Finite Group Databasebeta

← #16735950

Subgroups — #16735950

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
1#13128132C211yesmaximal, characteristic
2#13126227C212yesmaximal, complemented
3#13126219C212yesmaximal, complemented
4#13126203C214yesmaximal, complemented
5#13126178C212yesmaximal, complemented
6#13126167C214yesmaximal, complemented
7#13126148C212yesmaximal, complemented
8#13124645C212yesmaximal, complemented
9#13124641C212yesmaximal, complemented
10#13124462C214yesmaximal, complemented
11#13124319C212yesmaximal, complemented
12#13124308C212yesmaximal, complemented
13C2×#11718585C211yesmaximal, characteristic, complemented
14C2×C13×#533C211yesmaximal, characteristic, complemented
15C13×#533—21no—
16C13×#533—21no—
17C13×#533—21no—
18C13×#533—21no—
19C13×#533C2212yes—
20C13×#533C2212yes—
21C13×#533C2212yes—
22C13×#533C2212yes—
23C2×C13×C4⋊Q8C2211yescharacteristic
24C2×C13×C4⋊Q8C2211yescharacteristic
25C2×C13×#125—21no—
26C2×C13×C22⋊Q8—21no—
27C2×C13×C22⋊Q8C2212yes—
28C2×C4×Q8×C13—21no—
29C2×C4×Q8×C13C2212yes—
30C2×C13×#117—21no—
31C22×C42×C13C2211yescharacteristic
32C2×#88196C2214yes—
33#11719496—21no—
34#11719496—21no—
35#11719496C2212yes—
36C22×#6099C2212yes—
37#11719184—21no—
38#11719184—21no—
39#11719184—21no—
40#11719184—21no—
41#11719184C2212yes—
42#11719184C2212yes—
43#11719182C2211yescharacteristic
44#11719182C2211yescharacteristic
45#11719182C2211yescharacteristic
46C4×#6127—21no—
47C4×#6127—21no—
48C4×#6127C2212yes—
49#11719175C2211yescharacteristic
50#11719175C2211yescharacteristic
51#11719175C2211yescharacteristic
52#11718886C2214yes—
53#11718755C2214yescomplemented
54#11718752C2214yescomplemented
55#11718751C2214yescomplemented
56#11718751C2214yescomplemented
57#11718748C2214yescomplemented
58#11718745C2214yescomplemented
59#11718744C2214yescomplemented
60#11718744C2214yescomplemented
61#11718713C2218yes—
62#11718712C2218yes—
63#11718710C2218yes—
64#11718709C2218yes—
65#11718692C2214yescomplemented
66#11718689C2218yescomplemented
67#11718688C2214yescomplemented
68#11718683C2218yescomplemented
69#11718682C2214yescomplemented
70#11718681C2214yescomplemented
71#11718627C2214yes—
72#11718625C2214yes—
73#11718585C2212yes—
74#11718585C2212yes—
75#11718585C2212yes—
76#11718585C2212yes—
77C2×C4⋊#1055C2212yes—
78C2×C4⋊#1055C2212yes—
79C22×Q8×C13—21no—
80C22×Q8×C13C2312yes—
81C23×C4×C13D411yescharacteristic
82C23×C4×C13D411yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C2×#6127—21no—
85C2×#6127—21no—
86C2×#6127C2312yes—
87C13×C4⋊Q8—21no—
88C13×C4⋊Q8—21no—
89C13×C4⋊Q8—21no—
90C13×C4⋊Q8—21no—
91C13×C4⋊Q8C2312yes—
92C13×C4⋊Q8C2312yes—
93C13×C4⋊Q8C2312yes—
94C13×C4⋊Q8C2312yes—
95C13×#125—22no—
96C13×#125—22no—
97C13×#125—22no—
98C13×#125—22no—
99C13×C22⋊Q8—22no—
100C13×C22⋊Q8—22no—
101C13×C22⋊Q8—22no—
102C13×C22⋊Q8—22no—
103C13×C22⋊Q8—22no—
104C13×C22⋊Q8—22no—
105C13×C22⋊Q8C2314yes—
106C13×C22⋊Q8C2314yes—
107C4×Q8×C13—22no—
108C4×Q8×C13—22no—
109C4×Q8×C13—22no—
110C4×Q8×C13—22no—
111C4×Q8×C13—22no—
112C4×Q8×C13—22no—
113C4×Q8×C13C2314yes—
114C4×Q8×C13C2314yes—
