Finite Group Databasebeta

← C2×#428×D67 #31719482

Subgroups — C2×#428×D67 #31719482

Order 17152.

3182 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D67C211yesmaximal, characteristic
2C2×#117×D67C211yesmaximal, characteristic
3C22×C4⋊C4×D67C211yesmaximal, characteristic
4C2×#16863439C211yesmaximal, characteristic, complemented
5C2×#16863438C211yesmaximal, characteristic, complemented
6C2×#16863437C212yesmaximal, complemented
7C2×#16863436C211yesmaximal, characteristic, complemented
8C2×#16863435C212yesmaximal, complemented
9#428×D67C2116yesmaximal, direct product factor
10C2×#107×D67C212yesmaximal, complemented
11C2×#106×D67C212yesmaximal, complemented
12C2×#428×C67C211yesmaximal, characteristic, complemented
13C23×C4×D67—21no—
14C23×C4×D67C2211yescharacteristic
15C22×#11761612C2211yescharacteristic
16C22×#11761611C2212yes—
17C2×M16×D67C4116yescomplemented
18C2×M16×D67C2218yes—
19C22×C8×D67C2212yes—
20C2×#14524002C2211yescharacteristic
21C2×#14524001C2211yescharacteristic
22C2×#14524001C2211yescharacteristic
23C2×#14524000—21no—
24C2×#14523999—21no—
25#117×D67—24no—
26#117×D67C2218yes—
27C22×C4⋊Dic67C2211yescharacteristic
28C22×Dic67⋊C4—21no—
29C2×C4⋊C4×D67—21no—
30C2×C4⋊C4×D67—24no—
31C2×C4⋊C4×D67—21no—
32C2×C4⋊C4×D67C2212yes—
33C2×C4⋊C4×D67C2218yes—
34C2×C4⋊C4×D67C2212yes—
35C2×C4⋊C4×D67C2211yescharacteristic
36C2×C4⋊C4×D67C2211yescharacteristic
37C2×C22⋊C4×D67—21no—
38C2×C42×D67—21no—
39#16863439C2218yescomplemented
40#16863438C2218yescomplemented
41#16863437C22116yescomplemented
42#16863436C2218yescomplemented
43#16863435C22116yescomplemented
44C2×#14523977C2212yescomplemented
45C2×#14523976C2212yescomplemented
46C2×#14523976C2212yescomplemented
47#107×D67C22116yescomplemented
48C2×#14523975C2212yescomplemented
49C2×#14523974C2212yescomplemented
50C2×#14523974C2212yescomplemented
51#106×D67C22116yescomplemented
52C22×M16×C67C2211yescharacteristic
53C2×#117×C67C2211yescharacteristic
54C22×C4⋊C4×C67C2211yescharacteristic
55#428×C67C2218yescomplemented
56C2×#107×C67C2212yescomplemented
57C2×#106×C67C2212yescomplemented
58C24×D67D411yescharacteristic
59C23×Dic67—21no—
60C23×Dic67D411yescharacteristic
61C22×C4×D67—21no—
62C22×C4×D67—21no—
63C22×C4×D67—28no—
64C22×C4×D67—22no—
65C22×C4×D67—22no—
66C22×C4×D67—48no—
67C22×C4×D67C2×C418yes—
68C22×C4×D67D411yescharacteristic
69C22×C4×D67D414yes—
70C22×C4×D67D411yescharacteristic
71C22×C4×D67Q818yes—
72C22×C4×D67C2311yescharacteristic
73C22×C4×D67C2314yes—
74C22×C4×D67C2311yescharacteristic
75C2×#11761612C2×C418yescomplemented
76C2×#11761612C2314yes—
77C2×#11761611C2×C4116yescomplemented
78C2×#11761611C2318yes—
79M16×D67C2×C4164yescomplemented
80C22×C67⋊C8C2312yes—
81C2×C8×D67C2×C4116yescomplemented
82C2×C8×D67C2318yes—
83#14524002—22no—
84#14524002C2314yes—
85#14524001—22no—
86#14524001—22no—
87#14524001C2314yes—
