Subgroups — C₂×#20252272 #27080442

Order 12032.

2806 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689606	C₂	1	2	yes	maximal, complemented
2	#20252272	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689235	C₂	1	2	yes	maximal, complemented
4	C₂×#15689230	C₂	1	2	yes	maximal, complemented
5	C₂×SD₁₆×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689124	C₂	1	2	yes	maximal, complemented
8	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#15689606	—	2	8	no	—
12	#15689606	C₂²	1	16	yes	complemented
13	C₂×Q₈×Dic₄₇	C₂²	1	4	yes	—
14	C₂×D₄×Dic₄₇	—	2	4	no	—
15	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
16	C₂×#13093983	—	2	2	no	—
17	C₂×#13093983	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
19	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
20	#15689235	C₂²	1	16	yes	complemented
21	#15689230	C₂²	1	16	yes	complemented
22	SD₁₆×Dic₄₇	C₂²	1	32	yes	complemented
23	C₂×#13093956	C₂²	1	2	yes	—
24	C₂×#13093956	C₂²	1	2	yes	—
25	C₂×#13093956	C₂²	1	8	yes	complemented
26	#15689124	C₂²	1	16	yes	complemented
27	C₂×#13093948	C₂²	1	4	yes	—
28	C₂×#13093945	C₂²	1	4	yes	—
29	#15689078	C₂²	1	8	yes	complemented
30	C₂×#13093934	C₂²	1	2	yes	—
31	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
32	C₂²×#41×C₄₇	C₂²	1	2	yes	—
33	C₂×#135×C₄₇	C₄	1	16	yes	complemented
34	C₂×#135×C₄₇	C₂²	1	8	yes	—
35	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
37	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂³×Dic₄₇	—	2	2	no	—
40	C₂³×Dic₄₇	—	2	4	no	—
41	C₂×#10625329	—	2	4	no	—
42	C₂×#10625329	C₂³	1	4	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	Q₈×Dic₄₇	—	2	8	no	—
45	Q₈×Dic₄₇	C₂³	1	16	yes	—
46	D₄×Dic₄₇	—	2	32	no	—
47	D₄×Dic₄₇	—	2	8	no	—
48	D₄×Dic₄₇	C₂³	1	16	yes	—
49	#13093983	—	2	16	no	—
50	#13093983	D₄	1	4	yes	—
51	#13093983	C₂³	1	4	yes	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	—	2	4	no	—
54	C₂×C₄⋊Dic₄₇	—	2	4	no	—
55	C₂×C₄⋊Dic₄₇	—	2	16	no	—
56	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
59	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
60	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
61	C₂×C₄×Dic₄₇	—	2	4	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	#13093956	C₂³	1	8	yes	—
64	#13093956	C₂³	1	8	yes	—
65	#13093948	C₂³	1	16	yes	—
66	#13093945	C₂³	1	16	yes	—
67	#13093934	C₂³	1	8	yes	—
68	C₈×Dic₄₇	C₂³	1	8	yes	—
69	C₂×#41×C₄₇	—	2	4	no	—
70	C₂×#41×C₄₇	—	2	8	no	—
71	C₂×#41×C₄₇	C₂×C₄	1	16	yes	complemented
72	C₂×#41×C₄₇	C₂³	1	8	yes	—
73	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
74	C₂²×D₄×C₄₇	—	2	2	no	—
75	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	—	2	2	no	—
77	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	#135×C₄₇	C₂×C₄	1	64	yes	complemented
79	C₂×Q₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
80	C₂×Q₁₆×C₄₇	C₂³	1	4	yes	—
81	C₂×SD₁₆×C₄₇	C₂×C₄	1	16	yes	complemented
82	C₂×SD₁₆×C₄₇	C₂³	1	8	yes	—
83	C₂×D₈×C₄₇	C₂×C₄	1	8	yes	complemented
84	C₂×D₈×C₄₇	C₂³	1	4	yes	—
85	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
89	C₂⁴×C₄₇	—	2	2	no	—
90	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
91	#41×C₄₇	—	2	32	no	—
92	#41×C₄₇	—	2	16	no	—
93	#41×C₄₇	C₂²×C₄	1	32	yes	complemented
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	8	yes	—
97	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
98	C₂×D₄×C₄₇	—	2	16	no	—
99	C₂×D₄×C₄₇	—	2	8	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
103	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	16	no	—
