Subgroups — C₂×#10589122 #11796771

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 405 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64113	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10589122	C₂	1	4	yes	maximal, direct product factor
5	C₂×#4510	—	3	1	no	maximal
6	C₂×#4497	—	3	1	no	maximal
7	C₂×#3828	—	2	1	no	—
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×#3746	C₄	1	1	yes	characteristic
10	#64113	—	2	1	no	—
11	#64113	—	2	1	no	—
12	#64113	C₄	1	2	yes	—
13	#64113	C₂²	1	2	yes	—
14	C₂×#3745	C₄	1	1	yes	characteristic
15	C₂×#3744	—	2	1	no	—
16	C₂×C₃×#208	—	2	1	no	—
17	C₃×#819	—	2	1	no	—
18	C₃×#819	C₂²	1	2	yes	complemented
19	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
20	C₂×C₃×C₃⋊C₁₆	—	2	1	no	—
21	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	complemented
22	C₂×#904	—	3	1	no	—
23	C₂×#904	—	3	1	no	—
24	C₂×#904	—	6	1	no	—
25	C₂²×C₃×C₁₆	—	3	1	no	—
26	C₂×C₃×#108	—	3	1	no	—
27	C₂×#819	D₃	1	1	yes	characteristic, complemented
28	C₂²×C₃⋊C₁₆	D₃	1	1	yes	characteristic, complemented
29	#4510	—	3	4	no	—
30	#4497	—	3	4	no	—
31	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
32	C₂×#638	—	4	1	no	—
33	#3828	—	2	2	no	—
34	#3828	—	2	2	no	—
35	#3828	—	4	1	no	—
36	#3828	—	4	1	no	—
37	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
38	C₂×C₄×C₃⋊D₃	—	4	1	no	—
39	C₂×#634	—	2	1	no	—
40	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
43	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
44	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
45	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
46	#3746	—	2	1	no	—
47	#3746	C₂×C₄	1	2	yes	—
48	#3745	—	2	1	no	—
49	#3745	C₂×C₄	1	2	yes	—
50	#3744	—	2	2	no	—
51	#3744	—	2	2	no	—
52	C₃×#208	—	2	2	no	—
53	C₃×#208	—	4	1	no	—
54	C₂×C₃×C₃⋊C₈	—	4	1	no	—
55	C₃×C₃⋊C₁₆	—	2	2	no	—
56	C₂×#359	—	9	1	no	Sylow
57	C₂×#235	—	6	2	no	—
58	C₂×#235	—	6	1	no	—
59	C₂×#235	—	6	1	no	—
60	C₂×C₃×M₁₆	—	6	1	no	—
61	C₂²×C₃×C₈	—	2	1	no	—
62	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
64	C₂×#208	—	2	1	no	—
65	C₂×Dic₁₂	—	3	1	no	—
66	C₂×Dic₁₂	—	3	1	no	—
67	C₂×Dic₁₂	—	6	1	no	—
68	#904	—	3	2	no	—
69	#904	—	3	2	no	—
70	#904	—	3	2	no	—
71	#904	—	3	2	no	—
72	#904	—	6	2	no	—
73	#904	—	6	2	no	—
74	#904	—	6	2	no	—
75	#904	—	6	2	no	—
76	#904	—	6	1	no	—
77	#904	—	6	1	no	—
78	#904	—	6	1	no	—
79	#904	—	6	1	no	—
80	C₂×D₂₄	—	3	1	no	—
81	C₂×D₂₄	—	3	1	no	—
82	C₂×D₂₄	—	6	1	no	—
83	C₂×#204	—	6	2	no	—
84	C₂×#204	—	6	1	no	—
85	C₂×#204	—	6	1	no	—
86	C₂×C₃×C₁₆	—	3	2	no	—
87	C₂×C₃×C₁₆	—	6	1	no	—
88	C₂×C₃×C₁₆	—	6	1	no	—
89	C₃×#108	—	3	2	no	—
90	C₃×#108	—	6	1	no	—
91	#819	—	2	1	no	—
92	#819	C₂×D₃	1	2	yes	complemented
93	C₂×C₃⋊C₁₆	—	2	1	no	—
94	C₂×C₃⋊C₁₆	—	2	1	no	—
95	C₂×C₃⋊C₁₆	C₂×D₃	1	2	yes	complemented
96	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
97	C₂²×C₃⋊D₃	—	4	1	no	—
98	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
101	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
102	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
