Finite Group Databasebeta

← #84095⋊C3 #11921371

Subgroups — #84095⋊C3 #11921371

Order 1152.

414 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 31 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⋊C3)C211yesmaximal, characteristic, complemented
3C3⋊(#395⋊C3)C211yesmaximal, characteristic, complemented
4#84095C311yesmaximal, characteristic, complemented
5#2388⋊C3—31nomaximal
6C3×C22⋊SL(2,𝔽3)C2211yescharacteristic
7C4×D3×A4—41nomaximal
8C22×C3×#41C2×C311yescharacteristic, complemented
9#5948—21no—
10#5948D311yescharacteristic, complemented
11C2×C4×#67—31no—
12#5231C2×C311yescharacteristic
13#5230C2×C311yescharacteristic, complemented
14#5223—31no—
15#5222—31no—
16C4×#217—31no—
17#395⋊C3—31no—
18#393⋊C3—31no—
19C2×D3×A4—41no—
20C3×#41⋊C3—82no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23#2388—31noSylow
24C2×C3×#41—62no—
25C2×C3×#41—62no—
26C22×C3×Q8C22×C311yescharacteristic
27C22×C3×D4—31no—
28C23×C3×C4—31no—
29C22×#67—31no—
30C22×C4×D3A411yescharacteristic
31C22⋊SL(2,𝔽3)—21no—
32C22⋊SL(2,𝔽3)C2×D311yescharacteristic
33C2×C4×A4—121no—
34C2×#217—32no—
35C2×#217—31no—
36C4×#67—62no—
37C4×#67—62no—
38C2×(C2×D3)⋊C4—31no—
39C2×Dic3⋊C4—31no—
40C2×C4×Dic3—31no—
41C3⋊#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—41no—
44D3×A4—42no—
45C3×C4×D3—161no—
46C3×SL(2,𝔽3)—82no—
47C22×#41C3×D311yescharacteristic, complemented
48C2×C4×D4—91no—
49#395—31no—
50#394—91no—
51#393—31no—
52#392—91no—
53C4×C22⋊C4—91no—
54C24×C3—31no—
55C23×D3C2×A411yescharacteristic
56C22×A4—121no—
57C3×#41—22no—
58C3×#41—62no—
59C3×#41—64no—
60C3×#41—62no—
61C3×#41—62no—
62C2×C3×Q8—62no—
63C2×C3×D4—62no—
64C2×C3×D4—64no—
65C22×C3×C4—32no—
66C22×C3×C4—32no—
67C22×C3×C4—31no—
68C22×C3×C4—62no—
69C22×C3×C4—62no—
70C22×C3×C4C2×A411yescharacteristic
71C2×#67—62no—
72C2×#67—62no—
73C2×#67—62no—
74C22×Dic3—31no—
75C22×Dic3—31no—
76C22×Dic3C2×A411yescharacteristic
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79#41⋊C3—82no—
80#41⋊C3—84no—
81C4×A4—41no—
82C4×A4—81no—
83C4×A4—121no—
84#217—64no—
85#217—62no—
86(C2×D3)⋊C4—62no—
87Dic3⋊C4—62no—
88C4×Dic3—61no—
89C4×Dic3—61no—
90C2×C3×D3—161no—
91C3×A4—41no—
92C32×C4—161no—
93C3×Dic3—161no—
94C2×#41—62no—
95C2×#41—62no—
96C22×Q8C2×C3×D311yescharacteristic
97C22×D4—31no—
98C22×D4—91no—
99C23×C4—31no—
100C23×C4—31no—
101C4×D4—182no—
102C4×D4—182no—
103C2×C4⋊C4—91no—
104C2×C22⋊C4—91no—
105C2×C22⋊C4—91no—
106C2×C22⋊C4—92no—
107C2×C42—91no—
108#95—91no—
109#95—91no—
110C23×C3—32no—
111C23×C3—62no—
112C23×C3—61no—
113C23×C3—62no—
114C23×C3—61no—
115C23×C3C22×A411yescharacteristic
116C22×D3—61no—
117C22×D3—61no—
118C22×D3#41⋊C312yescomplemented
119C2×A4—41no—
120C2×A4—81no—
121C2×A4—122no—
122C3×Q8—22no—
123C3×Q8—62no—
124C3×D4—62no—
125C3×D4—62no—
126C3×D4—64no—
127C2×C3×C4—31no—
128C2×C3×C4—31no—
