Finite Group Databasebeta

← C3×#73134 #11920912

Subgroups — C3×#73134 #11920912

Order 1152.

232 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 36 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
1C3×A4×D8C211yesmaximal, characteristic
2C3×#5398C211yesmaximal, characteristic, complemented
3C3×A4⋊C16C211yesmaximal, characteristic, complemented
4#73134C311yesmaximal, characteristic, direct product factor
5C3×#2187—31nomaximal
6C3×D4×A4—21no—
7C3×A4⋊Q8—21no—
8C3×C8×A4C2211yescharacteristic
9C3×#827—41nomaximal
10C22×C3×D8D311yescharacteristic
11A4×D8—21no—
12A4×D8C2×C311yescharacteristic
13#5398C2×C311yescharacteristic, complemented
14C2×C3×SD32—31no—
15C2×C3×SD32—31no—
16C3×#467—31no—
17A4⋊C16C2×C311yescharacteristic, complemented
18C3×#357—31no—
19C3×#357—31no—
20C3×C22⋊C16—31no—
21C22×C3×A4—41no—
22C3×C4×A4D411yescharacteristic
23C3×SL(2,ℤ/4)—41no—
24C32×D8—41no—
25C3×Dic12—41no—
26C3×C3⋊C16—41no—
27#2187—31noSylow
28C22×C3×D4—21no—
29D4×A4—22no—
30D4×A4—21no—
31A4⋊Q8—21no—
32C2×C3×Q16—31no—
33C2×C3×D8—31no—
34C2×C3×D8—31no—
35C2×C3×D8—61no—
36C22×C3×C8C2×D311yescharacteristic
37C3×C22⋊Q8—61no—
38C8×A4—21no—
39C8×A4C22×C311yescharacteristic
40C3×SD32—62no—
41C3×SD32—61no—
42C3×SD32—61no—
43C2×C3×C16—31no—
44C2×C3×C16—31no—
45C3×#107—31no—
46C3×#103—61no—
47#827—41no—
48C2×C3×A4—81no—
49C2×C3×A4D811yescharacteristic
50C32×D4—81no—
51C3×Dic6—81no—
52C32×C8—41no—
53C22×D8C3×D311yescharacteristic
54C2×SD32—31no—
55C2×SD32—31no—
56#467—31no—
57#357—31no—
58#357—31no—
59C22⋊C16—31no—
60C24×C3—41no—
61C22×A4—42no—
62C22×A4—41no—
63C2×C3×Q8—61no—
64C2×C3×D4—61no—
65C2×C3×D4—61no—
66C2×C3×D4—121no—
67C22×C3×C4#6711yescharacteristic
68C4×A4—21no—
69C4×A4C3×D411yescharacteristic
70SL(2,ℤ/4)—41no—
71C3×Q16—61no—
72C3×Q16—61no—
73C3×D8—32no—
74C3×D8—31no—
75C3×D8—41no—
76C3×D8—61no—
77C3×D8—81no—
78C3×D8S411yescharacteristic
79C2×C3×C8—31no—
80C2×C3×C8—31no—
81C3×C4⋊C4—61no—
82C3×C4⋊C4—121no—
83C3×C22⋊C4—121no—
84Dic12—41no—
85C3×C16—61no—
86C3×C16—61no—
87C3⋊C16—41no—
88C22×C32—161no—
89C3×A4SD3211yescharacteristic, complemented
90C32×C4—41no—
91C3×Dic3—161no—
92C22×D4—21no—
93C2×Q16—31no—
94C2×D8—31no—
95C2×D8—31no—
96C2×D8—61no—
97C22×C8C2×C3×D311yescharacteristic
98C22⋊Q8—61no—
99SD32—62no—
100SD32—61no—
101SD32—61no—
102C2×C16—31no—
103C2×C16—31no—
104#107—31no—
105#103—61no—
106C23×C3—81no—
107C23×C3—121no—
108C23×C3—121no—
109C23×C3—241no—
110C23×C3#21311yescharacteristic
111C2×A4—21no—
112C2×A4—82no—
113C2×A4—81no—
114C2×A4C3×D811yescharacteristic
115C3×Q8—121no—
116C3×Q8—121no—
117C3×D4—21no—
118C3×D4—61no—
