Finite Group Databasebeta

← C2×#86752 #11703407

Subgroups — C2×#86752 #11703407

Order 768.

7022 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C2×Q8×#67C211yesmaximal, characteristic, complemented
3C2×Q8×#67C211yesmaximal, characteristic, complemented
4C2×#5812C211yesmaximal, characteristic, complemented
5C22×Q8×Dic3C211yesmaximal, characteristic, complemented
6#86752C2132yesmaximal, direct product factor
7C2×#5731C213yesmaximal, complemented
8C2×#5721C213yesmaximal, complemented
9C2×#5641C213yesmaximal, complemented
10C2×#5642C213yesmaximal, complemented
11C2×#5625C213yesmaximal, complemented
12C2×#5622C213yesmaximal, complemented
13C2×#5572C211yesmaximal, characteristic, complemented
14C2×#5569C211yesmaximal, characteristic, complemented
15C2×#5541C213yesmaximal, complemented
16C2×#5538C213yesmaximal
17C2×#3523—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic
21C3×D4×Q8C22116yescomplemented
22C2×C3×C4⋊Q8C2213yes—
23C2×C3×C22⋊Q8C2213yes—
24C2×C3×C22⋊Q8C2213yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2213yes—
27Q8×#67C22116yescomplemented
28Q8×#67C22116yescomplemented
29C2×#946C2213yes—
30C2×#946C2213yes—
31#5812C22116yescomplemented
32C2×Q8×Dic3C2211yescharacteristic
33C2×Q8×Dic3C2211yescharacteristic
34C2×Q8×Dic3C2211yescharacteristic
35C2×Q8×Dic3C2213yes—
36C2×Q8×Dic3C2213yes—
37C2×Q8×Dic3C2213yes—
38C2×Q8×Dic3C2213yes—
39C2×Q8×Dic3C22116yescomplemented
40C2×#944C2213yes—
41C2×#944C2213yes—
42C2×#939C2211yescharacteristic
43C2×#935C2213yes—
44C2×C4×#67C2213yes—
45C2×C4×#67C2213yes—
46C2×#926C2213yes—
47C2×#926C2213yes—
48C22×C4⋊Dic3C2213yes—
49C2×#924C2213yes—
50C2×#924C2213yes—
51C22×C4×Dic3C2213yes—
52#5731C22148yescomplemented
53#5721C22148yescomplemented
54#5642C22148yescomplemented
55#5641C22148yescomplemented
56#5625C22148yescomplemented
57#5622C22148yescomplemented
58#5572C22116yescomplemented
59#5569C22116yescomplemented
60#5541C22148yescomplemented
61#5538C22148yes—
62C2×#898C2213yes—
63C2×#898C2216yes—
64C2×#892C2213yes—
65C2×#890C2213yes—
66C2×#890C2216yes—
67C2×#889C2213yes—
68C2×#889C2216yes—
69C2×#889C2216yes—
70C2×#888C2213yes—
71C2×#887C2213yes—
72C2×#887C2216yes—
73C2×#886C2213yes—
74C2×#885C2213yes—
75C2×#879C2213yes—
76C2×#879C2216yes—
77C2×#878C2213yes—
78C2×#877C2216yes—
79C2×#872C2213yes—
80C2×#870C2213yes—
81C2×C4×Dic6C2213yes—
82C2×C4×Dic6C2213yes—
83#3523—332no—
84C2×#557—33no—
85C2×#557—31no—
86C2×#556—33no—
87C2×#552—33no—
88C2×#552—33no—
89C2×D4×Q8—31no—
90C2×D4×Q8—31no—
91C2×D4×Q8D311yescharacteristic, complemented
92C2×#541—33no—
93C2×#541—33no—
94C2×#533—33no—
