Finite Group Databasebeta

← C3×#10619679 #14517692

Subgroups — C3×#10619679 #14517692

Order 1944.

634 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 634 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C22×C3×AΣL(1,𝔽27)C211yesmaximal, characteristic, complemented
2C2×C3×#4183C211yesmaximal, characteristic, complemented
3C3×#66330C211yesmaximal, characteristic, complemented
4C32×#638—31nomaximal
5C3×#611⋊C3—32nomaximal
6C3×#638⋊C3—31nomaximal
7#10619679C311yesmaximal, characteristic, direct product factor
8C2×C3×AΣL(1,𝔽27)—21no—
9C2×C3×AΣL(1,𝔽27)C2211yescharacteristic
10C3×#4183—21no—
11C22×C34D311yescharacteristic, complemented
12C2×C32×C3⋊D3—31no—
13C32×C3⋊Dic3—31no—
14C22×C3×3−1+2D312yescomplemented
15C22×C3×H(3,𝔽3)D311yescharacteristic, complemented
16C2×C3×AGL(1,ℤ/9)—32no—
17C2×C3×(C3⋊D3)⋊C3—31no—
18C3×3−1+2⋊C4—32no—
19C3×(C3⋊Dic3)⋊C3—31no—
20C22×AΣL(1,𝔽27)—21no—
21C22×AΣL(1,𝔽27)—22no—
22C22×AΣL(1,𝔽27)—21no—
23C22×AΣL(1,𝔽27)C2×C311yescharacteristic, complemented
24C2×#4183C2×C311yescharacteristic, complemented
25#66330C2×C311yescharacteristic, complemented
26C3×AΣL(1,𝔽27)D411yescharacteristic, complemented, Sylow
27C3×#638—31no—
28C3×#638—32no—
29C3×#638—31no—
30C3×#638—31no—
31C32×#67—93no—
32C32×#67—91no—
33#611⋊C3—34no—
34#611⋊C3—32no—
35#638⋊C3—32no—
36#638⋊C3—31no—
37C3×#611—32no—
38C2×C34—21no—
39C2×C34C2×D311yescharacteristic
40C32×C3⋊D3—61no—
41C2×C3×3−1+2—22no—
42C2×C3×3−1+2C2×D312yes—
43C2×C3×H(3,𝔽3)—21no—
44C2×C3×H(3,𝔽3)C2×D311yescharacteristic
45C3×AGL(1,ℤ/9)—62no—
46C3×(C3⋊D3)⋊C3—61no—
47C2×AΣL(1,𝔽27)—22no—
48C2×AΣL(1,𝔽27)—24no—
49C2×AΣL(1,𝔽27)—22no—
50C2×AΣL(1,𝔽27)—21no—
51C2×AΣL(1,𝔽27)—21no—
52C2×AΣL(1,𝔽27)—22no—
53C2×AΣL(1,𝔽27)—21no—
54C2×AΣL(1,𝔽27)C22×C311yescharacteristic
55#4183—21no—
56C22×C33—21no—
57C22×C33—33no—
58C22×C33—32no—
59C22×C33—31no—
60C22×C33—31no—
61C22×C33—63no—
62C22×C33C3×D311yescharacteristic, complemented
63C22×C33C3⋊D311yescharacteristic
64C2×C3×C3⋊D3—31no—
65C2×C3×C3⋊D3—32no—
66C2×C3×C3⋊D3—31no—
67C2×C3×C3⋊D3—31no—
68C2×C32×D3—93no—
69C2×C32×D3—91no—
70C3×C3⋊Dic3—31no—
71C3×C3⋊Dic3—32no—
72C3×C3⋊Dic3—31no—
73C3×C3⋊Dic3—31no—
74C32×Dic3—93no—
75C32×Dic3—91no—
76C22×3−1+2—22no—
77C22×3−1+2—34no—
78C22×3−1+2C3×D312yescomplemented
79C22×H(3,𝔽3)—21no—
80C22×H(3,𝔽3)—32no—
81C22×H(3,𝔽3)C3×D311yescharacteristic, complemented
82C22×C3×C9—32no—
83C2×AGL(1,ℤ/9)—34no—
84C2×AGL(1,ℤ/9)—32no—
85C2×(C3⋊D3)⋊C3—32no—
86C2×(C3⋊D3)⋊C3—31no—
87C2×C3×D9—32no—
883−1+2⋊C4—34no—
893−1+2⋊C4—32no—
90(C3⋊Dic3)⋊C3—32no—
91(C3⋊Dic3)⋊C3—31no—
92C3×Dic9—32no—
93C34#6711yescharacteristic, complemented
94C3×3−1+2#6712yescomplemented
95C3×H(3,𝔽3)#6711yescharacteristic, complemented
96AΣL(1,𝔽27)—21no—
97AΣL(1,𝔽27)—22no—
98AΣL(1,𝔽27)—21no—
