Finite Group Databasebeta

← C2×#86749 #11703385

Subgroups — C2×#86749 #11703385

Order 768.

7130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#5817C211yesmaximal, characteristic, complemented
3C2×#5817C211yesmaximal, characteristic, complemented
4C2×#5812C211yesmaximal, characteristic, complemented
5C22×Q8×Dic3C211yesmaximal, characteristic, complemented
6#86749C2132yesmaximal, direct product factor
7C2×#5731C213yesmaximal, complemented
8C2×#5732C213yesmaximal, complemented
9C2×#5639C213yesmaximal, complemented
10C2×#5635C213yesmaximal, complemented
11C2×#5643C213yesmaximal, complemented
12C2×#5624C213yesmaximal, complemented
13C2×#5569C211yesmaximal, characteristic, complemented
14C2×#5574C211yesmaximal, characteristic, complemented
15C2×#5565C213yesmaximal, complemented
16C2×#5538C213yesmaximal, complemented
17C2×#3516—31nomaximal, Sylow
18C23×C3×Q8C2211yescharacteristic
19C23×C3×Q8C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C3×D4×Q8C22116yescomplemented
22C2×C3×C4⋊Q8C2213yes—
23C2×C3×C22⋊Q8C2213yes—
24C2×C3×C22⋊Q8C2213yes—
25C2×C3×C4×Q8C2211yescharacteristic
26C2×C3×C4×D4C2213yes—
27#5817C22116yescomplemented
28#5817C22116yescomplemented
29C2×#947C2213yes—
30C2×#947C2213yes—
31C2×#946C2213yes—
32C2×#946C2213yes—
33#5812C22116yescomplemented
34C2×Q8×Dic3C2211yescharacteristic
35C2×Q8×Dic3C2211yescharacteristic
36C2×Q8×Dic3C2211yescharacteristic
37C2×Q8×Dic3C2213yes—
38C2×Q8×Dic3C2213yes—
39C2×Q8×Dic3C2213yes—
40C2×Q8×Dic3C2213yes—
41C2×Q8×Dic3C22116yescomplemented
42C2×#939C2213yes—
43C2×#935C2211yescharacteristic
44C2×#930C2213yes—
45C2×#930C2213yes—
46C2×C4×#67C2213yes—
47C2×C4×#67C2213yes—
48C2×#926C2213yes—
49C2×#926C2213yes—
50C22×C4⋊Dic3C2213yes—
51C22×C4×Dic3C2213yes—
52#5732C22148yescomplemented
53#5731C22148yescomplemented
54#5643C22148yescomplemented
55#5639C22148yescomplemented
56#5635C22148yescomplemented
57#5624C22148yescomplemented
58#5574C22116yescomplemented
59#5569C22116yescomplemented
60#5565C22148yescomplemented
61#5538C22148yescomplemented
62C2×#898C2213yes—
63C2×#898C2216yes—
64C2×#898C2216yes—
65C2×#897C2216yes—
66C2×#893C2213yes—
67C2×#892C2216yes—
68C2×D3×C4⋊C4C2213yes—
69C2×#890C2213yes—
70C2×#889C2213yes—
71C2×#889C2216yes—
72C2×#888C2213yes—
73C2×#886C2213yes—
74C2×#885C2213yes—
75C2×#883C2216yes—
76C2×#67⋊C4C2216yes—
77C2×#879C2213yes—
78C2×#878C2213yes—
79C2×C4×D12C2213yes—
80C2×#872C2213yes—
81C2×#870C2213yes—
82C2×C4×Dic6C2213yes—
83#3516—332no—
84C2×#557—31no—
85C2×#556—33no—
86C2×#554—33no—