115C13×#117—22no—
116C13×#117—22no—
117C13×#117—22no—
118C13×#117—22no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—22no—
123C2×C13×C4⋊C4—22no—
124C2×C13×C4⋊C4C2312yes—
125C2×C13×C22⋊C4—22no—
126C2×C42×C13—22no—
127C2×C42×C13D411yescharacteristic
128C2×C42×C13D411yescharacteristic
129C2×C42×C13D411yescharacteristic
130C2×C42×C13D411yescharacteristic
131C2×C42×C13D411yescharacteristic
132C2×C42×C13D411yescharacteristic
133C2×C42×C13C2311yescharacteristic
134C2×C42×C13C2311yescharacteristic
135C2×C42×C13C2311yescharacteristic
136C2×C42×C13C2311yescharacteristic
137C2×C42×C13C2311yescharacteristic
138C2×C42×C13C2311yescharacteristic
139#88207—22no—
140C2×#6107C2318yes—
141#88196—48no—
142C2×#6106C2318yes—
143#88184—21no—
144#88184—21no—
145#88184—21no—
146#88184—21no—
147#88184C2312yes—
148#88184C2312yes—
149#88183—22no—
150#88183—22no—
151#88183—22no—
152C4×C22⋊D13—22no—
153C4×C22⋊D13—22no—
154C4×C22⋊D13—22no—
155C4×C22⋊D13—22no—
156C4×C22⋊D13—22no—
157C4×C22⋊D13—22no—
158#88180—21no—
159#88180—21no—
160#88180C2312yes—
161#88178—21no—
162#88178—21no—
163#88178—21no—
164#88178—21no—
165#88178C2312yes—
166#88178C2312yes—
167C2×#6099—44no—
168C2×#6099C2314yes—
169C2×#6099C2314yes—
170C22×#1055C2314yes—
171#88130—22no—
172#88130—22no—
173#88129—21no—
174#88129—21no—
175#88129C2312yes—
176#88128C2311yescharacteristic
177C4×D52—21no—
178C4×D52—21no—
179C4×D52—21no—
180C4×D52—21no—
181C4×D52C2312yes—
182C4×D52C2312yes—
183#88126—22no—
184#88126—22no—
185#88126—22no—
186C42×D13—22no—
187#88124—21no—
188#88124—21no—
189#88124C2312yes—
190#88123C2311yescharacteristic
191#88123C2311yescharacteristic
192#88123C2311yescharacteristic
193C4×Dic26—21no—
194C4×Dic26—21no—
195C4×Dic26—21no—
196C4×Dic26—21no—
197C4×Dic26C2312yes—
198C4×Dic26C2312yes—
199#88075C2318yes—
200#88075C2318yes—
201#88050C2318yes—
202#88049C2318yes—
203#88048C2318yes—
204#88047C2318yes—
205C4⋊#1055C2314yes—
206C4⋊#1055C2314yes—
207C4⋊#1055C2314yes—
208C4⋊#1055C2314yes—
209#60918—131nomaximal, Sylow
210C24×C13C2×D411yescharacteristic
211C2×Q8×C13—22no—
212C2×Q8×C13—22no—
213C2×Q8×C13—22no—
214C2×Q8×C13—24no—
215C2×Q8×C13—24no—
216C2×Q8×C13—44no—
217C2×Q8×C13C2414yes—
218C22×C4×C13—24no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—22no—
223C22×C4×C13—42no—
224C22×C4×C13C2×D411yescharacteristic
225C22×C4×C13C2×D411yescharacteristic
226C22×C4×C13C2×D411yescharacteristic
227C22×C4×C13C2×D411yescharacteristic
228C22×C4×C13C2×D411yescharacteristic
229C22×C4×C13C2×D411yescharacteristic
230C22×C4×C13C2×D411yescharacteristic
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×C13C2411yescharacteristic
240C22×C4×C13C2411yescharacteristic
241C22×C4×C13C2411yescharacteristic
242C2×C22⋊D13—22no—
243C2×C22⋊D13—22no—
244C2×C22⋊D13—22no—
245#6127—24no—
246#6127—24no—
247#6127—44no—
248#6127—44no—
249C2×D52—21no—
250C2×D52—21no—
251C2×D52C2412yes—
252C2×C4×D13—22no—
253C2×C4×D13—22no—
254C2×C4×D13—22no—
255C2×Dic26—21no—
256C2×Dic26—21no—
257C2×Dic26C2412yes—
258C13×C4⋊C4—22no—
259C13×C4⋊C4—22no—
260C13×C4⋊C4—22no—
