Finite Group Databasebeta

← #28336562

Subgroups — #28336562

Order 13696.

262 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 81 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#41×Dic107C211yesmaximal, characteristic
2#20292611C211yesmaximal, characteristic
3#20292386C212yesmaximal, complemented
4#20292383C212yesmaximal, complemented
5#410×C107C211yesmaximal, characteristic
6C2×#13133802C2212yes—
7Q8×Dic107—21no—
8D4×Dic107—21no—
9D4×Dic107—22no—
10#16812068C412yescomplemented
11#16812068C2211yescharacteristic
12C2×C4×Dic107C412yescomplemented
13C2×C4×Dic107C2211yescharacteristic
14#16812028—21no—
15#16812026—21no—
16C2×#41×C107C2211yescharacteristic
17#117×C107C2212yes—
18#99×C107—22no—
19C22×Dic107—22no—
20C22×Dic107—21no—
21#13133802—22no—
22#13133802—22no—
23C2×C107⋊C8—22no—
24C4⋊Dic107—22no—
25C4⋊Dic107—21no—
26C22⋊Dic107—22no—
27C22⋊Dic107—21no—
28C4×Dic107—22no—
29C4×Dic107—21no—
30C4×Dic107C2×C411yescharacteristic
31C4×Dic107C2×C412yes—
32C4×Dic107C2×C411yescharacteristic
33#41×C107—22no—
34#41×C107—22no—
35C2×Q8×C107D411yescharacteristic
36C2×D4×C107D411yescharacteristic
37C2×D4×C107D412yes—
38C22×C4×C107C2×C412yes—
39C22×C4×C107C2311yescharacteristic
40C4⋊C4×C107—22no—
41C22⋊C4×C107—22no—
42C42×C107—22no—
43C23×C107C22⋊C412yes—
44C23×C107C2×D411yescharacteristic
45Q8×C107—22no—
46D4×C107—24no—
47D4×C107—22no—
48C2×C4×C107—22no—
49C2×C4×C107—22no—
50C2×C4×C107—42no—
51C2×C4×C107C22⋊C412yes—
52C2×C4×C107C22×C411yescharacteristic
53C2×C4×C107C2×D411yescharacteristic
54C2×C4×C107#4112yes—
55C2×C4×C107#4112yes—
56C2×Dic107—21no—
57C2×Dic107—22no—
58C2×Dic107—21no—
59C2×Dic107—42no—
60C2×Dic107—44no—
61C107⋊C8—42no—
62C22×C107—22no—
63C22×C107—41no—
64C22×C107—42no—
65C22×C107C2×C22⋊C411yescharacteristic
66C22×C107#12312yes—
67C4×C107—22no—
68C4×C107—82no—
69C4×C107#11711yescharacteristic
70C4×C107#11711yescharacteristic
71C4×C107#12312yes—
72Dic107—22no—
73Dic107—42no—
74Dic107—41no—
75C2×C107—21no—
76C2×C107—22no—
77C2×C107—42no—
78C2×C107#38111yescharacteristic
79#1827—1071nomaximal, Sylow
80C107#182711yescharacteristic, complemented, Sylow
81C4×#41—1071no—
82#413—1071no—
83#410D10711yescharacteristic
84#339—1072no—
85H(3,ℤ/4)—1072no—
86C2×#41C2×D10711yescharacteristic
87C2×M16—1072no—
88C4×Q8—2141no—
89C4×D4—2141no—
90C4×D4—2142no—
91#117—1072no—
92#117—1071no—
93#117C2×D10712yes—
94C2×C42—1072no—
95C2×C42—1071no—
96#101—2141no—
97#100—2141no—
98#99—22no—
99#41—22no—
100#41—22no—
101C2×Q8D42811yescharacteristic
102C2×D4D42811yescharacteristic
103C2×D4C22⋊D10712yes—
104C22×C4—2142no—
105C22×C4—2141no—
106C22×C4C4×D10712yes—
107C22×C4C22×D10711yescharacteristic
108M16—2142no—
109M16—2142no—
110C2×C8—2142no—
111C4⋊C4—22no—
112C4⋊C4—2142no—
113C4⋊C4—2141no—
114C22⋊C4—22no—
115C22⋊C4—2142no—
116C22⋊C4—2141no—
117C42—22no—
118C42—1071no—
119C42—1072no—
120C42—1071no—
121C42—2142no—
122C42—2141no—
123C23(C2×D107)⋊C412yes—
124C23C2×C22⋊D10711yescharacteristic
125Q8—22no—
126D4—24no—
127D4—22no—
128C2×C4—22no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—4282no—
132C2×C4—4284no—
133C2×C4—2142no—
134C2×C4—2141no—
135C2×C4—2141no—
136C2×C4(C2×D107)⋊C412yes—
137C2×C4C2×C4×D10711yescharacteristic
138C2×C4C2×D42811yescharacteristic
139C2×C4#1313381712yes—
140C2×C4#1313381712yes—
141C8—4282no—
142C22—22no—
143C22—41no—
144C22—42no—
145C22C2×(C2×D107)⋊C411yescharacteristic
146C22#1681209012yes—
147C4—22no—
148C4—82no—
149C4—4281no—
150C4—4282no—
151C4—2142no—
152C4#1681206511yescharacteristic
153C4#1681206511yescharacteristic
154C4#1681209312yes—
155C2—22no—
156C2—21no—
157C2—42no—
158C2#2029248811yescharacteristic
subgroupG/H
centerC4#16812065
commutatorC2×C4×C107C22×C4
FrattiniC22×C4C22×D107
Fitting#410×C107C2
socleC2×C107#381
prime radicalC2×#41×C107C22
cosocleC22×C4×C107C23
hypercenter#410D107
hypocenterC107#1827
LCSG ▷ C2×C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #20292386C2semidirect
4. #20292383C2semidirect
10. #16812068C4semidirect
12. C2×C4×Dic107C4semidirect
80. C107#1827semidirect

Maximal subgroups

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

subgroupindex
#41×Dic1072
#202926112
#202923862
#202923832
#410×C1072
#1827107