Finite Group Databasebeta

← #28292317

Subgroups — #28292317

Order 13568.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288802C214yesmaximal, complemented
2#20288791C214yesmaximal, complemented
3#20288709C214yesmaximal, complemented
4#20288697C214yesmaximal, complemented
5#20288579C216yesmaximal, complemented
6#20288521C211yesmaximal, characteristic, complemented
7#20288482C211yesmaximal, characteristic, complemented
8#20288421C216yesmaximal, complemented
9#20288366C211yesmaximal, characteristic, complemented
10#20288336C214yesmaximal, complemented
11#20288331C214yesmaximal, complemented
12#20288305C214yesmaximal, complemented
13Q8×#11719947C214yesmaximal, complemented
14#20288139C216yesmaximal, complemented
15#20288007C216yesmaximal, complemented
162−1+4×Dic53C211yesmaximal, characteristic, complemented
17#20287924C211yesmaximal, characteristic, complemented
18C22×Q8×Dic53C211yesmaximal, characteristic, complemented
19C53×#3486C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21#16811355C22112yescomplemented
22Q8×Dic106C2214yescomplemented
23#16811352C2214yescomplemented
24#16811349C2214yescomplemented
25#16811349C2214yescomplemented
26#16811348C22112yescomplemented
27#16811347C22112yescomplemented
28#16811344C22112yescomplemented
29#16811342C22112yescomplemented
30#16811331C22112yes—
31#16811331C22112yescomplemented
32#16811330C22112yes—
33#16811325C22112yes—
34#16811319C22112yes—
35#16811315C22112yes—
36#16811315C22112yescomplemented
37#16811313C22112yes—
38#16811307C22112yescomplemented
39#16811292C2214yescomplemented
40Q8×C22⋊D53C2214yes—
41Q8×C22⋊D53C2214yes—
42Q8×C22⋊D53C2214yescomplemented
43#16811284C2214yes—
44#16811284C2214yes—
45#16811284C2214yescomplemented
46#16811280C2214yescomplemented
47#16811277C22112yes—
48#16811273C22112yes—
49#16811251C2216yes—
50#16811246C22112yescomplemented
51#16811242C22112yescomplemented
52#16811234C22112yescomplemented
53#16811233C22112yescomplemented
54#16811217C22124yes—
55#16811201C2216yes—
56#16811197C2216yes—
57#16811178C22112yescomplemented
58#16811176C2216yes—
59#16811175C2216yes—
60#16811175C2216yes—
61#16811175C22112yescomplemented
62#16811169C2216yes—
63#16811168C2216yes—
64#16811168C2216yes—
65#16811159C2216yes—
66#16811159C2216yes—
67#16811159C22112yescomplemented
68#16811154C2216yes—
69#16811154C2216yes—
70#16811153C22112yes—
71#16811153C22112yes—
72#16811152C22112yescomplemented
73#16811150C22112yes—
74#16811150C22112yes—
75#16811134C2216yes—
76#16811129C2214yes—
77#16811129C22112yes—
78#16811106C2216yes—
79#16811106C2214yescomplemented
80#16811105C2214yescomplemented
81#16811103C2216yes—
82#16811101C2211yescharacteristic
83#16811101C2214yescomplemented
84#16811099C2214yescomplemented