87C2×#553—33no—
88C2×#552—33no—
89C2×D4×Q8D311yescharacteristic, complemented
90C2×#548—31no—
91C2×#548—31no—
92C2×#542—33no—
93C2×#541—33no—
94C2×#529—33no—
95C2×#529—33no—
96C2×#520—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×#67C2313yes—
110C22×#67C2313yes—
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2313yes—
113C2×#239—28no—
114C2×#239C2318yes—
115C22×D12C2313yes—
116C22×C4×D3C2313yes—
117C22×C4×D3C2316yes—
118C22×Dic6C2313yes—
119C3×C4⋊Q8C23124yes—
120C3×C22⋊Q8C23124yes—
121C3×C22⋊Q8C23124yes—
122C3×C4×Q8C2318yes—
123C3×C4×D4C23124yes—
124C2×C3×C4⋊C4C2313yes—
125C2×C3×C4⋊C4C2316yes—
126C2×C3×C4⋊C4C2313yes—
127C2×C3×C22⋊C4C2313yes—
128C2×C3×C22⋊C4C2313yes—
129C2×C3×C42C2313yes—
130C2×#217C2311yescharacteristic
131C2×#217C2311yescharacteristic
132C2×#217C2313yes—
133C2×#217C2311yescharacteristic
134#947C23124yes—
135#947C23124yes—
136#946C23124yes—
137#946C23124yes—
138Q8×Dic3C23124yes—
139Q8×Dic3C23124yes—
140Q8×Dic3C23124yes—
141Q8×Dic3C23124yes—
142Q8×Dic3C2318yes—
143Q8×Dic3C2318yes—
144Q8×Dic3C2318yes—
145#939C23124yes—
146#935C2318yes—
147#930C23124yes—
148#930C23124yes—
149C4×#67C23124yes—
150C4×#67C23124yes—
151C2×(C2×D3)⋊C4C2313yes—
152C2×(C2×D3)⋊C4C2313yes—
153C2×(C2×D3)⋊C4C2316yes—
154C2×(C2×D3)⋊C4C2316yes—
155C2×(C2×D3)⋊C4C2313yes—
156C2×(C2×D3)⋊C4C2313yes—
157#926C23124yes—
158#926C23124yes—
159C2×C4⋊Dic3C23124yes—
160C2×C4⋊Dic3C2313yes—
161C2×C4⋊Dic3C2313yes—
162C2×C4⋊Dic3C2313yes—
163C2×C4⋊Dic3C2313yes—
164C2×C4⋊Dic3C2313yes—
165C2×C4⋊Dic3C2316yes—
166C2×C4⋊Dic3C2313yes—
167C2×Dic3⋊C4C2311yescharacteristic
168C2×Dic3⋊C4C2313yes—
169C2×Dic3⋊C4C2316yes—
170C2×Dic3⋊C4C2311yescharacteristic
171C2×Dic3⋊C4C2313yes—
172C2×Dic3⋊C4C2313yes—
173C2×Dic3⋊C4C2313yes—
174C2×C4×Dic3C2313yes—
175C2×C4×Dic3C2313yes—
176C2×C4×Dic3C2313yes—
177C2×C4×Dic3C2313yes—
178C2×C4×Dic3C2316yes—
179C2×C4×Dic3C2313yes—
180C2×C4×Dic3C23124yes—
181#898C23148yes—
182#898C23148yes—
183#898C23124yes—
184#897C23148yes—
185#893C23124yes—
186#892C23148yes—
187D3×C4⋊C4C23124yes—
188#890C23124yes—
189#889C23148yes—
190#889C23124yes—
191#888C23124yes—
192#886C23124yes—
193#885C23124yes—
194#883C23148yes—
195#67⋊C4C23148yes—
196#879C23124yes—
197#878C23124yes—
198C4×D12C23124yes—
199#872C23124yes—
200#870C23124yes—
201C4×Dic6C23124yes—
202C22×#41—31no—
203C23×Q8C2×D311yescharacteristic
204C23×Q8C2×D311yescharacteristic
205#557—316no—
206#556—348no—
207#554—348no—
208#553—348no—
209#552—348no—
210D4×Q8C2×D3116yescomplemented
211#548—316no—
212#548—316no—
