Finite Group Databasebeta

← C2×#20289145 #28291704

Subgroups — C2×#20289145 #28291704

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289145C2132yesmaximal, direct product factor
2C2×#16811375C214yesmaximal, complemented
3C2×#16811352C211yesmaximal, characteristic, complemented
4C2×#16811331C212yesmaximal, complemented
5C2×#16811317C212yesmaximal, complemented
6C2×Q8×D212C212yesmaximal, complemented
7C2×#16811288C211yesmaximal, characteristic, complemented
8C2×#16811281C212yesmaximal, complemented
9C2×#16811277C211yesmaximal, characteristic, complemented
10C2×#16811251C212yesmaximal, complemented
11C2×#16811246C212yesmaximal, complemented
12C2×#16811231C212yesmaximal, complemented
13C2×#16811214C214yesmaximal, complemented
14C2×#16811193C212yesmaximal, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811160C211yesmaximal, characteristic, complemented
17C2×#16811155C211yesmaximal, characteristic, complemented
18C2×C53×#556C211yesmaximal, characteristic, complemented
19C22×#11719947C2212yes—
20C22×Q8×D53C2212yes—
21C22×Q8×D53C2212yes—
22#16811375C22164yescomplemented
23#16811352C22116yescomplemented
24#16811331C22132yescomplemented
25#16811317C22132yescomplemented
26Q8×D212C22132yescomplemented
27#16811288C22116yescomplemented
28#16811281C22132yescomplemented
29#16811277C22116yescomplemented
30#16811251C22132yescomplemented
31#16811246C22132yescomplemented
32#16811231C22132yescomplemented
33#16811214C22164yescomplemented
34#16811193C22132yescomplemented
35C2×#13133217C2212yes—
36C2×#13133217C2211yescharacteristic
37C2×#13133217C2214yes—
38C2×#13133216C2212yes—
39C2×#13133216C2212yes—
40C2×#13133216C2212yes—
41C2×#13133215C2212yes—
42C4⋊Q8×D53C22116yescomplemented
43#16811160C22116yescomplemented
44#16811155C22116yescomplemented
45C2×#13133212C2214yes—
46C2×#13133212C2212yes—
47C2×#13133211C2214yes—
48C2×#13133210C2212yes—
49C2×#13133209C2214yes—
50C2×#13133208C2214yes—
51C2×#13133208C2212yes—
52C2×#13133208C2211yescharacteristic
53C2×#13133208C2211yescharacteristic
54C2×#13133207C2214yes—
55C2×#13133206C2211yescharacteristic
56C2×#13133204C2211yescharacteristic
57C2×#13133203C2214yes—
58C2×#13133202C2212yes—
59C2×#13133201C2214yes—
60C2×#13133199C2214yes—
61C2×#13133199C2214yes—
62C2×#13133199C2212yes—
63C2×#13133197C2214yes—
64C2×#13133197C2212yes—
65C2×#13133197C2214yes—
66C2×#13133197C2211yescharacteristic
67C2×#13133195C2214yes—
68C2×#13133194C2214yes—
69C2×#13133194C2214yes—
70C2×#13133194C2214yes—
71C2×#13133193C2212yes—
72C2×#13133193C2211yescharacteristic
73C2×#13133192C2211yescharacteristic
74C2×#13133191C2212yes—
75C2×#13133190C2214yes—
76C2×#13133188C2211yescharacteristic
77C2×Q8×Dic53C2212yes—
78C2×C4×Dic106C2212yes—
79C2×C4×Dic106C2211yescharacteristic
80C2×C4×D212C2214yes—
81C2×C4×D212C2211yescharacteristic
82C2×C4×D212C2212yes—
83C2×#13133179C2212yes—
84C2×C4×C22⋊D53C2212yes—
85C2×#13133177C2214yes—
86C2×#13133176C2212yes—
