Finite Group Databasebeta

← #31808075

Subgroups — #31808075

Order 17792.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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#22581517C211yesmaximal, characteristic
2#22580927C211yesmaximal, characteristic, complemented
3#22580745C214yesmaximal, complemented
4#410×C139C211yesmaximal, characteristic, complemented
5C22×D556C411yescharacteristic, complemented
6#17984838C2212yes—
7#17984831C412yescomplemented
8#17984816—21no—
9#17984816—21no—
10#17984810—21no—
11#17984810—21no—
12#17984801—21no—
13#17984801C411yescharacteristic, complemented
14#17984757—21no—
15#17984757C2212yescomplemented
16C2×#41×C139C2211yescharacteristic
17#117×C139—21no—
18#99×C139—21no—
19#99×C139C2212yescomplemented
20C23×D139—21no—
21C2×D556—21no—
22C2×D556—41no—
23C2×D556—41no—
24C2×D556C2×C412yes—
25C2×C22⋊D139—22no—
26C2×C22⋊D139—22no—
27C4⋊Dic139—21no—
28C4⋊Dic139—41no—
29C22⋊Dic139—21no—
30C22⋊Dic139—22no—
31(C2×D139)⋊C4—22no—
32(C2×D139)⋊C4—22no—
33C4×Dic139—41no—
34C4×Dic139C2×C412yes—
35#41×C139—41no—
36#41×C139—41no—
37C2×Q8×C139C2×C411yescharacteristic
38C2×D4×C139D411yescharacteristic
39C2×D4×C139D411yescharacteristic
40C2×D4×C139C2311yescharacteristic
41C22×C4×C139C2×C411yescharacteristic
42C22×C4×C139D411yescharacteristic
43C22×C4×C139D411yescharacteristic
44C4⋊C4×C139—41no—
45C22⋊C4×C139—22no—
46C42×C139—41no—
47C22×D139—22no—
48C22×D139—42no—
49C22×D139—82no—
50D556—42no—
51D556—41no—
52D556—41no—
53C22⋊D139—82no—
54C22⋊D139—82no—
55C2×Dic139—22no—
56C2×Dic139—42no—
57C23×C139C22⋊C411yescharacteristic
58C23×C139C2×D411yescharacteristic
59C23×C139C2×D411yescharacteristic
60Q8×C139—41no—
61D4×C139—41no—
62D4×C139—41no—
63D4×C139—41no—
64C2×C4×C139—21no—
65C2×C4×C139—21no—
66C2×C4×C139—21no—
67C2×C4×C139—21no—
68C2×C4×C139—21no—
69C2×C4×C139—21no—
70C2×C4×C139—42no—
71C2×C4×C139C22⋊C411yescharacteristic
72C2×C4×C139C22⋊C411yescharacteristic
73C2×C4×C139C22⋊C411yescharacteristic
74C2×C4×C139C22×C411yescharacteristic
75C22×C139—21no—
76C22×C139—21no—
77C22×C139—21no—
78C22×C139—41no—
79C22×C139—41no—
80C22×C139—41no—
81C22×C139C2×C22⋊C411yescharacteristic
82C2×D139—42no—
83C2×D139—42no—
84C2×D139—42no—
85C2×D139—84no—
86C4×C139—21no—
87C4×C139—21no—
88C4×C139—21no—
89C4×C139—82no—
90C4×C139#9911yescharacteristic
91C4×C139#9911yescharacteristic
92Dic139—42no—
93Dic139—82no—
94C2×C139—21no—
95C2×C139—41no—
96C2×C139—41no—
97C2×C139—41no—
98C2×C139C2×#9911yescharacteristic
99D139—82no—
100C139#212811yescharacteristic, complemented, Sylow
101#2128—1391nomaximal, Sylow
102#535—1391no—
103#410—1391no—
104#410D13911yescharacteristic, complemented
105#353—1394no—
106C2×#41C2×D13911yescharacteristic
107C22×D4—1391no—
108#127—1392no—
109#124—1392no—
110#121—2781no—
111#121—2781no—
112#120—2781no—
113#120—2781no—
114#117—21no—
115#117—2781no—
116#117—1391no—
117#99—21no—
118#99—2781no—
119#99—1392no—
120#99C2×D13912yescomplemented
121C24—2781no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D13911yescharacteristic
125C2×D4—2782no—
126C2×D4—2782no—
127C2×D4—2781no—
128C2×D4—5561no—
129C2×D4—5561no—
130C2×D4—1392no—
131C2×D4C22⋊D13911yescharacteristic
132C2×D4D55611yescharacteristic
133C2×D4C22×D13911yescharacteristic
134C22×C4C4×D13911yescharacteristic
135C22×C4C22⋊D13911yescharacteristic
136C22×C4D55611yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—2781no—
139C4⋊C4—5561no—
140C22⋊C4—22no—
141C22⋊C4—2781no—
142C22⋊C4—2782no—
143C22⋊C4—2782no—
144C22⋊C4—2782no—
145C42—41no—
146C42—5561no—
147C42—1392no—
148C23—2782no—
149C23—5562no—
150C23—11122no—
151C23(C2×D139)⋊C411yescharacteristic
152C23C2×C22⋊D13911yescharacteristic
153C23C2×D55611yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—5562no—
159D4—5561no—
160D4—5561no—
161D4—11122no—
162D4—11122no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—2782no—
171C2×C4—5562no—
172C2×C4(C2×D139)⋊C411yescharacteristic
173C2×C4(C2×D139)⋊C411yescharacteristic
174C2×C4(C2×D139)⋊C411yescharacteristic
175C2×C4C2×C4×D13911yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—5562no—
183C22—5562no—
184C22—5562no—
185C22—11124no—
186C22C2×(C2×D139)⋊C411yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—5562no—
192C4—11122no—
193C4#1798475611yescharacteristic
194C4#1798475611yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—11122no—
200C2C2×#1798475611yescharacteristic
subgroupG/H
centerC2C2×#17984756
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#410×C139C2
socleC2×C139C2×#99
prime radical#22581517C2
cosocleC2×D4×C139C23
hypercenter#410D139
hypocenterC139#2128
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #22580927C2semidirect
3. #22580745C2semidirect
4. #410×C139C2semidirect
5. C22×D556C4semidirect
7. #17984831C4semidirect
13. #17984801C4semidirect
15. #17984757C22semidirect
19. #99×C139C22semidirect
100. C139#2128semidirect
104. #410D139semidirect
120. #99C2×D139semidirect

Maximal subgroups

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

subgroupindex
#225815172
#225809272
#225807452
#410×C1392
#2128139