Finite Group Databasebeta

← C2×#22602147 #32905634

Subgroups — C2×#22602147 #32905634

Order 18176.

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#22602147C2132yesmaximal, direct product factor
2C2×Q8×Dic142C211yesmaximal, characteristic, complemented
3C2×#17986729C213yesmaximal, complemented
4C2×#17986727C213yesmaximal, complemented
5C2×#17986726C213yesmaximal, complemented
6C2×#17986726C213yesmaximal, complemented
7C2×#17986725C211yesmaximal, characteristic, complemented
8C2×#17986725C211yesmaximal, characteristic, complemented
9C2×#17986629C213yesmaximal
10C2×#17986626C213yesmaximal
11C2×#17986555C213yesmaximal
12C2×#17986553C213yesmaximal
13C2×#17986475C211yesmaximal, characteristic
14C2×#17986475C211yesmaximal, characteristic
15C2×C4×Q8×D71C211yesmaximal, characteristic
16C2×#557×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18Q8×Dic142C22116yescomplemented
19#17986729C22148yescomplemented
20#17986727C22148yescomplemented
21#17986726C22148yescomplemented
22#17986726C22148yescomplemented
23#17986725C22116yescomplemented
24#17986725C22116yescomplemented
25#17986629C22148yes—
26#17986626C22148yes—
27#17986555C22148yes—
28#17986553C22148yes—
29C2×#14556128C2213yes—
30C2×#14556127C2213yes—
31C2×#14556127C2213yes—
32C2×#14556127C2216yes—
33C2×#14556127C2213yes—
34C2×#14556127C2213yes—
35C2×#14556127C2213yes—
36C2×#14556126C2216yes—
37C2×#14556126C2213yes—
38C2×#14556120C2213yes—
39C2×#14556120C2213yes—
40C2×#14556119C2213yes—
41C2×#14556119C2213yes—
42C2×#14556118C2216yes—
43C2×#14556118C2216yes—
44C2×#14556118C2213yes—
45C2×#14556118C2213yes—
46C2×#14556108C2213yes—
47C2×#14556106C2216yes—
48C2×#14556106C2211yescharacteristic
49C2×#14556106C2213yes—
50C2×#14556104C2213yes—
51#17986475C22116yes—
52#17986475C22116yes—
53C2×Q8×Dic71C2211yescharacteristic
54C2×Q8×Dic71C2211yescharacteristic
55C2×Q8×Dic71C2211yescharacteristic
56C2×C4×Dic142C2213yes—
57C2×C4×Dic142C2213yes—
58C2×C4×Dic142C2213yes—
59C2×C4×Dic142C2213yes—
60C2×C4×Dic142C2213yes—
61C2×C4×Dic142C2213yes—
62C2×#14556093C2213yes—
63C2×#14556093C2213yes—
64C2×#14556093C2213yes—
65C2×#14556093C2216yes—
66C2×#14556093C2216yes—
67C4×Q8×D71C22116yes—
68C2×#14556086C2213yes—
69C2×#14556086C2213yes—
70C2×#14556085C2213yes—
71C2×#14556085C2213yes—
72C2×C4⋊C4×D71C2213yes—
73C2×C42×D71C2213yes—
74#557×C71C22116yescomplemented
75C2×C4⋊Q8×C71C2213yes—
76C2×#125×C71C2213yes—
77C2×#125×C71C2213yes—
78C2×C4×Q8×C71C2211yescharacteristic
79C2×C4×Q8×C71C2211yescharacteristic
80C2×C4×Q8×C71C2211yescharacteristic
81C2×C4×Q8×C71C2213yes—
82C22×Dic142C2313yes—
83C22×Dic142C2311yescharacteristic
