Finite Group Databasebeta

← C2×#22562741 #31014278

Subgroups — C2×#22562741 #31014278

Order 17152.

3854 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524020C211yesmaximal, characteristic
2C22×#14524008C211yesmaximal, characteristic, complemented
3C23×C4×Dic67C211yesmaximal, characteristic
4#22562741C2116yesmaximal, direct product factor
5C2×#16863300C211yesmaximal, characteristic, complemented
6C2×#16863291C211yesmaximal, characteristic, complemented
7C2×#16863281C211yesmaximal, characteristic, complemented
8C2×#16863277C211yesmaximal, characteristic, complemented
9C2×#16863269C211yesmaximal, characteristic
10C2×#16863254C211yesmaximal, characteristic
11C2×C4⋊C4×Dic67C211yesmaximal, characteristic, complemented
12C2×#16863247C211yesmaximal, characteristic, complemented
13C2×#16863247C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic67C211yesmaximal, characteristic
15C2×C22⋊C4×Dic67C211yesmaximal, characteristic
16C2×#385×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C24×Dic67C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C2×#14524020C4116yescomplemented
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×C4×Dic67—28no—
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2218yes—
37C22×C4×Dic67C2211yescharacteristic
38C22×C4×Dic67C2211yescharacteristic
39C22×C4×Dic67C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43#16863300C2218yescomplemented
44#16863291C2218yescomplemented
45#16863281C2218yescomplemented
46#16863277C2218yescomplemented
47#16863269C2218yes—
48#16863254C2218yes—
49C4⋊C4×Dic67C2218yescomplemented
50#16863247C2218yescomplemented
51#16863247C2218yescomplemented
52C22⋊C4×Dic67C2218yes—
53C22⋊C4×Dic67C2218yes—
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C24×C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65C22×C22⋊C4×C67C2211yescharacteristic
66C22×C22⋊C4×C67C2211yescharacteristic
67#385×C67C2218yes—
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
70C22×Dic134—24no—
71C22×Dic134—24no—
72C22×Dic134C2×C418yescomplemented
73C22×Dic134C2314yes—
74C23×Dic67—24no—
75C23×Dic67—24no—
76C23×Dic67—24no—
77C23×Dic67—24no—
78C23×Dic67C2×C418yes—
79C23×Dic67Q818yescomplemented
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2314yes—
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2314yes—
88C23×Dic67C2311yescharacteristic
89C23×Dic67C2311yescharacteristic
90#14524020C2×C4164yescomplemented
91#14524008—232no—
92C2×C4⋊Dic67C2×C418yescomplemented
93C2×C4⋊Dic67C2314yes—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—24no—
96C2×Dic67⋊C4—24no—
97C2×Dic67⋊C4—24no—
98C2×Dic67⋊C4C2×C418yescomplemented
99C2×Dic67⋊C4C2×C418yescomplemented
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×Dic67⋊C4C2314yes—
104C2×Dic67⋊C4C2314yes—
105C2×Dic67⋊C4C2314yes—
