Finite Group Databasebeta

← C2×#20288624 #28292465

Subgroups — C2×#20288624 #28292465

Order 13568.

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#20288624C2132yesmaximal, direct product factor
2C2×#16811344C212yesmaximal, complemented
3C2×#16811337C212yesmaximal, complemented
4C2×#16811331C212yesmaximal, complemented
5C2×#16811316C214yesmaximal, complemented
6C2×#16811279C214yesmaximal, complemented
7C2×#16811273C212yesmaximal, complemented
8C2×#16811246C212yesmaximal, complemented
9C2×#16811240C212yesmaximal, complemented
10C2×#16811201C211yesmaximal, characteristic, complemented
11C2×#16811175C212yesmaximal, complemented
12C2×#16811169C211yesmaximal, characteristic, complemented
13C2×#16811168C212yesmaximal, complemented
14C22×#13133216C211yesmaximal, characteristic, complemented
15C2×#16811106C211yesmaximal, characteristic, complemented
16C2×#16811104C211yesmaximal, characteristic, complemented
17C2×#41×Dic53C211yesmaximal, characteristic, complemented
18C2×C53×#537C211yesmaximal, characteristic, complemented
19C22×#11719945C2211yescharacteristic
20C22×#11719947C2214yes—
21C23×Dic106C2212yes—
22#16811344C22132yescomplemented
23#16811337C22132yescomplemented
24#16811331C22132yescomplemented
25#16811316C22164yescomplemented
26#16811279C22164yescomplemented
27#16811273C22132yescomplemented
28#16811246C22132yescomplemented
29#16811240C22132yescomplemented
30#16811201C22116yescomplemented
31#16811175C22132yescomplemented
32#16811169C22116yescomplemented
33#16811168C22132yescomplemented
34C2×#13133216C2212yes—
35C2×#13133216C2212yes—
36C2×#13133216C2212yes—
37C2×#13133216C2212yes—
38C2×#13133216C22116yescomplemented
39C2×#13133215C2211yescharacteristic
40C2×#13133213C2211yescharacteristic
41C2×#13133212C2214yes—
42C2×#13133210C2214yes—
43C2×#13133207C2214yes—
44C2×#13133206C2211yescharacteristic
45C2×#13133204C2211yescharacteristic
46C2×#13133204C2214yes—
47C2×#13133203C2214yes—
48C2×#13133203C2214yes—
49C2×#13133199C2214yes—
50C2×#13133198C2214yes—
51C2×#13133197C2214yes—
52C2×#13133196C2212yes—
53C2×#13133194C2214yes—
54C2×#13133194C2214yes—
55C2×#13133193C2212yes—
56C2×#13133191C2212yes—
57C2×#13133189C2214yes—
58C2×#13133189C2212yes—
59C2×#13133189C2212yes—
60C2×#13133189C2214yes—
61C2×#13133188C2212yes—
62#16811106C22116yescomplemented
63#16811104C22116yescomplemented
64#41×Dic53C22116yescomplemented
65C2×Q8×Dic53C2212yes—
66C2×Q8×Dic53C2211yescharacteristic
67C2×Q8×Dic53C2211yescharacteristic
68C2×#13133182C2214yes—
69C2×#13133182C2212yes—
70C2×D4×Dic53C2212yes—
71C2×D4×Dic53C2211yescharacteristic
72C2×D4×Dic53C2212yes—
73C2×D4×Dic53C2212yes—
74C2×D4×Dic53C2211yescharacteristic
75C2×D4×Dic53C2214yes—
