Finite Group Databasebeta

← C2×#20286167 #28257047

Subgroups — C2×#20286167 #28257047

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×#16811234C211yesmaximal, characteristic
2C2×#16811231C211yesmaximal, characteristic
3#20286167C2116yesmaximal, direct product factor
4C2×#16810932C211yesmaximal, characteristic, complemented
5C2×#16810931C211yesmaximal, characteristic, complemented
6C2×#16810930C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810880C211yesmaximal, characteristic
9C2×#16810878C211yesmaximal, characteristic
10C2×#16810863C211yesmaximal, characteristic
11C2×#16810861C211yesmaximal, characteristic
12C2×#16810831C211yesmaximal, characteristic, complemented
13C2×#16810831C211yesmaximal, characteristic, complemented
14C2×#16810830C211yesmaximal, characteristic, complemented
15C2×#16810648C211yesmaximal, characteristic
16C2×C53×#462C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C22×C8×D53C2211yescharacteristic
21#16811234—24no—
22#16811234C2218yes—
23#16811231—24no—
24#16811231C2218yes—
25C2×#13133215C2211yescharacteristic
26C2×#13133212—21no—
27C2×#13133212—21no—
28C2×#13133212—21no—
29C2×#13133211—21no—
30C2×#13133209—21no—
31C2×#13133209C2211yescharacteristic
32C2×#13133208C2211yescharacteristic
33C2×#13133207—21no—
34C2×#13133207—21no—
35C2×#13133207—21no—
36C2×#13133197C2211yescharacteristic
37C2×#13133193C2211yescharacteristic
38C2×#13133193C2211yescharacteristic
39C2×#13133193C2211yescharacteristic
40C2×Q8×Dic53C2211yescharacteristic
41C2×Q8×Dic53C2211yescharacteristic
42C2×C4×Dic106C2211yescharacteristic
43C2×#13133174C2211yescharacteristic
44#16810932C2218yescomplemented
45#16810931C2218yescomplemented
46#16810930C2218yescomplemented
47#16810928C2218yescomplemented
48#16810880C2218yes—
49#16810878C2218yes—
50#16810863C2218yes—
51#16810861C2218yes—
52#16810831C2218yescomplemented
53#16810831C2218yescomplemented
54#16810830C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59#16810648C2218yes—
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133141C2211yescharacteristic
67C2×#13133141C2211yescharacteristic
68C2×#13133141C2211yescharacteristic
69C22×Q16×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C2×C4⋊Q8×C53C2211yescharacteristic
72C2×C4×Q8×C53C2211yescharacteristic
73C53×#462C2218yescomplemented
74C2×C4⋊C8×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2211yescharacteristic
77C22×Dic106C2311yescharacteristic
78C22×C4×D53C2311yescharacteristic
79C2×#11719925—42no—
80C2×#11719925—42no—
81C2×#11719925C2314yes—
82C2×#11719925C2314yes—
83C2×#11719912—42no—
84C2×#11719912C2314yes—
85C22×#88322C2311yescharacteristic
86C22×#88322C2311yescharacteristic
87C2×C8×D53—42no—
88C2×C8×D53C2314yes—
89#13133215—22no—
90#13133215C2314yes—
91#13133212—28no—
92#13133212—28no—
93#13133212—28no—
94#13133211—28no—
95#13133209—22no—
96#13133209—28no—
97#13133209C2314yes—
98#13133208—22no—
99#13133208C2314yes—
100#13133207—28no—
101#13133207—28no—
102#13133207—28no—
103#13133197—22no—
104#13133197C2314yes—
105#13133193—22no—
106#13133193—22no—
107#13133193—22no—
108#13133193C2314yes—
109#13133193C2314yes—
110#13133193C2314yes—
111Q8×Dic53—22no—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114Q8×Dic53C2314yes—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117#13133174D414yes—
118#13133174C2314yes—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53—21no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53C2311yescharacteristic
