Finite Group Databasebeta

← #13128857

Subgroups — #13128857

Order 1664.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#546C211yesmaximal, characteristic, complemented
2#11719537C211yesmaximal, characteristic, complemented
3#11719534C211yesmaximal, characteristic, complemented
4C2×#88193C211yesmaximal, characteristic, complemented
5D4×C22⋊D13C211yesmaximal, characteristic, complemented
6#11719383C211yesmaximal, characteristic, complemented
7#11719375C211yesmaximal, characteristic, complemented
8#11719368C211yesmaximal, characteristic, complemented
9#11719366C211yesmaximal, characteristic, complemented
10#11719359C211yesmaximal, characteristic, complemented
11#11719354C211yesmaximal, characteristic, complemented
12#11719349C211yesmaximal, characteristic, complemented
13#11719341C211yesmaximal, characteristic, complemented
14#11719320C211yesmaximal, characteristic, complemented
15#11719318C211yesmaximal, characteristic, complemented
16#11719315C211yesmaximal, characteristic, complemented
17D13×#121C211yesmaximal, characteristic, complemented
18#11719306C211yesmaximal, characteristic, complemented
19#11719304C211yesmaximal, characteristic, complemented
20#11719298C211yesmaximal, characteristic, complemented
21#11719295C211yesmaximal, characteristic, complemented
22#11719295C211yesmaximal, characteristic, complemented
23#11719291C211yesmaximal, characteristic, complemented
24#11719252C211yesmaximal, characteristic, complemented
25#11719250C211yesmaximal, characteristic, complemented
26#11719245C211yesmaximal, characteristic, complemented
27#11719245C211yesmaximal, characteristic, complemented
28#11719195C211yesmaximal, characteristic, complemented
29#11719195C211yesmaximal, characteristic, complemented
30#11719191C211yesmaximal, characteristic, complemented
31C2×#88135C211yesmaximal, characteristic, complemented
32C2×C13×#41C2211yescharacteristic, complemented
33C22×D4×C13C2211yescharacteristic, complemented
34C22×C22⋊D13C2211yescharacteristic
35C22×C22⋊D13C2211yescharacteristic
36C22×C22⋊D13C2211yescharacteristic, complemented
37C22×C22⋊D13C2211yescharacteristic, complemented
38C23×Dic13C2211yescharacteristic, complemented
39C2×#6129C2211yescharacteristic, complemented
40C2×D4×D13C2211yescharacteristic
41C2×D4×D13C2211yescharacteristic, complemented
42C2×D4×D13C2211yescharacteristic, complemented
43C2×D4×D13C2211yescharacteristic, complemented
44C2×#6127C2211yescharacteristic, complemented
45C2×#6127C2211yescharacteristic, complemented
46C22×C4×D13C2211yescharacteristic, complemented
47C13×#124C2211yescharacteristic, complemented
48C13×#123C2211yescharacteristic, complemented
49C13×#123C2211yescharacteristic, complemented
50C13×C22⋊Q8C2211yescharacteristic, complemented
51C13×#121C2211yescharacteristic, complemented
52C13×#121C2211yescharacteristic, complemented
53C13×#121C2211yescharacteristic, complemented
54C13×#120C2211yescharacteristic, complemented
55C13×#120C2211yescharacteristic, complemented
56C4×D4×C13C2211yescharacteristic, complemented
57C4×D4×C13C2211yescharacteristic, complemented
58C2×C13×C22⋊C4C2211yescharacteristic, complemented
59C2×C13×C22⋊C4C2211yescharacteristic, complemented
60#88207C2211yescharacteristic, complemented
61#88207C2211yescharacteristic, complemented
62C2×C22⋊Dic13C2211yescharacteristic, complemented
63#88201C2211yescharacteristic, complemented
64#88201C2211yescharacteristic, complemented
65#88200C2211yescharacteristic, complemented
66#88198C2211yescharacteristic, complemented
67#88194C2211yescharacteristic, complemented
68#88194C2211yescharacteristic, complemented
69#88194C2211yescharacteristic, complemented
70#88193C2211yescharacteristic
71#88193C2211yescharacteristic, complemented
72#88193C2211yescharacteristic, complemented
73#88193C2211yescharacteristic, complemented
74#88193C2211yescharacteristic, complemented
75#88193C2211yescharacteristic, complemented
76#88193C2211yescharacteristic, complemented
77#88193C2211yescharacteristic, complemented
78#88193C2211yescharacteristic, complemented
79#88193C2211yescharacteristic, complemented
80#88193C2211yescharacteristic, complemented
81#88193C2211yescharacteristic, complemented
82#88193C2211yescharacteristic, complemented
