Subgroups — C₂×#10589169 #11783454

Order 1152.

925 conjugacy classes of subgroups.

The subgroup lattice has 639 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#3748	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic
4	#10589169	C₂	1	4	yes	maximal, direct product factor
5	C₂×#4556	—	3	1	no	maximal
6	C₂×#4533	—	3	1	no	maximal
7	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₂×#3748	—	2	1	no	—
9	C₂×#3748	—	2	1	no	—
10	C₂×#3748	—	2	1	no	—
11	C₂×#3748	C₄	1	2	yes	complemented
12	C₂×#3748	C₄	1	2	yes	complemented
13	C₂×#3748	C₂²	1	2	yes	—
14	C₂²×C₃⋊(C₃⋊C₈)	—	2	1	no	—
15	C₂×C₃×#217	C₄	1	2	yes	—
16	C₃×#926	—	2	1	no	—
17	C₃×#926	—	2	1	no	—
18	C₃×#926	C₄	1	2	yes	—
19	C₃×#926	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
21	C₂×C₃×C₄×Dic₃	—	2	1	no	—
22	C₂×C₃×#208	—	2	1	no	—
23	C₂×C₃×#208	—	2	1	no	—
24	C₂×C₃×#208	—	2	1	no	—
25	C₂×C₃×#208	—	2	1	no	—
26	C₂×C₃×#208	C₄	1	2	yes	complemented
27	C₂×C₃×#208	C₂²	1	2	yes	—
28	C₂²×C₃×C₃⋊C₈	C₄	1	2	yes	complemented
29	C₂²×C₃×M₁₆	—	3	1	no	—
30	C₂×C₃×#117	—	3	1	no	—
31	C₂×#926	D₃	1	1	yes	characteristic
32	C₂²×#208	—	3	1	no	—
33	C₂²×#208	—	3	1	no	—
34	C₂²×#208	—	6	1	no	—
35	C₂²×#208	D₃	1	1	yes	characteristic
36	#4556	—	3	4	no	—
37	#4533	—	3	4	no	—
38	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
46	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
47	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
48	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
49	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
50	C₂²×C₃²×C₄	Q₈	1	1	yes	characteristic
51	C₂²×C₃²×C₄	Q₈	1	1	yes	characteristic
52	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
53	C₂²×C₃×Dic₃	—	2	2	no	—
54	#3748	—	2	2	no	—
55	#3748	—	2	2	no	—
56	#3748	—	2	2	no	—
57	#3748	C₂×C₄	1	4	yes	complemented
58	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
59	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
60	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
61	C₃×#217	—	2	2	no	—
62	C₃×#217	C₂×C₄	1	4	yes	—
63	C₃×C₄⋊Dic₃	—	2	2	no	—
64	C₃×C₄⋊Dic₃	—	2	2	no	—
65	C₃×C₄×Dic₃	—	2	2	no	—
66	C₃×C₄×Dic₃	—	2	2	no	—
67	C₃×#208	—	2	2	no	—
68	C₃×#208	—	2	2	no	—
69	C₃×#208	—	2	2	no	—
70	C₃×#208	—	2	2	no	—
71	C₂×C₃×C₃⋊C₈	—	2	2	no	—
72	C₂×C₃×C₃⋊C₈	—	2	2	no	—
73	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
74	C₂×#344	—	9	1	no	Sylow
75	C₂³×C₃×C₄	—	2	1	no	—
76	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
77	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₃×M₁₆	—	3	2	no	—
79	C₂×C₃×M₁₆	—	3	2	no	—
80	C₂×C₃×M₁₆	—	6	1	no	—
81	C₂×C₃×M₁₆	—	6	1	no	—
82	C₂×C₃×M₁₆	—	6	1	no	—
83	C₂×C₃×M₁₆	—	6	1	no	—
84	C₂²×C₃×C₈	—	3	2	no	—
85	C₃×#117	—	3	2	no	—
86	C₃×#117	—	3	2	no	—
87	C₃×#117	—	6	1	no	—
88	C₃×#117	—	6	1	no	—
89	C₂×C₃×C₄⋊C₄	—	6	1	no	—
90	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
91	C₂×C₃×C₄²	—	6	1	no	—
92	C₂×#217	Dic₃	1	2	yes	—
93	#926	—	2	1	no	—
94	#926	—	2	1	no	—
95	#926	Dic₃	1	2	yes	—
96	#926	C₂×D₃	1	2	yes	—
97	C₂×C₄⋊Dic₃	—	2	1	no	—
98	C₂×C₄×Dic₃	—	2	1	no	—
99	C₂×#208	—	2	1	no	—
100	C₂×#208	—	2	1	no	—
101	C₂×#208	—	2	1	no	—
102	C₂×#208	—	2	1	no	—
103	C₂×#208	—	3	2	no	—
104	C₂×#208	—	3	2	no	—
105	C₂×#208	—	3	2	no	—
106	C₂×#208	—	3	2	no	—
107	C₂×#208	—	3	2	no	—
108	C₂×#208	—	3	2	no	—
109	C₂×#208	—	6	2	no	—
110	C₂×#208	—	6	2	no	—
111	C₂×#208	—	6	2	no	—
