Finite Group Databasebeta

← C2×#352×C233 #44448151

Subgroups — C2×#352×C233 #44448151

Order 29824.

278 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 88 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×#123×C233C211yesmaximal, characteristic
2C2×#100×C233C211yesmaximal, characteristic
3C2×#99×C233C211yesmaximal, characteristic
4#352×C233C214yesmaximal, direct product factor
5C22×D4×C233C2211yescharacteristic
6C23×C4×C233C411yescharacteristic, complemented
7C2×M16×C233—21no—
8#123×C233—21no—
9#123×C233—21no—
10#123×C233C412yescomplemented
11#123×C233C2212yes—
12C2×C4⋊C4×C233—21no—
13C2×C22⋊C4×C233—21no—
14C2×C22⋊C4×C233—21no—
15C2×C22⋊C4×C233C411yescharacteristic, complemented
16#100×C233—21no—
17#100×C233C2212yes—
18#99×C233—21no—
19#99×C233C2212yes—
20C24×C233C2×C411yescharacteristic
21C24×C233D411yescharacteristic
22C2×D4×C233—41no—
23C2×D4×C233—41no—
24C2×D4×C233C2×C411yescharacteristic
25C2×D4×C233D411yescharacteristic
26C2×D4×C233D411yescharacteristic
27C2×D4×C233C2311yescharacteristic
28C22×C4×C233—21no—
29C22×C4×C233—21no—
30C22×C4×C233—21no—
31C22×C4×C233—41no—
32C22×C4×C233—41no—
33C22×C4×C233—41no—
34C22×C4×C233C2×C412yescomplemented
35C22×C4×C233D411yescharacteristic
36M16×C233—22no—
37M16×C233—41no—
38C2×C8×C233—41no—
39C4⋊C4×C233—22no—
40C4⋊C4×C233—22no—
41C22⋊C4×C233—22no—
42C22⋊C4×C233—21no—
43C22⋊C4×C233—22no—
44C22⋊C4×C233—22no—
45C22⋊C4×C233—41no—
46C22⋊C4×C233C2×C412yescomplemented
47C23×C233—21no—
48C23×C233—21no—
49C23×C233—21no—
50C23×C233—21no—
51C23×C233—42no—
52C23×C233—42no—
53C23×C233C22⋊C411yescharacteristic
54C23×C233C22⋊C411yescharacteristic
55C23×C233C22⋊C411yescharacteristic
56C23×C233C22×C411yescharacteristic
57C23×C233C2×D411yescharacteristic
58D4×C233—41no—
59D4×C233—41no—
60D4×C233—41no—
61D4×C233—41no—
62C2×C4×C233—21no—
63C2×C4×C233—21no—
64C2×C4×C233—22no—
65C2×C4×C233—22no—
66C2×C4×C233—42no—
67C2×C4×C233—42no—
68C2×C4×C233—41no—
69C2×C4×C233—41no—
70C2×C4×C233—42no—
71C2×C4×C233—42no—
72C2×C4×C233—82no—
73C2×C4×C233C22⋊C411yescharacteristic
74C2×C4×C233C2×D411yescharacteristic
75C8×C233—42no—
76C22×C233—22no—
77C22×C233—21no—
78C22×C233—21no—
79C22×C233—21no—
80C22×C233—21no—
81C22×C233—41no—
82C22×C233—41no—
83C22×C233—41no—
84C22×C233—41no—
85C22×C233—42no—
86C22×C233—42no—
87C22×C233—42no—
88C22×C233—81no—
89C22×C233#9911yescharacteristic
90C22×C233#9911yescharacteristic
91C22×C233C2×C22⋊C411yescharacteristic
92C4×C233—21no—
93C4×C233—21no—
94C4×C233—42no—
95C4×C233—42no—
96C4×C233—82no—
97C2×C233—21no—
98C2×C233—21no—
99C2×C233—41no—
100C2×C233—41no—
101C2×C233—41no—
102C2×C233—41no—
103C2×C233#35212yesdirect product factor
104C2×C233C2×#9911yescharacteristic
105C233C2×#35211yescharacteristic, direct product factor, Sylow
106C2×#352C23311yesmaximal, characteristic, direct product factor, Sylow
