Finite Group Databasebeta

← C2×#22564422 #31024328

Subgroups — C2×#22564422 #31024328

Order 17152.

2638 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×#14524036C211yesmaximal, characteristic
2C22×#14524002C211yesmaximal, characteristic
3#22564422C2116yesmaximal, direct product factor
4C2×#16863329C211yesmaximal, characteristic, complemented
5C2×#16863328C211yesmaximal, characteristic, complemented
6C2×#16863324C211yesmaximal, characteristic
7C2×#16863321C211yesmaximal, characteristic
8C2×#16863293C211yesmaximal, characteristic, complemented
9C2×#16863291C211yesmaximal, characteristic, complemented
10C2×#16863290C211yesmaximal, characteristic
11C2×#16863283C211yesmaximal, characteristic, complemented
12C2×#16863282C211yesmaximal, characteristic, complemented
13C2×#16863278C211yesmaximal, characteristic, complemented
14C2×#16863269C211yesmaximal, characteristic
15C2×C4⋊C4×Dic67C211yesmaximal, characteristic, complemented
16C2×#385×C67C211yesmaximal, characteristic
17C2×#14524036—28no—
18C2×#14524036C2218yes—
19C2×#14524002—28no—
20C2×#14524002C2218yes—
21C22×C4⋊Dic67C2211yescharacteristic
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2211yescharacteristic
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×C22⋊Dic67C2211yescharacteristic
32C22×C22⋊Dic67C2211yescharacteristic
33C22×C22⋊Dic67C2211yescharacteristic
34C22×C22⋊Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39#16863329C2218yescomplemented
40#16863328C2218yescomplemented
41#16863324C2218yes—
42#16863321C2218yes—
43#16863293C2218yescomplemented
44#16863291C2218yescomplemented
45#16863290C2218yes—
46#16863283C2218yescomplemented
47#16863282C2218yescomplemented
48#16863278C2218yescomplemented
49#16863269C2218yes—
50C4⋊C4×Dic67C2218yescomplemented
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
60C2×C67⋊#95C2211yescharacteristic
61C24×C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66#385×C67C2218yes—
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C23×Dic67C2311yescharacteristic
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77#14524036—232no—
78#14524002—232no—
79C2×C4⋊Dic67—24no—
80C2×C4⋊Dic67—24no—
81C2×C4⋊Dic67—24no—
82C2×C4⋊Dic67—24no—
83C2×C4⋊Dic67C2314yes—
84C2×C4⋊Dic67C2314yes—
85C2×C4⋊Dic67C2314yes—
86C2×C4⋊Dic67C2314yes—
87C2×Dic67⋊C4—24no—
88C2×Dic67⋊C4—24no—
89C2×Dic67⋊C4—24no—
90C2×Dic67⋊C4—24no—
91C2×Dic67⋊C4—24no—
92C2×Dic67⋊C4—24no—
93C2×Dic67⋊C4C2314yes—
94C2×Dic67⋊C4C2314yes—
95C2×Dic67⋊C4C2314yes—
96C2×Dic67⋊C4C2314yes—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×C22⋊Dic67—24no—
100C2×C22⋊Dic67—24no—
101C2×C22⋊Dic67—24no—
102C2×C22⋊Dic67D418yes—
103C2×C22⋊Dic67C2314yes—
104C2×C22⋊Dic67C2314yes—
105C2×C22⋊Dic67C2314yes—
106C2×C22⋊Dic67C2314yes—
107C2×C4×Dic67—24no—
108C2×C4×Dic67—24no—
109C2×C4×Dic67—24no—
110C2×C4×Dic67—24no—
111C2×C4×Dic67C2314yes—
112C2×C4×Dic67C2314yes—
113C2×C4×Dic67C2314yes—
114C2×C4×Dic67C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C25×C67C2311yescharacteristic
126C23×C4×C67—24no—
127C23×C4×C67—24no—
128C23×C4×C67—24no—
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2314yes—
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C2×C4⋊C4×C67—24no—
137C2×C4⋊C4×C67—24no—
138C2×C4⋊C4×C67C2314yes—
139C2×C4⋊C4×C67C2314yes—
140C2×C22⋊C4×C67—24no—
141C2×C22⋊C4×C67—24no—
142C2×C22⋊C4×C67C2314yes—
143C2×C22⋊C4×C67C2314yes—
144#95×C67C2314yes—
145#95×C67C2314yes—