84C22×Dic142C2316yes—
85C22×Dic142C2313yes—
86C22×Dic142C2313yes—
87C2×Q8×D71Q8116yescomplemented
88C2×Q8×D71C2318yes—
89C22×C4×D71C2311yescharacteristic
90C22×C4×D71C2313yes—
91C22×C4×D71C2313yes—
92#14556128C23124yes—
93#14556127C23124yes—
94#14556127C23124yes—
95#14556127C23148yes—
96#14556127C23124yes—
97#14556127C23124yes—
98#14556127C23124yes—
99#14556126C23148yes—
100#14556126C23124yes—
101#14556120C23124yes—
102#14556120C23124yes—
103#14556119C23124yes—
104#14556119C23124yes—
105#14556118C23148yes—
106#14556118C23148yes—
107#14556118C23124yes—
108#14556118C23124yes—
109#14556108C23124yes—
110#14556106C23148yes—
111#14556106C2318yes—
112#14556106C23124yes—
113#14556104C23124yes—
114Q8×Dic71C2318yes—
115Q8×Dic71C2318yes—
116Q8×Dic71C2318yes—
117C4×Dic142C23124yes—
118C4×Dic142C23124yes—
119C4×Dic142C23124yes—
120C4×Dic142C23124yes—
121C4×Dic142C23124yes—
122C4×Dic142C23124yes—
123#14556093C23124yes—
124#14556093C23124yes—
125#14556093C23148yes—
126#14556093C23124yes—
127#14556093C23148yes—
128#14556086C23124yes—
129#14556086C23124yes—
130#14556085C23124yes—
131#14556085C23124yes—
132C2×C4⋊Dic71C2313yes—
133C2×C4⋊Dic71C2313yes—
134C2×C4⋊Dic71C2313yes—
135C2×C4⋊Dic71C2313yes—
136C2×C4⋊Dic71C2313yes—
137C2×C4⋊Dic71C2313yes—
138C2×Dic71⋊C4C2316yes—
139C2×Dic71⋊C4C2313yes—
140C2×Dic71⋊C4C2313yes—
141C2×Dic71⋊C4C2313yes—
142C2×Dic71⋊C4C2313yes—
143C2×Dic71⋊C4C2313yes—
144C2×Dic71⋊C4C2313yes—
145C2×Dic71⋊C4C2316yes—
146C2×Dic71⋊C4C2316yes—
147C2×Dic71⋊C4C2311yescharacteristic
148C2×Dic71⋊C4C2311yescharacteristic
149C2×Dic71⋊C4C2313yes—
150C2×Dic71⋊C4C2313yes—
151C4⋊C4×D71C23124yes—
152C2×(C2×D71)⋊C4C2311yescharacteristic
153C2×(C2×D71)⋊C4C2311yescharacteristic
154C2×(C2×D71)⋊C4C2313yes—
155C2×(C2×D71)⋊C4C2313yes—
156C2×C4×Dic71C2313yes—
157C2×C4×Dic71C2313yes—
158C2×C4×Dic71C2313yes—
159C2×C4×Dic71C2313yes—
160C2×C4×Dic71C2313yes—
161C2×C4×Dic71C2316yes—
162C2×C4×Dic71C2316yes—
163C42×D71C23124yes—
164C22×Q8×C71C2313yes—
165C22×Q8×C71C2311yescharacteristic
166C4⋊Q8×C71C23124yes—
167#125×C71C23124yes—
168#125×C71C23124yes—
169C4×Q8×C71C2318yes—
170C4×Q8×C71C2318yes—
171C4×Q8×C71C23124yes—
172C4×Q8×C71C2318yes—
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2313yes—
175C2×C4⋊C4×C71C2313yes—
176C2×C4⋊C4×C71C2313yes—
177C2×C4⋊C4×C71C2313yes—
178C2×C4⋊C4×C71C2313yes—
179C2×C4⋊C4×C71C2316yes—
180C2×C42×C71C2313yes—
181C2×C42×C71C2313yes—
182C2×C42×C71C2313yes—
183C23×D71C2411yescharacteristic
184C2×Dic142—212no—
185C2×Dic142—24no—
186C2×Dic142—412no—
187C2×Dic142—46no—
188C2×Dic142C2×Q8124yes—
189C2×Dic142C24112yes—
190C2×Dic142C2414yes—
191C2×Dic142C24124yes—