106	C₂²×C₄×C₄₇	—	2	8	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	#41	1	4	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
113	C₂²×Dic₄₇	—	2	4	no	—
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	2	16	no	—
116	C₂²×Dic₄₇	—	8	8	no	—
117	C₂²×Dic₄₇	—	8	4	no	—
118	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
119	Q₁₆×C₄₇	C₂²×C₄	1	16	yes	complemented
120	SD₁₆×C₄₇	C₂²×C₄	1	32	yes	complemented
121	D₈×C₄₇	C₂²×C₄	1	16	yes	complemented
122	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
125	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
126	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
127	C₂²⋊Dic₄₇	—	2	16	no	—
128	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
129	C₄⋊Dic₄₇	—	2	8	no	—
130	C₄⋊Dic₄₇	—	2	4	no	—
131	C₄⋊Dic₄₇	—	2	16	no	—
132	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
133	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
134	C₄×Dic₄₇	—	2	16	no	—
135	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
136	C₄×Dic₄₇	C₂⁴	1	4	yes	—
137	#10625329	—	2	8	no	—
138	C₂×C₄₇⋊C₈	—	2	4	no	—
139	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	8	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	—	4	4	no	—
145	C₂³×C₄₇	C₄×D₄	1	4	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₄₇	—	2	8	no	—
149	Q₈×C₄₇	—	2	4	no	—
150	Q₈×C₄₇	C₂³×C₄	1	8	yes	—
151	D₄×C₄₇	—	2	32	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	C₂³×C₄	1	8	yes	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	32	no	—
158	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
160	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
166	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	8	no	—
168	C₂×Dic₄₇	—	2	8	no	—
169	C₂×Dic₄₇	—	4	8	no	—
170	C₂×Dic₄₇	—	8	16	no	—
171	C₂×Dic₄₇	—	8	8	no	—
172	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
173	C₈×C₄₇	C₂³×C₄	1	4	yes	—
174	C₈×C₄₇	C₂³×C₄	1	4	yes	—
175	C₄₇⋊C₈	—	2	4	no	—
176	C₂×#2952	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	8	no	—
180	C₂²×C₄₇	—	4	16	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
184	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
185	C₂²×C₄₇	#577	1	4	yes	—
186	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
187	C₄×C₄₇	—	2	8	no	—
188	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
189	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
190	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
191	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
192	Dic₄₇	—	2	8	no	—
193	Dic₄₇	—	4	8	no	—
194	C₂²×#135	D₄₇	1	1	yes	characteristic
195	C₂×#520	—	47	2	no	—
196	#2952	—	47	16	no	—
197	C₂×#442	—	47	2	no	—
198	C₂×#441	—	47	2	no	—
199	C₂×C₄×SD₁₆	—	47	4	no	—
200	C₂²×#106	—	47	1	no	—
201	C₂×#417	—	47	2	no	—
202	C₂×#405	—	47	1	no	—
203	C₂×C₄₇	—	2	4	no	—
204	C₂×C₄₇	—	4	8	no	—
205	C₂×C₄₇	#2952	1	4	yes	complemented
206	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#577	1	2	yes	—
208	C₂²×#41	C₂×D₄₇	1	2	yes	—
209	C₂×#135	Dic₄₇	1	16	yes	complemented
210	C₂×#135	C₂×D₄₇	1	8	yes	—
211	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
212	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
213	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
214	C₂²×M₁₆	—	47	1	no	—
215	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
216	#520	—	47	16	no	—
217	#520	—	94	8	no	—
218	C₂×C₄×Q₈	—	47	4	no	—
219	C₂×C₄×D₄	—	47	4	no	—
220	C₂×C₄×D₄	—	94	4	no	—
