Finite Group Databasebeta

← #28293327

Subgroups — #28293327

Order 13568.

7498 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289064C214yesmaximal, complemented
2#20289042C214yesmaximal, complemented
3#20289035C218yesmaximal, complemented
4#20289026C218yesmaximal, complemented
5#20288895C218yesmaximal, complemented
6#20288886C214yesmaximal, complemented
7#20288876C214yesmaximal, complemented
8#20288870C214yesmaximal, complemented
9#20288867C214yesmaximal, complemented
10#20288411C212yesmaximal, complemented
11#20288404C212yesmaximal, complemented
12#20288402C212yesmaximal, complemented
13#20288353C212yesmaximal, complemented
14#20288350C212yesmaximal, complemented
15#20288344C212yesmaximal, complemented
16C2×#16811190C211yesmaximal, characteristic, complemented
17C2×#16811182C211yesmaximal, characteristic, complemented
18C2×C53×#534C211yesmaximal, characteristic, complemented
19C2×#13133262C2212yescomplemented
20C22×#11719945C2211yescharacteristic, complemented
21C23×C22⋊D53C2211yescharacteristic, complemented
22#16811376C2214yescomplemented
23#16811370C2218yescomplemented
24#16811368C2218yescomplemented
25#16811368C2218yescomplemented
26#16811366C2214yescomplemented
27#16811363C2214yescomplemented
28#16811362C2214yescomplemented
29#16811362C2218yescomplemented
30#16811361C2218yescomplemented
31#16811361C2218yescomplemented
32#16811357C2214yescomplemented
33#16811337C2218yescomplemented
34#16811320C2218yescomplemented
35#16811318C2218yescomplemented
36#16811310C2218yescomplemented
37#16811308C2218yescomplemented
38#16811304C2214yescomplemented
39#16811304C2218yescomplemented
40#16811301C2214yescomplemented
41#16811299C2218yescomplemented
42#16811299C2218yescomplemented
43#16811299C2218yescomplemented
44#16811299C2218yescomplemented
45#16811296C2218yescomplemented
46#16811291C2218yescomplemented
47#16811274C2218yescomplemented
48#16811271C2218yescomplemented
49#16811270C2218yescomplemented
50#16811267C2218yescomplemented
51#16811267C2218yescomplemented
52#16811267C2218yescomplemented
53#16811265C2218yescomplemented
54#16811263C2218yescomplemented
55#16811263C2218yescomplemented
56#16811263C2218yescomplemented
57#16811263C2218yescomplemented
58#16811260C2218yescomplemented
59#16811260C2218yescomplemented
60#16811260C2218yescomplemented
61D4×C22⋊D53C2218yescomplemented
62D4×C22⋊D53C2218yescomplemented
63D4×C22⋊D53C2218yescomplemented
64#16811255C2214yescomplemented
65#16811255C2218yescomplemented
66#16811249C2212yescomplemented
67#16811241C2218yescomplemented
68#16811240C2218yescomplemented
69#16811226C2218yescomplemented
70#16811225C2218yescomplemented
71#16811223C2218yescomplemented
72#16811223C2218yescomplemented
73#16811217C2218yescomplemented
74#16811216C2218yescomplemented
75#16811211C2218yescomplemented
76#16811209C2218yescomplemented
77#16811208C2218yescomplemented
78#16811208C2218yescomplemented
79#16811208C2218yescomplemented
80#16811205C2218yescomplemented
81#16811205C2218yescomplemented
82#16811202C2218yescomplemented
83#16811195C2214yescomplemented
84#16811190C2214yescomplemented
85#16811190C2214yescomplemented
86#16811190C2214yescomplemented
87#16811190C2214yescomplemented
88#16811190C2214yescomplemented
89#16811189C2218yescomplemented
90#16811188C2214yescomplemented
91#16811188C2218yescomplemented
92#16811185C2212yescomplemented
93#16811184C2214yescomplemented
94#16811183C2218yescomplemented
95#16811183C2214yescomplemented
96#16811182C2212yes—
97#16811182C2214yescomplemented
98#16811182C2214yescomplemented
99#16811182C2212yescomplemented
100#16811182C2214yescomplemented
101#16811182C2214yescomplemented
102#16811182C2214yescomplemented
103C2×#13133213C2212yescomplemented
104#16811150C2218yescomplemented
105C2×#13133204C2212yescomplemented
106#16811134C2218yescomplemented
107#16811134C2214yescomplemented
108#16811131C2214yescomplemented
109#16811129C2218yescomplemented
110#16811129C2214yescomplemented
111C2×#13133200C2212yescomplemented
112C2×#13133198C2212yescomplemented
113#123×D53C2214yescomplemented
114C2×#13133189C2214yescomplemented
115C2×#13133188C2214yescomplemented
116C2×#13133186C2212yescomplemented
117C2×#13133186C2212yescomplemented
118C2×#13133186C2212yescomplemented
119C2×#13133186C2214yescomplemented
120C2×#13133185C2212yescomplemented
121#120×D53C2214yescomplemented
122#16811098C2212yescomplemented
123#16811096C2212yescomplemented
124#16811096C2212yescomplemented
125C2×#13133176C2211yescharacteristic, complemented
126C22×C22⋊Dic53C2211yescharacteristic, complemented
127C23×D4×C53C2211yescharacteristic, complemented
128C23×D4×C53C2211yescharacteristic, complemented
129C53×#534C2214yescomplemented
130C53×#534C2214yescomplemented
131C53×#534C2214yescomplemented
132C53×#534C2214yescomplemented
133C2×#123×C53C2212yescomplemented
134C2×#123×C53C2212yescomplemented
135C2×#121×C53C2214yescomplemented
136C2×#120×C53C2212yescomplemented
137C2×#120×C53C2212yescomplemented
138C22×C22⋊C4×C53C2211yescharacteristic, complemented
139C24×D53C2311yescharacteristic, complemented
140#13133262—48no—
141C2×#11719945—44no—
142C2×#11719945C2314yes—
143C2×#11719945C2314yescomplemented
144C2×#11719945C2314yescomplemented
145C2×#11719945C2318yescomplemented
146C2×#11719947C2314yes—
147C2×#11719947C2314yes—
148C2×#11719947C2318yescomplemented