99AΣL(1,𝔽27)C3×D411yescharacteristic, complemented
100C32×D4—271no—
101#638—31no—
102#638—31no—
103C3×#67—93no—
104C3×#67—96no—
105C3×#67—93no—
106C3×#67—91no—
107C3×#67—92no—
108C3×#67—91no—
109C3×#67—271no—
110#611—32no—
111C2×C33—21no—
112C2×C33—22no—
113C2×C33—21no—
114C2×C33—21no—
115C2×C33—33no—
116C2×C33—32no—
117C2×C33—31no—
118C2×C33—31no—
119C2×C33—61no—
120C2×C33—62no—
121C2×C33—61no—
122C2×C33—63no—
123C2×C33—63no—
124C2×C33—66no—
125C2×C33C2×C3×D311yescharacteristic
126C2×C33C2×C3⋊D311yescharacteristic
127C3×C3⋊D3—61no—
128C3×C3⋊D3—62no—
129C3×C3⋊D3—61no—
130C3×C3⋊D3—61no—
131C32×D3—183no—
132C32×D3—181no—
133C2×3−1+2—24no—
134C2×3−1+2—22no—
135C2×3−1+2—22no—
136C2×3−1+2—34no—
137C2×3−1+2—64no—
138C2×3−1+2C2×C3×D312yes—
139C2×H(3,𝔽3)—22no—
140C2×H(3,𝔽3)—21no—
141C2×H(3,𝔽3)—21no—
142C2×H(3,𝔽3)—32no—
143C2×H(3,𝔽3)—62no—
144C2×H(3,𝔽3)C2×C3×D311yescharacteristic
145C2×C3×C9—32no—
146C2×C3×C9—62no—
147AGL(1,ℤ/9)—64no—
148AGL(1,ℤ/9)—62no—
149(C3⋊D3)⋊C3—62no—
150(C3⋊D3)⋊C3—61no—
151C3×D9—62no—
152C22×C32—31no—
153C22×C32—31no—
154C22×C32—33no—
155C22×C32—36no—
156C22×C32—33no—
157C22×C32—31no—
158C22×C32—61no—
159C22×C32—63no—
160C22×C32—66no—
161C22×C32—63no—
162C22×C32—61no—
163C22×C32—61no—
164C22×C32—91no—
165C22×C32—181no—
166C22×C32—271no—
167C22×C32#27211yescharacteristic
168C22×C32#27212yes—
169C22×C32C3×C3⋊D311yescharacteristic
170C2×C3⋊D3—31no—
171C2×C3⋊D3—31no—
172C2×C3×D3—93no—
173C2×C3×D3—96no—
174C2×C3×D3—93no—
175C2×C3×D3—91no—
176C2×C3×D3—92no—
177C2×C3×D3—91no—
178C2×C3×D3—271no—
179C32×C4—271no—
180C3⋊Dic3—31no—
181C3⋊Dic3—31no—
182C3×Dic3—93no—
183C3×Dic3—96no—
184C3×Dic3—93no—
185C3×Dic3—91no—
186C3×Dic3—92no—
187C3×Dic3—91no—
188C3×Dic3—271no—
189C22×C9—32no—
190C22×C9—62no—
191C2×D9—32no—
192Dic9—32no—
193C33—21no—
194C33—33no—
195C33—32no—
196C33—31no—
197C33—31no—
198C33—63no—
199C33C3×#6711yescharacteristic, complemented
200C33#63811yescharacteristic
2013−1+2—22no—
2023−1+2—34no—
2033−1+2C3×#6712yescomplemented
204H(3,𝔽3)—21no—
205H(3,𝔽3)—32no—
206H(3,𝔽3)C3×#6711yescharacteristic, complemented
207C3×C9—32no—
208C3×D4—272no—
209C3×D4—271no—
210C3×D4—271no—
211#67—93no—
212#67—91no—
213#67—271no—
214C2×C32—21no—
215C2×C32—22no—
216C2×C32—21no—
217C2×C32—31no—
218C2×C32—31no—
219C2×C32—33no—
220C2×C32—36no—
221C2×C32—33no—
222C2×C32—31no—
223C2×C32—61no—
224C2×C32—63no—
225C2×C32—61no—
226C2×C32—61no—
227C2×C32—63no—
228C2×C32—62no—
229C2×C32—62no—
230C2×C32—66no—
231C2×C32—61no—
232C2×C32—62no—
233C2×C32—66no—
234C2×C32—63no—
235C2×C32—66no—
236C2×C32—612no—
237C2×C32—61no—
238C2×C32—63no—
239C2×C32—66no—
240C2×C32—61no—
241C2×C32—91no—
242C2×C32—181no—
243C2×C32—181no—
244C2×C32—182no—
245C2×C32—541no—
246C2×C32C2×#27211yescharacteristic
247C2×C32C2×#27212yes—
