Finite Group Databasebeta

← C2×#20289207 #28291927

Subgroups — C2×#20289207 #28291927

Order 13568.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289207C2132yesmaximal, direct product factor
2C2×C53⋊#564C214yesmaximal, complemented
3C2×#16811352C211yesmaximal, characteristic, complemented
4C2×#16811351C211yesmaximal, characteristic, complemented
5C2×#16811351C212yesmaximal, complemented
6C2×#16811350C212yesmaximal, complemented
7C2×#16811349C212yesmaximal, complemented
8C2×#16811348C211yesmaximal, characteristic, complemented
9C2×#16811348C212yesmaximal, complemented
10C2×#16811236C212yesmaximal
11C2×#16811234C212yesmaximal
12C2×#16811232C214yesmaximal
13C2×#16811231C212yesmaximal
14C2×#16811231C212yesmaximal
15C2×#16811178C211yesmaximal, characteristic
16C2×#16811177C211yesmaximal, characteristic
17C2×#16811177C211yesmaximal, characteristic
18C2×C53×#557C211yesmaximal, characteristic, complemented
19C53⋊#564C22164yescomplemented
20#16811352C22116yescomplemented
21#16811351C22116yescomplemented
22#16811351C22132yescomplemented
23#16811350C22132yescomplemented
24#16811349C22132yescomplemented
25#16811348C22116yescomplemented
26#16811348C22132yescomplemented
27#16811236C22132yes—
28#16811234C22132yes—
29#16811232C22164yes—
30#16811231C22132yes—
31#16811231C22132yes—
32#16811178C22116yes—
33#16811177C22116yes—
34#16811177C22116yes—
35C2×#13133217C2211yescharacteristic
36C2×#13133217C2212yes—
37C2×#13133216C2211yescharacteristic
38C2×#13133216C2211yescharacteristic
39C2×#13133216C2214yes—
40C2×#13133215C2211yescharacteristic
41C2×#13133215C2211yescharacteristic
42C2×#13133215C2212yes—
43C2×#13133215C2212yes—
44C2×#13133212C2214yes—
45C2×#13133212C2214yes—
46C2×#13133212C2214yes—
47C2×#13133211C2214yes—
48C2×#13133209C2212yes—
49C2×#13133209C2214yes—
50C2×#13133209C2214yes—
51C2×#13133208C2212yes—
52C2×#13133208C2212yes—
53C2×#13133208C2214yes—
54C2×#13133208C2212yes—
55C2×#13133208C2214yes—
56C2×#13133208C2214yes—
57C2×#13133207C2212yes—
58C2×#13133207C2212yes—
59C2×#13133207C2214yes—
60C2×#13133207C2214yes—
61C2×#13133207C2214yes—
62C2×#13133207C2214yes—
63C2×#13133207C2214yes—
64C2×#13133207C2214yes—
65C2×#13133207C2214yes—
66C2×#13133197C2211yescharacteristic
67C2×#13133197C2211yescharacteristic
68C2×#13133197C2212yes—
69C2×#13133195C2212yes—
70C2×#13133195C2212yes—
71C2×#13133193C2211yescharacteristic
72C2×#13133193C2211yescharacteristic
73C2×#13133193C2212yes—
74C2×Q8×Dic53C2212yes—
75C2×Q8×Dic53C2212yes—
76C2×Q8×Dic53C2212yes—
77C2×C4×Dic106C2212yes—
78C2×C4×Dic106C2211yescharacteristic
79C2×C4×Dic106C2211yescharacteristic
80C2×C4×Dic106C2212yes—
81C2×C4×Dic106C2212yes—
82C2×C4×Dic106C2214yes—
