Finite Group Databasebeta

← #41006616

Subgroups — #41006616

Order 26973.

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

normal subgroups only

This group has 446 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#22582651C311yesmaximal, characteristic, complemented
3#22582651C311yesmaximal, characteristic, complemented
4#22582651C311yesmaximal, characteristic, complemented
5#22582644C311yesmaximal, characteristic, complemented
6#22582644C311yesmaximal, characteristic, complemented
7#22582644C311yesmaximal, characteristic, complemented
8#22582639C311yesmaximal, characteristic, complemented
9C3×#15688514C311yesmaximal, characteristic, complemented
10C3×#15688514C311yesmaximal, characteristic, complemented
11#22582551C311yesmaximal, characteristic, complemented
12#22582551C311yesmaximal, characteristic, complemented
13C37×#6912C311yesmaximal, characteristic, complemented
14C33×C37⋊C3C3211yescharacteristic
15#15688532—33no—
16#15688532—33no—
17#15688531—33no—
18C3×#11758608C3211yescharacteristic
19C3×#11758608C3211yescharacteristic
20C3×#11758608C3211yescharacteristic
21C3×#11758608C3211yescharacteristic
22C3×#11758608C3211yescharacteristic
23C3×#11758608C3211yescharacteristic
243−1+2×C37⋊C3—33no—
25C3×C32⋊(C37⋊C3)C3211yescharacteristic
26C3×C32⋊(C37⋊C3)C3211yescharacteristic
27#15688520—33no—
28#15688520—33no—
29#15688520—33no—
30#15688517—33no—
31#15688517—33no—
32#15688517—33no—
33#15688514—33no—
34#15688514—33no—
35#15688514—33no—
36#15688502—33no—
37#15688502—33no—
38C3×3−1+2×C37C3211yescharacteristic
39C3×3−1+2×C37C3211yescharacteristic
40C3×3−1+2×C37C3211yescharacteristic
41C3×3−1+2×C37C3211yescharacteristic
42C37×#733—33no—
43C33×C37C3311yescharacteristic
44C32×C37⋊C3—31no—
45C32×C37⋊C3—31no—
46C32×C37⋊C3—31no—
47C32×C37⋊C3—31no—
48C32×C37⋊C3—31no—
49C32×C37⋊C3—31no—
50C32×C37⋊C3—93no—
513−1+2×C37—31no—
523−1+2×C37—31no—
533−1+2×C37—31no—
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)13yes—
63C3×C9×C37—31no—
64C3×C9×C37—31no—
65C3×C9×C37—31no—
66C3×C9×C37—31no—
67C32⋊(C37⋊C3)—31no—
68C32⋊(C37⋊C3)—31no—
69C32⋊(C37⋊C3)—31no—
70C32⋊(C37⋊C3)—31no—
71C32⋊(C37⋊C3)—31no—
72C32⋊(C37⋊C3)H(3,𝔽3)13yes—
73#11758608—31no—
74#11758608—31no—
75#11758608—31no—
76#11758608—31no—
77#11758608—31no—
78#11758608—31no—
79#11758608—31no—
80#11758608—31no—
81#11758608—31no—
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—
91C3×#66524—31no—
92C3×#66524—31no—
93C3×#66524—31no—
94C3×#66524—31no—
95C3×#66524H(3,𝔽3)13yes—
96C3×#66524H(3,𝔽3)13yes—
97#11758606—39no—
98#11758605—39no—
99C9×C37⋊C3—39no—
100#10624752—371nomaximal, Sylow
101C32×C37—91no—
102C32×C37C3×H(3,𝔽3)11yescharacteristic
103C32×C37C3×H(3,𝔽3)11yescharacteristic
104C32×C37C3×H(3,𝔽3)11yescharacteristic
105C32×C37C3×H(3,𝔽3)11yescharacteristic
106C3×C37⋊C3—33no—
107C3×C37⋊C3—33no—
108C3×C37⋊C3—33no—
109C3×C37⋊C3—92no—
110C3×C37⋊C3—92no—
111C3×C37⋊C3—91no—
112C3×C37⋊C3—93no—
113C3×C37⋊C3—93no—
114C3×C37⋊C3—91no—
115C3×C37⋊C3—271no—
116C3×C37⋊C3—271no—
117C9×C37—33no—
118C9×C37—91no—
119C9×C37—91no—
120C9×C37—91no—
121#66524—33no—
122#66524—33no—
123#66524—91no—
124#66524—91no—
125#66524—91no—
126#66524—91no—
1273−1+4—371no—
128#6912—371no—
129#6912—371no—
130#6912—371no—
131#6912C37⋊C311yescharacteristic, complemented
132#6910—371no—
133#6910—371no—
