Finite Group Databasebeta

← #30822877

Subgroups — #30822877

Order 17152.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22569334C211yesmaximal, characteristic, complemented
2#22568853C211yesmaximal, characteristic, complemented
3#22558682C211yesmaximal, characteristic, complemented
4#22558674C211yesmaximal, characteristic, complemented
5#22558669C211yesmaximal, characteristic, complemented
6#22558656C211yesmaximal, characteristic, complemented
7#22558643C211yesmaximal, characteristic, complemented
8#22558638C211yesmaximal, characteristic, complemented
9#22558622C211yesmaximal, characteristic, complemented
10#22558617C211yesmaximal, characteristic, complemented
11#22558612C211yesmaximal, characteristic, complemented
12#22558604C211yesmaximal, characteristic, complemented
13#22558596C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C67⋊C8)C211yesmaximal, characteristic, complemented
15C67×#3482C211yesmaximal, characteristic
16#16863527—21no—
17#16863468—21no—
18#16863468—21no—
19D4×C67⋊C8—21no—
20#16863457—21no—
21#16863457—21no—
22#16863453C2211yescharacteristic
23#16863453C2211yescharacteristic
24#16863449C2211yescharacteristic
25#16863449C2211yescharacteristic
26#16863449C2211yescharacteristic
27#16863449C2211yescharacteristic
28#16863449C2211yescharacteristic
29#16863423—21no—
30#16863420C2211yescharacteristic
31C2×C4⋊(C67⋊C8)C2211yescharacteristic
32C2×C4⋊(C67⋊C8)C2211yescharacteristic
33#16863363—21no—
34C4×#11761612C2211yescharacteristic
35C2×C4×C67⋊C8C2211yescharacteristic
36Q8⋊(C67⋊C8)C2211yescharacteristic
37Q8⋊(C67⋊C8)C2211yescharacteristic
38Q8⋊(C67⋊C8)C2211yescharacteristic
39Q8⋊(C67⋊C8)C2211yescharacteristic
40Q8⋊(C67⋊C8)C2211yescharacteristic
41Q8⋊(C67⋊C8)C2211yescharacteristic
42Q8⋊(C67⋊C8)C2211yescharacteristic
43Q8⋊(C67⋊C8)C2211yescharacteristic
44Q8⋊(C67⋊C8)C2211yescharacteristic
45Q8⋊(C67⋊C8)C2211yescharacteristic
46Q8⋊(C67⋊C8)C2211yescharacteristic
47Q8⋊(C67⋊C8)C2211yescharacteristic
48D4⋊(C67⋊C8)C2211yescharacteristic
49D4⋊(C67⋊C8)C2211yescharacteristic
50D4⋊(C67⋊C8)C2211yescharacteristic
51D4⋊(C67⋊C8)C2211yescharacteristic
52#557×C67C411yescharacteristic
53#556×C67—21no—
54#556×C67C411yescharacteristic
55#552×C67—21no—
56#552×C67—21no—
57#552×C67C411yescharacteristic
58#552×C67C411yescharacteristic
59D4×Q8×C67C411yescharacteristic
60#548×C67C411yescharacteristic
61#548×C67C411yescharacteristic
62#547×C67—21no—
63#547×C67C411yescharacteristic
64#533×C67—21no—
65#533×C67C2211yescharacteristic
66#529×C67—21no—
67#529×C67—21no—
68#529×C67C2211yescharacteristic
69#529×C67C2211yescharacteristic
70C4×#41×C67—21no—
71C4×#41×C67C2211yescharacteristic
72C4×#41×C67C2211yescharacteristic
73C2×C4×Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×#11761612—21no—
76C2×#11761612—21no—
77C22×C67⋊C8—21no—
