Finite Group Databasebeta

← C2×#20285962 #28256275

Subgroups — C2×#20285962 #28256275

Order 13568.

1806 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811251C211yesmaximal, characteristic, complemented
2#20285962C2116yesmaximal, direct product factor
3C2×#16811033C211yesmaximal, characteristic, complemented
4C2×#16811022C211yesmaximal, characteristic, complemented
5C2×#16810987C211yesmaximal, characteristic, complemented
6C2×#16810969C211yesmaximal, characteristic, complemented
7C2×#16810939C211yesmaximal, characteristic, complemented
8C2×#16810944C211yesmaximal, characteristic, complemented
9C2×#16810944C211yesmaximal, characteristic, complemented
10C2×#16810934C211yesmaximal, characteristic, complemented
11C2×#16810923C211yesmaximal, characteristic, complemented
12C2×#16810923C211yesmaximal, characteristic, complemented
13C2×#16810913C211yesmaximal, characteristic, complemented
14C2×#16810903C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#540C211yesmaximal, characteristic
17#16811251—24no—
18#16811251C2218yescomplemented
19C2×#13133217C2211yescharacteristic
20C2×#13133217C2211yescharacteristic
21C2×#13133216—21no—
22C2×#13133209C2211yescharacteristic
23C2×#13133209C2211yescharacteristic
24C2×#13133208—21no—
25C2×#13133194—21no—
26C2×#13133194—21no—
27C2×#13133176C2211yescharacteristic
28C22×C4⋊Dic53C2211yescharacteristic
29#16811033C2218yescomplemented
30#16811022C2218yescomplemented
31#16810987C2218yescomplemented
32#16810969C2218yescomplemented
33#16810944C2218yescomplemented
34#16810944C2218yescomplemented
35#16810939C2218yescomplemented
36#16810934C2218yescomplemented
37#16810923C2218yescomplemented
38#16810923C2218yescomplemented
39#16810913C2218yescomplemented
40#16810903C2218yescomplemented
41#16810684C2218yescomplemented
42C2×#13133150C2211yescharacteristic
43C2×#13133150C2211yescharacteristic
44C2×#13133150C2211yescharacteristic
45C2×#13133150C2211yescharacteristic
46C2×#13133148C2211yescharacteristic
47C2×#13133148C2211yescharacteristic
48C2×#13133148C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133138C2211yescharacteristic
53C2×#13133138C2211yescharacteristic
54C2×#13133138C2211yescharacteristic
55C2×#13133138C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133138C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#540—24no—
65C53×#540C2218yes—
66C2×#127×C53C2211yescharacteristic
67C2×#125×C53C2211yescharacteristic
68C2×#123×C53—21no—
69C2×#123×C53—21no—
70C2×#121×C53—21no—
71C2×#121×C53—21no—
72C2×#121×C53C2211yescharacteristic
73C2×#121×C53C2211yescharacteristic
74C2×C4×D4×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C23×Dic53—21no—
80C22×#88322C2311yescharacteristic
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C22×#88322C2311yescharacteristic
84#13133217—22no—
85#13133217—22no—
86#13133217C2314yes—
87#13133217C2314yes—
88#13133216—28no—
89#13133209—22no—
90#13133209—22no—
91#13133209C2314yes—
92#13133209C2314yes—
93#13133208—28no—
94#13133194—28no—
95#13133194—28no—
96#13133176—22no—
97#13133176C2314yes—
98C2×C4⋊Dic53—21no—
99C2×C4⋊Dic53—22no—
100C2×C4⋊Dic53—21no—
101C2×C4⋊Dic53—21no—
102C2×C4⋊Dic53C2311yescharacteristic
103C2×C4⋊Dic53C2311yescharacteristic