106C2×C22⋊Dic67—24no—
107C2×C22⋊Dic67C2×C418yes—
108C2×C22⋊Dic67C2314yes—
109C2×C22⋊Dic67C2314yes—
110C2×C4×Dic67—24no—
111C2×C4×Dic67—24no—
112C2×C4×Dic67—24no—
113C2×C4×Dic67—24no—
114C2×C4×Dic67—24no—
115C2×C4×Dic67—24no—
116C2×C4×Dic67—232no—
117C2×C4×Dic67—24no—
118C2×C4×Dic67D418yes—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C2×C4×Dic67C2314yes—
122C2×C4×Dic67C2314yes—
123C2×C4×Dic67C2314yes—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C25×C67C2311yescharacteristic
136C23×C4×C67—24no—
137C23×C4×C67—24no—
138C23×C4×C67—24no—
139C23×C4×C67C2311yescharacteristic
140C23×C4×C67C2311yescharacteristic
141C23×C4×C67C2314yes—
142C23×C4×C67C2311yescharacteristic
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C2×C4⋊C4×C67—24no—
147C2×C4⋊C4×C67—24no—
148C2×C4⋊C4×C67C2314yes—
149C2×C4⋊C4×C67C2314yes—
150C2×C22⋊C4×C67—24no—
151C2×C22⋊C4×C67C2×C418yes—
152C2×C22⋊C4×C67C2314yes—
153C2×C22⋊C4×C67C2314yes—
154#95×C67C2314yes—
155#95×C67C2314yes—
156C2×Dic134—232no—
157C2×Dic134—28no—
158C2×Dic134—28no—
159C2×Dic134C22×C4116yescomplemented
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—232no—
169C22×Dic67—232no—
170C22×Dic67—28no—
171C22×Dic67—28no—
172C22×Dic67—28no—
173C22×Dic67—28no—
174C22×Dic67—22no—
175C22×Dic67—22no—
176C22×Dic67—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67C22×C414yes—
181C22×Dic67C22×C414yes—
182C22×Dic67C22×C414yes—
183C22×Dic67C22×C4116yes—
184C22×Dic67C22×C414yes—
185C22×Dic67C2×D414yes—
186C22×Dic67C2×D414yes—
187C22×Dic67C2×Q814yes—
188C22×Dic67C2×Q814yes—
189C22×Dic67C2×Q8116yescomplemented
190C22×Dic67#4114yes—
191C22×Dic67#4114yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C22×Dic67C2412yes—
199C22×Dic67C2412yes—
200C4⋊Dic67C22×C4116yescomplemented
201Dic67⋊C4—28no—
202Dic67⋊C4—28no—
203Dic67⋊C4—28no—
204Dic67⋊C4—28no—
205Dic67⋊C4C22×C4116yescomplemented
206Dic67⋊C4C22×C4116yescomplemented
207C22⋊Dic67—28no—
208C22⋊Dic67C22×C4116yes—
209C4×Dic67—28no—
210C4×Dic67—28no—
211C4×Dic67—28no—
212C4×Dic67—28no—
213C4×Dic67—28no—
214C4×Dic67—28no—
215C4×Dic67—28no—
216C4×Dic67C2×D4116yes—
217C24×C67—22no—
218C24×C67—22no—
219C24×C67—22no—
220C24×C67—22no—
221C24×C67C22×C414yes—
222C24×C67C2×Q814yes—
223C24×C67#4114yes—
224C24×C67C2412yes—
225C24×C67C2411yescharacteristic
226C22×C4×C67—232no—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—28no—
231C22×C4×C67—22no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—28no—
237C22×C4×C67—28no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67C22×C414yes—
245C22×C4×C67C22×C414yes—
246C22×C4×C67C2×D414yes—
247C22×C4×C67#4114yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2412yes—
251C22×C4×C67C2412yes—
252C22×C4×C67C2412yes—
253C22×C4×C67C2412yes—
254C4⋊C4×C67—28no—
255C4⋊C4×C67—28no—
