Finite Group Databasebeta

← #44533738

Subgroups — #44533738

Order 31347.

488 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 61 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#23782924C311yesmaximal, characteristic, complemented
2#23782891C311yesmaximal, characteristic, complemented
3#23782888C311yesmaximal, characteristic, complemented
4#23782888C311yesmaximal, characteristic, complemented
5#23782887C311yesmaximal, characteristic, complemented
6#23782883C311yesmaximal, characteristic, complemented
7#23782882C311yesmaximal, characteristic, complemented
8#23782882C311yesmaximal, characteristic, complemented
9C3×#16812508C311yesmaximal, characteristic, complemented
10C3×#16812506C311yesmaximal, characteristic, complemented
11#23782795C311yesmaximal, characteristic, complemented
12(C3×C43⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
13C43×#6909C311yesmaximal, characteristic, complemented
14C33×C43⋊C3C3211yescharacteristic
15#16812524—33no—
16#16812524—33no—
17#16812524—33no—
18C3×#11923958—33no—
19C3×#11923958C3211yescharacteristic
20C3×#11923958C3211yescharacteristic
21C3×#11923958C3211yescharacteristic
22C3×#11923958C3211yescharacteristic
23C3×#11923958C3211yescharacteristic
24C3×C32⋊(C43⋊C3)—33no—
25C3×C32⋊(C43⋊C3)C3211yescharacteristic
26C3×C32⋊(C43⋊C3)C3211yescharacteristic
27C3×C32⋊(C43⋊C3)C3211yescharacteristic
28#16812512—33no—
29#16812511—33no—
30#16812511—33no—
31#16812510—33no—
32#16812508—33no—
33#16812508—33no—
34#16812507—33no—
35#16812507—33no—
36#16812506—33no—
37(C3×C43⋊C3)⋊C9—33no—
38C3×3−1+2×C43C3211yescharacteristic
39C3×3−1+2×C43C3211yescharacteristic
40C3×H(3,𝔽3)×C43C3211yescharacteristic
41C3×H(3,𝔽3)×C43C3211yescharacteristic
42C43×AΣL(1,𝔽27)—33no—
43C32×C43⋊C3—31no—
44C32×C43⋊C3—31no—
45C32×C43⋊C3—31no—
46C32×C43⋊C3—31no—
47C32×C43⋊C3—31no—
48C32×C43⋊C3—31no—
49C32×C43⋊C3—31no—
50C32×C43⋊C3—93no—
51#11923958—318no—
52#11923958—31no—
53#11923958—31no—
54#11923958—31no—
55#11923958—31no—
56#11923958—31no—
57#11923958—31no—
58#11923958—31no—
59#11923958—31no—
60#11923958—31no—
61#11923958—31no—
62#11923958—31no—
63#11923958—31no—
64#11923958—31no—
65#11923958H(3,𝔽3)13yescomplemented
66#11923958H(3,𝔽3)13yescomplemented
67C32⋊(C43⋊C3)—31no—
68C32⋊(C43⋊C3)—31no—
69C32⋊(C43⋊C3)—31no—
70C32⋊(C43⋊C3)—31no—
71C32⋊(C43⋊C3)—31no—
72C32⋊(C43⋊C3)—31no—
73C32⋊(C43⋊C3)—31no—
74C32⋊(C43⋊C3)—31no—
75C32⋊(C43⋊C3)—31no—
76C32⋊(C43⋊C3)—99no—
77C3×C43⋊C9—39no—
78C3×C43⋊C9—31no—
79C3×C43⋊C9—31no—
80C3×C43⋊C9—31no—
