Finite Group Databasebeta

← C2×#22563202 #31015335

Subgroups — C2×#22563202 #31015335

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×#14524025C211yesmaximal, characteristic
2C22×C4×C22⋊D67C211yesmaximal, characteristic
3C22×#14524000C211yesmaximal, characteristic, complemented
4#22563202C2116yesmaximal, direct product factor
5C2×#16863294C211yesmaximal, characteristic, complemented
6C2×#16863289C211yesmaximal, characteristic, complemented
7C2×#16863284C211yesmaximal, characteristic, complemented
8C2×#16863280C211yesmaximal, characteristic, complemented
9C2×#16863279C211yesmaximal, characteristic, complemented
10C2×#16863272C211yesmaximal, characteristic
11C2×#16863270C211yesmaximal, characteristic, complemented
12C2×#16863269C211yesmaximal, characteristic, complemented
13C2×#16863247C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D67C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C67C211yesmaximal, characteristic, complemented
17C23×C22⋊D67C2211yescharacteristic
18C23×C4×D67C2211yescharacteristic
19C23×C4×D67C2211yescharacteristic
20C23×C4×D67C2211yescharacteristic
21C2×#14524025C4116yescomplemented
22C2×#14524025C2218yes—
23C2×C4×C22⋊D67—28no—
24C2×C4×C22⋊D67C2218yes—
25C2×#14524000—28no—
26C2×#14524000C2218yescomplemented
27C22×C4⋊Dic67C2211yescharacteristic
28C22×C4⋊Dic67C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×Dic67⋊C4C2211yescharacteristic
32C22×Dic67⋊C4C2211yescharacteristic
33C22×Dic67⋊C4C2211yescharacteristic
34C22×C22⋊Dic67C2211yescharacteristic
35C22×C22⋊Dic67C2211yescharacteristic
36C22×C22⋊Dic67C2211yescharacteristic
37C22×(C2×D67)⋊C4C2211yescharacteristic
38C22×(C2×D67)⋊C4C2211yescharacteristic
39C22×(C2×D67)⋊C4C2211yescharacteristic
40C22×C4×Dic67C2211yescharacteristic
41C22×C4×Dic67C2211yescharacteristic
42C22×C4×Dic67C2211yescharacteristic
43#16863294C2218yescomplemented
44#16863289C2218yescomplemented
45#16863284C2218yescomplemented
46#16863280C2218yescomplemented
47#16863279C2218yescomplemented
48#16863272C2218yes—
49#16863270C2218yescomplemented
50#16863269C2218yescomplemented
51#16863247C2218yescomplemented
52C4×(C2×D67)⋊C4C2218yescomplemented
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×C67⋊#95C2211yescharacteristic
61#95×D67C2218yescomplemented
62C24×C4×C67C2211yescharacteristic
63C22×C22⋊C4×C67C2211yescharacteristic
64C22×C22⋊C4×C67C2211yescharacteristic
65C22×C42×C67C2211yescharacteristic
66C22×C42×C67C2211yescharacteristic
67C4×C22⋊C4×C67C2218yescomplemented
68C2×#95×C67C2211yescharacteristic
69C2×#95×C67C2211yescharacteristic
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—24no—
85C22×C4×D67—24no—
86C22×C4×D67—24no—
87C22×C4×D67—24no—
88C22×C4×D67—42no—
89C22×C4×D67—42no—
90C22×C4×D67C2×C418yescomplemented
91C22×C4×D67C2314yes—
92C22×C4×D67C2314yes—
93C22×C4×D67C2314yes—
94#14524025C2×C4164yescomplemented
95C4×C22⋊D67—232no—
96#14524000—232no—
97C2×C4⋊Dic67—42no—
98C2×C4⋊Dic67C2×C418yescomplemented
99C2×C4⋊Dic67C2314yes—
100C2×C4⋊Dic67C2314yes—
101C2×Dic67⋊C4—24no—
102C2×Dic67⋊C4—24no—
103C2×Dic67⋊C4—24no—
104C2×Dic67⋊C4—24no—
105C2×Dic67⋊C4C2×C418yescomplemented
106C2×Dic67⋊C4C2314yes—
107C2×Dic67⋊C4C2314yes—
