Finite Group Databasebeta

← C2×#20288809 #28292309

Subgroups — C2×#20288809 #28292309

Order 13568.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288809C2132yesmaximal, direct product factor
2C2×#16811352C211yesmaximal, characteristic, complemented
3C2×#16811351C211yesmaximal, characteristic, complemented
4C2×#16811350C212yesmaximal, complemented
5C2×#16811343C211yesmaximal, characteristic, complemented
6C2×#16811342C212yesmaximal, complemented
7C2×#16811313C212yesmaximal, complemented
8C2×#16811310C214yesmaximal, complemented
9C2×D4×Dic106C211yesmaximal, characteristic, complemented
10C2×D4×Dic106C212yesmaximal, complemented
11C2×#16811235C212yesmaximal, complemented
12C2×#16811230C214yesmaximal, complemented
13C2×#16811180C211yesmaximal, characteristic, complemented
14C2×#16811175C212yesmaximal, complemented
15C2×#16811154C212yesmaximal
16C2×#16811100C212yesmaximal, complemented
17C22×C4×Dic106C211yesmaximal, characteristic, complemented
18C2×C53×#529C211yesmaximal, characteristic
19C23×Dic106C2211yescharacteristic
20C23×Dic106C2212yes—
21#16811352C22116yescomplemented
22#16811351C22116yescomplemented
23#16811350C22132yescomplemented
24#16811343C22116yescomplemented
25#16811342C22132yescomplemented
26#16811313C22132yescomplemented
27#16811310C22164yescomplemented
28D4×Dic106C22132yescomplemented
29D4×Dic106C22116yescomplemented
30#16811235C22132yescomplemented
31#16811230C22164yescomplemented
32#16811180C22116yescomplemented
33#16811175C22132yescomplemented
34C2×#13133217C2211yescharacteristic
35C2×#13133217C2211yescharacteristic
36C2×#13133217C2212yes—
37C2×#13133216C2212yes—
38C2×#13133216C2214yes—
39C2×#13133215C2212yes—
40#16811154C22132yes—
41C2×#13133210C2214yes—
42C2×#13133210C2214yes—
43C2×#13133210C2214yes—
44C2×#13133210C2214yes—
45C2×#13133209C2212yes—
46C2×#13133209C2212yes—
47C2×#13133208C2212yes—
48C2×#13133208C2214yes—
49C2×#13133207C2214yes—
50C2×#13133207C2214yes—
51C2×#13133207C2214yes—
52C2×#13133207C2214yes—
53C2×#13133204C2212yes—
54C2×#13133198C2214yes—
55C2×#13133196C2212yes—
56C2×#13133196C2212yes—
57C2×#13133196C2212yes—
58C2×#13133196C2212yes—
59C2×#13133194C2214yes—
60C2×#13133194C2214yes—
61C2×#13133194C2214yes—
62#16811100C22132yescomplemented
63C2×Q8×Dic53C2212yes—
64C2×C4×Dic106C2212yes—
65C2×C4×Dic106C2212yes—
66C2×C4×Dic106C2211yescharacteristic
67C2×C4×Dic106C2212yes—
68C2×C4×Dic106C2211yescharacteristic
69C2×C4×Dic106C2212yes—
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2212yes—
72C2×C4×Dic106C2211yescharacteristic
73C2×C4×Dic106C2211yescharacteristic
74C2×C4×Dic106C22116yescomplemented
75C2×#13133182C2212yes—
76C2×#13133182C2214yes—
77C2×#13133182C2212yes—
78C2×#13133182C2214yes—
79C2×D4×Dic53C2212yes—
80C2×D4×Dic53C2214yes—
81C2×#13133176C2212yes—
82C2×#13133176C2212yes—
83C2×#13133173C2214yes—
84C2×#13133173C2214yes—
85C2×#13133173C2214yes—
