Finite Group Databasebeta

← C2×#20277523 #27543006

Subgroups — C2×#20277523 #27543006

Order 13568.

3046 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133203C211yesmaximal, characteristic
2#20277523C2116yesmaximal, direct product factor
3C2×#16810529C211yesmaximal, characteristic, complemented
4C2×#16810527C211yesmaximal, characteristic, complemented
5C2×#16810517C211yesmaximal, characteristic, complemented
6C2×#16810516C211yesmaximal, characteristic, complemented
7C2×#16810514C211yesmaximal, characteristic, complemented
8C2×#16810512C211yesmaximal, characteristic, complemented
9C2×#16810502C211yesmaximal, characteristic
10C2×#16810499C211yesmaximal, characteristic
11C2×#16810497C211yesmaximal, characteristic, complemented
12C2×#16810496C211yesmaximal, characteristic, complemented
13C2×#16810490C211yesmaximal, characteristic, complemented
14C2×C4×#11719919C211yesmaximal, characteristic, complemented
15C2×C4×#11719921C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C23×C22⋊D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133203C4116yescomplemented
21C2×#13133203C2218yes—
22C22×C4⋊Dic53C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37#16810529C2218yescomplemented
38#16810527C2218yescomplemented
39#16810517C2218yescomplemented
40#16810516C2218yescomplemented
41#16810514C2218yescomplemented
42#16810512C2218yescomplemented
43#16810502C2218yes—
44#16810499C2218yes—
45#16810497C2218yescomplemented
46#16810496C2218yescomplemented
47#16810490C2218yescomplemented
48C4×#11719919C2218yescomplemented
49C4×#11719921C2218yescomplemented
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C24×C4×C53C2211yescharacteristic
61C22×C22⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C22×C42×C53C2211yescharacteristic
65C4×C22⋊C4×C53C2218yescomplemented
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C24×D53C2311yescharacteristic
69C22×Dic106—42no—
70C22×Dic106—42no—
71C22×Dic106C2×C418yescomplemented
72C22×Dic106C2314yes—
73C22×C22⋊D53—42no—
74C22×C22⋊D53—42no—
75C22×C22⋊D53C2×C418yes—
76C22×C22⋊D53C2314yes—
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C23×Dic53C2311yescharacteristic
81C23×Dic53C2311yescharacteristic
82C23×Dic53C2311yescharacteristic
83C23×Dic53C2311yescharacteristic
84C22×C4×D53—24no—
85C22×C4×D53—42no—
86C22×C4×D53—42no—
87C22×C4×D53C2314yes—
88#13133203C2×C4164yescomplemented
89C2×C4⋊Dic53—42no—
90C2×C4⋊Dic53C2314yes—
91C2×#11719919—24no—
92C2×#11719919—24no—
93C2×#11719919—42no—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×C22⋊Dic53—42no—
98C2×C22⋊Dic53—42no—
99C2×C22⋊Dic53C2×C418yescomplemented
100C2×C22⋊Dic53C2314yes—
101C2×C22⋊Dic53C2314yes—
102C2×C22⋊Dic53C2314yes—
103C2×#11719921—24no—
104C2×#11719921—42no—
105C2×#11719921—42no—
106C2×#11719921C2×C418yescomplemented
107C2×#11719921C2×C418yescomplemented
108C2×#11719921C2314yes—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113C2×C4×Dic53—42no—
114C2×C4×Dic53—42no—
115C2×C4×Dic53C2×C418yescomplemented
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—
127#13133124C2314yes—
128#13133124C2314yes—
129C25×C53C2311yescharacteristic
130C23×C4×C53—24no—
