Finite Group Databasebeta

← #28293158

Subgroups — #28293158

Order 13568.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288785C218yesmaximal, complemented
2#20288754C218yesmaximal, complemented
3#20288683C218yesmaximal, complemented
4#20288657C218yesmaximal, complemented
5#20288580C212yesmaximal, complemented
6#20288554C214yesmaximal, complemented
7#20288518C211yesmaximal, characteristic, complemented
8#20288479C211yesmaximal, characteristic, complemented
9#20288424C212yesmaximal, complemented
10#20288413C214yesmaximal, complemented
11#20288359C212yesmaximal, complemented
12#20288148C212yesmaximal, complemented
13#20288124C214yesmaximal, complemented
14#20288105C212yesmaximal, complemented
15C2×#16811220C214yesmaximal, complemented
16C4×#13133262C212yesmaximal, complemented
17C2×C53×#520C211yesmaximal, characteristic, complemented
18C2×#13133262C2212yes—
19#16811358C2214yescomplemented
20#16811351C2214yescomplemented
21#16811346C2214yescomplemented
22#16811345C2218yescomplemented
23#16811333C2214yescomplemented
24#16811332C2218yescomplemented
25#16811330C2214yescomplemented
26#16811328C2218yescomplemented
27#16811322C22116yescomplemented
28#16811321C2218yescomplemented
29#16811319C2218yescomplemented
30#16811314C2218yescomplemented
31#16811313C2218yescomplemented
32#16811308C2218yescomplemented
33#16811306C22116yescomplemented
34#16811306C22116yescomplemented
35#16811302C22116yescomplemented
36#16811297C22116yescomplemented
37#16811297C22116yescomplemented
38D4×Dic106C2214yescomplemented
39#16811282C2218yescomplemented
40#16811277C2214yescomplemented
41#16811274C2218yescomplemented
42#16811272C2218yescomplemented
43#16811272C2218yescomplemented
44#16811269C2218yescomplemented
45#16811268C2218yescomplemented
46#16811261C2218yescomplemented
47#16811261C2218yescomplemented
48D4×D212C2214yescomplemented
49#16811254C2212yescomplemented
50#16811249C2214yescomplemented
51#16811245C2218yescomplemented
52#16811244C2214yescomplemented
53#16811244C2214yescomplemented
54#16811235C2214yescomplemented
55#16811231C2218yescomplemented
56#16811228C2214yescomplemented
57#16811220C22116yescomplemented
58#16811220C2218yescomplemented
59#16811220C2214yescomplemented
60#16811220C2218yescomplemented
61#16811220C22116yescomplemented
62#16811220C2218yescomplemented
63#16811220C2214yescomplemented
64#16811215C22116yescomplemented
65#16811211C2214yescomplemented
66#16811211C2214yescomplemented
67#16811206C22116yescomplemented
68#16811204C2212yes—
69#16811197C2214yescomplemented
70#16811185C2214yes—
71#16811182C2218yescomplemented
72#16811180C2212yescomplemented
73#16811177C2218yescomplemented
74#16811173C2212yes—
75#16811160C2218yescomplemented
76#16811157C2218yescomplemented
77#16811157C2218yescomplemented
78#16811153C22116yescomplemented
79#16811151C2218yescomplemented
80#16811151C2218yescomplemented
81C2×#13133212C2218yescomplemented
82C2×#13133207C2218yescomplemented
83#16811134C2218yescomplemented
84#16811134C2214yescomplemented
85#16811132C22116yescomplemented
86C2×#13133202C2218yescomplemented
87C2×#13133200C2218yescomplemented
88C2×#13133196C2214yescomplemented
89C2×#13133195C2218yescomplemented
90C2×#13133191C2214yes—
91#16811104C2214yescomplemented