76C2×#13133179C2212yes—
77C2×C4×C22⋊D53C2212yes—
78C2×C4×C22⋊D53C2214yes—
79C2×C4×C22⋊D53C2212yes—
80C2×#13133177C2214yes—
81C2×#13133176C2212yes—
82C2×#13133176C2212yes—
83C2×#13133176C2211yescharacteristic
84C2×#13133175C2212yes—
85C2×#13133173C2214yes—
86C22×C4⋊Dic53C2211yescharacteristic
87C22×C4⋊Dic53C2212yes—
88C22×#11719919C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2212yes—
91C22×C4×Dic53C2211yescharacteristic
92C22×#41×C53C2211yescharacteristic
93C22×#41×C53C2211yescharacteristic
94C53×#537C22116yescomplemented
95C2×C22⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×#121×C53C2212yes—
98C2×#121×C53C2212yes—
99C2×#121×C53C2214yes—
100C22×C4⋊C4×C53C2211yescharacteristic
101C2×#11719945—28no—
102C2×#11719945C2318yes—
103C2×#11719947—416no—
104C2×#11719947C23132yes—
105C22×Dic106—48no—
106C22×Dic106C2311yescharacteristic
107C22×Dic106C2314yes—
108C22×Dic106C23116yes—
109C22×Dic106C2314yes—
110C22×D212C2311yescharacteristic
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2312yes—
113C22×C22⋊D53C2312yes—
114C22×C22⋊D53C2314yes—
115C23×Dic53C2311yescharacteristic
116C23×Dic53C2312yes—
117C23×Dic53C2311yescharacteristic
118C23×Dic53C2312yes—
119C23×Dic53C2312yes—
120C23×Dic53C2314yes—
121C22×C4×D53C2312yes—
122C22×C4×D53C2314yes—
123#13133216C23116yes—
124#13133216C23116yes—
125#13133216C23116yes—
126#13133216C23116yes—
127#13133215C2318yes—
128#13133213C2318yes—
129#13133212C23132yes—
130#13133210C23132yes—
131#13133207C23132yes—
132#13133206C2318yes—
133#13133204C23132yes—
134#13133204C2318yes—
135#13133203C23132yes—
136#13133203C23132yes—
137#13133199C23132yes—
138#13133198C23132yes—
139#13133197C23132yes—
140#13133196C23116yes—
141#13133194C23132yes—
142#13133194C23132yes—
143#13133193C23116yes—
144#13133191C23116yes—
145#13133189C23116yes—
146#13133189C23132yes—
147#13133189C23116yes—
148#13133189C23132yes—
149#13133188C23116yes—
150Q8×Dic53C2318yes—
151Q8×Dic53C2318yes—
152Q8×Dic53C23116yes—
153#13133182C23132yes—
154#13133182C23116yes—
155D4×Dic53C2318yes—
156D4×Dic53C23116yes—
157D4×Dic53C23132yes—
158D4×Dic53C23116yes—
159D4×Dic53C2318yes—
160D4×Dic53C23116yes—
161#13133179C23116yes—
162C4×C22⋊D53C23116yes—
163C4×C22⋊D53C23132yes—
164C4×C22⋊D53C23116yes—
165#13133177C23132yes—
166#13133176C23116yes—
167#13133176C2318yes—
168#13133176C23116yes—
169#13133175C23116yes—
170#13133173C23132yes—
171C2×C4⋊Dic53C23116yes—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2318yes—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2312yes—
180C2×#11719919C23116yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2314yes—
187C4⋊C4×D53C23116yes—
188C2×C22⋊Dic53C2314yes—
