Finite Group Databasebeta

← #11920709

Subgroups — #11920709

Order 1152.

263 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 263 conjugacy classes of subgroups — too many to draw. Only its 41 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#5819⋊C3C211yesmaximal, characteristic
2C2×C3⋊GU(2,𝔽3)C211yesmaximal, characteristic
3C3×#5423C211yesmaximal, characteristic
4#73129—31nomaximal
5#70398—31nomaximal
6C2×C3×#41⋊C3C2211yescharacteristic
7C3⋊(#131⋊C3)—21no—
8C3⋊GU(2,𝔽3)C411yescharacteristic, complemented
9C3⋊GU(2,𝔽3)C411yescharacteristic, complemented
10C3×GU(2,𝔽3)—21no—
11#63578—41nomaximal
12#5819D311yescharacteristic
13#568⋊C3—31no—
14#5423D311yescharacteristic
15C2×GU(2,𝔽3)—31no—
16C2×GU(2,𝔽3)—61no—
17C3×#421—31no—
18C2×#837—31no—
19#5124—31no—
20#5118—31no—
21#4533—31no—
22#4532—31no—
23C3×#41⋊C3C2×C411yescharacteristic
24C3×#41⋊C3D411yescharacteristic
25C2×C3×SL(2,𝔽3)Q811yescharacteristic
26C2×C3⋊(C3⋊C8)—41no—
27C3×#208—41no—
28C3×#208—41no—
29#1861—91noSylow
30C2×C3×#41C2×D311yescharacteristic
31C2×#41⋊C3—21no—
32C2×#41⋊C3C2×D311yescharacteristic
33C2×C3×M16—31no—
34C3×#117—31no—
35#948—21no—
36#948—61no—
37C2×C4×Dic3—31no—
38C2×#208—31no—
39C2×#208—31no—
40C2×#208—31no—
41#131⋊C3—61no—
42GU(2,𝔽3)—21no—
43GU(2,𝔽3)—31no—
44GU(2,𝔽3)—31no—
45GU(2,𝔽3)—61no—
46GU(2,𝔽3)—61no—
47C3×#104—61no—
48C3×#104—61no—
49#837—31no—
50#837—31no—
51#837—31no—
52#837—31no—
53#822—61no—
54#822—61no—
55#822—121no—
56Dic3⋊C8—62no—
57C2×C32×C4—41no—
58C3×SL(2,𝔽3)C4⋊C411yescharacteristic
59C3⋊(C3⋊C8)—41no—
60C3⋊(C3⋊C8)—41no—
61C3×C3⋊C8—81no—
62C3×C3⋊C8—81no—
63#568—31no—
64#430—91no—
65#423—91no—
66#421—31no—
67C2×#104—91no—
68#344—91no—
69#339—91no—
70C3×#41—31no—
71C3×#41—31no—
72C3×#41C4×D311yescharacteristic
73C3×#41#6711yescharacteristic
74C2×C3×Q8Dic611yescharacteristic
75C2×C3×D4—31no—
76C22×C3×C4—31no—
77C22×Dic3—61no—
78#41⋊C3—21no—
79#41⋊C3—21no—
80#41⋊C3C4×D311yescharacteristic
81#41⋊C3#6711yescharacteristic
82C2×SL(2,𝔽3)—21no—
83C2×SL(2,𝔽3)Dic611yescharacteristic
84C3×M16—61no—
85C3×M16—61no—
86C3×M16—121no—
87C2×C3×C8—61no—
88C3×C4⋊C4—61no—
89C3×C22⋊C4—61no—
90C3×C42—61no—
91C4×Dic3—31no—
92C4×Dic3—31no—
93C4×Dic3—61no—
94#208—31no—
95#208—31no—
96#208—31no—
97#208—41no—
98#208—61no—
99#208—61no—
100#208—61no—
101#208S411yescharacteristic
102C2×C3⋊C8—32no—
103C2×C3⋊C8—61no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—121no—
106C2×C3⋊C8—241no—
107C22×C32—41no—
108C32×C4—41no—
109C32×C4—41no—
110C2×#41D3211yescharacteristic
111#131—61no—
112#131—181no—
113C2×M16—31no—
114C2×M16—91no—
115C2×M16—91no—
116C2×M16—91no—
117#117—31no—
118C2×C42—91no—
119#108—181no—
120#108—181no—
121C4⋊C8—182no—
122#104—61no—
123#104—61no—
124#104—91no—
125#104—91no—
