Finite Group Databasebeta

← #16034630

Subgroups — #16034630

Order 3328.

1692 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#13120306C211yesmaximal, characteristic
2#13120298C211yesmaximal, characteristic
3#13120276C211yesmaximal, characteristic
4#13120268C211yesmaximal, characteristic
5#13120218C211yesmaximal, characteristic
6#13120197C211yesmaximal, characteristic
7#13120022C211yesmaximal, characteristic
8#13119852C211yesmaximal, characteristic
9#13119526C211yesmaximal, characteristic
10#13119524C211yesmaximal, characteristic
11#13119371C211yesmaximal, characteristic
12#13119351C211yesmaximal, characteristic
13#13118812C211yesmaximal, characteristic
14#13118694C211yesmaximal, characteristic
15#13118674C211yesmaximal, characteristic
16#13118140C211yesmaximal, characteristic
17#13118140C211yesmaximal, characteristic
18#13118126C211yesmaximal, characteristic
19#13118126C211yesmaximal, characteristic
20#13117407C211yesmaximal, characteristic
21#125×Dic13C211yesmaximal, characteristic
22#13117393C211yesmaximal, characteristic
23#13117393C211yesmaximal, characteristic
24#13117393C211yesmaximal, characteristic
25#13117309C211yesmaximal, characteristic
26#13117309C211yesmaximal, characteristic
27#13117309C211yesmaximal, characteristic
28#13117307C211yesmaximal, characteristic
29C4×Q8×Dic13C211yesmaximal, characteristic
30C4×#88141C211yesmaximal, characteristic
31C13×#2462C211yesmaximal, characteristic
32C2×C13×#125C2211yescharacteristic
33C2×C4×Q8×C13C2211yescharacteristic
34C2×Q8×Dic13C2211yescharacteristic
35C2×Q8×Dic13C2211yescharacteristic
36C2×#88143C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88143C2211yescharacteristic
39C2×#88142C2211yescharacteristic
40C2×#88141C2211yescharacteristic
41C2×#88141C2211yescharacteristic
42C2×#88141C2211yescharacteristic
43C2×#88141C2211yescharacteristic
44C2×C4×Dic26C2211yescharacteristic
45C13×#398C2211yescharacteristic
46C13×#398C2211yescharacteristic
47C13×#395C2211yescharacteristic
48C13×#395C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C13×#387C2211yescharacteristic
56C13×#387C2211yescharacteristic
57C4×C13×C4⋊C4C2211yescharacteristic
58#11718890C2211yescharacteristic
59#11718890C2211yescharacteristic
60#11718647C2211yescharacteristic
61#11718647C2211yescharacteristic
62#11718646C2211yescharacteristic
63#11718646C2211yescharacteristic
64#11718646C2211yescharacteristic
65#11718645C2211yescharacteristic
66#11718645C2211yescharacteristic
67#11718645C2211yescharacteristic
68#11718645C2211yescharacteristic
69#11718645C2211yescharacteristic
70#11718645C2211yescharacteristic
71#11718644C2211yescharacteristic
72#11718644C2211yescharacteristic
73#11718644C2211yescharacteristic
74#11718644C2211yescharacteristic
75#11718643C2211yescharacteristic
76#11718643C2211yescharacteristic
77#11718642C2211yescharacteristic
78#11718642C2211yescharacteristic
79#11718642C2211yescharacteristic
80#11718642C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718642C2211yescharacteristic
84#11718639C2211yescharacteristic
85#11718639C2211yescharacteristic
86#11718637C2211yescharacteristic
87C4⋊C4×Dic13C2211yescharacteristic
88C4⋊C4×Dic13C2211yescharacteristic
89C4⋊C4×Dic13C2211yescharacteristic
90C4⋊C4×Dic13C2211yescharacteristic
91C4⋊C4×Dic13C2211yescharacteristic
92C4⋊C4×Dic13C2211yescharacteristic
93C4⋊C4×Dic13C2211yescharacteristic
