Subgroups — C₂²×#15689124 #27079812

Order 12032.

5502 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689124	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#13093948	C₂	1	2	yes	maximal, complemented
5	C₂²×#13093945	C₂	1	2	yes	maximal, complemented
6	C₂³×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×Dic₄₇	—	2	1	no	—
8	C₂²×#10625329	—	2	8	no	—
9	C₂²×#10625329	C₂²	1	12	yes	complemented
10	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
11	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
12	C₂²×C₄⋊Dic₄₇	—	2	6	no	—
13	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₄₇	C₂²	1	12	yes	complemented
15	#15689124	C₂²	1	64	yes	direct product factor
16	C₂×#13093948	C₂²	1	24	yes	complemented
17	C₂×#13093945	C₂²	1	24	yes	complemented
18	C₂²×#41×C₄₇	—	2	8	no	—
19	C₂²×#41×C₄₇	—	2	6	no	—
20	C₂²×#41×C₄₇	C₄	1	16	yes	complemented
21	C₂²×#41×C₄₇	C₂²	1	12	yes	—
22	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂³×D₄×C₄₇	—	2	1	no	—
24	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	—	2	1	no	—
26	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂³×Dic₄₇	—	2	12	no	—
29	C₂³×Dic₄₇	—	4	8	no	—
30	C₂×#10625329	—	2	48	no	—
31	C₂×#10625329	C₂³	1	16	yes	complemented
32	C₂²×C₄₇⋊C₈	—	2	8	no	—
33	C₂²×C₄₇⋊C₈	C₂³	1	12	yes	—
34	C₂×C₄⋊Dic₄₇	—	2	6	no	—
35	C₂×C₄⋊Dic₄₇	—	2	24	no	—
36	C₂×C₄⋊Dic₄₇	—	2	12	no	—
37	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
38	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	complemented
39	#13093948	C₂³	1	32	yes	complemented
40	#13093945	C₂³	1	32	yes	complemented
41	C₂⁵×C₄₇	—	2	1	no	—
42	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
43	C₂×#41×C₄₇	—	2	96	no	—
44	C₂×#41×C₄₇	—	2	48	no	—
45	C₂×#41×C₄₇	—	2	24	no	—
46	C₂×#41×C₄₇	C₂×C₄	1	96	yes	complemented
47	C₂×#41×C₄₇	C₂³	1	16	yes	—
48	C₂²×Q₈×C₄₇	—	2	4	no	—
49	C₂²×Q₈×C₄₇	—	2	3	no	—
50	C₂²×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₄₇	C₂³	1	6	yes	—
52	C₂²×D₄×C₄₇	—	2	16	no	—
53	C₂²×D₄×C₄₇	—	2	12	no	—
54	C₂²×D₄×C₄₇	—	2	3	no	—
55	C₂²×D₄×C₄₇	—	2	4	no	—
56	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
57	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
58	C₂³×C₄×C₄₇	—	2	1	no	—
59	C₂³×C₄×C₄₇	—	2	16	no	—
60	C₂³×C₄×C₄₇	—	2	12	no	—
61	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	D₄	1	6	yes	—
64	C₂³×C₄×C₄₇	D₄	1	8	yes	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	8	no	—
70	C₂⁴×C₄₇	—	2	6	no	—
71	C₂⁴×C₄₇	—	4	4	no	—
72	C₂⁴×C₄₇	—	4	4	no	—
73	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
74	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
75	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
76	#41×C₄₇	—	2	192	no	—
77	#41×C₄₇	—	2	32	no	—
78	#41×C₄₇	C₂²×C₄	1	64	yes	complemented
79	C₂×Q₈×C₄₇	—	2	24	no	—
80	C₂×Q₈×C₄₇	—	2	12	no	—
81	C₂×Q₈×C₄₇	—	2	6	no	—
82	C₂×Q₈×C₄₇	C₂²×C₄	1	24	yes	complemented
83	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
84	C₂×D₄×C₄₇	—	2	96	no	—
85	C₂×D₄×C₄₇	—	2	16	no	—
86	C₂×D₄×C₄₇	—	2	24	no	—
87	C₂×D₄×C₄₇	—	2	6	no	—
88	C₂×D₄×C₄₇	—	2	12	no	—
89	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	complemented
90	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	6	no	—
93	C₂²×C₄×C₄₇	—	2	96	no	—
94	C₂²×C₄×C₄₇	—	2	16	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	48	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	12	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	24	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
