Finite Group Databasebeta

← C2×#479×D67 #31723316

Subgroups — C2×#479×D67 #31723316

Order 17152.

2142 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D67C211yesmaximal, characteristic
2C2×C4×Q8×D67C211yesmaximal, characteristic
3C2×#16863706C211yesmaximal, characteristic, complemented
4C2×#16863705C211yesmaximal, characteristic, complemented
5C2×#16863704C211yesmaximal, characteristic, complemented
6C2×#16863703C211yesmaximal, characteristic, complemented
7C2×#16863702C211yesmaximal, characteristic, complemented
8C2×#16863701C211yesmaximal, characteristic, complemented
9C2×#16863700C211yesmaximal, characteristic, complemented
10#479×D67C2116yesmaximal, direct product factor
11C2×#107×D67C211yesmaximal, characteristic
12C2×#106×D67C211yesmaximal, characteristic
13C2×C4⋊C8×D67C211yesmaximal, characteristic
14C2×#103×D67C211yesmaximal, characteristic
15C2×#103×D67C211yesmaximal, characteristic
16C2×#479×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18C22×C8×D67C2211yescharacteristic
19C22×C8×D67C2211yescharacteristic
20C2×#14524035C2211yescharacteristic
21C2×#14524034C2211yescharacteristic
22C2×#14524034C2211yescharacteristic
23C2×#14524033—21no—
24C2×#14524033—21no—
25#125×D67—24no—
26#125×D67C2218yes—
27C2×Q8×Dic67C2211yescharacteristic
28C2×C4×Dic134—21no—
29C2×C4×Dic134C2211yescharacteristic
30C2×#14524008—21no—
31C2×#14524008C2211yescharacteristic
32C4×Q8×D67—24no—
33C4×Q8×D67C2218yes—
34C2×C4⋊C4×D67—21no—
35C2×C4⋊C4×D67—21no—
36C2×C4⋊C4×D67—21no—
37C2×C4⋊C4×D67C2211yescharacteristic
38C2×C4⋊C4×D67C2211yescharacteristic
39C2×C4⋊C4×D67C2211yescharacteristic
40C2×C42×D67—21no—
41C2×C42×D67C2211yescharacteristic
42#16863706C2218yescomplemented
43#16863705C2218yescomplemented
44#16863704C2218yescomplemented
45#16863703C2218yescomplemented
46#16863702C2218yescomplemented
47#16863701C2218yescomplemented
48#16863700C2218yescomplemented
49C2×#14523977C2211yescharacteristic
50C2×#14523976C2211yescharacteristic
51C2×#14523976C2211yescharacteristic
52#107×D67C2218yes—
53C2×#14523975C2211yescharacteristic
54C2×#14523974C2211yescharacteristic
55C2×#14523974C2211yescharacteristic
56#106×D67C2218yes—
57C2×C4⋊(C67⋊C8)C2211yescharacteristic
58C2×Dic67⋊C8C2211yescharacteristic
59C2×Dic67⋊C8C2211yescharacteristic
60C4⋊C8×D67C2218yes—
61C2×#14523968C2211yescharacteristic
62C2×#14523968C2211yescharacteristic
63C2×#14523967C2211yescharacteristic
64C2×#14523967C2211yescharacteristic
65C2×#14523966C2211yescharacteristic
66C2×#14523966C2211yescharacteristic
67#103×D67C2218yes—
68#103×D67C2218yes—
69C2×#125×C67C2211yescharacteristic
70C2×C4×Q8×C67C2211yescharacteristic
71#479×C67C2218yescomplemented
72C2×#107×C67C2211yescharacteristic
73C2×#106×C67C2211yescharacteristic
