Finite Group Databasebeta

← #28293285

Subgroups — #28293285

Order 13568.

10986 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811458C211yesmaximal, characteristic, complemented
2C22×#13133264C211yesmaximal, characteristic, complemented
3#20288501C218yesmaximal, complemented
4#20288494C218yesmaximal, complemented
5#20288389C218yesmaximal, complemented
6#20288386C218yesmaximal, complemented
7#20288364C212yesmaximal, complemented
8#20288362C212yesmaximal, complemented
9#20288360C211yesmaximal, characteristic, complemented
10#20288359C211yesmaximal, characteristic, complemented
11#20288356C214yesmaximal, complemented
12#20288355C211yesmaximal, characteristic, complemented
13#20288353C214yesmaximal, complemented
14#20288045C212yesmaximal, complemented
15#20288041C214yesmaximal, complemented
16C2×#16811195C214yesmaximal, complemented
17#536×D53C212yesmaximal, complemented
18#20287913C211yesmaximal, characteristic, complemented
19C53×#3485C211yesmaximal, characteristic, complemented
20#16811458—216no—
21C2×#13133264—216no—
22C2×#13133264C2212yes—
23C2×#13133264C2218yescomplemented
24C2×#13133264C2214yescomplemented
25C2×#13133264C2218yescomplemented
26C2×#13133262C2214yes—
27C2×#13133262C2211yescharacteristic
28C2×#13133262C2214yescomplemented
29C22×#11719945C2211yescharacteristic, complemented
30C22×#11719945C2212yescomplemented
31C22×#11719947C2214yes—
32C22×#11719947C2211yescharacteristic
33C22×#11719947C2212yescomplemented
34C22×#11719947C2211yescharacteristic, complemented
35C22×#11719947C2212yescomplemented
36C22×#11719947C2214yescomplemented
37C2×#41×D53C2212yes—
38C2×#41×D53C2214yescomplemented
39C23×Dic106C2212yescomplemented
40C23×Dic106C2211yescharacteristic, complemented
41C22×Q8×D53C2211yescharacteristic, complemented
42C22×Q8×D53C2211yescharacteristic, complemented
43D4×Dic106C2218yescomplemented
44#16811288C2218yescomplemented
45#16811286C2218yescomplemented
46#16811286C2218yescomplemented
47#16811283C2218yescomplemented
48#16811282C2218yescomplemented
49#16811281C2218yescomplemented
50#16811279C2218yescomplemented
51#16811277C2218yescomplemented
52#16811274C22116yescomplemented
53#16811273C22116yescomplemented
54#16811272C2218yescomplemented
55#16811272C2218yescomplemented
56#16811271C22116yescomplemented
57#16811271C22116yescomplemented
58#16811268C2218yescomplemented
59#16811267C2218yescomplemented
60#16811265C22116yescomplemented
61#16811263C22116yescomplemented
62#16811262C22116yescomplemented
63#16811261C2218yescomplemented
64#16811260C22116yescomplemented
65#16811203C2214yescomplemented
66#16811202C2214yescomplemented
67#16811200C22116yescomplemented
68#16811199C2212yescomplemented
69#16811198C2214yescomplemented
70#16811197C2212yescomplemented
71#16811196C2218yescomplemented
72#16811196C2214yescomplemented
73#16811195C2218yescomplemented
74#16811195C2214yescomplemented
75#16811195C2218yescomplemented
76#16811195C2218yescomplemented
77#16811195C22116yescomplemented
78#16811195C22116yescomplemented
79#16811195C2218yescomplemented
80#16811194C2212yescomplemented
81#16811193C2214yescomplemented
82#16811189C2214yescomplemented
83#16811188C2214yescomplemented
84#16811188C2218yescomplemented
85#16811185C2214yescomplemented
86#16811184C2214yescomplemented
87#16811183C2214yescomplemented
88#16811182C2214yescomplemented
89#16811182C2214yescomplemented
90#16811170C2218yescomplemented
91#16811168C22116yescomplemented
92C2×#13133216C2218yescomplemented
93C4⋊Q8×D53C2214yescomplemented
94C2×#13133203C2218yescomplemented
95#124×D53C2214yescomplemented
96#16811135C2212yescomplemented
97#16811134C2212yescomplemented
98#16811132C2218yescomplemented
99#16811131C2218yescomplemented
100#16811131C2218yescomplemented
101#16811130C2212yescomplemented
102#16811129C2218yescomplemented
103#16811129C2218yescomplemented
104C2×#13133201C2214yescomplemented
105C2×#13133200C2214yescomplemented
106C2×#13133198C2214yescomplemented
107#123×D53C2218yescomplemented
108C2×#13133195C2218yescomplemented
109C2×#13133194C2218yescomplemented
