Finite Group Databasebeta

← C2×#20291533 #28329642

Subgroups — C2×#20291533 #28329642

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20291533C2116yesmaximal, direct product factor
2C2×#16811675C211yesmaximal, characteristic, complemented
3C2×#16811672C211yesmaximal, characteristic, complemented
4C2×#16811656C211yesmaximal, characteristic, complemented
5C2×#16811655C211yesmaximal, characteristic, complemented
6C2×#16811653C211yesmaximal, characteristic, complemented
7C2×#16811651C211yesmaximal, characteristic, complemented
8C2×#16811650C211yesmaximal, characteristic, complemented
9C2×#16811650C211yesmaximal, characteristic, complemented
10C2×#16811648C211yesmaximal, characteristic, complemented
11C2×#16811647C211yesmaximal, characteristic, complemented
12C2×#16811646C211yesmaximal, characteristic, complemented
13C2×#16811588C211yesmaximal, characteristic, complemented
14C2×#16811587C211yesmaximal, characteristic, complemented
15C2×C4×D53⋊C8C211yesmaximal, characteristic, complemented
16C2×#16811156C211yesmaximal, characteristic
17C22×#11719936C2211yescharacteristic
18C22×#11719940C2211yescharacteristic
19C22×D53⋊C8C2211yescharacteristic
20C22×D53⋊C8C2211yescharacteristic
21C22×D53⋊C8C2211yescharacteristic
22C23×#88324C2211yescharacteristic
23#16811675C2218yescomplemented
24#16811672C2218yescomplemented
25#16811656C2218yescomplemented
26#16811655C2218yescomplemented
27#16811653C2218yescomplemented
28#16811651C2218yescomplemented
29#16811650C2218yescomplemented
30#16811650C2218yescomplemented
31#16811648C2218yescomplemented
32#16811647C2218yescomplemented
33#16811646C2218yescomplemented
34C2×#13133284C2211yescharacteristic
35C2×#13133284C2211yescharacteristic
36C2×#13133284C2211yescharacteristic
37C2×#13133284C2211yescharacteristic
38C2×C4⋊#88324C2211yescharacteristic
39C2×C4⋊#88324C2211yescharacteristic
40C2×#13133274C2211yescharacteristic
41C2×#13133274C2211yescharacteristic
42C2×#13133274C2211yescharacteristic
43C2×#13133274C2211yescharacteristic
44C2×C22⋊#88324C2211yescharacteristic
45C2×C22⋊#88324C2211yescharacteristic
46#16811588C2218yescomplemented
47#16811587C2218yescomplemented
48C2×#13133272C2211yescharacteristic
49C2×#13133272C2211yescharacteristic
50C2×#13133272C2211yescharacteristic
51C2×#13133272C2211yescharacteristic
52C4×D53⋊C8C2218yescomplemented
53C2×C4×#88324C2211yescharacteristic
54C2×C4×#88324C2211yescharacteristic
55C2×C4×#88324C2211yescharacteristic
56C2×C4×#88324C2211yescharacteristic
57C2×C4×#88324C2211yescharacteristic
58C2×C4×#88324C2211yescharacteristic
59#16811156C418yes—
60#16811156C2218yes—
61C2×#13133211C411yescharacteristic
62C2×#13133207C411yescharacteristic
63C2×#13133203C411yescharacteristic
64C2×#13133202C411yescharacteristic
65C2×#13133199C411yescharacteristic
66C2×#13133195C411yescharacteristic
67C2×#13133190C411yescharacteristic
68C2×#13133182C2211yescharacteristic
69C2×#13133179C2211yescharacteristic
70C2×#13133177C2211yescharacteristic
71C2×#13133177C2211yescharacteristic
