Finite Group Databasebeta

← C2×#22570227 #31723846

Subgroups — C2×#22570227 #31723846

Order 17152.

2202 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863930C211yesmaximal, characteristic, complemented
2#22570227C2116yesmaximal, direct product factor
3C2×#16863737C211yesmaximal, characteristic, complemented
4C2×#16863720C211yesmaximal, characteristic, complemented
5C2×#16863703C211yesmaximal, characteristic, complemented
6C2×#16863696C211yesmaximal, characteristic, complemented
7C2×#16863618C211yesmaximal, characteristic, complemented
8C2×#16863611C211yesmaximal, characteristic, complemented
9C2×#16863558C211yesmaximal, characteristic, complemented
10C2×#16863541C211yesmaximal, characteristic
11C2×C4×#11761618C211yesmaximal, characteristic, complemented
12C2×C4×#11761615C211yesmaximal, characteristic, complemented
13C2×C4×#11761616C211yesmaximal, characteristic, complemented
14C2×C4×#11761613C211yesmaximal, characteristic, complemented
15C2×#16863449C211yesmaximal, characteristic, complemented
16C2×C4×#41×C67C211yesmaximal, characteristic, complemented
17C22×#11761618C2211yescharacteristic
18C22×#11761616C2211yescharacteristic
19C22×#11761615C2211yescharacteristic
20C22×#11761613C2211yescharacteristic
21#16863930—24no—
22#16863930C2218yescomplemented
23C2×#14524037—21no—
24C2×#14524035C2211yescharacteristic
25C2×#14524031C2211yescharacteristic
26C2×#14524026—21no—
27C2×#14524022C2211yescharacteristic
28C2×#14524017C2211yescharacteristic
29C2×C4×Dic134C2211yescharacteristic
30C2×C4×D268C2211yescharacteristic
31C2×C4×C22⋊D67—21no—
32C2×#14524000—21no—
33#16863737C2218yescomplemented
34#16863720C2218yescomplemented
35#16863703C2218yescomplemented
36#16863696C2218yescomplemented
37#16863618C2218yescomplemented
38#16863611C2218yescomplemented
39#16863558C2218yescomplemented
40#16863541C2218yes—
41C4×#11761618C2218yescomplemented
42C4×#11761615C2218yescomplemented
43C4×#11761616C2218yescomplemented
44C4×#11761613C2218yescomplemented
45#16863449C2218yescomplemented
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×C4⋊(C67⋊C8)C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523966C2211yescharacteristic
55C2×#14523966C2211yescharacteristic
56C2×#14523964C2211yescharacteristic
57C2×#14523964C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C4×C67⋊C8C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64C22×#41×C67C2211yescharacteristic
65C4×#41×C67—24no—
66C4×#41×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×C42×C67—21no—
76C22×C42×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C22×D268C2311yescharacteristic
79C22×C22⋊D67—21no—
80C22×C4×D67—21no—
81C2×#11761618—24no—
82C2×#11761618C2314yes—
83C2×#11761616—24no—
84C2×#11761616C2314yes—
85C2×#11761615—24no—
86C2×#11761615C2314yes—
87C2×#11761613—24no—
88C2×#11761613C2314yes—
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93#14524037—28no—
94#14524035—22no—
95#14524035C2314yes—
96#14524031—22no—
97#14524031C2314yes—
98#14524026—28no—
99#14524022—22no—
100#14524022C2314yes—
101#14524017—22no—
102#14524017C2314yes—
103C4×Dic134—22no—
104C4×Dic134C2314yes—
105C4×D268—22no—
106C4×D268C2314yes—
107C4×C22⋊D67—28no—
108#14524000—28no—
109C2×C4⋊Dic67C2311yescharacteristic
110C2×C4⋊Dic67C2311yescharacteristic
111C2×Dic67⋊C4—21no—
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×Dic67⋊C4—21no—
115C2×C22⋊Dic67—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×(C2×D67)⋊C4—21no—
