Finite Group Databasebeta

← C2×#20288724 #28292354

Subgroups — C2×#20288724 #28292354

Order 13568.

7118 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#20288724C2132yesmaximal, direct product factor
2C2×#16811353C211yesmaximal, characteristic, complemented
3C2×#16811347C211yesmaximal, characteristic, complemented
4C2×#16811345C214yesmaximal, complemented
5C2×#16811344C212yesmaximal, complemented
6C2×#16811341C212yesmaximal, complemented
7C2×#16811339C211yesmaximal, characteristic, complemented
8C2×#16811336C212yesmaximal, complemented
9C2×#16811288C211yesmaximal, characteristic, complemented
10C2×#16811283C212yesmaximal, complemented
11C2×#16811245C212yesmaximal, complemented
12C2×#16811243C214yesmaximal, complemented
13C2×#16811179C212yesmaximal, complemented
14C2×#16811158C212yesmaximal, complemented
15C2×#16811157C211yesmaximal, characteristic, complemented
16C2×#16811099C212yesmaximal, complemented
17C2×C4×#11719945C211yesmaximal, characteristic, complemented
18C2×C53×#533C211yesmaximal, characteristic, complemented
19C22×#11719945C2211yescharacteristic
20C22×Q8×D53C2212yes—
21#16811353C22116yescomplemented
22#16811347C22116yescomplemented
23#16811345C22164yescomplemented
24#16811344C22132yescomplemented
25#16811341C22132yescomplemented
26#16811339C22116yescomplemented
27#16811336C22132yescomplemented
28#16811288C22116yescomplemented
29#16811283C22132yescomplemented
30#16811245C22132yescomplemented
31#16811243C22164yescomplemented
32#16811179C22132yescomplemented
33C2×#13133216C2212yes—
34C2×#13133216C2212yes—
35C2×#13133216C2212yes—
36C2×#13133215C2214yes—
37#16811158C22132yescomplemented
38#16811157C22116yescomplemented
39C2×#13133212C2214yes—
40C2×#13133212C2214yes—
41C2×#13133211C2214yes—
42C2×#13133211C2212yes—
43C2×#13133210C2214yes—
44C2×#13133209C2211yescharacteristic
45C2×#13133206C2214yes—
46C2×#13133206C2212yes—
47C2×#13133205C2214yes—
48C2×#13133205C2211yescharacteristic
49C2×#13133203C2214yes—
50C2×#13133203C2214yes—
51C2×#13133202C2214yes—
52C2×#13133200C2212yes—
53C2×#13133197C2212yes—
54C2×#13133196C2211yescharacteristic
55C2×#13133195C2214yes—
56C2×#13133195C2214yes—
57C2×#13133195C2214yes—
58C2×#13133193C2212yes—
59C2×#13133192C2212yes—
60C2×#13133192C2212yes—
61C2×#13133191C2211yescharacteristic
62C2×#13133190C2214yes—
63#16811099C22132yescomplemented
64C4×#11719945C22116yescomplemented
65C2×Q8×Dic53C2212yes—
66C2×C4×Dic106C2214yes—
67C2×C4×Dic106C2211yescharacteristic
68C2×C4×Dic106C2211yescharacteristic
69C2×C4×Dic106C2211yescharacteristic
70C2×#13133182C2212yes—
71C2×#13133182C2214yes—
72C2×#13133182C2214yes—
73C2×#13133182C2212yes—
74C2×C4×D212C2211yescharacteristic
75C2×C4×D212C2211yescharacteristic
76C2×C4×D212C2211yescharacteristic
77C2×#13133179C2214yes—
78C2×#13133179C2212yes—
79C2×C4×C22⋊D53C2212yes—
80C2×C4×C22⋊D53C2212yes—
81C2×C4×C22⋊D53C2212yes—
82C2×#13133176C2211yescharacteristic
83C2×#13133175C2212yes—
84C2×#13133175C2212yes—