112	C₂×#208	—	6	2	no	—
113	C₂×#208	—	6	2	no	—
114	C₂×#208	—	6	2	no	—
115	C₂×#208	—	6	1	no	—
116	C₂×#208	—	6	1	no	—
117	C₂×#208	—	6	1	no	—
118	C₂×#208	—	6	1	no	—
119	C₂×#208	—	6	1	no	—
120	C₂×#208	—	6	1	no	—
121	C₂×#208	Dic₃	1	2	yes	complemented
122	C₂×#208	C₂×D₃	1	2	yes	—
123	C₂²×C₃⋊C₈	—	6	2	no	—
124	C₂²×C₃⋊C₈	—	6	1	no	—
125	C₂²×C₃⋊C₈	—	6	1	no	—
126	C₂²×C₃⋊C₈	Dic₃	1	2	yes	complemented
127	C₂³×C₃²	—	4	2	no	—
128	C₂³×C₃²	C₄²	1	1	yes	characteristic
129	C₂³×C₃²	C₄²	1	1	yes	characteristic
130	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
132	C₂³×C₃²	C₄⋊C₄	1	1	yes	characteristic
133	C₂³×C₃²	C₄⋊C₄	1	1	yes	characteristic
134	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
136	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
163	C₂×C₃×Dic₃	—	2	4	no	—
164	C₂×C₃×Dic₃	—	4	4	no	—
165	C₃⋊(C₃⋊C₈)	—	2	4	no	—
166	C₃×C₃⋊C₈	—	2	4	no	—
167	C₂²×M₁₆	—	3	1	no	—
168	C₂²×M₁₆	—	9	1	no	—
169	C₂×#117	—	3	1	no	—
170	#344	—	9	4	no	—
171	C₂⁴×C₃	—	2	1	no	—
172	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
173	C₂⁴×C₃	C₂×Dic₃	1	1	yes	characteristic
174	C₂²×C₃×C₄	—	2	1	no	—
175	C₂²×C₃×C₄	—	2	1	no	—
176	C₂²×C₃×C₄	—	2	1	no	—
177	C₂²×C₃×C₄	—	2	1	no	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	1	no	—
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	1	no	—
182	C₂²×C₃×C₄	—	2	1	no	—
183	C₂²×C₃×C₄	—	2	1	no	—
184	C₂²×C₃×C₄	—	2	1	no	—
185	C₂²×C₃×C₄	—	2	1	no	—
186	C₂²×C₃×C₄	—	2	1	no	—
187	C₂²×C₃×C₄	—	2	1	no	—
188	C₂²×C₃×C₄	—	6	2	no	—
189	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
190	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
191	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
192	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
198	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
199	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
200	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
201	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
202	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
203	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
207	C₂²×C₃×C₄	#67	1	1	yes	characteristic
208	C₂²×C₃×C₄	#67	1	1	yes	characteristic
209	C₂²×C₃×C₄	#67	1	1	yes	characteristic
210	C₂²×C₃×C₄	#67	1	1	yes	characteristic
211	C₂²×C₃×C₄	#67	1	1	yes	characteristic
212	C₂²×C₃×C₄	#67	1	1	yes	characteristic
213	C₂²×C₃×C₄	#67	1	1	yes	characteristic
214	C₂²×C₃×C₄	#67	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
217	C₂²×Dic₃	—	2	2	no	—
218	C₃×M₁₆	—	6	2	no	—
219	C₃×M₁₆	—	6	2	no	—
220	C₃×M₁₆	—	6	2	no	—
221	C₃×M₁₆	—	6	2	no	—
222	C₂×C₃×C₈	—	3	4	no	—
223	C₂×C₃×C₈	—	6	2	no	—
224	C₂×C₃×C₈	—	6	2	no	—
225	C₃×C₄⋊C₄	—	6	2	no	—
226	C₃×C₄⋊C₄	—	6	2	no	—
227	C₃×C₂²⋊C₄	—	3	4	no	—
228	C₃×C₂²⋊C₄	—	6	2	no	—
229	C₃×C₄²	—	6	2	no	—
230	C₃×C₄²	—	6	2	no	—
231	#217	—	2	2	no	—
232	#217	C₂×Dic₃	1	4	yes	—
233	C₄⋊Dic₃	—	2	2	no	—
234	C₄⋊Dic₃	—	2	2	no	—
235	C₄×Dic₃	—	2	2	no	—
236	C₄×Dic₃	—	2	2	no	—
237	#208	—	2	2	no	—
238	#208	—	2	2	no	—
239	#208	—	2	2	no	—
240	#208	—	2	2	no	—
241	#208	—	3	4	no	—
242	#208	—	3	4	no	—
243	#208	—	6	4	no	—
244	#208	—	6	4	no	—
245	#208	—	6	4	no	—
246	#208	—	6	4	no	—
247	#208	—	6	2	no	—
248	#208	—	6	2	no	—
249	#208	—	6	2	no	—
250	#208	—	6	2	no	—
251	#208	—	6	2	no	—
252	#208	—	6	2	no	—
253	C₂×C₃⋊C₈	—	2	2	no	—
254	C₂×C₃⋊C₈	—	2	2	no	—
255	C₂×C₃⋊C₈	—	6	4	no	—
