Finite Group Databasebeta

← #16735320

Subgroups — #16735320

Order 3328.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719224C211yesmaximal, characteristic, complemented
2#13126128C214yesmaximal, complemented
3#13126098C214yesmaximal, complemented
4#13126054C212yesmaximal, complemented
5#13126038C212yesmaximal, complemented
6#13126000C212yesmaximal, complemented
7#13125977C212yesmaximal, complemented
8#13125362C212yesmaximal, complemented
9#13125201C212yesmaximal, complemented
10#13124780C211yesmaximal, characteristic, complemented
11#13124756C211yesmaximal, characteristic
12#13124745C211yesmaximal, characteristic
13C2×#11718704C211yesmaximal, characteristic, complemented
14#13124698C212yesmaximal, complemented
15#13124678C212yesmaximal, complemented
16#13123494C211yesmaximal, characteristic, complemented
17C13×#3495C211yesmaximal, characteristic
18C13×#556—21no—
19C13×#554—21no—
20C13×#552—22no—
21C13×#552—21no—
22C13×#552—21no—
23C13×#551—22no—
24C13×#544C2211yescharacteristic
25C13×#542C2212yes—
26C13×#541C2212yes—
27C13×#536C2211yescharacteristic
28C13×#533C2212yes—
29C13×#529C2212yes—
30C13×#525C2211yescharacteristic
31C2×C13×C22⋊Q8C2211yescharacteristic
32C13×#520C2211yescharacteristic
33C13×#519C2211yescharacteristic
34C2×C13×#117C2211yescharacteristic
35C2×#88180C2211yescharacteristic
36C22×C4⋊Dic13C2211yescharacteristic
37#11719224—21no—
38#11719224—22no—
39#11719224—21no—
40#11719224C2212yes—
41#11719224C2212yes—
42#11719224C2214yes—
43C2×#88144—21no—
44C2×#88142—21no—
45C2×#88132—22no—
46C2×#88124C2212yes—
47C2×#88123C2212yes—
48#11718894C2212yes—
49#11718893C2212yes—
50#11718886C2212yes—
51C2×#88075C2212yes—
52#11718868C2211yescharacteristic
53C2×C22⋊#1055C2211yescharacteristic
54#11718743C2214yescomplemented
55#11718742C2214yescomplemented
56#11718741C2214yescomplemented
57#11718740C2214yescomplemented
58#11718726C2214yescomplemented
59#11718725C2214yescomplemented
60#11718717C2214yescomplemented
61#11718716C2214yescomplemented
62#11718706C2212yes—
63#11718706C2214yes—
64#11718705C2212yes—
65#11718705C2211yescharacteristic
66#11718705C2212yes—
67#11718704C2211yescharacteristic
68#11718704C2212yes—
69#11718704C2212yes—
70#11718704C2212yes—
71#11718704C2212yes—
72#11718704C2214yes—
73#11718696C2212yes—
74#11718695C2211yescharacteristic
75#11718695C2212yes—
76#11718694C2212yes—
77#11718694C2211yescharacteristic
78#11718683C2214yescomplemented
79#11718683C2214yescomplemented
80#11718683C2214yescomplemented
81#11718682C2214yescomplemented
82#11718681C2214yescomplemented
83#11718681C2214yescomplemented
84#11718670C2214yescomplemented
85#11718669C2214yescomplemented
86#11718661C2214yes—
87#11718660C2212yes—
88#11718659C2212yes—
89#11718658C2212yes—
90#11718656C2212yes—
91#11718625C2212yes—
92C2×#88048C2212yes—
93#11718587C2212yes—
94#11718586C2212yes—
95C2×C13×#41C2311yescharacteristic
96C22×Q8×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×Dic13—21no—
99C22×Dic26—22no—
100C13×C4⋊Q8—21no—
101C13×C4⋊Q8C2312yes—
102C13×C4⋊Q8C2312yes—
103C13×#126—22no—
104C13×#126—22no—
105C13×#126—22no—