85C2×#13133175C2212yes—
86C2×#13133175C2214yes—
87C2×#13133174C2212yes—
88C2×#13133174C2214yes—
89C2×#13133174C2212yes—
90C2×C42×D53C2212yes—
91C53×#533C22116yescomplemented
92C2×C4⋊Q8×C53C2211yescharacteristic
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#125×C53C2212yes—
95C2×C22⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2212yes—
98C2×C4×Q8×C53C2212yes—
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719945—28no—
102C2×#11719945C2318yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2314yes—
105C22×Dic106C2314yes—
106C22×Dic106C2311yescharacteristic
107C2×Q8×D53—216no—
108C2×Q8×D53C23116yes—
109C22×D212C2311yescharacteristic
110C22×D212C2311yescharacteristic
111C22×D212C2314yes—
112C22×C22⋊D53C2312yes—
113C22×C22⋊D53C2312yes—
114C22×C4×D53C2312yes—
115C22×C4×D53C2312yes—
116C22×C4×D53C2312yes—
117C22×C4×D53C2314yes—
118C22×C4×D53C2312yes—
119#13133216C23116yes—
120#13133216C23116yes—
121#13133216C23116yes—
122#13133215C23132yes—
123#13133212C23132yes—
124#13133212C23132yes—
125#13133211C23132yes—
126#13133211C23116yes—
127#13133210C23132yes—
128#13133209C2318yes—
129#13133206C23116yes—
130#13133206C23132yes—
131#13133205C23132yes—
132#13133205C2318yes—
133#13133203C23132yes—
134#13133203C23132yes—
135#13133202C23132yes—
136#13133200C23116yes—
137#13133197C23116yes—
138#13133196C2318yes—
139#13133195C23132yes—
140#13133195C23132yes—
141#13133195C23132yes—
142#13133193C23116yes—
143#13133192C23116yes—
144#13133192C23116yes—
145#13133191C2318yes—
146#13133190C23132yes—
147Q8×Dic53C23116yes—
148C4×Dic106C2318yes—
149C4×Dic106C23132yes—
150C4×Dic106C2318yes—
151C4×Dic106C2318yes—
152#13133182C23116yes—
153#13133182C23116yes—
154#13133182C23132yes—
155#13133182C23132yes—
156C4×D212C2318yes—
157C4×D212C2318yes—
158C4×D212C2318yes—
159#13133179C23132yes—
160#13133179C23116yes—
161C4×C22⋊D53C23116yes—
162C4×C22⋊D53C23116yes—
163C4×C22⋊D53C23116yes—
164#13133176C2318yes—
165#13133175C23116yes—
166#13133175C23116yes—
167#13133175C23116yes—
168#13133175C23132yes—
169#13133174C23132yes—
170#13133174C23116yes—
171#13133174C23116yes—
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2311yescharacteristic
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2311yescharacteristic
177C2×#11719919C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2312yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2312yes—
186C2×C22⋊Dic53C2312yes—
187C2×C22⋊Dic53C2312yes—
188C2×#11719921C2312yes—
189C2×#11719921C2314yes—
190C2×#11719921C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2312yes—
193C2×#11719921C2314yes—
194C2×#11719921C2314yes—
195C2×#11719921C2312yes—
196C2×#11719921C2314yes—
197C2×#11719921C2314yes—
198C2×#11719921C2312yes—
199C2×C4×Dic53C2312yes—
200C2×C4×Dic53C2312yes—
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2314yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2314yes—
205C2×C4×Dic53C2314yes—
206C42×D53C23116yes—