189C2×C22⋊Dic53C2312yes—
190C2×C22⋊Dic53C2314yes—
191C2×C22⋊Dic53C2312yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2312yes—
194C2×C22⋊Dic53C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×C4×Dic53C2311yescharacteristic
200C2×C4×Dic53C2312yes—
201C2×C4×Dic53C2311yescharacteristic
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2318yes—
207C2×C4×Dic53C23116yes—
208C2×C4×Dic53C2314yes—
209C2×C4×Dic53C2314yes—
210C2×#41×C53—28no—
211C2×#41×C53—28no—
212C2×#41×C53C2318yes—
213C2×#41×C53C2318yes—
214C22×Q8×C53C2311yescharacteristic
215C22×Q8×C53C2311yescharacteristic
216C22×D4×C53C2311yescharacteristic
217C22×D4×C53C2312yes—
218C22×D4×C53C2312yes—
219C22×D4×C53C2311yescharacteristic
220C22×D4×C53C2314yes—
221C23×C4×C53C2312yes—
222C23×C4×C53C2312yes—
223C23×C4×C53C2312yes—
224C23×C4×C53C2311yescharacteristic
225C22⋊Q8×C53C23116yes—
226C22⋊Q8×C53C23116yes—
227#121×C53C23116yes—
228#121×C53C23132yes—
229#121×C53C23116yes—
230C2×C4⋊C4×C53C2312yes—
231C2×C4⋊C4×C53C2312yes—
232C2×C4⋊C4×C53C2318yes—
233C2×C4⋊C4×C53C2314yes—
234C2×C22⋊C4×C53C2314yes—
235C2×C22⋊C4×C53C2314yes—
236C24×C53C2412yes—
237C24×C53C2412yes—
238C24×C53C2411yescharacteristic
239C23×D53C2412yes—
240#41×C53—232no—
241#41×C53—232no—
242C2×Q8×C53—24no—
243C2×Q8×C53—24no—
244C2×Q8×C53C2414yes—
245C2×Q8×C53C2414yes—
246C2×D4×C53—28no—
247C2×D4×C53—28no—
248C2×D4×C53—24no—
249C2×D4×C53—24no—
250C2×D4×C53—48no—
251C2×D4×C53C2414yes—
252C2×D4×C53C2418yes—
253C2×D4×C53C2418yes—
254C2×D4×C53C2414yes—
255C2×D4×C53C24116yes—
256C22×C4×C53—28no—
257C22×C4×C53—28no—
258C22×C4×C53—44no—
259C22×C4×C53#4118yescomplemented
260C22×C4×C53C2414yes—
261C22×C4×C53C2412yes—
262C22×C4×C53C2412yes—
263C22×C4×C53C2418yes—
264C22×C4×C53C2418yes—
265C22×C4×C53C2418yes—
266C22×C4×C53C2411yescharacteristic
267C22×C4×C53C2411yescharacteristic
268C22×C4×C53C2414yes—
269C2×C22⋊D53—28no—
270C2×C22⋊D53—28no—
271C2×C22⋊D53—28no—
272C2×C22⋊D53—48no—
273C2×C22⋊D53C2418yes—
274C2×C22⋊D53C2418yes—
275C2×C22⋊D53C2418yes—
276C2×C22⋊D53C24116yes—
277C22×Dic53—24no—
278C22×Dic53—28no—
279C22×Dic53—24no—
280C22×Dic53—28no—
281C22×Dic53—44no—
282C22×Dic53—48no—
283C22×Dic53C2412yes—
284C22×Dic53C2411yescharacteristic
285C22×Dic53C2411yescharacteristic
286C22×Dic53C2412yes—
287C22×Dic53C2412yes—
288C22×Dic53C2414yes—
289C22×Dic53C2418yes—
290C22×Dic53C2414yes—
291C22×Dic53C2418yes—
292C22×Dic53C2414yes—
293C22×Dic53C2418yes—
294C22×Dic53C24116yes—
295C22×Dic53C2411yescharacteristic
296C22×Dic53C2411yescharacteristic
297#11719947—464no—
298#11719945—232no—
299C2×D212—24no—
300C2×D212C2414yes—
301C2×C4×D53—28no—
302C2×C4×D53—48no—
303C2×C4×D53C2418yes—
304C2×C4×D53C24116yes—
