Finite Group Databasebeta

← #16735944

Subgroups — #16735944

Order 3328.

1888 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719175C211yesmaximal, characteristic, complemented
2#13126227C212yesmaximal, complemented
3#13126223C212yesmaximal, complemented
4#13126209C214yesmaximal, complemented
5#13126178C212yesmaximal, complemented
6#13126173C214yesmaximal, complemented
7#13126152C212yesmaximal, complemented
8#13124651C212yesmaximal, complemented
9#13124637C212yesmaximal, complemented
10#13124468C214yesmaximal, complemented
11#13124323C212yesmaximal, complemented
12#13124304C212yesmaximal, complemented
13C2×#11718585C211yesmaximal, characteristic, complemented
14C13×#3444C211yesmaximal, characteristic
15C13×#533C2211yescharacteristic
16C13×#533C2211yescharacteristic
17C13×#533C2211yescharacteristic
18C13×#532C2211yescharacteristic
19C13×#532C2211yescharacteristic
20C13×#532C2211yescharacteristic
21C13×#529—21no—
22C13×#529—21no—
23C13×#529—21no—
24C13×#529—21no—
25C13×#529C2212yes—
26C13×#529C2212yes—
27C13×#525—21no—
28C13×#525—21no—
29C13×#525C2212yes—
30C4×C13×#41—21no—
31C4×C13×#41—21no—
32C4×C13×#41C2212yes—
33C22×C42×C13C2211yescharacteristic
34C2×#88205C2214yes—
35C2×#88180—21no—
36C2×#88178—21no—
37C2×#88178C2212yes—
38C22×#6099C2212yes—
39#11719175—21no—
40#11719175—21no—
41#11719175—21no—
42#11719175—21no—
43#11719175C2212yes—
44#11719175C2212yes—
45#11719175C2212yes—
46#11719175C2212yes—
47C2×#88124—21no—
48C2×#88123C2211yescharacteristic
49C2×#88123C2211yescharacteristic
50C2×C4×Dic26—21no—
51C2×C4×Dic26C2212yes—
52#11718893C2214yes—
53#11718755C2214yescomplemented
54#11718752C2214yescomplemented
55#11718751C2214yescomplemented
56#11718736C2214yescomplemented
57#11718724C2218yescomplemented
58#11718715C2218yescomplemented
59#11718713C2218yes—
60#11718712C2218yes—
61#11718703C2218yes—
62#11718702C2218yes—
63#11718692C2214yescomplemented
64#11718692C2214yescomplemented
65#11718682C2214yescomplemented
66#11718681C2214yescomplemented
67#11718680C2214yescomplemented
68#11718680C2214yescomplemented
69#11718669C2214yescomplemented
70#11718668C2214yescomplemented
71#11718665C2214yes—
72#11718656C2214yes—
73#11718585C2212yes—
74#11718585C2212yes—
75#11718585C2212yes—
76#11718585C2212yes—
77C2×C4⋊#1055C2212yes—
78C2×C4⋊#1055C2212yes—
79C2×C13×#41—21no—
80C2×C13×#41—21no—
81C2×C13×#41C2312yes—
82C23×C4×C13D411yescharacteristic
83C23×C4×C13D411yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C22×Dic26—21no—
86C22×Dic26C2312yes—
87C13×C4⋊Q8C2311yescharacteristic
88C13×C4⋊Q8C2311yescharacteristic
89C13×C4⋊Q8C2311yescharacteristic
90C13×#127C2311yescharacteristic
91C13×#126—22no—
92C13×#126—22no—
93C13×#125—21no—
94C13×#125—21no—
95C13×#125C2312yes—
96C13×#124—21no—
97C13×#124—21no—
98C13×#124C2312yes—
99C13×#123—22no—
100C13×#123—22no—
101C13×#123—22no—
102C13×C22⋊Q8—21no—
103C13×C22⋊Q8—21no—
104C13×C22⋊Q8—21no—
105C13×C22⋊Q8—21no—
106C13×C22⋊Q8C2312yes—
107C13×C22⋊Q8C2312yes—
108C13×#121—21no—
109C13×#121—21no—
110C13×#121—21no—
111C13×#121—21no—
112C13×#121C2312yes—
113C13×#121C2312yes—
114C13×#120—22no—
