Finite Group Databasebeta

← C2×#20289055 #28291774

Subgroups — C2×#20289055 #28291774

Order 13568.

7086 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#20289055C2132yesmaximal, direct product factor
2C2×#16811375C214yesmaximal, complemented
3C2×Q8×Dic106C211yesmaximal, characteristic, complemented
4C2×#16811338C211yesmaximal, characteristic, complemented
5C2×#16811333C211yesmaximal, characteristic, complemented
6C2×#16811330C211yesmaximal, characteristic, complemented
7C2×#16811315C212yesmaximal, complemented
8C2×#16811313C212yesmaximal, complemented
9C2×#16811277C212yesmaximal, complemented
10C2×#16811273C212yesmaximal, complemented
11C2×#16811253C212yesmaximal, complemented
12C2×#16811251C212yesmaximal, complemented
13C2×#16811244C212yesmaximal, complemented
14C2×#16811242C212yesmaximal, complemented
15C2×#16811195C214yesmaximal, complemented
16C22×#13133217C211yesmaximal, characteristic, complemented
17C2×#16811157C211yesmaximal, characteristic, complemented
18C2×C53×#529C211yesmaximal, characteristic, complemented
19C22×#11719947C2214yes—
20C23×Dic106C2212yes—
21#16811375C22164yescomplemented
22Q8×Dic106C22116yescomplemented
23#16811338C22116yescomplemented
24#16811333C22116yescomplemented
25#16811330C22116yescomplemented
26#16811315C22132yescomplemented
27#16811313C22132yescomplemented
28#16811277C22132yescomplemented
29#16811273C22132yescomplemented
30#16811253C22132yescomplemented
31#16811251C22132yescomplemented
32#16811244C22132yescomplemented
33#16811242C22132yescomplemented
34#16811195C22164yescomplemented
35C2×#13133217C2212yes—
36C2×#13133217C2211yescharacteristic
37C2×#13133217C2212yes—
38C2×#13133217C2212yes—
39C2×#13133217C2212yes—
40C2×#13133217C2211yescharacteristic
41C2×#13133217C22116yescomplemented
42C2×#13133216C2214yes—
43C2×#13133216C2214yes—
44C2×#13133216C2212yes—
45#16811157C22116yescomplemented
46C2×#13133212C2214yes—
47C2×#13133211C2212yes—
48C2×#13133210C2214yes—
49C2×#13133209C2211yescharacteristic
50C2×#13133209C2212yes—
51C2×#13133208C2214yes—
52C2×#13133208C2212yes—
53C2×#13133207C2214yes—
54C2×#13133205C2211yescharacteristic
55C2×#13133203C2214yes—
56C2×#13133203C2214yes—
57C2×#13133201C2214yes—
58C2×#13133201C2214yes—
59C2×#13133200C2212yes—
60C2×#13133199C2214yes—
61C2×#13133198C2214yes—
62C2×#13133197C2214yes—
63C2×#13133196C2212yes—
64C2×#13133196C2211yescharacteristic
65C2×#13133195C2214yes—
66C2×#13133195C2214yes—
67C2×#13133194C2214yes—
68C2×#13133194C2214yes—
69C2×#13133194C2214yes—
70C2×#13133193C2212yes—
71C2×#13133191C2212yes—
72C2×#13133191C2211yescharacteristic
73C2×#13133188C2212yes—
74C2×Q8×Dic53C2212yes—
75C2×C4×Dic106C2212yes—
76C2×C4×Dic106C2211yescharacteristic
77C2×C4×D212C2212yes—
78C2×C4×D212C2211yescharacteristic
79C2×D4×Dic53C2212yes—
80C2×C4×C22⋊D53C2212yes—
81C2×#13133176C2212yes—
82C2×#13133175C2212yes—
