Finite Group Databasebeta

← #16029089

Subgroups — #16029089

Order 3328.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13⋊#564C211yesmaximal, characteristic
2#13118019C211yesmaximal, characteristic
3#13118018C211yesmaximal, characteristic
4#13118018C211yesmaximal, characteristic
5#13117940C211yesmaximal, characteristic
6#13117940C211yesmaximal, characteristic
7#13117939C211yesmaximal, characteristic
8#13117939C211yesmaximal, characteristic
9#13117939C211yesmaximal, characteristic
10#13117938C211yesmaximal, characteristic
11#13117937C211yesmaximal, characteristic
12#13117935C211yesmaximal, characteristic
13#13117933C211yesmaximal, characteristic
14#13117932C211yesmaximal, characteristic
15#13117930C211yesmaximal, characteristic
16#13117642C211yesmaximal, characteristic
17#13117641C211yesmaximal, characteristic
18#13117640C211yesmaximal, characteristic
19#13117640C211yesmaximal, characteristic
20#13117636C211yesmaximal, characteristic
21#13117635C211yesmaximal, characteristic
22#13117576C211yesmaximal, characteristic
23#13117574C211yesmaximal, characteristic
24#13117574C211yesmaximal, characteristic
25#13117574C211yesmaximal, characteristic
26#13117573C211yesmaximal, characteristic
27#13117572C211yesmaximal, characteristic
28C4×#88144C211yesmaximal, characteristic
29#13117393C211yesmaximal, characteristic
30C4×#88143C211yesmaximal, characteristic
31C13×#2370C211yesmaximal, characteristic
32C2×C13×#125C2211yescharacteristic
33C13⋊#564C4116yescomplemented
34C2×#88144C2211yescharacteristic
35C2×#88144C2211yescharacteristic
36C2×#88144C2211yescharacteristic
37C2×#88144C2211yescharacteristic
38C2×#88143C2211yescharacteristic
39C2×#88143C2211yescharacteristic
40C2×#88143C2211yescharacteristic
41C2×#88143C2211yescharacteristic
42C2×#88143C2211yescharacteristic
43C2×#88143C2211yescharacteristic
44C2×#88143C2211yescharacteristic
45C2×#88143C2211yescharacteristic
46C2×#88124C2211yescharacteristic
47C2×#88124C2211yescharacteristic
48C13×#389C2211yescharacteristic
49C13×#389C2211yescharacteristic
50C13×#389C2211yescharacteristic
51C13×#389C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#387C2211yescharacteristic
55C13×#387C2211yescharacteristic
56C4×C13×C4⋊C4C2211yescharacteristic
57C4×C13×C4⋊C4C2211yescharacteristic
58C4×C13×C4⋊C4C2211yescharacteristic
59C4×C13×C4⋊C4C2211yescharacteristic
60C4×C13×C4⋊C4C2211yescharacteristic
61C4×C13×C4⋊C4C2211yescharacteristic
62#11718646C2211yescharacteristic
63#11718646C2211yescharacteristic
64#11718642C2211yescharacteristic
65#11718642C2211yescharacteristic
66#11718642C2211yescharacteristic
67#11718642C2211yescharacteristic
68#11718642C2211yescharacteristic
69#11718642C2211yescharacteristic
70#11718642C2211yescharacteristic
71#11718642C2211yescharacteristic
72#11718639C2211yescharacteristic
73#11718639C2211yescharacteristic
74#11718639C2211yescharacteristic
75#11718639C2211yescharacteristic
