Finite Group Databasebeta

← #44450770

Subgroups — #44450770

Order 29824.

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

normal subgroups only

This group has 244 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#28417030C211yesmaximal, characteristic
2#28416591C211yesmaximal, characteristic, complemented
3#28416354C211yesmaximal, characteristic, complemented
4#28416173C211yesmaximal, characteristic, complemented
5#28416169C211yesmaximal, characteristic
6#28416160C211yesmaximal, characteristic, complemented
7#448×C233C211yesmaximal, characteristic
8C2×#16836584—21no—
9#21418528—21no—
10#21418525—21no—
11#21418516—21no—
12#21418516—21no—
13#21418514C2211yescharacteristic
14#21418512—21no—
15D4×Dic233—21no—
16C2×#16836573—21no—
17C2×#16836573C2211yescharacteristic
18#21418459—21no—
19C22⋊#14272338C2211yescharacteristic
20#21418442—21no—
21#21418442C2211yescharacteristic
22C22×Q8×C233C2211yescharacteristic
23C2×SD16×C233—21no—
24#121×C233C2211yescharacteristic
25#103×C233—21no—
26C22⋊C8×C233C2211yescharacteristic
27C2×Dic466D411yescharacteristic
28C22×Dic233—21no—
29C22×Dic233—21no—
30C22×Dic233D411yescharacteristic
31C22×Dic233D411yescharacteristic
32#16836584—42no—
33C2×#14272338—21no—
34C4⋊Dic233—21no—
35C4⋊Dic233D411yescharacteristic
36#16836573—21no—
37#16836573—21no—
38#16836573—21no—
39#16836573—21no—
40#16836573—21no—
41#16836573—42no—
42C22⋊Dic233—21no—
43C22⋊Dic233—21no—
44C22⋊Dic233—21no—
45C22⋊Dic233—21no—
46C4×Dic233—21no—
47C2×Q8×C233—21no—
48C2×Q8×C233—21no—
49C2×Q8×C233—42no—
50C2×D4×C233—21no—
51C2×D4×C233D411yescharacteristic
52C22×C4×C233—21no—
53C22×C4×C233C2311yescharacteristic
54SD16×C233—42no—
55C2×C8×C233—21no—
56C4⋊C4×C233D411yescharacteristic
57C22⋊C4×C233—21no—
58Dic466—41no—
59C2×Dic233—22no—
60C2×Dic233—21no—
61C2×Dic233—21no—
62C2×Dic233—21no—
63C2×Dic233—21no—
64C2×Dic233—21no—
65C2×Dic233—21no—
66C2×Dic233—41no—
67C2×Dic233—41no—
68C2×Dic233—41no—
69C2×Dic233—81no—
70#14272338—41no—
71C23×C233—21no—
72C23×C233C2×D411yescharacteristic
73Q8×C233—22no—
74Q8×C233—22no—
75Q8×C233—41no—
76Q8×C233—41no—
77D4×C233—41no—
78D4×C233—41no—
79D4×C233—41no—
80C2×C4×C233—22no—
81C2×C4×C233—21no—
82C2×C4×C233—41no—
83C2×C4×C233—41no—
84C2×C4×C233—41no—
85C2×C4×C233C2×D411yescharacteristic
86C2×C4×C233C2×D411yescharacteristic
87C8×C233—41no—
88C22×C233—21no—
89C22×C233—21no—
90C22×C233—41no—
91C22×C233—41no—
92C22×C233—41no—
93C22×C233#12011yescharacteristic
94C22×C233#13511yescharacteristic
95C22×C233#13711yescharacteristic
96C4×C233—21no—
97C4×C233—21no—
98C4×C233—41no—
99C4×C233—42no—
100Dic233—42no—
101Dic233—41no—
102Dic233—41no—
103Dic233—41no—
104Dic233—41no—
105C2×C233—21no—
106C2×C233—21no—
107C2×C233—81no—
108C2×C233#45211yescharacteristic
109C2×C233#45611yescharacteristic
110C2×C233B(4,𝔽2)11yescharacteristic
111C233#160311yescharacteristic, complemented, Sylow
112#1603—2331nomaximal, Sylow
113#539—2331no—
114#451—2331no—
115#448D23311yescharacteristic
116#395—2331no—
117#328—2331no—
118#327—2331no—
119#324—2331no—
120C22×Q8C2×D23311yescharacteristic
121C2×Q16—4661no—
122C2×SD16—21no—
123#126—4661no—
124#125—4661no—
125#123—4661no—
126#123—4661no—
127C22⋊Q8—4661no—
128C22⋊Q8—2331no—
129#121C2×D23311yescharacteristic
130C4×D4—4661no—
131C2×C4⋊C4—4661no—
132C2×C4⋊C4—2331no—
133#103—21no—
134#103—4661no—
135C22⋊C8—2331no—
136C22⋊C8C2×D23311yescharacteristic
137#95—4661no—
138#95—2331no—
139C2×Q8—21no—
140C2×Q8—21no—
141C2×Q8—42no—
142C2×Q8—2331no—
143C2×D4—21no—
144C2×D4C22⋊D23311yescharacteristic
145C22×C4—21no—
146C22×C4—4661no—
147C22×C4—4661no—
148C22×C4—2331no—
149C22×C4—2331no—
150C22×C4C22×D23311yescharacteristic
151Q16—9322no—
152SD16—42no—
153C2×C8—21no—
154C2×C8—4661no—
155C4⋊C4—9322no—
156C4⋊C4—4661no—
157C4⋊C4—4661no—
158C4⋊C4—4661no—
159C4⋊C4—4661no—
160C4⋊C4—4661no—
161C4⋊C4—4661no—
162C4⋊C4—2331no—
163C4⋊C4C22⋊D23311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—4661no—
166C22⋊C4—4661no—
167C22⋊C4—4661no—
168C22⋊C4—4661no—
169C42—4661no—
170C23—21no—
171C23D4×D23311yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—41no—
175Q8—41no—
176Q8—9321no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—18641no—
186C2×C4—9321no—
187C2×C4—9321no—
188C2×C4—9321no—
189C2×C4—4662no—
190C2×C4—4661no—
191C2×C4—4661no—
192C2×C4—4661no—
193C2×C4—4661no—
194C2×C4—4661no—
195C2×C4—4661no—
196C2×C4D4×D23311yescharacteristic
197C2×C4C2×C22⋊D23311yescharacteristic
198C8—41no—
199C8—9321no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#2141850311yescharacteristic
206C22#2141855611yescharacteristic
207C22#2141856411yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—42no—
212C4—9322no—
213C4—9321no—
214C4—9321no—
215C4—9321no—
216C4—9321no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#2841659411yescharacteristic
221C2#2841661611yescharacteristic
222C2#2841662111yescharacteristic
subgroupG/H
centerC22#21418503
commutator, cosocleC22×C4×C233C23
FrattiniC22×C4C22×D233
Fitting#448×C233C2
socleC22×C233#120
prime radical#121×C233C22
hypercenter#448D233
hypocenterC233#1603
LCSG ▷ C22×C4×C233 ▷ C22×C233 ▷ C233
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #28416591C2semidirect
3. #28416354C2semidirect
4. #28416173C2semidirect
6. #28416160C2semidirect
111. C233#1603semidirect

Maximal subgroups

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

subgroupindex
#284170302
#284165912
#284163542
#284161732
#284161692
#284161602
#448×C2332
#1603233