Finite Group Databasebeta

← #30822679

Subgroups — #30822679

Order 17152.

890 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22569326C211yesmaximal, characteristic, complemented
2#22569176C211yesmaximal, characteristic, complemented
3#22558682C211yesmaximal, characteristic, complemented
4#22558674C211yesmaximal, characteristic, complemented
5#22558669C211yesmaximal, characteristic, complemented
6#22558664C211yesmaximal, characteristic, complemented
7#22558656C211yesmaximal, characteristic, complemented
8#22558648C211yesmaximal, characteristic, complemented
9#22558643C211yesmaximal, characteristic, complemented
10#22558638C211yesmaximal, characteristic, complemented
11#22558630C211yesmaximal, characteristic, complemented
12#22558622C211yesmaximal, characteristic, complemented
13#22558617C211yesmaximal, characteristic, complemented
14#22558612C211yesmaximal, characteristic, complemented
15C67×#3461C211yesmaximal, characteristic
16#16863527—21no—
17#16863527—21no—
18#16863474—21no—
19#16863474—21no—
20#16863468—21no—
21#16863468—21no—
22#16863468—21no—
23#16863468—21no—
24#16863453C2211yescharacteristic
25#16863453C2211yescharacteristic
26#16863449C2211yescharacteristic
27#16863449C2211yescharacteristic
28#16863449C2211yescharacteristic
29#16863449C2211yescharacteristic
30#16863420C2211yescharacteristic
31#16863420C2211yescharacteristic
32C2×C4⋊(C67⋊C8)C2211yescharacteristic
33C4×#11761612C2211yescharacteristic
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#544×C67C411yescharacteristic
53#542×C67—21no—
54#542×C67C411yescharacteristic
55#542×C67C411yescharacteristic
56#541×C67—21no—
57#541×C67C411yescharacteristic
58#541×C67C411yescharacteristic
59#539×C67—21no—
60#539×C67—21no—
61#537×C67C411yescharacteristic
62#536×C67C411yescharacteristic
63#536×C67C411yescharacteristic
64#533×C67—21no—
65#533×C67C2211yescharacteristic
66#533×C67C2211yescharacteristic
67#529×C67—21no—
68#529×C67—21no—
69#529×C67—21no—
70#529×C67C2211yescharacteristic
71#529×C67C2211yescharacteristic
72C4×#41×C67C2211yescharacteristic
73C4×#41×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×#11761612—21no—
76C2×#11761612—21no—
77C2×#11761612—21no—
78C2×#11761612—21no—
79C22×C67⋊C8—21no—
80C22×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—
97#14523954—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×C67C2×C411yescharacteristic
108C2×#41×C67C2×C411yescharacteristic
109C22×Q8×C67C2×C411yescharacteristic
110C4⋊Q8×C67—21no—
111C4⋊Q8×C67—21no—
112C4⋊Q8×C67C2×C411yescharacteristic
113C4⋊Q8×C67C2×C411yescharacteristic
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#126×C67—21no—
123#126×C67—21no—
124#125×C67—21no—
125#125×C67—21no—
126#125×C67—21no—
127#125×C67—21no—
128#125×C67—21no—
129#125×C67—21no—
130#125×C67—21no—
131#125×C67C2×C411yescharacteristic
132#125×C67C2×C411yescharacteristic
133#124×C67—21no—
134#124×C67—21no—
135#124×C67—21no—
136#124×C67C2×C411yescharacteristic
