Finite Group Databasebeta

← #16027109

Subgroups — #16027109

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719406C211yesmaximal, characteristic
2#13118018C211yesmaximal, characteristic, complemented
3#13118014C211yesmaximal, characteristic, complemented
4#13118003C211yesmaximal, characteristic
5#13117960C211yesmaximal, characteristic
6#13117954C211yesmaximal, characteristic
7#13117951C211yesmaximal, characteristic
8#13117940C211yesmaximal, characteristic, complemented
9#13117937C211yesmaximal, characteristic, complemented
10#13117929C211yesmaximal, characteristic, complemented
11#13117922C211yesmaximal, characteristic, complemented
12#13117917C211yesmaximal, characteristic
13#13117796C211yesmaximal, characteristic, complemented
14#13117795C211yesmaximal, characteristic, complemented
15#13117726C211yesmaximal, characteristic
16#13117694C211yesmaximal, characteristic
17#13117638C211yesmaximal, characteristic, complemented
18#13117637C211yesmaximal, characteristic, complemented
19#13117634C211yesmaximal, characteristic, complemented
20#13117634C211yesmaximal, characteristic, complemented
21#13117618C211yesmaximal, characteristic
22#13117612C211yesmaximal, characteristic
23#13117612C211yesmaximal, characteristic
24#13117593C211yesmaximal, characteristic
25#13117575C211yesmaximal, characteristic, complemented
26#13117567C211yesmaximal, characteristic
27#13117485C211yesmaximal, characteristic, complemented
28#13117393C211yesmaximal, characteristic, complemented
29#13117390C211yesmaximal, characteristic
30#13117307C211yesmaximal, characteristic, complemented
31C13×#2383C211yesmaximal, characteristic
32C2×C13×#126C2211yescharacteristic
33#11719406C4116yescomplemented
34C2×#88144C2211yescharacteristic
35C2×#88143C2211yescharacteristic
36C2×#88143C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×#88141C2211yescharacteristic
40C2×#88133C2211yescharacteristic
41C2×#88133C2211yescharacteristic
42C2×#88133C2211yescharacteristic
43C2×#88132C2211yescharacteristic
44C2×#88132C2211yescharacteristic
45C2×#88131C2211yescharacteristic
46C2×#88124C2211yescharacteristic
47C2×C4×Dic26C2211yescharacteristic
48C13×#389C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#388C2211yescharacteristic
52C13×#388C2211yescharacteristic
53C13×#388C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C13×#387C2211yescharacteristic
56C13×#387C2211yescharacteristic
57C13×#385C2211yescharacteristic
58C13×#385C2211yescharacteristic
59C13×#385C2211yescharacteristic
60C13×#384C2211yescharacteristic
61C13×#383C2211yescharacteristic
62#11718871C2211yescharacteristic
63C4×C22⋊Dic13C2211yescharacteristic
64C4×C22⋊Dic13C2211yescharacteristic
65C2×#88071C2211yescharacteristic
66#11718646C2211yescharacteristic
67#11718642C2211yescharacteristic
68#11718642C2211yescharacteristic
69#11718642C2211yescharacteristic
70#11718639C2211yescharacteristic
71#11718639C2211yescharacteristic
72#11718639C2211yescharacteristic
73#11718639C2211yescharacteristic
74#11718639C2211yescharacteristic
75#11718639C2211yescharacteristic
76#11718639C2211yescharacteristic
77#11718639C2211yescharacteristic
78#11718639C2211yescharacteristic
79#11718639C2211yescharacteristic
