Finite Group Databasebeta

← C2×#20291530 #28329638

Subgroups — C2×#20291530 #28329638

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#20291530C2116yesmaximal, direct product factor
2C2×#16811675C211yesmaximal, characteristic, complemented
3C2×#16811672C211yesmaximal, characteristic, complemented
4C2×#16811656C211yesmaximal, characteristic, complemented
5C2×#16811654C211yesmaximal, characteristic, complemented
6C2×#16811652C211yesmaximal, characteristic, complemented
7C2×#16811650C211yesmaximal, characteristic, complemented
8C2×#16811650C211yesmaximal, characteristic, complemented
9C2×D4×#88324C211yesmaximal, characteristic, complemented
10C2×#16811648C211yesmaximal, characteristic, complemented
11C2×#16811647C211yesmaximal, characteristic, complemented
12C2×#16811643C211yesmaximal, characteristic, complemented
13C2×#16811588C211yesmaximal, characteristic, complemented
14C2×#16811587C211yesmaximal, characteristic, complemented
15C22×C4×#88324C211yesmaximal, characteristic, complemented
16C2×#16811150C211yesmaximal, characteristic
17C22×#11719936C2211yescharacteristic
18C22×#11719940C2211yescharacteristic
19C22×D53⋊C8C2211yescharacteristic
20C23×#88324C2211yescharacteristic
21C23×#88324C2211yescharacteristic
22C23×#88324C2211yescharacteristic
23#16811675C2218yescomplemented
24#16811672C2218yescomplemented
25#16811656C2218yescomplemented
26#16811654C2218yescomplemented
27#16811652C2218yescomplemented
28#16811650C2218yescomplemented
29#16811650C2218yescomplemented
30D4×#88324C2218yescomplemented
31#16811648C2218yescomplemented
32#16811647C2218yescomplemented
33#16811643C2218yescomplemented
34C2×#13133284C2211yescharacteristic
35C2×#13133284C2211yescharacteristic
36C2×#13133284C2211yescharacteristic
37C2×#13133284C2211yescharacteristic
38C2×C4⋊#88324C2211yescharacteristic
39C2×C4⋊#88324C2211yescharacteristic
40C2×#13133274C2211yescharacteristic
41C2×#13133274C2211yescharacteristic
42C2×C22⋊#88324C2211yescharacteristic
43C2×C22⋊#88324C2211yescharacteristic
44C2×C22⋊#88324C2211yescharacteristic
45C2×C22⋊#88324C2211yescharacteristic
46#16811588C2218yescomplemented
47#16811587C2218yescomplemented
48C2×#13133272C2211yescharacteristic
49C2×#13133272C2211yescharacteristic
50C2×#13133272C2211yescharacteristic
51C2×#13133272C2211yescharacteristic
52C2×C4×#88324C2211yescharacteristic
53C2×C4×#88324C2211yescharacteristic
54C2×C4×#88324C2211yescharacteristic
55C2×C4×#88324C2211yescharacteristic
56C2×C4×#88324C2211yescharacteristic
57C2×C4×#88324C2211yescharacteristic
58C2×C4×#88324C2218yescomplemented
59#16811150C418yes—
60#16811150C2218yes—
61C2×#13133212C411yescharacteristic
62C2×#13133210C411yescharacteristic
63C2×#13133207C411yescharacteristic
64C2×#13133203C411yescharacteristic
65C2×#13133200C411yescharacteristic
66C2×#13133194C411yescharacteristic
67C2×#13133189C411yescharacteristic
68C2×#13133182C2211yescharacteristic
69C2×D4×Dic53C2211yescharacteristic
70C2×#13133177C2211yescharacteristic
71C2×#13133177C2211yescharacteristic
72C2×#13133175C2211yescharacteristic
73C2×#13133173C2211yescharacteristic
74C22×C4×Dic53C2211yescharacteristic
75C2×#123×C53C411yescharacteristic
76C2×#11719936—24no—
77C2×#11719936C2314yes—
78C2×#11719940—24no—
79C2×#11719940C2314yes—
80C2×D53⋊C8—24no—
