Finite Group Databasebeta

← #11819057

Subgroups — #11819057

Order 1152.

1133 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63982C211yesmaximal, characteristic
2C2×#63839C211yesmaximal, characteristic, complemented
3#10592641C211yesmaximal, characteristic
4C3×#4947C211yesmaximal, characteristic
5C3×#4944C211yesmaximal, characteristic
6#10591705C211yesmaximal, characteristic
7#10591702C211yesmaximal, characteristic
8#10591692C211yesmaximal, characteristic
9#10591341C211yesmaximal, characteristic, complemented
10#10591261C211yesmaximal, characteristic, complemented
11#10591243C211yesmaximal, characteristic, complemented
12#10591236C211yesmaximal, characteristic, complemented
13#10591236C211yesmaximal, characteristic, complemented
14#10591207C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#76793—31nomaximal
17#75547—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32#63982—24no—
33C2×#3724C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63839—24no—
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#944—31no—
56C2×#888—31no—
57C2×#878—31no—
58C2×#878—31no—
59C3×#393—31no—
60C3×#388—31no—
61#5229—31no—
62#4986—31no—
63#4951—31no—
64#4947—31no—
65#4947—31no—
66#4947D311yescharacteristic
67#4945—31no—
68#4944D311yescharacteristic
69#4942—31no—
70#4942—31no—
71#4942—61no—
72Dic3×C22⋊C4—31no—
73Dic3×C22⋊C4—31no—
74C4×Dic3⋊C4—31no—
75#4929—31no—
76#4660—31no—
77#4659—31no—
78#4658—31no—
79#4649—31no—
80#4646—31no—
81#4646—31no—
82#4646—31no—
83#4646—31no—
84#4646—31no—
85#4646—31no—
86C24×C32C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3—22no—
91C22×C3⋊Dic3—22no—
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×Dic6—22no—
105C2×C3×Dic6—22no—
106C2×C3×Dic6—41no—
107C2×#627—22no—
108C2×#627—22no—
109C2×#627—22no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627—41no—
113C32×C22⋊C4—41no—
114#3757—41no—
115#3750—22no—
116#3750—22no—
117C3×#217—22no—
118C3×#217—22no—
119C3×#217—22no—
120C3×#217Q814yescomplemented
121C3×Dic3⋊C4—22no—
122C3×C4×Dic3—41no—
123#3724D414yes—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126Dic3⋊Dic3—22no—
127Dic32—22no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—31no—
132C23×Dic3—31no—
133C23×Dic3—31no—
134C23×Dic3—61no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C22×Dic6C2×D311yescharacteristic
140C2×C3×C4⋊C4—31no—
141C2×C3×C22⋊C4—21no—
142C2×C3×C22⋊C4—31no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—61no—
152C2×#217C2×D311yescharacteristic
153C2×#217C2×D311yescharacteristic
154C2×#217C2×D311yescharacteristic
155C2×#217C2×D311yescharacteristic
156#944—64no—
157C2×C4⋊Dic3—31no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—61no—
170C2×Dic3⋊C4—61no—
171C2×Dic3⋊C4C2×D311yescharacteristic
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3C2×D311yescharacteristic
179#888—64no—
180#878—64no—
181#878—64no—
182C3×#95—31no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—31no—
203C3⋊#95—31no—
204C3⋊#95—31no—
205C3⋊#95—61no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32—21no—
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32C2×Q812yes—
219C23×C32C2411yescharacteristic
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3—21no—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3—44no—
236C2×C3⋊Dic3C2×D412yes—
237C2×C3⋊Dic3#4112yes—
238C2×C3⋊Dic3#4112yes—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×D412yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3C2×Q812yes—
262C2×C3×Dic3#4112yes—
263C3×Dic6—44no—
264#627—44no—
265#627—44no—
266C2×C4⋊Q8—91no—
267C2×C22⋊Q8—91no—
268#400—91no—
269#400—91no—
270#393—31no—
271#393—91no—
272#391—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#388—31no—
277#388—91no—
278#380—91no—
279C4×C4⋊C4—91no—
280C4×C22⋊C4—91no—
281C24×C3—21no—