74C2×C4⋊C8×C67C2211yescharacteristic
75C2×#103×C67C2211yescharacteristic
76C2×#103×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C2×Q8×D67—22no—
80C2×Q8×D67—24no—
81C2×Q8×D67Q818yes—
82C2×Q8×D67C2314yes—
83C22×C4×D67—21no—
84C22×C4×D67—21no—
85C22×C4×D67—21no—
86C22×C4×D67—21no—
87C22×C4×D67D411yescharacteristic
88C22×C4×D67D411yescharacteristic
89C22×C4×D67C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C2×C8×D67—24no—
93C2×C8×D67—24no—
94C2×C8×D67C2314yes—
95C2×C8×D67C2314yes—
96#14524035—22no—
97#14524035C2314yes—
98#14524034—22no—
99#14524034—22no—
100#14524034C2314yes—
101#14524034C2314yes—
102#14524033—28no—
103#14524033—28no—
104Q8×Dic67—22no—
105Q8×Dic67C2314yes—
106C4×Dic134—28no—
107C4×Dic134—22no—
108C4×Dic134C2314yes—
109#14524008—22no—
110#14524008—28no—
111#14524008C2314yes—
112C2×C4⋊Dic67—21no—
113C2×C4⋊Dic67—21no—
114C2×C4⋊Dic67—21no—
115C2×C4⋊Dic67C2311yescharacteristic
116C2×C4⋊Dic67C2311yescharacteristic
117C2×C4⋊Dic67C2311yescharacteristic
118C2×Dic67⋊C4—21no—
119C2×Dic67⋊C4—21no—
120C2×Dic67⋊C4—21no—
121C2×Dic67⋊C4—21no—
122C2×Dic67⋊C4—21no—
123C2×Dic67⋊C4—21no—
124C2×Dic67⋊C4—21no—
125C2×Dic67⋊C4—21no—
126C2×Dic67⋊C4—21no—
127C4⋊C4×D67—28no—
128C4⋊C4×D67—28no—
129C4⋊C4×D67—28no—
130C4⋊C4×D67—22no—
131C4⋊C4×D67—22no—
132C4⋊C4×D67—22no—
133C4⋊C4×D67C2314yes—
134C4⋊C4×D67C2314yes—
135C4⋊C4×D67C2314yes—
136C2×C4×Dic67—21no—
137C2×C4×Dic67—21no—
138C2×C4×Dic67—21no—
139C2×C4×Dic67D411yescharacteristic
140C2×C4×Dic67D411yescharacteristic
141C2×C4×Dic67C2311yescharacteristic
142C42×D67—28no—
143C42×D67D414yes—
144C42×D67C2314yes—
145#14523977C2314yes—
146#14523976C2314yes—
147#14523976C2314yes—
148#14523975C2314yes—
149#14523974C2314yes—
150#14523974C2314yes—
151C4⋊(C67⋊C8)C2314yes—
152Dic67⋊C8C2314yes—
153Dic67⋊C8C2314yes—
154#14523968C2314yes—
155#14523968C2314yes—
156#14523967C2314yes—
157#14523967C2314yes—
158#14523966C2314yes—
159#14523966C2314yes—
160C22×Q8×C67C2311yescharacteristic
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163#125×C67—22no—
164#125×C67C2314yes—
165C4×Q8×C67—22no—
166C4×Q8×C67C2314yes—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C42×C67—21no—
174C2×C42×C67C2311yescharacteristic
175#107×C67C2314yes—
176#106×C67C2314yes—
177C4⋊C8×C67C2314yes—
178#103×C67C2314yes—
179#103×C67C2314yes—
180C23×D67C2×D411yescharacteristic
181C2×Dic134—21no—
182C2×Dic134—22no—
183C2×Dic134—28no—
184C2×Dic134—24no—
185C2×Dic134C2×Q814yes—
186C2×Dic134C2412yes—
187Q8×D67—216no—
188Q8×D67—28no—
189Q8×D67C2×Q8116yes—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67C2×D411yescharacteristic
195C22×Dic67C2×D411yescharacteristic
196C22×Dic67C2×D411yescharacteristic
197C2×C4×D67—28no—
198C2×C4×D67—24no—
