Finite Group Databasebeta

← #44450386

Subgroups — #44450386

Order 29824.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#28416971C211yesmaximal, characteristic
2#28416485C211yesmaximal, characteristic, complemented
3#28416302C211yesmaximal, characteristic, complemented
4#28416172C211yesmaximal, characteristic, complemented
5#28416170C211yesmaximal, characteristic
6#28416168C211yesmaximal, characteristic
7#328×C233C211yesmaximal, characteristic, complemented
8#21418530—21no—
9#21418526C411yescharacteristic, complemented
10#21418524C411yescharacteristic, complemented
11#21418519—21no—
12#21418509C2211yescharacteristic
13Q8×Dic233C411yescharacteristic, complemented
14#21418497C411yescharacteristic, complemented
15#21418495—21no—
16#21418493—21no—
17C2×C4×Dic233C2211yescharacteristic
18#21418464—21no—
19C22⋊#14272338C2211yescharacteristic
20C8×Dic233—21no—
21#21418442—21no—
22#21418442—21no—
23#21418442C2211yescharacteristic
24C22⋊Q8×C233C2211yescharacteristic
25C22⋊C8×C233C2211yescharacteristic
26#95×C233C2211yescharacteristic
27C2×D932C2×C411yescharacteristic
28C2×C22⋊D233—21no—
29C22×Dic233—21no—
30C22×Dic233D411yescharacteristic
31C22×Dic233D411yescharacteristic
32C2×C4×D233—21no—
33C2×#14272338—21no—
34C4⋊Dic233—21no—
35C4⋊Dic233—21no—
36C4⋊Dic233C2×C411yescharacteristic
37#16836573—21no—
38#16836571—21no—
39#16836571—21no—
40#16836571—21no—
41#16836571—21no—
42C4×Dic233—21no—
43C4×Dic233C2×C411yescharacteristic
44C4×Dic233C2×C411yescharacteristic
45C4×Dic233D411yescharacteristic
46C4×Dic233D411yescharacteristic
47C2×Q8×C233C2×C411yescharacteristic
48C22×C4×C233—21no—
49C22×C4×C233C2311yescharacteristic
50C2×C8×C233—21no—
51C4⋊C4×C233—21no—
52C4⋊C4×C233C2×C411yescharacteristic
53C22⋊C4×C233—21no—
54C22×D233—21no—
55D932—41no—
56C22⋊D233—41no—
57C22⋊D233—41no—
58C2×Dic233—21no—
59C2×Dic233—21no—
60C2×Dic233—21no—
61C2×Dic233—41no—
62C2×Dic233—41no—
63C2×Dic233—41no—
64C2×Dic233—41no—
65C2×Dic233C22⋊C411yescharacteristic
66C2×Dic233C22⋊C411yescharacteristic
67C2×Dic233C22⋊C411yescharacteristic
68C2×Dic233C22⋊C411yescharacteristic
69C4×D233—42no—
70#14272338—41no—
71C23×C233C2×D411yescharacteristic
72Q8×C233—41no—
73C2×C4×C233—21no—
74C2×C4×C233—21no—
75C2×C4×C233—41no—
76C2×C4×C233—41no—
77C2×C4×C233—41no—
78C2×C4×C233—41no—
79C2×C4×C233C22×C411yescharacteristic
80C2×C4×C233C2×D411yescharacteristic
81C8×C233—41no—
82C22×C233—21no—
83C22×C233—21no—
84C22×C233C2×C22⋊C411yescharacteristic
85C22×C233#13511yescharacteristic
86C22×C233#13511yescharacteristic
87C2×D233—41no—
88C2×D233—41no—
89C2×D233—41no—
90C4×C233—21no—
91C4×C233—21no—
92C4×C233—41no—
93C4×C233—41no—
94C4×C233—81no—
95Dic233—21no—
96Dic233—21no—
97Dic233—21no—
98Dic233—21no—
99Dic233—41no—
100Dic233—81no—
101C2×C233—21no—
102C2×C233—21no—
103C2×C233#41011yescharacteristic