149C22×Dic106C2311yescharacteristic, complemented
150C22×D212C2311yescharacteristic, complemented
151C22×C22⋊D53—44no—
152C22×C22⋊D53C2312yes—
153C22×C22⋊D53C2312yes—
154C22×C22⋊D53C2314yes—
155C22×C22⋊D53C2314yes—
156C22×C22⋊D53C2314yes—
157C22×C22⋊D53C2312yescomplemented
158C22×C22⋊D53C2314yescomplemented
159C22×C22⋊D53C2314yescomplemented
160C22×C22⋊D53C2314yescomplemented
161C22×C22⋊D53C2318yescomplemented
162C2×D4×D53C2314yes—
163C2×D4×D53C2314yes—
164C2×D4×D53C2318yescomplemented
165C23×Dic53C2311yescharacteristic, complemented
166C23×Dic53C2312yescomplemented
167C22×C4×D53C2312yescomplemented
168#13133216C2318yescomplemented
169#13133213C2314yes—
170#13133213C2314yescomplemented
171#13133213C2318yescomplemented
172#13133213C2318yescomplemented
173#13133213C2314yescomplemented
174#13133213C2314yescomplemented
175#13133212C2318yescomplemented
176#13133212C2318yescomplemented
177#13133210C2318yescomplemented
178#13133210C2318yescomplemented
179#13133210C2318yescomplemented
180#13133210C2318yescomplemented
181#13133210C2318yescomplemented
182#13133210C2318yescomplemented
183#13133208C2318yescomplemented
184#13133207C2318yescomplemented
185#13133207C2318yescomplemented
186#13133204C2314yes—
187#13133204C2318yescomplemented
188#13133204C2318yescomplemented
189#13133204C2314yescomplemented
190#13133204C2314yescomplemented
191#13133204C2314yescomplemented
192#13133203C2318yescomplemented
193#13133203C2318yescomplemented
194#13133203C2318yescomplemented
195#13133203C2318yescomplemented
196#13133203C2318yescomplemented
197#13133203C2318yescomplemented
198#13133202C2318yescomplemented
199#13133202C2318yescomplemented
200#13133201C2314yescomplemented
201#13133201C2318yescomplemented
202#13133201C2314yescomplemented
203#13133201C2318yescomplemented
204#13133200C2318yes—
205#13133200C2314yes—
206#13133200C2314yescomplemented
207#13133200C2318yescomplemented
208#13133200C2318yescomplemented
209#13133200C2314yescomplemented
210#13133200C2314yescomplemented
211#13133199C2318yescomplemented
212#13133199C2318yescomplemented
213#13133199C2318yescomplemented
214#13133199C2318yescomplemented
215#13133199C2318yescomplemented
216#13133199C2318yescomplemented
217#13133198C2314yes—
218#13133198C2314yes—
219#13133198C2314yes—
220#13133198C2314yescomplemented
221#13133198C2318yescomplemented
222#13133198C2318yescomplemented
223#13133198C2318yescomplemented
224#13133198C2314yescomplemented
225#13133198C2314yescomplemented
226#13133197C2318yescomplemented
227#13133196C2318yescomplemented
228#13133196C2318yescomplemented
229#13133196C2318yescomplemented
230#13133195C2318yescomplemented
231#13133195C2318yescomplemented
232#13133194C2318yescomplemented
233#13133194C2318yescomplemented
234#13133194C2318yescomplemented
235#13133194C2318yescomplemented
236#13133194C2318yescomplemented
237#13133194C2318yescomplemented
238#13133192C2318yescomplemented
239#13133191C2318yes—
240#13133191C2318yescomplemented
241#13133191C2318yescomplemented
242#13133190C2318yescomplemented
243#13133190C2318yescomplemented
244#13133190C2318yescomplemented
245#13133190C2318yescomplemented
246#13133190C2318yescomplemented
247#13133190C2318yescomplemented
248#13133189C2318yes—
249#13133189C2318yes—
250#13133189C2318yes—
251#13133189C2318yes—
252#13133189C2318yescomplemented
253#13133189C2318yescomplemented
254#13133189C2318yescomplemented
255#13133189C2318yescomplemented
256#13133189C2318yescomplemented
257#13133189C2318yescomplemented
258#13133189C2318yescomplemented
259#13133189C2318yescomplemented
260#13133188C2318yes—
261#13133188C2318yescomplemented
262#13133188C2318yescomplemented
263#13133188C2318yescomplemented
264#13133188C2318yescomplemented
265#13133188C2318yescomplemented
266#13133188C2318yescomplemented
267#13133188C2318yescomplemented
268#13133187C2314yescomplemented
269#13133187C2318yescomplemented
270#13133187C2318yescomplemented
271#13133187C2314yescomplemented
272#13133186C2318yes—
273#13133186C2318yes—
274#13133186C2318yes—
275#13133186C2314yes—
276#13133186C2314yes—
277#13133186C2314yes—
278#13133186C2314yescomplemented
279#13133186C2318yescomplemented
280#13133186C2318yescomplemented
281#13133186C2314yescomplemented
282#13133186C2314yescomplemented
283#13133186C2314yescomplemented
284#13133186C2314yescomplemented
285#13133185C2314yes—
286#13133185C2314yes—
287#13133185C2314yes—
288#13133185C2314yescomplemented
289#13133185C2318yescomplemented
290#13133185C2318yescomplemented
291#13133185C2318yescomplemented
292#13133185C2314yescomplemented
293#13133185C2314yescomplemented
294#13133182C2318yescomplemented
295D4×Dic53C2318yes—
296D4×Dic53C2318yescomplemented
297D4×Dic53C2318yescomplemented
298D4×Dic53C2318yescomplemented
299#13133179C2318yescomplemented
300C4×C22⋊D53C2318yes—
301C4×C22⋊D53C2318yescomplemented
302C4×C22⋊D53C2318yescomplemented
303C4×C22⋊D53C2318yescomplemented
304C4×C22⋊D53C2318yescomplemented
305C4×C22⋊D53C2318yescomplemented
306#13133177C2318yescomplemented
307#13133177C2318yescomplemented
308#13133177C2318yescomplemented
309#13133177C2318yescomplemented
310#13133177C2318yescomplemented
311#13133177C2318yescomplemented
312#13133176C2314yescomplemented
313#13133176C2314yescomplemented
314#13133176C2314yescomplemented
315#13133176C2318yescomplemented
316#13133175C2318yescomplemented