137#124×C67C2×C411yescharacteristic
138#123×C67—21no—
139#123×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—
146C22⋊Q8×C67—21no—
147C22⋊Q8×C67—21no—
148C22⋊Q8×C67—21no—
149C22⋊Q8×C67—21no—
150C22⋊Q8×C67—21no—
151C22⋊Q8×C67—21no—
152C22⋊Q8×C67—21no—
153C22⋊Q8×C67—21no—
154C22⋊Q8×C67—21no—
155C22⋊Q8×C67C2×C411yescharacteristic
156C22⋊Q8×C67C2×C411yescharacteristic
157C22⋊Q8×C67C2×C411yescharacteristic
158C22⋊Q8×C67C2×C411yescharacteristic
159C22⋊Q8×C67C2×C411yescharacteristic
160C22⋊Q8×C67C2×C411yescharacteristic
161#121×C67—21no—
162#121×C67—21no—
163#121×C67—21no—
164#121×C67C2×C411yescharacteristic
165#121×C67C2×C411yescharacteristic
166C4×Q8×C67—21no—
167C4×Q8×C67—21no—
168C4×Q8×C67—21no—
169C4×Q8×C67—21no—
170C4×Q8×C67C2×C411yescharacteristic
171C4×Q8×C67C2×C411yescharacteristic
172C4×Q8×C67C2×C411yescharacteristic
173C4×Q8×C67D411yescharacteristic
174C4×Q8×C67D411yescharacteristic
175C4×Q8×C67C2311yescharacteristic
176C4×Q8×C67C2311yescharacteristic
177C4×Q8×C67C2311yescharacteristic
178C4×D4×C67—21no—
179C4×D4×C67—21no—
180C4×D4×C67—21no—
181C4×D4×C67—21no—
182C4×D4×C67C2×C411yescharacteristic
183C4×D4×C67D411yescharacteristic
184C4×D4×C67D411yescharacteristic
185C4×D4×C67D411yescharacteristic
186C4×D4×C67D411yescharacteristic
187C4×D4×C67D411yescharacteristic
188C4×D4×C67D411yescharacteristic
189C4×D4×C67C2311yescharacteristic
190#117×C67—21no—
191#117×C67—21no—
192#117×C67—21no—
193#117×C67—21no—
194#117×C67—21no—
195#117×C67C2×C411yescharacteristic
196#117×C67C2×C411yescharacteristic
197#117×C67C2×C411yescharacteristic
198#117×C67C2×C411yescharacteristic
199C2×C4⋊C4×C67—21no—
200C2×C4⋊C4×C67C2×C411yescharacteristic
201C2×C42×C67—21no—
202C2×C42×C67—21no—
203C2×C42×C67C2311yescharacteristic
204C2×C42×C67C2311yescharacteristic
205C2×C42×C67C2311yescharacteristic
206#11761612—42no—
207#11761612—42no—
208#11761612—81no—
209#11761612—81no—
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—21no—
217C2×C67⋊C8—21no—
218C2×C67⋊C8—42no—
219C2×C67⋊C8—81no—
220#41×C67—42no—
221#41×C67—42no—
222C2×Q8×C67—21no—
223C2×Q8×C67—21no—
224C2×Q8×C67—21no—
225C2×Q8×C67—42no—
226C2×Q8×C67C22⋊C411yescharacteristic
227C2×Q8×C67C22×C411yescharacteristic
228C2×Q8×C67C22×C411yescharacteristic
229C2×Q8×C67C22×C411yescharacteristic
230C2×D4×C67—21no—
231C2×D4×C67—21no—
232C2×D4×C67—21no—
233C2×D4×C67C22⋊C411yescharacteristic
234C2×D4×C67C22⋊C411yescharacteristic
235C2×D4×C67C22⋊C411yescharacteristic
236C2×D4×C67C22×C411yescharacteristic
237C22×C4×C67—21no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—21no—
242C22×C4×C67C22×C411yescharacteristic
243C22×C4×C67C22×C411yescharacteristic
244C22×C4×C67C22×C411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—21no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
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×C67C22⋊C411yescharacteristic
275C4⋊C4×C67C22⋊C411yescharacteristic
276C4⋊C4×C67C22⋊C411yescharacteristic
277C4⋊C4×C67C22⋊C411yescharacteristic
