Finite Group Databasebeta

← C2×#20289186 #28291721

Subgroups — C2×#20289186 #28291721

Order 13568.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289186C2132yesmaximal, direct product factor
2C2×#16811369C214yesmaximal, complemented
3C2×#16811358C211yesmaximal, characteristic, complemented
4C2×#16811358C212yesmaximal, complemented
5C2×#16811351C211yesmaximal, characteristic, complemented
6C2×#16811333C212yesmaximal, complemented
7C2×#16811295C211yesmaximal, characteristic, complemented
8C2×Q8×D212C211yesmaximal, characteristic, complemented
9C2×#16811283C212yesmaximal, complemented
10C2×#16811275C212yesmaximal, complemented
11C2×#16811247C212yesmaximal, complemented
12C2×#16811244C212yesmaximal, complemented
13C2×#16811228C212yesmaximal, complemented
14C2×#16811221C214yesmaximal, complemented
15C2×#16811198C212yesmaximal, complemented
16C2×#16811173C211yesmaximal, characteristic, complemented
17C2×#16811157C211yesmaximal, characteristic, complemented
18C2×C53×#533C211yesmaximal, characteristic, complemented
19C22×#11719949C2212yes—
20C22×#11719945C2212yes—
21C22×Q8×D53C2212yes—
22#16811369C22164yescomplemented
23#16811358C22116yescomplemented
24#16811358C22132yescomplemented
25#16811351C22116yescomplemented
26#16811333C22132yescomplemented
27#16811295C22116yescomplemented
28Q8×D212C22116yescomplemented
29#16811283C22132yescomplemented
30#16811275C22132yescomplemented
31#16811247C22132yescomplemented
32#16811244C22132yescomplemented
33#16811228C22132yescomplemented
34#16811221C22164yescomplemented
35#16811198C22132yescomplemented
36#16811173C22116yescomplemented
37C2×#13133217C2211yescharacteristic
38C2×#13133217C2212yes—
39C2×#13133215C2212yes—
40C2×#13133214C2212yes—
41C2×#13133214C2211yescharacteristic
42#16811157C22116yescomplemented
43C2×#13133212C2214yes—
44C2×#13133211C2212yes—
45C2×#13133209C2212yes—
46C2×#13133209C2211yescharacteristic
47C2×#13133207C2214yes—
48C2×#13133206C2212yes—
49C2×#13133206C2214yes—
50C2×#13133205C2212yes—
51C2×#13133205C2212yes—
52C2×#13133205C2211yescharacteristic
53C2×#13133203C2214yes—
54C2×#13133202C2214yes—
55C2×#13133202C2214yes—
56C2×#13133202C2214yes—
57C2×#13133202C2214yes—
58C2×#13133202C2214yes—
59C2×#13133200C2212yes—
60C2×#13133199C2214yes—
61C2×#13133197C2214yes—
62C2×#13133197C2212yes—
63C2×#13133196C2211yescharacteristic
64C2×#13133195C2214yes—
65C2×#13133195C2214yes—
66C2×#13133195C2214yes—
67C2×#13133193C2214yes—
68C2×#13133192C2214yes—
69C2×#13133192C2212yes—
70C2×#13133191C2212yes—
71C2×#13133191C2211yescharacteristic
72C2×#13133191C2212yes—
73C2×#13133190C2214yes—
74C2×#13133190C2214yes—
75C2×C4×Dic106C2212yes—
76C2×C4×Dic106C2211yescharacteristic
77C2×#13133182C2212yes—
78C2×C4×D212C2212yes—
79C2×C4×D212C2212yes—
80C2×C4×D212C2212yes—
81C2×C4×D212C2212yes—
82C2×C4×D212C2212yes—
83C2×C4×D212C2211yescharacteristic
84C2×#13133179C2214yes—
85C2×#13133179C2212yes—
86C2×C4×C22⋊D53C2212yes—
