Finite Group Databasebeta

← #10586079

Subgroups — #10586079

Order 512.

33733 conjugacy classes of subgroups.

The subgroup lattice has 1059 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#63010C218yesmaximal, complemented
2#63009C218yesmaximal, complemented
3#63001C218yesmaximal, complemented
4#63000C218yesmaximal, complemented
5#62995C2116yesmaximal, complemented
6#62993C2116yesmaximal, complemented
7#62860C216yesmaximal, complemented
8#62859C212yesmaximal, complemented
9#62850C214yesmaximal, complemented
10#62847C2112yesmaximal, complemented
11#62845C216yesmaximal, complemented
12#62815C216yesmaximal, complemented
13#62813C211yesmaximal, characteristic, complemented
14#62812C211yesmaximal, characteristic, complemented
15#62788C214yesmaximal, complemented
16#62781C2112yesmaximal, complemented
17C2×#3507C216yesmaximal, complemented
18#62654C212yesmaximal, complemented
19C2×C4×2−1+4C211yesmaximal, characteristic, complemented
20C2×#585C2212yes—
21C22×2−1+4C2211yescharacteristic
22#3524C22132yescomplemented
23#3523C22132yescomplemented
24#3523C22116yescomplemented
25#3522C22116yescomplemented
26#3521C22196yescomplemented
27#3521C22196yescomplemented
28#3520C22196yescomplemented
29#3518C22132yescomplemented
30#3516C22132yescomplemented
31#3516C22132yescomplemented
32#3515C22196yescomplemented
33#3515C22148yescomplemented
34#3514C22148yescomplemented
35#3513C22196yescomplemented
36#3512C22124yescomplemented
37#3511C22112yescomplemented
38#3511C22112yescomplemented
39#3510C22124yescomplemented
40#3510C22148yescomplemented
41#3509C22148yescomplemented
42#3509C22112yescomplemented
43#3508C22112yescomplemented
44#3507C22124yescomplemented
45#3507C22124yescomplemented
46#3507C22148yescomplemented
47#3507C22124yescomplemented
48#3507C22124yescomplemented
49#3507C22112yescomplemented
50#3507C22124yescomplemented
51#3507C22124yescomplemented
52#3507C22124yescomplemented
53#3507C22112yescomplemented
54#3506C22148yescomplemented
55#3506C2214yescomplemented
56#3506C22112yescomplemented
57#3505C22124yescomplemented
58#3505C22124yescomplemented
59#3504C2218yescomplemented
60#3503C2214yescomplemented
61#3503C2214yescomplemented
62#3502C2212yescomplemented
63#3502C2212yescomplemented
64#3501C2216yescomplemented
65#3501C2216yescomplemented
66#3500C2218yescomplemented
67#3500C22116yescomplemented
68#3499C22116yescomplemented
69#3499C2214yescomplemented
70#3498C2214yescomplemented
71#3497C2212yes—
72#3497C2212yes—
73#3496C2216yes—
74#3496C2216yes—
75#3495C22148yescomplemented
76#3495C22148yescomplemented
77#3493C22148yescomplemented
78#3493C22124yescomplemented
79#3492C22148yescomplemented
80#3492C22124yescomplemented
81#3491C22148yescomplemented
82#3489C22116yescomplemented
83#3489C22116yescomplemented
84#3486C2218yescomplemented
85#3485C22124yescomplemented
86#3482C22132yescomplemented
87#3482C22148yescomplemented
88#3481C22148yescomplemented
89#3480C22124yescomplemented
90#3480C22124yescomplemented
91#3480C22116yescomplemented
92C2×#559C22112yescomplemented
93Q8×#41C2218yescomplemented
94Q8×#41C22116yescomplemented
95Q8×#41C2218yescomplemented
96C2×#557C22112yescomplemented
97#3475C22124yescomplemented
