Finite Group Databasebeta

← C2×#20278438 #27552177

Subgroups — C2×#20278438 #27552177

Order 13568.

2942 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×#13133207C211yesmaximal, characteristic, complemented
2C23×#11719919C211yesmaximal, characteristic
3#20278438C2116yesmaximal, direct product factor
4C2×#16810564C211yesmaximal, characteristic, complemented
5C2×#16810563C211yesmaximal, characteristic, complemented
6C2×#16810556C211yesmaximal, characteristic, complemented
7C2×#16810554C211yesmaximal, characteristic, complemented
8C2×#16810520C211yesmaximal, characteristic, complemented
9C2×#16810518C211yesmaximal, characteristic, complemented
10C2×#16810495C211yesmaximal, characteristic
11C2×#16810487C211yesmaximal, characteristic, complemented
12C2×#16810483C211yesmaximal, characteristic
13C2×#16810481C211yesmaximal, characteristic
14C2×#16810481C211yesmaximal, characteristic
15C2×C22⋊C4×Dic53C211yesmaximal, characteristic
16C2×C53×#385C211yesmaximal, characteristic
17C24×Dic53C2211yescharacteristic
18C24×Dic53C2211yescharacteristic
19C2×#13133207—28no—
20C2×#13133207C2218yescomplemented
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×#11719919—28no—
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2218yes—
29C22×#11719919C2211yescharacteristic
30C22×#11719919C2211yescharacteristic
31C22×#11719919C2211yescharacteristic
32C22×#11719919C2211yescharacteristic
33C22×#11719919C2211yescharacteristic
34C22×#11719919C2211yescharacteristic
35C22×C22⋊Dic53C2211yescharacteristic
36C22×C22⋊Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810564C2218yescomplemented
40#16810563C2218yescomplemented
41#16810556C2218yescomplemented
42#16810554C2218yescomplemented
43#16810520C2218yescomplemented
44#16810518C2218yescomplemented
45#16810495C2218yes—
46#16810487C2218yescomplemented
47#16810483C2218yes—
48#16810481C2218yes—
49#16810481C2218yes—
50C22⋊C4×Dic53C2218yes—
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C2×#13133124C2211yescharacteristic
61C24×C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C53×#385C2218yes—
67C2×#95×C53C2211yescharacteristic
68C2×#95×C53C2211yescharacteristic
69C23×Dic53—24no—
70C23×Dic53—24no—
71C23×Dic53—24no—
72C23×Dic53—24no—
73C23×Dic53—42no—
74C23×Dic53Q818yes—
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2314yes—
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2314yes—
84C23×Dic53C2311yescharacteristic
85#13133207—232no—
86C2×C4⋊Dic53—24no—
87C2×C4⋊Dic53—42no—
88C2×C4⋊Dic53C2314yes—
89C2×C4⋊Dic53C2314yes—
90C2×#11719919—232no—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—24no—
94C2×#11719919—24no—
95C2×#11719919—24no—
96C2×#11719919—24no—
97C2×#11719919—24no—
98C2×#11719919—42no—
99C2×#11719919—42no—
100C2×#11719919D418yes—
101C2×#11719919C2314yes—
102C2×#11719919C2314yes—
103C2×#11719919C2314yes—
104C2×#11719919C2314yes—
105C2×#11719919C2314yes—
106C2×#11719919C2314yes—
107C2×#11719919C2314yes—
108C2×#11719919C2314yes—
109C2×#11719919C2314yes—
110C2×#11719919C2314yes—
111C2×C22⋊Dic53—24no—
112C2×C22⋊Dic53—24no—
113C2×C22⋊Dic53C2314yes—
114C2×C22⋊Dic53C2314yes—
115C2×C4×Dic53—24no—
116C2×C4×Dic53—24no—
117C2×C4×Dic53C2314yes—
118C2×C4×Dic53C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127#13133124C2314yes—
128#13133124C2314yes—
129C25×C53C2311yescharacteristic
130C23×C4×C53—24no—
131C23×C4×C53—24no—
132C23×C4×C53—42no—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2314yes—
139C23×C4×C53C2311yescharacteristic
