Finite Group Databasebeta

← C2×#20289180 #28291717

Subgroups — C2×#20289180 #28291717

Order 13568.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289180C2132yesmaximal, direct product factor
2C2×#16811368C214yesmaximal, complemented
3C2×#16811359C211yesmaximal, characteristic, complemented
4C2×#16811356C212yesmaximal, complemented
5C2×#16811348C211yesmaximal, characteristic, complemented
6C2×#16811332C212yesmaximal, complemented
7C2×#16811293C211yesmaximal, characteristic, complemented
8C2×#16811288C211yesmaximal, characteristic, complemented
9C2×#16811280C212yesmaximal, complemented
10C2×#16811272C212yesmaximal, complemented
11C2×#16811242C212yesmaximal, complemented
12C2×#16811240C212yesmaximal, complemented
13C2×#16811226C212yesmaximal, complemented
14C2×#16811215C214yesmaximal, complemented
15C2×#16811193C212yesmaximal, complemented
16C2×#16811180C211yesmaximal, characteristic, complemented
17C2×#16811157C211yesmaximal, characteristic, complemented
18C2×C53×#532C211yesmaximal, characteristic, complemented
19C22×#11719947C2212yes—
20C22×Q8×D53C2212yes—
21#16811368C22164yescomplemented
22#16811359C22116yescomplemented
23#16811356C22132yescomplemented
24#16811348C22116yescomplemented
25#16811332C22132yescomplemented
26#16811293C22116yescomplemented
27#16811288C22116yescomplemented
28#16811280C22132yescomplemented
29#16811272C22132yescomplemented
30#16811242C22132yescomplemented
31#16811240C22132yescomplemented
32#16811226C22132yescomplemented
33#16811215C22164yescomplemented
34#16811193C22132yescomplemented
35#16811180C22116yescomplemented
36C2×#13133217C2211yescharacteristic
37C2×#13133217C2211yescharacteristic
38C2×#13133216C2212yes—
39C2×#13133215C2212yes—
40C2×#13133213C2212yes—
41#16811157C22116yescomplemented
42C2×#13133211C2212yes—
43C2×#13133210C2214yes—
44C2×#13133209C2212yes—
45C2×#13133209C2211yescharacteristic
46C2×#13133208C2212yes—
47C2×#13133207C2214yes—
48C2×#13133205C2211yescharacteristic
49C2×#13133204C2212yes—
50C2×#13133204C2212yes—
51C2×#13133204C2214yes—
52C2×#13133203C2214yes—
53C2×#13133201C2214yes—
54C2×#13133200C2214yes—
55C2×#13133200C2212yes—
56C2×#13133199C2214yes—
57C2×#13133199C2214yes—
58C2×#13133198C2214yes—
59C2×#13133198C2214yes—
60C2×#13133196C2212yes—
61C2×#13133196C2211yescharacteristic
62C2×#13133196C2211yescharacteristic
63C2×#13133196C2214yes—
64C2×#13133196C2211yescharacteristic
65C2×#13133195C2214yes—
66C2×#13133194C2214yes—
67C2×#13133194C2214yes—
68C2×#13133194C2214yes—
69C2×#13133193C2212yes—
70C2×#13133191C2211yescharacteristic
71C2×#13133189C2214yes—
72C2×#13133189C2214yes—
73C2×#13133188C2214yes—
74C2×#13133188C2212yes—
75C2×Q8×Dic53C2212yes—
76C2×C4×Dic106C2211yescharacteristic
77C2×C4×Dic106C2212yes—
78C2×C4×Dic106C2211yescharacteristic
79C2×C4×Dic106C2211yescharacteristic
80C2×#13133182C2212yes—
81C2×C4×D212C2211yescharacteristic
82C2×D4×Dic53C2212yes—
83C2×D4×Dic53C2212yes—
84C2×D4×Dic53C2212yes—
85C2×#13133179C2212yes—
