Finite Group Databasebeta

← #11805576

Subgroups — #11805576

Order 1152.

1221 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2C2×#63837C211yesmaximal, characteristic
3C2×#63837C211yesmaximal, characteristic
4#10592346C211yesmaximal, characteristic
5C3×#4649C211yesmaximal, characteristic
6C3×#4647C211yesmaximal, characteristic
7#10591349C211yesmaximal, characteristic
8#10591330C211yesmaximal, characteristic
9#10591327C211yesmaximal, characteristic
10#10591268C211yesmaximal, characteristic
11#10591264C211yesmaximal, characteristic
12#10591244C211yesmaximal, characteristic
13#10591244C211yesmaximal, characteristic
14#10591241C211yesmaximal, characteristic
15Dic3×Dic3⋊C4C211yesmaximal, characteristic
16#75981—31nomaximal
17C4⋊C4×Dic6—31nomaximal
18C22×#627C2211yescharacteristic
19C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×#3750C2211yescharacteristic
22C2×#3750C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45C2×Dic32C2211yescharacteristic
46C2×Dic32C2211yescharacteristic
47C4×#627—24no—
48#63837—24no—
49#63837C418yescomplemented
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56C2×#887—31no—
57C2×#887—31no—
58C2×C4×Dic6—31no—
59C2×C4×Dic6—31no—
60C2×C4×Dic6—31no—
61C2×C4×Dic6—31no—
62C3×#389—31no—
63C3×C4×C4⋊C4—31no—
64#4984—31no—
65#4976—31no—
66#4976—31no—
67#4975—31no—
68#4975—31no—
69#4975—31no—
70#4975—31no—
71#4975—31no—
72Dic3×C4⋊C4—31no—
73Dic3×C4⋊C4—31no—
74#4935—31no—
75C4×Dic3⋊C4—31no—
76#4928—31no—
77#4928—31no—
78#4649—31no—
79#4649D311yescharacteristic
80#4647—31no—
81#4647—31no—
82#4647—31no—
83#4647—31no—
84#4647—31no—
85#4647—61no—
86#4647D311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
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
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C2×#627C2×C414yes—
103C2×#627D414yes—
104C2×#627Q814yes—
105C4⋊(C3⋊Dic3)—41no—
106#3750—22no—
107#3750—41no—
108#3750C2×C414yes—
109C4×C3⋊Dic3—22no—
110C3×C4⋊Dic3—41no—
111C3×Dic3⋊C4—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—41no—
114C3×Dic3⋊C4C2×C414yes—
115C3×Dic3⋊C4Q814yescomplemented
116C3×C4×Dic3—22no—
117C3×C4×Dic3—22no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3C2×C414yes—
120#3724—22no—
121#3724—41no—
122Dic3⋊Dic3—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3—22no—
125Dic3⋊Dic3—22no—
126Dic3⋊Dic3—22no—
127Dic3⋊Dic3—41no—
128Dic3⋊Dic3C2×C414yes—
129Dic32—22no—
130Dic32—22no—
131Dic32C2×C414yes—
132Dic32C2×C414yes—
133Q8×C4⋊C4—91noSylow
134C22×Dic6—31no—
135C22×Dic6—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C42—31no—
143C2×C3×C42—31no—
144C2×C3×C42—31no—
145C2×C3×C42—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—31no—
149C2×C4⋊Dic3—31no—
150C2×C4⋊Dic3—31no—
151C2×C4⋊Dic3—31no—
152C2×C4⋊Dic3—31no—
153C2×C4⋊Dic3—31no—
154C2×C4⋊Dic3—31no—
155C2×C4⋊Dic3—61no—
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×Dic3⋊C4—31no—
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⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—61no—
175C2×Dic3⋊C4—61no—
176C2×Dic3⋊C4—61no—
177C2×Dic3⋊C4C2×D311yescharacteristic
178C2×Dic3⋊C4C2×D311yescharacteristic
179C2×Dic3⋊C4C2×D311yescharacteristic
180C2×Dic3⋊C4C2×D311yescharacteristic
