Finite Group Databasebeta

← C2×#20287781 #28265098

Subgroups — C2×#20287781 #28265098

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×#16811358C211yesmaximal, characteristic, complemented
2#20287781C2116yesmaximal, direct product factor
3C2×#16811015C211yesmaximal, characteristic, complemented
4C2×#16811013C211yesmaximal, characteristic
5C2×#16811005C211yesmaximal, characteristic, complemented
6C2×#16810845C211yesmaximal, characteristic, complemented
7C2×#16810842C211yesmaximal, characteristic, complemented
8C2×#16810823C211yesmaximal, characteristic, complemented
9C2×#16810838C211yesmaximal, characteristic, complemented
10C2×#16810835C211yesmaximal, characteristic, complemented
11C2×#16810825C211yesmaximal, characteristic, complemented
12C2×#16810754C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic, complemented
14C2×#16810728C211yesmaximal, characteristic, complemented
15C2×C4×#11719924C211yesmaximal, characteristic, complemented
16C2×C53×#556C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×#11719924C2211yescharacteristic
22C22×#11719924C2211yescharacteristic
23C22×#11719924C2211yescharacteristic
24C22×#11719922C2211yescharacteristic
25C22×#11719922C2211yescharacteristic
26#16811358—24no—
27#16811358C2218yescomplemented
28C2×#13133214C2211yescharacteristic
29C2×#13133206—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133205C2211yescharacteristic
32C2×#13133202—21no—
33C2×#13133202—21no—
34C2×C4×Dic106C2211yescharacteristic
35C2×C4×D212C2211yescharacteristic
36C2×C4×D212C2211yescharacteristic
37C2×#13133179—21no—
38#16811015C2218yescomplemented
39#16811013C2218yes—
40#16811005C2218yescomplemented
41#16810845C2218yescomplemented
42#16810842C2218yescomplemented
43#16810838C2218yescomplemented
44#16810835C2218yescomplemented
45#16810825C2218yescomplemented
46#16810823C2218yescomplemented
47#16810754C2218yescomplemented
48#16810733C2218yescomplemented
49#16810728C2218yescomplemented
50C4×#11719924C2218yescomplemented
51C2×#13133148C2211yescharacteristic
52C2×C4⋊#88322C2211yescharacteristic
53C2×C4⋊#88322C2211yescharacteristic
54C2×C4⋊#88322C2211yescharacteristic
55C2×#13133141C2211yescharacteristic
56C2×#13133141C2211yescharacteristic
57C2×#13133140C2211yescharacteristic
58C2×#13133138C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×#13133137C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#556—24no—
65C53×#556C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#126×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#124×C53C2211yescharacteristic
71C2×C22⋊Q8×C53—21no—
72C2×C4×Q8×C53C2211yescharacteristic
73C2×C4×Q8×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53—21no—
77C22×Dic106C2311yescharacteristic
78C22×D212—21no—
79C22×D212—21no—
80C22×D212C2311yescharacteristic
81C22×D212C2311yescharacteristic
82C22×C4×D53—21no—
83C22×C4×D53—21no—
84C2×#11719925—24no—
85C2×#11719925—42no—
86C2×#11719925C2314yes—
87C2×#11719925C2314yes—
88C2×#11719923—42no—
89C2×#11719923C2314yes—
90C2×#11719924—24no—
91C2×#11719924—42no—
92C2×#11719924—42no—
93C2×#11719924—42no—
94C2×#11719924C2314yes—
95C2×#11719924C2314yes—
96C2×#11719924C2314yes—
97C2×#11719924C2314yes—
98C2×#11719922—24no—
99C2×#11719922—42no—
100C2×#11719922C2314yes—
101C2×#11719922C2314yes—
102C22×#88322C2311yescharacteristic
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C22×#88322C2311yescharacteristic
106#13133214—22no—
107#13133214C2314yes—
108#13133206—28no—
109#13133205—22no—
110#13133205—22no—
111#13133205C2314yes—
112#13133205C2314yes—
113#13133202—28no—
114#13133202—28no—
115C4×Dic106—22no—
116C4×Dic106C2314yes—
117C4×D212—22no—
118C4×D212—22no—
119C4×D212C2314yes—
120C4×D212C2314yes—
121#13133179—28no—
122C2×C4⋊Dic53C2311yescharacteristic
123C2×#11719919—21no—
124C2×#11719921—21no—
125C2×#11719921—21no—
126C2×#11719921—21no—
127C2×#11719921—21no—
128C2×#11719921—21no—
129C2×#11719921—21no—
130C2×C4×Dic53—21no—
131#13133148C2314yes—