76#11718639C2211yescharacteristic
77#11718639C2211yescharacteristic
78#11718639C2211yescharacteristic
79#11718639C2211yescharacteristic
80#11718639C2211yescharacteristic
81#11718638C2211yescharacteristic
82#11718637C2211yescharacteristic
83#11718637C2211yescharacteristic
84C4⋊C4×Dic13C2211yescharacteristic
85C4⋊C4×Dic13C2211yescharacteristic
86C4⋊C4×Dic13C2211yescharacteristic
87C4⋊C4×Dic13C2211yescharacteristic
88C4⋊C4×Dic13C2211yescharacteristic
89C4⋊C4×Dic13C2211yescharacteristic
90#11718634C2211yescharacteristic
91#11718634C2211yescharacteristic
92#11718634C2211yescharacteristic
93#11718634C2211yescharacteristic
94#11718634C2211yescharacteristic
95#11718633C2211yescharacteristic
96#11718633C2211yescharacteristic
97#11718633C2211yescharacteristic
98#11718633C2211yescharacteristic
99#11718633C2211yescharacteristic
100#11718633C2211yescharacteristic
101#11718633C2211yescharacteristic
102#11718633C2211yescharacteristic
103#11718633C2211yescharacteristic
104#11718633C2211yescharacteristic
105#11718633C2211yescharacteristic
106#11718598C2211yescharacteristic
107C4×C4⋊Dic13C2211yescharacteristic
108C4×C4⋊Dic13C2211yescharacteristic
109C4×C4⋊Dic13C2211yescharacteristic
110C4×C4⋊Dic13C2211yescharacteristic
111C4×C4⋊Dic13C2211yescharacteristic
112C4×C4⋊Dic13C2211yescharacteristic
113#11718594C2211yescharacteristic
114#11718594C2211yescharacteristic
115#11718594C2211yescharacteristic
116#11718594C2211yescharacteristic
117#11718594C2211yescharacteristic
118#11718594C2211yescharacteristic
119#11718594C2211yescharacteristic
120#11718594C2211yescharacteristic
121#11718594C2211yescharacteristic
122#11718594C2211yescharacteristic
123#11718594C2211yescharacteristic
124#11718593C2211yescharacteristic
125#11718593C2211yescharacteristic
126C4×#6101C2211yescharacteristic
127C4×#6101C2211yescharacteristic
128C4×#6101C2211yescharacteristic
129C4×#6101C2211yescharacteristic
130C4×#6101C2211yescharacteristic
131C4×#6101C2211yescharacteristic
132C4×#6101C2211yescharacteristic
133C4×#6101C2211yescharacteristic
134C4×#6101C2211yescharacteristic
135C4×#6101C2211yescharacteristic
136C42×Dic13C2211yescharacteristic
137#11718589C2211yescharacteristic
138#11718589C2211yescharacteristic
139#11718589C2211yescharacteristic
140#11718316C2211yescharacteristic
141#11718316C2211yescharacteristic
142#11718316C2211yescharacteristic
143#11718316C2211yescharacteristic
144#11718316C2211yescharacteristic
145#11718316C2211yescharacteristic
146#11718316C2211yescharacteristic
147#11718315C2211yescharacteristic
148#11718315C2211yescharacteristic
149#11718315C2211yescharacteristic
150#11718315C2211yescharacteristic
151#11718315C2211yescharacteristic
152#11718315C2211yescharacteristic
153#11718315C2211yescharacteristic
154#11718315C2211yescharacteristic
155#11718314C2211yescharacteristic
156#11718314C2211yescharacteristic
157#11718314C2211yescharacteristic
158#11718314C2211yescharacteristic