106	C₂²×Dic₄₇	—	2	12	no	—
107	C₂²×Dic₄₇	—	2	16	no	—
108	C₂²×Dic₄₇	—	4	48	no	—
109	C₂²×Dic₄₇	—	4	8	no	—
110	C₄⋊Dic₄₇	—	2	12	no	—
111	C₄⋊Dic₄₇	—	2	16	no	—
112	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
113	#10625329	—	2	32	no	—
114	C₂×C₄₇⋊C₈	—	2	24	no	—
115	C₂×C₄₇⋊C₈	C₂⁴	1	8	yes	—
116	C₂³×C₄₇	—	2	12	no	—
117	C₂³×C₄₇	—	2	12	no	—
118	C₂³×C₄₇	—	2	32	no	—
119	C₂³×C₄₇	—	2	24	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	4	12	no	—
122	C₂³×C₄₇	—	4	12	no	—
123	C₂³×C₄₇	—	4	32	no	—
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	24	yes	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
126	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₄₇	#137	1	4	yes	—
128	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
129	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
130	Q₈×C₄₇	—	2	24	no	—
131	Q₈×C₄₇	—	2	4	no	—
132	Q₈×C₄₇	C₂³×C₄	1	8	yes	complemented
133	D₄×C₄₇	—	2	64	no	—
134	D₄×C₄₇	—	2	24	no	—
135	D₄×C₄₇	—	2	4	no	—
136	D₄×C₄₇	C₂³×C₄	1	8	yes	complemented
137	C₂×C₄×C₄₇	—	2	24	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	64	no	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	24	yes	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	12	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	48	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
147	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
148	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
149	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	8	no	—
151	C₂×Dic₄₇	—	4	32	no	—
152	C₂×Dic₄₇	—	4	24	no	—
153	C₄₇⋊C₈	—	2	8	no	—
154	C₂²×#417	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	48	no	—
156	C₂²×C₄₇	—	2	4	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	8	no	—
159	C₂²×C₄₇	—	4	48	no	—
160	C₂²×C₄₇	—	4	4	no	—
161	C₂²×C₄₇	—	4	4	no	—
162	C₂²×C₄₇	#417	1	16	yes	complemented
163	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
164	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	6	yes	—
165	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
166	C₂²×C₄₇	C₂×#137	1	6	yes	—
167	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
168	C₄×C₄₇	—	2	8	no	—
169	C₄×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
170	C₄×C₄₇	C₂²×C₂²⋊C₄	1	6	yes	—
171	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
172	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
173	Dic₄₇	—	4	8	no	—
174	C₂³×#41	D₄₇	1	1	yes	characteristic
175	C₂³×M₁₆	—	47	1	no	—
176	C₂³×C₄⋊C₄	—	47	1	no	—
177	C₂×#417	—	47	24	no	—
178	C₂²×#103	—	47	2	no	—
179	C₂²×#102	—	47	2	no	—
180	C₂×C₄₇	—	2	8	no	—
181	C₂×C₄₇	—	4	8	no	—
182	C₂×C₄₇	C₂×#417	1	12	yes	complemented
183	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂×C₄₇	C₂²×#137	1	1	yes	characteristic
186	C₂²×#41	—	2	8	no	—
187	C₂²×#41	—	2	6	no	—
188	C₂²×#41	Dic₄₇	1	16	yes	complemented
189	C₂²×#41	C₂×D₄₇	1	12	yes	—
190	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
191	C₂³×D₄	—	2	1	no	—
192	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
193	C₂⁴×C₄	—	2	1	no	—
194	C₂⁴×C₄	—	94	1	no	—
195	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
196	C₂²×M₁₆	—	47	12	no	—
197	C₂²×M₁₆	—	94	8	no	—
198	C₂³×C₈	—	47	2	no	—
199	C₂²×C₄⋊C₄	—	47	2	no	—
200	C₂²×C₄⋊C₄	—	47	12	no	—