110C22⋊Q8×D53C2218yescomplemented
111#16811102C2218yescomplemented
112#16811100C2212yescomplemented
113#16811098C2211yescharacteristic, complemented
114#16811096C2214yescomplemented
115C4×#11719947C2218yescomplemented
116C2×#13133173C2214yescomplemented
117#117×D53C2212yescomplemented
118C2×H(5,𝔽2)×C53C2211yescharacteristic
119C22×#41×C53C2211yescharacteristic, complemented
120C53×#547C2218yescomplemented
121C53×#546C2218yescomplemented
122C53×#536C2212yescomplemented
123C53×#534C2214yescomplemented
124C53×#525C2212yescomplemented
125C2×#123×C53C2214yescomplemented
126C53×#518C2211yescharacteristic, complemented
127#13133264—264no—
128#13133264—264no—
129#13133264—232no—
130#13133264—216no—
131#13133262—28no—
132#13133262—232no—
133#13133262—232no—
134C2×#11719949C2312yes—
135C2×#11719945—216no—
136C2×#11719945—28no—
137C2×#11719945C23116yes—
138C2×#11719945C2318yes—
139C2×#11719945C2314yes—
140C2×#11719945C2314yes—
141C2×#11719945C2312yes—
142C2×#11719945C2314yes—
143C2×#11719945C2314yes—
144C2×#11719947—28no—
145C2×#11719947—216no—
146C2×#11719947—232no—
147C2×#11719947—216no—
148C2×#11719947—232no—
149C2×#11719947D4116yescomplemented
150C2×#11719947C2318yes—
151C2×#11719947C2318yes—
152C2×#11719947C23116yes—
153C2×#11719947C2314yes—
154C2×#11719947C2314yes—
155C2×#11719947C2318yes—
156C2×#11719947C2318yes—
157C2×#11719947C2318yes—
158C2×#11719947C2318yes—
159C2×#11719947C2314yes—
160C2×#11719947C2312yes—
161C2×#11719947C2318yes—
162C2×#11719947C2314yes—
163C2×#11719947C2314yes—
164#41×D53—232no—
165#41×D53—216no—
166C22×Dic106—216no—
167C22×Dic106—28no—
168C22×Dic106C2318yes—
169C22×Dic106C2314yes—
170C22×Dic106C2318yes—
171C22×Dic106C2318yes—
172C22×Dic106C2314yes—
173C22×Dic106C2311yescharacteristic
174C22×Dic106C2312yes—
175C22×Dic106C2312yes—
176C22×Dic106C2311yescharacteristic
177C22×Dic106C2312yes—
178C22×Dic106C2311yescharacteristic
179C2×Q8×D53—28no—
180C2×Q8×D53—28no—
181C2×Q8×D53C2318yes—
182C2×Q8×D53C2314yes—
183C2×Q8×D53C2314yes—
184C2×Q8×D53C2314yes—
185C2×Q8×D53C2312yes—
186C22×D212C2311yescharacteristic
187C22×C22⋊D53C2314yes—
188C22×C22⋊D53C2314yes—
189C22×C22⋊D53C2312yes—
190C22×C22⋊D53C2311yescharacteristic
191C22×C22⋊D53C2311yescharacteristic
192C22×C22⋊D53C2318yes—
193C22×C22⋊D53C2312yes—
194C2×D4×D53C2318yes—
195C2×D4×D53C2314yes—
196C2×D4×D53C2314yes—
197C2×D4×D53C2312yes—
198C23×Dic53C2314yes—
199C23×Dic53C2312yes—
200C23×Dic53C2312yes—
201C23×Dic53C2312yes—
202C22×C4×D53C2314yes—
203C22×C4×D53C2314yes—
204C22×C4×D53C2312yes—
205C22×C4×D53C2311yescharacteristic
206C22×C4×D53C2312yes—
207C22×C4×D53C2311yescharacteristic
208#13133217C2314yes—
209#13133216C23116yes—
210#13133216C23116yes—
211#13133216C23116yes—
212#13133216C2318yes—
213#13133215C2314yes—
214#13133215C2314yes—
215#13133213C2318yes—
216#13133206C2314yes—
217#13133205C2314yes—
218#13133204C2314yes—
219#13133203C23116yes—
220#13133203C23116yes—
221#13133203C23116yes—
222#13133203C2318yes—
223#13133203C2318yes—
224#13133202C23116yes—
225#13133202C2318yes—
226#13133201C23116yes—
227#13133201C2318yes—
228#13133201C2318yes—
229#13133201C2314yes—
230#13133200C2318yes—
231#13133200C23116yes—
232#13133200C2318yes—
233#13133200C2314yes—
234#13133199C2318yes—
235#13133199C23116yes—
236#13133198C23116yes—
237#13133198C2318yes—
238#13133198C2318yes—
239#13133198C2314yes—
240#13133197C2318yes—
241#13133197C2314yes—
242#13133196C2318yes—
243#13133196C2314yes—
244#13133195C23116yes—
245#13133195C23116yes—
246#13133195C23116yes—
247#13133195C23116yes—
248#13133195C2318yes—
249#13133194C23116yes—
250#13133194C23116yes—
251#13133194C23116yes—
252#13133194C23116yes—
253#13133194C2318yes—
254#13133193C2314yes—
255#13133193C2318yes—
256#13133192C2318yes—
257#13133192C2314yes—
258#13133191C23116yes—
259#13133191C2314yes—
260#13133190C23116yes—
261#13133190C2318yes—
262#13133190C2318yes—
263#13133190C2318yes—
264#13133189C23116yes—
265#13133189C23116yes—
266#13133189C23116yes—
267#13133189C2318yes—
268#13133188C2314yes—
269#13133188C2318yes—
