Finite Group Databasebeta

← #16771463

Subgroups — #16771463

Order 3328.

11346 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719650C212yesmaximal, complemented
2#13128628C216yesmaximal, complemented
3#13128624C212yesmaximal, complemented
4#13128621C211yesmaximal, characteristic, complemented
5#13128616C213yesmaximal, complemented
6#13128612C213yesmaximal, complemented
7#13128601C214yesmaximal, complemented
8#13128592C2112yesmaximal, complemented
9#13128326C214yesmaximal, complemented
10D4×#6129C2112yesmaximal, complemented
11#13128167C216yesmaximal, complemented
12C2×#11719421C213yesmaximal, complemented
13D13×#532C213yesmaximal, complemented
14C4×#41×D13C211yesmaximal, characteristic, complemented
15C13×#3498C211yesmaximal, characteristic, complemented
16C2×C13×H(5,𝔽2)C2212yescomplemented
17#11719650—232no—
18C2×#88257C2214yescomplemented
19C2×#88257C2216yescomplemented
20C2×#88257C2212yescomplemented
21C2×#41×D13C2211yescharacteristic
22C2×#41×D13C2214yescomplemented
23C2×#41×D13C2216yescomplemented
24C2×#88251C22112yescomplemented
25C2×#88251C2216yescomplemented
26C22×#6129C22112yescomplemented
27C22×#6129C2216yescomplemented
28C13×#550C2214yescomplemented
29D42×C13C22112yescomplemented
30C13×#535C2216yescomplemented
31C13×#532C2213yescomplemented
32C2×C13×#127C2213yescomplemented
33C4×C13×#41C2211yescharacteristic, complemented
34#11719537C2216yescomplemented
35#11719536C2218yescomplemented
36#41×Dic13C2211yescharacteristic, complemented
37#11719530C2216yescomplemented
38#11719511C22124yescomplemented
39#11719510C2216yescomplemented
40D4×C22⋊D13C22124yescomplemented
41C2×#88192C22112yescomplemented
42C2×#88190C2216yescomplemented
43C2×D4×Dic13C22112yescomplemented
44#11719430C2211yescharacteristic, complemented
45D13×C4⋊Q8C2213yescomplemented
46#11719423C22112yescomplemented
47#11719422C22112yescomplemented
48#11719421C22112yescomplemented
49#11719421C22112yescomplemented
50#11719421C2216yescomplemented
51#11719421C2213yescomplemented
52#11719421C2216yescomplemented
53#11719421C2216yescomplemented
54#11719420C22112yescomplemented
55D13×#127C2213yescomplemented
56#11719380C22112yescomplemented
57D13×#124C2216yescomplemented
58#11719373C2216yescomplemented
59#11719317C22124yescomplemented
60#11719316C22124yescomplemented
61#11719313C22124yescomplemented
62#11719311C22124yescomplemented
63D13×#121C22112yescomplemented
64#11719303C22124yescomplemented
65#11719301C22112yescomplemented
66#11719296C22148yescomplemented
67#11719294C22124yescomplemented
68#11719291C22124yescomplemented
69Q8×D52C2214yescomplemented
