Finite Group Databasebeta

← C2×#20287007 #28260987

Subgroups — C2×#20287007 #28260987

Order 13568.

2146 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811336C211yesmaximal, characteristic
2C2×#16811286C211yesmaximal, characteristic, complemented
3#20287007C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810967C211yesmaximal, characteristic, complemented
6C2×#16810917C211yesmaximal, characteristic, complemented
7C2×#16810871C211yesmaximal, characteristic, complemented
8C2×#16810870C211yesmaximal, characteristic, complemented
9C2×#16810827C211yesmaximal, characteristic, complemented
10C2×#16810764C211yesmaximal, characteristic, complemented
11C2×#16810763C211yesmaximal, characteristic, complemented
12C2×#16810710C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic, complemented
14C2×#16810631C211yesmaximal, characteristic, complemented
15C2×#16810630C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×#11719912C2211yescharacteristic
24#16811336—24no—
25#16811336C2218yes—
26#16811286—24no—
27#16811286C2218yescomplemented
28C2×#13133216—21no—
29C2×#13133216C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133205—21no—
32C2×#13133203—21no—
33C2×#13133197C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133194—21no—
36C2×#13133192C2211yescharacteristic
37C2×#13133191C2211yescharacteristic
38C2×#13133190—21no—
39C2×#13133182C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53C2211yescharacteristic
42C2×#13133177—21no—
43C2×#13133175C2211yescharacteristic
44C2×#13133174—21no—
45#16810972C2218yescomplemented
46#16810967C2218yescomplemented
47#16810917C2218yescomplemented
48#16810871C2218yescomplemented
49#16810870C2218yescomplemented
50#16810827C2218yescomplemented
51#16810764C2218yescomplemented
52#16810763C2218yescomplemented
53#16810710C2218yescomplemented
54#16810698C2218yescomplemented
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810631C2218yescomplemented
58#16810630C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—22no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—21no—
82C22×Dic106—42no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2314yes—
85C22×Dic106C2311yescharacteristic
86C2×Q8×D53—22no—
87C2×Q8×D53—24no—
88C2×Q8×D53—42no—
89C2×Q8×D53C2314yes—
90C22×D212—21no—
91C22×D212C2311yescharacteristic
92C22×C22⋊D53—21no—
93C22×C22⋊D53D411yescharacteristic
94C23×Dic53—21no—
95C22×C4×D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53C2311yescharacteristic
98C2×#11719913—24no—
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101C2×#11719913C2314yes—
102C2×#11719924—42no—
103C2×#11719924C2314yes—
104C2×#11719917—42no—
105C2×#11719917C2314yes—
106C2×#11719912—42no—
107C2×#11719912C2314yes—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110#13133216—28no—
111#13133216—22no—
112#13133216C2314yes—
113#13133215—22no—
114#13133215C2314yes—
115#13133205—28no—
116#13133203—28no—
117#13133197—22no—
118#13133197C2314yes—
119#13133195—28no—
120#13133194—28no—
121#13133192—22no—
122#13133192C2314yes—
123#13133191—22no—
124#13133191C2314yes—
125#13133190—28no—
126#13133182—22no—
127#13133182C2314yes—
128#13133179—22no—
129#13133179C2314yes—
130C4×C22⋊D53D414yes—
131C4×C22⋊D53C2314yes—
132#13133177—28no—
133#13133175—22no—
134#13133175C2314yes—
135#13133174—28no—
136C2×C4⋊Dic53—21no—
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919D411yescharacteristic
143C2×C22⋊Dic53D411yescharacteristic
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133150C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22⋊Q8×C53—22no—
170C22⋊Q8×C53C2314yes—
171#117×C53—22no—
172#117×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180#107×C53C2314yes—
181#106×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187C23×D53C2×D411yescharacteristic
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53C2412yes—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C2×C22⋊D53—24no—