83C2×#13133174C2212yes—
84C2×#13133173C2214yes—
85C22×C4⋊Dic53C2212yes—
86C22×C4⋊Dic53C2212yes—
87C22×C4⋊Dic53C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C53×#529C22116yescomplemented
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×C53C2212yes—
98C2×C4×D4×C53C2211yescharacteristic
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719947—416no—
102C2×#11719947C23132yes—
103C22×Dic106—48no—
104C22×Dic106C2311yescharacteristic
105C22×Dic106C2312yes—
106C22×Dic106C2314yes—
107C22×Dic106C2314yes—
108C22×Dic106C2312yes—
109C22×Dic106C23116yes—
110C22×D212C2311yescharacteristic
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2314yes—
113C23×Dic53C2314yes—
114C23×Dic53C2314yes—
115C22×C4×D53C2312yes—
116C22×C4×D53C2314yes—
117#13133217C23116yes—
118#13133217C2318yes—
119#13133217C2318yes—
120#13133217C23116yes—
121#13133217C23116yes—
122#13133217C23116yes—
123#13133216C23116yes—
124#13133216C23132yes—
125#13133216C23132yes—
126#13133212C23132yes—
127#13133211C23116yes—
128#13133210C23132yes—
129#13133209C23116yes—
130#13133209C2318yes—
131#13133208C23116yes—
132#13133208C23132yes—
133#13133207C23132yes—
134#13133205C2318yes—
135#13133203C23132yes—
136#13133203C23132yes—
137#13133201C23132yes—
138#13133201C23132yes—
139#13133200C23116yes—
140#13133199C23132yes—
141#13133198C23132yes—
142#13133197C23132yes—
143#13133196C2318yes—
144#13133196C23116yes—
145#13133195C23132yes—
146#13133195C23132yes—
147#13133194C23132yes—
148#13133194C23132yes—
149#13133194C23132yes—
150#13133193C23116yes—
151#13133191C2318yes—
152#13133191C23116yes—
153#13133188C23116yes—
154Q8×Dic53C23116yes—
155C4×Dic106C23116yes—
156C4×Dic106C2318yes—
157C4×D212C23116yes—
158C4×D212C2318yes—
159D4×Dic53C23116yes—
160C4×C22⋊D53C23116yes—
161#13133176C23116yes—
162#13133175C23116yes—
163#13133174C23116yes—
164#13133173C23132yes—
165C2×C4⋊Dic53C23116yes—
166C2×C4⋊Dic53C23116yes—
167C2×C4⋊Dic53C23116yes—
168C2×C4⋊Dic53C2312yes—
169C2×C4⋊Dic53C2312yes—
170C2×C4⋊Dic53C2311yescharacteristic
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2314yes—
175C2×C4⋊Dic53C2314yes—
176C2×C4⋊Dic53C2311yescharacteristic
177C2×C4⋊Dic53C2314yes—
178C2×#11719919C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2312yes—
182C2×#11719919C2312yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2314yes—
186C4⋊C4×D53C23116yes—
187C2×C22⋊Dic53C2312yes—
188C2×C22⋊Dic53C2314yes—
189C2×C22⋊Dic53C2314yes—
190C2×#11719921C2312yes—
191C2×#11719921C2312yes—
192C2×#11719921C2314yes—
193C2×#11719921C2312yes—
194C2×#11719921C2314yes—
195C2×#11719921C2312yes—
196C2×C4×Dic53C2314yes—
197C2×C4×Dic53C2314yes—
198C2×C4×Dic53C2312yes—
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
235C23×D53C2412yes—
236C2×Q8×C53—24no—
237C2×Q8×C53C2414yes—
238C2×D4×C53—28no—
239C2×D4×C53—24no—
240C2×D4×C53C2418yes—
241C2×D4×C53C2414yes—
