Finite Group Databasebeta

← C2×#20277506 #27542987

Subgroups — C2×#20277506 #27542987

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×#13133198C211yesmaximal, characteristic
2#20277506C2116yesmaximal, direct product factor
3C2×#16810526C211yesmaximal, characteristic
4C2×#16810520C211yesmaximal, characteristic, complemented
5C2×#16810517C211yesmaximal, characteristic, complemented
6C2×#16810517C211yesmaximal, characteristic, complemented
7C2×#16810517C211yesmaximal, characteristic, complemented
8C2×#16810511C211yesmaximal, characteristic, complemented
9C2×#16810510C211yesmaximal, characteristic, complemented
10C2×#16810505C211yesmaximal, characteristic, complemented
11C2×#16810496C211yesmaximal, characteristic, complemented
12C2×#16810481C211yesmaximal, characteristic, complemented
13C2×#16810474C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic53C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
16C2×C53×#386C211yesmaximal, characteristic
17C24×Dic53C2211yescharacteristic
18C2×#13133198C4116yescomplemented
19C2×#13133198C2218yes—
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C22⋊Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36C22×C4×Dic53C2211yescharacteristic
37C22×C4×Dic53C2211yescharacteristic
38C22×C4×Dic53C2211yescharacteristic
39#16810526C2218yes—
40#16810520C2218yescomplemented
41#16810517C2218yescomplemented
42#16810517C2218yescomplemented
43#16810517C2218yescomplemented
44#16810511C2218yescomplemented
45#16810510C2218yescomplemented
46#16810505C2218yescomplemented
47#16810496C2218yescomplemented
48#16810481C2218yescomplemented
49#16810474C2218yescomplemented
50C22⋊C4×Dic53C2218yescomplemented
51C4×C22⋊Dic53C2218yescomplemented
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#13133124C2211yescharacteristic
60C23×D4×C53C2211yescharacteristic
61C24×C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C53×#386C2218yes—
66C2×#95×C53C2211yescharacteristic
67C2×#95×C53C2211yescharacteristic
68C23×Dic53—42no—
69C23×Dic53—42no—
70C23×Dic53C2×C418yescomplemented
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2314yes—
80#13133198C2×C4164yescomplemented
81C2×C4⋊Dic53—42no—
82C2×C4⋊Dic53C2314yes—
83C2×#11719919—24no—
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×C22⋊Dic53—24no—
96C2×C22⋊Dic53—24no—
97C2×C22⋊Dic53—42no—
98C2×C22⋊Dic53—42no—
99C2×C22⋊Dic53C2×C418yes—
100C2×C22⋊Dic53C2×C418yes—
101C2×C22⋊Dic53C2×C418yescomplemented
102C2×C22⋊Dic53C2314yes—
103C2×C22⋊Dic53C2314yes—
104C2×C22⋊Dic53C2314yes—
105C2×C22⋊Dic53C2314yes—
106C2×C22⋊Dic53C2314yes—
107C2×C22⋊Dic53C2314yes—
108C2×C22⋊Dic53C2314yes—
109C2×C4×Dic53—24no—
110C2×C4×Dic53—42no—
111C2×C4×Dic53—42no—
112C2×C4×Dic53—42no—
113C2×C4×Dic53—42no—
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—
127C25×C53C2311yescharacteristic
128C25×C53C2311yescharacteristic
129C22×D4×C53—42no—
130C22×D4×C53—42no—
131C22×D4×C53C2×C418yes—
132C22×D4×C53C2314yes—
133C23×C4×C53—24no—
134C23×C4×C53—42no—
135C23×C4×C53—42no—
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2314yes—
142C2×C22⋊C4×C53—24no—
143C2×C22⋊C4×C53—42no—
144C2×C22⋊C4×C53—42no—
145C2×C22⋊C4×C53C2314yes—
146C2×C22⋊C4×C53C2314yes—
147C2×C22⋊C4×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×C53—22no—
157C24×C53—22no—
158C24×C53—22no—
159C24×C53—22no—
160C24×C53—22no—
161C24×C53—22no—
162C24×C53C22×C414yes—
163C24×C53C22×C414yes—
164C24×C53C2412yes—
165C24×C53C2412yes—
