Finite Group Databasebeta

← C2×#20257291 #27124647

Subgroups — C2×#20257291 #27124647

Order 12032.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257291C2132yesmaximal, direct product factor
2C2×#15689841C212yesmaximal, complemented
3C2×#15689836C212yesmaximal, complemented
4C2×#15689828C212yesmaximal, complemented
5C2×#15689822C214yesmaximal, complemented
6C2×#15689782C214yesmaximal, complemented
7C2×#15689774C212yesmaximal, complemented
8C2×#15689745C212yesmaximal, complemented
9C2×#15689738C212yesmaximal, complemented
10C2×#15689704C211yesmaximal, characteristic, complemented
11C2×#15689701C211yesmaximal, characteristic, complemented
12C2×#15689677C212yesmaximal, complemented
13C2×#15689670C212yesmaximal, complemented
14C2×#15689669C211yesmaximal, characteristic, complemented
15C22×#13094023C211yesmaximal, characteristic, complemented
16C2×#15689603C211yesmaximal, characteristic, complemented
17C2×#15689591C211yesmaximal, characteristic, complemented
18C2×C47×#520C211yesmaximal, characteristic, complemented
19C22×#10625350C2211yescharacteristic
20C22×#10625350C2211yescharacteristic
21C22×#10625350C2214yes—
22C23×Dic94C2212yes—
23#15689841C22132yescomplemented
24#15689836C22132yescomplemented
25#15689828C22132yescomplemented
26#15689822C22164yescomplemented
27#15689782C22164yescomplemented
28#15689774C22132yescomplemented
29#15689745C22132yescomplemented
30#15689738C22132yescomplemented
31#15689704C22116yescomplemented
32#15689701C22116yescomplemented
33#15689677C22132yescomplemented
34#15689670C22132yescomplemented
35#15689669C22116yescomplemented
36C2×#13094023C2212yes—
37C2×#13094023C2212yes—
38C2×#13094023C2212yes—
39C2×#13094023C2212yes—
40C2×#13094023C22116yescomplemented
41C2×#13094022C2211yescharacteristic
42C2×#13094020C2211yescharacteristic
43C2×#13094018C2214yes—
44C2×#13094017C2214yes—
45C2×#13094014C2214yes—
46C2×#13094013C2211yescharacteristic
47C2×#13094012C2214yes—
48C2×#13094011C2211yescharacteristic
49C2×#13094010C2214yes—
50C2×#13094010C2214yes—
51C2×#13094009C2214yes—
52C2×#13094007C2214yes—
53C2×#13094004C2212yes—
54C2×#13094004C2212yes—
55C2×#13094003C2214yes—
56C2×#13094003C2212yes—
57C2×#13094002C2214yes—
58C2×#13094002C2214yes—
59C2×#13094000C2212yes—
60C2×#13093999C2212yes—
61C2×#13093999C2212yes—
62C2×#13093998C2212yes—
63C2×#13093998C2214yes—
64C2×#13093997C2214yes—
65C2×#13093996C2212yes—
66C2×#13093996C2214yes—
67C2×#13093996C2212yes—
68C2×#13093995C2212yes—
69#15689603C22116yescomplemented
70#15689591C22116yescomplemented
71C2×C4×Dic94C2212yes—
72C2×C4×Dic94C2214yes—
73C2×#13093989C2211yescharacteristic
74C2×#13093989C2211yescharacteristic
75C2×C4×D188C2212yes—