256	C₂×C₃⋊C₈	—	6	4	no	—
257	C₂×C₃⋊C₈	—	6	4	no	—
258	C₂×C₃⋊C₈	—	6	2	no	—
259	C₂×C₃⋊C₈	—	6	2	no	—
260	C₂×C₃⋊C₈	—	6	2	no	—
261	C₂×C₃⋊C₈	—	6	2	no	—
262	C₂×C₃⋊C₈	—	6	2	no	—
263	C₂×C₃⋊C₈	—	6	2	no	—
264	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	complemented
265	C₂²×C₃²	—	2	2	no	—
266	C₂²×C₃²	—	2	2	no	—
267	C₂²×C₃²	—	2	2	no	—
268	C₂²×C₃²	—	4	1	no	—
269	C₂²×C₃²	—	4	1	no	—
270	C₂²×C₃²	—	4	1	no	—
271	C₂²×C₃²	—	4	1	no	—
272	C₂²×C₃²	#95	1	1	yes	characteristic
273	C₂²×C₃²	#95	1	1	yes	characteristic
274	C₂²×C₃²	#95	1	1	yes	characteristic
275	C₂²×C₃²	#95	1	1	yes	characteristic
276	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
277	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₃²×C₄	#95	1	1	yes	characteristic
280	C₃²×C₄	#95	1	1	yes	characteristic
281	C₃²×C₄	#95	1	1	yes	characteristic
282	C₃²×C₄	#95	1	1	yes	characteristic
283	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
286	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
287	C₃×Dic₃	—	4	4	no	—
288	C₂³×C₄	D₃²	1	1	yes	characteristic
289	C₂×M₁₆	—	3	2	no	—
290	C₂×M₁₆	—	3	2	no	—
291	C₂×M₁₆	—	6	1	no	—
292	C₂×M₁₆	—	6	1	no	—
293	C₂×M₁₆	—	6	1	no	—
294	C₂×M₁₆	—	6	1	no	—
295	C₂×M₁₆	—	9	2	no	—
296	C₂×M₁₆	—	9	2	no	—
297	C₂×M₁₆	—	9	2	no	—
298	C₂×M₁₆	—	18	1	no	—
299	C₂×M₁₆	—	18	1	no	—
300	C₂×M₁₆	—	18	1	no	—
301	C₂²×C₈	—	3	2	no	—
302	C₂²×C₈	—	18	1	no	—
303	#117	—	3	2	no	—
304	#117	—	3	2	no	—
305	#117	—	6	1	no	—
306	#117	—	6	1	no	—
307	C₂×C₄⋊C₄	—	6	1	no	—
308	C₂×C₂²⋊C₄	—	3	2	no	—
309	C₂×C₄²	—	6	1	no	—
310	C₂³×C₃	—	2	1	no	—
311	C₂³×C₃	—	2	1	no	—
312	C₂³×C₃	—	2	1	no	—
313	C₂³×C₃	—	2	1	no	—
314	C₂³×C₃	—	2	1	no	—
315	C₂³×C₃	—	2	1	no	—
316	C₂³×C₃	—	2	1	no	—
317	C₂³×C₃	—	4	2	no	—
318	C₂³×C₃	—	4	2	no	—
319	C₂³×C₃	—	4	4	no	—
320	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
321	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
322	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
323	C₂³×C₃	C₄×Dic₃	1	1	yes	characteristic
324	C₂³×C₃	Dic₃⋊C₄	1	1	yes	characteristic
325	C₂³×C₃	Dic₃⋊C₄	1	1	yes	characteristic
326	C₂³×C₃	C₄⋊Dic₃	1	1	yes	characteristic
327	C₂³×C₃	C₄⋊Dic₃	1	1	yes	characteristic
328	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
329	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
330	C₂³×C₃	#217	1	1	yes	characteristic
331	C₂³×C₃	#217	1	1	yes	characteristic
332	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
333	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	6	4	no	—
363	C₂×C₃×C₄	—	12	4	no	—
364	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
365	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
366	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
367	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
368	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
369	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
370	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
371	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
372	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
373	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
374	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
375	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
376	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
377	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