261C13×C4⋊C4—22no—
262C13×C4⋊C4—22no—
263C13×C4⋊C4—22no—
264C13×C4⋊C4—24no—
265C13×C4⋊C4—24no—
266C13×C4⋊C4—24no—
267C13×C4⋊C4—24no—
268C13×C4⋊C4—22no—
269C13×C4⋊C4C2414yes—
270C13×C22⋊C4—24no—
271C13×C22⋊C4—24no—
272C42×C13—24no—
273C42×C13—24no—
274C42×C13C2×D411yescharacteristic
275C42×C13C2×D411yescharacteristic
276C42×C13C2×D411yescharacteristic
277C42×C13C2×D411yescharacteristic
278C42×C13C2×D411yescharacteristic
279C42×C13C2×D411yescharacteristic
280C42×C13C2×D411yescharacteristic
281C42×C13C2×D411yescharacteristic
282C42×C13C2×D411yescharacteristic
283C42×C13C2×D411yescharacteristic
284C42×C13C2×D411yescharacteristic
285C42×C13C2×D411yescharacteristic
286C42×C13C2411yescharacteristic
287C42×C13C2411yescharacteristic
288C42×C13C2411yescharacteristic
289C42×C13C2411yescharacteristic
290C22⋊Dic13—22no—
291C22⋊Dic13—22no—
292C22⋊Dic13—22no—
293#6107—48no—
294#6106—48no—
295#6103—22no—
296#6103—22no—
297#6103—22no—
298#6103—22no—
299#6103—22no—
300#6103—22no—
301C4⋊Dic13—21no—
302C4⋊Dic13—21no—
303C4⋊Dic13—21no—
304C4⋊Dic13—21no—
305C4⋊Dic13C2412yes—
306C4⋊Dic13C2412yes—
307#6101—22no—
308#6101—22no—
309#6101—22no—
310#6101—22no—
311#6101—22no—
312#6101—22no—
313C4×Dic13—22no—
314C4×Dic13—22no—
315C4×Dic13—22no—
316#6099—28no—
317#6099—44no—
318C2×#1055—44no—
319C2×#1055C2418yes—
320#3444—131no—
321C2×#533D1311yescharacteristic, complemented
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—41no—
337C23×C13C22×D411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C22×D411yescharacteristic
340C22×D13—22no—
341Q8×C13—24no—
342Q8×C13—24no—
343Q8×C13—44no—
344Q8×C13—44no—
345Q8×C13—44no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—21no—
358C2×C4×C13—21no—
359C2×C4×C13—21no—
360C2×C4×C13—21no—
361C2×C4×C13—24no—
362C2×C4×C13—24no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—44no—
367C2×C4×C13—44no—
368C2×C4×C13#13714yescomplemented
369C2×C4×C13C22×D411yescharacteristic
370C2×C4×C13C22×D411yescharacteristic
371C2×C4×C13C22×D411yescharacteristic
372C2×C4×C13C22×D411yescharacteristic
373C2×C4×C13C22×D411yescharacteristic
374C2×C4×C13C22×D411yescharacteristic
375C2×C4×C13C22×D411yescharacteristic
376C2×C4×C13C22×D411yescharacteristic
377C2×C4×C13C22×D411yescharacteristic
378C2×C4×C13C22×D411yescharacteristic
379C2×C4×C13C22×D411yescharacteristic
380C2×C4×C13H(5,𝔽2)12yes—
381C2×C4×C132−1+412yes—
382C2×C4×C13C2511yescharacteristic
383C22⋊D13—44no—
384C22⋊D13—44no—
385C22⋊D13—44no—
386C2×Dic13—22no—
387C2×Dic13—22no—
388C2×Dic13—22no—
389D52—22no—
390D52—22no—
391D52—42no—
392D52—42no—
393C4×D13—44no—
394C4×D13—44no—
395C4×D13—44no—
396Dic26—22no—
397Dic26—22no—
398Dic26—42no—
399Dic26—42no—
400#1055—28no—
401C2×#137—134no—
402C22×M16—132no—
403#533—21no—
404#533—21no—
405#533—21no—
406#533—21no—
407#533—131no—
408#533—131no—
409#533—131no—
410#533C2×D1312yes—
411#533C2×D1312yes—
412#533C2×D1312yes—
413#533C2×D1312yes—
414#532—131no—
415#532—131no—
416#532—131no—
417C2×C4⋊Q8C2×D1311yescharacteristic
418C2×C4⋊Q8C2×D1311yescharacteristic
419#529—132no—
420#529—132no—
