Finite Group Databasebeta

← C2×#20288693 #28292206

Subgroups — C2×#20288693 #28292206

Order 13568.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288693C2132yesmaximal, direct product factor
2C2×#16811351C211yesmaximal, characteristic, complemented
3C2×#16811333C211yesmaximal, characteristic, complemented
4C2×#16811330C211yesmaximal, characteristic, complemented
5C2×#16811319C212yesmaximal, complemented
6C2×#16811313C212yesmaximal, complemented
7C2×#16811312C212yesmaximal, complemented
8C2×#16811306C214yesmaximal, complemented
9C2×#16811277C211yesmaximal, characteristic, complemented
10C2×#16811272C212yesmaximal, complemented
11C2×#16811231C212yesmaximal, complemented
12C2×#16811215C214yesmaximal, complemented
13C2×#16811180C211yesmaximal, characteristic, complemented
14C2×#16811157C211yesmaximal, characteristic, complemented
15C2×#16811157C212yesmaximal, complemented
16C22×#13133209C212yesmaximal, complemented
17C2×#16811102C212yesmaximal, complemented
18C2×C4×#41×C53C211yesmaximal, characteristic, complemented
19C22×#11719947C2212yes—
20#16811351C22116yescomplemented
21#16811333C22116yescomplemented
22#16811330C22116yescomplemented
23#16811319C22132yescomplemented
24#16811313C22132yescomplemented
25#16811312C22132yescomplemented
26#16811306C22164yescomplemented
27#16811277C22116yescomplemented
28#16811272C22132yescomplemented
29#16811231C22132yescomplemented
30#16811215C22164yescomplemented
31#16811180C22116yescomplemented
32C2×#13133217C2211yescharacteristic
33C2×#13133217C2211yescharacteristic
34C2×#13133215C2212yes—
35#16811157C22132yescomplemented
36#16811157C22116yescomplemented
37C2×#13133212C2214yes—
38C2×#13133211C2214yes—
39C2×#13133211C2212yes—
40C2×#13133210C2214yes—
41C2×#13133209C2212yes—
42C2×#13133209C2212yes—
43C2×#13133209C2214yes—
44C2×#13133209C2214yes—
45C2×#13133209C2211yescharacteristic
46C2×#13133209C2212yes—
47C2×#13133209C22132yescomplemented
48C2×#13133208C2212yes—
49C2×#13133207C2214yes—
50C2×#13133207C2214yes—
51C2×#13133205C2211yescharacteristic
52C2×#13133201C2214yes—
53C2×#13133200C2212yes—
54C2×#13133200C2214yes—
55C2×#13133199C2214yes—
56C2×#13133198C2214yes—
57C2×#13133197C2212yes—
58C2×#13133196C2212yes—
59C2×#13133196C2212yes—
60C2×#13133196C2211yescharacteristic
61C2×#13133196C2212yes—
62C2×#13133195C2214yes—
63C2×#13133194C2214yes—
64C2×#13133193C2212yes—
65C2×#13133191C2212yes—
66C2×#13133191C2211yescharacteristic
67C2×#13133189C2214yes—
68#16811102C22132yescomplemented
69C2×C4×Dic106C2212yes—
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2212yes—
72C2×C4×Dic106C2211yescharacteristic
73C2×#13133182C2212yes—
74C2×C4×D212C2211yescharacteristic
75C2×C4×D212C2212yes—
76C2×D4×Dic53C2212yes—
77C2×C4×C22⋊D53C2214yes—
78C2×C4×C22⋊D53C2212yes—
79C2×#13133177C2214yes—
80C2×#13133176C2212yes—
81C2×#13133174C2212yes—
82C2×#13133174C2214yes—
83C2×#13133173C2214yes—
84C22×C4⋊Dic53C2212yes—
85C22×C4⋊Dic53C2212yes—
86C22×#11719919C2214yes—
