Subgroups — C₂×#20252240 #27080406

Order 12032.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689598	C₂	1	2	yes	maximal, complemented
2	#20252240	C₂	1	16	yes	maximal, direct product factor
3	C₂×#15689235	C₂	1	4	yes	maximal, complemented
4	C₂×D₈×Dic₄₇	C₂	1	4	yes	maximal, complemented
5	C₂×#15689161	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15689128	C₂	1	2	yes	maximal, complemented
7	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	#15689598	—	2	8	no	—
11	#15689598	C₂²	1	16	yes	complemented
12	C₂×D₄×Dic₄₇	—	2	4	no	—
13	C₂×D₄×Dic₄₇	C₂²	1	8	yes	complemented
14	C₂×#13093983	C₂²	1	2	yes	—
15	C₂×#13093983	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊Dic₄₇	—	2	4	no	—
17	#15689235	C₂²	1	32	yes	complemented
18	D₈×Dic₄₇	C₂²	1	32	yes	complemented
19	#15689161	C₂²	1	8	yes	complemented
20	C₂×#13093958	C₂²	1	2	yes	complemented
21	C₂×#13093956	C₂²	1	2	yes	complemented
22	#15689128	C₂²	1	16	yes	complemented
23	C₂×#13093945	C₂²	1	8	yes	complemented
24	#15689078	C₂²	1	8	yes	complemented
25	C₂×#13093934	C₂²	1	2	yes	complemented
26	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
27	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
28	C₂²×D₈×C₄₇	C₄	1	16	yes	complemented
29	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
30	C₂²×D₈×C₄₇	C₂²	1	8	yes	—
31	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
32	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂³×Dic₄₇	—	2	8	no	—
34	C₂×#10625329	—	2	4	no	—
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
37	D₄×Dic₄₇	—	2	32	no	—
38	D₄×Dic₄₇	—	2	16	no	—
39	D₄×Dic₄₇	C₂³	1	32	yes	complemented
40	#13093983	—	2	4	no	—
41	#13093983	D₄	1	4	yes	—
42	#13093983	C₂³	1	8	yes	—
43	#13093983	C₂³	1	4	yes	—
44	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
46	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
47	C₂×C₂²⋊Dic₄₇	—	2	8	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	32	no	—
49	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
52	#13093958	C₂³	1	8	yes	complemented
53	#13093956	C₂³	1	8	yes	complemented
54	#13093945	C₂³	1	32	yes	complemented
55	#13093934	C₂³	1	8	yes	complemented
56	C₈×Dic₄₇	C₂³	1	8	yes	complemented
57	C₂⁵×C₄₇	—	2	2	no	—
58	C₂²×D₄×C₄₇	—	2	2	no	—
59	C₂²×D₄×C₄₇	—	2	4	no	—
60	C₂²×D₄×C₄₇	—	2	8	no	—
61	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
62	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
63	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×D₈×C₄₇	C₂×C₄	1	16	yes	complemented
66	C₂×D₈×C₄₇	C₂×C₄	1	16	yes	complemented
67	C₂×D₈×C₄₇	C₂×C₄	1	64	yes	complemented
68	C₂×D₈×C₄₇	C₂³	1	8	yes	—
69	C₂×D₈×C₄₇	C₂³	1	8	yes	—
70	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
74	C₂⁴×C₄₇	—	2	4	no	—
75	C₂⁴×C₄₇	—	2	16	no	—
76	C₂⁴×C₄₇	—	2	8	no	—
77	C₂⁴×C₄₇	—	8	8	no	—
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₄₇	—	2	32	no	—
80	C₂×D₄×C₄₇	—	2	16	no	—
81	C₂×D₄×C₄₇	—	2	8	no	—
82	C₂×D₄×C₄₇	—	2	4	no	—
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	16	no	—
85	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
86	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	complemented
87	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	—	2	32	no	—
