Finite Group Databasebeta

← #28378349

Subgroups — #28378349

Order 13952.

234 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C2×C4⋊#11724786C211yesmaximal, characteristic, complemented
2C4×#13182038C211yesmaximal, characteristic, complemented
3Q8⋊#11724786C212yesmaximal, complemented
4#20295874C212yesmaximal, complemented
5#20295562C211yesmaximal, characteristic
6C2×#13182038—21no—
7C22×#11724786—21no—
8C4⋊#11724786—21no—
9C4⋊#11724786C2212yes—
10#16812754—21no—
11C4×#11724786C2212yes—
12#16812694—21no—
13#16812690C411yescharacteristic
14#16812688C411yescharacteristic
15#16812683—21no—
16#16812673C411yescharacteristic
17Q8×Dic109C2211yescharacteristic
18#16812661C2211yescharacteristic
19#16812659—21no—
20#16812657—21no—
21C2×C4×Dic109C2211yescharacteristic
22C22⋊Q8×C109C411yescharacteristic
23#13182038—24no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×#11724786—42no—
27C2×D436C2×C411yescharacteristic
28C2×C22⋊D109—21no—
29C22×Dic109D411yescharacteristic
30C22×Dic109D411yescharacteristic
31C2×C4×D109—21no—
32C4⋊Dic109—21no—
33C4⋊Dic109—21no—
34C4⋊Dic109C2×C411yescharacteristic
35#13182008—21no—
36#13182006—21no—
37#13182006—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C22×C4×C109C2×C411yescharacteristic
47C4⋊C4×C109—21no—
48C4⋊C4×C109C2×C411yescharacteristic
49C22⋊C4×C109—21no—
50C23×C109C22⋊C411yescharacteristic
51C22×D109—21no—
52Q8×C109—22no—
53C2×C4×C109—22no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—42no—
59C2×Dic109—22no—
60C2×Dic109—21no—
61C2×Dic109—21no—
62C2×Dic109—21no—
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C22⋊C411yescharacteristic
65C2×Dic109C2×D411yescharacteristic
66C2×Dic109C2×D411yescharacteristic
67D436—22no—
68C4×D109—41no—
69C4×D109—41no—
70#11724786—24no—
71#11724786—42no—
72C22×C109—21no—
73C22×C109—21no—
74C22×C109#10412yes—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—41no—
77C2×D109—41no—
78C2×D109—41no—
79C4×C109—21no—
80C4×C109—41no—
81C4×C109—41no—
82C4×C109#13112yes—
83Dic109—21no—
84Dic109—21no—
85Dic109—21no—
86Dic109—41no—
87Dic109AGL(1,ℤ/8)11yescharacteristic
88Dic109#13711yescharacteristic
89C2×C109—22no—
90C2×C109#40811yescharacteristic
91C2×C109#41711yescharacteristic
92C2×C109C2×#10411yescharacteristic
93D109—81no—
94#1483—1091nomaximal, Sylow
95C109#148311yescharacteristic, complemented, Sylow
96#529—1091no—
97C2×C4⋊C8—1091no—
98C4×M16—1091no—
99Q8⋊C8—1092no—
100D4⋊C8—1092no—
101C2×M16—2181no—
102C22×C8—2181no—
103#126—2181no—
104#125—1091no—
105#124—1091no—
106#123—2181no—
107C22⋊Q8#8913711yescharacteristic
108#121—1091no—
109C4×Q8—1091no—
110C4×D4—1091no—
111C4×D4—2181no—
112#117—2181no—
113C2×C42—1091no—
114C4⋊C8—1092no—
115C4⋊C8—2181no—
116#97—2181no—
117C4×C8—1092no—
118C2×Q8C2×#8913711yescharacteristic
119C2×D4—1091no—
120C2×D4—2181no—
121C22×C4—1091no—
122C22×C4—1091no—
123C22×C4—2181no—
124C22×C4C2×#8913711yescharacteristic
125M16—2184no—
126C2×C8—4362no—
127C2×C8—2182no—
128C2×C8—2182no—
129C4⋊C4—21no—
130C4⋊C4—1091no—
131C4⋊C4—2181no—
132C4⋊C4—2181no—
133C4⋊C4—2181no—
134C4⋊C4C2×#8913711yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—2181no—
137C22⋊C4—2181no—
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C42—1091no—
141C42—1091no—
142C42—1091no—
143C42—1091no—
144C42—2181no—
145C23—2181no—
146C23C22⋊#8913711yescharacteristic
147Q8—22no—
148D4—4362no—
149D4—2182no—
150C2×C4—22no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1091no—
154C2×C4—1091no—
155C2×C4—1091no—
156C2×C4—1091no—
157C2×C4—4361no—
158C2×C4—4361no—
159C2×C4—2181no—
160C2×C4—2181no—
161C2×C4—2181no—
162C2×C4—2182no—
163C2×C4C22⋊#8913711yescharacteristic
164C2×C4C22×#8913711yescharacteristic
165C8—4362no—
166C8—2184no—
167C22—21no—
168C22—21no—
169C22—4361no—
170C22—4361no—
171C22—4361no—
172C22#1681276412yes—
173C22C2×C22⋊#8913711yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—1091no—
178C4—1091no—
179C4—4361no—
180C4—2181no—
181C4—2181no—
182C4—2181no—
183C4#1681278612yes—
184C2—22no—
185C2—8721no—
186C2#2029599911yescharacteristic
187C2#2029601711yescharacteristic
188C2C2×#1681276411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC22⋊Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radical#16812673C4
cosocleC4×Dic109C23
hypercenterC22⋊Q8#89137
hypocenterC109#1483
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11724786C2semidirect
2. C4×#13182038C2semidirect
3. Q8⋊#11724786C2semidirect
4. #20295874C2semidirect
95. C109#1483semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#117247862
C4×#131820382
Q8⋊#117247862
#202958742
#202955622
#1483109