87C2×#13133174C2212yes—
88C22×C4⋊Dic53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C2×C4⋊C4×D53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#556C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#126×C53C2214yes—
95C2×#124×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2212yes—
99C2×C4×D4×C53C2211yescharacteristic
100C2×#117×C53C2212yes—
101C2×#11719947—48no—
102C2×#11719947C23116yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2312yes—
105C22×Dic106C2314yes—
106C22×Dic106C2314yes—
107C2×Q8×D53—48no—
108C2×Q8×D53—48no—
109C2×Q8×D53C23116yes—
110C2×Q8×D53C23116yes—
111C22×D212C2311yescharacteristic
112C22×D212C2312yes—
113C22×C22⋊D53C2312yes—
114C22×C22⋊D53C2314yes—
115C23×Dic53C2314yes—
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2311yescharacteristic
119C22×C4×D53C2312yes—
120C22×C4×D53C2314yes—
121C22×C4×D53C2314yes—
122#13133217C2318yes—
123#13133217C23116yes—
124#13133217C23132yes—
125#13133216C23116yes—
126#13133216C23116yes—
127#13133216C23116yes—
128#13133215C23116yes—
129#13133212C23116yes—
130#13133212C23132yes—
131#13133211C23132yes—
132#13133210C23116yes—
133#13133209C23132yes—
134#13133208C23116yes—
135#13133208C23132yes—
136#13133208C2318yes—
137#13133208C2318yes—
138#13133207C23132yes—
139#13133206C2318yes—
140#13133204C2318yes—
141#13133203C23132yes—
142#13133202C23116yes—
143#13133201C23132yes—
144#13133199C23132yes—
145#13133199C23116yes—
146#13133199C23132yes—
147#13133197C23116yes—
148#13133197C2318yes—
149#13133197C23132yes—
150#13133197C23132yes—
151#13133195C23132yes—
152#13133194C23132yes—
153#13133194C23132yes—
154#13133194C23132yes—
155#13133193C23116yes—
156#13133193C2318yes—
157#13133192C2318yes—
158#13133191C23116yes—
159#13133190C23132yes—
160#13133188C2318yes—
161Q8×Dic53C23116yes—
162C4×Dic106C23116yes—
163C4×Dic106C2318yes—
164C4×D212C2318yes—
165C4×D212C23116yes—
166C4×D212C23132yes—
167#13133179C23116yes—
168C4×C22⋊D53C23116yes—
169#13133177C23132yes—
170#13133176C23116yes—
171#13133174C23116yes—
172C2×C4⋊Dic53C23116yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2314yes—
177C2×C4⋊Dic53C2312yes—
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2312yes—
180C2×C4⋊Dic53C2314yes—
181C2×C4⋊Dic53C2311yescharacteristic
182C2×C4⋊Dic53C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2314yes—
188C2×#11719919C2312yes—
189C2×#11719919C2314yes—
190C2×#11719919C2312yes—
191C4⋊C4×D53C23116yes—
192C4⋊C4×D53C23116yes—
193C2×C22⋊Dic53C2312yes—
194C2×C22⋊Dic53C2312yes—
195C2×C22⋊Dic53C2312yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×#11719921C2312yes—
200C2×#11719921C2314yes—
201C2×#11719921C2314yes—
202C2×#11719921C2312yes—
203C2×#11719921C2312yes—
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2311yescharacteristic
206C2×C4×Dic53C2311yescharacteristic
207C2×C4×Dic53C2312yes—
208C2×C4×Dic53C2314yes—
209C42×D53C2318yes—
