Finite Group Databasebeta

← #16743531

Subgroups — #16743531

Order 3328.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719272C211yesmaximal, characteristic, complemented
2#13127799C214yesmaximal, complemented
3#13127781C214yesmaximal, complemented
4#13127764C212yesmaximal, complemented
5#13127757C212yesmaximal, complemented
6#13127723C212yesmaximal, complemented
7#13127711C212yesmaximal, complemented
8#13125389C212yesmaximal, complemented
9#13125383C211yesmaximal, characteristic, complemented
10#13124658C212yesmaximal
11#13124651C211yesmaximal, characteristic
12#13124637C212yesmaximal, complemented
13#13124637C211yesmaximal, characteristic, complemented
14Q8×#6099C211yesmaximal, characteristic, complemented
15C4×#88205C212yesmaximal
16C4×#88205C211yesmaximal, characteristic
17Q8×C13×#41C211yesmaximal, characteristic
18Q82×C13C2211yescharacteristic
19C13×#557C2211yescharacteristic
20C13×#557C2212yes—
21C13×#554—21no—
22C13×#554—22no—
23C13×#554C2211yescharacteristic
24C13×#554C2212yes—
25D4×Q8×C13—21no—
26D4×Q8×C13C2211yescharacteristic
27C13×#533—21no—
28C13×#533—22no—
29C13×#533C2211yescharacteristic
30C13×#533C2212yes—
31C4×C13×#41C2211yescharacteristic
32C4×C13×#41C2212yes—
33C2×C4×Q8×C13—21no—
34C2×C4×Q8×C13C2211yescharacteristic
35C2×#88205C2211yescharacteristic
36C2×#88198—21no—
37#11719272—21no—
38#11719272—22no—
39#11719272—21no—
40#11719272C2212yes—
41#11719272C2212yes—
42#11719272C2214yes—
43C2×#88143—22no—
44C2×#88141—21no—
45C2×#88124C2212yes—
46C2×#88123C2211yescharacteristic
47C2×C4×Dic26C2212yes—
48C2×C4×Dic26C2211yescharacteristic
49#11718893C2212yes—
50#11718893C2211yescharacteristic
51#11718755C2212yes—
52#11718755C2214yes—
53#11718752C2212yes—
54#11718752C2214yes—
55#11718741C2214yes—
56#11718741C2214yes—
57#11718740C2212yes—
58#11718739C2212yes—
59#11718726C2214yes—
60#11718725C2214yes—
61#11718725C2214yes—
62#11718724C2214yes—
63#11718724C2214yes—
64#11718724C2214yes—
65#11718691C2214yes—
66#11718691C2212yes—
67C4×#6107C2212yes—
68C4×#6107C2214yes—
69#11718685C2212yes—
70#11718685C2214yes—
71Q8×#1055C2212yes—
72#11718683C2214yes—
73#11718683C2214yes—
74#11718682C2212yes—
75#11718681C2212yes—
76#11718679C2214yes—
77#11718679C2212yes—
78C4×#6105C2212yes—
79C4×#6105C2214yes—
80#11718670C2214yes—
81#11718670C2214yes—
82#11718669C2212yes—
83#11718668C2212yes—
84#11718665C2211yescharacteristic
85#11718665C2212yes—
86#11718656C2212yes—
87#11718656C2212yes—
88#11718656C2211yescharacteristic
89#11718656C2212yes—
90#11718656C2212yes—
91#11718585C2211yescharacteristic
92#11718585C2212yes—
93C4×#6099C2211yescharacteristic
94C4×#6099C2212yes—
