Finite Group Databasebeta

← #76809⋊C3 #11921175

Subgroups — #76809⋊C3 #11921175

Order 1152.

408 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 28 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⋊#5948C211yesmaximal, characteristic, complemented
2C3×#393⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#393⋊C3)C211yesmaximal, characteristic, complemented
4#76809C311yesmaximal, characteristic, complemented
5#2615⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7A4×#67—41nomaximal
8C22×#239C2×C311yescharacteristic, complemented
9#5948—31no—
10C2×#884—31no—
11C3×#393C2×C311yescharacteristic, complemented
12#5231C2×C311yescharacteristic, complemented
13#4960—31no—
14#4671—31no—
15#4667—31no—
16#393⋊C3—21no—
17#393⋊C3—31no—
18#393⋊C3D311yescharacteristic, complemented
19C22×C3×A4—41no—
20C2×D3×A4—41no—
21Dic3×A4—41no—
22C3⋊(#41⋊C3)—82no—
23#2615—31noSylow
24C22×C3×Q8C22×C311yescharacteristic
25C22×#67—31no—
26C22×#67A411yescharacteristic
27C2×#239—62no—
28C2×#239—62no—
29C22×D12—31no—
30C22×D12—31no—
31C22×C4×D3—31no—
32C22⋊SL(2,𝔽3)—21no—
33C22⋊SL(2,𝔽3)C2×D311yescharacteristic
34D4×A4—121no—
35C2×C3×C22⋊C4—31no—
36C2×(C2×D3)⋊C4—31no—
37C2×(C2×D3)⋊C4—32no—
38C2×Dic3⋊C4—31no—
39#884—62no—
40#884—62no—
41C3×#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—41no—
44C2×C3×A4—81no—
45D3×A4—81no—
46C3×#67—161no—
47C3×SL(2,𝔽3)—82no—
48C22×#41—31no—
49C2×#121—91no—
50#393—31no—
51#393C3×D311yescharacteristic, complemented
52#392—91no—
53#392—91no—
54#380—91no—
55C24×C3C2×A411yescharacteristic
56C23×D3—31no—
57C23×D3C2×A411yescharacteristic
58C22×A4—41no—
59C22×A4—81no—
60C22×A4—121no—
61C2×C3×Q8—62no—
62C22×C3×C4—31no—
63C22×C3×C4—31no—
64C2×#67—61no—
65C2×#67—61no—
66C2×#67—62no—
67C2×#67—122no—
68C22×Dic3—31no—
69C22×Dic3C2×A411yescharacteristic
70#239—22no—
71#239—62no—
72#239—64no—
73#239—62no—
74#239—62no—
75C2×D12—62no—
76C2×D12—64no—
77C2×D12—62no—
78C2×D12—122no—
79C2×C4×D3—32no—
80C2×C4×D3—32no—
81C2×C4×D3—62no—
82C2×C4×D3—62no—
83#41⋊C3—242no—
84C4×A4—121no—
85C3×C22⋊C4—62no—
86(C2×D3)⋊C4—62no—
87(C2×D3)⋊C4—122no—
88Dic3⋊C4—61no—
89Dic3⋊C4—61no—
90C22×C32—161no—
91C2×C3×D3—161no—
92C3×A4—41no—
93C3×Dic3—161no—
94C2×#41—182no—
95C2×#41—182no—
96C22×Q8C2×C3×D311yescharacteristic
97C22×D4—31no—
98C22×D4—91no—
99C22×D4—91no—
100C22×D4—91no—
101C23×C4—91no—
102#121—182no—
103#121—182no—
104C2×C4⋊C4—91no—
105C2×C22⋊C4—31no—
106C2×C22⋊C4—91no—
107C2×C22⋊C4—92no—
108#95—31no—
109#95—91no—
110C23×C3—21no—
111C23×C3—61no—
112C23×C3—61no—
113C23×C3C22×A411yescharacteristic
114C22×D3—21no—
115C22×D3—32no—
116C22×D3—61no—
117C22×D3—61no—
118C22×D3—62no—
119C22×D3—62no—
120C22×D3—61no—
121C22×D3—61no—
122C2×A4—41no—
123C2×A4—81no—
124C2×A4—82no—
125C2×A4—81no—
126C2×A4—241no—
127C3×Q8—22no—
128C3×Q8—62no—
129C3×D4—481no—
130C2×C3×C4—32no—
131C2×C3×C4—62no—
132C2×C3×C4—61no—
133C2×C3×C4—62no—
134#67—41no—
135#67—121no—
136#67—124no—