115C4×Q8×C13—21no—
116C4×Q8×C13—21no—
117C4×Q8×C13—21no—
118C4×Q8×C13—21no—
119C4×Q8×C13C2312yes—
120C4×Q8×C13C2312yes—
121C4×D4×C13—22no—
122C4×D4×C13—22no—
123C4×D4×C13—22no—
124C4×D4×C13—22no—
125C4×D4×C13—22no—
126C4×D4×C13—22no—
127C4×D4×C13—21no—
128C4×D4×C13—21no—
129C4×D4×C13—21no—
130C4×D4×C13—21no—
131C4×D4×C13C2312yes—
132C4×D4×C13C2312yes—
133C13×#117—21no—
134C13×#117—21no—
135C13×#117—22no—
136C13×#117—22no—
137C13×#117—22no—
138C13×#117C2312yes—
139C2×C42×C13—22no—
140C2×C42×C13D411yescharacteristic
141C2×C42×C13D411yescharacteristic
142C2×C42×C13D411yescharacteristic
143C2×C42×C13D411yescharacteristic
144C2×C42×C13D411yescharacteristic
145C2×C42×C13D411yescharacteristic
146C2×C42×C13C2311yescharacteristic
147C2×C42×C13C2311yescharacteristic
148C2×C42×C13C2311yescharacteristic
149C2×C42×C13C2311yescharacteristic
150C2×C42×C13C2311yescharacteristic
151C2×C42×C13C2311yescharacteristic
152C2×C22⋊Dic13—22no—
153#88205—48no—
154C2×#6107C2318yes—
155C2×#6105C2318yes—
156#88180—22no—
157#88180—22no—
158#88180—22no—
159#88180—22no—
160C2×C4⋊Dic13—21no—
161C2×C4⋊Dic13—21no—
162C2×C4⋊Dic13—21no—
163C2×C4⋊Dic13C2312yes—
164#88178—22no—
165#88178—22no—
166#88178—22no—
167#88178—22no—
168#88178—22no—
169#88178—22no—
170#88178C2314yes—
171#88178C2314yes—
172C2×#6101—22no—
173C2×#6101—22no—
174C2×C4×Dic13—22no—
175C2×#6099—44no—
176C2×#6099C2314yes—
177C2×#6099C2314yes—
178C22×#1055C2314yes—
179#88124—22no—
180#88124—22no—
181#88124—22no—
182#88124—22no—
183#88123—21no—
184#88123—21no—
185#88123—21no—
186#88123—21no—
187#88123C2312yes—
188#88123C2312yes—
189#88123C2312yes—
190#88123C2312yes—
191C4×Dic26—22no—
192C4×Dic26—22no—
193C4×Dic26—22no—
194C4×Dic26—22no—
195C4×Dic26—22no—
196C4×Dic26—22no—
197C4×Dic26C2314yes—
198C4×Dic26C2314yes—
199#88075C2318yes—
200#88072C2318yes—
201#88050C2318yes—
202#88050C2318yes—
203#88048C2318yes—
204#88047C2318yes—
205C4⋊#1055C2314yes—
206C4⋊#1055C2314yes—
207C4⋊#1055C2314yes—
208C4⋊#1055C2314yes—
209#60918—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C13×#41—24no—
212C13×#41—24no—
213C13×#41—44no—
214C13×#41—44no—
215C2×Q8×C13—21no—
216C2×Q8×C13—21no—
217C2×Q8×C13C2412yes—
218C2×D4×C13—22no—
219C2×D4×C13—22no—
220C2×D4×C13—22no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13C2412yes—
224C22×C4×C13—24no—
225C22×C4×C13—22no—
226C22×C4×C13—22no—
227C22×C4×C13—22no—
228C22×C4×C13—22no—
229C22×C4×C13—22no—
230C22×C4×C13—42no—
231C22×C4×C13C2×D411yescharacteristic
232C22×C4×C13C2×D411yescharacteristic
233C22×C4×C13C2×D411yescharacteristic
234C22×C4×C13C2×D411yescharacteristic
235C22×C4×C13C2×D411yescharacteristic
236C22×C4×C13C2×D411yescharacteristic
237C22×C4×C13C2×D411yescharacteristic
238C22×C4×C13C2×D411yescharacteristic
239C22×C4×C13C2×D411yescharacteristic
240C22×C4×C13C2×D411yescharacteristic
241C22×C4×C13C2×D411yescharacteristic
242C22×C4×C13C2×D411yescharacteristic
243C22×C4×C13C2×D411yescharacteristic
244C22×C4×C13C2×D411yescharacteristic
245C22×C4×C13C2×D411yescharacteristic
246C22×C4×C13C2411yescharacteristic
247C22×C4×C13C2411yescharacteristic
