Finite Group Databasebeta

← C2×#22562963 #31014686

Subgroups — C2×#22562963 #31014686

Order 17152.

2678 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524021C211yesmaximal, characteristic
2#22562963C2116yesmaximal, direct product factor
3C2×#16863301C211yesmaximal, characteristic, complemented
4C2×#16863300C211yesmaximal, characteristic, complemented
5C2×#16863288C211yesmaximal, characteristic
6C2×#16863286C211yesmaximal, characteristic
7C2×#16863285C211yesmaximal, characteristic
8C2×#16863285C211yesmaximal, characteristic
9C2×#16863283C211yesmaximal, characteristic, complemented
10C2×#16863280C211yesmaximal, characteristic, complemented
11C2×#16863278C211yesmaximal, characteristic, complemented
12C2×#16863258C211yesmaximal, characteristic
13C2×C4⋊C4×Dic67C211yesmaximal, characteristic, complemented
14C2×#16863247C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic
16C2×#387×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C2×#14524021C4116yescomplemented
20C2×#14524021C2218yes—
21C22×C4⋊Dic67C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×(C2×D67)⋊C4C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863301C2218yescomplemented
38#16863300C2218yescomplemented
39#16863288C2218yes—
40#16863286C2218yes—
41#16863285C2218yes—
42#16863285C2218yes—
43#16863283C2218yescomplemented
44#16863280C2218yescomplemented
45#16863278C2218yescomplemented
46#16863258C2218yes—
47C4⋊C4×Dic67C2218yescomplemented
48#16863247C2218yescomplemented
49C4×(C2×D67)⋊C4C2218yes—
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C42×C67C2211yescharacteristic
63#387×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C24×D67C2311yescharacteristic
69C22×Dic134—42no—
70C22×Dic134—42no—
71C22×Dic134C2×C418yes—
72C22×Dic134C2314yes—
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C22×C4×D67—42no—
81C22×C4×D67—42no—
82C22×C4×D67C2×C418yes—
83C22×C4×D67C2314yes—
84#14524021C2×C4164yescomplemented
85C2×C4⋊Dic67—24no—
86C2×C4⋊Dic67C2314yes—
87C2×Dic67⋊C4—24no—
88C2×Dic67⋊C4—42no—
89C2×Dic67⋊C4C2×C418yes—
90C2×Dic67⋊C4C2×C418yes—
91C2×Dic67⋊C4C2314yes—
92C2×Dic67⋊C4C2314yes—
93C2×Dic67⋊C4C2314yes—
94C2×Dic67⋊C4C2314yes—
95C2×(C2×D67)⋊C4—24no—
96C2×(C2×D67)⋊C4—24no—
97C2×(C2×D67)⋊C4—42no—
98C2×(C2×D67)⋊C4—42no—
99C2×(C2×D67)⋊C4C2×C418yes—
100C2×(C2×D67)⋊C4C2×C418yes—
101C2×(C2×D67)⋊C4C2314yes—
102C2×(C2×D67)⋊C4C2314yes—
103C2×(C2×D67)⋊C4C2314yes—
104C2×(C2×D67)⋊C4C2314yes—
105C2×(C2×D67)⋊C4C2314yes—
106C2×(C2×D67)⋊C4C2314yes—
107C2×C4×Dic67—24no—
108C2×C4×Dic67—24no—
109C2×C4×Dic67—42no—
110C2×C4×Dic67—42no—
111C2×C4×Dic67—42no—
112C2×C4×Dic67C2314yes—
113C2×C4×Dic67C2314yes—
114C2×C4×Dic67C2314yes—
115C2×C4×Dic67C2314yes—
116C2×C4×Dic67C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C2×C4⋊C4×C67—42no—
135C2×C4⋊C4×C67C2×C418yes—