83C2×C4×Dic106C2212yes—
84C2×#13133182C2212yes—
85C2×#13133182C2214yes—
86C2×#13133182C2212yes—
87C2×#13133182C2212yes—
88C2×#13133175C2212yes—
89C2×#13133174C2212yes—
90C2×#13133174C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#557C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×C4⋊Q8×C53C2212yes—
95C2×#125×C53C2212yes—
96C2×#125×C53C2214yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×Q8×C53C2212yes—
100C2×C4×Q8×C53C2212yes—
101C22×Dic106C2312yes—
102C22×Dic106C2312yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2312yes—
105C22×Dic106C2311yescharacteristic
106C22×C4×D53C2311yescharacteristic
107C22×C4×D53C2311yescharacteristic
108C22×C4×D53C2311yescharacteristic
109#13133217C2318yes—
110#13133217C23116yes—
111#13133216C2318yes—
112#13133216C23132yes—
113#13133216C2318yes—
114#13133215C2318yes—
115#13133215C23116yes—
116#13133215C2318yes—
117#13133215C23116yes—
118#13133212C23132yes—
119#13133212C23132yes—
120#13133212C23132yes—
121#13133211C23132yes—
122#13133209C23116yes—
123#13133209C23132yes—
124#13133209C23132yes—
125#13133208C23116yes—
126#13133208C23132yes—
127#13133208C23116yes—
128#13133208C23132yes—
129#13133208C23132yes—
130#13133208C23116yes—
131#13133207C23132yes—
132#13133207C23132yes—
133#13133207C23132yes—
134#13133207C23132yes—
135#13133207C23132yes—
136#13133207C23132yes—
137#13133207C23132yes—
138#13133207C23116yes—
139#13133207C23116yes—
140#13133197C2318yes—
141#13133197C2318yes—
142#13133197C23116yes—
143#13133195C23116yes—
144#13133195C23116yes—
145#13133193C2318yes—
146#13133193C2318yes—
147#13133193C23116yes—
148Q8×Dic53C23116yes—
149Q8×Dic53C23116yes—
150Q8×Dic53C23116yes—
151C4×Dic106C23116yes—
152C4×Dic106C2318yes—
153C4×Dic106C23116yes—
154C4×Dic106C2318yes—
155C4×Dic106C23132yes—
156C4×Dic106C23116yes—
157C4×Dic106C23116yes—
158#13133182C23132yes—
159#13133182C23116yes—
160#13133182C23116yes—
161#13133182C23116yes—
162#13133175C23116yes—
163#13133174C23116yes—
164#13133174C23116yes—
165C2×C4⋊Dic53C2312yes—
166C2×C4⋊Dic53C2311yescharacteristic
167C2×C4⋊Dic53C2312yes—
168C2×C4⋊Dic53C2311yescharacteristic
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2312yes—
171C2×C4⋊Dic53C2314yes—
172C2×C4⋊Dic53C2314yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2314yes—
175C2×#11719919C2312yes—
176C2×#11719919C2312yes—
177C2×#11719919C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2312yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2312yes—
189C2×#11719919C2314yes—
190C2×#11719919C2314yes—
191C2×#11719919C2314yes—
192C2×#11719921C2312yes—
193C2×#11719921C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×#11719921C2314yes—
197C2×C4×Dic53C2311yescharacteristic