132C4⋊#88322C2314yes—
133C4⋊#88322C2314yes—
134C4⋊#88322C2314yes—
135#13133141C2314yes—
136#13133141C2314yes—
137#13133140C2314yes—
138#13133138C2314yes—
139#13133137C2314yes—
140#13133137C2314yes—
141#13133128C2314yes—
142#13133128C2314yes—
143C4×#88322C2314yes—
144C22×Q8×C53D411yescharacteristic
145C22×Q8×C53C2311yescharacteristic
146C22×Q8×C53C2311yescharacteristic
147C22×D4×C53C2311yescharacteristic
148C23×C4×C53—21no—
149C4⋊Q8×C53—22no—
150C4⋊Q8×C53C2314yes—
151#126×C53—28no—
152#126×C53—28no—
153#124×C53—22no—
154#124×C53—22no—
155#124×C53C2314yes—
156#124×C53C2314yes—
157C22⋊Q8×C53—28no—
158C4×Q8×C53—22no—
159C4×Q8×C53—22no—
160C4×Q8×C53D414yes—
161C4×Q8×C53C2314yes—
162C4×Q8×C53C2314yes—
163C4×Q8×C53C2314yes—
164C4×D4×C53—22no—
165C4×D4×C53C2314yes—
166#117×C53—28no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—21no—
169C2×C4⋊C4×C53—21no—
170C2×C4⋊C4×C53—21no—
171C2×C4⋊C4×C53D411yescharacteristic
172C2×C4⋊C4×C53D411yescharacteristic
173C2×C4⋊C4×C53D411yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181C2×C42×C53—21no—
182C2×C42×C53C2311yescharacteristic
183C2×C42×C53C2311yescharacteristic
184C2×C42×C53C2311yescharacteristic
185C24×C53—21no—
186C23×D53—21no—
187C23×D53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—21no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53—22no—
194C2×Q8×C53—42no—
195C2×Q8×C53C2×D414yes—
196C2×Q8×C53C2412yes—
197C2×Q8×C53C2412yes—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53C2412yes—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—24no—
206C22×C4×C53—44no—
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D411yescharacteristic
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2411yescharacteristic
214C22×Dic53—21no—
215C22×Dic53—21no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—22no—
220C2×D212—24no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—24no—
224C2×D212—44no—
225C2×D212—82no—
226C2×D212C2412yes—
227C2×D212C2412yes—
228C2×C4×D53—24no—
229C2×C4×D53—24no—
230C2×C4×D53—82no—
231C2×C4×D53—82no—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—21no—
235C2×Dic106C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—24no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C2×D414yes—
242C4⋊C4×C53C2×D414yes—
243C4⋊C4×C53C2×D414yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53—24no—
249C22⋊C4×C53—24no—
250C42×C53—24no—
251C42×C53—24no—
252C42×C53C2×D412yes—
253C42×C53C2×D412yes—
254C42×C53C2×D412yes—
255C42×C53C2412yes—
256C42×C53C2412yes—
257C42×C53C2412yes—
258#11719925—28no—
259#11719925—44no—
260#11719924—28no—
261#11719924—44no—
262#11719924—44no—
263#11719924—44no—
264#11719923—44no—
265#11719922—28no—
266#11719922—44no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273C4⋊Dic53—21no—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276C4×Dic53—24no—
277C2×#88322—22no—
278C2×#88322—22no—
279C2×#88322—22no—
280C2×#88322#4114yes—
281C2×#88322C2412yes—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53C22×D411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53—44no—
303Q8×C53—42no—
304Q8×C53—42no—
305D4×C53—22no—
306D4×C53—22no—
307D4×C53—42no—
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—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—48no—
318C2×C4×C53—42no—
319C2×C4×C53—42no—
320C2×C4×C53—42no—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C2×#4112yes—
329C2×C4×C53H(5,𝔽2)12yes—
330C2×C4×C53C2511yescharacteristic
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335D212—22no—
336D212—22no—
337D212—22no—
338D212—22no—
339D212—48no—
340D212—42no—
341D212—42no—
342D212—84no—
343C4×D53—84no—
344C4×D53—84no—
345Dic106—22no—
346Dic106—22no—
347Dic106—42no—
348#88322—22no—
349#88322—22no—
350#88322—22no—
351#88322C2×#4114yes—
352C2×#3401—531nomaximal, Sylow
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—84no—
357C22×C53#55012yes—
358C22×C53#57512yes—
