Finite Group Databasebeta

← C3×#2036 #72751

Subgroups — C3×#2036 #72751

Order 384.

316 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 104 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×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#107C211yesmaximal, characteristic, complemented
3C2×C3×#103C211yesmaximal, characteristic, complemented
4C2×C3×#103C211yesmaximal, characteristic, complemented
5C2×C3×C22⋊C8C211yesmaximal, characteristic
6C3×#380C211yesmaximal, characteristic
7C3×#340C211yesmaximal, characteristic, complemented
8#2036C311yesmaximal, characteristic, direct product factor, Sylow
9C22×C3×Q8C2211yescharacteristic
10C23×C3×C4C2211yescharacteristic
11C22×C3×C8C2211yescharacteristic
12C22×C3×C8C2211yescharacteristic
13C3×C22⋊Q8—22no—
14C3×C22⋊Q8—22no—
15C2×C3×C4⋊C4—21no—
16C2×C3×C4⋊C4C2211yescharacteristic
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×C3×C4⋊C4C2211yescharacteristic
19C2×C3×C22⋊C4—21no—
20C2×C3×C22⋊C4—21no—
21C3×#107—22no—
22C3×#103—22no—
23C3×#103—22no—
24C3×C22⋊C8—22no—
25C3×#95—21no—
26C2×C22⋊Q8C2×C311yescharacteristic
27C2×#107C2×C311yescharacteristic, complemented
28C2×#103C2×C311yescharacteristic, complemented
29C2×#103C2×C311yescharacteristic, complemented
30C2×C22⋊C8C2×C311yescharacteristic
31#380C2×C311yescharacteristic
32#340C2×C311yescharacteristic, complemented
33C24×C3D411yescharacteristic
34C2×C3×Q8—21no—
35C2×C3×Q8—21no—
36C2×C3×Q8—21no—
37C2×C3×Q8—21no—
38C2×C3×Q8—21no—
39C2×C3×Q8D412yes—
40C22×C3×C4—21no—
41C22×C3×C4—21no—
42C22×C3×C4—21no—
43C22×C3×C4—21no—
44C22×C3×C4—21no—
45C22×C3×C4—21no—
46C22×C3×C4—21no—
47C22×C3×C4—21no—
48C22×C3×C4—21no—
49C22×C3×C4—21no—
50C22×C3×C4D411yescharacteristic
51C22×C3×C4C2311yescharacteristic
52C2×C3×C8—21no—
53C2×C3×C8—21no—
54C2×C3×C8—21no—
55C2×C3×C8—21no—
56C2×C3×C8—21no—
57C2×C3×C8D412yes—
58C3×C4⋊C4—24no—
59C3×C4⋊C4—21no—
60C3×C4⋊C4—21no—
61C3×C4⋊C4—21no—
62C3×C4⋊C4—21no—
63C3×C4⋊C4—21no—
64C3×C4⋊C4D412yes—
65C3×C22⋊C4—24no—
66C3×C22⋊C4—42no—
67C22×Q8C22×C311yescharacteristic
68C23×C4C22×C311yescharacteristic
69C22×C8C22×C311yescharacteristic
70C22×C8C22×C311yescharacteristic
71C22⋊Q8—22no—
72C22⋊Q8—22no—
73C2×C4⋊C4—21no—
74C2×C4⋊C4C22×C311yescharacteristic
75C2×C4⋊C4C22×C311yescharacteristic
76C2×C4⋊C4C22×C311yescharacteristic
77C2×C22⋊C4—21no—
78C2×C22⋊C4—21no—
79#107—22no—
80#103—22no—
81#103—22no—
82C22⋊C8—22no—
83#95—21no—
84C23×C3—21no—
85C23×C3—21no—
86C23×C3—21no—
87C23×C3—21no—
88C23×C3—21no—
89C23×C3—21no—
90C23×C3Q1612yes—
91C23×C3C2×D411yescharacteristic
92C3×Q8—22no—
93C3×Q8—22no—
94C3×Q8—41no—
95C3×Q8—41no—
96C2×C3×C4—22no—
97C2×C3×C4—22no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—41no—
102C2×C3×C4—41no—
103C2×C3×C4—41no—
104C2×C3×C4—41no—
105C2×C3×C4—41no—
106C2×C3×C4—41no—
107C2×C3×C4—41no—
108C2×C3×C4—41no—
109C2×C3×C4—41no—
110C2×C3×C4—41no—
111C2×C3×C4—41no—
112C2×C3×C4—41no—
113C2×C3×C4—41no—
114C2×C3×C4—41no—
115C2×C3×C4C2×D411yescharacteristic
116C2×C3×C4C2×D411yescharacteristic
117C2×C3×C4C2×D411yescharacteristic
118C2×C3×C4#4111yescharacteristic
119C2×C3×C4#4111yescharacteristic
