Finite Group Databasebeta

← C2×#20288726 #28292357

Subgroups — C2×#20288726 #28292357

Order 13568.

7118 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
1#20288726C2132yesmaximal, direct product factor
2C2×Q8×Dic106C211yesmaximal, characteristic, complemented
3C2×#16811346C213yesmaximal, complemented
4C2×#16811345C213yesmaximal, complemented
5C2×#16811341C213yesmaximal, complemented
6C2×#16811336C213yesmaximal, complemented
7C2×Q8×C22⋊D53C211yesmaximal, characteristic, complemented
8C2×#16811285C211yesmaximal, characteristic, complemented
9C2×#16811284C211yesmaximal, characteristic, complemented
10C2×#16811245C213yesmaximal, complemented
11C2×#16811244C213yesmaximal, complemented
12C2×#16811177C213yesmaximal, complemented
13C2×#16811151C213yesmaximal, complemented
14C2×#16811099C211yesmaximal, characteristic, complemented
15C2×C4×#11719949C211yesmaximal, characteristic, complemented
16C2×C53×#519C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19Q8×Dic106C22116yescomplemented
20#16811346C22148yescomplemented
21#16811345C22148yescomplemented
22#16811341C22148yescomplemented
23#16811336C22148yescomplemented
24Q8×C22⋊D53C22116yescomplemented
25#16811285C22116yescomplemented
26#16811284C22116yescomplemented
27#16811245C22148yescomplemented
28#16811244C22148yescomplemented
29#16811177C22148yescomplemented
30C2×#13133217C2213yes—
31C2×#13133216C2213yes—
32C2×#13133216C2213yes—
33C2×#13133215C2213yes—
34#16811151C22148yescomplemented
35C2×#13133212C2216yes—
36C2×#13133212C2213yes—
37C2×#13133211C2216yes—
38C2×#13133210C2213yes—
39C2×#13133207C2213yes—
40C2×#13133206C2213yes—
41C2×#13133205C2213yes—
42C2×#13133205C2216yes—
43C2×#13133203C2216yes—
44C2×#13133203C2211yescharacteristic
45C2×#13133202C2213yes—
46C2×#13133199C2213yes—
47C2×#13133197C2213yes—
48C2×#13133196C2213yes—
49C2×#13133195C2216yes—
50C2×#13133195C2213yes—
51C2×#13133193C2213yes—
52C2×#13133193C2213yes—
53C2×#13133192C2213yes—
54C2×#13133191C2213yes—
55C2×#13133190C2213yes—
56#16811099C22116yescomplemented
57C4×#11719949C22116yescomplemented
58C2×Q8×Dic53C2211yescharacteristic
59C2×Q8×Dic53C2211yescharacteristic
60C2×C4×Dic106C2216yes—
61C2×C4×Dic106C2213yes—
62C2×C4×Dic106C2213yes—
63C2×#13133182C2213yes—
64C2×C4×D212C2213yes—
65C2×C4×D212C2213yes—
66C2×#13133179C2213yes—
67C2×C4×C22⋊D53C2213yes—
68C2×C4×C22⋊D53C2213yes—
69C2×#13133175C2213yes—
70C2×#13133175C2213yes—
71C2×#13133174C2216yes—
72C2×#13133174C2213yes—
73C2×C42×D53C2213yes—
74C23×Q8×C53C2211yescharacteristic
75C53×#519C22116yescomplemented
76C2×C4×Q8×C53C2213yes—
77C2×C4×Q8×C53C2213yes—
78C2×C4×Q8×C53C2211yescharacteristic
79C2×C4×Q8×C53C2211yescharacteristic
80C2×#117×C53C2213yes—
81C2×#117×C53C2213yes—
82C2×#11719949—28no—
83C2×#11719949C2318yes—
84C22×Dic106C2313yes—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2316yes—
