Finite Group Databasebeta

← #31814674

Subgroups — #31814674

Order 17792.

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

normal subgroups only

This group has 348 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#22580887C212yesmaximal
3#22580885C212yesmaximal
4#22580883C212yesmaximal
5#22580874C212yesmaximal
6#22580873C211yesmaximal, characteristic
7#22580822C211yesmaximal, characteristic
8#22580820C212yesmaximal
9#400×C139C211yesmaximal, characteristic
10C22×Dic278C2211yescharacteristic
11C2×C4⋊Dic139C2211yescharacteristic
12C2×C4⋊Dic139C2212yes—
13C2×C4⋊Dic139C2212yes—
14C2×Dic139⋊C4C2212yes—
15C2×Dic139⋊C4C2212yes—
16C2×Dic139⋊C4C2212yes—
17C2×Dic139⋊C4C2212yes—
18C2×C4×Dic139C2211yescharacteristic
19C139⋊#95C2212yes—
20C139⋊#95C2212yes—
21C139⋊#95C2212yes—
22C139⋊#95C2212yes—
23C139⋊#95C2212yes—
24C139⋊#95C2211yescharacteristic
25C139⋊#95C2212yes—
26C2×C4⋊C4×C139C2211yescharacteristic
27C2×C4⋊C4×C139C2211yescharacteristic
28#95×C139C2212yes—
29#95×C139C2212yes—
30#95×C139C2211yescharacteristic
31C2×Dic278—41no—
32C2×Dic278—42no—
33C22×Dic139C2312yes—
34C22×Dic139C2312yes—
35C22×Dic139C2312yes—
36C22×Dic139C2312yes—
37C4⋊Dic139—41no—
38C4⋊Dic139—42no—
39C4⋊Dic139—42no—
40Dic139⋊C4—42no—
41Dic139⋊C4—42no—
42Dic139⋊C4—42no—
43Dic139⋊C4—42no—
44C4×Dic139Q814yescomplemented
45C22×C4×C139C2311yescharacteristic
46C22×C4×C139C2311yescharacteristic
47C22×C4×C139C2312yes—
48C22×C4×C139C2312yes—
49C22×C4×C139C2311yescharacteristic
50C4⋊C4×C139—41no—
51C4⋊C4×C139—41no—
52Dic278—44no—
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—22no—
70C2×C4×C139—21no—
71C2×C4×C139—22no—
72C2×C4×C139—22no—
73C2×C4×C139—22no—
74C2×C4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—24no—
77C2×C4×C139C2×Q812yes—
78C22×C139C22×Q811yescharacteristic
79C22×C139H(5,𝔽2)11yescharacteristic
80C22×C139H(5,𝔽2)12yes—
81C22×C1392−1+411yescharacteristic
82C22×C1392−1+412yes—
83C4×C139—22no—
84C4×C139—41no—
85C4×C139—41no—
86C4×C139—42no—
87C4×C139—42no—
88Dic139—24no—
89Dic139—42no—
90Dic139—42no—
91Dic139—42no—
92C2×C139#54411yescharacteristic
93C2×C139#54412yes—
94C2×C139#56011yescharacteristic
95C2×C139#56311yescharacteristic
96C2×C139#56312yes—
97C139#284311yescharacteristic, complemented, Sylow
98#2843—1391nomaximal, Sylow
99#400—1392no—
100#400D13911yescharacteristic
101#398—1392no—
102#398—1392no—
103#398—1392no—
104#395—1391no—
105#395—1392no—
106#384—1391no—
107#383—1392no—
108C22×Q8—1391no—
109C2×C4⋊C4—1392no—
110C2×C4⋊C4—1392no—
111C2×C4⋊C4—1392no—
112C2×C4⋊C4—1392no—
113C2×C4⋊C4—1391no—
114C2×C4⋊C4—1392no—
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—1391no—
125#95—1392no—
126#95C2×D13912yes—
127#95C2×D13912yes—
128#95C2×D13911yescharacteristic
129C2×Q8—5561no—
130C2×Q8—5562no—
131C22×C4—1392no—
132C22×C4—1392no—
133C22×C4—1392no—
134C22×C4—1392no—
135C22×C4C22×D13912yes—
136C22×C4C22×D13912yes—
137C22×C4C22×D13911yescharacteristic
138C22×C4C22×D13911yescharacteristic
139C22×C4C22×D13911yescharacteristic
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—5562no—
143C4⋊C4—5562no—
144C4⋊C4—5562no—
145C4⋊C4—5562no—
146C4⋊C4—5561no—
147C4⋊C4—5562no—
148C4⋊C4—5562no—
149C42—1394no—
150C23C23×D13911yescharacteristic
151Q8—5564no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—24no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—2782no—
164C2×C4—2782no—
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—1394no—
175C2×C4Q8×D13912yes—
176C22C2×Q8×D13911yescharacteristic
177C22#1798488711yescharacteristic
178C22#1798488812yes—
179C22#1798488911yescharacteristic
180C22#1798488912yes—
181C4—22no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—2784no—
187C4—5562no—
188C4—5562no—
189C4—5562no—
190C2#2258158211yescharacteristic
191C2#2258158312yes—
192C2#2258169311yescharacteristic
193C2#2258170311yescharacteristic
194C2#2258170512yes—
subgroupG/H
center, FrattiniC23C23×D139
commutator, socle, prime radical, cosocleC23×C139C24
Fitting#400×C139C2
hypercenter#400D139
hypocenterC139#2843
LCSG ▷ C23×C139 ▷ C139
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
44. C4×Dic139Q8semidirect
97. C139#2843semidirect

Maximal subgroups

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

subgroupindex
#225808942
#225808872
#225808852
#225808832
#225808742
#225808732
#225808222
#225808202
#400×C1392
#2843139