86C2×C4×C22⋊D53C2214yes—
87C2×C4×C22⋊D53C2212yes—
88C2×#13133176C2212yes—
89C2×#13133174C2212yes—
90C22×#11719919C2214yes—
91C22×#41×C53C2212yes—
92C53×#532C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#127×C53C2211yescharacteristic
95C2×#124×C53C2212yes—
96C2×#121×C53C2212yes—
97C2×#121×C53C2212yes—
98C2×C4×D4×C53C2212yes—
99C2×C4×D4×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719947—48no—
102C2×#11719947C23116yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2311yescharacteristic
106C22×Dic106C2312yes—
107C22×Dic106C2314yes—
108C2×Q8×D53—48no—
109C2×Q8×D53C23116yes—
110C22×D212C2311yescharacteristic
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2314yes—
113C22×C22⋊D53C2314yes—
114C23×Dic53C2314yes—
115C23×Dic53C2314yes—
116C22×C4×D53C2312yes—
117C22×C4×D53C2314yes—
118#13133217C2318yes—
119#13133217C2318yes—
120#13133216C23116yes—
121#13133215C23116yes—
122#13133213C23116yes—
123#13133211C23116yes—
124#13133210C23132yes—
125#13133209C2318yes—
126#13133209C23116yes—
127#13133208C23116yes—
128#13133207C23132yes—
129#13133205C2318yes—
130#13133204C23116yes—
131#13133204C23132yes—
132#13133204C23116yes—
133#13133203C23132yes—
134#13133201C23132yes—
135#13133200C23132yes—
136#13133200C23116yes—
137#13133199C23132yes—
138#13133199C23132yes—
139#13133198C23132yes—
140#13133198C23132yes—
141#13133196C2318yes—
142#13133196C2318yes—
143#13133196C23132yes—
144#13133196C23116yes—
145#13133196C2318yes—
146#13133195C23132yes—
147#13133194C23132yes—
148#13133194C23132yes—
149#13133194C23132yes—
150#13133193C23116yes—
151#13133191C2318yes—
152#13133189C23132yes—
153#13133189C23132yes—
154#13133188C23116yes—
155#13133188C23132yes—
156Q8×Dic53C23116yes—
157C4×Dic106C2318yes—
158C4×Dic106C2318yes—
159C4×Dic106C23116yes—
160C4×Dic106C2318yes—
161#13133182C23116yes—
162C4×D212C2318yes—
163D4×Dic53C23116yes—
164D4×Dic53C23116yes—
165D4×Dic53C23116yes—
166#13133179C23116yes—
167C4×C22⋊D53C23116yes—
168C4×C22⋊D53C23132yes—
169#13133176C23116yes—
170#13133174C23116yes—
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2311yescharacteristic
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2311yescharacteristic
177C2×C4⋊Dic53C2312yes—
178C2×C4⋊Dic53C2314yes—
179C2×#11719919C23132yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2314yes—
188C2×#11719919C2312yes—
189C2×#11719919C2312yes—
190C2×#11719919C2312yes—
191C2×C22⋊Dic53C2312yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2314yes—
194C2×C22⋊Dic53C2312yes—
195C2×C22⋊Dic53C2314yes—
196C2×C22⋊Dic53C2314yes—
197C2×C22⋊Dic53C2314yes—
198C2×#11719921C2312yes—
199C2×#11719921C2312yes—
200C2×#11719921C2312yes—
201C2×#11719921C2314yes—
202C2×#11719921C2312yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2312yes—
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2314yes—
207C2×#41×C53—48no—
208C2×#41×C53C23116yes—
209C22×Q8×C53C2312yes—
210C22×D4×C53C2312yes—
211C22×D4×C53C2312yes—
212C22×D4×C53C2312yes—