270#13133187C2318yes—
271#13133187C2318yes—
272#13133187C2314yes—
273#13133186C2318yes—
274#13133186C2314yes—
275#13133185C2314yes—
276#13133185C2318yes—
277#13133185C2318yes—
278C4×Dic106C2318yes—
279#13133182C2318yes—
280C4×D212C2318yes—
281D4×Dic53C2318yes—
282D4×Dic53C23116yes—
283#13133179C23116yes—
284C4×C22⋊D53C2318yes—
285C4×C22⋊D53C2318yes—
286C4×C22⋊D53C23116yes—
287#13133177C23116yes—
288#13133177C23116yes—
289#13133177C23116yes—
290#13133176C2312yes—
291#13133175C2314yes—
292#13133174C2314yes—
293#13133173C2314yes—
294#13133173C2318yes—
295#13133173C2318yes—
296#13133173C2318yes—
297C2×C4⋊Dic53C2318yes—
298C2×#11719919C2318yes—
299C2×#11719919C2318yes—
300C2×#11719919C2318yes—
301C4⋊C4×D53C23116yes—
302C4⋊C4×D53C2314yes—
303C2×C22⋊Dic53C2318yes—
304C2×C22⋊Dic53C2314yes—
305C2×#11719921C2318yes—
306C2×#11719921C2318yes—
307C22⋊C4×D53C23116yes—
308C22⋊C4×D53C2314yes—
309C2×C4×Dic53C2318yes—
310C42×D53C2314yes—
311H(5,𝔽2)×C53—28no—
312C2×#41×C53—28no—
313C2×#41×C53C2314yes—
314C2×#41×C53C2318yes—
315C2×#41×C53C2312yes—
316C22×Q8×C53C2311yescharacteristic
317C22×D4×C53C2314yes—
318C22×D4×C53C2314yes—
319C22×D4×C53C2312yes—
320C22×D4×C53C2311yescharacteristic
321C23×C4×C53C2312yes—
322C23×C4×C53C2311yescharacteristic
323C4⋊Q8×C53C2314yes—
324#124×C53C2314yes—
325#123×C53C23116yes—
326#123×C53C2318yes—
327#123×C53C2314yes—
328#123×C53C2318yes—
329C22⋊Q8×C53C2318yes—
330C22⋊Q8×C53C2314yes—
331#121×C53C23116yes—
332#121×C53C2314yes—
333#120×C53C2314yes—
334#120×C53C2318yes—
335C4×D4×C53C2318yes—
336C4×D4×C53C2318yes—
337#117×C53C2312yes—
338C2×C4⋊C4×C53C2318yes—
339C2×C22⋊C4×C53C2314yes—
340C2×C22⋊C4×C53C2318yes—
341C24×C53C2414yes—
342C24×C53C2411yescharacteristic
343C24×C53C2412yes—
344C23×D53C2414yes—
345C23×D53C2414yes—
346C23×D53C2411yescharacteristic
347C23×D53C2411yescharacteristic
348#41×C53—232no—
349#41×C53—216no—
350#41×C53—28no—
351C2×Q8×C53—24no—
352C2×Q8×C53C2414yes—
353C2×Q8×C53C2412yes—
354C2×D4×C53—28no—
355C2×D4×C53—216no—
356C2×D4×C53—216no—
357C2×D4×C53C2×D418yes—
358C2×D4×C53C2418yes—
359C2×D4×C53C2414yes—
360C2×D4×C53C2418yes—
361C2×D4×C53C2412yes—
362C2×D4×C53C2418yes—
363C2×D4×C53C2414yes—
364C22×C4×C53—28no—
365C22×C4×C53—24no—
366C22×C4×C53C2418yes—
367C22×C4×C53C2414yes—
368C22×C4×C53C2414yes—
369C22×C4×C53C2414yes—
370C22×C4×C53C2411yescharacteristic
371C22×C4×C53C2412yes—
372C22×C4×C53C2418yes—
373C22×C4×C53C2411yescharacteristic
374C2×C22⋊D53—28no—
375C2×C22⋊D53—216no—
376C2×C22⋊D53—24no—
377C2×C22⋊D53—232no—
378C2×C22⋊D53—24no—
379C2×C22⋊D53—216no—
380C2×C22⋊D53C2×D4116yes—
381C2×C22⋊D53C2414yes—
382C2×C22⋊D53C2418yes—
383C2×C22⋊D53C2414yes—
384C2×C22⋊D53C2414yes—
385C2×C22⋊D53C2412yes—
386C2×C22⋊D53C2418yes—
387C2×C22⋊D53C2418yes—
388C2×C22⋊D53C2414yes—
389C2×C22⋊D53C2412yes—
390C2×C22⋊D53C2418yes—
391C2×C22⋊D53C2418yes—
392C2×C22⋊D53C2418yes—
393C22×Dic53—28no—
394C22×Dic53—28no—
395C22×Dic53—216no—
396C22×Dic53C2×D4116yes—
397C22×Dic53C2418yes—
398C22×Dic53C2414yes—
399C22×Dic53C2418yes—
400C22×Dic53C2418yes—
401C22×Dic53C2414yes—
402C22×Dic53C2412yes—
403C22×Dic53C2411yescharacteristic
404C22×Dic53C2418yes—
405C22×Dic53C2414yes—
406C22×Dic53C2414yes—
407C22×Dic53C2411yescharacteristic
408C22×Dic53C2412yes—
409#11719949—28no—
410Q8×D53—216no—
411Q8×D53—216no—
412Q8×D53—28no—
413Q8×D53—232no—
414Q8×D53—216no—
415#11719947—216no—
416#11719947—232no—
417#11719947—232no—
418#11719947—264no—
419#11719947—216no—
420#11719947—232no—
421#11719947—232no—
422#11719947—232no—
423#11719947—232no—
424#11719947—232no—
425#11719947—28no—
426#11719947—216no—
427#11719947C2×D4132yes—
428#11719947C2×D4132yes—
429D4×D53—216no—
430D4×D53—216no—
431D4×D53—232no—
432D4×D53—28no—
433#11719945—28no—
434#11719945—232no—
435#11719945—264no—
436#11719945—216no—
437#11719945—216no—
438#11719945—216no—
439#11719945—216no—
440C2×D212—24no—
441C2×D212C2414yes—
442C2×D212C2414yes—
443C2×D212C2412yes—
444C2×D212C2418yes—
445C2×C4×D53—28no—
446C2×C4×D53—24no—
447C2×C4×D53—28no—
448C2×C4×D53—216no—
449C2×C4×D53—216no—
