Subgroups — C₃×#10589937 #13153743

Order 1728.

970 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63715	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63513	C₂	1	3	yes	maximal, complemented
4	C₃×#63512	C₂	1	3	yes	maximal, complemented
5	C₃×#63510	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#63495	C₂	1	3	yes	maximal, complemented
7	C₂×C₃×#3673	C₂	1	3	yes	maximal, complemented
8	C₃×#5835	—	3	1	no	maximal
9	#10589937	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×C₉×#41	—	2	1	no	—
11	C₃×C₉×#41	C₂²	1	1	yes	characteristic
12	C₃×C₉×#41	C₂²	1	3	yes	complemented
13	C₂×C₃×D₄×C₉	—	2	3	no	—
14	C₂×C₃×D₄×C₉	C₂²	1	3	yes	complemented
15	C₃×#3701	—	2	1	no	—
16	C₃×D₄×D₉	—	2	3	no	—
17	C₃×#3697	C₂²	1	3	yes	complemented
18	C₂×C₃×D₃₆	C₂²	1	3	yes	complemented
19	C₃×#3675	C₂²	1	3	yes	complemented
20	C₃×#3674	C₂²	1	1	yes	characteristic, complemented
21	C₃×#3673	C₂²	1	3	yes	complemented
22	C₃×#3673	C₂²	1	6	yes	complemented
23	C₃×#3672	C₂²	1	3	yes	complemented
24	C₃×#3667	C₂²	1	3	yes	complemented
25	C₂×C₃×C₉⋊C₈	C₂²	1	3	yes	complemented
26	C₃²×H(5,𝔽₂)	D₃	1	1	yes	characteristic
27	C₃×#1009	—	3	1	no	—
28	C₃×#950	—	3	3	no	—
29	C₃×#949	—	3	3	no	—
30	C₃×#948	—	3	1	no	—
31	C₃×#932	—	3	3	no	—
32	C₂×C₃×#213	—	3	3	no	—
33	C₉×H(5,𝔽₂)	—	2	1	no	—
34	C₉×H(5,𝔽₂)	C₂×C₃	1	1	yes	characteristic, complemented
35	#63715	C₂×C₃	1	1	yes	characteristic, complemented
36	#63513	C₂×C₃	1	3	yes	complemented
37	#63512	C₂×C₃	1	3	yes	complemented
38	#63510	C₂×C₃	1	1	yes	characteristic, complemented
39	#63495	C₂×C₃	1	3	yes	complemented
40	C₂×#3673	C₂×C₃	1	3	yes	complemented
41	C₂³×C₃×C₉	—	2	3	no	—
42	C₂²×C₃×D₉	—	2	3	no	—
43	C₃×Q₈×C₉	D₄	1	1	yes	characteristic
44	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
45	C₃×D₄×C₉	—	2	3	no	—
46	C₃×D₄×C₉	—	2	3	no	—
47	C₃×D₄×C₉	D₄	1	3	yes	—
48	C₃×D₄×C₉	C₂³	1	3	yes	—
49	C₂×C₃×C₄×C₉	—	2	3	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	3	yes	—
51	C₃×#611	—	2	3	no	—
52	C₃×D₃₆	—	2	3	no	—
53	C₃×D₃₆	C₂³	1	3	yes	—
54	C₃×C₄×D₉	—	2	3	no	—
55	C₃×Dic₁₈	C₂³	1	1	yes	characteristic
56	C₃×C₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₃×C₉⋊C₈	C₂³	1	3	yes	—
