Finite Group Databasebeta

← #16029905

Subgroups — #16029905

Order 3328.

1536 conjugacy classes of subgroups.

The subgroup lattice has 1266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13121027C211yesmaximal, characteristic, complemented
2#13121017C211yesmaximal, characteristic, complemented
3#13120999C211yesmaximal, characteristic
4#13120997C211yesmaximal, characteristic
5#13120933C211yesmaximal, characteristic, complemented
6#13120929C211yesmaximal, characteristic, complemented
7#13120927C211yesmaximal, characteristic, complemented
8#13120925C211yesmaximal, characteristic, complemented
9#13120920C211yesmaximal, characteristic
10#13120910C211yesmaximal, characteristic
11#13120856C211yesmaximal, characteristic
12#13120852C211yesmaximal, characteristic
13#13120750C211yesmaximal, characteristic
14#13120746C211yesmaximal, characteristic
15#13120716C211yesmaximal, characteristic, complemented
16#13120713C211yesmaximal, characteristic, complemented
17#13118144C211yesmaximal, characteristic, complemented
18#13118143C211yesmaximal, characteristic, complemented
19#13118143C211yesmaximal, characteristic, complemented
20#13118137C211yesmaximal, characteristic
21#13118137C211yesmaximal, characteristic
22#13118130C211yesmaximal, characteristic, complemented
23#13118112C211yesmaximal, characteristic
24#13118112C211yesmaximal, characteristic
25C4×#88143C211yesmaximal, characteristic, complemented
26C4×#88152C211yesmaximal, characteristic
27C4×#88130C211yesmaximal, characteristic
28#13117329C211yesmaximal, characteristic
29#13117312C211yesmaximal, characteristic, complemented
30C42×Dic26C211yesmaximal, characteristic, complemented
31C4×C13×#125C211yesmaximal, characteristic, complemented
32C2×C13×#125C2211yescharacteristic
33C2×#88152C2211yescharacteristic
34C2×#88143C2211yescharacteristic
35C2×#88130C2211yescharacteristic
36C2×#88126C2211yescharacteristic
37C2×C4×Dic26C2211yescharacteristic
38C2×C4×Dic26C2211yescharacteristic
39C2×C4×Dic26C2211yescharacteristic
40C2×C4×Dic26C2211yescharacteristic
41C13×#389C2211yescharacteristic
42C13×#389C2211yescharacteristic
43C13×#387C2211yescharacteristic
44C13×#387C2211yescharacteristic
45C13×#387C2211yescharacteristic
46C13×#387C2211yescharacteristic
47C13×#382C2211yescharacteristic
48C4×C13×C4⋊C4C2211yescharacteristic
49C4×C13×C4⋊C4C2211yescharacteristic
50C4×C13×C4⋊C4C2211yescharacteristic
51C4×C13×C4⋊C4C2211yescharacteristic
52C4×C13×C4⋊C4C2211yescharacteristic
53C4×C13×C4⋊C4C2211yescharacteristic
54C43×C13C2211yescharacteristic
55#11718655C2211yescharacteristic
56#11718655C2211yescharacteristic
57#11718655C2211yescharacteristic
58#11718655C2211yescharacteristic
59#11718654C2211yescharacteristic
60#11718654C2211yescharacteristic
61#11718653C2211yescharacteristic
62#11718653C2211yescharacteristic
63#11718651C2211yescharacteristic
64#11718651C2211yescharacteristic
65#11718651C2211yescharacteristic
66#11718647C2211yescharacteristic
67#11718647C2211yescharacteristic
68#11718647C2211yescharacteristic
69#11718647C2211yescharacteristic
70#11718645C2211yescharacteristic
