Finite Group Databasebeta

← #11802810

Subgroups — #11802810

Order 1152.

1101 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C4⋊C4C211yesmaximal, characteristic
2#10592679C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4#10591313C211yesmaximal, characteristic
5#10591295C211yesmaximal, characteristic
6#10591294C211yesmaximal, characteristic
7#10591294C211yesmaximal, characteristic
8C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
9#10591272C211yesmaximal, characteristic, complemented
10#10591270C211yesmaximal, characteristic, complemented
11#10591269C211yesmaximal, characteristic, complemented
12#10591262C211yesmaximal, characteristic, complemented
13#10591237C211yesmaximal, characteristic
14#10591201C211yesmaximal, characteristic, complemented
15#10591192C211yesmaximal, characteristic, complemented
16#82155—31nomaximal
17#75296—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C2×C32×C4⋊C4C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C3×D3×C4⋊C4C418yescomplemented
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×(C2×D3)⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×Dic32C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38#63658C2211yescharacteristic
39#63658C2211yescharacteristic
40#63658C2211yescharacteristic
41#63658C2211yescharacteristic
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
54C22×C3×C4⋊C4—31no—
55C2×D3×C4⋊C4D311yescharacteristic
56C3×#387—31no—
57#5212—31no—
58#5212—31no—
59#5211—31no—
60#5211—31no—
61C4×#217—31no—
62C4×#217—31no—
63#4987—31no—
64#4980—31no—
65#4980—31no—
66#4980—31no—
67#4980—31no—
68#4980—31no—
69#4980—31no—
70#4980—31no—
71#4980—31no—
72#4980—61no—
73#4980D311yescharacteristic, complemented
74#4978—31no—
75C4×(C2×D3)⋊C4—31no—
76#4933—31no—
77#4667—31no—
78#4666—31no—
79#4664—31no—
80#4664—31no—
81#4655—31no—
82#4654—31no—
83#4653—31no—
84#4652—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×C3×C4×D3—41no—
104C2×C3×C4×D3—41no—
105C2×C3×C4×D3—41no—
106C2×C3×C4×D3C2×C414yes—
107C2×C3×C4×D3C2×C414yes—
108C2×C3×C4×D3C2×C414yes—
109C32×C4⋊C4C2×C414yes—
110C4⋊(C3⋊Dic3)—41no—
111C4×C3⋊Dic3—41no—
112C3×C4⋊Dic3—41no—
113C3×C4⋊Dic3C2×C414yes—
114C3×Dic3⋊C4C2×C414yes—
115C3×Dic3⋊C4C2×C414yes—
116C3×C4×Dic3—41no—
117Dic3⋊Dic3—41no—
118Dic3⋊Dic3—41no—
119(C2×D3)⋊Dic3—22no—
120(C2×D3)⋊Dic3—22no—
121(C2×D3)⋊Dic3—22no—
122(C2×D3)⋊Dic3—22no—
123Dic32—41no—
124Dic32—41no—
125#2313—91noSylow
126C23×C3×C4—31no—
127C23×C3×C4—31no—
128C23×C3×C4—31no—
129C22×C4×D3C2×D311yescharacteristic
130C22×C4×D3C2×D311yescharacteristic
131C22×C4×D3C2×D311yescharacteristic
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—38no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4C2×D311yescharacteristic
139C2×C3×C4⋊C4C2×D311yescharacteristic
140C2×C3×C42—31no—
141C2×#217—31no—
142C2×#217—31no—
143C2×#217—31no—
144C2×#217—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—61no—
154C2×C4⋊Dic3C2×D311yescharacteristic
155C2×C4⋊Dic3C2×D311yescharacteristic
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4C2×D311yescharacteristic
159C2×Dic3⋊C4C2×D311yescharacteristic
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×Dic3C2×D311yescharacteristic
168D3×C4⋊C4Dic318yescomplemented
169C3×#95—31no—
170C3×#95—31no—
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⋊#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×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×C4C22×C412yes—
220C2×C32×C4C22×C412yes—
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⋊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—21no—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3C22×C412yes—
255C3×C4×D3—28no—
256C3×C4×D3—44no—
257C3×C4×D3—44no—
258C22×C4⋊C4—31no—
259#387—31no—
260#387—91no—
261#387—91no—
262#387—91no—
263#387—91no—
264#387—91no—
265#387—91no—
266#387—91no—
267#381—91no—
268#381—91no—
269#380—91no—
270#380—91no—
271C4×C22⋊C4—91no—