159#11718314C2211yescharacteristic
160#11718314C2211yescharacteristic
161#11718314C2211yescharacteristic
162#11718314C2211yescharacteristic
163#11718313C2211yescharacteristic
164#11718313C2211yescharacteristic
165#11718313C2211yescharacteristic
166#11718313C2211yescharacteristic
167#11718313C2211yescharacteristic
168#11718312C2211yescharacteristic
169#11718311C2211yescharacteristic
170#11718311C2211yescharacteristic
171#11718310C2211yescharacteristic
172#11718310C2211yescharacteristic
173#11718310C2211yescharacteristic
174#11718310C2211yescharacteristic
175#11718310C2211yescharacteristic
176#11718310C2211yescharacteristic
177#11718310C2211yescharacteristic
178#11718310C2211yescharacteristic
179#11718309C2211yescharacteristic
180#11718309C2211yescharacteristic
181#11718309C2211yescharacteristic
182#11718309C2211yescharacteristic
183#11718308C2211yescharacteristic
184#11718308C2211yescharacteristic
185#11718308C2211yescharacteristic
186#11718308C2211yescharacteristic
187#11718308C2211yescharacteristic
188C13×#125C2×C418yes—
189C2×C13×C4⋊C4C2311yescharacteristic
190C2×C13×C4⋊C4C2311yescharacteristic
191C2×C13×C4⋊C4C2311yescharacteristic
192C2×C13×C4⋊C4C2311yescharacteristic
193C2×C13×C4⋊C4C2311yescharacteristic
194C2×C13×C4⋊C4C2311yescharacteristic
195C2×C13×C4⋊C4C2311yescharacteristic
196C2×C13×C4⋊C4C2311yescharacteristic
197C2×C13×C4⋊C4C2311yescharacteristic
198C2×C13×C4⋊C4C2311yescharacteristic
199C2×C13×C4⋊C4C2311yescharacteristic
200C2×C13×C4⋊C4C2311yescharacteristic
201C2×C13×C4⋊C4C2311yescharacteristic
202C2×C13×C4⋊C4C2311yescharacteristic
203C2×C42×C13C2311yescharacteristic
204C2×C42×C13C2311yescharacteristic
205C2×C42×C13C2311yescharacteristic
206C2×C42×C13C2311yescharacteristic
207C2×C42×C13C2311yescharacteristic
208C2×C42×C13C2311yescharacteristic
209C2×C42×C13C2311yescharacteristic
210C2×C42×C13C2311yescharacteristic
211C2×C42×C13C2311yescharacteristic
212C2×C4⋊Dic13C2311yescharacteristic
213C2×C4⋊Dic13C2311yescharacteristic
214C2×C4⋊Dic13C2311yescharacteristic
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×#6101C2311yescharacteristic
227C2×#6101C2311yescharacteristic
228C2×#6101C2311yescharacteristic
229C2×#6101C2311yescharacteristic
230C2×#6101C2311yescharacteristic
231C2×#6101C2311yescharacteristic
232C2×#6101C2311yescharacteristic
233C2×#6101C2311yescharacteristic
234C2×#6101C2311yescharacteristic
235C2×#6101C2311yescharacteristic
236C2×#6101C2311yescharacteristic
237C2×#6101C2311yescharacteristic
238C2×#6101C2311yescharacteristic
239C2×#6101C2311yescharacteristic
240C2×#6101C2311yescharacteristic
241C2×#6101C2311yescharacteristic
242C2×#6101C2311yescharacteristic
243C2×#6101C2311yescharacteristic
244C2×#6101C2311yescharacteristic
245C2×#6101C2311yescharacteristic
246C2×#6101C2311yescharacteristic
247C2×#6101C2311yescharacteristic
248C2×#6101C2311yescharacteristic
249C2×#6101C2311yescharacteristic
250C2×#6101C2311yescharacteristic