94C4⋊C4×Dic13C2211yescharacteristic
95C4⋊C4×Dic13C2211yescharacteristic
96C4⋊C4×Dic13C2211yescharacteristic
97C4⋊C4×Dic13C2211yescharacteristic
98C4⋊C4×Dic13C2211yescharacteristic
99C4⋊C4×Dic13C2211yescharacteristic
100C4⋊C4×Dic13C2211yescharacteristic
101C4⋊C4×Dic13C2211yescharacteristic
102C4⋊C4×Dic13C2211yescharacteristic
103#11718635C2211yescharacteristic
104#11718633C2211yescharacteristic
105#11718633C2211yescharacteristic
106#11718633C2211yescharacteristic
107#11718633C2211yescharacteristic
108#11718633C2211yescharacteristic
109#11718633C2211yescharacteristic
110#11718633C2211yescharacteristic
111#11718633C2211yescharacteristic
112#11718597C2211yescharacteristic
113C4×C4⋊Dic13C2211yescharacteristic
114C4×C4⋊Dic13C2211yescharacteristic
115C4×C4⋊Dic13C2211yescharacteristic
116#11718594C2211yescharacteristic
117#11718594C2211yescharacteristic
118#11718594C2211yescharacteristic
119#11718594C2211yescharacteristic
120#11718594C2211yescharacteristic
121#11718594C2211yescharacteristic
122C4×#6101C2211yescharacteristic
123C4×#6101C2211yescharacteristic
124C42×Dic13C2211yescharacteristic
125C42×Dic13C2211yescharacteristic
126C42×Dic13C2211yescharacteristic
127C42×Dic13C2211yescharacteristic
128C42×Dic13C2211yescharacteristic
129#11718590C2211yescharacteristic
130#11718589C2211yescharacteristic
131#11718322C2211yescharacteristic
132#11718322C2211yescharacteristic
133#11718322C2211yescharacteristic
134#11718322C2211yescharacteristic
135#11718321C2211yescharacteristic
136#11718321C2211yescharacteristic
137#11718320C2211yescharacteristic
138#11718320C2211yescharacteristic
139#11718317C2211yescharacteristic
140#11718317C2211yescharacteristic
141#11718317C2211yescharacteristic
142#11718317C2211yescharacteristic
143#11718316C2211yescharacteristic
144#11718316C2211yescharacteristic
145#11718316C2211yescharacteristic
146#11718316C2211yescharacteristic
147#11718316C2211yescharacteristic
148#11718315C2211yescharacteristic
149#11718315C2211yescharacteristic
150#11718315C2211yescharacteristic
151#11718313C2211yescharacteristic
152#11718313C2211yescharacteristic
153#11718313C2211yescharacteristic
154#11718311C2211yescharacteristic
155#11718311C2211yescharacteristic
156#11718311C2211yescharacteristic
157#11718310C2211yescharacteristic
158#11718310C2211yescharacteristic
159#11718310C2211yescharacteristic
160#11718310C2211yescharacteristic
161#11718310C2211yescharacteristic
162#11718310C2211yescharacteristic
163#11718310C2211yescharacteristic
164#11718310C2211yescharacteristic
165#11718310C2211yescharacteristic
166#11718310C2211yescharacteristic
167#11718310C2211yescharacteristic
168#11718310C2211yescharacteristic
169#11718309C2211yescharacteristic
170#11718309C2211yescharacteristic
171#11718309C2211yescharacteristic
172#11718309C2211yescharacteristic
173#11718308C2211yescharacteristic
174#11718308C2211yescharacteristic
175#11718308C2211yescharacteristic
176#11718308C2211yescharacteristic
177#11718308C2211yescharacteristic
178#11718308C2211yescharacteristic
179#11718307C2211yescharacteristic
180#11718307C2211yescharacteristic
181#11718307C2211yescharacteristic
182#11718307C2211yescharacteristic
183#11718307C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C22×Q8×C13C2311yescharacteristic
188C22×Dic26C2311yescharacteristic
189C22×Dic26C2311yescharacteristic
190C22×Dic26C2311yescharacteristic
191C13×#125—24no—
