Finite Group Databasebeta

← C2×#20277799 #27543726

Subgroups — C2×#20277799 #27543726

Order 13568.

3094 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic
2#20277799C2116yesmaximal, direct product factor
3C2×#16810529C211yesmaximal, characteristic, complemented
4C2×#16810527C211yesmaximal, characteristic, complemented
5C2×#16810509C211yesmaximal, characteristic, complemented
6C2×#16810507C211yesmaximal, characteristic, complemented
7C2×#16810507C211yesmaximal, characteristic, complemented
8C2×#16810504C211yesmaximal, characteristic, complemented
9C2×#16810497C211yesmaximal, characteristic
10C2×#16810494C211yesmaximal, characteristic
11C2×#16810474C211yesmaximal, characteristic, complemented
12C2×C4×#11719921C211yesmaximal, characteristic
13C2×C4×#11719921C211yesmaximal, characteristic
14C2×C4×#11719921C211yesmaximal, characteristic
15C2×#95×D53C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C23×C4×D53C2211yescharacteristic
21C2×#13133195C4116yescomplemented
22C2×#13133195C2218yes—
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810529C2218yescomplemented
36#16810527C2218yescomplemented
37#16810509C2218yescomplemented
38#16810507C2218yescomplemented
39#16810507C2218yescomplemented
40#16810504C2218yescomplemented
41#16810497C2218yes—
42#16810494C2218yes—
43#16810474C2218yescomplemented
44C4×#11719921C2218yes—
45C4×#11719921C2218yes—
46C4×#11719921C2218yes—
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59#95×D53C2218yes—
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C42×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C22×C42×C53C2211yescharacteristic
65C4×C4⋊C4×C53C2218yescomplemented
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C24×D53C2311yescharacteristic
69C22×Dic106—42no—
70C22×Dic106—42no—
71C22×Dic106C2×C418yescomplemented
72C22×Dic106C2314yes—
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C22×C4×D53—24no—
81C22×C4×D53—24no—
82C22×C4×D53—24no—
83C22×C4×D53—24no—
84C22×C4×D53—42no—
85C22×C4×D53—42no—
86C22×C4×D53—42no—
87C22×C4×D53—42no—
88C22×C4×D53C2×C418yes—
89C22×C4×D53C2314yes—
90C22×C4×D53C2314yes—
91C22×C4×D53C2314yes—
92#13133195C2×C4164yescomplemented
93C2×C4⋊Dic53—42no—
94C2×C4⋊Dic53C2314yes—
95C2×#11719919—24no—
96C2×#11719919—42no—
97C2×#11719919C2×C418yescomplemented
98C2×#11719919C2×C418yescomplemented
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719921—24no—
104C2×#11719921C2×C418yes—
105C2×#11719921C2×C418yes—
106C2×#11719921Q818yescomplemented
107C2×#11719921C2314yes—
108C2×#11719921C2314yes—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×C4×Dic53—24no—
112C2×C4×Dic53—42no—
113C2×C4×Dic53—42no—
114C2×C4×Dic53C2314yes—
115C2×C4×Dic53C2314yes—
116C2×C4×Dic53C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53—24no—
137C2×C4⋊C4×C53C2×C418yescomplemented
138C2×C4⋊C4×C53C2314yes—
139C2×C4⋊C4×C53C2314yes—
140C2×C42×C53—24no—
141C2×C42×C53—42no—
142C2×C42×C53—42no—
