Finite Group Databasebeta

← #27206977

Subgroups — #27206977

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#20268476C211yesmaximal, characteristic, complemented
2#20268432C211yesmaximal, characteristic
3#20268147C211yesmaximal, characteristic, complemented
4#20268117C211yesmaximal, characteristic, complemented
5#20268090C211yesmaximal, characteristic, complemented
6#20268030C211yesmaximal, characteristic, complemented
7#20268021C211yesmaximal, characteristic, complemented
8#20268016C211yesmaximal, characteristic, complemented
9#20267956C211yesmaximal, characteristic, complemented
10#20267944C211yesmaximal, characteristic, complemented
11#20267878C211yesmaximal, characteristic, complemented
12(C22⋊D103)⋊C8C211yesmaximal, characteristic, complemented
13#20267786C211yesmaximal, characteristic, complemented
14C2×#15692941C211yesmaximal, characteristic, complemented
15#483×C103C211yesmaximal, characteristic, complemented
16C2×#13110106C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C2×#13110095C2211yescharacteristic, complemented
19C2×#13110094C2211yescharacteristic
20C2×#13110094C2211yescharacteristic
21C22×C103⋊C8C2211yescharacteristic
22C2×C8×D103C2211yescharacteristic, complemented
23#15693016—21no—
24#15693012C2211yescharacteristic, complemented
25#15693011—21no—
26#15693010C2211yescharacteristic
27#15693006—21no—
28#15693004—21no—
29#15693001C2211yescharacteristic, complemented
30#15693000C2211yescharacteristic
31#15692996—21no—
32#15692996C2211yescharacteristic
33#15692991—21no—
34#15692986C2211yescharacteristic, complemented
35#15692983C2211yescharacteristic
36C4×C22⋊D103C2211yescharacteristic
37#15692980—21no—
38#15692979C2211yescharacteristic, complemented
39C22⋊C4×D103—21no—
40#15692954C2211yescharacteristic, complemented
41Dic103⋊C8C2211yescharacteristic, complemented
42#15692945C2211yescharacteristic, complemented
43#15692944C2211yescharacteristic, complemented
44#15692943C2211yescharacteristic
45#15692943C2211yescharacteristic
46#15692941C2211yescharacteristic
47#15692941C2211yescharacteristic
48#15692941C2211yescharacteristic
49#15692941C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic, complemented
51C8×Dic103C2211yescharacteristic, complemented
52C22⋊Q8×C103C2211yescharacteristic
53C2×C4⋊C4×C103C2211yescharacteristic
54#106×C103C2211yescharacteristic, complemented
55#106×C103C2211yescharacteristic, complemented
56#103×C103C2211yescharacteristic, complemented
57#103×C103C2211yescharacteristic, complemented
58C22⋊C8×C103C2211yescharacteristic
59C23×D103—21no—
60#13110106—22no—
61#13110106—41no—
62C2×Dic206C2311yescharacteristic
63C2×D412—22no—
64C2×D412—21no—
65C2×D412—21no—
66C2×D412—21no—
67C2×D412—41no—
68C2×D412C2311yescharacteristic
69C2×D412C2311yescharacteristic
70C2×C22⋊D103D411yescharacteristic
71C2×C4×D103—21no—
72C2×C4×D103—21no—
73C2×C4×D103C2311yescharacteristic
74#13110095—41no—
75#13110094—22no—
76#13110094—41no—
77C2×C103⋊C8—41no—
78C2×C103⋊C8C2311yescharacteristic
79C2×C103⋊C8C2311yescharacteristic
80C8×D103—41no—
81C4⋊Dic103—21no—
82C4⋊Dic103—21no—
83C4⋊Dic103C2311yescharacteristic
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4D411yescharacteristic
88C22⋊Dic103—21no—
89C22⋊Dic103D411yescharacteristic
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4—21no—
94(C2×D103)⋊C4—21no—
95(C2×D103)⋊C4—21no—
96(C2×D103)⋊C4D411yescharacteristic
97C4×Dic103—21no—
98C4×Dic103—21no—
99C4×Dic103C2311yescharacteristic
100C2×Q8×C103C2311yescharacteristic
101C22×C4×C103—21no—
102C22×C4×C103C2311yescharacteristic
103C2×C8×C103C2311yescharacteristic
104C2×C8×C103C2311yescharacteristic
105C4⋊C4×C103—21no—
106C4⋊C4×C103—21no—
107C4⋊C4×C103C2311yescharacteristic
108C4⋊C4×C103C2311yescharacteristic
109C4⋊C4×C103C2311yescharacteristic