248C22×C4×C13C2411yescharacteristic
249C22×Dic13—22no—
250C22×Dic13—22no—
251C2×Dic26—24no—
252C2×Dic26—24no—
253C2×Dic26—22no—
254C2×Dic26—22no—
255C2×Dic26—22no—
256C2×Dic26—44no—
257C2×Dic26C2414yes—
258C13×C4⋊C4—21no—
259C13×C4⋊C4—21no—
260C13×C4⋊C4—21no—
261C13×C4⋊C4—21no—
262C13×C4⋊C4—22no—
263C13×C4⋊C4—22no—
264C13×C4⋊C4—22no—
265C13×C4⋊C4—22no—
266C13×C4⋊C4—22no—
267C13×C4⋊C4—22no—
268C13×C4⋊C4C2412yes—
269C13×C4⋊C4C2412yes—
270C13×C22⋊C4—22no—
271C13×C22⋊C4—22no—
272C13×C22⋊C4—22no—
273C13×C22⋊C4—22no—
274C13×C22⋊C4—22no—
275C13×C22⋊C4—22no—
276C13×C22⋊C4—22no—
277C13×C22⋊C4—22no—
278C13×C22⋊C4—22no—
279C42×C13—22no—
280C42×C13—22no—
281C42×C13—22no—
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2×D411yescharacteristic
287C42×C13C2×D411yescharacteristic
288C42×C13C2×D411yescharacteristic
289C42×C13C2×D411yescharacteristic
290C42×C13C2×D411yescharacteristic
291C42×C13C2×D411yescharacteristic
292C42×C13C2×D411yescharacteristic
293C42×C13C2×D411yescharacteristic
294C42×C13C2411yescharacteristic
295C42×C13C2411yescharacteristic
296C42×C13C2411yescharacteristic
297C42×C13C2411yescharacteristic
298C22⋊Dic13—24no—
299C22⋊Dic13—24no—
300#6107—48no—
301#6105—48no—
302C4⋊Dic13—22no—
303C4⋊Dic13—22no—
304C4⋊Dic13—22no—
305C4⋊Dic13—22no—
306C4⋊Dic13—22no—
307C4⋊Dic13—22no—
308C4⋊Dic13—22no—
309C4⋊Dic13C2414yes—
310#6101—24no—
311#6101—24no—
312#6101—24no—
313#6101—24no—
314C4×Dic13—24no—
315C4×Dic13—24no—
316#6099—28no—
317#6099—44no—
318C2×#1055—44no—
319C2×#1055C2418yes—
320#3444D1311yescharacteristic
321C2×#533—131no—
322#3255—132no—
323#3254—132no—
324#3252—134no—
325#3249—132no—
326#3248—134no—
327#3246—132no—
328#3079—132no—
329#3078—132no—
330#3056—134no—
331#3039—132no—
332#3037—132no—
333C2×#423—131no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—41no—
338C23×C13C22×D411yescharacteristic
339C23×C13C22×D411yescharacteristic
340C23×C13C22×D411yescharacteristic
341Q8×C13—22no—
342Q8×C13—22no—
343Q8×C13—42no—
344Q8×C13—42no—
345D4×C13—22no—
346D4×C13—22no—
347D4×C13—42no—
348D4×C13—44no—
349D4×C13—44no—
350D4×C13—44no—
351D4×C13—42no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—21no—
364C2×C4×C13—21no—
365C2×C4×C13—21no—
366C2×C4×C13—21no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—44no—
374C2×C4×C13—44no—
375C2×C4×C13—44no—
376C2×C4×C13#13714yescomplemented
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13C22×D411yescharacteristic
381C2×C4×C13C22×D411yescharacteristic
382C2×C4×C13C22×D411yescharacteristic
383C2×C4×C13C22×D411yescharacteristic
384C2×C4×C13C22×D411yescharacteristic
385C2×C4×C13C22×D411yescharacteristic
386C2×C4×C13C22×D411yescharacteristic
387C2×C4×C13C22×D411yescharacteristic
388C2×C4×C13H(5,𝔽2)12yes—
389C2×C4×C132−1+412yes—
390C2×C4×C13C2511yescharacteristic
391C2×Dic13—24no—
392C2×Dic13—24no—
393C2×Dic13—44no—
394C2×Dic13—44no—
395Dic26—24no—
396Dic26—24no—
397Dic26—44no—
398Dic26—44no—
399Dic26—44no—
400#1055—28no—
401C2×#137—134no—
402C22×M16—132no—
403#533—132no—
404#533—132no—
405#533—132no—
406#533—132no—
407#533—261no—
408#533—261no—
409#533—261no—
410#533—261no—
