Finite Group Databasebeta

← C2×#20288711 #28292292

Subgroups — C2×#20288711 #28292292

Order 13568.

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
1#20288711C2132yesmaximal, direct product factor
2C2×#16811346C213yesmaximal, complemented
3C2×#16811334C213yesmaximal, complemented
4C2×#16811326C213yesmaximal, complemented
5C2×#16811311C213yesmaximal, complemented
6C2×Q8×D212C211yesmaximal, characteristic, complemented
7C2×#16811285C211yesmaximal, characteristic, complemented
8C2×#16811285C211yesmaximal, characteristic, complemented
9C2×#16811247C213yesmaximal, complemented
10C2×#16811236C213yesmaximal, complemented
11C2×#16811160C213yesmaximal, complemented
12C2×#16811158C213yesmaximal, complemented
13C2×#16811105C211yesmaximal, characteristic, complemented
14C2×#16811099C211yesmaximal, characteristic, complemented
15C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
16C2×C53×#557C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Q8×D53C2211yescharacteristic
20#16811346C22148yescomplemented
21#16811334C22148yescomplemented
22#16811326C22148yescomplemented
23#16811311C22148yescomplemented
24Q8×D212C22116yescomplemented
25#16811285C22116yescomplemented
26#16811285C22116yescomplemented
27#16811247C22148yescomplemented
28#16811236C22148yescomplemented
29C2×#13133217C2213yes—
30#16811160C22148yescomplemented
31#16811158C22148yescomplemented
32C2×#13133212C2213yes—
33C2×#13133212C2216yes—
34C2×#13133212C2216yes—
35C2×#13133212C2213yes—
36C2×#13133208C2213yes—
37C2×#13133208C2216yes—
38C2×#13133206C2213yes—
39C2×#13133205C2213yes—
40C2×#13133205C2213yes—
41C2×#13133202C2216yes—
42C2×#13133202C2213yes—
43C2×#13133202C2211yescharacteristic
44C2×#13133197C2213yes—
45C2×#13133197C2213yes—
46C2×#13133197C2213yes—
47C2×#13133197C2213yes—
48C2×#13133193C2216yes—
49C2×#13133193C2213yes—
50C2×#13133192C2213yes—
51C2×#13133192C2213yes—
52C2×#13133192C2213yes—
53#16811105C22116yescomplemented
54#16811099C22116yescomplemented
55C2×Q8×Dic53C2211yescharacteristic
56C2×C4×Dic106C2213yes—
57C2×C4×Dic106C2213yes—
58C2×#13133182C2213yes—
59C2×#13133182C2213yes—
60C4×Q8×D53C22116yescomplemented
61C2×C4×D212C2213yes—
62C2×C4×D212C2213yes—
63C2×C4×D212C2213yes—
64C2×C4×D212C2213yes—
65C2×#13133179C2213yes—
66C2×#13133179C2216yes—
67C2×#13133175C2216yes—
68C2×#13133175C2213yes—
69C2×#13133174C2213yes—
70C2×#13133174C2213yes—
71C2×C4⋊C4×D53C2213yes—
72C2×C4⋊C4×D53C2213yes—
73C2×C42×D53C2213yes—
74C53×#557C22116yescomplemented
75C2×C4⋊Q8×C53C2213yes—
76C2×#125×C53C2213yes—
77C2×#125×C53C2213yes—
78C2×C4×Q8×C53C2213yes—
79C2×C4×Q8×C53C2211yescharacteristic
80C2×C4×Q8×C53C2211yescharacteristic
81C2×C4×Q8×C53C2211yescharacteristic
82C2×#11719949—28no—
83C2×#11719949C2318yes—
84C22×Dic106C2313yes—
85C22×Dic106C2313yes—
86C2×Q8×D53—28no—
87C2×Q8×D53—28no—
88C2×Q8×D53C2318yes—