76C2×#13093986C2211yescharacteristic
77C2×#13093986C2211yescharacteristic
78C2×C4×C22⋊D47C2212yes—
79C2×C4×C22⋊D47C2214yes—
80C2×C4×C22⋊D47C2212yes—
81C2×(C22⋊D47)⋊C4C2212yes—
82C2×(C22⋊D47)⋊C4C2212yes—
83C2×(C22⋊D47)⋊C4C2214yes—
84C2×#13093982C2212yes—
85C2×#13093981C2212yes—
86C2×#13093981C2214yes—
87C22×C4⋊Dic47C2211yescharacteristic
88C22×Dic47⋊C4C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C22×C4×Dic47C2211yescharacteristic
91C2×C42×D47C2212yes—
92C22×#41×C47C2211yescharacteristic
93C47×#520C22116yescomplemented
94C2×C4×Q8×C47C2212yes—
95C2×C4×D4×C47C2214yes—
96C2×C4×D4×C47C2212yes—
97C2×#117×C47C2211yescharacteristic
98C2×#117×C47C2212yes—
99C22×C4⋊C4×C47C2212yes—
100C22×C4⋊C4×C47C2211yescharacteristic
101C2×#10625350—28no—
102C2×#10625350—28no—
103C2×#10625350—416no—
104C2×#10625350C2318yes—
105C2×#10625350C2318yes—
106C2×#10625350C23132yes—
107C22×Dic94—48no—
108C22×Dic94C2311yescharacteristic
109C22×Dic94C2311yescharacteristic
110C22×Dic94C2314yes—
111C22×Dic94C23116yes—
112C22×Dic94C2314yes—
113C22×D188C2311yescharacteristic
114C22×D188C2311yescharacteristic
115C22×D188C2314yes—
116C22×C22⋊D47C2312yes—
117C22×C22⋊D47C2312yes—
118C22×C22⋊D47C2312yes—
119C22×C22⋊D47C2312yes—
120C22×C22⋊D47C2314yes—
121C23×Dic47C2311yescharacteristic
122C23×Dic47C2311yescharacteristic
123C23×Dic47C2312yes—
124C22×C4×D47C2312yes—
125C22×C4×D47C2312yes—
126C22×C4×D47C2312yes—
127C22×C4×D47C2312yes—
128C22×C4×D47C2314yes—
129#13094023C23116yes—
130#13094023C23116yes—
131#13094023C23116yes—
132#13094023C23116yes—
133#13094022C2318yes—
134#13094020C2318yes—
135#13094018C23132yes—
136#13094017C23132yes—
137#13094014C23132yes—
138#13094013C2318yes—
139#13094012C23132yes—
140#13094011C2318yes—
141#13094010C23132yes—
142#13094010C23132yes—
143#13094009C23132yes—
144#13094007C23132yes—
145#13094004C23116yes—
146#13094004C23116yes—
147#13094003C23132yes—
148#13094003C23116yes—
149#13094002C23132yes—
150#13094002C23132yes—
151#13094000C23116yes—
152#13093999C23116yes—
153#13093999C23116yes—
154#13093998C23116yes—
155#13093998C23132yes—
156#13093997C23132yes—
157#13093996C23116yes—
158#13093996C23132yes—
159#13093996C23116yes—
160#13093995C23116yes—
161C4×Dic94C23116yes—
162C4×Dic94C23132yes—
163#13093989C2318yes—
164#13093989C2318yes—
165C4×D188C23116yes—
166#13093986C2318yes—
167#13093986C2318yes—
168C4×C22⋊D47C23116yes—
169C4×C22⋊D47C23132yes—
170C4×C22⋊D47C23116yes—
171(C22⋊D47)⋊C4C23116yes—
172(C22⋊D47)⋊C4C23132yes—
173(C22⋊D47)⋊C4C23116yes—
174#13093982C23116yes—
175#13093981C23116yes—
176#13093981C23132yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2318yes—
180C2×C4⋊Dic47C2314yes—