411#533C2×D1311yescharacteristic
412#533C2×D1311yescharacteristic
413#533C2×D1311yescharacteristic
414#532C2×D1311yescharacteristic
415#532C2×D1311yescharacteristic
416#532C2×D1311yescharacteristic
417C2×C4⋊Q8—131no—
418C2×C4⋊Q8—131no—
419#529—21no—
420#529—21no—
421#529—21no—
422#529—21no—
423#529C2×D1312yes—
424#529C2×D1312yes—
425C2×#125—261no—
426#525—21no—
427#525—21no—
428#525C2×D1312yes—
429C2×C22⋊Q8—132no—
430C2×C22⋊Q8—261no—
431C4×#41—21no—
432C4×#41—21no—
433C4×#41C2×D1312yes—
434C2×C4×Q8—132no—
435C2×C4×Q8—261no—
436C2×#117—261no—
437C22×C42C2×D1311yescharacteristic
438#479—138no—
439#477—134no—
440#477—134no—
441#476—134no—
442#475—134no—
443#475—134no—
444#474—134no—
445#470—138no—
446#468—138no—
447#467—138no—
448#465—138no—
449#464—138no—
450#462—134no—
451#462—134no—
452#462—134no—
453#461—134no—
454#461—134no—
455#460—134no—
456#428—134no—
457#423—132no—
458#423—132no—
459#423—132no—
460#423—132no—
461C2×C4⋊C8—132no—
462C2×C4⋊C8—132no—
463#419—134no—
464#417—134no—
465C22×C13—21no—
466C22×C13—21no—
467C22×C13—21no—
468C22×C13—21no—
469C22×C13—21no—
470C22×C13—21no—
471C22×C13—21no—
472C22×C13—44no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13#53712yes—
477C22×C13C2×#13712yes—
478C22×C13C23×D411yescharacteristic
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—42no—
487C4×C13—42no—
488C4×C13—42no—
489C4×C13#53712yes—
490C4×C13C2×#13712yes—
491C4×C13C2×#13712yes—
492C4×C13#57512yes—
493C4×C13C2×H(5,𝔽2)11yescharacteristic
494C4×C13C2×2−1+411yescharacteristic
495Dic13—44no—
496Dic13—44no—
497C2×#41—21no—
498C2×#41—21no—
499C2×#41C22×D1312yes—
500C22×Q8—132no—
501C22×Q8—261no—
502C23×C4C22⋊D1311yescharacteristic
503C23×C4C22⋊D1311yescharacteristic
504C23×C4C22×D1311yescharacteristic
505#137—528no—
506C2×Q16—138no—
507C2×SD16—138no—
508C2×M16—134no—
509C2×M16—134no—
510C2×M16—524no—
511C22×C8—134no—
512C4⋊Q8—132no—
513C4⋊Q8—132no—
514C4⋊Q8—132no—
515C4⋊Q8—132no—
516C4⋊Q8—261no—
517C4⋊Q8—261no—
518C4⋊Q8—261no—
519C4⋊Q8—261no—
520C4⋊Q8C22×D1311yescharacteristic
521C4⋊Q8C22×D1311yescharacteristic
522C4⋊Q8C22×D1311yescharacteristic
523#127C22×D1311yescharacteristic
524#126—22no—
525#126—22no—
526#125—21no—
527#125—21no—
528#125—262no—
529#125—262no—
530#125—262no—
531#125—262no—
532#125C22×D1312yes—
533#124—21no—
534#124—21no—
535#124C22×D1312yes—
536#123—22no—
537#123—22no—
538#123—22no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—134no—
544C22⋊Q8—134no—
545C22⋊Q8—262no—
546C22⋊Q8—262no—
547C22⋊Q8—262no—
548C22⋊Q8—262no—
549C22⋊Q8—262no—
550C22⋊Q8—262no—
551C22⋊Q8C22×D1312yes—
552C22⋊Q8C22×D1312yes—
553#121—21no—
554#121—21no—
555#121—21no—
556#121—21no—
557#121C22×D1312yes—
558#121C22×D1312yes—
559#120—22no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—21no—
563C4×Q8—21no—
564C4×Q8—134no—
565C4×Q8—134no—
566C4×Q8—262no—
567C4×Q8—262no—
568C4×Q8—262no—
569C4×Q8—262no—
570C4×Q8—262no—
571C4×Q8—262no—
572C4×Q8C22×D1312yes—
573C4×Q8C22×D1312yes—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4C22×D1312yes—
585C4×D4C22×D1312yes—
586#117—21no—
587#117—21no—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—262no—