89C2×Q8×D53C2318yes—
90C22×D212C2313yes—
91C22×D212C2313yes—
92C22×D212C2311yescharacteristic
93C22×D212C2313yes—
94C22×C4×D53C2311yescharacteristic
95C22×C4×D53C2313yes—
96C22×C4×D53C2313yes—
97C22×C4×D53C2313yes—
98C22×C4×D53C2313yes—
99C22×C4×D53C2316yes—
100#13133217C23124yes—
101#13133212C23124yes—
102#13133212C23148yes—
103#13133212C23124yes—
104#13133212C23148yes—
105#13133208C23148yes—
106#13133208C23124yes—
107#13133206C23124yes—
108#13133205C23124yes—
109#13133205C23124yes—
110#13133202C23148yes—
111#13133202C23124yes—
112#13133202C2318yes—
113#13133197C23124yes—
114#13133197C23124yes—
115#13133197C23124yes—
116#13133197C23124yes—
117#13133193C23124yes—
118#13133193C23148yes—
119#13133192C23124yes—
120#13133192C23124yes—
121#13133192C23124yes—
122Q8×Dic53C2318yes—
123C4×Dic106C23124yes—
124C4×Dic106C23124yes—
125#13133182C23124yes—
126#13133182C23124yes—
127C4×D212C23124yes—
128C4×D212C23124yes—
129C4×D212C23124yes—
130C4×D212C23124yes—
131#13133179C23148yes—
132#13133179C23124yes—
133#13133175C23124yes—
134#13133175C23148yes—
135#13133174C23124yes—
136#13133174C23124yes—
137C2×C4⋊Dic53C2313yes—
138C2×C4⋊Dic53C2316yes—
139C2×C4⋊Dic53C2313yes—
140C2×C4⋊Dic53C2313yes—
141C2×C4⋊Dic53C2313yes—
142C2×#11719919C2313yes—
143C2×#11719919C2316yes—
144C2×#11719919C2311yescharacteristic
145C2×#11719919C2313yes—
146C2×#11719919C2313yes—
147C4⋊C4×D53C23124yes—
148C4⋊C4×D53C23124yes—
149C2×#11719921C2311yescharacteristic
150C2×#11719921C2313yes—
151C2×#11719921C2313yes—
152C2×#11719921C2313yes—
153C2×#11719921C2313yes—
154C2×#11719921C2316yes—
155C2×#11719921C2313yes—
156C2×#11719921C2316yes—
157C2×#11719921C2311yescharacteristic
158C2×#11719921C2311yescharacteristic
159C2×#11719921C2313yes—
160C2×#11719921C2313yes—
161C2×C4×Dic53C2313yes—
162C2×C4×Dic53C2313yes—
163C2×C4×Dic53C2313yes—
164C2×C4×Dic53C2316yes—
165C42×D53C23124yes—
166C22×Q8×C53C2313yes—
167C22×Q8×C53C2311yescharacteristic
168C4⋊Q8×C53C23124yes—
169#125×C53C23124yes—
170#125×C53C23124yes—
171C4×Q8×C53C2318yes—
172C4×Q8×C53C2318yes—
173C4×Q8×C53C2318yes—
174C4×Q8×C53C23124yes—
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2313yes—
177C2×C4⋊C4×C53C2313yes—
178C2×C4⋊C4×C53C2313yes—
179C2×C4⋊C4×C53C2313yes—
180C2×C4⋊C4×C53C2313yes—
181C2×C4⋊C4×C53C2316yes—
182C2×C42×C53C2313yes—
183C2×C42×C53C2313yes—
184C2×C42×C53C2313yes—
185C23×D53C2411yescharacteristic
186C23×D53C2413yes—
187C23×D53C2411yescharacteristic
188C2×Q8×C53—46no—
189C2×Q8×C53#4118yes—
190C2×Q8×C53C24112yes—
191C2×Q8×C53C2414yes—
192C22×C4×C53C2411yescharacteristic
193C22×C4×C53C2411yescharacteristic
194C22×C4×C53C2411yescharacteristic
195C22×C4×C53C2413yes—
196C22×C4×C53C2413yes—
197C22×C4×C53C2413yes—
198C22×C4×C53C2413yes—
199C22×Dic53C2411yescharacteristic
200C22×Dic53C2413yes—
201C22×Dic53C2413yes—