143C2×C42×C53C2314yes—
144C2×C42×C53C2314yes—
145C2×C42×C53C2314yes—
146#95×C53C2314yes—
147#95×C53C2314yes—
148C24×C53C2411yescharacteristic
149C23×D53—22no—
150C23×D53—22no—
151C23×D53—22no—
152C23×D53—22no—
153C23×D53C22×C414yes—
154C23×D53C2×Q814yes—
155C23×D53#4114yes—
156C23×D53C2412yes—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53C22×C414yes—
173C22×C4×C53C22×C414yes—
174C22×C4×C53C22×C414yes—
175C22×C4×C53C2×Q814yes—
176C22×C4×C53#4114yes—
177C22×C4×C53#4114yes—
178C22×C4×C53C2412yes—
179C22×C4×C53C2412yes—
180C22×C4×C53C2412yes—
181C22×C4×C53C2412yes—
182C22×C4×C53C2412yes—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53C22×C414yes—
203C22×Dic53C22×C414yes—
204C22×Dic53C22×C414yes—
205C22×Dic53C2×Q814yes—
206C22×Dic53C2412yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C2×C4×D53—28no—
214C2×C4×D53—28no—
215C2×C4×D53—28no—
216C2×C4×D53—28no—
217C2×C4×D53—416no—
218C2×C4×D53—44no—
219C2×C4×D53—44no—
220C2×C4×D53—44no—
221C2×C4×D53—44no—
222C2×C4×D53—416no—
223C2×C4×D53—416no—
224C2×C4×D53C22×C4116yes—
225C2×Dic106—416no—
226C2×Dic106—44no—
227C2×Dic106—44no—
228C2×Dic106C22×C4116yescomplemented
229C4⋊C4×C53—28no—
230C4⋊C4×C53C22×C4116yescomplemented
231C42×C53—28no—
232C42×C53—44no—
233C42×C53—44no—
234#11719921—28no—
235#11719921C22×C4116yes—
236#11719921C22×C4116yes—
237#11719921C2×Q8116yescomplemented
238C4⋊Dic53—44no—
239#11719919—28no—
240#11719919—44no—
241#11719919C22×C4116yescomplemented
242#11719919C22×C4116yescomplemented
243C4×Dic53—28no—
244C4×Dic53—44no—
245C4×Dic53—44no—
246C23×C53C23×C412yes—
247C23×C53C22×Q812yes—
248C23×C53C2×#4112yes—
249C23×C53C2×#4112yes—
250C23×C53C2×#4112yes—
251C23×C53H(5,𝔽2)12yes—
252C23×C53H(5,𝔽2)12yes—
253C23×C53C2511yescharacteristic
254C22×D53—28no—
255C22×D53—28no—
256C22×D53—28no—
257C22×D53—28no—
258C22×D53—28no—
259C22×D53—28no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—22no—
263C22×D53—22no—
264C22×D53C4×Q8116yes—
265C22×D53C23×C414yes—
266C22×D53C22×Q814yes—
267C22×D53C2×#4114yes—
268C2×C4×C53—28no—
269C2×C4×C53—28no—
270C2×C4×C53—28no—
271C2×C4×C53—28no—
272C2×C4×C53—28no—
273C2×C4×C53—28no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—44no—
290C2×C4×C53C23×C414yes—
291C2×C4×C53C23×C414yes—
292C2×C4×C53C23×C414yes—
293C2×C4×C53C22×Q814yes—
294C2×C4×C53C2×#4114yes—
295C2×C4×C53C2×#4114yes—
296C2×Dic53—28no—
297C2×Dic53—28no—
298C2×Dic53—28no—
299C2×Dic53—28no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—44no—
318C2×Dic53—44no—
319C2×Dic53—44no—
320C2×Dic53C23×C414yes—
321C2×Dic53C23×C414yes—
322C2×Dic53C23×C414yes—
323C2×Dic53C22×Q814yes—
324C4×D53—416no—
325C4×D53—416no—
326C4×D53—416no—
327Dic106—416no—
328C2×#2368—531nomaximal, Sylow
329C22×C53C2×C4×Q814yes—
330C22×C53C4×#4114yes—
331C22×C53#51814yes—
332C22×C53#55114yes—
333C22×C53#55114yes—
334C22×C53#55414yes—
335C22×C53#55414yes—
336C22×C53C24×C411yescharacteristic
