Finite Group Databasebeta

← C2×#22563705 #31024070

Subgroups — C2×#22563705 #31024070

Order 17152.

2702 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524020C211yesmaximal, characteristic
2C22×#14524008C211yesmaximal, characteristic, complemented
3#22563705C2116yesmaximal, direct product factor
4C2×#16863338C211yesmaximal, characteristic, complemented
5C2×#16863334C211yesmaximal, characteristic, complemented
6C2×#16863324C211yesmaximal, characteristic
7C2×#16863300C211yesmaximal, characteristic, complemented
8C2×#16863293C211yesmaximal, characteristic, complemented
9C2×#16863289C211yesmaximal, characteristic
10C2×#16863284C211yesmaximal, characteristic
11C2×#16863283C211yesmaximal, characteristic, complemented
12C2×#16863281C211yesmaximal, characteristic, complemented
13C2×#16863260C211yesmaximal, characteristic, complemented
14C2×#16863254C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#397×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C2×#14524020—28no—
20C2×#14524020C2218yes—
21C2×#14524008—28no—
22C2×#14524008C2218yescomplemented
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×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37C22×C4×Dic67C2211yescharacteristic
38#16863338C2218yescomplemented
39#16863334C2218yescomplemented
40#16863324C2218yes—
41#16863300C2218yescomplemented
42#16863293C2218yescomplemented
43#16863289C2218yes—
44#16863284C2218yes—
45#16863283C2218yescomplemented
46#16863281C2218yescomplemented
47#16863260C2218yescomplemented
48#16863254C2218yes—
49C22⋊C4×Dic67C2218yes—
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
60C2×C67⋊#95C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65#397×C67C2218yes—
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C22×Dic134—24no—
70C22×Dic134—24no—
71C22×Dic134D418yes—
72C22×Dic134C2314yes—
73C23×Dic67—24no—
74C23×Dic67—24no—
75C23×Dic67—24no—
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2314yes—
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85#14524020—232no—
86#14524008—232no—
87C2×C4⋊Dic67—24no—
88C2×C4⋊Dic67—24no—
89C2×C4⋊Dic67C2314yes—
90C2×C4⋊Dic67C2314yes—
91C2×Dic67⋊C4—24no—
92C2×Dic67⋊C4—24no—
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×C22⋊Dic67—24no—
104C2×C22⋊Dic67—24no—
105C2×C22⋊Dic67—24no—
106C2×C22⋊Dic67C2314yes—
107C2×C22⋊Dic67C2314yes—
108C2×C22⋊Dic67C2314yes—
109C2×C4×Dic67—24no—
110C2×C4×Dic67—24no—
111C2×C4×Dic67—24no—
112C2×C4×Dic67—24no—
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—
127C67⋊#95C2314yes—
128C25×C67C2311yescharacteristic
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C2×C4⋊C4×C67—24no—
136C2×C4⋊C4×C67C2314yes—
137C2×C22⋊C4×C67—24no—
138C2×C22⋊C4×C67—24no—
139C2×C22⋊C4×C67—24no—
140C2×C22⋊C4×C67C2314yes—
141C2×C22⋊C4×C67C2314yes—
142C2×C22⋊C4×C67C2314yes—
143#95×C67C2314yes—
144#95×C67C2314yes—
145#95×C67C2314yes—
146C2×Dic134—232no—
147C2×Dic134—28no—
148C2×Dic134—28no—
149C2×Dic134C2×D4116yes—
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—22no—
169C22×Dic67—28no—
170C22×Dic67—28no—
171C22×Dic67—28no—
172C22×Dic67—416no—
173C22×Dic67C2×D414yes—
174C22×Dic67C2×D414yes—
