Finite Group Databasebeta

← C2×#20287102 #28262548

Subgroups — C2×#20287102 #28262548

Order 13568.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811331C211yesmaximal, characteristic
2C2×#16811328C211yesmaximal, characteristic
3#20287102C2116yesmaximal, direct product factor
4C2×#16811027C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810959C211yesmaximal, characteristic, complemented
7C2×#16810957C211yesmaximal, characteristic, complemented
8C2×#16810917C211yesmaximal, characteristic, complemented
9C2×#16810916C211yesmaximal, characteristic, complemented
10C2×#16810863C211yesmaximal, characteristic, complemented
11C2×#16810862C211yesmaximal, characteristic, complemented
12C2×#16810715C211yesmaximal, characteristic, complemented
13C2×#16810686C211yesmaximal, characteristic
14C22×#13133150C211yesmaximal, characteristic, complemented
15C2×#107×D53C211yesmaximal, characteristic, complemented
16C2×C53×#484C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C23×#88322C2211yescharacteristic
19C22×C8×D53C2211yescharacteristic
20#16811331—24no—
21#16811331C2218yes—
22#16811328—24no—
23#16811328C2218yes—
24C2×#13133216C2211yescharacteristic
25C2×#13133216C2211yescharacteristic
26C2×#13133207—21no—
27C2×#13133207—21no—
28C2×#13133197—21no—
29C2×#13133197C2211yescharacteristic
30C2×#13133196—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133194—21no—
34C2×#13133193C2211yescharacteristic
35C2×Q8×Dic53C2211yescharacteristic
36C2×#13133182C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×C4×C22⋊D53C2211yescharacteristic
39C2×#13133177—21no—
40C22×C4⋊Dic53C2211yescharacteristic
41C2×C4⋊C4×D53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16811027C2218yescomplemented
44#16810960C2218yescomplemented
45#16810959C2218yescomplemented
46#16810957C2218yescomplemented
47#16810917C2218yescomplemented
48#16810916C2218yescomplemented
49#16810863C2218yescomplemented
50#16810862C2218yescomplemented
51#16810715C2218yescomplemented
52#16810686C2218yes—
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133150C2211yescharacteristic
59C2×#13133150C2211yescharacteristic
60C2×#13133150C2218yescomplemented
61#107×D53C2218yescomplemented
62C2×#13133146C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133141C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C22×C4⋊C4×C53C2211yescharacteristic
71C53×#484C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×C22⋊D53D411yescharacteristic
81C23×Dic53—21no—
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53C2311yescharacteristic
85C2×#11719925—24no—
86C2×#11719925C2314yes—
87C22×#88322—24no—
88C22×#88322C2311yescharacteristic
89C22×#88322C2314yes—
90C22×#88322C2311yescharacteristic
91C2×C8×D53—24no—
92C2×C8×D53C2314yes—
93#13133216—22no—
94#13133216—22no—
95#13133216C2314yes—
96#13133216C2314yes—
97#13133207—28no—
98#13133207—28no—
99#13133197—28no—
100#13133197—22no—
101#13133197C2314yes—
102#13133196—28no—
103#13133196—22no—
104#13133196C2314yes—
105#13133195—28no—
106#13133194—28no—
107#13133193—22no—
108#13133193C2314yes—
109Q8×Dic53—22no—
110Q8×Dic53C2314yes—
111#13133182—22no—
112#13133182C2314yes—
113C4×C22⋊D53—28no—
114C4×C22⋊D53D414yes—
115C4×C22⋊D53C2314yes—
