Finite Group Databasebeta

← #28292323

Subgroups — #28292323

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#20288805C214yesmaximal, complemented
2#20288794C214yesmaximal, complemented
3#20288710C214yesmaximal, complemented
4#20288700C214yesmaximal, complemented
5#20288573C216yesmaximal, complemented
6#20288521C211yesmaximal, characteristic, complemented
7#20288482C211yesmaximal, characteristic, complemented
8#20288418C216yesmaximal, complemented
9#20288367C211yesmaximal, characteristic, complemented
10#20288363C211yesmaximal, characteristic, complemented
11#20288337C214yesmaximal, complemented
12#20288332C214yesmaximal, complemented
13#20288313C214yesmaximal, complemented
14Q8×#11719945C214yesmaximal, complemented
15#20288142C216yesmaximal, complemented
16#20288008C216yesmaximal, complemented
17C4×#13133265C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
19C4×2−1+4×C53C211yesmaximal, characteristic, complemented
20C2×#13133265C2211yescharacteristic
21C22×Q8×D53C2211yescharacteristic
22#16811356C22112yescomplemented
23Q8×Dic106C2214yescomplemented
24#16811352C2214yescomplemented
25#16811351C22112yescomplemented
26#16811349C2214yescomplemented
27#16811349C2214yescomplemented
28#16811345C22112yescomplemented
29#16811343C22112yescomplemented
30#16811341C22112yescomplemented
31#16811333C22112yes—
32#16811328C22112yes—
33#16811328C22112yescomplemented
34#16811323C22112yes—
35#16811317C22112yes—
36#16811314C22112yes—
37#16811312C22112yes—
38#16811312C22112yescomplemented
39#16811308C22112yescomplemented
40#16811292C2214yescomplemented
41Q8×D212C2214yes—
42Q8×D212C2214yes—
43Q8×C22⋊D53C2214yes—
44Q8×C22⋊D53C2214yes—
45Q8×C22⋊D53C2214yescomplemented
46#16811285C2214yes—
47#16811285C2214yes—
48#16811284C2214yescomplemented
49#16811280C2214yes—
50#16811280C2214yes—
51#16811280C2214yescomplemented
52#16811278C22112yes—
53#16811274C22112yes—
54#16811251C2216yes—
55#16811244C22112yescomplemented
56#16811238C22112yescomplemented
57#16811235C22112yescomplemented
58#16811231C22112yescomplemented
59#16811215C22124yes—
60#16811201C2216yes—
61#16811199C2216yes—
62#16811194C2216yes—
63#16811180C22112yescomplemented
64#16811177C2216yes—
65#16811177C2216yes—
66#16811177C22112yescomplemented
67#16811176C2216yes—
68#16811170C2216yes—
69#16811170C2216yes—
70#16811169C2216yes—
71#16811160C2216yes—
72#16811160C2216yes—
73#16811157C22112yescomplemented
74#16811155C2216yes—
75#16811155C2216yes—
76#16811155C22112yescomplemented
77#16811153C22112yes—
78#16811153C22112yes—
79#16811151C22112yes—
80#16811151C22112yes—
81#16811135C2216yes—
82#16811132C2214yes—
83#16811132C22112yes—
84#16811130C2216yes—