136C2×C4⋊C4×C67C2314yes—
137C2×C4⋊C4×C67C2314yes—
138C2×C42×C67—42no—
139C2×C42×C67C2314yes—
140#95×C67C2314yes—
141#95×C67C2314yes—
142#95×C67C2314yes—
143#95×C67C2314yes—
144C23×D67—22no—
145C23×D67—22no—
146C23×D67—22no—
147C23×D67—22no—
148C23×D67—22no—
149C23×D67—22no—
150C23×D67C22×C414yes—
151C23×D67C2412yes—
152C2×Dic134—416no—
153C2×Dic134—44no—
154C2×Dic134—44no—
155C2×Dic134C22×C4116yes—
156C22×Dic67—22no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67C22×C414yes—
173C22×Dic67C22×C414yes—
174C22×Dic67C22×C414yes—
175C22×Dic67#4114yes—
176C22×Dic67#4114yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C2×C4×D67—416no—
185C2×C4×D67—44no—
186C2×C4×D67—44no—
187C2×C4×D67C22×C4116yes—
188C4⋊Dic67—28no—
189Dic67⋊C4—28no—
190Dic67⋊C4—44no—
191Dic67⋊C4C22×C4116yes—
192Dic67⋊C4C22×C4116yes—
193(C2×D67)⋊C4—28no—
194(C2×D67)⋊C4—28no—
195(C2×D67)⋊C4—44no—
196(C2×D67)⋊C4—44no—
197(C2×D67)⋊C4C22×C4116yes—
198(C2×D67)⋊C4C22×C4116yes—
199C4×Dic67—28no—
200C4×Dic67—28no—
201C4×Dic67—44no—
202C4×Dic67—44no—
203C4×Dic67—44no—
204C24×C67C2411yescharacteristic
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67—22no—
219C22×C4×C67—22no—
220C22×C4×C67—22no—
221C22×C4×C67—22no—
222C22×C4×C67—22no—
223C22×C4×C67C22×C414yes—
224C22×C4×C67C22×C414yes—
225C22×C4×C67C22×C414yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C22×C4×C67C2412yes—
232C22×C4×C67C2412yes—
233C4⋊C4×C67—44no—
234C4⋊C4×C67C22×C4116yes—
235C42×C67—44no—
236C23×C67C23×C412yes—
237C23×C67C2×#4112yes—
238C23×C67C2×#4112yes—
239C23×C67H(5,𝔽2)12yes—
240C23×C67H(5,𝔽2)12yes—
241C23×C672−1+412yes—
242C23×C672−1+412yes—
243C23×C67C2511yescharacteristic
244C22×D67—28no—
245C22×D67—28no—
246C22×D67—28no—
247C22×D67—22no—
248C22×D67—22no—
249C22×D67—22no—
250C22×D67—22no—
251C22×D67—22no—
252C22×D67—22no—
253C22×D67—44no—
254C22×D67—44no—
255C22×D67—44no—
256C22×D67—44no—
257C22×D67C23×C414yes—
258C2×C4×C67—28no—
259C2×C4×C67—28no—
260C2×C4×C67—28no—
261C2×C4×C67—22no—
262C2×C4×C67—22no—
263C2×C4×C67—22no—
264C2×C4×C67—22no—
265C2×C4×C67—22no—
266C2×C4×C67—22no—
267C2×C4×C67—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—44no—
280C2×C4×C67—44no—
281C2×C4×C67—44no—
282C2×C4×C67—44no—
283C2×C4×C67C23×C414yes—
284C2×C4×C67C23×C414yes—
285C2×C4×C67C23×C414yes—
286C2×Dic67—28no—
287C2×Dic67—28no—
288C2×Dic67—28no—
289C2×Dic67—28no—
290C2×Dic67—28no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—44no—
308C2×Dic67—44no—
309C2×Dic67C23×C414yes—
310C2×Dic67C23×C414yes—
311C2×Dic67C23×C414yes—
312C2×Dic67C2×#4114yes—
313C2×Dic67C2×#4114yes—
314C4×D67—416no—
315Dic134—416no—
316C22×C67C4×#4114yes—
317C22×C67#51814yes—
318C22×C67#51914yes—
319C22×C67#53914yes—
320C22×C67#53914yes—
321C22×C67#54214yes—
322C22×C67#54214yes—
323C22×C67C24×C411yescharacteristic