78C22×C67⋊C8—21no—
79C22×C67⋊C8—21no—
80C4⋊(C67⋊C8)—21no—
81C4⋊(C67⋊C8)—21no—
82C4⋊(C67⋊C8)—21no—
83C4⋊(C67⋊C8)—21no—
84C4⋊(C67⋊C8)—21no—
85C4⋊(C67⋊C8)—21no—
86C4⋊(C67⋊C8)—21no—
87C4⋊(C67⋊C8)C2311yescharacteristic
88C4⋊(C67⋊C8)C2311yescharacteristic
89C4⋊(C67⋊C8)C2311yescharacteristic
90C4⋊(C67⋊C8)C2311yescharacteristic
91C22⋊(C67⋊C8)—21no—
92C22⋊(C67⋊C8)—21no—
93C22⋊(C67⋊C8)—21no—
94C22⋊(C67⋊C8)—21no—
95C22⋊(C67⋊C8)—21no—
96C22⋊(C67⋊C8)—21no—
97C22⋊(C67⋊C8)—21no—
98#14523954—21no—
99#14523954—21no—
100#14523954—21no—
101C4×C67⋊C8—21no—
102C4×C67⋊C8—21no—
103C4×C67⋊C8C2311yescharacteristic
104C4×C67⋊C8C2311yescharacteristic
105C4×C67⋊C8C2311yescharacteristic
106C4×C67⋊C8C2311yescharacteristic
107C2×#41×C67—21no—
108C2×#41×C67C2×C411yescharacteristic
109C2×#41×C67D411yescharacteristic
110C22×Q8×C67C2×C411yescharacteristic
111C22×Q8×C67C2×C411yescharacteristic
112C4⋊Q8×C67—21no—
113C4⋊Q8×C67—21no—
114C4⋊Q8×C67C2×C411yescharacteristic
115C4⋊Q8×C67C2×C411yescharacteristic
116#126×C67—21no—
117#126×C67—21no—
118#126×C67—21no—
119#126×C67—21no—
120#126×C67—21no—
121#126×C67—21no—
122#125×C67—21no—
123#125×C67—21no—
124#125×C67—21no—
125#125×C67—21no—
126#125×C67—21no—
127#125×C67C2×C411yescharacteristic
128#125×C67C2×C411yescharacteristic
129#124×C67—21no—
130#124×C67—21no—
131#124×C67C2×C411yescharacteristic
132#124×C67C2×C411yescharacteristic
133#123×C67—21no—
134#123×C67—21no—
135#123×C67—21no—
136#123×C67—21no—
137#123×C67—21no—
138#123×C67—21no—
139C22⋊Q8×C67—21no—
140C22⋊Q8×C67—21no—
141C22⋊Q8×C67—21no—
142C22⋊Q8×C67—21no—
143C22⋊Q8×C67—21no—
144C22⋊Q8×C67—21no—
145C22⋊Q8×C67—21no—
146C22⋊Q8×C67C2×C411yescharacteristic
147C22⋊Q8×C67C2×C411yescharacteristic
148C22⋊Q8×C67C2×C411yescharacteristic
149C22⋊Q8×C67C2×C411yescharacteristic
150#121×C67—21no—
151#121×C67—21no—
152#121×C67C2×C411yescharacteristic
153#121×C67C2×C411yescharacteristic
154C4×Q8×C67—21no—
155C4×Q8×C67—21no—
156C4×Q8×C67—21no—
157C4×Q8×C67—21no—
158C4×Q8×C67—21no—
159C4×Q8×C67—21no—
160C4×Q8×C67C2×C411yescharacteristic
161C4×Q8×C67C2×C411yescharacteristic
162C4×Q8×C67C2×C411yescharacteristic
163C4×Q8×C67C2×C411yescharacteristic
164C4×Q8×C67C2×C411yescharacteristic
165C4×Q8×C67C2×C411yescharacteristic
166C4×Q8×C67D411yescharacteristic
167C4×Q8×C67C2311yescharacteristic
168C4×Q8×C67C2311yescharacteristic
169C4×Q8×C67C2311yescharacteristic
170C4×D4×C67—21no—
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×C67C2×C411yescharacteristic
178C4×D4×C67C2×C411yescharacteristic
179C4×D4×C67C2×C411yescharacteristic
180C4×D4×C67C2×C411yescharacteristic
181C4×D4×C67D411yescharacteristic
182C4×D4×C67D411yescharacteristic
183C4×D4×C67D411yescharacteristic
184C4×D4×C67C2311yescharacteristic
185#117×C67—21no—
186#117×C67—21no—
187#117×C67—21no—
188#117×C67—21no—
189#117×C67—21no—
