Finite Group Databasebeta

← C2×#22574016 #31764013

Subgroups — C2×#22574016 #31764013

Order 17152.

6826 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574016C2132yesmaximal, direct product factor
2C2×Q8×Dic134C211yesmaximal, characteristic, complemented
3C2×#16864126C213yesmaximal, complemented
4C2×#16864124C213yesmaximal, complemented
5C2×#16864123C213yesmaximal, complemented
6C2×#16864123C213yesmaximal, complemented
7C2×#16864122C211yesmaximal, characteristic, complemented
8C2×#16864122C211yesmaximal, characteristic, complemented
9C2×#16864026C213yesmaximal
10C2×#16864023C213yesmaximal
11C2×#16863952C213yesmaximal
12C2×#16863950C213yesmaximal
13C2×#16863872C211yesmaximal, characteristic
14C2×#16863872C211yesmaximal, characteristic
15C2×C4×Q8×D67C211yesmaximal, characteristic
16C2×#557×C67C211yesmaximal, characteristic, complemented
17C22×Q8×D67C2211yescharacteristic
18Q8×Dic134C22116yescomplemented
19#16864126C22148yescomplemented
20#16864124C22148yescomplemented
21#16864123C22148yescomplemented
22#16864123C22148yescomplemented
23#16864122C22116yescomplemented
24#16864122C22116yescomplemented
25#16864026C22148yes—
26#16864023C22148yes—
27#16863952C22148yes—
28#16863950C22148yes—
29C2×#14524043C2213yes—
30C2×#14524042C2213yes—
31C2×#14524042C2213yes—
32C2×#14524042C2216yes—
33C2×#14524042C2213yes—
34C2×#14524042C2213yes—
35C2×#14524042C2213yes—
36C2×#14524041C2216yes—
37C2×#14524041C2213yes—
38C2×#14524035C2213yes—
39C2×#14524035C2213yes—
40C2×#14524034C2213yes—
41C2×#14524034C2213yes—
42C2×#14524033C2216yes—
43C2×#14524033C2216yes—
44C2×#14524033C2213yes—
45C2×#14524033C2213yes—
46C2×#14524023C2213yes—
47C2×#14524021C2216yes—
48C2×#14524021C2211yescharacteristic
49C2×#14524021C2213yes—
50C2×#14524019C2213yes—
51#16863872C22116yes—
52#16863872C22116yes—
53C2×Q8×Dic67C2211yescharacteristic
54C2×Q8×Dic67C2211yescharacteristic
55C2×Q8×Dic67C2211yescharacteristic
56C2×C4×Dic134C2213yes—
57C2×C4×Dic134C2213yes—
58C2×C4×Dic134C2213yes—
59C2×C4×Dic134C2213yes—
60C2×C4×Dic134C2213yes—
61C2×C4×Dic134C2213yes—
62C2×#14524008C2213yes—
63C2×#14524008C2213yes—
64C2×#14524008C2213yes—
65C2×#14524008C2216yes—
66C2×#14524008C2216yes—
67C4×Q8×D67C22116yes—
68C2×#14524001C2213yes—
69C2×#14524001C2213yes—
70C2×#14524000C2213yes—
71C2×#14524000C2213yes—
72C2×C4⋊C4×D67C2213yes—
73C2×C42×D67C2213yes—
74#557×C67C22116yescomplemented
75C2×C4⋊Q8×C67C2213yes—
76C2×#125×C67C2213yes—
77C2×#125×C67C2213yes—
78C2×C4×Q8×C67C2211yescharacteristic
79C2×C4×Q8×C67C2211yescharacteristic
80C2×C4×Q8×C67C2211yescharacteristic
81C2×C4×Q8×C67C2213yes—
82C22×Dic134C2313yes—
83C22×Dic134C2311yescharacteristic