198C2×C4×Dic53C2311yescharacteristic
199C2×C4×Dic53C2311yescharacteristic
200C2×C4×Dic53C2312yes—
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2314yes—
203C2×C4×Dic53C2314yes—
204C2×C4×Dic53C2314yes—
205C2×C4×Dic53C2314yes—
206C42×D53C2318yes—
207C22×Q8×C53C2311yescharacteristic
208C22×Q8×C53C2311yescharacteristic
209C22×Q8×C53C2312yes—
210C4⋊Q8×C53C2318yes—
211C4⋊Q8×C53C23116yes—
212#125×C53C23116yes—
213#125×C53C23132yes—
214C4×Q8×C53C23116yes—
215C4×Q8×C53C2318yes—
216C4×Q8×C53C23116yes—
217C4×Q8×C53C2318yes—
218C2×C4⋊C4×C53C2311yescharacteristic
219C2×C4⋊C4×C53C2311yescharacteristic
220C2×C4⋊C4×C53C2312yes—
221C2×C4⋊C4×C53C2312yes—
222C2×C4⋊C4×C53C2314yes—
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C2314yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2314yes—
227C2×C42×C53C2312yes—
228C2×C42×C53C2314yes—
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2312yes—
231C23×D53C2411yescharacteristic
232C2×Q8×C53—24no—
233C2×Q8×C53—28no—
234C2×Q8×C53—24no—
235C2×Q8×C53C2414yes—
236C2×Q8×C53C2418yes—
237C2×Q8×C53C2414yes—
238C22×C4×C53C2412yes—
239C22×C4×C53C2412yes—
240C22×C4×C53C2412yes—
241C22×C4×C53C2411yescharacteristic
242C22×C4×C53C2412yes—
243C22×C4×C53C2414yes—
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2411yescharacteristic
246C22×Dic53C2412yes—
247C22×Dic53C2412yes—
248C22×Dic53C2412yes—
249C22×Dic53C2412yes—
250C22×Dic53C2414yes—
251C22×Dic53C2411yescharacteristic
252C22×Dic53C2411yescharacteristic
253C22×Dic53C2411yescharacteristic
254C2×C4×D53—24no—
255C2×C4×D53—24no—
256C2×C4×D53—24no—
257C2×C4×D53C2414yes—
258C2×C4×D53C2414yes—
259C2×C4×D53C2414yes—
260C2×Dic106—24no—
261C2×Dic106—28no—
262C2×Dic106—24no—
263C2×Dic106—28no—
264C2×Dic106—28no—
265C2×Dic106C2418yes—
266C2×Dic106C2414yes—
267C2×Dic106C2418yes—
268C2×Dic106C2418yes—
269C2×Dic106C2414yes—
270C4⋊C4×C53C2414yes—
271C4⋊C4×C53C2414yes—
272C4⋊C4×C53C2418yes—
273C4⋊C4×C53C2418yes—
274C4⋊C4×C53C24116yes—
275C4⋊C4×C53C2418yes—
276C4⋊C4×C53C24116yes—
277C4⋊C4×C53C2418yes—
278C4⋊C4×C53C24116yes—
279C42×C53C2418yes—
280C42×C53C24116yes—
281C42×C53C2414yes—
282C42×C53C2418yes—
283#11719921C2418yes—
284#11719921C2418yes—
285#11719921C2418yes—
286#11719921C2418yes—
287#11719921C24116yes—
288C4⋊Dic53C2418yes—
289C4⋊Dic53C2414yes—
290C4⋊Dic53C2418yes—
291C4⋊Dic53C2414yes—
292C4⋊Dic53C2418yes—
293C4⋊Dic53C2418yes—
294C4⋊Dic53C24116yes—
295C4⋊Dic53C24116yes—
296C4⋊Dic53C24116yes—
297C4⋊Dic53C24116yes—
298#11719919C2418yes—
299#11719919C2418yes—
300#11719919C2418yes—
301#11719919C2418yes—
302#11719919C2418yes—
303#11719919C24116yes—
304#11719919C24116yes—
305#11719919C24116yes—
306#11719919C24116yes—
