Finite Group Databasebeta

← C2×#20287786 #28265103

Subgroups — C2×#20287786 #28265103

Order 13568.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811356C211yesmaximal, characteristic, complemented
2C2×#16811343C211yesmaximal, characteristic, complemented
3#20287786C2116yesmaximal, direct product factor
4C2×#16811017C211yesmaximal, characteristic, complemented
5C2×#16811011C211yesmaximal, characteristic
6C2×#16811006C211yesmaximal, characteristic, complemented
7C2×#16810844C211yesmaximal, characteristic, complemented
8C2×#16810844C211yesmaximal, characteristic, complemented
9C2×#16810822C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810837C211yesmaximal, characteristic, complemented
12C2×#16810828C211yesmaximal, characteristic, complemented
13C2×#16810751C211yesmaximal, characteristic, complemented
14C2×#16810729C211yesmaximal, characteristic, complemented
15C2×#16810710C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×Dic212C2211yescharacteristic
18C22×Dic212C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×#11719923C2211yescharacteristic
22C22×#11719923C2211yescharacteristic
23C22×#11719923C2211yescharacteristic
24C22×#11719922C2211yescharacteristic
25#16811356—24no—
26#16811356C2218yescomplemented
27#16811343—24no—
28#16811343C2218yescomplemented
29C2×#13133217C2211yescharacteristic
30C2×#13133213C2211yescharacteristic
31C2×#13133210—21no—
32C2×#13133210—21no—
33C2×#13133205C2211yescharacteristic
34C2×#13133204C2211yescharacteristic
35C2×#13133204C2211yescharacteristic
36C2×#13133204C2211yescharacteristic
37C2×#13133203—21no—
38C2×#13133200—21no—
39C2×#13133199—21no—
40C2×#13133196—21no—
41C2×C4×Dic106C2211yescharacteristic
42C2×#13133182C2211yescharacteristic
43C2×#13133182C2211yescharacteristic
44C2×#13133182C2211yescharacteristic
45C2×#13133179C2211yescharacteristic
46C2×C4×C22⋊D53—21no—
47C2×#13133176—21no—
48#16811017C2218yescomplemented
49#16811011C2218yes—
50#16811006C2218yescomplemented
51#16810844C2218yescomplemented
52#16810844C2218yescomplemented
53#16810838C2218yescomplemented
54#16810837C2218yescomplemented
55#16810828C2218yescomplemented
56#16810822C2218yescomplemented
57#16810751C2218yescomplemented
58#16810729C2218yescomplemented
59#16810710C2218yescomplemented
60C2×C4⋊#88322C2211yescharacteristic
61C2×#13133146C2211yescharacteristic
62C2×#13133146C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106D411yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C4×D53—21no—
85C2×Dic212—24no—
86C2×Dic212—42no—
87C2×Dic212C2314yes—
88C2×Dic212C2314yes—
89C2×#11719913—24no—
90C2×#11719913—42no—
91C2×#11719913C2314yes—
92C2×#11719913C2314yes—
93C2×#11719923—42no—
94C2×#11719923—42no—
95C2×#11719923—42no—
96C2×#11719923C2314yes—
97C2×#11719923C2314yes—
98C2×#11719923C2314yes—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C22×#88322C2311yescharacteristic
102C22×#88322C2311yescharacteristic
103#13133217—22no—
104#13133217C2314yes—
105#13133213—22no—
106#13133213C2314yes—
107#13133210—28no—
108#13133210—28no—
109#13133205—22no—
110#13133205C2314yes—
111#13133204—22no—
112#13133204—22no—
113#13133204—22no—
114#13133204C2314yes—
115#13133204C2314yes—
116#13133204C2314yes—
117#13133203—28no—
118#13133200—28no—
119#13133199—28no—
120#13133196—28no—
121C4×Dic106D414yes—
122C4×Dic106C2314yes—
123#13133182—22no—
124#13133182—22no—
125#13133182—22no—
126#13133182C2314yes—
127#13133182C2314yes—
128#13133182C2314yes—
129#13133179—22no—
130#13133179C2314yes—
131C4×C22⋊D53—28no—
132#13133176—28no—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919D411yescharacteristic
140C2×#11719919D411yescharacteristic
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153C2×C4×Dic53C2311yescharacteristic
154C2×C4×Dic53C2311yescharacteristic
155C4⋊#88322C2314yes—
156#13133146C2314yes—
157#13133146C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133137C2314yes—
