Finite Group Databasebeta

← C2×#85896 #11703440

Subgroups — C2×#85896 #11703440

Order 768.

7854 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2C2×#5834C211yesmaximal, characteristic, complemented
3C2×#5834C211yesmaximal, characteristic, complemented
4#85896C2132yesmaximal, direct product factor
5C2×#5569C211yesmaximal, characteristic, complemented
6C2×#5577C211yesmaximal, characteristic, complemented
7C2×#5574C211yesmaximal, characteristic, complemented
8C2×C4×#239C211yesmaximal, characteristic, complemented
9C2×#5558C213yesmaximal, complemented
10C2×#5562C213yesmaximal, complemented
11C2×#5548C213yesmaximal, complemented
12C2×#5553C213yesmaximal, complemented
13C2×#5535C213yesmaximal, complemented
14C2×#5528C213yesmaximal, complemented
15C2×#5514C213yesmaximal, complemented
16C2×#5507C213yesmaximal, complemented
17C2×#3517—31nomaximal, Sylow
18C22×C3×#41C2211yescharacteristic
19C22×#239C2211yescharacteristic
20C22×#239C2211yescharacteristic
21C22×#235C2216yes—
22C3×#520C22116yescomplemented
23C2×C3×C4×Q8C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic
25C2×C3×C4×D4C2213yes—
26C2×C3×C4×D4C2213yes—
27C2×C3×#117C2213yes—
28C22×C3×C4⋊C4C2213yes—
29#5834C22116yescomplemented
30#5834C22116yescomplemented
31C2×Q8×Dic3C2211yescharacteristic
32C2×Q8×Dic3C2211yescharacteristic
33C2×#940C2213yes—
34C2×#940C2213yes—
35C2×#938C2213yes—
36C2×#938C2213yes—
37C2×#930C2216yes—
38C2×#930C2213yes—
39C2×#930C2213yes—
40C2×#929C2216yes—
41C2×C4×#67C2216yes—
42C2×C4×#67C2213yes—
43C2×C4×#67C2213yes—
44#5577C22116yescomplemented
45#5574C22116yescomplemented
46C4×#239C22116yescomplemented
47#5569C22116yescomplemented
48#5562C22148yescomplemented
49#5558C22148yescomplemented
50#5553C22148yescomplemented
51#5548C22148yescomplemented
52#5535C22148yescomplemented
53#5528C22148yescomplemented
54#5514C22148yescomplemented
55C2×#898C2213yes—
56C2×#896C2213yes—
57#5507C22148yescomplemented
58C2×#895C2213yes—
59C2×#895C2213yes—
60C2×#894C2216yes—
61C2×#894C2213yes—
62C2×#893C2213yes—
63C2×#893C2213yes—
64C2×#892C2213yes—
65C2×D3×C4⋊C4C2213yes—
66C2×#890C2213yes—
67C2×#889C2211yescharacteristic
68C2×#888C2213yes—
69C2×#885C2213yes—
70C2×#884C2216yes—
71C2×#884C2216yes—
72C2×#884C2213yes—
73C2×#883C2213yes—
74C2×#879C2213yes—
75C2×#874C2213yes—
76C2×C4×D12C2213yes—
77C2×C4×D12C2213yes—
78C2×C4×D12C2213yes—
79C2×#872C2213yes—
80C2×C42×D3C2213yes—
81C2×#870C2213yes—
82C2×C4×Dic6C2213yes—
83#3517—332no—
84C2×#557—31no—
85C2×#553—33no—
86C2×#553—33no—
87C2×#550—31no—
88C2×#550—31no—
89C2×#550—31no—
90C2×#550—33no—
91C2×#547—33no—
92C2×#540—33no—
93C2×#540—33no—
94C2×#532—33no—
95C2×#529—33no—
96C2×#520—31no—
97C2×#520D311yescharacteristic, complemented