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C22×D4×C53C2311yescharacteristic
213C23×C4×C53C2312yes—
214C4⋊Q8×C53C2318yes—
215#126×C53C23132yes—
216#124×C53C23116yes—
217C22⋊Q8×C53C23116yes—
218C4×Q8×C53C23116yes—
219C4×Q8×C53C2318yes—
220C4×D4×C53C2318yes—
221#117×C53C23116yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2312yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2314yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C22⋊C4×C53C2314yes—
229C2×C22⋊C4×C53C2312yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C42×C53C2314yes—
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C23×D53C2412yes—
236C23×D53C2411yescharacteristic
237C2×Q8×C53—28no—
238C2×Q8×C53—24no—
239C2×Q8×C53C2414yes—
240C2×Q8×C53C2418yes—
241C2×D4×C53—24no—
242C2×D4×C53C2414yes—
243C22×C4×C53—28no—
244C22×C4×C53C2412yes—
245C22×C4×C53C2412yes—
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2412yes—
248C22×C4×C53C2414yes—
249C22×C4×C53C2418yes—
250C22×C4×C53C2411yescharacteristic
251C22×C4×C53C2411yescharacteristic
252C2×C22⋊D53—28no—
253C2×C22⋊D53—48no—
254C2×C22⋊D53C2418yes—
255C2×C22⋊D53C24116yes—
256C22×Dic53—48no—
257C22×Dic53C2412yes—
258C22×Dic53C2411yescharacteristic
259C22×Dic53C2411yescharacteristic
260C22×Dic53C2411yescharacteristic
261C22×Dic53C2412yes—
262C22×Dic53C2414yes—
263C22×Dic53C2412yes—
264C22×Dic53C24116yes—
265Q8×D53—432no—
266Q8×D53—432no—
267#11719947—432no—
268C2×D212—28no—
269C2×D212—24no—
270C2×D212C2414yes—
271C2×D212C2418yes—
272C2×C4×D53—24no—
273C2×C4×D53—24no—
274C2×C4×D53—28no—
275C2×C4×D53—24no—
276C2×C4×D53—48no—
277C2×C4×D53—48no—
278C2×C4×D53C2414yes—
279C2×C4×D53C2414yes—
280C2×C4×D53C2414yes—
281C2×C4×D53C2418yes—
282C2×C4×D53C24116yes—
283C2×C4×D53C24116yes—
284C2×Dic106—24no—
285C2×Dic106—28no—
286C2×Dic106—48no—
287C2×Dic106—48no—
288C2×Dic106C2414yes—
289C2×Dic106C2418yes—
290C2×Dic106C24116yes—
291C2×Dic106C24116yes—
292C4⋊C4×C53C2414yes—
293C4⋊C4×C53C2418yes—
294C4⋊C4×C53C2414yes—
295C4⋊C4×C53C24116yes—
296C4⋊C4×C53C2418yes—
297C4⋊C4×C53C2418yes—
298C22⋊C4×C53C24116yes—
299C22⋊C4×C53C2418yes—
300C22⋊C4×C53C24116yes—
301C42×C53C24116yes—
302C42×C53C2414yes—
303C42×C53C2418yes—
304C22⋊Dic53C2418yes—
305C22⋊Dic53C2418yes—
306C22⋊Dic53C2418yes—
307#11719921C2418yes—
308#11719921C2418yes—
309#11719921C2418yes—
310#11719921C2418yes—
311#11719921C24116yes—
312#11719921C24116yes—
313#11719921C2418yes—
314#11719921C2418yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C2418yes—
317C4⋊Dic53C2414yes—
318C4⋊Dic53C24116yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C2418yes—
321C4⋊Dic53C2418yes—
322C4⋊Dic53C24116yes—
323C4⋊Dic53C2414yes—
324C4⋊Dic53C24116yes—
325#11719919C24116yes—
326#11719919C24116yes—
327#11719919C2418yes—
328#11719919C2418yes—
329#11719919C24116yes—
330#11719919C2418yes—
331#11719919C24116yes—
332#11719919C2418yes—
333C4×Dic53C2414yes—
334C4×Dic53C2414yes—
335C4×Dic53C2414yes—
336C4×Dic53C2418yes—