116#13133177—28no—
117C2×C4⋊Dic53—22no—
118C2×C4⋊Dic53—21no—
119C2×C4⋊Dic53—21no—
120C2×C4⋊Dic53—21no—
121C2×C4⋊Dic53C2311yescharacteristic
122C2×C4⋊Dic53C2311yescharacteristic
123C2×C4⋊Dic53C2314yes—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×#11719919—21no—
126C2×#11719919—21no—
127C2×#11719919—21no—
128C2×#11719919—21no—
129C2×#11719919—21no—
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C4⋊C4×D53—22no—
134C4⋊C4×D53—22no—
135C4⋊C4×D53C2314yes—
136C4⋊C4×D53C2314yes—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53D411yescharacteristic
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921D411yescharacteristic
142C2×C4×Dic53—21no—
143C2×C4×Dic53—21no—
144C2×C4×Dic53C2311yescharacteristic
145#13133151C2314yes—
146#13133151C2314yes—
147#13133150C2314yes—
148#13133150C2314yes—
149#13133150C2314yes—
150#13133150C2314yes—
151#13133150C2314yes—
152#13133146C2314yes—
153#13133142C2314yes—
154#13133142C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133129C2314yes—
158C8×Dic53C2314yes—
159C22×Q8×C53C2311yescharacteristic
160C23×C4×C53—21no—
161C23×C4×C53C2311yescharacteristic
162C22×C8×C53C2311yescharacteristic
163C22×C8×C53C2311yescharacteristic
164C22⋊Q8×C53—22no—
165C22⋊Q8×C53C2314yes—
166C2×C4⋊C4×C53—22no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53C2311yescharacteristic
170C2×C4⋊C4×C53C2314yes—
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C22⋊C4×C53—21no—
174#107×C53C2314yes—
175#107×C53C2314yes—
176#103×C53C2314yes—
177#103×C53C2314yes—
178C22⋊C8×C53C2314yes—
179C24×C53C2×D411yescharacteristic
180C23×D53C2×D411yescharacteristic
181C2×Q8×C53—21no—
182C2×Q8×C53—22no—
183C2×Q8×C53—22no—
184C2×Q8×C53C2412yes—
185C22×C4×C53—22no—
186C22×C4×C53—22no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—24no—
192C22×C4×C53—82no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D412yes—
195C22×C4×C53C2412yes—
196C22×C4×C53C2411yescharacteristic
197C2×C22⋊D53Q1618yescomplemented
198C2×C22⋊D53C2×D414yes—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—24no—
204C22×Dic53—82no—
205C22×Dic53C2×D411yescharacteristic
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208C2×C4×D53—22no—
209C2×C4×D53—22no—
210C2×C4×D53—24no—
211C2×C4×D53—24no—
212C2×C4×D53—82no—
213C2×C4×D53—82no—
214C2×C4×D53C2×D412yes—
215C2×C4×D53C2412yes—
216C2×Dic106—22no—
217C2×Dic106—22no—
218C2×Dic106—21no—
219C2×Dic106—24no—
220C2×Dic106—24no—
221C2×Dic106—82no—
222C2×Dic106—82no—
223C2×Dic106C2412yes—
224C2×C8×C53—22no—
225C2×C8×C53—22no—
226C2×C8×C53C2412yes—
227C2×C8×C53C2412yes—
228C4⋊C4×C53—21no—
229C4⋊C4×C53—24no—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—24no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53C2412yes—
234C4⋊C4×C53C2412yes—
235C4⋊C4×C53C2412yes—
236C22⋊C4×C53—24no—
237C22⋊Dic53—24no—
238C22⋊Dic53C2×D414yes—
239#11719925—28no—
240#11719921—24no—
241#11719921—24no—
242#11719921C2×D414yes—
243C4⋊Dic53—21no—
244C4⋊Dic53—21no—
245C4⋊Dic53—21no—
246C4⋊Dic53—24no—
247C4⋊Dic53—24no—
248C4⋊Dic53—24no—
249C4⋊Dic53C2412yes—
250C4⋊Dic53C2412yes—
251C4⋊Dic53C2412yes—
252#11719919—24no—
253#11719919—24no—
254#11719919—24no—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258#11719919—24no—
