Finite Group Databasebeta

← C2×#20277828 #27543773

Subgroups — C2×#20277828 #27543773

Order 13568.

2726 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×#13133212C211yesmaximal, characteristic
2#20277828C2116yesmaximal, direct product factor
3C2×#16810520C211yesmaximal, characteristic, complemented
4C2×#16810515C211yesmaximal, characteristic
5C2×#16810512C211yesmaximal, characteristic
6C2×#16810512C211yesmaximal, characteristic
7C2×#16810508C211yesmaximal, characteristic, complemented
8C2×#16810505C211yesmaximal, characteristic, complemented
9C2×#16810494C211yesmaximal, characteristic
10C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
12C2×#16810474C211yesmaximal, characteristic, complemented
13C2×C4×#11719921C211yesmaximal, characteristic
14C2×#16810470C211yesmaximal, characteristic
15C2×#16810469C211yesmaximal, characteristic, complemented
16C2×C53×#387C211yesmaximal, characteristic, complemented
17C23×C4×D53C2211yescharacteristic
18C2×#13133212C4116yescomplemented
19C2×#13133212C2218yes—
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810520C2218yescomplemented
40#16810515C2218yes—
41#16810512C2218yes—
42#16810512C2218yes—
43#16810508C2218yescomplemented
44#16810505C2218yescomplemented
45#16810494C2218yes—
46C4⋊C4×Dic53C2218yescomplemented
47C4⋊C4×Dic53C2218yescomplemented
48#16810474C2218yescomplemented
49C4×#11719921C2218yes—
50#16810470C2218yes—
51#16810469C2218yescomplemented
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C42×C53C2211yescharacteristic
63C53×#387C2218yescomplemented
64C2×#95×C53C2211yescharacteristic
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C24×D53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C22×C4×D53—24no—
77C22×C4×D53—24no—
78C22×C4×D53—42no—
79C22×C4×D53C2314yes—
80#13133212C2×C4164yescomplemented
81C2×C4⋊Dic53—24no—
82C2×C4⋊Dic53C2×C418yescomplemented
83C2×C4⋊Dic53C2314yes—
84C2×C4⋊Dic53C2314yes—
85C2×#11719919—24no—
86C2×#11719919—24no—
87C2×#11719919—42no—
88C2×#11719919C2×C418yescomplemented
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719921—24no—
94C2×#11719921—24no—
95C2×#11719921—42no—
96C2×#11719921C2×C418yes—
97C2×#11719921C2×C418yes—
98C2×#11719921C2×C418yes—
99C2×#11719921C2314yes—
100C2×#11719921C2314yes—
101C2×#11719921C2314yes—
102C2×#11719921C2314yes—
103C2×#11719921C2314yes—
104C2×#11719921C2314yes—
105C2×C4×Dic53—24no—
106C2×C4×Dic53—24no—
107C2×C4×Dic53—24no—
108C2×C4×Dic53—42no—
109C2×C4×Dic53—42no—
110C2×C4×Dic53—42no—
111C2×C4×Dic53C2×C418yescomplemented
112C2×C4×Dic53C2314yes—
113C2×C4×Dic53C2314yes—
114C2×C4×Dic53C2314yes—
115C2×C4×Dic53C2314yes—
116C2×C4×Dic53C2314yes—
117C2×C4×Dic53C2314yes—
118C2×C4×Dic53C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123#13133124C2314yes—
124#13133124C2314yes—
125#13133124C2314yes—
126#13133124C2314yes—
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C2×C4⋊C4×C53—24no—
135C2×C4⋊C4×C53C2×C418yescomplemented
136C2×C4⋊C4×C53C2314yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C42×C53—24no—
139C2×C42×C53C2314yes—
140#95×C53C2314yes—
141#95×C53C2314yes—
142#95×C53C2314yes—
143#95×C53C2314yes—
144C24×C53C2411yescharacteristic
145C23×D53—22no—
146C23×D53—22no—
147C23×D53—22no—
148C23×D53—22no—
149C23×D53—22no—
150C23×D53—22no—
151C23×D53C22×C414yes—
152C23×D53C2412yes—
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—22no—
170C22×C4×C53C22×C414yes—