203C2×C22⋊D53—24no—
204C2×C22⋊D53—82no—
205C2×C22⋊D53C2×D414yes—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—24no—
210C22×Dic53—44no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214Q8×D53—28no—
215Q8×D53—44no—
216Q8×D53—48no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—21no—
220C2×D212—24no—
221C2×D212—82no—
222C2×D212C2412yes—
223C2×C4×D53—22no—
224C2×C4×D53—22no—
225C2×C4×D53—24no—
226C2×C4×D53—24no—
227C2×C4×D53—44no—
228C2×C4×D53—44no—
229C2×C4×D53C2×D412yes—
230C2×C4×D53C2412yes—
231C2×Dic106—21no—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—22no—
235C2×Dic106—28no—
236C2×Dic106—24no—
237C2×Dic106—21no—
238C2×Dic106—24no—
239C2×Dic106—24no—
240C2×Dic106—44no—
241C2×Dic106—48no—
242C2×Dic106—44no—
243C2×Dic106—44no—
244C2×Dic106—82no—
245C2×Dic106#4114yes—
246C2×Dic106C2412yes—
247C2×Dic106C2412yes—
248C2×C8×C53—22no—
249C2×C8×C53—22no—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53—24no—
253C4⋊C4×C53—21no—
254C4⋊C4×C53—21no—
255C4⋊C4×C53—21no—
256C4⋊C4×C53C2412yes—
257C4⋊C4×C53C2412yes—
258C4⋊C4×C53C2412yes—
259C22⋊C4×C53—24no—
260C22⋊C4×C53—24no—
261C42×C53—24no—
262C22⋊Dic53C2×D414yes—
263#11719924—44no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—24no—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919C2×D414yes—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C4×Dic53C2×D412yes—
281C4×Dic53C2412yes—
282#11719917—44no—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287#11719913—28no—
288#11719913—44no—
289#11719912—44no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53C22×D412yes—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—42no—
300C22×D53—42no—
301C22×D53—42no—
302C22×D53C22×D412yes—
303Q8×C53—22no—
304Q8×C53—22no—
305Q8×C53—42no—
306C2×C4×C53—22no—
307C2×C4×C53—24no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D411yescharacteristic
320C2×C4×C53C2×#4112yes—
321C2×C4×C53H(5,𝔽2)12yes—
322C2×C4×C53C2511yescharacteristic
323C22⋊D53—28no—
324C22⋊D53—84no—
325C2×Dic53—24no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—48no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53#13714yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337C2×Dic53C22×D412yes—
338D212—22no—
339D212—22no—
340D212—42no—
341D212—84no—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—48no—
346C4×D53—48no—
347Dic106—24no—
348Dic106—22no—
349Dic106—22no—
350Dic106—22no—
351Dic106—48no—
352Dic106—48no—
353Dic106—42no—
354Dic106—84no—
355Dic106C2×#4114yes—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3329—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—44no—
365C22×C53#54612yes—
366C22×C53C2×#13712yes—
367C22×C53#57712yes—
368C22×C53C23×D411yescharacteristic
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—22no—
372C2×D53—44no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—84no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53—42no—
382C4×C53#54612yes—
383C4×C53C22×#4111yescharacteristic
384C4×C53C2×H(5,𝔽2)11yescharacteristic
385Dic53—24no—
386Dic53—22no—
387Dic53—22no—
388Dic53—42no—
389Dic53—42no—
390Dic53C2×#13714yes—
391C2×#555—531no—
392C2×D4×Q8—531no—
393#3329—5316no—
394C2×#487—531no—
395C2×#485—531no—
396C2×#485D5311yescharacteristic, complemented
397C2×#477—531no—
398C2×#468—531no—
399C2×#468—531no—
400C2×#461—531no—
401C2×#448—531no—
402C2×#448—531no—
403C2×C4×SD16—531no—
404C2×#436—531no—
405C2×#419—531no—
406C2×#419—531no—
407C2×C53—42no—
408C2×C53#332914yescomplemented
409C2×C53C2×#54611yescharacteristic
410C2×C53C22×#13711yescharacteristic
411C2×C53C2×#57711yescharacteristic
412D53—42no—
413D53—82no—
414C23×Q8—531no—
415C23×Q8—531no—
416C22×SD16—531no—
417C22×SD16—531no—
418C22×SD16—531no—
419C22×M16—531no—
420C22×M16—531no—
421#555—538no—
422#555—1064no—
423D4×Q8—538no—
424D4×Q8—1064no—
