Finite Group Databasebeta

← #10828107

Subgroups — #10828107

Order 768.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3488C211yesmaximal, characteristic
2#84072C211yesmaximal, characteristic, complemented
3#82915C211yesmaximal, characteristic, complemented
4#82663C211yesmaximal, characteristic, complemented
5#72140C211yesmaximal, characteristic, complemented
6#72140C211yesmaximal, characteristic, complemented
7#72138C211yesmaximal, characteristic, complemented
8#71877C211yesmaximal, characteristic, complemented
9#71876C211yesmaximal, characteristic, complemented
10#71852C211yesmaximal, characteristic, complemented
11#71852C211yesmaximal, characteristic, complemented
12#71713C211yesmaximal, characteristic, complemented
13#71683C211yesmaximal, characteristic, complemented
14#71665C211yesmaximal, characteristic, complemented
15#71664C211yesmaximal, characteristic, complemented
16#24031—31nomaximal, Sylow
17C2×C3×H(5,𝔽2)C2211yescharacteristic
18C22×C3×#41C2211yescharacteristic
19C3×#550—21no—
20C3×#548—21no—
21C3×#546—21no—
22C3×#546—22no—
23C3×D42—22no—
24C3×D42—21no—
25C3×#537—21no—
26C3×#537C2211yescharacteristic
27C3×#535—21no—
28C3×#535C2211yescharacteristic
29C3×#525—21no—
30C3×#525C2211yescharacteristic
31C2×C3×#121—21no—
32C2×C3×#121C2211yescharacteristic
33C3×#520C2211yescharacteristic
34C2×#926C2211yescharacteristic, complemented
35C22×#208C2211yescharacteristic, complemented
36C2×#837C2211yescharacteristic
37C2×#837C2211yescharacteristic
38C2×#837C2211yescharacteristic, complemented
39C2×#837C2211yescharacteristic, complemented
40C2×#837C2211yescharacteristic, complemented
41C2×#837C2211yescharacteristic, complemented
42#5233—21no—
43#5233—21no—
44#5232C2211yescharacteristic
45#5232C2211yescharacteristic
46#5232C2211yescharacteristic, complemented
47#5232C2211yescharacteristic, complemented
48#5232C2211yescharacteristic, complemented
49#5232C2211yescharacteristic, complemented
50#5225—21no—
51#5222—22no—
52#5221C2211yescharacteristic, complemented
53#5221C2211yescharacteristic, complemented
54C2×#833C2211yescharacteristic, complemented
55C2×#833C2211yescharacteristic, complemented
56#5215—21no—
57C4×#217C2211yescharacteristic, complemented
58#5207C2211yescharacteristic, complemented
59#5045—21no—
60#5045—21no—
61#5035—21no—
62#5035—21no—
63#4995C2211yescharacteristic, complemented
64#4995C2211yescharacteristic, complemented
65#4977C2211yescharacteristic, complemented
66#4975C2211yescharacteristic, complemented
67#4944—22no—
68#4532C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#4530C2211yescharacteristic, complemented
71#4530C2211yescharacteristic, complemented
72#3488D311yescharacteristic
73#3093—31no—
74#2896—31no—
75#2500—31no—
76#2040—31no—
77#2039—31no—
78#2037—31no—
79#2037—31no—
80#1900—31no—
81#1871—31no—
82#1860—31no—
83#1859—31no—
84#1792—31no—
85#1792—31no—
86#1789—31no—
87C3×H(5,𝔽2)—22no—
88C3×H(5,𝔽2)—22no—
89C3×H(5,𝔽2)—41no—
90C3×H(5,𝔽2)—41no—
91C2×C3×#41—21no—
92C2×C3×#41—21no—
93C2×C3×#41—21no—
94C2×C3×#41—21no—
95C2×C3×#41—22no—
96C2×C3×#41—22no—
97C2×C3×#41—41no—
98C2×C3×#41—41no—
99C2×C3×#41D411yescharacteristic
100C2×C3×#41D411yescharacteristic
101C2×C3×#41C2311yescharacteristic
102C2×C3×#41C2311yescharacteristic
