Subgroups — C₂×#20244299 #26220273

Order 12032.

1694 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689128	C₂	1	2	yes	maximal, complemented
3	C₂²×#13093941	C₂	1	2	yes	maximal, complemented
4	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244299	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×#10625329	C₂²	1	1	yes	characteristic
9	C₂×#13093983	C₂²	1	1	yes	characteristic
10	C₂×#13093960	—	2	4	no	—
11	C₂×#13093960	C₂²	1	4	yes	complemented
12	#15689128	—	2	4	no	—
13	#15689128	C₂²	1	8	yes	complemented
14	C₂×#13093945	—	2	4	no	—
15	C₂×#13093941	—	2	8	no	—
16	C₂×#13093941	C₂²	1	8	yes	complemented
17	#15689078	—	2	2	no	—
18	#15689078	C₂²	1	4	yes	complemented
19	C₂×#13093934	—	2	1	no	—
20	C₂×C₈×Dic₄₇	—	2	1	no	—
21	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×D₈×C₄₇	—	2	1	no	—
23	C₂²×D₈×C₄₇	—	2	1	no	—
24	C₂²×D₈×C₄₇	—	2	2	no	—
25	C₂²×D₈×C₄₇	—	2	4	no	—
26	C₂²×D₈×C₄₇	C₄	1	8	yes	complemented
27	C₂²×D₈×C₄₇	C₂²	1	4	yes	—
28	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#10625329	—	2	1	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	D₄	1	4	yes	—
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂×#10625329	C₂³	1	2	yes	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	—	2	2	no	—
39	#13093983	—	2	1	no	—
40	#13093983	—	2	1	no	—
41	#13093983	D₄	1	2	yes	—
42	#13093983	C₂³	1	2	yes	—
43	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
44	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄×Dic₄₇	—	2	1	no	—
46	#13093960	—	2	8	no	—
47	#13093945	—	2	16	no	—
48	#13093941	—	2	16	no	—
49	#13093934	—	2	4	no	—
50	C₈×Dic₄₇	—	2	4	no	—
51	C₂⁵×C₄₇	—	2	2	no	—
52	C₂²×D₄×C₄₇	—	2	2	no	—
53	C₂²×D₄×C₄₇	—	2	2	no	—
54	C₂²×D₄×C₄₇	—	2	4	no	—
55	C₂²×D₄×C₄₇	—	2	2	no	—
56	C₂²×D₄×C₄₇	—	2	2	no	—
57	C₂²×D₄×C₄₇	—	2	4	no	—
58	C₂²×D₄×C₄₇	—	2	4	no	—
59	C₂²×D₄×C₄₇	—	2	2	no	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
61	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
62	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×D₈×C₄₇	—	2	8	no	—
64	C₂×D₈×C₄₇	—	2	8	no	—
65	C₂×D₈×C₄₇	—	2	16	no	—
66	C₂×D₈×C₄₇	—	2	4	no	—
67	C₂×D₈×C₄₇	—	2	4	no	—
68	C₂×D₈×C₄₇	—	2	8	no	—
69	C₂×D₈×C₄₇	C₂×C₄	1	16	yes	complemented
70	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
71	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	D₄	1	2	yes	—
74	C₂²×C₈×C₄₇	D₄	1	4	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂⁴×C₄₇	—	2	8	no	—
77	C₂⁴×C₄₇	—	2	4	no	—
78	C₂⁴×C₄₇	—	4	2	no	—
79	C₂⁴×C₄₇	—	4	2	no	—
80	C₂⁴×C₄₇	—	4	4	no	—
81	C₂⁴×C₄₇	—	8	8	no	—
82	C₂⁴×C₄₇	#41	1	1	yes	characteristic
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	8	no	—
85	C₂×D₄×C₄₇	—	2	8	no	—
86	C₂×D₄×C₄₇	—	2	8	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	4	no	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	4	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	—	4	4	no	—
98	C₂×D₄×C₄₇	—	4	4	no	—
99	C₂×D₄×C₄₇	—	4	4	no	—
100	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	2	no	—
112	D₈×C₄₇	—	2	16	no	—
113	D₈×C₄₇	—	2	16	no	—
114	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
116	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
121	C₂²⋊Dic₄₇	—	2	2	no	—
122	C₂²⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂×D₄	1	4	yes	—
125	C₄×Dic₄₇	—	2	2	no	—
126	C₄×Dic₄₇	—	2	2	no	—
127	#10625329	—	2	4	no	—
128	#10625329	—	2	2	no	—
129	#10625329	—	2	4	no	—
130	#10625329	—	2	4	no	—
131	#10625329	—	4	4	no	—
132	#10625329	C₂×D₄	1	4	yes	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	4	no	—
136	C₂×C₄₇⋊C₈	—	4	4	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	4	no	—
141	C₂³×C₄₇	—	4	8	no	—
142	C₂³×C₄₇	—	4	8	no	—
143	C₂³×C₄₇	—	8	16	no	—
144	C₂³×C₄₇	—	8	8	no	—
145	C₂³×C₄₇	—	8	16	no	—
146	C₂³×C₄₇	—	8	8	no	—
147	C₂³×C₄₇	—	8	8	no	—
148	C₂³×C₄₇	C₄×D₄	1	2	yes	—
149	C₂³×C₄₇	#121	1	1	yes	characteristic
150	C₂³×C₄₇	#121	1	1	yes	characteristic