80#11718639C2211yescharacteristic
81#11718639C2211yescharacteristic
82#11718639C2211yescharacteristic
83#11718638C2211yescharacteristic
84#11718638C2211yescharacteristic
85C4⋊C4×Dic13C2211yescharacteristic
86C4⋊C4×Dic13C2211yescharacteristic
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
96#11718635C2211yescharacteristic
97#11718635C2211yescharacteristic
98#11718635C2211yescharacteristic
99#11718634C2211yescharacteristic
100#11718634C2211yescharacteristic
101#11718634C2211yescharacteristic
102#11718634C2211yescharacteristic
103#11718633C2211yescharacteristic
104#11718633C2211yescharacteristic
105#11718633C2211yescharacteristic
106#11718633C2211yescharacteristic
107#11718633C2211yescharacteristic
108#11718612C2211yescharacteristic
109#11718612C2211yescharacteristic
110#11718612C2211yescharacteristic
111#11718611C2211yescharacteristic
112#11718607C2211yescharacteristic
113#11718606C2211yescharacteristic
114#11718606C2211yescharacteristic
115#11718606C2211yescharacteristic
116#11718606C2211yescharacteristic
117#11718606C2211yescharacteristic
118#11718605C2211yescharacteristic
119#11718604C2211yescharacteristic
120#11718603C2211yescharacteristic
121C22⋊C4×Dic13C2211yescharacteristic
122C22⋊C4×Dic13C2211yescharacteristic
123C22⋊C4×Dic13C2211yescharacteristic
124C22⋊C4×Dic13C2211yescharacteristic
125C22⋊C4×Dic13C2211yescharacteristic
126C4×C4⋊Dic13C2211yescharacteristic
127C4×C4⋊Dic13C2211yescharacteristic
128C4×C4⋊Dic13C2211yescharacteristic
129#11718594C2211yescharacteristic
130#11718594C2211yescharacteristic
131#11718594C2211yescharacteristic
132#11718594C2211yescharacteristic
133#11718593C2211yescharacteristic
134C4×#6101C2211yescharacteristic
135C4×#6101C2211yescharacteristic
136C4×#6101C2211yescharacteristic
137C4×#6101C2211yescharacteristic
138C42×Dic13C2211yescharacteristic
139#11718590C2211yescharacteristic
140#11718316C2211yescharacteristic
141#11718316C2211yescharacteristic
142#11718316C2211yescharacteristic
143#11718316C2211yescharacteristic
144#11718316C2211yescharacteristic
145#11718315C2211yescharacteristic
146#11718315C2211yescharacteristic
147#11718315C2211yescharacteristic
148#11718315C2211yescharacteristic
149#11718315C2211yescharacteristic
150#11718315C2211yescharacteristic
151#11718314C2211yescharacteristic
152#11718314C2211yescharacteristic
153#11718314C2211yescharacteristic
154#11718314C2211yescharacteristic
155#11718313C2211yescharacteristic
156#11718313C2211yescharacteristic
157#11718313C2211yescharacteristic
158#11718313C2211yescharacteristic
159#11718313C2211yescharacteristic
160#11718313C2211yescharacteristic
161#11718312C2211yescharacteristic
162#11718312C2211yescharacteristic
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#11718309C2211yescharacteristic
177#11718309C2211yescharacteristic
178#11718309C2211yescharacteristic
179#11718308C2211yescharacteristic
180#11718308C2211yescharacteristic
181#11718308C2211yescharacteristic
182#11718308C2211yescharacteristic
183#11718308C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187#11718307C2211yescharacteristic
188C23×C4×C13C2311yescharacteristic
189C23×Dic13C2311yescharacteristic
190C23×Dic13C2311yescharacteristic
191C22×Dic26C2311yescharacteristic