175C22×Dic67#4114yes—
176C22×Dic67#4114yes—
177C22×Dic67#4114yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C22×Dic67C2412yes—
183C22×Dic67C2412yes—
184C22×Dic67C2412yes—
185C22×Dic67C2412yes—
186C4⋊Dic67—28no—
187C4⋊Dic67—28no—
188Dic67⋊C4—28no—
189Dic67⋊C4—28no—
190Dic67⋊C4—28no—
191Dic67⋊C4—28no—
192Dic67⋊C4—28no—
193Dic67⋊C4—28no—
194C22⋊Dic67—28no—
195C22⋊Dic67—28no—
196C22⋊Dic67—28no—
197C4×Dic67—28no—
198C4×Dic67—28no—
199C4×Dic67—28no—
200C4×Dic67—28no—
201C24×C67—22no—
202C24×C67—22no—
203C24×C67—22no—
204C24×C67—22no—
205C24×C67—22no—
206C24×C67—22no—
207C24×C67#4114yes—
208C24×C67C2412yes—
209C24×C67C2411yescharacteristic
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×C67—22no—
224C22×C4×C67—22no—
225C22×C4×C67—22no—
226C22×C4×C67—22no—
227C22×C4×C67C2×D414yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C22×C4×C67C2412yes—
232C22×C4×C67C2412yes—
233C22×C4×C67C2412yes—
234C4⋊C4×C67—28no—
235C22⋊C4×C67—28no—
236C22⋊C4×C67—28no—
237C22⋊C4×C67—28no—
238C23×C67—28no—
239C23×C67—28no—
240C23×C67—28no—
241C23×C67—22no—
242C23×C67—22no—
243C23×C67—22no—
244C23×C67—22no—
245C23×C67—22no—
246C23×C67—22no—
247C23×C67—44no—
248C23×C67—44no—
249C23×C67—44no—
250C23×C67—44no—
251C23×C67C22×D412yes—
252C23×C67C2×#4112yes—
253C23×C67C2×#4112yes—
254C23×C67C2×#4112yes—
255C23×C67C2×#4114yes—
256C23×C67C2×#4112yes—
257C23×C672−1+412yes—
258C23×C672−1+412yes—
259C23×C67C2511yescharacteristic
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—44no—
279C2×C4×C67—44no—
280C2×C4×C67—44no—
281C2×C4×C67—44no—
282C2×C4×C67—44no—
283C2×C4×C67C22×D414yes—
284C2×Dic67—28no—
285C2×Dic67—28no—
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—416no—
311C2×Dic67#123116yes—
312C2×Dic67C22×D414yes—
313C2×Dic67C22×D414yes—
314C2×Dic67C2×#4114yes—
315C2×Dic67C2×#4114yes—
316C2×Dic67C2×#4114yes—
317Dic134—232no—
318C22×C67—24no—
319C22×C67—24no—
320C22×C67—24no—
321C22×C67—42no—
322C22×C67—416no—
323C22×C67—42no—
324C22×C67—42no—
325C22×C67—42no—
326C22×C67C2×#12314yes—
327C22×C67#52914yes—
328C22×C67#54114yes—
329C22×C67#54814yes—
330C22×C67#54814yes—
331C22×C67#55214yes—
332C22×C67#55614yes—
333C22×C67C23×D411yescharacteristic
334C22×C67C22×#4111yescharacteristic
335C22×C67C22×#4111yescharacteristic
336C22×C67C22×#4111yescharacteristic
337C22×C67C22×#4111yescharacteristic
338C22×C67C2×2−1+411yescharacteristic
339C22×C67C2×2−1+411yescharacteristic
340C4×C67—24no—
341C4×C67—42no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67—42no—
345C4×C67—42no—
346Dic67—24no—
347Dic67—24no—
348Dic67—42no—
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352Dic67—42no—
353Dic67C2×#12318yes—
354C2×#2421—671nomaximal, Sylow
355C2×C67—44no—
356C2×C67#242118yescomplemented
357C2×C67C22×#12311yescharacteristic
358C2×C67C2×#52911yescharacteristic
359C2×C67C2×#54111yescharacteristic
360C2×C67C2×#54811yescharacteristic
361C2×C67C2×#54811yescharacteristic
362C2×C67C2×#55211yescharacteristic
363C2×C67C2×#55611yescharacteristic
364C22×C22⋊Q8—671no—
365C22×C4×Q8—671no—
366#2421—6716no—
367C2×#400—671no—
368C2×#400—671no—
369C2×#397—671no—
370C2×#397D6711yescharacteristic
371C2×#391—671no—
