Finite Group Databasebeta

← #31809205

Subgroups — #31809205

Order 17792.

428 conjugacy classes of subgroups; only the 177 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 177 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
1C2×#17984834C211yesmaximal, characteristic
2#22580850C212yesmaximal
3#22580840C212yesmaximal
4#22580838C212yesmaximal
5#22580836C212yesmaximal
6#22580835C212yesmaximal
7C4×C4⋊Dic139C211yesmaximal, characteristic
8#22580804C212yesmaximal
9#383×C139C211yesmaximal, characteristic
10#17984834C418yescomplemented
11C2×C4⋊Dic139C2212yes—
12C2×C4⋊Dic139C2211yescharacteristic
13C2×C4⋊Dic139C2211yescharacteristic
14C2×Dic139⋊C4C2212yes—
15C2×Dic139⋊C4C2212yes—
16C2×Dic139⋊C4C2212yes—
17C2×Dic139⋊C4C2212yes—
18C2×C4×Dic139C2212yes—
19C2×C4×Dic139C2211yescharacteristic
20C2×C4×Dic139C2212yes—
21C2×C4×Dic139C2211yescharacteristic
22C139⋊#95C2212yes—
23C139⋊#95C2212yes—
24C139⋊#95C2212yes—
25C139⋊#95C2212yes—
26C139⋊#95C2212yes—
27C2×C42×C139C2211yescharacteristic
28#95×C139C2212yes—
29#95×C139C2212yes—
30#95×C139C2211yescharacteristic
31#95×C139C2211yescharacteristic
32C22×Dic139C2312yes—
33C22×Dic139C2312yes—
34C22×Dic139C2312yes—
35C22×Dic139C2312yes—
36C4⋊Dic139—24no—
37C4⋊Dic139C2×C414yes—
38C4⋊Dic139C2×C414yes—
39Dic139⋊C4—24no—
40Dic139⋊C4—42no—
41Dic139⋊C4C2×C418yes—
42Dic139⋊C4C2×C418yes—
43C4×Dic139—24no—
44C4×Dic139—41no—
45C4×Dic139—41no—
46C4×Dic139—42no—
47C22×C4×C139C2312yes—
48C22×C4×C139C2312yes—
49C22×C4×C139C2311yescharacteristic
50C22×C4×C139C2311yescharacteristic
51C22×C4×C139C2311yescharacteristic
52C42×C139C2×C414yes—
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×Dic139C22×C414yes—
63C2×Dic139C22×C414yes—
64C2×Dic139#4114yes—
65C23×C139C2411yescharacteristic
66C2×C4×C139—22no—
67C2×C4×C139—21no—
68C2×C4×C139—22no—
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×C139C22×C412yes—
77C2×C4×C139C22×C412yes—
78C2×C4×C139C22×C412yes—
79C22×C139C23×C411yescharacteristic
80C22×C139C2×#4112yes—
81C22×C139H(5,𝔽2)11yescharacteristic
82C22×C1392−1+412yes—
83C22×C1392−1+411yescharacteristic
84C4×C139—22no—
85C4×C139—22no—
86C4×C139—22no—
87C4×C139—42no—
88C4×C139—42no—
89Dic139—24no—
90Dic139—24no—
91Dic139—24no—
92Dic139—42no—
93C2×C139C4×#4111yescharacteristic
94C2×C139#51911yescharacteristic
95C2×C139#52011yescharacteristic
96C2×C139#53912yes—
97C2×C139#54112yes—
98C139#233611yescharacteristic, complemented, Sylow
99#2336—1391nomaximal, Sylow
100C2×#125—1391no—
101#389—1392no—
102#387—1392no—
103#387—1392no—
104#387—1392no—
105#387—1392no—
106#383D13911yescharacteristic
107C4×C4⋊C4—1391no—
108C4×C4⋊C4—1392no—
109#125—1398no—
110C2×C4⋊C4—1392no—
111C2×C4⋊C4—1392no—
112C2×C4⋊C4—1392no—
113C2×C4⋊C4—1392no—
114C2×C4⋊C4—1392no—
115C2×C4⋊C4—1391no—
116C2×C4⋊C4—1391no—
117C2×C42—1392no—
118C2×C42—1391no—
119C2×C42—1391no—
120C2×C42—1392no—
121C2×C42C2×D13911yescharacteristic
122#95—1392no—
123#95—1392no—
124#95—1392no—
125#95—1392no—
126#95—1392no—
127#95C2×D13912yes—
128#95C2×D13911yescharacteristic
129#95C2×D13912yes—
130#95C2×D13911yescharacteristic
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—2784no—
141C4⋊C4—2784no—
142C4⋊C4—5562no—
143C4⋊C4—1398no—
144C4⋊C4—1398no—
145C4⋊C4—1394no—
146C4⋊C4—1394no—
147C42—2784no—
148C42—5561no—
149C42—5561no—
150C42—5562no—
151C42C4×D13914yes—
152C23C23×D13911yescharacteristic
153C2×C4—22no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—22no—
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—1394no—
173C2×C4—1394no—
174C2×C4—1394no—
175C2×C4C2×C4×D13912yes—
176C2×C4C2×C4×D13912yes—
177C2×C4C2×C4×D13912yes—
178C22C22×C4×D13911yescharacteristic
179C22#41×D13912yes—
180C22#1798488811yescharacteristic
181C22#1798488912yes—
182C22#1798488911yescharacteristic
183C4—22no—
184C4—22no—
185C4—22no—
186C4—42no—
187C4—42no—
188C4—2784no—
189C4—2784no—
190C4—2784no—
191C4—5562no—
192C2#2258142111yescharacteristic
193C2#2258143011yescharacteristic
194C2#2258143311yescharacteristic
195C2#2258154412yes—
196C2#2258156012yes—
subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
Fitting#383×C139C2
socle, prime radical, cosocleC23×C139C24
hypercenter#383D139
hypocenterC139#2336
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
10. #17984834C4semidirect
98. C139#2336semidirect

Maximal subgroups

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

subgroupindex
C2×#179848342
#225808502
#225808402
#225808382
#225808362
#225808352
C4×C4⋊Dic1392
#225808042
#383×C1392
#2336139