84C22×Dic134C2316yes—
85C22×Dic134C2313yes—
86C22×Dic134C2313yes—
87C2×Q8×D67Q8116yescomplemented
88C2×Q8×D67C2318yes—
89C22×C4×D67C2311yescharacteristic
90C22×C4×D67C2313yes—
91C22×C4×D67C2313yes—
92#14524043C23124yes—
93#14524042C23124yes—
94#14524042C23124yes—
95#14524042C23148yes—
96#14524042C23124yes—
97#14524042C23124yes—
98#14524042C23124yes—
99#14524041C23148yes—
100#14524041C23124yes—
101#14524035C23124yes—
102#14524035C23124yes—
103#14524034C23124yes—
104#14524034C23124yes—
105#14524033C23148yes—
106#14524033C23148yes—
107#14524033C23124yes—
108#14524033C23124yes—
109#14524023C23124yes—
110#14524021C23148yes—
111#14524021C2318yes—
112#14524021C23124yes—
113#14524019C23124yes—
114Q8×Dic67C2318yes—
115Q8×Dic67C2318yes—
116Q8×Dic67C2318yes—
117C4×Dic134C23124yes—
118C4×Dic134C23124yes—
119C4×Dic134C23124yes—
120C4×Dic134C23124yes—
121C4×Dic134C23124yes—
122C4×Dic134C23124yes—
123#14524008C23124yes—
124#14524008C23124yes—
125#14524008C23148yes—
126#14524008C23124yes—
127#14524008C23148yes—
128#14524001C23124yes—
129#14524001C23124yes—
130#14524000C23124yes—
131#14524000C23124yes—
132C2×C4⋊Dic67C2313yes—
133C2×C4⋊Dic67C2313yes—
134C2×C4⋊Dic67C2313yes—
135C2×C4⋊Dic67C2313yes—
136C2×C4⋊Dic67C2313yes—
137C2×C4⋊Dic67C2313yes—
138C2×Dic67⋊C4C2316yes—
139C2×Dic67⋊C4C2313yes—
140C2×Dic67⋊C4C2313yes—
141C2×Dic67⋊C4C2313yes—
142C2×Dic67⋊C4C2313yes—
143C2×Dic67⋊C4C2313yes—
144C2×Dic67⋊C4C2313yes—
145C2×Dic67⋊C4C2316yes—
146C2×Dic67⋊C4C2316yes—
147C2×Dic67⋊C4C2311yescharacteristic
148C2×Dic67⋊C4C2311yescharacteristic
149C2×Dic67⋊C4C2313yes—
150C2×Dic67⋊C4C2313yes—
151C4⋊C4×D67C23124yes—
152C2×(C2×D67)⋊C4C2311yescharacteristic
153C2×(C2×D67)⋊C4C2311yescharacteristic
154C2×(C2×D67)⋊C4C2313yes—
155C2×(C2×D67)⋊C4C2313yes—
156C2×C4×Dic67C2313yes—
157C2×C4×Dic67C2313yes—
158C2×C4×Dic67C2313yes—
159C2×C4×Dic67C2313yes—
160C2×C4×Dic67C2313yes—
161C2×C4×Dic67C2316yes—
162C2×C4×Dic67C2316yes—
163C42×D67C23124yes—
164C22×Q8×C67C2313yes—
165C22×Q8×C67C2311yescharacteristic
166C4⋊Q8×C67C23124yes—
167#125×C67C23124yes—
168#125×C67C23124yes—
169C4×Q8×C67C2318yes—
170C4×Q8×C67C2318yes—
171C4×Q8×C67C23124yes—
172C4×Q8×C67C2318yes—
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C4⋊C4×C67C2313yes—
175C2×C4⋊C4×C67C2313yes—
176C2×C4⋊C4×C67C2313yes—
177C2×C4⋊C4×C67C2313yes—
178C2×C4⋊C4×C67C2313yes—
179C2×C4⋊C4×C67C2316yes—
180C2×C42×C67C2313yes—
181C2×C42×C67C2313yes—
182C2×C42×C67C2313yes—
183C23×D67C2411yescharacteristic
184C2×Dic134—212no—
185C2×Dic134—24no—
186C2×Dic134—412no—
187C2×Dic134—46no—
188C2×Dic134C2×Q8124yes—
189C2×Dic134C24112yes—
190C2×Dic134C2414yes—