192C4×Q8×C13—24no—
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×C13×C4⋊C4C2311yescharacteristic
204C2×C13×C4⋊C4C2311yescharacteristic
205C2×C13×C4⋊C4C2311yescharacteristic
206C2×C13×C4⋊C4C2311yescharacteristic
207C2×C13×C4⋊C4C2311yescharacteristic
208C2×C42×C13C2311yescharacteristic
209C2×C42×C13C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C42×C13C2311yescharacteristic
213Q8×Dic13—24no—
214Q8×Dic13—24no—
215C2×C4⋊Dic13C2311yescharacteristic
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×C4⋊Dic13C2311yescharacteristic
227C2×C4⋊Dic13C2311yescharacteristic
228C2×C4⋊Dic13C2311yescharacteristic
229C2×C4⋊Dic13C2311yescharacteristic
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
279C2×C4×Dic13C2311yescharacteristic
280C2×C4×Dic13C2311yescharacteristic
281C2×C4×Dic13C2311yescharacteristic
282C2×C4×Dic13C2311yescharacteristic
283C2×C4×Dic13C2311yescharacteristic
284C2×C4×Dic13C2311yescharacteristic
285C2×C4×Dic13C2311yescharacteristic
286#88143—24no—
287#88143—24no—
288#88143—24no—
289#88142—24no—
290#88141—24no—
291#88141—24no—
292#88141—24no—
293#88141Q818yescomplemented
294C4×Dic26—24no—
295C13×#95C2311yescharacteristic
296C13×#95C2311yescharacteristic
297C13×#95C2311yescharacteristic
298C13×#95C2311yescharacteristic
299C13×#95C2311yescharacteristic
300C13×#95C2311yescharacteristic
301C13×#95C2311yescharacteristic
302C13×#95C2311yescharacteristic
303C13×#95C2311yescharacteristic
304C13×#95C2311yescharacteristic
305C13×#95C2311yescharacteristic
306C13×#95C2311yescharacteristic
307C13×#95C2311yescharacteristic
308C13×#95C2311yescharacteristic
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#88071C2311yescharacteristic
352#88071C2311yescharacteristic
353#88071C2311yescharacteristic
354#88071C2311yescharacteristic
355#34920—131nomaximal, Sylow
356C2×Q8×C13—22no—
357C2×Q8×C13—22no—
358C2×Q8×C13—22no—
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×C4×C13C2411yescharacteristic
372C22×C4×C13C2411yescharacteristic
373C22×C4×C13C2411yescharacteristic
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
389C22×Dic13C2411yescharacteristic
390C2×Dic26—22no—
391C2×Dic26—22no—
392C2×Dic26—22no—
393C2×Dic26—22no—
394C2×Dic26—22no—
395C2×Dic26—22no—
396C2×Dic26—41no—
397C2×Dic26—41no—
398C2×Dic26C2×Q814yes—
399C13×C4⋊C4—22no—
400C13×C4⋊C4—22no—
401C13×C4⋊C4—22no—
402C13×C4⋊C4—22no—
403C13×C4⋊C4—22no—
404C13×C4⋊C4—22no—
405C13×C4⋊C4—22no—
406C13×C4⋊C4—22no—
407C13×C4⋊C4—22no—
408C13×C4⋊C4—22no—
409C13×C4⋊C4—22no—
410C13×C4⋊C4—22no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4C2×Q814yes—
413C13×C4⋊C4#4114yes—
414C42×C13—22no—
415C42×C13—22no—
416C42×C13—22no—
417C42×C13—22no—
418C42×C13—22no—
419C4⋊Dic13—22no—
420C4⋊Dic13—22no—
421C4⋊Dic13—22no—
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—41no—
431C4⋊Dic13—41no—
432C4⋊Dic13—41no—
433C4⋊Dic13—41no—
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—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—
457#6101C2×Q814yes—
458#6101C2×Q814yes—
459#6101#4114yes—
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—22no—
475C4×Dic13—22no—
476C4×Dic13—22no—
477C4×Dic13—22no—
478C4×Dic13—22no—
479C4×Dic13—22no—
480C4×Dic13—41no—
481C4×Dic13—41no—
482C4×Dic13—41no—
483C4×Dic13—41no—
484C4×Dic13—41no—
485C4×Dic13C2×Q814yes—
486C4×Dic13C2×Q814yes—
487C4×Dic13C2×Q814yes—
488C4×Dic13#4114yes—