71#11718645C2211yescharacteristic
72#11718645C2211yescharacteristic
73#11718645C2211yescharacteristic
74#11718645C2211yescharacteristic
75#11718645C2211yescharacteristic
76#11718644C2211yescharacteristic
77#11718644C2211yescharacteristic
78#11718643C2211yescharacteristic
79#11718643C2211yescharacteristic
80#11718643C2211yescharacteristic
81#11718643C2211yescharacteristic
82#11718642C2211yescharacteristic
83#11718642C2211yescharacteristic
84#11718641C2211yescharacteristic
85#11718641C2211yescharacteristic
86#11718641C2211yescharacteristic
87#11718641C2211yescharacteristic
88#11718640C2211yescharacteristic
89#11718640C2211yescharacteristic
90#11718640C2211yescharacteristic
91#11718640C2211yescharacteristic
92#11718639C2211yescharacteristic
93#11718639C2211yescharacteristic
94#11718639C2211yescharacteristic
95#11718639C2211yescharacteristic
96#11718639C2211yescharacteristic
97#11718639C2211yescharacteristic
98#11718633C2211yescharacteristic
99#11718633C2211yescharacteristic
100#11718633C2211yescharacteristic
101#11718601C2211yescharacteristic
102#11718601C2211yescharacteristic
103#11718601C2211yescharacteristic
104C4×#6103C2211yescharacteristic
105C4×#6103C2211yescharacteristic
106C4×#6103C2211yescharacteristic
107C4×#6103C2211yescharacteristic
108C4×#6103C2211yescharacteristic
109C4×#6103C2211yescharacteristic
110#11718598C2211yescharacteristic
111C4×C4⋊Dic13C2211yescharacteristic
112C4×C4⋊Dic13C2211yescharacteristic
113C4×C4⋊Dic13C2211yescharacteristic
114C4×C4⋊Dic13C2211yescharacteristic
115C4×C4⋊Dic13C2211yescharacteristic
116C4×C4⋊Dic13C2211yescharacteristic
117#11718594C2211yescharacteristic
118#11718594C2211yescharacteristic
119#11718594C2211yescharacteristic
120#11718593C2211yescharacteristic
121#11718593C2211yescharacteristic
122#11718593C2211yescharacteristic
123C4×#6101C2211yescharacteristic
124C4×#6101C2211yescharacteristic
125C4×#6101C2211yescharacteristic
126C4×#6101C2211yescharacteristic
127C4×#6101C2211yescharacteristic
128C4×#6101C2211yescharacteristic
129C4×#6101C2211yescharacteristic
130C4×#6101C2211yescharacteristic
131C4×#6101C2211yescharacteristic
132C4×#6101C2211yescharacteristic
133C4×#6101C2211yescharacteristic
134C4×#6101C2211yescharacteristic
135C4×#6101C2211yescharacteristic
136C4×#6101C2211yescharacteristic
137C42×Dic13C2211yescharacteristic
138C42×Dic13C2211yescharacteristic
139#11718337C2211yescharacteristic
140#11718337C2211yescharacteristic
141#11718336C2211yescharacteristic
142#11718336C2211yescharacteristic
143#11718335C2211yescharacteristic
144#11718335C2211yescharacteristic
145#11718334C2211yescharacteristic
146#11718334C2211yescharacteristic
147#11718331C2211yescharacteristic
148#11718331C2211yescharacteristic
149#11718331C2211yescharacteristic
150#11718330C2211yescharacteristic
151C13⋊#401C2211yescharacteristic
152C13⋊#401C2211yescharacteristic
153#11718322C2211yescharacteristic
154#11718322C2211yescharacteristic
155#11718321C2211yescharacteristic
156#11718321C2211yescharacteristic
157#11718321C2211yescharacteristic
158#11718321C2211yescharacteristic
159#11718320C2211yescharacteristic
