Subgroups — C₂×#13091566 #72244012

Order 2916.

694 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13091566	C₂	1	2	yes	maximal, direct product factor
2	C₂×#10624918	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4208	C₃	1	1	yes	maximal, characteristic
4	C₂×#92319	C₃	1	3	yes	maximal, complemented
5	C₂×D₃×C₂₇⋊C₃	—	3	1	no	maximal
6	C₂×D₃×C₂₇⋊C₃	—	3	1	no	maximal
7	C₂×D₃×C₂₇⋊C₃	—	3	1	no	maximal
8	C₂×D₃×C₂₇⋊C₃	—	3	1	no	maximal
9	#10624918	C₂²	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃×#737	C₂×C₃	1	1	yes	characteristic
11	C₃×#4208	C₂×C₃	1	2	yes	—
12	C₂×#6903	—	2	3	no	—
13	C₂×#6903	—	2	3	no	—
14	C₂×#6903	—	2	3	no	—
15	C₂×#6903	—	2	3	no	—
16	C₂×#6903	C₂×C₃	1	3	yes	complemented
17	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
18	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
19	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
20	C₂×C₃×C₂₇⋊C₃	—	2	1	no	—
21	C₂×C₃×C₂₇⋊C₃	D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×C₂₇⋊C₃	D₃	1	1	yes	characteristic, complemented
23	C₂×C₃×C₂₇⋊C₃	D₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₂₇⋊C₃	D₃	1	1	yes	characteristic, complemented
25	#92319	C₂×C₃	1	6	yes	complemented
26	D₃×C₂₇⋊C₃	—	3	2	no	—
27	D₃×C₂₇⋊C₃	—	3	2	no	—
28	D₃×C₂₇⋊C₃	—	3	2	no	—
29	D₃×C₂₇⋊C₃	—	3	2	no	—
30	C₂×#4208	C₉	1	2	yes	—
31	C₂×#4208	C₃²	1	1	yes	characteristic
32	C₂×C₃×#272	C₉	1	1	yes	characteristic
33	C₂×C₃×D₃×C₉	—	3	1	no	—
34	C₂×C₃×D₃×C₉	—	3	1	no	—
35	C₂×C₃×D₃×C₉	—	3	1	no	—
36	C₂×C₃×D₃×C₉	—	3	1	no	—
37	C₂²×C₂₇⋊C₃	—	9	1	no	—
38	C₂×D₃×C₂₇	—	3	3	no	—
39	C₂×D₃×C₂₇	—	3	3	no	—
40	C₂×D₃×C₂₇	—	3	3	no	—
41	C₂×D₃×C₂₇	—	3	3	no	—
42	C₃×#737	C₂²×C₃	1	1	yes	characteristic
43	#6903	—	2	3	no	—
44	#6903	—	2	3	no	—
45	#6903	—	2	3	no	—
46	#6903	—	2	3	no	—
47	#6903	C₂²×C₃	1	3	yes	complemented
48	C₃×C₂₇⋊C₃	—	2	1	no	—
49	C₃×C₂₇⋊C₃	—	2	1	no	—
50	C₃×C₂₇⋊C₃	—	2	1	no	—
51	C₃×C₂₇⋊C₃	—	2	1	no	—
52	C₃×C₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
53	C₃×C₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
54	C₃×C₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
55	C₃×C₂₇⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