140C2×C4⋊C4×C53—24no—
141C2×C4⋊C4×C53—42no—
142C2×C4⋊C4×C53C2314yes—
143C2×C4⋊C4×C53C2314yes—
144C2×C22⋊C4×C53—24no—
145C2×C22⋊C4×C53—24no—
146C2×C22⋊C4×C53C2314yes—
147C2×C22⋊C4×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53C2×Q814yes—
155C24×C53#4114yes—
156C24×C53#4114yes—
157C24×C53C2412yes—
158C24×C53C2411yescharacteristic
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—28no—
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×C53—28no—
178C22×C4×C53—44no—
179C22×C4×C53—416no—
180C22×C4×C53C2×D414yes—
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—232no—
192C22×Dic53—28no—
193C22×Dic53—28no—
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×Dic53—28no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—28no—
211C22×Dic53—44no—
212C22×Dic53—416no—
213C22×Dic53C2×D414yes—
214C22×Dic53C2×D414yes—
215C22×Dic53C2×Q814yes—
216C22×Dic53C2×Q8116yes—
217C22×Dic53C2×Q814yes—
218C22×Dic53#4114yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C4⋊C4×C53—28no—
228C4⋊C4×C53—44no—
229C22⋊C4×C53—28no—
230C22⋊C4×C53—28no—
231C22⋊Dic53—28no—
232C22⋊Dic53—28no—
233C4⋊Dic53—28no—
234C4⋊Dic53—44no—
235#11719919—28no—
236#11719919—28no—
237#11719919—28no—
238#11719919—28no—
239#11719919—28no—
240#11719919—28no—
241#11719919—28no—
242#11719919—44no—
243#11719919—44no—
244#11719919C2×D4116yes—
245C4×Dic53—28no—
246C4×Dic53—28no—
247C23×C53—28no—
248C23×C53—28no—
249C23×C53—28no—
250C23×C53—28no—
251C23×C53—28no—
252C23×C53—28no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—22no—
256C23×C53—22no—
257C23×C53#125116yescomplemented
258C23×C53C22×D412yes—
259C23×C53C22×Q814yes—
260C23×C53C22×Q812yes—
261C23×C53C2×#4112yes—
262C23×C53C2×#4114yes—
263C23×C53C2×#4112yes—
264C23×C53C2×#4114yes—
265C23×C53C2×#4112yes—
266C23×C53H(5,𝔽2)12yes—
267C23×C532−1+412yes—
268C23×C53C2511yescharacteristic
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—416no—
288C2×C4×C53—44no—
289C2×C4×C53—44no—
290C2×C4×C53—44no—
291C2×C4×C53—44no—
292C2×C4×C53—44no—
293C2×C4×C53C22×D414yes—
294C2×Dic53—28no—
295C2×Dic53—28no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—232no—
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—416no—
317C2×Dic53—44no—
318C2×Dic53—44no—
319C2×Dic53—44no—
320C2×Dic53—44no—
321C2×Dic53—44no—
322C2×Dic53C22⋊Q8116yes—
323C2×Dic53C22×D414yes—
324C2×Dic53C22×D414yes—
325C2×Dic53C22×Q814yes—
326C2×Dic53C22×Q814yes—
327C2×Dic53C2×#4114yes—
328C2×#2442—531nomaximal, Sylow
329C22×C53—24no—
330C22×C53—24no—
331C22×C53—24no—
332C22×C53—24no—
333C22×C53—232no—
334C22×C53—24no—
335C22×C53—24no—
336C22×C53C2×C22⋊Q814yes—
337C22×C53C2×#12514yes—
338C22×C53C2×#12518yescomplemented
339C22×C53#54414yes—
340C22×C53#54614yes—
341C22×C53#54814yes—
342C22×C53#55214yes—
343C22×C53#55314yes—
344C22×C53C23×D411yescharacteristic
345C22×C53C23×Q811yescharacteristic
346C22×C53C22×#4111yescharacteristic
347C22×C53C22×#4111yescharacteristic
348C22×C53C22×#4111yescharacteristic
349C22×C53C2×H(5,𝔽2)11yescharacteristic
350C22×C53C2×2−1+411yescharacteristic
351C4×C53—24no—
352C4×C53—42no—
353C4×C53—42no—
354C4×C53—42no—
355C4×C53—42no—
356C4×C53—42no—
357Dic53—24no—
358Dic53—24no—
359Dic53—42no—
360Dic53—42no—
361Dic53—42no—
362Dic53—42no—
363Dic53—42no—
364Dic53C2×C22⋊Q818yes—
365C22×#125—531no—
366C23×C4⋊C4—531no—
367#2442—5316no—
368C2×#400—531no—
369C2×#400—531no—
370C2×#398—531no—
371C2×#398—531no—
372C2×#389—531no—
373C2×#389—531no—
374C2×#385—531no—
375C2×#385D5311yescharacteristic
