Subgroups — C₂×#20245115 #26369205

Order 12032.

1154 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094046	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093964	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245115	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688929	C₂	1	4	yes	maximal, complemented
5	C₂²×#108×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10625350	—	2	1	no	—
7	C₂×#13094046	—	2	2	no	—
8	C₂×#13094046	—	2	1	no	—
9	C₂×#13094046	—	2	1	no	—
10	C₂×#13094046	—	2	2	no	—
11	C₂×#13094046	C₄	1	2	yes	—
12	C₂×#13094046	C₄	1	4	yes	—
13	C₂×#13094046	C₂²	1	2	yes	—
14	C₂×#13094046	C₂²	1	4	yes	—
15	C₂²×Dic₁₈₈	C₄	1	1	yes	characteristic
16	C₂²×#10625325	—	2	1	no	—
17	C₂²×D₃₇₆	C₄	1	1	yes	characteristic
18	C₂×#13093964	—	2	1	no	—
19	C₂×#13093964	—	2	1	no	—
20	C₂×#13093964	—	2	2	no	—
21	C₂×#13093964	C₂²	1	4	yes	complemented
22	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
23	#15688929	C₂²	1	16	yes	complemented
24	C₂²×M₁₆×C₄₇	—	2	1	no	—
25	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#108×C₄₇	—	2	2	no	—
27	C₂×#108×C₄₇	—	2	1	no	—
28	C₂×#108×C₄₇	C₂²	1	2	yes	complemented
29	C₂×#108×C₄₇	C₂²	1	4	yes	complemented
30	C₂×#10625350	—	2	2	no	—
31	C₂×#10625350	—	2	4	no	—
32	C₂×#10625350	—	2	2	no	—
33	C₂×#10625350	—	2	4	no	—
34	C₂×#10625350	—	4	1	no	—
35	C₂×#10625350	—	4	2	no	—
36	C₂×#10625350	—	4	1	no	—
37	C₂×#10625350	—	4	2	no	—
38	C₂²×Dic₉₄	—	2	1	no	—
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×C₂²⋊D₄₇	—	4	1	no	—
41	C₂²×C₄×D₄₇	—	4	1	no	—
42	#13094046	—	2	4	no	—
43	#13094046	—	2	4	no	—
44	#13094046	—	2	4	no	—
45	#13094046	—	2	2	no	—
46	#13094046	—	2	4	no	—
47	#13094046	—	2	2	no	—
48	#13094046	—	2	4	no	—
49	#13094046	C₂×C₄	1	4	yes	—
50	#13094046	C₂×C₄	1	8	yes	—
51	#13094046	C₂³	1	4	yes	—
52	C₂×Dic₁₈₈	—	2	2	no	—
53	C₂×Dic₁₈₈	—	2	1	no	—
54	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
55	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
56	C₂×#10625325	—	2	4	no	—
57	C₂×#10625325	—	2	2	no	—
58	C₂×#10625325	—	2	2	no	—
59	C₂×#10625325	—	2	4	no	—
60	C₂×D₃₇₆	—	2	2	no	—
61	C₂×D₃₇₆	—	2	1	no	—
62	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
63	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
64	#13093964	—	2	4	no	—
65	#13093964	—	2	4	no	—
66	C₂×C₄₇⋊C₁₆	—	2	2	no	—
67	C₂×C₄₇⋊C₁₆	—	2	2	no	—
68	C₂×C₄₇⋊C₁₆	C₂³	1	4	yes	complemented
69	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	4	no	—
72	C₂×M₁₆×C₄₇	—	4	1	no	—
73	C₂×M₁₆×C₄₇	—	4	2	no	—
74	C₂²×C₈×C₄₇	—	4	1	no	—
75	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
78	C₂²×C₈×C₄₇	D₄	1	2	yes	—
79	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	D₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
85	#108×C₄₇	—	2	2	no	—
86	#108×C₄₇	—	2	4	no	—
87	#108×C₄₇	C₂³	1	4	yes	complemented
88	C₂⁴×C₄₇	SD₁₆	1	1	yes	characteristic
89	C₂³×D₄₇	—	4	1	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	D₈	1	2	yes	—