88#14524001C2314yes—
89#14524000—28no—
90#14523999—28no—
91C2×C4⋊Dic67—21no—
92C2×C4⋊Dic67—22no—
93C2×C4⋊Dic67C2312yes—
94C2×C4⋊Dic67C2314yes—
95C2×C4⋊Dic67C2311yescharacteristic
96C2×C4⋊Dic67C2311yescharacteristic
97C2×Dic67⋊C4—22no—
98C2×Dic67⋊C4—22no—
99C2×Dic67⋊C4—28no—
100C2×Dic67⋊C4—21no—
101C2×Dic67⋊C4—21no—
102C4⋊C4×D67—28no—
103C4⋊C4×D67—24no—
104C4⋊C4×D67—28no—
105C4⋊C4×D67—24no—
106C4⋊C4×D67—22no—
107C4⋊C4×D67—22no—
108C4⋊C4×D67C2318yes—
109C4⋊C4×D67C2318yes—
110C4⋊C4×D67C2314yes—
111C4⋊C4×D67C2314yes—
112C2×C22⋊Dic67—21no—
113C2×(C2×D67)⋊C4—21no—
114C2×(C2×D67)⋊C4—21no—
115C22⋊C4×D67—28no—
116C2×C4×Dic67—21no—
117C2×C4×Dic67—21no—
118C2×C4×Dic67—21no—
119C42×D67—28no—
120#14523977C2318yescomplemented
121#14523976C2318yescomplemented
122#14523976C2318yescomplemented
123#14523975C2318yescomplemented
124#14523974C2318yescomplemented
125#14523974C2318yescomplemented
126C23×C4×C67—21no—
127C23×C4×C67C2311yescharacteristic
128C2×M16×C67C2×C418yescomplemented
129C2×M16×C67C2314yes—
130C22×C8×C67C2312yes—
131#117×C67—22no—
132#117×C67C2314yes—
133C2×C4⋊C4×C67—21no—
134C2×C4⋊C4×C67—22no—
135C2×C4⋊C4×C67C2312yes—
136C2×C4⋊C4×C67C2314yes—
137C2×C4⋊C4×C67C2311yescharacteristic
138C2×C4⋊C4×C67C2311yescharacteristic
139C2×C22⋊C4×C67—21no—
140C2×C42×C67—21no—
141#107×C67C2318yescomplemented
142#106×C67C2318yescomplemented
143C23×D67—24no—
144C23×D67—24no—
145C23×D67C4⋊C418yes—
146C23×D67C2×D414yes—
147C23×D67C2×D411yescharacteristic
148C23×D67C2×D411yescharacteristic
149C22×Dic67—21no—
150C22×Dic67—21no—
151C22×Dic67—24no—
152C22×Dic67—22no—
153C22×Dic67—44no—
154C22×Dic67C4⋊C418yes—
155C22×Dic67C2×D411yescharacteristic
156C22×Dic67C2×D411yescharacteristic
157C22×Dic67C2×D414yes—
158C2×C4×D67—24no—
159C2×C4×D67—24no—
160C2×C4×D67—28no—
161C2×C4×D67—28no—
162C2×C4×D67—48no—
163C2×C4×D67—432no—
164C2×C4×D67—44no—
165C2×C4×D67—48no—
166C2×C4×D67—44no—
167C2×C4×D67C4⋊C4132yes—
168C2×C4×D67C4⋊C418yes—
169C2×C4×D67C4⋊C418yes—
170C2×C4×D67C22×C414yes—
171C2×C4×D67C22×C4116yes—
172C2×C4×D67C22×C414yes—
173C2×C4×D67C2×D414yes—
174C2×C4×D67C2×D412yes—
175C2×C4×D67C2×D414yes—
176C2×C4×D67C2×D412yes—
177C2×C4×D67C2×Q8116yes—
178C2×C4×D67C2×Q814yes—
179C2×C4×D67C2×Q814yes—
180C2×C4×D67C2412yes—
181C2×C4×D67C2412yes—
182#11761612C22×C4116yescomplemented
183#11761611C22×C4132yescomplemented
184C2×C67⋊C8C22×C418yescomplemented
185C2×C67⋊C8C2414yes—
186C8×D67C22×C4132yescomplemented
187C4⋊Dic67—24no—
188C4⋊Dic67—22no—
189C4⋊Dic67—21no—
190C4⋊Dic67—21no—
191C4⋊Dic67C2412yes—
192C4⋊Dic67C2414yes—
193C4⋊Dic67C2412yes—
194Dic67⋊C4—28no—
195Dic67⋊C4—28no—
196Dic67⋊C4—24no—
197Dic67⋊C4—24no—
198C22⋊Dic67—24no—
199(C2×D67)⋊C4—24no—
200(C2×D67)⋊C4—24no—
201C4×Dic67—24no—
202C4×Dic67—24no—
203C4×Dic67—24no—
204C24×C67C2×D411yescharacteristic
205C22×C4×C67—21no—
206C22×C4×C67—21no—
207C22×C4×C67—24no—
