Finite Group Databasebeta

← C2×#22570408 #31724078

Subgroups — C2×#22570408 #31724078

Order 17152.

2198 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864001C211yesmaximal, characteristic, complemented
2#22570408C2116yesmaximal, direct product factor
3C2×#16863714C211yesmaximal, characteristic, complemented
4C2×#16863709C211yesmaximal, characteristic, complemented
5C2×#16863703C211yesmaximal, characteristic, complemented
6C2×#16863696C211yesmaximal, characteristic, complemented
7C2×#16863596C211yesmaximal, characteristic, complemented
8C2×#16863591C211yesmaximal, characteristic, complemented
9C2×#16863541C211yesmaximal, characteristic, complemented
10C2×#16863541C211yesmaximal, characteristic, complemented
11C2×#16863506C211yesmaximal, characteristic, complemented
12C2×#16863494C211yesmaximal, characteristic, complemented
13C2×C4×#11761615C211yesmaximal, characteristic, complemented
14C2×C4×#11761613C211yesmaximal, characteristic, complemented
15C2×#16863457C211yesmaximal, characteristic, complemented
16C2×#520×C67C211yesmaximal, characteristic, complemented
17C22×#11761615C2211yescharacteristic
18C22×#11761615C2211yescharacteristic
19C22×#11761613C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21#16864001—24no—
22#16864001C2218yescomplemented
23C2×#14524040C2211yescharacteristic
24C2×#14524035C2211yescharacteristic
25C2×#14524028—21no—
26C2×#14524028—21no—
27C2×#14524017C2211yescharacteristic
28C2×#14524017C2211yescharacteristic
29C2×#14524016—21no—
30C2×#14524016—21no—
31C2×C4×D268C2211yescharacteristic
32C2×C4×D268C2211yescharacteristic
33#16863714C2218yescomplemented
34#16863709C2218yescomplemented
35#16863703C2218yescomplemented
36#16863696C2218yescomplemented
37#16863596C2218yescomplemented
38#16863591C2218yescomplemented
39#16863541C2218yescomplemented
40#16863541C2218yescomplemented
41#16863506C2218yescomplemented
42#16863494C2218yescomplemented
43C4×#11761615C2218yescomplemented
44C4×#11761613C2218yescomplemented
45#16863457C2218yescomplemented
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523964C2211yescharacteristic
55C2×#14523964C2211yescharacteristic
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64C22×#41×C67C2211yescharacteristic
65#520×C67—24no—
66#520×C67C2218yescomplemented
67C2×C4×Q8×C67C2211yescharacteristic
68C2×C4×Q8×C67C2211yescharacteristic
69C2×C4×D4×C67—21no—
70C2×C4×D4×C67—21no—
71C2×C4×D4×C67C2211yescharacteristic
72C2×C4×D4×C67C2211yescharacteristic
73C2×#117×C67—21no—
74C2×#117×C67C2211yescharacteristic
75C22×C4⋊C4×C67—21no—
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×D268—21no—
78C22×D268—21no—
79C22×D268C2311yescharacteristic
80C22×D268C2311yescharacteristic
81C22×C22⋊D67—21no—
82C22×C22⋊D67—21no—
83C22×C4×D67—21no—
84C22×C4×D67—21no—
85C2×#11761615—24no—
86C2×#11761615—24no—
87C2×#11761615C2314yes—
88C2×#11761615C2314yes—
89C2×#11761613—24no—
90C2×#11761613—24no—