85#41×Dic53C2216yes—
86#41×Dic53C2214yescomplemented
87C4×#11719949C2214yescomplemented
88#16811091C2216yes—
89C4×#11719947C22112yes—
90C4×#11719947C22112yes—
91C2×Q8×Dic53C2211yescharacteristic
92C2×Q8×Dic53C2214yes—
93C2×Q8×Dic53C2214yes—
94C2×Q8×Dic53C2213yes—
95C2×Q8×Dic53C2214yes—
96C2×Q8×Dic53C2213yes—
97C2×Q8×Dic53C2211yescharacteristic
98C2×Q8×Dic53C2214yes—
99C2×Q8×Dic53C2214yescomplemented
100C4×Q8×D53C2214yescomplemented
101C22×C4⋊Dic53C2213yes—
102C22×C4×Dic53C2213yes—
103C2×2−1+4×C53C2211yescharacteristic
104C23×Q8×C53C2211yescharacteristic
105D4×Q8×C53C2214yes—
106D4×Q8×C53C2214yes—
107C53×#548C2214yes—
108C53×#548C2214yes—
109C53×#536C2216yes—
110C53×#525C2216yes—
111C53×#519C2211yescharacteristic
112#13133265—28no—
113C2×#11719949C2314yes—
114C2×#11719945C2316yes—
115C2×#11719947C2314yes—
116C2×#11719947C23112yes—
117C2×Q8×D53C2314yes—
118C23×Dic53C2311yescharacteristic
119C23×Dic53C2313yes—
120#13133217C23112yes—
121#13133216C23112yes—
122#13133216C2316yes—
123#13133216C2316yes—
124#13133215C23112yes—
125#13133215C2316yes—
126#13133213C2316yes—
127#13133212C23124yes—
128#13133212C23112yes—
129#13133212C23112yes—
130#13133210C23112yes—
131#13133210C23124yes—
132#13133210C23112yes—
133#13133209C23112yes—
134#13133208C2316yes—
135#13133208C23124yes—
136#13133208C23112yes—
137#13133208C2316yes—
138#13133207C23124yes—
139#13133207C23112yes—
140#13133207C23112yes—
141#13133206C23112yes—
142#13133206C2316yes—
143#13133204C2316yes—
144#13133203C23112yes—
145#13133203C23112yes—
146#13133201C23112yes—
147#13133201C23124yes—
148#13133201C2314yes—
149#13133200C23112yes—
150#13133199C23124yes—
151#13133198C23112yes—
152#13133198C2314yes—
153#13133197C23124yes—
154#13133196C23112yes—
155#13133196C2316yes—
156#13133196C2316yes—
157#13133194C23124yes—
158#13133194C23112yes—
159#13133194C2314yes—
160#13133194C23112yes—
161#13133194C2314yes—
162#13133193C23112yes—
163#13133193C23112yes—
164#13133193C23112yes—
165#13133191C2316yes—
166#13133191C23112yes—
167#13133191C2316yes—
168#13133189C23112yes—
169#13133189C2314yes—
170#13133189C23112yes—
171#13133189C2314yes—
172#13133188C23112yes—
173#13133186C2314yes—
174Q8×Dic53C2314yes—
175Q8×Dic53C2314yes—
176Q8×Dic53C2314yes—
177Q8×Dic53C2314yes—
178Q8×Dic53C23112yes—
179Q8×Dic53C23112yes—
180Q8×Dic53C23112yes—
181Q8×Dic53C2314yes—
182Q8×Dic53C2314yes—
183Q8×Dic53C23112yes—
184Q8×Dic53C23112yes—
185Q8×Dic53C2316yes—
186Q8×Dic53C2316yes—
187C4×Dic106C23112yes—
188C4×Dic106C23112yes—
189C4×Dic106C23112yes—
190#13133182C2316yes—
191#13133182C23112yes—
192#13133182C23112yes—
193#13133182C2316yes—
194C4×D212C23112yes—
195D4×Dic53C23112yes—
196D4×Dic53C23112yes—
197D4×Dic53C2314yes—
198D4×Dic53C2314yes—
199D4×Dic53C2316yes—