131C23×C4×C53—42no—
132C23×C4×C53—42no—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2314yes—
140C2×C22⋊C4×C53—24no—
141C2×C22⋊C4×C53C2×C418yescomplemented
142C2×C22⋊C4×C53C2314yes—
143C2×C22⋊C4×C53C2314yes—
144C2×C42×C53—42no—
145C2×C42×C53—42no—
146C2×C42×C53C2314yes—
147C2×C42×C53C2314yes—
148#95×C53C2314yes—
149#95×C53C2314yes—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53C22×C414yes—
157C24×C53C2412yes—
158C24×C53C2411yescharacteristic
159C23×D53—22no—
160C23×D53—22no—
161C23×D53—22no—
162C23×D53—22no—
163C23×D53—22no—
164C23×D53—22no—
165C23×D53C22×C414yes—
166C23×D53C2412yes—
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×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—22no—
180C22×C4×C53—22no—
181C22×C4×C53—28no—
182C22×C4×C53—44no—
183C22×C4×C53—44no—
184C22×C4×C53—416no—
185C22×C4×C53C22×C414yes—
186C22×C4×C53C22×C414yes—
187C22×C4×C53#4114yes—
188C22×C4×C53#4114yes—
189C22×C4×C53C2412yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
195C2×C22⋊D53—416no—
196C2×C22⋊D53—44no—
197C2×C22⋊D53—44no—
198C2×C22⋊D53C22×C4116yes—
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—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—22no—
215C22×Dic53—22no—
216C22×Dic53—22no—
217C22×Dic53C22×C414yes—
218C22×Dic53C22×C414yes—
219C22×Dic53C22×C414yes—
220C22×Dic53C2412yes—
221C22×Dic53C2412yes—
222C22×Dic53C2412yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C2×C4×D53—28no—
228C2×C4×D53—44no—
229C2×C4×D53—44no—
230C2×C4×D53—416no—
231C2×Dic106—416no—
232C2×Dic106—44no—
233C2×Dic106—44no—
234C2×Dic106C22×C4116yescomplemented
235C22⋊C4×C53—28no—
236C22⋊C4×C53C22×C4116yescomplemented
237C42×C53—44no—
238C42×C53—44no—
239C22⋊Dic53—44no—
240C22⋊Dic53—44no—
241C22⋊Dic53C22×C4116yescomplemented
242#11719921—28no—
243#11719921—44no—
244#11719921—44no—
245#11719921C22×C4116yescomplemented
246#11719921C22×C4116yescomplemented
247C4⋊Dic53—44no—
248#11719919—28no—
249#11719919—28no—
250#11719919—44no—
251C4×Dic53—44no—
252C4×Dic53—44no—
253C4×Dic53C22×C4116yescomplemented
254C23×C53—28no—
255C23×C53—28no—
256C23×C53—28no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—44no—
264C23×C53—44no—
265C23×C53—44no—
266C23×C53—44no—
267C23×C53C23×C414yes—
268C23×C53C23×C412yes—
269C23×C53C2×#4112yes—
270C23×C53C2×#4112yes—
271C23×C53H(5,𝔽2)12yes—
272C23×C53H(5,𝔽2)12yes—
273C23×C53H(5,𝔽2)12yes—
274C23×C532−1+412yes—
275C23×C53C2511yescharacteristic
276C22×D53—28no—
277C22×D53—28no—
278C22×D53—28no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—22no—
285C22×D53—44no—
286C22×D53—44no—
287C22×D53—44no—
288C22×D53—44no—
289C22×D53C23×C414yes—
290C2×C4×C53—28no—
291C2×C4×C53—28no—
292C2×C4×C53—28no—
293C2×C4×C53—28no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—22no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—416no—
309C2×C4×C53—44no—
310C2×C4×C53—44no—
311C2×C4×C53C23×C414yes—
312C2×C4×C53C23×C414yes—
313C2×C4×C53C2×#4114yes—
314C2×C4×C53C2×#4114yes—
315C22⋊D53—416no—
316C2×Dic53—28no—
317C2×Dic53—28no—
318C2×Dic53—28no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—44no—
338C2×Dic53—44no—
339C2×Dic53—44no—
340C2×Dic53—44no—