95C2×C13×#41C2311yescharacteristic
96C22×Q8×C13—21no—
97C22×Q8×C13D411yescharacteristic
98C22×Dic26—21no—
99C22×Dic26C2311yescharacteristic
100C13×C4⋊Q8—21no—
101C13×C4⋊Q8—22no—
102C13×C4⋊Q8—21no—
103C13×C4⋊Q8—22no—
104C13×C4⋊Q8C2311yescharacteristic
105C13×C4⋊Q8C2311yescharacteristic
106C13×C4⋊Q8C2312yes—
107C13×C4⋊Q8C2312yes—
108C13×#125—22no—
109C13×#125—22no—
110C13×#125—22no—
111C13×#125C2312yes—
112C13×#125C2312yes—
113C13×#125C2312yes—
114C13×C22⋊Q8—21no—
115C13×C22⋊Q8—22no—
116C13×C22⋊Q8—21no—
117C13×C22⋊Q8—22no—
118C13×C22⋊Q8—22no—
119C13×C22⋊Q8—21no—
120C13×C22⋊Q8—21no—
121C13×C22⋊Q8—22no—
122C13×C22⋊Q8—22no—
123C13×C22⋊Q8—22no—
124C13×C22⋊Q8—22no—
125C4×Q8×C13—21no—
126C4×Q8×C13—21no—
127C4×Q8×C13—22no—
128C4×Q8×C13—21no—
129C4×Q8×C13—22no—
130C4×Q8×C13—21no—
131C4×Q8×C13—22no—
132C4×Q8×C13D411yescharacteristic
133C4×Q8×C13D411yescharacteristic
134C4×Q8×C13D412yes—
135C4×Q8×C13C2311yescharacteristic
136C4×Q8×C13C2311yescharacteristic
137C4×Q8×C13C2312yes—
138C4×Q8×C13C2312yes—
139C4×Q8×C13C2311yescharacteristic
140C4×Q8×C13C2311yescharacteristic
141C4×Q8×C13C2312yes—
142C4×D4×C13—21no—
143C4×D4×C13—22no—
144C4×D4×C13—22no—
145C4×D4×C13—21no—
146C4×D4×C13C2311yescharacteristic
147C4×D4×C13C2311yescharacteristic
148C4×D4×C13C2312yes—
149C4×D4×C13C2312yes—
150C13×#117—21no—
151C13×#117—22no—
152C13×#117C2312yes—
153C13×#117C2311yescharacteristic
154C2×C13×C4⋊C4—21no—
155C2×C13×C4⋊C4—22no—
156C2×C13×C4⋊C4D411yescharacteristic
157C2×C13×C4⋊C4D412yes—
158C2×C42×C13—21no—
159C2×C42×C13—22no—
160C2×C42×C13C2311yescharacteristic
161C2×C42×C13C2312yes—
162#88205Q818yescomplemented
163#88198—22no—
164#88198—22no—
165#88198—24no—
166C2×#6107C2312yes—
167C2×#6105C2312yes—
168C2×C4⋊Dic13—21no—
169C2×C4⋊Dic13C2312yes—
170C2×C4⋊Dic13C2311yescharacteristic
171C2×#6101—21no—
172C2×#6101—22no—
173C2×#6101—22no—
174C2×#6101—22no—
175C2×C4×Dic13—22no—
176C2×C4×Dic13—21no—
177C2×#6099C2311yescharacteristic
178C2×#6099C2312yes—
179C2×#6099C2311yescharacteristic
180#88143—24no—
181#88143—24no—
182#88143—24no—
183#88143—24no—
184#88141—22no—
185#88141—24no—
186#88141—22no—
187#88124—22no—
188#88124—22no—
189#88124C2314yes—
190#88124C2314yes—
191#88123—21no—
192#88123—21no—
193#88123C2312yes—
194#88123C2312yes—
195C4×Dic26—22no—
196C4×Dic26—22no—
197C4×Dic26—21no—
198C4×Dic26—21no—
199C4×Dic26C2314yes—
200C4×Dic26C2312yes—
201C4×Dic26C2312yes—
202C4×Dic26C2314yes—
203#88075C2314yes—
204#88075C2312yes—
205#88072C2314yes—
206#88072C2312yes—
207#88050C2312yes—
208#88050C2314yes—
209#88050C2314yes—
210#88050C2312yes—
211#88048C2314yes—
212#88048C2314yes—
213#88048C2314yes—