192C22×Dic26C2311yescharacteristic
193C13×#126C2×C418yes—
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×C13×C4⋊C4C2311yescharacteristic
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C4⋊C4C2311yescharacteristic
206C2×C13×C22⋊C4C2311yescharacteristic
207C2×C13×C22⋊C4C2311yescharacteristic
208C2×C13×C22⋊C4C2311yescharacteristic
209C2×C13×C22⋊C4C2311yescharacteristic
210C2×C13×C22⋊C4C2311yescharacteristic
211C2×C13×C22⋊C4C2311yescharacteristic
212C2×C42×C13C2311yescharacteristic
213C2×C42×C13C2311yescharacteristic
214C2×C42×C13C2311yescharacteristic
215C2×C42×C13C2311yescharacteristic
216C2×C22⋊Dic13C2311yescharacteristic
217C2×C22⋊Dic13C2311yescharacteristic
218C2×C22⋊Dic13C2311yescharacteristic
219C2×C22⋊Dic13C2311yescharacteristic
220C2×C22⋊Dic13C2311yescharacteristic
221C2×C22⋊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×#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
279C2×C4×Dic13C2311yescharacteristic
280C2×C4×Dic13C2311yescharacteristic
281C2×C4×Dic13C2311yescharacteristic
282C2×C4×Dic13C2311yescharacteristic
283C2×C4×Dic13C2311yescharacteristic
284#88144C2×C418yescomplemented
285#88143C2×C418yescomplemented
286#88143C2×C418yescomplemented
287#88143C2×C418yescomplemented
288#88142C2×C418yescomplemented
289#88141C2×C418yescomplemented
290#88133C2×C418yes—
291#88133C2×C418yes—
292#88133C2×C418yes—
293#88132C2×C418yes—
294#88132C2×C418yes—
295#88131C2×C418yes—
296#88124C2×C418yescomplemented
297C4×Dic26C2×C418yescomplemented
298C13×#95C2311yescharacteristic
299C13×#95C2311yescharacteristic
300C13×#95C2311yescharacteristic
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
305C13×#95C2311yescharacteristic
306C13×#95C2311yescharacteristic
307C13×#95C2311yescharacteristic
308C13×#95C2311yescharacteristic
309C13×#95C2311yescharacteristic
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#88071C2311yescharacteristic
352#88071C2311yescharacteristic
353#88071C2311yescharacteristic
354#88071C2311yescharacteristic
355#88071C2311yescharacteristic
356#88071C2311yescharacteristic
357#88071C2311yescharacteristic
358#34445—131nomaximal, Sylow
359C24×C13C2411yescharacteristic
360C22×C4×C13—41no—
361C22×C4×C13—41no—
362C22×C4×C13—41no—
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×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
374C22×C4×C13C2411yescharacteristic
375C22×C4×C13C2411yescharacteristic
376C22×C4×C13C2411yescharacteristic
377C22×Dic13—22no—
378C22×Dic13—41no—
379C22×Dic13—41no—
380C22×Dic13—41no—
381C22×Dic13—41no—
382C22×Dic13C22×C414yes—
383C22×Dic13C2411yescharacteristic
384C22×Dic13C2411yescharacteristic
385C22×Dic13C2411yescharacteristic
386C22×Dic13C2411yescharacteristic
387C22×Dic13C2411yescharacteristic
388C22×Dic13C2411yescharacteristic
389C22×Dic13C2411yescharacteristic
390C22×Dic13C2411yescharacteristic
391C22×Dic13C2411yescharacteristic
392C22×Dic13C2411yescharacteristic
393C22×Dic13C2411yescharacteristic
394C22×Dic13C2411yescharacteristic
395C22×Dic13C2411yescharacteristic
396C22×Dic13C2411yescharacteristic
397C22×Dic13C2411yescharacteristic
398C22×Dic13C2411yescharacteristic
399C2×Dic26—41no—
400C2×Dic26—41no—
401C2×Dic26—41no—
402C2×Dic26—41no—
403C2×Dic26C22×C414yes—