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×Dic67C2×D414yes—
168C22×Dic67C2×D414yes—
169C22×Dic67#4114yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174C22×Dic67C2412yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C4⋊Dic67—28no—
179C4⋊Dic67—28no—
180C4⋊Dic67—28no—
181C4⋊Dic67—28no—
182Dic67⋊C4—28no—
183Dic67⋊C4—28no—
184Dic67⋊C4—28no—
185Dic67⋊C4—28no—
186Dic67⋊C4—28no—
187Dic67⋊C4—28no—
188C22⋊Dic67—28no—
189C22⋊Dic67—28no—
190C22⋊Dic67—28no—
191C22⋊Dic67C2×D4116yes—
192C4×Dic67—28no—
193C4×Dic67—28no—
194C4×Dic67—28no—
195C4×Dic67—28no—
196C24×C67—22no—
197C24×C67—22no—
198C24×C67—22no—
199C24×C67—22no—
200C24×C67—22no—
201C24×C67—22no—
202C24×C67C2×D414yes—
203C24×C67C2412yes—
204C24×C67C2411yescharacteristic
205C22×C4×C67—232no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—28no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—28no—
214C22×C4×C67—28no—
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×C67—22no—
224C22×C4×C67#4114yes—
225C22×C4×C67#4114yes—
226C22×C4×C67#4114yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C22×C4×C67C2412yes—
232C22×C4×C67C2412yes—
233C4⋊C4×C67—28no—
234C4⋊C4×C67—28no—
235C22⋊C4×C67—28no—
236C22⋊C4×C67—28no—
237C23×C67—28no—
238C23×C67—28no—
239C23×C67—28no—
240C23×C67—22no—
241C23×C67—22no—
242C23×C67—22no—
243C23×C67—22no—
244C23×C67—22no—
245C23×C67—22no—
246C23×C67—44no—
247C23×C67—44no—
248C23×C67—44no—
249C23×C67—44no—
250C23×C67C22×D414yes—
251C23×C67C22×D412yes—
252C23×C67C2×#4112yes—
253C23×C67C2×#4112yes—
254C23×C67C2×#4112yes—
255C23×C67C2×#4112yes—
256C23×C672−1+412yes—
257C23×C672−1+412yes—
258C23×C67C2511yescharacteristic
259C2×C4×C67—232no—
260C2×C4×C67—28no—
261C2×C4×C67—28no—
262C2×C4×C67—28no—
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—44no—
279C2×C4×C67—44no—
280C2×C4×C67—44no—
281C2×C4×C67C2×#4114yes—
282C2×C4×C67C2×#4114yes—
283C2×C4×C67C2×#4114yes—
284C2×Dic67—28no—
285C2×Dic67—28no—
286C2×Dic67—28no—
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—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—44no—
309C2×Dic67—44no—
310C2×Dic67—44no—
311C2×Dic67—44no—
312C2×Dic67—44no—
313C2×Dic67C22×D414yes—
314C2×Dic67C22×D414yes—
315C2×Dic67C2×#4114yes—
316C22×C67—24no—
317C22×C67—24no—
318C22×C67—24no—
319C22×C67—42no—
320C22×C67—42no—
321C22×C67—42no—
322C22×C67—42no—
323C22×C67—416no—
324C22×C67#52514yes—
325C22×C67#52914yes—
326C22×C67#54114yes—
327C22×C67#54714yes—
328C22×C67#54714yes—
329C22×C67#55214yes—
330C22×C67#55614yes—
331C22×C67C23×D411yescharacteristic
332C22×C67C22×#4111yescharacteristic
333C22×C67C22×#4111yescharacteristic
334C22×C67C22×#4111yescharacteristic
335C22×C67C22×#4111yescharacteristic
336C22×C67C2×2−1+411yescharacteristic
337C22×C67C2×2−1+411yescharacteristic
338C4×C67—24no—
339C4×C67—24no—
340C4×C67—24no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67—42no—
344Dic67—24no—
345Dic67—24no—
346Dic67—24no—
347Dic67—42no—
348Dic67—42no—
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352C2×#2478—671nomaximal, Sylow
353C2×C67—44no—
354C2×C67#247818yescomplemented
355C2×C67C2×#52511yescharacteristic
356C2×C67C2×#52911yescharacteristic
357C2×C67C2×#54111yescharacteristic
358C2×C67C2×#54711yescharacteristic
359C2×C67C2×#54711yescharacteristic
360C2×C67C2×#55211yescharacteristic
361C2×C67C2×#55611yescharacteristic
362C22×#126—671no—
363C22×#117—671no—
364#2478—6716no—
365C2×#398—671no—
