Finite Group Databasebeta

← C2×#20277903 #27546751

Subgroups — C2×#20277903 #27546751

Order 13568.

2502 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133210C211yesmaximal, characteristic
2#20277903C2116yesmaximal, direct product factor
3C2×#16810520C211yesmaximal, characteristic, complemented
4C2×#16810519C211yesmaximal, characteristic, complemented
5C2×#16810518C211yesmaximal, characteristic, complemented
6C2×#16810517C211yesmaximal, characteristic
7C2×#16810516C211yesmaximal, characteristic
8C2×#16810511C211yesmaximal, characteristic
9C2×#16810506C211yesmaximal, characteristic, complemented
10C2×#16810505C211yesmaximal, characteristic, complemented
11C2×#16810504C211yesmaximal, characteristic, complemented
12C2×#16810496C211yesmaximal, characteristic
13C2×#16810496C211yesmaximal, characteristic
14C2×#16810492C211yesmaximal, characteristic, complemented
15C2×#16810490C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic
17C2×#13133210C4116yescomplemented
18C2×#13133210C2218yes—
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719919C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37#16810520C2218yescomplemented
38#16810519C2218yescomplemented
39#16810518C2218yescomplemented
40#16810517C2218yes—
41#16810516C2218yes—
42#16810511C2218yes—
43#16810506C2218yescomplemented
44#16810505C2218yescomplemented
45#16810504C2218yescomplemented
46#16810496C2218yes—
47#16810496C2218yes—
48#16810492C2218yescomplemented
49#16810490C2218yescomplemented
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C24×C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C53×#385C2218yes—
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76#13133210C2×C4164yescomplemented
77C2×C4⋊Dic53—42no—
78C2×C4⋊Dic53C2×C418yescomplemented
79C2×C4⋊Dic53C2314yes—
80C2×C4⋊Dic53C2314yes—
81C2×#11719919—42no—
82C2×#11719919—42no—
83C2×#11719919—42no—
84C2×#11719919—42no—
85C2×#11719919—42no—
86C2×#11719919—42no—
87C2×#11719919C2×C418yescomplemented
88C2×#11719919C2×C418yescomplemented
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×C22⋊Dic53—42no—
98C2×C22⋊Dic53—42no—
99C2×C22⋊Dic53C2×C418yes—
100C2×C22⋊Dic53C2×C418yes—
101C2×C22⋊Dic53C2314yes—
102C2×C22⋊Dic53C2314yes—
103C2×C22⋊Dic53C2314yes—
104C2×C22⋊Dic53C2314yes—
105C2×C4×Dic53—42no—
106C2×C4×Dic53—42no—
107C2×C4×Dic53—42no—
108C2×C4×Dic53C2×C418yescomplemented
109C2×C4×Dic53C2314yes—
110C2×C4×Dic53C2314yes—
111C2×C4×Dic53C2314yes—
112C2×C4×Dic53C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123C25×C53C2311yescharacteristic
124C23×C4×C53—42no—
125C23×C4×C53—42no—
126C23×C4×C53—42no—
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2314yes—
134C2×C4⋊C4×C53—42no—
135C2×C4⋊C4×C53—42no—
136C2×C4⋊C4×C53C2314yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C22⋊C4×C53—42no—
139C2×C22⋊C4×C53C2×C418yes—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142#95×C53C2314yes—
143#95×C53C2314yes—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53C22×C414yes—
151C24×C53C2412yes—
152C24×C53C2411yescharacteristic
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
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—44no—
170C22×C4×C53—44no—
171C22×C4×C53—44no—
172C22×C4×C53—416no—
173C22×C4×C53C22×C414yes—