104C2×C4⋊Dic53C2314yes—
105C2×C4⋊Dic53C2311yescharacteristic
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×#11719919—21no—
110C2×#11719919—21no—
111C2×C22⋊Dic53—21no—
112C2×C4×Dic53—21no—
113#13133150C2314yes—
114#13133150C2314yes—
115#13133150C2314yes—
116#13133150C2314yes—
117#13133148C2314yes—
118#13133148C2314yes—
119#13133148C2314yes—
120#13133148C2314yes—
121C4⋊#88322C2314yes—
122C4⋊#88322C2314yes—
123#13133138C2314yes—
124#13133138C2314yes—
125#13133138C2314yes—
126#13133138C2314yes—
127#13133138C2314yes—
128#13133138C2314yes—
129#13133138C2314yes—
130#13133138C2314yes—
131C22⋊#88322C2314yes—
132C22⋊#88322C2314yes—
133#13133128C2314yes—
134C4×#88322C2314yes—
135C22×D4×C53—21no—
136C22×D4×C53—21no—
137C22×D4×C53—21no—
138C22×D4×C53—21no—
139C22×D4×C53C2311yescharacteristic
140C22×D4×C53C2311yescharacteristic
141C23×C4×C53—21no—
142C23×C4×C53—21no—
143C23×C4×C53C2311yescharacteristic
144#127×C53—22no—
145#127×C53C2314yes—
146#125×C53—22no—
147#125×C53C2314yes—
148#123×C53—28no—
149#123×C53—28no—
150#121×C53—28no—
151#121×C53—28no—
152#121×C53—22no—
153#121×C53—22no—
154#121×C53C2314yes—
155#121×C53C2314yes—
156C4×D4×C53—22no—
157C4×D4×C53—22no—
158C4×D4×C53C2314yes—
159C4×D4×C53C2314yes—
160#117×C53D414yes—
161#117×C53C2314yes—
162C2×C4⋊C4×C53—21no—
163C2×C4⋊C4×C53—21no—
164C2×C4⋊C4×C53D411yescharacteristic
165C2×C4⋊C4×C53D411yescharacteristic
166C2×C4⋊C4×C53C2311yescharacteristic
167C2×C4⋊C4×C53C2311yescharacteristic
168C2×C22⋊C4×C53—21no—
169C2×C22⋊C4×C53—21no—
170C2×C22⋊C4×C53—21no—
171C2×C22⋊C4×C53—21no—
172C2×C22⋊C4×C53D411yescharacteristic
173C2×C22⋊C4×C53D411yescharacteristic
174C2×C42×C53C2311yescharacteristic
175C2×C42×C53C2311yescharacteristic
176C24×C53—21no—
177C24×C53—21no—
178C24×C53C2×D411yescharacteristic
179C2×D4×C53—24no—
180C2×D4×C53—24no—
181C2×D4×C53—21no—
182C2×D4×C53—21no—
183C2×D4×C53—24no—
184C2×D4×C53—24no—
185C2×D4×C53—22no—
186C2×D4×C53—22no—
187C2×D4×C53—22no—
188C2×D4×C53—22no—
189C2×D4×C53—82no—
190C2×D4×C53—82no—
191C2×D4×C53—82no—
192C2×D4×C53—82no—
193C2×D4×C53C2412yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—22no—
196C22×C4×C53—22no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—24no—
200C22×C4×C53—24no—
201C22×C4×C53—82no—
202C22×C4×C53—82no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D412yes—
209C22×C4×C53C2412yes—
210C22×C4×C53C2411yescharacteristic
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—24no—
216C22×Dic53—82no—
217C2×Dic106—24no—
218C2×Dic106—24no—
219C2×Dic106—82no—
220C2×Dic106—82no—
221C4⋊C4×C53—24no—
222C4⋊C4×C53—24no—
223C4⋊C4×C53—21no—
224C4⋊C4×C53—21no—
225C4⋊C4×C53C2×D414yes—
226C4⋊C4×C53C2×D414yes—
227C4⋊C4×C53C2412yes—
228C4⋊C4×C53C2412yes—
229C22⋊C4×C53—24no—
230C22⋊C4×C53—24no—
231C22⋊C4×C53—24no—
232C22⋊C4×C53—24no—
233C22⋊C4×C53C2×D414yes—
234C22⋊C4×C53C2×D414yes—
235C42×C53C2×D412yes—
236C42×C53C2×D412yes—
237C42×C53C2412yes—
238C42×C53C2412yes—
239C22⋊Dic53—24no—
240C4⋊Dic53—24no—
241C4⋊Dic53—21no—
242C4⋊Dic53—21no—
243C4⋊Dic53—24no—
244C4⋊Dic53—24no—
245C4⋊Dic53—21no—
246C4⋊Dic53—21no—
247C4⋊Dic53C2412yes—
248C4⋊Dic53C2412yes—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251#11719919—24no—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255C4×Dic53—24no—