199C2×C4×D67—24no—
200C2×C4×D67—24no—
201C2×C4×D67—24no—
202C2×C4×D67—24no—
203C2×C4×D67—24no—
204C2×C4×D67—44no—
205C2×C4×D67—44no—
206C2×C4×D67—44no—
207C2×C4×D67C2×D414yes—
208C2×C4×D67C2×D414yes—
209C2×C4×D67C2×D412yes—
210C2×C4×D67C2×Q814yes—
211C2×C4×D67#4114yes—
212C2×C4×D67C2412yes—
213C2×C67⋊C8—22no—
214C2×C67⋊C8—22no—
215C2×C67⋊C8C2412yes—
216C2×C67⋊C8C2412yes—
217C8×D67—28no—
218C8×D67—28no—
219C4⋊Dic67—21no—
220C4⋊Dic67—21no—
221C4⋊Dic67—21no—
222C4⋊Dic67—24no—
223C4⋊Dic67—24no—
224C4⋊Dic67—24no—
225C4⋊Dic67C2412yes—
226C4⋊Dic67C2412yes—
227C4⋊Dic67C2412yes—
228Dic67⋊C4—24no—
229Dic67⋊C4—24no—
230Dic67⋊C4—24no—
231Dic67⋊C4—24no—
232Dic67⋊C4—24no—
233Dic67⋊C4—24no—
234Dic67⋊C4—24no—
235Dic67⋊C4—24no—
236Dic67⋊C4—24no—
237C4×Dic67—24no—
238C4×Dic67—24no—
239C4×Dic67—24no—
240C4×Dic67C2×D412yes—
241C4×Dic67C2×D414yes—
242C4×Dic67C2×D414yes—
243C4×Dic67C2412yes—
244C2×Q8×C67—21no—
245C2×Q8×C67—22no—
246C2×Q8×C67C2×Q814yes—
247C2×Q8×C67C2412yes—
248C22×C4×C67—21no—
249C22×C4×C67—21no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67C2×D411yescharacteristic
253C22×C4×C67C2×D411yescharacteristic
254C22×C4×C67C2411yescharacteristic
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67C2412yes—
258C2×C8×C67C2412yes—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—24no—
262C4⋊C4×C67—21no—
263C4⋊C4×C67—21no—
264C4⋊C4×C67—21no—
265C4⋊C4×C67C2412yes—
266C4⋊C4×C67C2412yes—
267C4⋊C4×C67C2412yes—
268C42×C67—24no—
269C42×C67C2×D412yes—
270C42×C67C2412yes—
271C23×C67C22×D411yescharacteristic
272C22×D67C22⋊Q814yes—
273C22×D67#13514yes—
274C22×D67#13714yes—
275C22×D67C22×D412yes—
276Q8×C67—24no—
277Q8×C67—22no—
278Q8×C67C22×Q814yes—
279C2×C4×C67—24no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—42no—
287C2×C4×C67—42no—
288C2×C4×C67—42no—
289C2×C4×C67C22×D412yes—
290C2×C4×C67C22×D412yes—
291C2×C4×C67C22×D411yescharacteristic
292C2×C4×C67C22×Q812yes—
293C2×C4×C67C2×#4112yes—
294C2×C4×C67C2511yescharacteristic
295C2×Dic67—24no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—42no—
303C2×Dic67—42no—
304C2×Dic67—42no—
305C2×Dic67C22⋊Q814yes—
306C2×Dic67C22×D412yes—
307C2×Dic67C22×D412yes—
308C2×Dic67C22×D412yes—
309C4×D67—216no—
310C4×D67—28no—
311C4×D67—28no—
312C4×D67—48no—
313C4×D67—48no—
314C4×D67—48no—
315C4×D67C22⋊Q818yes—
316C4×D67C22×Q814yes—
317C4×D67C2×#4114yes—
318Dic134—24no—
319Dic134—22no—
320Dic134—216no—
321Dic134C22×Q814yes—
322C8×C67—22no—
323C8×C67—22no—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C22×C67C2×C22⋊Q812yes—
327C22×C67C2×#13512yes—
328C22×C67C2×#13712yes—
329C22×C67C23×D411yescharacteristic
330C2×D67#479116yesdirect product factor
331C2×D67C2×C22⋊Q814yes—
332C2×D67C2×#13514yes—
333C2×D67C2×#13714yes—