83#88193C2211yescharacteristic, complemented
84#88193C2211yescharacteristic, complemented
85#88193C2211yescharacteristic, complemented
86#88192C2211yescharacteristic, complemented
87#88192C2211yescharacteristic, complemented
88#88191C2211yescharacteristic, complemented
89#88191C2211yescharacteristic, complemented
90#88191C2211yescharacteristic, complemented
91#88191C2211yescharacteristic, complemented
92#88190C2211yescharacteristic, complemented
93#88189C2211yescharacteristic, complemented
94#88189C2211yescharacteristic, complemented
95D4×Dic13C2211yescharacteristic, complemented
96D4×Dic13C2211yescharacteristic, complemented
97D4×Dic13C2211yescharacteristic, complemented
98#88184C2211yescharacteristic, complemented
99#88184C2211yescharacteristic, complemented
100#88184C2211yescharacteristic, complemented
101#88183C2211yescharacteristic, complemented
102#88183C2211yescharacteristic, complemented
103#88183C2211yescharacteristic, complemented
104C4×C22⋊D13C2211yescharacteristic
105C4×C22⋊D13C2211yescharacteristic, complemented
106C4×C22⋊D13C2211yescharacteristic, complemented
107C4×C22⋊D13C2211yescharacteristic, complemented
108C4×C22⋊D13C2211yescharacteristic, complemented
109C4×C22⋊D13C2211yescharacteristic, complemented
110C4×C22⋊D13C2211yescharacteristic, complemented
111C4×C22⋊D13C2211yescharacteristic, complemented
112C4×C22⋊D13C2211yescharacteristic, complemented
113C2×#6103C2211yescharacteristic, complemented
114C2×#6103C2211yescharacteristic, complemented
115C2×#6103C2211yescharacteristic, complemented
116C2×#6101C2211yescharacteristic, complemented
117C2×#6101C2211yescharacteristic, complemented
118C2×C4×Dic13C2211yescharacteristic, complemented
119#88152C2211yescharacteristic, complemented
120#88152C2211yescharacteristic, complemented
121#88150C2211yescharacteristic, complemented
122#88150C2211yescharacteristic, complemented
123#88149C2211yescharacteristic, complemented
124#88149C2211yescharacteristic, complemented
125#88148C2211yescharacteristic, complemented
126#88148C2211yescharacteristic, complemented
127#88148C2211yescharacteristic, complemented
128#88147C2211yescharacteristic, complemented
129#88146C2211yescharacteristic, complemented
130C4⋊C4×D13C2211yescharacteristic, complemented
131#88143C2211yescharacteristic, complemented
132#88143C2211yescharacteristic, complemented
133#88143C2211yescharacteristic, complemented
134#88141C2211yescharacteristic, complemented
135#88140C2211yescharacteristic, complemented
136#88139C2211yescharacteristic, complemented
137#88139C2211yescharacteristic, complemented
138#88139C2211yescharacteristic, complemented
139#88138C2211yescharacteristic, complemented
140#88138C2211yescharacteristic, complemented
141#88138C2211yescharacteristic, complemented
142#88138C2211yescharacteristic, complemented
143#88138C2211yescharacteristic, complemented
144#88138C2211yescharacteristic, complemented
145#88138C2211yescharacteristic, complemented
146#88138C2211yescharacteristic, complemented
147#88138C2211yescharacteristic, complemented
148#88137C2211yescharacteristic, complemented
149#88137C2211yescharacteristic, complemented
150#88137C2211yescharacteristic, complemented
151#88136C2211yescharacteristic, complemented
152#88136C2211yescharacteristic, complemented
153#88136C2211yescharacteristic, complemented
154#88136C2211yescharacteristic, complemented
155#88135C2211yescharacteristic
156#88135C2211yescharacteristic
157#88135C2211yescharacteristic
158#88135C2211yescharacteristic, complemented
159#88135C2211yescharacteristic, complemented
160#88135C2211yescharacteristic, complemented
161#88135C2211yescharacteristic, complemented
162#88135C2211yescharacteristic, complemented
163#88135C2211yescharacteristic, complemented
164#88135C2211yescharacteristic, complemented
165#88135C2211yescharacteristic, complemented
166#88135C2211yescharacteristic, complemented
167#88135C2211yescharacteristic, complemented
168#88135C2211yescharacteristic, complemented
169#88135C2211yescharacteristic, complemented
170C22⋊C4×D13C2211yescharacteristic, complemented
171C22⋊C4×D13C2211yescharacteristic, complemented
172C22⋊C4×D13C2211yescharacteristic, complemented
173C22⋊C4×D13C2211yescharacteristic, complemented
