Subgroups — C₂×#20243447 #26215952

Order 12032.

1374 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689124	C₂	1	2	yes	maximal
4	#20243447	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688891	C₂	1	2	yes	maximal, complemented
6	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂×#13093960	—	2	4	no	—
10	C₂×#13093960	C₂²	1	4	yes	complemented
11	C₂×#13093956	—	2	1	no	—
12	C₂×#13093956	—	2	1	no	—
13	C₂×#13093956	—	2	2	no	—
14	C₂×#13093956	C₂²	1	4	yes	complemented
15	#15689124	—	2	4	no	—
16	#15689124	C₂²	1	8	yes	—
17	C₂×#13093948	—	2	2	no	—
18	C₂×#13093945	—	2	2	no	—
19	#15688891	C₂²	1	8	yes	complemented
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#131×C₄₇	—	2	4	no	—
22	C₂×#131×C₄₇	—	2	2	no	—
23	C₂×#131×C₄₇	C₄	1	8	yes	complemented
24	C₂×#131×C₄₇	C₂²	1	4	yes	—
25	C₂²×M₁₆×C₄₇	—	2	1	no	—
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₄₇	—	2	1	no	—
28	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×Dic₄₇	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	4	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	C₂³	1	4	yes	—
34	C₂²×C₄₇⋊C₈	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
41	#13093960	—	2	8	no	—
42	#13093956	—	2	4	no	—
43	#13093956	—	2	4	no	—
44	#13093948	—	2	8	no	—
45	#13093945	—	2	8	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	1	no	—
48	C₂×#41×C₄₇	—	2	1	no	—
49	C₂×#41×C₄₇	—	2	2	no	—
50	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
51	C₂×#41×C₄₇	D₄	1	2	yes	—
52	C₂×#41×C₄₇	Q₈	1	4	yes	—
53	C₂×#41×C₄₇	C₂³	1	2	yes	—
54	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
55	C₂²×D₄×C₄₇	—	2	1	no	—
56	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	—	2	1	no	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	#131×C₄₇	—	2	16	no	—
60	#131×C₄₇	—	2	8	no	—
61	#131×C₄₇	C₂×C₄	1	16	yes	complemented
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	1	no	—
64	C₂×M₁₆×C₄₇	—	2	8	no	—
65	C₂×M₁₆×C₄₇	—	2	4	no	—
66	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
67	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₇	—	2	1	no	—
69	C₂²×C₈×C₄₇	—	2	8	no	—
70	C₂²×C₈×C₄₇	—	2	4	no	—
71	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
72	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	D₄	1	2	yes	—
75	C₂²×C₈×C₄₇	D₄	1	4	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂⁴×C₄₇	—	2	1	no	—
78	C₂⁴×C₄₇	#41	1	1	yes	characteristic
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	—	2	4	no	—
84	#41×C₄₇	—	2	2	no	—
85	#41×C₄₇	—	2	2	no	—
86	#41×C₄₇	C₄⋊C₄	1	8	yes	—
87	#41×C₄₇	C₂²×C₄	1	4	yes	—
88	#41×C₄₇	C₂×Q₈	1	4	yes	—
89	C₂×Q₈×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
92	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₄₇	—	2	4	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	4	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	2	4	no	—
117	C₂²×Dic₄₇	—	4	2	no	—
118	C₂²×Dic₄₇	—	4	2	no	—
119	C₂²×Dic₄₇	—	8	4	no	—
120	M₁₆×C₄₇	—	2	4	no	—
121	M₁₆×C₄₇	—	2	2	no	—
122	M₁₆×C₄₇	—	2	16	no	—
123	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	16	no	—
127	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
128	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
129	C₂×C₈×C₄₇	C₂²⋊C₄	1	8	yes	—
130	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
134	C₄⋊Dic₄₇	—	2	4	no	—
135	C₄⋊Dic₄₇	—	2	4	no	—
136	C₄⋊Dic₄₇	—	4	2	no	—
137	C₄⋊Dic₄₇	—	4	2	no	—
138	#10625329	—	2	4	no	—
139	#10625329	—	2	4	no	—
140	#10625329	—	4	4	no	—
141	C₂×C₄₇⋊C₈	—	2	4	no	—
142	C₂×C₄₇⋊C₈	—	4	4	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	4	4	no	—
147	C₂³×C₄₇	#117	1	2	yes	—
148	C₂³×C₄₇	#121	1	1	yes	characteristic
149	C₂³×C₄₇	#121	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
151	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
152	Q₈×C₄₇	—	2	2	no	—
153	Q₈×C₄₇	—	2	4	no	—
154	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
155	D₄×C₄₇	—	2	4	no	—
156	D₄×C₄₇	—	2	4	no	—
157	D₄×C₄₇	—	2	8	no	—