337C4×Dic53C24116yes—
338C23×C53—24no—
339C23×C53—24no—
340C23×C53—24no—
341C23×C53C2514yes—
342C23×C53C2511yescharacteristic
343C22×D53—22no—
344C22×D53—22no—
345C22×D53—24no—
346C22×D53—24no—
347C22×D53—24no—
348C22×D532−1+414yes—
349C22×D53C2514yes—
350C22×D53C2512yes—
351Q8×C53—216no—
352Q8×C53—28no—
353D4×C53—28no—
354C2×C4×C53—28no—
355C2×C4×C53—22no—
356C2×C4×C53—24no—
357C2×C4×C53—24no—
358C2×C4×C53—24no—
359C2×C4×C53—216no—
360C2×C4×C53H(5,𝔽2)14yes—
361C2×C4×C532−1+414yes—
362C2×C4×C53C2518yes—
363C2×C4×C53C2512yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2514yes—
367C2×C4×C53C2512yes—
368C2×C4×C53C2512yes—
369C22⋊D53—216no—
370C22⋊D53—416no—
371C2×Dic53—24no—
372C2×Dic53—28no—
373C2×Dic53—22no—
374C2×Dic53—24no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—24no—
378C2×Dic53—416no—
379C2×Dic53C2512yes—
380C2×Dic53C2514yes—
381C2×Dic53C2514yes—
382C2×Dic53C2518yes—
383C2×Dic53C2512yes—
384C2×Dic53C2512yes—
385C2×Dic53C2514yes—
386D212—216no—
387D212—28no—
388C4×D53—28no—
389C4×D53—216no—
390C4×D53—28no—
391C4×D53—28no—
392C4×D53—416no—
393C4×D53—416no—
394Dic106—216no—
395Dic106—28no—
396Dic106—416no—
397Dic106—416no—
398C2×#3552—531nomaximal, Sylow
399C22×C53—24no—
400C22×C53—24no—
401C22×C53—24no—
402C22×C53—48no—
403C22×C53C2×H(5,𝔽2)12yes—
404C22×C53C2×2−1+412yes—
405C22×C53C2×2−1+412yes—
406C22×C53C2611yescharacteristic
407C2×D53—22no—
408C2×D53—22no—
409C2×D53—28no—
410C2×D53—24no—
411C2×D53—24no—
412C2×D53—24no—
413C2×D53—48no—
414C2×D53C2×2−1+414yes—
415C4×C53—28no—
416C4×C53—22no—
417C4×C53—24no—
418C4×C53—24no—
419C4×C53—24no—
420C4×C53C2×H(5,𝔽2)14yes—
421C4×C53C2×2−1+414yes—
422Dic53—24no—
423Dic53—28no—
424Dic53—22no—
425Dic53—24no—
426Dic53—22no—
427Dic53—22no—
428Dic53—24no—
429#3552—5332no—
430C2×#563—534no—
431C2×#557—531no—
432C2×#556D5311yescharacteristic, complemented
433C2×#554—532no—
434C2×#553—532no—
435C2×D4×Q8—531no—
436C2×D4×Q8—532no—
437C2×#548—532no—
438C2×#547—531no—
439C2×#544—532no—
440C2×#542—532no—
441C2×#541—532no—
442C2×#539—534no—
443C2×#536—532no—
444C22×C4⋊Q8—531no—
445C2×#529—531no—
446C2×#529—531no—
447C2×C53—44no—
448C2×C53#355214yescomplemented
449C2×C53C22×H(5,𝔽2)11yescharacteristic
450C2×C53C22×2−1+411yescharacteristic
451C2×C53C22×2−1+411yescharacteristic
452D53—24no—
453D53—44no—
454C22×#41—532no—
455C23×Q8—532no—
456C23×Q8—532no—
457#563—5364no—
458#557—5316no—
459#556C2×D53116yescomplemented
460#554—5332no—
461#553—5332no—
462D4×Q8—5316no—
463D4×Q8—5332no—
464#548—5332no—
465#547—5316no—
466#544—5332no—
467#542—5332no—
468#541—5332no—
469#539—5364no—
470#536—5332no—
471C2×C4⋊Q8—532no—
472C2×C4⋊Q8—5316no—
473C2×C4⋊Q8—532no—
474C2×C4⋊Q8—532no—
475C2×C4⋊Q8—532no—
476C2×C4⋊Q8—531no—
477C2×C4⋊Q8—532no—
478C2×C4⋊Q8—534no—
479C2×C4⋊Q8C2×D5311yescharacteristic
480#529—5316no—
481#529—5316no—
482C2×#126—532no—
483C2×#126—534no—
484C2×#126—532no—
485C2×#126—534no—
