Finite Group Databasebeta

← C2×#20288824 #28292376

Subgroups — C2×#20288824 #28292376

Order 13568.

7226 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288824C2132yesmaximal, direct product factor
2C2×#16811356C213yesmaximal, complemented
3C2×#16811349C211yesmaximal, characteristic, complemented
4C2×#16811336C213yesmaximal, complemented
5C2×#16811323C213yesmaximal, complemented
6C2×#16811312C213yesmaximal, complemented
7C2×#16811292C211yesmaximal, characteristic, complemented
8C2×#16811285C211yesmaximal, characteristic, complemented
9C2×#16811280C211yesmaximal, characteristic, complemented
10C2×#16811238C213yesmaximal, complemented
11C2×#16811224C213yesmaximal, complemented
12C2×#16811157C213yesmaximal, complemented
13C2×#16811157C213yesmaximal, complemented
14C2×#16811105C211yesmaximal, characteristic, complemented
15C2×#16811099C211yesmaximal, characteristic, complemented
16C2×C4×#41×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19#16811356C22148yescomplemented
20#16811349C22116yescomplemented
21#16811336C22148yescomplemented
22#16811323C22148yescomplemented
23#16811312C22148yescomplemented
24#16811292C22116yescomplemented
25#16811285C22116yescomplemented
26#16811280C22116yescomplemented
27#16811238C22148yescomplemented
28#16811224C22148yescomplemented
29C2×#13133216C2213yes—
30C2×#13133213C2213yes—
31#16811157C22148yescomplemented
32#16811157C22148yescomplemented
33C2×#13133211C2211yescharacteristic
34C2×#13133211C2213yes—
35C2×#13133210C2216yes—
36C2×#13133209C2213yes—
37C2×#13133209C2213yes—
38C2×#13133208C2213yes—
39C2×#13133205C2213yes—
40C2×#13133205C2213yes—
41C2×#13133204C2213yes—
42C2×#13133203C2216yes—
43C2×#13133200C2213yes—
44C2×#13133200C2216yes—
45C2×#13133200C2213yes—
46C2×#13133199C2216yes—
47C2×#13133197C2213yes—
48C2×#13133196C2213yes—
49C2×#13133196C2213yes—
50C2×#13133192C2213yes—
51C2×#13133191C2213yes—
52C2×#13133191C2213yes—
53C2×#13133190C2216yes—
54C2×#13133188C2213yes—
55C2×#13133188C2213yes—
56#16811105C22116yescomplemented
57#16811099C22116yescomplemented
58C2×Q8×Dic53C2211yescharacteristic
59C2×Q8×Dic53C2211yescharacteristic
60C2×C4×Dic106C2213yes—
61C2×C4×Dic106C2213yes—
62C2×#13133182C2213yes—
63C2×C4×D212C2213yes—
64C2×C4×D212C2213yes—
65C2×#13133179C2213yes—
66C2×C4×C22⋊D53C2216yes—
67C2×C4×C22⋊D53C2213yes—
68C2×C4×C22⋊D53C2213yes—
69C2×#13133175C2213yes—
70C2×#13133174C2213yes—
71C2×#13133174C2213yes—
72C2×#13133174C2216yes—
73C2×C4⋊C4×D53C2213yes—
74C22×#41×C53C2211yescharacteristic
75C4×#41×C53C22116yescomplemented
76C2×C4×Q8×C53C2211yescharacteristic
77C2×C4×Q8×C53C2211yescharacteristic
78C2×C4×D4×C53C2213yes—
79C2×C4×D4×C53C2213yes—
80C2×#117×C53C2213yes—
81C22×C42×C53C2213yes—
82C2×#11719949—28no—
83C2×#11719949C2318yes—
84C22×Dic106C2313yes—
85C22×Dic106C2313yes—
86C2×Q8×D53—28no—
87C2×Q8×D53C2318yes—
88C22×D212C2313yes—
