Finite Group Databasebeta

← C2×#22568467 #31062252

Subgroups — C2×#22568467 #31062252

Order 17152.

2110 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#22568467C2116yesmaximal, direct product factor
2C2×#16863335C211yesmaximal, characteristic, complemented
3C2×#16863334C211yesmaximal, characteristic, complemented
4C2×#16863331C211yesmaximal, characteristic
5C2×#16863330C211yesmaximal, characteristic, complemented
6C2×#16863330C211yesmaximal, characteristic, complemented
7C2×#16863326C211yesmaximal, characteristic, complemented
8C2×#16863318C211yesmaximal, characteristic
9C2×#16863318C211yesmaximal, characteristic
10C2×#16863317C211yesmaximal, characteristic, complemented
11C2×#16863316C211yesmaximal, characteristic, complemented
12C2×#16863309C211yesmaximal, characteristic
13C2×#16863258C211yesmaximal, characteristic
14C2×#16863255C211yesmaximal, characteristic
15C2×#16863253C211yesmaximal, characteristic
16C2×#398×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×C4⋊Dic67C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×(C2×D67)⋊C4C2211yescharacteristic
34#16863335C2218yescomplemented
35#16863334C2218yescomplemented
36#16863331C2218yes—
37#16863330C2218yescomplemented
38#16863330C2218yescomplemented
39#16863326C2218yescomplemented
40#16863318C2218yes—
41#16863318C2218yes—
42#16863317C2218yescomplemented
43#16863316C2218yescomplemented
44#16863309C2218yes—
45#16863258C2218yes—
46#16863255C2218yes—
47#16863253C2218yes—
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×C4⋊C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63#398×C67C2218yescomplemented
64C2×#95×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C24×D67C2311yescharacteristic
68C22×Dic134—42no—
69C22×Dic134—42no—
70C22×Dic134—42no—
71C22×Dic134C2314yes—
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C22×C4×D67—42no—
80C22×C4×D67—42no—
81C22×C4×D67Q818yescomplemented
82C22×C4×D67C2314yes—
83C2×C4⋊Dic67—42no—
84C2×C4⋊Dic67—42no—
85C2×C4⋊Dic67—42no—
86C2×C4⋊Dic67C2314yes—
87C2×C4⋊Dic67C2314yes—
88C2×C4⋊Dic67C2314yes—
89C2×Dic67⋊C4—42no—
90C2×Dic67⋊C4—42no—
91C2×Dic67⋊C4—42no—
92C2×Dic67⋊C4—42no—
93C2×Dic67⋊C4—42no—
94C2×Dic67⋊C4—42no—
95C2×Dic67⋊C4C2314yes—
96C2×Dic67⋊C4C2314yes—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×(C2×D67)⋊C4—42no—
102C2×(C2×D67)⋊C4—42no—
103C2×(C2×D67)⋊C4—42no—
104C2×(C2×D67)⋊C4—42no—
105C2×(C2×D67)⋊C4—42no—
106C2×(C2×D67)⋊C4—42no—
107C2×(C2×D67)⋊C4C2314yes—
108C2×(C2×D67)⋊C4C2314yes—
109C2×(C2×D67)⋊C4C2314yes—
110C2×(C2×D67)⋊C4C2314yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C23×C4×C67C2311yescharacteristic
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C2×C4⋊C4×C67—42no—
132C2×C4⋊C4×C67—42no—
133C2×C4⋊C4×C67—42no—
134C2×C4⋊C4×C67—42no—
135C2×C4⋊C4×C67C2314yes—
136C2×C4⋊C4×C67C2314yes—
137C2×C4⋊C4×C67C2314yes—
138C2×C4⋊C4×C67C2314yes—
139#95×C67C2314yes—
140#95×C67C2314yes—
141#95×C67C2314yes—
142C23×D67—22no—
143C23×D67—22no—
144C23×D67—22no—
145C23×D67—22no—
146C23×D67—22no—
147C23×D67—22no—
148C23×D67C2×Q814yes—
149C23×D67C2412yes—
150C2×Dic134—44no—
151C2×Dic134—44no—
152C2×Dic134—44no—
153C2×Dic134—416no—