256C22⋊C4×C67—28no—
257C22⋊C4×C67C22×C4116yes—
258C23×C67—28no—
259C23×C67—28no—
260C23×C67—28no—
261C23×C67—28no—
262C23×C67—28no—
263C23×C67—28no—
264C23×C67—22no—
265C23×C67—22no—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67C4×Q8116yescomplemented
269C23×C67C23×C414yes—
270C23×C67C23×C412yes—
271C23×C67C22×D412yes—
272C23×C67C22×Q814yes—
273C23×C67C22×Q812yes—
274C23×C67C2×#4112yes—
275C23×C67C2×#4112yes—
276C23×C67C2×#4114yes—
277C23×C67C2×#4112yes—
278C23×C67C2×#4112yes—
279C23×C67C2511yescharacteristic
280C2×C4×C67—232no—
281C2×C4×C67—28no—
282C2×C4×C67—28no—
283C2×C4×C67—28no—
284C2×C4×C67—28no—
285C2×C4×C67—22no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—44no—
300C2×C4×C67—44no—
301C2×C4×C67C23×C414yes—
302C2×C4×C67C23×C414yes—
303C2×C4×C67C22×D414yes—
304C2×C4×C67C2×#4114yes—
305C2×Dic67—28no—
306C2×Dic67—28no—
307C2×Dic67—28no—
308C2×Dic67—28no—
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—232no—
318C2×Dic67—232no—
319C2×Dic67—22no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—44no—
326C2×Dic67—44no—
327C2×Dic67C4×D4116yes—
328C2×Dic67C22⋊Q8116yescomplemented
329C2×Dic67C23×C414yes—
330C2×Dic67C23×C414yes—
331C2×Dic67C23×C414yes—
332C2×Dic67C23×C414yes—
333C2×Dic67C22×D414yes—
334C2×Dic67C22×D414yes—
335C2×Dic67C22×Q814yes—
336C2×Dic67C22×Q814yes—
337C2×Dic67C2×#4114yes—
338C2×Dic67C2×#4114yes—
339Dic134—232no—
340C22×C67—24no—
341C22×C67—24no—
342C22×C67—24no—
343C22×C67—24no—
344C22×C67—24no—
345C22×C67—24no—
346C22×C67—232no—
347C22×C67C2×C4×D414yes—
348C22×C67C2×C4×Q814yes—
349C22×C67C2×C4×Q818yescomplemented
350C22×C67C4×#4114yes—
351C22×C67C2×C22⋊Q814yes—
352C22×C67#52514yes—
353C22×C67#52914yes—
354C22×C67#53314yes—
355C22×C67C24×C411yescharacteristic
356C22×C67C23×D411yescharacteristic
357C22×C67C23×Q811yescharacteristic
358C22×C67C22×#4111yescharacteristic
359C22×C67C22×#4111yescharacteristic
360C22×C67C22×#4111yescharacteristic
361C22×C67C22×#4111yescharacteristic
362C4×C67—24no—
363C4×C67—24no—
364C4×C67—24no—
365C4×C67—24no—
366C4×C67—42no—
367C4×C67—42no—
368Dic67—24no—
369Dic67—24no—
370Dic67—24no—
371Dic67—24no—
372Dic67—42no—
373Dic67—42no—
374Dic67C2×C4×D418yes—
375Dic67C2×C22⋊Q818yescomplemented
376C2×C4×C22⋊Q8—671nomaximal, Sylow
377C2×C67—28no—
378C2×C67C4×C22⋊Q818yescomplemented
379C2×C67C22×C4×D411yescharacteristic
380C2×C67C22×C4×Q811yescharacteristic
381C2×C67C2×C4×#4111yescharacteristic
382C2×C67C22×C22⋊Q811yescharacteristic
383C2×C67C2×#52511yescharacteristic
384C2×C67C2×#52911yescharacteristic
385C2×C67C2×#53311yescharacteristic
386C22×C22⋊Q8—671no—
387C22×C4×Q8—671no—
388C23×C42—671no—
389C4×C22⋊Q8—6716no—
390C2×#391—671no—
391C2×#389—671no—
392C2×#387—671no—
393C2×#387—671no—
394C2×#385—671no—
395C2×#385D6711yescharacteristic
396C2×#380—671no—