324C22×C67C22×#4111yescharacteristic
325C22×C67C22×#4111yescharacteristic
326C22×C67C2×H(5,𝔽2)11yescharacteristic
327C22×C67C2×H(5,𝔽2)11yescharacteristic
328C22×C67C2×2−1+411yescharacteristic
329C22×C67C2×2−1+411yescharacteristic
330C2×D67—24no—
331C2×D67—24no—
332C2×D67—24no—
333C2×D67—416no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—42no—
338C4×C67—24no—
339C4×C67—24no—
340C4×C67—24no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67—42no—
345Dic67—24no—
346Dic67—24no—
347Dic67—24no—
348Dic67—24no—
349Dic67—24no—
350Dic67—42no—
351Dic67—42no—
352C2×#2332—671nomaximal, Sylow
353C2×C67#233218yescomplemented
354C2×C67C2×C4×#4111yescharacteristic
355C2×C67C2×#51811yescharacteristic
356C2×C67C2×#51911yescharacteristic
357C2×C67C2×#53911yescharacteristic
358C2×C67C2×#53911yescharacteristic
359C2×C67C2×#54211yescharacteristic
360C2×C67C2×#54211yescharacteristic
361D67—44no—
362C22×C22⋊Q8—671no—
363#2332—6716no—
364C2×#391—671no—
365C2×#391—671no—
366C2×#388—671no—
367C2×#388—671no—
368C2×#388—671no—
369C2×#388—671no—
370C2×#387—671no—
371C2×#387—671no—
372C2×#387—671no—
373C2×#387D6711yescharacteristic, complemented
374C2×#381—671no—
375C2×C4×C4⋊C4—671no—
376C2×C4×C4⋊C4—671no—
377C2×C4×C22⋊C4—671no—
378C67C2×#233211yescharacteristic, complemented, Sylow
379C23×Q8—671no—
380C24×C4—671no—
381C2×C22⋊Q8—6716no—
382C2×C22⋊Q8—678no—
383C22×C4⋊C4—671no—
384C22×C4⋊C4—671no—
385C22×C4⋊C4—671no—
386C22×C4⋊C4—671no—
387C22×C4⋊C4—671no—
388C22×C4⋊C4C2×D6711yescharacteristic
389C22×C4⋊C4C2×D6711yescharacteristic
390C22×C22⋊C4—671no—
391C22×C22⋊C4—671no—
392C22×C22⋊C4—671no—
393C22×C22⋊C4—671no—
394C22×C22⋊C4—671no—
395C22×C22⋊C4—671no—
396C22×C42—671no—
397C22×C42—671no—
398C22×C42—671no—
399C22×C42—671no—
400C22×C42—671no—
401C22×C42C2×D6711yescharacteristic
402#391—678no—
403#391—678no—
404#388—678no—
405#388—678no—
406#388—678no—
407#388—678no—
408#387—678no—
409#387—678no—
410#387—678no—
411#387C2×D6718yescomplemented
412#381—678no—
413C4×C4⋊C4—678no—
414C4×C4⋊C4—678no—
415C4×C22⋊C4—678no—
416C2×#95—671no—
417C2×#95—671no—
418C2×#95—671no—
419C2×#95—671no—
420C2×#95—671no—
421C2×#95—671no—
422C2×#95—671no—
423C2×#95—671no—
424C2×#95—671no—
425C2×#95—671no—
426C2×#95C2×D6711yescharacteristic
427C2×#95C2×D6711yescharacteristic
428C2×#95C2×D6711yescharacteristic
429C2×#95C2×D6711yescharacteristic
430C25—671no—
431C22×Q8—2682no—
432C22×Q8—2682no—
433C22×Q8—678no—
434C22×Q8—674no—
435C23×C4—2682no—
436C23×C4—2682no—
437C23×C4—678no—
438C23×C4—674no—
439C23×C4—671no—
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4—671no—
444C23×C4—671no—
445C23×C4—671no—
446C23×C4C22×D6711yescharacteristic
447C23×C4C22×D6711yescharacteristic
448C23×C4C22×D6711yescharacteristic
449C23×C4C22×D6711yescharacteristic
450C23×C4C22×D6711yescharacteristic
