Finite Group Databasebeta

← #16070877

Subgroups — #16070877

Order 3328.

1482 conjugacy classes of subgroups.

The subgroup lattice has 1278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123187C211yesmaximal, characteristic
2#13123147C211yesmaximal, characteristic
3#13122756C211yesmaximal, characteristic, complemented
4#13122754C211yesmaximal, characteristic, complemented
5#13122661C211yesmaximal, characteristic, complemented
6#13122654C211yesmaximal, characteristic, complemented
7#13122595C211yesmaximal, characteristic, complemented
8#13122590C211yesmaximal, characteristic, complemented
9#13122428C211yesmaximal, characteristic, complemented
10#13122426C211yesmaximal, characteristic, complemented
11#13122282C211yesmaximal, characteristic, complemented
12#13122192C211yesmaximal, characteristic, complemented
13#13122185C211yesmaximal, characteristic, complemented
14#13121705C211yesmaximal, characteristic, complemented
15#13121701C211yesmaximal, characteristic, complemented
16#13121624C211yesmaximal, characteristic, complemented
17#13121615C211yesmaximal, characteristic, complemented
18#13120654C211yesmaximal, characteristic
19#13120654C211yesmaximal, characteristic
20#13119344C211yesmaximal, characteristic
21#13119332C211yesmaximal, characteristic
22#13119220C211yesmaximal, characteristic
23#13119218C211yesmaximal, characteristic
24#13119216C211yesmaximal, characteristic
25#13119214C211yesmaximal, characteristic
26#13118978C211yesmaximal, characteristic
27#13118975C211yesmaximal, characteristic
28#13117570C211yesmaximal, characteristic
29#13117563C211yesmaximal, characteristic
30D13×#387C211yesmaximal, characteristic
31C13×#2766C211yesmaximal, characteristic, complemented
32C2×#88150C2211yescharacteristic
33C2×#88150C2211yescharacteristic
34C2×C4⋊C4×D13C2211yescharacteristic
35C2×C4⋊C4×D13C2211yescharacteristic
36C2×#88143C2211yescharacteristic
37C2×#88143C2211yescharacteristic
38C2×#88142C2211yescharacteristic
39C2×C42×D13C2211yescharacteristic
40C2×#88124C2211yescharacteristic
41C13×#401C2211yescharacteristic
42C13×#400C2211yescharacteristic
43C13×#400C2211yescharacteristic
44C13×#398C2211yescharacteristic
45C13×#398C2211yescharacteristic
46C13×#398C2211yescharacteristic
47C13×#389C2211yescharacteristic
48C13×#389C2211yescharacteristic
49C13×#387C2211yescharacteristic
50C13×#387C2211yescharacteristic
51C13×#387C2211yescharacteristic
52C13×#387C2211yescharacteristic
53C13×#387C2211yescharacteristic
54C13×#383C2211yescharacteristic
55C13×#382C2211yescharacteristic
56#11718650C2211yescharacteristic
57#11718650C2211yescharacteristic
58#11718650C2211yescharacteristic
59#11718650C2211yescharacteristic
60#11718648C2211yescharacteristic
61#11718648C2211yescharacteristic
62#11718648C2211yescharacteristic
63#11718648C2211yescharacteristic
64#11718647C2211yescharacteristic
65#11718646C2211yescharacteristic
66#11718646C2211yescharacteristic
67#11718646C2211yescharacteristic
68#11718646C2211yescharacteristic
69#11718645C2211yescharacteristic
70#11718645C2211yescharacteristic
71#11718645C2211yescharacteristic
72#11718645C2211yescharacteristic
73#11718645C2211yescharacteristic
74#11718644C2211yescharacteristic
75#11718644C2211yescharacteristic
