Finite Group Databasebeta

← #14550697

Subgroups — #14550697

Order 2187.

471 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 471 conjugacy classes of subgroups — too many to draw. Only its 80 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×#6912C311yesmaximal, characteristic
2#10624886C311yesmaximal, characteristic
3#10624699C311yesmaximal, characteristic
4#10624699C311yesmaximal, characteristic
5#10624699C311yesmaximal, characteristic
6#10624699C311yesmaximal, characteristic
7#10624699C311yesmaximal, characteristic
8#10624699C311yesmaximal, characteristic
9#10624699C311yesmaximal, characteristic
10C3×3−1+2⋊C9C311yesmaximal, characteristic
11C3×3−1+2⋊C9C311yesmaximal, characteristic
12#10624558C311yesmaximal, characteristic
13#10624558C311yesmaximal, characteristic
14C32×3−1+2C3211yescharacteristic
15C32×3−1+2C3211yescharacteristic
16C32×3−1+2C3211yescharacteristic
17C32×3−1+2C3211yescharacteristic
18C33×C9C3211yescharacteristic
19#6912—33no—
20#6912—33no—
21#6912—33no—
22C3×#733—33no—
23#6895—33no—
24#6894—33no—
25#6894—33no—
26#6894—33no—
27C3×C32⋊C9C3211yescharacteristic
28C3×C32⋊C9C3211yescharacteristic
29C3×C32⋊C9C3211yescharacteristic
30C3×C32⋊C9C3211yescharacteristic
31C3×C32⋊C9C3211yescharacteristic
32C3×C32⋊C9C3211yescharacteristic
33C3×C32⋊C9C3211yescharacteristic
34C3×C32⋊C9C3211yescharacteristic
353−1+2⋊C9—33no—
363−1+2⋊C9—33no—
373−1+2⋊C9—33no—
383−1+2⋊C9—33no—
393−1+2⋊C9—33no—
403−1+2⋊C9—33no—
413−1+2⋊C9—33no—
423−1+2⋊C9—33no—
433−1+2⋊C9—33no—
44#6855—33no—
45#6855—33no—
46C34C3311yescharacteristic
47C3×3−1+2—31no—
48C3×3−1+2—31no—
49C3×3−1+2—31no—
50C3×3−1+2—31no—
51C3×3−1+2—31no—
52C3×3−1+2—31no—
53C3×3−1+2—31no—
54C3×3−1+2—31no—
55C3×3−1+2—31no—
56C3×3−1+2—31no—
57C3×3−1+2—31no—
58C3×3−1+2—31no—
59C3×3−1+2—31no—
60C3×3−1+2—31no—
61C3×3−1+2—31no—
62C3×3−1+2—31no—
63C3×3−1+2—31no—
64C3×3−1+2—31no—
65C3×3−1+2—31no—
66C3×3−1+2—31no—
67C3×3−1+2—31no—
68C3×3−1+2—31no—
69C3×3−1+2—31no—
70C3×3−1+2—31no—
71C3×3−1+2—31no—
72C3×3−1+2—31no—
73C3×3−1+2—31no—
74C3×3−1+2—31no—
75C3×3−1+2—31no—
76C3×3−1+2—31no—
77C3×3−1+2—31no—
78C3×3−1+2—31no—
79C3×3−1+2—31no—
80C3×3−1+2—31no—
81C3×3−1+2—31no—
82C3×3−1+2—31no—
83C3×3−1+2—31no—
84C3×3−1+2—31no—
85C3×3−1+2—31no—
86C3×3−1+2—31no—
87C3×3−1+2—31no—
88C3×3−1+2—31no—
89C3×3−1+2—31no—
90C3×3−1+2—31no—
91C3×3−1+2H(3,𝔽3)13yes—
92C3×3−1+23−1+213yes—
93C3×3−1+23−1+213yes—
94C3×3−1+23−1+213yes—
95C32×C9—31no—
96C32×C9—31no—
97C32×C9—31no—
98C32×C9—31no—
99C32×C9—31no—
100C32×C9—31no—
101C32×C9—31no—
102C32×C9—31no—
103C32×C9—31no—
104C32×C9—31no—
105C32×C9—31no—
106C32×C9—31no—
107C32×C9—31no—
108C32×C9—31no—
109C32×C9—93no—
110C32×C9H(3,𝔽3)13yes—
111C32×C9H(3,𝔽3)13yes—
112#733—327no—
113C9⋊C9—327no—
114C32⋊C9—31no—
115C32⋊C9—31no—
116C32⋊C9—31no—
117C32⋊C9—31no—
118C32⋊C9—31no—
119C32⋊C9—31no—
120C32⋊C9—31no—
121C32⋊C9—31no—
122C32⋊C9—31no—
123C32⋊C9—31no—
124C32⋊C9—31no—
125C32⋊C9—31no—
126C32⋊C9—31no—
127C32⋊C9—31no—
128C32⋊C9—31no—
129C32⋊C9—31no—
130C32⋊C9—31no—
131C32⋊C9—31no—
132C32⋊C9—31no—
133C32⋊C9—31no—
134C32⋊C9—31no—
135C32⋊C9—31no—
136C32⋊C9—31no—
