Finite Group Databasebeta

← C2×#22565656 #31026124

Subgroups — C2×#22565656 #31026124

Order 17152.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22565656C2116yesmaximal, direct product factor
2C2×#16863335C211yesmaximal, characteristic, complemented
3C2×#16863332C211yesmaximal, characteristic
4C2×#16863328C211yesmaximal, characteristic, complemented
5C2×#16863308C211yesmaximal, characteristic
6C2×#16863302C211yesmaximal, characteristic, complemented
7C2×#16863300C211yesmaximal, characteristic, complemented
8C2×#16863295C211yesmaximal, characteristic, complemented
9C2×#16863289C211yesmaximal, characteristic
10C2×#16863283C211yesmaximal, characteristic, complemented
11C2×#16863279C211yesmaximal, characteristic, complemented
12C2×#16863271C211yesmaximal, characteristic
13C2×#16863271C211yesmaximal, characteristic
14C2×C4×C4⋊Dic67C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#388×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×C4⋊Dic67C2211yescharacteristic
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×C22⋊Dic67C2211yescharacteristic
28C22×C22⋊Dic67C2211yescharacteristic
29C22×C22⋊Dic67C2211yescharacteristic
30C22×C4×Dic67C2211yescharacteristic
31C22×C4×Dic67C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33#16863335C2218yescomplemented
34#16863332C2218yes—
35#16863328C2218yescomplemented
36#16863308C2218yes—
37#16863302C2218yescomplemented
38#16863300C2218yescomplemented
39#16863295C2218yescomplemented
40#16863289C2218yes—
41#16863283C2218yescomplemented
42#16863279C2218yescomplemented
43#16863271C2218yes—
44#16863271C2218yes—
45C4×C4⋊Dic67C2218yescomplemented
46C22⋊C4×Dic67C2218yes—
47C2×C67⋊#95C2211yescharacteristic
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
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
59C22×C4⋊C4×C67C2211yescharacteristic
60C22×C22⋊C4×C67C2211yescharacteristic
61C22×C22⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C42×C67C2211yescharacteristic
64#388×C67C2218yes—
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C22×Dic134—24no—
68C22×Dic134—24no—
69C22×Dic134—42no—
70C22×Dic134C2314yes—
71C23×Dic67—24no—
72C23×Dic67—42no—
73C23×Dic67—42no—
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2314yes—
83C2×C4⋊Dic67—24no—
84C2×C4⋊Dic67—24no—
85C2×C4⋊Dic67—24no—
86C2×C4⋊Dic67—42no—
87C2×C4⋊Dic67—42no—
88C2×C4⋊Dic67—42no—
89C2×C4⋊Dic67C2314yes—
90C2×C4⋊Dic67C2314yes—
91C2×C4⋊Dic67C2314yes—
92C2×C4⋊Dic67C2314yes—
93C2×C4⋊Dic67C2314yes—
94C2×C4⋊Dic67C2314yes—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—42no—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×C22⋊Dic67—24no—
100C2×C22⋊Dic67—42no—
101C2×C22⋊Dic67—42no—
102C2×C22⋊Dic67C2314yes—
103C2×C22⋊Dic67C2314yes—
104C2×C22⋊Dic67C2314yes—
105C2×C4×Dic67—42no—
106C2×C4×Dic67—42no—
107C2×C4×Dic67—42no—
108C2×C4×Dic67C2314yes—
109C2×C4×Dic67C2314yes—
110C2×C4×Dic67C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C25×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C23×C4×C67C2311yescharacteristic
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129C23×C4×C67C2311yescharacteristic
130C2×C4⋊C4×C67—24no—
131C2×C4⋊C4×C67C2314yes—
132C2×C22⋊C4×C67—24no—
133C2×C22⋊C4×C67—24no—
134C2×C22⋊C4×C67Q818yescomplemented
135C2×C22⋊C4×C67C2314yes—
136C2×C22⋊C4×C67C2314yes—
137C2×C22⋊C4×C67C2314yes—
138C2×C42×C67—24no—
139C2×C42×C67C2314yes—
140#95×C67C2314yes—
141#95×C67C2314yes—
142C2×Dic134—28no—
143C2×Dic134—28no—
144C2×Dic134—44no—
145C2×Dic134—416no—
146C22×Dic67—22no—
147C22×Dic67—22no—