208C22×C4×C67—22no—
209C22×C4×C67—44no—
210C22×C4×C67C22×C414yes—
211C22×C4×C67C2×D411yescharacteristic
212C22×C4×C67C2×D412yes—
213C22×C4×C67C2×Q814yes—
214C22×C4×C67C2411yescharacteristic
215C22×C4×C67C2412yes—
216M16×C67C22×C4116yescomplemented
217C2×C8×C67C22×C418yescomplemented
218C2×C8×C67C2414yes—
219C4⋊C4×C67—24no—
220C4⋊C4×C67—22no—
221C4⋊C4×C67—21no—
222C4⋊C4×C67—21no—
223C4⋊C4×C67C2412yes—
224C4⋊C4×C67C2414yes—
225C4⋊C4×C67C2412yes—
226C22⋊C4×C67—24no—
227C42×C67—24no—
228C23×C67—22no—
229C23×C67—22no—
230C23×C67C2×C4⋊C414yes—
231C23×C67C22×D412yes—
232C23×C67C22×D411yescharacteristic
233C22×D67—22no—
234C22×D67—22no—
235C22×D67—28no—
236C22×D67—28no—
237C22×D67—232no—
238C22×D67C2×C4⋊C414yes—
239C22×D67C2×C4⋊C4116yes—
240C22×D67C2×C4⋊C414yes—
241C22×D67AGL(1,ℤ/8)14yes—
242C22×D67#13714yes—
243C22×D67C22×D412yes—
244C22×D67C22×D412yes—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—24no—
248C2×C4×C67—48no—
249C2×C4×C67—44no—
250C2×C4×C67—42no—
251C2×C4×C67—42no—
252C2×C4×C67C2×C4⋊C418yes—
253C2×C4×C67C2×C4⋊C414yes—
254C2×C4×C67C23×C412yes—
255C2×C4×C67C23×C414yes—
256C2×C4×C67C22×D412yes—
257C2×C4×C67C22×D411yescharacteristic
258C2×C4×C67C22×Q814yes—
259C2×C4×C67C22×Q812yes—
260C2×C4×C67C2511yescharacteristic
261C2×Dic67—22no—
262C2×Dic67—22no—
263C2×Dic67—24no—
264C2×Dic67—48no—
265C2×Dic67—44no—
266C2×Dic67—42no—
267C2×Dic67—42no—
268C2×Dic67C2×C4⋊C4116yes—
269C2×Dic67C2×C4⋊C414yes—
270C2×Dic67C2×C4⋊C414yes—
271C2×Dic67C22×D412yes—
272C2×Dic67C22×D412yes—
273C4×D67—416no—
274C4×D67—48no—
275C4×D67—416no—
276C4×D67—48no—
277C4×D67C2×C4⋊C4116yes—
278C4×D67C2×C4⋊C418yes—
279C4×D67C2×C4⋊C418yes—
280C4×D67C2×C4⋊C4116yes—
281C4×D67C23×C414yes—
282C4×D67C23×C414yes—
283C4×D67C22×Q814yes—
284C4×D67C22×Q814yes—
285C8×C67C23×C418yescomplemented
286C67⋊C8C23×C418yescomplemented
287C22×C67—28no—
288C22×C67—22no—
289C22×C67—22no—
290C22×C67C22×C4⋊C414yes—
291C22×C67C22×C4⋊C412yes—
292C22×C67C2×AGL(1,ℤ/8)12yes—
293C22×C67C2×#13712yes—
294C22×C67C23×D411yescharacteristic
295C2×D67—28no—
296C2×D67—22no—
297C2×D67—22no—
298C2×D67—232no—
299C2×D67#428116yesdirect product factor
300C2×D67C22×C4⋊C414yes—
301C2×D67C22×C4⋊C414yes—
302C2×D67C2×AGL(1,ℤ/8)14yes—
303C2×D67C2×#13714yes—
304C4×C67—44no—
305C4×C67—42no—
306C4×C67—42no—
307C4×C67C22×C4⋊C412yes—
308C4×C67C22×C4⋊C414yes—
309C4×C67C24×C411yescharacteristic
310C4×C67C23×Q811yescharacteristic
311Dic67—44no—
312Dic67—42no—
313Dic67—42no—
314Dic67C22×C4⋊C414yes—
315Dic67C22×C4⋊C414yes—
316C22×#428—671nomaximal, Sylow
317C2×C67—24no—
318C2×C67C2×#42814yescomplemented
319C2×C67C23×C4⋊C411yescharacteristic
320C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
321C2×C67C22×#13711yescharacteristic
322D67—24no—
323D67C2×#42818yesdirect product factor
324C23×M16—671no—
325C22×#117—671no—
326C23×C4⋊C4—671no—
327C2×#428—6716no—