174#88133C2211yescharacteristic, complemented
175#88133C2211yescharacteristic, complemented
176#88133C2211yescharacteristic, complemented
177#88132C2211yescharacteristic, complemented
178#88132C2211yescharacteristic, complemented
179#88132C2211yescharacteristic, complemented
180#88131C2211yescharacteristic, complemented
181#88131C2211yescharacteristic, complemented
182#88131C2211yescharacteristic, complemented
183#88130C2211yescharacteristic, complemented
184C4×D52C2211yescharacteristic, complemented
185#88126C2211yescharacteristic, complemented
186#88126C2211yescharacteristic, complemented
187C24×C13C2311yescharacteristic
188C24×C13C2311yescharacteristic
189C23×D13C2311yescharacteristic
190C23×D13C2311yescharacteristic
191C23×D13C2311yescharacteristic
192C23×D13C2311yescharacteristic
193C13×#41—42no—
194C2×Q8×C13C2311yescharacteristic
195C2×D4×C13—42no—
196C2×D4×C13C2311yescharacteristic
197C2×D4×C13C2311yescharacteristic
198C2×D4×C13C2311yescharacteristic
199C2×D4×C13C2311yescharacteristic
200C2×D4×C13C2311yescharacteristic
201C2×D4×C13C2311yescharacteristic
202C2×D4×C13C2311yescharacteristic
203C2×D4×C13C2311yescharacteristic
204C2×D4×C13C2311yescharacteristic
205C22×C4×C13C2311yescharacteristic
206C22×C4×C13C2311yescharacteristic
207C22×C4×C13C2311yescharacteristic
208C22×C4×C13C2311yescharacteristic
209C22×C4×C13C2311yescharacteristic
210C22×C4×C13C2311yescharacteristic
211C2×C22⋊D13—24no—
212C2×C22⋊D13—24no—
213C2×C22⋊D13—42no—
214C2×C22⋊D13—42no—
215C2×C22⋊D13C2311yescharacteristic
216C2×C22⋊D13C2311yescharacteristic
217C2×C22⋊D13C2311yescharacteristic
218C2×C22⋊D13C2311yescharacteristic
219C2×C22⋊D13C2311yescharacteristic
220C2×C22⋊D13C2311yescharacteristic
221C2×C22⋊D13C2311yescharacteristic
222C2×C22⋊D13C2311yescharacteristic
223C2×C22⋊D13C2311yescharacteristic
224C2×C22⋊D13C2311yescharacteristic
225C2×C22⋊D13C2311yescharacteristic
226C2×C22⋊D13C2311yescharacteristic
227C2×C22⋊D13C2311yescharacteristic
228C2×C22⋊D13C2311yescharacteristic
229C2×C22⋊D13C2311yescharacteristic
230C2×C22⋊D13C2311yescharacteristic
231C2×C22⋊D13C2311yescharacteristic
232C2×C22⋊D13C2311yescharacteristic
233C2×C22⋊D13C2311yescharacteristic
234C2×C22⋊D13C2311yescharacteristic
235C2×C22⋊D13C2311yescharacteristic
236C2×C22⋊D13C2311yescharacteristic
237C22×Dic13—42no—
238C22×Dic13C2311yescharacteristic
239C22×Dic13C2311yescharacteristic
240C22×Dic13C2311yescharacteristic
241C22×Dic13C2311yescharacteristic
242C22×Dic13C2311yescharacteristic
243C22×Dic13C2311yescharacteristic
244C22×Dic13C2311yescharacteristic
245C22×Dic13C2311yescharacteristic
246C22×Dic13C2311yescharacteristic
247C22×Dic13C2311yescharacteristic
248#6129—42no—
249D4×D13—24no—
250D4×D13—42no—
251D4×D13—42no—
252D4×D13—42no—
253#6127—42no—
254#6127—42no—
255C2×D52C2311yescharacteristic
256C2×D52C2311yescharacteristic
257C2×D52C2311yescharacteristic
258C2×D52C2311yescharacteristic
259C2×D52C2311yescharacteristic
260C2×D52C2311yescharacteristic
261C2×C4×D13—42no—
262C2×C4×D13C2311yescharacteristic
263C2×C4×D13C2311yescharacteristic
264C2×C4×D13C2311yescharacteristic
265C2×C4×D13C2311yescharacteristic
266C2×C4×D13C2311yescharacteristic
267C2×C4×D13C2311yescharacteristic
268C2×C4×D13C2311yescharacteristic
269C2×C4×D13C2311yescharacteristic
270C2×C4×D13C2311yescharacteristic
271C2×C4×D13C2311yescharacteristic
272C2×C4×D13C2311yescharacteristic
273C2×Dic26C2311yescharacteristic
274C2×Dic26C2311yescharacteristic
275C13×C4⋊C4C2311yescharacteristic
276C13×C4⋊C4C2311yescharacteristic
277C13×C4⋊C4C2311yescharacteristic
278C13×C4⋊C4C2311yescharacteristic
279C13×C22⋊C4C2311yescharacteristic
280C13×C22⋊C4C2311yescharacteristic
281C13×C22⋊C4C2311yescharacteristic
282C13×C22⋊C4C2311yescharacteristic
283C13×C22⋊C4C2311yescharacteristic
284C13×C22⋊C4C2311yescharacteristic
285C13×C22⋊C4C2311yescharacteristic
286C13×C22⋊C4C2311yescharacteristic
287C13×C22⋊C4C2311yescharacteristic
288C13×C22⋊C4C2311yescharacteristic
289C13×C22⋊C4C2311yescharacteristic
290C13×C22⋊C4C2311yescharacteristic
291C42×C13C2311yescharacteristic
292C22⋊Dic13C2311yescharacteristic
293C22⋊Dic13C2311yescharacteristic
294C22⋊Dic13C2311yescharacteristic
295C22⋊Dic13C2311yescharacteristic
296C22⋊Dic13C2311yescharacteristic
