Finite Group Databasebeta

← C2×#22569355 #31720918

Subgroups — C2×#22569355 #31720918

Order 17152.

1926 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16863926C211yesmaximal, characteristic
2#22569355C2116yesmaximal, direct product factor
3C2×#16863525C211yesmaximal, characteristic, complemented
4C2×C8×Dic134C211yesmaximal, characteristic, complemented
5C2×#16863472C211yesmaximal, characteristic, complemented
6C2×#16863471C211yesmaximal, characteristic, complemented
7C2×#16863468C211yesmaximal, characteristic, complemented
8C2×#16863465C211yesmaximal, characteristic, complemented
9C2×(C22⋊D67)⋊C8C211yesmaximal, characteristic, complemented
10C2×#16863455C211yesmaximal, characteristic, complemented
11C2×#16863454C211yesmaximal, characteristic, complemented
12C2×#16863446C211yesmaximal, characteristic, complemented
13C2×#16863424C211yesmaximal, characteristic, complemented
14C2×#16863421C211yesmaximal, characteristic, complemented
15C2×#16863419C211yesmaximal, characteristic, complemented
16C2×#436×C67C211yesmaximal, characteristic, complemented
17C22×#11761612C2211yescharacteristic
18C22×#11761611C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20C22×C8×D67C2211yescharacteristic
21#16863926C418yes—
22#16863926C2218yes—
23C2×#14524038C411yescharacteristic
24C2×#14524036C411yescharacteristic
25C2×#14524033C411yescharacteristic
26C2×#14524029C411yescharacteristic
27C2×#14524027C411yescharacteristic
28C2×#14524024C411yescharacteristic
29C2×#14524020C411yescharacteristic
30C2×#14524015C411yescharacteristic
31C2×C4×Dic134C2211yescharacteristic
32C2×C4×C22⋊D67C2211yescharacteristic
33C2×C4×C22⋊D67C2211yescharacteristic
34C2×#14524002C2211yescharacteristic
35C2×#14524000C2211yescharacteristic
36C22×C4×Dic67C2211yescharacteristic
37#16863525C2218yescomplemented
38C8×Dic134C2218yescomplemented
39#16863472C2218yescomplemented
40#16863471C2218yescomplemented
41#16863468C2218yescomplemented
42#16863465C2218yescomplemented
43(C22⋊D67)⋊C8C2218yescomplemented
44#16863455C2218yescomplemented
45#16863454C2218yescomplemented
46#16863446C2218yescomplemented
47#16863424C2218yescomplemented
48#16863421C2218yescomplemented
49#16863419C2218yescomplemented
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×Dic67⋊C8C2211yescharacteristic
52C2×Dic67⋊C8C2211yescharacteristic
53C2×Dic67⋊C8C2211yescharacteristic
54C2×Dic67⋊C8C2211yescharacteristic
55C2×Dic67⋊C8C2211yescharacteristic
56C2×Dic67⋊C8C2211yescharacteristic
57C2×Dic67⋊C8C2211yescharacteristic
58C2×Dic67⋊C8C2211yescharacteristic
59C2×C22⋊(C67⋊C8)C2211yescharacteristic
60C2×C22⋊(C67⋊C8)C2211yescharacteristic
61C2×(C2×D67)⋊C8C2211yescharacteristic
