Finite Group Databasebeta

← #16029909

Subgroups — #16029909

Order 3328.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13121021C211yesmaximal, characteristic, complemented
2#13121014C211yesmaximal, characteristic, complemented
3#13121001C211yesmaximal, characteristic
4#13120996C211yesmaximal, characteristic
5#13120934C211yesmaximal, characteristic, complemented
6#13120928C211yesmaximal, characteristic, complemented
7#13120925C211yesmaximal, characteristic, complemented
8#13120923C211yesmaximal, characteristic, complemented
9#13120921C211yesmaximal, characteristic
10#13120912C211yesmaximal, characteristic
11#13120851C211yesmaximal, characteristic
12#13120748C211yesmaximal, characteristic
13#13120745C211yesmaximal, characteristic
14#13120716C211yesmaximal, characteristic, complemented
15#13120714C211yesmaximal, characteristic, complemented
16#13118142C211yesmaximal, characteristic, complemented
17#13118142C211yesmaximal, characteristic, complemented
18#13118142C211yesmaximal, characteristic, complemented
19#13118133C211yesmaximal, characteristic
20#13118133C211yesmaximal, characteristic
21#13118126C211yesmaximal, characteristic, complemented
22#13118111C211yesmaximal, characteristic
23#13118103C211yesmaximal, characteristic
24#13117393C211yesmaximal, characteristic, complemented
25#13117393C211yesmaximal, characteristic, complemented
26#13117390C211yesmaximal, characteristic
27#13117390C211yesmaximal, characteristic
28#13117330C211yesmaximal, characteristic
29#13117311C211yesmaximal, characteristic, complemented
30C4×#88141C211yesmaximal, characteristic, complemented
31C13×#2650C211yesmaximal, characteristic
32C2×Q8×Dic13C2211yescharacteristic
33C2×#88143C2211yescharacteristic
34C2×#88143C2211yescharacteristic
35C2×#88141C2211yescharacteristic
36C2×#88141C2211yescharacteristic
37C2×#88133C2211yescharacteristic
38C2×#88133C2211yescharacteristic
39C2×#88131C2211yescharacteristic
40C2×C4×Dic26C2211yescharacteristic
41C13×#400C2211yescharacteristic
42C13×#400C2211yescharacteristic
43C13×#400C2211yescharacteristic
44C13×#397C2211yescharacteristic
45C13×#397C2211yescharacteristic
46C13×#396C2211yescharacteristic
47C13×#395C2211yescharacteristic
48C13×#393C2211yescharacteristic
49C13×#391C2211yescharacteristic
50C13×#388C2211yescharacteristic
51C13×#388C2211yescharacteristic
52C13×#388C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C4×C13×C4⋊C4C2211yescharacteristic
56#11718891C2211yescharacteristic
57#11718890C2211yescharacteristic
58#11718890C2211yescharacteristic
59#11718645C2211yescharacteristic
60#11718645C2211yescharacteristic
61#11718645C2211yescharacteristic
62#11718645C2211yescharacteristic
63#11718645C2211yescharacteristic
64#11718645C2211yescharacteristic
65#11718644C2211yescharacteristic
66#11718644C2211yescharacteristic
67#11718643C2211yescharacteristic
68#11718643C2211yescharacteristic
69#11718641C2211yescharacteristic
70#11718641C2211yescharacteristic
71#11718641C2211yescharacteristic
72#11718640C2211yescharacteristic
73#11718639C2211yescharacteristic
74#11718639C2211yescharacteristic
75#11718639C2211yescharacteristic
76C4⋊C4×Dic13C2211yescharacteristic
77C4⋊C4×Dic13C2211yescharacteristic
78C4⋊C4×Dic13C2211yescharacteristic
79C4⋊C4×Dic13C2211yescharacteristic
80C4⋊C4×Dic13C2211yescharacteristic
81C4⋊C4×Dic13C2211yescharacteristic