89C22×D212C2313yes—
90C22×C22⋊D53C2313yes—
91C22×C22⋊D53C2316yes—
92C22×C22⋊D53C2313yes—
93C22×C4×D53C2313yes—
94C22×C4×D53C2313yes—
95C22×C4×D53C2316yes—
96#13133216C23124yes—
97#13133213C23124yes—
98#13133211C2318yes—
99#13133211C23124yes—
100#13133210C23148yes—
101#13133209C23124yes—
102#13133209C23124yes—
103#13133208C23124yes—
104#13133205C23124yes—
105#13133205C23124yes—
106#13133204C23124yes—
107#13133203C23148yes—
108#13133200C23124yes—
109#13133200C23124yes—
110#13133200C23148yes—
111#13133199C23148yes—
112#13133197C23124yes—
113#13133196C23124yes—
114#13133196C23124yes—
115#13133192C23124yes—
116#13133191C23124yes—
117#13133191C23124yes—
118#13133190C23148yes—
119#13133188C23124yes—
120#13133188C23124yes—
121Q8×Dic53C2318yes—
122Q8×Dic53C2318yes—
123C4×Dic106C23124yes—
124C4×Dic106C23124yes—
125#13133182C23124yes—
126C4×D212C23124yes—
127C4×D212C23124yes—
128#13133179C23124yes—
129C4×C22⋊D53C23124yes—
130C4×C22⋊D53C23124yes—
131C4×C22⋊D53C23148yes—
132#13133175C23124yes—
133#13133174C23148yes—
134#13133174C23124yes—
135#13133174C23124yes—
136C2×C4⋊Dic53C2313yes—
137C2×C4⋊Dic53C2313yes—
138C2×C4⋊Dic53C2313yes—
139C2×C4⋊Dic53C2313yes—
140C2×#11719919C2313yes—
141C2×#11719919C2311yescharacteristic
142C2×#11719919C2313yes—
143C2×#11719919C2313yes—
144C2×#11719919C2313yes—
145C2×#11719919C2316yes—
146C2×#11719919C2311yescharacteristic
147C2×#11719919C2313yes—
148C2×#11719919C2311yescharacteristic
149C4⋊C4×D53C23124yes—
150C2×C22⋊Dic53C2313yes—
151C2×C22⋊Dic53C2316yes—
152C2×C22⋊Dic53C2313yes—
153C2×#11719921C2311yescharacteristic
154C2×#11719921C2313yes—
155C2×#11719921C2313yes—
156C2×#11719921C2313yes—
157C2×#11719921C2313yes—
158C2×#11719921C2316yes—
159C2×#11719921C2311yescharacteristic
160C2×#11719921C2313yes—
161C2×#11719921C2311yescharacteristic
162C2×C4×Dic53C2316yes—
163C2×C4×Dic53C2313yes—
164C2×C4×Dic53C2313yes—
165C2×#41×C53—28no—
166C2×#41×C53C2318yes—
167C22×Q8×C53C2311yescharacteristic
168C22×D4×C53C2313yes—
169C23×C4×C53C2313yes—
170C23×C4×C53C2313yes—
171C23×C4×C53C2313yes—
172C4×Q8×C53C2318yes—
173C4×Q8×C53C2318yes—
174C4×D4×C53C23124yes—
175C4×D4×C53C23124yes—
176#117×C53C23124yes—
177C2×C4⋊C4×C53C2313yes—
178C2×C4⋊C4×C53C2313yes—
179C2×C22⋊C4×C53C2316yes—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2313yes—
182C2×C42×C53C2313yes—
183C2×C42×C53C2313yes—
184C2×C42×C53C23124yes—
185C24×C53C2413yes—
186C23×D53C2411yescharacteristic
187C23×D53C2413yes—
188#41×C53—232no—
189C2×Q8×C53#4118yes—
190C2×Q8×C53C2414yes—
191C2×D4×C53—212no—
192C2×D4×C53C24112yes—
193C22×C4×C53—212no—
194C22×C4×C53—46no—
195C22×C4×C53—46no—
196C22×C4×C53C2411yescharacteristic
197C22×C4×C53C2411yescharacteristic
198C22×C4×C53C2411yescharacteristic
199C22×C4×C53C2413yes—
200C22×C4×C53C2413yes—
201C22×C4×C53C24112yes—
202C22×C4×C53C24112yes—
203C22×C4×C53C24112yes—
