Finite Group Databasebeta

← #16029910

Subgroups — #16029910

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#13121022C211yesmaximal, characteristic, complemented
2#13121002C211yesmaximal, characteristic
3#13120995C211yesmaximal, characteristic
4#13120935C211yesmaximal, characteristic, complemented
5#13120935C211yesmaximal, characteristic, complemented
6#13120932C211yesmaximal, characteristic, complemented
7#13120928C211yesmaximal, characteristic, complemented
8#13120920C211yesmaximal, characteristic
9#13120913C211yesmaximal, characteristic
10#13120860C211yesmaximal, characteristic
11#13120857C211yesmaximal, characteristic
12#13120751C211yesmaximal, characteristic
13#13120746C211yesmaximal, characteristic
14#13120718C211yesmaximal, characteristic, complemented
15#13120715C211yesmaximal, characteristic, complemented
16#13118140C211yesmaximal, characteristic, complemented
17#13118140C211yesmaximal, characteristic, complemented
18#13118140C211yesmaximal, characteristic, complemented
19#13118135C211yesmaximal, characteristic
20#13118135C211yesmaximal, characteristic
21#13118126C211yesmaximal, characteristic, complemented
22#13118113C211yesmaximal, characteristic
23#13118107C211yesmaximal, characteristic
24#13117395C211yesmaximal, characteristic, complemented
25#13117391C211yesmaximal, characteristic, complemented
26#13117386C211yesmaximal, characteristic
27#13117384C211yesmaximal, characteristic
28#13117328C211yesmaximal, characteristic
29#13117311C211yesmaximal, characteristic, complemented
30C4×#88141C211yesmaximal, characteristic, complemented
31C13×#2666C211yesmaximal, characteristic, complemented
32C2×Q8×Dic13C2211yescharacteristic
33C2×#88152C2211yescharacteristic
34C2×#88146C2211yescharacteristic
35C2×#88144C2211yescharacteristic
36C2×#88141C2211yescharacteristic
37C2×#88141C2211yescharacteristic
38C2×#88130C2211yescharacteristic
39C2×#88124C2211yescharacteristic
40C2×C4×Dic26C2211yescharacteristic
41C13×#400C2211yescharacteristic
42C13×#400C2211yescharacteristic
43C13×#398C2211yescharacteristic
44C13×#398C2211yescharacteristic
45C13×#398C2211yescharacteristic
46C13×#398C2211yescharacteristic
47C13×#395C2211yescharacteristic
48C13×#395C2211yescharacteristic
49C13×#391C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#383C2211yescharacteristic
54C13×#382C2211yescharacteristic
55C4×C13×C4⋊C4C2211yescharacteristic
56#11718892C2211yescharacteristic
57#11718891C2211yescharacteristic
58#11718890C2211yescharacteristic
59#11718655C2211yescharacteristic
60#11718655C2211yescharacteristic
61#11718655C2211yescharacteristic
62#11718655C2211yescharacteristic
63#11718655C2211yescharacteristic
64#11718655C2211yescharacteristic
65#11718654C2211yescharacteristic
66#11718654C2211yescharacteristic
67#11718653C2211yescharacteristic
68#11718651C2211yescharacteristic
69#11718651C2211yescharacteristic
70#11718647C2211yescharacteristic
71#11718647C2211yescharacteristic
72#11718647C2211yescharacteristic
73#11718647C2211yescharacteristic
74#11718645C2211yescharacteristic
75#11718645C2211yescharacteristic
76#11718645C2211yescharacteristic
77#11718645C2211yescharacteristic
78#11718645C2211yescharacteristic
79#11718645C2211yescharacteristic
80#11718644C2211yescharacteristic
81#11718644C2211yescharacteristic
82#11718644C2211yescharacteristic
83#11718644C2211yescharacteristic
84#11718643C2211yescharacteristic
85#11718643C2211yescharacteristic
86#11718643C2211yescharacteristic
87#11718642C2211yescharacteristic
88#11718639C2211yescharacteristic
89#11718639C2211yescharacteristic
90#11718638C2211yescharacteristic
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
101C4⋊C4×Dic13C2211yescharacteristic
102C4⋊C4×Dic13C2211yescharacteristic
103#11718634C2211yescharacteristic
104#11718634C2211yescharacteristic
105#11718634C2211yescharacteristic
106#11718601C2211yescharacteristic
107#11718601C2211yescharacteristic
108C4×#6101C2211yescharacteristic
109C4×#6101C2211yescharacteristic
110C42×Dic13C2211yescharacteristic
111C42×Dic13C2211yescharacteristic
112C42×Dic13C2211yescharacteristic