62C2×(C2×D67)⋊C8C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64C2×#14523953C2211yescharacteristic
65C2×C8×Dic67C2211yescharacteristic
66C2×C8×Dic67C2211yescharacteristic
67C2×C8×Dic67C2211yescharacteristic
68C22×M16×C67C2211yescharacteristic
69C22×M16×C67C2211yescharacteristic
70C2×C4×D4×C67C2211yescharacteristic
71#436×C67C2218yescomplemented
72C2×C4⋊C8×C67C2211yescharacteristic
73C2×C22⋊C8×C67C2211yescharacteristic
74C2×C22⋊C8×C67C2211yescharacteristic
75C2×C4×C8×C67C2211yescharacteristic
76C22×Dic134C2×C411yescharacteristic
77C22×C22⋊D67C2×C411yescharacteristic
78C22×C22⋊D67C2×C411yescharacteristic
79C23×Dic67C2×C411yescharacteristic
80C23×Dic67C2×C411yescharacteristic
81C22×C4×D67C2311yescharacteristic
82C2×#11761612—42no—
83C2×#11761612C2314yes—
84C2×#11761611—42no—
85C2×#11761611C2314yes—
86C22×C67⋊C8—42no—
87C22×C67⋊C8C2311yescharacteristic
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2314yes—
92C2×C8×D67—42no—
93C2×C8×D67C2314yes—
94#14524038C2×C418yes—
95#14524036C2×C418yes—
96#14524033C2×C418yes—
97#14524029C2×C418yes—
98#14524027C2×C418yes—
99#14524024C2×C418yes—
100#14524020C2×C418yes—
101#14524015C2×C418yes—
102C4×Dic134C2×C414yes—
103C4×Dic134C2314yes—
104C4×C22⋊D67C2×C414yes—
105C4×C22⋊D67C2×C414yes—
106C4×C22⋊D67C2314yes—
107C4×C22⋊D67C2314yes—
108#14524002C2×C414yes—
109#14524002C2314yes—
110#14524000C2×C414yes—
111#14524000C2314yes—
112C2×C4⋊Dic67C2×C411yescharacteristic
113C2×C4⋊Dic67C2×C411yescharacteristic
114C2×C4⋊Dic67C2×C411yescharacteristic
115C2×Dic67⋊C4C2×C411yescharacteristic
116C2×Dic67⋊C4C2×C411yescharacteristic
117C2×Dic67⋊C4C2×C411yescharacteristic
118C2×Dic67⋊C4C2×C411yescharacteristic
119C2×Dic67⋊C4C2×C411yescharacteristic
120C2×Dic67⋊C4C2×C411yescharacteristic
121C2×C22⋊Dic67C2×C411yescharacteristic
122C2×C22⋊Dic67C2×C411yescharacteristic
123C2×C22⋊Dic67C2×C411yescharacteristic
124C2×C22⋊Dic67C2×C411yescharacteristic
125C2×(C2×D67)⋊C4C2×C411yescharacteristic
126C2×(C2×D67)⋊C4C2×C411yescharacteristic
127C2×(C2×D67)⋊C4C2×C411yescharacteristic
128C2×(C2×D67)⋊C4C2×C411yescharacteristic
129C2×C4×Dic67C2×C411yescharacteristic
130C2×C4×Dic67C2×C411yescharacteristic
131C2×C4×Dic67C2×C414yes—
132C2×C4×Dic67C2311yescharacteristic
133C2×C4×Dic67C2311yescharacteristic
134C2×C4×Dic67C2314yes—
135C2×C4×Dic67C2311yescharacteristic
136C4⋊(C67⋊C8)C2314yes—
137Dic67⋊C8C2314yes—
138Dic67⋊C8C2314yes—
139Dic67⋊C8C2314yes—
140Dic67⋊C8C2314yes—
141Dic67⋊C8C2314yes—
142Dic67⋊C8C2314yes—
143Dic67⋊C8C2314yes—
144Dic67⋊C8C2314yes—
145C22⋊(C67⋊C8)C2314yes—
146C22⋊(C67⋊C8)C2314yes—
147(C2×D67)⋊C8C2314yes—
148(C2×D67)⋊C8C2314yes—
149#14523954C2314yes—