317#13133173C2314yescomplemented
318#13133173C2314yescomplemented
319#13133173C2318yescomplemented
320#13133173C2318yescomplemented
321C2×C4⋊Dic53C2312yescomplemented
322C2×#11719919C2314yescomplemented
323C4⋊C4×D53C2318yescomplemented
324C2×C22⋊Dic53C2314yes—
325C2×C22⋊Dic53C2314yes—
326C2×C22⋊Dic53C2312yes—
327C2×C22⋊Dic53C2312yes—
328C2×C22⋊Dic53C2314yescomplemented
329C2×C22⋊Dic53C2314yescomplemented
330C2×C22⋊Dic53C2318yescomplemented
331C2×C22⋊Dic53C2314yescomplemented
332C2×C22⋊Dic53C2314yescomplemented
333C2×C22⋊Dic53C2312yescomplemented
334C2×#11719921C2314yescomplemented
335C22⋊C4×D53C2318yescomplemented
336C22⋊C4×D53C2318yescomplemented
337C22⋊C4×D53C2314yescomplemented
338C22⋊C4×D53C2314yescomplemented
339C2×C4×Dic53C2312yescomplemented
340C25×C53C2311yescharacteristic
341C25×C53C2311yescharacteristic
342C25×C53C2311yescharacteristic, complemented
343C22×D4×C53—44no—
344C22×D4×C53—44no—
345C22×D4×C53C2312yes—
346C22×D4×C53C2314yes—
347C22×D4×C53C2312yes—
348C22×D4×C53C2312yes—
349C22×D4×C53C2312yes—
350C22×D4×C53C2312yes—
351C22×D4×C53C2312yes—
352C22×D4×C53C2312yes—
353C22×D4×C53C2314yes—
354C22×D4×C53C2314yescomplemented
355C22×D4×C53C2312yescomplemented
356C23×C4×C53C2311yescharacteristic
357C23×C4×C53C2311yescharacteristic, complemented
358C23×C4×C53C2312yescomplemented
359#123×C53C2318yes—
360#123×C53C2314yes—
361#123×C53C2314yes—
362#123×C53C2314yescomplemented
363#123×C53C2314yescomplemented
364#123×C53C2314yescomplemented
365#123×C53C2314yescomplemented
366#121×C53C2318yes—
367#121×C53C2318yes—
368#121×C53C2318yescomplemented
369#121×C53C2318yescomplemented
370#120×C53C2314yes—
371#120×C53C2318yes—
372#120×C53C2314yes—
373#120×C53C2314yes—
374#120×C53C2314yes—
375#120×C53C2314yescomplemented
376#120×C53C2314yescomplemented
377C2×C4⋊C4×C53C2314yescomplemented
378C2×C22⋊C4×C53C2314yes—
379C2×C22⋊C4×C53C2312yes—
380C2×C22⋊C4×C53C2314yes—
381C2×C22⋊C4×C53C2314yescomplemented
382C2×C22⋊C4×C53C2312yescomplemented
383C2×C22⋊C4×C53C2314yescomplemented
384C24×C53—24no—
385C24×C53—24no—
386C24×C53—42no—
387C24×C53—82no—
388C24×C53—82no—
389C24×C53—82no—
390C24×C53C2412yes—
391C24×C53C2412yes—
392C24×C53C2411yescharacteristic
393C24×C53C2412yes—
394C24×C53C2412yes—
395C24×C53C2412yes—
396C24×C53C2411yescharacteristic
397C24×C53C2411yescharacteristic
398C24×C53C2411yescharacteristic
399C24×C53C2414yes—
400C24×C53C2411yescharacteristic
401C23×D53—42no—
402C23×D53—82no—
403C23×D53C2412yes—
404C23×D53C2412yes—
405C23×D53C2414yes—
406C23×D53C2414yes—
407C2×D4×C53—28no—
408C2×D4×C53—44no—
409C2×D4×C53—44no—
410C2×D4×C53—44no—
411C2×D4×C53—44no—
412C2×D4×C53—44no—
413C2×D4×C53—44no—
414C2×D4×C53—44no—
415C2×D4×C53—48no—
416C2×D4×C53—48no—
417C2×D4×C53—84no—
418C2×D4×C53C2414yes—
419C2×D4×C53C2414yes—
420C2×D4×C53C2418yes—
421C2×D4×C53C2418yes—
422C2×D4×C53C2412yes—
423C2×D4×C53C2412yes—
424C2×D4×C53C2412yes—
425C2×D4×C53C2412yes—
426C2×D4×C53C2412yes—
427C2×D4×C53C2412yes—
428C2×D4×C53C2418yes—
429C2×D4×C53C2412yes—
430C2×D4×C53C2412yes—
431C22×C4×C53—24no—
432C22×C4×C53—42no—
433C22×C4×C53—82no—
434C22×C4×C53C2412yes—
435C22×C4×C53C2412yes—
436C22×C4×C53C2412yes—
437C22×C4×C53C2411yescharacteristic
438C22×C4×C53C2411yescharacteristic
439C22×C4×C53C2414yes—
440C22×C4×C53C2418yes—
441C22×C4×C53C2414yes—
442C2×C22⋊D53—28no—
443C2×C22⋊D53—28no—
444C2×C22⋊D53—44no—
445C2×C22⋊D53—48no—
446C2×C22⋊D53—48no—
447C2×C22⋊D53—48no—
448C2×C22⋊D53—84no—
449C2×C22⋊D53—88no—
450C2×C22⋊D53—84no—
451C2×C22⋊D53—84no—
452C2×C22⋊D53C2414yes—
453C2×C22⋊D53C2414yes—
454C2×C22⋊D53C2414yes—
455C2×C22⋊D53C2414yes—
456C2×C22⋊D53C2418yes—
457C2×C22⋊D53C2418yes—
458C2×C22⋊D53C2418yes—
459C2×C22⋊D53C2418yes—
460C2×C22⋊D53C2418yes—
461C2×C22⋊D53C2418yes—
462C2×C22⋊D53C2418yes—
463C2×C22⋊D53C2418yes—
464C2×C22⋊D53C2414yes—
465C2×C22⋊D53C2418yes—
466C2×C22⋊D53C2414yes—
467C22×Dic53—42no—
468C22×Dic53—82no—
469C22×Dic53C2412yes—
470C22×Dic53C2412yes—
471C22×Dic53C2414yes—
472C22×Dic53C2414yes—
473C22×Dic53C2418yes—
474C22×Dic53C2418yes—
475C22×Dic53C2414yes—
476C22×Dic53C2414yes—
477#11719947—48no—
478#11719947—48no—
479#11719947—88no—
480D4×D53—48no—
481D4×D53—48no—
482D4×D53—88no—
483#11719945—48no—
484#11719945—48no—
485#11719945—48no—
486#11719945—88no—
487C2×D212—42no—
488C2×D212C2418yes—
489C2×D212C2414yes—
490C2×D212C2414yes—
491C2×C4×D53—44no—
492C2×C4×D53C2418yes—
493C2×C4×D53C2418yes—
494C2×C4×D53C2414yes—
495C2×C4×D53C2418yes—
496C2×C4×D53C2414yes—
497C2×Dic106—42no—
498C2×Dic106C2418yes—
499C2×Dic106C2414yes—
500C2×Dic106C2414yes—
501C4⋊C4×C53C2418yes—
502C4⋊C4×C53C2418yes—
503C22⋊C4×C53C2414yes—
504C22⋊C4×C53C2414yes—
505C22⋊C4×C53C2414yes—
506C22⋊C4×C53C2414yes—
507C22⋊C4×C53C2418yes—
508C22⋊C4×C53C2418yes—
509C22⋊C4×C53C2418yes—
510C22⋊C4×C53C2418yes—
511C22⋊Dic53C2414yes—
512C22⋊Dic53C2414yes—
513C22⋊Dic53C2418yes—
514C22⋊Dic53C2418yes—
515C22⋊Dic53C2414yes—
516C22⋊Dic53C2414yes—
517C22⋊Dic53C2414yes—
518C22⋊Dic53C2414yes—
519C22⋊Dic53C2418yes—
520C22⋊Dic53C2418yes—
521C22⋊Dic53C2418yes—
522C22⋊Dic53C2418yes—
523C22⋊Dic53C2418yes—
524C22⋊Dic53C2418yes—
525C22⋊Dic53C2418yes—
526#11719921C2418yes—
527#11719921C2418yes—
528#11719921C2418yes—
529#11719921C2418yes—
530#11719921C2418yes—
531#11719921C2418yes—
532#11719921C2418yes—
533#11719921C2418yes—