372C2×#389—671no—
373C2×#388—671no—
374C2×#388—671no—
375C2×#387—671no—
376C2×#387—671no—
377C2×#382—671no—
378C2×#380—671no—
379C2×C4×C22⋊C4—671no—
380C67C2×#242111yescharacteristic, complemented, Sylow
381C23×Q8—671no—
382C24×C4—671no—
383C2×C22⋊Q8—678no—
384C2×C22⋊Q8—1348no—
385C2×C4×Q8—678no—
386C2×C4×Q8—1348no—
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⋊C4—671no—
395C22×C4⋊C4C2×D6711yescharacteristic
396C22×C22⋊C4—671no—
397C22×C22⋊C4—671no—
398C22×C22⋊C4—671no—
399C22×C22⋊C4C2×D6711yescharacteristic
400C22×C22⋊C4C2×D6711yescharacteristic
401C22×C22⋊C4C2×D6711yescharacteristic
402C22×C42—671no—
403C22×C42—671no—
404C22×C42—671no—
405C22×C42—671no—
406#400—678no—
407#400—678no—
408#397—678no—
409#397C2×D6718yes—
410#391—678no—
411#389—678no—
412#388—678no—
413#388—678no—
414#387—678no—
415#387—678no—
416#382—678no—
417#380—678no—
418C4×C22⋊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×#95—671no—
430C2×#95C2×D6711yescharacteristic
431C2×#95C2×D6711yescharacteristic
432C2×#95C2×D6711yescharacteristic
433C25C22×D6711yescharacteristic
434C22×Q8—678no—
435C22×Q8—674no—
436C22×Q8—1344no—
437C22×Q8—1344no—
438C23×C4—671no—
439C23×C4—671no—
440C23×C4—671no—
441C23×C4—674no—
442C23×C4—671no—
443C23×C4—671no—
444C23×C4—671no—
445C23×C4—671no—
446C23×C4—671no—
447C23×C4—1344no—
448C23×C4—1344no—
449C23×C4—1344no—
450C23×C4C22×D6711yescharacteristic
451C23×C4C22×D6711yescharacteristic
452C23×C4C22×D6711yescharacteristic
453C23×C4C22×D6711yescharacteristic
454C23×C4C22×D6711yescharacteristic
455C23×C4C22×D6711yescharacteristic
456C22⋊Q8—13432no—
457C4×Q8—13432no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—674no—
460C2×C4⋊C4—674no—
461C2×C4⋊C4—674no—
462C2×C4⋊C4—674no—
463C2×C4⋊C4—674no—
464C2×C4⋊C4—674no—
465C2×C4⋊C4—674no—
466C2×C4⋊C4—674no—
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⋊C4—1344no—
475C2×C4⋊C4C22×D6714yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—674no—
480C2×C22⋊C4—674no—
481C2×C22⋊C4—674no—
482C2×C22⋊C4—1344no—
483C2×C22⋊C4—1344no—
484C2×C22⋊C4—1344no—
485C2×C22⋊C4C22×D6714yes—
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#95—674no—
507#95C22×D6714yes—
508#95C22×D6714yes—
509#95C22×D6714yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24#1176162714yes—
517C24C23×D6712yes—
518C24C23×D6711yescharacteristic
519C2×Q8—6716no—
520C2×Q8—13432no—
521C2×Q8—1348no—
522C2×Q8—1348no—
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—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—26816no—
541C22×C4—674no—
542C22×C4—674no—
543C22×C4—674no—
544C22×C4—672no—
545C22×C4—674no—
546C22×C4—674no—
547C22×C4—672no—
548C22×C4—672no—
549C22×C4—672no—
550C22×C4—672no—
551C22×C4—672no—
552C22×C4—672no—
553C22×C4—672no—
554C22×C4—1348no—
555C22×C4—1348no—
556C22×C4—1348no—
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×C4—1342no—
570C22×C4—1342no—
571C22×C4—1342no—
572C22×C4—1342no—
573C22×C4—1342no—
574C22×C4—1342no—
575C22×C4—1342no—
576C22×C4D4×D6714yes—
577C22×C4C23×D6712yes—
578C22×C4C23×D6712yes—
579C22×C4C23×D6712yes—
580C22×C4C23×D6712yes—
581C22×C4C23×D6712yes—
582C22×C4C23×D6712yes—