87C22×#11719919C2214yes—
88C2×C4⋊C4×D53C2212yes—
89C22×#41×C53C2211yescharacteristic
90C4×#41×C53C22116yescomplemented
91C2×C4×Q8×C53C2211yescharacteristic
92C2×C4×Q8×C53C2211yescharacteristic
93C2×C4×D4×C53C2212yes—
94C2×C4×D4×C53C2211yescharacteristic
95C2×C4×D4×C53C2211yescharacteristic
96C2×C4×D4×C53C2212yes—
97C2×#117×C53C2212yes—
98C2×#117×C53C2211yescharacteristic
99C22×C42×C53C2211yescharacteristic
100C22×C42×C53C2212yes—
101C2×#11719947—216no—
102C2×#11719947C23116yes—
103C22×Dic106C2312yes—
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2312yes—
106C22×D212C2311yescharacteristic
107C22×C22⋊D53C2314yes—
108C22×C22⋊D53C2312yes—
109C23×Dic53C2314yes—
110C23×Dic53C2314yes—
111C22×C4×D53C2312yes—
112C22×C4×D53C2314yes—
113#13133217C2318yes—
114#13133217C2318yes—
115#13133215C23116yes—
116#13133212C23132yes—
117#13133211C23116yes—
118#13133211C23132yes—
119#13133210C23132yes—
120#13133209C23132yes—
121#13133209C23116yes—
122#13133209C23116yes—
123#13133209C2318yes—
124#13133209C23116yes—
125#13133209C23132yes—
126#13133208C23116yes—
127#13133207C23132yes—
128#13133207C23132yes—
129#13133205C2318yes—
130#13133201C23132yes—
131#13133200C23132yes—
132#13133200C23116yes—
133#13133199C23132yes—
134#13133198C23132yes—
135#13133197C23116yes—
136#13133196C23116yes—
137#13133196C2318yes—
138#13133196C23116yes—
139#13133196C23116yes—
140#13133195C23132yes—
141#13133194C23132yes—
142#13133193C23116yes—
143#13133191C23116yes—
144#13133191C2318yes—
145#13133189C23132yes—
146C4×Dic106C23116yes—
147C4×Dic106C23116yes—
148C4×Dic106C2318yes—
149C4×Dic106C23116yes—
150#13133182C23116yes—
151C4×D212C2318yes—
152C4×D212C23116yes—
153D4×Dic53C23116yes—
154C4×C22⋊D53C23116yes—
155C4×C22⋊D53C23132yes—
156#13133177C23132yes—
157#13133176C23116yes—
158#13133174C23132yes—
159#13133174C23116yes—
160#13133173C23132yes—
161C2×C4⋊Dic53C23116yes—
162C2×C4⋊Dic53C23116yes—
163C2×C4⋊Dic53C2312yes—
164C2×C4⋊Dic53C2311yescharacteristic
165C2×C4⋊Dic53C2311yescharacteristic
166C2×C4⋊Dic53C2312yes—
167C2×C4⋊Dic53C2312yes—
168C2×C4⋊Dic53C2314yes—
169C2×C4⋊Dic53C2314yes—
170C2×C4⋊Dic53C2312yes—
171C2×#11719919C23132yes—
172C2×#11719919C2314yes—
173C2×#11719919C2312yes—
174C2×#11719919C2312yes—
175C2×#11719919C2314yes—
176C2×#11719919C2314yes—
177C2×#11719919C2314yes—
178C2×#11719919C23132yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2312yes—
184C2×#11719919C2314yes—
185C4⋊C4×D53C23116yes—
186C2×C22⋊Dic53C2314yes—
187C2×C22⋊Dic53C2314yes—
188C2×C22⋊Dic53C2312yes—
189C2×#11719921C2312yes—
190C2×#11719921C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2314yes—
193C2×#11719921C2314yes—
194C2×#11719921C2312yes—
195C2×C4×Dic53C2314yes—
196C2×C4×Dic53C2314yes—
197C2×C4×Dic53C2312yes—
198C2×#41×C53—28no—
199C2×#41×C53C2318yes—
200C22×Q8×C53C2311yescharacteristic
201C22×D4×C53C2312yes—
202C22×D4×C53C2311yescharacteristic
203C23×C4×C53C2312yes—
204C23×C4×C53C2311yescharacteristic
205C23×C4×C53C2312yes—
206C23×C4×C53C2311yescharacteristic
