Finite Group Databasebeta

← #10828731

Subgroups — #10828731

Order 768.

984 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3495C211yesmaximal, characteristic
2#82915C211yesmaximal, characteristic
3#82774C211yesmaximal, characteristic, complemented
4#82207C211yesmaximal, characteristic, complemented
5#71901C211yesmaximal, characteristic, complemented
6#71900C211yesmaximal, characteristic, complemented
7#71863C211yesmaximal, characteristic, complemented
8#71863C211yesmaximal, characteristic, complemented
9#71713C211yesmaximal, characteristic
10#71698C211yesmaximal, characteristic, complemented
11#71665C211yesmaximal, characteristic, complemented
12#71664C211yesmaximal, characteristic, complemented
13#71658C211yesmaximal, characteristic, complemented
14#71658C211yesmaximal, characteristic, complemented
15#71590C211yesmaximal, characteristic, complemented
16#24087—31nomaximal, Sylow
17C3×#556—21no—
18C3×#554—21no—
19C3×#552—21no—
20C3×#552—22no—
21C3×#552—21no—
22C3×#551—22no—
23C3×#544C2211yescharacteristic
24C3×#542—21no—
25C3×#541—21no—
26C3×#536C2211yescharacteristic
27C3×#533—21no—
28C3×#529—21no—
29C3×#525C2211yescharacteristic
30C2×C3×C22⋊Q8C2211yescharacteristic
31C3×#520C2211yescharacteristic
32C3×#519C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C2×#926C2211yescharacteristic
35C22×#208C2211yescharacteristic
36C2×#837C2211yescharacteristic
37C2×#837C2211yescharacteristic
38#5232C2211yescharacteristic
39#5232C2211yescharacteristic
40#5229C2211yescharacteristic
41#5229C2211yescharacteristic
42C2×#836C2211yescharacteristic
43C2×#836C2211yescharacteristic
44C4×#217C2211yescharacteristic
45#5207C2211yescharacteristic
46#5045—21no—
47#5045—21no—
48#5035—21no—
49#5035—21no—
50#4998—21no—
51#4998—21no—
52#4995C2211yescharacteristic
53#4995C2211yescharacteristic
54#4995C2211yescharacteristic
55#4995C2211yescharacteristic
56#4995C2211yescharacteristic
57#4995C2211yescharacteristic
58#4978—22no—
59#4977C2211yescharacteristic
60#4975C2211yescharacteristic
61#4964—21no—
62#4964—21no—
63#4952—22no—
64#4532C2211yescharacteristic
65#4532C2211yescharacteristic
66#4532C2211yescharacteristic
67#4532C2211yescharacteristic
68#4532C2211yescharacteristic
69#4532C2211yescharacteristic
70#4530C2211yescharacteristic
71#4530C2211yescharacteristic
72#3495D311yescharacteristic
73#3093—31no—
74#2911—31no—
75#2499—31no—
76#2061—31no—
77#2060—31no—
78#2038—31no—
79#2038—31no—
80#1901—31no—
81#1871—31no—
82#1860—31no—
83#1859—31no—
84#1857—31no—
85#1857—31no—
86#1826—31no—
87C2×C3×#41C2311yescharacteristic
88C22×C3×Q8C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C3×C4⋊Q8—21no—
91C3×C4⋊Q8—21no—
92C3×C4⋊Q8—21no—
93C3×#126—22no—
94C3×#126—22no—
95C3×#126—22no—
96C3×#126—22no—
97C3×#125—22no—
98C3×#125—22no—
99C3×#125—22no—
100C3×#125—21no—
101C3×#125—21no—
102C3×#124—22no—
103C3×#124—21no—
104C3×#123—22no—
105C3×#123—22no—
106C3×#123—21no—
107C3×#123—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8—22no—
110C3×C22⋊Q8—21no—
111C3×C22⋊Q8—21no—
112C3×C22⋊Q8—21no—
113C3×C22⋊Q8—21no—
114C3×C22⋊Q8—22no—
115C3×C22⋊Q8—21no—
116C3×C22⋊Q8—21no—
117C3×C22⋊Q8D411yescharacteristic
118C3×C22⋊Q8D411yescharacteristic
119C3×#121D411yescharacteristic
120C3×#121D411yescharacteristic
121C3×#120—21no—
122C3×C4×Q8—22no—
123C3×C4×Q8—21no—
124C3×C4×Q8—21no—
125C3×C4×Q8—21no—
126C3×C4×Q8—21no—
127C3×C4×Q8—21no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—22no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×#117—22no—
134C3×#117—22no—
135C3×#117—21no—
136C3×#117—21no—
137C3×#117—22no—
138C3×#117—21no—
139C3×#117D411yescharacteristic
140C3×#117D411yescharacteristic
141C3×#117C2311yescharacteristic
142C3×#117C2311yescharacteristic
143C3×#117C2311yescharacteristic
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4D412yes—
146C2×C3×C4⋊C4D411yescharacteristic