160#11718320C2211yescharacteristic
161#11718319C2211yescharacteristic
162#11718319C2211yescharacteristic
163#11718319C2211yescharacteristic
164#11718319C2211yescharacteristic
165#11718319C2211yescharacteristic
166#11718319C2211yescharacteristic
167#11718318C2211yescharacteristic
168#11718318C2211yescharacteristic
169#11718318C2211yescharacteristic
170#11718318C2211yescharacteristic
171#11718318C2211yescharacteristic
172#11718318C2211yescharacteristic
173#11718317C2211yescharacteristic
174#11718317C2211yescharacteristic
175#11718316C2211yescharacteristic
176#11718316C2211yescharacteristic
177#11718315C2211yescharacteristic
178#11718314C2211yescharacteristic
179#11718314C2211yescharacteristic
180#11718314C2211yescharacteristic
181#11718313C2211yescharacteristic
182#11718312C2211yescharacteristic
183#11718311C2211yescharacteristic
184#11718308C2211yescharacteristic
185#11718307C2211yescharacteristic
186#11718307C2211yescharacteristic
187C22×C4×D13C2311yescharacteristic
188C22×Dic26C2311yescharacteristic
189C22×Dic26C2311yescharacteristic
190C13×#125—24no—
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×C42×C13C2311yescharacteristic
213C2×C42×C13C2311yescharacteristic
214C2×#6103C2311yescharacteristic
215C2×#6103C2311yescharacteristic
216C2×#6103C2311yescharacteristic
217C2×#6103C2311yescharacteristic
218C2×#6103C2311yescharacteristic
219C2×#6103C2311yescharacteristic
220C2×#6103C2311yescharacteristic
221C2×#6103C2311yescharacteristic
222C2×#6103C2311yescharacteristic
223C2×#6103C2311yescharacteristic
224C2×#6103C2311yescharacteristic
225C2×#6103C2311yescharacteristic
226C2×#6103C2311yescharacteristic
227C2×#6103C2311yescharacteristic
228C2×C4⋊Dic13C2311yescharacteristic
229C2×C4⋊Dic13C2311yescharacteristic
230C2×C4⋊Dic13C2311yescharacteristic
231C2×C4⋊Dic13C2311yescharacteristic
232C2×C4⋊Dic13C2311yescharacteristic
233C2×C4⋊Dic13C2311yescharacteristic
234C2×C4⋊Dic13C2311yescharacteristic
235C2×C4⋊Dic13C2311yescharacteristic
236C2×C4⋊Dic13C2311yescharacteristic
237C2×C4⋊Dic13C2311yescharacteristic
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×#6101C2311yescharacteristic
259C2×#6101C2311yescharacteristic
260C2×#6101C2311yescharacteristic
261C2×#6101C2311yescharacteristic
262C2×#6101C2311yescharacteristic
263C2×#6101C2311yescharacteristic
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
279#88152—24no—
280#88143—24no—
281#88130—24no—
282#88126—24no—
283C4×Dic26—24no—
284C4×Dic26—24no—
285C4×Dic26—24no—
286C4×Dic26—24no—
287C13×#95C2311yescharacteristic
288C13×#95C2311yescharacteristic
289C13×#95C2311yescharacteristic
290C13×#95C2311yescharacteristic
291C13×#95C2311yescharacteristic
292C13×#95C2311yescharacteristic
293C13×#95C2311yescharacteristic
294C13×#95C2311yescharacteristic
295C13×#95C2311yescharacteristic
296C13×#95C2311yescharacteristic
297C13×#95C2311yescharacteristic
298C13×#95C2311yescharacteristic
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#34604—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×Dic26—22no—
387C2×Dic26—22no—
388C2×Dic26—22no—
389C2×Dic26—22no—
390C2×Dic26—41no—