181C2×Dic47⋊C4C23116yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2312yes—
189C2×Dic47⋊C4C2314yes—
190C4⋊C4×D47C23116yes—
191C2×C22⋊Dic47C2314yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2314yes—
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2311yescharacteristic
206C2×C4×Dic47C2311yescharacteristic
207C2×C4×Dic47C2311yescharacteristic
208C2×C4×Dic47C2318yes—
209C2×C4×Dic47C2314yes—
210C42×D47C23116yes—
211C2×#41×C47—28no—
212C2×#41×C47C2318yes—
213C22×Q8×C47C2311yescharacteristic
214C22×D4×C47C2311yescharacteristic
215C22×D4×C47C2312yes—
216C23×C4×C47C2312yes—
217C23×C4×C47C2312yes—
218C23×C4×C47C2314yes—
219C23×C4×C47C2311yescharacteristic
220C4×Q8×C47C23116yes—
221C4×D4×C47C23116yes—
222C4×D4×C47C23132yes—
223#117×C47C23116yes—
224#117×C47C2318yes—
225C2×C4⋊C4×C47C23116yes—
226C2×C4⋊C4×C47C2311yescharacteristic
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2312yes—
229C2×C4⋊C4×C47C2314yes—
230C2×C4⋊C4×C47C2318yes—
231C2×C4⋊C4×C47C2311yescharacteristic
232C2×C22⋊C4×C47C2312yes—
233C2×C22⋊C4×C47C2314yes—
234C2×C42×C47C2312yes—
235C2×C42×C47C2314yes—
236C24×C47C2412yes—
237C24×C47C2411yescharacteristic
238C23×D47C2412yes—
239C23×D47C2412yes—
240#41×C47—232no—
241C2×Q8×C47—24no—
242C2×Q8×C47C2414yes—
243C2×D4×C47—28no—
244C2×D4×C47—24no—
245C2×D4×C47C2414yes—
246C2×D4×C47C2418yes—
247C22×C4×C47—28no—
248C22×C4×C47—44no—
249C22×C4×C47—48no—
250C22×C4×C47#4118yescomplemented
251C22×C4×C47C2412yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2412yes—
254C22×C4×C47C2414yes—
255C22×C4×C47C2418yes—
256C22×C4×C47C2418yes—
257C22×C4×C47C24116yes—
258C22×C4×C47C2411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260C22×C4×C47C2414yes—
261C2×C22⋊D47—28no—
262C2×C22⋊D47—28no—
263C2×C22⋊D47—28no—
264C2×C22⋊D47—28no—
265C2×C22⋊D47—48no—
266C2×C22⋊D47C2418yes—
267C2×C22⋊D47C2418yes—
268C2×C22⋊D47C2418yes—
269C2×C22⋊D47C2418yes—
270C2×C22⋊D47C24116yes—
271C22×Dic47—24no—
272C22×Dic47—24no—
273C22×Dic47—44no—
274C22×Dic47C2411yescharacteristic
275C22×Dic47C2411yescharacteristic
276C22×Dic47C2412yes—
277C22×Dic47C2412yes—
278C22×Dic47C2414yes—
279C22×Dic47C2414yes—
280C22×Dic47C2414yes—
281C22×Dic47C2418yes—
282C22×Dic47C2411yescharacteristic
283C22×Dic47C2411yescharacteristic
284#10625350—232no—
285#10625350—232no—
286#10625350—464no—
287C2×D188—24no—
288C2×D188—24no—
289C2×D188—48no—
290C2×D188C2414yes—
291C2×D188C2414yes—
292C2×D188C24116yes—
293C2×C4×D47—28no—
294C2×C4×D47—28no—
295C2×C4×D47—28no—
296C2×C4×D47—28no—
297C2×C4×D47—48no—
298C2×C4×D47C2418yes—
299C2×C4×D47C2418yes—
300C2×C4×D47C2418yes—
301C2×C4×D47C2418yes—
302C2×C4×D47C24116yes—
303C2×Dic94—24no—
304C2×Dic94—24no—
305C2×Dic94—216no—
306C2×Dic94—432no—
