Finite Group Databasebeta

← #16069642

Subgroups — #16069642

Order 3328.

1304 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123110C211yesmaximal, characteristic
2#13123087C211yesmaximal, characteristic
3#13123085C211yesmaximal, characteristic
4#13123083C211yesmaximal, characteristic
5#13123081C211yesmaximal, characteristic
6#13123079C211yesmaximal, characteristic
7#13123078C211yesmaximal, characteristic
8#13123077C211yesmaximal, characteristic
9#13123076C211yesmaximal, characteristic
10#13123075C211yesmaximal, characteristic
11#13123074C211yesmaximal, characteristic
12#13123073C211yesmaximal, characteristic
13#13122906C211yesmaximal, characteristic
14#13122905C211yesmaximal, characteristic
15#13122902C211yesmaximal, characteristic
16#13118142C211yesmaximal, characteristic
17#13118142C211yesmaximal, characteristic
18#13118142C211yesmaximal, characteristic
19#13118142C211yesmaximal, characteristic
20#13118142C211yesmaximal, characteristic
21#13118142C211yesmaximal, characteristic
22#13118142C211yesmaximal, characteristic
23#13118140C211yesmaximal, characteristic
24#13118140C211yesmaximal, characteristic
25#13118140C211yesmaximal, characteristic
26#13118140C211yesmaximal, characteristic
27#13118140C211yesmaximal, characteristic
28#13117395C211yesmaximal, characteristic
29#13117393C211yesmaximal, characteristic
30#13117393C211yesmaximal, characteristic
31C13×#2839C211yesmaximal, characteristic
32C2×#88144C2211yescharacteristic
33C2×#88143C2211yescharacteristic
34C2×#88143C2211yescharacteristic
35C13×#400C2211yescharacteristic
36C13×#400C2211yescharacteristic
37C13×#400C2211yescharacteristic
38C13×#400C2211yescharacteristic
39C13×#400C2211yescharacteristic
40C13×#400C2211yescharacteristic
41C13×#400C2211yescharacteristic
42C13×#398C2211yescharacteristic
43C13×#398C2211yescharacteristic
44C13×#398C2211yescharacteristic
45C13×#398C2211yescharacteristic
46C13×#398C2211yescharacteristic
47C13×#389C2211yescharacteristic
48C13×#387C2211yescharacteristic
49C13×#387C2211yescharacteristic
50#11718647C2211yescharacteristic
51#11718647C2211yescharacteristic
52#11718647C2211yescharacteristic
53#11718647C2211yescharacteristic
54#11718647C2211yescharacteristic
55#11718645C2211yescharacteristic
56#11718645C2211yescharacteristic
57#11718645C2211yescharacteristic
58#11718645C2211yescharacteristic
59#11718645C2211yescharacteristic
60#11718645C2211yescharacteristic
61#11718645C2211yescharacteristic
62#11718645C2211yescharacteristic
63#11718645C2211yescharacteristic
64#11718645C2211yescharacteristic
65#11718645C2211yescharacteristic
66#11718645C2211yescharacteristic
67#11718644C2211yescharacteristic
68#11718644C2211yescharacteristic
69#11718644C2211yescharacteristic
70#11718644C2211yescharacteristic
71#11718644C2211yescharacteristic
72#11718643C2211yescharacteristic
73#11718643C2211yescharacteristic
74#11718643C2211yescharacteristic
75#11718643C2211yescharacteristic
76#11718643C2211yescharacteristic
77#11718641C2211yescharacteristic
78#11718641C2211yescharacteristic
79#11718641C2211yescharacteristic
80#11718641C2211yescharacteristic
81#11718641C2211yescharacteristic
82#11718641C2211yescharacteristic
83#11718641C2211yescharacteristic
84#11718639C2211yescharacteristic
85#11718639C2211yescharacteristic
86#11718638C2211yescharacteristic
87C4⋊C4×Dic13C2211yescharacteristic
88C4⋊C4×Dic13C2211yescharacteristic
89C4⋊C4×Dic13C2211yescharacteristic
90C4⋊C4×Dic13C2211yescharacteristic
91C4⋊C4×Dic13C2211yescharacteristic
92C4⋊C4×Dic13C2211yescharacteristic
93C4⋊C4×Dic13C2211yescharacteristic
