Finite Group Databasebeta

← #11807828

Subgroups — #11807828

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#878C211yesmaximal, characteristic
2#10592650C211yesmaximal, characteristic
3C3×#4951C211yesmaximal, characteristic
4#10591716C211yesmaximal, characteristic
5#10591702C211yesmaximal, characteristic
6#10591702C211yesmaximal, characteristic
7#10591696C211yesmaximal, characteristic
8#10591357C211yesmaximal, characteristic, complemented
9#10591269C211yesmaximal, characteristic, complemented
10#10591268C211yesmaximal, characteristic, complemented
11#10591262C211yesmaximal, characteristic, complemented
12#10591261C211yesmaximal, characteristic, complemented
13#10591220C211yesmaximal, characteristic, complemented
14#10591201C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82750—31nomaximal
17#75492—31nomaximal
18C23×C3×Dic3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×C32×C22⋊C4C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C3×#878C418yescomplemented
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×C3×C22⋊Q8—31no—
55C2×#878D311yescharacteristic
56C3×#388—31no—
57#5229—31no—
58#5229—31no—
59#5212—31no—
60#5211—31no—
61#4984—31no—
62#4984—31no—
63#4980—31no—
64#4980—31no—
65#4980—31no—
66#4980—31no—
67#4978—31no—
68#4972—31no—
69#4951—31no—
70#4951—31no—
71#4951—31no—
72#4951—31no—
73#4951—61no—
74#4951D311yescharacteristic
75#4945—31no—
76#4945—31no—
77#4943—31no—
78#4942—31no—
79#4933—31no—
80#4929—31no—
81#4653—31no—
82#4652—31no—
83#4647—31no—
84#4646—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3×Dic3—41no—
93C22×C3×Dic3—41no—
94C22×C3×Dic3C2×C414yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×C3×Dic6—41no—
104C2×C3×Dic6—41no—
105C2×C3×Dic6C2×C414yes—
106C32×C22⋊C4C2×C414yes—
107#3757—41no—
108#3757—41no—
109C4⋊(C3⋊Dic3)—41no—
110C4×C3⋊Dic3—41no—
111C3×#217—41no—
112C3×#217—41no—
113C3×#217C2×C414yes—
114C3×C4⋊Dic3—41no—
115C3×C4⋊Dic3C2×C414yes—
116C3×Dic3⋊C4C2×C414yes—
117C3×Dic3⋊C4C2×C414yes—
118C3×C4×Dic3—41no—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3—41no—
121Dic3⋊Dic3—41no—
122Dic3⋊Dic3—41no—
123Dic32—41no—
124Dic32—41no—
125#2378—91noSylow
126C22×C3×Q8—31no—
127C23×C3×C4—31no—
128C23×Dic3C2×D311yescharacteristic
129C22×Dic6C2×D311yescharacteristic
130C3×C22⋊Q8—38no—
131C2×C3×C4⋊C4—31no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C22⋊C4—31no—
137C2×C3×C22⋊C4—31no—
138C2×C3×C22⋊C4—31no—
139C2×C3×C22⋊C4C2×D311yescharacteristic
140C2×C3×C22⋊C4C2×D311yescharacteristic
141C2×C3×C42—31no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×#217—31no—
146C2×#217—61no—
147C2×#217—61no—
148C2×#217C2×D311yescharacteristic
149C2×#217C2×D311yescharacteristic
150C2×#217C2×D311yescharacteristic
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3—61no—
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×C4⋊Dic3C2×D311yescharacteristic
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4C2×D311yescharacteristic
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174#878Dic318yescomplemented
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—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—61no—
202C3⋊#95—61no—
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C23×C32—21no—
206C23×C32—21no—
207C23×C32—21no—
208C23×C32—21no—
209C23×C32—21no—
210C23×C32—21no—
211C23×C32C22×C412yes—
212C23×C32C2411yescharacteristic
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4C22×C412yes—
218C2×C32×C4C22×C412yes—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
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×Dic3—21no—
233C2×C3×Dic3—21no—
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—44no—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C2×C3×Dic3C22×C412yes—
256C3×Dic6—44no—
257C2×C22⋊Q8—31no—
258#391—91no—
259#391—91no—
260#389—91no—