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C2×#11719919D411yescharacteristic
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133151C2314yes—
148#13133150C2314yes—
149#13133149C2314yes—
150#13133148C2314yes—
151C4⋊#88322C2314yes—
152#13133146C2314yes—
153#13133146C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133141C2314yes—
160C22×Q8×C53C2311yescharacteristic
161C22×Q8×C53C2311yescharacteristic
162C22×Q8×C53C2311yescharacteristic
163C2×Q16×C53—42no—
164C2×Q16×C53—42no—
165C2×Q16×C53C2314yes—
166C2×Q16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yes—
171C4×Q8×C53—22no—
172C4×Q8×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179C4⋊C8×C53C2314yes—
180#103×C53C2314yes—
181#103×C53C2314yes—
182C23×D53C2×D411yescharacteristic
183C2×Q8×C53—21no—
184C2×Q8×C53—21no—
185C2×Q8×C53—21no—
186C2×Q8×C53—22no—
187C2×Q8×C53—22no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53C2412yes—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C22×Dic53C2×D411yescharacteristic
209C2×C4×D53—22no—
210C2×C4×D53—22no—
211C2×C4×D53C2×D412yes—
212C2×C4×D53C2412yes—
213C2×Dic106—22no—
214C2×Dic106—22no—
215C2×Dic106—21no—
216C2×Dic106C2412yes—
217Q16×C53—44no—
218Q16×C53—44no—
219C2×C8×C53—22no—
220C2×C8×C53—22no—
221C2×C8×C53C2412yes—
222C2×C8×C53C2412yes—
223C4⋊C4×C53—24no—
224C4⋊C4×C53—24no—
225C4⋊C4×C53—24no—
226C4⋊C4×C53—21no—
227C4⋊C4×C53C2412yes—
228C42×C53—24no—
229C42×C53C2×D412yes—
230C42×C53C2412yes—
231#11719925—44no—
232#11719925—44no—
233#11719921—24no—
234#11719921—24no—
235#11719921—24no—
236#11719921—24no—
237#11719921C2×D414yes—
238#11719921C2×D414yes—
239C4⋊Dic53—21no—
240C4⋊Dic53—21no—
241C4⋊Dic53—21no—
242C4⋊Dic53—24no—
243C4⋊Dic53—24no—
244C4⋊Dic53—24no—
245C4⋊Dic53—24no—
246C4⋊Dic53C2412yes—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249#11719919—24no—
250#11719919—24no—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919C2×D414yes—
259#11719919C2×D414yes—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53—24no—
263C4×Dic53C2×D412yes—
264C4×Dic53C2412yes—
265C2×#88322—22no—
266C2×#88322—22no—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
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—22no—
279Q8×C53—22no—
280Q8×C53—22no—
281Q8×C53—22no—
282Q8×C53—42no—
283Q8×C53—42no—
284Q8×C53—42no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D412yes—
297C2×C4×C53C22×D411yescharacteristic
298C2×C4×C53H(5,𝔽2)12yes—
299C2×C4×C532−1+412yes—
300C2×C4×C53C2511yescharacteristic
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—42no—
312C2×Dic53C22×D412yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C4×D53—24no—
316C4×D53—22no—
317C4×D53—22no—
318Dic106—22no—
319Dic106—22no—
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×#479—531no—
357C2×#470—531no—
358C2×#470—531no—
359C2×#467—531no—
360C2×#467—531no—
361C2×#462—531no—
362C2×#462—531no—
363C2×#462—531no—
364C2×#462D5311yescharacteristic, complemented
365C2×#424—531no—
366C2×C53#326114yescomplemented
367C2×C53C2×#53711yescharacteristic
368C2×C53C2×#57811yescharacteristic
369C2×C53C2×#57811yescharacteristic
370D53—42no—
371C22×Q16—531no—
372C22×Q16—531no—
373C22×Q16C2×D5311yescharacteristic
374C22×Q16C2×D5311yescharacteristic
375C22×M16—531no—
376C23×C8—531no—
377#541—538no—
378#541—538no—
379#541—1064no—
380#541—1064no—
381C2×C4⋊Q8—531no—
382C2×C4⋊Q8C2×D5311yescharacteristic
383C2×#126—1061no—
384C2×#126—1061no—
385C2×#126—1061no—
386C2×#126—1061no—
387C2×#125—531no—
388C2×#125—531no—
389C2×#125—1061no—
390C2×#125—1061no—
391C2×#125—1061no—