86C22×C4⋊Dic53C2211yescharacteristic
87C22×#11719919C2212yes—
88C22×C4×Dic53C2212yes—
89C53×#529C22116yes—
90C2×#126×C53C2212yes—
91C2×#125×C53C2211yescharacteristic
92C2×#124×C53C2211yescharacteristic
93C2×#123×C53C2212yes—
94C2×C22⋊Q8×C53C2211yescharacteristic
95C2×#121×C53C2211yescharacteristic
96C2×C4×Q8×C53C2211yescharacteristic
97C2×C4×D4×C53C2211yescharacteristic
98C2×C4×D4×C53C2212yes—
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C22×Dic106—28no—
102C22×Dic106—216no—
103C22×Dic106C2318yes—
104C22×Dic106C23116yes—
105C22×Dic106C2312yes—
106C22×Dic106C2314yes—
107C22×Dic106C2312yes—
108C22×Dic106C2311yescharacteristic
109C22×Dic106C2312yes—
110C22×Dic106C2311yescharacteristic
111C23×Dic53C2312yes—
112C23×Dic53C2312yes—
113C23×Dic53C2314yes—
114#13133217C2318yes—
115#13133217C23116yes—
116#13133217C2318yes—
117#13133216C23116yes—
118#13133216C23132yes—
119#13133215C23116yes—
120#13133210C23132yes—
121#13133210C23132yes—
122#13133210C23132yes—
123#13133210C23132yes—
124#13133209C23116yes—
125#13133209C23116yes—
126#13133208C23132yes—
127#13133208C23116yes—
128#13133207C23132yes—
129#13133207C23132yes—
130#13133207C23132yes—
131#13133207C23132yes—
132#13133204C23116yes—
133#13133198C23132yes—
134#13133196C23116yes—
135#13133196C23116yes—
136#13133196C23116yes—
137#13133196C23116yes—
138#13133194C23132yes—
139#13133194C23132yes—
140#13133194C23132yes—
141Q8×Dic53C23116yes—
142C4×Dic106C2318yes—
143C4×Dic106C23116yes—
144C4×Dic106C23116yes—
145C4×Dic106C23116yes—
146C4×Dic106C23116yes—
147C4×Dic106C2318yes—
148C4×Dic106C2318yes—
149C4×Dic106C23116yes—
150C4×Dic106C2318yes—
151C4×Dic106C23116yes—
152#13133182C23132yes—
153#13133182C23116yes—
154#13133182C23116yes—
155#13133182C23132yes—
156D4×Dic53C23132yes—
157D4×Dic53C23116yes—
158#13133176C23116yes—
159#13133176C23116yes—
160#13133173C23132yes—
161#13133173C23132yes—
162#13133173C23132yes—
163C2×C4⋊Dic53C2318yes—
164C2×C4⋊Dic53C2311yescharacteristic
165C2×C4⋊Dic53C2311yescharacteristic
166C2×C4⋊Dic53C2312yes—
167C2×C4⋊Dic53C2312yes—
168C2×C4⋊Dic53C2312yes—
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2314yes—
172C2×C4⋊Dic53C2314yes—
173C2×#11719919C23116yes—
174C2×#11719919C2312yes—
175C2×#11719919C2312yes—
176C2×#11719919C2312yes—
177C2×#11719919C2312yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2314yes—
186C2×C22⋊Dic53C2314yes—
187C2×C22⋊Dic53C2314yes—
188C2×C22⋊Dic53C2314yes—
189C2×C22⋊Dic53C2314yes—
190C2×C4×Dic53C2312yes—
191C2×C4×Dic53C2312yes—
192C2×C4×Dic53C2312yes—
193C2×C4×Dic53C2312yes—
194C2×C4×Dic53C23116yes—
195C2×C4×Dic53C2314yes—
196C2×C4×Dic53C2314yes—
197C2×C4×Dic53C2314yes—
198C2×C4×Dic53C2314yes—
199C22×Q8×C53C2311yescharacteristic
200C22×D4×C53C2312yes—
201C22×D4×C53C2311yescharacteristic
202C23×C4×C53C2311yescharacteristic
203C23×C4×C53C2311yescharacteristic
204C23×C4×C53C2311yescharacteristic
205C23×C4×C53C2312yes—