108C2×Dic67⋊C4C2314yes—
109C2×Dic67⋊C4C2314yes—
110C2×Dic67⋊C4C2314yes—
111C2×C22⋊Dic67—24no—
112C2×C22⋊Dic67—42no—
113C2×C22⋊Dic67C2×C418yescomplemented
114C2×C22⋊Dic67C2314yes—
115C2×C22⋊Dic67C2314yes—
116C2×C22⋊Dic67C2314yes—
117C2×(C2×D67)⋊C4—24no—
118C2×(C2×D67)⋊C4C2×C418yescomplemented
119C2×(C2×D67)⋊C4D418yes—
120C2×(C2×D67)⋊C4C2314yes—
121C2×(C2×D67)⋊C4C2314yes—
122C2×(C2×D67)⋊C4C2314yes—
123C2×C4×Dic67—24no—
124C2×C4×Dic67—24no—
125C2×C4×Dic67—24no—
126C2×C4×Dic67C2314yes—
127C2×C4×Dic67C2314yes—
128C2×C4×Dic67C2314yes—
129C67⋊#95C2314yes—
130C67⋊#95C2314yes—
131C67⋊#95C2314yes—
132C67⋊#95C2314yes—
133C67⋊#95C2314yes—
134C67⋊#95C2314yes—
135C67⋊#95C2314yes—
136C67⋊#95C2314yes—
137C25×C67C2311yescharacteristic
138C23×C4×C67—24no—
139C23×C4×C67—24no—
140C23×C4×C67—42no—
141C23×C4×C67C2311yescharacteristic
142C23×C4×C67C2314yes—
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C23×C4×C67C2311yescharacteristic
146C23×C4×C67C2311yescharacteristic
147C23×C4×C67C2311yescharacteristic
148C2×C22⋊C4×C67—24no—
149C2×C22⋊C4×C67C2×C418yescomplemented
150C2×C22⋊C4×C67C2314yes—
151C2×C22⋊C4×C67C2314yes—
152C2×C42×C67—24no—
153C2×C42×C67—42no—
154C2×C42×C67C2314yes—
155C2×C42×C67C2314yes—
156#95×C67C2314yes—
157#95×C67C2314yes—
158C23×D67—22no—
159C23×D67—22no—
160C23×D67—22no—
161C23×D67—22no—
162C23×D67C22×C414yes—
163C23×D67C2×D414yes—
164C23×D67#4114yes—
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×Dic67—22no—
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C414yes—
189C22×Dic67C22×C414yes—
190C22×Dic67C2×D414yes—
191C22×Dic67C2412yes—
192C22×Dic67C2412yes—
193C22×Dic67C2412yes—
194C22×Dic67C2412yes—
195C22×Dic67C2412yes—
196C22×Dic67C2412yes—
197C22×Dic67C2412yes—
198C2×C4×D67—232no—
199C2×C4×D67—28no—
200C2×C4×D67—28no—
201C2×C4×D67—28no—
202C2×C4×D67—28no—
203C2×C4×D67—28no—
204C2×C4×D67—28no—
205C2×C4×D67—44no—
206C2×C4×D67—44no—
207C2×C4×D67—416no—
208C2×C4×D67—416no—
209C2×C4×D67C22×C4116yescomplemented
210C4⋊Dic67—44no—
211C4⋊Dic67C22×C4116yescomplemented
212Dic67⋊C4—28no—
213Dic67⋊C4—28no—
214Dic67⋊C4—28no—
215Dic67⋊C4—28no—
216Dic67⋊C4C22×C4116yescomplemented
217C22⋊Dic67—28no—
218C22⋊Dic67—44no—
219C22⋊Dic67C22×C4116yescomplemented
220(C2×D67)⋊C4—28no—
221(C2×D67)⋊C4C22×C4116yescomplemented
222(C2×D67)⋊C4C2×D4116yes—
223C4×Dic67—28no—
224C4×Dic67—28no—
225C4×Dic67—28no—
226C24×C67—22no—
227C24×C67—22no—
228C24×C67—22no—
229C24×C67—22no—
230C24×C67—22no—
231C24×C67—22no—
232C24×C67C22×C414yes—
233C24×C67C2412yes—
234C24×C67C2411yescharacteristic
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×C67—22no—
242C22×C4×C67—22no—
243C22×C4×C67—22no—
244C22×C4×C67—22no—
245C22×C4×C67—22no—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—28no—
249C22×C4×C67—28no—
250C22×C4×C67—44no—
251C22×C4×C67—416no—
252C22×C4×C67C22×C414yes—
253C22×C4×C67C22×C414yes—
254C22×C4×C67C2×D414yes—
255C22×C4×C67#4114yes—
256C22×C4×C67#4114yes—
257C22×C4×C67C2412yes—
258C22×C4×C67C2412yes—
259C22×C4×C67C2412yes—
260C22×C4×C67C2412yes—
261C22×C4×C67C2412yes—
262C22×C4×C67C2412yes—
263C22⋊C4×C67—28no—
264C22⋊C4×C67C22×C4116yescomplemented
265C42×C67—28no—
266C42×C67—44no—