392C2×#125—1061no—
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#479—538no—
406#470—538no—
407#470—538no—
408#467—538no—
409#467—538no—
410#462—538no—
411#462—538no—
412#462—538no—
413#462C2×D5318yescomplemented
414C2×#107—531no—
415C2×#107—531no—
416C2×#106—531no—
417C2×#106—531no—
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×Q8C22×D5311yescharacteristic
434C22×Q8C22×D5311yescharacteristic
435C22×Q8C22×D5311yescharacteristic
436C23×C4—531no—
437C2×Q16—42no—
438C2×Q16—42no—
439C2×Q16—534no—
440C2×Q16—534no—
441C2×Q16—2122no—
442C2×Q16—2122no—
443C2×Q16C22×D5314yes—
444C2×Q16C22×D5314yes—
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—22no—
454C4⋊Q8—534no—
455C4⋊Q8—1062no—
456C4⋊Q8C22×D5314yes—
457#126—1068no—
458#126—1068no—
459#126—1068no—
460#126—1068no—
461#125—534no—
462#125—534no—
463#125—1068no—
464#125—1062no—
465#125—1068no—
466#125—1068no—
467#125—1068no—
468#125—1062no—
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—531no—
494C2×C4⋊C4—531no—
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⋊C4—1061no—
507C2×C4⋊C4—1061no—
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#107—534no—
523#106—534no—
524#106—534no—
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—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—532no—
548C2×Q8—1061no—
549C2×Q8—1062no—
550C2×Q8—1062no—
551C2×Q8C23×D5312yes—
552C2×Q8C23×D5312yes—
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—44no—
573Q16—44no—
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—534no—
591C4⋊C4—534no—
592C4⋊C4—532no—
593C4⋊C4—532no—
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—1061no—
607C4⋊C4—1061no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
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—22no—
634Q8—22no—
635Q8—22no—
636Q8—22no—
637Q8—42no—
638Q8—42no—
639Q8—42no—
640Q8—1062no—
641Q8—1062no—
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#1313326212yes—
674C2×C4#1313326412yes—
675C2×C4C24×D5311yescharacteristic
676C8—22no—
677C8—22no—
678C8—1062no—
679C8—1062no—
680C22—1062no—
681C22—1062no—
682C22—1062no—
683C22—2124no—
684C22#1681120212yes—
685C22#1681143612yes—
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#1681120212yes—
702C4C2×#1313326211yescharacteristic
703C4C2×#1313326411yescharacteristic
704C2—2122no—
705C2#2028616714yesdirect product factor
706C2C2×#1681120211yescharacteristic
707C2C2×#1681143611yescharacteristic
708C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#462C2
socleC23×C53C22×D4
prime radicalC23×D53C2×D4
hypercenterC2×#462D53
hypocenterC53C2×#3261
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20286167C2direct (N × H)
4. C2×#16810932C2semidirect
5. C2×#16810931C2semidirect
6. C2×#16810930C2semidirect
7. C2×#16810928C2semidirect
12. C2×#16810831C2semidirect
13. C2×#16810831C2semidirect
14. C2×#16810830C2semidirect
16. C2×C53×#462C2semidirect
44. #16810932C22semidirect
45. #16810931C22semidirect
46. #16810930C22semidirect
47. #16810928C22semidirect
52. #16810831C22semidirect
53. #16810831C22semidirect
54. #16810830C22semidirect
73. C53×#462C22semidirect
364. C2×#462D53semidirect
366. C2×C53#3261semidirect
413. #462C2×D53semidirect
431. C53C2×#3261semidirect
705. C2#20286167direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112342
C2×#168112312
#202861672
C2×#168109322
C2×#168109312
C2×#168109302
C2×#168109282
C2×#168108802
C2×#168108782
C2×#168108632
C2×#168108612
C2×#168108312
C2×#168108302
C2×#168106482
C2×C53×#4622
C2×#326153