91C2×#11761613C2314yes—
92C2×#11761613C2314yes—
93C22×C67⋊C8C2311yescharacteristic
94C22×C67⋊C8C2311yescharacteristic
95C22×C67⋊C8C2311yescharacteristic
96C22×C67⋊C8C2311yescharacteristic
97#14524040—22no—
98#14524040C2314yes—
99#14524035—22no—
100#14524035C2314yes—
101#14524028—28no—
102#14524028—28no—
103#14524017—22no—
104#14524017—22no—
105#14524017C2314yes—
106#14524017C2314yes—
107#14524016—28no—
108#14524016—28no—
109C4×D268—22no—
110C4×D268—22no—
111C4×D268C2314yes—
112C4×D268C2314yes—
113C2×C4⋊Dic67C2311yescharacteristic
114C2×C4⋊Dic67C2311yescharacteristic
115C2×Dic67⋊C4—21no—
116C2×Dic67⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×(C2×D67)⋊C4—21no—
119C2×(C2×D67)⋊C4—21no—
120C2×(C2×D67)⋊C4—21no—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125C4⋊(C67⋊C8)C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523964C2314yes—
130#14523964C2314yes—
131#14523963C2314yes—
132#14523963C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C4×C67⋊C8C2314yes—
139C2×#41×C67—24no—
140C2×#41×C67—24no—
141C2×#41×C67—22no—
142C2×#41×C67C2314yes—
143C22×Q8×C67C2311yescharacteristic
144C22×D4×C67—21no—
145C22×D4×C67C2311yescharacteristic
146C23×C4×C67—21no—
147C23×C4×C67—21no—
148C23×C4×C67—21no—
149C23×C4×C67—21no—
150C23×C4×C67C2311yescharacteristic
151C4×Q8×C67—22no—
152C4×Q8×C67—22no—
153C4×Q8×C67C2314yes—
154C4×Q8×C67C2314yes—
155C4×D4×C67—28no—
156C4×D4×C67—28no—
157C4×D4×C67—22no—
158C4×D4×C67—22no—
159C4×D4×C67C2314yes—
160C4×D4×C67C2314yes—
161#117×C67—28no—
162#117×C67D414yes—
163#117×C67C2314yes—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67—22no—
168C2×C4⋊C4×C67—28no—
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67D411yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C4⋊C4×C67C2314yes—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C42×C67—21no—
179C2×C42×C67—21no—
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2311yescharacteristic
182C23×D67—21no—
183C23×D67—21no—
184C2×D268—22no—
185C2×D268—22no—
186C2×D268—22no—
187C2×D268—22no—
188C2×D268—21no—
189C2×D268—21no—
190C2×D268—24no—
191C2×D268—24no—
192C2×D268—82no—
193C2×D268—82no—
194C2×D268C2412yes—
195C2×D268C2412yes—
196C2×C22⋊D67—24no—
197C2×C22⋊D67—24no—
198C2×C22⋊D67—82no—
199C2×C22⋊D67—82no—
200C22×Dic67—21no—
201C22×Dic67—21no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—82no—
205C2×C4×D67—82no—
206#11761615—28no—
207#11761615—28no—
208#11761613—28no—
209#11761613—28no—
210C2×C67⋊C8—22no—
211C2×C67⋊C8—22no—
212C2×C67⋊C8—22no—
213C2×C67⋊C8—22no—
214C2×C67⋊C8C2412yes—
215C2×C67⋊C8C2412yes—
216C2×C67⋊C8C2412yes—
217C2×C67⋊C8C2412yes—
218C4⋊Dic67—21no—
219C4⋊Dic67—21no—
220C4⋊Dic67C2412yes—
221C4⋊Dic67C2412yes—
222Dic67⋊C4—24no—
223Dic67⋊C4—24no—
224(C2×D67)⋊C4—24no—
225(C2×D67)⋊C4—24no—
226(C2×D67)⋊C4—24no—
227(C2×D67)⋊C4—24no—
228C24×C67—21no—
229C24×C67C2×D411yescharacteristic
230#41×C67—216no—
231#41×C67—28no—
232#41×C67—28no—