96	C₂²×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₄₇	—	4	2	no	—
101	C₂×C₂²⋊D₄₇	—	4	4	no	—
102	C₂×C₂²⋊D₄₇	—	4	2	no	—
103	C₂×C₂²⋊D₄₇	—	4	4	no	—
104	C₂²×Dic₄₇	—	4	1	no	—
105	#10625350	—	2	4	no	—
106	#10625350	—	2	8	no	—
107	#10625350	—	2	4	no	—
108	#10625350	—	4	4	no	—
109	#10625350	—	4	4	no	—
110	#10625350	—	4	4	no	—
111	#10625350	—	4	4	no	—
112	#10625350	—	4	2	no	—
113	#10625350	—	4	2	no	—
114	#10625350	—	4	4	no	—
115	C₂×D₁₈₈	—	2	4	no	—
116	C₂×D₁₈₈	—	2	2	no	—
117	C₂×D₁₈₈	—	4	2	no	—
118	C₂×D₁₈₈	—	4	1	no	—
119	C₂×C₄×D₄₇	—	4	4	no	—
120	C₂×C₄×D₄₇	—	4	2	no	—
121	C₂×C₄×D₄₇	—	4	4	no	—
122	C₂×C₄×D₄₇	—	4	2	no	—
123	C₂×Dic₉₄	—	2	4	no	—
124	C₂×Dic₉₄	—	2	2	no	—
125	C₂×Dic₉₄	—	4	2	no	—
126	C₂×Dic₉₄	—	4	1	no	—
127	M₁₆×C₄₇	—	2	4	no	—
128	M₁₆×C₄₇	—	4	4	no	—
129	M₁₆×C₄₇	—	4	2	no	—
130	C₂×C₈×C₄₇	—	4	4	no	—
131	C₂×C₈×C₄₇	—	4	2	no	—
132	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
135	C₂×C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
137	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
150	Dic₁₈₈	—	2	2	no	—
151	Dic₁₈₈	—	2	4	no	—
152	Dic₁₈₈	C₂²×C₄	1	4	yes	—
153	D₃₇₆	—	2	2	no	—
154	D₃₇₆	—	2	4	no	—
155	D₃₇₆	C₂²×C₄	1	4	yes	—
156	#10625325	—	2	4	no	—
157	#10625325	—	2	8	no	—
158	#10625325	—	2	4	no	—
159	C₄₇⋊C₁₆	—	2	4	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	#102	1	1	yes	characteristic
162	C₂³×C₄₇	#102	1	1	yes	characteristic
163	C₂³×C₄₇	#102	1	2	yes	—
164	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
165	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
166	C₂²×D₄₇	—	4	4	no	—
167	C₂²×D₄₇	—	4	2	no	—
168	C₂²×D₄₇	—	8	4	no	—
169	C₂×C₄×C₄₇	#102	1	2	yes	—
170	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#102	1	2	yes	—
172	C₂×C₄×C₄₇	#102	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#102	1	2	yes	—
174	C₂×C₄×C₄₇	#102	1	2	yes	—
175	C₂×C₄×C₄₇	#102	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₂²⋊D₄₇	—	4	4	no	—
188	C₂²⋊D₄₇	—	4	8	no	—
189	C₂²⋊D₄₇	—	4	4	no	—
190	C₂×Dic₄₇	—	4	4	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	D₁₈₈	—	2	4	no	—
193	D₁₈₈	—	4	4	no	—
194	D₁₈₈	—	4	2	no	—
195	C₄×D₄₇	—	4	4	no	—
196	C₄×D₄₇	—	4	8	no	—
197	C₄×D₄₇	—	4	4	no	—
198	Dic₉₄	—	2	4	no	—
199	Dic₉₄	—	4	4	no	—
200	Dic₉₄	—	4	2	no	—
201	C₈×C₄₇	—	4	4	no	—
202	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
204	C₈×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₈×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
206	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
207	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×#2143	—	47	1	no	maximal, Sylow
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	2	2	no	—
212	C₂²×C₄₇	—	4	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	C₂×#102	1	2	yes	—
215	C₂²×C₄₇	C₂×#102	1	2	yes	—
216	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
218	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂×D₄₇	—	4	4	no	—
