Finite Group Databasebeta

← #28293149

Subgroups — #28293149

Order 13568.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288788C214yesmaximal, complemented
2#20288782C214yesmaximal, complemented
3#20288763C214yesmaximal, complemented
4#20288760C214yesmaximal, complemented
5#20288692C214yesmaximal, complemented
6#20288689C214yesmaximal, complemented
7#20288660C214yesmaximal, complemented
8#20288654C214yesmaximal, complemented
9#20288580C211yesmaximal, characteristic, complemented
10#20288547C214yesmaximal, complemented
11#20288516C211yesmaximal, characteristic, complemented
12#20288477C211yesmaximal, characteristic, complemented
13#20288418C212yesmaximal, complemented
14#20288407C214yesmaximal, complemented
15#20288358C212yesmaximal, complemented
16#20288139C212yesmaximal, complemented
17#20288125C214yesmaximal, complemented
18#20288107C211yesmaximal, characteristic, complemented
19#20288104C211yesmaximal, characteristic, complemented
20#539×D53C214yesmaximal, complemented
21#20287921C212yesmaximal, complemented
22C2×#16811105C211yesmaximal, characteristic, complemented
23C53×#3507C211yesmaximal, characteristic, complemented
24C2×#13133263C2212yes—
25C22×#11719949C2211yescharacteristic
26#16811358C2212yescomplemented
27#16811351C2212yescomplemented
28#16811346C2212yescomplemented
29#16811345C2214yescomplemented
30#16811334C2212yescomplemented
31#16811333C2212yescomplemented
32#16811333C2214yescomplemented
33#16811333C2212yescomplemented
34#16811333C2214yescomplemented
35#16811329C2214yescomplemented
36#16811328C2214yescomplemented
37#16811326C2218yescomplemented
38#16811324C2218yescomplemented
39#16811323C2214yescomplemented
40#16811318C2218yescomplemented
41#16811317C2214yescomplemented
42#16811314C2214yescomplemented
43#16811314C2218yescomplemented
44#16811314C2214yescomplemented
45#16811312C2214yescomplemented
46#16811312C2218yescomplemented
47#16811309C2218yescomplemented
48#16811305C2218yescomplemented
49#16811305C2218yescomplemented
50#16811303C2218yescomplemented
51#16811302C2218yescomplemented
52#16811300C2218yescomplemented
53#16811298C2218yescomplemented
54#16811298C2218yescomplemented
55#16811297C2218yescomplemented
56Q8×D212C2212yescomplemented
57#16811288C2212yescomplemented
58#16811283C2218yescomplemented
59#16811278C2214yescomplemented
60#16811278C2212yescomplemented
61#16811276C2214yescomplemented
62#16811276C2214yescomplemented
63#16811276C2212yescomplemented
64#16811275C2214yescomplemented
65#16811275C2214yescomplemented
66#16811274C2214yescomplemented
67#16811269C2214yescomplemented
68#16811266C2214yescomplemented
69#16811266C2214yescomplemented
70#16811266C2214yescomplemented
71#16811265C2218yescomplemented
72#16811264C2214yescomplemented
73#16811264C2214yescomplemented
74D4×D212C2212yescomplemented
75#16811258C2212yescomplemented
76#16811251C2212yescomplemented
77#16811248C2214yescomplemented
78#16811247C2212yescomplemented
79#16811247C2212yescomplemented
80#16811246C2214yescomplemented
81#16811242C2212yescomplemented
82#16811242C2212yescomplemented
83#16811242C2214yescomplemented
84#16811236C2212yescomplemented
85#16811234C2214yescomplemented
86#16811234C2212yescomplemented
87#16811233C2214yescomplemented
88#16811229C2212yescomplemented
89#16811227C2212yescomplemented
90#16811222C2212yescomplemented
91#16811222C2212yescomplemented
92#16811221C2218yescomplemented
93#16811221C2218yescomplemented
94#16811220C2214yescomplemented
95#16811219C2218yescomplemented
96#16811218C2212yescomplemented
97#16811218C2212yescomplemented
98#16811217C2218yescomplemented
99#16811216C2218yescomplemented
100#16811215C2218yescomplemented
101#16811214C2218yescomplemented
102#16811214C2218yescomplemented
103#16811213C2212yescomplemented
104#16811213C2212yescomplemented
105#16811212C2218yescomplemented
106#16811210C2212yescomplemented
107#16811210C2212yescomplemented
108#16811207C2218yescomplemented
109#16811201C2212yes—
110#16811197C2212yescomplemented
111#16811184C2218yescomplemented
112#16811181C2214yes—
113#16811180C2211yescharacteristic, complemented
114#16811178C2214yescomplemented
115#16811175C2214yescomplemented
116#16811173C2211yescharacteristic
117#16811160C2214yescomplemented
118#16811160C2218yescomplemented
119#16811160C2214yescomplemented
120#16811159C2214yescomplemented
121#16811157C2214yescomplemented
122#16811153C2214yescomplemented
123#16811153C2214yescomplemented
124#16811152C2214yescomplemented
125#16811151C2218yescomplemented
126#16811150C2218yescomplemented
127#126×D53C2218yescomplemented
128#125×D53C2218yescomplemented
129#16811135C2212yescomplemented
130#16811135C2218yescomplemented
131#16811132C2218yescomplemented
132#16811132C2218yescomplemented
133#16811130C2212yescomplemented
134#123×D53C2218yescomplemented
135#123×D53C2218yescomplemented
136C22⋊Q8×D53C2214yescomplemented
137C22⋊Q8×D53C2218yescomplemented
138#121×D53C2214yes—
139#16811105C2214yescomplemented