191C2×Dic134C24124yes—
192C2×Dic134C24112yes—
193C2×Dic134C24112yes—
194Q8×D67C2×Q8164yescomplemented
195C22×Dic67C2411yescharacteristic
196C22×Dic67C2413yes—
197C22×Dic67C2411yescharacteristic
198C22×Dic67C2413yes—
199C22×Dic67C2413yes—
200C22×Dic67C2413yes—
201C22×Dic67C2411yescharacteristic
202C2×C4×D67—24no—
203C2×C4×D67—46no—
204C2×C4×D67C2×Q8124yes—
205C2×C4×D67C2414yes—
206C2×C4×D67C24112yes—
207C2×C4×D67C24112yes—
208C4⋊Dic67C24112yes—
209C4⋊Dic67C24112yes—
210C4⋊Dic67C24112yes—
211C4⋊Dic67C24112yes—
212C4⋊Dic67C24112yes—
213C4⋊Dic67C24112yes—
214Dic67⋊C4C24124yes—
215Dic67⋊C4C24112yes—
216Dic67⋊C4C24112yes—
217Dic67⋊C4C24112yes—
218Dic67⋊C4C24112yes—
219Dic67⋊C4C24112yes—
220Dic67⋊C4C24112yes—
221Dic67⋊C4C24124yes—
222Dic67⋊C4C24124yes—
223Dic67⋊C4C2414yes—
224Dic67⋊C4C2414yes—
225Dic67⋊C4C24112yes—
226Dic67⋊C4C24112yes—
227(C2×D67)⋊C4C2414yes—
228(C2×D67)⋊C4C2414yes—
229(C2×D67)⋊C4C24112yes—
230(C2×D67)⋊C4C24112yes—
231C4×Dic67C24112yes—
232C4×Dic67C24112yes—
233C4×Dic67C24112yes—
234C4×Dic67C24112yes—
235C4×Dic67C24112yes—
236C4×Dic67C24124yes—
237C4×Dic67C24124yes—
238C2×Q8×C67—46no—
239C2×Q8×C67C2×Q818yes—
240C2×Q8×C67C24112yes—
241C2×Q8×C67C2414yes—
242C22×C4×C67C2411yescharacteristic
243C22×C4×C67C2411yescharacteristic
244C22×C4×C67C2411yescharacteristic
245C22×C4×C67C2413yes—
246C22×C4×C67C2413yes—
247C22×C4×C67C2413yes—
248C22×C4×C67C2413yes—
249C4⋊C4×C67C2414yes—
250C4⋊C4×C67C24112yes—
251C4⋊C4×C67C24112yes—
252C4⋊C4×C67C24112yes—
253C4⋊C4×C67C24112yes—
254C4⋊C4×C67C24112yes—
255C4⋊C4×C67C24124yes—
256C42×C67C24112yes—
257C42×C67C24112yes—
258C42×C67C24112yes—
259C23×C67C2511yescharacteristic
260C22×D67—22no—
261C22×D67—22no—
262C22×D67C22×Q814yes—
263C22×D67C2512yes—
264Q8×C67—412no—
265Q8×C67C22×Q8116yes—
266C2×C4×C67—22no—
267C2×C4×C67—22no—
268C2×C4×C67—26no—
269C2×C4×C67—22no—
270C2×C4×C67—26no—
271C2×C4×C67—26no—
272C2×C4×C67C22×Q8112yes—
273C2×C4×C67C2512yes—
274C2×C4×C67C2512yes—
275C2×C4×C67C2512yes—
276C2×C4×C67C2516yes—
277C2×C4×C67C2516yes—
278C2×C4×C67C2516yes—
279C2×C4×C67C2516yes—
280C2×Dic67—22no—
281C2×Dic67—26no—
282C2×Dic67—26no—
283C2×Dic67—22no—
284C2×Dic67—26no—
285C2×Dic67C22×Q8112yes—
286C2×Dic672−1+414yes—
287C2×Dic67C2512yes—
288C2×Dic67C2516yes—
289C2×Dic67C2512yes—
290C2×Dic67C2516yes—
291C2×Dic67C2516yes—
292C2×Dic67C2516yes—
293C2×Dic67C2512yes—
294C4×D67—28no—
295C4×D67—412no—
296C4×D67C22×Q8148yes—
297Dic134—224no—
298Dic134—28no—
299Dic134—412no—
300Dic134—424no—
301Dic134C22×Q8148yes—
302C22×C67C23×Q812yes—
303C22×C67C2×2−1+412yes—
304C22×C67#58512yes—
305C22×C67C2611yescharacteristic
306C2×D67—22no—
307C2×D67—22no—
