Finite Group Databasebeta

← C2×#22563023 #31014751

Subgroups — C2×#22563023 #31014751

Order 17152.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524029C211yesmaximal, characteristic
2#22563023C2116yesmaximal, direct product factor
3C2×#16863301C211yesmaximal, characteristic, complemented
4C2×#16863300C211yesmaximal, characteristic, complemented
5C2×#16863289C211yesmaximal, characteristic, complemented
6C2×#16863286C211yesmaximal, characteristic, complemented
7C2×#16863286C211yesmaximal, characteristic, complemented
8C2×#16863284C211yesmaximal, characteristic, complemented
9C2×#16863275C211yesmaximal, characteristic
10C2×#16863272C211yesmaximal, characteristic
11C2×#16863270C211yesmaximal, characteristic, complemented
12C2×#16863263C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic67C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic67C211yesmaximal, characteristic, complemented
15C2×#16863243C211yesmaximal, characteristic, complemented
16C2×#385×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C22⋊D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C2×#14524029C4116yescomplemented
21C2×#14524029C2218yes—
22C22×C4⋊Dic67C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×C22⋊Dic67C2211yescharacteristic
25C22×C22⋊Dic67C2211yescharacteristic
26C22×C22⋊Dic67C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863301C2218yescomplemented
38#16863300C2218yescomplemented
39#16863289C2218yescomplemented
40#16863286C2218yescomplemented
41#16863286C2218yescomplemented
42#16863284C2218yescomplemented
43#16863275C2218yes—
44#16863272C2218yes—
45#16863270C2218yescomplemented
46#16863263C2218yescomplemented
47C4⋊C4×Dic67C2218yescomplemented
48C4×C22⋊Dic67C2218yescomplemented
49#16863243C2218yescomplemented
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
60C24×C4×C67C2211yescharacteristic
61C22×C4⋊C4×C67C2211yescharacteristic
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65#385×C67C2218yescomplemented
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C24×D67C2311yescharacteristic
69C22×Dic134—42no—
70C22×Dic134—42no—
71C22×Dic134C2×C418yescomplemented
72C22×Dic134C2314yes—
73C22×C22⋊D67—42no—
74C22×C22⋊D67—42no—
75C22×C22⋊D67C2×C418yes—
76C22×C22⋊D67C2314yes—
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C22×C4×D67—24no—
85C22×C4×D67—42no—
86C22×C4×D67—42no—
87C22×C4×D67C2314yes—
88#14524029C2×C4164yescomplemented
89C2×C4⋊Dic67—24no—
90C2×C4⋊Dic67C2314yes—
91C2×Dic67⋊C4—42no—
92C2×Dic67⋊C4C2314yes—
93C2×C22⋊Dic67—24no—
94C2×C22⋊Dic67—42no—
95C2×C22⋊Dic67C2×C418yescomplemented
96C2×C22⋊Dic67C2314yes—
97C2×C22⋊Dic67C2314yes—
98C2×C22⋊Dic67C2314yes—
99C2×(C2×D67)⋊C4—24no—
100C2×(C2×D67)⋊C4—42no—
101C2×(C2×D67)⋊C4—42no—
102C2×(C2×D67)⋊C4C2×C418yescomplemented
103C2×(C2×D67)⋊C4C2×C418yescomplemented
