Finite Group Databasebeta

← #28379296

Subgroups — #28379296

Order 13952.

234 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 54 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#20296012C211yesmaximal, characteristic
2#20296005C211yesmaximal, characteristic
3#20295929C214yesmaximal, complemented
4#20295602C211yesmaximal, characteristic
5D109⋊M16—21no—
6#16812778—21no—
7#16812760—21no—
8#16812759C2212yes—
9#16812758—21no—
10#16812757C2212yes—
11C2×#13182029C2211yescharacteristic
12C22×Dic218C411yescharacteristic, complemented
13#16812699—21no—
14#16812687—21no—
15#16812683C412yescomplemented
16#16812683C2212yes—
17#16812679—21no—
18#16812679—21no—
19#117×C109C411yescharacteristic, complemented
20#13182039—41no—
21#13182038—22no—
22D109⋊C8—41no—
23C4⋊#89137—41no—
24C22⋊#89137—22no—
25C4×#89137—41no—
26#13182029—41no—
27#13182029—41no—
28C2×Dic218—21no—
29C2×Dic218—21no—
30C2×Dic218—41no—
31C2×Dic218—41no—
32C2×Dic218D411yescharacteristic
33C2×D436D411yescharacteristic
34C2×C22⋊D109C2×C411yescharacteristic
35C2×C22⋊D109C2311yescharacteristic
36C22×Dic109C2×C412yes—
37C2×C4×D109D411yescharacteristic
38C2×C4×D109D411yescharacteristic
39C4⋊Dic109—22no—
40C4⋊Dic109—22no—
41#13182006—22no—
42#13182006—22no—
43C22×C4×C109C2×C411yescharacteristic
44C4⋊C4×C109—21no—
45C22⋊C4×C109C2×C412yes—
46C42×C109—21no—
47C23×C109C22×C411yescharacteristic
48C22×D109C22⋊C411yescharacteristic
49C22×D109C2×D411yescharacteristic
50C2×#89137—42no—
51C2×C4×C109—21no—
52C2×C4×C109—21no—
53C2×C4×C109—22no—
54C2×C4×C109C22⋊C411yescharacteristic
55C2×C4×C109C22⋊C411yescharacteristic
56C22⋊D109—41no—
57C22⋊D109—41no—
58C2×Dic109—22no—
59C2×Dic109—42no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62D436—41no—
63C4×D109—21no—
64C4×D109—21no—
65C4×D109—21no—
66C4×D109—21no—
67Dic218—41no—
68Dic218—42no—
69Dic218—41no—
70Dic218—41no—
71#11724786—42no—
72C22×C109—21no—
73C22×C109—41no—
74C22×C109C2×C22⋊C411yescharacteristic
75C2×D109—21no—
76C2×D109—21no—
77C2×D109—41no—
78C2×D109—41no—
79#89137—82no—
80C4×C109—21no—
81C4×C109—42no—
82C4×C109#9911yescharacteristic
83C4×C109#9911yescharacteristic
84Dic109—21no—
85Dic109—21no—
86Dic109—42no—
87C2×C109—21no—
88C2×C109—41no—
89C2×C109C2×#9911yescharacteristic
90D109—41no—
91D109—41no—
92#2123—1091nomaximal, Sylow
93C109#212311yescharacteristic, complemented, Sylow
94#536—1091no—
95#413—1091no—
96#410—1091no—
97#352—1094no—
98C2×#41—1091no—
99C22×Q8—1091no—
100C2×M16—2181no—
101C4⋊Q8—2181no—
102#124—2181no—
103#123—1092no—
104#123—1092no—
105C22⋊Q8—2181no—
106C22⋊Q8—2181no—
107#117—2181no—
108#117#8913711yescharacteristic, complemented
109#101—2181no—
110#100—1092no—
111#99—1092no—
112#99—2181no—
113#41—4361no—
114#41—4361no—
115C2×Q8—1091no—
116C2×Q8—4361no—
117C2×Q8—4361no—
118C2×Q8—2181no—
119C2×Q8—2181no—
120C2×D4—1091no—
121C2×D4—1091no—
122C2×D4—1091no—
123C22×C4—1091no—
124C22×C4—1091no—
125C22×C4—1092no—
126C22×C4C2×#8913711yescharacteristic
127M16—4361no—
128M16—2182no—
129C2×C8—4361no—
130C4⋊C4—21no—
131C4⋊C4—4361no—
132C4⋊C4—2182no—
133C4⋊C4—2182no—
134C22⋊C4—2182no—
135C22⋊C4—2182no—
136C22⋊C4—2182no—
137C22⋊C4C2×#8913712yes—
138C42—21no—
139C42—4361no—
140C23—1091no—
141C23—1091no—
142C23C22×#8913711yescharacteristic
143Q8—4362no—
144Q8—4361no—
145Q8—4361no—
146Q8—4361no—
147D4—4361no—
148D4—4361no—
149D4—4361no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—22no—
153C2×C4—1091no—
154C2×C4—1091no—
155C2×C4—4362no—
156C2×C4—4362no—
157C2×C4—2182no—
158C2×C4—2181no—
159C2×C4—2181no—
160C2×C4—2181no—
161C2×C4—2181no—
162C2×C4C22⋊#8913711yescharacteristic
163C2×C4C22⋊#8913711yescharacteristic
164C8—4362no—
165C22—21no—
166C22—41no—
167C22—4361no—
168C22—4361no—
169C22—2181no—
170C22—2181no—
171C22C2×C22⋊#8913711yescharacteristic
172C4—21no—
173C4—42no—
174C4—8722no—
175C4—4362no—
176C4—2181no—
177C4—2181no—
178C4#1681275811yescharacteristic
179C4#1681275811yescharacteristic
180C2—21no—
181C2—41no—
182C2—4361no—
183C2—4361no—
184C2C2×#1681275811yescharacteristic
subgroupG/H
centerC2C2×#16812758
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
Fitting#117×C109C4
socleC2×C109C2×#99
prime radicalC2×#13182029C22
cosocleC2×C22⋊D109C23
hypercenter#117#89137
hypocenterC109#2123
LCSG ▷ C23×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
3. #20295929C2semidirect
12. C22×Dic218C4semidirect
15. #16812683C4semidirect
19. #117×C109C4semidirect
93. C109#2123semidirect
108. #117#89137semidirect

Maximal subgroups

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

subgroupindex
#202960122
#202960052
#202959292
#202956022
#2123109