486C2×#126C2×D5314yes—
487C2×#125—531no—
488C2×#125—531no—
489C2×#125—534no—
490C2×#125—534no—
491C2×#125—532no—
492C2×#125—534no—
493C2×#124—531no—
494C2×#124—531no—
495C2×#124—534no—
496C2×#124C2×D5312yes—
497C2×#123—532no—
498C2×#123—532no—
499C2×#123—534no—
500C2×#123—534no—
501C2×#123—534no—
502C2×C22⋊Q8—531no—
503C2×C22⋊Q8—532no—
504C2×C22⋊Q8—531no—
505C2×C22⋊Q8—534no—
506C2×C22⋊Q8—534no—
507C2×C22⋊Q8—532no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—534no—
511C2×C22⋊Q8—534no—
512C2×C22⋊Q8C2×D5312yes—
513C2×#121—531no—
514C2×#121—532no—
515C2×#121—531no—
516C2×#121—534no—
517C2×C4×Q8—532no—
518C2×C4×Q8—531no—
519C2×C4×Q8—532no—
520C2×C4×Q8C2×D5311yescharacteristic
521C2×C4×Q8C2×D5312yes—
522C2×C4×D4—532no—
523C2×C4×D4—532no—
524C2×C4×D4—534no—
525C2×C4×D4—531no—
526C2×C4×D4—532no—
527C2×C4×D4—534no—
528C2×C4×D4C2×D5311yescharacteristic
529C2×#117—532no—
530C2×#117—532no—
531C2×#117C2×D5312yes—
532C22×C4⋊C4—532no—
533C22×C4⋊C4—532no—
534C22×C4⋊C4—532no—
535C22×C42—531no—
536C53C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—5316no—
538C2×#41—2128no—
539C22×Q8—5316no—
540C22×Q8—5316no—
541C22×Q8—531no—
542C22×Q8—532no—
543C22×Q8—534no—
544C22×Q8—534no—
545C22×Q8—2128no—
546C22×Q8—2128no—
547C22×Q8C22×D5311yescharacteristic
548C22×Q8C22×D5312yes—
549C22×D4—532no—
550C22×D4—534no—
551C22×D4—532no—
552C22×D4—531no—
553C22×D4C22×D5311yescharacteristic
554C23×C4—534no—
555C23×C4—531no—
556C23×C4—531no—
557C23×C4—532no—
558C23×C4—531no—
559C23×C4—534no—
560C23×C4—534no—
561C23×C4C22×D5312yes—
562C4⋊Q8—5316no—
563C4⋊Q8—5316no—
564C4⋊Q8—5316no—
565C4⋊Q8—5316no—
566C4⋊Q8—538no—
567C4⋊Q8—5316no—
568C4⋊Q8—5332no—
569C4⋊Q8C22×D5318yes—
570#126—5316no—
571#126—5332no—
572#126—5316no—
573#126—5332no—
574#126C22×D53132yes—
575#125—538no—
576#125—538no—
577#125—5332no—
578#125—5332no—
579#125—5316no—
580#125—5332no—
581#124—538no—
582#124—538no—
583#124—5332no—
584#124C22×D53116yes—
585#123—5316no—
586#123—5316no—
587#123—5332no—
588#123—5332no—
589#123—5332no—
590C22⋊Q8—538no—
591C22⋊Q8—5316no—
592C22⋊Q8—538no—
593C22⋊Q8—5332no—
594C22⋊Q8—5332no—
595C22⋊Q8—5316no—
596C22⋊Q8—5332no—
597C22⋊Q8—5332no—
598C22⋊Q8—5332no—
599C22⋊Q8—5332no—
600C22⋊Q8C22×D53116yes—
601#121—538no—
602#121—5316no—
603#121—538no—
604#121—5332no—
605C4×Q8—5316no—
606C4×Q8—538no—
607C4×Q8—5316no—
608C4×Q8C22×D5318yes—
609C4×Q8C22×D53116yes—
610C4×D4—5316no—
611C4×D4—5316no—
612C4×D4—5332no—
613C4×D4—538no—
614C4×D4—5316no—
615C4×D4—5332no—
616C4×D4C22×D5318yes—
617#117—5316no—
618#117—5316no—
619#117C22×D53116yes—
620C2×C4⋊C4—531no—
621C2×C4⋊C4—532no—
622C2×C4⋊C4—534no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—5316no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—534no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—531no—
636C2×C4⋊C4—534no—
637C2×C4⋊C4—534no—
638C2×C4⋊C4—532no—
639C2×C4⋊C4—5316no—
640C2×C4⋊C4—5316no—
641C2×C4⋊C4C22×D5312yes—