166C24×C53C2411yescharacteristic
167C2×D4×C53—416no—
168C2×D4×C53—44no—
169C2×D4×C53—44no—
170C2×D4×C53C22×C4116yes—
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—22no—
182C22×C4×C53—22no—
183C22×C4×C53—22no—
184C22×C4×C53—28no—
185C22×C4×C53—44no—
186C22×C4×C53—44no—
187C22×C4×C53—416no—
188C22×C4×C53C22×C414yes—
189C22×C4×C53#4114yes—
190C22×C4×C53C2412yes—
191C22×C4×C53C2412yes—
192C22×C4×C53C2412yes—
193C22×C4×C53C2412yes—
194C22×C4×C53C2412yes—
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—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53—416no—
215C22×Dic53—44no—
216C22×Dic53—44no—
217C22×Dic53C22×C414yes—
218C22×Dic53C22×C414yes—
219C22×Dic53C22×C414yes—
220C22×Dic53C22×C414yes—
221C22×Dic53C22×C4116yescomplemented
222C22×Dic53#4114yes—
223C22×Dic53C2412yes—
224C22×Dic53C2412yes—
225C22×Dic53C2412yes—
226C22×Dic53C2412yes—
227C22×Dic53C2412yes—
228C22×Dic53C2412yes—
229C22×Dic53C2412yes—
230C22×Dic53C2412yes—
231C22⋊C4×C53—28no—
232C22⋊C4×C53—44no—
233C22⋊C4×C53—44no—
234C22⋊Dic53—28no—
235C22⋊Dic53—28no—
236C22⋊Dic53—44no—
237C22⋊Dic53—44no—
238C22⋊Dic53C22×C4116yes—
239C22⋊Dic53C22×C4116yes—
240C22⋊Dic53C22×C4116yescomplemented
241C4⋊Dic53—44no—
242#11719919—28no—
243#11719919—44no—
244#11719919—44no—
245#11719919—44no—
246#11719919C22×C4116yescomplemented
247#11719919C22×C4116yescomplemented
248C4×Dic53—28no—
249C4×Dic53—44no—
250C4×Dic53—44no—
251C4×Dic53—44no—
252C4×Dic53—44no—
253C23×C53—28no—
254C23×C53—28no—
255C23×C53—28no—
256C23×C53—28no—
257C23×C53—28no—
258C23×C53—28no—
259C23×C53—22no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—22no—
264C23×C53—22no—
265C23×C53—22no—
266C23×C53—22no—
267C23×C53—22no—
268C23×C53—22no—
269C23×C53—22no—
270C23×C53—22no—
271C23×C53—44no—
272C23×C53—44no—
273C23×C53—44no—
274C23×C53—44no—
275C23×C53—44no—
276C23×C53—44no—
277C23×C53—44no—
278C23×C53—44no—
279C23×C53C23×C414yes—
280C23×C53C23×C414yes—
281C23×C53C23×C412yes—
282C23×C53C2×#4112yes—
283C23×C53C2×#4112yes—
284C23×C53H(5,𝔽2)12yes—
285C23×C53H(5,𝔽2)12yes—
286C23×C53H(5,𝔽2)12yes—
287C23×C532−1+412yes—
288C23×C53C2511yescharacteristic
289D4×C53—416no—
290C2×C4×C53—28no—
291C2×C4×C53—28no—
292C2×C4×C53—22no—
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—416no—
306C2×C4×C53—44no—
307C2×C4×C53—44no—
308C2×C4×C53—44no—
309C2×C4×C53C23×C414yes—
310C2×C4×C53C2×#4114yes—
311C2×Dic53—28no—
312C2×Dic53—28no—
313C2×Dic53—28no—
314C2×Dic53—28no—
315C2×Dic53—28no—
316C2×Dic53—22no—
317C2×Dic53—22no—
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—416no—
336C2×Dic53—44no—
337C2×Dic53—44no—
338C2×Dic53—44no—
339C2×Dic53C23×C414yes—
340C2×Dic53C23×C414yes—
341C2×Dic53C23×C414yes—
342C2×Dic53C23×C414yes—
343C2×Dic53C2×#4114yes—
344C2×#2335—531nomaximal, Sylow
345C22×C53—24no—
346C22×C53—24no—
347C22×C53—24no—
348C22×C53—24no—
349C22×C53—24no—
350C22×C53—24no—
351C22×C53—416no—
352C22×C53—416no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—42no—
360C22×C53—42no—
361C22×C53C4×#4114yes—
362C22×C53#51814yes—
363C22×C53#52014yes—
364C22×C53#53814yes—
365C22×C53#53914yes—
366C22×C53#54014yes—
367C22×C53#54214yes—
368C22×C53C24×C411yescharacteristic
369C22×C53C22×#4111yescharacteristic
370C22×C53C22×#4111yescharacteristic
371C22×C53C2×H(5,𝔽2)11yescharacteristic
372C22×C53C2×H(5,𝔽2)11yescharacteristic
373C22×C53C2×H(5,𝔽2)11yescharacteristic
374C22×C53C2×2−1+411yescharacteristic
375C4×C53—24no—
