Finite Group Databasebeta

← #70635

Subgroups — #70635

Order 384.

316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 87 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×#897C211yesmaximal, characteristic
2C2×C3×#107C211yesmaximal, characteristic, complemented
3C2×(C2×D3)⋊C8C211yesmaximal, characteristic
4C2×#816C211yesmaximal, characteristic, complemented
5#4987C211yesmaximal, characteristic
6C2×#810C211yesmaximal, characteristic, complemented
7#4529C211yesmaximal, characteristic, complemented
8#2036—31nomaximal, Sylow
9C22×C4×D3C2211yescharacteristic
10C22×Dic6C2211yescharacteristic
11C22×C3×C8C2211yescharacteristic
12C2×C3×C4⋊C4C2211yescharacteristic
13C2×C3×C4⋊C4C2211yescharacteristic
14C2×(C2×D3)⋊C4—21no—
15C2×(C2×D3)⋊C4—21no—
16C2×C4⋊Dic3—21no—
17C2×C4⋊Dic3C2211yescharacteristic
18C22×C3⋊C8C2211yescharacteristic
19#897—22no—
20#897—22no—
21C3×#107—22no—
22C3⋊#95—21no—
23(C2×D3)⋊C8—22no—
24#816—22no—
25#810—22no—
26C2×C22⋊Q8—31no—
27C2×#107D311yescharacteristic, complemented
28C2×#103—31no—
29C2×#103—31no—
30C2×C22⋊C8—31no—
31#380—31no—
32#340—31no—
33C23×D3D411yescharacteristic
34C22×C3×C4—21no—
35C22×C3×C4—21no—
36C22×C3×C4C2311yescharacteristic
37C22×Dic3—21no—
38C22×Dic3—21no—
39C22×Dic3D411yescharacteristic
40C2×C4×D3—21no—
41C2×C4×D3—21no—
42C2×C4×D3—21no—
43C2×C4×D3—21no—
44C2×C4×D3—21no—
45C2×C4×D3—21no—
46C2×Dic6—21no—
47C2×Dic6—21no—
48C2×Dic6—21no—
49C2×Dic6—21no—
50C2×Dic6—21no—
51C2×Dic6D412yes—
52C2×C3×C8—21no—
53C2×C3×C8—21no—
54C2×C3×C8D412yes—
55C3×C4⋊C4—21no—
56C3×C4⋊C4—21no—
57C3×C4⋊C4—21no—
58C3×C4⋊C4D412yes—
59(C2×D3)⋊C4—24no—
60(C2×D3)⋊C4—42no—
61C4⋊Dic3—24no—
62C4⋊Dic3—21no—
63C4⋊Dic3—21no—
64C2×C3⋊C8—21no—
65C2×C3⋊C8—21no—
66C2×C3⋊C8—21no—
67C22×Q8—31no—
68C23×C4—31no—
69C22×C8—31no—
70C22×C8C2×D311yescharacteristic
71C22⋊Q8—62no—
72C22⋊Q8—62no—
73C2×C4⋊C4—31no—
74C2×C4⋊C4—61no—
75C2×C4⋊C4C2×D311yescharacteristic
76C2×C4⋊C4C2×D311yescharacteristic
77C2×C22⋊C4—61no—
78C2×C22⋊C4—61no—
79#107—22no—
80#103—62no—
81#103—62no—
82C22⋊C8—62no—
83#95—61no—
84C23×C3C2×D411yescharacteristic
85C22×D3—21no—
86C22×D3—21no—
87C22×D3—21no—
88C22×D3—21no—
89C22×D3—21no—
90C22×D3—21no—
91C22×D3Q1612yes—
92C2×C3×C4—22no—
93C2×C3×C4—41no—
94C2×C3×C4—41no—
95C2×C3×C4—41no—
96C2×C3×C4—41no—
97C2×C3×C4—41no—
98C2×C3×C4C2×D411yescharacteristic
99C2×C3×C4C2×D411yescharacteristic
100C2×C3×C4C2×D411yescharacteristic
101C2×C3×C4#4111yescharacteristic
102C2×C3×C4#4111yescharacteristic
103C2×C3×C4#4111yescharacteristic
104C2×Dic3—21no—
105C2×Dic3—22no—
106C2×Dic3—21no—
107C2×Dic3—21no—
108C2×Dic3—41no—
109C2×Dic3—41no—
110C2×Dic3—41no—
111C2×Dic3—41no—
112C2×Dic3—41no—
113C4×D3—41no—
114C4×D3—41no—
115C4×D3—41no—
116C4×D3—41no—
117Dic6—22no—
118Dic6—22no—
119Dic6—41no—
120Dic6—41no—
121C3×C8—22no—
122C3⋊C8—41no—
123C24—31no—
124C2×Q8—32no—
125C2×Q8—61no—
126C2×Q8—61no—
127C2×Q8—61no—
128C2×Q8—61no—
129C2×Q8—61no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—31no—
133C22×C4—61no—
134C22×C4—61no—
135C22×C4—61no—
136C22×C4—61no—
137C22×C4—61no—