98#3475C22196yescomplemented
99#3475C22124yescomplemented
100C2×#556C22124yescomplemented
101C2×#556C22112yescomplemented
102C2×#554C22112yescomplemented
103C2×#552C22124yescomplemented
104D4×#41C2218yescomplemented
105D4×#41C2218yescomplemented
106#3461C22124yescomplemented
107#3461C22124yescomplemented
108#3459C22148yescomplemented
109#3458C2216yescomplemented
110#3455C22124yescomplemented
111C2×#539C22124yescomplemented
112#3449C2216yes—
113#3449C22112yescomplemented
114C2×#536C22112yescomplemented
115#3444C22124yescomplemented
116C2×#533C2216yescomplemented
117C2×#532C2216yes—
118C2×#529C22124yescomplemented
119C4×2−1+4C2218yescomplemented
120C4×2−1+4C2218yescomplemented
121C4×2−1+4C22116yescomplemented
122C4×2−1+4C2218yescomplemented
123C4×2−1+4C2218yescomplemented
124C4×2−1+4C2218yescomplemented
125C4×H(5,𝔽2)C22116yescomplemented
126C4×H(5,𝔽2)C22124yescomplemented
127#3428C2212yes—
128#3428C22116yescomplemented
129#3428C22112yescomplemented
130C2×#520C2211yescharacteristic
131C2×#520C22116yescomplemented
132C2×#520C22112yescomplemented
133C2×#520C2213yescomplemented
134C2×#520C2216yescomplemented
135C2×#519C2212yescomplemented
136C2×#519C2213yescomplemented
137C2×C4×#41C2211yescharacteristic
138C2×C4×#41C2216yescomplemented
139C2×C4×#41C2213yescomplemented
140C22×C4×Q8C2213yescomplemented
141C22×C4×Q8C2212yescomplemented
142#585—232no—
143C2×2−1+4—216no—
144C2×2−1+4C2318yes—
145C2×2−1+4C2318yes—
146C2×2−1+4C2314yes—
147C2×2−1+4C2318yes—
148C2×H(5,𝔽2)C23112yes—
149C2×H(5,𝔽2)C2318yes—
150C22×#41C2313yes—
151C22×#41C2316yes—
152C22×#41C23112yes—
153C22×#41C23116yes—
154C22×#41C2311yescharacteristic
155C23×Q8C2313yes—
156C23×Q8C2312yes—
157#559C23124yes—
158#559C23148yes—
159#559C23148yes—
160#559C23148yes—
161#559C23116yes—
162#559C23148yes—
163#559C23124yes—
164Q82C2318yes—
165Q82C2318yes—
166#557C23124yes—
167#557C23148yes—
168#557C23148yes—
169#557C23148yes—
170#557C2318yes—
171#557C23116yes—
172#557C2318yes—
173#557C23116yes—
174#557C23124yes—
175#556C23124yes—
176#556C23148yes—
177#556C23196yes—
178#556C23148yes—
179#556C23148yes—
180#556C23196yes—
181#556C23196yes—
182#556C23148yes—
183#556C23124yes—
184#556C2318yes—
185#556C23124yes—
186#556C23148yes—
187#556C23196yes—
188#555C2318yes—
189#555C23124yes—
190#555C23196yes—
191#554C23124yes—
192#554C23148yes—
193#554C23148yes—
194#554C23148yes—
195#554C23148yes—
196#554C23124yes—
197#554C23124yes—
198#554C23196yes—
199#554C23124yes—
200#554C23148yes—
201#553C23116yes—
202#553C23196yes—
203#553C23148yes—
204#553C23148yes—
205#553C23196yes—
206#553C23148yes—
207#553C23196yes—
208#553C23196yes—
209#552C23148yes—
210#552C23196yes—
211#552C23196yes—
212#552C23196yes—
213#552C23148yes—
214#552C231192yes—
215#552C23196yes—
216#552C23148yes—
217#552C23148yes—
218#552C231192yes—
219#552C23196yes—
220#551C23196yes—
221#551C231192yes—
222#551C23196yes—
223#551C231192yes—
224#550C2318yes—
225#550C2318yes—
226#550C2318yes—
227#550C23124yes—
228D4×Q8C2318yes—
229D4×Q8C2318yes—
230D4×Q8C23124yes—
231D4×Q8C23132yes—
232D4×Q8C23124yes—
233D4×Q8C23132yes—
234#548C23116yes—
235#548C23116yes—
236#548C23148yes—
237#548C23132yes—
238#548C23148yes—