92#16811102C2218yescomplemented
93#16811098C2212yes—
94#16811096C2218yescomplemented
95#16811095C2218yescomplemented
96C4×#11719945C2214yescomplemented
97C4×#11719947C2218yescomplemented
98C2×C4×C22⋊D53C2218yescomplemented
99C4×D4×D53C2218yescomplemented
100C22×#41×C53C2211yescharacteristic
101C53×#520C2218yescomplemented
102C53×#520C2218yescomplemented
103C2×C4×Q8×C53C2211yescharacteristic, complemented
104C2×C4×Q8×C53C2211yescharacteristic, complemented
105C2×C4×D4×C53C2211yescharacteristic
106C2×C4×D4×C53C2211yescharacteristic
107C2×C4×D4×C53C2212yescomplemented
108C2×C4×D4×C53C2212yescomplemented
109C2×#117×C53C2211yescharacteristic, complemented
110C2×#117×C53C2212yescomplemented
111C22×C4⋊C4×C53C2212yescomplemented
112C22×C4⋊C4×C53C2211yescharacteristic, complemented
113#13133262—216no—
114C2×#11719945C2314yes—
115C2×#11719945C2318yes—
116C2×#11719947C2318yes—
117C22×Dic106C2314yes—
118C22×D212C2314yes—
119C22×C22⋊D53C2318yes—
120C2×D4×D53C2318yes—
121C22×C4×D53C2318yes—
122#13133217C2312yes—
123#13133217C2312yes—
124#13133217C2312yes—
125#13133216C2318yes—
126#13133215C2318yes—
127#13133214C2312yes—
128#13133212C2318yes—
129#13133212C23116yes—
130#13133212C23116yes—
131#13133212C2318yes—
132#13133212C23116yes—
133#13133211C23116yes—
134#13133211C23116yes—
135#13133210C2318yes—
136#13133210C2318yes—
137#13133209C2318yes—
138#13133209C2318yes—
139#13133209C2314yes—
140#13133208C2318yes—
141#13133207C2318yes—
142#13133207C23116yes—
143#13133207C23116yes—
144#13133207C2318yes—
145#13133207C23116yes—
146#13133206C2318yes—
147#13133205C2314yes—
148#13133205C2318yes—
149#13133205C2318yes—
150#13133203C2318yes—
151#13133203C2318yes—
152#13133202C23116yes—
153#13133202C23116yes—
154#13133202C2318yes—
155#13133202C2318yes—
156#13133202C23116yes—
157#13133201C23116yes—
158#13133200C23116yes—
159#13133200C23116yes—
160#13133200C23116yes—
161#13133200C2318yes—
162#13133200C23116yes—
163#13133199C2318yes—
164#13133199C2318yes—
165#13133198C23116yes—
166#13133197C2318yes—
167#13133196C2318yes—
168#13133196C2314yes—
169#13133196C2314yes—
170#13133196C2318yes—
171#13133196C2318yes—
172#13133196C2314yes—
173#13133196C2318yes—
174#13133196C2314yes—
175#13133195C23116yes—
176#13133195C23116yes—
177#13133195C2318yes—
178#13133195C2318yes—
179#13133195C23116yes—
180#13133194C23116yes—
181#13133194C23116yes—
182#13133193C2318yes—
183#13133193C2318yes—
184#13133192C2318yes—
185#13133191C2318yes—
186#13133191C2318yes—
187#13133191C2314yes—
188#13133191C2318yes—
189#13133191C2314yes—
190#13133191C2314yes—
191#13133191C2318yes—
192#13133191C2314yes—
193#13133190C2318yes—
194#13133190C2318yes—
195#13133189C23116yes—
196#13133189C23116yes—
197#13133187C23116yes—
198#13133186C2318yes—
199#13133185C23116yes—
200C4×Dic106C2318yes—
201C4×Dic106C2314yes—
202C4×Dic106C2318yes—
203C4×Dic106C2314yes—
204C4×Dic106C2314yes—
205C4×Dic106C2314yes—
206#13133182C2318yes—
207C4×D212C2314yes—
208C4×D212C2318yes—
209C4×D212C2314yes—
210C4×D212C2318yes—
211C4×D212C2314yes—
212C4×D212C2314yes—
213D4×Dic53C2318yes—
214D4×Dic53C2318yes—
215#13133179C2318yes—
216C4×C22⋊D53C2318yes—
217C4×C22⋊D53C2318yes—
218C4×C22⋊D53C23116yes—
219C4×C22⋊D53C23116yes—
220C4×C22⋊D53C2318yes—