214#88048C2312yes—
215#88048C2314yes—
216#88047C2314yes—
217#88047C2314yes—
218#88047C2314yes—
219#88047C2312yes—
220#88047C2314yes—
221C4⋊#1055C2312yes—
222C4⋊#1055C2312yes—
223C4⋊#1055C2314yes—
224C4⋊#1055C2314yes—
225#88043C2312yes—
226#88043C2314yes—
227C4×#1055C2314yes—
228C4×#1055C2312yes—
229#61369—131nomaximal, Sylow
230C13×#41—22no—
231C13×#41C2×Q814yes—
232C2×Q8×C13—22no—
233C2×Q8×C13—21no—
234C2×Q8×C13—22no—
235C2×Q8×C13—21no—
236C2×Q8×C13—42no—
237C2×Q8×C13—44no—
238C2×Q8×C13C2×D411yescharacteristic
239C2×Q8×C13C2×D411yescharacteristic
240C2×Q8×C13C2×D412yes—
241C2×Q8×C13C2411yescharacteristic
242C2×D4×C13—21no—
243C2×D4×C13C2411yescharacteristic
244C22×C4×C13—21no—
245C22×C4×C13—22no—
246C22×C4×C13—21no—
247C22×C4×C13—22no—
248C22×C4×C13—21no—
249C22×C4×C13C2×D411yescharacteristic
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13C2×D411yescharacteristic
253C22×C4×C13C2411yescharacteristic
254C22×Dic13—21no—
255C22×Dic13—21no—
256C22×Dic13—22no—
257C2×Dic26—21no—
258C2×Dic26—22no—
259C2×Dic26—22no—
260C2×Dic26—22no—
261C2×Dic26—44no—
262C2×Dic26C2×Q814yescomplemented
263C2×Dic26C2412yes—
264C13×C4⋊C4—22no—
265C13×C4⋊C4—22no—
266C13×C4⋊C4—22no—
267C13×C4⋊C4—22no—
268C13×C4⋊C4—21no—
269C13×C4⋊C4—22no—
270C13×C4⋊C4—21no—
271C13×C4⋊C4—22no—
272C13×C4⋊C4—21no—
273C13×C4⋊C4—22no—
274C13×C4⋊C4—21no—
275C13×C4⋊C4—22no—
276C13×C4⋊C4—22no—
277C13×C4⋊C4—22no—
278C13×C4⋊C4C2×D411yescharacteristic
279C13×C4⋊C4C2×D412yes—
280C13×C4⋊C4C2×D411yescharacteristic
281C13×C4⋊C4C2×D412yes—
282C13×C4⋊C4C2×D412yes—
283C13×C4⋊C4C2×D412yes—
284C13×C4⋊C4C2×D412yes—
285C13×C4⋊C4C2411yescharacteristic
286C13×C4⋊C4C2412yes—
287C13×C4⋊C4C2411yescharacteristic
288C13×C4⋊C4C2412yes—
289C13×C22⋊C4—22no—
290C13×C22⋊C4—21no—
291C13×C22⋊C4—22no—
292C13×C22⋊C4—21no—
293C13×C22⋊C4—22no—
294C13×C22⋊C4—21no—
295C42×C13—21no—
296C42×C13—22no—
297C42×C13—22no—
298C42×C13—21no—
299C42×C13—22no—
300C42×C13—21no—
301C42×C13C2×D411yescharacteristic
302C42×C13C2×D411yescharacteristic
303C42×C13C2×D412yes—
304C42×C13C2×D412yes—
305C42×C13C2411yescharacteristic
306C42×C13C2411yescharacteristic
307C42×C13C2412yes—
308C42×C13C2412yes—
309#6107C2×Q818yescomplemented
310#6105C2×Q818yescomplemented
311C4⋊Dic13—22no—
312C4⋊Dic13—21no—
313C4⋊Dic13—22no—
314C4⋊Dic13—22no—
315C4⋊Dic13C2414yes—
316C4⋊Dic13C2412yes—
317#6101—22no—
318#6101—22no—
319#6101—24no—
320#6101—24no—
321#6101—24no—
322#6101—24no—
323#6101—24no—
324#6101—24no—
325C4×Dic13—24no—
326C4×Dic13—24no—
327C4×Dic13—22no—
328C4×Dic13—22no—
329#6099—22no—
330#6099—24no—
331#6099C2×Q814yescomplemented
332C2×#1055C2414yes—
333C2×#1055C2412yes—