534C4⋊Dic53C2418yes—
535C4⋊Dic53C2418yes—
536C4⋊Dic53C2418yes—
537C4⋊Dic53C2418yes—
538#11719919C2418yes—
539#11719919C2418yes—
540#11719919C2418yes—
541#11719919C2418yes—
542#11719919C2418yes—
543#11719919C2418yes—
544#11719919C2418yes—
545#11719919C2418yes—
546C4×Dic53C2414yes—
547C4×Dic53C2414yes—
548C4×Dic53C2418yes—
549C4×Dic53C2418yes—
550C4×Dic53C2418yes—
551C23×C53—22no—
552C23×C53—22no—
553C23×C53—22no—
554C23×C53—22no—
555C23×C53—24no—
556C23×C53—24no—
557C23×C53—24no—
558C23×C53—24no—
559C23×C53—24no—
560C23×C53—42no—
561C23×C53—42no—
562C23×C53—42no—
563C23×C53—42no—
564C23×C53—42no—
565C23×C53—44no—
566C23×C53—44no—
567C23×C53—44no—
568C23×C53—48no—
569C23×C53—44no—
570C23×C53—44no—
571C23×C53—44no—
572C23×C53—88no—
573C23×C53—88no—
574C23×C53—88no—
575C23×C53H(5,𝔽2)14yes—
576C23×C53C2512yes—
577C23×C53C2514yes—
578C23×C53C2512yes—
579C23×C53C2512yes—
580C23×C53C2512yes—
581C23×C53C2511yescharacteristic
582C23×C53C2511yescharacteristic
583C23×C53C2511yescharacteristic
584C22×D53—24no—
585C22×D53—24no—
586C22×D53—48no—
587C22×D53—44no—
588C22×D53—44no—
589C22×D53—44no—
590C22×D53—44no—
591C22×D53—48no—
592C22×D53—88no—
593C22×D53C2514yes—
594C22×D53C2514yes—
595D4×C53—28no—
596D4×C53—28no—
597D4×C53—48no—
598D4×C53—48no—
599D4×C53—42no—
600D4×C53—42no—
601D4×C53—42no—
602D4×C53—42no—
603D4×C53—48no—
604D4×C53—42no—
605D4×C53—42no—
606D4×C53—42no—
607D4×C53—42no—
608C2×C4×C53—22no—
609C2×C4×C53—22no—
610C2×C4×C53—24no—
611C2×C4×C53—24no—
612C2×C4×C53—24no—
613C2×C4×C53—48no—
614C2×C4×C53—44no—
615C2×C4×C53—44no—
616C2×C4×C53C2512yes—
617C2×C4×C53C2514yes—
618C2×C4×C53C2518yes—
619C2×C4×C53C2512yes—
620C22⋊D53—28no—
621C22⋊D53—28no—
622C22⋊D53—28no—
623C22⋊D53—28no—
624C22⋊D53—48no—
625C22⋊D53—48no—
626C22⋊D53—44no—
627C22⋊D53—44no—
628C22⋊D53—48no—
629C22⋊D53—48no—
630C22⋊D53—48no—
631C22⋊D53—48no—
632C22⋊D53—48no—
633C22⋊D53—48no—
634C22⋊D53—48no—
635C2×Dic53—24no—
636C2×Dic53—24no—
637C2×Dic53—44no—
638C2×Dic53—48no—
639C2×Dic53—48no—
640C2×Dic53—44no—
641C2×Dic53—44no—
642C2×Dic53—44no—
643C2×Dic53C2514yes—
644C2×Dic53C2514yes—
645C2×Dic53C2518yes—
646C2×Dic53C2518yes—
647D212—44no—
648D212—44no—
649D212—48no—
650C4×D53—48no—
651C4×D53—44no—
652C4×D53—44no—
653C4×D53—48no—
654C4×D53—48no—
655Dic106—44no—
656Dic106—44no—
657Dic106—48no—
658#62862—531nomaximal, Sylow
659C22×C53—22no—
660C22×C53—22no—
661C22×C53—22no—
662C22×C53—22no—
663C22×C53—24no—
664C22×C53—22no—
665C22×C53—22no—
666C22×C53—22no—
667C22×C53—24no—
668C22×C53—28no—
669C22×C53—24no—
670C22×C53—24no—
671C22×C53—24no—
672C22×C53—44no—
673C22×C53—44no—
674C22×C53—44no—
675C22×C53—44no—
676C22×C53—44no—
677C22×C53—84no—
678C22×C53—84no—
679C22×C53—84no—
680C22×C53—84no—
681C22×C53—84no—
682C22×C53—88no—
683C22×C53C2×H(5,𝔽2)12yes—
684C22×C53C2×H(5,𝔽2)12yes—
685C22×C53C2×H(5,𝔽2)12yes—
686C22×C53C2611yescharacteristic
687C2×D53—24no—
688C2×D53—24no—
689C2×D53—28no—
690C2×D53—28no—
691C2×D53—84no—
692C2×D53—84no—
693C2×D53—88no—
694C2×D53—164no—
695C4×C53—22no—
696C4×C53—24no—
697C4×C53—22no—
698C4×C53—28no—
699Dic53—24no—
700Dic53—24no—
701Dic53—28no—
702Dic53—28no—
703#3545—534no—
704#3543—534no—
705#3542—538no—
706#3542—538no—
707#3534—538no—
708#3533—534no—
709#3533—534no—
710#3532—534no—
711#3532—534no—
712#3491—532no—
713#3490—532no—
714#3490—532no—
715#3485—532no—
716#3484—532no—
717#3484—532no—
718C2×#535—531no—
719C2×#534—531no—
720C2×#534D5311yescharacteristic, complemented
721C2×C53—22no—
722C2×C53—22no—
723C2×C53—22no—
724C2×C53—42no—
725C2×C53—44no—
726C2×C53—42no—
727C2×C53—42no—
728C2×C53—42no—
729C2×C53C22×H(5,𝔽2)11yescharacteristic
730C2×C53H(7,𝔽2)12yes—
731D53—44no—
732D53—44no—
733C2×H(5,𝔽2)—532no—
734C22×#41—531no—
735C23×D4—531no—
736C23×D4C2×D5311yescharacteristic, complemented
737C23×D4C2×D5311yescharacteristic, complemented
738#563—534no—
739#562—538no—
740#562—538no—
741#562—538no—
742H(3,𝔽4)—534no—
743#560—534no—
744#560—538no—
745#560—538no—
746#560—534no—
747#560—538no—
748#559—534no—
749#555—538no—
750#553—538no—
751#553—538no—
752#552—538no—
753#552—538no—
754#551—538no—
755#551—534no—
756#551—538no—
757#551—534no—
758#551—538no—
759#551—538no—
760#551—538no—
761#551—538no—
762#550—538no—
763#547—538no—
764#547—538no—
765#546—538no—
766#546—538no—
767#546—538no—
768#546—538no—
769#546—538no—
770#546—538no—
771#546—538no—
772#546—538no—
773#546—538no—
774#546—538no—
775#546—538no—
776#546—538no—
777D42—538no—
778D42—538no—
779D42—538no—
780D42—538no—
781D42—534no—
782#543—532no—
783#542—538no—
784#542—538no—
785#540—538no—
786#540—538no—
787#540—538no—
788#540—538no—
789#539—538no—
790#539—538no—
791#538—538no—
792#538—538no—
793#538—538no—
794#538—538no—
795#538—538no—
796#538—538no—
797#538—538no—
798#537—538no—
799#536—534no—
800#535—534no—
801#535—534no—
802#535—534no—
803#535—534no—
804#535—534no—
805#535—538no—
806#535—534no—
807#535—538no—
808#534—534no—
809#534—534no—
810#534—534no—
811#534—534no—
812#534—532no—
813#534—532no—
814#534—534no—
815#534—534no—
816#534—534no—
817#534—538no—
818#534—532no—
819#534C2×D5314yescomplemented
820#534C2×D5314yescomplemented
821#534C2×D5314yescomplemented
822#534C2×D5314yescomplemented
823C2×#127—532no—
824#529—538no—
825C2×#124—532no—
826#525—534no—
827#525—538no—
828#525—534no—
829#525—534no—
830#525—538no—
