Finite Group Databasebeta

← #28378366

Subgroups — #28378366

Order 13952.

246 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 66 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, complemented
2#20296045C211yesmaximal, characteristic, complemented
3Q8⋊#11724786C212yesmaximal, complemented
4#20295874C212yesmaximal, complemented
5C4×#13182030C211yesmaximal, characteristic
6C4⋊#11724786—21no—
7C4⋊#11724786C2212yes—
8#16812756—21no—
9#16812756—21no—
10#16812754—21no—
11C4×#11724786C2212yes—
12C2×#13182030C411yescharacteristic
13Q8×Dic109C2211yescharacteristic
14C4×D436—21no—
15C4×D436C411yescharacteristic
16#16812661—21no—
17#16812661C2211yescharacteristic
18#16812657—21no—
19#16812657C411yescharacteristic
20C42×D109—21no—
21C42×D109C2211yescharacteristic
22C4×Q8×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25#13182030—22no—
26#13182030—22no—
27C2×D436—21no—
28C2×D436C2×C411yescharacteristic
29C2×C4×D109—21no—
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#13182006—21no—
38#13182006—21no—
39#13182006—21no—
40C4×Dic109—21no—
41C4×Dic109—21no—
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C2×Q8×C109C2×C411yescharacteristic
46C4⋊C4×C109—21no—
47C4⋊C4×C109C2×C411yescharacteristic
48C42×C109—21no—
49C42×C109C2×C411yescharacteristic
50C22×D109—21no—
51C22×D109C22⋊C411yescharacteristic
52Q8×C109—21no—
53Q8×C109M1612yes—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22⋊C411yescharacteristic
58C2×C4×C109C22×C411yescharacteristic
59C2×Dic109—21no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63D436—24no—
64D436—21no—
65D436M1612yes—
66C4×D109—24no—
67C4×D109—21no—
68C4×D109—21no—
69C4×D109—22no—
70C4×D109—41no—
71C4×D109—42no—
72C4×D109—42no—
73#11724786—42no—
74#11724786—42no—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—21no—
77C2×D109—22no—
78C2×D109—21no—
79C2×D109—21no—
80C2×D109—41no—
81C2×D109—41no—
82C4×C109—22no—
83C4×C109—21no—
84C4×C109—21no—
85C4×C109—41no—
86C4×C109C2×M1611yescharacteristic
87C4×C109C2×M1611yescharacteristic
88Dic109—21no—
89Dic109—21no—
90Dic109—41no—
91Dic109#13512yes—
92C2×C109#40711yescharacteristic
93C2×C109#41611yescharacteristic
94C2×C109#42111yescharacteristic
95D109—41no—
96D109—42no—
97#1488—1091nomaximal, Sylow
98C109#148811yescharacteristic, complemented, Sylow
99C4×#41—1091no—
100#432—1091no—
101#431—1091no—
102Q8⋊C8—1092no—
103D4⋊C8—1092no—
104C2×#41—1091no—
105C4×Q8—1091no—
106C4×Q8#8913711yescharacteristic
107C4×D4—1091no—
108C4×D4—1091no—
109C4×D4—2181no—
110C4×D4—2181no—
111#117—1091no—
112#117—2181no—
113C2×C42—1091no—
114C2×C42—2181no—
115C4⋊C8—1092no—
116C4⋊C8—2181no—
117C22⋊C8—2181no—
118C22⋊C8—2181no—
119#97—2181no—
120C4×C8—1092no—
121#41—2182no—
122#41—2182no—
123C2×Q8C2×#8913711yescharacteristic
124C2×D4—1091no—
125C2×D4—2181no—
126C22×C4—1091no—
127C22×C4—1091no—
128C22×C4—1091no—
129C22×C4—2181no—
130C22×C4—2181no—
131C22×C4—2181no—
132C2×C8—2182no—
133C2×C8—2182no—
134C4⋊C4—21no—
135C4⋊C4—1091no—
136C4⋊C4—2181no—
137C4⋊C4C2×#8913711yescharacteristic
138C22⋊C4—2181no—
139C22⋊C4—2181no—
140C22⋊C4—2181no—
141C42—21no—
142C42—1091no—
143C42—1091no—
144C42—1091no—
145C42—2181no—
146C42—2181no—
147C42C2×#8913711yescharacteristic
148C23—1091no—
149C23—2181no—
150Q8—21no—
151Q8#1318203912yes—
152D4—1092no—
153D4—2184no—
154D4—2181no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—1091no—
158C2×C4—1091no—
159C2×C4—1091no—
160C2×C4—4362no—
161C2×C4—4361no—
162C2×C4—4362no—
163C2×C4—2182no—
164C2×C4—2184no—
165C2×C4—2181no—
166C2×C4—2181no—
167C2×C4—2181no—
168C2×C4C22⋊#8913711yescharacteristic
169C2×C4C22⋊#8913711yescharacteristic
170C2×C4C22×#8913711yescharacteristic
171C8—4362no—
172C8—4362no—
173C22—4361no—
174C22—4361no—
175C22—2182no—
176C22—2181no—
177C22—2181no—
178C22—2181no—
179C22C2×C22⋊#8913711yescharacteristic
180C4—22no—
181C4—21no—
182C4—21no—
183C4—41no—
184C4—1092no—
185C4—4361no—
186C4—2181no—
187C4—2181no—
188C4D109⋊M1611yescharacteristic
189C4C2×#1318203911yescharacteristic
190C2—4362no—
191C2—4361no—
192C2#2029599711yescharacteristic
193C2#2029601611yescharacteristic
194C2#2029602511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4×Q8×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#13182030C4
cosocleC4×Dic109C23
hypercenterC4×Q8#89137
hypocenterC109#1488
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
1. #20296048C2semidirect
2. #20296045C2semidirect
3. Q8⋊#11724786C2semidirect
4. #20295874C2semidirect
98. C109#1488semidirect

Maximal subgroups

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

subgroupindex
#202960482
#202960452
Q8⋊#117247862
#202958742
C4×#131820302
#1488109