85#16811105C2214yescomplemented
86#16811104C2216yes—
87#16811101C2211yescharacteristic
88#16811099C2214yescomplemented
89C4×#11719949C2214yescomplemented
90C4×#11719945C22112yes—
91C4×#11719945C22112yes—
92C4×#11719945C2216yes—
93C2×Q8×Dic53C2211yescharacteristic
94C2×C4×Dic106C2213yes—
95C2×#13133182C2213yes—
96C4×Q8×D53C2214yes—
97C4×Q8×D53C2214yes—
98C4×Q8×D53C2214yes—
99C4×Q8×D53C2214yes—
100C4×Q8×D53C2214yescomplemented
101C2×C4⋊C4×D53C2213yes—
102C2×C42×D53C2213yes—
103C2×2−1+4×C53C2211yescharacteristic
104C53×#520C2216yes—
105C53×#520C2214yescomplemented
106C53×#519C2211yescharacteristic
107C53×#519C2214yescomplemented
108C4×#41×C53C2216yes—
109C4×#41×C53C2214yescomplemented
110C2×C4×Q8×C53C2211yescharacteristic
111C2×C4×Q8×C53C2214yescomplemented
112#13133265—28no—
113C2×#11719949C2314yes—
114C2×#11719945C2314yes—
115C2×#11719945C2316yes—
116C2×#11719945C23112yes—
117C22×Dic106C2313yes—
118C2×Q8×D53—28no—
119C2×Q8×D53C2314yes—
120C2×Q8×D53C2314yes—
121C2×Q8×D53C2314yes—
122C22×C4×D53C2311yescharacteristic
123C22×C4×D53C2313yes—
124C22×C4×D53C2313yes—
125#13133217C23112yes—
126#13133217C23112yes—
127#13133216C23112yes—
128#13133216C2316yes—
129#13133216C2316yes—
130#13133215C23112yes—
131#13133215C2316yes—
132#13133213C2316yes—
133#13133212C23112yes—
134#13133212C23112yes—
135#13133211C23124yes—
136#13133210C23124yes—
137#13133210C23112yes—
138#13133210C23112yes—
139#13133209C23124yes—
140#13133209C23112yes—
141#13133208C2316yes—
142#13133208C23112yes—
143#13133208C2316yes—
144#13133207C23124yes—
145#13133207C23112yes—
146#13133207C23112yes—
147#13133206C2316yes—
148#13133205C23112yes—
149#13133204C23112yes—
150#13133204C2316yes—
151#13133203C23112yes—
152#13133203C23112yes—
153#13133202C23112yes—
154#13133202C2314yes—
155#13133201C23112yes—
156#13133200C23124yes—
157#13133199C23112yes—
158#13133199C23124yes—
159#13133199C2314yes—
160#13133198C23112yes—
161#13133197C23112yes—
162#13133197C23112yes—
163#13133197C2316yes—
164#13133197C2316yes—
165#13133196C23124yes—
166#13133196C23112yes—
167#13133196C23112yes—
168#13133196C23112yes—
169#13133195C23124yes—
170#13133195C23112yes—
171#13133195C2314yes—
172#13133194C2314yes—
173#13133194C23112yes—
174#13133193C23112yes—
175#13133193C2316yes—
176#13133193C2316yes—
177#13133192C2316yes—
178#13133192C2316yes—
179#13133191C23112yes—
180#13133190C23112yes—
181#13133190C2314yes—
182#13133189C2314yes—
183#13133189C23112yes—
184#13133188C2316yes—
185#13133188C23112yes—
186#13133188C2316yes—
187#13133187C2314yes—
188#13133185C2314yes—
189Q8×Dic53C2314yes—
190Q8×Dic53C2314yes—
191Q8×Dic53C2314yes—
192Q8×Dic53C2314yes—
193C4×Dic106C23112yes—