70C4×#6131C2212yescomplemented
71C4×Q8×D13C2212yescomplemented
72#11719260C22112yescomplemented
73#11719256C22112yescomplemented
74#11719253C22112yescomplemented
75C4×D4×D13C2216yescomplemented
76C4×D4×D13C22112yescomplemented
77D4×Dic26C22112yescomplemented
78C4×#6129C2216yescomplemented
79#11719231C2216yescomplemented
80#11719227C2213yescomplemented
81D13×#117C2213yescomplemented
82#11719182C2213yescomplemented
83C4×#6127C2213yescomplemented
84C2×C42×D13C2213yescomplemented
85C2×#88123C2213yescomplemented
86C13×H(5,𝔽2)—216no—
87C2×C13×#41C2316yes—
88C2×C13×#41C2314yes—
89C2×C13×#41C2311yescharacteristic
90C22×D4×C13C2316yes—
91C22×D4×C13C23112yes—
92C22×D4×C13C23112yes—
93C22×C22⋊D13C23112yes—
94C22×C22⋊D13C23124yes—
95C23×Dic13C23112yes—
96#88257—216no—
97#88257—232no—
98#88257—248no—
99#41×D13—232no—
100#41×D13—248no—
101#41×D13D4116yescomplemented
102C2×#6131C2312yes—
103C2×#6131C2311yescharacteristic
104C2×Q8×D13C2316yes—
105C2×Q8×D13C2314yes—
106C2×Q8×D13C2311yescharacteristic
107#88251—296no—
108#88251—248no—
109C2×#6129—296no—
110C2×#6129—248no—
111C2×#6129C23112yes—
112C2×#6129C23112yes—
113C2×#6129C23124yes—
114C2×#6129C23112yes—
115C2×#6129C23112yes—
116C2×#6129C23112yes—
117C2×#6129C2316yes—
118C2×#6129C23112yes—
119C2×#6129C2313yes—
120C2×D4×D13C23112yes—
121C2×D4×D13C23112yes—
122C2×D4×D13C2316yes—
123C2×D4×D13C23112yes—
124C2×D4×D13C2313yes—
125C2×#6127C2316yes—
126C2×#6127C23112yes—
127C2×#6127C23112yes—
128C2×#6127C2313yes—
129C22×C4×D13C23112yes—
130C22×C4×D13C2316yes—
131C22×C4×D13C2313yes—
132C22×Dic26C2316yes—
133C22×Dic26C23112yes—
134C13×C4⋊Q8C2311yescharacteristic
135C13×#127C2313yes—
136C13×#127C2316yes—
137C13×#127C23112yes—
138C13×#124C2316yes—
139C13×#121C23112yes—
140C13×#121C23124yes—
141C13×#120C23124yes—
142C4×Q8×C13C2312yes—
143C4×D4×C13C2316yes—
144C4×D4×C13C23112yes—
145C13×#117C2313yes—
146C2×C42×C13C2313yes—
147#88207C23124yes—
148C2×C22⋊Dic13C23124yes—
149#88201C2312yes—
150Q8×Dic13C2312yes—
151#88198C2316yes—
152#88194C23112yes—
153#88194C2316yes—
154#88193C23148yes—
155#88193C23124yes—
156#88192C23112yes—
157#88192C23124yes—
158#88192C23124yes—
159#88192C23124yes—
160#88192C23124yes—
161#88191C23148yes—
162#88190C2316yes—
163#88190C23112yes—
164#88190C23124yes—
165#88189C23124yes—
166D4×Dic13C2316yes—
167D4×Dic13C23124yes—
168D4×Dic13C23112yes—
169D4×Dic13C23124yes—
170D4×Dic13C23124yes—
171#88184C23112yes—
172C4×C22⋊D13C23112yes—
173C4×C22⋊D13C23124yes—
174#88180C2313yes—
175C2×C4⋊Dic13C23112yes—
176#88178C23124yes—
177C2×C4×Dic13C2313yes—
178C2×C4×Dic13C2316yes—
179#88151C23124yes—
