Finite Group Databasebeta

← C2×#20278790 #27552298

Subgroups — C2×#20278790 #27552298

Order 13568.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133212C211yesmaximal, characteristic
2#20278790C2116yesmaximal, direct product factor
3C2×#16810562C211yesmaximal, characteristic, complemented
4C2×#16810545C211yesmaximal, characteristic
5C2×#16810542C211yesmaximal, characteristic, complemented
6C2×#16810534C211yesmaximal, characteristic
7C2×#16810521C211yesmaximal, characteristic, complemented
8C2×#16810514C211yesmaximal, characteristic
9C2×#16810514C211yesmaximal, characteristic
10C2×#16810514C211yesmaximal, characteristic
11C2×#16810513C211yesmaximal, characteristic
12C2×#16810509C211yesmaximal, characteristic, complemented
13C2×#16810507C211yesmaximal, characteristic, complemented
14C2×#16810504C211yesmaximal, characteristic, complemented
15C2×C4×#11719919C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C53C211yesmaximal, characteristic, complemented
17C2×#13133212—28no—
18C2×#13133212C2218yes—
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810562C2218yescomplemented
36#16810545C2218yes—
37#16810542C2218yescomplemented
38#16810534C2218yes—
39#16810521C2218yescomplemented
40#16810514C2218yes—
41#16810514C2218yes—
42#16810514C2218yes—
43#16810513C2218yes—
44#16810509C2218yescomplemented
45#16810507C2218yescomplemented
46#16810504C2218yescomplemented
47C4×#11719919C2218yescomplemented
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C23×Q8×C53C2211yescharacteristic
61C2×C4×Q8×C53—28no—
62C2×C4×Q8×C53C2218yescomplemented
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C4⋊C4×C53C2211yescharacteristic
65C22×C4⋊C4×C53C2211yescharacteristic
66C22×C42×C53C2211yescharacteristic
67C22×C42×C53C2211yescharacteristic
68C22×C42×C53C2211yescharacteristic
69C24×D53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77#13133212—232no—
78C2×C4⋊Dic53—24no—
79C2×C4⋊Dic53—24no—
80C2×C4⋊Dic53C2314yes—
81C2×C4⋊Dic53C2314yes—
82C2×#11719919—24no—
83C2×#11719919—24no—
84C2×#11719919—24no—
85C2×#11719919—24no—
86C2×#11719919—24no—
87C2×#11719919C2314yes—
88C2×#11719919C2314yes—
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×#11719919C2314yes—
92C2×#11719921—24no—
93C2×#11719921—24no—
94C2×#11719921—24no—
95C2×#11719921—24no—
96C2×#11719921—24no—
97C2×#11719921—24no—
98C2×#11719921—24no—
99C2×#11719921C2314yes—
100C2×#11719921C2314yes—
101C2×#11719921C2314yes—
102C2×#11719921C2314yes—
103C2×#11719921C2314yes—
104C2×#11719921C2314yes—
105C2×#11719921C2314yes—
106C2×C4×Dic53—24no—
107C2×C4×Dic53—24no—
108C2×C4×Dic53C2314yes—
109C2×C4×Dic53C2314yes—
110#13133124C2314yes—
111#13133124C2314yes—
112#13133124C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122C22×Q8×C53—24no—
123C22×Q8×C53—24no—
124C22×Q8×C53—24no—
125C22×Q8×C53C2314yes—
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C4×Q8×C53—232no—
134C2×C4⋊C4×C53—24no—
135C2×C4⋊C4×C53—24no—
136C2×C4⋊C4×C53D418yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C4⋊C4×C53C2314yes—
139C2×C4⋊C4×C53C2314yes—
140C2×C42×C53—24no—
141C2×C42×C53—24no—
142C2×C42×C53—24no—
143C2×C42×C53C2314yes—
144C2×C42×C53C2314yes—
145C2×C42×C53C2314yes—
146C24×C53C2411yescharacteristic
147C23×D53—22no—
148C23×D53—22no—
149C23×D53—22no—
150C23×D53—22no—
151C23×D53—22no—