148C22×Dic67—22no—
149C22×Dic67—22no—
150C22×Dic67—22no—
151C22×Dic67—22no—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
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—28no—
169C22×Dic67—44no—
170C22×Dic67—44no—
171C22×Dic67—416no—
172C22×Dic67#4114yes—
173C22×Dic67#4114yes—
174C22×Dic67C2412yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C4⋊Dic67—28no—
183C4⋊Dic67—28no—
184C4⋊Dic67—28no—
185C4⋊Dic67—44no—
186C4⋊Dic67—44no—
187C4⋊Dic67—44no—
188Dic67⋊C4—28no—
189Dic67⋊C4—44no—
190C22⋊Dic67—28no—
191C22⋊Dic67—44no—
192C22⋊Dic67—44no—
193C4×Dic67—44no—
194C4×Dic67—44no—
195C4×Dic67—44no—
196C24×C67—22no—
197C24×C67—22no—
198C24×C67—22no—
199C24×C67—22no—
200C24×C67—22no—
201C24×C67—22no—
202C24×C67C2×Q814yes—
203C24×C67C2412yes—
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×C67C2×Q814yes—
220C22×C4×C67C2×Q814yes—
221C22×C4×C67#4114yes—
222C22×C4×C67#4114yes—
223C22×C4×C67C2412yes—
224C22×C4×C67C2412yes—
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C4⋊C4×C67—28no—
230C22⋊C4×C67—28no—
231C22⋊C4×C67—28no—
232C22⋊C4×C67C2×Q8116yescomplemented
233C42×C67—28no—
234C23×C67—28no—
235C23×C67—28no—
236C23×C67—28no—
237C23×C67—22no—
238C23×C67—22no—
239C23×C67—22no—
240C23×C67—22no—
241C23×C67—22no—
242C23×C67—22no—
243C23×C67—44no—
244C23×C67—44no—
245C23×C67—44no—
246C23×C67—44no—
247C23×C67C22×Q814yes—
248C23×C67C22×Q812yes—
249C23×C67C2×#4112yes—
250C23×C67C2×#4112yes—
251C23×C67C2×#4112yes—
252C23×C67C2×#4112yes—
253C23×C67H(5,𝔽2)12yes—
254C23×C67H(5,𝔽2)12yes—
255C23×C67C2511yescharacteristic
256C2×C4×C67—28no—
257C2×C4×C67—28no—
258C2×C4×C67—28no—
259C2×C4×C67—28no—
260C2×C4×C67—22no—
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—44no—
275C2×C4×C67—44no—
276C2×C4×C67C22×Q814yes—
277C2×C4×C67C22×Q814yes—
278C2×C4×C67C2×#4114yes—
279C2×C4×C67C2×#4114yes—
280C2×Dic67—28no—
281C2×Dic67—28no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—22no—
286C2×Dic67—22no—
287C2×Dic67—22no—
288C2×Dic67—22no—
289C2×Dic67—22no—
290C2×Dic67—22no—
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—416no—
305C2×Dic67—44no—
306C2×Dic67—44no—
307C2×Dic67—44no—
308C2×Dic67—44no—
309C2×Dic67—44no—
310C2×Dic67—44no—
311C2×Dic67C2×#4114yes—
312C2×Dic67C2×#4114yes—
313Dic134—416no—
314C22×C67—24no—
315C22×C67—24no—
316C22×C67—24no—
317C22×C67—416no—
318C22×C67—42no—
319C22×C67—42no—
320C22×C67—42no—
321C22×C67—42no—
322C22×C67#52914yes—
323C22×C67#53314yes—
324C22×C67#53814yes—
325C22×C67#55114yes—
326C22×C67#55414yes—
327C22×C67#55414yes—
328C22×C67#55914yes—
329C22×C67C23×Q811yescharacteristic
330C22×C67C22×#4111yescharacteristic
331C22×C67C22×#4111yescharacteristic
332C22×C67C22×#4111yescharacteristic
333C22×C67C22×#4111yescharacteristic
334C22×C67C2×H(5,𝔽2)11yescharacteristic
335C22×C67C2×H(5,𝔽2)11yescharacteristic
336C4×C67—24no—
337C4×C67—24no—
338C4×C67—24no—
339C4×C67—24no—
340C4×C67—42no—
341C4×C67—42no—
342Dic67—24no—
343Dic67—24no—
344Dic67—42no—
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349Dic67—42no—
350C2×#2589—671nomaximal, Sylow
351C2×C67—44no—
352C2×C67#258918yescomplemented
353C2×C67C2×#52911yescharacteristic
354C2×C67C2×#53311yescharacteristic
355C2×C67C2×#53811yescharacteristic
356C2×C67C2×#55111yescharacteristic
357C2×C67C2×#55411yescharacteristic
358C2×C67C2×#55411yescharacteristic
359C2×C67C2×#55911yescharacteristic
360#2589—6716no—
361C2×#400—671no—
362C2×#399—671no—
363C2×#398—671no—
364C2×#393—671no—
365C2×#391—671no—
366C2×#391—671no—
367C2×#389—671no—
368C2×#388—671no—
369C2×#388D6711yescharacteristic