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—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67C2×Q814yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C2×C4×D67—416no—
183C2×C4×D67—44no—
184C2×C4×D67—44no—
185C2×C4×D67C2×Q8116yescomplemented
186C4⋊Dic67—44no—
187C4⋊Dic67—44no—
188C4⋊Dic67—44no—
189Dic67⋊C4—44no—
190Dic67⋊C4—44no—
191Dic67⋊C4—44no—
192Dic67⋊C4—44no—
193Dic67⋊C4—44no—
194Dic67⋊C4—44no—
195(C2×D67)⋊C4—44no—
196(C2×D67)⋊C4—44no—
197(C2×D67)⋊C4—44no—
198(C2×D67)⋊C4—44no—
199(C2×D67)⋊C4—44no—
200(C2×D67)⋊C4—44no—
201C24×C67C2411yescharacteristic
202C22×C4×C67—22no—
203C22×C4×C67—22no—
204C22×C4×C67—22no—
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×C67C2×Q814yes—
223C22×C4×C67C2412yes—
224C22×C4×C67C2412yes—
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C4⋊C4×C67—44no—
231C4⋊C4×C67—44no—
232C4⋊C4×C67—44no—
233C4⋊C4×C67—44no—
234C23×C67C22×Q812yes—
235C23×C67H(5,𝔽2)12yes—
236C23×C67H(5,𝔽2)12yes—
237C23×C67H(5,𝔽2)12yes—
238C23×C67H(5,𝔽2)12yes—
239C23×C672−1+412yes—
240C23×C672−1+412yes—
241C23×C67C2511yescharacteristic
242C22×D67—28no—
243C22×D67—28no—
244C22×D67—28no—
245C22×D67—22no—
246C22×D67—22no—
247C22×D67—22no—
248C22×D67—22no—
249C22×D67—22no—
250C22×D67—22no—
251C22×D67—44no—
252C22×D67—44no—
253C22×D67—44no—
254C22×D67—44no—
255C22×D67C22×Q814yes—
256C2×C4×C67—28no—
257C2×C4×C67—22no—
258C2×C4×C67—22no—
259C2×C4×C67—22no—
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—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—44no—
278C2×C4×C67—44no—
279C2×C4×C67—44no—
280C2×C4×C67—44no—
281C2×C4×C67—44no—
282C2×C4×C67—44no—
283C2×C4×C67C22×Q814yes—
284C2×Dic67—28no—
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—22no—
305C2×Dic67—44no—
306C2×Dic67—44no—
307C2×Dic67—44no—
308C2×Dic67—44no—
309C2×Dic67—44no—
310C2×Dic67—44no—
311C2×Dic67C22×Q814yes—
312C4×D67—416no—
313Dic134—416no—
314C22×C67#54314yes—
315C22×C67#54414yes—
316C22×C67#54414yes—
317C22×C67#56014yes—
318C22×C67#56214yes—
319C22×C67#56214yes—
320C22×C67#56314yes—
321C22×C67C23×Q811yescharacteristic
322C22×C67C2×H(5,𝔽2)11yescharacteristic
323C22×C67C2×H(5,𝔽2)11yescharacteristic
324C22×C67C2×H(5,𝔽2)11yescharacteristic
325C22×C67C2×H(5,𝔽2)11yescharacteristic
326C22×C67C2×2−1+411yescharacteristic
327C22×C67C2×2−1+411yescharacteristic
328C2×D67—24no—
329C2×D67—24no—
330C2×D67—24no—
331C2×D67—416no—
332C2×D67—42no—
333C2×D67—42no—
334C2×D67—42no—
335C2×D67—42no—
336C4×C67—24no—
337C4×C67—42no—
338C4×C67—42no—
339C4×C67—42no—
340C4×C67—42no—
341C4×C67—42no—
342C4×C67—42no—
343Dic67—24no—
344Dic67—42no—
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349Dic67—42no—
350C2×#2841—671nomaximal, Sylow
351C2×C67#284118yescomplemented
352C2×C67C2×#54311yescharacteristic
353C2×C67C2×#54411yescharacteristic
354C2×C67C2×#54411yescharacteristic
355C2×C67C2×#56011yescharacteristic
356C2×C67C2×#56211yescharacteristic
357C2×C67C2×#56211yescharacteristic
358C2×C67C2×#56311yescharacteristic
359D67—44no—
360#2841—6716no—
361C2×#400—671no—
362C2×#400—671no—
363C2×#399—671no—
364C2×#398—671no—
365C2×#398—671no—
366C2×#398—671no—
367C2×#398D6711yescharacteristic, complemented
368C2×#396—671no—
