Finite Group Databasebeta

← C2×#22563020 #31014748

Subgroups — C2×#22563020 #31014748

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#22563020C2116yesmaximal, direct product factor
3C2×#16863301C211yesmaximal, characteristic, complemented
4C2×#16863300C211yesmaximal, characteristic, complemented
5C2×#16863287C211yesmaximal, characteristic, complemented
6C2×#16863285C211yesmaximal, characteristic, complemented
7C2×#16863284C211yesmaximal, characteristic, complemented
8C2×#16863273C211yesmaximal, characteristic
9C2×#16863272C211yesmaximal, characteristic
10C2×#16863268C211yesmaximal, characteristic, complemented
11C2×#16863267C211yesmaximal, characteristic, complemented
12C2×#16863263C211yesmaximal, characteristic, complemented
13C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic67C211yesmaximal, characteristic, complemented
15C2×#16863243C211yesmaximal, characteristic, complemented
16C2×#388×C67C211yesmaximal, characteristic, complemented
17C23×Dic134C2211yescharacteristic
18C23×C22⋊D67C2211yescharacteristic
19C24×Dic67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C2×#14524029C4116yescomplemented
22C2×#14524029C2218yes—
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×C22⋊Dic67C2211yescharacteristic
27C22×C22⋊Dic67C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35C22×C4×Dic67C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863301C2218yescomplemented
38#16863300C2218yescomplemented
39#16863287C2218yescomplemented
40#16863285C2218yescomplemented
41#16863284C2218yescomplemented
42#16863273C2218yes—
43#16863272C2218yes—
44#16863268C2218yescomplemented
45#16863267C2218yescomplemented
46#16863263C2218yescomplemented
47C4×Dic67⋊C4C2218yescomplemented
48C22⋊C4×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
60C22×C4⋊C4×C67C2211yescharacteristic
61C22×C22⋊C4×C67C2211yescharacteristic
62C22×C22⋊C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C42×C67C2211yescharacteristic
65#388×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×Dic67—24no—
78C23×Dic67—42no—
79C23×Dic67—42no—
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C23×Dic67C2311yescharacteristic
83C23×Dic67C2311yescharacteristic
84C23×Dic67C2311yescharacteristic
85C23×Dic67C2311yescharacteristic
86C23×Dic67C2311yescharacteristic
87C23×Dic67C2314yes—
88C22×C4×D67—24no—
89C22×C4×D67—42no—
90C22×C4×D67—42no—
91C22×C4×D67C2314yes—
92#14524029C2×C4164yescomplemented
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—42no—
96C2×Dic67⋊C4C2314yes—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×C22⋊Dic67—24no—
100C2×C22⋊Dic67C2×C418yescomplemented
101C2×C22⋊Dic67C2314yes—
102C2×C22⋊Dic67C2314yes—
103C2×(C2×D67)⋊C4—24no—
104C2×(C2×D67)⋊C4—42no—
105C2×(C2×D67)⋊C4—42no—
106C2×(C2×D67)⋊C4C2×C418yescomplemented
107C2×(C2×D67)⋊C4C2×C418yescomplemented
108C2×(C2×D67)⋊C4C2314yes—
109C2×(C2×D67)⋊C4C2314yes—
110C2×(C2×D67)⋊C4C2314yes—
111C2×(C2×D67)⋊C4C2314yes—
112C2×(C2×D67)⋊C4C2314yes—
113C2×C4×Dic67—42no—
114C2×C4×Dic67—42no—
115C2×C4×Dic67—42no—
116C2×C4×Dic67C2×C418yescomplemented