171C22×C4×C53C22×C414yes—
172C22×C4×C53C22×C414yes—
173C22×C4×C53#4114yes—
174C22×C4×C53C2412yes—
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×Dic53C22×C414yes—
197C22×Dic53C22×C414yes—
198C22×Dic53C22×C414yes—
199C22×Dic53#4114yes—
200C22×Dic53#4114yes—
201C22×Dic53#4114yes—
202C22×Dic53C2412yes—
203C22×Dic53C2412yes—
204C22×Dic53C2412yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C2×C4×D53—28no—
210C2×C4×D53—28no—
211C2×C4×D53—44no—
212C2×C4×D53—416no—
213C4⋊C4×C53—28no—
214C4⋊C4×C53C22×C4116yescomplemented
215C42×C53—28no—
216#11719921—28no—
217#11719921—28no—
218#11719921—44no—
219#11719921C22×C4116yes—
220#11719921C22×C4116yes—
221#11719921C22×C4116yes—
222C4⋊Dic53—28no—
223C4⋊Dic53C22×C4116yescomplemented
224#11719919—28no—
225#11719919—28no—
226#11719919—44no—
227#11719919C22×C4116yescomplemented
228C4×Dic53—28no—
229C4×Dic53—28no—
230C4×Dic53—28no—
231C4×Dic53—44no—
232C4×Dic53—44no—
233C4×Dic53—44no—
234C4×Dic53C22×C4116yescomplemented
235C23×C53C23×C412yes—
236C23×C53C2×#4112yes—
237C23×C53C2×#4112yes—
238C23×C53C2×#4112yes—
239C23×C53C2×#4112yes—
240C23×C53H(5,𝔽2)12yes—
241C23×C532−1+412yes—
242C23×C53C2511yescharacteristic
243C22×D53—28no—
244C22×D53—28no—
245C22×D53—28no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—44no—
253C22×D53—44no—
254C22×D53—44no—
255C22×D53—44no—
256C22×D53C23×C414yes—
257C2×C4×C53—28no—
258C2×C4×C53—28no—
259C2×C4×C53—28no—
260C2×C4×C53—28no—
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—22no—
276C2×C4×C53—22no—
277C2×C4×C53—22no—
278C2×C4×C53—44no—
279C2×C4×C53—44no—
280C2×C4×C53—44no—
281C2×C4×C53C23×C414yes—
282C2×C4×C53C23×C414yes—
283C2×C4×C53C23×C414yes—
284C2×C4×C53C2×#4114yes—
285C2×Dic53—28no—
286C2×Dic53—28no—
287C2×Dic53—28no—
288C2×Dic53—28no—
289C2×Dic53—28no—
290C2×Dic53—28no—
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×Dic53C23×C414yes—
308C2×Dic53C23×C414yes—
309C2×Dic53C23×C414yes—
310C2×Dic53C2×#4114yes—
311C2×Dic53C2×#4114yes—
312C2×Dic53C2×#4114yes—
313C4×D53—416no—
314C2×#2373—531nomaximal, Sylow
315C22×C53C4×#4114yes—
316C22×C53C4×#4114yes—
317C22×C53#52014yes—
318C22×C53#55114yes—
319C22×C53#55214yes—
320C22×C53#55314yes—
321C22×C53#55614yes—
322C22×C53C24×C411yescharacteristic
323C22×C53C22×#4111yescharacteristic
324C22×C53C22×#4111yescharacteristic
325C22×C53C22×#4111yescharacteristic
326C22×C53C22×#4111yescharacteristic
327C22×C53C2×H(5,𝔽2)11yescharacteristic
328C22×C53C2×2−1+411yescharacteristic
329C2×D53—24no—
330C2×D53—24no—
331C2×D53—24no—
332C2×D53—416no—
333C2×D53—42no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C4×C53—24no—
338C4×C53—24no—
339C4×C53—24no—
340C4×C53—24no—
341C4×C53—42no—
342C4×C53—42no—
343C4×C53—42no—
344Dic53—24no—
345Dic53—24no—
346Dic53—24no—
347Dic53—24no—
348Dic53—24no—
349Dic53—24no—
350Dic53—42no—
351C22×#126—531no—
352#2373—5316no—
353C2×#389—531no—
354C2×#388—531no—
355C2×#388—531no—
356C2×#388—531no—
357C2×#387—531no—
358C2×#387—531no—
359C2×#387D5311yescharacteristic, complemented
360C2×#385—531no—
361C2×C4×C4⋊C4—531no—
362C2×C4×C4⋊C4—531no—
363C2×C4×C4⋊C4—531no—
364C2×C4×C22⋊C4—531no—
365C2×C4×C22⋊C4—531no—
366C2×#376—531no—
367C2×C53#237318yescomplemented
368C2×C53C2×C4×#4111yescharacteristic
369C2×C53C2×C4×#4111yescharacteristic
370C2×C53C2×#52011yescharacteristic
371C2×C53C2×#55111yescharacteristic
372C2×C53C2×#55211yescharacteristic