251C2×#6101C2311yescharacteristic
252C2×#6101C2311yescharacteristic
253C2×#6101C2311yescharacteristic
254C2×#6101C2311yescharacteristic
255C2×#6101C2311yescharacteristic
256C2×#6101C2311yescharacteristic
257C2×#6101C2311yescharacteristic
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×C418yes—
285#88144C2×C418yes—
286#88144C2×C418yes—
287#88144C2×C418yes—
288#88143C2×C418yes—
289#88143C2×C418yes—
290#88143C2×C418yes—
291#88143C2×C418yes—
292#88143C2×C418yes—
293#88143C2×C418yes—
294#88143C2×C418yes—
295#88143C2×C418yes—
296#88124C2×C418yes—
297#88124C2×C418yes—
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#34530—131nomaximal, Sylow
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
390C13×C4⋊C4—22no—
391C13×C4⋊C4—22no—
392C13×C4⋊C4—41no—
393C13×C4⋊C4—41no—
394C13×C4⋊C4—41no—
395C13×C4⋊C4—41no—
396C13×C4⋊C4—41no—
397C13×C4⋊C4—41no—
398C13×C4⋊C4C22×C414yes—
399C13×C4⋊C4C22×C414yes—
400C13×C4⋊C4C22×C414yes—
401C13×C4⋊C4C22×C414yes—
402C13×C4⋊C4C22×C414yes—
403C13×C4⋊C4C22×C414yes—
404C42×C13—22no—
405C42×C13—22no—
406C42×C13—41no—
407C42×C13—41no—
408C42×C13—41no—
409C42×C13—41no—
410C42×C13—41no—
411C42×C13—41no—
412C42×C13C22×C414yes—
413C4⋊Dic13—22no—
414C4⋊Dic13—22no—
415C4⋊Dic13—41no—
416C4⋊Dic13—41no—
417C4⋊Dic13—41no—
418C4⋊Dic13—41no—
419C4⋊Dic13C22×C414yes—
420C4⋊Dic13C22×C414yes—
421C4⋊Dic13C22×C414yes—
422C4⋊Dic13C22×C414yes—
423C4⋊Dic13C22×C414yes—
424C4⋊Dic13C22×C414yes—
425C4⋊Dic13C22×C414yes—
426C4⋊Dic13C22×C414yes—
427#6101—22no—
428#6101—22no—
429#6101—41no—
430#6101—41no—
431#6101—41no—
432#6101—41no—
433#6101—41no—
434#6101—41no—
435#6101—41no—
436#6101—41no—
437#6101—41no—
438#6101—41no—
439#6101—41no—
440#6101—41no—
441#6101—41no—
442#6101—41no—
443#6101C22×C414yes—
444#6101C22×C414yes—
445#6101C22×C414yes—
446#6101C22×C414yes—
447#6101C22×C414yes—
448#6101C22×C414yes—
449#6101C22×C414yes—
450#6101C22×C414yes—
451#6101C22×C414yes—
452#6101C22×C414yes—
453#6101C22×C414yes—
454#6101C22×C414yes—
455#6101C22×C414yes—
456#6101C22×C414yes—
457#6101C22×C414yes—
458#6101C22×C414yes—
459C4×Dic13—22no—
460C4×Dic13—22no—
461C4×Dic13—22no—
462C4×Dic13—22no—
463C4×Dic13—22no—
464C4×Dic13—22no—
465C4×Dic13—22no—
466C4×Dic13—41no—
467C4×Dic13—41no—
468C4×Dic13—41no—
469C4×Dic13—41no—
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×Dic13C22×C414yes—
482C4×Dic13C22×C414yes—
483C4×Dic13C22×C414yes—
484C4×Dic13C22×C414yes—
485C2×#564—131no—
486#2382—131no—
487#2382—131no—
488#2382—131no—
489#2371—131no—
490#2371—131no—
491#2371—131no—
492#2371—131no—
493#2371—131no—
494#2371—131no—
495#2370—131no—
496#2370—131no—
497#2370—131no—
498#2370—131no—
499#2370—131no—
500#2370D1311yescharacteristic
501#2336—131no—
502#2336—131no—
503#2336—131no—
504#2336—131no—
505#2336—131no—
506#2336—131no—
507#2330—131no—
508#2330—131no—
509#2330—131no—
510#2330—131no—
511#2330—131no—
512#2330—131no—
513C4×#125—131no—
514C4×#125—131no—
515C4×#125—131no—