87C2×Q8×D53—28no—
88C2×Q8×D53C2318yes—
89C22×D212C2313yes—
90C22×D212C2313yes—
91C22×C22⋊D53C2311yescharacteristic
92C22×C22⋊D53C2313yes—
93C22×C4×D53C2313yes—
94C22×C4×D53C2313yes—
95C22×C4×D53C2313yes—
96C22×C4×D53C2313yes—
97#13133217C23124yes—
98#13133216C23124yes—
99#13133216C23124yes—
100#13133215C23124yes—
101#13133212C23148yes—
102#13133212C23124yes—
103#13133211C23148yes—
104#13133210C23124yes—
105#13133207C23124yes—
106#13133206C23124yes—
107#13133205C23124yes—
108#13133205C23148yes—
109#13133203C23148yes—
110#13133203C2318yes—
111#13133202C23124yes—
112#13133199C23124yes—
113#13133197C23124yes—
114#13133196C23124yes—
115#13133195C23124yes—
116#13133195C23148yes—
117#13133193C23124yes—
118#13133193C23124yes—
119#13133192C23124yes—
120#13133191C23124yes—
121#13133190C23124yes—
122Q8×Dic53C2318yes—
123Q8×Dic53C2318yes—
124C4×Dic106C23148yes—
125C4×Dic106C23124yes—
126C4×Dic106C23124yes—
127#13133182C23124yes—
128C4×D212C23124yes—
129C4×D212C23124yes—
130#13133179C23124yes—
131C4×C22⋊D53C23124yes—
132C4×C22⋊D53C23124yes—
133#13133175C23124yes—
134#13133175C23124yes—
135#13133174C23148yes—
136#13133174C23124yes—
137C2×C4⋊Dic53C2313yes—
138C2×C4⋊Dic53C2313yes—
139C2×C4⋊Dic53C2313yes—
140C2×C4⋊Dic53C2313yes—
141C2×#11719919C2313yes—
142C2×#11719919C2313yes—
143C2×#11719919C2313yes—
144C2×#11719919C2313yes—
145C2×#11719919C2313yes—
146C2×#11719919C2316yes—
147C2×#11719919C2313yes—
148C2×C22⋊Dic53C2311yescharacteristic
149C2×C22⋊Dic53C2313yes—
150C2×#11719921C2311yescharacteristic
151C2×#11719921C2313yes—
152C2×#11719921C2316yes—
153C2×#11719921C2316yes—
154C2×#11719921C2316yes—
155C2×#11719921C2313yes—
156C2×#11719921C2313yes—
157C2×#11719921C2311yescharacteristic
158C2×#11719921C2313yes—
159C2×C4×Dic53C2311yescharacteristic
160C2×C4×Dic53C2313yes—
161C2×C4×Dic53C2313yes—
162C2×C4×Dic53C2316yes—
163C2×C4×Dic53C2313yes—
164C42×D53C23124yes—
165C22×Q8×C53—28no—
166C22×Q8×C53C2318yes—
167C22×Q8×C53C2313yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53C2313yes—
170C4×Q8×C53C2318yes—
171C4×Q8×C53C23124yes—
172C4×Q8×C53C2318yes—
173C4×Q8×C53C23124yes—
174#117×C53C23124yes—
175#117×C53C23124yes—
176C2×C4⋊C4×C53C2313yes—
177C2×C4⋊C4×C53C2313yes—
178C2×C4⋊C4×C53C2313yes—
179C2×C4⋊C4×C53C2313yes—
180C2×C22⋊C4×C53C2313yes—
181C2×C22⋊C4×C53C2311yescharacteristic
182C2×C42×C53C2313yes—
183C2×C42×C53C2316yes—
184C2×C42×C53C2313yes—
185C24×C53C2411yescharacteristic
186C23×D53C2411yescharacteristic
187C23×D53C2413yes—
188C2×Q8×C53—232no—
189C2×Q8×C53—212no—
190C2×Q8×C53#4118yes—
191C2×Q8×C53C24112yes—
192C2×Q8×C53C2414yes—
193C22×C4×C53—212no—
194C22×C4×C53C2413yes—
195C22×C4×C53C2411yescharacteristic
196C22×C4×C53C2411yescharacteristic
197C22×C4×C53C2413yes—
198C22×C4×C53C2413yes—
199C22×C4×C53C24112yes—
200C22×C4×C53C2413yes—
201C2×C22⋊D53—24no—
202C2×C22⋊D53—46no—
203C2×C22⋊D53C2414yes—