76#11718644C2211yescharacteristic
77#11718644C2211yescharacteristic
78#11718643C2211yescharacteristic
79#11718642C2211yescharacteristic
80#11718642C2211yescharacteristic
81#11718642C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718641C2211yescharacteristic
84#11718640C2211yescharacteristic
85#11718640C2211yescharacteristic
86#11718639C2211yescharacteristic
87#11718639C2211yescharacteristic
88#11718639C2211yescharacteristic
89#11718639C2211yescharacteristic
90#11718639C2211yescharacteristic
91#11718637C2211yescharacteristic
92#11718635C2211yescharacteristic
93#11718634C2211yescharacteristic
94#11718633C2211yescharacteristic
95#11718633C2211yescharacteristic
96#11718633C2211yescharacteristic
97C4×#6103C2211yescharacteristic
98C4×#6103C2211yescharacteristic
99#11718598C2211yescharacteristic
100#11718594C2211yescharacteristic
101#11718594C2211yescharacteristic
102#11718594C2211yescharacteristic
103#11718590C2211yescharacteristic
104#11718589C2211yescharacteristic
105#11718589C2211yescharacteristic
106#11718589C2211yescharacteristic
107#11718329C2211yescharacteristic
108#11718329C2211yescharacteristic
109#11718329C2211yescharacteristic
110#11718329C2211yescharacteristic
111#11718329C2211yescharacteristic
112#11718329C2211yescharacteristic
113#11718329C2211yescharacteristic
114#11718329C2211yescharacteristic
115#11718328C2211yescharacteristic
116#11718328C2211yescharacteristic
117#11718327C2211yescharacteristic
118#11718327C2211yescharacteristic
119#11718325C2211yescharacteristic
120#11718325C2211yescharacteristic
121#11718325C2211yescharacteristic
122#11718325C2211yescharacteristic
123D13×#95C2211yescharacteristic
124D13×#95C2211yescharacteristic
125D13×#95C2211yescharacteristic
126D13×#95C2211yescharacteristic
127C13⋊#401C2211yescharacteristic
128C13⋊#401C2211yescharacteristic
129C13⋊#401C2211yescharacteristic
130#11718322C2211yescharacteristic
131#11718322C2211yescharacteristic
132#11718321C2211yescharacteristic
133#11718321C2211yescharacteristic
134#11718321C2211yescharacteristic
135#11718321C2211yescharacteristic
136#11718321C2211yescharacteristic
137#11718321C2211yescharacteristic
138#11718321C2211yescharacteristic
139#11718321C2211yescharacteristic
140#11718321C2211yescharacteristic
141#11718320C2211yescharacteristic
142#11718320C2211yescharacteristic
143#11718320C2211yescharacteristic
144#11718320C2211yescharacteristic
145#11718319C2211yescharacteristic
146#11718319C2211yescharacteristic
147#11718319C2211yescharacteristic
148#11718319C2211yescharacteristic
149#11718319C2211yescharacteristic
150#11718319C2211yescharacteristic
151#11718319C2211yescharacteristic
152#11718318C2211yescharacteristic
153#11718317C2211yescharacteristic
154#11718317C2211yescharacteristic
155#11718316C2211yescharacteristic
156#11718316C2211yescharacteristic
157#11718316C2211yescharacteristic
158#11718316C2211yescharacteristic
159#11718316C2211yescharacteristic
160#11718316C2211yescharacteristic
161#11718316C2211yescharacteristic
162#11718316C2211yescharacteristic
163#11718315C2211yescharacteristic
164#11718315C2211yescharacteristic
165#11718315C2211yescharacteristic
166#11718315C2211yescharacteristic
167#11718314C2211yescharacteristic
168#11718314C2211yescharacteristic