96	C₂²×Dic₄₇	—	8	16	no	—
97	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
98	D₈×C₄₇	C₂²×C₄	1	32	yes	complemented
99	D₈×C₄₇	C₂²×C₄	1	32	yes	complemented
100	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	complemented
103	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
104	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
105	C₂²⋊Dic₄₇	—	2	8	no	—
106	C₂²⋊Dic₄₇	—	2	32	no	—
107	C₂²⋊Dic₄₇	C₂×D₄	1	8	yes	—
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	C₂×D₄	1	8	yes	—
110	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
111	C₄×Dic₄₇	—	2	8	no	—
112	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
113	C₄×Dic₄₇	C₂⁴	1	4	yes	—
114	#10625329	—	2	8	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	2	16	no	—
119	C₂³×C₄₇	—	2	8	no	—
120	C₂³×C₄₇	—	2	32	no	—
121	C₂³×C₄₇	—	4	16	no	—
122	C₂³×C₄₇	—	8	32	no	—
123	C₂³×C₄₇	—	8	16	no	—
124	C₂³×C₄₇	C₄×D₄	1	4	yes	—
125	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
126	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
127	D₄×C₄₇	—	2	16	no	—
128	D₄×C₄₇	—	2	32	no	—
129	D₄×C₄₇	—	2	8	no	—
130	D₄×C₄₇	C₂³×C₄	1	16	yes	—
131	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
132	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
133	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
134	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
135	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
136	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
139	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
140	C₂×Dic₄₇	—	2	8	no	—
141	C₂×Dic₄₇	—	2	8	no	—
142	C₂×Dic₄₇	—	4	8	no	—
143	C₂×Dic₄₇	—	8	32	no	—
144	C₂×Dic₄₇	C₂²×D₄	1	8	yes	—
145	C₈×C₄₇	C₂³×C₄	1	4	yes	—
146	C₈×C₄₇	C₂³×C₄	1	4	yes	—
147	C₄₇⋊C₈	—	2	4	no	—
148	C₂×#2948	—	47	1	no	maximal, Sylow
149	C₂²×C₄₇	—	2	8	no	—
150	C₂²×C₄₇	—	2	4	no	—
151	C₂²×C₄₇	—	2	16	no	—
152	C₂²×C₄₇	—	4	32	no	—
153	C₂²×C₄₇	—	4	16	no	—
154	C₂²×C₄₇	—	8	32	no	—
155	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
156	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
157	C₂²×C₄₇	#576	1	4	yes	—
158	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
159	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
160	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
161	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
162	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
163	Dic₄₇	—	2	8	no	—
164	Dic₄₇	—	4	8	no	—
165	C₂³×D₈	D₄₇	1	1	yes	characteristic
166	C₂×#518	—	47	2	no	—
167	#2948	—	47	16	no	—
168	C₂×#442	—	47	4	no	—
169	C₂×C₄×D₈	—	47	4	no	—
170	C₂×#427	—	47	1	no	—
171	C₂×#418	—	47	2	no	—
172	C₂×#405	—	47	1	no	—
173	C₂×C₄₇	—	2	4	no	—
174	C₂×C₄₇	—	4	16	no	—
175	C₂×C₄₇	#2948	1	4	yes	complemented
176	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
177	C₂×C₄₇	C₂×#576	1	2	yes	—
178	C₂³×D₄	C₂×D₄₇	1	2	yes	—
179	C₂²×D₈	Dic₄₇	1	16	yes	complemented
180	C₂²×D₈	C₂×D₄₇	1	2	yes	—
181	C₂²×D₈	C₂×D₄₇	1	2	yes	—
182	C₂²×D₈	C₂×D₄₇	1	8	yes	—
183	C₂²×M₁₆	—	47	1	no	—
184	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
185	#518	—	47	16	no	—
186	#518	—	94	8	no	—
187	C₂×C₄×D₄	—	47	8	no	—
188	C₂×C₄×D₄	—	94	4	no	—
189	C₂×#117	—	47	1	no	—
190	C₂×#117	—	47	2	no	—
191	C₂²×C₂²⋊C₄	—	94	4	no	—