207C22×Q8×C53C2312yes—
208C22×Q8×C53C2312yes—
209C23×C4×C53C2311yescharacteristic
210C23×C4×C53C2311yescharacteristic
211C23×C4×C53C2311yescharacteristic
212C4⋊Q8×C53C2318yes—
213C4⋊Q8×C53C2318yes—
214#125×C53C23116yes—
215C22⋊Q8×C53C23116yes—
216C22⋊Q8×C53C23116yes—
217C4×Q8×C53C23116yes—
218C4×Q8×C53C23116yes—
219#117×C53C23116yes—
220C2×C4⋊C4×C53C2312yes—
221C2×C4⋊C4×C53C2312yes—
222C2×C4⋊C4×C53C2314yes—
223C2×C4⋊C4×C53C2314yes—
224C2×C4⋊C4×C53C2312yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C22⋊C4×C53C2314yes—
227C2×C42×C53C2311yescharacteristic
228C2×C42×C53C2311yescharacteristic
229C2×C42×C53C2311yescharacteristic
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2318yes—
232C2×C42×C53C2314yes—
233C24×C53C2411yescharacteristic
234C23×D53C2412yes—
235C23×D53C2412yes—
236C2×Q8×C53—28no—
237C2×Q8×C53—44no—
238C2×Q8×C53C2418yes—
239C2×Q8×C53C2418yes—
240C22×C4×C53—24no—
241C22×C4×C53—24no—
242C22×C4×C53—42no—
243C22×C4×C53C2411yescharacteristic
244C22×C4×C53C2411yescharacteristic
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2414yes—
248C22×C4×C53C2414yes—
249C22×C4×C53C2414yes—
250C22×C4×C53C2414yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2411yescharacteristic
253C22×C4×C53C2411yescharacteristic
254C2×C22⋊D53—28no—
255C2×C22⋊D53—44no—
256C2×C22⋊D53C2418yes—
257C2×C22⋊D53C2418yes—
258C22×Dic53C2412yes—
259C22×Dic53C2412yes—
260C22×Dic53C2412yes—
261C22×Dic53C2412yes—
262C22×Dic53C2412yes—
263C22×Dic53C2412yes—
264Q8×D53—264no—
265#11719945—232no—
266C2×D212—24no—
267C2×D212—24no—
268C2×D212—48no—
269C2×D212C2414yes—
270C2×D212C2414yes—
271C2×D212C24116yes—
272C2×C4×D53—28no—
273C2×C4×D53—28no—
274C2×C4×D53—216no—
275C2×C4×D53—28no—
276C2×C4×D53—44no—
277C2×C4×D53C2418yes—
278C2×C4×D53C2418yes—
279C2×C4×D53C2418yes—
280C2×C4×D53C24116yes—
281C2×C4×D53C2418yes—
282C2×Dic106—24no—
283C2×Dic106—216no—
284C2×Dic106—48no—
285C2×Dic106#4118yes—
286C2×Dic106C2414yes—
287C2×Dic106C24116yes—
288C2×Dic106C24116yes—
289C2×Dic106C2414yes—
290C4⋊C4×C53C2418yes—
291C4⋊C4×C53C2418yes—
292C4⋊C4×C53C24116yes—
293C4⋊C4×C53C24116yes—
294C4⋊C4×C53C2418yes—
295C4⋊C4×C53C2418yes—
296C22⋊C4×C53C24116yes—
297C42×C53C2414yes—
298C42×C53C2414yes—
299C42×C53C2414yes—
300C42×C53C2414yes—
301C42×C53C24116yes—
302C22⋊Dic53C2418yes—
303C22⋊Dic53C2418yes—
304#11719921C2418yes—
305#11719921C24116yes—
306#11719921C2418yes—
307#11719921C2418yes—
308#11719921C2418yes—
309#11719921C24116yes—
310#11719921C24116yes—
311#11719921C2418yes—
312#11719921C24116yes—
313#11719921C24116yes—
314#11719921C2418yes—
315C4⋊Dic53C2414yes—
316C4⋊Dic53C2414yes—
317C4⋊Dic53C2414yes—
318C4⋊Dic53C24116yes—
319C4⋊Dic53C2414yes—
320#11719919C2418yes—
321#11719919C2418yes—
322#11719919C24116yes—
323#11719919C2418yes—
324#11719919C2418yes—
325#11719919C2418yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C2418yes—
329C4×Dic53C2418yes—
330C4×Dic53C2418yes—
331C4×Dic53C2418yes—
