Finite Group Databasebeta

← #41006591

Subgroups — #41006591

Order 26973.

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#22582679C311yesmaximal, characteristic, complemented
2#22582647C311yesmaximal, characteristic, complemented
3#22582644C311yesmaximal, characteristic, complemented
4#22582642C311yesmaximal, characteristic, complemented
5#22582639C311yesmaximal, characteristic, complemented
6#22582639C311yesmaximal, characteristic, complemented
7#22582639C311yesmaximal, characteristic, complemented
8#22582639C311yesmaximal, characteristic, complemented
9C3×#15688514C311yesmaximal, characteristic, complemented
10C3×#15688514C311yesmaximal, characteristic, complemented
11#22582551C311yesmaximal, characteristic, complemented
12(C3×C37⋊C3)⋊H(3,𝔽3)C311yesmaximal, characteristic, complemented
13C37×#6910C311yesmaximal, characteristic, complemented
14C33×C37⋊C3C3211yescharacteristic
15#15688532—33no—
16#15688532—33no—
17#15688531—33no—
18C3×#11758608C3211yescharacteristic
19C3×#11758608C3211yescharacteristic
20C3×#11758608C3211yescharacteristic
21C3×#11758608C3211yescharacteristic
223−1+2×C37⋊C3—33no—
23C3×C32⋊(C37⋊C3)—33no—
24C3×C32⋊(C37⋊C3)C3211yescharacteristic
25C3×C32⋊(C37⋊C3)C3211yescharacteristic
26C3×C32⋊(C37⋊C3)C3211yescharacteristic
27C3×C32⋊(C37⋊C3)C3211yescharacteristic
28#15688518—33no—
29#15688517—33no—
30#15688515—33no—
31#15688514—33no—
32#15688514—33no—
33#15688514—33no—
34#15688514—33no—
35#15688514—33no—
36#15688514—33no—
37#15688502—33no—
38C3×3−1+2×C37C3211yescharacteristic
39C3×3−1+2×C37C3211yescharacteristic
40C3×3−1+2×C37C3211yescharacteristic
41C3×H(3,𝔽3)×C37C3211yescharacteristic
42C37×#731—33no—
43C33×C37—31no—
44C33×C37C3311yescharacteristic
45C32×C37⋊C3—31no—
46C32×C37⋊C3—31no—
47C32×C37⋊C3—31no—
48C32×C37⋊C3—31no—
49C32×C37⋊C3—31no—
50C32×C37⋊C3—31no—
51C32×C37⋊C3—31no—
52C32×C37⋊C3—93no—
53C32×C37⋊C3H(3,𝔽3)13yes—
543−1+2×C37—31no—
553−1+2×C37—31no—
563−1+2×C37—31no—
573−1+2×C37—31no—
583−1+2×C37—31no—
593−1+2×C37—31no—
603−1+2×C37—31no—
613−1+2×C37—31no—
623−1+2×C37H(3,𝔽3)13yescomplemented
63H(3,𝔽3)×C37—31no—
64H(3,𝔽3)×C37—31no—
65H(3,𝔽3)×C37—31no—
66C3×C9×C37—31no—
67C3×C9×C37—31no—
68C3×C9×C37—31no—
69C32⋊(C37⋊C3)—31no—
70C32⋊(C37⋊C3)—31no—
71C32⋊(C37⋊C3)—31no—
72C32⋊(C37⋊C3)—31no—
73C32⋊(C37⋊C3)—31no—
74C32⋊(C37⋊C3)—31no—
75C32⋊(C37⋊C3)—31no—
76C32⋊(C37⋊C3)—31no—
77C32⋊(C37⋊C3)—31no—
78C32⋊(C37⋊C3)—31no—
79C32⋊(C37⋊C3)—31no—
80C32⋊(C37⋊C3)—31no—
81C32⋊(C37⋊C3)—99no—
82#11758608—31no—
