Finite Group Databasebeta

← #11802453

Subgroups — #11802453

Order 1152.

1127 conjugacy classes of subgroups.

The subgroup lattice has 795 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63956C211yesmaximal, characteristic
2#10592644C211yesmaximal, characteristic
3C3×#4944C211yesmaximal, characteristic
4C3×Dic3×C22⋊C4C211yesmaximal, characteristic
5#10591701C211yesmaximal, characteristic
6Dic3×#217C211yesmaximal, characteristic
7Dic3×#217C211yesmaximal, characteristic
8#10591335C211yesmaximal, characteristic, complemented
9#10591332C211yesmaximal, characteristic, complemented
10#10591255C211yesmaximal, characteristic, complemented
11#10591248C211yesmaximal, characteristic, complemented
12#10591243C211yesmaximal, characteristic, complemented
13#10591242C211yesmaximal, characteristic, complemented
14Dic3×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C4×Dic32C211yesmaximal, characteristic, complemented
16#75455—31nomaximal
17C4×#879—31nomaximal
18C23×C3×Dic3C2211yescharacteristic
19C2×C32×C22⋊C4C2211yescharacteristic
20C2×#3757C2211yescharacteristic
21C2×#3757C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35#63956C418yescomplemented
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41C2×Dic32C2211yescharacteristic
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×#879—31no—
55C2×#879—31no—
56C3×#388—31no—
57C3×C4×C22⋊C4—31no—
58C4×#217—31no—
59C4×#217—31no—
60#4978—31no—
61Dic3×C4⋊C4—31no—
62#4951—31no—
63#4945—31no—
64#4945—31no—
65#4945—61no—
66#4944—31no—
67#4944D311yescharacteristic
68Dic3×C22⋊C4—31no—
69Dic3×C22⋊C4—31no—
70Dic3×C22⋊C4D311yescharacteristic
71C4×C4⋊Dic3—31no—
72#4933—31no—
73C4×Dic3⋊C4—31no—
74C4×Dic3⋊C4—31no—
75C42×Dic3—31no—
76C42×Dic3—31no—
77#4655—31no—
78#4654—31no—
79#4653—31no—
80#4652—31no—
81#4651—31no—
82#4651—31no—
83#4649—31no—
84#4649—31no—
85C24×C32C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3×Dic3—22no—
93C22×C3×Dic3—22no—
94C22×C3×Dic3—22no—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C32×C22⋊C4—22no—
104#3757—22no—
105#3757C2×C414yes—
106#3750—22no—
107C4×C3⋊Dic3—22no—
108C3×#217—22no—
109C3×#217C2×C414yes—
110C3×#217C2×C414yes—
111C3×Dic3⋊C4—22no—
112C3×C4×Dic3—22no—
113C3×C4×Dic3—22no—
114C3×C4×Dic3—22no—
115#3724C2×C414yescomplemented
116Dic3⋊Dic3—22no—
117Dic3⋊Dic3C2×C414yescomplemented
118Dic3⋊Dic3C2×C414yescomplemented
119Dic32—22no—
120Dic32—22no—
121Dic32—22no—
122Dic32—22no—
123Dic32—22no—
124Dic32C2×C414yescomplemented
125C4×#126—91noSylow
126C23×C3×C4—31no—
127C23×Dic3C2×D311yescharacteristic
128C2×C3×C4⋊C4—31no—
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—31no—
131C2×C3×C22⋊C4—31no—
132C2×C3×C22⋊C4—31no—
133C2×C3×C22⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×C3×C42—31no—
138C2×#217—31no—
139C2×#217—31no—
140C2×#217—31no—
141C2×#217—31no—
142C2×#217—61no—
143C2×#217—61no—
144C2×#217C2×D311yescharacteristic
145C2×#217C2×D311yescharacteristic
146C2×#217C2×D311yescharacteristic
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—61no—
158C2×Dic3⋊C4C2×D311yescharacteristic
159C2×C4×Dic3—31no—
160C2×C4×Dic3—31no—
161C2×C4×Dic3—31no—
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
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—31no—
173C2×C4×Dic3—61no—
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#879—38no—
178#879—38no—
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—61no—
200C3⋊#95—61no—
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
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×C4—21no—
218C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
229C2×C3⋊Dic3C22×C412yes—
230C2×C3⋊Dic3#4112yes—
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—44no—
248C2×C3×Dic3C22×C412yes—
249C2×C3×Dic3C22×C412yes—
250C2×C3×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3#4112yes—
253C2×C3×Dic3#4112yes—
254C2×C3×Dic3#4112yes—
255C2×C3×Dic3#4112yes—
256C2×#126—91no—
257#388—31no—
258#388—91no—
259#388—91no—
260#387—91no—
261#387—91no—
262#387—91no—
263#383—91no—
264C4×C4⋊C4—91no—
265C4×C4⋊C4—91no—
266C4×C4⋊C4—91no—