305C2×Dic106—24no—
306C2×Dic106—216no—
307C2×Dic106—432no—
308C2×Dic106—48no—
309C2×Dic106C2414yes—
310C2×Dic106C24116yes—
311C2×Dic106C24116yes—
312C4⋊C4×C53C2418yes—
313C4⋊C4×C53C2418yes—
314C4⋊C4×C53C24116yes—
315C22⋊C4×C53C24116yes—
316C22⋊C4×C53C24116yes—
317C22⋊Dic53C24116yes—
318C22⋊Dic53C2418yes—
319C22⋊Dic53C24116yes—
320C22⋊Dic53C2418yes—
321C22⋊Dic53C2418yes—
322C22⋊Dic53C2418yes—
323C22⋊Dic53C2418yes—
324#11719921C24116yes—
325#11719921C24116yes—
326#11719921C2418yes—
327#11719921C2418yes—
328C4⋊Dic53C2414yes—
329C4⋊Dic53C2418yes—
330C4⋊Dic53C2418yes—
331C4⋊Dic53C24116yes—
332C4⋊Dic53C2414yes—
333C4⋊Dic53C2418yes—
334C4⋊Dic53C2418yes—
335#11719919C24116yes—
336#11719919C24116yes—
337#11719919C24116yes—
338#11719919C2418yes—
339#11719919C2418yes—
340#11719919C24116yes—
341C4×Dic53C2414yes—
342C4×Dic53C2418yes—
343C4×Dic53C2414yes—
344C4×Dic53C2418yes—
345C4×Dic53C2414yes—
346C4×Dic53C2414yes—
347C4×Dic53C2418yes—
348C4×Dic53C24116yes—
349C4×Dic53C24116yes—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—24no—
353C23×C53—24no—
354C23×C53—24no—
355C23×C53—24no—
356C23×C53—24no—
357C23×C53—24no—
358C23×C53C2×#4114yes—
359C23×C53C2514yes—
360C23×C53C2514yes—
361C23×C53C2512yes—
362C23×C53C2511yescharacteristic
363C22×D53—24no—
364C22×D53—24no—
365C22×D53—24no—
366C22×D53C2514yes—
367Q8×C53—28no—
368Q8×C53—28no—
369D4×C53—216no—
370D4×C53—216no—
371D4×C53—28no—
372D4×C53—28no—
373D4×C53—416no—
374C2×C4×C53—24no—
375C2×C4×C53—24no—
376C2×C4×C53—28no—
377C2×C4×C53—216no—
378C2×C4×C53—216no—
379C2×C4×C53—48no—
380C2×C4×C53C2×#4114yes—
381C2×C4×C53C2×#4114yes—
382C2×C4×C53C2×#41116yescomplemented
383C2×C4×C53C2518yes—
384C2×C4×C53C2514yes—
385C2×C4×C53C2514yes—
386C2×C4×C53C2512yes—
387C2×C4×C53C2512yes—
388C22⋊D53—216no—
389C22⋊D53—216no—
390C22⋊D53—216no—
391C22⋊D53—416no—
392C2×Dic53—24no—
393C2×Dic53—28no—
394C2×Dic53—22no—
395C2×Dic53—24no—
396C2×Dic53—24no—
397C2×Dic53—22no—
398C2×Dic53—28no—
399C2×Dic53—216no—
400C2×Dic53—28no—
401C2×Dic53—216no—
402C2×Dic53—48no—
403C2×Dic53—416no—
404C2×Dic53H(5,𝔽2)14yes—
405C2×Dic532−1+414yes—
406C2×Dic53C2512yes—
407C2×Dic53C2518yes—
408C2×Dic53C2514yes—
409C2×Dic53C2514yes—
410C2×Dic53C2514yes—
411C2×Dic53C2512yes—
412C2×Dic53C2512yes—
413C2×Dic53C2512yes—
414D212—28no—
415C4×D53—216no—
416C4×D53—416no—
417Dic106—28no—
418Dic106—232no—
419Dic106—416no—
420C2×#3511—531nomaximal, Sylow
421C22×C53—22no—
422C22×C53—22no—
423C22×C53—28no—
424C22×C53—24no—
425C22×C53—24no—
426C22×C53—24no—
427C22×C53—24no—
428C22×C53—24no—
429C22×C53—24no—
430C22×C53—48no—
431C22×C53—48no—
432C22×C53C22×#4114yes—
433C22×C53C22×#4112yes—
434C22×C53C2×H(5,𝔽2)12yes—
435C22×C53C2×2−1+412yes—
