Finite Group Databasebeta

← C2×#20286168 #28257048

Subgroups — C2×#20286168 #28257048

Order 13568.

1754 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811236C211yesmaximal, characteristic
2C2×#16811231C211yesmaximal, characteristic
3#20286168C2116yesmaximal, direct product factor
4C2×#16810933C211yesmaximal, characteristic, complemented
5C2×#16810929C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic
8C2×#16810880C211yesmaximal, characteristic
9C2×#16810865C211yesmaximal, characteristic
10C2×#16810863C211yesmaximal, characteristic
11C2×#16810834C211yesmaximal, characteristic, complemented
12C2×#16810833C211yesmaximal, characteristic, complemented
13C2×#16810832C211yesmaximal, characteristic, complemented
14C2×#16810832C211yesmaximal, characteristic, complemented
15C2×#16810648C211yesmaximal, characteristic
16C2×C53×#479C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719925C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719912C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811236—24no—
24#16811236C2218yes—
25#16811231—24no—
26#16811231C2218yes—
27C2×#13133217C2211yescharacteristic
28C2×#13133215C2211yescharacteristic
29C2×#13133212—21no—
30C2×#13133212—21no—
31C2×#13133212—21no—
32C2×#13133211—21no—
33C2×#13133209—21no—
34C2×#13133208—21no—
35C2×#13133208—21no—
36C2×#13133208C2211yescharacteristic
37C2×#13133207—21no—
38C2×#13133197C2211yescharacteristic
39C2×#13133197C2211yescharacteristic
40C2×#13133197C2211yescharacteristic
41C2×#13133193C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133174C2211yescharacteristic
46#16810933C2218yescomplemented
47#16810929C2218yescomplemented
48#16810927C2218yescomplemented
49#16810882C2218yes—
50#16810880C2218yes—
51#16810865C2218yes—
52#16810863C2218yes—
53#16810834C2218yescomplemented
54#16810833C2218yescomplemented
55#16810832C2218yescomplemented
56#16810832C2218yescomplemented
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810648C2218yes—
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133140C2211yescharacteristic
68C2×#13133140C2211yescharacteristic
69C2×#125×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C53×#479C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×C4×D53C2311yescharacteristic
81C2×Dic212—42no—
82C2×Dic212—42no—
83C2×Dic212C2314yes—
84C2×Dic212C2314yes—
85C2×#11719925—42no—
86C2×#11719925—42no—
87C2×#11719925C2314yes—
88C2×#11719925C2314yes—
89C2×#11719912—42no—
90C2×#11719912C2314yes—
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C2×C8×D53—42no—
94C2×C8×D53C2314yes—
95#13133217—22no—
96#13133217C2314yes—
97#13133215—22no—
98#13133215C2314yes—
99#13133212—28no—
100#13133212—28no—
101#13133212—28no—
102#13133211—28no—
103#13133209—28no—
104#13133208—28no—
105#13133208—28no—
106#13133208—22no—
107#13133208C2314yes—
108#13133207—28no—
109#13133197—22no—
110#13133197—22no—
111#13133197—22no—
112#13133197C2314yes—
113#13133197C2314yes—
114#13133197C2314yes—
115#13133193—22no—
116#13133193C2314yes—
117C4×Dic106—22no—
118C4×Dic106C2314yes—
119#13133182—22no—
120#13133182—22no—
121#13133182C2314yes—
122#13133182C2314yes—
123#13133174D414yes—
124#13133174C2314yes—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921D411yescharacteristic
146C2×#11719921D411yescharacteristic
147C2×C4×Dic53—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53C2311yescharacteristic
151#13133150C2314yes—
152#13133148C2314yes—
153C4⋊#88322C2314yes—
154#13133146C2314yes—
155#13133146C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22×C8×C53C2311yescharacteristic
165#125×C53—22no—
166#125×C53C2314yes—