204C2×C22⋊D53C24112yes—
205C22×Dic53C2411yescharacteristic
206C22×Dic53C2411yescharacteristic
207C22×Dic53C2413yes—
208C22×Dic53C2413yes—
209C22×Dic53C2413yes—
210C22×Dic53C2411yescharacteristic
211#11719949—232no—
212Q8×D53—232no—
213C2×D212—212no—
214C2×D212—46no—
215C2×D212C24112yes—
216C2×D212C24112yes—
217C2×C4×D53—212no—
218C2×C4×D53—212no—
219C2×C4×D53—212no—
220C2×C4×D53—46no—
221C2×C4×D53C24112yes—
222C2×C4×D53C24112yes—
223C2×C4×D53C24112yes—
224C2×C4×D53C24112yes—
225C2×Dic106—212no—
226C2×Dic106—24no—
227C2×Dic106—412no—
228C2×Dic106C24112yes—
229C2×Dic106C2414yes—
230C2×Dic106C24124yes—
231C4⋊C4×C53C24112yes—
232C4⋊C4×C53C24112yes—
233C4⋊C4×C53C24112yes—
234C4⋊C4×C53C24112yes—
235C22⋊C4×C53C24112yes—
236C22⋊C4×C53C2414yes—
237C42×C53C24112yes—
238C42×C53C24124yes—
239C42×C53C24112yes—
240C22⋊Dic53C2414yes—
241C22⋊Dic53C24112yes—
242#11719921C2414yes—
243#11719921C24112yes—
244#11719921C24124yes—
245#11719921C24124yes—
246#11719921C24124yes—
247#11719921C24112yes—
248#11719921C24112yes—
249#11719921C2414yes—
250#11719921C24112yes—
251C4⋊Dic53C24112yes—
252C4⋊Dic53C24112yes—
253C4⋊Dic53C24112yes—
254C4⋊Dic53C24112yes—
255#11719919C24112yes—
256#11719919C24112yes—
257#11719919C24112yes—
258#11719919C24112yes—
259#11719919C24112yes—
260#11719919C24124yes—
261#11719919C24112yes—
262C4×Dic53C2414yes—
263C4×Dic53C24112yes—
264C4×Dic53C24112yes—
265C4×Dic53C24124yes—
266C4×Dic53C24112yes—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53C2512yes—
271C23×C53C2511yescharacteristic
272C22×D53—22no—
273C22×D53—26no—
274C22×D53—26no—
275C22×D53—22no—
276C22×D53—26no—
277C22×D53—22no—
278C22×D53C2512yes—
279C22×D53C2516yes—
280Q8×C53—224no—
281Q8×C53C2×#41116yes—
282C2×C4×C53—26no—
283C2×C4×C53—22no—
284C2×C4×C53—26no—
285C2×C4×C53—26no—
286C2×C4×C53—22no—
287C2×C4×C53—224no—
288C2×C4×C53C2×#41112yes—
289C2×C4×C53C2516yes—
290C2×C4×C53C2512yes—
291C2×C4×C53C2512yes—
292C2×C4×C53C2516yes—
293C2×C4×C53C2516yes—
294C2×C4×C53C2516yes—
295C22⋊D53—28no—
296C22⋊D53—412no—
297C2×Dic53—26no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—26no—
301C2×Dic53—26no—
302C2×Dic532−1+414yes—
303C2×Dic53C2516yes—
304C2×Dic53C2516yes—
305C2×Dic53C2516yes—
306C2×Dic53C2512yes—
307C2×Dic53C2512yes—
308C2×Dic53C2512yes—
309D212—224no—
310D212—412no—
311C4×D53—224no—
312C4×D53—224no—
313C4×D53—224no—
314C4×D53—412no—
315Dic106—224no—
316Dic106—28no—
317Dic106—424no—
318C2×#3518—531nomaximal, Sylow
319C22×C53—22no—
320C22×C53—22no—
321C22×C53—22no—
322C22×C53—44no—
323C22×C53C22×#4112yes—
324C22×C53C2×2−1+412yes—
325C22×C53#58512yes—
326C22×C53C2611yescharacteristic
327C2×D53—22no—
328C2×D53—26no—
329C2×D53—26no—
330C2×D53—22no—
331C2×D53—26no—
332C2×D53—22no—
333C2×D53—44no—
334C2×D53—412no—
335C4×C53—26no—
336C4×C53—22no—
337C4×C53—26no—
338C4×C53—26no—
339C4×C53—22no—