106C13×#126—22no—
107C13×#125—22no—
108C13×#125—22no—
109C13×#125—21no—
110C13×#125—22no—
111C13×#125C2312yes—
112C13×#124—22no—
113C13×#124C2312yes—
114C13×#123—21no—
115C13×#123—22no—
116C13×#123—22no—
117C13×#123—22no—
118C13×C22⋊Q8—21no—
119C13×C22⋊Q8—21no—
120C13×C22⋊Q8—22no—
121C13×C22⋊Q8—21no—
122C13×C22⋊Q8—21no—
123C13×C22⋊Q8—22no—
124C13×C22⋊Q8—22no—
125C13×C22⋊Q8C2312yes—
126C13×C22⋊Q8C2311yescharacteristic
127C13×C22⋊Q8C2312yes—
128C13×C22⋊Q8C2311yescharacteristic
129C13×#121C2311yescharacteristic
130C13×#121C2311yescharacteristic
131C13×#120—21no—
132C4×Q8×C13—21no—
133C4×Q8×C13—21no—
134C4×Q8×C13—22no—
135C4×Q8×C13C2312yes—
136C4×Q8×C13C2312yes—
137C4×Q8×C13C2312yes—
138C4×D4×C13—21no—
139C4×D4×C13—21no—
140C4×D4×C13—22no—
141C4×D4×C13—22no—
142C4×D4×C13C2312yes—
143C13×#117—22no—
144C13×#117—21no—
145C13×#117—22no—
146C13×#117—22no—
147C13×#117D411yescharacteristic
148C13×#117D412yes—
149C13×#117D411yescharacteristic
150C13×#117C2311yescharacteristic
151C13×#117C2311yescharacteristic
152C13×#117C2311yescharacteristic
153C13×#117C2312yes—
154C2×C13×C4⋊C4—21no—
155C2×C13×C4⋊C4—21no—
156C2×C13×C4⋊C4D411yescharacteristic
157C2×C13×C4⋊C4D411yescharacteristic
158C2×C13×C4⋊C4C2311yescharacteristic
159C2×C13×C22⋊C4—21no—
160C2×C13×C22⋊C4D412yes—
161C2×C42×C13C2312yes—
162C2×C22⋊Dic13—21no—
163#88180—21no—
164#88180—21no—
165#88180C2312yes—
166#88180C2312yes—
167C2×C4⋊Dic13—22no—
168C2×C4⋊Dic13—21no—
169C2×C4⋊Dic13—21no—
170C2×C4⋊Dic13—21no—
171C2×C4⋊Dic13C2312yes—
172C2×C4⋊Dic13C2311yescharacteristic
173C2×C4⋊Dic13C2312yes—
174C2×C4⋊Dic13C2311yescharacteristic
175C2×C4⋊Dic13C2312yes—
176C2×#6101—22no—
177C2×#6101—22no—
178C2×C4×Dic13—21no—
179C2×#6099C2312yes—
180C22×#1055C2312yes—
181#88144—22no—
182#88144—24no—
183#88144—22no—
184#88142—22no—
185#88142—22no—
186#88142—24no—
187#88132—24no—
188#88132—24no—
189#88132—24no—
190#88132—24no—
191#88124—22no—
192#88124—22no—
193#88124C2314yes—
194#88124C2314yes—
195#88123—22no—
196#88123—22no—
197#88123C2314yes—
198#88123C2314yes—
199#88075C2312yes—
200#88075C2314yes—
201#88075C2314yes—
202#88075C2314yes—
203#88075C2314yes—
204#88075C2314yes—
205#88075C2312yes—
206#88072C2312yes—
207#88072C2314yes—
208#88072C2312yes—
209C22⋊#1055C2312yes—
210C22⋊#1055C2312yes—
211C22⋊#1055C2312yes—
212C22⋊#1055C2311yescharacteristic
213C22⋊#1055C2311yescharacteristic
214#88048C2314yes—
215#88048C2312yes—
216#88048C2312yes—
217#88048C2314yes—
218#88048C2314yes—
219#88048C2314yes—
220#88047C2314yes—
221#88047C2312yes—
222#88047C2312yes—
223#88047C2314yes—
224C4⋊#1055C2314yes—
225C4⋊#1055C2314yes—
226#88043C2314yes—
227C4×#1055C2314yes—
228#60872—131nomaximal, Sylow
229C24×C13C2×D411yescharacteristic
230C13×#41—24no—
231C2×Q8×C13—21no—
232C2×Q8×C13—22no—
233C2×Q8×C13—24no—
234C2×Q8×C13C2412yes—
235C2×Q8×C13C2411yescharacteristic
236C2×D4×C13—21no—
237C2×D4×C13—21no—
238C2×D4×C13—21no—
239C2×D4×C13C2411yescharacteristic
240C22×C4×C13—24no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—22no—
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D411yescharacteristic