207C23×C4×C53C2312yes—
208C23×C4×C53C2311yescharacteristic
209C4×Q8×C53C2318yes—
210C4×Q8×C53C2318yes—
211C4×D4×C53C2318yes—
212C4×D4×C53C23116yes—
213C4×D4×C53C2318yes—
214C4×D4×C53C23116yes—
215#117×C53C23116yes—
216#117×C53C2318yes—
217C2×C4⋊C4×C53C2311yescharacteristic
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2311yescharacteristic
220C2×C4⋊C4×C53C2312yes—
221C2×C22⋊C4×C53C2312yes—
222C2×C22⋊C4×C53C2312yes—
223C2×C22⋊C4×C53C2312yes—
224C2×C42×C53C2311yescharacteristic
225C2×C42×C53C2312yes—
226C2×C42×C53C2311yescharacteristic
227C2×C42×C53C2311yescharacteristic
228C2×C42×C53C2312yes—
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2312yes—
231C2×C42×C53C23116yes—
232C2×C42×C53C2318yes—
233C24×C53C2411yescharacteristic
234C24×C53C2412yes—
235C23×D53C2412yes—
236#41×C53—232no—
237C2×Q8×C53—24no—
238C2×Q8×C53C2414yes—
239C2×D4×C53—28no—
240C2×D4×C53#4118yes—
241C2×D4×C53C2418yes—
242C2×D4×C53C2414yes—
243C22×C4×C53—28no—
244C22×C4×C53—24no—
245C22×C4×C53—28no—
246C22×C4×C53—24no—
247C22×C4×C53—42no—
248C22×C4×C53—44no—
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2411yescharacteristic
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2411yescharacteristic
255C22×C4×C53C2412yes—
256C22×C4×C53C2418yes—
257C22×C4×C53C2414yes—
258C22×C4×C53C2418yes—
259C22×C4×C53C2414yes—
260C22×C4×C53C2418yes—
261C22×C4×C53C2414yes—
262C22×C4×C53C2411yescharacteristic
263C22×C4×C53C2411yescharacteristic
264C2×C22⋊D53—216no—
265C2×C22⋊D53—44no—
266C2×C22⋊D53C24116yes—
267C2×C22⋊D53C2418yes—
268C22×Dic53—216no—
269C22×Dic53—48no—
270C22×Dic53C2412yes—
271C22×Dic53C2414yes—
272C22×Dic53C2414yes—
273C22×Dic53C2412yes—
274C22×Dic53C2412yes—
275C22×Dic53C24116yes—
276C22×Dic53C24116yes—
277#11719947—264no—
278C2×D212—24no—
279C2×D212C2414yes—
280C2×C4×D53—28no—
281C2×C4×D53—48no—
282C2×C4×D53C2418yes—
283C2×C4×D53C24116yes—
284C2×Dic106—28no—
285C2×Dic106—24no—
286C2×Dic106—44no—
287C2×Dic106C2418yes—
288C2×Dic106C2414yes—
289C2×Dic106C2418yes—
290C4⋊C4×C53C2414yes—
291C4⋊C4×C53C2418yes—
292C4⋊C4×C53C2414yes—
293C4⋊C4×C53C2418yes—
294C22⋊C4×C53C2418yes—
295C22⋊C4×C53C2418yes—
296C22⋊C4×C53C2418yes—
297C42×C53C2414yes—
298C42×C53C2418yes—
299C42×C53C2414yes—
300C42×C53C2414yes—
301C42×C53C2418yes—
302C42×C53C2414yes—
303C42×C53C2418yes—
304C22⋊Dic53C24116yes—
305C22⋊Dic53C24116yes—
306C22⋊Dic53C2418yes—
307#11719921C2418yes—
308#11719921C2418yes—
309#11719921C2418yes—
310#11719921C24116yes—
311#11719921C24116yes—
312#11719921C2418yes—
313C4⋊Dic53C2418yes—
314C4⋊Dic53C2414yes—
315C4⋊Dic53C2414yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C2418yes—
318C4⋊Dic53C24116yes—
319C4⋊Dic53C24116yes—
320C4⋊Dic53C2418yes—
321#11719919C24116yes—
322#11719919C2418yes—
323#11719919C2418yes—
324#11719919C24116yes—
325#11719919C24116yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C24116yes—
329#11719919C2418yes—
330#11719919C24116yes—
331#11719919C2418yes—
332#11719919C24116yes—