140#16811105C2214yescomplemented
141#16811105C2214yescomplemented
142#16811105C2214yescomplemented
143#16811105C2214yescomplemented
144#16811104C2212yescomplemented
145#16811104C2214yescomplemented
146#16811097C2212yes—
147#16811097C2214yescomplemented
148#16811095C2214yescomplemented
149#16811095C2218yescomplemented
150#41×Dic53C2212yescomplemented
151C4×#11719949C2214yescomplemented
152#16811091C2214yescomplemented
153#16811091C2212yescomplemented
154C2×Q8×Dic53C2211yescharacteristic, complemented
155C2×C4×D212C2211yescharacteristic
156C2×C4×D212C2212yescomplemented
157C2×#13133179C2211yescharacteristic
158C2×#13133179C2212yescomplemented
159C2×#13133179C2214yescomplemented
160C4×D4×D53C2218yescomplemented
161C4×D4×D53C2214yescomplemented
162C2×#13133174C2211yescharacteristic, complemented
163C2×#13133174C2212yescomplemented
164C2×C4⋊C4×D53C2212yescomplemented
165C2×C4⋊C4×D53C2211yescharacteristic, complemented
166C53×#559C2212yescomplemented
167C53×#557C2212yescomplemented
168C53×#556C2214yescomplemented
169C53×#556C2212yescomplemented
170C53×#554C2212yescomplemented
171C53×#552C2214yescomplemented
172C53×#539C2214yescomplemented
173C53×#536C2212yescomplemented
174C53×#533C2211yescharacteristic, complemented
175C53×#532C2211yescharacteristic
176C53×#529C2214yescomplemented
177C53×#520C2212yescomplemented
178C2×C4×Q8×C53C2211yescharacteristic, complemented
179#13133263—216no—
180C2×#11719949—28no—
181C2×#11719949C2314yes—
182C2×#11719949C2314yes—
183C2×#11719949C2314yes—
184C2×#11719945C2314yes—
185C2×#11719945C2312yes—
186C2×#11719945C2318yes—
187C2×Q8×D53C2314yes—
188C22×D212C2314yes—
189C22×D212C2312yes—
190C22×D212C2311yescharacteristic
191C2×D4×D53C2314yes—
192C2×D4×D53C2318yes—
193C2×D4×D53C2314yes—
194C22×C4×D53C2312yes—
195C22×C4×D53C2311yescharacteristic
196C22×C4×D53C2312yes—
197C22×C4×D53C2312yes—
198C22×C4×D53C2312yes—
199C22×C4×D53C2318yes—
200#13133217C2311yescharacteristic
201#13133217C2314yes—
202#13133217C2311yescharacteristic
203#13133217C2311yescharacteristic
204#13133216C2314yes—
205#13133215C2314yes—
206#13133214C2311yescharacteristic
207#13133212C2318yes—
208#13133212C2318yes—
209#13133212C2314yes—
210#13133212C2314yes—
211#13133212C2314yes—
212#13133212C2314yes—
213#13133212C2318yes—
214#13133212C2314yes—
215#13133212C2314yes—
216#13133211C2318yes—
217#13133211C2318yes—
218#13133210C2314yes—
219#13133210C2318yes—
220#13133210C2318yes—
221#13133210C2314yes—
222#13133210C2318yes—
223#13133209C2318yes—
224#13133209C2314yes—
225#13133209C2312yes—
226#13133209C2314yes—
227#13133208C2314yes—
228#13133208C2314yes—
229#13133208C2314yes—
230#13133208C2318yes—
231#13133207C2314yes—
232#13133207C2318yes—
233#13133207C2318yes—
234#13133207C2318yes—
235#13133207C2314yes—
236#13133207C2318yes—
237#13133206C2314yes—
238#13133206C2314yes—
239#13133206C2314yes—
240#13133205C2312yes—
241#13133205C2314yes—
242#13133203C2318yes—
243#13133203C2314yes—
244#13133203C2314yes—
245#13133202C2318yes—
246#13133202C2318yes—
247#13133202C2318yes—
248#13133202C2318yes—
249#13133202C2318yes—
250#13133202C2318yes—
251#13133202C2318yes—
252#13133202C2314yes—
253#13133202C2314yes—
254#13133202C2314yes—
255#13133202C2314yes—
256#13133201C2314yes—
257#13133201C2314yes—
258#13133201C2318yes—
259#13133201C2314yes—
260#13133200C2318yes—
261#13133200C2318yes—
262#13133199C2318yes—
263#13133199C2318yes—
264#13133199C2318yes—
265#13133199C2318yes—
266#13133199C2318yes—
267#13133199C2318yes—
268#13133198C2314yes—
269#13133198C2314yes—
270#13133198C2314yes—
271#13133197C2312yes—
272#13133197C2312yes—
273#13133197C2314yes—
274#13133197C2318yes—
275#13133197C2318yes—
276#13133196C2314yes—
277#13133196C2318yes—
278#13133196C2312yes—
279#13133196C2312yes—
280#13133195C2318yes—
281#13133195C2318yes—
282#13133195C2318yes—
283#13133195C2318yes—
284#13133195C2318yes—
285#13133195C2318yes—
286#13133194C2314yes—
287#13133194C2314yes—
288#13133194C2318yes—
289#13133194C2318yes—
290#13133193C2314yes—
291#13133193C2314yes—
292#13133193C2314yes—
293#13133193C2312yes—
294#13133193C2312yes—
295#13133193C2314yes—
296#13133193C2314yes—
297#13133193C2318yes—
298#13133193C2314yes—
299#13133192C2312yes—
300#13133192C2312yes—
301#13133192C2318yes—
302#13133192C2318yes—
303#13133192C2314yes—
304#13133192C2314yes—
305#13133192C2314yes—
306#13133191C2314yes—
307#13133191C2312yes—
308#13133191C2312yes—
309#13133190C2318yes—
310#13133190C2318yes—
311#13133190C2318yes—
312#13133190C2318yes—
313#13133189C2314yes—
314#13133189C2318yes—
315#13133189C2314yes—
316#13133188C2312yes—
317#13133188C2312yes—
318#13133188C2314yes—
319#13133188C2314yes—
320#13133187C2318yes—
321#13133187C2318yes—
322#13133187C2318yes—
323#13133187C2314yes—
324#13133185C2318yes—
325#13133185C2314yes—
326Q8×Dic53C2314yes—
327Q8×Dic53C2314yes—
328Q8×Dic53C2312yes—
329Q8×Dic53C2312yes—
330C4×Dic106C2312yes—
331C4×Dic106C2314yes—
332C4×Dic106C2312yes—
333#13133182C2318yes—
