Finite Group Databasebeta

← C4×#16864065 #31015682

Subgroups — C4×#16864065 #31015682

Order 17152.

3420 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864065C211yesmaximal, characteristic
2C2×C4×#11761629C211yesmaximal, characteristic, complemented
3#22563271C213yesmaximal, complemented
4#22563247C213yesmaximal, complemented
5#22563243C213yesmaximal, complemented
6#22563159C213yesmaximal, complemented
7Q8×Dic67⋊C4C211yesmaximal, characteristic, complemented
8#22563050C211yesmaximal, characteristic, complemented
9#22563047C211yesmaximal, characteristic, complemented
10C4×#14524039C213yesmaximal, complemented
11C4×#14524017C213yesmaximal, complemented
12C4×#14524014C213yesmaximal, complemented
13C4×Q8×Dic67C211yesmaximal, characteristic, complemented
14C42×C22⋊D67C213yesmaximal, complemented
15C2×C4×#41×C67C211yesmaximal, characteristic, complemented
16C22×#11761629C2211yescharacteristic
17#16864065C4116yesdirect product factor
18C2×#14524039C2213yes—
19C2×#14524017C2213yes—
20C2×#14524014C2213yes—
21C4×#11761629—28no—
22C2×Q8×Dic67C2211yescharacteristic
23C2×Q8×Dic67C2211yescharacteristic
24C2×Q8×Dic67C2211yescharacteristic
25C2×C4×D268C2213yes—
26C2×#14524005C2213yes—
27C2×C4×C22⋊D67C2213yes—
28C2×C4×C22⋊D67C2213yes—
29C2×C4×C22⋊D67C2216yes—
30C2×C4×C22⋊D67C2213yes—
31C2×#14524001C2213yes—
32C2×C42×D67C2213yes—
33#16863299C2213yes—
34#16863299C2213yes—
35#16863298C2213yes—
36#16863297C2213yes—
37#16863296C2216yes—
38#16863296C2216yes—
39#16863294C2213yes—
40#16863292C2213yes—
41#16863287C2216yes—
42#16863284C2216yes—
43#16863275C2216yes—
44#16863272C2216yes—
45#16863265C2213yes—
46#16863256C2213yes—
47#16863253C2213yes—
48C4⋊C4×Dic67C2213yes—
49C4⋊C4×Dic67C2213yes—
50C4×Dic67⋊C4C2213yes—
51C4×Dic67⋊C4C2213yes—
52C4×Dic67⋊C4C2211yescharacteristic
53C4×C4⋊Dic67C2213yes—
54C4×(C2×D67)⋊C4C2213yes—
55C4×(C2×D67)⋊C4C2213yes—
56C4×(C2×D67)⋊C4C2213yes—
57C4×C22⋊Dic67C2213yes—
58C4×C22⋊Dic67C2213yes—
59C4×C22⋊Dic67C2213yes—
60C42×Dic67C2213yes—
61C22×#41×C67C2211yescharacteristic
62C4×#41×C67—28no—
63C2×C4×Q8×C67C2211yescharacteristic
64C2×C4×Q8×C67C2211yescharacteristic
65C2×C4×D4×C67C2213yes—
66C2×C4×D4×C67C2213yes—
67C2×#117×C67C2213yes—
68C22×C42×C67C2213yes—
69C2×#11761629—24no—
70C2×#11761629—24no—
71C2×#11761629C2×C418yescomplemented
72C22×D268C2313yes—
73C22×C22⋊D67C2313yes—
74C22×C22⋊D67C2316yes—
75C22×C4×D67C2313yes—
76C22×C4×D67C2313yes—
77C22×C4×D67C2313yes—
78#14524039C2×C4124yescomplemented
79#14524017C2×C4124yescomplemented
80#14524014C2×C4124yescomplemented
81Q8×Dic67—24no—
82Q8×Dic67—24no—
83Q8×Dic67C2×C418yescomplemented
84C4×D268—212no—
85#14524005—212no—
86C4×C22⋊D67—212no—
87C4×C22⋊D67—212no—
88C4×C22⋊D67—412no—
