Finite Group Databasebeta

← C2×#22564231 #31023808

Subgroups — C2×#22564231 #31023808

Order 17152.

2854 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524020C211yesmaximal, characteristic
2C22×#14524008C211yesmaximal, characteristic, complemented
3#22564231C2116yesmaximal, direct product factor
4C2×#16863316C211yesmaximal, characteristic, complemented
5C2×#16863316C211yesmaximal, characteristic, complemented
6C2×#16863308C211yesmaximal, characteristic
7C2×#16863301C211yesmaximal, characteristic, complemented
8C2×#16863293C211yesmaximal, characteristic, complemented
9C2×#16863290C211yesmaximal, characteristic
10C2×#16863284C211yesmaximal, characteristic
11C2×#16863282C211yesmaximal, characteristic, complemented
12C2×#16863278C211yesmaximal, characteristic, complemented
13C2×#16863277C211yesmaximal, characteristic, complemented
14C2×#16863268C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#396×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C23×Dic134C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C2×#14524020—28no—
21C2×#14524020C2218yes—
22C2×#14524008—28no—
23C2×#14524008C2218yescomplemented
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#16863316C2218yescomplemented
39#16863316C2218yescomplemented
40#16863308C2218yes—
41#16863301C2218yescomplemented
42#16863293C2218yescomplemented
43#16863290C2218yes—
44#16863284C2218yes—
45#16863282C2218yescomplemented
46#16863278C2218yescomplemented
47#16863277C2218yescomplemented
48#16863268C2218yes—
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×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66C22×C22⋊C4×C67C2211yescharacteristic
67#396×C67C2218yes—
68C2×#95×C67C2211yescharacteristic
69C22×Dic134—24no—
70C22×Dic134—24no—
71C22×Dic134—24no—
72C22×Dic134—24no—
73C22×Dic134—24no—
74C22×Dic134—42no—
75C22×Dic134C2314yes—
76C22×Dic134C2314yes—
77C23×Dic67—24no—
78C23×Dic67—24no—
79C23×Dic67—42no—
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2314yes—
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2311yescharacteristic
88C23×Dic67C2311yescharacteristic
89#14524020—232no—
90#14524008—232no—
91C2×C4⋊Dic67—24no—
92C2×C4⋊Dic67C2314yes—
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—42no—
98C2×Dic67⋊C4D418yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×C22⋊Dic67—24no—
106C2×C22⋊Dic67—24no—
107C2×C22⋊Dic67Q818yescomplemented
108C2×C22⋊Dic67C2314yes—
109C2×C22⋊Dic67C2314yes—
110C2×C22⋊Dic67C2314yes—
111C2×C4×Dic67—24no—
112C2×C4×Dic67—24no—
113C2×C4×Dic67—24no—
114C2×C4×Dic67—42no—
115C2×C4×Dic67C2314yes—
116C2×C4×Dic67C2314yes—
117C2×C4×Dic67C2314yes—
118C2×C4×Dic67C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C25×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C2×C4⋊C4×C67—24no—
138C2×C4⋊C4×C67—24no—
139C2×C4⋊C4×C67—42no—
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C4⋊C4×C67C2314yes—
