Finite Group Databasebeta

← C2×#20278425 #27552577

Subgroups — C2×#20278425 #27552577

Order 13568.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133207C211yesmaximal, characteristic, complemented
2C22×#13133174C211yesmaximal, characteristic
3#20278425C2116yesmaximal, direct product factor
4C2×#16810558C211yesmaximal, characteristic
5C2×#16810558C211yesmaximal, characteristic
6C2×#16810545C211yesmaximal, characteristic
7C2×#16810545C211yesmaximal, characteristic
8C2×#16810520C211yesmaximal, characteristic, complemented
9C2×#16810518C211yesmaximal, characteristic, complemented
10C2×#16810518C211yesmaximal, characteristic, complemented
11C2×#16810510C211yesmaximal, characteristic, complemented
12C2×#16810507C211yesmaximal, characteristic, complemented
13C2×#16810492C211yesmaximal, characteristic, complemented
14C2×#16810482C211yesmaximal, characteristic
15C2×#16810470C211yesmaximal, characteristic
16C2×C53×#389C211yesmaximal, characteristic, complemented
17C23×C4×D53C2211yescharacteristic
18C2×#13133207—28no—
19C2×#13133207C2218yescomplemented
20C2×#13133174—28no—
21C2×#13133174C2218yes—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C4⋊Dic53C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×#11719921C2211yescharacteristic
37C22×#11719921C2211yescharacteristic
38C22×#11719921C2211yescharacteristic
39C22×#11719921C2211yescharacteristic
40C22×C4×Dic53C2211yescharacteristic
41C22×C4×Dic53C2211yescharacteristic
42C22×C4×Dic53C2211yescharacteristic
43#16810558C2218yes—
44#16810558C2218yes—
45#16810545C2218yes—
46#16810545C2218yes—
47#16810520C2218yescomplemented
48#16810518C2218yescomplemented
49#16810518C2218yescomplemented
50#16810510C2218yescomplemented
51#16810507C2218yescomplemented
52#16810492C2218yescomplemented
53#16810482C2218yes—
54#16810470C2218yes—
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C22×C42×C53C2211yescharacteristic
66C53×#389C2218yescomplemented
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C22×C4×D53—24no—
78C22×C4×D53—24no—
79C22×C4×D53Q818yes—
80C22×C4×D53C2314yes—
81#13133207—232no—
82#13133174—232no—
83C2×C4⋊Dic53—24no—
84C2×C4⋊Dic53—42no—
85C2×C4⋊Dic53C2314yes—
86C2×C4⋊Dic53C2314yes—
87C2×#11719919—24no—
88C2×#11719919—24no—
89C2×#11719919—24no—
90C2×#11719919—24no—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—24no—
94C2×#11719919—24no—
95C2×#11719919—42no—
96C2×#11719919D418yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×#11719919C2314yes—
100C2×#11719919C2314yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719921—24no—
108C2×#11719921—24no—
109C2×#11719921—24no—
110C2×#11719921—24no—
111C2×#11719921—42no—
112C2×#11719921—42no—
113C2×#11719921C2314yes—
114C2×#11719921C2314yes—
115C2×#11719921C2314yes—
116C2×#11719921C2314yes—
117C2×#11719921C2314yes—
118C2×#11719921C2314yes—
119C2×C4×Dic53—24no—
120C2×C4×Dic53—24no—
121C2×C4×Dic53—24no—
122C2×C4×Dic53C2314yes—
123C2×C4×Dic53C2314yes—
124C2×C4×Dic53C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129#13133124C2314yes—
130#13133124C2314yes—
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C2×C4⋊C4×C53—24no—
139C2×C4⋊C4×C53—24no—
140C2×C4⋊C4×C53—42no—
141C2×C4⋊C4×C53—42no—
142C2×C4⋊C4×C53C2314yes—
143C2×C4⋊C4×C53C2314yes—
144C2×C4⋊C4×C53C2314yes—
145C2×C4⋊C4×C53C2314yes—
146C2×C42×C53—24no—
147C2×C42×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150C24×C53C2411yescharacteristic
151C23×D53—22no—
152C23×D53—22no—
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53C2×Q814yes—
