Finite Group Databasebeta

← C2×#22563197 #31015330

Subgroups — C2×#22563197 #31015330

Order 17152.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524026C211yesmaximal, characteristic
2C22×C4×C22⋊D67C211yesmaximal, characteristic
3C22×#14524002C211yesmaximal, characteristic, complemented
4#22563197C2116yesmaximal, direct product factor
5C2×#16863293C211yesmaximal, characteristic, complemented
6C2×#16863288C211yesmaximal, characteristic, complemented
7C2×#16863285C211yesmaximal, characteristic, complemented
8C2×#16863283C211yesmaximal, characteristic, complemented
9C2×#16863278C211yesmaximal, characteristic, complemented
10C2×#16863275C211yesmaximal, characteristic
11C2×#16863270C211yesmaximal, characteristic, complemented
12C2×#16863269C211yesmaximal, characteristic, complemented
13C2×#16863247C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic67C211yesmaximal, characteristic, complemented
15C2×#16863243C211yesmaximal, characteristic, complemented
16C22×#95×C67C211yesmaximal, characteristic, complemented
17C23×C22⋊D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C2×#14524026C4116yescomplemented
20C2×#14524026C2218yes—
21C2×C4×C22⋊D67—28no—
22C2×C4×C22⋊D67C2218yes—
23C2×#14524002—28no—
24C2×#14524002C2218yescomplemented
25C22×C4⋊Dic67C2211yescharacteristic
26C22×C4⋊Dic67C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×C22⋊Dic67C2211yescharacteristic
33C22×C22⋊Dic67C2211yescharacteristic
34C22×C22⋊Dic67C2211yescharacteristic
35C22×(C2×D67)⋊C4C2211yescharacteristic
36C22×(C2×D67)⋊C4C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×(C2×D67)⋊C4C2211yescharacteristic
39C22×(C2×D67)⋊C4C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43C22×C4×Dic67C2211yescharacteristic
44C22×C4×Dic67C2211yescharacteristic
45#16863293C2218yescomplemented
46#16863288C2218yescomplemented
47#16863285C2218yescomplemented
48#16863283C2218yescomplemented
49#16863278C2218yescomplemented
50#16863275C2218yes—
51#16863270C2218yescomplemented
52#16863269C2218yescomplemented
53#16863247C2218yescomplemented
54C4×C22⋊Dic67C2218yescomplemented
55#16863243C2218yescomplemented
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61C2×C67⋊#95C2211yescharacteristic
62C24×C4×C67C2211yescharacteristic
63C24×C4×C67C2211yescharacteristic
64C24×C4×C67C2211yescharacteristic
65C2×#95×C67C2211yescharacteristic
66C2×#95×C67C2211yescharacteristic
67C2×#95×C67C2211yescharacteristic
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2218yescomplemented
70C24×D67C2311yescharacteristic
71C22×C22⋊D67—24no—
72C22×C22⋊D67—24no—
73C22×C22⋊D67C2×C418yes—
74C22×C22⋊D67C2314yes—
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77C23×Dic67C2311yescharacteristic
78C23×Dic67C2311yescharacteristic
79C23×Dic67C2311yescharacteristic
80C23×Dic67C2311yescharacteristic
81C23×Dic67C2311yescharacteristic
82C22×C4×D67—24no—
83C22×C4×D67—24no—
84C22×C4×D67—42no—
85C22×C4×D67C2314yes—
86#14524026C2×C4164yescomplemented
87C4×C22⋊D67—232no—
88#14524002—232no—
89C2×C4⋊Dic67—24no—
90C2×C4⋊Dic67—24no—
91C2×C4⋊Dic67C2314yes—