194C4×Dic106C23112yes—
195C4×Dic106C23112yes—
196C4×Dic106C2316yes—
197C4×Dic106C23112yes—
198C4×Dic106C23112yes—
199C4×Dic106C2316yes—
200C4×Dic106C23112yes—
201#13133182C23112yes—
202#13133182C23112yes—
203#13133182C23112yes—
204C4×D212C23112yes—
205C4×D212C23112yes—
206C4×D212C23112yes—
207C4×D212C2314yes—
208C4×D212C2316yes—
209C4×D212C2316yes—
210#13133179C23112yes—
211C4×C22⋊D53C23112yes—
212C4×C22⋊D53C23112yes—
213C4×C22⋊D53C23112yes—
214C4×C22⋊D53C23112yes—
215C4×C22⋊D53C23112yes—
216C4×C22⋊D53C23112yes—
217C4×C22⋊D53C2314yes—
218C4×C22⋊D53C2314yes—
219C4×C22⋊D53C23112yes—
220C4×C22⋊D53C23112yes—
221#13133176C23112yes—
222#13133176C2316yes—
223#13133176C23112yes—
224#13133175C23112yes—
225#13133174C23112yes—
226#13133174C23112yes—
227#13133174C2314yes—
228#13133174C23112yes—
229#13133174C23112yes—
230C2×C4⋊Dic53C2313yes—
231C2×#11719919C2316yes—
232C4⋊C4×D53C23112yes—
233C4⋊C4×D53C23112yes—
234C4⋊C4×D53C23112yes—
235C2×C4×Dic53C2313yes—
236C2×C4×Dic53C2313yes—
237C2×C4×Dic53C2313yes—
238C42×D53C2316yes—
239C42×D53C2316yes—
240C42×D53C2316yes—
241C42×D53C2316yes—
242C42×D53C23112yes—
2432−1+4×C53—28no—
244C2×#41×C53C2314yes—
245C2×#41×C53C2316yes—
246C22×Q8×C53C2314yes—
247C22×Q8×C53C2311yescharacteristic
248C4×Q8×C53C2314yes—
249C4×Q8×C53C2314yes—
250C4×Q8×C53C2314yes—
251C4×Q8×C53C2314yes—
252C4×Q8×C53C2316yes—
253C4×Q8×C53C23112yes—
254C4×Q8×C53C2316yes—
255C4×D4×C53C23112yes—
256C4×D4×C53C2314yes—
257C4×D4×C53C2316yes—
258C4×D4×C53C23112yes—
259C4×D4×C53C2316yes—
260#117×C53C2316yes—
261#117×C53C23112yes—
262#117×C53C23112yes—
263C2×C4⋊C4×C53C23112yes—
264C2×C4⋊C4×C53C2313yes—
265C2×C42×C53C2313yes—
266C2×C42×C53C23112yes—
267C23×D53C2411yescharacteristic
268#41×C53—216no—
269#41×C53—224no—
270C2×Q8×C53—216no—
271C2×Q8×C53#4118yescomplemented
272C2×Q8×C53C2416yes—
273C2×Q8×C53C2414yes—
274C2×D4×C53C2414yes—
275C2×D4×C53C2416yes—
276C22×C4×C53C2411yescharacteristic
277C22×C4×C53C2414yes—
278C22×C4×C53C24112yes—
279C22×C4×C53C2413yes—
280C22×C4×C53C24112yes—
281C22×C4×C53C2413yes—
282C2×C22⋊D53C2414yes—
283C2×C22⋊D53C2414yes—
284C2×C22⋊D53C2414yes—
285C2×C22⋊D53C2414yes—
286C2×C22⋊D53C24112yes—
287C22×Dic53C2411yescharacteristic
288C22×Dic53C2413yes—
289C22×Dic53C2413yes—
290#11719949—216no—
291Q8×D53—216no—
292Q8×D53—216no—
293Q8×D53—216no—
294#11719945—224no—
295#11719945—216no—
296#11719945—424no—
297C2×D212C2416yes—
298C2×D212C2414yes—
299C2×D212C2414yes—
300C2×C4×D53—212no—
301C2×C4×D53—24no—
302C2×C4×D53—46no—
303C2×C4×D53C2411yescharacteristic
304C2×C4×D53C2411yescharacteristic
305C2×C4×D53C2411yescharacteristic
306C2×C4×D53C2414yes—
307C2×C4×D53C2416yes—