98C2×C4×#41—31no—
99C2×C3×#41—28no—
100C2×C3×#41C2318yes—
101C22×C3×Q8C2311yescharacteristic
102C22×C3×D4C2313yes—
103C23×C3×C4C2313yes—
104C23×C3×C4C2316yes—
105C22×#67C2313yes—
106C22×#67C2316yes—
107C22×#67C2313yes—
108C22×#67C2316yes—
109C2×#239—28no—
110C2×#239—28no—
111C2×#239C2318yes—
112C2×#239C2318yes—
113C2×#235—424no—
114C2×#235C23148yes—
115C22×D12C2313yes—
116C22×D12C2313yes—
117C22×D12C2316yes—
118C22×D12C2313yes—
119C22×C4×D3C2313yes—
120C22×C4×D3C2313yes—
121C22×C4×D3C2313yes—
122C22×C4×D3C2316yes—
123C22×C4×D3C2313yes—
124C22×Dic6C2313yes—
125C3×C4×Q8C2318yes—
126C3×C4×Q8C2318yes—
127C3×C4×D4C23124yes—
128C3×C4×D4C23124yes—
129C3×#117C23124yes—
130C2×C3×C4⋊C4C2313yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2313yes—
133C2×C3×C4⋊C4C2313yes—
134C2×C3×C4⋊C4C23124yes—
135C2×C3×C22⋊C4C2313yes—
136C2×C3×C22⋊C4C2313yes—
137C2×C3×C42C2313yes—
138C2×C3×C42C2313yes—
139C2×#217C2313yes—
140C2×#217C2313yes—
141Q8×Dic3C2318yes—
142Q8×Dic3C2318yes—
143#940C23124yes—
144#940C23124yes—
145#938C23124yes—
146#938C23124yes—
147#930C23124yes—
148#930C23124yes—
149#930C23148yes—
150#929C23148yes—
151C4×#67C23124yes—
152C4×#67C23124yes—
153C4×#67C23148yes—
154C2×(C2×D3)⋊C4C2313yes—
155C2×(C2×D3)⋊C4C2313yes—
156C2×(C2×D3)⋊C4C2313yes—
157C2×(C2×D3)⋊C4C2316yes—
158C2×(C2×D3)⋊C4C2313yes—
159C2×(C2×D3)⋊C4C2313yes—
160C2×(C2×D3)⋊C4C2313yes—
161C2×C4⋊Dic3C2313yes—
162C2×C4⋊Dic3C2313yes—
163C2×C4⋊Dic3C2313yes—
164C2×C4⋊Dic3C2311yescharacteristic
165C2×Dic3⋊C4C2311yescharacteristic
166C2×Dic3⋊C4C2313yes—
167C2×Dic3⋊C4C2316yes—
168C2×Dic3⋊C4C2311yescharacteristic
169C2×Dic3⋊C4C2313yes—
170C2×Dic3⋊C4C2311yescharacteristic
171C2×Dic3⋊C4C2311yescharacteristic
172C2×C4×Dic3C2313yes—
173C2×C4×Dic3C2313yes—
174C2×C4×Dic3C2311yescharacteristic
175C2×C4×Dic3C2313yes—
176#898C23124yes—
177#896C23124yes—
178#895C23124yes—
179#895C23124yes—
180#894C23148yes—
181#894C23124yes—
182#893C23124yes—
183#893C23124yes—
184#892C23124yes—
185D3×C4⋊C4C23124yes—
186#890C23124yes—
187#889C2318yes—
188#888C23124yes—
189#885C23124yes—
190#884C23124yes—
191#884C23148yes—
192#884C23148yes—
193#883C23124yes—
194#879C23124yes—
195#874C23124yes—
196C4×D12C23124yes—
197C4×D12C23124yes—
198C4×D12C23124yes—
199#872C23124yes—
200C42×D3C23124yes—
201#870C23124yes—
202C4×Dic6C23124yes—
203C22×#41—31no—
204C22×#41—31no—
205C22×#41—36no—
206C22×#41C2×D311yescharacteristic
207#557—316no—
208#553—348no—
209#553—348no—
210#550—316no—
211#550—316no—
212#550—316no—
213#550—348no—
214#547—348no—
215#540—348no—
216#540—348no—
217#532—348no—
218C2×C4⋊Q8—33no—
219C2×#127—33no—
220C2×#127—33no—
221C2×#127—33no—
222#529—348no—
223C2×#126—33no—
224C2×#126—33no—