220	C₂×D₄₇	—	8	8	no	—
221	C₂×D₄₇	—	8	4	no	—
222	C₄×C₄₇	C₂×#102	1	2	yes	—
223	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
224	C₄×C₄₇	C₂×#102	1	2	yes	—
225	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
226	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
227	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
228	Dic₄₇	—	4	4	no	—
229	C₂²×#135	—	47	1	no	—
230	C₂²×M₃₂	—	47	1	no	—
231	C₂²×#108	D₄₇	1	1	yes	characteristic, complemented
232	#2143	—	47	8	no	—
233	C₂×#359	—	47	4	no	—
234	C₂×C₄₇	—	2	2	no	—
235	C₂×C₄₇	—	2	1	no	—
236	C₂×C₄₇	—	2	2	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	#2143	1	2	yes	complemented
239	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
240	D₄₇	—	8	4	no	—
241	C₂²×#41	—	94	1	no	—
242	C₂×#135	—	47	2	no	—
243	C₂×#135	—	47	4	no	—
244	C₂×#135	—	47	2	no	—
245	C₂×#135	—	47	4	no	—
246	C₂×#135	—	94	1	no	—
247	C₂×#135	—	94	2	no	—
248	C₂×#135	—	94	2	no	—
249	C₂×#135	—	94	1	no	—
250	C₂²×Q₁₆	—	47	1	no	—
251	C₂²×SD₁₆	—	94	1	no	—
252	C₂²×D₈	—	47	1	no	—
253	C₂²×M₁₆	—	2	1	no	—
254	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
255	C₂×M₃₂	—	47	4	no	—
256	C₂×M₃₂	—	94	1	no	—
257	C₂×M₃₂	—	94	1	no	—
258	C₂×M₃₂	—	94	2	no	—
259	C₂²×C₁₆	—	47	2	no	—
260	C₂×#108	—	2	2	no	—
261	C₂×#108	—	2	1	no	—
262	C₂×#108	C₂×D₄₇	1	2	yes	complemented
263	C₂×#108	C₂×D₄₇	1	4	yes	complemented
264	#359	—	47	16	no	—
265	C₄₇	C₂×#2143	1	1	yes	characteristic, complemented, Sylow
266	C₂×#41	—	94	2	no	—
267	C₂×#41	—	94	4	no	—
268	C₂×#41	—	94	4	no	—
269	C₂×#41	—	94	2	no	—
270	C₂×#41	—	188	2	no	—
271	C₂×#41	—	188	1	no	—
272	C₂×#41	—	188	1	no	—
273	C₂×#41	—	188	2	no	—
274	C₂²×Q₈	—	94	1	no	—
275	C₂²×D₄	—	94	1	no	—
276	C₂²×D₄	—	188	1	no	—
277	C₂³×C₄	—	188	1	no	—
278	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
279	#135	—	47	4	no	—
280	#135	—	47	8	no	—
281	#135	—	47	4	no	—
282	#135	—	94	4	no	—
283	#135	—	94	4	no	—
284	#135	—	94	4	no	—
285	#135	—	94	2	no	—
286	#135	—	94	4	no	—
287	#135	—	94	2	no	—
288	#135	—	94	4	no	—
289	C₂×Q₁₆	—	47	2	no	—
290	C₂×Q₁₆	—	47	4	no	—
291	C₂×Q₁₆	—	94	2	no	—
292	C₂×Q₁₆	—	94	1	no	—
293	C₂×SD₁₆	—	94	4	no	—
294	C₂×SD₁₆	—	94	2	no	—
295	C₂×SD₁₆	—	94	2	no	—
296	C₂×SD₁₆	—	94	4	no	—
297	C₂×D₈	—	47	2	no	—
298	C₂×D₈	—	47	4	no	—
299	C₂×D₈	—	94	2	no	—
300	C₂×D₈	—	94	1	no	—
301	C₂×M₁₆	—	2	4	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	4	2	no	—
304	C₂×M₁₆	—	4	1	no	—
305	C₂²×C₈	—	4	1	no	—
306	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₈	C₄×D₄₇	1	2	yes	—
309	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
310	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
311	C₂²×C₈	D₁₈₈	1	2	yes	—
312	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
313	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
314	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
316	M₃₂	—	94	4	no	—
317	M₃₂	—	94	4	no	—
318	C₂×C₁₆	—	47	4	no	—
319	C₂×C₁₆	—	94	2	no	—
320	C₂×C₁₆	—	94	2	no	—