107C2×#123C2×C23311yescharacteristic
108C2×#100C2×C23311yescharacteristic
109C2×#99C2×C23311yescharacteristic
110#352C2×C23314yesdirect product factor
111C22×D4C22×C23311yescharacteristic
112C23×C4C4×C23311yescharacteristic, complemented
113C2×M16—21no—
114#123—21no—
115#123—21no—
116#123C4×C23312yescomplemented
117#123C22×C23312yes—
118C2×C4⋊C4—21no—
119C2×C22⋊C4—21no—
120C2×C22⋊C4—21no—
121C2×C22⋊C4C4×C23311yescharacteristic, complemented
122#100—21no—
123#100C22×C23312yes—
124#99—21no—
125#99C22×C23312yes—
126C24C2×C4×C23311yescharacteristic
127C24D4×C23311yescharacteristic
128C2×D4—41no—
129C2×D4—41no—
130C2×D4C2×C4×C23311yescharacteristic
131C2×D4D4×C23311yescharacteristic
132C2×D4D4×C23311yescharacteristic
133C2×D4C23×C23311yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—41no—
140C22×C4C2×C4×C23312yescomplemented
141C22×C4D4×C23311yescharacteristic
142M16—22no—
143M16—41no—
144C2×C8—41no—
145C4⋊C4—22no—
146C4⋊C4—22no—
147C22⋊C4—22no—
148C22⋊C4—21no—
149C22⋊C4—22no—
150C22⋊C4—22no—
151C22⋊C4—41no—
152C22⋊C4C2×C4×C23312yescomplemented
153C23—21no—
154C23—21no—
155C23—21no—
156C23—21no—
157C23—42no—
158C23—42no—
159C23C22⋊C4×C23311yescharacteristic
160C23C22⋊C4×C23311yescharacteristic
161C23C22⋊C4×C23311yescharacteristic
162C23C22×C4×C23311yescharacteristic
163C23C2×D4×C23311yescharacteristic
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—82no—
179C2×C4C22⋊C4×C23311yescharacteristic
180C2×C4C2×D4×C23311yescharacteristic
181C8—42no—
182C22—22no—
183C22—21no—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22#99×C23311yescharacteristic
196C22#99×C23311yescharacteristic
197C22C2×C22⋊C4×C23311yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—42no—
202C4—82no—
203C2—21no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—41no—
208C2—41no—
209C2#352×C23312yesdirect product factor
210C2C2×#99×C23311yescharacteristic
subgroupG/H
center, socleC22×C233#99
commutatorC23C22×C4×C233
Frattini, cosocleC2×D4C23×C233
prime radicalC22×D4×C233C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C233 ◁ C23×C233 ◁ C22×D4×C233 ◁ G

Complements

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

NH ≅ G/Ntype
4. #352×C233C2direct (N × H)
6. C23×C4×C233C4semidirect
10. #123×C233C4semidirect
15. C2×C22⋊C4×C233C4semidirect
34. C22×C4×C233C2×C4semidirect
46. C22⋊C4×C233C2×C4semidirect
103. C2×C233#352direct (N × H)
105. C233C2×#352direct (N × H)
106. C2×#352C233direct (N × H)
110. #352C2×C233direct (N × H)
112. C23×C4C4×C233semidirect
116. #123C4×C233semidirect
121. C2×C22⋊C4C4×C233semidirect
140. C22×C4C2×C4×C233semidirect
152. C22⋊C4C2×C4×C233semidirect
209. C2#352×C233direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#123×C2332
C2×#100×C2332
C2×#99×C2332
#352×C2332
C2×#352233