162#13133127C2314yes—
163C8×Dic53C2314yes—
164C22×D4×C53C2311yescharacteristic
165C22×D4×C53C2311yescharacteristic
166C23×C4×C53—21no—
167C23×C4×C53—21no—
168C2×D8×C53—24no—
169C2×D8×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C4×D4×C53—22no—
173C4×D4×C53—22no—
174C4×D4×C53C2314yes—
175C4×D4×C53C2314yes—
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C42×C53C2311yescharacteristic
181#106×C53C2314yes—
182#102×C53C2314yes—
183#102×C53C2314yes—
184#97×C53C2314yes—
185C24×C53—21no—
186C24×C53—21no—
187C23×D53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—21no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53C2412yes—
195C2×D4×C53C2412yes—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—24no—
200C22×C4×C53—44no—
201C22×C4×C53—82no—
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2411yescharacteristic
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—82no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215C22×Dic53C2×D411yescharacteristic
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—21no—
219C2×D212C2412yes—
220C2×C4×D53—24no—
221C2×C4×D53—82no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—22no—
228C2×Dic106—21no—
229C2×Dic106—21no—
230C2×Dic106—21no—
231C2×Dic106—42no—
232C2×Dic106C2×D414yes—
233C2×Dic106C2412yes—
234C2×Dic106C2412yes—
235C2×Dic106C2412yes—
236D8×C53—28no—
237C2×C8×C53—22no—
238C2×C8×C53#4114yes—
239C2×C8×C53C2412yes—
240C2×C8×C53C2412yes—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C42×C53C2×D412yes—
248C42×C53C2412yes—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251C22⋊Dic53—24no—
252C22⋊Dic53—24no—
253C22⋊Dic53—24no—
254C22⋊Dic53—24no—
255#11719923—44no—
256#11719923—44no—
257#11719923—44no—
258#11719922—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262C4⋊Dic53—24no—
263C4⋊Dic53—24no—
264C4⋊Dic53C2×D414yes—
265#11719919—24no—
266#11719919—24no—
267#11719919—24no—
268#11719919C2×D414yes—
269#11719919C2×D414yes—
270C4×Dic53—24no—
271C4×Dic53—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2×D412yes—
275C4×Dic53C2412yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281Dic212—28no—
282Dic212—44no—
283#11719913—28no—
284#11719913—44no—
285C23×C53—22no—
286C23×C53—22no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53C22×D411yescharacteristic
294C22×D53—22no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298D4×C53—22no—
299D4×C53—22no—
300D4×C53—22no—
301D4×C53—22no—
302D4×C53—42no—
303D4×C53—42no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—48no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—84no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C2×#4112yes—
316C2×C4×C53H(5,𝔽2)12yes—
317C2×C4×C53C2511yescharacteristic
318C22⋊D53—48no—
319C22⋊D53—84no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334D212—22no—
335D212—22no—
336D212—42no—
337C4×D53—84no—
338Dic106—22no—
339Dic106—22no—
340Dic106—22no—
341Dic106—22no—
342Dic106—22no—
343Dic106—22no—
344Dic106—44no—
345Dic106—42no—
346Dic106—42no—
347Dic106—42no—
348C8×C53—22no—
349C8×C53C2×#4114yes—
350#88322—22no—
351#88322—22no—
352C2×#3401—531nomaximal, Sylow
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—84no—
360C22×C53—84no—
361C22×C53#55012yes—
362C22×C53#57512yes—
363C22×C53#57712yes—
364C22×C53C23×D411yescharacteristic
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—84no—
369C4×C53—22no—
370C4×C53—22no—
371C4×C53—42no—
372C4×C53—42no—
373C4×C53#55012yes—
374C4×C53C22×#4111yescharacteristic
375C4×C53C2×H(5,𝔽2)11yescharacteristic
376Dic53—22no—
377Dic53—22no—
378Dic53—22no—
379Dic53—22no—
380Dic53—42no—
381Dic53—42no—
382Dic53—42no—
383C2×#559—531no—
384C2×#556—531no—
385#3401—5316no—
386C2×#497—531no—
387C2×#496—531no—
388C2×#495—531no—
389C2×#464—531no—
390C2×#464—531no—
391C2×#460—531no—
392C2×#463—531no—
393C2×#463—531no—