334#13133182C2314yes—
335#13133182C2312yes—
336#13133182C2312yes—
337C4×D212C2312yes—
338C4×D212C2312yes—
339C4×D212C2314yes—
340C4×D212C2314yes—
341C4×D212C2314yes—
342C4×D212C2314yes—
343C4×D212C2312yes—
344C4×D212C2312yes—
345C4×D212C2312yes—
346C4×D212C2312yes—
347C4×D212C2318yes—
348C4×D212C2314yes—
349C4×D212C2318yes—
350C4×D212C2318yes—
351C4×D212C2318yes—
352C4×D212C2318yes—
353D4×Dic53C2314yes—
354D4×Dic53C2312yes—
355D4×Dic53C2314yes—
356D4×Dic53C2312yes—
357#13133179C2314yes—
358#13133179C2314yes—
359#13133179C2318yes—
360#13133179C2314yes—
361#13133179C2318yes—
362#13133179C2318yes—
363#13133179C2314yes—
364#13133179C2318yes—
365#13133179C2314yes—
366#13133179C2312yes—
367#13133179C2312yes—
368C4×C22⋊D53C2314yes—
369C4×C22⋊D53C2314yes—
370C4×C22⋊D53C2318yes—
371C4×C22⋊D53C2318yes—
372C4×C22⋊D53C2318yes—
373C4×C22⋊D53C2318yes—
374#13133177C2318yes—
375#13133177C2318yes—
376#13133177C2318yes—
377#13133177C2314yes—
378#13133177C2314yes—
379#13133176C2312yes—
380#13133176C2314yes—
381#13133175C2318yes—
382#13133175C2318yes—
383#13133175C2314yes—
384#13133174C2318yes—
385#13133174C2318yes—
386#13133174C2318yes—
387#13133174C2318yes—
388#13133174C2318yes—
389#13133174C2312yes—
390#13133174C2312yes—
391#13133174C2312yes—
392#13133174C2312yes—
393#13133174C2314yes—
394#13133173C2318yes—
395C2×C4⋊Dic53C2311yescharacteristic
396C2×C4⋊Dic53C2312yes—
397C2×#11719919C2312yes—
398C2×#11719919C2311yescharacteristic
399C2×#11719919C2311yescharacteristic
400C4⋊C4×D53C2314yes—
401C4⋊C4×D53C2318yes—
402C4⋊C4×D53C2318yes—
403C4⋊C4×D53C2314yes—
404C4⋊C4×D53C2314yes—
405C4⋊C4×D53C2314yes—
406C4⋊C4×D53C2318yes—
407C4⋊C4×D53C2314yes—
408C4⋊C4×D53C2318yes—
409C4⋊C4×D53C2318yes—
410C4⋊C4×D53C2318yes—
411C2×#11719921C2318yes—
412C2×#11719921C2312yes—
413C2×#11719921C2311yescharacteristic
414C2×#11719921C2312yes—
415C2×#11719921C2311yescharacteristic
416C22⋊C4×D53C2318yes—
417C22⋊C4×D53C2318yes—
418C22⋊C4×D53C2318yes—
419C22⋊C4×D53C2318yes—
420C22⋊C4×D53C2318yes—
421C22⋊C4×D53C2318yes—
422C2×C4×Dic53C2311yescharacteristic
423C2×C4×Dic53C2312yes—
424C2×C4×Dic53C2314yes—
425C42×D53C2318yes—
426C42×D53C2314yes—
427C2×#41×C53C2312yes—
428C22×Q8×C53C2311yescharacteristic
429C4⋊Q8×C53C2311yescharacteristic
430C4⋊Q8×C53C2314yes—
431C4⋊Q8×C53C2311yescharacteristic
432C4⋊Q8×C53C2311yescharacteristic
433#127×C53C2311yescharacteristic
434#126×C53C2318yes—
435#126×C53C2318yes—
436#125×C53C2314yes—
437#125×C53C2318yes—
438#125×C53C2312yes—
439#124×C53C2312yes—
440#124×C53C2314yes—
441#124×C53C2314yes—
442#123×C53C2318yes—
443#123×C53C2318yes—
444C22⋊Q8×C53C2314yes—
445C22⋊Q8×C53C2314yes—
446C22⋊Q8×C53C2318yes—
447C22⋊Q8×C53C2312yes—
448C22⋊Q8×C53C2312yes—
449#121×C53C2312yes—
450#121×C53C2312yes—
451C4×Q8×C53C2312yes—
452C4×Q8×C53C2312yes—
453C4×Q8×C53C2312yes—
454C4×Q8×C53C2312yes—
455C4×Q8×C53C2312yes—
456C4×Q8×C53C2314yes—
457C4×Q8×C53C2314yes—
458C4×Q8×C53C2312yes—
459C4×D4×C53C2312yes—
460C4×D4×C53C2314yes—
461C4×D4×C53C2312yes—
462C4×D4×C53C2318yes—
463C4×D4×C53C2314yes—
464#117×C53C2318yes—
465#117×C53C2312yes—
466#117×C53C2314yes—
467C2×C4⋊C4×C53C2314yes—
468C2×C4⋊C4×C53C2311yescharacteristic
469C2×C4⋊C4×C53C2312yes—
470C2×C42×C53C2312yes—
471C2×C42×C53C2311yescharacteristic
472C23×D53C2418yes—
473C23×D53C2411yescharacteristic
474C23×D53C2412yes—
475#41×C53—28no—
476C2×Q8×C53—24no—
477C2×Q8×C53C2412yes—
478C2×Q8×C53C2412yes—
479C2×Q8×C53C2412yes—
480C2×Q8×C53C2412yes—
481C2×Q8×C53C2412yes—
482C2×D4×C53C2414yes—
483C2×D4×C53C2412yes—
484C2×D4×C53C2412yes—
485C2×D4×C53C2412yes—
486C22×C4×C53C2412yes—
487C22×C4×C53C2414yes—
488C22×C4×C53C2411yescharacteristic
489C22×C4×C53C2412yes—
490C22×C4×C53C2411yescharacteristic
491C22×C4×C53C2418yes—
492C22×C4×C53C2411yescharacteristic
493C2×C22⋊D53C2418yes—
494C2×C22⋊D53C2414yes—
495C2×C22⋊D53C2418yes—
496C2×C22⋊D53C2414yes—
497C2×C22⋊D53C2414yes—
498C22×Dic53C2411yescharacteristic
499C22×Dic53C2411yescharacteristic
500C22×Dic53C2414yes—
501C22×Dic53C2411yescharacteristic
502C22×Dic53C2412yes—
503C22×Dic53C2414yes—
504#11719949—216no—
505#11719949—216no—
506#11719949—216no—
507Q8×D53—84no—
508D4×D53—232no—
509D4×D53—216no—
510D4×D53—84no—
511#11719945—28no—
512#11719945—216no—
513#11719945—88no—
514C2×D212—28no—
515C2×D212—216no—
516C2×D212#4118yescomplemented
517C2×D212C2412yes—
518C2×D212C2418yes—
519C2×D212C2418yes—
520C2×D212C2412yes—
521C2×D212C2414yes—
522C2×D212C2414yes—
523C2×D212C2412yes—
524C2×D212C2412yes—
525C2×D212C2412yes—
526C2×C4×D53—28no—
527C2×C4×D53—24no—
528C2×C4×D53—82no—
529C2×C4×D53—88no—
530C2×C4×D53—82no—
531C2×C4×D53—82no—
532C2×C4×D53C2418yes—
533C2×C4×D53C2414yes—
534C2×C4×D53C2418yes—
535C2×C4×D53C2412yes—
536C2×C4×D53C2412yes—
537C2×C4×D53C2418yes—
538C2×C4×D53C2414yes—
539C2×C4×D53C2418yes—
540C2×C4×D53C2414yes—
541C2×C4×D53C2418yes—
542C2×C4×D53C2414yes—
543C2×C4×D53C2418yes—
544C2×C4×D53C2414yes—
545C2×C4×D53C2418yes—