242C22×C4×C53—24no—
243C22×C4×C53—24no—
244C22×C4×C53—28no—
245C22×C4×C53—24no—
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2411yescharacteristic
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2414yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2414yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2412yes—
255C22×C4×C53C2412yes—
256C22×C4×C53C2418yes—
257C22×C4×C53C2411yescharacteristic
258C22×C4×C53C2411yescharacteristic
259C2×C22⋊D53—28no—
260C2×C22⋊D53—48no—
261C2×C22⋊D53C2418yes—
262C2×C22⋊D53C24116yes—
263C22×Dic53—216no—
264C22×Dic53—48no—
265C22×Dic53C2412yes—
266C22×Dic53C2412yes—
267C22×Dic53C2414yes—
268C22×Dic53C2412yes—
269C22×Dic53C2414yes—
270C22×Dic53C24116yes—
271C22×Dic53C24116yes—
272#11719947—464no—
273C2×D212—24no—
274C2×D212C2414yes—
275C2×C4×D53—28no—
276C2×C4×D53—48no—
277C2×C4×D53C2418yes—
278C2×C4×D53C24116yes—
279C2×Dic106—24no—
280C2×Dic106—44no—
281C2×Dic106—48no—
282C2×Dic106—44no—
283C2×Dic106—432no—
284C2×Dic106—48no—
285C2×Dic106C2414yes—
286C2×Dic106C2418yes—
287C2×Dic106C24116yes—
288C2×Dic106C24116yes—
289C2×Dic106C2418yes—
290C4⋊C4×C53C2418yes—
291C4⋊C4×C53C2418yes—
292C4⋊C4×C53C2414yes—
293C4⋊C4×C53C2418yes—
294C4⋊C4×C53C2414yes—
295C4⋊C4×C53C2418yes—
296C22⋊C4×C53C2418yes—
297C22⋊C4×C53C2418yes—
298C22⋊C4×C53C2418yes—
299C22⋊C4×C53C2418yes—
300C22⋊C4×C53C2418yes—
301C42×C53C2414yes—
302C42×C53C2414yes—
303C42×C53C2414yes—
304C42×C53C2414yes—
305C42×C53C2418yes—
306C22⋊Dic53C2418yes—
307C22⋊Dic53C24116yes—
308C22⋊Dic53C24116yes—
309#11719921C2418yes—
310#11719921C2418yes—
311#11719921C24116yes—
312#11719921C2418yes—
313#11719921C24116yes—
314#11719921C2418yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C2414yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C24116yes—
321C4⋊Dic53C24116yes—
322C4⋊Dic53C24116yes—
323C4⋊Dic53C2414yes—
324C4⋊Dic53C24116yes—
325#11719919C24116yes—
326#11719919C24116yes—
327#11719919C24116yes—
328#11719919C2418yes—
329#11719919C2418yes—
330#11719919C2418yes—
331#11719919C2418yes—
332#11719919C24116yes—
333C4×Dic53C24116yes—
334C4×Dic53C24116yes—
335C4×Dic53C2418yes—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—24no—
339C23×C53—24no—
340C23×C53—24no—
341C23×C53H(5,𝔽2)14yes—
342C23×C53C2514yes—
343C23×C53C2512yes—
344C23×C53C2511yescharacteristic
345C22×D53—24no—
346C22×D53—24no—
347C22×D53—24no—
348C22×D53C2514yes—
349Q8×C53—28no—
350D4×C53—216no—
351D4×C53—28no—
352C2×C4×C53—28no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—24no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—24no—
359C2×C4×C53—24no—
360C2×C4×C53—28no—
361C2×C4×C53—216no—
362C2×C4×C53—28no—
363C2×C4×C532−1+414yes—
364C2×C4×C532−1+414yes—
365C2×C4×C53C2512yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2514yes—
368C2×C4×C53C2514yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2512yes—