213#542—348no—
214#541—348no—
215C2×C4⋊Q8—33no—
216C2×C4⋊Q8C2×D313yes—
217#529—348no—
218#529—348no—
219C2×#126—36no—
220C2×#126—33no—
221C2×#126—36no—
222C2×#126—33no—
223C2×#125—33no—
224C2×#125—33no—
225C2×#125—36no—
226C2×#125—33no—
227C2×#124—33no—
228C2×#124—33no—
229C2×#124—33no—
230C2×#123—31no—
231C2×#123—33no—
232C2×#123—36no—
233C2×C22⋊Q8—33no—
234C2×C22⋊Q8—33no—
235C2×C22⋊Q8—36no—
236C2×C22⋊Q8—33no—
237C2×C22⋊Q8C2×D313yes—
238C2×C22⋊Q8C2×D313yes—
239C2×#121—33no—
240C2×#121—33no—
241C2×#121—33no—
242#520—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×Q8C2×D311yescharacteristic
254C2×C4×D4—33no—
255C2×C4×D4—33no—
256C2×C4×D4—33no—
257C2×C4×D4—36no—
258C2×C4×D4—33no—
259C2×C4×D4C2×D313yes—
260C2×#117—33no—
261C2×#117—33no—
262C2×#117—36no—
263C2×#117—33no—
264C22×C4⋊C4—33no—
265C22×C4⋊C4—33no—
266C22×C42—33no—
267C24×C3C2411yescharacteristic
268C24×C3C2411yescharacteristic
269C23×D3C2413yes—
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×C4C24112yes—
285C22×C3×C4C2411yescharacteristic
286C22×C3×C4C2413yes—
287C22×C3×C4C24112yes—
288C22×C3×C4C2413yes—
289C2×#67—212no—
290C2×#67—46no—
291C2×#67C24112yes—
292C2×#67C24112yes—
293C22×Dic3—24no—
294C22×Dic3—46no—
295C22×Dic3C2414yes—
296C22×Dic3C2411yescharacteristic
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2413yes—
299C22×Dic3C2413yes—
300C22×Dic3C2411yescharacteristic
301C22×Dic3C2413yes—
302C22×Dic3C2411yescharacteristic
303C22×Dic3C24112yes—
304#239—232no—
305C2×D12—212no—
306C2×D12C24112yes—
307C2×C4×D3—212no—
308C2×C4×D3—412no—
309C2×C4×D3C24112yes—
310C2×C4×D3C24124yes—
311C2×Dic6—46no—
312C2×Dic6C24112yes—
313C3×C4⋊C4C24112yes—
314C3×C4⋊C4C24124yes—
315C3×C4⋊C4C24112yes—
316C3×C22⋊C4C24112yes—
317C3×C22⋊C4C24112yes—
318C3×C42C24112yes—
319#217C2414yes—
320#217C2414yes—
321#217C24112yes—
322#217C2414yes—
323(C2×D3)⋊C4C24112yes—
324(C2×D3)⋊C4C24112yes—
325(C2×D3)⋊C4C24124yes—
326(C2×D3)⋊C4C24124yes—
327(C2×D3)⋊C4C24112yes—
328(C2×D3)⋊C4C24112yes—
329C4⋊Dic3C24112yes—
330C4⋊Dic3C24112yes—
331C4⋊Dic3C24112yes—
332C4⋊Dic3C24112yes—
333C4⋊Dic3C24112yes—
334C4⋊Dic3C24124yes—
335C4⋊Dic3C24112yes—
336Dic3⋊C4C2414yes—
337Dic3⋊C4C24112yes—
338Dic3⋊C4C24124yes—
339Dic3⋊C4C2414yes—
340Dic3⋊C4C24112yes—
341Dic3⋊C4C24112yes—
342Dic3⋊C4C24112yes—
343C4×Dic3C24112yes—
344C4×Dic3C24112yes—
345C4×Dic3C24112yes—
346C4×Dic3C24112yes—
347C4×Dic3C24124yes—
348C4×Dic3C24112yes—
349C2×#41—38no—
350C2×#41—68no—
351C22×Q8—28no—
352C22×Q8—28no—
353C22×Q8—33no—
354C22×Q8C22×D313yes—
