Subgroups — C₂×#20245786 #26374565

Order 12032.

3246 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245786	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15688991	C₂	1	2	yes	maximal, complemented
3	C₂×#15688989	C₂	1	2	yes	maximal, complemented
4	C₂×#15688986	C₂	1	2	yes	maximal
5	C₂×#15688983	C₂	1	2	yes	maximal
6	C₂×C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
8	C₂×#15688969	C₂	1	2	yes	maximal, complemented
9	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	4	yes	—
11	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
12	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
13	#15688991	C₂²	1	16	yes	complemented
14	#15688989	C₂²	1	16	yes	complemented
15	#15688986	C₂²	1	16	yes	—
16	#15688983	C₂²	1	16	yes	—
17	C₄×C₄⋊Dic₄₇	C₂²	1	16	yes	complemented
18	C₄×C₂²⋊Dic₄₇	C₂²	1	16	yes	—
19	#15688969	C₂²	1	16	yes	complemented
20	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
21	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
22	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
23	C₂×C₄₇⋊#95	C₂²	1	4	yes	—
24	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₄	1	16	yes	complemented
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	8	yes	—
33	C₂³×Dic₄₇	C₂³	1	8	yes	—
34	C₂×C₄⋊Dic₄₇	—	2	16	no	—
35	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
36	C₂×C₂²⋊Dic₄₇	—	2	16	no	—
37	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
38	C₂×C₄×Dic₄₇	—	2	16	no	—
39	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
40	C₄₇⋊#95	C₂³	1	16	yes	—
41	C₄₇⋊#95	C₂³	1	16	yes	—
42	C₄₇⋊#95	C₂³	1	16	yes	—
43	C₄₇⋊#95	C₂³	1	16	yes	—
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	—	2	8	no	—
46	C₂³×C₄×C₄₇	—	2	8	no	—
47	C₂³×C₄×C₄₇	—	2	8	no	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
57	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	64	yes	complemented
65	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
69	C₂⁴×C₄₇	—	2	4	no	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
72	C₂⁴×C₄₇	#41	1	8	yes	—
73	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
74	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	—	2	32	no	—
76	C₂²×C₄×C₄₇	—	2	16	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	32	no	—
82	C₂²×C₄×C₄₇	—	2	32	no	—
83	C₂²×C₄×C₄₇	—	2	16	no	—
84	C₂²×C₄×C₄₇	—	2	16	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	#41	1	8	yes	—
95	C₂²×C₄×C₄₇	#41	1	8	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
102	C₂²×Dic₄₇	—	2	16	no	—
103	C₂²×Dic₄₇	—	2	16	no	—
104	C₂²×Dic₄₇	—	2	16	no	—
105	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
108	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
109	C₄²×C₄₇	C₂²×C₄	1	16	yes	—
110	C₂²⋊Dic₄₇	—	2	32	no	—
111	C₄⋊Dic₄₇	—	2	32	no	—
112	C₄×Dic₄₇	—	2	32	no	—
113	C₂³×C₄₇	—	2	8	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	32	no	—
116	C₂³×C₄₇	—	2	4	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	#117	1	16	yes	—
119	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
120	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
121	C₂³×C₄₇	C₂×#41	1	8	yes	—
122	C₂³×C₄₇	C₂×#41	1	4	yes	—
123	C₂³×C₄₇	C₂×#41	1	4	yes	—
124	C₂³×C₄₇	C₂×#41	1	4	yes	—
125	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
126	C₂×C₄×C₄₇	—	2	32	no	—
127	C₂×C₄×C₄₇	—	2	8	no	—
128	C₂×C₄×C₄₇	—	2	8	no	—
129	C₂×C₄×C₄₇	—	2	8	no	—
130	C₂×C₄×C₄₇	—	2	8	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	32	no	—
136	C₂×C₄×C₄₇	—	2	32	no	—
137	C₂×C₄×C₄₇	#117	1	16	yes	—
138	C₂×C₄×C₄₇	#117	1	16	yes	—
139	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
141	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
142	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
146	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
147	C₂×Dic₄₇	—	2	16	no	—
148	C₂×Dic₄₇	—	2	16	no	—
149	C₂×Dic₄₇	—	2	16	no	—