169#11718314C2211yescharacteristic
170#11718314C2211yescharacteristic
171#11718314C2211yescharacteristic
172#11718314C2211yescharacteristic
173#11718314C2211yescharacteristic
174#11718313C2211yescharacteristic
175#11718313C2211yescharacteristic
176#11718313C2211yescharacteristic
177#11718313C2211yescharacteristic
178#11718312C2211yescharacteristic
179#11718312C2211yescharacteristic
180#11718311C2211yescharacteristic
181#11718311C2211yescharacteristic
182#11718308C2211yescharacteristic
183#11718307C2211yescharacteristic
184#11718307C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C22×C4×D13C2311yescharacteristic
188C22×C4×D13C2311yescharacteristic
189C22×C4×D13C2311yescharacteristic
190C22×C4×D13C2311yescharacteristic
191C22×C4×D13C2311yescharacteristic
192C22×C4×D13C2311yescharacteristic
193C22×C4×D13C2311yescharacteristic
194C22×Dic26C2311yescharacteristic
195C22×Dic26C2311yescharacteristic
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×#6103C2311yescharacteristic
212C2×#6103C2311yescharacteristic
213C2×#6103C2311yescharacteristic
214C2×#6103C2311yescharacteristic
215C2×#6103C2311yescharacteristic
216C2×#6103C2311yescharacteristic
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
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×C4⋊Dic13C2311yescharacteristic
231C2×C4⋊Dic13C2311yescharacteristic
232C2×C4⋊Dic13C2311yescharacteristic
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×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
266#88150—24no—
267#88150—24no—
268C4⋊C4×D13—24no—
269C4⋊C4×D13—42no—
270#88143—42no—
271#88143—42no—
272#88142—42no—
273C42×D13—42no—
274#88124—42no—
275C13×#95C2311yescharacteristic
276C13×#95C2311yescharacteristic
277C13×#95C2311yescharacteristic
278C13×#95C2311yescharacteristic
279C13×#95C2311yescharacteristic
280C13×#95C2311yescharacteristic
281C13×#95C2311yescharacteristic
282C13×#95C2311yescharacteristic
283C13×#95C2311yescharacteristic
284C13×#95C2311yescharacteristic
285C13×#95C2311yescharacteristic
286C13×#95C2311yescharacteristic
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289C13×#95C2311yescharacteristic
290C13×#95C2311yescharacteristic
291C13×#95C2311yescharacteristic
292C13×#95C2311yescharacteristic
293C13×#95C2311yescharacteristic
294C13×#95C2311yescharacteristic
295#88071C2311yescharacteristic
296#88071C2311yescharacteristic
297#88071C2311yescharacteristic
298#88071C2311yescharacteristic
299#88071C2311yescharacteristic
300#88071C2311yescharacteristic
301#88071C2311yescharacteristic
302#88071C2311yescharacteristic
303#88071C2311yescharacteristic
304#88071C2311yescharacteristic
305#88071C2311yescharacteristic
306#88071C2311yescharacteristic
307#88071C2311yescharacteristic
308#88071C2311yescharacteristic
309#88071C2311yescharacteristic
310#88071C2311yescharacteristic
311#88071C2311yescharacteristic
312#88071C2311yescharacteristic
313#88071C2311yescharacteristic
314#88071C2311yescharacteristic
315#88071C2311yescharacteristic
316#88071C2311yescharacteristic
317#88071C2311yescharacteristic
318#88071C2311yescharacteristic
319#88071C2311yescharacteristic
320#88071C2311yescharacteristic
321#88071C2311yescharacteristic
322#88071C2311yescharacteristic
323#88071C2311yescharacteristic