328C2×#428—672no—
329C2×#428—672no—
330C2×#428—671no—
331C2×#428—671no—
332C2×#428—671no—
333C2×#428D6711yescharacteristic, direct product factor
334C22×#107—672no—
335C22×#106—672no—
336C67C22×#42811yescharacteristic, complemented, Sylow
337C24×C4—671no—
338C24×C4—1341no—
339C22×M16—671no—
340C22×M16—6716no—
341C22×M16—678no—
342C22×M16—672no—
343C22×M16C2×D6711yescharacteristic
344C23×C8—672no—
345C2×#117—671no—
346C2×#117—678no—
347C2×#117—671no—
348C2×#117—671no—
349C2×#117—1341no—
350C2×#117—1341no—
351C2×#117—1344no—
352C2×#117C2×D6711yescharacteristic
353C22×C4⋊C4—671no—
354C22×C4⋊C4—671no—
355C22×C4⋊C4—672no—
356C22×C4⋊C4—671no—
357C22×C4⋊C4—672no—
358C22×C4⋊C4—678no—
359C22×C4⋊C4—1344no—
360C22×C4⋊C4—1341no—
361C22×C4⋊C4—1341no—
362C22×C4⋊C4—1341no—
363C22×C4⋊C4C2×D6711yescharacteristic
364C22×C22⋊C4—1341no—
365C22×C42—1341no—
366#428—678no—
367#428—678no—
368#428—678no—
369#428—6716no—
370#428—6716no—
371#428C2×D6718yesdirect product factor
372C2×#107—672no—
373C2×#107—672no—
374C2×#107—672no—
375C2×#107—6716no—
376C2×#107C2×D6712yescomplemented
377C2×#106—672no—
378C2×#106—672no—
379C2×#106—672no—
380C2×#106—6716no—
381C2×#106C2×D6712yescomplemented
382C25—671no—
383C23×C4—21no—
384C23×C4—2688no—
385C23×C4—671no—
386C23×C4—678no—
387C23×C4—674no—
388C23×C4—671no—
389C23×C4—671no—
390C23×C4—678no—
391C23×C4—671no—
392C23×C4—674no—
393C23×C4—671no—
394C23×C4—1341no—
395C23×C4—1341no—
396C23×C4—1348no—
397C23×C4—1342no—
398C23×C4—1342no—
399C23×C4—1341no—
400C23×C4C22×D6711yescharacteristic
401C2×M16—678no—
402C2×M16—674no—
403C2×M16—6764no—
404C2×M16—6716no—
405C2×M16—678no—
406C2×M16C4×D6718yescomplemented
407C2×M16C22×D6714yes—
408C22×C8—672no—
409C22×C8—6716no—
410C22×C8—678no—
411C22×C8C22×D6712yes—
412#117—22no—
413#117—674no—
414#117—674no—
415#117—674no—
416#117—1348no—
417#117—1348no—
418#117—1342no—
419#117—1342no—
420#117—1342no—
421#117C22×D6714yes—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—672no—
425C2×C4⋊C4—674no—
426C2×C4⋊C4—671no—
427C2×C4⋊C4—671no—
428C2×C4⋊C4—678no—
429C2×C4⋊C4—678no—
430C2×C4⋊C4—674no—
431C2×C4⋊C4—674no—
432C2×C4⋊C4—1348no—
433C2×C4⋊C4—1344no—
434C2×C4⋊C4—1348no—
435C2×C4⋊C4—1344no—
436C2×C4⋊C4—1342no—
437C2×C4⋊C4—1342no—
438C2×C4⋊C4—1348no—
439C2×C4⋊C4—1342no—
440C2×C4⋊C4—1342no—
441C2×C4⋊C4—1341no—
442C2×C4⋊C4—1341no—
443C2×C4⋊C4—1342no—
444C2×C4⋊C4—1341no—
445C2×C4⋊C4C22×D6712yes—
446C2×C4⋊C4C22×D6714yes—
447C2×C4⋊C4C22×D6711yescharacteristic
448C2×C4⋊C4C22×D6711yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—1348no—
451C2×C22⋊C4—1341no—
452C2×C22⋊C4—1341no—
453C2×C22⋊C4—1341no—
454C2×C42—21no—
455C2×C42—1348no—
456C2×C42—1341no—
457C2×C42—1341no—
458C2×C42—1341no—
459#107—678no—
460#107—678no—
461#107—678no—
462#107C22×D6718yescomplemented
463#106—678no—
464#106—678no—
465#106—678no—