337C22×C53C23×Q811yescharacteristic
338C22×C53C22×#4111yescharacteristic
339C22×C53C22×#4111yescharacteristic
340C22×C53C22×#4111yescharacteristic
341C22×C53C2×H(5,𝔽2)11yescharacteristic
342C22×C53C2×H(5,𝔽2)11yescharacteristic
343C2×D53—232no—
344C2×D53—24no—
345C2×D53—24no—
346C2×D53—24no—
347C2×D53—24no—
348C2×D53—24no—
349C2×D53—24no—
350C2×D53C2×C4×Q818yes—
351C4×C53—24no—
352C4×C53—24no—
353C4×C53—24no—
354C4×C53—24no—
355C4×C53—24no—
356C4×C53—24no—
357C4×C53—42no—
358Dic53—24no—
359Dic53—24no—
360Dic53—24no—
361Dic53—24no—
362Dic53—42no—
363Dic53—42no—
364Dic53—42no—
365C22×C22⋊Q8—531no—
366#2368—5316no—
367C2×#391—531no—
368C2×#391—531no—
369C2×#387—531no—
370C2×#387—531no—
371C2×#387—531no—
372C2×#387—531no—
373C2×#385—531no—
374C2×#385—531no—
375C2×C4×C4⋊C4—531no—
376C2×C4×C4⋊C4D5311yescharacteristic, complemented
377C2×C4×C22⋊C4—531no—
378C2×C4×C22⋊C4—531no—
379C2×C4×C22⋊C4—531no—
380C22×#95—531no—
381C2×C53#236818yescomplemented
382C2×C53C22×C4×Q811yescharacteristic
383C2×C53C2×C4×#4111yescharacteristic
384C2×C53C2×#51811yescharacteristic
385C2×C53C2×#55111yescharacteristic
386C2×C53C2×#55111yescharacteristic
387C2×C53C2×#55411yescharacteristic
388C2×C53C2×#55411yescharacteristic
389D53—28no—
390C23×Q8—531no—
391C24×C4—531no—
392C24×C4—531no—
393C24×C4—531no—
394C2×C22⋊Q8—5316no—
395C2×C22⋊Q8—538no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4C2×D5311yescharacteristic
402C22×C4⋊C4C2×D5311yescharacteristic
403C22×C22⋊C4—531no—
404C22×C22⋊C4—531no—
405C22×C22⋊C4—531no—
406C22×C22⋊C4—531no—
407C22×C42—531no—
408C22×C42—531no—
409C22×C42—531no—
410C22×C42C2×D5311yescharacteristic
411C22×C42C2×D5311yescharacteristic
412C22×C42C2×D5311yescharacteristic
413#391—538no—
414#391—538no—
415#387—538no—
416#387—538no—
417#387—538no—
418#387—538no—
419#385—538no—
420#385—538no—
421C4×C4⋊C4—538no—
422C4×C4⋊C4C2×D5318yescomplemented
423C4×C22⋊C4—538no—
424C4×C22⋊C4—538no—
425C4×C22⋊C4—538no—
426C2×#95—531no—
427C2×#95—531no—
428C2×#95—531no—
429C2×#95—531no—
430C2×#95—531no—
431C2×#95—531no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—531no—
435C2×#95—531no—
436C2×#95—531no—
437C2×#95—531no—
438C2×#95—538no—
439C2×#95C2×D5311yescharacteristic
440C2×#95C2×D5311yescharacteristic
441C53C2×#236811yescharacteristic, complemented, Sylow
442C25—531no—
443C22×Q8—538no—
444C22×Q8—534no—
445C22×Q8—2122no—
446C22×Q8—2122no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—531no—
450C23×C4—531no—
451C23×C4—538no—
452C23×C4—534no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—534no—
457C23×C4—534no—
458C23×C4—1064no—
459C23×C4—1064no—
460C23×C4—1064no—
461C23×C4—1064no—
462C23×C4—2122no—
463C23×C4—2122no—
464C23×C4—2122no—
465C23×C4—2122no—
466C23×C4C22×D5311yescharacteristic
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C23×C4C22×D5311yescharacteristic
473C22⋊Q8—5364no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—538no—
