Subgroups — #26376291

Order 12032.

7734 conjugacy classes of subgroups.

The subgroup lattice has 370 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	D₄×C₂²⋊Dic₄₇	C₂	1	16	yes	maximal, complemented
3	#20245970	C₂	1	2	yes	maximal, complemented
4	#20245966	C₂	1	4	yes	maximal, complemented
5	#20245771	C₂	1	2	yes	maximal, complemented
6	C₂×#15688979	C₂	1	4	yes	maximal, complemented
7	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
8	#15689598	—	2	16	no	—
9	C₂×D₄×Dic₄₇	C₂²	1	16	yes	complemented
10	C₂×#13093983	C₂²	1	4	yes	complemented
11	C₂²×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
12	C₂²×C₂²⋊Dic₄₇	C₂²	1	16	yes	complemented
13	#15689026	C₂²	1	16	yes	complemented
14	#15689003	C₂²	1	32	yes	complemented
15	#15688986	C₂²	1	4	yes	complemented
16	#15688983	C₂²	1	8	yes	complemented
17	#15688979	C₂²	1	4	yes	—
18	#15688979	C₂²	1	16	yes	complemented
19	#15688979	C₂²	1	8	yes	complemented
20	C₄×C₂²⋊Dic₄₇	C₂²	1	8	yes	complemented
21	C₂⁶×C₄₇	C₂²	1	2	yes	—
22	C₂³×D₄×C₄₇	—	2	16	no	—
23	C₂³×D₄×C₄₇	C₄	1	16	yes	complemented
24	C₂³×D₄×C₄₇	C₂²	1	8	yes	—
25	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
26	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
28	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂³×Dic₄₇	C₂³	1	16	yes	complemented
30	D₄×Dic₄₇	—	2	64	no	—
31	#13093983	—	2	16	no	—
32	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	complemented
33	C₂×C₂²⋊Dic₄₇	—	2	32	no	—
34	C₂×C₂²⋊Dic₄₇	—	4	32	no	—
35	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	—
36	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
37	C₂×C₂²⋊Dic₄₇	C₂³	1	16	yes	complemented
38	C₂×C₂²⋊Dic₄₇	C₂³	1	32	yes	complemented
39	C₂×C₄×Dic₄₇	C₂³	1	8	yes	complemented
40	C₄₇⋊#95	C₂³	1	16	yes	complemented
41	C₂⁵×C₄₇	—	2	16	no	—
42	C₂⁵×C₄₇	—	4	16	no	—
43	C₂⁵×C₄₇	C₂×C₄	1	16	yes	complemented
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂⁵×C₄₇	C₂³	1	8	yes	—
46	C₂⁵×C₄₇	C₂³	1	2	yes	—
47	C₂⁵×C₄₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₇	—	2	16	no	—
49	C₂²×D₄×C₄₇	—	2	128	no	—
50	C₂²×D₄×C₄₇	—	2	64	no	—
51	C₂²×D₄×C₄₇	—	2	8	no	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
53	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
54	C₂²×D₄×C₄₇	C₂×C₄	1	64	yes	complemented
55	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
56	C₂²×D₄×C₄₇	D₄	1	16	yes	—
57	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
58	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
59	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
60	C₂³×C₄×C₄₇	—	2	8	no	—
61	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
62	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	8	no	—
67	C₂⁴×C₄₇	—	2	64	no	—
68	C₂⁴×C₄₇	—	2	32	no	—
69	C₂⁴×C₄₇	—	2	8	no	—
70	C₂⁴×C₄₇	—	2	32	no	—
71	C₂⁴×C₄₇	—	4	64	no	—
72	C₂⁴×C₄₇	—	4	8	no	—
73	C₂⁴×C₄₇	—	4	16	no	—
74	C₂⁴×C₄₇	—	4	8	no	—
75	C₂⁴×C₄₇	—	4	128	no	—
76	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂²×C₄	1	32	yes	—
78	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
80	C₂⁴×C₄₇	C₂×D₄	1	16	yes	—
81	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
82	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
84	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
85	C₂×D₄×C₄₇	—	2	64	no	—
86	C₂×D₄×C₄₇	—	2	32	no	—
87	C₂×D₄×C₄₇	—	2	256	no	—
88	C₂×D₄×C₄₇	—	2	32	no	—
89	C₂×D₄×C₄₇	—	2	16	no	—
90	C₂×D₄×C₄₇	C₂²⋊C₄	1	64	yes	complemented
91	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	—