450C2×C4×D53C2×D418yes—
451C2×C4×D53C2418yes—
452C2×C4×D53C2414yes—
453C2×C4×D53C2418yes—
454C2×C4×D53C2418yes—
455C2×C4×D53C2414yes—
456C2×C4×D53C2414yes—
457C2×C4×D53C2414yes—
458C2×C4×D53C2418yes—
459C2×C4×D53C2412yes—
460C2×C4×D53C2412yes—
461C2×Dic106—24no—
462C2×Dic106—28no—
463C2×Dic106—28no—
464C2×Dic106—24no—
465C2×Dic106—28no—
466C2×Dic106—232no—
467C2×Dic106—232no—
468C2×Dic106—216no—
469C2×Dic106—232no—
470C2×Dic106—216no—
471C2×Dic106C2×D418yes—
472C2×Dic106C2414yes—
473C2×Dic106C2412yes—
474C2×Dic106C2418yes—
475C2×Dic106C2418yes—
476C2×Dic106C2418yes—
477C2×Dic106C2414yes—
478C2×Dic106C2412yes—
479C2×Dic106C2414yes—
480C2×Dic106C2412yes—
481C2×Dic106C2414yes—
482C2×Dic106C2414yes—
483C4⋊C4×C53C2418yes—
484C4⋊C4×C53C24116yes—
485C4⋊C4×C53C2414yes—
486C22⋊C4×C53C2414yes—
487C22⋊C4×C53C2418yes—
488C22⋊C4×C53C2418yes—
489C22⋊C4×C53C24116yes—
490C22⋊C4×C53C2418yes—
491C42×C53C2414yes—
492C22⋊Dic53C2414yes—
493C22⋊Dic53C24116yes—
494C22⋊Dic53C2418yes—
495C22⋊Dic53C2418yes—
496C22⋊Dic53C2418yes—
497#11719921C24116yes—
498#11719921C24116yes—
499#11719921C2418yes—
500#11719921C2418yes—
501#11719921C2418yes—
502#11719921C2418yes—
503#11719921C2418yes—
504C4⋊Dic53C24116yes—
505C4⋊Dic53C2414yes—
506C4⋊Dic53C2418yes—
507#11719919C2418yes—
508#11719919C24116yes—
509#11719919C24116yes—
510#11719919C2418yes—
511#11719919C2418yes—
512#11719919C24116yes—
513C4×Dic53C2418yes—
514C4×Dic53C2414yes—
515C4×Dic53C24116yes—
516C23×C53—22no—
517C23×C53—28no—
518C23×C53—44no—
519C23×C53—42no—
520C23×C53—48no—
521C23×C53C22×D418yes—
522C23×C53C2512yes—
523C23×C53C2514yes—
524C23×C53C2514yes—
525C23×C53C2511yescharacteristic
526C22×D53—22no—
527C22×D53—28no—
528C22×D53—28no—
529C22×D53—42no—
530C22×D53—42no—
531C22×D53—48no—
532C22×D53—48no—
533C22×D53C22×D414yes—
534C22×D53C2512yes—
535C22×D53C2514yes—
536C22×D53C2512yes—
537Q8×C53—28no—
538Q8×C53—24no—
539D4×C53—28no—
540D4×C53—216no—
541D4×C53—216no—
542D4×C53—24no—
543D4×C53—48no—
544D4×C53C22×D4116yes—
545C2×C4×C53—22no—
546C2×C4×C53—24no—
547C2×C4×C53—216no—
548C2×C4×C53—28no—
549C2×C4×C53—28no—
550C2×C4×C53—28no—
551C2×C4×C53—48no—
552C2×C4×C53C22×D414yes—
553C2×C4×C53C2512yes—
554C2×C4×C53C2514yes—
555C2×C4×C53C2514yes—
556C2×C4×C53C2518yes—
557C2×C4×C53C2512yes—
558C22⋊D53—216no—
559C22⋊D53—28no—
560C22⋊D53—216no—
561C22⋊D53—28no—
562C22⋊D53—28no—
563C22⋊D53—24no—
564C22⋊D53—24no—
565C22⋊D53—28no—
566C22⋊D53—216no—
567C22⋊D53—48no—
568C22⋊D53—48no—
569C22⋊D53C22×D4132yes—
570C2×Dic53—24no—
571C2×Dic53—22no—
572C2×Dic53—216no—
573C2×Dic53—28no—
574C2×Dic53—216no—
575C2×Dic53—216no—
576C2×Dic53—28no—
577C2×Dic53—48no—
578C2×Dic53C22×D414yes—
579C2×Dic53C22×D4116yes—
580C2×Dic53C22×D418yes—
581C2×Dic53C22×D4116yes—
582C2×Dic53C2514yes—
583C2×Dic53C2512yes—
584C2×Dic53C2514yes—
585C2×Dic53C2518yes—
586C2×Dic53C2511yescharacteristic
587C2×Dic53C2514yes—
588C2×Dic53C2511yescharacteristic
589D212—28no—
590D212—28no—
591D212—24no—
592D212—48no—
593C4×D53—28no—
594C4×D53—216no—
595C4×D53—28no—
596C4×D53—28no—
597C4×D53—28no—
598C4×D53—216no—
599C4×D53—216no—
600C4×D53—48no—
601C4×D53C22×D418yes—
602C4×D53C22×D418yes—
603Dic106—28no—
604Dic106—24no—
605Dic106—24no—
606Dic106—216no—
607Dic106—24no—
608Dic106—28no—
609Dic106—216no—
610Dic106—28no—
611Dic106—28no—
612Dic106—216no—
613Dic106C22×D4116yes—
614#62859—531nomaximal, Sylow
615C22×C53—28no—
616C22×C53—22no—
617C22×C53—22no—
618C22×C53—24no—
619C22×C53—24no—
620C22×C53—28no—
621C22×C53—48no—
622C22×C53—44no—
623C22×C53—88no—
624C22×C53C23×D412yes—
625C22×C53C23×D418yes—
626C22×C53C2611yescharacteristic
627C2×D53—24no—
628C2×D53—22no—
629C2×D53—24no—
630C2×D53—24no—
631C2×D53—28no—
632C2×D53—44no—
633C2×D53—44no—
634C2×D53—88no—
635C2×D53—88no—
636C2×D53C23×D414yes—
637C4×C53—22no—
638C4×C53—24no—
639C4×C53—24no—
640C4×C53—28no—
641C4×C53C23×D414yes—
642Dic53—24no—
643Dic53—22no—
644Dic53—24no—
645Dic53—28no—
646Dic53C23×D412yes—
647Dic53C23×D418yes—
648Dic53C23×D412yes—
649C2×#585—531no—
650C22×2−1+4—531no—
651#3500—538no—