180#88149C2314yes—
181#88147C2314yes—
182#88147C2316yes—
183#88146C2316yes—
184C4⋊C4×D13C23112yes—
185C4⋊C4×D13C2316yes—
186#88142C23112yes—
187#88141C2316yes—
188#88140C23124yes—
189#88139C23124yes—
190#88138C23124yes—
191#88137C23148yes—
192#88135C23112yes—
193#88135C23124yes—
194C22⋊C4×D13C2316yes—
195C22⋊C4×D13C23124yes—
196#88132C23148yes—
197#88131C2316yes—
198#88129C2316yes—
199#88128C2311yescharacteristic
200C4×D52C2316yes—
201C4×D52C23112yes—
202#88126C2316yes—
203C42×D13C2313yes—
204C42×D13C2311yescharacteristic
205C42×D13C2313yes—
206C42×D13C2313yes—
207C42×D13C2316yes—
208C42×D13C2316yes—
209#88123C2313yes—
210#88123C2316yes—
211#88123C23112yes—
212C4×Dic26C2316yes—
213#62812—131nomaximal, Sylow
214C24×C13C24112yes—
215C23×D13C24112yes—
216C23×D13C2413yes—
217C13×#41—216no—
218C13×#41—224no—
219C13×#41C2×D418yescomplemented
220C2×Q8×C13C2412yes—
221C2×Q8×C13C2411yescharacteristic
222C2×D4×C13—248no—
223C2×D4×C13—224no—
224C2×D4×C13—424no—
225C2×D4×C13C24112yes—
226C2×D4×C13C24112yes—
227C2×D4×C13C2416yes—
228C2×D4×C13C24112yes—
229C2×D4×C13C24124yes—
230C2×D4×C13C2413yes—
231C22×C4×C13C2416yes—
232C22×C4×C13C24112yes—
233C22×C4×C13C2413yes—
234C2×C22⋊D13—248no—
235C2×C22⋊D13—296no—
236C2×C22⋊D13C24124yes—
237C2×C22⋊D13C24112yes—
238C2×C22⋊D13C24112yes—
239C2×C22⋊D13C24112yes—
240C2×C22⋊D13C24124yes—
241C2×C22⋊D13C2416yes—
242C22×Dic13—248no—
243C22×Dic13C24124yes—
244C22×Dic13C24112yes—
245C22×Dic13C24112yes—
246C22×Dic13C2416yes—
247C22×Dic13C2413yes—
248#6131—28no—
249#6131C2×D418yescomplemented
250Q8×D13—216no—
251Q8×D13—224no—
252Q8×D13C2×D418yescomplemented
253#6129—248no—
254#6129—296no—
255#6129—248no—
256#6129—248no—
257#6129—224no—
258#6129—248no—
259#6129—248no—
260#6129—248no—
261#6129C2×D4124yescomplemented
262D4×D13—248no—
263D4×D13—248no—
264D4×D13—224no—
265D4×D13—424no—
266D4×D13C2×D4124yescomplemented
267#6127—224no—
268#6127—248no—
269#6127—248no—
270#6127C2×D4124yescomplemented
271C2×D52C2414yes—
272C2×D52C2412yes—
273C2×D52C2414yes—
274C2×D52C2413yes—
275C2×C4×D13—248no—
276C2×C4×D13—412no—
277C2×C4×D13C2×D4124yescomplemented
278C2×C4×D13C2412yes—
279C2×C4×D13C2416yes—
280C2×C4×D13C24112yes—
281C2×C4×D13C24112yes—
282C2×C4×D13C2414yes—
283C2×C4×D13C2416yes—
284C2×C4×D13C2416yes—
285C2×C4×D13C2411yescharacteristic
286C2×C4×D13C2413yes—
287C2×C4×D13C2413yes—
288C2×C4×D13C2413yes—
289C2×Dic26—224no—
290C2×Dic26—248no—
291C2×Dic26C2416yes—
292C2×Dic26C24112yes—
293C2×Dic26C24112yes—
294C2×Dic26C2413yes—
295C13×C4⋊C4C2416yes—
296C13×C4⋊C4C2414yes—
297C13×C22⋊C4C2416yes—
298C13×C22⋊C4C24124yes—