113#11718589C2211yescharacteristic
114#11718589C2211yescharacteristic
115#11718338C2211yescharacteristic
116#11718336C2211yescharacteristic
117#11718336C2211yescharacteristic
118#11718335C2211yescharacteristic
119#11718335C2211yescharacteristic
120#11718334C2211yescharacteristic
121#11718331C2211yescharacteristic
122#11718331C2211yescharacteristic
123#11718330C2211yescharacteristic
124#11718330C2211yescharacteristic
125#11718330C2211yescharacteristic
126#11718330C2211yescharacteristic
127#11718327C2211yescharacteristic
128#11718327C2211yescharacteristic
129#11718327C2211yescharacteristic
130#11718327C2211yescharacteristic
131#11718327C2211yescharacteristic
132#11718327C2211yescharacteristic
133C13⋊#401C2211yescharacteristic
134C13⋊#401C2211yescharacteristic
135#11718322C2211yescharacteristic
136#11718322C2211yescharacteristic
137#11718322C2211yescharacteristic
138#11718322C2211yescharacteristic
139#11718322C2211yescharacteristic
140#11718322C2211yescharacteristic
141#11718321C2211yescharacteristic
142#11718321C2211yescharacteristic
143#11718321C2211yescharacteristic
144#11718321C2211yescharacteristic
145#11718321C2211yescharacteristic
146#11718321C2211yescharacteristic
147#11718320C2211yescharacteristic
148#11718320C2211yescharacteristic
149#11718320C2211yescharacteristic
150#11718320C2211yescharacteristic
151#11718320C2211yescharacteristic
152#11718317C2211yescharacteristic
153#11718317C2211yescharacteristic
154#11718317C2211yescharacteristic
155#11718316C2211yescharacteristic
156#11718315C2211yescharacteristic
157#11718315C2211yescharacteristic
158#11718315C2211yescharacteristic
159#11718314C2211yescharacteristic
160#11718314C2211yescharacteristic
161#11718314C2211yescharacteristic
162#11718314C2211yescharacteristic
163#11718314C2211yescharacteristic
164#11718314C2211yescharacteristic
165#11718313C2211yescharacteristic
166#11718313C2211yescharacteristic
167#11718313C2211yescharacteristic
168#11718313C2211yescharacteristic
169#11718313C2211yescharacteristic
170#11718313C2211yescharacteristic
171#11718313C2211yescharacteristic
172#11718312C2211yescharacteristic
173#11718310C2211yescharacteristic
174#11718310C2211yescharacteristic
175#11718310C2211yescharacteristic
176#11718310C2211yescharacteristic
177#11718310C2211yescharacteristic
178#11718310C2211yescharacteristic
179#11718310C2211yescharacteristic
180#11718310C2211yescharacteristic
181#11718310C2211yescharacteristic
182#11718310C2211yescharacteristic
183#11718310C2211yescharacteristic
184#11718309C2211yescharacteristic
185#11718309C2211yescharacteristic
186#11718309C2211yescharacteristic
187C22×Q8×C13C2311yescharacteristic
188C22×C4×D13C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
199C2×C13×C4⋊C4C2311yescharacteristic
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C13×C4⋊C4C2311yescharacteristic
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C42×C13C2311yescharacteristic
204C2×C42×C13C2311yescharacteristic
205C2×C42×C13C2311yescharacteristic
206Q8×Dic13—24no—
207C2×#6103C2311yescharacteristic
208C2×#6103C2311yescharacteristic
209C2×#6103C2311yescharacteristic
210C2×#6103C2311yescharacteristic
211C2×#6103C2311yescharacteristic
212C2×#6103C2311yescharacteristic
213C2×#6103C2311yescharacteristic
214C2×#6103C2311yescharacteristic
215C2×#6103C2311yescharacteristic
216C2×#6103C2311yescharacteristic
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
219C2×#6103C2311yescharacteristic
220C2×#6103C2311yescharacteristic
221C2×C4⋊Dic13C2311yescharacteristic
222C2×C4⋊Dic13C2311yescharacteristic
223C2×C4⋊Dic13C2311yescharacteristic
224C2×C4⋊Dic13C2311yescharacteristic
225C2×C4⋊Dic13C2311yescharacteristic
226C2×C4⋊Dic13C2311yescharacteristic
227C2×C4⋊Dic13C2311yescharacteristic
228C2×C4⋊Dic13C2311yescharacteristic
229C2×C4⋊Dic13C2311yescharacteristic
230C2×C4⋊Dic13C2311yescharacteristic
231C2×C4⋊Dic13C2311yescharacteristic
232C2×C4⋊Dic13C2311yescharacteristic
233C2×C4⋊Dic13C2311yescharacteristic
234C2×C4⋊Dic13C2311yescharacteristic
235C2×C4⋊Dic13C2311yescharacteristic
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#88152—24no—