642C2×C4⋊C4C22×D5312yes—
643C2×C4⋊C4C22×D5311yescharacteristic
644C2×C4⋊C4C22×D5311yescharacteristic
645C2×C4⋊C4C22×D5314yes—
646C2×C4⋊C4C22×D5312yes—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—532no—
652C2×C22⋊C4—532no—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—534no—
655C2×C22⋊C4—534no—
656C2×C22⋊C4—532no—
657C2×C22⋊C4—532no—
658C2×C22⋊C4C22×D5314yes—
659C2×C22⋊C4C22×D5314yes—
660C2×C22⋊C4C22×D5312yes—
661C2×C42—531no—
662C2×C42—531no—
663C2×C42—532no—
664C2×C42—534no—
665C2×C42—531no—
666C2×C42—538no—
667C2×C42C22×D5312yes—
668C2×C42C22×D5314yes—
669C2×C42C22×D5311yescharacteristic
670C24—531no—
671C24—532no—
672C24C23×D5312yes—
673#41—21232no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—534no—
677C2×Q8—538no—
678C2×Q8—5316no—
679C2×Q8—5316no—
680C2×Q8—1064no—
681C2×Q8—1068no—
682C2×Q8—2128no—
683C2×Q8—2128no—
684C2×Q8—21232no—
685C2×Q8—21232no—
686C2×Q8C23×D5314yes—
687C2×Q8C23×D5318yes—
688C2×D4—24no—
689C2×D4—538no—
690C2×D4—5316no—
691C2×D4—538no—
692C2×D4—534no—
693C2×D4—1068no—
694C2×D4—1068no—
695C2×D4—1064no—
696C2×D4—2128no—
697C2×D4C23×D5314yes—
698C22×C4—28no—
699C22×C4—532no—
700C22×C4—531no—
701C22×C4—531no—
702C22×C4—531no—
703C22×C4—532no—
704C22×C4—534no—
705C22×C4—532no—
706C22×C4—5316no—
707C22×C4—534no—
708C22×C4—534no—
709C22×C4—534no—
710C22×C4—538no—
711C22×C4—5316no—
712C22×C4—5316no—
713C22×C4—1064no—
714C22×C4—1064no—
715C22×C4—1068no—
716C22×C4—1064no—
717C22×C4—2128no—
718C22×C4—2128no—
719C22×C4—2128no—
720C22×C4C23×D5318yes—
721C22×C4C23×D5312yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5312yes—
724C22×C4C23×D5312yes—
725C22×C4C23×D5314yes—
726C22×C4C23×D5311yescharacteristic
727C22×C4C23×D5311yescharacteristic
728C4⋊C4—534no—
729C4⋊C4—538no—
730C4⋊C4—5316no—
731C4⋊C4—5316no—
732C4⋊C4—5316no—
733C4⋊C4—538no—
734C4⋊C4—538no—
735C4⋊C4—538no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—5316no—
739C4⋊C4—538no—
740C4⋊C4—5316no—
741C4⋊C4—538no—
742C4⋊C4—534no—
743C4⋊C4—5316no—
744C4⋊C4—5316no—
745C4⋊C4—538no—
746C4⋊C4C23×D5318yes—
747C4⋊C4C23×D5318yes—
748C4⋊C4C23×D5314yes—
749C4⋊C4C23×D5314yes—
750C4⋊C4C23×D53116yes—
751C4⋊C4C23×D5318yes—
752C22⋊C4—538no—
753C22⋊C4—538no—
754C22⋊C4—538no—
755C22⋊C4—538no—
756C22⋊C4—538no—
757C22⋊C4—538no—
758C22⋊C4—538no—
759C22⋊C4—5316no—
760C22⋊C4—5316no—
761C22⋊C4—538no—
762C22⋊C4—538no—
763C22⋊C4C23×D53116yes—
764C22⋊C4C23×D53116yes—
765C22⋊C4C23×D5318yes—
766C42—534no—
767C42—534no—
768C42—534no—
769C42—538no—
770C42—5316no—
771C42C23×D5314yes—
772C42C23×D5318yes—
773C42C23×D53116yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—534no—
778C23—532no—
779C23—534no—
780C23—1062no—
781C23—1062no—
782C23—1064no—
783C23—1064no—
784C23—1064no—
785C23C24×D5314yes—
786C23C24×D5311yescharacteristic
787Q8—216no—
788Q8—28no—
789Q8—1068no—
790Q8—10616no—
791Q8—21216no—
792Q8—21216no—
793D4—28no—
794D4—10616no—
795D4—10616no—
796D4—1068no—