233C2×Q8×C67—21no—
234C2×Q8×C67—22no—
235C2×Q8×C67#4114yes—
236C2×Q8×C67C2412yes—
237C2×D4×C67—28no—
238C2×D4×C67—24no—
239C2×D4×C67—21no—
240C2×D4×C67—22no—
241C2×D4×C67#4114yes—
242C2×D4×C67C2412yes—
243C22×C4×C67—28no—
244C22×C4×C67—21no—
245C22×C4×C67—24no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—24no—
251C22×C4×C67—24no—
252C22×C4×C67—24no—
253C22×C4×C67—82no—
254C22×C4×C67—82no—
255C22×C4×C67—82no—
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2×D411yescharacteristic
261C22×C4×C67C2×D412yes—
262C22×C4×C67C2412yes—
263C22×C4×C67C2411yescharacteristic
264C4⋊C4×C67—24no—
265C4⋊C4×C67—24no—
266C4⋊C4×C67—24no—
267C4⋊C4×C67—21no—
268C4⋊C4×C67—21no—
269C4⋊C4×C67C2×D414yes—
270C4⋊C4×C67C2×D414yes—
271C4⋊C4×C67C2412yes—
272C4⋊C4×C67C2412yes—
273C22⋊C4×C67—24no—
274C22⋊C4×C67—24no—
275C22⋊C4×C67C2×D414yes—
276C22⋊C4×C67C2×D414yes—
277C42×C67—24no—
278C42×C67—24no—
279C42×C67C2×D412yes—
280C42×C67C2×D412yes—
281C42×C67C2412yes—
282C42×C67C2412yes—
283C23×C67—22no—
284C23×C67—24no—
285C23×C67—22no—
286C23×C67—22no—
287C23×C67—22no—
288C23×C67—42no—
289C23×C67—42no—
290C23×C67C22×D412yes—
291C23×C67C22×D411yescharacteristic
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—42no—
295C22×D67—42no—
296C22×D67—42no—
297C22×D67—42no—
298C22×D67—42no—
299C22×D67—42no—
300Q8×C67—24no—
301Q8×C67—22no—
302Q8×C67C2×#4114yes—
303D4×C67—216no—
304D4×C67—24no—
305D4×C67—22no—
306D4×C67C2×#4114yes—
307C2×C4×C67—216no—
308C2×C4×C67—22no—
309C2×C4×C67—24no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—24no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—42no—
321C2×C4×C67—42no—
322C2×C4×C67—84no—
323C2×C4×C67—84no—
324C2×C4×C67—84no—
325C2×C4×C67C22×D412yes—
326C2×C4×C67C22×D412yes—
327C2×C4×C67C22×D412yes—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D412yes—
330C2×C4×C67C22×D411yescharacteristic
331C2×C4×C67C2×#4112yes—
332C2×C4×C67C2×#4112yes—
333C2×C4×C67C2511yescharacteristic
334C22⋊D67—84no—
335C22⋊D67—84no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—42no—
339C2×Dic67—42no—
340D268—22no—
341D268—22no—
342D268—22no—
343D268—22no—
344D268—42no—
345D268—42no—
346D268—84no—
347D268—84no—
348C4×D67—84no—
349C4×D67—84no—
350C67⋊C8—22no—
351C67⋊C8—22no—
352C67⋊C8—22no—
353C67⋊C8—22no—
354C22×C67—22no—
355C22×C67—24no—
356C22×C67—22no—
357C22×C67—22no—
358C22×C67—44no—
359C22×C67—48no—
360C22×C67—42no—
361C22×C67—42no—
362C22×C67#52512yes—
363C22×C67#57612yes—
364C22×C67#57712yes—
365C22×C67C23×D411yescharacteristic
366C2×D67—42no—
367C2×D67—42no—
368C2×D67—42no—
369C2×D67—42no—
370C2×D67—42no—
371C2×D67—42no—
372C2×D67—84no—
373C2×D67—84no—
374C4×C67—22no—
375C4×C67—24no—
376C4×C67—22no—
377C4×C67—22no—
378C4×C67—22no—
379C4×C67—22no—
380C4×C67—42no—
381C4×C67—42no—
382C4×C67#52512yes—
383C4×C67C22×#4111yescharacteristic
384C4×C67C22×#4111yescharacteristic
385Dic67—42no—
386Dic67—42no—
387C2×#3119—671nomaximal, Sylow