221	C₂×#117	—	47	1	no	—
222	C₂×#117	—	94	2	no	—
223	C₂²×C₄⋊C₄	—	47	2	no	—
224	C₂²×C₄⋊C₄	—	94	2	no	—
225	#442	—	47	16	no	—
226	#441	—	47	16	no	—
227	C₄×SD₁₆	—	47	32	no	—
228	C₂×#106	—	47	2	no	—
229	C₂×#106	—	47	2	no	—
230	C₂×#106	—	47	8	no	—
231	#417	—	47	16	no	—
232	C₂×#103	—	47	4	no	—
233	C₂×#102	—	47	4	no	—
234	#405	—	47	8	no	—
235	C₂×#97	—	47	2	no	—
236	C₂×C₄×C₈	—	47	2	no	—
237	C₄₇	C₂×#2952	1	1	yes	characteristic, complemented, Sylow
238	C₂×#41	—	2	4	no	—
239	C₂×#41	—	2	8	no	—
240	C₂×#41	C₂×Dic₄₇	1	16	yes	complemented
241	C₂×#41	C₂²×D₄₇	1	8	yes	—
242	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	94	4	no	—
247	C₂³×C₄	—	94	2	no	—
248	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
249	#135	C₂×Dic₄₇	1	64	yes	complemented
250	C₂×Q₁₆	C₂×Dic₄₇	1	8	yes	complemented
251	C₂×Q₁₆	C₂²×D₄₇	1	4	yes	—
252	C₂×SD₁₆	C₂×Dic₄₇	1	16	yes	complemented
253	C₂×SD₁₆	C₂²×D₄₇	1	8	yes	—
254	C₂×D₈	C₂×Dic₄₇	1	8	yes	complemented
255	C₂×D₈	C₂²×D₄₇	1	4	yes	—
256	C₂×M₁₆	—	47	4	no	—
257	C₂×M₁₆	—	94	4	no	—
258	C₂²×C₈	—	47	2	no	—
259	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
260	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
263	C₄×Q₈	—	47	16	no	—
264	C₄×Q₈	—	94	8	no	—
265	C₄×D₄	—	47	16	no	—
266	C₄×D₄	—	94	8	no	—
267	C₄×D₄	—	94	32	no	—
268	#117	—	47	4	no	—
269	#117	—	47	4	no	—
270	#117	—	94	16	no	—
271	C₂×C₄⋊C₄	—	47	2	no	—
272	C₂×C₄⋊C₄	—	47	4	no	—
273	C₂×C₄⋊C₄	—	47	8	no	—
274	C₂×C₄⋊C₄	—	94	16	no	—
275	C₂×C₄⋊C₄	—	94	4	no	—
276	C₂×C₄⋊C₄	—	94	2	no	—
277	C₂×C₄⋊C₄	—	94	4	no	—
278	C₂×C₂²⋊C₄	—	47	2	no	—
279	C₂×C₂²⋊C₄	—	94	4	no	—
280	C₂×C₄²	—	47	2	no	—
281	C₂×C₄²	—	94	4	no	—
282	#106	—	47	8	no	—
283	#106	—	47	8	no	—
284	#103	—	47	16	no	—
285	#102	—	47	16	no	—
286	#97	—	47	8	no	—
287	C₄×C₈	—	47	8	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
290	#41	—	2	32	no	—
291	#41	—	2	16	no	—
292	#41	C₂²×Dic₄₇	1	32	yes	complemented
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	C₂²×Dic₄₇	1	8	yes	—
296	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
297	C₂×D₄	—	2	16	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	4	no	—
301	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
302	C₂×D₄	C₂³×D₄₇	1	4	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	16	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	47	4	no	—
307	C₂²×C₄	—	94	16	no	—
308	C₂²×C₄	—	94	8	no	—
309	C₂²×C₄	—	94	4	no	—
310	C₂²×C₄	—	376	8	no	—
311	C₂²×C₄	—	376	4	no	—
312	C₂²×C₄	D₄×D₄₇	1	2	yes	—
313	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	#10625352	1	4	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
316	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
317	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
318	Q₁₆	C₂²×Dic₄₇	1	16	yes	complemented
319	SD₁₆	C₂²×Dic₄₇	1	32	yes	complemented
320	D₈	C₂²×Dic₄₇	1	16	yes	complemented
321	M₁₆	—	94	8	no	—
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	94	4	no	—
324	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
325	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
326	C₂×C₈	C₂²×Dic₄₇	1	16	yes	complemented
327	C₂×C₈	C₂³×D₄₇	1	2	yes	—
328	C₂×C₈	C₂³×D₄₇	1	2	yes	—
329	C₄⋊C₄	—	47	8	no	—
330	C₄⋊C₄	—	47	8	no	—
331	C₄⋊C₄	—	94	16	no	—
332	C₄⋊C₄	—	94	8	no	—
333	C₄⋊C₄	—	94	4	no	—
334	C₂²⋊C₄	—	47	8	no	—
335	C₂²⋊C₄	—	94	16	no	—
336	C₄²	—	47	4	no	—
337	C₄²	—	47	4	no	—
338	C₄²	—	94	16	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	2	8	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	4	no	—
