Finite Group Databasebeta

← #30872324

Subgroups — #30872324

Order 17152.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#11761612C211yesmaximal, characteristic, complemented
2#22562654C211yesmaximal, characteristic, complemented
3#22561191C211yesmaximal, characteristic, complemented
4#22561154C211yesmaximal, characteristic, complemented
5#22560658C211yesmaximal, characteristic, complemented
6#22560653C211yesmaximal, characteristic, complemented
7#22560512C211yesmaximal, characteristic, complemented
8#22560512C211yesmaximal, characteristic, complemented
9#22560308C211yesmaximal, characteristic, complemented
10#22560308C211yesmaximal, characteristic, complemented
11#22560229C211yesmaximal, characteristic, complemented
12#22560019C211yesmaximal, characteristic, complemented
13#22559918C211yesmaximal, characteristic, complemented
14C2×#16863155C211yesmaximal, characteristic, complemented
15C67×#3475C211yesmaximal, characteristic
16C22×#11761612C2211yescharacteristic
17C22×#11761612C2211yescharacteristic
18C2×#14524002C2211yescharacteristic
19C22×C4×Dic67C2211yescharacteristic
20#16863474—21no—
21#16863468—21no—
22#16863468—21no—
23D4×C67⋊C8—21no—
24#16863420C2211yescharacteristic
25C2×#14523970C2211yescharacteristic
26C2×#14523970C2211yescharacteristic
27C2×#14523970C2211yescharacteristic
28C2×#14523970C2211yescharacteristic
29#16863360C2211yescharacteristic
30#16863360C2211yescharacteristic
31C4×#11761612C2211yescharacteristic
32#16863289—21no—
33#16863282—21no—
34#16863276—21no—
35#16863271—21no—
36C4×C4⋊Dic67C2211yescharacteristic
37C4×C22⋊Dic67C2211yescharacteristic
38C4×C22⋊Dic67C2211yescharacteristic
39#16863242C2211yescharacteristic
40#16863155C2211yescharacteristic
41#16863155C2211yescharacteristic
42#16863155C2211yescharacteristic
43#16863155C2211yescharacteristic
44#16863155C2211yescharacteristic
45#16863155C2211yescharacteristic
46#16863155C2211yescharacteristic
47#16863155C2211yescharacteristic
48#16863155C2211yescharacteristic
49#16863155C2211yescharacteristic
50#16863155C2211yescharacteristic
51#16863155C2211yescharacteristic
52#556×C67C411yescharacteristic, complemented
53#555×C67C411yescharacteristic, complemented
54#554×C67C411yescharacteristic, complemented
55#553×C67C411yescharacteristic, complemented
56#553×C67C411yescharacteristic, complemented
57#552×C67—21no—
58#552×C67C411yescharacteristic, complemented
59#552×C67C411yescharacteristic, complemented
60#551×C67—21no—
61#551×C67—21no—
62#547×C67C411yescharacteristic, complemented
63#546×C67—21no—
64#533×C67C2211yescharacteristic
65#529×C67—21no—
66#529×C67—21no—
67#529×C67—21no—
68#525×C67C2211yescharacteristic
69#525×C67C2211yescharacteristic
70C4×#41×C67—21no—
71C4×#41×C67C2211yescharacteristic
72C2×C4×D4×C67C2211yescharacteristic
73C2×#117×C67C2211yescharacteristic
74C2×#117×C67C2211yescharacteristic
75C23×Dic67—21no—
76C2×#11761612—22no—
77C2×#11761612—22no—
78C2×#11761612—21no—
79C2×#11761612—21no—
80C2×#11761612—41no—
81C2×#11761612—41no—
82C2×#11761612C2311yescharacteristic
83C2×#11761612C2311yescharacteristic
84C2×#11761612C2311yescharacteristic
85C2×#11761612C2311yescharacteristic
86C22×C67⋊C8—21no—