94C4⋊C4×Dic13C2211yescharacteristic
95C4⋊C4×Dic13C2211yescharacteristic
96C4⋊C4×Dic13C2211yescharacteristic
97C4⋊C4×Dic13C2211yescharacteristic
98C4⋊C4×Dic13C2211yescharacteristic
99C4⋊C4×Dic13C2211yescharacteristic
100C4⋊C4×Dic13C2211yescharacteristic
101#11718633C2211yescharacteristic
102#11718633C2211yescharacteristic
103#11718594C2211yescharacteristic
104#11718594C2211yescharacteristic
105C42×Dic13C2211yescharacteristic
106#11718589C2211yescharacteristic
107#11718322C2211yescharacteristic
108#11718322C2211yescharacteristic
109#11718322C2211yescharacteristic
110#11718322C2211yescharacteristic
111#11718322C2211yescharacteristic
112#11718321C2211yescharacteristic
113#11718321C2211yescharacteristic
114#11718321C2211yescharacteristic
115#11718321C2211yescharacteristic
116#11718321C2211yescharacteristic
117#11718321C2211yescharacteristic
118#11718321C2211yescharacteristic
119#11718321C2211yescharacteristic
120#11718321C2211yescharacteristic
121#11718321C2211yescharacteristic
122#11718321C2211yescharacteristic
123#11718321C2211yescharacteristic
124#11718320C2211yescharacteristic
125#11718320C2211yescharacteristic
126#11718320C2211yescharacteristic
127#11718320C2211yescharacteristic
128#11718320C2211yescharacteristic
129#11718319C2211yescharacteristic
130#11718319C2211yescharacteristic
131#11718319C2211yescharacteristic
132#11718319C2211yescharacteristic
133#11718319C2211yescharacteristic
134#11718319C2211yescharacteristic
135#11718319C2211yescharacteristic
136#11718319C2211yescharacteristic
137#11718319C2211yescharacteristic
138#11718319C2211yescharacteristic
139#11718319C2211yescharacteristic
140#11718319C2211yescharacteristic
141#11718319C2211yescharacteristic
142#11718319C2211yescharacteristic
143#11718318C2211yescharacteristic
144#11718318C2211yescharacteristic
145#11718318C2211yescharacteristic
146#11718318C2211yescharacteristic
147#11718318C2211yescharacteristic
148#11718318C2211yescharacteristic
149#11718318C2211yescharacteristic
150#11718318C2211yescharacteristic
151#11718318C2211yescharacteristic
152#11718318C2211yescharacteristic
153#11718318C2211yescharacteristic
154#11718318C2211yescharacteristic
155#11718318C2211yescharacteristic
156#11718318C2211yescharacteristic
157#11718316C2211yescharacteristic
158#11718316C2211yescharacteristic
159#11718315C2211yescharacteristic
160#11718315C2211yescharacteristic
161#11718314C2211yescharacteristic
162#11718314C2211yescharacteristic
163#11718311C2211yescharacteristic
164#11718311C2211yescharacteristic
165#11718310C2211yescharacteristic
166#11718310C2211yescharacteristic
167#11718310C2211yescharacteristic
168#11718310C2211yescharacteristic
169#11718310C2211yescharacteristic
170#11718310C2211yescharacteristic
171#11718310C2211yescharacteristic
172#11718310C2211yescharacteristic
173#11718310C2211yescharacteristic
174#11718310C2211yescharacteristic
175#11718310C2211yescharacteristic
176#11718310C2211yescharacteristic
177#11718310C2211yescharacteristic
178#11718310C2211yescharacteristic
179#11718310C2211yescharacteristic
180#11718310C2211yescharacteristic
181#11718309C2211yescharacteristic
182#11718309C2211yescharacteristic
183#11718309C2211yescharacteristic
184#11718309C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718308C2211yescharacteristic
187C2×C13×C4⋊C4C2311yescharacteristic
188C2×C13×C4⋊C4C2311yescharacteristic
189C2×C13×C4⋊C4C2311yescharacteristic
190C2×C13×C4⋊C4C2311yescharacteristic
191C2×C13×C4⋊C4C2311yescharacteristic
192C2×C13×C4⋊C4C2311yescharacteristic
193C2×C13×C4⋊C4C2311yescharacteristic