167C4×Q8×C53—22no—
168C4×Q8×C53C2314yes—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53—21no—
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C42×C53—21no—
176C2×C42×C53C2311yescharacteristic
177#107×C53C2314yes—
178#106×C53C2314yes—
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—22no—
185C2×Q8×C53—22no—
186C2×Q8×C53C2412yes—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53C2×D411yescharacteristic
192C22×C4×C53C2×D411yescharacteristic
193C22×C4×C53C2411yescharacteristic
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—21no—
198C22×Dic53C2×D411yescharacteristic
199C22×Dic53C2×D411yescharacteristic
200C22×Dic53C2×D411yescharacteristic
201C2×C4×D53—22no—
202C2×C4×D53—22no—
203C2×C4×D53C2×D412yes—
204C2×C4×D53C2412yes—
205C2×Dic106—22no—
206C2×Dic106—22no—
207C2×Dic106—22no—
208C2×Dic106—22no—
209C2×Dic106—22no—
210C2×Dic106—22no—
211C2×Dic106—21no—
212C2×Dic106—21no—
213C2×Dic106—21no—
214C2×Dic106C2412yes—
215C2×Dic106C2412yes—
216C2×Dic106C2412yes—
217C2×C8×C53—22no—
218C2×C8×C53—22no—
219C2×C8×C53C2412yes—
220C2×C8×C53C2412yes—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53—21no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53C2412yes—
228C4⋊C4×C53C2412yes—
229C4⋊C4×C53C2412yes—
230C42×C53—24no—
231C42×C53C2×D412yes—
232C42×C53C2412yes—
233#11719925—44no—
234#11719925—44no—
235#11719921—24no—
236#11719921—24no—
237#11719921—24no—
238#11719921—24no—
239#11719921C2×D414yes—
240#11719921C2×D414yes—
241C4⋊Dic53—24no—
242C4⋊Dic53—24no—
243C4⋊Dic53—21no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919C2×D414yes—
257#11719919C2×D414yes—
258C4×Dic53—24no—
259C4×Dic53—24no—
260C4×Dic53—24no—
261C4×Dic53C2×D412yes—
262C4×Dic53C2412yes—
263C2×#88322—22no—
264C2×#88322—22no—
265C2×#88322C2412yes—
266C2×#88322C2412yes—
267Dic212—44no—
268Dic212—44no—
269#11719912—44no—
270C8×D53—44no—
271C23×C53C22×D411yescharacteristic
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53C22×D412yes—
276Q8×C53—22no—
277Q8×C53—22no—
278Q8×C53—42no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—42no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53C22×D412yes—
290C2×C4×C53C22×D412yes—
291C2×C4×C53C22×D411yescharacteristic
292C2×C4×C53H(5,𝔽2)12yes—
293C2×C4×C532−1+412yes—
294C2×C4×C53C2511yescharacteristic
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—42no—
303C2×Dic53—42no—
304C2×Dic53—42no—
305C2×Dic53—42no—
306C2×Dic53C22×D412yes—
307C2×Dic53C22×D412yes—
308C2×Dic53C22×D412yes—
309C4×D53—24no—
310C4×D53—22no—
311C4×D53—22no—
312Dic106—22no—
313Dic106—22no—
314Dic106—22no—
315Dic106—22no—
316Dic106—22no—
317Dic106—22no—
318Dic106—42no—
319Dic106—42no—
320Dic106—42no—
321C8×C53—22no—
322C8×C53—22no—
323#88322—22no—
324#88322—22no—
325C2×#3261—531nomaximal, Sylow
326C22×C53#53712yes—
327C22×C53#57812yes—
328C22×C53#57812yes—
329C22×C53C23×D411yescharacteristic
330C2×D53—22no—
331C2×D53—22no—
332C2×D53—22no—
333C2×D53—44no—
334C4×C53—22no—
335C4×C53—22no—
336C4×C53—42no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53#53712yes—
341C4×C53C2×H(5,𝔽2)11yescharacteristic
342C4×C53C2×2−1+411yescharacteristic
343Dic53—22no—
344Dic53—22no—
345Dic53—22no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350C2×#541—531no—
351C2×#541—531no—
352#3261—5316no—
353C2×#479—531no—
354C2×#479—531no—
355C2×#479—531no—
356C2×#479D5311yescharacteristic, complemented
357C2×#470—531no—
358C2×#470—531no—
359C2×#467—531no—
360C2×#467—531no—
361C2×#462—531no—
362C2×#462—531no—
363C2×#462—531no—
364C2×#462—531no—
365C2×#424—531no—
366C2×C53#326114yescomplemented