72C2×#13133175C2211yescharacteristic
73C2×#13133173C2211yescharacteristic
74C2×C42×D53C2211yescharacteristic
75C2×#126×C53C411yescharacteristic
76C2×#11719936—24no—
77C2×#11719936C2314yes—
78C2×#11719940—24no—
79C2×#11719940C2314yes—
80C2×D53⋊C8—24no—
81C2×D53⋊C8—24no—
82C2×D53⋊C8—24no—
83C2×D53⋊C8C2314yes—
84C2×D53⋊C8C2314yes—
85C2×D53⋊C8C2314yes—
86C22×#88324—24no—
87C22×#88324C2311yescharacteristic
88C22×#88324C2311yescharacteristic
89C22×#88324C2311yescharacteristic
90C22×#88324C2311yescharacteristic
91C22×#88324C2311yescharacteristic
92C22×#88324C2311yescharacteristic
93C22×#88324C2314yes—
94C22×#88324C2311yescharacteristic
95C22×#88324C2311yescharacteristic
96#13133284C2314yes—
97#13133284C2314yes—
98#13133284C2314yes—
99#13133284C2314yes—
100C4⋊#88324C2314yes—
101C4⋊#88324C2314yes—
102#13133274C2314yes—
103#13133274C2314yes—
104#13133274C2314yes—
105#13133274C2314yes—
106C22⋊#88324C2314yes—
107C22⋊#88324C2314yes—
108#13133272C2314yes—
109#13133272C2314yes—
110#13133272C2314yes—
111#13133272C2314yes—
112C4×#88324C2314yes—
113C4×#88324C2314yes—
114C4×#88324C2314yes—
115C4×#88324C2314yes—
116C4×#88324C2314yes—
117C4×#88324C2314yes—
118C22×Dic106C2×C411yescharacteristic
119C22×D212C2×C411yescharacteristic
120C22×C22⋊D53C2×C411yescharacteristic
121C22×C22⋊D53C2×C411yescharacteristic
122C23×Dic53C2311yescharacteristic
123C22×C4×D53C2×C411yescharacteristic
124C22×C4×D53C2×C411yescharacteristic
125C22×C4×D53C2311yescharacteristic
126C22×C4×D53C2311yescharacteristic
127#13133211C2×C418yes—
128#13133207C2×C418yes—
129#13133203C2×C418yes—
130#13133202C2×C418yes—
131#13133199C2×C418yes—
132#13133195C2×C418yes—
133#13133190C2×C418yes—
134#13133182C2×C414yes—
135#13133182C2314yes—
136#13133179C2×C414yes—
137#13133179C2314yes—
138#13133177C2×C414yes—
139#13133177C2×C414yes—
140#13133177C2314yes—
141#13133177C2314yes—
142#13133175C2×C414yes—
143#13133175C2314yes—
144#13133173C2×C414yes—
145#13133173C2314yes—
146C2×C4⋊Dic53C2×C411yescharacteristic
147C2×#11719919C2×C411yescharacteristic
148C2×#11719919C2×C411yescharacteristic
149C2×#11719919C2×C411yescharacteristic
150C2×#11719919C2×C411yescharacteristic
151C2×#11719919C2×C411yescharacteristic
152C2×#11719919C2×C411yescharacteristic
153C2×C22⋊Dic53C2×C411yescharacteristic
154C2×#11719921C2×C411yescharacteristic
155C2×#11719921C2×C411yescharacteristic
156C2×#11719921C2×C411yescharacteristic
157C2×#11719921C2×C411yescharacteristic
158C2×#11719921C2×C411yescharacteristic
159C2×#11719921C2×C411yescharacteristic
160C2×C4×Dic53C2×C411yescharacteristic
161C2×C4×Dic53C2311yescharacteristic
162C2×C4×Dic53C2311yescharacteristic
163C2×C4×Dic53C2311yescharacteristic
164C2×C4×Dic53C2311yescharacteristic
165C42×D53C2×C414yes—
166C42×D53C2314yes—
167#126×C53C2×C418yes—
168C2×C4⋊C4×C53C2×C411yescharacteristic
169C2×C4⋊C4×C53C2×C411yescharacteristic
170C2×C4⋊C4×C53C2×C411yescharacteristic
171C2×C22⋊C4×C53C2×C411yescharacteristic
172C2×C22⋊C4×C53C2×C411yescharacteristic
173C2×C22⋊C4×C53C2×C411yescharacteristic
