Finite Group Databasebeta

← C2×#20285796 #28255473

Subgroups — C2×#20285796 #28255473

Order 13568.

2022 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811233C211yesmaximal, characteristic, complemented
2C2×#16811194C211yesmaximal, characteristic
3#20285796C2116yesmaximal, direct product factor
4C2×#16811014C211yesmaximal, characteristic, complemented
5C2×#16811001C211yesmaximal, characteristic, complemented
6C2×#16810990C211yesmaximal, characteristic, complemented
7C2×#16810976C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810843C211yesmaximal, characteristic, complemented
10C2×#16810832C211yesmaximal, characteristic, complemented
11C2×#16810831C211yesmaximal, characteristic, complemented
12C2×#16810785C211yesmaximal, characteristic
13C2×#16810781C211yesmaximal, characteristic, complemented
14C2×#16810778C211yesmaximal, characteristic, complemented
15C2×#16810681C211yesmaximal, characteristic, complemented
16C2×C53×#452C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719925C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24#16811233—24no—
25#16811233C2218yescomplemented
26#16811194—24no—
27#16811194C2218yes—
28C2×#13133215C2211yescharacteristic
29C2×#13133215C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133210—21no—
32C2×#13133210—21no—
33C2×#13133208—21no—
34C2×#13133208C2211yescharacteristic
35C2×#13133207—21no—
36C2×#13133204C2211yescharacteristic
37C2×#13133204C2211yescharacteristic
38C2×#13133198—21no—
39C2×#13133198—21no—
40C2×#13133196—21no—
41C2×#13133196—21no—
42C2×#13133196C2211yescharacteristic
43C2×Q8×Dic53C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133176C2211yescharacteristic
46#16811014C2218yescomplemented
47#16811001C2218yescomplemented
48#16810990C2218yescomplemented
49#16810976C2218yescomplemented
50#16810844C2218yescomplemented
51#16810843C2218yescomplemented
52#16810832C2218yescomplemented
53#16810831C2218yescomplemented
54#16810785C2218yes—
55#16810781C2218yescomplemented
56#16810778C2218yescomplemented
57#16810681C2218yescomplemented
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×SD16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#452C2218yes—
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—22no—
79C22×Dic106—42no—
80C22×Dic106—42no—
81C22×Dic106C2311yescharacteristic
82C22×Dic106C2311yescharacteristic
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2314yes—
85C23×Dic53—21no—
86C2×Dic212—42no—
87C2×Dic212—42no—
88C2×Dic212C2314yes—
89C2×Dic212C2314yes—
90C2×#11719925—42no—
91C2×#11719925—42no—
92C2×#11719925—42no—
93C2×#11719925C2314yes—
94C2×#11719925C2314yes—
95C2×#11719925C2314yes—
96C2×#11719923—42no—
97C2×#11719923C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100#13133215—22no—
101#13133215—22no—
102#13133215—22no—
103#13133215C2314yes—
104#13133215C2314yes—
105#13133215C2314yes—
106#13133210—28no—
107#13133210—28no—
108#13133208—28no—
109#13133208—22no—
110#13133208C2314yes—
111#13133207—28no—
112#13133204—22no—
113#13133204—22no—
114#13133204C2314yes—
115#13133204C2314yes—
116#13133198—28no—
117#13133198—28no—
118#13133196—28no—
119#13133196—28no—
120#13133196—22no—
121#13133196C2314yes—
122Q8×Dic53—22no—
123Q8×Dic53C2314yes—
124#13133182—22no—
125#13133182C2314yes—
126#13133176D414yes—
127#13133176C2314yes—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53D411yescharacteristic
131C2×C4⋊Dic53D411yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53D411yescharacteristic
148C2×C22⋊Dic53D411yescharacteristic
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53C2311yescharacteristic
152C2×C4×Dic53C2311yescharacteristic
153#13133146C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133138C2314yes—
161C22⋊#88322C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C2×#41×C53—22no—
165C2×#41×C53—42no—
166C2×#41×C53—42no—