117C2×C4×Dic67C2314yes—
118C2×C4×Dic67C2314yes—
119C2×C4×Dic67C2314yes—
120C2×C4×Dic67C2314yes—
121C67⋊#95C2314yes—
122C67⋊#95C2314yes—
123C67⋊#95C2314yes—
124C67⋊#95C2314yes—
125C67⋊#95C2314yes—
126C67⋊#95C2314yes—
127C67⋊#95C2314yes—
128C67⋊#95C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C25×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C23×C4×C67C2311yescharacteristic
134C23×C4×C67C2311yescharacteristic
135C23×C4×C67C2311yescharacteristic
136C23×C4×C67C2311yescharacteristic
137C23×C4×C67C2311yescharacteristic
138C2×C4⋊C4×C67—42no—
139C2×C4⋊C4×C67C2314yes—
140C2×C22⋊C4×C67—42no—
141C2×C22⋊C4×C67—42no—
142C2×C22⋊C4×C67C2×C418yescomplemented
143C2×C22⋊C4×C67C2314yes—
144C2×C22⋊C4×C67C2314yes—
145C2×C22⋊C4×C67C2314yes—
146C2×C42×C67—42no—
147C2×C42×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—28no—
183C22×Dic67—44no—
184C22×Dic67—44no—
185C22×Dic67—416no—
186C22×Dic67C22×C414yes—
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C414yes—
189C22×Dic67#4114yes—
190C22×Dic67#4114yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C2×C4×D67—28no—
199C2×C4×D67—44no—
200C2×C4×D67—44no—
201C2×C4×D67—416no—
202Dic67⋊C4—28no—
203Dic67⋊C4—28no—
204Dic67⋊C4—44no—
205C22⋊Dic67—28no—
206C22⋊Dic67C22×C4116yescomplemented
207(C2×D67)⋊C4—28no—
208(C2×D67)⋊C4—44no—
209(C2×D67)⋊C4—44no—
210(C2×D67)⋊C4C22×C4116yescomplemented
211(C2×D67)⋊C4C22×C4116yescomplemented
212C4×Dic67—44no—
213C4×Dic67—44no—
214C4×Dic67—44no—
215C4×Dic67C22×C4116yescomplemented
216C24×C67—22no—
217C24×C67—22no—
218C24×C67—22no—
219C24×C67—22no—
220C24×C67—22no—
221C24×C67—22no—
222C24×C67C22×C414yes—
223C24×C67C2412yes—
224C24×C67C2411yescharacteristic
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—22no—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67C22×C414yes—
242C22×C4×C67C22×C414yes—
243C22×C4×C67C2412yes—
244C22×C4×C67C2412yes—
245C22×C4×C67C2412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2412yes—
248C22×C4×C67C2412yes—
249C4⋊C4×C67—44no—
250C22⋊C4×C67—44no—
251C22⋊C4×C67—44no—
252C22⋊C4×C67C22×C4116yescomplemented
253C42×C67—44no—
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—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—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—44no—
309C2×C4×C67—44no—
310C2×C4×C67—44no—
311C2×C4×C67—44no—
312C2×C4×C67C23×C414yes—
313C2×C4×C67C23×C414yes—
314C22⋊D67—416no—
315C2×Dic67—28no—
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—416no—
337C2×Dic67—44no—
338C2×Dic67—44no—
339C2×Dic67C23×C414yes—
340C2×Dic67C23×C414yes—
341C2×Dic67C23×C414yes—
342C2×Dic67C2×#4114yes—
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—42no—
379C4×C67—42no—
380C4×C67—42no—
381C4×C67—42no—
382Dic67—24no—
383Dic67—24no—
384Dic67—24no—
385Dic67—24no—
386Dic67—24no—
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×#388D6711yescharacteristic, complemented
408C2×#386—671no—
409C2×#386—671no—
410C2×#385—671no—
411C2×#385—671no—
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×C4—671no—
421C2×#124—6716no—
