Finite Group Databasebeta

← #11692190

Subgroups — #11692190

Order 768.

1684 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3559C211yesmaximal, characteristic
2#86129C211yesmaximal, characteristic, complemented
3#83644C212yesmaximal, complemented
4#83632C212yesmaximal, complemented
5#83620C212yesmaximal, complemented
6#83620C212yesmaximal, complemented
7#83611C212yesmaximal, complemented
8#83606C212yesmaximal, complemented
9#83531C212yesmaximal, complemented
10#83518C212yesmaximal, complemented
11#83481C212yesmaximal, complemented
12#83480C212yesmaximal, complemented
13#83441C212yesmaximal, complemented
14#83439C212yesmaximal, complemented
15#83320C211yesmaximal, characteristic, complemented
16#83316C211yesmaximal, characteristic, complemented
17#83130C211yesmaximal, characteristic, complemented
18#83021C211yesmaximal, characteristic, complemented
19C2×#5063C211yesmaximal, characteristic, complemented
20#62167—31nomaximal, Sylow
21C3×#563—21no—
22C3×#562—21no—
23C3×#554C2212yes—
24C3×#553C2212yes—
25C3×#553C2212yes—
26C3×#547—22no—
27C3×#547C2212yes—
28C3×#544C2212yes—
29C3×#540C2212yes—
30C3×#539—22no—
31C3×#539—21no—
32C3×#537—21no—
33C3×#532C2211yescharacteristic
34C3×#529C2211yescharacteristic
35C2×C3×#125C2211yescharacteristic
36#5701—22no—
37#5685—21no—
38#5671—21no—
39#5650—22no—
40#5622—21no—
41#5600—21no—
42#5570C2211yescharacteristic
43#5567C2211yescharacteristic
44#5542C2211yescharacteristic
45#5541C2212yes—
46D4×Dic6C2212yes—
47D4×Dic6C2211yescharacteristic
48#5518C2212yes—
49#5516C2212yes—
50#5470C2211yescharacteristic
51C2×C4×Dic6C2211yescharacteristic
52#5094C2212yes—
53#5094C2212yes—
54#5093C2212yes—
55#5091C2211yescharacteristic
56#5091C2212yes—
57#5091C2211yescharacteristic
58#5081C2212yes—
59#5075C2211yescharacteristic
60#5075C2211yescharacteristic
61#5075C2212yes—
62#5069C2212yes—
63#5069C2212yes—
64#5065C2212yes—
65#5064C2212yes—
66#5063C2212yes—
67#5063C2212yes—
68#5063C2212yes—
69#5063C2212yes—
70#5063C2212yes—
71#5063C2212yes—
72#5063C2212yes—
73#5063C2212yes—
74#5042C2212yes—
75#5042C2212yes—
76#5041C2212yes—
77#5041C2212yes—
78#5041C2212yes—
79#5041C2212yes—
80#5040C2212yes—
81#5040C2212yes—
82#5040C2212yes—
83#5035C2212yes—
84#5035C2212yes—
85#5033C2212yes—
86#5024C2212yes—
87#5019C2212yes—
88#5019C2212yes—
89#5019C2212yes—
90#5018C2212yes—
91#5018C2212yes—
92#5018C2212yes—
93#5018C2212yes—
94C4×#214C2212yes—
95C4×#214C2212yes—
96#5011C2212yes—
97#5011C2212yes—
98D4×C3⋊C8C2212yes—
99#5009C2212yes—
100#5009C2212yes—
101#5008C2212yes—
102#5004C2212yes—
103#5000C2212yes—
104#4999C2212yes—
105#4998C2212yes—
106#4996C2212yes—
107#4996C2212yes—
108#4971C2212yes—
109#4971C2212yes—
110#4970C2212yes—
111#4970C2212yes—
112C2×#810C2212yes—
113C2×#810C2211yescharacteristic
114C2×#810C2211yescharacteristic