194C2×C13×C4⋊C4C2311yescharacteristic
195C2×C13×C4⋊C4C2311yescharacteristic
196C2×C13×C4⋊C4C2311yescharacteristic
197C2×C13×C4⋊C4C2311yescharacteristic
198C2×C13×C4⋊C4C2311yescharacteristic
199C2×C13×C4⋊C4C2311yescharacteristic
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C42×C13C2311yescharacteristic
202C2×C4⋊Dic13C2311yescharacteristic
203C2×C4⋊Dic13C2311yescharacteristic
204C2×C4⋊Dic13C2311yescharacteristic
205C2×C4⋊Dic13C2311yescharacteristic
206C2×C4⋊Dic13C2311yescharacteristic
207C2×C4⋊Dic13C2311yescharacteristic
208C2×C4⋊Dic13C2311yescharacteristic
209C2×C4⋊Dic13C2311yescharacteristic
210C2×C4⋊Dic13C2311yescharacteristic
211C2×C4⋊Dic13C2311yescharacteristic
212C2×C4⋊Dic13C2311yescharacteristic
213C2×C4⋊Dic13C2311yescharacteristic
214C2×C4⋊Dic13C2311yescharacteristic
215C2×C4⋊Dic13C2311yescharacteristic
216C2×#6101C2311yescharacteristic
217C2×#6101C2311yescharacteristic
218C2×#6101C2311yescharacteristic
219C2×#6101C2311yescharacteristic
220C2×#6101C2311yescharacteristic
221C2×#6101C2311yescharacteristic
222C2×#6101C2311yescharacteristic
223C2×#6101C2311yescharacteristic
224C2×#6101C2311yescharacteristic
225C2×#6101C2311yescharacteristic
226C2×#6101C2311yescharacteristic
227C2×#6101C2311yescharacteristic
228C2×#6101C2311yescharacteristic
229C2×#6101C2311yescharacteristic
230C2×#6101C2311yescharacteristic
231C2×#6101C2311yescharacteristic
232C2×#6101C2311yescharacteristic
233C2×#6101C2311yescharacteristic
234C2×#6101C2311yescharacteristic
235C2×#6101C2311yescharacteristic
236C2×#6101C2311yescharacteristic
237C2×#6101C2311yescharacteristic
238C2×#6101C2311yescharacteristic
239C2×#6101C2311yescharacteristic
240C2×#6101C2311yescharacteristic
241C2×#6101C2311yescharacteristic
242C2×#6101C2311yescharacteristic
243C2×#6101C2311yescharacteristic
244C2×#6101C2311yescharacteristic
245C2×#6101C2311yescharacteristic
246C2×#6101C2311yescharacteristic
247C2×#6101C2311yescharacteristic
248C2×C4×Dic13C2311yescharacteristic
249C2×C4×Dic13C2311yescharacteristic
250C2×C4×Dic13C2311yescharacteristic
251C2×C4×Dic13C2311yescharacteristic
252C2×C4×Dic13C2311yescharacteristic
253C2×C4×Dic13C2311yescharacteristic
254C2×C4×Dic13C2311yescharacteristic
255C2×C4×Dic13C2311yescharacteristic
256C2×C4×Dic13C2311yescharacteristic
257C2×C4×Dic13C2311yescharacteristic
258C2×C4×Dic13C2311yescharacteristic
259C2×C4×Dic13C2311yescharacteristic
260C2×C4×Dic13C2311yescharacteristic
261C2×C4×Dic13C2311yescharacteristic
262C2×C4×Dic13C2311yescharacteristic
263C2×C4×Dic13C2311yescharacteristic
264C2×C4×Dic13C2311yescharacteristic
265C2×C4×Dic13C2311yescharacteristic
266#88144—24no—
267#88143—24no—
268#88143—24no—
269C13×#95C2311yescharacteristic
270C13×#95C2311yescharacteristic
271C13×#95C2311yescharacteristic
272C13×#95C2311yescharacteristic
273C13×#95C2311yescharacteristic
274C13×#95C2311yescharacteristic
275C13×#95C2311yescharacteristic
276C13×#95C2311yescharacteristic
277C13×#95C2311yescharacteristic
278C13×#95C2311yescharacteristic
279C13×#95C2311yescharacteristic
280C13×#95C2311yescharacteristic
281C13×#95C2311yescharacteristic
282C13×#95C2311yescharacteristic
283C13×#95C2311yescharacteristic
284C13×#95C2311yescharacteristic
285C13×#95C2311yescharacteristic
286C13×#95C2311yescharacteristic
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289#88071C2311yescharacteristic
290#88071C2311yescharacteristic
291#88071C2311yescharacteristic
292#88071C2311yescharacteristic
293#88071C2311yescharacteristic
294#88071C2311yescharacteristic
295#88071C2311yescharacteristic
296#88071C2311yescharacteristic