369C2×#396—671no—
370C2×#395—671no—
371C2×#395—671no—
372C2×#393—671no—
373C2×#381—671no—
374C2×#380—671no—
375C2×#380—671no—
376C67C2×#284111yescharacteristic, 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⋊C4—671no—
388C22×C4⋊C4C2×D6711yescharacteristic
389C22×C4⋊C4C2×D6711yescharacteristic
390C22×C4⋊C4C2×D6711yescharacteristic
391C22×C4⋊C4C2×D6711yescharacteristic
392C22×C22⋊C4—671no—
393C22×C22⋊C4—671no—
394C22×C22⋊C4—671no—
395C22×C22⋊C4—671no—
396C22×C22⋊C4—671no—
397C22×C22⋊C4—671no—
398#400—678no—
399#400—678no—
400#399—678no—
401#398—678no—
402#398—678no—
403#398—678no—
404#398C2×D6718yescomplemented
405#396—678no—
406#396—678no—
407#395—678no—
408#395—678no—
409#393—678no—
410#381—678no—
411#380—678no—
412#380—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×#95C2×D6711yescharacteristic
425C2×#95C2×D6711yescharacteristic
426C2×#95C2×D6711yescharacteristic
427C25—671no—
428C22×Q8—2682no—
429C22×Q8—2682no—
430C22×Q8—2682no—
431C22×Q8—674no—
432C23×C4—2682no—
433C23×C4—2682no—
434C23×C4—678no—
435C23×C4—674no—
436C23×C4—671no—
437C23×C4—671no—
438C23×C4—671no—
439C23×C4—671no—
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4C22×D6711yescharacteristic
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C23×C4C22×D6711yescharacteristic
447C23×C4C22×D6711yescharacteristic
448C23×C4C22×D6711yescharacteristic
449C23×C4C22×D6711yescharacteristic
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—2682no—
455C2×C4⋊C4—2682no—
456C2×C4⋊C4—2682no—
457C2×C4⋊C4—2682no—
458C2×C4⋊C4—2682no—
459C2×C4⋊C4—2682no—
460C2×C4⋊C4—2682no—
461C2×C4⋊C4—2682no—
462C2×C4⋊C4—2682no—
463C2×C4⋊C4—674no—
464C2×C4⋊C4—674no—
465C2×C4⋊C4—674no—
466C2×C4⋊C4—674no—
467C2×C4⋊C4—674no—
468C2×C4⋊C4—674no—
469C2×C4⋊C4—674no—
470C2×C4⋊C4—674no—
471C2×C4⋊C4—674no—
472C2×C4⋊C4C22×D6714yes—
473C2×C4⋊C4C22×D6714yes—
474C2×C4⋊C4C22×D6714yes—
475C2×C4⋊C4C22×D6714yes—
476C2×C22⋊C4—2682no—
477C2×C22⋊C4—2682no—
478C2×C22⋊C4—2682no—
479C2×C22⋊C4—2682no—
480C2×C22⋊C4—2682no—
481C2×C22⋊C4—2682no—
482C2×C22⋊C4—674no—
483C2×C22⋊C4—674no—
484C2×C22⋊C4—674no—
485C2×C22⋊C4—674no—
486C2×C22⋊C4—674no—
487C2×C22⋊C4—674no—
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#95C22×D6714yes—
500#95C22×D6714yes—
501#95C22×D6714yes—
502C24—674no—
503C24—672no—
504C24—1342no—
505C24—1342no—
506C24—1342no—
507C24—1342no—
508C24—1342no—
509C24—1342no—
510C24C23×D6711yescharacteristic
511C2×Q8—2684no—
512C2×Q8—2684no—
513C2×Q8—2684no—
514C2×Q8—26816no—
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—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—26816no—
536C22×C4—2684no—
537C22×C4—2684no—
538C22×C4—6716no—
539C22×C4—674no—
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×C4Q8×D6714yes—
568C22×C4C23×D6712yes—
569C22×C4C23×D6712yes—
570C22×C4C23×D6712yes—
571C22×C4C23×D6712yes—
572C22×C4C23×D6712yes—
573C22×C4C23×D6712yes—
574C22×C4C23×D6712yes—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—2684no—
580C4⋊C4—2684no—
581C4⋊C4—2684no—
582C4⋊C4—2684no—
583C4⋊C4—2684no—
584C4⋊C4—2684no—
585C4⋊C4—2684no—
586C4⋊C4—2684no—
587C4⋊C4—2684no—
588C22⋊C4—2684no—
589C22⋊C4—2684no—
590C22⋊C4—2684no—