202C22×Dic53C2413yes—
203C22×Dic53C2411yescharacteristic
204#11719949—232no—
205Q8×D53—232no—
206Q8×D53—232no—
207C2×D212—212no—
208C2×D212—24no—
209C2×D212—212no—
210C2×D212—46no—
211C2×D212C24112yes—
212C2×D212C24112yes—
213C2×D212C2414yes—
214C2×D212C24112yes—
215C2×C4×D53—24no—
216C2×C4×D53—212no—
217C2×C4×D53—212no—
218C2×C4×D53—212no—
219C2×C4×D53—412no—
220C2×C4×D53—46no—
221C2×C4×D53C2414yes—
222C2×C4×D53C24112yes—
223C2×C4×D53C24112yes—
224C2×C4×D53C24112yes—
225C2×C4×D53C24112yes—
226C2×C4×D53C24124yes—
227C2×Dic106—212no—
228C2×Dic106—212no—
229C2×Dic106C24112yes—
230C2×Dic106C24112yes—
231C4⋊C4×C53C2414yes—
232C4⋊C4×C53C24112yes—
233C4⋊C4×C53C24112yes—
234C4⋊C4×C53C24112yes—
235C4⋊C4×C53C24112yes—
236C4⋊C4×C53C24112yes—
237C4⋊C4×C53C24124yes—
238C42×C53C24112yes—
239C42×C53C24112yes—
240C42×C53C24112yes—
241#11719921C2414yes—
242#11719921C24112yes—
243#11719921C24112yes—
244#11719921C24112yes—
245#11719921C24112yes—
246#11719921C24124yes—
247#11719921C24112yes—
248#11719921C24124yes—
249#11719921C2414yes—
250#11719921C2414yes—
251#11719921C24112yes—
252#11719921C24112yes—
253C4⋊Dic53C24112yes—
254C4⋊Dic53C24124yes—
255C4⋊Dic53C24112yes—
256C4⋊Dic53C24112yes—
257C4⋊Dic53C24112yes—
258#11719919C24112yes—
259#11719919C24124yes—
260#11719919C2414yes—
261#11719919C24112yes—
262#11719919C24112yes—
263C4×Dic53C24112yes—
264C4×Dic53C24112yes—
265C4×Dic53C24112yes—
266C4×Dic53C24124yes—
267C23×C53C2511yescharacteristic
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—26no—
272C22×D53—22no—
273C22×D53—26no—
274C22×D53—26no—
275C22×D53—22no—
276C22×D532−1+414yes—
277C22×D53C2512yes—
278C22×D53C2516yes—
279C22×D53C2512yes—
280Q8×C53—412no—
281Q8×C53C2×#41116yes—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—26no—
285C2×C4×C53—26no—
286C2×C4×C53—26no—
287C2×C4×C53—22no—
288C2×C4×C53C2×#41112yes—
289C2×C4×C53C2516yes—
290C2×C4×C53C2516yes—
291C2×C4×C53C2512yes—
292C2×C4×C53C2516yes—
293C2×C4×C53C2512yes—
294C2×C4×C53C2512yes—
295C2×C4×C53C2516yes—
296C2×Dic53—26no—
297C2×Dic53—26no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—26no—
301C2×Dic53C2516yes—
302C2×Dic53C2516yes—
303C2×Dic53C2516yes—
304C2×Dic53C2512yes—
305C2×Dic53C2512yes—
306D212—224no—
307D212—28no—
308D212—224no—
309D212—412no—
310C4×D53—28no—
311C4×D53—224no—
312C4×D53—224no—
313C4×D53—224no—
314C4×D53—424no—
315C4×D53—412no—
316Dic106—224no—
317Dic106—224no—
318C2×#3516—531nomaximal, Sylow
319C22×C53C22×#4112yes—
320C22×C53C2×2−1+412yes—
321C22×C53#58512yes—
322C22×C53C2611yescharacteristic
323C2×D53—22no—
324C2×D53—22no—
325C2×D53—28no—
326C2×D53—22no—
327C2×D53—26no—
328C2×D53—22no—
329C2×D53—26no—
330C2×D53—26no—
331C2×D53—22no—
332C2×D53—44no—
333C2×D53—412no—
334C2×D53C2×2−1+414yes—
335C4×C53—22no—
336C4×C53—26no—
337C4×C53—22no—
338C4×C53—26no—
339C4×C53—26no—