267C4×C22⋊C4—31no—
268C4×C22⋊C4—91no—
269C4×C22⋊C4—91no—
270C43—91no—
271C24×C3—21no—
272C24×C3C22×D311yescharacteristic
273C24×C3C22×D311yescharacteristic
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—31no—
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×C4—62no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—22no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C3×C4⋊C4—62no—
315C3×C22⋊C4—22no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—34no—
318C3×C22⋊C4—34no—
319C3×C22⋊C4—42no—
320C3×C22⋊C4—62no—
321C3×C42—62no—
322C3×C42—62no—
323C3×C42—62no—
324#217—22no—
325#217—34no—
326#217—34no—
327#217—64no—
328#217—62no—
329#217—62no—
330#217—122no—
331#217C4×D314yes—
332#217C4×D314yes—
333C4⋊Dic3—34no—
334C4⋊Dic3—34no—
335C4⋊Dic3—62no—
336Dic3⋊C4—22no—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—34no—
340Dic3⋊C4—34no—
341Dic3⋊C4—62no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—122no—
345C4×Dic3—22no—
346C4×Dic3—22no—
347C4×Dic3—22no—
348C4×Dic3—34no—
349C4×Dic3—34no—
350C4×Dic3—62no—
351C4×Dic3—62no—
352C4×Dic3—62no—
353C4×Dic3—62no—
354C4×Dic3—62no—
355C4×Dic3—62no—
356C4×Dic3—62no—
357C4×Dic3—62no—
358C4×Dic3—62no—
359C4×Dic3—62no—
360C4×Dic3—62no—
361C4×Dic3—62no—
362C4×Dic3—122no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—41no—
369C22×C32—41no—
370C22×C32C23×C411yescharacteristic
371C22×C32C2×#4111yescharacteristic
372C22×C32C2×#4111yescharacteristic
373C22×C32C2×#4111yescharacteristic
374C22×C32C2×#4111yescharacteristic
375C22×C32C2×#4111yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C32×C4—22no—
378C32×C4—41no—
379C3⋊Dic3—22no—
380C3⋊Dic3—22no—
381C3⋊Dic3—22no—
382C3⋊Dic3—41no—
383C3×Dic3—22no—
384C3×Dic3—22no—
385C3×Dic3—22no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3#12614yescomplemented
391C23×C4—31no—
392#126—98no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—91no—
395C2×C4⋊C4—91no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C22⋊C4—31no—
400C2×C22⋊C4—31no—
401C2×C22⋊C4—31no—
402C2×C22⋊C4—91no—
403C2×C22⋊C4—91no—
404C2×C22⋊C4D3211yescharacteristic
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—31no—
408C2×C42—91no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412C2×C42—91no—
413C2×C42—91no—
414C2×C42—91no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427C23×C3—21no—
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—22no—
441C23×C3—41no—
442C23×C3—41no—
443C23×C3—41no—
444C23×C3—41no—
445C23×C3—41no—
446C23×C3—41no—
447C23×C3C2×C4×D312yes—
448C23×C3C2×C4×D312yes—
449C23×C3C23×D311yescharacteristic
450C23×C3C23×D311yescharacteristic
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—21no—
461C2×C3×C4—22no—
462C2×C3×C4—32no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
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×C4#23512yes—
493C2×C3×C4#23712yes—
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—21no—
510C2×Dic3—32no—
511C2×Dic3—32no—
512C2×Dic3—32no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—44no—
517C2×Dic3—62no—
518C2×Dic3—62no—
519C2×Dic3—62no—
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—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3C2×C4×D312yes—
548C2×Dic3C2×C4×D312yes—
549C2×Dic3C2×C4×D312yes—
550C2×Dic3C2×C4×D312yes—
551C2×Dic3#23512yes—
552C2×Dic3#23712yes—
553C2×Dic3#23712yes—
554C2×Dic3#23712yes—
555C2×C32—42no—
556C2×C32C4×#4111yescharacteristic
557C2×C32C4×#4111yescharacteristic
558C2×C32C4×#4111yescharacteristic
559C2×C32C2×#12611yescharacteristic
560C2×C32#52911yescharacteristic
561C2×C32#52911yescharacteristic
562C2×C32#52911yescharacteristic
563C24C2×D3211yescharacteristic
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—62no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—91no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4C2×D3211yescharacteristic
580C22×C4C2×D3211yescharacteristic
581C4⋊C4—62no—
582C4⋊C4—94no—
583C4⋊C4—94no—
584C4⋊C4—94no—
585C4⋊C4—182no—
586C4⋊C4—182no—
587C22⋊C4—22no—
588C22⋊C4—34no—
589C22⋊C4—34no—
590C22⋊C4—62no—
591C22⋊C4—94no—