174C22×C4×C53C22×C414yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
179C22×C4×C53C2412yes—
180C22×C4×C53C2412yes—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
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×Dic53C22×C414yes—
202C22×Dic53C22×C414yes—
203C22×Dic53C22×C414yes—
204C22×Dic53C22×C414yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C4⋊C4×C53—44no—
214C4⋊C4×C53—44no—
215C22⋊C4×C53—44no—
216C22⋊C4×C53C22×C4116yes—
217C22⋊Dic53—44no—
218C22⋊Dic53—44no—
219C22⋊Dic53C22×C4116yes—
220C22⋊Dic53C22×C4116yes—
221C4⋊Dic53—44no—
222C4⋊Dic53C22×C4116yescomplemented
223#11719919—44no—
224#11719919—44no—
225#11719919—44no—
226#11719919—44no—
227#11719919—44no—
228#11719919—44no—
229#11719919C22×C4116yescomplemented
230#11719919C22×C4116yescomplemented
231C4×Dic53—44no—
232C4×Dic53—44no—
233C4×Dic53—44no—
234C4×Dic53C22×C4116yescomplemented
235C23×C53—28no—
236C23×C53—28no—
237C23×C53—28no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—44no—
245C23×C53—44no—
246C23×C53—44no—
247C23×C53—44no—
248C23×C53C23×C414yes—
249C23×C53C23×C412yes—
250C23×C53H(5,𝔽2)12yes—
251C23×C53H(5,𝔽2)12yes—
252C23×C53H(5,𝔽2)12yes—
253C23×C532−1+412yes—
254C23×C532−1+412yes—
255C23×C532−1+412yes—
256C23×C53C2511yescharacteristic
257C2×C4×C53—28no—
258C2×C4×C53—28no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—416no—
276C2×C4×C53—44no—
277C2×C4×C53—44no—
278C2×C4×C53—44no—
279C2×C4×C53—44no—
280C2×C4×C53C23×C414yes—
281C2×C4×C53C23×C414yes—
282C2×Dic53—28no—
283C2×Dic53—28no—
284C2×Dic53—28no—
285C2×Dic53—28no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
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—44no—
307C2×Dic53—44no—
308C2×Dic53—44no—
309C2×Dic53—44no—
310C2×Dic53C23×C414yes—
311C2×Dic53C23×C414yes—
312C2×Dic53C23×C414yes—
313C2×Dic53C23×C414yes—
314C2×#2383—531nomaximal, Sylow
315C22×C53—24no—
316C22×C53—24no—
317C22×C53—24no—
318C22×C53—416no—
319C22×C53—42no—
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53#52014yes—
324C22×C53#52014yes—
325C22×C53#52014yes—
326C22×C53#56014yes—
327C22×C53#56314yes—
328C22×C53#56314yes—
329C22×C53#56314yes—
330C22×C53C24×C411yescharacteristic
331C22×C53C2×H(5,𝔽2)11yescharacteristic
332C22×C53C2×H(5,𝔽2)11yescharacteristic
333C22×C53C2×H(5,𝔽2)11yescharacteristic
334C22×C53C2×2−1+411yescharacteristic
335C22×C53C2×2−1+411yescharacteristic
336C22×C53C2×2−1+411yescharacteristic
337C4×C53—24no—
338C4×C53—24no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342C4×C53—42no—
343Dic53—24no—
344Dic53—24no—
345Dic53—24no—
346Dic53—24no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—42no—
351C22×#126—531no—
352#2383—5316no—
353C2×#389—531no—
354C2×#389—531no—
355C2×#389—531no—
356C2×#388—531no—
357C2×#388—531no—
358C2×#388—531no—
359C2×#387—531no—
360C2×#387—531no—
361C2×#387—531no—
362C2×#385—531no—
363C2×#385—531no—
364C2×#385D5311yescharacteristic
365C2×#384—531no—
366C2×#383—531no—
367C2×C53—44no—
368C2×C53#238318yescomplemented
369C2×C53C2×#52011yescharacteristic
370C2×C53C2×#52011yescharacteristic
371C2×C53C2×#52011yescharacteristic
372C2×C53C2×#56011yescharacteristic
373C2×C53C2×#56311yescharacteristic
374C2×C53C2×#56311yescharacteristic
375C2×C53C2×#56311yescharacteristic
