Finite Group Databasebeta

← #44506763

Subgroups — #44506763

Order 30848.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#29508461C211yesmaximal, characteristic
2#29508126C211yesmaximal, characteristic, complemented
3#29508112C211yesmaximal, characteristic, complemented
4#29508077C211yesmaximal, characteristic, complemented
5#29507458C211yesmaximal, characteristic, complemented
6#29507456C211yesmaximal, characteristic, complemented
7#329×C241C211yesmaximal, characteristic, complemented
8C2×#16838760—21no—
9C2×#16838758—21no—
10#21440642C2211yescharacteristic
11#21440634C2211yescharacteristic
12#21440630C2211yescharacteristic
13#21440626—21no—
14#21440624—21no—
15#21440619—21no—
16#21440618—21no—
17#21440615—21no—
18#21440614—21no—
19#21440576—21no—
20#21440574—21no—
21#21440567—21no—
22#21440564—21no—
23#21440553C2211yescharacteristic
24#124×C241C2211yescharacteristic
25#97×C241C2211yescharacteristic
26#97×C241C2211yescharacteristic
27C2×Dic482—21no—
28C2×Dic482D411yescharacteristic
29C2×D964D411yescharacteristic
30C2×C22⋊D241—21no—
31C2×C22⋊D241—21no—
32C22×Dic241—21no—
33C2×C4×D241—21no—
34#16838760—42no—
35#16838758—42no—
36C2×#14515349—21no—
37C4⋊Dic241—21no—
38C4⋊Dic241—21no—
39C4⋊Dic241—21no—
40C4⋊Dic241D411yescharacteristic
41C4⋊Dic241D411yescharacteristic
42#16838749—21no—
43#16838749—21no—
44#16838749—21no—
45C22⋊Dic241—21no—
46#16838747—21no—
47#16838747—21no—
48#16838747—21no—
49C2×Q8×C241D411yescharacteristic
50C2×D4×C241D411yescharacteristic
51C2×C8×C241—21no—
52C2×C8×C241—21no—
53C22⋊C4×C241—21no—
54C22⋊C4×C241—21no—
55C42×C241C2311yescharacteristic
56C22×D241—21no—
57Dic482—41no—
58Dic482—41no—
59Dic482—41no—
60D964—41no—
61C22⋊D241—81no—
62C22⋊D241—81no—
63C2×Dic241—21no—
64C2×Dic241—21no—
65C2×Dic241—21no—
66C2×Dic241—41no—
67C2×Dic241—81no—
68C4×D241—81no—
69#14515349—22no—
70C23×C241—21no—
71Q8×C241—41no—
72D4×C241—41no—
73C2×C4×C241—21no—
74C2×C4×C241C2×D411yescharacteristic
75C2×C4×C241C2×D411yescharacteristic
76C2×C4×C241C2×D411yescharacteristic
77C8×C241—22no—
78C8×C241—41no—
79C22×C241—41no—
80C22×C241—41no—
81C22×C241—41no—
82C22×C241#12011yescharacteristic
83C2×D241—41no—
84C2×D241—41no—
85C2×D241—41no—
86C4×C241—21no—
87C4×C241—21no—
88C4×C241—21no—
89C4×C241—41no—
90Dic241—41no—
91Dic241—41no—
92Dic241—41no—
93Dic241—81no—
94C2×C241—81no—
95C2×C241#45311yescharacteristic
96C2×C241#45511yescharacteristic
97C2×C241#45611yescharacteristic
98D241—81no—
99C241#166111yescharacteristic, complemented, Sylow
100#1661—2411nomaximal, Sylow
101#562—2411no—
102#501—2411no—
103#497—2411no—
104#489—2411no—
105#330—2411no—
106#329—2411no—
107#329D24111yescharacteristic, complemented
108C2×Q16—4821no—
109C2×SD16—4821no—
110C4⋊Q8—2411no—
111#125—2411no—
112#124—2411no—
113#124C2×D24111yescharacteristic
114#123—4821no—
115#123—4821no—
116C22⋊Q8—4821no—
117C22⋊Q8—4821no—
118#121—4821no—
119#121—4821no—
120#107—4821no—
121#106—4821no—
122#103—4821no—
123#102—4821no—
124#97—2411no—
125#97C2×D24111yescharacteristic
126#97C2×D24111yescharacteristic
127C2×Q8—4821no—
128C2×Q8—2411no—
129C2×Q8D96411yescharacteristic
130C2×D4—4821no—
131C2×D4—4821no—
132C2×D4—2411no—
133C2×D4D96411yescharacteristic
134C22×C4—4821no—
135C22×C4—4821no—
136Q16—9642no—
137SD16—9642no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—4821no—
141C4⋊C4—4821no—
142C4⋊C4—4821no—
143C4⋊C4—4821no—
144C4⋊C4—4821no—
145C4⋊C4—4821no—
146C4⋊C4—4821no—
147C4⋊C4—2411no—
148C4⋊C4—2411no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—4821no—
152C22⋊C4—4821no—
153C22⋊C4—4821no—
154C22⋊C4—4821no—
155C42C22×D24111yescharacteristic
156C23—21no—
157C23—4821no—
158Q8—41no—
159Q8—9641no—
160Q8—9641no—
161Q8—9641no—
162D4—41no—
163D4—19281no—
164D4—19281no—
165D4—9641no—
166C2×C4—21no—
167C2×C4—19281no—
168C2×C4—19281no—
169C2×C4—9641no—
170C2×C4—4821no—
171C2×C4—4821no—
172C2×C4—4821no—
173C2×C4D4×D24111yescharacteristic
174C2×C4D4×D24111yescharacteristic
175C2×C4C2×D96411yescharacteristic
176C8—22no—
177C8—41no—
178C8—4822no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—9641no—
183C22—9641no—
184C22—9641no—
185C22#2144061211yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—19281no—
191C4—9641no—
192C4—9641no—
193C4—9641no—
194C2—81no—
195C2—19281no—
196C2#2950788711yescharacteristic
197C2#2950789611yescharacteristic
198C2#2950790111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241#120
prime radical#29508461C2
hypercenter#329D241
hypocenterC241#1661
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #29508126C2semidirect
3. #29508112C2semidirect
4. #29508077C2semidirect
5. #29507458C2semidirect
6. #29507456C2semidirect
7. #329×C241C2semidirect
99. C241#1661semidirect
107. #329D241semidirect

Maximal subgroups

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

subgroupindex
#295084612
#295081262
#295081122
#295080772
#295074582
#295074562
#329×C2412
#1661241