Finite Group Databasebeta

← #28378365

Subgroups — #28378365

Order 13952.

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

normal subgroups only

This group has 246 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
1#20296047C211yesmaximal, characteristic, complemented
2#20296043C211yesmaximal, characteristic, complemented
3#20295876C212yesmaximal, complemented
4#20295874C212yesmaximal, complemented
5#20295494C211yesmaximal, characteristic
6#16812766—21no—
7C4⋊#11724786C2212yes—
8C22⋊#11724786—21no—
9C22⋊#11724786—21no—
10#16812754—21no—
11C4×#11724786C2212yes—
12C2×#13182029C411yescharacteristic
13#16812664C411yescharacteristic
14#16812664C2211yescharacteristic
15#16812661C411yescharacteristic
16#16812661C2211yescharacteristic
17#16812659—21no—
18#16812659—21no—
19#16812656—21no—
20C2×C4×Dic109C2211yescharacteristic
21C42×D109—21no—
22#117×C109C411yescharacteristic
23C2×#11724786—22no—
24C2×#11724786—22no—
25#13182029—22no—
26#13182029—22no—
27C2×Dic218C2×C411yescharacteristic
28C2×D436C2×C411yescharacteristic
29C2×C22⋊D109—21no—
30C22×Dic109D411yescharacteristic
31C22×Dic109D411yescharacteristic
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×C4×D109—21no—
35#13182008—21no—
36#13182008—21no—
37#13182006—21no—
38#13182006—21no—
39C4×Dic109—21no—
40C4×Dic109—21no—
41C4×Dic109C2×C411yescharacteristic
42C4×Dic109D411yescharacteristic
43C4×Dic109D411yescharacteristic
44C4×Dic109C2311yescharacteristic
45C22×C4×C109C2×C411yescharacteristic
46C4⋊C4×C109C2×C411yescharacteristic
47C4⋊C4×C109C2×C411yescharacteristic
48C22⋊C4×C109—21no—
49C42×C109—21no—
50C23×C109C22⋊C411yescharacteristic
51C22×D109—21no—
52C2×C4×C109—21no—
53C2×C4×C109—21no—
54C2×C4×C109—21no—
55C2×C4×C109—21no—
56C2×C4×C109C22⋊C411yescharacteristic
57C2×C4×C109C22×C411yescharacteristic
58C22⋊D109—24no—
59C2×Dic109—21no—
60C2×Dic109—22no—
61C2×Dic109—41no—
62C2×Dic109C22⋊C411yescharacteristic
63C2×Dic109C22⋊C411yescharacteristic
64C2×Dic109C2×D411yescharacteristic
65C2×Dic109C2×D411yescharacteristic
66D436—21no—
67D436M1612yes—
68C4×D109—24no—
69C4×D109—42no—
70C4×D109—42no—
71Dic218—21no—
72Dic218M1612yes—
73#11724786—42no—
74#11724786—42no—
75C22×C109—21no—
76C22×C109—21no—
77C22×C109—21no—
78C22×C109C2×C22⋊C411yescharacteristic
79C2×D109—22no—
80C2×D109—41no—
81C2×D109—41no—
82C4×C109—21no—
83C4×C109—41no—
84C4×C109—41no—
85C4×C109C2×M1611yescharacteristic
86C4×C109C2×M1611yescharacteristic
87Dic109—22no—
88Dic109—21no—
89Dic109—21no—
90Dic109—21no—
91Dic109#13512yes—
92C2×C109—41no—
93C2×C109#40711yescharacteristic
94C2×C109#41611yescharacteristic
95C2×C109#42111yescharacteristic
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—1091no—
107C4×D4—1091no—
108C4×D4—1091no—
109C4×D4—2181no—
110C4×D4—2181no—
111#117—2181no—
112#117#8913711yescharacteristic
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×Q8—1091no—
124C2×D4—1091no—
125C2×D4—2181no—
126C22×C4—1091no—
127C22×C4—1091no—
128C22×C4—2181no—
129C22×C4—2181no—
130C22×C4—2181no—
131C22×C4C2×#8913711yescharacteristic
132C2×C8—2182no—
133C2×C8—2182no—
134C4⋊C4—2181no—
135C4⋊C4—2181no—
136C4⋊C4C2×#8913711yescharacteristic
137C4⋊C4C2×#8913711yescharacteristic
138C22⋊C4—21no—
139C22⋊C4—2181no—
140C22⋊C4—2181no—
141C42—21no—
142C42—1091no—
143C42—1091no—
144C42—1091no—
145C42—1091no—
146C42—2181no—
147C42—2181no—
148C23—2181no—
149C23C22⋊#8913711yescharacteristic
150Q8—1092no—
151Q8—2181no—
152D4—1092no—
153D4—2184no—
154D4—2181no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—1091no—
160C2×C4—1091no—
161C2×C4—1091no—
162C2×C4—1091no—
163C2×C4—4362no—
164C2×C4—4362no—
165C2×C4—4361no—
166C2×C4—2184no—
167C2×C4—2182no—
168C2×C4—2181no—
169C2×C4C22⋊#8913711yescharacteristic
170C2×C4C22×#8913711yescharacteristic
171C8—4362no—
172C8—4362no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—4361no—
177C22—4361no—
178C22—2182no—
179C22C2×C22⋊#8913711yescharacteristic
180C4—21no—
181C4—41no—
182C4—41no—
183C4—1092no—
184C4—2182no—
185C4—2181no—
186C4—2181no—
187C4—2181no—
188C4D109⋊M1611yescharacteristic
189C4D109⋊M1611yescharacteristic
190C2—41no—
191C2—4362no—
192C2#2029599811yescharacteristic
193C2#2029601611yescharacteristic
194C2#2029602311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#117×C109C4
socleC22×C109C2×C22⋊C4
prime radicalC2×#13182029C4
cosocleC4×Dic109C23
hypercenter#117#89137
hypocenterC109#1488
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #20296047C2semidirect
2. #20296043C2semidirect
3. #20295876C2semidirect
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
#202960472
#202960432
#202958762
#202958742
#202954942
#1488109