466#106C22×D6718yescomplemented
467C24—671no—
468C24—678no—
469C24—674no—
470C24—671no—
471C24—1344no—
472C24—1344no—
473C24D4×D6711yescharacteristic
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—44no—
479C22×C4—2688no—
480C22×C4—2684no—
481C22×C4—2684no—
482C22×C4—26832no—
483C22×C4—2688no—
484C22×C4—2684no—
485C22×C4—678no—
486C22×C4—674no—
487C22×C4—671no—
488C22×C4—671no—
489C22×C4—678no—
490C22×C4—6732no—
491C22×C4—678no—
492C22×C4—674no—
493C22×C4—6716no—
494C22×C4—674no—
495C22×C4—674no—
496C22×C4—672no—
497C22×C4—672no—
498C22×C4—674no—
499C22×C4—674no—
500C22×C4—6716no—
501C22×C4—674no—
502C22×C4—672no—
503C22×C4—672no—
504C22×C4—1344no—
505C22×C4—1344no—
506C22×C4—1348no—
507C22×C4—1348no—
508C22×C4—1344no—
509C22×C4—1341no—
510C22×C4—1341no—
511C22×C4—1342no—
512C22×C4C2×C4×D6714yes—
513C22×C4D4×D6712yes—
514C22×C4D4×D6711yescharacteristic
515C22×C4Q8×D6714yes—
516C22×C4C23×D6712yes—
517C22×C4C23×D6711yescharacteristic
518M16—6716no—
519M16—6732no—
520M16C2×C4×D67116yescomplemented
521C2×C8—678no—
522C2×C8—674no—
523C2×C8—6732no—
524C2×C8C2×C4×D6718yescomplemented
525C2×C8C23×D6714yes—
526C4⋊C4—24no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—672no—
531C4⋊C4—674no—
532C4⋊C4—672no—
533C4⋊C4—1348no—
534C4⋊C4—1348no—
535C4⋊C4—1344no—
536C4⋊C4—1344no—
537C4⋊C4—1344no—
538C4⋊C4—1342no—
539C4⋊C4—1341no—
540C4⋊C4—1341no—
541C4⋊C4C23×D6712yes—
542C4⋊C4C23×D6714yes—
543C4⋊C4C23×D6712yes—
544C22⋊C4—24no—
545C22⋊C4—1344no—
546C22⋊C4—1344no—
547C22⋊C4—1344no—
548C42—24no—
549C42—1344no—
550C42—1344no—
551C42—1344no—
552C23—22no—
553C23—22no—
554C23—674no—
555C23—674no—
556C23—674no—
557C23—672no—
558C23—6716no—
559C23—674no—
560C23—672no—
561C23—1348no—
562C23—13432no—
563C23—1348no—
564C23—1342no—
565C23—1342no—
566C23C4⋊C4×D6714yes—
567C23C2×D4×D6712yes—
568C23C2×D4×D6711yescharacteristic
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—48no—
573C2×C4—44no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—26816no—
577C2×C4—2688no—
578C2×C4—2688no—
579C2×C4—26816no—
580C2×C4—2688no—
581C2×C4—2684no—
582C2×C4—2682no—
583C2×C4—2682no—
584C2×C4—6716no—
585C2×C4—674no—
586C2×C4—674no—
587C2×C4—672no—
588C2×C4—672no—
589C2×C4—678no—
590C2×C4—6716no—
591C2×C4—678no—
592C2×C4—6716no—
593C2×C4—674no—
594C2×C4—674no—
595C2×C4—674no—
596C2×C4—674no—
597C2×C4—1342no—
598C2×C4—1342no—
599C2×C4—1344no—
600C2×C4C4⋊C4×D6718yes—
601C2×C4C4⋊C4×D6714yes—
602C2×C4C22×C4×D6712yes—
603C2×C4C22×C4×D6714yes—
604C2×C4C2×D4×D6712yes—
605C2×C4C2×D4×D6711yescharacteristic
606C2×C4C2×Q8×D6714yes—
607C2×C4C2×Q8×D6712yes—
608C2×C4C24×D6711yescharacteristic
609C8—678no—
610C8C22×C4×D6718yescomplemented
611C22—28no—
612C22—22no—
613C22—22no—
614C22—674no—
615C22—6716no—
616C22—674no—
617C22—674no—
618C22—674no—
619C22—13432no—
620C22—1348no—
621C22—1342no—
622C22—1342no—
623C22C2×C4⋊C4×D6714yes—