104C2×(C2×D67)⋊C4C2314yes—
105C2×(C2×D67)⋊C4C2314yes—
106C2×(C2×D67)⋊C4C2314yes—
107C2×(C2×D67)⋊C4C2314yes—
108C2×(C2×D67)⋊C4C2314yes—
109C2×C4×Dic67—42no—
110C2×C4×Dic67—42no—
111C2×C4×Dic67—42no—
112C2×C4×Dic67—42no—
113C2×C4×Dic67C2×C418yescomplemented
114C2×C4×Dic67C2314yes—
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—
129C25×C67C2311yescharacteristic
130C23×C4×C67—24no—
131C23×C4×C67—42no—
132C23×C4×C67—42no—
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C23×C4×C67C2311yescharacteristic
139C23×C4×C67C2314yes—
140C2×C4⋊C4×C67—24no—
141C2×C4⋊C4×C67—42no—
142C2×C4⋊C4×C67C2314yes—
143C2×C4⋊C4×C67C2314yes—
144C2×C22⋊C4×C67—42no—
145C2×C22⋊C4×C67C2×C418yescomplemented
146C2×C22⋊C4×C67C2314yes—
147C2×C22⋊C4×C67C2314yes—
148#95×C67C2314yes—
149#95×C67C2314yes—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67—22no—
154C23×D67—22no—
155C23×D67—22no—
156C23×D67C22×C414yes—
157C23×D67C2412yes—
158C2×Dic134—416no—
159C2×Dic134—44no—
160C2×Dic134—44no—
161C2×Dic134C22×C4116yescomplemented
162C2×C22⋊D67—416no—
163C2×C22⋊D67—44no—
164C2×C22⋊D67—44no—
165C2×C22⋊D67C22×C4116yes—
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—22no—
177C22×Dic67—22no—
178C22×Dic67—22no—
179C22×Dic67—22no—
180C22×Dic67—22no—
181C22×Dic67—22no—
182C22×Dic67—22no—
183C22×Dic67C22×C414yes—
184C22×Dic67C22×C414yes—
185C22×Dic67C22×C414yes—
186C22×Dic67#4114yes—
187C22×Dic67C2412yes—
188C22×Dic67C2412yes—
189C22×Dic67C2412yes—
190C22×Dic67C2412yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C2×C4×D67—28no—
195C2×C4×D67—44no—
196C2×C4×D67—44no—
197C2×C4×D67—416no—
198C4⋊Dic67—28no—
199Dic67⋊C4—44no—
200C22⋊Dic67—28no—
201C22⋊Dic67—44no—
202C22⋊Dic67C22×C4116yescomplemented
203(C2×D67)⋊C4—28no—
204(C2×D67)⋊C4—44no—
205(C2×D67)⋊C4—44no—
206(C2×D67)⋊C4C22×C4116yescomplemented
207(C2×D67)⋊C4C22×C4116yescomplemented
208C4×Dic67—44no—
209C4×Dic67—44no—
210C4×Dic67—44no—
211C4×Dic67—44no—
212C4×Dic67C22×C4116yescomplemented
213C24×C67—22no—
214C24×C67—22no—
215C24×C67—22no—
216C24×C67—22no—
217C24×C67—22no—
218C24×C67—22no—
219C24×C67C22×C414yes—
220C24×C67C2412yes—
221C24×C67C2411yescharacteristic
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×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—28no—
238C22×C4×C67—44no—
239C22×C4×C67—44no—
240C22×C4×C67—416no—
241C22×C4×C67C22×C414yes—
242C22×C4×C67C22×C414yes—
243C22×C4×C67#4114yes—
244C22×C4×C67C2412yes—
245C22×C4×C67C2412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C4⋊C4×C67—28no—
251C4⋊C4×C67—44no—
252C22⋊C4×C67—44no—
253C22⋊C4×C67C22×C4116yescomplemented
254C23×C67—28no—
255C23×C67—28no—
256C23×C67—28no—
257C23×C67—22no—
258C23×C67—22no—
259C23×C67—22no—
260C23×C67—22no—
261C23×C67—22no—
262C23×C67—22no—
263C23×C67—44no—
264C23×C67—44no—
265C23×C67—44no—
266C23×C67—44no—
267C23×C67C23×C414yes—