82C4⋊C4×Dic13C2211yescharacteristic
83C4⋊C4×Dic13C2211yescharacteristic
84#11718634C2211yescharacteristic
85#11718633C2211yescharacteristic
86#11718633C2211yescharacteristic
87#11718613C2211yescharacteristic
88#11718613C2211yescharacteristic
89#11718613C2211yescharacteristic
90#11718613C2211yescharacteristic
91#11718612C2211yescharacteristic
92#11718610C2211yescharacteristic
93#11718610C2211yescharacteristic
94#11718609C2211yescharacteristic
95#11718609C2211yescharacteristic
96#11718609C2211yescharacteristic
97#11718609C2211yescharacteristic
98#11718609C2211yescharacteristic
99#11718608C2211yescharacteristic
100#11718606C2211yescharacteristic
101#11718606C2211yescharacteristic
102#11718606C2211yescharacteristic
103#11718605C2211yescharacteristic
104#11718605C2211yescharacteristic
105#11718605C2211yescharacteristic
106C22⋊C4×Dic13C2211yescharacteristic
107C22⋊C4×Dic13C2211yescharacteristic
108C22⋊C4×Dic13C2211yescharacteristic
109C22⋊C4×Dic13C2211yescharacteristic
110C22⋊C4×Dic13C2211yescharacteristic
111C22⋊C4×Dic13C2211yescharacteristic
112#11718594C2211yescharacteristic
113#11718594C2211yescharacteristic
114#11718594C2211yescharacteristic
115#11718594C2211yescharacteristic
116#11718594C2211yescharacteristic
117C4×#6101C2211yescharacteristic
118C4×#6101C2211yescharacteristic
119C42×Dic13C2211yescharacteristic
120C42×Dic13C2211yescharacteristic
121C42×Dic13C2211yescharacteristic
122#11718589C2211yescharacteristic
123C13⋊#401C2211yescharacteristic
124C13⋊#401C2211yescharacteristic
125#11718322C2211yescharacteristic
126#11718321C2211yescharacteristic
127#11718321C2211yescharacteristic
128#11718321C2211yescharacteristic
129#11718321C2211yescharacteristic
130#11718321C2211yescharacteristic
131#11718320C2211yescharacteristic
132#11718319C2211yescharacteristic
133#11718319C2211yescharacteristic
134#11718319C2211yescharacteristic
135#11718319C2211yescharacteristic
136#11718319C2211yescharacteristic
137#11718319C2211yescharacteristic
138#11718319C2211yescharacteristic
139#11718319C2211yescharacteristic
140#11718319C2211yescharacteristic
141#11718318C2211yescharacteristic
142#11718318C2211yescharacteristic
143#11718318C2211yescharacteristic
144#11718318C2211yescharacteristic
145#11718318C2211yescharacteristic
146#11718318C2211yescharacteristic
147#11718318C2211yescharacteristic
148#11718318C2211yescharacteristic
149#11718317C2211yescharacteristic
150#11718317C2211yescharacteristic
151#11718316C2211yescharacteristic
152#11718316C2211yescharacteristic
153#11718316C2211yescharacteristic
154#11718315C2211yescharacteristic
155#11718315C2211yescharacteristic
156#11718315C2211yescharacteristic
157#11718315C2211yescharacteristic
158#11718315C2211yescharacteristic
159#11718315C2211yescharacteristic
160#11718314C2211yescharacteristic
161#11718314C2211yescharacteristic
162#11718313C2211yescharacteristic
163#11718312C2211yescharacteristic
164#11718312C2211yescharacteristic
165#11718311C2211yescharacteristic
166#11718311C2211yescharacteristic
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#11718310C2211yescharacteristic
182#11718309C2211yescharacteristic
183#11718309C2211yescharacteristic
184#11718309C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718308C2211yescharacteristic
187C22×Q8×C13C2311yescharacteristic
188C23×Dic13C2311yescharacteristic