239#548C23132yes—
240#547C23124yes—
241#547C23124yes—
242#547C2318yes—
243#547C23196yes—
244#547C23124yes—
245#547C23196yes—
246#547C23196yes—
247#546C23148yes—
248#546C23148yes—
249#546C23148yes—
250#546C23196yes—
251#546C23148yes—
252#546C23196yes—
253D42C23124yes—
254D42C23124yes—
255#544C23112yes—
256#544C23112yes—
257#544C23124yes—
258#544C23124yes—
259#543C23124yes—
260#542C23148yes—
261#542C23148yes—
262#542C23196yes—
263#542C23196yes—
264#541C23148yes—
265#541C23196yes—
266#541C23196yes—
267#540C23148yes—
268#539C23148yes—
269#539C23196yes—
270#539C23196yes—
271#539C23196yes—
272#539C23148yes—
273#539C231192yes—
274#538C23116yes—
275#538C23148yes—
276#538C231192yes—
277#537C23112yes—
278#537C23112yes—
279#537C23124yes—
280#537C23124yes—
281#536C23124yes—
282#536C23148yes—
283#536C23148yes—
284#536C23148yes—
285#536C23124yes—
286#536C23124yes—
287#535C23124yes—
288#535C2318yes—
289#535C23124yes—
290#534C23124yes—
291#534C23148yes—
292#533C2314yes—
293#533C23112yes—
294#533C23112yes—
295#533C23112yes—
296#533C23112yes—
297#533C23112yes—
298#533C23112yes—
299#533C23112yes—
300#533C23124yes—
301#533C23124yes—
302#533C23148yes—
303#533C23196yes—
304#533C23196yes—
305#532C2314yes—
306#532C23112yes—
307#532C23112yes—
308#532C23112yes—
309#532C23112yes—
310#532C23112yes—
311#532C23112yes—
312#532C23112yes—
313#532C23124yes—
314#532C23124yes—
315#532C23148yes—
316C2×C4⋊Q8C2316yes—
317C2×C4⋊Q8C2316yes—
318C2×C4⋊Q8C2316yes—
319C2×C4⋊Q8C23124yes—
320C2×#127C2316yes—
321#529C23148yes—
322#529C23196yes—
323#529C23196yes—
324#529C23196yes—
325#529C23148yes—
326#529C23148yes—
327#529C23148yes—
328#529C23148yes—
329#529C23148yes—
330#529C23196yes—
331#529C23196yes—
332#529C231192yes—
333#529C23196yes—
334#529C23196yes—
335C2×#126C23148yes—
336C2×#126C23148yes—
337C2×#125C23124yes—
338C2×#125C23112yes—
339C2×#125C23148yes—
340C2×#124C23124yes—
341C2×#124C23112yes—
342C2×#124C23124yes—
343#525C23116yes—
344#525C23148yes—
345#525C23148yes—
346#525C23148yes—
347#525C23148yes—
348#525C231192yes—
349C2×#123C23148yes—
350C2×#123C23148yes—
351C2×C22⋊Q8C23112yes—
352C2×C22⋊Q8C23112yes—
353C2×C22⋊Q8C23124yes—
354C2×C22⋊Q8C23124yes—
355C2×C22⋊Q8C23148yes—
356C2×#121C23112yes—
357C2×#121C23112yes—
358#520C2318yes—
359#520C2318yes—
360#520C2318yes—
361#520C23148yes—
362#520C23124yes—
363#520C23124yes—
364#520C23148yes—
365#520C23148yes—
366#520C23196yes—
367#520C23132yes—
368#520C23124yes—
369#520C23124yes—
370#520C23148yes—
371#520C23148yes—
372#520C2318yes—
373#520C23124yes—
374#520C2318yes—
375#519C23124yes—
376#519C23124yes—
377#519C23116yes—
378#519C23116yes—
379#519C2314yes—
380#519C23124yes—
381#519C23132yes—
382#518C23112yes—
383#518C23148yes—
384#518C23124yes—
385#518C23196yes—
386C4×#41C2314yes—
387C4×#41C2314yes—
388C4×#41C2314yes—
389C4×#41C2314yes—
390C4×#41C23112yes—
391C4×#41C23112yes—
392C4×#41C23148yes—
393C4×#41C23112yes—
394C4×#41C23112yes—
395C4×#41C23148yes—
396C4×#41C23116yes—
397C4×#41C23148yes—
398C4×#41C23196yes—
399C4×#41C23148yes—
400C4×#41C23132yes—
401C4×#41C23148yes—
402C4×#41C23148yes—
403C2×C4×Q8C2311yescharacteristic
404C2×C4×Q8C2313yes—
405C2×C4×Q8C2316yes—
406C2×C4×Q8C2312yes—