324#88071C2311yescharacteristic
325#88071C2311yescharacteristic
326#88071C2311yescharacteristic
327#88071C2311yescharacteristic
328#88071C2311yescharacteristic
329#88071C2311yescharacteristic
330#88071C2311yescharacteristic
331#88071C2311yescharacteristic
332#88071C2311yescharacteristic
333#88071C2311yescharacteristic
334#88071C2311yescharacteristic
335#88071C2311yescharacteristic
336#88071C2311yescharacteristic
337#88071C2311yescharacteristic
338#88071C2311yescharacteristic
339#88071C2311yescharacteristic
340#88071C2311yescharacteristic
341#88071C2311yescharacteristic
342#88071C2311yescharacteristic
343#88071C2311yescharacteristic
344#88071C2311yescharacteristic
345#88071C2311yescharacteristic
346#88071C2311yescharacteristic
347#88071C2311yescharacteristic
348#88071C2311yescharacteristic
349#88071C2311yescharacteristic
350#88071C2311yescharacteristic
351#36762—131nomaximal, Sylow
352C23×D13C2411yescharacteristic
353C22×C4×C13C2411yescharacteristic
354C22×C4×C13C2411yescharacteristic
355C22×C4×C13C2411yescharacteristic
356C22×C4×C13C2411yescharacteristic
357C22×C4×C13C2411yescharacteristic
358C22×C4×C13C2411yescharacteristic
359C22×C4×C13C2411yescharacteristic
360C22×C4×C13C2411yescharacteristic
361C22×C4×C13C2411yescharacteristic
362C22×C4×C13C2411yescharacteristic
363C22×C4×C13C2411yescharacteristic
364C22×C4×C13C2411yescharacteristic
365C22×C4×C13C2411yescharacteristic
366C22×C4×C13C2411yescharacteristic
367C22×C4×C13C2411yescharacteristic
368C22×Dic13C2411yescharacteristic
369C22×Dic13C2411yescharacteristic
370C22×Dic13C2411yescharacteristic
371C22×Dic13C2411yescharacteristic
372C22×Dic13C2411yescharacteristic
373C22×Dic13C2411yescharacteristic
374C22×Dic13C2411yescharacteristic
375C22×Dic13C2411yescharacteristic
376C22×Dic13C2411yescharacteristic
377C22×Dic13C2411yescharacteristic
378C22×Dic13C2411yescharacteristic
379C22×Dic13C2411yescharacteristic
380C22×Dic13C2411yescharacteristic
381C22×Dic13C2411yescharacteristic
382C22×Dic13C2411yescharacteristic
383C2×C4×D13—22no—
384C2×C4×D13—22no—
385C2×C4×D13—22no—
386C2×C4×D13—22no—
387C2×C4×D13—22no—
388C2×C4×D13—22no—
389C2×C4×D13—22no—
390C2×C4×D13—22no—
391C2×C4×D13—22no—
392C2×C4×D13—22no—
393C2×C4×D13—41no—
394C2×C4×D13—41no—
395C2×C4×D13—41no—
396C2×C4×D13—41no—
397C2×C4×D13—41no—
398C2×C4×D13—41no—
399C2×C4×D13—41no—
400C2×C4×D13—41no—
401C2×C4×D13—41no—
402C2×C4×D13—41no—
403C2×C4×D13#4114yes—
404C2×Dic26—22no—
405C2×Dic26—22no—
406C2×Dic26—41no—
407C2×Dic26—41no—
408C2×Dic26—41no—
409C2×Dic26—41no—
410C13×C4⋊C4—22no—
411C13×C4⋊C4—22no—
412C13×C4⋊C4—22no—
413C13×C4⋊C4—22no—
414C13×C4⋊C4—22no—
415C13×C4⋊C4—41no—
416C13×C4⋊C4—41no—
417C13×C4⋊C4—41no—
418C13×C4⋊C4—41no—
419C13×C4⋊C4—41no—
420C13×C4⋊C4—41no—
421C13×C4⋊C4—41no—
422C42×C13—22no—
423C42×C13—41no—
424C42×C13—41no—
425#6103—22no—
426#6103—22no—
427#6103—22no—
428#6103—22no—
429#6103—22no—
430#6103—22no—
431#6103—22no—
432#6103—22no—
433C4⋊Dic13—22no—
434C4⋊Dic13—22no—
435C4⋊Dic13—22no—
436C4⋊Dic13—22no—
437C4⋊Dic13—41no—
438C4⋊Dic13—41no—
439C4⋊Dic13—41no—
440C4⋊Dic13—41no—
441C4⋊Dic13—41no—
442C4⋊Dic13—41no—
443C4⋊Dic13—41no—
444C4⋊Dic13—41no—
445C4⋊Dic13—41no—
446C4⋊Dic13—41no—
447#6101—22no—
448#6101—22no—
449#6101—22no—