278C4⋊C4×C67C22⋊C411yescharacteristic
279C4⋊C4×C67C22⋊C411yescharacteristic
280C4⋊C4×C67C22×C411yescharacteristic
281C4⋊C4×C67C22×C411yescharacteristic
282C4⋊C4×C67C22×C411yescharacteristic
283C4⋊C4×C67C22×C411yescharacteristic
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×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×C67C22⋊C411yescharacteristic
300C22⋊C4×C67C22⋊C411yescharacteristic
301C22⋊C4×C67C22⋊C411yescharacteristic
302C22⋊C4×C67C22⋊C411yescharacteristic
303C22⋊C4×C67C22⋊C411yescharacteristic
304C22⋊C4×C67C22⋊C411yescharacteristic
305C42×C67—21no—
306C42×C67—21no—
307C42×C67—21no—
308C42×C67—21no—
309C42×C67—21no—
310C42×C67—21no—
311C42×C67—21no—
312C42×C67C22×C411yescharacteristic
313C42×C67C22×C411yescharacteristic
314C42×C67C22×C411yescharacteristic
315C42×C67C2×D411yescharacteristic
316C42×C67C2×D411yescharacteristic
317C42×C67C2×D411yescharacteristic
318C42×C67C2×D411yescharacteristic
319C42×C67C2×D411yescharacteristic
320C42×C67C2×D411yescharacteristic
321C42×C67C2411yescharacteristic
322C23×C67—21no—
323C23×C67C2×C22⋊C411yescharacteristic
324C23×C67C2×C22⋊C411yescharacteristic
325C23×C67C2×C22⋊C411yescharacteristic
326Q8×C67—22no—
327Q8×C67—22no—
328Q8×C67—22no—
329Q8×C67—41no—
330Q8×C67—42no—
331Q8×C67—81no—
332Q8×C67—81no—
333D4×C67—22no—
334D4×C67—41no—
335D4×C67—41no—
336D4×C67—41no—
337D4×C67—42no—
338D4×C67—81no—
339D4×C67—81no—
340C2×C4×C67—22no—
341C2×C4×C67—22no—
342C2×C4×C67—22no—
343C2×C4×C67—21no—
344C2×C4×C67—21no—
345C2×C4×C67—21no—
346C2×C4×C67—21no—
347C2×C4×C67—21no—
348C2×C4×C67—21no—
349C2×C4×C67—21no—
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—41no—
357C2×C4×C67—41no—
358C2×C4×C67—41no—
359C2×C4×C67—42no—
360C2×C4×C67—42no—
361C2×C4×C67—41no—
362C2×C4×C67—41no—
363C2×C4×C67—81no—
364C2×C4×C67—81no—
365C2×C4×C67C2×C22⋊C411yescharacteristic
366C2×C4×C67C2×C22⋊C411yescharacteristic
367C2×C4×C67C2×C22⋊C411yescharacteristic
368C2×C4×C67C2×C22⋊C411yescharacteristic
369C2×C4×C67C2×C22⋊C411yescharacteristic
370C2×C4×C67C2×C22⋊C411yescharacteristic
371C2×C4×C67C2×C22⋊C411yescharacteristic
372C2×C4×C67C2×C22⋊C411yescharacteristic
373C2×C4×C67C2×C22⋊C411yescharacteristic
374C2×C4×C67C23×C411yescharacteristic
375C2×C4×C67C22×D411yescharacteristic
376C2×C4×C67C22×D411yescharacteristic
377C67⋊C8—22no—
378C67⋊C8—41no—
379C67⋊C8—41no—
380C67⋊C8—41no—
381C67⋊C8—41no—
382C67⋊C8—41no—
383C67⋊C8—41no—
384C67⋊C8—41no—
385C22×C67—21no—
386C22×C67—21no—
387C22×C67—21no—
388C22×C67—21no—
389C22×C67—21no—
390C22×C67—21no—
391C22×C67—21no—
392C22×C67—21no—
393C22×C67—21no—
394C22×C67—41no—
395C22×C67—41no—
396C22×C67—41no—
397C22×C67C22×C22⋊C411yescharacteristic
398C4×C67—21no—
399C4×C67—21no—
400C4×C67—21no—
401C4×C67—21no—
402C4×C67—21no—
403C4×C67—21no—
404C4×C67—21no—
405C4×C67—21no—
406C4×C67—21no—
407C4×C67—21no—
408C4×C67—41no—
409C4×C67—41no—
410C4×C67—41no—
411C4×C67—41no—
412C4×C67—41no—
413C4×C67—41no—
414C4×C67—41no—
