Finite Group Databasebeta

← #27206989

Subgroups — #27206989

Order 13184.

420 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268488C211yesmaximal, characteristic, complemented
2#20268438C211yesmaximal, characteristic, complemented
3#20268144C211yesmaximal, characteristic, complemented
4#20268128C211yesmaximal, characteristic, complemented
5#20268112C211yesmaximal, characteristic, complemented
6#20268094C211yesmaximal, characteristic, complemented
7#20268019C211yesmaximal, characteristic, complemented
8#20268004C211yesmaximal, characteristic, complemented
9#20267934C211yesmaximal, characteristic, complemented
10#20267923C211yesmaximal, characteristic, complemented
11#20267871C211yesmaximal, characteristic, complemented
12C8×C22⋊D103C211yesmaximal, characteristic, complemented
13#20267788C211yesmaximal, characteristic, complemented
14#102×D103C211yesmaximal, characteristic, complemented
15#466×C103C211yesmaximal, characteristic, complemented
16C2×#13110105C2211yescharacteristic
17C2×D4×D103C2211yescharacteristic
18C2×#13110093C2211yescharacteristic, complemented
19C2×#13110090C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21#15693014—21no—
22#15693012C2211yescharacteristic, complemented
23#15693008C2211yescharacteristic
24#15693003—21no—
25#15693002—21no—
26#15693001C2211yescharacteristic
27#15692992—21no—
28#15692992—21no—
29#15692992C2211yescharacteristic
30#15692989—21no—
31D4×Dic103C2211yescharacteristic, complemented
32#15692983C2211yescharacteristic
33C4×C22⋊D103C2211yescharacteristic
34(C22⋊D103)⋊C4—21no—
35#15692980C2211yescharacteristic, complemented
36C4⋊C4×D103C2211yescharacteristic
37C22⋊C4×D103—21no—
38#15692954C2211yescharacteristic, complemented
39#15692952C2211yescharacteristic, complemented
40Dic103⋊C8C2211yescharacteristic, complemented
41#15692946C2211yescharacteristic, complemented
42#15692946C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692942C2211yescharacteristic
47#15692942C2211yescharacteristic
48#15692941C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic, complemented
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic, complemented
52C2×D8×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic, complemented
54#121×C103C2211yescharacteristic
55#121×C103C2211yescharacteristic, complemented
56#107×C103C2211yescharacteristic, complemented
57#102×C103C2211yescharacteristic
58#102×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110105—22no—
61#13110105—41no—
62C2×Dic206C2311yescharacteristic
63C2×D412C2311yescharacteristic
64C2×C22⋊D103—21no—
65C2×C22⋊D103—21no—
66C2×C22⋊D103—21no—
67C2×C22⋊D103D411yescharacteristic
68D4×D103—22no—
69D4×D103—41no—
70C22×Dic103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103—21no—
74C2×C4×D103C2311yescharacteristic
75#13110093—41no—
76#13110090—22no—
77C2×C103⋊C8C2311yescharacteristic
78C2×C103⋊C8C2311yescharacteristic
79C8×D103—41no—
80C4⋊Dic103—21no—
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4D411yescharacteristic
87C22⋊Dic103—21no—
88C22⋊Dic103—21no—
89C22⋊Dic103—21no—
90C22⋊Dic103—21no—
91C22⋊Dic103—21no—
92C22⋊Dic103D411yescharacteristic
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4D411yescharacteristic
96C4×Dic103—21no—
97C4×Dic103C2311yescharacteristic
98C2×D4×C103—21no—
99C2×D4×C103—21no—
100C2×D4×C103C2311yescharacteristic
