Subgroups — C₂×#10590919 #11861021

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#904	C₂	1	1	yes	maximal, characteristic
2	C₂×#63815	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#63568	C₂	1	2	yes	maximal, complemented
6	#10590919	C₂	1	8	yes	maximal, direct product factor
7	C₂×#5196	—	3	1	no	maximal
8	C₂×#4895	—	3	1	no	maximal
9	C₂×C₃×#235	C₂²	1	2	yes	—
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₃×#208	C₂²	1	2	yes	—
14	C₂×C₃×Dic₁₂	C₄	1	1	yes	characteristic, complemented
15	C₃×#904	C₄	1	4	yes	complemented
16	C₃×#904	C₂²	1	4	yes	—
17	C₂×C₃×D₂₄	C₄	1	1	yes	characteristic, complemented
18	C₂×C₃×#204	C₄	1	2	yes	complemented
19	C₂×#3711	—	2	2	no	—
20	#63815	—	2	4	no	—
21	#63815	C₂²	1	8	yes	complemented
22	C₂×D₃×C₃⋊C₈	—	2	2	no	—
23	C₈×C₃⋊Dic₃	C₂²	1	4	yes	complemented
24	C₃×#819	C₂²	1	4	yes	complemented
25	#63568	C₂²	1	8	yes	complemented
26	C₂×C₃×#135	—	3	1	no	—
27	C₂×#948	—	3	2	no	—
28	C₂×#907	—	3	2	no	—
29	C₂×#904	D₃	1	1	yes	characteristic
30	C₂×C₃×#108	—	3	1	no	—
31	C₂×#837	—	3	2	no	—
32	#5196	—	3	8	no	—
33	C₂×#825	—	3	2	no	—
34	C₂×#819	D₃	1	1	yes	characteristic, complemented
35	C₂×C₈×Dic₃	—	3	1	no	—
36	C₂×C₈×Dic₃	—	3	1	no	—
37	C₂×C₈×Dic₃	—	6	1	no	—
38	#4895	—	3	8	no	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃⋊Dic₃	—	2	1	no	—
41	C₂×C₃×#67	—	2	2	no	—
42	C₃×#235	—	2	2	no	—
43	C₃×#235	—	2	2	no	—
44	C₃×#235	C₂×C₄	1	4	yes	—
45	C₃×#235	C₂³	1	4	yes	—
46	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
47	C₂×C₃×C₄×D₃	—	2	2	no	—
48	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
49	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
52	C₂×C₃²×C₈	C₂³	1	2	yes	—
53	C₄×C₃⋊Dic₃	—	2	1	no	—
54	C₄×C₃⋊Dic₃	C₂³	1	2	yes	—
55	C₂×C₃⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
56	C₂×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	—
57	C₂×C₃⋊(C₃⋊C₈)	D₄	1	1	yes	characteristic
58	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
59	C₃×#208	—	2	2	no	—
60	C₃×#208	C₂³	1	4	yes	—
61	C₂×C₃×C₃⋊C₈	—	2	2	no	—
62	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
63	C₃×D₂₄	C₂×C₄	1	4	yes	complemented
64	C₃×#204	C₂×C₄	1	8	yes	complemented
65	#3711	—	2	8	no	—
66	D₃×C₃⋊C₈	—	2	8	no	—
67	C₂×#443	—	9	1	no	Sylow
68	C₂×C₃×#41	—	3	2	no	—
69	C₂×#235	C₂×D₃	1	2	yes	—
70	C₃×#135	—	3	4	no	—
71	C₃×#135	—	3	4	no	—
72	C₂×C₃×Q₁₆	—	3	1	no	—
73	C₂×C₃×SD₁₆	—	3	2	no	—
74	C₂×C₃×D₈	—	3	1	no	—
75	C₂×C₃×M₁₆	—	3	2	no	—
76	C₂²×C₃×C₈	—	2	1	no	—
77	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
78	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
79	#948	—	3	8	no	—
80	#948	—	6	4	no	—
81	C₂×C₄×Dic₃	—	3	1	no	—
82	C₂×C₄×Dic₃	—	3	1	no	—
83	C₂×C₄×Dic₃	—	6	1	no	—
84	C₂×#208	—	6	2	no	—
85	C₂×#208	C₂×D₃	1	2	yes	—
86	C₂²×C₃⋊C₈	—	3	1	no	—