340C4×C53C22×#41112yes—
341Dic53—26no—
342Dic53—22no—
343Dic53—22no—
344Dic53—26no—
345Dic53—26no—
346Dic53C2×2−1+414yes—
347#3518—5332no—
348C2×Q82—531no—
349C2×#556—533no—
350C2×#556—533no—
351C2×#556—533no—
352C2×#555—533no—
353C2×D4×Q8—531no—
354C2×#548—531no—
355C2×#548—531no—
356C2×#542—533no—
357C2×#542—533no—
358C2×#533—533no—
359C2×#529—533no—
360C2×#519—531no—
361C2×#519D5311yescharacteristic, complemented
362C2×C4×#41—531no—
363C2×C53—42no—
364C2×C53#351814yescomplemented
365C2×C53C23×#4111yescharacteristic
366C2×C53C22×2−1+411yescharacteristic
367C2×C53C2×#58511yescharacteristic
368D53—42no—
369D53—46no—
370C22×#41—531no—
371C23×Q8—531no—
372C23×Q8C2×D5311yescharacteristic
373Q82—5316no—
374#556—5348no—
375#556—5348no—
376#556—5348no—
377#555—5348no—
378D4×Q8—5316no—
379#548—5316no—
380#548—5316no—
381#542—5348no—
382#542—5348no—
383#533—5348no—
384C2×C4⋊Q8—533no—
385C2×C4⋊Q8—533no—
386C2×C4⋊Q8—533no—
387C2×C4⋊Q8—533no—
388#529—5348no—
389C2×#126—533no—
390C2×#126—536no—
391C2×#126—533no—
392C2×#126—536no—
393C2×#125—533no—
394C2×#124—533no—
395C2×#124—531no—
396C2×#124—536no—
397C2×#124—533no—
398C2×#124—536no—
399C2×#123—533no—
400C2×#123—533no—
401C2×C22⋊Q8—533no—
402C2×C22⋊Q8—533no—
403C2×C22⋊Q8—533no—
404C2×C22⋊Q8—533no—
405C2×C22⋊Q8—536no—
406C2×C22⋊Q8—533no—
407C2×#121—533no—
408C2×#121—533no—
409C2×#121—533no—
410#519—5316no—
411#519C2×D53116yescomplemented
412C4×#41—5316no—
413C2×C4×Q8—531no—
414C2×C4×Q8—531no—
415C2×C4×Q8—533no—
416C2×C4×Q8—533no—
417C2×C4×Q8—533no—
418C2×C4×Q8—536no—
419C2×C4×Q8C2×D5311yescharacteristic
420C2×C4×Q8C2×D5313yes—
421C2×C4×Q8C2×D5311yescharacteristic
422C2×C4×Q8C2×D5313yes—
423C2×C4×D4—533no—
424C2×C4×D4—533no—
425C2×C4×D4—533no—
426C2×C4×D4—533no—
427C2×C4×D4—533no—
428C2×#117—533no—
429C2×#117—533no—
430C2×#117—533no—
431C2×#117—536no—
432C2×#117C2×D5313yes—
433C2×#117C2×D5313yes—
434C22×C42—533no—
435C53C2×#351811yescharacteristic, complemented, Sylow
436C2×#41—538no—
437C2×#41—1068no—
438C22×Q8—28no—
439C22×Q8—538no—
440C22×Q8—531no—
441C22×Q8—533no—
442C22×Q8—536no—
443C22×Q8—1068no—
444C22×Q8C22×D5313yes—
445C22×Q8C22×D5318yes—
446C22×Q8C22×D5311yescharacteristic
447C22×D4—531no—
448C22×D4—533no—
449C22×D4—533no—
450C22×D4—533no—
451C23×C4—533no—
452C23×C4—533no—
453C23×C4—533no—
454C23×C4—533no—
455C23×C4C22×D5313yes—
456C4⋊Q8—5324no—
457C4⋊Q8—5324no—
458C4⋊Q8—5324no—
459C4⋊Q8—5324no—
460#126—5324no—
461#126—5348no—
462#126—5324no—
463#126—5348no—
464#125—5324no—
465#124—5324no—
466#124—538no—
467#124—5348no—
468#124—5324no—
469#124—5348no—
470#123—5324no—
471#123—5324no—
472C22⋊Q8—5324no—
473C22⋊Q8—5324no—
474C22⋊Q8—5324no—
475C22⋊Q8—5324no—
476C22⋊Q8—5348no—
477C22⋊Q8—5324no—
478#121—5324no—
479#121—5324no—
480#121—5324no—
481C4×Q8—538no—
482C4×Q8—538no—
483C4×Q8—5324no—
484C4×Q8—5324no—
485C4×Q8—5324no—
486C4×Q8—5348no—