81C2×D53⋊C8C2314yes—
82C22×#88324—24no—
83C22×#88324—24no—
84C22×#88324—24no—
85C22×#88324C2311yescharacteristic
86C22×#88324C2311yescharacteristic
87C22×#88324C2311yescharacteristic
88C22×#88324C2311yescharacteristic
89C22×#88324C2314yes—
90C22×#88324C2314yes—
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—
104C22⋊#88324C2314yes—
105C22⋊#88324C2314yes—
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×C22⋊D53C2×C411yescharacteristic
120C22×C22⋊D53C2×C411yescharacteristic
121C23×Dic53C2×C411yescharacteristic
122C23×Dic53C2311yescharacteristic
123C23×Dic53C2311yescharacteristic
124C22×C4×D53C2311yescharacteristic
125#13133212C2×C418yes—
126#13133210C2×C418yes—
127#13133207C2×C418yes—
128#13133203C2×C418yes—
129#13133200C2×C418yes—
130#13133194C2×C418yes—
131#13133189C2×C418yes—
132#13133182C2×C414yes—
133#13133182C2314yes—
134D4×Dic53C2×C414yes—
135D4×Dic53C2314yes—
136#13133177C2×C414yes—
137#13133177C2×C414yes—
138#13133177C2314yes—
139#13133177C2314yes—
140#13133175C2×C414yes—
141#13133175C2314yes—
142#13133173C2×C414yes—
143#13133173C2314yes—
144C2×C4⋊Dic53C2×C411yescharacteristic
145C2×C4⋊Dic53C2×C411yescharacteristic
146C2×#11719919C2×C411yescharacteristic
147C2×#11719919C2×C411yescharacteristic
148C2×#11719919C2×C411yescharacteristic
149C2×#11719919C2×C411yescharacteristic
150C2×#11719919C2×C411yescharacteristic
151C2×#11719919C2×C411yescharacteristic
152C2×C22⋊Dic53C2×C411yescharacteristic
153C2×C22⋊Dic53C2×C411yescharacteristic
154C2×C22⋊Dic53C2×C411yescharacteristic
155C2×#11719921C2×C411yescharacteristic
156C2×#11719921C2×C411yescharacteristic
157C2×#11719921C2×C411yescharacteristic
158C2×#11719921C2×C411yescharacteristic
159C2×C4×Dic53C2×C411yescharacteristic
160C2×C4×Dic53C2×C411yescharacteristic
161C2×C4×Dic53C2×C414yes—
162C2×C4×Dic53C2311yescharacteristic
163C2×C4×Dic53C2311yescharacteristic
164C2×C4×Dic53C2311yescharacteristic
165C2×C4×Dic53C2311yescharacteristic
166C2×C4×Dic53C2314yes—
167C22×D4×C53C2×C411yescharacteristic
168C23×C4×C53C2×C411yescharacteristic
169#123×C53C2×C418yes—
170C2×C4⋊C4×C53C2×C411yescharacteristic
171C2×C4⋊C4×C53C2×C411yescharacteristic
172C2×C22⋊C4×C53C2×C411yescharacteristic
173C2×C22⋊C4×C53C2×C411yescharacteristic
174C2×C22⋊C4×C53C2×C411yescharacteristic
175C24×C53C22×C411yescharacteristic
176C24×C53C22×C411yescharacteristic
177C23×D53C22×C411yescharacteristic
178C2×D4×C53—24no—
179C2×D4×C53C22×C414yes—
180C22×C4×C53—24no—
181C22×C4×C53C22×C411yescharacteristic
182C22×C4×C53C22×C411yescharacteristic
183C22×C4×C53C22×C411yescharacteristic
184C22×C4×C53C22×C411yescharacteristic
185C22×C4×C53C22×C411yescharacteristic
186C22×C4×C53C22×C414yes—
187C2×C22⋊D53—24no—
188C2×C22⋊D53—24no—
189C2×C22⋊D53C22×C414yes—
190C2×C22⋊D53C22×C414yes—
191C22×Dic53—24no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53C22×C411yescharacteristic
197C22×Dic53C22×C412yes—
198C22×Dic53C22×C411yescharacteristic
199C22×Dic53C22×C414yes—
200C22×Dic53C22×C411yescharacteristic
201C22×Dic53C22×C411yescharacteristic
202C22×Dic53C22×C411yescharacteristic
203C22×Dic53C22×C412yes—
204C22×Dic53C22×C411yescharacteristic
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C22×Dic53C2411yescharacteristic
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53C22×C412yes—