115#4964C2212yes—
116C2×#808C2211yescharacteristic
117C2×#807C2211yescharacteristic
118#4926C2211yescharacteristic
119C2×C4⋊(C3⋊C8)C2211yescharacteristic
120#3559D311yescharacteristic
121#3523—31no—
122#3388—32no—
123#3372—32no—
124#3350—32no—
125#3343—32no—
126#3337—32no—
127#3320—32no—
128#3320—32no—
129#3298—32no—
130#3260—32no—
131#3246—31no—
132#3242—32no—
133#3236—31no—
134#3126—32no—
135#3112—31no—
136#3082—32no—
137C2×#479—31no—
138#2992—31no—
139C2×C3×#41—22no—
140C2×C3×#41—21no—
141C22×Dic6C2311yescharacteristic
142C22×Dic6C2312yes—
143C3×C4⋊Q8—22no—
144C3×C4⋊Q8C2312yes—
145C3×C4⋊Q8C2311yescharacteristic
146C3×#127C2311yescharacteristic
147C3×#126—22no—
148C3×#126—22no—
149C3×#126D412yes—
150C3×#125—22no—
151C3×#125—21no—
152C3×#125—21no—
153C3×#125D411yescharacteristic
154C3×#125C2312yes—
155C3×#125C2312yes—
156C3×#125C2312yes—
157C3×#124—21no—
158C3×#124D411yescharacteristic
159C3×#123—22no—
160C3×#123—22no—
161C3×#123—22no—
162C3×#123—22no—
163C3×#123—22no—
164C3×#123—22no—
165C3×#123D412yes—
166C3×C22⋊Q8—22no—
167C3×C22⋊Q8—22no—
168C3×C22⋊Q8—22no—
169C3×C22⋊Q8—22no—
170C3×C22⋊Q8—22no—
171C3×C22⋊Q8—22no—
172C3×C22⋊Q8D411yescharacteristic
173C3×#121—22no—
174C3×#121—22no—
175C3×#121—21no—
176C3×#121—22no—
177C3×#121—22no—
178C3×#121D411yescharacteristic
179C3×#121C2312yes—
180C3×#121C2312yes—
181C3×#121C2312yes—
182C3×C4×Q8C2311yescharacteristic
183C3×C4×D4—22no—
184C3×C4×D4—22no—
185C3×C4×D4—21no—
186C3×C4×D4C2312yes—
187C3×C4×D4C2312yes—
188C3×C4×D4C2312yes—
189C3×C4×D4C2312yes—
190C3×C4×D4C2311yescharacteristic
191C3×#117C2312yes—
192C3×#117C2312yes—
193C2×C3×C4⋊C4—21no—
194C2×C3×C4⋊C4—21no—
195C2×C3×C4⋊C4—22no—
196C2×C3×C4⋊C4C2311yescharacteristic
197C2×C3×C4⋊C4C2311yescharacteristic
198C2×C3×C4⋊C4C2312yes—
199C2×C3×C42C2311yescharacteristic
200Q8×Dic3—21no—
201#944—21no—
202#936—21no—
203#935—22no—
204D4×Dic3—22no—
205D4×Dic3—21no—
206C2×#214C2312yes—
207C2×#214C2312yes—
208C2×#214C2312yes—
209C2×#214C2312yes—
210#926—21no—
211#926C2312yes—
212C2×C4⋊Dic3C2311yescharacteristic
213#924—21no—
214#924C2312yes—
215#924C2312yes—
216#924C2312yes—
217C2×Dic3⋊C4—21no—
218C2×C4×Dic3—21no—
219C2×#208C2312yes—
220C22×C3⋊C8C2311yescharacteristic
221C22×C3⋊C8C2311yescharacteristic
222C22×C3⋊C8C2312yes—
223#890—22no—
224#890—21no—
225#889—22no—
226#889—22no—
227#889—22no—
228#889—22no—
229#888—22no—
230#888—21no—
231#887—22no—
232#887—21no—
233#887—21no—
234#887—22no—
235#879—22no—
236#879—22no—
237#879—22no—
238#879—22no—
239#878—22no—
240#878—22no—
241#878—22no—
242#877—22no—
243#877—22no—
244#877—22no—
245#870—21no—
246#870C2312yes—
247#869C2311yescharacteristic
248#869C2312yes—
249#869C2311yescharacteristic
250C4×Dic6—21no—
251C4×Dic6—21no—
252C4×Dic6—21no—
253C4×Dic6C2311yescharacteristic