415C4×C67#56812yes—
416C4×C67#57711yescharacteristic
417C4×C67#57811yescharacteristic
418#17506—671nomaximal, Sylow
419C2×C67—41no—
420C2×C67—41no—
421C2×C67—41no—
422C2×C67—81no—
423C2×C67#287911yescharacteristic
424C2×C67#289811yescharacteristic
425C2×C67#290111yescharacteristic
426#3461D6711yescharacteristic
427#2989—671no—
428#2965—671no—
429#1497—671no—
430#1495—671no—
431#1494—671no—
432#1493—671no—
433#1491—671no—
434#1489—671no—
435#1488—671no—
436#1487—671no—
437#1485—671no—
438#1483—671no—
439#1482—671no—
440#1481—671no—
441C67#1750611yescharacteristic, complemented, Sylow
442#544Dic6711yescharacteristic
443#542—21no—
444#542Dic6711yescharacteristic
445#542Dic6711yescharacteristic
446#541—21no—
447#541Dic6711yescharacteristic
448#541Dic6711yescharacteristic
449#539—21no—
450#539—21no—
451#537Dic6711yescharacteristic
452#536Dic6711yescharacteristic
453#536Dic6711yescharacteristic
454#533—21no—
455#533C2×D6711yescharacteristic
456#533C2×D6711yescharacteristic
457#529—21no—
458#529—21no—
459#529—21no—
460#529C2×D6711yescharacteristic
461#529C2×D6711yescharacteristic
462C4×#41C2×D6711yescharacteristic
463C4×#41C2×D6711yescharacteristic
464C2×C4×Q8C2×D6711yescharacteristic
465#446—1341no—
466#446—1341no—
467#436—1341no—
468#436—1341no—
469#435—1341no—
470#435—1341no—
471#435—1341no—
472#435—1341no—
473#432—671no—
474#432—671no—
475#431—671no—
476#431—671no—
477#431—671no—
478#431—671no—
479#423—671no—
480#423—671no—
481C2×C4⋊C8—671no—
482C4×M16—671no—
483C4×M16—671no—
484C2×C4×C8—671no—
485Q8⋊C8—671no—
486Q8⋊C8—671no—
487Q8⋊C8—671no—
488Q8⋊C8—671no—
489Q8⋊C8—671no—
490Q8⋊C8—671no—
491Q8⋊C8—671no—
492Q8⋊C8—671no—
493Q8⋊C8—671no—
494Q8⋊C8—671no—
495Q8⋊C8—671no—
496Q8⋊C8—671no—
497D4⋊C8—671no—
498D4⋊C8—671no—
499D4⋊C8—671no—
500D4⋊C8—671no—
501C2×#41C2×Dic6711yescharacteristic
502C2×#41C2×Dic6711yescharacteristic
503C22×Q8C2×Dic6711yescharacteristic
504C2×M16—1341no—
505C2×M16—1341no—
506C2×M16—1341no—
507C2×M16—1341no—
508C22×C8—1341no—
509C22×C8—1341no—
510C4⋊Q8—21no—
511C4⋊Q8—21no—
512C4⋊Q8C2×Dic6711yescharacteristic
513C4⋊Q8C2×Dic6711yescharacteristic
514C4⋊Q8C2×Dic6711yescharacteristic
515C4⋊Q8C2×Dic6711yescharacteristic
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#125—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125C2×Dic6711yescharacteristic
532#125C2×Dic6711yescharacteristic
533#124—21no—
534#124—21no—
535#124—21no—
536#124C2×Dic6711yescharacteristic
537#124C2×Dic6711yescharacteristic
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8C2×Dic6711yescharacteristic
556C22⋊Q8C2×Dic6711yescharacteristic
557C22⋊Q8C2×Dic6711yescharacteristic
558C22⋊Q8C2×Dic6711yescharacteristic
559C22⋊Q8C2×Dic6711yescharacteristic
560C22⋊Q8C2×Dic6711yescharacteristic
561#121—21no—
562#121—21no—
563#121—21no—
564#121C2×Dic6711yescharacteristic
565#121C2×Dic6711yescharacteristic
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8C2×Dic6711yescharacteristic
571C4×Q8C2×Dic6711yescharacteristic