189C22×Dic26C2311yescharacteristic
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×C22⋊C4C2311yescharacteristic
199C2×C13×C22⋊C4C2311yescharacteristic
200C2×C13×C22⋊C4C2311yescharacteristic
201C2×C13×C22⋊C4C2311yescharacteristic
202C2×C13×C22⋊C4C2311yescharacteristic
203C2×C13×C22⋊C4C2311yescharacteristic
204C2×C13×C22⋊C4C2311yescharacteristic
205C2×C42×C13C2311yescharacteristic
206C2×C42×C13C2311yescharacteristic
207C2×C42×C13C2311yescharacteristic
208C2×C22⋊Dic13C2311yescharacteristic
209C2×C22⋊Dic13C2311yescharacteristic
210C2×C22⋊Dic13C2311yescharacteristic
211C2×C22⋊Dic13C2311yescharacteristic
212C2×C22⋊Dic13C2311yescharacteristic
213C2×C22⋊Dic13C2311yescharacteristic
214C2×C22⋊Dic13C2311yescharacteristic
215Q8×Dic13—24no—
216C2×C4⋊Dic13C2311yescharacteristic
217C2×C4⋊Dic13C2311yescharacteristic
218C2×C4⋊Dic13C2311yescharacteristic
219C2×C4⋊Dic13C2311yescharacteristic
220C2×C4⋊Dic13C2311yescharacteristic
221C2×C4⋊Dic13C2311yescharacteristic
222C2×C4⋊Dic13C2311yescharacteristic
223C2×C4⋊Dic13C2311yescharacteristic
224C2×C4⋊Dic13C2311yescharacteristic
225C2×C4⋊Dic13C2311yescharacteristic
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×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×#6101C2311yescharacteristic
254C2×#6101C2311yescharacteristic
255C2×#6101C2311yescharacteristic
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
266C2×C4×Dic13C2311yescharacteristic
267C2×C4×Dic13C2311yescharacteristic
268C2×C4×Dic13C2311yescharacteristic
269C2×C4×Dic13C2311yescharacteristic
270C2×C4×Dic13C2311yescharacteristic
271C2×C4×Dic13C2311yescharacteristic
272C2×C4×Dic13C2311yescharacteristic
273C2×C4×Dic13C2311yescharacteristic
274C2×C4×Dic13C2311yescharacteristic
275C2×C4×Dic13C2311yescharacteristic
276C2×C4×Dic13C2311yescharacteristic
277C2×C4×Dic13C2311yescharacteristic
278C2×C4×Dic13C2311yescharacteristic
279#88143—24no—
280#88143—24no—
281#88141—24no—
282#88141—24no—
283#88133—24no—
284#88133—24no—
285#88131—24no—
286C4×Dic26—24no—
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289C13×#95C2311yescharacteristic
290C13×#95C2311yescharacteristic
291C13×#95C2311yescharacteristic
292C13×#95C2311yescharacteristic
293C13×#95C2311yescharacteristic
294C13×#95C2311yescharacteristic
295C13×#95C2311yescharacteristic
296C13×#95C2311yescharacteristic
297C13×#95C2311yescharacteristic
298C13×#95C2311yescharacteristic
299C13×#95C2311yescharacteristic
300C13×#95C2311yescharacteristic
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
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#88071C2311yescharacteristic
346#88071C2311yescharacteristic
347#88071C2311yescharacteristic
348#88071C2311yescharacteristic
349#88071C2311yescharacteristic
350#88071C2311yescharacteristic
351#34604—131nomaximal, Sylow
352C24×C13C2411yescharacteristic
353C2×Q8×C13—22no—
354C2×Q8×C13—41no—
355C2×Q8×C13—41no—
356C22×C4×C13C2411yescharacteristic
357C22×C4×C13C2411yescharacteristic
358C22×C4×C13C2411yescharacteristic
359C22×C4×C13C2411yescharacteristic
360C22×C4×C13C2411yescharacteristic
361C22×C4×C13C2411yescharacteristic
362C22×C4×C13C2411yescharacteristic
363C22×C4×C13C2411yescharacteristic
364C22×C4×C13C2411yescharacteristic
365C22×C4×C13C2411yescharacteristic
366C22×C4×C13C2411yescharacteristic
367C22×C4×C13C2411yescharacteristic
