Finite Group Databasebeta

← #44506697

Subgroups — #44506697

Order 30848.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic482C211yesmaximal, characteristic
2#29508122C211yesmaximal, characteristic, complemented
3#29507997C211yesmaximal, characteristic
4#29507928C211yesmaximal, characteristic, complemented
5#29507464C211yesmaximal, characteristic, complemented
6#29507449C211yesmaximal, characteristic, complemented
7D4⋊C8×C241C211yesmaximal, characteristic
8C22×Dic482—21no—
9C2×Dic964—21no—
10#21440642C2211yescharacteristic
11#21440642C2211yescharacteristic
12#21440641—21no—
13#21440621—21no—
14#21440619—22no—
15C4×Dic482C2211yescharacteristic
16D4×Dic241—21no—
17#21440576—22no—
18#21440575—21no—
19C4⋊#14515349C2211yescharacteristic
20#21440567—21no—
21#21440563—21no—
22C4×D4×C241C2211yescharacteristic
23C4⋊C8×C241C2211yescharacteristic
24C4×C8×C241C2211yescharacteristic
25C2×Dic482—22no—
26C2×Dic482—21no—
27C2×Dic482—21no—
28C2×Dic482—42no—
29C2×Dic482—42no—
30C2×Dic482D411yescharacteristic
31C22×Dic241—22no—
32Dic964—42no—
33C2×#14515349—21no—
34C4⋊Dic241—21no—
35C4⋊Dic241—21no—
36C4⋊Dic241—21no—
37C4⋊Dic241D411yescharacteristic
38C4⋊Dic241D412yes—
39#16838749—22no—
40#16838749—21no—
41C22⋊Dic241—22no—
42C4×Dic241—21no—
43C2×D4×C241D411yescharacteristic
44C22×C4×C241—21no—
45C2×C8×C241—21no—
46C2×C8×C241—21no—
47C4⋊C4×C241D411yescharacteristic
48C22⋊C4×C241—21no—
49C42×C241C2311yescharacteristic
50Dic482—21no—
51Dic482—44no—
52Dic482—41no—
53Dic482—41no—
54Dic482—41no—
55Dic482—41no—
56Dic482D812yes—
57C2×Dic241—21no—
58C2×Dic241—21no—
59C2×Dic241—22no—
60C2×Dic241—44no—
61C2×Dic241—41no—
62#14515349—41no—
63C23×C241—21no—
64D4×C241—21no—
65D4×C241Q1612yescomplemented
66C2×C4×C241—21no—
67C2×C4×C241—41no—
68C2×C4×C241—41no—
69C2×C4×C241C2×D411yescharacteristic
70C2×C4×C241C2×D411yescharacteristic
71C2×C4×C241C2×D411yescharacteristic
72C8×C241—22no—
73C8×C241—41no—
74C22×C241—22no—
75C22×C241—41no—
76C22×C241—41no—
77C22×C241#12011yescharacteristic
78C4×C241—21no—
79C4×C241—41no—
80C4×C241C2×D811yescharacteristic
81C4×C241C2×Q1611yescharacteristic
82C4×C241AGL(1,ℤ/8)11yescharacteristic
83C4×C241#13711yescharacteristic
84Dic241—22no—
85Dic241—42no—
86Dic241—41no—
87Dic241—81no—
88C2×C241—42no—
89C2×C241#44711yescharacteristic
90C2×C241#45111yescharacteristic
91C2×C241#45611yescharacteristic
92C241#164911yescharacteristic, complemented, Sylow
93#1649—2411nomaximal, Sylow
94D4×Q8—2411no—
95#500—2411no—
96#474—2411no—
97#462—2411no—
98#332—2411no—
99Q8⋊C8—2411no—
100D4⋊C8D24111yescharacteristic
101C22×Q8—4821no—
102C2×Q16—4821no—
103C4⋊Q8—4821no—
104C4⋊Q8—2411no—
105C4⋊Q8—2411no—
106C22⋊Q8—4822no—
107C22⋊Q8—4821no—
108C4×Q8—2411no—
109C4×D4—4821no—
110C4×D4C2×D24111yescharacteristic
111#107—4822no—
112#107—4821no—
113C4⋊C8—2411no—
114C4⋊C8C2×D24111yescharacteristic
115#103—4821no—
116#102—4821no—
117C4×C8C2×D24111yescharacteristic
118C2×Q8—9642no—
119C2×Q8—9642no—
120C2×Q8—4822no—
121C2×Q8—4821no—
122C2×Q8—4821no—
123C2×Q8—2411no—
124C2×D4D96411yescharacteristic
125C22×C4—21no—
126C22×C4—4822no—
127Q16—9642no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—4821no—
131C4⋊C4—4822no—
132C4⋊C4—4821no—
133C4⋊C4—4821no—
134C4⋊C4—4821no—
135C4⋊C4—4821no—
136C4⋊C4—2411no—
137C4⋊C4—2412no—
138C4⋊C4D96411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—4822no—
141C42—4821no—
142C42C22×D24111yescharacteristic
143C23—21no—
144Q8—9644no—
145Q8—9641no—
146Q8—9641no—
147Q8—9641no—
148Q8—9641no—
149Q8—4821no—
150Q8—2412no—
151D4—21no—
152D4Dic96412yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—9641no—
157C2×C4—9644no—
158C2×C4—4821no—
159C2×C4—4822no—
160C2×C4—4821no—
161C2×C4D4×D24111yescharacteristic
162C2×C4D4×D24111yescharacteristic
163C2×C4C2×D96411yescharacteristic
164C8—22no—
165C8—41no—
166C8—9641no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#2144061211yescharacteristic
171C4—21no—
172C4—41no—
173C4—19281no—
174C4—9642no—
175C4—9641no—
176C4—4822no—
177C4D8×D24111yescharacteristic
178C4C2×Dic96411yescharacteristic
179C4#2144066911yescharacteristic
180C4#2144067511yescharacteristic
181C2—42no—
182C2#2950785211yescharacteristic
183C2#2950787511yescharacteristic
184C2#2950790111yescharacteristic
subgroupG/H
centerC22#21440612
commutator, cosocleC42×C241C23
FrattiniC42C22×D241
FittingD4⋊C8×C241C2
socleC22×C241#120
prime radicalC2×D4×C241D4
hypercenterD4⋊C8D241
hypocenterC241#1649
LCSG ▷ C42×C241 ▷ C22×C241 ▷ C241
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29508122C2semidirect
4. #29507928C2semidirect
5. #29507464C2semidirect
6. #29507449C2semidirect
65. D4×C241Q16semidirect
92. C241#1649semidirect
152. D4Dic964semidirect

Maximal subgroups

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

subgroupindex
D4×Dic4822
#295081222
#295079972
#295079282
#295074642
#295074492
D4⋊C8×C2412
#1649241