397C2×C4×C4⋊C4—671no—
398C2×C4×C4⋊C4—671no—
399C2×C4×C4⋊C4—671no—
400C2×C4×C22⋊C4—671no—
401C2×C4×C22⋊C4—671no—
402C67C2×C4×C22⋊Q811yescharacteristic, complemented, Sylow
403C23×Q8—671no—
404C24×C4—671no—
405C24×C4—671no—
406C24×C4C2×D6711yescharacteristic
407C2×C22⋊Q8—6716no—
408C2×C22⋊Q8—678no—
409C2×C4×Q8—678no—
410C2×C4×Q8—1348no—
411C22×C4⋊C4—671no—
412C22×C4⋊C4—671no—
413C22×C4⋊C4—671no—
414C22×C4⋊C4—671no—
415C22×C4⋊C4—671no—
416C22×C4⋊C4—671no—
417C22×C4⋊C4—671no—
418C22×C4⋊C4C2×D6711yescharacteristic
419C22×C4⋊C4C2×D6711yescharacteristic
420C22×C22⋊C4—671no—
421C22×C22⋊C4—671no—
422C22×C22⋊C4C2×D6711yescharacteristic
423C22×C22⋊C4C2×D6711yescharacteristic
424C22×C42—671no—
425C22×C42—671no—
426C22×C42—671no—
427C22×C42—671no—
428C22×C42—678no—
429C22×C42—671no—
430C22×C42—671no—
431C22×C42—671no—
432C22×C42—671no—
433C22×C42—1348no—
434#391—678no—
435#389—678no—
436#387—678no—
437#387—678no—
438#385—678no—
439#385C2×D6718yes—
440#380—678no—
441C4×C4⋊C4—678no—
442C4×C4⋊C4—678no—
443C4×C4⋊C4—678no—
444C4×C22⋊C4—678no—
445C4×C22⋊C4—678no—
446C2×#95—671no—
447C2×#95—671no—
448C2×#95—671no—
449C2×#95—671no—
450C2×#95—671no—
451C2×#95—671no—
452C2×#95—671no—
453C2×#95—671no—
454C2×#95C2×D6711yescharacteristic
455C2×#95C2×D6711yescharacteristic
456C25C22×D6711yescharacteristic
457C22×Q8—678no—
458C22×Q8—674no—
459C22×Q8—1344no—
460C22×Q8—1344no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—24no—
464C23×C4—671no—
465C23×C4—671no—
466C23×C4—678no—
467C23×C4—678no—
468C23×C4—674no—
469C23×C4—674no—
470C23×C4—671no—
471C23×C4—671no—
472C23×C4—671no—
473C23×C4—671no—
474C23×C4—671no—
475C23×C4—671no—
476C23×C4—1344no—
477C23×C4—1344no—
478C23×C4—1344no—
479C23×C4—1344no—
480C23×C4C22×D6714yes—
481C23×C4C22×D6711yescharacteristic
482C23×C4C22×D6711yescharacteristic
483C23×C4C22×D6711yescharacteristic
484C23×C4C22×D6711yescharacteristic
485C23×C4C22×D6711yescharacteristic
486C23×C4C22×D6711yescharacteristic
487C22⋊Q8—6764no—
488C4×Q8—13432no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—678no—
492C2×C4⋊C4—678no—
493C2×C4⋊C4—678no—
494C2×C4⋊C4—674no—
495C2×C4⋊C4—674no—
496C2×C4⋊C4—674no—
497C2×C4⋊C4—674no—
498C2×C4⋊C4—674no—
499C2×C4⋊C4—674no—
500C2×C4⋊C4—674no—
501C2×C4⋊C4—1344no—
502C2×C4⋊C4—1344no—
503C2×C4⋊C4—1344no—
504C2×C4⋊C4—1344no—
505C2×C4⋊C4C22×D6714yes—
506C2×C4⋊C4C22×D6714yes—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—678no—
509C2×C22⋊C4—674no—
510C2×C22⋊C4—674no—
511C2×C22⋊C4—1344no—
512C2×C22⋊C4C4×D6718yes—
513C2×C22⋊C4C22×D6714yes—
514C2×C22⋊C4C22×D6714yes—
515C2×C42—678no—
516C2×C42—674no—
517C2×C42—674no—
518C2×C42—674no—
519C2×C42—674no—
520C2×C42—674no—
521C2×C42—674no—
522C2×C42—674no—
523C2×C42—674no—
524C2×C42—13432no—
525C2×C42—1344no—
526C2×C42—1344no—
527C2×C42—1344no—