158	D₄×C₄₇	—	2	2	no	—
159	D₄×C₄₇	—	2	4	no	—
160	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	8	no	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	#117	1	2	yes	—
171	C₂×C₄×C₄₇	#121	1	2	yes	—
172	C₂×C₄×C₄₇	#121	1	2	yes	—
173	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	4	4	no	—
185	C₂×Dic₄₇	—	8	4	no	—
186	C₂×Dic₄₇	—	8	4	no	—
187	C₂×Dic₄₇	—	8	4	no	—
188	C₈×C₄₇	—	2	4	no	—
189	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
190	C₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
191	C₄₇⋊C₈	—	4	4	no	—
192	C₂×#1815	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	2	4	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	4	no	—
198	C₂²×C₄₇	—	4	8	no	—
199	C₂²×C₄₇	—	4	4	no	—
200	C₂²×C₄₇	#380	1	2	yes	—
201	C₂²×C₄₇	#380	1	2	yes	—
202	C₂²×C₄₇	#471	1	4	yes	—
203	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×C₄₇	—	2	4	no	—
207	C₄×C₄₇	#380	1	2	yes	—
208	C₄×C₄₇	#380	1	2	yes	—
209	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
210	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
212	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	Dic₄₇	—	8	4	no	—
214	C₂²×#131	D₄₇	1	1	yes	characteristic
215	C₂²×#108	—	47	1	no	—
216	C₂²×#106	—	47	1	no	—
217	C₂×#417	—	47	2	no	—
218	#1815	—	47	8	no	—
219	C₂×#343	—	47	2	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	1	no	—
222	C₂×C₄₇	—	2	2	no	—
223	C₂×C₄₇	—	4	4	no	—
224	C₂×C₄₇	#1815	1	4	yes	complemented
225	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#471	1	2	yes	—
227	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
228	C₂×#131	—	2	4	no	—
229	C₂×#131	—	2	2	no	—
230	C₂×#131	Dic₄₇	1	8	yes	complemented
231	C₂×#131	C₂×D₄₇	1	4	yes	—
232	C₂²×M₁₆	—	2	1	no	—
233	C₂²×M₁₆	—	47	2	no	—
234	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
235	C₂³×C₈	—	2	1	no	—
236	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	—	47	2	no	—
238	C₂×#108	—	47	4	no	—
239	C₂×#108	—	94	4	no	—
240	C₂×#106	—	47	4	no	—
241	C₂×#106	—	94	1	no	—
242	C₂×#106	—	94	1	no	—
243	C₂×#106	—	94	2	no	—
244	#417	—	47	8	no	—
245	#417	—	94	4	no	—
246	C₂×#103	—	94	2	no	—
247	C₂×#102	—	94	2	no	—
248	#343	—	47	8	no	—
249	C₄₇	C₂×#1815	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	2	no	—
253	C₂×#41	—	2	1	no	—
254	C₂×#41	Dic₉₄	1	4	yes	—
255	C₂×#41	D₁₈₈	1	2	yes	—
256	C₂×#41	C₂×Dic₄₇	1	4	yes	—
257	C₂×#41	C₂²×D₄₇	1	2	yes	—
258	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	94	2	no	—
263	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
264	#131	—	2	16	no	—
265	#131	—	2	8	no	—
266	#131	C₂×Dic₄₇	1	16	yes	complemented
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	—	47	4	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂×M₁₆	—	94	4	no	—
274	C₂×M₁₆	—	94	4	no	—
275	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
276	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	8	no	—
279	C₂²×C₈	—	2	4	no	—
280	C₂²×C₈	—	94	2	no	—
281	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
282	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
285	C₂²×C₈	C₂²⋊D₄₇	1	4	yes	—
286	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	—	47	4	no	—
288	C₂×C₄⋊C₄	—	94	2	no	—
289	C₂×C₄⋊C₄	—	94	2	no	—
290	C₂×C₄⋊C₄	—	94	2	no	—
291	C₂×C₄⋊C₄	—	94	2	no	—
292	C₂×C₄⋊C₄	—	94	2	no	—
293	#108	—	94	8	no	—
294	#106	—	94	4	no	—
295	#106	—	94	4	no	—
296	#103	—	94	8	no	—
297	#102	—	94	8	no	—
298	C₂⁴	—	2	1	no	—
299	C₂⁴	#10625350	1	1	yes	characteristic
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	#41	—	2	4	no	—
305	#41	—	2	2	no	—
306	#41	—	2	2	no	—
307	#41	C₄⋊Dic₄₇	1	8	yes	—
308	#41	C₂×Dic₉₄	1	4	yes	—
309	#41	C₂²×Dic₄₇	1	4	yes	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
313	C₂×Q₈	C₂×D₁₈₈	1	2	yes	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
321	C₂×D₄	C₂×D₁₈₈	1	2	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	94	4	no	—
328	C₂²×C₄	—	376	4	no	—
329	C₂²×C₄	—	188	2	no	—
330	C₂²×C₄	—	188	2	no	—