583C4⋊C4—28no—
584C4⋊C4—1348no—
585C4⋊C4—1348no—
586C4⋊C4—1348no—
587C4⋊C4—1348no—
588C4⋊C4—1348no—
589C4⋊C4—1348no—
590C4⋊C4—1348no—
591C4⋊C4—1348no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—28no—
595C22⋊C4—1348no—
596C22⋊C4—1348no—
597C22⋊C4—1348no—
598C42—1348no—
599C42—1348no—
600C42—1348no—
601C42—1348no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D6712yes—
616C23#41×D6712yes—
617C23#41×D6712yes—
618C23#41×D6712yes—
619C23C2×#1176162714yes—
620C23C2×#1176162712yes—
621C23#1452409012yes—
622C23#1452409012yes—
623C23C24×D6711yescharacteristic
624Q8—13432no—
625C2×C4—28no—
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—22no—
643C2×C4—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—2684no—
649C2×C4—2684no—
650C2×C4—2684no—
651C2×C4—2684no—
652C2×C4—2684no—
653C2×C4—26816no—
654C2×C4—6716no—
655C2×C4—674no—
656C2×C4—674no—
657C2×C4—674no—
658C2×C4—674no—
659C2×C4—674no—
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—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1348no—
676C2×C4—1348no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4C2×D4×D6714yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—42no—
687C22—416no—
688C22—42no—
689C22—42no—
690C22#123×D6714yes—
691C22#1686392314yes—
692C22#1686400314yes—
693C22#1686405214yes—
694C22#1686405414yes—
695C22#1686408314yes—
696C22#1686411314yes—
697C22C22×D4×D6711yescharacteristic
698C22C2×#41×D6711yescharacteristic
699C22C2×#41×D6711yescharacteristic
700C22C2×#41×D6711yescharacteristic
701C22C22×#1176162711yescharacteristic
702C22C2×#1452409011yescharacteristic
703C22C2×#1452409011yescharacteristic
704C4—24no—
705C4—42no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—2682no—
711C4—2682no—
712C4—2682no—
713C4—2682no—
714C4—2682no—
715C4—678no—
716C4—1344no—
717C4—1344no—
718C2—44no—
719C2#2256370518yesdirect product factor
720C2C2×#123×D6711yescharacteristic
721C2C2×#1686392311yescharacteristic
722C2C2×#1686400311yescharacteristic
723C2C2×#1686405211yescharacteristic
724C2C2×#1686405411yescharacteristic
725C2C2×#1686408311yescharacteristic
726C2C2×#1686411311yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#397×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#397D67
hypocenterC67C2×#2421
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×#14524008C2semidirect
3. #22563705C2direct (N × H)
4. C2×#16863338C2semidirect
5. C2×#16863334C2semidirect
7. C2×#16863300C2semidirect
8. C2×#16863293C2semidirect
11. C2×#16863283C2semidirect
12. C2×#16863281C2semidirect
13. C2×#16863260C2semidirect
22. C2×#14524008C22semidirect
38. #16863338C22semidirect
39. #16863334C22semidirect
41. #16863300C22semidirect
42. #16863293C22semidirect
45. #16863283C22semidirect
46. #16863281C22semidirect
47. #16863260C22semidirect
356. C2×C67#2421semidirect
380. C67C2×#2421semidirect
719. C2#22563705direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240202
C22×#145240082
#225637052
C2×#168633382
C2×#168633342
C2×#168633242
C2×#168633002
C2×#168632932
C2×#168632892
C2×#168632842
C2×#168632832
C2×#168632812
C2×#168632602
C2×#168632542
C2×C22⋊C4×Dic672
C2×#397×C672
C2×#242167