89C4×C22⋊D67C2×C4124yescomplemented
90#14524001—212no—
91C2×C4⋊Dic67C2313yes—
92C2×C4⋊Dic67C2313yes—
93C2×C4⋊Dic67C2313yes—
94C2×Dic67⋊C4C2313yes—
95C2×Dic67⋊C4C2316yes—
96C2×Dic67⋊C4C2311yescharacteristic
97C2×Dic67⋊C4C2311yescharacteristic
98C2×C22⋊Dic67C2313yes—
99C2×C22⋊Dic67C2313yes—
100C2×C22⋊Dic67C2316yes—
101C2×C22⋊Dic67C2313yes—
102C2×(C2×D67)⋊C4C2313yes—
103C2×(C2×D67)⋊C4C2313yes—
104C2×(C2×D67)⋊C4C2316yes—
105C2×(C2×D67)⋊C4C2316yes—
106C2×(C2×D67)⋊C4C2313yes—
107C2×C4×Dic67C2313yes—
108C2×C4×Dic67C2313yes—
109C2×C4×Dic67C2313yes—
110C2×C4×Dic67C2311yescharacteristic
111C2×C4×Dic67C2313yes—
112C2×C4×Dic67C2313yes—
113C2×C4×Dic67C2313yes—
114C2×C4×Dic67C2313yes—
115C2×C4×Dic67C2311yescharacteristic
116C42×D67—212no—
117C67⋊#95C2311yescharacteristic
118C67⋊#95C2311yescharacteristic
119C67⋊#95C2313yes—
120C67⋊#95C2313yes—
121C67⋊#95C2313yes—
122C67⋊#95C2313yes—
123C67⋊#95C2316yes—
124C2×#41×C67—24no—
125C2×#41×C67—24no—
126C2×#41×C67C2×C418yescomplemented
127C22×Q8×C67C2311yescharacteristic
128C22×D4×C67C2313yes—
129C23×C4×C67C2313yes—
130C23×C4×C67C2313yes—
131C23×C4×C67C2313yes—
132C4×Q8×C67—24no—
133C4×Q8×C67D418yescomplemented
134C4×D4×C67—212no—
135C4×D4×C67—212no—
136#117×C67—212no—
137C2×C4⋊C4×C67C2313yes—
138C2×C4⋊C4×C67C2313yes—
139C2×C22⋊C4×C67C2316yes—
140C2×C42×C67—212no—
141C2×C42×C67C2311yescharacteristic
142C2×C42×C67C2313yes—
143C2×C42×C67C2313yes—
144C2×C42×C67C2313yes—
145C23×D67C2413yes—
146#11761629—232no—
147C2×D268—26no—
148C2×D268—26no—
149C2×D268C22×C4112yes—
150C2×C22⋊D67—26no—
151C2×C22⋊D67—26no—
152C2×C22⋊D67—46no—
153C2×C22⋊D67—46no—
154C2×C22⋊D67C22×C4112yes—
155C2×C22⋊D67C22×C4124yes—
156C22×Dic67C2413yes—
157C22×Dic67C2413yes—
158C22×Dic67C2411yescharacteristic
159C22×Dic67C2413yes—
160C22×Dic67C2411yescharacteristic
161C22×Dic67C2411yescharacteristic
162C22×Dic67C2411yescharacteristic
163C2×C4×D67—26no—
164C2×C4×D67—26no—
165C2×C4×D67—26no—
166C2×C4×D67—26no—
167C2×C4×D67—26no—
168C2×C4×D67—26no—
169C2×C4×D67—26no—
170C2×C4×D67—43no—
171C2×C4×D67C22×C4112yes—
172C4⋊Dic67—26no—
173C4⋊Dic67—26no—
174C4⋊Dic67C22×C4112yes—
175Dic67⋊C4—26no—
176Dic67⋊C4—46no—
177Dic67⋊C4C22×C414yes—
178Dic67⋊C4#4114yescomplemented
179C22⋊Dic67—26no—
180C22⋊Dic67—26no—
181C22⋊Dic67—46no—
182C22⋊Dic67C22×C4112yes—
183(C2×D67)⋊C4—212no—
184(C2×D67)⋊C4—26no—
185(C2×D67)⋊C4—26no—
186(C2×D67)⋊C4—46no—
187(C2×D67)⋊C4C22×C4112yes—
188C4×Dic67—22no—
189C4×Dic67—26no—
190C4×Dic67—26no—
191C4×Dic67—26no—
192C4×Dic67—26no—
193C4×Dic67—26no—
194C4×Dic67—43no—
195C4×Dic67C22×C4112yes—
196C4×Dic67#4114yescomplemented
197C24×C67C2413yes—
198#41×C67—232no—
199C2×Q8×C67C22×C414yes—
200C2×Q8×C67C2×D414yes—
201C2×Q8×C67#4114yes—