221C4×C22⋊D53C23116yes—
222C4×C22⋊D53C23116yes—
223C4×C22⋊D53C2318yes—
224#13133177C23116yes—
225#13133177C23116yes—
226#13133176C2318yes—
227#13133176C2314yes—
228#13133175C2318yes—
229#13133174C23116yes—
230#13133174C23116yes—
231#13133174C2318yes—
232#13133173C23116yes—
233C2×C4⋊Dic53C2314yes—
234C2×C4⋊Dic53C2314yes—
235C2×#11719919C2318yes—
236C2×#11719919C2318yes—
237C2×#11719919C2318yes—
238C2×#11719919C2318yes—
239C4⋊C4×D53C2318yes—
240C2×C22⋊Dic53C2318yes—
241C2×#11719921C2318yes—
242C2×#11719921C2318yes—
243C2×#11719921C2318yes—
244C2×#11719921C2318yes—
245C22⋊C4×D53C23116yes—
246C2×C4×Dic53C2318yes—
247C42×D53C2318yes—
248C2×#41×C53—28no—
249C2×#41×C53C2318yes—
250C22×Q8×C53C2311yescharacteristic
251C22×D4×C53C2312yes—
252C22×D4×C53C2311yescharacteristic
253C23×C4×C53C2312yes—
254C23×C4×C53C2311yescharacteristic
255C23×C4×C53C2312yes—
256C23×C4×C53C2312yes—
257C23×C4×C53C2312yes—
258C4×Q8×C53C2314yes—
259C4×Q8×C53C2314yes—
260C4×Q8×C53C2318yes—
261C4×D4×C53C2314yes—
262C4×D4×C53C2318yes—
263C4×D4×C53C2314yes—
264C4×D4×C53C2318yes—
265C4×D4×C53C2318yes—
266C4×D4×C53C23116yes—
267#117×C53C23116yes—
268#117×C53C2314yes—
269#117×C53C2314yes—
270C2×C4⋊C4×C53C2318yes—
271C2×C4⋊C4×C53C2311yescharacteristic
272C2×C4⋊C4×C53C2312yes—
273C2×C4⋊C4×C53C2311yescharacteristic
274C2×C4⋊C4×C53C2311yescharacteristic
275C2×C4⋊C4×C53C2312yes—
276C2×C4⋊C4×C53C2312yes—
277C2×C4⋊C4×C53C2318yes—
278C2×C4⋊C4×C53C2318yes—
279C2×C4⋊C4×C53C2311yescharacteristic
280C2×C22⋊C4×C53C2312yes—
281C2×C22⋊C4×C53C2312yes—
282C2×C22⋊C4×C53C2311yescharacteristic
283C2×C22⋊C4×C53C2311yescharacteristic
284C2×C42×C53C2311yescharacteristic
285C2×C42×C53C2311yescharacteristic
286C2×C42×C53C2312yes—
287C2×C42×C53C2312yes—
288C24×C53C2411yescharacteristic
289C24×C53C2412yes—
290C23×D53C2418yes—
291#41×C53—232no—
292C2×Q8×C53—24no—
293C2×Q8×C53C2414yes—
294C2×D4×C53—28no—
295C2×D4×C53#4118yescomplemented
296C2×D4×C53C2418yes—
297C2×D4×C53C2414yes—
298C22×C4×C53—28no—
299C22×C4×C53—24no—
300C22×C4×C53—82no—
301C22×C4×C53—82no—
302C22×C4×C53—82no—
303C22×C4×C53C2412yes—
304C22×C4×C53C2411yescharacteristic
305C22×C4×C53C2418yes—
306C22×C4×C53C2414yes—
307C22×C4×C53C2411yescharacteristic
308C22×C4×C53C2411yescharacteristic
309C22×C4×C53C2411yescharacteristic
310C22×C4×C53C2412yes—
311C22×C4×C53C2411yescharacteristic
312C22×C4×C53C2412yes—
313C22×C4×C53C2418yes—
314C22×C4×C53C2414yes—
315C22×C4×C53C2414yes—
316C22×C4×C53C2418yes—
317C22×C4×C53C2411yescharacteristic
318C2×C22⋊D53—232no—
319C2×C22⋊D53C24116yes—
320C2×C22⋊D53C2418yes—
321C2×C22⋊D53C2418yes—
322C2×C22⋊D53C2418yes—
323C22×Dic53C2418yes—
324C22×Dic53C2418yes—
325C22×Dic53C2418yes—
326#11719947—232no—
327D4×D53—232no—
328#11719945—216no—
329#11719945—88no—
330C2×D212—84no—
331C2×D212C2414yes—
332C2×D212C2414yes—
333C2×D212C2418yes—
334C2×D212C2414yes—
335C2×C4×D53—88no—
336C2×C4×D53C2418yes—
337C2×C4×D53C2418yes—
338C2×C4×D53C2418yes—
339C2×C4×D53C24116yes—
340C2×Dic106—84no—
341C2×Dic106C2414yes—
342C2×Dic106C2414yes—
343C2×Dic106C2418yes—
344C2×Dic106C2414yes—
345C4⋊C4×C53C2412yes—
346C4⋊C4×C53C2418yes—
347C4⋊C4×C53C2412yes—
348C4⋊C4×C53C2414yes—
349C4⋊C4×C53C2414yes—
350C4⋊C4×C53C2414yes—
351C4⋊C4×C53C2418yes—