376C24×C4C2×D5311yescharacteristic
377C2×#126—5316no—
378C2×#126—538no—
379C22×C4⋊C4—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—531no—
384C22×C4⋊C4—531no—
385C22×C4⋊C4—531no—
386C22×C4⋊C4—531no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4C2×D5311yescharacteristic
390C22×C4⋊C4C2×D5311yescharacteristic
391C22×C22⋊C4—531no—
392C22×C22⋊C4—531no—
393C22×C22⋊C4—531no—
394C22×C22⋊C4—531no—
395C22×C22⋊C4C2×D5311yescharacteristic
396C22×C22⋊C4C2×D5311yescharacteristic
397C22×C42—531no—
398C22×C42—531no—
399C22×C42—531no—
400C22×C42—531no—
401#389—538no—
402#389—538no—
403#389—538no—
404#388—538no—
405#388—538no—
406#388—538no—
407#387—538no—
408#387—538no—
409#387—538no—
410#385—538no—
411#385—538no—
412#385C2×D5318yes—
413#384—538no—
414#383—538no—
415C2×#95—531no—
416C2×#95—531no—
417C2×#95—531no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95—531no—
423C2×#95—531no—
424C2×#95—531no—
425C2×#95C2×D5311yescharacteristic
426C2×#95C2×D5311yescharacteristic
427C53C2×#238311yescharacteristic, complemented, Sylow
428C25C22×D5311yescharacteristic
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—531no—
438C23×C4—531no—
439C23×C4—531no—
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5314yes—
447#126—5364no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—538no—
451C2×C4⋊C4—538no—
452C2×C4⋊C4—538no—
453C2×C4⋊C4—534no—
454C2×C4⋊C4—534no—
455C2×C4⋊C4—534no—
456C2×C4⋊C4—534no—
457C2×C4⋊C4—534no—
458C2×C4⋊C4—534no—
459C2×C4⋊C4—534no—
460C2×C4⋊C4—534no—
461C2×C4⋊C4—534no—
462C2×C4⋊C4—534no—
463C2×C4⋊C4—2122no—
464C2×C4⋊C4—2122no—
465C2×C4⋊C4—2122no—
466C2×C4⋊C4—2122no—
467C2×C4⋊C4—2122no—
468C2×C4⋊C4—2122no—
469C2×C4⋊C4—2122no—
470C2×C4⋊C4C22×D5314yes—
471C2×C4⋊C4C22×D5314yes—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—538no—
474C2×C22⋊C4—538no—
475C2×C22⋊C4—534no—
476C2×C22⋊C4—534no—
477C2×C22⋊C4—534no—
478C2×C22⋊C4—534no—
479C2×C22⋊C4—2122no—
480C2×C22⋊C4—2122no—
481C2×C22⋊C4C4×D5318yes—
482C2×C22⋊C4C22×D5314yes—
483C2×C22⋊C4C22×D5314yes—
484C2×C42—538no—
485C2×C42—534no—
486C2×C42—534no—
487C2×C42—534no—
488C2×C42—534no—
489C2×C42—2122no—
490C2×C42—2122no—
491C2×C42—2122no—
492#95—534no—
493#95—534no—
494#95—534no—
495#95—534no—
496#95—534no—
497#95—534no—
498#95—534no—
499#95—534no—
500#95—534no—
501#95—534no—
502#95C22×D5314yes—
503#95C22×D5314yes—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C2×C4×D5314yes—
511C24C23×D5312yes—
512C24C23×D5311yescharacteristic
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—416no—
533C22×C4—534no—
534C22×C4—534no—
535C22×C4—534no—
536C22×C4—534no—
537C22×C4—532no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—532no—
543C22×C4—532no—
544C22×C4—532no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—1062no—
558C22×C4—1062no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4C2×C4×D5314yes—
566C22×C4C2×C4×D5314yes—
567C22×C4C23×D5312yes—
568C22×C4C23×D5312yes—
569C22×C4C23×D5312yes—
570C22×C4C23×D5312yes—
571C22×C4C23×D5312yes—
572C22×C4C23×D5312yes—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—5316no—
576C4⋊C4—5316no—
577C4⋊C4—5316no—
578C4⋊C4—2124no—
579C4⋊C4—2124no—
580C4⋊C4—2124no—
581C4⋊C4—2124no—
582C4⋊C4—2124no—
583C4⋊C4—2124no—