797D4—21216no—
798C2×C4—28no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—534no—
805C2×C4—532no—
806C2×C4—532no—
807C2×C4—532no—
808C2×C4—534no—
809C2×C4—538no—
810C2×C4—534no—
811C2×C4—1068no—
812C2×C4—1064no—
813C2×C4—1062no—
814C2×C4—1068no—
815C2×C4—1064no—
816C2×C4—1062no—
817C2×C4—1064no—
818C2×C4—1062no—
819C2×C4—1068no—
820C2×C4—10616no—
821C2×C4—1068no—
822C2×C4—21216no—
823C2×C4—21216no—
824C2×C4—21216no—
825C2×C4#1313326314yes—
826C2×C4#1313326414yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5314yes—
830C2×C4C24×D5314yes—
831C2×C4C24×D5318yes—
832C2×C4C24×D5312yes—
833C2×C4C24×D5312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—534no—
839C22—1068no—
840C22—1062no—
841C22—1062no—
842C22—1064no—
843C22—1064no—
844C22—1064no—
845C22—2128no—
846C22C2×#1313326312yes—
847C222−1+4×D5312yes—
848C22C2×#1313326412yes—
849C22C25×D5311yescharacteristic
850C4—28no—
851C4—22no—
852C4—24no—
853C4—24no—
854C4—24no—
855C4—1064no—
856C4—1062no—
857C4—1068no—
858C4—1064no—
859C4—1062no—
860C4—1064no—
861C4—1062no—
862C4C2×#1313326314yes—
863C4C2×#1313326414yes—
864C2—44no—
865C2—1064no—
866C2—2124no—
867C2#2028914514yesdirect product factor
868C2C22×#1313326311yescharacteristic
869C2C2×2−1+4×D5311yescharacteristic
870C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#556C2
socleC23×C53C25
hypercenterC2×#556D53
hypocenterC53C2×#3552
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20289145C2direct (N × H)
2. C2×#16811375C2semidirect
3. C2×#16811352C2semidirect
4. C2×#16811331C2semidirect
5. C2×#16811317C2semidirect
6. C2×Q8×D212C2semidirect
7. C2×#16811288C2semidirect
8. C2×#16811281C2semidirect
9. C2×#16811277C2semidirect
10. C2×#16811251C2semidirect
11. C2×#16811246C2semidirect
12. C2×#16811231C2semidirect
13. C2×#16811214C2semidirect
14. C2×#16811193C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
16. C2×#16811160C2semidirect
17. C2×#16811155C2semidirect
18. C2×C53×#556C2semidirect
22. #16811375C22semidirect
23. #16811352C22semidirect
24. #16811331C22semidirect
25. #16811317C22semidirect
26. Q8×D212C22semidirect
27. #16811288C22semidirect
28. #16811281C22semidirect
29. #16811277C22semidirect
30. #16811251C22semidirect
31. #16811246C22semidirect
32. #16811231C22semidirect
33. #16811214C22semidirect
34. #16811193C22semidirect
42. C4⋊Q8×D53C22semidirect
43. #16811160C22semidirect
44. #16811155C22semidirect
92. C53×#556C22semidirect
432. C2×#556D53semidirect
448. C2×C53#3552semidirect
459. #556C2×D53semidirect
536. C53C2×#3552semidirect
867. C2#20289145direct (N × H)

Maximal subgroups

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

subgroupindex
#202891452
C2×#168113752
C2×#168113522
C2×#168113312
C2×#168113172
C2×Q8×D2122
C2×#168112882
C2×#168112812
C2×#168112772
C2×#168112512
C2×#168112462
C2×#168112312
C2×#168112142
C2×#168111932
C2×C4⋊Q8×D532
C2×#168111602
C2×#168111552
C2×C53×#5562
C2×#355253