92C2×C4⋊Dic67C2314yes—
93C2×Dic67⋊C4—24no—
94C2×Dic67⋊C4—24no—
95C2×Dic67⋊C4—42no—
96C2×Dic67⋊C4C2×C418yescomplemented
97C2×Dic67⋊C4C2×C418yescomplemented
98C2×Dic67⋊C4C2314yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×Dic67⋊C4C2314yes—
103C2×C22⋊Dic67—24no—
104C2×C22⋊Dic67C2×C418yescomplemented
105C2×C22⋊Dic67D418yes—
106C2×C22⋊Dic67C2314yes—
107C2×C22⋊Dic67C2314yes—
108C2×C22⋊Dic67C2314yes—
109C2×(C2×D67)⋊C4—24no—
110C2×(C2×D67)⋊C4—24no—
111C2×(C2×D67)⋊C4—42no—
112C2×(C2×D67)⋊C4C2×C418yescomplemented
113C2×(C2×D67)⋊C4C2×C418yescomplemented
114C2×(C2×D67)⋊C4C2314yes—
115C2×(C2×D67)⋊C4C2314yes—
116C2×(C2×D67)⋊C4C2314yes—
117C2×(C2×D67)⋊C4C2314yes—
118C2×(C2×D67)⋊C4C2314yes—
119C2×C4×Dic67—24no—
120C2×C4×Dic67—24no—
121C2×C4×Dic67—24no—
122C2×C4×Dic67—24no—
123C2×C4×Dic67—42no—
124C2×C4×Dic67C2314yes—
125C2×C4×Dic67C2314yes—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C2×C4×Dic67C2314yes—
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×C67—24no—
140C23×C4×C67—24no—
141C23×C4×C67—24no—
142C23×C4×C67—42no—
143C23×C4×C67—42no—
144C23×C4×C67C2×C418yescomplemented
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2314yes—
148C23×C4×C67C2314yes—
149C23×C4×C67C2311yescharacteristic
150C23×C4×C67C2311yescharacteristic
151C23×C4×C67C2314yes—
152C23×C4×C67C2311yescharacteristic
153C23×C4×C67C2311yescharacteristic
154#95×C67C2314yes—
155#95×C67C2314yes—
156#95×C67C2314yes—
157#95×C67C2314yes—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67—22no—
163C23×D67—22no—
164C23×D67C22×C414yes—
165C23×D67C2412yes—
166C2×C22⋊D67—232no—
167C2×C22⋊D67—28no—
168C2×C22⋊D67—28no—
169C2×C22⋊D67C22×C4116yes—
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×Dic67—22no—
184C22×Dic67—22no—
185C22×Dic67—22no—
186C22×Dic67C22×C414yes—
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C414yes—
189C22×Dic67C2×D414yes—
190C22×Dic67C2×D414yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C2×C4×D67—28no—
199C2×C4×D67—28no—
200C2×C4×D67—44no—
201C2×C4×D67—416no—
202C4⋊Dic67—28no—
203C4⋊Dic67—28no—
204Dic67⋊C4—28no—
205Dic67⋊C4—28no—
206Dic67⋊C4—44no—
207Dic67⋊C4C22×C4116yescomplemented
208Dic67⋊C4C22×C4116yescomplemented
209C22⋊Dic67—28no—
210C22⋊Dic67C22×C4116yescomplemented
211C22⋊Dic67C2×D4116yes—
212(C2×D67)⋊C4—28no—
213(C2×D67)⋊C4—28no—
214(C2×D67)⋊C4—44no—
215(C2×D67)⋊C4C22×C4116yescomplemented
216(C2×D67)⋊C4C22×C4116yescomplemented
217C4×Dic67—28no—
218C4×Dic67—28no—
219C4×Dic67—28no—
220C4×Dic67—28no—
221C4×Dic67—44no—
222C24×C67—22no—
223C24×C67—22no—
224C24×C67—22no—
225C24×C67—22no—
226C24×C67C22×C414yes—
227C24×C67C2×D414yes—
228C24×C67#4114yes—
229C24×C67C2412yes—
230C24×C67C2411yescharacteristic
231C22×C4×C67—232no—
232C22×C4×C67—22no—
233C22×C4×C67—22no—
234C22×C4×C67—22no—
235C22×C4×C67—28no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—28no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—28no—
244C22×C4×C67—28no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67—22no—
250C22×C4×C67—28no—
251C22×C4×C67—28no—
252C22×C4×C67—44no—