201	C₂²×C₄⋊C₄	—	94	6	no	—
202	C₂²×C₄⋊C₄	—	94	1	no	—
203	#417	—	47	64	no	—
204	C₂×#103	—	47	24	no	—
205	C₂×#102	—	47	24	no	—
206	C₄₇	C₂²×#417	1	1	yes	characteristic, complemented, Sylow
207	C₂⁵	—	2	1	no	—
208	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
209	C₂×#41	—	2	96	no	—
210	C₂×#41	—	2	48	no	—
211	C₂×#41	—	2	24	no	—
212	C₂×#41	C₂×Dic₄₇	1	96	yes	complemented
213	C₂×#41	C₂²×D₄₇	1	16	yes	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	3	no	—
216	C₂²×Q₈	C₂×Dic₄₇	1	8	yes	complemented
217	C₂²×Q₈	C₂²×D₄₇	1	6	yes	—
218	C₂²×D₄	—	2	16	no	—
219	C₂²×D₄	—	2	12	no	—
220	C₂²×D₄	—	2	3	no	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	C₂×Dic₄₇	1	8	yes	complemented
223	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
224	C₂³×C₄	—	2	1	no	—
225	C₂³×C₄	—	2	16	no	—
226	C₂³×C₄	—	2	12	no	—
227	C₂³×C₄	—	94	12	no	—
228	C₂³×C₄	—	94	2	no	—
229	C₂³×C₄	—	188	8	no	—
230	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
231	C₂³×C₄	C₂²⋊D₄₇	1	6	yes	—
232	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²⋊D₄₇	1	8	yes	—
234	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
235	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
236	C₂×M₁₆	—	47	16	no	—
237	C₂×M₁₆	—	94	48	no	—
238	C₂²×C₈	—	47	12	no	—
239	C₂²×C₈	—	94	8	no	—
240	C₂×C₄⋊C₄	—	47	12	no	—
241	C₂×C₄⋊C₄	—	47	16	no	—
242	C₂×C₄⋊C₄	—	94	12	no	—
243	C₂×C₄⋊C₄	—	94	6	no	—
244	C₂×C₄⋊C₄	—	94	24	no	—
245	#103	—	47	32	no	—
246	#102	—	47	32	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	2	6	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	C₂²⋊Dic₄₇	1	8	yes	—
254	C₂⁴	C₂×C₂²⋊D₄₇	1	6	yes	—
255	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
256	#41	—	2	192	no	—
257	#41	—	2	32	no	—
258	#41	C₂²×Dic₄₇	1	64	yes	complemented
259	C₂×Q₈	—	2	24	no	—
260	C₂×Q₈	—	2	12	no	—
261	C₂×Q₈	—	2	6	no	—
262	C₂×Q₈	C₂²×Dic₄₇	1	24	yes	complemented
263	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
264	C₂×D₄	—	2	96	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	2	24	no	—
267	C₂×D₄	—	2	6	no	—
268	C₂×D₄	—	2	12	no	—
269	C₂×D₄	C₂²×Dic₄₇	1	24	yes	complemented
270	C₂×D₄	C₂³×D₄₇	1	4	yes	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	6	no	—
273	C₂²×C₄	—	2	96	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	94	16	no	—
276	C₂²×C₄	—	94	12	no	—
277	C₂²×C₄	—	188	48	no	—
278	C₂²×C₄	—	188	8	no	—
279	C₂²×C₄	C₂²⋊Dic₄₇	1	8	yes	—
280	C₂²×C₄	C₂²⋊Dic₄₇	1	48	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	24	yes	—
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	12	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	24	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
289	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
290	M₁₆	—	94	32	no	—
291	C₂×C₈	—	47	8	no	—
292	C₂×C₈	—	94	24	no	—
293	C₄⋊C₄	—	47	8	no	—
294	C₄⋊C₄	—	94	16	no	—
295	C₄⋊C₄	—	94	12	no	—
296	C₂³	—	2	32	no	—
297	C₂³	—	2	12	no	—
298	C₂³	—	2	12	no	—
299	C₂³	—	2	24	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	4	32	no	—
302	C₂³	—	4	12	no	—
303	C₂³	—	4	12	no	—
304	C₂³	C₂×C₂²⋊Dic₄₇	1	24	yes	—
305	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
306	C₂³	#13094049	1	4	yes	—
307	C₂³	#13094054	1	4	yes	—
308	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
309	C₂³	C₂²×C₂²⋊D₄₇	1	3	yes	—
310	Q₈	—	2	24	no	—
311	Q₈	—	2	4	no	—
312	Q₈	C₂³×Dic₄₇	1	8	yes	complemented
313	D₄	—	2	64	no	—