624C22C2×C4⋊C4×D6712yes—
625C22AGL(1,ℤ/8)×D6712yes—
626C22#137×D6712yes—
627C22C22×D4×D6711yescharacteristic
628C4—44no—
629C4—42no—
630C4—42no—
631C4—2684no—
632C4—2682no—
633C4—2682no—
634C4—674no—
635C4—674no—
636C4C2×C4⋊C4×D6712yes—
637C4C2×C4⋊C4×D6714yes—
638C4C23×C4×D6711yescharacteristic
639C4C22×Q8×D6711yescharacteristic
640C2—24no—
641C2—678no—
642C2—1344no—
643C2#428×D6714yesdirect product factor
644C2C22×C4⋊C4×D6711yescharacteristic
645C2C2×AGL(1,ℤ/8)×D6711yescharacteristic
646C2C2×#137×D6711yescharacteristic
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C24×C4
FrattiniC2×C4C24×D67
FittingC2×#428×C67C2
socleC23×C67C22×D4
prime radicalC24×D67D4
cosocleC2×C4×C67C25
hypercenterC2×#428D67
hypocenterC67C22×#428
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#16863439C2semidirect
5. C2×#16863438C2semidirect
6. C2×#16863437C2semidirect
7. C2×#16863436C2semidirect
8. C2×#16863435C2semidirect
9. #428×D67C2direct (N × H)
10. C2×#107×D67C2semidirect
11. C2×#106×D67C2semidirect
12. C2×#428×C67C2semidirect
17. C2×M16×D67C4semidirect
39. #16863439C22semidirect
40. #16863438C22semidirect
41. #16863437C22semidirect
42. #16863436C22semidirect
43. #16863435C22semidirect
44. C2×#14523977C22semidirect
45. C2×#14523976C22semidirect
46. C2×#14523976C22semidirect
47. #107×D67C22semidirect
48. C2×#14523975C22semidirect
49. C2×#14523974C22semidirect
50. C2×#14523974C22semidirect
51. #106×D67C22semidirect
55. #428×C67C22semidirect
56. C2×#107×C67C22semidirect
57. C2×#106×C67C22semidirect
75. C2×#11761612C2×C4semidirect
77. C2×#11761611C2×C4semidirect
79. M16×D67C2×C4semidirect
81. C2×C8×D67C2×C4semidirect
120. #14523977C23semidirect
121. #14523976C23semidirect
122. #14523976C23semidirect
123. #14523975C23semidirect
124. #14523974C23semidirect
125. #14523974C23semidirect
128. C2×M16×C67C2×C4semidirect
141. #107×C67C23semidirect
142. #106×C67C23semidirect
182. #11761612C22×C4semidirect
183. #11761611C22×C4semidirect
184. C2×C67⋊C8C22×C4semidirect
186. C8×D67C22×C4semidirect
216. M16×C67C22×C4semidirect
217. C2×C8×C67C22×C4semidirect
285. C8×C67C23×C4semidirect
286. C67⋊C8C23×C4semidirect
299. C2×D67#428direct (N × H)
318. C2×C67C2×#428semidirect
323. D67C2×#428direct (N × H)
333. C2×#428D67direct (N × H)
336. C67C22×#428semidirect
371. #428C2×D67direct (N × H)
376. C2×#107C2×D67semidirect
381. C2×#106C2×D67semidirect
406. C2×M16C4×D67semidirect
462. #107C22×D67semidirect
466. #106C22×D67semidirect
520. M16C2×C4×D67semidirect
524. C2×C8C2×C4×D67semidirect
610. C8C22×C4×D67semidirect
643. C2#428×D67direct (N × H)

Maximal subgroups

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

subgroupindex
C22×M16×D672
C2×#117×D672
C22×C4⋊C4×D672
C2×#168634392
C2×#168634382
C2×#168634372
C2×#168634362
C2×#168634352
#428×D672
C2×#107×D672
C2×#106×D672
C2×#428×C672
C22×#42867