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—21no—
273C24×C3C22×D311yescharacteristic
274C24×C3C22×D311yescharacteristic
275C2×C3×Q8—34no—
276C2×C3×Q8—121no—
277C2×C3×Q8—121no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—34no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—121no—
290C22×C3×C4—121no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—41no—
304C22×Dic3—41no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3C2×Dic314yes—
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C2×Dic6—41no—
319C2×Dic6—41no—
320C2×Dic6C2×Dic314yes—
321C3×C4⋊C4—34no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—121no—
325C3×C22⋊C4—24no—
326C3×C22⋊C4—34no—
327C3×C22⋊C4—121no—
328C3×C22⋊C4—121no—
329C3×C22⋊C4C4×D314yes—
330C3×C22⋊C4C2×Dic314yes—
331C3×C42—121no—
332#217—41no—
333#217—41no—
334#217—121no—
335#217—121no—
336#217—121no—
337#217—121no—
338#217—122no—
339#217—122no—
340#217C2×Dic314yes—
341C4⋊Dic3—41no—
342C4⋊Dic3—121no—
343C4⋊Dic3—121no—
344C4⋊Dic3—121no—
345C4⋊Dic3—121no—
346C4⋊Dic3—121no—
347C4⋊Dic3—121no—
348C4⋊Dic3—122no—
349C4⋊Dic3C2×Dic314yes—
350Dic3⋊C4—121no—
351Dic3⋊C4—121no—
352Dic3⋊C4—121no—
353Dic3⋊C4—121no—
354Dic3⋊C4C2×Dic314yes—
355Dic3⋊C4C2×Dic314yes—
356C4×Dic3—41no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—121no—
362C4×Dic3—121no—
363C4×Dic3—122no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32—41no—
371C22×C32C23×C411yescharacteristic
372C22×C32H(5,𝔽2)11yescharacteristic
373C22×C32H(5,𝔽2)11yescharacteristic
374C22×C32H(5,𝔽2)11yescharacteristic
375C22×C322−1+411yescharacteristic
376C22×C322−1+411yescharacteristic
377C22×C322−1+411yescharacteristic
378C32×C4—22no—
379C32×C4—22no—
380C3⋊Dic3—41no—
381C3⋊Dic3—41no—
382C3⋊Dic3—41no—
383C3⋊Dic3—41no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C22×Q8—31no—
393C23×C4—31no—
394C22⋊Q8—38no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—31no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C4⋊C4—91no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—31no—
407C2×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C22⋊C4D3211yescharacteristic
410C2×C42—31no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
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—
426#95—91no—
427#95—91no—
428C23×C3—21no—
429C23×C3—21no—
430C23×C3—21no—
431C23×C3—21no—
432C23×C3—21no—
433C23×C3—21no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—21no—
437C23×C3—21no—
438C23×C3—21no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3—41no—
448C23×C3C2×C4×D312yes—
449C23×C3C22×Dic312yes—
450C23×C3C23×D311yescharacteristic
451C23×C3C23×D311yescharacteristic
452C3×Q8—124no—
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—21no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
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×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—124no—
492C2×C3×C4C2×C4×D312yes—
493C2×C3×C4C2×C4×D312yes—
494C2×C3×C4C22×Dic312yes—
495C2×C3×C4C22×Dic312yes—
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—21no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—44no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
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—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3—121no—
553C2×Dic3C22×Dic312yes—
554C2×Dic3C22×Dic312yes—
555C2×Dic3C22×Dic312yes—
556C2×Dic3C22×Dic312yes—
557Dic6—44no—
558C2×C32—42no—
559C2×C32#51811yescharacteristic
560C2×C32#51911yescharacteristic
561C2×C32#52011yescharacteristic
562C2×C32#56211yescharacteristic
563C2×C32#56211yescharacteristic
564C2×C32#56311yescharacteristic
565C2×C32#56311yescharacteristic
566C24C2×D3211yescharacteristic
567C2×Q8—34no—
568C2×Q8—121no—
569C2×Q8—121no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—34no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—31no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4—91no—