280#88146—24no—
281#88144—24no—
282#88141—24no—
283#88141—24no—
284#88130—24no—
285#88124—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
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
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
352C23×D13C2411yescharacteristic
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×C4×C13C2411yescharacteristic
371C22×Dic13C2411yescharacteristic
372C22×Dic13C2411yescharacteristic
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
386C2×C4×D13—22no—
387C2×C4×D13—22no—
388C2×C4×D13—22no—
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—22no—
397C13×C4⋊C4—41no—
398C13×C4⋊C4—41no—
399C13×C4⋊C4—41no—
400C13×C4⋊C4—41no—
401C13×C4⋊C4—41no—
402C13×C4⋊C4—41no—
403C13×C4⋊C4—41no—
404C13×C4⋊C4—41no—
405C42×C13—41no—
406C42×C13—41no—
407C42×C13#4114yes—
408#6103—22no—
409#6103—22no—
410#6103—22no—
411#6103—22no—
412#6103—22no—
413#6103—22no—
414#6103—22no—
415#6103—22no—
416#6103—41no—
417#6103—41no—
418#6103—41no—
419#6103—41no—
420#6103—41no—
421#6103—41no—
422C4⋊Dic13—22no—
423C4⋊Dic13—22no—
424C4⋊Dic13—22no—
425C4⋊Dic13—22no—
426C4⋊Dic13—22no—
427C4⋊Dic13—22no—
428C4⋊Dic13—22no—
429C4⋊Dic13—22no—
430C4⋊Dic13—22no—
431C4⋊Dic13—22no—
432C4⋊Dic13—22no—
433C4⋊Dic13—41no—
434C4⋊Dic13—41no—
435C4⋊Dic13—41no—
436C4⋊Dic13—41no—
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—22no—
448#6101—22no—
449#6101—22no—
450#6101—22no—
451#6101—22no—
452#6101—22no—
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—22no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13—41no—
478C4×Dic13#4114yes—
479C4×Dic13#4114yes—
480#2666—131no—
481#2666D1311yescharacteristic, complemented
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#2650—131no—
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×C13C2511yescharacteristic
512C22×D13—21no—
513C22×D13—21no—
514C22×D13—21no—
515C22×D13—21no—
516C22×D13—21no—
517C22×D13—21no—
518C22×D13—21no—
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×C13—21no—
560C2×C4×C13C2×#4112yes—
561C2×C4×C13C2×#4112yes—
562C2×C4×C13C2×#4112yes—
563C2×C4×C13C2×#4112yes—
564C2×C4×C13C2×#4112yes—
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—21no—
603C2×Dic13—21no—
604C2×Dic13C2×#4112yes—
605C2×Dic13C2×#4112yes—
606C2×Dic13C2×#4112yes—
607C2×Dic13C2×#4112yes—
608C2×Dic132−1+412yes—
609C2×Dic132−1+412yes—
610C4×D13—44no—
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#400—131no—
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#398C2×D1311yescharacteristic
662#398C2×D1311yescharacteristic
663#398C2×D1311yescharacteristic
664#398C2×D1311yescharacteristic
665#397—131no—
666#397—131no—
667#397—131no—
668#397—131no—
669#397—131no—
670#397—131no—
671#396—131no—
672#396—131no—
673#396—131no—
674#396—131no—
675#396—131no—
676#396—131no—
677#395—131no—
678#395—131no—
679#395—131no—
680#395—131no—
681#395C2×D1311yescharacteristic
682#395C2×D1311yescharacteristic
683#393—131no—
684#393—131no—
685#391—131no—
686#391C2×D1311yescharacteristic
687#389—131no—
688#389—131no—
689#389—131no—
690#389—131no—
691#389—131no—
692#389C2×D1311yescharacteristic
693#388—131no—
694#388—131no—
695#388—131no—
696#388—131no—
697#388—131no—
698#388—131no—
699#388—131no—
700#388—131no—
701#388—131no—
702#388—131no—
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#383C2×D1311yescharacteristic
727#382—131no—
728#382C2×D1311yescharacteristic
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×C13C22×#4111yescharacteristic
768C22×C13C22×#4111yescharacteristic
769C22×C13C22×#4111yescharacteristic
770C22×C13C2×2−1+411yescharacteristic
771C22×C13C2×2−1+411yescharacteristic
772C22×C13#58511yescharacteristic
773C22×C13#58511yescharacteristic
774C2×D13—41no—
775C2×D13—41no—
776C2×D13—41no—
777C2×D13—41no—
778C2×D13—41no—
779C2×D13—41no—
780C2×D13—41no—
781C4×C13—22no—
782C4×C13—22no—
783C4×C13—22no—
784C4×C13—22no—
785C4×C13—22no—
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—
795C4×C13—41no—
796Dic13—22no—
797Dic13—22no—
798Dic13—22no—
799Dic13—41no—