378	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
379	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
380	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
381	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
383	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
384	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
385	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
386	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
387	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
388	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
389	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
390	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
391	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
392	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
393	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
394	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
395	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
396	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
397	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
398	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
399	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
400	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
401	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
402	C₂×C₃×C₄	#217	1	1	yes	characteristic
403	C₂×C₃×C₄	#217	1	1	yes	characteristic
404	C₂×C₃×C₄	#217	1	1	yes	characteristic
405	C₂×C₃×C₄	#217	1	1	yes	characteristic
406	C₂×C₃×C₄	#217	1	1	yes	characteristic
407	C₂×C₃×C₄	#217	1	1	yes	characteristic
408	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
409	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
410	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
420	C₂×Dic₃	—	2	4	no	—
421	C₂×Dic₃	—	4	4	no	—
422	C₃×C₈	—	6	4	no	—
423	C₃⋊C₈	—	2	4	no	—
424	C₃⋊C₈	—	6	8	no	—
425	C₃⋊C₈	—	6	4	no	—
426	C₃⋊C₈	—	6	4	no	—
427	C₂×C₃²	—	2	1	no	—
428	C₂×C₃²	—	2	1	no	—
429	C₂×C₃²	—	2	1	no	—
430	C₂×C₃²	—	2	1	no	—
431	C₂×C₃²	—	2	1	no	—
432	C₂×C₃²	—	2	1	no	—
433	C₂×C₃²	#344	1	2	yes	complemented
434	C₂×C₃²	C₂×#95	1	1	yes	characteristic
435	C₂⁴	D₃×Dic₃	1	1	yes	characteristic
436	C₂²×C₄	—	6	2	no	—
437	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
438	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
439	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
440	C₂²×C₄	#624	1	1	yes	characteristic
441	C₂²×C₄	#624	1	1	yes	characteristic
442	C₂²×C₄	#625	1	1	yes	characteristic
443	C₂²×C₄	#625	1	1	yes	characteristic
444	C₂²×C₄	#626	1	1	yes	characteristic
445	C₂²×C₄	#626	1	1	yes	characteristic
446	C₂²×C₄	#626	1	1	yes	characteristic
447	C₂²×C₄	#626	1	1	yes	characteristic
448	C₂²×C₄	#627	1	1	yes	characteristic
449	C₂²×C₄	#627	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
451	M₁₆	—	6	2	no	—
452	M₁₆	—	6	2	no	—
453	M₁₆	—	6	2	no	—
454	M₁₆	—	6	2	no	—
455	M₁₆	—	9	4	no	—
456	M₁₆	—	18	2	no	—
457	M₁₆	—	18	2	no	—
458	M₁₆	—	18	2	no	—
459	C₂×C₈	—	3	4	no	—
460	C₂×C₈	—	6	2	no	—
461	C₂×C₈	—	6	2	no	—
462	C₂×C₈	—	18	2	no	—
463	C₂×C₈	—	18	2	no	—
464	C₂×C₈	—	18	2	no	—
465	C₄⋊C₄	—	6	2	no	—
466	C₄⋊C₄	—	6	2	no	—
467	C₂²⋊C₄	—	3	4	no	—
468	C₂²⋊C₄	—	6	2	no	—
469	C₄²	—	6	2	no	—
470	C₄²	—	6	2	no	—
471	C₂²×C₃	—	2	4	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	2	1	no	—
481	C₂²×C₃	—	2	1	no	—