546C2×Dic106C2412yes—
547C2×Dic106C2418yes—
548C2×Dic106C2412yes—
549C2×Dic106C2412yes—
550C4⋊C4×C53C2412yes—
551C4⋊C4×C53C2412yes—
552C4⋊C4×C53C2412yes—
553C4⋊C4×C53C2418yes—
554C4⋊C4×C53C2414yes—
555C4⋊C4×C53C2414yes—
556C4⋊C4×C53C2412yes—
557C4⋊C4×C53C2414yes—
558C4⋊C4×C53C2418yes—
559C4⋊C4×C53C2412yes—
560C4⋊C4×C53C2412yes—
561C4⋊C4×C53C2412yes—
562C4⋊C4×C53C2414yes—
563C4⋊C4×C53C2418yes—
564C4⋊C4×C53C2412yes—
565C22⋊C4×C53C2414yes—
566C22⋊C4×C53C2414yes—
567C22⋊C4×C53C2418yes—
568C22⋊C4×C53C2418yes—
569C22⋊C4×C53C2414yes—
570C22⋊C4×C53C2418yes—
571C42×C53C2414yes—
572C42×C53C2411yescharacteristic
573C42×C53C2411yescharacteristic
574C42×C53C2414yes—
575C42×C53C2411yescharacteristic
576C42×C53C2411yescharacteristic
577C42×C53C2418yes—
578C42×C53C2414yes—
579C22⋊Dic53C2414yes—
580C22⋊Dic53C2414yes—
581C22⋊Dic53C2414yes—
582C22⋊Dic53C2414yes—
583C22⋊Dic53C2414yes—
584C22⋊Dic53C2418yes—
585#11719921C2418yes—
586#11719921C2414yes—
587#11719921C2414yes—
588#11719921C2414yes—
589#11719921C2414yes—
590#11719921C2418yes—
591#11719921C2418yes—
592#11719921C2418yes—
593#11719921C2418yes—
594#11719921C2418yes—
595#11719921C2418yes—
596#11719921C2414yes—
597#11719921C2412yes—
598#11719921C2412yes—
599#11719921C2414yes—
600#11719921C2414yes—
601#11719921C2412yes—
602#11719921C2412yes—
603#11719921C2414yes—
604#11719921C2414yes—
605#11719921C2414yes—
606#11719921C2414yes—
607#11719921C2414yes—
608C4⋊Dic53C2412yes—
609C4⋊Dic53C2412yes—
610C4⋊Dic53C2418yes—
611C4⋊Dic53C2412yes—
612C4⋊Dic53C2414yes—
613C4⋊Dic53C2412yes—
614C4⋊Dic53C2414yes—
615C4⋊Dic53C2414yes—
616C4⋊Dic53C2412yes—
617C4⋊Dic53C2418yes—
618C4⋊Dic53C2412yes—
619C4⋊Dic53C2414yes—
620C4⋊Dic53C2412yes—
621C4⋊Dic53C2412yes—
622#11719919C2412yes—
623#11719919C2418yes—
624#11719919C2412yes—
625#11719919C2414yes—
626#11719919C2418yes—
627#11719919C2414yes—
628#11719919C2414yes—
629#11719919C2414yes—
630#11719919C2418yes—
631#11719919C2418yes—
632#11719919C2418yes—
633#11719919C2418yes—
634#11719919C2418yes—
635#11719919C2412yes—
636#11719919C2412yes—
637#11719919C2414yes—
638#11719919C2414yes—
639C4×Dic53C2414yes—
640C4×Dic53C2412yes—
641C4×Dic53C2414yes—
642C4×Dic53C2414yes—
643C4×Dic53C2418yes—
644C4×Dic53C2412yes—
645C4×Dic53C2418yes—
646C4×Dic53C2414yes—
647C4×Dic53C2414yes—
648C23×C53C2514yes—
649C23×C53C2511yescharacteristic
650C22×D53—22no—
651C22×D53—216no—
652C22×D53—42no—
653C22×D53—41no—
654C22×D53—42no—
655C22×D53—41no—
656C22×D53—48no—
657C22×D53—48no—
658C22×D53C2×#4118yes—
659C22×D53C2512yes—
660C22×D53C2514yes—
661C22×D53C2514yes—
662Q8×C53—24no—
663Q8×C53—24no—
664Q8×C53—24no—
665Q8×C53—42no—
666Q8×C53—42no—
667D4×C53—28no—
668D4×C53—24no—
669D4×C53—42no—
670D4×C53—42no—
671C2×C4×C53—24no—
672C2×C4×C53—28no—
673C2×C4×C53—41no—
674C2×C4×C53—42no—
675C2×C4×C53—48no—
676C2×C4×C53—41no—
677C2×C4×C53C2×#4114yes—
678C2×C4×C53C2511yescharacteristic
679C2×C4×C53C2514yes—
680C2×C4×C53C2511yescharacteristic
681C2×C4×C53C2514yes—
682C2×C4×C53C2511yescharacteristic
683C2×C4×C53C2514yes—
684C2×C4×C53C2514yes—
685C2×C4×C53C2514yes—
686C2×C4×C53C2511yescharacteristic
687C2×C4×C53C2511yescharacteristic
688C2×C4×C53C2511yescharacteristic
689C22⋊D53—28no—
690C22⋊D53—216no—
691C22⋊D53—44no—
692C22⋊D53—48no—
693C22⋊D53—44no—
694C2×Dic53—22no—
695C2×Dic53—44no—
696C2×Dic53—42no—
697C2×Dic53—41no—
698C2×Dic53—44no—
699C2×Dic53—41no—
700C2×Dic53C2514yes—
701C2×Dic53C2514yes—
702C2×Dic53C2514yes—
703C2×Dic53C2514yes—
704C2×Dic53C2512yes—
705C2×Dic53C2512yes—
706C2×Dic53C2512yes—
707D212—216no—
708D212—216no—
709D212—24no—
710D212—42no—
711D212—44no—
712D212—44no—
713D212—42no—
714D212C2×#4118yes—
715D212C2×#4118yes—
716C4×D53—216no—
717C4×D53—216no—
718C4×D53—24no—
719C4×D53—24no—
720C4×D53—28no—
721C4×D53—44no—
722C4×D53—48no—
723C4×D53—48no—
724C4×D53—48no—
725C4×D53—44no—
726C4×D53—48no—
727C4×D53—44no—
728C4×D53—48no—
729C4×D53—44no—
730Dic106—24no—
731Dic106—42no—
732Dic106—48no—
733Dic106—42no—
734#62847—531nomaximal, Sylow
735C22×C53—21no—
736C22×C53—21no—
737C22×C53—24no—
738C22×C53—24no—
739C22×C53—24no—
740C22×C53C22×#4112yes—
741C22×C53C2611yescharacteristic
742C2×D53—24no—
743C2×D53—24no—
744C2×D53—22no—
745C2×D53—24no—
746C2×D53—22no—
747C2×D53—24no—
748C2×D53—24no—
749C2×D53—22no—
750C2×D53—48no—
751C2×D53—44no—
752C2×D53—816no—
753C2×D53C22×#4118yes—
754C4×C53—24no—
755C4×C53—24no—
756C4×C53—21no—
757C4×C53—24no—
758C4×C53—24no—
759C4×C53—21no—
760C4×C53—21no—
761C4×C53—24no—
762C4×C53—21no—
763C4×C53C22×#4112yes—
764C4×C53C22×#4112yes—
765Dic53—24no—
766Dic53—22no—
767Dic53—24no—
768Dic53—24no—
769Dic53—22no—
770Dic53—24no—
771Dic53—22no—
772#3521—534no—
773#3521—534no—
774#3520—534no—
775#3520—534no—
776#3515—534no—
777#3515—534no—
778#3513—534no—
779#3513—534no—
780#3507—531no—
781#3507D5311yescharacteristic, complemented
782#3505—534no—
783#3501—531no—
784#3496—531no—
785#3492—532no—
786#3491—534no—
787#3485—532no—
788#3461—532no—