299C42×C13C2416yes—
300C42×C13C2411yescharacteristic
301C42×C13C2413yes—
302C22⋊Dic13C2416yes—
303C22⋊Dic13C24148yes—
304C22⋊Dic13C24124yes—
305#6103C24112yes—
306#6103C24124yes—
307#6103C2418yes—
308C4⋊Dic13C2416yes—
309C4⋊Dic13C24112yes—
310C4⋊Dic13C24124yes—
311#6101C24112yes—
312#6101C24124yes—
313C4×Dic13C2416yes—
314C4×Dic13C2412yes—
315C4×Dic13C2411yescharacteristic
316C4×Dic13C2413yes—
317C4×Dic13C2416yes—
318C4×Dic13C2416yes—
319C4×Dic13C2416yes—
320C2×#585—132no—
321#3500—132no—
322#3500—136no—
323#3499—133no—
324#3499—131no—
325#3498—133no—
326#3498D1311yescharacteristic, complemented
327#3497—134no—
328#3496—1312no—
329D4×#41—134no—
330D4×#41—1312no—
331#3449—136no—
332C2×#532—133no—
333C2×#532—133no—
334C2×C4×#41—131no—
335C23×C13—224no—
336C23×C13—424no—
337C23×C13C25112yes—
338C23×C13C2513yes—
339C22×D13—224no—
340C22×D13—46no—
341C22×D13—424no—
342C22×D13C22×D4112yes—
343C22×D13C2514yes—
344C22×D13C2513yes—
345C22×D13C2511yescharacteristic
346Q8×C13—24no—
347Q8×C13C22×D414yes—
348D4×C13—224no—
349D4×C13—212no—
350D4×C13—224no—
351D4×C13—224no—
352D4×C13—424no—
353D4×C13C22×D4112yes—
354C2×C4×C13—224no—
355C2×C4×C13—212no—
356C2×C4×C13C22×D4112yes—
357C2×C4×C13C2516yes—
358C2×C4×C13C2514yes—
359C2×C4×C13C2511yescharacteristic
360C2×C4×C13C2513yes—
361C2×C4×C13C2512yes—
362C22⋊D13—224no—
363C22⋊D13—248no—
364C22⋊D13—224no—
365C22⋊D13—224no—
366C22⋊D13—424no—
367C22⋊D13C22×D4124yes—
368C2×Dic13—224no—
369C2×Dic13—248no—
370C2×Dic13—224no—
371C2×Dic13—46no—
372C2×Dic13C22×D4112yes—
373C2×Dic13C2512yes—
374C2×Dic13C2516yes—
375C2×Dic13C25112yes—
376C2×Dic13C2511yescharacteristic
377C2×Dic13C2513yes—
378D52—28no—
379D52—24no—
380D52—28no—
381D52C22×D4112yes—
382C4×D13—224no—
383C4×D13—224no—
384C4×D13—24no—
385C4×D13—212no—
386C4×D13—28no—
387C4×D13—46no—
388C4×D13—46no—
389C4×D13C22×D4112yes—
390C4×D13C22×D414yes—
391C4×D13C22×D4112yes—
392C4×D13C22×D4112yes—
393Dic26—212no—
394Dic26—224no—
395Dic26—224no—
396Dic26C22×D4112yes—
397#585—2632no—
398C2×2−1+4—134no—
399C2×2−1+4—136no—
400C2×2−1+4—132no—
401C2×H(5,𝔽2)—1312no—
402C2×H(5,𝔽2)—136no—
403C2×H(5,𝔽2)C2×D1312yescomplemented
404C22×#41—131no—
405C22×#41—136no—
406C22×#41—134no—
407C22×#41—136no—
408C22×#41—1312no—
409#550—1312no—
410#550C2×D1314yescomplemented
411D4×Q8—134no—
412D4×Q8—1312no—
413#548—138no—
414#548—1324no—
415#547—1324no—
416#547—1312no—
417#547—1312no—
418#546—1324no—
419#546—1324no—
420#546—1348no—
421D42—1324no—
422D42—1312no—
423D42C2×D13112yescomplemented
424#537—1324no—
425#536—136no—
426#536—1312no—
427#536—136no—
428#535—136no—
