Finite Group Databasebeta

← #11807856

Subgroups — #11807856

Order 1152.

1005 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63899C211yesmaximal, characteristic
2#10592677C211yesmaximal, characteristic, complemented
3C3×#4990C211yesmaximal, characteristic
4C3×#4972C211yesmaximal, characteristic, complemented
5#10591366C211yesmaximal, characteristic
6#10591362C211yesmaximal, characteristic
7#10591328C211yesmaximal, characteristic, complemented
8#10591305C211yesmaximal, characteristic
9#10591283C211yesmaximal, characteristic
10#10591282C211yesmaximal, characteristic
11#10591269C211yesmaximal, characteristic, complemented
12#10591235C211yesmaximal, characteristic, complemented
13#10591197C211yesmaximal, characteristic, complemented
14#10591193C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16#75992—31nomaximal
17#75492—31nomaximal
18C22×#627C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×C4×C3⋊Dic3C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63899C418yescomplemented
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#896—31no—
55C2×#878—31no—
56C3×#389—31no—
57C3×#388—31no—
58#4990—31no—
59#4990D311yescharacteristic
60#4987—31no—
61#4980—31no—
62#4978—31no—
63#4978—31no—
64#4978—31no—
65#4978—61no—
66#4973—31no—
67#4972D311yescharacteristic, complemented
68#4951—31no—
69#4945—31no—
70#4945—31no—
71#4943—31no—
72#4942—31no—
73#4940—31no—
74#4933—31no—
75#4933—31no—
76#4929—31no—
77#4669—31no—
78#4664—31no—
79#4653—31no—
80#4652—31no—
81#4647—31no—
82#4647—31no—
83#4646—31no—
84#4646—31no—
85C23×C3×D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C2×#627—41no—
101C2×#627—41no—
102C2×#627C2×C414yes—
103C2×D3×Dic3—41no—
104C2×D3×Dic3—41no—
105C2×D3×Dic3C2×C414yes—
106C32×C4⋊C4—41no—
107#3750C2×C414yes—
108C4×C3⋊Dic3—41no—
109C3×(C2×D3)⋊C4—41no—
110C3×(C2×D3)⋊C4—41no—
111C3×(C2×D3)⋊C4C2×C414yes—
112C3×C4⋊Dic3C2×C414yes—
113C3×Dic3⋊C4—41no—
114C3×Dic3⋊C4—41no—
115C3×C4×Dic3—41no—
116C3×C4×Dic3—41no—
117#3724—41no—
118#3724C2×C414yes—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3—41no—
121(C2×D3)⋊Dic3—41no—
122(C2×D3)⋊Dic3—41no—
123(C2×D3)⋊Dic3C2×C414yes—
124Dic32—41no—
125#2378—91noSylow
126C23×Dic3—31no—
127C22×C4×D3—31no—
128C22×Dic6—31no—
129C22×Dic6—31no—
130C2×C3×C4⋊C4—21no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4C2×D311yescharacteristic
135C2×C3×C4⋊C4C2×D311yescharacteristic
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×#217—31no—
142C2×#217—31no—
143C2×#217—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4C2×D311yescharacteristic
148C2×(C2×D3)⋊C4C2×D311yescharacteristic
149C2×(C2×D3)⋊C4C2×D311yescharacteristic
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—61no—
162C2×Dic3⋊C4C2×D311yescharacteristic
163C2×Dic3⋊C4C2×D311yescharacteristic
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—61no—
169C2×C4×Dic3C2×D311yescharacteristic
170C2×C4×Dic3C2×D311yescharacteristic
171#896—38no—
172#878—38no—
173C3×#95—31no—
174C3×#95—31no—
175C3×#95—31no—
176C3×#95—31no—
177C3⋊#95—31no—
178C3⋊#95—31no—
179C3⋊#95—31no—
180C3⋊#95—31no—
181C3⋊#95—31no—
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—61no—
198C3⋊#95—61no—
199C3⋊#95—61no—
200C3⋊#95—61no—
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32C2411yescharacteristic
206C22×C3×D3—21no—
207C22×C3×D3—21no—
208C22×C3×D3—21no—
209C22×C3×D3—21no—
210C22×C3×D3—21no—
211C22×C3×D3—21no—
212C22×C3×D3C22×C412yes—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4C22×C412yes—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—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⋊Dic3C22×C412yes—
233C2×C3⋊Dic3C22×C412yes—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
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×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255#627—44no—
256D3×Dic3—44no—
257C2×C22⋊Q8—91no—
