Finite Group Databasebeta

← #11804328

Subgroups — #11804328

Order 1152.

1047 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×#63868C211yesmaximal, characteristic
2#10592689C211yesmaximal, characteristic
3C3×#4978C211yesmaximal, characteristic, complemented
4C3×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5#10591378C211yesmaximal, characteristic
6#10591375C211yesmaximal, characteristic
7#10591331C211yesmaximal, characteristic, complemented
8C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
9#10591328C211yesmaximal, characteristic, complemented
10#10591265C211yesmaximal, characteristic, complemented
11#10591249C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic
13#10591206C211yesmaximal, characteristic, complemented
14#10591194C211yesmaximal, characteristic
15#10591194C211yesmaximal, characteristic
16#74954—31nomaximal
17#73628—31nomaximal
18C22×#624C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×#3752C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×#3722C2211yescharacteristic
39C2×#3722C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63868C418yescomplemented
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#898—31no—
55C2×#876—31no—
56C3×#387—31no—
57C3×C4×C4⋊C4—31no—
58#4990—31no—
59#4990—31no—
60#4990—61no—
61#4989—31no—
62#4984—31no—
63#4978D311yescharacteristic, complemented
64#4976—31no—
65Dic3×C4⋊C4D311yescharacteristic, complemented
66#4940—31no—
67#4940—31no—
68C4×(C2×D3)⋊C4—31no—
69#4936—31no—
70C4×C4⋊Dic3—31no—
71#4933—31no—
72C4×Dic3⋊C4—31no—
73#4670—31no—
74#4670—31no—
75#4668—31no—
76#4668—31no—
77#4668—31no—
78#4666—31no—
79#4655—31no—
80#4654—31no—
81#4652—31no—
82#4650—31no—
83#4647—31no—
84#4647—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×#624—22no—
101C2×#624—41no—
102C2×#624—41no—
103C32×C4⋊C4—22no—
104#3752—22no—
105#3752—41no—
106#3752C2×C414yes—
107C4×C3⋊Dic3—41no—
108C3×C4⋊Dic3—22no—
109C3×Dic3⋊C4C2×C414yescomplemented
110C3×C4×Dic3—22no—
111C3×C4×Dic3—41no—
112C3×C4×Dic3—41no—
113C3×C4×Dic3C2×C414yescomplemented
114#3724—41no—
115#3724C2×C414yescomplemented
116Dic3⋊Dic3—22no—
117Dic3⋊Dic3—41no—
118Dic3⋊Dic3—41no—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3C2×C414yescomplemented
121#3722—41no—
122#3722C2×C414yes—
123#3722C2×C414yes—
124Dic32—41no—
125#2334—91noSylow
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C2×C3×C4⋊C4—21no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C4⋊C4—31no—
131C2×C3×C4⋊C4C2×D311yescharacteristic
132C2×C3×C4⋊C4C2×D311yescharacteristic
133C2×C3×C42—31no—
134C2×C3×C42—31no—
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×(C2×D3)⋊C4—31no—
138C2×(C2×D3)⋊C4—31no—
139C2×(C2×D3)⋊C4—31no—
140C2×(C2×D3)⋊C4—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—61no—
150C2×(C2×D3)⋊C4—61no—
151C2×(C2×D3)⋊C4—61no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—31no—
156C2×C4⋊Dic3—31no—
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4C2×D311yescharacteristic
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#898—38no—
178#876—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—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⋊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×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⋊Dic3C22×C412yes—
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×Dic3C22×C412yes—
251C2×C3×Dic3C22×C412yes—
252C2×C3×Dic3C22×C412yes—
253C2×C3×Dic3C22×C412yes—
254C2×C3×Dic3#4112yes—
255#624—44no—
256C2×#126—91no—
257#389—91no—
258#389—91no—
259#388—91no—
260#388—91no—
261#388—91no—
262#387—31no—
263#387—91no—
264#387—91no—
265#385—91no—
266#385—91no—
267#382—91no—
268C4×C4⋊C4—31no—
269C4×C4⋊C4—91no—
270C4×C22⋊C4—91no—
271C23×D3—31no—
272C23×D3—31no—
273C23×D3—61no—
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×C4—31no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3—61no—
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C2×C4×D3—62no—
309C2×C4×D3—62no—
310C2×C4×D3—121no—
311C2×C4×D3—121no—