450#6101—22no—
451#6101—22no—
452#6101—22no—
453#6101—22no—
454#6101—22no—
455#6101—22no—
456#6101—22no—
457#6101—22no—
458#6101—41no—
459#6101—41no—
460#6101—41no—
461#6101—41no—
462#6101—41no—
463#6101—41no—
464#6101—41no—
465#6101—41no—
466#6101—41no—
467#6101—41no—
468#6101—41no—
469#6101—41no—
470#6101—41no—
471C4×Dic13—22no—
472C4×Dic13—41no—
473C4×Dic13—41no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13—41no—
478C4×Dic13—41no—
479C4×Dic13—41no—
480#2857—131no—
481#2851—131no—
482#2802—131no—
483#2802—131no—
484#2794—131no—
485#2794—131no—
486#2789—131no—
487#2789—131no—
488#2776—131no—
489#2776—131no—
490#2766—131no—
491#2766D1311yescharacteristic, complemented
492#2758—131no—
493#2758—131no—
494#2719—131no—
495#2719—131no—
496#2713—131no—
497#2713—131no—
498#2627—131no—
499#2627—131no—
500#2505—131no—
501#2505—131no—
502#2493—131no—
503#2493—131no—
504#2493—131no—
505#2493—131no—
506#2473—131no—
507#2473—131no—
508#2329—131no—
509#2329—131no—
510C2×#387—131no—
511C23×C13C2511yescharacteristic
512C22×D13—21no—
513C22×D13—21no—
514C22×D13—21no—
515C22×D13—21no—
516C22×D13C2×#4112yes—
517C22×D132−1+412yes—
518C22×D132−1+412yes—
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×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×C13C2×#4112yes—
563C2×C4×C13H(5,𝔽2)12yes—
564C2×Dic13—21no—
565C2×Dic13—21no—
566C2×Dic13—21no—
567C2×Dic13—21no—
568C2×Dic13—21no—
569C2×Dic13—21no—
570C2×Dic13—21no—
571C2×Dic13—21no—
572C2×Dic13—21no—
573C2×Dic13—21no—
574C2×Dic13—21no—
575C2×Dic13—21no—
576C2×Dic13—21no—
577C2×Dic13—21no—
578C2×Dic13—21no—
579C2×Dic13—21no—
580C2×Dic13—21no—
581C2×Dic13—21no—
582C2×Dic13—21no—
583C2×Dic13—21no—
584C2×Dic13—21no—
585C2×Dic13—21no—
586C2×Dic13—21no—
587C2×Dic13—21no—
588C2×Dic13—21no—
589C2×Dic13—21no—
590C2×Dic13—21no—
591C2×Dic13—21no—
592C2×Dic13—21no—
593C2×Dic13—21no—
594C2×Dic13—21no—
595C2×Dic13—21no—
596C2×Dic13—21no—
597C2×Dic13—21no—
598C2×Dic13—21no—
599C2×Dic13—21no—
600C2×Dic13—21no—
601C2×Dic13—21no—
602C2×Dic13—21no—
603C2×Dic13—21no—
604C2×Dic13—21no—
605C2×Dic13—21no—
606C2×Dic13—21no—
607C2×Dic13C2×#4112yes—
608C2×Dic132−1+412yes—
609C4×D13—44no—
610C4×D13—44no—
611C4×D13—44no—
612C4×D13—44no—
613C4×D13—44no—
614C4×D13—82no—
615C4×D13—82no—
616Dic26—82no—
617Dic26—82no—
618C2×C4⋊Q8—131no—
619C2×#125—131no—
620C2×#125—131no—
621C2×#125—131no—
622C2×C22⋊Q8—131no—
623C2×C22⋊Q8—131no—
624C22×C4⋊C4—131no—
625C22×C4⋊C4—131no—
626C22×C42—131no—
627#401—131no—
628#401—131no—
629#401—131no—
630#401C2×D1311yescharacteristic
631#400—131no—
632#400—131no—
633#400—131no—
634#400—131no—
635#400—131no—
636#400—131no—
637#400—131no—
638#400—131no—
639#400—131no—
640#400—131no—
641#400—131no—
642#400—131no—
643#400—131no—
644#400—131no—
645#400—131no—
646#400—131no—
647#400—131no—
648#400—131no—
649#400—131no—
650#400—131no—
651#400—131no—
652#400—131no—
653#400C2×D1311yescharacteristic
654#400C2×D1311yescharacteristic
655#398—131no—
656#398—131no—
657#398—131no—
658#398—131no—
659#398—131no—
660#398—131no—
661#398—131no—
662#398—131no—
663#398—131no—
664#398—131no—
665#398—131no—
666#398—131no—
667#398—131no—
668#398C2×D1311yescharacteristic
669#398C2×D1311yescharacteristic
670#398C2×D1311yescharacteristic