87C22×C67⋊C8—21no—
88#14524002—22no—
89#14524002—41no—
90C2×C4⋊Dic67—21no—
91C2×C4⋊Dic67—21no—
92C2×C22⋊Dic67—21no—
93C2×C22⋊Dic67—21no—
94C2×C22⋊Dic67—21no—
95C2×C4×Dic67—22no—
96C2×C4×Dic67—21no—
97C2×C4×Dic67—41no—
98C2×C4×Dic67C2311yescharacteristic
99C2×C4×Dic67C2311yescharacteristic
100C2×C4×Dic67C2311yescharacteristic
101C2×C4×Dic67C2311yescharacteristic
102C4⋊(C67⋊C8)—21no—
103C4⋊(C67⋊C8)—21no—
104#14523970—22no—
105#14523970—22no—
106#14523970—41no—
107#14523970—41no—
108C22⋊(C67⋊C8)—21no—
109C22⋊(C67⋊C8)—21no—
110C22⋊(C67⋊C8)—21no—
111C22⋊(C67⋊C8)—21no—
112#14523954—21no—
113C4×C67⋊C8—21no—
114C67⋊#95—21no—
115C67⋊#95—21no—
116C67⋊#95—21no—
117C67⋊#95—21no—
118C67⋊#95—21no—
119C2×#41×C67—21no—
120C2×#41×C67C2311yescharacteristic
121C22×D4×C67D411yescharacteristic
122C23×C4×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C4⋊Q8×C67C2×C411yescharacteristic, complemented
125C4⋊Q8×C67C2×C411yescharacteristic, complemented
126#126×C67—21no—
127#126×C67—21no—
128#126×C67—21no—
129#126×C67—21no—
130#126×C67—21no—
131#126×C67—21no—
132#125×C67—21no—
133#125×C67—21no—
134#125×C67—21no—
135#125×C67C2×C411yescharacteristic, complemented
136#125×C67C2×C411yescharacteristic, complemented
137#124×C67—21no—
138#124×C67—21no—
139#124×C67—21no—
140#123×C67—21no—
141#123×C67—21no—
142#123×C67—21no—
143#123×C67—21no—
144#123×C67—21no—
145#123×C67—21no—
146#123×C67—21no—
147#123×C67—21no—
148C22⋊Q8×C67—21no—
149C22⋊Q8×C67—21no—
150C22⋊Q8×C67—21no—
151C22⋊Q8×C67—21no—
152C22⋊Q8×C67—21no—
153C22⋊Q8×C67C2×C411yescharacteristic
154C22⋊Q8×C67C2×C411yescharacteristic
155C22⋊Q8×C67C2×C411yescharacteristic, complemented
156C22⋊Q8×C67C2×C411yescharacteristic, complemented
157#121×C67—21no—
158#121×C67—21no—
159#121×C67—21no—
160#121×C67C2×C411yescharacteristic
161#121×C67C2×C411yescharacteristic
162#121×C67C2×C411yescharacteristic, complemented
163#121×C67C2×C411yescharacteristic, complemented
164#120×C67—21no—
165#120×C67—21no—
166C4×Q8×C67—21no—
167C4×Q8×C67—21no—
168C4×Q8×C67—21no—
169C4×Q8×C67C2×C411yescharacteristic, complemented
170C4×Q8×C67C2×C411yescharacteristic, complemented
171C4×D4×C67—21no—
172C4×D4×C67—21no—
173C4×D4×C67—21no—
174C4×D4×C67—21no—
175C4×D4×C67—21no—
176C4×D4×C67—21no—
177C4×D4×C67—21no—
178C4×D4×C67—21no—
179C4×D4×C67—21no—
180C4×D4×C67C2×C411yescharacteristic
181C4×D4×C67C2×C411yescharacteristic
182C4×D4×C67C2×C411yescharacteristic
183C4×D4×C67C2×C411yescharacteristic
184C4×D4×C67C2×C411yescharacteristic, complemented
185C4×D4×C67C2×C411yescharacteristic, complemented
186C4×D4×C67D411yescharacteristic
187C4×D4×C67D411yescharacteristic
188C4×D4×C67D411yescharacteristic
189C4×D4×C67D411yescharacteristic
190#117×C67—21no—
191#117×C67—21no—
192#117×C67—21no—
193#117×C67—21no—
194#117×C67—21no—
195#117×C67—21no—
196#117×C67—21no—
197#117×C67—21no—
198#117×C67C2×C411yescharacteristic
199#117×C67C2×C411yescharacteristic
200#117×C67C2×C411yescharacteristic, complemented
201#117×C67C2×C411yescharacteristic, complemented
202#117×C67C2311yescharacteristic
203#117×C67C2311yescharacteristic
204#117×C67C2311yescharacteristic
205C2×C4⋊C4×C67C2×C411yescharacteristic