256C2×#88322—22no—
257C2×#88322—22no—
258C2×#88322—22no—
259C2×#88322—22no—
260C2×#88322C2412yes—
261C2×#88322C2412yes—
262C2×#88322C2412yes—
263C2×#88322C2412yes—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—42no—
270C23×C53—42no—
271C23×C53—42no—
272C23×C53—42no—
273C23×C53—42no—
274C23×C53—42no—
275C23×C53C22×D412yes—
276C23×C53C22×D411yescharacteristic
277D4×C53—22no—
278D4×C53—22no—
279D4×C53—22no—
280D4×C53—22no—
281D4×C53—42no—
282D4×C53—42no—
283D4×C53—84no—
284D4×C53—84no—
285D4×C53—84no—
286D4×C53—84no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—24no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—42no—
298C2×C4×C53—42no—
299C2×C4×C53—84no—
300C2×C4×C53—84no—
301C2×C4×C53C22×D412yes—
302C2×C4×C53C22×D412yes—
303C2×C4×C53C22×D412yes—
304C2×C4×C53C22×D412yes—
305C2×C4×C53C22×D412yes—
306C2×C4×C53C22×D411yescharacteristic
307C2×C4×C532−1+412yes—
308C2×C4×C532−1+412yes—
309C2×C4×C53C2511yescharacteristic
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—42no—
315C2×Dic53—42no—
316C2×Dic53—42no—
317C2×Dic53—42no—
318C2×Dic53—84no—
319Dic106—84no—
320Dic106—84no—
321#88322—22no—
322#88322—22no—
323#88322—22no—
324#88322—22no—
325C2×#3241—531nomaximal, Sylow
326C22×C53—22no—
327C22×C53—22no—
328C22×C53—22no—
329C22×C53—44no—
330C22×C53—42no—
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—84no—
337C22×C53—84no—
338C22×C53#53612yes—
339C22×C53#57612yes—
340C22×C53#57712yes—
341C22×C53C23×D411yescharacteristic
342C4×C53—22no—
343C4×C53—22no—
344C4×C53—22no—
345C4×C53—22no—
346C4×C53—22no—
347C4×C53—42no—
348C4×C53—42no—
349C4×C53#53612yes—
350C4×C53C2×2−1+411yescharacteristic
351C4×C53C2×2−1+411yescharacteristic
352Dic53—42no—
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356C2×#544—531no—
357C2×#540D5311yescharacteristic
358#3241—5316no—
359C2×#501—531no—
360C2×#499—531no—
361C2×#490—531no—
362C2×#486—531no—
363C2×#481—531no—
364C2×#482—531no—
365C2×#482—531no—
366C2×#480—531no—
367C2×#478—531no—
368C2×#478—531no—
369C2×#476—531no—
370C2×#474—531no—
371C2×#433—531no—
372C2×C53—42no—
373C2×C53—82no—
374C2×C53—82no—
375C2×C53#324114yescomplemented
376C2×C53C2×#53611yescharacteristic
377C2×C53C2×#57611yescharacteristic
378C2×C53C2×#57711yescharacteristic
379#544—538no—
380#544—1064no—
381#540—24no—
382#540C2×D5318yes—
383C2×C4⋊Q8—531no—
384C2×C4⋊Q8—531no—
385C2×C4⋊Q8—1061no—
386C2×#127C2×D5311yescharacteristic
387C2×#125—531no—
388C2×#125—531no—
389C2×#125—1061no—
390C2×#125C2×D5311yescharacteristic
391C2×#123—21no—
392C2×#123—21no—
393C2×C22⋊Q8—1061no—
394C2×C22⋊Q8—1061no—
395C2×#121—21no—
396C2×#121—21no—
397C2×#121C2×D5311yescharacteristic
398C2×#121C2×D5311yescharacteristic
399C2×C4×D4C2×D5311yescharacteristic
400C2×C4×D4C2×D5311yescharacteristic
401C2×#117—531no—
402C2×#117C2×D5311yescharacteristic
403C22×C4⋊C4—531no—
404#501—538no—
405#499—538no—
406#490—538no—
407#486—538no—
408#482—538no—
409#482—538no—
410#481—538no—
411#480—538no—
412#478—538no—
413#478—538no—
414#476—538no—
415#474—538no—
416#433—538no—
417C2×#107—531no—
418C2×#107—531no—
419C2×#107—531no—
420C2×#107—531no—
421C2×#106—531no—
422C2×#106—531no—
423C2×#106—531no—