331	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
332	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
334	C₂²×C₄	#10625350	1	1	yes	characteristic
335	C₂²×C₄	#10625350	1	2	yes	—
336	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
337	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
338	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	2	16	no	—
344	M₁₆	—	94	4	no	—
345	M₁₆	—	94	4	no	—
346	M₁₆	—	188	4	no	—
347	M₁₆	C₂²×Dic₄₇	1	4	yes	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	16	no	—
351	C₂×C₈	—	94	4	no	—
352	C₂×C₈	—	188	4	no	—
353	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
354	C₂×C₈	C₂²⋊Dic₄₇	1	4	yes	—
355	C₂×C₈	C₂²⋊Dic₄₇	1	8	yes	—
356	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
357	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
358	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
359	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
360	C₄⋊C₄	—	94	4	no	—
361	C₄⋊C₄	—	94	4	no	—
362	C₄⋊C₄	—	188	2	no	—
363	C₄⋊C₄	—	188	2	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	4	4	no	—
368	C₂³	#13093983	1	2	yes	—
369	C₂³	#13093998	1	1	yes	characteristic
370	C₂³	#13093998	1	1	yes	characteristic
371	C₂³	#13094003	1	2	yes	—
372	C₂³	C₂×#10625350	1	1	yes	characteristic
373	Q₈	—	2	4	no	—
374	Q₈	—	2	2	no	—
375	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	—
376	D₄	—	2	8	no	—
377	D₄	—	2	4	no	—
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	2	no	—
381	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	376	4	no	—
388	C₂×C₄	—	376	4	no	—
389	C₂×C₄	—	376	4	no	—
390	C₂×C₄	—	188	4	no	—
391	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
393	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
394	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
395	C₂×C₄	#13093983	1	2	yes	—
396	C₂×C₄	#13093998	1	1	yes	characteristic
397	C₂×C₄	#13093998	1	1	yes	characteristic
398	C₂×C₄	#13093998	1	2	yes	—
399	C₂×C₄	#13093998	1	2	yes	—
400	C₂×C₄	#13094003	1	2	yes	—
401	C₂×C₄	#13094003	1	2	yes	—
402	C₂×C₄	#13094003	1	2	yes	—
403	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
407	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
408	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	188	4	no	—
411	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
412	C₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	#15688983	1	2	yes	—
421	C₂²	#15688983	1	2	yes	—
422	C₂²	#15689386	1	4	yes	—
423	C₂²	C₂×#13093983	1	1	yes	characteristic
424	C₂²	C₂×#13093998	1	1	yes	characteristic
425	C₂²	C₂×#13094003	1	1	yes	characteristic
426	C₄	—	2	4	no	—
427	C₄	—	376	4	no	—
428	C₄	#15688983	1	2	yes	—
429	C₄	#15688983	1	2	yes	—
430	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
431	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
432	C₄	C₂×#13093998	1	1	yes	characteristic
433	C₄	C₂×#13094003	1	1	yes	characteristic
434	C₂	—	2	2	no	—
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	4	4	no	—
438	C₂	#20243447	1	4	yes	direct product factor
439	C₂	C₂×#15688983	1	1	yes	characteristic
440	C₂	C₂×#15689386	1	2	yes	—

	subgroup	G/H
center	C₂³	#13093998
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	C₂×#1815
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#13093960	C₂	semidirect
2. C₂²×#13093956	C₂	semidirect
4. #20243447	C₂	direct (N × H)
5. C₂×#15688891	C₂	semidirect
10. C₂×#13093960	C₂²	semidirect
14. C₂×#13093956	C₂²	semidirect
19. #15688891	C₂²	semidirect
23. C₂×#131×C₄₇	C₄	semidirect
61. #131×C₄₇	C₂×C₄	semidirect
224. C₂×C₄₇	#1815	semidirect
230. C₂×#131	Dic₄₇	semidirect
249. C₄₇	C₂×#1815	semidirect
266. #131	C₂×Dic₄₇	semidirect
438. C₂	#20243447	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×#13093956	2
C₂×#15689124	2
#20243447	2
C₂×#15688891	2
C₂²×#131×C₄₇	2
C₂×#1815	47

Subgroups — C2×#20243447 #26215952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243447 #26215952