206C2×C4⋊C4×C67C2×C411yescharacteristic
207C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
208C2×C4⋊C4×C67C2×C411yescharacteristic, complemented
209C2×C4⋊C4×C67D411yescharacteristic
210C2×C22⋊C4×C67—21no—
211C2×C22⋊C4×C67—21no—
212C2×C22⋊C4×C67D411yescharacteristic
213C2×C22⋊C4×C67D411yescharacteristic
214C2×C42×C67—21no—
215C2×C42×C67—21no—
216C2×C42×C67—21no—
217C2×C42×C67C2311yescharacteristic
218C22×Dic67—21no—
219C22×Dic67—21no—
220C22×Dic67—21no—
221C22×Dic67—21no—
222C22×Dic67—42no—
223C22×Dic67—42no—
224C22×Dic67—42no—
225#11761612—21no—
226#11761612—21no—
227#11761612—21no—
228#11761612—21no—
229#11761612—21no—
230#11761612—21no—
231#11761612—21no—
232#11761612—42no—
233#11761612—42no—
234#11761612#4112yescomplemented
235C2×C67⋊C8—21no—
236C2×C67⋊C8—21no—
237C2×C67⋊C8—21no—
238C2×C67⋊C8—21no—
239C2×C67⋊C8—42no—
240C2×C67⋊C8—42no—
241C4⋊Dic67—42no—
242C4⋊Dic67—42no—
243C22⋊Dic67—42no—
244C22⋊Dic67—42no—
245C22⋊Dic67—42no—
246C4×Dic67—21no—
247C4×Dic67—21no—
248C4×Dic67—21no—
249C4×Dic67—21no—
250C4×Dic67—21no—
251C4×Dic67—21no—
252C4×Dic67—21no—
253C4×Dic67—42no—
254C4×Dic67#4112yescomplemented
255C24×C67C2×D411yescharacteristic
256C24×C67C2×D411yescharacteristic
257#41×C67—21no—
258#41×C67—21no—
259#41×C67—21no—
260#41×C67—21no—
261#41×C67—44no—
262C2×Q8×C67—21no—
263C2×Q8×C67—21no—
264C2×Q8×C67C22×C411yescharacteristic
265C2×D4×C67—21no—
266C2×D4×C67—21no—
267C2×D4×C67—21no—
268C2×D4×C67—21no—
269C2×D4×C67—21no—
270C2×D4×C67—42no—
271C2×D4×C67C22⋊C411yescharacteristic
272C2×D4×C67C22⋊C411yescharacteristic
273C2×D4×C67C22⋊C411yescharacteristic
274C2×D4×C67C22⋊C411yescharacteristic
275C2×D4×C67C22×C411yescharacteristic
276C22×C4×C67—21no—
277C22×C4×C67—21no—
278C22×C4×C67—21no—
279C22×C4×C67—21no—
280C22×C4×C67—21no—
281C22×C4×C67—21no—
282C22×C4×C67—21no—
283C22×C4×C67—21no—
284C22×C4×C67—21no—
285C22×C4×C67—21no—
286C22×C4×C67—21no—
287C22×C4×C67—21no—
288C22×C4×C67—21no—
289C22×C4×C67—21no—
290C22×C4×C67—21no—
291C22×C4×C67C22×C411yescharacteristic
292C22×C4×C67C22×C411yescharacteristic
293C22×C4×C67C22×C411yescharacteristic
294C22×C4×C67C22×C411yescharacteristic
295C22×C4×C67C2×D411yescharacteristic
296C22×C4×C67C2×D411yescharacteristic
297C22×C4×C67C2×D411yescharacteristic
298C22×C4×C67C2×D411yescharacteristic
299C22×C4×C67C2×D411yescharacteristic
300C22×C4×C67C2×D411yescharacteristic
301C22×C4×C67C2×D411yescharacteristic
302C22×C4×C67C2×D411yescharacteristic
303C22×C4×C67C2411yescharacteristic
304C4⋊C4×C67—21no—
305C4⋊C4×C67—21no—
306C4⋊C4×C67—21no—
307C4⋊C4×C67—21no—
308C4⋊C4×C67—21no—
309C4⋊C4×C67—21no—
310C4⋊C4×C67—21no—
311C4⋊C4×C67—21no—
312C4⋊C4×C67—21no—
313C4⋊C4×C67—21no—
314C4⋊C4×C67—21no—
315C4⋊C4×C67—21no—
316C4⋊C4×C67—21no—
317C4⋊C4×C67—21no—
318C4⋊C4×C67—21no—
319C4⋊C4×C67—21no—
320C4⋊C4×C67C22⋊C411yescharacteristic
321C4⋊C4×C67C22⋊C411yescharacteristic
322C4⋊C4×C67C22⋊C411yescharacteristic
323C4⋊C4×C67C22⋊C411yescharacteristic
324C4⋊C4×C67C22×C411yescharacteristic
325C4⋊C4×C67C22×C411yescharacteristic
326C4⋊C4×C67C22×C411yescharacteristic
327C4⋊C4×C67C22×C411yescharacteristic
328C4⋊C4×C67C22×C411yescharacteristic
329C4⋊C4×C67C22×C411yescharacteristic
330C22⋊C4×C67—21no—
