Finite Group Databasebeta

← #31808053

Subgroups — #31808053

Order 17792.

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

normal subgroups only

This group has 266 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#22580937C211yesmaximal, characteristic, complemented
3#22580739C214yesmaximal, complemented
4#410×C139C211yesmaximal, characteristic, complemented
5C22×D556C411yescharacteristic, complemented
6C2×#14555769—21no—
7#17984838—21no—
8#17984831—21no—
9#17984816—21no—
10#17984816—21no—
11#17984810C412yescomplemented
12#17984810C2212yes—
13#17984801C411yescharacteristic, complemented
14#17984761—21no—
15#17984759C2212yes—
16C2×#41×C139C2211yescharacteristic
17#117×C139—21no—
18#99×C139—21no—
19#99×C139C2212yes—
20C23×D139C2×C412yes—
21C2×D556—21no—
22C2×D556—21no—
23C2×D556—41no—
24C2×D556—41no—
25C2×C22⋊D139—22no—
26C2×C22⋊D139—22no—
27#14555769—22no—
28#14555769—41no—
29C2×C139⋊C8—41no—
30C4⋊Dic139—21no—
31C22⋊Dic139C2×C412yes—
32(C2×D139)⋊C4—22no—
33(C2×D139)⋊C4—22no—
34C4×Dic139—21no—
35#41×C139—41no—
36#41×C139—41no—
37C2×Q8×C139D411yescharacteristic
38C2×D4×C139C2×C411yescharacteristic
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—
56C139⋊C8—42no—
57C23×C139C22⋊C411yescharacteristic
58C23×C139C22×C411yescharacteristic
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×C139C2×D411yescharacteristic
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—
93C2×C139—21no—
94C2×C139—41no—
95C2×C139—41no—
96C2×C139—41no—
97C2×C139C2×#9911yescharacteristic
98D139—82no—
99C139#212211yescharacteristic, complemented, Sylow
100#2122—1391nomaximal, Sylow
101#535—1391no—
102#413—1391no—
103#410D13911yescharacteristic, complemented
104AΣL(1,𝔽16)—1394no—
105C2×#41C2×D13911yescharacteristic
106C22×D4—1391no—
107C2×M16—2781no—
108#127—2781no—
109#124—2781no—
110#121—2781no—
111#121—2781no—
112#120—1392no—
113#120—1392no—
114#117—21no—
115#117—1391no—
116#101—2781no—
117#100—1392no—
118#99—21no—
119#99C2×D13912yes—
120C24—1392no—
121#41—41no—
122#41—41no—
123C2×Q8D55611yescharacteristic
124C2×D4—2782no—
125C2×D4—2782no—
126C2×D4—2781no—
127C2×D4—2781no—
128C2×D4—5561no—
129C2×D4—5561no—
130C2×D4C4×D13911yescharacteristic
131C2×D4C22⋊D13911yescharacteristic
132C2×D4C22×D13911yescharacteristic
133C22×C4C4×D13911yescharacteristic
134C22×C4C22⋊D13911yescharacteristic
135C22×C4D55611yescharacteristic
136M16—2782no—
137M16—5561no—
138C2×C8—5561no—
139C4⋊C4—41no—
140C4⋊C4—2781no—
141C22⋊C4—22no—
142C22⋊C4—2782no—
143C22⋊C4—2782no—
144C22⋊C4—1392no—
145C42—41no—
146C42—2781no—
147C23—2782no—
148C23—5562no—
149C23—11122no—
150C23(C2×D139)⋊C411yescharacteristic
151C23C2×C4×D13911yescharacteristic
152C23C2×C22⋊D13911yescharacteristic
153Q8—41no—
154D4—41no—
155D4—41no—
156D4—41no—
157D4—5562no—
158D4—5561no—
159D4—5561no—
160D4—11122no—
161D4—11122no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—2782no—
170C2×C4(C2×D139)⋊C411yescharacteristic
171C2×C4(C2×D139)⋊C411yescharacteristic
172C2×C4(C2×D139)⋊C411yescharacteristic
173C2×C4C2×D55611yescharacteristic
174C8—5562no—
175C22—21no—
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—5562no—
182C22—5562no—
183C22—5562no—
184C22—11124no—
185C22C2×(C2×D139)⋊C411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—82no—
190C4—5562no—
191C4#1798475611yescharacteristic
192C4#1798475611yescharacteristic
193C2—21no—
194C2—41no—
195C2—41no—
196C2—41no—
197C2—11122no—
198C2C2×#1798475611yescharacteristic
subgroupG/H
centerC2C2×#17984756
commutatorC23×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#410×C139C2
socleC2×C139C2×#99
prime radical#22581517C2
cosocleC2×D4×C139C23
hypercenter#410D139
hypocenterC139#2122
LCSG ▷ C23×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. #22580937C2semidirect
3. #22580739C2semidirect
4. #410×C139C2semidirect
5. C22×D556C4semidirect
11. #17984810C4semidirect
13. #17984801C4semidirect
99. C139#2122semidirect
103. #410D139semidirect

Maximal subgroups

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

subgroupindex
#225815172
#225809372
#225807392
#410×C1392
#2122139