Finite Group Databasebeta

← #44506753

Subgroups — #44506753

Order 30848.

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

normal subgroups only

This group has 228 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#29508459C211yesmaximal, characteristic
2#29508111C211yesmaximal, characteristic, complemented
3#29508077C211yesmaximal, characteristic, complemented
4#29508076C211yesmaximal, characteristic, complemented
5#29507456C211yesmaximal, characteristic, complemented
6#29507456C211yesmaximal, characteristic, complemented
7#329×C241C211yesmaximal, characteristic, complemented
8C2×Dic964—21no—
9C2×#16838759—21no—
10#21440642C2211yescharacteristic, complemented
11#21440631—21no—
12#21440630C2211yescharacteristic
13#21440630C2211yescharacteristic
14#21440628—21no—
15#21440628—21no—
16#21440612—21no—
17#21440612—21no—
18#21440610—21no—
19#21440567—21no—
20#21440566—21no—
21#21440564—21no—
22#21440563—21no—
23#21440553C2211yescharacteristic, complemented
24#124×C241C2211yescharacteristic
25#97×C241C2211yescharacteristic, complemented
26#97×C241C2211yescharacteristic, complemented
27C23×D241—21no—
28C2×Dic482—21no—
29C2×Dic482D411yescharacteristic
30C2×Dic482D411yescharacteristic
31C2×D964—21no—
32C2×D964D411yescharacteristic
33C2×D964D411yescharacteristic
34C2×C22⋊D241—21no—
35C2×C22⋊D241—21no—
36Dic964—42no—
37#16838759—42no—
38C2×#14515349—21no—
39C4⋊Dic241—21no—
40C4⋊Dic241—21no—
41C22⋊Dic241—21no—
42#16838747—21no—
43#16838747—21no—
44#16838747—21no—
45#16838747—21no—
46#16838747—21no—
47#16838747—21no—
48C4×Dic241—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—
57C22×D241—21no—
58C22×D241—81no—
59C22×D241—81no—
60C22×D241—81no—
61Dic482—41no—
62Dic482—41no—
63Dic482—41no—
64Dic482—41no—
65D964—41no—
66D964—41no—
67D964—81no—
68C22⋊D241—81no—
69C22⋊D241—81no—
70C2×Dic241—21no—
71C2×Dic241—21no—
72C2×Dic241—41no—
73#14515349—41no—
74C23×C241—21no—
75Q8×C241—41no—
76D4×C241—41no—
77C2×C4×C241—21no—
78C2×C4×C241C2×D411yescharacteristic
79C2×C4×C241C2×D411yescharacteristic
80C2×C4×C241C2×D411yescharacteristic
81C8×C241—22no—
82C8×C241—41no—
83C22×C241—41no—
84C22×C241—41no—
85C22×C241—41no—
86C22×C241#12011yescharacteristic
87C2×D241—41no—
88C2×D241—41no—
89C2×D241—41no—
90C2×D241—41no—
91C2×D241—41no—
92C2×D241—41no—
93C2×D241—84no—
94C4×C241—21no—
95C4×C241—21no—
96C4×C241—21no—
97C4×C241—41no—
98Dic241—41no—
99Dic241—41no—
100Dic241—81no—
101C2×C241—81no—
102C2×C241#45311yescharacteristic
103C2×C241#45511yescharacteristic
104C2×C241#45511yescharacteristic
105D241—81no—
106D241—81no—
107C241#165911yescharacteristic, complemented, Sylow
108#1659—2411nomaximal, Sylow
109H(3,𝔽4)—2411no—
110#497—2411no—
111#489—2411no—
112#489—2411no—
113#329—2411no—
114#329—2411no—
115#329D24111yescharacteristic, complemented
116C2×Q16—4821no—
117C2×SD16—4821no—
118C4⋊Q8—2411no—
119#124—4821no—
120#124—4821no—
121#124—4821no—
122#124—2411no—
123#124—2411no—
124#124C2×D24111yescharacteristic
125#120—4821no—
126#120—4821no—
127#120—4821no—
128#103—4821no—
129#103—4821no—
130#102—4821no—
131#102—4821no—
132#97—2411no—
133#97C2×D24111yescharacteristic, complemented
134#97C2×D24111yescharacteristic, complemented
135C24—4821no—
136C2×Q8—4821no—
137C2×Q8—2411no—
138C2×Q8—2411no—
139C2×Q8D96411yescharacteristic
140C2×D4—4821no—
141C2×D4—4821no—
142C2×D4—4821no—
143C2×D4—2411no—
144C2×D4—2411no—
145C2×D4D96411yescharacteristic
146Q16—9642no—
147SD16—9642no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—4821no—
151C4⋊C4—4821no—
152C4⋊C4—4821no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—4821no—
156C22⋊C4—4821no—
157C22⋊C4—4821no—
158C22⋊C4—4821no—
159C22⋊C4—4821no—
160C22⋊C4—4821no—
161C22⋊C4—4821no—
162C42—4821no—
163C42C22×D24111yescharacteristic
164C23—21no—
165C23—19281no—
166C23—19281no—
167C23—19281no—
168C23—4821no—
169C23—4821no—
170Q8—41no—
171Q8—9641no—
172Q8—9641no—
173Q8—9641no—
174Q8—9641no—
175D4—41no—
176D4—19281no—
177D4—19281no—
178D4—19281no—
179D4—9641no—
180D4—9641no—
181C2×C4—21no—
182C2×C4—9641no—
183C2×C4—4821no—
184C2×C4—4821no—
185C2×C4D4×D24111yescharacteristic
186C2×C4D4×D24111yescharacteristic
187C2×C4C2×D96411yescharacteristic
188C8—22no—
189C8—41no—
190C8—9641no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—19284no—
195C22—9641no—
196C22—9641no—
197C22—9641no—
198C22—9641no—
199C22—9641no—
200C22—9641no—
201C22#2144061211yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—19281no—
207C4—9641no—
208C4—9641no—
209C2—81no—
210C2—19281no—
211C2—19281no—
212C2#2950788611yescharacteristic
213C2#2950789611yescharacteristic
214C2#2950789711yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#329×C241C2
socleC22×C241#120
prime radical#29508459C2
hypercenter#329D241
hypocenterC241#1659
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. #29508111C2semidirect
3. #29508077C2semidirect
4. #29508076C2semidirect
5. #29507456C2semidirect
6. #29507456C2semidirect
7. #329×C241C2semidirect
10. #21440642C22semidirect
23. #21440553C22semidirect
25. #97×C241C22semidirect
26. #97×C241C22semidirect
107. C241#1659semidirect
115. #329D241semidirect
133. #97C2×D241semidirect
134. #97C2×D241semidirect

Maximal subgroups

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

subgroupindex
#295084592
#295081112
#295080772
#295080762
#295074562
#329×C2412
#1659241