Finite Group Databasebeta

← C2×#20277839 #27543784

Subgroups — C2×#20277839 #27543784

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
1#20277839C2116yesmaximal, direct product factor
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810516C211yesmaximal, characteristic
4C2×#16810516C211yesmaximal, characteristic
5C2×#16810516C211yesmaximal, characteristic
6C2×#16810509C211yesmaximal, characteristic, complemented
7C2×#16810509C211yesmaximal, characteristic, complemented
8C2×#16810509C211yesmaximal, characteristic, complemented
9C2×#16810498C211yesmaximal, characteristic
10C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
11C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
12C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic53C211yesmaximal, characteristic
14C2×C22⋊C4×Dic53C211yesmaximal, characteristic
15C2×#16810469C211yesmaximal, characteristic, complemented
16C22×#126×C53C211yesmaximal, characteristic
17C24×Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×C4⋊Dic53C2211yescharacteristic
21C22×C4⋊Dic53C2211yescharacteristic
22C22×C4⋊Dic53C2211yescharacteristic
23C22×C22⋊Dic53C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33#16810522C2218yescomplemented
34#16810516C2218yes—
35#16810516C2218yes—
36#16810516C2218yes—
37#16810509C2218yescomplemented
38#16810509C2218yescomplemented
39#16810509C2218yescomplemented
40#16810498C2218yes—
41C4⋊C4×Dic53C2218yescomplemented
42C4⋊C4×Dic53C2218yescomplemented
43C4×C4⋊Dic53C2218yescomplemented
44C22⋊C4×Dic53C2218yes—
45C22⋊C4×Dic53C2218yes—
46#16810469C2218yescomplemented
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C2×#126×C53C4116yescomplemented
60C2×#126×C53C2218yes—
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C4⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C22×C22⋊C4×C53C2211yescharacteristic
66C22×C22⋊C4×C53C2211yescharacteristic
67C22×C42×C53C2211yescharacteristic
68C23×Dic53—24no—
69C23×Dic53—24no—
70C23×Dic53—42no—
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2314yes—
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C23×Dic53C2311yescharacteristic
80C2×C4⋊Dic53—24no—
81C2×C4⋊Dic53—24no—
82C2×C4⋊Dic53—24no—
83C2×C4⋊Dic53—24no—
84C2×C4⋊Dic53—42no—
85C2×C4⋊Dic53C2314yes—
86C2×C4⋊Dic53C2314yes—
87C2×C4⋊Dic53C2314yes—
88C2×C4⋊Dic53C2314yes—
89C2×C4⋊Dic53C2314yes—
90C2×C22⋊Dic53—24no—
91C2×C22⋊Dic53—24no—
92C2×C22⋊Dic53—42no—
93C2×C22⋊Dic53C2314yes—
94C2×C22⋊Dic53C2314yes—
95C2×C22⋊Dic53C2314yes—
96C2×C4×Dic53—24no—
97C2×C4×Dic53—24no—
98C2×C4×Dic53—24no—
99C2×C4×Dic53—24no—
100C2×C4×Dic53—42no—
101C2×C4×Dic53—42no—
102C2×C4×Dic53—42no—
103C2×C4×Dic53C2314yes—
104C2×C4×Dic53C2314yes—
105C2×C4×Dic53C2314yes—
106C2×C4×Dic53C2314yes—
107C2×C4×Dic53C2314yes—
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—
122C25×C53C2311yescharacteristic