331C22⋊C4×C67—21no—
332C22⋊C4×C67—21no—
333C22⋊C4×C67—21no—
334C22⋊C4×C67—21no—
335C22⋊C4×C67—21no—
336C22⋊C4×C67—21no—
337C22⋊C4×C67—21no—
338C22⋊C4×C67—21no—
339C22⋊C4×C67—21no—
340C22⋊C4×C67—21no—
341C22⋊C4×C67—21no—
342C22⋊C4×C67—21no—
343C22⋊C4×C67—21no—
344C22⋊C4×C67—21no—
345C22⋊C4×C67—21no—
346C22⋊C4×C67—21no—
347C22⋊C4×C67C22⋊C411yescharacteristic
348C22⋊C4×C67C22⋊C411yescharacteristic
349C22⋊C4×C67C22⋊C411yescharacteristic
350C22⋊C4×C67C22⋊C411yescharacteristic
351C22⋊C4×C67C22⋊C411yescharacteristic
352C22⋊C4×C67C22⋊C411yescharacteristic
353C22⋊C4×C67C22⋊C411yescharacteristic
354C22⋊C4×C67C22⋊C411yescharacteristic
355C42×C67—21no—
356C42×C67—21no—
357C42×C67—21no—
358C42×C67—21no—
359C42×C67—21no—
360C42×C67—21no—
361C42×C67—21no—
362C42×C67—21no—
363C42×C67—21no—
364C42×C67C22×C411yescharacteristic
365C42×C67C22×C411yescharacteristic
366C42×C67C2×D411yescharacteristic
367C42×C67C2×D411yescharacteristic
368C23×C67—21no—
369C23×C67—21no—
370C23×C67—22no—
371C23×C67—21no—
372C23×C67—21no—
373C23×C67—21no—
374C23×C67—41no—
375C23×C67—41no—
376C23×C67—41no—
377C23×C67C2×C22⋊C411yescharacteristic
378C23×C67C2×C22⋊C411yescharacteristic
379C23×C67C2×C22⋊C411yescharacteristic
380C23×C67C2×C22⋊C411yescharacteristic
381C23×C67C22×D411yescharacteristic
382Q8×C67—21no—
383Q8×C67—21no—
384Q8×C67—42no—
385Q8×C67—81no—
386D4×C67—22no—
387D4×C67—22no—
388D4×C67—21no—
389D4×C67—21no—
390D4×C67—41no—
391D4×C67—41no—
392D4×C67—42no—
393D4×C67—41no—
394D4×C67—41no—
395D4×C67—42no—
396D4×C67—81no—
397D4×C67—81no—
398C2×C4×C67—21no—
399C2×C4×C67—21no—
400C2×C4×C67—21no—
401C2×C4×C67—21no—
402C2×C4×C67—21no—
403C2×C4×C67—21no—
404C2×C4×C67—21no—
405C2×C4×C67—21no—
406C2×C4×C67—21no—
407C2×C4×C67—21no—
408C2×C4×C67—21no—
409C2×C4×C67—21no—
410C2×C4×C67—21no—
411C2×C4×C67—21no—
412C2×C4×C67—21no—
413C2×C4×C67—21no—
414C2×C4×C67—21no—
415C2×C4×C67—21no—
416C2×C4×C67—21no—
417C2×C4×C67—21no—
418C2×C4×C67—21no—
419C2×C4×C67—21no—
420C2×C4×C67—21no—
421C2×C4×C67—21no—
422C2×C4×C67—21no—
423C2×C4×C67—21no—
424C2×C4×C67—21no—
425C2×C4×C67—41no—
426C2×C4×C67—41no—
427C2×C4×C67—42no—
428C2×C4×C67—42no—
429C2×C4×C67—42no—
430C2×C4×C67—41no—
431C2×C4×C67—41no—
432C2×C4×C67—81no—
433C2×C4×C67—81no—
434C2×C4×C67—81no—
435C2×C4×C67C2×C22⋊C411yescharacteristic
436C2×C4×C67C2×C22⋊C411yescharacteristic
437C2×C4×C67C2×C22⋊C411yescharacteristic
438C2×C4×C67C2×C22⋊C411yescharacteristic
439C2×C4×C67C2×C22⋊C411yescharacteristic
440C2×C4×C67C2×C22⋊C411yescharacteristic
441C2×C4×C67C2×C22⋊C411yescharacteristic
442C2×C4×C67C2×C22⋊C411yescharacteristic
443C2×C4×C67C23×C411yescharacteristic
444C2×C4×C67C22×D411yescharacteristic
445C2×C4×C67C2×#4111yescharacteristic
446C2×C4×C67C2×#4111yescharacteristic
447C2×C4×C67H(5,𝔽2)11yescharacteristic
448C2×C4×C672−1+411yescharacteristic
449C2×Dic67—22no—
450C2×Dic67—22no—
451C2×Dic67—41no—
452C2×Dic67—41no—
453C2×Dic67—41no—
454C2×Dic67—48no—
455C2×Dic67—41no—
456C2×Dic67—41no—
457C2×Dic67—41no—
458C2×Dic67—41no—
459C2×Dic67—41no—
460C2×Dic67—41no—
461C2×Dic67—41no—
462C67⋊C8—22no—
463C67⋊C8—41no—
464C67⋊C8—41no—
465C67⋊C8—41no—
466C22×C67—21no—
467C22×C67—21no—
468C22×C67—21no—