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	1	no	—
485	C₂²×C₃	—	4	2	no	—
486	C₂²×C₃	—	4	2	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	4	2	no	—
497	C₂²×C₃	—	4	2	no	—
498	C₂²×C₃	—	4	2	no	—
499	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
500	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
501	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
502	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
503	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
504	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
505	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
506	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
507	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
508	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
509	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
510	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
511	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
512	C₂²×C₃	C₂×#217	1	1	yes	characteristic
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	2	1	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	12	4	no	—
522	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
523	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
524	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
525	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
526	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
527	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
528	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
529	C₃×C₄	C₃⋊#95	1	1	yes	characteristic
530	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
531	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
532	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
533	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
534	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
535	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
536	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
537	C₃×C₄	C₂×#217	1	1	yes	characteristic
538	Dic₃	—	4	4	no	—
539	C₃²	C₂×#344	1	1	yes	characteristic, complemented, Sylow
540	C₂³	—	4	2	no	—
541	C₂³	Dic₃²	1	1	yes	characteristic
542	C₂³	Dic₃²	1	1	yes	characteristic
543	C₂³	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
544	C₂³	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
545	C₂³	Dic₃⋊Dic₃	1	1	yes	characteristic
546	C₂³	Dic₃⋊Dic₃	1	1	yes	characteristic
547	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
548	C₂×C₄	—	6	4	no	—
549	C₂×C₄	—	12	4	no	—
550	C₂×C₄	Dic₃²	1	1	yes	characteristic
551	C₂×C₄	Dic₃²	1	1	yes	characteristic
552	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
553	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
554	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
555	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
556	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
557	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
558	C₂×C₄	#3722	1	1	yes	characteristic
559	C₂×C₄	#3722	1	1	yes	characteristic
560	C₂×C₄	#3722	1	1	yes	characteristic
561	C₂×C₄	#3722	1	1	yes	characteristic
562	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
563	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
564	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