831C2×#123—532no—
832C2×#123—532no—
833C2×#123—534no—
834C2×#123C2×D5312yescomplemented
835C2×#123C2×D5312yescomplemented
836C2×#121—534no—
837C2×#121—534no—
838C2×#121C2×D5314yescomplemented
839C2×#120—532no—
840C2×#120—532no—
841C2×#120—532no—
842C2×#120—534no—
843C2×#120—532no—
844C2×#120—534no—
845C2×#120C2×D5312yescomplemented
846C2×#120C2×D5312yescomplemented
847#518—532no—
848#518—532no—
849#518—532no—
850C2×#117—531no—
851C22×C22⋊C4—531no—
852C22×C22⋊C4C2×D5311yescharacteristic, complemented
853C53#6286211yescharacteristic, complemented, Sylow
854C25—531no—
855C25C22×D5311yescharacteristic
856C25C22×D5311yescharacteristic
857C25C22×D5311yescharacteristic, complemented
858H(5,𝔽2)—2128no—
859C2×#41—538no—
860C2×#41—534no—
861C2×#41—534no—
862C2×#41—538no—
863C2×#41—534no—
864C2×#41—534no—
865C2×#41—534no—
866C2×#41—2124no—
867C22×Q8—531no—
868C22×D4—44no—
869C22×D4—44no—
870C22×D4—532no—
871C22×D4—532no—
872C22×D4—534no—
873C22×D4—534no—
874C22×D4—534no—
875C22×D4—538no—
876C22×D4—534no—
877C22×D4—532no—
878C22×D4—534no—
879C22×D4—534no—
880C22×D4—538no—
881C22×D4—534no—
882C22×D4—534no—
883C22×D4—531no—
884C22×D4—2124no—
885C22×D4C22×D5312yes—
886C22×D4C22×D5312yes—
887C22×D4C22×D5312yes—
888C22×D4C22×D5312yes—
889C22×D4C22×D5312yes—
890C22×D4C22×D5312yes—
891C22×D4C22×D5312yes—
892C22×D4C22×D5314yes—
893C22×D4C22×D5314yes—
894C22×D4C22×D5312yescomplemented
895C22×D4C22×D5314yescomplemented
896C23×C4—532no—
897C23×C4—531no—
898C23×C4—532no—
899C23×C4C22×D5311yescharacteristic
900C23×C4C22×D5311yescharacteristic, complemented
901C23×C4C22×D5312yescomplemented
902C4⋊Q8—538no—
903#127—534no—
904#127—534no—
905#127—534no—
906#127—534no—
907#127—538no—
908#127—538no—
909#126—538no—
910#126—538no—
911#126—538no—
912#126—538no—
913#126—538no—
914#126—538no—
915#126—538no—
916#126—538no—
917#125—538no—
918#125—538no—
919#125—538no—
920#124—534no—
921#124—534no—
922#124—534no—
923#124—534no—
924#124—538no—
925#124—538no—
926#124—538no—
927#124—538no—
928#124—538no—
929#124—538no—
930#124—538no—
931#124—538no—
932#123—534no—
933#123—534no—
934#123—534no—
935#123—534no—
936#123—534no—
937#123—534no—
938#123—538no—
939#123—538no—
940#123—538no—
941#123—534no—
942#123—534no—
943#123—538no—
944#123—534no—
945#123—534no—
946#123—538no—
947#123—538no—
948#123—538no—
949#123—538no—
950#123—534no—
951#123—538no—
952#123—534no—
953#123—538no—
954#123—538no—
955#123—538no—
956#123—538no—
957#123—538no—
958#123—538no—
959#123—538no—
960#123C22×D5314yes—
961#123C22×D5318yes—
962#123C22×D5314yes—
963#123C22×D5314yescomplemented
964#123C22×D5314yescomplemented
965#123C22×D5314yescomplemented
966#123C22×D5314yescomplemented
967C22⋊Q8—538no—
968C22⋊Q8—538no—
969C22⋊Q8—538no—
970C22⋊Q8—538no—
971C22⋊Q8—538no—
972C22⋊Q8—538no—
973C22⋊Q8—538no—
974C22⋊Q8—538no—
975C22⋊Q8—538no—
976C22⋊Q8—538no—
977C22⋊Q8—538no—
978C22⋊Q8—538no—
979#121—538no—
980#121—538no—
981#121—538no—
982#121—538no—
983#121—538no—
984#121—538no—
985#121—538no—
986#121—538no—
987#121—538no—
988#121—538no—
989#121—538no—
990#121—538no—
991#121—538no—
992#121—538no—
993#121—538no—
994#121—538no—
995#121—538no—
996#121—538no—
997#121—538no—
998#121—538no—
999#121—538no—
1000#121—538no—
1001#121—538no—
1002#121—538no—
1003#121—538no—
1004#121—538no—
1005#121—538no—
1006#121—538no—
1007#121—538no—
1008#121—538no—
1009#121C22×D5318yes—
1010#121C22×D5318yes—
1011#121C22×D5318yescomplemented
1012#121C22×D5318yescomplemented
1013#120—534no—
1014#120—534no—
1015#120—534no—
1016#120—534no—
1017#120—534no—
1018#120—534no—
1019#120—538no—
1020#120—534no—
1021#120—534no—
1022#120—538no—
1023#120—538no—
1024#120—538no—
1025#120—538no—
1026#120—534no—
1027#120—534no—
1028#120—534no—
1029#120—534no—
1030#120—534no—
1031#120—538no—
1032#120—534no—
1033#120—538no—
1034#120—538no—
1035#120—534no—
1036#120—538no—
1037#120—534no—
1038#120—538no—
1039#120C22×D5314yes—
1040#120C22×D5314yes—
1041#120C22×D5314yes—
1042#120C22×D5318yes—
1043#120C22×D5314yes—
1044#120C22×D5314yescomplemented
1045#120C22×D5314yescomplemented
1046C4×Q8—538no—
1047C4×D4—538no—
1048C4×D4—538no—
1049C4×D4—538no—
1050C4×D4—538no—
1051C4×D4—538no—
1052C4×D4—538no—
1053C4×D4—538no—
1054C4×D4—538no—
1055C4×D4—538no—
1056C4×D4—538no—
1057C4×D4—538no—
1058C4×D4—538no—
1059C4×D4—538no—
1060C4×D4—538no—
1061C4×D4—538no—
1062C4×D4—538no—
1063C4×D4—538no—
1064#117—534no—
1065#117—534no—
1066#117—534no—
1067#117—538no—
1068#117—538no—
1069#117—534no—
1070#117—534no—
1071#117—538no—
1072#117—538no—
1073C2×C4⋊C4—532no—
1074C2×C4⋊C4—534no—
1075C2×C4⋊C4—538no—
1076C2×C4⋊C4C22×D5314yescomplemented
1077C2×C22⋊C4—532no—
1078C2×C22⋊C4—532no—
1079C2×C22⋊C4—534no—
1080C2×C22⋊C4—534no—
1081C2×C22⋊C4—532no—
1082C2×C22⋊C4—534no—
1083C2×C22⋊C4—534no—
1084C2×C22⋊C4—534no—
1085C2×C22⋊C4—534no—
1086C2×C22⋊C4—538no—
1087C2×C22⋊C4—534no—
1088C2×C22⋊C4—534no—
1089C2×C22⋊C4—534no—
1090C2×C22⋊C4—538no—
1091C2×C22⋊C4—538no—
1092C2×C22⋊C4C22×D5312yes—
1093C2×C22⋊C4C22×D5314yes—
1094C2×C22⋊C4C22×D5314yes—
1095C2×C22⋊C4C22×D5312yescomplemented
1096C2×C22⋊C4C22×D5314yescomplemented
1097C2×C22⋊C4C22×D5314yescomplemented
1098C2×C42—532no—
1099C24—24no—
1100C24—24no—
1101C24—42no—
1102C24—82no—
1103C24—82no—
1104C24—82no—
1105C24—532no—
1106C24—532no—
1107C24—534no—
1108C24—534no—
1109C24—4242no—