376C4×C53—24no—
377C4×C53—42no—
378C4×C53—42no—
379C4×C53—42no—
380Dic53—24no—
381Dic53—24no—
382Dic53—24no—
383Dic53—24no—
384Dic53—24no—
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×#386D5311yescharacteristic
399C2×#385—531no—
400C2×#380—531no—
401C2×C4×C4⋊C4—531no—
402C2×C4×C22⋊C4—531no—
403C2×C4×C22⋊C4—531no—
404C2×C53—44no—
405C2×C53—44no—
406C2×C53#233518yescomplemented
407C2×C53C2×C4×#4111yescharacteristic
408C2×C53C2×#51811yescharacteristic
409C2×C53C2×#52011yescharacteristic
410C2×C53C2×#53811yescharacteristic
411C2×C53C2×#53911yescharacteristic
412C2×C53C2×#54011yescharacteristic
413C2×C53C2×#54211yescharacteristic
414C23×D4C2×D5311yescharacteristic
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⋊C4C2×D5311yescharacteristic
434C22×C22⋊C4C2×D5311yescharacteristic
435C22×C22⋊C4C2×D5311yescharacteristic
436C22×C42—531no—
437C22×C42—531no—
438C22×C42—531no—
439C22×C42—531no—
440C22×C42—531no—
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#386C2×D5318yes—
450#385—538no—
451#380—538no—
452C4×C4⋊C4—538no—
453C4×C22⋊C4—538no—
454C4×C22⋊C4—538no—
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
466C25C22×D5311yescharacteristic
467C25C22×D5311yescharacteristic
468C22×D4—42no—
469C22×D4—42no—
470C22×D4C4×D5318yes—
471C22×D4C22×D5314yes—
472C23×C4—24no—
473C23×C4—42no—
474C23×C4—42no—
475C23×C4—531no—
476C23×C4—531no—
477C23×C4—531no—
478C23×C4—531no—
479C23×C4—531no—
480C23×C4—538no—
481C23×C4—534no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4—531no—
485C23×C4—2122no—
486C23×C4—2122no—
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—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—538no—
512C2×C22⋊C4—538no—
513C2×C22⋊C4—538no—
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—534no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—1064no—
523C2×C22⋊C4—2122no—
524C2×C22⋊C4—2122no—
525C2×C22⋊C4C22×D5314yes—
526C2×C22⋊C4C22×D5314yes—
527C2×C22⋊C4C22×D5314yes—
528C2×C42—534no—
529C2×C42—534no—
530C2×C42—534no—
531C2×C42—534no—
532C2×C42—534no—
533C2×C42—1064no—
534C2×C42—2122no—
535C2×C42—2122no—
536C2×C42—2122no—
537C2×C42—2122no—
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—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24C2×C4×D5314yes—
561C24C2×C4×D5314yes—
562C24C23×D5312yes—
563C24C23×D5312yes—
564C24C23×D5311yescharacteristic
565C2×D4—416no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4C2×C4×D53116yes—
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—28no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4—416no—
586C22×C4—534no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—534no—
590C22×C4—534no—
591C22×C4—532no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—5316no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—532no—
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—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—21216no—
620C22×C4—2124no—
621C22×C4—2124no—
622C22×C4C2×C4×D5314yes—
623C22×C4#1171994714yes—
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—44no—
638C22⋊C4—44no—
639C22⋊C4—5316no—
640C22⋊C4—5316no—
641C22⋊C4—5316no—
642C22⋊C4—1068no—
643C22⋊C4—1068no—
644C22⋊C4—2124no—
645C22⋊C4—2124no—
646C42—1068no—
647C42—2124no—
648C42—2124no—
649C42—2124no—
650C42—2124no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—44no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—44no—
676C23—44no—
677C23C22×C4×D5314yes—