190#117×C67—21no—
191#117×C67—21no—
192#117×C67C2×C411yescharacteristic
193#117×C67D411yescharacteristic
194#117×C67D411yescharacteristic
195#117×C67D411yescharacteristic
196C2×C4⋊C4×C67—21no—
197C2×C4⋊C4×C67—21no—
198C2×C4⋊C4×C67C2×C411yescharacteristic
199C2×C4⋊C4×C67C2×C411yescharacteristic
200C2×C42×C67—21no—
201C2×C42×C67—21no—
202C2×C42×C67—21no—
203C2×C42×C67C2311yescharacteristic
204C2×C42×C67C2311yescharacteristic
205C2×C42×C67C2311yescharacteristic
206#11761612—42no—
207#11761612—81no—
208C2×C67⋊C8—21no—
209C2×C67⋊C8—21no—
210C2×C67⋊C8—21no—
211C2×C67⋊C8—21no—
212C2×C67⋊C8—21no—
213C2×C67⋊C8—21no—
214C2×C67⋊C8—21no—
215C2×C67⋊C8—21no—
216C2×C67⋊C8—42no—
217C2×C67⋊C8—81no—
218C2×C67⋊C8—81no—
219#41×C67—22no—
220#41×C67—42no—
221#41×C67—41no—
222#41×C67—44no—
223C2×Q8×C67—21no—
224C2×Q8×C67—21no—
225C2×Q8×C67—21no—
226C2×Q8×C67—22no—
227C2×Q8×C67—22no—
228C2×Q8×C67—41no—
229C2×Q8×C67—41no—
230C2×Q8×C67C22⋊C411yescharacteristic
231C2×Q8×C67C22×C411yescharacteristic
232C2×Q8×C67C22×C411yescharacteristic
233C2×Q8×C67C22×C411yescharacteristic
234C2×D4×C67—21no—
235C2×D4×C67—21no—
236C2×D4×C67—21no—
237C2×D4×C67C22⋊C411yescharacteristic
238C2×D4×C67C22⋊C411yescharacteristic
239C2×D4×C67C22⋊C411yescharacteristic
240C2×D4×C67C22×C411yescharacteristic
241C22×C4×C67—21no—
242C22×C4×C67—21no—
243C22×C4×C67—21no—
244C22×C4×C67—21no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—21no—
248C22×C4×C67C22×C411yescharacteristic
249C22×C4×C67C22×C411yescharacteristic
250C22×C4×C67C22×C411yescharacteristic
251C22×C4×C67C2×D411yescharacteristic
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2×D411yescharacteristic
255C22×C4×C67C2×D411yescharacteristic
256C22×C4×C67C2×D411yescharacteristic
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—21no—
260C4⋊C4×C67—21no—
261C4⋊C4×C67—21no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67—21no—
267C4⋊C4×C67—21no—
268C4⋊C4×C67—21no—
269C4⋊C4×C67—21no—
270C4⋊C4×C67—21no—
271C4⋊C4×C67—21no—
272C4⋊C4×C67—21no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67—21no—
275C4⋊C4×C67—21no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67C22⋊C411yescharacteristic
279C4⋊C4×C67C22⋊C411yescharacteristic
280C4⋊C4×C67C22⋊C411yescharacteristic
281C4⋊C4×C67C22⋊C411yescharacteristic
282C4⋊C4×C67C22⋊C411yescharacteristic
283C4⋊C4×C67C22⋊C411yescharacteristic
284C4⋊C4×C67C22×C411yescharacteristic
285C4⋊C4×C67C22×C411yescharacteristic
286C4⋊C4×C67C22×C411yescharacteristic
287C4⋊C4×C67C22×C411yescharacteristic
288C22⋊C4×C67—21no—
289C22⋊C4×C67—21no—
290C22⋊C4×C67—21no—
291C22⋊C4×C67—21no—
292C22⋊C4×C67—21no—
293C22⋊C4×C67—21no—
294C22⋊C4×C67—21no—
295C22⋊C4×C67—21no—
296C22⋊C4×C67—21no—
297C22⋊C4×C67—21no—
298C22⋊C4×C67—21no—
299C22⋊C4×C67—21no—
300C22⋊C4×C67—21no—
301C22⋊C4×C67C22⋊C411yescharacteristic