429#535—1312no—
430#535C2×D1316yescomplemented
431#534—1324no—
432#532—136no—
433#532—131no—
434#532—133no—
435#532—136no—
436#532—1312no—
437#532—1312no—
438#532—136no—
439#532—136no—
440#532—136no—
441#532—1312no—
442#532—1312no—
443#532—133no—
444#532C2×D1313yescomplemented
445C2×C4⋊Q8—133no—
446C2×C4⋊Q8—133no—
447C2×#127—133no—
448C2×#127C2×D1313yescomplemented
449C2×#124—136no—
450C2×#124—136no—
451#525—1324no—
452#525—1324no—
453C2×#121—1312no—
454C2×#121—1312no—
455C4×#41—131no—
456C4×#41—132no—
457C4×#41—136no—
458C4×#41—133no—
459C4×#41—133no—
460C4×#41C2×D1311yescharacteristic, complemented
461C2×C4×Q8—132no—
462C2×C4×D4—1312no—
463C2×C4×D4—136no—
464C2×C4×D4—1312no—
465C2×#117—133no—
466C22×C42—133no—
467C22×C13—26no—
468C22×C13—212no—
469C22×C13—224no—
470C22×C13—824no—
471C22×C13C23×D416yes—
472C22×C13C2611yescharacteristic
473C2×D13—22no—
474C2×D13—26no—
475C2×D13—24no—
476C2×D13—28no—
477C2×D13—412no—
478C2×D13—824no—
479C2×D13C23×D416yes—
480C2×D13C23×D412yes—
481C4×C13—24no—
482C4×C13—26no—
483C4×C13C23×D412yes—
484C4×C13C23×D416yes—
485C4×C13#58514yescomplemented
486Dic13—212no—
487Dic13—22no—
488Dic13—26no—
489Dic13C23×D416yes—
490Dic13C23×D412yes—
4912−1+4—2632no—
4922−1+4—2648no—
4932−1+4—2616no—
494H(5,𝔽2)—216no—
495H(5,𝔽2)—2696no—
496H(5,𝔽2)—2648no—
497C2×#41—1316no—
498C2×#41—131no—
499C2×#41—132no—
500C2×#41—133no—
501C2×#41—1312no—
502C2×#41—1312no—
503C2×#41—136no—
504C2×#41—1312no—
505C2×#41—1312no—
506C2×#41—1312no—
507C2×#41—1324no—
508C2×#41—1312no—
509C2×#41—133no—
510C2×#41—136no—
511C2×#41—1312no—
512C2×#41—1312no—
513C2×#41—2648no—
514C2×#41—2648no—
515C2×#41—2696no—
516C2×#41—2632no—
517C2×#41C22×D1316yes—
518C2×#41C22×D1314yes—
519C2×#41C22×D1311yescharacteristic
520C22×Q8—131no—
521C22×Q8—136no—
522C22×Q8—134no—
523C22×Q8—136no—
524C22×Q8—1312no—
525C22×D4—133no—
526C22×D4—1312no—
527C22×D4—1324no—
528C22×D4—1312no—
529C22×D4—136no—
530C22×D4—1312no—
531C22×D4—1312no—
532C22×D4C22×D1316yes—
533C22×D4C22×D13112yes—
534C22×D4C22×D13112yes—
535C23×C4—133no—
536C23×C4—1312no—
537C23×C4—1312no—
538C23×C4—136no—
539C4⋊Q8—136no—
540C4⋊Q8—1312no—
541C4⋊Q8—133no—
542C4⋊Q8—136no—
543C4⋊Q8—1312no—
544C4⋊Q8C22×D1311yescharacteristic
545#127—136no—
546#127—1312no—
547#127—131no—
548#127C22×D1313yes—
549#127C22×D1316yes—
550#127C22×D13112yes—
551#124—132no—
552#124—136no—
553#124—1312no—
554#124—1324no—
555#124—1324no—
556#124—136no—
557#124C22×D1316yes—
558#123—1324no—
559#123—1348no—
560#123—1324no—
561C22⋊Q8—1324no—
562C22⋊Q8—1324no—
563C22⋊Q8—1348no—
564#121—1312no—
565#121—1324no—
566#121—1324no—