152C23×D53—22no—
153C23×D53—22no—
154C23×D53C2412yes—
155C2×Q8×C53—232no—
156C2×Q8×C53—28no—
157C2×Q8×C53—28no—
158C2×Q8×C53—28no—
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×C53C2×D414yes—
175C22×C4×C53C2×D414yes—
176C22×C4×C53C2×D414yes—
177C22×C4×C53#4114yes—
178C22×C4×C53#4114yes—
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×Dic53—22no—
204C22×Dic53—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53#4114yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C4⋊C4×C53—28no—
216C4⋊C4×C53—28no—
217C4⋊C4×C53C2×D4116yes—
218C42×C53—28no—
219C42×C53—28no—
220C42×C53—28no—
221#11719921—28no—
222#11719921—28no—
223#11719921—28no—
224#11719921—28no—
225#11719921—28no—
226#11719921—28no—
227#11719921—28no—
228C4⋊Dic53—28no—
229C4⋊Dic53—28no—
230#11719919—28no—
231#11719919—28no—
232#11719919—28no—
233#11719919—28no—
234#11719919—28no—
235C4×Dic53—28no—
236C4×Dic53—28no—
237C23×C53C22×D412yes—
238C23×C53C2×#4112yes—
239C23×C53C2×#4112yes—
240C23×C53C2×#4112yes—
241C23×C53C2×#4112yes—
242C23×C532−1+412yes—
243C23×C532−1+412yes—
244C23×C53C2511yescharacteristic
245C22×D53—22no—
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×D53—44no—
257C22×D53—44no—
258C22×D53—44no—
259Q8×C53—232no—
260C2×C4×C53—28no—
261C2×C4×C53—28no—
262C2×C4×C53—28no—
263C2×C4×C53—28no—
264C2×C4×C53—28no—
265C2×C4×C53—28no—
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—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—44no—
282C2×C4×C53C22×D414yes—
283C2×C4×C53C22×D414yes—
284C2×C4×C53C22×D414yes—
285C2×C4×C53C2×#4114yes—
286C2×C4×C53C2×#4114yes—
287C2×C4×C53C2×#4114yes—
288C2×Dic53—28no—
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—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—44no—
310C2×Dic53—44no—
311C2×Dic53—44no—
312C2×Dic53—44no—
313C2×Dic53—44no—
314C2×Dic53—44no—
315C2×Dic53C2×#4114yes—
316C2×#2469—531nomaximal, Sylow
317C22×C53#52514yes—
318C22×C53#52914yes—
319C22×C53#54114yes—
320C22×C53#54714yes—
321C22×C53#54814yes—
322C22×C53#55614yes—
323C22×C53#55614yes—
324C22×C53C23×D411yescharacteristic
325C22×C53C22×#4111yescharacteristic
326C22×C53C22×#4111yescharacteristic
327C22×C53C22×#4111yescharacteristic
328C22×C53C22×#4111yescharacteristic
329C22×C53C2×2−1+411yescharacteristic
330C22×C53C2×2−1+411yescharacteristic
331C2×D53—42no—
332C2×D53—42no—
333C2×D53—42no—
334C2×D53—42no—
335C2×D53—42no—
336C2×D53—42no—
337C2×D53—42no—
338C2×D53—88no—
339C4×C53—24no—
340C4×C53—24no—
341C4×C53—24no—
342C4×C53—24no—
343C4×C53—24no—
344C4×C53—24no—
345C4×C53—42no—
346Dic53—24no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—42no—
351Dic53—42no—
352Dic53—42no—
353C22×#126—531no—
354C22×C4×Q8D5311yescharacteristic, complemented
355#2469—5316no—
356C2×#400—531no—
357C2×#396—531no—
358C2×#395—531no—
359C2×#393—531no—
360C2×#389—531no—
361C2×#388—531no—
362C2×#388—531no—
363C2×#388—531no—
364C2×#388—531no—
365C2×#387—531no—
366C2×#387—531no—
367C2×#387—531no—
368C2×C4×C4⋊C4—531no—
369C2×C53#246918yescomplemented
370C2×C53C2×#52511yescharacteristic
371C2×C53C2×#52911yescharacteristic
372C2×C53C2×#54111yescharacteristic
373C2×C53C2×#54711yescharacteristic
374C2×C53C2×#54811yescharacteristic
375C2×C53C2×#55611yescharacteristic
376C2×C53C2×#55611yescharacteristic
377D53—82no—
378C23×Q8C2×D5311yescharacteristic