572C4×Q8C2×Dic6711yescharacteristic
573C4×Q8C22⋊D6711yescharacteristic
574C4×Q8C22⋊D6711yescharacteristic
575C4×Q8C22×D6711yescharacteristic
576C4×Q8C22×D6711yescharacteristic
577C4×Q8C22×D6711yescharacteristic
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4C2×Dic6711yescharacteristic
583C4×D4C22⋊D6711yescharacteristic
584C4×D4C22⋊D6711yescharacteristic
585C4×D4C22⋊D6711yescharacteristic
586C4×D4C22⋊D6711yescharacteristic
587C4×D4C22⋊D6711yescharacteristic
588C4×D4C22⋊D6711yescharacteristic
589C4×D4C22×D6711yescharacteristic
590#117—21no—
591#117—21no—
592#117—21no—
593#117—21no—
594#117—21no—
595#117C2×Dic6711yescharacteristic
596#117C2×Dic6711yescharacteristic
597#117C2×Dic6711yescharacteristic
598#117C2×Dic6711yescharacteristic
599C2×C4⋊C4—21no—
600C2×C4⋊C4C2×Dic6711yescharacteristic
601C2×C42—21no—
602C2×C42—21no—
603C2×C42C22×D6711yescharacteristic
604C2×C42C22×D6711yescharacteristic
605C2×C42C22×D6711yescharacteristic
606C4⋊C8—671no—
607C4⋊C8—671no—
608C4⋊C8—671no—
609C4⋊C8—671no—
610C4⋊C8—1341no—
611C4⋊C8—1341no—
612C4⋊C8—1341no—
613C4⋊C8—1341no—
614C4⋊C8—1341no—
615C4⋊C8—1341no—
616C22⋊C8—1341no—
617C22⋊C8—1341no—
618C22⋊C8—1341no—
619C22⋊C8—1341no—
620C22⋊C8—1341no—
621C22⋊C8—1341no—
622#97—1341no—
623#97—1341no—
624#97—1341no—
625#97—1341no—
626C4×C8—671no—
627C4×C8—671no—
628C4×C8—671no—
629C4×C8—671no—
630C4×C8—1341no—
631C4×C8—1341no—
632#41—42no—
633#41—42no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—42no—
638C2×Q8C22⋊Dic6711yescharacteristic
639C2×Q8C22×Dic6711yescharacteristic
640C2×Q8C22×Dic6711yescharacteristic
641C2×Q8C22×Dic6711yescharacteristic
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4C22⋊Dic6711yescharacteristic
646C2×D4C22⋊Dic6711yescharacteristic
647C2×D4C22⋊Dic6711yescharacteristic
648C2×D4C22×Dic6711yescharacteristic
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4C22×Dic6711yescharacteristic
655C22×C4C22×Dic6711yescharacteristic
656C22×C4C22×Dic6711yescharacteristic
657C22×C4C2×C22⋊D6711yescharacteristic
658C22×C4C2×C22⋊D6711yescharacteristic
659C22×C4C2×C22⋊D6711yescharacteristic
660C22×C4C2×C22⋊D6711yescharacteristic
661C22×C4C2×C22⋊D6711yescharacteristic
662C22×C4C2×C22⋊D6711yescharacteristic
663M16—2682no—
664M16—2682no—
665M16—5361no—
666M16—5361no—
667C2×C8—2682no—
668C2×C8—5361no—
669C2×C8—1341no—
670C2×C8—1341no—
671C2×C8—1341no—
672C2×C8—1341no—
673C2×C8—1341no—
674C2×C8—1341no—
675C2×C8—1341no—
676C2×C8—1341no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4C22⋊Dic6711yescharacteristic
701C4⋊C4C22⋊Dic6711yescharacteristic
702C4⋊C4C22⋊Dic6711yescharacteristic
703C4⋊C4C22⋊Dic6711yescharacteristic
704C4⋊C4C22⋊Dic6711yescharacteristic
705C4⋊C4C22⋊Dic6711yescharacteristic
706C4⋊C4C22×Dic6711yescharacteristic
707C4⋊C4C22×Dic6711yescharacteristic
708C4⋊C4C22×Dic6711yescharacteristic
709C4⋊C4C22×Dic6711yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4C22⋊Dic6711yescharacteristic