340C4×C53—22no—
341C4×C53C22×#41112yes—
342Dic53—26no—
343Dic53—26no—
344Dic53—22no—
345Dic53—22no—
346Dic53—26no—
347#3516—5332no—
348C2×#557D5311yescharacteristic, complemented
349C2×#556—533no—
350C2×#554—533no—
351C2×#553—533no—
352C2×#552—533no—
353C2×D4×Q8—531no—
354C2×#548—531no—
355C2×#548—531no—
356C2×#542—533no—
357C2×#541—533no—
358C2×#529—533no—
359C2×#529—533no—
360C2×#520—531no—
361C2×#519—531no—
362C22×C4×Q8—531no—
363C2×C53#351614yescomplemented
364C2×C53C23×#4111yescharacteristic
365C2×C53C22×2−1+411yescharacteristic
366C2×C53C2×#58511yescharacteristic
367D53—24no—
368D53—42no—
369D53—46no—
370C22×#41—531no—
371C23×Q8—531no—
372C23×Q8—531no—
373#557C2×D53116yescomplemented
374#556—5348no—
375#554—5348no—
376#553—5348no—
377#552—5348no—
378D4×Q8—5316no—
379#548—5316no—
380#548—5316no—
381#542—5348no—
382#541—5348no—
383C2×C4⋊Q8—533no—
384C2×C4⋊Q8C2×D5313yes—
385#529—5348no—
386#529—5348no—
387C2×#126—536no—
388C2×#126—533no—
389C2×#126—533no—
390C2×#126—536no—
391C2×#125—533no—
392C2×#125—536no—
393C2×#125C2×D5313yes—
394C2×#125C2×D5313yes—
395C2×#124—533no—
396C2×#124—533no—
397C2×#124—533no—
398C2×#123—531no—
399C2×#123—533no—
400C2×#123—536no—
401C2×C22⋊Q8—533no—
402C2×C22⋊Q8—536no—
403C2×C22⋊Q8—533no—
404C2×C22⋊Q8—533no—
405C2×C22⋊Q8—533no—
406C2×C22⋊Q8—533no—
407C2×#121—533no—
408C2×#121—533no—
409C2×#121—533no—
410#520—5316no—
411#519—5316no—
412C2×C4×Q8—531no—
413C2×C4×Q8—5316no—
414C2×C4×Q8—533no—
415C2×C4×Q8—533no—
416C2×C4×Q8—533no—
417C2×C4×Q8—533no—
418C2×C4×Q8C2×D5311yescharacteristic
419C2×C4×Q8C2×D5311yescharacteristic
420C2×C4×Q8C2×D5311yescharacteristic
421C2×C4×Q8C2×D5313yes—
422C2×C4×D4—533no—
423C2×C4×D4—536no—
424C2×C4×D4—533no—
425C2×C4×D4—533no—
426C2×C4×D4—533no—
427C2×C4×D4—533no—
428C2×#117—533no—
429C2×#117—536no—
430C2×#117—533no—
431C2×#117—533no—
432C22×C4⋊C4—533no—
433C22×C4⋊C4—533no—
434C22×C42—533no—
435C53C2×#351611yescharacteristic, complemented, Sylow
436C2×#41—538no—
437C2×#41—1068no—
438C22×Q8—538no—
439C22×Q8—538no—
440C22×Q8—533no—
441C22×Q8—533no—
442C22×Q8—1068no—
443C22×Q8—1068no—
444C22×Q8C22×D5313yes—
445C22×Q8C22×D5311yescharacteristic
446C22×D4—533no—
447C22×D4—531no—
448C22×D4—533no—
449C22×D4—533no—
450C23×C4—533no—
451C23×C4—533no—
452C23×C4—533no—
453C23×C4—531no—
454C23×C4—533no—
455C23×C4—536no—
456C4⋊Q8—5324no—
457C4⋊Q8C22×D53124yes—
458#126—5348no—
459#126—5324no—
460#126—5324no—
461#126—5348no—
462#125—5324no—
463#125—5348no—
464#125C22×D53124yes—
465#125C22×D53124yes—
466#124—5324no—
467#124—5324no—
468#124—5324no—
469#123—538no—
470#123—5324no—
471#123—5348no—
472C22⋊Q8—5324no—
473C22⋊Q8—5348no—
474C22⋊Q8—5324no—
475C22⋊Q8—5324no—
476C22⋊Q8—5324no—
477C22⋊Q8—5324no—
478#121—5324no—
479#121—5324no—
480#121—5324no—
481C4×Q8—538no—
482C4×Q8—5324no—
483C4×Q8—5324no—
484C4×Q8—5324no—