258#391—91no—
259#391—91no—
260#389—31no—
261#389—91no—
262#388—31no—
263#388—91no—
264#388—91no—
265#388—91no—
266#387—91no—
267#387—91no—
268#387—91no—
269#387—91no—
270#381—91no—
271#380—91no—
272C24×C3—31no—
273C23×D3C22×D311yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—34no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—121no—
304C22×Dic3—121no—
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C2×C4×D3—34no—
313C2×C4×D3—121no—
314C2×C4×D3—121no—
315C2×Dic6—34no—
316C2×Dic6—34no—
317C2×Dic6—121no—
318C2×Dic6—121no—
319C2×Dic6—121no—
320C2×Dic6—121no—
321C3×C4⋊C4—34no—
322C3×C4⋊C4—41no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—42no—
325C3×C4⋊C4—121no—
326C3×C4⋊C4—121no—
327C3×C22⋊C4—34no—
328C3×C22⋊C4—121no—
329C3×C22⋊C4—121no—
330C3×C42—121no—
331C3×C42—121no—
332#217—34no—
333#217—121no—
334#217—121no—
335(C2×D3)⋊C4—34no—
336(C2×D3)⋊C4—41no—
337(C2×D3)⋊C4—41no—
338(C2×D3)⋊C4—121no—
339(C2×D3)⋊C4—121no—
340(C2×D3)⋊C4C4×D314yes—
341C4⋊Dic3—121no—
342C4⋊Dic3—121no—
343C4⋊Dic3C4×D314yes—
344Dic3⋊C4—34no—
345Dic3⋊C4—34no—
346Dic3⋊C4—34no—
347Dic3⋊C4—34no—
348Dic3⋊C4—41no—
349Dic3⋊C4—41no—
350Dic3⋊C4—64no—
351Dic3⋊C4—121no—
352Dic3⋊C4—121no—
353Dic3⋊C4—121no—
354Dic3⋊C4—121no—
355C4×Dic3—41no—
356C4×Dic3—41no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—122no—
362C22×C32C23×C411yescharacteristic
363C22×C32H(5,𝔽2)11yescharacteristic
364C22×C32H(5,𝔽2)11yescharacteristic
365C22×C32H(5,𝔽2)11yescharacteristic
366C22×C322−1+411yescharacteristic
367C22×C322−1+411yescharacteristic
368C22×C322−1+411yescharacteristic
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—41no—
373C2×C3×D3—41no—
374C2×C3×D3—41no—
375C2×C3×D3—41no—
376C32×C4—22no—
377C32×C4—41no—
378C32×C4—41no—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—41no—
382C3⋊Dic3—41no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—41no—
387C3×Dic3—41no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C22×Q8—91no—
391C23×C4—91no—
392C22⋊Q8—98no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4D3211yescharacteristic
402C2×C22⋊C4—31no—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C22⋊C4—91no—
408C2×C42—31no—
409C2×C42—31no—
410C2×C42—91no—
411C2×C42—91no—
412#95—31no—
413#95—31no—
414#95—31no—
415#95—31no—
416#95—91no—
417#95—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426C23×C3—21no—
427C23×C3—32no—
428C23×C3—61no—
429C23×C3—61no—
430C23×C3—61no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3C23×D311yescharacteristic
435C23×C3C23×D311yescharacteristic
436C22×D3—21no—
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3C2×C4×D312yes—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—32no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—61no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4C2×C4×D312yes—
490C2×C3×C4C2×C4×D312yes—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—21no—
508C2×Dic3—21no—
509C2×Dic3—32no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—62no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—124no—
546C2×Dic3C2×C4×D312yes—
547C2×Dic3C2×C4×D312yes—
548C2×Dic3C2×C4×D312yes—
549C4×D3—124no—
550Dic6—124no—
551Dic6—124no—
552C2×C32#51811yescharacteristic
553C2×C32#51911yescharacteristic
554C2×C32#52011yescharacteristic
555C2×C32#56211yescharacteristic
556C2×C32#56211yescharacteristic
557C2×C32#56311yescharacteristic
558C2×C32#56311yescharacteristic
559C3×D3—42no—
560C24—31no—
561C2×Q8—94no—
562C2×Q8—361no—
563C2×Q8—361no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—94no—
572C22×C4—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—91no—
576C22×C4—361no—
577C22×C4—361no—
578C22×C4C2×D3211yescharacteristic
579C22×C4C2×D3211yescharacteristic
580C22×C4C2×D3211yescharacteristic
581C4⋊C4—34no—
582C4⋊C4—41no—
583C4⋊C4—94no—
584C4⋊C4—94no—
585C4⋊C4—121no—
586C4⋊C4—121no—