334C2×#1055C2412yes—
335Q8×#41D1311yescharacteristic
336C2×#557—131no—
337#3390—134no—
338#3388—134no—
339#3387—132no—
340#3386—132no—
341#3383—132no—
342#3381—132no—
343#3166—132no—
344#3165—131no—
345#3080—132no—
346#3079—131no—
347#3078—131no—
348#3078—132no—
349Q8×M16—131no—
350C4×#137—131no—
351C4×#137—132no—
352C23×C13—21no—
353C23×C13C22×D411yescharacteristic
354Q8×C13—22no—
355Q8×C13—22no—
356Q8×C13—21no—
357Q8×C13—42no—
358Q8×C13—44no—
359Q8×C13—42no—
360Q8×C13—82no—
361Q8×C13—81no—
362Q8×C13C22×Q812yes—
363D4×C13—24no—
364D4×C13—21no—
365D4×C13C22×Q812yes—
366C2×C4×C13—21no—
367C2×C4×C13—24no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—21no—
371C2×C4×C13—22no—
372C2×C4×C13—21no—
373C2×C4×C13—42no—
374C2×C4×C13—41no—
375C2×C4×C13—42no—
376C2×C4×C13—44no—
377C2×C4×C13—42no—
378C2×C4×C13—82no—
379C2×C4×C13—81no—
380C2×C4×C13C22×D412yes—
381C2×C4×C13C22×D412yes—
382C2×C4×C13C22×D411yescharacteristic
383C2×C4×C13C22×D412yes—
384C2×C4×C13C22×D412yes—
385C2×C4×C13C22×D411yescharacteristic
386C2×C4×C13C22×D411yescharacteristic
387C2×C4×C13C22×D411yescharacteristic
388C2×C4×C13C22×D411yescharacteristic
389C2×C4×C13C22×Q812yes—
390C2×C4×C132−1+412yes—
391C2×C4×C13C2511yescharacteristic
392C2×Dic13—24no—
393C2×Dic13—22no—
394C2×Dic13—22no—
395C2×Dic13—24no—
396C2×Dic13—44no—
397C2×Dic13—42no—
398Dic26—24no—
399Dic26—22no—
400Dic26—44no—
401Dic26—44no—
402Dic26C22×Q814yes—
403#1055—24no—
404#1055—22no—
405#1055C22×Q814yes—
406C2×#137—131no—
407Q82C2×D1311yescharacteristic
408#557—132no—
409#557—132no—
410#557—134no—
411#557—261no—
412#557—262no—
413#557—261no—
414#557C2×D1311yescharacteristic
415#557C2×D1312yes—
416#554—21no—
417#554—22no—
418#554C2×D1311yescharacteristic
419#554C2×D1312yes—
420D4×Q8—21no—
421D4×Q8C2×D1311yescharacteristic
422#533—22no—
423#533—21no—
424#533C2×D1311yescharacteristic
425#533C2×D1312yes—
426C2×C4⋊Q8—131no—
427C2×C4⋊Q8—261no—
428C2×#125—132no—
429C2×#125—262no—
430C4×#41C2×D1311yescharacteristic
431C4×#41C2×D1312yes—
432C2×C4×Q8—21no—
433C2×C4×Q8—132no—
434C2×C4×Q8—131no—
435C2×C4×Q8—261no—
436C2×C4×Q8C2×D1311yescharacteristic
437#501—134no—
438#501—134no—
439#501—134no—
440#500—132no—
441#499—134no—
442#499—134no—
443#498—132no—
444#479—134no—
445#479—134no—
446#479—134no—
447#479—134no—
448#479—134no—
449#478—134no—
450#478—134no—
451#477—132no—
452#477—134no—
453#477—132no—
454#476—132no—
455#475—132no—
456#475—134no—
457#475—132no—
458#474—132no—
459#446—132no—
460#446—134no—
461C8×Q8—132no—
462#441—134no—
463#441—132no—
464#440—134no—
465#440—132no—
466C4×Q16—132no—
467C4×Q16—134no—
468C4×SD16—132no—