368C22×C4×C13C2411yescharacteristic
369C22×C4×C13C2411yescharacteristic
370C22×Dic13—22no—
371C22×Dic13—22no—
372C22×Dic13—22no—
373C22×Dic13C2411yescharacteristic
374C22×Dic13C2411yescharacteristic
375C22×Dic13C2411yescharacteristic
376C22×Dic13C2411yescharacteristic
377C22×Dic13C2411yescharacteristic
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2411yescharacteristic
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2411yescharacteristic
382C22×Dic13C2411yescharacteristic
383C22×Dic13C2411yescharacteristic
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2411yescharacteristic
386C22×Dic13C2411yescharacteristic
387C22×Dic13C2411yescharacteristic
388C22×Dic13C2411yescharacteristic
389C2×Dic26—22no—
390C2×Dic26—22no—
391C2×Dic26—22no—
392C13×C4⋊C4—22no—
393C13×C4⋊C4—22no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—22no—
396C13×C4⋊C4—41no—
397C13×C4⋊C4—41no—
398C13×C4⋊C4—41no—
399C13×C4⋊C4—41no—
400C13×C22⋊C4—22no—
401C13×C22⋊C4—22no—
402C13×C22⋊C4—22no—
403C13×C22⋊C4—41no—
404C13×C22⋊C4—41no—
405C13×C22⋊C4—41no—
406C13×C22⋊C4—41no—
407C42×C13—22no—
408C42×C13—41no—
409C42×C13—41no—
410C22⋊Dic13—22no—
411C22⋊Dic13—22no—
412C22⋊Dic13—22no—
413C22⋊Dic13—22no—
414C22⋊Dic13—22no—
415C22⋊Dic13—41no—
416C22⋊Dic13—41no—
417C4⋊Dic13—22no—
418C4⋊Dic13—22no—
419C4⋊Dic13—22no—
420C4⋊Dic13—22no—
421C4⋊Dic13—22no—
422C4⋊Dic13—22no—
423C4⋊Dic13—22no—
424C4⋊Dic13—22no—
425C4⋊Dic13—41no—
426C4⋊Dic13—41no—
427#6101—22no—
428#6101—22no—
429#6101—22no—
430#6101—22no—
431#6101—22no—
432#6101—22no—
433#6101—22no—
434#6101—22no—
435#6101—22no—
436#6101—22no—
437#6101—22no—
438#6101—22no—
439#6101—22no—
440#6101—22no—
441#6101—22no—
442#6101—22no—
443#6101—22no—
444#6101—22no—
445#6101—22no—
446#6101—22no—
447#6101—41no—
448#6101—41no—
449#6101—41no—
450#6101—41no—
451#6101—41no—
452#6101—41no—
453#6101—41no—
454#6101—41no—
455#6101—41no—
456#6101—41no—
457C4×Dic13—22no—
458C4×Dic13—22no—
459C4×Dic13—22no—
460C4×Dic13—22no—
461C4×Dic13—22no—
462C4×Dic13—22no—
463C4×Dic13—22no—
464C4×Dic13—22no—
465C4×Dic13—22no—
466C4×Dic13—22no—
467C4×Dic13—22no—
468C4×Dic13—22no—
469C4×Dic13—22no—
470C4×Dic13—22no—
471C4×Dic13—22no—
472C4×Dic13—22no—
473C4×Dic13—41no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13#4114yes—
478C4×Dic13#4114yes—
479C4×Dic13#4114yes—
480#2666—131no—
481#2666—131no—
482#2664—131no—
483#2664—131no—
484#2655—131no—
485#2655—131no—
486#2655—131no—
487#2655—131no—
488#2654—131no—
489#2654—131no—
490#2650—131no—
491#2650D1311yescharacteristic
492#2637—131no—
493#2637—131no—
494#2634—131no—
495#2634—131no—
496#2402—131no—
497#2402—131no—
498#2402—131no—
499#2401—131no—
500#2401—131no—
501#2399—131no—
502#2396—131no—
503#2396—131no—
504C4×#125—131no—
505C4×#125—131no—
506C4×#126—131no—
507C4×#126—131no—
508#2298—131no—
509#2295—131no—
510C42×Q8—131no—
511C23×C13—21no—
512C23×C13—21no—
513C23×C13—21no—
514C23×C13—21no—
515C23×C13—21no—
516C23×C13—21no—
517C23×C13—21no—
518C23×C13C2511yescharacteristic
519Q8×C13—44no—
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×C13—21no—
533C2×C4×C13—21no—
534C2×C4×C13—21no—
535C2×C4×C13—21no—
536C2×C4×C13—21no—
537C2×C4×C13—21no—
538C2×C4×C13—21no—
539C2×C4×C13—21no—
540C2×C4×C13—21no—
541C2×C4×C13—21no—
542C2×C4×C13—21no—
543C2×C4×C13—21no—
544C2×C4×C13—21no—
545C2×C4×C13—21no—
546C2×C4×C13—21no—