126#104—91no—
127#104—91no—
128C23×C3—31no—
129C3×Q8—31no—
130C3×Q8Dic3⋊C411yescharacteristic
131C3×D4—31no—
132C3×D4—31no—
133C3×D4—61no—
134C2×C3×C4—31no—
135C2×C3×C4—31no—
136C2×C3×C4—31no—
137C2×C3×C4—31no—
138C2×C3×C4—31no—
139C2×C3×C4—41no—
140C2×C3×C4—81no—
141C2×C3×C4—121no—
142C2×C3×C4C2×S411yescharacteristic
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—122no—
146SL(2,𝔽3)—21no—
147SL(2,𝔽3)Dic3⋊C411yescharacteristic
148C3×C8—121no—
149C3×C8—241no—
150C3⋊C8—21no—
151C3⋊C8—61no—
152C3⋊C8—61no—
153C3⋊C8—61no—
154C3⋊C8—81no—
155C3⋊C8—121no—
156C3⋊C8—121no—
157C3⋊C8—241no—
158C3⋊C8—241no—
159C2×C32—41no—
160C2×C32—81no—
161#41—31no—
162#41—31no—
163#41#62411yescharacteristic
164#41#62511yescharacteristic
165C2×Q8#62711yescharacteristic
166C2×D4—31no—
167C22×C4—31no—
168C22×C4—181no—
169M16—31no—
170M16—61no—
171M16—61no—
172M16—91no—
173M16—91no—
174M16—91no—
175M16—181no—
176M16—181no—
177M16—181no—
178C2×C8—61no—
179C2×C8—92no—
180C2×C8—181no—
181C2×C8—181no—
182C4⋊C4—61no—
183C22⋊C4—61no—
184C42—61no—
185C42—91no—
186C42—91no—
187C42—181no—
188C22×C3—31no—
189C22×C3—31no—
190C22×C3—41no—
191C22×C3—81no—
192C22×C3—121no—
193C22×C3A4⋊Q811yescharacteristic
194C3×C4—31no—
195C3×C4—31no—
196C3×C4—41no—
197C3×C4—41no—
198C3×C4—81no—
199C3×C4—81no—
200C3×C4—241no—
201C3×C4C4×S411yescharacteristic
202C3×C4GL(2,ℤ/4)11yescharacteristic
203Dic3—62no—
204Dic3—121no—
205C32—41noSylow
206C23—31no—
207Q8—31no—
208Q8#372411yescharacteristic
209D4—31no—
210D4—31no—
211D4—61no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—31no—
216C2×C4—31no—
217C2×C4—121no—
218C2×C4—181no—
219C2×C4—181no—
220C2×C4—362no—
221C2×C4D3×S411yescharacteristic
222C8—61no—
223C8—121no—
224C8—181no—
225C8—181no—
226C8—181no—
227C2×C3—21no—
228C2×C3—41no—
229C2×C3—61no—
230C2×C3—61no—
231C2×C3—81no—
232C2×C3—82no—
233C2×C3—81no—
234C2×C3SL(2,ℤ/4)⋊C411yescharacteristic
235C22—31no—
236C22—31no—
237C22—121no—
238C22#6420411yescharacteristic
239C4—31no—
240C4—31no—
241C4—182no—
242C4—241no—
243C4—361no—
244C4(C3⋊S4)⋊C411yescharacteristic
245C4#6420911yescharacteristic
246C3—41no—
247C3—81no—
248C3#7312911yescharacteristic, complemented
249C2—21no—
250C2—61no—
251C2—61no—
252C2#1059323811yescharacteristic
subgroupG/H
centerC4#64209
commutatorC3×#41⋊C3C2×C4
Frattini, hypercenterC2×C4D3×S4
FittingC2×C3×#41C2×D3
socleC2×C3SL(2,ℤ/4)⋊C4
prime radical, cosocleC2×C3×#41⋊C3C22
hypocenterC3×SL(2,𝔽3)C4⋊C4
LCSG ▷ C3×#41⋊C3 ▷ C3×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
8. C3⋊GU(2,𝔽3)C4semidirect
9. C3⋊GU(2,𝔽3)C4semidirect
248. C3#73129semidirect

Maximal subgroups

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

subgroupindex
#5819⋊C32
C2×C3⋊GU(2,𝔽3)2
C3×#54232
#731293
#703983
#635784