95C2×#529—33no—
96C2×#519—31no—
97C2×#519—31no—
98C22×C4×Q8—31no—
99C22×C3×Q8—28no—
100C22×C3×Q8—28no—
101C22×C3×Q8C2313yes—
102C22×C3×Q8C2313yes—
103C22×C3×Q8C2318yes—
104C22×C3×Q8C2318yes—
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4C2311yescharacteristic
107C23×C3×C4C2313yes—
108C23×C3×C4C2313yes—
109C22×#67C2311yescharacteristic
110C22×#67C2311yescharacteristic
111C23×Dic3C2313yes—
112C23×Dic3C2311yescharacteristic
113C2×D3×Q8—28no—
114C2×D3×Q8C2318yes—
115C22×C4×D3C2313yes—
116C22×Dic6C2313yes—
117C22×Dic6C2313yes—
118C3×C4⋊Q8C23124yes—
119C3×C22⋊Q8C23124yes—
120C3×C22⋊Q8C23124yes—
121C3×C4×Q8C2318yes—
122C3×C4×D4C23124yes—
123C2×C3×C4⋊C4C2313yes—
124C2×C3×C4⋊C4C2316yes—
125C2×C3×C4⋊C4C2313yes—
126C2×C3×C22⋊C4C2313yes—
127C2×C3×C22⋊C4C2313yes—
128C2×C3×C42C2313yes—
129C2×#217C2313yes—
130C2×#217C2313yes—
131C2×#217C2311yescharacteristic
132C2×#217C2313yes—
133#946C23124yes—
134#946C23124yes—
135Q8×Dic3C23124yes—
136Q8×Dic3C23124yes—
137Q8×Dic3C23124yes—
138Q8×Dic3C23124yes—
139Q8×Dic3C2318yes—
140Q8×Dic3C2318yes—
141Q8×Dic3C2318yes—
142#944C23124yes—
143#944C23124yes—
144#939C2318yes—
145#935C23124yes—
146C4×#67C23124yes—
147C4×#67C23124yes—
148C2×(C2×D3)⋊C4C2311yescharacteristic
149C2×(C2×D3)⋊C4C2313yes—
150C2×(C2×D3)⋊C4C2313yes—
151C2×(C2×D3)⋊C4C2313yes—
152#926C23124yes—
153#926C23124yes—
154C2×C4⋊Dic3C23124yes—
155C2×C4⋊Dic3C2313yes—
156C2×C4⋊Dic3C2313yes—
157C2×C4⋊Dic3C2313yes—
158C2×C4⋊Dic3C2313yes—
159C2×C4⋊Dic3C2313yes—
160C2×C4⋊Dic3C2316yes—
161C2×C4⋊Dic3C2313yes—
162#924C23124yes—
163#924C23124yes—
164C2×Dic3⋊C4C2311yescharacteristic
165C2×Dic3⋊C4C2313yes—
166C2×Dic3⋊C4C2313yes—
167C2×Dic3⋊C4C2316yes—
168C2×Dic3⋊C4C2313yes—
169C2×Dic3⋊C4C2316yes—
170C2×Dic3⋊C4C2313yes—
171C2×Dic3⋊C4C2316yes—
172C2×Dic3⋊C4C2313yes—
173C2×C4×Dic3C2316yes—
174C2×C4×Dic3C2313yes—
175C2×C4×Dic3C2313yes—
176C2×C4×Dic3C2313yes—
177C2×C4×Dic3C2316yes—
178C2×C4×Dic3C2313yes—
179C2×C4×Dic3C2313yes—
180C2×C4×Dic3C23124yes—
181#898C23148yes—
182#898C23124yes—
183#892C23124yes—
184#890C23148yes—
185#890C23124yes—
186#889C23124yes—
187#889C23148yes—
188#889C23148yes—
189#888C23124yes—
190#887C23148yes—
191#887C23124yes—
192#886C23124yes—
193#885C23124yes—
194#879C23148yes—
195#879C23124yes—
196#878C23124yes—
197#877C23148yes—
198#872C23124yes—
199#870C23124yes—
200C4×Dic6C23124yes—
201C4×Dic6C23124yes—
202C23×Q8—31no—
203C23×Q8C2×D311yescharacteristic
204C23×Q8C2×D311yescharacteristic
205#557—348no—
206#557—316no—
207#556—348no—
208#552—348no—
209#552—348no—
210D4×Q8—316no—
211D4×Q8—316no—
212D4×Q8C2×D3116yescomplemented