547C2×C4×C13—21no—
548C2×C4×C13—21no—
549C2×C4×C13—21no—
550C2×C4×C13—21no—
551C2×C4×C13—21no—
552C2×C4×C13—21no—
553C2×C4×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—21no—
556C2×C4×C13—21no—
557C2×C4×C13—21no—
558C2×C4×C13—21no—
559C2×C4×C13C2×#4112yes—
560C2×C4×C13C2×#4112yes—
561C2×C4×C13C2×#4112yes—
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×Dic13—21no—
577C2×Dic13—21no—
578C2×Dic13—21no—
579C2×Dic13—21no—
580C2×Dic13—21no—
581C2×Dic13—21no—
582C2×Dic13—21no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—21no—
589C2×Dic13—21no—
590C2×Dic13—21no—
591C2×Dic13—21no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—21no—
595C2×Dic13—21no—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13—21no—
602C2×Dic13—44no—
603C2×Dic13C2×#4112yes—
604C2×Dic13C2×#4112yes—
605C2×Dic13C2×#4112yes—
606C2×Dic13C2×#4112yes—
607C2×Dic13C2×#4112yes—
608C2×Dic13C2×#4112yes—
609C2×Dic132−1+412yes—
610C2×Dic132−1+412yes—
611Dic26—28no—
612C2×#126—131no—
613C2×#126—131no—
614C2×#125—131no—
615C2×#125—131no—
616C2×C4×Q8—131no—
617C2×C4×Q8—131no—
618C2×C4×Q8—131no—
619C2×C4×Q8—131no—
620C2×#117—131no—
621#401—131no—
622#401—131no—
623#400—131no—
624#400—131no—
625#400—131no—
626#400—131no—
627#400—131no—
628#400—131no—
629#400—131no—
630#400—131no—
631#400—131no—
632#400—131no—
633#400—131no—
634#400—131no—
635#400—131no—
636#400—131no—
637#400—131no—
638#400—131no—
639#400—131no—
640#400C2×D1311yescharacteristic
641#400C2×D1311yescharacteristic
642#400C2×D1311yescharacteristic
643#399—131no—
644#399—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#397—131no—
666#397—131no—
667#397—131no—
668#397—131no—
669#397C2×D1311yescharacteristic
670#397C2×D1311yescharacteristic
671#396—131no—
672#396—131no—
673#396—131no—
674#396—131no—
675#396—131no—
676#396C2×D1311yescharacteristic
677#395—131no—
678#395—131no—
679#395—131no—
680#395—131no—
681#395—131no—
682#395C2×D1311yescharacteristic
683#393—131no—
684#393C2×D1311yescharacteristic
685#391—131no—
686#391C2×D1311yescharacteristic
687#389—131no—
688#389—131no—
689#389—131no—
690#389—131no—
691#389—131no—
692#389—131no—
693#388—131no—
694#388—131no—
695#388—131no—
696#388—131no—
697#388—131no—
698#388—131no—
699#388—131no—
700#388C2×D1311yescharacteristic
701#388C2×D1311yescharacteristic
702#388C2×D1311yescharacteristic
703#387—131no—
704#387—131no—
705#387—131no—
706#387—131no—
707#387—131no—
708#387—131no—
709#387—131no—
710#387—131no—
711#387—131no—
712#387—131no—
713#387—131no—
714#387—131no—
715#387—131no—
716#387—131no—
717#387—131no—
718#387—131no—
719#387—131no—
720#387—131no—
721#387—131no—
722#387—131no—
723#387C2×D1311yescharacteristic
724#387C2×D1311yescharacteristic
725#383—131no—
726#383—131no—
727#382—131no—
728#382—131no—
729C4×C4⋊C4—131no—
730C4×C4⋊C4—131no—
731C4×C4⋊C4—131no—
732C4×C4⋊C4—131no—
733C4×C4⋊C4—131no—
734C4×C4⋊C4—131no—
735C4×C4⋊C4—131no—
736C4×C4⋊C4—131no—
737C4×C4⋊C4—131no—
738C4×C4⋊C4—131no—
739C4×C4⋊C4—131no—
740C4×C4⋊C4—131no—
741C4×C4⋊C4—131no—
742C4×C4⋊C4—131no—
743C4×C4⋊C4—131no—
744C4×C4⋊C4—131no—
745C4×C4⋊C4—131no—
746C4×C4⋊C4—131no—
747C4×C4⋊C4—131no—
748C4×C4⋊C4—131no—
749C4×C4⋊C4—131no—
750C4×C4⋊C4—131no—
751C4×C4⋊C4—131no—
752C4×C4⋊C4—131no—
753C4×C4⋊C4—131no—
754C4×C4⋊C4C2×D1311yescharacteristic
755C4×C22⋊C4—131no—
756C4×C22⋊C4—131no—