565	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
566	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
567	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
568	C₂×C₄	#3724	1	1	yes	characteristic
569	C₂×C₄	#3724	1	1	yes	characteristic
570	C₂×C₄	#3724	1	1	yes	characteristic
571	C₂×C₄	#3724	1	1	yes	characteristic
572	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
573	C₂×C₄	C₂×#624	1	1	yes	characteristic
574	C₂×C₄	C₂×#625	1	1	yes	characteristic
575	C₂×C₄	C₂×#626	1	1	yes	characteristic
576	C₂×C₄	C₂×#626	1	1	yes	characteristic
577	C₂×C₄	C₂×#627	1	1	yes	characteristic
578	C₈	—	6	4	no	—
579	C₈	—	18	4	no	—
580	C₂×C₃	—	2	2	no	—
581	C₂×C₃	—	2	2	no	—
582	C₂×C₃	—	2	1	no	—
583	C₂×C₃	—	2	1	no	—
584	C₂×C₃	—	2	1	no	—
585	C₂×C₃	—	2	1	no	—
586	C₂×C₃	—	2	1	no	—
587	C₂×C₃	—	2	1	no	—
588	C₂×C₃	—	2	1	no	—
589	C₂×C₃	—	2	1	no	—
590	C₂×C₃	—	2	1	no	—
591	C₂×C₃	—	2	1	no	—
592	C₂×C₃	—	2	1	no	—
593	C₂×C₃	—	2	1	no	—
594	C₂×C₃	—	2	1	no	—
595	C₂×C₃	—	2	2	no	—
596	C₂×C₃	—	4	1	no	—
597	C₂×C₃	—	4	1	no	—
598	C₂×C₃	—	4	1	no	—
599	C₂×C₃	—	4	1	no	—
600	C₂×C₃	#4533	1	2	yes	complemented
601	C₂×C₃	#4556	1	2	yes	complemented
602	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
603	C₂×C₃	C₂×C₃⋊#95	1	1	yes	characteristic
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	#63579	1	1	yes	characteristic
612	C₂²	#63579	1	1	yes	characteristic
613	C₂²	#63579	1	1	yes	characteristic
614	C₂²	#63579	1	1	yes	characteristic
615	C₂²	C₂×Dic₃²	1	1	yes	characteristic
616	C₂²	C₂×(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
617	C₂²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
618	C₄	—	12	4	no	—
619	C₄	#63579	1	1	yes	characteristic
620	C₄	#63579	1	1	yes	characteristic
621	C₄	#63579	1	1	yes	characteristic
622	C₄	#63579	1	1	yes	characteristic
623	C₄	C₂×(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
624	C₄	C₂×#3722	1	1	yes	characteristic
625	C₄	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
626	C₄	C₂×#3724	1	1	yes	characteristic
627	C₃	—	2	1	no	—
628	C₃	C₂×#4533	1	1	yes	characteristic, complemented
629	C₃	C₂×#4556	1	1	yes	characteristic, complemented
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	#10589169	1	2	yes	direct product factor
637	C₂	C₂×#63579	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₃)⋊Dic₃
commutator	C₂²×C₃²	C₂×C₄²
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂³×C₃²×C₄	C₂²
socle	C₂²×C₃²	#95
prime radical	C₂⁴×C₃²	C₂×C₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂³×C₄	D₃²
hypocenter	C₃²	C₂×#344
LCS	G ▷ C₂²×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
4. #10589169	C₂	direct (N × H)
11. C₂×#3748	C₄	semidirect
12. C₂×#3748	C₄	semidirect
26. C₂×C₃×#208	C₄	semidirect
28. C₂²×C₃×C₃⋊C₈	C₄	semidirect
57. #3748	C₂×C₄	semidirect
73. C₂×C₃×C₃⋊C₈	C₂×C₄	semidirect
121. C₂×#208	Dic₃	semidirect
126. C₂²×C₃⋊C₈	Dic₃	semidirect
264. C₂×C₃⋊C₈	C₂×Dic₃	semidirect
433. C₂×C₃²	#344	semidirect
539. C₃²	C₂×#344	semidirect
600. C₂×C₃	#4533	semidirect
601. C₂×C₃	#4556	semidirect
628. C₃	C₂×#4533	semidirect
629. C₃	C₂×#4556	semidirect
636. C₂	#10589169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#3748	2
C₂×C₃×#926	2
C₂²×C₃×#208	2
#10589169	2
C₂×#4556	3
C₂×#4533	3

Subgroups — C2×#10589169 #11783454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589169 #11783454