307#11719919C2418yes—
308#11719919C2418yes—
309#11719919C2418yes—
310#11719919C2418yes—
311#11719919C2418yes—
312#11719919C24116yes—
313#11719919C24116yes—
314#11719919C24116yes—
315C4×Dic53C2414yes—
316C4×Dic53C2414yes—
317C4×Dic53C2414yes—
318C4×Dic53C2418yes—
319C4×Dic53C2418yes—
320C4×Dic53C24116yes—
321C4×Dic53C24116yes—
322C4×Dic53C24116yes—
323C4×Dic53C24116yes—
324C23×C53C2511yescharacteristic
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53C2512yes—
329Q8×C53—216no—
330Q8×C53—28no—
331Q8×C53—28no—
332C2×C4×C53—24no—
333C2×C4×C53—24no—
334C2×C4×C53—22no—
335C2×C4×C53—24no—
336C2×C4×C53—28no—
337C2×C4×C53—24no—
338C2×C4×C532−1+414yes—
339C2×C4×C532−1+414yes—
340C2×C4×C53C2514yes—
341C2×C4×C53C2514yes—
342C2×C4×C53C2512yes—
343C2×C4×C53C2518yes—
344C2×C4×C53C2514yes—
345C2×C4×C53C2514yes—
346C2×C4×C53C2512yes—
347C2×C4×C53C2512yes—
348C2×Dic53—24no—
349C2×Dic53—24no—
350C2×Dic53—24no—
351C2×Dic53—24no—
352C2×Dic53—28no—
353C2×Dic53—22no—
354C2×Dic53—22no—
355C2×Dic532−1+414yes—
356C2×Dic53C2514yes—
357C2×Dic53C2514yes—
358C2×Dic53C2514yes—
359C2×Dic53C2514yes—
360C2×Dic53C2518yes—
361C2×Dic53C2512yes—
362C2×Dic53C2512yes—
363C2×Dic53C2512yes—
364C4×D53—28no—
365C4×D53—28no—
366C4×D53—28no—
367Dic106—28no—
368Dic106—28no—
369Dic106—216no—
370Dic106—216no—
371Dic106—216no—
372C2×#3556—531nomaximal, Sylow
373C22×C53C2×2−1+412yes—
374C22×C53C2×2−1+412yes—
375C22×C53C2×2−1+412yes—
376C22×C53C2611yescharacteristic
377C2×D53—22no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—44no—
381C4×C53—24no—
382C4×C53—24no—
383C4×C53—22no—
384C4×C53—28no—
385C4×C53—24no—
386C4×C53—24no—
387C4×C53C2×2−1+414yes—
388C4×C53C2×2−1+414yes—
389Dic53—24no—
390Dic53—24no—
391Dic53—24no—
392Dic53—24no—
393Dic53—28no—
394Dic53—22no—
395Dic53—22no—
396Dic53C2×2−1+414yes—
397#3556—5332no—
398C2×#564—534no—
399C2×#557—532no—
400C2×#557—531no—
401C2×#557—532no—
402C2×#557—532no—
403C2×#557—532no—
404C2×#557—531no—
405C2×#557—531no—
406C2×#557D5311yescharacteristic, complemented
407C2×#541—532no—
408C2×#541—534no—
409C2×#541—532no—
410C2×#541—532no—
411C2×#541—532no—
412C2×#533—531no—
413C2×#533—531no—
414C2×#533—531no—
415C2×C53#355614yescomplemented
416C2×C53C22×2−1+411yescharacteristic
417C2×C53C22×2−1+411yescharacteristic
418C2×C53C22×2−1+411yescharacteristic
419D53—42no—
420#564—5364no—
421#557—5332no—
422#557—5316no—
423#557—5332no—
424#557—5332no—
425#557—5332no—
426#557—5316no—
427#557—5316no—
428#557C2×D53116yescomplemented
429#541—5332no—
430#541—5364no—
431#541—5332no—
432#541—5332no—
433#541—5332no—
434#533—5316no—
435#533—5316no—
436#533—5316no—
437C2×C4⋊Q8—531no—
438C2×C4⋊Q8—531no—
439C2×C4⋊Q8—532no—
440C2×C4⋊Q8—532no—