254C4×Dic6C2311yescharacteristic
255C4×Dic6C2311yescharacteristic
256C4×Dic6C2311yescharacteristic
257C4×Dic6C2312yes—
258C4×Dic6C2312yes—
259C4×Dic6C2312yes—
260#832C2312yes—
261#832C2312yes—
262#832C2312yes—
263#832C2312yes—
264#830C2312yes—
265#830C2312yes—
266#830C2312yes—
267#810C2312yes—
268#810C2312yes—
269#810C2312yes—
270#810C2312yes—
271#810C2312yes—
272#810C2312yes—
273#810C2312yes—
274#810C2312yes—
275#810C2312yes—
276#810C2312yes—
277#810C2312yes—
278#810C2312yes—
279#808C2312yes—
280#808C2312yes—
281#808C2312yes—
282#808C2312yes—
283#808C2312yes—
284#808C2312yes—
285#807C2312yes—
286#807C2312yes—
287#807C2312yes—
288#807C2312yes—
289#807C2312yes—
290#807C2312yes—
291C4⋊(C3⋊C8)C2312yes—
292C4⋊(C3⋊C8)C2312yes—
293C4⋊(C3⋊C8)C2311yescharacteristic
294C4⋊(C3⋊C8)C2311yescharacteristic
295C4⋊(C3⋊C8)C2312yes—
296C4⋊(C3⋊C8)C2312yes—
297#803C2312yes—
298#803C2312yes—
299C4×C3⋊C8C2312yes—
300#563—21no—
301#562—21no—
302#557—31no—
303#557—31no—
304#557—61no—
305#556—31no—
306#556—61no—
307#554C2×D312yes—
308#553C2×D312yes—
309#553C2×D312yes—
310#552—32no—
311#552—62no—
312D4×Q8—32no—
313D4×Q8—31no—
314#547—22no—
315#547C2×D312yes—
316#544C2×D312yes—
317#541—32no—
318#541—62no—
319#540C2×D312yes—
320#539—22no—
321#539—21no—
322#537—21no—
323#533—31no—
324#533—61no—
325#532C2×D311yescharacteristic
326#529—61no—
327#529C2×D311yescharacteristic
328C2×#125C2×D311yescharacteristic
329#519—32no—
330C2×C4×Q8—31no—
331#501—32no—
332#501—32no—
333#499—32no—
334#491—32no—
335#491—32no—
336#487—32no—
337#485—32no—
338#485—32no—
339#484—32no—
340#484—32no—
341#483—32no—
342#483—32no—
343#482—32no—
344#482—32no—
345#480—32no—
346#479—32no—
347#479—32no—
348#479—32no—
349#479—32no—
350#479—32no—
351#479—32no—
352#479—32no—
353#479—32no—
354#478—32no—
355#478—32no—
356#477—31no—
357#477—32no—
358#477—31no—
359#476—32no—
360#475—32no—
361#475—32no—
362#468—32no—
363#468—32no—
364#465—32no—
365#465—32no—
366#465—32no—
367#465—32no—
368#461—32no—
369#461—32no—
370#461—32no—
371#460—31no—
372#460—31no—
373#460—32no—
374#448—32no—
375#448—32no—
376#448—32no—
377#446—32no—
378#440—32no—
379#440—32no—
380#440—32no—
381#440—32no—
382C4×SD16—32no—
383C4×SD16—32no—
384#435—32no—
385#435—32no—
386C8×D4—32no—
387#433—32no—
388#432—31no—
389#428—32no—
390#427—32no—
391C2×#107—31no—
392C2×#106—31no—
393#424—32no—
394C2×C4⋊C8—31no—
395#419—32no—
396C2×#103—31no—
397C2×#103—31no—
398C2×#103—32no—
399C3×#41—82no—
400C3×#41—84no—
401C2×C3×Q8—22no—
402C2×C3×Q8—21no—
403C2×C3×Q8C2×D411yescharacteristic
404C2×C3×D4—22no—
405C2×C3×D4—22no—
406C2×C3×D4—22no—
407C2×C3×D4—21no—
408C2×C3×D4—21no—
409C2×C3×D4C2×D412yes—
410C2×C3×D4C2×D411yescharacteristic
411C2×C3×D4C2412yes—
412C22×C3×C4—21no—
413C22×C3×C4—21no—
414C22×C3×C4—22no—
415C22×C3×C4—22no—
416C22×C3×C4—22no—