341C2×Dic53C23×C414yes—
342C2×Dic53C23×C414yes—
343C2×Dic53C23×C414yes—
344C4×D53—416no—
345Dic106—416no—
346C2×#2337—531nomaximal, Sylow
347C22×C53—24no—
348C22×C53—24no—
349C22×C53—24no—
350C22×C53—416no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53C4×#4114yes—
356C22×C53#51814yes—
357C22×C53#52014yes—
358C22×C53#53814yes—
359C22×C53#53814yes—
360C22×C53#54214yes—
361C22×C53#54214yes—
362C22×C53C24×C411yescharacteristic
363C22×C53C22×#4111yescharacteristic
364C22×C53C22×#4111yescharacteristic
365C22×C53C2×H(5,𝔽2)11yescharacteristic
366C22×C53C2×H(5,𝔽2)11yescharacteristic
367C22×C53C2×H(5,𝔽2)11yescharacteristic
368C22×C53C2×2−1+411yescharacteristic
369C2×D53—24no—
370C2×D53—24no—
371C2×D53—24no—
372C2×D53—416no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C4×C53—24no—
378C4×C53—24no—
379C4×C53—24no—
380C4×C53—24no—
381C4×C53—42no—
382C4×C53—42no—
383Dic53—24no—
384Dic53—24no—
385Dic53—24no—
386Dic53—42no—
387Dic53—42no—
388Dic53—42no—
389Dic53—42no—
390C22×#124—531no—
391#2337—5316no—
392C2×#391—531no—
393C2×#391—531no—
394C2×#388—531no—
395C2×#388—531no—
396C2×#388—531no—
397C2×#388—531no—
398C2×#386—531no—
399C2×#386—531no—
400C2×#385—531no—
401C2×#385—531no—
402C2×#383—531no—
403C2×C4×C4⋊C4—531no—
404C2×C4×C22⋊C4—531no—
405C2×C4×C22⋊C4D5311yescharacteristic, complemented
406C2×C53—44no—
407C2×C53#233718yescomplemented
408C2×C53C2×C4×#4111yescharacteristic
409C2×C53C2×#51811yescharacteristic
410C2×C53C2×#52011yescharacteristic
411C2×C53C2×#53811yescharacteristic
412C2×C53C2×#53811yescharacteristic
413C2×C53C2×#54211yescharacteristic
414C2×C53C2×#54211yescharacteristic
415D53—44no—
416C23×Q8—531no—
417C23×D4—531no—
418C24×C4—531no—
419C24×C4C2×D5311yescharacteristic
420C2×#124—5316no—
421C2×#124—538no—
422C22×C4⋊C4—531no—
423C22×C4⋊C4—531no—
424C22×C4⋊C4—531no—
425C22×C4⋊C4—531no—
426C22×C22⋊C4—531no—
427C22×C22⋊C4—531no—
428C22×C22⋊C4—531no—
429C22×C22⋊C4—531no—
430C22×C22⋊C4—531no—
431C22×C22⋊C4—531no—
432C22×C22⋊C4—531no—
433C22×C22⋊C4—531no—
434C22×C22⋊C4C2×D5311yescharacteristic
435C22×C22⋊C4C2×D5311yescharacteristic
436C22×C42—531no—
437C22×C42—531no—
438C22×C42—531no—
439C22×C42C2×D5311yescharacteristic
440C22×C42C2×D5311yescharacteristic
441#391—538no—
442#391—538no—
443#388—538no—
444#388—538no—
445#388—538no—
446#388—538no—
447#386—538no—
448#386—538no—
449#385—538no—
450#385—538no—
451#383—538no—
452C4×C4⋊C4—538no—
453C4×C22⋊C4—538no—
454C4×C22⋊C4C2×D5318yescomplemented
455C2×#95—531no—
456C2×#95—531no—
457C2×#95—531no—
458C2×#95—531no—
459C2×#95—531no—
460C2×#95—531no—
461C2×#95—531no—
462C2×#95—531no—
463C2×#95—531no—
464C2×#95—531no—
465C2×#95C2×D5311yescharacteristic
466C2×#95C2×D5311yescharacteristic
467C53C2×#233711yescharacteristic, complemented, Sylow
468C25—531no—
469C25C22×D5311yescharacteristic
470C22×Q8—538no—
471C22×Q8—534no—
472C22×Q8—2122no—
473C22×Q8—2122no—
474C22×D4—538no—
475C22×D4—534no—
476C22×D4—2122no—
477C22×D4—2122no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—531no—
486C23×C4—531no—
487C23×C4—531no—
488C23×C4—534no—
489C23×C4—1064no—
490C23×C4—2122no—
491C23×C4—2122no—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C23×C4C22×D5311yescharacteristic