213C22×D4×C53C2314yes—
214C23×C4×C53C2311yescharacteristic
215C23×C4×C53C2311yescharacteristic
216C23×C4×C53C2311yescharacteristic
217C23×C4×C53C2314yes—
218C4⋊Q8×C53C2318yes—
219#127×C53C2318yes—
220#124×C53C23116yes—
221#121×C53C23116yes—
222#121×C53C23116yes—
223C4×D4×C53C23116yes—
224C4×D4×C53C23116yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C22⋊C4×C53C2314yes—
228C2×C22⋊C4×C53C2314yes—
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2318yes—
234C24×C53C2414yes—
235C24×C53C2411yescharacteristic
236C23×D53C2412yes—
237#41×C53—432no—
238C2×Q8×C53—28no—
239C2×Q8×C53C2418yes—
240C2×D4×C53—28no—
241C2×D4×C53—28no—
242C2×D4×C53—44no—
243C2×D4×C53—48no—
244C2×D4×C53C2418yes—
245C2×D4×C53C2418yes—
246C2×D4×C53C2418yes—
247C2×D4×C53C24116yes—
248C22×C4×C53—24no—
249C22×C4×C53—24no—
250C22×C4×C53—42no—
251C22×C4×C53—48no—
252C22×C4×C53C2411yescharacteristic
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C2411yescharacteristic
255C22×C4×C53C2414yes—
256C22×C4×C53C2411yescharacteristic
257C22×C4×C53C2414yes—
258C22×C4×C53C2414yes—
259C22×C4×C53C2414yes—
260C22×C4×C53C24116yes—
261C22×C4×C53C2411yescharacteristic
262C22×C4×C53C2411yescharacteristic
263C2×C22⋊D53—48no—
264C2×C22⋊D53—44no—
265C2×C22⋊D53—48no—
266C2×C22⋊D53C2418yes—
267C2×C22⋊D53C24116yes—
268C2×C22⋊D53C24116yes—
269C22×Dic53—48no—
270C22×Dic53—48no—
271C22×Dic53C2412yes—
272C22×Dic53C2412yes—
273C22×Dic53C2412yes—
274C22×Dic53C2412yes—
275C22×Dic53C2412yes—
276C22×Dic53C2412yes—
277C22×Dic53C2412yes—
278C22×Dic53C24116yes—
279C22×Dic53C24116yes—
280Q8×D53—432no—
281#11719947—432no—
282C2×D212—24no—
283C2×D212C2414yes—
284C2×C4×D53—28no—
285C2×C4×D53—48no—
286C2×C4×D53C2418yes—
287C2×C4×D53C24116yes—
288C2×Dic106—24no—
289C2×Dic106—24no—
290C2×Dic106—24no—
291C2×Dic106—48no—
292C2×Dic106—44no—
293C2×Dic106C2414yes—
294C2×Dic106C2414yes—
295C2×Dic106C2414yes—
296C2×Dic106C2418yes—
297C2×Dic106C24116yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C2418yes—
300C22⋊C4×C53C24116yes—
301C22⋊C4×C53C24116yes—
302C42×C53C2414yes—
303C42×C53C2414yes—
304C42×C53C2414yes—
305C42×C53C2414yes—
306C22⋊Dic53C2418yes—
307C22⋊Dic53C2418yes—
308C22⋊Dic53C24116yes—
309C22⋊Dic53C2418yes—
310C22⋊Dic53C24116yes—
311C22⋊Dic53C24116yes—
312C22⋊Dic53C24116yes—
313#11719921C2418yes—
314#11719921C2418yes—
315#11719921C2418yes—
316#11719921C24116yes—
317#11719921C2418yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C2414yes—
321C4⋊Dic53C2414yes—
322C4⋊Dic53C2414yes—
323C4⋊Dic53C2414yes—
324C4⋊Dic53C2418yes—
325C4⋊Dic53C24116yes—
326#11719919C2418yes—
327#11719919C2418yes—
328#11719919C24116yes—
329#11719919C24116yes—
330#11719919C2418yes—
331#11719919C2418yes—
332#11719919C2418yes—
333#11719919C24116yes—
334#11719919C2418yes—
335#11719919C2418yes—
336#11719919C2418yes—
337C4×Dic53C2418yes—
338C4×Dic53C2418yes—
339C4×Dic53C2418yes—
340C4×Dic53C24116yes—
341C23×C53—28no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53—28no—