87	C₂²×C₃⋊C₈	—	3	1	no	—
88	C₂²×C₃⋊C₈	—	6	1	no	—
89	C₂²×C₃⋊C₈	—	6	2	no	—
90	#907	—	3	8	no	—
91	#907	—	6	4	no	—
92	C₂×Dic₁₂	Dic₃	1	1	yes	characteristic, complemented
93	#904	Dic₃	1	4	yes	complemented
94	#904	C₂×D₃	1	4	yes	—
95	C₂×D₂₄	Dic₃	1	1	yes	characteristic, complemented
96	C₂×#204	Dic₃	1	2	yes	complemented
97	C₂×ΓL(1,𝔽₂₅)	—	6	2	no	—
98	C₂×D₃×C₈	—	6	2	no	—
99	C₃×#108	—	3	4	no	—
100	#837	—	3	8	no	—
101	#825	—	3	8	no	—
102	#819	C₂×D₃	1	4	yes	complemented
103	C₈×Dic₃	—	3	4	no	—
104	C₈×Dic₃	—	3	4	no	—
105	C₈×Dic₃	—	6	4	no	—
106	C₂³×C₃²	#41	1	1	yes	characteristic
107	C₂²×C₃×D₃	—	2	2	no	—
108	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃²×C₄	#41	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
114	C₂×C₃⋊Dic₃	—	2	4	no	—
115	C₂×C₃⋊Dic₃	—	2	2	no	—
116	C₃×#67	—	2	4	no	—
117	C₃×#67	—	2	4	no	—
118	C₂×C₃×Dic₃	—	2	2	no	—
119	C₃×D₁₂	—	2	2	no	—
120	C₃×D₁₂	C₂²×C₄	1	4	yes	—
121	C₃×C₄×D₃	—	2	4	no	—
122	C₃×C₄×D₃	—	2	4	no	—
123	C₃×Dic₆	—	2	2	no	—
124	C₃×Dic₆	C₂²×C₄	1	4	yes	—
125	C₃²×C₈	C₂²×C₄	1	2	yes	—
126	C₃²×C₈	C₂²×C₄	1	2	yes	—
127	C₃⋊(C₃⋊C₈)	C₂×D₄	1	2	yes	—
128	C₃⋊(C₃⋊C₈)	C₂×D₄	1	2	yes	—
129	C₃×C₃⋊C₈	—	2	4	no	—
130	C₂×#135	—	3	1	no	—
131	C₂×#131	—	9	2	no	—
132	#443	—	9	8	no	—
133	C₂×#108	—	3	1	no	—
134	C₂×#104	—	9	2	no	—
135	C₂×C₄×C₈	—	9	1	no	—
136	C₃×#41	—	3	4	no	—
137	C₃×#41	—	3	4	no	—
138	C₃×#41	—	6	2	no	—
139	C₃×#41	—	6	2	no	—
140	C₂×C₃×Q₈	—	3	2	no	—
141	C₂×C₃×D₄	—	3	2	no	—
142	C₂×C₃×D₄	—	6	2	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	6	2	no	—
145	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
146	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂×#67	—	2	2	no	—
148	C₂²×Dic₃	—	6	2	no	—
149	C₂²×Dic₃	—	6	1	no	—
150	C₂²×Dic₃	—	6	1	no	—
151	#235	—	2	2	no	—
152	#235	—	2	2	no	—
153	#235	C₂×Dic₃	1	4	yes	—
154	#235	C₂²×D₃	1	4	yes	—
155	C₂×D₁₂	C₂×Dic₃	1	2	yes	—
156	C₂×C₄×D₃	—	2	2	no	—
157	C₂×Dic₆	C₂×Dic₃	1	2	yes	—
158	C₃×Q₁₆	—	3	4	no	—
159	C₃×SD₁₆	—	3	8	no	—
160	C₃×D₈	—	3	4	no	—
161	C₃×M₁₆	—	3	4	no	—
162	C₃×M₁₆	—	6	2	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	—	2	1	no	—
165	C₂×C₃×C₈	—	2	2	no	—
166	C₂×C₃×C₈	—	2	2	no	—
167	C₂×C₃×C₈	—	6	2	no	—
168	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
169	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
170	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
171	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
173	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
174	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
175	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
176	C₄×Dic₃	—	3	2	no	—
177	C₄×Dic₃	—	3	2	no	—
178	C₄×Dic₃	—	6	2	no	—
179	C₄×Dic₃	—	6	2	no	—
180	C₄×Dic₃	—	6	1	no	—
181	C₄×Dic₃	—	6	1	no	—
182	#208	—	2	2	no	—
183	#208	—	6	8	no	—
184	#208	C₂²×D₃	1	4	yes	—