333C4×Dic53C24116yes—
334C4×Dic53C24116yes—
335C4×Dic53C2418yes—
336C23×C53—24no—
337C23×C53—24no—
338C23×C53—22no—
339C23×C53—22no—
340C23×C53—22no—
341C23×C53C2×#4118yes—
342C23×C53C2512yes—
343C23×C53C2514yes—
344C23×C53C2511yescharacteristic
345C22×D53—24no—
346C22×D53—24no—
347C22×D53—24no—
348C22×D53C2514yes—
349Q8×C53—28no—
350D4×C53—216no—
351D4×C53C2×#41116yes—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—216no—
355C2×C4×C53—22no—
356C2×C4×C53—24no—
357C2×C4×C53—22no—
358C2×C4×C53—24no—
359C2×C4×C53—22no—
360C2×C4×C53—28no—
361C2×C4×C53—216no—
362C2×C4×C53—28no—
363C2×C4×C53—44no—
364C2×C4×C53—48no—
365C2×C4×C53C2×#4114yes—
366C2×C4×C532−1+414yes—
367C2×C4×C53C2512yes—
368C2×C4×C53C2514yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2512yes—
371C2×C4×C53C2514yes—
372C2×C4×C53C2512yes—
373C2×C4×C53C2514yes—
374C2×C4×C53C2512yes—
375C2×C4×C53C2512yes—
376C22⋊D53—232no—
377C22⋊D53—48no—
378C2×Dic53—28no—
379C2×Dic53—24no—
380C2×Dic53—232no—
381C2×Dic53—24no—
382C2×Dic53—28no—
383C2×Dic53—24no—
384C2×Dic53—416no—
385C2×Dic53C2518yes—
386C2×Dic53C2518yes—
387C2×Dic53C2514yes—
388C2×Dic53C2514yes—
389C2×Dic53C2514yes—
390D212—28no—
391C4×D53—216no—
392C4×D53—416no—
393Dic106—216no—
394Dic106—28no—
395Dic106—48no—
396C2×#3515—531nomaximal, Sylow
397C22×C53—24no—
398C22×C53—24no—
399C22×C53—216no—
400C22×C53—22no—
401C22×C53—22no—
402C22×C53—22no—
403C22×C53—44no—
404C22×C53C22×#4118yes—
405C22×C53C22×#4112yes—
406C22×C53C2×2−1+412yes—
407C22×C53#58512yes—
408C22×C53C2611yescharacteristic
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—48no—
413C4×C53—22no—
414C4×C53—24no—
415C4×C53—22no—
416C4×C53—24no—
417C4×C53—22no—
418C4×C53—24no—
419C4×C53—22no—
420C4×C53C22×#4114yes—
421C4×C53C2×2−1+414yes—
422Dic53—28no—
423Dic53—24no—
424Dic53—24no—
425Dic53—28no—
426Dic53—24no—
427#3515—5332no—
428C2×#557—531no—
429C2×#554—531no—
430C2×#554—531no—
431C2×#553—532no—
432C2×#552—532no—
433C2×#552—534no—
434C2×#552—532no—
435C2×#547—532no—
436C2×#547—531no—
437C2×#541—532no—
438C2×#539—534no—
439C2×#533—531no—
440C2×#529—531no—
441C2×#529—532no—
442C22×#125—532no—
443C2×#520—532no—
444C2×C4×#41D5311yescharacteristic, complemented
445C2×C53—28no—
446C2×C53—42no—
447C2×C53#351514yescomplemented
448C2×C53C23×#4111yescharacteristic
449C2×C53C22×2−1+411yescharacteristic
450C2×C53C2×#58511yescharacteristic
451D53—44no—
452C22×#41—532no—
453C22×#41C2×D5311yescharacteristic
454#557—5316no—
455#554—5316no—
456#554—5316no—
457#553—5332no—
458#552—5332no—
459#552—5364no—
460#552—5332no—
461#547—5332no—
462#547—5316no—
463#541—5332no—
464#539—5364no—
465#533—5316no—
466C2×C4⋊Q8—532no—
467C2×C4⋊Q8—531no—
468C2×C4⋊Q8—531no—
469#529—5332no—
470#529—5316no—
471C2×#126—534no—
472C2×#126—534no—
473C2×#126—534no—
474C2×#126—532no—
475C2×#125—534no—
476C2×#125—534no—
477C2×#125—532no—
478C2×#125—531no—
479C2×#125—532no—
480C2×#125—534no—
481C2×#125—534no—
482C2×#125—532no—
483C2×#125—532no—