150#14523953C2314yes—
151C8×Dic67C2314yes—
152C8×Dic67C2314yes—
153C8×Dic67C2314yes—
154C22×D4×C67C2×C411yescharacteristic
155C23×C4×C67C2311yescharacteristic
156C23×C4×C67C2311yescharacteristic
157C2×M16×C67—42no—
158C2×M16×C67—42no—
159C2×M16×C67C2314yes—
160C2×M16×C67C2314yes—
161C22×C8×C67C2311yescharacteristic
162C22×C8×C67C2311yescharacteristic
163C22×C8×C67C2311yescharacteristic
164C22×C8×C67C2311yescharacteristic
165C4×D4×C67C2×C414yes—
166C4×D4×C67C2314yes—
167C2×C4⋊C4×C67C2×C411yescharacteristic
168C2×C22⋊C4×C67C2×C411yescharacteristic
169C2×C22⋊C4×C67C2×C411yescharacteristic
170C2×C42×C67C2311yescharacteristic
171C4⋊C8×C67C2314yes—
172C22⋊C8×C67C2314yes—
173C22⋊C8×C67C2314yes—
174C4×C8×C67C2314yes—
175C23×D67C22×C411yescharacteristic
176C2×Dic134—24no—
177C2×Dic134C22×C414yes—
178C2×C22⋊D67—24no—
179C2×C22⋊D67—42no—
180C2×C22⋊D67C22×C414yes—
181C2×C22⋊D67C22×C414yes—
182C22×Dic67—24no—
183C22×Dic67—42no—
184C22×Dic67C22×C411yescharacteristic
185C22×Dic67C22×C411yescharacteristic
186C22×Dic67C22×C411yescharacteristic
187C22×Dic67C22×C414yes—
188C22×Dic67C22×C411yescharacteristic
189C22×Dic67C22×C411yescharacteristic
190C22×Dic67C22×C411yescharacteristic
191C22×Dic67C22×C414yes—
192C22×Dic67C22×C411yescharacteristic
193C2×C4×D67—22no—
194C2×C4×D67—22no—
195C2×C4×D67C22×C412yes—
196C2×C4×D67C2412yes—
197#11761612—44no—
198#11761611—44no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8—22no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—44no—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C2×C67⋊C8C2412yes—
207C2×C67⋊C8C2412yes—
208C8×D67—44no—
209C4⋊Dic67C22×C414yes—
210C4⋊Dic67C22×C414yes—
211C4⋊Dic67C22×C414yes—
212Dic67⋊C4C22×C414yes—
213Dic67⋊C4C22×C414yes—
214Dic67⋊C4C22×C414yes—
215Dic67⋊C4C22×C414yes—
216Dic67⋊C4C22×C414yes—
217Dic67⋊C4C22×C414yes—
218C22⋊Dic67C22×C414yes—
219C22⋊Dic67C22×C414yes—
220C22⋊Dic67C22×C414yes—
221C22⋊Dic67C22×C414yes—
222(C2×D67)⋊C4C22×C414yes—
223(C2×D67)⋊C4C22×C414yes—
224(C2×D67)⋊C4C22×C414yes—
225(C2×D67)⋊C4C22×C414yes—
226C4×Dic67C22×C412yes—
227C4×Dic67C22×C412yes—
228C4×Dic67C22×C414yes—
229C4×Dic67C22×C414yes—
230C4×Dic67C22×C412yes—
231C4×Dic67C2412yes—
232C4×Dic67C2412yes—
233C4×Dic67C2412yes—
234C24×C67C22×C411yescharacteristic
235C24×C67C22×C411yescharacteristic
236C2×D4×C67—42no—
237C2×D4×C67C22×C414yes—
238C22×C4×C67—22no—
239C22×C4×C67—22no—
240C22×C4×C67—22no—
241C22×C4×C67—22no—
242C22×C4×C67C22×C411yescharacteristic
243C22×C4×C67C22×C411yescharacteristic
244C22×C4×C67C22×C411yescharacteristic
245C22×C4×C67C22×C411yescharacteristic
246C22×C4×C67C22×C412yes—
247C22×C4×C67C22×C412yes—
248C22×C4×C67C2412yes—