58	C₃×#576	—	9	1	no	—
59	#5835	—	3	1	no	—
60	C₃²×#41	—	2	1	no	—
61	C₃²×#41	C₂×D₃	1	3	yes	—
62	C₃²×#41	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×D₄	—	2	3	no	—
64	C₂×C₃²×D₄	C₂×D₃	1	3	yes	—
65	C₃×#239	—	6	1	no	—
66	C₃×D₃×D₄	—	6	3	no	—
67	C₃×#235	—	3	3	no	—
68	C₂×C₃×D₁₂	—	3	3	no	—
69	C₃×#216	—	3	1	no	—
70	C₃×#215	—	3	3	no	—
71	C₃×#214	—	3	3	no	—
72	C₃×#213	—	3	3	no	—
73	C₃×#213	—	3	6	no	—
74	C₃×#208	—	3	3	no	—
75	C₂×C₃×C₃⋊C₈	—	3	3	no	—
76	C₉×#41	—	2	2	no	—
77	C₉×#41	—	2	1	no	—
78	C₉×#41	—	2	3	no	—
79	C₉×#41	—	2	1	no	—
80	C₉×#41	C₂²×C₃	1	1	yes	characteristic
81	C₉×#41	C₂²×C₃	1	3	yes	complemented
82	C₂×D₄×C₉	—	2	6	no	—
83	C₂×D₄×C₉	—	2	3	no	—
84	C₂×D₄×C₉	—	2	3	no	—
85	C₂×D₄×C₉	C₂²×C₃	1	3	yes	complemented
86	#3701	—	2	1	no	—
87	D₄×D₉	—	2	3	no	—
88	#3697	C₂²×C₃	1	3	yes	complemented
89	C₂×D₃₆	C₂²×C₃	1	3	yes	complemented
90	#3675	C₂²×C₃	1	3	yes	complemented
91	#3674	C₂²×C₃	1	1	yes	characteristic, complemented
92	#3673	C₂²×C₃	1	3	yes	complemented
93	#3673	C₂²×C₃	1	6	yes	complemented
94	#3672	C₂²×C₃	1	3	yes	complemented
95	#3667	C₂²×C₃	1	3	yes	complemented
96	C₂×C₉⋊C₈	C₂²×C₃	1	3	yes	complemented
97	C₂²×C₃×C₉	—	2	3	no	—
98	C₂²×C₃×C₉	—	8	3	no	—
99	C₂²×C₃×C₉	C₂×D₄	1	3	yes	—
100	C₂×C₃×D₉	—	2	3	no	—
101	C₂×C₃×D₉	—	8	3	no	—
102	C₃×C₄×C₉	—	2	1	no	—
103	C₃×C₄×C₉	C₂×D₄	1	3	yes	—
104	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
105	C₃×Dic₉	—	2	1	no	—
106	C₃×H(5,𝔽₂)	—	2	1	no	—
107	C₃×H(5,𝔽₂)	—	9	1	no	—
108	C₃×H(5,𝔽₂)	D₉	1	1	yes	characteristic, complemented
109	C₃×H(5,𝔽₂)	C₃×D₃	1	1	yes	characteristic
110	#1009	—	3	1	no	—
111	C₃×AGL(1,ℤ/8)	—	9	3	no	—
112	C₃×AGL(1,ℤ/8)	—	9	3	no	—
113	C₃×#135	—	9	3	no	—
114	C₂×C₃×D₈	—	9	3	no	—
115	C₃×#131	—	9	1	no	—
116	#950	—	3	3	no	—
117	#949	—	3	3	no	—
118	#948	—	3	1	no	—
119	#932	—	3	3	no	—
120	C₂×#213	—	3	3	no	—
121	C₂³×C₃²	—	2	3	no	—
122	C₂²×C₃×D₃	—	6	3	no	—
123	C₃²×Q₈	#67	1	1	yes	characteristic
124	C₃²×Q₈	C₂²×D₃	1	1	yes	characteristic
125	C₃²×D₄	—	2	3	no	—
126	C₃²×D₄	—	2	3	no	—
127	C₃²×D₄	#67	1	3	yes	—
128	C₃²×D₄	C₂²×D₃	1	3	yes	—
129	C₂×C₃²×C₄	—	2	3	no	—
130	C₂×C₃²×C₄	C₂²×D₃	1	3	yes	—