485C4×Q8—5324no—
486C4×Q8C22×D5318yes—
487C4×Q8C22×D5318yes—
488C4×Q8C22×D5318yes—
489C4×Q8C22×D53124yes—
490C4×D4—5324no—
491C4×D4—5348no—
492C4×D4—5324no—
493C4×D4—5324no—
494C4×D4—5324no—
495C4×D4—5324no—
496#117—5324no—
497#117—5348no—
498#117—5324no—
499#117—5324no—
500C2×C4⋊C4—533no—
501C2×C4⋊C4—533no—
502C2×C4⋊C4—536no—
503C2×C4⋊C4—531no—
504C2×C4⋊C4—533no—
505C2×C4⋊C4—533no—
506C2×C4⋊C4—536no—
507C2×C4⋊C4—533no—
508C2×C4⋊C4—533no—
509C2×C4⋊C4—533no—
510C2×C4⋊C4—5324no—
511C2×C4⋊C4—5324no—
512C2×C4⋊C4C22×D5313yes—
513C2×C4⋊C4C22×D5313yes—
514C2×C4⋊C4C22×D5313yes—
515C2×C4⋊C4C22×D5313yes—
516C2×C4⋊C4C22×D5316yes—
517C2×C4⋊C4C22×D5311yescharacteristic
518C2×C4⋊C4C22×D5313yes—
519C2×C22⋊C4—533no—
520C2×C22⋊C4—531no—
521C2×C22⋊C4—533no—
522C2×C22⋊C4—533no—
523C2×C22⋊C4—533no—
524C2×C22⋊C4—536no—
525C2×C22⋊C4—533no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—536no—
529C2×C22⋊C4—533no—
530C2×C22⋊C4—533no—
531C2×C42—533no—
532C2×C42—536no—
533C2×C42—533no—
534C2×C42—533no—
535C2×C42—5324no—
536C2×C42C22×D5313yes—
537C2×C42C22×D5313yes—
538C2×C42C22×D5313yes—
539C24—531no—
540C24—531no—
541C24—533no—
542#41—10632no—
543C2×Q8—46no—
544C2×Q8—5312no—
545C2×Q8—5312no—
546C2×Q8—10632no—
547C2×Q8—10632no—
548C2×Q8—10612no—
549C2×Q8—10612no—
550C2×Q8#1171994918yes—
551C2×Q8C23×D53112yes—
552C2×Q8C23×D5314yes—
553C2×D4—5312no—
554C2×D4—534no—
555C2×D4—5312no—
556C2×D4—5312no—
557C2×D4—10612no—
558C2×D4—1064no—
559C2×D4—10612no—
560C2×D4—2126no—
561C22×C4—531no—
562C22×C4—533no—
563C22×C4—533no—
564C22×C4—533no—
565C22×C4—531no—
566C22×C4—534no—
567C22×C4—5312no—
568C22×C4—5312no—
569C22×C4—5312no—
570C22×C4—5312no—
571C22×C4—5324no—
572C22×C4—1064no—
573C22×C4—10612no—
574C22×C4—10612no—
575C22×C4—10612no—
576C22×C4—21212no—
577C22×C4—2126no—
578C22×C4C23×D5311yescharacteristic
579C22×C4C23×D5313yes—
580C22×C4C23×D5313yes—
581C22×C4C23×D5311yescharacteristic
582C22×C4C23×D5311yescharacteristic
583C22×C4C23×D5313yes—
584C22×C4C23×D5313yes—
585C4⋊C4—5312no—
586C4⋊C4—5312no—
587C4⋊C4—5324no—
588C4⋊C4—534no—
589C4⋊C4—5312no—
590C4⋊C4—5312no—
591C4⋊C4—5324no—
592C4⋊C4—5312no—
593C4⋊C4—5312no—
594C4⋊C4—5312no—
595C4⋊C4C23×D53112yes—
596C4⋊C4C23×D53112yes—
597C4⋊C4C23×D53112yes—
598C4⋊C4C23×D53112yes—
599C4⋊C4C23×D53124yes—
600C4⋊C4C23×D5314yes—
601C4⋊C4C23×D53112yes—
602C22⋊C4—5312no—
603C22⋊C4—534no—
604C22⋊C4—5312no—
605C22⋊C4—5312no—
606C22⋊C4—5312no—
607C22⋊C4—5324no—
608C22⋊C4—5312no—
609C22⋊C4—534no—
610C22⋊C4—534no—
611C22⋊C4—5324no—
612C22⋊C4—5312no—
613C22⋊C4—5312no—
614C42—5312no—
615C42—5312no—
616C42—5312no—
617C42—5324no—
618C42C23×D53112yes—
619C42C23×D53112yes—
620C42C23×D53112yes—
621C23—534no—
622C23—532no—
623C23—532no—
624C23—536no—
625C23—1062no—
626C23—1062no—
627C23—1062no—
628C23—1066no—
629C23—1062no—
630C23—1066no—
631C23—1066no—