371C2×C4×C53C2514yes—
372C2×C4×C53C2512yes—
373C2×C4×C53C2512yes—
374C22⋊D53—216no—
375C22⋊D53—416no—
376C2×Dic53—28no—
377C2×Dic53—28no—
378C2×Dic53—232no—
379C2×Dic53—24no—
380C2×Dic53—24no—
381C2×Dic53—24no—
382C2×Dic53—416no—
383C2×Dic53C2518yes—
384C2×Dic53C2518yes—
385C2×Dic53C2514yes—
386C2×Dic53C2514yes—
387C2×Dic53C2514yes—
388D212—28no—
389C4×D53—216no—
390C4×D53—416no—
391Dic106—28no—
392Dic106—48no—
393Dic106—416no—
394Dic106—48no—
395Dic106—416no—
396C2×#3544—531nomaximal, Sylow
397C22×C53—22no—
398C22×C53—22no—
399C22×C53—28no—
400C22×C53—24no—
401C22×C53—24no—
402C22×C53—24no—
403C22×C53—48no—
404C22×C53C2×H(5,𝔽2)14yes—
405C22×C53C2×H(5,𝔽2)12yes—
406C22×C53C2×2−1+412yes—
407C22×C53C2×2−1+412yes—
408C22×C53C2611yescharacteristic
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—48no—
413C4×C53—22no—
414C4×C53—22no—
415C4×C53—24no—
416C4×C53—24no—
417C4×C53—22no—
418C4×C53—22no—
419C4×C53—24no—
420C4×C53C2×2−1+414yes—
421C4×C53C2×2−1+414yes—
422Dic53—28no—
423Dic53—28no—
424Dic53—24no—
425Dic53—24no—
426Dic53—24no—
427#3544—5332no—
428C2×#563—534no—
429C2×Q82—531no—
430C2×#555—531no—
431C2×#554—531no—
432C2×#554—531no—
433C2×#552—532no—
434C2×#552—532no—
435C2×#547—532no—
436C2×#547—532no—
437C2×#544—532no—
438C2×#544—532no—
439C2×#542—532no—
440C2×#542—532no—
441C2×#536—534no—
442C22×C4⋊Q8—531no—
443C2×#529—531no—
444C2×#529D5311yescharacteristic, complemented
445C2×C53—24no—
446C2×C53—44no—
447C2×C53#354414yescomplemented
448C2×C53C22×H(5,𝔽2)11yescharacteristic
449C2×C53C22×2−1+411yescharacteristic
450C2×C53C22×2−1+411yescharacteristic
451D53—44no—
452C22×#41—534no—
453C23×Q8—532no—
454#563—5364no—
455Q82—5316no—
456#555—5316no—
457#554—5316no—
458#554—5316no—
459#552—5332no—
460#552—5332no—
461#547—5332no—
462#547—5332no—
463#544—5332no—
464#544—5332no—
465#542—5332no—
466#542—5332no—
467#536—5364no—
468C2×C4⋊Q8—534no—
469C2×C4⋊Q8—534no—
470C2×C4⋊Q8—532no—
471C2×C4⋊Q8—532no—
472C2×C4⋊Q8—532no—
473C2×C4⋊Q8—531no—
474C2×C4⋊Q8—531no—
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—5316no—
477C2×C4⋊Q8—532no—
478#529—5316no—
479#529C2×D53116yescomplemented
480C2×#126—534no—
481C2×#126—534no—
482C2×#126—532no—
483C2×#126C2×D5312yes—
484C2×#125—534no—
485C2×#125—532no—
486C2×#125—534no—
487C2×#125—531no—
488C2×#125—532no—
489C2×#125C2×D5311yescharacteristic
490C2×#124—534no—
491C2×#124—534no—
492C2×#124—531no—
493C2×#124C2×D5311yescharacteristic
494C2×#123—534no—
495C2×#123—532no—
496C2×#123—534no—
497C2×#123—534no—
498C2×#123—534no—
499C2×#123C2×D5312yes—
500C2×C22⋊Q8—532no—
501C2×C22⋊Q8—531no—
502C2×C22⋊Q8—532no—
503C2×C22⋊Q8—534no—
504C2×C22⋊Q8—534no—
505C2×C22⋊Q8—534no—
506C2×C22⋊Q8—534no—
507C2×C22⋊Q8—534no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8C2×D5311yescharacteristic
510C2×#121—532no—
511C2×#121—531no—
512C2×#121—532no—