307C2×Dic94—48no—
308C2×Dic94C2414yes—
309C2×Dic94C2414yes—
310C2×Dic94C24116yes—
311C2×Dic94C24116yes—
312C4⋊C4×C47C2414yes—
313C4⋊C4×C47C2418yes—
314C4⋊C4×C47C2418yes—
315C4⋊C4×C47C24116yes—
316C4⋊C4×C47C2414yes—
317C22⋊C4×C47C2418yes—
318C22⋊C4×C47C24116yes—
319C42×C47C2418yes—
320C42×C47C24116yes—
321C22⋊Dic47C24116yes—
322C22⋊Dic47C2418yes—
323C22⋊Dic47C2418yes—
324(C2×D47)⋊C4C2418yes—
325(C2×D47)⋊C4C2418yes—
326(C2×D47)⋊C4C24116yes—
327(C2×D47)⋊C4C24116yes—
328(C2×D47)⋊C4C24116yes—
329(C2×D47)⋊C4C2418yes—
330(C2×D47)⋊C4C2418yes—
331(C2×D47)⋊C4C24116yes—
332C4⋊Dic47C2418yes—
333C4⋊Dic47C2418yes—
334C4⋊Dic47C24116yes—
335Dic47⋊C4C24116yes—
336Dic47⋊C4C24116yes—
337Dic47⋊C4C24116yes—
338Dic47⋊C4C2418yes—
339Dic47⋊C4C2418yes—
340Dic47⋊C4C2418yes—
341Dic47⋊C4C2418yes—
342Dic47⋊C4C24116yes—
343C4×Dic47C2414yes—
344C4×Dic47C2418yes—
345C4×Dic47C2418yes—
346C4×Dic47C2414yes—
347C4×Dic47C2414yes—
348C4×Dic47C2414yes—
349C4×Dic47C24116yes—
350C23×C47—22no—
351C23×C47—22no—
352C23×C47—24no—
353C23×C47—24no—
354C23×C47—24no—
355C23×C47C2×#4114yes—
356C23×C47C2514yes—
357C23×C47C2512yes—
358C23×C47C2511yescharacteristic
359C22×D47—24no—
360C22×D47—24no—
361C22×D47—24no—
362C22×D47—24no—
363C22×D47—24no—
364C22×D47—24no—
365C22×D47C2514yes—
366C22×D47C2514yes—
367Q8×C47—28no—
368D4×C47—216no—
369D4×C47—28no—
370C2×C4×C47—24no—
371C2×C4×C47—28no—
372C2×C4×C47—24no—
373C2×C4×C47—24no—
374C2×C4×C47—216no—
375C2×C4×C47—48no—
376C2×C4×C47—416no—
377C2×C4×C47C2×#4114yes—
378C2×C4×C47C2×#4114yes—
379C2×C4×C47C2×#41116yescomplemented
380C2×C4×C47C2514yes—
381C2×C4×C47C2514yes—
382C2×C4×C47C2514yes—
383C2×C4×C47C2518yes—
384C2×C4×C47C2512yes—
385C2×C4×C47C2512yes—
386C22⋊D47—216no—
387C22⋊D47—216no—
388C22⋊D47—216no—
389C22⋊D47—216no—
390C22⋊D47—416no—
391C2×Dic47—24no—
392C2×Dic47—24no—
393C2×Dic47—28no—
394C2×Dic47—22no—
395C2×Dic47—22no—
396C2×Dic47—28no—
397C2×Dic47—28no—
398C2×Dic47—48no—
399C2×Dic47H(5,𝔽2)14yes—
400C2×Dic472−1+414yes—
401C2×Dic47C2512yes—
402C2×Dic47C2514yes—
403C2×Dic47C2514yes—
404C2×Dic47C2512yes—
405C2×Dic47C2518yes—
406C2×Dic47C2512yes—
407C2×Dic47C2512yes—
408D188—28no—
409D188—28no—
410D188—416no—
411C4×D47—216no—
412C4×D47—216no—
413C4×D47—216no—
414C4×D47—216no—
415C4×D47—416no—
416Dic94—28no—
417Dic94—28no—
418Dic94—232no—
419Dic94—416no—
420C2×#3511—471nomaximal, Sylow
421C22×C47—22no—
422C22×C47—22no—
423C22×C47—28no—
424C22×C47—24no—
425C22×C47—24no—
426C22×C47—24no—
427C22×C47—48no—
428C22×C47C22×#4114yes—
429C22×C47C22×#4112yes—
430C22×C47C2×H(5,𝔽2)12yes—
431C22×C47C2×2−1+412yes—
432C22×C47C2611yescharacteristic
433C2×D47—24no—
434C2×D47—24no—
435C2×D47—24no—
436C2×D47—24no—