158C23×D53C2412yes—
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×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53C2×D414yes—
178C22×C4×C53C2×Q814yes—
179C22×C4×C53#4114yes—
180C22×C4×C53C2412yes—
181C22×C4×C53C2412yes—
182C22×C4×C53C2412yes—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
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×Dic53—22no—
203C22×Dic53C2×D414yes—
204C22×Dic53C2×D414yes—
205C22×Dic53C2×Q814yes—
206C22×Dic53#4114yes—
207C22×Dic53#4114yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C2×C4×D53—232no—
216C2×C4×D53—28no—
217C2×C4×D53—28no—
218C2×C4×D53C2×Q8116yes—
219C4⋊C4×C53—28no—
220C4⋊C4×C53—28no—
221C4⋊C4×C53—44no—
222C4⋊C4×C53—44no—
223C42×C53—28no—
224#11719921—28no—
225#11719921—28no—
226#11719921—28no—
227#11719921—28no—
228#11719921—44no—
229#11719921—44no—
230C4⋊Dic53—28no—
231C4⋊Dic53—44no—
232#11719919—28no—
233#11719919—28no—
234#11719919—28no—
235#11719919—28no—
236#11719919—28no—
237#11719919—28no—
238#11719919—28no—
239#11719919—28no—
240#11719919—44no—
241#11719919C2×D4116yes—
242C4×Dic53—28no—
243C4×Dic53—28no—
244C4×Dic53—28no—
245C23×C53C22×D412yes—
246C23×C53C22×Q812yes—
247C23×C53C2×#4112yes—
248C23×C53C2×#4112yes—
249C23×C53C2×#4112yes—
250C23×C53H(5,𝔽2)12yes—
251C23×C532−1+412yes—
252C23×C53C2511yescharacteristic
253C22×D53—28no—
254C22×D53—28no—
255C22×D53—28no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—22no—
261C22×D53—22no—
262C22×D53—44no—
263C22×D53—44no—
264C22×D53—44no—
265C22×D53—44no—
266C22×D53C22×Q814yes—
267C2×C4×C53—28no—
268C2×C4×C53—28no—
269C2×C4×C53—28no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
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—44no—
289C2×C4×C53—44no—
290C2×C4×C53—44no—
291C2×C4×C53—44no—
292C2×C4×C53C22×D414yes—
293C2×C4×C53C22×Q814yes—
294C2×C4×C53C2×#4114yes—
295C2×Dic53—28no—
296C2×Dic53—28no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
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—44no—
314C2×Dic53—44no—
315C2×Dic53—44no—
316C2×Dic53—44no—
317C2×Dic53C22⋊Q8116yes—
318C2×Dic53C22×D414yes—
319C2×Dic53C22×D414yes—
320C2×Dic53C22×Q814yes—
321C2×Dic53C2×#4114yes—
322C2×Dic53C2×#4114yes—
323C4×D53—232no—
324C2×#2441—531nomaximal, Sylow
325C22×C53C2×C22⋊Q814yes—
326C22×C53#53314yes—
327C22×C53#54414yes—
328C22×C53#54714yes—
329C22×C53#55014yes—
330C22×C53#55214yes—
331C22×C53#55314yes—
332C22×C53C23×D411yescharacteristic
333C22×C53C23×Q811yescharacteristic
334C22×C53C22×#4111yescharacteristic
335C22×C53C22×#4111yescharacteristic
336C22×C53C22×#4111yescharacteristic
337C22×C53C2×H(5,𝔽2)11yescharacteristic
338C22×C53C2×2−1+411yescharacteristic
339C2×D53—24no—
340C2×D53—24no—
341C2×D53—24no—
342C2×D53—42no—
343C2×D53—416no—
344C2×D53—42no—
345C2×D53—42no—
346C2×D53—42no—
347C4×C53—24no—
348C4×C53—24no—
349C4×C53—24no—
350C4×C53—42no—
351C4×C53—42no—
352C4×C53—42no—
353C4×C53—42no—
354Dic53—24no—
355Dic53—24no—
356Dic53—42no—
357Dic53—42no—
358Dic53—42no—
359Dic53—42no—
360Dic53C2×C22⋊Q818yes—
361C22×#125—531no—
362C22×#117—531no—
363#2441—5316no—
364C2×#399—531no—
365C2×#399—531no—
366C2×#396—531no—
367C2×#396—531no—
368C2×#389—531no—
369C2×#389—531no—
370C2×#389—531no—
371C2×#389D5311yescharacteristic, complemented
372C2×#387—531no—
373C2×#387—531no—
374C2×#384—531no—
375C2×#380—531no—
376C2×C4×C22⋊C4—531no—
377C2×C53#244118yescomplemented
378C2×C53C22×C22⋊Q811yescharacteristic
379C2×C53C2×#53311yescharacteristic
380C2×C53C2×#54411yescharacteristic