253C22×C4×C67—44no—
254C22×C4×C67—416no—
255C22×C4×C67—416no—
256C22×C4×C67C22×C414yes—
257C22×C4×C67C22×C414yes—
258C22×C4×C67C22×C4116yescomplemented
259C22×C4×C67#4114yes—
260C22×C4×C67#4114yes—
261C22×C4×C67C2412yes—
262C22×C4×C67C2412yes—
263C22×C4×C67C2412yes—
264C22×C4×C67C2412yes—
265C22×C4×C67C2412yes—
266C22×C4×C67C2412yes—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—28no—
270C23×C67—28no—
271C23×C67—28no—
272C23×C67—28no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67C4×D4116yes—
278C23×C67C23×C414yes—
279C23×C67C23×C412yes—
280C23×C67C22×D414yes—
281C23×C67C22×D412yes—
282C23×C67C2×#4114yes—
283C23×C67C2×#4112yes—
284C23×C67C2×#4112yes—
285C23×C67C2×#4112yes—
286C23×C67H(5,𝔽2)12yes—
287C23×C672−1+412yes—
288C23×C67C2511yescharacteristic
289C22×D67—28no—
290C22×D67—28no—
291C22×D67—28no—
292C22×D67—22no—
293C22×D67—22no—
294C22×D67—22no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—44no—
299C22×D67—44no—
300C22×D67—44no—
301C22×D67—44no—
302C22×D67C23×C414yes—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—232no—
306C2×C4×C67—28no—
307C2×C4×C67—28no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—416no—
323C2×C4×C67—416no—
324C2×C4×C67—44no—
325C2×C4×C67—44no—
326C2×C4×C67C23×C414yes—
327C2×C4×C67C23×C414yes—
328C2×C4×C67C2×#4114yes—
329C2×C4×C67C2×#4114yes—
330C22⋊D67—232no—
331C2×Dic67—28no—
332C2×Dic67—28no—
333C2×Dic67—28no—
334C2×Dic67—28no—
335C2×Dic67—28no—
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—22no—
345C2×Dic67—22no—
346C2×Dic67—22no—
347C2×Dic67—22no—
348C2×Dic67—22no—
349C2×Dic67—22no—
350C2×Dic67—22no—
351C2×Dic67—22no—
352C2×Dic67—44no—
353C2×Dic67—44no—
354C2×Dic67C23×C414yes—
355C2×Dic67C23×C414yes—
356C2×Dic67C23×C414yes—
357C2×Dic67C22×D414yes—
358C2×Dic67C22×D414yes—
359C4×D67—416no—
360C22×C67—232no—
361C22×C67—24no—
362C22×C67—24no—
363C22×C67—24no—
364C22×C67—24no—
365C22×C67—24no—
366C22×C67—24no—
367C22×C67C2×C4×D418yes—
368C22×C67C2×C4×D414yes—
369C22×C67C4×#4114yes—
370C22×C67#52014yes—
371C22×C67#54614yes—
372C22×C67#54714yes—
373C22×C67#55114yes—
374C22×C67#55214yes—
375C22×C67C24×C411yescharacteristic
376C22×C67C23×D411yescharacteristic
377C22×C67C22×#4111yescharacteristic
378C22×C67C22×#4111yescharacteristic
379C22×C67C22×#4111yescharacteristic
380C22×C67C2×H(5,𝔽2)11yescharacteristic
381C22×C67C2×2−1+411yescharacteristic
382C2×D67—24no—
383C2×D67—24no—
384C2×D67—24no—
385C2×D67—416no—
386C2×D67—42no—
387C2×D67—42no—
388C2×D67—42no—
389C2×D67—42no—
390C4×C67—24no—
391C4×C67—24no—
392C4×C67—24no—
393C4×C67—24no—
394C4×C67—42no—
395C4×C67—42no—
396Dic67—24no—
397Dic67—24no—
398Dic67—24no—
399Dic67—24no—
400Dic67—24no—
401Dic67—42no—
402Dic67—42no—
403C2×#2359—671nomaximal, Sylow
404C2×C67—28no—
405C2×C67#235918yescomplemented
406C2×C67C22×C4×D411yescharacteristic
407C2×C67C2×C4×#4111yescharacteristic
408C2×C67C2×#52011yescharacteristic
409C2×C67C2×#54611yescharacteristic
410C2×C67C2×#54711yescharacteristic
411C2×C67C2×#55111yescharacteristic
412C2×C67C2×#55211yescharacteristic
413D67—44no—