487C4×Q8C22×D5318yes—
488C4×Q8C22×D53124yes—
489C4×Q8C22×D5318yes—
490C4×Q8C22×D53124yes—
491C4×D4—5324no—
492C4×D4—5324no—
493C4×D4—5324no—
494C4×D4—5324no—
495C4×D4—5324no—
496#117—5324no—
497#117—5324no—
498#117—5324no—
499#117—5348no—
500#117C22×D53124yes—
501#117C22×D53124yes—
502C2×C4⋊C4—533no—
503C2×C4⋊C4—533no—
504C2×C4⋊C4—533no—
505C2×C4⋊C4—533no—
506C2×C4⋊C4—533no—
507C2×C4⋊C4—533no—
508C2×C4⋊C4—533no—
509C2×C4⋊C4—533no—
510C2×C4⋊C4—536no—
511C2×C4⋊C4—533no—
512C2×C4⋊C4—533no—
513C2×C4⋊C4C22×D5313yes—
514C2×C4⋊C4C22×D5313yes—
515C2×C4⋊C4C22×D5313yes—
516C2×C4⋊C4C22×D5313yes—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—533no—
519C2×C22⋊C4—533no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—536no—
522C2×C22⋊C4—536no—
523C2×C22⋊C4—536no—
524C2×C22⋊C4—531no—
525C2×C22⋊C4—533no—
526C2×C22⋊C4—533no—
527C2×C22⋊C4—533no—
528C2×C22⋊C4C22×D5313yes—
529C2×C22⋊C4C22×D5311yescharacteristic
530C2×C42—536no—
531C2×C42—533no—
532C2×C42—533no—
533C2×C42—533no—
534C2×C42—531no—
535C2×C42—5324no—
536C2×C42C22×D5313yes—
537C2×C42C22×D5316yes—
538C2×C42C22×D5313yes—
539C24—531no—
540C24—533no—
541C24C23×D5311yescharacteristic
542#41—10632no—
543C2×Q8—232no—
544C2×Q8—212no—
545C2×Q8—534no—
546C2×Q8—5312no—
547C2×Q8—5324no—
548C2×Q8—1064no—
549C2×Q8—10632no—
550C2×Q8—10612no—
551C2×Q8—21212no—
552C2×Q8#1171994518yes—
553C2×Q8C23×D53112yes—
554C2×Q8C23×D5314yes—
555C2×D4—534no—
556C2×D4—5312no—
557C2×D4—5312no—
558C2×D4—5312no—
559C2×D4—1064no—
560C2×D4—10612no—
561C2×D4—2126no—
562C2×D4—2126no—
563C22×C4—212no—
564C22×C4—531no—
565C22×C4—531no—
566C22×C4—531no—
567C22×C4—533no—
568C22×C4—533no—
569C22×C4—533no—
570C22×C4—5312no—
571C22×C4—5312no—
572C22×C4—5312no—
573C22×C4—5312no—
574C22×C4—10612no—
575C22×C4—10612no—
576C22×C4—10612no—
577C22×C4—2126no—
578C22×C4C23×D53112yes—
579C22×C4C23×D5313yes—
580C22×C4C23×D5311yescharacteristic
581C22×C4C23×D5311yescharacteristic
582C22×C4C23×D5313yes—
583C22×C4C23×D5313yes—
584C22×C4C23×D5313yes—
585C4⋊C4—5312no—
586C4⋊C4—5312no—
587C4⋊C4—5312no—
588C4⋊C4—5312no—
589C4⋊C4—5312no—
590C4⋊C4—5312no—
591C4⋊C4—5312no—
592C4⋊C4—5312no—
593C4⋊C4—5324no—
594C4⋊C4—5312no—
595C4⋊C4—5312no—
596C4⋊C4C23×D53112yes—
597C4⋊C4C23×D53112yes—
598C4⋊C4C23×D53112yes—
599C4⋊C4C23×D53112yes—
600C22⋊C4—534no—
601C22⋊C4—5312no—
602C22⋊C4—5312no—
603C22⋊C4—534no—
604C22⋊C4—5324no—
605C22⋊C4—5324no—
606C22⋊C4—5324no—
607C22⋊C4—534no—
608C22⋊C4—5312no—
609C22⋊C4—5312no—
610C22⋊C4—5312no—
611C22⋊C4C23×D53112yes—
612C22⋊C4C23×D5314yes—
613C42—534no—
614C42—5312no—
615C42—5312no—
616C42—5324no—
617C42—5312no—
618C42C23×D53112yes—
619C42C23×D53124yes—
620C42C23×D53112yes—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—532no—
625C23—536no—
626C23—1062no—
627C23—1066no—
628C23—1066no—
629C23—1062no—
630C23—1066no—
631C23—1062no—
632C23C24×D5312yes—
