Finite Group Databasebeta

← #41008508

Subgroups — #41008508

Order 26973.

404 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 87 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×C32⋊#66526C311yesmaximal, characteristic
2C3×C32⋊#66526C311yesmaximal, characteristic
3C3×C32⋊#66526C311yesmaximal, characteristic
43−1+2⋊#66526C319yesmaximal, complemented
5C3×3−1+2×C37⋊C3C311yesmaximal, characteristic
6C32×#66526—31no—
7C32×#66526—31no—
8C32×#66526C3213yes—
9C32⋊#66526—31no—
10C32⋊#66526—31no—
11C32⋊#66526—31no—
12C32⋊#66526—31no—
13C32⋊#66526—31no—
14C32⋊#66526—31no—
15C32⋊#66526—31no—
16C32⋊#66526C3213yes—
17C32⋊#66526C3213yes—
18C33×C37⋊C3C3211yescharacteristic
19C3×#11758608C912yescomplemented
20C3×#11758605—31no—
21C3×#11758606—31no—
223−1+2×C37⋊C3—31no—
233−1+2×C37⋊C3—31no—
243−1+2×C37⋊C3—31no—
253−1+2×C37⋊C3—31no—
263−1+2×C37⋊C3—31no—
273−1+2×C37⋊C3—31no—
283−1+2×C37⋊C3C913yescomplemented
293−1+2×C37⋊C3C913yescomplemented
303−1+2×C37⋊C3C3213yes—
31C3×C9×C37⋊C3—31no—
32C3×3−1+2×C37C911yescharacteristic, complemented
33C33×C37C3×C911yescharacteristic
34C32×C37⋊C3—91no—
35C32×C37⋊C3—91no—
36C32×C37⋊C3—91no—
37C32×C37⋊C3C3×C911yescharacteristic
38C32×C37⋊C3C3×C911yescharacteristic
39C32×C37⋊C3H(3,𝔽3)11yescharacteristic
40C32×C37⋊C3H(3,𝔽3)11yescharacteristic
41C32×C37⋊C3H(3,𝔽3)11yescharacteristic
42C32×C37⋊C33−1+211yescharacteristic
43C32×C37⋊C33−1+211yescharacteristic
44C32×C37⋊C33−1+211yescharacteristic
45C32×C37⋊C33−1+211yescharacteristic
46C32×C37⋊C33−1+211yescharacteristic
47C32×C37⋊C33−1+211yescharacteristic
48C32×C37⋊C3C3311yescharacteristic
49C3×#66526—33no—
50C3×#66526—33no—
51C3×#66526—33no—
52C3×#66526—93no—
53C3×#66526—93no—
54C3×#66526—93no—
553−1+2×C37—31no—
563−1+2×C37—31no—
573−1+2×C37C3×C913yescomplemented
58C3×C9×C37—31no—
59#11758608—32no—
60#11758608—32no—
61#11758608C3×C916yescomplemented
62C3×#66524—32no—
63#11758606—33no—
64#11758606—33no—
65#11758606—33no—
66#11758605—33no—
67#11758605—33no—
68#11758605—33no—
69C9×C37⋊C3—33no—
70C9×C37⋊C3—33no—
71C9×C37⋊C3—33no—
72#10624699—371nomaximal, Sylow
73C32×C37—91no—
74C32×C37C32⋊C911yescharacteristic
75C32×C37C32⋊C911yescharacteristic
76C32×C37C32⋊C911yescharacteristic
77C32×C37C32×C911yescharacteristic
78C3×C37⋊C3—31no—
79C3×C37⋊C3—31no—
80C3×C37⋊C3—31no—
81C3×C37⋊C3—31no—
82C3×C37⋊C3—31no—
83C3×C37⋊C3—31no—
84C3×C37⋊C3—31no—
85C3×C37⋊C3—31no—
86C3×C37⋊C3—31no—
87C3×C37⋊C3—31no—
88C3×C37⋊C3—31no—
89C3×C37⋊C3—31no—
90C3×C37⋊C3—91no—
91C3×C37⋊C3—91no—
92C3×C37⋊C3—91no—
93C3×C37⋊C3—91no—
94C3×C37⋊C3—91no—
95C3×C37⋊C3—91no—
96C3×C37⋊C3—91no—
97C3×C37⋊C3—91no—
98C3×C37⋊C3C32⋊C911yescharacteristic
99C3×C37⋊C3C32⋊C911yescharacteristic
100C3×C37⋊C3C32⋊C911yescharacteristic
101C3×C37⋊C3C32⋊C911yescharacteristic
102C3×C37⋊C3C32⋊C911yescharacteristic
103C3×C37⋊C3C32⋊C911yescharacteristic
104C3×C37⋊C3C3×H(3,𝔽3)11yescharacteristic
105C3×C37⋊C3C3×3−1+211yescharacteristic
106C3×C37⋊C3C3×3−1+211yescharacteristic
107#66526—93no—
108#66526—93no—
109#66526—93no—
110C9×C37—33no—
111#66524—36no—
112C32×3−1+2—371no—
113C3×C32⋊C9—371no—
114C3×C32⋊C9—371no—
115C3×C32⋊C9—371no—
1163−1+2⋊C9—379no—
117C3×C37—31no—
118C3×C37—31no—
119C3×C37—31no—
120C3×C37—31no—
121C3×C37C3×C32⋊C911yescharacteristic
