Subgroups — C₃×#70664 #11785478

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 413 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
2	C₃²×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5006	C₂	1	2	yes	maximal
5	C₃×#4531	C₂	1	2	yes	maximal, complemented
6	C₃×#1812	—	3	1	no	maximal
7	#70664	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#235	C₂²	1	1	yes	characteristic
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₃²×#117	C₂²	1	2	yes	—
11	C₃×#926	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	1	yes	characteristic
13	C₃×#901	—	2	1	no	—
14	C₃×#901	—	2	1	no	—
15	C₃×#901	—	2	1	no	—
16	C₃×#901	—	2	1	no	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₄	1	2	yes	complemented
18	C₂×C₃×D₃×C₈	C₄	1	2	yes	complemented
19	C₃²×#107	—	2	1	no	—
20	C₃²×#106	—	2	1	no	—
21	C₃×#818	—	2	1	no	—
22	C₃×#817	—	2	1	no	—
23	C₃×#806	—	2	4	no	—
24	C₂×C₃×#131	—	3	1	no	—
25	C₂×#901	C₂×C₃	1	1	yes	characteristic
26	C₃×#427	—	2	1	no	—
27	C₃×#427	—	3	1	no	—
28	C₃×#427	D₃	1	1	yes	characteristic, complemented
29	C₃×#427	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×#410	—	3	2	no	—
31	#5106	C₂×C₃	1	1	yes	characteristic, complemented
32	#5006	C₂×C₃	1	2	yes	—
33	C₃×H(3,ℤ/4)	—	3	2	no	—
34	#4531	C₂×C₃	1	2	yes	complemented
35	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
36	C₂×C₃×#67	D₄	1	2	yes	—
37	C₃×#235	—	2	1	no	—
38	C₃×#235	—	2	1	no	—
39	C₃×#235	—	2	1	no	—
40	C₃×#235	—	2	1	no	—
41	C₂×C₃×D₁₂	Q₈	1	1	yes	characteristic
42	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
43	C₂×C₃×Dic₆	Q₈	1	1	yes	characteristic
44	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
47	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
48	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
49	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
50	C₃²×C₄⋊C₄	—	2	2	no	—
51	C₃²×C₂²⋊C₄	—	2	2	no	—
52	C₃²×C₄²	—	2	2	no	—
53	C₃×#217	—	2	2	no	—
54	C₃×C₄⋊Dic₃	—	2	2	no	—
55	C₃×C₄×Dic₃	—	2	2	no	—
56	C₃×#208	—	2	1	no	—
57	C₃×#208	—	2	1	no	—
58	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
59	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
60	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
61	C₃×D₃×C₈	—	2	2	no	—
62	C₃×D₃×C₈	—	2	2	no	—
63	#1812	—	3	1	no	Sylow
64	C₂×C₃×#41	—	3	1	no	—
65	C₂×#235	C₂²×C₃	1	1	yes	characteristic
66	C₃×#131	—	6	1	no	—
67	C₃×#131	—	6	1	no	—
68	C₃×#131	—	6	1	no	—
69	C₃×#131	—	6	1	no	—
70	C₂×C₃×M₁₆	—	3	1	no	—
71	C₂×C₃×M₁₆	—	3	2	no	—
72	C₂²×C₃×C₈	—	2	1	no	—
73	C₂²×C₃×C₈	—	3	2	no	—
74	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×#117	—	2	2	no	—
77	C₃×#117	—	3	2	no	—
78	C₃×#117	C₂×D₃	1	2	yes	—
79	C₃×#117	C₂²×C₃	1	2	yes	—
80	#926	C₂²×C₃	1	2	yes	—
81	C₂×#208	C₂²×C₃	1	1	yes	characteristic
82	#901	—	2	1	no	—
83	#901	—	2	1	no	—
84	#901	—	2	1	no	—
85	#901	—	2	1	no	—
86	C₂×ΓL(1,𝔽₂₅)	C₃×C₄	1	2	yes	complemented
87	C₂×D₃×C₈	C₃×C₄	1	2	yes	complemented
88	C₃×#107	—	2	2	no	—
89	C₃×#107	—	2	1	no	—
90	C₃×#107	—	2	1	no	—
91	C₃×#107	—	6	1	no	—
92	C₃×#106	—	2	2	no	—
93	C₃×#106	—	2	1	no	—
94	C₃×#106	—	2	1	no	—
95	C₃×#106	—	6	1	no	—
96	C₃×#99	—	6	4	no	—
97	#818	—	2	1	no	—
98	#817	—	2	1	no	—
99	#806	—	2	4	no	—
100	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₃×D₃	C₄⋊C₄	1	2	yes	—
102	C₂×C₃²×C₄	—	4	2	no	—
103	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₃²×C₄	#41	1	1	yes	characteristic
108	C₂×C₃²×C₄	#41	1	1	yes	characteristic