437C2×D47—24no—
438C2×D47—24no—
439C2×D47—48no—
440C2×D47—48no—
441C4×C47—24no—
442C4×C47—28no—
443C4×C47—24no—
444C4×C47—24no—
445C4×C47C22×#4114yes—
446C4×C47C22×#4114yes—
447Dic47—24no—
448Dic47—24no—
449Dic47—28no—
450Dic47—22no—
451Dic47—22no—
452Dic47C2×H(5,𝔽2)14yes—
453Dic47C2×2−1+414yes—
454#3511—4732no—
455C2×#556—472no—
456C2×#555—472no—
457C2×#554—472no—
458C2×#553—474no—
459C2×#548—474no—
460C2×#547—472no—
461C2×#542—472no—
462C2×#542—472no—
463C2×#537—471no—
464C2×#537—471no—
465C2×#533—472no—
466C2×#532—471no—
467C2×#532—472no—
468C22×C4⋊Q8—471no—
469C2×#520—471no—
470C2×#520D4711yescharacteristic, complemented
471C2×C4×#41—471no—
472C2×C47—24no—
473C2×C47—44no—
474C2×C47#351114yescomplemented
475C2×C47C23×#4111yescharacteristic
476C2×C47C22×H(5,𝔽2)11yescharacteristic
477C2×C47C22×2−1+411yescharacteristic
478D47—44no—
479D47—44no—
480C22×#41—471no—
481C22×#41—471no—
482C22×#41—474no—
483C22×#41C2×D4711yescharacteristic
484C23×Q8—472no—
485#556—4732no—
486#555—4732no—
487#554—4732no—
488#553—4764no—
489#548—4764no—
490#547—4732no—
491#542—4732no—
492#542—4732no—
493#537—4716no—
494#537—4716no—
495#533—4732no—
496#532—4716no—
497#532—4732no—
498C2×C4⋊Q8—471no—
499C2×C4⋊Q8—472no—
500C2×C4⋊Q8—472no—
501C2×C4⋊Q8—472no—
502C2×C4⋊Q8—472no—
503C2×C4⋊Q8—4716no—
504C2×#127—471no—
505C2×#126—474no—
506C2×#126—474no—
507C2×#125—474no—
508C2×#124—471no—
509C2×#124—471no—
510C2×#124—474no—
511C2×#124—474no—
512C2×#124—474no—
513C2×#123—474no—
514C2×#123—474no—
515C2×C22⋊Q8—472no—
516C2×C22⋊Q8—472no—
517C2×C22⋊Q8—474no—
518C2×C22⋊Q8—472no—
519C2×C22⋊Q8—474no—
520C2×C22⋊Q8—472no—
521C2×C22⋊Q8—474no—
522C2×#121—472no—
523C2×#121—472no—
524C2×#121—472no—
525C2×#121—474no—
526C2×#121—472no—
527C2×#121—474no—
528C2×#121—472no—
529C2×#121—472no—
530C2×#121—474no—
531#520—4716no—
532#520C2×D47116yescomplemented
533C4×#41—4716no—
534C2×C4×Q8—471no—
535C2×C4×Q8—471no—
536C2×C4×Q8—472no—
537C2×C4×Q8—474no—
538C2×C4×Q8C2×D4712yes—
539C2×C4×D4—472no—
540C2×C4×D4—474no—
541C2×C4×D4—472no—
542C2×C4×D4—471no—
543C2×C4×D4—471no—
544C2×C4×D4—472no—
545C2×C4×D4—472no—
546C2×C4×D4—474no—
547C2×C4×D4—472no—
548C2×C4×D4C2×D4712yes—
549C2×C4×D4C2×D4714yes—
550C2×#117—472no—
551C2×#117—472no—
552C2×#117—474no—
553C2×#117C2×D4711yescharacteristic
554C2×#117C2×D4712yes—
555C22×C4⋊C4—471no—
556C22×C4⋊C4—472no—
557C22×C4⋊C4—472no—
558C22×C4⋊C4C2×D4711yescharacteristic
559C22×C4⋊C4C2×D4712yes—
560C22×C42—471no—
561C22×C42—472no—
562C47C2×#351111yescharacteristic, complemented, Sylow
563C2×#41—28no—
564C2×#41—478no—
565C2×#41—478no—
566C2×#41—4732no—
567C2×#41—948no—
568C2×#41—948no—
569C2×#41—18816no—
570C2×#41C22×D4718yes—
571C22×Q8—471no—