129C2×C3×C4—32no—
130C2×C3×C4—62no—
131C2×C3×C4—64no—
132C2×C3×C4—62no—
133C2×C3×C4—62no—
134C2×C3×C4—481no—
135#67—68no—
136C2×Dic3—32no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140C2×Dic3—61no—
141C2×Dic3—62no—
142C4×D3—41no—
143C4×D3—121no—
144SL(2,𝔽3)—82no—
145SL(2,𝔽3)—84no—
146C2×C32—161no—
147C3×D3—162no—
148C24—31no—
149C24—31no—
150#41—22no—
151#41—62no—
152#41—64no—
153#41—62no—
154#41—62no—
155C2×Q8—62no—
156C2×D4—62no—
157C2×D4—64no—
158C2×D4—182no—
159C2×D4—182no—
160C2×D4—182no—
161C22×C4—32no—
162C22×C4—32no—
163C22×C4—31no—
164C22×C4—31no—
165C22×C4—62no—
166C22×C4—62no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—181no—
170C22×C4—181no—
171C22×C4D3×A411yescharacteristic
172C4⋊C4—182no—
173C22⋊C4—182no—
174C22⋊C4—184no—
175C22⋊C4—182no—
176C42—181no—
177C42—181no—
178C22×C3—31no—
179C22×C3—31no—
180C22×C3—62no—
181C22×C3—62no—
182C22×C3—62no—
183C22×C3—122no—
184C22×C3—122no—
185C22×C3—481no—
186C22×C3C2×#41⋊C311yescharacteristic
187C2×D3—41no—
188C2×D3—62no—
189C2×D3—121no—
190A4—41no—
191A4—81no—
192C3×C4—31no—
193C3×C4—62no—
194C3×C4—161no—
195C3×C4—321no—
196C3×C4—481no—
197C3×C4#120⋊C311yescharacteristic
198Dic3—41no—
199Dic3—62no—
200Dic3—121no—
201C32—161noSylow
202C23—32no—
203C23—32no—
204C23—62no—
205C23—62no—
206C23—61no—
207C23—61no—
208C23—181no—
209C23—181no—
210C23C2×D3×A411yescharacteristic
211Q8—22no—
212Q8—62no—
213D4—62no—
214D4—62no—
215D4—64no—
216D4—188no—
217C2×C4—31no—
218C2×C4—31no—
219C2×C4—32no—
220C2×C4—62no—
221C2×C4—64no—
222C2×C4—62no—
223C2×C4—62no—
224C2×C4—92no—
225C2×C4—121no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—182no—
231C2×C4—361no—
232C2×C3—31no—
233C2×C3—31no—
234C2×C3—122no—
235C2×C3—161no—
236C2×C3—321no—
237C2×C3—482no—
238C2×C3C2×#120⋊C311yescharacteristic
239D3—42no—
240C22—31no—
241C22—31no—
242C22—62no—
243C22—62no—
244C22—62no—
245C22—122no—
246C22—122no—
247C22—121no—
248C22—182no—
249C22—361no—
250C22D3×#41⋊C311yescharacteristic
251C4—31no—
252C4—62no—
253C4—121no—
254C4—182no—
255C4—361no—
256C4C3⋊(#120⋊C3)11yescharacteristic
257C3—161no—
258C3—321no—
259C3#2388⋊C311yescharacteristic, complemented
260C2—31no—
261C2—31no—
262C2—122no—
263C2—122no—
264C2C2×C3⋊(#120⋊C3)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊(#120⋊C3)
commutator, cosocle, hypocenterC22×C3×Q8C22×C3
FrattiniC23C2×D3×A4
FittingC22×C3×#41C2×C3
socleC23×C3C22×A4
LCSG ▷ C22×C3×Q8
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C3×#5948C2semidirect
2. C3⋊(#393⋊C3)C2semidirect
3. C3⋊(#395⋊C3)C2semidirect
4. #84095C3semidirect
8. C22×C3×#41C2×C3semidirect
10. #5948D3semidirect
13. #5230C2×C3semidirect
47. C22×#41C3×D3semidirect
118. C22×D3#41⋊C3semidirect
259. C3#2388⋊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⋊C3)2
C3⋊(#395⋊C3)2
#840953
#2388⋊C33
C4×D3×A44