297C22⋊Dic13C2311yescharacteristic
298C22⋊Dic13C2311yescharacteristic
299C22⋊Dic13C2311yescharacteristic
300C22⋊Dic13C2311yescharacteristic
301C22⋊Dic13C2311yescharacteristic
302C22⋊Dic13C2311yescharacteristic
303C22⋊Dic13C2311yescharacteristic
304#6103C2311yescharacteristic
305#6103C2311yescharacteristic
306#6103C2311yescharacteristic
307#6103C2311yescharacteristic
308#6103C2311yescharacteristic
309#6103C2311yescharacteristic
310#6103C2311yescharacteristic
311#6103C2311yescharacteristic
312#6103C2311yescharacteristic
313#6103C2311yescharacteristic
314#6103C2311yescharacteristic
315#6103C2311yescharacteristic
316#6103C2311yescharacteristic
317#6103C2311yescharacteristic
318#6103C2311yescharacteristic
319#6103C2311yescharacteristic
320#6103C2311yescharacteristic
321#6103C2311yescharacteristic
322#6103C2311yescharacteristic
323#6103C2311yescharacteristic
324#6103C2311yescharacteristic
325#6103C2311yescharacteristic
326C4⋊Dic13C2311yescharacteristic
327C4⋊Dic13C2311yescharacteristic
328C4⋊Dic13C2311yescharacteristic
329C4⋊Dic13C2311yescharacteristic
330#6101C2311yescharacteristic
331#6101C2311yescharacteristic
332#6101C2311yescharacteristic
333#6101C2311yescharacteristic
334#6101C2311yescharacteristic
335#6101C2311yescharacteristic
336#6101C2311yescharacteristic
337#6101C2311yescharacteristic
338#6101C2311yescharacteristic
339#6101C2311yescharacteristic
340#6101C2311yescharacteristic
341#6101C2311yescharacteristic
342#6101C2311yescharacteristic
343#6101C2311yescharacteristic
344#6101C2311yescharacteristic
345#6101C2311yescharacteristic
346#6101C2311yescharacteristic
347#6101C2311yescharacteristic
348C4×Dic13C2311yescharacteristic
349C4×Dic13C2311yescharacteristic
350C4×Dic13C2311yescharacteristic
351C4×Dic13C2311yescharacteristic
352C4×Dic13C2311yescharacteristic
353C4×Dic13C2311yescharacteristic
354C4×Dic13C2311yescharacteristic
355C4×Dic13C2311yescharacteristic
356C4×Dic13C2311yescharacteristic
357#3519—131nomaximal, Sylow
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13C2411yescharacteristic
365C23×C13C2411yescharacteristic
366C23×C13C2411yescharacteristic
367C23×C13C2411yescharacteristic
368C23×C13C2411yescharacteristic
369C23×C13C2411yescharacteristic
370C22×D13—22no—
371C22×D13—22no—
372C22×D13—22no—
373C22×D13—22no—
374C22×D13—22no—
375C22×D13—41no—
376C22×D13—41no—
377C22×D13—41no—
378C22×D13—41no—
379C22×D13—41no—
380C22×D13—41no—
381C22×D13—41no—
382C22×D13C2411yescharacteristic
383C22×D13C2411yescharacteristic
384C22×D13C2411yescharacteristic
385C22×D13C2411yescharacteristic
386C22×D13C2411yescharacteristic
387Q8×C13—41no—
388D4×C13—22no—
389D4×C13—22no—
390D4×C13—22no—
391D4×C13—22no—
392D4×C13—41no—
393D4×C13—41no—
394D4×C13—41no—
395D4×C13—41no—
396D4×C13—41no—
397C2×C4×C13—22no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13C2411yescharacteristic
404C2×C4×C13C2411yescharacteristic
405C2×C4×C13C2411yescharacteristic
406C2×C4×C13C2411yescharacteristic
407C2×C4×C13C2411yescharacteristic
408C2×C4×C13C2411yescharacteristic
409C2×C4×C13C2411yescharacteristic
410C2×C4×C13C2411yescharacteristic
411C2×C4×C13C2411yescharacteristic
412C22⋊D13—22no—
413C22⋊D13—22no—
414C22⋊D13—22no—
415C22⋊D13—22no—
416C22⋊D13—22no—
417C22⋊D13—22no—
418C22⋊D13—22no—
419C22⋊D13—22no—
420C22⋊D13—22no—
421C22⋊D13—22no—
422C22⋊D13—22no—
423C22⋊D13—22no—
424C22⋊D13—22no—
425C22⋊D13—41no—
426C22⋊D13—41no—
427C22⋊D13—41no—
428C22⋊D13—41no—
429C22⋊D13—41no—
430C22⋊D13—41no—
431C22⋊D13—41no—
432C22⋊D13—41no—
433C22⋊D13#4114yescomplemented
434C2×Dic13—22no—
435C2×Dic13—22no—
436C2×Dic13—22no—
437C2×Dic13—22no—
438C2×Dic13—22no—
439C2×Dic13—41no—
440C2×Dic13—41no—
441C2×Dic13—41no—
442C2×Dic13—41no—
443C2×Dic13—41no—
444C2×Dic13C2411yescharacteristic
445C2×Dic13C2411yescharacteristic
446C2×Dic13C2411yescharacteristic
447C2×Dic13C2411yescharacteristic
448C2×Dic13C2411yescharacteristic
449C2×Dic13C2411yescharacteristic
450C2×Dic13C2411yescharacteristic
451C2×Dic13C2411yescharacteristic
452C2×Dic13C2411yescharacteristic
453C2×Dic13C2411yescharacteristic
454C2×Dic13C2411yescharacteristic
455D52—22no—
456D52—41no—
457D52—41no—
458D52—41no—
459D52—41no—
460D52—41no—
461C4×D13—22no—
462C4×D13—22no—
463C4×D13—22no—
464C4×D13—41no—
