Finite Group Databasebeta

← #11819062

Subgroups — #11819062

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64087C211yesmaximal, characteristic
2C2×#63839C211yesmaximal, characteristic, complemented
3C3×#4947C211yesmaximal, characteristic
4C3×#4945C211yesmaximal, characteristic
5#10591720C211yesmaximal, characteristic
6#10591705C211yesmaximal, characteristic
7#10591701C211yesmaximal, characteristic
8#10591692C211yesmaximal, characteristic
9#10591273C211yesmaximal, characteristic, complemented
10#10591273C211yesmaximal, characteristic, complemented
11#10591243C211yesmaximal, characteristic, complemented
12#10591236C211yesmaximal, characteristic, complemented
13#10591226C211yesmaximal, characteristic, complemented
14#10591220C211yesmaximal, characteristic, complemented
15#10591210C211yesmaximal, characteristic, complemented
16#76793—31nomaximal
17#75547—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C22⋊C4C2211yescharacteristic
23C2×#3757C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64087—24no—
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63839—24no—
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
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—
59C2×#878—61no—
60C3×#393—31no—
61C3×#388—31no—
62#5229—31no—
63#4986—31no—
64#4951—31no—
65#4947—31no—
66#4947—31no—
67#4947D311yescharacteristic
68#4945D311yescharacteristic
69#4944—31no—
70#4942—31no—
71#4942—31no—
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
96C2×#634—22no—
97C2×#634—22no—
98C2×#634—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×Dic6—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—41no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627—41no—
113C32×C22⋊C4—22no—
114#3757—22no—
115C4⋊(C3⋊Dic3)—22no—
116#3750—22no—
117#3750D414yes—
118C3×#217—22no—
119C3×#217—41no—
120C3×#217—41no—
121C3×#217Q814yescomplemented
122C3×Dic3⋊C4—22no—
123C3×C4×Dic3—41no—
124#3724—22no—
125#3724—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×Dic6—61no—
140C22×Dic6C2×D311yescharacteristic
141C2×C3×C4⋊C4—31no—
142C2×C3×C22⋊C4—21no—
143C2×C3×C22⋊C4—31no—
144C2×C3×C22⋊C4—31no—
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4C2×D311yescharacteristic
148C2×C3×C22⋊C4C2×D311yescharacteristic
149C2×C3×C42—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—61no—
153C2×#217C2×D311yescharacteristic
154C2×#217C2×D311yescharacteristic
155C2×#217C2×D311yescharacteristic
156C2×#217C2×D311yescharacteristic
157#944—64no—
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—61no—
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—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3C2×D311yescharacteristic
181#888—64no—
182#878—64no—
183#878—64no—
184#878—68no—
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—31no—
206C3⋊#95—31no—
207C3⋊#95—31no—
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C23×C32—21no—
214C23×C32—21no—
215C23×C32—21no—
216C23×C32—21no—
217C23×C32—21no—
218C23×C32—21no—
219C23×C32C2×Q812yes—
220C23×C32C2411yescharacteristic
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4C2×D412yes—
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⋊Dic3C2×D412yes—
238C2×C3⋊Dic3#4112yes—
239C2×C3⋊Dic3#4112yes—
240#634—44no—
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×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×Q812yes—
263C2×C3×Dic3C2×Q812yes—
264C2×C3×Dic3#4112yes—
265C3×Dic6—44no—
266#627—44no—
267C2×C4⋊Q8—91no—
268C2×C22⋊Q8—91no—
269#400—91no—
270#400—91no—
271#393—31no—
272#393—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#391—91no—
277#388—31no—
278#388—91no—
279#380—91no—
280C4×C4⋊C4—91no—
281C4×C22⋊C4—91no—
282C24×C3—21no—
283C24×C3C22×D311yescharacteristic
284C24×C3C22×D311yescharacteristic
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8—121no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
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×C4—31no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—62no—