103C2×C3×#41C2311yescharacteristic
104C22×C3×Q8D411yescharacteristic
105C22×C3×D4—21no—
106C22×C3×D4—22no—
107C22×C3×D4—22no—
108C22×C3×D4—21no—
109C22×C3×D4—21no—
110C22×C3×D4D411yescharacteristic
111C22×C3×D4D412yes—
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4C2311yescharacteristic
115C3×#127—22no—
116C3×#127—21no—
117C3×#124—22no—
118C3×#124—21no—
119C3×#123—22no—
120C3×#123—21no—
121C3×C22⋊Q8—22no—
122C3×C22⋊Q8—21no—
123C3×C22⋊Q8—21no—
124C3×C22⋊Q8D411yescharacteristic
125C3×C22⋊Q8D411yescharacteristic
126C3×#121—22no—
127C3×#121—22no—
128C3×#121—22no—
129C3×#121—22no—
130C3×#121—22no—
131C3×#121—21no—
132C3×#121—21no—
133C3×#121—21no—
134C3×#121—21no—
135C3×#121—21no—
136C3×#121—21no—
137C3×#121—22no—
138C3×#121—21no—
139C3×#121—21no—
140C3×#121D411yescharacteristic
141C3×#121D411yescharacteristic
142C3×#120—22no—
143C3×#120—22no—
144C3×#120—22no—
145C3×#120—21no—
146C3×#120—22no—
147C3×C4×Q8—21no—
148C3×C4×D4—22no—
149C3×C4×D4—22no—
150C3×C4×D4—21no—
151C3×C4×D4—22no—
152C3×C4×D4—21no—
153C3×C4×D4—21no—
154C3×#117—21no—
155C3×#117C2311yescharacteristic
156C2×C3×C4⋊C4—21no—
157C2×C3×C4⋊C4C2311yescharacteristic
158C2×C3×C22⋊C4—22no—
159C2×C3×C22⋊C4D412yes—
160C2×#217—22no—
161C2×#217—21no—
162C2×#217—21no—
163C2×#217—22no—
164#926—21no—
165#926—21no—
166#926—21no—
167#926—21no—
168C2×C4⋊Dic3C2311yescharacteristic
169C2×C4⋊Dic3C2311yescharacteristic
170C2×Dic3⋊C4—22no—
171C2×C4×Dic3—21no—
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2311yescharacteristic
174C2×#208—21no—
175C2×#208—41no—
176C2×#208—41no—
177C2×#208C2311yescharacteristic
178C2×#208C2311yescharacteristic
179C2×#208C2311yescharacteristic
180C2×#208C2311yescharacteristic
181C22×C3⋊C8—21no—
182#837—22no—
183#837—22no—
184#837—41no—
185#837—41no—
186#837—41no—
187#837—41no—
188#835—21no—
189#835—21no—
190#835—21no—
191#835—21no—
192#835—21no—
193#835—21no—
194#833—41no—
195#833—41no—
196#832—21no—
197#832—21no—
198#832—21no—
199#832—21no—
200#832—21no—
201#832—21no—
202C3⋊#95—21no—
203C3⋊#95—22no—
204#830—21no—
205#830—21no—
206#808—21no—
207#808—21no—
208#807—21no—
209#807—21no—
210C2×H(5,𝔽2)C2×D311yescharacteristic
211C22×#41C2×D311yescharacteristic
212C22×M16—31no—
213#550—21no—
214#548—21no—
215#546—21no—
216#546—22no—
217D42—22no—
218D42—21no—
219#537—21no—
220#537C2×D311yescharacteristic
221#535—21no—
222#535C2×D311yescharacteristic
223#525—21no—
224#525C2×D311yescharacteristic
225C2×#121—21no—
226C2×#121C2×D311yescharacteristic
227#520C2×D311yescharacteristic
228C2×#117—31no—
229#485—61no—
230#485—61no—
231#482—61no—
232#482—61no—
233#428—31no—
234#428—31no—
235C2×#104—31no—
236C2×#104—31no—
237C2×#104—31no—
238C2×#104—31no—
239C2×#104—31no—
240C2×#104—31no—
241#419—61no—
242#418—61no—
243#417—31no—
244#417—31no—
245#417—31no—
246#417—31no—
247#417—31no—
248#417—31no—
249#416—61no—
250#416—61no—
251C2×#100—31no—
252C2×#100—31no—
253#407—31no—
254#394—62no—
255#390—31no—
256#390—31no—
257#388—62no—
258#384—31no—
259#382—31no—
260C4×C22⋊C4—31no—
261#343—31no—
262#343—31no—
263#339—31no—
264#339—31no—
265C24×C3—22no—
266C24×C3—21no—
267C24×C3C2×D412yes—
268C24×C3C2×D411yescharacteristic
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—22no—
272C3×#41—22no—
273C3×#41—21no—
274C3×#41—21no—