436C22×C53C2611yescharacteristic
437C2×D53—24no—
438C2×D53—24no—
439C2×D53—24no—
440C2×D53—48no—
441C4×C53—24no—
442C4×C53—24no—
443C4×C53—28no—
444C4×C53C22×#4114yes—
445C4×C53C22×#4114yes—
446Dic53—24no—
447Dic53—28no—
448Dic53—22no—
449Dic53—24no—
450Dic53—24no—
451Dic53—22no—
452Dic53C2×H(5,𝔽2)14yes—
453Dic53C2×2−1+414yes—
454#3511—5332no—
455C2×#556—532no—
456C2×#555—532no—
457C2×#554—532no—
458C2×#553—534no—
459C2×#548—534no—
460C2×#547—532no—
461C2×#542—532no—
462C2×#542—532no—
463C2×#537—531no—
464C2×#537D5311yescharacteristic, complemented
465C2×#533—532no—
466C2×#532—531no—
467C2×#532—532no—
468C22×C4⋊Q8—531no—
469C2×#520—531no—
470C2×#520—531no—
471C2×C4×#41—531no—
472C2×C53—24no—
473C2×C53—44no—
474C2×C53—44no—
475C2×C53#351114yescomplemented
476C2×C53C23×#4111yescharacteristic
477C2×C53C22×H(5,𝔽2)11yescharacteristic
478C2×C53C22×2−1+411yescharacteristic
479D53—44no—
480C22×#41—534no—
481C22×#41—531no—
482C22×#41C2×D5311yescharacteristic
483C22×#41C2×D5311yescharacteristic
484C23×Q8—532no—
485#556—5332no—
486#555—5332no—
487#554—5332no—
488#553—5364no—
489#548—5364no—
490#547—5332no—
491#542—5332no—
492#542—5332no—
493#537—5316no—
494#537C2×D53116yescomplemented
495#533—5332no—
496#532—5316no—
497#532—5332no—
498C2×C4⋊Q8—531no—
499C2×C4⋊Q8—532no—
500C2×C4⋊Q8—532no—
501C2×C4⋊Q8—532no—
502C2×C4⋊Q8—532no—
503C2×C4⋊Q8—5316no—
504C2×#127—531no—
505C2×#126—534no—
506C2×#126—534no—
507C2×#125—534no—
508C2×#124—531no—
509C2×#124—531no—
510C2×#124—534no—
511C2×#124—534no—
512C2×#124—534no—
513C2×#123—534no—
514C2×#123—534no—
515C2×C22⋊Q8—532no—
516C2×C22⋊Q8—532no—
517C2×C22⋊Q8—534no—
518C2×C22⋊Q8—534no—
519C2×C22⋊Q8—534no—
520C2×C22⋊Q8C2×D5312yes—
521C2×C22⋊Q8C2×D5312yes—
522C2×#121—532no—
523C2×#121—532no—
524C2×#121—532no—
525C2×#121—534no—
526C2×#121—534no—
527C2×#121—532no—
528C2×#121C2×D5312yes—
529C2×#121C2×D5312yes—
530C2×#121C2×D5314yes—
531#520—5316no—
532#520—5316no—
533C4×#41—5316no—
534C2×C4×Q8—531no—
535C2×C4×Q8—531no—
536C2×C4×Q8—532no—
537C2×C4×Q8—532no—
538C2×C4×Q8—534no—
539C2×C4×D4—531no—
540C2×C4×D4—532no—
541C2×C4×D4—532no—
542C2×C4×D4—531no—
543C2×C4×D4—532no—
544C2×C4×D4—534no—
545C2×C4×D4—534no—
546C2×C4×D4—532no—
547C2×C4×D4—532no—
548C2×C4×D4—532no—
549C2×C4×D4—534no—
550C2×#117—531no—
551C2×#117—532no—
552C2×#117—532no—
553C2×#117—532no—
554C2×#117—534no—
555C22×C4⋊C4—532no—
556C22×C4⋊C4—531no—
557C22×C4⋊C4—532no—
558C22×C4⋊C4—532no—
559C22×C4⋊C4C2×D5311yescharacteristic
560C22×C42—531no—
561C22×C42—532no—
562C53C2×#351111yescharacteristic, complemented, Sylow
563C2×#41—28no—
564C2×#41—28no—
565C2×#41—5332no—
566C2×#41—538no—
567C2×#41—1068no—
568C2×#41—21216no—
569C2×#41C22×D5318yes—