332C4×Dic53C24116yes—
333C4×Dic53C2418yes—
334C4×Dic53C24116yes—
335C4×Dic53C24116yes—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53C2512yes—
340C23×C53C2511yescharacteristic
341C22×D53—24no—
342C22×D53—24no—
343C22×D53—24no—
344C22×D53—24no—
345C22×D53—24no—
346C22×D53—24no—
347C22×D53C2514yes—
348C22×D53C2514yes—
349Q8×C53—216no—
350Q8×C53—48no—
351C2×C4×C53—28no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—28no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—28no—
358C2×C4×C53—28no—
359C2×C4×C53—44no—
360C2×C4×C53C2×#4114yes—
361C2×C4×C532−1+414yes—
362C2×C4×C53C2518yes—
363C2×C4×C53C2518yes—
364C2×C4×C53C2512yes—
365C2×C4×C53C2512yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2512yes—
368C2×C4×C53C2512yes—
369C2×C4×C53C2512yes—
370C22⋊D53—216no—
371C22⋊D53—48no—
372C2×Dic53—24no—
373C2×Dic53—24no—
374C2×Dic53—24no—
375C2×Dic53—24no—
376C2×Dic53—24no—
377C2×Dic53C2×#4118yes—
378C2×Dic53C2514yes—
379C2×Dic53C2514yes—
380C2×Dic53C2514yes—
381C2×Dic53C2514yes—
382C2×Dic53C2514yes—
383C2×Dic53C2514yes—
384D212—28no—
385D212—28no—
386D212—416no—
387C4×D53—216no—
388C4×D53—216no—
389C4×D53—216no—
390C4×D53—232no—
391C4×D53—48no—
392Dic106—28no—
393Dic106—232no—
394Dic106—416no—
395Dic106C2×#41116yes—
396C2×#3518—531nomaximal, Sylow
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—22no—
400C22×C53—44no—
401C22×C53C22×#4112yes—
402C22×C53C2×2−1+412yes—
403C22×C53#58512yes—
404C22×C53C2611yescharacteristic
405C2×D53—24no—
406C2×D53—24no—
407C2×D53—24no—
408C2×D53—24no—
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—48no—
412C2×D53—48no—
413C4×C53—28no—
414C4×C53—22no—
415C4×C53—22no—
416C4×C53—28no—
417C4×C53—22no—
418C4×C53—22no—
419C4×C53C22×#4114yes—
420C4×C53C2×2−1+414yes—
421Dic53—24no—
422Dic53—24no—
423Dic53—24no—
424Dic53—24no—
425Dic53—24no—
426Dic53C22×#4118yes—
427#3518—5332no—
428C2×Q82—531no—
429C2×#556—531no—
430C2×#556—532no—
431C2×#556—534no—
432C2×#556—532no—
433C2×#555—531no—
434C2×#555—532no—
435C2×D4×Q8—531no—
436C2×#548—532no—
437C2×#542—534no—
438C2×#542—532no—
439C2×#533—532no—
440C2×#533D5311yescharacteristic, complemented
441C2×#529—531no—
442C2×#529—532no—
443C2×#519—532no—
444C2×C4×#41—531no—
445C2×C53—42no—
446C2×C53#351814yescomplemented
447C2×C53C23×#4111yescharacteristic
448C2×C53C22×2−1+411yescharacteristic
449C2×C53C2×#58511yescharacteristic
450D53—44no—
451D53—44no—
452C22×#41—531no—
453C23×Q8—532no—
454Q82—5316no—
455#556—5316no—
456#556—5332no—
457#556—5364no—
458#556—5332no—
459#555—5316no—
460#555—5332no—
461D4×Q8—5316no—
462#548—5332no—
463#542—5364no—
464#542—5332no—
465#533—5332no—
466#533C2×D53116yescomplemented
467C2×C4⋊Q8—534no—
468C2×C4⋊Q8—532no—
469C2×C4⋊Q8—532no—
470C2×C4⋊Q8—532no—
471C2×C4⋊Q8C2×D5311yescharacteristic
472C2×C4⋊Q8C2×D5311yescharacteristic
473#529—5332no—
474#529—5316no—
475C2×#126—534no—
476C2×#126—534no—
477C2×#126—534no—
478C2×#126—532no—
479C2×#126—534no—
480C2×#125—531no—