202C2×D4×C67—26no—
203C2×D4×C67—26no—
204C2×D4×C67C22×C4112yes—
205C22×C4×C67—26no—
206C22×C4×C67—26no—
207C22×C4×C67—26no—
208C22×C4×C67—26no—
209C22×C4×C67—26no—
210C22×C4×C67—26no—
211C22×C4×C67—26no—
212C22×C4×C67—43no—
213C22×C4×C67C22×C4112yes—
214C22×C4×C67C2413yes—
215C22×C4×C67C2411yescharacteristic
216C22×C4×C67C2413yes—
217C22×C4×C67C2411yescharacteristic
218C22×C4×C67C2413yes—
219C22×C4×C67C2411yescharacteristic
220C4⋊C4×C67—26no—
221C4⋊C4×C67C2×D4112yes—
222C22⋊C4×C67—212no—
223C42×C67—22no—
224C42×C67—26no—
225C42×C67—26no—
226C42×C67C2×D4112yes—
227C23×C67—23no—
228C23×C67—23no—
229C23×C67—23no—
230C23×C67—23no—
231C23×C67—23no—
232C23×C67—23no—
233C23×C67C23×C416yes—
234C23×C67C2511yescharacteristic
235C22×D67—23no—
236C22×D67—23no—
237C22×D67—23no—
238C22×D67—23no—
239C22×D67—23no—
240C22×D67—23no—
241C22×D67C23×C416yes—
242Q8×C67C4×D4116yescomplemented
243D4×C67—224no—
244C2×C4×C67—21no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—23no—
248C2×C4×C67—21no—
249C2×C4×C67—23no—
250C2×C4×C67—224no—
251C2×C4×C67—23no—
252C2×C4×C67—23no—
253C2×C4×C67—23no—
254C2×C4×C67—412no—
255C2×C4×C67—412no—
256C2×C4×C67C23×C412yes—
257C2×C4×C67C23×C416yes—
258C2×C4×C67C22×D416yes—
259C2×C4×C67C22×D416yes—
260C2×C4×C67C22×D412yes—
261C2×C4×C67C2×#4112yes—
262C2×C4×C67C2×#4112yes—
263C2×C4×C67C2×#4116yes—
264C2×C4×C67H(5,𝔽2)12yes—
265C22⋊D67—224no—
266C22⋊D67—424no—
267C2×Dic67—21no—
268C2×Dic67—21no—
269C2×Dic67—21no—
270C2×Dic67—21no—
271C2×Dic67—23no—
272C2×Dic67—21no—
273C2×Dic67—23no—
274C2×Dic67—21no—
275C2×Dic67—23no—
276C2×Dic67—23no—
277C2×Dic67—23no—
278C2×Dic67—23no—
279C2×Dic67—23no—
280C2×Dic67—23no—
281C2×Dic67C23×C416yes—
282C2×Dic67C23×C412yes—
283C2×Dic67C23×C412yes—
284C2×Dic67C2×#4112yes—
285C2×Dic67C2×#4112yes—
286C2×Dic67C2×#4112yes—
287C2×Dic67C2×#4112yes—
288D268—224no—
289C4×D67—224no—
290C4×D67—412no—
291C4×D67—412no—
292C22×C67—26no—
293C22×C67—26no—
294C22×C67—26no—
295C22×C67—43no—
296C22×C67—43no—
297C22×C67—43no—
298C22×C67—43no—
299C22×C67C24×C411yescharacteristic
300C22×C67C23×D411yescharacteristic
301C22×C67C22×#4111yescharacteristic
302C22×C67C22×#4111yescharacteristic
303C22×C67C22×#4111yescharacteristic
304C22×C67C2×H(5,𝔽2)11yescharacteristic
305C22×C67#58511yescharacteristic
306C2×D67—26no—
307C2×D67—26no—
308C2×D67—26no—
309C2×D67—43no—
310C2×D67—43no—
311C2×D67—43no—
312C2×D67—43no—
313C4×C67—22no—
314C4×C67—26no—
315C4×C67—22no—
316C4×C67—43no—
317C4×C67C2×C4×D4112yes—
318C4×C67#55014yescomplemented
319Dic67—22no—
320Dic67—26no—
321Dic67—22no—
322Dic67—22no—
323Dic67—43no—
324Dic67—43no—
325Dic67C4×#4114yescomplemented
326C4×#550—671nomaximal, Sylow
327C2×C67—46no—