87C2×#13133174C2212yes—
88C2×C4⋊C4×D53C2214yes—
89C53×#533C22116yescomplemented
90C2×C4⋊Q8×C53C2211yescharacteristic
91C2×C4⋊Q8×C53C2211yescharacteristic
92C2×#125×C53C2212yes—
93C2×C22⋊Q8×C53C2212yes—
94C2×C22⋊Q8×C53C2211yescharacteristic
95C2×C22⋊Q8×C53C2211yescharacteristic
96C2×C4×Q8×C53C2211yescharacteristic
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2212yes—
99C2×#117×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719949—48no—
102C2×#11719949C23116yes—
103C2×#11719945—48no—
104C2×#11719945C23116yes—
105C22×Dic106C2312yes—
106C22×Dic106C2311yescharacteristic
107C22×Dic106C2314yes—
108C2×Q8×D53—48no—
109C2×Q8×D53C23116yes—
110C22×D212C2312yes—
111C22×D212C2311yescharacteristic
112C22×D212C2312yes—
113C22×D212C2314yes—
114C22×D212C2312yes—
115C22×D212C2314yes—
116C22×C22⋊D53C2312yes—
117C22×C22⋊D53C2314yes—
118C22×C4×D53C2312yes—
119C22×C4×D53C2314yes—
120C22×C4×D53C2314yes—
121C22×C4×D53C2314yes—
122C22×C4×D53C2314yes—
123#13133217C23116yes—
124#13133217C2318yes—
125#13133215C23116yes—
126#13133214C2318yes—
127#13133214C23116yes—
128#13133212C23132yes—
129#13133211C23116yes—
130#13133209C2318yes—
131#13133209C23116yes—
132#13133207C23132yes—
133#13133206C23116yes—
134#13133206C23132yes—
135#13133205C2318yes—
136#13133205C23116yes—
137#13133205C23116yes—
138#13133203C23132yes—
139#13133202C23132yes—
140#13133202C23132yes—
141#13133202C23132yes—
142#13133202C23132yes—
143#13133202C23132yes—
144#13133200C23116yes—
145#13133199C23132yes—
146#13133197C23116yes—
147#13133197C23132yes—
148#13133196C2318yes—
149#13133195C23132yes—
150#13133195C23132yes—
151#13133195C23132yes—
152#13133193C23132yes—
153#13133192C23116yes—
154#13133192C23132yes—
155#13133191C23116yes—
156#13133191C2318yes—
157#13133191C23116yes—
158#13133190C23132yes—
159#13133190C23132yes—
160C4×Dic106C2318yes—
161C4×Dic106C23116yes—
162#13133182C23116yes—
163C4×D212C2318yes—
164C4×D212C23116yes—
165C4×D212C23116yes—
166C4×D212C23116yes—
167C4×D212C23116yes—
168C4×D212C23116yes—
169#13133179C23116yes—
170#13133179C23132yes—
171C4×C22⋊D53C23116yes—
172#13133174C23116yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2312yes—
178C2×#11719919C2312yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C4⋊C4×D53C23132yes—
186C2×C22⋊Dic53C2312yes—
187C2×#11719921C2312yes—
188C2×#11719921C2312yes—
189C2×#11719921C2312yes—
190C2×#11719921C2314yes—
191C2×#11719921C2314yes—
192C2×#11719921C2314yes—
193C2×#11719921C2314yes—
194C2×#11719921C2314yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×C4×Dic53C2312yes—
199C2×C4×Dic53C2314yes—
200C22×Q8×C53C2311yescharacteristic
201C22×Q8×C53C2311yescharacteristic
202C22×Q8×C53C2312yes—
203C23×C4×C53C2311yescharacteristic
204C23×C4×C53C2311yescharacteristic
205C23×C4×C53C2311yescharacteristic
206C4⋊Q8×C53C2318yes—
207C4⋊Q8×C53C2318yes—
208#125×C53C23116yes—
209C22⋊Q8×C53C2318yes—
210C22⋊Q8×C53C2318yes—
211C22⋊Q8×C53C23116yes—