496C23×C4C22×D5311yescharacteristic
497C23×C4C22×D5311yescharacteristic
498C23×C4C22×D5314yes—
499#124—5364no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—2122no—
507C2×C4⋊C4—2122no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—538no—
510C2×C22⋊C4—534no—
511C2×C22⋊C4—538no—
512C2×C22⋊C4—538no—
513C2×C22⋊C4—534no—
514C2×C22⋊C4—534no—
515C2×C22⋊C4—534no—
516C2×C22⋊C4—534no—
517C2×C22⋊C4—534no—
518C2×C22⋊C4—534no—
519C2×C22⋊C4—534no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—2122no—
522C2×C22⋊C4—2122no—
523C2×C22⋊C4—2122no—
524C2×C22⋊C4—2122no—
525C2×C22⋊C4C4×D5318yescomplemented
526C2×C22⋊C4C22×D5314yes—
527C2×C22⋊C4C22×D5314yes—
528C2×C42—42no—
529C2×C42—42no—
530C2×C42—538no—
531C2×C42—534no—
532C2×C42—534no—
533C2×C42—534no—
534C2×C42—2122no—
535C2×C42—2122no—
536C2×C42C22×D5314yes—
537C2×C42C22×D5314yes—
538#95—534no—
539#95—534no—
540#95—534no—
541#95—534no—
542#95—534no—
543#95—534no—
544#95—534no—
545#95—534no—
546#95—534no—
547#95—534no—
548#95C22×D5314yes—
549#95C22×D5314yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—534no—
557C24—532no—
558C24—1062no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24—1062no—
563C24—1062no—
564C24C2×C4×D5314yes—
565C24C23×D5312yes—
566C24C23×D5311yescharacteristic
567C2×Q8—5316no—
568C2×Q8—21216no—
569C2×Q8—2124no—
570C2×Q8—2124no—
571C2×D4—5316no—
572C2×D4—21216no—
573C2×D4—2124no—
574C2×D4—2124no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—28no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—416no—
593C22×C4—534no—
594C22×C4—534no—
595C22×C4—534no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1062no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1062no—
614C22×C4—1062no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1062no—
621C22×C4—1068no—
622C22×C4—2124no—
623C22×C4—2124no—
624C22×C4—21216no—
625C22×C4C2×C4×D5314yes—
626C22×C4C2×C4×D5314yes—
627C22×C4#1171994514yes—
628C22×C4#1171994514yes—
629C22×C4C23×D5312yes—
630C22×C4C23×D5312yes—
631C22×C4C23×D5312yes—
632C22×C4C23×D5312yes—
633C22×C4C23×D5312yes—
634C22×C4C23×D5312yes—
635C4⋊C4—1068no—
636C4⋊C4—1068no—
637C4⋊C4—2124no—
638C4⋊C4—2124no—
639C22⋊C4—28no—
640C22⋊C4—5316no—
641C22⋊C4—5316no—
642C22⋊C4—5316no—
643C22⋊C4—1068no—
644C22⋊C4—2124no—
645C22⋊C4—2124no—
646C22⋊C4—2124no—
647C22⋊C4—2124no—
648C22⋊C4C2×C4×D53116yescomplemented
649C42—44no—
650C42—44no—
651C42—5316no—
652C42—2124no—
653C42—2124no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—534no—
668C23—1068no—
669C23—1068no—
670C23—1068no—
671C23—1062no—
672C23—1062no—
673C23—1062no—
674C23—1062no—
675C23—1062no—
676C23—1062no—
677C23—2124no—
678C23—2124no—
679C23—2124no—
680C23—2124no—
681C23C22×C4×D5314yes—
682C23C22×C4×D5312yes—
683C23C2×#1171994512yes—
684C23C2×#1171994512yes—
685C23#1313326212yes—
686C23#1313326212yes—
687C23#1313326312yes—
688C23#1313326412yes—
689C23C24×D5311yescharacteristic
690Q8—21216no—
691D4—21216no—
692C2×C4—28no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—534no—
714C2×C4—534no—
715C2×C4—534no—
716C2×C4—1068no—
717C2×C4—1068no—