192	#442	—	47	32	no	—
193	C₄×D₈	—	47	32	no	—
194	#427	—	47	8	no	—
195	C₂×#107	—	47	2	no	—
196	C₂×#106	—	47	2	no	—
197	#418	—	47	16	no	—
198	C₂×#102	—	47	8	no	—
199	#405	—	47	8	no	—
200	C₂×#97	—	47	2	no	—
201	C₂×C₄×C₈	—	47	2	no	—
202	C₄₇	C₂×#2948	1	1	yes	characteristic, complemented, Sylow
203	C₂⁵	—	2	2	no	—
204	C₂²×D₄	—	2	2	no	—
205	C₂²×D₄	—	2	4	no	—
206	C₂²×D₄	—	2	8	no	—
207	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
208	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
209	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
210	C₂³×C₄	—	94	8	no	—
211	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
212	C₂×D₈	C₂×Dic₄₇	1	16	yes	complemented
213	C₂×D₈	C₂×Dic₄₇	1	16	yes	complemented
214	C₂×D₈	C₂×Dic₄₇	1	64	yes	complemented
215	C₂×D₈	C₂²×D₄₇	1	8	yes	—
216	C₂×D₈	C₂²×D₄₇	1	8	yes	—
217	C₂×M₁₆	—	47	4	no	—
218	C₂×M₁₆	—	94	4	no	—
219	C₂²×C₈	—	47	2	no	—
220	C₂²×C₈	C₂×Dic₄₇	1	8	yes	complemented
221	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
223	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
224	C₄×D₄	—	47	32	no	—
225	C₄×D₄	—	94	16	no	—
226	C₄×D₄	—	94	32	no	—
227	#117	—	47	4	no	—
228	#117	—	47	4	no	—
229	#117	—	47	8	no	—
230	#117	—	94	4	no	—
231	C₂×C₄⋊C₄	—	47	2	no	—
232	C₂×C₄⋊C₄	—	47	4	no	—
233	C₂×C₂²⋊C₄	—	47	2	no	—
234	C₂×C₂²⋊C₄	—	94	32	no	—
235	C₂×C₂²⋊C₄	—	94	8	no	—
236	C₂×C₂²⋊C₄	—	94	2	no	—
237	C₂×C₄²	—	47	2	no	—
238	C₂×C₄²	—	94	2	no	—
239	#107	—	47	8	no	—
240	#106	—	47	8	no	—
241	#102	—	47	32	no	—
242	#97	—	47	8	no	—
243	C₄×C₈	—	47	8	no	—
244	C₂⁴	—	2	4	no	—
245	C₂⁴	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	8	8	no	—
248	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
249	C₂×D₄	—	2	32	no	—
250	C₂×D₄	—	2	16	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
256	C₂×D₄	C₂²×Dic₄₇	1	32	yes	complemented
257	C₂×D₄	C₂³×D₄₇	1	8	yes	—
258	C₂²×C₄	—	47	4	no	—
259	C₂²×C₄	—	94	32	no	—
260	C₂²×C₄	—	94	4	no	—
261	C₂²×C₄	—	376	16	no	—
262	C₂²×C₄	D₄×D₄₇	1	2	yes	—
263	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
264	C₂²×C₄	#10625352	1	4	yes	—
265	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
266	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
267	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
268	D₈	C₂²×Dic₄₇	1	32	yes	complemented
269	D₈	C₂²×Dic₄₇	1	32	yes	complemented
270	M₁₆	—	94	8	no	—
271	C₂×C₈	—	47	4	no	—
272	C₂×C₈	—	94	4	no	—
273	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
274	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
275	C₂×C₈	C₂²×Dic₄₇	1	16	yes	complemented
276	C₂×C₈	C₂³×D₄₇	1	2	yes	—
277	C₂×C₈	C₂³×D₄₇	1	2	yes	—
278	C₄⋊C₄	—	47	8	no	—
279	C₄⋊C₄	—	47	8	no	—
280	C₄⋊C₄	—	94	4	no	—
281	C₂²⋊C₄	—	47	8	no	—
282	C₂²⋊C₄	—	94	32	no	—
283	C₂²⋊C₄	—	94	8	no	—
284	C₄²	—	47	4	no	—
285	C₄²	—	47	4	no	—
286	C₄²	—	94	8	no	—
287	C₂³	—	2	4	no	—
288	C₂³	—	2	16	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	32	no	—
291	C₂³	—	4	16	no	—
292	C₂³	—	8	32	no	—
293	C₂³	—	8	16	no	—
294	C₂³	D₄×Dic₄₇	1	4	yes	—
295	C₂³	C₂×D₄×D₄₇	1	2	yes	—
296	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
297	D₄	—	2	16	no	—
298	D₄	—	2	32	no	—
299	D₄	—	2	8	no	—
300	D₄	C₂³×Dic₄₇	1	16	yes	—
301	C₂×C₄	—	47	8	no	—
