Finite Group Databasebeta

← #16769777

Subgroups — #16769777

Order 3328.

7226 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128266C216yesmaximal, complemented
2#13128265C216yesmaximal, complemented
3#13128255C216yesmaximal, complemented
4#13128254C216yesmaximal, complemented
5#13128248C211yesmaximal, characteristic, complemented
6#13128245C213yesmaximal, complemented
7#13128242C213yesmaximal, complemented
8#13128238C211yesmaximal, characteristic, complemented
9#13128222C216yesmaximal, complemented
10#13128218C216yesmaximal, complemented
11#13128162C213yesmaximal, complemented
12#13128130C216yesmaximal, complemented
13#13128128C216yesmaximal, complemented
14C2×C4×#6129C213yesmaximal, complemented
15C13×#3459C211yesmaximal, characteristic, complemented
16C22×#6129C2213yes—
17C13×#543C2211yescharacteristic
18C13×#539C2216yescomplemented
19C13×#538C2216yescomplemented
20C13×#534C2213yes—
21C13×#529C2216yescomplemented
22C13×#525C2216yescomplemented
23C2×C4×D4×C13C2213yes—
24#11719537C2216yescomplemented
25#41×Dic13C2212yescomplemented
26#11719509C2216yes—
27C2×D4×Dic13C2213yes—
28#11719496C2216yescomplemented
29C2×C4×C22⋊D13C2213yes—
30C2×C4×C22⋊D13C2213yescomplemented
31C22×C4×Dic13C2211yescharacteristic
32C22×C4×Dic13C2213yescomplemented
33#11719415C22112yescomplemented
34#11719411C22112yescomplemented
35#11719411C22112yescomplemented
36#11719406C22112yescomplemented
37#11719401C22112yescomplemented
38#11719396C2216yescomplemented
39#11719393C2216yescomplemented
40#11719385C2216yescomplemented
41#11719374C22112yescomplemented
42#11719373C2216yescomplemented
43#11719370C22112yescomplemented
44#11719368C22112yescomplemented
45#11719367C22112yescomplemented
46#11719361C22112yescomplemented
47#11719354C22112yescomplemented
48#11719354C22112yescomplemented
49#11719354C22112yescomplemented
50#11719353C22112yescomplemented
51#11719350C2216yescomplemented
52#11719349C2216yescomplemented
53#11719345C22112yescomplemented
54#11719332C2216yescomplemented
55#11719329C2216yescomplemented
56#11719329C2216yescomplemented
57#11719328C2216yescomplemented
58#11719328C2216yescomplemented
59#11719327C2216yescomplemented
60#11719327C2216yescomplemented
61#11719327C2216yescomplemented
62#11719322C2216yescomplemented
63#11719320C22112yescomplemented
64#11719311C2216yescomplemented
65#11719307C2216yescomplemented
66#11719305C2216yescomplemented
67#11719305C2216yescomplemented
68#11719302C2216yes—
69#11719302C2216yes—
70#11719301C2216yes—
71#11719301C2216yes—
72#11719301C2216yescomplemented
73#11719298C22112yescomplemented
74#11719297C22112yescomplemented
75#11719291C22112yescomplemented
76#11719291C22112yescomplemented
77#11719283C2216yescomplemented
78C4×#6131C2212yescomplemented
79#11719269C22112yescomplemented
80#11719265C22112yescomplemented
81#11719253C2216yescomplemented
82#11719252C22112yescomplemented
83#11719243C22112yescomplemented