109	C₃×#67	—	2	2	no	—
110	C₃×#67	—	2	2	no	—
111	C₂×C₃×Dic₃	—	4	2	no	—
112	C₂×C₃×Dic₃	C₄⋊C₄	1	2	yes	—
113	C₃×D₁₂	—	2	1	no	—
114	C₃×D₁₂	—	2	1	no	—
115	C₃×C₄×D₃	—	2	2	no	—
116	C₃×C₄×D₃	—	2	2	no	—
117	C₃×Dic₆	—	2	1	no	—
118	C₃×Dic₆	—	2	1	no	—
119	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
120	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
121	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
122	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
123	C₃×C₃⋊C₈	—	2	2	no	—
124	C₂×#131	—	3	1	no	—
125	#427	—	3	1	no	—
126	#427	C₃×D₃	1	1	yes	characteristic, complemented
127	#410	—	3	2	no	—
128	H(3,ℤ/4)	—	3	2	no	—
129	C₃×#41	—	6	1	no	—
130	C₃×#41	—	6	1	no	—
131	C₃×#41	—	6	1	no	—
132	C₃×#41	—	6	1	no	—
133	C₂×C₃×Q₈	—	3	1	no	—
134	C₂×C₃×D₄	—	3	2	no	—
135	C₂×C₃×D₄	—	3	1	no	—
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	3	2	no	—
138	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂×#67	C₃×D₄	1	2	yes	—
141	#235	—	2	1	no	—
142	#235	—	2	1	no	—
143	#235	—	2	1	no	—
144	#235	—	2	1	no	—
145	C₂×D₁₂	C₃×Q₈	1	1	yes	characteristic
146	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
147	C₂×Dic₆	C₃×Q₈	1	1	yes	characteristic
148	C₃×M₁₆	—	6	1	no	—
149	C₃×M₁₆	—	6	1	no	—
150	C₃×M₁₆	—	6	2	no	—
151	C₃×M₁₆	—	6	2	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	2	1	no	—
155	C₂×C₃×C₈	—	2	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	3	2	no	—
159	C₂×C₃×C₈	—	6	2	no	—
160	C₂×C₃×C₈	—	6	2	no	—
161	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
162	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
163	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
164	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
165	C₂×C₃×C₈	#67	1	1	yes	characteristic
166	C₂×C₃×C₈	#67	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
170	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
171	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
172	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	2	no	—
175	C₃×C₄⋊C₄	—	2	2	no	—
176	C₃×C₄⋊C₄	—	6	2	no	—
177	C₃×C₂²⋊C₄	—	2	2	no	—
178	C₃×C₂²⋊C₄	—	2	2	no	—
179	C₃×C₂²⋊C₄	—	4	2	no	—
180	C₃×C₂²⋊C₄	—	6	2	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₃×C₄²	—	2	2	no	—
183	C₃×C₄²	—	4	2	no	—
184	C₃×C₄²	—	6	2	no	—
185	#217	—	2	2	no	—
186	C₄⋊Dic₃	—	2	2	no	—
187	C₄×Dic₃	—	2	2	no	—
188	#208	—	2	1	no	—
189	#208	—	2	1	no	—
190	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
191	ΓL(1,𝔽₂₅)	—	2	2	no	—
192	ΓL(1,𝔽₂₅)	—	2	2	no	—
193	D₃×C₈	—	2	2	no	—
194	D₃×C₈	—	2	2	no	—
195	C₂²×C₃²	—	4	1	no	—
196	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂²×C₃²	#121	1	1	yes	characteristic
198	C₂²×C₃²	#121	1	1	yes	characteristic
199	C₂×C₃×D₃	—	2	2	no	—
200	C₂×C₃×D₃	—	4	2	no	—
201	C₃²×C₄	—	8	2	no	—
202	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₃²×C₄	#117	1	1	yes	characteristic
204	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
205	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
206	C₃×Dic₃	—	2	2	no	—
207	C₃×Dic₃	—	8	2	no	—
208	C₂×#41	—	3	1	no	—
209	#131	—	6	1	no	—
210	#131	—	6	1	no	—
211	#131	—	6	1	no	—
212	#131	—	6	1	no	—
213	C₂×M₁₆	—	3	1	no	—
214	C₂×M₁₆	—	3	2	no	—
215	C₂²×C₈	—	3	2	no	—
216	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
217	#117	—	3	2	no	—
218	#117	C₂×C₃×D₃	1	2	yes	—
219	#107	—	2	1	no	—
220	#107	—	6	1	no	—
221	#106	—	2	1	no	—
222	#106	—	6	1	no	—