469C4×SD16—134no—
470#428—132no—
471#428—132no—
472#428—132no—
473#428—132no—
474#428—131no—
475#423—131no—
476#423—132no—
477#419—132no—
478#419—131no—
479#417—132no—
480#417—131no—
481C4×M16—131no—
482C4×M16—132no—
483C22×C13—21no—
484C22×C13—21no—
485C22×C13—22no—
486C22×C13—41no—
487C22×C13—41no—
488C22×C13D4×Q812yes—
489C22×C13C23×D411yescharacteristic
490C4×C13—22no—
491C4×C13—21no—
492C4×C13—22no—
493C4×C13—21no—
494C4×C13—22no—
495C4×C13—21no—
496C4×C13—22no—
497C4×C13—22no—
498C4×C13—42no—
499C4×C13—41no—
500C4×C13—42no—
501C4×C13—41no—
502C4×C13D4×Q812yes—
503C4×C13#57512yes—
504C4×C13C23×Q811yescharacteristic
505C4×C13C2×2−1+411yescharacteristic
506Dic13—24no—
507Dic13—42no—
508Dic13—44no—
509C2×#41C22×D1311yescharacteristic
510C22×Q8—21no—
511C22×Q8—131no—
512C22×Q8—261no—
513C22×Q8C22⋊D1311yescharacteristic
514#137—138no—
515C2×Q16—132no—
516C2×SD16—132no—
517C2×M16—131no—
518C2×M16—131no—
519C2×M16—132no—
520C4⋊Q8—21no—
521C4⋊Q8—22no—
522C4⋊Q8—21no—
523C4⋊Q8—22no—
524C4⋊Q8—132no—
525C4⋊Q8—132no—
526C4⋊Q8—262no—
527C4⋊Q8—262no—
528C4⋊Q8—264no—
529C4⋊Q8—261no—
530C4⋊Q8—261no—
531C4⋊Q8C22×D1311yescharacteristic
532C4⋊Q8C22×D1312yes—
533C4⋊Q8C22×D1312yes—
534C4⋊Q8C22×D1311yescharacteristic
535#125—22no—
536#125—22no—
537#125—22no—
538#125—134no—
539#125—134no—
540#125—264no—
541#125—264no—
542#125—264no—
543#125—264no—
544#125—262no—
545#125—262no—
546#125C22×D1312yes—
547#125C22×D1312yes—
548#125C22×D1312yes—
549C22⋊Q8—21no—
550C22⋊Q8—22no—
551C22⋊Q8—21no—
552C22⋊Q8—22no—
553C22⋊Q8—22no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—22no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—21no—
567C4×Q8—132no—
568C4×Q8—134no—
569C4×Q8—134no—
570C4×Q8—132no—
571C4×Q8—262no—
572C4×Q8—264no—
573C4×Q8—262no—
574C4×Q8—262no—
575C4×Q8—262no—
576C4×Q8—261no—
577C4×Q8—261no—
578C4×Q8C22⋊D1311yescharacteristic
579C4×Q8C22⋊D1312yes—
580C4×Q8C22⋊D1311yescharacteristic
581C4×Q8C22×D1312yes—
582C4×Q8C22×D1311yescharacteristic
583C4×Q8C22×D1311yescharacteristic
584C4×Q8C22×D1312yes—
585C4×Q8C22×D1311yescharacteristic
586C4×Q8C22×D1311yescharacteristic
587C4×Q8C22×D1312yes—
588C4×D4—21no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—21no—
592C4×D4C22×D1311yescharacteristic
593C4×D4C22×D1312yes—
594C4×D4C22×D1312yes—
595C4×D4C22×D1311yescharacteristic
596#117—22no—
597#117—21no—
598#117C22×D1311yescharacteristic
599#117C22×D1312yes—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—131no—
603C2×C4⋊C4—132no—
604C2×C4⋊C4—261no—
605C2×C4⋊C4—262no—
606C2×C4⋊C4—262no—
607C2×C4⋊C4—262no—
608C2×C4⋊C4—261no—
609C2×C4⋊C4C22⋊D1311yescharacteristic
610C2×C4⋊C4C22⋊D1312yes—