417C22×C3×C4—22no—
418C22×C3×C4C2×D411yescharacteristic
419C22×C3×C4C2×D411yescharacteristic
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2412yes—
422C22×Dic3—22no—
423C22×Dic3—21no—
424C22×Dic3—21no—
425C2×Dic6—22no—
426C2×Dic6—24no—
427C2×Dic6—21no—
428C2×Dic6—21no—
429C2×Dic6—22no—
430C2×Dic6—41no—
431C2×Dic6—42no—
432C2×Dic6C2411yescharacteristic
433C2×Dic6C2412yes—
434C2×Dic6C2411yescharacteristic
435C3×C4⋊C4—22no—
436C3×C4⋊C4—22no—
437C3×C4⋊C4—22no—
438C3×C4⋊C4—22no—
439C3×C4⋊C4—22no—
440C3×C4⋊C4—22no—
441C3×C4⋊C4—21no—
442C3×C4⋊C4—22no—
443C3×C4⋊C4—21no—
444C3×C4⋊C4—21no—
445C3×C4⋊C4—22no—
446C3×C4⋊C4C2×D411yescharacteristic
447C3×C4⋊C4C2×D412yes—
448C3×C4⋊C4C2×D412yes—
449C3×C4⋊C4C2×D411yescharacteristic
450C3×C4⋊C4C2×D412yes—
451C3×C4⋊C4C2×D412yes—
452C3×C4⋊C4C2412yes—
453C3×C4⋊C4C2412yes—
454C3×C4⋊C4C2412yes—
455C3×C22⋊C4—22no—
456C3×C22⋊C4—22no—
457C3×C22⋊C4—22no—
458C3×C22⋊C4—22no—
459C3×C22⋊C4—22no—
460C3×C22⋊C4—22no—
461C3×C22⋊C4—22no—
462C3×C22⋊C4C2×D412yes—
463C3×C22⋊C4C2×D412yes—
464C3×C22⋊C4C2×D412yes—
465C3×C22⋊C4C2×D412yes—
466C3×C22⋊C4C2×D412yes—
467C3×C42—22no—
468C3×C42C2×D411yescharacteristic
469C3×C42C2×D411yescharacteristic
470C3×C42C2412yes—
471C3×C42C2411yescharacteristic
472C3×C42C2411yescharacteristic
473#217—22no—
474#217—22no—
475#217—22no—
476#217—22no—
477#214—24no—
478#214—42no—
479#214—42no—
480#214—42no—
481C4⋊Dic3—21no—
482C4⋊Dic3—21no—
483C4⋊Dic3—21no—
484C4⋊Dic3—21no—
485C4⋊Dic3—22no—
486C4⋊Dic3—22no—
487C4⋊Dic3C2411yescharacteristic
488C4⋊Dic3C2411yescharacteristic
489C4⋊Dic3C2412yes—
490Dic3⋊C4—21no—
491Dic3⋊C4—21no—
492Dic3⋊C4—21no—
493Dic3⋊C4—21no—
494Dic3⋊C4—22no—
495Dic3⋊C4—22no—
496Dic3⋊C4—22no—
497Dic3⋊C4—22no—
498Dic3⋊C4—22no—
499Dic3⋊C4—22no—
500Dic3⋊C4—22no—
501Dic3⋊C4—22no—
502C4×Dic3—21no—
503C4×Dic3—22no—
504C4×Dic3—21no—
505C4×Dic3—21no—
506C4×Dic3—21no—
507C4×Dic3—22no—
508C4×Dic3—22no—
509C4×Dic3—22no—
510#208—42no—
511C2×C3⋊C8—41no—
512C2×C3⋊C8—42no—
513C2×C3⋊C8—41no—
514C2×C3⋊C8C2412yes—
515C2×C3⋊C8C2412yes—
516C2×C3⋊C8C2412yes—
517C2×C3⋊C8C2412yes—
518C2×#41—22no—
519C2×#41—21no—
520C22×Q8—31no—
521C22×Q8—32no—
522C2×SD16—32no—
523C2×SD16—32no—
524C2×SD16—32no—
525C2×SD16—32no—
526C2×M16—32no—
527C22×C8—31no—
528C22×C8—31no—
529C22×C8—32no—
530C4⋊Q8—22no—
531C4⋊Q8—31no—
532C4⋊Q8—31no—
533C4⋊Q8—32no—
534C4⋊Q8—61no—
535C4⋊Q8—61no—
536C4⋊Q8—62no—
537C4⋊Q8C22×D311yescharacteristic
538C4⋊Q8C22×D312yes—
539#127C22×D311yescharacteristic
540#126—22no—
541#126—22no—
542#126—62no—
543#126—62no—
544#126—62no—
545#126—62no—
546#126#6712yes—
547#125—22no—
548#125—21no—
549#125—21no—
550#125—32no—
551#125—61no—
552#125—62no—
553#125—62no—
554#125—62no—
555#125—62no—
556#125—62no—
557#125—61no—
558#125#6711yescharacteristic
559#125C22×D312yes—
560#125C22×D312yes—