425C2×C4⋊Q8—531no—
426C2×C4⋊Q8—531no—
427C2×C4⋊Q8—1061no—
428C2×#124—1061no—
429C2×#124—1061no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—1061no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8C2×D5311yescharacteristic
434C2×#121—531no—
435C2×#121—531no—
436C2×#121—1061no—
437C2×C4×Q8—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×#117—531no—
442C2×#117—1061no—
443C2×#117C2×D5311yescharacteristic
444#487—538no—
445#485—538no—
446#485C2×D5318yescomplemented
447#477—538no—
448#468—538no—
449#468—538no—
450#461—538no—
451#448—538no—
452#448—538no—
453C4×SD16—538no—
454#436—538no—
455C2×#107—531no—
456C2×#107C2×D5311yescharacteristic
457C2×#106C2×D5311yescharacteristic
458C2×C4⋊C8—531no—
459#419—538no—
460#419—538no—
461C2×#103—531no—
462C2×#103—531no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103C2×D5311yescharacteristic
469C2×#103C2×D5311yescharacteristic
470C2×#102—531no—
471C2×C22⋊C8—531no—
472C2×C22⋊C8C2×D5311yescharacteristic
473C2×C4×C8—531no—
474C53C2×#332911yescharacteristic, complemented, Sylow
475C22×Q8—534no—
476C22×Q8—531no—
477C22×Q8—531no—
478C22×Q8—534no—
479C22×Q8—1061no—
480C22×Q8—1061no—
481C22×Q8—1064no—
482C22×Q8—1062no—
483C22×Q8—1061no—
484C22×Q8—1062no—
485C22×Q8—1064no—
486C22×Q8—2122no—
487C22×Q8—2122no—
488C22×Q8C22×D5311yescharacteristic
489C22×D4—531no—
490C22×D4—531no—
491C22×D4—1061no—
492C22×D4—1061no—
493C23×C4—531no—
494C23×C4—1061no—
495C23×C4—1061no—
496C23×C4—1061no—
497C23×C4C22×D5311yescharacteristic
498C2×SD16—534no—
499C2×SD16—534no—
500C2×SD16—534no—
501C2×SD16—1064no—
502C2×SD16—2122no—
503C2×SD16—2122no—
504C2×M16—534no—
505C2×M16—534no—
506C2×M16—2122no—
507C2×M16—2122no—
508C22×C8—531no—
509C22×C8—531no—
510C22×C8C22×D5311yescharacteristic
511C22×C8C22×D5311yescharacteristic
512C4⋊Q8—534no—
513C4⋊Q8—534no—
514C4⋊Q8—1062no—
515C4⋊Q8—1062no—
516C4⋊Q8—1068no—
517#124—1068no—
518#124—1068no—
519C22⋊Q8—22no—
520C22⋊Q8—534no—
521C22⋊Q8—1068no—
522C22⋊Q8—1068no—
523C22⋊Q8—1062no—
524C22⋊Q8C22×D5314yes—
525#121—534no—
526#121—534no—
527#121—1068no—
528#121—1062no—
529#121—1062no—
530C4×Q8—534no—
531C4×Q8—1062no—
532C4×D4—534no—
533C4×D4—534no—
534C4×D4—534no—
535C4×D4—1062no—
536C4×D4—1068no—
537#117—22no—
538#117—534no—
539#117—1068no—
540#117—1062no—
541#117C22×D5314yes—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4C22×D5311yescharacteristic
551C2×C4⋊C4C22×D5311yescharacteristic
552C2×C4⋊C4C22×D5311yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—531no—
556C2×C22⋊C4—531no—
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C42—21no—
563C2×C42—531no—
564C2×C42—1061no—
565C2×C42—1061no—
566#107—534no—
567#107C22×D5314yes—
568#106C22×D5314yes—
569C4⋊C8—534no—
570#103—534no—
571#103—534no—
572#103—534no—
573#103—534no—
574#103—534no—
575#103—534no—
576#103—534no—
577#103C22×D5314yes—
578#103C22×D5314yes—
579#102—534no—
580C22⋊C8—534no—
581C22⋊C8C22×D5314yes—
582C4×C8—534no—
583C24—531no—
584C24—1061no—
585C24D4×D5311yescharacteristic
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—534no—
590C2×Q8—532no—
591C2×Q8—532no—
592C2×Q8—1064no—
593C2×Q8—1064no—
594C2×Q8—1068no—
595C2×Q8—1061no—
596C2×Q8—1064no—
597C2×Q8—1061no—
598C2×Q8—1062no—
599C2×Q8—1068no—
600C2×Q8—1062no—
601C2×Q8—1062no—
602C2×Q8—4242no—
603C2×Q8—2124no—
604C2×Q8—2124no—
605C2×Q8—2128no—
606C2×Q8—2124no—
607C2×Q8—2124no—
608C2×Q8—2128no—
609C2×Q8C23×D5312yes—
610C2×D4—534no—
611C2×D4—532no—
612C2×D4—1064no—
613C2×D4—1064no—
614C2×D4—1064no—
615C2×D4—1061no—
616C2×D4—1062no—
617C2×D4—1062no—
618C2×D4—4242no—
619C2×D4—4242no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—531no—
627C22×C4—531no—
628C22×C4—531no—
629C22×C4—532no—
630C22×C4—532no—
631C22×C4—1064no—
632C22×C4—1064no—
633C22×C4—1061no—
634C22×C4—1062no—
635C22×C4—1062no—
636C22×C4—1064no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—2124no—
