Finite Group Databasebeta

← C2×#20277507 #27542988

Subgroups — C2×#20277507 #27542988

Order 13568.

2982 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133199C211yesmaximal, characteristic
2#20277507C2116yesmaximal, direct product factor
3C2×#16810523C211yesmaximal, characteristic
4C2×#16810521C211yesmaximal, characteristic, complemented
5C2×#16810516C211yesmaximal, characteristic, complemented
6C2×#16810515C211yesmaximal, characteristic, complemented
7C2×#16810514C211yesmaximal, characteristic, complemented
8C2×#16810511C211yesmaximal, characteristic, complemented
9C2×#16810506C211yesmaximal, characteristic, complemented
10C2×#16810505C211yesmaximal, characteristic, complemented
11C2×#16810502C211yesmaximal, characteristic
12C2×#16810496C211yesmaximal, characteristic, complemented
13C2×#16810482C211yesmaximal, characteristic, complemented
14C2×C4×#11719919C211yesmaximal, characteristic, complemented
15C2×C4×#11719921C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
17C23×C22⋊D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C2×#13133199C4116yescomplemented
20C2×#13133199C2218yes—
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35C22×#11719921C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810523C2218yes—
40#16810521C2218yescomplemented
41#16810516C2218yescomplemented
42#16810515C2218yescomplemented
43#16810514C2218yescomplemented
44#16810511C2218yescomplemented
45#16810506C2218yescomplemented
46#16810505C2218yescomplemented
47#16810502C2218yes—
48#16810496C2218yescomplemented
49#16810482C2218yescomplemented
50C4×#11719919C2218yescomplemented
51C4×#11719921C2218yescomplemented
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×C22⋊D53—42no—
70C22×C22⋊D53—42no—
71C22×C22⋊D53C2×C418yes—
72C22×C22⋊D53C2314yes—
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C22×C4×D53—42no—
81C22×C4×D53—42no—
82C22×C4×D53C2×C418yescomplemented
83C22×C4×D53C2314yes—
84#13133199C2×C4164yescomplemented
85C2×C4⋊Dic53—42no—
86C2×C4⋊Dic53C2×C418yescomplemented
87C2×C4⋊Dic53C2314yes—
88C2×C4⋊Dic53C2314yes—
89C2×#11719919—24no—
90C2×#11719919—42no—
91C2×#11719919—42no—
92C2×#11719919—42no—
93C2×#11719919C2×C418yescomplemented
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×C22⋊Dic53—42no—
100C2×C22⋊Dic53—42no—
101C2×C22⋊Dic53C2×C418yes—
102C2×C22⋊Dic53C2314yes—
103C2×C22⋊Dic53C2314yes—
104C2×C22⋊Dic53C2314yes—
105C2×#11719921—24no—
106C2×#11719921—24no—
107C2×#11719921—42no—
108C2×#11719921—42no—
109C2×#11719921C2×C418yescomplemented
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113C2×#11719921C2314yes—
114C2×#11719921C2314yes—
115C2×C4×Dic53—24no—
116C2×C4×Dic53—42no—
117C2×C4×Dic53—42no—
118C2×C4×Dic53C2314yes—
119C2×C4×Dic53C2314yes—
120C2×C4×Dic53C2314yes—
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×C418yes—
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—416no—
228C2×C4×D53—44no—
229C2×C4×D53—44no—
230C2×C4×D53C22×C4116yescomplemented
231C22⋊C4×C53—28no—
232C22⋊C4×C53C22×C4116yes—
233C42×C53—44no—
234C42×C53—44no—
235C22⋊Dic53—44no—
236C22⋊Dic53—44no—
237C22⋊Dic53C22×C4116yes—
238#11719921—28no—
239#11719921—28no—
240#11719921—44no—
241#11719921—44no—
242#11719921C22×C4116yescomplemented
243C4⋊Dic53—44no—
244C4⋊Dic53C22×C4116yescomplemented
245#11719919—28no—
246#11719919—44no—
