Finite Group Databasebeta

← #27206985

Subgroups — #27206985

Order 13184.

408 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268483C211yesmaximal, characteristic, complemented
2#20268432C211yesmaximal, characteristic
3#20268147C211yesmaximal, characteristic, complemented
4#20268119C211yesmaximal, characteristic, complemented
5#20268118C211yesmaximal, characteristic, complemented
6#20268094C211yesmaximal, characteristic, complemented
7#20268023C211yesmaximal, characteristic, complemented
8#20268015C211yesmaximal, characteristic, complemented
9#20267952C211yesmaximal, characteristic, complemented
10#20267941C211yesmaximal, characteristic, complemented
11#20267876C211yesmaximal, characteristic, complemented
12C8×C22⋊D103C211yesmaximal, characteristic, complemented
13#20267786C211yesmaximal, characteristic, complemented
14C2×#15692943C211yesmaximal, characteristic, complemented
15#467×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110092C2211yescharacteristic
19C2×#13110092C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic, complemented
21#15693016—21no—
22#15693012—21no—
23#15693012C2211yescharacteristic, complemented
24#15693010C2211yescharacteristic
25#15693006—21no—
26#15693005—21no—
27#15692997C2211yescharacteristic, complemented
28#15692996—21no—
29#15692996C2211yescharacteristic
30#15692991—21no—
31Q8×Dic103C2211yescharacteristic, complemented
32#15692983C2211yescharacteristic
33C4×C22⋊D103C2211yescharacteristic
34#15692979C2211yescharacteristic, complemented
35#15692977—21no—
36C2×C4⋊Dic103C2211yescharacteristic
37C22⋊C4×D103—21no—
38#15692952C2211yescharacteristic, complemented
39#15692952C2211yescharacteristic, complemented
40Dic103⋊C8C2211yescharacteristic, complemented
41#15692945C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692943C2211yescharacteristic
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692943C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C2×Q16×C103C2211yescharacteristic, complemented
53C22×C8×C103C2211yescharacteristic
54C22⋊Q8×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#107×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58#103×C103C2211yescharacteristic, complemented
59C23×D103—21no—
60#13110106—22no—
61#13110106—41no—
62C2×D412—22no—
63C2×D412—21no—
64C2×D412—21no—
65C2×D412—21no—
66C2×D412—41no—
67C2×D412C2311yescharacteristic
68C2×D412C2311yescharacteristic
69C2×C22⋊D103D411yescharacteristic
70C22×Dic103—21no—
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103C2311yescharacteristic
74#13110092—22no—
75#13110092—41no—
76C2×C103⋊C8C2311yescharacteristic
77C2×C103⋊C8C2311yescharacteristic
78C8×D103—41no—
79C4⋊Dic103—21no—
80C4⋊Dic103—21no—
81C4⋊Dic103—21no—
82C4⋊Dic103C2311yescharacteristic
83C4⋊Dic103C2311yescharacteristic
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4D411yescharacteristic
87C22⋊Dic103D411yescharacteristic
88(C2×D103)⋊C4—21no—
89(C2×D103)⋊C4—21no—
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4D411yescharacteristic
95C4×Dic103—21no—
96C4×Dic103—21no—
97C4×Dic103C2311yescharacteristic
98C2×Q8×C103C2311yescharacteristic
99C2×Q8×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101Q16×C103—41no—
102C2×C8×C103—41no—
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C22⋊C4×C103—21no—
110C22⋊C4×C103—21no—
111C23×C103C2×D411yescharacteristic
112C22×D103—21no—
113C22×D103—21no—
114C22×D103—42no—
115C22×D103—42no—
116C22×D103—81no—
117C22×D103C2×D411yescharacteristic
118Q8×C103—21no—
119Q8×C103—21no—
120Q8×C103—21no—
121Q8×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103C2×D411yescharacteristic
129C2×C4×C103C2411yescharacteristic
130C22⋊D103—22no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—42no—
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137D412—21no—
138D412—21no—
139D412—21no—
140D412—42no—
141D412—42no—
142D412—81no—
143D412#4112yes—
144C4×D103—21no—
145C4×D103—21no—
146C4×D103—42no—
147C4×D103—81no—
148C8×C103—21no—
149C8×C103—21no—
150C103⋊C8—21no—
151C103⋊C8—21no—
152C22×C103—21no—
153C22×C103—21no—
154C22×C103#13512yes—
155C22×C103C22×D411yescharacteristic
156C2×D103—21no—
157C2×D103—22no—
158C2×D103—21no—
159C2×D103—21no—
160C2×D103—41no—
161C2×D103—41no—
162C2×D103—41no—
163C2×D103—41no—
164C2×D103—41no—
165C2×D103—84no—
166C4×C103—21no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103—41no—
171C4×C103C2×#4111yescharacteristic
172C4×C103H(5,𝔽2)11yescharacteristic
173Dic103—21no—
174Dic103—21no—
175Dic103—21no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—22no—
179C2×C103#54611yescharacteristic
180C2×C103C2×#13511yescharacteristic
181C2×C103#57711yescharacteristic
182D103—41no—
