Finite Group Databasebeta

← #27205671

Subgroups — #27205671

Order 13184.

340 conjugacy classes of subgroups.

The subgroup lattice has 310 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268421C211yesmaximal, characteristic
2#20268418C211yesmaximal, characteristic
3#20268200C211yesmaximal, characteristic, complemented
4#20268199C211yesmaximal, characteristic, complemented
5#20268198C211yesmaximal, characteristic, complemented
6#20268192C211yesmaximal, characteristic, complemented
7#20268190C211yesmaximal, characteristic, complemented
8#20268188C211yesmaximal, characteristic, complemented
9#20268187C211yesmaximal, characteristic, complemented
10#20267832C211yesmaximal, characteristic
11#20267830C211yesmaximal, characteristic
12#20267828C211yesmaximal, characteristic
13#106×D103C211yesmaximal, characteristic
14#20267748C211yesmaximal, characteristic
15#501×C103C211yesmaximal, characteristic, complemented
16C2×#13110088C2211yescharacteristic
17C2×C8×D103C2211yescharacteristic
18#15693021C2211yescharacteristic
19#15693020—21no—
20#15693020C2211yescharacteristic
21#15693020C2211yescharacteristic
22#15693019—21no—
23#15693013C2211yescharacteristic
24#15693012C2211yescharacteristic
25#15693012C2211yescharacteristic
26#15693011—21no—
27#15693011—21no—
28#15693001—21no—
29#15692999—21no—
30#15692999—21no—
31#15692997—21no—
32#15692979C2211yescharacteristic
33#15692979C2211yescharacteristic
34#15692978C2211yescharacteristic
35C4⋊C4×D103C2211yescharacteristic
36C4⋊C4×D103C2211yescharacteristic
37#15692955C2211yescharacteristic
38#15692955C2211yescharacteristic
39#15692954C2211yescharacteristic
40#15692954C2211yescharacteristic
41#15692953C2211yescharacteristic
42#15692953C2211yescharacteristic
43#15692952C2211yescharacteristic
44#15692952C2211yescharacteristic
45#15692952C2211yescharacteristic
46#15692952C2211yescharacteristic
47#15692952C2211yescharacteristic
48#15692952C2211yescharacteristic
49#15692931C2211yescharacteristic
50C4×C103⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C4⋊Q8×C103C2211yescharacteristic
53#125×C103C2211yescharacteristic
54#107×C103C2211yescharacteristic
55#107×C103C2211yescharacteristic
56#106×C103C2211yescharacteristic
57#106×C103C2211yescharacteristic
58#97×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206—21no—
61C2×Dic206—21no—
62C2×C4×D103—21no—
63C2×C4×D103—21no—
64C2×C4×D103C2311yescharacteristic
65#13110088Q814yescomplemented
66C2×C103⋊C8C2311yescharacteristic
67C2×C103⋊C8C2311yescharacteristic
68C8×D103Q814yescomplemented
69C4⋊Dic103—21no—
70C4⋊Dic103—21no—
71C4⋊Dic103—21no—
72C4⋊Dic103C2311yescharacteristic
73C4⋊Dic103C2311yescharacteristic
74C4⋊Dic103C2311yescharacteristic
75C4⋊Dic103C2311yescharacteristic
76Dic103⋊C4—21no—
77Dic103⋊C4—21no—
78Dic103⋊C4—21no—
79Dic103⋊C4—21no—
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4D411yescharacteristic
85Dic103⋊C4D411yescharacteristic
86(C2×D103)⋊C4—21no—
87(C2×D103)⋊C4—21no—
88(C2×D103)⋊C4D411yescharacteristic
89(C2×D103)⋊C4D411yescharacteristic
90C4×Dic103—21no—
91C4×Dic103—21no—
92C4×Dic103C2311yescharacteristic
93C2×Q8×C103—21no—
94C2×C8×C103C2311yescharacteristic
95C2×C8×C103C2311yescharacteristic
96C4⋊C4×C103—21no—
97C4⋊C4×C103—21no—
98C4⋊C4×C103—21no—
99C4⋊C4×C103C2311yescharacteristic
100C4⋊C4×C103C2311yescharacteristic
101C4⋊C4×C103C2311yescharacteristic
102C4⋊C4×C103C2311yescharacteristic
103C42×C103C2311yescharacteristic
104C22×D103C2×D411yescharacteristic
105Q8×C103—81no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103C2×D411yescharacteristic
111C2×C4×C103C2×D411yescharacteristic
112C2×C4×C103C2411yescharacteristic
113C2×Dic103—21no—
114C2×Dic103—21no—
115C2×Dic103—21no—
116C2×Dic103—21no—
117C2×Dic103C2×D411yescharacteristic
118C2×Dic103C2×D411yescharacteristic
119C2×Dic103C2×D411yescharacteristic
120C4×D103—81no—
121C4×D103—81no—
122C4×D103C2×Q812yes—
123C4×D103C2×Q812yes—
124Dic206—81no—
125Dic206—81no—
126Dic206—81no—
127C8×C103C2×Q812yes—
128C8×C103C2×Q812yes—
129C103⋊C8C2×Q812yes—
130C103⋊C8C2×Q812yes—
131C22×C103C22×D411yescharacteristic
132C2×D103—21no—
133C2×D103—21no—
134C2×D103C4⋊Q812yes—
135C4×C103—21no—
136C4×C103—21no—