476C2×C4⋊C4—538no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—534no—
482C2×C4⋊C4—1064no—
483C2×C4⋊C4—2122no—
484C2×C4⋊C4—2122no—
485C2×C4⋊C4C4×D5318yescomplemented
486C2×C4⋊C4C22×D5314yes—
487C2×C4⋊C4C22×D5314yes—
488C2×C22⋊C4—538no—
489C2×C22⋊C4—538no—
490C2×C22⋊C4—538no—
491C2×C22⋊C4—534no—
492C2×C22⋊C4—534no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—1064no—
496C2×C42—24no—
497C2×C42—42no—
498C2×C42—42no—
499C2×C42—534no—
500C2×C42—534no—
501C2×C42—534no—
502C2×C42—1064no—
503C2×C42—2122no—
504C2×C42—2122no—
505C2×C42C22×D5314yes—
506C2×C42C22×D5314yes—
507C2×C42C22×D5314yes—
508#95—534no—
509#95—534no—
510#95—534no—
511#95—534no—
512#95—534no—
513#95—534no—
514#95—534no—
515#95—534no—
516#95—534no—
517#95—534no—
518#95—534no—
519#95—534no—
520#95C22×D5314yes—
521#95C22×D5314yes—
522C24—534no—
523C24—534no—
524C24—534no—
525C24—532no—
526C24—1062no—
527C24—1062no—
528C24—1062no—
529C24—1062no—
530C24C23×D5311yescharacteristic
531C2×Q8—5316no—
532C2×Q8—21216no—
533C2×Q8—2124no—
534C2×Q8—2124no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—534no—
551C22×C4—534no—
552C22×C4—534no—
553C22×C4—534no—
554C22×C4—532no—
555C22×C4—532no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—5316no—
559C22×C4—532no—
560C22×C4—532no—
561C22×C4—532no—
562C22×C4—1068no—
563C22×C4—1068no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1062no—
568C22×C4—1062no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1068no—
582C22×C4—1068no—
583C22×C4—21216no—
584C22×C4—2124no—
585C22×C4—2124no—
586C22×C4—2124no—
587C22×C4—2124no—
588C22×C4—21216no—
589C22×C4—21216no—
590C22×C4C2×C4×D5314yes—
591C22×C4C2×C4×D5314yes—
592C22×C4C2×C4×D5314yes—
593C22×C4#1171994514yes—
594C22×C4#1171994514yes—
595C22×C4Q8×D5314yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5312yes—
598C22×C4C23×D5312yes—
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C22×C4C23×D5312yes—
602C22×C4C23×D5312yes—
603C4⋊C4—28no—
604C4⋊C4—5316no—
605C4⋊C4—5316no—
606C4⋊C4—1068no—
607C4⋊C4—2124no—
608C4⋊C4—2124no—
609C4⋊C4C2×C4×D53116yescomplemented
610C22⋊C4—5316no—
611C22⋊C4—5316no—
612C22⋊C4—5316no—
613C22⋊C4—1068no—
614C42—28no—
615C42—44no—
616C42—44no—
617C42—1068no—
618C42—2124no—
619C42—2124no—
620C23—5316no—
621C23—534no—
622C23—534no—
623C23—534no—
624C23—1068no—
625C23—1068no—
626C23—1068no—
627C23—1068no—
628C23—1068no—
629C23—1068no—
630C23—1062no—
631C23—1062no—
632C23—1062no—
633C23—1062no—
634C23C22×C4×D5312yes—
635C23C2×Q8×D5312yes—
636C23#41×D5312yes—
637C23C2×#1171994512yes—
638C23C2×#1171994512yes—
639C23#1313326212yes—
640C23#1313326312yes—
641C23C24×D5311yescharacteristic
642Q8—21216no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—534no—
666C2×C4—534no—
667C2×C4—534no—
668C2×C4—534no—
669C2×C4—1068no—
670C2×C4—1068no—
671C2×C4—1068no—
672C2×C4—1068no—
673C2×C4—1062no—
674C2×C4—1062no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1062no—
680C2×C4—1062no—