469C22×C67—21no—
470C22×C67—21no—
471C22×C67—21no—
472C22×C67—21no—
473C22×C67—21no—
474C22×C67—21no—
475C22×C67—21no—
476C22×C67—21no—
477C22×C67—21no—
478C22×C67—21no—
479C22×C67—42no—
480C22×C67—42no—
481C22×C67—41no—
482C22×C67—41no—
483C22×C67—41no—
484C22×C67—81no—
485C22×C67—81no—
486C22×C67#42112yes—
487C22×C67C22×C22⋊C411yescharacteristic
488C22×C67#54611yescharacteristic
489C22×C67#54711yescharacteristic
490C4×C67—21no—
491C4×C67—21no—
492C4×C67—21no—
493C4×C67—21no—
494C4×C67—21no—
495C4×C67—21no—
496C4×C67—21no—
497C4×C67—21no—
498C4×C67—41no—
499C4×C67—41no—
500C4×C67—41no—
501C4×C67—41no—
502C4×C67—41no—
503C4×C67—41no—
504C4×C67—41no—
505C4×C67C4×#4111yescharacteristic
506C4×C67#52011yescharacteristic
507C4×C67#54611yescharacteristic
508C4×C67#54711yescharacteristic
509Dic67—42no—
510Dic67—42no—
511Dic67—81no—
512Dic67—81no—
513#22506—671nomaximal, Sylow
514C2×C67—21no—
515C2×C67—21no—
516C2×C67—22no—
517C2×C67—41no—
518C2×C67—41no—
519C2×C67—41no—
520C2×C67—81no—
521C2×C67#233911yescharacteristic
522C2×C67C2×#42111yescharacteristic
523C2×C67#290111yescharacteristic
524#3475D6711yescharacteristic
525D4×M16—671no—
526#2290—671no—
527#1995—671no—
528#1986—671no—
529#1897—671no—
530#1896—671no—
531#1871—671no—
532#1871—671no—
533#1826—671no—
534#1826—671no—
535#1806—671no—
536#1759—671no—
537#1733—671no—
538C2×#339—671no—
539C67#2250611yescharacteristic, complemented, Sylow
540C22×M16—671no—
541C22×M16—671no—
542#556Dic6711yescharacteristic, complemented
543#555Dic6711yescharacteristic, complemented
544#554Dic6711yescharacteristic, complemented
545#553Dic6711yescharacteristic, complemented
546#553Dic6711yescharacteristic, complemented
547#552—21no—
548#552Dic6711yescharacteristic, complemented
549#552Dic6711yescharacteristic, complemented
550#551—21no—
551#551—21no—
552#547Dic6711yescharacteristic, complemented
553#546—21no—
554#533C2×D6711yescharacteristic
555#529—21no—
556#529—21no—
557#529—21no—
558#525C2×D6711yescharacteristic
559#525C2×D6711yescharacteristic
560C4×#41—21no—
561C4×#41C2×D6711yescharacteristic
562C2×C4×D4C2×D6711yescharacteristic
563C2×#117—671no—
564C2×#117C2×D6711yescharacteristic
565C2×#117C2×D6711yescharacteristic
566C22×C42—671no—
567#436—1341no—
568#435—1341no—
569#435—1341no—
570C8×D4—1341no—
571#423—671no—
572C2×#104—671no—
573C2×#104—671no—
574C2×#104—671no—
575C2×#104—671no—
576#407—671no—
577#407—671no—
578C4×M16—671no—
579#388—1341no—
580#387—1341no—
581#386—1341no—
582#385—1341no—
583C4×C4⋊C4—671no—
584C4×C22⋊C4—671no—
585C4×C22⋊C4—671no—
586#376—671no—
587#339—671no—
588#339—671no—
589#339—671no—
590#339—671no—
591#339—671no—
592#339—671no—
593#339—671no—
594#339—671no—
595#339—671no—
596#339—671no—
597#339—671no—
598#339—671no—
599C2×#41—21no—
600C2×#41C22×D6711yescharacteristic
601C22×D4C22⋊D6711yescharacteristic
602C23×C4—1341no—
603C23×C4C22×D6711yescharacteristic
604C23×C4C22×D6711yescharacteristic
605C2×M16—2681no—
606C2×M16—2681no—
607C2×M16—671no—
608C2×M16—671no—
609C2×M16—671no—
610C2×M16—671no—
611C2×M16—1342no—
612C2×M16—1342no—
613C2×M16—1341no—
614C2×M16—1341no—
615C22×C8—1341no—
616C22×C8—1341no—
617C4⋊Q8C2×Dic6711yescharacteristic, complemented
