Finite Group Databasebeta

← #31805037

Subgroups — #31805037

Order 17792.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#22581502C211yesmaximal, characteristic
2#22581008C212yesmaximal, complemented
3#22580693C211yesmaximal, characteristic, complemented
4#22580692C212yesmaximal, complemented
5#329×C139C211yesmaximal, characteristic, complemented
6C2×#14555786C411yescharacteristic
7C2×#14555784C411yescharacteristic
8#17984840C411yescharacteristic
9#17984838C411yescharacteristic
10#17984830C2211yescharacteristic
11#17984815—22no—
12(C22⋊D139)⋊C4—22no—
13C42×D139C2211yescharacteristic
14Dic139⋊C8—22no—
15(C2×D139)⋊C8—22no—
16#17984753C2212yes—
17#124×C139C2211yescharacteristic
18#97×C139C2212yes—
19#14555786—42no—
20#14555784—42no—
21C2×Dic278C2×C411yescharacteristic
22C2×D556—21no—
23C2×D556C2×C411yescharacteristic
24C2×C22⋊D139—21no—
25C2×C22⋊D139—22no—
26C22×Dic139—21no—
27C2×C4×D139—21no—
28C2×C4×D139C2×C411yescharacteristic
29C2×C4×D139D412yes—
30C2×C139⋊C8—22no—
31Dic139⋊C4—22no—
32(C2×D139)⋊C4—22no—
33C4×Dic139C2×C411yescharacteristic
34C4×Dic139D412yes—
35C2×Q8×C139C2×C411yescharacteristic
36C2×D4×C139C2×C411yescharacteristic
37C2×C8×C139—22no—
38C22⋊C4×C139—22no—
39C42×C139C2311yescharacteristic
40C22×D139—21no—
41C22×D139C22⋊C411yescharacteristic
42Dic278—41no—
43D556—41no—
44D556—42no—
45C22⋊D139—44no—
46C22⋊D139—42no—
47C2×Dic139—21no—
48C2×Dic139—42no—
49C2×Dic139C22⋊C412yes—
50C2×Dic139C22⋊C411yescharacteristic
51C4×D139—22no—
52C4×D139—42no—
53C4×D139—42no—
54C139⋊C8—42no—
55C23×C139—21no—
56Q8×C139—41no—
57D4×C139—41no—
58C2×C4×C139—21no—
59C2×C4×C139C22×C411yescharacteristic
60C2×C4×C139C2×D412yes—
61C8×C139—42no—
62C22×C139—41no—
63C22×C139—42no—
64C22×C139C2×C22⋊C411yescharacteristic
65C2×D139—21no—
66C2×D139—22no—
67C2×D139—41no—
68C2×D139—42no—
69C4×C139—21no—
70C4×C139—22no—
71C4×C139—41no—
72Dic139—22no—
73Dic139—41no—
74Dic139#10012yes—
75C2×C139—81no—
76C2×C139C2×#10011yescharacteristic
77C2×C139#42112yes—
78D139—41no—
79D139—81no—
80C139#153611yescharacteristic, complemented, Sylow
81#1536—1391nomaximal, Sylow
82#532—1391no—
83#432—1392no—
84#329—1391no—
85#329—1392no—
86#329D13911yescharacteristic, complemented
87C2×#41—1391no—
88C2×#41—1391no—
89C4⋊Q8—1391no—
90#127—1391no—
91#124—1391no—
92#124C2×D13911yescharacteristic
93#121—2782no—
94C4×D4—2782no—
95C2×C42—1391no—
96C4⋊C8—2782no—
97C22⋊C8—2782no—
98#97—1392no—
99#97C2×D13912yes—
100#41—5562no—
101#41—5562no—
102C2×Q8—1391no—
103C2×Q8C4×D13911yescharacteristic
104C2×D4—2781no—
105C2×D4—2781no—
106C2×D4—2782no—
107C2×D4—1391no—
108C2×D4C4×D13911yescharacteristic
109C22×C4—2781no—
110C22×C4—2781no—
111C22×C4—1391no—
112C22×C4—1392no—
113C2×C8—22no—
114C2×C8—2782no—
115C4⋊C4—2782no—
116C22⋊C4—22no—
117C22⋊C4—2782no—
118C42—1391no—
119C42—1392no—
120C42C22×D13911yescharacteristic
121C23—21no—
122C23—2781no—
123C23—1391no—
124Q8—41no—
125Q8—5561no—
126D4—41no—
127D4—5561no—
128D4—5562no—
129D4—5564no—
130D4—5562no—
131C2×C4—21no—
132C2×C4—2782no—
133C2×C4—2781no—
134C2×C4—5562no—
135C2×C4—5562no—
136C2×C4—5562no—
137C2×C4—1392no—
138C2×C4—1391no—
139C2×C4C2×C4×D13911yescharacteristic
140C2×C4D4×D13912yes—
141C8—42no—
142C8—5562no—
143C22—41no—
144C22—42no—
145C22—2781no—
146C22—2782no—
147C22—5561no—
148C22—5562no—
149C22C22⋊C4×D13911yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—2782no—
154C4—5561no—
155C4—1392no—
156C2—81no—
157C2—5561no—
158C2—11121no—
159C2#100×D13911yescharacteristic
160C2#2258096812yes—
subgroupG/H
centerC22C22⋊C4×D139
commutatorC2×C4×C139C22×C4
FrattiniC42C22×D139
Fitting#329×C139C2
socleC22×C139C2×C22⋊C4
prime radical#22581502C2
cosocleC42×C139C23
hypercenter#329D139
hypocenterC139#1536
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #22581008C2semidirect
3. #22580693C2semidirect
4. #22580692C2semidirect
5. #329×C139C2semidirect
80. C139#1536semidirect
86. #329D139semidirect

Maximal subgroups

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

subgroupindex
#225815022
#225810082
#225806932
#225806922
#329×C1392
#1536139