489C4×Dic13#4114yes—
490#2590—131no—
491#2590—131no—
492#2588—131no—
493#2588—131no—
494#2584—131no—
495#2581—131no—
496#2565—131no—
497#2550—131no—
498#2520—131no—
499#2520—131no—
500#2508—131no—
501#2506—131no—
502#2462—131no—
503#2462D1311yescharacteristic
504#2453—131no—
505#2451—131no—
506#2402—131no—
507#2402—131no—
508#2399—131no—
509#2399—131no—
510C4×C4⋊Q8—131no—
511C4×#125—131no—
512C4×#125—131no—
513C4×#125—131no—
514C4×#125—131no—
515#2295—131no—
516#2295—131no—
517#2295—131no—
518#2295—131no—
519C42×Q8—131no—
520C42×Q8—131no—
521C23×C13C2511yescharacteristic
522Q8×C13—28no—
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×C13C22×Q812yes—
560C2×C4×C13C22×Q812yes—
561C2×C4×C13C22×Q812yes—
562C2×C4×C13C2×#4112yes—
563C2×C4×C13C2×#4112yes—
564C2×C4×C13C2×#4112yes—
565C2×C4×C13C2×#4112yes—
566C2×C4×C13C2×#4112yes—
567C2×C4×C13C2×#4112yes—
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×Dic13—21no—
605C2×Dic13C22×Q812yes—
606C2×Dic13C22×Q812yes—
607C2×Dic13C22×Q812yes—
608C2×Dic13C22×Q812yes—
609C2×Dic13C2×#4112yes—
610C2×Dic13C2×#4112yes—
611C2×Dic13C2×#4112yes—
612C2×Dic13C2×#4112yes—
613C2×Dic13C2×#4112yes—
614C2×Dic13C2×#4112yes—
615C2×Dic132−1+412yes—
616Dic26—28no—
617Dic26—44no—
618Dic26—44no—
619C2×C4⋊Q8—131no—
620C2×#125—131no—
621C2×#125—131no—
622C2×#125—131no—
623C2×#125C2×D1311yescharacteristic
624C2×C4×Q8—131no—
625C2×C4×Q8—131no—
626C2×C4×Q8—131no—
627C2×C4×Q8—131no—
628C2×C4×Q8—131no—
629C2×C4×Q8—131no—
630C2×C4×Q8—131no—
631C2×C4×Q8C2×D1311yescharacteristic
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#398—131no—
641#398—131no—
642#398—131no—
643#398—131no—
644#398—131no—
645#398—131no—
646#398—131no—
647#398—131no—
648#398—131no—
649#398—131no—
650#398—131no—
651#398—131no—
652#398—131no—
653#398—131no—
654#398C2×D1311yescharacteristic
655#398C2×D1311yescharacteristic
656#395—131no—
657#395—131no—
658#395—131no—
659#395—131no—
660#395—131no—
661#395—131no—
662#395C2×D1311yescharacteristic
663#395C2×D1311yescharacteristic
664#391—131no—
665#391—131no—
666#391—131no—
667#391—131no—
668#391—131no—
669#391—131no—
670#391—131no—
671#391—131no—
672#391—131no—
673#391—131no—
674#389—131no—
675#389—131no—
676#389—131no—
677#389—131no—
678#389—131no—
679#389—131no—
680#389—131no—
681#389—131no—
682#389—131no—
683#389—131no—
684#389—131no—
685#389—131no—
686#389—131no—
687#389—131no—
688#389—131no—
689#389—131no—
690#389—131no—
691#389—131no—
692#389C2×D1311yescharacteristic
693#389C2×D1311yescharacteristic
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#387C2×D1311yescharacteristic
721#387C2×D1311yescharacteristic
722#387C2×D1311yescharacteristic
723#387C2×D1311yescharacteristic
724#387C2×D1311yescharacteristic
725#387C2×D1311yescharacteristic
726#384—131no—
727#382—131no—
728#382—131no—
729#382—131no—
730#382—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⋊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⋊C4C2×D1311yescharacteristic
765#376—131no—
766#376—131no—
767#376—131no—
768#376—131no—
769C43—131no—
770C43—131no—
771C43—131no—
772C43—131no—
773C43—131no—
774C22×C13C23×Q811yescharacteristic
775C22×C13C22×#4111yescharacteristic
776C22×C13C22×#4111yescharacteristic
777C22×C13C22×#4111yescharacteristic
778C22×C13C22×#4111yescharacteristic
779C22×C13C2×2−1+411yescharacteristic
780C22×C13#58511yescharacteristic
781C4×C13—22no—