407C2×C4×Q8C2316yes—
408C2×C4×Q8C2316yes—
409C2×C4×Q8C2316yes—
410C2×C4×Q8C23112yes—
411C2×C4×Q8C23112yes—
412C2×C4×Q8C23112yes—
413C2×C4×Q8C23112yes—
414C2×C4×Q8C23116yes—
415C2×C4×Q8C23116yes—
416C2×C4×Q8C2311yescharacteristic
417C2×C4×Q8C2316yes—
418C2×C4×Q8C2313yes—
419C2×C4×Q8C23124yes—
420C2×C4×Q8C23132yes—
421C2×C4×Q8C23124yes—
422C2×C4×Q8C23112yes—
423C2×C4×Q8C23112yes—
424C2×C4×D4C2313yes—
425C2×C4×D4C2313yes—
426C2×C4×D4C2316yes—
427C2×C4×D4C2311yescharacteristic
428C2×C4×D4C2316yes—
429C2×C4×D4C23112yes—
430C2×C4×D4C2316yes—
431C2×C4×D4C2313yes—
432C2×C4×D4C23148yes—
433C2×C4×D4C23124yes—
434C2×C4×D4C23196yes—
435C2×C4×D4C23124yes—
436C2×C4×D4C23112yes—
437C2×C4×D4C23112yes—
438C2×#117C2313yes—
439C2×#117C2313yes—
440C2×#117C2316yes—
441C2×#117C23112yes—
442C2×#117C2316yes—
443C2×#117C23112yes—
444C2×#117C23124yes—
445C2×#117C23148yes—
446C2×#117C23148yes—
447C22×C4⋊C4C2313yes—
448C22×C4⋊C4C2316yes—
449C22×C4⋊C4C2316yes—
450C22×C4⋊C4C23124yes—
451C22×C42C2313yes—
452C22×C42C2316yes—
453C22×C42C2316yes—
4542−1+4—264no—
4552−1+4—264no—
4562−1+4—264no—
4572−1+4—232no—
458H(5,𝔽2)—264no—
459H(5,𝔽2)—296no—
460C2×#41—2128no—
461C2×#41—248no—
462C2×#41—224no—
463C2×#41—296no—
464C2×#41#41116yescomplemented
465C2×#41C24112yes—
466C2×#41C24124yes—
467C2×#41C24112yes—
468C2×#41C24124yes—
469C2×#41C24148yes—
470C2×#41C24148yes—
471C2×#41C24116yes—
472C2×#41C24124yes—
473C2×#41C2418yes—
474C2×#41C24116yes—
475C2×#41C24148yes—
476C2×#41C2414yes—
477C2×#41C2414yes—
478C22×Q8—216no—
479C22×Q8—224no—
480C22×Q8C2413yes—
481C22×Q8C2416yes—
482C22×Q8C24112yes—
483C22×Q8C24112yes—
484C22×Q8C24112yes—
485C22×Q8C24116yes—
486C22×Q8C24116yes—
487C22×Q8C24112yes—
488C22×Q8C24112yes—
489C22×Q8C2411yescharacteristic
490C22×D4C2416yes—
491C22×D4C2411yescharacteristic
492C22×D4C24124yes—
493C22×D4C24112yes—
494C22×D4C24148yes—
495C22×D4C24112yes—
496C22×D4C24112yes—
497C22×D4C2413yes—
498C23×C4C24124yes—
499C23×C4C2416yes—
500C23×C4C2416yes—
501C23×C4C2413yes—
502C23×C4C2412yes—
503C23×C4C2416yes—
504C23×C4C2413yes—
505C23×C4C2416yes—
506C23×C4C24148yes—
507C23×C4C2413yes—
508C4⋊Q8C2414yes—
509C4⋊Q8C2414yes—
510C4⋊Q8C2414yes—
511C4⋊Q8C24148yes—
512C4⋊Q8C24112yes—
513C4⋊Q8C24112yes—
514C4⋊Q8C24112yes—
515C4⋊Q8C24112yes—
516C4⋊Q8C24112yes—
517C4⋊Q8C24196yes—
518C4⋊Q8C24112yes—
519C4⋊Q8C24112yes—
520C4⋊Q8C24112yes—
521C4⋊Q8C24112yes—
522C4⋊Q8C24148yes—
523C4⋊Q8C24148yes—
524#127C2414yes—
525#127C24112yes—
526#127C24112yes—
527#127C24112yes—
528#127C24116yes—
529#126C24196yes—
530#126C24196yes—
531#126C241192yes—
532#126C241192yes—
533#126C24196yes—
534#126C24132yes—
535#126C24196yes—
536#126C24196yes—
537#125C2418yes—
538#125C24148yes—
539#125C24196yes—
540#125C24124yes—
541#125C24196yes—
542#125C241192yes—
543#125C24124yes—
544#125C24124yes—
545#125C24148yes—
546#125C24148yes—
547#125C24148yes—
548#125C24196yes—
549#124C2418yes—
550#124C24148yes—
551#124C24148yes—
552#124C24124yes—
553#124C24196yes—
554#124C24196yes—
555#124C24124yes—
556#124C24124yes—
557#124C24196yes—
558#124C24132yes—
559#124C24148yes—
560#124C24116yes—
561#123C24196yes—
562#123C24196yes—
563#123C241192yes—
564#123C241192yes—
565#123C24196yes—
