Finite Group Databasebeta

← #11805120

Subgroups — #11805120

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63878C211yesmaximal, characteristic
2C4×#3750C211yesmaximal, characteristic, complemented
3C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic
4C3×#4933C211yesmaximal, characteristic, complemented
5#10591372C211yesmaximal, characteristic
6#10591368C211yesmaximal, characteristic
7#10591362C211yesmaximal, characteristic
8D3×C3⋊#95C211yesmaximal, characteristic
9#10591332C211yesmaximal, characteristic, complemented
10#10591278C211yesmaximal, characteristic
11#10591251C211yesmaximal, characteristic, complemented
12#10591245C211yesmaximal, characteristic, complemented
13#10591239C211yesmaximal, characteristic, complemented
14#10591229C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#75304—31nomaximal
17#73455—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×D3×Dic3C2211yescharacteristic
20C22×D3×Dic3C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×C4×C3⋊Dic3C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C3×(C2×D3)⋊C4C2211yescharacteristic
27C2×C3×(C2×D3)⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×Dic32C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37#63878C418yescomplemented
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
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
54C2×#892—31no—
55C2×#877—31no—
56C3×#387—31no—
57C3×C4×C22⋊C4—31no—
58#5210—31no—
59C2×C3⋊#95—31no—
60#4989—31no—
61#4980—31no—
62#4977—31no—
63#4946—31no—
64#4943—31no—
65Dic3×C22⋊C4—31no—
66C4×(C2×D3)⋊C4D311yescharacteristic
67#4933—31no—
68#4933D311yescharacteristic, complemented
69#4932—31no—
70C4×Dic3⋊C4—31no—
71C4×Dic3⋊C4—31no—
72C4×Dic3⋊C4—61no—
73#4668—31no—
74#4666—31no—
75#4664—31no—
76D3×#95—31no—
77#4654—31no—
78#4653—31no—
79#4652—31no—
80#4652—31no—
81#4651—31no—
82#4651—31no—
83#4650—31no—
84#4648—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×C3×C4×D3—22no—
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—41no—
103C2×D3×Dic3—22no—
104C2×D3×Dic3—22no—
105C2×D3×Dic3—22no—
106C2×D3×Dic3—22no—
107C2×D3×Dic3—41no—
108C2×D3×Dic3C2×C414yes—
109C32×C42—41no—
110#3750—22no—
111#3750—22no—
112C4×C3⋊Dic3—41no—
113C4×C3⋊Dic3C2×C414yescomplemented
114C3×(C2×D3)⋊C4—22no—
115C3×(C2×D3)⋊C4C2×C414yes—
116C3×Dic3⋊C4—41no—
117C3×Dic3⋊C4C2×C414yescomplemented
118C3×C4×Dic3—22no—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3C2×C414yescomplemented
121(C2×D3)⋊Dic3—22no—
122(C2×D3)⋊Dic3C2×C414yes—
123Dic32—22no—
124Dic32C2×C414yescomplemented
125#2343—91noSylow
126C23×C3×C4—31no—
127C23×Dic3—31no—
128C23×Dic3—31no—
129C22×C4×D3—31no—
130C22×C4×D3—31no—
131C22×C4×D3C2×D311yescharacteristic
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C22⋊C4—31no—
135C2×C3×C22⋊C4—31no—
136C2×C3×C42—21no—
137C2×C3×C42—31no—
138C2×C3×C42C2×D311yescharacteristic
139C2×C3×C42C2×D311yescharacteristic
140C2×#217—31no—
141C2×#217—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4C2×D311yescharacteristic
145C2×(C2×D3)⋊C4C2×D311yescharacteristic
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—61no—
155C2×Dic3⋊C4—61no—
156C2×Dic3⋊C4C2×D311yescharacteristic
157C2×Dic3⋊C4C2×D311yescharacteristic
158C2×C4×Dic3—31no—
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—61no—
167C2×C4×Dic3—61no—
168C2×C4×Dic3C2×D311yescharacteristic
169#892—38no—
170#877—38no—
171C3×#95—31no—
172C3×#95—31no—
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⋊#95C2×D311yescharacteristic
200C3⋊#95C2×D311yescharacteristic
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×D3C22×C412yes—
211C22×C3×D3#4112yes—
212C22×C3×D3#4112yes—
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×C4C22×C412yes—
221C2×C32×C4#4112yes—
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⋊Dic3C22×C412yes—
232C2×C3⋊Dic3C22×C412yes—
233C2×C3⋊Dic3#4112yes—
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—
255C3×C4×D3—44no—
256D3×Dic3—28no—
257D3×Dic3—44no—
258C2×#117—91no—
259#387—31no—
260#387—91no—
261#387—91no—
262#387—91no—
263#385—91no—
264#385—91no—
265#383—91no—
266#382—91no—
267#381—91no—
268C4×C4⋊C4—91no—
269C4×C22⋊C4—31no—
270C4×C22⋊C4—91no—
271#376—91no—
272C2×#95—91no—
273C24×C3—31no—