212C4×Q8×C53C2318yes—
213C4×Q8×C53C2318yes—
214C4×Q8×C53C23116yes—
215#117×C53C23116yes—
216C2×C4⋊C4×C53C2312yes—
217C2×C4⋊C4×C53C2312yes—
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2312yes—
220C2×C4⋊C4×C53C2312yes—
221C2×C4⋊C4×C53C2312yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊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—
233C2×C42×C53C2312yes—
234C24×C53C2411yescharacteristic
235C23×D53C2412yes—
236C23×D53C2414yes—
237C2×Q8×C53—24no—
238C2×Q8×C53—24no—
239C2×Q8×C53—44no—
240C2×Q8×C53C2414yes—
241C2×Q8×C53C2414yes—
242C2×Q8×C53C2418yes—
243C22×C4×C53—24no—
244C22×C4×C53—24no—
245C22×C4×C53—42no—
246C22×C4×C53C2411yescharacteristic
247C22×C4×C53C2411yescharacteristic
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2414yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2412yes—
255C22×C4×C53C2412yes—
256C22×C4×C53C2414yes—
257C22×C4×C53C2411yescharacteristic
258C22×C4×C53C2411yescharacteristic
259C2×C22⋊D53—44no—
260C2×C22⋊D53—48no—
261C2×C22⋊D53C2418yes—
262C2×C22⋊D53C24116yes—
263C22×Dic53C2412yes—
264C22×Dic53C2412yes—
265C22×Dic53C2414yes—
266C22×Dic53C2412yes—
267#11719949—432no—
268Q8×D53—432no—
269#11719945—432no—
270C2×D212—28no—
271C2×D212—24no—
272C2×D212—28no—
273C2×D212—44no—
274C2×D212—48no—
275C2×D212—48no—
276C2×D212C2418yes—
277C2×D212C2414yes—
278C2×D212C2418yes—
279C2×D212C24116yes—
280C2×D212C2418yes—
281C2×D212C24116yes—
282C2×C4×D53—28no—
283C2×C4×D53—48no—
284C2×C4×D53—48no—
285C2×C4×D53—48no—
286C2×C4×D53—48no—
287C2×C4×D53C2418yes—
288C2×C4×D53C24116yes—
289C2×C4×D53C24116yes—
290C2×C4×D53C24116yes—
291C2×C4×D53C24116yes—
292C2×Dic106—28no—
293C2×Dic106—24no—
294C2×Dic106—48no—
295C2×Dic106C2418yes—
296C2×Dic106C2414yes—
297C2×Dic106C24116yes—
298C4⋊C4×C53C2418yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C2418yes—
301C4⋊C4×C53C2418yes—
302C4⋊C4×C53C2418yes—
303C4⋊C4×C53C2418yes—
304C4⋊C4×C53C2414yes—
305C4⋊C4×C53C2414yes—
306C4⋊C4×C53C2418yes—
307C22⋊C4×C53C2418yes—
308C22⋊C4×C53C2418yes—
309C42×C53C2414yes—
310C42×C53C2414yes—
311C42×C53C2414yes—
312C42×C53C2414yes—
313C42×C53C2418yes—
314C42×C53C2418yes—
315C22⋊Dic53C2418yes—
316#11719921C2418yes—
317#11719921C2418yes—
318#11719921C2418yes—
319#11719921C24116yes—
320#11719921C24116yes—
321#11719921C24116yes—
322#11719921C24116yes—
323#11719921C24116yes—
324#11719921C24116yes—
325#11719921C24116yes—
326#11719921C2418yes—
327C4⋊Dic53C24116yes—
328C4⋊Dic53C2414yes—
329C4⋊Dic53C2414yes—
330C4⋊Dic53C2418yes—
331C4⋊Dic53C2418yes—
332#11719919C2418yes—
333#11719919C24116yes—
334#11719919C2418yes—
335#11719919C2418yes—
336#11719919C24116yes—
337#11719919C24116yes—
338#11719919C2418yes—
339C4×Dic53C2418yes—
340C4×Dic53C24116yes—
341C23×C53—22no—
342C23×C53—22no—
343C23×C53—22no—
344C23×C53C2512yes—
345C23×C53C2511yescharacteristic
346C22×D53—24no—
347C22×D53—28no—
348C22×D53—24no—
349C22×D53—28no—
350C22×D53—28no—
351C22×D53—24no—
