Finite Group Databasebeta

← C2×#22572763 #31734503

Subgroups — C2×#22572763 #31734503

Order 17152.

1898 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864086C211yesmaximal, characteristic, complemented
2#22572763C2116yesmaximal, direct product factor
3C2×#16863795C211yesmaximal, characteristic, complemented
4C2×#16863712C211yesmaximal, characteristic, complemented
5C2×#16863737C211yesmaximal, characteristic, complemented
6C2×#16863717C211yesmaximal, characteristic, complemented
7C2×#16863726C211yesmaximal, characteristic, complemented
8C2×#16863700C211yesmaximal, characteristic, complemented
9C2×#16863696C211yesmaximal, characteristic, complemented
10C2×#16863640C211yesmaximal, characteristic, complemented
11C2×#16863640C211yesmaximal, characteristic, complemented
12C2×C4×#11761616C211yesmaximal, characteristic, complemented
13C2×#16863474C211yesmaximal, characteristic, complemented
14C2×#16863439C211yesmaximal, characteristic, complemented
15C2×#16863436C211yesmaximal, characteristic, complemented
16C2×#553×C67C211yesmaximal, characteristic
17C22×#11761616C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C22×#11761612C2211yescharacteristic
20#16864086—24no—
21#16864086C2218yescomplemented
22C2×#14524036—21no—
23C2×#14524035C2211yescharacteristic
24C2×#14524033—21no—
25C2×#14524024—21no—
26C2×#14524022C2211yescharacteristic
27C2×#14524022C2211yescharacteristic
28C2×C4×Dic134C2211yescharacteristic
29C2×#14524002C2211yescharacteristic
30C2×#14523999—21no—
31C22×C4⋊Dic67C2211yescharacteristic
32#16863795C2218yescomplemented
33#16863737C2218yescomplemented
34#16863726C2218yescomplemented
35#16863717C2218yescomplemented
36#16863712C2218yescomplemented
37#16863700C2218yescomplemented
38#16863696C2218yescomplemented
39#16863640C2218yescomplemented
40#16863640C2218yescomplemented
41C4×#11761616C2218yescomplemented
42#16863474C2218yescomplemented
43#16863439C2218yescomplemented
44#16863436C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523966C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#553×C67—24no—
65#553×C67C2218yes—
66C2×#126×C67—21no—
67C2×#125×C67C2211yescharacteristic
68C2×#123×C67—21no—
69C2×#121×C67—21no—
70C2×#121×C67C2211yescharacteristic
71C2×#121×C67C2211yescharacteristic
72C2×C4×D4×C67—21no—
73C2×C4×D4×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C2×#117×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C23×Dic67—21no—
79C2×#11761616—24no—
80C2×#11761616C2314yes—
81C2×#11761612—24no—
82C2×#11761612—24no—
83C2×#11761612C2314yes—
84C2×#11761612C2314yes—
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89#14524036—28no—
90#14524035—22no—
91#14524035C2314yes—
92#14524033—28no—
93#14524024—28no—
94#14524022—22no—
95#14524022—22no—
96#14524022C2314yes—
97#14524022C2314yes—
98C4×Dic134—22no—
99C4×Dic134C2314yes—
100#14524002—22no—
101#14524002C2314yes—
102#14523999—28no—
103C2×C4⋊Dic67—22no—
104C2×C4⋊Dic67—21no—
105C2×C4⋊Dic67C2314yes—
106C2×C4⋊Dic67C2311yescharacteristic
107C2×C4⋊Dic67C2311yescharacteristic
108C2×C4⋊Dic67C2311yescharacteristic
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C2×Dic67⋊C4—21no—