681C2×C4—1062no—
682C2×C4—1062no—
683C2×C4—1062no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1062no—
689C2×C4—1062no—
690C2×C4—21216no—
691C2×C4—21216no—
692C2×C4—21216no—
693C2×C4—2124no—
694C2×C4—2124no—
695C2×C4—2124no—
696C2×C4C22×C4×D5314yes—
697C2×C4C22×C4×D5314yes—
698C2×C4C22×C4×D5314yes—
699C2×C4C2×Q8×D5314yes—
700C2×C4C2×#1171994514yes—
701C2×C4C2×#1171994514yes—
702C22—538no—
703C22—10632no—
704C22—1064no—
705C22—1064no—
706C22—1064no—
707C22—1064no—
708C22—1064no—
709C22—1064no—
710C22C4×Q8×D5314yes—
711C22C4×#1171994514yes—
712C22#1681109514yes—
713C22#1681129714yes—
714C22#1681130214yes—
715C22#1681132814yes—
716C22#1681133314yes—
717C22C23×C4×D5311yescharacteristic
718C22C22×Q8×D5311yescharacteristic
719C22C2×#41×D5311yescharacteristic
720C22C22×#1171994511yescharacteristic
721C22C22×#1171994511yescharacteristic
722C22C2×#1313326211yescharacteristic
723C22C2×#1313326311yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—24no—
729C4—24no—
730C4—42no—
731C4—1064no—
732C4—1064no—
733C4—1064no—
734C4—1064no—
735C4—2122no—
736C4—2122no—
737C4—2122no—
738C2—1068no—
739C2#2027779918yesdirect product factor
740C2C2×C4×Q8×D5311yescharacteristic
741C2C2×C4×#1171994511yescharacteristic
742C2C2×#1681109511yescharacteristic
743C2C2×#1681129711yescharacteristic
744C2C2×#1681130211yescharacteristic
745C2C2×#1681132811yescharacteristic
746C2C2×#1681133311yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C4×C4⋊C4×C53C2
socleC24×C53C24
prime radicalC24×D53C23
cosocleC23×C53C25
hypercenterC2×C4×C4⋊C4D53
hypocenterC53C2×#2368
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20277799C2direct (N × H)
3. C2×#16810529C2semidirect
4. C2×#16810527C2semidirect
5. C2×#16810509C2semidirect
6. C2×#16810507C2semidirect
7. C2×#16810507C2semidirect
8. C2×#16810504C2semidirect
11. C2×#16810474C2semidirect
16. C2×C4×C4⋊C4×C53C2semidirect
21. C2×#13133195C4semidirect
35. #16810529C22semidirect
36. #16810527C22semidirect
37. #16810509C22semidirect
38. #16810507C22semidirect
39. #16810507C22semidirect
40. #16810504C22semidirect
43. #16810474C22semidirect
65. C4×C4⋊C4×C53C22semidirect
71. C22×Dic106C2×C4semidirect
92. #13133195C2×C4semidirect
97. C2×#11719919C2×C4semidirect
98. C2×#11719919C2×C4semidirect
106. C2×#11719921Q8semidirect
137. C2×C4⋊C4×C53C2×C4semidirect
228. C2×Dic106C22×C4semidirect
230. C4⋊C4×C53C22×C4semidirect
237. #11719921C2×Q8semidirect
241. #11719919C22×C4semidirect
242. #11719919C22×C4semidirect
376. C2×C4×C4⋊C4D53semidirect
381. C2×C53#2368semidirect
422. C4×C4⋊C4C2×D53semidirect
441. C53C2×#2368semidirect
485. C2×C4⋊C4C4×D53semidirect
609. C4⋊C4C2×C4×D53semidirect
739. C2#20277799direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331952
#202777992
C2×#168105292
C2×#168105272
C2×#168105092
C2×#168105072
C2×#168105042
C2×#168104972
C2×#168104942
C2×#168104742
C2×C4×#117199212
C2×#95×D532
C2×C4×C4⋊C4×C532
C2×#236853