404C2×Dic26C22×C414yes—
405C13×C4⋊C4—41no—
406C13×C4⋊C4—41no—
407C13×C4⋊C4—41no—
408C13×C4⋊C4—41no—
409C13×C4⋊C4—41no—
410C13×C4⋊C4—41no—
411C13×C4⋊C4—41no—
412C13×C4⋊C4—41no—
413C13×C4⋊C4—41no—
414C13×C4⋊C4C22×C414yes—
415C13×C4⋊C4C22×C414yes—
416C13×C4⋊C4C22×C414yes—
417C13×C22⋊C4—41no—
418C13×C22⋊C4—41no—
419C13×C22⋊C4—41no—
420C13×C22⋊C4C22×C414yes—
421C13×C22⋊C4C22×C414yes—
422C13×C22⋊C4C22×C414yes—
423C42×C13—41no—
424C42×C13—41no—
425C42×C13—41no—
426C42×C13C22×C414yes—
427C22⋊Dic13—22no—
428C22⋊Dic13—41no—
429C22⋊Dic13—41no—
430C22⋊Dic13C22×C414yes—
431C22⋊Dic13C22×C414yes—
432C22⋊Dic13C22×C414yes—
433C4⋊Dic13—22no—
434C4⋊Dic13—22no—
435C4⋊Dic13—22no—
436C4⋊Dic13—41no—
437C4⋊Dic13—41no—
438C4⋊Dic13C22×C414yes—
439C4⋊Dic13C22×C414yes—
440C4⋊Dic13C22×C414yes—
441C4⋊Dic13C22×C414yes—
442C4⋊Dic13C22×C414yes—
443#6101—22no—
444#6101—22no—
445#6101—41no—
446#6101—41no—
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#6101C22×C414yes—
456#6101C22×C414yes—
457#6101C22×C414yes—
458#6101C22×C414yes—
459#6101C22×C414yes—
460#6101C22×C414yes—
461#6101C22×C414yes—
462#6101C22×C414yes—
463#6101C22×C414yes—
464#6101C22×C414yes—
465#6101C22×C414yes—
466#6101C22×C414yes—
467C4×Dic13—22no—
468C4×Dic13—22no—
469C4×Dic13—22no—
470C4×Dic13—41no—
471C4×Dic13—41no—
472C4×Dic13—41no—
473C4×Dic13—41no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13—41no—
478C4×Dic13—41no—
479C4×Dic13—41no—
480C4×Dic13—41no—
481C4×Dic13—41no—
482C4×Dic13—41no—
483C4×Dic13—41no—
484C4×Dic13—41no—
485C4×Dic13—41no—
486C4×Dic13—41no—
487C4×Dic13—41no—
488C4×Dic13—41no—
489C4×Dic13—41no—
490C4×Dic13C22×C414yes—
491C4×Dic13C22×C414yes—
492C4×Dic13C22×C414yes—
493C4×Dic13C22×C414yes—
494C4×Dic13C22×C414yes—
495C2×#541—131no—
496#2383D1311yescharacteristic
497#2382—131no—
498#2381—131no—
499#2378—131no—
500#2373—131no—
501#2373—131no—
502#2373—131no—
503#2371—131no—
504#2370—131no—
505#2370—131no—
506#2369—131no—
507#2368—131no—
508#2356—131no—
509#2355—131no—
510#2347—131no—
511#2343—131no—
512#2336—131no—
513#2336—131no—
514#2336—131no—
515#2336—131no—
516#2334—131no—
517#2334—131no—
518#2334—131no—
519#2332—131no—
520#2330—131no—
521#2329—131no—
522#2320—131no—
523C4×#125—131no—
524C4×#126—131no—
525#2295—131no—
526C23×C13—21no—
527C23×C13—21no—
528C23×C13—21no—
529C23×C13—21no—
530C23×C13—21no—
531C23×C13—21no—
532C23×C13C23×C412yes—
533C23×C13C2511yescharacteristic
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×C13—21no—
561C2×C4×C13—21no—
562C2×C4×C13—21no—
563C2×C4×C13—21no—
564C2×C4×C13—21no—
565C2×C4×C13—21no—
566C2×C4×C13—21no—
567C2×C4×C13—21no—
568C2×C4×C13—21no—
569C2×C4×C13—21no—
570C2×C4×C13—82no—
571C2×C4×C13C23×C412yes—
572C2×C4×C13C23×C412yes—
573C2×C4×C13C23×C412yes—
574C2×C4×C13C23×C412yes—
575C2×C4×C13C23×C412yes—
576C2×C4×C13C23×C412yes—
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×Dic13—21no—
605C2×Dic13—21no—
606C2×Dic13—21no—
607C2×Dic13—21no—
608C2×Dic13—21no—
609C2×Dic13—21no—
610C2×Dic13—21no—
611C2×Dic13—21no—
612C2×Dic13—21no—
613C2×Dic13—21no—
614C2×Dic13—21no—
615C2×Dic13—44no—
616C2×Dic13—82no—
617C2×Dic13C23×C412yes—
618C2×Dic13C23×C412yes—
619C2×Dic13C23×C412yes—
620C2×Dic13C23×C412yes—