370C2×#387—671no—
371C2×#387—671no—
372C2×#385—671no—
373C2×#385—671no—
374C2×C4×C4⋊C4—671no—
375C2×C4×C22⋊C4—671no—
376C67C2×#258911yescharacteristic, complemented, Sylow
377C23×Q8—671no—
378C24×C4—671no—
379C22×C4⋊C4—671no—
380C22×C4⋊C4—671no—
381C22×C4⋊C4—671no—
382C22×C4⋊C4—671no—
383C22×C4⋊C4—671no—
384C22×C4⋊C4—671no—
385C22×C4⋊C4—671no—
386C22×C4⋊C4—671no—
387C22×C4⋊C4C2×D6711yescharacteristic
388C22×C22⋊C4—671no—
389C22×C22⋊C4—671no—
390C22×C22⋊C4—671no—
391C22×C22⋊C4C2×D6711yescharacteristic
392C22×C22⋊C4C2×D6711yescharacteristic
393C22×C22⋊C4C2×D6711yescharacteristic
394C22×C42—671no—
395C22×C42—671no—
396C22×C42—671no—
397C22×C42C2×D6711yescharacteristic
398#400—678no—
399#399—678no—
400#398—678no—
401#393—678no—
402#391—678no—
403#391—678no—
404#389—678no—
405#388—678no—
406#388C2×D6718yes—
407#387—678no—
408#387—678no—
409#385—678no—
410#385—678no—
411C4×C4⋊C4—678no—
412C4×C22⋊C4—678no—
413C2×#95—671no—
414C2×#95—671no—
415C2×#95—671no—
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×#95C2×D6711yescharacteristic
426C2×#95C2×D6711yescharacteristic
427C25C22×D6711yescharacteristic
428C22×Q8—2682no—
429C22×Q8—674no—
430C22×Q8—1344no—
431C22×Q8—1344no—
432C23×C4—2682no—
433C23×C4—2682no—
434C23×C4—674no—
435C23×C4—671no—
436C23×C4—671no—
437C23×C4—671no—
438C23×C4—671no—
439C23×C4—671no—
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4—1344no—
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C23×C4C22×D6711yescharacteristic
447C23×C4C22×D6711yescharacteristic
448C23×C4C22×D6711yescharacteristic
449C23×C4C22×D6711yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—2682no—
452C2×C4⋊C4—2682no—
453C2×C4⋊C4—2682no—
454C2×C4⋊C4—2682no—
455C2×C4⋊C4—674no—
456C2×C4⋊C4—674no—
457C2×C4⋊C4—674no—
458C2×C4⋊C4—674no—
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⋊C4—1344no—
466C2×C4⋊C4—1344no—
467C2×C4⋊C4C22×D6714yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—2682no—
471C2×C22⋊C4—2682no—
472C2×C22⋊C4—674no—
473C2×C22⋊C4—674no—
474C2×C22⋊C4—674no—
475C2×C22⋊C4—1344no—
476C2×C22⋊C4Dic13418yescomplemented
477C2×C22⋊C4C22×D6714yes—
478C2×C22⋊C4C22×D6714yes—
479C2×C22⋊C4C22×D6714yes—
480C2×C42—24no—
481C2×C42—2682no—
482C2×C42—2682no—
483C2×C42—2682no—
484C2×C42—674no—
485C2×C42—674no—
486C2×C42—674no—
487C2×C42C22×D6714yes—
488#95—674no—
489#95—674no—
490#95—674no—
491#95—674no—
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#95C22×D6714yes—
501#95C22×D6714yes—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24C2×Dic13414yes—
509C24C23×D6712yes—
510C24C23×D6711yescharacteristic
511C2×Q8—26816no—
512C2×Q8—2684no—
513C2×Q8—1348no—
514C2×Q8—1348no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
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—26816no—
530C22×C4—2684no—
531C22×C4—2684no—
532C22×C4—674no—
533C22×C4—674no—
534C22×C4—672no—
535C22×C4—672no—
536C22×C4—672no—
537C22×C4—672no—
538C22×C4—672no—
539C22×C4—672no—
540C22×C4—672no—
541C22×C4—672no—
542C22×C4—1348no—
543C22×C4—1342no—
544C22×C4—1342no—
545C22×C4—1342no—
546C22×C4—1342no—
547C22×C4—1342no—
548C22×C4—1342no—
549C22×C4—1342no—
550C22×C4—1342no—
551C22×C4—1342no—
552C22×C4—1342no—
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×C4C2×Dic13414yes—
566C22×C4C2×Dic13414yes—
567C22×C4#1176162714yes—
568C22×C4#1176162714yes—
569C22×C4C23×D6712yes—
570C22×C4C23×D6712yes—
571C22×C4C23×D6712yes—
572C22×C4C23×D6712yes—
573C22×C4C23×D6712yes—
574C22×C4C23×D6712yes—
575C4⋊C4—28no—
576C4⋊C4—2684no—
577C4⋊C4—2684no—