84#11719243C22112yescomplemented
85C4×#6129C22112yescomplemented
86C4×#6129C22112yescomplemented
87C4×#6129C22112yescomplemented
88C4×#6129C22112yescomplemented
89C4×#6129C2216yescomplemented
90#11719233C22112yescomplemented
91#11719227C2216yescomplemented
92#11719222C2216yescomplemented
93#11719220C2216yescomplemented
94C2×#88146C2213yescomplemented
95C2×#88141C2213yescomplemented
96#11719199C2216yescomplemented
97#11719198C2213yes—
98C2×#88135C2213yes—
99C2×#88135C2213yescomplemented
100#11719188C2213yes—
101C2×#88131C2213yes—
102C2×#88131C2213yescomplemented
103#11719184C2216yescomplemented
104C2×C42×D13C2213yescomplemented
105C2×C4×Dic26C2213yescomplemented
106C2×C13×#41C2312yes—
107C22×D4×C13C2313yes—
108C23×C4×C13C2311yescharacteristic
109C23×C4×C13C2313yes—
110C22×C22⋊D13C2313yes—
111C22×C22⋊D13C2313yes—
112C23×Dic13C2313yes—
113C23×Dic13C2311yescharacteristic
114C23×Dic13C2313yes—
115C23×Dic13C2311yescharacteristic
116C2×#6131C2312yes—
117C2×#6129—224no—
118C2×#6129C23112yes—
119C2×#6129C23112yes—
120C2×#6129C2316yes—
121C2×#6127C2316yes—
122C22×C4×D13C2313yes—
123C22×C4×D13C2313yes—
124C22×C4×D13C2313yes—
125C22×Dic26C2313yes—
126C13×#126C23112yes—
127C13×#125C2316yes—
128C13×#124C2316yes—
129C13×#123C23112yes—
130C13×#123C23112yes—
131C13×C22⋊Q8C2316yes—
132C13×C22⋊Q8C2316yes—
133C13×C22⋊Q8C2316yes—
134C13×#121C2316yes—
135C13×#121C2316yes—
136C13×#121C2316yes—
137C13×#120C23112yes—
138C4×Q8×C13C2312yes—
139C4×D4×C13C23112yes—
140C4×D4×C13C23112yes—
141C4×D4×C13C2316yes—
142C13×#117C2316yes—
143C2×C13×C4⋊C4C2313yes—
144C2×C13×C22⋊C4C2313yes—
145C2×C13×C22⋊C4C2313yes—
146C2×C42×C13C2313yes—
147#88207C23112yes—
148C2×C22⋊Dic13C2313yes—
149C2×C22⋊Dic13C2313yes—
150#88201C2316yes—
151#88200C2316yes—
152Q8×Dic13C2312yes—
153Q8×Dic13C2312yes—
154Q8×Dic13C2312yes—
155#88198C2316yes—
156#88198C2316yes—
157#88194C2316yes—
158#88194C2316yes—
159#88193C23112yes—
160#88193C23112yes—
161#88193C23112yes—
162#88193C23112yes—
163#88193C23112yes—
164#88192C2316yes—
165#88191C23112yes—
166#88190C2316yes—
167#88189C23112yes—
168#88189C23112yes—
169D4×Dic13C23112yes—
170D4×Dic13C23112yes—
171D4×Dic13C2316yes—
172D4×Dic13C2316yes—
173D4×Dic13C2316yes—
174#88184C2316yes—
175#88184C2316yes—
176#88184C2316yes—
177#88183C23112yes—
178#88183C23112yes—
179C4×C22⋊D13C23112yes—
180C4×C22⋊D13C23112yes—
181C4×C22⋊D13C23112yes—
182C4×C22⋊D13C23112yes—
183C4×C22⋊D13C23112yes—
184C2×#6103C2313yes—
185C2×#6103C2313yes—
186#88180C2316yes—
187C2×C4⋊Dic13C2313yes—
188#88178C2316yes—
189#88178C2316yes—
190#88178C2316yes—
191C2×#6101C2313yes—
192C2×#6101C2313yes—
193C2×#6101C2313yes—
194C2×#6101C2313yes—
195C2×C4×Dic13C2313yes—
196C2×C4×Dic13C2313yes—
197C2×C4×Dic13C2313yes—
198C2×C4×Dic13C2313yes—
199C2×C4×Dic13C2313yes—
200C2×C4×Dic13C2313yes—
201C2×C4×Dic13C2313yes—
202C2×C4×Dic13C2313yes—
203C2×C4×Dic13C2313yes—
204C2×C4×Dic13C2316yes—