366C2×#398—671no—
367C2×#397—671no—
368C2×#397—671no—
369C2×#389—671no—
370C2×#389—671no—
371C2×#388—671no—
372C2×#387—671no—
373C2×#387—671no—
374C2×#387—671no—
375C2×#385—671no—
376C2×#385D6711yescharacteristic
377C2×C4×C4⋊C4—671no—
378C67C2×#247811yescharacteristic, complemented, Sylow
379C24×C4C2×D6711yescharacteristic
380C2×#126—678no—
381C2×#126—1348no—
382C2×#117—678no—
383C2×#117—1348no—
384C22×C4⋊C4—671no—
385C22×C4⋊C4—671no—
386C22×C4⋊C4—671no—
387C22×C4⋊C4—671no—
388C22×C4⋊C4—671no—
389C22×C4⋊C4—671no—
390C22×C4⋊C4—671no—
391C22×C4⋊C4—671no—
392C22×C4⋊C4—671no—
393C22×C4⋊C4—671no—
394C22×C4⋊C4C2×D6711yescharacteristic
395C22×C4⋊C4C2×D6711yescharacteristic
396C22×C22⋊C4—671no—
397C22×C22⋊C4—671no—
398C22×C22⋊C4—671no—
399C22×C22⋊C4—671no—
400C22×C22⋊C4C2×D6711yescharacteristic
401C22×C22⋊C4C2×D6711yescharacteristic
402C22×C42—671no—
403C22×C42—671no—
404C22×C42—671no—
405C22×C42—671no—
406#398—678no—
407#398—678no—
408#397—678no—
409#397—678no—
410#389—678no—
411#389—678no—
412#388—678no—
413#387—678no—
414#387—678no—
415#387—678no—
416#385—678no—
417#385C2×D6718yes—
418C4×C4⋊C4—678no—
419C2×#95—671no—
420C2×#95—671no—
421C2×#95—671no—
422C2×#95—671no—
423C2×#95—671no—
424C2×#95—671no—
425C2×#95—671no—
426C2×#95—671no—
427C2×#95—671no—
428C2×#95—671no—
429C2×#95C2×D6711yescharacteristic
430C2×#95C2×D6711yescharacteristic
431C25C22×D6711yescharacteristic
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—24no—
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×C4C22×D6714yes—
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C23×C4C22×D6711yescharacteristic
447C23×C4C22×D6711yescharacteristic
448C23×C4C22×D6711yescharacteristic
449C23×C4C22×D6711yescharacteristic
450#126—13432no—
451#117—13432no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—674no—
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—674no—
464C2×C4⋊C4—1344no—
465C2×C4⋊C4—1344no—
466C2×C4⋊C4—1344no—
467C2×C4⋊C4—1344no—
468C2×C4⋊C4—1344no—
469C2×C4⋊C4—1344no—
470C2×C4⋊C4—1344no—
471C2×C4⋊C4—1344no—
472C2×C4⋊C4—1344no—
473C2×C4⋊C4—1344no—
474C2×C4⋊C4C22×D6714yes—
475C2×C4⋊C4C22×D6714yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—678no—
479C2×C22⋊C4—674no—
480C2×C22⋊C4—674no—
481C2×C22⋊C4—674no—
482C2×C22⋊C4—674no—
483C2×C22⋊C4—1344no—
484C2×C22⋊C4—1344no—
485C2×C22⋊C4—1344no—
486C2×C22⋊C4C22×D6714yes—
487C2×C22⋊C4C22×D6714yes—
488C2×C42—674no—
489C2×C42—674no—
490C2×C42—674no—
491C2×C42—674no—
492C2×C42—1344no—
493C2×C42—1344no—
494C2×C42—1344no—
495C2×C42—1344no—
496#95—674no—
497#95—674no—
498#95—674no—
499#95—674no—
500#95—674no—
501#95—674no—
502#95—674no—
503#95—674no—
504#95—674no—
505#95—674no—
506#95C22×D6714yes—
507#95C22×D6714yes—
508C24—22no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24D4×D6714yes—
515C24C23×D6712yes—
516C24C23×D6711yescharacteristic
517C22×C4—232no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—28no—
526C22×C4—28no—
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—674no—
537C22×C4—674no—
538C22×C4—674no—
539C22×C4—672no—
540C22×C4—672no—
541C22×C4—672no—
542C22×C4—672no—
543C22×C4—672no—
544C22×C4—672no—
545C22×C4—672no—
546C22×C4—672no—
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×C4—1342no—
566C22×C4—1342no—
567C22×C4—1342no—
568C22×C4#1176162714yes—
569C22×C4#1176162714yes—
570C22×C4#1176162814yes—
571C22×C4C23×D6712yes—
572C22×C4C23×D6712yes—
573C22×C4C23×D6712yes—