376C2×#382—531no—
377C2×#380—531no—
378C2×#380—531no—
379C2×#380—531no—
380C2×C4×C22⋊C4—531no—
381C2×C53—28no—
382C2×C53#244218yescomplemented
383C2×C53C22×C22⋊Q811yescharacteristic
384C2×C53C22×#12511yescharacteristic
385C2×C53C2×#54411yescharacteristic
386C2×C53C2×#54611yescharacteristic
387C2×C53C2×#54811yescharacteristic
388C2×C53C2×#55211yescharacteristic
389C2×C53C2×#55311yescharacteristic
390C24×C4—531no—
391C24×C4—531no—
392C24×C4C2×D5311yescharacteristic
393C2×#125—538no—
394C2×#125—1068no—
395C22×C4⋊C4—531no—
396C22×C4⋊C4—531no—
397C22×C4⋊C4—531no—
398C22×C4⋊C4—531no—
399C22×C4⋊C4—531no—
400C22×C4⋊C4—538no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—531no—
408C22×C4⋊C4—1068no—
409C22×C4⋊C4C2×D5311yescharacteristic
410C22×C4⋊C4C2×D5311yescharacteristic
411C22×C22⋊C4—531no—
412C22×C22⋊C4—531no—
413C22×C22⋊C4C2×D5311yescharacteristic
414C22×C22⋊C4C2×D5311yescharacteristic
415C22×C42—531no—
416C22×C42—531no—
417#400—538no—
418#400—538no—
419#398—538no—
420#398—538no—
421#389—538no—
422#389—538no—
423#385—538no—
424#385C2×D5318yes—
425#382—538no—
426#380—538no—
427#380—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×#95—531no—
437C2×#95—531no—
438C2×#95—531no—
439C2×#95—531no—
440C2×#95C2×D5311yescharacteristic
441C2×#95C2×D5311yescharacteristic
442C53C2×#244211yescharacteristic, complemented, Sylow
443C25C22×D5311yescharacteristic
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—42no—
447C23×C4—531no—
448C23×C4—538no—
449C23×C4—534no—
450C23×C4—531no—
451C23×C4—531no—
452C23×C4—531no—
453C23×C4—531no—
454C23×C4—531no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—534no—
458C23×C4—1064no—
459C23×C4—1064no—
460C23×C4—1064no—
461C23×C4—1064no—
462C23×C4—2122no—
463C23×C4C22×D5311yescharacteristic
464C23×C4C22×D5311yescharacteristic
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5314yes—
469C23×C4C22×D5311yescharacteristic
470#125—10632no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—538no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—534no—
482C2×C4⋊C4—534no—
483C2×C4⋊C4—534no—
484C2×C4⋊C4—534no—
485C2×C4⋊C4—534no—
486C2×C4⋊C4—10632no—
487C2×C4⋊C4—1064no—
488C2×C4⋊C4—1064no—
489C2×C4⋊C4—1064no—
490C2×C4⋊C4—1064no—
491C2×C4⋊C4—1064no—
492C2×C4⋊C4—1064no—
493C2×C4⋊C4—1064no—
494C2×C4⋊C4—1064no—
495C2×C4⋊C4—2122no—
496C2×C4⋊C4—2122no—
497C2×C4⋊C4—2122no—
498C2×C4⋊C4C22×D5314yes—
499C2×C4⋊C4C22×D5314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—1064no—
505C2×C22⋊C4—1064no—
506C2×C22⋊C4C22×D5314yes—
507C2×C22⋊C4C22×D5314yes—
508C2×C42—534no—
509C2×C42—534no—
510C2×C42—1064no—
511C2×C42—1064no—
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#95—534no—
521#95—534no—
522#95C22×D5314yes—
523#95C22×D5314yes—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24#1171994514yes—
529C24#1171994714yes—
530C24Q8×D5314yes—
531C24C23×D5312yes—
532C24C23×D5311yescharacteristic
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—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—534no—
555C22×C4—534no—
556C22×C4—534no—
557C22×C4—532no—
558C22×C4—534no—
559C22×C4—5316no—
560C22×C4—534no—
561C22×C4—532no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—1068no—
569C22×C4—10632no—
570C22×C4—1068no—
571C22×C4—1068no—
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—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—2124no—
593C22×C4—21216no—
594C22×C4D4×D5314yes—
595C22×C4C23×D5312yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5312yes—