513C2×#121C2×D5311yescharacteristic
514C2×C4×Q8—532no—
515C2×C4×Q8—531no—
516C2×C4×Q8—532no—
517C2×C4×Q8C2×D5311yescharacteristic
518C2×C4×D4—532no—
519C2×C4×D4—532no—
520C2×C4×D4—531no—
521C2×C4×D4—532no—
522C2×C4×D4C2×D5312yes—
523C2×C4×D4C2×D5311yescharacteristic
524C2×#117—532no—
525C2×#117—532no—
526C2×#117—534no—
527C2×#117—532no—
528C2×#117C2×D5312yes—
529C22×C4⋊C4—532no—
530C22×C4⋊C4—532no—
531C22×C4⋊C4—532no—
532C22×C4⋊C4—532no—
533C22×C42C2×D5311yescharacteristic
534C53C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—5332no—
536C2×#41—21216no—
537C22×Q8—531no—
538C22×Q8—532no—
539C22×Q8—534no—
540C22×Q8—534no—
541C22×Q8—532no—
542C22×Q8—5316no—
543C22×Q8—2128no—
544C22×Q8C22×D5311yescharacteristic
545C22×D4—532no—
546C22×D4—534no—
547C22×D4—531no—
548C22×D4C22×D5311yescharacteristic
549C22×D4C22×D5312yes—
550C23×C4—534no—
551C23×C4—534no—
552C23×C4—532no—
553C23×C4—534no—
554C23×C4C22×D5311yescharacteristic
555C23×C4C22×D5311yescharacteristic
556C23×C4C22×D5312yes—
557C23×C4C22×D5311yescharacteristic
558C4⋊Q8—5332no—
559C4⋊Q8—5332no—
560C4⋊Q8—5316no—
561C4⋊Q8—5316no—
562C4⋊Q8—5316no—
563C4⋊Q8—538no—
564C4⋊Q8—538no—
565C4⋊Q8—5316no—
566C4⋊Q8—5316no—
567#126—5332no—
568#126—5332no—
569#126—5316no—
570#126C22×D53116yes—
571#125—5316no—
572#125—5332no—
573#125—5332no—
574#125—538no—
575#125—5316no—
576#125C22×D5318yes—
577#124—5332no—
578#124—5332no—
579#124—538no—
580#124C22×D5318yes—
581#123—5332no—
582#123—5316no—
583#123—5332no—
584#123—5332no—
585#123—5332no—
586#123C22×D53116yes—
587C22⋊Q8—5316no—
588C22⋊Q8—538no—
589C22⋊Q8—5316no—
590C22⋊Q8—5332no—
591C22⋊Q8—5332no—
592C22⋊Q8—5332no—
593C22⋊Q8—5332no—
594C22⋊Q8—5332no—
595C22⋊Q8—5332no—
596C22⋊Q8C22×D5318yes—
597#121—5316no—
598#121—538no—
599#121—5316no—
600#121C22×D5318yes—
601C4×Q8—5316no—
602C4×Q8—538no—
603C4×Q8—5316no—
604C4×Q8C22×D5318yes—
605C4×D4—5316no—
606C4×D4—5316no—
607C4×D4—538no—
608C4×D4—5316no—
609C4×D4C22×D53116yes—
610C4×D4C22×D5318yes—
611#117—5316no—
612#117—5316no—
613#117—5332no—
614#117—5316no—
615#117C22×D53116yes—
616C2×C4⋊C4—532no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—531no—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—532no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4—5316no—
626C2×C4⋊C4—5316no—
627C2×C4⋊C4—5316no—
628C2×C4⋊C4—531no—
629C2×C4⋊C4—534no—
630C2×C4⋊C4—534no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—532no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—534no—
636C2×C4⋊C4—534no—
637C2×C4⋊C4—5316no—
638C2×C4⋊C4C22×D5311yescharacteristic
639C2×C4⋊C4C22×D5311yescharacteristic
640C2×C4⋊C4C22×D5312yes—
641C2×C4⋊C4C22×D5312yes—
642C2×C4⋊C4C22×D5312yes—
643C2×C4⋊C4C22×D5312yes—
644C2×C22⋊C4—532no—
645C2×C22⋊C4—534no—
646C2×C22⋊C4—534no—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—534no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—534no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4—532no—