789#3459—534no—
790#3455—531no—
791#3455—531no—
792C2×#539—534no—
793C4×H(5,𝔽2)—532no—
794C2×#520—531no—
795C2×C53—22no—
796C2×C53—44no—
797C2×C53C23×#4111yescharacteristic
798C2×C53H(7,𝔽2)11yescharacteristic
799C2×C532−1+611yescharacteristic
800D53—28no—
801D53—42no—
802D53—44no—
803C2×H(5,𝔽2)—532no—
804C22×#41—531no—
805#559—532no—
806#559C2×D5312yescomplemented
807#557—532no—
808#557C2×D5312yescomplemented
809#556—534no—
810#556—532no—
811#556C2×D5314yescomplemented
812#556C2×D5312yescomplemented
813#554—532no—
814#554—534no—
815#554—534no—
816#554—534no—
817#554—532no—
818#554—532no—
819#554—534no—
820#554C2×D5312yescomplemented
821#553—538no—
822#553—538no—
823#553—538no—
824#553—534no—
825#553—534no—
826#552—538no—
827#552—538no—
828#552—538no—
829#552—538no—
830#552—534no—
831#552—534no—
832#552—538no—
833#552—534no—
834#552C2×D5314yescomplemented
835#551—538no—
836#551—538no—
837#551—538no—
838#551—538no—
839#551—538no—
840#551—538no—
841D4×Q8—532no—
842D4×Q8—532no—
843#548—538no—
844#547—534no—
845#547—534no—
846#547—532no—
847#547—534no—
848#547—534no—
849#547—534no—
850#547—532no—
851#547—534no—
852#546—534no—
853#546—534no—
854#546—534no—
855#546—538no—
856#546—534no—
857#546—534no—
858#546—534no—
859D42—532no—
860D42—532no—
861#544—532no—
862#543—534no—
863#542—532no—
864#542—532no—
865#542—532no—
866#542—532no—
867#542—534no—
868#542—534no—
869#541—532no—
870#541—534no—
871#541—532no—
872#541—534no—
873#540—532no—
874#540—532no—
875#539—538no—
876#539—538no—
877#539—538no—
878#539—538no—
879#539—538no—
880#539—538no—
881#539—532no—
882#539—538no—
883#539—532no—
884#539—532no—
885#539—532no—
886#539—538no—
887#539—534no—
888#539C2×D5314yescomplemented
889#538—538no—
890#538—538no—
891#538—532no—
892#538—532no—
893#538—532no—
894#538—532no—
895#537—532no—
896#536—532no—
897#536C2×D5312yescomplemented
898#534—538no—
899#534—534no—
900#533—534no—
901#533—534no—
902#533—531no—
903#533C2×D5311yescharacteristic, complemented
904#532—531no—
905#532C2×D5311yescharacteristic
906#529—534no—
907#529—538no—
908#529—534no—
909#529—534no—
910#529—534no—
911#529—538no—
912#529—534no—
913#529—534no—
914#529—538no—
915#529—534no—
916#529C2×D5314yescomplemented
917C2×#126—538no—
918C2×#125—538no—
919#525—532no—
920#525—538no—
921#525—538no—
922#525—532no—
923#525—538no—
924C2×#123—538no—
925C2×#123—538no—
926C2×C22⋊Q8—534no—
927C2×C22⋊Q8—538no—
928C2×#121—534no—
929#520—534no—
930#520—534no—
931#520—534no—
932#520—534no—
933#520—534no—
934#520—532no—
935#520—534no—
936#520C2×D5312yescomplemented
937#518—538no—
938#518—534no—
939#518—532no—
940#518—534no—
941C4×#41—532no—
942C4×#41—534no—
943C4×#41—532no—
944C4×#41—534no—
945C2×C4×Q8—531no—
946C2×C4×Q8C2×D5311yescharacteristic, complemented
947C2×C4×D4—538no—
948C2×C4×D4—534no—
949C2×C4×D4—531no—
950C2×C4×D4—532no—
951C2×C4×D4—534no—
952C2×C4×D4—531no—
953C2×C4×D4—532no—
954C2×#117—531no—
955C2×#117—532no—
956C22×C4⋊C4—532no—
957C22×C4⋊C4—531no—
958C53#6284711yescharacteristic, complemented, Sylow
959H(5,𝔽2)—10616no—
960C2×#41—534no—
961C2×#41—534no—
962C2×#41—534no—
963C2×#41—532no—
964C2×#41—534no—
965C2×#41—538no—
966C2×#41—1068no—
967C2×#41C22×D5312yes—
968C22×Q8—534no—
969C22×Q8C22×D5311yescharacteristic
970C22×D4—538no—
971C22×D4—534no—
972C22×D4—534no—
973C22×D4—531no—
974C22×D4—532no—
975C22×D4—534no—
976C23×C4—532no—
977C23×C4—531no—
978C23×C4—532no—
979C23×C4—532no—
980C23×C4—532no—
981C23×C4—538no—
982C4⋊Q8—534no—
983C4⋊Q8—534no—
984C4⋊Q8—531no—
985C4⋊Q8—531no—
986C4⋊Q8—531no—
987C4⋊Q8—534no—
988C4⋊Q8C22×D5311yescharacteristic
989C4⋊Q8C22×D5314yes—
990C4⋊Q8C22×D5311yescharacteristic
991C4⋊Q8C22×D5311yescharacteristic
992#127—531no—
993#127C22×D5311yescharacteristic
994#126—534no—
995#126—538no—
996#126—538no—
997#126—534no—
998#126—534no—
999#126—534no—
1000#126—534no—
1001#126—534no—
1002#126—538no—
1003#126—534no—
1004#126—538no—
1005#126—538no—
1006#126—534no—
1007#126—538no—
1008#126—538no—
1009#126—538no—
1010#126C22×D5318yes—
1011#126C22×D5318yes—
1012#125—534no—
1013#125—534no—
1014#125—538no—
1015#125—538no—
1016#125—538no—
1017#125—538no—
1018#125—534no—
1019#125—534no—
1020#125—538no—
1021#125—534no—
1022#125—538no—
1023#125—534no—
1024#125—534no—
1025#125—532no—
1026#125C22×D5318yes—
1027#125C22×D5314yes—
1028#125C22×D5312yes—
1029#124—534no—
1030#124—534no—
1031#124—534no—
1032#124—534no—
1033#124—534no—
1034#124—538no—
1035#124—534no—
1036#124—532no—
1037#124C22×D5314yes—
1038#124C22×D5314yes—
1039#124C22×D5312yes—
1040#123—534no—
1041#123—534no—
1042#123—534no—
1043#123—538no—
1044#123—538no—
1045#123—534no—
1046#123—538no—
1047#123—538no—
1048#123—538no—
1049#123—534no—
1050#123—538no—
1051#123—538no—
1052#123—538no—
1053#123—538no—
1054#123—534no—
1055#123—534no—
1056#123—534no—
1057#123—538no—
1058#123—538no—
1059#123—538no—
1060#123—538no—
1061#123—538no—
1062#123—534no—
1063#123—538no—
1064#123—538no—
1065#123—534no—