204C22×C4×C53C2413yes—
205C2×C22⋊D53—412no—
206C2×C22⋊D53—46no—
207C2×C22⋊D53—46no—
208C2×C22⋊D53C24112yes—
209C2×C22⋊D53C24124yes—
210C2×C22⋊D53C24112yes—
211C22×Dic53C2411yescharacteristic
212C22×Dic53C2413yes—
213C22×Dic53C2411yescharacteristic
214C22×Dic53C2413yes—
215C22×Dic53C2413yes—
216C22×Dic53C2411yescharacteristic
217#11719949—232no—
218Q8×D53—232no—
219C2×D212—212no—
220C2×D212—46no—
221C2×D212C24112yes—
222C2×D212C24112yes—
223C2×C4×D53—212no—
224C2×C4×D53—212no—
225C2×C4×D53—412no—
226C2×C4×D53C24112yes—
227C2×C4×D53C24112yes—
228C2×C4×D53C24124yes—
229C2×Dic106—212no—
230C2×Dic106—46no—
231C2×Dic106C24112yes—
232C2×Dic106C24112yes—
233C4⋊C4×C53C24112yes—
234C4⋊C4×C53C24112yes—
235C22⋊C4×C53C24124yes—
236C42×C53C2414yes—
237C42×C53C24112yes—
238C42×C53C24112yes—
239C42×C53C24112yes—
240C22⋊Dic53C24112yes—
241C22⋊Dic53C24124yes—
242C22⋊Dic53C24112yes—
243#11719921C2414yes—
244#11719921C24112yes—
245#11719921C24112yes—
246#11719921C24112yes—
247#11719921C24112yes—
248#11719921C24124yes—
249#11719921C2414yes—
250#11719921C24112yes—
251#11719921C2414yes—
252C4⋊Dic53C24112yes—
253C4⋊Dic53C24112yes—
254C4⋊Dic53C24112yes—
255C4⋊Dic53C24112yes—
256#11719919C24112yes—
257#11719919C2414yes—
258#11719919C24112yes—
259#11719919C24112yes—
260#11719919C24112yes—
261#11719919C24124yes—
262#11719919C2414yes—
263#11719919C24112yes—
264#11719919C2414yes—
265C4×Dic53C24124yes—
266C4×Dic53C24112yes—
267C4×Dic53C24112yes—
268C23×C53—26no—
269C23×C53—26no—
270C23×C53—26no—
271C23×C53C2516yes—
272C23×C53C2511yescharacteristic
273C22×D53—22no—
274C22×D53—26no—
275C22×D53—26no—
276C22×D53—22no—
277C22×D53—26no—
278C22×D53—22no—
279C22×D53C2512yes—
280C22×D53C2516yes—
281Q8×C53C2×#41116yes—
282D4×C53—224no—
283C2×C4×C53—22no—
284C2×C4×C53—26no—
285C2×C4×C53—26no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—224no—
289C2×C4×C53—412no—
290C2×C4×C53—412no—
291C2×C4×C53C2×#41112yes—
292C2×C4×C53C2516yes—
293C2×C4×C53C2516yes—
294C2×C4×C53C2512yes—
295C2×C4×C53C2512yes—
296C2×C4×C53C2512yes—
297C2×C4×C53C2516yes—
298C22⋊D53—424no—
299C22⋊D53—412no—
300C22⋊D53—412no—
301C2×Dic53—26no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—26no—
305C2×Dic53—26no—
306C2×Dic53—22no—
307C2×Dic53C2512yes—
308C2×Dic53C2516yes—
309C2×Dic53C2516yes—
310C2×Dic53C2512yes—
311C2×Dic53C2516yes—
312C2×Dic53C2512yes—
313D212—224no—
314D212—412no—
315C4×D53—224no—
316C4×D53—224no—
317C4×D53—424no—
318Dic106—224no—
319Dic106—412no—
320C2×#3524—531nomaximal, Sylow
321C22×C53—26no—
322C22×C53—26no—
323C22×C53—26no—
324C22×C53—412no—
325C22×C53C22×#4112yes—
326C22×C53#58512yes—
327C22×C53#58512yes—
328C22×C53C2611yescharacteristic
329C2×D53—22no—
330C2×D53—26no—
331C2×D53—26no—
332C2×D53—22no—
333C2×D53—26no—
334C2×D53—22no—
335C2×D53—44no—
336C2×D53—412no—
337C4×C53—22no—
338C4×C53—26no—
339C4×C53—26no—
340C4×C53—22no—