247#11719919—44no—
248#11719919—44no—
249#11719919C22×C4116yescomplemented
250C4×Dic53—28no—
251C4×Dic53—44no—
252C4×Dic53—44no—
253C23×C53—28no—
254C23×C53—28no—
255C23×C53—28no—
256C23×C53—22no—
257C23×C53—22no—
258C23×C53—22no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—44no—
263C23×C53—44no—
264C23×C53—44no—
265C23×C53—44no—
266C23×C53C23×C414yes—
267C23×C53C23×C412yes—
268C23×C53C2×#4112yes—
269C23×C53C2×#4112yes—
270C23×C53H(5,𝔽2)12yes—
271C23×C53H(5,𝔽2)12yes—
272C23×C53H(5,𝔽2)12yes—
273C23×C532−1+412yes—
274C23×C53C2511yescharacteristic
275C22×D53—28no—
276C22×D53—28no—
277C22×D53—28no—
278C22×D53—22no—
279C22×D53—22no—
280C22×D53—22no—
281C22×D53—22no—
282C22×D53—22no—
283C22×D53—22no—
284C22×D53—44no—
285C22×D53—44no—
286C22×D53—44no—
287C22×D53—44no—
288C22×D53C23×C414yes—
289C2×C4×C53—28no—
290C2×C4×C53—28no—
291C2×C4×C53—28no—
292C2×C4×C53—28no—
293C2×C4×C53—22no—
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—416no—
308C2×C4×C53—44no—
309C2×C4×C53—44no—
310C2×C4×C53C23×C414yes—
311C2×C4×C53C23×C414yes—
312C2×C4×C53C2×#4114yes—
313C2×C4×C53C2×#4114yes—
314C22⋊D53—416no—
315C2×Dic53—28no—
316C2×Dic53—28no—
317C2×Dic53—28no—
318C2×Dic53—22no—
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—44no—
337C2×Dic53—44no—
338C2×Dic53—44no—
339C2×Dic53—44no—
340C2×Dic53C23×C414yes—
341C2×Dic53C23×C414yes—
342C2×Dic53C23×C414yes—
343C4×D53—416no—
344C2×#2335—531nomaximal, Sylow
345C22×C53—24no—
346C22×C53—24no—
347C22×C53—24no—
348C22×C53—416no—
349C22×C53—42no—
350C22×C53—42no—
351C22×C53—42no—
352C22×C53—42no—
353C22×C53C4×#4114yes—
354C22×C53#51814yes—
355C22×C53#52014yes—
356C22×C53#53814yes—
357C22×C53#53914yes—
358C22×C53#54014yes—
359C22×C53#54214yes—
360C22×C53C24×C411yescharacteristic
361C22×C53C22×#4111yescharacteristic
362C22×C53C22×#4111yescharacteristic
363C22×C53C2×H(5,𝔽2)11yescharacteristic
364C22×C53C2×H(5,𝔽2)11yescharacteristic
365C22×C53C2×H(5,𝔽2)11yescharacteristic
366C22×C53C2×2−1+411yescharacteristic
367C2×D53—24no—
368C2×D53—24no—
369C2×D53—24no—
370C2×D53—416no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C4×C53—24no—
376C4×C53—24no—
377C4×C53—24no—
378C4×C53—24no—
379C4×C53—42no—
380C4×C53—42no—
381Dic53—24no—
382Dic53—24no—
383Dic53—24no—
384Dic53—42no—
385Dic53—42no—
386Dic53—42no—
387Dic53—42no—
388C22×#123—531no—
389#2335—5316no—
390C2×#390—531no—
391C2×#389—531no—
392C2×#388—531no—
393C2×#388—531no—
394C2×#388—531no—
395C2×#388—531no—
396C2×#387—531no—
397C2×#387—531no—
398C2×#386—531no—
399C2×#385—531no—
400C2×#380—531no—
401C2×C4×C4⋊C4—531no—
402C2×C4×C22⋊C4—531no—
403C2×C4×C22⋊C4D5311yescharacteristic, complemented
404C2×C53—44no—
405C2×C53#233518yescomplemented
406C2×C53C2×C4×#4111yescharacteristic
407C2×C53C2×#51811yescharacteristic
408C2×C53C2×#52011yescharacteristic
409C2×C53C2×#53811yescharacteristic
410C2×C53C2×#53911yescharacteristic
411C2×C53C2×#54011yescharacteristic
412C2×C53C2×#54211yescharacteristic
413D53—44no—
414C23×D4—531no—
415C24×C4—531no—
416C24×C4C2×D5311yescharacteristic
417C2×#123—5316no—
418C2×#123—538no—
419C22×C4⋊C4—531no—
420C22×C4⋊C4—531no—
421C22×C4⋊C4—531no—
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#390—538no—
442#389—538no—
443#388—538no—
444#388—538no—
445#388—538no—
446#388—538no—
447#387—538no—
448#387—538no—
