Subgroups — C₂×#20244277 #26220220

Order 12032.

1558 conjugacy classes of subgroups.

The subgroup lattice has 434 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	C₂²×#13093951	C₂	1	2	yes	maximal, complemented
3	C₂×#15689090	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244277	C₂	1	8	yes	maximal, direct product factor
6	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×#13093960	—	2	4	no	—
11	C₂×#13093960	C₂²	1	4	yes	complemented
12	C₂×#13093951	—	2	8	no	—
13	C₂×#13093951	C₂²	1	8	yes	complemented
14	#15689090	—	2	4	no	—
15	#15689090	C₂²	1	8	yes	complemented
16	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
17	C₂×C₈×Dic₄₇	—	2	4	no	—
18	C₂×C₈×Dic₄₇	C₂²	1	4	yes	complemented
19	C₂²×#41×C₄₇	C₂²	1	2	yes	—
20	C₂×#135×C₄₇	—	2	4	no	—
21	C₂×#135×C₄₇	—	2	4	no	—
22	C₂×#135×C₄₇	C₄	1	4	yes	complemented
23	C₂×#135×C₄₇	C₂²	1	4	yes	—
24	C₂²×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
25	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
26	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
27	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂³×Dic₄₇	—	2	1	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	2	4	no	—
32	C₂×#10625329	C₂³	1	4	yes	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
37	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	1	no	—
41	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
42	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
43	#13093960	—	2	8	no	—
44	#13093951	—	2	16	no	—
45	C₂²⋊(C₄₇⋊C₈)	—	2	16	no	—
46	C₈×Dic₄₇	—	2	8	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	—	2	4	no	—
50	C₂×#41×C₄₇	—	2	4	no	—
51	C₂×#41×C₄₇	—	2	4	no	—
52	C₂×#41×C₄₇	—	2	4	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
54	C₂×#41×C₄₇	C₂³	1	4	yes	—
55	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₄₇	—	2	2	no	—
57	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₄₇	—	2	2	no	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	#135×C₄₇	—	2	16	no	—
61	#135×C₄₇	—	2	8	no	—
62	#135×C₄₇	—	2	8	no	—
63	C₂×Q₁₆×C₄₇	—	2	4	no	—
64	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
65	C₂×SD₁₆×C₄₇	—	2	8	no	—
66	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
67	C₂×D₈×C₄₇	—	2	4	no	—
68	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
69	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	D₄	1	4	yes	—
73	C₂²×C₈×C₄₇	D₄	1	4	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂⁴×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	#41	1	1	yes	characteristic
77	#41×C₄₇	—	2	8	no	—
78	#41×C₄₇	—	2	8	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	#41×C₄₇	—	4	4	no	—
84	#41×C₄₇	—	4	4	no	—
85	#41×C₄₇	—	4	4	no	—
86	#41×C₄₇	—	4	4	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	—	2	4	no	—
90	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	4	no	—
94	C₂×D₄×C₄₇	—	2	4	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	4	4	no	—
97	C₂×D₄×C₄₇	—	4	4	no	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	2	4	no	—
102	C₂²×C₄×C₄₇	—	4	4	no	—
103	C₂²×C₄×C₄₇	—	4	4	no	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	2	4	no	—
116	C₂²×Dic₄₇	—	2	2	no	—
117	Q₁₆×C₄₇	—	2	8	no	—
118	SD₁₆×C₄₇	—	2	16	no	—
119	D₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
127	C₄×Dic₄₇	—	2	4	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
130	#10625329	—	2	4	no	—
131	#10625329	—	2	4	no	—
132	#10625329	—	4	4	no	—
133	C₂×C₄₇⋊C₈	—	2	4	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	4	no	—
138	C₂×C₄₇⋊C₈	—	4	4	no	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	8	no	—
144	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₄₇	#121	1	2	yes	—
147	C₂³×C₄₇	#124	1	2	yes	—
148	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
149	Q₈×C₄₇	—	2	4	no	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	4	4	no	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	4	4	no	—
155	D₄×C₄₇	—	4	4	no	—
156	D₄×C₄₇	—	4	8	no	—
157	D₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	—	4	8	no	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#121	1	2	yes	—