578C4⋊C4—2684no—
579C4⋊C4—2684no—
580C4⋊C4—1348no—
581C4⋊C4—1348no—
582C4⋊C4—1348no—
583C4⋊C4—1348no—
584C22⋊C4—28no—
585C22⋊C4—28no—
586C22⋊C4—2684no—
587C22⋊C4—2684no—
588C22⋊C4—1348no—
589C22⋊C4C2×Dic134116yescomplemented
590C42—28no—
591C42—2684no—
592C42—2684no—
593C42—2684no—
594C23—28no—
595C23—28no—
596C23—28no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—44no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23C22×Dic13414yes—
608C23C22×Dic13412yes—
609C23#41×D6712yes—
610C23#41×D6712yes—
611C23C2×#1176162712yes—
612C23C2×#1176162712yes—
613C23#1452408912yes—
614C23#1452408912yes—
615C23C24×D6711yescharacteristic
616Q8—26816no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
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—44no—
636C2×C4—44no—
637C2×C4—2684no—
638C2×C4—2684no—
639C2×C4—2684no—
640C2×C4—2684no—
641C2×C4—2684no—
642C2×C4—2684no—
643C2×C4—26816no—
644C2×C4—674no—
645C2×C4—674no—
646C2×C4—1342no—
647C2×C4—1342no—
648C2×C4—1342no—
649C2×C4—1342no—
650C2×C4—1342no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4—1342no—
656C2×C4—1342no—
657C2×C4—1342no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4—1342no—
661C2×C4—1342no—
662C2×C4—1342no—
663C2×C4—1342no—
664C2×C4—1348no—
665C2×C4—1342no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1348no—
670C2×C4C22×Dic13414yes—
671C2×C4C22×Dic13414yes—
672C2×C4C2×#1176162714yes—
673C2×C4C2×#1176162714yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—416no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#1686392714yes—
683C22#1686394914yes—
684C22#1686398514yes—
685C22#1686406914yes—
686C22#1686410314yes—
687C22#1686410314yes—
688C22#1686412814yes—
689C22C23×Dic13411yescharacteristic
690C22C2×#41×D6711yescharacteristic
691C22C2×#41×D6711yescharacteristic
692C22C22×#1176162711yescharacteristic
693C22C22×#1176162711yescharacteristic
694C22C2×#1452408911yescharacteristic
695C22C2×#1452408911yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—2682no—
703C4—2682no—
704C4—2682no—
705C4—2682no—
706C4—2682no—
707C4—2682no—
708C4—1344no—
709C4—1344no—
710C2—44no—
711C2#2256565618yesdirect product factor
712C2C2×#1686392711yescharacteristic
713C2C2×#1686394911yescharacteristic
714C2C2×#1686398511yescharacteristic
715C2C2×#1686406911yescharacteristic
716C2C2×#1686410311yescharacteristic
717C2C2×#1686410311yescharacteristic
718C2C2×#1686412811yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#388D67
hypocenterC67C2×#2589
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #22565656C2direct (N × H)
2. C2×#16863335C2semidirect
4. C2×#16863328C2semidirect
6. C2×#16863302C2semidirect
7. C2×#16863300C2semidirect
8. C2×#16863295C2semidirect
10. C2×#16863283C2semidirect
11. C2×#16863279C2semidirect
14. C2×C4×C4⋊Dic67C2semidirect
33. #16863335C22semidirect
35. #16863328C22semidirect
37. #16863302C22semidirect
38. #16863300C22semidirect
39. #16863295C22semidirect
41. #16863283C22semidirect
42. #16863279C22semidirect
45. C4×C4⋊Dic67C22semidirect
134. C2×C22⋊C4×C67Q8semidirect
232. C22⋊C4×C67C2×Q8semidirect
352. C2×C67#2589semidirect
376. C67C2×#2589semidirect
476. C2×C22⋊C4Dic134semidirect
589. C22⋊C4C2×Dic134semidirect
711. C2#22565656direct (N × H)

Maximal subgroups

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

subgroupindex
#225656562
C2×#168633352
C2×#168633322
C2×#168633282
C2×#168633082
C2×#168633022
C2×#168633002
C2×#168632952
C2×#168632892
C2×#168632832
C2×#168632792
C2×#168632712
C2×C4×C4⋊Dic672
C2×C22⋊C4×Dic672
C2×#388×C672
C2×#258967