582C22×C4—91no—
583C22×C4—121no—
584C22×C4—121no—
585C22×C4C2×D3211yescharacteristic
586C22×C4C2×D3211yescharacteristic
587C4⋊C4—34no—
588C4⋊C4—34no—
589C4⋊C4—34no—
590C4⋊C4—121no—
591C4⋊C4—361no—
592C4⋊C4—361no—
593C4⋊C4—361no—
594C4⋊C4—361no—
595C4⋊C4—361no—
596C22⋊C4—34no—
597C22⋊C4—121no—
598C22⋊C4—121no—
599C22⋊C4—361no—
600C22⋊C4—361no—
601C22⋊C4D3×Dic314yes—
602C42—121no—
603C42—361no—
604C42—361no—
605C42—361no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—22no—
610C22×C3—22no—
611C22×C3—22no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—42no—
620C22×C3—42no—
621C22×C3—42no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—81no—
631C22×C3—81no—
632C22×C3—81no—
633C22×C3—81no—
634C22×C3C22×C4×D311yescharacteristic
635C22×C3#100411yescharacteristic
636C22×C3#100411yescharacteristic
637C22×C3#100411yescharacteristic
638C22×C3#100411yescharacteristic
639C22×C3#100711yescharacteristic
640C22×C3#100711yescharacteristic
641C22×C3#100911yescharacteristic
642C22×C3#100911yescharacteristic
643C22×C3#101011yescharacteristic
644C22×C3#101011yescharacteristic
645C22×C3#101011yescharacteristic
646C22×C3#101011yescharacteristic
647C22×C3C23×Dic311yescharacteristic
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662Dic3—22no—
663Dic3—22no—
664Dic3—22no—
665Dic3—22no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—122no—
671Dic3—122no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—121no—
680Dic3—241no—
681Dic3—241no—
682C32#237811yescharacteristic, complemented, Sylow
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23C2×D3×Dic312yes—
690C23C22×D3211yescharacteristic
691Q8—124no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
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—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—124no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4C2×D3×Dic312yes—
734C2×C4C2×D3×Dic312yes—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3#551611yescharacteristic
746C2×C3#554511yescharacteristic
747C2×C3#554611yescharacteristic
748C2×C3#562111yescharacteristic
749C2×C3#564611yescharacteristic
750C2×C3#564611yescharacteristic
751C2×C3#564711yescharacteristic
752C2×C3#564711yescharacteristic
753C2×C3#565111yescharacteristic
754C2×C3#568411yescharacteristic
755C2×C3#571211yescharacteristic
756C2×C3#579811yescharacteristic
757C2×C3#581211yescharacteristic
758C2×C3#582711yescharacteristic
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22#6429711yescharacteristic
767C22#6429711yescharacteristic
768C22#6430911yescharacteristic
769C22#6431311yescharacteristic
770C22#6431411yescharacteristic
771C22#6431411yescharacteristic
772C22C22×D3×Dic311yescharacteristic
773C4—22no—
774C4—22no—
775C4—62no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—361no—
784C4—361no—
785C4—361no—
786C4—361no—
787C3—21no—
788C3#7549211yescharacteristic, complemented
789C3#8275011yescharacteristic, complemented
790C2—42no—
791C2#1059403411yescharacteristic
792C2#1059404211yescharacteristic
793C2#1059417811yescharacteristic
794C2#1059424011yescharacteristic
795C2#1059481811yescharacteristic
796C2#1059521511yescharacteristic
797C2#1059522211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591357C2semidirect
9. #10591269C2semidirect
10. #10591268C2semidirect
11. #10591262C2semidirect
12. #10591261C2semidirect
13. #10591220C2semidirect
14. #10591201C2semidirect
15. #10591192C2semidirect
33. C3×#878C4semidirect
174. #878Dic3semidirect
682. C32#2378semidirect
788. C3#75492semidirect
789. C3#82750semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8782
#105926502
C3×#49512
#105917162
#105917022
#105916962
#105913572
#105912692
#105912682
#105912622
#105912612
#105912202
#105912012
#105911922
#827503
#754923