248C2×C32C2×C3×C3⋊D311yescharacteristic
249C3⋊D3—61no—
250C3⋊D3—61no—
251C3×D3—183no—
252C3×D3—186no—
253C3×D3—183no—
254C3×D3—181no—
255C3×D3—182no—
256C3×D3—181no—
257C3×D3—541no—
258C2×C9—32no—
259C2×C9—62no—
260C2×C9—64no—
261C2×C9—62no—
262D9—62no—
263C22×C3—21no—
264C22×C3—33no—
265C22×C3—32no—
266C22×C3—31no—
267C22×C3—63no—
268C22×C3—91no—
269C22×C3—181no—
270C22×C3—272no—
271C22×C3—271no—
272C22×C3—271no—
273C22×C3#418311yescharacteristic, complemented
274C22×C3C3×#27211yescharacteristic
275C2×D3—93no—
276C2×D3—91no—
277C2×D3—271no—
278C3×C4—272no—
279C3×C4—271no—
280C3×C4—271no—
281Dic3—93no—
282Dic3—91no—
283Dic3—271no—
284C32—33no—
285C32—31no—
286C32—31no—
287C32—36no—
288C32—33no—
289C32—31no—
290C32—61no—
291C32—63no—
292C32—66no—
293C32—63no—
294C32—61no—
295C32—61no—
296C32—91no—
297C32—181no—
298C32#623511yescharacteristic
299C32#623512yes—
300C32C3×#63811yescharacteristic
301C9—32no—
302C9—62no—
303D4—271noSylow
304C2×C3—22no—
305C2×C3—21no—
306C2×C3—21no—
307C2×C3—21no—
308C2×C3—33no—
309C2×C3—32no—
310C2×C3—31no—
311C2×C3—62no—
312C2×C3—61no—
313C2×C3—63no—
314C2×C3—66no—
315C2×C3—63no—
316C2×C3—91no—
317C2×C3—181no—
318C2×C3—182no—
319C2×C3—181no—
320C2×C3—542no—
321C2×C3—541no—
322C2×C3—541no—
323C2×C3C2×#418311yescharacteristic
324C2×C3C2×C3×#27211yescharacteristic
325D3—183no—
326D3—181no—
327D3—541no—
328C22—271no—
329C22C3×#418311yescharacteristic, complemented
330C4—271no—
331C3—21no—
332C3—33no—
333C3—32no—
334C3—31no—
335C3—63no—
336C3—91no—
337C3—181no—
338C3#1061967911yescharacteristic, direct product factor
339C3C3×#623511yescharacteristic
340C2—21no—
341C2—541no—
342C2C2×C3×#418311yescharacteristic
subgroupG/H
centerC2×C3C2×#4183
commutator, cosocleC2×AΣL(1,𝔽27)C22×C3
FrattiniC2×C32C2×C3×C3⋊D3
FittingC22×C3×AΣL(1,𝔽27)C2
socleC2×C32C2×#272
hypercenterC22×C3#4183
hypocenterAΣL(1,𝔽27)C3×D4
LCSG ▷ C2×AΣL(1,𝔽27) ▷ AΣL(1,𝔽27)
UCSC1 ◁ C2×C3 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×AΣL(1,𝔽27)C2semidirect
2. C2×C3×#4183C2semidirect
3. C3×#66330C2semidirect
7. #10619679C3direct (N × H)
11. C22×C34D3semidirect
14. C22×C3×3−1+2D3semidirect
15. C22×C3×H(3,𝔽3)D3semidirect
23. C22×AΣL(1,𝔽27)C2×C3semidirect
24. C2×#4183C2×C3semidirect
25. #66330C2×C3semidirect
26. C3×AΣL(1,𝔽27)D4semidirect
62. C22×C33C3×D3semidirect
78. C22×3−1+2C3×D3semidirect
81. C22×H(3,𝔽3)C3×D3semidirect
93. C34#67semidirect
94. C3×3−1+2#67semidirect
95. C3×H(3,𝔽3)#67semidirect
99. AΣL(1,𝔽27)C3×D4semidirect
199. C33C3×#67semidirect
203. 3−1+2C3×#67semidirect
206. H(3,𝔽3)C3×#67semidirect
273. C22×C3#4183semidirect
329. C22C3×#4183semidirect
338. C3#10619679direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×AΣL(1,𝔽27)2
C2×C3×#41832
C3×#663302
C32×#6383
C3×#611⋊C33
C3×#638⋊C33
#106196793