104C2×C233#41611yescharacteristic
105C2×C233#42111yescharacteristic
106D233—81no—
107C233#152111yescharacteristic, complemented, Sylow
108#1521—2331nomaximal, Sylow
109#529—2331no—
110#431—2331no—
111#383—2331no—
112#328—2331no—
113#328D23311yescharacteristic, complemented
114#327—2331no—
115#327—2331no—
116#126—4661no—
117#125—2331no—
118#124—2331no—
119#123—4661no—
120C22⋊Q8C2×D23311yescharacteristic
121#121—2331no—
122C4×Q8—2331no—
123C4×D4—4661no—
124C4×D4—2331no—
125#117—4661no—
126C2×C42—2331no—
127C4⋊C8—4661no—
128C22⋊C8—2331no—
129C22⋊C8C2×D23311yescharacteristic
130C4×C8—4661no—
131#95—4661no—
132#95—4661no—
133#95—2331no—
134#95C2×D23311yescharacteristic
135C2×Q8C4×D23311yescharacteristic
136C2×D4—4661no—
137C2×D4—2331no—
138C22×C4—21no—
139C22×C4—4661no—
140C22×C4—4661no—
141C22×C4—2331no—
142C22×C4—2331no—
143C22×C4C22×D23311yescharacteristic
144C2×C8—21no—
145C2×C8—4661no—
146C4⋊C4—21no—
147C4⋊C4—4661no—
148C4⋊C4—4661no—
149C4⋊C4—4661no—
150C4⋊C4—2331no—
151C4⋊C4C4×D23311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—4661no—
154C22⋊C4—4661no—
155C22⋊C4—4661no—
156C22⋊C4—4661no—
157C42—4661no—
158C42—2331no—
159C42—2331no—
160C42—2331no—
161C42—2331no—
162C23—4661no—
163C23D4×D23311yescharacteristic
164Q8—41no—
165D4—9321no—
166D4—9321no—
167D4—9321no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—9322no—
175C2×C4—9321no—
176C2×C4—9321no—
177C2×C4—9321no—
178C2×C4—9321no—
179C2×C4—4661no—
180C2×C4—4661no—
181C2×C4—4661no—
182C2×C4—2331no—
183C2×C4—2331no—
184C2×C4—2331no—
185C2×C4—2331no—
186C2×C4C2×C4×D23311yescharacteristic
187C2×C4D4×D23311yescharacteristic
188C8—41no—
189C8—9321no—
190C22—21no—
191C22—21no—
192C22—9321no—
193C22—9321no—
194C22—9321no—
195C22C22⋊C4×D23311yescharacteristic
196C22#2141855611yescharacteristic
197C22#2141855811yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—18641no—
204C4—9321no—
205C4—4661no—
206C4—4661no—
207C4—4661no—
208C4—4661no—
209C2—21no—
210C2—21no—
211C2—18641no—
212C2#2841640711yescharacteristic
213C2#2841643011yescharacteristic
214C2#2841645011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D233
commutatorC2×C4×C233C22×C4
FrattiniC22×C4C22×D233
Fitting#328×C233C2
socleC22×C233C2×C22⋊C4
prime radical#21418509C22
cosocleC22×C4×C233C23
hypercenter#328D233
hypocenterC233#1521
LCSG ▷ C2×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #28416485C2semidirect
3. #28416302C2semidirect
4. #28416172C2semidirect
7. #328×C233C2semidirect
9. #21418526C4semidirect
10. #21418524C4semidirect
13. Q8×Dic233C4semidirect
14. #21418497C4semidirect
107. C233#1521semidirect
113. #328D233semidirect

Maximal subgroups

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

subgroupindex
#284169712
#284164852
#284163022
#284161722
#284161702
#284161682
#328×C2332
#1521233