272C4×C22⋊C4—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—34no—
282C22×C3×C4—34no—
283C22×C3×C4—34no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—62no—
289C22×C3×C4—62no—
290C22×C3×C4—121no—
291C22×C3×C4—121no—
292C22×C3×C4—121no—
293C22×C3×C4—121no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
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—41no—
322C2×C4×D3—41no—
323C2×C4×D3—41no—
324C2×C4×D3—41no—
325C2×C4×D3C2×Dic314yes—
326C2×C4×D3C2×Dic314yes—
327C2×C4×D3C2×Dic314yes—
328C3×C4⋊C4—24no—
329C3×C4⋊C4—34no—
330C3×C4⋊C4—34no—
331C3×C4⋊C4—34no—
332C3×C4⋊C4—121no—
333C3×C4⋊C4C4×D314yes—
334C3×C4⋊C4C2×Dic314yes—
335C3×C42—121no—
336#217—62no—
337#217—62no—
338#217—62no—
339#217—62no—
340(C2×D3)⋊C4—62no—
341(C2×D3)⋊C4—62no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4—62no—
344C4⋊Dic3—41no—
345C4⋊Dic3—121no—
346C4⋊Dic3—121no—
347C4⋊Dic3—121no—
348C4⋊Dic3—121no—
349C4⋊Dic3—122no—
350C4⋊Dic3C2×Dic314yes—
351Dic3⋊C4—121no—
352Dic3⋊C4—121no—
353Dic3⋊C4C2×Dic314yes—
354Dic3⋊C4C2×Dic314yes—
355C4×Dic3—41no—
356C4×Dic3—121no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—121no—
362C4×Dic3—122no—
363C22×C32C23×C411yescharacteristic
364C22×C32C2×#4111yescharacteristic
365C22×C32C2×#4111yescharacteristic
366C22×C32H(5,𝔽2)11yescharacteristic
367C22×C32H(5,𝔽2)11yescharacteristic
368C22×C322−1+411yescharacteristic
369C22×C322−1+411yescharacteristic
370C2×C3×D3—22no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—22no—
375C2×C3×D3—22no—
376C2×C3×D3#11714yes—
377C32×C4—22no—
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—41no—
388C3×Dic3—41no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C23×C4—31no—
392C23×C4—31no—
393C23×C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—38no—
398C2×C4⋊C4—31no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4D3211yescharacteristic
403C2×C22⋊C4—91no—
404C2×C22⋊C4—91no—
405C2×C22⋊C4—91no—
406C2×C22⋊C4—91no—
407C2×C42—31no—
408C2×C42—91no—
409C2×C42—91no—
410C2×C42—91no—
411#95—31no—
412#95—31no—
413#95—31no—
414#95—31no—
415#95—91no—
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—
427C23×C3—21no—
428C23×C3—32no—
429C23×C3—32no—
430C23×C3—32no—
431C23×C3—61no—
432C23×C3—61no—
433C23×C3—61no—
434C23×C3—61no—
435C23×C3C23×D311yescharacteristic
436C23×C3C23×D311yescharacteristic
437C22×D3—21no—
438C22×D3—21no—
439C22×D3—21no—
440C22×D3—21no—
441C22×D3#23512yes—
442C22×D3#23512yes—
443C22×D3C22×Dic312yes—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
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—22no—
458C2×C3×C4—22no—
459C2×C3×C4—32no—
460C2×C3×C4—32no—
461C2×C3×C4—32no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—68no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
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—124no—
488C2×C3×C4—124no—
489C2×C3×C4C2×C4×D312yes—
490C2×C3×C4C2×C4×D312yes—
491C2×C3×C4C2×C4×D312yes—
492C2×C3×C4C22×Dic312yes—
493C2×C3×C4C22×Dic312yes—
494C2×C3×C4C22×Dic312yes—
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—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—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—121no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3C22×Dic312yes—
550C2×Dic3C22×Dic312yes—
551C2×Dic3C22×Dic312yes—
552C4×D3—28no—
553C4×D3—44no—
554C4×D3—44no—
555C2×C32C2×#11711yescharacteristic
556C2×C32#51811yescharacteristic
557C2×C32#51911yescharacteristic
558C2×C32#53911yescharacteristic
559C2×C32#53911yescharacteristic
560C2×C32#53911yescharacteristic
561C2×C32#53911yescharacteristic
562C3×D3—24no—
563C24—31no—
564C22×C4—31no—
565C22×C4—31no—
566C22×C4—31no—
567C22×C4—34no—
568C22×C4—34no—
569C22×C4—34no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—62no—
575C22×C4—62no—
576C22×C4—91no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—121no—
581C22×C4—121no—
582C22×C4—121no—
583C22×C4—121no—
584C22×C4C2×D3211yescharacteristic