225C2×#125—31no—
226C2×#125—33no—
227C2×#125—33no—
228C2×#124—33no—
229C2×#123—36no—
230C2×#123—33no—
231C2×#123—36no—
232C2×#123—33no—
233C2×C22⋊Q8—33no—
234C2×#121—33no—
235C2×#121—33no—
236C2×#121—33no—
237C2×#121—36no—
238C2×#121—33no—
239C2×#121—33no—
240C2×#121—33no—
241C2×#121—33no—
242C2×#121—36no—
243C2×#121—36no—
244#520—316no—
245#520C2×D3116yescomplemented
246C4×#41—316no—
247C2×C4×Q8—31no—
248C2×C4×Q8—31no—
249C2×C4×Q8—33no—
250C2×C4×Q8C2×D311yescharacteristic
251C2×C4×Q8C2×D311yescharacteristic
252C2×C4×D4—33no—
253C2×C4×D4—33no—
254C2×C4×D4—36no—
255C2×C4×D4—33no—
256C2×C4×D4—33no—
257C2×C4×D4—33no—
258C2×C4×D4—33no—
259C2×C4×D4—33no—
260C2×C4×D4C2×D313yes—
261C2×C4×D4C2×D313yes—
262C2×#117—33no—
263C2×#117—33no—
264C2×#117C2×D313yes—
265C22×C4⋊C4—33no—
266C22×C4⋊C4C2×D313yes—
267C22×C42—33no—
268C24×C3C2413yes—
269C23×D3C2413yes—
270C23×D3C2413yes—
271C3×#41—232no—
272C2×C3×Q8#4118yescomplemented
273C2×C3×Q8C2414yes—
274C2×C3×D4—212no—
275C2×C3×D4C24112yes—
276C22×C3×C4—212no—
277C22×C3×C4—412no—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2413yes—
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2413yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C24112yes—
284C22×C3×C4C24124yes—
285C22×C3×C4C2413yes—
286C2×#67—212no—
287C2×#67—412no—
288C2×#67—412no—
289C2×#67—46no—
290C2×#67C24112yes—
291C2×#67C24112yes—
292C2×#67C24124yes—
293C2×#67C24124yes—
294C22×Dic3C2411yescharacteristic
295C22×Dic3C2411yescharacteristic
296C22×Dic3C2413yes—
297C22×Dic3C2413yes—
298C22×Dic3C2411yescharacteristic
299C22×Dic3C2411yescharacteristic
300#239—232no—
301#239—232no—
302#235—496no—
303C2×D12—212no—
304C2×D12—212no—
305C2×D12—46no—
306C2×D12—412no—
307C2×D12C24112yes—
308C2×D12C24112yes—
309C2×D12C24112yes—
310C2×D12C24124yes—
311C2×C4×D3—212no—
312C2×C4×D3—212no—
313C2×C4×D3—212no—
314C2×C4×D3—46no—
315C2×C4×D3—412no—
316C2×C4×D3C24112yes—
317C2×C4×D3C24112yes—
318C2×C4×D3C24112yes—
319C2×C4×D3C24112yes—
320C2×C4×D3C24124yes—
321C2×Dic6—212no—
322C2×Dic6C24112yes—
323C3×C4⋊C4C24112yes—
324C3×C4⋊C4C2414yes—
325C3×C4⋊C4C24112yes—
326C3×C4⋊C4C24112yes—
327C3×C22⋊C4C24112yes—
328C3×C22⋊C4C24112yes—
329C3×C42C24112yes—
330C3×C42C24112yes—
331#217C24112yes—
332#217C24112yes—
333(C2×D3)⋊C4C24112yes—
334(C2×D3)⋊C4C24112yes—
335(C2×D3)⋊C4C24112yes—
336(C2×D3)⋊C4C24124yes—
337(C2×D3)⋊C4C24112yes—
338(C2×D3)⋊C4C24112yes—
339(C2×D3)⋊C4C24112yes—
340C4⋊Dic3C24112yes—
341C4⋊Dic3C24112yes—
342C4⋊Dic3C24112yes—
343C4⋊Dic3C2414yes—
344Dic3⋊C4C2414yes—
345Dic3⋊C4C24112yes—
346Dic3⋊C4C24124yes—
347Dic3⋊C4C2414yes—
348Dic3⋊C4C24112yes—
349Dic3⋊C4C2414yes—
350Dic3⋊C4C2414yes—
351C4×Dic3C24112yes—
352C4×Dic3C24112yes—
353C4×Dic3C2414yes—