249C22×C4×C67C2412yes—
250C22×C4×C67C2411yescharacteristic
251M16×C67—44no—
252M16×C67—44no—
253C2×C8×C67—22no—
254C2×C8×C67—22no—
255C2×C8×C67—22no—
256C2×C8×C67—22no—
257C2×C8×C67C2412yes—
258C2×C8×C67C2412yes—
259C2×C8×C67C2412yes—
260C2×C8×C67C2412yes—
261C4⋊C4×C67C22×C414yes—
262C22⋊C4×C67C22×C414yes—
263C22⋊C4×C67C22×C414yes—
264C42×C67C22×C412yes—
265C42×C67C2412yes—
266C23×C67—22no—
267C23×C67—22no—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67C23×C412yes—
273C23×C67C23×C412yes—
274C23×C67C23×C411yescharacteristic
275C22×D67—22no—
276C22×D67—22no—
277C22×D67—22no—
278C22×D67C23×C412yes—
279D4×C67—44no—
280C2×C4×C67—22no—
281C2×C4×C67—22no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—24no—
285C2×C4×C67—24no—
286C2×C4×C67—22no—
287C2×C4×C67—22no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
290C2×C4×C67C23×C412yes—
291C2×C4×C67C23×C412yes—
292C2×C4×C67C23×C412yes—
293C2×C4×C67C23×C412yes—
294C2×C4×C67C23×C411yescharacteristic
295C2×C4×C67H(5,𝔽2)12yes—
296C2×C4×C672−1+412yes—
297C2×C4×C67C2511yescharacteristic
298C22⋊D67—28no—
299C22⋊D67—44no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—28no—
307C2×Dic67—44no—
308C2×Dic67#13114yes—
309C2×Dic67C23×C412yes—
310C2×Dic67C23×C412yes—
311C2×Dic67C23×C412yes—
312C2×Dic67C23×C412yes—
313C2×Dic67C23×C412yes—
314C2×Dic67C23×C412yes—
315C2×Dic67C23×C412yes—
316C4×D67—24no—
317C4×D67—22no—
318C4×D67—22no—
319Dic134—28no—
320C8×C67—22no—
321C8×C67—22no—
322C8×C67—22no—
323C8×C67—22no—
324C67⋊C8—22no—
325C67⋊C8—22no—
326C67⋊C8—22no—
327C67⋊C8—22no—
328C22×C67—22no—
329C22×C67—22no—
330C22×C67—22no—
331C22×C67—22no—
332C22×C67—22no—
333C22×C67—22no—
334C22×C67—44no—
335C22×C67—44no—
336C22×C67#52012yes—
337C22×C67C2×#13112yes—
338C22×C67#56812yes—
339C22×C67C24×C411yescharacteristic
340C2×D67—22no—
341C2×D67—22no—
342C2×D67—22no—
343C2×D67—44no—
344C4×C67—22no—
345C4×C67—22no—
346C4×C67—22no—
347C4×C67—22no—
348C4×C67#52012yes—
349C4×C67C2×H(5,𝔽2)11yescharacteristic
350C4×C67C2×2−1+411yescharacteristic
351Dic67—22no—
352Dic67—22no—
353Dic67—22no—
354Dic67—22no—
355Dic67—22no—
356Dic67—22no—
357Dic67C2×#13114yes—
358C2×#2993—671nomaximal, Sylow
359C2×C67—42no—
360C2×C67—42no—
361C2×C67#299314yescomplemented
362C2×C67C2×#52011yescharacteristic
363C2×C67C22×#13111yescharacteristic
364C2×C67C2×#56811yescharacteristic
365D67—42no—
366C2×#529—671no—
367#2993—6716no—
368C2×#446—671no—
369C2×C8×Q8—671no—
370C2×#436—671no—
371C2×#436—671no—
372C2×#436D6711yescharacteristic, complemented
373C2×#435—671no—
374C2×#435—671no—
375C2×C8×D4—671no—
376C2×#433—671no—
377C2×#433—671no—
378C2×#431—671no—
379C2×#424—671no—