259#11719919C2×D414yes—
260C4×Dic53—24no—
261C4×Dic53—24no—
262C4×Dic53C2×D412yes—
263C4×Dic53C2412yes—
264C2×#88322—22no—
265C2×#88322—28no—
266C2×#88322#4114yes—
267C2×#88322C2412yes—
268C2×#88322C2412yes—
269C8×D53—28no—
270C23×C53—22no—
271C23×C53—22no—
272C23×C53C2×Q1614yes—
273C23×C53C22×D412yes—
274C23×C53C22×D411yescharacteristic
275C22×D53—22no—
276C22×D53—22no—
277C22×D53C2×Q1614yes—
278C22×D53C22×D412yes—
279Q8×C53—22no—
280Q8×C53—22no—
281Q8×C53—42no—
282C2×C4×C53—22no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—84no—
295C2×C4×C53C22×D412yes—
296C2×C4×C53C22×D411yescharacteristic
297C2×C4×C53C2×#4112yes—
298C2×C4×C532−1+412yes—
299C2×C4×C53C2511yescharacteristic
300C22⋊D53C2×Q16116yescomplemented
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—84no—
312C2×Dic53C2×Q1614yes—
313C2×Dic53C22×D412yes—
314C2×Dic53C22×D412yes—
315C2×Dic53C22×D412yes—
316C4×D53—24no—
317C4×D53—22no—
318C4×D53—22no—
319C4×D53—84no—
320C4×D53—84no—
321Dic106—22no—
322Dic106—22no—
323Dic106—42no—
324Dic106—84no—
325Dic106—84no—
326C8×C53—22no—
327C8×C53—22no—
328#88322—22no—
329#88322C2×#4114yes—
330C2×#3338—531nomaximal, Sylow
331C22×C53—28no—
332C22×C53—22no—
333C22×C53—22no—
334C22×C53#54712yes—
335C22×C53C22×Q1614yes—
336C22×C53C22×Q1612yes—
337C22×C53#57612yes—
338C22×C53C23×D411yescharacteristic
339C2×D53—28no—
340C2×D53—22no—
341C2×D53—22no—
342C2×D53C22×Q1614yes—
343C4×C53—22no—
344C4×C53—42no—
345C4×C53—42no—
346C4×C53—42no—
347C4×C53—42no—
348C4×C53#54712yes—
349C4×C53C22×#4111yescharacteristic
350C4×C53C2×2−1+411yescharacteristic
351Dic53—22no—
352Dic53—22no—
353Dic53—42no—
354Dic53—42no—
355Dic53—42no—
356Dic53—42no—
357Dic53C22×Q1614yes—
358C2×#554—531no—
359C2×#554—531no—
360#3338—5316no—
361C2×#500—531no—
362C2×#484—531no—
363C2×#484—531no—
364C2×#484—531no—
365C2×#484D5311yescharacteristic, complemented
366C2×#477—531no—
367C2×#477—531no—
368C2×#467—531no—
369C2×#467—531no—
370C2×C4×Q16—531no—
371C2×C8×D4—531no—
372C22×#107—531no—
373C22×#107—531no—
374C2×C53—24no—
375C2×C53#333814yescomplemented
376C2×C53C2×#54711yescharacteristic
377C2×C53C23×Q1611yescharacteristic
378C2×C53C2×#57611yescharacteristic
379D53—24no—
380C22×Q16—531no—
381C23×C8—531no—
382C23×C8—531no—
383#554—538no—
384#554—538no—
385#554—1064no—
386#554—1064no—
387C2×C4⋊Q8—531no—
388C2×C4⋊Q8—531no—
389C2×#125—1061no—
390C2×#125—1061no—
391C2×C22⋊Q8—531no—
392C2×C22⋊Q8—531no—
393C2×C22⋊Q8—531no—
394C2×C22⋊Q8—1061no—
395C2×C22⋊Q8—1061no—
396C2×C22⋊Q8—1061no—
397C2×C22⋊Q8—1061no—
398C2×C22⋊Q8C2×D5311yescharacteristic
399C2×C4×Q8—531no—
400C2×C4×Q8—531no—
401C2×C4×D4—531no—
402C2×C4×D4—1061no—
403C2×C4×D4—1061no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4C2×D5311yescharacteristic
408#500—538no—
409#484—538no—
410#484—538no—
411#484—538no—
412#484C2×D5318yescomplemented
413#477—538no—
414#477—538no—
415#467—538no—
416#467—538no—
417C4×Q16—538no—
418C8×D4—538no—
419C2×#107—531no—
420C2×#107—531no—
421C2×#107—531no—
422C2×#107—531no—
423C2×#107—538no—
424C2×#107—531no—
425C2×#107—531no—
426C2×#107—531no—
427C2×#107—538no—
428C2×#107C2×D5311yescharacteristic
429C2×#107C2×D5311yescharacteristic
430C2×C4⋊C8—531no—
431C2×#103—531no—