653C2×C22⋊C4C22×D5312yes—
654C2×C22⋊C4C22×D5312yes—
655C2×C22⋊C4C22×D5312yes—
656C2×C22⋊C4C22×D5312yes—
657C2×C22⋊C4C22×D5312yes—
658C2×C42—534no—
659C2×C42—532no—
660C2×C42—534no—
661C2×C42C22×D5311yescharacteristic
662C2×C42C22×D5311yescharacteristic
663C2×C42C22×D5312yes—
664C2×C42C22×D5311yescharacteristic
665C2×C42C22×D5311yescharacteristic
666C2×C42C22×D5318yes—
667C24—532no—
668C24C23×D5312yes—
669C24C23×D5311yescharacteristic
670#41—21264no—
671C2×Q8—24no—
672C2×Q8—534no—
673C2×Q8—538no—
674C2×Q8—5316no—
675C2×Q8—5316no—
676C2×Q8—538no—
677C2×Q8—1064no—
678C2×Q8—2124no—
679C2×Q8—2128no—
680C2×Q8—2124no—
681C2×Q8—21232no—
682C2×Q8—2128no—
683C2×Q8C23×D5314yes—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—538no—
687C2×D4—5316no—
688C2×D4—534no—
689C2×D4—1068no—
690C2×D4—1064no—
691C2×D4—2128no—
692C2×D4C23×D5314yes—
693C2×D4C23×D5318yes—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—28no—
697C22×C4—24no—
698C22×C4—5316no—
699C22×C4—532no—
700C22×C4—532no—
701C22×C4—534no—
702C22×C4—532no—
703C22×C4—534no—
704C22×C4—5316no—
705C22×C4—538no—
706C22×C4—5316no—
707C22×C4—10616no—
708C22×C4—1068no—
709C22×C4—2128no—
710C22×C4—2128no—
711C22×C4C23×D5314yes—
712C22×C4C23×D5314yes—
713C22×C4C23×D5314yes—
714C22×C4C23×D5318yes—
715C22×C4C23×D5312yes—
716C22×C4C23×D5312yes—
717C22×C4C23×D5311yescharacteristic
718C22×C4C23×D5311yescharacteristic
719C22×C4C23×D5311yescharacteristic
720C22×C4C23×D5311yescharacteristic
721C22×C4C23×D5312yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—538no—
725C4⋊C4—538no—
726C4⋊C4—534no—
727C4⋊C4—538no—
728C4⋊C4—538no—
729C4⋊C4—5316no—
730C4⋊C4—5316no—
731C4⋊C4—5316no—
732C4⋊C4—5316no—
733C4⋊C4—534no—
734C4⋊C4—5316no—
735C4⋊C4—5316no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—538no—
739C4⋊C4—538no—
740C4⋊C4—5316no—
741C4⋊C4—5316no—
742C4⋊C4C23×D5314yes—
743C4⋊C4C23×D5314yes—
744C4⋊C4C23×D5318yes—
745C4⋊C4C23×D5318yes—
746C4⋊C4C23×D5318yes—
747C4⋊C4C23×D5318yes—
748C22⋊C4—538no—
749C22⋊C4—5316no—
750C22⋊C4—5316no—
751C22⋊C4—538no—
752C22⋊C4—5316no—
753C22⋊C4—538no—
754C22⋊C4—5316no—
755C22⋊C4—538no—
756C22⋊C4—538no—
757C22⋊C4C23×D5318yes—
758C22⋊C4C23×D5318yes—
759C22⋊C4C23×D5318yes—
760C22⋊C4C23×D5318yes—
761C22⋊C4C23×D5318yes—
762C42—5316no—
763C42—538no—
764C42—5316no—
765C42C23×D5314yes—
766C42C23×D5314yes—
767C42C23×D5314yes—
768C42C23×D5314yes—
769C42C23×D5318yes—
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—534no—
776C23—1064no—
777C23—1064no—
778C23—1064no—
779C23#1313326314yes—
780C23C24×D5314yes—
781C23C24×D5312yes—
782C23C24×D5311yescharacteristic
783Q8—28no—
784Q8—1068no—
785Q8—2128no—
786Q8—21216no—
787Q8—2128no—
788Q8—21216no—
789D4—216no—
790D4—28no—
791D4—10616no—
792D4—1068no—