274C23×D3C22×D311yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
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—31no—
285C22×C3×C4—62no—
286C22×C3×C4—62no—
287C22×C3×C4—121no—
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—34no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—62no—
308C22×Dic3—62no—
309C22×Dic3—62no—
310C22×Dic3—62no—
311C22×Dic3—121no—
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C2×C4×D3—22no—
320C2×C4×D3—22no—
321C2×C4×D3—34no—
322C2×C4×D3—41no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
327C2×C4×D3—121no—
328C3×C4⋊C4—34no—
329C3×C4⋊C4—121no—
330C3×C22⋊C4—34no—
331C3×C22⋊C4—62no—
332C3×C42—41no—
333C3×C42—41no—
334C3×C42—42no—
335C3×C42—62no—
336#217—34no—
337#217—62no—
338(C2×D3)⋊C4—22no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4C4×D314yes—
342C4⋊Dic3—34no—
343C4⋊Dic3—121no—
344Dic3⋊C4—34no—
345Dic3⋊C4—41no—
346Dic3⋊C4—62no—
347Dic3⋊C4—62no—
348Dic3⋊C4—64no—
349Dic3⋊C4—64no—
350Dic3⋊C4—62no—
351Dic3⋊C4—62no—
352Dic3⋊C4—121no—
353Dic3⋊C4C4×D314yescomplemented
354C4×Dic3—22no—
355C4×Dic3—34no—
356C4×Dic3—34no—
357C4×Dic3—34no—
358C4×Dic3—34no—
359C4×Dic3—64no—
360C4×Dic3—62no—
361C4×Dic3—62no—
362C4×Dic3—121no—
363C4×Dic3—121no—
364C4×Dic3—122no—
365C22×C32C23×C411yescharacteristic
366C22×C32C2×#4111yescharacteristic
367C22×C32C2×#4111yescharacteristic
368C22×C32C2×#4111yescharacteristic
369C22×C32C2×#4111yescharacteristic
370C22×C32H(5,𝔽2)11yescharacteristic
371C22×C322−1+411yescharacteristic
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3—22no—
377C2×C3×D3—22no—
378C2×C3×D3#11714yes—
379C32×C4—22no—
380C32×C4—22no—
381C32×C4—41no—
382C3⋊Dic3—22no—
383C3⋊Dic3—22no—
384C3⋊Dic3—22no—
385C3⋊Dic3—41no—
386C3×Dic3—22no—
387C3×Dic3—22no—
388C3×Dic3—22no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C23×C4—31no—
394C23×C4—91no—
395C23×C4—91no—
396#117—98no—
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×C22⋊C4—31no—
404C2×C22⋊C4—31no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C42—31no—
408C2×C42—91no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412C2×C42D3211yescharacteristic
413#95—31no—
414#95—31no—
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—
427#95—91no—
428#95—91no—
429C23×C3—21no—
430C23×C3—32no—
431C23×C3—32no—
432C23×C3—32no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3—61no—
436C23×C3—61no—
437C23×C3C23×D311yescharacteristic
438C23×C3C23×D311yescharacteristic
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C22×D3—21no—
443C22×D3C2×C4×D312yes—
444C22×D3#23512yes—
445C22×D3#23512yes—
446C2×C3×C4—22no—
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—22no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—22no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—41no—
471C2×C3×C4—41no—
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—124no—
491C2×C3×C4C2×C4×D312yes—
492C2×C3×C4C2×C4×D312yes—
493C2×C3×C4#23712yes—
494C2×C3×C4#23912yes—
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—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—32no—
514C2×Dic3—32no—
515C2×Dic3—32no—
516C2×Dic3—32no—
517C2×Dic3—32no—
518C2×Dic3—32no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—68no—
523C2×Dic3—62no—
524C2×Dic3—62no—
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—62no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—124no—
551C2×Dic3C2×C4×D312yes—
552C2×Dic3C2×C4×D312yes—
553C2×Dic3C2×C4×D312yes—
554C4×D3—44no—
555C4×D3—68no—
556C4×D3—124no—
557C2×C32C2×#11711yescharacteristic
558C2×C32C4×#4111yescharacteristic
559C2×C32#52011yescharacteristic
560C2×C32#55111yescharacteristic
561C2×C32#55111yescharacteristic
562C2×C32#55211yescharacteristic
563C2×C32#55211yescharacteristic
564C3×D3—24no—
565C24—31no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—31no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—62no—
574C22×C4—62no—
575C22×C4—94no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—121no—
581C22×C4—182no—
582C22×C4—182no—
583C22×C4—182no—
584C22×C4—182no—
585C22×C4—361no—
586C22×C4C2×D3211yescharacteristic
587C22×C4C2×D3211yescharacteristic
588C22×C4C2×D3211yescharacteristic
589C4⋊C4—34no—
590C4⋊C4—94no—
591C4⋊C4—121no—
592C4⋊C4—182no—
593C4⋊C4—182no—