137C2×Dic3—31no—
138C2×Dic3—31no—
139C2×Dic3—61no—
140C2×Dic3—62no—
141D12—62no—
142D12—62no—
143D12—64no—
144D12—124no—
145C4×D3—64no—
146C4×D3—62no—
147C4×D3—62no—
148SL(2,𝔽3)—82no—
149SL(2,𝔽3)—162no—
150C2×C32—161no—
151C2×C32—321no—
152C3×D3—321no—
153C24—31no—
154C24—91no—
155C24D3×A411yescharacteristic
156#41—62no—
157#41—182no—
158#41—184no—
159#41—182no—
160#41—182no—
161C2×Q8—62no—
162C2×D4—182no—
163C2×D4—184no—
164C2×D4—182no—
165C2×D4—181no—
166C2×D4—181no—
167C2×D4—182no—
168C2×D4—362no—
169C2×D4—362no—
170C22×C4—31no—
171C22×C4—31no—
172C22×C4—31no—
173C22×C4—92no—
174C22×C4—92no—
175C22×C4—91no—
176C22×C4—182no—
177C22×C4—182no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C22⋊C4—62no—
181C22⋊C4—182no—
182C22⋊C4—362no—
183C22×C3—31no—
184C22×C3—31no—
185C22×C3—41no—
186C22×C3—121no—
187C22×C3—121no—
188C22×C3—161no—
189C22×C3—321no—
190C22×C3—481no—
191C22×C32−1+4⋊C311yescharacteristic
192C2×D3—41no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—62no—
196C2×D3—121no—
197C2×D3—121no—
198C2×D3—122no—
199C2×D3—122no—
200A4—41no—
201A4—81no—
202C3×C4—62no—
203C3×C4—121no—
204C3×C4—481no—
205Dic3—31no—
206Dic3—121no—
207Dic3#120⋊C311yescharacteristic
208C32—161noSylow
209C23—21no—
210C23—61no—
211C23—61no—
212C23—61no—
213C23—92no—
214C23—181no—
215C23—181no—
216C23—182no—
217C23—182no—
218C23—181no—
219C23—181no—
220C23C2×D3×A411yescharacteristic
221Q8—22no—
222Q8—62no—
223D4—121no—
224D4—182no—
225D4—182no—
226D4—184no—
227D4—361no—
228D4—364no—
229D4—364no—
230C2×C4—32no—
231C2×C4—62no—
232C2×C4—61no—
233C2×C4—62no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—182no—
237C2×C4—182no—
238C2×C4—184no—
239C2×C4—181no—
240C2×C4—182no—
241C2×C3—31no—
242C2×C3—31no—
243C2×C3—81no—
244C2×C3—161no—
245C2×C3—321no—
246C2×C3—322no—
247C2×C3—321no—
248C2×C3—961no—
249C2×C3C2×#120⋊C311yescharacteristic
250D3—81no—
251D3—122no—
252C22—31no—
253C22—31no—
254C22—41no—
255C22—121no—
256C22—121no—
257C22—121no—
258C22—182no—
259C22—182no—
260C22—182no—
261C22—361no—
262C22—361no—
263C22—362no—
264C22—362no—
265C22#1007⋊C311yescharacteristic
266C4—31no—
267C4—62no—
268C4—91no—
269C4—121no—
270C4—361no—
271C3—161no—
272C3—321no—
273C3#2615⋊C311yescharacteristic, complemented
274C2—31no—
275C2—31no—
276C2—81no—
277C2—241no—
278C2—362no—
279C2D3×#120⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#120⋊C3
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC3×#393C2×C3
socleC23×C3C22×A4
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3⋊#5948C2semidirect
2. C3×#393⋊C3C2semidirect
3. C3⋊(#393⋊C3)C2semidirect
4. #76809C3semidirect
8. C22×#239C2×C3semidirect
11. C3×#393C2×C3semidirect
12. #5231C2×C3semidirect
18. #393⋊C3D3semidirect
51. #393C3×D3semidirect
273. C3#2615⋊C3semidirect

Maximal subgroups

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

subgroupindex
C3⋊#59482
C3×#393⋊C32
C3⋊(#393⋊C3)2
#768093
#2615⋊C33
A4×#674