Finite Group Databasebeta

← C2×#22565625 #31026115

Subgroups — C2×#22565625 #31026115

Order 17152.

2270 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22565625C2116yesmaximal, direct product factor
2C2×#16863337C211yesmaximal, characteristic, complemented
3C2×#16863327C211yesmaximal, characteristic, complemented
4C2×#16863319C211yesmaximal, characteristic
5C2×#16863292C211yesmaximal, characteristic, complemented
6C2×#16863291C211yesmaximal, characteristic, complemented
7C2×#16863291C211yesmaximal, characteristic, complemented
8C2×#16863290C211yesmaximal, characteristic
9C2×#16863284C211yesmaximal, characteristic
10C2×#16863282C211yesmaximal, characteristic, complemented
11C2×#16863277C211yesmaximal, characteristic, complemented
12C2×#16863268C211yesmaximal, characteristic
13C2×#16863268C211yesmaximal, characteristic
14C2×#16863247C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#396×C67C211yesmaximal, characteristic
17C24×Dic67C2211yescharacteristic
18C22×C4⋊Dic67C2211yescharacteristic
19C22×Dic67⋊C4C2211yescharacteristic
20C22×Dic67⋊C4C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×C22⋊Dic67C2211yescharacteristic
28C22×C22⋊Dic67C2211yescharacteristic
29C22×C22⋊Dic67C2211yescharacteristic
30C22×C4×Dic67C2211yescharacteristic
31C22×C4×Dic67C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34#16863337C2218yescomplemented
35#16863327C2218yescomplemented
36#16863319C2218yes—
37#16863292C2218yescomplemented
38#16863291C2218yescomplemented
39#16863291C2218yescomplemented
40#16863290C2218yes—
41#16863284C2218yes—
42#16863282C2218yescomplemented
43#16863277C2218yescomplemented
44#16863268C2218yes—
45#16863268C2218yes—
46#16863247C2218yescomplemented
47C22⋊C4×Dic67C2218yes—
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×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65#396×C67C2218yes—
66C2×#95×C67C2211yescharacteristic
67C23×Dic67—24no—
68C23×Dic67—42no—
69C23×Dic67—42no—
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2314yes—
79C2×C4⋊Dic67—24no—
80C2×C4⋊Dic67C2314yes—
81C2×Dic67⋊C4—24no—
82C2×Dic67⋊C4—24no—
83C2×Dic67⋊C4—24no—
84C2×Dic67⋊C4—24no—
85C2×Dic67⋊C4—24no—
86C2×Dic67⋊C4—42no—
87C2×Dic67⋊C4—42no—
88C2×Dic67⋊C4—42no—
89C2×Dic67⋊C4C2314yes—
90C2×Dic67⋊C4C2314yes—
91C2×Dic67⋊C4C2314yes—
92C2×Dic67⋊C4C2314yes—
93C2×Dic67⋊C4C2314yes—
94C2×Dic67⋊C4C2314yes—
95C2×Dic67⋊C4C2314yes—
96C2×Dic67⋊C4C2314yes—
97C2×C22⋊Dic67—24no—
98C2×C22⋊Dic67—24no—
99C2×C22⋊Dic67Q818yes—
100C2×C22⋊Dic67C2314yes—
101C2×C22⋊Dic67C2314yes—
102C2×C22⋊Dic67C2314yes—
103C2×C4×Dic67—24no—
104C2×C4×Dic67—42no—
105C2×C4×Dic67—42no—
106C2×C4×Dic67—42no—
107C2×C4×Dic67C2314yes—
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—
122C25×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C23×C4×C67C2311yescharacteristic
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129C2×C4⋊C4×C67—24no—
130C2×C4⋊C4×C67—42no—
131C2×C4⋊C4×C67—42no—
132C2×C4⋊C4×C67C2314yes—
133C2×C4⋊C4×C67C2314yes—
134C2×C4⋊C4×C67C2314yes—
135C2×C22⋊C4×C67—24no—
136C2×C22⋊C4×C67—42no—
137C2×C22⋊C4×C67—42no—
138C2×C22⋊C4×C67C2314yes—
139C2×C22⋊C4×C67C2314yes—
140C2×C22⋊C4×C67C2314yes—
