Finite Group Databasebeta

← #31809589

Subgroups — #31809589

Order 17792.

408 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 173 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#22580848C212yesmaximal
4#22580840C212yesmaximal
5#22580838C212yesmaximal
6#22580836C212yesmaximal
7#22580834C212yesmaximal
8#22580819C211yesmaximal, characteristic
9#382×C139C211yesmaximal, characteristic
10#17984834C418yescomplemented
11C2×C4⋊Dic139C2211yescharacteristic
12C2×C4⋊Dic139C2211yescharacteristic
13C2×C4⋊Dic139C2211yescharacteristic
14C2×C4⋊Dic139C2211yescharacteristic
15C2×Dic139⋊C4C2212yes—
16C2×Dic139⋊C4C2212yes—
17C2×Dic139⋊C4C2212yes—
18C2×Dic139⋊C4C2212yes—
19C2×C4×Dic139C2212yes—
20C2×C4×Dic139C2212yes—
21C139⋊#95C2212yes—
22C139⋊#95C2212yes—
23C139⋊#95C2212yes—
24C139⋊#95C2212yes—
25C139⋊#95C2212yes—
26C139⋊#95C2212yes—
27C2×C4⋊C4×C139C2211yescharacteristic
28C2×C4⋊C4×C139C2211yescharacteristic
29C2×C42×C139C2211yescharacteristic
30#95×C139C2212yes—
31#95×C139C2212yes—
32C22×Dic139C2312yes—
33C22×Dic139C2312yes—
34C22×Dic139C2312yes—
35C22×Dic139C2312yes—
36C4⋊Dic139—41no—
37C4⋊Dic139—41no—
38C4⋊Dic139C2×C414yes—
39C4⋊Dic139C2×C414yes—
40Dic139⋊C4—42no—
41Dic139⋊C4—42no—
42Dic139⋊C4C2×C418yes—
43Dic139⋊C4C2×C418yes—
44C4×Dic139—42no—
45C4×Dic139—42no—
46C22×C4×C139C2312yes—
47C22×C4×C139C2312yes—
48C22×C4×C139C2311yescharacteristic
49C22×C4×C139C2311yescharacteristic
50C22×C4×C139C2311yescharacteristic
51C4⋊C4×C139—41no—
52C4⋊C4×C139—41no—
53C42×C139C2×C414yes—
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×Dic139C22×C414yes—
65C2×Dic139C22×C414yes—
66C23×C139C2411yescharacteristic
67C2×C4×C139—21no—
68C2×C4×C139—21no—
69C2×C4×C139—21no—
70C2×C4×C139—21no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—22no—
74C2×C4×C139—22no—
75C2×C4×C139—22no—
76C2×C4×C139—22no—
77C2×C4×C139—22no—
78C2×C4×C139—22no—
79C2×C4×C139C22×C412yes—
80C2×C4×C139C22×C412yes—
81C2×C4×C139C22×C412yes—
82C22×C139C23×C411yescharacteristic
83C22×C139H(5,𝔽2)11yescharacteristic
84C22×C139H(5,𝔽2)11yescharacteristic
85C22×C1392−1+411yescharacteristic
86C22×C1392−1+411yescharacteristic
87C22×C1392−1+411yescharacteristic
88C22×C1392−1+411yescharacteristic
89C4×C139—22no—
90C4×C139—22no—
91C4×C139—22no—
92C4×C139—42no—
93C4×C139—42no—
94Dic139—24no—
95Dic139—24no—
96Dic139—42no—
97Dic139—42no—
98C2×C139#51911yescharacteristic
99C2×C139#52011yescharacteristic
100C2×C139#52011yescharacteristic
101C2×C139#56211yescharacteristic
102C2×C139#56311yescharacteristic
103C2×C139#56311yescharacteristic
104C2×C139#56411yescharacteristic
105C139#238211yescharacteristic, complemented, Sylow
106#2382—1391nomaximal, Sylow
107C2×#125—1391no—
108#389—1392no—
109#389—1392no—
110#387—1392no—
111#387—1392no—
112#387—1392no—
113#387—1392no—
114#382—1391no—
115#382D13911yescharacteristic
116#125—1398no—
117C2×C4⋊C4—1392no—
118C2×C4⋊C4—1392no—
119C2×C4⋊C4—1391no—
120C2×C4⋊C4—1391no—
121C2×C4⋊C4—1392no—
122C2×C4⋊C4—1392no—
123C2×C4⋊C4—1391no—
124C2×C4⋊C4—1391no—
125C2×C4⋊C4C2×D13911yescharacteristic
126C2×C4⋊C4C2×D13911yescharacteristic
127C2×C42—1392no—
128C2×C42—1392no—
129C2×C42C2×D13911yescharacteristic
130#95—1392no—
131#95—1392no—
132#95—1392no—
133#95—1392no—
134#95—1392no—
135#95—1392no—
136#95C2×D13912yes—
137#95C2×D13912yes—
138C22×C4—1392no—
139C22×C4—1392no—
140C22×C4—1392no—
141C22×C4—1392no—
142C22×C4C22×D13912yes—
143C22×C4C22×D13912yes—
144C22×C4C22×D13911yescharacteristic
145C22×C4C22×D13911yescharacteristic
146C22×C4C22×D13911yescharacteristic
147C4⋊C4—41no—
148C4⋊C4—41no—
149C4⋊C4—5562no—
150C4⋊C4—5562no—
151C4⋊C4—5561no—
152C4⋊C4—5561no—
153C4⋊C4—1398no—
154C4⋊C4—1398no—
155C4⋊C4—1394no—
156C4⋊C4—1394no—
157C42—5562no—
158C42—5562no—
159C42C4×D13914yes—
160C23C23×D13911yescharacteristic
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—2782no—
174C2×C4—2782no—
175C2×C4—2782no—
176C2×C4—2782no—
177C2×C4—2782no—
178C2×C4—2782no—
179C2×C4—2782no—
180C2×C4—2782no—
181C2×C4—2782no—
182C2×C4—2782no—
183C2×C4—1394no—
184C2×C4—1394no—
185C2×C4C2×C4×D13912yes—
186C2×C4C2×C4×D13912yes—
187C2×C4C2×C4×D13912yes—
188C22C22×C4×D13911yescharacteristic
189C22#1798488711yescharacteristic
190C22#1798488811yescharacteristic
191C22#1798488911yescharacteristic
192C22#1798488911yescharacteristic
193C22#1798488911yescharacteristic
194C22#1798489011yescharacteristic
195C4—22no—
196C4—22no—
197C4—22no—
198C4—42no—
199C4—42no—
200C4—2784no—
201C4—2784no—
202C4—5562no—
203C4—5562no—
204C2#2258143011yescharacteristic
205C2#2258143311yescharacteristic
206C2#2258143411yescharacteristic
207C2#2258169711yescharacteristic
208C2#2258170311yescharacteristic
209C2#2258170711yescharacteristic
210C2C139⋊#56411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D139
commutatorC22×C139C23×C4
Fitting#382×C139C2
socle, prime radical, cosocleC23×C139C24
hypercenter#382D139
hypocenterC139#2382
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
10. #17984834C4semidirect
105. C139#2382semidirect

Maximal subgroups

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

subgroupindex
C2×#179848342
#225808502
#225808482
#225808402
#225808382
#225808362
#225808342
#225808192
#382×C1392
#2382139