Finite Group Databasebeta

← #28335621

Subgroups — #28335621

Order 13696.

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

normal subgroups only

This group has 188 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#20293355C211yesmaximal, characteristic
2#20292978C211yesmaximal, characteristic
3#20292923C211yesmaximal, characteristic
4#20292922C211yesmaximal, characteristic
5#20292372C211yesmaximal, characteristic
6#20292359C211yesmaximal, characteristic
7Q8⋊C8×C107C211yesmaximal, characteristic
8#16812109C2211yescharacteristic
9#16812109C2211yescharacteristic
10#16812107—21no—
11#16812101—21no—
12#16812099—22no—
13C4×Dic214—21no—
14C4×Dic214C2211yescharacteristic
15#16812074—21no—
16#16812043—21no—
17#16812042—21no—
18C4⋊(C107⋊C8)C2211yescharacteristic
19#16812034—21no—
20#16812034—22no—
21#16812033—21no—
22C4×Q8×C107C2211yescharacteristic
23C4⋊C8×C107C2211yescharacteristic
24C4×C8×C107C2211yescharacteristic
25C2×Dic214—21no—
26C2×Dic214—21no—
27C2×Dic214D411yescharacteristic
28C2×C107⋊C8—21no—
29C4⋊Dic107—21no—
30C4⋊Dic107—21no—
31C4⋊Dic107—21no—
32C4⋊Dic107D412yes—
33C4⋊Dic107D411yescharacteristic
34Dic107⋊C4—22no—
35Dic107⋊C4—22no—
36Dic107⋊C4—22no—
37Dic107⋊C4—21no—
38C4×Dic107—22no—
39C4×Dic107—21no—
40C2×Q8×C107D411yescharacteristic
41C2×C8×C107—21no—
42C2×C8×C107—21no—
43C4⋊C4×C107—21no—
44C4⋊C4×C107D411yescharacteristic
45C42×C107—21no—
46C42×C107C2311yescharacteristic
47Q8×C107—21no—
48Q8×C107—21no—
49C2×C4×C107—21no—
50C2×C4×C107—21no—
51C2×C4×C107C2×D411yescharacteristic
52C2×C4×C107C2×D411yescharacteristic
53C2×C4×C107C2×D411yescharacteristic
54C2×Dic107—21no—
55C2×Dic107—21no—
56C2×Dic107—22no—
57C2×Dic107—41no—
58Dic214—21no—
59Dic214—41no—
60Dic214—41no—
61Dic214—42no—
62Dic214Q1612yes—
63C8×C107—41no—
64C8×C107—41no—
65C107⋊C8—41no—
66C22×C107#12011yescharacteristic
67C4×C107—21no—
68C4×C107—41no—
69C4×C107—41no—
70C4×C107C2×Q1611yescharacteristic
71C4×C107#13511yescharacteristic
72C4×C107#13711yescharacteristic
73C4×C107#13711yescharacteristic
74Dic107—22no—
75Dic107—42no—
76Dic107—41no—
77Dic107—81no—
78C2×C107#45111yescharacteristic
79C2×C107#45211yescharacteristic
80C2×C107#45411yescharacteristic
81#1636—1071nomaximal, Sylow
82C107#163611yescharacteristic, complemented, Sylow
83#557—1071no—
84#487—1071no—
85#477—1071no—
86#477—1071no—
87#332—1071no—
88Q8⋊C8—1071no—
89Q8⋊C8D10711yescharacteristic
90C4⋊Q8—1071no—
91C4⋊Q8—1071no—
92C4⋊Q8—2141no—
93#125—2141no—
94#125—2142no—
95C4×Q8—1071no—
96C4×Q8—2141no—
97C4×Q8—2141no—
98C4×Q8C2×D10711yescharacteristic
99#107—2141no—
100#107—2141no—
101C4⋊C8—1071no—
102C4⋊C8C2×D10711yescharacteristic
103#103—2142no—
104#103—2141no—
105#103—2141no—
106C4×C8C2×D10711yescharacteristic
107C2×Q8—1071no—
108C2×Q8—2141no—
109C2×Q8—2141no—
110C2×Q8D42811yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—2141no—
114C4⋊C4—21no—
115C4⋊C4—1072no—
116C4⋊C4—1071no—
117C4⋊C4—2142no—
118C4⋊C4—2142no—
119C4⋊C4—2142no—
120C4⋊C4—2141no—
121C4⋊C4—2141no—
122C4⋊C4—2141no—
123C4⋊C4—2141no—
124C4⋊C4D42811yescharacteristic
125C42—21no—
126C42—2142no—
127C42—2141no—
128C42C22×D10711yescharacteristic
129Q8—21no—
130Q8—21no—
131Q8—1072no—
132Q8—4282no—
133Q8—4281no—
134Q8—4281no—
135Q8—2141no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—4281no—
139C2×C4—2141no—
140C2×C4—2142no—
141C2×C4—2141no—
142C2×C4D4×D10711yescharacteristic
143C2×C4D4×D10711yescharacteristic
144C2×C4C2×D42811yescharacteristic
145C8—41no—
146C8—41no—
147C8—4281no—
148C22#1681207911yescharacteristic
149C4—21no—
150C4—41no—
151C4—41no—
152C4—8561no—
153C4—4282no—
154C4—4281no—
155C4—2142no—
156C4Q16×D10711yescharacteristic
157C4#1681213111yescharacteristic
158C4#1681213811yescharacteristic
159C4#1681214211yescharacteristic
160C2#2029278411yescharacteristic
161C2#2029279111yescharacteristic
162C2#2029280111yescharacteristic
subgroupG/H
centerC22#16812079
commutator, cosocleC42×C107C23
FrattiniC42C22×D107
FittingQ8⋊C8×C107C2
socle, prime radicalC22×C107#120
hypercenterQ8⋊C8D107
hypocenterC107#1636
LCSG ▷ C42×C107 ▷ C22×C107 ▷ C107
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
82. C107#1636semidirect

Maximal subgroups

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

subgroupindex
#202933552
#202929782
#202929232
#202929222
#202923722
#202923592
Q8⋊C8×C1072
#1636107