449#386—538no—
450#385—538no—
451#380—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×#95C2×D5311yescharacteristic
464C2×#95C2×D5311yescharacteristic
465C53C2×#233511yescharacteristic, complemented, Sylow
466C25—531no—
467C25C22×D5311yescharacteristic
468C22×D4—538no—
469C22×D4—534no—
470C22×D4—2122no—
471C22×D4—2122no—
472C23×C4—24no—
473C23×C4—42no—
474C23×C4—42no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—531no—
478C23×C4—538no—
479C23×C4—534no—
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—2122no—
485C23×C4—2122no—
486C23×C4C22×D5311yescharacteristic
487C23×C4C22×D5311yescharacteristic
488C23×C4C22×D5311yescharacteristic
489C23×C4C22×D5311yescharacteristic
490C23×C4C22×D5311yescharacteristic
491C23×C4C22×D5311yescharacteristic
492C23×C4C22×D5314yes—
493#123—5364no—
494C2×C4⋊C4—538no—
495C2×C4⋊C4—538no—
496C2×C4⋊C4—534no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—534no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—534no—
503C2×C4⋊C4—1064no—
504C2×C4⋊C4—2122no—
505C2×C4⋊C4—2122no—
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—534no—
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—1064no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—2122no—
522C2×C22⋊C4—2122no—
523C2×C22⋊C4—2122no—
524C2×C22⋊C4—2122no—
525C2×C22⋊C4C4×D5318yes—
526C2×C22⋊C4C22×D5314yes—
527C2×C22⋊C4C22×D5314yes—
528C2×C42—42no—
529C2×C42—42no—
530C2×C42—534no—
531C2×C42—534no—
532C2×C42—534no—
533C2×C42—1064no—
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#95C22×D5314yes—
547#95C22×D5314yes—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—534no—
555C24—532no—
556C24—1062no—
557C24—1062no—
558C24—1062no—
559C24—1062no—
560C24—1062no—
561C24—1062no—
562C24C2×C4×D5314yes—
563C24C23×D5312yes—
564C24C23×D5311yescharacteristic
565C2×D4—5316no—
566C2×D4—21216no—
567C2×D4—2124no—
568C2×D4—2124no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
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—28no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—416no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—534no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—5316no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4—1062no—
602C22×C4—1062no—
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—21216no—
617C22×C4—2124no—
618C22×C4—2124no—
619C22×C4C2×C4×D5314yes—
620C22×C4C2×C4×D5314yes—
621C22×C4#1171994514yes—
622C22×C4#1171994514yes—
623C22×C4C23×D5312yes—
624C22×C4C23×D5312yes—
625C22×C4C23×D5312yes—
626C22×C4C23×D5312yes—
627C22×C4C23×D5312yes—
628C22×C4C23×D5312yes—
629C4⋊C4—5316no—
630C4⋊C4—5316no—
631C4⋊C4—1068no—
632C4⋊C4—2124no—
633C4⋊C4—2124no—
634C4⋊C4—2124no—
635C4⋊C4—2124no—
636C22⋊C4—28no—
637C22⋊C4—5316no—
638C22⋊C4—5316no—
639C22⋊C4—1068no—
640C22⋊C4—1068no—
641C22⋊C4—2124no—
642C22⋊C4—2124no—
643C22⋊C4—2124no—
644C22⋊C4—2124no—
645C22⋊C4C2×C4×D53116yes—
646C42—44no—
647C42—44no—
648C42—1068no—
649C42—2124no—
650C42—2124no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—534no—
665C23—1068no—
666C23—1068no—
667C23—1068no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1062no—
672C23—1062no—
673C23—1062no—
674C23—2124no—
675C23—2124no—
676C23—2124no—
677C23—2124no—
678C23C22×C4×D5314yes—
679C23C22×C4×D5312yes—
680C23C2×#1171994512yes—
681C23C2×#1171994512yes—