205C2×C4×Dic13C2316yes—
206C2×C4×Dic13C2316yes—
207C2×C4×Dic13C2316yes—
208#88152C23112yes—
209#88152C23112yes—
210#88152C23112yes—
211#88151C2316yes—
212#88150C23112yes—
213#88150C23112yes—
214#88150C23112yes—
215#88149C2316yes—
216#88148C23112yes—
217#88148C23112yes—
218#88147C2316yes—
219#88147C2316yes—
220#88147C2316yes—
221#88146C23112yes—
222#88146C23112yes—
223#88146C2316yes—
224#88146C2316yes—
225#88144C2316yes—
226#88144C2316yes—
227#88143C23112yes—
228#88143C23112yes—
229#88143C23112yes—
230#88143C23112yes—
231#88142C2316yes—
232#88142C2316yes—
233#88142C2316yes—
234#88142C2316yes—
235#88141C23112yes—
236#88141C23112yes—
237#88141C2316yes—
238#88141C2316yes—
239#88141C2316yes—
240#88140C23112yes—
241#88140C23112yes—
242#88139C23112yes—
243#88139C23112yes—
244#88139C23112yes—
245#88139C23112yes—
246#88138C23112yes—
247#88138C23112yes—
248#88138C23112yes—
249#88137C23112yes—
250#88137C23112yes—
251#88136C23112yes—
252#88135C23112yes—
253#88135C23112yes—
254#88135C23112yes—
255#88135C23112yes—
256#88135C23112yes—
257#88135C23112yes—
258#88135C23112yes—
259#88133C23112yes—
260#88133C23112yes—
261#88133C23112yes—
262#88132C23112yes—
263#88132C23112yes—
264#88132C23112yes—
265#88132C23112yes—
266#88132C23112yes—
267#88131C23112yes—
268#88131C23112yes—
269#88131C23112yes—
270#88131C23112yes—
271#88131C23112yes—
272#88130C23112yes—
273#88129C2316yes—
274C4×D52C2316yes—
275#88126C23112yes—
276C42×D13C2316yes—
277C42×D13C2316yes—
278C42×D13C2316yes—
279C42×D13C2316yes—
280#88124C2316yes—
281C4×Dic26C23112yes—
282C4×Dic26C23112yes—
283C4×Dic26C2316yes—
284#62686—131nomaximal, Sylow
285C24×C13C2413yes—
286C24×C13C2411yescharacteristic
287C23×D13C2413yes—
288C13×#41—44no—
289C2×Q8×C13C2412yes—
290C2×Q8×C13C2412yes—
291C2×D4×C13—212no—
292C2×D4×C13C24112yes—
293C2×D4×C13C2416yes—
294C2×D4×C13C2416yes—
295C22×C4×C13—42no—
296C22×C4×C13—46no—
297C22×C4×C13C2413yes—
298C22×C4×C13C2416yes—
299C22×C4×C13C2413yes—
300C22×C4×C13C2413yes—
301C22×C4×C13C2413yes—
302C22×C4×C13C2416yes—
303C22×C4×C13C2413yes—
304C2×C22⋊D13—212no—
305C2×C22⋊D13—212no—
306C2×C22⋊D13C24112yes—
307C2×C22⋊D13C24112yes—
308C2×C22⋊D13C24112yes—
309C2×C22⋊D13C24112yes—
310C22×Dic13—212no—
311C22×Dic13—42no—
312C22×Dic13—46no—
313C22×Dic13#4118yescomplemented
314C22×Dic13C2416yes—
315C22×Dic13C2416yes—
316C22×Dic13C2416yes—
317C22×Dic13C2413yes—
318C22×Dic13C2413yes—
319C22×Dic13C2413yes—
320C22×Dic13C2413yes—
321C22×Dic13C2416yes—
322C22×Dic13C2413yes—
323C22×Dic13C2413yes—
324C22×Dic13C2413yes—
325#6131—44no—
326#6129—248no—
327#6129—248no—
328#6129—412no—
329#6127—412no—
330C2×D52C2416yes—
331C2×D52C2416yes—
332C2×C4×D13—212no—
333C2×C4×D13—46no—
334C2×C4×D13—46no—
335C2×C4×D13C2416yes—
336C2×C4×D13C2416yes—
337C2×C4×D13C2416yes—
338C2×C4×D13C2416yes—
339C2×C4×D13C2416yes—
340C2×C4×D13C2416yes—
341C2×Dic26—212no—
342C2×Dic26C24112yes—
343C2×Dic26C2416yes—
344C2×Dic26C2416yes—