267C23×C67—28no—
268C23×C67—28no—
269C23×C67—28no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—44no—
277C23×C67—44no—
278C23×C67—44no—
279C23×C67—44no—
280C23×C67C23×C414yes—
281C23×C67C23×C412yes—
282C23×C67C22×D412yes—
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—28no—
293C22×D67—28no—
294C22×D67—28no—
295C22×D67—22no—
296C22×D67—22no—
297C22×D67—22no—
298C22×D67—22no—
299C22×D67C4×D4116yes—
300C22×D67C23×C414yes—
301C22×D67C22×D414yes—
302C22×D67C2×#4114yes—
303C2×C4×C67—28no—
304C2×C4×C67—28no—
305C2×C4×C67—28no—
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—416no—
322C2×C4×C67—44no—
323C2×C4×C67C23×C414yes—
324C2×C4×C67C23×C414yes—
325C2×C4×C67C22×D414yes—
326C2×C4×C67C2×#4114yes—
327C2×C4×C67C2×#4114yes—
328C22⋊D67—232no—
329C2×Dic67—28no—
330C2×Dic67—28no—
331C2×Dic67—28no—
332C2×Dic67—28no—
333C2×Dic67—22no—
334C2×Dic67—22no—
335C2×Dic67—22no—
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—44no—
351C2×Dic67—44no—
352C2×Dic67—44no—
353C2×Dic67C23×C414yes—
354C2×Dic67C23×C414yes—
355C2×Dic67C23×C414yes—
356C2×Dic67C22×D414yes—
357C4×D67—232no—
358C4×D67—416no—
359C4×D67—416no—
360C22×C67—24no—
361C22×C67—24no—
362C22×C67—24no—
363C22×C67—416no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—42no—
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—232no—
383C2×D67—24no—
384C2×D67—24no—
385C2×D67—24no—
386C2×D67—24no—
387C2×D67—24no—
388C2×D67—24no—
389C2×D67C2×C4×D418yes—
390C4×C67—24no—
391C4×C67—24no—
392C4×C67—24no—
393C4×C67—24no—
394C4×C67—24no—
395C4×C67—42no—
396Dic67—24no—
397Dic67—24no—
398Dic67—24no—
399Dic67—24no—
400Dic67—42no—
401Dic67—42no—
402Dic67—42no—
403C2×#2359—671nomaximal, Sylow
404C2×C67—44no—
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—28no—
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⋊C4D6711yescharacteristic, complemented
429C22×#95—671no—
430C67C2×#235911yescharacteristic, complemented, Sylow
431C23×D4—671no—
432C24×C4—671no—
433C24×C4—671no—
434C24×C4—671no—
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⋊C4C2×D6711yescharacteristic
456C22×C22⋊C4C2×D6711yescharacteristic
457C22×C42—671no—
458C22×C42—671no—
459C22×C42—671no—
460C22×C42C2×D6711yescharacteristic
461C22×C42C2×D6711yescharacteristic
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⋊C4C2×D6718yescomplemented
473C2×#95—671no—
474C2×#95—671no—
475C2×#95—671no—
476C2×#95—671no—
477C2×#95—671no—
478C2×#95—671no—
479C2×#95—671no—
480C2×#95—671no—
481C2×#95—678no—
482C2×#95C2×D6711yescharacteristic
483C2×#95C2×D6711yescharacteristic
484C25—671no—
485C25C22×D6711yescharacteristic
486C22×D4—678no—
487C22×D4—674no—
488C22×D4—1344no—
489C22×D4—1344no—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—42no—
493C23×C4—2682no—
494C23×C4—2682no—
495C23×C4—674no—
496C23×C4—674no—
497C23×C4—671no—
498C23×C4—671no—
499C23×C4—671no—
500C23×C4—671no—
501C23×C4—678no—
502C23×C4—674no—
503C23×C4—671no—
504C23×C4—671no—
505C23×C4—671no—
506C23×C4—1344no—
507C23×C4—1344no—
508C23×C4—1344no—
509C23×C4—1344no—
510C23×C4—1344no—
511C23×C4—1344no—
512C23×C4C22×D6711yescharacteristic
513C23×C4C22×D6714yes—
514C23×C4C22×D6711yescharacteristic