441C2×C4⋊Q8—531no—
442C2×C4⋊Q8—531no—
443C2×C4⋊Q8—534no—
444C2×C4⋊Q8—531no—
445C2×C4⋊Q8—532no—
446C2×C4⋊Q8C2×D5311yescharacteristic
447C2×C4⋊Q8C2×D5312yes—
448C2×#126—534no—
449C2×#126—534no—
450C2×#126—534no—
451C2×#126—534no—
452C2×#125—532no—
453C2×#125—532no—
454C2×#125—532no—
455C2×#125—534no—
456C2×#125—534no—
457C2×#125—534no—
458C2×#125—534no—
459C2×#125—534no—
460C2×#125—534no—
461C2×#125—534no—
462C2×#125—532no—
463C2×#125—532no—
464C2×#125—534no—
465C2×#125—534no—
466C2×#125—534no—
467C2×#125—532no—
468C2×#125—534no—
469C2×#125—534no—
470C2×#125C2×D5312yes—
471C2×#125C2×D5314yes—
472C2×C22⋊Q8—531no—
473C2×C22⋊Q8—532no—
474C2×C22⋊Q8—531no—
475C2×C22⋊Q8—532no—
476C2×C22⋊Q8—532no—
477C2×C22⋊Q8—532no—
478C2×C22⋊Q8—531no—
479C2×C22⋊Q8—531no—
480C2×C4×Q8—532no—
481C2×C4×Q8—532no—
482C2×C4×Q8—532no—
483C2×C4×Q8—532no—
484C2×C4×Q8—534no—
485C2×C4×Q8—532no—
486C2×C4×Q8—532no—
487C2×C4×Q8—531no—
488C2×C4×Q8—531no—
489C2×C4×Q8—532no—
490C2×C4×Q8—532no—
491C2×C4×Q8—534no—
492C2×C4×Q8—532no—
493C2×C4×Q8—532no—
494C2×C4×Q8C2×D5311yescharacteristic
495C2×C4×Q8C2×D5311yescharacteristic
496C2×C4×Q8C2×D5312yes—
497C2×C4×Q8C2×D5312yes—
498C2×#117—532no—
499C2×#117—532no—
500C2×#117—532no—
501C22×C42—531no—
502C53C2×#355611yescharacteristic, complemented, Sylow
503C22×Q8—532no—
504C22×Q8—532no—
505C22×Q8—531no—
506C22×Q8—532no—
507C22×Q8—531no—
508C22×Q8C22×D5312yes—
509C22×Q8C22×D5311yescharacteristic
510C22×Q8C22×D5311yescharacteristic
511C23×C4—531no—
512C23×C4—531no—
513C23×C4—531no—
514C4⋊Q8—538no—
515C4⋊Q8—538no—
516C4⋊Q8—5316no—
517C4⋊Q8—5316no—
518C4⋊Q8—538no—
519C4⋊Q8—538no—
520C4⋊Q8—5332no—
521C4⋊Q8—538no—
522C4⋊Q8—5316no—
523C4⋊Q8C22×D5318yes—
524C4⋊Q8C22×D53116yes—
525#126—5332no—
526#126—5332no—
527#126—5332no—
528#126—5332no—
529#125—5316no—
530#125—5316no—
531#125—5316no—
532#125—5332no—
533#125—5316no—
534#125—5316no—
535#125—5332no—
536#125—5332no—
537#125—5332no—
538#125—5332no—
539#125—5332no—
540#125—5332no—
541#125—5332no—
542#125—5332no—
543#125—5332no—
544#125—5316no—
545#125—5332no—
546#125—5332no—
547#125C22×D53116yes—
548#125C22×D53132yes—
549C22⋊Q8—5316no—
550C22⋊Q8—538no—
551C22⋊Q8—538no—
552C22⋊Q8—5316no—
553C22⋊Q8—5316no—
554C22⋊Q8—5316no—
555C22⋊Q8—538no—
556C22⋊Q8—538no—
557C4×Q8—5316no—
558C4×Q8—5316no—
559C4×Q8—5316no—
560C4×Q8—5316no—
561C4×Q8—5332no—
562C4×Q8—5316no—
563C4×Q8—5316no—
564C4×Q8—5316no—
565C4×Q8—5316no—
566C4×Q8—538no—
567C4×Q8—538no—
568C4×Q8—5332no—
569C4×Q8—5316no—
570C4×Q8—5316no—
571C4×Q8C22×D5318yes—
572C4×Q8C22×D5318yes—
573C4×Q8C22×D53116yes—
574C4×Q8C22×D53116yes—
575#117—5316no—
576#117—5316no—
577#117—5316no—
578C2×C4⋊C4—532no—
579C2×C4⋊C4—532no—
580C2×C4⋊C4—532no—