345C13×C4⋊C4C24112yes—
346C13×C4⋊C4C2416yes—
347C13×C4⋊C4C2416yes—
348C13×C4⋊C4C2416yes—
349C13×C4⋊C4C2416yes—
350C13×C22⋊C4C24112yes—
351C13×C22⋊C4C24112yes—
352C13×C22⋊C4C24112yes—
353C13×C22⋊C4C24112yes—
354C42×C13C2416yes—
355C42×C13C2416yes—
356C22⋊Dic13C24112yes—
357C22⋊Dic13C24112yes—
358C22⋊Dic13C24112yes—
359C22⋊Dic13C24112yes—
360#6103C24112yes—
361#6103C24112yes—
362#6103C24112yes—
363#6103C24112yes—
364#6103C24112yes—
365#6103C24112yes—
366C4⋊Dic13C24112yes—
367C4⋊Dic13C2416yes—
368C4⋊Dic13C2416yes—
369C4⋊Dic13C2416yes—
370C4⋊Dic13C2416yes—
371#6101C24112yes—
372#6101C24112yes—
373#6101C24112yes—
374#6101C24112yes—
375#6101C24112yes—
376#6101C24112yes—
377#6101C24112yes—
378#6101C24112yes—
379C4×Dic13C2413yes—
380C4×Dic13C2416yes—
381C4×Dic13C2416yes—
382C4×Dic13C2416yes—
383C4×Dic13C2411yescharacteristic
384C4×Dic13C2416yes—
385C4×Dic13C2416yes—
386C4×Dic13C2413yes—
387C4×Dic13C2416yes—
388C4×Dic13C2416yes—
389C4×Dic13C2413yes—
390C4×Dic13C2416yes—
391C4×Dic13C2416yes—
392C4×Dic13C2416yes—
393C4×Dic13C2416yes—
394#3461—136no—
395#3461—136no—
396#3460—136no—
397#3460—136no—
398#3459—131no—
399#3459—133no—
400#3459—133no—
401#3459D1311yescharacteristic, complemented
402#3458—131no—
403#3455—136no—
404#3455—136no—
405#3449—133no—
406#3444—136no—
407#3444—136no—
408C2×C4×#41—133no—
409C23×C13—26no—
410C23×C13—41no—
411C23×C13—43no—
412C23×C13—41no—
413C23×C13—43no—
414C23×C13C2×#4114yes—
415C23×C13C2516yes—
416C23×C13C2513yes—
417C22×D13—26no—
418C22×D13—43no—
419C22×D13—43no—
420C22×D13C2516yes—
421Q8×C13—42no—
422Q8×C13—42no—
423D4×C13—224no—
424D4×C13—46no—
425D4×C13—46no—
426C2×C4×C13—26no—
427C2×C4×C13—26no—
428C2×C4×C13—212no—
429C2×C4×C13—43no—
430C2×C4×C13—43no—
431C2×C4×C13—46no—
432C2×C4×C13—43no—
433C2×C4×C13C2513yes—
434C2×C4×C13C2516yes—
435C2×C4×C13C2516yes—
436C2×C4×C13C2516yes—
437C2×C4×C13C2511yescharacteristic
438C22⋊D13—224no—
439C22⋊D13—224no—
440C22⋊D13—412no—
441C22⋊D13—412no—
442C2×Dic13—26no—
443C2×Dic13—212no—
444C2×Dic13—212no—
445C2×Dic13—26no—
446C2×Dic13—212no—
447C2×Dic13—43no—
448C2×Dic13—43no—
449C2×Dic13—46no—
450C2×Dic13—43no—
451C2×Dic13C2×#41112yes—
452C2×Dic13C2×#41112yes—
453C2×Dic13C2513yes—
454C2×Dic13C2516yes—
455C2×Dic13C2516yes—
456C2×Dic13C2516yes—
457C2×Dic13C2511yescharacteristic
458C2×Dic13C2513yes—
459C2×Dic13C2511yescharacteristic
460D52—46no—
461D52—46no—
462C4×D13—212no—
463C4×D13—212no—
464C4×D13—212no—
465C4×D13—212no—
466C4×D13—46no—
467C4×D13—46no—
468Dic26—224no—
469Dic26—46no—
470Dic26—46no—
471C22×#41—133no—
472#544—136no—
473#544—136no—
474#543—133no—
475#543C2×D1311yescharacteristic
476#542—1312no—
477#542—1312no—
478#542—1312no—
479#542—1312no—
480#541—1312no—
481#541—1312no—
482#540—1312no—
483#540—1312no—
484#539—1312no—
485#539—136no—
486#539—136no—
487#539—1312no—
488#539—136no—
489#539C2×D1316yescomplemented
490#538—136no—
491#538—136no—