1110C24—2122no—
1111C24C23×D5312yes—
1112C24C23×D5312yes—
1113C24C23×D5312yes—
1114C24C23×D5312yes—
1115C24C23×D5312yes—
1116C24C23×D5311yescharacteristic
1117C24C23×D5311yescharacteristic
1118C24C23×D5311yescharacteristic
1119C24C23×D5311yescharacteristic
1120C24C23×D5314yes—
1121C24C23×D5311yescharacteristic
1122#41—4248no—
1123#41—4248no—
1124#41—2128no—
1125#41—2128no—
1126#41—2128no—
1127#41—2128no—
1128#41—2128no—
1129C2×Q8—538no—
1130C2×Q8—534no—
1131C2×Q8—534no—
1132C2×Q8—2122no—
1133C2×D4—28no—
1134C2×D4—44no—
1135C2×D4—44no—
1136C2×D4—44no—
1137C2×D4—44no—
1138C2×D4—44no—
1139C2×D4—44no—
1140C2×D4—44no—
1141C2×D4—48no—
1142C2×D4—48no—
1143C2×D4—84no—
1144C2×D4—534no—
1145C2×D4—534no—
1146C2×D4—534no—
1147C2×D4—534no—
1148C2×D4—538no—
1149C2×D4—538no—
1150C2×D4—538no—
1151C2×D4—538no—
1152C2×D4—538no—
1153C2×D4—538no—
1154C2×D4—538no—
1155C2×D4—538no—
1156C2×D4—534no—
1157C2×D4—534no—
1158C2×D4—538no—
1159C2×D4—538no—
1160C2×D4—534no—
1161C2×D4—534no—
1162C2×D4—1068no—
1163C2×D4—1068no—
1164C2×D4—4248no—
1165C2×D4—4244no—
1166C2×D4—4244no—
1167C2×D4—4244no—
1168C2×D4—4248no—
1169C2×D4—2122no—
1170C2×D4—2124no—
1171C2×D4—2128no—
1172C2×D4—2128no—
1173C2×D4—2128no—
1174C2×D4—2128no—
1175C2×D4—2128no—
1176C2×D4C23×D5314yes—
1177C2×D4C23×D5314yes—
1178C2×D4C23×D5318yes—
1179C2×D4C23×D5318yes—
1180C2×D4C23×D5312yes—
1181C2×D4C23×D5312yes—
1182C2×D4C23×D5312yes—
1183C2×D4C23×D5312yes—
1184C2×D4C23×D5318yes—
1185C2×D4C23×D5312yes—
1186C2×D4C23×D5312yes—
1187C2×D4C23×D5312yes—
1188C2×D4C23×D5312yes—
1189C22×C4—24no—
1190C22×C4—42no—
1191C22×C4—82no—
1192C22×C4—532no—
1193C22×C4—532no—
1194C22×C4—534no—
1195C22×C4—534no—
1196C22×C4—538no—
1197C22×C4—538no—
1198C22×C4—534no—
1199C22×C4—534no—
1200C22×C4—538no—
1201C22×C4—538no—
1202C22×C4—534no—
1203C22×C4—538no—
1204C22×C4—534no—
1205C22×C4—4242no—
1206C22×C4—2124no—
1207C22×C4—2122no—
1208C22×C4C23×D5311yescharacteristic
1209C22×C4C23×D5312yes—
1210C22×C4C23×D5312yes—
1211C22×C4C23×D5312yes—
1212C22×C4C23×D5311yescharacteristic
1213C22×C4C23×D5314yes—
1214C22×C4C23×D5318yes—
1215C22×C4C23×D5314yes—
1216C4⋊C4—538no—
1217C4⋊C4—538no—
1218C4⋊C4—538no—
1219C4⋊C4—538no—
1220C4⋊C4—538no—
1221C4⋊C4—538no—
1222C4⋊C4—538no—
1223C4⋊C4—538no—
1224C4⋊C4—538no—
1225C4⋊C4—538no—
1226C4⋊C4—538no—
1227C4⋊C4—538no—
1228C4⋊C4C23×D5318yes—
1229C4⋊C4C23×D5318yes—
1230C22⋊C4—534no—
1231C22⋊C4—534no—
1232C22⋊C4—534no—
1233C22⋊C4—534no—
1234C22⋊C4—534no—
1235C22⋊C4—534no—
1236C22⋊C4—538no—
1237C22⋊C4—538no—
1238C22⋊C4—538no—
1239C22⋊C4—538no—
1240C22⋊C4—538no—
1241C22⋊C4—538no—
1242C22⋊C4—538no—
1243C22⋊C4—538no—
1244C22⋊C4—538no—
1245C22⋊C4—538no—
1246C22⋊C4—538no—
1247C22⋊C4—538no—
1248C22⋊C4—538no—
1249C22⋊C4—538no—
1250C22⋊C4—538no—
1251C22⋊C4—538no—
1252C22⋊C4—538no—
1253C22⋊C4C23×D5314yes—
1254C22⋊C4C23×D5314yes—
1255C22⋊C4C23×D5318yes—
1256C22⋊C4C23×D5318yes—
1257C22⋊C4C23×D5314yes—
1258C22⋊C4C23×D5314yes—
1259C22⋊C4C23×D5318yes—
1260C22⋊C4C23×D5318yes—
1261C42—534no—
1262C42—534no—
1263C42—538no—
1264C42—538no—
1265C42—538no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—24no—
1271C23—24no—
1272C23—24no—
1273C23—24no—
1274C23—24no—
1275C23—42no—
1276C23—42no—
1277C23—42no—
1278C23—42no—
1279C23—42no—
1280C23—44no—
1281C23—44no—
1282C23—44no—
1283C23—44no—
1284C23—44no—
1285C23—44no—
1286C23—48no—
1287C23—88no—
1288C23—88no—
1289C23—88no—
1290C23—534no—
1291C23—534no—
1292C23—1064no—
1293C23—1064no—
1294C23—4248no—
1295C23—2128no—
1296C23—2124no—
1297C23—2124no—
1298C23—2124no—
1299C23—2128no—
1300C23—2124no—
1301C23#1313326214yes—
1302C23C24×D5312yes—
1303C23C24×D5312yes—
1304C23C24×D5312yes—
1305C23C24×D5314yes—
1306C23C24×D5312yes—
1307C23C24×D5311yescharacteristic
1308C23C24×D5311yescharacteristic
1309C23C24×D5311yescharacteristic
1310Q8—2124no—
1311Q8—2128no—
1312Q8—2124no—
1313D4—28no—
1314D4—28no—
1315D4—42no—
1316D4—42no—
1317D4—42no—
1318D4—42no—
1319D4—42no—
1320D4—42no—
1321D4—42no—
1322D4—42no—
1323D4—48no—
1324D4—48no—
1325D4—48no—
1326D4—1068no—
1327D4—1068no—
1328D4—1068no—
1329D4—1068no—
1330D4—2128no—
1331D4—2124no—
1332D4—2124no—
1333D4—2128no—
1334D4—2128no—
1335D4—2128no—
1336D4—2128no—
1337D4—2128no—
1338D4—2128no—
1339D4—2128no—
1340D4—2128no—
1341D4—2128no—
1342D4—2124no—
1343D4—2124no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—44no—
1350C2×C4—44no—
1351C2×C4—48no—
1352C2×C4—538no—
1353C2×C4—538no—
1354C2×C4—534no—
1355C2×C4—534no—
1356C2×C4—1064no—
1357C2×C4—1064no—
1358C2×C4—2128no—
1359C2×C4—2128no—
1360C2×C4—2124no—
1361C2×C4—2124no—
1362C2×C4—2128no—
1363C2×C4—2124no—
1364C2×C4—2128no—
1365C2×C4—2124no—
1366C2×C4—2124no—
1367C2×C4—2128no—
1368C2×C4—2124no—
1369C2×C4C24×D5312yes—
1370C2×C4C24×D5318yes—
1371C2×C4C24×D5314yes—
1372C2×C4C24×D5312yes—
1373C22—22no—
1374C22—22no—
1375C22—22no—
1376C22—22no—
1377C22—22no—
1378C22—24no—
1379C22—22no—
1380C22—22no—
1381C22—24no—
1382C22—24no—
1383C22—28no—
1384C22—24no—
1385C22—24no—
1386C22—44no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—44no—
1391C22—84no—
1392C22—84no—
1393C22—84no—
1394C22—84no—
1395C22—84no—
1396C22—88no—
1397C22—8484no—
1398C22—1064no—
1399C22—1064no—
1400C22—1068no—
1401C22—1068no—
1402C22—4244no—
1403C22—4244no—
1404C22—4248no—
1405C22C2×#1313326212yes—
1406C22C2×#1313326212yes—
1407C22C2×#1313326212yes—