275C3×#41—21no—
276C3×#41—21no—
277C3×#41—21no—
278C3×#41—21no—
279C3×#41—21no—
280C3×#41—21no—
281C3×#41—42no—
282C3×#41—42no—
283C3×#41—41no—
284C3×#41—41no—
285C3×#41—42no—
286C3×#41—42no—
287C3×#41—42no—
288C3×#41—42no—
289C3×#41—42no—
290C3×#41—42no—
291C3×#41#4112yes—
292C3×#41#4112yes—
293C2×C3×Q8—21no—
294C2×C3×Q8—22no—
295C2×C3×Q8—41no—
296C2×C3×Q8C2×D411yescharacteristic
297C2×C3×Q8C2×D411yescharacteristic
298C2×C3×Q8C2×D411yescharacteristic
299C2×C3×D4—21no—
300C2×C3×D4—22no—
301C2×C3×D4—22no—
302C2×C3×D4—22no—
303C2×C3×D4—22no—
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—22no—
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—21no—
313C2×C3×D4—22no—
314C2×C3×D4—21no—
315C2×C3×D4—21no—
316C2×C3×D4—21no—
317C2×C3×D4—21no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4—21no—
321C2×C3×D4—41no—
322C2×C3×D4—42no—
323C2×C3×D4—42no—
324C2×C3×D4—42no—
325C2×C3×D4—42no—
326C2×C3×D4—44no—
327C2×C3×D4—44no—
328C2×C3×D4—42no—
329C2×C3×D4—42no—
330C2×C3×D4—82no—
331C2×C3×D4—84no—
332C2×C3×D4C2×D411yescharacteristic
333C2×C3×D4C2×D411yescharacteristic
334C2×C3×D4C2×D411yescharacteristic
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—21no—
340C22×C3×C4—22no—
341C22×C3×C4—21no—
342C22×C3×C4—22no—
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—42no—
348C22×C3×C4—42no—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D411yescharacteristic
351C22×C3×C4C2×D411yescharacteristic
352C22×C3×C4C2×D411yescharacteristic
353C22×C3×C4C2×D411yescharacteristic
354C22×C3×C4C2×D412yes—
355C22×C3×C4C2411yescharacteristic
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C3×C4⋊C4—22no—
361C3×C4⋊C4—22no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4C2×D411yescharacteristic
367C3×C4⋊C4C2×D411yescharacteristic
368C3×C22⋊C4—22no—
369C3×C22⋊C4—22no—
370C3×C22⋊C4—22no—
371C3×C22⋊C4—22no—
372C3×C22⋊C4—22no—
373C3×C22⋊C4—21no—
374C3×C22⋊C4—21no—
375C3×C22⋊C4—21no—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—22no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—21no—
380C3×C42—22no—
381C3×C42—21no—
382#217—42no—
383#217—44no—
384#217—41no—
385#217—41no—
386#217—82no—
387C4⋊Dic3—21no—
388C4⋊Dic3—21no—
389C4⋊Dic3—21no—
390C4⋊Dic3—21no—
391Dic3⋊C4—82no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—41no—
397C4×Dic3—41no—
398#208—21no—
399#208—21no—
400#208—21no—
401#208—21no—
402#208—21no—
403#208—21no—
404#208—21no—
405#208—21no—
406#208—42no—
407C2×C3⋊C8—21no—
408C2×C3⋊C8—21no—
409C2×C3⋊C8—21no—
410C2×C3⋊C8—21no—
411C2×C3⋊C8—42no—
412H(5,𝔽2)—22no—
413H(5,𝔽2)—22no—
414H(5,𝔽2)—41no—
415H(5,𝔽2)—41no—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—21no—
419C2×#41—21no—
420C2×#41—22no—
421C2×#41—22no—
422C2×#41—41no—
423C2×#41—41no—
424C2×#41#6711yescharacteristic
425C2×#41#6711yescharacteristic
426C2×#41C22×D311yescharacteristic
427C2×#41C22×D311yescharacteristic
428C2×#41C22×D311yescharacteristic
429C22×Q8#6711yescharacteristic
430C22×D4—21no—
431C22×D4—22no—
432C22×D4—22no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4#6711yescharacteristic
436C22×D4#6712yes—
437C22×D4C22×D311yescharacteristic
438C23×C4—21no—
439C23×C4C22×D311yescharacteristic
440C2×M16—31no—
441C2×M16—31no—
442C2×M16—31no—
443C2×M16—31no—
444C2×M16—61no—
445C2×M16—121no—