481C2×#125C2×D5312yes—
482C2×#124—532no—
483C2×#124—534no—
484C2×#124—534no—
485C2×#124—534no—
486C2×#124—531no—
487C2×#124—534no—
488C2×#123—532no—
489C2×#123—534no—
490C2×C22⋊Q8—532no—
491C2×C22⋊Q8—531no—
492C2×C22⋊Q8—532no—
493C2×C22⋊Q8—534no—
494C2×C22⋊Q8—534no—
495C2×C22⋊Q8—534no—
496C2×C22⋊Q8C2×D5312yes—
497C2×C22⋊Q8C2×D5312yes—
498C2×#121—531no—
499C2×#121—532no—
500C2×#121—532no—
501C2×#121—534no—
502#519—5332no—
503C4×#41—5316no—
504C2×C4×Q8—532no—
505C2×C4×Q8—534no—
506C2×C4×Q8—532no—
507C2×C4×Q8—532no—
508C2×C4×Q8—534no—
509C2×C4×Q8—531no—
510C2×C4×Q8—531no—
511C2×C4×Q8—534no—
512C2×C4×Q8—531no—
513C2×C4×Q8C2×D5312yes—
514C2×C4×Q8C2×D5312yes—
515C2×C4×D4—532no—
516C2×C4×D4—532no—
517C2×C4×D4—532no—
518C2×C4×D4—534no—
519C2×C4×D4—532no—
520C2×C4×D4—531no—
521C2×C4×D4—531no—
522C2×C4×D4—531no—
523C2×#117—531no—
524C2×#117—534no—
525C2×#117—532no—
526C2×#117—532no—
527C2×#117—532no—
528C2×#117—532no—
529C2×#117—532no—
530C2×#117—534no—
531C2×#117C2×D5312yes—
532C22×C42—532no—
533C22×C42C2×D5311yescharacteristic
534C53C2×#351811yescharacteristic, complemented, Sylow
535C2×#41—538no—
536C2×#41—1068no—
537C22×Q8—5316no—
538C22×Q8—531no—
539C22×Q8—531no—
540C22×Q8—534no—
541C22×Q8—534no—
542C22×Q8—10616no—
543C22×Q8C22×D5312yes—
544C22×Q8C22×D5312yes—
545C22×D4—532no—
546C22×D4—532no—
547C22×D4—531no—
548C22×D4—531no—
549C22×D4—534no—
550C23×C4—534no—
551C23×C4—532no—
552C23×C4—532no—
553C23×C4—532no—
554C23×C4—532no—
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5311yescharacteristic
557C23×C4C22×D5311yescharacteristic
558C4⋊Q8—5332no—
559C4⋊Q8—5316no—
560C4⋊Q8—5316no—
561C4⋊Q8—5316no—
562C4⋊Q8C22×D5318yes—
563C4⋊Q8C22×D5318yes—
564#126—5332no—
565#126—5332no—
566#126—5332no—
567#126—5316no—
568#126—5332no—
569#125—538no—
570#125C22×D53116yes—
571#124—5316no—
572#124—5332no—
573#124—5332no—
574#124—5332no—
575#124—538no—
576#124—5332no—
577#123—5316no—
578#123—5332no—
579C22⋊Q8—5316no—
580C22⋊Q8—538no—
581C22⋊Q8—5316no—
582C22⋊Q8—5332no—
583C22⋊Q8—5332no—
584C22⋊Q8—5332no—
585C22⋊Q8C22×D53116yes—
586C22⋊Q8C22×D53116yes—
587#121—538no—
588#121—5316no—
589#121—5316no—
590#121—5332no—
591C4×Q8—5316no—
592C4×Q8—5332no—
593C4×Q8—5316no—
594C4×Q8—5316no—
595C4×Q8—5332no—
596C4×Q8—538no—
597C4×Q8—538no—
598C4×Q8—5332no—
599C4×Q8—538no—
600C4×Q8C22×D53116yes—
601C4×Q8C22×D53116yes—
602C4×D4—5316no—
603C4×D4—5316no—
604C4×D4—5316no—
605C4×D4—5332no—
606C4×D4—5316no—
607C4×D4—538no—
608C4×D4—538no—
609C4×D4—538no—
610#117—538no—
611#117—5332no—
612#117—5316no—
613#117—5316no—
614#117—5316no—
615#117—5316no—
616#117—5316no—
617#117—5332no—
618#117C22×D53116yes—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—531no—
621C2×C4⋊C4—531no—
622C2×C4⋊C4—531no—
623C2×C4⋊C4—532no—
624C2×C4⋊C4—531no—
625C2×C4⋊C4—534no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—534no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—534no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4C22×D5312yes—