103	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
104	#638	—	4	2	no	—
105	#638	—	4	2	no	—
106	C₂×C₃⋊Dic₃	—	4	1	no	—
107	C₄⋊(C₃⋊D₃)	—	2	2	no	—
108	C₄⋊(C₃⋊D₃)	—	4	1	no	—
109	C₄×C₃⋊D₃	—	4	2	no	—
110	C₄×C₃⋊D₃	—	4	2	no	—
111	#634	—	2	2	no	—
112	#634	—	4	1	no	—
113	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
114	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
115	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
116	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
117	C₃×C₃⋊C₈	—	4	2	no	—
118	C₂×#135	—	9	1	no	—
119	C₂²×C₁₆	—	3	1	no	—
120	C₂×#108	—	3	1	no	—
121	#359	—	9	4	no	—
122	C₂²×C₃×C₄	—	2	1	no	—
123	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
124	C₂²×C₃×C₄	#67	1	1	yes	characteristic
125	C₂×#67	—	12	2	no	—
126	C₂×#67	—	12	1	no	—
127	C₂×#67	—	12	1	no	—
128	#235	—	6	4	no	—
129	#235	—	6	4	no	—
130	#235	—	6	2	no	—
131	#235	—	6	2	no	—
132	#235	—	6	2	no	—
133	#235	—	6	2	no	—
134	#235	—	12	2	no	—
135	#235	—	12	2	no	—
136	#235	—	12	1	no	—
137	#235	—	12	1	no	—
138	#235	—	12	1	no	—
139	#235	—	12	1	no	—
140	C₂×D₁₂	—	6	2	no	—
141	C₂×D₁₂	—	6	1	no	—
142	C₂×D₁₂	—	6	1	no	—
143	C₂×C₄×D₃	—	12	2	no	—
144	C₂×C₄×D₃	—	12	1	no	—
145	C₂×C₄×D₃	—	12	1	no	—
146	C₂×Dic₆	—	6	2	no	—
147	C₂×Dic₆	—	6	1	no	—
148	C₂×Dic₆	—	6	1	no	—
149	C₃×M₁₆	—	6	2	no	—
150	C₃×M₁₆	—	12	1	no	—
151	C₂×C₃×C₈	—	2	1	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	—	12	1	no	—
158	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
159	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
160	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
161	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
162	C₂×C₃×C₈	D₁₂	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	#67	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
170	#208	—	2	2	no	—
171	#208	—	4	1	no	—
172	C₂×C₃⋊C₈	—	4	1	no	—
173	Dic₁₂	—	3	2	no	—
174	Dic₁₂	—	3	2	no	—
175	Dic₁₂	—	6	2	no	—
176	Dic₁₂	—	6	2	no	—
177	Dic₁₂	—	6	1	no	—
178	Dic₁₂	—	6	1	no	—
179	D₂₄	—	3	2	no	—
180	D₂₄	—	3	2	no	—
181	D₂₄	—	6	2	no	—
182	D₂₄	—	6	2	no	—
183	D₂₄	—	6	1	no	—
184	D₂₄	—	6	1	no	—
185	#204	—	6	4	no	—
186	#204	—	6	4	no	—
187	#204	—	6	2	no	—
188	#204	—	6	2	no	—
189	#204	—	6	2	no	—
190	#204	—	6	2	no	—
191	C₃×C₁₆	—	6	2	no	—
192	C₃⋊C₁₆	—	2	2	no	—
193	C₂²×C₃²	—	2	2	no	—
194	C₂²×C₃²	#102	1	1	yes	characteristic
195	C₂²×C₃²	#102	1	1	yes	characteristic
196	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
197	C₂×C₃⋊D₃	—	4	2	no	—
198	C₂×C₃⋊D₃	—	8	2	no	—
199	C₃²×C₄	#102	1	1	yes	characteristic
200	C₃²×C₄	#102	1	1	yes	characteristic
201	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
203	C₃⋊Dic₃	—	4	2	no	—
204	C₂×#41	—	18	1	no	—
205	#135	—	9	2	no	—
206	#135	—	9	2	no	—
207	#135	—	18	1	no	—
208	#135	—	18	1	no	—
209	C₂×Q₁₆	—	9	1	no	—
210	C₂×SD₁₆	—	18	1	no	—
211	C₂×D₈	—	9	1	no	—
212	C₂×M₁₆	—	6	1	no	—
213	C₂²×C₈	D₃²	1	1	yes	characteristic
214	C₂×C₁₆	—	3	2	no	—
215	C₂×C₁₆	—	6	1	no	—
216	C₂×C₁₆	—	6	1	no	—
217	#108	—	3	2	no	—