170	C₂×C₄×C₄₇	#121	1	2	yes	—
171	C₂×C₄×C₄₇	#121	1	2	yes	—
172	C₂×C₄×C₄₇	#124	1	2	yes	—
173	C₂×C₄×C₄₇	#127	1	2	yes	—
174	C₂×C₄×C₄₇	#127	1	2	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₇	—	2	8	no	—
182	C₂×Dic₄₇	—	2	16	no	—
183	C₂×Dic₄₇	—	2	4	no	—
184	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
186	C₄₇⋊C₈	—	2	4	no	—
187	C₄₇⋊C₈	—	4	4	no	—
188	C₂×#1974	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	4	8	no	—
194	C₂²×C₄₇	—	4	4	no	—
195	C₂²×C₄₇	—	8	8	no	—
196	C₂²×C₄₇	#390	1	2	yes	—
197	C₂²×C₄₇	#390	1	2	yes	—
198	C₂²×C₄₇	#443	1	4	yes	—
199	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
202	C₄×C₄₇	—	4	4	no	—
203	C₄×C₄₇	#390	1	2	yes	—
204	C₄×C₄₇	#390	1	2	yes	—
205	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
206	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
208	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
209	Dic₄₇	—	2	8	no	—
210	C₂²×#135	D₄₇	1	1	yes	characteristic
211	C₂²×#108	—	47	1	no	—
212	C₂²×#104	—	47	2	no	—
213	C₂×#408	—	47	2	no	—
214	C₂²×C₄×C₈	—	47	1	no	—
215	#1974	—	47	8	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	8	4	no	—
220	C₂×C₄₇	#1974	1	4	yes	complemented
221	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
222	C₂×C₄₇	C₂×#443	1	2	yes	—
223	C₂²×#41	C₂×D₄₇	1	2	yes	—
224	C₂×#135	—	2	4	no	—
225	C₂×#135	—	2	4	no	—
226	C₂×#135	Dic₄₇	1	4	yes	complemented
227	C₂×#135	C₂×D₄₇	1	4	yes	—
228	C₂²×Q₁₆	Dic₄₇	1	1	yes	characteristic, complemented
229	C₂²×SD₁₆	Dic₄₇	1	2	yes	complemented
230	C₂²×D₈	Dic₄₇	1	1	yes	characteristic, complemented
231	C₂²×M₁₆	—	47	2	no	—
232	C₂³×C₈	—	47	1	no	—
233	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂²×C₄²	—	47	1	no	—
235	C₂×#108	—	47	4	no	—
236	C₂×#108	—	94	4	no	—
237	C₂×#104	—	47	8	no	—
238	C₂×#104	—	94	8	no	—
239	#408	—	47	8	no	—
240	#408	—	94	4	no	—
241	C₂×C₂²⋊C₈	—	94	4	no	—
242	C₂×C₄×C₈	—	47	4	no	—
243	C₂×C₄×C₈	—	94	4	no	—
244	C₄₇	C₂×#1974	1	1	yes	characteristic, complemented, Sylow
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	—	2	4	no	—
249	C₂×#41	—	2	4	no	—
250	C₂×#41	—	2	4	no	—
251	C₂×#41	C₂×Dic₄₇	1	4	yes	—
252	C₂×#41	C₂²×D₄₇	1	4	yes	—
253	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	—	94	1	no	—
258	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
259	#135	—	2	16	no	—
260	#135	—	2	8	no	—
261	#135	—	2	8	no	—
262	C₂×Q₁₆	—	2	4	no	—
263	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
264	C₂×SD₁₆	—	2	8	no	—
265	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
266	C₂×D₈	—	2	4	no	—
267	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
268	C₂×M₁₆	—	47	4	no	—
269	C₂×M₁₆	—	94	2	no	—
270	C₂×M₁₆	—	94	4	no	—
271	C₂×M₁₆	—	94	4	no	—
272	C₂²×C₈	—	47	2	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	—	94	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	2	no	—
278	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
279	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
280	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
281	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
282	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
283	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
284	C₂×C₄²	—	47	4	no	—
285	C₂×C₄²	—	47	2	no	—
286	C₂×C₄²	—	94	1	no	—
287	C₂×C₄²	—	94	2	no	—
288	#108	—	94	8	no	—
289	#104	—	94	16	no	—
290	C₂²⋊C₈	—	94	16	no	—
291	C₄×C₈	—	94	8	no	—
292	C₂⁴	—	2	2	no	—
293	C₂⁴	#10625352	1	1	yes	characteristic
294	#41	—	2	8	no	—
295	#41	—	2	8	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	4	4	no	—
301	#41	—	4	4	no	—
302	#41	—	4	4	no	—
303	#41	—	4	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	4	no	—
314	C₂×D₄	—	4	4	no	—
315	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	94	8	no	—
322	C₂²×C₄	—	94	4	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	D₄×D₄₇	1	2	yes	—
325	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	#10625352	1	1	yes	characteristic
328	C₂²×C₄	#10625352	1	2	yes	—
329	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