570C2×#41C22×D5318yes—
571C22×Q8—531no—
572C22×Q8—534no—
573C22×Q8—534no—
574C22×Q8—5316no—
575C22×Q8—2128no—
576C22×Q8C22×D5311yescharacteristic
577C22×Q8C22×D5311yescharacteristic
578C22×D4—532no—
579C22×D4—532no—
580C22×D4—532no—
581C22×D4—534no—
582C22×D4—531no—
583C22×D4C22×D5312yes—
584C22×D4C22×D5312yes—
585C22×D4C22×D5311yescharacteristic
586C22×D4C22×D5311yescharacteristic
587C22×D4C22×D5314yes—
588C23×C4—531no—
589C23×C4—532no—
590C23×C4—531no—
591C23×C4—532no—
592C23×C4—532no—
593C23×C4—534no—
594C23×C4—532no—
595C23×C4—534no—
596C23×C4C22×D5312yes—
597C23×C4C22×D5312yes—
598C23×C4C22×D5312yes—
599C23×C4C22×D5311yescharacteristic
600C4⋊Q8—538no—
601C4⋊Q8—5316no—
602C4⋊Q8—5316no—
603C4⋊Q8—5316no—
604C4⋊Q8—5316no—
605#127—538no—
606#126—5332no—
607#126—5332no—
608#125—5332no—
609#124—538no—
610#124—538no—
611#124—5332no—
612#124—5332no—
613#124—5332no—
614#123—5332no—
615#123—5332no—
616C22⋊Q8—5316no—
617C22⋊Q8—5316no—
618C22⋊Q8—5332no—
619C22⋊Q8—5332no—
620C22⋊Q8—5332no—
621C22⋊Q8C22×D53116yes—
622C22⋊Q8C22×D53116yes—
623#121—5316no—
624#121—5316no—
625#121—5332no—
626#121—5316no—
627#121—5332no—
628#121—5316no—
629#121C22×D53116yes—
630#121C22×D53116yes—
631#121C22×D53132yes—
632C4×Q8—538no—
633C4×Q8—538no—
634C4×Q8—5316no—
635C4×Q8—5316no—
636C4×Q8—5332no—
637C4×D4—538no—
638C4×D4—5316no—
639C4×D4—5316no—
640C4×D4—538no—
641C4×D4—5316no—
642C4×D4—5332no—
643C4×D4—5332no—
644C4×D4—5316no—
645C4×D4—5316no—
646C4×D4—5316no—
647C4×D4—5332no—
648#117—538no—
649#117—5316no—
650#117—5316no—
651#117—5316no—
652#117—5332no—
653C2×C4⋊C4—531no—
654C2×C4⋊C4—532no—
655C2×C4⋊C4—534no—
656C2×C4⋊C4—532no—
657C2×C4⋊C4—534no—
658C2×C4⋊C4—534no—
659C2×C4⋊C4—538no—
660C2×C4⋊C4—5316no—
661C2×C4⋊C4—534no—
662C2×C4⋊C4—5316no—
663C2×C4⋊C4—531no—
664C2×C4⋊C4—532no—
665C2×C4⋊C4—532no—
666C2×C4⋊C4—532no—
667C2×C4⋊C4—532no—
668C2×C4⋊C4—534no—
669C2×C4⋊C4—5316no—
670C2×C4⋊C4C22×D5312yes—
671C2×C4⋊C4C22×D5312yes—
672C2×C4⋊C4C22×D5318yes—
673C2×C4⋊C4C22×D5314yes—
674C2×C22⋊C4—532no—
675C2×C22⋊C4—534no—
676C2×C22⋊C4—532no—
677C2×C22⋊C4—532no—
678C2×C22⋊C4—534no—
679C2×C22⋊C4—532no—
680C2×C22⋊C4—532no—
681C2×C22⋊C4—534no—
682C2×C22⋊C4—534no—
683C2×C22⋊C4—532no—
684C2×C22⋊C4—532no—
685C2×C22⋊C4C22×D5314yes—
686C2×C22⋊C4C22×D5314yes—
687C2×C42—532no—
688C2×C42—534no—
689C2×C42—534no—
690C2×C42—531no—
691C2×C42—532no—
692C2×C42—531no—
693C2×C42—531no—
694C2×C42—532no—
695C2×C42—538no—
696C2×C42—5316no—
697C2×C42—531no—
698C24—532no—
699C24C23×D5312yes—
700C24C23×D5312yes—
701C24C23×D5311yescharacteristic
702#41—232no—
703#41—232no—
704#41—10632no—
705#41—21264no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—534no—
