Subgroups — C₂×#20246298 #26375574

Order 12032.

4198 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×Dic₄₇	C₂	1	2	yes	maximal
2	#20246298	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689022	C₂	1	2	yes	maximal, complemented
4	C₂×#15688998	C₂	1	4	yes	maximal, complemented
5	C₂×#15688989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688983	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄₇⋊#95	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂⁴×Dic₄₇	C₂²	1	4	yes	—
11	C₂×D₄×Dic₄₇	—	2	16	no	—
12	C₂×D₄×Dic₄₇	C₂²	1	16	yes	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
16	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
17	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
18	#15689022	C₂²	1	16	yes	complemented
19	#15688998	C₂²	1	32	yes	complemented
20	#15688989	C₂²	1	8	yes	complemented
21	#15688983	C₂²	1	16	yes	complemented
22	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
23	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
24	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
25	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
26	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
27	C₂×C₄₇⋊#95	C₂²	1	1	yes	characteristic
28	C₂×C₄₇⋊#95	C₂²	1	16	yes	complemented
29	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₄	1	16	yes	complemented
32	C₂×C₄×D₄×C₄₇	C₂²	1	8	yes	—
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×Dic₄₇	—	2	16	no	—
37	C₂³×Dic₄₇	—	2	16	no	—
38	C₂³×Dic₄₇	—	4	8	no	—
39	C₂³×Dic₄₇	C₂³	1	4	yes	—
40	C₂³×Dic₄₇	C₂³	1	2	yes	—
41	C₂³×Dic₄₇	C₂³	1	16	yes	—
42	C₂³×Dic₄₇	C₂³	1	2	yes	—
43	D₄×Dic₄₇	—	2	64	no	—
44	C₂×C₄⋊Dic₄₇	—	2	8	no	—
45	C₂×C₄⋊Dic₄₇	—	2	8	no	—
46	C₂×C₄⋊Dic₄₇	—	4	8	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
50	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
51	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
52	C₂×C₄×Dic₄₇	—	2	8	no	—
53	C₂×C₄×Dic₄₇	C₂³	1	8	yes	—
54	C₄₇⋊#95	C₂³	1	4	yes	—
55	C₄₇⋊#95	C₂³	1	8	yes	—
56	C₄₇⋊#95	C₂³	1	16	yes	—
57	C₄₇⋊#95	C₂³	1	4	yes	—
58	C₄₇⋊#95	C₂³	1	8	yes	—
59	C₂⁵×C₄₇	C₂³	1	2	yes	—
60	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
61	C₂²×D₄×C₄₇	D₄	1	8	yes	—
62	C₂²×D₄×C₄₇	Q₈	1	8	yes	—
63	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
64	C₂³×C₄×C₄₇	—	4	8	no	—
65	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	complemented
66	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
74	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
75	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
77	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
78	C₂⁴×C₄₇	—	2	8	no	—
79	C₂⁴×C₄₇	—	2	8	no	—
80	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
82	C₂⁴×C₄₇	C₂×Q₈	1	8	yes	—
83	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
84	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
85	C₂×D₄×C₄₇	C₄⋊C₄	1	64	yes	complemented
86	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
87	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	—
88	C₂×D₄×C₄₇	C₂×Q₈	1	16	yes	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	4	32	no	—
93	C₂²×C₄×C₄₇	—	4	16	no	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
99	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
105	C₂²×Dic₄₇	—	2	4	no	—
106	C₂²×Dic₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	8	no	—
109	C₂²×Dic₄₇	—	2	32	no	—
110	C₂²×Dic₄₇	—	2	4	no	—
111	C₂²×Dic₄₇	—	2	8	no	—
112	C₂²×Dic₄₇	—	2	4	no	—
113	C₂²×Dic₄₇	—	2	8	no	—
114	C₂²×Dic₄₇	—	2	32	no	—
115	C₂²×Dic₄₇	—	4	16	no	—
116	C₂²×Dic₄₇	—	4	64	no	—
117	C₂²×Dic₄₇	#41	1	8	yes	—
118	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