598C22×C4C23×D5312yes—
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C4⋊C4—28no—
602C4⋊C4—44no—
603C4⋊C4—5316no—
604C4⋊C4—1068no—
605C4⋊C4—1068no—
606C4⋊C4—1068no—
607C4⋊C4—1068no—
608C4⋊C4—1068no—
609C4⋊C4—1068no—
610C4⋊C4—1068no—
611C4⋊C4—1068no—
612C4⋊C4—2124no—
613C4⋊C4—2124no—
614C4⋊C4—2124no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—1068no—
618C22⋊C4—1068no—
619C42—1068no—
620C42—1068no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—28no—
630C23—28no—
631C23#13133207116yescomplemented
632C23C2×D4×D5312yes—
633C23C2×Q8×D5314yes—
634C23C2×Q8×D5312yes—
635C23#41×D5312yes—
636C23C2×#1171994714yes—
637C23C2×#1171994712yes—
638C23C2×#1171994514yes—
639C23C2×#1171994512yes—
640C23#1313326212yes—
641C23#1313326412yes—
642C23C24×D5311yescharacteristic
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—28no—
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—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—5316no—
668C2×C4—534no—
669C2×C4—534no—
670C2×C4—534no—
671C2×C4—534no—
672C2×C4—534no—
673C2×C4—10632no—
674C2×C4—1068no—
675C2×C4—1062no—
676C2×C4—1062no—
677C2×C4—1062no—
678C2×C4—1062no—
679C2×C4—1068no—
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—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—21216no—
696C2×C4—2124no—
697C2×C4—2124no—
698C2×C4—2124no—
699C2×C4—2124no—
700C2×C4—2124no—
701C2×C4C2×D4×D5314yes—
702C22—24no—
703C22—24no—
704C22—232no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—24no—
709C22C22⋊Q8×D5314yes—
710C22C2×#1313320714yes—
711C22C2×#1313320718yescomplemented
712C22#1681125214yes—
713C22#1681126014yes—
714C22#1681128214yes—
715C22#1681131014yes—
716C22#1681132214yes—
717C22C22×D4×D5311yescharacteristic
718C22C22×Q8×D5311yescharacteristic
719C22C2×#41×D5311yescharacteristic
720C22C22×#1171994711yescharacteristic
721C22C22×#1171994511yescharacteristic
722C22C2×#1313326211yescharacteristic
723C22C2×#1313326411yescharacteristic
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—538no—
731C4—1064no—
732C4—1064no—
733C4—2122no—
734C4—2122no—
735C4—2122no—
736C4—2122no—
737C4—2122no—
738C2—28no—
739C2#2027843818yesdirect product factor
740C2C2×C22⋊Q8×D5311yescharacteristic
741C2C22×#1313320711yescharacteristic
742C2C2×#1681125211yescharacteristic
743C2C2×#1681126011yescharacteristic
744C2C2×#1681128211yescharacteristic
745C2C2×#1681131011yescharacteristic
746C2C2×#1681132211yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53C2×#2442
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#13133207C2semidirect
3. #20278438C2direct (N × H)
4. C2×#16810564C2semidirect
5. C2×#16810563C2semidirect
6. C2×#16810556C2semidirect
7. C2×#16810554C2semidirect
8. C2×#16810520C2semidirect
9. C2×#16810518C2semidirect
11. C2×#16810487C2semidirect
20. C2×#13133207C22semidirect
39. #16810564C22semidirect
40. #16810563C22semidirect
41. #16810556C22semidirect
42. #16810554C22semidirect
43. #16810520C22semidirect
44. #16810518C22semidirect
46. #16810487C22semidirect
257. C23×C53#125semidirect
338. C22×C53C2×#125semidirect
382. C2×C53#2442semidirect
442. C53C2×#2442semidirect
631. C23#13133207semidirect
711. C22C2×#13133207semidirect
739. C2#20278438direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332072
C23×#117199192
#202784382
C2×#168105642
C2×#168105632
C2×#168105562
C2×#168105542
C2×#168105202
C2×#168105182
C2×#168104952
C2×#168104872
C2×#168104832
C2×#168104812
C2×C22⋊C4×Dic532
C2×C53×#3852
C2×#244253