492#538—1312no—
493#538—1312no—
494#538—136no—
495#538C2×D1316yescomplemented
496#537—136no—
497#537—136no—
498#536—1312no—
499#535—1312no—
500#534—136no—
501#534—133no—
502#534C2×D1313yes—
503#533—136no—
504#533—136no—
505#533—136no—
506#533—136no—
507#533—136no—
508#533—136no—
509#532—136no—
510#532—136no—
511#532—136no—
512#532—136no—
513#532—136no—
514#532—136no—
515#529—1312no—
516#529—1312no—
517#529—136no—
518#529—136no—
519#529—1312no—
520#529—1312no—
521#529—1312no—
522#529—136no—
523#529—136no—
524#529—136no—
525#529—136no—
526#529—1312no—
527#529—1312no—
528#529—1312no—
529#529—136no—
530#529C2×D1316yescomplemented
531#525—136no—
532#525—1312no—
533#525—136no—
534#525—136no—
535#525—1312no—
536#525—1312no—
537#525—1312no—
538#525C2×D1316yescomplemented
539C4×#41—132no—
540C4×#41—132no—
541C4×#41—1312no—
542C4×#41—1312no—
543C4×#41—1312no—
544C4×#41—1312no—
545C4×#41—136no—
546C4×#41—136no—
547C2×C4×Q8—133no—
548C2×C4×Q8—133no—
549C2×C4×D4—133no—
550C2×C4×D4—133no—
551C2×C4×D4—133no—
552C2×C4×D4—133no—
553C2×C4×D4—133no—
554C2×C4×D4C2×D1313yes—
555C2×#117—133no—
556C2×#117—133no—
557C2×#117—133no—
558C22×C42—131no—
559C22×C42—133no—
560C22×C42—133no—
561C22×C13—23no—
562C22×C13—23no—
563C22×C13—26no—
564C22×C13—26no—
565C22×C13—26no—
566C22×C13—44no—
567C22×C13—412no—
568C22×C13C22×#4116yes—
569C22×C13C2611yescharacteristic
570C2×D13—26no—
571C2×D13—26no—
572C2×D13—26no—
573C2×D13—412no—
574C4×C13—26no—
575C4×C13—26no—
576C4×C13—26no—
577C4×C13—23no—
578C4×C13#58512yes—
579Dic13—26no—
580Dic13—26no—
581Dic13—26no—
582Dic13—23no—
583Dic13C22×#4116yes—
584Dic13C22×#4112yes—
585Dic13#58512yes—
586C2×#41—132no—
587C2×#41—1312no—
588C2×#41—1312no—
589C2×#41—136no—
590C2×#41—136no—
591C2×#41—2624no—
592C2×#41C22×D1312yes—
593C22×Q8—133no—
594C22×D4—133no—
595C22×D4—133no—
596C22×D4C22×D1313yes—
597C23×C4—131no—
598C23×C4—133no—
599C23×C4—131no—
600C23×C4—133no—
601C23×C4—133no—
602C23×C4—133no—
603C23×C4—133no—
604C23×C4C22×D1311yescharacteristic
605C23×C4C22×D1313yes—
606C4⋊Q8—136no—
607C4⋊Q8—136no—
608C4⋊Q8—136no—
609C4⋊Q8—136no—
610C4⋊Q8—136no—
611C4⋊Q8—136no—
612#127—136no—
613#127—136no—
614#126—1312no—
615#126—1312no—
616#126—1312no—
617#126—1312no—
618#126—1312no—
619#126—1312no—
620#126—1312no—
621#126C22×D13112yes—
622#125—1312no—
623#125—1312no—
624#125—136no—
625#125—136no—
626#125—1312no—
627#125—1312no—
628#125—136no—
629#125C22×D1316yes—
630#124—136no—
631#124—136no—
632#124—1312no—
633#124—1312no—
634#124—1312no—
635#124—1312no—
636#124—136no—
637#124C22×D1316yes—
638#123—1312no—
639#123—1312no—
640#123—1312no—
641#123—1312no—
642#123—1312no—
643#123—1312no—
644#123—1312no—
645#123—1312no—
646#123—1312no—
647#123—1312no—
648#123C22×D13112yes—
649#123C22×D13112yes—
650C22⋊Q8—136no—
651C22⋊Q8—136no—
652C22⋊Q8—136no—
653C22⋊Q8—136no—
654C22⋊Q8—1312no—
655C22⋊Q8—1312no—
656C22⋊Q8—1312no—
657C22⋊Q8—136no—