192C2×Dic142C24112yes—
193C2×Dic142C24112yes—
194Q8×D71C2×Q8164yescomplemented
195C22×Dic71C2413yes—
196C22×Dic71C2413yes—
197C22×Dic71C2411yescharacteristic
198C22×Dic71C2413yes—
199C22×Dic71C2411yescharacteristic
200C22×Dic71C2413yes—
201C22×Dic71C2411yescharacteristic
202C2×C4×D71—24no—
203C2×C4×D71—46no—
204C2×C4×D71C2×Q8124yes—
205C2×C4×D71C2414yes—
206C2×C4×D71C24112yes—
207C2×C4×D71C24112yes—
208C4⋊Dic71C24112yes—
209C4⋊Dic71C24112yes—
210C4⋊Dic71C24112yes—
211C4⋊Dic71C24112yes—
212C4⋊Dic71C24112yes—
213C4⋊Dic71C24112yes—
214Dic71⋊C4C24124yes—
215Dic71⋊C4C24112yes—
216Dic71⋊C4C24112yes—
217Dic71⋊C4C24112yes—
218Dic71⋊C4C24112yes—
219Dic71⋊C4C24112yes—
220Dic71⋊C4C24112yes—
221Dic71⋊C4C24124yes—
222Dic71⋊C4C24124yes—
223Dic71⋊C4C2414yes—
224Dic71⋊C4C2414yes—
225Dic71⋊C4C24112yes—
226Dic71⋊C4C24112yes—
227(C2×D71)⋊C4C2414yes—
228(C2×D71)⋊C4C2414yes—
229(C2×D71)⋊C4C24112yes—
230(C2×D71)⋊C4C24112yes—
231C4×Dic71C24112yes—
232C4×Dic71C24112yes—
233C4×Dic71C24112yes—
234C4×Dic71C24112yes—
235C4×Dic71C24112yes—
236C4×Dic71C24124yes—
237C4×Dic71C24124yes—
238C2×Q8×C71—46no—
239C2×Q8×C71C2×Q818yes—
240C2×Q8×C71C24112yes—
241C2×Q8×C71C2414yes—
242C22×C4×C71C2413yes—
243C22×C4×C71C2411yescharacteristic
244C22×C4×C71C2413yes—
245C22×C4×C71C2411yescharacteristic
246C22×C4×C71C2413yes—
247C22×C4×C71C2411yescharacteristic
248C22×C4×C71C2413yes—
249C4⋊C4×C71C2414yes—
250C4⋊C4×C71C24112yes—
251C4⋊C4×C71C24112yes—
252C4⋊C4×C71C24112yes—
253C4⋊C4×C71C24112yes—
254C4⋊C4×C71C24112yes—
255C4⋊C4×C71C24124yes—
256C42×C71C24112yes—
257C42×C71C24112yes—
258C42×C71C24112yes—
259C23×C71C2511yescharacteristic
260C22×D71—22no—
261C22×D71—22no—
262C22×D71C22×Q814yes—
263C22×D71C2512yes—
264Q8×C71—412no—
265Q8×C71C22×Q8116yes—
266C2×C4×C71—22no—
267C2×C4×C71—22no—
268C2×C4×C71—26no—
269C2×C4×C71—22no—
270C2×C4×C71—26no—
271C2×C4×C71—26no—
272C2×C4×C71C22×Q8112yes—
273C2×C4×C71C2512yes—
274C2×C4×C71C2512yes—
275C2×C4×C71C2512yes—
276C2×C4×C71C2516yes—
277C2×C4×C71C2516yes—
278C2×C4×C71C2516yes—
279C2×C4×C71C2516yes—
280C2×Dic71—26no—
281C2×Dic71—22no—
282C2×Dic71—26no—
283C2×Dic71—26no—
284C2×Dic71—22no—
285C2×Dic71C22×Q8112yes—
286C2×Dic712−1+414yes—
287C2×Dic71C2512yes—
288C2×Dic71C2516yes—
289C2×Dic71C2512yes—
290C2×Dic71C2516yes—
291C2×Dic71C2516yes—
292C2×Dic71C2516yes—
293C2×Dic71C2512yes—
294C4×D71—28no—
295C4×D71—412no—
296C4×D71C22×Q8148yes—
297Dic142—224no—
298Dic142—28no—
299Dic142—412no—
300Dic142—424no—
301Dic142C22×Q8148yes—
302C22×C71C23×Q812yes—
303C22×C71C2×2−1+412yes—
304C22×C71#58512yes—
305C22×C71C2611yescharacteristic
306C2×D71—22no—
307C2×D71—22no—