312C2×C4×D3—121no—
313C2×C4×D3—121no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—34no—
317C3×C4⋊C4—42no—
318C3×C4⋊C4—62no—
319C3×C42—34no—
320C3×C42—62no—
321C3×C42—121no—
322C3×C42—121no—
323(C2×D3)⋊C4—34no—
324(C2×D3)⋊C4—34no—
325(C2×D3)⋊C4—34no—
326(C2×D3)⋊C4—34no—
327(C2×D3)⋊C4—34no—
328(C2×D3)⋊C4—34no—
329(C2×D3)⋊C4—64no—
330(C2×D3)⋊C4—62no—
331(C2×D3)⋊C4—62no—
332(C2×D3)⋊C4—122no—
333(C2×D3)⋊C4—121no—
334(C2×D3)⋊C4—121no—
335(C2×D3)⋊C4—121no—
336(C2×D3)⋊C4—121no—
337(C2×D3)⋊C4—122no—
338C4⋊Dic3—22no—
339C4⋊Dic3—34no—
340C4⋊Dic3—62no—
341C4⋊Dic3—121no—
342C4⋊Dic3—121no—
343C4⋊Dic3—121no—
344Dic3⋊C4—34no—
345Dic3⋊C4—34no—
346Dic3⋊C4—34no—
347Dic3⋊C4—62no—
348Dic3⋊C4—121no—
349Dic3⋊C4—121no—
350Dic3⋊C4—121no—
351Dic3⋊C4—121no—
352Dic3⋊C4—121no—
353Dic3⋊C4C4×D314yescomplemented
354C4×Dic3—22no—
355C4×Dic3—41no—
356C4×Dic3—41no—
357C4×Dic3—121no—
358C4×Dic3—121no—
359C4×Dic3—121no—
360C4×Dic3—121no—
361C4×Dic3—122no—
362C4×Dic3C4×D314yescomplemented
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—41no—
374C2×C3⋊D3—41no—
375C2×C3⋊D3—41no—
376C2×C3⋊D3—41no—
377C32×C4—22no—
378C32×C4—22no—
379C32×C4—41no—
380C3⋊Dic3—22no—
381C3⋊Dic3—41no—
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—41no—
391C23×C4—91no—
392#126—98no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—91no—
396C2×C4⋊C4—91no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
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×C22⋊C4—91no—
408C2×C22⋊C4—91no—
409C2×C42—31no—
410C2×C42—31no—
411C2×C42—31no—
412C2×C42—31no—
413C2×C42—91no—
414C2×C42—91no—
415#95—31no—
416#95—31no—
417#95—31no—
418#95—31no—
419#95—31no—
420#95—31no—
421#95—91no—
422#95—91no—
423#95—91no—
424#95—91no—
425#95—91no—
426#95—91no—
427C23×C3—21no—
428C23×C3C23×D311yescharacteristic
429C23×C3C23×D311yescharacteristic
430C22×D3—32no—
431C22×D3—32no—
432C22×D3—62no—
433C22×D3—61no—
434C22×D3—61no—
435C22×D3—61no—
436C22×D3—61no—
437C22×D3—61no—
438C22×D3—61no—
439C22×D3—61no—
440C22×D3—61no—
441C22×D3—61no—
442C22×D3—61no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—121no—
446C22×D3—121no—
447C22×D3—121no—
448C22×D3—121no—
449C22×D3—121no—
450C22×D3—121no—
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—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—32no—
472C2×C3×C4—41no—
473C2×C3×C4—41no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
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—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4C2×C4×D312yes—
499C2×C3×C4C2×C4×D312yes—
500C2×C3×C4#23512yes—
501C2×C3×C4#23712yes—
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—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—32no—
522C2×Dic3—32no—
523C2×Dic3—62no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—62no—
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—121no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3C2×C4×D312yes—
549C2×Dic3C2×C4×D312yes—
550C2×Dic3C2×C4×D312yes—
551C2×Dic3C2×C4×D312yes—
552C2×Dic3#23512yes—
553C4×D3—124no—
554C4×D3—124no—
555C2×C32C4×#4111yescharacteristic
556C2×C32#52011yescharacteristic
557C2×C32#52011yescharacteristic
558C2×C32#53811yescharacteristic
559C2×C32#53911yescharacteristic
560C2×C32#54111yescharacteristic
561C2×C32#54211yescharacteristic
562C3⋊D3—42no—
563C24—91no—
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—91no—
573C22×C4—91no—
574C22×C4—91no—
575C22×C4—182no—
576C22×C4—361no—
577C22×C4—361no—
578C22×C4C2×D3211yescharacteristic
579C22×C4C2×D3211yescharacteristic
580C22×C4C2×D3211yescharacteristic
581C4⋊C4—22no—
582C4⋊C4—34no—
583C4⋊C4—62no—
584C4⋊C4—94no—
585C4⋊C4—94no—
586C4⋊C4—182no—
587C4⋊C4—361no—
588C4⋊C4—361no—
589C4⋊C4—361no—
590C4⋊C4—361no—
591C22⋊C4—94no—
592C22⋊C4—94no—
593C22⋊C4—94no—
594C22⋊C4—182no—
595C22⋊C4—361no—
596C22⋊C4—361no—
597C42—34no—
598C42—62no—
599C42—121no—
600C42—121no—
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×C3C22×C4×D311yescharacteristic
611C22×C3C22×C4×D311yescharacteristic