367C2×C53C2×#53711yescharacteristic
368C2×C53C2×#57811yescharacteristic
369C2×C53C2×#57811yescharacteristic
370D53—42no—
371C22×Q16—531no—
372C22×Q16—531no—
373C22×Q16—531no—
374C22×Q16—531no—
375C22×M16—531no—
376C23×C8—531no—
377#541—538no—
378#541—538no—
379#541—1064no—
380#541—1064no—
381C2×C4⋊Q8—531no—
382C2×C4⋊Q8—531no—
383C2×#126—1061no—
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#126—1061no—
387C2×#125—531no—
388C2×#125—1061no—
389C2×#125—1061no—
390C2×#125—1061no—
391C2×#125—1061no—
392C2×#125C2×D5311yescharacteristic
393C2×C22⋊Q8—531no—
394C2×C22⋊Q8—531no—
395C2×C22⋊Q8—531no—
396C2×C22⋊Q8—531no—
397C2×C4×Q8—531no—
398C2×C4×Q8—531no—
399C2×C4×Q8—531no—
400C2×C4×Q8C2×D5311yescharacteristic
401C2×#117—531no—
402#479—538no—
403#479—538no—
404#479—538no—
405#479C2×D5318yescomplemented
406#470—538no—
407#470—538no—
408#467—538no—
409#467—538no—
410#462—538no—
411#462—538no—
412#462—538no—
413#462—538no—
414C2×#107—531no—
415C2×#107C2×D5311yescharacteristic
416C2×#106—531no—
417C2×#106C2×D5311yescharacteristic
418#424—538no—
419C2×C4⋊C8—531no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8—531no—
422C2×C4⋊C8C2×D5311yescharacteristic
423C2×#103—531no—
424C2×#103—531no—
425C2×#103—531no—
426C2×#103—531no—
427C2×#103—531no—
428C2×#103—531no—
429C2×#103C2×D5311yescharacteristic
430C2×#103C2×D5311yescharacteristic
431C53C2×#326111yescharacteristic, complemented, Sylow
432C22×Q8—531no—
433C22×Q8—531no—
434C22×Q8—531no—
435C22×Q8C22×D5311yescharacteristic
436C23×C4—531no—
437C2×Q16—534no—
438C2×Q16—534no—
439C2×Q16—534no—
440C2×Q16—534no—
441C2×Q16—2122no—
442C2×Q16—2122no—
443C2×Q16—2122no—
444C2×Q16—2122no—
445C2×M16—534no—
446C2×M16—2122no—
447C22×C8—531no—
448C22×C8—531no—
449C22×C8—534no—
450C22×C8—2122no—
451C22×C8C22×D5311yescharacteristic
452C22×C8C22×D5311yescharacteristic
453C4⋊Q8—534no—
454C4⋊Q8—534no—
455C4⋊Q8—1062no—
456C4⋊Q8—1062no—
457#126—1068no—
458#126—1068no—
459#126—1068no—
460#126—1068no—
461#125—22no—
462#125—534no—
463#125—1068no—
464#125—1062no—
465#125—1068no—
466#125—1068no—
467#125—1068no—
468#125C22×D5314yes—
469C22⋊Q8—534no—
470C22⋊Q8—534no—
471C22⋊Q8—534no—
472C22⋊Q8—534no—
473C22⋊Q8—1062no—
474C22⋊Q8—1062no—
475C22⋊Q8—1062no—
476C22⋊Q8—1062no—
477C4×Q8—22no—
478C4×Q8—534no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×Q8—1062no—
482C4×Q8—1062no—
483C4×Q8—1062no—
484C4×Q8C22×D5314yes—
485#117—534no—
486#117—534no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—1061no—
494C2×C4⋊C4—1061no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1061no—
497C2×C4⋊C4—1061no—
498C2×C4⋊C4—1061no—
499C2×C4⋊C4—1061no—
500C2×C4⋊C4—1061no—
501C2×C4⋊C4—1061no—
502C2×C4⋊C4—1061no—
503C2×C4⋊C4—1061no—
504C2×C4⋊C4—1061no—
505C2×C4⋊C4—1061no—
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C4⋊C4C22×D5311yescharacteristic
508C2×C4⋊C4C22×D5311yescharacteristic
509C2×C22⋊C4—531no—
510C2×C22⋊C4—531no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4—1061no—
513C2×C22⋊C4—1061no—
514C2×C22⋊C4—1061no—
515C2×C42—21no—
516C2×C42—531no—
517C2×C42—1061no—
518C2×C42—1061no—
519C2×C42—1061no—
520C2×C42C22×D5311yescharacteristic
521#107—534no—
522#107C22×D5314yes—
523#106—534no—
524#106C22×D5314yes—
525C4⋊C8—534no—
526C4⋊C8—534no—
527C4⋊C8—534no—
528C4⋊C8C22×D5314yes—
529#103—534no—
530#103—534no—
531#103—534no—
532#103—534no—
533#103—534no—
534#103—534no—
535#103C22×D5314yes—
536#103C22×D5314yes—
537C24—531no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—532no—
542C2×Q8—532no—
543C2×Q8—532no—
544C2×Q8—1061no—
545C2×Q8—1061no—
546C2×Q8—1061no—
547C2×Q8—1062no—