297#88071C2311yescharacteristic
298#88071C2311yescharacteristic
299#88071C2311yescharacteristic
300#88071C2311yescharacteristic
301#88071C2311yescharacteristic
302#88071C2311yescharacteristic
303#88071C2311yescharacteristic
304#88071C2311yescharacteristic
305#88071C2311yescharacteristic
306#88071C2311yescharacteristic
307#88071C2311yescharacteristic
308#88071C2311yescharacteristic
309#88071C2311yescharacteristic
310#88071C2311yescharacteristic
311#88071C2311yescharacteristic
312#88071C2311yescharacteristic
313#88071C2311yescharacteristic
314#88071C2311yescharacteristic
315#88071C2311yescharacteristic
316#88071C2311yescharacteristic
317#88071C2311yescharacteristic
318#88071C2311yescharacteristic
319#88071C2311yescharacteristic
320#88071C2311yescharacteristic
321#88071C2311yescharacteristic
322#88071C2311yescharacteristic
323#88071C2311yescharacteristic
324#88071C2311yescharacteristic
325#88071C2311yescharacteristic
326#88071C2311yescharacteristic
327#88071C2311yescharacteristic
328#88071C2311yescharacteristic
329#88071C2311yescharacteristic
330#88071C2311yescharacteristic
331#88071C2311yescharacteristic
332#88071C2311yescharacteristic
333#88071C2311yescharacteristic
334#88071C2311yescharacteristic
335#88071C2311yescharacteristic
336#88071C2311yescharacteristic
337#88071C2311yescharacteristic
338#88071C2311yescharacteristic
339#88071C2311yescharacteristic
340#88071C2311yescharacteristic
341#88071C2311yescharacteristic
342#88071C2311yescharacteristic
343#88071C2311yescharacteristic
344#88071C2311yescharacteristic
345#36701—131nomaximal, Sylow
346C22×C4×C13C2411yescharacteristic
347C22×C4×C13C2411yescharacteristic
348C22×C4×C13C2411yescharacteristic
349C22×C4×C13C2411yescharacteristic
350C22×C4×C13C2411yescharacteristic
351C22×C4×C13C2411yescharacteristic
352C22×C4×C13C2411yescharacteristic
353C22×C4×C13C2411yescharacteristic
354C22×C4×C13C2411yescharacteristic
355C22×C4×C13C2411yescharacteristic
356C22×C4×C13C2411yescharacteristic
357C22×C4×C13C2411yescharacteristic
358C22×C4×C13C2411yescharacteristic
359C22×C4×C13C2411yescharacteristic
360C22×C4×C13C2411yescharacteristic
361C22×Dic13C2411yescharacteristic
362C22×Dic13C2411yescharacteristic
363C22×Dic13C2411yescharacteristic
364C22×Dic13C2411yescharacteristic
365C22×Dic13C2411yescharacteristic
366C22×Dic13C2411yescharacteristic
367C22×Dic13C2411yescharacteristic
368C22×Dic13C2411yescharacteristic
369C22×Dic13C2411yescharacteristic
370C22×Dic13C2411yescharacteristic
371C22×Dic13C2411yescharacteristic
372C22×Dic13C2411yescharacteristic
373C22×Dic13C2411yescharacteristic
374C22×Dic13C2411yescharacteristic
375C22×Dic13C2411yescharacteristic
376C22×Dic13C2411yescharacteristic
377C13×C4⋊C4—22no—
378C13×C4⋊C4—22no—
379C13×C4⋊C4—22no—
380C13×C4⋊C4—41no—
381C13×C4⋊C4—41no—
382C13×C4⋊C4—41no—
383C13×C4⋊C4—41no—
384C13×C4⋊C4—41no—
385C13×C4⋊C4—41no—
386C13×C4⋊C4—41no—
387C13×C4⋊C4—41no—
388C13×C4⋊C4—41no—
389C13×C4⋊C4—41no—
390C13×C4⋊C4—41no—
391C42×C13—41no—
392C4⋊Dic13—22no—
393C4⋊Dic13—22no—
394C4⋊Dic13—22no—
395C4⋊Dic13—22no—
396C4⋊Dic13—22no—
397C4⋊Dic13—41no—
398C4⋊Dic13—41no—
399C4⋊Dic13—41no—
400C4⋊Dic13—41no—
401C4⋊Dic13—41no—
402C4⋊Dic13—41no—
403C4⋊Dic13—41no—
404C4⋊Dic13—41no—
405C4⋊Dic13—41no—
406#6101—22no—
407#6101—22no—
408#6101—22no—
409#6101—22no—
410#6101—22no—
411#6101—22no—
412#6101—22no—
413#6101—22no—
414#6101—22no—
415#6101—22no—
416#6101—41no—
417#6101—41no—
418#6101—41no—
419#6101—41no—
420#6101—41no—
421#6101—41no—
422#6101—41no—
423#6101—41no—
424#6101—41no—
425#6101—41no—
426#6101—41no—
427#6101—41no—