566#123C24132yes—
567#123C24196yes—
568#123C24196yes—
569#123C24196yes—
570#123C24132yes—
571#123C24196yes—
572C22⋊Q8C2418yes—
573C22⋊Q8C2418yes—
574C22⋊Q8C24148yes—
575C22⋊Q8C24148yes—
576C22⋊Q8C24196yes—
577C22⋊Q8C24124yes—
578C22⋊Q8C241192yes—
579C22⋊Q8C24124yes—
580C22⋊Q8C24124yes—
581C22⋊Q8C24124yes—
582C22⋊Q8C24196yes—
583C22⋊Q8C24196yes—
584C22⋊Q8C24124yes—
585C22⋊Q8C24124yes—
586C22⋊Q8C24196yes—
587C22⋊Q8C24116yes—
588C22⋊Q8C24148yes—
589C22⋊Q8C24148yes—
590C22⋊Q8C24148yes—
591C22⋊Q8C24148yes—
592C22⋊Q8C24148yes—
593C22⋊Q8C24196yes—
594C22⋊Q8C24196yes—
595#121C2418yes—
596#121C2418yes—
597#121C24124yes—
598#121C24124yes—
599#121C24124yes—
600#121C24124yes—
601#121C24124yes—
602#121C24124yes—
603#121C24116yes—
604#121C24116yes—
605#121C24196yes—
606#121C24196yes—
607#121C24116yes—
608#121C24148yes—
609#121C24148yes—
610#121C24148yes—
611#121C24148yes—
612#121C24148yes—
613#121C24132yes—
614#121C24196yes—
615#120C24132yes—
616#120C24196yes—
617#120C24196yes—
618C4×Q8C24116yes—
619C4×Q8C2414yes—
620C4×Q8C2414yes—
621C4×Q8C2416yes—
622C4×Q8C24124yes—
623C4×Q8C2416yes—
624C4×Q8C24124yes—
625C4×Q8C2416yes—
626C4×Q8C2416yes—
627C4×Q8C24148yes—
628C4×Q8C24124yes—
629C4×Q8C24124yes—
630C4×Q8C24124yes—
631C4×Q8C24124yes—
632C4×Q8C2418yes—
633C4×Q8C2418yes—
634C4×Q8C24148yes—
635C4×Q8C24116yes—
636C4×Q8C24196yes—
637C4×Q8C24148yes—
638C4×Q8C24148yes—
639C4×Q8C24148yes—
640C4×Q8C2414yes—
641C4×Q8C2414yes—
642C4×Q8C24112yes—
643C4×Q8C24112yes—
644C4×Q8C24124yes—
645C4×Q8C24124yes—
646C4×Q8C24124yes—
647C4×Q8C24196yes—
648C4×Q8C24124yes—
649C4×Q8C24124yes—
650C4×Q8C24124yes—
651C4×Q8C24148yes—
652C4×Q8C24116yes—
653C4×Q8C24116yes—
654C4×Q8C24148yes—
655C4×D4C24148yes—
656C4×D4C2418yes—
657C4×D4C2418yes—
658C4×D4C24196yes—
659C4×D4C241192yes—
660C4×D4C24148yes—
661C4×D4C24148yes—
662C4×D4C24196yes—
663C4×D4C24196yes—
664C4×D4C24148yes—
665C4×D4C24148yes—
666C4×D4C24112yes—
667C4×D4C24112yes—
668C4×D4C24124yes—
669C4×D4C2412yes—
670C4×D4C2412yes—
671C4×D4C24124yes—
672C4×D4C2412yes—
673C4×D4C2412yes—
674C4×D4C24196yes—
675C4×D4C24112yes—
676C4×D4C24112yes—
677C4×D4C24124yes—
678C4×D4C24112yes—
679C4×D4C24124yes—
680C4×D4C24112yes—
681C4×D4C24124yes—
682C4×D4C24124yes—
683C4×D4C24124yes—
684C4×D4C24124yes—
685C4×D4C24196yes—
686C4×D4C24124yes—
687C4×D4C24124yes—
688C4×D4C24132yes—
689C4×D4C24148yes—
690C4×D4C24148yes—
691C4×D4C24196yes—
692C4×D4C24116yes—
693C4×D4C24132yes—
694C4×D4C24196yes—
695C4×D4C24196yes—
696C4×D4C24196yes—
697C4×D4C24148yes—
698#117C24112yes—
699#117C24124yes—
700#117C2418yes—
701#117C24148yes—
702#117C24116yes—
703#117C24196yes—
704#117C24112yes—
705#117C24124yes—
706#117C24196yes—
707#117C24124yes—
708#117C24196yes—
709#117C24196yes—
710#117C24112yes—
711#117C24124yes—
712#117C24124yes—
713#117C24112yes—
714#117C24196yes—
715#117C24148yes—
716#117C241192yes—
717#117C24116yes—
718#117C24148yes—
719#117C24196yes—
720C2×C4⋊C4C24112yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2416yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C24112yes—
726C2×C4⋊C4C24112yes—
727C2×C4⋊C4C24148yes—
728C2×C4⋊C4C24112yes—
729C2×C4⋊C4C24148yes—
730C2×C4⋊C4C24196yes—
731C2×C4⋊C4C24124yes—