143C2×C22⋊C4×C67—24no—
144C2×C22⋊C4×C67—24no—
145C2×C22⋊C4×C67—42no—
146C2×C22⋊C4×C67C2314yes—
147C2×C22⋊C4×C67C2314yes—
148C2×C22⋊C4×C67C2314yes—
149#95×C67C2314yes—
150C2×Dic134—232no—
151C2×Dic134—28no—
152C2×Dic134—28no—
153C2×Dic134—28no—
154C2×Dic134—28no—
155C2×Dic134—28no—
156C2×Dic134—44no—
157C2×Dic134—416no—
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×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—28no—
177C22×Dic67—28no—
178C22×Dic67—44no—
179C22×Dic67—416no—
180C22×Dic67C2×D414yes—
181C22×Dic67C2×D414yes—
182C22×Dic67C2×Q814yes—
183C22×Dic67C2×Q814yes—
184C22×Dic67#4114yes—
185C22×Dic67#4114yes—
186C22×Dic67C2412yes—
187C22×Dic67C2412yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C4⋊Dic67—28no—
195Dic67⋊C4—28no—
196Dic67⋊C4—28no—
197Dic67⋊C4—28no—
198Dic67⋊C4—28no—
199Dic67⋊C4—44no—
200Dic67⋊C4C2×D4116yes—
201C22⋊Dic67—28no—
202C22⋊Dic67—28no—
203C22⋊Dic67C2×Q8116yescomplemented
204C4×Dic67—28no—
205C4×Dic67—28no—
206C4×Dic67—28no—
207C4×Dic67—44no—
208C24×C67—22no—
209C24×C67—22no—
210C24×C67—22no—
211C24×C67—22no—
212C24×C67—22no—
213C24×C67—22no—
214C24×C67C2×Q814yes—
215C24×C67C2412yes—
216C24×C67C2411yescharacteristic
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×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67C2×D414yes—
234C22×C4×C67#4114yes—
235C22×C4×C67C2412yes—
236C22×C4×C67C2412yes—
237C22×C4×C67C2412yes—
238C22×C4×C67C2412yes—
239C22×C4×C67C2412yes—
240C22×C4×C67C2412yes—
241C4⋊C4×C67—28no—
242C4⋊C4×C67—28no—
243C4⋊C4×C67—44no—
244C22⋊C4×C67—28no—
245C22⋊C4×C67—28no—
246C22⋊C4×C67—44no—
247C23×C67—28no—
248C23×C67—28no—
249C23×C67—28no—
250C23×C67—22no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—22no—
255C23×C67—22no—
256C23×C67—44no—
257C23×C67—44no—
258C23×C67—44no—
259C23×C67—44no—
260C23×C67C22×D412yes—
261C23×C67C22×Q814yes—
262C23×C67C22×Q812yes—
263C23×C67C2×#4112yes—
264C23×C67C2×#4112yes—
265C23×C67C2×#4112yes—
266C23×C67H(5,𝔽2)12yes—
267C23×C672−1+412yes—
268C23×C67C2511yescharacteristic
269C2×C4×C67—28no—
270C2×C4×C67—28no—
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—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—44no—
288C2×C4×C67—44no—
289C2×C4×C67—44no—
290C2×C4×C67—44no—
291C2×C4×C67C22×D414yes—
292C2×C4×C67C2×#4114yes—
293C2×Dic67—28no—
294C2×Dic67—28no—
295C2×Dic67—28no—
296C2×Dic67—28no—
297C2×Dic67—28no—
298C2×Dic67—28no—
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—22no—
309C2×Dic67—22no—
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—22no—
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—416no—
318C2×Dic67—44no—
319C2×Dic67—44no—
320C2×Dic67C22×D414yes—
321C2×Dic67C22×D414yes—
322C2×Dic67C22×Q814yes—
323C2×Dic67C22×Q814yes—
324C2×Dic67C2×#4114yes—
325C2×Dic67C2×#4114yes—
326Dic134—232no—
327Dic134—416no—
328C22×C67—24no—
329C22×C67—24no—
330C22×C67—24no—
331C22×C67—42no—