56	C₂×#737	—	2	2	no	—
57	C₂×#737	—	2	2	no	—
58	C₂×#737	—	2	2	no	—
59	C₂×#737	—	2	2	no	—
60	C₂×#737	—	2	1	no	—
61	C₂×#737	—	2	1	no	—
62	C₂×#737	—	2	1	no	—
63	C₂×#737	—	2	1	no	—
64	C₂×#737	C₂×C₉	1	2	yes	—
65	C₂×#737	C₂×C₃²	1	1	yes	characteristic
66	C₂×C₃×3₋¹⁺²	—	2	1	no	—
67	C₂×C₃×3₋¹⁺²	—	2	1	no	—
68	C₂×C₃×3₋¹⁺²	—	2	1	no	—
69	C₂×C₃×3₋¹⁺²	—	2	1	no	—
70	C₂×C₃×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
71	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
72	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
73	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
74	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
75	#4208	C₂×C₉	1	4	yes	—
76	#4208	C₂×C₃²	1	2	yes	—
77	C₃×#272	C₂×C₉	1	2	yes	—
78	C₃×D₃×C₉	—	3	2	no	—
79	C₃×D₃×C₉	—	3	2	no	—
80	C₃×D₃×C₉	—	3	2	no	—
81	C₃×D₃×C₉	—	3	2	no	—
82	C₂×C₂₇⋊C₃	—	2	3	no	—
83	C₂×C₂₇⋊C₃	—	2	3	no	—
84	C₂×C₂₇⋊C₃	—	2	3	no	—
85	C₂×C₂₇⋊C₃	—	2	3	no	—
86	C₂×C₂₇⋊C₃	—	2	3	no	—
87	C₂×C₂₇⋊C₃	—	2	3	no	—
88	C₂×C₂₇⋊C₃	—	2	3	no	—
89	C₂×C₂₇⋊C₃	—	2	3	no	—
90	C₂×C₂₇⋊C₃	—	2	1	no	—
91	C₂×C₂₇⋊C₃	—	2	1	no	—
92	C₂×C₂₇⋊C₃	—	2	1	no	—
93	C₂×C₂₇⋊C₃	—	2	1	no	—
94	C₂×C₂₇⋊C₃	—	2	3	no	—
95	C₂×C₂₇⋊C₃	—	2	3	no	—
96	C₂×C₂₇⋊C₃	—	2	3	no	—
97	C₂×C₂₇⋊C₃	—	2	3	no	—
98	C₂×C₂₇⋊C₃	—	9	2	no	—
99	C₂×C₂₇⋊C₃	C₃⋊D₃	1	1	yes	characteristic
100	C₂×C₃×C₂₇	—	2	3	no	—
101	C₂×C₃×C₂₇	—	2	3	no	—
102	C₂×C₃×C₂₇	—	2	3	no	—
103	C₂×C₃×C₂₇	—	2	3	no	—
104	C₂×C₃×C₂₇	C₃×D₃	1	3	yes	complemented
105	C₂×C₃×C₂₇	C₃×D₃	1	3	yes	complemented
106	C₂×C₃×C₂₇	C₃×D₃	1	3	yes	complemented
107	C₂×C₃×C₂₇	C₃×D₃	1	3	yes	complemented
108	D₃×C₂₇	—	3	6	no	—
109	D₃×C₂₇	—	3	6	no	—
110	D₃×C₂₇	—	3	6	no	—
111	D₃×C₂₇	—	3	6	no	—
112	C₂×C₃²×D₃	—	3	1	no	—
113	C₂×C₃²×D₃	—	3	1	no	—
114	C₂×C₃²×D₃	—	3	1	no	—
115	C₂×C₃²×D₃	—	3	1	no	—
116	C₂²×C₃×C₉	—	9	1	no	—
117	C₂×#272	C₃×C₉	1	1	yes	characteristic
118	C₂×D₃×C₉	—	3	2	no	—
119	C₂×D₃×C₉	—	3	2	no	—
120	C₂×D₃×C₉	—	3	2	no	—
121	C₂×D₃×C₉	—	3	2	no	—
122	C₂×D₃×C₉	—	3	1	no	—
123	C₂×D₃×C₉	—	3	1	no	—
124	C₂×D₃×C₉	—	3	1	no	—
125	C₂×D₃×C₉	—	3	1	no	—
126	C₂²×C₂₇	—	9	3	no	—
127	#737	—	2	2	no	—
128	#737	—	2	2	no	—
129	#737	—	2	2	no	—
130	#737	—	2	2	no	—
131	#737	—	2	1	no	—
132	#737	—	2	1	no	—