341C4×C53—22no—
342C4×C53C22×#41112yes—
343Dic53—26no—
344Dic53—22no—
345Dic53—22no—
346Dic53—26no—
347Dic53—26no—
348Dic53—22no—
349#3524—5332no—
350C2×#559—533no—
351C2×#557—531no—
352C2×#555—533no—
353C2×#553—533no—
354C2×#552—533no—
355C2×#550—531no—
356C2×#548—531no—
357C2×#548—531no—
358C2×#542—533no—
359C2×#540—533no—
360C2×#529—533no—
361C2×#529—533no—
362C2×#520—531no—
363C2×#519—531no—
364C2×C4×#41D5311yescharacteristic, complemented
365C2×C53—46no—
366C2×C53#352414yescomplemented
367C2×C53C23×#4111yescharacteristic
368C2×C53C2×#58511yescharacteristic
369C2×C53C2×#58511yescharacteristic
370D53—42no—
371D53—46no—
372C22×#41—531no—
373C22×#41C2×D5311yescharacteristic
374C23×Q8—531no—
375#559—5348no—
376#557—5316no—
377#555—5348no—
378#553—5348no—
379#552—5348no—
380#550—5316no—
381#548—5316no—
382#548—5316no—
383#542—5348no—
384#540—5348no—
385C2×C4⋊Q8—533no—
386C2×#127—533no—
387#529—5348no—
388#529—5348no—
389C2×#126—536no—
390C2×#126—531no—
391C2×#126—533no—
392C2×#125—533no—
393C2×#125—533no—
394C2×#125—533no—
395C2×#124—533no—
396C2×#124—536no—
397C2×#124—533no—
398C2×#124—533no—
399C2×#123—536no—
400C2×#123—533no—
401C2×#123—533no—
402C2×#123—536no—
403C2×C22⋊Q8—533no—
404C2×C22⋊Q8—533no—
405C2×C22⋊Q8—533no—
406C2×#121—533no—
407C2×#121—533no—
408C2×#121—533no—
409C2×#121—533no—
410C2×#121—533no—
411C2×#121—536no—
412#520—5316no—
413#519—5316no—
414C4×#41C2×D53116yescomplemented
415C2×C4×Q8—531no—
416C2×C4×Q8—531no—
417C2×C4×Q8—533no—
418C2×C4×Q8—533no—
419C2×C4×Q8—533no—
420C2×C4×Q8C2×D5311yescharacteristic
421C2×C4×Q8C2×D5311yescharacteristic
422C2×C4×D4—533no—
423C2×C4×D4—533no—
424C2×C4×D4—536no—
425C2×C4×D4—533no—
426C2×C4×D4—533no—
427C2×C4×D4—533no—
428C2×C4×D4C2×D5313yes—
429C2×C4×D4C2×D5313yes—
430C2×#117—533no—
431C2×#117—533no—
432C2×#117—533no—
433C2×#117—536no—
434C2×#117C2×D5313yes—
435C22×C4⋊C4—533no—
436C22×C42C2×D5313yes—
437C53C2×#352411yescharacteristic, complemented, Sylow
438C2×#41—28no—
439C2×#41—538no—
440C2×#41—1068no—
441C2×#41C22×D5318yes—
442C22×Q8—538no—
443C22×Q8—533no—
444C22×Q8—533no—
445C22×Q8—1068no—
446C22×Q8C22×D5311yescharacteristic
447C22×D4—533no—
448C22×D4—536no—
449C22×D4—533no—
450C22×D4—533no—
451C22×D4—533no—
452C22×D4C22×D5313yes—
453C23×C4—533no—
454C23×C4—533no—
455C23×C4—536no—
456C23×C4C22×D5313yes—
457C23×C4C22×D5313yes—
458C23×C4C22×D5313yes—
459C4⋊Q8—5324no—
460#127—5324no—
461#126—5348no—
462#126—538no—
463#126—5324no—
464#125—5324no—
465#125—5324no—
466#125—5324no—
467#124—5324no—
468#124—5348no—
469#124—5324no—
470#124—5324no—
471#123—5348no—
472#123—5324no—
473#123—5324no—
474#123—5348no—
475C22⋊Q8—5324no—
476C22⋊Q8—5324no—
477C22⋊Q8—5324no—
478#121—5324no—
479#121—5324no—
480#121—5324no—
481#121—5324no—
482#121—5324no—
483#121—5348no—
484C4×Q8—538no—
485C4×Q8—538no—
486C4×Q8—5324no—
487C4×Q8—5324no—