388C2×C67—42no—
389C2×C67—44no—
390C2×C67#311914yescomplemented
391C2×C67C2×#52511yescharacteristic
392C2×C67C2×#57611yescharacteristic
393C2×C67C2×#57711yescharacteristic
394D67—82no—
395D67—82no—
396C2×#540—671no—
397C2×#520D6711yescharacteristic, complemented
398#3119—6716no—
399C2×#481—671no—
400C2×#480—671no—
401C2×#479—671no—
402C2×#478—671no—
403C2×#460—671no—
404C2×#459—671no—
405C2×#449—671no—
406C2×#449—671no—
407C2×#442—671no—
408C2×#440—671no—
409C2×C4×SD16—671no—
410C2×C4×D8—671no—
411C2×#433—671no—
412C67C2×#311911yescharacteristic, complemented, Sylow
413C22×#41C2×D6711yescharacteristic
414C22×SD16—671no—
415C22×SD16—671no—
416C22×D8—671no—
417C22×D8—671no—
418#540—678no—
419#540—1344no—
420C2×#127—671no—
421C2×#125—671no—
422C2×#123—1341no—
423C2×#123—1341no—
424C2×#121—671no—
425C2×#121—671no—
426C2×#121—1341no—
427C2×#121—1341no—
428#520—24no—
429#520C2×D6718yescomplemented
430C2×C4×Q8C2×D6711yescharacteristic
431C2×C4×Q8C2×D6711yescharacteristic
432C2×C4×D4—21no—
433C2×C4×D4—21no—
434C2×C4×D4—671no—
435C2×C4×D4—671no—
436C2×C4×D4C2×D6711yescharacteristic
437C2×C4×D4C2×D6711yescharacteristic
438C2×#117—21no—
439C2×#117C2×D6711yescharacteristic
440C22×C4⋊C4—21no—
441C22×C4⋊C4C2×D6711yescharacteristic
442#481—678no—
443#480—678no—
444#479—678no—
445#478—678no—
446#460—678no—
447#459—678no—
448#449—678no—
449#449—678no—
450#442—678no—
451#440—678no—
452C4×SD16—678no—
453C4×D8—678no—
454#433—678no—
455C2×#107—671no—
456C2×#107—671no—
457C2×#106—671no—
458C2×#106—671no—
459C2×C4⋊C8—671no—
460C2×C4⋊C8—671no—
461C2×#103—671no—
462C2×#103—671no—
463C2×#102—671no—
464C2×#102—671no—
465C2×#102—671no—
466C2×#102—671no—
467C2×#102—671no—
468C2×#102—671no—
469C2×C22⋊C8—671no—
470C2×C22⋊C8—671no—
471C2×#97—671no—
472C2×C4×C8—671no—
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—22no—
476C2×#41C22×D6714yes—
477C22×Q8C22×D6711yescharacteristic
478C22×D4—21no—
479C22×D4—671no—
480C22×D4—671no—
481C22×D4—1341no—
482C22×D4—1341no—
483C22×D4—1341no—
484C22×D4—1341no—
485C22×D4C22×D6711yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—1341no—
491C23×C4—1341no—
492C23×C4C22×D6711yescharacteristic
493C2×SD16—674no—
494C2×SD16—674no—
495C2×SD16—1344no—
496C2×SD16—1344no—
497C2×D8—674no—
498C2×D8—674no—
499C2×D8—1344no—
500C2×D8—1344no—
501C22×C8—671no—
502C22×C8—671no—
503C22×C8—671no—
504C22×C8—671no—
505#127—674no—
506#127—1342no—
507#125—674no—
508#125—1342no—
509#123—1348no—
510#123—1348no—
511#121—674no—
512#121—674no—
513#121—1342no—
514#121—1342no—
515#121—1348no—
516#121—1348no—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×Q8C22×D6714yes—
520C4×Q8C22×D6714yes—
521C4×D4—28no—
522C4×D4—28no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—674no—
526C4×D4—674no—
527C4×D4—1342no—
528C4×D4—1342no—
529C4×D4C22×D6714yes—
530C4×D4C22×D6714yes—
531#117—28no—
532#117C22⋊D6714yes—
533#117C22×D6714yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—671no—