248C22×C4×C13C2×D411yescharacteristic
249C22×C4×C13C2×D412yes—
250C22×C4×C13C2411yescharacteristic
251C22×C4×C13C2411yescharacteristic
252C22×C4×C13C2411yescharacteristic
253C22×Dic13—21no—
254C22×Dic13—21no—
255C22×Dic13—22no—
256C22×Dic13—22no—
257C22×Dic13—22no—
258C22×Dic13—82no—
259C2×Dic26—24no—
260C2×Dic26—24no—
261C2×Dic26—84no—
262C13×C4⋊C4—21no—
263C13×C4⋊C4—22no—
264C13×C4⋊C4—22no—
265C13×C4⋊C4—22no—
266C13×C4⋊C4—22no—
267C13×C4⋊C4—22no—
268C13×C4⋊C4—22no—
269C13×C4⋊C4—22no—
270C13×C4⋊C4—22no—
271C13×C4⋊C4—21no—
272C13×C4⋊C4—22no—
273C13×C4⋊C4—21no—
274C13×C4⋊C4—22no—
275C13×C4⋊C4C2×D411yescharacteristic
276C13×C4⋊C4C2×D411yescharacteristic
277C13×C4⋊C4C2×D412yes—
278C13×C4⋊C4C2×D411yescharacteristic
279C13×C4⋊C4C2×D412yes—
280C13×C4⋊C4C2×D411yescharacteristic
281C13×C4⋊C4C2412yes—
282C13×C4⋊C4C2411yescharacteristic
283C13×C4⋊C4C2411yescharacteristic
284C13×C22⋊C4—22no—
285C13×C22⋊C4—22no—
286C13×C22⋊C4—21no—
287C13×C22⋊C4—21no—
288C13×C22⋊C4—21no—
289C13×C22⋊C4—21no—
290C13×C22⋊C4—22no—
291C13×C22⋊C4—22no—
292C13×C22⋊C4—21no—
293C13×C22⋊C4—22no—
294C13×C22⋊C4C2×D412yes—
295C13×C22⋊C4C2×D412yes—
296C13×C22⋊C4C2×D412yes—
297C13×C22⋊C4C2×D412yes—
298C42×C13—22no—
299C42×C13—22no—
300C42×C13—22no—
301C42×C13—21no—
302C42×C13C2×D412yes—
303C42×C13C2×D412yes—
304C42×C13C2412yes—
305C42×C13C2412yes—
306C22⋊Dic13—22no—
307C22⋊Dic13—22no—
308C4⋊Dic13—21no—
309C4⋊Dic13—22no—
310C4⋊Dic13—24no—
311C4⋊Dic13—24no—
312C4⋊Dic13—21no—
313C4⋊Dic13—22no—
314C4⋊Dic13—22no—
315C4⋊Dic13C2412yes—
316C4⋊Dic13C2414yes—
317C4⋊Dic13C2412yes—
318#6101—24no—
319#6101—24no—
320#6101—24no—
321#6101—24no—
322C4×Dic13—22no—
323C4×Dic13—22no—
324#6099—24no—
325C2×#1055—24no—
326C2×#1055C2412yes—
327C2×#1055C2412yes—
328C2×#1055C2414yes—
329#3495D1311yescharacteristic
330C2×#544—131no—
331#3244—134no—
332#3242—134no—
333#3238—132no—
334#3236—132no—
335#3232—132no—
336#3229—132no—
337#3163—132no—
338#3137—132no—
339#3095—131no—
340#3092—131no—
341#3091—131no—
342C2×#483—131no—
343#3084—132no—
344#3082—132no—
345#2924—131no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—21no—
349C23×C13—41no—
350C23×C13C22×D411yescharacteristic
351C23×C13C22×D411yescharacteristic
352C23×C13C22×D411yescharacteristic
353Q8×C13—24no—
354Q8×C13—22no—
355Q8×C13—42no—
356Q8×C13—82no—
357D4×C13—22no—
358D4×C13—42no—
359D4×C13—42no—
360D4×C13—81no—
361C2×C4×C13—22no—
362C2×C4×C13—24no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—21no—
368C2×C4×C13—21no—
369C2×C4×C13—22no—
370C2×C4×C13—21no—
371C2×C4×C13—22no—
372C2×C4×C13—42no—
373C2×C4×C13—42no—
374C2×C4×C13—42no—
375C2×C4×C13—82no—
376C2×C4×C13—81no—
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D412yes—
379C2×C4×C13C22×D412yes—
380C2×C4×C13C22×D412yes—
381C2×C4×C13C22×D412yes—
382C2×C4×C13C22×D411yescharacteristic
383C2×C4×C13C22×D411yescharacteristic
384C2×C4×C132−1+414yes—
385C2×C4×C13C2511yescharacteristic
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—24no—
389C2×Dic13—42no—
390C2×Dic13—42no—
391C2×Dic13—44no—
392C2×Dic13—82no—
393C2×Dic13—82no—