151	C₂³×C₄₇	#124	1	2	yes	—
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	2	8	no	—
155	D₄×C₄₇	—	4	4	no	—
156	D₄×C₄₇	—	4	4	no	—
157	D₄×C₄₇	—	4	8	no	—
158	D₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×C₄×C₄₇	#121	1	2	yes	—
166	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#124	1	2	yes	—
169	C₂×C₄×C₄₇	#127	1	2	yes	—
170	C₂×C₄×C₄₇	#127	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	4	4	no	—
179	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
180	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
181	C₄₇⋊C₈	—	2	4	no	—
182	C₄₇⋊C₈	—	4	4	no	—
183	C₂×#1978	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	4	8	no	—
189	C₂²×C₄₇	—	8	8	no	—
190	C₂²×C₄₇	—	8	8	no	—
191	C₂²×C₄₇	—	8	16	no	—
192	C₂²×C₄₇	—	8	16	no	—
193	C₂²×C₄₇	—	8	8	no	—
194	C₂²×C₄₇	#390	1	2	yes	—
195	C₂²×C₄₇	#390	1	2	yes	—
196	C₂²×C₄₇	#472	1	4	yes	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
200	C₄×C₄₇	#390	1	2	yes	—
201	C₄×C₄₇	#390	1	2	yes	—
202	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
206	Dic₄₇	—	4	4	no	—
207	C₂³×D₈	D₄₇	1	1	yes	characteristic
208	C₂²×#108	—	47	1	no	—
209	C₂×#418	—	47	2	no	—
210	C₂²×#100	—	47	2	no	—
211	C₂×#405	—	47	1	no	—
212	#1978	—	47	8	no	—
213	C₂×C₄₇	—	2	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	8	8	no	—
217	C₂×C₄₇	#1978	1	4	yes	complemented
218	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#472	1	2	yes	—
220	C₂³×D₄	C₂×D₄₇	1	2	yes	—
221	C₂²×D₈	—	2	1	no	—
222	C₂²×D₈	—	2	1	no	—
223	C₂²×D₈	—	2	2	no	—
224	C₂²×D₈	—	2	4	no	—
225	C₂²×D₈	Dic₄₇	1	8	yes	complemented
226	C₂²×D₈	C₂×D₄₇	1	4	yes	—
227	C₂²×M₁₆	—	47	1	no	—
228	C₂²×M₁₆	—	47	2	no	—
229	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₂×#117	—	47	1	no	—
231	C₂×#108	—	47	4	no	—
232	C₂×#108	—	94	4	no	—
233	#418	—	47	8	no	—
234	#418	—	94	4	no	—
235	C₂×#102	—	94	4	no	—
236	C₂×#100	—	47	8	no	—
237	C₂×#100	—	94	8	no	—
238	#405	—	47	4	no	—
239	#405	—	94	2	no	—
240	C₂×#97	—	94	1	no	—
241	C₂×C₄×C₈	—	94	1	no	—
242	C₄₇	C₂×#1978	1	1	yes	characteristic, complemented, Sylow
243	C₂⁵	—	2	2	no	—
244	C₂²×D₄	—	2	2	no	—
245	C₂²×D₄	—	2	2	no	—
246	C₂²×D₄	—	2	4	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	4	no	—
252	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
253	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
254	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×D₈	—	2	8	no	—
256	C₂×D₈	—	2	8	no	—
257	C₂×D₈	—	2	16	no	—
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	2	4	no	—
260	C₂×D₈	—	2	8	no	—
261	C₂×D₈	C₂×Dic₄₇	1	16	yes	complemented
262	C₂×M₁₆	—	47	4	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	47	4	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂×M₁₆	—	94	1	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂×M₁₆	—	94	4	no	—
269	C₂×M₁₆	—	94	4	no	—
270	C₂²×C₈	—	94	1	no	—
271	C₂²×C₈	—	94	2	no	—
272	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
273	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
276	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
277	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
278	#117	—	47	2	no	—
279	#117	—	47	2	no	—
280	#117	—	94	1	no	—
281	#117	—	94	1	no	—
282	C₂×C₄⋊C₄	—	47	2	no	—
283	C₂×C₂²⋊C₄	—	94	1	no	—
284	C₂×C₄²	—	94	1	no	—
285	#108	—	94	8	no	—
286	#102	—	94	16	no	—
287	#100	—	94	16	no	—
288	#97	—	94	4	no	—
289	C₄×C₈	—	94	4	no	—
290	C₂⁴	—	2	8	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	4	2	no	—
293	C₂⁴	—	4	2	no	—
294	C₂⁴	—	4	4	no	—
295	C₂⁴	—	8	8	no	—
296	C₂⁴	#10625352	1	1	yes	characteristic
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	4	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₄₇	1	2	yes	—
319	C₂²×C₄	#10625352	1	1	yes	characteristic
320	C₂²×C₄	#10625352	1	2	yes	—
321	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
325	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
326	D₈	—	2	16	no	—
327	D₈	—	2	16	no	—