581C2×C4⋊C4—532no—
582C2×C4⋊C4—532no—
583C2×C4⋊C4—532no—
584C2×C4⋊C4—532no—
585C2×C4⋊C4—532no—
586C2×C4⋊C4—531no—
587C2×C4⋊C4—531no—
588C2×C4⋊C4—532no—
589C2×C4⋊C4—532no—
590C2×C4⋊C4—534no—
591C2×C4⋊C4—532no—
592C2×C4⋊C4—532no—
593C2×C4⋊C4—534no—
594C2×C4⋊C4—532no—
595C2×C4⋊C4—532no—
596C2×C4⋊C4—534no—
597C2×C4⋊C4—534no—
598C2×C4⋊C4—534no—
599C2×C4⋊C4—534no—
600C2×C4⋊C4—534no—
601C2×C4⋊C4—534no—
602C2×C4⋊C4—534no—
603C2×C4⋊C4—534no—
604C2×C4⋊C4—534no—
605C2×C4⋊C4C22×D5312yes—
606C2×C4⋊C4C22×D5312yes—
607C2×C4⋊C4C22×D5311yescharacteristic
608C2×C4⋊C4C22×D5314yes—
609C2×C4⋊C4C22×D5311yescharacteristic
610C2×C4⋊C4C22×D5312yes—
611C2×C4⋊C4C22×D5312yes—
612C2×C4⋊C4C22×D5314yes—
613C2×C4⋊C4C22×D5314yes—
614C2×C22⋊C4—534no—
615C2×C22⋊C4—532no—
616C2×C22⋊C4—532no—
617C2×C22⋊C4—532no—
618C2×C22⋊C4—532no—
619C2×C42—534no—
620C2×C42—532no—
621C2×C42—532no—
622C2×C42—531no—
623C2×C42—531no—
624C2×C42—534no—
625C2×C42—534no—
626C2×C42—534no—
627C2×C42—531no—
628C2×C42—538no—
629C2×C42C22×D5312yes—
630C2×C42C22×D5312yes—
631C2×C42C22×D5311yescharacteristic
632C2×C42C22×D5314yes—
633C24—531no—
634C2×Q8—28no—
635C2×Q8—24no—
636C2×Q8—24no—
637C2×Q8—538no—
638C2×Q8—538no—
639C2×Q8—534no—
640C2×Q8—538no—
641C2×Q8—534no—
642C2×Q8—1068no—
643C2×Q8—1068no—
644C2×Q8—1064no—
645C2×Q8—1068no—
646C2×Q8—1064no—
647C2×Q8C23×D5318yes—
648C2×Q8C23×D5314yes—
649C2×Q8C23×D5314yes—
650C22×C4—531no—
651C22×C4—532no—
652C22×C4—532no—
653C22×C4—532no—
654C22×C4—532no—
655C22×C4—534no—
656C22×C4—531no—
657C22×C4—531no—
658C22×C4—534no—
659C22×C4—534no—
660C22×C4—534no—
661C22×C4—1064no—
662C22×C4—1064no—
663C22×C4—1064no—
664C22×C4C23×D5314yes—
665C22×C4C23×D5312yes—
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668C22×C4C23×D5312yes—
669C22×C4C23×D5312yes—
670C22×C4C23×D5311yescharacteristic
671C22×C4C23×D5311yescharacteristic
672C4⋊C4—538no—
673C4⋊C4—538no—
674C4⋊C4—538no—
675C4⋊C4—538no—
676C4⋊C4—538no—
677C4⋊C4—538no—
678C4⋊C4—538no—
679C4⋊C4—538no—
680C4⋊C4—534no—
681C4⋊C4—534no—
682C4⋊C4—538no—
683C4⋊C4—538no—
684C4⋊C4—5316no—
685C4⋊C4—538no—
686C4⋊C4—538no—
687C4⋊C4—5316no—
688C4⋊C4—538no—
689C4⋊C4—538no—
690C4⋊C4—5316no—
691C4⋊C4—5316no—
692C4⋊C4—5316no—
693C4⋊C4—5316no—
694C4⋊C4—5316no—
695C4⋊C4—5316no—
696C4⋊C4—5316no—
697C4⋊C4—5316no—
698C4⋊C4—5316no—
699C4⋊C4C23×D5318yes—
700C4⋊C4C23×D5318yes—
701C4⋊C4C23×D5314yes—
702C4⋊C4C23×D53116yes—
703C4⋊C4C23×D5314yes—
704C4⋊C4C23×D5318yes—
705C4⋊C4C23×D5318yes—
706C4⋊C4C23×D53116yes—
707C4⋊C4C23×D53116yes—
708C22⋊C4—5316no—
709C22⋊C4—538no—
710C22⋊C4—538no—
711C22⋊C4—538no—
712C22⋊C4—538no—
713C42—534no—
714C42—534no—
715C42—534no—
716C42—5316no—
717C42—538no—
718C42—538no—
719C42—5316no—