381C2×C53C2×#54711yescharacteristic
382C2×C53C2×#55011yescharacteristic
383C2×C53C2×#55211yescharacteristic
384C2×C53C2×#55311yescharacteristic
385D53—44no—
386C24×C4—531no—
387C2×#125—538no—
388C2×#125—1068no—
389C2×#117—538no—
390C2×#117—1068no—
391C22×C4⋊C4—531no—
392C22×C4⋊C4—531no—
393C22×C4⋊C4—531no—
394C22×C4⋊C4—531no—
395C22×C4⋊C4—531no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—531no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4C2×D5311yescharacteristic
404C22×C4⋊C4C2×D5311yescharacteristic
405C22×C4⋊C4C2×D5311yescharacteristic
406C22×C4⋊C4C2×D5311yescharacteristic
407C22×C22⋊C4—531no—
408C22×C22⋊C4—531no—
409C22×C22⋊C4—531no—
410C22×C22⋊C4—531no—
411C22×C22⋊C4—531no—
412C22×C22⋊C4—531no—
413C22×C42—531no—
414C22×C42—531no—
415C22×C42—531no—
416C22×C42C2×D5311yescharacteristic
417#399—538no—
418#399—538no—
419#396—538no—
420#396—538no—
421#389—538no—
422#389—538no—
423#389—538no—
424#389C2×D5318yescomplemented
425#387—538no—
426#387—538no—
427#384—538no—
428#380—538no—
429C4×C22⋊C4—538no—
430C2×#95—531no—
431C2×#95—531no—
432C2×#95—531no—
433C2×#95—531no—
434C2×#95—531no—
435C2×#95—531no—
436C2×#95C2×D5311yescharacteristic
437C2×#95C2×D5311yescharacteristic
438C53C2×#244111yescharacteristic, complemented, Sylow
439C25—531no—
440C23×C4—531no—
441C23×C4—531no—
442C23×C4—531no—
443C23×C4—538no—
444C23×C4—534no—
445C23×C4—531no—
446C23×C4—531no—
447C23×C4—531no—
448C23×C4—531no—
449C23×C4—1064no—
450C23×C4—1064no—
451C23×C4C22×D5311yescharacteristic
452C23×C4C22×D5311yescharacteristic
453C23×C4C22×D5311yescharacteristic
454C23×C4C22×D5311yescharacteristic
455C23×C4C22×D5311yescharacteristic
456C23×C4C22×D5311yescharacteristic
457C23×C4C22×D5311yescharacteristic
458#125—10632no—
459#117—10632no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—538no—
465C2×C4⋊C4—534no—
466C2×C4⋊C4—534no—
467C2×C4⋊C4—534no—
468C2×C4⋊C4—534no—
469C2×C4⋊C4—534no—
470C2×C4⋊C4—534no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—534no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—1064no—
478C2×C4⋊C4—1064no—
479C2×C4⋊C4—1064no—
480C2×C4⋊C4—1064no—
481C2×C4⋊C4—1064no—
482C2×C4⋊C4—1064no—
483C2×C4⋊C4—1064no—
484C2×C4⋊C4—1064no—
485C2×C4⋊C4—1064no—
486C2×C4⋊C4—2122no—
487C2×C4⋊C4—2122no—
488C2×C4⋊C4C22×D5314yes—
489C2×C4⋊C4C22×D5314yes—
490C2×C4⋊C4C22×D5314yes—
491C2×C4⋊C4C22×D5314yes—
492C2×C22⋊C4—534no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—534no—
497C2×C22⋊C4—534no—
498C2×C22⋊C4—1064no—
499C2×C22⋊C4—1064no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—2122no—
503C2×C22⋊C4—2122no—
504C2×C42—24no—
505C2×C42—534no—
506C2×C42—534no—
507C2×C42—534no—
508C2×C42—1064no—
509C2×C42—1064no—
510C2×C42—1064no—
511C2×C42C22×D5314yes—
512#95—534no—
513#95—534no—
514#95—534no—
515#95—534no—
516#95—534no—
517#95—534no—
518#95C22×D5314yes—
519#95C22×D5314yes—
520C24—534no—
521C24—532no—
522C24—1062no—
523C24—1062no—
524C24—1062no—
525C24—1062no—
526C24—1062no—
527C24—1062no—
528C24C23×D5311yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
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—534no—
548C22×C4—534no—
549C22×C4—534no—
550C22×C4—532no—
551C22×C4—534no—
552C22×C4—534no—
553C22×C4—532no—
554C22×C4—532no—
555C22×C4—5316no—
556C22×C4—532no—
557C22×C4—532no—
558C22×C4—532no—
559C22×C4—532no—
560C22×C4—1068no—
561C22×C4—10632no—
562C22×C4—1068no—
563C22×C4—1062no—
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#1171994514yes—
580C22×C4D4×D5314yes—
581C22×C4Q8×D5314yes—