181C2×Dic3⋊C4C2×D311yescharacteristic
182C2×C4×Dic3—31no—
183C2×C4×Dic3—31no—
184C2×C4×Dic3—31no—
185C2×C4×Dic3—31no—
186C2×C4×Dic3—31no—
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—61no—
193C2×C4×Dic3C2×D311yescharacteristic
194C2×C4×Dic3C2×D311yescharacteristic
195C2×C4×Dic3C2×D311yescharacteristic
196C2×C4×Dic3C2×D311yescharacteristic
197#887—38no—
198#887—64no—
199C4×Dic6—38no—
200C4×Dic6—64no—
201C4×Dic6—64no—
202C4×Dic6—64no—
203C3×#95—21no—
204C3×#95—31no—
205C3×#95—31no—
206C3×#95C2×D311yescharacteristic
207C3×#95C2×D311yescharacteristic
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—61no—
215C3⋊#95C2×D311yescharacteristic
216C3⋊#95C2×D311yescharacteristic
217C23×C32C2411yescharacteristic
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4C22×C412yes—
226C2×C32×C4C2×Q812yes—
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⋊Dic3C22×C412yes—
236C2×C3⋊Dic3C22×C412yes—
237C2×C3⋊Dic3C2×D412yes—
238C2×C3⋊Dic3C2×Q812yes—
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—
255C2×C3×Dic3C22×C412yes—
256C2×C3×Dic3C2×D412yes—
257C2×C3×Dic3C2×D412yes—
258C2×C3×Dic3C2×Q812yes—
259C2×C3×Dic3C2×Q812yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3C2×Q812yes—
262C2×C3×Dic3#4112yes—
263#627C4⋊C4116yescomplemented
264C2×C4×Q8—91no—
265C2×C4×Q8—91no—
266C2×C4×Q8—91no—
267#389—31no—
268#389—91no—
269#389—91no—
270#389—91no—
271#389—91no—
272#389—91no—
273#384—91no—
274#384—91no—
275#384—91no—
276C4×C4⋊C4—31no—
277C4×C4⋊C4—91no—
278C4×C4⋊C4—91no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C22×Dic3C22×D311yescharacteristic
311C22×Dic3C22×D311yescharacteristic
312C22×Dic3C22×D311yescharacteristic
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C2×Dic6—34no—
317C2×Dic6—34no—
318C2×Dic6—34no—
319C2×Dic6—34no—
320C2×Dic6—34no—
321C2×Dic6—34no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—62no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—121no—
327C3×C4⋊C4—121no—
328C3×C42—34no—
329C3×C42—62no—
330C3×C42—62no—
331C3×C42—62no—
332C4⋊Dic3—34no—
333C4⋊Dic3—41no—
334C4⋊Dic3—62no—
335C4⋊Dic3—62no—
336C4⋊Dic3—62no—
337C4⋊Dic3—62no—
338C4⋊Dic3—62no—
339C4⋊Dic3—121no—
340C4⋊Dic3—121no—
341C4⋊Dic3—121no—
342C4⋊Dic3—122no—
343Dic3⋊C4—22no—
344Dic3⋊C4—22no—
345Dic3⋊C4—34no—
346Dic3⋊C4—34no—
347Dic3⋊C4—34no—
348Dic3⋊C4—41no—
349Dic3⋊C4—64no—
350Dic3⋊C4—62no—
351Dic3⋊C4—62no—
352Dic3⋊C4—62no—
353Dic3⋊C4—62no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—62no—
358Dic3⋊C4—62no—
359Dic3⋊C4—122no—
360Dic3⋊C4—121no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365Dic3⋊C4—122no—
366Dic3⋊C4Dic614yescomplemented
367Dic3⋊C4C4×D314yes—
368C4×Dic3—22no—
369C4×Dic3—22no—
370C4×Dic3—22no—
371C4×Dic3—34no—
372C4×Dic3—34no—
373C4×Dic3—34no—
374C4×Dic3—34no—
375C4×Dic3—62no—
376C4×Dic3—62no—
377C4×Dic3—62no—
378C4×Dic3—62no—
379C4×Dic3—62no—
380C4×Dic3—62no—
381C4×Dic3—122no—
382C4×Dic3C4×D314yes—
383C22×C32C23×C411yescharacteristic
384C22×C32C22×D411yescharacteristic
385C22×C32C22×Q811yescharacteristic
386C22×C32C22×Q811yescharacteristic
387C22×C32C2×#4111yescharacteristic
388C22×C32H(5,𝔽2)11yescharacteristic
389C22×C322−1+411yescharacteristic
390C32×C4—22no—
391C32×C4—22no—
392C32×C4—41no—
393C3⋊Dic3—22no—
394C3⋊Dic3—41no—