373C2×C53C2×#55311yescharacteristic
374C2×C53C2×#55611yescharacteristic
375D53—44no—
376C24×C4—531no—
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⋊C4C2×D5311yescharacteristic
386C22×C4⋊C4C2×D5311yescharacteristic
387C22×C22⋊C4—531no—
388C22×C22⋊C4—531no—
389C22×C22⋊C4—531no—
390C22×C22⋊C4—531no—
391C22×C22⋊C4—531no—
392C22×C22⋊C4—531no—
393C22×C42—531no—
394C22×C42—531no—
395C22×C42—531no—
396C22×C42—531no—
397C22×C42—531no—
398C22×C42—531no—
399C22×C42—531no—
400C22×C42C2×D5311yescharacteristic
401#389—538no—
402#388—538no—
403#388—538no—
404#388—538no—
405#387—538no—
406#387—538no—
407#387C2×D5318yescomplemented
408#385—538no—
409C4×C4⋊C4—538no—
410C4×C4⋊C4—538no—
411C4×C4⋊C4—538no—
412C4×C22⋊C4—538no—
413C4×C22⋊C4—538no—
414#376—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×#95C2×D5311yescharacteristic
424C2×#95C2×D5311yescharacteristic
425C2×#95C2×D5311yescharacteristic
426C2×#95C2×D5311yescharacteristic
427C53C2×#237311yescharacteristic, complemented, Sylow
428C25—531no—
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—534no—
437C23×C4—1064no—
438C23×C4—1064no—
439C23×C4—2122no—
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5311yescharacteristic
447#126—5364no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—538no—
450C2×C4⋊C4—538no—
451C2×C4⋊C4—534no—
452C2×C4⋊C4—534no—
453C2×C4⋊C4—534no—
454C2×C4⋊C4—534no—
455C2×C4⋊C4—534no—
456C2×C4⋊C4—534no—
457C2×C4⋊C4—1064no—
458C2×C4⋊C4—1064no—
459C2×C4⋊C4—1064no—
460C2×C4⋊C4—2122no—
461C2×C4⋊C4C4×D5318yescomplemented
462C2×C4⋊C4C22×D5314yes—
463C2×C4⋊C4C22×D5314yes—
464C2×C22⋊C4—538no—
465C2×C22⋊C4—538no—
466C2×C22⋊C4—538no—
467C2×C22⋊C4—534no—
468C2×C22⋊C4—534no—
469C2×C22⋊C4—534no—
470C2×C22⋊C4—534no—
471C2×C22⋊C4—534no—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—1064no—
474C2×C22⋊C4—1064no—
475C2×C22⋊C4—2122no—
476C2×C42—24no—
477C2×C42—538no—
478C2×C42—534no—
479C2×C42—534no—
480C2×C42—534no—
481C2×C42—534no—
482C2×C42—534no—
483C2×C42—534no—
484C2×C42—534no—
485C2×C42—1064no—
486C2×C42—1064no—
487C2×C42—1064no—
488C2×C42—2122no—
489C2×C42—2122no—
490C2×C42—2122no—
491C2×C42C22×D5314yes—
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#95C22×D5314yes—
501#95C22×D5314yes—
502#95C22×D5314yes—
503#95C22×D5314yes—
504C24—534no—
505C24—532no—
506C24—1062no—
507C24—1062no—
508C24—1062no—
509C24—1062no—
510C24—1062no—
511C24—1062no—
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—22no—
530C22×C4—534no—
531C22×C4—534no—
532C22×C4—534no—
533C22×C4—534no—
534C22×C4—534no—
535C22×C4—534no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—532no—
539C22×C4—532no—
540C22×C4—532no—
541C22×C4—532no—
542C22×C4—532no—
543C22×C4—1068no—
544C22×C4—1062no—
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—1068no—
560C22×C4—2124no—
561C22×C4—21216no—
562C22×C4C2×C4×D5314yes—
563C22×C4C2×C4×D5314yes—
564C22×C4C2×C4×D5314yes—
565C22×C4#1171994714yes—
566C22×C4C23×D5312yes—
567C22×C4C23×D5312yes—
568C22×C4C23×D5312yes—
569C22×C4C23×D5312yes—
570C22×C4C23×D5312yes—
571C22×C4C23×D5312yes—
572C22×C4C23×D5312yes—
573C4⋊C4—28no—
574C4⋊C4—5316no—
575C4⋊C4—5316no—
576C4⋊C4—1068no—
577C4⋊C4—1068no—
578C4⋊C4—1068no—
579C4⋊C4—2124no—
580C4⋊C4C2×C4×D53116yescomplemented
581C22⋊C4—5316no—
582C22⋊C4—5316no—
583C22⋊C4—5316no—
584C22⋊C4—1068no—
585C22⋊C4—1068no—
586C22⋊C4—2124no—
587C42—28no—
588C42—5316no—
589C42—1068no—
590C42—1068no—
591C42—1068no—
