Finite Group Databasebeta

← #31804990

Subgroups — #31804990

Order 17792.

234 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 73 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#22581487C211yesmaximal, characteristic
2C4×#14555769C211yesmaximal, characteristic, complemented
3#22580694C212yesmaximal, complemented
4#22580692C212yesmaximal, complemented
5C2×#97×C139C211yesmaximal, characteristic, complemented
6C2×#14555769—21no—
7#17984836—21no—
8#17984834C2211yescharacteristic
9#17984830C2211yescharacteristic
10#17984825—21no—
11#17984821C411yescharacteristic
12#17984816C411yescharacteristic
13C4×Dic278C411yescharacteristic
14C4×D556C411yescharacteristic
15C4×C22⋊D139—21no—
16#17984799—21no—
17#17984753C2212yes—
18C4×C139⋊C8—21no—
19C22×C8×C139—21no—
20C2×C42×C139C2211yescharacteristic
21#97×C139—21no—
22#97×C139C2212yes—
23C2×Dic278C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26C2×C4×D139—21no—
27#14555769—24no—
28C2×C139⋊C8—22no—
29C4⋊Dic139C2×C411yescharacteristic
30C4⋊Dic139C2×C411yescharacteristic
31Dic139⋊C4—21no—
32Dic139⋊C4—21no—
33Dic139⋊C4—21no—
34Dic139⋊C4—21no—
35C22⋊Dic139—21no—
36(C2×D139)⋊C4—21no—
37(C2×D139)⋊C4—21no—
38(C2×D139)⋊C4—21no—
39(C2×D139)⋊C4—21no—
40C4×Dic139—21no—
41C22×C4×C139C2×C411yescharacteristic
42C22×C4×C139D411yescharacteristic
43C22×C4×C139D411yescharacteristic
44C2×C8×C139—24no—
45C2×C8×C139—22no—
46C42×C139C2×C411yescharacteristic
47C42×C139D411yescharacteristic
48C42×C139D411yescharacteristic
49C42×C139C2311yescharacteristic
50C22×D139—21no—
51Dic278—41no—
52D556—41no—
53C22⋊D139—42no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C2×Dic139—21no—
57C4×D139—42no—
58C139⋊C8—24no—
59C23×C139C22⋊C411yescharacteristic
60C2×C4×C139—22no—
61C2×C4×C139—22no—
62C2×C4×C139—41no—
63C2×C4×C139C22⋊C411yescharacteristic
64C2×C4×C139C22⋊C411yescharacteristic
65C2×C4×C139C22⋊C411yescharacteristic
66C2×C4×C139C22×C411yescharacteristic
67C2×C4×C139C2×D411yescharacteristic
68C2×C4×C139C2×D411yescharacteristic
69C8×C139—24no—
70C22×C139—21no—
71C22×C139—21no—
72C22×C139#10412yes—
73C22×C139C2×C22⋊C411yescharacteristic
74C2×D139—41no—
75C2×D139—41no—
76C2×D139—41no—
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—21no—
80C4×C139—21no—
81C4×C139—21no—
82C4×C139#10412yes—
83Dic139—41no—
84Dic139—41no—
85Dic139—41no—
86C2×C139—22no—
87C2×C139#41311yescharacteristic
88C2×C139C2×#10411yescharacteristic
89C2×C139C2×#10411yescharacteristic
90D139—81no—
91C139#152411yescharacteristic, complemented, Sylow
92#1524—1391nomaximal, Sylow
93#529—1391no—
94C4×M16—1391no—
95C2×#97D13911yescharacteristic, complemented
96#330—1392no—
97#329—1392no—
98C2×M16—2781no—
99C22×C8—21no—
100#126—2781no—
101#125—1391no—
102#124—1391no—
103#123—2781no—
104C22⋊Q8—1391no—
105#121—1391no—
106C4×Q8—1391no—
107C4×D4—2781no—
108C4×D4—1391no—
109#117—2781no—
110C2×C42C2×D13911yescharacteristic
111#97—21no—
112#97—1392no—
113#97C2×D13912yes—
114C4×C8—2781no—
115C2×Q8—1391no—
116C2×D4—2781no—
117C2×D4—1391no—
118C22×C4—2781no—
119C22×C4C4×D13911yescharacteristic
120C22×C4C22⋊D13911yescharacteristic
121C22×C4D55611yescharacteristic
122M16—2784no—
123C2×C8—24no—
124C2×C8—22no—
125C2×C8—2782no—
126C4⋊C4—2781no—
127C4⋊C4—2781no—
128C4⋊C4—2781no—
129C4⋊C4—2781no—
130C4⋊C4—1391no—
131C4⋊C4—1391no—
132C22⋊C4—2781no—
133C22⋊C4—2781no—
134C22⋊C4—2781no—
135C22⋊C4—2781no—
136C22⋊C4—2781no—
137C42—2781no—
138C42C4×D13911yescharacteristic
139C42C22⋊D13911yescharacteristic
140C42D55611yescharacteristic
141C42C22×D13911yescharacteristic
142C23—2781no—
143C23(C2×D139)⋊C411yescharacteristic
144Q8—5561no—
145D4—5561no—
146D4—5562no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—2781no—
151C2×C4—2781no—
152C2×C4—2781no—
153C2×C4—5562no—
154C2×C4(C2×D139)⋊C411yescharacteristic
155C2×C4(C2×D139)⋊C411yescharacteristic
156C2×C4(C2×D139)⋊C411yescharacteristic
157C2×C4C2×C4×D13911yescharacteristic
158C2×C4C2×C22⋊D13911yescharacteristic
159C2×C4C2×D55611yescharacteristic
160C8—24no—
161C8—2784no—
162C22—21no—
163C22—21no—
164C22—5561no—
165C22—5561no—
166C22—5561no—
167C22#1798476812yes—
168C22C2×(C2×D139)⋊C411yescharacteristic
169C4—21no—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—5561no—
175C4—5561no—
176C4—5561no—
177C4#1798477012yes—
178C2—22no—
179C2—11121no—
180C2#2258093511yescharacteristic
181C2C2×#1798476811yescharacteristic
182C2C2×#1798477011yescharacteristic
subgroupG/H
centerC2×C4(C2×D139)⋊C4
commutatorC2×C4×C139C22×C4
FrattiniC42C22×D139
FittingC2×#97×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C4
cosocleC42×C139C23
hypercenterC2×#97D139
hypocenterC139#1524
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C4×#14555769C2semidirect
3. #22580694C2semidirect
4. #22580692C2semidirect
5. C2×#97×C139C2semidirect
91. C139#1524semidirect
95. C2×#97D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
C4×#145557692
#225806942
#225806922
C2×#97×C1392
#1524139