282C24×C3C22×D311yescharacteristic
283C24×C3C22×D311yescharacteristic
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C2×C3×Q8—121no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—62no—
314C22×Dic3—62no—
315C22×Dic3—62no—
316C22×Dic3—62no—
317C22×Dic3—62no—
318C22×Dic3—62no—
319C22×Dic3—64no—
320C22×Dic3—122no—
321C22×Dic3—122no—
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C2×Dic6—22no—
331C2×Dic6—22no—
332C2×Dic6—41no—
333C2×Dic6—62no—
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—62no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—62no—
342C2×Dic6—62no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C3×C4⋊C4—62no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—42no—
350C3×C22⋊C4—62no—
351C3×C22⋊C4—62no—
352C3×C22⋊C4—62no—
353C3×C42—121no—
354#217—22no—
355#217—22no—
356#217—22no—
357#217—121no—
358#217—121no—
359#217—122no—
360#217Dic614yescomplemented
361C4⋊Dic3—62no—
362C4⋊Dic3—62no—
363C4⋊Dic3—62no—
364Dic3⋊C4—22no—
365Dic3⋊C4—34no—
366Dic3⋊C4—34no—
367Dic3⋊C4—62no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373Dic3⋊C4—62no—
374Dic3⋊C4—122no—
375Dic3⋊C4—122no—
376C4×Dic3—41no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—121no—
382C4×Dic3—121no—
383C22×C32—22no—
384C22×C32—22no—
385C22×C32—22no—
386C22×C32—41no—
387C22×C32—41no—
388C22×C32—41no—
389C22×C32—41no—
390C22×C32C22×D411yescharacteristic
391C22×C32C22×Q811yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32C2×#4111yescharacteristic
394C22×C32C2×#4111yescharacteristic
395C22×C32H(5,𝔽2)11yescharacteristic
396C22×C322−1+411yescharacteristic
397C32×C4—41no—
398C32×C4—41no—
399C3⋊Dic3—41no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3⋊Dic3#12414yes—
403C3×Dic3—22no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—41no—
409C3×Dic3—41no—
410C3×Dic3—41no—
411C22×Q8—31no—
412C22×Q8—91no—
413C22×Q8—91no—
414C23×C4—91no—
415C4⋊Q8—184no—
416C22⋊Q8—184no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C22⋊C4—31no—
425C2×C22⋊C4—31no—
426C2×C22⋊C4—31no—
427C2×C22⋊C4—31no—
428C2×C22⋊C4—91no—
429C2×C22⋊C4D3211yescharacteristic
430C2×C42—31no—
431C2×C42—91no—
432C2×C42—91no—
433C2×C42—91no—
434#95—31no—
435#95—31no—
436#95—31no—
437#95—31no—
438#95—31no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—21no—
451C23×C3—21no—
452C23×C3—21no—
453C23×C3—21no—
454C23×C3—21no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—21no—
462C23×C3—21no—
463C23×C3—22no—
464C23×C3—41no—
465C23×C3—41no—
466C23×C3—41no—
467C23×C3—41no—
468C23×C3C2×Dic612yes—
469C23×C3D3×Q812yes—
470C23×C3C23×D311yescharacteristic
471C23×C3C23×D311yescharacteristic
472C3×Q8—124no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—32no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
543C2×Dic3—62no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3—121no—
569C2×Dic3—121no—
570C2×Dic3—124no—
571C2×Dic3—124no—
572C2×Dic3—128no—
573C2×Dic3C2×Dic612yes—
574C2×Dic3C2×Dic612yes—
575C2×Dic3D3×D412yes—
576C2×Dic3D3×D412yes—
577C2×Dic3#23712yes—
578Dic6—44no—
579Dic6—124no—
580Dic6—124no—
581Dic6—124no—
582Dic6—124no—
583C2×C32—42no—
584C2×C32C2×#12411yescharacteristic
585C2×C32#53311yescharacteristic
586C2×C32#54211yescharacteristic
587C2×C32#54611yescharacteristic
588C2×C32D4×Q811yescharacteristic
589C2×C32#55411yescharacteristic
590C2×C32#55611yescharacteristic
591C24C2×D3211yescharacteristic
592C2×Q8—62no—
593C2×Q8—62no—
594C2×Q8—121no—
595C2×Q8—182no—
596C2×Q8—182no—
597C2×Q8—182no—
598C2×Q8—182no—
599C2×Q8—182no—
600C2×Q8—361no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—182no—
614C22×C4—182no—
615C22×C4—182no—
616C22×C4C2×D3211yescharacteristic
617C22×C4C2×D3211yescharacteristic
618C4⋊C4—62no—
619C4⋊C4—94no—
620C4⋊C4—182no—
621C4⋊C4—182no—
622C4⋊C4—182no—
623C4⋊C4—182no—
624C4⋊C4—182no—
625C22⋊C4—34no—