185	C₂×C₃⋊C₈	—	2	2	no	—
186	C₂×C₃⋊C₈	—	3	1	no	—
187	C₂×C₃⋊C₈	—	3	1	no	—
188	C₂×C₃⋊C₈	—	3	2	no	—
189	C₂×C₃⋊C₈	—	3	1	no	—
190	C₂×C₃⋊C₈	—	3	1	no	—
191	C₂×C₃⋊C₈	—	3	2	no	—
192	C₂×C₃⋊C₈	—	3	2	no	—
193	C₂×C₃⋊C₈	—	3	2	no	—
194	C₂×C₃⋊C₈	—	6	2	no	—
195	C₂×C₃⋊C₈	—	6	2	no	—
196	C₂×C₃⋊C₈	—	6	1	no	—
197	C₂×C₃⋊C₈	—	6	1	no	—
198	C₂×C₃⋊C₈	—	6	8	no	—
199	Dic₁₂	C₂×Dic₃	1	4	yes	complemented
200	D₂₄	C₂×Dic₃	1	4	yes	complemented
201	#204	C₂×Dic₃	1	8	yes	complemented
202	ΓL(1,𝔽₂₅)	—	6	8	no	—
203	D₃×C₈	—	6	8	no	—
204	C₂²×C₃²	—	2	2	no	—
205	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
206	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
207	C₂²×C₃²	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×D₃	—	2	4	no	—
209	C₂×C₃×D₃	—	4	4	no	—
210	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
211	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
212	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
213	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
214	C₃⋊Dic₃	—	2	4	no	—
215	C₃×Dic₃	—	2	4	no	—
216	C₂×#41	—	3	2	no	—
217	#135	—	3	4	no	—
218	#135	—	3	4	no	—
219	C₂×Q₁₆	—	3	1	no	—
220	C₂×SD₁₆	—	3	2	no	—
221	C₂×D₈	—	3	1	no	—
222	#131	—	9	8	no	—
223	#131	—	18	4	no	—
224	C₂×M₁₆	—	3	2	no	—
225	C₂×M₁₆	—	18	2	no	—
226	C₂²×C₈	—	9	1	no	—
227	C₂²×C₈	—	18	2	no	—
228	C₂²×C₈	D₃²	1	1	yes	characteristic
229	C₂×C₄²	—	9	1	no	—
230	#108	—	3	4	no	—
231	#104	—	9	8	no	—
232	C₄×C₈	—	9	4	no	—
233	C₂³×C₃	—	2	1	no	—
234	C₂³×C₃	—	6	2	no	—
235	C₂³×C₃	#237	1	1	yes	characteristic
236	C₂³×C₃	#239	1	1	yes	characteristic
237	C₂²×D₃	—	2	2	no	—
238	C₃×Q₈	—	3	4	no	—
239	C₃×Q₈	—	6	2	no	—
240	C₃×D₄	—	3	4	no	—
241	C₃×D₄	—	6	4	no	—
242	C₃×D₄	—	6	4	no	—
243	C₃×D₄	—	6	2	no	—
244	C₂×C₃×C₄	—	2	1	no	—
245	C₂×C₃×C₄	—	2	1	no	—
246	C₂×C₃×C₄	—	2	1	no	—
247	C₂×C₃×C₄	—	2	1	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	6	2	no	—
251	C₂×C₃×C₄	—	6	4	no	—
252	C₂×C₃×C₄	—	6	4	no	—
253	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
255	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
256	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
258	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
259	C₂×C₃×C₄	#237	1	1	yes	characteristic
260	C₂×C₃×C₄	#239	1	1	yes	characteristic
261	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
262	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
263	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
264	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
265	#67	—	2	4	no	—
266	#67	—	2	4	no	—
267	C₂×Dic₃	—	2	2	no	—
268	C₂×Dic₃	—	6	4	no	—
269	C₂×Dic₃	—	6	8	no	—
270	C₂×Dic₃	—	6	4	no	—
271	C₂×Dic₃	—	6	4	no	—
272	C₂×Dic₃	—	6	2	no	—
273	C₂×Dic₃	—	6	2	no	—
274	D₁₂	—	2	2	no	—
275	D₁₂	C₂²×Dic₃	1	4	yes	—
276	C₄×D₃	—	2	4	no	—