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—28no—
223C2×#88324—28no—
224C2×#88324#4114yes—
225C2×#88324#4114yes—
226C2×#88324C2412yes—
227C2×#88324C2412yes—
228C2×#88324C2412yes—
229C2×#88324C2412yes—
230C2×#88324C2412yes—
231C2×#88324C2412yes—
232C2×#88324C2412yes—
233C2×#88324C2412yes—
234#11719936—28no—
235D53⋊C8—28no—
236C4⋊C4×C53C22×C414yes—
237C4⋊C4×C53C22×C414yes—
238C22⋊C4×C53C22×C414yes—
239C22⋊C4×C53C22×C414yes—
240C22⋊C4×C53C22×C414yes—
241C22⋊Dic53C22×C414yes—
242C22⋊Dic53C22×C414yes—
243C22⋊Dic53C22×C414yes—
244#11719921C22×C414yes—
245#11719921C22×C414yes—
246#11719921C22×C414yes—
247#11719921C22×C414yes—
248C4⋊Dic53C22×C414yes—
249C4⋊Dic53C22×C414yes—
250#11719919C22×C414yes—
251#11719919C22×C414yes—
252#11719919C22×C414yes—
253#11719919C22×C414yes—
254#11719919C22×C414yes—
255#11719919C22×C414yes—
256C4×Dic53C22×C412yes—
257C4×Dic53C22×C412yes—
258C4×Dic53C22×C414yes—
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×C53—22no—
270C23×C53—22no—
271C23×C53#13114yes—
272C23×C53C23×C412yes—
273C23×C53C23×C412yes—
274C23×C53C23×C411yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53—22no—
278C22×D53C23×C412yes—
279D4×C53—28no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—28no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
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—22no—
298C2×Dic53—24no—
299C2×Dic53—24no—
300C2×Dic53—28no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53#13114yes—
306C2×Dic53C23×C412yes—
307C2×Dic53C23×C412yes—
308C2×Dic53C23×C412yes—
309C2×Dic53C23×C412yes—
310C2×Dic53C23×C412yes—
311C2×Dic53C23×C411yescharacteristic
312C2×Dic53C23×C412yes—
313C2×Dic53C2×#4112yes—
314C2×Dic53C2×#4112yes—
315C2×Dic53C2511yescharacteristic
316C4×D53—24no—
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—28no—
331C22×C53—22no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53—22no—
335C22×C53—44no—
336C22×C53C4×#4112yes—
337C22×C53C2×#13114yes—
338C22×C53C2×#13112yes—
339C22×C53C2×#13112yes—
340C22×C53C24×C411yescharacteristic
341C2×D53—22no—
342C2×D53—22no—
343C2×D53—22no—
344C2×D53—44no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—22no—
348C4×C53—22no—
349C4×C53—22no—
350Dic53—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—24no—
376C2×C53—42no—
377C2×C53#296614yescomplemented
378C2×C53C2×C4×#4111yescharacteristic
379C2×C53C22×#13111yescharacteristic
380C2×C53C22×#13111yescharacteristic
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—531no—
392C2×#125—531no—
393C2×#124—531no—
394C2×#123—531no—
395C2×#123#615711yescharacteristic
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×D4C2×#615711yescharacteristic
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4C2×#615711yescharacteristic
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#126—538no—
473#125—538no—
474#124—538no—
475#123—538no—
476#123C2×#615718yes—
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⋊C4—531no—
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—531no—
517C2×C42—534no—
518C2×C42—534no—
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—
542C24C22×#615711yescharacteristic
543C24C22×#615711yescharacteristic
544C2×Q8—534no—
545C2×Q8—1064no—
546C2×D4—24no—