268C23×C67C23×C412yes—
269C23×C67C2×#4112yes—
270C23×C67C2×#4112yes—
271C23×C67H(5,𝔽2)12yes—
272C23×C67H(5,𝔽2)12yes—
273C23×C67H(5,𝔽2)12yes—
274C23×C672−1+412yes—
275C23×C67C2511yescharacteristic
276C22×D67—28no—
277C22×D67—28no—
278C22×D67—28no—
279C22×D67—22no—
280C22×D67—22no—
281C22×D67—22no—
282C22×D67—22no—
283C22×D67—22no—
284C22×D67—22no—
285C22×D67—44no—
286C22×D67—44no—
287C22×D67—44no—
288C22×D67—44no—
289C22×D67C23×C414yes—
290C2×C4×C67—28no—
291C2×C4×C67—28no—
292C2×C4×C67—28no—
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—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—416no—
309C2×C4×C67—44no—
310C2×C4×C67—44no—
311C2×C4×C67—44no—
312C2×C4×C67C23×C414yes—
313C2×C4×C67C23×C414yes—
314C2×C4×C67C2×#4114yes—
315C22⋊D67—416no—
316C2×Dic67—28no—
317C2×Dic67—28no—
318C2×Dic67—28no—
319C2×Dic67—28no—
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—22no—
325C2×Dic67—22no—
326C2×Dic67—22no—
327C2×Dic67—22no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—22no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
336C2×Dic67—22no—
337C2×Dic67—44no—
338C2×Dic67—44no—
339C2×Dic67—44no—
340C2×Dic67C23×C414yes—
341C2×Dic67C23×C414yes—
342C2×Dic67C23×C414yes—
343C2×Dic67C2×#4114yes—
344C4×D67—416no—
345Dic134—416no—
346C22×C67—24no—
347C22×C67—24no—
348C22×C67—24no—
349C22×C67—416no—
350C22×C67—42no—
351C22×C67—42no—
352C22×C67—42no—
353C22×C67—42no—
354C22×C67C4×#4114yes—
355C22×C67#51814yes—
356C22×C67#52014yes—
357C22×C67#53814yes—
358C22×C67#53814yes—
359C22×C67#54214yes—
360C22×C67#54214yes—
361C22×C67C24×C411yescharacteristic
362C22×C67C22×#4111yescharacteristic
363C22×C67C22×#4111yescharacteristic
364C22×C67C2×H(5,𝔽2)11yescharacteristic
365C22×C67C2×H(5,𝔽2)11yescharacteristic
366C22×C67C2×H(5,𝔽2)11yescharacteristic
367C22×C67C2×2−1+411yescharacteristic
368C2×D67—24no—
369C2×D67—24no—
370C2×D67—24no—
371C2×D67—416no—
372C2×D67—42no—
373C2×D67—42no—
374C2×D67—42no—
375C2×D67—42no—
376C4×C67—24no—
377C4×C67—24no—
378C4×C67—24no—
379C4×C67—42no—
380C4×C67—42no—
381C4×C67—42no—
382Dic67—24no—
383Dic67—24no—
384Dic67—24no—
385Dic67—24no—
386Dic67—42no—
387Dic67—42no—
388Dic67—42no—
389C2×#2337—671nomaximal, Sylow
390C2×C67—44no—
391C2×C67#233718yescomplemented
392C2×C67C2×C4×#4111yescharacteristic
393C2×C67C2×#51811yescharacteristic
394C2×C67C2×#52011yescharacteristic
395C2×C67C2×#53811yescharacteristic
396C2×C67C2×#53811yescharacteristic
397C2×C67C2×#54211yescharacteristic
398C2×C67C2×#54211yescharacteristic
399D67—44no—
400C22×#124—671no—
401#2337—6716no—
402C2×#391—671no—
403C2×#391—671no—
404C2×#388—671no—
405C2×#388—671no—
406C2×#388—671no—
407C2×#388—671no—
408C2×#386—671no—
409C2×#386—671no—
410C2×#385—671no—
411C2×#385D6711yescharacteristic, complemented
412C2×#383—671no—
413C2×C4×C4⋊C4—671no—
414C2×C4×C22⋊C4—671no—