757C4×C22⋊C4—131no—
758C4×C22⋊C4—131no—
759C4×C22⋊C4—131no—
760C4×C22⋊C4—131no—
761#376—131no—
762#376—131no—
763#376—131no—
764C43—131no—
765C43—131no—
766C43—131no—
767C22×C13—41no—
768C22×C13—41no—
769C22×C13—41no—
770C22×C13—41no—
771C22×C13—41no—
772C22×C13—41no—
773C22×C13—41no—
774C22×C13C22×#4111yescharacteristic
775C22×C13C22×#4111yescharacteristic
776C22×C13C22×#4111yescharacteristic
777C22×C13C2×2−1+411yescharacteristic
778C22×C13C2×2−1+411yescharacteristic
779C22×C13#58511yescharacteristic
780C22×C13#58511yescharacteristic
781C4×C13—22no—
782C4×C13—22no—
783C4×C13—22no—
784C4×C13—41no—
785C4×C13—41no—
786C4×C13—41no—
787C4×C13—41no—
788C4×C13—41no—
789C4×C13—41no—
790C4×C13—41no—
791C4×C13—41no—
792C4×C13—41no—
793C4×C13—41no—
794C4×C13—41no—
795Dic13—22no—
796Dic13—22no—
797Dic13—22no—
798Dic13—22no—
799Dic13—22no—
800Dic13—41no—
801Dic13—41no—
802Dic13—41no—
803Dic13—41no—
804Dic13—41no—
805Dic13—41no—
806Dic13—41no—
807Dic13—41no—
808Dic13—41no—
809Dic13—41no—
810Dic13#54114yes—
811C22×Q8—131no—
812C22×Q8C22×D1311yescharacteristic
813C23×C4—131no—
814#126—264no—
815#126—264no—
816#125—264no—
817#125—264no—
818C4×Q8—264no—
819C4×Q8—264no—
820C4×Q8—264no—
821C4×Q8—264no—
822#117—264no—
823C2×C4⋊C4—131no—
824C2×C4⋊C4—131no—
825C2×C4⋊C4—131no—
826C2×C4⋊C4—131no—
827C2×C4⋊C4—131no—
828C2×C4⋊C4—131no—
829C2×C4⋊C4—131no—
830C2×C4⋊C4—131no—
831C2×C4⋊C4—131no—
832C2×C4⋊C4—131no—
833C2×C4⋊C4—131no—
834C2×C4⋊C4—131no—
835C2×C4⋊C4—131no—
836C2×C4⋊C4—131no—
837C2×C4⋊C4—131no—
838C2×C4⋊C4—131no—
839C2×C4⋊C4—131no—
840C2×C4⋊C4—131no—
841C2×C4⋊C4—131no—
842C2×C4⋊C4—131no—
843C2×C4⋊C4—131no—
844C2×C4⋊C4—131no—
845C2×C4⋊C4—131no—
846C2×C4⋊C4—131no—
847C2×C4⋊C4—131no—
848C2×C4⋊C4—131no—
849C2×C4⋊C4—131no—
850C2×C4⋊C4—131no—
851C2×C4⋊C4—131no—
852C2×C4⋊C4—131no—
853C2×C4⋊C4—131no—
854C2×C4⋊C4—131no—
855C2×C4⋊C4—131no—
856C2×C4⋊C4—131no—
857C2×C4⋊C4—131no—
858C2×C4⋊C4—131no—
859C2×C4⋊C4—131no—
860C2×C4⋊C4—131no—
861C2×C4⋊C4—131no—
862C2×C4⋊C4—131no—
863C2×C4⋊C4C22×D1311yescharacteristic
864C2×C4⋊C4C22×D1311yescharacteristic
865C2×C4⋊C4C22×D1311yescharacteristic
866C2×C4⋊C4C22×D1311yescharacteristic
867C2×C4⋊C4C22×D1311yescharacteristic
868C2×C4⋊C4C22×D1311yescharacteristic
869C2×C4⋊C4C22×D1311yescharacteristic
870C2×C4⋊C4C22×D1311yescharacteristic
871C2×C22⋊C4—131no—
872C2×C22⋊C4—131no—
873C2×C22⋊C4—131no—
874C2×C22⋊C4—131no—
875C2×C22⋊C4—131no—
876C2×C22⋊C4—131no—
877C2×C22⋊C4—131no—
878C2×C22⋊C4C22×D1311yescharacteristic
879C2×C22⋊C4C22×D1311yescharacteristic
880C2×C22⋊C4C22×D1311yescharacteristic
881C2×C22⋊C4C22×D1311yescharacteristic
882C2×C22⋊C4C22×D1311yescharacteristic
883C2×C22⋊C4C22×D1311yescharacteristic
884C2×C22⋊C4C22×D1311yescharacteristic
885C2×C42—131no—
886C2×C42—131no—
887C2×C42—131no—
888C2×C42—131no—
889C2×C42—131no—
890C2×C42—131no—
891C2×C42—131no—
892C2×C42—131no—
893C2×C42—131no—
894C2×C42—131no—
895C2×C42—131no—
896C2×C42—131no—
897C2×C42—131no—
898C2×C42—131no—
899C2×C42—131no—
900C2×C42—131no—
901C2×C42—131no—
902C2×C42—131no—
903C2×C42—131no—
904C2×C42—131no—
905C2×C42—131no—
906C2×C42—131no—
907C2×C42—131no—
908C2×C42C22×D1311yescharacteristic
909C2×C42C22×D1311yescharacteristic
910C2×C42C22×D1311yescharacteristic
911#95—131no—
912#95—131no—
913#95—131no—
914#95—131no—
915#95—131no—
916#95—131no—
917#95—131no—