540C2×C4⋊C4—671no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4C22⋊D6711yescharacteristic
544C2×C4⋊C4C22⋊D6711yescharacteristic
545C2×C4⋊C4C22×D6711yescharacteristic
546C2×C4⋊C4C22×D6711yescharacteristic
547C2×C4⋊C4C22×D6714yes—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—1341no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4C22⋊D6711yescharacteristic
555C2×C22⋊C4C22⋊D6711yescharacteristic
556C2×C42—21no—
557C2×C42—21no—
558C2×C42C22×D6711yescharacteristic
559C2×C42C22×D6711yescharacteristic
560#107—674no—
561#107—674no—
562#106—674no—
563#106—674no—
564C4⋊C8—674no—
565C4⋊C8—674no—
566#103—674no—
567#103—674no—
568#102—674no—
569#102—674no—
570#102—674no—
571#102—674no—
572#102—674no—
573#102—674no—
574C22⋊C8—674no—
575C22⋊C8—674no—
576#97—674no—
577C4×C8—674no—
578C24—21no—
579C24—1341no—
580C24—1341no—
581C24C2×C22⋊D6711yescharacteristic
582#41—216no—
583#41—28no—
584#41—28no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8#1176162814yes—
588C2×Q8C23×D6712yes—
589C2×D4—28no—
590C2×D4—24no—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—5362no—
594C2×D4—5362no—
595C2×D4—5362no—
596C2×D4—5362no—
597C2×D4—672no—
598C2×D4—672no—
599C2×D4—1344no—
600C2×D4—1344no—
601C2×D4—1341no—
602C2×D4—1341no—
603C2×D4—1344no—
604C2×D4—1344no—
605C2×D4—1342no—
606C2×D4—1342no—
607C2×D4—1342no—
608C2×D4—1342no—
609C2×D4#1176162814yes—
610C2×D4C23×D6712yes—
611C22×C4—28no—
612C22×C4—21no—
613C22×C4—24no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—82no—
622C22×C4—82no—
623C22×C4—82no—
624C22×C4—5362no—
625C22×C4—5362no—
626C22×C4—1341no—
627C22×C4—1341no—
628C22×C4—1344no—
629C22×C4—1344no—
630C22×C4C2×C22⋊D6712yes—
631C22×C4C2×C22⋊D6711yescharacteristic
632C22×C4C2×C22⋊D6711yescharacteristic
633C22×C4C2×C22⋊D6711yescharacteristic
634C22×C4C2×C22⋊D6711yescharacteristic
635C22×C4C2×C22⋊D6711yescharacteristic
636C22×C4C23×D6712yes—
637C22×C4C23×D6711yescharacteristic
638SD16—1348no—
639SD16—1348no—
640D8—1348no—
641D8—1348no—
642C2×C8—672no—
643C2×C8—672no—
644C2×C8—672no—
645C2×C8—672no—
646C2×C8—1342no—
647C2×C8—1342no—
648C2×C8—1342no—
649C2×C8—1342no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—672no—
656C4⋊C4—672no—
657C4⋊C4—1341no—
658C4⋊C4—1341no—
659C4⋊C4—1344no—
660C4⋊C4—1344no—
661C4⋊C4C2×C22⋊D6714yes—
662C4⋊C4C2×C22⋊D6714yes—
663C4⋊C4C23×D6712yes—
664C4⋊C4C23×D6712yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1344no—
668C22⋊C4—1344no—
669C22⋊C4—1344no—
670C22⋊C4—1344no—
671C22⋊C4C2×C22⋊D6714yes—
672C22⋊C4C2×C22⋊D6714yes—
673C42—24no—
674C42—24no—
675C42C2×C22⋊D6712yes—
676C42C2×C22⋊D6712yes—
677C42C23×D6712yes—
678C42C23×D6712yes—
679C23—22no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—42no—
685C23—42no—
686C23—2682no—
687C23—2682no—
688C23—2682no—
689C23—2682no—
690C23—2682no—
691C23—2682no—
692C23—1342no—
693C23—1342no—
694C23C22×C22⋊D6712yes—