302C22⋊C4×C67C22⋊C411yescharacteristic
303C22⋊C4×C67C22⋊C411yescharacteristic
304C22⋊C4×C67C22⋊C411yescharacteristic
305C22⋊C4×C67C22⋊C411yescharacteristic
306C22⋊C4×C67C22⋊C411yescharacteristic
307C42×C67—21no—
308C42×C67—21no—
309C42×C67—21no—
310C42×C67—21no—
311C42×C67—21no—
312C42×C67—21no—
313C42×C67—21no—
314C42×C67—21no—
315C42×C67—21no—
316C42×C67C22×C411yescharacteristic
317C42×C67C22×C411yescharacteristic
318C42×C67C22×C411yescharacteristic
319C42×C67C2×D411yescharacteristic
320C42×C67C2×D411yescharacteristic
321C42×C67C2×D411yescharacteristic
322C42×C67C2×D411yescharacteristic
323C42×C67C2×D411yescharacteristic
324C42×C67C2×D411yescharacteristic
325C42×C67C2411yescharacteristic
326C23×C67—21no—
327C23×C67C2×C22⋊C411yescharacteristic
328C23×C67C2×C22⋊C411yescharacteristic
329C23×C67C2×C22⋊C411yescharacteristic
330Q8×C67—21no—
331Q8×C67—21no—
332Q8×C67—21no—
333Q8×C67—21no—
334Q8×C67—21no—
335Q8×C67—41no—
336Q8×C67—42no—
337Q8×C67—42no—
338Q8×C67—42no—
339Q8×C67#13112yes—
340D4×C67—22no—
341D4×C67—22no—
342D4×C67—21no—
343D4×C67—21no—
344D4×C67—41no—
345D4×C67—42no—
346D4×C67—42no—
347D4×C67—42no—
348C2×C4×C67—21no—
349C2×C4×C67—22no—
350C2×C4×C67—21no—
351C2×C4×C67—21no—
352C2×C4×C67—21no—
353C2×C4×C67—21no—
354C2×C4×C67—21no—
355C2×C4×C67—21no—
356C2×C4×C67—21no—
357C2×C4×C67—21no—
358C2×C4×C67—21no—
359C2×C4×C67—21no—
360C2×C4×C67—21no—
361C2×C4×C67—21no—
362C2×C4×C67—21no—
363C2×C4×C67—21no—
364C2×C4×C67—21no—
365C2×C4×C67—21no—
366C2×C4×C67—21no—
367C2×C4×C67—21no—
368C2×C4×C67—41no—
369C2×C4×C67—41no—
370C2×C4×C67—42no—
371C2×C4×C67—42no—
372C2×C4×C67—42no—
373C2×C4×C67—42no—
374C2×C4×C67—42no—
375C2×C4×C67—42no—
376C2×C4×C67—41no—
377C2×C4×C67—41no—
378C2×C4×C67C2×C22⋊C411yescharacteristic
379C2×C4×C67C2×C22⋊C411yescharacteristic
380C2×C4×C67C2×C22⋊C411yescharacteristic
381C2×C4×C67C2×C22⋊C411yescharacteristic
382C2×C4×C67C2×C22⋊C411yescharacteristic
383C2×C4×C67C2×C22⋊C411yescharacteristic
384C2×C4×C67C2×C22⋊C411yescharacteristic
385C2×C4×C67C2×C22⋊C411yescharacteristic
386C2×C4×C67C2×C22⋊C411yescharacteristic
387C2×C4×C67C23×C411yescharacteristic
388C2×C4×C67C22×D411yescharacteristic
389C2×C4×C67C22×D411yescharacteristic
390C67⋊C8—41no—
391C67⋊C8—41no—
392C67⋊C8—41no—
393C67⋊C8—41no—
394C67⋊C8—41no—
395C67⋊C8—41no—
396C67⋊C8—41no—
397C67⋊C8—41no—
398C22×C67—21no—
399C22×C67—21no—
400C22×C67—21no—
401C22×C67—21no—
402C22×C67—21no—
403C22×C67—21no—
404C22×C67—21no—
405C22×C67—21no—
406C22×C67—41no—
407C22×C67—41no—
408C22×C67—41no—
409C22×C67#42112yes—
410C22×C67C22×C22⋊C411yescharacteristic
411C4×C67—21no—
412C4×C67—21no—
413C4×C67—21no—
414C4×C67—22no—
415C4×C67—21no—
416C4×C67—21no—
417C4×C67—21no—
418C4×C67—21no—
419C4×C67—21no—
420C4×C67—21no—
421C4×C67—21no—
422C4×C67—41no—
423C4×C67—41no—
424C4×C67—41no—