380C2×#424—671no—
381C2×#423—671no—
382C67C2×#299311yescharacteristic, complemented, Sylow
383C22×M16—671no—
384C22×M16—671no—
385C22×M16C2×D6711yescharacteristic
386C22×M16C2×D6711yescharacteristic
387C23×C8—671no—
388C23×C8—671no—
389#529—678no—
390#529—678no—
391C2×#126—671no—
392C2×#126—671no—
393C2×#125—671no—
394C2×#124—671no—
395C2×#123—671no—
396C2×#123—671no—
397C2×C22⋊Q8—671no—
398C2×#121—671no—
399C2×C4×Q8—671no—
400C2×C4×D4—671no—
401C2×C4×D4—671no—
402C2×C4×D4C2×D6711yescharacteristic
403C2×#117—671no—
404C2×#117—671no—
405C22×C42—671no—
406#446—678no—
407C8×Q8—678no—
408#436—678no—
409#436—678no—
410#436C2×D6718yescomplemented
411#435—678no—
412#435—678no—
413C8×D4—678no—
414#433—678no—
415#433—678no—
416#431—678no—
417#424—678no—
418#424—678no—
419#423—678no—
420C2×C4⋊C8—671no—
421C2×C4⋊C8—671no—
422C2×C4⋊C8—671no—
423C2×C4⋊C8—671no—
424C2×C4⋊C8—671no—
425C2×C4⋊C8—671no—
426C2×C4⋊C8—671no—
427C2×C4⋊C8—671no—
428C2×C4⋊C8—671no—
429C2×C4⋊C8C2×D6711yescharacteristic
430C2×C22⋊C8—671no—
431C2×C22⋊C8—671no—
432C2×C22⋊C8—671no—
433C2×C22⋊C8—671no—
434C2×C22⋊C8C2×D6711yescharacteristic
435C2×C22⋊C8C2×D6711yescharacteristic
436C2×#97—671no—
437C2×#97—671no—
438C2×C4×C8—671no—
439C2×C4×C8—671no—
440C2×C4×C8—671no—
441C2×C4×C8C2×D6711yescharacteristic
442C22×Q8—671no—
443C22×D4—671no—
444C22×D4—671no—
445C22×D4C4×D6711yescharacteristic
446C23×C4—671no—
447C23×C4—671no—
448C23×C4—671no—
449C23×C4C22×D6711yescharacteristic
450C23×C4C22×D6711yescharacteristic
451C2×M16—42no—
452C2×M16—42no—
453C2×M16—2682no—
454C2×M16—2682no—
455C2×M16—674no—
456C2×M16—674no—
457C2×M16C22×D6714yes—
458C2×M16C22×D6714yes—
459C22×C8—2682no—
460C22×C8—2682no—
461C22×C8—674no—
462C22×C8—674no—
463C22×C8—671no—
464C22×C8—671no—
465C22×C8—671no—
466C22×C8—671no—
467C22×C8C22×D6711yescharacteristic
468C22×C8C22×D6711yescharacteristic
469C22×C8C22×D6711yescharacteristic
470C22×C8C22×D6711yescharacteristic
471#126—678no—
472#126—678no—
473#125—678no—
474#124—678no—
475#123—678no—
476#123—678no—
477C22⋊Q8—678no—
478#121—678no—
479C4×Q8—674no—
480C4×Q8—674no—
481C4×D4—674no—
482C4×D4—674no—
483C4×D4—674no—
484C4×D4—674no—
485C4×D4C4×D6714yes—
486C4×D4C22×D6714yes—
487#117—674no—
488#117—674no—
489#117—674no—
490#117—674no—
491C2×C4⋊C4—671no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—671no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—671no—
497C2×C4⋊C4—671no—
498C2×C4⋊C4—671no—
499C2×C4⋊C4—671no—
500C2×C4⋊C4C4×D6711yescharacteristic
501C2×C22⋊C4—671no—
502C2×C22⋊C4—671no—
503C2×C22⋊C4—671no—
504C2×C22⋊C4—671no—
505C2×C22⋊C4—671no—
506C2×C22⋊C4—671no—
507C2×C22⋊C4—671no—
508C2×C22⋊C4—671no—