782C4×C13—22no—
783C4×C13—22no—
784C4×C13—22no—
785C4×C13—22no—
786C4×C13—22no—
787C4×C13—22no—
788C4×C13—22no—
789C4×C13—22no—
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—22no—
800Dic13—22no—
801Dic13—41no—
802Dic13—41no—
803Dic13—41no—
804Dic13—41no—
805Dic13—41no—
806Dic13—41no—
807Dic13—41no—
808Dic13—41no—
809Dic13—41no—
810Dic13#53314yes—
811Dic13#55714yes—
812C22×Q8—131no—
813C22×Q8—131no—
814C22×Q8—131no—
815C22×Q8C22×D1311yescharacteristic
816C4⋊Q8—264no—
817#125—24no—
818#125—264no—
819#125—264no—
820#125—264no—
821C4×Q8—24no—
822C4×Q8—138no—
823C4×Q8—264no—
824C4×Q8—264no—
825C4×Q8—264no—
826C4×Q8—264no—
827C4×Q8—264no—
828C4×Q8—264no—
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⋊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⋊C4C22×D1311yescharacteristic
871C2×C4⋊C4C22×D1311yescharacteristic
872C2×C4⋊C4C22×D1311yescharacteristic
873C2×C4⋊C4C22×D1311yescharacteristic
874C2×C4⋊C4C22×D1311yescharacteristic
875C2×C4⋊C4C22×D1311yescharacteristic
876C2×C4⋊C4C22×D1311yescharacteristic
877C2×C4⋊C4C22×D1311yescharacteristic
878C2×C4⋊C4C22×D1311yescharacteristic
879C2×C4⋊C4C22×D1311yescharacteristic
880C2×C4⋊C4C22×D1311yescharacteristic
881C2×C4⋊C4C22×D1311yescharacteristic
882C2×C4⋊C4C22×D1311yescharacteristic
883C2×C4⋊C4C22×D1311yescharacteristic
884C2×C4⋊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×C42—131no—
909C2×C42—131no—
910C2×C42—131no—
911C2×C42—131no—
912C2×C42—131no—
913C2×C42—131no—
914C2×C42—131no—
915C2×C42C22×D1311yescharacteristic
916C2×C42C22×D1311yescharacteristic
917C2×C42C22×D1311yescharacteristic
918C2×C42C22×D1311yescharacteristic
919C2×C42C22×D1311yescharacteristic
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#95—131no—
960#95—131no—
961#95—131no—
962#95—131no—
963#95—131no—
964#95—131no—
965#95—131no—
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
975#95C22×D1311yescharacteristic
976#95C22×D1311yescharacteristic
977#95C22×D1311yescharacteristic
978#95C22×D1311yescharacteristic
979#95C22×D1311yescharacteristic
980C2×C13C2×#53311yescharacteristic
981C2×C13#344411yescharacteristic
982C2×C13#346111yescharacteristic
983C2×C13#347511yescharacteristic
984C2×C13C2×#55711yescharacteristic
985C2×C13Q8×#4111yescharacteristic
986C2×C13#348211yescharacteristic
987C2×Q8—22no—
988C2×Q8—22no—
989C2×Q8—22no—
990C2×Q8—134no—
991C2×Q8—262no—
992C2×Q8—262no—
993C2×Q8—262no—
994C2×Q8—262no—
995C2×Q8—262no—
996C2×Q8—262no—
997C2×Q8—521no—
998C2×Q8—521no—
999C22×C4—131no—
1000C22×C4—131no—
1001C22×C4—131no—
1002C22×C4—131no—
1003C22×C4—131no—
1004C22×C4—131no—
1005C22×C4—131no—
1006C22×C4—131no—
1007C22×C4—131no—
1008C22×C4—131no—
1009C22×C4—131no—
1010C22×C4—131no—
1011C22×C4—131no—
1012C22×C4—131no—
1013C22×C4—131no—
1014C22×C4—131no—
1015C22×C4C23×D1311yescharacteristic
1016C22×C4C23×D1311yescharacteristic
1017C22×C4C23×D1311yescharacteristic
1018C22×C4C23×D1311yescharacteristic
1019C22×C4C23×D1311yescharacteristic
1020C22×C4C23×D1311yescharacteristic
1021C22×C4C23×D1311yescharacteristic
1022C22×C4C23×D1311yescharacteristic
1023C22×C4C23×D1311yescharacteristic
1024C22×C4C23×D1311yescharacteristic
1025C22×C4C23×D1311yescharacteristic
1026C22×C4C23×D1311yescharacteristic
1027C22×C4C23×D1311yescharacteristic
1028C22×C4C23×D1311yescharacteristic
1029C22×C4C23×D1311yescharacteristic
1030C4⋊C4—22no—
1031C4⋊C4—22no—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—22no—