206#126×C53C23116yes—
207#125×C53C2318yes—
208#124×C53C2318yes—
209#123×C53C23116yes—
210C22⋊Q8×C53C2318yes—
211#121×C53C2318yes—
212C4×Q8×C53C2318yes—
213C4×D4×C53C23116yes—
214C4×D4×C53C2318yes—
215#117×C53C23116yes—
216C2×C4⋊C4×C53C2312yes—
217C2×C4⋊C4×C53C2312yes—
218C2×C4⋊C4×C53C2311yescharacteristic
219C2×C4⋊C4×C53C2312yes—
220C2×C4⋊C4×C53C2311yescharacteristic
221C2×C4⋊C4×C53C2312yes—
222C2×C22⋊C4×C53C2312yes—
223C2×C22⋊C4×C53C2312yes—
224C2×C22⋊C4×C53C2312yes—
225C2×C22⋊C4×C53C2312yes—
226C2×C22⋊C4×C53C2312yes—
227C2×C42×C53C2311yescharacteristic
228C2×C42×C53C2311yescharacteristic
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2318yes—
232C2×C42×C53C2312yes—
233C24×C53C2412yes—
234C24×C53C2411yescharacteristic
235C2×Q8×C53—24no—
236C2×Q8×C53C2414yes—
237C2×D4×C53—28no—
238C2×D4×C53—24no—
239C2×D4×C53C2418yes—
240C2×D4×C53C2414yes—
241C22×C4×C53—24no—
242C22×C4×C53—24no—
243C22×C4×C53—28no—
244C22×C4×C53—24no—
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2411yescharacteristic
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2414yes—
250C22×C4×C53C2414yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2412yes—
255C22×C4×C53C2418yes—
256C22×C4×C53C2411yescharacteristic
257C22×C4×C53C2411yescharacteristic
258C22×Dic53—28no—
259C22×Dic53—28no—
260C22×Dic53—216no—
261C22×Dic53C2412yes—
262C22×Dic53C2414yes—
263C22×Dic53C2412yes—
264C22×Dic53C2412yes—
265C22×Dic53C2414yes—
266C22×Dic53C2418yes—
267C22×Dic53C2418yes—
268C22×Dic53C24116yes—
269C22×Dic53C2412yes—
270C2×Dic106—24no—
271C2×Dic106—28no—
272C2×Dic106—28no—
273C2×Dic106—216no—
274C2×Dic106—28no—
275C2×Dic106—232no—
276C2×Dic106—264no—
277C2×Dic106#4118yes—
278C2×Dic106C2418yes—
279C2×Dic106C24116yes—
280C2×Dic106C2418yes—
281C2×Dic106C2418yes—
282C2×Dic106C2414yes—
283C2×Dic106C2414yes—
284C4⋊C4×C53C2418yes—
285C4⋊C4×C53C2418yes—
286C4⋊C4×C53C2414yes—
287C4⋊C4×C53C2418yes—
288C4⋊C4×C53C2414yes—
289C4⋊C4×C53C2418yes—
290C22⋊C4×C53C2418yes—
291C22⋊C4×C53C2418yes—
292C22⋊C4×C53C2418yes—
293C22⋊C4×C53C2418yes—
294C22⋊C4×C53C2418yes—
295C42×C53C2414yes—
296C42×C53C2414yes—
297C42×C53C2414yes—
298C42×C53C2414yes—
299C42×C53C2418yes—
300C22⋊Dic53C24116yes—
301C22⋊Dic53C24116yes—
302C22⋊Dic53C24116yes—
303C22⋊Dic53C24116yes—
304C4⋊Dic53C2414yes—
305C4⋊Dic53C2414yes—
306C4⋊Dic53C2418yes—
307C4⋊Dic53C2418yes—
308C4⋊Dic53C2418yes—
309C4⋊Dic53C2418yes—
310C4⋊Dic53C2418yes—
311C4⋊Dic53C24116yes—
312C4⋊Dic53C24116yes—
313#11719919C2418yes—
314#11719919C2418yes—
315#11719919C2418yes—
316#11719919C2418yes—
317#11719919C24116yes—
318#11719919C24116yes—
319#11719919C24116yes—
320#11719919C24116yes—
321#11719919C24116yes—
322#11719919C24116yes—
323#11719919C24116yes—
324#11719919C24116yes—
325C4×Dic53C2418yes—
326C4×Dic53C2418yes—
327C4×Dic53C2418yes—
328C4×Dic53C2418yes—
329C4×Dic53C24116yes—
330C4×Dic53C24116yes—
331C4×Dic53C24116yes—