658C22⋊Q8—1312no—
659C22⋊Q8—1312no—
660C22⋊Q8—1312no—
661C22⋊Q8—1312no—
662C22⋊Q8—1312no—
663C22⋊Q8C22×D1316yes—
664C22⋊Q8C22×D1316yes—
665C22⋊Q8C22×D1316yes—
666#121—1312no—
667#121—1312no—
668#121—1312no—
669#121—1312no—
670#121—136no—
671#121—1312no—
672#121—136no—
673#121—136no—
674#121—136no—
675#121—136no—
676#121—1312no—
677#121—1312no—
678#121—1312no—
679#121C22×D1316yes—
680#121C22×D1316yes—
681#121C22×D1316yes—
682#120—1312no—
683#120—1312no—
684#120—1312no—
685#120C22×D13112yes—
686C4×Q8—132no—
687C4×Q8—132no—
688C4×Q8—132no—
689C4×Q8—1312no—
690C4×Q8—1312no—
691C4×Q8—136no—
692C4×Q8—136no—
693C4×Q8—136no—
694C4×Q8—1312no—
695C4×Q8—1312no—
696C4×Q8—136no—
697C4×Q8C22×D1312yes—
698C4×D4—1312no—
699C4×D4—1312no—
700C4×D4—136no—
701C4×D4—136no—
702C4×D4—136no—
703C4×D4—1312no—
704C4×D4—1312no—
705C4×D4—1312no—
706C4×D4—1312no—
707C4×D4—1312no—
708C4×D4—136no—
709C4×D4—136no—
710C4×D4—136no—
711C4×D4—1312no—
712C4×D4—1312no—
713C4×D4—1312no—
714C4×D4—1312no—
715C4×D4—1312no—
716C4×D4—1312no—
717C4×D4—1312no—
718C4×D4—136no—
719C4×D4C22×D13112yes—
720C4×D4C22×D13112yes—
721C4×D4C22×D1316yes—
722#117—136no—
723#117—1312no—
724#117—1312no—
725#117—136no—
726#117—136no—
727#117—1312no—
728#117—1312no—
729#117—1312no—
730#117—1312no—
731#117—1312no—
732#117—1312no—
733#117C22×D1316yes—
734C2×C4⋊C4—133no—
735C2×C4⋊C4—133no—
736C2×C4⋊C4—133no—
737C2×C4⋊C4—133no—
738C2×C4⋊C4—133no—
739C2×C4⋊C4C22×D1313yes—
740C2×C22⋊C4—133no—
741C2×C22⋊C4—133no—
742C2×C22⋊C4—133no—
743C2×C22⋊C4—133no—
744C2×C22⋊C4C22×D1313yes—
745C2×C22⋊C4C22×D1313yes—
746C2×C42—133no—
747C2×C42—133no—
748C2×C42—133no—
749C2×C42—133no—
750C2×C42—133no—
751C2×C42—133no—
752C2×C42—133no—
753C2×C42—133no—
754C2×C42—136no—
755C2×C42—133no—
756C2×C42—136no—
757C2×C42—136no—
758C2×C42—136no—
759C2×C42—136no—
760C2×C42—136no—
761C2×C42—136no—
762C2×C42—136no—
763C2×C42C22×D1313yes—
764C2×C13—26no—
765C2×C13—46no—
766C2×C13C23×#4111yescharacteristic
767C2×C13C2×#58511yescharacteristic
768C2×C13C2×#58511yescharacteristic
769D13—46no—
770C24—133no—
771C24C23×D1313yes—
772C24C23×D1311yescharacteristic
773#41—44no—
774#41—2648no—
775#41—2648no—
776#41—5212no—
777#41—5212no—
778#41—524no—
779C2×Q8—1312no—
780C2×Q8—136no—
781C2×Q8—136no—
782C2×Q8—2612no—
783C2×Q8C23×D1312yes—
784C2×Q8C23×D1312yes—
785C2×D4—212no—
786C2×D4—1312no—
787C2×D4—1312no—
788C2×D4—1312no—
789C2×D4—1312no—
790C2×D4—136no—
791C2×D4—136no—
792C2×D4—2612no—
793C2×D4—2612no—
794C2×D4C23×D13112yes—
795C2×D4C23×D1316yes—
796C2×D4C23×D1316yes—
797C22×C4—42no—
798C22×C4—46no—
799C22×C4—138no—
800C22×C4—133no—
801C22×C4—133no—
802C22×C4—133no—
803C22×C4—133no—
804C22×C4—136no—
805C22×C4—136no—
806C22×C4—136no—
807C22×C4—133no—
808C22×C4—133no—
809C22×C4—133no—
810C22×C4—136no—
811C22×C4—136no—
812C22×C4—136no—
813C22×C4—136no—
814C22×C4—136no—
815C22×C4—136no—
816C22×C4—136no—
817C22×C4—2612no—
818C22×C4—2612no—