718C2×C4—1068no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—21216no—
738C2×C4—2124no—
739C2×C4—2124no—
740C2×C4—2124no—
741C2×C4—2124no—
742C2×C4C22×C4×D5314yes—
743C2×C4C22×C4×D5314yes—
744C2×C4C2×#1171994514yes—
745C2×C4C2×#1171994514yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—1064no—
755C22—1064no—
756C22—1064no—
757C22—21216no—
758C22—2122no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22C4×#1171994514yes—
763C22#1681109514yes—
764C22#1681110214yes—
765C22#1681120614yes—
766C22#1681121114yes—
767C22#1681123814yes—
768C22#1681124414yes—
769C22C23×C4×D5311yescharacteristic
770C22C22×#1171994511yescharacteristic
771C22C22×#1171994511yescharacteristic
772C22C2×#1313326211yescharacteristic
773C22C2×#1313326211yescharacteristic
774C22C2×#1313326311yescharacteristic
775C22C2×#1313326411yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—1064no—
783C4—1064no—
784C4—1064no—
785C4—2122no—
786C4—2122no—
787C4—2122no—
788C4—2122no—
789C2—44no—
790C2—2124no—
791C2#2027752318yesdirect product factor
792C2C2×C4×#1171994511yescharacteristic
793C2C2×#1681109511yescharacteristic
794C2C2×#1681110211yescharacteristic
795C2C2×#1681120611yescharacteristic
796C2C2×#1681121111yescharacteristic
797C2C2×#1681123811yescharacteristic
798C2C2×#1681124411yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C4×C22⋊C4×C53C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
cosocleC23×C53C25
hypercenterC2×C4×C22⋊C4D53
hypocenterC53C2×#2337
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20277523C2direct (N × H)
3. C2×#16810529C2semidirect
4. C2×#16810527C2semidirect
5. C2×#16810517C2semidirect
6. C2×#16810516C2semidirect
7. C2×#16810514C2semidirect
8. C2×#16810512C2semidirect
11. C2×#16810497C2semidirect
12. C2×#16810496C2semidirect
13. C2×#16810490C2semidirect
14. C2×C4×#11719919C2semidirect
15. C2×C4×#11719921C2semidirect
16. C2×C4×C22⋊C4×C53C2semidirect
20. C2×#13133203C4semidirect
37. #16810529C22semidirect
38. #16810527C22semidirect
39. #16810517C22semidirect
40. #16810516C22semidirect
41. #16810514C22semidirect
42. #16810512C22semidirect
45. #16810497C22semidirect
46. #16810496C22semidirect
47. #16810490C22semidirect
48. C4×#11719919C22semidirect
49. C4×#11719921C22semidirect
65. C4×C22⋊C4×C53C22semidirect
71. C22×Dic106C2×C4semidirect
88. #13133203C2×C4semidirect
99. C2×C22⋊Dic53C2×C4semidirect
106. C2×#11719921C2×C4semidirect
107. C2×#11719921C2×C4semidirect
115. C2×C4×Dic53C2×C4semidirect
141. C2×C22⋊C4×C53C2×C4semidirect
234. C2×Dic106C22×C4semidirect
236. C22⋊C4×C53C22×C4semidirect
241. C22⋊Dic53C22×C4semidirect
245. #11719921C22×C4semidirect
246. #11719921C22×C4semidirect
253. C4×Dic53C22×C4semidirect
405. C2×C4×C22⋊C4D53semidirect
407. C2×C53#2337semidirect
454. C4×C22⋊C4C2×D53semidirect
467. C53C2×#2337semidirect
525. C2×C22⋊C4C4×D53semidirect
648. C22⋊C4C2×C4×D53semidirect
791. C2#20277523direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131332032
#202775232
C2×#168105292
C2×#168105272
C2×#168105172
C2×#168105162
C2×#168105142
C2×#168105122
C2×#168105022
C2×#168104992
C2×#168104972
C2×#168104962
C2×#168104902
C2×C4×#117199192
C2×C4×#117199212
C2×C4×C22⋊C4×C532
C2×#233753