302	C₂×C₄	—	94	8	no	—
303	C₂×C₄	—	94	8	no	—
304	C₂×C₄	—	376	32	no	—
305	C₂×C₄	—	188	8	no	—
306	C₂×C₄	D₄×Dic₄₇	1	8	yes	—
307	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
308	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
309	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
310	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
311	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
312	C₂×C₄	C₂×#10625352	1	2	yes	—
313	C₂×C₄	C₂×#10625352	1	4	yes	—
314	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
315	C₈	—	94	4	no	—
316	C₈	C₂³×Dic₄₇	1	4	yes	—
317	C₈	C₂³×Dic₄₇	1	4	yes	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	4	32	no	—
322	C₂²	—	4	16	no	—
323	C₂²	—	8	32	no	—
324	C₂²	C₂×D₄×Dic₄₇	1	4	yes	—
325	C₂²	C₂×D₄×Dic₄₇	1	2	yes	—
326	C₂²	#15689924	1	4	yes	—
327	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
328	C₄	—	94	8	no	—
329	C₄	—	188	8	no	—
330	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
331	C₄	C₂×D₄×Dic₄₇	1	4	yes	—
332	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
333	C₄	C₂²×#10625352	1	1	yes	characteristic
334	C₂	—	2	4	no	—
335	C₂	—	4	16	no	—
336	C₂	#20252240	1	4	yes	direct product factor
337	C₂	C₂²×D₄×Dic₄₇	1	1	yes	characteristic
338	C₂	C₂×#15689924	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂³×D₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×D₈	D₄₇
hypocenter	C₄₇	C₂×#2948
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#15689598	C₂	semidirect
2. #20252240	C₂	direct (N × H)
3. C₂×#15689235	C₂	semidirect
4. C₂×D₈×Dic₄₇	C₂	semidirect
5. C₂×#15689161	C₂	semidirect
6. C₂×#15689128	C₂	semidirect
7. C₂×#15689078	C₂	semidirect
11. #15689598	C₂²	semidirect
13. C₂×D₄×Dic₄₇	C₂²	semidirect
17. #15689235	C₂²	semidirect
18. D₈×Dic₄₇	C₂²	semidirect
19. #15689161	C₂²	semidirect
20. C₂×#13093958	C₂²	semidirect
21. C₂×#13093956	C₂²	semidirect
22. #15689128	C₂²	semidirect
23. C₂×#13093945	C₂²	semidirect
24. #15689078	C₂²	semidirect
25. C₂×#13093934	C₂²	semidirect
26. C₂×C₈×Dic₄₇	C₂²	semidirect
28. C₂²×D₈×C₄₇	C₄	semidirect
39. D₄×Dic₄₇	C₂³	semidirect
52. #13093958	C₂³	semidirect
53. #13093956	C₂³	semidirect
54. #13093945	C₂³	semidirect
55. #13093934	C₂³	semidirect
56. C₈×Dic₄₇	C₂³	semidirect
61. C₂²×D₄×C₄₇	C₂×C₄	semidirect
65. C₂×D₈×C₄₇	C₂×C₄	semidirect
66. C₂×D₈×C₄₇	C₂×C₄	semidirect
67. C₂×D₈×C₄₇	C₂×C₄	semidirect
70. C₂²×C₈×C₄₇	C₂×C₄	semidirect
86. C₂×D₄×C₄₇	C₂²×C₄	semidirect
98. D₈×C₄₇	C₂²×C₄	semidirect
99. D₈×C₄₇	C₂²×C₄	semidirect
102. C₂×C₈×C₄₇	C₂²×C₄	semidirect
175. C₂×C₄₇	#2948	semidirect
179. C₂²×D₈	Dic₄₇	semidirect
202. C₄₇	C₂×#2948	semidirect
207. C₂²×D₄	C₂×Dic₄₇	semidirect
212. C₂×D₈	C₂×Dic₄₇	semidirect
213. C₂×D₈	C₂×Dic₄₇	semidirect
214. C₂×D₈	C₂×Dic₄₇	semidirect
220. C₂²×C₈	C₂×Dic₄₇	semidirect
256. C₂×D₄	C₂²×Dic₄₇	semidirect
268. D₈	C₂²×Dic₄₇	semidirect
269. D₈	C₂²×Dic₄₇	semidirect
275. C₂×C₈	C₂²×Dic₄₇	semidirect
336. C₂	#20252240	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×#15689598	2
#20252240	2
C₂×#15689235	2
C₂×D₈×Dic₄₇	2
C₂×#15689161	2
C₂×#15689128	2
C₂×#15689078	2
C₂³×D₈×C₄₇	2
C₂×#2948	47

Subgroups — C2×#20252240 #27080406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252240 #27080406