584C4⋊C4—2124no—
585C22⋊C4—44no—
586C22⋊C4—5316no—
587C22⋊C4—5316no—
588C22⋊C4—2124no—
589C22⋊C4—2124no—
590C22⋊C4C2×C4×D53116yes—
591C42—5316no—
592C42—2124no—
593C42—2124no—
594C42—2124no—
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C22×C4×D5314yes—
609C23C22×C4×D5312yes—
610C23#1313326212yes—
611C23#1313326212yes—
612C23#1313326212yes—
613C23#1313326412yes—
614C23#1313326412yes—
615C23#1313326512yes—
616C23C24×D5311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—416no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—534no—
641C2×C4—534no—
642C2×C4—534no—
643C2×C4—534no—
644C2×C4—1068no—
645C2×C4—1068no—
646C2×C4—1068no—
647C2×C4—1068no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1062no—
663C2×C4—1062no—
664C2×C4—1062no—
665C2×C4—1062no—
666C2×C4—1062no—
667C2×C4—1062no—
668C2×C4—2124no—
669C2×C4—2124no—
670C2×C4—2124no—
671C2×C4—2124no—
672C2×C4C22×C4×D5314yes—
673C2×C4C22×C4×D5314yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—42no—
679C22—42no—
680C22—42no—
681C22—416no—
682C22#1681110214yes—
683C22#1681110214yes—
684C22#1681110414yes—
685C22#1681136214yes—
686C22#1681137414yes—
687C22#1681137414yes—
688C22#1681137614yes—
689C22C23×C4×D5311yescharacteristic
690C22C2×#1313326211yescharacteristic
691C22C2×#1313326211yescharacteristic
692C22C2×#1313326211yescharacteristic
693C22C2×#1313326411yescharacteristic
694C22C2×#1313326411yescharacteristic
695C22C2×#1313326511yescharacteristic
696C4—24no—
697C4—24no—
698C4—42no—
699C4—42no—
700C4—42no—
701C4—42no—
702C4—1064no—
703C4—1064no—
704C4—1064no—
705C4—1064no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C2—44no—
711C2#2027790318yesdirect product factor
712C2C2×#1681110211yescharacteristic
713C2C2×#1681110211yescharacteristic
714C2C2×#1681110411yescharacteristic
715C2C2×#1681136211yescharacteristic
716C2C2×#1681137411yescharacteristic
717C2C2×#1681137411yescharacteristic
718C2C2×#1681137611yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC25×C53C23
cosocleC23×C53C25
hypercenterC2×#385D53
hypocenterC53C2×#2383
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #20277903C2direct (N × H)
3. C2×#16810520C2semidirect
4. C2×#16810519C2semidirect
5. C2×#16810518C2semidirect
9. C2×#16810506C2semidirect
10. C2×#16810505C2semidirect
11. C2×#16810504C2semidirect
14. C2×#16810492C2semidirect
15. C2×#16810490C2semidirect
17. C2×#13133210C4semidirect
37. #16810520C22semidirect
38. #16810519C22semidirect
39. #16810518C22semidirect
43. #16810506C22semidirect
44. #16810505C22semidirect
45. #16810504C22semidirect
48. #16810492C22semidirect
49. #16810490C22semidirect
76. #13133210C2×C4semidirect
78. C2×C4⋊Dic53C2×C4semidirect
87. C2×#11719919C2×C4semidirect
88. C2×#11719919C2×C4semidirect
108. C2×C4×Dic53C2×C4semidirect
222. C4⋊Dic53C22×C4semidirect
229. #11719919C22×C4semidirect
230. #11719919C22×C4semidirect
234. C4×Dic53C22×C4semidirect
368. C2×C53#2383semidirect
427. C53C2×#2383semidirect
711. C2#20277903direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332102
#202779032
C2×#168105202
C2×#168105192
C2×#168105182
C2×#168105172
C2×#168105162
C2×#168105112
C2×#168105062
C2×#168105052
C2×#168105042
C2×#168104962
C2×#168104922
C2×#168104902
C2×C53×#3852
C2×#238353