509C2×C22⋊C4C4×D6711yescharacteristic
510C2×C22⋊C4C4×D6711yescharacteristic
511C2×C42—671no—
512C2×C42—671no—
513C2×C42—674no—
514C2×C42—674no—
515C2×C42—671no—
516C2×C42—671no—
517C2×C42—671no—
518C2×C42C22×D6711yescharacteristic
519C4⋊C8—674no—
520C4⋊C8—674no—
521C4⋊C8—674no—
522C4⋊C8—674no—
523C4⋊C8—674no—
524C4⋊C8—674no—
525C4⋊C8—674no—
526C4⋊C8—674no—
527C4⋊C8—674no—
528C4⋊C8C22×D6714yes—
529C22⋊C8—674no—
530C22⋊C8—674no—
531C22⋊C8—674no—
532C22⋊C8—674no—
533C22⋊C8C22×D6714yes—
534C22⋊C8C22×D6714yes—
535#97—674no—
536#97—674no—
537C4×C8—674no—
538C4×C8—674no—
539C4×C8—674no—
540C4×C8C22×D6714yes—
541C24—671no—
542C24C2×C4×D6711yescharacteristic
543C24C2×C4×D6711yescharacteristic
544C2×Q8—674no—
545C2×Q8—1344no—
546C2×D4—42no—
547C2×D4—2682no—
548C2×D4—674no—
549C2×D4—674no—
550C2×D4—1344no—
551C2×D4C2×C4×D6714yes—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—2682no—
557C22×C4—674no—
558C22×C4—671no—
559C22×C4—671no—
560C22×C4—671no—
561C22×C4—671no—
562C22×C4—674no—
563C22×C4—671no—
564C22×C4—671no—
565C22×C4—671no—
566C22×C4—672no—
567C22×C4—672no—
568C22×C4—1344no—
569C22×C4—1342no—
570C22×C4—1342no—
571C22×C4C2×C4×D6711yescharacteristic
572C22×C4C2×C4×D6712yes—
573C22×C4C2×C4×D6711yescharacteristic
574C22×C4C2×C4×D6711yescharacteristic
575C22×C4C2×C4×D6711yescharacteristic
576C22×C4C2×C4×D6712yes—
577C22×C4C23×D6712yes—
578C22×C4C23×D6712yes—
579C22×C4C23×D6711yescharacteristic
580M16—44no—
581M16—44no—
582M16—2684no—
583M16—2684no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—22no—
587C2×C8—22no—
588C2×C8—2684no—
589C2×C8—2684no—
590C2×C8—672no—
591C2×C8—672no—
592C2×C8—672no—
593C2×C8—672no—
594C2×C8—1342no—
595C2×C8—1342no—
596C2×C8—1342no—
597C2×C8—1342no—
598C2×C8C23×D6712yes—
599C2×C8C23×D6712yes—
600C2×C8C23×D6712yes—
601C2×C8C23×D6712yes—
602C4⋊C4—674no—
603C4⋊C4—674no—
604C4⋊C4—674no—
605C4⋊C4—674no—
606C4⋊C4—674no—
607C4⋊C4—674no—
608C4⋊C4—674no—
609C4⋊C4—674no—
610C4⋊C4—674no—
611C4⋊C4C2×C4×D6714yes—
612C22⋊C4—674no—
613C22⋊C4—674no—
614C22⋊C4—674no—
615C22⋊C4—674no—
616C22⋊C4—674no—
617C22⋊C4—674no—
618C22⋊C4—674no—
619C22⋊C4—674no—
620C22⋊C4C2×C4×D6714yes—
621C22⋊C4C2×C4×D6714yes—
622C42—672no—
623C42—672no—
624C42—674no—
625C42—674no—
626C42—672no—
627C42—672no—
628C42—672no—
629C42—672no—
630C42C2×C4×D6712yes—
631C42C23×D6712yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—672no—
639C23—1342no—
640C23—1342no—
641C23—1342no—
642C23C22×C4×D6712yes—
643C23C22×C4×D6712yes—
644C23C22×C4×D6711yescharacteristic
645Q8—1348no—
646D4—44no—
647D4—2684no—
648D4—1348no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—2684no—
660C2×C4—674no—
661C2×C4—672no—