678C23C22×C4×D5314yes—
679C23C22×C4×D5312yes—
680C23#41×D5312yes—
681C23C2×#1171994712yes—
682C23#1313326212yes—
683C23#1313326212yes—
684C23#1313326212yes—
685C23#1313326412yes—
686C23C24×D5311yescharacteristic
687D4—416no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
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—22no—
703C2×C4—416no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—534no—
708C2×C4—534no—
709C2×C4—534no—
710C2×C4—534no—
711C2×C4—534no—
712C2×C4—1068no—
713C2×C4—1068no—
714C2×C4—1068no—
715C2×C4—1068no—
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—1068no—
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—21216no—
737C2×C4—2124no—
738C2×C4—2124no—
739C2×C4—2124no—
740C2×C4C22×C4×D5314yes—
741C2×C4C2×#1171994714yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—24no—
746C22—24no—
747C22—24no—
748C22—416no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22C4×#1171994714yes—
759C22#1681109614yes—
760C22#1681110214yes—
761C22#1681120814yes—
762C22#1681121614yes—
763C22#1681122314yes—
764C22#1681124014yes—
765C22C23×C4×D5311yescharacteristic
766C22C2×#41×D5311yescharacteristic
767C22C22×#1171994711yescharacteristic
768C22C2×#1313326211yescharacteristic
769C22C2×#1313326211yescharacteristic
770C22C2×#1313326211yescharacteristic
771C22C2×#1313326411yescharacteristic
772C4—24no—
773C4—24no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—1064no—
778C4—1064no—
779C4—1064no—
780C4—1064no—
781C4—1064no—
782C4—2122no—
783C4—2122no—
784C4—2122no—
785C2—44no—
786C2—44no—
787C2#2027750618yesdirect product factor
788C2C2×C4×#1171994711yescharacteristic
789C2C2×#1681109611yescharacteristic
790C2C2×#1681110211yescharacteristic
791C2C2×#1681120811yescharacteristic
792C2C2×#1681121611yescharacteristic
793C2C2×#1681122311yescharacteristic
794C2C2×#1681124011yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC2×C53×#386C2
socleC24×C53C24
prime radicalC23×D4×C53C22
cosocleC23×C53C25
hypercenterC2×#386D53
hypocenterC53C2×#2335
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. #20277506C2direct (N × H)
4. C2×#16810520C2semidirect
5. C2×#16810517C2semidirect
6. C2×#16810517C2semidirect
7. C2×#16810517C2semidirect
8. C2×#16810511C2semidirect
9. C2×#16810510C2semidirect
10. C2×#16810505C2semidirect
11. C2×#16810496C2semidirect
12. C2×#16810481C2semidirect
13. C2×#16810474C2semidirect
14. C2×C22⋊C4×Dic53C2semidirect
15. C2×C4×C22⋊Dic53C2semidirect
18. C2×#13133198C4semidirect
40. #16810520C22semidirect
41. #16810517C22semidirect
42. #16810517C22semidirect
43. #16810517C22semidirect
44. #16810511C22semidirect
45. #16810510C22semidirect
46. #16810505C22semidirect
47. #16810496C22semidirect
48. #16810481C22semidirect
49. #16810474C22semidirect
50. C22⋊C4×Dic53C22semidirect
51. C4×C22⋊Dic53C22semidirect
70. C23×Dic53C2×C4semidirect
80. #13133198C2×C4semidirect
87. C2×#11719919C2×C4semidirect
88. C2×#11719919C2×C4semidirect
101. C2×C22⋊Dic53C2×C4semidirect
221. C22×Dic53C22×C4semidirect
240. C22⋊Dic53C22×C4semidirect
246. #11719919C22×C4semidirect
247. #11719919C22×C4semidirect
406. C2×C53#2335semidirect
465. C53C2×#2335semidirect
787. C2#20277506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131331982
#202775062
C2×#168105262
C2×#168105202
C2×#168105172
C2×#168105112
C2×#168105102
C2×#168105052
C2×#168104962
C2×#168104812
C2×#168104742
C2×C22⋊C4×Dic532
C2×C4×C22⋊Dic532
C2×C53×#3862
C2×#233553