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129#126×C53C2×C4164yescomplemented
130C2×C4⋊C4×C53C2×C418yescomplemented
131C2×C4⋊C4×C53C2×C418yescomplemented
132C2×C4⋊C4×C53C2×C418yescomplemented
133C2×C4⋊C4×C53C2314yes—
134C2×C4⋊C4×C53C2314yes—
135C2×C4⋊C4×C53C2314yes—
136C2×C22⋊C4×C53C2×C418yes—
137C2×C22⋊C4×C53C2×C418yes—
138C2×C22⋊C4×C53C2×C418yes—
139C2×C22⋊C4×C53C2314yes—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142C2×C42×C53C2×C418yescomplemented
143C2×C42×C53C2314yes—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53C22×C414yes—
151C24×C53C2412yes—
152C24×C53C2411yescharacteristic
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×C53C22×C414yes—
166C22×C4×C53C22×C414yes—
167C22×C4×C53C22×C414yes—
168C22×C4×C53C22×C414yes—
169C22×C4×C53C22×C414yes—
170C22×C4×C53C22×C414yes—
171C22×C4×C53C2412yes—
172C22×C4×C53C2412yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×Dic53—22no—
178C22×Dic53—22no—
179C22×Dic53—22no—
180C22×Dic53—22no—
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×Dic53—22no—
197C22×Dic53—28no—
198C22×Dic53—28no—
199C22×Dic53—44no—
200C22×Dic53—416no—
201C22×Dic53#4114yes—
202C22×Dic53#4114yes—
203C22×Dic53#4114yes—
204C22×Dic53#4114yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C22×Dic53C2412yes—
208C22×Dic53C2412yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C4⋊C4×C53C22×C4116yescomplemented
214C4⋊C4×C53C22×C4116yescomplemented
215C4⋊C4×C53C22×C4116yescomplemented
216C22⋊C4×C53C22×C4116yes—
217C22⋊C4×C53C22×C4116yes—
218C22⋊C4×C53C22×C4116yes—
219C42×C53C22×C4116yescomplemented
220C22⋊Dic53—28no—
221C22⋊Dic53—28no—
222C22⋊Dic53—44no—
223C4⋊Dic53—28no—
224C4⋊Dic53—28no—
225C4⋊Dic53—28no—
226C4⋊Dic53—28no—
227C4⋊Dic53—44no—
228C4×Dic53—28no—
229C4×Dic53—28no—
230C4×Dic53—28no—
231C4×Dic53—28no—
232C4×Dic53—44no—
233C4×Dic53—44no—
234C4×Dic53—44no—
235C23×C53—28no—
236C23×C53—28no—
237C23×C53—28no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—44no—
245C23×C53—44no—
246C23×C53—44no—
247C23×C53—44no—
248C23×C53C23×C414yes—
249C23×C53C23×C412yes—
250C23×C53C2×#4112yes—
251C23×C53C2×#4112yes—
252C23×C53C2×#4112yes—
253C23×C53C2×#4112yes—
254C23×C53H(5,𝔽2)12yes—
255C23×C532−1+412yes—
256C23×C53C2511yescharacteristic
257C2×C4×C53—28no—
258C2×C4×C53—28no—
259C2×C4×C53—28no—
260C2×C4×C53—28no—
261C2×C4×C53—28no—
262C2×C4×C53—28no—
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×C53C23×C414yes—
276C2×C4×C53C23×C414yes—
277C2×C4×C53C23×C414yes—
278C2×C4×C53C23×C414yes—
279C2×C4×C53C23×C414yes—
280C2×C4×C53C23×C414yes—
281C2×Dic53—28no—
282C2×Dic53—28no—
283C2×Dic53—28no—
284C2×Dic53—28no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
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—416no—
306C2×Dic53—44no—
307C2×Dic53—44no—
308C2×Dic53—44no—
309C2×Dic53—44no—
310C2×Dic53C2×#4114yes—