618C4⋊Q8C2×Dic6711yescharacteristic, complemented
619#126—21no—
620#126—21no—
621#126—21no—
622#126—21no—
623#126—21no—
624#126—21no—
625#125—21no—
626#125—21no—
627#125—21no—
628#125C2×Dic6711yescharacteristic, complemented
629#125C2×Dic6711yescharacteristic, complemented
630#124—21no—
631#124—21no—
632#124—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640#123—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8—21no—
646C22⋊Q8C2×Dic6711yescharacteristic
647C22⋊Q8C2×Dic6711yescharacteristic
648C22⋊Q8C2×Dic6711yescharacteristic, complemented
649C22⋊Q8C2×Dic6711yescharacteristic, complemented
650#121—21no—
651#121—21no—
652#121—21no—
653#121C2×Dic6711yescharacteristic
654#121C2×Dic6711yescharacteristic
655#121C2×Dic6711yescharacteristic, complemented
656#121C2×Dic6711yescharacteristic, complemented
657#120—21no—
658#120—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8C2×Dic6711yescharacteristic, complemented
663C4×Q8C2×Dic6711yescharacteristic, complemented
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4—21no—
673C4×D4C2×Dic6711yescharacteristic
674C4×D4C2×Dic6711yescharacteristic
675C4×D4C2×Dic6711yescharacteristic
676C4×D4C2×Dic6711yescharacteristic
677C4×D4C2×Dic6711yescharacteristic, complemented
678C4×D4C2×Dic6711yescharacteristic, complemented
679C4×D4C22⋊D6711yescharacteristic
680C4×D4C22⋊D6711yescharacteristic
681C4×D4C22⋊D6711yescharacteristic
682C4×D4C22⋊D6711yescharacteristic
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—21no—
691#117—2681no—
692#117—1342no—
693#117C2×Dic6711yescharacteristic
694#117C2×Dic6711yescharacteristic
695#117C2×Dic6711yescharacteristic, complemented
696#117C2×Dic6711yescharacteristic, complemented
697#117C22×D6711yescharacteristic
698#117C22×D6711yescharacteristic
699#117C22×D6711yescharacteristic
700C2×C4⋊C4—1341no—
701C2×C4⋊C4—1341no—
702C2×C4⋊C4C2×Dic6711yescharacteristic
703C2×C4⋊C4C2×Dic6711yescharacteristic
704C2×C4⋊C4C2×Dic6711yescharacteristic, complemented
705C2×C4⋊C4C2×Dic6711yescharacteristic, complemented
706C2×C4⋊C4C22⋊D6711yescharacteristic
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—1341no—
710C2×C22⋊C4—1341no—
711C2×C22⋊C4—1341no—
712C2×C22⋊C4C22⋊D6711yescharacteristic
713C2×C22⋊C4C22⋊D6711yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—2681no—
718C2×C42—671no—
719C2×C42—671no—
720C2×C42—671no—
721C2×C42—671no—
722C2×C42—1341no—
723C2×C42—1342no—
724C2×C42C22×D6711yescharacteristic
725C4⋊C8—1341no—
726C4⋊C8—1341no—
727#104—2681no—
728#104—2681no—
729#104—1342no—
730#104—1342no—
731C22⋊C8—1341no—
732C22⋊C8—1341no—
733C22⋊C8—1341no—
734C22⋊C8—1341no—
735#97—1341no—
736C4×C8—1341no—
737#95—1341no—
738#95—1341no—
739#95—1341no—
740#95—1341no—
741#95—1341no—
742C24C2×C22⋊D6711yescharacteristic
743C24C2×C22⋊D6711yescharacteristic
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8C22×Dic6711yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—42no—
758C2×D4C22⋊Dic6711yescharacteristic
759C2×D4C22⋊Dic6711yescharacteristic
760C2×D4C22⋊Dic6711yescharacteristic
761C2×D4C22⋊Dic6711yescharacteristic
762C2×D4C22×Dic6711yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—2682no—