1066#123C22×D5318yes—
1067#123C22×D5318yes—
1068C22⋊Q8—534no—
1069C22⋊Q8—534no—
1070C22⋊Q8—532no—
1071C22⋊Q8—532no—
1072C22⋊Q8—534no—
1073C22⋊Q8—538no—
1074C22⋊Q8—534no—
1075C22⋊Q8—534no—
1076C22⋊Q8—534no—
1077C22⋊Q8—532no—
1078C22⋊Q8—538no—
1079C22⋊Q8—532no—
1080C22⋊Q8—534no—
1081C22⋊Q8—538no—
1082C22⋊Q8—538no—
1083C22⋊Q8—538no—
1084C22⋊Q8—538no—
1085C22⋊Q8—534no—
1086C22⋊Q8—538no—
1087C22⋊Q8—538no—
1088C22⋊Q8—538no—
1089C22⋊Q8—532no—
1090C22⋊Q8—532no—
1091C22⋊Q8—538no—
1092C22⋊Q8—534no—
1093C22⋊Q8—538no—
1094C22⋊Q8—538no—
1095C22⋊Q8—534no—
1096C22⋊Q8C22×D5312yes—
1097C22⋊Q8C22×D5318yes—
1098C22⋊Q8C22×D5314yes—
1099C22⋊Q8C22×D5312yes—
1100C22⋊Q8C22×D5314yes—
1101#121—538no—
1102#121—534no—
1103#121—534no—
1104#121—532no—
1105#121—532no—
1106#121—534no—
1107#121—534no—
1108#121—532no—
1109#121—532no—
1110#121—534no—
1111#121—534no—
1112#121—534no—
1113#121—538no—
1114#121—532no—
1115#121—532no—
1116#121—538no—
1117#121—534no—
1118#121—538no—
1119#121—538no—
1120#121—538no—
1121#121—538no—
1122#121C22×D5312yes—
1123#121C22×D5312yes—
1124#120—534no—
1125#120—538no—
1126#120—534no—
1127#120—538no—
1128#120—538no—
1129#120—538no—
1130C4×Q8—534no—
1131C4×Q8—534no—
1132C4×Q8—532no—
1133C4×Q8—532no—
1134C4×Q8—532no—
1135C4×Q8—532no—
1136C4×Q8—534no—
1137C4×Q8—538no—
1138C4×Q8—534no—
1139C4×Q8—532no—
1140C4×Q8—532no—
1141C4×Q8C22×D5312yes—
1142C4×Q8C22×D5312yes—
1143C4×Q8C22×D5312yes—
1144C4×Q8C22×D5312yes—
1145C4×Q8C22×D5314yes—
1146C4×Q8C22×D5314yes—
1147C4×Q8C22×D5312yes—
1148C4×Q8C22×D5312yes—
1149C4×D4—534no—
1150C4×D4—532no—
1151C4×D4—534no—
1152C4×D4—532no—
1153C4×D4—538no—
1154C4×D4—538no—
1155C4×D4—538no—
1156C4×D4—538no—
1157C4×D4—534no—
1158C4×D4—534no—
1159C4×D4—534no—
1160C4×D4—534no—
1161C4×D4—538no—
1162C4×D4—532no—
1163C4×D4—534no—
1164C4×D4—534no—
1165C4×D4—538no—
1166C4×D4—538no—
1167C4×D4—538no—
1168C4×D4—532no—
1169C4×D4—534no—
1170C4×D4—538no—
1171C4×D4—534no—
1172C4×D4—534no—
1173C4×D4—538no—
1174C4×D4—538no—
1175C4×D4—538no—
1176C4×D4—534no—
1177C4×D4—538no—
1178C4×D4—538no—
1179C4×D4—532no—
1180C4×D4—532no—
1181C4×D4—532no—
1182C4×D4—532no—
1183C4×D4—534no—
1184C4×D4—538no—
1185C4×D4—534no—
1186C4×D4—538no—
1187C4×D4—534no—
1188C4×D4—534no—
1189C4×D4—532no—
1190C4×D4—532no—
1191C4×D4C22×D5318yes—
1192C4×D4C22×D5314yes—
1193C4×D4C22×D5314yes—
1194C4×D4C22×D5312yes—
1195C4×D4C22×D5312yes—
1196#117—532no—
1197#117—534no—
1198#117—538no—
1199#117—534no—
1200#117—538no—
1201#117—538no—
1202#117—532no—
1203#117—532no—
1204#117—532no—
1205#117—532no—
1206#117—538no—
1207#117—538no—
1208#117—534no—
1209#117—538no—
1210#117—538no—
1211#117—538no—
1212#117C22×D5312yes—
1213#117C22×D5314yes—
1214#117C22×D5318yes—
1215C2×C4⋊C4—531no—
1216C2×C4⋊C4—532no—
1217C2×C4⋊C4—531no—
1218C2×C4⋊C4—532no—
1219C2×C4⋊C4—531no—
1220C2×C4⋊C4—538no—
1221C2×C4⋊C4—538no—
1222C2×C4⋊C4—534no—
1223C2×C4⋊C4—534no—
1224C2×C4⋊C4—538no—
1225C2×C4⋊C4—534no—
1226C2×C4⋊C4—534no—
1227C2×C4⋊C4—538no—
1228C2×C4⋊C4—538no—
1229C2×C4⋊C4—534no—
1230C2×C4⋊C4—538no—
1231C2×C4⋊C4C22×D5311yescharacteristic
1232C2×C4⋊C4C22×D5312yes—
1233C2×C4⋊C4C22×D5314yes—
1234C2×C22⋊C4—532no—
1235C2×C22⋊C4—532no—
1236C2×C22⋊C4—531no—
1237C2×C22⋊C4—531no—
1238C2×C22⋊C4—538no—
1239C2×C22⋊C4—538no—
1240C2×C22⋊C4—538no—
1241C2×C22⋊C4—538no—
1242C2×C22⋊C4—538no—
1243C2×C22⋊C4—538no—
1244C2×C22⋊C4—538no—
1245C2×C42—531no—
1246C2×C42—532no—
1247C2×C42—534no—
1248C2×C42—538no—
1249C2×C42—534no—
1250C2×C42C22×D5312yes—
1251C2×C42C22×D5311yescharacteristic
1252C24—532no—
1253C24—538no—
1254C24—531no—
1255#41—28no—
1256#41—10616no—
1257#41—10616no—
1258#41—10616no—
1259#41—10616no—
1260#41—1068no—
1261#41—4248no—
1262C2×Q8—24no—
1263C2×Q8—532no—
1264C2×Q8—532no—
1265C2×Q8—532no—
1266C2×Q8—538no—
1267C2×Q8—4244no—
1268C2×Q8C23×D5312yes—
1269C2×Q8C23×D5312yes—
1270C2×Q8C23×D5312yes—
1271C2×Q8C23×D5312yes—
1272C2×Q8C23×D5312yes—
1273C2×D4—538no—
1274C2×D4—534no—
1275C2×D4—534no—
1276C2×D4—534no—
1277C2×D4—538no—
1278C2×D4—538no—
1279C2×D4—532no—
1280C2×D4—532no—
1281C2×D4—538no—
1282C2×D4—538no—
1283C2×D4—532no—
1284C2×D4—532no—
1285C2×D4—534no—
1286C2×D4—534no—
1287C2×D4—532no—
1288C2×D4—10616no—
1289C2×D4—1068no—
1290C2×D4—10616no—
1291C2×D4—10632no—
1292C2×D4—4244no—
1293C2×D4C23×D5314yes—
1294C2×D4C23×D5312yes—
1295C2×D4C23×D5312yes—
1296C2×D4C23×D5312yes—
1297C22×C4—531no—
1298C22×C4—531no—
1299C22×C4—534no—
1300C22×C4—531no—
1301C22×C4—532no—
1302C22×C4—534no—
1303C22×C4—538no—
1304C22×C4—534no—
1305C22×C4—538no—
1306C22×C4—532no—
1307C22×C4—532no—
1308C22×C4—538no—
1309C22×C4—534no—
1310C22×C4—538no—
1311C22×C4—534no—
1312C22×C4—538no—
1313C22×C4—534no—
1314C22×C4—538no—
1315C22×C4—534no—
1316C22×C4—538no—
1317C22×C4—1068no—
1318C22×C4—1064no—
1319C22×C4—4242no—
1320C22×C4—4242no—
1321C22×C4—4242no—
1322C22×C4—4248no—
1323C22×C4C23×D5312yes—
1324C22×C4C23×D5314yes—
1325C22×C4C23×D5311yescharacteristic
1326C22×C4C23×D5312yes—
1327C22×C4C23×D5311yescharacteristic