147C2×C3×C4⋊C4D411yescharacteristic
148C2×C3×C4⋊C4C2311yescharacteristic
149C2×C3×C22⋊C4—21no—
150C2×C3×C22⋊C4D412yes—
151C2×C3×C42—21no—
152C2×#217—21no—
153C2×#217—21no—
154#926—21no—
155#926—21no—
156#926—21no—
157#926—21no—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2311yescharacteristic
160C2×Dic3⋊C4—22no—
161C2×C4×Dic3—21no—
162C2×C4×Dic3C2311yescharacteristic
163C2×C4×Dic3C2311yescharacteristic
164C2×#208—21no—
165C2×#208—22no—
166C2×#208—22no—
167C2×#208C2311yescharacteristic
168C2×#208C2311yescharacteristic
169C2×#208C2311yescharacteristic
170C2×#208C2311yescharacteristic
171C22×C3⋊C8—21no—
172#837—22no—
173#837—22no—
174#836—22no—
175#836—22no—
176#835—21no—
177#835—21no—
178#832—21no—
179#832—21no—
180C3⋊#95—22no—
181C3⋊#95—22no—
182C3⋊#95—22no—
183C3⋊#95—21no—
184#830—21no—
185#830—21no—
186#808—21no—
187#808—21no—
188#808—21no—
189#808—21no—
190#808—21no—
191#808—21no—
192#807—21no—
193#807—21no—
194#807—21no—
195#807—21no—
196#807—21no—
197#807—21no—
198C22×M16—31no—
199#556—21no—
200#554—21no—
201#552—21no—
202#552—22no—
203#552—21no—
204#551—22no—
205#544C2×D311yescharacteristic
206#542—21no—
207#541—21no—
208#536C2×D311yescharacteristic
209#533—21no—
210#529—21no—
211#525C2×D311yescharacteristic
212C2×C22⋊Q8C2×D311yescharacteristic
213#520C2×D311yescharacteristic
214#519C2×D311yescharacteristic
215C2×#117—31no—
216C2×#117C2×D311yescharacteristic
217#485—61no—
218#485—61no—
219#482—61no—
220#482—61no—
221#428—31no—
222#428—31no—
223#428—31no—
224#428—31no—
225#428—31no—
226#428—31no—
227#428—61no—
228#428—61no—
229#427—61no—
230#427—61no—
231C2×#104—31no—
232C2×#104—31no—
233#417—31no—
234#417—31no—
235C2×#101—31no—
236C2×#101—31no—
237#407—31no—
238#397—62no—
239#391—31no—
240#391—31no—
241#387—62no—
242#384—31no—
243#382—31no—
244C4×C22⋊C4—31no—
245#343—31no—
246#343—31no—
247#339—31no—
248#339—31no—
249#339—31no—
250#339—31no—
251#339—31no—
252#339—31no—
253C24×C3C2×D411yescharacteristic
254C3×#41—21no—
255C3×#41—21no—
256C3×#41—21no—
257C3×#41—21no—
258C2×C3×Q8—22no—
259C2×C3×Q8—21no—
260C2×C3×Q8—21no—
261C2×C3×Q8—21no—
262C2×C3×Q8—21no—
263C2×C3×Q8—21no—
264C2×C3×Q8—21no—
265C2×C3×Q8C2×D411yescharacteristic
266C2×C3×D4—21no—
267C2×C3×D4—21no—
268C2×C3×D4—21no—
269C2×C3×D4C2×D411yescharacteristic
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—22no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4C2×D412yes—
279C22×C3×C4C2×D411yescharacteristic
280C22×C3×C4C2×D411yescharacteristic
281C22×C3×C4C2×D411yescharacteristic
282C22×C3×C4C2×D411yescharacteristic
283C22×C3×C4C2×D411yescharacteristic
284C22×C3×C4C2×D412yes—
285C22×C3×C4C2411yescharacteristic
286C22×Dic3—21no—
287C22×Dic3—21no—
288C22×Dic3—21no—
289C22×Dic3—21no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—22no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—22no—
295C3×C4⋊C4—22no—
296C3×C4⋊C4—22no—
297C3×C4⋊C4—22no—
298C3×C4⋊C4—21no—
299C3×C4⋊C4—21no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—22no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—21no—
305C3×C4⋊C4—21no—
306C3×C4⋊C4C2×D411yescharacteristic
307C3×C4⋊C4C2×D411yescharacteristic
308C3×C4⋊C4C2×D411yescharacteristic
309C3×C4⋊C4C2×D411yescharacteristic
310C3×C4⋊C4C2×D411yescharacteristic
311C3×C4⋊C4C2×D411yescharacteristic
312C3×C22⋊C4—22no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—21no—
316C3×C22⋊C4—21no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—21no—
320C3×C22⋊C4—21no—
321C3×C22⋊C4—21no—
322C3×C22⋊C4—21no—
323C3×C22⋊C4—21no—
324C3×C22⋊C4—21no—
325C3×C22⋊C4—21no—
326C3×C42—22no—
327C3×C42—22no—
328C3×C42—22no—
329C3×C42—21no—
330C3×C42—21no—
331C3×C42—21no—
332C3×C42—21no—
333C3×C42—21no—
334#217—42no—
335#217—41no—
336#217—41no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339C4⋊Dic3—21no—
340C4⋊Dic3—21no—
341Dic3⋊C4—44no—