621C2×Dic13C23×C412yes—
622C2×Dic13C23×C412yes—
623C2×Dic13C23×C412yes—
624C2×Dic13C23×C412yes—
625C2×Dic132−1+412yes—
626C2×Dic132−1+412yes—
627Dic26—44no—
628Dic26—44no—
629#541—1316no—
630C2×C4⋊Q8—131no—
631C2×#126—131no—
632C2×#126—131no—
633C2×#126—131no—
634C2×#126C2×D1311yescharacteristic
635C2×#125—131no—
636C2×#125—131no—
637C2×#125—131no—
638C2×#125—131no—
639C2×#125—131no—
640C2×C22⋊Q8—131no—
641C2×C22⋊Q8—131no—
642C2×C4×Q8—131no—
643C2×C4×Q8—131no—
644C2×#117—131no—
645#391—131no—
646#391—131no—
647#391—131no—
648#391—131no—
649#391—131no—
650#391—131no—
651#391—131no—
652#391—131no—
653#389—131no—
654#389—131no—
655#389—131no—
656#389—131no—
657#389—131no—
658#389—131no—
659#389—131no—
660#389—131no—
661#389—131no—
662#389—131no—
663#389—131no—
664#389—131no—
665#389—131no—
666#389—131no—
667#389—131no—
668#389C2×D1311yescharacteristic
669#389C2×D1311yescharacteristic
670#389C2×D1311yescharacteristic
671#388—131no—
672#388—131no—
673#388—131no—
674#388—131no—
675#388—131no—
676#388—131no—
677#388—131no—
678#388—131no—
679#388—131no—
680#388C2×D1311yescharacteristic
681#388C2×D1311yescharacteristic
682#388C2×D1311yescharacteristic
683#387—131no—
684#387—131no—
685#387—131no—
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#387—131no—
697#387—131no—
698#387—131no—
699#387—131no—
700#387—131no—
701#387—131no—
702#387—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#387—131no—
724#387C2×D1311yescharacteristic
725#387C2×D1311yescharacteristic
726#387C2×D1311yescharacteristic
727#385—131no—
728#385—131no—
729#385—131no—
730#385C2×D1311yescharacteristic
731#385C2×D1311yescharacteristic
732#385C2×D1311yescharacteristic
733#384C2×D1311yescharacteristic
734#383—131no—
735#383—131no—
736#383—131no—
737#383—131no—
738#383C2×D1311yescharacteristic
739#382—131no—
740#382—131no—
741#382—131no—
742#382—131no—
743#381—131no—
744#380—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⋊C4—131no—
755C4×C4⋊C4—131no—
756C4×C4⋊C4—131no—
757C4×C4⋊C4—131no—
758C4×C4⋊C4—131no—
759C4×C4⋊C4—131no—
760C4×C4⋊C4—131no—
761C4×C4⋊C4—131no—
762C4×C4⋊C4—131no—
763C4×C4⋊C4—131no—
764C4×C4⋊C4—131no—
765C4×C4⋊C4—131no—
766C4×C4⋊C4—131no—
767C4×C4⋊C4—131no—
768C4×C4⋊C4—131no—
769C4×C4⋊C4—131no—
770C4×C4⋊C4—131no—
771C4×C4⋊C4—131no—
772C4×C22⋊C4—131no—
773C4×C22⋊C4—131no—
774C4×C22⋊C4—131no—
775C4×C22⋊C4—131no—
776C4×C22⋊C4—131no—
777C4×C22⋊C4—131no—
778C4×C22⋊C4—131no—
779#376—131no—
780#376—131no—
781#376—131no—
782#376—131no—
783C2×#95—131no—
784C43—131no—
785C22×C13—22no—
786C22×C13—22no—
787C22×C13—22no—
788C22×C13—41no—
789C22×C13—41no—
790C22×C13—41no—
791C22×C13—41no—
792C22×C13C24×C411yescharacteristic
793C22×C13C2×2−1+411yescharacteristic
794C22×C13C2×2−1+411yescharacteristic
795C22×C13#58511yescharacteristic
796C22×C13#58511yescharacteristic
797C22×C13#58511yescharacteristic
798C22×C13#58511yescharacteristic
799C4×C13—22no—
800C4×C13—22no—
801C4×C13—22no—
802C4×C13—22no—
803C4×C13—22no—
804C4×C13—22no—
805C4×C13—41no—
806C4×C13—41no—
807C4×C13—41no—
808C4×C13—41no—
809C4×C13—41no—
810C4×C13—41no—
811C4×C13—41no—
812C4×C13—41no—
813Dic13—22no—
814Dic13—22no—
815Dic13—22no—
816Dic13—22no—
817Dic13—22no—
818Dic13—22no—
819Dic13—22no—
