Finite Group Databasebeta

← #28378540

Subgroups — #28378540

Order 13952.

344 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 70 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#20296044C211yesmaximal, characteristic, complemented
2#20296031C211yesmaximal, characteristic, complemented
3#20295884C214yesmaximal, complemented
4#127×D109C211yesmaximal, characteristic
5C2×#13182039—21no—
6#16812766—21no—
7#16812766C2212yescomplemented
8#16812766C2212yescomplemented
9#16812756—21no—
10C4×#11724786—21no—
11C2×D4×D109—21no—
12C2×D4×D109—21no—
13C2×D4×D109C412yes—
14#16812696C411yescharacteristic
15#16812695—21no—
16#16812695—21no—
17#16812695C2212yes—
18C42×D109C2211yescharacteristic
19#127×C109C411yescharacteristic
20#13182039—42no—
21C2×#11724786—22no—
22C2×#11724786—22no—
23C23×D109—22no—
24C2×D436—21no—
25C2×D436—21no—
26C2×D436C2×C412yes—
27C2×C22⋊D109—22no—
28C2×C22⋊D109—22no—
29C2×C22⋊D109—22no—
30D4×D109—44no—
31D4×D109—44no—
32D4×D109—42no—
33D4×D109—42no—
34C2×C4×D109C2×C411yescharacteristic
35C2×C4×D109D411yescharacteristic
36C2×C4×D109D411yescharacteristic
37C4×Dic109D411yescharacteristic
38C4×Dic109D411yescharacteristic
39C4×Dic109C2311yescharacteristic
40C2×D4×C109—21no—
41C2×D4×C109—21no—
42C2×D4×C109C2×C412yes—
43C42×C109C2×C411yescharacteristic
44C23×C109—22no—
45C22×D109—22no—
46C22×D109—44no—
47C22×D109—44no—
48C22×D109—44no—
49C22×D109C22⋊C411yescharacteristic
50D4×C109—42no—
51D4×C109—42no—
52D4×C109—42no—
53C2×C4×C109C22⋊C411yescharacteristic
54C2×C4×C109C22⋊C411yescharacteristic
55C2×C4×C109C22×C411yescharacteristic
56C22⋊D109—44no—
57C22⋊D109—42no—
58C22⋊D109—42no—
59C22⋊D109—44no—
60C2×Dic109C22⋊C411yescharacteristic
61C2×Dic109C2×D411yescharacteristic
62C2×Dic109C2×D411yescharacteristic
63D436—42no—
64D436—42no—
65D436—42no—
66C4×D109—22no—
67C4×D109—22no—
68C4×D109D812yes—
69C4×D109SD1612yes—
70#11724786—42no—
71#11724786—42no—
72C22×C109—42no—
73C22×C109—42no—
74C22×C109—42no—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—21no—
77C2×D109—21no—
78C2×D109—42no—
79C2×D109—42no—
80C2×D109—42no—
81C2×D109—88no—
82C2×D109#10212yes—
83C4×C109—21no—
84C4×C109—21no—
85C4×C109#10212yes—
86Dic109#10012yes—
87Dic109C2×D811yescharacteristic
88Dic109C2×SD1611yescharacteristic
89Dic109AGL(1,ℤ/8)12yes—
90C2×C109—82no—
91C2×C109C2×#10011yescharacteristic
92C2×C109C2×#10211yescharacteristic
93C2×C109#41811yescharacteristic
94D109—22no—
95D109—82no—
96#1545—1091nomaximal, Sylow
97C109#154511yescharacteristic, complemented, Sylow
98C2×#127—1091no—
99#431—1091no—
100#423—1091no—
101#331—1094no—
102C22×D4—1092no—
103C22×D4—2181no—
104C22×D4—2181no—
105C2×M16—2181no—
106#127—1092no—
107#127—1091no—
108#127—2181no—
109#127—2181no—
110#127#8913711yescharacteristic
111C2×C42—1091no—
112C4⋊C8—1092no—
113C4⋊C8—1092no—
114C4⋊C8—2181no—
115C22⋊C8—2181no—
116C4×C8—2181no—
117C24—2182no—
118C2×D4—21no—
119C2×D4—21no—
120C2×D4—1092no—
121C2×D4—4362no—
122C2×D4—4362no—
123C2×D4—4364no—
124C2×D4—4364no—
125C2×D4—2182no—
126C2×D4—2182no—
127C2×D4—2182no—
128C2×D4—2181no—
129C2×D4—2181no—
130C2×D4C2×#8913712yes—
131C22×C4—1091no—
132C22×C4—1091no—
133C22×C4—1091no—
134M16—4362no—
135C2×C8—2182no—
136C2×C8—2182no—
137C42—1091no—
138C42—1091no—
139C42—1091no—
140C42C2×#8913711yescharacteristic
141C23—22no—
142C23—1091no—
143C23—4364no—
144C23—4364no—
145C23—4364no—
146C23—2182no—
147D4—42no—
148D4—42no—
149D4—42no—
150D4—4362no—
151D4—4362no—
152D4—4362no—
153D4—4362no—
154D4—4364no—
155D4—4364no—
156D4—4362no—
157C2×C4—1091no—
158C2×C4—1091no—
159C2×C4—1091no—
160C2×C4—1092no—
161C2×C4—1092no—
162C2×C4—2182no—
163C2×C4—2182no—
164C2×C4C22⋊#8913711yescharacteristic
165C2×C4C22⋊#8913711yescharacteristic
166C2×C4C22×#8913711yescharacteristic
167C8—4362no—
168C8—4362no—
169C22—42no—
170C22—42no—
171C22—42no—
172C22—8728no—
173C22—1092no—
174C22—4362no—
175C22—4362no—
176C22—4362no—
177C22—2181no—
178C22—2181no—
179C22C2×C22⋊#8913711yescharacteristic
180C4—21no—
181C4—21no—
182C4—1092no—
183C4—1091no—
184C4—1091no—
185C4—1092no—
186C4#1681276112yes—
187C2—82no—
188C2—8722no—
189C2—2182no—
190C2D109⋊#10011yescharacteristic
191C2C2×#1681276111yescharacteristic
192C2#2029601811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#89137
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#127×C109C4
socleC22×C109C2×C22⋊C4
prime radical#127×D109C2
cosocleC4×Dic109C23
hypercenter#127#89137
hypocenterC109#1545
LCSG ▷ C2×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #20296044C2semidirect
2. #20296031C2semidirect
3. #20295884C2semidirect
7. #16812766C22semidirect
8. #16812766C22semidirect
97. C109#1545semidirect

Maximal subgroups

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

subgroupindex
#202960442
#202960312
#202958842
#127×D1092
#1545109