574C22×C4C23×D6712yes—
575C22×C4C23×D6712yes—
576C22×C4C23×D6712yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—1348no—
580C4⋊C4—1348no—
581C4⋊C4—1348no—
582C4⋊C4—1348no—
583C4⋊C4—1348no—
584C4⋊C4—1348no—
585C4⋊C4—1348no—
586C4⋊C4—1348no—
587C4⋊C4—1348no—
588C4⋊C4—1348no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—6716no—
592C22⋊C4—1348no—
593C22⋊C4—1348no—
594C22⋊C4—1348no—
595C42—1348no—
596C42—1348no—
597C42—1348no—
598C42—1348no—
599C23—28no—
600C23—28no—
601C23—28no—
602C23—22no—
603C23—22no—
604C23—22no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—44no—
609C23—44no—
610C23—44no—
611C23—44no—
612C23C2×D4×D6714yes—
613C23C2×D4×D6712yes—
614C23#41×D6712yes—
615C23C2×#1176162712yes—
616C23C2×#1176162712yes—
617C23C2×#1176162812yes—
618C23#1452409012yes—
619C23#1452409112yes—
620C23C24×D6711yescharacteristic
621C2×C4—232no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
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—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—2684no—
644C2×C4—2684no—
645C2×C4—2684no—
646C2×C4—2684no—
647C2×C4—2684no—
648C2×C4—674no—
649C2×C4—674no—
650C2×C4—674no—
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—1342no—
665C2×C4—1342no—
666C2×C4—1348no—
667C2×C4—1348no—
668C2×C4—1348no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4C2×#1176162714yes—
676C2×C4C2×#1176162714yes—
677C2×C4C2×#1176162814yes—
678C22—24no—
679C22—24no—
680C22—24no—
681C22—42no—
682C22—416no—
683C22—42no—
684C22—42no—
685C22—42no—
686C22#1686390214yes—
687C22#1686392614yes—
688C22#1686400614yes—
689C22#1686404414yes—
690C22#1686404714yes—
691C22#1686408014yes—
692C22#1686411614yes—
693C22C22×D4×D6711yescharacteristic
694C22C2×#41×D6711yescharacteristic
695C22C22×#1176162711yescharacteristic
696C22C22×#1176162711yescharacteristic
697C22C22×#1176162811yescharacteristic
698C22C2×#1452409011yescharacteristic
699C22C2×#1452409111yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2682no—
707C4—2682no—
708C4—2682no—
709C4—2682no—
710C4—2682no—
711C4—1344no—
712C4—1344no—
713C4—1344no—
714C2—44no—
715C2#2256442218yesdirect product factor
716C2C2×#1686390211yescharacteristic
717C2C2×#1686392611yescharacteristic
718C2C2×#1686400611yescharacteristic
719C2C2×#1686404411yescharacteristic
720C2C2×#1686404711yescharacteristic
721C2C2×#1686408011yescharacteristic
722C2C2×#1686411611yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#385×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#385D67
hypocenterC67C2×#2478
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #22564422C2direct (N × H)
4. C2×#16863329C2semidirect
5. C2×#16863328C2semidirect
8. C2×#16863293C2semidirect
9. C2×#16863291C2semidirect
11. C2×#16863283C2semidirect
12. C2×#16863282C2semidirect
13. C2×#16863278C2semidirect
15. C2×C4⋊C4×Dic67C2semidirect
39. #16863329C22semidirect
40. #16863328C22semidirect
43. #16863293C22semidirect
44. #16863291C22semidirect
46. #16863283C22semidirect
47. #16863282C22semidirect
48. #16863278C22semidirect
50. C4⋊C4×Dic67C22semidirect
354. C2×C67#2478semidirect
378. C67C2×#2478semidirect
715. C2#22564422direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240362
C22×#145240022
#225644222
C2×#168633292
C2×#168633282
C2×#168633242
C2×#168633212
C2×#168632932
C2×#168632912
C2×#168632902
C2×#168632832
C2×#168632822
C2×#168632782
C2×#168632692
C2×C4⋊C4×Dic672
C2×#385×C672
C2×#247867