516C23×C13C2511yescharacteristic
517C2×C4×C13—21no—
518C2×C4×C13—21no—
519C2×C4×C13—21no—
520C2×C4×C13—21no—
521C2×C4×C13—21no—
522C2×C4×C13—21no—
523C2×C4×C13—21no—
524C2×C4×C13—21no—
525C2×C4×C13—21no—
526C2×C4×C13—21no—
527C2×C4×C13—21no—
528C2×C4×C13—21no—
529C2×C4×C13—21no—
530C2×C4×C13—21no—
531C2×C4×C13—21no—
532C2×C4×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×C13C23×C412yes—
554C2×C4×C13C23×C412yes—
555C2×C4×C13C23×C412yes—
556C2×C4×C13C23×C412yes—
557C2×C4×C13C23×C412yes—
558C2×C4×C13C23×C412yes—
559C2×C4×C13C23×C412yes—
560C2×C4×C132−1+412yes—
561C2×C4×C132−1+412yes—
562C2×Dic13—21no—
563C2×Dic13—21no—
564C2×Dic13—21no—
565C2×Dic13—21no—
566C2×Dic13—21no—
567C2×Dic13—21no—
568C2×Dic13—21no—
569C2×Dic13—21no—
570C2×Dic13—21no—
571C2×Dic13—21no—
572C2×Dic13—21no—
573C2×Dic13—21no—
574C2×Dic13—21no—
575C2×Dic13—21no—
576C2×Dic13—21no—
577C2×Dic13—21no—
578C2×Dic13—21no—
579C2×Dic13—21no—
580C2×Dic13—21no—
581C2×Dic13—21no—
582C2×Dic13—21no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—21no—
589C2×Dic13—21no—
590C2×Dic13—21no—
591C2×Dic13—21no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—21no—
595C2×Dic13—21no—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13C23×C412yes—
602C2×Dic13C23×C412yes—
603C2×Dic13C23×C412yes—
604C2×Dic13C23×C412yes—
605C2×Dic13C23×C412yes—
606C2×Dic13C23×C412yes—
607C2×Dic13C23×C412yes—
608C2×Dic13C23×C412yes—
609C2×Dic132−1+412yes—
610#564—1316no—
611C2×#125—131no—
612C2×#125—131no—
613C2×#125—131no—
614C2×#125—131no—
615C2×#125—131no—
616C2×#125—131no—
617C2×#125—131no—
618C2×#125—131no—
619C2×#125—131no—
620C2×#125—131no—
621C2×#125—131no—
622C2×#125—131no—
623C2×#125—131no—
624C2×#125—131no—
625C2×#125C2×D1311yescharacteristic
626#389—131no—
627#389—131no—
628#389—131no—
629#389—131no—
630#389—131no—
631#389—131no—
632#389—131no—
633#389—131no—
634#389—131no—
635#389—131no—
636#389—131no—
637#389—131no—
638#389—131no—
639#389—131no—
640#389—131no—
641#389—131no—
642#389—131no—
643#389—131no—
644#389—131no—
645#389—131no—
646#389—131no—
647#389—131no—
648#389—131no—
649#389—131no—
650#389—131no—
651#389—131no—
652#389C2×D1311yescharacteristic
653#389C2×D1311yescharacteristic
654#389C2×D1311yescharacteristic
655#389C2×D1311yescharacteristic
656#387—131no—
657#387—131no—
658#387—131no—
659#387—131no—
660#387—131no—
661#387—131no—
662#387—131no—
663#387—131no—
664#387—131no—
665#387—131no—
666#387—131no—
667#387—131no—
668#387—131no—
669#387—131no—
670#387—131no—
671#387—131no—
672#387—131no—
673#387—131no—
674#387—131no—
675#387—131no—
676#387—131no—
677#387—131no—
678#387—131no—
679#387—131no—
680#387—131no—
681#387—131no—
682#387—131no—
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#387C2×D1311yescharacteristic
713#387C2×D1311yescharacteristic
714#387C2×D1311yescharacteristic
715#387C2×D1311yescharacteristic
716#384—131no—
717#384—131no—
718#383—131no—
719#383—131no—