119C2×(C2×D67)⋊C4—21no—
120C2×C4×Dic67—21no—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125C4⋊(C67⋊C8)C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523966C2314yes—
130#14523966C2314yes—
131#14523964C2314yes—
132#14523964C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137C4×C67⋊C8C2314yes—
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×C67D411yescharacteristic
150C23×C4×C67D411yescharacteristic
151C23×C4×C67C2311yescharacteristic
152C4×Q8×C67—22no—
153C4×Q8×C67—22no—
154C4×Q8×C67C2314yes—
155C4×Q8×C67C2314yes—
156C4×D4×C67—28no—
157C4×D4×C67—28no—
158C4×D4×C67—22no—
159C4×D4×C67—22no—
160C4×D4×C67C2314yes—
161C4×D4×C67C2314yes—
162#117×C67—22no—
163#117×C67—28no—
164#117×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C22⋊C4×C67—21no—
170C2×C22⋊C4×C67—21no—
171C2×C22⋊C4×C67—21no—
172C2×C42×C67—21no—
173C2×C42×C67—21no—
174C2×C42×C67—21no—
175C2×C42×C67—28no—
176C2×C42×C67D411yescharacteristic
177C2×C42×C67D411yescharacteristic
178C2×C42×C67D414yes—
179C2×C42×C67C2311yescharacteristic
180C2×C42×C67C2311yescharacteristic
181C2×C42×C67C2314yes—
182C23×D67—21no—
183C2×Dic134—22no—
184C2×Dic134—22no—
185C2×Dic134—21no—
186C2×Dic134C2412yes—
187C2×D268—22no—
188C2×D268—22no—
189C2×D268—21no—
190C2×D268C2412yes—
191C2×C22⋊D67—24no—
192C2×C22⋊D67—44no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195C22×Dic67—21no—
196C2×C4×D67—24no—
197C2×C4×D67—44no—
198#11761618—28no—
199#11761616—28no—
200#11761615—28no—
201#11761613—28no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—22no—
204C2×C67⋊C8—22no—
205C2×C67⋊C8—22no—
206C2×C67⋊C8C2412yes—
207C2×C67⋊C8C2412yes—
208C2×C67⋊C8C2412yes—
209C2×C67⋊C8C2412yes—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214Dic67⋊C4—24no—
215Dic67⋊C4—24no—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218C22⋊Dic67—24no—
219(C2×D67)⋊C4—24no—
220(C2×D67)⋊C4—24no—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223C4×Dic67—24no—
224C24×C67—21no—
225C24×C67C2×D411yescharacteristic
226#41×C67—216no—
227#41×C67—28no—
228#41×C67—28no—
229C2×Q8×C67—21no—
230C2×Q8×C67—22no—
231C2×Q8×C67#4114yes—
232C2×Q8×C67C2412yes—
233C2×D4×C67—28no—
234C2×D4×C67—24no—
235C2×D4×C67—21no—
236C2×D4×C67—22no—
237C2×D4×C67#4114yes—
238C2×D4×C67C2412yes—
239C22×C4×C67—28no—
240C22×C4×C67—21no—
241C22×C4×C67—24no—
242C22×C4×C67—24no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—21no—
246C22×C4×C67—21no—
247C22×C4×C67—24no—
248C22×C4×C67—24no—
249C22×C4×C67—42no—
250C22×C4×C67—44no—
251C22×C4×C67—44no—
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2×D412yes—
255C22×C4×C67C2×D411yescharacteristic
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×D414yes—
258C22×C4×C67C2×D414yes—
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2412yes—
261C22×C4×C67C2411yescharacteristic
262C4⋊C4×C67—24no—
263C4⋊C4×C67—24no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67—21no—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C22⋊C4×C67—24no—
269C22⋊C4×C67—24no—
270C22⋊C4×C67—24no—
271C42×C67—24no—
272C42×C67—24no—
273C42×C67—24no—
274C42×C67C2×D414yes—
275C42×C67C2×D414yes—
276C42×C67C2×D412yes—
277C42×C67C2×D412yes—
278C42×C67C2412yes—
279C42×C67C2412yes—
280C23×C67—22no—
281C23×C67—24no—
282C23×C67—22no—
283C23×C67—22no—
284C23×C67—22no—
285C23×C67—42no—
286C23×C67—42no—
287C23×C67C22×D412yes—
288C23×C67C22×D411yescharacteristic