484C2×#125—5332no—
485C2×#124—531no—
486C2×#123—534no—
487C2×#123—532no—
488C2×#123—534no—
489C2×#123—534no—
490C2×#123—534no—
491C2×C22⋊Q8—532no—
492C2×C22⋊Q8—531no—
493C2×C22⋊Q8—532no—
494C2×C22⋊Q8—532no—
495C2×C22⋊Q8—532no—
496C2×C22⋊Q8—534no—
497C2×C22⋊Q8—532no—
498C2×C22⋊Q8—534no—
499C2×#121—534no—
500C2×#121—532no—
501C2×#121—531no—
502#520—5332no—
503C4×#41C2×D53116yescomplemented
504C2×C4×Q8—532no—
505C2×C4×Q8—532no—
506C2×C4×Q8—532no—
507C2×C4×Q8—531no—
508C2×C4×Q8—532no—
509C2×C4×Q8C2×D5311yescharacteristic
510C2×C4×Q8C2×D5311yescharacteristic
511C2×C4×D4—532no—
512C2×C4×D4—534no—
513C2×C4×D4—532no—
514C2×C4×D4—534no—
515C2×C4×D4—531no—
516C2×C4×D4—532no—
517C2×C4×D4C2×D5311yescharacteristic
518C2×C4×D4C2×D5312yes—
519C2×C4×D4C2×D5311yescharacteristic
520C2×C4×D4C2×D5312yes—
521C2×#117—532no—
522C2×#117—534no—
523C2×#117—532no—
524C2×#117—534no—
525C2×#117C2×D5311yescharacteristic
526C2×#117C2×D5312yes—
527C22×C4⋊C4—534no—
528C22×C4⋊C4—534no—
529C22×C4⋊C4—532no—
530C22×C4⋊C4—532no—
531C22×C4⋊C4—532no—
532C22×C42C2×D5312yes—
533C22×C42C2×D5311yescharacteristic
534C53C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—28no—
536C2×#41—5316no—
537C2×#41—10616no—
538C2×#41C22×D5318yes—
539C22×Q8—531no—
540C22×Q8—532no—
541C22×Q8—532no—
542C22×Q8C22×D5311yescharacteristic
543C22×D4—534no—
544C22×D4—532no—
545C22×D4—531no—
546C22×D4C22×D5312yes—
547C22×D4C22×D5311yescharacteristic
548C23×C4—534no—
549C23×C4—534no—
550C23×C4—532no—
551C23×C4—534no—
552C23×C4C22×D5312yes—
553C23×C4C22×D5312yes—
554C23×C4C22×D5311yescharacteristic
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5312yes—
557C23×C4C22×D5311yescharacteristic
558C4⋊Q8—5316no—
559C4⋊Q8—538no—
560C4⋊Q8—538no—
561#126—5332no—
562#126—5332no—
563#126—5332no—
564#126—5316no—
565#125—5332no—
566#125—5332no—
567#125—5316no—
568#125—538no—
569#125—5316no—
570#125—5332no—
571#125—5332no—
572#125—5316no—
573#125—5316no—
574#124—538no—
575#123—5332no—
576#123—5316no—
577#123—5332no—
578#123—5332no—
579#123—5332no—
580C22⋊Q8—5316no—
581C22⋊Q8—538no—
582C22⋊Q8—5316no—
583C22⋊Q8—5316no—
584C22⋊Q8—5316no—
585C22⋊Q8—5332no—
586C22⋊Q8—5316no—
587C22⋊Q8—5332no—
588#121—5332no—
589#121—5316no—
590#121—538no—
591C4×Q8—5316no—
592C4×Q8—5316no—
593C4×Q8—5316no—
594C4×Q8—538no—
595C4×Q8—5316no—
596C4×Q8C22×D5318yes—
597C4×Q8C22×D5318yes—
598C4×D4—5316no—
599C4×D4—5332no—
600C4×D4—5316no—
601C4×D4—5332no—
602C4×D4—538no—
603C4×D4—5316no—
604C4×D4C22×D5318yes—
605C4×D4C22×D53116yes—
606C4×D4C22×D5318yes—
607C4×D4C22×D53116yes—
608#117—5316no—
609#117—5332no—
610#117—5316no—
611#117—5332no—
612#117C22×D5318yes—
613#117C22×D53116yes—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—532no—
616C2×C4⋊C4—531no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—531no—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—532no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—532no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4—5332no—
