Finite Group Databasebeta

← #31807536

Subgroups — #31807536

Order 17792.

430 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 75 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#22581515C211yesmaximal, characteristic
2C2×#17984826C212yesmaximal, complemented
3C2×#17984756C212yesmaximal, complemented
4#22580814C211yesmaximal, characteristic, complemented
5#342×C139C211yesmaximal, characteristic, complemented
6C22×C22⋊D139C2212yes—
7C23×Dic139C2211yescharacteristic
8#17984826—22no—
9#17984826—24no—
10#17984826—24no—
11#17984816—22no—
12#17984812—22no—
13C2×C4⋊Dic139—22no—
14C2×C22⋊Dic139C2211yescharacteristic
15C2×(C2×D139)⋊C4—22no—
16#17984756—24no—
17C139⋊#95—22no—
18C2×C22⋊C4×C139C2211yescharacteristic
19C2×C22⋊C4×C139C2212yes—
20C23×D139D412yes—
21C2×D556—22no—
22C2×C22⋊D139—22no—
23C2×C22⋊D139—22no—
24C2×C22⋊D139—22no—
25C2×C22⋊D139—22no—
26C2×C22⋊D139—22no—
27C2×C22⋊D139—22no—
28C22×Dic139—22no—
29C22×Dic139—22no—
30C22×Dic139—21no—
31C22×Dic139—21no—
32C22×Dic139—21no—
33C22×Dic139D412yes—
34C22×Dic139D412yescomplemented
35C4⋊Dic139—28no—
36C4⋊Dic139—22no—
37C22⋊Dic139—22no—
38(C2×D139)⋊C4—28no—
39(C2×D139)⋊C4—24no—
40C24×C139C2311yescharacteristic
41C22×C4×C139—22no—
42C22×C4×C139D412yes—
43C22⋊C4×C139—22no—
44C22⋊C4×C139—22no—
45C22⋊C4×C139D414yescomplemented
46C22×D139—22no—
47C22×D139—22no—
48C22×D139—22no—
49C22×D139—44no—
50D556—82no—
51C22⋊D139—42no—
52C22⋊D139—42no—
53C22⋊D139—42no—
54C22⋊D139—42no—
55C2×Dic139—24no—
56C2×Dic139—22no—
57C2×Dic139—22no—
58C2×Dic139—22no—
59C2×Dic139—22no—
60C2×Dic139—41no—
61C2×Dic139—42no—
62C2×Dic139—41no—
63C2×Dic139—42no—
64C2×Dic139—41no—
65C23×C139—42no—
66C23×C139C2×D412yes—
67C23×C139C2×D411yescharacteristic
68C23×C139C2×D411yescharacteristic
69C23×C139C2×D412yes—
70C23×C139#4111yescharacteristic
71C2×C4×C139—22no—
72C2×C4×C139—24no—
73C2×C4×C139—44no—
74C2×C4×C139—42no—
75C22×C139—22no—
76C22×C139—24no—
77C22×C139—41no—
78C22×C139—42no—
79C22×C139—41no—
80C22×C139#12012yes—
81C22×C139#12011yescharacteristic
82C22×C139#12111yescharacteristic
83C22×C139#12112yes—
84C22×C139#12711yescharacteristic
85C2×D139—44no—
86C2×D139—42no—
87C2×D139—44no—
88C2×D139—82no—
89C4×C139—44no—
90C4×C139—42no—
91Dic139—42no—
92Dic139—42no—
93Dic139—81no—
94C2×C139—21no—
95C2×C139—22no—
96C2×C139—22no—
97C2×C139—21no—
98C2×C139#39211yescharacteristic
99C2×C139#45812yes—
100D139—82no—
101C139#202211yescharacteristic, complemented, Sylow
102#2022—1391nomaximal, Sylow
103#534—1391no—
104C2×#123—1392no—
105C2×#99—1392no—
106#381—1391no—
107#342D13911yescharacteristic, complemented
108C22×D4—1392no—
109C23×C4—1391no—
110#123—2784no—
111#123—2782no—
112#123—2784no—
113#121—2782no—
114#120—2782no—
115C2×C4⋊C4—2782no—
116C2×C22⋊C4—2782no—
117C2×C22⋊C4—1391no—
118C2×C22⋊C4C2×D13911yescharacteristic
119C2×C22⋊C4C2×D13912yes—
120#99—2784no—
121#95—2782no—
122C24—1392no—
123C24C22×D13911yescharacteristic
124C2×D4—2782no—
125C2×D4—2782no—
126C2×D4—2782no—
127C2×D4—2782no—
128C2×D4—2782no—
129C2×D4—2782no—
130C2×D4—2782no—
131C22×C4—22no—
132C22×C4—2782no—
133C22×C4—2781no—
134C22×C4—2782no—
135C22×C4—2781no—
136C22×C4—2781no—
137C22×C4—1392no—
138C22×C4—1392no—
139C22×C4D55612yes—
140C4⋊C4—2788no—
141C4⋊C4—2782no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—2788no—
145C22⋊C4—2784no—
146C22⋊C4—2782no—
147C22⋊C4D55614yescomplemented
148C23—42no—
149C23—2782no—
150C23—2782no—
151C23—2782no—
152C23—5564no—
153C23D4×D13912yes—
154C23D4×D13911yescharacteristic
155C23C2×D55611yescharacteristic
156C23C2×D55612yes—
157C23#1455578611yescharacteristic
158D4—5562no—
159D4—5562no—
160D4—5562no—
161D4—5562no—
162D4—11122no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—44no—
166C2×C4—42no—
167C2×C4—2784no—
168C2×C4—2782no—
169C2×C4—2782no—
170C2×C4—2782no—
171C2×C4—2782no—
172C2×C4—5561no—
173C2×C4—5562no—
174C2×C4—5561no—
175C2×C4—5562no—
176C2×C4—5561no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—42no—
181C22—41no—
182C22—5564no—
183C22—5562no—
184C22—5564no—
185C22—11122no—
186C22#1798481212yes—
187C22#1798481211yescharacteristic
188C22#1798481711yescharacteristic
189C22#1798481712yes—
190C22#1798483911yescharacteristic
191C4—44no—
192C4—42no—
193C4—5562no—
194C4—5562no—
195C4—11121no—
196C2—22no—
197C2—21no—
198C2—22no—
199C2—21no—
200C2—11122no—
201C2#2258086311yescharacteristic
202C2#2258114412yes—
subgroupG/H
centerC22#17984812
commutator, cosocleC24×C139C23
FrattiniC24C22×D139
Fitting#342×C139C2
socleC22×C139#120
prime radical#22581515C2
hypercenter#342D139
hypocenterC139#2022
LCSG ▷ C24×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#17984826C2semidirect
3. C2×#17984756C2semidirect
4. #22580814C2semidirect
5. #342×C139C2semidirect
34. C22×Dic139D4semidirect
45. C22⋊C4×C139D4semidirect
101. C139#2022semidirect
107. #342D139semidirect
147. C22⋊C4D556semidirect

Maximal subgroups

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

subgroupindex
#225815152
C2×#179848262
C2×#179847562
#225808142
#342×C1392
#2022139