150	C₂×Dic₄₇	—	4	32	no	—
151	C₂×#2283	—	47	1	no	maximal, Sylow
152	C₂²×C₄₇	—	2	4	no	—
153	C₂²×C₄₇	—	2	4	no	—
154	C₂²×C₄₇	—	2	16	no	—
155	C₂²×C₄₇	—	2	32	no	—
156	C₂²×C₄₇	C₂×#117	1	8	yes	—
157	C₂²×C₄₇	C₂×#117	1	4	yes	—
158	C₂²×C₄₇	C₂×#117	1	4	yes	—
159	C₂²×C₄₇	C₂×#117	1	4	yes	—
160	C₂²×C₄₇	#529	1	16	yes	—
161	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
162	C₂²×C₄₇	C₂²×#41	1	2	yes	—
163	C₂²×C₄₇	C₂²×#41	1	2	yes	—
164	C₂²×C₄₇	C₂²×#41	1	2	yes	—
165	C₄×C₄₇	—	2	4	no	—
166	C₄×C₄₇	—	2	4	no	—
167	C₄×C₄₇	—	2	4	no	—
168	C₄×C₄₇	—	2	4	no	—
169	C₄×C₄₇	C₂×#117	1	8	yes	—
170	C₄×C₄₇	C₂×#117	1	8	yes	—
171	Dic₄₇	—	4	16	no	—
172	C₂³×C₄²	D₄₇	1	1	yes	characteristic
173	#2283	—	47	16	no	—
174	C₂×#383	—	47	2	no	—
175	C₂×#382	—	47	2	no	—
176	C₂×#381	—	47	2	no	—
177	C₂×#380	—	47	2	no	—
178	C₂×C₄×C₄⋊C₄	—	47	2	no	—
179	C₂×C₄×C₂²⋊C₄	—	47	2	no	—
180	C₂×#376	—	47	2	no	—
181	C₂×C₄₇	—	2	8	no	—
182	C₂×C₄₇	#2283	1	8	yes	complemented
183	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
184	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
185	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
186	C₂×C₄₇	C₂×#529	1	4	yes	—
187	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
188	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
189	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	—	47	4	no	—
191	C₂²×C₂²⋊C₄	—	47	4	no	—
192	C₂²×C₄²	—	47	4	no	—
193	C₂²×C₄²	Dic₄₇	1	16	yes	complemented
194	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
195	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
198	C₂²×C₄²	C₂×D₄₇	1	8	yes	—
199	#383	—	47	16	no	—
200	#382	—	47	16	no	—
201	#381	—	47	16	no	—
202	#380	—	47	16	no	—
203	C₄×C₄⋊C₄	—	47	16	no	—
204	C₄×C₂²⋊C₄	—	47	16	no	—
205	#376	—	47	16	no	—
206	C₂×#95	—	47	4	no	—
207	C₂×#95	—	47	4	no	—
208	C₂×#95	—	47	4	no	—
209	C₂×#95	—	47	4	no	—
210	C₄₇	C₂×#2283	1	1	yes	characteristic, complemented, Sylow
211	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
212	C₂³×C₄	—	2	8	no	—
213	C₂³×C₄	—	2	8	no	—
214	C₂³×C₄	—	2	8	no	—
215	C₂³×C₄	—	47	8	no	—
216	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
217	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
218	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
219	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
220	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
224	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
225	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
226	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
228	C₂×C₄⋊C₄	—	47	16	no	—
229	C₂×C₄⋊C₄	—	94	16	no	—
230	C₂×C₂²⋊C₄	—	47	16	no	—
231	C₂×C₂²⋊C₄	—	94	16	no	—
232	C₂×C₄²	—	47	16	no	—
233	C₂×C₄²	—	94	16	no	—
234	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
235	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
236	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
237	C₂×C₄²	C₂×Dic₄₇	1	8	yes	—
238	C₂×C₄²	C₂×Dic₄₇	1	64	yes	complemented
239	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
240	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
241	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
242	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
243	#95	—	47	16	no	—
244	#95	—	47	16	no	—
245	#95	—	47	16	no	—
246	#95	—	47	16	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	#10625350	1	8	yes	—
250	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
251	C₂⁴	C₂³×D₄₇	1	2	yes	—
252	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
253	C₂²×C₄	—	2	32	no	—
254	C₂²×C₄	—	2	16	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	32	no	—
260	C₂²×C₄	—	2	32	no	—
261	C₂²×C₄	—	2	16	no	—
262	C₂²×C₄	—	2	16	no	—
263	C₂²×C₄	—	47	16	no	—
264	C₂²×C₄	—	94	16	no	—
265	C₂²×C₄	—	94	16	no	—
266	C₂²×C₄	—	94	16	no	—
267	C₂²×C₄	#10625350	1	8	yes	—
268	C₂²×C₄	#10625350	1	8	yes	—