428#6101—41no—
429#6101—41no—
430#6101—41no—
431#6101—41no—
432#6101—41no—
433#6101—41no—
434#6101—41no—
435#6101—41no—
436#6101—41no—
437#6101—41no—
438C4×Dic13—22no—
439C4×Dic13—22no—
440C4×Dic13—22no—
441C4×Dic13—22no—
442C4×Dic13—22no—
443C4×Dic13—22no—
444C4×Dic13—22no—
445C4×Dic13—22no—
446C4×Dic13—22no—
447C4×Dic13—22no—
448C4×Dic13—22no—
449C4×Dic13—22no—
450C4×Dic13—22no—
451C4×Dic13—22no—
452C4×Dic13—22no—
453C4×Dic13—41no—
454C4×Dic13—41no—
455C4×Dic13#4114yes—
456#2845—131no—
457#2839—131no—
458#2839—131no—
459#2839—131no—
460#2839—131no—
461#2839—131no—
462#2839—131no—
463#2839—131no—
464#2839—131no—
465#2839—131no—
466#2839—131no—
467#2839—131no—
468#2839D1311yescharacteristic
469#2822—131no—
470#2822—131no—
471#2822—131no—
472#2402—131no—
473#2402—131no—
474#2402—131no—
475#2402—131no—
476#2402—131no—
477#2402—131no—
478#2402—131no—
479#2402—131no—
480#2402—131no—
481#2402—131no—
482#2402—131no—
483#2402—131no—
484C4×#125—131no—
485C4×#125—131no—
486C4×#125—131no—
487C23×C13C2511yescharacteristic
488C2×C4×C13—21no—
489C2×C4×C13—21no—
490C2×C4×C13—21no—
491C2×C4×C13—21no—
492C2×C4×C13—21no—
493C2×C4×C13—21no—
494C2×C4×C13—21no—
495C2×C4×C13—21no—
496C2×C4×C13—21no—
497C2×C4×C13—21no—
498C2×C4×C13—21no—
499C2×C4×C13—21no—
500C2×C4×C13—21no—
501C2×C4×C13—21no—
502C2×C4×C13—21no—
503C2×C4×C13—21no—
504C2×C4×C13—21no—
505C2×C4×C13—21no—
506C2×C4×C13—21no—
507C2×C4×C13—21no—
508C2×C4×C13—21no—
509C2×C4×C13—21no—
510C2×C4×C13—21no—
511C2×C4×C13—21no—
512C2×C4×C13—21no—
513C2×C4×C13—21no—
514C2×C4×C13—21no—
515C2×C4×C13—21no—
516C2×C4×C13—21no—
517C2×C4×C13—21no—
518C2×C4×C13—21no—
519C2×C4×C13—21no—
520C2×C4×C13—21no—
521C2×C4×C13—21no—
522C2×C4×C13—21no—
523C2×C4×C13—21no—
524C2×C4×C13—21no—
525C2×C4×C13—21no—
526C2×C4×C13—21no—
527C2×C4×C13—21no—
528C2×C4×C13—21no—
529C2×C4×C13—21no—
530C2×C4×C13—21no—
531C2×C4×C13—21no—
532C2×C4×C13C2×#4112yes—
533C2×Dic13—21no—
534C2×Dic13—21no—
535C2×Dic13—21no—
536C2×Dic13—21no—
537C2×Dic13—21no—
538C2×Dic13—21no—
539C2×Dic13—21no—
540C2×Dic13—21no—
541C2×Dic13—21no—
542C2×Dic13—21no—
543C2×Dic13—21no—
544C2×Dic13—21no—
545C2×Dic13—21no—
546C2×Dic13—21no—
547C2×Dic13—21no—
548C2×Dic13—21no—
549C2×Dic13—21no—
550C2×Dic13—21no—
551C2×Dic13—21no—
552C2×Dic13—21no—
553C2×Dic13—21no—
554C2×Dic13—21no—
555C2×Dic13—21no—
556C2×Dic13—21no—
557C2×Dic13—21no—
558C2×Dic13—21no—
559C2×Dic13—21no—
560C2×Dic13—21no—
561C2×Dic13—21no—
562C2×Dic13—21no—
563C2×Dic13—21no—
564C2×Dic13—21no—
565C2×Dic13—21no—
566C2×Dic13—21no—
567C2×Dic13—21no—
568C2×Dic13—21no—
569C2×Dic13—21no—
570C2×Dic13—21no—
571C2×Dic13—21no—
572C2×Dic13—21no—
573C2×Dic13—21no—
574C2×Dic13—21no—
575C2×Dic13—21no—
576C2×Dic13C2×#4112yes—
577C2×Dic13C2×#4112yes—
578C2×Dic132−1+412yes—
579C2×Dic132−1+412yes—
580C2×Dic132−1+412yes—
581C2×#125—131no—
582C2×#125—131no—
583C2×#125—131no—
584#400—131no—
585#400—131no—
586#400—131no—
587#400—131no—
588#400—131no—
589#400—131no—
590#400—131no—
591#400—131no—
592#400—131no—
593#400—131no—
594#400—131no—
595#400—131no—
596#400—131no—
597#400—131no—
598#400—131no—
599#400—131no—
600#400—131no—
601#400—131no—
602#400—131no—
603#400—131no—
604#400—131no—
605#400—131no—
606#400—131no—
607#400—131no—
608#400—131no—
609#400—131no—
610#400—131no—
611#400—131no—
612#400—131no—
613#400—131no—
614#400—131no—
615#400—131no—
616#400—131no—
617#400—131no—
618#400—131no—
619#400—131no—
620#400—131no—
621#400—131no—
622#400—131no—
623#400—131no—
624#400—131no—
625#400C2×D1311yescharacteristic
626#400C2×D1311yescharacteristic