333	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
334	Q₁₆	—	2	8	no	—
335	SD₁₆	—	2	16	no	—
336	D₈	—	2	8	no	—
337	M₁₆	—	94	4	no	—
338	M₁₆	—	94	4	no	—
339	M₁₆	—	188	4	no	—
340	C₂×C₈	—	47	4	no	—
341	C₂×C₈	—	94	4	no	—
342	C₂×C₈	—	94	4	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	4	no	—
346	C₂×C₈	—	188	4	no	—
347	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
348	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
349	C₂×C₈	C₂²⋊Dic₄₇	1	8	yes	—
350	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
351	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
352	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
353	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
354	C₄²	—	47	4	no	—
355	C₄²	—	94	4	no	—
356	C₄²	—	94	2	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	8	no	—
360	C₂³	—	4	4	no	—
361	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
362	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
363	C₂³	#13093995	1	2	yes	—
364	C₂³	#13094011	1	2	yes	—
365	C₂³	C₂×#10625352	1	1	yes	characteristic
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	4	no	—
369	D₄	—	2	4	no	—
370	D₄	—	2	4	no	—
371	D₄	—	4	8	no	—
372	D₄	—	4	4	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	94	16	no	—
381	C₂×C₄	—	94	8	no	—
382	C₂×C₄	—	94	4	no	—
383	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
384	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
385	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
386	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
387	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
388	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
389	C₂×C₄	#13093995	1	2	yes	—
390	C₂×C₄	#13093995	1	2	yes	—
391	C₂×C₄	#13093995	1	2	yes	—
392	C₂×C₄	#13094011	1	2	yes	—
393	C₂×C₄	#13094020	1	2	yes	—
394	C₂×C₄	#13094020	1	2	yes	—
395	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
401	C₈	—	94	4	no	—
402	C₈	—	188	4	no	—
403	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
404	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	8	8	no	—
412	C₂²	#15689026	1	2	yes	—
413	C₂²	#15689026	1	2	yes	—
414	C₂²	#15689240	1	4	yes	—
415	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
416	C₂²	C₂×#13093995	1	1	yes	characteristic
417	C₂²	C₂×#13094011	1	1	yes	characteristic
418	C₄	—	4	4	no	—
419	C₄	—	94	8	no	—
420	C₄	#15689026	1	2	yes	—
421	C₄	#15689026	1	2	yes	—
422	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
423	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
424	C₄	C₂×#13093995	1	1	yes	characteristic
425	C₄	C₂×#13094020	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	2	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	4	no	—
430	C₂	#20244277	1	4	yes	direct product factor
431	C₂	C₂×#15689026	1	1	yes	characteristic
432	C₂	C₂×#15689240	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	C₂×#1974
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093960	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. C₂×#15689090	C₂	semidirect
4. C₂²×C₈×Dic₄₇	C₂	semidirect
5. #20244277	C₂	direct (N × H)
11. C₂×#13093960	C₂²	semidirect
13. C₂×#13093951	C₂²	semidirect
15. #15689090	C₂²	semidirect
18. C₂×C₈×Dic₄₇	C₂²	semidirect
22. C₂×#135×C₄₇	C₄	semidirect
24. C₂²×Q₁₆×C₄₇	C₄	semidirect
25. C₂²×SD₁₆×C₄₇	C₄	semidirect
26. C₂²×D₈×C₄₇	C₄	semidirect
64. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
66. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
68. C₂×D₈×C₄₇	C₂×C₄	semidirect
220. C₂×C₄₇	#1974	semidirect
226. C₂×#135	Dic₄₇	semidirect
228. C₂²×Q₁₆	Dic₄₇	semidirect
229. C₂²×SD₁₆	Dic₄₇	semidirect
230. C₂²×D₈	Dic₄₇	semidirect
244. C₄₇	C₂×#1974	semidirect
263. C₂×Q₁₆	C₂×Dic₄₇	semidirect
265. C₂×SD₁₆	C₂×Dic₄₇	semidirect
267. C₂×D₈	C₂×Dic₄₇	semidirect
430. C₂	#20244277	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
C₂²×#13093951	2
C₂×#15689090	2
C₂²×C₈×Dic₄₇	2
#20244277	2
C₂²×#135×C₄₇	2
C₂×#1974	47

Subgroups — C2×#20244277 #26220220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244277 #26220220