311C2×Dic53C2×#4114yes—
312C2×Dic53C2×#4114yes—
313C2×Dic53C2×#4114yes—
314C2×#2373—531nomaximal, Sylow
315C22×C53—24no—
316C22×C53—24no—
317C22×C53—24no—
318C22×C53—416no—
319C22×C53—42no—
320C22×C53—42no—
321C22×C53—42no—
322C22×C53—42no—
323C22×C53C4×#4114yes—
324C22×C53C4×#4114yes—
325C22×C53#52014yes—
326C22×C53#55114yes—
327C22×C53#55214yes—
328C22×C53#55314yes—
329C22×C53#55614yes—
330C22×C53C24×C411yescharacteristic
331C22×C53C22×#4111yescharacteristic
332C22×C53C22×#4111yescharacteristic
333C22×C53C22×#4111yescharacteristic
334C22×C53C22×#4111yescharacteristic
335C22×C53C2×H(5,𝔽2)11yescharacteristic
336C22×C53C2×2−1+411yescharacteristic
337C4×C53—24no—
338C4×C53—24no—
339C4×C53—24no—
340C4×C53—24no—
341C4×C53—24no—
342C4×C53—24no—
343Dic53—24no—
344Dic53—24no—
345Dic53—24no—
346Dic53—24no—
347Dic53—42no—
348Dic53—42no—
349Dic53—42no—
350Dic53—42no—
351C22×#126D5311yescharacteristic
352#2373—5316no—
353C2×#389—531no—
354C2×#388—531no—
355C2×#388—531no—
356C2×#388—531no—
357C2×#387—531no—
358C2×#387—531no—
359C2×#387—531no—
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—44no—
368C2×C53#237318yescomplemented
369C2×C53C2×C4×#4111yescharacteristic
370C2×C53C2×C4×#4111yescharacteristic
371C2×C53C2×#52011yescharacteristic
372C2×C53C2×#55111yescharacteristic
373C2×C53C2×#55211yescharacteristic
374C2×C53C2×#55311yescharacteristic
375C2×C53C2×#55611yescharacteristic
376C24×C4—531no—
377C2×#126Dic53116yescomplemented
378C2×#126C2×D5318yes—
379C22×C4⋊C4—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—531no—
384C22×C4⋊C4C2×D5311yescharacteristic
385C22×C4⋊C4C2×D5311yescharacteristic
386C22×C4⋊C4C2×D5311yescharacteristic
387C22×C22⋊C4—531no—
388C22×C22⋊C4—531no—
389C22×C22⋊C4—531no—
390C22×C22⋊C4C2×D5311yescharacteristic
391C22×C22⋊C4C2×D5311yescharacteristic
392C22×C22⋊C4C2×D5311yescharacteristic
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#387—538no—
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×#95—531no—
424C2×#95—531no—
425C2×#95—531no—
426C2×#95—531no—
427C53C2×#237311yescharacteristic, complemented, Sylow
428C25C22×D5311yescharacteristic
429C23×C4—531no—
430C23×C4—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—531no—
437C23×C4—534no—
438C23×C4—1064no—
439C23×C4—1064no—
440C23×C4—2122no—
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C23×C4C22×D5311yescharacteristic
445C23×C4C22×D5311yescharacteristic
446C23×C4C22×D5311yescharacteristic
447#126C2×Dic53164yescomplemented
448C2×C4⋊C4—534no—
449C2×C4⋊C4—534no—
450C2×C4⋊C4—534no—
451C2×C4⋊C4—534no—
452C2×C4⋊C4—534no—
453C2×C4⋊C4—1064no—
454C2×C4⋊C4—1064no—
455C2×C4⋊C4—1064no—
456C2×C4⋊C4—1064no—
457C2×C4⋊C4—2122no—
458C2×C4⋊C4C2×Dic5318yescomplemented
459C2×C4⋊C4C2×Dic5318yescomplemented
460C2×C4⋊C4C2×Dic5318yescomplemented
461C2×C4⋊C4C22×D5314yes—
462C2×C4⋊C4C22×D5314yes—
