Finite Group Databasebeta

← #1020⋊C4 #72990

Subgroups — #1020⋊C4 #72990

Order 384.

241 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 241 conjugacy classes of subgroups — too many to draw. Only its 16 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
1C2×#1020C211yesmaximal, characteristic
2#5936C211yesmaximal, characteristic, complemented
3#379⋊C3C211yesmaximal, characteristic, complemented
4#1889—31nomaximal, Sylow
5C2×C22⋊A4C2211yescharacteristic
6#1020C412yescomplemented
7C4×S4—41nomaximal
8C2×#120—31no—
9#518—31no—
10C2×#99—31no—
11#379—31no—
12#379D311yescharacteristic, complemented
13#342—31no—
14#342—31no—
15C22⋊A4C2×C411yescharacteristic, complemented
16C2×S4—41no—
17C2×S4—81no—
18C4×A4—41no—
19SL(2,ℤ/4)—41no—
20SL(2,ℤ/4)—81no—
21C25C2×D311yescharacteristic
22C22×D4—31no—
23C22×D4—61no—
24#120—32no—
25#120—32no—
26#120—62no—
27C4×D4—61no—
28C4×D4—61no—
29C4×D4—61no—
30C4×D4—61no—
31#117—61no—
32C2×C22⋊C4—31no—
33C2×C22⋊C4—31no—
34C2×C22⋊C4—31no—
35C2×C22⋊C4—31no—
36C2×C22⋊C4—31no—
37C2×C22⋊C4—61no—
38C2×C22⋊C4—61no—
39C2×C22⋊C4—61no—
40C2×C22⋊C4—61no—
41#99—62no—
42C2×A4—41no—
43C2×A4—81no—
44C2×A4—81no—
45S4—42no—
46S4—82no—
47C4×D3—161no—
48C24—31no—
49C24—31no—
50C24—31no—
51C24—61no—
52C24—61no—
53C24—61no—
54C24—61no—
55C24C4×D311yescharacteristic, complemented
56C2×D4—32no—
57C2×D4—32no—
58C2×D4—61no—
59C2×D4—61no—
60C2×D4—61no—
61C2×D4—61no—
62C2×D4—62no—
63C2×D4—62no—
64C2×D4—121no—
65C2×D4—121no—
66C2×D4—121no—
67C2×D4—121no—
68C22×C4—31no—
69C22×C4—31no—
70C22×C4—31no—
71C22×C4—31no—
72C22×C4—61no—
73C22×C4—61no—
74C22×C4—61no—
75C22×C4—61no—
76C22×C4S411yescharacteristic, complemented
77C4⋊C4—61no—
78C4⋊C4—61no—
79C22⋊C4—32no—
80C22⋊C4—62no—
81C22⋊C4—62no—
82C22⋊C4—61no—
83C22⋊C4—61no—
84C22⋊C4—61no—
85C22⋊C4—61no—
86C22⋊C4—61no—
87C22⋊C4—61no—
88C22⋊C4—61no—
89C22⋊C4—61no—
90C22⋊C4—61no—
91C22⋊C4—61no—
92C22⋊C4—61no—
93C22⋊C4—121no—
94C22⋊C4—121no—
95C22⋊C4—121no—
96C22⋊C4—121no—
97C42—61no—
98C42—61no—
99C2×D3—161no—
100A4—41no—
101A4—81no—
102A4—81no—
103C3×C4—161no—
104Dic3—161no—
105C23—21no—
106C23—21no—
107C23—31no—
108C23—31no—
109C23—31no—
110C23—31no—
111C23—31no—
112C23—31no—
113C23—32no—
114C23—61no—
115C23—61no—
116C23—61no—
117C23—61no—
118C23—61no—
119C23—61no—
120C23—61no—
121C23—61no—
122C23—61no—
123C23—61no—
124C23—61no—
125C23—61no—
126C23—121no—
127C23—121no—
128C23—121no—
129C23—121no—
130C23—121no—
131C23—121no—
132C23—121no—
133C23—121no—
134C23C2×S411yescharacteristic
135D4—62no—
136D4—62no—
137D4—62no—
138D4—62no—
139D4—122no—
140D4—122no—
141D4—122no—
142D4—122no—
143C2×C4—32no—
144C2×C4—61no—
145C2×C4—61no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—62no—
151C2×C4—121no—
152C2×C4—121no—
153C2×C4—121no—
154C2×C4—121no—
155C2×C4—121no—
156C2×C4—121no—
157C2×C4—121no—
158C2×C4—121no—
159C2×C4—241no—
160C2×C4—241no—
161C2×C3—161no—
162D3—162no—
163C22—21no—
164C22—21no—
165C22—31no—
166C22—31no—
167C22—31no—
168C22—31no—
169C22—31no—
170C22—31no—
171C22—61no—
172C22—61no—
173C22—62no—
174C22—61no—
175C22—61no—
176C22—61no—
177C22—61no—
178C22—61no—
179C22—61no—
180C22—61no—
181C22—61no—
182C22—121no—
183C22—121no—
184C22—121no—
185C22—121no—
186C22—121no—
187C22—121no—
188C22—121no—
189C22—122no—
190C22—121no—
191C22—241no—
192C22C4×S411yescharacteristic
193C4—41no—
194C4—62no—
195C4—121no—
196C4—121no—
197C4—122no—
198C4—121no—
199C4—241no—
200C3—161noSylow
201C2—31no—
202C2—31no—
203C2—61no—
204C2—61no—
205C2—61no—
206C2—61no—
207C2—122no—
208C2#1020⋊C211yescharacteristic
subgroupG/H
center, hypercenterC2#1020⋊C2
commutator, hypocenterC22⋊A4C2×C4
Frattini, socleC23C2×S4
Fitting#379D3
prime radicalC2×#1020C2
cosocleC2×C22⋊A4C22
LCSG ▷ C22⋊A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. #5936C2semidirect
3. #379⋊C3C2semidirect
6. #1020C4semidirect
12. #379D3semidirect
15. C22⋊A4C2×C4semidirect
55. C24C4×D3semidirect
76. C22×C4S4semidirect

Maximal subgroups

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

subgroupindex
C2×#10202
#59362
#379⋊C32
#18893
C4×S44