Finite Group Databasebeta

← #22581639

Subgroups — #22581639

Order 8896.

214 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17984835C211yesmaximal, characteristic, complemented
2#17984833C211yesmaximal, characteristic, complemented
3#17984832C211yesmaximal, characteristic, complemented
4#17984832C211yesmaximal, characteristic, complemented
5#17984824C211yesmaximal, characteristic
6#17984824C211yesmaximal, characteristic
7#17984820C211yesmaximal, characteristic, complemented
8#17984819C211yesmaximal, characteristic, complemented
9C4×Dic278C211yesmaximal, characteristic, complemented
10(C22⋊D139)⋊C4C211yesmaximal, characteristic
11#17984800C211yesmaximal, characteristic, complemented
12#17984799C211yesmaximal, characteristic, complemented
13#17984798C211yesmaximal, characteristic, complemented
14C4⋊C4×D139C211yesmaximal, characteristic, complemented
15#126×C139C211yesmaximal, characteristic, complemented
16C2×Dic278C2211yescharacteristic
17C2×C22⋊D139C2211yescharacteristic
18C22×Dic139C2211yescharacteristic
19C2×C4×D139C2211yescharacteristic
20C2×C4×D139C2211yescharacteristic
21C2×C4×D139C2211yescharacteristic
22C4⋊Dic139C2211yescharacteristic
23C4⋊Dic139C2211yescharacteristic
24C4⋊Dic139C2211yescharacteristic
25C4⋊Dic139C2211yescharacteristic
26Dic139⋊C4C2211yescharacteristic
27Dic139⋊C4C2211yescharacteristic
28Dic139⋊C4C2211yescharacteristic
29Dic139⋊C4C2211yescharacteristic
30Dic139⋊C4C2211yescharacteristic
31Dic139⋊C4C2211yescharacteristic
32Dic139⋊C4C2211yescharacteristic
33Dic139⋊C4C2211yescharacteristic
34Dic139⋊C4C2211yescharacteristic
35C22⋊Dic139C2211yescharacteristic
36C22⋊Dic139C2211yescharacteristic
37(C2×D139)⋊C4C2211yescharacteristic
38(C2×D139)⋊C4C2211yescharacteristic
39(C2×D139)⋊C4C2211yescharacteristic
40C4×Dic139C2211yescharacteristic
41C4×Dic139C2211yescharacteristic
42C4×Dic139C2211yescharacteristic
43C4×Dic139C2211yescharacteristic
44C4⋊C4×C139C2211yescharacteristic
45C4⋊C4×C139C2211yescharacteristic
46C4⋊C4×C139C2211yescharacteristic
47C22⋊C4×C139C2211yescharacteristic
48C22⋊C4×C139C2211yescharacteristic
49C22⋊C4×C139C2211yescharacteristic
50C42×C139C2211yescharacteristic
51C22×D139C2311yescharacteristic
52Dic278—22no—
53C22⋊D139—22no—
54C2×Dic139—22no—
55C2×Dic139C2311yescharacteristic
56C2×Dic139C2311yescharacteristic
57C2×Dic139C2311yescharacteristic
58C2×Dic139C2311yescharacteristic
59C2×Dic139C2311yescharacteristic
60C2×Dic139C2311yescharacteristic
61C2×Dic139C2311yescharacteristic
62C4×D139—22no—
63C4×D139—22no—
64C4×D139—22no—
65C23×C139C2311yescharacteristic
66C2×C4×C139C2311yescharacteristic
67C2×C4×C139C2311yescharacteristic
68C2×C4×C139C2311yescharacteristic
69C2×C4×C139C2311yescharacteristic
70C2×C4×C139C2311yescharacteristic
71C2×C4×C139C2311yescharacteristic
72C22×C139—21no—
73C22×C139—21no—
74C22×C139—21no—
75C22×C139C2411yescharacteristic
76C2×D139—21no—
77C2×D139—21no—