137C4×C103—41no—
138C4×C103—41no—
139C4×C103—41no—
140C4×C103—41no—
141C4×C103C22×Q811yescharacteristic
142C4×C103C22×Q811yescharacteristic
143Dic103—21no—
144Dic103—21no—
145Dic103—41no—
146Dic103—41no—
147Dic103—41no—
148Dic103—41no—
149Dic103C4⋊Q812yes—
150C2×C103C2×C4⋊Q811yescharacteristic
151C2×C103#57711yescharacteristic
152C2×C103#57711yescharacteristic
153D103—22no—
154#3163—1031nomaximal, Sylow
155C103#316311yescharacteristic, complemented, Sylow
156#544—1031no—
157#544—1031no—
158#501—1031no—
159#501—1031no—
160#501—1031no—
161#501D10311yescharacteristic, complemented
162#499—1031no—
163#499—1031no—
164#498—1031no—
165#498—1031no—
166#428—1031no—
167#428—1031no—
168#427—1031no—
169C2×#106—1031no—
170#405—1031no—
171C2×M16—1031no—
172C22×C8—1031no—
173C4⋊Q8—1031no—
174C4⋊Q8—1031no—
175C4⋊Q8—1031no—
176C4⋊Q8—2061no—
177C4⋊Q8—2061no—
178C4⋊Q8C2×D10311yescharacteristic
179#125—1031no—
180#125—1031no—
181#125—1031no—
182#125—2061no—
183#125—2061no—
184#125C2×D10311yescharacteristic
185C22⋊Q8—2061no—
186C22⋊Q8—2061no—
187C22⋊Q8—2061no—
188C22⋊Q8—2061no—
189#117—1031no—
190#117—1031no—
191#117—1031no—
192C2×C4⋊C4—1031no—
193C2×C4⋊C4—1031no—
194#107—1031no—
195#107—1031no—
196#107—1031no—
197#107—1031no—
198#107C2×D10311yescharacteristic
199#107C2×D10311yescharacteristic
200#106—1031no—
201#106—1031no—
202#106—1031no—
203#106—1031no—
204#106—1031no—
205#106—1031no—
206#106—1031no—
207#106—1031no—
208#106C2×D10311yescharacteristic
209#106C2×D10311yescharacteristic
210#97—1031no—
211#97C2×D10311yescharacteristic
212C4×C8—1031no—
213C4×C8—1031no—
214C2×Q8—21no—
215C2×Q8—2061no—
216C2×Q8—2061no—
217C2×Q8—2061no—
218C22×C4—1031no—
219C22×C4—2061no—
220C22×C4—2061no—
221M16—1034no—
222C2×C8—1031no—
223C2×C8—1031no—
224C2×C8—1034no—
225C2×C8C22×D10311yescharacteristic
226C2×C8C22×D10311yescharacteristic
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—1031no—
231C4⋊C4—1031no—
232C4⋊C4—1031no—
233C4⋊C4—1031no—
234C4⋊C4—1031no—
235C4⋊C4—1031no—
236C4⋊C4—2061no—
237C4⋊C4—2061no—
238C4⋊C4—2061no—
239C4⋊C4—2061no—
240C4⋊C4—2061no—
241C4⋊C4—2061no—
242C4⋊C4—2061no—
243C4⋊C4—2061no—
244C4⋊C4—2061no—
245C4⋊C4—2061no—
246C4⋊C4—2061no—
247C4⋊C4C22×D10311yescharacteristic
248C4⋊C4C22×D10311yescharacteristic
249C4⋊C4C22×D10311yescharacteristic
250C4⋊C4C22×D10311yescharacteristic
251C22⋊C4—1031no—
252C22⋊C4—1031no—
253C22⋊C4—2061no—
254C22⋊C4—2061no—
255C42—1031no—
256C42—2061no—
257C42—2061no—
258C42C22×D10311yescharacteristic
259C23—1031no—
260Q8—81no—
261Q8—8241no—
262Q8—8241no—
263Q8—8241no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—8241no—
269C2×C4—8241no—
270C2×C4—1031no—
271C2×C4—1032no—
272C2×C4—1032no—
273C2×C4—1031no—
274C2×C4—1031no—
275C2×C4—2061no—
276C2×C4—2061no—
277C2×C4—2061no—
278C2×C4—2061no—
279C2×C4D4×D10311yescharacteristic
280C2×C4D4×D10311yescharacteristic
281C2×C4C23×D10311yescharacteristic
282C8—1032no—
283C8—1032no—
284C8Q8×D10312yes—
285C8Q8×D10312yes—
286C22—1032no—
287C22—2061no—
288C22—2061no—
289C22C2×D4×D10311yescharacteristic
290C4—21no—
291C4—21no—
292C4—41no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—1032no—
297C4—4121no—
298C4—4121no—
299C4—4121no—
300C4—4121no—
301C4—2061no—
302C4—2061no—
303C4C2×Q8×D10311yescharacteristic
304C4C2×Q8×D10311yescharacteristic
305C2—2062no—
306C2C4⋊Q8×D10311yescharacteristic
307C2#2026860011yescharacteristic
308C2#2026860111yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#501×C103C2
socleC22×C103C22×D4
prime radicalC22×D103C2×D4
hypercenter#501D103
hypocenterC103#3163
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #20268200C2semidirect
4. #20268199C2semidirect
5. #20268198C2semidirect
6. #20268192C2semidirect
7. #20268190C2semidirect
8. #20268188C2semidirect
9. #20268187C2semidirect
15. #501×C103C2semidirect
65. #13110088Q8semidirect
68. C8×D103Q8semidirect
155. C103#3163semidirect
161. #501D103semidirect

Maximal subgroups

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

subgroupindex
#202684212
#202684182
#202682002
#202681992
#202681982
#202681922
#202681902
#202681882
#202681872
#202678322
#202678302
#202678282
#106×D1032
#202677482
#501×C1032
#3163103