Finite Group Databasebeta

← #44506420

Subgroups — #44506420

Order 30848.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#29508346C211yesmaximal, characteristic
2#29507875C211yesmaximal, characteristic
3#29507872C211yesmaximal, characteristic
4#29507638C211yesmaximal, characteristic
5#29507453C211yesmaximal, characteristic
6#29507442C211yesmaximal, characteristic
7#328×C241C211yesmaximal, characteristic
8C22×Dic482C2211yescharacteristic
9C2×Dic964—21no—
10C2×#16838760—21no—
11#21440641—21no—
12#21440640—21no—
13#21440632—21no—
14#21440632—21no—
15#21440621C2211yescharacteristic
16#21440619—21no—
17#21440598—21no—
18C2×C4⋊Dic241—21no—
19C2×#16838749C2211yescharacteristic
20#21440567—21no—
21#21440565—21no—
22C22⋊#14515349C2211yescharacteristic
23#21440549—21no—
24C22⋊Q8×C241C2211yescharacteristic
25C22⋊C8×C241C2211yescharacteristic
26#95×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482—21no—
29C2×Dic482—21no—
30C2×Dic482—42no—
31C2×Dic482D411yescharacteristic
32C22×Dic241—21no—
33C22×Dic241D411yescharacteristic
34C22×Dic241D411yescharacteristic
35Dic964—42no—
36#16838760—42no—
37C2×#14515349—21no—
38C4⋊Dic241—21no—
39C4⋊Dic241—42no—
40C4⋊Dic241D411yescharacteristic
41#16838749—21no—
42#16838749—21no—
43#16838749—21no—
44#16838749—21no—
45#16838749—21no—
46#16838749—21no—
47#16838749—21no—
48C22⋊Dic241—21no—
49C4×Dic241—21no—
50C4×Dic241—21no—
51C2×Q8×C241D411yescharacteristic
52C22×C4×C241—21no—
53C22×C4×C241C2311yescharacteristic
54C2×C8×C241—21no—
55C4⋊C4×C241—21no—
56C4⋊C4×C241D411yescharacteristic
57C22⋊C4×C241—21no—
58Dic482—22no—
59Dic482—22no—
60Dic482—41no—
61Dic482—41no—
62Dic482—41no—
63Dic482—81no—
64C2×Dic241—21no—
65C2×Dic241—21no—
66C2×Dic241—22no—
67C2×Dic241—21no—
68C2×Dic241—21no—
69C2×Dic241—21no—
70C2×Dic241—41no—
71C2×Dic241—41no—
72C2×Dic241—41no—
73C2×Dic241Q1612yescomplemented
74#14515349—41no—
75C23×C241C2×D411yescharacteristic
76Q8×C241—41no—
77C2×C4×C241—22no—
78C2×C4×C241—21no—
79C2×C4×C241—21no—
80C2×C4×C241—41no—
81C2×C4×C241—41no—
82C2×C4×C241—41no—
83C2×C4×C241C2×D411yescharacteristic
84C2×C4×C241C2×D411yescharacteristic
85C8×C241—41no—
86C22×C241—21no—
87C22×C241—21no—
88C22×C241#12011yescharacteristic
89C22×C241C2×Q1611yescharacteristic
90C22×C241#13711yescharacteristic
91C4×C241—21no—
92C4×C241—21no—
93C4×C241—42no—
94C4×C241—41no—
95C4×C241—41no—
96Dic241—22no—
97Dic241—41no—
98Dic241—42no—
99Dic241—41no—
100Dic241—41no—
101C2×C241—21no—
102C2×C241—21no—
103C2×C241#45111yescharacteristic
104C2×C241#45611yescharacteristic
105C2×C241B(4,𝔽2)11yescharacteristic
106C241#160511yescharacteristic, complemented, Sylow
107#1605—2411nomaximal, Sylow
108#544—2411no—
109#451—2411no—
110#451—2411no—
111#395—2411no—
112#328—2411no—
113#328D24111yescharacteristic
114#324—2411no—
115C22×Q8—2411no—
116C2×Q16—4821no—
117C2×Q16—4821no—
118C4⋊Q8—4821no—
119C4⋊Q8—4821no—
120#125—4821no—
121#125—4821no—
122C22⋊Q8—4821no—
123C22⋊Q8—2411no—
124C22⋊Q8C2×D24111yescharacteristic
125#117—4821no—
126C2×C4⋊C4—4821no—
127C2×C4⋊C4—2411no—
128#103—4821no—
129#103—4821no—
130C22⋊C8—2411no—
131C22⋊C8C2×D24111yescharacteristic
132#95—4821no—
133#95C2×D24111yescharacteristic
134C2×Q8—9642no—
135C2×Q8—4821no—
136C2×Q8—4821no—
137C2×Q8—4821no—
138C2×Q8—2411no—
139C2×Q8D96411yescharacteristic
140C22×C4—21no—
141C22×C4—4821no—
142C22×C4—2411no—
143C22×C4—2411no—
144C22×C4C22×D24111yescharacteristic
145Q16—9642no—
146Q16—9642no—
147C2×C8—21no—
148C2×C8—4821no—
149C4⋊C4—21no—
150C4⋊C4—9642no—
151C4⋊C4—4821no—
152C4⋊C4—4821no—
153C4⋊C4—4821no—
154C4⋊C4—4821no—
155C4⋊C4—4821no—
156C4⋊C4—4821no—
157C4⋊C4—4821no—
158C4⋊C4—4821no—
159C4⋊C4—2411no—
160C4⋊C4D96411yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—4821no—
163C42—4821no—
164C42—4821no—
165C23D4×D24111yescharacteristic
166Q8—41no—
167Q8—19281no—
168Q8—9641no—
169Q8—9641no—
170Q8—9641no—
171Q8—4822no—
172Q8—4822no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—9641no—
180C2×C4—9641no—
181C2×C4—9641no—
182C2×C4—4822no—
183C2×C4—4821no—
184C2×C4—4821no—
185C2×C4—4821no—
186C2×C4—4821no—
187C2×C4—4821no—
188C2×C4—2412no—
189C2×C4D4×D24111yescharacteristic
190C2×C4C2×D96411yescharacteristic
191C8—41no—
192C8—9641no—
193C22—21no—
194C22—21no—
195C22#2144061211yescharacteristic
196C22Q16×D24111yescharacteristic
197C22#2144067111yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—9641no—
204C4—9642no—
205C4—9641no—
206C4—9641no—
207C4—4822no—
208C2—21no—
209C2—21no—
210C2#2950787411yescharacteristic
211C2#2950790111yescharacteristic
212C2#2950790511yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC22×C4×C241C23
FrattiniC22×C4C22×D241
Fitting#328×C241C2
socleC22×C241#120
prime radicalC23×C241C2×D4
hypercenter#328D241
hypocenterC241#1605
LCSG ▷ C22×C4×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
73. C2×Dic241Q16semidirect
106. C241#1605semidirect

Maximal subgroups

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

subgroupindex
#295083462
#295078752
#295078722
#295076382
#295074532
#295074422
#328×C2412
#1605241