918#95—131no—
919#95—131no—
920#95—131no—
921#95—131no—
922#95—131no—
923#95—131no—
924#95—131no—
925#95—131no—
926#95—131no—
927#95—131no—
928#95—131no—
929#95—131no—
930#95—131no—
931#95—131no—
932#95—131no—
933#95—131no—
934#95—131no—
935#95—131no—
936#95—131no—
937#95—131no—
938#95—131no—
939#95—131no—
940#95—131no—
941#95—131no—
942#95—131no—
943#95—131no—
944#95—131no—
945#95—131no—
946#95—131no—
947#95—131no—
948#95—131no—
949#95—131no—
950#95—131no—
951#95—131no—
952#95—131no—
953#95—131no—
954#95—131no—
955#95—131no—
956#95—131no—
957#95—131no—
958#95—131no—
959#95C22×D1311yescharacteristic
960#95C22×D1311yescharacteristic
961#95C22×D1311yescharacteristic
962#95C22×D1311yescharacteristic
963#95C22×D1311yescharacteristic
964#95C22×D1311yescharacteristic
965#95C22×D1311yescharacteristic
966#95C22×D1311yescharacteristic
967#95C22×D1311yescharacteristic
968#95C22×D1311yescharacteristic
969#95C22×D1311yescharacteristic
970#95C22×D1311yescharacteristic
971#95C22×D1311yescharacteristic
972#95C22×D1311yescharacteristic
973#95C22×D1311yescharacteristic
974#95C22×D1311yescharacteristic
975C2×C13—81no—
976C2×C13#344411yescharacteristic
977C2×C13C2×#54111yescharacteristic
978C2×C13#345511yescharacteristic
979C2×C13#346111yescharacteristic
980C2×C13#346111yescharacteristic
981C2×C13#346111yescharacteristic
982C2×C13#346111yescharacteristic
983C24C23×D1311yescharacteristic
984C2×Q8—22no—
985C2×Q8—41no—
986C2×Q8—41no—
987C2×Q8—262no—
988C2×Q8—262no—
989C2×Q8—262no—
990C22×C4—131no—
991C22×C4—131no—
992C22×C4—131no—
993C22×C4—131no—
994C22×C4—131no—
995C22×C4—131no—
996C22×C4—131no—
997C22×C4—131no—
998C22×C4—131no—
999C22×C4—131no—
1000C22×C4—131no—
1001C22×C4—131no—
1002C22×C4—131no—
1003C22×C4—131no—
1004C22×C4—131no—
1005C22×C4—131no—
1006C22×C4—262no—
1007C22×C4—262no—
1008C22×C4—262no—
1009C22×C4C23×D1311yescharacteristic
1010C22×C4C23×D1311yescharacteristic
1011C22×C4C23×D1311yescharacteristic
1012C22×C4C23×D1311yescharacteristic
1013C22×C4C23×D1311yescharacteristic
1014C22×C4C23×D1311yescharacteristic
1015C22×C4C23×D1311yescharacteristic
1016C22×C4C23×D1311yescharacteristic
1017C22×C4C23×D1311yescharacteristic
1018C22×C4C23×D1311yescharacteristic
1019C22×C4C23×D1311yescharacteristic
1020C22×C4C23×D1311yescharacteristic
1021C22×C4C23×D1311yescharacteristic
1022C22×C4C23×D1311yescharacteristic
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—262no—
1032C4⋊C4—262no—
1033C4⋊C4—262no—
1034C4⋊C4—262no—
1035C4⋊C4—262no—
1036C4⋊C4—262no—
1037C4⋊C4—262no—
1038C4⋊C4—262no—
1039C4⋊C4—262no—
1040C4⋊C4—262no—
1041C4⋊C4—262no—
1042C4⋊C4—262no—
1043C4⋊C4—262no—
1044C4⋊C4—262no—
1045C4⋊C4—262no—
1046C4⋊C4—262no—
1047C4⋊C4—262no—
1048C4⋊C4—262no—
1049C4⋊C4—262no—
1050C4⋊C4—262no—
1051C4⋊C4—262no—
1052C4⋊C4—262no—
1053C4⋊C4—262no—
1054C4⋊C4—262no—
1055C4⋊C4—262no—
1056C4⋊C4—262no—
1057C4⋊C4—262no—
1058C4⋊C4—262no—
1059C4⋊C4—521no—
1060C4⋊C4—521no—
1061C4⋊C4—521no—
1062C4⋊C4—521no—
1063C4⋊C4—521no—
1064C4⋊C4—521no—
1065C4⋊C4—521no—
1066C4⋊C4—521no—
1067C4⋊C4—521no—
1068C4⋊C4—521no—
1069C4⋊C4—521no—
1070C4⋊C4—521no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—262no—
1079C22⋊C4—262no—
1080C22⋊C4—262no—
1081C22⋊C4—262no—
1082C22⋊C4—262no—
1083C22⋊C4—521no—
1084C22⋊C4—521no—
1085C42—22no—
1086C42—41no—
1087C42—41no—
1088C42—134no—
1089C42—134no—