1328C22×C4C23×D5318yes—
1329C22×C4C23×D5311yescharacteristic
1330C4⋊C4—532no—
1331C4⋊C4—538no—
1332C4⋊C4—532no—
1333C4⋊C4—532no—
1334C4⋊C4—532no—
1335C4⋊C4—538no—
1336C4⋊C4—532no—
1337C4⋊C4—534no—
1338C4⋊C4—538no—
1339C4⋊C4—534no—
1340C4⋊C4—532no—
1341C4⋊C4—534no—
1342C4⋊C4—534no—
1343C4⋊C4—534no—
1344C4⋊C4—534no—
1345C4⋊C4—534no—
1346C4⋊C4—532no—
1347C4⋊C4—532no—
1348C4⋊C4—532no—
1349C4⋊C4—538no—
1350C4⋊C4—538no—
1351C4⋊C4—538no—
1352C4⋊C4—538no—
1353C4⋊C4—538no—
1354C4⋊C4—538no—
1355C4⋊C4—532no—
1356C4⋊C4—534no—
1357C4⋊C4—534no—
1358C4⋊C4—534no—
1359C4⋊C4—532no—
1360C4⋊C4—532no—
1361C4⋊C4C23×D5312yes—
1362C4⋊C4C23×D5312yes—
1363C4⋊C4C23×D5314yes—
1364C4⋊C4C23×D5314yes—
1365C4⋊C4C23×D5312yes—
1366C4⋊C4C23×D5314yes—
1367C4⋊C4C23×D5312yes—
1368C4⋊C4C23×D5318yes—
1369C4⋊C4C23×D5318yes—
1370C4⋊C4C23×D5318yes—
1371C4⋊C4C23×D5312yes—
1372C4⋊C4C23×D5312yes—
1373C4⋊C4C23×D5314yes—
1374C4⋊C4C23×D5312yes—
1375C4⋊C4C23×D5312yes—
1376C22⋊C4—534no—
1377C22⋊C4—534no—
1378C22⋊C4—534no—
1379C22⋊C4—534no—
1380C22⋊C4—534no—
1381C22⋊C4—538no—
1382C22⋊C4—538no—
1383C22⋊C4—538no—
1384C22⋊C4—538no—
1385C22⋊C4—534no—
1386C22⋊C4—538no—
1387C22⋊C4—534no—
1388C22⋊C4—534no—
1389C22⋊C4—534no—
1390C22⋊C4—534no—
1391C22⋊C4—534no—
1392C22⋊C4—534no—
1393C22⋊C4—532no—
1394C22⋊C4—532no—
1395C22⋊C4—532no—
1396C22⋊C4—532no—
1397C22⋊C4—538no—
1398C22⋊C4—538no—
1399C22⋊C4—538no—
1400C22⋊C4—534no—
1401C22⋊C4—534no—
1402C22⋊C4—534no—
1403C22⋊C4—534no—
1404C22⋊C4—534no—
1405C22⋊C4C23×D5314yes—
1406C22⋊C4C23×D5318yes—
1407C22⋊C4C23×D5314yes—
1408C22⋊C4C23×D5318yes—
1409C22⋊C4C23×D5318yes—
1410C22⋊C4C23×D5314yes—
1411C42—532no—
1412C42—532no—
1413C42—534no—
1414C42—534no—
1415C42—538no—
1416C42—534no—
1417C42—534no—
1418C42—538no—
1419C42—534no—
1420C42C23×D5318yes—
1421C42C23×D5314yes—
1422C42C23×D5314yes—
1423C42C23×D5314yes—
1424C42C23×D5311yescharacteristic
1425C42C23×D5311yescharacteristic
1426C42C23×D5311yescharacteristic
1427C42C23×D5311yescharacteristic
1428C23—534no—
1429C23—538no—
1430C23—534no—
1431C23—532no—
1432C23—10616no—
1433C23—1062no—
1434C23—2128no—
1435C23—2128no—
1436C23—2122no—
1437C23—2121no—
1438C23—2122no—
1439C23—2121no—
1440C23C24×D5314yes—
1441C23C24×D5311yescharacteristic
1442Q8—24no—
1443Q8—24no—
1444Q8—24no—
1445Q8—42no—
1446Q8—42no—
1447Q8—1064no—
1448Q8—2122no—
1449Q8—2122no—
1450Q8—2128no—
1451D4—28no—
1452D4—24no—
1453D4—42no—
1454D4—42no—
1455D4—538no—
1456D4—538no—
1457D4—10616no—
1458D4—10616no—
1459D4—10616no—
1460D4—1068no—
1461D4—1064no—
1462D4—2122no—
1463D4—2124no—
1464D4—2122no—
1465D4—2124no—
1466D4—2124no—
1467D4—2128no—
1468D4—2124no—
1469C2×C4—24no—
1470C2×C4—28no—
1471C2×C4—42no—
1472C2×C4—41no—
1473C2×C4—48no—
1474C2×C4—41no—
1475C2×C4—532no—
1476C2×C4—532no—
1477C2×C4—534no—
1478C2×C4—534no—
1479C2×C4—534no—
1480C2×C4—534no—
1481C2×C4—532no—
1482C2×C4—10616no—
1483C2×C4—10616no—
1484C2×C4—1062no—
1485C2×C4—1064no—
1486C2×C4—1064no—
1487C2×C4—1068no—
1488C2×C4—2124no—
1489C2×C4—2128no—
1490C2×C4—2128no—
1491C2×C4—2124no—
1492C2×C4—2124no—
1493C2×C4—2128no—
1494C2×C4—2124no—
1495C2×C4—2128no—
1496C2×C4—2128no—
1497C2×C4—2121no—
1498C2×C4—2124no—
1499C2×C4—2121no—
1500C2×C4—2124no—
1501C2×C4—2122no—
1502C2×C4#41×D5314yes—
1503C2×C4C24×D5314yes—
1504C2×C4C24×D5314yes—
1505C2×C4C24×D5314yes—
1506C2×C4C24×D5314yes—
1507C2×C4C24×D5314yes—
1508C2×C4C24×D5311yescharacteristic
1509C2×C4C24×D5311yescharacteristic
1510C2×C4C24×D5311yescharacteristic
1511C2×C4C24×D5311yescharacteristic
1512C2×C4C24×D5311yescharacteristic
1513C2×C4C24×D5311yescharacteristic
1514C22—21no—
1515C22—21no—
1516C22—24no—
1517C22—24no—
1518C22—24no—
1519C22—538no—
1520C22—1064no—
1521C22—1064no—
1522C22—1062no—
1523C22—1064no—
1524C22—1062no—
1525C22—1064no—
1526C22—1064no—
1527C22—1062no—
1528C22—42416no—
1529C22—2128no—
1530C22—2124no—
1531C22C2×#41×D5312yes—
1532C22C25×D5311yescharacteristic
1533C4—24no—
1534C4—24no—
1535C4—24no—
1536C4—24no—
1537C4—21no—
1538C4—21no—
1539C4—21no—
1540C4—21no—
1541C4—24no—
1542C4—1062no—
1543C4—1064no—
1544C4—1062no—
1545C4—1064no—
1546C4—1064no—
1547C4—1062no—
1548C4—1064no—
1549C4C2×#41×D5312yes—
1550C4C2×#41×D5312yes—
1551C2—22no—
1552C2—44no—
1553C2—1068no—
1554C2—2124no—
1555C2—2122no—
1556C2C22×#41×D5311yescharacteristic
1557C2#2028952611yescharacteristic
1558C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3507C2
hypercenter#3507D53
hypocenterC53#62847
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. #20288788C2semidirect
2. #20288782C2semidirect
3. #20288763C2semidirect
4. #20288760C2semidirect
5. #20288692C2semidirect
6. #20288689C2semidirect
7. #20288660C2semidirect
8. #20288654C2semidirect
9. #20288580C2semidirect
10. #20288547C2semidirect
11. #20288516C2semidirect
12. #20288477C2semidirect
13. #20288418C2semidirect
14. #20288407C2semidirect
15. #20288358C2semidirect
16. #20288139C2semidirect
17. #20288125C2semidirect
18. #20288107C2semidirect