488C4×Q8—5324no—
489C4×Q8C22×D5318yes—
490C4×Q8C22×D5318yes—
491C4×D4—5324no—
492C4×D4—5324no—
493C4×D4—5348no—
494C4×D4—5324no—
495C4×D4—5324no—
496C4×D4—5324no—
497C4×D4C22×D53124yes—
498C4×D4C22×D53124yes—
499#117—5324no—
500#117—5324no—
501#117—5324no—
502#117—5348no—
503#117C22×D53124yes—
504C2×C4⋊C4—533no—
505C2×C4⋊C4—533no—
506C2×C4⋊C4—531no—
507C2×C4⋊C4—533no—
508C2×C4⋊C4—533no—
509C2×C4⋊C4—533no—
510C2×C4⋊C4—533no—
511C2×C4⋊C4—536no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—533no—
514C2×C4⋊C4—533no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—533no—
517C2×C4⋊C4—5324no—
518C2×C4⋊C4C22×D5313yes—
519C2×C4⋊C4C22×D5313yes—
520C2×C22⋊C4—533no—
521C2×C22⋊C4—536no—
522C2×C22⋊C4—533no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—533no—
525C2×C22⋊C4—533no—
526C2×C22⋊C4—533no—
527C2×C22⋊C4—533no—
528C2×C22⋊C4—536no—
529C2×C22⋊C4—531no—
530C2×C22⋊C4—533no—
531C2×C22⋊C4—531no—
532C2×C22⋊C4C22×D5316yes—
533C2×C42—536no—
534C2×C42—533no—
535C2×C42—533no—
536C2×C42C22×D5313yes—
537C2×C42C22×D5313yes—
538C2×C42C22×D5313yes—
539C2×C42C22×D53124yes—
540C2×C42C22×D5311yescharacteristic
541C24—531no—
542C24—533no—
543C24C23×D5313yes—
544#41—232no—
545#41—10632no—
546C2×Q8—5312no—
547C2×Q8—5312no—
548C2×Q8—10632no—
549C2×Q8—10612no—
550C2×Q8—2126no—
551C2×Q8#1171994518yes—
552C2×Q8C23×D5314yes—
553C2×D4—212no—
554C2×D4—5312no—
555C2×D4—5324no—
556C2×D4—5312no—
557C2×D4—5312no—
558C2×D4—5312no—
559C2×D4—10612no—
560C2×D4—2126no—
561C2×D4—2126no—
562C2×D4—2126no—
563C2×D4—21212no—
564C2×D4C23×D53112yes—
565C22×C4—212no—
566C22×C4—46no—
567C22×C4—46no—
568C22×C4—531no—
569C22×C4—533no—
570C22×C4—531no—
571C22×C4—533no—
572C22×C4—533no—
573C22×C4—531no—
574C22×C4—5312no—
575C22×C4—5312no—
576C22×C4—5324no—
577C22×C4—10612no—
578C22×C4—10612no—
579C22×C4—21212no—
580C22×C4C23×D53112yes—
581C22×C4C23×D5313yes—
582C22×C4C23×D5311yescharacteristic
583C22×C4C23×D5311yescharacteristic
584C22×C4C23×D5311yescharacteristic
585C22×C4C23×D5313yes—
586C22×C4C23×D53112yes—
587C22×C4C23×D53112yes—
588C22×C4C23×D5313yes—
589C4⋊C4—5312no—
590C4⋊C4—5312no—
591C4⋊C4—534no—
592C4⋊C4—5312no—
593C4⋊C4—5312no—
594C4⋊C4—5312no—
595C4⋊C4—5312no—
596C4⋊C4—5324no—
597C4⋊C4—534no—
598C4⋊C4—5312no—
599C4⋊C4—5312no—
600C4⋊C4—534no—
601C4⋊C4—5312no—
602C4⋊C4C23×D53112yes—
603C4⋊C4C23×D53112yes—
604C22⋊C4—5312no—
605C22⋊C4—5324no—
606C22⋊C4—5312no—
607C22⋊C4—534no—
608C22⋊C4—5312no—
609C22⋊C4—5312no—
610C22⋊C4—5312no—
611C22⋊C4—5312no—
612C22⋊C4—5324no—
613C22⋊C4—534no—
614C22⋊C4—5312no—
615C22⋊C4—534no—
616C22⋊C4C23×D53124yes—
617C42—5324no—
618C42—5312no—
619C42—5312no—
620C42C23×D5314yes—
621C42C23×D53112yes—
622C42C23×D53112yes—
623C42C23×D53112yes—
624C23—26no—
625C23—26no—
626C23—26no—
627C23—532no—
628C23—536no—
629C23—1062no—
630C23—1066no—
631C23—1066no—
632C23—1062no—
633C23—1066no—
634C23—1062no—