463C2×C4⋊C4C22×D5314yes—
464C2×C22⋊C4—534no—
465C2×C22⋊C4—534no—
466C2×C22⋊C4—534no—
467C2×C22⋊C4—1064no—
468C2×C22⋊C4—1064no—
469C2×C22⋊C4—2122no—
470C2×C22⋊C4C2×Dic5318yes—
471C2×C22⋊C4C2×Dic5318yes—
472C2×C22⋊C4C2×Dic5318yes—
473C2×C22⋊C4C22×D5314yes—
474C2×C22⋊C4C22×D5314yes—
475C2×C22⋊C4C22×D5314yes—
476C2×C42—534no—
477C2×C42—534no—
478C2×C42—534no—
479C2×C42—534no—
480C2×C42—534no—
481C2×C42—534no—
482C2×C42—534no—
483C2×C42—1064no—
484C2×C42—1064no—
485C2×C42—1064no—
486C2×C42—1064no—
487C2×C42—2122no—
488C2×C42—2122no—
489C2×C42—2122no—
490C2×C42C2×Dic5318yescomplemented
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#95—534no—
501#95—534no—
502#95—534no—
503#95—534no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—22no—
509C24—22no—
510C24C22×Dic5314yes—
511C24C23×D5312yes—
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—534no—
526C22×C4—534no—
527C22×C4—534no—
528C22×C4—534no—
529C22×C4—532no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—532no—
533C22×C4—532no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—1068no—
538C22×C4—1068no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
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—2124no—
560C22×C4—21216no—
561C22×C4C22×Dic5314yes—
562C22×C4C22×Dic5314yes—
563C22×C4C22×Dic5314yes—
564C22×C4C22×Dic5314yes—
565C22×C4C22×Dic5314yes—
566C22×C4C22×Dic5314yes—
567C22×C4C23×D5312yes—
568C22×C4C23×D5312yes—
569C22×C4C23×D5312yes—
570C22×C4C23×D5312yes—
571C22×C4C23×D5312yes—
572C22×C4C23×D5312yes—
573C4⋊C4—1068no—
574C4⋊C4—1068no—
575C4⋊C4—1068no—
576C4⋊C4—1068no—
577C4⋊C4—2124no—
578C4⋊C4C22×Dic53116yescomplemented
579C4⋊C4C22×Dic53116yescomplemented
580C4⋊C4C22×Dic53116yescomplemented
581C22⋊C4—1068no—
582C22⋊C4—1068no—
583C22⋊C4—2124no—
584C22⋊C4C22×Dic53116yes—
585C22⋊C4C22×Dic53116yes—
586C22⋊C4C22×Dic53116yes—
587C42—1068no—
588C42—1068no—
589C42—1068no—
590C42—1068no—
591C42—2124no—
592C42—2124no—
593C42—2124no—
594C42C22×Dic53116yescomplemented
595C23—28no—
596C23—28no—
597C23—28no—
598C23—22no—
599C23—22no—
600C23—22no—
601C23—22no—
602C23—22no—
603C23—22no—
604C23—44no—
605C23—44no—
606C23—44no—
607C23—44no—
608C23C23×Dic5314yes—
609C23C23×Dic5312yes—
610C23#41×D5312yes—
611C23#41×D5312yes—
612C23#41×D5312yes—
613C23#41×D5312yes—
614C23#1313326312yes—
615C23#1313326412yes—
616C23C24×D5311yescharacteristic
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—28no—
621C2×C4—28no—
622C2×C4—28no—
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—534no—
636C2×C4—534no—
637C2×C4—534no—
638C2×C4—534no—
639C2×C4—1068no—
640C2×C4—1068no—
641C2×C4—1068no—
642C2×C4—1068no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1062no—
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—21216no—
664C2×C4—2124no—
665C2×C4—2124no—
666C2×C4—2124no—
667C2×C4—2124no—