591C22⋊C4—2684no—
592C22⋊C4—2684no—
593C22⋊C4—2684no—
594C23—2684no—
595C23—2684no—
596C23—2684no—
597C23—2684no—
598C23—674no—
599C23—1348no—
600C23—1348no—
601C23—1348no—
602C23—1342no—
603C23—1342no—
604C23—1342no—
605C23—1342no—
606C23—1342no—
607C23—1342no—
608C23C2×Q8×D6712yes—
609C23#1452408812yes—
610C23#1452408812yes—
611C23#1452408912yes—
612C23#1452408912yes—
613C23#1452409012yes—
614C23#1452409112yes—
615C23C24×D6711yescharacteristic
616Q8—26816no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
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—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—44no—
642C2×C4—44no—
643C2×C4—44no—
644C2×C4—26816no—
645C2×C4—2684no—
646C2×C4—2684no—
647C2×C4—2684no—
648C2×C4—2684no—
649C2×C4—2684no—
650C2×C4—2684no—
651C2×C4—674no—
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—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1342no—
670C2×C4—1348no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4C2×Q8×D6714yes—
674C22—2682no—
675C22—26816no—
676C22—2682no—
677C22—2682no—
678C22—2682no—
679C22—1344no—
680C22—1344no—
681C22—1344no—
682C22#1686402114yes—
683C22#1686402314yes—
684C22#1686402614yes—
685C22#1686413614yes—
686C22#1686414114yes—
687C22#1686414214yes—
688C22#1686415014yes—
689C22C22×Q8×D6711yescharacteristic
690C22C2×#1452408811yescharacteristic
691C22C2×#1452408811yescharacteristic
692C22C2×#1452408911yescharacteristic
693C22C2×#1452408911yescharacteristic
694C22C2×#1452409011yescharacteristic
695C22C2×#1452409111yescharacteristic
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—2682no—
704C4—2682no—
705C4—2682no—
706C4—2682no—
707C4—2682no—
708C4—2682no—
709C4—1344no—
710C2—2684no—
711C2#2256846718yesdirect product factor
712C2C2×#1686402111yescharacteristic
713C2C2×#1686402311yescharacteristic
714C2C2×#1686402611yescharacteristic
715C2C2×#1686413611yescharacteristic
716C2C2×#1686414111yescharacteristic
717C2C2×#1686414211yescharacteristic
718C2C2×#1686415011yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#398×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC2×#398D67
hypocenterC67C2×#2841
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. #22568467C2direct (N × H)
2. C2×#16863335C2semidirect
3. C2×#16863334C2semidirect
5. C2×#16863330C2semidirect
6. C2×#16863330C2semidirect
7. C2×#16863326C2semidirect
10. C2×#16863317C2semidirect
11. C2×#16863316C2semidirect
16. C2×#398×C67C2semidirect
34. #16863335C22semidirect
35. #16863334C22semidirect
37. #16863330C22semidirect
38. #16863330C22semidirect
39. #16863326C22semidirect
42. #16863317C22semidirect
43. #16863316C22semidirect
63. #398×C67C22semidirect
81. C22×C4×D67Q8semidirect
185. C2×C4×D67C2×Q8semidirect
351. C2×C67#2841semidirect
367. C2×#398D67semidirect
376. C67C2×#2841semidirect
404. #398C2×D67semidirect
711. C2#22568467direct (N × H)

Maximal subgroups

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

subgroupindex
#225684672
C2×#168633352
C2×#168633342
C2×#168633312
C2×#168633302
C2×#168633262
C2×#168633182
C2×#168633172
C2×#168633162
C2×#168633092
C2×#168632582
C2×#168632552
C2×#168632532
C2×#398×C672
C2×#284167