612C22×C3C2×#23511yescharacteristic
613C22×C3C2×#23511yescharacteristic
614C22×C3C2×#23711yescharacteristic
615C22×C3#100411yescharacteristic
616C22×C3#100711yescharacteristic
617C22×C3#100711yescharacteristic
618C22×C3D3×#4111yescharacteristic
619C22×C3#100911yescharacteristic
620C22×C3#100911yescharacteristic
621C22×C3#100911yescharacteristic
622C22×C3#101011yescharacteristic
623C22×C3#101011yescharacteristic
624C2×D3—62no—
625C2×D3—62no—
626C2×D3—62no—
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—122no—
631C2×D3—122no—
632C2×D3—122no—
633C2×D3—121no—
634C2×D3—121no—
635C2×D3—121no—
636C2×D3—121no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—241no—
642C2×D3—241no—
643C2×D3—241no—
644C2×D3—241no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—42no—
650C3×C4—42no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—62no—
654C3×C4—62no—
655C3×C4—62no—
656C3×C4—62no—
657C3×C4—62no—
658C3×C4—81no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4—121no—
662Dic3—22no—
663Dic3—22no—
664Dic3—22no—
665Dic3—22no—
666Dic3—22no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—62no—
672Dic3—122no—
673Dic3—122no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—241no—
679C32#233411yescharacteristic, complemented, Sylow
680C23—92no—
681C23—181no—
682C23—181no—
683C23—181no—
684C23—181no—
685C23—181no—
686C23—181no—
687C23C22×D3211yescharacteristic
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—32no—
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—92no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—181no—
724C2×C4—181no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—364no—
729C2×C4C4×D3212yes—
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×C3C4×#23511yescharacteristic
739C2×C3#550411yescharacteristic
740C2×C3#552311yescharacteristic
741C2×C3#552311yescharacteristic
742C2×C3C4×#23711yescharacteristic
743C2×C3#556011yescharacteristic
744C2×C3#556411yescharacteristic
745C2×C3#557411yescharacteristic
746C2×C3#558211yescharacteristic
747C2×C3#558311yescharacteristic
748C2×C3#564311yescharacteristic
749C2×C3#566511yescharacteristic
750C2×C3#569611yescharacteristic
751C2×C3#570411yescharacteristic
752D3—122no—
753D3—122no—
754D3—242no—
755C22—182no—
756C22—182no—
757C22—182no—
758C22—361no—
759C22—361no—
760C22—361no—
761C22—361no—
762C22C2×C4×D3211yescharacteristic
763C22D3×#23511yescharacteristic
764C22#6430911yescharacteristic
765C22#6431411yescharacteristic
766C22#6431611yescharacteristic
767C22#6432011yescharacteristic
768C22C2×#380411yescharacteristic
769C4—22no—
770C4—22no—
771C4—41no—
772C4—62no—
773C4—62no—
774C4—62no—
775C4—62no—
776C4—62no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—182no—
781C4—361no—
782C4—361no—
783C3—21no—
784C3#7362811yescharacteristic, complemented
785C3#7495411yescharacteristic, complemented
786C2—362no—
787C2#1059432711yescharacteristic
788C2#1059434811yescharacteristic
789C2#1059451111yescharacteristic
790C2#1059463811yescharacteristic
791C2C4×#380411yescharacteristic
792C2#1059512711yescharacteristic
793C2#1059534611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2334
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4978C2semidirect
4. C3×Dic3×C4⋊C4C2semidirect
7. #10591331C2semidirect
8. C4×Dic3⋊Dic3C2semidirect
9. #10591328C2semidirect
10. #10591265C2semidirect
11. #10591249C2semidirect
13. #10591206C2semidirect
41. #63868C4semidirect
63. #4978D3semidirect
65. Dic3×C4⋊C4D3semidirect
109. C3×Dic3⋊C4C2×C4semidirect
113. C3×C4×Dic3C2×C4semidirect
115. #3724C2×C4semidirect
120. Dic3⋊Dic3C2×C4semidirect
353. Dic3⋊C4C4×D3semidirect
362. C4×Dic3C4×D3semidirect
679. C32#2334semidirect
784. C3#73628semidirect
785. C3#74954semidirect

Maximal subgroups

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

subgroupindex
C2×#638682
#105926892
C3×#49782
C3×Dic3×C4⋊C42
#105913782
#105913752
#105913312
C4×Dic3⋊Dic32
#105913282
#105912652
#105912492
#105912332
#105912062
#105911942
#749543
#736283