81C3×C43⋊C9—31no—
82C3×C43⋊C9H(3,𝔽3)13yescomplemented
83C33×C43—31no—
84C33×C43H(3,𝔽3)13yes—
85C33×C43C3311yescharacteristic
863−1+2×C43—31no—
873−1+2×C43—31no—
883−1+2×C43—31no—
893−1+2×C43—31no—
903−1+2×C43—31no—
913−1+2×C43—31no—
92H(3,𝔽3)×C43—31no—
93H(3,𝔽3)×C43—31no—
94H(3,𝔽3)×C43—31no—
95H(3,𝔽3)×C43—31no—
96H(3,𝔽3)×C43—31no—
97H(3,𝔽3)×C43—31no—
98C3×C9×C43—31no—
99C3×C9×C43—31no—
100#10624749—431nomaximal, Sylow
101C32×C43—33no—
102C32×C43—91no—
103C32×C43—93no—
104C32×C43—91no—
105C32×C43—271no—
106C32×C43C3×H(3,𝔽3)11yescharacteristic
107C32×C43C3×H(3,𝔽3)11yescharacteristic
108C32×C43C3×H(3,𝔽3)11yescharacteristic
109C32×C43C3×H(3,𝔽3)11yescharacteristic
110C3×C43⋊C3—33no—
111C3×C43⋊C3—33no—
112C3×C43⋊C3—92no—
113C3×C43⋊C3—92no—
114C3×C43⋊C3—91no—
115C3×C43⋊C3—93no—
116C3×C43⋊C3—93no—
117C3×C43⋊C3—93no—
118C3×C43⋊C3—93no—
119C3×C43⋊C3—91no—
120C3×C43⋊C3—91no—
121C3×C43⋊C3—91no—
122C3×C43⋊C3—271no—
123C9×C43—91no—
124C9×C43—91no—
125C43⋊C9—33no—
126C43⋊C9—33no—
127C43⋊C9—33no—
128C43⋊C9—91no—
129C43⋊C9—91no—
1303−1+4—431no—
131#6911—431no—
132#6910—431no—
133#6910—431no—
134#6910—431no—
135#6909—431no—
136#6909—431no—
137#6909—431no—
138#6909C43⋊C311yescharacteristic, complemented
139C3×AΣL(1,𝔽27)—431no—
140C3×AΣL(1,𝔽27)—431no—
141#6891—431no—
142C32⋊H(3,𝔽3)—431no—
143C3×C43—31no—
144C3×C43—31no—
145C3×C43—31no—
146C3×C43—31no—
147C3×C43—93no—
148C3×C43—271no—
149C3×C43C32⋊H(3,𝔽3)11yescharacteristic
150C43⋊C3—93no—
151C43⋊C3—271no—
152C43⋊C3—271no—
153C43⋊C3—271no—
154C34—431no—
155#737—1293no—
156#737—1293no—
157#737—1293no—
158C3×3−1+2—431no—
159C3×3−1+2—431no—
160C3×3−1+2—431no—
161C3×3−1+2—431no—
162C3×3−1+2—431no—
163C3×3−1+2—1293no—
164C3×3−1+2C3×C43⋊C311yescharacteristic
165C3×3−1+2C3×C43⋊C311yescharacteristic
166C3×H(3,𝔽3)—431no—
167C3×H(3,𝔽3)—431no—
168C3×H(3,𝔽3)—431no—
169C3×H(3,𝔽3)—1293no—
170C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
171C3×H(3,𝔽3)C3×C43⋊C311yescharacteristic
172#732—1293no—
173#731—1293no—
174#731—1293no—
175#731—1293no—
176AΣL(1,𝔽27)—33no—
177AΣL(1,𝔽27)—1293no—
178AΣL(1,𝔽27)—1293no—
179AΣL(1,𝔽27)—1293no—
180AΣL(1,𝔽27)—1293no—
181AΣL(1,𝔽27)—1293no—
182C32⋊C9—1293no—
183C43#1062474911yescharacteristic, complemented, Sylow
184C33—31no—
185C33—1291no—
186C33—1291no—
187C33—1291no—
188C33—1291no—
189C33—1291no—
190C33—1291no—
191C33—1291no—
192C33—3873no—
193C33C32⋊(C43⋊C3)13yes—
194C33C32×C43⋊C311yescharacteristic
1953−1+2—31no—
1963−1+2—31no—
1973−1+2—31no—
1983−1+2—31no—