359C22×C53#57712yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—42no—
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—84no—
368C2×D53—84no—
369C4×C53—22no—
370C4×C53—22no—
371C4×C53—22no—
372C4×C53—22no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53#55012yes—
379C4×C53C22×#4111yescharacteristic
380C4×C53C2×H(5,𝔽2)11yescharacteristic
381Dic53—42no—
382Dic53—42no—
383C2×#559—531no—
384C2×#556D5311yescharacteristic, complemented
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×#442—531no—
397C2×#441—531no—
398C2×C4×SD16—531no—
399C2×C53—82no—
400C2×C53#340114yescomplemented
401C2×C53C2×#55011yescharacteristic
402C2×C53C2×#57511yescharacteristic
403C2×C53C2×#57711yescharacteristic
404D53—82no—
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×D8—531no—
415#559—538no—
416#559—1064no—
417#556—24no—
418#556C2×D5318yescomplemented
419C2×C4⋊Q8C2×D5311yescharacteristic
420C2×#127—531no—
421C2×#126—21no—
422C2×#126—21no—
423C2×#124—531no—
424C2×#124—531no—
425C2×#124—1061no—
426C2×#124C2×D5311yescharacteristic
427C2×#124C2×D5311yescharacteristic
428C2×#123—1061no—
429C2×#123—1061no—
430C2×C22⋊Q8—21no—
431C2×C4×Q8—531no—
432C2×C4×Q8C2×D5311yescharacteristic
433C2×C4×Q8C2×D5311yescharacteristic
434C2×C4×Q8C2×D5311yescharacteristic
435C2×C4×D4—531no—
436C2×C4×D4—531no—
437C2×C4×D4—1061no—
438C2×C4×D4C2×D5311yescharacteristic
439C2×#117—21no—
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#442—538no—
451#441—538no—
452C4×SD16—538no—
453C2×#106—531no—
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×#102—531no—
462C2×#102—531no—
463C2×#97—531no—
464C2×#97—531no—
465C2×C4×C8—531no—
466C53C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—531no—
468C22×Q8C22⋊D5311yescharacteristic
469C22×Q8C22×D5311yescharacteristic
470C22×Q8C22×D5311yescharacteristic
471C22×D4—531no—
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4C22×D5311yescharacteristic
476C23×C4—21no—
477C23×C4—1061no—
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—534no—
494C2×D8—534no—
495C2×D8—1064no—
496C2×D8—2122no—
497C22×C8—531no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C4⋊Q8—22no—
502C4⋊Q8C22×D5314yes—
503#127—534no—
504#127—1062no—
505#126—28no—
506#126—28no—
507#124—22no—
508#124—22no—
509#124—534no—
510#124—534no—
511#124—1068no—
512#124—1062no—
513#124—1062no—
514#124C22×D5314yes—
515#124C22×D5314yes—
516#123—1068no—
517#123—1068no—
518C22⋊Q8—28no—
519C4×Q8—22no—
520C4×Q8—22no—
521C4×Q8—534no—
522C4×Q8—1062no—
523C4×Q8C22⋊D5314yes—
524C4×Q8C22×D5314yes—
525C4×Q8C22×D5314yes—
526C4×Q8C22×D5314yes—
527C4×D4—22no—
528C4×D4—534no—
529C4×D4—534no—
530C4×D4—1068no—
531C4×D4—1062no—
532C4×D4—1062no—
533C4×D4C22×D5314yes—
534#117—28no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4C22⋊D5311yescharacteristic
542C2×C4⋊C4C22⋊D5311yescharacteristic
543C2×C4⋊C4C22⋊D5311yescharacteristic
544C2×C4⋊C4C22×D5311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
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—21no—
557C2×C42—21no—
558C2×C42—1061no—
559C2×C42C22×D5311yescharacteristic
560C2×C42C22×D5311yescharacteristic
561C2×C42C22×D5311yescharacteristic
562#106—534no—
563C4⋊C8—534no—
564C4⋊C8—534no—
565C4⋊C8—534no—
566#103—534no—
567#103—534no—
568#103—534no—
569#102—534no—
570#102—534no—
571#102—534no—
572#97—534no—
573#97—534no—
574C4×C8—534no—
575C24—21no—
576C24—1061no—
577C24—1061no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—42no—
585C2×Q8—532no—
586C2×Q8—1061no—
587C2×Q8—1062no—
588C2×Q8—1062no—
589C2×Q8C2×C22⋊D5314yes—
590C2×Q8C23×D5312yes—
591C2×Q8C23×D5312yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—532no—
596C2×D4—532no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1061no—
600C2×D4—1061no—
601C2×D4—1062no—
602C2×D4—1062no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—4242no—
606C2×D4—2124no—
607C2×D4C23×D5312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1064no—
616C22×C4—1064no—
617C22×C4—4242no—