561#125C22×D312yes—
562#124—21no—
563#124—61no—
564#124#6711yescharacteristic
565#123—22no—
566#123—22no—
567#123—22no—
568#123—22no—
569#123—22no—
570#123—22no—
571#123—62no—
572#123#6712yes—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—32no—
580C22⋊Q8—32no—
581C22⋊Q8—32no—
582C22⋊Q8—61no—
583C22⋊Q8—62no—
584C22⋊Q8—62no—
585C22⋊Q8—62no—
586C22⋊Q8#6711yescharacteristic
587#121—22no—
588#121—22no—
589#121—21no—
590#121—22no—
591#121—22no—
592#121#6711yescharacteristic
593#121C22×D312yes—
594#121C22×D312yes—
595#121C22×D312yes—
596C4×Q8—31no—
597C4×Q8—31no—
598C4×Q8—31no—
599C4×Q8—31no—
600C4×Q8—32no—
601C4×Q8—32no—
602C4×Q8—32no—
603C4×Q8—61no—
604C4×Q8—62no—
605C4×Q8—62no—
606C4×Q8—61no—
607C4×Q8—61no—
608C4×Q8—61no—
609C4×Q8—61no—
610C4×Q8—61no—
611C4×Q8C22×D311yescharacteristic
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—21no—
615C4×D4—62no—
616C4×D4—61no—
617C4×D4C22×D312yes—
618C4×D4C22×D312yes—
619C4×D4C22×D312yes—
620C4×D4C22×D312yes—
621C4×D4C22×D311yescharacteristic
622#117—32no—
623#117—61no—
624#117—62no—
625#117—62no—
626#117—62no—
627#117C22×D312yes—
628#117C22×D312yes—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—31no—
633C2×C4⋊C4—61no—
634C2×C4⋊C4C22×D311yescharacteristic
635C2×C4⋊C4C22×D311yescharacteristic
636C2×C4⋊C4C22×D312yes—
637C2×C42—61no—
638C2×C42C22×D311yescharacteristic
639#107—32no—
640#107—32no—
641#107—32no—
642#107—32no—
643#107—32no—
644#107—32no—
645#106—32no—
646#106—32no—
647#106—32no—
648#106—32no—
649#106—32no—
650#106—32no—
651C4⋊C8—32no—
652C4⋊C8—32no—
653C4⋊C8—31no—
654C4⋊C8—32no—
655C4⋊C8—32no—
656C4⋊C8—31no—
657#103—32no—
658#103—32no—
659#103—32no—
660#103—32no—
661#103—32no—
662#103—32no—
663#103—32no—
664#103—32no—
665#103—32no—
666#103—32no—
667#103—32no—
668#103—32no—
669#102—32no—
670#102—32no—
671#102—32no—
672#102—32no—
673C22⋊C8—32no—
674C22⋊C8—32no—
675C22⋊C8—32no—
676#97—32no—
677#97—32no—
678C4×C8—32no—
679C23×C3—22no—
680C23×C3C22×D412yes—
681C23×C3C22×D411yescharacteristic
682C3×Q8—41no—
683C3×Q8—81no—
684C3×Q8—82no—
685C3×D4—24no—
686C3×D4—22no—
687C3×D4—22no—
688C3×D4—41no—
689C3×D4—44no—
690C3×D4—81no—
691C3×D4—81no—
692C3×D4—82no—
693C3×D4—82no—
694C2×C3×C4—22no—
695C2×C3×C4—21no—
696C2×C3×C4—22no—
697C2×C3×C4—21no—
698C2×C3×C4—22no—
699C2×C3×C4—22no—
700C2×C3×C4—22no—
701C2×C3×C4—22no—
702C2×C3×C4—41no—
703C2×C3×C4—42no—
704C2×C3×C4—82no—
705C2×C3×C4—82no—
706C2×C3×C4—82no—
707C2×C3×C4—81no—
708C2×C3×C4—82no—
709C2×C3×C4C22×D411yescharacteristic
710C2×C3×C4C22×D411yescharacteristic
711C2×C3×C4C22×D411yescharacteristic
712C2×C3×C4C22×D412yes—
713C2×C3×C4C22×D412yes—
714C2×C3×C4C22×D412yes—
715C2×C3×C4C22×D411yescharacteristic
716C2×C3×C4C22×D411yescharacteristic
717C2×C3×C4C2511yescharacteristic
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—22no—
