Finite Group Databasebeta

← #68908

Subgroups — #68908

Order 384.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×Dic12C211yesmaximal, characteristic
2C2×#887C211yesmaximal, characteristic
3#4973C211yesmaximal, characteristic
4C2×#810C211yesmaximal, characteristic
5C2×#810C211yesmaximal, characteristic
6C3×#340C211yesmaximal, characteristic
7#4550C211yesmaximal, characteristic
8#1878—31nomaximal, Sylow
9C22×Dic6C2211yescharacteristic
10C22×Dic6C2211yescharacteristic
11C22×C3×C8C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×Dic3⋊C4—21no—
15C2×C4×Dic3—21no—
16C2×C4×Dic3C2211yescharacteristic
17C22×C3⋊C8C2211yescharacteristic
18C2×Dic12—22no—
19C2×Dic12—22no—
20C2×Dic12C414yescomplemented
21#887—22no—
22#887—22no—
23C3⋊#95—21no—
24C3⋊#95—21no—
25#810—22no—
26#810—22no—
27C22×Q16—31no—
28C2×C4×Q8—31no—
29C2×#103—31no—
30C2×#103—31no—
31#391—31no—
32#340D311yescharacteristic
33#336—31no—
34C22×C3×C4—21no—
35C22×C3×C4—21no—
36C22×C3×C4C2311yescharacteristic
37C22×Dic3—21no—
38C22×Dic3—21no—
39C22×Dic3D411yescharacteristic
40C22×Dic3D411yescharacteristic
41C2×Dic6—21no—
42C2×Dic6—21no—
43C2×Dic6—21no—
44C2×Dic6—21no—
45C2×Dic6—21no—
46C2×Dic6—21no—
47C2×Dic6—21no—
48C2×Dic6—21no—
49C2×Dic6C2×C412yes—
50C2×Dic6C2×C412yes—
51C2×Dic6D412yes—
52C2×Dic6D412yes—
53C2×C3×C8—21no—
54C2×C3×C8—21no—
55C2×C3×C8C2×C412yes—
56C3×C4⋊C4—21no—
57C3×C4⋊C4—21no—
58C3×C4⋊C4—21no—
59C3×C4⋊C4D412yes—
60Dic3⋊C4—24no—
61C4×Dic3—24no—
62C4×Dic3—21no—
63C4×Dic3—21no—
64C2×C3⋊C8—21no—
65C2×C3⋊C8—21no—
66C2×C3⋊C8—21no—
67Dic12—28no—
68C22×Q8—31no—
69C22×Q8—31no—
70C2×Q16—34no—
71C2×Q16—62no—
72C2×Q16—62no—
73C22×C8—31no—
74C22×C8C2×D311yescharacteristic
75C4×Q8—62no—
76C4×Q8—62no—
77C2×C4⋊C4—61no—
78C2×C4⋊C4C2×D311yescharacteristic
79C2×C4⋊C4C2×D311yescharacteristic
80C2×C42—31no—
81C2×C42—61no—
82#103—62no—
83#103—62no—
84#95—61no—
85#95—61no—
86C23×C3C2×D411yescharacteristic
87C2×C3×C4—22no—
88C2×C3×C4—41no—
89C2×C3×C4—41no—
90C2×C3×C4—41no—
91C2×C3×C4—41no—
92C2×C3×C4—41no—
93C2×C3×C4C22×C411yescharacteristic
94C2×C3×C4C2×D411yescharacteristic
95C2×C3×C4C2×D411yescharacteristic
96C2×C3×C4C2×D411yescharacteristic
97C2×C3×C4#4111yescharacteristic
98C2×C3×C4#4111yescharacteristic
99C2×Dic3—22no—
100C2×Dic3—21no—
101C2×Dic3—22no—
102C2×Dic3—22no—
103C2×Dic3—21no—
104C2×Dic3—22no—
105C2×Dic3—21no—
106C2×Dic3—21no—
107C2×Dic3—21no—
108C2×Dic3—41no—
109C2×Dic3—41no—
110C2×Dic3Q1612yescomplemented
111Dic6—22no—
112Dic6—22no—
113Dic6—22no—
114Dic6—22no—
115Dic6—22no—
116Dic6—41no—
117Dic6—41no—
118Dic6C22⋊C414yes—
119C3×C8—22no—
120C3⋊C8—41no—
121C2×Q8—32no—
122C2×Q8—32no—
123C2×Q8—32no—
124C2×Q8—32no—
125C2×Q8—61no—
126C2×Q8—61no—
127C2×Q8—61no—
128C2×Q8—61no—
129C2×Q8—61no—
130C2×Q8—61no—
131C2×Q8—61no—
132C2×Q8—61no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—31no—