682C23#1313326212yes—
683C23#1313326212yes—
684C23#1313326312yes—
685C23#1313326412yes—
686C23C24×D5311yescharacteristic
687D4—21216no—
688C2×C4—28no—
689C2×C4—28no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—416no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—534no—
710C2×C4—534no—
711C2×C4—534no—
712C2×C4—1068no—
713C2×C4—1068no—
714C2×C4—1068no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
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—21216no—
734C2×C4—2124no—
735C2×C4—2124no—
736C2×C4—2124no—
737C2×C4—2124no—
738C2×C4C22×C4×D5314yes—
739C2×C4C22×C4×D5314yes—
740C2×C4C2×#1171994514yes—
741C2×C4C2×#1171994514yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—1064no—
751C22—1064no—
752C22—1064no—
753C22—21216no—
754C22—2122no—
755C22—2122no—
756C22—2122no—
757C22—2122no—
758C22C4×#1171994514yes—
759C22#1681109514yes—
760C22#1681110214yes—
761C22#1681121114yes—
762C22#1681121514yes—
763C22#1681122414yes—
764C22#1681124414yes—
765C22C23×C4×D5311yescharacteristic
766C22C22×#1171994511yescharacteristic
767C22C22×#1171994511yescharacteristic
768C22C2×#1313326211yescharacteristic
769C22C2×#1313326211yescharacteristic
770C22C2×#1313326311yescharacteristic
771C22C2×#1313326411yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—24no—
776C4—42no—
777C4—42no—
778C4—1064no—
779C4—1064no—
780C4—1064no—
781C4—2122no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C2—44no—
786C2—2124no—
787C2#2027750718yesdirect product factor
788C2C2×C4×#1171994511yescharacteristic
789C2C2×#1681109511yescharacteristic
790C2C2×#1681110211yescharacteristic
791C2C2×#1681121111yescharacteristic
792C2C2×#1681121511yescharacteristic
793C2C2×#1681122411yescharacteristic
794C2C2×#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×#2335
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. #20277507C2direct (N × H)
4. C2×#16810521C2semidirect
5. C2×#16810516C2semidirect
6. C2×#16810515C2semidirect
7. C2×#16810514C2semidirect
8. C2×#16810511C2semidirect
9. C2×#16810506C2semidirect
10. C2×#16810505C2semidirect
12. C2×#16810496C2semidirect
13. C2×#16810482C2semidirect
14. C2×C4×#11719919C2semidirect
15. C2×C4×#11719921C2semidirect
16. C2×C4×C22⋊C4×C53C2semidirect
19. C2×#13133199C4semidirect
40. #16810521C22semidirect
41. #16810516C22semidirect
42. #16810515C22semidirect
43. #16810514C22semidirect
44. #16810511C22semidirect
45. #16810506C22semidirect
46. #16810505C22semidirect
48. #16810496C22semidirect
49. #16810482C22semidirect
50. C4×#11719919C22semidirect
51. C4×#11719921C22semidirect
65. C4×C22⋊C4×C53C22semidirect
82. C22×C4×D53C2×C4semidirect
84. #13133199C2×C4semidirect
86. C2×C4⋊Dic53C2×C4semidirect
93. C2×#11719919C2×C4semidirect
109. C2×#11719921C2×C4semidirect
230. C2×C4×D53C22×C4semidirect
242. #11719921C22×C4semidirect
244. C4⋊Dic53C22×C4semidirect
249. #11719919C22×C4semidirect
403. C2×C4×C22⋊C4D53semidirect
405. C2×C53#2335semidirect
454. C4×C22⋊C4C2×D53semidirect
465. C53C2×#2335semidirect
787. C2#20277507direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331992
#202775072
C2×#168105232
C2×#168105212
C2×#168105162
C2×#168105152
C2×#168105142
C2×#168105112
C2×#168105062
C2×#168105052
C2×#168105022
C2×#168104962
C2×#168104822
C2×C4×#117199192
C2×C4×#117199212
C2×C4×C22⋊C4×C532
C2×#233553