138C22×C4—61no—
139C22×C4—61no—
140C22×C4—61no—
141C22×C4C22×D311yescharacteristic
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—61no—
145C2×C8—61no—
146C2×C8—61no—
147C2×C8D1212yes—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—64no—
152C4⋊C4—61no—
153C4⋊C4—61no—
154C4⋊C4#6712yes—
155C22⋊C4—64no—
156C22⋊C4—122no—
157C22×C3#12011yescharacteristic
158C22×C3#12111yescharacteristic
159C22×C3#12311yescharacteristic
160C22×C3C2×Q1611yescharacteristic
161C22×C3#13511yescharacteristic
162C22×C3AGL(1,ℤ/8)11yescharacteristic
163C22×C3#13711yescharacteristic
164C2×D3—22no—
165C2×D3—22no—
166C2×D3—22no—
167C2×D3—41no—
168C2×D3—41no—
169C2×D3—41no—
170C2×D3—41no—
171C3×C4—42no—
172C3×C4—81no—
173C3×C4#12111yescharacteristic
174C3×C4#12111yescharacteristic
175C3×C4#12311yescharacteristic
176C3×C4#12411yescharacteristic
177Dic3—42no—
178Dic3—41no—
179Dic3—81no—
180C23—32no—
181C23—61no—
182C23—61no—
183C23—61no—
184C23—61no—
185C23—61no—
186C23—61no—
187C23D3×D411yescharacteristic
188Q8—62no—
189Q8—62no—
190Q8—121no—
191Q8—121no—
192C2×C4—22no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—62no—
201C2×C4—61no—
202C2×C4—121no—
203C2×C4—121no—
204C2×C4—121no—
205C2×C4—121no—
206C2×C4—121no—
207C2×C4—121no—
208C2×C4—121no—
209C2×C4—121no—
210C2×C4—121no—
211C2×C4C2×D1211yescharacteristic
212C2×C4#23511yescharacteristic
213C2×C4D3×D411yescharacteristic
214C2×C4#23911yescharacteristic
215C2×C4#23911yescharacteristic
216C2×C4C2×#6711yescharacteristic
217C8—22no—
218C8—121no—
219C2×C3#39411yescharacteristic
220C2×C3#44911yescharacteristic
221C2×C3#45111yescharacteristic
222C2×C3#46711yescharacteristic
223C2×C3#46811yescharacteristic
224C2×C3#48411yescharacteristic
225C2×C3#48511yescharacteristic
226D3—42no—
227C22—62no—
228C22—62no—
229C22—62no—
230C22—121no—
231C22—121no—
232C22—121no—
233C22—121no—
234C22#89411yescharacteristic
235C22#89511yescharacteristic
236C22#91111yescharacteristic
237C22#91211yescharacteristic
238C22D3×Q1611yescharacteristic
239C22#91811yescharacteristic
240C22#93711yescharacteristic
241C4—42no—
242C4—81no—
243C4—121no—
244C4—122no—
245C4—241no—
246C4#89411yescharacteristic
247C4#89511yescharacteristic
248C4#93011yescharacteristic
249C4#94711yescharacteristic
250C3#203611yescharacteristic, complemented, Sylow
251C2—122no—
252C2#488411yescharacteristic
253C2#488611yescharacteristic
254C2#488711yescharacteristic
255C2#488811yescharacteristic
256C2#499111yescharacteristic
257C2#515811yescharacteristic
258C2#518611yescharacteristic
subgroupG/H
centerC23D3×D4
commutator, cosocleC22×C3×C4C23
FrattiniC22×C4C22×D3
FittingC2×C3×#107C2
socleC23×C3C2×D4
prime radicalC23×D3D4
hypercenterC2×#107D3
hypocenterC3#2036
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×C3×#107C2semidirect
4. C2×#816C2semidirect
6. C2×#810C2semidirect
7. #4529C2semidirect
27. C2×#107D3semidirect
250. C3#2036semidirect

Maximal subgroups

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

subgroupindex
C2×#8972
C2×C3×#1072
C2×(C2×D3)⋊C82
C2×#8162
#49872
C2×#8102
#45292
#20363