321	#108	—	2	2	no	—
322	#108	—	2	4	no	—
323	#108	C₂²×D₄₇	1	4	yes	complemented
324	C₂⁴	—	188	1	no	—
325	C₂⁴	#10625336	1	1	yes	characteristic
326	#41	—	94	8	no	—
327	#41	—	94	4	no	—
328	#41	—	94	4	no	—
329	#41	—	188	4	no	—
330	#41	—	188	4	no	—
331	#41	—	188	4	no	—
332	#41	—	188	4	no	—
333	#41	—	188	2	no	—
334	#41	—	188	4	no	—
335	#41	—	188	2	no	—
336	C₂×Q₈	—	94	4	no	—
337	C₂×Q₈	—	94	2	no	—
338	C₂×Q₈	—	188	2	no	—
339	C₂×Q₈	—	188	1	no	—
340	C₂×D₄	—	94	4	no	—
341	C₂×D₄	—	94	2	no	—
342	C₂×D₄	—	188	2	no	—
343	C₂×D₄	—	188	4	no	—
344	C₂×D₄	—	188	2	no	—
345	C₂×D₄	—	188	4	no	—
346	C₂×D₄	—	188	2	no	—
347	C₂×D₄	—	188	1	no	—
348	C₂²×C₄	—	188	1	no	—
349	C₂²×C₄	—	188	4	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	—	188	4	no	—
352	C₂²×C₄	—	188	2	no	—
353	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
356	C₂²×C₄	#10625334	1	2	yes	—
357	C₂²×C₄	#10625334	1	1	yes	characteristic
358	C₂²×C₄	#10625334	1	1	yes	characteristic
359	C₂²×C₄	#10625336	1	1	yes	characteristic
360	C₂²×C₄	#10625336	1	2	yes	—
361	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
363	Q₁₆	—	47	4	no	—
364	Q₁₆	—	94	2	no	—
365	Q₁₆	—	94	4	no	—
366	SD₁₆	—	94	4	no	—
367	SD₁₆	—	94	8	no	—
368	SD₁₆	—	94	4	no	—
369	D₈	—	47	4	no	—
370	D₈	—	94	2	no	—
371	D₈	—	94	4	no	—
372	M₁₆	—	2	4	no	—
373	M₁₆	—	4	4	no	—
374	M₁₆	—	4	2	no	—
375	C₂×C₈	—	4	4	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
378	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
379	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
380	C₂×C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
381	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
382	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
383	C₂×C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
384	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
386	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
388	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
389	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
390	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
391	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
392	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
394	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
395	C₁₆	—	94	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	376	4	no	—
398	C₂³	—	188	4	no	—
399	C₂³	—	188	2	no	—
400	C₂³	#13093944	1	1	yes	characteristic
401	C₂³	#13093944	1	1	yes	characteristic
402	C₂³	#13093944	1	2	yes	—
403	C₂³	C₂×#10625336	1	1	yes	characteristic
404	C₂³	C₂×#10625336	1	2	yes	—
405	Q₈	—	94	4	no	—
406	Q₈	—	188	4	no	—
407	Q₈	—	188	2	no	—
408	D₄	—	94	4	no	—
409	D₄	—	188	8	no	—
410	D₄	—	188	4	no	—
411	D₄	—	188	4	no	—
412	D₄	—	188	4	no	—
413	D₄	—	188	2	no	—
414	C₂×C₄	—	188	4	no	—
415	C₂×C₄	—	188	2	no	—
416	C₂×C₄	—	188	8	no	—
417	C₂×C₄	—	188	4	no	—
418	C₂×C₄	—	188	4	no	—
419	C₂×C₄	#13093944	1	1	yes	characteristic
420	C₂×C₄	#13093944	1	2	yes	—