308C2×D67—28no—
309C2×D67C23×Q814yes—
310C4×C67—22no—
311C4×C67—26no—
312C4×C67—22no—
313C4×C67—26no—
314C4×C67—26no—
315C4×C67—22no—
316C4×C67C23×Q8112yes—
317Dic67—26no—
318Dic67—22no—
319Dic67—22no—
320Dic67—26no—
321Dic67—26no—
322Dic67C23×Q8112yes—
323Dic67C2×2−1+414yes—
324C2×#3502—671nomaximal, Sylow
325C2×C67#350214yescomplemented
326C2×C67C24×Q811yescharacteristic
327C2×C67C22×2−1+411yescharacteristic
328C2×C67C2×#58511yescharacteristic
329D67—24no—
330#3502—6732no—
331C2×Q82—673no—
332C2×Q82—671no—
333C2×#557—673no—
334C2×#557—673no—
335C2×#557—671no—
336C2×#557—671no—
337C2×#557—673no—
338C2×#557D6711yescharacteristic, complemented
339C2×#544—673no—
340C2×#544—673no—
341C2×#533—673no—
342C2×#533—673no—
343C2×#519—671no—
344C2×#519—671no—
345C22×C4×Q8—671no—
346C67C2×#350211yescharacteristic, complemented, Sylow
347C23×Q8—671no—
348Q82—6748no—
349Q82—6716no—
350#557—6748no—
351#557—6748no—
352#557—6716no—
353#557—6716no—
354#557—6748no—
355#557C2×D67116yescomplemented
356#544—6748no—
357#544—6748no—
358#533—6748no—
359#533—6748no—
360C2×C4⋊Q8—673no—
361C2×C4⋊Q8—676no—
362C2×C4⋊Q8—673no—
363C2×C4⋊Q8—673no—
364C2×C4⋊Q8—673no—
365C2×C4⋊Q8—676no—
366C2×C4⋊Q8—673no—
367C2×C4⋊Q8—673no—
368C2×C4⋊Q8—673no—
369C2×C4⋊Q8C2×D6713yes—
370C2×#125—673no—
371C2×#125—673no—
372C2×#125—676no—
373C2×#125—676no—
374C2×#125—673no—
375C2×#125—673no—
376C2×#125—673no—
377C2×#125—673no—
378C2×#125C2×D6713yes—
379C2×#125C2×D6713yes—
380C2×C22⋊Q8—673no—
381C2×C22⋊Q8—673no—
382C2×C22⋊Q8—671no—
383C2×C22⋊Q8—676no—
384C2×C22⋊Q8—673no—
385#519—6716no—
386#519—6716no—
387C2×C4×Q8—671no—
388C2×C4×Q8—671no—
389C2×C4×Q8—671no—
390C2×C4×Q8—6716no—
391C2×C4×Q8—673no—
392C2×C4×Q8—673no—
393C2×C4×Q8—673no—
394C2×C4×Q8—676no—
395C2×C4×Q8—676no—
396C2×C4×Q8—673no—
397C2×C4×Q8—673no—
398C2×C4×Q8—673no—
399C2×C4×Q8—673no—
400C2×C4×Q8—673no—
401C2×C4×Q8—673no—
402C2×C4×Q8C2×D6711yescharacteristic
403C2×C4×Q8C2×D6711yescharacteristic
404C2×C4×Q8C2×D6711yescharacteristic
405C2×C4×Q8C2×D6713yes—
406C2×#117—673no—
407C2×#117—673no—
408C2×#117—673no—
409C2×#117—673no—
410C22×C4⋊C4—673no—
411C22×C42—673no—
412C22×Q8—6716no—
413C22×Q8—678no—
414C22×Q8—673no—
415C22×Q8—676no—
416C22×Q8—673no—
417C22×Q8—673no—
418C22×Q8—671no—
419C22×Q8C22×D6713yes—
420C22×Q8C22×D6711yescharacteristic
421C23×C4—673no—
422C23×C4—673no—
423C23×C4—671no—
424C4⋊Q8—6724no—
425C4⋊Q8—6748no—
426C4⋊Q8—6724no—
427C4⋊Q8—6724no—
428C4⋊Q8—6724no—
429C4⋊Q8—6748no—
430C4⋊Q8—6724no—
431C4⋊Q8—6724no—
432C4⋊Q8—6724no—
433C4⋊Q8C22×D67124yes—
434#125—6724no—
435#125—6724no—
436#125—6748no—
437#125—6748no—
438#125—6724no—
439#125—6724no—