345C23×C53—28no—
346C23×C53—22no—
347C23×C53C2518yes—
348C23×C53C2512yes—
349C23×C53C2511yescharacteristic
350C22×D53—24no—
351C22×D53—24no—
352C22×D53—24no—
353C22×D53C2514yes—
354Q8×C53—216no—
355D4×C53—216no—
356D4×C53—216no—
357D4×C53—48no—
358D4×C53—416no—
359C2×C4×C53—28no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—28no—
365C2×C4×C53—28no—
366C2×C4×C53—44no—
367C2×C4×C53—416no—
368C2×C4×C53H(5,𝔽2)14yes—
369C2×C4×C532−1+414yes—
370C2×C4×C53C2512yes—
371C2×C4×C53C2518yes—
372C2×C4×C53C2512yes—
373C2×C4×C53C2512yes—
374C2×C4×C53C2512yes—
375C2×C4×C53C2512yes—
376C2×C4×C53C2512yes—
377C22⋊D53—416no—
378C22⋊D53—416no—
379C22⋊D53—48no—
380C2×Dic53—24no—
381C2×Dic53—24no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53—24no—
385C2×Dic53—24no—
386C2×Dic53—24no—
387C2×Dic53—416no—
388C2×Dic53—416no—
389C2×Dic53C2514yes—
390C2×Dic53C2514yes—
391C2×Dic53C2514yes—
392C2×Dic53C2514yes—
393C2×Dic53C2514yes—
394C2×Dic53C2514yes—
395C2×Dic53C2514yes—
396D212—28no—
397C4×D53—216no—
398C4×D53—416no—
399Dic106—28no—
400Dic106—28no—
401Dic106—28no—
402Dic106—48no—
403Dic106—416no—
404C2×#3554—531nomaximal, Sylow
405C22×C53—28no—
406C22×C53—22no—
407C22×C53—22no—
408C22×C53—28no—
409C22×C53—28no—
410C22×C53—22no—
411C22×C53—416no—
412C22×C53—44no—
413C22×C53C2×H(5,𝔽2)12yes—
414C22×C53C2×2−1+412yes—
415C22×C53#58512yes—
416C22×C53C2611yescharacteristic
417C2×D53—24no—
418C2×D53—24no—
419C2×D53—24no—
420C2×D53—48no—
421C4×C53—28no—
422C4×C53—22no—
423C4×C53—22no—
424C4×C53—22no—
425C4×C53—22no—
426C4×C53C2×H(5,𝔽2)14yes—
427C4×C53C2×2−1+414yes—
428Dic53—24no—
429Dic53—24no—
430Dic53—24no—
431Dic53—24no—
432Dic53—24no—
433Dic53—24no—
434Dic53—24no—
435#3554—5332no—
436C2×#562—534no—
437C2×#559—531no—
438C2×#559—532no—
439C2×#557—531no—
440C2×#554—532no—
441C2×#550—531no—
442C2×D4×Q8—531no—
443C2×#548—532no—
444C2×#547—532no—
445C2×#542—532no—
446C2×#542—532no—
447C2×#540—532no—
448C2×#539—534no—
449C2×#536—532no—
450C2×#533—531no—
451C2×#532D5311yescharacteristic, complemented
452C2×#529—531no—
453C2×C53—48no—
454C2×C53—42no—
455C2×C53#355414yescomplemented
456C2×C53C22×H(5,𝔽2)11yescharacteristic
457C2×C53C22×2−1+411yescharacteristic
458C2×C53C2×#58511yescharacteristic
459D53—44no—
460C22×#41—532no—
461C22×#41C2×D5312yes—
462C23×Q8—532no—
463#562—5364no—
464#559—5316no—
465#559—5332no—
466#557—5316no—
467#554—5332no—
468#550—5316no—
469D4×Q8—5316no—
470#548—5332no—
471#547—5332no—
472#542—5332no—
473#542—5332no—
474#540—5332no—
475#539—5364no—
476#536—5332no—
477#533—5316no—
478#532C2×D53116yescomplemented
479C2×C4⋊Q8—532no—
480C2×C4⋊Q8—532no—
481C2×C4⋊Q8—531no—
482C2×C4⋊Q8—531no—
483C2×C4⋊Q8C2×D5311yescharacteristic
484C2×#127—532no—
485C2×#127C2×D5311yescharacteristic
486#529—5316no—
487C2×#126—534no—
488C2×#126—532no—
489C2×#125—534no—
490C2×#125—532no—
491C2×#125—531no—
492C2×#125—532no—
493C2×#124—532no—
494C2×#124—534no—
495C2×#124—532no—
496C2×#124—534no—