548C2×Q8—1062no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8—1062no—
552C2×Q8—1062no—
553C2×Q8C23×D5312yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—531no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1061no—
566C22×C4—1061no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4D4×D5311yescharacteristic
570C22×C4D4×D5311yescharacteristic
571C22×C4C23×D5311yescharacteristic
572Q16—2124no—
573Q16—2124no—
574Q16—2124no—
575Q16—2124no—
576M16—2124no—
577C2×C8—22no—
578C2×C8—22no—
579C2×C8—532no—
580C2×C8—532no—
581C2×C8—1062no—
582C2×C8—1062no—
583C2×C8—2124no—
584C2×C8C23×D5312yes—
585C2×C8C23×D5312yes—
586C4⋊C4—24no—
587C4⋊C4—24no—
588C4⋊C4—24no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—534no—
593C4⋊C4—534no—
594C4⋊C4—532no—
595C4⋊C4—1064no—
596C4⋊C4—1064no—
597C4⋊C4—1064no—
598C4⋊C4—1064no—
599C4⋊C4—1064no—
600C4⋊C4—1064no—
601C4⋊C4—1064no—
602C4⋊C4—1064no—
603C4⋊C4—1064no—
604C4⋊C4—1064no—
605C4⋊C4—1061no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4C23×D5312yes—
610C4⋊C4C23×D5312yes—
611C4⋊C4C23×D5312yes—
612C22⋊C4—534no—
613C22⋊C4—534no—
614C22⋊C4—1064no—
615C22⋊C4—1064no—
616C22⋊C4—1064no—
617C22⋊C4—1064no—
618C42—24no—
619C42—532no—
620C42—532no—
621C42—1064no—
622C42—1064no—
623C42—1064no—
624C42D4×D5312yes—
625C42C23×D5312yes—
626C23—532no—
627C23—1062no—
628C23—1062no—
629C23—1062no—
630C23C2×D4×D5311yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—1062no—
635Q8—1062no—
636Q8—1062no—
637Q8—1062no—
638Q8—1062no—
639Q8—1062no—
640Q8—2122no—
641Q8—2122no—
642Q8—2122no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—532no—
654C2×C4—532no—
655C2×C4—532no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1064no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4C2×D4×D5312yes—
671C2×C4C2×D4×D5312yes—
672C2×C4C2×D4×D5311yescharacteristic
673C2×C4#1313326312yes—
674C2×C4#1313326512yes—
675C2×C4C24×D5311yescharacteristic
676C8—22no—
677C8—22no—
678C8—1062no—
679C8—1062no—
680C22—1062no—
681C22—1062no—
682C22—1062no—
683C22—2124no—
684C22#1681120312yes—
685C22#1681143712yes—
686C22#1681143912yes—
687C22C22×D4×D5311yescharacteristic
688C4—22no—
689C4—22no—
690C4—42no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—1062no—
695C4—1062no—
696C4—1062no—
697C4—2122no—
698C4—2122no—
699C4—2122no—
700C4—2122no—
701C4#1681120312yes—
702C4C2×#1313326311yescharacteristic
703C4C2×#1313326511yescharacteristic
704C2—2122no—
705C2#2028616814yesdirect product factor
706C2C2×#1681120311yescharacteristic
707C2C2×#1681143711yescharacteristic
708C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#479C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#479D53
hypocenterC53C2×#3261
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #20286168C2direct (N × H)
4. C2×#16810933C2semidirect
5. C2×#16810929C2semidirect
6. C2×#16810927C2semidirect
11. C2×#16810834C2semidirect
12. C2×#16810833C2semidirect
13. C2×#16810832C2semidirect
14. C2×#16810832C2semidirect
16. C2×C53×#479C2semidirect
46. #16810933C22semidirect
47. #16810929C22semidirect
48. #16810927C22semidirect
53. #16810834C22semidirect
54. #16810833C22semidirect
55. #16810832C22semidirect
56. #16810832C22semidirect
71. C53×#479C22semidirect
356. C2×#479D53semidirect
366. C2×C53#3261semidirect
405. #479C2×D53semidirect
431. C53C2×#3261semidirect
705. C2#20286168direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112362
C2×#168112312
#202861682
C2×#168109332
C2×#168109292
C2×#168109272
C2×#168108822
C2×#168108802
C2×#168108652
C2×#168108632
C2×#168108342
C2×#168108332
C2×#168108322
C2×#168106482
C2×C53×#4792
C2×#326153