721C2×Dic3—21no—
722C2×Dic3—22no—
723C2×Dic3—21no—
724C2×Dic3—42no—
725C2×Dic3—44no—
726C2×Dic3—42no—
727Dic6—21no—
728Dic6—21no—
729Dic6—22no—
730Dic6—22no—
731Dic6—21no—
732Dic6—42no—
733Dic6—44no—
734Dic6—42no—
735Dic62−1+412yes—
736C3⋊C8—22no—
737C3⋊C8—22no—
738C3⋊C8—22no—
739C3⋊C8—22no—
740#41—82no—
741#41—84no—
742C2×Q8—22no—
743C2×Q8—21no—
744C2×Q8—31no—
745C2×Q8—32no—
746C2×Q8—31no—
747C2×Q8—62no—
748C2×Q8—64no—
749C2×Q8—61no—
750C2×Q8—62no—
751C2×Q8—61no—
752C2×Q8—121no—
753C2×Q8—122no—
754C2×Q8C2×#6711yescharacteristic
755C2×D4—22no—
756C2×D4—22no—
757C2×D4—22no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4C2×#6712yes—
761C2×D4C2×#6711yescharacteristic
762C2×D4C23×D312yes—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—62no—
772C22×C4C2×#6711yescharacteristic
773C22×C4C2×#6711yescharacteristic
774C22×C4C23×D311yescharacteristic
775C22×C4C23×D312yes—
776SD16—64no—
777SD16—122no—
778SD16—122no—
779SD16—122no—
780M16—122no—
781C2×C8—32no—
782C2×C8—32no—
783C2×C8—32no—
784C2×C8—32no—
785C2×C8—121no—
786C2×C8—122no—
787C2×C8—121no—
788C4⋊C4—22no—
789C4⋊C4—22no—
790C4⋊C4—22no—
791C4⋊C4—22no—
792C4⋊C4—22no—
793C4⋊C4—22no—
794C4⋊C4—21no—
795C4⋊C4—22no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—22no—
799C4⋊C4—32no—
800C4⋊C4—31no—
801C4⋊C4—31no—
802C4⋊C4—61no—
803C4⋊C4—61no—
804C4⋊C4—61no—
805C4⋊C4—61no—
806C4⋊C4—61no—
807C4⋊C4—62no—
808C4⋊C4—62no—
809C4⋊C4—62no—
810C4⋊C4—62no—
811C4⋊C4—61no—
812C4⋊C4—62no—
813C4⋊C4—61no—
814C4⋊C4—61no—
815C4⋊C4—62no—
816C4⋊C4—62no—
817C4⋊C4—62no—
818C4⋊C4—62no—
819C4⋊C4—62no—
820C4⋊C4C2×#6712yes—
821C4⋊C4C2×#6712yes—
822C4⋊C4C2×#6712yes—
823C4⋊C4C2×#6711yescharacteristic
824C4⋊C4C2×#6712yes—
825C4⋊C4C2×#6711yescharacteristic
826C4⋊C4C23×D312yes—
827C4⋊C4C23×D312yes—
828C4⋊C4C23×D312yes—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—22no—
832C22⋊C4—22no—
833C22⋊C4—22no—
834C22⋊C4—22no—
835C22⋊C4—22no—
836C22⋊C4—62no—
837C22⋊C4—62no—
838C22⋊C4—62no—
839C22⋊C4—62no—
840C22⋊C4C2×#6712yes—
841C22⋊C4C2×#6712yes—
842C22⋊C4C2×#6712yes—
843C22⋊C4C2×#6712yes—
844C22⋊C4C2×#6712yes—
845C42—22no—
846C42—61no—
847C42—61no—
848C42—61no—
849C42—61no—
850C42—62no—
851C42—62no—
852C42—62no—
853C42—62no—
854C42C2×#6711yescharacteristic
855C42C2×#6711yescharacteristic
856C42C23×D312yes—
857C42C23×D311yescharacteristic
858C42C23×D311yescharacteristic
859C22×C3—21no—
860C22×C3—21no—
861C22×C3—22no—
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—42no—
865C22×C3—42no—
866C22×C3—42no—
867C22×C3#57712yes—
868C22×C3C23×D411yescharacteristic
869C3×C4—21no—
870C3×C4—21no—
871C3×C4—22no—
872C3×C4—21no—
873C3×C4—22no—
874C3×C4—21no—
875C3×C4—21no—
876C3×C4—22no—
877C3×C4—42no—
878C3×C4—42no—
879C3×C4—42no—
880C3×C4C2×2−1+411yescharacteristic
881C3×C4#58511yescharacteristic