352C4⋊C4×C53C2414yes—
353C4⋊C4×C53C2414yes—
354C22⋊C4×C53C2418yes—
355C22⋊C4×C53C2418yes—
356C22⋊C4×C53C2412yes—
357C22⋊C4×C53C2414yes—
358C22⋊C4×C53C2412yes—
359C42×C53C2414yes—
360C42×C53C2418yes—
361C42×C53C2418yes—
362C42×C53C2412yes—
363C42×C53C2412yes—
364C22⋊Dic53C24116yes—
365C22⋊Dic53C2418yes—
366C22⋊Dic53C2418yes—
367C22⋊Dic53C2418yes—
368#11719921C2418yes—
369#11719921C24116yes—
370#11719921C2418yes—
371#11719921C2418yes—
372#11719921C2418yes—
373#11719921C2418yes—
374#11719921C24116yes—
375#11719921C24116yes—
376#11719921C24116yes—
377#11719921C2418yes—
378C4⋊Dic53C2414yes—
379C4⋊Dic53C2414yes—
380C4⋊Dic53C2414yes—
381C4⋊Dic53C2418yes—
382C4⋊Dic53C2418yes—
383C4⋊Dic53C2414yes—
384C4⋊Dic53C2414yes—
385C4⋊Dic53C2414yes—
386#11719919C24116yes—
387#11719919C2418yes—
388#11719919C2418yes—
389#11719919C2418yes—
390#11719919C2418yes—
391#11719919C24116yes—
392#11719919C24116yes—
393#11719919C24116yes—
394#11719919C2418yes—
395#11719919C2418yes—
396C4×Dic53C2418yes—
397C4×Dic53C2418yes—
398C4×Dic53C2418yes—
399C4×Dic53C24116yes—
400C23×C53—22no—
401C23×C53—42no—
402C23×C53—41no—
403C23×C53—42no—
404C23×C53—41no—
405C23×C53C2×#4118yes—
406C23×C53C2512yes—
407C23×C53C2514yes—
408C23×C53C2511yescharacteristic
409C22×D53—216no—
410C22×D53—48no—
411C22×D53—48no—
412C22×D53C2518yes—
413Q8×C53—28no—
414D4×C53—216no—
415D4×C53C2×#41116yes—
416C2×C4×C53—22no—
417C2×C4×C53—24no—
418C2×C4×C53—216no—
419C2×C4×C53—28no—
420C2×C4×C53—44no—
421C2×C4×C53—48no—
422C2×C4×C53—44no—
423C2×C4×C53—48no—
424C2×C4×C53—41no—
425C2×C4×C53—42no—
426C2×C4×C53—41no—
427C2×C4×C53—42no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53C2×#4114yes—
431C2×C4×C53C2511yescharacteristic
432C2×C4×C53C2514yes—
433C2×C4×C53C2512yes—
434C2×C4×C53C2512yes—
435C2×C4×C53C2514yes—
436C2×C4×C53C2512yes—
437C2×C4×C53C2511yescharacteristic
438C2×C4×C53C2512yes—
439C2×C4×C53C2514yes—
440C2×C4×C53C2512yes—
441C22⋊D53—216no—
442C22⋊D53—232no—
443C22⋊D53—48no—
444C22⋊D53—48no—
445C2×Dic53—216no—
446C2×Dic53—48no—
447C2×Dic53—48no—
448C2×Dic53C2518yes—
449C2×Dic53C2518yes—
450C2×Dic53C2518yes—
451D212—28no—
452D212—44no—
453D212—48no—
454D212—44no—
455C4×D53—216no—
456C4×D53—48no—
457C4×D53—416no—
458C4×D53—48no—
459Dic106—28no—
460Dic106—44no—
461Dic106—48no—
462Dic106—44no—
463#62847—531nomaximal, Sylow
464C22×C53—24no—
465C22×C53—21no—
466C22×C53—24no—
467C22×C53—21no—
468C22×C53—22no—
469C22×C53—22no—
470C22×C53—22no—
471C22×C53—48no—
472C22×C53—44no—
473C22×C53C22×#4118yes—
474C22×C53C22×#4112yes—
475C22×C53C2611yescharacteristic
476C2×D53—28no—
477C2×D53—28no—
478C2×D53—28no—
479C2×D53—816no—
480C4×C53—22no—
481C4×C53—24no—
482C4×C53—21no—
483C4×C53—24no—
484C4×C53—22no—
485C4×C53—24no—
486C4×C53—21no—
487C4×C53—22no—
488C4×C53—22no—
489C4×C53C22×#4114yes—
490Dic53—28no—
491Dic53—28no—
492Dic53—28no—
493#3521—538no—
494#3520—538no—
495#3515—538no—
496#3513—538no—
497#3507—532no—
498#3505—534no—
499#3501—531no—
500#3496—531no—
501#3492—532no—
502#3491—534no—
503#3485—532no—
504#3461—532no—
505#3459—534no—
506#3455—532no—
507C2×#539—534no—
508C4×H(5,𝔽2)—532no—
509C2×#520D5311yescharacteristic, complemented
510C2×C53—28no—
511C2×C53—22no—
512C2×C53—42no—
513C2×C53C23×#4111yescharacteristic