122C37⋊C3—31no—
123C37⋊C3—31no—
124C37⋊C3—31no—
125C37⋊C3—31no—
126C37⋊C3—31no—
127C37⋊C3—31no—
128C37⋊C3—31no—
129C37⋊C3—31no—
130C37⋊C3#690911yescharacteristic
131C37⋊C3#691011yescharacteristic
132C37⋊C3#691211yescharacteristic
133C34—371no—
134C3×3−1+2—372no—
135C3×3−1+2—373no—
136C3×3−1+2—373no—
137C3×3−1+2—373no—
138C3×3−1+2—1111no—
139C3×3−1+2—1111no—
140C3×3−1+2—1111no—
141C3×3−1+2—1111no—
142C3×3−1+2—1111no—
143C3×3−1+2—1111no—
144C3×3−1+2—1111no—
145C3×3−1+2—1111no—
146C3×3−1+2#6652611yescharacteristic, complemented
147C32×C9—373no—
148C32×C9—1111no—
149C32×C9—1111no—
150C32×C9—1111no—
151C32⋊C9—373no—
152C32⋊C9—373no—
153C32⋊C9—1111no—
154C32⋊C9—1111no—
155C32⋊C9—1111no—
156C32⋊C9—1111no—
157C32⋊C9—1111no—
158C32⋊C9—1111no—
159C32⋊C9—1111no—
160C37#1062469911yescharacteristic, complemented, Sylow
161C33—371no—
162C33—371no—
163C33—371no—
164C33—371no—
165C33—371no—
166C33—371no—
167C33—371no—
168C33—371no—
169C33—371no—
170C33—371no—
171C33—371no—
172C33—371no—
173C33—3331no—
174C33—3331no—
175C33—3331no—
176C33C3×#6652611yescharacteristic
1773−1+2—31no—
1783−1+2—31no—
1793−1+2—376no—
1803−1+2—1113no—
1813−1+2—1113no—
1823−1+2—1113no—
1833−1+2—1113no—
1843−1+2—1113no—
1853−1+2—1113no—
1863−1+2—1112no—
1873−1+2—1112no—
1883−1+2C3×#6652613yescomplemented
189C3×C9—31no—
190C3×C9—3333no—
191C3×C9—3333no—
192C3×C9—3333no—
193C3×C9—1113no—
194C3×C9—1113no—
195C3×C9—1113no—
196C3×C9—1113no—
197C3×C9—1113no—
198C3×C9—1113no—
199C3×C9—1112no—
200C32—91no—
201C32—371no—
202C32—371no—
203C32—371no—
204C32—371no—
205C32—371no—
206C32—371no—
207C32—371no—
208C32—371no—
209C32—371no—
210C32—3331no—
211C32—3331no—
212C32—3331no—
213C32—3331no—
214C32—3331no—
215C32—3331no—
216C32—3331no—
217C32—3331no—
218C32—1111no—
219C32—1111no—
220C32—1111no—
221C32—1111no—
222C32—1111no—
223C32—1111no—
224C32—1111no—
225C32—1111no—
226C32—1111no—
227C32—1111no—
228C32—1111no—
229C32—1111no—
230C32C32⋊#6652611yescharacteristic
231C32C32⋊#6652611yescharacteristic
232C32C32⋊#6652611yescharacteristic
233C32C32×#6652611yescharacteristic
234C9—33no—
235C9—3333no—
236C9—3333no—
237C9—3333no—
238C9—1116no—
239C3—31no—
240C3—31no—
241C3—31no—
242C3—31no—
243C3—371no—
244C3—371no—
245C3—371no—
246C3—1111no—
247C3—1111no—
248C3—1111no—
249C3—1111no—
250C3—1111no—
251C3—1111no—
252C3—1111no—
253C3—1111no—
254C3C3×C32⋊#6652611yescharacteristic
subgroupG/H
centerC3C3×C32⋊#66526
commutatorC32×C37C32×C9
FrattiniC32C32×#66526
FittingC3×3−1+2×C37C9
socleC3×C37C3×C32⋊C9
prime radicalC33×C37⋊C3C32
cosocleC32×C37⋊C3C33
hypercenterC3×3−1+2#66526
hypocenterC37#10624699
LCSG ▷ C32×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C33 ◁ C3×3−1+2

Complements

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

NH ≅ G/Ntype
4. 3−1+2⋊#66526C3semidirect
19. C3×#11758608C9semidirect
28. 3−1+2×C37⋊C3C9semidirect
29. 3−1+2×C37⋊C3C9semidirect
32. C3×3−1+2×C37C9semidirect
57. 3−1+2×C37C3×C9semidirect
61. #11758608C3×C9semidirect
146. C3×3−1+2#66526semidirect
160. C37#10624699semidirect
188. 3−1+2C3×#66526semidirect

Maximal subgroups

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

subgroupindex
C3×C32⋊#665263
3−1+2⋊#665263
C3×3−1+2×C37⋊C33
#1062469937