425C4×C67—41no—
426C4×C67—41no—
427C4×C67—41no—
428C4×C67C2×#13111yescharacteristic
429C4×C67#56811yescharacteristic
430C4×C67#57711yescharacteristic
431C4×C67#57811yescharacteristic
432#17524—671nomaximal, Sylow
433C2×C67—22no—
434C2×C67—41no—
435C2×C67—41no—
436C2×C67—81no—
437C2×C67#288011yescharacteristic
438C2×C67#289811yescharacteristic
439C2×C67C2×#42111yescharacteristic
440#3482D6711yescharacteristic
441#2990—671no—
442#2922—671no—
443#1497—671no—
444#1495—671no—
445#1494—671no—
446#1491—671no—
447#1488—671no—
448#1487—671no—
449#1483—671no—
450#1482—671no—
451#1481—671no—
452#1479—671no—
453#1477—671no—
454C2×Q8⋊C8—671no—
455C67#1752411yescharacteristic, complemented, Sylow
456#557Dic6711yescharacteristic
457#556—21no—
458#556Dic6711yescharacteristic
459#552—21no—
460#552—21no—
461#552Dic6711yescharacteristic
462#552Dic6711yescharacteristic
463D4×Q8Dic6711yescharacteristic
464#548Dic6711yescharacteristic
465#548Dic6711yescharacteristic
466#547—21no—
467#547Dic6711yescharacteristic
468#533—21no—
469#533C2×D6711yescharacteristic
470#529—21no—
471#529—21no—
472#529C2×D6711yescharacteristic
473#529C2×D6711yescharacteristic
474C4×#41—21no—
475C4×#41C2×D6711yescharacteristic
476C4×#41C2×D6711yescharacteristic
477C2×C4×Q8C2×D6711yescharacteristic
478C2×C4×Q8C2×D6711yescharacteristic
479#446—1341no—
480#435—1341no—
481#435—1341no—
482C8×D4—1341no—
483#433—1341no—
484#433—1341no—
485#432—671no—
486#432—671no—
487#431—671no—
488#431—671no—
489#431—671no—
490#431—671no—
491#431—671no—
492#424—1341no—
493#423—671no—
494C2×C4⋊C8—671no—
495C2×C4⋊C8—671no—
496#408—1341no—
497C4×M16—671no—
498C2×C4×C8—671no—
499Q8⋊C8—671no—
500Q8⋊C8—671no—
501Q8⋊C8—671no—
502Q8⋊C8—671no—
503Q8⋊C8—671no—
504Q8⋊C8—671no—
505Q8⋊C8—671no—
506Q8⋊C8—671no—
507Q8⋊C8—671no—
508Q8⋊C8—671no—
509Q8⋊C8—671no—
510Q8⋊C8—671no—
511D4⋊C8—671no—
512D4⋊C8—671no—
513D4⋊C8—671no—
514D4⋊C8—671no—
515C2×#41—21no—
516C2×#41C2×Dic6711yescharacteristic
517C2×#41C22⋊D6711yescharacteristic
518C22×Q8C2×Dic6711yescharacteristic
519C22×Q8C2×Dic6711yescharacteristic
520C2×M16—1341no—
521C2×M16—1341no—
522C22×C8—1341no—
523C22×C8—1341no—
524C22×C8—1341no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×Dic6711yescharacteristic
528C4⋊Q8C2×Dic6711yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×Dic6711yescharacteristic
541#125C2×Dic6711yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×Dic6711yescharacteristic
545#124C2×Dic6711yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×Dic6711yescharacteristic
560C22⋊Q8C2×Dic6711yescharacteristic
561C22⋊Q8C2×Dic6711yescharacteristic
562C22⋊Q8C2×Dic6711yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×Dic6711yescharacteristic
566#121C2×Dic6711yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×Dic6711yescharacteristic