627#400C2×D1311yescharacteristic
628#400C2×D1311yescharacteristic
629#400C2×D1311yescharacteristic
630#400C2×D1311yescharacteristic
631#400C2×D1311yescharacteristic
632#398—131no—
633#398—131no—
634#398—131no—
635#398—131no—
636#398—131no—
637#398—131no—
638#398—131no—
639#398—131no—
640#398—131no—
641#398—131no—
642#398—131no—
643#398—131no—
644#398—131no—
645#398—131no—
646#398—131no—
647#398—131no—
648#398—131no—
649#398—131no—
650#398—131no—
651#398—131no—
652#398—131no—
653#398—131no—
654#398—131no—
655#398—131no—
656#398—131no—
657#398—131no—
658#398—131no—
659#398—131no—
660#398—131no—
661#398—131no—
662#398—131no—
663#398—131no—
664#398—131no—
665#398—131no—
666#398—131no—
667#398—131no—
668#398—131no—
669#398—131no—
670#398—131no—
671#398—131no—
672#398—131no—
673#398—131no—
674#398—131no—
675#398C2×D1311yescharacteristic
676#398C2×D1311yescharacteristic
677#398C2×D1311yescharacteristic
678#398C2×D1311yescharacteristic
679#398C2×D1311yescharacteristic
680#389—131no—
681#389—131no—
682#389—131no—
683#389—131no—
684#389—131no—
685#389C2×D1311yescharacteristic
686#387—131no—
687#387—131no—
688#387—131no—
689#387—131no—
690#387—131no—
691#387—131no—
692#387—131no—
693#387—131no—
694#387—131no—
695#387—131no—
696#387C2×D1311yescharacteristic
697#387C2×D1311yescharacteristic
698#382—131no—
699#382—131no—
700#382—131no—
701C4×C4⋊C4—131no—
702C4×C4⋊C4—131no—
703C4×C4⋊C4—131no—
704C4×C4⋊C4—131no—
705C4×C4⋊C4—131no—
706C4×C4⋊C4—131no—
707C4×C4⋊C4—131no—
708C4×C4⋊C4—131no—
709C4×C4⋊C4—131no—
710C4×C4⋊C4—131no—
711C4×C4⋊C4—131no—
712C4×C4⋊C4—131no—
713C4×C4⋊C4—131no—
714C4×C4⋊C4—131no—
715C4×C4⋊C4—131no—
716C4×C4⋊C4—131no—
717C4×C4⋊C4—131no—
718C4×C4⋊C4—131no—
719C4×C4⋊C4—131no—
720C4×C4⋊C4—131no—
721C4×C4⋊C4—131no—
722C4×C4⋊C4—131no—
723C4×C4⋊C4—131no—
724C4×C4⋊C4—131no—
725C4×C4⋊C4—131no—
726C4×C4⋊C4—131no—
727C4×C4⋊C4—131no—
728C4×C4⋊C4—131no—
729C4×C4⋊C4—131no—
730C4×C4⋊C4—131no—
731#376—131no—
732#376—131no—
733#376—131no—
734#376—131no—
735C43—131no—
736C22×C13C22×#4111yescharacteristic
737C22×C13C2×2−1+411yescharacteristic
738C22×C13C2×2−1+411yescharacteristic
739C22×C13C2×2−1+411yescharacteristic
740C22×C13#58511yescharacteristic
741C22×C13#58511yescharacteristic
742C22×C13#58511yescharacteristic
743C4×C13—22no—
744C4×C13—41no—
745C4×C13—41no—
746C4×C13—41no—
747C4×C13—41no—
748C4×C13—41no—
749C4×C13—41no—
750C4×C13—41no—
751C4×C13—41no—
752C4×C13—41no—
753C4×C13—41no—
754C4×C13—41no—
755C4×C13—41no—
756C4×C13—41no—
757C4×C13—41no—
758Dic13—22no—
759Dic13—22no—
760Dic13—41no—
761Dic13—41no—
762Dic13—41no—
763Dic13—41no—
764Dic13—41no—
765Dic13—41no—
766Dic13—41no—
767Dic13—41no—
768Dic13—41no—
769Dic13—41no—
770Dic13—41no—
771Dic13—41no—
772Dic13—41no—
773Dic13#56414yes—
774#125—264no—
775#125—264no—
776#125—264no—
777C2×C4⋊C4—131no—
778C2×C4⋊C4—131no—
779C2×C4⋊C4—131no—
780C2×C4⋊C4—131no—
781C2×C4⋊C4—131no—
782C2×C4⋊C4—131no—
783C2×C4⋊C4—131no—
784C2×C4⋊C4—131no—
785C2×C4⋊C4—131no—
786C2×C4⋊C4—131no—
787C2×C4⋊C4—131no—
788C2×C4⋊C4—131no—
789C2×C4⋊C4—131no—
790C2×C4⋊C4—131no—
791C2×C4⋊C4—131no—
792C2×C4⋊C4—131no—
793C2×C4⋊C4—131no—
794C2×C4⋊C4—131no—
795C2×C4⋊C4—131no—
796C2×C4⋊C4—131no—
797C2×C4⋊C4—131no—
798C2×C4⋊C4—131no—
799C2×C4⋊C4—131no—
800C2×C4⋊C4—131no—
801C2×C4⋊C4—131no—
802C2×C4⋊C4—131no—
803C2×C4⋊C4—131no—
804C2×C4⋊C4—131no—
805C2×C4⋊C4—131no—
806C2×C4⋊C4—131no—
807C2×C4⋊C4—131no—
808C2×C4⋊C4—131no—
809C2×C4⋊C4—131no—
810C2×C4⋊C4—131no—
811C2×C4⋊C4—131no—
812C2×C4⋊C4—131no—
813C2×C4⋊C4—131no—
814C2×C4⋊C4—131no—
815C2×C4⋊C4—131no—
816C2×C4⋊C4—131no—