394Dic26—84no—
395Dic26—84no—
396#1055—22no—
397#1055—22no—
398#1055—24no—
399#556—21no—
400#554—21no—
401#552—22no—
402#552—21no—
403#552—21no—
404#551—22no—
405#544—132no—
406#544—132no—
407#544—134no—
408#544—262no—
409#544—261no—
410#544—261no—
411#544C2×D1311yescharacteristic
412#542C2×D1312yes—
413#541C2×D1312yes—
414#536C2×D1311yescharacteristic
415#533C2×D1312yes—
416C2×C4⋊Q8—132no—
417C2×C4⋊Q8—261no—
418#529C2×D1312yes—
419C2×#125—132no—
420C2×#125—261no—
421#525C2×D1311yescharacteristic
422C2×C22⋊Q8—262no—
423C2×C22⋊Q8C2×D1311yescharacteristic
424#520C2×D1311yescharacteristic
425#519C2×D1311yescharacteristic
426C2×#117—131no—
427C2×#117C2×D1311yescharacteristic
428C22×C4⋊C4—131no—
429#501—134no—
430#501—134no—
431#499—134no—
432#498—134no—
433#491—134no—
434#489—134no—
435#488—134no—
436#487—134no—
437#485—132no—
438#485—134no—
439#484—131no—
440#484—132no—
441#484—132no—
442#483—132no—
443#483—132no—
444#483—134no—
445#483—131no—
446#483—132no—
447#483—132no—
448#482—132no—
449#481—131no—
450#481—132no—
451#480—131no—
452#480—132no—
453#479—134no—
454#479—134no—
455#479—134no—
456#478—134no—
457#477—134no—
458#476—134no—
459#475—134no—
460#475—134no—
461#433—134no—
462#432—132no—
463#431—132no—
464#428—132no—
465#428—132no—
466#427—132no—
467C2×#106—132no—
468#424—132no—
469#419—132no—
470#417—132no—
471#416—132no—
472C2×#103—132no—
473#407—131no—
474C2×C22⋊C8—131no—
475#405—132no—
476C22×C13—21no—
477C22×C13—21no—
478C22×C13—21no—
479C22×C13—21no—
480C22×C13—21no—
481C22×C13—21no—
482C22×C13—21no—
483C22×C13—44no—
484C22×C13—41no—
485C22×C13—41no—
486C22×C13—41no—
487C22×C13#53612yes—
488C22×C13#57712yes—
489C22×C13C23×D411yescharacteristic
490C4×C13—22no—
491C4×C13—22no—
492C4×C13—21no—
493C4×C13—21no—
494C4×C13—22no—
495C4×C13—22no—
496C4×C13—42no—
497C4×C13—41no—
498C4×C13—41no—
499C4×C13—42no—
500C4×C13—41no—
501C4×C13#53612yes—
502C4×C13C2×2−1+412yes—
503Dic13—42no—
504Dic13—42no—
505Dic13—44no—
506C2×#41C22×D1311yescharacteristic
507C22×Q8—262no—
508C22×Q8C22×D1311yescharacteristic
509C23×C4—261no—
510C23×C4C22×D1311yescharacteristic
511C2×M16—132no—
512C22×C8—132no—
513C4⋊Q8—21no—
514C4⋊Q8—134no—
515C4⋊Q8—134no—
516C4⋊Q8—262no—
517C4⋊Q8—262no—
518C4⋊Q8—264no—
519C4⋊Q8—262no—
520C4⋊Q8—262no—
521C4⋊Q8C22×D1312yes—
522C4⋊Q8C22×D1312yes—
523#126—22no—
524#126—22no—
525#126—22no—
526#126—22no—
527#125—22no—
528#125—22no—
529#125—21no—
530#125—22no—
531#125—134no—
532#125—134no—
533#125—262no—
534#125—264no—
535#125—262no—
536#125—262no—
537#125—262no—
538#125C22×D1312yes—
539#124—22no—
540#124C22×D1312yes—
541#123—21no—
542#123—22no—
543#123—22no—
544#123—22no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—22no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—264no—
553C22⋊Q8—264no—
554C22⋊Q8—264no—
555C22⋊Q8—264no—
556C22⋊Q8C22×D1312yes—
557C22⋊Q8C22×D1312yes—
558C22⋊Q8C22×D1311yescharacteristic
559C22⋊Q8C22×D1311yescharacteristic
560#121C22×D1311yescharacteristic
561#121C22×D1311yescharacteristic
562#120—21no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8C22×D1312yes—