652#3499—538no—
653#3489—538no—
654#3489—538no—
655#3486—532no—
656#3486—532no—
657#3485—531no—
658#3485—531no—
659#3485—534no—
660#3485—534no—
661#3485—531no—
662#3485D5311yescharacteristic, complemented
663#3449—534no—
664#3449—532no—
665C2×#536—532no—
666C2×#536—534no—
667#3428—531no—
668C2×C53—22no—
669C2×C53—28no—
670C2×C53—44no—
671C2×C53—42no—
672C2×C53C24×D411yescharacteristic
673C2×C532−1+612yes—
674D53—24no—
675D53—42no—
676D53—44no—
677#585—10616no—
678C2×2−1+4—538no—
679C2×2−1+4—538no—
680C2×2−1+4—532no—
681C2×2−1+4—534no—
682C2×2−1+4—10616no—
683C2×H(5,𝔽2)—534no—
684C2×H(5,𝔽2)—531no—
685C2×H(5,𝔽2)—534no—
686C2×H(5,𝔽2)C2×D5311yescharacteristic
687C22×#41—532no—
688C22×#41—534no—
689C22×#41—531no—
690C22×#41—532no—
691C22×#41—531no—
692C22×#41—532no—
693C22×#41—534no—
694C22×#41—534no—
695C22×#41—531no—
696C22×#41—532no—
697C22×#41C2×D5311yescharacteristic, complemented
698C23×Q8—531no—
699C23×Q8—531no—
700C23×Q8—532no—
701C23×Q8—531no—
702D4×Q8—538no—
703D4×Q8—538no—
704D4×Q8—538no—
705D4×Q8—538no—
706#548—538no—
707#548—538no—
708#548—538no—
709#548—538no—
710#547—538no—
711#547—538no—
712#547—5316no—
713#547—5316no—
714#547—5316no—
715#547—538no—
716#547—5316no—
717#547C2×D5318yescomplemented
718#546—538no—
719#546—538no—
720#546—5316no—
721#546—5316no—
722#546—5316no—
723#546—538no—
724#546—5316no—
725#546C2×D5318yescomplemented
726#537—534no—
727#537—5316no—
728#537—534no—
729#536—532no—
730#536—532no—
731#536—534no—
732#536—534no—
733#536—538no—
734#536—534no—
735#536—538no—
736#536—538no—
737#536—5316no—
738#536—5316no—
739#536—538no—
740#536—538no—
741#536—534no—
742#536—532no—
743#536C2×D5312yescomplemented
744#535—534no—
745#535—534no—
746#535—538no—
747#534—534no—
748#534—534no—
749#534—534no—
750#534—534no—
751#534—534no—
752#534C2×D5314yescomplemented
753#532—5316no—
754#532—538no—
755C2×C4⋊Q8—534no—
756C2×C4⋊Q8—538no—
757C2×#124—534no—
758C2×#124—538no—
759#525—532no—
760#525—532no—
761#525—538no—
762#525—538no—
763#525—538no—
764#525—538no—
765#525—538no—
766#525—532no—
767#525C2×D5312yescomplemented
768C2×#123—534no—
769C2×#123—534no—
770C2×#123—538no—
771C2×#123—534no—
772C2×#123C2×D5314yescomplemented
773C2×C22⋊Q8—538no—
774C2×C22⋊Q8—538no—
775C2×C22⋊Q8—538no—
776#520—538no—
777#519—532no—
778#518—531no—
779#518—534no—
780#518C2×D5311yescharacteristic, complemented
781C4×#41—538no—
782C2×#117—532no—
783C2×#117—534no—
784C53#6285911yescharacteristic, complemented, Sylow
7852−1+4—10616no—
7862−1+4—10664no—
7872−1+4—10664no—
7882−1+4—10632no—
789H(5,𝔽2)—28no—
790H(5,𝔽2)—10632no—
791H(5,𝔽2)—10632no—
792H(5,𝔽2)—1068no—
793C2×#41—28no—
794C2×#41—532no—
795C2×#41—5316no—
796C2×#41—534no—
797C2×#41—534no—
798C2×#41—538no—
799C2×#41—538no—
800C2×#41—538no—
801C2×#41—538no—
802C2×#41—534no—
803C2×#41—538no—
804C2×#41—532no—
805C2×#41—538no—
806C2×#41—5316no—
807C2×#41—534no—
808C2×#41—538no—
809C2×#41—534no—
810C2×#41—532no—
811C2×#41—534no—
812C2×#41—534no—
813C2×#41—534no—
814C2×#41—5316no—
815C2×#41—538no—
816C2×#41—534no—
817C2×#41—1068no—
818C2×#41—10616no—
819C2×#41—10616no—
820C2×#41—10632no—
821C2×#41—10616no—
822C2×#41—10616no—
823C2×#41—10632no—
824C2×#41—10632no—
825C2×#41—1068no—
826C2×#41C22×D5312yes—
827C2×#41C22×D5318yes—
828C2×#41C22×D5314yes—
829C22×Q8—534no—
830C22×Q8—534no—
831C22×Q8—532no—
832C22×Q8—538no—
833C22×Q8—534no—
834C22×Q8—531no—
835C22×Q8—538no—
836C22×Q8—538no—
837C22×Q8—534no—
838C22×Q8—532no—
839C22×Q8—532no—
840C22×Q8—531no—
841C22×Q8—532no—
842C22×Q8—531no—
843C22×Q8—538no—
844C22×Q8—534no—
845C22×Q8—10616no—
846C22×Q8—1068no—
847C22×Q8—1068no—
848C22×Q8—1068no—
849C22×Q8C22×D5311yescharacteristic
850C22×D4—532no—
851C22×D4—534no—
852C22×D4—534no—
853C22×D4—531no—
854C22×D4—532no—
855C22×D4—531no—
856C22×D4—538no—
857C22×D4—534no—
858C22×D4—532no—
859C22×D4—538no—
860C22×D4—534no—
861C22×D4—531no—
862C22×D4C22×D5314yes—
863C22×D4C22×D5312yes—
864C22×D4C22×D5314yes—
865C22×D4C22×D5311yescharacteristic
866C23×C4—532no—
867C23×C4—531no—
868C23×C4—534no—
869C23×C4—532no—
