Finite Group Databasebeta

← #44506597

Subgroups — #44506597

Order 30848.

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

normal subgroups only

This group has 234 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#29508370C211yesmaximal, characteristic
2#29508069C211yesmaximal, characteristic, complemented
3#29508008C211yesmaximal, characteristic, complemented
4#29508008C211yesmaximal, characteristic, complemented
5#29507444C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic, complemented
7#332×C241C211yesmaximal, characteristic, complemented
8C2×#16838771—21no—
9#21440642C2211yescharacteristic
10#21440627—22no—
11#21440618—21no—
12#21440617—21no—
13C4×D964C2211yescharacteristic
14C4×D964C2211yescharacteristic
15C4⋊C4×D241—21no—
16#21440574—21no—
17#21440574—21no—
18#21440565—22no—
19#21440564—21no—
20#21440564—21no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25#16838771—42no—
26#16838771—42no—
27C2×Dic482—21no—
28C2×D964—22no—
29C2×D964D411yescharacteristic
30C2×D964D411yescharacteristic
31C2×C4×D241—22no—
32C2×C4×D241—21no—
33C2×C4×D241—21no—
34C2×#14515349—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241D411yescharacteristic
38C4⋊Dic241D411yescharacteristic
39#16838749—22no—
40#16838747—22no—
41#16838747—21no—
42#16838747—21no—
43C2×Q8×C241—21no—
44C2×C8×C241—21no—
45C2×C8×C241—21no—
46C4⋊C4×C241—21no—
47C4⋊C4×C241D412yes—
48C42×C241C2311yescharacteristic
49C22×D241—21no—
50C22×D241—21no—
51Dic482—42no—
52D964—21no—
53D964—21no—
54D964—21no—
55D964—44no—
56D964SD1612yes—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—41no—
60C4×D241—44no—
61C4×D241—41no—
62C4×D241—41no—
63C4×D241—41no—
64C4×D241—41no—
65#14515349—41no—
66Q8×C241—41no—
67Q8×C241—41no—
68C2×C4×C241—22no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C8×C241—41no—
73C8×C241—41no—
74C22×C241#12011yescharacteristic
75C2×D241—22no—
76C2×D241—41no—
77C2×D241—41no—
78C2×D241—41no—
79C2×D241—41no—
80C2×D241—41no—
81C4×C241—21no—
82C4×C241—42no—
83C4×C241C2×SD1611yescharacteristic
84C4×C241#13511yescharacteristic
85C4×C241AGL(1,ℤ/8)11yescharacteristic
86C4×C241#13711yescharacteristic
87Dic241—41no—
88Dic241—41no—
89Dic241—81no—
90C2×C241#45011yescharacteristic
91C2×C241#45211yescharacteristic
92C2×C241#45411yescharacteristic
93D241—42no—
94D241—81no—
95C241#163511yescharacteristic, complemented, Sylow
96#1635—2411nomaximal, Sylow
97#547—2411no—
98#487—2411no—
99#476—2411no—
100#476—2411no—
101#332D24111yescharacteristic, complemented
102D4⋊C8—2411no—
103D4⋊C8—2411no—
104C2×#41—4821no—
105C4⋊Q8—2411no—
106C4⋊Q8C2×D24111yescharacteristic
107#123—4822no—
108C22⋊Q8—4821no—
109#121—4821no—
110C4×D4—2411no—
111C4×D4—2411no—
112C2×C4⋊C4—4821no—
113#106—4821no—
114#106—4821no—
115C4⋊C8C2×D24111yescharacteristic
116C4⋊C8C2×D24111yescharacteristic
117#103—4822no—
118#102—4821no—
119#102—4821no—
120C4×C8—2411no—
121#41—9642no—
122#41—9642no—
123C2×Q8—21no—
124C2×Q8—4821no—
125C2×D4—4822no—
126C2×D4—2411no—
127C2×D4—2411no—
128C22×C4—4822no—
129C22×C4—4821no—
130C22×C4—4821no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—4821no—
134C4⋊C4—21no—
135C4⋊C4—4822no—
136C4⋊C4—4821no—
137C4⋊C4—4821no—
138C4⋊C4—2411no—
139C4⋊C4—2411no—
140C4⋊C4D96412yes—
141C22⋊C4—4822no—
142C22⋊C4—4821no—
143C22⋊C4—4821no—
144C42C22×D24111yescharacteristic
145C23—4821no—
146C23—4821no—
147Q8—41no—
148Q8—41no—
149Q8—9642no—
150D4—9644no—
151D4—4821no—
152D4—4821no—
153D4—4821no—
154D4—2412no—
155C2×C4—22no—
156C2×C4—9644no—
157C2×C4—9641no—
158C2×C4—9641no—
159C2×C4—9641no—
160C2×C4—9641no—
161C2×C4—9641no—
162C2×C4—4821no—
163C2×C4—4821no—
164C2×C4D4×D24111yescharacteristic
165C2×C4D4×D24111yescharacteristic
166C2×C4C2×D96411yescharacteristic
167C8—41no—
168C8—41no—
169C8—9641no—
170C22—9641no—
171C22—9641no—
172C22—9641no—
173C22—9641no—
174C22—9641no—
175C22—4822no—
176C22#2144061211yescharacteristic
177C4—21no—
178C4—42no—
179C4—19281no—
180C4—9641no—
181C4—9641no—
182C4SD16×D24111yescharacteristic
183C4#2144066311yescharacteristic
184C4#2144066611yescharacteristic
185C4#2144067411yescharacteristic
186C2—19281no—
187C2—9642no—
188C2#2950786911yescharacteristic
189C2#2950788211yescharacteristic
190C2#2950789211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241#120
prime radical#29508370C2
hypercenter#332D241
hypocenterC241#1635
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #29508069C2semidirect
3. #29508008C2semidirect
4. #29508008C2semidirect
5. #29507444C2semidirect
6. #29507444C2semidirect
7. #332×C241C2semidirect
95. C241#1635semidirect
101. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295083702
#295080692
#295080082
#295074442
#332×C2412
#1635241