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⋊C4C22×D1311yescharacteristic
859C2×C4⋊C4C22×D1311yescharacteristic
860C2×C4⋊C4C22×D1311yescharacteristic
861C2×C4⋊C4C22×D1311yescharacteristic
862C2×C4⋊C4C22×D1311yescharacteristic
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⋊C4—131no—
879C2×C22⋊C4—131no—
880C2×C22⋊C4—131no—
881C2×C22⋊C4—131no—
882C2×C22⋊C4—131no—
883C2×C22⋊C4—131no—
884C2×C22⋊C4—131no—
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#95C22×D1311yescharacteristic
958#95C22×D1311yescharacteristic
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#344411yescharacteristic
976C2×C13C2×#54111yescharacteristic
977C2×C13#345511yescharacteristic
978C2×C13#346111yescharacteristic
979C2×C13#346111yescharacteristic
980C2×C13#346111yescharacteristic
981C2×C13#346111yescharacteristic
982D13—81no—
983C24—131no—
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—262no—
1006C22×C4—262no—
1007C22×C4—262no—
1008C22×C4C23×D1311yescharacteristic
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—22no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
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—262no—
1060C4⋊C4—262no—
1061C4⋊C4—262no—
1062C4⋊C4—262no—
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—262no—
1072C22⋊C4—262no—
1073C22⋊C4—262no—
1074C22⋊C4—262no—
1075C22⋊C4—262no—
1076C22⋊C4—262no—
1077C22⋊C4—262no—
1078C22⋊C4—262no—
1079C22⋊C4—521no—
1080C22⋊C4—521no—
1081C22⋊C4—521no—
1082C22⋊C4—521no—
1083C22⋊C4—521no—
1084C22⋊C4—521no—
1085C42—41no—
1086C42—41no—
1087C42—134no—
1088C42—134no—
1089C42—262no—
1090C42—262no—
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—521no—
1107C42—521no—
1108C42—521no—
1109C42—521no—
1110C42#613114yes—
1111C13#3460411yescharacteristic, complemented, Sylow
1112C23—261no—
1113C23—261no—
1114C23—261no—
1115C23—261no—
1116C23—261no—
1117C23—261no—
1118C23—261no—
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—21no—
1162C2×C4—132no—
1163C2×C4—132no—
1164C2×C4—132no—
1165C2×C4—132no—
1166C2×C4—132no—
1167C2×C4—132no—
1168C2×C4—261no—
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—524no—
1208C2×C4C2×#613112yes—
1209C2×C4C2×#613112yes—
1210C2×C4C2×#613112yes—
1211C2×C4#41×D1312yes—
1212C2×C4#41×D1312yes—
1213C22—521no—
1214C22—521no—
1215C22—521no—
1216C22—521no—
1217C22—521no—
1218C22—521no—
1219C22—521no—
1220C22C22×#613111yescharacteristic
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—22no—
1231C4—22no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—134no—
1243C4—262no—
1244C4—262no—
1245C4—262no—
1246C4—521no—
1247C4—521no—
1248C4—521no—
1249C4—521no—
1250C4—521no—
1251C4—521no—
1252C4—521no—
1253C4—521no—
1254C4—521no—
1255C4—521no—
1256C4—521no—
1257C2—1041no—
1258C2#1312813311yescharacteristic
1259C2D13×#54111yescharacteristic
1260C2#1312821811yescharacteristic
1261C2#1312826211yescharacteristic
1262C2#1312826611yescharacteristic
1263C2#1312827011yescharacteristic
1264C2#1312827011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2666C2
prime radicalC23×D13C24
hypercenter#2666D13
hypocenterC13#34604
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2666

Complements

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

NH ≅ G/Ntype
1. #13121022C2semidirect
4. #13120935C2semidirect
5. #13120935C2semidirect
6. #13120932C2semidirect
7. #13120928C2semidirect
14. #13120718C2semidirect
15. #13120715C2semidirect
16. #13118140C2semidirect
17. #13118140C2semidirect
18. #13118140C2semidirect
21. #13118126C2semidirect
24. #13117395C2semidirect
25. #13117391C2semidirect
29. #13117311C2semidirect
30. C4×#88141C2semidirect
31. C13×#2666C2semidirect
481. #2666D13semidirect
1111. C13#34604semidirect

Maximal subgroups

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

subgroupindex
#131210222
#131210022
#131209952
#131209352
#131209322
#131209282
#131209202
#131209132
#131208602
#131208572
#131207512
#131207462
#131207182
#131207152
#131181402
#131181352
#131181262
#131181132
#131181072
#131173952
#131173912
#131173862
#131173842
#131173282
#131173112
C4×#881412
C13×#26662
#3460413