183D103—42no—
184D103—81no—
185#3296—1031nomaximal, Sylow
186C103#329611yescharacteristic, complemented, Sylow
187#552—1031no—
188#546—1031no—
189#488—1031no—
190#483—1031no—
191#482—1031no—
192#478—1031no—
193#467D10311yescharacteristic, complemented
194#465—1031no—
195#464—1031no—
196#452—1031no—
197#450—1031no—
198C4×SD16—1031no—
199C8×D4—1031no—
200#416—1031no—
201C2×#102—1031no—
202C2×#41—1031no—
203C22×D4—1031no—
204C2×Q16C2×D10311yescharacteristic, complemented
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8C2×D10311yescharacteristic
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
213#123—2061no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8C2×D10311yescharacteristic
217C22⋊Q8C2×D10311yescharacteristic
218#121—1031no—
219#121—2061no—
220#120—2061no—
221C4×Q8—1031no—
222C4×D4—1031no—
223C4×D4—1031no—
224#117—1031no—
225#117—2061no—
226C2×C4⋊C4—1031no—
227C2×C22⋊C4—2061no—
228#107C2×D10311yescharacteristic, complemented
229#106—1031no—
230#106—1031no—
231C4⋊C8—1031no—
232#103—1031no—
233#103—1031no—
234#103C2×D10311yescharacteristic, complemented
235#103C2×D10311yescharacteristic, complemented
236#102—1031no—
237#102—1031no—
238#102—1031no—
239#102—1031no—
240#102—1031no—
241#102—1031no—
242C22⋊C8—1031no—
243C22⋊C8—1031no—
244C4×C8—1031no—
245C24—2061no—
246#41—4121no—
247#41—2062no—
248C2×Q8C22×D10311yescharacteristic
249C2×Q8C22×D10311yescharacteristic
250C2×D4—1031no—
251C2×D4—1031no—
252C2×D4—1031no—
253C2×D4—4121no—
254C2×D4—2061no—
255C2×D4—2062no—
256C2×D4—2061no—
257C2×D4—2061no—
258C22×C4—1031no—
259C22×C4—2061no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263Q16—41no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—41no—
267C2×C8—1031no—
268C2×C8—1031no—
269C2×C8—4121no—
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—1031no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4—2061no—
282C4⋊C4C22×D10311yescharacteristic
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—1031no—
287C22⋊C4—1031no—
288C22⋊C4—2061no—
289C22⋊C4—2061no—
290C22⋊C4—2061no—
291C22⋊C4—2061no—
292C22⋊C4—2061no—
293C22⋊C4—2061no—
294C42—1031no—
295C42—2061no—
296C42—2061no—
297C23—8241no—
298C23—1031no—
299C23—4122no—
300C23—4122no—
301C23—2061no—
302C23—2061no—
303C23D4×D10311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—21no—
308D4—8241no—
309D4—1032no—
310D4—4122no—
311D4—4122no—
312D4—2062no—
313D4—2061no—
314D4—2061no—
315D4—2061no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—8241no—
323C2×C4—1031no—
324C2×C4—1031no—
325C2×C4—1031no—
326C2×C4—4122no—
327C2×C4—4122no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4D4×D10311yescharacteristic
333C2×C4C23×D10311yescharacteristic
334C8—21no—
335C8—21no—
336C8—2061no—
337C8—2061no—
338C22—21no—
339C22—21no—
340C22—8244no—
341C22—4121no—
342C22—4121no—
343C22—4121no—
344C22—4121no—
345C22—4121no—
346C22—2061no—
347C22—2061no—
348C22—2062no—
349C22—2061no—
350C22#1569304412yes—
351C22C2×D4×D10311yescharacteristic
352C4—21no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4121no—
358C4—4121no—
359C4—2061no—
360C4—2061no—
361C4—2061no—
362C4#41×D10311yescharacteristic
363C4#1569306611yescharacteristic
364C2—22no—
365C2—8241no—
366C2—4122no—
367C2—4121no—
368C2#2026843011yescharacteristic
369C2C2×#1569304411yescharacteristic
370C2#2026859811yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#467×C103C2
socleC22×C103C22×D4
prime radical#20268432C2
hypercenter#467D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
1. #20268483C2semidirect
3. #20268147C2semidirect
4. #20268119C2semidirect
5. #20268118C2semidirect
6. #20268094C2semidirect
7. #20268023C2semidirect
8. #20268015C2semidirect
9. #20267952C2semidirect
10. #20267941C2semidirect
11. #20267876C2semidirect
12. C8×C22⋊D103C2semidirect
13. #20267786C2semidirect
14. C2×#15692943C2semidirect
15. #467×C103C2semidirect
20. C2×C8×D103C22semidirect
23. #15693012C22semidirect
27. #15692997C22semidirect
31. Q8×Dic103C22semidirect
34. #15692979C22semidirect
38. #15692952C22semidirect
39. #15692952C22semidirect
40. Dic103⋊C8C22semidirect
41. #15692945C22semidirect
42. #15692945C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
52. C2×Q16×C103C22semidirect
56. #107×C103C22semidirect
57. #103×C103C22semidirect
58. #103×C103C22semidirect
186. C103#3296semidirect
193. #467D103semidirect
204. C2×Q16C2×D103semidirect
228. #107C2×D103semidirect
234. #103C2×D103semidirect
235. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202684832
#202684322
#202681472
#202681192
#202681182
#202680942
#202680232
#202680152
#202679522
#202679412
#202678762
C8×C22⋊D1032
#202677862
C2×#156929432
#467×C1032
#3296103