Finite Group Databasebeta

← #44506611

Subgroups — #44506611

Order 30848.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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#29508382C211yesmaximal, characteristic
2#29508069C211yesmaximal, characteristic, complemented
3#29508013C211yesmaximal, characteristic, complemented
4#29508008C211yesmaximal, characteristic
5#29507447C211yesmaximal, characteristic, complemented
6#29507444C211yesmaximal, characteristic
7#332×C241C211yesmaximal, characteristic, complemented
8C2×Q8×D241—21no—
9#21440642C2211yescharacteristic
10#21440641—21no—
11#21440620—22no—
12#21440618—21no—
13C4×Dic482C2211yescharacteristic
14C4×D964C2211yescharacteristic
15#21440604—21no—
16#21440576—21no—
17#21440574—21no—
18#21440567—21no—
19#21440565—22no—
20#21440564—21no—
21C4×#14515349C2211yescharacteristic
22C4⋊Q8×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4⋊C8×C241C2211yescharacteristic
25C2×Dic482—22no—
26C2×Dic482—21no—
27C2×Dic482D411yescharacteristic
28Q8×D241—42no—
29Q8×D241—42no—
30C2×D964D411yescharacteristic
31C2×C4×D241—22no—
32C2×C4×D241—21no—
33C2×#14515349—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241D411yescharacteristic
37C4⋊Dic241D411yescharacteristic
38#16838749—22no—
39#16838749—21no—
40#16838747—22no—
41#16838747—21no—
42C4×Dic241—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—
50Dic482—21no—
51Dic482—44no—
52Dic482—42no—
53Dic482SD1612yes—
54D964—21no—
55D964Q1612yes—
56C2×Dic241—21no—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—41no—
60C4×D241—44no—
61C4×D241—41no—
62C4×D241—41no—
63#14515349—41no—
64Q8×C241—41no—
65Q8×C241—41no—
66C2×C4×C241—22no—
67C2×C4×C241C2×D411yescharacteristic
68C2×C4×C241C2×D411yescharacteristic
69C2×C4×C241C2×D411yescharacteristic
70C8×C241—41no—
71C8×C241—41no—
72C22×C241#12011yescharacteristic
73C2×D241—22no—
74C2×D241—41no—
75C2×D241—41no—
76C4×C241—21no—
77C4×C241—42no—
78C4×C241C2×SD1611yescharacteristic
79C4×C241C2×Q1611yescharacteristic
80C4×C241AGL(1,ℤ/8)11yescharacteristic
81C4×C241#13711yescharacteristic
82Dic241—22no—
83Dic241—41no—
84Dic241—41no—
85Dic241—81no—
86C2×C241#45011yescharacteristic
87C2×C241#45111yescharacteristic
88C2×C241#45411yescharacteristic
89D241—42no—
90C241#163711yescharacteristic, complemented, Sylow
91#1637—2411nomaximal, Sylow
92D4×Q8—2411no—
93#487—2411no—
94#477—2411no—
95#476—2411no—
96#332D24111yescharacteristic, complemented
97Q8⋊C8—2411no—
98D4⋊C8—2411no—
99C22×Q8—4821no—
100C4⋊Q8—4821no—
101C4⋊Q8—2411no—
102C4⋊Q8C2×D24111yescharacteristic
103C22⋊Q8—4821no—
104C22⋊Q8—4822no—
105C4×Q8—2411no—
106C4×D4—4821no—
107C4×D4—2411no—
108#107—4821no—
109#106—4821no—
110C4⋊C8C2×D24111yescharacteristic
111C4⋊C8C2×D24111yescharacteristic
112#103—4821no—
113#103—4822no—
114#102—4821no—
115C4×C8—2411no—
116C2×Q8—21no—
117C2×Q8—9642no—
118C2×Q8—9642no—
119C2×Q8—4822no—
120C2×Q8—4821no—
121C2×Q8—2411no—
122C2×D4—2411no—
123C22×C4—4822no—
124C22×C4—4821no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—4821no—
128C4⋊C4—21no—
129C4⋊C4—4822no—
130C4⋊C4—4821no—
131C4⋊C4—4821no—
132C4⋊C4—4821no—
133C4⋊C4—2411no—
134C4⋊C4—2411no—
135C4⋊C4D96412yes—
136C22⋊C4—4822no—
137C22⋊C4—4821no—
138C42—4821no—
139C42C22×D24111yescharacteristic
140C23—4821no—
141Q8—41no—
142Q8—41no—
143Q8—9642no—
144Q8—9644no—
145Q8—4821no—
146Q8—2412no—
147D4—4821no—
148D4—2412no—
149C2×C4—22no—
150C2×C4—9644no—
151C2×C4—9641no—
152C2×C4—9641no—
153C2×C4—9641no—
154C2×C4—4821no—
155C2×C4—4821no—
156C2×C4—4821no—
157C2×C4D4×D24111yescharacteristic
158C2×C4D4×D24111yescharacteristic
159C2×C4C2×D96411yescharacteristic
160C8—41no—
161C8—41no—
162C8—9641no—
163C22—9641no—
164C22—9641no—
165C22—4822no—
166C22#2144061211yescharacteristic
167C4—21no—
168C4—42no—
169C4—19281no—
170C4—9641no—
171C4—9641no—
172C4—4822no—
173C4SD16×D24111yescharacteristic
174C4Q16×D24111yescharacteristic
175C4#2144066611yescharacteristic
176C4#2144067111yescharacteristic
177C2—9642no—
178C2#2950786911yescharacteristic
179C2#2950787411yescharacteristic
180C2#2950789211yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
Fitting#332×C241C2
socleC22×C241#120
prime radicalC2×D964D4
hypercenter#332D241
hypocenterC241#1637
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. #29508013C2semidirect
5. #29507447C2semidirect
7. #332×C241C2semidirect
90. C241#1637semidirect
96. #332D241semidirect

Maximal subgroups

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

subgroupindex
#295083822
#295080692
#295080132
#295080082
#295074472
#295074442
#332×C2412
#1637241