440#125—6724no—
441#125—6724no—
442#125C22×D67124yes—
443#125C22×D67124yes—
444C22⋊Q8—6724no—
445C22⋊Q8—6724no—
446C22⋊Q8—678no—
447C22⋊Q8—6748no—
448C22⋊Q8—6724no—
449C4×Q8—678no—
450C4×Q8—678no—
451C4×Q8—678no—
452C4×Q8—6724no—
453C4×Q8—6724no—
454C4×Q8—6724no—
455C4×Q8—6748no—
456C4×Q8—6748no—
457C4×Q8—6724no—
458C4×Q8—6724no—
459C4×Q8—6724no—
460C4×Q8—6724no—
461C4×Q8—6724no—
462C4×Q8—6724no—
463C4×Q8C22×D6718yes—
464C4×Q8C22×D6718yes—
465C4×Q8C22×D6718yes—
466C4×Q8C22×D67124yes—
467#117—6724no—
468#117—6724no—
469#117—6724no—
470#117—6724no—
471C2×C4⋊C4—676no—
472C2×C4⋊C4—673no—
473C2×C4⋊C4—673no—
474C2×C4⋊C4—673no—
475C2×C4⋊C4—673no—
476C2×C4⋊C4—673no—
477C2×C4⋊C4—673no—
478C2×C4⋊C4—673no—
479C2×C4⋊C4—673no—
480C2×C4⋊C4—671no—
481C2×C4⋊C4—673no—
482C2×C4⋊C4—671no—
483C2×C4⋊C4—676no—
484C2×C4⋊C4—673no—
485C2×C4⋊C4—676no—
486C2×C4⋊C4—673no—
487C2×C4⋊C4—673no—
488C2×C4⋊C4—673no—
489C2×C4⋊C4—673no—
490C2×C4⋊C4—6724no—
491C2×C4⋊C4C22×D6713yes—
492C2×C4⋊C4C22×D6713yes—
493C2×C4⋊C4C22×D6713yes—
494C2×C4⋊C4C22×D6713yes—
495C2×C4⋊C4C22×D6716yes—
496C2×C4⋊C4C22×D6711yescharacteristic
497C2×C4⋊C4C22×D6713yes—
498C2×C22⋊C4—673no—
499C2×C22⋊C4—671no—
500C2×C22⋊C4—673no—
501C2×C22⋊C4—671no—
502C2×C42—676no—
503C2×C42—676no—
504C2×C42—673no—
505C2×C42—673no—
506C2×C42—673no—
507C2×C42—673no—
508C2×C42—673no—
509C2×C42—6724no—
510C2×C42C22×D6713yes—
511C2×C42C22×D6713yes—
512C2×C42C22×D6713yes—
513C24—671no—
514C2×Q8—46no—
515C2×Q8—2686no—
516C2×Q8—26812no—
517C2×Q8—6764no—
518C2×Q8—6724no—
519C2×Q8—6712no—
520C2×Q8—6724no—
521C2×Q8—6712no—
522C2×Q8—6712no—
523C2×Q8—674no—
524C2×Q8—13412no—
525C2×Q8—1344no—
526C2×Q8Q8×D6718yes—
527C2×Q8C23×D67112yes—
528C2×Q8C23×D6714yes—
529C22×C4—2686no—
530C22×C4—6712no—
531C22×C4—673no—
532C22×C4—671no—
533C22×C4—6724no—
534C22×C4—6712no—
535C22×C4—671no—
536C22×C4—673no—
537C22×C4—671no—
538C22×C4—673no—
539C22×C4—673no—
540C22×C4—674no—
541C22×C4—1344no—
542C22×C4C23×D6711yescharacteristic
543C22×C4C23×D6713yes—
544C22×C4C23×D6713yes—
545C22×C4C23×D6713yes—
546C22×C4C23×D6711yescharacteristic
547C22×C4C23×D6711yescharacteristic
548C22×C4C23×D6713yes—
549C4⋊C4—6724no—
550C4⋊C4—6712no—
551C4⋊C4—6712no—
552C4⋊C4—6712no—
553C4⋊C4—6712no—
554C4⋊C4—6712no—
555C4⋊C4—6712no—
556C4⋊C4—6712no—
557C4⋊C4—6712no—
558C4⋊C4—674no—
559C4⋊C4—6712no—
560C4⋊C4—674no—
561C4⋊C4—6724no—
562C4⋊C4—6712no—
563C4⋊C4—6724no—
564C4⋊C4—6712no—
565C4⋊C4—6712no—
566C4⋊C4—6712no—
567C4⋊C4—6712no—
568C4⋊C4C23×D67112yes—
569C4⋊C4C23×D67112yes—
570C4⋊C4C23×D67112yes—
571C4⋊C4C23×D67112yes—
572C4⋊C4C23×D67124yes—
573C4⋊C4C23×D6714yes—
574C4⋊C4C23×D67112yes—