587C4⋊C4—361no—
588C4⋊C4—361no—
589C4⋊C4—361no—
590C22⋊C4—34no—
591C22⋊C4—94no—
592C22⋊C4—121no—
593C22⋊C4—121no—
594C22⋊C4—361no—
595C22⋊C4—361no—
596C42—121no—
597C42—121no—
598C42—361no—
599C42—361no—
600C22×C3—21no—
601C22×C3—21no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—62no—
608C22×C3—62no—
609C22×C3—62no—
610C22×C3—121no—
611C22×C3—121no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3C22×C4×D311yescharacteristic
615C22×C3C22×C4×D311yescharacteristic
616C22×C3#100411yescharacteristic
617C22×C3#100411yescharacteristic
618C22×C3#100411yescharacteristic
619C22×C3#100411yescharacteristic
620C22×C3#100711yescharacteristic
621C22×C3#100711yescharacteristic
622C22×C3#100911yescharacteristic
623C22×C3#100911yescharacteristic
624C22×C3#101011yescharacteristic
625C22×C3#101011yescharacteristic
626C22×C3#101011yescharacteristic
627C22×C3#101011yescharacteristic
628C2×D3—22no—
629C2×D3—22no—
630C2×D3—22no—
631C2×D3—41no—
632C2×D3—41no—
633C2×D3—41no—
634C2×D3—41no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—42no—
638C3×C4—42no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—62no—
644C3×C4—62no—
645C3×C4—62no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650C3×C4—121no—
651Dic3—22no—
652Dic3—22no—
653Dic3—22no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—41no—
658Dic3—62no—
659Dic3—62no—
660Dic3—62no—
661Dic3—62no—
662Dic3—122no—
663Dic3—122no—
664Dic3—122no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—241no—
670C32#237811yescharacteristic, complemented, Sylow
671C23—32no—
672C23—61no—
673C23—61no—
674C23—61no—
675C23—61no—
676C23—61no—
677C23—61no—
678C23C22×D3211yescharacteristic
679Q8—364no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—92no—
710C2×C4—92no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—364no—
722C2×C4C4×D3212yes—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—122no—
731C2×C3#550411yescharacteristic
732C2×C3#551611yescharacteristic
733C2×C3#554511yescharacteristic
734C2×C3#554511yescharacteristic
735C2×C3#554611yescharacteristic
736C2×C3#557211yescharacteristic
737C2×C3#562111yescharacteristic
738C2×C3#562111yescharacteristic
739C2×C3#564711yescharacteristic
740C2×C3#565111yescharacteristic
741C2×C3#568411yescharacteristic
742C2×C3#569911yescharacteristic
743C2×C3#571211yescharacteristic
744C2×C3#573511yescharacteristic
745D3—42no—
746C22—62no—
747C22—62no—
748C22—62no—
749C22—121no—
750C22—121no—
751C22—121no—
752C22—121no—
753C22#6429711yescharacteristic
754C22C2×C4×D3211yescharacteristic
755C22#6430911yescharacteristic
756C22#6431311yescharacteristic
757C22#6431511yescharacteristic
758C22#6432011yescharacteristic
759C22#6433011yescharacteristic
760C4—22no—
761C4—41no—
762C4—41no—
763C4—62no—
764C4—62no—
765C4—62no—
766C4—121no—
767C4—121no—
768C4—121no—
769C4—121no—
770C4—182no—
771C4—182no—
772C4—361no—
773C4—361no—
774C3—21no—
775C3#7549211yescharacteristic, complemented
776C3#7599211yescharacteristic, complemented
777C2—122no—
778C2#1059435711yescharacteristic
779C2#1059449511yescharacteristic
780C2#1059450611yescharacteristic
781C2#1059460611yescharacteristic
782C2#1059487411yescharacteristic
783C2#1059526011yescharacteristic
784C2#1059541711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592677C2semidirect
4. C3×#4972C2semidirect
7. #10591328C2semidirect
11. #10591269C2semidirect
12. #10591235C2semidirect
13. #10591197C2semidirect
14. #10591193C2semidirect
15. #10591191C2semidirect
39. #63899C4semidirect
67. #4972D3semidirect
670. C32#2378semidirect
775. C3#75492semidirect
776. C3#75992semidirect

Maximal subgroups

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

subgroupindex
C2×#638992
#105926772
C3×#49902
C3×#49722
#105913662
#105913622
#105913282
#105913052
#105912832
#105912822
#105912692
#105912352
#105911972
#105911932
#105911912
#759923
#754923