515C23×C4C22×D6711yescharacteristic
516C23×C4C22×D6711yescharacteristic
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—24no—
537C2×C22⋊C4—2682no—
538C2×C22⋊C4—674no—
539C2×C22⋊C4—678no—
540C2×C22⋊C4—674no—
541C2×C22⋊C4—678no—
542C2×C22⋊C4—678no—
543C2×C22⋊C4—674no—
544C2×C22⋊C4—674no—
545C2×C22⋊C4—674no—
546C2×C22⋊C4—674no—
547C2×C22⋊C4—1344no—
548C2×C22⋊C4—1344no—
549C2×C22⋊C4C4×D6718yescomplemented
550C2×C22⋊C4C22×D6714yes—
551C2×C22⋊C4C22×D6714yes—
552C2×C42—24no—
553C2×C42—42no—
554C2×C42—674no—
555C2×C42—674no—
556C2×C42—674no—
557C2×C42—1344no—
558C2×C42—1344no—
559C2×C42—1344no—
560C2×C42C22×D6714yes—
561C2×C42C22×D6714yes—
562#95—674no—
563#95—674no—
564#95—674no—
565#95—674no—
566#95—674no—
567#95—674no—
568#95—674no—
569#95—674no—
570#95C22×D6714yes—
571#95C22×D6714yes—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—674no—
579C24—674no—
580C24—674no—
581C24—672no—
582C24—1342no—
583C24—1342no—
584C24—1342no—
585C24—1342no—
586C24C2×C4×D6714yes—
587C24C23×D6712yes—
588C24C23×D6711yescharacteristic
589C2×D4—6716no—
590C2×D4—1348no—
591C2×D4—13432no—
592C2×D4—1348no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—416no—
610C22×C4—26816no—
611C22×C4—26816no—
612C22×C4—2684no—
613C22×C4—2684no—
614C22×C4—674no—
615C22×C4—674no—
616C22×C4—674no—
617C22×C4—674no—
618C22×C4—672no—
619C22×C4—672no—
620C22×C4—672no—
621C22×C4—672no—
622C22×C4—6716no—
623C22×C4—672no—
624C22×C4—672no—
625C22×C4—672no—
626C22×C4—1348no—
627C22×C4—1348no—
628C22×C4—1348no—
629C22×C4—13432no—
630C22×C4—1348no—
631C22×C4—1342no—
632C22×C4—1342no—
633C22×C4—1342no—
634C22×C4—1342no—
635C22×C4—1342no—
636C22×C4—1342no—
637C22×C4—1342no—
638C22×C4—1342no—
639C22×C4—1342no—
640C22×C4—1348no—
641C22×C4—1348no—
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×C4D4×D6714yes—
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—28no—
669C22⋊C4—2684no—
670C22⋊C4—6716no—
671C22⋊C4—6716no—
672C22⋊C4—6716no—
673C22⋊C4—1348no—
674C22⋊C4—1348no—
675C22⋊C4C2×C4×D67116yescomplemented
676C42—28no—
677C42—44no—
678C42—1348no—
679C42—1348no—
680C42—1348no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—6716no—
695C23—674no—
696C23—674no—
697C23—674no—
698C23—1348no—
699C23—1348no—
700C23—1348no—
701C23—1348no—
702C23—1348no—
703C23—1348no—
704C23—1342no—
705C23—1342no—
706C23—1342no—
707C23—1342no—
708C23C22×C4×D6714yes—
709C23C22×C4×D6712yes—
710C23C2×D4×D6712yes—
711C23#41×D6712yes—
712C23C2×#1176162812yes—
713C23C2×#1176162812yes—
714C23#1452408812yes—
715C23#1452409012yes—
716C23C24×D6711yescharacteristic
717D4—13432no—
718C2×C4—28no—
719C2×C4—28no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
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—416no—
737C2×C4—44no—
738C2×C4—26816no—
739C2×C4—26816no—
740C2×C4—2684no—
741C2×C4—2684no—
742C2×C4—2684no—
743C2×C4—674no—
744C2×C4—674no—
745C2×C4—674no—
746C2×C4—674no—
747C2×C4—13432no—
748C2×C4—1342no—
749C2×C4—1342no—
750C2×C4—1342no—
751C2×C4—1342no—
752C2×C4—1342no—
753C2×C4—1342no—
754C2×C4—1342no—
755C2×C4—1342no—
756C2×C4—1342no—
757C2×C4—1348no—
758C2×C4—1348no—
759C2×C4—1348no—
760C2×C4—1348no—