101C2×D4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103D8×C103—41no—
104C2×C8×C103—41no—
105C2×C8×C103C2311yescharacteristic
106C2×C8×C103C2311yescharacteristic
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C22⋊C4×C103—21no—
110C22⋊C4×C103—21no—
111C23×C103—21no—
112C23×C103—21no—
113C23×C103C2×D411yescharacteristic
114C22×D103—21no—
115C22×D103—42no—
116C22×D103—42no—
117C22×D103—81no—
118C22×D103C2×D411yescharacteristic
119D4×C103—21no—
120D4×C103—21no—
121D4×C103—21no—
122D4×C103—21no—
123D4×C103—81no—
124D4×C103—81no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103C2×D411yescharacteristic
130C2×C4×C103C2411yescharacteristic
131C22⋊D103—22no—
132C22⋊D103—42no—
133C22⋊D103—42no—
134C22⋊D103—42no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—81no—
139C2×Dic103C2×D411yescharacteristic
140C2×Dic103C2×D411yescharacteristic
141C2×Dic103C2×D411yescharacteristic
142D412—21no—
143D412#4112yes—
144C4×D103—21no—
145C4×D103—21no—
146C4×D103—42no—
147C4×D103—81no—
148C4×D103—81no—
149Dic206—21no—
150Dic206—21no—
151C8×C103—21no—
152C8×C103—21no—
153C103⋊C8—21no—
154C103⋊C8—21no—
155C22×C103—21no—
156C22×C103—21no—
157C22×C103—21no—
158C22×C103—41no—
159C22×C103—41no—
160C22×C103—41no—
161C22×C103—41no—
162C22×C103—41no—
163C22×C103—41no—
164C22×C103C22×D411yescharacteristic
165C2×D103—21no—
166C2×D103—21no—
167C2×D103—22no—
168C2×D103—41no—
169C2×D103—41no—
170C2×D103—84no—
171C2×D103#13512yes—
172C4×C103—21no—
173C4×C103—41no—
174C4×C103—41no—
175C4×C103C2×#4111yescharacteristic
176C4×C103H(5,𝔽2)11yescharacteristic
177Dic103—21no—
178Dic103—21no—
179Dic103—21no—
180Dic103—41no—
181Dic103—41no—
182Dic103—41no—
183C2×C103—41no—
184C2×C103—81no—
185C2×C103—81no—
186C2×C103#54611yescharacteristic
187C2×C103C2×#13511yescharacteristic
188C2×C103#57611yescharacteristic
189D103—22no—
190D103—42no—
191#3297—1031nomaximal, Sylow
192C103#329711yescharacteristic, complemented, Sylow
193#553—1031no—
194#546—1031no—
195#488—1031no—
196#484—1031no—
197#482—1031no—
198#478—1031no—
199#466D10311yescharacteristic, complemented
200#465—1031no—
201#463—1031no—
202#449—1031no—
203#447—1031no—
204C4×D8—1031no—
205C8×D4—1031no—
206#416—1031no—
207C2×#102—1031no—
208C2×#41—1031no—
209C22×D4—1031no—
210C2×SD16—1031no—
211C2×D8—1031no—
212C2×D8C2×D10311yescharacteristic
213C22×C8—1031no—
214C22×C8C2×D10311yescharacteristic, complemented
215#126—2061no—
216#125—1031no—
217#124—1031no—
218#123—2061no—
219#123—2061no—
220C22⋊Q8—1031no—
221#121—1031no—
222#121—2061no—
223#121—2061no—
224#121C2×D10311yescharacteristic
225#121C2×D10311yescharacteristic, complemented
226#120—2061no—
227C4×D4—1031no—
228C4×D4—1031no—
229C4×D4—1031no—
230C4×D4—2061no—
231#117—1031no—
232C2×C4⋊C4—1031no—
233C2×C22⋊C4—2061no—
234#107—1031no—
235#107C2×D10311yescharacteristic, complemented
236#106—1031no—
237C4⋊C8—1031no—
238#103—1031no—
239#103—1031no—
240#103—1031no—
241#102—1031no—
242#102—1031no—
243#102—1031no—
244#102—1031no—
245#102—1031no—
246#102C2×D10311yescharacteristic
247#102C2×D10311yescharacteristic, complemented
248C22⋊C8—1031no—
249C22⋊C8—1031no—
250C4×C8—1031no—
251C24—2061no—
252#41—4121no—
253#41—2062no—
254C2×Q8—1031no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—1031no—
258C2×D4—1031no—
259C2×D4—4121no—
260C2×D4—2061no—
261C2×D4—2062no—
262C2×D4—2061no—
263C2×D4—2061no—
264C2×D4C22×D10311yescharacteristic