567#121—1324no—
568#121—1324no—
569#121—1324no—
570#121—1348no—
571#121—1312no—
572#121—134no—
573#121—1324no—
574#121C22×D13112yes—
575#121C22×D13124yes—
576#120—1324no—
577#120—1348no—
578#120C22×D13124yes—
579C4×Q8—132no—
580C4×Q8—136no—
581C4×Q8—136no—
582C4×Q8C22×D1312yes—
583C4×D4—1312no—
584C4×D4—136no—
585C4×D4—1324no—
586C4×D4—1324no—
587C4×D4—1324no—
588C4×D4—1312no—
589C4×D4—1324no—
590C4×D4—134no—
591C4×D4—136no—
592C4×D4—1312no—
593C4×D4—1324no—
594C4×D4—136no—
595C4×D4—1312no—
596C4×D4C22×D1316yes—
597C4×D4C22×D13112yes—
598#117—133no—
599#117—136no—
600#117—136no—
601#117—136no—
602#117C22×D1313yes—
603C2×C4⋊C4—1312no—
604C2×C4⋊C4—136no—
605C2×C4⋊C4—1312no—
606C2×C22⋊C4—1324no—
607C2×C22⋊C4—136no—
608C2×C22⋊C4—1324no—
609C2×C42—136no—
610C2×C42—133no—
611C2×C42—133no—
612C2×C42—136no—
613C2×C42—136no—
614C2×C42—133no—
615C2×C42—133no—
616C2×C42—131no—
617C2×C42C22×D1313yes—
618C2×C13—26no—
619C2×C13—412no—
620C2×C13C24×D411yescharacteristic
621C2×C13C2×#58512yes—
622D13—22no—
623D13—26no—
624D13—44no—
625C24—133no—
626C24—1312no—
627C24C23×D13112yes—
628#41—216no—
629#41—224no—
630#41—138no—
631#41—1324no—
632#41—1324no—
633#41—2648no—
634#41—2648no—
635#41—2648no—
636#41—2624no—
637#41—2648no—
638#41—2648no—
639#41—2648no—
640#41—268no—
641#41—2696no—
642#41—2648no—
643#41—2648no—
644#41—2624no—
645#41D4×D1318yescomplemented
646C2×Q8—138no—
647C2×Q8—133no—
648C2×Q8—1312no—
649C2×Q8—1312no—
650C2×Q8—136no—
651C2×Q8—2648no—
652C2×Q8—2624no—
653C2×Q8—2616no—
654C2×Q8—2624no—
655C2×Q8C23×D1312yes—
656C2×Q8C23×D1311yescharacteristic
657C2×D4—248no—
658C2×D4—224no—
659C2×D4—424no—
660C2×D4—136no—
661C2×D4—1324no—
662C2×D4—1324no—
663C2×D4—1312no—
664C2×D4—1312no—
665C2×D4—1312no—
666C2×D4—1324no—
667C2×D4—133no—
668C2×D4—134no—
669C2×D4—134no—
670C2×D4—132no—
671C2×D4—2624no—
672C2×D4—2648no—
673C2×D4—2648no—
674C2×D4—2696no—
675C2×D4—2648no—
676C2×D4—5224no—
677C2×D4C23×D13112yes—
678C2×D4C23×D13112yes—
679C2×D4C23×D13112yes—
680C2×D4C23×D1316yes—
681C2×D4C23×D13124yes—
682C2×D4C23×D1313yes—
683C22×C4—133no—
684C22×C4—1324no—
685C22×C4—131no—
686C22×C4—133no—
687C22×C4—133no—
688C22×C4—133no—
689C22×C4—1312no—
690C22×C4—1312no—
691C22×C4—1324no—
692C22×C4—136no—
693C22×C4—132no—
694C22×C4—136no—
695C22×C4—1312no—
696C22×C4—134no—
697C22×C4—1312no—
698C22×C4—136no—
699C22×C4—136no—
700C22×C4—2648no—
701C22×C4—2648no—
702C22×C4—5212no—
703C22×C4C23×D1316yes—
704C22×C4C23×D13112yes—
705C22×C4C23×D1313yes—
706C4⋊C4—1312no—
707C4⋊C4—1312no—
708C4⋊C4—136no—
709C4⋊C4—1324no—
710C4⋊C4—1324no—
711C4⋊C4C23×D1314yes—