626C22⋊C4—41no—
627C22⋊C4—62no—
628C22⋊C4—62no—
629C22⋊C4—62no—
630C22⋊C4—361no—
631C42—121no—
632C42—182no—
633C42—182no—
634C42—361no—
635C22×C3—24no—
636C22×C3—22no—
637C22×C3—22no—
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—42no—
650C22×C3—42no—
651C22×C3—42no—
652C22×C3—42no—
653C22×C3—42no—
654C22×C3—42no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3C22×Dic611yescharacteristic
664C22×C3C2×D3×D411yescharacteristic
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×#23711yescharacteristic
667C22×C3#100411yescharacteristic
668C22×C3#100411yescharacteristic
669C22×C3C2×D3×Q811yescharacteristic
670C22×C3D3×#4111yescharacteristic
671C22×C3D3×#4111yescharacteristic
672C22×C3D3×#4111yescharacteristic
673C22×C3D3×#4111yescharacteristic
674C22×C3D3×#4111yescharacteristic
675C22×C3#101011yescharacteristic
676C22×C3#101011yescharacteristic
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—62no—
682C3×C4—62no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—62no—
686C3×C4—81no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691Dic3—22no—
692Dic3—22no—
693Dic3—22no—
694Dic3—22no—
695Dic3—22no—
696Dic3—34no—
697Dic3—34no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—64no—
702Dic3—122no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—241no—
710Dic3—241no—
711C32#249211yescharacteristic, complemented, Sylow
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23D3×Dic612yes—
719C23C22×D3211yescharacteristic
720Q8—124no—
721Q8—364no—
722Q8—364no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—32no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—92no—
754C2×C4—92no—
755C2×C4—92no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—364no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3—21no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—44no—
774C2×C3—42no—
775C2×C3—42no—
776C2×C3#551711yescharacteristic
777C2×C3D4×Dic611yescharacteristic
778C2×C3#553911yescharacteristic
779C2×C3#559111yescharacteristic
780C2×C3#561011yescharacteristic
781C2×C3#562211yescharacteristic
782C2×C3#563211yescharacteristic
783C2×C3#563611yescharacteristic
784C2×C3#566211yescharacteristic
785C2×C3#566911yescharacteristic
786C2×C3#567111yescharacteristic
787C2×C3D3×#12411yescharacteristic
788C2×C3D3×#12411yescharacteristic
789C2×C3#570211yescharacteristic
790C22—22no—
791C22—22no—
792C22—22no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22C2×D3×Dic611yescharacteristic
798C22#6430611yescharacteristic
799C22#6430911yescharacteristic
800C22D32×D411yescharacteristic
801C22D3×#23711yescharacteristic
802C22#6431211yescharacteristic
803C22#6433011yescharacteristic
804C4—41no—
805C4—41no—
806C4—62no—
807C4—62no—
808C4—62no—
809C4—62no—
810C4—62no—
811C4—94no—
812C4—121no—
813C4—121no—
814C4—121no—
815C4—361no—
816C4—361no—
817C4—361no—
818C3—21no—
819C3#7554711yescharacteristic, complemented
820C3#7679311yescharacteristic, complemented
821C2—42no—
822C2#1059402911yescharacteristic
823C2#1059407111yescharacteristic
824C2#1059414511yescharacteristic
825C2#1059428811yescharacteristic
826C2#1059495911yescharacteristic
827C2#1059521111yescharacteristic
828C2#1059529011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63839C2semidirect
9. #10591341C2semidirect
10. #10591261C2semidirect
11. #10591243C2semidirect
12. #10591236C2semidirect
13. #10591236C2semidirect
14. #10591207C2semidirect
15. #10591191C2semidirect
120. C3×#217Q8semidirect
360. #217Dic6semidirect
711. C32#2492semidirect
819. C3#75547semidirect
820. C3#76793semidirect

Maximal subgroups

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

subgroupindex
C2×#639822
C2×#638392
#105926412
C3×#49472
C3×#49442
#105917052
#105917022
#105916922
#105913412
#105912612
#105912432
#105912362
#105912072
#105911912
#767933
#755473