567C4×Q8C22×D1312yes—
568C4×Q8C22×D1312yes—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4C22×D1312yes—
574#117—22no—
575#117—21no—
576#117—22no—
577#117—22no—
578#117—132no—
579#117—132no—
580#117—261no—
581#117—261no—
582#117C22⋊D1311yescharacteristic
583#117C22⋊D1312yes—
584#117C22⋊D1311yescharacteristic
585#117C22×D1311yescharacteristic
586#117C22×D1311yescharacteristic
587#117C22×D1311yescharacteristic
588#117C22×D1312yes—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—132no—
592C2×C4⋊C4—132no—
593C2×C4⋊C4—132no—
594C2×C4⋊C4—131no—
595C2×C4⋊C4—131no—
596C2×C4⋊C4—261no—
597C2×C4⋊C4—261no—
598C2×C4⋊C4—261no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—262no—
602C2×C4⋊C4C22⋊D1311yescharacteristic
603C2×C4⋊C4C22⋊D1311yescharacteristic
604C2×C4⋊C4C22×D1311yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—261no—
607C2×C22⋊C4C22⋊D1312yes—
608C2×C42—261no—
609C2×C42C22×D1312yes—
610#107—132no—
611#107—132no—
612#107—134no—
613#107—134no—
614#106—134no—
615#106—134no—
616#106—132no—
617#106—132no—
618#106—134no—
619#106—134no—
620C4⋊C8—134no—
621C4⋊C8—134no—
622#103—134no—
623#103—134no—
624#103—132no—
625#103—132no—
626#103—134no—
627#103—134no—
628#103—134no—
629#102—132no—
630#102—132no—
631#102—134no—
632C22⋊C8—131no—
633C22⋊C8—131no—
634C22⋊C8—132no—
635C22⋊C8—132no—
636C22⋊C8—132no—
637#97—134no—
638C4×C8—134no—
639C2×C13—22no—
640C2×C13—22no—
641C2×C13—41no—
642C2×C13—81no—
643C2×C13C2×#53611yescharacteristic
644C2×C13C2×#57711yescharacteristic
645C2×C13#358611yescharacteristic
646C24C2×C22⋊D1311yescharacteristic
647#41—24no—
648C2×Q8—21no—
649C2×Q8—22no—
650C2×Q8—24no—
651C2×Q8—264no—
652C2×Q8—264no—
653C2×Q8—1044no—
654C2×Q8C23×D1312yes—
655C2×Q8C23×D1311yescharacteristic
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4C23×D1311yescharacteristic
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—261no—
666C22×C4—261no—
667C22×C4—262no—
668C22×C4—262no—
669C22×C4—262no—
670C22×C4—1042no—
671C22×C4C2×C22⋊D1311yescharacteristic
672C22×C4C2×C22⋊D1312yes—
673C22×C4C2×C22⋊D1311yescharacteristic
674C22×C4C2×C22⋊D1311yescharacteristic
675C22×C4C2×C22⋊D1312yes—
676C22×C4C23×D1311yescharacteristic
677C22×C4C23×D1311yescharacteristic
678C22×C4C23×D1311yescharacteristic
679M16—264no—
680C2×C8—132no—
681C2×C8—134no—
682C2×C8—132no—
683C2×C8—264no—
684C4⋊C4—21no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—134no—
698C4⋊C4—132no—
699C4⋊C4—132no—
700C4⋊C4—262no—
701C4⋊C4—262no—
702C4⋊C4—262no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—264no—
706C4⋊C4—264no—
707C4⋊C4—264no—
708C4⋊C4—264no—
709C4⋊C4—264no—
710C4⋊C4—264no—
711C4⋊C4C2×C22⋊D1311yescharacteristic
712C4⋊C4C2×C22⋊D1311yescharacteristic
713C4⋊C4C2×C22⋊D1312yes—
714C4⋊C4C2×C22⋊D1311yescharacteristic
715C4⋊C4C2×C22⋊D1311yescharacteristic
716C4⋊C4C2×C22⋊D1312yes—
717C4⋊C4C23×D1312yes—
718C4⋊C4C23×D1311yescharacteristic
719C4⋊C4C23×D1311yescharacteristic
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—21no—
729C22⋊C4—22no—
730C22⋊C4—262no—
731C22⋊C4—262no—
732C22⋊C4C2×C22⋊D1312yes—
733C22⋊C4C2×C22⋊D1312yes—