328C2×C67C22×C4×D411yescharacteristic
329C2×C67C2×C4×#4111yescharacteristic
330C2×C67C4×H(5,𝔽2)11yescharacteristic
331C2×C67C2×#55011yescharacteristic
332C2×C67D4×#4111yescharacteristic
333C2×C67#348011yescharacteristic
334C2×C67#348311yescharacteristic
335D67—46no—
336C2×#550—671no—
337C2×C4×#41—671no—
338C2×C4×#41D6711yescharacteristic, complemented
339#2366—673no—
340#2363—673no—
341#2363—673no—
342#2354—673no—
343Q8×C4⋊C4—671no—
344#2341—671no—
345#2341—671no—
346C4×#127—673no—
347C4×#121—673no—
348C4×#121—673no—
349C42×Q8—671no—
350C42×D4—673no—
351C67C4×#55011yescharacteristic, complemented, Sylow
352C22×#41—671no—
353C22×#41C2×D6711yescharacteristic
354#550—6716no—
355C2×#127—673no—
356C2×#121—673no—
357C2×#121—673no—
358C4×#41—28no—
359C4×#41—1348no—
360C2×C4×Q8—671no—
361C2×C4×Q8—671no—
362C2×C4×Q8—671no—
363C2×C4×Q8C2×D6711yescharacteristic
364C2×C4×Q8C2×D6711yescharacteristic
365C2×C4×D4—676no—
366C2×C4×D4—673no—
367C2×C4×D4—673no—
368C2×C4×D4—673no—
369C2×C4×D4—673no—
370C2×C4×D4—673no—
371C2×C4×D4C2×D6713yes—
372C2×C4×D4C2×D6713yes—
373C2×#117—673no—
374C2×#117C2×D6713yes—
375C22×C42—673no—
376C22×C42C2×D6713yes—
377#390—673no—
378#390—673no—
379#390—673no—
380#390—676no—
381#390—676no—
382#390—673no—
383#389—673no—
384#389—673no—
385#388—676no—
386#388—676no—
387#386—676no—
388#386—676no—
389#384—673no—
390#380—673no—
391#380—673no—
392C4×C4⋊C4—673no—
393C4×C4⋊C4—673no—
394C4×C4⋊C4—673no—
395C4×C4⋊C4—673no—
396C4×C4⋊C4—673no—
397C4×C4⋊C4—671no—
398C4×C22⋊C4—673no—
399C4×C22⋊C4—673no—
400C4×C22⋊C4—673no—
401C4×C22⋊C4—673no—
402C4×C22⋊C4—673no—
403C4×C22⋊C4—673no—
404C43—673no—
405C2×#41—24no—
406C2×#41—24no—
407C2×#41—678no—
408C2×#41—1344no—
409C2×#41—1344no—
410C2×#41C4×D6718yescomplemented
411C22×Q8C22×D6711yescharacteristic
412C22×D4—676no—
413C22×D4—673no—
414C22×D4—673no—
415C22×D4C22×D6713yes—
416C23×C4—673no—
417C23×C4—673no—
418C23×C4—673no—
419C23×C4C22×D6713yes—
420C23×C4C22×D6713yes—
421C23×C4C22×D6713yes—
422#127—6724no—
423#121—6724no—
424#121—6724no—
425C4×Q8—24no—
426C4×Q8—678no—
427C4×Q8—1344no—
428C4×Q8—1344no—
429C4×Q8C22⋊D6718yescomplemented
430C4×D4—212no—
431C4×D4—212no—
432C4×D4—26812no—
433C4×D4—6724no—
434C4×D4—13412no—
435C4×D4—13412no—
436C4×D4—13412no—
437C4×D4—13412no—
438#117—212no—
439#117—13412no—
440C2×C4⋊C4—676no—
441C2×C4⋊C4—671no—
442C2×C4⋊C4—671no—
443C2×C4⋊C4—673no—
444C2×C4⋊C4—673no—
445C2×C4⋊C4—673no—
446C2×C4⋊C4—673no—
447C2×C4⋊C4C22×D6713yes—
448C2×C4⋊C4C22×D6713yes—
449C2×C22⋊C4—676no—
450C2×C22⋊C4—676no—
451C2×C22⋊C4—673no—
452C2×C22⋊C4—673no—
453C2×C22⋊C4—673no—
454C2×C22⋊C4—673no—
455C2×C22⋊C4—676no—
456C2×C22⋊C4—673no—
457C2×C22⋊C4—673no—
458C2×C22⋊C4C22×D6716yes—
459C2×C42—212no—