432C2×#103—531no—
433C2×#103—531no—
434C2×#103—531no—
435C2×#103C2×D5311yescharacteristic
436C2×#103C2×D5311yescharacteristic
437C2×C22⋊C8—531no—
438C2×C22⋊C8C2×D5311yescharacteristic
439C2×C4×C8—531no—
440C53C2×#333811yescharacteristic, complemented, Sylow
441C22×Q8—531no—
442C22×Q8—1061no—
443C22×Q8—1061no—
444C22×Q8C22×D5311yescharacteristic
445C22×D4—531no—
446C23×C4—21no—
447C23×C4—531no—
448C23×C4—1061no—
449C23×C4—1061no—
450C23×C4—1061no—
451C23×C4C22×D5311yescharacteristic
452C2×Q16—534no—
453C2×Q16—1064no—
454C22×C8—531no—
455C22×C8—531no—
456C22×C8—534no—
457C22×C8—534no—
458C22×C8—1064no—
459C22×C8—1064no—
460C22×C8C22×D5311yescharacteristic
461C22×C8C22×D5311yescharacteristic
462C4⋊Q8—534no—
463C4⋊Q8—534no—
464C4⋊Q8—1062no—
465C4⋊Q8—1062no—
466#125—1068no—
467#125—1068no—
468C22⋊Q8—22no—
469C22⋊Q8—534no—
470C22⋊Q8—534no—
471C22⋊Q8—534no—
472C22⋊Q8—1068no—
473C22⋊Q8—1068no—
474C22⋊Q8—1068no—
475C22⋊Q8—1068no—
476C22⋊Q8—1062no—
477C22⋊Q8—1062no—
478C22⋊Q8—1062no—
479C22⋊Q8C22×D5314yes—
480C4×Q8—534no—
481C4×Q8—534no—
482C4×Q8—1062no—
483C4×Q8—1062no—
484C4×D4—534no—
485C4×D4—534no—
486C4×D4—1068no—
487C4×D4—1068no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—531no—
492C2×C4⋊C4—531no—
493C2×C4⋊C4—531no—
494C2×C4⋊C4—531no—
495C2×C4⋊C4—534no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
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⋊C4—1061no—
509C2×C4⋊C4—1062no—
510C2×C4⋊C4—1061no—
511C2×C4⋊C4C22×D5311yescharacteristic
512C2×C4⋊C4C22×D5311yescharacteristic
513C2×C4⋊C4C22×D5311yescharacteristic
514C2×C4⋊C4C22×D5314yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—531no—
517C2×C22⋊C4—531no—
518C2×C22⋊C4—1061no—
519C2×C22⋊C4—1061no—
520C2×C22⋊C4—1061no—
521C2×C42—531no—
522C2×C42—1061no—
523C2×C42—1061no—
524#107—534no—
525#107—534no—
526#107—534no—
527#107—534no—
528#107—534no—
529#107—534no—
530#107—534no—
531#107C22×D5314yes—
532#107C22×D5314yes—
533C4⋊C8—534no—
534#103—534no—
535#103—534no—
536#103—534no—
537#103—534no—
538#103C22×D5314yes—
539#103C22×D5314yes—
540C22⋊C8—534no—
541C22⋊C8C22×D5314yes—
542C4×C8—534no—
543C24—531no—
544C24D4×D5311yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—532no—
549C2×Q8—1064no—
550C2×Q8—1064no—
551C2×Q8—1061no—
552C2×Q8—1062no—
553C2×Q8—1062no—
554C2×Q8—4242no—
555C2×Q8—4242no—
556C2×Q8C23×D5312yes—
557C2×D4—538no—
558C2×D4—534no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—531no—
568C22×C4—531no—
569C22×C4—531no—
570C22×C4—532no—
571C22×C4—532no—
572C22×C4—1064no—
573C22×C4—1064no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1064no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1061no—
580C22×C4—1061no—
581C22×C4—4242no—
582C22×C4—4242no—
583C22×C4—4242no—
584C22×C4D4×D5312yes—
585C22×C4D4×D5311yescharacteristic
586C22×C4C23×D5312yes—
587C22×C4C23×D5311yescharacteristic
588Q16—1068no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—534no—
592C2×C8—532no—
593C2×C8—532no—
594C2×C8—1068no—
595C2×C8—1068no—
596C2×C8—1062no—
597C2×C8C23×D5312yes—
598C2×C8C23×D5312yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—534no—
605C4⋊C4—532no—
606C4⋊C4—532no—
607C4⋊C4—532no—
608C4⋊C4—1064no—
609C4⋊C4—1064no—
610C4⋊C4—1064no—