391C2×Dic26—41no—
392C13×C4⋊C4—22no—
393C13×C4⋊C4—22no—
394C13×C4⋊C4—22no—
395C13×C4⋊C4—22no—
396C13×C4⋊C4—22no—
397C13×C4⋊C4—22no—
398C13×C4⋊C4—22no—
399C13×C4⋊C4—22no—
400C13×C4⋊C4—41no—
401C13×C4⋊C4—41no—
402C13×C4⋊C4—41no—
403C13×C4⋊C4—41no—
404C42×C13—22no—
405C42×C13—22no—
406C42×C13—22no—
407C42×C13—22no—
408C42×C13—22no—
409C42×C13—22no—
410C42×C13—22no—
411C42×C13—22no—
412C42×C13—41no—
413C42×C13—41no—
414C42×C13#4114yes—
415#6103—22no—
416#6103—22no—
417#6103—22no—
418#6103—22no—
419#6103—22no—
420#6103—22no—
421#6103—22no—
422#6103—22no—
423#6103—41no—
424#6103—41no—
425#6103—41no—
426#6103—41no—
427#6103—41no—
428#6103—41no—
429C4⋊Dic13—22no—
430C4⋊Dic13—22no—
431C4⋊Dic13—22no—
432C4⋊Dic13—22no—
433C4⋊Dic13—22no—
434C4⋊Dic13—22no—
435C4⋊Dic13—41no—
436C4⋊Dic13—41no—
437C4⋊Dic13—41no—
438C4⋊Dic13—41no—
439#6101—22no—
440#6101—22no—
441#6101—22no—
442#6101—22no—
443#6101—22no—
444#6101—22no—
445#6101—22no—
446#6101—22no—
447#6101—22no—
448#6101—22no—
449#6101—22no—
450#6101—22no—
451#6101—22no—
452#6101—22no—
453#6101—22no—
454#6101—22no—
455#6101—22no—
456#6101—22no—
457#6101—41no—
458#6101—41no—
459#6101—41no—
460#6101—41no—
461#6101—41no—
462#6101—41no—
463#6101—41no—
464#6101—41no—
465C4×Dic13—22no—
466C4×Dic13—22no—
467C4×Dic13—22no—
468C4×Dic13—22no—
469C4×Dic13—22no—
470C4×Dic13—22no—
471C4×Dic13—22no—
472C4×Dic13—22no—
473C4×Dic13—22no—
474C4×Dic13—41no—
475C4×Dic13—41no—
476C4×Dic13—41no—
477C4×Dic13—41no—
478C4×Dic13#4114yes—
479C4×Dic13#4114yes—
480#2666—131no—
481#2666—131no—
482#2664—131no—
483#2664—131no—
484#2655—131no—
485#2655—131no—
486#2655—131no—
487#2655—131no—
488#2654—131no—
489#2654—131no—
490#2650—131no—
491#2650—131no—
492#2637—131no—
493#2637—131no—
494#2634—131no—
495#2634—131no—
496#2402—131no—
497#2402—131no—
498#2402—131no—
499#2401—131no—
500#2401—131no—
501#2399—131no—
502#2396—131no—
503#2396—131no—
504C4×#125—131no—
505C4×#125D1311yescharacteristic, complemented
506C4×#126—131no—
507C4×#126—131no—
508#2298—131no—
509#2295—131no—
510C42×Q8—131no—
511C23×C13C2511yescharacteristic
512C22×D13—21no—
513C22×D13—21no—
514C22×D13—21no—
515C22×D13—21no—
516C22×D13—21no—
517C22×D13—21no—
518C22×D13—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×C13—21no—
554C2×C4×C13—21no—
555C2×C4×C13—21no—
556C2×C4×C13—21no—
557C2×C4×C13C2×#4112yes—
558C2×C4×C13C2×#4112yes—
559C2×C4×C13C2×#4112yes—
560C2×C4×C13C2×#4112yes—
561C2×C4×C13C2×#4112yes—
562C2×C4×C132−1+412yes—
563C2×C4×C132−1+412yes—
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×Dic13C2×#4112yes—
606C2×Dic13C2×#4112yes—
607C2×Dic13C2×#4112yes—
608C2×Dic13C2×#4112yes—
609C4×D13—44no—
610Dic26—28no—
611Dic26—44no—
612C2×#126—131no—
613C2×#126—131no—
614C2×#125—131no—
615C2×#125C2×D1311yescharacteristic
616C2×C4×Q8—131no—
617C2×C4×Q8—131no—
618C2×C4×Q8—131no—
619C2×C4×Q8—131no—
620C2×#117—131no—
621#401—131no—
622#401—131no—
623#400—131no—
624#400—131no—
625#400—131no—
626#400—131no—
627#400—131no—
628#400—131no—
629#400—131no—
630#400—131no—
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#399—131no—
644#399—131no—