709C2×Q8—5316no—
710C2×Q8—5316no—
711C2×Q8—10616no—
712C2×Q8—1064no—
713C2×Q8—2128no—
714C2×Q8—21232no—
715C2×Q8C23×D5314yes—
716C2×Q8C23×D5314yes—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—48no—
722C2×D4—538no—
723C2×D4—538no—
724C2×D4—538no—
725C2×D4—5316no—
726C2×D4—534no—
727C2×D4—1068no—
728C2×D4—1068no—
729C2×D4—1068no—
730C2×D4—1064no—
731C2×D4—2128no—
732C2×D4C23×D5318yes—
733C2×D4C23×D5318yes—
734C2×D4C23×D5314yes—
735C2×D4C23×D5314yes—
736C2×D4C23×D53116yes—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—44no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—534no—
743C22×C4—538no—
744C22×C4—534no—
745C22×C4—538no—
746C22×C4—532no—
747C22×C4—531no—
748C22×C4—531no—
749C22×C4—532no—
750C22×C4—532no—
751C22×C4—534no—
752C22×C4—538no—
753C22×C4—5316no—
754C22×C4—538no—
755C22×C4—5316no—
756C22×C4—1064no—
757C22×C4—1068no—
758C22×C4—1064no—
759C22×C4—1068no—
760C22×C4—1068no—
761C22×C4—2128no—
762C22×C4—2124no—
763C22×C4—2128no—
764C22×C4#1171994718yescomplemented
765C22×C4C23×D5318yes—
766C22×C4C23×D5318yes—
767C22×C4C23×D5312yes—
768C22×C4C23×D5312yes—
769C22×C4C23×D5314yes—
770C22×C4C23×D5318yes—
771C22×C4C23×D5311yescharacteristic
772C22×C4C23×D5311yescharacteristic
773C22×C4C23×D5314yes—
774C4⋊C4—534no—
775C4⋊C4—538no—
776C4⋊C4—5316no—
777C4⋊C4—538no—
778C4⋊C4—5316no—
779C4⋊C4—5316no—
780C4⋊C4—5316no—
781C4⋊C4—534no—
782C4⋊C4—538no—
783C4⋊C4—538no—
784C4⋊C4—538no—
785C4⋊C4—538no—
786C4⋊C4—5316no—
787C4⋊C4C23×D5318yes—
788C4⋊C4C23×D5318yes—
789C4⋊C4C23×D53116yes—
790C22⋊C4—538no—
791C22⋊C4—5316no—
792C22⋊C4—538no—
793C22⋊C4—538no—
794C22⋊C4—5316no—
795C22⋊C4—538no—
796C22⋊C4—538no—
797C22⋊C4—5316no—
798C22⋊C4—5316no—
799C22⋊C4—538no—
800C22⋊C4—538no—
801C22⋊C4C23×D53116yes—
802C22⋊C4C23×D53116yes—
803C42—534no—
804C42—538no—
805C42—534no—
806C42—538no—
807C42—534no—
808C42—534no—
809C42—538no—
810C42—5316no—
811C42—5316no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—534no—
821C23—1064no—
822C23—1064no—
823C23—1064no—
824C23C2×#1171994714yes—
825C23C24×D5314yes—
826C23C24×D5314yes—
827C23C24×D5312yes—
828C23C24×D5311yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—10632no—
832Q8—1068no—
833Q8—21216no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—10616no—
840D4—10616no—
841D4—10616no—
842D4—1068no—
843D4—21216no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—534no—
851C2×C4—534no—
852C2×C4—532no—
853C2×C4—532no—
854C2×C4—534no—
855C2×C4—532no—
856C2×C4—532no—
857C2×C4—534no—
858C2×C4—534no—
859C2×C4—538no—
860C2×C4—1068no—
861C2×C4—10616no—
862C2×C4—1068no—
863C2×C4—10616no—
864C2×C4—1064no—
865C2×C4—1064no—
866C2×C4—1062no—
867C2×C4—1068no—
868C2×C4—1064no—