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×C22⋊Dic67—21no—
115C2×C22⋊Dic67—21no—
116C2×C22⋊Dic67—21no—
117C2×C4×Dic67—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523976C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523966C2314yes—
130#14523966C2314yes—
131#14523966C2314yes—
132#14523964C2314yes—
133#14523964C2314yes—
134#14523964C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137C4×C67⋊C8C2314yes—
138C22×D4×C67—21no—
139C22×D4×C67—21no—
140C22×D4×C67D411yescharacteristic
141C22×D4×C67C2311yescharacteristic
142C23×C4×C67—21no—
143C23×C4×C67—21no—
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146#126×C67—28no—
147#125×C67—22no—
148#125×C67C2314yes—
149#123×C67—28no—
150#121×C67—28no—
151#121×C67—22no—
152#121×C67—22no—
153#121×C67C2314yes—
154#121×C67C2314yes—
155C4×D4×C67—28no—
156C4×D4×C67—22no—
157C4×D4×C67D414yes—
158C4×D4×C67C2314yes—
159C4×D4×C67C2314yes—
160#117×C67—22no—
161#117×C67C2314yes—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—22no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67D411yescharacteristic
167C2×C4⋊C4×C67C2311yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2314yes—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C22⋊C4×C67—21no—
172C2×C22⋊C4×C67—21no—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C42×C67—21no—
178C2×C42×C67C2311yescharacteristic
179C2×Dic134—22no—
180C2×Dic134—22no—
181C2×Dic134—21no—
182C2×Dic134C2412yes—
183C22×Dic67—21no—
184C22×Dic67—21no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—24no—
188C22×Dic67—44no—
189#11761616—28no—
190#11761612—28no—
191#11761612—28no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8—22no—
194C2×C67⋊C8—22no—
195C2×C67⋊C8#4114yes—
196C2×C67⋊C8C2412yes—
197C2×C67⋊C8C2412yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C4⋊Dic67—21no—
201C4⋊Dic67—21no—
202C4⋊Dic67—24no—
203C4⋊Dic67—21no—
204C4⋊Dic67C2412yes—
205C4⋊Dic67C2412yes—
206C4⋊Dic67C2412yes—
207Dic67⋊C4—24no—
208Dic67⋊C4—24no—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212C22⋊Dic67—24no—
213C22⋊Dic67—24no—
214C22⋊Dic67—24no—
215C4×Dic67—24no—
216C4×Dic67—24no—
217C24×C67—21no—
218C24×C67C2×D411yescharacteristic
219C24×C67C2×D411yescharacteristic
220C2×D4×C67—24no—
221C2×D4×C67—24no—
222C2×D4×C67—21no—
223C2×D4×C67—22no—
224C2×D4×C67—22no—
225C2×D4×C67—42no—
226C2×D4×C67—44no—
227C2×D4×C67—82no—
228C2×D4×C67C2×D414yes—
229C2×D4×C67C2412yes—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—21no—
237C22×C4×C67—24no—
238C22×C4×C67—24no—
239C22×C4×C67—82no—
240C22×C4×C67—82no—
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D412yes—
246C22×C4×C67C2×D412yes—
247C22×C4×C67C2412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2411yescharacteristic
250C4⋊C4×C67—21no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—24no—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67C2×D414yes—
257C4⋊C4×C67C2412yes—
258C4⋊C4×C67C2412yes—
259C4⋊C4×C67C2412yes—
260C22⋊C4×C67—24no—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67—24no—
264C22⋊C4×C67C2×D414yes—
265C22⋊C4×C67C2×D414yes—
266C42×C67—24no—
267C42×C67C2×D412yes—
268C42×C67C2412yes—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—42no—