414C22×#123—671no—
415C22×C4×D4—671no—
416C22×#117—671no—
417#2359—6716no—
418C2×#389—671no—
419C2×#388—671no—
420C2×#388—671no—
421C2×#387—671no—
422C2×#387—671no—
423C2×#386—671no—
424C2×#385—671no—
425C2×#385—671no—
426C2×C4×C4⋊C4—671no—
427C2×C4×C22⋊C4—671no—
428C2×C4×C22⋊C4—671no—
429C22×#95D6711yescharacteristic, complemented
430C67C2×#235911yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4C2×D6711yescharacteristic
434C24×C4C2×D6711yescharacteristic
435C24×C4C2×D6711yescharacteristic
436C2×#123—6716no—
437C2×#123—678no—
438C2×C4×D4—678no—
439C2×C4×D4—1348no—
440C2×#117—678no—
441C2×#117—1348no—
442C22×C4⋊C4—671no—
443C22×C4⋊C4—671no—
444C22×C4⋊C4—671no—
445C22×C4⋊C4—671no—
446C22×C4⋊C4—671no—
447C22×C4⋊C4—671no—
448C22×C4⋊C4—671no—
449C22×C22⋊C4—671no—
450C22×C22⋊C4—671no—
451C22×C22⋊C4—671no—
452C22×C22⋊C4—671no—
453C22×C22⋊C4—671no—
454C22×C22⋊C4—671no—
455C22×C22⋊C4—671no—
456C22×C22⋊C4—671no—
457C22×C42—671no—
458C22×C42—671no—
459C22×C42—671no—
460C22×C42—671no—
461C22×C42—671no—
462#389—678no—
463#388—678no—
464#388—678no—
465#387—678no—
466#387—678no—
467#386—678no—
468#385—678no—
469#385—678no—
470C4×C4⋊C4—678no—
471C4×C22⋊C4—678no—
472C4×C22⋊C4—678no—
473C2×#95—671no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95C2×D6711yescharacteristic
480C2×#95C2×D6711yescharacteristic
481C2×#95C2×D6711yescharacteristic
482C2×#95C2×D6711yescharacteristic
483C2×#95C2×D6718yescomplemented
484C25—671no—
485C25C22×D6711yescharacteristic
486C22×D4—678no—
487C22×D4—674no—
488C22×D4—1344no—
489C22×D4—1344no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—24no—
495C23×C4—24no—
496C23×C4—42no—
497C23×C4—42no—
498C23×C4—2682no—
499C23×C4—674no—
500C23×C4—671no—
501C23×C4—671no—
502C23×C4—671no—
503C23×C4—671no—
504C23×C4—671no—
505C23×C4—671no—
506C23×C4—671no—
507C23×C4—1344no—
508C23×C4—1344no—
509C23×C4C4×D6718yescomplemented
510C23×C4C22×D6711yescharacteristic
511C23×C4C22×D6711yescharacteristic
512C23×C4C22×D6714yes—
513C23×C4C22×D6714yes—
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6714yes—
517C23×C4C22×D6711yescharacteristic
518C23×C4C22×D6711yescharacteristic
519#123—6764no—
520C4×D4—13432no—
521#117—13432no—
522C2×C4⋊C4—2682no—
523C2×C4⋊C4—674no—
524C2×C4⋊C4—678no—
525C2×C4⋊C4—678no—
526C2×C4⋊C4—674no—
527C2×C4⋊C4—674no—
528C2×C4⋊C4—674no—
529C2×C4⋊C4—674no—
530C2×C4⋊C4—674no—
531C2×C4⋊C4—674no—
532C2×C4⋊C4—1344no—
533C2×C4⋊C4—1344no—
534C2×C4⋊C4—1344no—
535C2×C4⋊C4—1344no—
536C2×C22⋊C4—2682no—
537C2×C22⋊C4—674no—
538C2×C22⋊C4—678no—
539C2×C22⋊C4—678no—
540C2×C22⋊C4—674no—
541C2×C22⋊C4—674no—
542C2×C22⋊C4—678no—
543C2×C22⋊C4—678no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—674no—
546C2×C22⋊C4—674no—
547C2×C22⋊C4—674no—
548C2×C22⋊C4—674no—
549C2×C22⋊C4—1344no—
550C2×C22⋊C4—1344no—
551C2×C22⋊C4—1344no—
552C2×C42—2682no—
553C2×C42—674no—
554C2×C42—674no—
555C2×C42—674no—
556C2×C42—674no—
557C2×C42—674no—
558C2×C42—1344no—
559C2×C42—1344no—
560C2×C42—1344no—
561C2×C42—1344no—
562#95—674no—
563#95—674no—
564#95—674no—
565#95—674no—