817C2×C4⋊C4—131no—
818C2×C4⋊C4—131no—
819C2×C4⋊C4—131no—
820C2×C4⋊C4—131no—
821C2×C4⋊C4—131no—
822C2×C4⋊C4—131no—
823C2×C4⋊C4C22×D1311yescharacteristic
824C2×C4⋊C4C22×D1311yescharacteristic
825C2×C4⋊C4C22×D1311yescharacteristic
826C2×C4⋊C4C22×D1311yescharacteristic
827C2×C4⋊C4C22×D1311yescharacteristic
828C2×C4⋊C4C22×D1311yescharacteristic
829C2×C4⋊C4C22×D1311yescharacteristic
830C2×C4⋊C4C22×D1311yescharacteristic
831C2×C4⋊C4C22×D1311yescharacteristic
832C2×C4⋊C4C22×D1311yescharacteristic
833C2×C4⋊C4C22×D1311yescharacteristic
834C2×C4⋊C4C22×D1311yescharacteristic
835C2×C4⋊C4C22×D1311yescharacteristic
836C2×C4⋊C4C22×D1311yescharacteristic
837C2×C42—131no—
838C2×C42—131no—
839C2×C42—131no—
840C2×C42—131no—
841C2×C42—131no—
842C2×C42—131no—
843C2×C42—131no—
844C2×C42—131no—
845C2×C42—131no—
846C2×C42—131no—
847C2×C42—131no—
848C2×C42—131no—
849C2×C42—131no—
850C2×C42—131no—
851C2×C42—131no—
852C2×C42—131no—
853C2×C42—131no—
854C2×C42—131no—
855C2×C42C22×D1311yescharacteristic
856#95—131no—
857#95—131no—
858#95—131no—
859#95—131no—
860#95—131no—
861#95—131no—
862#95—131no—
863#95—131no—
864#95—131no—
865#95—131no—
866#95—131no—
867#95—131no—
868#95—131no—
869#95—131no—
870#95—131no—
871#95—131no—
872#95—131no—
873#95—131no—
874#95—131no—
875#95—131no—
876#95—131no—
877#95—131no—
878#95—131no—
879#95—131no—
880#95—131no—
881#95—131no—
882#95—131no—
883#95—131no—
884#95—131no—
885#95—131no—
886#95—131no—
887#95—131no—
888#95—131no—
889#95—131no—
890#95—131no—
891#95—131no—
892#95—131no—
893#95—131no—
894#95—131no—
895#95—131no—
896#95—131no—
897#95—131no—
898#95—131no—
899#95—131no—
900#95—131no—
901#95—131no—
902#95—131no—
903#95—131no—
904#95—131no—
905#95—131no—
906#95—131no—
907#95—131no—
908#95—131no—
909#95—131no—
910#95—131no—
911#95—131no—
912#95C22×D1311yescharacteristic
913#95C22×D1311yescharacteristic
914#95C22×D1311yescharacteristic
915#95C22×D1311yescharacteristic
916#95C22×D1311yescharacteristic
917#95C22×D1311yescharacteristic
918#95C22×D1311yescharacteristic
919#95C22×D1311yescharacteristic
920#95C22×D1311yescharacteristic
921#95C22×D1311yescharacteristic
922#95C22×D1311yescharacteristic
923#95C22×D1311yescharacteristic
924#95C22×D1311yescharacteristic
925#95C22×D1311yescharacteristic
926#95C22×D1311yescharacteristic
927#95C22×D1311yescharacteristic
928#95C22×D1311yescharacteristic
929#95C22×D1311yescharacteristic
930#95C22×D1311yescharacteristic
931#95C22×D1311yescharacteristic
932C2×C13#346111yescharacteristic
933C2×C13#346111yescharacteristic
934C2×C13#346111yescharacteristic
935C2×C13C2×#56411yescharacteristic
936C2×C13#353111yescharacteristic
937C2×C13#353111yescharacteristic
938C2×C13#353111yescharacteristic
939C22×C4—131no—
940C22×C4—131no—
941C22×C4—131no—
942C22×C4—131no—
943C22×C4—131no—
944C22×C4—131no—
945C22×C4—131no—
946C22×C4—131no—
947C22×C4—131no—
948C22×C4—131no—
949C22×C4—131no—
950C22×C4—131no—
951C22×C4—131no—
952C22×C4—131no—
953C22×C4—131no—
954C22×C4—131no—
955C22×C4C23×D1311yescharacteristic
956C22×C4C23×D1311yescharacteristic
957C22×C4C23×D1311yescharacteristic
958C22×C4C23×D1311yescharacteristic
959C22×C4C23×D1311yescharacteristic
960C22×C4C23×D1311yescharacteristic
961C22×C4C23×D1311yescharacteristic
962C22×C4C23×D1311yescharacteristic
963C22×C4C23×D1311yescharacteristic
964C22×C4C23×D1311yescharacteristic
965C22×C4C23×D1311yescharacteristic
966C22×C4C23×D1311yescharacteristic
967C22×C4C23×D1311yescharacteristic
968C22×C4C23×D1311yescharacteristic
969C22×C4C23×D1311yescharacteristic
970C4⋊C4—22no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—41no—