174C2×C42×C53C2×C411yescharacteristic
175C24×C53C22×C411yescharacteristic
176C23×D53C22×C411yescharacteristic
177C23×D53C22×C411yescharacteristic
178C22×C4×C53C22×C411yescharacteristic
179C22×C4×C53C22×C411yescharacteristic
180C22×C4×C53C22×C411yescharacteristic
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C22×C411yescharacteristic
183C22×C4×C53C22×C411yescharacteristic
184C2×C22⋊D53—24no—
185C2×C22⋊D53—24no—
186C2×C22⋊D53C22×C414yes—
187C2×C22⋊D53C22×C414yes—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53C22×C411yescharacteristic
191C22×Dic53C22×C411yescharacteristic
192C22×Dic53C22×C411yescharacteristic
193C22×Dic53C22×C411yescharacteristic
194C22×Dic53C22×C412yes—
195C22×Dic53C22×C411yescharacteristic
196C22×Dic53C2412yes—
197C22×Dic53C2411yescharacteristic
198C2×D212—24no—
199C2×D212C22×C414yes—
200C2×C4×D53—24no—
201C2×C4×D53—24no—
202C2×C4×D53—22no—
203C2×C4×D53—22no—
204C2×C4×D53—22no—
205C2×C4×D53—22no—
206C2×C4×D53C22×C412yes—
207C2×C4×D53C22×C414yes—
208C2×C4×D53C22×C414yes—
209C2×C4×D53C22×C412yes—
210C2×C4×D53C2412yes—
211C2×C4×D53C2412yes—
212C2×Dic106—24no—
213C2×Dic106C22×C414yes—
214#11719940—28no—
215C2×#88324—22no—
216C2×#88324—22no—
217C2×#88324—22no—
218C2×#88324—22no—
219C2×#88324—22no—
220C2×#88324—22no—
221C2×#88324—28no—
222C2×#88324#4114yes—
223C2×#88324#4114yes—
224C2×#88324C2412yes—
225C2×#88324C2412yes—
226C2×#88324C2412yes—
227C2×#88324C2412yes—
228C2×#88324C2412yes—
229C2×#88324C2412yes—
230C2×#88324C2412yes—
231C2×#88324C2412yes—
232#11719936—28no—
233D53⋊C8—28no—
234D53⋊C8—28no—
235D53⋊C8—28no—
236C4⋊C4×C53C22×C414yes—
237C4⋊C4×C53C22×C414yes—
238C4⋊C4×C53C22×C414yes—
239C22⋊C4×C53C22×C414yes—
240C22⋊C4×C53C22×C414yes—
241C22⋊C4×C53C22×C414yes—
242C42×C53C22×C414yes—
243C22⋊Dic53C22×C414yes—
244#11719921C22×C414yes—
245#11719921C22×C414yes—
246#11719921C22×C414yes—
247#11719921C22×C414yes—
248#11719921C22×C414yes—
249#11719921C22×C414yes—
250C4⋊Dic53C22×C414yes—
251#11719919C22×C414yes—
252#11719919C22×C414yes—
253#11719919C22×C414yes—
254#11719919C22×C414yes—
255#11719919C22×C414yes—
256#11719919C22×C414yes—
257C4×Dic53C22×C412yes—
258C4×Dic53C22×C412yes—
259C4×Dic53C22×C414yes—
260C4×Dic53C22×C412yes—
261C4×Dic53C22×C412yes—
262C4×Dic53C2412yes—
263C4×Dic53C2412yes—
264C4×Dic53C2412yes—
265C4×Dic53C2412yes—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53C23×C412yes—
270C23×C53C23×C411yescharacteristic
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—22no—
276C22×D53#13114yes—
277C22×D53C23×C412yes—
278C22×D53C23×C412yes—
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×C53C23×C412yes—
286C2×C4×C53C23×C412yes—
287C2×C4×C53C23×C412yes—
288C2×C4×C53C23×C412yes—
289C2×C4×C53C23×C412yes—
290C2×C4×C53C23×C412yes—
291C22⋊D53—28no—
292C22⋊D53—28no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—24no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53#13114yes—
301C2×Dic53C23×C412yes—
302C2×Dic53C23×C412yes—
303C2×Dic53C23×C412yes—
304C2×Dic53C23×C412yes—