332C4×Dic53C24116yes—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—24no—
336C23×C53—24no—
337C23×C53—24no—
338C23×C532−1+414yes—
339C23×C53C2514yes—
340C23×C53C2512yes—
341C23×C53C2511yescharacteristic
342Q8×C53—28no—
343D4×C53—216no—
344D4×C53—28no—
345C2×C4×C53—22no—
346C2×C4×C53—24no—
347C2×C4×C53—28no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—24no—
352C2×C4×C53—24no—
353C2×C4×C53—28no—
354C2×C4×C53—216no—
355C2×C4×C53—28no—
356C2×C4×C53C2×#4114yes—
357C2×C4×C532−1+414yes—
358C2×C4×C53C2514yes—
359C2×C4×C53C2512yes—
360C2×C4×C53C2512yes—
361C2×C4×C53C2512yes—
362C2×C4×C53C2512yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2512yes—
366C2×C4×C53C2512yes—
367C2×Dic53—28no—
368C2×Dic53—24no—
369C2×Dic53—28no—
370C2×Dic53—216no—
371C2×Dic53—24no—
372C2×Dic53—24no—
373C2×Dic53—216no—
374C2×Dic53—232no—
375C2×Dic53C2×#4118yes—
376C2×Dic53C2518yes—
377C2×Dic53C2514yes—
378C2×Dic53C2518yes—
379C2×Dic53C2514yes—
380C2×Dic53C2514yes—
381C2×Dic53C2514yes—
382Dic106—28no—
383Dic106—216no—
384Dic106—216no—
385Dic106—232no—
386Dic106—216no—
387Dic106C2×#41116yes—
388C2×#3523—531nomaximal, Sylow
389C22×C53—22no—
390C22×C53—22no—
391C22×C53—28no—
392C22×C53—24no—
393C22×C53—24no—
394C22×C53—24no—
395C22×C53—48no—
396C22×C53C22×#4112yes—
397C22×C53C2×2−1+414yes—
398C22×C53C2×2−1+412yes—
399C22×C53C2×2−1+412yes—
400C22×C53C2611yescharacteristic
401C4×C53—24no—
402C4×C53—22no—
403C4×C53—22no—
404C4×C53—22no—
405C4×C53—22no—
406C4×C53—24no—
407C4×C53—24no—
408C4×C53C22×#4114yes—
409C4×C53C2×2−1+414yes—
410Dic53—28no—
411Dic53—24no—
412Dic53—28no—
413Dic53—24no—
414Dic53—24no—
415Dic53C22×#4118yes—
416#3523—5332no—
417C2×#557—532no—
418C2×#557—531no—
419C2×#557—531no—
420C2×#556—532no—
421C2×#556—531no—
422C2×#552—534no—
423C2×#552—532no—
424C2×D4×Q8—532no—
425C2×D4×Q8—531no—
426C2×#541—534no—
427C2×#541—532no—
428C2×#533—531no—
429C2×#533—532no—
430C2×#529—532no—
431C2×#529D5311yescharacteristic
432C2×#519—532no—
433C22×C4×Q8—531no—
434C2×C53—24no—
435C2×C53—44no—
436C2×C53#352314yescomplemented
437C2×C53C23×#4111yescharacteristic
438C2×C53C22×2−1+411yescharacteristic
439C2×C53C22×2−1+411yescharacteristic
440C23×Q8—531no—
441C23×Q8—532no—
442#557—5332no—
443#557—5316no—
444#557—5316no—
445#556—5332no—
446#556—5316no—
447#552—5364no—
448#552—5332no—
449D4×Q8—5332no—
450D4×Q8—5316no—
451#541—5364no—
452#541—5332no—
453#533—5332no—
454#533—5316no—
455C2×C4⋊Q8—532no—
456C2×C4⋊Q8—532no—
457C2×C4⋊Q8—534no—
458C2×C4⋊Q8—531no—
459C2×C4⋊Q8—531no—
460C2×C4⋊Q8—532no—
461#529—5332no—
462#529C2×D53116yes—
463C2×#126—534no—
464C2×#126—534no—
465C2×#126—534no—
466C2×#126—534no—
467C2×#126C2×D5312yes—
468C2×#125—532no—
469C2×#125—534no—
470C2×#125—534no—
471C2×#125—534no—
472C2×#125—534no—
473C2×#125—534no—
474C2×#125—532no—
475C2×#125—532no—
476C2×#125C2×D5311yescharacteristic
477C2×#124—532no—