671#395—131no—
672#395—131no—
673#395—131no—
674#395—131no—
675#391—131no—
676#391—131no—
677#391—131no—
678#391—131no—
679#391—131no—
680#391—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#389—131no—
693#389C2×D1311yescharacteristic
694#389C2×D1311yescharacteristic
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#387—131no—
725#387—131no—
726#387—131no—
727#387—131no—
728#387—131no—
729#387—131no—
730#387C2×D1311yescharacteristic
731#387C2×D1311yescharacteristic
732#387C2×D1311yescharacteristic
733#387C2×D1311yescharacteristic
734#387C2×D1311yescharacteristic
735#385—131no—
736#385—131no—
737#385—131no—
738#385—131no—
739#385—131no—
740#385—131no—
741#385—131no—
742#385—131no—
743#385—131no—
744#385—131no—
745#385—131no—
746#385—131no—
747#384—131no—
748#383—131no—
749#383—131no—
750#383—131no—
751#383C2×D1311yescharacteristic
752#382—131no—
753#382—131no—
754#382C2×D1311yescharacteristic
755#381—131no—
756#381—131no—
757#381—131no—
758#381—131no—
759#380—131no—
760#380—131no—
761#380—131no—
762#380—131no—
763#380—131no—
764#380—131no—
765C4×C22⋊C4—131no—
766C4×C22⋊C4—131no—
767C4×C22⋊C4—131no—
768C4×C22⋊C4—131no—
769C2×#95—131no—
770C2×#95—131no—
771C2×#95—131no—
772C2×#95—131no—
773C22×C13C22×#4111yescharacteristic
774C22×C13C2×H(5,𝔽2)11yescharacteristic
775C22×C13C2×2−1+411yescharacteristic
776C22×C13C2×2−1+411yescharacteristic
777C22×C13C2×2−1+411yescharacteristic
778C22×C13#58511yescharacteristic
779C22×C13#58511yescharacteristic
780C2×D13—22no—
781C2×D13—22no—
782C2×D13—22no—
783C2×D13—22no—
784C2×D13—22no—
785C2×D13—22no—
786C2×D13#54114yes—
787C4×C13—22no—
788C4×C13—22no—
789C4×C13—41no—
790C4×C13—41no—
791C4×C13—41no—
792C4×C13—41no—
793C4×C13—41no—
794C4×C13—41no—
795C4×C13—41no—
796C4×C13—41no—
797C4×C13—41no—
798C4×C13—41no—
799C4×C13—41no—
800C4×C13—41no—
801C4×C13—41no—
802Dic13—22no—
803Dic13—22no—
804Dic13—41no—
805Dic13—41no—
806Dic13—41no—
807Dic13—41no—
808Dic13—41no—
809Dic13—41no—
810Dic13—41no—
811Dic13—41no—
812Dic13—41no—
813Dic13—41no—
814Dic13—41no—
815Dic13—41no—
816Dic13—41no—
817C22×Q8—131no—
818C22×Q8—131no—
819C23×C4—131no—
820C23×C4—131no—
821C23×C4—131no—
822C23×C4—131no—
823C23×C4—131no—
824C23×C4—131no—
825C23×C4—131no—
826C4⋊Q8—522no—
827#125—522no—
828#125—522no—
829#125—522no—
830C22⋊Q8—264no—
831C22⋊Q8—264no—
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⋊C4—264no—
871C2×C4⋊C4—522no—
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×C22⋊C4—131no—
885C2×C22⋊C4—131no—
886C2×C22⋊C4—131no—
887C2×C22⋊C4—131no—
888C2×C22⋊C4—131no—
889C2×C22⋊C4—131no—
890C2×C22⋊C4—131no—
891C2×C22⋊C4—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—522no—
902C2×C42C22×D1311yescharacteristic
903C2×C42C22×D1311yescharacteristic
904C2×C42C22×D1311yescharacteristic
905#95—131no—
906#95—131no—
907#95—131no—
908#95—131no—
909#95—131no—
910#95—131no—
911#95—131no—
912#95—131no—
913#95—131no—
914#95—131no—
915#95—131no—
916#95—131no—
917#95—131no—
918#95—131no—
919#95—131no—
920#95—131no—
921#95—131no—
922#95—131no—
923#95—131no—
924#95—131no—
925#95—131no—
926#95—131no—
927#95—131no—
928#95—131no—
929#95—131no—
930#95—131no—
931#95—131no—
932#95—131no—
933#95—131no—
934#95—131no—
935#95—131no—
936#95—131no—