355C22×Q8C22×D313yes—
356C22×Q8C22×D318yes—
357C22×Q8C22×D318yes—
358C22×Q8C22×D311yescharacteristic
359C22×D4—33no—
360C22×D4—33no—
361C22×D4—33no—
362C22×D4C22×D311yescharacteristic
363C23×C4—31no—
364C23×C4—33no—
365C23×C4—33no—
366C23×C4—36no—
367C23×C4C22×D313yes—
368C23×C4C22×D313yes—
369C4⋊Q8—324no—
370C4⋊Q8C22×D3124yes—
371#126—348no—
372#126—324no—
373#126—348no—
374#126—324no—
375#125—324no—
376#125—324no—
377#125—348no—
378#125—324no—
379#124—324no—
380#124—324no—
381#124—324no—
382#123—38no—
383#123—324no—
384#123—348no—
385C22⋊Q8—324no—
386C22⋊Q8—324no—
387C22⋊Q8—348no—
388C22⋊Q8—324no—
389C22⋊Q8C22×D3124yes—
390C22⋊Q8C22×D3124yes—
391#121—324no—
392#121—324no—
393#121—324no—
394C4×Q8—38no—
395C4×Q8—324no—
396C4×Q8—38no—
397C4×Q8—324no—
398C4×Q8—324no—
399C4×Q8—38no—
400C4×Q8—324no—
401C4×Q8—324no—
402C4×Q8C22×D318yes—
403C4×D4—324no—
404C4×D4—324no—
405C4×D4—324no—
406C4×D4—348no—
407C4×D4—324no—
408C4×D4C22×D3124yes—
409#117—324no—
410#117—324no—
411#117—348no—
412#117—324no—
413C2×C4⋊C4—33no—
414C2×C4⋊C4—33no—
415C2×C4⋊C4—33no—
416C2×C4⋊C4—36no—
417C2×C4⋊C4—324no—
418C2×C4⋊C4—31no—
419C2×C4⋊C4—33no—
420C2×C4⋊C4—33no—
421C2×C4⋊C4—33no—
422C2×C4⋊C4—33no—
423C2×C4⋊C4—33no—
424C2×C4⋊C4—33no—
425C2×C4⋊C4—36no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—33no—
428C2×C4⋊C4—324no—
429C2×C4⋊C4C22×D313yes—
430C2×C4⋊C4C22×D316yes—
431C2×C4⋊C4C22×D313yes—
432C2×C22⋊C4—33no—
433C2×C22⋊C4—31no—
434C2×C22⋊C4—31no—
435C2×C22⋊C4—31no—
436C2×C22⋊C4—33no—
437C2×C22⋊C4—33no—
438C2×C22⋊C4—33no—
439C2×C22⋊C4—36no—
440C2×C22⋊C4—36no—
441C2×C22⋊C4—33no—
442C2×C22⋊C4C22×D313yes—
443C2×C22⋊C4C22×D313yes—
444C2×C42—33no—
445C2×C42—36no—
446C2×C42—33no—
447C2×C42—33no—
448C2×C42—33no—
449C2×C42—33no—
450C2×C42—324no—
451C2×C42C22×D313yes—
452C23×C3—22no—
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C32−1+414yes—
458C23×C3C2512yes—
459C23×C3C2512yes—
460C23×C3C2511yescharacteristic
461C22×D3—26no—
462C22×D3—26no—
463C22×D3—26no—
464C22×D3C2516yes—
465C3×Q8—224no—
466C3×Q8—224no—
467C3×Q8C2×#41116yes—
468C3×D4—28no—
469C2×C3×C4—26no—
470C2×C3×C4—26no—
471C2×C3×C4—22no—
472C2×C3×C4—26no—
473C2×C3×C4—224no—
474C2×C3×C4—224no—
475C2×C3×C4C2×#41112yes—
476C2×C3×C4C2516yes—
477C2×C3×C4C2516yes—
478C2×C3×C4C2512yes—
479C2×C3×C4C2516yes—
480C2×C3×C4C2516yes—
481#67—224no—
482#67—412no—
483C2×Dic3—22no—
484C2×Dic3—28no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—26no—
488C2×Dic3—22no—
489C2×Dic3—26no—
490C2×Dic3—26no—
491C2×Dic3—412no—
492C2×Dic3C2512yes—