424C2×#106—531no—
425C2×C4⋊C8—531no—
426C2×C4⋊C8—531no—
427C2×#102—531no—
428C2×#102—531no—
429C2×#102—531no—
430C2×#102—531no—
431C2×#102—531no—
432C2×#102—531no—
433C2×#102—531no—
434C2×#102—531no—
435C2×C22⋊C8—531no—
436C2×C22⋊C8—531no—
437C2×#97—531no—
438C2×C4×C8—531no—
439C53C2×#324111yescharacteristic, complemented, Sylow
440C22×Q8—1061no—
441C22×Q8—1061no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4—21no—
445C22×D4—21no—
446C22×D4C22×D5311yescharacteristic
447C22×D4C22×D5311yescharacteristic
448C23×C4—21no—
449C23×C4—21no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C22×C8—531no—
453C22×C8—531no—
454C22×C8—531no—
455C22×C8—531no—
456C4⋊Q8—534no—
457C4⋊Q8—534no—
458C4⋊Q8—1068no—
459C4⋊Q8—1062no—
460C4⋊Q8—1062no—
461#127—22no—
462#127C22×D5314yes—
463#125—22no—
464#125—534no—
465#125—534no—
466#125—1068no—
467#125—1062no—
468#125—1062no—
469#125C22×D5314yes—
470#123—28no—
471#123—28no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474#121—22no—
475#121—22no—
476#121—28no—
477#121—28no—
478#121C22×D5314yes—
479#121C22×D5314yes—
480C4×D4—22no—
481C4×D4—22no—
482C4×D4C22×D5314yes—
483C4×D4C22×D5314yes—
484#117—534no—
485#117—1062no—
486#117C22⋊D5314yes—
487#117C22×D5314yes—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—531no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—534no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—1061no—
496C2×C4⋊C4—1062no—
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⋊C4C22⋊D5311yescharacteristic
504C2×C4⋊C4C22⋊D5311yescharacteristic
505C2×C4⋊C4C22×D5311yescharacteristic
506C2×C4⋊C4C22×D5311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1061no—
512C2×C22⋊C4C22⋊D5311yescharacteristic
513C2×C22⋊C4C22⋊D5311yescharacteristic
514C2×C42—1061no—
515C2×C42C22×D5311yescharacteristic
516C2×C42C22×D5311yescharacteristic
517#107—534no—
518#107—534no—
519#107—534no—
520#107—534no—
521#106—534no—
522#106—534no—
523#106—534no—
524#106—534no—
525C4⋊C8—534no—
526C4⋊C8—534no—
527#102—534no—
528#102—534no—
529#102—534no—
530#102—534no—
531#102—534no—
532#102—534no—
533#102—534no—
534#102—534no—
535C22⋊C8—534no—
536C22⋊C8—534no—
537#97—534no—
538C4×C8—534no—
539C24—21no—
540C24—21no—
541C24C2×C22⋊D5311yescharacteristic
542C2×Q8—1064no—
543C2×Q8—1064no—
544C2×Q8—4242no—
545C2×Q8—4242no—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—82no—
557C2×D4—82no—
558C2×D4—82no—
559C2×D4—82no—
560C2×D4C23×D5312yes—
561C2×D4C23×D5312yes—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—24no—
568C22×C4—82no—
569C22×C4—82no—
570C22×C4—1064no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1061no—
574C22×C4—1061no—
575C22×C4—4242no—
576C22×C4C2×C22⋊D5312yes—
577C22×C4C2×C22⋊D5311yescharacteristic
578C22×C4C2×C22⋊D5311yescharacteristic
579C22×C4C2×C22⋊D5311yescharacteristic
580C22×C4C2×C22⋊D5311yescharacteristic
581C22×C4C2×C22⋊D5311yescharacteristic
582C22×C4C23×D5312yes—
583C22×C4C23×D5311yescharacteristic
584C2×C8—532no—
585C2×C8—532no—
586C2×C8—532no—
587C2×C8—532no—
588C2×C8—1062no—
589C2×C8—1062no—
590C2×C8—1062no—
591C2×C8—1062no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—532no—
597C4⋊C4—532no—
598C4⋊C4—532no—
599C4⋊C4—532no—
600C4⋊C4—1064no—