308C2×C4×D53C2416yes—
309C2×C4×D53C2416yes—
310C2×C4×D53C24112yes—
311C2×C4×D53C2416yes—
312C2×C4×D53C24112yes—
313C2×C4×D53C2411yescharacteristic
314C2×Dic106—212no—
315C2×Dic106C24112yes—
316C2×Dic106C2416yes—
317C2×Dic106C2414yes—
318C2×Dic106C24112yes—
319C4⋊C4×C53C24112yes—
320C4⋊C4×C53C2416yes—
321C4⋊C4×C53C24112yes—
322C4⋊C4×C53C2416yes—
323C4⋊C4×C53C2414yes—
324C22⋊C4×C53C2414yes—
325C22⋊C4×C53C24112yes—
326C22⋊C4×C53C2414yes—
327C42×C53C2416yes—
328C42×C53C2414yes—
329C42×C53C2416yes—
330C42×C53C24112yes—
331C42×C53C24112yes—
332C22⋊Dic53C2414yes—
333C22⋊Dic53C2414yes—
334C22⋊Dic53C24112yes—
335C22⋊Dic53C24112yes—
336C22⋊Dic53C24112yes—
337#11719921C2414yes—
338#11719921C2414yes—
339#11719921C2414yes—
340#11719921C2414yes—
341#11719921C24112yes—
342#11719921C2414yes—
343#11719921C2414yes—
344#11719921C24112yes—
345#11719921C24112yes—
346#11719921C24112yes—
347C4⋊Dic53C24112yes—
348C4⋊Dic53C2416yes—
349C4⋊Dic53C2416yes—
350C4⋊Dic53C2414yes—
351C4⋊Dic53C24112yes—
352C4⋊Dic53C24112yes—
353C4⋊Dic53C24112yes—
354#11719919C24124yes—
355#11719919C24112yes—
356#11719919C2414yes—
357#11719919C2414yes—
358#11719919C2414yes—
359#11719919C2414yes—
360#11719919C24112yes—
361#11719919C24112yes—
362#11719919C24112yes—
363#11719919C24112yes—
364#11719919C24112yes—
365C4×Dic53C2414yes—
366C4×Dic53C2416yes—
367C4×Dic53C2416yes—
368C4×Dic53C2416yes—
369C4×Dic53C2416yes—
370C4×Dic53C2416yes—
371C4×Dic53C2416yes—
372C4×Dic53C24112yes—
373C4×Dic53C24112yes—
374C23×C53C2514yes—
375C23×C53C2511yescharacteristic
376C22×D53—22no—
377C22×D53—22no—
378C22×D53—22no—
379C22×D53C2514yes—
380C22×D53C2511yescharacteristic
381C22×D53C2511yescharacteristic
382Q8×C53—212no—
383Q8×C53C2×#41116yes—
384D4×C53—28no—
385D4×C53—212no—
386C2×C4×C53—224no—
387C2×C4×C53—22no—
388C2×C4×C53—28no—
389C2×C4×C53—43no—
390C2×C4×C53—412no—
391C2×C4×C53C2×#41112yes—
392C2×C4×C53C2514yes—
393C2×C4×C53C2514yes—
394C2×C4×C53C2516yes—
395C2×C4×C53C2511yescharacteristic
396C2×C4×C53C2514yes—
397C2×C4×C53C2516yes—
398C2×C4×C53C2511yescharacteristic
399C22⋊D53—28no—
400C22⋊D53—28no—
401C22⋊D53—28no—
402C22⋊D53—28no—
403C22⋊D53—412no—
404C2×Dic53—26no—
405C2×Dic53—22no—
406C2×Dic53—43no—
407C2×Dic53C2516yes—
408C2×Dic53C2514yes—
409C2×Dic53C2514yes—
410C2×Dic53C2516yes—
411C2×Dic53C2514yes—
412C2×Dic53C2511yescharacteristic
413C2×Dic53C2511yescharacteristic
414D212—28no—
415D212—28no—
416D212—212no—
417C4×D53—22no—
418C4×D53—212no—
419C4×D53—212no—
420C4×D53—212no—
421C4×D53—224no—
422C4×D53—22no—
423C4×D53—28no—
424C4×D53—22no—
425C4×D53—46no—
426C4×D53—412no—
427C4×D532−1+414yescomplemented
428Dic106—224no—
429Dic106—212no—
430Dic106—28no—