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—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—42no—
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2411yescharacteristic
129C22⋊D103—22no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103C2×D411yescharacteristic
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135D412—21no—
136D412—21no—
137D412—21no—
138D412—42no—
139D412—42no—
140D412—81no—
141D412#4112yes—
142C4×D103—21no—
143C4×D103—21no—
144C4×D103—42no—
145C4×D103—81no—
146Dic206—21no—
147Dic206—21no—
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#483D10311yescharacteristic, complemented
191#482—1031no—
192#478—1031no—
193#467—1031no—
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×Q16—1031no—
205C2×SD16—1031no—
206C2×SD16—1031no—
207C22×C8—1031no—
208C22×C8—1031no—
209#126—2061no—
210#125—1031no—
211#125—2061no—
212#124—1031no—
213#123—2061no—
214#123—2061no—
215C22⋊Q8—1031no—
216C22⋊Q8—1031no—
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⋊C4C2×D10311yescharacteristic
227C2×C22⋊C4—2061no—
228#107—1031no—
229#106C2×D10311yescharacteristic, complemented
230#106C2×D10311yescharacteristic, complemented
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⋊C8C2×D10311yescharacteristic
244C4×C8—1031no—
245C24—2061no—
246#41—4121no—
247#41—2062no—
248C2×Q8—1031no—
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—21no—
259C22×C4—1031no—
260C22×C4—2061no—
261C22×C4—2061no—
262C22×C4C22×D10311yescharacteristic
263Q16—4121no—
264SD16—4121no—
265SD16—2062no—
266C2×C8—1031no—
267C2×C8—1031no—
268C2×C8—4121no—
269C2×C8—4121no—
270C2×C8C22×D10311yescharacteristic
271C2×C8C22×D10311yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—1031no—
275C4⋊C4—1031no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4—2061no—
279C4⋊C4—2061no—
280C4⋊C4—2061no—
281C4⋊C4C22×D10311yescharacteristic
282C4⋊C4C22×D10311yescharacteristic
283C4⋊C4C22×D10311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—1031no—
286C22⋊C4—1031no—
287C22⋊C4—2061no—
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—2061no—
307Q8—2061no—
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—42no—
323C2×C4—8241no—
324C2×C4—1031no—
325C2×C4—1031no—
326C2×C4—1031no—
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#1569304212yes—
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#1569306711yescharacteristic
364C2—22no—
365C2—8241no—
366C2—4122no—
367C2—4121no—
368C2#2026843311yescharacteristic
369C2C2×#1569304211yescharacteristic
370C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#483×C103C2
socleC22×C103C22×D4
prime radical#20268432C2
hypercenter#483D103
hypocenterC103#3296
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
1. #20268476C2semidirect
3. #20268147C2semidirect
4. #20268117C2semidirect
5. #20268090C2semidirect
6. #20268030C2semidirect
7. #20268021C2semidirect
8. #20268016C2semidirect
9. #20267956C2semidirect
10. #20267944C2semidirect
11. #20267878C2semidirect
12. (C22⋊D103)⋊C8C2semidirect
13. #20267786C2semidirect
14. C2×#15692941C2semidirect
15. #483×C103C2semidirect
18. C2×#13110095C22semidirect
22. C2×C8×D103C22semidirect
24. #15693012C22semidirect
29. #15693001C22semidirect
34. #15692986C22semidirect
38. #15692979C22semidirect
40. #15692954C22semidirect
41. Dic103⋊C8C22semidirect
42. #15692945C22semidirect
43. #15692944C22semidirect
50. (C2×D103)⋊C8C22semidirect
51. C8×Dic103C22semidirect
54. #106×C103C22semidirect
55. #106×C103C22semidirect
56. #103×C103C22semidirect
57. #103×C103C22semidirect
186. C103#3296semidirect
190. #483D103semidirect
229. #106C2×D103semidirect
230. #106C2×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
#202684762
#202684322
#202681472
#202681172
#202680902
#202680302
#202680212
#202680162
#202679562
#202679442
#202678782
(C22⋊D103)⋊C82
#202677862
C2×#156929412
#483×C1032
#3296103