133	#737	—	2	1	no	—
134	#737	—	2	1	no	—
135	#737	C₂²×C₉	1	2	yes	—
136	#737	C₂²×C₃²	1	1	yes	characteristic
137	C₃×3₋¹⁺²	—	2	1	no	—
138	C₃×3₋¹⁺²	—	2	1	no	—
139	C₃×3₋¹⁺²	—	2	1	no	—
140	C₃×3₋¹⁺²	—	2	1	no	—
141	C₃×H(3,𝔽₃)	C₂²×C₉	1	1	yes	characteristic
142	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
143	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
144	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
145	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
146	C₂₇⋊C₃	—	2	3	no	—
147	C₂₇⋊C₃	—	2	3	no	—
148	C₂₇⋊C₃	—	2	3	no	—
149	C₂₇⋊C₃	—	2	3	no	—
150	C₂₇⋊C₃	—	2	3	no	—
151	C₂₇⋊C₃	—	2	3	no	—
152	C₂₇⋊C₃	—	2	3	no	—
153	C₂₇⋊C₃	—	2	3	no	—
154	C₂₇⋊C₃	—	2	1	no	—
155	C₂₇⋊C₃	—	2	1	no	—
156	C₂₇⋊C₃	—	2	1	no	—
157	C₂₇⋊C₃	—	2	1	no	—
158	C₂₇⋊C₃	—	2	3	no	—
159	C₂₇⋊C₃	—	2	3	no	—
160	C₂₇⋊C₃	—	2	3	no	—
161	C₂₇⋊C₃	—	2	3	no	—
162	C₂₇⋊C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
163	C₃×C₂₇	—	2	3	no	—
164	C₃×C₂₇	—	2	3	no	—
165	C₃×C₂₇	—	2	3	no	—
166	C₃×C₂₇	—	2	3	no	—
167	C₃×C₂₇	C₂×C₃×D₃	1	3	yes	complemented
168	C₃×C₂₇	C₂×C₃×D₃	1	3	yes	complemented
169	C₃×C₂₇	C₂×C₃×D₃	1	3	yes	complemented
170	C₃×C₂₇	C₂×C₃×D₃	1	3	yes	complemented
171	C₂×C₃³	D₃×C₉	1	1	yes	characteristic
172	C₂×C₃³	D₃×C₉	1	1	yes	characteristic
173	C₂×C₃³	D₃×C₉	1	1	yes	characteristic
174	C₂×C₃³	D₃×C₉	1	1	yes	characteristic
175	C₃²×D₃	—	3	2	no	—
176	C₃²×D₃	—	3	2	no	—
177	C₃²×D₃	—	3	2	no	—
178	C₃²×D₃	—	3	2	no	—
179	C₂×3₋¹⁺²	—	2	2	no	—
180	C₂×3₋¹⁺²	—	2	2	no	—
181	C₂×3₋¹⁺²	—	2	2	no	—
182	C₂×3₋¹⁺²	—	2	2	no	—
183	C₂×3₋¹⁺²	—	2	2	no	—
184	C₂×3₋¹⁺²	—	2	2	no	—
185	C₂×3₋¹⁺²	—	2	2	no	—
186	C₂×3₋¹⁺²	—	2	2	no	—
187	C₂×3₋¹⁺²	—	2	2	no	—
188	C₂×3₋¹⁺²	—	2	2	no	—
189	C₂×3₋¹⁺²	—	2	2	no	—
190	C₂×3₋¹⁺²	—	2	2	no	—
191	C₂×3₋¹⁺²	—	2	2	no	—
192	C₂×3₋¹⁺²	—	2	2	no	—
193	C₂×3₋¹⁺²	—	2	2	no	—
194	C₂×3₋¹⁺²	—	2	2	no	—
195	C₂×3₋¹⁺²	—	2	1	no	—
196	C₂×3₋¹⁺²	—	2	1	no	—
197	C₂×3₋¹⁺²	—	2	1	no	—
198	C₂×3₋¹⁺²	—	2	1	no	—
199	C₂×H(3,𝔽₃)	—	2	1	no	—
200	C₂×H(3,𝔽₃)	—	2	1	no	—
201	C₂×H(3,𝔽₃)	—	2	1	no	—
202	C₂×H(3,𝔽₃)	—	2	1	no	—
203	C₂×H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
204	C₂×C₃×C₉	—	2	1	no	—
205	C₂×C₃×C₉	—	2	1	no	—
