Finite Group Databasebeta

← #31805578

Subgroups — #31805578

Order 17792.

194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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#22581673C211yesmaximal, characteristic
2#22581304C211yesmaximal, characteristic, complemented
3#22581249C211yesmaximal, characteristic, complemented
4#22581243C211yesmaximal, characteristic
5#22580698C211yesmaximal, characteristic, complemented
6#22580685C211yesmaximal, characteristic, complemented
7D4⋊C8×C139C211yesmaximal, characteristic
8#17984842C2211yescharacteristic
9#17984842C2211yescharacteristic
10#17984835—22no—
11#17984829—21no—
12#17984821—21no—
13C4×Dic278C2211yescharacteristic
14#17984807—21no—
15#17984801—21no—
16#17984776—21no—
17#17984773—21no—
18C4⋊(C139⋊C8)C2211yescharacteristic
19#17984767—21no—
20#17984767—22no—
21#17984763—21no—
22C4×D4×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4×C8×C139C2211yescharacteristic
25C2×Dic278—21no—
26C2×Dic278—21no—
27C2×Dic278D411yescharacteristic
28C2×C139⋊C8—21no—
29C4⋊Dic139—21no—
30C4⋊Dic139—21no—
31C4⋊Dic139—21no—
32C4⋊Dic139D411yescharacteristic
33C4⋊Dic139D412yes—
34Dic139⋊C4—22no—
35Dic139⋊C4—21no—
36C22⋊Dic139—22no—
37C22⋊Dic139—22no—
38C4×Dic139—22no—
39C4×Dic139—21no—
40C2×D4×C139D411yescharacteristic
41C22×C4×C139—21no—
42C2×C8×C139—21no—
43C2×C8×C139—21no—
44C4⋊C4×C139D411yescharacteristic
45C22⋊C4×C139—21no—
46C42×C139C2311yescharacteristic
47Dic278—21no—
48Dic278—21no—
49Dic278—41no—
50Dic278—41no—
51Dic278—42no—
52C2×Dic139—21no—
53C2×Dic139—21no—
54C2×Dic139—22no—
55C2×Dic139—41no—
56C139⋊C8—41no—
57C23×C139—21no—
58D4×C139—21no—
59D4×C139—21no—
60C2×C4×C139—21no—
61C2×C4×C139—41no—
62C2×C4×C139—41no—
63C2×C4×C139C2×D411yescharacteristic
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139C2×D411yescharacteristic
66C8×C139—41no—
67C8×C139—41no—
68C22×C139—41no—
69C22×C139—41no—
70C22×C139—41no—
71C22×C139#12011yescharacteristic
72C4×C139—21no—
73C4×C139—41no—
74C4×C139#13511yescharacteristic
75C4×C139#13511yescharacteristic
76C4×C139#13711yescharacteristic
77C4×C139#13711yescharacteristic
78Dic139—41no—
79Dic139—42no—
80Dic139—41no—
81Dic139—81no—
82C2×C139—81no—
83C2×C139#45211yescharacteristic
84C2×C139#45211yescharacteristic
85C2×C139#45411yescharacteristic
86C139#163811yescharacteristic, complemented, Sylow
87#1638—1391nomaximal, Sylow
88#556—1391no—
89#487—1391no—
90#477—1391no—
91#476—1391no—
92#332—1391no—
93Q8⋊C8—1391no—
94D4⋊C8D13911yescharacteristic
95C4⋊Q8—1391no—
96C4⋊Q8—1391no—
97#126—2782no—
98#124—2781no—
99C22⋊Q8—2781no—
100C4×Q8—2781no—
101C4×Q8—1391no—
102C4×D4C2×D13911yescharacteristic
103#117—2781no—
104#107—2781no—
105#106—2781no—
106C4⋊C8—1391no—
107C4⋊C8C2×D13911yescharacteristic
108#103—2781no—
109#103—2782no—
110#102—2781no—
111C4×C8C2×D13911yescharacteristic
112C2×Q8—2781no—
113C2×Q8—2781no—
114C2×Q8—1391no—
115C2×D4D55611yescharacteristic
116C22×C4—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2781no—
120C4⋊C4—2782no—
121C4⋊C4—2781no—
122C4⋊C4—2781no—
123C4⋊C4—2781no—
124C4⋊C4—2781no—
125C4⋊C4—1392no—
126C4⋊C4—1391no—
127C4⋊C4D55611yescharacteristic
128C22⋊C4—21no—
129C22⋊C4—2782no—
130C22⋊C4—2782no—
131C42—2782no—
132C42—2781no—
133C42C22×D13911yescharacteristic
134C23—21no—
135Q8—2781no—
136Q8—2781no—
137Q8—5562no—
138Q8—5561no—
139Q8—5561no—
140D4—21no—
141D4—21no—
142C2×C4—21no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—2781no—
146C2×C4—2781no—
147C2×C4—2782no—
148C2×C4—5561no—
149C2×C4D4×D13911yescharacteristic
150C2×C4D4×D13911yescharacteristic
151C2×C4C2×D55611yescharacteristic
152C8—41no—
153C8—41no—
154C8—5561no—
155C22—41no—
156C22—41no—
157C22—41no—
158C22#1798481211yescharacteristic
159C4—21no—
160C4—41no—
161C4—5561no—
162C4—5562no—
163C4—5561no—
164C4—11121no—
165C4#1798486111yescharacteristic
166C4#1798486411yescharacteristic
167C4#1798487111yescharacteristic
168C4#1798487511yescharacteristic
169C2—81no—
170C2#2258111611yescharacteristic
171C2#2258111711yescharacteristic
172C2#2258112711yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
FittingD4⋊C8×C139C2
socleC22×C139#120
prime radicalC2×D4×C139D4
hypercenterD4⋊C8D139
hypocenterC139#1638
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #22581304C2semidirect
3. #22581249C2semidirect
5. #22580698C2semidirect
6. #22580685C2semidirect
86. C139#1638semidirect

Maximal subgroups

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

subgroupindex
#225816732
#225813042
#225812492
#225812432
#225806982
#225806852
D4⋊C8×C1392
#1638139