352C22×D53C2514yes—
353C22×D53C2518yes—
354Q8×C53—28no—
355Q8×C53—28no—
356Q8×C53—48no—
357C2×C4×C53—24no—
358C2×C4×C53—22no—
359C2×C4×C53—24no—
360C2×C4×C53—22no—
361C2×C4×C53—24no—
362C2×C4×C53—22no—
363C2×C4×C53—24no—
364C2×C4×C53—22no—
365C2×C4×C53—28no—
366C2×C4×C53—28no—
367C2×C4×C53—44no—
368C2×C4×C53H(5,𝔽2)14yes—
369C2×C4×C532−1+414yes—
370C2×C4×C53C2514yes—
371C2×C4×C53C2512yes—
372C2×C4×C53C2514yes—
373C2×C4×C53C2514yes—
374C2×C4×C53C2512yes—
375C2×C4×C53C2514yes—
376C2×C4×C53C2512yes—
377C2×C4×C53C2512yes—
378C2×C4×C53C2512yes—
379C2×C4×C53C2512yes—
380C22⋊D53—416no—
381C22⋊D53—48no—
382C2×Dic53—28no—
383C2×Dic53—24no—
384C2×Dic53—24no—
385C2×Dic53—24no—
386C2×Dic53C2514yes—
387C2×Dic53C2518yes—
388C2×Dic53C2514yes—
389C2×Dic53C2514yes—
390D212—216no—
391D212—28no—
392D212—216no—
393D212—48no—
394D212—416no—
395D212—416no—
396C4×D53—216no—
397C4×D53—416no—
398C4×D53—416no—
399C4×D53—416no—
400C4×D53—416no—
401Dic106—216no—
402Dic106—28no—
403Dic106—416no—
404C2×#3554—531nomaximal, Sylow
405C22×C53—22no—
406C22×C53—22no—
407C22×C53—22no—
408C22×C53—44no—
409C22×C53C2×H(5,𝔽2)12yes—
410C22×C53C2×2−1+412yes—
411C22×C53#58512yes—
412C22×C53C2611yescharacteristic
413C2×D53—24no—
414C2×D53—28no—
415C2×D53—24no—
416C2×D53—28no—
417C2×D53—28no—
418C2×D53—24no—
419C2×D53—48no—
420C2×D53—416no—
421C4×C53—24no—
422C4×C53—22no—
423C4×C53—24no—
424C4×C53—22no—
425C4×C53—24no—
426C4×C53—22no—
427C4×C53—24no—
428C4×C53—22no—
429C4×C53C2×H(5,𝔽2)14yes—
430C4×C53C2×2−1+414yes—
431Dic53—28no—
432Dic53—24no—
433Dic53—24no—
434Dic53—24no—
435#3554—5332no—
436C2×#562—534no—
437C2×#559—532no—
438C2×#559—531no—
439C2×#557—531no—
440C2×#554—532no—
441C2×#550—531no—
442C2×D4×Q8—531no—
443C2×#548—532no—
444C2×#547—532no—
445C2×#542—532no—
446C2×#542—532no—
447C2×#540—532no—
448C2×#539—534no—
449C2×#536—532no—
450C2×#533D5311yescharacteristic, complemented
451C2×#532—531no—
452C2×#529—531no—
453C2×C53—42no—
454C2×C53#355414yescomplemented
455C2×C53C22×H(5,𝔽2)11yescharacteristic
456C2×C53C22×2−1+411yescharacteristic
457C2×C53C2×#58511yescharacteristic
458D53—44no—
459D53—48no—
460C22×#41—532no—
461C22×#41—532no—
462C23×Q8—532no—
463#562—5364no—
464#559—5332no—
465#559—5316no—
466#557—5316no—
467#554—5332no—
468#550—5316no—
469D4×Q8—5316no—
470#548—5332no—
471#547—5332no—
472#542—5332no—
473#542—5332no—
474#540—5332no—
475#539—5364no—
476#536—5332no—
477#533C2×D53116yescomplemented
478#532—5316no—
479C2×C4⋊Q8—532no—
480C2×C4⋊Q8—531no—
481C2×C4⋊Q8—532no—
482C2×C4⋊Q8C2×D5311yescharacteristic
483C2×C4⋊Q8C2×D5311yescharacteristic
484C2×#127—531no—
485C2×#127—532no—
486#529—5316no—
487C2×#126—534no—
488C2×#126—532no—
489C2×#125—534no—
490C2×#125—531no—
491C2×#125—532no—
492C2×#125C2×D5312yes—
493C2×#124—532no—
494C2×#124—534no—
495C2×#124—534no—
496C2×#124—531no—
497C2×#124—532no—
498C2×#124—532no—
499C2×#123—532no—
500C2×#123—534no—
501C2×#123—534no—
502C2×#123—534no—
