Finite Group Databasebeta

← #31805589

Subgroups — #31805589

Order 17792.

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

normal subgroups only

This group has 212 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#22581688C211yesmaximal, characteristic
2#22581301C211yesmaximal, characteristic
3#22581160C211yesmaximal, characteristic, complemented
4#22580696C211yesmaximal, characteristic
5Q8⋊(C139⋊C8)C211yesmaximal, characteristic, complemented
6#22580683C211yesmaximal, characteristic, complemented
7#475×C139C211yesmaximal, characteristic, complemented
8C2×#14555775—21no—
9#17984839C2211yescharacteristic
10#17984831—21no—
11#17984830—21no—
12#17984827—22no—
13C4×Dic278C2211yescharacteristic
14C4×D556—21no—
15#17984804—21no—
16C4⋊(C139⋊C8)C2211yescharacteristic
17#17984766—21no—
18#17984762—22no—
19C4×C139⋊C8C2211yescharacteristic
20C4⋊Q8×C139C2211yescharacteristic
21C4×Q8×C139C2211yescharacteristic
22#106×C139—21no—
23C4⋊C8×C139C2211yescharacteristic
24#103×C139—21no—
25C2×Dic278D411yescharacteristic
26C2×D556—21no—
27C2×D556—21no—
28C2×D556D412yes—
29C2×C4×D139—22no—
30#14555775—42no—
31C2×C139⋊C8—21no—
32C2×C139⋊C8—21no—
33C4⋊Dic139D411yescharacteristic
34Dic139⋊C4—21no—
35(C2×D139)⋊C4—22no—
36(C2×D139)⋊C4—22no—
37(C2×D139)⋊C4—22no—
38C4×Dic139—21no—
39C2×Q8×C139—21no—
40C2×Q8×C139D411yescharacteristic
41C2×C8×C139—21no—
42C4⋊C4×C139—21no—
43C4⋊C4×C139—21no—
44C4⋊C4×C139—21no—
45C4⋊C4×C139D411yescharacteristic
46C42×C139—21no—
47C42×C139C2311yescharacteristic
48C22×D139—22no—
49Dic278—21no—
50Dic278—21no—
51D556—42no—
52D556—41no—
53D556—41no—
54D556—41no—
55D556—41no—
56C2×Dic139—21no—
57C2×Dic139—21no—
58C4×D139—82no—
59C139⋊C8—41no—
60C139⋊C8—41no—
61Q8×C139—21no—
62Q8×C139—21no—
63Q8×C139—41no—
64Q8×C139—41no—
65C2×C4×C139—21no—
66C2×C4×C139—21no—
67C2×C4×C139—41no—
68C2×C4×C139C2×D411yescharacteristic
69C2×C4×C139C2×D411yescharacteristic
70C2×C4×C139C2×D411yescharacteristic
71C8×C139—41no—
72C22×C139#12011yescharacteristic
73C2×D139—42no—
74C2×D139—42no—
75C2×D139—42no—
76C4×C139—21no—
77C4×C139—41no—
78C4×C139—41no—
79C4×C139—81no—
80C4×C139#13511yescharacteristic
81C4×C139#13511yescharacteristic
82C4×C139AGL(1,ℤ/8)11yescharacteristic
83C4×C139#13711yescharacteristic
84Dic139—41no—
85Dic139—41no—
86C2×C139#44911yescharacteristic
87C2×C139#45211yescharacteristic
88C2×C139#45511yescharacteristic
89D139—82no—
90C139#164011yescharacteristic, complemented, Sylow
91#1640—1391nomaximal, Sylow
92#559—1391no—
93#486—1391no—
94#475D13911yescharacteristic, complemented
95#462—1391no—
96#331—1391no—
97Q8⋊C8—1391no—
98Q8⋊C8—1391no—
99C2×Q16—2781no—
100C4⋊Q8C2×D13911yescharacteristic
101#127—1391no—
102#124—2781no—
103#124—2781no—
104#123—2782no—
105C4×Q8—1391no—
106C4×Q8C2×D13911yescharacteristic
107C4×D4—2781no—
108C4×D4—2781no—
109#106—21no—
110C4⋊C8—1391no—
111C4⋊C8C2×D13911yescharacteristic
112#103—21no—
113#103—2781no—
114#102—2782no—
115C4×C8—1391no—
116C2×Q8—21no—
117C2×Q8—1391no—
118C2×Q8C22⋊D13911yescharacteristic
119C2×D4—2781no—
120C2×D4—2781no—
121C2×D4—1392no—
122C22×C4—2782no—
123Q16—5562no—
124C2×C8—21no—
125C2×C8—2781no—
126C2×C8—2781no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—2781no—
131C4⋊C4—1391no—
132C4⋊C4C22⋊D13911yescharacteristic
133C22⋊C4—2782no—
134C22⋊C4—2782no—
135C22⋊C4—2782no—
136C42—21no—
137C42—2781no—
138C42C22×D13911yescharacteristic
139C23—2782no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—2781no—
145Q8—2781no—
146D4—5562no—
147D4—5561no—
148D4—5561no—
149D4—5561no—
150D4—5561no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—2781no—
155C2×C4—2781no—
156C2×C4—11122no—
157C2×C4D4×D13911yescharacteristic
158C2×C4D4×D13911yescharacteristic
159C2×C4C2×C22⋊D13911yescharacteristic
160C8—41no—
161C8—5561no—
162C8—5561no—
163C22—5562no—
164C22—5562no—
165C22—5562no—
166C22#1798481011yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—5561no—
172C4—5561no—
173C4#1798486211yescharacteristic
174C4#1798486311yescharacteristic
175C4#1798486911yescharacteristic
176C4#1798487311yescharacteristic
177C2—11122no—
178C2#2258109711yescharacteristic
179C2#2258111311yescharacteristic
180C2#2258112911yescharacteristic
subgroupG/H
centerC22#17984810
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#475×C139C2
socleC22×C139#120
prime radical#17984839C22
hypercenter#475D139
hypocenterC139#1640
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
3. #22581160C2semidirect
5. Q8⋊(C139⋊C8)C2semidirect
6. #22580683C2semidirect
7. #475×C139C2semidirect
90. C139#1640semidirect
94. #475D139semidirect

Maximal subgroups

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

subgroupindex
#225816882
#225813012
#225811602
#225806962
Q8⋊(C139⋊C8)2
#225806832
#475×C1392
#1640139