634C2×C4⋊C4C22×D5312yes—
635C2×C4⋊C4C22×D5312yes—
636C2×C4⋊C4C22×D5314yes—
637C2×C4⋊C4C22×D5314yes—
638C2×C4⋊C4C22×D5312yes—
639C2×C22⋊C4—532no—
640C2×C22⋊C4—532no—
641C2×C22⋊C4—534no—
642C2×C22⋊C4—532no—
643C2×C22⋊C4—532no—
644C2×C22⋊C4—532no—
645C2×C22⋊C4—532no—
646C2×C22⋊C4—534no—
647C2×C22⋊C4—534no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—534no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—534no—
652C2×C22⋊C4C22×D5314yes—
653C2×C42—532no—
654C2×C42—534no—
655C2×C42—534no—
656C2×C42—532no—
657C2×C42—534no—
658C2×C42—532no—
659C2×C42—532no—
660C2×C42—5316no—
661C2×C42C22×D5311yescharacteristic
662C2×C42C22×D5311yescharacteristic
663C2×C42C22×D5314yes—
664C2×C42C22×D5311yescharacteristic
665C2×C42C22×D5318yes—
666C2×C42C22×D5311yescharacteristic
667C24—532no—
668C24—532no—
669C24C23×D5311yescharacteristic
670#41—10632no—
671C2×Q8—28no—
672C2×Q8—44no—
673C2×Q8—538no—
674C2×Q8—534no—
675C2×Q8—534no—
676C2×Q8—5316no—
677C2×Q8—5316no—
678C2×Q8—10616no—
679C2×Q8—10664no—
680C2×Q8—1064no—
681C2×Q8—2128no—
682C2×Q8C23×D5318yes—
683C2×Q8C23×D5318yes—
684C2×D4—538no—
685C2×D4—538no—
686C2×D4—534no—
687C2×D4—534no—
688C2×D4—5316no—
689C2×D4—1068no—
690C2×D4—1064no—
691C2×D4—1064no—
692C2×D4—2128no—
693C2×D4—2124no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—42no—
697C22×C4—532no—
698C22×C4—532no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—538no—
704C22×C4—538no—
705C22×C4—5316no—
706C22×C4—538no—
707C22×C4—538no—
708C22×C4—10616no—
709C22×C4—1068no—
710C22×C4—1068no—
711C22×C4—1068no—
712C22×C4—2124no—
713C22×C4C23×D5314yes—
714C22×C4C23×D5314yes—
715C22×C4C23×D5311yescharacteristic
716C22×C4C23×D5311yescharacteristic
717C22×C4C23×D5314yes—
718C22×C4C23×D5314yes—
719C22×C4C23×D5311yescharacteristic
720C22×C4C23×D5311yescharacteristic
721C22×C4C23×D5314yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—538no—
725C4⋊C4—534no—
726C4⋊C4—534no—
727C4⋊C4—534no—
728C4⋊C4—538no—
729C4⋊C4—534no—
730C4⋊C4—5316no—
731C4⋊C4—538no—
732C4⋊C4—538no—
733C4⋊C4—5316no—
734C4⋊C4—538no—
735C4⋊C4—5316no—
736C4⋊C4—538no—
737C4⋊C4—5316no—
738C4⋊C4C23×D5318yes—
739C4⋊C4C23×D5318yes—
740C4⋊C4C23×D5318yes—
741C4⋊C4C23×D53116yes—
742C4⋊C4C23×D53116yes—
743C4⋊C4C23×D5318yes—
744C22⋊C4—538no—
745C22⋊C4—538no—
746C22⋊C4—5316no—
747C22⋊C4—538no—
748C22⋊C4—538no—
749C22⋊C4—538no—
750C22⋊C4—538no—
751C22⋊C4—5316no—
752C22⋊C4—5316no—
753C22⋊C4—538no—
754C22⋊C4—5316no—
755C22⋊C4—538no—
756C22⋊C4—5316no—
757C22⋊C4C23×D53116yes—
758C42—538no—
759C42—538no—
760C42—538no—
761C42—5316no—
762C42—5316no—
763C42—5316no—
764C42—538no—
765C42C23×D5314yes—
766C42C23×D5314yes—
767C42C23×D5314yes—
768C42C23×D5314yes—
769C42C23×D53116yes—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—534no—
774C23—534no—
775C23—1064no—
776C23—1064no—
777C23—1064no—
778C23—1064no—
779C23—1064no—
780C23—1064no—
781C23C24×D5312yes—