431Dic106—412no—
432#62788—531nomaximal, Sylow
433C22×C53—21no—
434C22×C53—21no—
435C22×C53—24no—
436C22×C53—24no—
437C22×C53—24no—
438C22×C53C22×#4112yes—
439C22×C53C2611yescharacteristic
440C2×D53—28no—
441C2×D53—21no—
442C2×D53—21no—
443C2×D53—21no—
444C2×D53—21no—
445C2×D53—24no—
446C2×D53—24no—
447C2×D53—24no—
448C2×D53C2×2−1+412yes—
449C2×D53#58512yes—
450C4×C53—24no—
451C4×C53—24no—
452C4×C53—21no—
453C4×C53—24no—
454C4×C53—26no—
455C4×C53C22×#41112yes—
456C4×C53C2×2−1+412yes—
457Dic53—26no—
458Dic53—24no—
459Dic53—24no—
460Dic53—21no—
461Dic53—24no—
462Dic53—26no—
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#3486—531no—
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+4D5311yescharacteristic, complemented
482C22×C4×Q8—531no—
483C2×C53—22no—
484C2×C53—44no—
485C2×C53C23×#4111yescharacteristic
486C2×C53C22×2−1+411yescharacteristic
487C2×C53C2×#58511yescharacteristic
488D53—22no—
489D53—22no—
490D53—44no—
491C2×2−1+4—531no—
492C2×2−1+4C2×D5311yescharacteristic
493C23×Q8—531no—
494#559—5312no—
495Q82—534no—
496#557—534no—
497#557—534no—
498#557—5312no—
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×Q8—534no—
517D4×Q8—534no—
518#548—534no—
519#548—534no—
520#548—534no—
521#548—534no—
522#548—534no—
523#548—534no—
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#536—536no—
535#533—536no—
536#533—536no—
537#533—5312no—
538#533—536no—
539#533—5312no—
540#532—536no—
541#532—536no—
542#532—536no—
543#529—536no—
544#529—536no—
545#529—5312no—
546#529—5312no—
547#529—536no—
548#529—536no—
549#529—5312no—
550#529—5312no—
551#529—5312no—
552#529—5312no—
553#525—536no—
554#525—534no—
555#525—5312no—
556#525—536no—
557#520—534no—
558#520—536no—
559#520C2×D5316yes—
560#520C2×D5314yescomplemented
561#519—531no—
562#519—534no—
563#519C2×D5311yescharacteristic
564#519C2×D5314yescomplemented
565C4×#41—534no—
566C4×#41—536no—
567C4×#41—5312no—
568C4×#41—5312no—
569C4×#41C2×D5316yes—
570C4×#41C2×D5314yescomplemented
571C2×C4×Q8—531no—
572C2×C4×Q8—534no—
573C2×C4×Q8—534no—
574C2×C4×Q8—534no—
575C2×C4×Q8—534no—
576C2×C4×Q8—534no—
577C2×C4×Q8—533no—
578C2×C4×Q8—533no—
579C2×C4×Q8C2×D5311yescharacteristic
580C2×C4×Q8C2×D5314yescomplemented
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—536no—
589C2×#41—5312no—
590C2×#41C22×D5316yes—
591C2×#41C22×D5314yes—
592C22×Q8—534no—
593C22×Q8—534no—
594C22×Q8—534no—
595C22×Q8—533no—
596C22×Q8—1068no—
597C22×Q8C22×D5314yes—
598C22×Q8C22×D5311yescharacteristic
599C23×C4—533no—
600C23×C4—531no—
601C23×C4—533no—
602C4⋊Q8—536no—
603C4⋊Q8—5312no—
604C4⋊Q8—536no—
605C4⋊Q8—536no—
606C4⋊Q8—5312no—
607C4⋊Q8—5312no—
608C4⋊Q8—5312no—