478C2×#124C2×D5311yescharacteristic
479C2×#123—534no—
480C2×#123C2×D5312yes—
481C2×C22⋊Q8—532no—
482C2×C22⋊Q8—532no—
483C2×C22⋊Q8—532no—
484C2×C22⋊Q8—532no—
485C2×C22⋊Q8—534no—
486C2×C22⋊Q8—534no—
487C2×C22⋊Q8—534no—
488C2×C22⋊Q8C2×D5311yescharacteristic
489C2×#121C2×D5311yescharacteristic
490#519—5332no—
491C2×C4×Q8—532no—
492C2×C4×Q8—534no—
493C2×C4×Q8—534no—
494C2×C4×Q8—532no—
495C2×C4×Q8—532no—
496C2×C4×Q8—531no—
497C2×C4×Q8—532no—
498C2×C4×Q8—531no—
499C2×C4×Q8—531no—
500C2×C4×Q8—532no—
501C2×C4×Q8—531no—
502C2×C4×Q8—532no—
503C2×C4×Q8—532no—
504C2×C4×Q8—532no—
505C2×C4×Q8—532no—
506C2×C4×Q8—5316no—
507C2×C4×Q8C2×D5311yescharacteristic
508C2×C4×D4—534no—
509C2×C4×D4—532no—
510C2×C4×D4C2×D5312yes—
511C2×C4×D4C2×D5311yescharacteristic
512C2×#117—532no—
513C2×#117—532no—
514C2×#117—534no—
515C2×#117—534no—
516C2×#117—534no—
517C2×#117C2×D5312yes—
518C22×C4⋊C4—532no—
519C22×C4⋊C4—531no—
520C22×C42—532no—
521C22×C42C2×D5311yescharacteristic
522C53C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—531no—
524C22×Q8—532no—
525C22×Q8—534no—
526C22×Q8—532no—
527C22×Q8—531no—
528C22×Q8—532no—
529C22×Q8—538no—
530C22×Q8—5316no—
531C22×Q8—1068no—
532C22×Q8—10616no—
533C22×Q8C22×D5311yescharacteristic
534C22×D4C22×D5312yes—
535C22×D4C22×D5311yescharacteristic
536C23×C4—532no—
537C23×C4—532no—
538C23×C4—534no—
539C23×C4C22×D5311yescharacteristic
540C23×C4C22×D5311yescharacteristic
541C23×C4C22×D5312yes—
542C23×C4C22×D5311yescharacteristic
543C4⋊Q8—5316no—
544C4⋊Q8—5316no—
545C4⋊Q8—5332no—
546C4⋊Q8—538no—
547C4⋊Q8—538no—
548C4⋊Q8—5316no—
549#126—5332no—
550#126—5332no—
551#126—5332no—
552#126—5332no—
553#126C22×D53116yes—
554#125—5316no—
555#125—5332no—
556#125—5332no—
557#125—5332no—
558#125—5332no—
559#125—5332no—
560#125—5316no—
561#125—5316no—
562#125C22×D5318yes—
563#124—5316no—
564#124C22×D5318yes—
565#123—5332no—
566#123C22×D53116yes—
567C22⋊Q8—5316no—
568C22⋊Q8—5316no—
569C22⋊Q8—5316no—
570C22⋊Q8—5316no—
571C22⋊Q8—5332no—
572C22⋊Q8—5332no—
573C22⋊Q8—5332no—
574C22⋊Q8C22×D5318yes—
575#121C22×D5318yes—
576C4×Q8—5316no—
577C4×Q8—5332no—
578C4×Q8—5332no—
579C4×Q8—5316no—
580C4×Q8—5316no—
581C4×Q8—538no—
582C4×Q8—5316no—
583C4×Q8—538no—
584C4×Q8—538no—
585C4×Q8—5316no—
586C4×Q8—538no—
587C4×Q8—5316no—
588C4×Q8—5316no—
589C4×Q8—5316no—
590C4×Q8—5316no—
591C4×Q8C22×D5318yes—
592C4×D4—5332no—
593C4×D4—5316no—
594C4×D4C22×D53116yes—
595C4×D4C22×D5318yes—
596#117—5316no—
597#117—5316no—
598#117—5332no—
599#117—5332no—
600#117—5332no—
601#117C22×D53116yes—
602C2×C4⋊C4—532no—
603C2×C4⋊C4—531no—
604C2×C4⋊C4—532no—
605C2×C4⋊C4—531no—
606C2×C4⋊C4—532no—
607C2×C4⋊C4—532no—
608C2×C4⋊C4—532no—
609C2×C4⋊C4—5316no—
610C2×C4⋊C4—538no—
611C2×C4⋊C4—534no—
612C2×C4⋊C4—532no—
613C2×C4⋊C4—534no—
614C2×C4⋊C4—534no—
615C2×C4⋊C4—534no—
616C2×C4⋊C4—532no—
617C2×C4⋊C4—534no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—534no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4C22×D5312yes—