937#95—131no—
938#95—131no—
939#95—131no—
940#95—131no—
941#95—131no—
942#95—131no—
943#95—131no—
944#95—131no—
945#95—131no—
946#95—131no—
947#95—131no—
948#95—131no—
949#95—131no—
950#95—131no—
951#95—131no—
952#95—131no—
953#95—131no—
954#95—131no—
955#95—131no—
956#95—131no—
957#95—131no—
958#95—131no—
959#95—131no—
960#95—131no—
961#95C22×D1311yescharacteristic
962#95C22×D1311yescharacteristic
963#95C22×D1311yescharacteristic
964#95C22×D1311yescharacteristic
965#95C22×D1311yescharacteristic
966#95C22×D1311yescharacteristic
967#95C22×D1311yescharacteristic
968#95C22×D1311yescharacteristic
969#95C22×D1311yescharacteristic
970#95C22×D1311yescharacteristic
971#95C22×D1311yescharacteristic
972#95C22×D1311yescharacteristic
973#95C22×D1311yescharacteristic
974#95C22×D1311yescharacteristic
975#95C22×D1311yescharacteristic
976#95C22×D1311yescharacteristic
977#95C22×D1311yescharacteristic
978#95C22×D1311yescharacteristic
979#95C22×D1311yescharacteristic
980#95C22×D1311yescharacteristic
981C2×C13C2×#54111yescharacteristic
982C2×C13#350511yescharacteristic
983C2×C13#350711yescharacteristic
984C2×C13#353511yescharacteristic
985C2×C13#353811yescharacteristic
986C2×C13#356311yescharacteristic
987C2×C13#356411yescharacteristic
988D13—24no—
989C24—131no—
990C2×Q8—262no—
991C2×Q8—262no—
992C2×Q8—521no—
993C2×Q8—521no—
994C2×Q8—521no—
995C2×Q8—521no—
996C22×C4—131no—
997C22×C4—131no—
998C22×C4—134no—
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—262no—
1013C22×C4—262no—
1014C22×C4—262no—
1015C22×C4—262no—
1016C22×C4—262no—
1017C22×C4—262no—
1018C22×C4—262no—
1019C22×C4—262no—
1020C22×C4—262no—
1021C22×C4—262no—
1022C22×C4—521no—
1023C22×C4—521no—
1024C22×C4—521no—
1025C22×C4—521no—
1026C22×C4—521no—
1027C22×C4—521no—
1028C22×C4—521no—
1029C22×C4—521no—
1030C22×C4—521no—
1031C22×C4—521no—
1032C22×C4C23×D1311yescharacteristic
1033C22×C4C23×D1311yescharacteristic
1034C22×C4C23×D1311yescharacteristic
1035C22×C4C23×D1311yescharacteristic
1036C22×C4C23×D1311yescharacteristic
1037C22×C4C23×D1311yescharacteristic
1038C22×C4C23×D1311yescharacteristic
1039C22×C4C23×D1311yescharacteristic
1040C22×C4C23×D1311yescharacteristic
1041C22×C4C23×D1311yescharacteristic
1042C22×C4C23×D1311yescharacteristic
1043C22×C4C23×D1311yescharacteristic
1044C22×C4C23×D1311yescharacteristic
1045C22×C4C23×D1311yescharacteristic
1046C22×C4C23×D1311yescharacteristic
1047C4⋊C4—22no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—22no—
1052C4⋊C4—41no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—41no—
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—521no—
1075C4⋊C4—521no—
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—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⋊C4—521no—
1097C22⋊C4—262no—
1098C22⋊C4—262no—
1099C22⋊C4—262no—
1100C22⋊C4—262no—
1101C22⋊C4—262no—
1102C22⋊C4—262no—
1103C22⋊C4—262no—
1104C22⋊C4—262no—
1105C42—22no—
1106C42—41no—
1107C42—41no—
1108C42—262no—
1109C42—521no—
1110C42—521no—
1111C42—521no—
1112C42—521no—
1113C42—521no—
1114C42—521no—
1115C42—521no—
1116C42—521no—
1117C13#3676211yescharacteristic, complemented, Sylow
1118C23—132no—
1119C23—132no—
1120C23—132no—
1121C23—261no—
1122C23—261no—
1123C23—261no—
1124C23—261no—