869C2×C4—1062no—
870C2×C4—10616no—
871C2×C4—21216no—
872C2×C4—2128no—
873C2×C4—21216no—
874C2×C4C2×#1171994714yes—
875C2×C4C2×#1171994714yes—
876C2×C4C2×#11719947116yescomplemented
877C2×C4C24×D5314yes—
878C2×C4C24×D5314yes—
879C2×C4C24×D5318yes—
880C2×C4C24×D5312yes—
881C2×C4C24×D5312yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—1064no—
894C22—1064no—
895C22—1064no—
896C22—2128no—
897C22C22×#1171994714yes—
898C22C22×#1171994712yes—
899C22H(5,𝔽2)×D5312yes—
900C222−1+4×D5312yes—
901C22C25×D5311yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—534no—
906C4—534no—
907C4—1064no—
908C4—1064no—
909C4—1062no—
910C4—1068no—
911C4—1064no—
912C4—1062no—
913C4C22×#1171994714yes—
914C4C22×#1171994714yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—2124no—
919C2#2028862414yesdirect product factor
920C2C23×#1171994711yescharacteristic
921C2C2×H(5,𝔽2)×D5311yescharacteristic
922C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#537C2
socleC23×C53C25
hypercenterC2×#537D53
hypocenterC53C2×#3511
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #20288624C2direct (N × H)
2. C2×#16811344C2semidirect
3. C2×#16811337C2semidirect
4. C2×#16811331C2semidirect
5. C2×#16811316C2semidirect
6. C2×#16811279C2semidirect
7. C2×#16811273C2semidirect
8. C2×#16811246C2semidirect
9. C2×#16811240C2semidirect
10. C2×#16811201C2semidirect
11. C2×#16811175C2semidirect
12. C2×#16811169C2semidirect
13. C2×#16811168C2semidirect
14. C22×#13133216C2semidirect
15. C2×#16811106C2semidirect
16. C2×#16811104C2semidirect
17. C2×#41×Dic53C2semidirect
18. C2×C53×#537C2semidirect
22. #16811344C22semidirect
23. #16811337C22semidirect
24. #16811331C22semidirect
25. #16811316C22semidirect
26. #16811279C22semidirect
27. #16811273C22semidirect
28. #16811246C22semidirect
29. #16811240C22semidirect
30. #16811201C22semidirect
31. #16811175C22semidirect
32. #16811169C22semidirect
33. #16811168C22semidirect
38. C2×#13133216C22semidirect
62. #16811106C22semidirect
63. #16811104C22semidirect
64. #41×Dic53C22semidirect
94. C53×#537C22semidirect
259. C22×C4×C53#41semidirect
382. C2×C4×C53C2×#41semidirect
464. C2×#537D53semidirect
475. C2×C53#3511semidirect
494. #537C2×D53semidirect
562. C53C2×#3511semidirect
764. C22×C4#11719947semidirect
876. C2×C4C2×#11719947semidirect
919. C2#20288624direct (N × H)

Maximal subgroups

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

subgroupindex
#202886242
C2×#168113442
C2×#168113372
C2×#168113312
C2×#168113162
C2×#168112792
C2×#168112732
C2×#168112462
C2×#168112402
C2×#168112012
C2×#168111752
C2×#168111692
C2×#168111682
C22×#131332162
C2×#168111062
C2×#168111042
C2×#41×Dic532
C2×C53×#5372
C2×#351153