626C2×C4⋊C4C22×D5312yes—
627C2×C4⋊C4C22×D5311yescharacteristic
628C2×C4⋊C4C22×D5312yes—
629C2×C4⋊C4C22×D5311yescharacteristic
630C2×C4⋊C4C22×D5312yes—
631C2×C22⋊C4—534no—
632C2×C22⋊C4—534no—
633C2×C22⋊C4—534no—
634C2×C22⋊C4—534no—
635C2×C22⋊C4C22×D5312yes—
636C2×C22⋊C4C22×D5312yes—
637C2×C22⋊C4C22×D5312yes—
638C2×C22⋊C4C22×D5312yes—
639C2×C22⋊C4C22×D5312yes—
640C2×C42—532no—
641C2×C42—534no—
642C2×C42—534no—
643C2×C42—534no—
644C2×C42—534no—
645C2×C42—532no—
646C2×C42—532no—
647C2×C42—532no—
648C2×C42—5316no—
649C2×C42C22×D5311yescharacteristic
650C2×C42C22×D5312yes—
651C2×C42C22×D5311yescharacteristic
652C2×C42C22×D5311yescharacteristic
653C2×C42C22×D5311yescharacteristic
654C2×C42C22×D5318yes—
655C24C23×D5312yes—
656C24C23×D5311yescharacteristic
657C2×Q8—24no—
658C2×Q8—538no—
659C2×Q8—534no—
660C2×Q8—538no—
661C2×Q8—5316no—
662C2×Q8—538no—
663C2×Q8—534no—
664C2×Q8—538no—
665C2×Q8—10616no—
666C2×Q8—1068no—
667C2×Q8—10632no—
668C2×Q8—10664no—
669C2×Q8—1064no—
670C2×Q8—1068no—
671C2×Q8—1068no—
672C2×Q8C23×D5314yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4C23×D5318yes—
676C2×D4C23×D5314yes—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—28no—
680C22×C4—24no—
681C22×C4—532no—
682C22×C4—538no—
683C22×C4—538no—
684C22×C4—5316no—
685C22×C4—532no—
686C22×C4—534no—
687C22×C4—532no—
688C22×C4—534no—
689C22×C4—532no—
690C22×C4—1068no—
691C22×C4—10616no—
692C22×C4—1068no—
693C22×C4C23×D5314yes—
694C22×C4C23×D5314yes—
695C22×C4C23×D5314yes—
696C22×C4C23×D5318yes—
697C22×C4C23×D5311yescharacteristic
698C22×C4C23×D5311yescharacteristic
699C22×C4C23×D5312yes—
700C22×C4C23×D5312yes—
701C22×C4C23×D5312yes—
702C22×C4C23×D5311yescharacteristic
703C22×C4C23×D5311yescharacteristic
704C22×C4C23×D5311yescharacteristic
705C22×C4C23×D5311yescharacteristic
706C4⋊C4—538no—
707C4⋊C4—534no—
708C4⋊C4—538no—
709C4⋊C4—534no—
710C4⋊C4—538no—
711C4⋊C4—538no—
712C4⋊C4—538no—
713C4⋊C4—5316no—
714C4⋊C4—538no—
715C4⋊C4—5316no—
716C4⋊C4—5316no—
717C4⋊C4—5316no—
718C4⋊C4—538no—
719C4⋊C4—5316no—
720C4⋊C4—538no—
721C4⋊C4—538no—
722C4⋊C4—5316no—
723C4⋊C4—5316no—
724C4⋊C4—5316no—
725C4⋊C4—5316no—
726C4⋊C4—5316no—
727C4⋊C4C23×D5318yes—
728C4⋊C4C23×D5318yes—
729C4⋊C4C23×D5314yes—
730C4⋊C4C23×D5318yes—
731C4⋊C4C23×D5314yes—
732C4⋊C4C23×D5318yes—
733C22⋊C4—5316no—
734C22⋊C4—5316no—
735C22⋊C4—5316no—
736C22⋊C4—5316no—
737C22⋊C4C23×D5318yes—
738C22⋊C4C23×D5318yes—
739C22⋊C4C23×D5318yes—
740C22⋊C4C23×D5318yes—
741C22⋊C4C23×D5318yes—
742C42—538no—
743C42—538no—
744C42—538no—
745C42—538no—
746C42—5316no—
747C42—5316no—
748C42—5316no—
749C42—5316no—
750C42C23×D5314yes—
751C42C23×D5314yes—
752C42C23×D5314yes—
753C42C23×D5314yes—
754C42C23×D5318yes—
755C23—22no—
756C23—22no—
757C23—24no—
758C23—24no—
759C23—24no—
760C23#1313326414yes—
761C23C24×D5314yes—
762C23C24×D5312yes—