134#6910—371no—
135#6909—371no—
136C3×AΣL(1,𝔽27)—371no—
137C3×AΣL(1,𝔽27)—371no—
138#6891—371no—
139#6891—371no—
140C3×C37—31no—
141C3×C37—31no—
142C3×C37—31no—
143C3×C37—31no—
144C3×C37C32⋊H(3,𝔽3)11yescharacteristic
145C37⋊C3—93no—
146C37⋊C3—93no—
147C37⋊C3—271no—
148C34—371no—
149#737—1113no—
150#737—1113no—
151#737—1113no—
152C3×3−1+2—371no—
153C3×3−1+2—371no—
154C3×3−1+2—371no—
155C3×3−1+2—371no—
156C3×3−1+2—371no—
157C3×3−1+2—371no—
158C3×3−1+2—1113no—
159C3×3−1+2C3×C37⋊C311yescharacteristic
160C3×3−1+2C3×C37⋊C311yescharacteristic
161C3×3−1+2C3×C37⋊C311yescharacteristic
162C3×3−1+2C3×C37⋊C311yescharacteristic
163C3×H(3,𝔽3)—371no—
164C3×H(3,𝔽3)—371no—
165#733—33no—
166#733—1113no—
167#733—1113no—
168#733—1113no—
169#731—1113no—
170#731—1113no—
171#731—1113no—
172AΣL(1,𝔽27)—1113no—
173AΣL(1,𝔽27)—1113no—
174AΣL(1,𝔽27)—1113no—
175C32⋊C9—1113no—
176C32⋊C9—1113no—
177C37#1062475211yescharacteristic, complemented, Sylow
178C33—3333no—
179C33—1111no—
180C33—1111no—
181C33—1111no—
182C33—1111no—
183C33—1111no—
184C33—1111no—
185C33C32×C37⋊C311yescharacteristic
1863−1+2—31no—
1873−1+2—31no—
1883−1+2—31no—
1893−1+2—31no—
1903−1+2—31no—
1913−1+2—31no—
1923−1+2—31no—
1933−1+2—31no—
1943−1+2—31no—
1953−1+2—31no—
1963−1+2—31no—
1973−1+2—1119no—
1983−1+2—1119no—
1993−1+2—1111no—
2003−1+2—1111no—
2013−1+2—1111no—
2023−1+2—1111no—
2033−1+2—1111no—
2043−1+2—1111no—
2053−1+2—1111no—
2063−1+2—1111no—
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+2C32⋊(C37⋊C3)13yes—
218H(3,𝔽3)—373no—
219H(3,𝔽3)—1111no—
220H(3,𝔽3)—1111no—
221H(3,𝔽3)—1111no—
222H(3,𝔽3)—1111no—
223H(3,𝔽3)—1111no—
224C3×C9—31no—
225C3×C9—31no—
226C3×C9—31no—
227C3×C9—31no—
228C3×C9—373no—
229C3×C9—373no—
230C3×C9—1119no—
231C3×C9—1111no—
232C3×C9—1111no—
233C3×C9—1111no—
234C3×C9—1111no—
235C32—91no—
236C32—3333no—
237C32—3333no—
238C32—3332no—
239C32—3332no—
240C32—3331no—
241C32—3331no—
242C32—1113no—
243C32—1113no—
244C32—1113no—
245C32—9991no—
246C32—9991no—
247C32H(3,𝔽3)×C37⋊C311yescharacteristic
248C32H(3,𝔽3)×C37⋊C311yescharacteristic
249C32H(3,𝔽3)×C37⋊C311yescharacteristic
250C32C3×C32⋊(C37⋊C3)11yescharacteristic
251C9—33no—
252C9—91no—
253C9—91no—
254C9—91no—
255C9—3331no—
256C9—3331no—
257C9—3331no—
258C9—3331no—
259C9—1113no—
260C9—1113no—
261C3—31no—
262C3—31no—
263C3—31no—
264C3—31no—
265C3—3333no—
266C3—3333no—
267C3—9991no—
268C3(C3×C37⋊C3)⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
centerC3(C3×C37⋊C3)⋊H(3,𝔽3)
commutator, cosocleC33×C37C33
FrattiniC33C32×C37⋊C3
FittingC37×#6912C3
socleC3×C37C32⋊H(3,𝔽3)
hypercenter#6912C37⋊C3
hypocenterC37#10624752
LCSG ▷ C33×C37 ▷ C3×C37 ▷ C37
UCSC1 ◁ C3 ◁ C33 ◁ #6912

Complements

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

NH ≅ G/Ntype
1. #22582679C3semidirect
2. #22582651C3semidirect
3. #22582651C3semidirect
4. #22582651C3semidirect
5. #22582644C3semidirect
6. #22582644C3semidirect
7. #22582644C3semidirect
8. #22582639C3semidirect
9. C3×#15688514C3semidirect
10. C3×#15688514C3semidirect
11. #22582551C3semidirect
12. #22582551C3semidirect
13. C37×#6912C3semidirect
131. #6912C37⋊C3semidirect
177. C37#10624752semidirect

Maximal subgroups

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

subgroupindex
#225826793
#225826513
#225826443
#225826393
C3×#156885143
#225825513
C37×#69123
#1062475237