308C2×D71—28no—
309C2×D71C23×Q814yes—
310C4×C71—22no—
311C4×C71—26no—
312C4×C71—22no—
313C4×C71—26no—
314C4×C71—26no—
315C4×C71—22no—
316C4×C71C23×Q8112yes—
317Dic71—26no—
318Dic71—22no—
319Dic71—22no—
320Dic71—26no—
321Dic71—26no—
322Dic71C23×Q8112yes—
323Dic71C2×2−1+414yes—
324C2×#3502—711nomaximal, Sylow
325C2×C71#350214yescomplemented
326C2×C71C24×Q811yescharacteristic
327C2×C71C22×2−1+411yescharacteristic
328C2×C71C2×#58511yescharacteristic
329D71—24no—
330#3502—7132no—
331C2×Q82—713no—
332C2×Q82—711no—
333C2×#557—713no—
334C2×#557—713no—
335C2×#557—711no—
336C2×#557—711no—
337C2×#557—713no—
338C2×#557D7111yescharacteristic, complemented
339C2×#544—713no—
340C2×#544—713no—
341C2×#533—713no—
342C2×#533—713no—
343C2×#519—711no—
344C2×#519—711no—
345C22×C4×Q8—711no—
346C71C2×#350211yescharacteristic, complemented, Sylow
347C23×Q8—711no—
348Q82—7148no—
349Q82—7116no—
350#557—7148no—
351#557—7148no—
352#557—7116no—
353#557—7116no—
354#557—7148no—
355#557C2×D71116yescomplemented
356#544—7148no—
357#544—7148no—
358#533—7148no—
359#533—7148no—
360C2×C4⋊Q8—713no—
361C2×C4⋊Q8—716no—
362C2×C4⋊Q8—713no—
363C2×C4⋊Q8—713no—
364C2×C4⋊Q8—713no—
365C2×C4⋊Q8—716no—
366C2×C4⋊Q8—713no—
367C2×C4⋊Q8—713no—
368C2×C4⋊Q8—713no—
369C2×C4⋊Q8C2×D7113yes—
370C2×#125—713no—
371C2×#125—713no—
372C2×#125—716no—
373C2×#125—716no—
374C2×#125—713no—
375C2×#125—713no—
376C2×#125—713no—
377C2×#125—713no—
378C2×#125C2×D7113yes—
379C2×#125C2×D7113yes—
380C2×C22⋊Q8—713no—
381C2×C22⋊Q8—713no—
382C2×C22⋊Q8—711no—
383C2×C22⋊Q8—716no—
384C2×C22⋊Q8—713no—
385#519—7116no—
386#519—7116no—
387C2×C4×Q8—711no—
388C2×C4×Q8—711no—
389C2×C4×Q8—711no—
390C2×C4×Q8—7116no—
391C2×C4×Q8—713no—
392C2×C4×Q8—713no—
393C2×C4×Q8—713no—
394C2×C4×Q8—716no—
395C2×C4×Q8—716no—
396C2×C4×Q8—713no—
397C2×C4×Q8—713no—
398C2×C4×Q8—713no—
399C2×C4×Q8—713no—
400C2×C4×Q8—713no—
401C2×C4×Q8—713no—
402C2×C4×Q8C2×D7111yescharacteristic
403C2×C4×Q8C2×D7111yescharacteristic
404C2×C4×Q8C2×D7111yescharacteristic
405C2×C4×Q8C2×D7113yes—
406C2×#117—713no—
407C2×#117—713no—
408C2×#117—713no—
409C2×#117—713no—
410C22×C4⋊C4—713no—
411C22×C42—713no—
412C22×Q8—7116no—
413C22×Q8—718no—
414C22×Q8—713no—
415C22×Q8—716no—
416C22×Q8—713no—
417C22×Q8—713no—
418C22×Q8—711no—
419C22×Q8C22×D7113yes—
420C22×Q8C22×D7111yescharacteristic
421C23×C4—713no—
422C23×C4—713no—
423C23×C4—711no—
424C4⋊Q8—7124no—
425C4⋊Q8—7148no—
426C4⋊Q8—7124no—
427C4⋊Q8—7124no—
428C4⋊Q8—7124no—
429C4⋊Q8—7148no—
430C4⋊Q8—7124no—
431C4⋊Q8—7124no—
432C4⋊Q8—7124no—
433C4⋊Q8C22×D71124yes—
434#125—7124no—
435#125—7124no—
436#125—7148no—
437#125—7148no—
438#125—7124no—