609#127—536no—
610#126—5312no—
611#126—5312no—
612#126—5312no—
613#126—5312no—
614#126—5324no—
615#126—5324no—
616#125—5312no—
617#125—536no—
618#125—536no—
619#125—5312no—
620#125—5312no—
621#125—5324no—
622#125—5312no—
623#125—5324no—
624#124—536no—
625#124—536no—
626#124—5312no—
627#124—5312no—
628#124—5312no—
629#124—5312no—
630#123—5312no—
631#123—5324no—
632#123—534no—
633#123—5312no—
634#123—534no—
635#123—5312no—
636#123—5312no—
637#123—5324no—
638C22⋊Q8—536no—
639C22⋊Q8—536no—
640C22⋊Q8—5312no—
641C22⋊Q8—5312no—
642C22⋊Q8—5312no—
643C22⋊Q8—5312no—
644C22⋊Q8—5324no—
645C22⋊Q8—534no—
646C22⋊Q8—536no—
647C22⋊Q8—536no—
648C22⋊Q8—5312no—
649C22⋊Q8—5312no—
650C22⋊Q8—5312no—
651C22⋊Q8—5324no—
652C22⋊Q8—534no—
653C22⋊Q8—5312no—
654#121—534no—
655#121—5312no—
656#121—536no—
657#121—536no—
658#121—5312no—
659#121—5312no—
660#121—536no—
661#121—536no—
662#121—534no—
663#121—5312no—
664#120—534no—
665#120—534no—
666C4×Q8—534no—
667C4×Q8—534no—
668C4×Q8—534no—
669C4×Q8—534no—
670C4×Q8—5312no—
671C4×Q8—5312no—
672C4×Q8—5312no—
673C4×Q8—5312no—
674C4×Q8—5312no—
675C4×Q8—536no—
676C4×Q8—536no—
677C4×Q8—5312no—
678C4×Q8—5312no—
679C4×Q8—5312no—
680C4×Q8—5312no—
681C4×Q8C22×D5314yes—
682C4×Q8C22×D5314yes—
683C4×Q8C22×D5316yes—
684C4×Q8C22×D5314yes—
685C4×Q8C22×D53112yes—
686C4×Q8C22×D5316yes—
687C4×Q8C22×D5314yes—
688C4×D4—534no—
689C4×D4—534no—
690C4×D4—5312no—
691C4×D4—5312no—
692C4×D4—5312no—
693C4×D4—5312no—
694C4×D4—5312no—
695C4×D4—5312no—
696C4×D4—5312no—
697C4×D4—5312no—
698C4×D4—5312no—
699C4×D4—534no—
700C4×D4—536no—
701C4×D4—536no—
702C4×D4—5312no—
703C4×D4—5312no—
704C4×D4—5312no—
705C4×D4C22×D5314yes—
706C4×D4C22×D5316yes—
707C4×D4C22×D53112yes—
708C4×D4C22×D5316yes—
709C4×D4C22×D53112yes—
710#117—536no—
711#117—5312no—
712#117—5312no—
713#117—5312no—
714#117—534no—
715#117—5312no—
716#117—5312no—
717#117—5312no—
718#117—5312no—
719#117C22×D5316yes—
720#117C22×D53112yes—
721#117C22×D53112yes—
722C2×C4⋊C4—533no—
723C2×C4⋊C4—536no—
724C2×C4⋊C4—5312no—
725C2×C4⋊C4—5312no—
726C2×C4⋊C4—5312no—
727C2×C4⋊C4C22×D5313yes—
728C2×C4⋊C4C22×D53112yes—
729C2×C42—533no—
730C2×C42—533no—
731C2×C42—533no—
732C2×C42—536no—
733C2×C42—536no—
734C2×C42—536no—
735C2×C42—536no—
736C2×C42—5312no—
737C2×C42C22×D5313yes—
738C2×C42C22×D53112yes—
739C24—531no—
740#41—216no—
741#41—224no—
742#41—10616no—
743#41—10616no—
744#41—10624no—
745#41—21224no—
746C2×Q8—216no—
747C2×Q8—534no—
748C2×Q8—5312no—
749C2×Q8—536no—
750C2×Q8—5312no—
751C2×Q8—10616no—
752C2×Q8—10616no—
753C2×Q8—10616no—
754C2×Q8—10612no—
755C2×Q8#1171994518yescomplemented
756C2×Q8C23×D5316yes—
757C2×Q8C23×D5314yes—
758C2×D4—534no—
759C2×D4—534no—