305C2×Dic53C23×C411yescharacteristic
306C2×Dic53C23×C412yes—
307C2×Dic53C2×#4112yes—
308C2×Dic53C2×#4112yes—
309C2×Dic53C2511yescharacteristic
310D212—28no—
311C4×D53—28no—
312C4×D53—24no—
313C4×D53—24no—
314C4×D53—28no—
315C4×D53—22no—
316C4×D53—22no—
317C4×D53—22no—
318C4×D53—22no—
319Dic106—28no—
320#88324—22no—
321#88324—22no—
322#88324—22no—
323#88324—22no—
324#88324—22no—
325#88324—22no—
326#88324C2×#4114yes—
327#88324C2×#4114yes—
328C2×#2966—531nomaximal, Sylow
329C22×C53—22no—
330C22×C53—22no—
331C22×C53—22no—
332C22×C53—44no—
333C22×C53C4×#4112yes—
334C22×C53C2×#13112yes—
335C22×C53C2×#13112yes—
336C22×C53C24×C411yescharacteristic
337C2×D53—22no—
338C2×D53—28no—
339C2×D53—22no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—44no—
344C2×D53C2×#13114yes—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350C4×C53—22no—
351Dic53—22no—
352Dic53—22no—
353Dic53—22no—
354Dic53—22no—
355Dic53C4×#4112yes—
356Dic53C2×#13114yes—
357Dic53C22×#4111yescharacteristic
358Dic53C22×#4111yescharacteristic
359C2×#529—531no—
360#2966—5316no—
361C2×#446—531no—
362C2×C8×Q8—531no—
363C2×#436—531no—
364C2×#435—531no—
365C2×#435—531no—
366C2×C8×D4—531no—
367C2×C8×D4—531no—
368C2×C8×D4—531no—
369C2×#433—531no—
370C2×#433—531no—
371C2×#432—531no—
372C2×#405—531no—
373C2×#405—531no—
374C22×C4×C8—531no—
375C2×C53—42no—
376C2×C53#296614yescomplemented
377C2×C53C2×C4×#4111yescharacteristic
378C2×C53C22×#13111yescharacteristic
379C2×C53C22×#13111yescharacteristic
380D53—24no—
381D53—42no—
382C22×M16—531no—
383C22×M16—531no—
384C23×C8—531no—
385C23×C8—531no—
386C23×C8—531no—
387C23×C8—531no—
388#529—538no—
389#529—538no—
390C2×#126—531no—
391C2×#126#615711yescharacteristic
392C2×#125—531no—
393C2×#124—531no—
394C2×#123—531no—
395C2×#123—531no—
396C2×C22⋊Q8—531no—
397C2×#121—531no—
398C2×C4×Q8—531no—
399C2×C4×D4—531no—
400C2×C4×D4—531no—
401C2×C4×D4—531no—
402C2×#117—531no—
403C2×#117—531no—
404C22×C42—531no—
405#446—538no—
406C8×Q8—538no—
407#436—538no—
408#435—538no—
409#435—538no—
410C8×D4—538no—
411C8×D4—538no—
412C8×D4—538no—
413#433—538no—
414#433—538no—
415#432—538no—
416C2×C4⋊C8—531no—
417C2×C4⋊C8—531no—
418C2×C4⋊C8—531no—
419C2×C4⋊C8—531no—
420C2×C4⋊C8—531no—
421C2×C4⋊C8—531no—
422C2×C22⋊C8—531no—
423C2×C22⋊C8—531no—
424C2×C22⋊C8—531no—
425C2×C22⋊C8—531no—
426C2×C22⋊C8—531no—
427C2×C22⋊C8—531no—
428#405—538no—
429#405—538no—
430C2×#97—531no—
431C2×#97—531no—
432C2×#97—531no—
433C2×#97—531no—
434C2×C4×C8—531no—
435C2×C4×C8—531no—
436C2×C4×C8—531no—
437C2×C4×C8—531no—
438C2×C4×C8—538no—
439C2×C4×C8—531no—
440C2×C4×C8—531no—
441C53C2×#296611yescharacteristic, complemented, Sylow
442C22×Q8—531no—
443C22×D4—531no—
444C22×D4—531no—
445C22×D4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4—531no—
451C2×M16—534no—
452C2×M16—534no—
453C2×M16—1064no—
454C2×M16—1064no—
455C22×C8—531no—
456C22×C8—531no—
457C22×C8—531no—
458C22×C8—531no—
459C22×C8—534no—
460C22×C8—534no—
461C22×C8—531no—
462C22×C8—531no—
463C22×C8—534no—
464C22×C8—534no—
465C22×C8—531no—