726C22⋊C4C22⋊Dic6711yescharacteristic
727C22⋊C4C22⋊Dic6711yescharacteristic
728C22⋊C4C22⋊Dic6711yescharacteristic
729C22⋊C4C22⋊Dic6711yescharacteristic
730C22⋊C4C22⋊Dic6711yescharacteristic
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42C22×Dic6711yescharacteristic
739C42C22×Dic6711yescharacteristic
740C42C22×Dic6711yescharacteristic
741C42C2×C22⋊D6711yescharacteristic
742C42C2×C22⋊D6711yescharacteristic
743C42C2×C22⋊D6711yescharacteristic
744C42C2×C22⋊D6711yescharacteristic
745C42C2×C22⋊D6711yescharacteristic
746C42C2×C22⋊D6711yescharacteristic
747C42C23×D6711yescharacteristic
748C23—21no—
749C23C2×C22⋊Dic6711yescharacteristic
750C23C2×C22⋊Dic6711yescharacteristic
751C23C2×C22⋊Dic6711yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—22no—
755Q8—41no—
756Q8—42no—
757Q8—81no—
758Q8—81no—
759D4—22no—
760D4—41no—
761D4—41no—
762D4—41no—
763D4—42no—
764D4—81no—
765D4—81no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4C2×C22⋊Dic6711yescharacteristic
792C2×C4C2×C22⋊Dic6711yescharacteristic
793C2×C4C2×C22⋊Dic6711yescharacteristic
794C2×C4C2×C22⋊Dic6711yescharacteristic
795C2×C4C2×C22⋊Dic6711yescharacteristic
796C2×C4C2×C22⋊Dic6711yescharacteristic
797C2×C4C2×C22⋊Dic6711yescharacteristic
798C2×C4C2×C22⋊Dic6711yescharacteristic
799C2×C4C2×C22⋊Dic6711yescharacteristic
800C2×C4C23×Dic6711yescharacteristic
801C2×C4C22×C22⋊D6711yescharacteristic
802C2×C4C22×C22⋊D6711yescharacteristic
803C8—2681no—
804C8—2681no—
805C8—2681no—
806C8—2681no—
807C8—2681no—
808C8—2681no—
809C8—2681no—
810C8—1342no—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22C22×C22⋊Dic6711yescharacteristic
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—21no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4#1686416312yes—
842C4#1686420411yescharacteristic
843C4#1686421111yescharacteristic
844C2—41no—
845C2—41no—
846C2—41no—
847C2—81no—
848C2#2256865411yescharacteristic
849C2#2256874211yescharacteristic
850C2#2256875611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D67
commutatorC2×C4×C67C23×C4
FrattiniC42C23×D67
FittingC67×#3461C2
socleC22×C67C22×C22⋊C4
prime radical#537×C67C4
cosocleC42×C67C24
hypercenter#3461D67
hypocenterC67#17506
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3461

Complements

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

NH ≅ G/Ntype
1. #22569326C2semidirect
2. #22569176C2semidirect
3. #22558682C2semidirect
4. #22558674C2semidirect
5. #22558669C2semidirect
6. #22558664C2semidirect
7. #22558656C2semidirect
8. #22558648C2semidirect
9. #22558643C2semidirect
10. #22558638C2semidirect
11. #22558630C2semidirect
12. #22558622C2semidirect
13. #22558617C2semidirect
14. #22558612C2semidirect
441. C67#17506semidirect

Maximal subgroups

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

subgroupindex
#225693262
#225691762
#225586822
#225586742
#225586692
#225586642
#225586562
#225586482
#225586432
#225586382
#225586302
#225586222
#225586172
#225586122
C67×#34612
#1750667