395C3⋊Dic3—41no—
396C3⋊Dic3C2×C4⋊C414yes—
397C3×Dic3—22no—
398C3×Dic3—22no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C3×Dic3—41no—
402C3×Dic3C2×C4⋊C414yes—
403C3×Dic3C2×C4⋊C414yes—
404C3×Dic3C4×Q814yescomplemented
405C22×Q8—91no—
406C4×Q8—98no—
407C4×Q8—184no—
408C4×Q8—184no—
409C2×C4⋊C4—31no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—31no—
412C2×C4⋊C4—31no—
413C2×C4⋊C4—31no—
414C2×C4⋊C4—31no—
415C2×C4⋊C4—91no—
416C2×C4⋊C4—91no—
417C2×C4⋊C4—91no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4—91no—
422C2×C4⋊C4—91no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—91no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—31no—
432C2×C42—91no—
433C2×C42—91no—
434C2×C42—91no—
435C2×C42—91no—
436C2×C42—91no—
437#95—31no—
438#95—31no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95D3211yescharacteristic
443C23×C3—21no—
444C23×C3C23×D311yescharacteristic
445C23×C3C23×D311yescharacteristic
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—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
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—32no—
471C2×C3×C4—32no—
472C2×C3×C4—32no—
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—41no—
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×C4C2×Dic612yes—
494C2×C3×C4C2×C4×D312yes—
495C2×C3×C4C2×C4×D312yes—
496C2×C3×C4D3×Q812yes—
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—32no—
517C2×Dic3—32no—
518C2×Dic3—62no—
519C2×Dic3—62no—
520C2×Dic3—62no—
521C2×Dic3—62no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—62no—
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×Dic3C2×Dic612yes—
547C2×Dic3C2×Dic612yes—
548C2×Dic3C2×C4×D312yes—
549C2×Dic3C2×C4×D312yes—
550C2×Dic3C2×C4×D312yes—
551C2×Dic3C2×C4×D312yes—
552C2×Dic3#23512yes—
553C2×Dic3D3×D412yes—
554C2×Dic3D3×D412yes—
555C2×Dic3D3×Q812yes—
556C2×Dic3D3×Q812yes—
557Dic6—316no—
558Dic6—316no—
559C2×C32C22×C4⋊C411yescharacteristic
560C2×C32C2×C4×Q811yescharacteristic
561C2×C32#52011yescharacteristic
562C2×C32D4×Q811yescharacteristic
563C2×C32#55011yescharacteristic
564C2×C32#55711yescharacteristic
565C2×C32Q8211yescharacteristic
566C2×Q8—94no—
567C2×Q8—94no—
568C2×Q8—94no—
569C22×C4—31no—
570C22×C4—31no—
571C22×C4—31no—
572C22×C4—31no—
573C22×C4—31no—
574C22×C4—31no—
575C22×C4—31no—
576C22×C4—31no—
577C22×C4—91no—
578C22×C4—91no—
579C22×C4—91no—
580C22×C4—91no—
581C22×C4C2×D3211yescharacteristic
582C22×C4C2×D3211yescharacteristic
583C22×C4C2×D3211yescharacteristic
584C4⋊C4—34no—
585C4⋊C4—34no—
586C4⋊C4—62no—
587C4⋊C4—62no—
588C4⋊C4—94no—
589C4⋊C4—94no—
590C4⋊C4—121no—
591C4⋊C4—121no—
592C4⋊C4—182no—
593C4⋊C4—182no—
594C4⋊C4—182no—
595C4⋊C4—182no—
596C4⋊C4—182no—
597C4⋊C4—182no—
598C4⋊C4—182no—
599C4⋊C4—361no—
600C4⋊C4—361no—
601C4⋊C4—361no—
602C4⋊C4—361no—
603C42—34no—
604C42—62no—
605C42—62no—
606C42—62no—
607C42—94no—
608C42—94no—
609C42—182no—
610C42—182no—
611C42—182no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3C22×Dic611yescharacteristic
620C22×C3C22×C4×D311yescharacteristic
621C22×C3C22×C4×D311yescharacteristic
622C22×C3C2×#23511yescharacteristic
623C22×C3C2×D3×D411yescharacteristic
624C22×C3C2×D3×D411yescharacteristic
625C22×C3#100411yescharacteristic