574C4×Q8C2×Dic6711yescharacteristic
575C4×Q8C2×Dic6711yescharacteristic
576C4×Q8C2×Dic6711yescharacteristic
577C4×Q8C2×Dic6711yescharacteristic
578C4×Q8C2×Dic6711yescharacteristic
579C4×Q8C22⋊D6711yescharacteristic
580C4×Q8C22×D6711yescharacteristic
581C4×Q8C22×D6711yescharacteristic
582C4×Q8C22×D6711yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×Dic6711yescharacteristic
591C4×D4C2×Dic6711yescharacteristic
592C4×D4C2×Dic6711yescharacteristic
593C4×D4C2×Dic6711yescharacteristic
594C4×D4C22⋊D6711yescharacteristic
595C4×D4C22⋊D6711yescharacteristic
596C4×D4C22⋊D6711yescharacteristic
597C4×D4C22×D6711yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×Dic6711yescharacteristic
606#117C22⋊D6711yescharacteristic
607#117C22⋊D6711yescharacteristic
608#117C22⋊D6711yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×Dic6711yescharacteristic
612C2×C4⋊C4C2×Dic6711yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C22×D6711yescharacteristic
617C2×C42C22×D6711yescharacteristic
618C2×C42C22×D6711yescharacteristic
619C4⋊C8—671no—
620C4⋊C8—671no—
621C4⋊C8—671no—
622C4⋊C8—671no—
623C4⋊C8—1341no—
624C4⋊C8—1341no—
625C4⋊C8—1341no—
626C4⋊C8—1341no—
627C4⋊C8—1341no—
628C4⋊C8—1341no—
629C4⋊C8—1341no—
630C22⋊C8—1341no—
631C22⋊C8—1341no—
632C22⋊C8—1341no—
633C22⋊C8—1341no—
634C22⋊C8—1341no—
635C22⋊C8—1341no—
636C22⋊C8—1341no—
637#97—1341no—
638#97—1341no—
639#97—1341no—
640C4×C8—671no—
641C4×C8—671no—
642C4×C8—671no—
643C4×C8—671no—
644C4×C8—1341no—
645C4×C8—1341no—
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊Dic6711yescharacteristic
658C2×Q8C22×Dic6711yescharacteristic
659C2×Q8C22×Dic6711yescharacteristic
660C2×Q8C22×Dic6711yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊Dic6711yescharacteristic
665C2×D4C22⋊Dic6711yescharacteristic
666C2×D4C22⋊Dic6711yescharacteristic
667C2×D4C22×Dic6711yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×Dic6711yescharacteristic
676C22×C4C22×Dic6711yescharacteristic
677C22×C4C22×Dic6711yescharacteristic
678C22×C4C2×C22⋊D6711yescharacteristic
679C22×C4C2×C22⋊D6711yescharacteristic
680C22×C4C2×C22⋊D6711yescharacteristic
681C22×C4C2×C22⋊D6711yescharacteristic
682C22×C4C2×C22⋊D6711yescharacteristic
683C22×C4C2×C22⋊D6711yescharacteristic
684M16—2682no—
685M16—5361no—
686C2×C8—2682no—
687C2×C8—5361no—
688C2×C8—5361no—
689C2×C8—1341no—
690C2×C8—1341no—
691C2×C8—1341no—
692C2×C8—1341no—
693C2×C8—1341no—
694C2×C8—1341no—
695C2×C8—1341no—
696C2×C8—1341no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊Dic6711yescharacteristic
719C4⋊C4C22⋊Dic6711yescharacteristic
720C4⋊C4C22⋊Dic6711yescharacteristic
721C4⋊C4C22⋊Dic6711yescharacteristic
722C4⋊C4C22⋊Dic6711yescharacteristic
723C4⋊C4C22⋊Dic6711yescharacteristic
724C4⋊C4C22×Dic6711yescharacteristic
725C4⋊C4C22×Dic6711yescharacteristic