277	C₄×D₃	—	2	4	no	—
278	Dic₆	—	2	2	no	—
279	Dic₆	C₂²×Dic₃	1	4	yes	—
280	C₃×C₈	—	2	2	no	—
281	C₃×C₈	—	2	2	no	—
282	C₃×C₈	—	6	4	no	—
283	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
284	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
285	C₃×C₈	C₂²×Dic₃	1	2	yes	—
286	C₃×C₈	C₂²×Dic₃	1	2	yes	—
287	C₃⋊C₈	—	2	4	no	—
288	C₃⋊C₈	—	3	2	no	—
289	C₃⋊C₈	—	3	2	no	—
290	C₃⋊C₈	—	3	2	no	—
291	C₃⋊C₈	—	3	2	no	—
292	C₃⋊C₈	—	6	2	no	—
293	C₃⋊C₈	—	6	2	no	—
294	C₂×C₃²	—	2	1	no	—
295	C₂×C₃²	—	2	1	no	—
296	C₂×C₃²	#443	1	2	yes	complemented
297	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
298	C₃×D₃	—	4	4	no	—
299	#41	—	3	4	no	—
300	#41	—	3	4	no	—
301	#41	—	6	2	no	—
302	#41	—	6	2	no	—
303	C₂×Q₈	—	3	2	no	—
304	C₂×D₄	—	3	2	no	—
305	C₂×D₄	—	6	2	no	—
306	C₂²×C₄	—	6	2	no	—
307	C₂²×C₄	—	18	1	no	—
308	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
309	Q₁₆	—	3	4	no	—
310	SD₁₆	—	3	8	no	—
311	D₈	—	3	4	no	—
312	M₁₆	—	3	4	no	—
313	M₁₆	—	6	2	no	—
314	M₁₆	—	18	8	no	—
315	C₂×C₈	—	6	2	no	—
316	C₂×C₈	—	9	2	no	—
317	C₂×C₈	—	9	2	no	—
318	C₂×C₈	—	9	1	no	—
319	C₂×C₈	—	9	1	no	—
320	C₂×C₈	—	18	8	no	—
321	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
322	C₂×C₈	D₃×Dic₃	1	1	yes	characteristic
323	C₂×C₈	D₃×Dic₃	1	2	yes	—
324	C₂×C₈	C₂×D₃²	1	2	yes	—
325	C₄²	—	9	2	no	—
326	C₄²	—	18	1	no	—
327	C₂²×C₃	—	2	4	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	1	no	—
331	C₂²×C₃	—	2	1	no	—
332	C₂²×C₃	—	2	1	no	—
333	C₂²×C₃	—	6	4	no	—
334	C₂²×C₃	—	12	4	no	—
335	C₂²×C₃	#893	1	1	yes	characteristic
336	C₂²×C₃	#893	1	1	yes	characteristic
337	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
338	C₂²×C₃	D₄×Dic₃	1	1	yes	characteristic
339	C₂²×C₃	C₂×#237	1	1	yes	characteristic
340	C₂²×C₃	C₂×#239	1	1	yes	characteristic
341	C₂×D₃	—	2	4	no	—
342	C₂×D₃	—	4	4	no	—
343	C₃×C₄	—	2	1	no	—
344	C₃×C₄	—	2	1	no	—
345	C₃×C₄	—	2	1	no	—
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	6	4	no	—
348	C₃×C₄	#893	1	1	yes	characteristic
349	C₃×C₄	#893	1	1	yes	characteristic
350	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
351	C₃×C₄	D₄×Dic₃	1	1	yes	characteristic
352	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
353	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
354	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
355	C₃×C₄	C₂³×Dic₃	1	1	yes	characteristic
356	Dic₃	—	2	4	no	—
357	Dic₃	—	6	8	no	—
358	Dic₃	—	6	4	no	—
359	Dic₃	—	6	4	no	—
360	C₃²	C₂×#443	1	1	yes	characteristic, complemented, Sylow
361	C₂³	—	6	2	no	—
362	C₂³	#3796	1	1	yes	characteristic
363	Q₈	—	3	4	no	—
364	Q₈	—	6	2	no	—
365	D₄	—	3	4	no	—
366	D₄	—	6	4	no	—
367	D₄	—	6	4	no	—
368	D₄	—	6	2	no	—
369	C₂×C₄	—	6	2	no	—
370	C₂×C₄	—	6	4	no	—
371	C₂×C₄	—	6	4	no	—
372	C₂×C₄	—	18	4	no	—
373	C₂×C₄	—	18	2	no	—