439#125—7124no—
440#125—7124no—
441#125—7124no—
442#125C22×D71124yes—
443#125C22×D71124yes—
444C22⋊Q8—7124no—
445C22⋊Q8—7124no—
446C22⋊Q8—718no—
447C22⋊Q8—7148no—
448C22⋊Q8—7124no—
449C4×Q8—718no—
450C4×Q8—718no—
451C4×Q8—718no—
452C4×Q8—7124no—
453C4×Q8—7124no—
454C4×Q8—7124no—
455C4×Q8—7148no—
456C4×Q8—7148no—
457C4×Q8—7124no—
458C4×Q8—7124no—
459C4×Q8—7124no—
460C4×Q8—7124no—
461C4×Q8—7124no—
462C4×Q8—7124no—
463C4×Q8C22×D7118yes—
464C4×Q8C22×D7118yes—
465C4×Q8C22×D7118yes—
466C4×Q8C22×D71124yes—
467#117—7124no—
468#117—7124no—
469#117—7124no—
470#117—7124no—
471C2×C4⋊C4—716no—
472C2×C4⋊C4—713no—
473C2×C4⋊C4—713no—
474C2×C4⋊C4—713no—
475C2×C4⋊C4—713no—
476C2×C4⋊C4—713no—
477C2×C4⋊C4—713no—
478C2×C4⋊C4—713no—
479C2×C4⋊C4—713no—
480C2×C4⋊C4—711no—
481C2×C4⋊C4—713no—
482C2×C4⋊C4—711no—
483C2×C4⋊C4—716no—
484C2×C4⋊C4—713no—
485C2×C4⋊C4—716no—
486C2×C4⋊C4—713no—
487C2×C4⋊C4—713no—
488C2×C4⋊C4—713no—
489C2×C4⋊C4—713no—
490C2×C4⋊C4—7124no—
491C2×C4⋊C4C22×D7113yes—
492C2×C4⋊C4C22×D7113yes—
493C2×C4⋊C4C22×D7113yes—
494C2×C4⋊C4C22×D7113yes—
495C2×C4⋊C4C22×D7116yes—
496C2×C4⋊C4C22×D7111yescharacteristic
497C2×C4⋊C4C22×D7113yes—
498C2×C22⋊C4—713no—
499C2×C22⋊C4—711no—
500C2×C22⋊C4—713no—
501C2×C22⋊C4—711no—
502C2×C42—716no—
503C2×C42—716no—
504C2×C42—713no—
505C2×C42—713no—
506C2×C42—713no—
507C2×C42—713no—
508C2×C42—713no—
509C2×C42—7124no—
510C2×C42C22×D7113yes—
511C2×C42C22×D7113yes—
512C2×C42C22×D7113yes—
513C24—711no—
514C2×Q8—46no—
515C2×Q8—2846no—
516C2×Q8—28412no—
517C2×Q8—7164no—
518C2×Q8—7124no—
519C2×Q8—7112no—
520C2×Q8—7124no—
521C2×Q8—7112no—
522C2×Q8—7112no—
523C2×Q8—714no—
524C2×Q8—14212no—
525C2×Q8—1424no—
526C2×Q8Q8×D7118yes—
527C2×Q8C23×D71112yes—
528C2×Q8C23×D7114yes—
529C22×C4—2846no—
530C22×C4—7112no—
531C22×C4—713no—
532C22×C4—711no—
533C22×C4—7124no—
534C22×C4—7112no—
535C22×C4—711no—
536C22×C4—713no—
537C22×C4—711no—
538C22×C4—713no—
539C22×C4—713no—
540C22×C4—714no—
541C22×C4—1424no—
542C22×C4C23×D7111yescharacteristic
543C22×C4C23×D7113yes—
544C22×C4C23×D7113yes—
545C22×C4C23×D7113yes—
546C22×C4C23×D7111yescharacteristic
547C22×C4C23×D7111yescharacteristic
548C22×C4C23×D7113yes—
549C4⋊C4—7124no—
550C4⋊C4—7112no—
551C4⋊C4—7112no—
552C4⋊C4—7112no—
553C4⋊C4—7112no—
554C4⋊C4—7112no—
555C4⋊C4—714no—
556C4⋊C4—7112no—
557C4⋊C4—714no—
558C4⋊C4—7124no—
559C4⋊C4—7124no—
560C4⋊C4—7112no—
561C4⋊C4—7112no—
562C4⋊C4—7112no—
563C4⋊C4—7112no—
564C4⋊C4—7112no—
565C4⋊C4—7112no—
566C4⋊C4—7112no—
567C4⋊C4—7112no—
568C4⋊C4C23×D71112yes—
569C4⋊C4C23×D71112yes—
570C4⋊C4C23×D71112yes—
571C4⋊C4C23×D71112yes—
572C4⋊C4C23×D71124yes—
573C4⋊C4C23×D7114yes—
