Finite Group Databasebeta

← #28378332

Subgroups — #28378332

Order 13952.

312 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 78 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#20296045C211yesmaximal, characteristic, complemented
2#20296044C211yesmaximal, characteristic, complemented
3#20295874C212yesmaximal, complemented
4D4⋊#11724786C212yesmaximal, complemented
5C4×D4×D109C211yesmaximal, characteristic
6#16812766—21no—
7C4⋊#11724786C2212yescomplemented
8#16812756—21no—
9#16812756—21no—
10C4×#11724786—21no—
11C4×#11724786C2212yescomplemented
12C2×D4×D109C411yescharacteristic
13C22×C4×D109—21no—
14C4×D436C411yescharacteristic
15D4×Dic109C2211yescharacteristic
16#16812661C2211yescharacteristic
17C4×C22⋊D109—21no—
18#16812659—21no—
19C4⋊C4×D109C411yescharacteristic
20C22⋊C4×D109—21no—
21C42×D109C2211yescharacteristic
22C4×D4×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25C23×D109—21no—
26C2×D436C2×C411yescharacteristic
27C2×C22⋊D109—21no—
28D4×D109—22no—
29D4×D109C814yescomplemented
30C22×Dic109—21no—
31C2×C4×D109—21no—
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—44no—
35C2×C4×D109C2×C411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C2×C4×D109D411yescharacteristic
38C4⋊Dic109C2×C411yescharacteristic
39#13182008—21no—
40C22⋊Dic109—21no—
41#13182006—21no—
42#13182006—21no—
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109C2311yescharacteristic
46C2×D4×C109C2×C411yescharacteristic
47C22×C4×C109—21no—
48C4⋊C4×C109C2×C411yescharacteristic
49C22⋊C4×C109—21no—
50C42×C109C2×C411yescharacteristic
51C23×C109—21no—
52C22×D109—21no—
53C22×D109—24no—
54C22×D109—42no—
55C22×D109—42no—
56C22×D109C22⋊C411yescharacteristic
57D4×C109—21no—
58D4×C109C2×C812yes—
59C2×C4×C109—21no—
60C2×C4×C109—42no—
61C2×C4×C109C22⋊C411yescharacteristic
62C2×C4×C109C22⋊C411yescharacteristic
63C2×C4×C109C22×C411yescharacteristic
64C22⋊D109—24no—
65C2×Dic109—21no—
66C2×Dic109—42no—
67C2×Dic109C22⋊C411yescharacteristic
68C2×Dic109C2×D411yescharacteristic
69C2×Dic109C2×D411yescharacteristic
70D436—21no—
71D436C2×C812yes—
72C4×D109—22no—
73C4×D109—41no—
74C4×D109—42no—
75C4×D109—42no—
76C4×D109—42no—
77C4×D109C2×C812yes—
78C4×D109M1612yes—
79#11724786—42no—
80#11724786—42no—
81C22×C109—22no—
82C22×C109—41no—
83C22×C109—41no—
84C22×C109C2×C22⋊C411yescharacteristic
85C2×D109—21no—
86C2×D109—21no—
87C2×D109—22no—
88C2×D109—48no—
89C2×D109—41no—
90C2×D109—41no—
91C2×D109C22⋊C812yes—
92C4×C109—21no—
93C4×C109—21no—
94C4×C109—41no—
95C4×C109C22×C811yescharacteristic
96C4×C109C2×M1611yescharacteristic
97Dic109—21no—
98Dic109—41no—
99Dic109C22⋊C812yes—
100Dic109AGL(1,ℤ/8)12yes—
101C2×C109—42no—
102C2×C109C2×C22⋊C811yescharacteristic
103C2×C109#41811yescharacteristic
104C2×C109#42111yescharacteristic
105D109—22no—
106D109—42no—
107#1478—1091nomaximal, Sylow
108C109#147811yescharacteristic, complemented, Sylow
109C2×C4×D4—1091no—
110#431—1091no—
111#431—1091no—
112D4⋊C8—1092no—
113D4⋊C8—1092no—
114C22×D4—1091no—
115C23×C4—2181no—
116C4×D4—1091no—
117C4×D4—1091no—
118C4×D4—1091no—
119C4×D4—2181no—
120C4×D4—2181no—
121C4×D4#8913711yescharacteristic
122C2×C4⋊C4—1091no—
123C2×C22⋊C4—2181no—
124C2×C42—1091no—
125C4⋊C8—1092no—
126C4⋊C8—2181no—
127C22⋊C8—2181no—
128C22⋊C8—2181no—
129C4×C8—1092no—
130C4×C8—2181no—
131C24—2181no—
132C2×D4—1094no—
133C2×D4—1091no—
134C2×D4—2182no—
135C2×D4—2181no—
136C2×D4C2×#8913711yescharacteristic
137C22×C4—21no—
138C22×C4—1091no—
139C22×C4—1091no—
140C22×C4—1091no—
141C22×C4—4364no—
142C22×C4—2181no—
143C22×C4—2181no—
144C22×C4—2181no—
145C22×C4—2181no—
146C2×C8—2182no—
147C2×C8—2182no—
148C4⋊C4—1091no—
149C4⋊C4—2181no—
150C4⋊C4C2×#8913711yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—2181no—
153C22⋊C4—2181no—
154C22⋊C4—2181no—
155C42—1091no—
156C42—1091no—
157C42—1091no—
158C42C2×#8913711yescharacteristic
159C23—21no—
160C23—1091no—
161C23—4362no—
162C23—4362no—
163C23—2184no—
164C23—2181no—
165D4—21no—
166D4—1092no—
167D4—2184no—
168D4—2181no—
169D4D109⋊C812yes—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—1091no—
173C2×C4—1091no—
174C2×C4—1092no—
175C2×C4—1092no—
176C2×C4—1091no—
177C2×C4—4362no—
178C2×C4—4361no—
179C2×C4—4362no—
180C2×C4—4362no—
181C2×C4—4362no—
182C2×C4—2182no—
183C2×C4—2181no—
184C2×C4C22⋊#8913711yescharacteristic
185C2×C4C22⋊#8913711yescharacteristic
186C2×C4C22×#8913711yescharacteristic
187C8—4362no—
188C8—4362no—
189C22—22no—
190C22—41no—
191C22—41no—
192C22—1092no—
193C22—4368no—
194C22—4361no—
195C22—4361no—
196C22—2182no—
197C22—2181no—
198C22—2181no—
199C22C2×C22⋊#8913711yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—1092no—
204C4—1092no—
205C4—4361no—
206C4—2181no—
207C4C2×D109⋊C811yescharacteristic
208C4D109⋊M1611yescharacteristic
209C2—42no—
210C2—4362no—
211C2—2182no—
212C2D109⋊(C22⋊C8)11yescharacteristic
213C2#2029601811yescharacteristic
214C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC4×C109C22×C8
FrattiniC2×C4C22×#89137
FittingC4×D4×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×D4×D109C4
cosocleC4×Dic109C23
hypercenterC4×D4#89137
hypocenterC109#1478
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #20296045C2semidirect
2. #20296044C2semidirect
3. #20295874C2semidirect
4. D4⋊#11724786C2semidirect
7. C4⋊#11724786C22semidirect
11. C4×#11724786C22semidirect
29. D4×D109C8semidirect
108. C109#1478semidirect

Maximal subgroups

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

subgroupindex
#202960452
#202960442
#202958742
D4⋊#117247862
C4×D4×D1092
#1478109