514C2×C53H(7,𝔽2)11yescharacteristic
515C2×C532−1+611yescharacteristic
516D53—48no—
517C2×H(5,𝔽2)—532no—
518C22×#41C2×D5311yescharacteristic
519#559—534no—
520#557—534no—
521#556—538no—
522#556—534no—
523#554—534no—
524#554—534no—
525#554—538no—
526#554—538no—
527#553—538no—
528#553—5316no—
529#553—538no—
530#552—538no—
531#552—538no—
532#552—5316no—
533#552—5316no—
534#552—538no—
535#551—5316no—
536#551—5316no—
537#551—5316no—
538D4×Q8—534no—
539#548—538no—
540#547—538no—
541#547—538no—
542#547—534no—
543#547—538no—
544#546—538no—
545#546—538no—
546#546—538no—
547#546—538no—
548D42—534no—
549#544—532no—
550#543—534no—
551#542—538no—
552#542—534no—
553#542—534no—
554#541—538no—
555#541—534no—
556#540—534no—
557#539—5316no—
558#539—534no—
559#539—538no—
560#539—538no—
561#539—538no—
562#539—5316no—
563#539—5316no—
564#539—534no—
565#538—5316no—
566#538—534no—
567#538—534no—
568#537—532no—
569#536—534no—
570#534—538no—
571#534—534no—
572#533—538no—
573#533—532no—
574#532—532no—
575#529—538no—
576#529—5316no—
577#529—538no—
578#529—538no—
579#529—538no—
580#529—538no—
581C2×#126—538no—
582C2×#125—538no—
583#525—534no—
584#525—538no—
585#525—5316no—
586C2×#123—538no—
587C2×#123—538no—
588C2×C22⋊Q8—534no—
589C2×C22⋊Q8—538no—
590C2×#121—534no—
591#520—538no—
592#520—534no—
593#520C2×D5318yescomplemented
594#520C2×D5318yescomplemented
595#518—532no—
596#518—538no—
597#518—538no—
598C4×#41—538no—
599C4×#41—534no—
600C2×C4×Q8C2×D5311yescharacteristic, complemented
601C2×C4×Q8C2×D5311yescharacteristic, complemented
602C2×C4×D4—538no—
603C2×C4×D4—538no—
604C2×C4×D4C2×D5311yescharacteristic
605C2×C4×D4C2×D5311yescharacteristic
606C2×C4×D4C2×D5312yescomplemented
607C2×C4×D4C2×D5312yescomplemented
608C2×#117C2×D5311yescharacteristic, complemented
609C2×#117C2×D5312yescomplemented
610C22×C4⋊C4C2×D5312yescomplemented
611C22×C4⋊C4C2×D5311yescharacteristic, complemented
612C53#6284711yescharacteristic, complemented, Sylow
613H(5,𝔽2)—10616no—
614C2×#41—28no—
615C2×#41—538no—
616C2×#41—534no—
617C2×#41—538no—
618C2×#41C22×D5318yes—
619C22×Q8—534no—
620C22×Q8C22×D5311yescharacteristic
621C22×D4—538no—
622C22×D4—538no—
623C22×D4—534no—
624C22×D4C22×D5312yes—
625C22×D4C22×D5311yescharacteristic
626C23×C4—538no—
627C23×C4C22×D5312yes—
628C23×C4C22×D5311yescharacteristic
629C23×C4C22×D5312yes—
630C23×C4C22×D5312yes—
631C23×C4C22×D5312yes—
632C4⋊Q8—538no—
633C4⋊Q8—538no—
634C4⋊Q8—532no—
635C4⋊Q8—532no—
636C4⋊Q8—532no—
637#127—532no—
638#126—538no—
639#126—5316no—
640#126—5316no—
641#126—5316no—
642#126—538no—
643#126—538no—
644#126—538no—
645#126—5316no—
646#126—5316no—
647#125—538no—
648#125—5316no—
649#125—5316no—
650#125—5316no—
651#125—538no—
652#125—538no—
653#125—538no—
654#125—538no—
655#125—534no—
656#124—538no—
657#124—538no—
658#124—538no—
659#124—538no—
660#124—538no—
661#124—534no—
662#123—5316no—
663#123—538no—
664#123—5316no—
665#123—5316no—
666#123—5316no—
667#123—5316no—
668#123—538no—
669#123—5316no—
670#123—5316no—
671#123—5316no—
672#123—538no—
673#123—538no—
674#123—5316no—
675#123—538no—
676C22⋊Q8—538no—
677C22⋊Q8—538no—
678C22⋊Q8—534no—
679C22⋊Q8—538no—
680C22⋊Q8—538no—
681C22⋊Q8—538no—
682C22⋊Q8—538no—
683C22⋊Q8—534no—