83#11758608—31no—
84#11758608—31no—
85#11758608—31no—
86#11758608—31no—
87#11758608—31no—
88#11758608—31no—
89#11758608—31no—
90#11758608—31no—
91#11758608—31no—
92#11758608—31no—
93#11758608H(3,𝔽3)13yescomplemented
94C3×#66524—31no—
95C3×#66524—31no—
96C3×#66524—31no—
97C3×#66524H(3,𝔽3)13yescomplemented
98#11758606—39no—
99#11758605—39no—
100C9×C37⋊C3—39no—
101#10624749—371nomaximal, Sylow
102C32×C37—91no—
103C32×C37—93no—
104C32×C37—91no—
105C32×C37C3×H(3,𝔽3)11yescharacteristic
106C32×C37C3×H(3,𝔽3)11yescharacteristic
107C32×C37C3×H(3,𝔽3)11yescharacteristic
108C32×C37C3×H(3,𝔽3)11yescharacteristic
109C3×C37⋊C3—33no—
110C3×C37⋊C3—33no—
111C3×C37⋊C3—33no—
112C3×C37⋊C3—92no—
113C3×C37⋊C3—92no—
114C3×C37⋊C3—91no—
115C3×C37⋊C3—93no—
116C3×C37⋊C3—93no—
117C3×C37⋊C3—93no—
118C3×C37⋊C3—93no—
119C3×C37⋊C3—91no—
120C3×C37⋊C3—91no—
121C3×C37⋊C3—91no—
122C3×C37⋊C3—271no—
123C3×C37⋊C3—271no—
124C9×C37—33no—
125C9×C37—91no—
126C9×C37—91no—
127#66524—33no—
128#66524—33no—
129#66524—91no—
130#66524—91no—
1313−1+4—371no—
132#6911—371no—
133#6910—371no—
134#6910—371no—
135#6910C37⋊C311yescharacteristic, complemented
136#6909—371no—
137#6909—371no—
138#6909—371no—
139#6909—371no—
140C3×AΣL(1,𝔽27)—371no—
141C3×AΣL(1,𝔽27)—371no—
142#6891—371no—
143C32⋊H(3,𝔽3)—371no—
144C3×C37—31no—
145C3×C37—31no—
146C3×C37—31no—
147C3×C37—31no—
148C3×C37—271no—
149C3×C37C32⋊H(3,𝔽3)11yescharacteristic
150C37⋊C3—93no—
151C37⋊C3—93no—
152C37⋊C3—271no—
153C37⋊C3—271no—
154C37⋊C3—271no—
155C34—371no—
156#737—1113no—
157#737—1113no—
158#737—1113no—
159C3×3−1+2—371no—
160C3×3−1+2—371no—
161C3×3−1+2—371no—
162C3×3−1+2—371no—
163C3×3−1+2—1113no—
164C3×3−1+2C3×C37⋊C311yescharacteristic
165C3×3−1+2C3×C37⋊C311yescharacteristic
166C3×3−1+2C3×C37⋊C311yescharacteristic
167C3×H(3,𝔽3)—371no—
168C3×H(3,𝔽3)—371no—
169C3×H(3,𝔽3)—371no—
170C3×H(3,𝔽3)—371no—
171C3×H(3,𝔽3)—1113no—
172C3×H(3,𝔽3)C3×C37⋊C311yescharacteristic
173#732—1113no—
174#731—33no—
175#731—1113no—
176#731—1113no—
177AΣL(1,𝔽27)—1113no—
178AΣL(1,𝔽27)—1113no—
179AΣL(1,𝔽27)—1113no—
180AΣL(1,𝔽27)—1113no—
181AΣL(1,𝔽27)—1113no—
182AΣL(1,𝔽27)—1113no—
183C32⋊C9—1113no—
184C37#1062474911yescharacteristic, complemented, Sylow
185C33—31no—
186C33—373no—
187C33—3333no—
188C33—1111no—
189C33—1111no—
190C33—1111no—
191C33—1111no—
192C33—1111no—
193C33—1111no—
194C33—1111no—
195C33C32×C37⋊C311yescharacteristic
1963−1+2—31no—
1973−1+2—31no—
1983−1+2—31no—
1993−1+2—31no—
2003−1+2—31no—
2013−1+2—31no—
2023−1+2—31no—
2033−1+2—31no—
2043−1+2—373no—