712C4⋊C4C23×D1316yes—
713C22⋊C4—1324no—
714C22⋊C4—136no—
715C22⋊C4—1348no—
716C22⋊C4—138no—
717C22⋊C4—1312no—
718C22⋊C4—1324no—
719C22⋊C4C23×D1316yes—
720C22⋊C4C23×D13124yes—
721C42—132no—
722C42—131no—
723C42—136no—
724C42—133no—
725C42—136no—
726C42—136no—
727C42—136no—
728C42C23×D1311yescharacteristic
729C42C23×D1313yes—
730C42C23×D1316yes—
731C13#6281211yescharacteristic, complemented, Sylow
732C23—224no—
733C23—424no—
734C23—133no—
735C23—131no—
736C23—1312no—
737C23—134no—
738C23—2624no—
739C23—526no—
740C23—5224no—
741C23C24×D13112yes—
742C23C24×D1313yes—
743Q8—24no—
744Q8—1312no—
745Q8—2624no—
746Q8—2624no—
747Q8—2612no—
748Q8C2×D4×D1314yes—
749D4—224no—
750D4—224no—
751D4—212no—
752D4—224no—
753D4—424no—
754D4—1324no—
755D4—1312no—
756D4—268no—
757D4—2624no—
758D4—2624no—
759D4—2648no—
760D4—2624no—
761D4—264no—
762D4—268no—
763D4—5224no—
764D4C2×D4×D13112yes—
765C2×C4—224no—
766C2×C4—212no—
767C2×C4—1312no—
768C2×C4—131no—
769C2×C4—133no—
770C2×C4—134no—
771C2×C4—1312no—
772C2×C4—1312no—
773C2×C4—1312no—
774C2×C4—132no—
775C2×C4—136no—
776C2×C4—1312no—
777C2×C4—268no—
778C2×C4—2624no—
779C2×C4—2624no—
780C2×C4—2648no—
781C2×C4—2624no—
782C2×C4—2624no—
783C2×C4—264no—
784C2×C4—2612no—
785C2×C4—526no—
786C2×C4—526no—
787C2×C4—526no—
788C2×C4C2×D4×D13112yes—
789C2×C4C24×D1316yes—
790C2×C4C24×D1314yes—
791C2×C4C24×D1311yescharacteristic
792C2×C4C24×D1313yes—
793C2×C4C24×D1312yes—
794C22—26no—
795C22—212no—
796C22—224no—
797C22—824no—
798C22—132no—
799C22—136no—
800C22—262no—
801C22—266no—
802C22—264no—
803C22—268no—
804C22—5212no—
805C22—10424no—
806C22C22×D4×D1316yes—
807C22C25×D1311yescharacteristic
808C4—24no—
809C4—26no—
810C4—132no—
811C4—136no—
812C4—2612no—
813C4—262no—
814C4—266no—
815C4C22×D4×D1316yes—
816C4C22×D4×D1312yes—
817C4#1171965014yescomplemented
818C2—26no—
819C2—412no—
820C2—262no—
821C2—266no—
822C2—524no—
823C2C23×D4×D1311yescharacteristic
824C2C2×#1171965012yes—
subgroupG/H
center, FrattiniC22C25×D13
commutator, socle, cosocleC22×C13C26
FittingC13×#3498C2
hypercenter#3498D13
hypocenterC13#62812
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. C2×#11719650C2semidirect
2. #13128628C2semidirect
3. #13128624C2semidirect
4. #13128621C2semidirect
5. #13128616C2semidirect
6. #13128612C2semidirect
7. #13128601C2semidirect
8. #13128592C2semidirect
9. #13128326C2semidirect
10. D4×#6129C2semidirect
11. #13128167C2semidirect
12. C2×#11719421C2semidirect
13. D13×#532C2semidirect
14. C4×#41×D13C2semidirect
15. C13×#3498C2semidirect
16. C2×C13×H(5,𝔽2)C22semidirect
18. C2×#88257C22semidirect