379C2×#126—538no—
380C2×#126—1068no—
381C2×C4×Q8—28no—
382C2×C4×Q8C2×D5318yescomplemented
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⋊C4—531no—
390C22×C4⋊C4C2×D5311yescharacteristic
391C22×C4⋊C4C2×D5311yescharacteristic
392C22×C4⋊C4C2×D5311yescharacteristic
393C22×C22⋊C4—531no—
394C22×C22⋊C4—531no—
395C22×C22⋊C4—531no—
396C22×C22⋊C4—531no—
397C22×C22⋊C4—531no—
398C22×C22⋊C4—531no—
399C22×C22⋊C4—531no—
400C22×C42—531no—
401C22×C42—531no—
402C22×C42C2×D5311yescharacteristic
403C22×C42C2×D5311yescharacteristic
404C22×C42C2×D5311yescharacteristic
405#400—538no—
406#396—538no—
407#395—538no—
408#393—538no—
409#389—538no—
410#388—538no—
411#388—538no—
412#388—538no—
413#388—538no—
414#387—538no—
415#387—538no—
416#387—538no—
417C4×C4⋊C4—538no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95—531no—
423C2×#95—531no—
424C2×#95—531no—
425C2×#95—531no—
426C2×#95—531no—
427C2×#95—531no—
428C2×#95—531no—
429C2×#95—531no—
430C53C2×#246911yescharacteristic, complemented, Sylow
431C25—531no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C22×D5314yes—
436C23×C4—531no—
437C23×C4—531no—
438C23×C4—531no—
439C23×C4—531no—
440C23×C4—531no—
441C23×C4—531no—
442C23×C4—531no—
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5311yescharacteristic
447C23×C4C22×D5311yescharacteristic
448C23×C4C22×D5311yescharacteristic
449C23×C4C22×D5311yescharacteristic
450#126—10632no—
451C4×Q8—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
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—1064no—
462C2×C4⋊C4—1064no—
463C2×C4⋊C4—1064no—
464C2×C4⋊C4—1064no—
465C2×C4⋊C4—1064no—
466C2×C4⋊C4—1064no—
467C2×C4⋊C4—1064no—
468C2×C4⋊C4C22⋊D5318yes—
469C2×C4⋊C4C22×D5314yes—
470C2×C4⋊C4C22×D5314yes—
471C2×C4⋊C4C22×D5314yes—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—534no—
474C2×C22⋊C4—534no—
475C2×C22⋊C4—534no—
476C2×C22⋊C4—534no—
477C2×C22⋊C4—534no—
478C2×C22⋊C4—534no—
479C2×C22⋊C4—1064no—
480C2×C22⋊C4—1064no—
481C2×C22⋊C4—1064no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—1064no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—534no—
490C2×C42—534no—
491C2×C42—1064no—
492C2×C42—1064no—
493C2×C42C22×D5314yes—
494C2×C42C22×D5314yes—
495C2×C42C22×D5314yes—
496#95—534no—
497#95—534no—
498#95—534no—
499#95—534no—
500#95—534no—
501#95—534no—
502#95—534no—
503#95—534no—
504#95—534no—
505#95—534no—
506#95—534no—
507#95—534no—
508C24—532no—
509C24—1062no—
510C24—1062no—
511C24—1062no—
512C24—1062no—
513C24—1062no—
514C24—1062no—
515C24—1062no—
516C24C23×D5311yescharacteristic
517C2×Q8—232no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
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—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
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—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—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4#1171994514yes—
565C22×C4#1171994514yes—
566C22×C4#1171994914yes—
567C22×C4C2×C22⋊D5314yes—
568C22×C4C2×C22⋊D5314yes—
569C22×C4C2×C22⋊D5314yes—
570C22×C4C23×D5312yes—
571C22×C4C23×D5312yes—
572C22×C4C23×D5312yes—
573C22×C4C23×D5312yes—
574C22×C4C23×D5312yes—
575C22×C4C23×D5312yes—
576C22×C4C23×D5312yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—1068no—
580C4⋊C4—1068no—
581C4⋊C4—1068no—
