Finite Group Databasebeta

← #31808077

Subgroups — #31808077

Order 17792.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#22581523C211yesmaximal, characteristic
2#22580925C212yesmaximal
3#22580748C211yesmaximal, characteristic, complemented
4#22580747C212yesmaximal, complemented
5#354×C139C211yesmaximal, characteristic, complemented
6C2×#14555784C2211yescharacteristic
7C2×Q8×D139C411yescharacteristic, complemented
8#17984842C411yescharacteristic, complemented
9#17984840C411yescharacteristic, complemented
10#17984829C2211yescharacteristic
11#17984824—22no—
12#17984819—22no—
13#17984799C411yescharacteristic, complemented
14#17984798—22no—
15#17984757C2212yes—
16#17984756—22no—
17#124×C139C2211yescharacteristic
18#99×C139C2212yes—
19#14555784—42no—
20C2×Dic278—21no—
21C2×Dic278C2×C411yescharacteristic
22C2×Dic278C2×C411yescharacteristic
23Q8×D139—42no—
24C2×C22⋊D139D412yes—
25C22×Dic139D412yes—
26C2×C4×D139—21no—
27C2×C4×D139C2×C411yescharacteristic
28C4⋊Dic139—22no—
29Dic139⋊C4—21no—
30Dic139⋊C4—22no—
31Dic139⋊C4—42no—
32C22⋊Dic139—22no—
33C22⋊Dic139—22no—
34(C2×D139)⋊C4—21no—
35C4×Dic139—42no—
36C4×Dic139C2×C411yescharacteristic
37C2×Q8×C139C2×C411yescharacteristic
38C2×D4×C139C2311yescharacteristic
39C22⋊C4×C139—22no—
40C22⋊C4×C139—22no—
41C42×C139C2×C411yescharacteristic
42C22×D139C22⋊C411yescharacteristic
43Dic278—41no—
44Dic278—42no—
45Dic278—41no—
46C22⋊D139—42no—
47C2×Dic139—22no—
48C2×Dic139—22no—
49C2×Dic139—21no—
50C2×Dic139—21no—
51C2×Dic139—42no—
52C2×Dic139C22⋊C412yes—
53C2×Dic139C22⋊C411yescharacteristic
54C4×D139—22no—
55C4×D139—42no—
56C23×C139C2×D412yes—
57Q8×C139—41no—
58D4×C139—41no—
59C2×C4×C139—21no—
60C2×C4×C139—21no—
61C2×C4×C139—42no—
62C2×C4×C139C22×C411yescharacteristic
63C22×C139—22no—
64C22×C139—42no—
65C22×C139C2×C22⋊C411yescharacteristic
66C2×D139—21no—
67C2×D139—41no—
68C4×C139—21no—
69C4×C139—41no—
70C4×C139—41no—
71C4×C139—82no—
72Dic139—22no—
73Dic139—41no—
74Dic139—41no—
75Dic139—82no—
76Dic139#9912yes—
77C2×C139—21no—
78C2×C139—42no—
79C2×C139C2×#9911yescharacteristic
80D139—41no—
81C139#212911yescharacteristic, complemented, Sylow
82#2129—1391nomaximal, Sylow
83#536—1391no—
84#410—1392no—
85#354—1391no—
86#354—1392no—
87#354D13911yescharacteristic, complemented
88C2×#41—1391no—
89C22×Q8—1391no—
90C4⋊Q8—1391no—
91C4⋊Q8—1391no—
92#124—1391no—
93#124C2×D13911yescharacteristic
94#123—2782no—
95C22⋊Q8—2782no—
96#117—2782no—
97#117—1391no—
98#99—2782no—
99#99—1392no—
100#99C2×D13912yes—
101#41—5562no—
102C2×Q8—2781no—
103C2×Q8—5562no—
104C2×Q8—1391no—
105C2×Q8—1391no—
106C2×Q8C4×D13911yescharacteristic
107C2×D4—1392no—
108C2×D4C22×D13911yescharacteristic
109C22×C4—2781no—
110C22×C4—1392no—
111C22×C4—1391no—
112C4⋊C4—2781no—
113C4⋊C4—2782no—
114C4⋊C4—2782no—
115C4⋊C4—5562no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—2781no—
119C22⋊C4—2782no—
120C22⋊C4—2782no—
121C42—5562no—
122C42—1391no—
123C42C4×D13911yescharacteristic
124C23—1391no—
125C23D4×D13912yes—
126Q8—41no—
127Q8—5561no—
128Q8—5561no—
129Q8—5562no—
130D4—41no—
131D4—5562no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—2782no—
136C2×C4—2782no—
137C2×C4—2782no—
138C2×C4—2781no—
139C2×C4—2781no—
140C2×C4—5562no—
141C2×C4—5562no—
142C2×C4—1392no—
143C2×C4—1391no—
144C2×C4C2×C4×D13911yescharacteristic
145C22—22no—
146C22—42no—
147C22—2781no—
148C22—5561no—
149C22C22⋊C4×D13911yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—2782no—
155C4—5561no—
156C4—5561no—
157C4—11122no—
158C4—1392no—
159C2—21no—
160C2—42no—
161C2—5561no—
162C2#99×D13911yescharacteristic
subgroupG/H
centerC2#99×D139
commutatorC2×C4×C139C22×C4
FrattiniC2×D4C22×D139
Fitting#354×C139C2
socleC2×C139C2×#99
prime radicalC2×#14555784C22
cosocleC2×D4×C139C23
hypercenter#354D139
hypocenterC139#2129
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #22580748C2semidirect
4. #22580747C2semidirect
5. #354×C139C2semidirect
7. C2×Q8×D139C4semidirect
8. #17984842C4semidirect
9. #17984840C4semidirect
13. #17984799C4semidirect
81. C139#2129semidirect
87. #354D139semidirect

Maximal subgroups

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

subgroupindex
#225815232
#225809252
#225807482
#225807472
#354×C1392
#2129139