820Dic13—22no—
821Dic13—22no—
822Dic13—22no—
823Dic13—41no—
824Dic13—41no—
825Dic13—41no—
826Dic13—41no—
827Dic13—41no—
828Dic13—41no—
829C22×Q8—131no—
830C22×Q8—131no—
831C23×C4—131no—
832C23×C4—131no—
833C23×C4C22×D1311yescharacteristic
834C4⋊Q8—138no—
835#126—138no—
836#126—138no—
837#126—138no—
838#126C4×D1318yes—
839#125—138no—
840#125—138no—
841#125—138no—
842#125—138no—
843#125—138no—
844C22⋊Q8—138no—
845C22⋊Q8—138no—
846C4×Q8—138no—
847C4×Q8—138no—
848#117—138no—
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⋊C4—131no—
864C2×C4⋊C4—131no—
865C2×C4⋊C4—131no—
866C2×C4⋊C4—131no—
867C2×C4⋊C4—131no—
868C2×C4⋊C4—131no—
869C2×C4⋊C4—131no—
870C2×C4⋊C4—131no—
871C2×C4⋊C4—131no—
872C2×C4⋊C4—131no—
873C2×C4⋊C4—131no—
874C2×C4⋊C4—131no—
875C2×C4⋊C4—131no—
876C2×C4⋊C4—131no—
877C2×C4⋊C4—131no—
878C2×C4⋊C4—131no—
879C2×C4⋊C4—131no—
880C2×C4⋊C4—131no—
881C2×C4⋊C4—131no—
882C2×C4⋊C4—131no—
883C2×C4⋊C4C22×D1311yescharacteristic
884C2×C4⋊C4C22×D1311yescharacteristic
885C2×C4⋊C4C22×D1311yescharacteristic
886C2×C4⋊C4C22×D1311yescharacteristic
887C2×C4⋊C4C22×D1311yescharacteristic
888C2×C4⋊C4C22×D1311yescharacteristic
889C2×C4⋊C4C22×D1311yescharacteristic
890C2×C4⋊C4C22×D1311yescharacteristic
891C2×C4⋊C4C22×D1311yescharacteristic
892C2×C4⋊C4C22×D1311yescharacteristic
893C2×C4⋊C4C22×D1311yescharacteristic
894C2×C4⋊C4C22×D1311yescharacteristic
895C2×C22⋊C4—131no—
896C2×C22⋊C4—131no—
897C2×C22⋊C4—131no—
898C2×C22⋊C4—131no—
899C2×C22⋊C4—131no—
900C2×C22⋊C4—131no—
901C2×C22⋊C4C22×D1311yescharacteristic
902C2×C22⋊C4C22×D1311yescharacteristic
903C2×C22⋊C4C22×D1311yescharacteristic
904C2×C22⋊C4C22×D1311yescharacteristic
905C2×C22⋊C4C22×D1311yescharacteristic
906C2×C22⋊C4C22×D1311yescharacteristic
907C2×C42—131no—
908C2×C42—131no—
909C2×C42—131no—
910C2×C42—131no—
911C2×C42—131no—
912C2×C42—131no—
913C2×C42—131no—
914C2×C42—131no—
915C2×C42—131no—
916C2×C42—131no—
917C2×C42—131no—
918C2×C42—131no—
919C2×C42—131no—
920C2×C42—131no—
921C2×C42—131no—
922C2×C42—131no—
923C2×C42—131no—
924C2×C42—131no—
925C2×C42—131no—
926C2×C42—131no—
927C2×C42—131no—
928C2×C42—131no—
929C2×C42—131no—
930C2×C42—131no—
931C2×C42—131no—
932C2×C42—131no—
933C2×C42—131no—
934C2×C42—131no—
935C2×C42C22×D1311yescharacteristic
936C2×C42C22×D1311yescharacteristic
937C2×C42C22×D1311yescharacteristic
938C2×C42C22×D1311yescharacteristic
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#95—131no—
960#95—131no—
961#95—131no—
962#95—131no—
963#95—131no—
964#95—131no—
965#95—131no—
966#95—131no—
967#95—131no—
968#95—131no—
969#95—131no—
970#95—131no—
971#95—131no—
972#95—131no—
973#95—131no—
974#95—131no—
975#95—131no—
976#95—131no—
977#95—131no—
978#95—131no—
979#95—131no—
980#95—131no—
981#95—131no—
982#95—131no—
983#95—131no—
984#95—131no—
985#95—131no—
986#95—131no—
987#95C22×D1311yescharacteristic
988#95C22×D1311yescharacteristic
989#95C22×D1311yescharacteristic
990#95C22×D1311yescharacteristic
991#95C22×D1311yescharacteristic
992#95C22×D1311yescharacteristic
993#95C22×D1311yescharacteristic
994#95C22×D1311yescharacteristic
995#95C22×D1311yescharacteristic
996#95C22×D1311yescharacteristic
997#95C22×D1311yescharacteristic
998#95C22×D1311yescharacteristic
999C2×C13—42no—