819C22×C4—526no—
820C22×C4—526no—
821C22×C4—522no—
822C22×C4—526no—
823C22×C4C23×D1313yes—
824C22×C4C23×D1313yes—
825C22×C4C23×D1316yes—
826C22×C4C23×D1313yes—
827C22×C4C23×D1313yes—
828C22×C4C23×D1316yes—
829C22×C4C23×D1313yes—
830C4⋊C4—1312no—
831C4⋊C4—1312no—
832C4⋊C4—1312no—
833C4⋊C4—1312no—
834C4⋊C4—1312no—
835C4⋊C4—1312no—
836C4⋊C4—1312no—
837C4⋊C4—1312no—
838C4⋊C4—1312no—
839C4⋊C4—136no—
840C4⋊C4—136no—
841C4⋊C4—136no—
842C4⋊C4—136no—
843C4⋊C4C23×D13112yes—
844C4⋊C4C23×D1316yes—
845C4⋊C4C23×D1316yes—
846C4⋊C4C23×D1316yes—
847C4⋊C4C23×D1316yes—
848C22⋊C4—1312no—
849C22⋊C4—1312no—
850C22⋊C4—1312no—
851C22⋊C4—1312no—
852C22⋊C4—1312no—
853C22⋊C4—1312no—
854C22⋊C4—1312no—
855C22⋊C4—1312no—
856C22⋊C4—1312no—
857C22⋊C4—1312no—
858C22⋊C4C23×D13112yes—
859C22⋊C4C23×D13112yes—
860C22⋊C4C23×D13112yes—
861C22⋊C4C23×D13112yes—
862C42—133no—
863C42—133no—
864C42—136no—
865C42—136no—
866C42—136no—
867C42—136no—
868C42—136no—
869C42—136no—
870C42—136no—
871C42—136no—
872C42—136no—
873C42—136no—
874C42—131no—
875C42—133no—
876C42—136no—
877C42C23×D1316yes—
878C42C23×D1316yes—
879C13#6268611yescharacteristic, complemented, Sylow
880C23—26no—
881C23—41no—
882C23—43no—
883C23—41no—
884C23—43no—
885C23—136no—
886C23—266no—
887C23—523no—
888C23—523no—
889C23#41×D1314yes—
890C23C24×D1316yes—
891C23C24×D1313yes—
892Q8—42no—
893Q8—42no—
894Q8—2624no—
895Q8—526no—
896Q8—526no—
897D4—224no—
898D4—46no—
899D4—46no—
900D4—2624no—
901D4—2624no—
902D4—526no—
903D4—526no—
904D4—5212no—
905D4—5212no—
906C2×C4—26no—
907C2×C4—26no—
908C2×C4—212no—
909C2×C4—43no—
910C2×C4—46no—
911C2×C4—43no—
912C2×C4—43no—
913C2×C4—1312no—
914C2×C4—1312no—
915C2×C4—131no—
916C2×C4—131no—
917C2×C4—133no—
918C2×C4—133no—
919C2×C4—136no—
920C2×C4—136no—
921C2×C4—136no—
922C2×C4—2612no—
923C2×C4—2612no—
924C2×C4—2612no—
925C2×C4—2612no—
926C2×C4—2612no—
927C2×C4—266no—
928C2×C4—2612no—
929C2×C4—266no—
930C2×C4—2612no—
931C2×C4—526no—
932C2×C4—526no—
933C2×C4—523no—
934C2×C4—526no—
935C2×C4—523no—
936C2×C4—523no—
937C2×C4C24×D1313yes—
938C2×C4C24×D1316yes—
939C2×C4C24×D1316yes—
940C2×C4C24×D1316yes—
941C2×C4C24×D1311yescharacteristic
942C22—23no—
943C22—23no—
944C22—26no—
945C22—26no—
946C22—26no—
947C22—44no—
948C22—412no—
949C22—266no—
950C22—266no—
951C22—266no—
952C22—5212no—
953C22C2×#41×D1316yes—
954C22C25×D1311yescharacteristic
955C4—26no—
956C4—26no—
957C4—23no—
958C4—26no—
959C4—132no—
960C4—136no—
961C4—132no—
962C4—266no—
963C4—263no—
964C4—266no—
965C4—266no—
966C4#1171965012yes—
967C2—26no—
968C2—46no—
969C2—526no—
970C2C22×#41×D1311yescharacteristic
971C2D13×#58511yescharacteristic
972C2C2×#1171965011yescharacteristic
subgroupG/H
centerC2×C4C24×D13
commutator, socle, cosocleC22×C13C26
FrattiniC22C25×D13
FittingC13×#3459C2
hypercenter#3459D13
hypocenterC13#62686
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #3459

Complements