415C2×C4×C22⋊C4—671no—
416C67C2×#233711yescharacteristic, complemented, Sylow
417C23×Q8—671no—
418C23×D4—671no—
419C24×C4—671no—
420C24×C4C2×D6711yescharacteristic
421C2×#124—6716no—
422C2×#124—678no—
423C22×C4⋊C4—671no—
424C22×C4⋊C4—671no—
425C22×C4⋊C4C2×D6711yescharacteristic
426C22×C4⋊C4C2×D6711yescharacteristic
427C22×C22⋊C4—671no—
428C22×C22⋊C4—671no—
429C22×C22⋊C4—671no—
430C22×C22⋊C4—671no—
431C22×C22⋊C4—671no—
432C22×C22⋊C4—671no—
433C22×C22⋊C4—671no—
434C22×C22⋊C4—671no—
435C22×C22⋊C4C2×D6711yescharacteristic
436C22×C22⋊C4C2×D6711yescharacteristic
437C22×C42—671no—
438C22×C42—671no—
439C22×C42—671no—
440C22×C42—671no—
441C22×C42—671no—
442#391—678no—
443#391—678no—
444#388—678no—
445#388—678no—
446#388—678no—
447#388—678no—
448#386—678no—
449#386—678no—
450#385—678no—
451#385C2×D6718yescomplemented
452#383—678no—
453C4×C4⋊C4—678no—
454C4×C22⋊C4—678no—
455C4×C22⋊C4—678no—
456C2×#95—671no—
457C2×#95—671no—
458C2×#95—671no—
459C2×#95—671no—
460C2×#95—671no—
461C2×#95—671no—
462C2×#95—671no—
463C2×#95—671no—
464C2×#95—671no—
465C2×#95—671no—
466C2×#95C2×D6711yescharacteristic
467C2×#95C2×D6711yescharacteristic
468C25—671no—
469C25C22×D6711yescharacteristic
470C22×Q8—2682no—
471C22×Q8—2682no—
472C22×Q8—678no—
473C22×Q8—674no—
474C22×D4—2682no—
475C22×D4—2682no—
476C22×D4—678no—
477C22×D4—674no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—2682no—
482C23×C4—2682no—
483C23×C4—674no—
484C23×C4—671no—
485C23×C4—671no—
486C23×C4—671no—
487C23×C4—671no—
488C23×C4—671no—
489C23×C4—671no—
490C23×C4—671no—
491C23×C4—1344no—
492C23×C4C22×D6711yescharacteristic
493C23×C4C22×D6711yescharacteristic
494C23×C4C22×D6711yescharacteristic
495C23×C4C22×D6711yescharacteristic
496C23×C4C22×D6711yescharacteristic
497C23×C4C22×D6711yescharacteristic
498C23×C4C22×D6714yes—
499#124—6764no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—2682no—
503C2×C4⋊C4—674no—
504C2×C4⋊C4—674no—
505C2×C4⋊C4—1344no—
506C2×C4⋊C4C22×D6714yes—
507C2×C4⋊C4C22×D6714yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—2682no—
510C2×C22⋊C4—2682no—
511C2×C22⋊C4—2682no—
512C2×C22⋊C4—674no—
513C2×C22⋊C4—674no—
514C2×C22⋊C4—674no—
515C2×C22⋊C4—678no—
516C2×C22⋊C4—674no—
517C2×C22⋊C4—678no—
518C2×C22⋊C4—678no—
519C2×C22⋊C4—674no—
520C2×C22⋊C4—674no—
521C2×C22⋊C4—674no—
522C2×C22⋊C4—674no—
523C2×C22⋊C4—1344no—
524C2×C22⋊C4—1344no—
525C2×C22⋊C4C4×D6718yescomplemented
526C2×C22⋊C4C22×D6714yes—
527C2×C22⋊C4C22×D6714yes—
528C2×C42—2682no—
529C2×C42—2682no—
530C2×C42—2682no—
531C2×C42—2682no—
532C2×C42—674no—
533C2×C42—674no—
534C2×C42—674no—
535C2×C42—674no—
536C2×C42—678no—
537C2×C42—674no—
538#95—674no—
539#95—674no—
540#95—674no—
541#95—674no—
542#95—674no—
543#95—674no—
544#95—674no—
545#95—674no—
546#95—674no—
547#95—674no—
548#95C22×D6714yes—