720#382—131no—
721#382—131no—
722#382—131no—
723C4×C4⋊C4—131no—
724C4×C4⋊C4—131no—
725C4×C4⋊C4—131no—
726C4×C4⋊C4—131no—
727C4×C4⋊C4—131no—
728C4×C4⋊C4—131no—
729C4×C4⋊C4—131no—
730C4×C4⋊C4—131no—
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⋊C4C2×D1311yescharacteristic
754C4×C4⋊C4C2×D1311yescharacteristic
755C4×C4⋊C4C2×D1311yescharacteristic
756C4×C4⋊C4C2×D1311yescharacteristic
757C4×C4⋊C4C2×D1311yescharacteristic
758C4×C4⋊C4C2×D1311yescharacteristic
759#376—131no—
760#376—131no—
761#376—131no—
762#376—131no—
763#376—131no—
764#376—131no—
765C43—131no—
766C22×C13C24×C411yescharacteristic
767C22×C13C2×2−1+411yescharacteristic
768C22×C13C2×2−1+411yescharacteristic
769C22×C13C2×2−1+411yescharacteristic
770C22×C13#58511yescharacteristic
771C22×C13#58511yescharacteristic
772C22×C13#58511yescharacteristic
773C4×C13—22no—
774C4×C13—22no—
775C4×C13—22no—
776C4×C13—22no—
777C4×C13—22no—
778C4×C13—22no—
779C4×C13—22no—
780C4×C13—22no—
781C4×C13—22no—
782C4×C13—41no—
783C4×C13—41no—
784C4×C13—41no—
785C4×C13—41no—
786C4×C13—41no—
787C4×C13—41no—
788Dic13—22no—
789Dic13—22no—
790Dic13—22no—
791Dic13—22no—
792Dic13—22no—
793Dic13—22no—
794Dic13—22no—
795Dic13—22no—
796Dic13—22no—
797Dic13—41no—
798Dic13—41no—
799Dic13—41no—
800Dic13—41no—
801Dic13—41no—
802Dic13—41no—
803Dic13—41no—
804#125—138no—
805#125—138no—
806#125—138no—
807#125—138no—
808#125—138no—
809#125—138no—
810#125—138no—
811#125—138no—
812#125—138no—
813#125—138no—
814#125—138no—
815#125—138no—
816#125—138no—
817#125—138no—
818#125C4×D1318yes—
819C2×C4⋊C4—131no—
820C2×C4⋊C4—131no—
821C2×C4⋊C4—131no—
822C2×C4⋊C4—131no—
823C2×C4⋊C4—131no—
824C2×C4⋊C4—131no—
825C2×C4⋊C4—131no—
826C2×C4⋊C4—131no—
827C2×C4⋊C4—131no—
828C2×C4⋊C4—131no—
829C2×C4⋊C4—131no—
830C2×C4⋊C4—131no—
831C2×C4⋊C4—131no—
832C2×C4⋊C4—131no—
833C2×C4⋊C4—131no—
834C2×C4⋊C4—131no—
835C2×C4⋊C4—131no—
836C2×C4⋊C4—131no—
837C2×C4⋊C4—131no—
838C2×C4⋊C4—131no—
839C2×C4⋊C4—131no—
840C2×C4⋊C4—131no—
841C2×C4⋊C4—131no—
842C2×C4⋊C4—131no—
843C2×C4⋊C4—131no—
844C2×C4⋊C4—131no—
845C2×C4⋊C4—131no—
846C2×C4⋊C4—131no—
847C2×C4⋊C4—131no—
848C2×C4⋊C4—131no—
849C2×C4⋊C4—131no—
850C2×C4⋊C4—131no—
851C2×C4⋊C4—131no—
852C2×C4⋊C4—131no—
853C2×C4⋊C4—131no—
854C2×C4⋊C4—131no—
855C2×C4⋊C4—131no—
856C2×C4⋊C4—131no—
857C2×C4⋊C4—131no—
858C2×C4⋊C4—131no—
859C2×C4⋊C4—131no—
860C2×C4⋊C4—131no—
861C2×C4⋊C4—131no—
862C2×C4⋊C4—131no—
863C2×C4⋊C4—131no—
864C2×C4⋊C4—131no—
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×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×C42—131no—
880C2×C42—131no—
881C2×C42—131no—
882C2×C42—131no—
883C2×C42—131no—
884C2×C42—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×C42C22×D1311yescharacteristic
906C2×C42C22×D1311yescharacteristic
907C2×C42C22×D1311yescharacteristic
908C2×C42C22×D1311yescharacteristic
909C2×C42C22×D1311yescharacteristic
910C2×C42C22×D1311yescharacteristic
911C2×C42C22×D1311yescharacteristic