645#398—131no—
646#398—131no—
647#398—131no—
648#398—131no—
649#398—131no—
650#398—131no—
651#398—131no—
652#398—131no—
653#398—131no—
654#398—131no—
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#397—131no—
666#397—131no—
667#397—131no—
668#397—131no—
669#397—131no—
670#397—131no—
671#396—131no—
672#396—131no—
673#396—131no—
674#396—131no—
675#396—131no—
676#396—131no—
677#395—131no—
678#395—131no—
679#395—131no—
680#395—131no—
681#395—131no—
682#395—131no—
683#393—131no—
684#393—131no—
685#391—131no—
686#391—131no—
687#389—131no—
688#389—131no—
689#389—131no—
690#389—131no—
691#389C2×D1311yescharacteristic
692#389C2×D1311yescharacteristic
693#388—131no—
694#388—131no—
695#388—131no—
696#388—131no—
697#388—131no—
698#388—131no—
699#388—131no—
700#388—131no—
701#388—131no—
702#388—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#387C2×D1311yescharacteristic
722#387C2×D1311yescharacteristic
723#387C2×D1311yescharacteristic
724#387C2×D1311yescharacteristic
725#383—131no—
726#383—131no—
727#382—131no—
728#382C2×D1311yescharacteristic
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⋊C4C2×D1311yescharacteristic
750C4×C4⋊C4C2×D1311yescharacteristic
751C4×C4⋊C4C2×D1311yescharacteristic
752C4×C4⋊C4C2×D1311yescharacteristic
753C4×C4⋊C4C2×D1311yescharacteristic
754C4×C4⋊C4C2×D1311yescharacteristic
755C4×C22⋊C4—131no—
756C4×C22⋊C4—131no—
757C4×C22⋊C4—131no—
758C4×C22⋊C4—131no—
759C4×C22⋊C4—131no—
760C4×C22⋊C4—131no—
761#376—131no—
762#376—131no—
763#376—131no—
764C43—131no—
765C43—131no—
766C43C2×D1311yescharacteristic
767C22×C13C22×#4111yescharacteristic
768C22×C13C22×#4111yescharacteristic
769C22×C13C22×#4111yescharacteristic
770C22×C13C2×2−1+411yescharacteristic
771C22×C13C2×2−1+411yescharacteristic
772C22×C13#58511yescharacteristic
773C22×C13#58511yescharacteristic
774C2×D13—41no—
775C2×D13—41no—
776C2×D13—41no—
777C2×D13—41no—
778C2×D13—41no—
779C2×D13—41no—
780C2×D13—41no—
781C4×C13—22no—
782C4×C13—22no—
783C4×C13—22no—
784C4×C13—22no—
785C4×C13—41no—
786C4×C13—41no—
787C4×C13—41no—
788C4×C13—41no—
789C4×C13—41no—
790C4×C13—41no—
791C4×C13—41no—
792C4×C13—41no—
793C4×C13—41no—
794C4×C13—41no—
795C4×C13#54114yes—
796Dic13—22no—
797Dic13—22no—
798Dic13—22no—
799Dic13—22no—
800Dic13—41no—
801Dic13—41no—
802Dic13—41no—
803Dic13—41no—
804Dic13—41no—
805Dic13—41no—
806Dic13—41no—
807Dic13—41no—
808Dic13—41no—
809Dic13—41no—
810Dic13—41no—
811C22×Q8—131no—
812C22×Q8—131no—
813C23×C4—131no—
814#126—264no—
815#126—264no—
816#125—24no—
817#125—264no—
818C4×Q8—264no—
819C4×Q8—264no—
820C4×Q8—264no—
821C4×Q8—264no—
822#117—264no—
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⋊C4C22×D1311yescharacteristic
860C2×C4⋊C4C22×D1311yescharacteristic
861C2×C4⋊C4C22×D1311yescharacteristic
862C2×C4⋊C4C22×D1311yescharacteristic
863C2×C4⋊C4C22×D1311yescharacteristic
864C2×C4⋊C4C22×D1311yescharacteristic
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×C22⋊C4—131no—
872C2×C22⋊C4—131no—
873C2×C22⋊C4—131no—
874C2×C22⋊C4—131no—
875C2×C22⋊C4—131no—
876C2×C22⋊C4—131no—
877C2×C22⋊C4—131no—
878C2×C22⋊C4—131no—
879C2×C22⋊C4—131no—