734C22⋊C4C2×C22⋊D1312yes—
735C22⋊C4C2×C22⋊D1312yes—
736C42—22no—
737C42—22no—
738C42—22no—
739C42—21no—
740C42—262no—
741C42—262no—
742C42C2×C22⋊D1312yes—
743C42C2×C22⋊D1312yes—
744C42C23×D1312yes—
745C42C23×D1312yes—
746C13#6087211yescharacteristic, complemented, Sylow
747C23—22no—
748C23—22no—
749C23—21no—
750C23—41no—
751C23C22×C22⋊D1311yescharacteristic
752C23C22×C22⋊D1311yescharacteristic
753C23C22×C22⋊D1311yescharacteristic
754Q8—24no—
755Q8—22no—
756Q8—42no—
757Q8—82no—
758Q8—1044no—
759Q8—1044no—
760D4—22no—
761D4—42no—
762D4—42no—
763D4—81no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—22no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—82no—
779C2×C4—81no—
780C2×C4—262no—
781C2×C4—262no—
782C2×C4—264no—
783C2×C4—522no—
784C2×C4—524no—
785C2×C4—522no—
786C2×C4—1042no—
787C2×C4—1042no—
788C2×C4#8825714yes—
789C2×C4C22×C22⋊D1312yes—
790C2×C4C22×C22⋊D1312yes—
791C2×C4C22×C22⋊D1311yescharacteristic
792C2×C4C22×C22⋊D1311yescharacteristic
793C2×C4C22×C22⋊D1312yes—
794C2×C4C22×C22⋊D1312yes—
795C2×C4C22×C22⋊D1311yescharacteristic
796C2×C4C24×D1311yescharacteristic
797C8—262no—
798C8—262no—
799C8—264no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—44no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22#1171953012yes—
812C22#1171954212yes—
813C22C23×C22⋊D1311yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—41no—
821C4—42no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—524no—
826C4—522no—
827C4—522no—
828C4#1171953012yes—
829C4C2×#8825712yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—81no—
834C2C2×#1171953011yescharacteristic
835C2C2×#1171954211yescharacteristic
836C2#1312962211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC13×#3495C2
socleC22×C13C23×D4
prime radicalC13×#525C22
hypercenter#3495D13
hypocenterC13#60872
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3495

Complements

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

NH ≅ G/Ntype
1. C2×#11719224C2semidirect
2. #13126128C2semidirect
3. #13126098C2semidirect
4. #13126054C2semidirect
5. #13126038C2semidirect
6. #13126000C2semidirect
7. #13125977C2semidirect
8. #13125362C2semidirect
9. #13125201C2semidirect
10. #13124780C2semidirect
13. C2×#11718704C2semidirect
14. #13124698C2semidirect
15. #13124678C2semidirect
16. #13123494C2semidirect
54. #11718743C22semidirect
55. #11718742C22semidirect
56. #11718741C22semidirect
57. #11718740C22semidirect
58. #11718726C22semidirect
59. #11718725C22semidirect
60. #11718717C22semidirect
61. #11718716C22semidirect
78. #11718683C22semidirect
79. #11718683C22semidirect
80. #11718683C22semidirect
81. #11718682C22semidirect
82. #11718681C22semidirect
83. #11718681C22semidirect
84. #11718670C22semidirect
85. #11718669C22semidirect
746. C13#60872semidirect

Maximal subgroups

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

subgroupindex
C2×#117192242
#131261282
#131260982
#131260542
#131260382
#131260002
#131259772
#131253622
#131252012
#131247802
#131247562
#131247452
C2×#117187042
#131246982
#131246782
#131234942
C13×#34952
#6087213