592#117—262no—
593#117—262no—
594#117—262no—
595#117C22×D1312yes—
596C2×C4⋊C4—132no—
597C2×C4⋊C4—261no—
598C2×C4⋊C4—261no—
599C2×C4⋊C4—262no—
600C2×C4⋊C4—262no—
601C2×C4⋊C4—261no—
602C2×C22⋊C4—262no—
603C2×C42—22no—
604C2×C42—262no—
605C2×C42C22⋊D1311yescharacteristic
606C2×C42C22⋊D1311yescharacteristic
607C2×C42C22⋊D1311yescharacteristic
608C2×C42C22⋊D1311yescharacteristic
609C2×C42C22⋊D1311yescharacteristic
610C2×C42C22⋊D1311yescharacteristic
611C2×C42C22×D1311yescharacteristic
612C2×C42C22×D1311yescharacteristic
613C2×C42C22×D1311yescharacteristic
614C2×C42C22×D1311yescharacteristic
615C2×C42C22×D1311yescharacteristic
616C2×C42C22×D1311yescharacteristic
617#107—138no—
618#106—138no—
619C4⋊C8—134no—
620C4⋊C8—134no—
621C4⋊C8—134no—
622C4⋊C8—134no—
623#103—138no—
624#103—138no—
625#103—138no—
626#102—138no—
627C2×C13—22no—
628C2×C13—22no—
629C2×C13—41no—
630C2×C13—82no—
631C2×C13C2×#53711yescharacteristic
632C2×C13C22×#13711yescharacteristic
633C2×C13C2×#57511yescharacteristic
634C24C2×C22⋊D1311yescharacteristic
635#41—24no—
636#41—24no—
637#41—44no—
638#41—44no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—134no—
642C2×Q8—262no—
643C2×Q8—262no—
644C2×Q8—262no—
645C2×Q8—264no—
646C2×Q8—264no—
647C2×Q8—524no—
648C2×Q8C23×D1312yes—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4C23×D1312yes—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—42no—
662C22×C4—262no—
663C22×C4—262no—
664C22×C4C2×C22⋊D1311yescharacteristic
665C22×C4C2×C22⋊D1311yescharacteristic
666C22×C4C2×C22⋊D1311yescharacteristic
667C22×C4C2×C22⋊D1311yescharacteristic
668C22×C4C2×C22⋊D1311yescharacteristic
669C22×C4C2×C22⋊D1311yescharacteristic
670C22×C4C2×C22⋊D1311yescharacteristic
671C22×C4C2×C22⋊D1311yescharacteristic
672C22×C4C2×C22⋊D1311yescharacteristic
673C22×C4C2×C22⋊D1311yescharacteristic
674C22×C4C2×C22⋊D1311yescharacteristic
675C22×C4C2×C22⋊D1311yescharacteristic
676C22×C4C2×C22⋊D1311yescharacteristic
677C22×C4C2×C22⋊D1311yescharacteristic
678C22×C4C2×C22⋊D1311yescharacteristic
679C22×C4C23×D1311yescharacteristic
680C22×C4C23×D1311yescharacteristic
681C22×C4C23×D1311yescharacteristic
682Q16—528no—
683SD16—528no—
684M16—268no—
685M16—524no—
686C2×C8—138no—
687C2×C8—524no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—134no—
699C4⋊C4—262no—
700C4⋊C4—262no—
701C4⋊C4—262no—
702C4⋊C4—262no—
703C4⋊C4—262no—
704C4⋊C4—264no—
705C4⋊C4—264no—
706C4⋊C4—264no—
707C4⋊C4—264no—
708C4⋊C4—262no—
709C4⋊C4—262no—
710C4⋊C4C23×D1312yes—
711C4⋊C4C23×D1312yes—
712C22⋊C4—22no—
713C22⋊C4—22no—
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—264no—
722C22⋊C4—264no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—264no—
727C42—264no—
728C42C2×C22⋊D1311yescharacteristic
729C42C2×C22⋊D1311yescharacteristic
730C42C2×C22⋊D1311yescharacteristic
731C42C2×C22⋊D1311yescharacteristic
732C42C2×C22⋊D1311yescharacteristic
733C42C2×C22⋊D1311yescharacteristic
734C42C2×C22⋊D1311yescharacteristic
735C42C2×C22⋊D1311yescharacteristic
736C42C2×C22⋊D1311yescharacteristic
737C42C2×C22⋊D1311yescharacteristic