289C22×D67—22no—
290C22×D67—42no—
291C22×D67—42no—
292C22×D67—42no—
293Q8×C67—24no—
294Q8×C67—22no—
295Q8×C67C2×#4114yes—
296D4×C67—216no—
297D4×C67—24no—
298D4×C67—22no—
299D4×C67C2×#4114yes—
300C2×C4×C67—216no—
301C2×C4×C67—22no—
302C2×C4×C67—24no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—24no—
308C2×C4×C67—28no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—44no—
314C2×C4×C67—48no—
315C2×C4×C67—42no—
316C2×C4×C67—42no—
317C2×C4×C67—48no—
318C2×C4×C67#13514yes—
319C2×C4×C67C22×D412yes—
320C2×C4×C67C22×D412yes—
321C2×C4×C67C22×D412yes—
322C2×C4×C67C22×D412yes—
323C2×C4×C67C22×D411yescharacteristic
324C2×C4×C67C22×D412yes—
325C2×C4×C67C2×#4112yes—
326C2×C4×C67C2×#4112yes—
327C2×C4×C67C2511yescharacteristic
328C22⋊D67—48no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—42no—
333C2×Dic67—42no—
334C2×Dic67—42no—
335D268—22no—
336D268—22no—
337D268—42no—
338C4×D67—48no—
339Dic134—22no—
340Dic134—22no—
341Dic134—42no—
342C67⋊C8—22no—
343C67⋊C8—22no—
344C67⋊C8—22no—
345C67⋊C8—22no—
346C22×C67—22no—
347C22×C67—24no—
348C22×C67—22no—
349C22×C67—22no—
350C22×C67—44no—
351C22×C67—48no—
352C22×C67—42no—
353C22×C67—42no—
354C22×C67#52512yes—
355C22×C67C2×#13512yes—
356C22×C67#57512yes—
357C22×C67C23×D411yescharacteristic
358C2×D67—42no—
359C2×D67—42no—
360C2×D67—42no—
361C2×D67—84no—
362C4×C67—22no—
363C4×C67—24no—
364C4×C67—22no—
365C4×C67—22no—
366C4×C67—22no—
367C4×C67—42no—
368C4×C67—42no—
369C4×C67#52512yes—
370C4×C67C2×#13514yes—
371C4×C67C22×#4111yescharacteristic
372C4×C67C22×#4111yescharacteristic
373Dic67—42no—
374Dic67—42no—
375Dic67—42no—
376C2×#3102—671nomaximal, Sylow
377C2×C67—42no—
378C2×C67—44no—
379C2×C67#310214yescomplemented
380C2×C67C2×#52511yescharacteristic
381C2×C67C22×#13511yescharacteristic
382C2×C67C2×#57511yescharacteristic
383D67—82no—
384C2×#529—671no—
385C2×C4×#41D6711yescharacteristic, complemented
386#3102—6716no—
387C2×#485—671no—
388C2×#482—671no—
389C2×#479—671no—
390C2×#478—671no—
391C2×#464—671no—
392C2×#463—671no—
393C2×#452—671no—
394C2×#449—671no—
395C2×C4×Q16—671no—
396C2×C4×SD16—671no—
397C2×C4×SD16—671no—
398C2×C4×D8—671no—
399C2×#431—671no—
400C67C2×#310211yescharacteristic, complemented, Sylow
401C22×#41C2×D6711yescharacteristic
402C22×Q16—671no—
403C22×SD16—671no—
404C22×SD16—671no—
405C22×D8—671no—
406#529—678no—
407#529—1344no—
408C2×#126—1341no—
409C2×#125—671no—
410C2×#124—671no—
411C2×#123—1341no—
412C2×C22⋊Q8—671no—
413C2×#121—671no—
414C4×#41—24no—
415C4×#41C2×D6718yescomplemented
416C2×C4×Q8—671no—
417C2×C4×Q8C2×D6711yescharacteristic
418C2×C4×Q8C2×D6711yescharacteristic
419C2×C4×D4—21no—
420C2×C4×D4—21no—
421C2×C4×D4—671no—
422C2×C4×D4—1341no—
423C2×C4×D4C2×D6711yescharacteristic
424C2×C4×D4C2×D6711yescharacteristic
425C2×#117—21no—
426C2×#117—1341no—
427C2×#117C2×D6711yescharacteristic
428C22×C42—21no—
429C22×C42C2×D6711yescharacteristic
430#485—678no—
431#482—678no—
432#479—678no—
433#478—678no—
434#464—678no—
435#463—678no—
436#452—678no—
437#449—678no—
438C4×Q16—678no—
439C4×SD16—678no—
440C4×SD16—678no—
441C4×D8—678no—
442#431—678no—
443C2×#107—671no—
444C2×#107—671no—
445C2×#106—671no—
446C2×#106—671no—
447C2×C4⋊C8—671no—
448C2×C4⋊C8—671no—
449C2×#103—671no—
450C2×#103—671no—
451C2×#103—671no—
452C2×#103—671no—
453C2×#102—671no—
454C2×#102—671no—
455C2×#102—671no—
456C2×#102—671no—
457C2×C22⋊C8—671no—
458C2×C22⋊C8—671no—
459C2×C4×C8—671no—