572C22×Q8—471no—
573C22×Q8—474no—
574C22×Q8—474no—
575C22×Q8—4716no—
576C22×Q8—1888no—
577C22×Q8C22×D4711yescharacteristic
578C22×D4—472no—
579C22×D4—472no—
580C22×D4—472no—
581C22×D4—472no—
582C22×D4—474no—
583C22×D4—471no—
584C22×D4—471no—
585C22×D4—474no—
586C22×D4C22×D4712yes—
587C22×D4C22×D4711yescharacteristic
588C23×C4—471no—
589C23×C4—471no—
590C23×C4—472no—
591C23×C4—472no—
592C23×C4—472no—
593C23×C4—472no—
594C23×C4—472no—
595C23×C4—474no—
596C23×C4C22×D4712yes—
597C23×C4C22×D4712yes—
598C23×C4C22×D4714yes—
599C23×C4C22×D4711yescharacteristic
600C4⋊Q8—478no—
601C4⋊Q8—4716no—
602C4⋊Q8—4716no—
603C4⋊Q8—4716no—
604C4⋊Q8—4716no—
605#127—478no—
606#126—4732no—
607#126—4732no—
608#125—4732no—
609#124—478no—
610#124—478no—
611#124—4732no—
612#124—4732no—
613#124—4732no—
614#123—4732no—
615#123—4732no—
616C22⋊Q8—4716no—
617C22⋊Q8—4716no—
618C22⋊Q8—4732no—
619C22⋊Q8—4716no—
620C22⋊Q8—4732no—
621C22⋊Q8—4716no—
622C22⋊Q8—4732no—
623#121—4716no—
624#121—4716no—
625#121—4716no—
626#121—4732no—
627#121—4716no—
628#121—4732no—
629#121—4716no—
630#121—4716no—
631#121—4732no—
632C4×Q8—478no—
633C4×Q8—478no—
634C4×Q8—4716no—
635C4×Q8—4732no—
636C4×Q8C22×D47116yes—
637C4×D4—4716no—
638C4×D4—4732no—
639C4×D4—4716no—
640C4×D4—478no—
641C4×D4—478no—
642C4×D4—4716no—
643C4×D4—4716no—
644C4×D4—4732no—
645C4×D4—4716no—
646C4×D4C22×D47116yes—
647C4×D4C22×D47132yes—
648#117—4716no—
649#117—4716no—
650#117—4732no—
651#117C22×D4718yes—
652#117C22×D47116yes—
653C2×C4⋊C4—472no—
654C2×C4⋊C4—474no—
655C2×C4⋊C4—472no—
656C2×C4⋊C4—474no—
657C2×C4⋊C4—478no—
658C2×C4⋊C4—474no—
659C2×C4⋊C4—4716no—
660C2×C4⋊C4—472no—
661C2×C4⋊C4—472no—
662C2×C4⋊C4—472no—
663C2×C4⋊C4—472no—
664C2×C4⋊C4—474no—
665C2×C4⋊C4—474no—
666C2×C4⋊C4—4716no—
667C2×C4⋊C4C22×D4711yescharacteristic
668C2×C4⋊C4C22×D4712yes—
669C2×C4⋊C4C22×D4712yes—
670C2×C4⋊C4C22×D4714yes—
671C2×C4⋊C4C22×D4718yes—
672C2×C4⋊C4C22×D47116yes—
673C2×C4⋊C4C22×D4711yescharacteristic
674C2×C22⋊C4—474no—
675C2×C22⋊C4—472no—
676C2×C22⋊C4—472no—
677C2×C22⋊C4—474no—
678C2×C22⋊C4—472no—
679C2×C22⋊C4—472no—
680C2×C22⋊C4—474no—
681C2×C22⋊C4—474no—
682C2×C22⋊C4—474no—
683C2×C22⋊C4—472no—
684C2×C22⋊C4—472no—
685C2×C22⋊C4C22×D4712yes—
686C2×C22⋊C4C22×D4714yes—
687C2×C42—474no—
688C2×C42—471no—
689C2×C42—472no—
690C2×C42—471no—
691C2×C42—471no—
692C2×C42—472no—
693C2×C42—478no—
694C2×C42—471no—
695C2×C42—4716no—
696C2×C42C22×D4712yes—
697C2×C42C22×D4714yes—
698C24—472no—
699C24—472no—
700C24C23×D4712yes—
701C24C23×D4711yescharacteristic
702#41—232no—
703#41—9432no—
704#41—9432no—
705#41—18864no—
706C2×Q8—24no—
707C2×Q8—474no—
708C2×Q8—474no—
709C2×Q8—4716no—
710C2×Q8—4716no—
711C2×Q8—9416no—
712C2×Q8—944no—