738C42C2×C22⋊D1311yescharacteristic
739C42C2×C22⋊D1311yescharacteristic
740C42C23×D1311yescharacteristic
741C42C23×D1311yescharacteristic
742C42C23×D1311yescharacteristic
743C42C23×D1311yescharacteristic
744C13#6091811yescharacteristic, complemented, Sylow
745C23—22no—
746C23—22no—
747C23—22no—
748C23—41no—
749C23C22×C22⋊D1311yescharacteristic
750C23C22×C22⋊D1311yescharacteristic
751C23C22×C22⋊D1311yescharacteristic
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—264no—
757Q8—264no—
758Q8—524no—
759Q8—524no—
760Q8—524no—
761D4—22no—
762D4—22no—
763D4—42no—
764D4—44no—
765D4—44no—
766D4—44no—
767D4—42no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—264no—
793C2×C4—264no—
794C2×C4—524no—
795C2×C4—524no—
796C2×C4#8820514yescomplemented
797C2×C4#8825612yes—
798C2×C4#8825712yes—
799C2×C4C22×C22⋊D1311yescharacteristic
800C2×C4C22×C22⋊D1311yescharacteristic
801C2×C4C22×C22⋊D1311yescharacteristic
802C2×C4C22×C22⋊D1311yescharacteristic
803C2×C4C22×C22⋊D1311yescharacteristic
804C2×C4C22×C22⋊D1311yescharacteristic
805C2×C4C22×C22⋊D1311yescharacteristic
806C2×C4C22×C22⋊D1311yescharacteristic
807C2×C4C22×C22⋊D1311yescharacteristic
808C2×C4C22×C22⋊D1311yescharacteristic
809C2×C4C22×C22⋊D1311yescharacteristic
810C2×C4C24×D1311yescharacteristic
811C8—268no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—44no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22C2×#8820512yes—
824C22#1171953812yes—
825C22C23×C22⋊D1311yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—42no—
834C4—42no—
835C4—42no—
836C4—524no—
837C4—524no—
838C4#1171952712yes—
839C4C2×#8820512yes—
840C4C2×#8820512yes—
841C4#1171953812yes—
842C4C2×#8825611yescharacteristic
843C4C2×#8825711yescharacteristic
844C2—22no—
845C2—22no—
846C2—41no—
847C2—82no—
848C2C2×#1171953811yescharacteristic
849C2C22×#8820511yescharacteristic
850C2C2×#1171952711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
Fitting, prime radicalC13×#3444C2
socleC22×C13C23×D4
hypercenter#3444D13
hypocenterC13#60918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#11719175C2semidirect
2. #13126227C2semidirect
3. #13126223C2semidirect
4. #13126209C2semidirect
5. #13126178C2semidirect
6. #13126173C2semidirect
7. #13126152C2semidirect
8. #13124651C2semidirect
9. #13124637C2semidirect
10. #13124468C2semidirect
11. #13124323C2semidirect
12. #13124304C2semidirect
13. C2×#11718585C2semidirect
53. #11718755C22semidirect
54. #11718752C22semidirect
55. #11718751C22semidirect
56. #11718736C22semidirect
57. #11718724C22semidirect
58. #11718715C22semidirect
63. #11718692C22semidirect
64. #11718692C22semidirect
65. #11718682C22semidirect
66. #11718681C22semidirect
67. #11718680C22semidirect
68. #11718680C22semidirect
69. #11718669C22semidirect
70. #11718668C22semidirect
376. C2×C4×C13#137semidirect
744. C13#60918semidirect
796. C2×C4#88205semidirect

Maximal subgroups

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

subgroupindex
C2×#117191752
#131262272
#131262232
#131262092
#131261782
#131261732
#131261522
#131246512
#131246372
#131244682
#131243232
#131243042
C2×#117185852
C13×#34442
#6091813