446C2×M16—121no—
447C22×C8—61no—
448#127—22no—
449#127—21no—
450#124—22no—
451#124—21no—
452#123—22no—
453#123—21no—
454C22⋊Q8—22no—
455C22⋊Q8—21no—
456C22⋊Q8—21no—
457C22⋊Q8#6711yescharacteristic
458C22⋊Q8#6711yescharacteristic
459#121—22no—
460#121—22no—
461#121—22no—
462#121—22no—
463#121—22no—
464#121—21no—
465#121—21no—
466#121—21no—
467#121—21no—
468#121—21no—
469#121—21no—
470#121—22no—
471#121—21no—
472#121—21no—
473#121#6711yescharacteristic
474#121#6711yescharacteristic
475#120—22no—
476#120—22no—
477#120—22no—
478#120—21no—
479#120—22no—
480C4×Q8—21no—
481C4×D4—22no—
482C4×D4—22no—
483C4×D4—21no—
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487#117—21no—
488#117—61no—
489#117—61no—
490#117—61no—
491#117—61no—
492#117C22×D311yescharacteristic
493C2×C4⋊C4—21no—
494C2×C4⋊C4—31no—
495C2×C4⋊C4—31no—
496C2×C4⋊C4—62no—
497C2×C4⋊C4C22×D311yescharacteristic
498C2×C22⋊C4—22no—
499C2×C22⋊C4—61no—
500C2×C22⋊C4—61no—
501C2×C22⋊C4—62no—
502C2×C22⋊C4—62no—
503C2×C22⋊C4#6712yes—
504C2×C42—31no—
505C2×C42—31no—
506C2×C42—61no—
507#107—61no—
508#107—61no—
509#106—61no—
510#106—61no—
511#104—62no—
512#104—62no—
513#104—121no—
514#104—121no—
515#104—121no—
516#104—121no—
517#103—61no—
518#103—61no—
519#103—61no—
520#103—61no—
521#103—61no—
522#103—61no—
523#102—61no—
524#102—61no—
525#102—61no—
526#102—61no—
527#102—61no—
528#102—61no—
529#100—121no—
530#100—121no—
531C22⋊C8—61no—
532C22⋊C8—61no—
533#95—61no—
534#95—62no—
535C23×C3—21no—
536C23×C3—21no—
537C23×C3—21no—
538C23×C3—22no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—22no—
542C23×C3—22no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—42no—
546C23×C3—42no—
547C23×C3—44no—
548C23×C3—42no—
549C23×C3—42no—
550C23×C3—81no—
551C23×C3—82no—
552C23×C3—82no—
553C23×C3#12011yescharacteristic
554C23×C3#12011yescharacteristic
555C23×C3C22×D411yescharacteristic
556C3×Q8—21no—
557C3×Q8—21no—
558C3×Q8—21no—
559C3×Q8—21no—
560C3×Q8—21no—
561C3×Q8—42no—
562C3×Q8#12312yes—
563C3×D4—22no—
564C3×D4—22no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—21no—
570C3×D4—42no—
571C3×D4—42no—
572C3×D4—44no—
573C3×D4—42no—
574C3×D4—44no—
575C3×D4—44no—
576C3×D4—42no—
577C3×D4—41no—
578C3×D4—41no—
579C3×D4—41no—
580C3×D4—41no—
581C3×D4—41no—
582C3×D4—41no—
583C3×D4—41no—
584C3×D4—41no—
585C3×D4—81no—
586C3×D4—82no—
587C3×D4—82no—
588C3×D4—82no—
589C3×D4—82no—
590C3×D4#12312yes—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—21no—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—42no—
610C2×C3×C4—42no—
611C2×C3×C4—42no—
612C2×C3×C4—44no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—42no—
618C2×C3×C4—82no—
619C2×C3×C4#12011yescharacteristic
620C2×C3×C4#12011yescharacteristic
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C2×#4111yescharacteristic
624C2×C3×C4C2×#4111yescharacteristic
625C2×C3×C4H(5,𝔽2)11yescharacteristic
626C2×C3×C4H(5,𝔽2)11yescharacteristic
627C2×Dic3—22no—
628C2×Dic3—41no—
629C2×Dic3—41no—
630C2×Dic3—42no—
631C2×Dic3—41no—
632C2×Dic3—42no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C3⋊C8—41no—
638C3⋊C8—41no—
639C3⋊C8—41no—
640C3⋊C8—41no—
641C24—22no—
642C24—21no—
643C24C2×#6712yes—
644C24C2×#6711yescharacteristic
645#41—21no—
646#41—21no—
647#41—22no—
648#41—22no—