635C23C24×D5316yes—
636C23C24×D5311yescharacteristic
637Q8—10624no—
638Q8—21212no—
639Q8C2×#11719945116yes—
640D4—224no—
641D4—10624no—
642D4—21212no—
643D4—21212no—
644D4—21212no—
645D4—21224no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—26no—
650C2×C4—26no—
651C2×C4—224no—
652C2×C4—412no—
653C2×C4—412no—
654C2×C4—532no—
655C2×C4—536no—
656C2×C4—532no—
657C2×C4—536no—
658C2×C4—536no—
659C2×C4—532no—
660C2×C4—1062no—
661C2×C4—1066no—
662C2×C4—1066no—
663C2×C4—1062no—
664C2×C4—1066no—
665C2×C4—1062no—
666C2×C4—10624no—
667C2×C4—10624no—
668C2×C4—21224no—
669C2×C4C2×#11719945112yes—
670C2×C4C24×D5316yes—
671C2×C4C24×D5312yes—
672C2×C4C24×D5312yes—
673C2×C4C24×D5312yes—
674C2×C4C24×D5316yes—
675C2×C4C24×D5316yes—
676C22—26no—
677C22—26no—
678C22—26no—
679C22—412no—
680C22—1062no—
681C22—1066no—
682C22—1066no—
683C22—1062no—
684C22—1066no—
685C22—1062no—
686C22—2124no—
687C22—21212no—
688C22C22×#1171994512yes—
689C22#1681145912yes—
690C22#1681145912yes—
691C22C25×D5311yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—26no—
696C4—26no—
697C4—1062no—
698C4—1066no—
699C4—1066no—
700C4—1062no—
701C4—1066no—
702C4—1062no—
703C4C22×#11719945112yes—
704C2—46no—
705C2—2122no—
706C2—2126no—
707C2#2028882414yesdirect product factor
708C2C23×#1171994511yescharacteristic
709C2C2×#1681145911yescharacteristic
710C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C4×#41×C53C2
socleC23×C53C25
hypercenterC2×C4×#41D53
hypocenterC53C2×#3524
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20288824C2direct (N × H)
2. C2×#16811356C2semidirect
3. C2×#16811349C2semidirect
4. C2×#16811336C2semidirect
5. C2×#16811323C2semidirect
6. C2×#16811312C2semidirect
7. C2×#16811292C2semidirect
8. C2×#16811285C2semidirect
9. C2×#16811280C2semidirect
10. C2×#16811238C2semidirect
11. C2×#16811224C2semidirect
12. C2×#16811157C2semidirect
13. C2×#16811157C2semidirect
14. C2×#16811105C2semidirect
15. C2×#16811099C2semidirect
16. C2×C4×#41×C53C2semidirect
19. #16811356C22semidirect
20. #16811349C22semidirect
21. #16811336C22semidirect
22. #16811323C22semidirect
23. #16811312C22semidirect
24. #16811292C22semidirect
25. #16811285C22semidirect
26. #16811280C22semidirect
27. #16811238C22semidirect
28. #16811224C22semidirect
31. #16811157C22semidirect
32. #16811157C22semidirect
56. #16811105C22semidirect
57. #16811099C22semidirect
75. C4×#41×C53C22semidirect
364. C2×C4×#41D53semidirect
366. C2×C53#3524semidirect
414. C4×#41C2×D53semidirect
437. C53C2×#3524semidirect
707. C2#20288824direct (N × H)

Maximal subgroups

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

subgroupindex
#202888242
C2×#168113562
C2×#168113492
C2×#168113362
C2×#168113232
C2×#168113122
C2×#168112922
C2×#168112852
C2×#168112802
C2×#168112382
C2×#168112242
C2×#168111572
C2×#168111052
C2×#168110992
C2×C4×#41×C532
C2×#352453