200D4×Dic53C23112yes—
201D4×Dic53C2316yes—
202#13133179C2316yes—
203#13133179C2316yes—
204C4×C22⋊D53C23112yes—
205C4×C22⋊D53C23112yes—
206C4×C22⋊D53C23112yes—
207C4×C22⋊D53C23112yes—
208#13133177C23112yes—
209#13133177C23112yes—
210#13133177C2314yes—
211#13133177C23112yes—
212#13133177C2314yes—
213#13133177C23112yes—
214#13133176C23112yes—
215#13133176C2316yes—
216#13133176C23112yes—
217#13133175C23112yes—
218#13133175C23112yes—
219#13133175C23112yes—
220#13133174C23112yes—
221#13133173C23112yes—
222#13133173C23112yes—
223#13133173C2314yes—
224#13133173C23112yes—
225C2×C4⋊Dic53C23112yes—
226C2×C4⋊Dic53C23112yes—
227C2×C4⋊Dic53C23112yes—
228C2×C4⋊Dic53C2313yes—
229C2×C4⋊Dic53C2313yes—
230C2×C4⋊Dic53C2316yes—
231C4⋊C4×D53C23112yes—
232C2×C4×Dic53C2316yes—
233C2×C4×Dic53C2316yes—
234C2×C4×Dic53C2313yes—
235C2×C4×Dic53C2313yes—
236C2×C4×Dic53C2313yes—
237C2×C4×Dic53C2316yes—
238C2×C4×Dic53C2316yes—
239C2×C4×Dic53C2313yes—
240C2×C4×Dic53C23112yes—
241C42×D53C23112yes—
2422−1+4×C53—28no—
243C2×#41×C53C2314yes—
244C2×#41×C53C2316yes—
245C22×Q8×C53—28no—
246C22×Q8×C53C2314yes—
247C22×Q8×C53C2314yes—
248C22×Q8×C53C2314yes—
249C22×Q8×C53C2313yes—
250C22×Q8×C53C2311yescharacteristic
251C23×C4×C53C2313yes—
252C4⋊Q8×C53C23112yes—
253#124×C53C23112yes—
254#123×C53C23112yes—
255C22⋊Q8×C53C2316yes—
256C22⋊Q8×C53C2316yes—
257C22⋊Q8×C53C23112yes—
258C22⋊Q8×C53C23112yes—
259#121×C53C2316yes—
260#121×C53C2316yes—
261#120×C53C2314yes—
262C4×Q8×C53C2314yes—
263C4×Q8×C53C2314yes—
264C4×D4×C53C23112yes—
265C4×D4×C53C23112yes—
266#117×C53C2316yes—
267C24×C53C2411yescharacteristic
268#41×C53—216no—
269#41×C53—224no—
270C2×Q8×C53—216no—
271C2×Q8×C53—216no—
272C2×Q8×C53—216no—
273C2×Q8×C53—212no—
274C2×Q8×C53#4118yescomplemented
275C2×Q8×C53C24112yes—
276C2×Q8×C53C2416yes—
277C2×Q8×C53C2414yes—
278C2×D4×C53C2414yes—
279C2×D4×C53C2414yes—
280C2×D4×C53C2414yes—
281C2×D4×C53C2416yes—
282C22×C4×C53—212no—
283C22×C4×C53C2416yes—
284C22×C4×C53C2416yes—
285C22×C4×C53C24112yes—
286C22×C4×C53C2413yes—
287C22×C4×C53C2413yes—
288C2×C22⋊D53C2414yes—
289C2×C22⋊D53C2414yes—
290C2×C22⋊D53C2414yes—
291C2×C22⋊D53C2414yes—
292C2×C22⋊D53C24112yes—
293C22×Dic53—24no—
294C22×Dic53—46no—
295C22×Dic53C2411yescharacteristic
296C22×Dic53C2411yescharacteristic
297C22×Dic53C2411yescharacteristic
298C22×Dic53C2411yescharacteristic
299C22×Dic53C2411yescharacteristic
300C22×Dic53C2414yes—
301C22×Dic53C2416yes—
302C22×Dic53C2413yes—
303C22×Dic53C2416yes—
304C22×Dic53C2413yes—
305C22×Dic53C24112yes—
306C22×Dic53C2411yescharacteristic
307#11719949—216no—
308Q8×D53—216no—
309#11719947—216no—
310#11719947—424no—
311#11719945—224no—
312C2×D212C2416yes—
313C2×C4×D53C2414yes—
314C2×C4×D53C24112yes—
315C2×C4×D53C24112yes—