465C4×D13—41no—
466C4×D13—41no—
467C4×D13—41no—
468C4×D13—41no—
469C4×D13—41no—
470C4×D13—41no—
471C4×D13—41no—
472Dic26—22no—
473Dic26—41no—
474#555—131no—
475#554—131no—
476#553—131no—
477#553—131no—
478#553—131no—
479#553—131no—
480#550—131no—
481#546—131no—
482#546—131no—
483#546—131no—
484#546—131no—
485#546—131no—
486#546D1311yescharacteristic, complemented
487D42—131no—
488D42—131no—
489D42—131no—
490#540—131no—
491#540—131no—
492#538—131no—
493#538—131no—
494#538—131no—
495#538—131no—
496#532—131no—
497#529—131no—
498#525—131no—
499#525—131no—
500C2×#121—131no—
501C2×#121—131no—
502#518—131no—
503#518—131no—
504C2×C4×D4—131no—
505C22×C13—21no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—21no—
509C22×C13—21no—
510C22×C13—21no—
511C22×C13—21no—
512C22×C13—21no—
513C22×C13—21no—
514C22×C13—21no—
515C22×C13—21no—
516C22×C13—21no—
517C22×C13—21no—
518C22×C13—21no—
519C22×C13—21no—
520C22×C13—21no—
521C22×C13—44no—
522C22×C13—82no—
523C22×C13C2×#4112yes—
524C22×C13H(5,𝔽2)12yes—
525C22×C13C2511yescharacteristic
526C2×D13—21no—
527C2×D13—21no—
528C2×D13—21no—
529C2×D13—21no—
530C2×D13—21no—
531C2×D13—21no—
532C2×D13—21no—
533C2×D13—21no—
534C2×D13—21no—
535C2×D13—21no—
536C2×D13—21no—
537C2×D13—21no—
538C2×D13—21no—
539C2×D13—21no—
540C2×D13—44no—
541C2×D13—82no—
542C2×D13—82no—
543C2×D13—82no—
544C2×D13C2×#4112yes—
545C4×C13—21no—
546C4×C13—21no—
547C4×C13—21no—
548C4×C13—21no—
549C4×C13—21no—
550C4×C13—21no—
551C4×C13—21no—
552C4×C13—21no—
553C4×C13—21no—
554Dic13—21no—
555Dic13—21no—
556Dic13—21no—
557Dic13—21no—
558Dic13—21no—
559Dic13—21no—
560Dic13—21no—
561Dic13—21no—
562Dic13—21no—
563Dic13C2×#4112yes—
564Dic13H(5,𝔽2)12yes—
565C2×#41—131no—
566C2×#41—131no—
567C2×#41—131no—
568C2×#41C2×D1311yescharacteristic, complemented
569C22×D4—131no—
570C22×D4—131no—
571C22×D4—131no—
572C22×D4—131no—
573C22×D4—131no—
574C22×D4—131no—
575C22×D4—131no—
576C22×D4—131no—
577C22×D4C2×D1311yescharacteristic, complemented
578C23×C4—131no—
579C23×C4—131no—
580C4⋊Q8—131no—
581#127—131no—
582#127—131no—
583#127—131no—
584#126—131no—
585#126—131no—
586#126—131no—
587#126—131no—
588#126—131no—
589#126—131no—
590#125—131no—
591#125—131no—
592#125—131no—
593#124—131no—
594#124—131no—
595#124—131no—
596#124—131no—
597#124—131no—
598#124—131no—
599#124C2×D1311yescharacteristic, complemented
600#123—131no—
601#123—131no—
602#123—131no—
603#123—131no—
604#123—131no—
605#123—131no—
606#123—131no—
607#123—131no—
608#123—131no—
609#123—131no—
610#123—131no—
611#123—131no—
612#123C2×D1311yescharacteristic, complemented
613#123C2×D1311yescharacteristic, complemented
614C22⋊Q8—131no—
615C22⋊Q8—131no—
616C22⋊Q8—131no—
617C22⋊Q8—131no—
618C22⋊Q8—131no—
619C22⋊Q8—131no—
620C22⋊Q8C2×D1311yescharacteristic, complemented
621#121—131no—
622#121—131no—
623#121—131no—
624#121—131no—
625#121—131no—
626#121—131no—
627#121—131no—
628#121—131no—
629#121—131no—
630#121—131no—
631#121—131no—
632#121—131no—
633#121—131no—
634#121—131no—
635#121—131no—
636#121—131no—
637#121—131no—
638#121—131no—
639#121—131no—
640#121—131no—
641#121—131no—
642#121—131no—
643#121—131no—
644#121—131no—
645#121—131no—
646#121—131no—
647#121—131no—
648#121—131no—
649#121—131no—
650#121—131no—
651#121—131no—
652#121—131no—
653#121C2×D1311yescharacteristic, complemented
654#121C2×D1311yescharacteristic, complemented
655#121C2×D1311yescharacteristic, complemented
656#120—131no—
657#120—131no—
658#120—131no—
659#120—131no—
660#120—131no—
661#120—131no—
662#120—131no—
663#120—131no—
664#120—131no—
665#120—131no—
666#120C2×D1311yescharacteristic, complemented
667#120C2×D1311yescharacteristic, complemented
668C4×Q8—131no—
669C4×D4—131no—
670C4×D4—131no—
671C4×D4—131no—
672C4×D4—131no—
673C4×D4—131no—
674C4×D4—131no—
675C4×D4—131no—
676C4×D4—131no—
677C4×D4—131no—
678C4×D4—131no—
679C4×D4—131no—
680C4×D4—131no—
681C4×D4—131no—
682C4×D4—131no—
683C4×D4—131no—
684C4×D4—131no—
685C4×D4—131no—
686C4×D4—131no—
687C4×D4—131no—
688C4×D4—131no—
689C4×D4—131no—
690C4×D4—131no—
691C4×D4—131no—
692C4×D4—131no—
693C4×D4—131no—
694C4×D4—131no—
695C4×D4—131no—
696C4×D4—131no—
697C4×D4—131no—
698C4×D4C2×D1311yescharacteristic, complemented
699C4×D4C2×D1311yescharacteristic, complemented