2053−1+2—1119no—
2063−1+2—1119no—
2073−1+2—1111no—
2083−1+2—1111no—
2093−1+2—1111no—
2103−1+2—1111no—
2113−1+2—1111no—
2123−1+2—1111no—
2133−1+2—1111no—
2143−1+2—1111no—
2153−1+2—1111no—
2163−1+2—1111no—
2173−1+2—1111no—
2183−1+2C32⋊(C37⋊C3)13yescomplemented
219H(3,𝔽3)—31no—
220H(3,𝔽3)—31no—
221H(3,𝔽3)—31no—
222H(3,𝔽3)—3339no—
223H(3,𝔽3)—1111no—
224H(3,𝔽3)—1111no—
225H(3,𝔽3)—1111no—
226H(3,𝔽3)—1111no—
227H(3,𝔽3)—1111no—
228H(3,𝔽3)—1111no—
229H(3,𝔽3)—1111no—
230H(3,𝔽3)—1111no—
231H(3,𝔽3)—1111no—
232H(3,𝔽3)—1111no—
233H(3,𝔽3)—1111no—
234H(3,𝔽3)—1111no—
235C3×C9—31no—
236C3×C9—31no—
237C3×C9—31no—
238C3×C9—373no—
239C3×C9—1119no—
240C3×C9—1111no—
241C3×C9—1111no—
242C3×C9—1111no—
243C32—91no—
244C32—93no—
245C32—91no—
246C32—3333no—
247C32—3333no—
248C32—3333no—
249C32—3332no—
250C32—3332no—
251C32—3333no—
252C32—3331no—
253C32—3331no—
254C32—3331no—
255C32—3331no—
256C32—1113no—
257C32—1113no—
258C32—1113no—
259C32—9991no—
260C32—9991no—
261C32H(3,𝔽3)×C37⋊C311yescharacteristic
262C32H(3,𝔽3)×C37⋊C311yescharacteristic
263C32H(3,𝔽3)×C37⋊C311yescharacteristic
264C32C3×C32⋊(C37⋊C3)11yescharacteristic
265C9—33no—
266C9—91no—
267C9—91no—
268C9—3331no—
269C9—3331no—
270C9—1113no—
271C9—1113no—
272C3—31no—
273C3—31no—
274C3—31no—
275C3—31no—
276C3—271no—
277C3—3333no—
278C3—3333no—
279C3—9991no—
280C3—9991no—
281C3—9991no—
282C3(C3×C37⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C37⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C37C33
FrattiniC33C32×C37⋊C3
FittingC37×#6910C3
socleC3×C37C32⋊H(3,𝔽3)
hypercenter#6910C37⋊C3
hypocenterC37#10624749
LCSG ▷ C33×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C33 ◁ #6910

Complements

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

NH ≅ G/Ntype
1. #22582679C3semidirect
2. #22582647C3semidirect
3. #22582644C3semidirect
4. #22582642C3semidirect
5. #22582639C3semidirect
6. #22582639C3semidirect
7. #22582639C3semidirect
8. #22582639C3semidirect
9. C3×#15688514C3semidirect
10. C3×#15688514C3semidirect
11. #22582551C3semidirect
12. (C3×C37⋊C3)⋊H(3,𝔽3)C3semidirect
13. C37×#6910C3semidirect
62. 3−1+2×C37H(3,𝔽3)semidirect
93. #11758608H(3,𝔽3)semidirect
97. C3×#66524H(3,𝔽3)semidirect
135. #6910C37⋊C3semidirect
184. C37#10624749semidirect
218. 3−1+2C32⋊(C37⋊C3)semidirect

Maximal subgroups

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

subgroupindex
#225826793
#225826473
#225826443
#225826423
#225826393
C3×#156885143
#225825513
(C3×C37⋊C3)⋊H(3,𝔽3)3
C37×#69103
#1062474937