316C2×Dic106C2414yes—
317C2×Dic106C2416yes—
318C2×Dic106C24112yes—
319C4⋊C4×C53C2416yes—
320C4⋊C4×C53C2416yes—
321C4⋊C4×C53C24112yes—
322C4⋊C4×C53C24112yes—
323C22⋊C4×C53C2414yes—
324C22⋊C4×C53C2414yes—
325C22⋊C4×C53C2414yes—
326C22⋊C4×C53C24112yes—
327C22⋊C4×C53C24112yes—
328C42×C53C24112yes—
329C22⋊Dic53C2414yes—
330C22⋊Dic53C2414yes—
331C22⋊Dic53C2414yes—
332C22⋊Dic53C24112yes—
333C22⋊Dic53C2414yes—
334C22⋊Dic53C24112yes—
335C22⋊Dic53C2414yes—
336#11719921C2414yes—
337#11719921C24112yes—
338#11719921C2414yes—
339#11719921C24112yes—
340#11719921C24112yes—
341#11719921C24112yes—
342C4⋊Dic53C24112yes—
343C4⋊Dic53C24112yes—
344C4⋊Dic53C24124yes—
345C4⋊Dic53C2416yes—
346C4⋊Dic53C24112yes—
347C4⋊Dic53C2414yes—
348C4⋊Dic53C24112yes—
349C4⋊Dic53C2416yes—
350C4⋊Dic53C2414yes—
351#11719919C24112yes—
352#11719919C2414yes—
353#11719919C2414yes—
354#11719919C24112yes—
355#11719919C24112yes—
356#11719919C2414yes—
357#11719919C24112yes—
358#11719919C24112yes—
359#11719919C24112yes—
360#11719919C2414yes—
361C4×Dic53C2414yes—
362C4×Dic53C2416yes—
363C4×Dic53C24112yes—
364C4×Dic53C2416yes—
365C4×Dic53C2416yes—
366C4×Dic53C2414yes—
367C4×Dic53C2416yes—
368C4×Dic53C2416yes—
369C4×Dic53C2416yes—
370C4×Dic53C2416yes—
371C4×Dic53C2416yes—
372C4×Dic53C24112yes—
373C4×Dic53C24112yes—
374C23×C53—22no—
375C23×C53—22no—
376C23×C53—22no—
377C23×C53C2514yes—
378C23×C53C2511yescharacteristic
379C23×C53C2511yescharacteristic
380C23×C53C2511yescharacteristic
381C22×D53C2514yes—
382Q8×C53—224no—
383Q8×C53—212no—
384Q8×C53C2×#41116yes—
385D4×C53—28no—
386D4×C53—28no—
387D4×C53—28no—
388D4×C53—212no—
389C2×C4×C53—26no—
390C2×C4×C53—212no—
391C2×C4×C53—212no—
392C2×C4×C53—224no—
393C2×C4×C53C2×#41112yes—
394C2×C4×C53C2514yes—
395C2×C4×C53C2514yes—
396C2×C4×C53C2514yes—
397C2×C4×C53C2516yes—
398C2×C4×C53C2516yes—
399C22⋊D53—28no—
400C22⋊D53—28no—
401C22⋊D53—28no—
402C22⋊D53—28no—
403C22⋊D53—412no—
404C2×Dic53—22no—
405C2×Dic53—212no—
406C2×Dic53—28no—
407C2×Dic53—22no—
408C2×Dic53—22no—
409C2×Dic53—22no—
410C2×Dic53—22no—
411C2×Dic53—412no—
412C2×Dic53—43no—
413C2×Dic53—46no—
414C2×Dic53—43no—
415C2×Dic532−1+414yescomplemented
416C2×Dic53C2514yes—
417C2×Dic53C2514yes—
418C2×Dic53C2516yes—
419C2×Dic53C2514yes—
420C2×Dic53C2516yes—
421C2×Dic53C2511yescharacteristic
422C2×Dic53C2511yescharacteristic
423C2×Dic53C2511yescharacteristic
424C2×Dic53C2511yescharacteristic
425D212—212no—
426C4×D53—224no—
427C4×D53—28no—
428C4×D53—412no—
429Dic106—212no—
430Dic106—28no—
431Dic106—412no—
432#62788—531nomaximal, Sylow
433C22×C53—28no—
434C22×C53—21no—
435C22×C53—21no—
436C22×C53—21no—
437C22×C53—21no—
438C22×C53—21no—
439C22×C53—21no—
440C22×C53—24no—
441C22×C53—24no—
442C22×C53—24no—
443C22×C53C22×#4112yes—