700#117—131no—
701#117—131no—
702#117—131no—
703#117—131no—
704#117—131no—
705#117—131no—
706C2×C4⋊C4—131no—
707C2×C4⋊C4—131no—
708C2×C4⋊C4—131no—
709C2×C22⋊C4—131no—
710C2×C22⋊C4—131no—
711C2×C22⋊C4—131no—
712C2×C22⋊C4—131no—
713C2×C22⋊C4—131no—
714C2×C22⋊C4—131no—
715C2×C22⋊C4—131no—
716C2×C22⋊C4—131no—
717C2×C22⋊C4C2×D1311yescharacteristic, complemented
718C2×C22⋊C4C2×D1311yescharacteristic, complemented
719C2×C42—131no—
720C2×C13—22no—
721C2×C13—22no—
722C2×C13—41no—
723C2×C13—41no—
724C2×C13—41no—
725C2×C13—41no—
726C2×C13C22×#4111yescharacteristic
727C2×C13C2×H(5,𝔽2)11yescharacteristic
728C2×C13C2×H(5,𝔽2)11yescharacteristic
729D13—22no—
730D13—41no—
731D13—41no—
732D13—41no—
733D13—41no—
734C24—131no—
735C24—131no—
736C24—131no—
737C24—131no—
738C24C22×D1311yescharacteristic
739C24C22×D1311yescharacteristic
740#41—42no—
741#41—522no—
742#41—522no—
743#41—522no—
744C2×Q8—131no—
745C2×Q8—131no—
746C2×Q8C22×D1311yescharacteristic
747C2×D4—42no—
748C2×D4—131no—
749C2×D4—131no—
750C2×D4—131no—
751C2×D4—131no—
752C2×D4—131no—
753C2×D4—131no—
754C2×D4—131no—
755C2×D4—131no—
756C2×D4—131no—
757C2×D4—131no—
758C2×D4—131no—
759C2×D4—131no—
760C2×D4—131no—
761C2×D4—131no—
762C2×D4—131no—
763C2×D4—131no—
764C2×D4—131no—
765C2×D4—131no—
766C2×D4—131no—
767C2×D4—131no—
768C2×D4—131no—
769C2×D4—131no—
770C2×D4—131no—
771C2×D4—131no—
772C2×D4—131no—
773C2×D4—131no—
774C2×D4—131no—
775C2×D4—131no—
776C2×D4—264no—
777C2×D4—264no—
778C2×D4—264no—
779C2×D4—522no—
780C2×D4—522no—
781C2×D4—522no—
782C2×D4—522no—
783C2×D4—522no—
784C2×D4C22×D1311yescharacteristic
785C2×D4C22×D1311yescharacteristic
786C2×D4C22×D1311yescharacteristic
787C2×D4C22×D1311yescharacteristic
788C2×D4C22×D1311yescharacteristic
789C2×D4C22×D1311yescharacteristic
790C2×D4C22×D1311yescharacteristic
791C2×D4C22×D1311yescharacteristic
792C2×D4C22×D1311yescharacteristic
793C22×C4—131no—
794C22×C4—131no—
795C22×C4—131no—
796C22×C4—131no—
797C22×C4—131no—
798C22×C4—131no—
799C22×C4—131no—
800C22×C4—131no—
801C22×C4—131no—
802C22×C4—131no—
803C22×C4—131no—
804C22×C4—131no—
805C22×C4—131no—
806C22×C4—131no—
807C22×C4—131no—
808C22×C4—131no—
809C22×C4—131no—
810C22×C4—131no—
811C22×C4—131no—
812C22×C4—131no—
813C22×C4—131no—
814C22×C4—522no—
815C22×C4—522no—
816C22×C4C22×D1311yescharacteristic
817C22×C4C22×D1311yescharacteristic
818C22×C4C22×D1311yescharacteristic
819C22×C4C22×D1311yescharacteristic
820C22×C4C22×D1311yescharacteristic
821C22×C4C22×D1311yescharacteristic
822C4⋊C4—131no—
823C4⋊C4—131no—
824C4⋊C4—131no—
825C4⋊C4—131no—
826C4⋊C4—131no—
827C4⋊C4—131no—
828C4⋊C4—131no—
829C4⋊C4—131no—
830C4⋊C4—131no—
831C4⋊C4—131no—
832C4⋊C4—131no—
833C4⋊C4—131no—
834C4⋊C4—131no—
835C4⋊C4—131no—
836C4⋊C4—131no—
837C4⋊C4—131no—
838C4⋊C4—131no—
839C4⋊C4—131no—
840C4⋊C4—131no—
841C4⋊C4—131no—
842C4⋊C4—131no—
843C4⋊C4—131no—
844C4⋊C4C22×D1311yescharacteristic
845C4⋊C4C22×D1311yescharacteristic
846C4⋊C4C22×D1311yescharacteristic
847C4⋊C4C22×D1311yescharacteristic
848C22⋊C4—131no—
849C22⋊C4—131no—
850C22⋊C4—131no—
851C22⋊C4—131no—
852C22⋊C4—131no—
853C22⋊C4—131no—
854C22⋊C4—131no—
855C22⋊C4—131no—
856C22⋊C4—131no—
857C22⋊C4—131no—
858C22⋊C4—131no—
859C22⋊C4—131no—
860C22⋊C4—131no—
861C22⋊C4—131no—
862C22⋊C4—131no—
863C22⋊C4—131no—
864C22⋊C4—131no—
865C22⋊C4—131no—
866C22⋊C4—131no—
867C22⋊C4—131no—
868C22⋊C4—131no—
869C22⋊C4—131no—
870C22⋊C4—131no—
871C22⋊C4—131no—
872C22⋊C4—131no—
873C22⋊C4—131no—
874C22⋊C4—131no—
875C22⋊C4—131no—
876C22⋊C4—131no—
877C22⋊C4—131no—
878C22⋊C4—131no—
879C22⋊C4—131no—
880C22⋊C4—131no—
881C22⋊C4—131no—
882C22⋊C4C22×D1311yescharacteristic
883C22⋊C4C22×D1311yescharacteristic
884C22⋊C4C22×D1311yescharacteristic
885C22⋊C4C22×D1311yescharacteristic
886C22⋊C4C22×D1311yescharacteristic
887C22⋊C4C22×D1311yescharacteristic
888C22⋊C4C22×D1311yescharacteristic
889C22⋊C4C22×D1311yescharacteristic
890C22⋊C4C22×D1311yescharacteristic
891C22⋊C4C22×D1311yescharacteristic
892C22⋊C4C22×D1311yescharacteristic
893C22⋊C4C22×D1311yescharacteristic
894C42—131no—
895C42—131no—
896C42—131no—
897C42—131no—
898C42—131no—
899C42—131no—
900C42—131no—
901C42—131no—
902C42—131no—
903C42C22×D1311yescharacteristic
904C13#351911yescharacteristic, complemented, Sylow
