Finite Group Databasebeta

← #44450809

Subgroups — #44450809

Order 29824.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#28417032C211yesmaximal, characteristic
2#28416766C211yesmaximal, characteristic, complemented
3#28416749C211yesmaximal, characteristic
4#28416365C211yesmaximal, characteristic, complemented
5#28416173C211yesmaximal, characteristic, complemented
6#28416170C211yesmaximal, characteristic
7#324×C233C211yesmaximal, characteristic, complemented
8#21418530—21no—
9#21418525—21no—
10#21418520—21no—
11#21418518—21no—
12#21418514C2211yescharacteristic
13#21418513—21no—
14#21418509C2211yescharacteristic
15C4×C22⋊D233—21no—
16C2×C4⋊Dic233C2211yescharacteristic
17C2×#16836573—21no—
18#21418469—21no—
19#21418467—21no—
20#21418460—21no—
21#21418457—21no—
22#21418442—21no—
23#21418442C2211yescharacteristic
24C2×C4⋊C4×C233C2211yescharacteristic
25C22⋊C8×C233C2211yescharacteristic
26C22⋊C8×C233C2211yescharacteristic
27C2×Dic466D411yescharacteristic
28C2×D932D411yescharacteristic
29C2×C22⋊D233—21no—
30C22×Dic233—21no—
31C22×Dic233—21no—
32C2×C4×D233—21no—
33C4⋊Dic233—21no—
34C4⋊Dic233—21no—
35C4⋊Dic233D411yescharacteristic
36C4⋊Dic233D411yescharacteristic
37#16836573—21no—
38#16836573—21no—
39#16836573—21no—
40#16836573—21no—
41#16836573—42no—
42C22⋊Dic233—21no—
43#16836571—21no—
44#16836571—21no—
45#16836571—21no—
46#16836571—21no—
47C4×Dic233—21no—
48C22×C4×C233D411yescharacteristic
49C22×C4×C233D411yescharacteristic
50C22×C4×C233C2311yescharacteristic
51C2×C8×C233—21no—
52C2×C8×C233—21no—
53C4⋊C4×C233—21no—
54C4⋊C4×C233—21no—
55C22×D233—21no—
56Dic466—41no—
57D932—41no—
58C22⋊D233—41no—
59C22⋊D233—41no—
60C2×Dic233—22no—
61C2×Dic233—21no—
62C2×Dic233—21no—
63C2×Dic233—21no—
64C2×Dic233—41no—
65C2×Dic233—41no—
66C2×Dic233—41no—
67C2×Dic233—41no—
68C2×Dic233—41no—
69C4×D233—81no—
70C23×C233C2×D411yescharacteristic
71C2×C4×C233—21no—
72C2×C4×C233—21no—
73C2×C4×C233—21no—
74C2×C4×C233—21no—
75C2×C4×C233—41no—
76C2×C4×C233—41no—
77C2×C4×C233C2×D411yescharacteristic
78C2×C4×C233C2×D411yescharacteristic
79C8×C233—41no—
80C8×C233—41no—
81C22×C233—21no—
82C22×C233—21no—
83C22×C233#12011yescharacteristic
84C22×C233#13511yescharacteristic
85C22×C233AGL(1,ℤ/8)11yescharacteristic
86C2×D233—41no—
87C2×D233—41no—
88C2×D233—41no—
89C4×C233—21no—
90C4×C233—21no—
91C4×C233—41no—
92C4×C233—41no—
93Dic233—42no—
94Dic233—41no—
95Dic233—41no—
96Dic233—41no—
97Dic233—81no—
98C2×C233—21no—
99C2×C233—21no—
100C2×C233#44911yescharacteristic
101C2×C233#45611yescharacteristic
102C2×C233#45811yescharacteristic
103D233—81no—
104C233#160911yescharacteristic, complemented, Sylow
105#1609—2331nomaximal, Sylow
106#539—2331no—
107#483—2331no—
108#480—2331no—
109#398—2331no—
110#328—2331no—
111#327—2331no—
112#324D23311yescharacteristic, complemented
113#126—4661no—
114#125—4661no—
115#123—4661no—
116#123—4661no—
117C22⋊Q8—4661no—
118C22⋊Q8—2331no—
119#121—2331no—
120C4×D4—4661no—
121C2×C4⋊C4—4661no—
122C2×C4⋊C4—2331no—
123C2×C4⋊C4C2×D23311yescharacteristic
124#107—4661no—
125#106—4661no—
126#103—4661no—
127#102—4661no—
128C22⋊C8C2×D23311yescharacteristic
129C22⋊C8C2×D23311yescharacteristic
130#95—4661no—
131#95—2331no—
132C2×Q8—2331no—
133C2×D4—4661no—
134C2×D4—2331no—
135C22×C4—4661no—
136C22×C4—4661no—
137C22×C4—4661no—
138C22×C4D93211yescharacteristic
139C22×C4D93211yescharacteristic
140C22×C4C22×D23311yescharacteristic
141C2×C8—21no—
142C2×C8—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—9322no—
146C4⋊C4—4661no—
147C4⋊C4—4661no—
148C4⋊C4—4661no—
149C4⋊C4—4661no—
150C4⋊C4—4661no—
151C4⋊C4—4661no—
152C4⋊C4—2331no—
153C4⋊C4—2331no—
154C22⋊C4—4661no—
155C22⋊C4—4661no—
156C22⋊C4—4661no—
157C22⋊C4—4661no—
158C22⋊C4—4661no—
159C42—4661no—
160C23—4661no—
161C23C2×D93211yescharacteristic
162Q8—9321no—
163D4—9321no—
164D4—9321no—
165D4—9321no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—18641no—
173C2×C4—9321no—
174C2×C4—9321no—
175C2×C4—9321no—
176C2×C4—9321no—
177C2×C4—9321no—
178C2×C4—4662no—
179C2×C4—4661no—
180C2×C4—4661no—
181C2×C4—4661no—
182C2×C4D4×D23311yescharacteristic
183C2×C4D4×D23311yescharacteristic
184C8—41no—
185C8—41no—
186C22—21no—
187C22—21no—
188C22—9321no—
189C22—9321no—
190C22—9321no—
191C22#2141850511yescharacteristic
192C22#2141855711yescharacteristic
193C22#2141856311yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—18641no—
199C4—9322no—
200C4—9321no—
201C4—9321no—
202C4—9321no—
203C2—21no—
204C2—21no—
205C2—18641no—
206C2#2841658211yescharacteristic
207C2#2841662011yescharacteristic
208C2#2841662611yescharacteristic
subgroupG/H
centerC22#21418505
commutator, cosocleC22×C4×C233C23
FrattiniC22×C4C22×D233
Fitting#324×C233C2
socleC22×C233#120
prime radical#21418509C22
hypercenter#324D233
hypocenterC233#1609
LCSG ▷ C22×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #28416766C2semidirect
4. #28416365C2semidirect
5. #28416173C2semidirect
7. #324×C233C2semidirect
104. C233#1609semidirect
112. #324D233semidirect

Maximal subgroups

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

subgroupindex
#284170322
#284167662
#284167492
#284163652
#284161732
#284161702
#324×C2332
#1609233