92	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
93	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	—
94	C₂×D₄×C₄₇	C₂×D₄	1	32	yes	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	32	no	—
97	C₂²×C₄×C₄₇	—	2	16	no	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
104	C₂²×Dic₄₇	—	2	32	no	—
105	C₂²×Dic₄₇	—	4	32	no	—
106	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
107	C₂²⋊Dic₄₇	—	2	16	no	—
108	C₂²⋊Dic₄₇	—	2	32	no	—
109	C₂²⋊Dic₄₇	—	2	32	no	—
110	C₂²⋊Dic₄₇	—	4	32	no	—
111	C₄⋊Dic₄₇	—	2	16	no	—
112	C₄×Dic₄₇	—	2	16	no	—
113	C₂³×C₄₇	—	2	32	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	16	no	—
116	C₂³×C₄₇	—	2	4	no	—
117	C₂³×C₄₇	—	2	16	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	2	64	no	—
121	C₂³×C₄₇	—	2	16	no	—
122	C₂³×C₄₇	—	2	64	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	16	no	—
125	C₂³×C₄₇	—	4	16	no	—
126	C₂³×C₄₇	—	4	32	no	—
127	C₂³×C₄₇	—	4	16	no	—
128	C₂³×C₄₇	—	4	32	no	—
129	C₂³×C₄₇	—	4	128	no	—
130	C₂³×C₄₇	—	4	256	no	—
131	C₂³×C₄₇	—	4	32	no	—
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	32	yes	complemented
133	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
135	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
137	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
138	C₂³×C₄₇	C₂²×D₄	1	16	yes	—
139	C₂³×C₄₇	H(5,𝔽₂)	1	8	yes	—
140	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
141	D₄×C₄₇	—	2	64	no	—
142	D₄×C₄₇	—	2	32	no	—
143	D₄×C₄₇	C₂×C₂²⋊C₄	1	64	yes	complemented
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	32	no	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	complemented
148	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
150	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
151	C₂×Dic₄₇	—	2	16	no	—
152	C₂×Dic₄₇	—	2	32	no	—
153	C₂×Dic₄₇	—	8	32	no	—
154	#34171	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	32	no	—
156	C₂²×C₄₇	—	2	4	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	16	no	—
160	C₂²×C₄₇	—	2	32	no	—
161	C₂²×C₄₇	—	2	8	no	—
162	C₂²×C₄₇	—	2	16	no	—
163	C₂²×C₄₇	—	2	8	no	—
164	C₂²×C₄₇	—	2	16	no	—
165	C₂²×C₄₇	—	4	32	no	—
166	C₂²×C₄₇	—	4	128	no	—
167	C₂²×C₄₇	—	4	32	no	—
168	C₂²×C₄₇	—	4	16	no	—
169	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	4	yes	—
170	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	16	yes	—
171	C₂²×C₄₇	#518	1	8	yes	complemented
172	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
173	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
174	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
175	C₄×C₄₇	—	2	4	no	—
176	C₄×C₄₇	C₂²×C₂²⋊C₄	1	8	yes	—
177	Dic₄₇	—	4	16	no	—
178	C₂⁴×D₄	D₄₇	1	1	yes	characteristic
179	C₂×#518	—	47	2	no	—
180	D₄×C₂²⋊C₄	—	47	16	no	—
181	#2309	—	47	2	no	—
182	#2308	—	47	4	no	—
183	#2280	—	47	2	no	—
184	C₂×#379	—	47	4	no	—
185	C₂×C₄₇	—	2	4	no	—
186	C₂×C₄₇	—	2	8	no	—
187	C₂×C₄₇	—	2	16	no	—
188	C₂×C₄₇	—	4	8	no	—
189	C₂×C₄₇	C₂³×C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₄₇	C₂×#518	1	2	yes	—
191	C₂×C₄₇	#3484	1	4	yes	—
192	C₂⁶	C₂×D₄₇	1	2	yes	—
193	C₂³×D₄	—	2	16	no	—
194	C₂³×D₄	Dic₄₇	1	16	yes	complemented
195	C₂³×D₄	C₂×D₄₇	1	2	yes	—
196	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
197	C₂³×D₄	C₂×D₄₇	1	8	yes	—
198	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
199	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
200	#518	—	94	16	no	—
201	C₂×C₄×D₄	—	47	16	no	—
202	C₂×#117	—	47	4	no	—
203	C₂²×C₂²⋊C₄	—	47	8	no	—