328	M₁₆	—	47	4	no	—
329	M₁₆	—	94	4	no	—
330	M₁₆	—	94	2	no	—
331	M₁₆	—	94	4	no	—
332	M₁₆	—	94	4	no	—
333	M₁₆	—	188	4	no	—
334	C₂×C₈	—	94	4	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	4	no	—
337	C₂×C₈	—	188	4	no	—
338	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
339	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
340	C₂×C₈	C₂²⋊Dic₄₇	1	8	yes	—
341	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
344	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
345	C₄⋊C₄	—	47	4	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₂²⋊C₄	—	94	2	no	—
348	C₂²⋊C₄	—	94	2	no	—
349	C₄²	—	94	2	no	—
350	C₄²	—	94	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	4	8	no	—
354	C₂³	—	4	8	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	8	16	no	—
358	C₂³	—	8	8	no	—
359	C₂³	—	8	16	no	—
360	C₂³	—	8	8	no	—
361	C₂³	—	8	8	no	—
362	C₂³	D₄×Dic₄₇	1	2	yes	—
363	C₂³	#13093995	1	1	yes	characteristic
364	C₂³	#13093995	1	1	yes	characteristic
365	C₂³	#13094011	1	2	yes	—
366	C₂³	C₂×#10625352	1	1	yes	characteristic
367	D₄	—	2	8	no	—
368	D₄	—	2	8	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	8	no	—
371	D₄	—	4	4	no	—
372	D₄	—	4	4	no	—
373	C₂×C₄	—	94	4	no	—
374	C₂×C₄	—	188	4	no	—
375	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
376	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
377	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
378	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
379	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
380	C₂×C₄	#13093995	1	1	yes	characteristic
381	C₂×C₄	#13093995	1	1	yes	characteristic
382	C₂×C₄	#13093995	1	2	yes	—
383	C₂×C₄	#13093995	1	2	yes	—
384	C₂×C₄	#13094011	1	2	yes	—
385	C₂×C₄	#13094020	1	2	yes	—
386	C₂×C₄	#13094020	1	2	yes	—
387	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
393	C₈	—	94	4	no	—
394	C₈	—	188	4	no	—
395	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
396	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	8	no	—
402	C₂²	—	8	8	no	—
403	C₂²	—	8	16	no	—
404	C₂²	—	8	8	no	—
405	C₂²	—	8	16	no	—
406	C₂²	—	8	8	no	—
407	C₂²	#15689026	1	2	yes	—
408	C₂²	#15689026	1	2	yes	—
409	C₂²	#15689390	1	4	yes	—
410	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
411	C₂²	C₂×#13093995	1	1	yes	characteristic
412	C₂²	C₂×#13094011	1	1	yes	characteristic
413	C₄	—	188	4	no	—
414	C₄	#15689026	1	2	yes	—
415	C₄	#15689026	1	2	yes	—
416	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
417	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
418	C₄	C₂×#13093995	1	1	yes	characteristic
419	C₄	C₂×#13094020	1	1	yes	characteristic
420	C₂	—	2	2	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	8	8	no	—
424	C₂	#20244299	1	4	yes	direct product factor
425	C₂	C₂×#15689026	1	1	yes	characteristic
426	C₂	C₂×#15689390	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093995
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂³×D₈×C₄₇	C₂
socle	C₂³×C₄₇	#121
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂³×D₈	D₄₇
hypocenter	C₄₇	C₂×#1978
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×D₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093960	C₂	semidirect
2. C₂×#15689128	C₂	semidirect
3. C₂²×#13093941	C₂	semidirect
4. C₂×#15689078	C₂	semidirect
5. #20244299	C₂	direct (N × H)
11. C₂×#13093960	C₂²	semidirect
13. #15689128	C₂²	semidirect
16. C₂×#13093941	C₂²	semidirect
18. #15689078	C₂²	semidirect
26. C₂²×D₈×C₄₇	C₄	semidirect
69. C₂×D₈×C₄₇	C₂×C₄	semidirect
217. C₂×C₄₇	#1978	semidirect
225. C₂²×D₈	Dic₄₇	semidirect
242. C₄₇	C₂×#1978	semidirect
261. C₂×D₈	C₂×Dic₄₇	semidirect
424. C₂	#20244299	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×#13093960	2
C₂×#15689128	2
C₂²×#13093941	2
C₂×#15689078	2
#20244299	2
C₂³×D₈×C₄₇	2
C₂×#1978	47

Subgroups — C2×#20244299 #26220273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244299 #26220273