421	C₂×C₄	#13093944	1	2	yes	—
422	C₂×C₄	#13093944	1	1	yes	characteristic
423	C₂×C₄	#13093944	1	2	yes	—
424	C₂×C₄	#13093944	1	2	yes	—
425	C₂×C₄	#13093944	1	2	yes	—
426	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
427	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
428	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
429	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
430	C₂×C₄	C₂×#10625334	1	2	yes	—
431	C₂×C₄	C₂×#10625334	1	2	yes	—
432	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
434	C₂×C₄	C₂×#10625336	1	2	yes	—
435	C₂×C₄	C₂×#10625336	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
437	C₈	—	4	4	no	—
438	C₈	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
439	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
440	C₈	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
441	C₈	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
442	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
443	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	376	8	no	—
450	C₂²	—	376	4	no	—
451	C₂²	—	188	4	no	—
452	C₂²	C₂×#13093944	1	2	yes	—
453	C₂²	C₂×#13093944	1	2	yes	—
454	C₂²	C₂×#13093944	1	1	yes	characteristic
455	C₂²	C₂×#13093944	1	1	yes	characteristic
456	C₂²	C₂²×#10625336	1	1	yes	characteristic
457	C₄	—	188	4	no	—
458	C₄	C₂×#13093944	1	2	yes	—
459	C₄	C₂×#13093944	1	1	yes	characteristic
460	C₄	C₂×#13093944	1	2	yes	—
461	C₄	C₂×#13093944	1	1	yes	characteristic
462	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
463	C₄	C₂²×#10625334	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	2	2	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	376	4	no	—
469	C₂	#20245115	1	2	yes	direct product factor
470	C₂	C₂²×#13093944	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#10625334
commutator	C₈×C₄₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂²×#108×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#102
prime radical	C₂²×#13094046	C₂
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂²×#108	D₄₇
hypocenter	C₄₇	C₂×#2143
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093964	C₂	semidirect
3. #20245115	C₂	direct (N × H)
4. C₂×#15688929	C₂	semidirect
5. C₂²×#108×C₄₇	C₂	semidirect
21. C₂×#13093964	C₂²	semidirect
22. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
23. #15688929	C₂²	semidirect
28. C₂×#108×C₄₇	C₂²	semidirect
29. C₂×#108×C₄₇	C₂²	semidirect
68. C₂×C₄₇⋊C₁₆	C₂³	semidirect
87. #108×C₄₇	C₂³	semidirect
231. C₂²×#108	D₄₇	semidirect
238. C₂×C₄₇	#2143	semidirect
262. C₂×#108	C₂×D₄₇	semidirect
263. C₂×#108	C₂×D₄₇	semidirect
265. C₄₇	C₂×#2143	semidirect
323. #108	C₂²×D₄₇	semidirect
469. C₂	#20245115	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×#13094046	2
C₂²×#13093964	2
#20245115	2
C₂×#15688929	2
C₂²×#108×C₄₇	2
C₂×#2143	47

Subgroups — C2×#20245115 #26369205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245115 #26369205