422C2×#124—678no—
423C22×C4⋊C4—671no—
424C22×C4⋊C4—671no—
425C22×C4⋊C4—671no—
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⋊C4C2×D6711yescharacteristic
435C22×C22⋊C4C2×D6711yescharacteristic
436C22×C22⋊C4C2×D6711yescharacteristic
437C22×C42—671no—
438C22×C42—671no—
439C22×C42—671no—
440C22×C42—671no—
441C22×C42C2×D6711yescharacteristic
442#391—678no—
443#391—678no—
444#388—678no—
445#388—678no—
446#388—678no—
447#388C2×D6718yescomplemented
448#386—678no—
449#386—678no—
450#385—678no—
451#385—678no—
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—2682no—
479C23×C4—2682no—
480C23×C4—2682no—
481C23×C4—2682no—
482C23×C4—674no—
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×C4—1344no—
493C23×C4C22×D6711yescharacteristic
494C23×C4C22×D6711yescharacteristic
495C23×C4C22×D6711yescharacteristic
496C23×C4C22×D6711yescharacteristic
497C23×C4C22×D6711yescharacteristic
498C23×C4C22×D6711yescharacteristic
499#124—6764no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—2682no—
502C2×C4⋊C4—674no—
503C2×C4⋊C4—674no—
504C2×C4⋊C4—674no—
505C2×C4⋊C4—1344no—
506C2×C4⋊C4—1344no—
507C2×C4⋊C4C22×D6714yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—2682no—
511C2×C22⋊C4—2682no—
512C2×C22⋊C4—674no—
513C2×C22⋊C4—674no—
514C2×C22⋊C4—678no—
515C2×C22⋊C4—674no—
516C2×C22⋊C4—678no—
517C2×C22⋊C4—678no—
518C2×C22⋊C4—674no—
519C2×C22⋊C4—674no—
520C2×C22⋊C4—674no—
521C2×C22⋊C4—674no—
522C2×C22⋊C4—1344no—
523C2×C22⋊C4—1344no—
524C2×C22⋊C4C4×D6718yescomplemented
525C2×C22⋊C4C22×D6714yes—
526C2×C22⋊C4C22×D6714yes—
527C2×C22⋊C4C22×D6714yes—
528C2×C42—42no—
529C2×C42—2682no—
530C2×C42—2682no—
531C2×C42—2682no—
532C2×C42—674no—
533C2×C42—674no—
534C2×C42—674no—
535C2×C42—678no—
536C2×C42—674no—
537C2×C42C22×D6714yes—
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—22no—
591C22×C4—2684no—
592C22×C4—2684no—
593C22×C4—26816no—
594C22×C4—26816no—
595C22×C4—2684no—
596C22×C4—2684no—
597C22×C4—674no—
598C22×C4—674no—
599C22×C4—674no—
600C22×C4—674no—
601C22×C4—674no—
602C22×C4—672no—
603C22×C4—672no—
604C22×C4—672no—
605C22×C4—672no—
606C22×C4—672no—
607C22×C4—672no—
608C22×C4—672no—
609C22×C4—1348no—
610C22×C4—1348no—
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×C4—1342no—
627C22×C4C2×C4×D6714yes—
628C22×C4C2×C4×D6714yes—
629C22×C4C23×D6712yes—
630C22×C4C23×D6712yes—
631C22×C4C23×D6712yes—
632C22×C4C23×D6712yes—
633C22×C4C23×D6712yes—
634C22×C4C23×D6712yes—
635C4⋊C4—44no—
636C4⋊C4—2684no—
637C4⋊C4—1348no—
638C4⋊C4—1348no—
639C22⋊C4—44no—
640C22⋊C4—44no—
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—44no—
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—
684C23#41×D6712yes—
685C23#1452408812yes—
686C23#1452408812yes—
687C23#1452408912yes—
688C23#1452409012yes—
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—22no—
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—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—26816no—
715C2×C4—2684no—
716C2×C4—2684no—
717C2×C4—26816no—
718C2×C4—674no—
719C2×C4—674no—
720C2×C4—674no—
721C2×C4—674no—
722C2×C4—674no—