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×C4C22×C4×D6714yes—
770C2×C4C22×C4×D6714yes—
771C2×C4C2×D4×D6714yes—
772C2×C4C2×#1176162814yes—
773C2×C4C2×#1176162814yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—416no—
780C22—42no—
781C22—42no—
782C22—678no—
783C22—1344no—
784C22—1344no—
785C22—1344no—
786C22—1344no—
787C22—13432no—
788C22—1344no—
789C22—1344no—
790C22C4×D4×D6714yes—
791C22C4×#1176162814yes—
792C22#1686387514yes—
793C22#1686403614yes—
794C22#1686405114yes—
795C22#1686407514yes—
796C22#1686408514yes—
797C22C23×C4×D6711yescharacteristic
798C22C22×D4×D6711yescharacteristic
799C22C2×#41×D6711yescharacteristic
800C22C22×#1176162811yescharacteristic
801C22C22×#1176162811yescharacteristic
802C22C2×#1452408811yescharacteristic
803C22C2×#1452409011yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—24no—
809C4—42no—
810C4—2682no—
811C4—2682no—
812C4—2682no—
813C4—1344no—
814C4—1344no—
815C4—1344no—
816C4—1344no—
817C2—44no—
818C2—1348no—
819C2#2256320218yesdirect product factor
820C2C2×C4×D4×D6711yescharacteristic
821C2C2×C4×#1176162811yescharacteristic
822C2C2×#1686387511yescharacteristic
823C2C2×#1686403611yescharacteristic
824C2C2×#1686405111yescharacteristic
825C2C2×#1686407511yescharacteristic
826C2C2×#1686408511yescharacteristic
subgroupG/H
centerC24C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×C22⋊C4×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
cosocleC23×C67C25
hypercenterC2×C4×C22⋊C4D67
hypocenterC67C2×#2359
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C22×#14524000C2semidirect
4. #22563202C2direct (N × H)
5. C2×#16863294C2semidirect
6. C2×#16863289C2semidirect
7. C2×#16863284C2semidirect
8. C2×#16863280C2semidirect
9. C2×#16863279C2semidirect
11. C2×#16863270C2semidirect
12. C2×#16863269C2semidirect
13. C2×#16863247C2semidirect
14. C2×C4×(C2×D67)⋊C4C2semidirect
15. C2×#95×D67C2semidirect
16. C2×C4×C22⋊C4×C67C2semidirect
21. C2×#14524025C4semidirect
26. C2×#14524000C22semidirect
43. #16863294C22semidirect
44. #16863289C22semidirect
45. #16863284C22semidirect
46. #16863280C22semidirect
47. #16863279C22semidirect
49. #16863270C22semidirect
50. #16863269C22semidirect
51. #16863247C22semidirect
52. C4×(C2×D67)⋊C4C22semidirect
61. #95×D67C22semidirect
67. C4×C22⋊C4×C67C22semidirect
90. C22×C4×D67C2×C4semidirect
94. #14524025C2×C4semidirect
98. C2×C4⋊Dic67C2×C4semidirect
105. C2×Dic67⋊C4C2×C4semidirect
113. C2×C22⋊Dic67C2×C4semidirect
118. C2×(C2×D67)⋊C4C2×C4semidirect
149. C2×C22⋊C4×C67C2×C4semidirect
209. C2×C4×D67C22×C4semidirect
211. C4⋊Dic67C22×C4semidirect
216. Dic67⋊C4C22×C4semidirect
219. C22⋊Dic67C22×C4semidirect
221. (C2×D67)⋊C4C22×C4semidirect
264. C22⋊C4×C67C22×C4semidirect
405. C2×C67#2359semidirect
428. C2×C4×C22⋊C4D67semidirect
430. C67C2×#2359semidirect
472. C4×C22⋊C4C2×D67semidirect
549. C2×C22⋊C4C4×D67semidirect
675. C22⋊C4C2×C4×D67semidirect
819. C2#22563202direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240252
C22×C4×C22⋊D672
C22×#145240002
#225632022
C2×#168632942
C2×#168632892
C2×#168632842
C2×#168632802
C2×#168632792
C2×#168632722
C2×#168632702
C2×#168632692
C2×#168632472
C2×C4×(C2×D67)⋊C42
C2×#95×D672
C2×C4×C22⋊C4×C672
C2×#235967