732C2×C4⋊C4C24124yes—
733C2×C4⋊C4C24148yes—
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C24112yes—
738C2×C4⋊C4C24116yes—
739C2×C4⋊C4C24124yes—
740C2×C4⋊C4C24148yes—
741C2×C4⋊C4C24112yes—
742C2×C4⋊C4C24112yes—
743C2×C4⋊C4C24112yes—
744C2×C4⋊C4C24124yes—
745C2×C4⋊C4C24148yes—
746C2×C4⋊C4C24112yes—
747C2×C22⋊C4C2416yes—
748C2×C22⋊C4C2416yes—
749C2×C22⋊C4C2412yes—
750C2×C22⋊C4C2416yes—
751C2×C22⋊C4C24124yes—
752C2×C22⋊C4C24124yes—
753C2×C22⋊C4C24148yes—
754C2×C22⋊C4C24196yes—
755C2×C22⋊C4C24148yes—
756C2×C22⋊C4C24124yes—
757C2×C22⋊C4C24148yes—
758C2×C42C2416yes—
759C2×C42C2416yes—
760C2×C42C24112yes—
761C2×C42C2413yes—
762C2×C42C2413yes—
763C2×C42C24148yes—
764C2×C42C24124yes—
765C2×C42C24124yes—
766C2×C42C24196yes—
767C2×C42C2416yes—
768C2×C42C2416yes—
769C2×C42C24124yes—
770C2×C42C2416yes—
771C2×C42C2411yescharacteristic
772C2×C42C2413yes—
773C2×C42C2416yes—
774C2×C42C2416yes—
775C2×C42C24124yes—
776C2×C42C24124yes—
777C24C25124yes—
778C24C2512yes—
779C24C2513yes—
780#41—264no—
781#41—2192no—
782#41—2192no—
783#41—296no—
784#41—232no—
785#41—296no—
786#41—296no—
787#41—248no—
788#41—248no—
789#41—432no—
790#41—848no—
791#41C2×#41132yes—
792#41C2×#41132yes—
793C2×Q8—264no—
794C2×Q8—264no—
795C2×Q8—224no—
796C2×Q8—212no—
797C2×Q8—248no—
798C2×Q8—248no—
799C2×Q8—248no—
800C2×Q8—424no—
801C2×Q8—812no—
802C2×Q8C2×#4118yes—
803C2×Q8C2518yes—
804C2×Q8C2516yes—
805C2×Q8C25124yes—
806C2×Q8C25124yes—
807C2×Q8C2516yes—
808C2×Q8C2518yes—
809C2×Q8C25124yes—
810C2×Q8C2518yes—
811C2×Q8C25124yes—
812C2×Q8C2514yes—
813C2×D4—224no—
814C2×D4—296no—
815C2×D4—2192no—
816C2×D4—24no—
817C2×D4—248no—
818C2×D4—424no—
819C2×D4—812no—
820C2×D4C2×#41124yes—
821C2×D4C2518yes—
822C2×D4C25124yes—
823C2×D4C25116yes—
824C2×D4C25148yes—
825C2×D4C2512yes—
826C2×D4C25124yes—
827C2×D4C2518yes—
828C2×D4C2512yes—
829C2×D4C25132yes—
830C2×D4C25124yes—
831C2×D4C25132yes—
832C2×D4C25124yes—
833C2×D4C2518yes—
834C2×D4C25112yes—
835C22×C4—224no—
836C22×C4—224no—
837C22×C4—296no—
838C22×C4—46no—
839C22×C4—44no—
840C22×C4—86no—
841C22×C4—83no—
842C22×C4—86no—
843C22×C4—848no—
844C22×C4C2×#41124yes—
845C22×C4C2511yescharacteristic
846C22×C4C2516yes—
847C22×C4C2514yes—
848C22×C4C2516yes—
849C22×C4C25124yes—
850C22×C4C25124yes—
851C22×C4C25124yes—
852C22×C4C25148yes—
853C22×C4C25116yes—
854C22×C4C2512yes—
855C22×C4C2516yes—
856C22×C4C2513yes—
857C22×C4C2514yes—
858C22×C4C2516yes—
859C22×C4C25124yes—
860C22×C4C2511yescharacteristic
861C22×C4C2513yes—
862C22×C4C25124yes—
863C22×C4C25132yes—
864C22×C4C2516yes—
865C22×C4C2516yes—
866C22×C4C25124yes—
867C22×C4C25124yes—
868C22×C4C25196yes—
869C22×C4C2516yes—
870C22×C4C2513yes—
871C22×C4C2511yescharacteristic
872C22×C4C2516yes—
873C4⋊C4C2516yes—
874C4⋊C4C2512yes—
875C4⋊C4C25124yes—
876C4⋊C4C2518yes—
877C4⋊C4C2518yes—
878C4⋊C4C2516yes—
879C4⋊C4C25124yes—
880C4⋊C4C25196yes—
881C4⋊C4C25112yes—
882C4⋊C4C25112yes—
883C4⋊C4C25148yes—
884C4⋊C4C25112yes—
885C4⋊C4C25116yes—
886C4⋊C4C2518yes—
887C4⋊C4C2518yes—
888C4⋊C4C2518yes—
889C4⋊C4C25116yes—
890C4⋊C4C2518yes—
891C4⋊C4C25196yes—
892C4⋊C4C25196yes—
893C4⋊C4C2512yes—
894C4⋊C4C25124yes—
895C4⋊C4C25132yes—
896C4⋊C4C25112yes—
897C4⋊C4C25124yes—