601C4⋊C4—1061no—
602C4⋊C4—1061no—
603C4⋊C4—1061no—
604C4⋊C4—1061no—
605C4⋊C4—1064no—
606C4⋊C4—1064no—
607C4⋊C4—1064no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4C2×C22⋊D5314yes—
612C4⋊C4C2×C22⋊D5314yes—
613C4⋊C4C23×D5312yes—
614C4⋊C4C23×D5312yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—24no—
619C22⋊C4—1064no—
620C22⋊C4C2×C22⋊D5314yes—
621C22⋊C4C2×C22⋊D5314yes—
622C42—1064no—
623C42C2×C22⋊D5312yes—
624C42C2×C22⋊D5312yes—
625C42C23×D5312yes—
626C42C23×D5312yes—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23C22×C22⋊D5312yes—
639C23C22×C22⋊D5311yescharacteristic
640Q8—4244no—
641Q8—4244no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—42no—
647D4—42no—
648D4—84no—
649D4—84no—
650D4—84no—
651D4—84no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—24no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—84no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—1062no—
669C2×C4—1062no—
670C2×C4—4244no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4C22×C22⋊D5312yes—
676C2×C4C22×C22⋊D5312yes—
677C2×C4C22×C22⋊D5312yes—
678C2×C4C22×C22⋊D5312yes—
679C2×C4C22×C22⋊D5312yes—
680C2×C4C22×C22⋊D5311yescharacteristic
681C2×C4#1313326412yes—
682C2×C4#1313326412yes—
683C2×C4C24×D5311yescharacteristic
684C8—1062no—
685C8—1062no—
686C8—1062no—
687C8—1062no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—44no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22—42no—
698C22—84no—
699C22—84no—
700C22#1681119412yes—
701C22#1681142612yes—
702C22#1681143412yes—
703C22C23×C22⋊D5311yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C4—2122no—
715C4#1681119412yes—
716C4C2×#1313326411yescharacteristic
717C4C2×#1313326411yescharacteristic
718C2—42no—
719C2—82no—
720C2—82no—
721C2#2028596214yesdirect product factor
722C2C2×#1681119411yescharacteristic
723C2C2×#1681142611yescharacteristic
724C2C2×#1681143411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
Fitting, prime radicalC2×C53×#540C2
socleC23×C53C22×D4
hypercenterC2×#540D53
hypocenterC53C2×#3241
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#16811251C2semidirect
2. #20285962C2direct (N × H)
3. C2×#16811033C2semidirect
4. C2×#16811022C2semidirect
5. C2×#16810987C2semidirect
6. C2×#16810969C2semidirect
7. C2×#16810939C2semidirect
8. C2×#16810944C2semidirect
9. C2×#16810944C2semidirect
10. C2×#16810934C2semidirect
11. C2×#16810923C2semidirect
12. C2×#16810923C2semidirect
13. C2×#16810913C2semidirect
14. C2×#16810903C2semidirect
15. C2×#16810684C2semidirect
18. #16811251C22semidirect
29. #16811033C22semidirect
30. #16811022C22semidirect
31. #16810987C22semidirect
32. #16810969C22semidirect
33. #16810944C22semidirect
34. #16810944C22semidirect
35. #16810939C22semidirect
36. #16810934C22semidirect
37. #16810923C22semidirect
38. #16810923C22semidirect
39. #16810913C22semidirect
40. #16810903C22semidirect
41. #16810684C22semidirect
375. C2×C53#3241semidirect
439. C53C2×#3241semidirect
721. C2#20285962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112512
#202859622
C2×#168110332
C2×#168110222
C2×#168109872
C2×#168109692
C2×#168109392
C2×#168109442
C2×#168109342
C2×#168109232
C2×#168109132
C2×#168109032
C2×#168106842
C2×C53×#5402
C2×#324153