626C2×C4⋊C4—534no—
627C2×C4⋊C4—534no—
628C2×C4⋊C4—534no—
629C2×C4⋊C4—534no—
630C2×C4⋊C4—5332no—
631C2×C4⋊C4—5316no—
632C2×C4⋊C4—5316no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—534no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—534no—
638C2×C4⋊C4—5316no—
639C2×C4⋊C4C22×D5311yescharacteristic
640C2×C4⋊C4C22×D5312yes—
641C2×C4⋊C4C22×D5311yescharacteristic
642C2×C4⋊C4C22×D5312yes—
643C2×C22⋊C4—534no—
644C2×C22⋊C4—534no—
645C2×C22⋊C4—532no—
646C2×C22⋊C4—532no—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—534no—
650C2×C22⋊C4—534no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4C22×D5312yes—
653C2×C22⋊C4C22×D5312yes—
654C2×C22⋊C4C22×D5312yes—
655C2×C42—534no—
656C2×C42—534no—
657C2×C42—532no—
658C2×C42C22×D5312yes—
659C2×C42C22×D5311yescharacteristic
660C2×C42C22×D5311yescharacteristic
661C2×C42C22×D5312yes—
662C2×C42C22×D5311yescharacteristic
663C2×C42C22×D5312yes—
664C2×C42C22×D53116yes—
665C2×C42C22×D5318yes—
666C2×C42C22×D5311yescharacteristic
667C24—532no—
668C24C23×D5311yescharacteristic
669C24C23×D5312yes—
670#41—232no—
671#41—10664no—
672C2×Q8—24no—
673C2×Q8—534no—
674C2×Q8—538no—
675C2×Q8—538no—
676C2×Q8—1068no—
677C2×Q8—1064no—
678C2×Q8—2124no—
679C2×Q8C23×D5314yes—
680C2×D4—28no—
681C2×D4—5316no—
682C2×D4—538no—
683C2×D4—534no—
684C2×D4—10616no—
685C2×D4—1064no—
686C2×D4—2124no—
687C2×D4#1171994518yes—
688C2×D4C23×D5318yes—
689C2×D4C23×D5314yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—5316no—
697C22×C4—532no—
698C22×C4—534no—
699C22×C4—534no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—5316no—
703C22×C4—538no—
704C22×C4—5316no—
705C22×C4—10616no—
706C22×C4—1068no—
707C22×C4—2128no—
708C22×C4—2128no—
709C22×C4C23×D5318yes—
710C22×C4C23×D5318yes—
711C22×C4C23×D5314yes—
712C22×C4C23×D5314yes—
713C22×C4C23×D5311yescharacteristic
714C22×C4C23×D5312yes—
715C22×C4C23×D5311yescharacteristic
716C22×C4C23×D5311yescharacteristic
717C22×C4C23×D5312yes—
718C22×C4C23×D5311yescharacteristic
719C22×C4C23×D5312yes—
720C22×C4C23×D5318yes—
721C22×C4C23×D5314yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—5316no—
725C4⋊C4—538no—
726C4⋊C4—534no—
727C4⋊C4—538no—
728C4⋊C4—534no—
729C4⋊C4—538no—
730C4⋊C4—538no—
731C4⋊C4—5316no—
732C4⋊C4—538no—
733C4⋊C4—5316no—
734C4⋊C4—5316no—
735C4⋊C4—5316no—
736C4⋊C4—5316no—
737C4⋊C4—5316no—
738C4⋊C4—5316no—
739C4⋊C4—538no—
740C4⋊C4—5316no—
741C4⋊C4—538no—
742C4⋊C4—538no—
743C4⋊C4—5316no—
744C4⋊C4C23×D5314yes—
745C4⋊C4C23×D5318yes—
746C4⋊C4C23×D5314yes—
747C4⋊C4C23×D5318yes—
748C22⋊C4—5316no—
749C22⋊C4—5316no—
750C22⋊C4—538no—
751C22⋊C4—538no—
752C22⋊C4—538no—
753C22⋊C4—538no—
754C22⋊C4—5316no—
755C22⋊C4—5316no—
756C22⋊C4—538no—
757C22⋊C4C23×D5318yes—
758C22⋊C4C23×D5318yes—
759C22⋊C4C23×D5318yes—
760C42—5316no—
761C42—5316no—
762C42—538no—
763C42C23×D5314yes—
764C42C23×D5318yes—
765C42C23×D5314yes—
766C42C23×D5314yes—
767C42C23×D5318yes—
768C42C23×D5314yes—
769C42C23×D5318yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—534no—