204	C₂²×C₂²⋊C₄	—	47	16	no	—
205	#390	—	47	16	no	—
206	#386	—	47	32	no	—
207	#381	—	47	4	no	—
208	#380	—	47	8	no	—
209	#379	—	47	8	no	—
210	#379	—	47	4	no	—
211	#379	—	47	16	no	—
212	C₄×C₂²⋊C₄	—	47	8	no	—
213	C₄₇	#34171	1	1	yes	characteristic, complemented, Sylow
214	C₂⁵	—	2	16	no	—
215	C₂⁵	—	4	16	no	—
216	C₂⁵	C₂×Dic₄₇	1	16	yes	complemented
217	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
218	C₂⁵	C₂²×D₄₇	1	8	yes	—
219	C₂⁵	C₂²×D₄₇	1	2	yes	—
220	C₂⁵	C₂²×D₄₇	1	2	yes	—
221	C₂²×D₄	—	2	16	no	—
222	C₂²×D₄	—	2	128	no	—
223	C₂²×D₄	—	2	64	no	—
224	C₂²×D₄	—	2	8	no	—
225	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
226	C₂²×D₄	C₂×Dic₄₇	1	16	yes	complemented
227	C₂²×D₄	C₂×Dic₄₇	1	64	yes	complemented
228	C₂²×D₄	C₂×Dic₄₇	1	8	yes	complemented
229	C₂²×D₄	C₂²⋊D₄₇	1	16	yes	—
230	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
231	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
232	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
233	C₂³×C₄	—	2	8	no	—
234	C₂³×C₄	—	47	16	no	—
235	C₂³×C₄	C₂×Dic₄₇	1	8	yes	complemented
236	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
237	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₄×D₄	—	94	64	no	—
240	#117	—	94	16	no	—
241	C₂×C₄⋊C₄	—	47	8	no	—
242	C₂×C₂²⋊C₄	—	47	8	no	—
243	C₂×C₂²⋊C₄	—	47	16	no	—
244	C₂×C₂²⋊C₄	—	47	16	no	—
245	C₂×C₂²⋊C₄	—	47	32	no	—
246	C₂×C₂²⋊C₄	—	94	32	no	—
247	C₂×C₂²⋊C₄	—	188	32	no	—
248	C₂×C₄²	—	47	8	no	—
249	#95	—	47	16	no	—
250	C₂⁴	—	2	4	no	—
251	C₂⁴	—	2	8	no	—
252	C₂⁴	—	2	64	no	—
253	C₂⁴	—	2	32	no	—
254	C₂⁴	—	2	8	no	—
255	C₂⁴	—	2	32	no	—
256	C₂⁴	—	4	64	no	—
257	C₂⁴	—	4	8	no	—
258	C₂⁴	—	4	16	no	—
259	C₂⁴	—	4	8	no	—
260	C₂⁴	—	4	128	no	—
261	C₂⁴	C₂²×Dic₄₇	1	4	yes	—
262	C₂⁴	C₂²×Dic₄₇	1	32	yes	—
263	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
264	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
265	C₂⁴	C₂×C₂²⋊D₄₇	1	16	yes	—
266	C₂⁴	C₂³×D₄₇	1	4	yes	—
267	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
268	C₂⁴	C₂³×D₄₇	1	4	yes	—
269	C₂⁴	C₂³×D₄₇	1	2	yes	—
270	C₂×D₄	—	2	64	no	—
271	C₂×D₄	—	2	32	no	—
272	C₂×D₄	—	2	256	no	—
273	C₂×D₄	—	2	32	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	C₂²⋊Dic₄₇	1	64	yes	complemented
276	C₂×D₄	C₂²×Dic₄₇	1	32	yes	—
277	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
278	C₂×D₄	C₂²×Dic₄₇	1	16	yes	—
279	C₂×D₄	C₂×C₂²⋊D₄₇	1	32	yes	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	32	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	47	16	no	—
284	C₂²×C₄	—	94	32	no	—
285	C₂²×C₄	—	188	32	no	—
286	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
287	C₂²×C₄	C₂²×Dic₄₇	1	16	yes	—
288	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
290	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
291	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
292	C₄⋊C₄	—	94	16	no	—
293	C₂²⋊C₄	—	94	16	no	—
294	C₂²⋊C₄	—	94	32	no	—
295	C₂²⋊C₄	—	94	32	no	—
296	C₂²⋊C₄	—	188	32	no	—
297	C₄²	—	94	16	no	—
298	C₂³	—	2	32	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	16	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	16	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	4	no	—
305	C₂³	—	2	64	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	2	64	no	—
308	C₂³	—	2	8	no	—
309	C₂³	—	2	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	32	no	—
312	C₂³	—	4	16	no	—
313	C₂³	—	4	32	no	—
314	C₂³	—	4	128	no	—
315	C₂³	—	4	256	no	—
316	C₂³	—	4	32	no	—