167C2×#41×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C22×Q8×C53C2311yescharacteristic
170C22×D4×C53—21no—
171C22×D4×C53C2311yescharacteristic
172C23×C4×C53—21no—
173C23×C4×C53C2311yescharacteristic
174C2×Q16×C53—42no—
175C2×Q16×C53C2314yes—
176C2×SD16×C53—42no—
177C2×SD16×C53C2314yes—
178C22×C8×C53C2311yescharacteristic
179C22×C8×C53C2311yescharacteristic
180C22⋊Q8×C53—22no—
181C22⋊Q8×C53C2314yes—
182C2×C4⋊C4×C53—21no—
183C2×C4⋊C4×C53C2311yescharacteristic
184C2×C22⋊C4×C53—21no—
185#103×C53C2314yes—
186#102×C53C2314yes—
187C22⋊C8×C53C2314yes—
188C24×C53—21no—
189C24×C53C2×D411yescharacteristic
190#41×C53—44no—
191#41×C53—44no—
192#41×C53—48no—
193C2×Q8×C53—21no—
194C2×Q8×C53—21no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—22no—
198C2×Q8×C53—22no—
199C2×Q8×C53C2412yes—
200C2×Q8×C53C2412yes—
201C2×D4×C53—24no—
202C2×D4×C53—21no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53C2412yes—
207C22×C4×C53—22no—
208C22×C4×C53—22no—
209C22×C4×C53—21no—
210C22×C4×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—24no—
213C22×C4×C53—44no—
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2412yes—
217C22×C4×C53C2411yescharacteristic
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—44no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228C2×Dic106—22no—
229C2×Dic106—22no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—21no—
235C2×Dic106—24no—
236C2×Dic106—21no—
237C2×Dic106—21no—
238C2×Dic106—44no—
239C2×Dic106—44no—
240C2×Dic106—44no—
241C2×Dic106—48no—
242C2×Dic106C2412yes—
243C2×Dic106C2412yes—
244C2×Dic106C2412yes—
245Q16×C53—44no—
246SD16×C53—44no—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—24no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2412yes—
254C22⋊C4×C53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53C2×D414yes—
261C22⋊Dic53C2×D414yes—
262#11719925—44no—
263#11719925—44no—
264#11719925—44no—
265#11719923—44no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2×D414yes—
270C4⋊Dic53C2×D414yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53C2×D412yes—
284C4×Dic53C2×D412yes—
285C4×Dic53C2412yes—
286C4×Dic53C2412yes—
287C2×#88322—22no—
288C2×#88322—22no—
289C2×#88322C2412yes—
290C2×#88322C2412yes—
291Dic212—44no—
292Dic212—44no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53—42no—
300C23×C53C22×D412yes—
301C23×C53C22×D411yescharacteristic
302Q8×C53—22no—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—22no—
306Q8×C53—42no—
307Q8×C53—42no—
308D4×C53—22no—
309D4×C53—22no—
310D4×C53—48no—
311D4×C53—42no—
312C2×C4×C53—22no—
313C2×C4×C53—24no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—48no—
320C2×C4×C53—42no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53H(5,𝔽2)12yes—
327C2×C4×C53C2511yescharacteristic
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—48no—
337C2×Dic53—42no—
338C2×Dic53—42no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53C22×D412yes—
342C2×Dic53C22×D412yes—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345Dic106—22no—
346Dic106—22no—
347Dic106—22no—
348Dic106—22no—
349Dic106—22no—
350Dic106—22no—
351Dic106—48no—
352Dic106—42no—
353Dic106—42no—
354Dic106—42no—
355C8×C53—22no—
356C8×C53—22no—
357#88322—22no—
358#88322—22no—
359C2×#3223—531nomaximal, Sylow
360C22×C53—22no—
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—44no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53—42no—
367C22×C53—84no—
368C22×C53#53512yes—
369C22×C53#57812yes—
370C22×C53#57812yes—
371C22×C53C23×D411yescharacteristic
372C4×C53—22no—
373C4×C53—42no—
374C4×C53—42no—
375C4×C53—42no—
376C4×C53#53512yes—
377C4×C53C2×H(5,𝔽2)11yescharacteristic
378C4×C53C2×H(5,𝔽2)11yescharacteristic
379Dic53—22no—
380Dic53—22no—
381Dic53—22no—
382Dic53—22no—
383Dic53—42no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387C2×#541—531no—
388C2×#536—531no—
389#3223—5316no—
390C2×#497—531no—