1000C2×C13#342811yescharacteristic
1001C2×C13C4×2−1+411yescharacteristic
1002C2×C13C4×2−1+411yescharacteristic
1003C2×C13#355311yescharacteristic
1004C2×C13#355511yescharacteristic
1005C2×C13#356411yescharacteristic
1006C2×C13#356611yescharacteristic
1007C24C23×D1311yescharacteristic
1008C2×Q8—134no—
1009C2×Q8—134no—
1010C2×Q8—521no—
1011C2×Q8—521no—
1012C2×Q8—521no—
1013C2×Q8—521no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—131no—
1018C22×C4—131no—
1019C22×C4—131no—
1020C22×C4—131no—
1021C22×C4—131no—
1022C22×C4—131no—
1023C22×C4—131no—
1024C22×C4—131no—
1025C22×C4—131no—
1026C22×C4—131no—
1027C22×C4—134no—
1028C22×C4—131no—
1029C22×C4—131no—
1030C22×C4—131no—
1031C22×C4—131no—
1032C22×C4—131no—
1033C22×C4—131no—
1034C22×C4—262no—
1035C22×C4—521no—
1036C22×C4—521no—
1037C22×C4—521no—
1038C22×C4—521no—
1039C22×C4C23×D1311yescharacteristic
1040C22×C4C23×D1311yescharacteristic
1041C22×C4C23×D1311yescharacteristic
1042C22×C4C23×D1311yescharacteristic
1043C22×C4C23×D1311yescharacteristic
1044C22×C4C23×D1311yescharacteristic
1045C22×C4C23×D1311yescharacteristic
1046C22×C4C23×D1311yescharacteristic
1047C22×C4C23×D1311yescharacteristic
1048C22×C4C23×D1311yescharacteristic
1049C22×C4C23×D1311yescharacteristic
1050C22×C4C23×D1311yescharacteristic
1051C22×C4C23×D1311yescharacteristic
1052C22×C4C23×D1311yescharacteristic
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
1059C4⋊C4—41no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—134no—
1063C4⋊C4—134no—
1064C4⋊C4—134no—
1065C4⋊C4—134no—
1066C4⋊C4—134no—
1067C4⋊C4—134no—
1068C4⋊C4—134no—
1069C4⋊C4—134no—
1070C4⋊C4—134no—
1071C4⋊C4—134no—
1072C4⋊C4—134no—
1073C4⋊C4—134no—
1074C4⋊C4—134no—
1075C4⋊C4—134no—
1076C4⋊C4—134no—
1077C4⋊C4—134no—
1078C4⋊C4—134no—
1079C4⋊C4—262no—
1080C4⋊C4—262no—
1081C4⋊C4—262no—
1082C4⋊C4—262no—
1083C4⋊C4—262no—
1084C4⋊C4—521no—
1085C4⋊C4—521no—
1086C4⋊C4—521no—
1087C4⋊C4—521no—
1088C4⋊C4—521no—
1089C4⋊C4—521no—
1090C4⋊C4—521no—
1091C4⋊C4—521no—
1092C4⋊C4—521no—
1093C4⋊C4—521no—
1094C4⋊C4—521no—
1095C4⋊C4—521no—
1096C4⋊C4C2×C4×D1314yes—
1097C4⋊C4C2×C4×D1314yes—
1098C4⋊C4C2×C4×D1314yes—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—134no—
1103C22⋊C4—134no—
1104C22⋊C4—134no—
1105C22⋊C4—262no—
1106C22⋊C4—521no—
1107C22⋊C4—521no—
1108C22⋊C4C2×C4×D1314yes—
1109C22⋊C4C2×C4×D1314yes—
1110C22⋊C4C2×C4×D1314yes—
1111C42—41no—
1112C42—41no—
1113C42—41no—
1114C42—134no—
1115C42—134no—
1116C42—134no—
1117C42—134no—
1118C42—134no—
1119C42—262no—
1120C42—262no—
1121C42—262no—
1122C42—521no—
1123C42—521no—
1124C42—521no—
1125C42—521no—
1126C42—521no—
1127C42—521no—
1128C42—521no—
1129C42—521no—
1130C42—521no—
1131C42—521no—
1132C42—521no—
1133C42—521no—
1134C42—521no—
1135C42—521no—
1136C42—521no—
1137C42—521no—
1138C42—521no—
1139C42—521no—
1140C42—521no—
1141C42—521no—
1142C42C2×C4×D1314yes—
1143C13#3444511yescharacteristic, complemented, Sylow
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23C22×C4×D1312yes—
1151C23C24×D1311yescharacteristic
1152Q8—524no—
1153Q8—524no—
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—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—82no—
1191C2×C4—132no—
1192C2×C4—132no—
1193C2×C4—132no—