223	#99	—	6	4	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	3	2	no	—
226	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
227	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
228	C₂²×D₃	C₃×C₄⋊C₄	1	2	yes	—
229	C₃×Q₈	—	6	1	no	—
230	C₃×Q₈	—	6	1	no	—
231	C₃×D₄	—	6	2	no	—
232	C₃×D₄	—	6	2	no	—
233	C₃×D₄	—	6	1	no	—
234	C₃×D₄	—	6	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	3	2	no	—
242	C₂×C₃×C₄	—	4	4	no	—
243	C₂×C₃×C₄	—	4	2	no	—
244	C₂×C₃×C₄	—	4	2	no	—
245	C₂×C₃×C₄	—	6	2	no	—
246	C₂×C₃×C₄	—	6	2	no	—
247	C₂×C₃×C₄	—	12	2	no	—
248	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
250	C₂×C₃×C₄	#237	1	1	yes	characteristic
251	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
252	C₂×C₃×C₄	#239	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
258	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
259	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
260	#67	—	2	2	no	—
261	#67	—	2	2	no	—
262	C₂×Dic₃	—	4	2	no	—
263	C₂×Dic₃	C₃×C₄⋊C₄	1	2	yes	—
264	D₁₂	—	2	1	no	—
265	D₁₂	—	2	1	no	—
266	C₄×D₃	—	2	2	no	—
267	C₄×D₃	—	2	2	no	—
268	Dic₆	—	2	1	no	—
269	Dic₆	—	2	1	no	—
270	C₃×C₈	—	2	1	no	—
271	C₃×C₈	—	2	1	no	—
272	C₃×C₈	—	2	1	no	—
273	C₃×C₈	—	2	1	no	—
274	C₃×C₈	—	6	2	no	—
275	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
276	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
277	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
278	C₃×C₈	(C₂×D₃)⋊C₄	1	1	yes	characteristic
279	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
280	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
281	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
282	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
283	C₃⋊C₈	—	2	2	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	—	2	1	no	—
286	C₂×C₃²	—	2	1	no	—
287	C₂×C₃²	#380	1	1	yes	characteristic
288	C₃×D₃	—	4	2	no	—
289	#41	—	6	1	no	—
290	#41	—	6	1	no	—
291	#41	—	6	1	no	—
292	#41	—	6	1	no	—
293	C₂×Q₈	—	3	1	no	—
294	C₂×D₄	—	3	2	no	—
295	C₂×D₄	—	3	1	no	—
296	C₂²×C₄	—	3	2	no	—
297	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
298	M₁₆	—	6	1	no	—
299	M₁₆	—	6	1	no	—
300	M₁₆	—	6	2	no	—
301	M₁₆	—	6	2	no	—
302	C₂×C₈	—	3	2	no	—
303	C₂×C₈	—	6	2	no	—
304	C₂×C₈	—	6	2	no	—
305	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
306	C₂×C₈	C₃×C₄×D₃	1	1	yes	characteristic
307	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
308	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
309	C₂×C₈	C₃×#67	1	1	yes	characteristic
310	C₂×C₈	C₃×#67	1	1	yes	characteristic
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	6	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	6	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	6	2	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	2	1	no	—
320	C₂²×C₃	—	4	1	no	—
321	C₂²×C₃	—	4	1	no	—
322	C₂²×C₃	—	4	2	no	—
323	C₂²×C₃	—	6	2	no	—
324	C₂²×C₃	—	12	2	no	—
325	C₂²×C₃	D₃×C₄⋊C₄	1	1	yes	characteristic
326	C₂²×C₃	#895	1	1	yes	characteristic
327	C₂²×C₃	#938	1	1	yes	characteristic
328	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
329	C₂²×C₃	C₃×#121	1	1	yes	characteristic
330	C₂²×C₃	C₃×#121	1	1	yes	characteristic
331	C₂×D₃	—	2	2	no	—
332	C₂×D₃	—	4	2	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	6	2	no	—
338	C₃×C₄	—	8	4	no	—
339	C₃×C₄	—	8	2	no	—
340	C₃×C₄	—	8	2	no	—
341	C₃×C₄	—	24	2	no	—
342	C₃×C₄	#892	1	1	yes	characteristic