213#541—348no—
214#541—348no—
215#533—348no—
216C2×C4⋊Q8—33no—
217C2×C4⋊Q8—33no—
218C2×C4⋊Q8—33no—
219C2×C4⋊Q8C2×D313yes—
220#529—348no—
221C2×#126—33no—
222C2×#126—36no—
223C2×#126—33no—
224C2×#126—36no—
225C2×#125—33no—
226C2×#125—36no—
227C2×#125—36no—
228C2×#125—36no—
229C2×#125—33no—
230C2×#125—33no—
231C2×#124—33no—
232C2×#123—33no—
233C2×#123—33no—
234C2×C22⋊Q8—33no—
235C2×C22⋊Q8—33no—
236C2×C22⋊Q8—33no—
237C2×C22⋊Q8—33no—
238C2×C22⋊Q8—33no—
239C2×C22⋊Q8C2×D313yes—
240C2×C22⋊Q8C2×D313yes—
241C2×#121—31no—
242#519—316no—
243#519—316no—
244C2×C4×Q8—31no—
245C2×C4×Q8—33no—
246C2×C4×Q8—31no—
247C2×C4×Q8—33no—
248C2×C4×Q8—316no—
249C2×C4×Q8—33no—
250C2×C4×Q8—31no—
251C2×C4×Q8—33no—
252C2×C4×Q8—33no—
253C2×C4×Q8—36no—
254C2×C4×Q8—33no—
255C2×C4×Q8—33no—
256C2×C4×Q8C2×D311yescharacteristic
257C2×C4×D4—33no—
258C2×C4×D4—33no—
259C2×C4×D4C2×D313yes—
260C2×#117—33no—
261C2×#117—33no—
262C2×#117—33no—
263C2×#117—36no—
264C2×#117—33no—
265C22×C4⋊C4—33no—
266C22×C42—33no—
267C24×C3C2411yescharacteristic
268C24×C3C2411yescharacteristic
269C23×D3C2411yescharacteristic
270C2×C3×Q8—232no—
271C2×C3×Q8—232no—
272C2×C3×Q8—212no—
273C2×C3×Q8—212no—
274C2×C3×Q8#4118yes—
275C2×C3×Q8C24112yes—
276C2×C3×Q8C24112yes—
277C2×C3×Q8C2414yes—
278C2×C3×D4—24no—
279C2×C3×D4C2414yes—
280C22×C3×C4—212no—
281C22×C3×C4—212no—
282C22×C3×C4C2413yes—
283C22×C3×C4C2413yes—
284C22×C3×C4C2413yes—
285C22×C3×C4C24112yes—
286C22×C3×C4C2411yescharacteristic
287C22×C3×C4C24112yes—
288C22×C3×C4C2413yes—
289C2×#67—24no—
290C2×#67—24no—
291C2×#67C2414yes—
292C2×#67C2414yes—
293C22×Dic3—212no—
294C22×Dic3—24no—
295C22×Dic3C24112yes—
296C22×Dic3C2414yes—
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2413yes—
299C22×Dic3C2413yes—
300C22×Dic3C2411yescharacteristic
301C22×Dic3C2413yes—
302C22×Dic3C2413yes—
303C22×Dic3C2411yescharacteristic
304D3×Q8—232no—
305C2×C4×D3—212no—
306C2×C4×D3C24112yes—
307C2×Dic6—212no—
308C2×Dic6—212no—
309C2×Dic6C24112yes—
310C2×Dic6C24112yes—
311C3×C4⋊C4C24112yes—
312C3×C4⋊C4C24124yes—
313C3×C4⋊C4C24112yes—
314C3×C22⋊C4C24112yes—
315C3×C22⋊C4C24112yes—
316C3×C42C24112yes—
317#217C24112yes—
318#217C24112yes—
319#217C2414yes—
320#217C24112yes—
321(C2×D3)⋊C4C2414yes—
322(C2×D3)⋊C4C24112yes—
323(C2×D3)⋊C4C24112yes—
324(C2×D3)⋊C4C24112yes—
325C4⋊Dic3C24112yes—
326C4⋊Dic3C24112yes—
327C4⋊Dic3C24112yes—
328C4⋊Dic3C24112yes—
329C4⋊Dic3C24112yes—
330C4⋊Dic3C24124yes—
331C4⋊Dic3C24112yes—
332Dic3⋊C4C2414yes—
333Dic3⋊C4C24112yes—
334Dic3⋊C4C24112yes—
335Dic3⋊C4C24124yes—
336Dic3⋊C4C24112yes—
337Dic3⋊C4C24124yes—
338Dic3⋊C4C24112yes—