592C42—2124no—
593C42—2124no—
594C42—2124no—
595C23—534no—
596C23—1068no—
597C23—1068no—
598C23—1068no—
599C23—1062no—
600C23—1062no—
601C23—1062no—
602C23—1062no—
603C23—1062no—
604C23—1062no—
605C23—2124no—
606C23—2124no—
607C23—2124no—
608C23—2124no—
609C23C22×C4×D5312yes—
610C23#41×D5312yes—
611C23#41×D5312yes—
612C23#41×D5312yes—
613C23C2×#1171994712yes—
614C23#1313326312yes—
615C23#1313326512yes—
616C23C24×D5311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
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—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—534no—
642C2×C4—534no—
643C2×C4—534no—
644C2×C4—534no—
645C2×C4—534no—
646C2×C4—534no—
647C2×C4—1068no—
648C2×C4—1068no—
649C2×C4—1068no—
650C2×C4—1068no—
651C2×C4—1068no—
652C2×C4—1068no—
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—21216no—
669C2×C4—2124no—
670C2×C4C22×C4×D5314yes—
671C2×C4C22×C4×D5314yes—
672C2×C4C22×C4×D5314yes—
673C2×C4C2×#1171994714yes—
674C22—1064no—
675C22—1064no—
676C22—1064no—
677C22—2122no—
678C22—21216no—
679C22—2122no—
680C22—2122no—
681C22—2122no—
682C22C4×#1171994714yes—
683C22#1681109114yes—
684C22#1681110514yes—
685C22#1681129614yes—
686C22#1681130514yes—
687C22#1681132414yes—
688C22#1681134414yes—
689C22C23×C4×D5311yescharacteristic
690C22C2×#41×D5311yescharacteristic
691C22C2×#41×D5311yescharacteristic
692C22C2×#41×D5311yescharacteristic
693C22C22×#1171994711yescharacteristic
694C22C2×#1313326311yescharacteristic
695C22C2×#1313326511yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—1064no—
704C4—1064no—
705C4—1064no—
706C4—1064no—
707C4—1064no—
708C4—1064no—
709C4—2122no—
710C2—2124no—
711C2#2027782818yesdirect product factor
712C2C2×C4×#1171994711yescharacteristic
713C2C2×#1681109111yescharacteristic
714C2C2×#1681110511yescharacteristic
715C2C2×#1681129611yescharacteristic
716C2C2×#1681130511yescharacteristic
717C2C2×#1681132411yescharacteristic
718C2C2×#1681134411yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#387C2
socleC24×C53C24
prime radicalC24×D53C23
cosocleC23×C53C25
hypercenterC2×#387D53
hypocenterC53C2×#2373
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #20277828C2direct (N × H)
3. C2×#16810520C2semidirect
7. C2×#16810508C2semidirect
8. C2×#16810505C2semidirect
10. C2×C4⋊C4×Dic53C2semidirect
11. C2×C4⋊C4×Dic53C2semidirect
12. C2×#16810474C2semidirect
15. C2×#16810469C2semidirect
16. C2×C53×#387C2semidirect
18. C2×#13133212C4semidirect
39. #16810520C22semidirect
43. #16810508C22semidirect
44. #16810505C22semidirect
46. C4⋊C4×Dic53C22semidirect
47. C4⋊C4×Dic53C22semidirect
48. #16810474C22semidirect
51. #16810469C22semidirect
63. C53×#387C22semidirect
80. #13133212C2×C4semidirect
82. C2×C4⋊Dic53C2×C4semidirect
88. C2×#11719919C2×C4semidirect
111. C2×C4×Dic53C2×C4semidirect
135. C2×C4⋊C4×C53C2×C4semidirect
214. C4⋊C4×C53C22×C4semidirect
223. C4⋊Dic53C22×C4semidirect
227. #11719919C22×C4semidirect
234. C4×Dic53C22×C4semidirect
359. C2×#387D53semidirect
367. C2×C53#2373semidirect
407. #387C2×D53semidirect
427. C53C2×#2373semidirect
461. C2×C4⋊C4C4×D53semidirect
580. C4⋊C4C2×C4×D53semidirect
711. C2#20277828direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332122
#202778282
C2×#168105202
C2×#168105152
C2×#168105122
C2×#168105082
C2×#168105052
C2×#168104942
C2×C4⋊C4×Dic532
C2×#168104742
C2×C4×#117199212
C2×#168104702
C2×#168104692
C2×C53×#3872
C2×#237353