782C23C24×D5311yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—5316no—
786Q8—10632no—
787Q8—1068no—
788Q8—21216no—
789D4—10616no—
790D4—1068no—
791D4—1068no—
792D4—21216no—
793D4—2128no—
794C2×C4—22no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—44no—
803C2×C4—538no—
804C2×C4—534no—
805C2×C4—534no—
806C2×C4—534no—
807C2×C4—534no—
808C2×C4—534no—
809C2×C4—534no—
810C2×C4—10632no—
811C2×C4—10616no—
812C2×C4—1064no—
813C2×C4—1064no—
814C2×C4—1064no—
815C2×C4—1064no—
816C2×C4—1064no—
817C2×C4—10616no—
818C2×C4—10616no—
819C2×C4—2128no—
820C2×C4#41×D5314yes—
821C2×C4#1313326514yes—
822C2×C4C24×D5312yes—
823C2×C4C24×D5312yes—
824C2×C4C24×D5318yes—
825C2×C4C24×D5318yes—
826C2×C4C24×D5312yes—
827C2×C4C24×D5312yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—1064no—
835C22—1064no—
836C22—1064no—
837C22—1064no—
838C22—1064no—
839C22—1064no—
840C22—2128no—
841C22—2128no—
842C22C2×#41×D5312yes—
843C22C2×#1313326512yes—
844C22#1681145912yes—
845C22C25×D5311yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—538no—
853C4—1064no—
854C4—1064no—
855C4—1064no—
856C4—1064no—
857C4—1064no—
858C4C2×#41×D5314yes—
859C4C2×#1313326514yes—
860C2—42no—
861C2—2124no—
862C2—2124no—
863C2#2028872414yesdirect product factor
864C2C22×#41×D5311yescharacteristic
865C2C22×#1313326511yescharacteristic
866C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#533C2
socleC23×C53C25
hypercenterC2×#533D53
hypocenterC53C2×#3518
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20288724C2direct (N × H)
2. C2×#16811353C2semidirect
3. C2×#16811347C2semidirect
4. C2×#16811345C2semidirect
5. C2×#16811344C2semidirect
6. C2×#16811341C2semidirect
7. C2×#16811339C2semidirect
8. C2×#16811336C2semidirect
9. C2×#16811288C2semidirect
10. C2×#16811283C2semidirect
11. C2×#16811245C2semidirect
12. C2×#16811243C2semidirect
13. C2×#16811179C2semidirect
14. C2×#16811158C2semidirect
15. C2×#16811157C2semidirect
16. C2×#16811099C2semidirect
17. C2×C4×#11719945C2semidirect
18. C2×C53×#533C2semidirect
21. #16811353C22semidirect
22. #16811347C22semidirect
23. #16811345C22semidirect
24. #16811344C22semidirect
25. #16811341C22semidirect
26. #16811339C22semidirect
27. #16811336C22semidirect
28. #16811288C22semidirect
29. #16811283C22semidirect
30. #16811245C22semidirect
31. #16811243C22semidirect
32. #16811179C22semidirect
37. #16811158C22semidirect
38. #16811157C22semidirect
63. #16811099C22semidirect
64. C4×#11719945C22semidirect
91. C53×#533C22semidirect
440. C2×#533D53semidirect
446. C2×C53#3518semidirect
466. #533C2×D53semidirect
534. C53C2×#3518semidirect
863. C2#20288724direct (N × H)

Maximal subgroups

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

subgroupindex
#202887242
C2×#168113532
C2×#168113472
C2×#168113452
C2×#168113442
C2×#168113412
C2×#168113392
C2×#168113362
C2×#168112882
C2×#168112832
C2×#168112452
C2×#168112432
C2×#168111792
C2×#168111582
C2×#168111572
C2×#168110992
C2×C4×#117199452
C2×C53×#5332
C2×#351853