566#95—674no—
567#95—674no—
568#95C22×D6714yes—
569#95C22×D6714yes—
570#95C22×D6714yes—
571#95C22×D6714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—674no—
577C24—672no—
578C24—1342no—
579C24—1342no—
580C24—1342no—
581C24—1342no—
582C24—1342no—
583C24—1342no—
584C24C2×C4×D6714yes—
585C24D4×D6714yes—
586C24#1176162714yes—
587C24C23×D6712yes—
588C24C23×D6711yescharacteristic
589C2×D4—6716no—
590C2×D4—13432no—
591C2×D4—1348no—
592C2×D4—1348no—
593C22×C4—232no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—28no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—28no—
613C22×C4—28no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—416no—
617C22×C4—416no—
618C22×C4—26816no—
619C22×C4—2684no—
620C22×C4—674no—
621C22×C4—674no—
622C22×C4—674no—
623C22×C4—674no—
624C22×C4—674no—
625C22×C4—672no—
626C22×C4—672no—
627C22×C4—672no—
628C22×C4—672no—
629C22×C4—672no—
630C22×C4—672no—
631C22×C4—672no—
632C22×C4—1348no—
633C22×C4—1342no—
634C22×C4—1342no—
635C22×C4—1342no—
636C22×C4—1342no—
637C22×C4—1342no—
638C22×C4—1342no—
639C22×C4—1348no—
640C22×C4—1342no—
641C22×C4—1342no—
642C22×C4—1342no—
643C22×C4—1342no—
644C22×C4—1342no—
645C22×C4—1342no—
646C22×C4—1342no—
647C22×C4—1342no—
648C22×C4—1342no—
649C22×C4—1342no—
650C22×C4C2×C4×D6714yes—
651C22×C4C2×C4×D6714yes—
652C22×C4C2×C4×D67116yescomplemented
653C22×C4#1176162814yes—
654C22×C4#1176162814yes—
655C22×C4C23×D6712yes—
656C22×C4C23×D6712yes—
657C22×C4C23×D6712yes—
658C22×C4C23×D6712yes—
659C22×C4C23×D6712yes—
660C22×C4C23×D6712yes—
661C4⋊C4—2684no—
662C4⋊C4—6716no—
663C4⋊C4—6716no—
664C4⋊C4—1348no—
665C4⋊C4—1348no—
666C4⋊C4—1348no—
667C4⋊C4—1348no—
668C22⋊C4—2684no—
669C22⋊C4—6716no—
670C22⋊C4—6716no—
671C22⋊C4—6716no—
672C22⋊C4—6716no—
673C22⋊C4—1348no—
674C22⋊C4—1348no—
675C22⋊C4—1348no—
676C42—2684no—
677C42—1348no—
678C42—1348no—
679C42—1348no—
680C42—1348no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—28no—
686C23—28no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—2684no—
692C23—2684no—
693C23—2684no—
694C23—2684no—
695C23—674no—
696C23—1348no—
697C23—1348no—
698C23—1348no—
699C23—1342no—
700C23—1342no—
701C23—1342no—
702C23—1342no—
703C23—1342no—
704C23—1342no—
705C23(C22⋊D67)⋊C4116yes—
706C23C22×C4×D6714yes—
707C23C22×C4×D6712yes—
708C23C2×D4×D6714yes—
709C23C2×D4×D6712yes—
710C23C2×#1176162714yes—
711C23C2×#1176162712yes—
712C23C2×#1176162812yes—
713C23C2×#1176162812yes—
714C23#1452408812yes—
715C23#1452409112yes—
716C23C24×D6711yescharacteristic
717D4—13432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—416no—
738C2×C4—416no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—26816no—
742C2×C4—2684no—
743C2×C4—2684no—
744C2×C4—674no—
745C2×C4—674no—
746C2×C4—674no—
747C2×C4—674no—
748C2×C4—674no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4—1342no—
754C2×C4—1342no—
755C2×C4—1348no—
756C2×C4—1348no—
757C2×C4—1348no—
758C2×C4—1348no—
759C2×C4—1348no—
760C2×C4—1342no—
761C2×C4—1342no—
762C2×C4—1342no—
763C2×C4—1342no—
764C2×C4—1342no—
765C2×C4—1342no—
766C2×C4—1342no—