626C22×C3C2×D3×Q811yescharacteristic
627C22×C3C2×D3×Q811yescharacteristic
628C22×C3C2×D3×Q811yescharacteristic
629C22×C3D3×#4111yescharacteristic
630C22×C3#100911yescharacteristic
631C22×C3#101011yescharacteristic
632C22×C3#101011yescharacteristic
633C3×C4—22no—
634C3×C4—22no—
635C3×C4—22no—
636C3×C4—22no—
637C3×C4—34no—
638C3×C4—34no—
639C3×C4—34no—
640C3×C4—42no—
641C3×C4—42no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—62no—
645C3×C4—62no—
646C3×C4—81no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4—121no—
650Dic3—22no—
651Dic3—22no—
652Dic3—34no—
653Dic3—34no—
654Dic3—41no—
655Dic3—41no—
656Dic3—41no—
657Dic3—64no—
658Dic3—62no—
659Dic3—62no—
660Dic3—122no—
661Dic3—122no—
662Dic3—121no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3C4×Dic614yescomplemented
668Dic3D3×C4⋊C414yes—
669Dic3D3×C4⋊C414yes—
670C32Q8×C4⋊C411yescharacteristic, complemented, Sylow
671C23C22×D3211yescharacteristic
672Q8—916no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—32no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—32no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—32no—
687C2×C4—32no—
688C2×C4—32no—
689C2×C4—32no—
690C2×C4—32no—
691C2×C4—61no—
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—92no—
705C2×C4—92no—
706C2×C4—92no—
707C2×C4—92no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4D3×Dic612yes—
717C2×C4C4×D3212yes—
718C2×C3—21no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3C2×C4×Dic611yescharacteristic
726C2×C3C2×D3×C4⋊C411yescharacteristic
727C2×C3C2×D3×C4⋊C411yescharacteristic
728C2×C3#552311yescharacteristic
729C2×C3D4×Dic611yescharacteristic
730C2×C3#554611yescharacteristic
731C2×C3#555311yescharacteristic
732C2×C3Q8×Dic611yescharacteristic
733C2×C3#556711yescharacteristic
734C2×C3C4×D3×Q811yescharacteristic
735C2×C3#559911yescharacteristic
736C2×C3#563211yescharacteristic
737C2×C3#568511yescharacteristic
738C2×C3#572211yescharacteristic
739C22C2×D3×Dic611yescharacteristic
740C22C2×C4×D3211yescharacteristic
741C22D3×#23511yescharacteristic
742C22#6430911yescharacteristic
743C22D32×D411yescharacteristic
744C22#6431411yescharacteristic
745C22D32×Q811yescharacteristic
746C4—22no—
747C4—22no—
748C4—34no—
749C4—34no—
750C4—34no—
751C4—41no—
752C4—62no—
753C4—62no—
754C4—94no—
755C4—121no—
756C4—121no—
757C4—121no—
758C4—182no—
759C4—361no—
760C4—361no—
761C3—21no—
762C3C4⋊C4×Dic611yescharacteristic, complemented
763C3#7598111yescharacteristic, complemented
764C2C4×D3×Dic611yescharacteristic
765C2#1059404911yescharacteristic
766C2#1059407111yescharacteristic
767C2#1059424611yescharacteristic
768C2#1059431211yescharacteristic
769C2#1059459611yescharacteristic
770C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32Q8×C4⋊C4
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
49. #63837C4semidirect
115. C3×Dic3⋊C4Q8semidirect
263. #627C4⋊C4semidirect
366. Dic3⋊C4Dic6semidirect
404. C3×Dic3C4×Q8semidirect
667. Dic3C4×Dic6semidirect
670. C32Q8×C4⋊C4semidirect
762. C3C4⋊C4×Dic6semidirect
763. C3#75981semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638372
#105923462
C3×#46492
C3×#46472
#105913492
#105913302
#105913272
#105912682
#105912642
#105912442
#105912412
Dic3×Dic3⋊C42
#759813
C4⋊C4×Dic63