640C22×C4—2124no—
641C22×C4—2124no—
642C22×C4D4×D5312yes—
643C22×C4D4×D5311yescharacteristic
644C22×C4C23×D5312yes—
645C22×C4C23×D5311yescharacteristic
646SD16—1068no—
647SD16—2124no—
648SD16—2124no—
649M16—2124no—
650M16—2124no—
651C2×C8—22no—
652C2×C8—22no—
653C2×C8—532no—
654C2×C8—532no—
655C2×C8—1062no—
656C2×C8—1062no—
657C2×C8C23×D5312yes—
658C2×C8C23×D5312yes—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—534no—
664C4⋊C4—532no—
665C4⋊C4—1064no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1064no—
670C4⋊C4—1061no—
671C4⋊C4C23×D5312yes—
672C4⋊C4C23×D5312yes—
673C4⋊C4C23×D5312yes—
674C22⋊C4—24no—
675C22⋊C4—24no—
676C22⋊C4—534no—
677C22⋊C4—534no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C22⋊C4—1064no—
681C22⋊C4—1064no—
682C22⋊C4—1064no—
683C42—24no—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—532no—
692C23—1062no—
693C23—1062no—
694C23—1062no—
695C23—1062no—
696C23—2122no—
697C23—2122no—
698C23—2122no—
699C23C2×D4×D5312yes—
700C23C2×D4×D5311yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—42no—
704Q8—534no—
705Q8—1064no—
706Q8—1062no—
707Q8—1062no—
708Q8—1062no—
709Q8—4244no—
710Q8—2128no—
711Q8—2128no—
712Q8—2122no—
713D4—1068no—
714D4—1062no—
715D4—1062no—
716D4—4244no—
717D4—4244no—
718D4—2122no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—534no—
732C2×C4—532no—
733C2×C4—532no—
734C2×C4—532no—
735C2×C4—1062no—
736C2×C4—1064no—
737C2×C4—1062no—
738C2×C4—1062no—
739C2×C4—1064no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—2128no—
745C2×C4—2128no—
746C2×C4—2128no—
747C2×C4—2122no—
748C2×C4—2122no—
749C2×C4C2×D4×D5312yes—
750C2×C4C2×D4×D5311yescharacteristic
751C2×C4#41×D5312yes—
752C2×C4#1313326312yes—
753C2×C4C24×D5311yescharacteristic
754C8—22no—
755C8—22no—
756C8—1062no—
757C8—1062no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—44no—
762C22—1062no—
763C22—1062no—
764C22—1062no—
765C22—4244no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22—2124no—
770C22#1681126512yes—
771C22#137×D5312yes—
772C22#1681143012yes—
773C22C22×D4×D5311yescharacteristic
774C4—22no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—534no—
780C4—1062no—
781C4—1064no—
782C4—1062no—
783C4—2122no—
784C4—2122no—
785C4#1681126512yes—
786C4C2×#41×D5311yescharacteristic
787C4C2×#1313326311yescharacteristic
788C2—42no—
789C2—4242no—
790C2—2122no—
791C2#2028700714yesdirect product factor
792C2C2×#1681126511yescharacteristic
793C2C2×#137×D5311yescharacteristic
794C2C2×#1681143011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC2×#16811336C2
hypercenterC2×#485D53
hypocenterC53C2×#3329
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×#16811286C2semidirect
3. #20287007C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810967C2semidirect
6. C2×#16810917C2semidirect
7. C2×#16810871C2semidirect
8. C2×#16810870C2semidirect
9. C2×#16810827C2semidirect
10. C2×#16810764C2semidirect
11. C2×#16810763C2semidirect
12. C2×#16810710C2semidirect
13. C2×#16810698C2semidirect
14. C2×#16810631C2semidirect
15. C2×#16810630C2semidirect
16. C2×C53×#485C2semidirect
27. #16811286C22semidirect
45. #16810972C22semidirect
46. #16810967C22semidirect
47. #16810917C22semidirect
48. #16810871C22semidirect
49. #16810870C22semidirect
50. #16810827C22semidirect
51. #16810764C22semidirect
52. #16810763C22semidirect
53. #16810710C22semidirect
54. #16810698C22semidirect
57. #16810631C22semidirect
58. #16810630C22semidirect
71. C53×#485C22semidirect
396. C2×#485D53semidirect
408. C2×C53#3329semidirect
446. #485C2×D53semidirect
474. C53C2×#3329semidirect
791. C2#20287007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113362
C2×#168112862
#202870072
C2×#168109722
C2×#168109672
C2×#168109172
C2×#168108712
C2×#168108702
C2×#168108272
C2×#168107642
C2×#168107632
C2×#168107102
C2×#168106982
C2×#168106312
C2×#168106302
C2×C53×#4852
C2×#332953