870C23×C4—532no—
871C23×C4—534no—
872C23×C4—534no—
873C23×C4—532no—
874C23×C4—532no—
875C23×C4—531no—
876C23×C4C22×D5312yes—
877C23×C4C22×D5311yescharacteristic
878C4⋊Q8—534no—
879C4⋊Q8—534no—
880C4⋊Q8—5316no—
881C4⋊Q8—538no—
882C4⋊Q8—5316no—
883C4⋊Q8—5316no—
884C4⋊Q8—534no—
885C4⋊Q8C22×D5314yes—
886#127—538no—
887#124—534no—
888#124—534no—
889#124—5316no—
890#124—538no—
891#124—5316no—
892#124—5316no—
893#124—538no—
894#124—534no—
895#124C22×D5314yes—
896#123—534no—
897#123—538no—
898#123—5316no—
899#123—538no—
900#123—538no—
901#123—534no—
902#123—5316no—
903#123—538no—
904#123—5316no—
905#123—538no—
906#123—538no—
907#123—534no—
908#123—5316no—
909#123—5316no—
910#123—538no—
911#123—538no—
912#123C22×D5318yes—
913#123C22×D5314yes—
914#123C22×D53116yes—
915#123C22×D5318yes—
916C22⋊Q8—538no—
917C22⋊Q8—534no—
918C22⋊Q8—538no—
919C22⋊Q8—534no—
920C22⋊Q8—5316no—
921C22⋊Q8—538no—
922C22⋊Q8—5316no—
923C22⋊Q8—5316no—
924C22⋊Q8—538no—
925C22⋊Q8—5316no—
926C22⋊Q8—534no—
927C22⋊Q8—5316no—
928C22⋊Q8—538no—
929C22⋊Q8—5316no—
930C22⋊Q8—5316no—
931C22⋊Q8—5316no—
932C22⋊Q8C22×D5318yes—
933C22⋊Q8C22×D5314yes—
934#121—538no—
935#121—534no—
936#121—5316no—
937#121—538no—
938#121—5316no—
939#121—5316no—
940#121—534no—
941#121—5316no—
942#121—534no—
943#121—538no—
944#121—538no—
945#121—5316no—
946#121—538no—
947#121—538no—
948#121C22×D5314yes—
949#121C22×D53116yes—
950#120—534no—
951#120—538no—
952#120—534no—
953#120—538no—
954#120—538no—
955#120—534no—
956#120—538no—
957#120—538no—
958#120C22×D5314yes—
959#120C22×D5318yes—
960C4×Q8—538no—
961C4×Q8—538no—
962C4×D4—538no—
963C4×D4—5316no—
964C4×D4—5316no—
965C4×D4—538no—
966C4×D4—538no—
967C4×D4—5316no—
968C4×D4—5316no—
969C4×D4—5316no—
970C4×D4—5316no—
971C4×D4—538no—
972C4×D4C22×D5318yes—
973C4×D4C22×D5318yes—
974#117—532no—
975#117—534no—
976#117—534no—
977#117—538no—
978#117—538no—
979#117—538no—
980#117—534no—
981#117C22×D5312yes—
982C2×C4⋊C4—538no—
983C2×C4⋊C4—538no—
984C2×C4⋊C4—538no—
985C2×C4⋊C4—538no—
986C2×C4⋊C4—534no—
987C2×C4⋊C4—5316no—
988C2×C4⋊C4C22×D5318yes—
989C2×C22⋊C4—534no—
990C2×C22⋊C4—538no—
991C2×C22⋊C4—538no—
992C2×C22⋊C4—538no—
993C2×C22⋊C4—534no—
994C2×C22⋊C4—5316no—
995C2×C22⋊C4C22×D5314yes—
996C2×C22⋊C4C22×D5318yes—
997C2×C42—538no—
998C2×C42—534no—
999C24—531no—
1000C24—534no—
1001C24—534no—
1002C24—531no—
1003C24C23×D5314yes—
1004C24C23×D5311yescharacteristic
1005C24C23×D5312yes—
1006#41—232no—
1007#41—216no—
1008#41—28no—
1009#41—5332no—
1010#41—5332no—
1011#41—10616no—
1012#41—10616no—
1013#41—10616no—
1014#41—10632no—
1015#41—10664no—
1016#41—10616no—
1017#41—10616no—
1018#41—10632no—
1019#41—1068no—
1020#41—10632no—
1021#41—10632no—
1022#41—10632no—
1023#41—10632no—
1024#41—1068no—
1025#41—10632no—
1026#41—10664no—
1027#41—10616no—
1028#41—10616no—
1029#41—10632no—
1030#41—1068no—
1031C2×Q8—24no—
1032C2×Q8—538no—
1033C2×Q8—534no—
1034C2×Q8—534no—
1035C2×Q8—532no—
1036C2×Q8—538no—
1037C2×Q8—538no—
1038C2×Q8—534no—
1039C2×Q8—538no—
1040C2×Q8—532no—
1041C2×Q8—534no—
1042C2×Q8—532no—
1043C2×Q8—534no—
1044C2×Q8—1064no—
1045C2×Q8—1068no—
1046C2×Q8—1068no—
1047C2×Q8—1068no—
1048C2×Q8—10632no—
1049C2×Q8—10632no—
1050C2×Q8—10616no—
1051C2×Q8—10632no—
1052C2×Q8—10616no—
1053C2×Q8—10616no—
1054C2×Q8—10616no—
1055C2×Q8—1068no—
1056C2×Q8—10632no—
1057C2×Q8—10616no—
1058C2×Q8—1064no—
1059C2×Q8C23×D5314yes—
1060C2×Q8C23×D5312yes—
1061C2×D4—28no—
1062C2×D4—216no—
1063C2×D4—216no—
1064C2×D4—5316no—
1065C2×D4—538no—
1066C2×D4—534no—
1067C2×D4—538no—
1068C2×D4—534no—
1069C2×D4—532no—
1070C2×D4—534no—
1071C2×D4—538no—
1072C2×D4—538no—
1073C2×D4—534no—
1074C2×D4—532no—
1075C2×D4—538no—
1076C2×D4—538no—
1077C2×D4—534no—
1078C2×D4—534no—
1079C2×D4—532no—
1080C2×D4—538no—
1081C2×D4—1064no—
1082C2×D4—1068no—
1083C2×D4—1064no—
1084C2×D4—10616no—
1085C2×D4—10632no—
1086C2×D4—10616no—
1087C2×D4—10632no—
1088C2×D4—1064no—
1089C2×D4—1068no—
1090C2×D4—10616no—
1091C2×D4—10616no—
1092C2×D4D4×D5318yes—
1093C2×D4C23×D5318yes—
1094C2×D4C23×D5314yes—
1095C2×D4C23×D5318yes—
1096C2×D4C23×D5312yes—