317	C₂³	C₂×C₂²⋊Dic₄₇	1	32	yes	complemented
318	C₂³	C₂³×Dic₄₇	1	8	yes	—
319	C₂³	C₂³×Dic₄₇	1	2	yes	—
320	C₂³	C₂³×Dic₄₇	1	8	yes	—
321	C₂³	C₂³×Dic₄₇	1	4	yes	—
322	C₂³	C₂²×C₂²⋊D₄₇	1	4	yes	—
323	C₂³	C₂²×C₂²⋊D₄₇	1	16	yes	—
324	C₂³	#13094069	1	8	yes	—
325	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
326	D₄	—	2	64	no	—
327	D₄	—	2	32	no	—
328	D₄	C₂×C₂²⋊Dic₄₇	1	64	yes	complemented
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	32	no	—
332	C₂×C₄	—	94	16	no	—
333	C₂×C₄	—	94	32	no	—
334	C₂×C₄	—	376	32	no	—
335	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	16	yes	complemented
336	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
337	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
338	C₂×C₄	C₂²×C₂²⋊D₄₇	1	8	yes	—
339	C₂²	—	2	32	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	16	no	—
344	C₂²	—	2	32	no	—
345	C₂²	—	2	8	no	—
346	C₂²	—	2	16	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	16	no	—
349	C₂²	—	4	32	no	—
350	C₂²	—	4	128	no	—
351	C₂²	—	4	32	no	—
352	C₂²	—	4	16	no	—
353	C₂²	C₂²×C₂²⋊Dic₄₇	1	4	yes	—
354	C₂²	C₂²×C₂²⋊Dic₄₇	1	16	yes	—
355	C₂²	#15689598	1	8	yes	complemented
356	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
357	C₂²	C₂³×C₂²⋊D₄₇	1	2	yes	—
358	C₂²	C₂×#13094069	1	4	yes	—
359	C₄	—	2	4	no	—
360	C₄	—	188	16	no	—
361	C₄	C₂²×C₂²⋊Dic₄₇	1	8	yes	—
362	C₂	—	2	4	no	—
363	C₂	—	2	8	no	—
364	C₂	—	2	16	no	—
365	C₂	—	4	8	no	—
366	C₂	C₂³×C₂²⋊Dic₄₇	1	1	yes	characteristic
367	C₂	C₂×#15689598	1	2	yes	—
368	C₂	#20257023	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₂⁴×D₄×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂⁴×D₄	D₄₇
hypocenter	C₄₇	#34171
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689598	C₂	semidirect
2. D₄×C₂²⋊Dic₄₇	C₂	semidirect
3. #20245970	C₂	semidirect
4. #20245966	C₂	semidirect
5. #20245771	C₂	semidirect
6. C₂×#15688979	C₂	semidirect
9. C₂×D₄×Dic₄₇	C₂²	semidirect
10. C₂×#13093983	C₂²	semidirect
11. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
12. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
13. #15689026	C₂²	semidirect
14. #15689003	C₂²	semidirect
15. #15688986	C₂²	semidirect
16. #15688983	C₂²	semidirect
18. #15688979	C₂²	semidirect
19. #15688979	C₂²	semidirect
20. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
23. C₂³×D₄×C₄₇	C₄	semidirect
29. C₂³×Dic₄₇	C₂³	semidirect
32. C₂×C₄⋊Dic₄₇	C₂³	semidirect
37. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
38. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
39. C₂×C₄×Dic₄₇	C₂³	semidirect
40. C₄₇⋊#95	C₂³	semidirect
43. C₂⁵×C₄₇	C₂×C₄	semidirect
53. C₂²×D₄×C₄₇	C₂×C₄	semidirect
54. C₂²×D₄×C₄₇	C₂×C₄	semidirect
55. C₂²×D₄×C₄₇	C₂×C₄	semidirect
61. C₂³×C₄×C₄₇	C₂×C₄	semidirect
90. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
132. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
143. D₄×C₄₇	C₂×C₂²⋊C₄	semidirect
147. C₂×C₄×C₄₇	C₂×C₂²⋊C₄	semidirect
171. C₂²×C₄₇	#518	semidirect
194. C₂³×D₄	Dic₄₇	semidirect
213. C₄₇	#34171	semidirect
216. C₂⁵	C₂×Dic₄₇	semidirect
226. C₂²×D₄	C₂×Dic₄₇	semidirect
227. C₂²×D₄	C₂×Dic₄₇	semidirect
228. C₂²×D₄	C₂×Dic₄₇	semidirect
235. C₂³×C₄	C₂×Dic₄₇	semidirect
275. C₂×D₄	C₂²⋊Dic₄₇	semidirect
317. C₂³	C₂×C₂²⋊Dic₄₇	semidirect
328. D₄	C₂×C₂²⋊Dic₄₇	semidirect
335. C₂×C₄	C₂×C₂²⋊Dic₄₇	semidirect
355. C₂²	#15689598	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689598	2
D₄×C₂²⋊Dic₄₇	2
#20245970	2
#20245966	2
#20245771	2
C₂×#15688979	2
C₂⁴×D₄×C₄₇	2
#34171	47