131	C₃×#67	—	6	3	no	—
132	C₃×D₁₂	—	3	3	no	—
133	C₃×D₁₂	—	6	3	no	—
134	C₃×C₄×D₃	—	6	3	no	—
135	C₃×Dic₆	—	3	1	no	—
136	C₂³×C₉	—	2	6	no	—
137	C₂³×C₉	—	2	3	no	—
138	C₂²×D₉	—	2	3	no	—
139	C₃×C₃⋊C₈	—	3	1	no	—
140	C₃×C₃⋊C₈	—	3	3	no	—
141	Q₈×C₉	—	2	1	no	—
142	Q₈×C₉	—	2	1	no	—
143	Q₈×C₉	C₃×D₄	1	1	yes	characteristic
144	Q₈×C₉	C₂³×C₃	1	1	yes	characteristic
145	D₄×C₉	—	2	6	no	—
146	D₄×C₉	—	2	6	no	—
147	D₄×C₉	—	2	3	no	—
148	D₄×C₉	—	2	3	no	—
149	D₄×C₉	—	2	3	no	—
150	D₄×C₉	—	2	3	no	—
151	D₄×C₉	C₃×D₄	1	3	yes	—
152	D₄×C₉	C₂³×C₃	1	3	yes	—
153	C₂×C₄×C₉	—	2	6	no	—
154	C₂×C₄×C₉	—	2	3	no	—
155	C₂×C₄×C₉	—	2	3	no	—
156	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
157	#611	—	2	3	no	—
158	D₃₆	—	2	3	no	—
159	D₃₆	C₂³×C₃	1	3	yes	—
160	C₄×D₉	—	2	3	no	—
161	Dic₁₈	C₂³×C₃	1	1	yes	characteristic
162	C₉⋊C₈	C₂³×C₃	1	1	yes	characteristic
163	C₉⋊C₈	C₂³×C₃	1	3	yes	—
164	#576	—	9	1	no	Sylow
165	C₂×C₃×C₉	—	2	3	no	—
166	C₂×C₃×C₉	—	4	3	no	—
167	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
168	C₃×D₉	—	4	3	no	—
169	C₃×#41	—	2	2	no	—
170	C₃×#41	—	2	1	no	—
171	C₃×#41	—	2	1	no	—
172	C₃×#41	—	2	1	no	—
173	C₃×#41	—	2	3	no	—
174	C₃×#41	—	9	3	no	—
175	C₃×#41	—	18	1	no	—
176	C₃×#41	C₂×D₉	1	1	yes	characteristic
177	C₃×#41	C₂×D₉	1	3	yes	complemented
178	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
179	C₃×#41	C₂×C₃×D₃	1	3	yes	—
180	C₂×C₃×D₄	—	2	6	no	—
181	C₂×C₃×D₄	—	2	3	no	—
182	C₂×C₃×D₄	—	2	3	no	—
183	C₂×C₃×D₄	—	2	3	no	—
184	C₂×C₃×D₄	—	9	3	no	—
185	C₂×C₃×D₄	—	18	3	no	—
186	C₂×C₃×D₄	C₂×D₉	1	3	yes	complemented
187	C₂×C₃×D₄	C₂×C₃×D₃	1	3	yes	—
188	#239	—	6	1	no	—
189	D₃×D₄	—	6	3	no	—
190	#235	—	3	3	no	—
191	C₂×D₁₂	—	3	3	no	—
192	C₃×Q₁₆	—	9	1	no	—
193	C₃×SD₁₆	—	9	3	no	—
194	C₃×SD₁₆	—	9	3	no	—
195	C₃×D₈	—	9	3	no	—
196	C₃×D₈	—	9	6	no	—
197	C₃×M₁₆	—	9	3	no	—
198	C₂×C₃×C₈	—	9	3	no	—
199	#216	—	3	1	no	—
200	#215	—	3	3	no	—
201	#214	—	3	3	no	—
202	#213	—	3	3	no	—
203	#213	—	3	6	no	—
204	#208	—	3	3	no	—
205	C₂×C₃⋊C₈	—	3	3	no	—
206	C₂²×C₃²	—	2	3	no	—
207	C₂²×C₃²	—	8	3	no	—
208	C₂²×C₃²	C₂×#67	1	3	yes	—
209	C₂×C₃×D₃	—	6	3	no	—
210	C₂×C₃×D₃	—	24	3	no	—
211	C₃²×C₄	—	2	1	no	—