880C2×C22⋊C4—131no—
881C2×C22⋊C4—131no—
882C2×C22⋊C4—131no—
883C2×C22⋊C4—131no—
884C2×C22⋊C4—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×C42C22×D1311yescharacteristic
901C2×C42C22×D1311yescharacteristic
902C2×C42C22×D1311yescharacteristic
903C2×C42C22×D1311yescharacteristic
904C2×C42C22×D1311yescharacteristic
905C2×C42C22×D1311yescharacteristic
906C2×C42C22×D1311yescharacteristic
907C2×C42C22×D1311yescharacteristic
908C2×C42C22×D1311yescharacteristic
909C2×C42C22×D1311yescharacteristic
910C2×C42C22×D1311yescharacteristic
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#95—131no—
962#95—131no—
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
975C2×C13#344411yescharacteristic
976C2×C13C2×#54111yescharacteristic
977C2×C13#345511yescharacteristic
978C2×C13#346111yescharacteristic
979C2×C13#346111yescharacteristic
980C2×C13#346111yescharacteristic
981C2×C13#346111yescharacteristic
982D13—81no—
983C24—131no—
984C2×Q8—262no—
985C2×Q8—262no—
986C2×Q8—262no—
987C2×Q8—262no—
988C2×Q8—521no—
989C2×Q8—521no—
990C22×C4—131no—
991C22×C4—131no—
992C22×C4—131no—
993C22×C4—131no—
994C22×C4—131no—
995C22×C4—131no—
996C22×C4—131no—
997C22×C4—131no—
998C22×C4—131no—
999C22×C4—131no—
1000C22×C4—131no—
1001C22×C4—131no—
1002C22×C4—131no—
1003C22×C4—131no—
1004C22×C4—131no—
1005C22×C4—262no—
1006C22×C4—262no—
1007C22×C4—262no—
1008C22×C4C23×D1311yescharacteristic
1009C22×C4C23×D1311yescharacteristic
1010C22×C4C23×D1311yescharacteristic
1011C22×C4C23×D1311yescharacteristic
1012C22×C4C23×D1311yescharacteristic
1013C22×C4C23×D1311yescharacteristic
1014C22×C4C23×D1311yescharacteristic
1015C22×C4C23×D1311yescharacteristic
1016C22×C4C23×D1311yescharacteristic
1017C22×C4C23×D1311yescharacteristic
1018C22×C4C23×D1311yescharacteristic
1019C22×C4C23×D1311yescharacteristic
1020C22×C4C23×D1311yescharacteristic
1021C22×C4C23×D1311yescharacteristic
1022C22×C4C23×D1311yescharacteristic
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—22no—
1028C4⋊C4—22no—
1029C4⋊C4—22no—
1030C4⋊C4—22no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—262no—
1036C4⋊C4—262no—
1037C4⋊C4—262no—
1038C4⋊C4—262no—
1039C4⋊C4—262no—
1040C4⋊C4—262no—
1041C4⋊C4—262no—
1042C4⋊C4—262no—
1043C4⋊C4—262no—
1044C4⋊C4—262no—
1045C4⋊C4—262no—
1046C4⋊C4—262no—
1047C4⋊C4—262no—
1048C4⋊C4—262no—
1049C4⋊C4—262no—
1050C4⋊C4—262no—
1051C4⋊C4—262no—
1052C4⋊C4—262no—
1053C4⋊C4—262no—
1054C4⋊C4—262no—
1055C4⋊C4—262no—
1056C4⋊C4—262no—
1057C4⋊C4—262no—
1058C4⋊C4—262no—
1059C4⋊C4—521no—
1060C4⋊C4—521no—
1061C4⋊C4—521no—
1062C4⋊C4—521no—
1063C4⋊C4—521no—
1064C4⋊C4—521no—
1065C4⋊C4—521no—
1066C4⋊C4—521no—
1067C4⋊C4—521no—
1068C4⋊C4—521no—
1069C4⋊C4—521no—
1070C4⋊C4—521no—
1071C22⋊C4—262no—
1072C22⋊C4—262no—
1073C22⋊C4—262no—
1074C22⋊C4—262no—
1075C22⋊C4—262no—
1076C22⋊C4—262no—
1077C22⋊C4—262no—
1078C22⋊C4—262no—
1079C22⋊C4—521no—
1080C22⋊C4—521no—
1081C22⋊C4—521no—
1082C22⋊C4—521no—
1083C22⋊C4—521no—
1084C22⋊C4—521no—
1085C42—22no—
1086C42—22no—
1087C42—22no—
1088C42—22no—
1089C42—22no—
1090C42—22no—
1091C42—22no—
1092C42—22no—
1093C42—41no—
1094C42—41no—