611C2×C42—22no—
612C2×C42—21no—
613C2×C42—262no—
614C2×C42—261no—
615C2×C42C22×D1312yes—
616C2×C42C22×D1311yescharacteristic
617#107—132no—
618#107—134no—
619#107—134no—
620#107—134no—
621#107—134no—
622#106—134no—
623#106—132no—
624#106—134no—
625#106—134no—
626#106—134no—
627C4⋊C8—132no—
628C4⋊C8—134no—
629C4⋊C8—134no—
630C4⋊C8—132no—
631#103—134no—
632#103—132no—
633#103—134no—
634#103—132no—
635#103—132no—
636#103—134no—
637#102—134no—
638#102—132no—
639#97—134no—
640#97—132no—
641C4×C8—132no—
642C4×C8—134no—
643C2×C13—22no—
644C2×C13—42no—
645C2×C13C2×D4×Q811yescharacteristic
646C2×C13C2×#57511yescharacteristic
647C2×C13#358611yescharacteristic
648#41—22no—
649#41Q8×D1314yes—
650C2×Q8—22no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—21no—
654C2×Q8—42no—
655C2×Q8—44no—
656C2×Q8—134no—
657C2×Q8—132no—
658C2×Q8—262no—
659C2×Q8—261no—
660C2×Q8—262no—
661C2×Q8—262no—
662C2×Q8—524no—
663C2×Q8C2×C22⋊D1311yescharacteristic
664C2×Q8C2×C22⋊D1311yescharacteristic
665C2×Q8C2×C22⋊D1312yes—
666C2×Q8C23×D1311yescharacteristic
667C2×D4—21no—
668C2×D4C23×D1311yescharacteristic
669C22×C4—21no—
670C22×C4—22no—
671C22×C4—21no—
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—261no—
675C22×C4—261no—
676C22×C4—262no—
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1312yes—
679C22×C4C2×C22⋊D1311yescharacteristic
680C22×C4C2×C22⋊D1312yes—
681C22×C4C23×D1311yescharacteristic
682Q16—138no—
683SD16—138no—
684M16—134no—
685M16—262no—
686M16—264no—
687C2×C8—132no—
688C2×C8—132no—
689C2×C8—134no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—22no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—22no—
703C4⋊C4—22no—
704C4⋊C4—132no—
705C4⋊C4—134no—
706C4⋊C4—261no—
707C4⋊C4—262no—
708C4⋊C4—262no—
709C4⋊C4—262no—
710C4⋊C4—264no—
711C4⋊C4—264no—
712C4⋊C4—264no—
713C4⋊C4—264no—
714C4⋊C4—264no—
715C4⋊C4—264no—
716C4⋊C4—262no—
717C4⋊C4—262no—
718C4⋊C4C2×C22⋊D1311yescharacteristic
719C4⋊C4C2×C22⋊D1312yes—
720C4⋊C4C2×C22⋊D1312yes—
721C4⋊C4C2×C22⋊D1311yescharacteristic
722C4⋊C4C2×C22⋊D1312yes—
723C4⋊C4C2×C22⋊D1312yes—
724C4⋊C4C2×C22⋊D1312yes—
725C4⋊C4C23×D1312yes—
726C4⋊C4C23×D1311yescharacteristic
727C4⋊C4C23×D1311yescharacteristic
728C4⋊C4C23×D1312yes—
729C22⋊C4—21no—
730C22⋊C4—22no—
731C22⋊C4—21no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—21no—
735C42—22no—
736C42—21no—
737C42—22no—
738C42—21no—
739C42—22no—
740C42—21no—
741C42—264no—
742C42—264no—
743C42—262no—
744C42—262no—
745C42C2×C22⋊D1312yes—
746C42C2×C22⋊D1311yescharacteristic
747C42C2×C22⋊D1312yes—
748C42C2×C22⋊D1311yescharacteristic
749C42C23×D1312yes—
750C42C23×D1311yescharacteristic