344	C₂³	D₄×Dic₄₇	1	4	yes	—
345	C₂³	C₂×D₄×D₄₇	1	2	yes	—
346	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
347	Q₈	—	2	8	no	—
348	Q₈	—	2	4	no	—
349	Q₈	C₂³×Dic₄₇	1	8	yes	—
350	D₄	—	2	32	no	—
351	D₄	—	2	8	no	—
352	D₄	—	2	4	no	—
353	D₄	C₂³×Dic₄₇	1	8	yes	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	32	no	—
357	C₂×C₄	—	47	8	no	—
358	C₂×C₄	—	94	8	no	—
359	C₂×C₄	—	94	8	no	—
360	C₂×C₄	—	376	16	no	—
361	C₂×C₄	—	376	8	no	—
362	C₂×C₄	—	188	8	no	—
363	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
364	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
365	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
366	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
367	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
369	C₂×C₄	C₂×#10625352	1	2	yes	—
370	C₂×C₄	C₂×#10625352	1	4	yes	—
371	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
372	C₈	—	94	4	no	—
373	C₈	C₂³×Dic₄₇	1	4	yes	—
374	C₈	C₂³×Dic₄₇	1	4	yes	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	16	no	—
381	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
382	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
383	C₂²	#15689930	1	4	yes	—
384	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
385	C₄	—	2	8	no	—
386	C₄	—	94	8	no	—
387	C₄	—	188	8	no	—
388	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
389	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
390	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
391	C₄	C₂²×#10625352	1	1	yes	characteristic
392	C₂	—	2	4	no	—
393	C₂	—	4	8	no	—
394	C₂	#20252272	1	4	yes	direct product factor
395	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
396	C₂	C₂×#15689930	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	C₂×#2952
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#15689606	C₂	semidirect
2. #20252272	C₂	direct (N × H)
3. C₂×#15689235	C₂	semidirect
4. C₂×#15689230	C₂	semidirect
5. C₂×SD₁₆×Dic₄₇	C₂	semidirect
6. C₂²×#13093956	C₂	semidirect
7. C₂×#15689124	C₂	semidirect
8. C₂×#15689078	C₂	semidirect
12. #15689606	C₂²	semidirect
20. #15689235	C₂²	semidirect
21. #15689230	C₂²	semidirect
22. SD₁₆×Dic₄₇	C₂²	semidirect
25. C₂×#13093956	C₂²	semidirect
26. #15689124	C₂²	semidirect
29. #15689078	C₂²	semidirect
33. C₂×#135×C₄₇	C₄	semidirect
71. C₂×#41×C₄₇	C₂×C₄	semidirect
78. #135×C₄₇	C₂×C₄	semidirect
79. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
81. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
83. C₂×D₈×C₄₇	C₂×C₄	semidirect
85. C₂²×C₈×C₄₇	C₂×C₄	semidirect
93. #41×C₄₇	C₂²×C₄	semidirect
119. Q₁₆×C₄₇	C₂²×C₄	semidirect
120. SD₁₆×C₄₇	C₂²×C₄	semidirect
121. D₈×C₄₇	C₂²×C₄	semidirect
124. C₂×C₈×C₄₇	C₂²×C₄	semidirect
205. C₂×C₄₇	#2952	semidirect
209. C₂×#135	Dic₄₇	semidirect
237. C₄₇	C₂×#2952	semidirect
240. C₂×#41	C₂×Dic₄₇	semidirect
249. #135	C₂×Dic₄₇	semidirect
250. C₂×Q₁₆	C₂×Dic₄₇	semidirect
252. C₂×SD₁₆	C₂×Dic₄₇	semidirect
254. C₂×D₈	C₂×Dic₄₇	semidirect
259. C₂²×C₈	C₂×Dic₄₇	semidirect
292. #41	C₂²×Dic₄₇	semidirect
318. Q₁₆	C₂²×Dic₄₇	semidirect
319. SD₁₆	C₂²×Dic₄₇	semidirect
320. D₈	C₂²×Dic₄₇	semidirect
326. C₂×C₈	C₂²×Dic₄₇	semidirect
394. C₂	#20252272	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689606	2
#20252272	2
C₂×#15689235	2
C₂×#15689230	2
C₂×SD₁₆×Dic₄₇	2
C₂²×#13093956	2
C₂×#15689124	2
C₂×#15689078	2
C₂²×#135×C₄₇	2
C₂×#2952	47

Subgroups — C2×#20252272 #27080442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252272 #27080442