354C4×Dic3C24112yes—
355C2×#41—28no—
356C2×#41—38no—
357C2×#41—38no—
358C2×#41—348no—
359C2×#41—68no—
360C2×#41—68no—
361C2×#41—1224no—
362C2×#41C22×D318yes—
363C22×Q8—33no—
364C22×Q8C22×D311yescharacteristic
365C22×D4—33no—
366C22×D4—36no—
367C22×D4—33no—
368C22×D4—36no—
369C22×D4—33no—
370C22×D4—33no—
371C22×D4—33no—
372C22×D4—36no—
373C22×D4C22×D313yes—
374C23×C4—33no—
375C23×C4—33no—
376C23×C4—33no—
377C23×C4—36no—
378C23×C4—33no—
379C23×C4C22×D313yes—
380C23×C4C22×D316yes—
381C4⋊Q8—324no—
382#127—324no—
383#127—324no—
384#127—324no—
385#126—324no—
386#126—324no—
387#125—38no—
388#125—324no—
389#125—324no—
390#124—324no—
391#123—348no—
392#123—324no—
393#123—348no—
394#123—324no—
395C22⋊Q8—324no—
396#121—324no—
397#121—324no—
398#121—324no—
399#121—348no—
400#121—324no—
401#121—324no—
402#121—324no—
403#121—324no—
404#121—348no—
405#121—348no—
406C4×Q8—38no—
407C4×Q8—38no—
408C4×Q8—324no—
409C4×Q8C22×D318yes—
410C4×Q8C22×D318yes—
411C4×D4—324no—
412C4×D4—324no—
413C4×D4—348no—
414C4×D4—324no—
415C4×D4—324no—
416C4×D4—324no—
417C4×D4—324no—
418C4×D4—324no—
419C4×D4C22×D3124yes—
420C4×D4C22×D3124yes—
421#117—324no—
422#117—324no—
423#117C22×D3124yes—
424C2×C4⋊C4—33no—
425C2×C4⋊C4—33no—
426C2×C4⋊C4—31no—
427C2×C4⋊C4—33no—
428C2×C4⋊C4—31no—
429C2×C4⋊C4—31no—
430C2×C4⋊C4—31no—
431C2×C4⋊C4—36no—
432C2×C4⋊C4—31no—
433C2×C4⋊C4—33no—
434C2×C4⋊C4—33no—
435C2×C4⋊C4—324no—
436C2×C4⋊C4C22×D313yes—
437C2×C4⋊C4C22×D313yes—
438C2×C4⋊C4C22×D313yes—
439C2×C4⋊C4C22×D3124yes—
440C2×C4⋊C4C22×D311yescharacteristic
441C2×C22⋊C4—33no—
442C2×C22⋊C4—33no—
443C2×C22⋊C4—33no—
444C2×C22⋊C4—36no—
445C2×C22⋊C4—33no—
446C2×C22⋊C4—33no—
447C2×C22⋊C4—33no—
448C2×C22⋊C4—33no—
449C2×C22⋊C4—33no—
450C2×C22⋊C4C22×D313yes—
451C2×C22⋊C4C22×D313yes—
452C2×C42—33no—
453C2×C42—33no—
454C2×C42—33no—
455C2×C42—31no—
456C2×C42—324no—
457C2×C42C22×D313yes—
458C2×C42C22×D313yes—
459C23×C3—26no—
460C23×C3—26no—
461C23×C3—26no—
462C23×C3C2516yes—
463C23×C3C2511yescharacteristic
464C22×D3—26no—
465C22×D3—26no—
466C22×D3—26no—
467C22×D3—26no—
468C22×D3—26no—
469C22×D3—26no—
470C22×D3C2516yes—
471C22×D3C2516yes—
472C3×Q8C2×#41116yescomplemented
473C3×D4—224no—
474C2×C3×C4—22no—
475C2×C3×C4—26no—
476C2×C3×C4—26no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—224no—
480C2×C3×C4—424no—
481C2×C3×C4C2×#41112yes—
482C2×C3×C4C2512yes—
483C2×C3×C4C2516yes—
484C2×C3×C4C2512yes—
485C2×C3×C4C2516yes—
486C2×C3×C4C2512yes—
487C2×C3×C4C2516yes—
488#67—224no—
489#67—424no—
490#67—424no—
491#67—412no—
492C2×Dic3—22no—
493C2×Dic3—22no—
494C2×Dic3—26no—
495C2×Dic3—26no—
496C2×Dic3—22no—
497C2×Dic3H(5,𝔽2)14yes—
498C2×Dic3C2512yes—
499C2×Dic3C2512yes—
500C2×Dic3C2516yes—