444C22×C53C2×2−1+412yes—
445C22×C53#58512yes—
446C22×C53C2611yescharacteristic
447C2×D53—24no—
448C2×D53—24no—
449C2×D53—24no—
450C4×C53—24no—
451C4×C53—26no—
452C4×C53—24no—
453C4×C53—24no—
454C4×C53C22×#41112yes—
455Dic53—24no—
456Dic53—24no—
457Dic53—21no—
458Dic53—21no—
459Dic53—24no—
460Dic53—26no—
461Dic53—26no—
462Dic53C2×2−1+412yes—
463Dic53C2×2−1+412yes—
464#3523—534no—
465#3522—534no—
466#3516—534no—
467#3516—534no—
468#3507—536no—
469#3502—531no—
470#3497—531no—
471#3492—536no—
472#3486—531no—
473#3486D5311yescharacteristic, complemented
474#3482—534no—
475#3482—534no—
476#3480—534no—
477Q8×#41—534no—
478#3461—536no—
479#3444—536no—
480C4×2−1+4—531no—
481C4×2−1+4—531no—
482C22×C4×Q8—531no—
483C2×C53—22no—
484C2×C53—22no—
485C2×C53—22no—
486C2×C53—44no—
487C2×C53C23×#4111yescharacteristic
488C2×C53C22×2−1+411yescharacteristic
489C2×C53C2×#58511yescharacteristic
490D53—44no—
491C2×2−1+4—531no—
492C2×2−1+4C2×D5311yescharacteristic
493C23×Q8C2×D5311yescharacteristic
494#559—5312no—
495Q82—534no—
496#557—5312no—
497#557—534no—
498#557—534no—
499#557—534no—
500#556—5312no—
501#556—5312no—
502#556—5312no—
503#554—5312no—
504#554—5312no—
505#554—5312no—
506#553—5312no—
507#553—5312no—
508#552—5312no—
509#552—5312no—
510#552—5312no—
511#552—5312no—
512#550—534no—
513D4×Q8—534no—
514D4×Q8—534no—
515D4×Q8—534no—
516D4×Q8C2×D5314yes—
517D4×Q8C2×D5314yes—
518#548—534no—
519#548—534no—
520#548—534no—
521#548—534no—
522#548C2×D5314yes—
523#548C2×D5314yes—
524#547—5312no—
525#547—5312no—
526#544—536no—
527#542—5312no—
528#542—5312no—
529#541—5312no—
530#541—5312no—
531#539—5324no—
532#537—536no—
533#536—536no—
534#536C2×D5316yes—
535#533—5312no—
536#533—536no—
537#533—536no—
538#533—5312no—
539#533—536no—
540#532—536no—
541#532—536no—
542#532—536no—
543#529—5312no—
544#529—5312no—
545#529—5312no—
546#529—536no—
547#529—536no—
548#529—5312no—
549#529—536no—
550#529—536no—
551#529—5312no—
552#529—5312no—
553#525—536no—
554#525—534no—
555#525—5312no—
556#525C2×D5316yes—
557#520—536no—
558#520—534no—
559#520—534no—
560#520—536no—
561#519—531no—
562#519—534no—
563#519—534no—
564#519C2×D5311yescharacteristic
565C4×#41—536no—
566C4×#41—534no—
567C4×#41—534no—
568C4×#41—5312no—
569C4×#41—5312no—
570C4×#41—536no—
571C2×C4×Q8—531no—
572C2×C4×Q8—533no—
573C2×C4×Q8—534no—
574C2×C4×Q8—534no—
575C2×C4×Q8—531no—
576C2×C4×Q8—533no—
577C2×C4×Q8—534no—
578C2×C4×Q8—534no—
579C2×C4×Q8—534no—
580C2×C4×Q8—534no—
581C22×C4⋊C4—533no—
582C22×C42—533no—
583C53#6278811yescharacteristic, complemented, Sylow
5842−1+4—28no—
5852−1+4—1068no—
586C2×#41—534no—
587C2×#41—534no—
588C2×#41—5312no—
589C2×#41—536no—
590C2×#41C22×D5316yes—
591C2×#41C22×D5314yes—
592C22×Q8—28no—
593C22×Q8—534no—
594C22×Q8C22×D5313yes—