394C2×#461—531no—
395C2×#446—531no—
396C2×#442D5311yescharacteristic, complemented
397C2×#441—531no—
398C2×C4×SD16—531no—
399C2×C53—82no—
400C2×C53—82no—
401C2×C53#340114yescomplemented
402C2×C53C2×#55011yescharacteristic
403C2×C53C2×#57511yescharacteristic
404C2×C53C2×#57711yescharacteristic
405D53—82no—
406C22×Q16—531no—
407C22×Q16—531no—
408C22×SD16—531no—
409C22×SD16—531no—
410C22×SD16—531no—
411C22×SD16—531no—
412C22×SD16—531no—
413C22×D8—531no—
414C22×D8C2×D5311yescharacteristic
415#559—538no—
416#559—1064no—
417#556—538no—
418#556—1064no—
419C2×C4⋊Q8—531no—
420C2×#127—531no—
421C2×#126—1061no—
422C2×#126—1061no—
423C2×#124—531no—
424C2×#124—531no—
425C2×#124—531no—
426C2×#124—531no—
427C2×#124—1061no—
428C2×#123—1061no—
429C2×#123—1061no—
430C2×C22⋊Q8—1061no—
431C2×C4×Q8—531no—
432C2×C4×Q8—531no—
433C2×C4×Q8—531no—
434C2×C4×Q8—531no—
435C2×C4×D4—531no—
436C2×C4×D4—1061no—
437C2×C4×D4C2×D5311yescharacteristic
438C2×C4×D4C2×D5311yescharacteristic
439C2×#117—1061no—
440#497—538no—
441#496—538no—
442#495—538no—
443#464—538no—
444#464—538no—
445#463—538no—
446#463—538no—
447#461—538no—
448#460—538no—
449#446—538no—
450#442C2×D5318yescomplemented
451#441—538no—
452C4×SD16—538no—
453C2×#106C2×D5311yescharacteristic
454C2×C4⋊C8—531no—
455C2×C4⋊C8—531no—
456C2×C4⋊C8—531no—
457C2×#103—531no—
458C2×#103—531no—
459C2×#103—531no—
460C2×#102—531no—
461C2×#102C2×D5311yescharacteristic
462C2×#102C2×D5311yescharacteristic
463C2×#97—531no—
464C2×#97C2×D5311yescharacteristic
465C2×C4×C8—531no—
466C53C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—531no—
468C22×Q8—531no—
469C22×Q8—531no—
470C22×Q8—531no—
471C22×D4—531no—
472C22×D4—1061no—
473C22×D4—1061no—
474C22×D4C22×D5311yescharacteristic
475C22×D4C22×D5311yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
478C23×C4—1061no—
479C2×Q16—534no—
480C2×Q16—534no—
481C2×Q16—1064no—
482C2×Q16—2122no—
483C2×SD16—534no—
484C2×SD16—534no—
485C2×SD16—534no—
486C2×SD16—534no—
487C2×SD16—534no—
488C2×SD16—1064no—
489C2×SD16—2122no—
490C2×SD16—2122no—
491C2×SD16—2122no—
492C2×SD16—2122no—
493C2×D8—24no—
494C2×D8—534no—
495C2×D8—2122no—
496C2×D8C22×D5314yes—
497C22×C8—531no—
498C22×C8—531no—
499C22×C8C22×D5311yescharacteristic
500C22×C8C22×D5311yescharacteristic
501C4⋊Q8—534no—
502C4⋊Q8—1062no—
503#127—534no—
504#127—1062no—
505#126—1068no—
506#126—1068no—
507#124—534no—
508#124—534no—
509#124—534no—
510#124—534no—
511#124—1062no—
512#124—1062no—
513#124—1062no—
514#124—1068no—
515#124—1062no—
516#123—1068no—
517#123—1068no—
518C22⋊Q8—1068no—
519C4×Q8—534no—
520C4×Q8—534no—
521C4×Q8—534no—
522C4×Q8—534no—
523C4×Q8—534no—
524C4×Q8—1062no—
525C4×Q8—1062no—
526C4×Q8—1062no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—534no—
530C4×D4—1062no—
531C4×D4—1068no—
532C4×D4C22×D5314yes—
533C4×D4C22×D5314yes—
534#117—1068no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—531no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4C22×D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C42—531no—
557C2×C42—531no—
558C2×C42—1061no—
559C2×C42—1061no—
560C2×C42—1061no—
561C2×C42C22×D5311yescharacteristic
562#106C22×D5314yes—
563C4⋊C8—534no—
564C4⋊C8—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#102—534no—
570#102C22×D5314yes—
571#102C22×D5314yes—
572#97—534no—
573#97C22×D5314yes—
574C4×C8—534no—
575C24—21no—
576C24—21no—
577C24—1061no—
578C2×Q8—534no—
579C2×Q8—532no—
580C2×Q8—532no—
581C2×Q8—532no—
582C2×Q8—1061no—
583C2×Q8—1061no—
584C2×Q8—1061no—
585C2×Q8—1062no—
586C2×Q8—1062no—
587C2×Q8—1062no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8—2122no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—532no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1061no—
602C2×D4—1062no—
603C2×D4—1062no—
604C2×D4—4242no—
605C2×D4—2124no—
606C2×D4C23×D5312yes—
607C2×D4C23×D5312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—82no—