1194C2×C4—132no—
1195C2×C4—132no—
1196C2×C4—132no—
1197C2×C4—132no—
1198C2×C4—132no—
1199C2×C4—132no—
1200C2×C4—132no—
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—261no—
1210C2×C4—261no—
1211C2×C4—261no—
1212C2×C4—261no—
1213C2×C4—261no—
1214C2×C4—261no—
1215C2×C4—261no—
1216C2×C4—261no—
1217C2×C4—261no—
1218C2×C4—261no—
1219C2×C4—261no—
1220C2×C4—261no—
1221C2×C4—261no—
1222C2×C4—261no—
1223C2×C4—261no—
1224C2×C4—261no—
1225C2×C4—261no—
1226C2×C4—261no—
1227C2×C4—261no—
1228C2×C4—261no—
1229C2×C4—261no—
1230C2×C4—261no—
1231C2×C4—261no—
1232C2×C4—261no—
1233C2×C4—261no—
1234C2×C4—261no—
1235C2×C4—261no—
1236C2×C4—261no—
1237C2×C4—261no—
1238C2×C4—261no—
1239C2×C4—524no—
1240C2×C4—1042no—
1241C2×C4C22×C4×D1312yes—
1242C2×C4C22×C4×D1312yes—
1243C2×C4C22×C4×D1312yes—
1244C2×C4C22×C4×D1312yes—
1245C2×C4C22×C4×D1312yes—
1246C2×C4C22×C4×D1312yes—
1247C22—22no—
1248C22—22no—
1249C22—22no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22C23×C4×D1311yescharacteristic
1255C22#1171965011yescharacteristic
1256C22#1171965011yescharacteristic
1257C22#1171965011yescharacteristic
1258C22D13×2−1+411yescharacteristic
1259C22D13×2−1+411yescharacteristic
1260C22#1171965211yescharacteristic
1261C4—22no—
1262C4—22no—
1263C4—22no—
1264C4—22no—
1265C4—22no—
1266C4—22no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—262no—
1276C4—262no—
1277C4—262no—
1278C4—262no—
1279C4—262no—
1280C4—262no—
1281C4—262no—
1282C4—262no—
1283C4—262no—
1284C4—262no—
1285C4—521no—
1286C4—521no—
1287C4—521no—
1288C4—521no—
1289C4—521no—
1290C4—521no—
1291C2—42no—
1292C2#1312803611yescharacteristic
1293C2#1312804711yescharacteristic
1294C2#1312804711yescharacteristic
1295C2#1312928711yescharacteristic
1296C2#1312931511yescharacteristic
1297C2#1312945111yescharacteristic
1298C2#1312949311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2383C2
socle, cosocleC23×C13C25
prime radicalC24×C13C24
hypercenter#2383D13
hypocenterC13#34445
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2383

Complements

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

NH ≅ G/Ntype
2. #13118018C2semidirect
3. #13118014C2semidirect
8. #13117940C2semidirect
9. #13117937C2semidirect
10. #13117929C2semidirect
11. #13117922C2semidirect
13. #13117796C2semidirect
14. #13117795C2semidirect
17. #13117638C2semidirect
18. #13117637C2semidirect
19. #13117634C2semidirect
20. #13117634C2semidirect
25. #13117575C2semidirect
27. #13117485C2semidirect
28. #13117393C2semidirect
30. #13117307C2semidirect
33. #11719406C4semidirect
284. #88144C2×C4semidirect
285. #88143C2×C4semidirect
286. #88143C2×C4semidirect
287. #88143C2×C4semidirect
288. #88142C2×C4semidirect
289. #88141C2×C4semidirect
296. #88124C2×C4semidirect
297. C4×Dic26C2×C4semidirect
1143. C13#34445semidirect

Maximal subgroups

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

subgroupindex
C2×#117194062
#131180182
#131180142
#131180032
#131179602
#131179542
#131179512
#131179402
#131179372
#131179292
#131179222
#131179172
#131177962
#131177952
#131177262
#131176942
#131176382
#131176372
#131176342
#131176182
#131176122
#131175932
#131175752
#131175672
#131174852
#131173932
#131173902
#131173072
C13×#23832
#3444513