1408C22C25×D5311yescharacteristic
1409C4—22no—
1410C4—22no—
1411C4—24no—
1412C4—28no—
1413C4—1064no—
1414C4—1064no—
1415C4—1068no—
1416C4—1068no—
1417C2—22no—
1418C2—22no—
1419C2—22no—
1420C2—42no—
1421C2—42no—
1422C2—42no—
1423C2—42no—
1424C2—44no—
1425C2—2124no—
1426C2—2124no—
1427C2C22×#1313326211yescharacteristic
1428C2#2028952512yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#534C2
hypercenterC2×#534D53
hypocenterC53#62862
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#534

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289064C2semidirect
2. #20289042C2semidirect
3. #20289035C2semidirect
4. #20289026C2semidirect
5. #20288895C2semidirect
6. #20288886C2semidirect
7. #20288876C2semidirect
8. #20288870C2semidirect
9. #20288867C2semidirect
10. #20288411C2semidirect
11. #20288404C2semidirect
12. #20288402C2semidirect
13. #20288353C2semidirect
14. #20288350C2semidirect
15. #20288344C2semidirect
16. C2×#16811190C2semidirect
17. C2×#16811182C2semidirect
18. C2×C53×#534C2semidirect
19. C2×#13133262C22semidirect
20. C22×#11719945C22semidirect
21. C23×C22⋊D53C22semidirect
22. #16811376C22semidirect
23. #16811370C22semidirect
24. #16811368C22semidirect
25. #16811368C22semidirect
26. #16811366C22semidirect
27. #16811363C22semidirect
28. #16811362C22semidirect
29. #16811362C22semidirect
30. #16811361C22semidirect
31. #16811361C22semidirect
32. #16811357C22semidirect
33. #16811337C22semidirect
34. #16811320C22semidirect
35. #16811318C22semidirect
36. #16811310C22semidirect
37. #16811308C22semidirect
38. #16811304C22semidirect
39. #16811304C22semidirect
40. #16811301C22semidirect
41. #16811299C22semidirect
42. #16811299C22semidirect
43. #16811299C22semidirect
44. #16811299C22semidirect
45. #16811296C22semidirect
46. #16811291C22semidirect
47. #16811274C22semidirect
48. #16811271C22semidirect
49. #16811270C22semidirect
50. #16811267C22semidirect
51. #16811267C22semidirect
52. #16811267C22semidirect
53. #16811265C22semidirect
54. #16811263C22semidirect
55. #16811263C22semidirect
56. #16811263C22semidirect
57. #16811263C22semidirect
58. #16811260C22semidirect
59. #16811260C22semidirect
60. #16811260C22semidirect
61. D4×C22⋊D53C22semidirect
62. D4×C22⋊D53C22semidirect
63. D4×C22⋊D53C22semidirect
64. #16811255C22semidirect
65. #16811255C22semidirect
66. #16811249C22semidirect
67. #16811241C22semidirect
68. #16811240C22semidirect
69. #16811226C22semidirect
70. #16811225C22semidirect
71. #16811223C22semidirect
72. #16811223C22semidirect
73. #16811217C22semidirect
74. #16811216C22semidirect
75. #16811211C22semidirect
76. #16811209C22semidirect
77. #16811208C22semidirect
78. #16811208C22semidirect
79. #16811208C22semidirect
80. #16811205C22semidirect
81. #16811205C22semidirect
82. #16811202C22semidirect
83. #16811195C22semidirect
84. #16811190C22semidirect
85. #16811190C22semidirect
86. #16811190C22semidirect
87. #16811190C22semidirect
88. #16811190C22semidirect
89. #16811189C22semidirect
90. #16811188C22semidirect
91. #16811188C22semidirect
92. #16811185C22semidirect
93. #16811184C22semidirect
94. #16811183C22semidirect
95. #16811183C22semidirect
97. #16811182C22semidirect
98. #16811182C22semidirect
99. #16811182C22semidirect
100. #16811182C22semidirect
101. #16811182C22semidirect
102. #16811182C22semidirect
103. C2×#13133213C22semidirect
104. #16811150C22semidirect
105. C2×#13133204C22semidirect
106. #16811134C22semidirect
107. #16811134C22semidirect
108. #16811131C22semidirect
109. #16811129C22semidirect
110. #16811129C22semidirect
111. C2×#13133200C22semidirect
112. C2×#13133198C22semidirect
113. #123×D53C22semidirect
114. C2×#13133189C22semidirect
115. C2×#13133188C22semidirect
116. C2×#13133186C22semidirect
117. C2×#13133186C22semidirect
118. C2×#13133186C22semidirect
119. C2×#13133186C22semidirect
120. C2×#13133185C22semidirect
121. #120×D53C22semidirect
122. #16811098C22semidirect
123. #16811096C22semidirect
124. #16811096C22semidirect
125. C2×#13133176C22semidirect
126. C22×C22⋊Dic53C22semidirect
127. C23×D4×C53C22semidirect
128. C23×D4×C53C22semidirect
129. C53×#534C22semidirect
130. C53×#534C22semidirect
131. C53×#534C22semidirect
132. C53×#534C22semidirect
133. C2×#123×C53C22semidirect
134. C2×#123×C53C22semidirect
135. C2×#121×C53C22semidirect
136. C2×#120×C53C22semidirect
137. C2×#120×C53C22semidirect
138. C22×C22⋊C4×C53C22semidirect
139. C24×D53C23semidirect
143. C2×#11719945C23semidirect
144. C2×#11719945C23semidirect
145. C2×#11719945C23semidirect
148. C2×#11719947C23semidirect
149. C22×Dic106C23semidirect
150. C22×D212C23semidirect
157. C22×C22⋊D53C23semidirect
158. C22×C22⋊D53C23semidirect
159. C22×C22⋊D53C23semidirect
160. C22×C22⋊D53C23semidirect
161. C22×C22⋊D53C23semidirect
164. C2×D4×D53C23semidirect
165. C23×Dic53C23semidirect
166. C23×Dic53C23semidirect
167. C22×C4×D53C23semidirect
168. #13133216C23semidirect
170. #13133213C23semidirect
171. #13133213C23semidirect
172. #13133213C23semidirect
173. #13133213C23semidirect
174. #13133213C23semidirect
175. #13133212C23semidirect
176. #13133212C23semidirect
177. #13133210C23semidirect
178. #13133210C23semidirect
179. #13133210C23semidirect
180. #13133210C23semidirect
181. #13133210C23semidirect
182. #13133210C23semidirect
183. #13133208C23semidirect
184. #13133207C23semidirect