882Dic3—22no—
883Dic3—42no—
884Dic3—41no—
885Dic3—42no—
886Dic3—41no—
887Dic3—41no—
888C23—22no—
889C23C22×#6712yes—
890C23C22×#6711yescharacteristic
891Q8—32no—
892Q8—41no—
893Q8—61no—
894Q8—62no—
895Q8—61no—
896Q8—62no—
897Q8—61no—
898Q8—81no—
899Q8—82no—
900Q8—122no—
901Q8—124no—
902Q8—122no—
903D4—24no—
904D4—22no—
905D4—22no—
906D4—41no—
907D4—44no—
908D4—81no—
909D4—81no—
910D4—82no—
911D4—82no—
912C2×C4—22no—
913C2×C4—21no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—41no—
921C2×C4—42no—
922C2×C4—61no—
923C2×C4—61no—
924C2×C4—62no—
925C2×C4—61no—
926C2×C4—61no—
927C2×C4—62no—
928C2×C4—82no—
929C2×C4—82no—
930C2×C4—82no—
931C2×C4—82no—
932C2×C4—81no—
933C2×C4—122no—
934C2×C4—124no—
935C2×C4—122no—
936C2×C4C22×#6712yes—
937C2×C4C22×#6711yescharacteristic
938C2×C4C22×#6711yescharacteristic
939C2×C4C22×#6711yescharacteristic
940C2×C4C22×#6712yes—
941C2×C4C22×#6712yes—
942C2×C4C22×#6711yescharacteristic
943C2×C4C22×#6711yescharacteristic
944C2×C4C24×D311yescharacteristic
945C8—62no—
946C8—62no—
947C8—62no—
948C8—62no—
949C2×C3—22no—
950C2×C3—42no—
951C2×C3—82no—
952C2×C3#348911yescharacteristic
953C2×C3C2×#57711yescharacteristic
954C2×C3#358611yescharacteristic
955C22—21no—
956C22—21no—
957C22—22no—
958C22—22no—
959C22—22no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22#583612yes—
964C22C23×#6711yescharacteristic
965C4—21no—
966C4—21no—
967C4—22no—
968C4—21no—
969C4—21no—
970C4—22no—
971C4—21no—
972C4—22no—
973C4—42no—
974C4—42no—
975C4—42no—
976C4—62no—
977C4—122no—
978C4—121no—
979C4—121no—
980C4—121no—
981C4—122no—
982C4D3×2−1+411yescharacteristic
983C4#596811yescharacteristic
984C3#6216711yescharacteristic, complemented, Sylow
985C2—22no—
986C2—42no—
987C2—82no—
988C2C2×#583611yescharacteristic
989C2#8729511yescharacteristic
990C2#8729911yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
Fitting, prime radicalC3×#3559C2
socleC22×C3C23×D4
hypercenter#3559D3
hypocenterC3#62167
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #529 ◁ #3559

Complements

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

NH ≅ G/Ntype
2. #86129C2semidirect
3. #83644C2semidirect
4. #83632C2semidirect
5. #83620C2semidirect
6. #83620C2semidirect
7. #83611C2semidirect
8. #83606C2semidirect
9. #83531C2semidirect
10. #83518C2semidirect
11. #83481C2semidirect
12. #83480C2semidirect
13. #83441C2semidirect
14. #83439C2semidirect
15. #83320C2semidirect
16. #83316C2semidirect
17. #83130C2semidirect
18. #83021C2semidirect
19. C2×#5063C2semidirect
984. C3#62167semidirect

Maximal subgroups

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

subgroupindex
C3×#35592
#861292
#836442
#836322
#836202
#836112
#836062
#835312
#835182
#834812
#834802
#834412
#834392
#833202
#833162
#831302
#830212
C2×#50632
#621673