763C23C24×D5311yescharacteristic
764Q8—28no—
765Q8—5316no—
766Q8—10632no—
767Q8—10616no—
768Q8—1068no—
769Q8—10616no—
770Q8—10616no—
771D4—216no—
772D4—28no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—28no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—28no—
782C2×C4—216no—
783C2×C4—28no—
784C2×C4—538no—
785C2×C4—534no—
786C2×C4—534no—
787C2×C4—538no—
788C2×C4—534no—
789C2×C4—534no—
790C2×C4—538no—
791C2×C4—10616no—
792C2×C4—10632no—
793C2×C4—1068no—
794C2×C4—1064no—
795C2×C4—10616no—
796C2×C4—1064no—
797C2×C4—1064no—
798C2×C4—1068no—
799C2×C4#41×D5314yes—
800C2×C4#1313326414yes—
801C2×C4C24×D5312yes—
802C2×C4C24×D5312yes—
803C2×C4C24×D5314yes—
804C2×C4C24×D5314yes—
805C2×C4C24×D5314yes—
806C2×C4C24×D5312yes—
807C2×C4C24×D5312yes—
808C2×C4C24×D5312yes—
809C2×C4C24×D5312yes—
810C22—28no—
811C22—22no—
812C22—22no—
813C22—24no—
814C22—24no—
815C22—24no—
816C22—48no—
817C22C2×#41×D5312yes—
818C22C2×#1313326414yes—
819C22C2×#1313326412yes—
820C22C2×#1313326412yes—
821C22C25×D5311yescharacteristic
822C4—24no—
823C4—22no—
824C4—22no—
825C4—22no—
826C4—22no—
827C4—24no—
828C4—24no—
829C4—538no—
830C4—1064no—
831C4—1068no—
832C4—1064no—
833C4—1064no—
834C4—1068no—
835C4C2×#41×D5314yes—
836C4C2×#1313326414yes—
837C2—24no—
838C2—44no—
839C2#2028880914yesdirect product factor
840C2C22×#41×D5311yescharacteristic
841C2C22×#1313326411yescharacteristic
842C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#529C2
socleC23×C53C25
prime radicalC2×#121×C53C22
hypercenterC2×#529D53
hypocenterC53C2×#3523
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #20288809C2direct (N × H)
2. C2×#16811352C2semidirect
3. C2×#16811351C2semidirect
4. C2×#16811350C2semidirect
5. C2×#16811343C2semidirect
6. C2×#16811342C2semidirect
7. C2×#16811313C2semidirect
8. C2×#16811310C2semidirect
9. C2×D4×Dic106C2semidirect
10. C2×D4×Dic106C2semidirect
11. C2×#16811235C2semidirect
12. C2×#16811230C2semidirect
13. C2×#16811180C2semidirect
14. C2×#16811175C2semidirect
16. C2×#16811100C2semidirect
17. C22×C4×Dic106C2semidirect
21. #16811352C22semidirect
22. #16811351C22semidirect
23. #16811350C22semidirect
24. #16811343C22semidirect
25. #16811342C22semidirect
26. #16811313C22semidirect
27. #16811310C22semidirect
28. D4×Dic106C22semidirect
29. D4×Dic106C22semidirect
30. #16811235C22semidirect
31. #16811230C22semidirect
32. #16811180C22semidirect
33. #16811175C22semidirect
62. #16811100C22semidirect
74. C2×C4×Dic106C22semidirect
436. C2×C53#3523semidirect
522. C53C2×#3523semidirect
839. C2#20288809direct (N × H)

Maximal subgroups

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

subgroupindex
#202888092
C2×#168113522
C2×#168113512
C2×#168113502
C2×#168113432
C2×#168113422
C2×#168113132
C2×#168113102
C2×D4×Dic1062
C2×#168112352
C2×#168112302
C2×#168111802
C2×#168111752
C2×#168111542
C2×#168111002
C22×C4×Dic1062
C2×C53×#5292
C2×#352353