1097C2×D4C23×D5318yes—
1098C2×D4C23×D5314yes—
1099C22×C4—28no—
1100C22×C4—24no—
1101C22×C4—5316no—
1102C22×C4—534no—
1103C22×C4—534no—
1104C22×C4—531no—
1105C22×C4—532no—
1106C22×C4—538no—
1107C22×C4—532no—
1108C22×C4—532no—
1109C22×C4—538no—
1110C22×C4—534no—
1111C22×C4—538no—
1112C22×C4—538no—
1113C22×C4—534no—
1114C22×C4—531no—
1115C22×C4—532no—
1116C22×C4—538no—
1117C22×C4—538no—
1118C22×C4—534no—
1119C22×C4—538no—
1120C22×C4—534no—
1121C22×C4—538no—
1122C22×C4—534no—
1123C22×C4—534no—
1124C22×C4—538no—
1125C22×C4—1068no—
1126C22×C4—10616no—
1127C22×C4—10616no—
1128C22×C4—1068no—
1129C22×C4—1068no—
1130C22×C4—10616no—
1131C22×C4—1068no—
1132C22×C4—1064no—
1133C22×C4C23×D5318yes—
1134C22×C4C23×D5314yes—
1135C22×C4C23×D5314yes—
1136C22×C4C23×D5314yes—
1137C22×C4C23×D5312yes—
1138C22×C4C23×D5311yescharacteristic
1139C22×C4C23×D5318yes—
1140C22×C4C23×D5311yescharacteristic
1141C4⋊C4—538no—
1142C4⋊C4—538no—
1143C4⋊C4—5316no—
1144C4⋊C4—5316no—
1145C4⋊C4—538no—
1146C4⋊C4—538no—
1147C4⋊C4—5316no—
1148C4⋊C4—5316no—
1149C4⋊C4—534no—
1150C4⋊C4C23×D53116yes—
1151C4⋊C4C23×D5314yes—
1152C4⋊C4C23×D5318yes—
1153C22⋊C4—534no—
1154C22⋊C4—538no—
1155C22⋊C4—5316no—
1156C22⋊C4—538no—
1157C22⋊C4—538no—
1158C22⋊C4—5316no—
1159C22⋊C4—538no—
1160C22⋊C4—538no—
1161C22⋊C4—5316no—
1162C22⋊C4—538no—
1163C22⋊C4—538no—
1164C22⋊C4—538no—
1165C22⋊C4C23×D5314yes—
1166C22⋊C4C23×D53116yes—
1167C22⋊C4C23×D5318yes—
1168C22⋊C4C23×D5318yes—
1169C22⋊C4C23×D5318yes—
1170C42—538no—
1171C42—5316no—
1172C42—534no—
1173C42C23×D5314yes—
1174C23—22no—
1175C23—28no—
1176C23—44no—
1177C23—42no—
1178C23—48no—
1179C23—532no—
1180C23—534no—
1181C23—534no—
1182C23—532no—
1183C23—1068no—
1184C23—1068no—
1185C23—1062no—
1186C23—2128no—
1187C23—2128no—
1188C23—2122no—
1189C23—2122no—
1190C23C2×D4×D5318yes—
1191C23C24×D5314yes—
1192C23C24×D5312yes—
1193C23C24×D5311yescharacteristic
1194C23C24×D5314yes—
1195Q8—28no—
1196Q8—24no—
1197Q8—5316no—
1198Q8—1064no—
1199Q8—1064no—
1200Q8—10616no—
1201Q8—1068no—
1202Q8—1068no—
1203Q8—10616no—
1204Q8—1068no—
1205Q8—10616no—
1206Q8—1068no—
1207Q8—1064no—
1208D4—28no—
1209D4—216no—
1210D4—216no—
1211D4—24no—
1212D4—48no—
1213D4—5332no—
1214D4—1068no—
1215D4—1068no—
1216D4—1068no—
1217D4—10616no—
1218D4—1064no—
1219D4—1064no—
1220D4—1068no—
1221D4—1068no—
1222D4—1068no—
1223D4—10616no—
1224D4—10616no—
1225D4—1064no—
1226D4—2128no—
1227D4—2128no—
1228D4—2128no—
1229D4C2×D4×D53116yes—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—216no—
1233C2×C4—28no—
1234C2×C4—28no—
1235C2×C4—28no—
1236C2×C4—48no—
1237C2×C4—534no—
1238C2×C4—538no—
1239C2×C4—5316no—
1240C2×C4—5316no—
1241C2×C4—531no—
1242C2×C4—534no—
1243C2×C4—531no—
1244C2×C4—538no—
1245C2×C4—538no—
1246C2×C4—538no—
1247C2×C4—532no—
1248C2×C4—534no—
1249C2×C4—534no—
1250C2×C4—1068no—
1251C2×C4—10616no—
1252C2×C4—10616no—
1253C2×C4—1068no—
1254C2×C4—10616no—
1255C2×C4—1068no—
1256C2×C4—10616no—
1257C2×C4—10616no—
1258C2×C4—1064no—
1259C2×C4—1062no—
1260C2×C4—1068no—
1261C2×C4—10616no—
1262C2×C4—1068no—
1263C2×C4—1068no—
1264C2×C4—2128no—
1265C2×C4—2128no—
1266C2×C4C2×D4×D5314yes—
1267C2×C4C24×D5318yes—
1268C2×C4C24×D5314yes—
1269C2×C4C24×D5312yes—
1270C2×C4C24×D5314yes—
1271C2×C4C24×D5312yes—
1272C22—28no—
1273C22—22no—
1274C22—22no—
1275C22—24no—
1276C22—24no—
1277C22—28no—
1278C22—48no—
1279C22—44no—
1280C22—88no—
1281C22—534no—
1282C22—1064no—
1283C22—1062no—
1284C22—1064no—
1285C22—1064no—
1286C22—1068no—
1287C22—4248no—
1288C22—4248no—
1289C22—2124no—
1290C22—2124no—
1291C22C22×D4×D5312yes—
1292C22C22×D4×D5318yes—
1293C22C25×D5311yescharacteristic
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—28no—
1298C4—532no—
1299C4—532no—
1300C4—538no—
1301C4—1064no—
1302C4—1064no—
1303C4—1062no—
1304C4—1068no—
1305C4C22×D4×D5314yes—
1306C2—22no—
1307C2—28no—
1308C2—42no—
1309C2—44no—
1310C2—1064no—
1311C2—2124no—
1312C2—2122no—
1313C2C23×D4×D5311yescharacteristic
1314C2#2028952812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3485C2
hypercenter#3485D53