503C2×#123—534no—
504C2×#123—534no—
505C2×#123—534no—
506C2×C22⋊Q8—534no—
507C2×C22⋊Q8—531no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—534no—
511C2×C22⋊Q8—534no—
512C2×C22⋊Q8—532no—
513C2×C22⋊Q8C2×D5311yescharacteristic
514C2×C22⋊Q8C2×D5311yescharacteristic
515C2×C22⋊Q8C2×D5312yes—
516C2×#121—531no—
517C2×#121—532no—
518C2×#121—532no—
519C2×#121—534no—
520C2×#121—532no—
521C2×#121—534no—
522C2×#121—534no—
523C2×C4×Q8—532no—
524C2×C4×Q8—531no—
525C2×C4×Q8—532no—
526C2×C4×Q8C2×D5311yescharacteristic
527C2×C4×Q8C2×D5311yescharacteristic
528C2×C4×Q8C2×D5312yes—
529C2×C4×D4—532no—
530C2×C4×D4—534no—
531C2×C4×D4—532no—
532C2×C4×D4—531no—
533C2×C4×D4—532no—
534C2×C4×D4—532no—
535C2×C4×D4—532no—
536C2×C4×D4—532no—
537C2×C4×D4—532no—
538C2×#117—532no—
539C2×#117C2×D5312yes—
540C22×C4⋊C4—534no—
541C22×C42C2×D5311yescharacteristic
542C53C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—5316no—
544C2×#41—5316no—
545C2×#41—2128no—
546C2×#41—2128no—
547C22×Q8—5316no—
548C22×Q8—531no—
549C22×Q8—532no—
550C22×Q8—534no—
551C22×Q8—2128no—
552C22×Q8C22×D5311yescharacteristic
553C22×Q8C22×D5311yescharacteristic
554C22×Q8C22×D5312yes—
555C22×D4—532no—
556C22×D4—534no—
557C22×D4—531no—
558C22×D4—532no—
559C22×D4—532no—
560C22×D4—532no—
561C22×D4—534no—
562C22×D4—534no—
563C23×C4—532no—
564C23×C4—534no—
565C23×C4—534no—
566C23×C4—534no—
567C23×C4—534no—
568C23×C4C22×D5311yescharacteristic
569C23×C4C22×D5311yescharacteristic
570C23×C4C22×D5311yescharacteristic
571C4⋊Q8—5316no—
572C4⋊Q8—538no—
573C4⋊Q8—5316no—
574C4⋊Q8C22×D5318yes—
575C4⋊Q8C22×D5318yes—
576#127—538no—
577#127—5316no—
578#126—5332no—
579#126—5316no—
580#125—5332no—
581#125—538no—
582#125—5316no—
583#125C22×D53116yes—
584#124—5316no—
585#124—5332no—
586#124—5332no—
587#124—538no—
588#124—5316no—
589#124—5316no—
590#123—5316no—
591#123—5332no—
592#123—5332no—
593#123—5332no—
594#123—5332no—
595#123—5332no—
596#123—5332no—
597C22⋊Q8—5332no—
598C22⋊Q8—538no—
599C22⋊Q8—5332no—
600C22⋊Q8—5332no—
601C22⋊Q8—5332no—
602C22⋊Q8—5332no—
603C22⋊Q8—5316no—
604C22⋊Q8C22×D5318yes—
605C22⋊Q8C22×D5318yes—
606C22⋊Q8C22×D53116yes—
607#121—538no—
608#121—5316no—
609#121—5316no—
610#121—5332no—
611#121—5316no—
612#121—5332no—
613#121—5332no—
614C4×Q8—5316no—
615C4×Q8—538no—
616C4×Q8—5316no—
617C4×Q8C22×D5318yes—
618C4×Q8C22×D5318yes—
619C4×Q8C22×D53116yes—
620C4×D4—5316no—
621C4×D4—5332no—
622C4×D4—5316no—
623C4×D4—538no—
624C4×D4—5316no—
625C4×D4—5316no—
626C4×D4—5316no—
627C4×D4—5316no—
628C4×D4—5316no—
629#117—5316no—
630#117C22×D53116yes—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—531no—
637C2×C4⋊C4—531no—
638C2×C4⋊C4—532no—
639C2×C4⋊C4—532no—
640C2×C4⋊C4—534no—
641C2×C4⋊C4—534no—
642C2×C4⋊C4—532no—
643C2×C4⋊C4—5332no—
644C2×C4⋊C4C22×D5312yes—
645C2×C4⋊C4C22×D5312yes—
646C2×C4⋊C4C22×D5312yes—
647C2×C4⋊C4C22×D5312yes—
648C2×C4⋊C4C22×D5311yescharacteristic
649C2×C4⋊C4C22×D5311yescharacteristic