779C22×C4—2682no—
780C22×C4—2682no—
781C22×C4—1341no—
782C22×C4—1341no—
783C22×C4—1341no—
784C22×C4—1341no—
785C22×C4C22×Dic6711yescharacteristic
786C22×C4C22×Dic6711yescharacteristic
787C22×C4C22×Dic6711yescharacteristic
788C22×C4C22×Dic6711yescharacteristic
789C22×C4C2×C22⋊D6711yescharacteristic
790C22×C4C2×C22⋊D6711yescharacteristic
791C22×C4C2×C22⋊D6711yescharacteristic
792C22×C4C2×C22⋊D6711yescharacteristic
793C22×C4C2×C22⋊D6711yescharacteristic
794C22×C4C2×C22⋊D6711yescharacteristic
795C22×C4C2×C22⋊D6711yescharacteristic
796C22×C4C2×C22⋊D6711yescharacteristic
797C22×C4C23×D6711yescharacteristic
798M16—2682no—
799M16—2682no—
800M16—672no—
801M16—1341no—
802M16—1341no—
803M16—1341no—
804M16—1341no—
805M16—1341no—
806M16—1341no—
807M16—1341no—
808C2×C8—2682no—
809C2×C8—2682no—
810C2×C8—1341no—
811C2×C8—1341no—
812C2×C8—1341no—
813C2×C8—1341no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—2682no—
831C4⋊C4—2682no—
832C4⋊C4C22⋊Dic6711yescharacteristic
833C4⋊C4C22⋊Dic6711yescharacteristic
834C4⋊C4C22⋊Dic6711yescharacteristic
835C4⋊C4C22⋊Dic6711yescharacteristic
836C4⋊C4C22×Dic6711yescharacteristic
837C4⋊C4C22×Dic6711yescharacteristic
838C4⋊C4C22×Dic6711yescharacteristic
839C4⋊C4C22×Dic6711yescharacteristic
840C4⋊C4C22×Dic6711yescharacteristic
841C4⋊C4C22×Dic6711yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—2682no—
860C22⋊C4—2682no—
861C22⋊C4—2682no—
862C22⋊C4C22⋊Dic6711yescharacteristic
863C22⋊C4C22⋊Dic6711yescharacteristic
864C22⋊C4C22⋊Dic6711yescharacteristic
865C22⋊C4C22⋊Dic6711yescharacteristic
866C22⋊C4C22⋊Dic6711yescharacteristic
867C22⋊C4C22⋊Dic6711yescharacteristic
868C22⋊C4C22⋊Dic6711yescharacteristic
869C22⋊C4C22⋊Dic6711yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—2682no—
880C42—672no—
881C42—1341no—
882C42—1341no—
883C42—1341no—
884C42—1341no—
885C42—1341no—
886C42—1341no—
887C42—1341no—
888C42C22×Dic6711yescharacteristic
889C42C22×Dic6711yescharacteristic
890C42C2×C22⋊D6711yescharacteristic
891C42C2×C22⋊D6711yescharacteristic
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊Dic6711yescharacteristic
902C23C2×C22⋊Dic6711yescharacteristic
903C23C2×C22⋊Dic6711yescharacteristic
904C23C2×C22⋊Dic6711yescharacteristic
905C23C22×C22⋊D6711yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—41no—
918D4—41no—
919D4—42no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—21no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—42no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—81no—
957C2×C4—81no—
958C2×C4—81no—
959C2×C4—2681no—
960C2×C4—2681no—
961C2×C4—2681no—
962C2×C4—2688no—
963C2×C4—2681no—
964C2×C4—2681no—
965C2×C4—2681no—
966C2×C4—2681no—
967C2×C4—2681no—
968C2×C4—2681no—
969C2×C4—2681no—
970C2×C4—1342no—
971C2×C4—1342no—
972C2×C4C2×C22⋊Dic6711yescharacteristic
973C2×C4C2×C22⋊Dic6711yescharacteristic
974C2×C4C2×C22⋊Dic6711yescharacteristic
975C2×C4C2×C22⋊Dic6711yescharacteristic
976C2×C4C2×C22⋊Dic6711yescharacteristic
977C2×C4C2×C22⋊Dic6711yescharacteristic
978C2×C4C2×C22⋊Dic6711yescharacteristic
979C2×C4C2×C22⋊Dic6711yescharacteristic
980C2×C4C23×Dic6711yescharacteristic
981C2×C4C22×C22⋊D6711yescharacteristic