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⋊C4D3×Dic314yes—
595C22⋊C4—182no—
596C22⋊C4—182no—
597C22⋊C4—182no—
598C22⋊C4—182no—
599C42—121no—
600C42—361no—
601C42—361no—
602C42—361no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—34no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3C22×C4×D311yescharacteristic
618C22×C3C2×#23511yescharacteristic
619C22×C3C2×#23511yescharacteristic
620C22×C3#100411yescharacteristic
621C22×C3#100411yescharacteristic
622C22×C3#100411yescharacteristic
623C22×C3#100711yescharacteristic
624C22×C3#100711yescharacteristic
625C22×C3#100711yescharacteristic
626C22×C3D3×#4111yescharacteristic
627C22×C3D3×#4111yescharacteristic
628C22×C3#100911yescharacteristic
629C22×C3#101011yescharacteristic
630C22×C3C23×Dic311yescharacteristic
631C2×D3—22no—
632C2×D3—22no—
633C2×D3—22no—
634C2×D3—22no—
635C2×D3—22no—
636C2×D3—22no—
637C2×D3#92614yes—
638C3×C4—22no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—22no—
642C3×C4—22no—
643C3×C4—22no—
644C3×C4—42no—
645C3×C4—42no—
646C3×C4—42no—
647C3×C4—62no—
648C3×C4—62no—
649C3×C4—62no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4—121no—
654Dic3—22no—
655Dic3—22no—
656Dic3—22no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—41no—
661Dic3—122no—
662Dic3—122no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—241no—
672Dic3—241no—
673C32#231311yescharacteristic, complemented, Sylow
674C23—32no—
675C23—32no—
676C23—32no—
677C23—61no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23C22×D3211yescharacteristic
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—68no—
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—61no—
710C2×C4—124no—
711C2×C4—124no—
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—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4C2×D3×Dic312yes—
725C2×C4C2×D3×Dic312yes—
726C2×C4C2×D3×Dic312yes—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—21no—
730C2×C3—21no—
731C2×C3—21no—
732C2×C3—21no—
733C2×C3—21no—
734C2×C3—64no—
735C2×C3#551511yescharacteristic
736C2×C3#551511yescharacteristic
737C2×C3#551511yescharacteristic
738C2×C3#551511yescharacteristic
739C2×C3D3×#11711yescharacteristic
740C2×C3#554511yescharacteristic
741C2×C3#557211yescharacteristic
742C2×C3#563811yescharacteristic
743C2×C3#566011yescharacteristic
744C2×C3#569211yescharacteristic
745C2×C3#570711yescharacteristic
746C2×C3C2×#92611yescharacteristic
747C2×C3#579811yescharacteristic
748C2×C3#581211yescharacteristic
749D3—24no—
750C22—34no—
751C22—62no—
752C22—62no—
753C22—62no—
754C22—62no—
755C22—62no—
756C22—62no—
757C22D3×#23511yescharacteristic
758C22D3×#23511yescharacteristic
759C22#6431311yescharacteristic
760C22#6431411yescharacteristic
761C22#6431511yescharacteristic
762C22#6431611yescharacteristic
763C22C22×D3×Dic311yescharacteristic
764C4—22no—
765C4—22no—
766C4—22no—
767C4—62no—
768C4—62no—
769C4—62no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4—361no—
776C4—361no—
777C4—361no—
778C3—21no—
779C3#7529611yescharacteristic, complemented
780C3#8215511yescharacteristic, complemented
781C2—64no—
782C2#1059453911yescharacteristic
783C2#1059454011yescharacteristic
784C2#1059454111yescharacteristic
785C2#1059454211yescharacteristic
786C2D3×#92611yescharacteristic
787C2#1059521511yescharacteristic
788C2#1059534711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10592679C2semidirect
3. C3×#4980C2semidirect
9. #10591272C2semidirect
10. #10591270C2semidirect
11. #10591269C2semidirect
12. #10591262C2semidirect
14. #10591201C2semidirect
15. #10591192C2semidirect
29. C3×D3×C4⋊C4C4semidirect
73. #4980D3semidirect
168. D3×C4⋊C4Dic3semidirect
673. C32#2313semidirect
779. C3#75296semidirect
780. C3#82155semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C4⋊C42
#105926792
C3×#49802
#105913132
#105912952
#105912942
C4×(C2×D3)⋊Dic32
#105912722
#105912702
#105912692
#105912622
#105912372
#105912012
#105911922
#821553
#752963