374	C₂×C₄	#3796	1	1	yes	characteristic
375	C₂×C₄	#3802	1	1	yes	characteristic
376	C₂×C₄	#3802	1	1	yes	characteristic
377	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
378	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
380	C₈	—	6	4	no	—
381	C₈	—	9	2	no	—
382	C₈	—	9	2	no	—
383	C₈	C₂×D₃×Dic₃	1	2	yes	—
384	C₈	C₂×D₃×Dic₃	1	2	yes	—
385	C₂×C₃	—	2	2	no	—
386	C₂×C₃	—	2	2	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	1	no	—
390	C₂×C₃	—	2	1	no	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	12	4	no	—
394	C₂×C₃	#4895	1	2	yes	complemented
395	C₂×C₃	#5196	1	2	yes	complemented
396	C₂×C₃	C₂×#893	1	1	yes	characteristic
397	C₂×C₃	C₂×D₄×Dic₃	1	1	yes	characteristic
398	D₃	—	4	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	6	4	no	—
401	C₂²	—	12	4	no	—
402	C₂²	#63898	1	1	yes	characteristic
403	C₂²	#63898	1	1	yes	characteristic
404	C₂²	C₂×#3796	1	1	yes	characteristic
405	C₄	—	6	4	no	—
406	C₄	—	18	4	no	—
407	C₄	#63898	1	1	yes	characteristic
408	C₄	#63898	1	1	yes	characteristic
409	C₄	C₂×#3802	1	1	yes	characteristic
410	C₄	C₂²×D₃×Dic₃	1	1	yes	characteristic
411	C₃	—	2	1	no	—
412	C₃	C₂×#4895	1	1	yes	characteristic, complemented
413	C₃	C₂×#5196	1	1	yes	characteristic, complemented
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	12	4	no	—
417	C₂	#10590919	1	2	yes	direct product factor
418	C₂	C₂×#63898	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3802
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#904	C₂
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#443
LCS	G ▷ 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×#63815	C₂	semidirect
3. C₂×C₈×C₃⋊Dic₃	C₂	semidirect
4. C₂×C₃×#819	C₂	semidirect
5. C₂×#63568	C₂	semidirect
6. #10590919	C₂	direct (N × H)
14. C₂×C₃×Dic₁₂	C₄	semidirect
15. C₃×#904	C₄	semidirect
17. C₂×C₃×D₂₄	C₄	semidirect
18. C₂×C₃×#204	C₄	semidirect
21. #63815	C₂²	semidirect
23. C₈×C₃⋊Dic₃	C₂²	semidirect
24. C₃×#819	C₂²	semidirect
25. #63568	C₂²	semidirect
34. C₂×#819	D₃	semidirect
62. C₃×Dic₁₂	C₂×C₄	semidirect
63. C₃×D₂₄	C₂×C₄	semidirect
64. C₃×#204	C₂×C₄	semidirect
92. C₂×Dic₁₂	Dic₃	semidirect
93. #904	Dic₃	semidirect
95. C₂×D₂₄	Dic₃	semidirect
96. C₂×#204	Dic₃	semidirect
102. #819	C₂×D₃	semidirect
199. Dic₁₂	C₂×Dic₃	semidirect
200. D₂₄	C₂×Dic₃	semidirect
201. #204	C₂×Dic₃	semidirect
296. C₂×C₃²	#443	semidirect
360. C₃²	C₂×#443	semidirect
394. C₂×C₃	#4895	semidirect
395. C₂×C₃	#5196	semidirect
412. C₃	C₂×#4895	semidirect
413. C₃	C₂×#5196	semidirect
417. C₂	#10590919	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×C₃×#904	2
C₂×#63815	2
C₂×C₈×C₃⋊Dic₃	2
C₂×C₃×#819	2
C₂×#63568	2
#10590919	2
C₂×#5196	3
C₂×#4895	3

Subgroups — C2×#10590919 #11861021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590919 #11861021