Finite Group Databasebeta

← #28361665

Subgroups — #28361665

Order 13952.

238 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 59 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#20295575C211yesmaximal, characteristic
2#20295081C212yesmaximal, complemented
3#20294766C211yesmaximal, characteristic, complemented
4#20294765C212yesmaximal, complemented
5#329×C109C211yesmaximal, characteristic, complemented
6C2×#13182030C411yescharacteristic
7C2×#13182028C411yescharacteristic
8#16812697C411yescharacteristic
9#16812695C411yescharacteristic
10#16812687C2211yescharacteristic
11#16812672—22no—
12#16812659—22no—
13C42×D109C2211yescharacteristic
14#16812628—22no—
15#16812611—22no—
16#16812610C2212yes—
17#124×C109C2211yescharacteristic
18#97×C109C2212yes—
19#13182030—42no—
20#13182028—42no—
21C2×Dic218C2×C411yescharacteristic
22C2×D436—21no—
23C2×D436C2×C411yescharacteristic
24C2×C22⋊D109—21no—
25C2×C22⋊D109—22no—
26C22×Dic109—21no—
27C2×C4×D109—21no—
28C2×C4×D109C2×C411yescharacteristic
29C2×C4×D109D412yes—
30C2×#11724784—22no—
31#13182008—22no—
32#13182006—22no—
33C4×Dic109C2×C411yescharacteristic
34C4×Dic109D412yes—
35C2×Q8×C109C2×C411yescharacteristic
36C2×D4×C109C2×C411yescharacteristic
37C2×C8×C109—22no—
38C22⋊C4×C109—22no—
39C42×C109C2311yescharacteristic
40C23×C109—21no—
41C22×D109—21no—
42C22×D109C22⋊C411yescharacteristic
43Q8×C109—41no—
44D4×C109—41no—
45C2×C4×C109—21no—
46C2×C4×C109C22×C411yescharacteristic
47C2×C4×C109C2×D412yes—
48C22⋊D109—44no—
49C22⋊D109—42no—
50C2×Dic109—21no—
51C2×Dic109—42no—
52C2×Dic109C22⋊C412yes—
53C2×Dic109C22⋊C411yescharacteristic
54D436—41no—
55D436—42no—
56C4×D109—22no—
57C4×D109—42no—
58C4×D109—42no—
59Dic218—41no—
60C8×C109—42no—
61#11724784—42no—
62C22×C109—41no—
63C22×C109—42no—
64C22×C109C2×C22⋊C411yescharacteristic
65C2×D109—21no—
66C2×D109—22no—
67C2×D109—41no—
68C2×D109—42no—
69C4×C109—21no—
70C4×C109—22no—
71C4×C109—41no—
72Dic109—22no—
73Dic109—41no—
74Dic109#10012yes—
75C2×C109—81no—
76C2×C109C2×#10011yescharacteristic
77C2×C109#42112yes—
78D109—41no—
79D109—81no—
80#1536—1091nomaximal, Sylow
81C109#153611yescharacteristic, complemented, Sylow
82#532—1091no—
83#432—1092no—
84#329—1091no—
85#329—1092no—
86#329D10911yescharacteristic, complemented
87C2×#41—1091no—
88C2×#41—1091no—
89C4⋊Q8—1091no—
90#127—1091no—
91#124—1091no—
92#124C2×D10911yescharacteristic
93#121—2182no—
94C4×D4—2182no—
95C2×C42—1091no—
96C4⋊C8—2182no—
97C22⋊C8—2182no—
98#97—1092no—
99#97C2×D10912yes—
100#41—4362no—
101#41—4362no—
102C2×Q8—1091no—
103C2×Q8C4×D10911yescharacteristic
104C2×D4—1091no—
105C2×D4—2181no—
106C2×D4—2182no—
107C2×D4—2181no—
108C2×D4C4×D10911yescharacteristic
109C22×C4—1092no—
110C22×C4—1091no—
111C22×C4—2181no—
112C22×C4—2181no—
113C2×C8—22no—
114C2×C8—2182no—
115C4⋊C4—2182no—
116C22⋊C4—22no—
117C22⋊C4—2182no—
118C42—1091no—
119C42—1092no—
120C42C22×D10911yescharacteristic
121C23—21no—
122C23—1091no—
123C23—2181no—
124Q8—41no—
125Q8—4361no—
126D4—41no—
127D4—4361no—
128D4—4362no—
129D4—4362no—
130D4—4364no—
131C2×C4—21no—
132C2×C4—1091no—
133C2×C4—1092no—
134C2×C4—4362no—
135C2×C4—4362no—
136C2×C4—4362no—
137C2×C4—2182no—
138C2×C4—2181no—
139C2×C4C2×C4×D10911yescharacteristic
140C2×C4D4×D10912yes—
141C8—42no—
142C8—4362no—
143C22—41no—
144C22—42no—
145C22—4361no—
146C22—4362no—
147C22—2181no—
148C22—2182no—
149C22C22⋊C4×D10911yescharacteristic
150C4—21no—
151C4—22no—
152C4—41no—
153C4—1092no—
154C4—4361no—
155C4—2182no—
156C2—81no—
157C2—8721no—
158C2—4361no—
159C2#100×D10911yescharacteristic
160C2#2029504112yes—
subgroupG/H
centerC22C22⋊C4×D109
commutatorC2×C4×C109C22×C4
FrattiniC42C22×D109
Fitting#329×C109C2
socleC22×C109C2×C22⋊C4
prime radical#20295575C2
cosocleC42×C109C23
hypercenter#329D109
hypocenterC109#1536
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20295081C2semidirect
3. #20294766C2semidirect
4. #20294765C2semidirect
5. #329×C109C2semidirect
81. C109#1536semidirect
86. #329D109semidirect

Maximal subgroups

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

subgroupindex
#202955752
#202950812
#202947662
#202947652
#329×C1092
#1536109