528C2×C42—1344no—
529C2×C42—1344no—
530C2×C42—1344no—
531C2×C42—1344no—
532#95—674no—
533#95—674no—
534#95—674no—
535#95—674no—
536#95—674no—
537#95—674no—
538#95—674no—
539#95—674no—
540#95C22×D6714yes—
541#95C22×D6714yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D6714yes—
547C24Q8×D6714yes—
548C24#1176162714yes—
549C24C23×D6712yes—
550C24C23×D6711yescharacteristic
551C2×Q8—6716no—
552C2×Q8—1348no—
553C2×Q8—13432no—
554C2×Q8—1348no—
555C22×C4—232no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—28no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—674no—
574C22×C4—674no—
575C22×C4—674no—
576C22×C4—674no—
577C22×C4—674no—
578C22×C4—674no—
579C22×C4—672no—
580C22×C4—672no—
581C22×C4—674no—
582C22×C4—674no—
583C22×C4—674no—
584C22×C4—6716no—
585C22×C4—674no—
586C22×C4—6716no—
587C22×C4—672no—
588C22×C4—672no—
589C22×C4—672no—
590C22×C4—672no—
591C22×C4—672no—
592C22×C4—672no—
593C22×C4—1342no—
594C22×C4—1342no—
595C22×C4—1342no—
596C22×C4—1342no—
597C22×C4—1342no—
598C22×C4—1342no—
599C22×C4—1348no—
600C22×C4—1348no—
601C22×C4—13432no—
602C22×C4—13432no—
603C22×C4—1348no—
604C22×C4—1348no—
605C22×C4—1342no—
606C22×C4—1342no—
607C22×C4—1342no—
608C22×C4—1342no—
609C22×C4—1342no—
610C22×C4—1342no—
611C22×C4—1342no—
612C22×C4—1342no—
613C22×C4C2×C4×D6714yes—
614C22×C4C2×C4×D6714yes—
615C22×C4D4×D6714yes—
616C22×C4#1176162714yes—
617C22×C4C23×D6712yes—
618C22×C4C23×D6712yes—
619C22×C4C23×D6712yes—
620C22×C4C23×D6712yes—
621C22×C4C23×D6712yes—
622C22×C4C23×D6712yes—
623C4⋊C4—28no—
624C4⋊C4—28no—
625C4⋊C4—6716no—
626C4⋊C4—6716no—
627C4⋊C4—6716no—
628C4⋊C4—1348no—
629C4⋊C4—1348no—
630C4⋊C4—1348no—
631C4⋊C4—1348no—
632C22⋊C4—28no—
633C22⋊C4—6716no—
634C22⋊C4—1348no—
635C22⋊C4C2×C4×D67116yes—
636C42—6716no—
637C42—1348no—
638C42—1348no—
639C42—1348no—
640C42—1348no—
641C42—1348no—
642C42—1348no—
643C42—1348no—
644C23—28no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23#14524008116yescomplemented
655C23C22×C4×D6714yes—
656C23C22×C4×D6712yes—
657C23C2×D4×D6712yes—
658C23C2×Q8×D6714yes—
659C23C2×Q8×D6712yes—
660C23#41×D6712yes—
661C23#41×D6712yes—
662C23C2×#1176162714yes—
663C23C2×#1176162712yes—
664C23C2×#1176162712yes—
665C23C24×D6711yescharacteristic
666Q8—13432no—
667C2×C4—232no—
668C2×C4—28no—
669C2×C4—28no—
670C2×C4—28no—
671C2×C4—28no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—2684no—
689C2×C4—2684no—
690C2×C4—6716no—
691C2×C4—6716no—
692C2×C4—674no—
693C2×C4—674no—
694C2×C4—674no—
695C2×C4—674no—
696C2×C4—674no—
697C2×C4—674no—
698C2×C4—674no—
699C2×C4—674no—
700C2×C4—674no—
701C2×C4—674no—
702C2×C4—1342no—
703C2×C4—1342no—
704C2×C4—1342no—
705C2×C4—1342no—
706C2×C4—1342no—
707C2×C4—1342no—
708C2×C4—13432no—
709C2×C4—13432no—
710C2×C4—1348no—
711C2×C4—1348no—
712C2×C4—1348no—