595C22×Q8C22×D5314yes—
596C22×Q8C22×D5314yes—
597C22×Q8C22×D5314yes—
598C22×Q8C22×D5311yescharacteristic
599C23×C4—531no—
600C23×C4—533no—
601C23×C4C22×D5313yes—
602C4⋊Q8—536no—
603C4⋊Q8—5312no—
604C4⋊Q8—536no—
605C4⋊Q8—536no—
606C4⋊Q8—5312no—
607C4⋊Q8—5312no—
608C4⋊Q8C22×D53112yes—
609#127—536no—
610#126—5312no—
611#126—5312no—
612#126—5324no—
613#126—5312no—
614#126—5312no—
615#126—5324no—
616#125—5312no—
617#125—536no—
618#125—536no—
619#125—5312no—
620#125—5312no—
621#125—5324no—
622#125—5324no—
623#125—5312no—
624#124—536no—
625#124—5312no—
626#124—536no—
627#124—5312no—
628#124—5312no—
629#124C22×D53112yes—
630#123—534no—
631#123—5312no—
632#123—5312no—
633#123—534no—
634#123—5312no—
635#123—5324no—
636#123—5324no—
637#123C22×D53112yes—
638C22⋊Q8—5312no—
639C22⋊Q8—5312no—
640C22⋊Q8—5312no—
641C22⋊Q8—536no—
642C22⋊Q8—536no—
643C22⋊Q8—5312no—
644C22⋊Q8—5324no—
645C22⋊Q8—534no—
646C22⋊Q8—534no—
647C22⋊Q8—5312no—
648C22⋊Q8—5312no—
649C22⋊Q8—5324no—
650C22⋊Q8C22×D5316yes—
651C22⋊Q8C22×D5316yes—
652C22⋊Q8C22×D53112yes—
653C22⋊Q8C22×D53112yes—
654#121—534no—
655#121—534no—
656#121—5312no—
657#121—5312no—
658#121—5312no—
659#121—536no—
660#121—536no—
661#121—5312no—
662#121C22×D5316yes—
663#121C22×D5316yes—
664#120—534no—
665#120C22×D5314yes—
666C4×Q8—534no—
667C4×Q8—534no—
668C4×Q8—5312no—
669C4×Q8—5312no—
670C4×Q8—534no—
671C4×Q8—534no—
672C4×Q8—5312no—
673C4×Q8—5312no—
674C4×Q8—536no—
675C4×Q8—534no—
676C4×Q8—5312no—
677C4×Q8—536no—
678C4×Q8—534no—
679C4×Q8—536no—
680C4×Q8—536no—
681C4×Q8—5312no—
682C4×Q8—5312no—
683C4×Q8—5312no—
684C4×Q8—5312no—
685C4×Q8—5312no—
686C4×Q8C22×D5314yes—
687C4×Q8C22×D5314yes—
688C4×D4—534no—
689C4×D4—534no—
690C4×D4—536no—
691C4×D4—5312no—
692C4×D4—536no—
693C4×D4—5312no—
694C4×D4—5312no—
695C4×D4—5312no—
696C4×D4—5312no—
697C4×D4—5312no—
698C4×D4—5312no—
699C4×D4—536no—
700C4×D4—536no—
701C4×D4—534no—
702C4×D4—534no—
703C4×D4—5312no—
704C4×D4—5312no—
705C4×D4—5312no—
706C4×D4—5312no—
707C4×D4—5312no—
708C4×D4C22×D53112yes—
709C4×D4C22×D53112yes—
710#117—536no—
711#117—5312no—
712#117—5312no—
713#117—5312no—
714#117—5312no—
715#117—5312no—
716#117—534no—
717#117—5312no—
718#117—5312no—
719#117—5312no—
720#117—5312no—
721#117C22×D5316yes—
722C2×C4⋊C4—533no—
723C2×C4⋊C4—533no—
724C2×C4⋊C4—536no—
725C2×C4⋊C4—5312no—
726C2×C4⋊C4—5312no—
727C2×C4⋊C4—5312no—
728C2×C4⋊C4—5312no—
729C2×C42—533no—
730C2×C42—536no—
731C2×C42—536no—
732C2×C42—533no—
733C2×C42—536no—
734C2×C42—533no—
735C2×C42—536no—
736C2×C42—533no—
737C2×C42—5312no—
738C2×C42—5312no—
739C24C23×D5311yescharacteristic
740#41—216no—
741#41—224no—
742#41—10616no—
743#41—10616no—
744#41—10624no—
745#41—21224no—
746C2×Q8—216no—
747C2×Q8—216no—
748C2×Q8—216no—
749C2×Q8—212no—