594C4⋊C4—361no—
595C22⋊C4—34no—
596C22⋊C4—62no—
597C22⋊C4—94no—
598C22⋊C4—182no—
599C42—41no—
600C42—62no—
601C42—94no—
602C42—94no—
603C42—182no—
604C42—361no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—34no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—62no—
618C22×C3—62no—
619C22×C3C22×C4×D311yescharacteristic
620C22×C3C22×C4×D311yescharacteristic
621C22×C3C2×#23511yescharacteristic
622C22×C3C2×#23511yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3#100411yescharacteristic
625C22×C3#100411yescharacteristic
626C22×C3C2×#23911yescharacteristic
627C22×C3D3×#4111yescharacteristic
628C22×C3D3×#4111yescharacteristic
629C22×C3D3×#4111yescharacteristic
630C22×C3D3×#4111yescharacteristic
631C22×C3#101011yescharacteristic
632C22×C3#101011yescharacteristic
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3—22no—
638C2×D3—22no—
639C2×D3#87214yes—
640C3×C4—24no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—22no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—62no—
650C3×C4—62no—
651C3×C4—62no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656Dic3—22no—
657Dic3—22no—
658Dic3—22no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—41no—
663Dic3—64no—
664Dic3—62no—
665Dic3—62no—
666Dic3—62no—
667Dic3—62no—
668Dic3—62no—
669Dic3—62no—
670Dic3—122no—
671Dic3—122no—
672Dic3—122no—
673Dic3—121no—
674Dic3—121no—
675C32#234311yescharacteristic, complemented, Sylow
676C23—32no—
677C23—32no—
678C23—32no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23C22×D3211yescharacteristic
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—32no—
692C2×C4—32no—
693C2×C4—32no—
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—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—92no—
713C2×C4—92no—
714C2×C4—92no—
715C2×C4—124no—
716C2×C4—188no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—181no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—364no—
727C2×C4#379612yes—
728C2×C4C4×D3212yes—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—64no—
737C2×C3C2×#87211yescharacteristic
738C2×C3#549511yescharacteristic
739C2×C3D3×#11711yescharacteristic
740C2×C3#553111yescharacteristic
741C2×C3C4×#23711yescharacteristic
742C2×C3#554111yescharacteristic
743C2×C3#554611yescharacteristic
744C2×C3#554611yescharacteristic
745C2×C3#555611yescharacteristic
746C2×C3C4×#23911yescharacteristic
747C2×C3#563711yescharacteristic
748C2×C3#565911yescharacteristic
749C2×C3#569411yescharacteristic
750C2×C3#570811yescharacteristic
751D3—24no—
752C22—34no—
753C22—62no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—62no—
759C22C2×#379611yescharacteristic
760C22#6429811yescharacteristic
761C22C2×C4×D3211yescharacteristic
762C22D3×#23511yescharacteristic
763C22D3×#23511yescharacteristic
764C22#6430611yescharacteristic
765C22#6433011yescharacteristic
766C4—22no—
767C4—22no—
768C4—41no—
769C4—62no—
770C4—62no—
771C4—62no—
772C4—121no—
773C4—121no—
774C4—121no—
775C4—121no—
776C4—182no—
777C4—182no—
778C4—182no—
779C4—361no—
780C3—21no—
781C3#7345511yescharacteristic, complemented
782C3#7530411yescharacteristic, complemented
783C2—64no—
784C2C4×#379611yescharacteristic
785C2#1059391911yescharacteristic
786C2#1059392011yescharacteristic
787C2D3×#87211yescharacteristic
788C2#1059487611yescharacteristic
789C2#1059494111yescharacteristic
790C2#1059508811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C42D32
hypocenterC32#2343
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C4×#3750C2semidirect
4. C3×#4933C2semidirect
9. #10591332C2semidirect
11. #10591251C2semidirect
12. #10591245C2semidirect
13. #10591239C2semidirect
14. #10591229C2semidirect
15. #10591192C2semidirect
37. #63878C4semidirect
68. #4933D3semidirect
113. C4×C3⋊Dic3C2×C4semidirect
117. C3×Dic3⋊C4C2×C4semidirect
120. Dic3⋊Dic3C2×C4semidirect
124. Dic32C2×C4semidirect
353. Dic3⋊C4C4×D3semidirect
675. C32#2343semidirect
781. C3#73455semidirect
782. C3#75304semidirect

Maximal subgroups

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

subgroupindex
C2×#638782
C4×#37502
C3×C4×(C2×D3)⋊C42
C3×#49332
#105913722
#105913682
#105913622
D3×C3⋊#952
#105913322
#105912782
#105912512
#105912452
#105912392
#105912292
#105911922
#753043
#734553