547C2×D4—534no—
548C2×D4—534no—
549C2×D4—1064no—
550C2×D4—1064no—
551C2×D4C22×#615714yes—
552C22×C4—24no—
553C22×C4—531no—
554C22×C4—531no—
555C22×C4—532no—
556C22×C4—534no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—531no—
561C22×C4—531no—
562C22×C4—531no—
563C22×C4—531no—
564C22×C4—531no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1064no—
574C22×C4C22×#615714yes—
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⋊C4—534no—
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—534no—
630C42—532no—
631C42—532no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—532no—
638C23—1062no—
639C23—1062no—
640C23—1062no—
641C23#1313330414yes—
642C23C23×#615712yes—
643C23C23×#615712yes—
644C23C23×#615711yescharacteristic
645Q8—1068no—
646D4—28no—
647D4—1068no—
648D4—1068no—
649C2×C4—22no—
650C2×C4—28no—
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—532no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1064no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1062no—
672C2×C4—1062no—
673C2×C4—1064no—
674C2×C4—1064no—
675C2×C4—1068no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
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—28no—
697C22—22no—
698C22—22no—
699C22—22no—
700C22—44no—
701C22—1062no—
702C22—1062no—
703C22—1062no—
704C22—2124no—
705C22#41×#615712yes—
706C22C2×#1313330414yes—
707C22C2×#1313330412yes—
708C22D53⋊#13112yes—
709C22C24×#615711yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—531no—
716C4—531no—
717C4—532no—
718C4—534no—
719C4—1062no—
720C4—1062no—
721C4—1062no—
722C4—1062no—
723C4—1062no—
724C2—24no—
725C2—42no—
726C2—2122no—
727C2#2029153014yesdirect product factor
728C2C2×#41×#615711yescharacteristic
729C2C22×#1313330411yescharacteristic
730C2C2×D53⋊#13111yescharacteristic
subgroupG/H
centerC23C23×#6157
commutatorC22×C53C24×C4
FrattiniC22C24×#6157
FittingC2×#123×C53C4
socleC23×C53C23×C4
prime radicalC2×#13133189C4
cosocleC2×Dic53C25
hypercenterC2×#123#6157
hypocenterC53C2×#2966
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #20291530C2direct (N × H)
2. C2×#16811675C2semidirect
3. C2×#16811672C2semidirect
4. C2×#16811656C2semidirect
5. C2×#16811654C2semidirect
6. C2×#16811652C2semidirect
7. C2×#16811650C2semidirect
8. C2×#16811650C2semidirect
9. C2×D4×#88324C2semidirect
10. C2×#16811648C2semidirect
11. C2×#16811647C2semidirect
12. C2×#16811643C2semidirect
13. C2×#16811588C2semidirect
14. C2×#16811587C2semidirect
15. C22×C4×#88324C2semidirect
23. #16811675C22semidirect
24. #16811672C22semidirect
25. #16811656C22semidirect
26. #16811654C22semidirect
27. #16811652C22semidirect
28. #16811650C22semidirect
29. #16811650C22semidirect
30. D4×#88324C22semidirect
31. #16811648C22semidirect
32. #16811647C22semidirect
33. #16811643C22semidirect
46. #16811588C22semidirect
47. #16811587C22semidirect
58. C2×C4×#88324C22semidirect
377. C2×C53#2966semidirect
441. C53C2×#2966semidirect
727. C2#20291530direct (N × H)

Maximal subgroups

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

subgroupindex
#202915302
C2×#168116752
C2×#168116722
C2×#168116562
C2×#168116542
C2×#168116522
C2×#168116502
C2×D4×#883242
C2×#168116482
C2×#168116472
C2×#168116432
C2×#168115882
C2×#168115872
C22×C4×#883242
C2×#168111502
C2×#296653