1090C42—134no—
1091C42—262no—
1092C42—262no—
1093C42—262no—
1094C42—262no—
1095C42—262no—
1096C42—262no—
1097C42—262no—
1098C42—262no—
1099C42—262no—
1100C42—262no—
1101C42—262no—
1102C42—262no—
1103C42—262no—
1104C42—262no—
1105C42—262no—
1106C42—262no—
1107C42—521no—
1108C42—521no—
1109C42—521no—
1110C42—521no—
1111C13#3460411yescharacteristic, complemented, Sylow
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23C24×D1311yescharacteristic
1120Q8—44no—
1121Q8—268no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—132no—
1162C2×C4—132no—
1163C2×C4—132no—
1164C2×C4—132no—
1165C2×C4—132no—
1166C2×C4—132no—
1167C2×C4—132no—
1168C2×C4—132no—
1169C2×C4—261no—
1170C2×C4—261no—
1171C2×C4—261no—
1172C2×C4—261no—
1173C2×C4—261no—
1174C2×C4—261no—
1175C2×C4—261no—
1176C2×C4—261no—
1177C2×C4—261no—
1178C2×C4—261no—
1179C2×C4—261no—
1180C2×C4—261no—
1181C2×C4—261no—
1182C2×C4—261no—
1183C2×C4—261no—
1184C2×C4—261no—
1185C2×C4—261no—
1186C2×C4—261no—
1187C2×C4—261no—
1188C2×C4—261no—
1189C2×C4—261no—
1190C2×C4—261no—
1191C2×C4—261no—
1192C2×C4—261no—
1193C2×C4—261no—
1194C2×C4—261no—
1195C2×C4—261no—
1196C2×C4—261no—
1197C2×C4—261no—
1198C2×C4—261no—
1199C2×C4—261no—
1200C2×C4—261no—
1201C2×C4—261no—
1202C2×C4—261no—
1203C2×C4—261no—
1204C2×C4—261no—
1205C2×C4—261no—
1206C2×C4—261no—
1207C2×C4—261no—
1208C2×C4—261no—
1209C2×C4—524no—
1210C2×C4#41×D1312yes—
1211C2×C4#41×D1312yes—
1212C2×C4#41×D1312yes—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22C2×#41×D1311yescharacteristic
1221C22C2×#41×D1311yescharacteristic
1222C22C2×#41×D1311yescharacteristic
1223C22#1171965011yescharacteristic
1224C22#1171965011yescharacteristic
1225C22D13×2−1+411yescharacteristic
1226C22D13×2−1+411yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—134no—
1242C4—262no—
1243C4—262no—
1244C4—262no—
1245C4—262no—
1246C4—262no—
1247C4—521no—
1248C4—521no—
1249C4—521no—
1250C4—521no—
1251C4—521no—
1252C4—521no—
1253C4—521no—
1254C4—521no—
1255C4—521no—
1256C4—521no—
1257C2—81no—
1258C2#1312813011yescharacteristic
1259C2D13×#54111yescharacteristic
1260C2#1312821811yescharacteristic
1261C2#1312826211yescharacteristic
1262C2#1312826211yescharacteristic
1263C2#1312826211yescharacteristic
1264C2#1312826611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2650C2
prime radicalC24×C13C24
hypercenter#2650D13
hypocenterC13#34604
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2650

Complements

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

NH ≅ G/Ntype
1. #13121021C2semidirect
2. #13121014C2semidirect
5. #13120934C2semidirect
6. #13120928C2semidirect
7. #13120925C2semidirect
8. #13120923C2semidirect
14. #13120716C2semidirect
15. #13120714C2semidirect
16. #13118142C2semidirect
17. #13118142C2semidirect
18. #13118142C2semidirect
21. #13118126C2semidirect
24. #13117393C2semidirect
25. #13117393C2semidirect
29. #13117311C2semidirect
30. C4×#88141C2semidirect
1111. C13#34604semidirect

Maximal subgroups

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

subgroupindex
#131210212
#131210142
#131210012
#131209962
#131209342
#131209282
#131209252
#131209232
#131209212
#131209122
#131208512
#131207482
#131207452
#131207162
#131207142
#131181422
#131181332
#131181262
#131181112
#131181032
#131173932
#131173902
#131173302
#131173112
C4×#881412
C13×#26502
#3460413