119	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
120	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
122	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
123	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
124	C₂²⋊Dic₄₇	—	2	32	no	—
125	C₄⋊Dic₄₇	—	2	16	no	—
126	C₄⋊Dic₄₇	—	2	16	no	—
127	C₄⋊Dic₄₇	—	4	16	no	—
128	C₄×Dic₄₇	—	2	16	no	—
129	C₂³×C₄₇	—	2	16	no	—
130	C₂³×C₄₇	—	2	16	no	—
131	C₂³×C₄₇	—	2	32	no	—
132	C₂³×C₄₇	—	2	32	no	—
133	C₂³×C₄₇	—	2	8	no	—
134	C₂³×C₄₇	—	2	8	no	—
135	C₂³×C₄₇	C₂×C₄⋊C₄	1	32	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
137	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
139	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
140	C₂³×C₄₇	C₂²×Q₈	1	8	yes	—
141	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
142	C₂³×C₄₇	C₂×#41	1	4	yes	—
143	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
144	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
145	D₄×C₄₇	C₂×C₄⋊C₄	1	64	yes	complemented
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	2	8	no	—
148	C₂×C₄×C₄₇	—	2	16	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	4	32	no	—
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	16	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
157	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
160	C₂×Dic₄₇	—	2	16	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	2	4	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	2	8	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	8	no	—
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	8	no	—
169	C₂×Dic₄₇	—	4	64	no	—
170	C₂×Dic₄₇	—	4	8	no	—
171	C₂×Dic₄₇	—	4	16	no	—
172	C₂×Dic₄₇	C₂×#41	1	8	yes	—
173	C₂×#2349	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	64	no	—
175	C₂²×C₄₇	—	2	8	no	—
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	2	16	no	—
178	C₂²×C₄₇	—	2	16	no	—
179	C₂²×C₄₇	C₂²×C₄⋊C₄	1	16	yes	—
180	C₂²×C₄₇	C₂²×C₄⋊C₄	1	4	yes	—
181	C₂²×C₄₇	C₄×#41	1	4	yes	—
182	C₂²×C₄₇	#518	1	4	yes	—
183	C₂²×C₄₇	#546	1	8	yes	—
184	C₂²×C₄₇	#554	1	8	yes	—
185	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
187	C₂²×C₄₇	C₂³×Q₈	1	1	yes	characteristic
188	C₂²×C₄₇	C₂²×#41	1	2	yes	—
189	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	—	2	4	no	—
192	C₄×C₄₇	—	2	8	no	—
193	C₄×C₄₇	C₂²×C₄⋊C₄	1	8	yes	—
194	Dic₄₇	—	2	8	no	—
195	Dic₄₇	—	4	4	no	—
196	Dic₄₇	—	4	8	no	—
197	C₂²×C₄×D₄	—	47	2	no	—
198	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
199	#2349	—	47	16	no	—
200	C₂×#389	—	47	2	no	—
201	C₂×#385	—	47	4	no	—
202	C₂×#382	—	47	1	no	—
203	C₂×#380	—	47	2	no	—
204	C₂×C₄×C₄⋊C₄	—	47	1	no	—
205	C₂²×#95	—	47	2	no	—
206	C₂×C₄₇	—	2	16	no	—
207	C₂×C₄₇	#2349	1	8	yes	complemented
208	C₂×C₄₇	C₂³×C₄⋊C₄	1	1	yes	characteristic
209	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#546	1	2	yes	—
212	C₂×C₄₇	C₂×#554	1	2	yes	—
213	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
214	C₂⁴×C₄	—	47	4	no	—
215	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
216	C₂×C₄×D₄	—	47	16	no	—
217	C₂×C₄×D₄	—	94	16	no	—
218	C₂×C₄×D₄	Dic₄₇	1	16	yes	complemented
219	C₂×C₄×D₄	C₂×D₄₇	1	8	yes	—
220	C₂²×C₄⋊C₄	—	47	2	no	—
221	C₂²×C₄⋊C₄	—	47	2	no	—
222	C₂²×C₄⋊C₄	—	47	4	no	—
223	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
224	C₂²×C₂²⋊C₄	—	47	4	no	—
225	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
226	C₂²×C₄²	—	47	2	no	—
227	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
228	#389	—	47	16	no	—
229	#385	—	47	32	no	—
230	#382	—	47	8	no	—
231	#380	—	47	16	no	—
232	C₄×C₄⋊C₄	—	47	8	no	—
233	C₂×#95	—	47	1	no	—
234	C₂×#95	—	47	2	no	—
235	C₂×#95	—	47	4	no	—
236	C₂×#95	—	47	1	no	—
237	C₂×#95	—	47	2	no	—
238	C₂×#95	—	47	16	no	—