575C22⋊C4—6712no—
576C22⋊C4—674no—
577C22⋊C4—6712no—
578C22⋊C4—674no—
579C42—6712no—
580C42—6712no—
581C42—6712no—
582C42—6724no—
583C42—6724no—
584C42—6712no—
585C42—6712no—
586C42C23×D67112yes—
587C42C23×D67112yes—
588C42C23×D67112yes—
589C23—674no—
590C23—672no—
591C23—1342no—
592C23—1342no—
593C23C24×D6711yescharacteristic
594Q8—412no—
595Q8—26812no—
596Q8—26824no—
597Q8—6748no—
598Q8—13424no—
599Q8—1348no—
600Q8C2×Q8×D67116yes—
601C2×C4—22no—
602C2×C4—26no—
603C2×C4—22no—
604C2×C4—26no—
605C2×C4—22no—
606C2×C4—26no—
607C2×C4—26812no—
608C2×C4—6712no—
609C2×C4—674no—
610C2×C4—676no—
611C2×C4—672no—
612C2×C4—6748no—
613C2×C4—672no—
614C2×C4—676no—
615C2×C4—672no—
616C2×C4—676no—
617C2×C4—676no—
618C2×C4—1348no—
619C2×C4—1342no—
620C2×C4—1346no—
621C2×C4—1346no—
622C2×C4—1342no—
623C2×C4—1346no—
624C2×C4C2×Q8×D67112yes—
625C2×C4C24×D6712yes—
626C2×C4C24×D6716yes—
627C2×C4C24×D6716yes—
628C2×C4C24×D6716yes—
629C2×C4C24×D6712yes—
630C2×C4C24×D6712yes—
631C2×C4C24×D6716yes—
632C22—674no—
633C22—1342no—
634C22—1342no—
635C22—1348no—
636C22C22×Q8×D6712yes—
637C222−1+4×D6712yes—
638C22#1686423212yes—
639C22C25×D6711yescharacteristic
640C4—22no—
641C4—26no—
642C4—22no—
643C4—26no—
644C4—22no—
645C4—26no—
646C4—6712no—
647C4—674no—
648C4—1342no—
649C4—1346no—
650C4—1346no—
651C4—1342no—
652C4—1346no—
653C4C22×Q8×D67112yes—
654C2—1344no—
655C2#2257401614yesdirect product factor
656C2C23×Q8×D6711yescharacteristic
657C2C2×2−1+4×D6711yescharacteristic
658C2C2×#1686423211yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#557×C67C2
socleC23×C67C25
prime radicalC23×D67C24
hypercenterC2×#557D67
hypocenterC67C2×#3502
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22574016C2direct (N × H)
2. C2×Q8×Dic134C2semidirect
3. C2×#16864126C2semidirect
4. C2×#16864124C2semidirect
5. C2×#16864123C2semidirect
6. C2×#16864123C2semidirect
7. C2×#16864122C2semidirect
8. C2×#16864122C2semidirect
16. C2×#557×C67C2semidirect
18. Q8×Dic134C22semidirect
19. #16864126C22semidirect
20. #16864124C22semidirect
21. #16864123C22semidirect
22. #16864123C22semidirect
23. #16864122C22semidirect
24. #16864122C22semidirect
74. #557×C67C22semidirect
87. C2×Q8×D67Q8semidirect
194. Q8×D67C2×Q8semidirect
325. C2×C67#3502semidirect
338. C2×#557D67semidirect
346. C67C2×#3502semidirect
355. #557C2×D67semidirect
655. C2#22574016direct (N × H)

Maximal subgroups

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

subgroupindex
#225740162
C2×Q8×Dic1342
C2×#168641262
C2×#168641242
C2×#168641232
C2×#168641222
C2×#168640262
C2×#168640232
C2×#168639522
C2×#168639502
C2×#168638722
C2×C4×Q8×D672
C2×#557×C672
C2×#350267