339Dic3⋊C4C24124yes—
340Dic3⋊C4C24112yes—
341C4×Dic3C24124yes—
342C4×Dic3C24112yes—
343C4×Dic3C24112yes—
344C4×Dic3C24112yes—
345C4×Dic3C24124yes—
346C4×Dic3C24112yes—
347C4×Dic3C24112yes—
348C22×Q8—28no—
349C22×Q8—28no—
350C22×Q8—38no—
351C22×Q8—33no—
352C22×Q8—33no—
353C22×Q8—68no—
354C22×Q8C22×D313yes—
355C22×Q8C22×D313yes—
356C22×Q8C22×D318yes—
357C22×Q8C22×D318yes—
358C22×Q8C22×D311yescharacteristic
359C22×D4—31no—
360C22×D4—31no—
361C22×D4C22×D311yescharacteristic
362C23×C4—33no—
363C23×C4—31no—
364C23×C4—33no—
365C23×C4C22×D313yes—
366C23×C4C22×D313yes—
367C4⋊Q8—324no—
368C4⋊Q8—324no—
369C4⋊Q8—324no—
370C4⋊Q8C22×D3124yes—
371#126—324no—
372#126—348no—
373#126—324no—
374#126—348no—
375#125—324no—
376#125—348no—
377#125—348no—
378#125—348no—
379#125—324no—
380#125—324no—
381#124—324no—
382#123—324no—
383#123—324no—
384C22⋊Q8—324no—
385C22⋊Q8—324no—
386C22⋊Q8—324no—
387C22⋊Q8—324no—
388C22⋊Q8—324no—
389C22⋊Q8C22×D3124yes—
390C22⋊Q8C22×D3124yes—
391#121—38no—
392C4×Q8—38no—
393C4×Q8—324no—
394C4×Q8—38no—
395C4×Q8—324no—
396C4×Q8—324no—
397C4×Q8—38no—
398C4×Q8—324no—
399C4×Q8—324no—
400C4×Q8—348no—
401C4×Q8—324no—
402C4×Q8—324no—
403C4×Q8C22×D318yes—
404C4×D4—324no—
405C4×D4—324no—
406C4×D4C22×D3124yes—
407#117—324no—
408#117—324no—
409#117—324no—
410#117—348no—
411#117—324no—
412C2×C4⋊C4—33no—
413C2×C4⋊C4—33no—
414C2×C4⋊C4—36no—
415C2×C4⋊C4—324no—
416C2×C4⋊C4—33no—
417C2×C4⋊C4—33no—
418C2×C4⋊C4—33no—
419C2×C4⋊C4—33no—
420C2×C4⋊C4—33no—
421C2×C4⋊C4—36no—
422C2×C4⋊C4—36no—
423C2×C4⋊C4—33no—
424C2×C4⋊C4—33no—
425C2×C4⋊C4—31no—
426C2×C4⋊C4—36no—
427C2×C4⋊C4—33no—
428C2×C4⋊C4—33no—
429C2×C4⋊C4C22×D313yes—
430C2×C4⋊C4C22×D313yes—
431C2×C4⋊C4C22×D316yes—
432C2×C22⋊C4—31no—
433C2×C22⋊C4—33no—
434C2×C22⋊C4—33no—
435C2×C22⋊C4—33no—
436C2×C22⋊C4—31no—
437C2×C22⋊C4—33no—
438C2×C22⋊C4—33no—
439C2×C22⋊C4—33no—
440C2×C22⋊C4C22×D313yes—
441C2×C22⋊C4C22×D313yes—
442C2×C42—33no—
443C2×C42—36no—
444C2×C42—36no—
445C2×C42—33no—
446C2×C42—33no—
447C2×C42—33no—
448C2×C42—33no—
449C2×C42—324no—
450C2×C42C22×D313yes—
451C23×C3—22no—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C32−1+414yes—
457C23×C3C2512yes—
458C23×C3C2512yes—
459C23×C3C2511yescharacteristic
460C22×D3—22no—
461C22×D3—22no—
462C22×D3—22no—
463C22×D3C2512yes—
464C3×Q8—224no—
465C3×Q8—224no—
466C3×Q8C2×#41116yes—
467C3×D4—28no—
468C2×C3×C4—26no—
469C2×C3×C4—26no—
470C2×C3×C4—26no—
471C2×C3×C4—22no—
472C2×C3×C4—224no—
473C2×C3×C4—224no—
474C2×C3×C4C2×#41112yes—
475C2×C3×C4C2516yes—
476C2×C3×C4C2516yes—
477C2×C3×C4C2516yes—
478C2×C3×C4C2512yes—
479C2×C3×C4C2516yes—