633C23C24×D5311yescharacteristic
634Q8—224no—
635Q8—1068no—
636Q8—10624no—
637Q8—21224no—
638Q8C2×#11719945116yes—
639D4—1068no—
640D4—10624no—
641D4—21212no—
642D4—21212no—
643C2×C4—26no—
644C2×C4—26no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—26no—
648C2×C4—224no—
649C2×C4—534no—
650C2×C4—532no—
651C2×C4—532no—
652C2×C4—532no—
653C2×C4—536no—
654C2×C4—536no—
655C2×C4—536no—
656C2×C4—10624no—
657C2×C4—1062no—
658C2×C4—1066no—
659C2×C4—1062no—
660C2×C4—1066no—
661C2×C4—1066no—
662C2×C4—10624no—
663C2×C4—10624no—
664C2×C4—21212no—
665C2×C4C2×#11719945112yes—
666C2×C4C24×D5316yes—
667C2×C4C24×D5312yes—
668C2×C4C24×D5312yes—
669C2×C4C24×D5316yes—
670C2×C4C24×D5316yes—
671C2×C4C24×D5316yes—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—44no—
676C22—1062no—
677C22—1066no—
678C22—1066no—
679C22—1062no—
680C22—1066no—
681C22—1062no—
682C22—2124no—
683C22—21212no—
684C22C22×#1171994512yes—
685C222−1+4×D5312yes—
686C22#1681146012yes—
687C22C25×D5311yescharacteristic
688C4—26no—
689C4—26no—
690C4—22no—
691C4—22no—
692C4—26no—
693C4—534no—
694C4—1062no—
695C4—1066no—
696C4—1062no—
697C4—1066no—
698C4—1066no—
699C4C22×#11719945112yes—
700C2—42no—
701C2—2122no—
702C2—2126no—
703C2#2028872614yesdirect product factor
704C2C23×#1171994511yescharacteristic
705C2C2×2−1+4×D5311yescharacteristic
706C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#519C2
socleC23×C53C25
hypercenterC2×#519D53
hypocenterC53C2×#3518
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #20288726C2direct (N × H)
2. C2×Q8×Dic106C2semidirect
3. C2×#16811346C2semidirect
4. C2×#16811345C2semidirect
5. C2×#16811341C2semidirect
6. C2×#16811336C2semidirect
7. C2×Q8×C22⋊D53C2semidirect
8. C2×#16811285C2semidirect
9. C2×#16811284C2semidirect
10. C2×#16811245C2semidirect
11. C2×#16811244C2semidirect
12. C2×#16811177C2semidirect
13. C2×#16811151C2semidirect
14. C2×#16811099C2semidirect
15. C2×C4×#11719949C2semidirect
16. C2×C53×#519C2semidirect
19. Q8×Dic106C22semidirect
20. #16811346C22semidirect
21. #16811345C22semidirect
22. #16811341C22semidirect
23. #16811336C22semidirect
24. Q8×C22⋊D53C22semidirect
25. #16811285C22semidirect
26. #16811284C22semidirect
27. #16811245C22semidirect
28. #16811244C22semidirect
29. #16811177C22semidirect
34. #16811151C22semidirect
56. #16811099C22semidirect
57. C4×#11719949C22semidirect
75. C53×#519C22semidirect
361. C2×#519D53semidirect
364. C2×C53#3518semidirect
411. #519C2×D53semidirect
435. C53C2×#3518semidirect
703. C2#20288726direct (N × H)

Maximal subgroups

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

subgroupindex
#202887262
C2×Q8×Dic1062
C2×#168113462
C2×#168113452
C2×#168113412
C2×#168113362
C2×Q8×C22⋊D532
C2×#168112852
C2×#168112842
C2×#168112452
C2×#168112442
C2×#168111772
C2×#168111512
C2×#168110992
C2×C4×#117199492
C2×C53×#5192
C2×#351853