265C2×D4C22×D10311yescharacteristic
266C22×C4—1031no—
267C22×C4—2061no—
268C22×C4—2061no—
269C22×C4—2061no—
270C22×C4—2061no—
271C22×C4C22×D10311yescharacteristic
272SD16—4121no—
273D8—41no—
274D8—2062no—
275C2×C8—41no—
276C2×C8—1031no—
277C2×C8—1031no—
278C2×C8—4121no—
279C2×C8C22×D10311yescharacteristic
280C2×C8C22×D10311yescharacteristic
281C4⋊C4—1031no—
282C4⋊C4—1031no—
283C4⋊C4—1031no—
284C4⋊C4—2061no—
285C4⋊C4—2061no—
286C4⋊C4—2061no—
287C4⋊C4—2061no—
288C4⋊C4C22×D10311yescharacteristic
289C4⋊C4C22×D10311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—1031no—
293C22⋊C4—1031no—
294C22⋊C4—2061no—
295C22⋊C4—2061no—
296C22⋊C4—2061no—
297C22⋊C4—2061no—
298C22⋊C4—2061no—
299C22⋊C4—2061no—
300C22⋊C4—2061no—
301C42—1031no—
302C42—2061no—
303C23—21no—
304C23—21no—
305C23—8241no—
306C23—1031no—
307C23—4122no—
308C23—4122no—
309C23—2061no—
310C23D4×D10311yescharacteristic
311Q8—2061no—
312Q8—2061no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—81no—
318D4—81no—
319D4—1032no—
320D4—4122no—
321D4—4122no—
322D4—4122no—
323D4—2062no—
324D4—2061no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—8241no—
330C2×C4—8241no—
331C2×C4—8241no—
332C2×C4—1031no—
333C2×C4—1031no—
334C2×C4—1031no—
335C2×C4—4122no—
336C2×C4—2061no—
337C2×C4—2061no—
338C2×C4—2061no—
339C2×C4—2061no—
340C2×C4—2061no—
341C2×C4D4×D10311yescharacteristic
342C2×C4C23×D10311yescharacteristic
343C8—21no—
344C8—21no—
345C8—2061no—
346C8—2061no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—8244no—
357C22—1032no—
358C22—4121no—
359C22—4121no—
360C22—2062no—
361C22—2061no—
362C22—2061no—
363C22C2×D4×D10311yescharacteristic
364C4—21no—
365C4—41no—
366C4—41no—
367C4—4121no—
368C4—4121no—
369C4—4121no—
370C4—2061no—
371C4—2061no—
372C4—2061no—
373C4#41×D10311yescharacteristic
374C4#1569306611yescharacteristic
375C2—41no—
376C2—81no—
377C2—81no—
378C2—4122no—
379C2—2062no—
380C2#2026843011yescharacteristic
381C2#135×D10311yescharacteristic
382C2#2026859211yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#466×C103C2
socleC22×C103C22×D4
hypercenter#466D103
hypocenterC103#3297
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. #20268488C2semidirect
2. #20268438C2semidirect
3. #20268144C2semidirect
4. #20268128C2semidirect
5. #20268112C2semidirect
6. #20268094C2semidirect
7. #20268019C2semidirect
8. #20268004C2semidirect
9. #20267934C2semidirect
10. #20267923C2semidirect
11. #20267871C2semidirect
12. C8×C22⋊D103C2semidirect
13. #20267788C2semidirect
14. #102×D103C2semidirect
15. #466×C103C2semidirect
18. C2×#13110093C22semidirect
22. #15693012C22semidirect
31. D4×Dic103C22semidirect
35. #15692980C22semidirect
38. #15692954C22semidirect
39. #15692952C22semidirect
40. Dic103⋊C8C22semidirect
41. #15692946C22semidirect
42. #15692946C22semidirect
43. #15692944C22semidirect
49. C22⋊(C103⋊C8)C22semidirect
51. C8×Dic103C22semidirect
53. C22×C8×C103C22semidirect
55. #121×C103C22semidirect
56. #107×C103C22semidirect
58. #102×C103C22semidirect
192. C103#3297semidirect
199. #466D103semidirect
214. C22×C8C2×D103semidirect
225. #121C2×D103semidirect
235. #107C2×D103semidirect
247. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684882
#202684382
#202681442
#202681282
#202681122
#202680942
#202680192
#202680042
#202679342
#202679232
#202678712
C8×C22⋊D1032
#202677882
#102×D1032
#466×C1032
#3297103