611C4⋊C4—1064no—
612C4⋊C4—1064no—
613C4⋊C4—1064no—
614C4⋊C4—1064no—
615C4⋊C4—1064no—
616C4⋊C4—1061no—
617C4⋊C4—1064no—
618C4⋊C4—1061no—
619C4⋊C4—1061no—
620C4⋊C4—1064no—
621C4⋊C4C23×D5312yes—
622C4⋊C4C23×D5312yes—
623C4⋊C4C23×D5312yes—
624C22⋊C4—24no—
625C22⋊C4—534no—
626C22⋊C4—534no—
627C22⋊C4—1064no—
628C22⋊C4—1064no—
629C22⋊C4—1064no—
630C42—532no—
631C42—532no—
632C42—1064no—
633C42—1064no—
634C23—22no—
635C23—22no—
636C23—534no—
637C23—532no—
638C23—1062no—
639C23—1062no—
640C23Q16×D5314yes—
641C23C2×D4×D5312yes—
642C23C2×D4×D5311yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—1062no—
647Q8—1062no—
648Q8—4244no—
649Q8—4244no—
650Q8—2122no—
651D4—5316no—
652C2×C4—22no—
653C2×C4—24no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—534no—
666C2×C4—532no—
667C2×C4—532no—
668C2×C4—532no—
669C2×C4—1062no—
670C2×C4—1062no—
671C2×C4—1064no—
672C2×C4—1062no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—4244no—
679C2×C4—4244no—
680C2×C4—4244no—
681C2×C4—2122no—
682C2×C4—2122no—
683C2×C4—2122no—
684C2×C4—2122no—
685C2×C4C2×D4×D5312yes—
686C2×C4C2×D4×D5311yescharacteristic
687C2×C4#41×D5312yes—
688C2×C4#1313326412yes—
689C2×C4C24×D5311yescharacteristic
690C8—22no—
691C8—22no—
692C8—534no—
693C8—1062no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—534no—
698C22—1068no—
699C22—1062no—
700C22—1062no—
701C22#1681127112yes—
702C22C2×Q16×D5314yes—
703C22C2×Q16×D5312yes—
704C22#1681142712yes—
705C22C22×D4×D5311yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—534no—
712C4—1062no—
713C4—1062no—
714C4—2122no—
715C4—2122no—
716C4—2122no—
717C4—2122no—
718C4#1681127112yes—
719C4C2×#41×D5311yescharacteristic
720C4C2×#1313326411yescharacteristic
721C2—24no—
722C2—1064no—
723C2#2028710214yesdirect product factor
724C2C2×#1681127111yescharacteristic
725C2C22×Q16×D5311yescharacteristic
726C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#484C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#484D53
hypocenterC53C2×#3338
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #20287102C2direct (N × H)
4. C2×#16811027C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810959C2semidirect
7. C2×#16810957C2semidirect
8. C2×#16810917C2semidirect
9. C2×#16810916C2semidirect
10. C2×#16810863C2semidirect
11. C2×#16810862C2semidirect
12. C2×#16810715C2semidirect
14. C22×#13133150C2semidirect
15. C2×#107×D53C2semidirect
16. C2×C53×#484C2semidirect
43. #16811027C22semidirect
44. #16810960C22semidirect
45. #16810959C22semidirect
46. #16810957C22semidirect
47. #16810917C22semidirect
48. #16810916C22semidirect
49. #16810863C22semidirect
50. #16810862C22semidirect
51. #16810715C22semidirect
60. C2×#13133150C22semidirect
61. #107×D53C22semidirect
71. C53×#484C22semidirect
197. C2×C22⋊D53Q16semidirect
300. C22⋊D53C2×Q16semidirect
365. C2×#484D53semidirect
375. C2×C53#3338semidirect
412. #484C2×D53semidirect
440. C53C2×#3338semidirect
723. C2#20287102direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113312
C2×#168113282
#202871022
C2×#168110272
C2×#168109602
C2×#168109592
C2×#168109572
C2×#168109172
C2×#168109162
C2×#168108632
C2×#168108622
C2×#168107152
C2×#168106862
C22×#131331502
C2×#107×D532
C2×C53×#4842
C2×#333853