480#67—28no—
481#67—28no—
482C2×Dic3—26no—
483C2×Dic3—26no—
484C2×Dic3—224no—
485C2×Dic3—26no—
486C2×Dic3—26no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—28no—
490C2×Dic32−1+414yes—
491C2×Dic3C2512yes—
492C2×Dic3C2516yes—
493C2×Dic3C2516yes—
494C2×Dic3C2512yes—
495C2×Dic3C2516yes—
496C2×Dic3C2516yes—
497C2×Dic3C2512yes—
498C4×D3—224no—
499Dic6—224no—
500Dic6—224no—
501C24—31no—
502C24C23×D311yescharacteristic
503C24C23×D311yescharacteristic
504C2×Q8—232no—
505C2×Q8—232no—
506C2×Q8—212no—
507C2×Q8—212no—
508C2×Q8—312no—
509C2×Q8—312no—
510C2×Q8—612no—
511C2×Q8—632no—
512C2×Q8—612no—
513C2×Q8#23718yes—
514C2×Q8C23×D3112yes—
515C2×Q8C23×D3112yes—
516C2×Q8C23×D314yes—
517C2×D4—24no—
518C2×D4—34no—
519C2×D4—34no—
520C2×D4—64no—
521C2×D4—64no—
522C2×D4C23×D314yes—
523C22×C4—212no—
524C22×C4—212no—
525C22×C4—31no—
526C22×C4—34no—
527C22×C4—312no—
528C22×C4—33no—
529C22×C4—31no—
530C22×C4—33no—
531C22×C4—31no—
532C22×C4—33no—
533C22×C4—33no—
534C22×C4—312no—
535C22×C4—64no—
536C22×C4—612no—
537C22×C4—612no—
538C22×C4C23×D3112yes—
539C22×C4C23×D3112yes—
540C22×C4C23×D313yes—
541C22×C4C23×D313yes—
542C22×C4C23×D313yes—
543C22×C4C23×D311yescharacteristic
544C22×C4C23×D313yes—
545C4⋊C4—312no—
546C4⋊C4—312no—
547C4⋊C4—324no—
548C4⋊C4—312no—
549C4⋊C4—312no—
550C4⋊C4—312no—
551C4⋊C4—312no—
552C4⋊C4—312no—
553C4⋊C4—324no—
554C4⋊C4—324no—
555C4⋊C4—312no—
556C4⋊C4—312no—
557C4⋊C4—34no—
558C4⋊C4—324no—
559C4⋊C4—312no—
560C4⋊C4—312no—
561C4⋊C4C23×D3112yes—
562C4⋊C4C23×D3112yes—
563C4⋊C4C23×D3124yes—
564C22⋊C4—34no—
565C22⋊C4—312no—
566C22⋊C4—312no—
567C22⋊C4—312no—
568C22⋊C4—34no—
569C22⋊C4—312no—
570C22⋊C4—312no—
571C22⋊C4—312no—
572C22⋊C4C23×D3112yes—
573C22⋊C4C23×D3112yes—
574C42—312no—
575C42—312no—
576C42—312no—
577C42—312no—
578C42—324no—
579C42—324no—
580C42—312no—
581C42C23×D3112yes—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—28no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—44no—
589C22×C3C22×#4112yes—
590C22×C3C2×2−1+414yes—
591C22×C3C2×2−1+412yes—
592C22×C3C2×2−1+412yes—
593C22×C3C2611yescharacteristic
594C2×D3—22no—
595C2×D3—22no—
596C2×D3—22no—
597C2×D3—44no—
598C3×C4—26no—
599C3×C4—26no—
600C3×C4—26no—
601C3×C4—22no—
602C3×C4C22×#41112yes—
603Dic3—26no—
604Dic3—26no—
605Dic3—26no—
606Dic3—26no—
607Dic3—22no—
608Dic3—22no—
609Dic3C2×2−1+414yes—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—32no—
616C23—62no—
617C23—62no—
618C23—62no—
619C23#100714yes—
620C23C24×D312yes—
621C23C24×D312yes—
622C23C24×D311yescharacteristic
623Q8—224no—
624Q8—224no—
625Q8—624no—
626Q8—624no—