750C2×Q8—534no—
751C2×Q8—536no—
752C2×Q8—5312no—
753C2×Q8—10616no—
754C2×Q8#1171994718yescomplemented
755C2×Q8C23×D53112yes—
756C2×Q8C23×D5316yes—
757C2×Q8C23×D5314yes—
758C2×D4—534no—
759C2×D4—534no—
760C2×D4—534no—
761C2×D4—534no—
762C2×D4—5312no—
763C2×D4—536no—
764C2×D4C23×D5314yes—
765C2×D4C23×D5316yes—
766C2×D4C23×D5314yes—
767C2×D4C23×D5314yes—
768C22×C4—212no—
769C22×C4—531no—
770C22×C4—531no—
771C22×C4—531no—
772C22×C4—531no—
773C22×C4—531no—
774C22×C4—531no—
775C22×C4—534no—
776C22×C4—536no—
777C22×C4—533no—
778C22×C4—536no—
779C22×C4—533no—
780C22×C4—5312no—
781C22×C4—534no—
782C22×C4—5312no—
783C22×C4—5312no—
784C22×C4—1064no—
785C22×C4—2126no—
786C22×C4C23×D5316yes—
787C22×C4C23×D5316yes—
788C22×C4C23×D5313yes—
789C22×C4C23×D53112yes—
790C22×C4C23×D5313yes—
791C4⋊C4—5312no—
792C4⋊C4—5312no—
793C4⋊C4—5324no—
794C4⋊C4—536no—
795C4⋊C4—5312no—
796C4⋊C4—5312no—
797C4⋊C4—536no—
798C4⋊C4—534no—
799C4⋊C4—534no—
800C4⋊C4—534no—
801C4⋊C4—534no—
802C4⋊C4—534no—
803C4⋊C4—534no—
804C4⋊C4—5312no—
805C4⋊C4—5312no—
806C4⋊C4—5312no—
807C4⋊C4—5312no—
808C4⋊C4—5312no—
809C4⋊C4—5312no—
810C4⋊C4C23×D5316yes—
811C4⋊C4C23×D5316yes—
812C4⋊C4C23×D53112yes—
813C4⋊C4C23×D53112yes—
814C22⋊C4—534no—
815C22⋊C4—534no—
816C22⋊C4—5312no—
817C22⋊C4—534no—
818C22⋊C4—534no—
819C22⋊C4—534no—
820C22⋊C4—5312no—
821C22⋊C4—5312no—
822C22⋊C4—534no—
823C22⋊C4—534no—
824C22⋊C4—5312no—
825C22⋊C4—5312no—
826C22⋊C4—5312no—
827C22⋊C4C23×D5314yes—
828C22⋊C4C23×D5314yes—
829C22⋊C4C23×D53112yes—
830C22⋊C4C23×D53112yes—
831C22⋊C4C23×D5314yes—
832C42—536no—
833C42—534no—
834C42—534no—
835C42—536no—
836C42—536no—
837C42—536no—
838C42—536no—
839C42—536no—
840C42—536no—
841C42—536no—
842C42—5312no—
843C42—5312no—
844C42—5312no—
845C42C23×D53112yes—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—534no—
850C23C24×D5314yes—
851C23C24×D5311yescharacteristic
852C23C24×D5311yescharacteristic
853C23C24×D5311yescharacteristic
854Q8—224no—
855Q8—212no—
856Q8—1068no—
857Q8—10612no—
858Q8—21212no—
859Q8C2×#11719947116yes—
860D4—28no—
861D4—28no—
862D4—28no—
863D4—212no—
864D4—1068no—
865D4—1068no—
866D4—1068no—
867D4—1068no—
868D4—10612no—
869D4—21212no—
870C2×C4—26no—
871C2×C4—212no—
872C2×C4—212no—
873C2×C4—224no—
874C2×C4—534no—
875C2×C4—531no—
876C2×C4—531no—
877C2×C4—531no—
878C2×C4—531no—
879C2×C4—536no—
880C2×C4—534no—
881C2×C4—534no—
882C2×C4—534no—
883C2×C4—536no—
884C2×C4—1068no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1068no—
890C2×C4—1062no—
891C2×C4—10612no—
892C2×C4—10624no—
893C2×C4—21212no—
894C2×C4—2123no—
895C2×C4—2126no—
896C2×C4—2123no—
897C2×C4—21212no—
898C2×C4C2×#11719947112yes—
899C2×C4C24×D5316yes—
900C2×C4C24×D5314yes—
901C2×C4C24×D5314yes—
902C2×C4C24×D5314yes—