695C23C22×C22⋊D6711yescharacteristic
696Q8—24no—
697Q8—22no—
698Q8C2×#1176162814yes—
699D4—216no—
700D4—24no—
701D4—22no—
702D4—2682no—
703D4—2682no—
704D4—5364no—
705D4—5364no—
706D4—5364no—
707D4—5364no—
708D4—1342no—
709D4—1342no—
710D4—1342no—
711D4—1342no—
712D4C2×#1176162814yes—
713C2×C4—216no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4—84no—
731C2×C4—2682no—
732C2×C4—2682no—
733C2×C4—5364no—
734C2×C4—5364no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4C22×C22⋊D6712yes—
738C2×C4C22×C22⋊D6712yes—
739C2×C4C22×C22⋊D6712yes—
740C2×C4C22×C22⋊D6712yes—
741C2×C4C22×C22⋊D6712yes—
742C2×C4C22×C22⋊D6711yescharacteristic
743C2×C4C2×#1176162812yes—
744C2×C4C2×#1176162812yes—
745C2×C4C24×D6711yescharacteristic
746C8—1342no—
747C8—1342no—
748C8—1342no—
749C8—1342no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—24no—
754C22—42no—
755C22—42no—
756C22—44no—
757C22—48no—
758C22—2682no—
759C22—2682no—
760C22—2682no—
761C22—2682no—
762C22—2682no—
763C22—2682no—
764C22—5364no—
765C22—5364no—
766C22#1686390712yes—
767C22#1686419912yes—
768C22#1686420412yes—
769C22C23×C22⋊D6711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—2682no—
779C4—2682no—
780C4#1686390712yes—
781C4C22×#1176162811yescharacteristic
782C4C22×#1176162811yescharacteristic
783C2—42no—
784C2—44no—
785C2—5362no—
786C2—5362no—
787C2#2257040814yesdirect product factor
788C2C2×#1686390711yescharacteristic
789C2C2×#1686419911yescharacteristic
790C2C2×#1686420411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#520×C67C2
socleC23×C67C22×D4
hypercenterC2×#520D67
hypocenterC67C2×#3119
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#16864001C2semidirect
2. #22570408C2direct (N × H)
3. C2×#16863714C2semidirect
4. C2×#16863709C2semidirect
5. C2×#16863703C2semidirect
6. C2×#16863696C2semidirect
7. C2×#16863596C2semidirect
8. C2×#16863591C2semidirect
9. C2×#16863541C2semidirect
10. C2×#16863541C2semidirect
11. C2×#16863506C2semidirect
12. C2×#16863494C2semidirect
13. C2×C4×#11761615C2semidirect
14. C2×C4×#11761613C2semidirect
15. C2×#16863457C2semidirect
16. C2×#520×C67C2semidirect
22. #16864001C22semidirect
33. #16863714C22semidirect
34. #16863709C22semidirect
35. #16863703C22semidirect
36. #16863696C22semidirect
37. #16863596C22semidirect
38. #16863591C22semidirect
39. #16863541C22semidirect
40. #16863541C22semidirect
41. #16863506C22semidirect
42. #16863494C22semidirect
43. C4×#11761615C22semidirect
44. C4×#11761613C22semidirect
45. #16863457C22semidirect
66. #520×C67C22semidirect
390. C2×C67#3119semidirect
397. C2×#520D67semidirect
412. C67C2×#3119semidirect
429. #520C2×D67semidirect
787. C2#22570408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640012
#225704082
C2×#168637142
C2×#168637092
C2×#168637032
C2×#168636962
C2×#168635962
C2×#168635912
C2×#168635412
C2×#168635062
C2×#168634942
C2×C4×#117616152
C2×C4×#117616132
C2×#168634572
C2×#520×C672
C2×#311967