767C2×C4—1342no—
768C2×C4—1342no—
769C2×C4—1342no—
770C2×C4C22×C4×D6714yes—
771C2×C4C22×C4×D6714yes—
772C2×C4C2×#1176162814yes—
773C2×C4C2×#1176162814yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—2682no—
782C22—2682no—
783C22—26816no—
784C22—2682no—
785C22—2682no—
786C22—1344no—
787C22—1344no—
788C22—1344no—
789C22C2×(C22⋊D67)⋊C418yes—
790C22C2×(C22⋊D67)⋊C414yes—
791C22C4×#1176162814yes—
792C22#1686387714yes—
793C22#1686403614yes—
794C22#1686404714yes—
795C22#1686407214yes—
796C22#1686408114yes—
797C22C23×C4×D6711yescharacteristic
798C22C22×D4×D6711yescharacteristic
799C22C22×#1176162711yescharacteristic
800C22C22×#1176162811yescharacteristic
801C22C22×#1176162811yescharacteristic
802C22C2×#1452408811yescharacteristic
803C22C2×#1452409111yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—2682no—
811C4—2682no—
812C4—1344no—
813C4—1344no—
814C4—1344no—
815C4—1344no—
816C4—1344no—
817C2—28no—
818C2—2684no—
819C2#2256319718yesdirect product factor
820C2C22×(C22⋊D67)⋊C411yescharacteristic
821C2C2×C4×#1176162811yescharacteristic
822C2C2×#1686387711yescharacteristic
823C2C2×#1686403611yescharacteristic
824C2C2×#1686404711yescharacteristic
825C2C2×#1686407211yescharacteristic
826C2C2×#1686408111yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC22×#95×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC22×#95D67
hypocenterC67C2×#2359
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C22×#14524002C2semidirect
4. #22563197C2direct (N × H)
5. C2×#16863293C2semidirect
6. C2×#16863288C2semidirect
7. C2×#16863285C2semidirect
8. C2×#16863283C2semidirect
9. C2×#16863278C2semidirect
11. C2×#16863270C2semidirect
12. C2×#16863269C2semidirect
13. C2×#16863247C2semidirect
14. C2×C4×C22⋊Dic67C2semidirect
15. C2×#16863243C2semidirect
16. C22×#95×C67C2semidirect
19. C2×#14524026C4semidirect
24. C2×#14524002C22semidirect
45. #16863293C22semidirect
46. #16863288C22semidirect
47. #16863285C22semidirect
48. #16863283C22semidirect
49. #16863278C22semidirect
51. #16863270C22semidirect
52. #16863269C22semidirect
53. #16863247C22semidirect
54. C4×C22⋊Dic67C22semidirect
55. #16863243C22semidirect
69. C2×#95×C67C22semidirect
86. #14524026C2×C4semidirect
96. C2×Dic67⋊C4C2×C4semidirect
97. C2×Dic67⋊C4C2×C4semidirect
104. C2×C22⋊Dic67C2×C4semidirect
112. C2×(C2×D67)⋊C4C2×C4semidirect
113. C2×(C2×D67)⋊C4C2×C4semidirect
144. C23×C4×C67C2×C4semidirect
207. Dic67⋊C4C22×C4semidirect
208. Dic67⋊C4C22×C4semidirect
210. C22⋊Dic67C22×C4semidirect
215. (C2×D67)⋊C4C22×C4semidirect
216. (C2×D67)⋊C4C22×C4semidirect
258. C22×C4×C67C22×C4semidirect
405. C2×C67#2359semidirect
429. C22×#95D67semidirect
430. C67C2×#2359semidirect
483. C2×#95C2×D67semidirect
509. C23×C4C4×D67semidirect
652. C22×C4C2×C4×D67semidirect
819. C2#22563197direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240262
C22×C4×C22⋊D672
C22×#145240022
#225631972
C2×#168632932
C2×#168632882
C2×#168632852
C2×#168632832
C2×#168632782
C2×#168632752
C2×#168632702
C2×#168632692
C2×#168632472
C2×C4×C22⋊Dic672
C2×#168632432
C22×#95×C672
C2×#235967