751C42C23×D1312yes—
752C42C23×D1311yescharacteristic
753C13#6136911yescharacteristic, complemented, Sylow
754C23—21no—
755C23C22×C22⋊D1311yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—21no—
759Q8—42no—
760Q8—44no—
761Q8—42no—
762Q8—82no—
763Q8—81no—
764Q8—134no—
765Q8—264no—
766Q8—262no—
767Q8—524no—
768Q8—524no—
769Q8C2×Q8×D1312yes—
770D4—24no—
771D4—21no—
772D4C2×Q8×D1312yes—
773C2×C4—21no—
774C2×C4—24no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—42no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—82no—
786C2×C4—81no—
787C2×C4—264no—
788C2×C4—262no—
789C2×C4—262no—
790C2×C4—264no—
791C2×C4—522no—
792C2×C4—524no—
793C2×C4C2×Q8×D1312yes—
794C2×C4#8825412yes—
795C2×C4C22×C22⋊D1312yes—
796C2×C4C22×C22⋊D1311yescharacteristic
797C2×C4C22×C22⋊D1312yes—
798C2×C4C22×C22⋊D1311yescharacteristic
799C2×C4C22×C22⋊D1312yes—
800C2×C4C22×C22⋊D1312yes—
801C2×C4C22×C22⋊D1311yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C2×C4C22×C22⋊D1311yescharacteristic
804C2×C4C24×D1311yescharacteristic
805C8—134no—
806C8—262no—
807C8—264no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22Q8×C22⋊D1312yes—
814C22C23×C22⋊D1311yescharacteristic
815C4—21no—
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—21no—
821C4—22no—
822C4—21no—
823C4—42no—
824C4—41no—
825C4—42no—
826C4—41no—
827C4—264no—
828C4—524no—
829C4—522no—
830C4Q8×C22⋊D1312yes—
831C4#1171952712yes—
832C4C22×Q8×D1311yescharacteristic
833C4C2×#8825411yescharacteristic
834C2—22no—
835C2—42no—
836C2C2×Q8×C22⋊D1311yescharacteristic
837C2C2×#1171952711yescharacteristic
838C2#1312962211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingQ8×C13×#41C2
socleC22×C13C23×D4
prime radicalC2×C13×#41C23
hypercenterQ8×#41D13
hypocenterC13#61369
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×#41

Complements

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

NH ≅ G/Ntype
1. C2×#11719272C2semidirect
2. #13127799C2semidirect
3. #13127781C2semidirect
4. #13127764C2semidirect
5. #13127757C2semidirect
6. #13127723C2semidirect
7. #13127711C2semidirect
8. #13125389C2semidirect
9. #13125383C2semidirect
12. #13124637C2semidirect
13. #13124637C2semidirect
14. Q8×#6099C2semidirect
162. #88205Q8semidirect
262. C2×Dic26C2×Q8semidirect
309. #6107C2×Q8semidirect
310. #6105C2×Q8semidirect
331. #6099C2×Q8semidirect
753. C13#61369semidirect

Maximal subgroups

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

subgroupindex
C2×#117192722
#131277992
#131277812
#131277642
#131277572
#131277232
#131277112
#131253892
#131253832
#131246582
#131246512
#131246372
Q8×#60992
C4×#882052
Q8×C13×#412
#6136913