668C2×C4C23×Dic5314yes—
669C2×C4C23×Dic5314yes—
670C2×C4C23×Dic5314yes—
671C2×C4C23×Dic5314yes—
672C2×C4C23×Dic5314yes—
673C2×C4C23×Dic5314yes—
674C22—24no—
675C22—24no—
676C22—24no—
677C22—42no—
678C22—416no—
679C22—42no—
680C22—42no—
681C22—42no—
682C22#41×Dic5314yes—
683C22#41×Dic5314yes—
684C22#1681110614yes—
685C22#1681129814yes—
686C22#1681130914yes—
687C22#1681132414yes—
688C22#1681134014yes—
689C22C24×Dic5311yescharacteristic
690C22C2×#41×D5311yescharacteristic
691C22C2×#41×D5311yescharacteristic
692C22C2×#41×D5311yescharacteristic
693C22C2×#41×D5311yescharacteristic
694C22C2×#1313326311yescharacteristic
695C22C2×#1313326411yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—24no—
701C4—24no—
702C4—1064no—
703C4—1064no—
704C4—1064no—
705C4—1064no—
706C4—2122no—
707C4—2122no—
708C4—2122no—
709C4—2122no—
710C2—44no—
711C2#2027783918yesdirect product factor
712C2C2×#41×Dic5311yescharacteristic
713C2C2×#41×Dic5311yescharacteristic
714C2C2×#1681110611yescharacteristic
715C2C2×#1681129811yescharacteristic
716C2C2×#1681130911yescharacteristic
717C2C2×#1681132411yescharacteristic
718C2C2×#1681134011yescharacteristic
subgroupG/H
centerC24C23×D53
commutatorC22×C53C24×C4
FrattiniC23C24×D53
FittingC22×#126×C53C2
socleC24×C53C24
prime radicalC25×C53C23
cosocleC23×C53C25
hypercenterC22×#126D53
hypocenterC53C2×#2373
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. #20277839C2direct (N × H)
2. C2×#16810522C2semidirect
6. C2×#16810509C2semidirect
7. C2×#16810509C2semidirect
8. C2×#16810509C2semidirect
10. C2×C4⋊C4×Dic53C2semidirect
11. C2×C4⋊C4×Dic53C2semidirect
12. C2×C4×C4⋊Dic53C2semidirect
15. C2×#16810469C2semidirect
33. #16810522C22semidirect
37. #16810509C22semidirect
38. #16810509C22semidirect
39. #16810509C22semidirect
41. C4⋊C4×Dic53C22semidirect
42. C4⋊C4×Dic53C22semidirect
43. C4×C4⋊Dic53C22semidirect
46. #16810469C22semidirect
59. C2×#126×C53C4semidirect
129. #126×C53C2×C4semidirect
130. C2×C4⋊C4×C53C2×C4semidirect
131. C2×C4⋊C4×C53C2×C4semidirect
132. C2×C4⋊C4×C53C2×C4semidirect
142. C2×C42×C53C2×C4semidirect
213. C4⋊C4×C53C22×C4semidirect
214. C4⋊C4×C53C22×C4semidirect
215. C4⋊C4×C53C22×C4semidirect
219. C42×C53C22×C4semidirect
368. C2×C53#2373semidirect
377. C2×#126Dic53semidirect
427. C53C2×#2373semidirect
447. #126C2×Dic53semidirect
458. C2×C4⋊C4C2×Dic53semidirect
459. C2×C4⋊C4C2×Dic53semidirect
460. C2×C4⋊C4C2×Dic53semidirect
490. C2×C42C2×Dic53semidirect
578. C4⋊C4C22×Dic53semidirect
579. C4⋊C4C22×Dic53semidirect
580. C4⋊C4C22×Dic53semidirect
594. C42C22×Dic53semidirect
711. C2#20277839direct (N × H)

Maximal subgroups

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

subgroupindex
#202778392
C2×#168105222
C2×#168105162
C2×#168105092
C2×#168104982
C2×C4⋊C4×Dic532
C2×C4×C4⋊Dic532
C2×C22⋊C4×Dic532
C2×#168104692
C22×#126×C532
C2×#237353