977C4⋊C4—41no—
978C4⋊C4—41no—
979C4⋊C4—41no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—262no—
985C4⋊C4—262no—
986C4⋊C4—262no—
987C4⋊C4—262no—
988C4⋊C4—262no—
989C4⋊C4—262no—
990C4⋊C4—262no—
991C4⋊C4—262no—
992C4⋊C4—262no—
993C4⋊C4—262no—
994C4⋊C4—262no—
995C4⋊C4—262no—
996C4⋊C4—262no—
997C4⋊C4—262no—
998C4⋊C4—262no—
999C4⋊C4—521no—
1000C4⋊C4—521no—
1001C4⋊C4—521no—
1002C4⋊C4—521no—
1003C4⋊C4—521no—
1004C4⋊C4—521no—
1005C4⋊C4—521no—
1006C4⋊C4—521no—
1007C4⋊C4—521no—
1008C4⋊C4—521no—
1009C4⋊C4—521no—
1010C4⋊C4—521no—
1011C4⋊C4—521no—
1012C4⋊C4—521no—
1013C4⋊C4—521no—
1014C4⋊C4—521no—
1015C4⋊C4—521no—
1016C4⋊C4—521no—
1017C4⋊C4—521no—
1018C4⋊C4—521no—
1019C4⋊C4—521no—
1020C4⋊C4—521no—
1021C4⋊C4—521no—
1022C4⋊C4—521no—
1023C4⋊C4—521no—
1024C4⋊C4—521no—
1025C4⋊C4—521no—
1026C4⋊C4—521no—
1027C4⋊C4—521no—
1028C4⋊C4—521no—
1029C4⋊C4—521no—
1030C42—41no—
1031C42—134no—
1032C42—262no—
1033C42—262no—
1034C42—262no—
1035C42—262no—
1036C42—262no—
1037C42—262no—
1038C42—262no—
1039C42—262no—
1040C42—262no—
1041C42—262no—
1042C42—262no—
1043C42—262no—
1044C42—262no—
1045C42—262no—
1046C42—262no—
1047C42—521no—
1048C42—521no—
1049C13#3670111yescharacteristic, complemented, Sylow
1050C23C24×D1311yescharacteristic
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—132no—
1096C2×C4—132no—
1097C2×C4—132no—
1098C2×C4—132no—
1099C2×C4—132no—
1100C2×C4—261no—
1101C2×C4—261no—
1102C2×C4—261no—
1103C2×C4—261no—
1104C2×C4—261no—
1105C2×C4—261no—
1106C2×C4—261no—
1107C2×C4—261no—
1108C2×C4—261no—
1109C2×C4—261no—
1110C2×C4—261no—
1111C2×C4—261no—
1112C2×C4—261no—
1113C2×C4—261no—
1114C2×C4—261no—
1115C2×C4—261no—
1116C2×C4—261no—
1117C2×C4—261no—
1118C2×C4—261no—
1119C2×C4—261no—
1120C2×C4—261no—
1121C2×C4—261no—
1122C2×C4—261no—
1123C2×C4—261no—
1124C2×C4—261no—
1125C2×C4—261no—
1126C2×C4—261no—
1127C2×C4—261no—
1128C2×C4—261no—
1129C2×C4—261no—
1130C2×C4—261no—
1131C2×C4—261no—
1132C2×C4—261no—
1133C2×C4—261no—
1134C2×C4—261no—
1135C2×C4—261no—
1136C2×C4—261no—
1137C2×C4—261no—
1138C2×C4—261no—
1139C2×C4—261no—
1140C2×C4—261no—
1141C2×C4—261no—
1142C2×C4—261no—
1143C2×C4#41×D1312yes—
1144C22C2×#41×D1311yescharacteristic
1145C22#1171965011yescharacteristic
1146C22#1171965011yescharacteristic
1147C22D13×2−1+411yescharacteristic
1148C22D13×2−1+411yescharacteristic
1149C22D13×2−1+411yescharacteristic
1150C22#1171965211yescharacteristic
1151C4—22no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—134no—
1167C4—262no—
1168C4—262no—
1169C4—521no—
1170C4—521no—
1171C4—521no—
1172C4—521no—
1173C4—521no—
1174C4—521no—
1175C4—521no—
1176C4—521no—
1177C4—521no—
1178C4—521no—
1179C4—521no—
1180C4—521no—
1181C4—521no—
1182C2#1312826211yescharacteristic
1183C2#1312826611yescharacteristic
1184C2#1312826811yescharacteristic
1185C2D13×#56411yescharacteristic
1186C2#1312898011yescharacteristic
1187C2#1312898211yescharacteristic
1188C2#1312898211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, prime radical, cosocleC23×C13C25
FittingC13×#2839C2
hypercenter#2839D13
hypocenterC13#36701
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2839

Complements

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

NH ≅ G/Ntype
1049. C13#36701semidirect

Maximal subgroups

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

subgroupindex
#131231102
#131230872
#131230852
#131230832
#131230812
#131230792
#131230782
#131230772
#131230762
#131230752
#131230742
#131230732
#131229062
#131229052
#131229022
#131181422
#131181402
#131173952
#131173932
C13×#28392
#3670113