713C2×Q8—944no—
714C2×Q8—1888no—
715C2×Q8—18832no—
716C2×Q8C23×D4714yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—478no—
720C2×D4—478no—
721C2×D4—478no—
722C2×D4—478no—
723C2×D4—4716no—
724C2×D4—474no—
725C2×D4—474no—
726C2×D4—4716no—
727C2×D4—948no—
728C2×D4—948no—
729C2×D4—948no—
730C2×D4—948no—
731C2×D4—944no—
732C2×D4—944no—
733C2×D4—1888no—
734C2×D4—1888no—
735C2×D4C23×D4718yes—
736C2×D4C23×D4714yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—471no—
741C22×C4—471no—
742C22×C4—474no—
743C22×C4—474no—
744C22×C4—471no—
745C22×C4—471no—
746C22×C4—472no—
747C22×C4—472no—
748C22×C4—474no—
749C22×C4—478no—
750C22×C4—478no—
751C22×C4—478no—
752C22×C4—478no—
753C22×C4—478no—
754C22×C4—4716no—
755C22×C4—948no—
756C22×C4—948no—
757C22×C4—944no—
758C22×C4—944no—
759C22×C4—948no—
760C22×C4—948no—
761C22×C4—1888no—
762C22×C4—1884no—
763C22×C4#1062535018yescomplemented
764C22×C4C23×D4718yes—
765C22×C4C23×D4712yes—
766C22×C4C23×D4712yes—
767C22×C4C23×D4712yes—
768C22×C4C23×D4714yes—
769C22×C4C23×D4718yes—
770C22×C4C23×D47116yes—
771C22×C4C23×D4711yescharacteristic
772C22×C4C23×D4711yescharacteristic
773C22×C4C23×D4714yes—
774C4⋊C4—4716no—
775C4⋊C4—4716no—
776C4⋊C4—4716no—
777C4⋊C4—478no—
778C4⋊C4—478no—
779C4⋊C4—478no—
780C4⋊C4—478no—
781C4⋊C4—4716no—
782C4⋊C4—478no—
783C4⋊C4—478no—
784C4⋊C4—4716no—
785C4⋊C4C23×D4714yes—
786C4⋊C4C23×D4718yes—
787C4⋊C4C23×D4718yes—
788C4⋊C4C23×D47116yes—
789C4⋊C4C23×D4714yes—
790C22⋊C4—4716no—
791C22⋊C4—478no—
792C22⋊C4—478no—
793C22⋊C4—4716no—
794C22⋊C4—478no—
795C22⋊C4—478no—
796C22⋊C4—4716no—
797C22⋊C4—4716no—
798C22⋊C4—4716no—
799C22⋊C4—478no—
800C22⋊C4—478no—
801C22⋊C4C23×D4718yes—
802C22⋊C4C23×D47116yes—
803C42—474no—
804C42—474no—
805C42—478no—
806C42—474no—
807C42—474no—
808C42—478no—
809C42—4716no—
810C42C23×D4718yes—
811C42C23×D47116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—474no—
818C23—474no—
819C23—944no—
820C23—944no—
821C23—944no—
822C23—944no—
823C23—944no—
824C23—944no—
825C23C2×#1062535014yes—
826C23C24×D4714yes—
827C23C24×D4712yes—
828C23C24×D4711yescharacteristic
829Q8—28no—
830Q8—9432no—
831Q8—948no—
832Q8—948no—
833Q8—18816no—
834D4—216no—
835D4—28no—
836D4—9416no—
837D4—9416no—
838D4—9416no—
839D4—9416no—
840D4—948no—
841D4—948no—
842D4—18816no—
843D4—18816no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—474no—
852C2×C4—474no—
853C2×C4—472no—
854C2×C4—472no—
855C2×C4—472no—
856C2×C4—472no—
857C2×C4—474no—
858C2×C4—474no—
859C2×C4—478no—
860C2×C4—9416no—
861C2×C4—9416no—
862C2×C4—948no—
863C2×C4—948no—
864C2×C4—944no—
865C2×C4—944no—
866C2×C4—942no—
867C2×C4—948no—
868C2×C4—942no—
869C2×C4—9416no—
870C2×C4—9416no—