582C4⋊C4—1068no—
583C4⋊C4—1068no—
584C4⋊C4—1068no—
585C4⋊C4—1068no—
586C4⋊C4C2×C22⋊D53116yes—
587C22⋊C4—1068no—
588C22⋊C4—1068no—
589C22⋊C4—1068no—
590C22⋊C4—1068no—
591C22⋊C4—1068no—
592C22⋊C4—1068no—
593C22⋊C4—1068no—
594C42—28no—
595C42—28no—
596C42—28no—
597C42—1068no—
598C42—1068no—
599C23—1062no—
600C23—1062no—
601C23—1062no—
602C23—1062no—
603C23—1062no—
604C23—1062no—
605C23—1062no—
606C23—2124no—
607C23—2124no—
608C23—2124no—
609C23—2124no—
610C23—2124no—
611C23—2124no—
612C23—2124no—
613C23C22×C22⋊D5312yes—
614C23#41×D5312yes—
615C23C2×#1171994512yes—
616C23C2×#1171994512yes—
617C23C2×#1171994912yes—
618C23#1313326412yes—
619C23#1313326512yes—
620C23C24×D5311yescharacteristic
621Q8—232no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
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—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—534no—
645C2×C4—1068no—
646C2×C4—1062no—
647C2×C4—1062no—
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—2124no—
667C2×C4—2124no—
668C2×C4—2124no—
669C2×C4—2124no—
670C2×C4—2124no—
671C2×C4—2124no—
672C2×C4C22×C22⋊D5314yes—
673C2×C4C22×C22⋊D5314yes—
674C2×C4C22×C22⋊D5314yes—
675C2×C4C2×#1171994514yes—
676C2×C4C2×#1171994514yes—
677C2×C4C2×#1171994914yes—
678C22—4248no—
679C22—2122no—
680C22—2122no—
681C22—2122no—
682C22—2122no—
683C22—2122no—
684C22—2122no—
685C22—2122no—
686C22#1681113414yes—
687C22#1681116014yes—
688C22#1681123114yes—
689C22#1681127214yes—
690C22#1681128414yes—
691C22#1681134514yes—
692C22#1681134614yes—
693C22C23×C22⋊D5311yescharacteristic
694C22C2×#41×D5311yescharacteristic
695C22C22×#1171994511yescharacteristic
696C22C22×#1171994511yescharacteristic
697C22C22×#1171994911yescharacteristic
698C22C2×#1313326411yescharacteristic
699C22C2×#1313326511yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—1064no—
708C4—2122no—
709C4—2122no—
710C4—2122no—
711C4—2122no—
712C4—2122no—
713C4—2122no—
714C2—4242no—
715C2#2027879018yesdirect product factor
716C2C2×#1681113411yescharacteristic
717C2C2×#1681116011yescharacteristic
718C2C2×#1681123111yescharacteristic
719C2C2×#1681127211yescharacteristic
720C2C2×#1681128411yescharacteristic
721C2C2×#1681134511yescharacteristic
722C2C2×#1681134611yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC22×C4×Q8×C53C2
socleC24×C53C24
prime radicalC24×D53C23
hypercenterC22×C4×Q8D53
hypocenterC53C2×#2469
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #20278790C2direct (N × H)
3. C2×#16810562C2semidirect
5. C2×#16810542C2semidirect
7. C2×#16810521C2semidirect
12. C2×#16810509C2semidirect
13. C2×#16810507C2semidirect
14. C2×#16810504C2semidirect
15. C2×C4×#11719919C2semidirect
16. C22×C4×Q8×C53C2semidirect
35. #16810562C22semidirect
37. #16810542C22semidirect
39. #16810521C22semidirect
44. #16810509C22semidirect
45. #16810507C22semidirect
46. #16810504C22semidirect
47. C4×#11719919C22semidirect
62. C2×C4×Q8×C53C22semidirect
354. C22×C4×Q8D53semidirect
369. C2×C53#2469semidirect
382. C2×C4×Q8C2×D53semidirect
430. C53C2×#2469semidirect
715. C2#20278790direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332122
#202787902
C2×#168105622
C2×#168105452
C2×#168105422
C2×#168105342
C2×#168105212
C2×#168105142
C2×#168105132
C2×#168105092
C2×#168105072
C2×#168105042
C2×C4×#117199192
C22×C4×Q8×C532
C2×#246953