315C22×Dic3—62no—
316C22×Dic3—62no—
317C22×Dic3—62no—
318C22×Dic3—62no—
319C22×Dic3—62no—
320C22×Dic3—64no—
321C22×Dic3—122no—
322C22×Dic3—122no—
323C22×Dic3C22×D311yescharacteristic
324C22×Dic3C22×D311yescharacteristic
325C22×Dic3C22×D311yescharacteristic
326C22×Dic3C22×D311yescharacteristic
327C22×Dic3C22×D311yescharacteristic
328C22×Dic3C22×D311yescharacteristic
329C22×Dic3C22×D311yescharacteristic
330C22×Dic3C22×D311yescharacteristic
331C2×Dic6—22no—
332C2×Dic6—22no—
333C2×Dic6—41no—
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—64no—
344C2×Dic6—62no—
345C2×Dic6—122no—
346C2×Dic6—122no—
347C2×Dic6—121no—
348C2×Dic6—121no—
349C3×C4⋊C4—62no—
350C3×C22⋊C4—24no—
351C3×C22⋊C4—22no—
352C3×C22⋊C4—22no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—121no—
356C3×C22⋊C4—121no—
357C3×C42—121no—
358#217—22no—
359#217—41no—
360#217—41no—
361#217—62no—
362#217—62no—
363#217—64no—
364#217Dic614yescomplemented
365C4⋊Dic3—62no—
366C4⋊Dic3—64no—
367C4⋊Dic3—62no—
368C4⋊Dic3—62no—
369Dic3⋊C4—22no—
370Dic3⋊C4—34no—
371Dic3⋊C4—34no—
372Dic3⋊C4—64no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—64no—
381C4×Dic3—41no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C22×C32—22no—
389C22×C32—22no—
390C22×C32—22no—
391C22×C32—41no—
392C22×C32—41no—
393C22×C32—41no—
394C22×C32—41no—
395C22×C32C22×D411yescharacteristic
396C22×C32C22×Q811yescharacteristic
397C22×C32C2×#4111yescharacteristic
398C22×C32C2×#4111yescharacteristic
399C22×C32C2×#4111yescharacteristic
400C22×C32H(5,𝔽2)11yescharacteristic
401C22×C322−1+411yescharacteristic
402C32×C4—22no—
403C32×C4—41no—
404C3⋊Dic3—22no—
405C3⋊Dic3—41no—
406C3⋊Dic3—41no—
407C3⋊Dic3#12414yes—
408C3×Dic3—22no—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C22×Q8—31no—
417C22×Q8—91no—
418C22×Q8—91no—
419C23×C4—91no—
420C4⋊Q8—184no—
421C22⋊Q8—184no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4—91no—
429C2×C22⋊C4—31no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4D3211yescharacteristic
435C2×C42—31no—
436C2×C42—91no—
437C2×C42—91no—
438C2×C42—91no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—31no—
444#95—91no—
445#95—91no—
446#95—91no—
447#95—91no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453C23×C3—22no—
454C23×C3—22no—
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—21no—
464C23×C3—21no—
465C23×C3—21no—
466C23×C3—21no—
467C23×C3—21no—
468C23×C3—22no—
469C23×C3—41no—
470C23×C3—41no—
471C23×C3—41no—
472C23×C3—41no—
473C23×C3C2×Dic612yes—
474C23×C3D3×Q812yes—
475C23×C3C23×D311yescharacteristic
476C23×C3C23×D311yescharacteristic
477C3×Q8—124no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—41no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
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×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4D3×D412yes—
519C2×C3×C4D3×D412yes—
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—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—32no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—62no—
558C2×Dic3—62no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—124no—
578C2×Dic3—124no—
579C2×Dic3—128no—
580C2×Dic3C2×Dic612yes—
581C2×Dic3C2×Dic612yes—
582C2×Dic3#23712yes—
583Dic6—44no—
584Dic6—124no—
585Dic6—124no—
586Dic6—124no—
587Dic6—124no—
588Dic6—128no—
589C2×C32—42no—
590C2×C32C2×#12411yescharacteristic
591C2×C32#53311yescharacteristic
592C2×C32#54211yescharacteristic
593C2×C32#54611yescharacteristic
594C2×C32D4×Q811yescharacteristic
595C2×C32#55411yescharacteristic
596C2×C32#55611yescharacteristic
597C24C2×D3211yescharacteristic
598C2×Q8—62no—
599C2×Q8—62no—
600C2×Q8—121no—
601C2×Q8—182no—
602C2×Q8—182no—
603C2×Q8—182no—
604C2×Q8—182no—
605C2×Q8—182no—
606C2×Q8—361no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—91no—
619C22×C4—182no—
620C22×C4—182no—
621C22×C4—182no—
622C22×C4C2×D3211yescharacteristic
623C22×C4C2×D3211yescharacteristic
624C4⋊C4—62no—
625C4⋊C4—94no—
626C4⋊C4—182no—