460C2×C42—673no—
461C2×C42—673no—
462C2×C42—671no—
463C2×C42—673no—
464C2×C42—673no—
465C2×C42—673no—
466C2×C42—673no—
467C2×C42—673no—
468C2×C42—671no—
469C2×C42—13412no—
470C2×C42C22×D6713yes—
471C2×C42C22×D6713yes—
472C2×C42C22×D6711yescharacteristic
473C2×C42C22×D6713yes—
474#95—671no—
475#95—671no—
476#95—673no—
477#95—673no—
478#95—673no—
479#95—673no—
480#95—676no—
481C24—673no—
482C24C23×D6713yes—
483#41—232no—
484#41—13432no—
485C2×Q8C2×C4×D6714yes—
486C2×Q8C2×C22⋊D6714yes—
487C2×Q8#1176162814yes—
488C2×D4—26no—
489C2×D4—26no—
490C2×D4—2686no—
491C2×D4—2686no—
492C2×D4—6724no—
493C2×D4—6712no—
494C2×D4—6712no—
495C2×D4—1346no—
496C2×D4—1346no—
497C2×D4—1346no—
498C2×D4—1346no—
499C2×D4C2×C4×D67112yes—
500C22×C4—26no—
501C22×C4—26no—
502C22×C4—26no—
503C22×C4—26no—
504C22×C4—26no—
505C22×C4—26no—
506C22×C4—26no—
507C22×C4—43no—
508C22×C4—2683no—
509C22×C4—671no—
510C22×C4—671no—
511C22×C4—671no—
512C22×C4—673no—
513C22×C4—671no—
514C22×C4—6712no—
515C22×C4—673no—
516C22×C4—673no—
517C22×C4—1346no—
518C22×C4—1346no—
519C22×C4—1346no—
520C22×C4—1346no—
521C22×C4—1346no—
522C22×C4—1346no—
523C22×C4—1346no—
524C22×C4C2×C4×D67112yes—
525C22×C4C23×D6713yes—
526C22×C4C23×D6711yescharacteristic
527C22×C4C23×D6713yes—
528C22×C4C23×D6711yescharacteristic
529C22×C4C23×D6713yes—
530C22×C4C23×D6711yescharacteristic
531C4⋊C4—26no—
532C4⋊C4—2686no—
533C4⋊C4—674no—
534C4⋊C4—6712no—
535C4⋊C4—674no—
536C4⋊C4—1346no—
537C4⋊C4—1346no—
538C4⋊C4—1346no—
539C4⋊C4C2×C22⋊D67112yes—
540C22⋊C4—212no—
541C22⋊C4—2686no—
542C22⋊C4—2686no—
543C22⋊C4—6712no—
544C22⋊C4—6712no—
545C22⋊C4—1346no—
546C22⋊C4—1346no—
547C22⋊C4—1346no—
548C22⋊C4—13412no—
549C22⋊C4—1346no—
550C42—22no—
551C42—26no—
552C42—26no—
553C42—2683no—
554C42—6712no—
555C42—674no—
556C42—1346no—
557C42—1342no—
558C42—1346no—
559C42—1346no—
560C42—1346no—
561C42—1346no—
562C42C2×C22⋊D67112yes—
563C23—23no—
564C23—23no—
565C23—23no—
566C23—23no—
567C23—23no—
568C23—23no—
569C23—676no—
570C23—1343no—
571C23—1343no—
572C23—1343no—
573C23—1343no—
574C23—1343no—
575C23—1343no—
576C23C22×C4×D6716yes—
577C23C24×D6711yescharacteristic
578Q8C4×C22⋊D67116yescomplemented
579D4—224no—
580D4—26824no—
581D4—13424no—
582D4—13424no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—23no—
586C2×C4—21no—
587C2×C4—23no—
588C2×C4—21no—
589C2×C4—224no—
590C2×C4—23no—
591C2×C4—23no—
592C2×C4—23no—
593C2×C4—412no—
594C2×C4—412no—
595C2×C4—26812no—
596C2×C4—26812no—
597C2×C4—672no—
598C2×C4—672no—
599C2×C4—672no—
600C2×C4—676no—
601C2×C4—672no—
602C2×C4—672no—
603C2×C4—672no—
604C2×C4—1343no—
605C2×C4—1343no—
606C2×C4—1343no—
607C2×C4—1343no—
608C2×C4—1343no—
609C2×C4—1343no—
610C2×C4—1341no—
