Finite Group Databasebeta

← #28378375

Subgroups — #28378375

Order 13952.

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

normal subgroups only

This group has 252 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#20296048C211yesmaximal, characteristic
2C4×#13182039C211yesmaximal, characteristic
3#20295876C212yesmaximal, complemented
4Q8⋊#11724786C212yesmaximal, complemented
5C4×Q8×D109C211yesmaximal, characteristic
6C2×#13182039—21no—
7C4⋊#11724786C2212yes—
8#16812756—21no—
9#16812754—21no—
10#16812754—21no—
11C4×#11724786C2212yes—
12C2×Q8×D109C411yescharacteristic
13Q8×Dic109C2211yescharacteristic
14C4×Dic218—21no—
15C4×Dic218C411yescharacteristic
16#16812664—21no—
17#16812664C2211yescharacteristic
18C4⋊C4×D109—21no—
19C4⋊C4×D109C411yescharacteristic
20C42×D109—21no—
21C42×D109C2211yescharacteristic
22C4×Q8×C109C411yescharacteristic
23#13182039—24no—
24C2×#11724786—22no—
25C2×#11724786—22no—
26C2×Dic218—21no—
27C2×Dic218C2×C411yescharacteristic
28Q8×D109—22no—
29Q8×D109—22no—
30C2×C4×D109—21no—
31C2×C4×D109—21no—
32C2×C4×D109C2×C411yescharacteristic
33C2×C4×D109D411yescharacteristic
34C2×C4×D109D411yescharacteristic
35C4⋊Dic109—21no—
36C4⋊Dic109C2×C411yescharacteristic
37#13182008—21no—
38#13182008—21no—
39#13182008—21no—
40C4×Dic109—21no—
41C4×Dic109—21no—
42C4×Dic109—21no—
43C4×Dic109D411yescharacteristic
44C4×Dic109D411yescharacteristic
45C4×Dic109C2311yescharacteristic
46C2×Q8×C109C2×C411yescharacteristic
47C4⋊C4×C109—21no—
48C4⋊C4×C109C2×C411yescharacteristic
49C42×C109—21no—
50C42×C109C2×C411yescharacteristic
51C22×D109C22⋊C411yescharacteristic
52Q8×C109—21no—
53Q8×C109M1612yescomplemented
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109—21no—
61C2×Dic109C22⋊C411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63C2×Dic109C2×D411yescharacteristic
64C4×D109—24no—
65C4×D109—22no—
66C4×D109—21no—
67C4×D109—21no—
68C4×D109—22no—
69C4×D109—42no—
70Dic218—24no—
71Dic218—21no—
72Dic218M1612yescomplemented
73#11724786—24no—
74#11724786—42no—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—21no—
77C2×D109—21no—
78C2×D109#10412yes—
79C4×C109—22no—
80C4×C109—21no—
81C4×C109—21no—
82C4×C109—41no—
83C4×C109C2×M1611yescharacteristic
84C4×C109C2×M1611yescharacteristic
85Dic109—21no—
86Dic109—22no—
87Dic109—21no—
88Dic109—41no—
89Dic109#13712yes—
90C2×C109#40711yescharacteristic
91C2×C109#41911yescharacteristic
92C2×C109C2×#10411yescharacteristic
93D109—22no—
94#1491—1091nomaximal, Sylow
95C109#149111yescharacteristic, complemented, Sylow
96C2×C4×Q8—1091no—
97#432—1091no—
98C4×M16—1091no—
99Q8⋊C8—1092no—
100Q8⋊C8—1092no—
101C22×Q8—1091no—
102C2×M16—2181no—
103C4×Q8—1091no—
104C4×Q8—1091no—
105C4×Q8—1091no—
106C4×Q8—2181no—
107C4×Q8—2181no—
108C4×Q8#8913711yescharacteristic
109C2×C4⋊C4—1091no—
110C2×C4⋊C4—2181no—
111C2×C42—1091no—
112C2×C42—2181no—
113C4⋊C8—1092no—
114C22⋊C8—2181no—
115#97—2181no—
116#97—2181no—
117C4×C8—1092no—
118C2×Q8—1091no—
119C2×Q8—2181no—
120C2×Q8—2182no—
121C2×Q8—2182no—
122C2×Q8C2×#8913711yescharacteristic
123C22×C4—1091no—
124C22×C4—1091no—
125C22×C4—1091no—
126C22×C4—2181no—
127C22×C4—2181no—
128M16—2184no—
129C2×C8—2182no—
130C2×C8—2182no—
131C4⋊C4—21no—
132C4⋊C4—1091no—
133C4⋊C4—2181no—
134C4⋊C4—2181no—
135C4⋊C4—2181no—
136C4⋊C4—2181no—
137C4⋊C4C2×#8913711yescharacteristic
138C42—21no—
139C42—1091no—
140C42—1091no—
141C42—1091no—
142C42—2181no—
143C42—2181no—
144C42—2181no—
145C42C2×#8913711yescharacteristic
146C23—1091no—
147Q8—21no—
148Q8—1092no—
149Q8—2184no—
150Q8—2181no—
151Q8#1318203912yescomplemented
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—1091no—
155C2×C4—1091no—
156C2×C4—1091no—
157C2×C4—4362no—
158C2×C4—2182no—
159C2×C4—2182no—
160C2×C4—2184no—
161C2×C4—2181no—
162C2×C4—2181no—
163C2×C4—2181no—
164C2×C4—2181no—
165C2×C4C22⋊#8913711yescharacteristic
166C2×C4C22⋊#8913711yescharacteristic
167C2×C4C22×#8913711yescharacteristic
168C8—4362no—
169C8—2184no—
170C22—1092no—
171C22—2181no—
172C22—2181no—
173C22C2×C22⋊#8913711yescharacteristic
174C4—22no—
175C4—21no—
176C4—21no—
177C4—41no—
178C4—1092no—
179C4—4361no—
180C4—2181no—
181C4—2182no—
182C4—2181no—
183C4D109⋊M1611yescharacteristic
184C4C2×#1318203911yescharacteristic
185C2—2182no—
186C2#2029599711yescharacteristic
187C2#2029601911yescharacteristic
188C2D109⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC22×D109C22⋊C4
cosocleC4×Dic109C23
hypercenterC4×Q8#89137
hypocenterC109#1491
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20295876C2semidirect
4. Q8⋊#11724786C2semidirect
53. Q8×C109M16semidirect
72. Dic218M16semidirect
95. C109#1491semidirect
151. Q8#13182039semidirect

Maximal subgroups

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

subgroupindex
#202960482
C4×#131820392
#202958762
Q8⋊#117247862
C4×Q8×D1092
#1491109