Finite Group Databasebeta

← #44450878

Subgroups — #44450878

Order 29824.

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

normal subgroups only

This group has 278 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#28417106C211yesmaximal, characteristic, complemented
2#28416812C211yesmaximal, characteristic, complemented
3#28416636C211yesmaximal, characteristic, complemented
4#28416630C211yesmaximal, characteristic, complemented
5#28416178C211yesmaximal, characteristic, complemented
6#28416167C211yesmaximal, characteristic, complemented
7D4⋊C8×C233C211yesmaximal, characteristic, complemented
8C2×#16836594—21no—
9C2×#16836583—21no—
10C2×D1864—22no—
11C2×#16836579—21no—
12#21418532C2211yescharacteristic
13#21418532C2211yescharacteristic
14#21418531—21no—
15#21418509—21no—
16#21418508—22no—
17C4×Dic466C2211yescharacteristic
18#21418497—21no—
19C4⋊#14272338C2211yescharacteristic
20#21418457—21no—
21#21418455—21no—
22C4×D4×C233C2211yescharacteristic
23C4⋊C8×C233C2211yescharacteristic
24C4×C8×C233C2211yescharacteristic
25#16836594—42no—
26#16836594—42no—
27C2×Dic466D411yescharacteristic
28C2×D932—21no—
29C2×D932—21no—
30C2×D932—21no—
31C2×D932—21no—
32C2×D932—21no—
33C2×D932D412yes—
34C2×C22⋊D233—22no—
35C2×C22⋊D233—22no—
36C2×C4×D233—22no—
37#16836583—42no—
38D1864—44no—
39#16836579—42no—
40C2×#14272338—21no—
41C4⋊Dic233D411yescharacteristic
42#16836573—21no—
43#16836571—22no—
44C4×Dic233—21no—
45C2×D4×C233D411yescharacteristic
46C22×C4×C233—21no—
47C2×C8×C233—21no—
48C2×C8×C233—21no—
49C4⋊C4×C233D411yescharacteristic
50C22⋊C4×C233—21no—
51C42×C233C2311yescharacteristic
52C22×D233—22no—
53C22×D233—41no—
54Dic466—21no—
55Dic466D812yescomplemented
56D932—42no—
57D932—42no—
58D932—41no—
59D932—41no—
60D932—41no—
61D932—41no—
62D932—41no—
63D932—41no—
64D932—41no—
65D932—41no—
66C22⋊D233—44no—
67C22⋊D233—82no—
68C2×Dic233—21no—
69C2×Dic233—21no—
70C4×D233—44no—
71#14272338—41no—
72C23×C233—21no—
73D4×C233—21no—
74D4×C233—21no—
75C2×C4×C233—21no—
76C2×C4×C233—41no—
77C2×C4×C233—41no—
78C2×C4×C233C2×D411yescharacteristic
79C2×C4×C233C2×D411yescharacteristic
80C2×C4×C233C2×D411yescharacteristic
81C8×C233—22no—
82C8×C233—41no—
83C22×C233—41no—
84C22×C233—41no—
85C22×C233—41no—
86C22×C233#12011yescharacteristic
87C2×D233—42no—
88C2×D233—42no—
89C2×D233—42no—
90C2×D233—81no—
91C2×D233—81no—
92C2×D233—81no—
93C4×C233—21no—
94C4×C233—41no—
95C4×C233C2×D811yescharacteristic
96C4×C233#13511yescharacteristic
97C4×C233AGL(1,ℤ/8)11yescharacteristic
98C4×C233AGL(1,ℤ/8)11yescharacteristic
99Dic233—22no—
100Dic233—41no—
101C2×C233—81no—
102C2×C233#44711yescharacteristic
103C2×C233#44911yescharacteristic
104C2×C233#45311yescharacteristic
105D233—82no—
106D233—161no—
107C233#162111yescharacteristic, complemented, Sylow
108#1621—2331nomaximal, Sylow
109#550—2331no—
110#493—2331no—
111#460—2331no—
112#459—2331no—
113#331—2331no—
114Q8⋊C8—2331no—
115D4⋊C8D23311yescharacteristic, complemented
116C2×#41—4661no—
117C2×SD16—4661no—
118C2×D8—4662no—
119C2×D8—4661no—
120#127—4661no—
121#127—2331no—
122#127—2331no—
123#121—4662no—
124#121—4661no—
125C4×Q8—2331no—
126C4×D4—4661no—
127C4×D4C2×D23311yescharacteristic
128C4⋊C8—2331no—
129C4⋊C8C2×D23311yescharacteristic
130#102—4661no—
131#102—4661no—
132C4×C8C2×D23311yescharacteristic
133#41—9322no—
134#41—9322no—
135C2×Q8—2331no—
136C2×D4—4662no—
137C2×D4—4662no—
138C2×D4—4661no—
139C2×D4—4661no—
140C2×D4—4661no—
141C2×D4—4661no—
142C2×D4—4661no—
143C2×D4—2332no—
144C2×D4D93211yescharacteristic
145C22×C4—21no—
146C22×C4—4662no—
147SD16—9322no—
148D8—9324no—
149D8—9322no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—4661no—
153C4⋊C4—4661no—
154C4⋊C4—2331no—
155C4⋊C4D93211yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—4662no—
158C42—4661no—
159C42C22×D23311yescharacteristic
160C23—21no—
161C23—9321no—
162C23—4662no—
163Q8—4661no—
164Q8—2332no—
165D4—21no—
166D4—21no—
167D4—18642no—
168D4—9322no—
169D4—9322no—
170D4—9324no—
171D4—9321no—
172D4—9321no—
173D4—9321no—
174D4—9321no—
175D4—9321no—
176D4—9321no—
177D4—9321no—
178D4—9321no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—9324no—
183C2×C4—4661no—
184C2×C4—4661no—
185C2×C4D4×D23311yescharacteristic
186C2×C4D4×D23311yescharacteristic
187C2×C4C2×D93211yescharacteristic
188C8—22no—
189C8—41no—
190C8—9321no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—18641no—
195C22—18641no—
196C22—18641no—
197C22—9322no—
198C22—9322no—
199C22—9322no—
200C22#2141850511yescharacteristic
201C4—21no—
202C4—41no—
203C4—9321no—
204C4—4662no—
205C4D8×D23311yescharacteristic
206C4#2141855711yescharacteristic
207C4#2141856211yescharacteristic
208C4#2141856311yescharacteristic
209C2—81no—
210C2—18642no—
211C2—37281no—
212C2#2841657011yescharacteristic
213C2#2841658211yescharacteristic
214C2#2841660411yescharacteristic
subgroupG/H
centerC22#21418505
commutator, cosocleC42×C233C23
FrattiniC42C22×D233
FittingD4⋊C8×C233C2
socleC22×C233#120
hypercenterD4⋊C8D233
hypocenterC233#1621
LCSG ▷ C42×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #28417106C2semidirect
2. #28416812C2semidirect
3. #28416636C2semidirect
4. #28416630C2semidirect
5. #28416178C2semidirect
6. #28416167C2semidirect
7. D4⋊C8×C233C2semidirect
55. Dic466D8semidirect
107. C233#1621semidirect
115. D4⋊C8D233semidirect

Maximal subgroups

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

subgroupindex
#284171062
#284168122
#284166362
#284166302
#284161782
#284161672
D4⋊C8×C2332
#1621233