592C22⋊C4—182no—
593C42—62no—
594C42—62no—
595C42—62no—
596C42—94no—
597C42—182no—
598C42—182no—
599C42—182no—
600C42—182no—
601C42—182no—
602C42—182no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—42no—
617C22×C3—42no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—81no—
628C22×C3—81no—
629C22×C3—81no—
630C22×C3—81no—
631C22×C3C22×C4×D311yescharacteristic
632C22×C3C22×C4×D311yescharacteristic
633C22×C3C2×#23511yescharacteristic
634C22×C3C2×#23511yescharacteristic
635C22×C3C2×#23711yescharacteristic
636C22×C3C2×#23711yescharacteristic
637C22×C3C2×#23711yescharacteristic
638C22×C3C2×#23711yescharacteristic
639C22×C3D3×#4111yescharacteristic
640C22×C3D3×#4111yescharacteristic
641C22×C3D3×#4111yescharacteristic
642C22×C3D3×#4111yescharacteristic
643C22×C3D3×#4111yescharacteristic
644C22×C3D3×#4111yescharacteristic
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—34no—
648C3×C4—42no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—62no—
652C3×C4—62no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—81no—
657C3×C4—121no—
658C3×C4—121no—
659Dic3—22no—
660Dic3—22no—
661Dic3—22no—
662Dic3—22no—
663Dic3—22no—
664Dic3—41no—
665Dic3—41no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—62no—
670Dic3—62no—
671Dic3—62no—
672Dic3—122no—
673Dic3—122no—
674Dic3—122no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3#87914yescomplemented
679C32C4×#12611yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23C4×D3212yes—
687C23C22×D3211yescharacteristic
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—32no—
694C2×C4—32no—
695C2×C4—32no—
696C2×C4—32no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—32no—
700C2×C4—32no—
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—92no—
718C2×C4—92no—
719C2×C4—92no—
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#380412yes—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—42no—
739C2×C3—42no—
740C2×C3—82no—
741C2×C3C4×#23511yescharacteristic
742C2×C3C2×#87911yescharacteristic
743C2×C3#552211yescharacteristic
744C2×C3#552811yescharacteristic
745C2×C3C4×#23711yescharacteristic
746C2×C3C4×#23711yescharacteristic
747C2×C3C4×#23711yescharacteristic
748C2×C3C4×#23711yescharacteristic
749C2×C3#553811yescharacteristic
750C2×C3#555711yescharacteristic
751C2×C3#560011yescharacteristic
752C2×C3#564911yescharacteristic
753C2×C3#568011yescharacteristic
754C2×C3D3×#12611yescharacteristic
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22C2×C4×D3211yescharacteristic
763C22D3×#23511yescharacteristic
764C22D3×#23711yescharacteristic
765C22D3×#23711yescharacteristic
766C22D3×#23711yescharacteristic
767C22#6431211yescharacteristic
768C22C2×#380411yescharacteristic
769C4—22no—
770C4—34no—
771C4—41no—
772C4—62no—
773C4—62no—
774C4—62no—
775C4—62no—
776C4—62no—
777C4—121no—
778C4—121no—
779C4—182no—
780C4—182no—
781C4—182no—
782C4—361no—
783C3—21no—
784C3C4×#87911yescharacteristic, complemented
785C3#7545511yescharacteristic, complemented
786C2—42no—
787C2#1059404811yescharacteristic
788C2#1059405011yescharacteristic
789C2D3×#87911yescharacteristic
790C2#1059409911yescharacteristic
791C2C4×#380411yescharacteristic
792C2#1059511611yescharacteristic
793C2#1059517211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#126
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591335C2semidirect
9. #10591332C2semidirect
10. #10591255C2semidirect
11. #10591248C2semidirect
12. #10591243C2semidirect
13. #10591242C2semidirect
14. Dic3×Dic3⋊C4C2semidirect
15. C4×Dic32C2semidirect
35. #63956C4semidirect
115. #3724C2×C4semidirect
117. Dic3⋊Dic3C2×C4semidirect
118. Dic3⋊Dic3C2×C4semidirect
124. Dic32C2×C4semidirect
390. C3×Dic3#126semidirect
678. Dic3#879semidirect
679. C32C4×#126semidirect
784. C3C4×#879semidirect
785. C3#75455semidirect

Maximal subgroups

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

subgroupindex
C2×#639562
#105926442
C3×#49442
C3×Dic3×C22⋊C42
#105917012
Dic3×#2172
#105913352
#105913322
#105912552
#105912482
#105912432
#105912422
Dic3×Dic3⋊C42
C4×Dic322
#754553
C4×#8793