451C23×C4C22×D6711yescharacteristic
452C23×C4C22×D6711yescharacteristic
453C22⋊Q8—6764no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—2682no—
456C2×C4⋊C4—674no—
457C2×C4⋊C4—678no—
458C2×C4⋊C4—678no—
459C2×C4⋊C4—674no—
460C2×C4⋊C4—674no—
461C2×C4⋊C4—674no—
462C2×C4⋊C4—674no—
463C2×C4⋊C4—1344no—
464C2×C4⋊C4—1344no—
465C2×C4⋊C4C4×D6718yes—
466C2×C4⋊C4C22×D6714yes—
467C2×C4⋊C4C22×D6714yes—
468C2×C22⋊C4—2682no—
469C2×C22⋊C4—2682no—
470C2×C22⋊C4—674no—
471C2×C22⋊C4—674no—
472C2×C22⋊C4—678no—
473C2×C22⋊C4—678no—
474C2×C22⋊C4—674no—
475C2×C22⋊C4—674no—
476C2×C22⋊C4—674no—
477C2×C22⋊C4—674no—
478C2×C22⋊C4—1344no—
479C2×C22⋊C4—1344no—
480C2×C42—42no—
481C2×C42—2682no—
482C2×C42—2682no—
483C2×C42—2682no—
484C2×C42—674no—
485C2×C42—674no—
486C2×C42—674no—
487C2×C42—674no—
488C2×C42—674no—
489C2×C42—1344no—
490C2×C42—1344no—
491C2×C42C22×D6714yes—
492#95—674no—
493#95—674no—
494#95—674no—
495#95—674no—
496#95—674no—
497#95—674no—
498#95—674no—
499#95—674no—
500#95—674no—
501#95—674no—
502#95C22×D6714yes—
503#95C22×D6714yes—
504#95C22×D6714yes—
505#95C22×D6714yes—
506C24—674no—
507C24—672no—
508C24—1342no—
509C24—1342no—
510C24—1342no—
511C24—1342no—
512C24—1342no—
513C24—1342no—
514C24C23×D6711yescharacteristic
515C2×Q8—26816no—
516C2×Q8—2684no—
517C2×Q8—2684no—
518C2×Q8—6716no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—26816no—
538C22×C4—2684no—
539C22×C4—2684no—
540C22×C4—6716no—
541C22×C4—674no—
542C22×C4—674no—
543C22×C4—674no—
544C22×C4—674no—
545C22×C4—674no—
546C22×C4—672no—
547C22×C4—672no—
548C22×C4—672no—
549C22×C4—672no—
550C22×C4—672no—
551C22×C4—672no—
552C22×C4—672no—
553C22×C4—1342no—
554C22×C4—1342no—
555C22×C4—1342no—
556C22×C4—1342no—
557C22×C4—1342no—
558C22×C4—1342no—
559C22×C4—1342no—
560C22×C4—1342no—
561C22×C4—1342no—
562C22×C4—1342no—
563C22×C4—1342no—
564C22×C4—1342no—
565C22×C4—1342no—
566C22×C4—1342no—
567C22×C4—1342no—
568C22×C4—1342no—
569C22×C4C2×C4×D6714yes—
570C22×C4C2×C4×D6714yes—
571C22×C4C2×C4×D6714yes—
572C22×C4C23×D6712yes—
573C22×C4C23×D6712yes—
574C22×C4C23×D6712yes—
575C22×C4C23×D6712yes—
576C22×C4C23×D6712yes—
577C22×C4C23×D6712yes—
578C22×C4C23×D6712yes—
579C4⋊C4—44no—
580C4⋊C4—2684no—
581C4⋊C4—6716no—
582C4⋊C4—6716no—
583C4⋊C4—1348no—
584C4⋊C4—1348no—
585C4⋊C4C2×C4×D67116yes—
586C22⋊C4—2684no—
587C22⋊C4—2684no—
588C22⋊C4—6716no—
589C22⋊C4—6716no—
590C22⋊C4—1348no—
591C22⋊C4—1348no—
592C42—44no—
593C42—2684no—
594C42—2684no—
595C42—2684no—
596C42—1348no—
597C42—1348no—
598C23—2684no—
599C23—2684no—
600C23—2684no—
601C23—2684no—
602C23—674no—
603C23—1348no—
604C23—1348no—
605C23—1348no—
606C23—1342no—
607C23—1342no—
608C23—1342no—
609C23—1342no—
610C23—1342no—
611C23—1342no—
612C23C22×C4×D6712yes—
613C23#41×D6712yes—
614C23#41×D6712yes—
615C23#1452408812yes—