466C22×C8—531no—
467C22×C8—1064no—
468C22×C8—1064no—
469C22×C8—1064no—
470C22×C8—1064no—
471#126—538no—
472#126C2×#615718yes—
473#125—538no—
474#124—538no—
475#123—538no—
476#123—538no—
477C22⋊Q8—538no—
478#121—538no—
479C4×Q8—534no—
480C4×Q8—534no—
481C4×D4—534no—
482C4×D4—534no—
483C4×D4—534no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—534no—
487#117—534no—
488#117—534no—
489#117—534no—
490#117—534no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—531no—
496C2×C4⋊C4—531no—
497C2×C4⋊C4—531no—
498C2×C4⋊C4C2×#615711yescharacteristic
499C2×C4⋊C4C2×#615711yescharacteristic
500C2×C4⋊C4C2×#615711yescharacteristic
501C2×C22⋊C4—531no—
502C2×C22⋊C4—531no—
503C2×C22⋊C4—531no—
504C2×C22⋊C4—531no—
505C2×C22⋊C4—531no—
506C2×C22⋊C4—531no—
507C2×C22⋊C4—531no—
508C2×C22⋊C4C2×#615711yescharacteristic
509C2×C22⋊C4C2×#615711yescharacteristic
510C2×C22⋊C4C2×#615711yescharacteristic
511C2×C42—531no—
512C2×C42—531no—
513C2×C42—531no—
514C2×C42—531no—
515C2×C42—531no—
516C2×C42—534no—
517C2×C42—534no—
518C2×C42C2×#615711yescharacteristic
519C4⋊C8—534no—
520C4⋊C8—534no—
521C4⋊C8—534no—
522C4⋊C8—534no—
523C4⋊C8—534no—
524C4⋊C8—534no—
525C22⋊C8—534no—
526C22⋊C8—534no—
527C22⋊C8—534no—
528C22⋊C8—534no—
529C22⋊C8—534no—
530C22⋊C8—534no—
531#97—534no—
532#97—534no—
533#97—534no—
534#97—534no—
535C4×C8—534no—
536C4×C8—534no—
537C4×C8—534no—
538C4×C8—534no—
539C4×C8—534no—
540C4×C8—534no—
541C24—531no—
542C24—531no—
543C24C22×#615711yescharacteristic
544C2×Q8—534no—
545C2×Q8—1064no—
546C2×D4—534no—
547C2×D4—534no—
548C2×D4—534no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4—1064no—
552C22×C4—531no—
553C22×C4—531no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—531no—
557C22×C4—531no—
558C22×C4—531no—
559C22×C4—531no—
560C22×C4—532no—
561C22×C4—534no—
562C22×C4—534no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1064no—
571C22×C4—1064no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4C22×#615711yescharacteristic
575C22×C4C22×#615711yescharacteristic
576C22×C4C22×#615711yescharacteristic
577C22×C4C22×#615711yescharacteristic
578C22×C4C22×#615711yescharacteristic
579C22×C4C22×#615711yescharacteristic
580M16—1068no—
581M16—1068no—
582C2×C8—534no—
583C2×C8—534no—
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—532no—
589C2×C8—532no—
590C2×C8—532no—
591C2×C8—532no—
592C2×C8—1068no—
593C2×C8—1068no—
594C2×C8—1068no—
595C2×C8—1068no—
596C2×C8—1062no—
597C2×C8—1062no—
598C2×C8—1062no—
599C2×C8—1062no—
600C2×C8—1062no—
601C2×C8—1062no—
602C4⋊C4—534no—
603C4⋊C4—534no—
604C4⋊C4—534no—
605C4⋊C4—534no—
606C4⋊C4—534no—
607C4⋊C4—534no—
608C4⋊C4—534no—
609C4⋊C4C22×#615714yes—
610C4⋊C4C22×#615714yes—
611C4⋊C4C22×#615714yes—
612C22⋊C4—534no—
613C22⋊C4—534no—
614C22⋊C4—534no—
615C22⋊C4—534no—
616C22⋊C4—534no—
617C22⋊C4—534no—
618C22⋊C4—534no—
619C22⋊C4C22×#615714yes—
620C22⋊C4C22×#615714yes—
621C22⋊C4C22×#615714yes—
622C42—532no—
623C42—532no—
624C42—532no—
625C42—532no—
626C42—532no—
627C42—532no—
628C42—534no—
629C42—532no—