493C2×Dic3C2512yes—
494C2×Dic3C2516yes—
495C2×Dic3C2516yes—
496C2×Dic3C2512yes—
497C2×Dic3C2516yes—
498C2×Dic3C2512yes—
499D12—224no—
500C4×D3—224no—
501C4×D3—424no—
502Dic6—412no—
503C24—33no—
504C24C23×D311yescharacteristic
505C24C23×D311yescharacteristic
506#41—632no—
507C2×Q8—232no—
508C2×Q8—232no—
509C2×Q8—212no—
510C2×Q8—212no—
511C2×Q8—312no—
512C2×Q8—126no—
513C2×Q8#23718yes—
514C2×Q8C23×D3112yes—
515C2×Q8C23×D3112yes—
516C2×Q8C23×D314yes—
517C2×D4—24no—
518C2×D4—312no—
519C2×D4—312no—
520C2×D4—312no—
521C2×D4—612no—
522C2×D4—612no—
523C2×D4—126no—
524C2×D4C23×D314yes—
525C22×C4—212no—
526C22×C4—212no—
527C22×C4—34no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—33no—
531C22×C4—31no—
532C22×C4—33no—
533C22×C4—33no—
534C22×C4—31no—
535C22×C4—312no—
536C22×C4—312no—
537C22×C4—324no—
538C22×C4—64no—
539C22×C4—612no—
540C22×C4—1212no—
541C22×C4—126no—
542C22×C4C23×D3112yes—
543C22×C4C23×D3112yes—
544C22×C4C23×D313yes—
545C22×C4C23×D313yes—
546C22×C4C23×D311yescharacteristic
547C22×C4C23×D313yes—
548C22×C4C23×D313yes—
549C4⋊C4—312no—
550C4⋊C4—312no—
551C4⋊C4—312no—
552C4⋊C4—324no—
553C4⋊C4—34no—
554C4⋊C4—312no—
555C4⋊C4—312no—
556C4⋊C4—312no—
557C4⋊C4—312no—
558C4⋊C4—312no—
559C4⋊C4—312no—
560C4⋊C4—324no—
561C4⋊C4—34no—
562C4⋊C4—312no—
563C4⋊C4C23×D3112yes—
564C4⋊C4C23×D3124yes—
565C4⋊C4C23×D3112yes—
566C22⋊C4—312no—
567C22⋊C4—34no—
568C22⋊C4—34no—
569C22⋊C4—34no—
570C22⋊C4—312no—
571C22⋊C4—312no—
572C22⋊C4—312no—
573C22⋊C4—324no—
574C22⋊C4—324no—
575C22⋊C4—312no—
576C22⋊C4C23×D3112yes—
577C22⋊C4C23×D3112yes—
578C42—312no—
579C42—312no—
580C42—312no—
581C42—312no—
582C42—324no—
583C42—312no—
584C42C23×D3112yes—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—28no—
588C22×C3—22no—
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—44no—
592C22×C3C22×#4112yes—
593C22×C3C2×2−1+414yes—
594C22×C3C2×2−1+412yes—
595C22×C3#58512yes—
596C22×C3C2611yescharacteristic
597C2×D3—26no—
598C2×D3—26no—
599C2×D3—26no—
600C2×D3—412no—
601C3×C4—26no—
602C3×C4—26no—
603C3×C4—22no—
604C3×C4—26no—
605C3×C4C22×#41112yes—
606Dic3—22no—
607Dic3—22no—
608Dic3—22no—
609Dic3—26no—
610Dic3—22no—
611Dic3—26no—
612Dic3—26no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—36no—
619C23—66no—
620C23—66no—
621C23—66no—
622C23#100714yes—
623C23C24×D312yes—
624C23C24×D312yes—
625C23C24×D311yescharacteristic
626Q8—224no—
627Q8—224no—
628Q8—1212no—
629Q8C2×#237116yes—
630D4—28no—
631D4—624no—
632D4—624no—
633D4—1212no—
634C2×C4—26no—
635C2×C4—26no—
636C2×C4—22no—