650C2×C4⋊C4C22×D5312yes—
651C2×C4⋊C4C22×D5312yes—
652C2×C4⋊C4C22×D5312yes—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4—532no—
657C2×C22⋊C4—532no—
658C2×C22⋊C4—534no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—534no—
661C2×C22⋊C4—534no—
662C2×C22⋊C4—534no—
663C2×C22⋊C4—534no—
664C2×C22⋊C4—534no—
665C2×C22⋊C4C22×D5312yes—
666C2×C22⋊C4C22×D5312yes—
667C2×C42—532no—
668C2×C42—534no—
669C2×C42C22×D5311yescharacteristic
670C2×C42C22×D5312yes—
671C2×C42C22×D5312yes—
672C2×C42C22×D5311yescharacteristic
673C2×C42C22×D5311yescharacteristic
674C2×C42C22×D5311yescharacteristic
675C2×C42C22×D5318yes—
676C24—532no—
677C24—534no—
678C24C23×D5311yescharacteristic
679#41—21232no—
680#41—21232no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—534no—
685C2×Q8—538no—
686C2×Q8—5316no—
687C2×Q8—1068no—
688C2×Q8—1064no—
689C2×Q8—2128no—
690C2×Q8—21232no—
691C2×Q8C23×D5314yes—
692C2×Q8C23×D5314yes—
693C2×Q8C23×D5318yes—
694C2×D4—538no—
695C2×D4—5316no—
696C2×D4—534no—
697C2×D4—538no—
698C2×D4—538no—
699C2×D4—538no—
700C2×D4—5316no—
701C2×D4—5316no—
702C2×D4—1068no—
703C2×D4—1064no—
704C2×D4—1068no—
705C2×D4—2124no—
706C2×D4—2128no—
707C2×D4—2128no—
708C2×D4—2124no—
709C2×D4—2128no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—532no—
714C22×C4—532no—
715C22×C4—534no—
716C22×C4—532no—
717C22×C4—538no—
718C22×C4—5316no—
719C22×C4—5316no—
720C22×C4—5316no—
721C22×C4—5316no—
722C22×C4—1068no—
723C22×C4—2128no—
724C22×C4—2128no—
725C22×C4—2128no—
726C22×C4—2128no—
727C22×C4C23×D5314yes—
728C22×C4C23×D5314yes—
729C22×C4C23×D5312yes—
730C22×C4C23×D5311yescharacteristic
731C22×C4C23×D5311yescharacteristic
732C22×C4C23×D5311yescharacteristic
733C22×C4C23×D5311yescharacteristic
734C22×C4C23×D5312yes—
735C22×C4C23×D5312yes—
736C22×C4C23×D5312yes—
737C22×C4C23×D5314yes—
738C22×C4C23×D5311yescharacteristic
739C22×C4C23×D5311yescharacteristic
740C4⋊C4—538no—
741C4⋊C4—5316no—
742C4⋊C4—5316no—
743C4⋊C4—538no—
744C4⋊C4—538no—
745C4⋊C4—534no—
746C4⋊C4—534no—
747C4⋊C4—538no—
748C4⋊C4—538no—
749C4⋊C4—5316no—
750C4⋊C4—5316no—
751C4⋊C4—538no—
752C4⋊C4C23×D5318yes—
753C4⋊C4C23×D5318yes—
754C4⋊C4C23×D5318yes—
755C4⋊C4C23×D5318yes—
756C4⋊C4C23×D5314yes—
757C4⋊C4C23×D5314yes—
758C4⋊C4C23×D5318yes—
759C4⋊C4C23×D5318yes—
760C4⋊C4C23×D5318yes—
761C22⋊C4—538no—
762C22⋊C4—538no—
763C22⋊C4—538no—
764C22⋊C4—538no—
765C22⋊C4—538no—
766C22⋊C4—5316no—
767C22⋊C4—5316no—
768C22⋊C4—5316no—
769C22⋊C4—5316no—
770C22⋊C4—5316no—
771C22⋊C4—5316no—
772C22⋊C4—5316no—
773C22⋊C4C23×D5318yes—
774C22⋊C4C23×D5318yes—
775C42—538no—
776C42—5316no—
777C42C23×D5314yes—
778C42C23×D5314yes—
779C42C23×D5314yes—
780C42C23×D5314yes—
781C42C23×D5318yes—
782C42C23×D5318yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—534no—
787C23—538no—
788C23—1064no—
789C23—1068no—
790C23—1064no—
791C23—1068no—
792C23—1068no—
793C23—1064no—
794C23C24×D5312yes—
795C23C24×D5311yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—10616no—