342C4×Dic3—21no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C4×Dic3—21no—
346C4×Dic3—41no—
347C4×Dic3—41no—
348#208—24no—
349#208—21no—
350#208—21no—
351#208—21no—
352#208—21no—
353#208—21no—
354#208—21no—
355#208#4112yes—
356#208#4112yes—
357C2×C3⋊C8—24no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×#41C22×D311yescharacteristic
363C22×Q8C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C2×M16—31no—
366C2×M16—31no—
367C2×M16—31no—
368C2×M16—31no—
369C2×M16—62no—
370C2×M16—62no—
371C2×M16—61no—
372C22×C8—61no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376#126—22no—
377#126—22no—
378#126—22no—
379#126—22no—
380#125—22no—
381#125—22no—
382#125—22no—
383#125—21no—
384#125—21no—
385#124—22no—
386#124—21no—
387#123—22no—
388#123—22no—
389#123—21no—
390#123—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8#6711yescharacteristic
401C22⋊Q8#6711yescharacteristic
402#121#6711yescharacteristic
403#121#6711yescharacteristic
404#120—21no—
405C4×Q8—22no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×D4—22no—
412C4×D4—21no—
413C4×D4—22no—
414C4×D4—21no—
415C4×D4—21no—
416#117—22no—
417#117—22no—
418#117—21no—
419#117—21no—
420#117—22no—
421#117—21no—
422#117—61no—
423#117—61no—
424#117—61no—
425#117—61no—
426#117#6711yescharacteristic
427#117#6711yescharacteristic
428#117C22×D311yescharacteristic
429#117C22×D311yescharacteristic
430#117C22×D311yescharacteristic
431C2×C4⋊C4—21no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—31no—
434C2×C4⋊C4—62no—
435C2×C4⋊C4#6712yes—
436C2×C4⋊C4#6711yescharacteristic
437C2×C4⋊C4#6711yescharacteristic
438C2×C4⋊C4C22×D311yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—61no—
441C2×C22⋊C4—61no—
442C2×C22⋊C4#6712yes—
443C2×C42—21no—
444C2×C42—31no—
445C2×C42—31no—
446C2×C42—61no—
447#107—61no—
448#107—61no—
449#107—61no—
450#107—61no—
451#107—61no—
452#107—61no—
453#106—61no—
454#106—61no—
455#106—61no—
456#106—61no—
457#106—61no—
458#106—61no—
459#104—62no—
460#104—62no—
461#103—61no—
462#103—61no—
463#102—61no—
464#102—61no—
465#101—62no—
466#101—62no—
467C22⋊C8—61no—
468C22⋊C8—61no—
469#95—61no—
470#95—62no—
471#95—62no—
472#95—62no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—41no—
477C23×C3—41no—
478C23×C3#12011yescharacteristic
479C23×C3#12011yescharacteristic
480C23×C3C22×D411yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—41no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—82no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—42no—
491C3×D4—41no—
492C3×D4—41no—
493C3×D4—81no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—22no—
513C2×C3×C4—22no—
514C2×C3×C4—22no—
515C2×C3×C4—42no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—81no—
520C2×C3×C4—82no—
521C2×C3×C4#12011yescharacteristic
522C2×C3×C4#12011yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C22×D411yescharacteristic
525C2×C3×C4C2×#4111yescharacteristic
526C2×C3×C4C2×#4111yescharacteristic
527C2×C3×C42−1+411yescharacteristic
528C2×C3×C42−1+411yescharacteristic
529C2×Dic3—22no—
530C2×Dic3—41no—
531C2×Dic3—41no—
532C2×Dic3—42no—
533C2×Dic3—41no—
534C2×Dic3—41no—
535C2×Dic3—42no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C3⋊C8—22no—
540C3⋊C8—22no—
541C3⋊C8—41no—
542C3⋊C8—41no—
543C24C2×#6711yescharacteristic
544#41—21no—
545#41—21no—
546#41—21no—
547#41—21no—
548C2×Q8—22no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8C2×#6711yescharacteristic
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4C2×#6711yescharacteristic
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4C2×#6712yes—
573C22×C4C2×#6711yescharacteristic
574C22×C4C2×#6711yescharacteristic
575C22×C4C2×#6711yescharacteristic
576C22×C4C2×#6711yescharacteristic
577C22×C4C2×#6711yescharacteristic
578C22×C4C2×#6712yes—
579C22×C4C23×D311yescharacteristic
580M16—32no—
581M16—32no—
582M16—64no—
583M16—61no—