760C2×D4—534no—
761C2×D4—534no—
762C2×D4—5312no—
763C2×D4—534no—
764C2×D4—534no—
765C2×D4—536no—
766C2×D4C23×D5314yes—
767C2×D4C23×D5316yes—
768C22×C4—531no—
769C22×C4—531no—
770C22×C4—533no—
771C22×C4—533no—
772C22×C4—531no—
773C22×C4—531no—
774C22×C4—536no—
775C22×C4—536no—
776C22×C4—536no—
777C22×C4—5312no—
778C22×C4—531no—
779C22×C4—534no—
780C22×C4—536no—
781C22×C4—5312no—
782C22×C4—1064no—
783C22×C4—10612no—
784C22×C4—2126no—
785C22×C4C23×D53112yes—
786C22×C4C23×D5311yescharacteristic
787C22×C4C23×D5314yes—
788C22×C4C23×D5313yes—
789C22×C4C23×D53112yes—
790C22×C4C23×D5313yes—
791C4⋊C4—5312no—
792C4⋊C4—5324no—
793C4⋊C4—536no—
794C4⋊C4—5312no—
795C4⋊C4—536no—
796C4⋊C4—534no—
797C4⋊C4—534no—
798C4⋊C4—534no—
799C4⋊C4—534no—
800C4⋊C4—534no—
801C4⋊C4—5312no—
802C4⋊C4—5312no—
803C4⋊C4—5312no—
804C4⋊C4—5312no—
805C4⋊C4—5312no—
806C4⋊C4—5312no—
807C4⋊C4—5312no—
808C4⋊C4—5312no—
809C4⋊C4C23×D53112yes—
810C4⋊C4C23×D5316yes—
811C4⋊C4C23×D53112yes—
812C4⋊C4C23×D5316yes—
813C4⋊C4C23×D5314yes—
814C22⋊C4—534no—
815C22⋊C4—534no—
816C22⋊C4—5312no—
817C22⋊C4—5312no—
818C22⋊C4—5312no—
819C22⋊C4—534no—
820C22⋊C4—534no—
821C22⋊C4—5312no—
822C22⋊C4—534no—
823C22⋊C4—534no—
824C22⋊C4—534no—
825C22⋊C4—534no—
826C22⋊C4—5312no—
827C22⋊C4—5312no—
828C22⋊C4—5312no—
829C22⋊C4C23×D5314yes—
830C22⋊C4C23×D53112yes—
831C22⋊C4C23×D5314yes—
832C42—536no—
833C42—536no—
834C42—536no—
835C42—536no—
836C42—536no—
837C42—5312no—
838C42—5312no—
839C42—536no—
840C42—534no—
841C42C23×D5316yes—
842C42C23×D53112yes—
843C42C23×D53112yes—
844C42C23×D5316yes—
845C42C23×D5314yes—
846C23—531no—
847C23—531no—
848C23—534no—
849C23—1062no—
850C23—1062no—
851C23—1062no—
852C23C24×D5314yes—
853C23C24×D5311yescharacteristic
854Q8—212no—
855Q8—1068no—
856Q8—10624no—
857Q8—10612no—
858Q8—21212no—
859Q8C2×#11719945116yes—
860D4—28no—
861D4—212no—
862D4—1068no—
863D4—1068no—
864D4—1068no—
865D4—1068no—
866D4—1068no—
867D4—1068no—
868D4—10612no—
869D4—21212no—
870C2×C4—224no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—531no—
876C2×C4—534no—
877C2×C4—531no—
878C2×C4—534no—
879C2×C4—536no—
880C2×C4—534no—
881C2×C4—534no—
882C2×C4—536no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—10612no—
886C2×C4—1062no—
887C2×C4—1066no—
888C2×C4—10612no—
889C2×C4—10612no—
890C2×C4—10624no—
891C2×C4—1062no—
892C2×C4—1068no—
893C2×C4—2126no—
894C2×C4—21212no—
895C2×C4—2123no—
896C2×C4C2×#11719945112yes—
897C2×C4C24×D5311yescharacteristic
898C2×C4C24×D5316yes—
899C2×C4C24×D5314yes—
900C2×C4C24×D5314yes—
901C2×C4C24×D5314yes—
902C2×C4C24×D5316yes—
903C2×C4C24×D5311yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—532no—
910C22—532no—