1095C42—134no—
1096C42—134no—
1097C42—262no—
1098C42—262no—
1099C42—262no—
1100C42—262no—
1101C42—262no—
1102C42—262no—
1103C42—262no—
1104C42—262no—
1105C42—262no—
1106C42—521no—
1107C42—521no—
1108C42—521no—
1109C42—521no—
1110C42#612714yes—
1111C13#3460411yescharacteristic, complemented, Sylow
1112C23—261no—
1113C23—261no—
1114C23—261no—
1115C23—261no—
1116C23—261no—
1117C23—261no—
1118C23—261no—
1119C23C24×D1311yescharacteristic
1120Q8—268no—
1121Q8—524no—
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—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—132no—
1161C2×C4—132no—
1162C2×C4—132no—
1163C2×C4—132no—
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×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—524no—
1206C2×C4C2×#612712yes—
1207C2×C4C2×#612712yes—
1208C2×C4C2×#612712yes—
1209C2×C4#8825412yes—
1210C2×C4#41×D1312yes—
1211C2×C4#41×D1312yes—
1212C2×C4#8825712yes—
1213C22—521no—
1214C22—521no—
1215C22—521no—
1216C22—521no—
1217C22—521no—
1218C22—521no—
1219C22—521no—
1220C22C22×#612711yescharacteristic
1221C22C2×#8825411yescharacteristic
1222C22C2×#41×D1311yescharacteristic
1223C22C2×#41×D1311yescharacteristic
1224C22C2×#8825711yescharacteristic
1225C22#1171964811yescharacteristic
1226C22#1171964811yescharacteristic
1227C4—22no—
1228C4—22no—
1229C4—22no—
1230C4—22no—
1231C4—41no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—41no—
1241C4—262no—
1242C4—262no—
1243C4—262no—
1244C4—262no—
1245C4—521no—
1246C4—521no—
1247C4—521no—
1248C4—521no—
1249C4—521no—
1250C4—521no—
1251C4—521no—
1252C4—521no—
1253C4—521no—
1254C4—521no—
1255C4—521no—
1256C4#1171940114yes—
1257C2—1041no—
1258C2#1312812911yescharacteristic
1259C2C2×#1171940111yescharacteristic
1260C2#1312821911yescharacteristic
1261C2#1312826311yescharacteristic
1262C2#1312826511yescharacteristic
1263C2#1312826711yescharacteristic
1264C2#1312826911yescharacteristic
subgroupG/H
centerC22×C4C23×D13
commutator, socle, cosocleC23×C13C25
FrattiniC23C24×D13
FittingC4×C13×#125C2
prime radicalC23×D13C24
hypercenterC4×#125D13
hypocenterC13#34604
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C4×#125

Complements

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

NH ≅ G/Ntype
1. #13121027C2semidirect
2. #13121017C2semidirect
5. #13120933C2semidirect
6. #13120929C2semidirect
7. #13120927C2semidirect
8. #13120925C2semidirect
15. #13120716C2semidirect
16. #13120713C2semidirect
17. #13118144C2semidirect
18. #13118143C2semidirect
19. #13118143C2semidirect
22. #13118130C2semidirect
25. C4×#88143C2semidirect
29. #13117312C2semidirect
30. C42×Dic26C2semidirect
31. C4×C13×#125C2semidirect
505. C4×#125D13semidirect
1111. C13#34604semidirect

Maximal subgroups

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

subgroupindex
#131210272
#131210172
#131209992
#131209972
#131209332
#131209292
#131209272
#131209252
#131209202
#131209102
#131208562
#131208522
#131207502
#131207462
#131207162
#131207132
#131181442
#131181432
#131181372
#131181302
#131181122
C4×#881432
C4×#881522
C4×#881302
#131173292
#131173122
C42×Dic262
C4×C13×#1252
#3460413