391C2×#494—531no—
392C2×#491—531no—
393C2×#488—531no—
394C2×#464—531no—
395C2×#464—531no—
396C2×#462—531no—
397C2×#462—531no—
398C2×#452—531no—
399C2×#452D5311yescharacteristic
400C2×#451—531no—
401C2×#451—531no—
402C2×#433—531no—
403C2×C53—42no—
404C2×C53—82no—
405C2×C53#322314yescomplemented
406C2×C53C2×#53511yescharacteristic
407C2×C53C2×#57811yescharacteristic
408C2×C53C2×#57811yescharacteristic
409C22×#41C2×D5311yescharacteristic
410C23×Q8—531no—
411C22×Q16—531no—
412C22×Q16—531no—
413C22×Q16—531no—
414C22×Q16—531no—
415C22×Q16—531no—
416C22×Q16C2×D5311yescharacteristic
417C22×SD16—531no—
418C22×SD16C2×D5311yescharacteristic
419#541—538no—
420#541—1064no—
421#536—538no—
422#536—1064no—
423C2×C4⋊Q8—531no—
424C2×C4⋊Q8—531no—
425C2×C4⋊Q8—531no—
426C2×#126—1061no—
427C2×#126—1061no—
428C2×#125—531no—
429C2×#125—1061no—
430C2×#125—1061no—
431C2×#124—531no—
432C2×#124—531no—
433C2×#123—1061no—
434C2×#123—1061no—
435C2×C22⋊Q8—531no—
436C2×C22⋊Q8—1061no—
437C2×C22⋊Q8—1061no—
438C2×C22⋊Q8C2×D5311yescharacteristic
439C2×C4×Q8—531no—
440C2×C4×Q8—531no—
441C2×#117—531no—
442#497—538no—
443#494—538no—
444#491—538no—
445#488—538no—
446#464—538no—
447#464—538no—
448#462—538no—
449#462—538no—
450#452—538no—
451#452C2×D5318yes—
452#451—538no—
453#451—538no—
454#433—538no—
455C2×C4⋊C8—531no—
456C2×C4⋊C8—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#103—531no—
461C2×#103—531no—
462C2×#103C2×D5311yescharacteristic
463C2×#102—531no—
464C2×#102C2×D5311yescharacteristic
465C2×C22⋊C8—531no—
466C2×C22⋊C8C2×D5311yescharacteristic
467C2×#97—531no—
468C2×C4×C8—531no—
469C53C2×#322311yescharacteristic, complemented, Sylow
470C2×#41—22no—
471C2×#41—42no—
472C2×#41—42no—
473C2×#41C22×D5314yes—
474C22×Q8—531no—
475C22×Q8—531no—
476C22×Q8—531no—
477C22×Q8—534no—
478C22×Q8—1061no—
479C22×Q8—1062no—
480C22×Q8—2122no—
481C22×Q8—2122no—
482C22×Q8C22×D5311yescharacteristic
483C22×Q8C22×D5311yescharacteristic
484C22×D4—21no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—1061no—
488C23×C4C22×D5311yescharacteristic
489C2×Q16—42no—
490C2×Q16—534no—
491C2×Q16—534no—
492C2×Q16—534no—
493C2×Q16—534no—
494C2×Q16—534no—
495C2×Q16—2122no—
496C2×Q16—2122no—
497C2×Q16—2122no—
498C2×Q16—2122no—
499C2×Q16—2122no—
500C2×Q16C22×D5314yes—
501C2×SD16—42no—
502C2×SD16—534no—
503C2×SD16—2122no—
504C2×SD16C22×D5314yes—
505C22×C8—531no—
506C22×C8—531no—
507C22×C8C22×D5311yescharacteristic
508C22×C8C22×D5311yescharacteristic
509C4⋊Q8—534no—
510C4⋊Q8—534no—
511C4⋊Q8—534no—
512C4⋊Q8—1062no—
513C4⋊Q8—1062no—
514C4⋊Q8—1062no—
515#126—1068no—
516#126—1068no—
517#125—534no—
518#125—1062no—
519#125—1068no—
520#125—1068no—
521#124—534no—
522#124—534no—
523#124—1062no—
524#124—1062no—
525#123—1068no—
526#123—1068no—
527C22⋊Q8—22no—
528C22⋊Q8—534no—
529C22⋊Q8—1068no—
530C22⋊Q8—1068no—
531C22⋊Q8—1062no—
532C22⋊Q8C22×D5314yes—
533C4×Q8—534no—
534C4×Q8—534no—
535C4×Q8—1062no—
536C4×Q8—1062no—
537#117—534no—
538#117—534no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C22⋊C4—21no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—531no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C42—531no—
564C2×C42—531no—
565C2×C42—1061no—
566C2×C42—1061no—
567C4⋊C8—534no—
568C4⋊C8—534no—
569#103—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103C22×D5314yes—
575#102—534no—
576#102C22×D5314yes—
577C22⋊C8—534no—
578C22⋊C8C22×D5314yes—
579#97—534no—
580C4×C8—534no—
581C24—21no—
582C24D4×D5311yescharacteristic
583#41—44no—
584#41—44no—
585#41—48no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—532no—
593C2×Q8—532no—
594C2×Q8—532no—
595C2×Q8—1061no—
596C2×Q8—1064no—
597C2×Q8—1061no—
598C2×Q8—1061no—
599C2×Q8—1062no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—1062no—
603C2×Q8—1062no—
604C2×Q8—1062no—
605C2×Q8—2124no—
606C2×Q8—2124no—
607C2×Q8—2124no—
608C2×Q8—2128no—
609C2×Q8C23×D5312yes—