19. C2×#88257C22semidirect
20. C2×#88257C22semidirect
22. C2×#41×D13C22semidirect
23. C2×#41×D13C22semidirect
24. C2×#88251C22semidirect
25. C2×#88251C22semidirect
26. C22×#6129C22semidirect
27. C22×#6129C22semidirect
28. C13×#550C22semidirect
29. D42×C13C22semidirect
30. C13×#535C22semidirect
31. C13×#532C22semidirect
32. C2×C13×#127C22semidirect
33. C4×C13×#41C22semidirect
34. #11719537C22semidirect
35. #11719536C22semidirect
36. #41×Dic13C22semidirect
37. #11719530C22semidirect
38. #11719511C22semidirect
39. #11719510C22semidirect
40. D4×C22⋊D13C22semidirect
41. C2×#88192C22semidirect
42. C2×#88190C22semidirect
43. C2×D4×Dic13C22semidirect
44. #11719430C22semidirect
45. D13×C4⋊Q8C22semidirect
46. #11719423C22semidirect
47. #11719422C22semidirect
48. #11719421C22semidirect
49. #11719421C22semidirect
50. #11719421C22semidirect
51. #11719421C22semidirect
52. #11719421C22semidirect
53. #11719421C22semidirect
54. #11719420C22semidirect
55. D13×#127C22semidirect
56. #11719380C22semidirect
57. D13×#124C22semidirect
58. #11719373C22semidirect
59. #11719317C22semidirect
60. #11719316C22semidirect
61. #11719313C22semidirect
62. #11719311C22semidirect
63. D13×#121C22semidirect
64. #11719303C22semidirect
65. #11719301C22semidirect
66. #11719296C22semidirect
67. #11719294C22semidirect
68. #11719291C22semidirect
69. Q8×D52C22semidirect
70. C4×#6131C22semidirect
71. C4×Q8×D13C22semidirect
72. #11719260C22semidirect
73. #11719256C22semidirect
74. #11719253C22semidirect
75. C4×D4×D13C22semidirect
76. C4×D4×D13C22semidirect
77. D4×Dic26C22semidirect
78. C4×#6129C22semidirect
79. #11719231C22semidirect
80. #11719227C22semidirect
81. D13×#117C22semidirect
82. #11719182C22semidirect
83. C4×#6127C22semidirect
84. C2×C42×D13C22semidirect
85. C2×#88123C22semidirect
101. #41×D13D4semidirect
219. C13×#41C2×D4semidirect
249. #6131C2×D4semidirect
252. Q8×D13C2×D4semidirect
261. #6129C2×D4semidirect
266. D4×D13C2×D4semidirect
270. #6127C2×D4semidirect
277. C2×C4×D13C2×D4semidirect
326. #3498D13semidirect
403. C2×H(5,𝔽2)C2×D13semidirect
410. #550C2×D13semidirect
423. D42C2×D13semidirect
430. #535C2×D13semidirect
444. #532C2×D13semidirect
448. C2×#127C2×D13semidirect
460. C4×#41C2×D13semidirect
485. C4×C13#585semidirect
645. #41D4×D13semidirect
731. C13#62812semidirect
817. C4#11719650semidirect

Maximal subgroups

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

subgroupindex
C2×#117196502
#131286282
#131286242
#131286212
#131286162
#131286122
#131286012
#131285922
#131283262
D4×#61292
#131281672
C2×#117194212
D13×#5322
C4×#41×D132
C13×#34982
#6281213