982C2×C4#41×D6711yescharacteristic
983C2×C4#41×D6711yescharacteristic
984C2×C4#1452408911yescharacteristic
985C2×C4#1452409011yescharacteristic
986C8—2681no—
987C8—2681no—
988C8—2681no—
989C8—1342no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22#1686341312yes—
1011C22C22×C22⋊Dic6711yescharacteristic
1012C22#1686403411yescharacteristic
1013C22#1686404511yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—41no—
1023C4—41no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—2682no—
1030C4—2682no—
1031C4—5361no—
1032C4—5361no—
1033C4#41×Dic6711yescharacteristic
1034C4#1686387911yescharacteristic
1035C4#1686403411yescharacteristic
1036C4#1686404511yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2#2256303911yescharacteristic
1045C2C2×#1686341311yescharacteristic
1046C2#2256875611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
Fitting, prime radicalC67×#3475C2
socleC22×C67C22×C22⋊C4
cosocleC22×C4×C67C24
hypercenter#3475D67
hypocenterC67#22506
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ #3475

Complements

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

NH ≅ G/Ntype
1. D4×#11761612C2semidirect
2. #22562654C2semidirect
3. #22561191C2semidirect
4. #22561154C2semidirect
5. #22560658C2semidirect
6. #22560653C2semidirect
7. #22560512C2semidirect
8. #22560512C2semidirect
9. #22560308C2semidirect
10. #22560308C2semidirect
11. #22560229C2semidirect
12. #22560019C2semidirect
13. #22559918C2semidirect
14. C2×#16863155C2semidirect
52. #556×C67C4semidirect
53. #555×C67C4semidirect
54. #554×C67C4semidirect
55. #553×C67C4semidirect
56. #553×C67C4semidirect
58. #552×C67C4semidirect
59. #552×C67C4semidirect
62. #547×C67C4semidirect
124. C4⋊Q8×C67C2×C4semidirect
125. C4⋊Q8×C67C2×C4semidirect
135. #125×C67C2×C4semidirect
136. #125×C67C2×C4semidirect
155. C22⋊Q8×C67C2×C4semidirect
156. C22⋊Q8×C67C2×C4semidirect
162. #121×C67C2×C4semidirect
163. #121×C67C2×C4semidirect
169. C4×Q8×C67C2×C4semidirect
170. C4×Q8×C67C2×C4semidirect
184. C4×D4×C67C2×C4semidirect
185. C4×D4×C67C2×C4semidirect
200. #117×C67C2×C4semidirect
201. #117×C67C2×C4semidirect
207. C2×C4⋊C4×C67C2×C4semidirect
208. C2×C4⋊C4×C67C2×C4semidirect
234. #11761612#41semidirect
254. C4×Dic67#41semidirect
539. C67#22506semidirect
542. #556Dic67semidirect
543. #555Dic67semidirect
544. #554Dic67semidirect
545. #553Dic67semidirect
546. #553Dic67semidirect
548. #552Dic67semidirect
549. #552Dic67semidirect
552. #547Dic67semidirect
617. C4⋊Q8C2×Dic67semidirect
618. C4⋊Q8C2×Dic67semidirect
628. #125C2×Dic67semidirect
629. #125C2×Dic67semidirect
648. C22⋊Q8C2×Dic67semidirect
649. C22⋊Q8C2×Dic67semidirect
655. #121C2×Dic67semidirect
656. #121C2×Dic67semidirect
662. C4×Q8C2×Dic67semidirect
663. C4×Q8C2×Dic67semidirect
677. C4×D4C2×Dic67semidirect
678. C4×D4C2×Dic67semidirect
695. #117C2×Dic67semidirect
696. #117C2×Dic67semidirect
704. C2×C4⋊C4C2×Dic67semidirect
705. C2×C4⋊C4C2×Dic67semidirect

Maximal subgroups

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

subgroupindex
D4×#117616122
#225626542
#225611912
#225611542
#225606582
#225606532
#225605122
#225603082
#225602292
#225600192
#225599182
C2×#168631552
C67×#34752
#2250667