19. #20288104C2semidirect
20. #539×D53C2semidirect
21. #20287921C2semidirect
22. C2×#16811105C2semidirect
23. C53×#3507C2semidirect
26. #16811358C22semidirect
27. #16811351C22semidirect
28. #16811346C22semidirect
29. #16811345C22semidirect
30. #16811334C22semidirect
31. #16811333C22semidirect
32. #16811333C22semidirect
33. #16811333C22semidirect
34. #16811333C22semidirect
35. #16811329C22semidirect
36. #16811328C22semidirect
37. #16811326C22semidirect
38. #16811324C22semidirect
39. #16811323C22semidirect
40. #16811318C22semidirect
41. #16811317C22semidirect
42. #16811314C22semidirect
43. #16811314C22semidirect
44. #16811314C22semidirect
45. #16811312C22semidirect
46. #16811312C22semidirect
47. #16811309C22semidirect
48. #16811305C22semidirect
49. #16811305C22semidirect
50. #16811303C22semidirect
51. #16811302C22semidirect
52. #16811300C22semidirect
53. #16811298C22semidirect
54. #16811298C22semidirect
55. #16811297C22semidirect
56. Q8×D212C22semidirect
57. #16811288C22semidirect
58. #16811283C22semidirect
59. #16811278C22semidirect
60. #16811278C22semidirect
61. #16811276C22semidirect
62. #16811276C22semidirect
63. #16811276C22semidirect
64. #16811275C22semidirect
65. #16811275C22semidirect
66. #16811274C22semidirect
67. #16811269C22semidirect
68. #16811266C22semidirect
69. #16811266C22semidirect
70. #16811266C22semidirect
71. #16811265C22semidirect
72. #16811264C22semidirect
73. #16811264C22semidirect
74. D4×D212C22semidirect
75. #16811258C22semidirect
76. #16811251C22semidirect
77. #16811248C22semidirect
78. #16811247C22semidirect
79. #16811247C22semidirect
80. #16811246C22semidirect
81. #16811242C22semidirect
82. #16811242C22semidirect
83. #16811242C22semidirect
84. #16811236C22semidirect
85. #16811234C22semidirect
86. #16811234C22semidirect
87. #16811233C22semidirect
88. #16811229C22semidirect
89. #16811227C22semidirect
90. #16811222C22semidirect
91. #16811222C22semidirect
92. #16811221C22semidirect
93. #16811221C22semidirect
94. #16811220C22semidirect
95. #16811219C22semidirect
96. #16811218C22semidirect
97. #16811218C22semidirect
98. #16811217C22semidirect
99. #16811216C22semidirect
100. #16811215C22semidirect
101. #16811214C22semidirect
102. #16811214C22semidirect
103. #16811213C22semidirect
104. #16811213C22semidirect
105. #16811212C22semidirect
106. #16811210C22semidirect
107. #16811210C22semidirect
108. #16811207C22semidirect
110. #16811197C22semidirect
111. #16811184C22semidirect
113. #16811180C22semidirect
114. #16811178C22semidirect
115. #16811175C22semidirect
117. #16811160C22semidirect
118. #16811160C22semidirect
119. #16811160C22semidirect
120. #16811159C22semidirect
121. #16811157C22semidirect
122. #16811153C22semidirect
123. #16811153C22semidirect
124. #16811152C22semidirect
125. #16811151C22semidirect
126. #16811150C22semidirect
127. #126×D53C22semidirect
128. #125×D53C22semidirect
129. #16811135C22semidirect
130. #16811135C22semidirect
131. #16811132C22semidirect
132. #16811132C22semidirect
133. #16811130C22semidirect
134. #123×D53C22semidirect
135. #123×D53C22semidirect
136. C22⋊Q8×D53C22semidirect
137. C22⋊Q8×D53C22semidirect
139. #16811105C22semidirect
140. #16811105C22semidirect
141. #16811105C22semidirect
142. #16811105C22semidirect
143. #16811105C22semidirect
144. #16811104C22semidirect
145. #16811104C22semidirect
147. #16811097C22semidirect
148. #16811095C22semidirect
149. #16811095C22semidirect
150. #41×Dic53C22semidirect
151. C4×#11719949C22semidirect
152. #16811091C22semidirect
153. #16811091C22semidirect
154. C2×Q8×Dic53C22semidirect
156. C2×C4×D212C22semidirect
158. C2×#13133179C22semidirect
159. C2×#13133179C22semidirect
160. C4×D4×D53C22semidirect
161. C4×D4×D53C22semidirect
162. C2×#13133174C22semidirect
163. C2×#13133174C22semidirect
164. C2×C4⋊C4×D53C22semidirect
165. C2×C4⋊C4×D53C22semidirect
166. C53×#559C22semidirect
167. C53×#557C22semidirect
168. C53×#556C22semidirect
169. C53×#556C22semidirect
170. C53×#554C22semidirect
171. C53×#552C22semidirect
172. C53×#539C22semidirect
173. C53×#536C22semidirect
174. C53×#533C22semidirect
176. C53×#529C22semidirect
177. C53×#520C22semidirect
178. C2×C4×Q8×C53C22semidirect
516. C2×D212#41semidirect
781. #3507D53semidirect
806. #559C2×D53semidirect
808. #557C2×D53semidirect
811. #556C2×D53semidirect
812. #556C2×D53semidirect
820. #554C2×D53semidirect
834. #552C2×D53semidirect
888. #539C2×D53semidirect
897. #536C2×D53semidirect
903. #533C2×D53semidirect
916. #529C2×D53semidirect
936. #520C2×D53semidirect
946. C2×C4×Q8C2×D53semidirect
958. C53#62847semidirect

Maximal subgroups

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

subgroupindex
#202887882
#202887822
#202887632
#202887602
#202886922
#202886892
#202886602
#202886542
#202885802
#202885472
#202885162
#202884772
#202884182
#202884072
#202883582
#202881392
#202881252
#202881072
#202881042
#539×D532
#202879212
C2×#168111052
C53×#35072
#6284753