549#95C22×D6714yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—674no—
557C24—672no—
558C24—1342no—
559C24—1342no—
560C24—1342no—
561C24—1342no—
562C24—1342no—
563C24—1342no—
564C24C2×C4×D6714yes—
565C24C23×D6712yes—
566C24C23×D6711yescharacteristic
567C2×Q8—26816no—
568C2×Q8—2684no—
569C2×Q8—2684no—
570C2×Q8—6716no—
571C2×D4—26816no—
572C2×D4—2684no—
573C2×D4—2684no—
574C2×D4—6716no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—28no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—416no—
594C22×C4—2684no—
595C22×C4—2684no—
596C22×C4—26816no—
597C22×C4—674no—
598C22×C4—674no—
599C22×C4—674no—
600C22×C4—674no—
601C22×C4—672no—
602C22×C4—672no—
603C22×C4—672no—
604C22×C4—672no—
605C22×C4—672no—
606C22×C4—672no—
607C22×C4—672no—
608C22×C4—1348no—
609C22×C4—1342no—
610C22×C4—1342no—
611C22×C4—1342no—
612C22×C4—1342no—
613C22×C4—1342no—
614C22×C4—1342no—
615C22×C4—1342no—
616C22×C4—1342no—
617C22×C4—1342no—
618C22×C4—1342no—
619C22×C4—1342no—
620C22×C4—1342no—
621C22×C4—1342no—
622C22×C4—1342no—
623C22×C4—1342no—
624C22×C4—1342no—
625C22×C4—1342no—
626C22×C4C2×C4×D6714yes—
627C22×C4C2×C4×D6714yes—
628C22×C4#1176162714yes—
629C22×C4C23×D6712yes—
630C22×C4C23×D6712yes—
631C22×C4C23×D6712yes—
632C22×C4C23×D6712yes—
633C22×C4C23×D6712yes—
634C22×C4C23×D6712yes—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—2684no—
638C4⋊C4—1348no—
639C22⋊C4—44no—
640C22⋊C4—2684no—
641C22⋊C4—2684no—
642C22⋊C4—2684no—
643C22⋊C4—6716no—
644C22⋊C4—6716no—
645C22⋊C4—6716no—
646C22⋊C4—1348no—
647C22⋊C4—1348no—
648C22⋊C4C2×C4×D67116yescomplemented
649C42—2684no—
650C42—2684no—
651C42—2684no—
652C42—2684no—
653C42—6716no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—2684no—
668C23—2684no—
669C23—2684no—
670C23—2684no—
671C23—674no—
672C23—1348no—
673C23—1348no—
674C23—1348no—
675C23—1342no—
676C23—1342no—
677C23—1342no—
678C23—1342no—
679C23—1342no—
680C23—1342no—
681C23C22×C4×D6714yes—
682C23C22×C4×D6712yes—
683C23#41×D6712yes—
684C23C2×#1176162712yes—
685C23#1452408812yes—
686C23#1452408812yes—
687C23#1452408912yes—
688C23#1452409112yes—
689C23C24×D6711yescharacteristic
690Q8—26816no—
691D4—26816no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—26816no—
715C2×C4—2684no—
716C2×C4—2684no—
717C2×C4—2684no—
718C2×C4—674no—
719C2×C4—674no—
720C2×C4—674no—
721C2×C4—674no—
722C2×C4—1342no—
723C2×C4—1342no—
724C2×C4—1342no—
725C2×C4—1342no—
726C2×C4—1342no—
727C2×C4—1342no—
728C2×C4—1342no—
729C2×C4—1342no—
730C2×C4—1342no—
731C2×C4—1348no—
732C2×C4—1348no—
733C2×C4—1348no—
734C2×C4—1342no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1342no—
738C2×C4—1342no—
739C2×C4—1342no—
740C2×C4—1342no—
741C2×C4—1342no—
742C2×C4—1348no—
743C2×C4C22×C4×D6714yes—
744C2×C4C22×C4×D6714yes—
745C2×C4C2×#1176162714yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—416no—
752C22—42no—
