Finite Group Databasebeta

← #28379038

Subgroups — #28379038

Order 13952.

324 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 68 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#20296094C211yesmaximal, characteristic
2#20296019C212yesmaximal
3D109⋊#101C211yesmaximal, characteristic
4#20295897C212yesmaximal
5C4⋊Q8×D109C211yesmaximal, characteristic
6D109⋊M16C2212yes—
7Q8×#89137—24no—
8#16812778—22no—
9#16812778C2212yes—
10#16812762—24no—
11#16812760—22no—
12C2×Q8×D109C2211yescharacteristic
13C2×Q8×D109C2211yescharacteristic
14#16812699C411yescharacteristic, complemented
15#16812698—22no—
16#16812697C411yescharacteristic, complemented
17#16812697C411yescharacteristic, complemented
18C4⋊C4×D109—22no—
19C42×D109C2211yescharacteristic
20C4⋊Q8×C109C411yescharacteristic, complemented
21#13182039—22no—
22#13182038—22no—
23D109⋊C8—22no—
24C4⋊#89137—24no—
25C4⋊#89137D414yes—
26C22⋊#89137—22no—
27C4×#89137—24no—
28C4×#89137—22no—
29C2×Dic218—21no—
30C2×Dic218C2×C411yescharacteristic
31C2×Dic218C2×C411yescharacteristic
32C2×Dic218D412yes—
33Q8×D109—22no—
34Q8×D109—22no—
35Q8×D109—22no—
36Q8×D109—22no—
37C2×C4×D109—21no—
38C2×C4×D109—21no—
39C2×C4×D109D412yes—
40C2×C4×D109C2311yescharacteristic
41C4⋊Dic109—22no—
42#13182008—22no—
43#13182008—22no—
44C4×Dic109—21no—
45C4×Dic109C2×C411yescharacteristic
46C2×Q8×C109C2×C411yescharacteristic
47C2×Q8×C109C2×C411yescharacteristic
48C4⋊C4×C109—22no—
49C42×C109C2×C411yescharacteristic
50C22×D109C2×D411yescharacteristic
51C2×#89137—24no—
52Q8×C109—22no—
53Q8×C109—22no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C412yes—
57C2×C4×C109C22×C411yescharacteristic
58C2×Dic109—21no—
59C2×Dic109—21no—
60C2×Dic109C22⋊C412yes—
61C2×Dic109C2×D411yescharacteristic
62C4×D109—24no—
63C4×D109—22no—
64C4×D109—22no—
65C4×D109—41no—
66C4×D109—41no—
67C4×D109C2×D412yes—
68C4×D109#4112yes—
69Dic218—22no—
70Dic218—24no—
71Dic218—22no—
72Dic218—42no—
73#11724786—42no—
74C22×C109C2×C22⋊C411yescharacteristic
75C2×D109—22no—
76C2×D109#12011yescharacteristic
77C2×D109#12311yescharacteristic
78#89137—44no—
79C4×C109—22no—
80C4×C109—22no—
81C4×C109—41no—
82C4×C109C4×D412yes—
83Dic109—22no—
84Dic109—22no—
85Dic109—41no—
86Dic109#12112yes—
87C2×C109—21no—
88C2×C109#38611yescharacteristic
89D109—21no—
90D109#45612yes—
91#1886—1091nomaximal, Sylow
92C109#188611yescharacteristic, complemented, Sylow
93C2×C4⋊Q8—1091no—
94#519—1091no—
95#419—1092no—
96C2×#101—1091no—
97#339—1092no—
98C22×Q8—1091no—
99C22×Q8—1091no—
100C2×M16—1092no—
101C4⋊Q8—1091no—
102C4⋊Q8—1091no—
103C4⋊Q8—1091no—
104C4⋊Q8—2182no—
105C4⋊Q8#8913711yescharacteristic, complemented
106C4×Q8—2184no—
107#117—1092no—
108#117—2182no—
109C2×C4⋊C4—2182no—
110C2×C42—1091no—
111#103—2184no—
112#101—2182no—
113C2×Q8—1092no—
114C2×Q8—1091no—
115C2×Q8—1091no—
116C2×Q8—2181no—
117C2×Q8—2182no—
118C2×Q8—2182no—
119C2×Q8—2182no—
120C2×Q8—2182no—
121C2×Q8C2×#8913711yescharacteristic
122C2×Q8C2×#8913711yescharacteristic
123C22×C4—1091no—
124C22×C4—1092no—
125C22×C4—2181no—
126C22×C4—2181no—
127M16—2182no—
128M16—2182no—
129C2×C8—2182no—
130C4⋊C4—22no—
131C4⋊C4—1094no—
132C4⋊C4—2182no—
133C4⋊C4—2182no—
134C4⋊C4—2184no—
135C4⋊C4—2182no—
136C22⋊C4—2182no—
137C42—1091no—
138C42—2181no—
139C42—2182no—
140C42—2184no—
141C42C2×#8913711yescharacteristic
142C23—1091no—
143Q8—22no—
144Q8—22no—
145Q8—4362no—
146Q8—2184no—
147Q8—2182no—
148Q8—2182no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—1091no—
152C2×C4—1092no—
153C2×C4—1092no—
154C2×C4—1092no—
155C2×C4—4361no—
156C2×C4—4361no—
157C2×C4—2182no—
158C2×C4—2182no—
159C2×C4—2184no—
160C2×C4—2184no—
161C2×C4—2181no—
162C2×C4—2181no—
163C2×C4C22⋊#8913712yes—
164C2×C4C22×#8913711yescharacteristic
165C8—4362no—
166C22—1091no—
167C22—1091no—
168C22—2182no—
169C22C2×C22⋊#8913711yescharacteristic
170C4—22no—
171C4—22no—
172C4—41no—
173C4—1092no—
174C4—4364no—
175C4—4361no—
176C4—2182no—
177C4—2182no—
178C4D4×#8913712yes—
179C2—21no—
180C2—1092no—
181C2—2181no—
182C2#2029597411yescharacteristic
subgroupG/H
centerC2#20295974
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4⋊Q8×C109C4
socleC2×C109#386
prime radicalC22×D109C2×D4
cosocleC2×C4×D109C23
hypercenterC4⋊Q8#89137
hypocenterC109#1886
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. #16812699C4semidirect
16. #16812697C4semidirect
17. #16812697C4semidirect
20. C4⋊Q8×C109C4semidirect
92. C109#1886semidirect
105. C4⋊Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202960942
#202960192
D109⋊#1012
#202958972
C4⋊Q8×D1092
#1886109