206	C₂×C₃×C₉	—	2	1	no	—
207	C₂×C₃×C₉	—	2	1	no	—
208	C₂×C₃×C₉	—	2	2	no	—
209	C₂×C₃×C₉	—	2	2	no	—
210	C₂×C₃×C₉	—	2	2	no	—
211	C₂×C₃×C₉	—	2	2	no	—
212	C₂×C₃×C₉	—	2	1	no	—
213	C₂×C₃×C₉	—	2	1	no	—
214	C₂×C₃×C₉	—	2	1	no	—
215	C₂×C₃×C₉	—	2	1	no	—
216	C₂×C₃×C₉	—	9	2	no	—
217	C₂×C₃×C₉	D₃×C₉	1	2	yes	—
218	C₂×C₃×C₉	D₃×C₉	1	2	yes	—
219	C₂×C₃×C₉	D₃×C₉	1	2	yes	—
220	C₂×C₃×C₉	D₃×C₉	1	2	yes	—
221	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
222	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
223	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
224	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
225	C₂×C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
226	#272	C₂×C₃×C₉	1	2	yes	—
227	D₃×C₉	—	3	4	no	—
228	D₃×C₉	—	3	4	no	—
229	D₃×C₉	—	3	4	no	—
230	D₃×C₉	—	3	4	no	—
231	D₃×C₉	—	3	2	no	—
232	D₃×C₉	—	3	2	no	—
233	D₃×C₉	—	3	2	no	—
234	D₃×C₉	—	3	2	no	—
235	C₂×C₂₇	—	2	3	no	—
236	C₂×C₂₇	—	2	3	no	—
237	C₂×C₂₇	—	2	3	no	—
238	C₂×C₂₇	—	2	3	no	—
239	C₂×C₂₇	—	9	6	no	—
240	C₂×C₂₇	C₃×C₃⋊D₃	1	3	yes	—
241	C₂²×C₃²	—	9	1	no	—
242	C₂×C₃×D₃	—	3	1	no	—
243	C₂×C₃×D₃	—	3	1	no	—
244	C₂×C₃×D₃	—	3	1	no	—
245	C₂×C₃×D₃	—	3	1	no	—
246	C₂×C₃×D₃	—	9	1	no	—
247	C₂×C₃×D₃	—	9	1	no	—
248	C₂×C₃×D₃	—	9	1	no	—
249	C₂×C₃×D₃	—	9	1	no	—
250	C₂²×C₉	—	9	2	no	—
251	C₂²×C₉	—	9	1	no	—
252	C₃³	C₂×D₃×C₉	1	1	yes	characteristic
253	C₃³	C₂×D₃×C₉	1	1	yes	characteristic
254	C₃³	C₂×D₃×C₉	1	1	yes	characteristic
255	C₃³	C₂×D₃×C₉	1	1	yes	characteristic
256	3₋¹⁺²	—	2	2	no	—
257	3₋¹⁺²	—	2	2	no	—
258	3₋¹⁺²	—	2	2	no	—
259	3₋¹⁺²	—	2	2	no	—
260	3₋¹⁺²	—	2	2	no	—
261	3₋¹⁺²	—	2	2	no	—
262	3₋¹⁺²	—	2	2	no	—
263	3₋¹⁺²	—	2	2	no	—
264	3₋¹⁺²	—	2	2	no	—
265	3₋¹⁺²	—	2	2	no	—
266	3₋¹⁺²	—	2	2	no	—
267	3₋¹⁺²	—	2	2	no	—
268	3₋¹⁺²	—	2	2	no	—
269	3₋¹⁺²	—	2	2	no	—
270	3₋¹⁺²	—	2	2	no	—
271	3₋¹⁺²	—	2	2	no	—
272	3₋¹⁺²	—	2	1	no	—
273	3₋¹⁺²	—	2	1	no	—
274	3₋¹⁺²	—	2	1	no	—
275	3₋¹⁺²	—	2	1	no	—
276	H(3,𝔽₃)	—	2	1	no	—
277	H(3,𝔽₃)	—	2	1	no	—
278	H(3,𝔽₃)	—	2	1	no	—
279	H(3,𝔽₃)	—	2	1	no	—
280	H(3,𝔽₃)	C₂²×C₃×C₉	1	1	yes	characteristic
281	C₃×C₉	—	2	1	no	—
282	C₃×C₉	—	2	1	no	—
283	C₃×C₉	—	2	1	no	—
284	C₃×C₉	—	2	1	no	—
285	C₃×C₉	—	2	2	no	—
286	C₃×C₉	—	2	2	no	—