277C23×C67—42no—
278C23×C67—42no—
279C23×C67C22×D412yes—
280C23×C67C22×D412yes—
281C23×C67C22×D411yescharacteristic
282D4×C67—22no—
283D4×C67—22no—
284D4×C67—44no—
285D4×C67—48no—
286D4×C67—42no—
287D4×C67—84no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—24no—
293C2×C4×C67—24no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—42no—
302C2×C4×C67—42no—
303C2×C4×C67—42no—
304C2×C4×C67—84no—
305C2×C4×C67—84no—
306C2×C4×C67C22×D412yes—
307C2×C4×C67C22×D412yes—
308C2×C4×C67C22×D412yes—
309C2×C4×C67C22×D412yes—
310C2×C4×C67C22×D411yescharacteristic
311C2×C4×C67C2×#4112yes—
312C2×C4×C672−1+412yes—
313C2×C4×C67C2511yescharacteristic
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—22no—
318C2×Dic67—48no—
319C2×Dic67—42no—
320C2×Dic67—42no—
321C2×Dic67—42no—
322C2×Dic67—42no—
323Dic134—22no—
324Dic134—22no—
325Dic134—42no—
326C67⋊C8—22no—
327C67⋊C8—22no—
328C67⋊C8—22no—
329C67⋊C8C2×#4114yes—
330C22×C67—22no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67—22no—
334C22×C67—22no—
335C22×C67—22no—
336C22×C67—44no—
337C22×C67—44no—
338C22×C67—42no—
339C22×C67—42no—
340C22×C67—42no—
341C22×C67—84no—
342C22×C67#54712yes—
343C22×C67#57512yes—
344C22×C67#57712yes—
345C22×C67C23×D411yescharacteristic
346C4×C67—22no—
347C4×C67—22no—
348C4×C67—22no—
349C4×C67—22no—
350C4×C67—42no—
351C4×C67—42no—
352C4×C67—42no—
353C4×C67#54712yes—
354C4×C67C22×#4111yescharacteristic
355C4×C67C2×2−1+411yescharacteristic
356Dic67—42no—
357Dic67—42no—
358Dic67—42no—
359Dic67—42no—
360C2×#3351—671nomaximal, Sylow
361C2×C67—42no—
362C2×C67—42no—
363C2×C67—82no—
364C2×C67#335114yescomplemented
365C2×C67C2×#54711yescharacteristic
366C2×C67C2×#57511yescharacteristic
367C2×C67C2×#57711yescharacteristic
368C2×#553D6711yescharacteristic
369C2×#552—671no—
370#3351—6716no—
371C2×#499—671no—
372C2×#481—671no—
373C2×#485—671no—
374C2×#482—671no—
375C2×#483—671no—
376C2×#479—671no—
377C2×#478—671no—
378C2×#468—671no—
379C2×#468—671no—
380C2×C4×SD16—671no—
381C2×#436—671no—
382C2×#428—671no—
383C2×#428—671no—
384C67C2×#335111yescharacteristic, complemented, Sylow
385C22×SD16—671no—
386C22×M16—671no—
387C22×M16—671no—
388#553—24no—
389#553C2×D6718yes—
390#552—678no—
391#552—1344no—
392C2×#126—21no—
393C2×#126—1341no—
394C2×#125—671no—
395C2×#125—1341no—
396C2×#125C2×D6711yescharacteristic
397C2×#123—21no—
398C2×#123—1341no—
399C2×C22⋊Q8—671no—
400C2×C22⋊Q8—671no—
401C2×#121—21no—
402C2×#121C2×D6711yescharacteristic
403C2×#121C2×D6711yescharacteristic
404C2×C4×Q8—671no—
405C2×C4×D4—21no—
406C2×C4×D4C2×D6711yescharacteristic
407C2×C4×D4C2×D6711yescharacteristic
408C2×#117—671no—
409C2×#117—1341no—
410C2×#117C2×D6711yescharacteristic
411C22×C4⋊C4—671no—
412C22×C4⋊C4C2×D6711yescharacteristic
413#499—678no—
414#485—678no—
415#483—678no—
416#482—678no—
417#481—678no—
418#479—678no—
419#478—678no—
420#468—678no—
421#468—678no—
422C4×SD16—678no—
423#436—678no—
424#428—678no—
425#428—678no—
426C2×#107—671no—
427C2×#107—671no—
428C2×#107—671no—
429C2×#107—671no—
430C2×#106—671no—
431C2×#106—671no—
432C2×#106—671no—
433C2×#106—671no—
434C2×#106—671no—
435C2×C4⋊C8—671no—
436C2×#103—671no—
437C2×#103—671no—
438C2×#103—671no—