800Q8—1068no—
801Q8—21216no—
802D4—10616no—
803D4—1068no—
804D4—10616no—
805D4—2128no—
806D4—21216no—
807D4—21216no—
808D4—2128no—
809D4—21216no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—534no—
822C2×C4—534no—
823C2×C4—538no—
824C2×C4—534no—
825C2×C4—1064no—
826C2×C4—1068no—
827C2×C4—1064no—
828C2×C4—1064no—
829C2×C4—10616no—
830C2×C4—21216no—
831C2×C4—21216no—
832C2×C4—21216no—
833C2×C4—21216no—
834C2×C4#1313326314yes—
835C2×C4#1313326514yes—
836C2×C4C24×D5314yes—
837C2×C4C24×D5312yes—
838C2×C4C24×D5312yes—
839C2×C4C24×D5312yes—
840C2×C4C24×D5312yes—
841C2×C4C24×D5314yes—
842C2×C4C24×D5314yes—
843C2×C4C24×D5314yes—
844C2×C4C24×D5312yes—
845C2×C4C24×D5312yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—1064no—
851C22—1068no—
852C22—1064no—
853C22—1068no—
854C22—1068no—
855C22—1064no—
856C22—2128no—
857C22—21216no—
858C22C2×#1313326312yes—
859C22C2×#1313326512yes—
860C22#1681145912yes—
861C22C25×D5311yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1064no—
871C4—1068no—
872C4—1064no—
873C4—1064no—
874C4C2×#1313326314yes—
875C4C2×#1313326514yes—
876C2—42no—
877C2—2124no—
878C2—2128no—
879C2#2028918614yesdirect product factor
880C2C22×#1313326311yescharacteristic
881C2C22×#1313326511yescharacteristic
882C2C2×#1681145911yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#533C2
socleC23×C53C25
hypercenterC2×#533D53
hypocenterC53C2×#3554
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20289186C2direct (N × H)
2. C2×#16811369C2semidirect
3. C2×#16811358C2semidirect
4. C2×#16811358C2semidirect
5. C2×#16811351C2semidirect
6. C2×#16811333C2semidirect
7. C2×#16811295C2semidirect
8. C2×Q8×D212C2semidirect
9. C2×#16811283C2semidirect
10. C2×#16811275C2semidirect
11. C2×#16811247C2semidirect
12. C2×#16811244C2semidirect
13. C2×#16811228C2semidirect
14. C2×#16811221C2semidirect
15. C2×#16811198C2semidirect
16. C2×#16811173C2semidirect
17. C2×#16811157C2semidirect
18. C2×C53×#533C2semidirect
22. #16811369C22semidirect
23. #16811358C22semidirect
24. #16811358C22semidirect
25. #16811351C22semidirect
26. #16811333C22semidirect
27. #16811295C22semidirect
28. Q8×D212C22semidirect
29. #16811283C22semidirect
30. #16811275C22semidirect
31. #16811247C22semidirect
32. #16811244C22semidirect
33. #16811228C22semidirect
34. #16811221C22semidirect
35. #16811198C22semidirect
36. #16811173C22semidirect
42. #16811157C22semidirect
89. C53×#533C22semidirect
450. C2×#533D53semidirect
454. C2×C53#3554semidirect
477. #533C2×D53semidirect
542. C53C2×#3554semidirect
879. C2#20289186direct (N × H)

Maximal subgroups

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

subgroupindex
#202891862
C2×#168113692
C2×#168113582
C2×#168113512
C2×#168113332
C2×#168112952
C2×Q8×D2122
C2×#168112832
C2×#168112752
C2×#168112472
C2×#168112442
C2×#168112282
C2×#168112212
C2×#168111982
C2×#168111732
C2×#168111572
C2×C53×#5332
C2×#355453