212	C₃²×C₄	C₂×#67	1	3	yes	—
213	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
214	C₃×Dic₃	—	6	1	no	—
215	C₂²×C₉	—	2	6	no	—
216	C₂²×C₉	—	2	3	no	—
217	C₂²×C₉	—	2	3	no	—
218	C₂²×C₉	—	8	3	no	—
219	C₂²×C₉	—	8	6	no	—
220	C₂²×C₉	C₂×C₃×D₄	1	3	yes	—
221	C₂×D₉	—	2	3	no	—
222	C₂×D₉	—	8	3	no	—
223	C₄×C₉	—	2	2	no	—
224	C₄×C₉	—	2	1	no	—
225	C₄×C₉	—	2	1	no	—
226	C₄×C₉	—	2	3	no	—
227	C₄×C₉	C₂×C₃×D₄	1	3	yes	—
228	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
229	Dic₉	—	2	1	no	—
230	H(5,𝔽₂)	—	9	1	no	—
231	H(5,𝔽₂)	C₃×D₉	1	1	yes	characteristic, complemented
232	AGL(1,ℤ/8)	—	9	3	no	—
233	AGL(1,ℤ/8)	—	9	3	no	—
234	#135	—	9	3	no	—
235	C₂×D₈	—	9	3	no	—
236	#131	—	9	1	no	—
237	C₃×C₉	#576	1	1	yes	characteristic, complemented, Sylow
238	C₂³×C₃	—	2	6	no	—
239	C₂³×C₃	—	2	3	no	—
240	C₂³×C₃	—	2	3	no	—
241	C₂³×C₃	—	18	3	no	—
242	C₂²×D₃	—	6	3	no	—
243	C₃×Q₈	—	2	1	no	—
244	C₃×Q₈	—	2	1	no	—
245	C₃×Q₈	—	9	1	no	—
246	C₃×Q₈	#611	1	1	yes	characteristic
247	C₃×Q₈	C₂²×D₉	1	1	yes	characteristic
248	C₃×Q₈	C₃×#67	1	1	yes	characteristic
249	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
250	C₃×D₄	—	2	6	no	—
251	C₃×D₄	—	2	6	no	—
252	C₃×D₄	—	2	3	no	—
253	C₃×D₄	—	2	3	no	—
254	C₃×D₄	—	2	3	no	—
255	C₃×D₄	—	2	3	no	—
256	C₃×D₄	—	2	3	no	—
257	C₃×D₄	—	2	3	no	—
258	C₃×D₄	—	9	3	no	—
259	C₃×D₄	—	18	3	no	—
260	C₃×D₄	—	18	3	no	—
261	C₃×D₄	#611	1	3	yes	—
262	C₃×D₄	C₂²×D₉	1	3	yes	—
263	C₃×D₄	C₃×#67	1	3	yes	—
264	C₃×D₄	C₂²×C₃×D₃	1	3	yes	—
265	C₂×C₃×C₄	—	2	6	no	—
266	C₂×C₃×C₄	—	2	3	no	—
267	C₂×C₃×C₄	—	2	3	no	—
268	C₂×C₃×C₄	—	2	3	no	—
269	C₂×C₃×C₄	—	18	3	no	—
270	C₂×C₃×C₄	C₂²×D₉	1	3	yes	—
271	C₂×C₃×C₄	C₂²×C₃×D₃	1	3	yes	—
272	#67	—	6	3	no	—
273	D₁₂	—	3	3	no	—
274	D₁₂	—	6	3	no	—
275	C₄×D₃	—	6	3	no	—
276	Dic₆	—	3	1	no	—
277	C₃×C₈	—	9	1	no	—
278	C₃×C₈	—	9	3	no	—
279	C₃⋊C₈	—	3	1	no	—
280	C₃⋊C₈	—	3	3	no	—
281	C₂×C₃²	—	2	3	no	—
282	C₂×C₃²	—	4	3	no	—
283	C₂×C₃²	C₂²×#67	1	1	yes	characteristic
284	C₃×D₃	—	12	3	no	—
285	C₂×C₉	—	2	3	no	—
286	C₂×C₉	—	2	1	no	—
287	C₂×C₉	—	4	3	no	—
288	C₂×C₉	—	4	6	no	—
289	C₂×C₉	—	4	3	no	—
290	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
291	D₉	—	4	3	no	—
