Finite Group Databasebeta

← #31805033

Subgroups — #31805033

Order 17792.

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

normal subgroups only

This group has 200 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#22581487C211yesmaximal, characteristic
2#22581010C211yesmaximal, characteristic, complemented
3#22580694C212yesmaximal, complemented
4#22580692C212yesmaximal, complemented
5#432×C139C211yesmaximal, characteristic, complemented
6#17984836—21no—
7#17984834C2211yescharacteristic
8#17984830C2211yescharacteristic
9#17984825—21no—
10#17984821C411yescharacteristic
11#17984816C411yescharacteristic
12C4×Dic278C411yescharacteristic
13C4×D556C411yescharacteristic
14C4×C22⋊D139—21no—
15#17984799—21no—
16C4⋊(C139⋊C8)—21no—
17C22⋊(C139⋊C8)—21no—
18#17984753C2212yes—
19C2×C42×C139C2211yescharacteristic
20C4⋊C8×C139—21no—
21C22⋊C8×C139—21no—
22#97×C139C2212yes—
23C2×Dic278C2×C411yescharacteristic
24C2×D556C2×C411yescharacteristic
25C2×C22⋊D139—21no—
26C2×C4×D139—21no—
27C2×C139⋊C8—22no—
28C4⋊Dic139C2×C411yescharacteristic
29C4⋊Dic139C2×C411yescharacteristic
30Dic139⋊C4—21no—
31Dic139⋊C4—21no—
32Dic139⋊C4—21no—
33Dic139⋊C4—21no—
34C22⋊Dic139—21no—
35(C2×D139)⋊C4—21no—
36(C2×D139)⋊C4—21no—
37(C2×D139)⋊C4—21no—
38(C2×D139)⋊C4—21no—
39C4×Dic139—21no—
40C22×C4×C139C2×C411yescharacteristic
41C22×C4×C139D411yescharacteristic
42C22×C4×C139D411yescharacteristic
43C2×C8×C139—22no—
44C42×C139C2×C411yescharacteristic
45C42×C139D411yescharacteristic
46C42×C139D411yescharacteristic
47C42×C139C2311yescharacteristic
48C22×D139—21no—
49Dic278—41no—
50D556—41no—
51C22⋊D139—42no—
52C2×Dic139—21no—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C4×D139—42no—
56C139⋊C8—42no—
57C23×C139C22⋊C411yescharacteristic
58C2×C4×C139—41no—
59C2×C4×C139—41no—
60C2×C4×C139—41no—
61C2×C4×C139C22⋊C411yescharacteristic
62C2×C4×C139C22⋊C411yescharacteristic
63C2×C4×C139C22⋊C411yescharacteristic
64C2×C4×C139C22×C411yescharacteristic
65C2×C4×C139C2×D411yescharacteristic
66C2×C4×C139C2×D411yescharacteristic
67C8×C139—42no—
68C22×C139—21no—
69C22×C139—21no—
70C22×C139—21no—
71C22×C139C2×C22⋊C411yescharacteristic
72C2×D139—41no—
73C2×D139—41no—
74C2×D139—41no—
75C4×C139—21no—
76C4×C139—21no—
77C4×C139—21no—
78C4×C139—21no—
79C4×C139—21no—
80C4×C139—21no—
81Dic139—41no—
82Dic139—41no—
83Dic139—41no—
84C2×C139—41no—
85C2×C139#41311yescharacteristic
86C2×C139#42111yescharacteristic
87C2×C139#42111yescharacteristic
88D139—81no—
89C139#153511yescharacteristic, complemented, Sylow
90#1535—1391nomaximal, Sylow
91#529—1391no—
92#432—1391no—
93#432D13911yescharacteristic, complemented
94#330—1392no—
95#329—1392no—
96#126—2781no—
97#125—1391no—
98#124—1391no—
99#123—2781no—
100C22⋊Q8—1391no—
101#121—1391no—
102C4×Q8—1391no—
103C4×D4—2781no—
104C4×D4—1391no—
105#117—2781no—
106C2×C42C2×D13911yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—2781no—
109C22⋊C8—21no—
110C22⋊C8—2781no—
111#97—1392no—
112#97C2×D13912yes—
113C2×Q8—1391no—
114C2×D4—2781no—
115C2×D4—1391no—
116C22×C4—2781no—
117C22×C4C4×D13911yescharacteristic
118C22×C4C22⋊D13911yescharacteristic
119C22×C4D55611yescharacteristic
120C2×C8—22no—
121C2×C8—2782no—
122C4⋊C4—2781no—
123C4⋊C4—2781no—
124C4⋊C4—2781no—
125C4⋊C4—2781no—
126C4⋊C4—1391no—
127C4⋊C4—1391no—
128C22⋊C4—2781no—
129C22⋊C4—2781no—
130C22⋊C4—2781no—
131C22⋊C4—2781no—
132C22⋊C4—2781no—
133C42—2781no—
134C42C4×D13911yescharacteristic
135C42C22⋊D13911yescharacteristic
136C42D55611yescharacteristic
137C42C22×D13911yescharacteristic
138C23—2781no—
139C23(C2×D139)⋊C411yescharacteristic
140Q8—5561no—
141D4—5561no—
142D4—5562no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—2781no—
147C2×C4—2781no—
148C2×C4—2781no—
149C2×C4—5562no—
150C2×C4(C2×D139)⋊C411yescharacteristic
151C2×C4(C2×D139)⋊C411yescharacteristic
152C2×C4(C2×D139)⋊C411yescharacteristic
153C2×C4C2×C4×D13911yescharacteristic
154C2×C4C2×C22⋊D13911yescharacteristic
155C2×C4C2×D55611yescharacteristic
156C8—42no—
157C8—5562no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—5561no—
162C22—5561no—
163C22—5561no—
164C22C2×(C2×D139)⋊C411yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—5561no—
172C4—5561no—
173C4—5561no—
174C2—41no—
175C2—11121no—
176C2#2258093511yescharacteristic
177C2#2258096911yescharacteristic
178C2#2258097111yescharacteristic
subgroupG/H
centerC22C2×(C2×D139)⋊C4
commutatorC2×C4×C139C22×C4
FrattiniC42C22×D139
Fitting#432×C139C2
socleC22×C139C2×C22⋊C4
prime radical#17984816C4
cosocleC42×C139C23
hypercenter#432D139
hypocenterC139#1535
LCSG ▷ C2×C4×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #22581010C2semidirect
3. #22580694C2semidirect
4. #22580692C2semidirect
5. #432×C139C2semidirect
89. C139#1535semidirect
93. #432D139semidirect

Maximal subgroups

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

subgroupindex
#225814872
#225810102
#225806942
#225806922
#432×C1392
#1535139