218	#108	—	6	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	#204	1	1	yes	characteristic
221	C₂³×C₃	#215	1	1	yes	characteristic
222	C₂²×D₃	—	12	2	no	—
223	C₂²×D₃	—	12	1	no	—
224	C₂²×D₃	—	12	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	1	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	#204	1	1	yes	characteristic
232	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
233	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
234	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
238	C₂×C₃×C₄	#213	1	1	yes	characteristic
239	C₂×C₃×C₄	#213	1	1	yes	characteristic
240	C₂×C₃×C₄	#215	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
243	#67	—	12	4	no	—
244	#67	—	12	4	no	—
245	#67	—	12	2	no	—
246	#67	—	12	2	no	—
247	#67	—	12	2	no	—
248	#67	—	12	2	no	—
249	C₂×Dic₃	—	12	2	no	—
250	C₂×Dic₃	—	12	1	no	—
251	C₂×Dic₃	—	12	1	no	—
252	D₁₂	—	6	4	no	—
253	D₁₂	—	6	2	no	—
254	D₁₂	—	6	2	no	—
255	D₁₂	—	12	2	no	—
256	D₁₂	—	12	1	no	—
257	D₁₂	—	12	1	no	—
258	C₄×D₃	—	12	4	no	—
259	C₄×D₃	—	12	4	no	—
260	C₄×D₃	—	12	2	no	—
261	C₄×D₃	—	12	2	no	—
262	C₄×D₃	—	12	2	no	—
263	C₄×D₃	—	12	2	no	—
264	Dic₆	—	6	4	no	—
265	Dic₆	—	6	2	no	—
266	Dic₆	—	6	2	no	—
267	Dic₆	—	12	2	no	—
268	Dic₆	—	12	1	no	—
269	Dic₆	—	12	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	—	12	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	C₂×C₄×D₃	1	1	yes	characteristic
280	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
281	C₃×C₈	C₂×D₁₂	1	1	yes	characteristic
282	C₃×C₈	C₂×#67	1	1	yes	characteristic
283	C₃⋊C₈	—	4	2	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	—	2	1	no	—
286	C₂×C₃²	#359	1	2	yes	complemented
287	C₂×C₃²	C₂×#102	1	1	yes	characteristic
288	C₃⋊D₃	—	8	2	no	—
289	#41	—	18	2	no	—
290	#41	—	18	2	no	—
291	#41	—	36	1	no	—
292	#41	—	36	1	no	—
293	C₂×Q₈	—	18	1	no	—
294	C₂×D₄	—	18	1	no	—
295	C₂×D₄	—	36	1	no	—
296	C₂²×C₄	—	36	1	no	—
297	C₂²×C₄	#626	1	1	yes	characteristic
298	Q₁₆	—	9	2	no	—
299	Q₁₆	—	18	1	no	—
300	SD₁₆	—	18	2	no	—
301	SD₁₆	—	18	2	no	—
302	D₈	—	9	2	no	—
303	D₈	—	18	1	no	—
304	M₁₆	—	6	2	no	—
305	M₁₆	—	12	1	no	—
306	C₂×C₈	—	12	1	no	—
307	C₂×C₈	#624	1	1	yes	characteristic
308	C₂×C₈	#624	1	1	yes	characteristic
309	C₂×C₈	#626	1	1	yes	characteristic
310	C₂×C₈	#626	1	1	yes	characteristic
311	C₂×C₈	#626	1	1	yes	characteristic
312	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
313	C₁₆	—	6	2	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	2	2	no	—
316	C₂²×C₃	—	2	1	no	—
317	C₂²×C₃	—	2	1	no	—
318	C₂²×C₃	—	2	1	no	—
319	C₂²×C₃	—	4	2	no	—
320	C₂²×C₃	#809	1	1	yes	characteristic
321	C₂²×C₃	#809	1	1	yes	characteristic
322	C₂²×C₃	#821	1	1	yes	characteristic
323	C₂²×C₃	#821	1	1	yes	characteristic
324	C₂²×C₃	C₂×#204	1	1	yes	characteristic
325	C₂²×C₃	C₂×#215	1	1	yes	characteristic
326	C₂×D₃	—	12	4	no	—
327	C₂×D₃	—	12	2	no	—
328	C₂×D₃	—	12	2	no	—
329	C₂×D₃	—	24	4	no	—
330	C₂×D₃	—	24	2	no	—
331	C₂×D₃	—	24	2	no	—
332	C₃×C₄	—	2	1	no	—
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	#809	1	1	yes	characteristic
337	C₃×C₄	#809	1	1	yes	characteristic