497C2×#124—531no—
498C2×#124C2×D5312yes—
499C2×#123—534no—
500C2×#123—534no—
501C2×#123—532no—
502C2×#123—534no—
503C2×#123—534no—
504C2×#123—534no—
505C2×#123—534no—
506C2×C22⋊Q8—532no—
507C2×C22⋊Q8—531no—
508C2×C22⋊Q8—531no—
509C2×C22⋊Q8—531no—
510C2×C22⋊Q8—532no—
511C2×C22⋊Q8—534no—
512C2×C22⋊Q8—534no—
513C2×C22⋊Q8—534no—
514C2×C22⋊Q8—534no—
515C2×C22⋊Q8—534no—
516C2×#121—534no—
517C2×#121—532no—
518C2×#121—534no—
519C2×#121—534no—
520C2×#121—531no—
521C2×#121C2×D5312yes—
522C2×#121C2×D5312yes—
523C2×C4×Q8—532no—
524C2×C4×Q8—532no—
525C2×C4×Q8—531no—
526C2×C4×Q8—531no—
527C2×C4×Q8—531no—
528C2×C4×Q8—532no—
529C2×C4×D4—532no—
530C2×C4×D4—532no—
531C2×C4×D4—532no—
532C2×C4×D4—532no—
533C2×C4×D4—534no—
534C2×C4×D4—532no—
535C2×C4×D4—531no—
536C2×C4×D4C2×D5312yes—
537C2×C4×D4C2×D5312yes—
538C2×#117—532no—
539C2×#117—532no—
540C22×C4⋊C4—534no—
541C22×C42C2×D5311yescharacteristic
542C53C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—48no—
544C2×#41—5316no—
545C2×#41—2128no—
546C2×#41C22×D53116yes—
547C22×Q8—5316no—
548C22×Q8—531no—
549C22×Q8—531no—
550C22×Q8—531no—
551C22×Q8—532no—
552C22×Q8—534no—
553C22×Q8—2128no—
554C22×Q8C22×D5312yes—
555C22×D4—532no—
556C22×D4—534no—
557C22×D4—534no—
558C22×D4—531no—
559C22×D4C22×D5312yes—
560C22×D4C22×D5312yes—
561C22×D4C22×D5312yes—
562C22×D4C22×D5314yes—
563C23×C4—534no—
564C23×C4—534no—
565C23×C4—532no—
566C23×C4—534no—
567C23×C4C22×D5311yescharacteristic
568C23×C4C22×D5311yescharacteristic
569C23×C4C22×D5314yes—
570C23×C4C22×D5311yescharacteristic
571C4⋊Q8—5316no—
572C4⋊Q8—5316no—
573C4⋊Q8—538no—
574C4⋊Q8—538no—
575C4⋊Q8C22×D5318yes—
576#127—5316no—
577#127C22×D5318yes—
578#126—5332no—
579#126—5316no—
580#125—5332no—
581#125—5316no—
582#125—538no—
583#125—5316no—
584#124—5316no—
585#124—5332no—
586#124—5316no—
587#124—5332no—
588#124—538no—
589#124C22×D53116yes—
590#123—5332no—
591#123—5332no—
592#123—5316no—
593#123—5332no—
594#123—5332no—
595#123—5332no—
596#123—5332no—
597C22⋊Q8—5316no—
598C22⋊Q8—538no—
599C22⋊Q8—538no—
600C22⋊Q8—538no—
601C22⋊Q8—5316no—
602C22⋊Q8—5332no—
603C22⋊Q8—5332no—
604C22⋊Q8—5332no—
605C22⋊Q8—5332no—
606C22⋊Q8—5332no—
607#121—5332no—
608#121—5332no—
609#121—5332no—
610#121—5316no—
611#121—538no—
612#121C22×D53116yes—
613#121C22×D53116yes—
614C4×Q8—5316no—
615C4×Q8—5316no—
616C4×Q8—538no—
617C4×Q8—538no—
618C4×Q8—538no—
619C4×Q8—5316no—
620C4×D4—5316no—
621C4×D4—5316no—
622C4×D4—5316no—
623C4×D4—5316no—
624C4×D4—5332no—
625C4×D4—5316no—
626C4×D4—538no—
627C4×D4C22×D53116yes—
628C4×D4C22×D53116yes—
629#117—5316no—
630#117—5316no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—534no—
635C2×C4⋊C4—5332no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—532no—
639C2×C4⋊C4—532no—
640C2×C4⋊C4—531no—
641C2×C4⋊C4—531no—
642C2×C4⋊C4—532no—
643C2×C4⋊C4—531no—
644C2×C4⋊C4—531no—
645C2×C4⋊C4—532no—
646C2×C4⋊C4—534no—
647C2×C4⋊C4—532no—
648C2×C4⋊C4—532no—
649C2×C4⋊C4—534no—
650C2×C4⋊C4—532no—
651C2×C4⋊C4C22×D5312yes—