726C4⋊C4C22×Dic6711yescharacteristic
727C4⋊C4C22×Dic6711yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4C22⋊Dic6711yescharacteristic
742C22⋊C4C22⋊Dic6711yescharacteristic
743C22⋊C4C22⋊Dic6711yescharacteristic
744C22⋊C4C22⋊Dic6711yescharacteristic
745C22⋊C4C22⋊Dic6711yescharacteristic
746C22⋊C4C22⋊Dic6711yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×Dic6711yescharacteristic
757C42C22×Dic6711yescharacteristic
758C42C22×Dic6711yescharacteristic
759C42C2×C22⋊D6711yescharacteristic
760C42C2×C22⋊D6711yescharacteristic
761C42C2×C22⋊D6711yescharacteristic
762C42C2×C22⋊D6711yescharacteristic
763C42C2×C22⋊D6711yescharacteristic
764C42C2×C22⋊D6711yescharacteristic
765C42C23×D6711yescharacteristic
766C23—21no—
767C23C2×C22⋊Dic6711yescharacteristic
768C23C2×C22⋊Dic6711yescharacteristic
769C23C2×C22⋊Dic6711yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#1452405012yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊Dic6711yescharacteristic
819C2×C4C2×C22⋊Dic6711yescharacteristic
820C2×C4C2×C22⋊Dic6711yescharacteristic
821C2×C4C2×C22⋊Dic6711yescharacteristic
822C2×C4C2×C22⋊Dic6711yescharacteristic
823C2×C4C2×C22⋊Dic6711yescharacteristic
824C2×C4C2×C22⋊Dic6711yescharacteristic
825C2×C4C2×C22⋊Dic6711yescharacteristic
826C2×C4C2×C22⋊Dic6711yescharacteristic
827C2×C4C23×Dic6711yescharacteristic
828C2×C4C22×C22⋊D6711yescharacteristic
829C2×C4C22×C22⋊D6711yescharacteristic
830C8—2681no—
831C8—2681no—
832C8—2681no—
833C8—2681no—
834C8—2681no—
835C8—2681no—
836C8—2681no—
837C8—2681no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#1686341312yes—
850C22C22×C22⋊Dic6711yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#1452405011yescharacteristic
869C4#1686416311yescharacteristic
870C4#1686420411yescharacteristic
871C4#1686421111yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2#2256865811yescharacteristic
877C2#2256874211yescharacteristic
878C2C2×#1686341311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC42C23×D67
Fitting, prime radicalC67×#3482C2
socleC22×C67C22×C22⋊C4
cosocleC42×C67C24
hypercenter#3482D67
hypocenterC67#17524
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #22569334C2semidirect
2. #22568853C2semidirect
3. #22558682C2semidirect
4. #22558674C2semidirect
5. #22558669C2semidirect
6. #22558656C2semidirect
7. #22558643C2semidirect
8. #22558638C2semidirect
9. #22558622C2semidirect
10. #22558617C2semidirect
11. #22558612C2semidirect
12. #22558604C2semidirect
13. #22558596C2semidirect
14. C2×Q8⋊(C67⋊C8)C2semidirect
455. C67#17524semidirect

Maximal subgroups

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

subgroupindex
#225693342
#225688532
#225586822
#225586742
#225586692
#225586562
#225586432
#225586382
#225586222
#225586172
#225586122
#225586042
#225585962
C2×Q8⋊(C67⋊C8)2
C67×#34822
#1752467