632C23—1062no—
633C23C24×D5311yescharacteristic
634Q8—412no—
635Q8—10624no—
636Q8—10624no—
637Q8C2×#11719949116yes—
638D4—10624no—
639D4—1068no—
640D4—10624no—
641D4—21212no—
642C2×C4—22no—
643C2×C4—26no—
644C2×C4—22no—
645C2×C4—26no—
646C2×C4—26no—
647C2×C4—22no—
648C2×C4—532no—
649C2×C4—536no—
650C2×C4—536no—
651C2×C4—536no—
652C2×C4—532no—
653C2×C4—1068no—
654C2×C4—1062no—
655C2×C4—1066no—
656C2×C4—1066no—
657C2×C4—1062no—
658C2×C4—1066no—
659C2×C4—10624no—
660C2×C4—10624no—
661C2×C4—10624no—
662C2×C4—21224no—
663C2×C4—21212no—
664C2×C4C2×#11719949112yes—
665C2×C4C24×D5312yes—
666C2×C4C24×D5316yes—
667C2×C4C24×D5316yes—
668C2×C4C24×D5312yes—
669C2×C4C24×D5312yes—
670C2×C4C24×D5316yes—
671C2×C4C24×D5316yes—
672C22—534no—
673C22—1068no—
674C22—1062no—
675C22—1062no—
676C22—1062no—
677C22—1066no—
678C22—1062no—
679C22—1066no—
680C22—1066no—
681C22—1062no—
682C22—2124no—
683C22—21212no—
684C22C22×#1171994912yes—
685C222−1+4×D5312yes—
686C22#1681145912yes—
687C22C25×D5311yescharacteristic
688C4—22no—
689C4—26no—
690C4—22no—
691C4—26no—
692C4—26no—
693C4—22no—
694C4—1062no—
695C4—1066no—
696C4—1066no—
697C4—1062no—
698C4—1066no—
699C4C22×#11719949112yes—
700C2—1064no—
701C2—2122no—
702C2—2126no—
703C2#2028871114yesdirect product factor
704C2C23×#1171994911yescharacteristic
705C2C2×2−1+4×D5311yescharacteristic
706C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#557C2
socleC23×C53C25
hypercenterC2×#557D53
hypocenterC53C2×#3516
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20288711C2direct (N × H)
2. C2×#16811346C2semidirect
3. C2×#16811334C2semidirect
4. C2×#16811326C2semidirect
5. C2×#16811311C2semidirect
6. C2×Q8×D212C2semidirect
7. C2×#16811285C2semidirect
8. C2×#16811285C2semidirect
9. C2×#16811247C2semidirect
10. C2×#16811236C2semidirect
11. C2×#16811160C2semidirect
12. C2×#16811158C2semidirect
13. C2×#16811105C2semidirect
14. C2×#16811099C2semidirect
15. C2×C4×Q8×D53C2semidirect
16. C2×C53×#557C2semidirect
20. #16811346C22semidirect
21. #16811334C22semidirect
22. #16811326C22semidirect
23. #16811311C22semidirect
24. Q8×D212C22semidirect
25. #16811285C22semidirect
26. #16811285C22semidirect
27. #16811247C22semidirect
28. #16811236C22semidirect
30. #16811160C22semidirect
31. #16811158C22semidirect
53. #16811105C22semidirect
54. #16811099C22semidirect
60. C4×Q8×D53C22semidirect
74. C53×#557C22semidirect
348. C2×#557D53semidirect
363. C2×C53#3516semidirect
373. #557C2×D53semidirect
435. C53C2×#3516semidirect
703. C2#20288711direct (N × H)

Maximal subgroups

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

subgroupindex
#202887112
C2×#168113462
C2×#168113342
C2×#168113262
C2×#168113112
C2×Q8×D2122
C2×#168112852
C2×#168112472
C2×#168112362
C2×#168111602
C2×#168111582
C2×#168111052
C2×#168110992
C2×C4×Q8×D532
C2×C53×#5572
C2×#351653