332C22×C67—42no—
333C22×C67—42no—
334C22×C67—42no—
335C22×C67—416no—
336C22×C67#52514yes—
337C22×C67#53314yes—
338C22×C67#54214yes—
339C22×C67#54614yes—
340C22×C67D4×Q814yes—
341C22×C67#55414yes—
342C22×C67#55614yes—
343C22×C67C23×D411yescharacteristic
344C22×C67C23×Q811yescharacteristic
345C22×C67C22×#4111yescharacteristic
346C22×C67C22×#4111yescharacteristic
347C22×C67C22×#4111yescharacteristic
348C22×C67C2×H(5,𝔽2)11yescharacteristic
349C22×C67C2×2−1+411yescharacteristic
350C4×C67—24no—
351C4×C67—24no—
352C4×C67—42no—
353C4×C67—42no—
354C4×C67—42no—
355C4×C67—42no—
356Dic67—24no—
357Dic67—24no—
358Dic67—24no—
359Dic67—24no—
360Dic67—24no—
361Dic67—24no—
362Dic67—42no—
363Dic67—42no—
364C2×#2465—671nomaximal, Sylow
365C2×C67—44no—
366C2×C67#246518yescomplemented
367C2×C67C2×#52511yescharacteristic
368C2×C67C2×#53311yescharacteristic
369C2×C67C2×#54211yescharacteristic
370C2×C67C2×#54611yescharacteristic
371C2×C67C2×D4×Q811yescharacteristic
372C2×C67C2×#55411yescharacteristic
373C2×C67C2×#55611yescharacteristic
374C22×C22⋊Q8—671no—
375C22×C4×Q8—671no—
376#2465—6716no—
377C2×#396D6711yescharacteristic
378C2×#395—671no—
379C2×#395—671no—
380C2×#393—671no—
381C2×#391—671no—
382C2×#389—671no—
383C2×#388—671no—
384C2×#388—671no—
385C2×#387—671no—
386C2×#387—671no—
387C2×#387—671no—
388C2×#385—671no—
389C2×C4×C22⋊C4—671no—
390C67C2×#246511yescharacteristic, complemented, Sylow
391C23×Q8—671no—
392C23×Q8—671no—
393C24×C4—671no—
394C2×C22⋊Q8—678no—
395C2×C22⋊Q8—1348no—
396C2×C4×Q8—678no—
397C2×C4×Q8—1348no—
398C22×C4⋊C4—671no—
399C22×C4⋊C4—671no—
400C22×C4⋊C4—671no—
401C22×C4⋊C4—671no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4—671no—
404C22×C4⋊C4—671no—
405C22×C4⋊C4C2×D6711yescharacteristic
406C22×C4⋊C4C2×D6711yescharacteristic
407C22×C4⋊C4C2×D6711yescharacteristic
408C22×C22⋊C4—671no—
409C22×C22⋊C4—671no—
410C22×C22⋊C4—671no—
411C22×C22⋊C4C2×D6711yescharacteristic
412C22×C22⋊C4C2×D6711yescharacteristic
413C22×C22⋊C4C2×D6711yescharacteristic
414C22×C42—671no—
415C22×C42—671no—
416C22×C42—671no—
417C22×C42—671no—
418#396C2×D6718yes—
419#395—678no—
420#395—678no—
421#393—678no—
422#391—678no—
423#389—678no—
424#388—678no—
425#388—678no—
426#387—678no—
427#387—678no—
428#387—678no—
429#385—678no—
430C4×C22⋊C4—678no—
431C2×#95—671no—
432C2×#95—671no—
433C2×#95—671no—
434C2×#95—671no—
435C2×#95—671no—
436C2×#95—671no—
437C2×#95—671no—
438C2×#95—671no—
439C2×#95—671no—
440C2×#95—671no—
441C2×#95—671no—
442C2×#95C2×D6711yescharacteristic
443C25C22×D6711yescharacteristic
444C22×Q8—2682no—
445C22×Q8—674no—
446C22×Q8—674no—
447C22×Q8—1344no—
448C22×Q8—1344no—
449C22×Q8—1344no—
450C22×Q8—1344no—
451C22×Q8—1344no—
452C23×C4—2682no—
453C23×C4—674no—
454C23×C4—671no—
455C23×C4—671no—
456C23×C4—671no—
457C23×C4—671no—
458C23×C4—671no—
459C23×C4—671no—
460C23×C4—671no—
461C23×C4—671no—
462C23×C4—1344no—
463C23×C4—1344no—