1993−1+2—31no—
2003−1+2—31no—
2013−1+2—433no—
2023−1+2—433no—
2033−1+2—12918no—
2043−1+2—1291no—
2053−1+2—1291no—
2063−1+2—1291no—
2073−1+2—1291no—
2083−1+2—1291no—
2093−1+2—1291no—
2103−1+2—1291no—
2113−1+2—1291no—
2123−1+2—1291no—
2133−1+2—1291no—
2143−1+2—1291no—
2153−1+2—1291no—
2163−1+2—1291no—
217H(3,𝔽3)—31no—
218H(3,𝔽3)—31no—
219H(3,𝔽3)—31no—
220H(3,𝔽3)—31no—
221H(3,𝔽3)—31no—
222H(3,𝔽3)—31no—
223H(3,𝔽3)—1291no—
224H(3,𝔽3)—1291no—
225H(3,𝔽3)—1291no—
226H(3,𝔽3)—1291no—
227H(3,𝔽3)—1291no—
228H(3,𝔽3)—1291no—
229H(3,𝔽3)—1291no—
230H(3,𝔽3)—1291no—
231H(3,𝔽3)—1291no—
232H(3,𝔽3)—3879no—
233C3×C9—31no—
234C3×C9—31no—
235C3×C9—433no—
236C3×C9—1299no—
237C3×C9—1291no—
238C3×C9—1291no—
239C3×C9—1291no—
240C3×C9—1291no—
241C32—33no—
242C32—91no—
243C32—93no—
244C32—91no—
245C32—271no—
246C32—1293no—
247C32—1293no—
248C32—3873no—
249C32—3873no—
250C32—3872no—
251C32—3872no—
252C32—3873no—
253C32—3873no—
254C32—3871no—
255C32—3871no—
256C32—3871no—
257C32—3871no—
258C32—11611no—
259C32H(3,𝔽3)×C43⋊C311yescharacteristic
260C32H(3,𝔽3)×C43⋊C311yescharacteristic
261C32H(3,𝔽3)×C43⋊C311yescharacteristic
262C32C3×C32⋊(C43⋊C3)11yescharacteristic
263C9—91no—
264C9—91no—
265C9—1293no—
266C9—1293no—
267C9—1293no—
268C9—3871no—
269C9—3871no—
270C3—31no—
271C3—31no—
272C3—31no—
273C3—31no—
274C3—93no—
275C3—271no—
276C3—3873no—
277C3—11611no—
278C3—11611no—
279C3—11611no—
280C3(C3×C43⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C43⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C43C33
FrattiniC33C32×C43⋊C3
FittingC43×#6909C3
socleC3×C43C32⋊H(3,𝔽3)
hypercenter#6909C43⋊C3
hypocenterC43#10624749
LCSG ▷ C33×C43 ▷ C3×C43 ▷ C43
UCSC1 ◁ C3 ◁ C33 ◁ #6909

Complements

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

NH ≅ G/Ntype
1. #23782924C3semidirect
2. #23782891C3semidirect
3. #23782888C3semidirect
4. #23782888C3semidirect
5. #23782887C3semidirect
6. #23782883C3semidirect
7. #23782882C3semidirect
8. #23782882C3semidirect
9. C3×#16812508C3semidirect
10. C3×#16812506C3semidirect
11. #23782795C3semidirect
12. (C3×C43⋊C3)⋊H(3,𝔽3)C3semidirect
13. C43×#6909C3semidirect
65. #11923958H(3,𝔽3)semidirect
66. #11923958H(3,𝔽3)semidirect
82. C3×C43⋊C9H(3,𝔽3)semidirect
138. #6909C43⋊C3semidirect
183. C43#10624749semidirect

Maximal subgroups

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

subgroupindex
#237829243
#237828913
#237828883
#237828873
#237828833
#237828823
C3×#168125083
C3×#168125063
#237827953
(C3×C43⋊C3)⋊H(3,𝔽3)3
C43×#69093
#1062474943