136C22×C4—31no—
137C22×C4—61no—
138C22×C4—61no—
139C22×C4C22×D311yescharacteristic
140Q16—68no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—61no—
144C2×C8—61no—
145C2×C8—61no—
146C2×C8C4×D312yes—
147C4⋊C4—21no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—64no—
151C4⋊C4D1212yes—
152C42—64no—
153C42—61no—
154C42—61no—
155C22×C3C4×D411yescharacteristic
156C22×C3#12011yescharacteristic
157C22×C3#12111yescharacteristic
158C22×C3C2×Q1611yescharacteristic
159C22×C3#13511yescharacteristic
160C22×C3#13711yescharacteristic
161C22×C3#13711yescharacteristic
162C3×C4—42no—
163C3×C4—81no—
164C3×C4C2×C22⋊C411yescharacteristic
165C3×C4C4×D411yescharacteristic
166C3×C4#12111yescharacteristic
167C3×C4#12311yescharacteristic
168Dic3—24no—
169Dic3—22no—
170Dic3—42no—
171Dic3—41no—
172C23D3×D411yescharacteristic
173Q8—34no—
174Q8—62no—
175Q8—62no—
176Q8—62no—
177Q8—62no—
178Q8—62no—
179Q8—121no—
180Q8—121no—
181C2×C4—22no—
182C2×C4—32no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—61no—
189C2×C4—62no—
190C2×C4—62no—
191C2×C4—62no—
192C2×C4—61no—
193C2×C4—61no—
194C2×C4—62no—
195C2×C4—61no—
196C2×C4—61no—
197C2×C4—121no—
198C2×C4—121no—
199C2×C4C2×C4×D311yescharacteristic
200C2×C4C2×D1211yescharacteristic
201C2×C4#23511yescharacteristic
202C2×C4D3×D411yescharacteristic
203C2×C4D3×D411yescharacteristic
204C2×C4#23911yescharacteristic
205C8—22no—
206C8—121no—
207C2×C3#38611yescharacteristic
208C2×C3C4×Q1611yescharacteristic
209C2×C3#44111yescharacteristic
210C2×C3#45111yescharacteristic
211C2×C3#45211yescharacteristic
212C2×C3#46211yescharacteristic
213C2×C3#46411yescharacteristic
214C22#88211yescharacteristic
215C22#88411yescharacteristic
216C22#89311yescharacteristic
217C22#91211yescharacteristic
218C22#91511yescharacteristic
219C22#91511yescharacteristic
220C22D3×Q1611yescharacteristic
221C4—42no—
222C4—64no—
223C4—62no—
224C4—81no—
225C4—122no—
226C4—121no—
227C4C4×D1211yescharacteristic
228C4D3×C22⋊C411yescharacteristic
229C4#89411yescharacteristic
230C4#89511yescharacteristic
231C3#187811yescharacteristic, complemented, Sylow
232C2#466511yescharacteristic
233C2#476711yescharacteristic
234C2#478311yescharacteristic
235C2#479511yescharacteristic
236C2#480911yescharacteristic
237C2#485311yescharacteristic
238C2#487311yescharacteristic
subgroupG/H
centerC23D3×D4
commutatorC2×C3×C4C22×C4
FrattiniC22×C4C22×D3
FittingC3×#340C2
socle, prime radicalC23×C3C2×D4
cosocleC22×C3×C4C23
hypercenter#340D3
hypocenterC3#1878
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
20. C2×Dic12C4semidirect
110. C2×Dic3Q16semidirect
231. C3#1878semidirect

Maximal subgroups

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

subgroupindex
C22×Dic122
C2×#8872
#49732
C2×#8102
C3×#3402
#45502
#18783