684C22⋊Q8—534no—
685C22⋊Q8—534no—
686C22⋊Q8—538no—
687C22⋊Q8—5316no—
688C22⋊Q8—5316no—
689C22⋊Q8—5316no—
690C22⋊Q8—538no—
691C22⋊Q8—538no—
692C22⋊Q8—5316no—
693C22⋊Q8—5316no—
694#121—5316no—
695#121—5316no—
696#121—534no—
697#121—538no—
698#121—538no—
699#121—538no—
700#121—538no—
701#121—534no—
702#121—534no—
703#121—534no—
704#121—538no—
705#121—538no—
706#121—538no—
707#120—538no—
708#120—5316no—
709#120—5316no—
710C4×Q8—538no—
711C4×Q8—534no—
712C4×Q8—534no—
713C4×Q8—538no—
714C4×Q8—534no—
715C4×Q8—534no—
716C4×Q8—538no—
717C4×Q8C22×D5318yes—
718C4×Q8C22×D5314yes—
719C4×Q8C22×D5314yes—
720C4×D4—538no—
721C4×D4—538no—
722C4×D4—5316no—
723C4×D4—538no—
724C4×D4—5316no—
725C4×D4—5316no—
726C4×D4—538no—
727C4×D4—5316no—
728C4×D4—538no—
729C4×D4—538no—
730C4×D4—538no—
731C4×D4—5316no—
732C4×D4—5316no—
733C4×D4—534no—
734C4×D4—534no—
735C4×D4—538no—
736C4×D4—538no—
737C4×D4—534no—
738C4×D4—534no—
739C4×D4C22×D5318yes—
740C4×D4C22×D5314yes—
741C4×D4C22×D5314yes—
742C4×D4C22×D53116yes—
743C4×D4C22×D5318yes—
744C4×D4C22×D5318yes—
745#117—534no—
746#117—538no—
747#117—538no—
748#117—5316no—
749#117—538no—
750#117—5316no—
751#117—5316no—
752#117C22×D5314yes—
753#117C22×D5314yes—
754#117C22×D53116yes—
755C2×C4⋊C4—538no—
756C2×C4⋊C4—534no—
757C2×C4⋊C4—538no—
758C2×C4⋊C4—538no—
759C2×C4⋊C4—534no—
760C2×C4⋊C4—538no—
761C2×C4⋊C4—538no—
762C2×C4⋊C4C22×D5311yescharacteristic
763C2×C4⋊C4C22×D5312yes—
764C2×C4⋊C4C22×D5311yescharacteristic
765C2×C4⋊C4C22×D5311yescharacteristic
766C2×C4⋊C4C22×D5312yes—
767C2×C4⋊C4C22×D5312yes—
768C2×C4⋊C4C22×D5318yes—
769C2×C4⋊C4C22×D5318yes—
770C2×C4⋊C4C22×D5318yes—
771C2×C4⋊C4C22×D5311yescharacteristic
772C2×C22⋊C4—538no—
773C2×C22⋊C4—538no—
774C2×C22⋊C4—538no—
775C2×C22⋊C4—538no—
776C2×C22⋊C4—538no—
777C2×C22⋊C4—5316no—
778C2×C22⋊C4C22×D5312yes—
779C2×C22⋊C4C22×D5312yes—
780C2×C22⋊C4C22×D5311yescharacteristic
781C2×C22⋊C4C22×D5311yescharacteristic
782C2×C42—538no—
783C2×C42—538no—
784C2×C42C22×D5311yescharacteristic
785C2×C42C22×D5311yescharacteristic
786C2×C42C22×D5312yes—
787C2×C42C22×D5312yes—
788C24—538no—
789C24C23×D5311yescharacteristic
790C24C23×D5312yes—
791#41—232no—
792#41—10632no—
793#41—10616no—
794#41—4248no—
795C2×Q8—24no—
796C2×Q8—534no—
797C2×Q8—534no—
798C2×Q8—534no—
799C2×Q8—538no—
800C2×Q8—4244no—
801C2×Q8C23×D5314yes—
802C2×D4—28no—
803C2×D4—538no—
804C2×D4—5316no—
805C2×D4—538no—
806C2×D4—538no—
807C2×D4—534no—
808C2×D4—534no—
809C2×D4—538no—
810C2×D4—534no—
811C2×D4—10632no—
812C2×D4—10632no—
813C2×D4—4244no—
814C2×D4#1171994518yescomplemented
815C2×D4C23×D5318yes—
816C2×D4C23×D5314yes—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—82no—
820C22×C4—82no—
821C22×C4—82no—
822C22×C4—538no—
823C22×C4—538no—
824C22×C4—538no—
825C22×C4—538no—
826C22×C4—538no—
827C22×C4—538no—
828C22×C4—5316no—
829C22×C4—4248no—
830C22×C4C23×D5312yes—
831C22×C4C23×D5318yes—
832C22×C4C23×D5311yescharacteristic
833C22×C4C23×D5314yes—
834C22×C4C23×D5318yes—
835C22×C4C23×D5311yescharacteristic
836C22×C4C23×D5311yescharacteristic
837C22×C4C23×D5311yescharacteristic
838C22×C4C23×D5312yes—
839C22×C4C23×D5311yescharacteristic
840C22×C4C23×D5312yes—
841C22×C4C23×D5314yes—
842C22×C4C23×D5314yes—
843C22×C4C23×D5318yes—