137C32⋊C9H(3,𝔽3)13yes—
138C33—91no—
139C33—91no—
140C33—91no—
141C33C3×H(3,𝔽3)11yescharacteristic
142C33C3×H(3,𝔽3)11yescharacteristic
143C33C3×H(3,𝔽3)11yescharacteristic
144C33C3×H(3,𝔽3)11yescharacteristic
145C33C3×3−1+211yescharacteristic
146C33C3×3−1+211yescharacteristic
147C33C3×3−1+211yescharacteristic
148C33#73711yescharacteristic
149C33#73711yescharacteristic
150C33#73711yescharacteristic
151C33#73711yescharacteristic
152C33#73711yescharacteristic
153C33#73711yescharacteristic
1543−1+2—33no—
1553−1+2—33no—
1563−1+2—33no—
1573−1+2—33no—
1583−1+2—33no—
1593−1+2—33no—
1603−1+2—33no—
1613−1+2—33no—
1623−1+2—33no—
1633−1+2—33no—
1643−1+2—33no—
1653−1+2—33no—
1663−1+2—91no—
1673−1+2—91no—
1683−1+2—91no—
1693−1+2—91no—
1703−1+2—91no—
1713−1+2—91no—
1723−1+2—91no—
1733−1+2—91no—
1743−1+2—91no—
1753−1+2—91no—
1763−1+2—91no—
1773−1+2—91no—
1783−1+2—91no—
1793−1+2—91no—
1803−1+2—91no—
1813−1+2—91no—
1823−1+2—91no—
1833−1+2—91no—
1843−1+2—91no—
1853−1+2—91no—
1863−1+2—91no—
1873−1+2—91no—
1883−1+2—91no—
1893−1+2—91no—
190C3×C9—33no—
191C3×C9—33no—
192C3×C9—33no—
193C3×C9—33no—
194C3×C9—33no—
195C3×C9—33no—
196C3×C9—33no—
197C3×C9—33no—
198C3×C9—33no—
199C3×C9—92no—
200C3×C9—92no—
201C3×C9—91no—
202C3×C9—91no—
203C3×C9—91no—
204C3×C9—91no—
205C3×C9—91no—
206C3×C9—91no—
207C3×C9—91no—
208C3×C9—91no—
209C3×C9—91no—
210C3×C9—91no—
211C3×C9—91no—
212C3×C9—91no—
213C3×C9—91no—
214C3×C9—93no—
215C3×C9—93no—
216C3×C9—93no—
217C3×C9—93no—
218C3×C9—93no—
219C3×C9—93no—
220C3×C9—91no—
221C3×C9—91no—
222C3×C9—91no—
223C3×C9—91no—
224C3×C9—91no—
225C3×C9—271no—
226C3×C9—271no—
227C3×C9—271no—
228C3×C9—271no—
229C32—31no—
230C32—31no—
231C32—31no—
232C32—31no—
233C32—31no—
234C32—31no—
235C32—31no—
236C32—31no—
237C32—31no—
238C32—31no—
239C32—31no—
240C32—31no—
241C32—91no—
242C32—91no—
243C32—91no—
244C32—91no—
245C32—91no—
246C32—91no—
247C32—91no—
248C32—91no—
249C32—91no—
250C32C32⋊H(3,𝔽3)11yescharacteristic
251C32#689111yescharacteristic
252C32C9⋊H(3,𝔽3)11yescharacteristic
253C32C9⋊H(3,𝔽3)11yescharacteristic
254C32C9⋊H(3,𝔽3)11yescharacteristic
255C32C9⋊H(3,𝔽3)11yescharacteristic
256C32C9⋊H(3,𝔽3)11yescharacteristic
257C32C9⋊H(3,𝔽3)11yescharacteristic
258C32C9⋊H(3,𝔽3)11yescharacteristic
259C32C9⋊H(3,𝔽3)11yescharacteristic
260C32C9⋊H(3,𝔽3)11yescharacteristic
261C32#689311yescharacteristic
262C32#689311yescharacteristic
263C9—93no—
264C9—93no—
265C9—93no—
266C9—93no—
267C9—93no—
268C9—93no—
269C9—93no—
270C9—93no—
271C9—271no—
272C9—271no—
273C9—271no—
274C9—271no—
275C9—271no—
276C3—31no—
277C3—31no—
278C3—31no—
279C3—31no—
280C3—31no—
281C3—31no—
282C3—31no—
283C3—31no—
284C3—31no—
285C3—31no—
286C3—31no—
287C3—31no—
288C3#1062456311yescharacteristic
289C3#1062475011yescharacteristic
290C3#1062475011yescharacteristic
291C3#1062475211yescharacteristic
subgroupG/H
center, socleC32C32⋊H(3,𝔽3)
commutator, Frattini, prime radical, cosocleC34C33
LCSG ▷ C34 ▷ C3 ▷ C1
UCSC1 ◁ C32 ◁ C34 ◁ G
LECSG ▷ C34 ▷ C3 ▷ C1

Maximal subgroups

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

subgroupindex
C3×#69123
#106248863
#106246993
C3×3−1+2⋊C93
#106245583