78C2×D139#4112yes—
79C4×C139—21no—
80C4×C139—21no—
81C4×C139—21no—
82C4×C139—21no—
83C4×C139—21no—
84C4×C139—21no—
85Dic139—21no—
86Dic139—21no—
87Dic139—21no—
88Dic139—21no—
89Dic139—21no—
90Dic139—21no—
91Dic139#4112yes—
92C2×C139—41no—
93C2×C139C2×#4111yescharacteristic
94C2×C139C2×#4111yescharacteristic
95C2×C1392−1+411yescharacteristic
96D139—22no—
97C139#55211yescharacteristic, complemented, Sylow
98#552—1391nomaximal, Sylow
99#126—1391no—
100#126D13911yescharacteristic, complemented
101#125—1391no—
102#125—1391no—
103#125—1391no—
104#123—1391no—
105#123—1391no—
106C22⋊Q8—1391no—
107C22⋊Q8—1391no—
108C4×Q8—1391no—
109C4×D4—1391no—
110#117—1391no—
111#117—1391no—
112#117—1391no—
113C2×C4⋊C4—1391no—
114C2×Q8—1391no—
115C2×D4—1391no—
116C22×C4—1391no—
117C22×C4—1391no—
118C22×C4—1391no—
119C22×C4—1391no—
120C4⋊C4—1391no—
121C4⋊C4—1391no—
122C4⋊C4—1391no—
123C4⋊C4—1391no—
124C4⋊C4—1391no—
125C4⋊C4—1391no—
126C4⋊C4—1391no—
127C4⋊C4—1391no—
128C4⋊C4—1391no—
129C4⋊C4—1391no—
130C4⋊C4—1391no—
131C4⋊C4—1391no—
132C4⋊C4—1391no—
133C4⋊C4C2×D13911yescharacteristic
134C4⋊C4C2×D13911yescharacteristic
135C4⋊C4C2×D13911yescharacteristic
136C22⋊C4—1391no—
137C22⋊C4—1391no—
138C22⋊C4—1391no—
139C22⋊C4—1391no—
140C22⋊C4—1391no—
141C22⋊C4C2×D13911yescharacteristic
142C22⋊C4C2×D13911yescharacteristic
143C22⋊C4C2×D13911yescharacteristic
144C42—1391no—
145C42—1391no—
146C42—1391no—
147C42—1391no—
148C42C2×D13911yescharacteristic
149C23—1391no—
150C23C22×D13911yescharacteristic
151Q8—2782no—
152D4—2782no—
153C2×C4—2782no—
154C2×C4—2782no—
155C2×C4—2782no—
156C2×C4—2782no—
157C2×C4—1391no—
158C2×C4—1391no—
159C2×C4—1391no—
160C2×C4—1391no—
161C2×C4—1391no—
162C2×C4—1391no—
163C2×C4—1391no—
164C2×C4C22×D13911yescharacteristic
165C2×C4C22×D13911yescharacteristic
166C2×C4C22×D13911yescharacteristic
167C2×C4C22×D13911yescharacteristic
168C2×C4C22×D13911yescharacteristic
169C2×C4C22×D13911yescharacteristic
170C22—21no—
171C22—21no—
172C22—21no—
173C22—2781no—
174C22—2781no—
175C22—1392no—
176C22C23×D13911yescharacteristic
177C4—21no—
178C4—21no—
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—2781no—
184C4—2781no—
185C4—2781no—
186C4—2781no—
187C4—2781no—
188C4—2781no—
189C4—1392no—
190C2—41no—
191C2—2782no—
192C2#41×D13911yescharacteristic
193C2#41×D13911yescharacteristic
194C2#1798488911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D139
commutator, socleC22×C139C24
Fitting#126×C139C2
hypercenter#126D139
hypocenterC139#552
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #17984835C2semidirect
2. #17984833C2semidirect
3. #17984832C2semidirect
4. #17984832C2semidirect
7. #17984820C2semidirect
8. #17984819C2semidirect
9. C4×Dic278C2semidirect
11. #17984800C2semidirect
12. #17984799C2semidirect
13. #17984798C2semidirect
14. C4⋊C4×D139C2semidirect
15. #126×C139C2semidirect
97. C139#552semidirect
100. #126D139semidirect