292	#41	—	2	1	no	—
293	#41	—	9	3	no	—
294	#41	—	18	1	no	—
295	#41	C₂×C₃×D₉	1	1	yes	characteristic
296	#41	C₂×C₃×D₉	1	3	yes	complemented
297	C₂×D₄	—	2	3	no	—
298	C₂×D₄	—	9	3	no	—
299	C₂×D₄	—	18	3	no	—
300	C₂×D₄	C₂×C₃×D₉	1	3	yes	complemented
301	Q₁₆	—	9	1	no	—
302	SD₁₆	—	9	3	no	—
303	SD₁₆	—	9	3	no	—
304	D₈	—	9	3	no	—
305	D₈	—	9	6	no	—
306	M₁₆	—	9	3	no	—
307	C₂×C₈	—	9	3	no	—
308	C₂²×C₃	—	2	6	no	—
309	C₂²×C₃	—	2	3	no	—
310	C₂²×C₃	—	2	3	no	—
311	C₂²×C₃	—	2	3	no	—
312	C₂²×C₃	—	8	3	no	—
313	C₂²×C₃	—	8	3	no	—
314	C₂²×C₃	—	8	6	no	—
315	C₂²×C₃	—	18	3	no	—
316	C₂²×C₃	—	72	3	no	—
317	C₂²×C₃	C₂×#611	1	3	yes	—
318	C₂²×C₃	C₂×C₃×#67	1	3	yes	—
319	C₂×D₃	—	6	3	no	—
320	C₂×D₃	—	24	3	no	—
321	C₃×C₄	—	2	2	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	2	1	no	—
324	C₃×C₄	—	2	1	no	—
325	C₃×C₄	—	2	3	no	—
326	C₃×C₄	—	18	1	no	—
327	C₃×C₄	C₂×#611	1	3	yes	—
328	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
329	C₃×C₄	C₂×C₃×#67	1	3	yes	—
330	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
331	Dic₃	—	6	1	no	—
332	C₃²	#5835	1	1	yes	characteristic
333	C₉	—	2	1	no	—
334	C₉	C₃×#576	1	1	yes	characteristic, complemented
335	C₂³	—	2	3	no	—
336	C₂³	—	18	3	no	—
337	Q₈	—	9	1	no	—
338	Q₈	C₃×#611	1	1	yes	characteristic
339	Q₈	C₂²×C₃×D₉	1	1	yes	characteristic
340	D₄	—	2	3	no	—
341	D₄	—	2	3	no	—
342	D₄	—	9	3	no	—
343	D₄	—	18	3	no	—
344	D₄	—	18	3	no	—
345	D₄	C₃×#611	1	3	yes	—
346	D₄	C₂²×C₃×D₉	1	3	yes	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	18	3	no	—
349	C₂×C₄	C₂²×C₃×D₉	1	3	yes	—
350	C₈	—	9	1	no	—
351	C₈	—	9	3	no	—
352	C₂×C₃	—	2	3	no	—
353	C₂×C₃	—	2	3	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	4	3	no	—
356	C₂×C₃	—	4	6	no	—
357	C₂×C₃	—	4	3	no	—
358	C₂×C₃	—	4	3	no	—
359	C₂×C₃	—	36	3	no	—
360	C₂×C₃	C₂²×#611	1	1	yes	characteristic
361	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
362	D₃	—	12	3	no	—
363	C₂²	—	2	3	no	—
364	C₂²	—	8	3	no	—
365	C₂²	—	18	3	no	—
366	C₂²	—	72	3	no	—
367	C₂²	C₂×C₃×#611	1	3	yes	—
368	C₄	—	2	1	no	—
369	C₄	—	18	1	no	—
370	C₄	C₂×C₃×#611	1	3	yes	—
371	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
372	C₃	—	2	1	no	—