627C4⋊C4—182no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C22⋊C4—22no—
632C22⋊C4—34no—
633C22⋊C4—62no—
634C22⋊C4—121no—
635C22⋊C4—121no—
636C22⋊C4—182no—
637C42—121no—
638C42—182no—
639C42—182no—
640C42—361no—
641C22×C3—24no—
642C22×C3—22no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—22no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—42no—
656C22×C3—42no—
657C22×C3—42no—
658C22×C3—42no—
659C22×C3—42no—
660C22×C3—42no—
661C22×C3—41no—
662C22×C3—41no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—41no—
667C22×C3—41no—
668C22×C3—41no—
669C22×C3C22×Dic611yescharacteristic
670C22×C3C2×D3×D411yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C22×C3C2×#23711yescharacteristic
673C22×C3#100411yescharacteristic
674C22×C3#100411yescharacteristic
675C22×C3C2×D3×Q811yescharacteristic
676C22×C3D3×#4111yescharacteristic
677C22×C3D3×#4111yescharacteristic
678C22×C3D3×#4111yescharacteristic
679C22×C3D3×#4111yescharacteristic
680C22×C3D3×#4111yescharacteristic
681C22×C3#101011yescharacteristic
682C22×C3#101011yescharacteristic
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4—121no—
697Dic3—22no—
698Dic3—22no—
699Dic3—22no—
700Dic3—34no—
701Dic3—34no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—41no—
707Dic3—64no—
708Dic3—62no—
709Dic3—62no—
710Dic3—122no—
711Dic3—122no—
712Dic3—122no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717C32#249211yescharacteristic, complemented, Sylow
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23D3×Dic612yes—
725C23C22×D3211yescharacteristic
726Q8—124no—
727Q8—364no—
728Q8—364no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—32no—
735C2×C4—32no—
736C2×C4—32no—
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—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—92no—
759C2×C4—92no—
760C2×C4—92no—
761C2×C4—92no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—364no—
771C2×C4#381112yes—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—44no—
780C2×C3—42no—
781C2×C3—42no—
782C2×C3#551711yescharacteristic
783C2×C3D4×Dic611yescharacteristic
784C2×C3#553911yescharacteristic
785C2×C3#559111yescharacteristic
786C2×C3#561011yescharacteristic
787C2×C3#562211yescharacteristic
788C2×C3#563211yescharacteristic
789C2×C3#563611yescharacteristic
790C2×C3#566211yescharacteristic
791C2×C3#566911yescharacteristic
792C2×C3#567111yescharacteristic
793C2×C3D3×#12411yescharacteristic
794C2×C3D3×#12411yescharacteristic
795C2×C3#570211yescharacteristic
796C22—22no—
797C22—22no—
798C22—22no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22C2×D3×Dic611yescharacteristic
804C22#6429811yescharacteristic
805C22D3×#23711yescharacteristic
806C22#6431211yescharacteristic
807C22#6431211yescharacteristic
808C22#6431311yescharacteristic
809C22C2×#381111yescharacteristic
810C4—22no—
811C4—41no—
812C4—62no—
813C4—62no—
814C4—62no—
815C4—94no—
816C4—121no—
817C4—121no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—182no—
822C4—361no—
823C4—361no—
824C3—21no—
825C3#7554711yescharacteristic, complemented
826C3#7679311yescharacteristic, complemented
827C2—42no—
828C2#1059402911yescharacteristic
829C2#1059414711yescharacteristic
830C2#1059415611yescharacteristic
831C2#1059416011yescharacteristic
832C2#1059491511yescharacteristic
833C2#1059517011yescharacteristic
834C2#1059530711yescharacteristic
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. #10591273C2semidirect
10. #10591273C2semidirect
11. #10591243C2semidirect
12. #10591236C2semidirect
13. #10591226C2semidirect
14. #10591220C2semidirect
15. #10591210C2semidirect
121. C3×#217Q8semidirect
364. #217Dic6semidirect
717. C32#2492semidirect
825. C3#75547semidirect
826. C3#76793semidirect

Maximal subgroups

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

subgroupindex
C2×#640872
C2×#638392
C3×#49472
C3×#49452
#105917202
#105917052
#105917012
#105916922
#105912732
#105912432
#105912362
#105912262
#105912202
#105912102
#767933
#755473