652C2×C4⋊C4C22×D5312yes—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—534no—
656C2×C22⋊C4—534no—
657C2×C22⋊C4—532no—
658C2×C22⋊C4—534no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—532no—
661C2×C22⋊C4—532no—
662C2×C22⋊C4—532no—
663C2×C22⋊C4—532no—
664C2×C22⋊C4—534no—
665C2×C22⋊C4C22×D5314yes—
666C2×C22⋊C4C22×D5314yes—
667C2×C42—532no—
668C2×C42—532no—
669C2×C42—532no—
670C2×C42—534no—
671C2×C42C22×D5311yescharacteristic
672C2×C42C22×D5311yescharacteristic
673C2×C42C22×D5311yescharacteristic
674C2×C42C22×D5311yescharacteristic
675C2×C42C22×D5318yes—
676C24—532no—
677C24C23×D5311yescharacteristic
678C24C23×D5314yes—
679#41—432no—
680#41—21232no—
681C2×Q8—28no—
682C2×Q8—534no—
683C2×Q8—534no—
684C2×Q8—534no—
685C2×Q8—538no—
686C2×Q8—5316no—
687C2×Q8—1064no—
688C2×Q8—1064no—
689C2×Q8—1064no—
690C2×Q8—2124no—
691C2×Q8—2128no—
692C2×Q8—21232no—
693C2×Q8C23×D5318yes—
694C2×D4—28no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—48no—
698C2×D4—538no—
699C2×D4—5316no—
700C2×D4—5316no—
701C2×D4—534no—
702C2×D4—1064no—
703C2×D4—2124no—
704C2×D4—2128no—
705C2×D4—2128no—
706C2×D4C23×D5318yes—
707C2×D4C23×D5318yes—
708C2×D4C23×D5318yes—
709C2×D4C23×D53116yes—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—48no—
714C22×C4—532no—
715C22×C4—532no—
716C22×C4—532no—
717C22×C4—532no—
718C22×C4—532no—
719C22×C4—532no—
720C22×C4—532no—
721C22×C4—5316no—
722C22×C4—5316no—
723C22×C4—538no—
724C22×C4—5316no—
725C22×C4—1068no—
726C22×C4—2128no—
727C22×C4—2128no—
728C22×C4—2128no—
729C22×C4C23×D5314yes—
730C22×C4C23×D5314yes—
731C22×C4C23×D5314yes—
732C22×C4C23×D5311yescharacteristic
733C22×C4C23×D5311yescharacteristic
734C22×C4C23×D5311yescharacteristic
735C22×C4C23×D5311yescharacteristic
736C22×C4C23×D5314yes—
737C22×C4C23×D53116yes—
738C22×C4C23×D5311yescharacteristic
739C22×C4C23×D5311yescharacteristic
740C4⋊C4—538no—
741C4⋊C4—538no—
742C4⋊C4—5316no—
743C4⋊C4—5316no—
744C4⋊C4—538no—
745C4⋊C4—538no—
746C4⋊C4—538no—
747C4⋊C4—538no—
748C4⋊C4—534no—
749C4⋊C4—534no—
750C4⋊C4—538no—
751C4⋊C4—534no—
752C4⋊C4—534no—
753C4⋊C4—538no—
754C4⋊C4—5316no—
755C4⋊C4—538no—
756C4⋊C4—538no—
757C4⋊C4—5316no—
758C4⋊C4—538no—
759C4⋊C4C23×D5318yes—
760C4⋊C4C23×D5318yes—
761C22⋊C4—538no—
762C22⋊C4—538no—
763C22⋊C4—5316no—
764C22⋊C4—5316no—
765C22⋊C4—538no—
766C22⋊C4—5316no—
767C22⋊C4—5316no—
768C22⋊C4—538no—
769C22⋊C4—538no—
770C22⋊C4—538no—
771C22⋊C4—538no—
772C22⋊C4—5316no—
773C22⋊C4C23×D53116yes—
774C22⋊C4C23×D53116yes—
775C42—538no—
776C42—538no—
777C42—538no—
778C42—5316no—
779C42C23×D5314yes—
780C42C23×D5314yes—
781C42C23×D5314yes—
782C42C23×D5314yes—
783C23—22no—
784C23—28no—
785C23—22no—
786C23—28no—
787C23—22no—
788C23—28no—
789C23—534no—
790C23—1064no—
791C23—1064no—
792C23—1064no—
793C23C24×D5312yes—
794C23C24×D5318yes—
795C23C24×D5311yescharacteristic
796Q8—216no—
797Q8—1068no—
798Q8—1068no—
799Q8—1068no—
800Q8—2128no—
801Q8—21216no—
802D4—216no—
803D4—216no—
804D4—48no—
805D4—416no—