723C2×C4—1342no—
724C2×C4—1342no—
725C2×C4—1342no—
726C2×C4—1342no—
727C2×C4—1342no—
728C2×C4—1342no—
729C2×C4—1348no—
730C2×C4—1348no—
731C2×C4—1348no—
732C2×C4—1342no—
733C2×C4—1342no—
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×C4—1348no—
744C2×C4C22×C4×D6714yes—
745C2×C4C22×C4×D6714yes—
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—
762C22#1686386414yes—
763C22#1686386814yes—
764C22#1686387514yes—
765C22#1686397814yes—
766C22#1686398214yes—
767C22#1686401014yes—
768C22#1686401214yes—
769C22C23×C4×D6711yescharacteristic
770C22C2×#41×D6711yescharacteristic
771C22C2×#41×D6711yescharacteristic
772C22C2×#1452408811yescharacteristic
773C22C2×#1452408811yescharacteristic
774C22C2×#1452408911yescharacteristic
775C22C2×#1452409011yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—2682no—
783C4—2682no—
784C4—1344no—
785C4—1344no—
786C4—1344no—
787C4—1344no—
788C4—1344no—
789C2—44no—
790C2—2684no—
791C2#2256302018yesdirect product factor
792C2C2×#1686386411yescharacteristic
793C2C2×#1686386811yescharacteristic
794C2C2×#1686387511yescharacteristic
795C2C2×#1686397811yescharacteristic
796C2C2×#1686398211yescharacteristic
797C2C2×#1686401011yescharacteristic
798C2C2×#1686401211yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#388×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×#388D67
hypocenterC67C2×#2337
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #22563020C2direct (N × H)
3. C2×#16863301C2semidirect
4. C2×#16863300C2semidirect
5. C2×#16863287C2semidirect
6. C2×#16863285C2semidirect
7. C2×#16863284C2semidirect
10. C2×#16863268C2semidirect
11. C2×#16863267C2semidirect
12. C2×#16863263C2semidirect
13. C2×C4×Dic67⋊C4C2semidirect
14. C2×C22⋊C4×Dic67C2semidirect
15. C2×#16863243C2semidirect
16. C2×#388×C67C2semidirect
21. C2×#14524029C4semidirect
37. #16863301C22semidirect
38. #16863300C22semidirect
39. #16863287C22semidirect
40. #16863285C22semidirect
41. #16863284C22semidirect
44. #16863268C22semidirect
45. #16863267C22semidirect
46. #16863263C22semidirect
47. C4×Dic67⋊C4C22semidirect
48. C22⋊C4×Dic67C22semidirect
49. #16863243C22semidirect
65. #388×C67C22semidirect
71. C22×Dic134C2×C4semidirect
92. #14524029C2×C4semidirect
100. C2×C22⋊Dic67C2×C4semidirect
106. C2×(C2×D67)⋊C4C2×C4semidirect
107. C2×(C2×D67)⋊C4C2×C4semidirect
116. C2×C4×Dic67C2×C4semidirect
142. C2×C22⋊C4×C67C2×C4semidirect
161. C2×Dic134C22×C4semidirect
206. C22⋊Dic67C22×C4semidirect
210. (C2×D67)⋊C4C22×C4semidirect
211. (C2×D67)⋊C4C22×C4semidirect
215. C4×Dic67C22×C4semidirect
252. C22⋊C4×C67C22×C4semidirect
391. C2×C67#2337semidirect
407. C2×#388D67semidirect
416. C67C2×#2337semidirect
447. #388C2×D67semidirect
524. C2×C22⋊C4C4×D67semidirect
648. C22⋊C4C2×C4×D67semidirect
791. C2#22563020direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240292
#225630202
C2×#168633012
C2×#168633002
C2×#168632872
C2×#168632852
C2×#168632842
C2×#168632732
C2×#168632722
C2×#168632682
C2×#168632672
C2×#168632632
C2×C4×Dic67⋊C42
C2×C22⋊C4×Dic672
C2×#168632432
C2×#388×C672
C2×#233767