141#95×C67C2314yes—
142C22×Dic67—22no—
143C22×Dic67—22no—
144C22×Dic67—22no—
145C22×Dic67—22no—
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—28no—
162C22×Dic67—44no—
163C22×Dic67—44no—
164C22×Dic67—416no—
165C22×Dic67C2×Q814yes—
166C22×Dic67C2×Q814yes—
167C22×Dic67#4114yes—
168C22×Dic67#4114yes—
169C22×Dic67#4114yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174C22×Dic67C2412yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C4⋊Dic67—28no—
179Dic67⋊C4—28no—
180Dic67⋊C4—28no—
181Dic67⋊C4—28no—
182Dic67⋊C4—28no—
183Dic67⋊C4—28no—
184Dic67⋊C4—44no—
185Dic67⋊C4—44no—
186Dic67⋊C4—44no—
187C22⋊Dic67—28no—
188C22⋊Dic67—28no—
189C22⋊Dic67C2×Q8116yes—
190C4×Dic67—28no—
191C4×Dic67—44no—
192C4×Dic67—44no—
193C4×Dic67—44no—
194C24×C67—22no—
195C24×C67—22no—
196C24×C67—22no—
197C24×C67—22no—
198C24×C67—22no—
199C24×C67—22no—
200C24×C67C2×Q814yes—
201C24×C67C2412yes—
202C24×C67C2411yescharacteristic
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#4114yes—
221C22×C4×C67C2412yes—
222C22×C4×C67C2412yes—
223C22×C4×C67C2412yes—
224C22×C4×C67C2412yes—
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C4⋊C4×C67—28no—
228C4⋊C4×C67—44no—
229C4⋊C4×C67—44no—
230C22⋊C4×C67—28no—
231C22⋊C4×C67—44no—
232C22⋊C4×C67—44no—
233C23×C67—28no—
234C23×C67—28no—
235C23×C67—28no—
236C23×C67—22no—
237C23×C67—22no—
238C23×C67—22no—
239C23×C67—22no—
240C23×C67—22no—
241C23×C67—22no—
242C23×C67—44no—
243C23×C67—44no—
244C23×C67—44no—
245C23×C67—44no—
246C23×C67C22×Q814yes—
247C23×C67C22×Q812yes—
248C23×C67C2×#4112yes—
249C23×C67C2×#4112yes—
250C23×C67C2×#4112yes—
251C23×C67C2×#4112yes—
252C23×C67H(5,𝔽2)12yes—
253C23×C67H(5,𝔽2)12yes—
254C23×C67C2511yescharacteristic
255C2×C4×C67—28no—
256C2×C4×C67—22no—
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—44no—
274C2×C4×C67—44no—
275C2×C4×C67—44no—
276C2×C4×C67—44no—
277C2×C4×C67—44no—
278C2×C4×C67C2×#4114yes—
279C2×Dic67—28no—
280C2×Dic67—28no—
281C2×Dic67—28no—
282C2×Dic67—28no—
283C2×Dic67—28no—
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—416no—
304C2×Dic67—44no—
305C2×Dic67—44no—
306C2×Dic67—44no—
307C2×Dic67C22×Q814yes—
308C2×Dic67C22×Q814yes—
309C2×Dic67C2×#4114yes—
310C2×Dic67C2×#4114yes—
311C2×Dic67C2×#4114yes—
312C22×C67—24no—
313C22×C67—24no—
314C22×C67—24no—
315C22×C67—416no—
316C22×C67—42no—
317C22×C67—42no—
318C22×C67—42no—
319C22×C67—42no—
320C22×C67#52914yes—
321C22×C67#53314yes—
322C22×C67#53814yes—
323C22×C67#55314yes—
324C22×C67#55314yes—
325C22×C67#55414yes—
326C22×C67#55414yes—
327C22×C67C23×Q811yescharacteristic
328C22×C67C22×#4111yescharacteristic
329C22×C67C22×#4111yescharacteristic
330C22×C67C22×#4111yescharacteristic
331C22×C67C22×#4111yescharacteristic
332C22×C67C2×H(5,𝔽2)11yescharacteristic
333C22×C67C2×H(5,𝔽2)11yescharacteristic
334C4×C67—24no—
335C4×C67—42no—
336C4×C67—42no—
337C4×C67—42no—
338C4×C67—42no—
339C4×C67—42no—
340Dic67—24no—
341Dic67—24no—
342Dic67—24no—
343Dic67—24no—
344Dic67—24no—
345Dic67—42no—
346Dic67—42no—
347Dic67—42no—
348C2×#2587—671nomaximal, Sylow
349C2×C67—44no—
350C2×C67#258718yescomplemented
351C2×C67C2×#52911yescharacteristic
352C2×C67C2×#53311yescharacteristic