793D4—21216no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—28no—
803C2×C4—216no—
804C2×C4—28no—
805C2×C4—534no—
806C2×C4—534no—
807C2×C4—538no—
808C2×C4—534no—
809C2×C4—538no—
810C2×C4—1068no—
811C2×C4—1068no—
812C2×C4—10632no—
813C2×C4—1064no—
814C2×C4—1064no—
815C2×C4—1064no—
816C2×C4—10616no—
817C2×C4—21216no—
818C2×C4—21216no—
819C2×C4#1313326414yes—
820C2×C4#1313326414yes—
821C2×C4C24×D5314yes—
822C2×C4C24×D5314yes—
823C2×C4C24×D5312yes—
824C2×C4C24×D5312yes—
825C2×C4C24×D5312yes—
826C2×C4C24×D5312yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—28no—
831C22—22no—
832C22—22no—
833C22—24no—
834C22—24no—
835C22—24no—
836C22—48no—
837C22—1064no—
838C22—1064no—
839C22—1064no—
840C22—2128no—
841C22C2×#1313326314yes—
842C22C2×#1313326312yes—
843C22C2×#1313326412yes—
844C22C2×#1313326412yes—
845C22C25×D5311yescharacteristic
846C4—22no—
847C4—22no—
848C4—24no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1068no—
854C4—1068no—
855C4—1064no—
856C4—1064no—
857C4—1064no—
858C4C2×#1313326414yes—
859C4C2×#1313326414yes—
860C2—24no—
861C2—44no—
862C2—2124no—
863C2#2028905514yesdirect product factor
864C2C22×#1313326311yescharacteristic
865C2C22×#1313326411yescharacteristic
866C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#529C2
socleC23×C53C25
hypercenterC2×#529D53
hypocenterC53C2×#3544
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #20289055C2direct (N × H)
2. C2×#16811375C2semidirect
3. C2×Q8×Dic106C2semidirect
4. C2×#16811338C2semidirect
5. C2×#16811333C2semidirect
6. C2×#16811330C2semidirect
7. C2×#16811315C2semidirect
8. C2×#16811313C2semidirect
9. C2×#16811277C2semidirect
10. C2×#16811273C2semidirect
11. C2×#16811253C2semidirect
12. C2×#16811251C2semidirect
13. C2×#16811244C2semidirect
14. C2×#16811242C2semidirect
15. C2×#16811195C2semidirect
16. C22×#13133217C2semidirect
17. C2×#16811157C2semidirect
18. C2×C53×#529C2semidirect
21. #16811375C22semidirect
22. Q8×Dic106C22semidirect
23. #16811338C22semidirect
24. #16811333C22semidirect
25. #16811330C22semidirect
26. #16811315C22semidirect
27. #16811313C22semidirect
28. #16811277C22semidirect
29. #16811273C22semidirect
30. #16811253C22semidirect
31. #16811251C22semidirect
32. #16811244C22semidirect
33. #16811242C22semidirect
34. #16811195C22semidirect
41. C2×#13133217C22semidirect
45. #16811157C22semidirect
89. C53×#529C22semidirect
444. C2×#529D53semidirect
447. C2×C53#3544semidirect
479. #529C2×D53semidirect
534. C53C2×#3544semidirect
863. C2#20289055direct (N × H)

Maximal subgroups

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

subgroupindex
#202890552
C2×#168113752
C2×Q8×Dic1062
C2×#168113382
C2×#168113332
C2×#168113302
C2×#168113152
C2×#168113132
C2×#168112772
C2×#168112732
C2×#168112532
C2×#168112512
C2×#168112442
C2×#168112422
C2×#168111952
C22×#131332172
C2×#168111572
C2×C53×#5292
C2×#354453