911C22—1068no—
912C22—1061no—
913C22—1061no—
914C22—1061no—
915C22—1061no—
916C22—1064no—
917C22—1064no—
918C22—1064no—
919C22C22×#1171994512yes—
920C22C25×D5311yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—532no—
927C4—1064no—
928C4—1066no—
929C4—1061no—
930C4—1064no—
931C4—1066no—
932C4—1064no—
933C4C22×#11719945112yes—
934C42−1+4×D5312yes—
935C2—22no—
936C2—44no—
937C2—1062no—
938C2—1062no—
939C2—2124no—
940C2C23×#1171994511yescharacteristic
941C2C2×2−1+4×D5311yescharacteristic
942C2#585×D5311yescharacteristic
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC4×2−1+4×C53C2
hypercenterC4×2−1+4D53
hypocenterC53#62788
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #20288805C2semidirect
2. #20288794C2semidirect
3. #20288710C2semidirect
4. #20288700C2semidirect
5. #20288573C2semidirect
6. #20288521C2semidirect
7. #20288482C2semidirect
8. #20288418C2semidirect
9. #20288367C2semidirect
10. #20288363C2semidirect
11. #20288337C2semidirect
12. #20288332C2semidirect
13. #20288313C2semidirect
14. Q8×#11719945C2semidirect
15. #20288142C2semidirect
16. #20288008C2semidirect
17. C4×#13133265C2semidirect
18. C2×C4×Q8×D53C2semidirect
19. C4×2−1+4×C53C2semidirect
22. #16811356C22semidirect
23. Q8×Dic106C22semidirect
24. #16811352C22semidirect
25. #16811351C22semidirect
26. #16811349C22semidirect
27. #16811349C22semidirect
28. #16811345C22semidirect
29. #16811343C22semidirect
30. #16811341C22semidirect
33. #16811328C22semidirect
38. #16811312C22semidirect
39. #16811308C22semidirect
40. #16811292C22semidirect
45. Q8×C22⋊D53C22semidirect
48. #16811284C22semidirect
51. #16811280C22semidirect
55. #16811244C22semidirect
56. #16811238C22semidirect
57. #16811235C22semidirect
58. #16811231C22semidirect
63. #16811180C22semidirect
66. #16811177C22semidirect
73. #16811157C22semidirect
76. #16811155C22semidirect
85. #16811105C22semidirect
88. #16811099C22semidirect
89. C4×#11719949C22semidirect
100. C4×Q8×D53C22semidirect
105. C53×#520C22semidirect
107. C53×#519C22semidirect
109. C4×#41×C53C22semidirect
111. C2×C4×Q8×C53C22semidirect
271. C2×Q8×C53#41semidirect
427. C4×D532−1+4semidirect
481. C4×2−1+4D53semidirect
560. #520C2×D53semidirect
564. #519C2×D53semidirect
570. C4×#41C2×D53semidirect
580. C2×C4×Q8C2×D53semidirect
583. C53#62788semidirect
755. C2×Q8#11719945semidirect

Maximal subgroups

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

subgroupindex
#202888052
#202887942
#202887102
#202887002
#202885732
#202885212
#202884822
#202884182
#202883672
#202883632
#202883372
#202883322
#202883132
Q8×#117199452
#202881422
#202880082
C4×#131332652
C2×C4×Q8×D532
C4×2−1+4×C532
#6278853