353C2×C67C2×#53811yescharacteristic
354C2×C67C2×#55311yescharacteristic
355C2×C67C2×#55311yescharacteristic
356C2×C67C2×#55411yescharacteristic
357C2×C67C2×#55411yescharacteristic
358#2587—6716no—
359C2×#400—671no—
360C2×#398—671no—
361C2×#396—671no—
362C2×#396D6711yescharacteristic
363C2×#389—671no—
364C2×#389—671no—
365C2×#389—671no—
366C2×#388—671no—
367C2×#388—671no—
368C2×#387—671no—
369C2×#387—671no—
370C2×#385—671no—
371C2×#385—671no—
372C2×C4×C4⋊C4—671no—
373C2×C4×C22⋊C4—671no—
374C67C2×#258711yescharacteristic, complemented, Sylow
375C24×C4—671no—
376C22×C4⋊C4—671no—
377C22×C4⋊C4—671no—
378C22×C4⋊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⋊C4C2×D6711yescharacteristic
386C22×C4⋊C4C2×D6711yescharacteristic
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×C42—671no—
398#400—678no—
399#398—678no—
400#396—678no—
401#396C2×D6718yes—
402#389—678no—
403#389—678no—
404#389—678no—
405#388—678no—
406#388—678no—
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×#95C2×D6711yescharacteristic
425C25C22×D6711yescharacteristic
426C23×C4—2682no—
427C23×C4—2682no—
428C23×C4—674no—
429C23×C4—671no—
430C23×C4—671no—
431C23×C4—671no—
432C23×C4—671no—
433C23×C4—671no—
434C23×C4—671no—
435C23×C4—671no—
436C23×C4—671no—
437C23×C4—1344no—
438C23×C4C22×D6711yescharacteristic
439C23×C4C22×D6711yescharacteristic
440C23×C4C22×D6711yescharacteristic
441C23×C4C22×D6711yescharacteristic
442C23×C4C22×D6711yescharacteristic
443C23×C4C22×D6711yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—2682no—
448C2×C4⋊C4—2682no—
449C2×C4⋊C4—2682no—
450C2×C4⋊C4—674no—
451C2×C4⋊C4—674no—
452C2×C4⋊C4—674no—
453C2×C4⋊C4—674no—
454C2×C4⋊C4—674no—
455C2×C4⋊C4—674no—
456C2×C4⋊C4—674no—
457C2×C4⋊C4—674no—
458C2×C4⋊C4—674no—
459C2×C4⋊C4—1344no—
460C2×C4⋊C4—1344no—
461C2×C4⋊C4—1344no—
462C2×C4⋊C4—1344no—
463C2×C4⋊C4—1344no—
464C2×C4⋊C4—1344no—
465C2×C4⋊C4C22×D6714yes—
466C2×C4⋊C4C22×D6714yes—
467C2×C4⋊C4C22×D6714yes—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—678no—
472C2×C22⋊C4—674no—
473C2×C22⋊C4—674no—
474C2×C22⋊C4—674no—
475C2×C22⋊C4—1344no—
476C2×C22⋊C4—1344no—
477C2×C22⋊C4C22×D6714yes—
478C2×C22⋊C4C22×D6714yes—
479C2×C22⋊C4C22×D6714yes—
480C2×C42—2682no—
481C2×C42—2682no—
482C2×C42—2682no—
483C2×C42—674no—
484C2×C42—674no—
485C2×C42—674no—
486C2×C42—674no—
487C2×C42—1344no—
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—
500C24—22no—
501C24—22no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24Q8×D6714yes—
507C24C23×D6712yes—
508C24C23×D6711yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
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—26816no—
527C22×C4—2684no—
528C22×C4—2684no—
529C22×C4—674no—
530C22×C4—674no—
531C22×C4—674no—
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#1176162714yes—
563C22×C4C23×D6712yes—
564C22×C4C23×D6712yes—
565C22×C4C23×D6712yes—
566C22×C4C23×D6712yes—
567C22×C4C23×D6712yes—
568C22×C4C23×D6712yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—2684no—
573C4⋊C4—2684no—
574C4⋊C4—2684no—
575C4⋊C4—1348no—
576C4⋊C4—1348no—
577C4⋊C4—1348no—
578C4⋊C4—1348no—
579C4⋊C4—1348no—
580C4⋊C4—1348no—
581C22⋊C4—28no—