649#41—21no—
650#41—21no—
651#41—21no—
652#41—21no—
653#41—21no—
654#41—21no—
655#41—21no—
656#41—21no—
657#41—42no—
658#41—42no—
659#41—41no—
660#41—41no—
661#41—42no—
662#41—42no—
663#41—42no—
664#41—42no—
665#41—42no—
666#41—42no—
667#41#23712yes—
668#41#23712yes—
669C2×Q8—21no—
670C2×Q8—22no—
671C2×Q8—41no—
672C2×Q8C2×#6711yescharacteristic
673C2×Q8C2×#6711yescharacteristic
674C2×Q8C2×#6711yescharacteristic
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—22no—
686C2×D4—22no—
687C2×D4—22no—
688C2×D4—21no—
689C2×D4—22no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—41no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—82no—
707C2×D4—84no—
708C2×D4C2×#6711yescharacteristic
709C2×D4C2×#6711yescharacteristic
710C2×D4C2×#6711yescharacteristic
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—21no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—61no—
726C22×C4—61no—
727C22×C4—61no—
728C22×C4—61no—
729C22×C4C2×#6711yescharacteristic
730C22×C4C2×#6711yescharacteristic
731C22×C4C2×#6711yescharacteristic
732C22×C4C2×#6711yescharacteristic
733C22×C4C2×#6711yescharacteristic
734C22×C4C2×#6712yes—
735C22×C4C23×D311yescharacteristic
736M16—61no—
737M16—61no—
738M16—61no—
739M16—61no—
740M16—61no—
741M16—61no—
742M16—61no—
743M16—61no—
744M16—122no—
745C2×C8—61no—
746C2×C8—61no—
747C2×C8—61no—
748C2×C8—61no—
749C2×C8—122no—
750C4⋊C4—22no—
751C4⋊C4—22no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—61no—
757C4⋊C4—61no—
758C4⋊C4—61no—
759C4⋊C4—61no—
760C4⋊C4—242no—
761C4⋊C4C2×#6711yescharacteristic
762C4⋊C4C2×#6711yescharacteristic
763C22⋊C4—22no—
764C22⋊C4—22no—
765C22⋊C4—22no—
766C22⋊C4—22no—
767C22⋊C4—22no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—22no—
773C22⋊C4—22no—
774C22⋊C4—21no—
775C22⋊C4—122no—
776C22⋊C4—124no—
777C22⋊C4—121no—
778C22⋊C4—121no—
779C22⋊C4—242no—
780C42—22no—
781C42—21no—
782C42—61no—
783C42—61no—
784C42—61no—
785C42—61no—
786C42—121no—
787C42—121no—
788C22×C3—21no—
789C22×C3—21no—
790C22×C3—21no—
791C22×C3—21no—
792C22×C3—22no—
793C22×C3—21no—
794C22×C3—21no—
795C22×C3—21no—
796C22×C3—21no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—42no—
802C22×C3—41no—
803C22×C3—42no—
804C22×C3—41no—
805C22×C3—42no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—82no—
811C22×C3—82no—
812C22×C3—84no—
813C22×C3—164no—
814C22×C3C2×#12011yescharacteristic
815C22×C3#54611yescharacteristic
816C22×C3#54611yescharacteristic
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—22no—
820C3×C4—41no—
821C3×C4—41no—
822C3×C4—41no—
823C3×C4—42no—
824C3×C4—41no—
825C3×C4C2×#12311yescharacteristic
826C3×C4#53411yescharacteristic
827C3×C4#54611yescharacteristic
828C3×C4#54611yescharacteristic
829Dic3—42no—
830Dic3—81no—
831Dic3—81no—
832Dic3—81no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—22no—
840C23—22no—
841C23—41no—
842C23—41no—
843C23—42no—
844C23—42no—
845C23—44no—
846C23—42no—
847C23—42no—
848C23—81no—
849C23—82no—
850C23—82no—
851C23#95311yescharacteristic
852C23#95311yescharacteristic
853C23C22×#6711yescharacteristic
854Q8—21no—
855Q8—21no—
856Q8—21no—
857Q8—21no—
858Q8—21no—
859Q8—42no—
860Q8#93512yes—
861D4—22no—
862D4—22no—
863D4—21no—
864D4—21no—
865D4—21no—
866D4—21no—
867D4—21no—
868D4—42no—
869D4—42no—
870D4—44no—