584M16—61no—
585M16—61no—
586M16—61no—
587M16—61no—
588M16—61no—
589C2×C8—64no—
590C2×C8—61no—
591C2×C8—61no—
592C2×C8—61no—
593C2×C8—61no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—22no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—61no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—124no—
615C4⋊C4C2×#6711yescharacteristic
616C4⋊C4C2×#6711yescharacteristic
617C4⋊C4C2×#6711yescharacteristic
618C4⋊C4C2×#6711yescharacteristic
619C4⋊C4C2×#6711yescharacteristic
620C4⋊C4C2×#6711yescharacteristic
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—122no—
636C22⋊C4—121no—
637C22⋊C4—121no—
638C42—22no—
639C42—22no—
640C42—22no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—21no—
645C42—21no—
646C42—61no—
647C42—61no—
648C42—61no—
649C42—61no—
650C42—121no—
651C42—121no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—81no—
664C22×C3—81no—
665C22×C3C2×#12011yescharacteristic
666C22×C3#54711yescharacteristic
667C22×C3#54711yescharacteristic
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—42no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4#52511yescharacteristic
680C3×C4#53611yescharacteristic
681C3×C4#54711yescharacteristic
682C3×C4#54711yescharacteristic
683Dic3—42no—
684Dic3—81no—
685Dic3—81no—
686Dic3—81no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—41no—
691C23—41no—
692C23#95311yescharacteristic
693C23#95311yescharacteristic
694C23C22×#6711yescharacteristic
695Q8—21no—
696Q8—21no—
697Q8—41no—
698Q8—41no—
699Q8—41no—
700Q8—41no—
701Q8—82no—
702D4—21no—
703D4—21no—
704D4—42no—
705D4—41no—
706D4—41no—
707D4—81no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—22no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—62no—
734C2×C4—81no—
735C2×C4—82no—
736C2×C4—121no—
737C2×C4—121no—
738C2×C4—121no—
739C2×C4—122no—
740C2×C4—121no—
741C2×C4—122no—
742C2×C4—121no—
743C2×C4—121no—
744C2×C4—121no—
745C2×C4#95311yescharacteristic
746C2×C4#95311yescharacteristic
747C2×C4D3×#4111yescharacteristic
748C2×C4D3×#4111yescharacteristic
749C2×C4#101011yescharacteristic
750C2×C4#101011yescharacteristic
751C2×C4C22×#6711yescharacteristic
752C2×C4C22×#6711yescharacteristic
753C8—62no—
754C8—62no—
755C8—121no—
756C8—121no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—41no—
760C2×C3—41no—
761C2×C3—81no—
762C2×C3#240611yescharacteristic
763C2×C3#301811yescharacteristic
764C2×C3#302011yescharacteristic
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—81no—
777C22—81no—
778C22#582411yescharacteristic
779C22#582411yescharacteristic
780C22C2×#95311yescharacteristic
781C4—21no—
782C4—21no—
783C4—42no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—42no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—122no—
793C4—241no—
794C4—241no—
795C4—241no—
796C4#582411yescharacteristic
797C4#582411yescharacteristic
798C4#582511yescharacteristic
799C4#582811yescharacteristic
800C3#2408711yescharacteristic, complemented, Sylow
801C2—21no—
802C2—21no—
803C2—41no—
804C2—41no—
805C2—81no—
806C2#8409011yescharacteristic
807C2#8411611yescharacteristic
808C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#3495C2
socleC22×C3C2×#120
prime radicalC3×#525C22
hypercenter#3495D3
hypocenterC3#24087
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3495

Complements

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

NH ≅ G/Ntype
3. #82774C2semidirect
4. #82207C2semidirect
5. #71901C2semidirect
6. #71900C2semidirect
7. #71863C2semidirect
8. #71863C2semidirect
10. #71698C2semidirect
11. #71665C2semidirect
12. #71664C2semidirect
13. #71658C2semidirect
14. #71658C2semidirect
15. #71590C2semidirect
800. C3#24087semidirect

Maximal subgroups

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

subgroupindex
C3×#34952
#829152
#827742
#822072
#719012
#719002
#718632
#717132
#716982
#716652
#716642
#716582
#715902
#240873