334C4×C67—24no—
335C4×C67—22no—
336C4×C67—22no—
337C4×C67—42no—
338C4×C67—42no—
339C4×C67—42no—
340C4×C67C2×C22⋊Q812yes—
341C4×C67C23×Q811yescharacteristic
342C4×C67C22×#4111yescharacteristic
343Dic67—24no—
344Dic67—22no—
345Dic67—22no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349Dic67C2×C22⋊Q814yes—
350C22×#479—671nomaximal, Sylow
351C2×C67C2×#47914yescomplemented
352C2×C67C22×C22⋊Q811yescharacteristic
353C2×C67C22×#13511yescharacteristic
354C2×C67C22×#13711yescharacteristic
355D67C2×#47918yesdirect product factor
356C22×#125—671no—
357C22×C4×Q8—671no—
358C2×#479—6716no—
359C2×#479—671no—
360C2×#479—671no—
361C2×#479—671no—
362C2×#479—671no—
363C2×#479—671no—
364C2×#479—671no—
365C2×#479—671no—
366C2×#479D6711yescharacteristic, direct product factor
367C22×#107—671no—
368C22×#106—671no—
369C22×C4⋊C8—671no—
370C22×#103—671no—
371C22×#103—671no—
372C67C22×#47911yescharacteristic, complemented, Sylow
373C23×Q8—671no—
374C23×C8—671no—
375C23×C8—671no—
376C2×#125—678no—
377C2×#125—671no—
378C2×#125—671no—
379C2×#125—671no—
380C2×#125—1341no—
381C2×#125—1341no—
382C2×#125—1344no—
383C2×#125C2×D6711yescharacteristic
384C2×C4×Q8—671no—
385C2×C4×Q8—678no—
386C2×C4×Q8—671no—
387C2×C4×Q8—671no—
388C2×C4×Q8—1341no—
389C2×C4×Q8—1341no—
390C2×C4×Q8—1344no—
391C2×C4×Q8C2×D6711yescharacteristic
392C22×C4⋊C4—671no—
393C22×C4⋊C4—671no—
394C22×C4⋊C4—671no—
395C22×C4⋊C4—1341no—
396C22×C4⋊C4—1341no—
397C22×C4⋊C4—1341no—
398C22×C42—671no—
399C22×C42—1341no—
400#479—678no—
401#479—678no—
402#479—678no—
403#479—678no—
404#479—678no—
405#479—678no—
406#479—678no—
407#479C2×D6718yesdirect product factor
408C2×#107—671no—
409C2×#107—671no—
410C2×#107—671no—
411C2×#107—678no—
412C2×#107C2×D6711yescharacteristic
413C2×#106—671no—
414C2×#106—671no—
415C2×#106—671no—
416C2×#106—678no—
417C2×#106C2×D6711yescharacteristic
418C2×C4⋊C8—671no—
419C2×C4⋊C8—671no—
420C2×C4⋊C8—671no—
421C2×C4⋊C8—678no—
422C2×C4⋊C8C2×D6711yescharacteristic
423C2×#103—671no—
424C2×#103—671no—
425C2×#103—671no—
426C2×#103—671no—
427C2×#103—671no—
428C2×#103—671no—
429C2×#103—678no—
430C2×#103—678no—
431C2×#103C2×D6711yescharacteristic
432C2×#103C2×D6711yescharacteristic
433C22×Q8—678no—
434C22×Q8—674no—
435C22×Q8—671no—
436C22×Q8—1341no—
437C22×Q8—1342no—
438C22×Q8—1344no—
439C22×Q8C22×D6711yescharacteristic
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4—1341no—
444C23×C4—1341no—
445C23×C4—1341no—
446C23×C4—1341no—
447C22×C8—671no—
448C22×C8—671no—
449C22×C8—674no—
450C22×C8—674no—
451C22×C8—1344no—
452C22×C8—1344no—
453C22×C8C22×D6711yescharacteristic
454C22×C8C22×D6711yescharacteristic
455#125—22no—
456#125—674no—
457#125—674no—
458#125—674no—
459#125—1348no—
460#125—1348no—
461#125—1342no—