630C42—532no—
631C42C22×#615714yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—534no—
636C23—532no—
637C23—532no—
638C23—1062no—
639C23—1062no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23C23×#615712yes—
644C23C23×#615711yescharacteristic
645Q8—1068no—
646D4—1068no—
647D4—1068no—
648D4—1068no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—532no—
656C2×C4—532no—
657C2×C4—534no—
658C2×C4—531no—
659C2×C4—532no—
660C2×C4—531no—
661C2×C4—532no—
662C2×C4—532no—
663C2×C4—532no—
664C2×C4—532no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1064no—
670C2×C4—1064no—
671C2×C4—1068no—
672C2×C4—1068no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1064no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4C23×#615712yes—
681C2×C4C23×#615712yes—
682C2×C4C23×#615712yes—
683C2×C4C23×#615712yes—
684C2×C4C23×#615712yes—
685C2×C4C23×#615712yes—
686C8—534no—
687C8—534no—
688C8—1062no—
689C8—1062no—
690C8—1062no—
691C8—1062no—
692C8—1062no—
693C8—1062no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—534no—
699C22—1062no—
700C22—1062no—
701C22—1068no—
702C22—1062no—
703C22—1062no—
704C22—1062no—
705C22—2124no—
706C22#41×#615712yes—
707C22D53⋊#13112yes—
708C22D53⋊#13112yes—
709C22C24×#615711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—22no—
716C4—531no—
717C4—531no—
718C4—532no—
719C4—534no—
720C4—1062no—
721C4—1062no—
722C4—1062no—
723C4—1062no—
724C2—42no—
725C2—1064no—
726C2—2122no—
727C2#2029153314yesdirect product factor
728C2C2×#41×#615711yescharacteristic
729C2C2×D53⋊#13111yescharacteristic
730C2C2×D53⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#126×C53C4
socleC23×C53C23×C4
prime radicalC2×#13133190C4
cosocleC2×Dic53C25
hypercenterC2×#126#6157
hypocenterC53C2×#2966
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. #20291533C2direct (N × H)
2. C2×#16811675C2semidirect
3. C2×#16811672C2semidirect
4. C2×#16811656C2semidirect
5. C2×#16811655C2semidirect
6. C2×#16811653C2semidirect
7. C2×#16811651C2semidirect
8. C2×#16811650C2semidirect
9. C2×#16811650C2semidirect
10. C2×#16811648C2semidirect
11. C2×#16811647C2semidirect
12. C2×#16811646C2semidirect
13. C2×#16811588C2semidirect
14. C2×#16811587C2semidirect
15. C2×C4×D53⋊C8C2semidirect
23. #16811675C22semidirect
24. #16811672C22semidirect
25. #16811656C22semidirect
26. #16811655C22semidirect
27. #16811653C22semidirect
28. #16811651C22semidirect
29. #16811650C22semidirect
30. #16811650C22semidirect
31. #16811648C22semidirect
32. #16811647C22semidirect
33. #16811646C22semidirect
46. #16811588C22semidirect
47. #16811587C22semidirect
52. C4×D53⋊C8C22semidirect
376. C2×C53#2966semidirect
441. C53C2×#2966semidirect
727. C2#20291533direct (N × H)

Maximal subgroups

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

subgroupindex
#202915332
C2×#168116752
C2×#168116722
C2×#168116562
C2×#168116552
C2×#168116532
C2×#168116512
C2×#168116502
C2×#168116482
C2×#168116472
C2×#168116462
C2×#168115882
C2×#168115872
C2×C4×D53⋊C82
C2×#168111562
C2×#296653