614C22×C4—531no—
615C22×C4—531no—
616C22×C4—531no—
617C22×C4—531no—
618C22×C4—1064no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—4242no—
623C22×C4D4×D5311yescharacteristic
624C22×C4D4×D5311yescharacteristic
625C22×C4C23×D5311yescharacteristic
626Q16—1068no—
627Q16—2124no—
628SD16—1068no—
629SD16—2124no—
630SD16—2124no—
631SD16—2124no—
632SD16—2124no—
633D8—28no—
634D8—2124no—
635C2×C8—22no—
636C2×C8—532no—
637C2×C8—532no—
638C2×C8—1062no—
639C2×C8—1062no—
640C2×C8#1171994514yes—
641C2×C8C23×D5312yes—
642C2×C8C23×D5312yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—534no—
646C4⋊C4—534no—
647C4⋊C4—534no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4C23×D5312yes—
654C4⋊C4C23×D5312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—1064no—
658C22⋊C4—1064no—
659C22⋊C4—1064no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C42—532no—
667C42—532no—
668C42—532no—
669C42—532no—
670C42—1064no—
671C42—1064no—
672C42—1064no—
673C42D4×D5312yes—
674C42C23×D5312yes—
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—1062no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23C2×D4×D5311yescharacteristic
688Q8—1062no—
689Q8—1062no—
690Q8—1062no—
691Q8—1062no—
692Q8—1062no—
693Q8—1062no—
694Q8—2124no—
695Q8—2122no—
696Q8—2122no—
697Q8—2122no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—1062no—
705D4—1062no—
706D4—4244no—
707D4—2128no—
708D4—2122no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—532no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—532no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—4244no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4C2×D4×D5312yes—
733C2×C4C2×D4×D5312yes—
734C2×C4C2×D4×D5311yescharacteristic
735C2×C4C2×#1171994512yes—
736C2×C4#1313326312yes—
737C2×C4C24×D5311yescharacteristic
738C8—22no—
739C8—1062no—
740C8—1062no—
741C8C2×#1171994514yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—4244no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22#1681129412yes—
755C22#1681141912yes—
756C22#1681143312yes—
757C22C22×D4×D5311yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—1062no—
763C4—1062no—
764C4—1062no—
765C4—1062no—
766C4—2122no—
767C4—2122no—
768C4—2122no—
769C4#1681129412yes—
770C4C22×#1171994511yescharacteristic
771C4C2×#1313326311yescharacteristic
772C2—82no—
773C2—82no—
774C2—4242no—
775C2#2028778614yesdirect product factor
776C2C2×#1681129411yescharacteristic
777C2C2×#1681141911yescharacteristic
778C2C2×#1681143311yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
prime radicalC2×#16811011C2
hypercenterC2×#442D53
hypocenterC53C2×#3401
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811356C2semidirect
2. C2×#16811343C2semidirect
3. #20287786C2direct (N × H)
4. C2×#16811017C2semidirect
6. C2×#16811006C2semidirect
7. C2×#16810844C2semidirect
8. C2×#16810844C2semidirect
9. C2×#16810822C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810837C2semidirect
12. C2×#16810828C2semidirect
13. C2×#16810751C2semidirect
14. C2×#16810729C2semidirect
15. C2×#16810710C2semidirect
16. C2×C53×#442C2semidirect
26. #16811356C22semidirect
28. #16811343C22semidirect
48. #16811017C22semidirect
50. #16811006C22semidirect
51. #16810844C22semidirect
52. #16810844C22semidirect
53. #16810838C22semidirect
54. #16810837C22semidirect
55. #16810828C22semidirect
56. #16810822C22semidirect
57. #16810751C22semidirect
58. #16810729C22semidirect
59. #16810710C22semidirect
72. C53×#442C22semidirect
396. C2×#442D53semidirect
401. C2×C53#3401semidirect
450. #442C2×D53semidirect
466. C53C2×#3401semidirect
775. C2#20287786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113562
C2×#168113432
#202877862
C2×#168110172
C2×#168110112
C2×#168110062
C2×#168108442
C2×#168108222
C2×#168108382
C2×#168108372
C2×#168108282
C2×#168107512
C2×#168107292
C2×#168107102
C2×C53×#4422
C2×#340153