464C23×C4C22×D6711yescharacteristic
465C23×C4C22×D6711yescharacteristic
466C23×C4C22×D6711yescharacteristic
467C23×C4C22×D6711yescharacteristic
468C23×C4C22×D6711yescharacteristic
469C23×C4C22×D6711yescharacteristic
470C22⋊Q8—13432no—
471C4×Q8—13432no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—2682no—
476C2×C4⋊C4—674no—
477C2×C4⋊C4—678no—
478C2×C4⋊C4—674no—
479C2×C4⋊C4—674no—
480C2×C4⋊C4—674no—
481C2×C4⋊C4—674no—
482C2×C4⋊C4—674no—
483C2×C4⋊C4—674no—
484C2×C4⋊C4—1344no—
485C2×C4⋊C4—1344no—
486C2×C4⋊C4—1344no—
487C2×C4⋊C4—1344no—
488C2×C4⋊C4—1344no—
489C2×C4⋊C4C22×D6714yes—
490C2×C4⋊C4C22×D6714yes—
491C2×C4⋊C4C22×D6714yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—678no—
496C2×C22⋊C4—674no—
497C2×C22⋊C4—674no—
498C2×C22⋊C4—674no—
499C2×C22⋊C4—1344no—
500C2×C22⋊C4—1344no—
501C2×C22⋊C4C22×D6714yes—
502C2×C22⋊C4C22×D6714yes—
503C2×C22⋊C4C22×D6714yes—
504C2×C42—2682no—
505C2×C42—674no—
506C2×C42—674no—
507C2×C42—674no—
508C2×C42—674no—
509C2×C42—1344no—
510C2×C42—1344no—
511C2×C42—1344no—
512#95—674no—
513#95—674no—
514#95—674no—
515#95—674no—
516#95—674no—
517#95—674no—
518#95—674no—
519#95—674no—
520#95—674no—
521#95—674no—
522#95—674no—
523#95C22×D6714yes—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24Q8×D6714yes—
531C24C23×D6712yes—
532C24C23×D6711yescharacteristic
533C2×Q8—26816no—
534C2×Q8—2684no—
535C2×Q8—1348no—
536C2×Q8—1348no—
537C2×Q8—1348no—
538C2×Q8—13432no—
539C2×Q8—1348no—
540C2×Q8—1348no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—2684no—
558C22×C4—26816no—
559C22×C4—674no—
560C22×C4—674no—
561C22×C4—674no—
562C22×C4—674no—
563C22×C4—674no—
564C22×C4—674no—
565C22×C4—672no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—672no—
569C22×C4—672no—
570C22×C4—672no—
571C22×C4—672no—
572C22×C4—672no—
573C22×C4—1348no—
574C22×C4—1348no—
575C22×C4—1342no—
576C22×C4—1342no—
577C22×C4—1342no—
578C22×C4—1342no—
579C22×C4—1342no—
580C22×C4—1342no—
581C22×C4—1342no—
582C22×C4—1342no—
583C22×C4—1342no—
584C22×C4—1342no—
585C22×C4—1342no—
586C22×C4—1342no—
587C22×C4—1342no—
588C22×C4—1342no—
589C22×C4—1342no—
590C22×C4—1342no—
591C22×C4—1342no—
592C22×C4—1342no—
593C22×C4D4×D6714yes—
594C22×C4#1176162714yes—
595C22×C4C23×D6712yes—
596C22×C4C23×D6712yes—
597C22×C4C23×D6712yes—
598C22×C4C23×D6712yes—
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C4⋊C4—28no—
602C4⋊C4—28no—
603C4⋊C4—44no—
604C4⋊C4—2684no—
605C4⋊C4—6716no—
606C4⋊C4—1348no—
607C4⋊C4—1348no—
608C4⋊C4—1348no—
609C4⋊C4—1348no—
610C4⋊C4—1348no—
611C22⋊C4—28no—
612C22⋊C4—28no—
613C22⋊C4—44no—
614C22⋊C4—6716no—
615C22⋊C4—1348no—
616C22⋊C4—1348no—
617C42—2684no—
618C42—1348no—
619C42—1348no—
620C42—1348no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—44no—
631C23—44no—
632C23—44no—
633C23—44no—
634C23C2×D4×D6712yes—
635C23C2×Q8×D6714yes—
636C23C2×Q8×D6712yes—
637C23#41×D6712yes—
638C23#41×D6712yes—