421#529—261no—
422#529—261no—
423#529—261no—
424#529—261no—
425C2×#125—21no—
426#525—132no—
427#525—261no—
428#525—261no—
429C2×C22⋊Q8—21no—
430C2×C22⋊Q8C2×D1312yes—
431C4×#41—132no—
432C4×#41—261no—
433C4×#41—261no—
434C2×C4×Q8—21no—
435C2×C4×Q8C2×D1312yes—
436C2×#117—21no—
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#53712yes—
474C22×C13C2×#13712yes—
475C22×C13C23×D411yescharacteristic
476C2×D13—42no—
477C2×D13—42no—
478C2×D13—42no—
479C4×C13—21no—
480C4×C13—21no—
481C4×C13—21no—
482C4×C13—21no—
483C4×C13—21no—
484C4×C13—21no—
485C4×C13—21no—
486C4×C13—44no—
487C4×C13—44no—
488C4×C13#53712yes—
489C4×C13C2×#13712yes—
490C4×C13C2×#13712yes—
491C4×C13#57512yes—
492C4×C13C2×H(5,𝔽2)11yescharacteristic
493C4×C13C2×2−1+411yescharacteristic
494Dic13—42no—
495Dic13—42no—
496Dic13—42no—
497C2×#41—132no—
498C2×#41—261no—
499C2×#41—261no—
500C22×Q8—21no—
501C22×Q8C22×D1312yes—
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—21no—
513C4⋊Q8—21no—
514C4⋊Q8—21no—
515C4⋊Q8—21no—
516C4⋊Q8—131no—
517C4⋊Q8—131no—
518C4⋊Q8—131no—
519C4⋊Q8C22×D1312yes—
520C4⋊Q8C22×D1312yes—
521C4⋊Q8C22×D1312yes—
522C4⋊Q8C22×D1312yes—
523#127—131no—
524#126—262no—
525#126—262no—
526#125—22no—
527#125—22no—
528#125—22no—
529#125—22no—
530#125—132no—
531#125—261no—
532#125—261no—
533#124—132no—
534#124—261no—
535#124—261no—
536#123—262no—
537#123—262no—
538#123—262no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—132no—
546C22⋊Q8—132no—
547C22⋊Q8—261no—
548C22⋊Q8—261no—
549C22⋊Q8—261no—
550C22⋊Q8—261no—
551C22⋊Q8C22×D1314yes—
552C22⋊Q8C22×D1314yes—
553#121—132no—
554#121—132no—
555#121—261no—
556#121—261no—
557#121—261no—
558#121—261no—
559#120—262no—
560C4×Q8—22no—
561C4×Q8—22no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—22no—
566C4×Q8—132no—
567C4×Q8—132no—
568C4×Q8—261no—
569C4×Q8—261no—
570C4×Q8—261no—
571C4×Q8—261no—
572C4×Q8C22×D1314yes—
573C4×Q8C22×D1314yes—
574C4×D4—132no—
575C4×D4—132no—
576C4×D4—262no—
577C4×D4—262no—
578C4×D4—262no—
579C4×D4—262no—
580C4×D4—262no—
581C4×D4—262no—
582C4×D4—261no—
583C4×D4—261no—
584C4×D4—261no—
585C4×D4—261no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—132no—
591#117—261no—
592#117—261no—
593#117—262no—
594#117—262no—
595#117—262no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4C22×D1312yes—
602C2×C22⋊C4—22no—
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×C13C2×#53711yescharacteristic
631C2×C13C22×#13711yescharacteristic
632C2×C13C2×#57511yescharacteristic
633D13—82no—
634C24C2×C22⋊D1311yescharacteristic
635#41—264no—
636#41—264no—
637#41—524no—
638#41—524no—
639C2×Q8—22no—
640C2×Q8—22no—
641C2×Q8—22no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—44no—
645C2×Q8—132no—
646C2×Q8—261no—
647C2×Q8—261no—
648C2×Q8C23×D1314yes—
649C2×D4—132no—
650C2×D4—262no—
651C2×D4—262no—
652C2×D4—262no—
653C2×D4—261no—
654C2×D4—261no—
655C22×C4—24no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—42no—
661C22×C4—262no—
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—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—24no—