460C2×C4×C8—671no—
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D6714yes—
465C22×Q8—671no—
466C22×Q8C22×D6711yescharacteristic
467C22×D4—21no—
468C22×D4—671no—
469C22×D4—1341no—
470C22×D4C22×D6711yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—1341no—
475C23×C4C22⋊D6711yescharacteristic
476C23×C4C22⋊D6711yescharacteristic
477C23×C4C22×D6711yescharacteristic
478C2×Q16—674no—
479C2×Q16—1344no—
480C2×SD16—674no—
481C2×SD16—674no—
482C2×SD16—1344no—
483C2×SD16—1344no—
484C2×D8—674no—
485C2×D8—1344no—
486C22×C8—671no—
487C22×C8—671no—
488C22×C8—671no—
489C22×C8—671no—
490#126—1348no—
491#125—674no—
492#125—1342no—
493#124—674no—
494#124—1342no—
495#123—1348no—
496C22⋊Q8—674no—
497C22⋊Q8—1342no—
498#121—674no—
499#121—1342no—
500C4×Q8—22no—
501C4×Q8—22no—
502C4×Q8—674no—
503C4×Q8—1342no—
504C4×Q8C22×D6714yes—
505C4×Q8C22×D6714yes—
506C4×D4—28no—
507C4×D4—28no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—674no—
511C4×D4—1348no—
512C4×D4—1342no—
513C4×D4C22×D6714yes—
514C4×D4C22×D6714yes—
515#117—22no—
516#117—28no—
517#117—1348no—
518#117C22×D6714yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—671no—
522C2×C4⋊C4—671no—
523C2×C4⋊C4—1341no—
524C2×C4⋊C4—1341no—
525C2×C4⋊C4—1341no—
526C2×C4⋊C4—1341no—
527C2×C4⋊C4C22×D6711yescharacteristic
528C2×C4⋊C4C22×D6711yescharacteristic
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—1341no—
533C2×C22⋊C4—1341no—
534C2×C22⋊C4—1341no—
535C2×C22⋊C4—1341no—
536C2×C22⋊C4—1341no—
537C2×C42—21no—
538C2×C42—21no—
539C2×C42—21no—
540C2×C42—28no—
541C2×C42—1341no—
542C2×C42C22⋊D6711yescharacteristic
543C2×C42C22⋊D6714yes—
544C2×C42C22⋊D6711yescharacteristic
545C2×C42C22×D6711yescharacteristic
546C2×C42C22×D6714yes—
547C2×C42C22×D6711yescharacteristic
548#107—674no—
549#107—674no—
550#106—674no—
551#106—674no—
552C4⋊C8—674no—
553C4⋊C8—674no—
554#103—674no—
555#103—674no—
556#103—674no—
557#103—674no—
558#102—674no—
559#102—674no—
560#102—674no—
561#102—674no—
562C22⋊C8—674no—
563C22⋊C8—674no—
564C4×C8—674no—
565C4×C8—674no—
566C24—21no—
567C24—1341no—
568C24C2×C22⋊D6711yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—672no—
575C2×Q8—1342no—
576C2×Q8—1342no—
577C2×Q8—1341no—
578C2×Q8#1176162814yes—
579C2×Q8C23×D6712yes—
580C2×D4—28no—
581C2×D4—24no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—2684no—
585C2×D4—672no—
586C2×D4—1344no—
587C2×D4—1341no—
588C2×D4—1342no—
589C2×D4—1342no—
590C2×D4#1176162814yes—
591C2×D4C23×D6712yes—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—24no—
601C22×C4—24no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4—2684no—
606C22×C4—1341no—
607C22×C4—1341no—
608C22×C4—1341no—
609C22×C4—1344no—
610C22×C4C2×C22⋊D6711yescharacteristic
611C22×C4C2×C22⋊D6711yescharacteristic
612C22×C4C2×C22⋊D6712yes—
613C22×C4C2×C22⋊D6711yescharacteristic
614C22×C4C2×C22⋊D6711yescharacteristic
615C22×C4C2×C22⋊D6714yes—
616C22×C4C2×C22⋊D6714yes—
617C22×C4C2×C22⋊D6711yescharacteristic
618C22×C4C23×D6712yes—
619C22×C4C23×D6711yescharacteristic
620Q16—1348no—
621SD16—1348no—
622SD16—1348no—
623D8—1348no—
624C2×C8—672no—
625C2×C8—672no—
626C2×C8—672no—
627C2×C8—672no—
628C2×C8—1342no—
629C2×C8—1342no—
630C2×C8—1342no—
631C2×C8—1342no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—672no—
637C4⋊C4—672no—
638C4⋊C4—1341no—
639C4⋊C4—1341no—
640C4⋊C4—1344no—
641C4⋊C4—1344no—
642C4⋊C4—1344no—
643C4⋊C4—1344no—
644C4⋊C4C23×D6712yes—