287	C₃×C₉	—	2	2	no	—
288	C₃×C₉	—	2	2	no	—
289	C₃×C₉	—	2	1	no	—
290	C₃×C₉	—	2	1	no	—
291	C₃×C₉	—	2	1	no	—
292	C₃×C₉	—	2	1	no	—
293	C₃×C₉	C₂×D₃×C₉	1	2	yes	—
294	C₃×C₉	C₂×D₃×C₉	1	2	yes	—
295	C₃×C₉	C₂×D₃×C₉	1	2	yes	—
296	C₃×C₉	C₂×D₃×C₉	1	2	yes	—
297	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
298	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
299	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
300	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
301	C₃×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
302	C₂₇	—	2	3	no	—
303	C₂₇	—	2	3	no	—
304	C₂₇	—	2	3	no	—
305	C₂₇	—	2	3	no	—
306	C₂₇	C₂×C₃×C₃⋊D₃	1	3	yes	—
307	C₂×C₃²	—	2	1	no	—
308	C₂×C₃²	—	2	1	no	—
309	C₂×C₃²	—	2	1	no	—
310	C₂×C₃²	—	2	1	no	—
311	C₂×C₃²	—	9	1	no	—
312	C₂×C₃²	—	9	1	no	—
313	C₂×C₃²	—	9	2	no	—
314	C₂×C₃²	—	18	1	no	—
315	C₂×C₃²	—	18	1	no	—
316	C₂×C₃²	C₃×D₃×C₉	1	1	yes	characteristic
317	C₂×C₃²	C₃×D₃×C₉	1	1	yes	characteristic
318	C₂×C₃²	C₃×D₃×C₉	1	1	yes	characteristic
319	C₂×C₃²	C₃×D₃×C₉	1	1	yes	characteristic
320	C₂×C₃²	C₉×C₃⋊D₃	1	1	yes	characteristic
321	C₃×D₃	—	3	2	no	—
322	C₃×D₃	—	3	2	no	—
323	C₃×D₃	—	3	2	no	—
324	C₃×D₃	—	3	2	no	—
325	C₃×D₃	—	9	2	no	—
326	C₃×D₃	—	9	2	no	—
327	C₃×D₃	—	9	2	no	—
328	C₃×D₃	—	9	2	no	—
329	C₂×C₉	—	2	2	no	—
330	C₂×C₉	—	2	2	no	—
331	C₂×C₉	—	2	2	no	—
332	C₂×C₉	—	2	2	no	—
333	C₂×C₉	—	2	1	no	—
334	C₂×C₉	—	2	1	no	—
335	C₂×C₉	—	2	1	no	—
336	C₂×C₉	—	2	1	no	—
337	C₂×C₉	—	9	4	no	—
338	C₂×C₉	—	9	2	no	—
339	C₂×C₉	C₉×C₃⋊D₃	1	2	yes	—
340	C₂×C₉	C₃²×C₃⋊D₃	1	1	yes	characteristic
341	C₂²×C₃	—	9	1	no	—
342	C₂²×C₃	—	27	1	no	—
343	C₂×D₃	—	3	1	no	—
344	C₂×D₃	—	3	1	no	—
345	C₂×D₃	—	3	1	no	—
346	C₂×D₃	—	3	1	no	—
347	C₃²	—	2	1	no	—
348	C₃²	—	2	1	no	—
349	C₃²	—	2	1	no	—
350	C₃²	—	2	1	no	—
351	C₃²	—	9	1	no	—
352	C₃²	—	9	1	no	—
353	C₃²	—	18	1	no	—
354	C₃²	—	18	1	no	—
355	C₃²	C₂×C₃×D₃×C₉	1	1	yes	characteristic
356	C₃²	C₂×C₃×D₃×C₉	1	1	yes	characteristic
357	C₃²	C₂×C₃×D₃×C₉	1	1	yes	characteristic
358	C₃²	C₂×C₃×D₃×C₉	1	1	yes	characteristic
359	C₃²	C₂×C₉×C₃⋊D₃	1	1	yes	characteristic
360	C₉	—	2	2	no	—
361	C₉	—	2	2	no	—
362	C₉	—	2	2	no	—
363	C₉	—	2	2	no	—
364	C₉	—	2	1	no	—