698C4⋊C4—22no—
699C4⋊C4—132no—
700C4⋊C4—132no—
701C4⋊C4—262no—
702C4⋊C4—262no—
703C4⋊C4—261no—
704C4⋊C4—261no—
705C4⋊C4—261no—
706C4⋊C4—261no—
707C4⋊C4—262no—
708C4⋊C4—262no—
709C4⋊C4—262no—
710C4⋊C4—262no—
711C4⋊C4C23×D1314yes—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—262no—
715C22⋊C4—262no—
716C22⋊C4—262no—
717C22⋊C4—262no—
718C22⋊C4—262no—
719C22⋊C4—262no—
720C22⋊C4—262no—
721C22⋊C4—262no—
722C22⋊C4—262no—
723C42—24no—
724C42—24no—
725C42—262no—
726C42—262no—
727C42—262no—
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—41no—
748C23—262no—
749C23C22×C22⋊D1311yescharacteristic
750C23C22×C22⋊D1311yescharacteristic
751C23C22×C22⋊D1311yescharacteristic
752Q8—24no—
753Q8—24no—
754Q8—44no—
755Q8—44no—
756Q8—44no—
757Q8—262no—
758Q8—262no—
759Q8—522no—
760Q8—522no—
761D4—262no—
762D4—262no—
763D4—522no—
764D4—524no—
765D4—524no—
766D4—524no—
767D4—522no—
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—24no—
784C2×C4—24no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—262no—
791C2×C4—262no—
792C2×C4—262no—
793C2×C4—524no—
794C2×C4—524no—
795C2×C4—524no—
796C2×C4#8819614yescomplemented
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—522no—
821C22—522no—
822C22—522no—
823C22C2×#8819612yes—
824C22#1171953812yes—
825C22C23×C22⋊D1311yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—21no—
833C4—44no—
834C4—44no—
835C4—522no—
836C4—522no—
837C4—522no—
838C4C2×#8819612yes—
839C4C2×#8819612yes—
840C4#1171952712yes—
841C4#1171953812yes—
842C4C2×#8825611yescharacteristic
843C4C2×#8825711yescharacteristic
844C2—22no—
845C2—22no—
846C2—41no—
847C2—1042no—
848C2C2×#1171953811yescharacteristic
849C2C22×#8819611yescharacteristic
850C2C2×#1171952711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D13
commutator, cosocleC2×C4×C13C25
FrattiniC2×C4C24×D13
FittingC2×C13×#533C2
socleC22×C13C23×D4
prime radical#13128132C2
hypercenterC2×#533D13
hypocenterC13#60918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13126227C2semidirect
3. #13126219C2semidirect
4. #13126203C2semidirect
5. #13126178C2semidirect
6. #13126167C2semidirect
7. #13126148C2semidirect
8. #13124645C2semidirect
9. #13124641C2semidirect
10. #13124462C2semidirect
11. #13124319C2semidirect
12. #13124308C2semidirect
13. C2×#11718585C2semidirect
14. C2×C13×#533C2semidirect
53. #11718755C22semidirect
54. #11718752C22semidirect
55. #11718751C22semidirect
56. #11718751C22semidirect
57. #11718748C22semidirect
58. #11718745C22semidirect
59. #11718744C22semidirect
60. #11718744C22semidirect
65. #11718692C22semidirect
66. #11718689C22semidirect
67. #11718688C22semidirect
68. #11718683C22semidirect
69. #11718682C22semidirect
70. #11718681C22semidirect
321. C2×#533D13semidirect
368. C2×C4×C13#137semidirect
744. C13#60918semidirect
796. C2×C4#88196semidirect

Maximal subgroups

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

subgroupindex
#131281322
#131262272
#131262192
#131262032
#131261782
#131261672
#131261482
#131246452
#131246412
#131244622
#131243192
#131243082
C2×#117185852
C2×C13×#5332
#6091813