Finite Group Databasebeta

← C2×#20295928 #28379280

Subgroups — C2×#20295928 #28379280

Order 13952.

278 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 58 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
1C2×#16812759C211yesmaximal, characteristic
2C2×#16812757C211yesmaximal, characteristic
3#20295928C214yesmaximal, direct product factor
4C2×#16812682C211yesmaximal, characteristic
5C2×#13182038—21no—
6C2×C22⋊#89137—21no—
7#16812759—21no—
8#16812759C2212yes—
9#16812757—21no—
10#16812757C2212yes—
11C22×C22⋊D109C2211yescharacteristic
12#16812682—21no—
13#16812682—21no—
14#16812682C412yescomplemented
15#16812682C2212yes—
16C2×#13182008—21no—
17C2×C22⋊Dic109C411yescharacteristic, complemented
18C2×#13182006—21no—
19C23×C4×C109C411yescharacteristic, complemented
20C22×#89137—41no—
21#13182038—22no—
22#13182038—41no—
23C2×#11724786—41no—
24C22⋊#89137—22no—
25C22⋊#89137—41no—
26C23×D109D411yescharacteristic
27C2×C22⋊D109—41no—
28C2×C22⋊D109—41no—
29C2×C22⋊D109C2×C411yescharacteristic
30C2×C22⋊D109D411yescharacteristic
31C2×C22⋊D109D411yescharacteristic
32C2×C22⋊D109C2311yescharacteristic
33C22×Dic109—21no—
34C22×Dic109D411yescharacteristic
35#13182008—22no—
36#13182008—22no—
37C22⋊Dic109—21no—
38C22⋊Dic109C2×C412yescomplemented
39#13182006—22no—
40#13182006—22no—
41C24×C109C2×C411yescharacteristic
42C22×C4×C109—21no—
43C22×C4×C109—21no—
44C22×C4×C109—41no—
45C22×C4×C109—41no—
46C22×C4×C109C2×C412yescomplemented
47C23×C109—21no—
48C23×C109—21no—
49C23×C109—42no—
50C23×C109C22⋊C411yescharacteristic
51C23×C109C22⋊C411yescharacteristic
52C23×C109C22×C411yescharacteristic
53C22×D109—21no—
54C22×D109—21no—
55C22×D109—42no—
56C22×D109C22⋊C411yescharacteristic
57C22×D109C2×D411yescharacteristic
58C2×#89137—42no—
59C2×#89137—82no—
60C2×C4×C109—22no—
61C2×C4×C109—42no—
62C2×C4×C109—41no—
63C2×C4×C109—41no—
64C2×C4×C109—42no—
65C22⋊D109—41no—
66C22⋊D109—41no—
67C22⋊D109—41no—
68C22⋊D109—41no—
69C2×Dic109—21no—
70C2×Dic109—21no—
71C2×Dic109—22no—
72C2×Dic109—42no—
73C2×Dic109C22⋊C411yescharacteristic
74C2×Dic109C2×D411yescharacteristic
75#11724786—42no—
76C22×C109—22no—
77C22×C109—21no—
78C22×C109—21no—
79C22×C109—41no—
80C22×C109—41no—
81C22×C109—42no—
82C22×C109—42no—
83C22×C109#9911yescharacteristic
84C22×C109#9911yescharacteristic
85C22×C109C2×C22⋊C411yescharacteristic
86C2×D109—21no—
87C2×D109—21no—
88C2×D109—42no—
89C2×D109—41no—
90C2×D109—41no—
91C2×D109—81no—
92#89137—82no—
93C4×C109—42no—
94Dic109—21no—
95Dic109—21no—
96Dic109—42no—
97C2×C109—21no—
98C2×C109—21no—
99C2×C109—41no—
100C2×C109—41no—
101C2×C109#35212yescomplemented
102C2×C109C2×#9911yescharacteristic
103D109—41no—
104D109—41no—
105C2×#352—1091nomaximal, Sylow
106C109C2×#35211yescharacteristic, complemented, Sylow
107C2×#123—1091no—
108C2×#100—1091no—
109C2×#99—1091no—
110#352—1094no—
111C22×D4—1091no—
112C23×C4#8913711yescharacteristic, complemented
113C2×M16—2181no—
114#123—1092no—
115#123—1092no—
116#123—2181no—
117#123—2181no—
118C2×C4⋊C4—2181no—
119C2×C22⋊C4—1091no—
120C2×C22⋊C4—2181no—
121C2×C22⋊C4—2181no—
122#100—1092no—
123#100—2181no—
124#99—1092no—
125#99—2181no—
126C24—1091no—
127C24C2×#8913711yescharacteristic
128C2×D4—1091no—
129C2×D4—1091no—
130C2×D4—1091no—
131C2×D4—1091no—
132C2×D4—4361no—
133C2×D4—4361no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—41no—
137C22×C4—41no—
138C22×C4—1091no—
139C22×C4—4361no—
140C22×C4—2181no—
141C22×C4C2×#8913712yescomplemented
142M16—4361no—
143M16—2182no—
144C2×C8—4361no—
145C4⋊C4—2182no—
146C4⋊C4—2182no—
147C22⋊C4—1092no—
148C22⋊C4—4361no—
149C22⋊C4—2182no—
150C22⋊C4—2182no—
151C22⋊C4—2182no—
152C22⋊C4—2181no—
153C23—21no—
154C23—21no—
155C23—42no—
156C23—1091no—
157C23—1091no—
158C23—4362no—
159C23—2181no—
160C23—2181no—
161C23C22⋊#8913711yescharacteristic
162C23C22⋊#8913711yescharacteristic
163C23C22×#8913711yescharacteristic
164D4—4361no—
165D4—4361no—
166D4—4361no—
167D4—4361no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—42no—
173C2×C4—8722no—
174C2×C4—1091no—
175C2×C4—1091no—
176C2×C4—4362no—
177C2×C4—4362no—
178C2×C4—2182no—
179C2×C4—2181no—
180C2×C4—2181no—
181C8—4362no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—41no—
186C22—41no—
187C22—42no—
188C22—42no—
189C22—8721no—
190C22—4361no—
191C22—4361no—
192C22—4362no—
193C22—2181no—
194C22—2181no—
195C22#1681275711yescharacteristic
196C22#1681275711yescharacteristic
197C22C2×C22⋊#8913711yescharacteristic
198C4—42no—
199C4—8722no—
200C4—4362no—
201C4—2181no—
202C4—2181no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—4361no—
208C2—4361no—
209C2#2029592812yesdirect product factor
210C2C2×#1681275711yescharacteristic
subgroupG/H
centerC22#16812757
commutatorC23×C109C22×C4
FrattiniC23C22×#89137
FittingC23×C4×C109C4
socleC22×C109#99
prime radicalC22×C22⋊D109C22
cosocleC2×C22⋊D109C23
hypercenterC23×C4#89137
hypocenterC109C2×#352
LCSG ▷ C23×C109 ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #20295928C2direct (N × H)
14. #16812682C4semidirect
17. C2×C22⋊Dic109C4semidirect
19. C23×C4×C109C4semidirect
38. C22⋊Dic109C2×C4semidirect
46. C22×C4×C109C2×C4semidirect
101. C2×C109#352semidirect
106. C109C2×#352semidirect
112. C23×C4#89137semidirect
141. C22×C4C2×#89137semidirect
209. C2#20295928direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168127592
C2×#168127572
#202959282
C2×#168126822
C2×#352109