hypocenterC53#62859
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3485

Complements

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

NH ≅ G/Ntype
1. C2×#16811458C2semidirect
2. C22×#13133264C2semidirect
3. #20288501C2semidirect
4. #20288494C2semidirect
5. #20288389C2semidirect
6. #20288386C2semidirect
7. #20288364C2semidirect
8. #20288362C2semidirect
9. #20288360C2semidirect
10. #20288359C2semidirect
11. #20288356C2semidirect
12. #20288355C2semidirect
13. #20288353C2semidirect
14. #20288045C2semidirect
15. #20288041C2semidirect
16. C2×#16811195C2semidirect
17. #536×D53C2semidirect
18. #20287913C2semidirect
19. C53×#3485C2semidirect
23. C2×#13133264C22semidirect
24. C2×#13133264C22semidirect
25. C2×#13133264C22semidirect
28. C2×#13133262C22semidirect
29. C22×#11719945C22semidirect
30. C22×#11719945C22semidirect
33. C22×#11719947C22semidirect
34. C22×#11719947C22semidirect
35. C22×#11719947C22semidirect
36. C22×#11719947C22semidirect
38. C2×#41×D53C22semidirect
39. C23×Dic106C22semidirect
40. C23×Dic106C22semidirect
41. C22×Q8×D53C22semidirect
42. C22×Q8×D53C22semidirect
43. D4×Dic106C22semidirect
44. #16811288C22semidirect
45. #16811286C22semidirect
46. #16811286C22semidirect
47. #16811283C22semidirect
48. #16811282C22semidirect
49. #16811281C22semidirect
50. #16811279C22semidirect
51. #16811277C22semidirect
52. #16811274C22semidirect
53. #16811273C22semidirect
54. #16811272C22semidirect
55. #16811272C22semidirect
56. #16811271C22semidirect
57. #16811271C22semidirect
58. #16811268C22semidirect
59. #16811267C22semidirect
60. #16811265C22semidirect
61. #16811263C22semidirect
62. #16811262C22semidirect
63. #16811261C22semidirect
64. #16811260C22semidirect
65. #16811203C22semidirect
66. #16811202C22semidirect
67. #16811200C22semidirect
68. #16811199C22semidirect
69. #16811198C22semidirect
70. #16811197C22semidirect
71. #16811196C22semidirect
72. #16811196C22semidirect
73. #16811195C22semidirect
74. #16811195C22semidirect
75. #16811195C22semidirect
76. #16811195C22semidirect
77. #16811195C22semidirect
78. #16811195C22semidirect
79. #16811195C22semidirect
80. #16811194C22semidirect
81. #16811193C22semidirect
82. #16811189C22semidirect
83. #16811188C22semidirect
84. #16811188C22semidirect
85. #16811185C22semidirect
86. #16811184C22semidirect
87. #16811183C22semidirect
88. #16811182C22semidirect
89. #16811182C22semidirect
90. #16811170C22semidirect
91. #16811168C22semidirect
92. C2×#13133216C22semidirect
93. C4⋊Q8×D53C22semidirect
94. C2×#13133203C22semidirect
95. #124×D53C22semidirect
96. #16811135C22semidirect
97. #16811134C22semidirect
98. #16811132C22semidirect
99. #16811131C22semidirect
100. #16811131C22semidirect
101. #16811130C22semidirect
102. #16811129C22semidirect
103. #16811129C22semidirect
104. C2×#13133201C22semidirect
105. C2×#13133200C22semidirect
106. C2×#13133198C22semidirect
107. #123×D53C22semidirect
108. C2×#13133195C22semidirect
109. C2×#13133194C22semidirect
110. C22⋊Q8×D53C22semidirect
111. #16811102C22semidirect
112. #16811100C22semidirect
113. #16811098C22semidirect
114. #16811096C22semidirect
115. C4×#11719947C22semidirect
116. C2×#13133173C22semidirect
117. #117×D53C22semidirect
119. C22×#41×C53C22semidirect
120. C53×#547C22semidirect
121. C53×#546C22semidirect
122. C53×#536C22semidirect
123. C53×#534C22semidirect
124. C53×#525C22semidirect
125. C2×#123×C53C22semidirect
126. C53×#518C22semidirect
149. C2×#11719947D4semidirect
662. #3485D53semidirect
697. C22×#41C2×D53semidirect
717. #547C2×D53semidirect
725. #546C2×D53semidirect
743. #536C2×D53semidirect
752. #534C2×D53semidirect
767. #525C2×D53semidirect
772. C2×#123C2×D53semidirect
780. #518C2×D53semidirect
784. C53#62859semidirect

Maximal subgroups

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

subgroupindex
C2×#168114582
C22×#131332642
#202885012
#202884942
#202883892
#202883862
#202883642
#202883622
#202883602
#202883592
#202883562
#202883552
#202883532
#202880452
#202880412
C2×#168111952
#536×D532
#202879132
C53×#34852
#6285953