905C23—22no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—131no—
912C23—131no—
913C23—131no—
914C23—131no—
915C23—131no—
916C23—262no—
917C23—262no—
918C23—262no—
919C23—262no—
920C23—262no—
921C23—521no—
922C23—521no—
923C23—521no—
924C23—521no—
925C23—521no—
926C23—521no—
927C23—521no—
928C23C23×D1311yescharacteristic
929C23C23×D1311yescharacteristic
930C23C23×D1311yescharacteristic
931C23C23×D1311yescharacteristic
932C23C23×D1311yescharacteristic
933C23C23×D1311yescharacteristic
934Q8—41no—
935Q8—262no—
936Q8—521no—
937D4—22no—
938D4—22no—
939D4—22no—
940D4—22no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—134no—
947D4—262no—
948D4—262no—
949D4—262no—
950D4—262no—
951D4—262no—
952D4—262no—
953D4—262no—
954D4—262no—
955D4—262no—
956D4—262no—
957D4—262no—
958D4—262no—
959D4—262no—
960D4—262no—
961D4—521no—
962D4—521no—
963D4—521no—
964D4—521no—
965D4—521no—
966D4—521no—
967D4—521no—
968D4—521no—
969D4—521no—
970D4—521no—
971D4—521no—
972D4—521no—
973D4—521no—
974C2×C4—22no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—131no—
981C2×C4—131no—
982C2×C4—131no—
983C2×C4—131no—
984C2×C4—131no—
985C2×C4—131no—
986C2×C4—131no—
987C2×C4—131no—
988C2×C4—131no—
989C2×C4—131no—
990C2×C4—131no—
991C2×C4—262no—
992C2×C4—262no—
993C2×C4—262no—
994C2×C4—262no—
995C2×C4—262no—
996C2×C4—262no—
997C2×C4—262no—
998C2×C4—262no—
999C2×C4—521no—
1000C2×C4—521no—
1001C2×C4—521no—
1002C2×C4—521no—
1003C2×C4—521no—
1004C2×C4—521no—
1005C2×C4—521no—
1006C2×C4—521no—
1007C2×C4—521no—
1008C2×C4—521no—
1009C2×C4—521no—
1010C2×C4—521no—
1011C2×C4—521no—
1012C2×C4C23×D1311yescharacteristic
1013C2×C4C23×D1311yescharacteristic
1014C2×C4C23×D1311yescharacteristic
1015C2×C4C23×D1311yescharacteristic
1016C2×C4C23×D1311yescharacteristic
1017C2×C4C23×D1311yescharacteristic
1018C2×C4C23×D1311yescharacteristic
1019C2×C4C23×D1311yescharacteristic
1020C2×C4C23×D1311yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—44no—
1038C22—82no—
1039C22—132no—
1040C22—261no—
1041C22—261no—
1042C22—261no—
1043C22—261no—
1044C22—261no—
1045C22—261no—
1046C22—261no—
1047C22—261no—
1048C22—261no—
1049C22—261no—
1050C22—261no—
1051C22—261no—
1052C22—261no—
1053C22—261no—
1054C22—524no—
1055C22—1042no—
1056C22—1042no—
1057C22—1042no—
1058C22#8825112yes—
1059C22#41×D1312yes—
1060C22C24×D1311yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—132no—
1071C4—132no—
1072C4—261no—
1073C4—261no—
1074C4—261no—
1075C4—261no—
1076C4—261no—
1077C4—261no—
1078C4—261no—
1079C4—261no—
1080C4—261no—
1081C2—22no—
1082C2—22no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—41no—
1087C2—262no—
1088C2—521no—
1089C2—521no—
1090C2—521no—
1091C2—521no—
1092C2C2×#8825111yescharacteristic
1093C2C2×#41×D1311yescharacteristic
1094C2D13×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×D13
commutator, socle, cosocleC22×C13C25
FittingC13×#546C2
hypercenter#546D13
hypocenterC13#3519
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C13×#546C2semidirect
2. #11719537C2semidirect
3. #11719534C2semidirect
4. C2×#88193C2semidirect
5. D4×C22⋊D13C2semidirect
6. #11719383C2semidirect
7. #11719375C2semidirect
8. #11719368C2semidirect
9. #11719366C2semidirect
10. #11719359C2semidirect
11. #11719354C2semidirect
12. #11719349C2semidirect
13. #11719341C2semidirect
14. #11719320C2semidirect
15. #11719318C2semidirect
16. #11719315C2semidirect
17. D13×#121C2semidirect
18. #11719306C2semidirect
19. #11719304C2semidirect
20. #11719298C2semidirect
21. #11719295C2semidirect
22. #11719295C2semidirect
23. #11719291C2semidirect
24. #11719252C2semidirect
25. #11719250C2semidirect
26. #11719245C2semidirect
27. #11719245C2semidirect
28. #11719195C2semidirect
29. #11719195C2semidirect
30. #11719191C2semidirect
31. C2×#88135C2semidirect
32. C2×C13×#41C22semidirect
33. C22×D4×C13C22semidirect
36. C22×C22⋊D13C22semidirect
37. C22×C22⋊D13C22semidirect
38. C23×Dic13C22semidirect
39. C2×#6129C22semidirect
41. C2×D4×D13C22semidirect
42. C2×D4×D13C22semidirect
43. C2×D4×D13C22semidirect
44. C2×#6127C22semidirect
45. C2×#6127C22semidirect
46. C22×C4×D13C22semidirect
47. C13×#124C22semidirect
48. C13×#123C22semidirect
49. C13×#123C22semidirect
50. C13×C22⋊Q8C22semidirect
51. C13×#121C22semidirect