844C22×C4C23×D5311yescharacteristic
845C4⋊C4—534no—
846C4⋊C4—538no—
847C4⋊C4—5316no—
848C4⋊C4—534no—
849C4⋊C4—538no—
850C4⋊C4—538no—
851C4⋊C4—538no—
852C4⋊C4—534no—
853C4⋊C4—538no—
854C4⋊C4—5316no—
855C4⋊C4—538no—
856C4⋊C4—5316no—
857C4⋊C4—5316no—
858C4⋊C4—534no—
859C4⋊C4—538no—
860C4⋊C4—538no—
861C4⋊C4—534no—
862C4⋊C4—534no—
863C4⋊C4C23×D5314yes—
864C4⋊C4C23×D5312yes—
865C4⋊C4C23×D5318yes—
866C4⋊C4C23×D5312yes—
867C4⋊C4C23×D5314yes—
868C4⋊C4C23×D5314yes—
869C4⋊C4C23×D5318yes—
870C4⋊C4C23×D5314yes—
871C4⋊C4C23×D5314yes—
872C22⋊C4—538no—
873C22⋊C4—5316no—
874C22⋊C4—538no—
875C22⋊C4—538no—
876C22⋊C4—538no—
877C22⋊C4—5316no—
878C22⋊C4—538no—
879C22⋊C4—538no—
880C22⋊C4—538no—
881C22⋊C4—538no—
882C22⋊C4—5316no—
883C22⋊C4—5316no—
884C22⋊C4—5316no—
885C22⋊C4—538no—
886C22⋊C4C23×D5318yes—
887C22⋊C4C23×D5318yes—
888C22⋊C4C23×D5312yes—
889C22⋊C4C23×D5314yes—
890C22⋊C4C23×D5312yes—
891C42—538no—
892C42—5316no—
893C42—538no—
894C42—538no—
895C42C23×D5314yes—
896C42C23×D5318yes—
897C42C23×D5318yes—
898C42C23×D5312yes—
899C42C23×D5312yes—
900C23—22no—
901C23—42no—
902C23—41no—
903C23—42no—
904C23—41no—
905C23—538no—
906C23—10616no—
907C23—2128no—
908C23—2128no—
909C23C2×#1171994518yes—
910C23C24×D5312yes—
911C23C24×D5311yescharacteristic
912C23C24×D5314yes—
913Q8—28no—
914Q8—1068no—
915Q8—2124no—
916Q8—2124no—
917Q8—2128no—
918D4—216no—
919D4—10616no—
920D4—10632no—
921D4—1068no—
922D4—2124no—
923D4—2124no—
924D4—2128no—
925D4—2128no—
926D4—2128no—
927D4C2×#11719945116yes—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—216no—
931C2×C4—28no—
932C2×C4—41no—
933C2×C4—42no—
934C2×C4—41no—
935C2×C4—42no—
936C2×C4—48no—
937C2×C4—44no—
938C2×C4—44no—
939C2×C4—48no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—538no—
943C2×C4—538no—
944C2×C4—538no—
945C2×C4—10616no—
946C2×C4—10616no—
947C2×C4—2128no—
948C2×C4—2128no—
949C2×C4—21216no—
950C2×C4—2128no—
951C2×C4—2128no—
952C2×C4C2×#1171994514yes—
953C2×C4C24×D5312yes—
954C2×C4C24×D5312yes—
955C2×C4C24×D5314yes—
956C2×C4C24×D5312yes—
957C2×C4C24×D5314yes—
958C2×C4C24×D5311yescharacteristic
959C2×C4C24×D5314yes—
960C2×C4C24×D5311yescharacteristic
961C2×C4C24×D5312yes—
962C2×C4C24×D5312yes—
963C22—21no—
964C22—24no—
965C22—21no—
966C22—24no—
967C22—22no—
968C22—22no—
969C22—22no—
970C22—48no—
971C22—44no—
972C22—1068no—
973C22—1068no—
974C22—1068no—
975C22—42416no—
976C22C22×#1171994512yes—
977C22C22×#1171994518yes—
978C22C25×D5311yescharacteristic
979C4—22no—
980C4—24no—
981C4—22no—
982C4—24no—
983C4—21no—
984C4—24no—
985C4—21no—
986C4—22no—
987C4—22no—
988C4—1068no—
989C4—1068no—
990C4—1068no—
991C4C22×#1171994514yes—
992C2—22no—
993C2—28no—
994C2—42no—
995C2—2128no—
996C2C23×#1171994511yescharacteristic
997C2#2028952511yescharacteristic
998C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#520C2
hypercenterC2×#520D53
hypocenterC53#62847
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20288785C2semidirect
2. #20288754C2semidirect
3. #20288683C2semidirect
4. #20288657C2semidirect
5. #20288580C2semidirect
6. #20288554C2semidirect
7. #20288518C2semidirect
8. #20288479C2semidirect
9. #20288424C2semidirect
10. #20288413C2semidirect
11. #20288359C2semidirect
12. #20288148C2semidirect
13. #20288124C2semidirect