1125C23C24×D1311yescharacteristic
1126Q8—1042no—
1127Q8—1042no—
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—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—132no—
1172C2×C4—132no—
1173C2×C4—261no—
1174C2×C4—261no—
1175C2×C4—261no—
1176C2×C4—261no—
1177C2×C4—261no—
1178C2×C4—261no—
1179C2×C4—261no—
1180C2×C4—261no—
1181C2×C4—261no—
1182C2×C4—261no—
1183C2×C4—261no—
1184C2×C4—261no—
1185C2×C4—261no—
1186C2×C4—261no—
1187C2×C4—261no—
1188C2×C4—261no—
1189C2×C4—261no—
1190C2×C4—261no—
1191C2×C4—261no—
1192C2×C4—261no—
1193C2×C4—261no—
1194C2×C4—261no—
1195C2×C4—261no—
1196C2×C4—261no—
1197C2×C4—261no—
1198C2×C4—261no—
1199C2×C4—261no—
1200C2×C4—261no—
1201C2×C4—261no—
1202C2×C4—261no—
1203C2×C4—261no—
1204C2×C4—261no—
1205C2×C4—261no—
1206C2×C4—261no—
1207C2×C4—261no—
1208C2×C4—261no—
1209C2×C4—261no—
1210C2×C4—261no—
1211C2×C4—261no—
1212C2×C4—261no—
1213C2×C4—261no—
1214C2×C4—261no—
1215C2×C4—261no—
1216C2×C4—524no—
1217C2×C4—524no—
1218C2×C4—524no—
1219C2×C4—524no—
1220C2×C4—524no—
1221C2×C4—1042no—
1222C2×C4—1042no—
1223C2×C4#41×D1312yes—
1224C2×C4#8825612yes—
1225C22—134no—
1226C22—262no—
1227C22—262no—
1228C22—262no—
1229C22—262no—
1230C22—262no—
1231C22—262no—
1232C22C2×#41×D1311yescharacteristic
1233C22C2×#8825611yescharacteristic
1234C22#1171964811yescharacteristic
1235C22#1171965011yescharacteristic
1236C22D13×2−1+411yescharacteristic
1237C22D13×2−1+411yescharacteristic
1238C22D13×2−1+411yescharacteristic
1239C4—22no—
1240C4—22no—
1241C4—41no—
1242C4—41no—
1243C4—41no—
1244C4—41no—
1245C4—41no—
1246C4—41no—
1247C4—41no—
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—262no—
1255C4—262no—
1256C4—521no—
1257C4—521no—
1258C4—521no—
1259C4—521no—
1260C4—521no—
1261C4—521no—
1262C4—521no—
1263C4—521no—
1264C4—521no—
1265C4—521no—
1266C4—521no—
1267C4—521no—
1268C4—521no—
1269C2—264no—
1270C2D13×#54111yescharacteristic
1271C2#1312866511yescharacteristic
1272C2#1312869511yescharacteristic
1273C2#1312904811yescharacteristic
1274C2#1312908411yescharacteristic
1275C2#1312943611yescharacteristic
1276C2#1312946111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2766C2
prime radicalC23×D13C24
hypercenter#2766D13
hypocenterC13#36762
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2766

Complements

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

NH ≅ G/Ntype
3. #13122756C2semidirect
4. #13122754C2semidirect
5. #13122661C2semidirect
6. #13122654C2semidirect
7. #13122595C2semidirect
8. #13122590C2semidirect
9. #13122428C2semidirect
10. #13122426C2semidirect
11. #13122282C2semidirect
12. #13122192C2semidirect
13. #13122185C2semidirect
14. #13121705C2semidirect
15. #13121701C2semidirect
16. #13121624C2semidirect
17. #13121615C2semidirect
31. C13×#2766C2semidirect
491. #2766D13semidirect
1117. C13#36762semidirect

Maximal subgroups

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

subgroupindex
#131231872
#131231472
#131227562
#131227542
#131226612
#131226542
#131225952
#131225902
#131224282
#131224262
#131222822
#131221922
#131221852
#131217052
#131217012
#131216242
#131216152
#131206542
#131193442
#131193322
#131192202
#131192182
#131192162
#131192142
#131189782
#131189752
#131175702
#131175632
D13×#3872
C13×#27662
#3676213