52. C13×#121C22semidirect
53. C13×#121C22semidirect
54. C13×#120C22semidirect
55. C13×#120C22semidirect
56. C4×D4×C13C22semidirect
57. C4×D4×C13C22semidirect
58. C2×C13×C22⋊C4C22semidirect
59. C2×C13×C22⋊C4C22semidirect
60. #88207C22semidirect
61. #88207C22semidirect
62. C2×C22⋊Dic13C22semidirect
63. #88201C22semidirect
64. #88201C22semidirect
65. #88200C22semidirect
66. #88198C22semidirect
67. #88194C22semidirect
68. #88194C22semidirect
69. #88194C22semidirect
71. #88193C22semidirect
72. #88193C22semidirect
73. #88193C22semidirect
74. #88193C22semidirect
75. #88193C22semidirect
76. #88193C22semidirect
77. #88193C22semidirect
78. #88193C22semidirect
79. #88193C22semidirect
80. #88193C22semidirect
81. #88193C22semidirect
82. #88193C22semidirect
83. #88193C22semidirect
84. #88193C22semidirect
85. #88193C22semidirect
86. #88192C22semidirect
87. #88192C22semidirect
88. #88191C22semidirect
89. #88191C22semidirect
90. #88191C22semidirect
91. #88191C22semidirect
92. #88190C22semidirect
93. #88189C22semidirect
94. #88189C22semidirect
95. D4×Dic13C22semidirect
96. D4×Dic13C22semidirect
97. D4×Dic13C22semidirect
98. #88184C22semidirect
99. #88184C22semidirect
100. #88184C22semidirect
101. #88183C22semidirect
102. #88183C22semidirect
103. #88183C22semidirect
105. C4×C22⋊D13C22semidirect
106. C4×C22⋊D13C22semidirect
107. C4×C22⋊D13C22semidirect
108. C4×C22⋊D13C22semidirect
109. C4×C22⋊D13C22semidirect
110. C4×C22⋊D13C22semidirect
111. C4×C22⋊D13C22semidirect
112. C4×C22⋊D13C22semidirect
113. C2×#6103C22semidirect
114. C2×#6103C22semidirect
115. C2×#6103C22semidirect
116. C2×#6101C22semidirect
117. C2×#6101C22semidirect
118. C2×C4×Dic13C22semidirect
119. #88152C22semidirect
120. #88152C22semidirect
121. #88150C22semidirect
122. #88150C22semidirect
123. #88149C22semidirect
124. #88149C22semidirect
125. #88148C22semidirect
126. #88148C22semidirect
127. #88148C22semidirect
128. #88147C22semidirect
129. #88146C22semidirect
130. C4⋊C4×D13C22semidirect
131. #88143C22semidirect
132. #88143C22semidirect
133. #88143C22semidirect
134. #88141C22semidirect
135. #88140C22semidirect
136. #88139C22semidirect
137. #88139C22semidirect
138. #88139C22semidirect
139. #88138C22semidirect
140. #88138C22semidirect
141. #88138C22semidirect
142. #88138C22semidirect
143. #88138C22semidirect
144. #88138C22semidirect
145. #88138C22semidirect
146. #88138C22semidirect
147. #88138C22semidirect
148. #88137C22semidirect
149. #88137C22semidirect
150. #88137C22semidirect
151. #88136C22semidirect
152. #88136C22semidirect
153. #88136C22semidirect
154. #88136C22semidirect
158. #88135C22semidirect
159. #88135C22semidirect
160. #88135C22semidirect
161. #88135C22semidirect
162. #88135C22semidirect
163. #88135C22semidirect
164. #88135C22semidirect
165. #88135C22semidirect
166. #88135C22semidirect
167. #88135C22semidirect
168. #88135C22semidirect
169. #88135C22semidirect
170. C22⋊C4×D13C22semidirect
171. C22⋊C4×D13C22semidirect
172. C22⋊C4×D13C22semidirect
173. C22⋊C4×D13C22semidirect
174. #88133C22semidirect
175. #88133C22semidirect
176. #88133C22semidirect
177. #88132C22semidirect
178. #88132C22semidirect
179. #88132C22semidirect
180. #88131C22semidirect
181. #88131C22semidirect
182. #88131C22semidirect
183. #88130C22semidirect
184. C4×D52C22semidirect
185. #88126C22semidirect
186. #88126C22semidirect
433. C22⋊D13#41semidirect
486. #546D13semidirect
568. C2×#41C2×D13semidirect
577. C22×D4C2×D13semidirect
599. #124C2×D13semidirect
612. #123C2×D13semidirect
613. #123C2×D13semidirect
620. C22⋊Q8C2×D13semidirect
653. #121C2×D13semidirect
654. #121C2×D13semidirect
655. #121C2×D13semidirect
666. #120C2×D13semidirect
667. #120C2×D13semidirect
698. C4×D4C2×D13semidirect
699. C4×D4C2×D13semidirect
717. C2×C22⋊C4C2×D13semidirect
718. C2×C22⋊C4C2×D13semidirect
904. C13#3519semidirect

Maximal subgroups

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

subgroupindex
C13×#5462
#117195372
#117195342
C2×#881932
D4×C22⋊D132
#117193832
#117193752
#117193682
#117193662
#117193592
#117193542
#117193492
#117193412
#117193202
#117193182
#117193152
D13×#1212
#117193062
#117193042
#117192982
#117192952
#117192912
#117192522
#117192502
#117192452
#117191952
#117191912
C2×#881352
#351913