119C3×D4—81no—
120C3×D4—82no—
121C3×D4—121no—
122C3×D4—121no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—121no—
126C2×C3×C4—121no—
127Dic6—81no—
128C3×C8—31no—
129C3×C8—41no—
130C3×C8—81no—
131C3×C8C2×S411yescharacteristic
132C2×C32—41no—
133C2×C32—321no—
134C24—41no—
135C2×Q8—61no—
136C2×D4—61no—
137C2×D4—61no—
138C2×D4—121no—
139C22×C4C3×#6711yescharacteristic
140Q16—61no—
141Q16—61no—
142D8—32no—
143D8—31no—
144D8—61no—
145D8C3×S411yescharacteristic
146C2×C8—31no—
147C2×C8—31no—
148C4⋊C4—61no—
149C4⋊C4—121no—
150C22⋊C4—121no—
151C16—61no—
152C16—61no—
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—41no—
156C22×C3—121no—
157C22×C3—161no—
158C22×C3—162no—
159C22×C3—241no—
160C22×C3—241no—
161C22×C3—241no—
162C22×C3—241no—
163C22×C3#82711yescharacteristic, complemented
164A4—21no—
165A4C3×SD3211yescharacteristic, complemented
166C3×C4—31no—
167C3×C4—41no—
168C3×C4—81no—
169C3×C4—241no—
170C3×C4—241no—
171C3×C4GL(2,ℤ/4)11yescharacteristic
172Dic3—161no—
173C32—41noSylow
174C23—81no—
175C23—121no—
176C23—121no—
177C23—241no—
178C23C3×#21311yescharacteristic
179Q8—121no—
180Q8—121no—
181D4—21no—
182D4—61no—
183D4—121no—
184D4—121no—
185C2×C4—31no—
186C2×C4—31no—
187C2×C4—121no—
188C2×C4—121no—
189C8—31no—
190C8C2×C3×S411yescharacteristic
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—41no—
194C2×C3—81no—
195C2×C3—81no—
196C2×C3—241no—
197C2×C3—321no—
198C2×C3—322no—
199C2×C3#541511yescharacteristic
200C22—31no—
201C22—31no—
202C22—41no—
203C22—121no—
204C22—241no—
205C22—241no—
206C22—241no—
207C22—241no—
208C22C3×#82711yescharacteristic, complemented
209C4—31no—
210C4—241no—
211C4—241no—
212C4C3×GL(2,ℤ/4)11yescharacteristic
213C3—41no—
214C3—81no—
215C3#7313411yescharacteristic, direct product factor
216C2—31no—
217C2—31no—
218C2—81no—
219C2—241no—
220C2C3×#541511yescharacteristic
subgroupG/H
centerC2×C3#5415
commutator, cosocleC8×A4C22×C3
FrattiniC8C2×C3×S4
FittingC22×C3×D8D3
socleC23×C3#213
prime radicalC3×A4×D8C2
hypercenterC3×D8S4
hypocenterA4C3×SD32
LCSG ▷ C8×A4 ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×C8 ◁ C3×D8

Complements

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

NH ≅ G/Ntype
2. C3×#5398C2semidirect
3. C3×A4⋊C16C2semidirect
4. #73134C3direct (N × H)
13. #5398C2×C3semidirect
17. A4⋊C16C2×C3semidirect
89. C3×A4SD32semidirect
163. C22×C3#827semidirect
165. A4C3×SD32semidirect
208. C22C3×#827semidirect
215. C3#73134direct (N × H)

Maximal subgroups

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

subgroupindex
C3×A4×D82
C3×#53982
C3×A4⋊C162
#731343
C3×#21873
C3×#8274