898C4⋊C4C25148yes—
899C4⋊C4C25124yes—
900C4⋊C4C25124yes—
901C4⋊C4C25148yes—
902C4⋊C4C25124yes—
903C4⋊C4C25124yes—
904C22⋊C4C25124yes—
905C22⋊C4C25116yes—
906C22⋊C4C25116yes—
907C22⋊C4C25148yes—
908C22⋊C4C25132yes—
909C22⋊C4C25196yes—
910C22⋊C4C25116yes—
911C22⋊C4C25196yes—
912C22⋊C4C25196yes—
913C22⋊C4C25124yes—
914C22⋊C4C2514yes—
915C22⋊C4C25124yes—
916C22⋊C4C2514yes—
917C22⋊C4C25148yes—
918C22⋊C4C25148yes—
919C22⋊C4C25132yes—
920C22⋊C4C25132yes—
921C42C25124yes—
922C42C25112yes—
923C42C2511yescharacteristic
924C42C2511yescharacteristic
925C42C2516yes—
926C42C25112yes—
927C42C2516yes—
928C42C2511yescharacteristic
929C42C2511yescharacteristic
930C42C25132yes—
931C42C25196yes—
932C42C25124yes—
933C42C25148yes—
934C42C2516yes—
935C42C25148yes—
936C42C2516yes—
937C42C2516yes—
938C42C25116yes—
939C42C2516yes—
940C23—24no—
941C23—248no—
942C23—43no—
943C23—42no—
944C23—43no—
945C23—42no—
946C23—424no—
947C23—424no—
948C23C22×#41112yes—
949C23C26116yes—
950C23C2614yes—
951C23C2616yes—
952C23C2611yescharacteristic
953Q8—212no—
954Q8—248no—
955Q8—212no—
956Q8—248no—
957Q8—216no—
958Q8—216no—
959Q8—424no—
960Q8—48no—
961Q8—424no—
962Q8C22×#41116yes—
963D4—296no—
964D4—232no—
965D4—248no—
966D4—248no—
967D4—216no—
968D4—24no—
969D4—24no—
970D4—216no—
971D4—424no—
972D4—48no—
973D4—424no—
974D4—432no—
975D4—432no—
976D4C22×#41148yes—
977C2×C4—212no—
978C2×C4—248no—
979C2×C4—248no—
980C2×C4—232no—
981C2×C4—296no—
982C2×C4—248no—
983C2×C4—22no—
984C2×C4—212no—
985C2×C4—28no—
986C2×C4—42no—
987C2×C4—44no—
988C2×C4—46no—
989C2×C4—43no—
990C2×C4—46no—
991C2×C4—424no—
992C2×C4—41no—
993C2×C4—43no—
994C2×C4—424no—
995C2×C4—496no—
996C2×C4—46no—
997C2×C4—46no—
998C2×C4—424no—
999C2×C4—424no—
1000C2×C4—432no—
1001C2×C4C22×#41124yes—
1002C2×C4C22×#41112yes—
1003C2×C4C22×#4114yes—
1004C2×C4C22×#41124yes—
1005C2×C4C2614yes—
1006C2×C4C2611yescharacteristic
1007C2×C4C26112yes—
1008C2×C4C2616yes—
1009C2×C4C26116yes—
1010C2×C4C2611yescharacteristic
1011C2×C4C26112yes—
1012C2×C4C26116yes—
1013C2×C4C2616yes—
1014C2×C4C2611yescharacteristic
1015C2×C4C26116yes—
1016C2×C4C2611yescharacteristic
1017C2×C4C2616yes—
1018C2×C4C2611yescharacteristic
1019C2×C4C2611yescharacteristic
1020C22—21no—
1021C22—26no—
1022C22—21no—
1023C22—26no—
1024C22—24no—
1025C22—216no—
1026C22—24no—
1027C22—216no—
1028C22—24no—
1029C22—216no—
1030C22—412no—
1031C22—48no—
1032C22—848no—
1033C22C23×#41112yes—
1034C22C23×#4112yes—
1035C22C2711yescharacteristic
1036C4—216no—
1037C4—212no—
1038C4—21no—
1039C4—24no—
1040C4—26no—
1041C4—216no—
1042C4—212no—
1043C4—216no—
1044C4—21no—
1045C4—26no—
1046C4—21no—
1047C4C23×#4112yes—
1048C4C23×#41112yes—
1049C4C23×#4112yes—
1050C42−1+612yes—
1051C2—22no—
1052C2—212no—
1053C2—44no—
1054C2—416no—
1055C2C24×#4111yescharacteristic
1056C2C2×2−1+611yescharacteristic
1057C2#6310311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC22C27
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #63010C2semidirect
2. #63009C2semidirect
3. #63001C2semidirect
4. #63000C2semidirect
5. #62995C2semidirect
6. #62993C2semidirect
7. #62860C2semidirect
8. #62859C2semidirect
9. #62850C2semidirect
10. #62847C2semidirect