439C2×#102—671no—
440C2×#102—671no—
441C2×#102—671no—
442C2×C22⋊C8—671no—
443C2×C22⋊C8—671no—
444C2×C4×C8—671no—
445C22×Q8—671no—
446C22×D4—21no—
447C22×D4—21no—
448C22×D4C22⋊D6711yescharacteristic
449C22×D4C22×D6711yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—1341no—
453C23×C4C22×D6711yescharacteristic
454C23×C4C22×D6711yescharacteristic
455C2×SD16—674no—
456C2×SD16—1344no—
457C2×M16—674no—
458C2×M16—674no—
459C2×M16—1344no—
460C2×M16—1344no—
461C22×C8—671no—
462C22×C8—671no—
463C22×C8—671no—
464C22×C8—671no—
465#126—28no—
466#126—1348no—
467#125—22no—
468#125—674no—
469#125—1348no—
470#125—1342no—
471#125C22×D6714yes—
472#123—28no—
473#123—1348no—
474C22⋊Q8—674no—
475C22⋊Q8—674no—
476C22⋊Q8—1342no—
477C22⋊Q8—1342no—
478#121—28no—
479#121—22no—
480#121—22no—
481#121C22×D6714yes—
482#121C22×D6714yes—
483C4×Q8—674no—
484C4×Q8—1342no—
485C4×D4—28no—
486C4×D4—22no—
487C4×D4C22⋊D6714yes—
488C4×D4C22×D6714yes—
489C4×D4C22×D6714yes—
490#117—22no—
491#117—674no—
492#117—1342no—
493#117—1348no—
494#117C22×D6714yes—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—671no—
500C2×C4⋊C4—671no—
501C2×C4⋊C4—674no—
502C2×C4⋊C4—671no—
503C2×C4⋊C4—1341no—
504C2×C4⋊C4—1342no—
505C2×C4⋊C4—1341no—
506C2×C4⋊C4—1341no—
507C2×C4⋊C4—1341no—
508C2×C4⋊C4—1341no—
509C2×C4⋊C4—1341no—
510C2×C4⋊C4C22⋊D6711yescharacteristic
511C2×C4⋊C4C22×D6711yescharacteristic
512C2×C4⋊C4C22×D6711yescharacteristic
513C2×C4⋊C4C22×D6714yes—
514C2×C4⋊C4C22×D6711yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—1341no—
520C2×C22⋊C4—1341no—
521C2×C22⋊C4—1341no—
522C2×C22⋊C4C22⋊D6711yescharacteristic
523C2×C22⋊C4C22⋊D6711yescharacteristic
524C2×C42—21no—
525C2×C42—1341no—
526C2×C42—1341no—
527C2×C42C22×D6711yescharacteristic
528#107—674no—
529#107—674no—
530#107—674no—
531#107—674no—
532#106—674no—
533#106—674no—
534#106—674no—
535#106—674no—
536#106—674no—
537C4⋊C8—674no—
538#103—674no—
539#103—674no—
540#103—674no—
541#102—674no—
542#102—674no—
543#102—674no—
544C22⋊C8—674no—
545C22⋊C8—674no—
546C4×C8—674no—
547C24—21no—
548C24C2×C22⋊D6711yescharacteristic
549C24C2×C22⋊D6711yescharacteristic
550C2×Q8—672no—
551C2×Q8—1342no—
552C2×Q8—1342no—
553C2×Q8—1341no—
554C2×D4—24no—
555C2×D4—24no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—42no—
560C2×D4—44no—
561C2×D4—82no—
562C2×D4C2×C22⋊D6714yes—
563C2×D4C23×D6712yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—82no—
574C22×C4—82no—
575C22×C4—2684no—
576C22×C4—1344no—
577C22×C4—1341no—
578C22×C4—1341no—
579C22×C4—1341no—
580C22×C4—1341no—
581C22×C4C2×C22⋊D6712yes—
582C22×C4C2×C22⋊D6712yes—
583C22×C4C2×C22⋊D6711yescharacteristic
584C22×C4C2×C22⋊D6711yescharacteristic
585C22×C4C2×C22⋊D6711yescharacteristic
586C22×C4C2×C22⋊D6711yescharacteristic
587C22×C4C23×D6712yes—
588C22×C4C23×D6712yes—
589C22×C4C23×D6711yescharacteristic
590SD16—1348no—
591M16—1348no—
592M16—1348no—
593C2×C8—674no—
594C2×C8—672no—
595C2×C8—672no—
596C2×C8—672no—
597C2×C8—672no—
598C2×C8—1342no—
599C2×C8—1342no—
600C2×C8—1342no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—21no—
607C4⋊C4—672no—
608C4⋊C4—672no—
609C4⋊C4—672no—
610C4⋊C4—1341no—
611C4⋊C4—1341no—
612C4⋊C4—1344no—