912C2×C42C22×D1311yescharacteristic
913C2×C42C22×D1311yescharacteristic
914#95—131no—
915#95—131no—
916#95—131no—
917#95—131no—
918#95—131no—
919#95—131no—
920#95—131no—
921#95—131no—
922#95—131no—
923#95—131no—
924#95—131no—
925#95—131no—
926#95—131no—
927#95—131no—
928#95—131no—
929#95—131no—
930#95—131no—
931#95—131no—
932#95—131no—
933#95—131no—
934#95—131no—
935#95—131no—
936#95—131no—
937#95—131no—
938#95—131no—
939#95—131no—
940#95—131no—
941#95—131no—
942#95—131no—
943#95—131no—
944#95—131no—
945#95—131no—
946#95—131no—
947#95—131no—
948#95—131no—
949#95—131no—
950#95—131no—
951#95—131no—
952#95—131no—
953#95—131no—
954#95—131no—
955#95—131no—
956#95—131no—
957#95—131no—
958#95—131no—
959#95—131no—
960#95—131no—
961#95—131no—
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
974C2×C13C4×2−1+411yescharacteristic
975C2×C13C4×2−1+411yescharacteristic
976C2×C13C4×2−1+411yescharacteristic
977C2×C13#356311yescharacteristic
978C2×C13#356311yescharacteristic
979C2×C13#356311yescharacteristic
980C2×C13#356711yescharacteristic
981C22×C4—131no—
982C22×C4—131no—
983C22×C4—131no—
984C22×C4—131no—
985C22×C4—131no—
986C22×C4—131no—
987C22×C4—131no—
988C22×C4—131no—
989C22×C4—131no—
990C22×C4—131no—
991C22×C4—131no—
992C22×C4—131no—
993C22×C4—131no—
994C22×C4—131no—
995C22×C4—131no—
996C22×C4—131no—
997C22×C4C23×D1311yescharacteristic
998C22×C4C23×D1311yescharacteristic
999C22×C4C23×D1311yescharacteristic
1000C22×C4C23×D1311yescharacteristic
1001C22×C4C23×D1311yescharacteristic
1002C22×C4C23×D1311yescharacteristic
1003C22×C4C23×D1311yescharacteristic
1004C22×C4C23×D1311yescharacteristic
1005C22×C4C23×D1311yescharacteristic
1006C22×C4C23×D1311yescharacteristic
1007C22×C4C23×D1311yescharacteristic
1008C22×C4C23×D1311yescharacteristic
1009C22×C4C23×D1311yescharacteristic
1010C22×C4C23×D1311yescharacteristic
1011C22×C4C23×D1311yescharacteristic
1012C4⋊C4—22no—
1013C4⋊C4—22no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—134no—
1021C4⋊C4—134no—
1022C4⋊C4—134no—
1023C4⋊C4—134no—
1024C4⋊C4—134no—
1025C4⋊C4—134no—
1026C4⋊C4—134no—
1027C4⋊C4—134no—
1028C4⋊C4—134no—
1029C4⋊C4—134no—
1030C4⋊C4—134no—
1031C4⋊C4—134no—
1032C4⋊C4—134no—
1033C4⋊C4—134no—
1034C4⋊C4—134no—
1035C4⋊C4—134no—
1036C4⋊C4—134no—
1037C4⋊C4—134no—
1038C4⋊C4—134no—
1039C4⋊C4—134no—
1040C4⋊C4—134no—
1041C4⋊C4—134no—
1042C4⋊C4—134no—
1043C4⋊C4—134no—
1044C4⋊C4—262no—
1045C4⋊C4—262no—
1046C4⋊C4—262no—
1047C4⋊C4—262no—
1048C4⋊C4—521no—
1049C4⋊C4—521no—
1050C4⋊C4—521no—
1051C4⋊C4—521no—
1052C4⋊C4—521no—
1053C4⋊C4—521no—
1054C4⋊C4—521no—
1055C4⋊C4—521no—
1056C4⋊C4—521no—
1057C4⋊C4—521no—
1058C4⋊C4—521no—
1059C4⋊C4—521no—
1060C4⋊C4—521no—
1061C4⋊C4—521no—
1062C4⋊C4—521no—
1063C4⋊C4—521no—
1064C4⋊C4—521no—
1065C4⋊C4—521no—
1066C4⋊C4C2×C4×D1314yes—
1067C4⋊C4C2×C4×D1314yes—
1068C4⋊C4C2×C4×D1314yes—
1069C4⋊C4C2×C4×D1314yes—
1070C4⋊C4C2×C4×D1314yes—
1071C4⋊C4C2×C4×D1314yes—
1072C42—22no—