365	C₉	—	2	1	no	—
366	C₉	—	2	1	no	—
367	C₉	—	2	1	no	—
368	C₉	C₂×C₉×C₃⋊D₃	1	2	yes	—
369	C₉	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
370	C₂×C₃	—	3	1	no	—
371	C₂×C₃	—	3	1	no	—
372	C₂×C₃	—	3	1	no	—
373	C₂×C₃	—	6	1	no	—
374	C₂×C₃	—	6	1	no	—
375	C₂×C₃	—	6	1	no	—
376	C₂×C₃	—	6	1	no	—
377	C₂×C₃	—	6	1	no	—
378	C₂×C₃	—	6	1	no	—
379	C₂×C₃	—	9	2	no	—
380	C₂×C₃	—	27	2	no	—
381	C₂×C₃	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
382	D₃	—	3	2	no	—
383	D₃	—	3	2	no	—
384	D₃	—	3	2	no	—
385	D₃	—	3	2	no	—
386	C₂²	—	9	1	no	Sylow
387	C₃	—	3	1	no	—
388	C₃	—	3	1	no	—
389	C₃	—	3	1	no	—
390	C₃	—	6	1	no	—
391	C₃	—	6	1	no	—
392	C₃	—	6	1	no	—
393	C₃	—	6	1	no	—
394	C₃	—	6	1	no	—
395	C₃	—	6	1	no	—
396	C₃	C₂×C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
397	C₂	—	9	2	no	—
398	C₂	#13091566	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₉	C₃²×C₃⋊D₃
commutator, hypocenter	H(3,𝔽₃)	C₂²×C₃×C₉
Frattini	C₉	C₂×C₃²×C₃⋊D₃
Fitting	C₂×#10624918	C₂
socle	C₂×C₃	C₃×C₉×C₃⋊D₃
prime radical	C₂×C₃×#272	C₉
cosocle	#737	C₂²×C₃²
hypercenter	C₂×C₂₇⋊C₃	C₃⋊D₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
1. #13091566	C₂	direct (N × H)
2. C₂×#10624918	C₂	semidirect
4. C₂×#92319	C₃	semidirect
9. #10624918	C₂²	semidirect
16. C₂×#6903	C₂×C₃	semidirect
21. C₂×C₃×C₂₇⋊C₃	D₃	semidirect
22. C₂×C₃×C₂₇⋊C₃	D₃	semidirect
23. C₂×C₃×C₂₇⋊C₃	D₃	semidirect
24. C₂×C₃×C₂₇⋊C₃	D₃	semidirect
25. #92319	C₂×C₃	semidirect
47. #6903	C₂²×C₃	semidirect
52. C₃×C₂₇⋊C₃	C₂×D₃	semidirect
53. C₃×C₂₇⋊C₃	C₂×D₃	semidirect
54. C₃×C₂₇⋊C₃	C₂×D₃	semidirect
55. C₃×C₂₇⋊C₃	C₂×D₃	semidirect
104. C₂×C₃×C₂₇	C₃×D₃	semidirect
105. C₂×C₃×C₂₇	C₃×D₃	semidirect
106. C₂×C₃×C₂₇	C₃×D₃	semidirect
107. C₂×C₃×C₂₇	C₃×D₃	semidirect
167. C₃×C₂₇	C₂×C₃×D₃	semidirect
168. C₃×C₂₇	C₂×C₃×D₃	semidirect
169. C₃×C₂₇	C₂×C₃×D₃	semidirect
170. C₃×C₂₇	C₂×C₃×D₃	semidirect
398. C₂	#13091566	direct (N × H)

Maximal subgroups

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

subgroup	index
#13091566	2
C₂×#10624918	2
C₂×C₃×#4208	3
C₂×#92319	3
C₂×D₃×C₂₇⋊C₃	3

Subgroups — C2×#13091566 #72244012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13091566 #72244012