501C2×Dic3C2516yes—
502C2×Dic3C2512yes—
503C2×Dic3C2512yes—
504D12—224no—
505D12—224no—
506D12—412no—
507D12—424no—
508C4×D3—224no—
509C4×D3—224no—
510C4×D3—224no—
511C4×D3—412no—
512C4×D3—424no—
513Dic6—224no—
514C24—33no—
515C24—33no—
516C24C23×D313yes—
517#41—232no—
518#41—632no—
519#41—632no—
520#41—1296no—
521C2×Q8—312no—
522C2×Q8—612no—
523C2×Q8#23518yescomplemented
524C2×Q8C23×D314yes—
525C2×D4—212no—
526C2×D4—312no—
527C2×D4—324no—
528C2×D4—312no—
529C2×D4—324no—
530C2×D4—312no—
531C2×D4—312no—
532C2×D4—312no—
533C2×D4—324no—
534C2×D4—612no—
535C2×D4—612no—
536C2×D4—612no—
537C2×D4—1212no—
538C2×D4—126no—
539C2×D4—1212no—
540C2×D4—1212no—
541C2×D4—126no—
542C2×D4C23×D3112yes—
543C22×C4—212no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—31no—
547C22×C4—33no—
548C22×C4—33no—
549C22×C4—31no—
550C22×C4—312no—
551C22×C4—312no—
552C22×C4—312no—
553C22×C4—312no—
554C22×C4—324no—
555C22×C4—412no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—1212no—
560C22×C4—126no—
561C22×C4C23×D3112yes—
562C22×C4C23×D311yescharacteristic
563C22×C4C23×D313yes—
564C22×C4C23×D311yescharacteristic
565C22×C4C23×D313yes—
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D3124yes—
568C22×C4C23×D313yes—
569C4⋊C4—312no—
570C4⋊C4—312no—
571C4⋊C4—34no—
572C4⋊C4—312no—
573C4⋊C4—34no—
574C4⋊C4—34no—
575C4⋊C4—34no—
576C4⋊C4—324no—
577C4⋊C4—34no—
578C4⋊C4—312no—
579C4⋊C4—312no—
580C4⋊C4C23×D3112yes—
581C4⋊C4C23×D3112yes—
582C4⋊C4C23×D3112yes—
583C4⋊C4C23×D314yes—
584C22⋊C4—312no—
585C22⋊C4—312no—
586C22⋊C4—312no—
587C22⋊C4—324no—
588C22⋊C4—312no—
589C22⋊C4—312no—
590C22⋊C4—312no—
591C22⋊C4—312no—
592C22⋊C4—312no—
593C22⋊C4C23×D3112yes—
594C22⋊C4C23×D3112yes—
595C42—34no—
596C42—312no—
597C42—312no—
598C42—312no—
599C42C23×D3112yes—
600C42C23×D3112yes—
601C22×C3—26no—
602C22×C3—26no—
603C22×C3—26no—
604C22×C3—412no—
605C22×C3C22×#4112yes—
606C22×C3C2×H(5,𝔽2)12yes—
607C22×C3#58512yes—
608C22×C3C2611yescharacteristic
609C2×D3—26no—
610C2×D3—26no—
611C2×D3—26no—
612C2×D3—26no—
613C2×D3—26no—
614C2×D3—26no—
615C2×D3—412no—
616C2×D3—412no—
617C3×C4—22no—
618C3×C4—26no—
619C3×C4—26no—
620C3×C4—22no—
621C3×C4—22no—
622C3×C4C22×#41112yes—
623Dic3—22no—
624Dic3—22no—
625Dic3—26no—
626Dic3—26no—
627Dic3—22no—
628Dic3C2×H(5,𝔽2)14yes—
629C23—26no—
630C23—26no—
631C23—26no—
632C23—36no—
633C23—36no—
634C23—66no—
635C23—66no—
636C23—66no—
637C23—66no—
638C23—66no—
639C23—66no—
640C23C24×D316yes—
641C23C24×D311yescharacteristic
642Q8—624no—
643Q8C2×#235116yescomplemented
644D4—224no—
645D4—624no—
646D4—624no—
647D4—624no—
648D4—1224no—
649D4—1212no—
650D4—1224no—
651D4—1224no—
652D4—1212no—
653C2×C4—22no—
654C2×C4—26no—