806D4—1068no—
807D4—2128no—
808D4—21216no—
809D4—21216no—
810C2×C4—22no—
811C2×C4—28no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—44no—
818C2×C4—416no—
819C2×C4—534no—
820C2×C4—534no—
821C2×C4—534no—
822C2×C4—534no—
823C2×C4—534no—
824C2×C4—534no—
825C2×C4—534no—
826C2×C4—1064no—
827C2×C4—1064no—
828C2×C4—1064no—
829C2×C4—1064no—
830C2×C4—1064no—
831C2×C4—1064no—
832C2×C4—1064no—
833C2×C4—10616no—
834C2×C4—21216no—
835C2×C4—21216no—
836C2×C4—21216no—
837C2×C4#1313326214yes—
838C2×C4#1313326414yes—
839C2×C4C24×D5318yes—
840C2×C4C24×D5312yes—
841C2×C4C24×D5312yes—
842C2×C4C24×D5312yes—
843C2×C4C24×D5312yes—
844C2×C4C24×D5312yes—
845C2×C4C24×D5312yes—
846C22—22no—
847C22—28no—
848C22—22no—
849C22—28no—
850C22—22no—
851C22—28no—
852C22—44no—
853C22—416no—
854C22—1064no—
855C22—1064no—
856C22—1064no—
857C22—2128no—
858C22C2×#1313326212yes—
859C22C2×#1313326412yes—
860C22#1681145912yes—
861C22C25×D5311yescharacteristic
862C4—22no—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—1064no—
868C4—1064no—
869C4—1064no—
870C4—1064no—
871C4—1064no—
872C4—1064no—
873C4—1064no—
874C4C2×#1313326214yes—
875C4C2×#1313326414yes—
876C2—42no—
877C2—48no—
878C2—2124no—
879C2#2028918014yesdirect product factor
880C2C22×#1313326211yescharacteristic
881C2C22×#1313326411yescharacteristic
882C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#532C2
socleC23×C53C25
hypercenterC2×#532D53
hypocenterC53C2×#3554
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20289180C2direct (N × H)
2. C2×#16811368C2semidirect
3. C2×#16811359C2semidirect
4. C2×#16811356C2semidirect
5. C2×#16811348C2semidirect
6. C2×#16811332C2semidirect
7. C2×#16811293C2semidirect
8. C2×#16811288C2semidirect
9. C2×#16811280C2semidirect
10. C2×#16811272C2semidirect
11. C2×#16811242C2semidirect
12. C2×#16811240C2semidirect
13. C2×#16811226C2semidirect
14. C2×#16811215C2semidirect
15. C2×#16811193C2semidirect
16. C2×#16811180C2semidirect
17. C2×#16811157C2semidirect
18. C2×C53×#532C2semidirect
21. #16811368C22semidirect
22. #16811359C22semidirect
23. #16811356C22semidirect
24. #16811348C22semidirect
25. #16811332C22semidirect
26. #16811293C22semidirect
27. #16811288C22semidirect
28. #16811280C22semidirect
29. #16811272C22semidirect
30. #16811242C22semidirect
31. #16811240C22semidirect
32. #16811226C22semidirect
33. #16811215C22semidirect
34. #16811193C22semidirect
35. #16811180C22semidirect
41. #16811157C22semidirect
92. C53×#532C22semidirect
451. C2×#532D53semidirect
455. C2×C53#3554semidirect
478. #532C2×D53semidirect
542. C53C2×#3554semidirect
879. C2#20289180direct (N × H)

Maximal subgroups

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

subgroupindex
#202891802
C2×#168113682
C2×#168113592
C2×#168113562
C2×#168113482
C2×#168113322
C2×#168112932
C2×#168112882
C2×#168112802
C2×#168112722
C2×#168112422
C2×#168112402
C2×#168112262
C2×#168112152
C2×#168111932
C2×#168111802
C2×#168111572
C2×C53×#5322
C2×#355453