Finite Group Databasebeta

← #71285

Subgroups — #71285

Order 384.

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

normal subgroups only

This group has 278 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#5718C211yesmaximal, characteristic, complemented
2C3×#493C211yesmaximal, characteristic, complemented
3#5075C211yesmaximal, characteristic, complemented
4#5072C211yesmaximal, characteristic, complemented
5#4544C211yesmaximal, characteristic, complemented
6#4459C211yesmaximal, characteristic, complemented
7#4456C211yesmaximal, characteristic, complemented
8#1621—31nomaximal, Sylow
9C2×#237—21no—
10C2×C3×D8—22no—
11C3×#127C2211yescharacteristic
12C3×#127C2211yescharacteristic
13#940—21no—
14#939—22no—
15#938—21no—
16D4×Dic3—21no—
17C2×#214—21no—
18C2×#213—21no—
19C4×D12C2211yescharacteristic
20C4×Dic6C2211yescharacteristic
21C3×C4×C8C2211yescharacteristic
22#832—21no—
23#832—21no—
24C4⋊(C3⋊C8)C2211yescharacteristic
25C4⋊(C3⋊C8)C2211yescharacteristic
26#550—31no—
27#493D311yescharacteristic, complemented
28#460—31no—
29#459—31no—
30#331—31no—
31Q8⋊C8—31no—
32D4⋊C8—31no—
33C2×C3×D4—21no—
34C2×C3×D4—21no—
35C2×C3×D4—21no—
36C2×C3×D4—21no—
37C2×C3×D4—21no—
38C2×C3×D4D412yes—
39C2×#67—22no—
40C2×#67—22no—
41C22×Dic3—22no—
42#237—42no—
43#237—42no—
44C2×D12D411yescharacteristic
45C2×C4×D3—21no—
46C2×Dic6D411yescharacteristic
47C3×D8—44no—
48C2×C3×C8—21no—
49C3×C42C2311yescharacteristic
50#217—22no—
51#214—42no—
52#213—42no—
53(C2×D3)⋊C4—21no—
54C4⋊Dic3D411yescharacteristic
55C4⋊Dic3D411yescharacteristic
56Dic3⋊C4—21no—
57C4×Dic3—21no—
58C2×C3⋊C8—21no—
59C2×C3⋊C8—21no—
60C2×#41—61no—
61C2×SD16—61no—
62C2×D8—22no—
63C2×D8—61no—
64#127—61no—
65#127C2×D311yescharacteristic
66#127C2×D311yescharacteristic
67#121—61no—
68#121—62no—
69C4×Q8—31no—
70C4×D4—31no—
71C4×D4—61no—
72C4⋊C8—31no—
73C4⋊C8—31no—
74#102—61no—
75#102—61no—
76C4×C8C2×D311yescharacteristic
77C23×C3—22no—
78C23×C3—41no—
79C22×D3—21no—
80C3×D4—42no—
81C3×D4—42no—
82C3×D4—41no—
83C3×D4—41no—
84C3×D4—41no—
85C3×D4—41no—
86C3×D4—41no—
87C3×D4—41no—
88C3×D4—41no—
89C3×D4—41no—
90C2×C3×C4C2×D411yescharacteristic
91C2×C3×C4C2×D411yescharacteristic
92C2×C3×C4C2×D411yescharacteristic
93#67—44no—
94#67—82no—
95C2×Dic3—21no—
96C2×Dic3—21no—
97C2×Dic3—21no—
98C2×Dic3—44no—
99D12—21no—
100D12—21no—
101C4×D3—41no—
102C4×D3—41no—
103Dic6—21no—
104Dic6D812yescomplemented
105C3×C8—22no—
106C3⋊C8—41no—
107C3⋊C8—41no—
108#41—122no—
109#41—122no—
110C2×Q8—31no—
111C2×D4—21no—
112C2×D4—21no—
113C2×D4—21no—
114C2×D4—21no—
115C2×D4—21no—
116C2×D4—31no—
117C2×D4—62no—
118C2×D4—62no—
119C2×D4#6712yes—
120C22×C4—62no—
121C22×C4—61no—
122SD16—122no—
123D8—44no—
124D8—122no—
125C2×C8—21no—
126C2×C8—61no—
127C2×C8—61no—
128C4⋊C4—31no—
129C4⋊C4—31no—
130C4⋊C4—61no—
131C22⋊C4—62no—
132C22⋊C4—61no—
133C42—61no—
134C42C22×D311yescharacteristic
135C22×C3—42no—
136C22×C3—42no—
137C22×C3—42no—
138C22×C3—81no—
139C22×C3—81no—
140C22×C3—81no—
141C22×C3#12011yescharacteristic
142C2×D3—41no—
143C2×D3—41no—
144C2×D3—41no—
145C3×C4—21no—
146C3×C4C2×D811yescharacteristic
147C3×C4#13511yescharacteristic
148C3×C4AGL(1,ℤ/8)11yescharacteristic
149C3×C4AGL(1,ℤ/8)11yescharacteristic
150Dic3—22no—
151Dic3—41no—
152Dic3—41no—
153C23—22no—
154C23—41no—
155C23—61no—
156Q8—32no—
157Q8—61no—
158D4—42no—
159D4—42no—
160D4—41no—
161D4—41no—
162D4—41no—
163D4—41no—
164D4—41no—
165D4—41no—
166D4—41no—
167D4—41no—
168D4—61no—
169D4—61no—
170D4—124no—
171D4—242no—
172C2×C4—61no—
173C2×C4—61no—
174C2×C4—61no—
175C2×C4—124no—
176C2×C4—121no—
177C2×C4—121no—
178C2×C4D3×D411yescharacteristic
179C2×C4D3×D411yescharacteristic
180C2×C4C2×#6711yescharacteristic
181C8—22no—
182C8—121no—
183C8—121no—
184C2×C3—82no—
185C2×C3—161no—
186C2×C3#44711yescharacteristic
187C2×C3#44911yescharacteristic
188C2×C3#45311yescharacteristic
189D3—81no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—81no—
194C22—81no—
195C22—81no—
196C22—121no—
197C22—121no—
198C22—121no—
199C22#93711yescharacteristic
200C4—21no—
201C4—62no—
202C4—121no—
203C4—121no—
204C4D3×D811yescharacteristic
205C4#91111yescharacteristic
206C4#91111yescharacteristic
207C4#91211yescharacteristic
208C3#162111yescharacteristic, complemented, Sylow
209C2—82no—
210C2—161no—
211C2—241no—
212C2#507711yescharacteristic
213C2#515611yescharacteristic
214C2#515811yescharacteristic
subgroupG/H
centerC22#937
commutator, cosocleC3×C42C23
FrattiniC42C22×D3
FittingC3×#493C2
socleC22×C3#120
hypercenter#493D3
hypocenterC3#1621
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #5718C2semidirect
2. C3×#493C2semidirect
3. #5075C2semidirect
4. #5072C2semidirect
5. #4544C2semidirect
6. #4459C2semidirect
7. #4456C2semidirect
27. #493D3semidirect
104. Dic6D8semidirect
208. C3#1621semidirect

Maximal subgroups

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

subgroupindex
#57182
C3×#4932
#50752
#50722
#45442
#44592
#44562
#16213