582C22×C4C23×D5312yes—
583C22×C4C23×D5312yes—
584C22×C4C23×D5312yes—
585C22×C4C23×D5312yes—
586C22×C4C23×D5312yes—
587C22×C4C23×D5312yes—
588C22×C4C23×D5312yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—5316no—
594C4⋊C4—1068no—
595C4⋊C4—1068no—
596C4⋊C4—1068no—
597C4⋊C4—1068no—
598C4⋊C4—1068no—
599C4⋊C4—1068no—
600C4⋊C4—1068no—
601C4⋊C4—1068no—
602C4⋊C4—1068no—
603C4⋊C4—2124no—
604C4⋊C4—2124no—
605C22⋊C4—1068no—
606C22⋊C4—1068no—
607C22⋊C4—1068no—
608C22⋊C4—1068no—
609C22⋊C4—2124no—
610C22⋊C4—2124no—
611C42—28no—
612C42—1068no—
613C42—1068no—
614C42—1068no—
615C23—534no—
616C23—1068no—
617C23—1068no—
618C23—1062no—
619C23—1062no—
620C23—1062no—
621C23—1062no—
622C23—1062no—
623C23—1062no—
624C23—1068no—
625C23—2124no—
626C23—2124no—
627C23—2124no—
628C23—2124no—
629C23C2×D4×D5312yes—
630C23C2×Q8×D5312yes—
631C23#41×D5312yes—
632C23#41×D5312yes—
633C23C2×#1171994512yes—
634C23#1313326212yes—
635C23#1313326512yes—
636C23C24×D5311yescharacteristic
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
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—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—5316no—
663C2×C4—534no—
664C2×C4—534no—
665C2×C4—534no—
666C2×C4—534no—
667C2×C4—534no—
668C2×C4—10632no—
669C2×C4—1068no—
670C2×C4—1068no—
671C2×C4—1062no—
672C2×C4—1062no—
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—2124no—
688C2×C4—2124no—
689C2×C4—2124no—
690C2×C4—2124no—
691C2×C4C2×D4×D5314yes—
692C2×C4C2×Q8×D5314yes—
693C2×C4C2×#1171994514yes—
694C22—1064no—
695C22—1064no—
696C22—1064no—
697C22—21216no—
698C22—2122no—
699C22—2122no—
700C22—2122no—
701C22—2122no—
702C22C22⋊Q8×D5314yes—
703C22#1681117714yes—
704C22#1681125014yes—
705C22#1681127414yes—
706C22#1681129114yes—
707C22#1681130514yes—
708C22#1681132214yes—
709C22C22×D4×D5311yescharacteristic
710C22C22×Q8×D5311yescharacteristic
711C22C2×#41×D5311yescharacteristic
712C22C2×#41×D5311yescharacteristic
713C22C22×#1171994511yescharacteristic
714C22C2×#1313326211yescharacteristic
715C22C2×#1313326511yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—538no—
724C4—1064no—
725C4—1064no—
726C4—2122no—
727C4—2122no—
728C4—2122no—
729C4—2122no—
730C2—2124no—
731C2#2027842518yesdirect product factor
732C2C2×C22⋊Q8×D5311yescharacteristic
733C2C2×#1681117711yescharacteristic
734C2C2×#1681125011yescharacteristic
735C2C2×#1681127411yescharacteristic
736C2C2×#1681129111yescharacteristic
737C2C2×#1681130511yescharacteristic
738C2C2×#1681132211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#389C2
socleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53C2×#2441
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#13133207C2semidirect
3. #20278425C2direct (N × H)
8. C2×#16810520C2semidirect
9. C2×#16810518C2semidirect
10. C2×#16810518C2semidirect
11. C2×#16810510C2semidirect
12. C2×#16810507C2semidirect
13. C2×#16810492C2semidirect
16. C2×C53×#389C2semidirect
19. C2×#13133207C22semidirect
47. #16810520C22semidirect
48. #16810518C22semidirect
49. #16810518C22semidirect
50. #16810510C22semidirect
51. #16810507C22semidirect
52. #16810492C22semidirect
66. C53×#389C22semidirect
371. C2×#389D53semidirect
377. C2×C53#2441semidirect
424. #389C2×D53semidirect
438. C53C2×#2441semidirect
731. C2#20278425direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332072
C22×#131331742
#202784252
C2×#168105582
C2×#168105452
C2×#168105202
C2×#168105182
C2×#168105102
C2×#168105072
C2×#168104922
C2×#168104822
C2×#168104702
C2×C53×#3892
C2×#244153