613C4⋊C4—1341no—
614C4⋊C4—1344no—
615C4⋊C4—1344no—
616C4⋊C4—1344no—
617C4⋊C4—1344no—
618C4⋊C4—1344no—
619C4⋊C4C2×C22⋊D6714yes—
620C4⋊C4C23×D6712yes—
621C4⋊C4C23×D6712yes—
622C4⋊C4C23×D6712yes—
623C22⋊C4—24no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—1344no—
628C22⋊C4—1344no—
629C22⋊C4—1344no—
630C22⋊C4C2×C22⋊D6714yes—
631C22⋊C4C2×C22⋊D6714yes—
632C42—24no—
633C42—1344no—
634C42—1344no—
635C42C2×C22⋊D6712yes—
636C42C23×D6712yes—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23C22×C22⋊D6712yes—
648C23C22×C22⋊D6712yes—
649C23C22×C22⋊D6711yescharacteristic
650Q8—2682no—
651Q8—1342no—
652Q8—1342no—
653D4—22no—
654D4—22no—
655D4—44no—
656D4—48no—
657D4—42no—
658D4—84no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—84no—
676C2×C4—84no—
677C2×C4—2688no—
678C2×C4—2682no—
679C2×C4—2682no—
680C2×C4—2682no—
681C2×C4—2682no—
682C2×C4—1342no—
683C2×C4—1342no—
684C2×C4—1342no—
685C2×C4—1342no—
686C2×C4C22×C22⋊D6712yes—
687C2×C4C22×C22⋊D6712yes—
688C2×C4C22×C22⋊D6712yes—
689C2×C4C22×C22⋊D6712yes—
690C2×C4C22×C22⋊D6711yescharacteristic
691C2×C4#41×D6712yes—
692C2×C4#1452409012yes—
693C2×C4C24×D6711yescharacteristic
694C8—674no—
695C8—1342no—
696C8—1342no—
697C8—1342no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—44no—
705C22—44no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—84no—
710C22#1686404512yes—
711C22#1686419412yes—
712C22#1686420712yes—
713C22C23×C22⋊D6711yescharacteristic
714C4—22no—
715C4—22no—
716C4—22no—
717C4—22no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—2682no—
722C4—2682no—
723C4—2682no—
724C4—2682no—
725C4#1686404512yes—
726C4C2×#41×D6711yescharacteristic
727C4C2×#1452409011yescharacteristic
728C2—42no—
729C2—42no—
730C2—82no—
731C2#2257276314yesdirect product factor
732C2C2×#1686404511yescharacteristic
733C2C2×#1686419411yescharacteristic
734C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#553×C67C2
socleC23×C67C22×D4
hypercenterC2×#553D67
hypocenterC67C2×#3351
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#16864086C2semidirect
2. #22572763C2direct (N × H)
3. C2×#16863795C2semidirect
4. C2×#16863712C2semidirect
5. C2×#16863737C2semidirect
6. C2×#16863717C2semidirect
7. C2×#16863726C2semidirect
8. C2×#16863700C2semidirect
9. C2×#16863696C2semidirect
10. C2×#16863640C2semidirect
11. C2×#16863640C2semidirect
12. C2×C4×#11761616C2semidirect
13. C2×#16863474C2semidirect
14. C2×#16863439C2semidirect
15. C2×#16863436C2semidirect
21. #16864086C22semidirect
32. #16863795C22semidirect
33. #16863737C22semidirect
34. #16863726C22semidirect
35. #16863717C22semidirect
36. #16863712C22semidirect
37. #16863700C22semidirect
38. #16863696C22semidirect
39. #16863640C22semidirect
40. #16863640C22semidirect
41. C4×#11761616C22semidirect
42. #16863474C22semidirect
43. #16863439C22semidirect
44. #16863436C22semidirect
364. C2×C67#3351semidirect
384. C67C2×#3351semidirect
731. C2#22572763direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640862
#225727632
C2×#168637952
C2×#168637122
C2×#168637372
C2×#168637172
C2×#168637262
C2×#168637002
C2×#168636962
C2×#168636402
C2×C4×#117616162
C2×#168634742
C2×#168634392
C2×#168634362
C2×#553×C672
C2×#335167