713C2×C4—1348no—
714C2×C4—1342no—
715C2×C4—1342no—
716C2×C4—1342no—
717C2×C4—1342no—
718C2×C4—1342no—
719C2×C4—1342no—
720C2×C4—1342no—
721C2×C4—1342no—
722C2×C4C22×C4×D6714yes—
723C2×C4C22×C4×D6714yes—
724C2×C4C2×D4×D6714yes—
725C2×C4C2×#1176162714yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—232no—
732C22—24no—
733C22C4×D4×D6714yes—
734C22C2×#1452400814yes—
735C22C2×#1452400818yescomplemented
736C22C4×#1176162714yes—
737C22C22⋊Q8×D6714yes—
738C22#1686390214yes—
739C22#1686392314yes—
740C22#1686394814yes—
741C22C23×C4×D6711yescharacteristic
742C22C22×D4×D6711yescharacteristic
743C22C22×Q8×D6711yescharacteristic
744C22C2×#41×D6711yescharacteristic
745C22C2×#41×D6711yescharacteristic
746C22C22×#1176162711yescharacteristic
747C22C22×#1176162711yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2682no—
755C4—2682no—
756C4—678no—
757C4—678no—
758C4—1344no—
759C4—1344no—
760C4—1344no—
761C4—1344no—
762C2—28no—
763C2#2256274118yesdirect product factor
764C2C2×C4×D4×D6711yescharacteristic
765C2C22×#1452400811yescharacteristic
766C2C2×C4×#1176162711yescharacteristic
767C2C2×C22⋊Q8×D6711yescharacteristic
768C2C2×#1686390211yescharacteristic
769C2C2×#1686392311yescharacteristic
770C2C2×#1686394811yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#385×C67C2
socleC24×C67C24
prime radicalC25×C67C23
cosocleC23×C67C25
hypercenterC2×#385D67
hypocenterC67C2×C4×C22⋊Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14524008C2semidirect
4. #22562741C2direct (N × H)
5. C2×#16863300C2semidirect
6. C2×#16863291C2semidirect
7. C2×#16863281C2semidirect
8. C2×#16863277C2semidirect
11. C2×C4⋊C4×Dic67C2semidirect
12. C2×#16863247C2semidirect
13. C2×#16863247C2semidirect
20. C2×#14524020C4semidirect
23. C2×#14524008C22semidirect
43. #16863300C22semidirect
44. #16863291C22semidirect
45. #16863281C22semidirect
46. #16863277C22semidirect
49. C4⋊C4×Dic67C22semidirect
50. #16863247C22semidirect
51. #16863247C22semidirect
72. C22×Dic134C2×C4semidirect
79. C23×Dic67Q8semidirect
90. #14524020C2×C4semidirect
92. C2×C4⋊Dic67C2×C4semidirect
98. C2×Dic67⋊C4C2×C4semidirect
99. C2×Dic67⋊C4C2×C4semidirect
159. C2×Dic134C22×C4semidirect
189. C22×Dic67C2×Q8semidirect
200. C4⋊Dic67C22×C4semidirect
205. Dic67⋊C4C22×C4semidirect
206. Dic67⋊C4C22×C4semidirect
268. C23×C67C4×Q8semidirect
328. C2×Dic67C22⋊Q8semidirect
349. C22×C67C2×C4×Q8semidirect
375. Dic67C2×C22⋊Q8semidirect
378. C2×C67C4×C22⋊Q8semidirect
402. C67C2×C4×C22⋊Q8semidirect
654. C23#14524008semidirect
735. C22C2×#14524008semidirect
763. C2#22562741direct (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
C23×C4×Dic672
#225627412
C2×#168633002
C2×#168632912
C2×#168632812
C2×#168632772
C2×#168632692
C2×#168632542
C2×C4⋊C4×Dic672
C2×#168632472
C2×C22⋊C4×Dic672
C2×#385×C672
C2×C4×C22⋊Q867