343	C₃×C₄	#897	1	1	yes	characteristic
344	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₃×C₄	#946	1	1	yes	characteristic
346	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
347	C₃×C₄	C₃×#117	1	1	yes	characteristic
348	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
349	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
350	Dic₃	—	2	2	no	—
351	Dic₃	—	8	2	no	—
352	C₃²	#1812	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	3	2	no	—
354	C₂³	C₃×D₃×D₄	1	1	yes	characteristic
355	Q₈	—	6	1	no	—
356	Q₈	—	6	1	no	—
357	D₄	—	6	2	no	—
358	D₄	—	6	2	no	—
359	D₄	—	6	1	no	—
360	D₄	—	6	1	no	—
361	C₂×C₄	—	3	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	6	2	no	—
364	C₂×C₄	—	6	2	no	—
365	C₂×C₄	—	12	2	no	—
366	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
367	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
368	C₂×C₄	C₃×#237	1	1	yes	characteristic
369	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
370	C₂×C₄	C₃×#239	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
372	C₈	—	6	2	no	—
373	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
374	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
375	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
376	C₈	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
377	C₂×C₃	—	2	2	no	—
378	C₂×C₃	—	2	1	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	1	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	—	2	1	no	—
383	C₂×C₃	—	2	1	no	—
384	C₂×C₃	—	2	1	no	—
385	C₂×C₃	—	4	1	no	—
386	C₂×C₃	—	4	1	no	—
387	C₂×C₃	—	12	2	no	—
388	C₂×C₃	#4987	1	1	yes	characteristic
389	C₂×C₃	C₃×#380	1	1	yes	characteristic
390	D₃	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	6	2	no	—
393	C₂²	—	12	2	no	—
394	C₂²	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
395	C₂²	C₃×#895	1	1	yes	characteristic
396	C₂²	C₃×#938	1	1	yes	characteristic
397	C₄	—	6	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	24	2	no	—
400	C₄	C₃×#892	1	1	yes	characteristic
401	C₄	C₃×#897	1	1	yes	characteristic
402	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
403	C₄	C₃×#946	1	1	yes	characteristic
404	C₃	—	2	1	no	—
405	C₃	#70664	1	1	yes	characteristic, direct product factor
406	C₃	C₃×#1812	1	1	yes	characteristic, complemented
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	12	2	no	—
411	C₂	C₃×#4987	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#892
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#427	C₂
socle	C₂×C₃²	#380
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#427	D₃
hypocenter	C₃	C₃×#1812
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#427

Complements

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

N	H ≅ G/N	type
2. C₃²×#427	C₂	semidirect
3. C₃×#5106	C₂	semidirect
5. C₃×#4531	C₂	semidirect
7. #70664	C₃	direct (N × H)
17. C₂×C₃×ΓL(1,𝔽₂₅)	C₄	semidirect
18. C₂×C₃×D₃×C₈	C₄	semidirect
28. C₃×#427	D₃	semidirect
29. C₃×#427	C₂×C₃	semidirect
31. #5106	C₂×C₃	semidirect
34. #4531	C₂×C₃	semidirect
86. C₂×ΓL(1,𝔽₂₅)	C₃×C₄	semidirect
87. C₂×D₃×C₈	C₃×C₄	semidirect
126. #427	C₃×D₃	semidirect
352. C₃²	#1812	semidirect
405. C₃	#70664	direct (N × H)
406. C₃	C₃×#1812	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₃²×#427	2
C₃×#5106	2
C₃×#5006	2
C₃×#4531	2
C₃×#1812	3
#70664	3

Subgroups — C3×#70664 #11785478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70664 #11785478