120C2×C3×C4#4111yescharacteristic
121C3×C8—22no—
122C3×C8—41no—
123C24C3×D411yescharacteristic
124C2×Q8—21no—
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8C3×D412yes—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4C3×D411yescharacteristic
141C22×C4C23×C311yescharacteristic
142C2×C8—21no—
143C2×C8—21no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8C3×D412yes—
148C4⋊C4—24no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4C3×D412yes—
155C22⋊C4—24no—
156C22⋊C4—42no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C22×C3—41no—
161C22×C3—41no—
162C22×C3—41no—
163C22×C3—41no—
164C22×C3#12011yescharacteristic
165C22×C3#12111yescharacteristic
166C22×C3#12311yescharacteristic
167C22×C3C2×Q1611yescharacteristic
168C22×C3#13511yescharacteristic
169C22×C3AGL(1,ℤ/8)11yescharacteristic
170C22×C3#13711yescharacteristic
171C3×C4—41no—
172C3×C4—42no—
173C3×C4—42no—
174C3×C4—81no—
175C3×C4—81no—
176C3×C4#12111yescharacteristic
177C3×C4#12111yescharacteristic
178C3×C4#12311yescharacteristic
179C3×C4#12411yescharacteristic
180C23—21no—
181C23—21no—
182C23—21no—
183C23—21no—
184C23—21no—
185C23—21no—
186C23C3×Q1612yes—
187C23C2×C3×D411yescharacteristic
188Q8—22no—
189Q8—22no—
190Q8—41no—
191Q8—41no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4C2×C3×D411yescharacteristic
212C2×C4C2×C3×D411yescharacteristic
213C2×C4C2×C3×D411yescharacteristic
214C2×C4C3×#4111yescharacteristic
215C2×C4C3×#4111yescharacteristic
216C2×C4C3×#4111yescharacteristic
217C8—22no—
218C8—41no—
219C2×C3—42no—
220C2×C3#39411yescharacteristic
221C2×C3#44911yescharacteristic
222C2×C3#45111yescharacteristic
223C2×C3#46711yescharacteristic
224C2×C3#46811yescharacteristic
225C2×C3#48411yescharacteristic
226C2×C3#48511yescharacteristic
227C22—22no—
228C22—22no—
229C22—22no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22C3×#12011yescharacteristic
235C22C3×#12111yescharacteristic
236C22C3×#12311yescharacteristic
237C22C2×C3×Q1611yescharacteristic
238C22C3×#13511yescharacteristic
239C22C3×AGL(1,ℤ/8)11yescharacteristic
240C22C3×#13711yescharacteristic
241C4—41no—
242C4—42no—
243C4—42no—
244C4—81no—
245C4—81no—
246C4C3×#12111yescharacteristic
247C4C3×#12111yescharacteristic
248C4C3×#12311yescharacteristic
249C4C3×#12411yescharacteristic
250C3#203611yescharacteristic, direct product factor, Sylow
251C2—42no—
252C2C3×#39411yescharacteristic
253C2C3×#44911yescharacteristic
254C2C3×#45111yescharacteristic
255C2C3×#46711yescharacteristic
256C2C3×#46811yescharacteristic
257C2C3×#48411yescharacteristic
258C2C3×#48511yescharacteristic
subgroupG/H
center, socleC23×C3C2×D4
commutator, Frattini, cosocleC22×C4C23×C3
prime radicalC24×C3D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#107C2semidirect
3. C2×C3×#103C2semidirect
4. C2×C3×#103C2semidirect
7. C3×#340C2semidirect
8. #2036C3direct (N × H)
27. C2×#107C2×C3semidirect
28. C2×#103C2×C3semidirect
29. C2×#103C2×C3semidirect
32. #340C2×C3semidirect
250. C3#2036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊Q82
C2×C3×#1072
C2×C3×#1032
C2×C3×C22⋊C82
C3×#3802
C3×#3402
#20363