Finite Group Databasebeta

← #31804982

Subgroups — #31804982

Order 17792.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#22581487C211yesmaximal, characteristic
2#22580821C211yesmaximal, characteristic, complemented
3#22580691C212yesmaximal, complemented
4#22580688C212yesmaximal
5#431×C139C211yesmaximal, characteristic, complemented
6#17984836—21no—
7#17984834C411yescharacteristic, complemented
8#17984830C411yescharacteristic, complemented
9#17984825—21no—
10#17984821C2211yescharacteristic
11#17984816C2211yescharacteristic
12C4×Dic278C411yescharacteristic, complemented
13C4×D556C411yescharacteristic, complemented
14C4×C22⋊D139—21no—
15#17984799—21no—
16C139⋊#95—21no—
17C139⋊#95—21no—
18C139⋊#95C2212yes—
19C2×C42×C139C2211yescharacteristic
20C4⋊C8×C139—21no—
21C22⋊C8×C139C2212yes—
22C4×C8×C139—21no—
23C2×Dic278C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26C22×Dic139—22no—
27C2×C4×D139—21no—
28C4⋊Dic139C2×C411yescharacteristic
29C4⋊Dic139C2×C411yescharacteristic
30Dic139⋊C4—21no—
31Dic139⋊C4—21no—
32Dic139⋊C4—21no—
33Dic139⋊C4—21no—
34C22⋊Dic139—21no—
35(C2×D139)⋊C4—21no—
36(C2×D139)⋊C4—21no—
37(C2×D139)⋊C4—21no—
38(C2×D139)⋊C4—21no—
39C4×Dic139—21no—
40C22×C4×C139D411yescharacteristic
41C22×C4×C139D411yescharacteristic
42C22×C4×C139C2311yescharacteristic
43C2×C8×C139—22no—
44C42×C139C2×C411yescharacteristic
45C42×C139C2×C411yescharacteristic
46C42×C139D411yescharacteristic
47C42×C139D411yescharacteristic
48C22×D139—21no—
49Dic278—41no—
50D556—41no—
51C22⋊D139—42no—
52C2×Dic139—21no—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C2×Dic139—42no—
56C2×Dic139—42no—
57C2×Dic139—42no—
58C4×D139—42no—
59C23×C139C2×D411yescharacteristic
60C2×C4×C139—22no—
61C2×C4×C139—41no—
62C2×C4×C139—41no—
63C2×C4×C139C22⋊C411yescharacteristic
64C2×C4×C139C22⋊C411yescharacteristic
65C2×C4×C139C22⋊C411yescharacteristic
66C2×C4×C139C22⋊C411yescharacteristic
67C2×C4×C139C22×C411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C8×C139—42no—
70C22×C139—21no—
71C22×C139—21no—
72C22×C139C2×C22⋊C411yescharacteristic
73C22×C139#13512yes—
74C2×D139—41no—
75C2×D139—41no—
76C2×D139—41no—
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—21no—
80C4×C139—21no—
81C4×C139—21no—
82C4×C139—21no—
83Dic139—41no—
84Dic139—41no—
85Dic139—41no—
86Dic139—82no—
87C2×C139—22no—
88C2×C139#41011yescharacteristic
89C2×C139#41611yescharacteristic
90C2×C139#42111yescharacteristic
91D139—81no—
92C139#152111yescharacteristic, complemented, Sylow
93#1521—1391nomaximal, Sylow
94#529—1391no—
95#431D13911yescharacteristic, complemented
96#383—1391no—
97#328—1392no—
98#327—1392no—
99#126—2781no—
100#125—1391no—
101#124—1391no—
102#123—2781no—
103C22⋊Q8—1391no—
104#121—1391no—
105C4×Q8—1391no—
106C4×D4—2781no—
107C4×D4—1391no—
108#117—2781no—
109C2×C42C2×D13911yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D13912yes—
112C4×C8—21no—
113#95—2781no—
114#95—2781no—
115#95—1392no—
116C2×Q8—1391no—
117C2×D4—2781no—
118C2×D4—1391no—
119C22×C4—2781no—
120C22×C4—2782no—
121C22×C4D55611yescharacteristic
122C22×C4D55611yescharacteristic
123C22×C4C22×D13911yescharacteristic
124C2×C8—22no—
125C4⋊C4—2781no—
126C4⋊C4—2781no—
127C4⋊C4—2781no—
128C4⋊C4—2781no—
129C4⋊C4—1391no—
130C4⋊C4—1391no—
131C22⋊C4—2781no—
132C22⋊C4—2781no—
133C22⋊C4—2781no—
134C22⋊C4—2781no—
135C22⋊C4—2781no—
136C42—2781no—
137C42C4×D13911yescharacteristic
138C42C4×D13911yescharacteristic
139C42C22⋊D13911yescharacteristic
140C42C22⋊D13911yescharacteristic
141C23—2781no—
142C23C2×D55611yescharacteristic
143Q8—5561no—
144D4—5561no—
145D4—5562no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—2781no—
150C2×C4—2781no—
151C2×C4—2781no—
152C2×C4—5562no—
153C2×C4—5562no—
154C2×C4—5562no—
155C2×C4—5562no—
156C2×C4(C2×D139)⋊C411yescharacteristic
157C2×C4(C2×D139)⋊C411yescharacteristic
158C2×C4(C2×D139)⋊C411yescharacteristic
159C2×C4(C2×D139)⋊C411yescharacteristic
160C2×C4C2×C4×D13911yescharacteristic
161C2×C4C2×C22⋊D13911yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—5561no—
166C22—5561no—
167C22—5561no—
168C22C2×(C2×D139)⋊C411yescharacteristic
169C22#1798486412yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—5561no—
177C4—5561no—
178C4—5561no—
179C4—11122no—
180C2—22no—
181C2—11121no—
182C2#2258092611yescharacteristic
183C2#2258095011yescharacteristic
184C2#2258096911yescharacteristic
subgroupG/H
centerC22C2×(C2×D139)⋊C4
commutatorC2×C4×C139C22×C4
FrattiniC22×C4C22×D139
Fitting#431×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C22
cosocleC22×C4×C139C23
hypercenter#431D139
hypocenterC139#1521
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #22580821C2semidirect
3. #22580691C2semidirect
5. #431×C139C2semidirect
7. #17984834C4semidirect
8. #17984830C4semidirect
12. C4×Dic278C4semidirect
13. C4×D556C4semidirect
92. C139#1521semidirect
95. #431D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225808212
#225806912
#225806882
#431×C1392
#1521139