314	D₄	—	2	24	no	—
315	D₄	—	2	4	no	—
316	D₄	C₂³×Dic₄₇	1	8	yes	complemented
317	C₂×C₄	—	2	24	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	64	no	—
320	C₂×C₄	—	94	8	no	—
321	C₂×C₄	—	188	32	no	—
322	C₂×C₄	—	188	24	no	—
323	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	24	yes	—
324	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	12	yes	—
325	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	48	yes	—
326	C₂×C₄	C₂³×Dic₄₇	1	6	yes	—
327	C₂×C₄	C₂³×Dic₄₇	1	8	yes	—
328	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
329	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
330	C₂×C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
331	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
332	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
333	C₈	—	94	8	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	48	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	4	48	no	—
341	C₂²	#15689124	1	16	yes	direct product factor
342	C₂²	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
343	C₂²	C₂²×C₂²⋊Dic₄₇	1	6	yes	—
344	C₂²	C₂×#13094049	1	6	yes	—
345	C₂²	C₂×#13094054	1	6	yes	—
346	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	188	8	no	—
349	C₄	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
350	C₄	C₂²×C₂²⋊Dic₄₇	1	6	yes	—
351	C₄	C₂⁴×Dic₄₇	1	1	yes	characteristic
352	C₄	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂	—	2	8	no	—
354	C₂	—	4	8	no	—
355	C₂	C₂×#15689124	1	12	yes	direct product factor
356	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
357	C₂	C₂²×#13094049	1	1	yes	characteristic
358	C₂	C₂²×#13094054	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting, prime radical	C₂³×#41×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×#41	D₄₇
hypocenter	C₄₇	C₂²×#417
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625329	C₂	semidirect
2. C₂³×C₄⋊Dic₄₇	C₂	semidirect
3. C₂×#15689124	C₂	direct (N × H)
4. C₂²×#13093948	C₂	semidirect
5. C₂²×#13093945	C₂	semidirect
9. C₂²×#10625329	C₂²	semidirect
14. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
15. #15689124	C₂²	direct (N × H)
16. C₂×#13093948	C₂²	semidirect
17. C₂×#13093945	C₂²	semidirect
20. C₂²×#41×C₄₇	C₄	semidirect
31. C₂×#10625329	C₂³	semidirect
38. C₂×C₄⋊Dic₄₇	C₂³	semidirect
39. #13093948	C₂³	semidirect
40. #13093945	C₂³	semidirect
46. C₂×#41×C₄₇	C₂×C₄	semidirect
50. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
56. C₂²×D₄×C₄₇	C₂×C₄	semidirect
78. #41×C₄₇	C₂²×C₄	semidirect
82. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
89. C₂×D₄×C₄₇	C₂²×C₄	semidirect
132. Q₈×C₄₇	C₂³×C₄	semidirect
136. D₄×C₄₇	C₂³×C₄	semidirect
162. C₂²×C₄₇	#417	semidirect
182. C₂×C₄₇	C₂×#417	semidirect
188. C₂²×#41	Dic₄₇	semidirect
206. C₄₇	C₂²×#417	semidirect
212. C₂×#41	C₂×Dic₄₇	semidirect
216. C₂²×Q₈	C₂×Dic₄₇	semidirect
222. C₂²×D₄	C₂×Dic₄₇	semidirect
258. #41	C₂²×Dic₄₇	semidirect
262. C₂×Q₈	C₂²×Dic₄₇	semidirect
269. C₂×D₄	C₂²×Dic₄₇	semidirect
312. Q₈	C₂³×Dic₄₇	semidirect
316. D₄	C₂³×Dic₄₇	semidirect
341. C₂²	#15689124	direct (N × H)
355. C₂	C₂×#15689124	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625329	2
C₂³×C₄⋊Dic₄₇	2
C₂×#15689124	2
C₂²×#13093948	2
C₂²×#13093945	2
C₂³×#41×C₄₇	2
C₂²×#417	47

Subgroups — C22×#15689124 #27079812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689124 #27079812