Finite Group Databasebeta

← #31805577

Subgroups — #31805577

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#22581677C211yesmaximal, characteristic
2#22581305C211yesmaximal, characteristic, complemented
3#22581249C211yesmaximal, characteristic, complemented
4#22581244C211yesmaximal, characteristic
5#22580683C211yesmaximal, characteristic, complemented
6#22580680C211yesmaximal, characteristic
7#332×C139C211yesmaximal, characteristic, complemented
8#17984842C2211yescharacteristic
9#17984837—22no—
10#17984831—21no—
11#17984822—21no—
12Q8×Dic139—21no—
13C4×Dic278C2211yescharacteristic
14C4×D556C2211yescharacteristic
15#17984800—21no—
16#17984776—21no—
17#17984774—21no—
18#17984767—21no—
19#17984765—22no—
20#17984764—21no—
21C4×C139⋊C8C2211yescharacteristic
22C4⋊Q8×C139C2211yescharacteristic
23C4⋊C8×C139C2211yescharacteristic
24C4⋊C8×C139C2211yescharacteristic
25C2×Dic278—21no—
26C2×Dic278D411yescharacteristic
27C2×D556D411yescharacteristic
28C2×C4×D139—21no—
29C2×C139⋊C8—21no—
30C4⋊Dic139—22no—
31C4⋊Dic139—21no—
32C4⋊Dic139—21no—
33C4⋊Dic139D411yescharacteristic
34C4⋊Dic139D411yescharacteristic
35Dic139⋊C4—21no—
36(C2×D139)⋊C4—22no—
37(C2×D139)⋊C4—22no—
38(C2×D139)⋊C4—21no—
39C4×Dic139—22no—
40C4×Dic139—21no—
41C2×Q8×C139—21no—
42C2×C8×C139—21no—
43C2×C8×C139—21no—
44C4⋊C4×C139—21no—
45C4⋊C4×C139D412yes—
46C42×C139C2311yescharacteristic
47C22×D139—21no—
48Dic278—21no—
49Dic278—21no—
50Dic278—42no—
51D556—21no—
52D556—21no—
53C2×Dic139—21no—
54C2×Dic139—21no—
55C2×Dic139—21no—
56C2×Dic139—41no—
57C4×D139—41no—
58C4×D139—41no—
59C139⋊C8—41no—
60Q8×C139—41no—
61Q8×C139—41no—
62C2×C4×C139—22no—
63C2×C4×C139C2×D411yescharacteristic
64C2×C4×C139C2×D411yescharacteristic
65C2×C4×C139C2×D411yescharacteristic
66C8×C139—41no—
67C8×C139—41no—
68C22×C139#12011yescharacteristic
69C2×D139—41no—
70C2×D139—41no—
71C2×D139—41no—
72C4×C139—21no—
73C4×C139—42no—
74C4×C139#13511yescharacteristic
75C4×C139#13511yescharacteristic
76C4×C139#13711yescharacteristic
77C4×C139#13711yescharacteristic
78Dic139—41no—
79Dic139—41no—
80Dic139—41no—
81Dic139—81no—
82C2×C139#45211yescharacteristic
83C2×C139#45211yescharacteristic
84C2×C139#45411yescharacteristic
85D139—81no—
86C139#163811yescharacteristic, complemented, Sylow
87#1638—1391nomaximal, Sylow
88#556—1391no—
89#487—1391no—
90#477—1391no—
91#476—1391no—
92#332D13911yescharacteristic, complemented
93Q8⋊C8—1391no—
94D4⋊C8—1391no—
95C4⋊Q8—1391no—
96C4⋊Q8C2×D13911yescharacteristic
97#126—2782no—
98#124—2781no—
99C22⋊Q8—2781no—
100C4×Q8—2781no—
101C4×Q8—1391no—
102C4×D4—1391no—
103#117—2781no—
104#107—2781no—
105#106—2781no—
106C4⋊C8C2×D13911yescharacteristic
107C4⋊C8C2×D13911yescharacteristic
108#103—2781no—
109#103—2782no—
110#102—2781no—
111C4×C8—1391no—
112C2×Q8—21no—
113C2×Q8—2781no—
114C2×Q8—1391no—
115C2×D4—1391no—
116C22×C4—2781no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—2781no—
120C4⋊C4—21no—
121C4⋊C4—2782no—
122C4⋊C4—2781no—
123C4⋊C4—2781no—
124C4⋊C4—2781no—
125C4⋊C4—1391no—
126C4⋊C4—1391no—
127C4⋊C4D55612yes—
128C22⋊C4—2782no—
129C22⋊C4—2782no—
130C22⋊C4—2781no—
131C42—2782no—
132C42—2781no—
133C42C22×D13911yescharacteristic
134C23—2781no—
135Q8—41no—
136Q8—41no—
137Q8—2781no—
138Q8—2781no—
139Q8—5562no—
140D4—2781no—
141D4—2781no—
142C2×C4—22no—
143C2×C4—2781no—
144C2×C4—2781no—
145C2×C4—2781no—
146C2×C4—5561no—
147C2×C4—5561no—
148C2×C4—5561no—
149C2×C4D4×D13911yescharacteristic
150C2×C4D4×D13911yescharacteristic
151C2×C4C2×D55611yescharacteristic
152C8—41no—
153C8—41no—
154C8—5561no—
155C22—5561no—
156C22—5561no—
157C22—5561no—
158C22#1798481211yescharacteristic
159C4—21no—
160C4—42no—
161C4—5561no—
162C4—5561no—
163C4—5561no—
164C4—11121no—
165C4#1798486111yescharacteristic
166C4#1798486311yescharacteristic
167C4#1798487111yescharacteristic
168C4#1798487411yescharacteristic
169C2—11121no—
170C2#2258111611yescharacteristic
171C2#2258111811yescharacteristic
172C2#2258112811yescharacteristic
subgroupG/H
centerC22#17984812
commutator, cosocleC42×C139C23
FrattiniC42C22×D139
Fitting#332×C139C2
socleC22×C139#120
prime radicalC2×D556D4
hypercenter#332D139
hypocenterC139#1638
LCSG ▷ C42×C139 ▷ C22×C139 ▷ C139
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #22581305C2semidirect
3. #22581249C2semidirect
5. #22580683C2semidirect
7. #332×C139C2semidirect
86. C139#1638semidirect
92. #332D139semidirect

Maximal subgroups

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

subgroupindex
#225816772
#225813052
#225812492
#225812442
#225806832
#225806802
#332×C1392
#1638139