611C2×C4—1341no—
612C2×C4—1341no—
613C2×C4—1341no—
614C2×C4—1343no—
615C2×C4—1341no—
616C2×C4—1343no—
617C2×C4—1341no—
618C2×C4—13424no—
619C2×C4C22×C4×D6712yes—
620C2×C4C22×C4×D6716yes—
621C2×C4C22×C22⋊D6716yes—
622C2×C4C22×C22⋊D6712yes—
623C2×C4C22×C22⋊D6716yes—
624C2×C4#41×D6712yes—
625C2×C4#41×D6712yes—
626C2×C4C2×#1176162816yes—
627C2×C4#1452408912yes—
628C22—26no—
629C22—26no—
630C22—26no—
631C22—43no—
632C22—43no—
633C22—43no—
634C22—43no—
635C22—2683no—
636C22—2683no—
637C22—2683no—
638C22—2683no—
639C22—1346no—
640C22—1346no—
641C22—1346no—
642C22C23×C4×D6711yescharacteristic
643C22C23×C22⋊D6711yescharacteristic
644C22C2×#41×D6711yescharacteristic
645C22C2×#41×D6711yescharacteristic
646C22C22×#1176162811yescharacteristic
647C22C2×#1452408911yescharacteristic
648C22#1686423211yescharacteristic
649C4—22no—
650C4—22no—
651C4—26no—
652C4—43no—
653C4—2683no—
654C4—2683no—
655C4—674no—
656C4—1342no—
657C4—1346no—
658C4—1342no—
659C4—1342no—
660C4C2×C4×C22⋊D67112yes—
661C4#1686406514yesdirect product factor
662C2—46no—
663C2—2686no—
664C2C22×C4×C22⋊D6711yescharacteristic
665C2C4×#41×D6711yescharacteristic
666C2C4×#1452408911yescharacteristic
667C2C2×#1686406511yescharacteristic
668C2#41×C22⋊D6711yescharacteristic
669C2#2257380711yescharacteristic
670C2#2257383511yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×C4×#41×C67C2
socle, cosocleC23×C67C25
prime radicalC2×#16864065C2
hypercenterC2×C4×#41D67
hypocenterC67C4×#550
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11761629C2semidirect
3. #22563271C2semidirect
4. #22563247C2semidirect
5. #22563243C2semidirect
6. #22563159C2semidirect
7. Q8×Dic67⋊C4C2semidirect
8. #22563050C2semidirect
9. #22563047C2semidirect
10. C4×#14524039C2semidirect
11. C4×#14524017C2semidirect
12. C4×#14524014C2semidirect
13. C4×Q8×Dic67C2semidirect
14. C42×C22⋊D67C2semidirect
15. C2×C4×#41×C67C2semidirect
17. #16864065C4direct (N × H)
71. C2×#11761629C2×C4semidirect
78. #14524039C2×C4semidirect
79. #14524017C2×C4semidirect
80. #14524014C2×C4semidirect
83. Q8×Dic67C2×C4semidirect
89. C4×C22⋊D67C2×C4semidirect
126. C2×#41×C67C2×C4semidirect
133. C4×Q8×C67D4semidirect
178. Dic67⋊C4#41semidirect
196. C4×Dic67#41semidirect
242. Q8×C67C4×D4semidirect
318. C4×C67#550semidirect
325. Dic67C4×#41semidirect
338. C2×C4×#41D67semidirect
351. C67C4×#550semidirect
410. C2×#41C4×D67semidirect
429. C4×Q8C22⋊D67semidirect
578. Q8C4×C22⋊D67semidirect
661. C4#16864065direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640652
C2×C4×#117616292
#225632712
#225632472
#225632432
#225631592
Q8×Dic67⋊C42
#225630502
#225630472
C4×#145240392
C4×#145240172
C4×#145240142
C4×Q8×Dic672
C42×C22⋊D672
C2×C4×#41×C672
C4×#55067