1073C42—22no—
1074C42—41no—
1075C42—41no—
1076C42—41no—
1077C42—41no—
1078C42—41no—
1079C42—41no—
1080C42—134no—
1081C42—134no—
1082C42—134no—
1083C42—134no—
1084C42—262no—
1085C42—262no—
1086C42—262no—
1087C42—262no—
1088C42—262no—
1089C42—262no—
1090C42—262no—
1091C42—521no—
1092C42—521no—
1093C42—521no—
1094C42—521no—
1095C42—521no—
1096C42—521no—
1097C42—521no—
1098C42—521no—
1099C42—521no—
1100C42—521no—
1101C42—521no—
1102C42—521no—
1103C42—521no—
1104C42—521no—
1105C42—521no—
1106C42C2×C4×D1314yes—
1107C13#3453011yescharacteristic, complemented, Sylow
1108C23C24×D1311yescharacteristic
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
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—132no—
1146C2×C4—132no—
1147C2×C4—132no—
1148C2×C4—132no—
1149C2×C4—132no—
1150C2×C4—132no—
1151C2×C4—132no—
1152C2×C4—132no—
1153C2×C4—132no—
1154C2×C4—261no—
1155C2×C4—261no—
1156C2×C4—261no—
1157C2×C4—261no—
1158C2×C4—261no—
1159C2×C4—261no—
1160C2×C4—261no—
1161C2×C4—261no—
1162C2×C4—261no—
1163C2×C4—261no—
1164C2×C4—261no—
1165C2×C4—261no—
1166C2×C4—261no—
1167C2×C4—261no—
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×C4C22×C4×D1312yes—
1194C2×C4C22×C4×D1312yes—
1195C2×C4C22×C4×D1312yes—
1196C2×C4C22×C4×D1312yes—
1197C2×C4C22×C4×D1312yes—
1198C2×C4C22×C4×D1312yes—
1199C2×C4C22×C4×D1312yes—
1200C2×C4#8825412yes—
1201C2×C4#8825712yes—
1202C22C23×C4×D1311yescharacteristic
1203C22C2×#8825411yescharacteristic
1204C22C2×#8825711yescharacteristic
1205C22#1171964811yescharacteristic
1206C22#1171964811yescharacteristic
1207C22#1171965011yescharacteristic
1208C22D13×2−1+411yescharacteristic
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—22no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—262no—
1225C4—262no—
1226C4—262no—
1227C4—262no—
1228C4—262no—
1229C4—262no—
1230C4—262no—
1231C4—262no—
1232C4—262no—
1233C4—521no—
1234C4—521no—
1235C4—521no—
1236C4—521no—
1237C4—521no—
1238C4—521no—
1239C4—521no—
1240C2C4×#8825711yescharacteristic
1241C2#1312804711yescharacteristic
1242C2C4×#8825411yescharacteristic
1243C2#1312943211yescharacteristic
1244C2#1312943311yescharacteristic
1245C2#1312944011yescharacteristic
1246C2#1312952011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutatorC22×C13C24×C4
FittingC13×#2370C2
socle, prime radical, cosocleC23×C13C25
hypercenter#2370D13
hypocenterC13#34530
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2370

Complements

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

NH ≅ G/Ntype
33. C13⋊#564C4semidirect
1107. C13#34530semidirect

Maximal subgroups

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

subgroupindex
C2×C13⋊#5642
#131180192
#131180182
#131179402
#131179392
#131179382
#131179372
#131179352
#131179332
#131179322
#131179302
#131176422
#131176412
#131176402
#131176362
#131176352
#131175762
#131175742
#131175732
#131175722
C4×#881442
#131173932
C4×#881432
C13×#23702
#3453013