373	C₃	#10589937	1	1	yes	characteristic, direct product factor
374	C₃	C₃×#5835	1	1	yes	characteristic
375	C₂	—	2	3	no	—
376	C₂	—	4	3	no	—
377	C₂	—	36	3	no	—
378	C₂	C₂²×C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×#611
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×H(5,𝔽₂)	C₂
socle	C₂×C₃²	C₂²×#67
hypercenter	C₃×H(5,𝔽₂)	D₉
hypocenter	C₉	C₃×#576
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×#41 ◁ C₃×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×H(5,𝔽₂)	C₂	semidirect
2. C₃×#63715	C₂	semidirect
3. C₃×#63513	C₂	semidirect
4. C₃×#63512	C₂	semidirect
5. C₃×#63510	C₂	semidirect
6. C₃×#63495	C₂	semidirect
7. C₂×C₃×#3673	C₂	semidirect
9. #10589937	C₃	direct (N × H)
12. C₃×C₉×#41	C₂²	semidirect
14. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₃×#3697	C₂²	semidirect
18. C₂×C₃×D₃₆	C₂²	semidirect
19. C₃×#3675	C₂²	semidirect
20. C₃×#3674	C₂²	semidirect
21. C₃×#3673	C₂²	semidirect
22. C₃×#3673	C₂²	semidirect
23. C₃×#3672	C₂²	semidirect
24. C₃×#3667	C₂²	semidirect
25. C₂×C₃×C₉⋊C₈	C₂²	semidirect
34. C₉×H(5,𝔽₂)	C₂×C₃	semidirect
35. #63715	C₂×C₃	semidirect
36. #63513	C₂×C₃	semidirect
37. #63512	C₂×C₃	semidirect
38. #63510	C₂×C₃	semidirect
39. #63495	C₂×C₃	semidirect
40. C₂×#3673	C₂×C₃	semidirect
81. C₉×#41	C₂²×C₃	semidirect
85. C₂×D₄×C₉	C₂²×C₃	semidirect
88. #3697	C₂²×C₃	semidirect
89. C₂×D₃₆	C₂²×C₃	semidirect
90. #3675	C₂²×C₃	semidirect
91. #3674	C₂²×C₃	semidirect
92. #3673	C₂²×C₃	semidirect
93. #3673	C₂²×C₃	semidirect
94. #3672	C₂²×C₃	semidirect
95. #3667	C₂²×C₃	semidirect
96. C₂×C₉⋊C₈	C₂²×C₃	semidirect
108. C₃×H(5,𝔽₂)	D₉	semidirect
177. C₃×#41	C₂×D₉	semidirect
186. C₂×C₃×D₄	C₂×D₉	semidirect
231. H(5,𝔽₂)	C₃×D₉	semidirect
237. C₃×C₉	#576	semidirect
296. #41	C₂×C₃×D₉	semidirect
300. C₂×D₄	C₂×C₃×D₉	semidirect
334. C₉	C₃×#576	semidirect
373. C₃	#10589937	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₉×H(5,𝔽₂)	2
C₃×#63715	2
C₃×#63513	2
C₃×#63512	2
C₃×#63510	2
C₃×#63495	2
C₂×C₃×#3673	2
C₃×#5835	3
#10589937	3

Subgroups — C3×#10589937 #13153743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589937 #13153743