574C4⋊C4C23×D71112yes—
575C22⋊C4—7112no—
576C22⋊C4—714no—
577C22⋊C4—7112no—
578C22⋊C4—714no—
579C42—7112no—
580C42—7112no—
581C42—7112no—
582C42—7124no—
583C42—7124no—
584C42—7112no—
585C42—7112no—
586C42C23×D71112yes—
587C42C23×D71112yes—
588C42C23×D71112yes—
589C23—714no—
590C23—712no—
591C23—1422no—
592C23—1422no—
593C23C24×D7111yescharacteristic
594Q8—412no—
595Q8—28412no—
596Q8—28424no—
597Q8—7148no—
598Q8—14224no—
599Q8—1428no—
600Q8C2×Q8×D71116yes—
601C2×C4—22no—
602C2×C4—26no—
603C2×C4—22no—
604C2×C4—26no—
605C2×C4—22no—
606C2×C4—26no—
607C2×C4—28412no—
608C2×C4—7112no—
609C2×C4—714no—
610C2×C4—716no—
611C2×C4—712no—
612C2×C4—7148no—
613C2×C4—712no—
614C2×C4—716no—
615C2×C4—712no—
616C2×C4—716no—
617C2×C4—716no—
618C2×C4—1428no—
619C2×C4—1422no—
620C2×C4—1426no—
621C2×C4—1426no—
622C2×C4—1422no—
623C2×C4—1426no—
624C2×C4C2×Q8×D71112yes—
625C2×C4C24×D7112yes—
626C2×C4C24×D7116yes—
627C2×C4C24×D7116yes—
628C2×C4C24×D7116yes—
629C2×C4C24×D7112yes—
630C2×C4C24×D7112yes—
631C2×C4C24×D7116yes—
632C22—714no—
633C22—1422no—
634C22—1422no—
635C22—1428no—
636C22C22×Q8×D7112yes—
637C222−1+4×D7112yes—
638C22#1798683512yes—
639C22C25×D7111yescharacteristic
640C4—22no—
641C4—26no—
642C4—22no—
643C4—26no—
644C4—22no—
645C4—26no—
646C4—7112no—
647C4—714no—
648C4—1422no—
649C4—1426no—
650C4—1426no—
651C4—1422no—
652C4—1426no—
653C4C22×Q8×D71112yes—
654C2—1424no—
655C2#2260214714yesdirect product factor
656C2C23×Q8×D7111yescharacteristic
657C2C2×2−1+4×D7111yescharacteristic
658C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
prime radicalC23×D71C24
hypercenterC2×#557D71
hypocenterC71C2×#3502
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602147C2direct (N × H)
2. C2×Q8×Dic142C2semidirect
3. C2×#17986729C2semidirect
4. C2×#17986727C2semidirect
5. C2×#17986726C2semidirect
6. C2×#17986726C2semidirect
7. C2×#17986725C2semidirect
8. C2×#17986725C2semidirect
16. C2×#557×C71C2semidirect
18. Q8×Dic142C22semidirect
19. #17986729C22semidirect
20. #17986727C22semidirect
21. #17986726C22semidirect
22. #17986726C22semidirect
23. #17986725C22semidirect
24. #17986725C22semidirect
74. #557×C71C22semidirect
87. C2×Q8×D71Q8semidirect
194. Q8×D71C2×Q8semidirect
325. C2×C71#3502semidirect
338. C2×#557D71semidirect
346. C71C2×#3502semidirect
355. #557C2×D71semidirect
655. C2#22602147direct (N × H)

Maximal subgroups

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

subgroupindex
#226021472
C2×Q8×Dic1422
C2×#179867292
C2×#179867272
C2×#179867262
C2×#179867252
C2×#179866292
C2×#179866262
C2×#179865552
C2×#179865532
C2×#179864752
C2×C4×Q8×D712
C2×#557×C712
C2×#350271