610C2×Q8C23×D5312yes—
611C2×D4—24no—
612C2×D4—21no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—44no—
616C2×D4C23×D5312yes—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—44no—
624C22×C4—531no—
625C22×C4—531no—
626C22×C4—531no—
627C22×C4—531no—
628C22×C4—1064no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1061no—
633C22×C4—2124no—
634C22×C4D4×D5312yes—
635C22×C4D4×D5311yescharacteristic
636C22×C4C23×D5312yes—
637C22×C4C23×D5311yescharacteristic
638Q16—44no—
639Q16—2124no—
640Q16—2124no—
641Q16—2124no—
642Q16—2124no—
643Q16—2124no—
644SD16—44no—
645SD16—2124no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—532no—
649C2×C8—532no—
650C2×C8—1062no—
651C2×C8—1062no—
652C2×C8C23×D5312yes—
653C2×C8C23×D5312yes—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—534no—
657C4⋊C4—534no—
658C4⋊C4—532no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1064no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1061no—
670C4⋊C4—1064no—
671C4⋊C4C23×D5312yes—
672C22⋊C4—24no—
673C22⋊C4—534no—
674C22⋊C4—534no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C42—532no—
681C42—532no—
682C42—532no—
683C42—532no—
684C42—1064no—
685C42—1064no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23C2×D4×D5312yes—
694C23C2×D4×D5311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—1062no—
702Q8—1062no—
703Q8—1062no—
704Q8—1062no—
705Q8—1062no—
706Q8—1062no—
707Q8—2128no—
708Q8—2122no—
709Q8—2122no—
710Q8—2122no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—42no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—48no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—532no—
729C2×C4—532no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—1062no—
738C2×C4—2128no—
739C2×C4—2122no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4—2122no—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4#1313326212yes—
746C2×C4#1313326212yes—
747C2×C4C24×D5311yescharacteristic
748C8—22no—
749C8—22no—
750C8—1062no—
751C8—1062no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—44no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—84no—
760C22#1681118812yes—
761C22#1681143712yes—
762C22#1681143912yes—
763C22C22×D4×D5311yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—1062no—
769C4—1062no—
770C4—1062no—
771C4—1062no—
772C4—2122no—
773C4—2122no—
774C4—2122no—
775C4—2122no—
776C4#1681118812yes—
777C4C2×#1313326211yescharacteristic
778C4C2×#1313326211yescharacteristic
779C2—42no—
780C2—82no—
781C2#2028579614yesdirect product factor
782C2C2×#1681118811yescharacteristic
783C2C2×#1681143711yescharacteristic
784C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#452C2
socleC23×C53C22×D4
prime radicalC22×#41×C53C22
hypercenterC2×#452D53
hypocenterC53C2×#3223
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. C2×#16811233C2semidirect
3. #20285796C2direct (N × H)
4. C2×#16811014C2semidirect
5. C2×#16811001C2semidirect
6. C2×#16810990C2semidirect
7. C2×#16810976C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810843C2semidirect
10. C2×#16810832C2semidirect
11. C2×#16810831C2semidirect
13. C2×#16810781C2semidirect
14. C2×#16810778C2semidirect
15. C2×#16810681C2semidirect
25. #16811233C22semidirect
46. #16811014C22semidirect
47. #16811001C22semidirect
48. #16810990C22semidirect
49. #16810976C22semidirect
50. #16810844C22semidirect
51. #16810843C22semidirect
52. #16810832C22semidirect
53. #16810831C22semidirect
55. #16810781C22semidirect
56. #16810778C22semidirect
57. #16810681C22semidirect
405. C2×C53#3223semidirect
469. C53C2×#3223semidirect
781. C2#20285796direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112332
C2×#168111942
#202857962
C2×#168110142
C2×#168110012
C2×#168109902
C2×#168109762
C2×#168108442
C2×#168108432
C2×#168108322
C2×#168108312
C2×#168107852
C2×#168107812
C2×#168107782
C2×#168106812
C2×C53×#4522
C2×#322353