616C23#1452408912yes—
617C23#1452409012yes—
618C23#1452409112yes—
619C23C24×D6711yescharacteristic
620Q8—26816no—
621C2×C4—28no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—26816no—
647C2×C4—2684no—
648C2×C4—2684no—
649C2×C4—674no—
650C2×C4—674no—
651C2×C4—674no—
652C2×C4—674no—
653C2×C4—674no—
654C2×C4—1342no—
655C2×C4—1342no—
656C2×C4—1342no—
657C2×C4—1342no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4—1348no—
661C2×C4—1348no—
662C2×C4—1348no—
663C2×C4—1342no—
664C2×C4—1342no—
665C2×C4—1342no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1348no—
674C2×C4—1348no—
675C2×C4C22×C4×D6714yes—
676C2×C4C22×C4×D6714yes—
677C2×C4C22×C4×D6714yes—
678C22—2682no—
679C22—2682no—
680C22—26816no—
681C22—2682no—
682C22—2682no—
683C22—1344no—
684C22—1344no—
685C22—1344no—
686C22#1686386414yes—
687C22#1686386814yes—
688C22#1686387214yes—
689C22#1686398714yes—
690C22#1686399414yes—
691C22#1686401414yes—
692C22#1686401614yes—
693C22C23×C4×D6711yescharacteristic
694C22C2×#41×D6711yescharacteristic
695C22C2×#41×D6711yescharacteristic
696C22C2×#1452408811yescharacteristic
697C22C2×#1452408911yescharacteristic
698C22C2×#1452409011yescharacteristic
699C22C2×#1452409111yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—2682no—
708C4—2682no—
709C4—1344no—
710C4—1344no—
711C4—1344no—
712C4—1344no—
713C4—1344no—
714C2—2684no—
715C2#2256296318yesdirect product factor
716C2C2×#1686386411yescharacteristic
717C2C2×#1686386811yescharacteristic
718C2C2×#1686387211yescharacteristic
719C2C2×#1686398711yescharacteristic
720C2C2×#1686399411yescharacteristic
721C2C2×#1686401411yescharacteristic
722C2C2×#1686401611yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#387×C67C2
socleC24×C67C24
prime radicalC24×D67C23
cosocleC23×C67C25
hypercenterC2×#387D67
hypocenterC67C2×#2332
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #22562963C2direct (N × H)
3. C2×#16863301C2semidirect
4. C2×#16863300C2semidirect
9. C2×#16863283C2semidirect
10. C2×#16863280C2semidirect
11. C2×#16863278C2semidirect
13. C2×C4⋊C4×Dic67C2semidirect
14. C2×#16863247C2semidirect
16. C2×#387×C67C2semidirect
19. C2×#14524021C4semidirect
37. #16863301C22semidirect
38. #16863300C22semidirect
43. #16863283C22semidirect
44. #16863280C22semidirect
45. #16863278C22semidirect
47. C4⋊C4×Dic67C22semidirect
48. #16863247C22semidirect
63. #387×C67C22semidirect
84. #14524021C2×C4semidirect
353. C2×C67#2332semidirect
373. C2×#387D67semidirect
378. C67C2×#2332semidirect
411. #387C2×D67semidirect
715. C2#22562963direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240212
#225629632
C2×#168633012
C2×#168633002
C2×#168632882
C2×#168632862
C2×#168632852
C2×#168632832
C2×#168632802
C2×#168632782
C2×#168632582
C2×C4⋊C4×Dic672
C2×#168632472
C2×C4×(C2×D67)⋊C42
C2×#387×C672
C2×#233267