239	C₄₇	C₂×#2349	1	1	yes	characteristic, complemented, Sylow
240	C₂⁵	C₂²×D₄₇	1	2	yes	—
241	C₂²×D₄	Dic₉₄	1	8	yes	—
242	C₂²×D₄	D₁₈₈	1	8	yes	—
243	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
244	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
245	C₂³×C₄	—	4	8	no	—
246	C₂³×C₄	—	47	2	no	—
247	C₂³×C₄	—	47	2	no	—
248	C₂³×C₄	—	47	4	no	—
249	C₂³×C₄	—	47	16	no	—
250	C₂³×C₄	—	94	16	no	—
251	C₂³×C₄	—	94	16	no	—
252	C₂³×C₄	—	188	8	no	—
253	C₂³×C₄	C₂×Dic₄₇	1	16	yes	complemented
254	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
255	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
256	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
257	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
258	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
259	C₄×D₄	—	94	64	no	—
260	C₄×D₄	C₂×Dic₄₇	1	64	yes	complemented
261	C₂×C₄⋊C₄	—	47	8	no	—
262	C₂×C₄⋊C₄	—	47	8	no	—
263	C₂×C₄⋊C₄	—	47	16	no	—
264	C₂×C₄⋊C₄	—	94	8	no	—
265	C₂×C₄⋊C₄	—	94	8	no	—
266	C₂×C₄⋊C₄	—	188	8	no	—
267	C₂×C₄⋊C₄	C₂×Dic₄₇	1	8	yes	complemented
268	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
269	C₂×C₂²⋊C₄	—	47	16	no	—
270	C₂×C₂²⋊C₄	—	94	16	no	—
271	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
272	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
273	C₂×C₄²	—	47	8	no	—
274	C₂×C₄²	—	94	8	no	—
275	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
276	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
277	#95	—	47	4	no	—
278	#95	—	47	8	no	—
279	#95	—	47	16	no	—
280	#95	—	47	4	no	—
281	#95	—	47	8	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	8	no	—
284	C₂⁴	C₂×Dic₉₄	1	8	yes	—
285	C₂⁴	C₂×D₁₈₈	1	8	yes	—
286	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
287	C₂⁴	C₂³×D₄₇	1	4	yes	—
288	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
289	C₂×D₄	C₄⋊Dic₄₇	1	64	yes	complemented
290	C₂×D₄	C₂×Dic₉₄	1	16	yes	—
291	C₂×D₄	C₂×D₁₈₈	1	16	yes	—
292	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	4	32	no	—
297	C₂²×C₄	—	4	16	no	—
298	C₂²×C₄	—	47	8	no	—
299	C₂²×C₄	—	47	4	no	—
300	C₂²×C₄	—	47	8	no	—
301	C₂²×C₄	—	47	4	no	—
302	C₂²×C₄	—	94	32	no	—
303	C₂²×C₄	—	94	4	no	—
304	C₂²×C₄	—	94	4	no	—
305	C₂²×C₄	—	94	4	no	—
306	C₂²×C₄	—	94	8	no	—
307	C₂²×C₄	—	94	32	no	—
308	C₂²×C₄	—	94	4	no	—
309	C₂²×C₄	—	94	8	no	—
310	C₂²×C₄	—	94	4	no	—
311	C₂²×C₄	—	94	8	no	—
312	C₂²×C₄	—	188	16	no	—
313	C₂²×C₄	—	188	64	no	—
314	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
315	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
316	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
317	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
318	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
319	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
320	C₂²×C₄	C₂²×Dic₄₇	1	32	yes	complemented
321	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
322	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
323	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
324	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
325	C₄⋊C₄	—	94	16	no	—
326	C₄⋊C₄	—	94	16	no	—
327	C₄⋊C₄	—	188	16	no	—
328	C₄⋊C₄	C₂²×Dic₄₇	1	16	yes	complemented
329	C₂²⋊C₄	—	94	32	no	—
330	C₂²⋊C₄	C₂²×Dic₄₇	1	32	yes	complemented
331	C₄²	—	94	16	no	—
332	C₄²	C₂²×Dic₄₇	1	16	yes	complemented
333	C₂³	—	2	32	no	—
334	C₂³	—	2	32	no	—
335	C₂³	—	2	16	no	—
336	C₂³	—	2	16	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	8	no	—
339	C₂³	C₂×C₄⋊Dic₄₇	1	32	yes	—
340	C₂³	C₂³×Dic₄₇	1	8	yes	—
341	C₂³	C₂³×Dic₄₇	1	2	yes	—
342	C₂³	C₂²×D₁₈₈	1	8	yes	—
343	C₂³	C₂²×D₁₈₈	1	2	yes	—
344	C₂³	C₂²×Dic₉₄	1	8	yes	—
345	C₂³	C₂²×Dic₉₄	1	2	yes	—
346	C₂³	#41×D₄₇	1	4	yes	—
347	C₂³	#13094069	1	4	yes	—