269	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
270	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
271	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
272	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
275	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
276	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
277	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
278	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
279	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
280	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
281	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
282	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
283	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
284	C₄⋊C₄	—	94	32	no	—
285	C₂²⋊C₄	—	94	32	no	—
286	C₄²	—	94	32	no	—
287	C₄²	C₂²×Dic₄₇	1	16	yes	—
288	C₄²	C₂²×Dic₄₇	1	16	yes	—
289	C₄²	C₂²×Dic₄₇	1	16	yes	—
290	C₄²	C₂²×Dic₄₇	1	16	yes	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	32	no	—
294	C₂³	—	2	4	no	—
295	C₂³	—	2	4	no	—
296	C₂³	#13093983	1	16	yes	—
297	C₂³	C₂³×Dic₄₇	1	4	yes	—
298	C₂³	C₂³×Dic₄₇	1	2	yes	—
299	C₂³	C₂×#10625350	1	8	yes	—
300	C₂³	C₂×#10625350	1	4	yes	—
301	C₂³	C₂×#10625350	1	4	yes	—
302	C₂³	C₂×#10625350	1	4	yes	—
303	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
304	C₂×C₄	—	2	32	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	32	no	—
314	C₂×C₄	—	2	32	no	—
315	C₂×C₄	—	94	16	no	—
316	C₂×C₄	—	94	16	no	—
317	C₂×C₄	—	94	16	no	—
318	C₂×C₄	—	188	32	no	—
319	C₂×C₄	#13093983	1	16	yes	—
320	C₂×C₄	#13093983	1	16	yes	—
321	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
322	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
323	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
324	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
325	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
326	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
327	C₂×C₄	C₂×#10625350	1	8	yes	—
328	C₂×C₄	C₂×#10625350	1	8	yes	—
329	C₂²	—	2	32	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	2	16	no	—
333	C₂²	C₂×#13093983	1	8	yes	—
334	C₂²	C₂×#13093983	1	4	yes	—
335	C₂²	C₂×#13093983	1	4	yes	—
336	C₂²	C₂×#13093983	1	4	yes	—
337	C₂²	#15689657	1	16	yes	—
338	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
339	C₂²	C₂²×#10625350	1	2	yes	—
340	C₂²	C₂²×#10625350	1	2	yes	—
341	C₂²	C₂²×#10625350	1	2	yes	—
342	C₄	—	2	4	no	—
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	2	4	no	—
346	C₄	—	188	16	no	—
347	C₄	C₂×#13093983	1	8	yes	—
348	C₄	C₂×#13093983	1	8	yes	—
349	C₂	—	2	8	no	—
350	C₂	#20245786	1	8	yes	direct product factor
351	C₂	C₂²×#13093983	1	1	yes	characteristic
352	C₂	C₂²×#13093983	1	1	yes	characteristic
353	C₂	C₂²×#13093983	1	1	yes	characteristic
354	C₂	C₂×#15689657	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂⁵×C₄₇	C₂³
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×#2283
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. #20245786	C₂	direct (N × H)
2. C₂×#15688991	C₂	semidirect
3. C₂×#15688989	C₂	semidirect
6. C₂×C₄×C₄⋊Dic₄₇	C₂	semidirect
8. C₂×#15688969	C₂	semidirect
13. #15688991	C₂²	semidirect
14. #15688989	C₂²	semidirect
17. C₄×C₄⋊Dic₄₇	C₂²	semidirect
19. #15688969	C₂²	semidirect
27. C₂²×C₄²×C₄₇	C₄	semidirect
64. C₂×C₄²×C₄₇	C₂×C₄	semidirect
182. C₂×C₄₇	#2283	semidirect
193. C₂²×C₄²	Dic₄₇	semidirect
210. C₄₇	C₂×#2283	semidirect
238. C₂×C₄²	C₂×Dic₄₇	semidirect
350. C₂	#20245786	direct (N × H)

Maximal subgroups

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

subgroup	index
#20245786	2
C₂×#15688991	2
C₂×#15688989	2
C₂×#15688986	2
C₂×#15688983	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄×C₂²⋊Dic₄₇	2
C₂×#15688969	2
C₂³×C₄²×C₄₇	2
C₂×#2283	47

Subgroups — C2×#20245786 #26374565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245786 #26374565