462#125—1342no—
463#125—1342no—
464#125C22×D6714yes—
465C4×Q8—22no—
466C4×Q8—674no—
467C4×Q8—674no—
468C4×Q8—674no—
469C4×Q8—1348no—
470C4×Q8—1348no—
471C4×Q8—1342no—
472C4×Q8—1342no—
473C4×Q8—1342no—
474C4×Q8C22×D6714yes—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—671no—
479C2×C4⋊C4—671no—
480C2×C4⋊C4—671no—
481C2×C4⋊C4—674no—
482C2×C4⋊C4—674no—
483C2×C4⋊C4—674no—
484C2×C4⋊C4—1342no—
485C2×C4⋊C4—1342no—
486C2×C4⋊C4—1342no—
487C2×C4⋊C4—1348no—
488C2×C4⋊C4—1348no—
489C2×C4⋊C4—1348no—
490C2×C4⋊C4—1341no—
491C2×C4⋊C4—1341no—
492C2×C4⋊C4—1341no—
493C2×C4⋊C4—1341no—
494C2×C4⋊C4—1341no—
495C2×C4⋊C4—1341no—
496C2×C4⋊C4—1341no—
497C2×C4⋊C4—1341no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4C22×D6711yescharacteristic
503C2×C4⋊C4C22×D6711yescharacteristic
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C42—21no—
506C2×C42—671no—
507C2×C42—671no—
508C2×C42—671no—
509C2×C42—674no—
510C2×C42—674no—
511C2×C42—1348no—
512C2×C42—1341no—
513C2×C42—1341no—
514C2×C42—1341no—
515C2×C42C22×D6711yescharacteristic
516#107—674no—
517#107—674no—
518#107—674no—
519#107C22×D6714yes—
520#106—674no—
521#106—674no—
522#106—674no—
523#106C22×D6714yes—
524C4⋊C8—674no—
525C4⋊C8—674no—
526C4⋊C8—674no—
527C4⋊C8C22×D6714yes—
528#103—674no—
529#103—674no—
530#103—674no—
531#103—674no—
532#103—674no—
533#103—674no—
534#103C22×D6714yes—
535#103C22×D6714yes—
536C24—671no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—6716no—
540C2×Q8—674no—
541C2×Q8—672no—
542C2×Q8—1344no—
543C2×Q8—1348no—
544C2×Q8—13416no—
545C2×Q8—1348no—
546C2×Q8—1341no—
547C2×Q8—1342no—
548C2×Q8Q8×D6714yes—
549C2×Q8C23×D6712yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—2684no—
555C22×C4—2684no—
556C22×C4—2684no—
557C22×C4—671no—
558C22×C4—672no—
559C22×C4—674no—
560C22×C4—674no—
561C22×C4—672no—
562C22×C4—671no—
563C22×C4—671no—
564C22×C4—674no—
565C22×C4—674no—
566C22×C4—1344no—
567C22×C4—1344no—
568C22×C4—1344no—
569C22×C4—1344no—
570C22×C4—1344no—
571C22×C4—1344no—
572C22×C4—1348no—
573C22×C4—1341no—
574C22×C4—1341no—
575C22×C4—1341no—
576C22×C4—1341no—
577C22×C4D4×D6711yescharacteristic
578C22×C4D4×D6711yescharacteristic
579C22×C4C23×D6711yescharacteristic
580C2×C8—22no—
581C2×C8—22no—
582C2×C8—672no—
583C2×C8—672no—
584C2×C8—1348no—
585C2×C8—1348no—
586C2×C8—1342no—
587C2×C8—1342no—
588C2×C8C23×D6712yes—
589C2×C8C23×D6712yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—672no—
597C4⋊C4—672no—
598C4⋊C4—672no—
599C4⋊C4—1344no—
600C4⋊C4—1344no—
601C4⋊C4—1344no—
602C4⋊C4—1344no—
603C4⋊C4—1344no—
604C4⋊C4—1344no—
605C4⋊C4—1344no—
606C4⋊C4—1344no—
607C4⋊C4—1344no—
608C4⋊C4—1341no—
609C4⋊C4—1341no—
610C4⋊C4—1341no—
611C4⋊C4—1344no—
612C4⋊C4—1344no—
613C4⋊C4—1344no—
614C4⋊C4C23×D6712yes—