338	C₃×C₄	#821	1	1	yes	characteristic
339	C₃×C₄	#821	1	1	yes	characteristic
340	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
341	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
342	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
343	C₃×C₄	C₂×#213	1	1	yes	characteristic
344	Dic₃	—	12	4	no	—
345	Dic₃	—	12	2	no	—
346	Dic₃	—	12	2	no	—
347	C₃²	C₂×#359	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	36	1	no	—
349	C₂³	#3717	1	1	yes	characteristic
350	Q₈	—	18	2	no	—
351	Q₈	—	36	1	no	—
352	D₄	—	18	2	no	—
353	D₄	—	36	2	no	—
354	D₄	—	36	2	no	—
355	D₄	—	36	1	no	—
356	C₂×C₄	—	36	1	no	—
357	C₂×C₄	—	36	2	no	—
358	C₂×C₄	—	36	2	no	—
359	C₂×C₄	#3714	1	1	yes	characteristic
360	C₂×C₄	#3714	1	1	yes	characteristic
361	C₂×C₄	#3717	1	1	yes	characteristic
362	C₂×C₄	#3722	1	1	yes	characteristic
363	C₂×C₄	#3722	1	1	yes	characteristic
364	C₂×C₄	C₂×#626	1	1	yes	characteristic
365	C₈	—	12	2	no	—
366	C₈	#3722	1	1	yes	characteristic
367	C₈	#3722	1	1	yes	characteristic
368	C₈	C₂×#624	1	1	yes	characteristic
369	C₈	C₂×#626	1	1	yes	characteristic
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	2	2	no	—
376	C₂×C₃	—	4	1	no	—
377	C₂×C₃	—	4	1	no	—
378	C₂×C₃	#4497	1	2	yes	complemented
379	C₂×C₃	#4510	1	2	yes	complemented
380	C₂×C₃	C₂×#809	1	1	yes	characteristic
381	C₂×C₃	C₂×#821	1	1	yes	characteristic
382	D₃	—	24	4	no	—
383	D₃	—	24	2	no	—
384	D₃	—	24	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	36	2	no	—
387	C₂²	—	72	2	no	—
388	C₂²	#63564	1	1	yes	characteristic
389	C₂²	#63564	1	1	yes	characteristic
390	C₂²	C₂×#3717	1	1	yes	characteristic
391	C₄	—	36	2	no	—
392	C₄	#63564	1	1	yes	characteristic
393	C₄	#63564	1	1	yes	characteristic
394	C₄	C₂×#3714	1	1	yes	characteristic
395	C₄	C₂×#3722	1	1	yes	characteristic
396	C₃	—	2	1	no	—
397	C₃	C₂×#4497	1	1	yes	characteristic, complemented
398	C₃	C₂×#4510	1	1	yes	characteristic, complemented
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	72	2	no	—
402	C₂	#10589122	1	2	yes	direct product factor
403	C₂	C₂×#63564	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3714
commutator	C₃²×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	#102
prime radical	C₂×#64113	C₂
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#359
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#819	C₂	semidirect
3. C₂²×C₃×C₃⋊C₁₆	C₂	semidirect
4. #10589122	C₂	direct (N × H)
18. C₃×#819	C₂²	semidirect
21. C₂×C₃×C₃⋊C₁₆	C₂²	semidirect
27. C₂×#819	D₃	semidirect
28. C₂²×C₃⋊C₁₆	D₃	semidirect
92. #819	C₂×D₃	semidirect
95. C₂×C₃⋊C₁₆	C₂×D₃	semidirect
286. C₂×C₃²	#359	semidirect
347. C₃²	C₂×#359	semidirect
378. C₂×C₃	#4497	semidirect
379. C₂×C₃	#4510	semidirect
397. C₃	C₂×#4497	semidirect
398. C₃	C₂×#4510	semidirect
402. C₂	#10589122	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#64113	2
C₂×C₃×#819	2
C₂²×C₃×C₃⋊C₁₆	2
#10589122	2
C₂×#4510	3
C₂×#4497	3

Subgroups — C2×#10589122 #11796771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589122 #11796771