639C23C2×#1176162712yes—
640C23#1452408812yes—
641C23#1452409012yes—
642C23C24×D6711yescharacteristic
643Q8—26816no—
644Q8—13432no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—2684no—
668C2×C4—2684no—
669C2×C4—26816no—
670C2×C4—674no—
671C2×C4—674no—
672C2×C4—674no—
673C2×C4—674no—
674C2×C4—674no—
675C2×C4—674no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4—1342no—
679C2×C4—1342no—
680C2×C4—1342no—
681C2×C4—1342no—
682C2×C4—1348no—
683C2×C4—1348no—
684C2×C4—1348no—
685C2×C4—1348no—
686C2×C4—1348no—
687C2×C4—1348no—
688C2×C4—1342no—
689C2×C4—1342no—
690C2×C4—1342no—
691C2×C4—1342no—
692C2×C4—1342no—
693C2×C4—1342no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1342no—
697C2×C4—1342no—
698C2×C4—1342no—
699C2×C4—1342no—
700C2×C4C2×D4×D6714yes—
701C2×C4C2×#1176162714yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—42no—
706C22—42no—
707C22—416no—
708C22—42no—
709C22—42no—
710C22#1686390614yes—
711C22#1686394814yes—
712C22#1686401314yes—
713C22#1686403514yes—
714C22#1686405914yes—
715C22#1686410014yes—
716C22#1686411314yes—
717C22C22×D4×D6711yescharacteristic
718C22C22×Q8×D6711yescharacteristic
719C22C2×#41×D6711yescharacteristic
720C22C2×#41×D6711yescharacteristic
721C22C22×#1176162711yescharacteristic
722C22C2×#1452408811yescharacteristic
723C22C2×#1452409011yescharacteristic
724C4—24no—
725C4—24no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—2682no—
731C4—2682no—
732C4—1344no—
733C4—1344no—
734C4—1344no—
735C4—1344no—
736C4—1344no—
737C4—1344no—
738C2—44no—
739C2#2256423118yesdirect product factor
740C2C2×#1686390611yescharacteristic
741C2C2×#1686394811yescharacteristic
742C2C2×#1686401311yescharacteristic
743C2C2×#1686403511yescharacteristic
744C2C2×#1686405911yescharacteristic
745C2C2×#1686410011yescharacteristic
746C2C2×#1686411311yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC2×#396×C67C2
socleC24×C67C24
prime radicalC25×C67C23
hypercenterC2×#396D67
hypocenterC67C2×#2465
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
2. C22×#14524008C2semidirect
3. #22564231C2direct (N × H)
4. C2×#16863316C2semidirect
5. C2×#16863316C2semidirect
7. C2×#16863301C2semidirect
8. C2×#16863293C2semidirect
11. C2×#16863282C2semidirect
12. C2×#16863278C2semidirect
13. C2×#16863277C2semidirect
23. C2×#14524008C22semidirect
38. #16863316C22semidirect
39. #16863316C22semidirect
41. #16863301C22semidirect
42. #16863293C22semidirect
45. #16863282C22semidirect
46. #16863278C22semidirect
47. #16863277C22semidirect
107. C2×C22⋊Dic67Q8semidirect
203. C22⋊Dic67C2×Q8semidirect
366. C2×C67#2465semidirect
390. C67C2×#2465semidirect
739. C2#22564231direct (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
#225642312
C2×#168633162
C2×#168633082
C2×#168633012
C2×#168632932
C2×#168632902
C2×#168632842
C2×#168632822
C2×#168632782
C2×#168632772
C2×#168632682
C2×C22⋊C4×Dic672
C2×#396×C672
C2×#246567