903C2×C4C24×D5316yes—
904C22—28no—
905C22—21no—
906C22—21no—
907C22—21no—
908C22—21no—
909C22—21no—
910C22—21no—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—1064no—
915C22—1064no—
916C22—1064no—
917C22C22×#1171994712yes—
918C222−1+4×D5312yes—
919C22#1681146012yes—
920C22C25×D5311yescharacteristic
921C4—24no—
922C4—26no—
923C4—24no—
924C4—24no—
925C4—532no—
926C4—532no—
927C4—1064no—
928C4—1061no—
929C4—1061no—
930C4—1064no—
931C4—1066no—
932C4—1066no—
933C4—1064no—
934C4C22×#11719947112yes—
935C2—22no—
936C2—22no—
937C2—22no—
938C2—44no—
939C2—2124no—
940C2C23×#1171994711yescharacteristic
941C2C2×2−1+4×D5311yescharacteristic
942C2C2×#1681146011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3486C2
hypercenter#3486D53
hypocenterC53#62788
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3486

Complements

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

NH ≅ G/Ntype
1. #20288802C2semidirect
2. #20288791C2semidirect
3. #20288709C2semidirect
4. #20288697C2semidirect
5. #20288579C2semidirect
6. #20288521C2semidirect
7. #20288482C2semidirect
8. #20288421C2semidirect
9. #20288366C2semidirect
10. #20288336C2semidirect
11. #20288331C2semidirect
12. #20288305C2semidirect
13. Q8×#11719947C2semidirect
14. #20288139C2semidirect
15. #20288007C2semidirect
16. 2−1+4×Dic53C2semidirect
17. #20287924C2semidirect
18. C22×Q8×Dic53C2semidirect
19. C53×#3486C2semidirect
21. #16811355C22semidirect
22. Q8×Dic106C22semidirect
23. #16811352C22semidirect
24. #16811349C22semidirect
25. #16811349C22semidirect
26. #16811348C22semidirect
27. #16811347C22semidirect
28. #16811344C22semidirect
29. #16811342C22semidirect
31. #16811331C22semidirect
36. #16811315C22semidirect
38. #16811307C22semidirect
39. #16811292C22semidirect
42. Q8×C22⋊D53C22semidirect
45. #16811284C22semidirect
46. #16811280C22semidirect
50. #16811246C22semidirect
51. #16811242C22semidirect
52. #16811234C22semidirect
53. #16811233C22semidirect
57. #16811178C22semidirect
61. #16811175C22semidirect
67. #16811159C22semidirect
72. #16811152C22semidirect
79. #16811106C22semidirect
80. #16811105C22semidirect
83. #16811101C22semidirect
84. #16811099C22semidirect
86. #41×Dic53C22semidirect
87. C4×#11719949C22semidirect
99. C2×Q8×Dic53C22semidirect
100. C4×Q8×D53C22semidirect
274. C2×Q8×C53#41semidirect
415. C2×Dic532−1+4semidirect
473. #3486D53semidirect
583. C53#62788semidirect
754. C2×Q8#11719947semidirect

Maximal subgroups

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

subgroupindex
#202888022
#202887912
#202887092
#202886972
#202885792
#202885212
#202884822
#202884212
#202883662
#202883362
#202883312
#202883052
Q8×#117199472
#202881392
#202880072
2−1+4×Dic532
#202879242
C22×Q8×Dic532
C53×#34862
#6278853