645C4⋊C4C23×D6712yes—
646C22⋊C4—24no—
647C22⋊C4—24no—
648C22⋊C4—24no—
649C22⋊C4—1344no—
650C22⋊C4—1344no—
651C22⋊C4—1344no—
652C22⋊C4—1344no—
653C22⋊C4—1344no—
654C42—24no—
655C42—24no—
656C42—24no—
657C42—1344no—
658C42C2×C22⋊D6714yes—
659C42C2×C22⋊D6714yes—
660C42C2×C22⋊D6712yes—
661C42C2×C22⋊D6712yes—
662C42C23×D6712yes—
663C42C23×D6712yes—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—2682no—
672C23—2682no—
673C23—2682no—
674C23—1342no—
675C23C22×C22⋊D6712yes—
676C23C22×C22⋊D6711yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—2682no—
680Q8—1342no—
681Q8—1342no—
682Q8C2×#1176162814yes—
683D4—216no—
684D4—24no—
685D4—22no—
686D4—2688no—
687D4—2682no—
688D4—1342no—
689D4—1342no—
690D4C2×#1176162814yes—
691C2×C4—216no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—44no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—48no—
709C2×C4—2682no—
710C2×C4—2682no—
711C2×C4—2682no—
712C2×C4—2688no—
713C2×C4—1342no—
714C2×C4—1342no—
715C2×C4—1342no—
716C2×C4#1452406314yes—
717C2×C4C22×C22⋊D6712yes—
718C2×C4C22×C22⋊D6712yes—
719C2×C4C22×C22⋊D6712yes—
720C2×C4C22×C22⋊D6712yes—
721C2×C4C22×C22⋊D6711yescharacteristic
722C2×C4C22×C22⋊D6712yes—
723C2×C4C2×#1176162812yes—
724C2×C4C2×#1176162812yes—
725C2×C4C24×D6711yescharacteristic
726C8—1342no—
727C8—1342no—
728C8—1342no—
729C8—1342no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—44no—
737C22—48no—
738C22—2682no—
739C22—2682no—
740C22—2682no—
741C22—5364no—
742C22#1686390712yes—
743C22C2×#1452406312yes—
744C22#1686419412yes—
745C22C23×C22⋊D6711yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—2682no—
754C4—2682no—
755C4—2682no—
756C4#1686390712yes—
757C4C2×#1452406314yes—
758C4C22×#1176162811yescharacteristic
759C4C22×#1176162811yescharacteristic
760C2—42no—
761C2—44no—
762C2—5362no—
763C2#2257022714yesdirect product factor
764C2C2×#1686390711yescharacteristic
765C2C22×#1452406311yescharacteristic
766C2C2×#1686419411yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×C4×#41×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863541C2
hypercenterC2×C4×#41D67
hypocenterC67C2×#3102
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16863930C2semidirect
2. #22570227C2direct (N × H)
3. C2×#16863737C2semidirect
4. C2×#16863720C2semidirect
5. C2×#16863703C2semidirect
6. C2×#16863696C2semidirect
7. C2×#16863618C2semidirect
8. C2×#16863611C2semidirect
9. C2×#16863558C2semidirect
11. C2×C4×#11761618C2semidirect
12. C2×C4×#11761615C2semidirect
13. C2×C4×#11761616C2semidirect
14. C2×C4×#11761613C2semidirect
15. C2×#16863449C2semidirect
16. C2×C4×#41×C67C2semidirect
22. #16863930C22semidirect
33. #16863737C22semidirect
34. #16863720C22semidirect
35. #16863703C22semidirect
36. #16863696C22semidirect
37. #16863618C22semidirect
38. #16863611C22semidirect
39. #16863558C22semidirect
41. C4×#11761618C22semidirect
42. C4×#11761615C22semidirect
43. C4×#11761616C22semidirect
44. C4×#11761613C22semidirect
45. #16863449C22semidirect
66. C4×#41×C67C22semidirect
379. C2×C67#3102semidirect
385. C2×C4×#41D67semidirect
400. C67C2×#3102semidirect
415. C4×#41C2×D67semidirect
763. C2#22570227direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639302
#225702272
C2×#168637372
C2×#168637202
C2×#168637032
C2×#168636962
C2×#168636182
C2×#168636112
C2×#168635582
C2×#168635412
C2×C4×#117616182
C2×C4×#117616152
C2×C4×#117616162
C2×C4×#117616132
C2×#168634492
C2×C4×#41×C672
C2×#310267