720C42—5316no—
721C42—5316no—
722C42C23×D5314yes—
723C42C23×D5318yes—
724C42C23×D5318yes—
725C42C23×D53116yes—
726C23—532no—
727C23—1062no—
728C23—1062no—
729C23—1062no—
730C23C24×D5311yescharacteristic
731Q8—216no—
732Q8—28no—
733Q8—28no—
734Q8—10616no—
735Q8—10616no—
736Q8—1068no—
737Q8—10616no—
738Q8—1068no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—28no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—534no—
746C2×C4—532no—
747C2×C4—534no—
748C2×C4—534no—
749C2×C4—534no—
750C2×C4—534no—
751C2×C4—538no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—1068no—
755C2×C4—1064no—
756C2×C4—1064no—
757C2×C4—1062no—
758C2×C4—1064no—
759C2×C4—1062no—
760C2×C4—1064no—
761C2×C4—1068no—
762C2×C4—1068no—
763C2×C4—1068no—
764C2×C4#1313326414yes—
765C2×C4#1313326514yes—
766C2×C4C24×D5318yes—
767C2×C4C24×D5314yes—
768C2×C4C24×D5314yes—
769C2×C4C24×D5312yes—
770C2×C4C24×D5314yes—
771C2×C4C24×D5314yes—
772C2×C4C24×D5312yes—
773C2×C4C24×D5312yes—
774C22—1062no—
775C22—1062no—
776C22—1062no—
777C22—2124no—
778C222−1+4×D5312yes—
779C22C2×#1313326412yes—
780C22C2×#1313326512yes—
781C22C25×D5311yescharacteristic
782C4—22no—
783C4—24no—
784C4—24no—
785C4—28no—
786C4—24no—
787C4—24no—
788C4—534no—
789C4—1064no—
790C4—1064no—
791C4—1062no—
792C4—1064no—
793C4—1062no—
794C4—1064no—
795C4—1068no—
796C4C2×#1313326414yes—
797C4C2×#1313326514yes—
798C2—2122no—
799C2#2028920714yesdirect product factor
800C2C2×2−1+4×D5311yescharacteristic
801C2C22×#1313326411yescharacteristic
802C2C22×#1313326511yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#557C2
socleC23×C53C25
prime radicalC23×D53C24
hypercenterC2×#557D53
hypocenterC53C2×#3556
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20289207C2direct (N × H)
2. C2×C53⋊#564C2semidirect
3. C2×#16811352C2semidirect
4. C2×#16811351C2semidirect
5. C2×#16811351C2semidirect
6. C2×#16811350C2semidirect
7. C2×#16811349C2semidirect
8. C2×#16811348C2semidirect
9. C2×#16811348C2semidirect
18. C2×C53×#557C2semidirect
19. C53⋊#564C22semidirect
20. #16811352C22semidirect
21. #16811351C22semidirect
22. #16811351C22semidirect
23. #16811350C22semidirect
24. #16811349C22semidirect
25. #16811348C22semidirect
26. #16811348C22semidirect
92. C53×#557C22semidirect
406. C2×#557D53semidirect
415. C2×C53#3556semidirect
428. #557C2×D53semidirect
502. C53C2×#3556semidirect
799. C2#20289207direct (N × H)

Maximal subgroups

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

subgroupindex
#202892072
C2×C53⋊#5642
C2×#168113522
C2×#168113512
C2×#168113502
C2×#168113492
C2×#168113482
C2×#168112362
C2×#168112342
C2×#168112322
C2×#168112312
C2×#168111782
C2×#168111772
C2×C53×#5572
C2×#355653