871C2×C4—18816no—
872C2×C4—1888no—
873C2×C4C2×#1062535014yes—
874C2×C4C2×#1062535014yes—
875C2×C4C2×#10625350116yescomplemented
876C2×C4C24×D4714yes—
877C2×C4C24×D4714yes—
878C2×C4C24×D4714yes—
879C2×C4C24×D4718yes—
880C2×C4C24×D4712yes—
881C2×C4C24×D4712yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—944no—
890C22—944no—
891C22—944no—
892C22—944no—
893C22—944no—
894C22—944no—
895C22—1888no—
896C22—1888no—
897C22C22×#1062535014yes—
898C22C22×#1062535012yes—
899C22H(5,𝔽2)×D4712yes—
900C222−1+4×D4712yes—
901C22C25×D4711yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—474no—
907C4—474no—
908C4—944no—
909C4—944no—
910C4—942no—
911C4—948no—
912C4—942no—
913C4C22×#1062535014yes—
914C4C22×#1062535014yes—
915C2—24no—
916C2—44no—
917C2—1884no—
918C2—1884no—
919C2#2025729114yesdirect product factor
920C2C23×#1062535011yescharacteristic
921C2C2×H(5,𝔽2)×D4711yescharacteristic
922C2C2×2−1+4×D4711yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#520C2
socleC23×C47C25
hypercenterC2×#520D47
hypocenterC47C2×#3511
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20257291C2direct (N × H)
2. C2×#15689841C2semidirect
3. C2×#15689836C2semidirect
4. C2×#15689828C2semidirect
5. C2×#15689822C2semidirect
6. C2×#15689782C2semidirect
7. C2×#15689774C2semidirect
8. C2×#15689745C2semidirect
9. C2×#15689738C2semidirect
10. C2×#15689704C2semidirect
11. C2×#15689701C2semidirect
12. C2×#15689677C2semidirect
13. C2×#15689670C2semidirect
14. C2×#15689669C2semidirect
15. C22×#13094023C2semidirect
16. C2×#15689603C2semidirect
17. C2×#15689591C2semidirect
18. C2×C47×#520C2semidirect
23. #15689841C22semidirect
24. #15689836C22semidirect
25. #15689828C22semidirect
26. #15689822C22semidirect
27. #15689782C22semidirect
28. #15689774C22semidirect
29. #15689745C22semidirect
30. #15689738C22semidirect
31. #15689704C22semidirect
32. #15689701C22semidirect
33. #15689677C22semidirect
34. #15689670C22semidirect
35. #15689669C22semidirect
40. C2×#13094023C22semidirect
69. #15689603C22semidirect
70. #15689591C22semidirect
93. C47×#520C22semidirect
250. C22×C4×C47#41semidirect
379. C2×C4×C47C2×#41semidirect
470. C2×#520D47semidirect
474. C2×C47#3511semidirect
532. #520C2×D47semidirect
562. C47C2×#3511semidirect
763. C22×C4#10625350semidirect
875. C2×C4C2×#10625350semidirect
919. C2#20257291direct (N × H)

Maximal subgroups

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

subgroupindex
#202572912
C2×#156898412
C2×#156898362
C2×#156898282
C2×#156898222
C2×#156897822
C2×#156897742
C2×#156897452
C2×#156897382
C2×#156897042
C2×#156897012
C2×#156896772
C2×#156896702
C2×#156896692
C22×#130940232
C2×#156896032
C2×#156895912
C2×C47×#5202
C2×#351147