753C22—42no—
754C22—2682no—
755C22—2682no—
756C22—26816no—
757C22—2682no—
758C22—2682no—
759C22—1344no—
760C22—1344no—
761C22—1344no—
762C22C4×#1176162714yes—
763C22#1686386814yes—
764C22#1686387714yes—
765C22#1686398114yes—
766C22#1686398214yes—
767C22#1686401614yes—
768C22#1686401914yes—
769C22C23×C4×D6711yescharacteristic
770C22C2×#41×D6711yescharacteristic
771C22C22×#1176162711yescharacteristic
772C22C2×#1452408811yescharacteristic
773C22C2×#1452408811yescharacteristic
774C22C2×#1452408911yescharacteristic
775C22C2×#1452409111yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2682no—
783C4—2682no—
784C4—2682no—
785C4—1344no—
786C4—1344no—
787C4—1344no—
788C4—1344no—
789C2—44no—
790C2—2684no—
791C2#2256302318yesdirect product factor
792C2C2×C4×#1176162711yescharacteristic
793C2C2×#1686386811yescharacteristic
794C2C2×#1686387711yescharacteristic
795C2C2×#1686398111yescharacteristic
796C2C2×#1686398211yescharacteristic
797C2C2×#1686401611yescharacteristic
798C2C2×#1686401911yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#385×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×#385D67
hypocenterC67C2×#2337
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #22563023C2direct (N × H)
3. C2×#16863301C2semidirect
4. C2×#16863300C2semidirect
5. C2×#16863289C2semidirect
6. C2×#16863286C2semidirect
7. C2×#16863286C2semidirect
8. C2×#16863284C2semidirect
11. C2×#16863270C2semidirect
12. C2×#16863263C2semidirect
13. C2×C4⋊C4×Dic67C2semidirect
14. C2×C4×C22⋊Dic67C2semidirect
15. C2×#16863243C2semidirect
16. C2×#385×C67C2semidirect
20. C2×#14524029C4semidirect
37. #16863301C22semidirect
38. #16863300C22semidirect
39. #16863289C22semidirect
40. #16863286C22semidirect
41. #16863286C22semidirect
42. #16863284C22semidirect
45. #16863270C22semidirect
46. #16863263C22semidirect
47. C4⋊C4×Dic67C22semidirect
48. C4×C22⋊Dic67C22semidirect
49. #16863243C22semidirect
65. #385×C67C22semidirect
71. C22×Dic134C2×C4semidirect
88. #14524029C2×C4semidirect
95. C2×C22⋊Dic67C2×C4semidirect
102. C2×(C2×D67)⋊C4C2×C4semidirect
103. C2×(C2×D67)⋊C4C2×C4semidirect
113. C2×C4×Dic67C2×C4semidirect
145. C2×C22⋊C4×C67C2×C4semidirect
161. C2×Dic134C22×C4semidirect
202. C22⋊Dic67C22×C4semidirect
206. (C2×D67)⋊C4C22×C4semidirect
207. (C2×D67)⋊C4C22×C4semidirect
212. C4×Dic67C22×C4semidirect
253. C22⋊C4×C67C22×C4semidirect
391. C2×C67#2337semidirect
411. C2×#385D67semidirect
416. C67C2×#2337semidirect
451. #385C2×D67semidirect
525. C2×C22⋊C4C4×D67semidirect
648. C22⋊C4C2×C4×D67semidirect
791. C2#22563023direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240292
#225630232
C2×#168633012
C2×#168633002
C2×#168632892
C2×#168632862
C2×#168632842
C2×#168632752
C2×#168632722
C2×#168632702
C2×#168632632
C2×C4⋊C4×Dic672
C2×C4×C22⋊Dic672
C2×#168632432
C2×#385×C672
C2×#233767