615C4⋊C4C23×D6712yes—
616C4⋊C4C23×D6712yes—
617C42—24no—
618C42—674no—
619C42—674no—
620C42—672no—
621C42—672no—
622C42—1344no—
623C42—1344no—
624C42—1344no—
625C42D4×D6712yes—
626C42C23×D6712yes—
627C23—674no—
628C23—674no—
629C23—674no—
630C23—672no—
631C23C2×D4×D6711yescharacteristic
632Q8—24no—
633Q8—22no—
634Q8—674no—
635Q8—13416no—
636Q8—1344no—
637Q8—1342no—
638Q8C2×Q8×D6714yes—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—2688no—
650C2×C4—2688no—
651C2×C4—2688no—
652C2×C4—2682no—
653C2×C4—2682no—
654C2×C4—2682no—
655C2×C4—674no—
656C2×C4—672no—
657C2×C4—678no—
658C2×C4—674no—
659C2×C4—674no—
660C2×C4—672no—
661C2×C4—672no—
662C2×C4—1348no—
663C2×C4—1348no—
664C2×C4—13416no—
665C2×C4—1342no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1344no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4C2×D4×D6712yes—
673C2×C4C2×D4×D6712yes—
674C2×C4C2×D4×D6711yescharacteristic
675C2×C4C2×Q8×D6712yes—
676C2×C4#41×D6712yes—
677C2×C4C24×D6711yescharacteristic
678C8—22no—
679C8—22no—
680C8—1342no—
681C8—1342no—
682C22—674no—
683C22—674no—
684C22—674no—
685C22—6716no—
686C22C22⋊Q8×D6712yes—
687C22#135×D6712yes—
688C22#137×D6712yes—
689C22C22×D4×D6711yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—2682no—
697C4—2682no—
698C4—2682no—
699C4—674no—
700C4—1342no—
701C4—1342no—
702C4—1344no—
703C4C22⋊Q8×D6712yes—
704C4C22×Q8×D6711yescharacteristic
705C4C2×#41×D6711yescharacteristic
706C2—678no—
707C2#479×D6714yesdirect product factor
708C2C2×C22⋊Q8×D6711yescharacteristic
709C2C2×#135×D6711yescharacteristic
710C2C2×#137×D6711yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#479×C67C2
socleC23×C67C22×D4
prime radicalC23×D67C2×D4
hypercenterC2×#479D67
hypocenterC67C22×#479
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. C2×#16863706C2semidirect
4. C2×#16863705C2semidirect
5. C2×#16863704C2semidirect
6. C2×#16863703C2semidirect
7. C2×#16863702C2semidirect
8. C2×#16863701C2semidirect
9. C2×#16863700C2semidirect
10. #479×D67C2direct (N × H)
16. C2×#479×C67C2semidirect
42. #16863706C22semidirect
43. #16863705C22semidirect
44. #16863704C22semidirect
45. #16863703C22semidirect
46. #16863702C22semidirect
47. #16863701C22semidirect
48. #16863700C22semidirect
71. #479×C67C22semidirect
330. C2×D67#479direct (N × H)
351. C2×C67C2×#479semidirect
355. D67C2×#479direct (N × H)
366. C2×#479D67direct (N × H)
372. C67C22×#479semidirect
407. #479C2×D67direct (N × H)
707. C2#479×D67direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#125×D672
C2×C4×Q8×D672
C2×#168637062
C2×#168637052
C2×#168637042
C2×#168637032
C2×#168637022
C2×#168637012
C2×#168637002
#479×D672
C2×#107×D672
C2×#106×D672
C2×C4⋊C8×D672
C2×#103×D672
C2×#479×C672
C22×#47967