11. #62845C2semidirect
12. #62815C2semidirect
13. #62813C2semidirect
14. #62812C2semidirect
15. #62788C2semidirect
16. #62781C2semidirect
17. C2×#3507C2semidirect
18. #62654C2semidirect
19. C2×C4×2−1+4C2semidirect
22. #3524C22semidirect
23. #3523C22semidirect
24. #3523C22semidirect
25. #3522C22semidirect
26. #3521C22semidirect
27. #3521C22semidirect
28. #3520C22semidirect
29. #3518C22semidirect
30. #3516C22semidirect
31. #3516C22semidirect
32. #3515C22semidirect
33. #3515C22semidirect
34. #3514C22semidirect
35. #3513C22semidirect
36. #3512C22semidirect
37. #3511C22semidirect
38. #3511C22semidirect
39. #3510C22semidirect
40. #3510C22semidirect
41. #3509C22semidirect
42. #3509C22semidirect
43. #3508C22semidirect
44. #3507C22semidirect
45. #3507C22semidirect
46. #3507C22semidirect
47. #3507C22semidirect
48. #3507C22semidirect
49. #3507C22semidirect
50. #3507C22semidirect
51. #3507C22semidirect
52. #3507C22semidirect
53. #3507C22semidirect
54. #3506C22semidirect
55. #3506C22semidirect
56. #3506C22semidirect
57. #3505C22semidirect
58. #3505C22semidirect
59. #3504C22semidirect
60. #3503C22semidirect
61. #3503C22semidirect
62. #3502C22semidirect
63. #3502C22semidirect
64. #3501C22semidirect
65. #3501C22semidirect
66. #3500C22semidirect
67. #3500C22semidirect
68. #3499C22semidirect
69. #3499C22semidirect
70. #3498C22semidirect
75. #3495C22semidirect
76. #3495C22semidirect
77. #3493C22semidirect
78. #3493C22semidirect
79. #3492C22semidirect
80. #3492C22semidirect
81. #3491C22semidirect
82. #3489C22semidirect
83. #3489C22semidirect
84. #3486C22semidirect
85. #3485C22semidirect
86. #3482C22semidirect
87. #3482C22semidirect
88. #3481C22semidirect
89. #3480C22semidirect
90. #3480C22semidirect
91. #3480C22semidirect
92. C2×#559C22semidirect
93. Q8×#41C22semidirect
94. Q8×#41C22semidirect
95. Q8×#41C22semidirect
96. C2×#557C22semidirect
97. #3475C22semidirect
98. #3475C22semidirect
99. #3475C22semidirect
100. C2×#556C22semidirect
101. C2×#556C22semidirect
102. C2×#554C22semidirect
103. C2×#552C22semidirect
104. D4×#41C22semidirect
105. D4×#41C22semidirect
106. #3461C22semidirect
107. #3461C22semidirect
108. #3459C22semidirect
109. #3458C22semidirect
110. #3455C22semidirect
111. C2×#539C22semidirect
113. #3449C22semidirect
114. C2×#536C22semidirect
115. #3444C22semidirect
116. C2×#533C22semidirect
118. C2×#529C22semidirect
119. C4×2−1+4C22semidirect
120. C4×2−1+4C22semidirect
121. C4×2−1+4C22semidirect
122. C4×2−1+4C22semidirect
123. C4×2−1+4C22semidirect
124. C4×2−1+4C22semidirect
125. C4×H(5,𝔽2)C22semidirect
126. C4×H(5,𝔽2)C22semidirect
128. #3428C22semidirect
129. #3428C22semidirect
131. C2×#520C22semidirect
132. C2×#520C22semidirect
133. C2×#520C22semidirect
134. C2×#520C22semidirect
135. C2×#519C22semidirect
136. C2×#519C22semidirect
138. C2×C4×#41C22semidirect
139. C2×C4×#41C22semidirect
140. C22×C4×Q8C22semidirect
141. C22×C4×Q8C22semidirect
464. C2×#41#41semidirect

Maximal subgroups

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

subgroupindex
#630102
#630092
#630012
#630002
#629952
#629932
#628602
#628592
#628502
#628472
#628452
#628152
#628132
#628122
#627882
#627812
C2×#35072
#626542
C2×C4×2−1+42