Finite Group Databasebeta

← #31814677

Subgroups — #31814677

Order 17792.

356 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 125 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#22580894C212yesmaximal
2#22580893C212yesmaximal
3#22580892C211yesmaximal, characteristic
4#22580874C212yesmaximal
5#22580874C212yesmaximal
6#22580873C212yesmaximal
7#22580818C211yesmaximal, characteristic
8#22580817C212yesmaximal
9#400×C139C211yesmaximal, characteristic
10C22×Dic278C2212yes—
11C2×C4⋊Dic139C2211yescharacteristic
12C2×C4⋊Dic139C2211yescharacteristic
13C2×C4⋊Dic139C2212yes—
14C2×Dic139⋊C4C2212yes—
15C2×Dic139⋊C4C2212yes—
16C2×Dic139⋊C4C2212yes—
17C2×C4×Dic139C2211yescharacteristic
18C139⋊#95C2212yes—
19C139⋊#95C2212yes—
20C139⋊#95C2212yes—
21C139⋊#95C2212yes—
22C139⋊#95C2212yes—
23C139⋊#95C2212yes—
24C139⋊#95C2212yes—
25C139⋊#95C2211yescharacteristic
26C2×C4⋊C4×C139C2211yescharacteristic
27C2×C4⋊C4×C139C2211yescharacteristic
28#95×C139C2212yes—
29#95×C139C2212yes—
30#95×C139C2211yescharacteristic
31C2×Dic278—42no—
32C2×Dic278—42no—
33C2×Dic278—42no—
34C22×Dic139C2312yes—
35C22×Dic139C2312yes—
36C22×Dic139C2312yes—
37C22×Dic139C2312yes—
38C4⋊Dic139—41no—
39C4⋊Dic139—41no—
40C4⋊Dic139—42no—
41Dic139⋊C4—42no—
42Dic139⋊C4—42no—
43Dic139⋊C4—42no—
44C4×Dic139Q814yescomplemented
45C22×C4×C139C2312yes—
46C22×C4×C139C2312yes—
47C22×C4×C139C2311yescharacteristic
48C22×C4×C139C2311yescharacteristic
49C22×C4×C139C2311yescharacteristic
50C4⋊C4×C139—41no—
51C4⋊C4×C139—41no—
52Dic278—48no—
53C2×Dic139—22no—
54C2×Dic139—22no—
55C2×Dic139—22no—
56C2×Dic139—22no—
57C2×Dic139—22no—
58C2×Dic139—22no—
59C2×Dic139—22no—
60C2×Dic139—22no—
61C2×Dic139—22no—
62C2×Dic139—22no—
63C2×Dic139—22no—
64C2×Dic139C2×Q814yes—
65C23×C139C2411yescharacteristic
66C2×C4×C139—21no—
67C2×C4×C139—21no—
68C2×C4×C139—21no—
69C2×C4×C139—21no—
70C2×C4×C139—22no—
71C2×C4×C139—22no—
72C2×C4×C139—22no—
73C2×C4×C139—22no—
74C2×C4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139C2×Q812yes—
79C22×C139C22×Q811yescharacteristic
80C22×C139H(5,𝔽2)11yescharacteristic
81C22×C139H(5,𝔽2)12yes—
82C22×C1392−1+411yescharacteristic
83C22×C1392−1+412yes—
84C4×C139—22no—
85C4×C139—42no—
86C4×C139—42no—
87C4×C139—41no—
88C4×C139—41no—
89Dic139—24no—
90Dic139—42no—
91Dic139—42no—
92Dic139—42no—
93C2×C139#54411yescharacteristic
94C2×C139#54412yes—
95C2×C139H(3,𝔽4)11yescharacteristic
96C2×C139#56312yes—
97C2×C139#56311yescharacteristic
98C139#284411yescharacteristic, complemented, Sylow
99#2844—1391nomaximal, Sylow
100#400—1391no—
101#400—1392no—
102#400—1392no—
103#400D13911yescharacteristic
104#395—1392no—
105#395—1392no—
106#395—1392no—
107#382—1391no—
108#382—1392no—
109C22×Q8—1392no—
110C2×C4⋊C4—1392no—
111C2×C4⋊C4—1392no—
112C2×C4⋊C4—1392no—
113C2×C4⋊C4—1391no—
114C2×C4⋊C4—1391no—
115C2×C4⋊C4—1392no—
116C2×C4⋊C4C2×D13911yescharacteristic
117C2×C4⋊C4C2×D13911yescharacteristic
118C2×C42—1391no—
119#95—1392no—
120#95—1392no—
121#95—1392no—
122#95—1392no—
123#95—1392no—
124#95—1392no—
125#95—1392no—
126#95—1391no—
127#95C2×D13912yes—
128#95C2×D13912yes—
129#95C2×D13911yescharacteristic
130C2×Q8—5562no—
131C2×Q8—5562no—
132C2×Q8—5562no—
133C22×C4—1392no—
134C22×C4—1392no—
135C22×C4—1392no—
136C22×C4—1392no—
137C22×C4C22×D13911yescharacteristic
138C22×C4C22×D13911yescharacteristic
139C22×C4C22×D13912yes—
140C22×C4C22×D13912yes—
141C22×C4C22×D13911yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—5562no—
145C4⋊C4—5562no—
146C4⋊C4—5562no—
147C4⋊C4—5561no—
148C4⋊C4—5561no—
149C4⋊C4—5562no—
150C42—1394no—
151C23C23×D13911yescharacteristic
152Q8—5568no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—2782no—
166C2×C4—2782no—
167C2×C4—2782no—
168C2×C4—2782no—
169C2×C4—2782no—
170C2×C4—2782no—
171C2×C4—2782no—
172C2×C4—2782no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—2782no—
176C2×C4—1394no—
177C2×C4Q8×D13912yes—
178C22C2×Q8×D13911yescharacteristic
179C22#1798488711yescharacteristic
180C22#1798488812yes—
181C22#1798488911yescharacteristic
182C22#1798488912yes—
183C4—22no—
184C4—42no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—2784no—
189C4—5562no—
190C4—5562no—
191C4—5562no—
192C2#2258158211yescharacteristic
193C2#2258158312yes—
194C2#2258169511yescharacteristic
195C2#2258170512yes—
196C2#2258170611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, prime radical, cosocleC23×C139C24
Fitting#400×C139C2
hypercenter#400D139
hypocenterC139#2844
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic139Q8semidirect
98. C139#2844semidirect

Maximal subgroups

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

subgroupindex
#225808942
#225808932
#225808922
#225808742
#225808732
#225808182
#225808172
#400×C1392
#2844139