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

NH ≅ G/Ntype
1. #13128266C2semidirect
2. #13128265C2semidirect
3. #13128255C2semidirect
4. #13128254C2semidirect
5. #13128248C2semidirect
6. #13128245C2semidirect
7. #13128242C2semidirect
8. #13128238C2semidirect
9. #13128222C2semidirect
10. #13128218C2semidirect
11. #13128162C2semidirect
12. #13128130C2semidirect
13. #13128128C2semidirect
14. C2×C4×#6129C2semidirect
15. C13×#3459C2semidirect
18. C13×#539C22semidirect
19. C13×#538C22semidirect
21. C13×#529C22semidirect
22. C13×#525C22semidirect
24. #11719537C22semidirect
25. #41×Dic13C22semidirect
28. #11719496C22semidirect
30. C2×C4×C22⋊D13C22semidirect
32. C22×C4×Dic13C22semidirect
33. #11719415C22semidirect
34. #11719411C22semidirect
35. #11719411C22semidirect
36. #11719406C22semidirect
37. #11719401C22semidirect
38. #11719396C22semidirect
39. #11719393C22semidirect
40. #11719385C22semidirect
41. #11719374C22semidirect
42. #11719373C22semidirect
43. #11719370C22semidirect
44. #11719368C22semidirect
45. #11719367C22semidirect
46. #11719361C22semidirect
47. #11719354C22semidirect
48. #11719354C22semidirect
49. #11719354C22semidirect
50. #11719353C22semidirect
51. #11719350C22semidirect
52. #11719349C22semidirect
53. #11719345C22semidirect
54. #11719332C22semidirect
55. #11719329C22semidirect
56. #11719329C22semidirect
57. #11719328C22semidirect
58. #11719328C22semidirect
59. #11719327C22semidirect
60. #11719327C22semidirect
61. #11719327C22semidirect
62. #11719322C22semidirect
63. #11719320C22semidirect
64. #11719311C22semidirect
65. #11719307C22semidirect
66. #11719305C22semidirect
67. #11719305C22semidirect
72. #11719301C22semidirect
73. #11719298C22semidirect
74. #11719297C22semidirect
75. #11719291C22semidirect
76. #11719291C22semidirect
77. #11719283C22semidirect
78. C4×#6131C22semidirect
79. #11719269C22semidirect
80. #11719265C22semidirect
81. #11719253C22semidirect
82. #11719252C22semidirect
83. #11719243C22semidirect
84. #11719243C22semidirect
85. C4×#6129C22semidirect
86. C4×#6129C22semidirect
87. C4×#6129C22semidirect
88. C4×#6129C22semidirect
89. C4×#6129C22semidirect
90. #11719233C22semidirect
91. #11719227C22semidirect
92. #11719222C22semidirect
93. #11719220C22semidirect
94. C2×#88146C22semidirect
95. C2×#88141C22semidirect
96. #11719199C22semidirect
99. C2×#88135C22semidirect
102. C2×#88131C22semidirect
103. #11719184C22semidirect
104. C2×C42×D13C22semidirect
105. C2×C4×Dic26C22semidirect
313. C22×Dic13#41semidirect
401. #3459D13semidirect
489. #539C2×D13semidirect
495. #538C2×D13semidirect
530. #529C2×D13semidirect
538. #525C2×D13semidirect
879. C13#62686semidirect

Maximal subgroups

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

subgroupindex
#131282662
#131282652
#131282552
#131282542
#131282482
#131282452
#131282422
#131282382
#131282222
#131282182
#131281622
#131281302
#131281282
C2×C4×#61292
C13×#34592
#6268613