627Q8C2×#237116yes—
628D4—28no—
629D4—68no—
630D4—68no—
631C2×C4—26no—
632C2×C4—26no—
633C2×C4—22no—
634C2×C4—26no—
635C2×C4—224no—
636C2×C4—224no—
637C2×C4—34no—
638C2×C4—32no—
639C2×C4—36no—
640C2×C4—32no—
641C2×C4—36no—
642C2×C4—32no—
643C2×C4—36no—
644C2×C4—36no—
645C2×C4—68no—
646C2×C4—66no—
647C2×C4—624no—
648C2×C4—66no—
649C2×C4—66no—
650C2×C4—62no—
651C2×C4—62no—
652C2×C4—66no—
653C2×C4—624no—
654C2×C4C2×#237112yes—
655C2×C4C24×D316yes—
656C2×C4C24×D316yes—
657C2×C4C24×D316yes—
658C2×C4C24×D312yes—
659C2×C4C24×D316yes—
660C2×C3—24no—
661C2×C3—42no—
662C2×C3#352314yescomplemented
663C2×C3C23×#4111yescharacteristic
664C2×C3C22×2−1+411yescharacteristic
665C2×C3C22×2−1+411yescharacteristic
666D3—42no—
667C22—22no—
668C22—22no—
669C22—28no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—44no—
674C22—62no—
675C22—62no—
676C22—62no—
677C22—124no—
678C22C22×#23712yes—
679C22C2×#100714yes—
680C22C2×#100712yes—
681C22D3×2−1+412yes—
682C22C25×D311yescharacteristic
683C4—26no—
684C4—26no—
685C4—22no—
686C4—26no—
687C4—34no—
688C4—66no—
689C4—66no—
690C4—66no—
691C4—62no—
692C4—62no—
693C4—66no—
694C4C22×#237112yes—
695C3C2×#352311yescharacteristic, complemented, Sylow
696C2—24no—
697C2—42no—
698C2—122no—
699C2#8675214yesdirect product factor
700C2C23×#23711yescharacteristic
701C2C22×#100711yescharacteristic
702C2C2×D3×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×D4×Q8C2
socleC23×C3C25
prime radicalC2×#939C22
hypercenterC2×D4×Q8D3
hypocenterC3C2×#3523
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×Q8C2semidirect
2. C2×Q8×#67C2semidirect
3. C2×Q8×#67C2semidirect
4. C2×#5812C2semidirect
5. C22×Q8×Dic3C2semidirect
6. #86752C2direct (N × H)
7. C2×#5731C2semidirect
8. C2×#5721C2semidirect
9. C2×#5641C2semidirect
10. C2×#5642C2semidirect
11. C2×#5625C2semidirect
12. C2×#5622C2semidirect
13. C2×#5572C2semidirect
14. C2×#5569C2semidirect
15. C2×#5541C2semidirect
21. C3×D4×Q8C22semidirect
27. Q8×#67C22semidirect
28. Q8×#67C22semidirect
31. #5812C22semidirect
39. C2×Q8×Dic3C22semidirect
52. #5731C22semidirect
53. #5721C22semidirect
54. #5642C22semidirect
55. #5641C22semidirect
56. #5625C22semidirect
57. #5622C22semidirect
58. #5572C22semidirect
59. #5569C22semidirect
60. #5541C22semidirect
91. C2×D4×Q8D3semidirect
212. D4×Q8C2×D3semidirect
662. C2×C3#3523semidirect
695. C3C2×#3523semidirect
699. C2#86752direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Q82
C2×Q8×#672
C2×#58122
C22×Q8×Dic32
#867522
C2×#57312
C2×#57212
C2×#56412
C2×#56422
C2×#56252
C2×#56222
C2×#55722
C2×#55692
C2×#55412
C2×#55382
C2×#35233