Finite Group Databasebeta

← #44450883

Subgroups — #44450883

Order 29824.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#28417146C211yesmaximal, characteristic, complemented
2#28416809C211yesmaximal, characteristic, complemented
3#28416636C211yesmaximal, characteristic, complemented
4#28416631C211yesmaximal, characteristic
5#28416165C211yesmaximal, characteristic, complemented
6#28416162C211yesmaximal, characteristic, complemented
7#333×C233C211yesmaximal, characteristic, complemented
8C2×#16836583—21no—
9C2×#16836581—22no—
10C2×D1864—21no—
11#21418532C2211yescharacteristic
12#21418526—21no—
13#21418515—21no—
14#21418511—22no—
15C4×Dic466C2211yescharacteristic
16C4×D932C2211yescharacteristic
17#21418497—21no—
18C4⋊C4×D233—21no—
19#21418457—21no—
20#21418457—21no—
21C4×#14272338C2211yescharacteristic
22C4⋊Q8×C233C2211yescharacteristic
23C4⋊C8×C233C2211yescharacteristic
24C4⋊C8×C233C2211yescharacteristic
25C2×Dic466D411yescharacteristic
26C2×D932—21no—
27C2×D932—21no—
28C2×D932—21no—
29C2×D932D411yescharacteristic
30C2×C4×D233—22no—
31C2×C4×D233—21no—
32#16836583—42no—
33#16836581—44no—
34D1864—42no—
35C2×#14272338—21no—
36C4⋊Dic233—22no—
37C4⋊Dic233D411yescharacteristic
38C4⋊Dic233D411yescharacteristic
39#16836573—22no—
40#16836573—21no—
41#16836571—22no—
42#16836571—21no—
43C4×Dic233—21no—
44C2×Q8×C233D412yes—
45C2×C8×C233—21no—
46C2×C8×C233—21no—
47C4⋊C4×C233—21no—
48C4⋊C4×C233—21no—
49C42×C233C2311yescharacteristic
50C22×D233—21no—
51C22×D233—41no—
52Dic466—21no—
53Dic466—21no—
54D932—21no—
55D932—42no—
56D932—41no—
57D932—41no—
58D932—41no—
59D932—41no—
60D932SD1612yescomplemented
61C2×Dic233—21no—
62C2×Dic233—21no—
63C2×Dic233—21no—
64C4×D233—41no—
65C4×D233—41no—
66C4×D233—82no—
67#14272338—22no—
68Q8×C233—42no—
69C2×C4×C233—22no—
70C2×C4×C233C2×D411yescharacteristic
71C2×C4×C233C2×D411yescharacteristic
72C2×C4×C233C2×D411yescharacteristic
73C8×C233—41no—
74C8×C233—41no—
75C22×C233#12011yescharacteristic
76C2×D233—22no—
77C2×D233—41no—
78C2×D233—41no—
79C2×D233—81no—
80C2×D233—81no—
81C2×D233—81no—
82C4×C233—21no—
83C4×C233—42no—
84C4×C233C2×SD1611yescharacteristic
85C4×C233#13511yescharacteristic
86C4×C233AGL(1,ℤ/8)11yescharacteristic
87C4×C233#13711yescharacteristic
88Dic233—41no—
89Dic233—41no—
90Dic233—41no—
91C2×C233#44811yescharacteristic
92C2×C233#44911yescharacteristic
93C2×C233#45311yescharacteristic
94D233—42no—
95D233—161no—
96C233#162211yescharacteristic, complemented, Sylow
97#1622—2331nomaximal, Sylow
98#554—2331no—
99#492—2331no—
100#460—2331no—
101#459—2331no—
102#333D23311yescharacteristic, complemented
103Q8⋊C8—2331no—
104D4⋊C8—2331no—
105C2×SD16—4661no—
106C2×SD16—4662no—
107C2×D8—4661no—
108C4⋊Q8C2×D23311yescharacteristic
109#127—2331no—
110#125—4661no—
111C22⋊Q8—4661no—
112C22⋊Q8—4662no—
113C4×Q8—2331no—
114C4×D4—4661no—
115C4×D4—2331no—
116C2×C4⋊C4—4661no—
117C4⋊C8C2×D23311yescharacteristic
118C4⋊C8C2×D23311yescharacteristic
119#102—4661no—
120#102—4661no—
121C4×C8—2331no—
122C2×Q8—2331no—
123C2×Q8D93212yes—
124C2×D4—4661no—
125C2×D4—4661no—
126C2×D4—4661no—
127C2×D4—2331no—
128C22×C4—4662no—
129C22×C4—4661no—
130SD16—9322no—
131SD16—9324no—
132D8—9322no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—4661no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—4662no—
139C4⋊C4—4662no—
140C4⋊C4—4661no—
141C4⋊C4—2331no—
142C4⋊C4—2331no—
143C22⋊C4—4662no—
144C22⋊C4—4661no—
145C42—4661no—
146C42C22×D23311yescharacteristic
147C23—9321no—
148C23—4661no—
149Q8—42no—
150Q8—4661no—
151Q8—4661no—
152D4—9322no—
153D4—9321no—
154D4—9321no—
155D4—9321no—
156D4—9321no—
157D4—4661no—
158D4—2332no—
159C2×C4—22no—
160C2×C4—18642no—
161C2×C4—9321no—
162C2×C4—9321no—
163C2×C4—4661no—
164C2×C4—4661no—
165C2×C4—4661no—
166C2×C4D4×D23311yescharacteristic
167C2×C4D4×D23311yescharacteristic
168C2×C4C2×D93211yescharacteristic
169C8—41no—
170C8—41no—
171C8—4662no—
172C22—18641no—
173C22—18641no—
174C22—18641no—
175C22—9321no—
176C22—9321no—
177C22—4662no—
178C22#2141850511yescharacteristic
179C4—21no—
180C4—42no—
181C4—9321no—
182C4—9321no—
183C4—9321no—
184C4SD16×D23311yescharacteristic
185C4#2141855811yescharacteristic
186C4#2141856211yescharacteristic
187C4#2141856711yescharacteristic
188C2—37281no—
189C2—9322no—
190C2#2841657511yescharacteristic
191C2#2841658311yescharacteristic
192C2#2841660511yescharacteristic
subgroupG/H
centerC22#21418505
commutator, cosocleC42×C233C23
FrattiniC42C22×D233
Fitting#333×C233C2
socleC22×C233#120
prime radical#28416631C2
hypercenter#333D233
hypocenterC233#1622
LCSG ▷ C42×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #28417146C2semidirect
2. #28416809C2semidirect
3. #28416636C2semidirect
5. #28416165C2semidirect
6. #28416162C2semidirect
7. #333×C233C2semidirect
60. D932SD16semidirect
96. C233#1622semidirect
102. #333D233semidirect

Maximal subgroups

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

subgroupindex
#284171462
#284168092
#284166362
#284166312
#284161652
#284161622
#333×C2332
#1622233