637C2×C4—26no—
638C2×C4—224no—
639C2×C4—224no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—36no—
643C2×C4—32no—
644C2×C4—36no—
645C2×C4—36no—
646C2×C4—32no—
647C2×C4—62no—
648C2×C4—68no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—66no—
652C2×C4—66no—
653C2×C4—66no—
654C2×C4—62no—
655C2×C4—624no—
656C2×C4—1224no—
657C2×C4—1212no—
658C2×C4C2×#237112yes—
659C2×C4C24×D316yes—
660C2×C4C24×D316yes—
661C2×C4C24×D312yes—
662C2×C4C24×D316yes—
663C2×C4C24×D316yes—
664C2×C3—24no—
665C2×C3—42no—
666C2×C3#351614yescomplemented
667C2×C3C23×#4111yescharacteristic
668C2×C3C22×2−1+411yescharacteristic
669C2×C3C2×#58511yescharacteristic
670D3—46no—
671C22—22no—
672C22—22no—
673C22—28no—
674C22—22no—
675C22—22no—
676C22—22no—
677C22—44no—
678C22—66no—
679C22—66no—
680C22—66no—
681C22—1212no—
682C22C22×#23712yes—
683C22C2×#100714yes—
684C22C2×#100712yes—
685C22#596812yes—
686C22C25×D311yescharacteristic
687C4—26no—
688C4—26no—
689C4—22no—
690C4—26no—
691C4—62no—
692C4—62no—
693C4—62no—
694C4—66no—
695C4—66no—
696C4—66no—
697C4—62no—
698C4C22×#237112yes—
699C3C2×#351611yescharacteristic, complemented, Sylow
700C2—24no—
701C2—42no—
702C2—126no—
703C2#8674914yesdirect product factor
704C2C23×#23711yescharacteristic
705C2C22×#100711yescharacteristic
706C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×D4×Q8C2
socleC23×C3C25
hypercenterC2×D4×Q8D3
hypocenterC3C2×#3516
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×#5817C2semidirect
3. C2×#5817C2semidirect
4. C2×#5812C2semidirect
5. C22×Q8×Dic3C2semidirect
6. #86749C2direct (N × H)
7. C2×#5731C2semidirect
8. C2×#5732C2semidirect
9. C2×#5639C2semidirect
10. C2×#5635C2semidirect
11. C2×#5643C2semidirect
12. C2×#5624C2semidirect
13. C2×#5569C2semidirect
14. C2×#5574C2semidirect
15. C2×#5565C2semidirect
16. C2×#5538C2semidirect
21. C3×D4×Q8C22semidirect
27. #5817C22semidirect
28. #5817C22semidirect
33. #5812C22semidirect
41. C2×Q8×Dic3C22semidirect
52. #5732C22semidirect
53. #5731C22semidirect
54. #5643C22semidirect
55. #5639C22semidirect
56. #5635C22semidirect
57. #5624C22semidirect
58. #5574C22semidirect
59. #5569C22semidirect
60. #5565C22semidirect
61. #5538C22semidirect
89. C2×D4×Q8D3semidirect
210. D4×Q8C2×D3semidirect
666. C2×C3#3516semidirect
699. C3C2×#3516semidirect
703. C2#86749direct (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×#58172
C2×#58122
C22×Q8×Dic32
#867492
C2×#57312
C2×#57322
C2×#56392
C2×#56352
C2×#56432
C2×#56242
C2×#55692
C2×#55742
C2×#55652
C2×#55382
C2×#35163