618C22×C4—4242no—
619C22×C4C2×C22⋊D5311yescharacteristic
620C22×C4C2×C22⋊D5311yescharacteristic
621C22×C4C2×C22⋊D5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C2×C22⋊D5311yescharacteristic
625C22×C4C23×D5311yescharacteristic
626Q16—1068no—
627Q16—2124no—
628SD16—1068no—
629SD16—2124no—
630SD16—2124no—
631SD16—2124no—
632SD16—2124no—
633D8—1068no—
634D8—2124no—
635C2×C8—534no—
636C2×C8—532no—
637C2×C8—532no—
638C2×C8—532no—
639C2×C8—532no—
640C2×C8—1062no—
641C2×C8—1062no—
642C2×C8—1062no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—21no—
648C4⋊C4—532no—
649C4⋊C4—1061no—
650C4⋊C4—1064no—
651C4⋊C4C2×C22⋊D5314yes—
652C4⋊C4C2×C22⋊D5314yes—
653C4⋊C4C2×C22⋊D5314yes—
654C4⋊C4C23×D5312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C42—24no—
667C42—24no—
668C42—1064no—
669C42C2×C22⋊D5312yes—
670C42C2×C22⋊D5312yes—
671C42C2×C22⋊D5312yes—
672C42C23×D5312yes—
673C42C23×D5312yes—
674C42C23×D5312yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—1062no—
680C23—1062no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23—2122no—
687C23C22×C22⋊D5311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—22no—
691Q8—22no—
692Q8—44no—
693Q8—42no—
694Q8—42no—
695Q8—1062no—
696Q8—1062no—
697Q8—2122no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—1062no—
702D4—1062no—
703D4—1062no—
704D4—1062no—
705D4—4244no—
706D4—2128no—
707D4—2122no—
708D4—2122no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—48no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—4244no—
725C2×C4—4244no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4C22×C22⋊D5312yes—
729C2×C4C22×C22⋊D5312yes—
730C2×C4C22×C22⋊D5312yes—
731C2×C4C22×C22⋊D5312yes—
732C2×C4C22×C22⋊D5312yes—
733C2×C4C22×C22⋊D5312yes—
734C2×C4C22×C22⋊D5311yescharacteristic
735C2×C4#41×D5312yes—
736C2×C4#1313326312yes—
737C2×C4C24×D5311yescharacteristic
738C8—534no—
739C8—1062no—
740C8—1062no—
741C8—1062no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—4244no—
747C22—4244no—
748C22—2122no—
749C22—2122no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22#1681129212yes—
755C22#1681142112yes—
756C22#1681143112yes—
757C22C23×C22⋊D5311yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—42no—
765C4—42no—
766C4—42no—
767C4—2122no—
768C4—2122no—
769C4#1681129212yes—
770C4C2×#41×D5311yescharacteristic
771C4C2×#1313326311yescharacteristic
772C2—82no—
773C2—4242no—
774C2—4242no—
775C2#2028778114yesdirect product factor
776C2C2×#1681129211yescharacteristic
777C2C2×#1681142111yescharacteristic
778C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#556C2
socleC23×C53C22×D4
prime radicalC2×#16811013C2
hypercenterC2×#556D53
hypocenterC53C2×#3401
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#16811358C2semidirect
2. #20287781C2direct (N × H)
3. C2×#16811015C2semidirect
5. C2×#16811005C2semidirect
6. C2×#16810845C2semidirect
7. C2×#16810842C2semidirect
8. C2×#16810823C2semidirect
9. C2×#16810838C2semidirect
10. C2×#16810835C2semidirect
11. C2×#16810825C2semidirect
12. C2×#16810754C2semidirect
13. C2×#16810733C2semidirect
14. C2×#16810728C2semidirect
15. C2×C4×#11719924C2semidirect
16. C2×C53×#556C2semidirect
27. #16811358C22semidirect
38. #16811015C22semidirect
40. #16811005C22semidirect
41. #16810845C22semidirect
42. #16810842C22semidirect
43. #16810838C22semidirect
44. #16810835C22semidirect
45. #16810825C22semidirect
46. #16810823C22semidirect
47. #16810754C22semidirect
48. #16810733C22semidirect
49. #16810728C22semidirect
50. C4×#11719924C22semidirect
65. C53×#556C22semidirect
384. C2×#556D53semidirect
400. C2×C53#3401semidirect
418. #556C2×D53semidirect
466. C53C2×#3401semidirect
775. C2#20287781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113582
#202877812
C2×#168110152
C2×#168110132
C2×#168110052
C2×#168108452
C2×#168108422
C2×#168108232
C2×#168108382
C2×#168108352
C2×#168108252
C2×#168107542
C2×#168107332
C2×#168107282
C2×C4×#117199242
C2×C53×#5562
C2×#340153