582C22⋊C4—44no—
583C22⋊C4—44no—
584C22⋊C4—6716no—
585C22⋊C4—1348no—
586C22⋊C4—1348no—
587C42—2684no—
588C42—2684no—
589C42—2684no—
590C42—1348no—
591C23—28no—
592C23—28no—
593C23—28no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23—22no—
598C23—22no—
599C23—22no—
600C23—44no—
601C23—44no—
602C23—44no—
603C23—44no—
604C23C2×Q8×D6714yes—
605C23C2×Q8×D6712yes—
606C23#41×D6712yes—
607C23#41×D6712yes—
608C23#41×D6712yes—
609C23C2×#1176162712yes—
610C23#1452408812yes—
611C23#1452408812yes—
612C23C24×D6711yescharacteristic
613C2×C4—28no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
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—44no—
632C2×C4—44no—
633C2×C4—44no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—2684no—
637C2×C4—2684no—
638C2×C4—2684no—
639C2×C4—26816no—
640C2×C4—674no—
641C2×C4—674no—
642C2×C4—674no—
643C2×C4—674no—
644C2×C4—674no—
645C2×C4—1342no—
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—1348no—
655C2×C4—1348no—
656C2×C4—1348no—
657C2×C4—1348no—
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—1348no—
669C2×C4C2×#1176162714yes—
670C22—24no—
671C22—24no—
672C22—24no—
673C22—42no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—416no—
678C22#1686392914yes—
679C22#1686394814yes—
680C22#1686397814yes—
681C22#1686408914yes—
682C22#1686409314yes—
683C22#1686410014yes—
684C22#1686410014yes—
685C22C22×Q8×D6711yescharacteristic
686C22C2×#41×D6711yescharacteristic
687C22C2×#41×D6711yescharacteristic
688C22C2×#41×D6711yescharacteristic
689C22C22×#1176162711yescharacteristic
690C22C2×#1452408811yescharacteristic
691C22C2×#1452408811yescharacteristic
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—2682no—
699C4—2682no—
700C4—2682no—
701C4—1344no—
702C4—1344no—
703C4—1344no—
704C4—1344no—
705C4—1344no—
706C2—44no—
707C2#2256562518yesdirect product factor
708C2C2×#1686392911yescharacteristic
709C2C2×#1686394811yescharacteristic
710C2C2×#1686397811yescharacteristic
711C2C2×#1686408911yescharacteristic
712C2C2×#1686409311yescharacteristic
713C2C2×#1686410011yescharacteristic
714C2C2×#1686410011yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#396×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#396D67
hypocenterC67C2×#2587
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. #22565625C2direct (N × H)
2. C2×#16863337C2semidirect
3. C2×#16863327C2semidirect
5. C2×#16863292C2semidirect
6. C2×#16863291C2semidirect
7. C2×#16863291C2semidirect
10. C2×#16863282C2semidirect
11. C2×#16863277C2semidirect
14. C2×#16863247C2semidirect
34. #16863337C22semidirect
35. #16863327C22semidirect
37. #16863292C22semidirect
38. #16863291C22semidirect
39. #16863291C22semidirect
42. #16863282C22semidirect
43. #16863277C22semidirect
46. #16863247C22semidirect
350. C2×C67#2587semidirect
374. C67C2×#2587semidirect
707. C2#22565625direct (N × H)

Maximal subgroups

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

subgroupindex
#225656252
C2×#168633372
C2×#168633272
C2×#168633192
C2×#168632922
C2×#168632912
C2×#168632902
C2×#168632842
C2×#168632822
C2×#168632772
C2×#168632682
C2×#168632472
C2×C22⋊C4×Dic672
C2×#396×C672
C2×#258767