662C2×C4—672no—
663C2×C4—672no—
664C2×C4—672no—
665C2×C4—672no—
666C2×C4—672no—
667C2×C4—672no—
668C2×C4—1348no—
669C2×C4—1342no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4—1342no—
675C2×C4—1344no—
676C2×C4—1342no—
677C2×C4—1342no—
678C2×C4C22×C4×D6712yes—
679C2×C4C22×C4×D6712yes—
680C2×C4C22×C4×D6712yes—
681C2×C4C22×C4×D6712yes—
682C2×C4C22×C4×D6711yescharacteristic
683C2×C4#1452408812yes—
684C2×C4#1452409012yes—
685C2×C4C24×D6711yescharacteristic
686C8—22no—
687C8—22no—
688C8—22no—
689C8—22no—
690C8—1342no—
691C8—1342no—
692C8—1342no—
693C8—1342no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—44no—
702C22—2684no—
703C22—1342no—
704C22—1342no—
705C22—1342no—
706C22#1686387512yes—
707C22#131×D6712yes—
708C22#1686416212yes—
709C22C23×C4×D6711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—674no—
715C4—1342no—
716C4—1342no—
717C4—1342no—
718C4—1342no—
719C4—1342no—
720C4—1342no—
721C4#1686387512yes—
722C4C2×#1452408811yescharacteristic
723C4C2×#1452409011yescharacteristic
724C2—42no—
725C2—42no—
726C2—2682no—
727C2#2256935514yesdirect product factor
728C2C2×#1686387511yescharacteristic
729C2C2×#131×D6711yescharacteristic
730C2C2×#1686416211yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#436×C67C2
socleC23×C67C23×C4
prime radicalC2×#14524015C4
cosocleC2×C4×C67C25
hypercenterC2×#436D67
hypocenterC67C2×#2993
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. #22569355C2direct (N × H)
3. C2×#16863525C2semidirect
4. C2×C8×Dic134C2semidirect
5. C2×#16863472C2semidirect
6. C2×#16863471C2semidirect
7. C2×#16863468C2semidirect
8. C2×#16863465C2semidirect
9. C2×(C22⋊D67)⋊C8C2semidirect
10. C2×#16863455C2semidirect
11. C2×#16863454C2semidirect
12. C2×#16863446C2semidirect
13. C2×#16863424C2semidirect
14. C2×#16863421C2semidirect
15. C2×#16863419C2semidirect
16. C2×#436×C67C2semidirect
37. #16863525C22semidirect
38. C8×Dic134C22semidirect
39. #16863472C22semidirect
40. #16863471C22semidirect
41. #16863468C22semidirect
42. #16863465C22semidirect
43. (C22⋊D67)⋊C8C22semidirect
44. #16863455C22semidirect
45. #16863454C22semidirect
46. #16863446C22semidirect
47. #16863424C22semidirect
48. #16863421C22semidirect
49. #16863419C22semidirect
71. #436×C67C22semidirect
361. C2×C67#2993semidirect
372. C2×#436D67semidirect
382. C67C2×#2993semidirect
410. #436C2×D67semidirect
727. C2#22569355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168639262
#225693552
C2×#168635252
C2×C8×Dic1342
C2×#168634722
C2×#168634712
C2×#168634682
C2×#168634652
C2×(C22⋊D67)⋊C82
C2×#168634552
C2×#168634542
C2×#168634462
C2×#168634242
C2×#168634212
C2×#168634192
C2×#436×C672
C2×#299367