776C23—1064no—
777C23—1064no—
778C23—1064no—
779C23C2×#1171994518yes—
780C23C24×D5312yes—
781C23C24×D5314yes—
782C23C24×D5311yescharacteristic
783Q8—28no—
784Q8—10616no—
785Q8—1068no—
786Q8—2128no—
787D4—216no—
788D4—10632no—
789D4—1068no—
790D4—2128no—
791D4C2×#11719945116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—534no—
806C2×C4—538no—
807C2×C4—538no—
808C2×C4—534no—
809C2×C4—534no—
810C2×C4—1064no—
811C2×C4—1068no—
812C2×C4—10632no—
813C2×C4—1064no—
814C2×C4—1064no—
815C2×C4—1068no—
816C2×C4—10616no—
817C2×C4—21216no—
818C2×C4—21216no—
819C2×C4C2×#1171994514yes—
820C2×C4#1313326414yes—
821C2×C4C24×D5312yes—
822C2×C4C24×D5314yes—
823C2×C4C24×D5312yes—
824C2×C4C24×D5312yes—
825C2×C4C24×D5314yes—
826C2×C4C24×D5312yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—1064no—
838C22—1064no—
839C22—1064no—
840C22—2128no—
841C22C22×#1171994518yes—
842C22C22×#1171994512yes—
843C22C2×#1313326412yes—
844C22#1681145912yes—
845C22C25×D5311yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1064no—
854C4—1068no—
855C4—1064no—
856C4—1064no—
857C4—1068no—
858C4C22×#1171994514yes—
859C4C2×#1313326414yes—
860C2—28no—
861C2—42no—
862C2—2124no—
863C2#2028869314yesdirect product factor
864C2C23×#1171994511yescharacteristic
865C2C22×#1313326411yescharacteristic
866C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C4×#41×C53C2
socleC23×C53C25
hypercenterC2×C4×#41D53
hypocenterC53C2×#3515
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #20288693C2direct (N × H)
2. C2×#16811351C2semidirect
3. C2×#16811333C2semidirect
4. C2×#16811330C2semidirect
5. C2×#16811319C2semidirect
6. C2×#16811313C2semidirect
7. C2×#16811312C2semidirect
8. C2×#16811306C2semidirect
9. C2×#16811277C2semidirect
10. C2×#16811272C2semidirect
11. C2×#16811231C2semidirect
12. C2×#16811215C2semidirect
13. C2×#16811180C2semidirect
14. C2×#16811157C2semidirect
15. C2×#16811157C2semidirect
16. C22×#13133209C2semidirect
17. C2×#16811102C2semidirect
18. C2×C4×#41×C53C2semidirect
20. #16811351C22semidirect
21. #16811333C22semidirect
22. #16811330C22semidirect
23. #16811319C22semidirect
24. #16811313C22semidirect
25. #16811312C22semidirect
26. #16811306C22semidirect
27. #16811277C22semidirect
28. #16811272C22semidirect
29. #16811231C22semidirect
30. #16811215C22semidirect
31. #16811180C22semidirect
35. #16811157C22semidirect
36. #16811157C22semidirect
47. C2×#13133209C22semidirect
68. #16811102C22semidirect
90. C4×#41×C53C22semidirect
444. C2×C4×#41D53semidirect
447. C2×C53#3515semidirect
503. C4×#41C2×D53semidirect
534. C53C2×#3515semidirect
863. C2#20288693direct (N × H)

Maximal subgroups

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

subgroupindex
#202886932
C2×#168113512
C2×#168113332
C2×#168113302
C2×#168113192
C2×#168113132
C2×#168113122
C2×#168113062
C2×#168112772
C2×#168112722
C2×#168112312
C2×#168112152
C2×#168111802
C2×#168111572
C22×#131332092
C2×#168111022
C2×C4×#41×C532
C2×#351553