185. #13133207C23semidirect
187. #13133204C23semidirect
188. #13133204C23semidirect
189. #13133204C23semidirect
190. #13133204C23semidirect
191. #13133204C23semidirect
192. #13133203C23semidirect
193. #13133203C23semidirect
194. #13133203C23semidirect
195. #13133203C23semidirect
196. #13133203C23semidirect
197. #13133203C23semidirect
198. #13133202C23semidirect
199. #13133202C23semidirect
200. #13133201C23semidirect
201. #13133201C23semidirect
202. #13133201C23semidirect
203. #13133201C23semidirect
206. #13133200C23semidirect
207. #13133200C23semidirect
208. #13133200C23semidirect
209. #13133200C23semidirect
210. #13133200C23semidirect
211. #13133199C23semidirect
212. #13133199C23semidirect
213. #13133199C23semidirect
214. #13133199C23semidirect
215. #13133199C23semidirect
216. #13133199C23semidirect
220. #13133198C23semidirect
221. #13133198C23semidirect
222. #13133198C23semidirect
223. #13133198C23semidirect
224. #13133198C23semidirect
225. #13133198C23semidirect
226. #13133197C23semidirect
227. #13133196C23semidirect
228. #13133196C23semidirect
229. #13133196C23semidirect
230. #13133195C23semidirect
231. #13133195C23semidirect
232. #13133194C23semidirect
233. #13133194C23semidirect
234. #13133194C23semidirect
235. #13133194C23semidirect
236. #13133194C23semidirect
237. #13133194C23semidirect
238. #13133192C23semidirect
240. #13133191C23semidirect
241. #13133191C23semidirect
242. #13133190C23semidirect
243. #13133190C23semidirect
244. #13133190C23semidirect
245. #13133190C23semidirect
246. #13133190C23semidirect
247. #13133190C23semidirect
252. #13133189C23semidirect
253. #13133189C23semidirect
254. #13133189C23semidirect
255. #13133189C23semidirect
256. #13133189C23semidirect
257. #13133189C23semidirect
258. #13133189C23semidirect
259. #13133189C23semidirect
261. #13133188C23semidirect
262. #13133188C23semidirect
263. #13133188C23semidirect
264. #13133188C23semidirect
265. #13133188C23semidirect
266. #13133188C23semidirect
267. #13133188C23semidirect
268. #13133187C23semidirect
269. #13133187C23semidirect
270. #13133187C23semidirect
271. #13133187C23semidirect
278. #13133186C23semidirect
279. #13133186C23semidirect
280. #13133186C23semidirect
281. #13133186C23semidirect
282. #13133186C23semidirect
283. #13133186C23semidirect
284. #13133186C23semidirect
288. #13133185C23semidirect
289. #13133185C23semidirect
290. #13133185C23semidirect
291. #13133185C23semidirect
292. #13133185C23semidirect
293. #13133185C23semidirect
294. #13133182C23semidirect
296. D4×Dic53C23semidirect
297. D4×Dic53C23semidirect
298. D4×Dic53C23semidirect
299. #13133179C23semidirect
301. C4×C22⋊D53C23semidirect
302. C4×C22⋊D53C23semidirect
303. C4×C22⋊D53C23semidirect
304. C4×C22⋊D53C23semidirect
305. C4×C22⋊D53C23semidirect
306. #13133177C23semidirect
307. #13133177C23semidirect
308. #13133177C23semidirect
309. #13133177C23semidirect
310. #13133177C23semidirect
311. #13133177C23semidirect
312. #13133176C23semidirect
313. #13133176C23semidirect
314. #13133176C23semidirect
315. #13133176C23semidirect
316. #13133175C23semidirect
317. #13133173C23semidirect
318. #13133173C23semidirect
319. #13133173C23semidirect
320. #13133173C23semidirect
321. C2×C4⋊Dic53C23semidirect
322. C2×#11719919C23semidirect
323. C4⋊C4×D53C23semidirect
328. C2×C22⋊Dic53C23semidirect
329. C2×C22⋊Dic53C23semidirect
330. C2×C22⋊Dic53C23semidirect
331. C2×C22⋊Dic53C23semidirect
332. C2×C22⋊Dic53C23semidirect
333. C2×C22⋊Dic53C23semidirect
334. C2×#11719921C23semidirect
335. C22⋊C4×D53C23semidirect
336. C22⋊C4×D53C23semidirect
337. C22⋊C4×D53C23semidirect
338. C22⋊C4×D53C23semidirect
339. C2×C4×Dic53C23semidirect
342. C25×C53C23semidirect
354. C22×D4×C53C23semidirect
355. C22×D4×C53C23semidirect
357. C23×C4×C53C23semidirect
358. C23×C4×C53C23semidirect
362. #123×C53C23semidirect
363. #123×C53C23semidirect
364. #123×C53C23semidirect
365. #123×C53C23semidirect
368. #121×C53C23semidirect
369. #121×C53C23semidirect
375. #120×C53C23semidirect
376. #120×C53C23semidirect
377. C2×C4⋊C4×C53C23semidirect
381. C2×C22⋊C4×C53C23semidirect
382. C2×C22⋊C4×C53C23semidirect
383. C2×C22⋊C4×C53C23semidirect
720. C2×#534D53semidirect
736. C23×D4C2×D53semidirect
737. C23×D4C2×D53semidirect
819. #534C2×D53semidirect
820. #534C2×D53semidirect
821. #534C2×D53semidirect
822. #534C2×D53semidirect
834. C2×#123C2×D53semidirect
835. C2×#123C2×D53semidirect
838. C2×#121C2×D53semidirect
845. C2×#120C2×D53semidirect
846. C2×#120C2×D53semidirect
852. C22×C22⋊C4C2×D53semidirect
853. C53#62862semidirect
857. C25C22×D53semidirect
894. C22×D4C22×D53semidirect
895. C22×D4C22×D53semidirect
900. C23×C4C22×D53semidirect
901. C23×C4C22×D53semidirect
963. #123C22×D53semidirect
964. #123C22×D53semidirect
965. #123C22×D53semidirect
966. #123C22×D53semidirect
1011. #121C22×D53semidirect
1012. #121C22×D53semidirect
1044. #120C22×D53semidirect
1045. #120C22×D53semidirect
1076. C2×C4⋊C4C22×D53semidirect
1095. C2×C22⋊C4C22×D53semidirect
1096. C2×C22⋊C4C22×D53semidirect
1097. C2×C22⋊C4C22×D53semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202890642
#202890422
#202890352
#202890262
#202888952
#202888862
#202888762
#202888702
#202888672
#202884112
#202884042
#202884022
#202883532
#202883502
#202883442
C2×#168111902
C2×#168111822
C2×C53×#5342
#6286253