1036C4⋊C4—22no—
1037C4⋊C4—22no—
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—134no—
1044C4⋊C4—134no—
1045C4⋊C4—134no—
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—262no—
1064C4⋊C4—262no—
1065C4⋊C4—262no—
1066C4⋊C4—262no—
1067C4⋊C4—262no—
1068C4⋊C4—262no—
1069C4⋊C4—262no—
1070C4⋊C4—262no—
1071C4⋊C4—262no—
1072C4⋊C4—262no—
1073C4⋊C4—262no—
1074C4⋊C4—262no—
1075C4⋊C4—262no—
1076C4⋊C4—521no—
1077C4⋊C4—521no—
1078C4⋊C4—521no—
1079C4⋊C4—521no—
1080C4⋊C4—521no—
1081C4⋊C4—521no—
1082C4⋊C4—521no—
1083C4⋊C4—521no—
1084C4⋊C4#612914yes—
1085C4⋊C4Q8×D1314yes—
1086C42—22no—
1087C42—22no—
1088C42—22no—
1089C42—22no—
1090C42—22no—
1091C42—134no—
1092C42—134no—
1093C42—134no—
1094C42—134no—
1095C42—134no—
1096C42—262no—
1097C42—262no—
1098C42—262no—
1099C42—262no—
1100C42—262no—
1101C42—262no—
1102C42—262no—
1103C42—262no—
1104C42—262no—
1105C42—262no—
1106C42—262no—
1107C42—262no—
1108C42—262no—
1109C42—262no—
1110C42—262no—
1111C42—262no—
1112C42—262no—
1113C42—262no—
1114C42—262no—
1115C42—262no—
1116C42—521no—
1117C42—521no—
1118C42—521no—
1119C42—521no—
1120C42—521no—
1121C13#3492011yescharacteristic, complemented, Sylow
1122C23C24×D1311yescharacteristic
1123Q8—28no—
1124Q8—268no—
1125Q8—524no—
1126Q8—524no—
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—21no—
1163C2×C4—132no—
1164C2×C4—132no—
1165C2×C4—132no—
1166C2×C4—132no—
1167C2×C4—132no—
1168C2×C4—132no—
1169C2×C4—132no—
1170C2×C4—132no—
1171C2×C4—132no—
1172C2×C4—132no—
1173C2×C4—132no—
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—261no—
1210C2×C4—261no—
1211C2×C4C2×#612912yes—
1212C2×C4C2×#612912yes—
1213C2×C4C2×#612912yes—
1214C2×C4C2×Q8×D1312yes—
1215C2×C4C2×Q8×D1312yes—
1216C2×C4C2×Q8×D1312yes—
1217C2×C4#41×D1312yes—
1218C2×C4#41×D1312yes—
1219C2×C4#41×D1312yes—
1220C22C22×#612911yescharacteristic
1221C22C22×Q8×D1311yescharacteristic
1222C22C2×#41×D1311yescharacteristic
1223C22C2×#41×D1311yescharacteristic
1224C22C2×#41×D1311yescharacteristic
1225C22D13×2−1+411yescharacteristic
1226C22#1171965211yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—22no—
1232C4—22no—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—41no—
1242C4—134no—
1243C4—134no—
1244C4—262no—
1245C4—262no—
1246C4—262no—
1247C4—262no—
1248C4—262no—
1249C4—521no—
1250C4—521no—
1251C4—521no—
1252C4—521no—
1253C4—521no—
1254C4—521no—
1255C4—521no—
1256C4—521no—
1257C4—521no—
1258C2D13×#53311yescharacteristic
1259C2#1312812811yescharacteristic
1260C2#1312826811yescharacteristic
1261C2#1312838911yescharacteristic
1262C2D13×#55711yescharacteristic
1263C2Q8×#612911yescharacteristic
1264C2#1312844811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, prime radical, cosocleC23×C13C25
FittingC13×#2462C2
hypercenter#2462D13
hypocenterC13#34920
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2462

Complements

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

NH ≅ G/Ntype
293. #88141Q8semidirect
1121. C13#34920semidirect

Maximal subgroups

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

subgroupindex
#131203062
#131202982
#131202762
#131202682
#131202182
#131201972
#131200222
#131198522
#131195262
#131195242
#131193712
#131193512
#131188122
#131186942
#131186742
#131181402
#131181262
#131174072
#125×Dic132
#131173932
#131173092
#131173072
C4×Q8×Dic132
C4×#881412
C13×#24622
#3492013