14. #20288105C2semidirect
15. C2×#16811220C2semidirect
16. C4×#13133262C2semidirect
17. C2×C53×#520C2semidirect
19. #16811358C22semidirect
20. #16811351C22semidirect
21. #16811346C22semidirect
22. #16811345C22semidirect
23. #16811333C22semidirect
24. #16811332C22semidirect
25. #16811330C22semidirect
26. #16811328C22semidirect
27. #16811322C22semidirect
28. #16811321C22semidirect
29. #16811319C22semidirect
30. #16811314C22semidirect
31. #16811313C22semidirect
32. #16811308C22semidirect
33. #16811306C22semidirect
34. #16811306C22semidirect
35. #16811302C22semidirect
36. #16811297C22semidirect
37. #16811297C22semidirect
38. D4×Dic106C22semidirect
39. #16811282C22semidirect
40. #16811277C22semidirect
41. #16811274C22semidirect
42. #16811272C22semidirect
43. #16811272C22semidirect
44. #16811269C22semidirect
45. #16811268C22semidirect
46. #16811261C22semidirect
47. #16811261C22semidirect
48. D4×D212C22semidirect
49. #16811254C22semidirect
50. #16811249C22semidirect
51. #16811245C22semidirect
52. #16811244C22semidirect
53. #16811244C22semidirect
54. #16811235C22semidirect
55. #16811231C22semidirect
56. #16811228C22semidirect
57. #16811220C22semidirect
58. #16811220C22semidirect
59. #16811220C22semidirect
60. #16811220C22semidirect
61. #16811220C22semidirect
62. #16811220C22semidirect
63. #16811220C22semidirect
64. #16811215C22semidirect
65. #16811211C22semidirect
66. #16811211C22semidirect
67. #16811206C22semidirect
69. #16811197C22semidirect
71. #16811182C22semidirect
72. #16811180C22semidirect
73. #16811177C22semidirect
75. #16811160C22semidirect
76. #16811157C22semidirect
77. #16811157C22semidirect
78. #16811153C22semidirect
79. #16811151C22semidirect
80. #16811151C22semidirect
81. C2×#13133212C22semidirect
82. C2×#13133207C22semidirect
83. #16811134C22semidirect
84. #16811134C22semidirect
85. #16811132C22semidirect
86. C2×#13133202C22semidirect
87. C2×#13133200C22semidirect
88. C2×#13133196C22semidirect
89. C2×#13133195C22semidirect
91. #16811104C22semidirect
92. #16811102C22semidirect
94. #16811096C22semidirect
95. #16811095C22semidirect
96. C4×#11719945C22semidirect
97. C4×#11719947C22semidirect
98. C2×C4×C22⋊D53C22semidirect
99. C4×D4×D53C22semidirect
101. C53×#520C22semidirect
102. C53×#520C22semidirect
103. C2×C4×Q8×C53C22semidirect
104. C2×C4×Q8×C53C22semidirect
107. C2×C4×D4×C53C22semidirect
108. C2×C4×D4×C53C22semidirect
109. C2×#117×C53C22semidirect
110. C2×#117×C53C22semidirect
111. C22×C4⋊C4×C53C22semidirect
112. C22×C4⋊C4×C53C22semidirect
295. C2×D4×C53#41semidirect
509. C2×#520D53semidirect
593. #520C2×D53semidirect
594. #520C2×D53semidirect
600. C2×C4×Q8C2×D53semidirect
601. C2×C4×Q8C2×D53semidirect
606. C2×C4×D4C2×D53semidirect
607. C2×C4×D4C2×D53semidirect
608. C2×#117C2×D53semidirect
609. C2×#117C2×D53semidirect
610. C22×C4⋊C4C2×D53semidirect
611. C22×C4⋊C4C2×D53semidirect
612. C53#62847semidirect
814. C2×D4#11719945semidirect

Maximal subgroups

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

subgroupindex
#202887852
#202887542
#202886832
#202886572
#202885802
#202885542
#202885182
#202884792
#202884242
#202884132
#202883592
#202881482
#202881242
#202881052
C2×#168112202
C4×#131332622
C2×C53×#5202
#6284753