871D4—42no—
872D4—44no—
873D4—44no—
874D4—42no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—82no—
884D4—81no—
885D4—82no—
886D4—82no—
887D4—82no—
888D4#93512yes—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—42no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—44no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—42no—
916C2×C4—62no—
917C2×C4—82no—
918C2×C4—121no—
919C2×C4—121no—
920C2×C4—121no—
921C2×C4—122no—
922C2×C4—121no—
923C2×C4—122no—
924C2×C4—121no—
925C2×C4—121no—
926C2×C4—121no—
927C2×C4#95311yescharacteristic
928C2×C4#95311yescharacteristic
929C2×C4C2×#23711yescharacteristic
930C2×C4C2×#23711yescharacteristic
931C2×C4#100411yescharacteristic
932C2×C4#100411yescharacteristic
933C2×C4C22×#6711yescharacteristic
934C2×C4C22×#6711yescharacteristic
935C8—121no—
936C8—121no—
937C8—121no—
938C8—121no—
939C2×C3—21no—
940C2×C3—21no—
941C2×C3—41no—
942C2×C3—41no—
943C2×C3—42no—
944C2×C3—81no—
945C2×C3—82no—
946C2×C3—81no—
947C2×C3#240511yescharacteristic
948C2×C3#301811yescharacteristic
949C2×C3#301911yescharacteristic
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—22no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—42no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—42no—
969C22—41no—
970C22—81no—
971C22—81no—
972C22—82no—
973C22—82no—
974C22—84no—
975C22—164no—
976C22#580611yescharacteristic
977C22#580611yescharacteristic
978C22C2×#95311yescharacteristic
979C4—21no—
980C4—21no—
981C4—22no—
982C4—41no—
983C4—41no—
984C4—42no—
985C4—41no—
986C4—41no—
987C4—122no—
988C4—241no—
989C4—241no—
990C4—241no—
991C4C2×#93511yescharacteristic
992C4#580411yescharacteristic
993C4#580611yescharacteristic
994C4#580611yescharacteristic
995C3#2403111yescharacteristic, complemented, Sylow
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#8404711yescharacteristic
1005C2#8410411yescharacteristic
1006C2#8412111yescharacteristic
subgroupG/H
centerC22C2×#953
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
Fitting, prime radicalC3×#3488C2
socleC22×C3C2×#120
hypercenter#3488D3
hypocenterC3#24031
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
2. #84072C2semidirect
3. #82915C2semidirect
4. #82663C2semidirect
5. #72140C2semidirect
6. #72140C2semidirect
7. #72138C2semidirect
8. #71877C2semidirect
9. #71876C2semidirect
10. #71852C2semidirect
11. #71852C2semidirect
12. #71713C2semidirect
13. #71683C2semidirect
14. #71665C2semidirect
15. #71664C2semidirect
34. C2×#926C22semidirect
35. C22×#208C22semidirect
38. C2×#837C22semidirect
39. C2×#837C22semidirect
40. C2×#837C22semidirect
41. C2×#837C22semidirect
46. #5232C22semidirect
47. #5232C22semidirect
48. #5232C22semidirect
49. #5232C22semidirect
52. #5221C22semidirect
53. #5221C22semidirect
54. C2×#833C22semidirect
55. C2×#833C22semidirect
57. C4×#217C22semidirect
58. #5207C22semidirect
63. #4995C22semidirect
64. #4995C22semidirect
65. #4977C22semidirect
66. #4975C22semidirect
68. #4532C22semidirect
69. #4532C22semidirect
70. #4530C22semidirect
71. #4530C22semidirect
995. C3#24031semidirect

Maximal subgroups

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

subgroupindex
C3×#34882
#840722
#829152
#826632
#721402
#721382
#718772
#718762
#718522
#717132
#716832
#716652
#716642
#240313