655C2×C4—26no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—224no—
659C2×C4—34no—
660C2×C4—32no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—36no—
664C2×C4—36no—
665C2×C4—32no—
666C2×C4—424no—
667C2×C4—624no—
668C2×C4—62no—
669C2×C4—62no—
670C2×C4—66no—
671C2×C4—66no—
672C2×C4—62no—
673C2×C4—624no—
674C2×C4—624no—
675C2×C4—1224no—
676C2×C4—1212no—
677C2×C4C2×#235112yes—
678C2×C4C24×D312yes—
679C2×C4C24×D316yes—
680C2×C4C24×D312yes—
681C2×C4C24×D316yes—
682C2×C4C24×D312yes—
683C2×C4C24×D316yes—
684C2×C3—46no—
685C2×C3#351714yescomplemented
686C2×C3C23×#4111yescharacteristic
687C2×C3C22×H(5,𝔽2)11yescharacteristic
688C2×C3C2×#58511yescharacteristic
689D3—46no—
690D3—46no—
691C22—26no—
692C22—26no—
693C22—26no—
694C22—412no—
695C22—66no—
696C22—66no—
697C22—66no—
698C22—66no—
699C22—66no—
700C22—66no—
701C22—1212no—
702C22—1212no—
703C22C22×#23512yes—
704C22D3×H(5,𝔽2)12yes—
705C22#596812yes—
706C22C25×D311yescharacteristic
707C4—22no—
708C4—26no—
709C4—26no—
710C4—22no—
711C4—22no—
712C4—34no—
713C4—62no—
714C4—62no—
715C4—66no—
716C4—66no—
717C4—62no—
718C4C22×#235112yes—
719C3C2×#351711yescharacteristic, complemented, Sylow
720C2—46no—
721C2—126no—
722C2—126no—
723C2#8589614yesdirect product factor
724C2C23×#23511yescharacteristic
725C2C2×D3×H(5,𝔽2)11yescharacteristic
726C2C2×#596811yescharacteristic
subgroupG/H
centerC23C24×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC2×C3×#520C2
socleC23×C3C25
hypercenterC2×#520D3
hypocenterC3C2×#3517
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×C3×#520C2semidirect
2. C2×#5834C2semidirect
3. C2×#5834C2semidirect
4. #85896C2direct (N × H)
5. C2×#5569C2semidirect
6. C2×#5577C2semidirect
7. C2×#5574C2semidirect
8. C2×C4×#239C2semidirect
9. C2×#5558C2semidirect
10. C2×#5562C2semidirect
11. C2×#5548C2semidirect
12. C2×#5553C2semidirect
13. C2×#5535C2semidirect
14. C2×#5528C2semidirect
15. C2×#5514C2semidirect
16. C2×#5507C2semidirect
22. C3×#520C22semidirect
29. #5834C22semidirect
30. #5834C22semidirect
44. #5577C22semidirect
45. #5574C22semidirect
46. C4×#239C22semidirect
47. #5569C22semidirect
48. #5562C22semidirect
49. #5558C22semidirect
50. #5553C22semidirect
51. #5548C22semidirect
52. #5535C22semidirect
53. #5528C22semidirect
54. #5514C22semidirect
57. #5507C22semidirect
97. C2×#520D3semidirect
245. #520C2×D3semidirect
272. C2×C3×Q8#41semidirect
472. C3×Q8C2×#41semidirect
523. C2×Q8#235semidirect
643. Q8C2×#235semidirect
685. C2×C3#3517semidirect
719. C3C2×#3517semidirect
723. C2#85896direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5202
C2×#58342
#858962
C2×#55692
C2×#55772
C2×#55742
C2×C4×#2392
C2×#55582
C2×#55622
C2×#55482
C2×#55532
C2×#55352
C2×#55282
C2×#55142
C2×#55072
C2×#35173