348	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
349	D₄	C₂×C₄⋊Dic₄₇	1	64	yes	complemented
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	32	no	—
357	C₂×C₄	—	47	8	no	—
358	C₂×C₄	—	94	16	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	94	8	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	8	no	—
365	C₂×C₄	—	94	4	no	—
366	C₂×C₄	—	94	8	no	—
367	C₂×C₄	—	188	64	no	—
368	C₂×C₄	—	188	8	no	—
369	C₂×C₄	—	188	16	no	—
370	C₂×C₄	C₂×C₄⋊Dic₄₇	1	16	yes	—
371	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
372	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
373	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
374	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
375	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
376	C₂×C₄	C₂²×Dic₉₄	1	4	yes	—
377	C₂²	—	2	64	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	16	no	—
381	C₂²	—	2	16	no	—
382	C₂²	C₂²×C₄⋊Dic₄₇	1	16	yes	—
383	C₂²	C₂²×C₄⋊Dic₄₇	1	4	yes	—
384	C₂²	#41×Dic₄₇	1	4	yes	—
385	C₂²	#15689598	1	4	yes	—
386	C₂²	#15689768	1	8	yes	—
387	C₂²	#15689832	1	8	yes	—
388	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
389	C₂²	C₂³×D₁₈₈	1	1	yes	characteristic
390	C₂²	C₂³×Dic₉₄	1	1	yes	characteristic
391	C₂²	C₂×#41×D₄₇	1	2	yes	—
392	C₂²	C₂×#13094069	1	2	yes	—
393	C₄	—	2	4	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	8	no	—
396	C₄	—	94	8	no	—
397	C₄	—	188	8	no	—
398	C₄	—	188	4	no	—
399	C₄	C₂²×C₄⋊Dic₄₇	1	8	yes	—
400	C₂	—	2	16	no	—
401	C₂	#20246298	1	8	yes	direct product factor
402	C₂	C₂³×C₄⋊Dic₄₇	1	1	yes	characteristic
403	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
404	C₂	C₂×#15689598	1	1	yes	characteristic
405	C₂	C₂×#15689768	1	2	yes	—
406	C₂	C₂×#15689832	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂×#2349
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #20246298	C₂	direct (N × H)
3. C₂×#15689022	C₂	semidirect
4. C₂×#15688998	C₂	semidirect
5. C₂×#15688989	C₂	semidirect
6. C₂×#15688983	C₂	semidirect
7. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
8. C₂²×C₄₇⋊#95	C₂	semidirect
18. #15689022	C₂²	semidirect
19. #15688998	C₂²	semidirect
20. #15688989	C₂²	semidirect
21. #15688983	C₂²	semidirect
22. C₄×C₄⋊Dic₄₇	C₂²	semidirect
28. C₂×C₄₇⋊#95	C₂²	semidirect
31. C₂×C₄×D₄×C₄₇	C₄	semidirect
65. C₂³×C₄×C₄₇	C₂×C₄	semidirect
71. C₄×D₄×C₄₇	C₂×C₄	semidirect
72. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
74. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
76. C₂×C₄²×C₄₇	C₂×C₄	semidirect
85. C₂×D₄×C₄₇	C₄⋊C₄	semidirect
98. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
121. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
122. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
123. C₄²×C₄₇	C₂²×C₄	semidirect
145. D₄×C₄₇	C₂×C₄⋊C₄	semidirect
207. C₂×C₄₇	#2349	semidirect
218. C₂×C₄×D₄	Dic₄₇	semidirect
239. C₄₇	C₂×#2349	semidirect
253. C₂³×C₄	C₂×Dic₄₇	semidirect
260. C₄×D₄	C₂×Dic₄₇	semidirect
267. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
271. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
275. C₂×C₄²	C₂×Dic₄₇	semidirect
289. C₂×D₄	C₄⋊Dic₄₇	semidirect
320. C₂²×C₄	C₂²×Dic₄₇	semidirect
328. C₄⋊C₄	C₂²×Dic₄₇	semidirect
330. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
332. C₄²	C₂²×Dic₄₇	semidirect
349. D₄	C₂×C₄⋊Dic₄₇	semidirect
401. C₂	#20246298	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×D₄×Dic₄₇	2
#20246298	2
C₂×#15689022	2
C₂×#15688998	2
C₂×#15688989	2
C₂×#15688983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂²×C₄₇⋊#95	2
C₂²×C₄×D₄×C₄₇	2
C₂×#2349	47

Subgroups — C2×#20246298 #26375574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20246298 #26375574