Subgroups — C₂²×#15689233 #27080321

Order 12032.

3654 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625334	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689233	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13093945	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄×D₄₇	—	2	1	no	—
11	C₂²×#10625334	C₄	1	16	yes	complemented
12	C₂²×#10625334	C₂²	1	12	yes	—
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₈₈	—	2	6	no	—
16	C₂×C₄×D₁₈₈	C₂²	1	12	yes	complemented
17	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂²×(C₂×D₄₇)⋊C₄	—	2	1	no	—
19	#15689233	C₂²	1	64	yes	direct product factor
20	C₂×#13093955	C₂²	1	12	yes	complemented
21	C₂×#13093945	C₂²	1	12	yes	complemented
22	C₂×#13093944	C₂²	1	12	yes	complemented
23	C₂×#13093935	C₂²	1	12	yes	complemented
24	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	—	2	6	no	—
27	C₂×C₄×D₄×C₄₇	C₂²	1	12	yes	complemented
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂⁴×D₄₇	—	2	1	no	—
32	C₂²×D₁₈₈	—	2	3	no	—
33	C₂²×D₁₈₈	—	2	4	no	—
34	C₂²×D₁₈₈	C₂×C₄	1	8	yes	complemented
35	C₂²×D₁₈₈	C₂³	1	6	yes	—
36	C₂³×Dic₄₇	—	2	1	no	—
37	C₂²×C₄×D₄₇	—	2	12	no	—
38	C₂²×C₄×D₄₇	—	4	8	no	—
39	C₂×#10625334	C₂×C₄	1	96	yes	complemented
40	C₂×#10625334	C₂³	1	16	yes	—
41	C₂²×C₄₇⋊C₈	—	2	4	no	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
43	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
45	C₄×D₁₈₈	—	2	24	no	—
46	C₄×D₁₈₈	C₂³	1	16	yes	complemented
47	C₂×C₄⋊Dic₄₇	—	2	3	no	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
49	C₂×(C₂×D₄₇)⋊C₄	—	2	12	no	—
50	#13093955	C₂³	1	16	yes	complemented
51	#13093945	C₂³	1	16	yes	complemented
52	#13093944	C₂³	1	16	yes	complemented
53	#13093935	C₂³	1	16	yes	complemented
54	C₂⁵×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	—	2	3	no	—
56	C₂²×D₄×C₄₇	—	2	4	no	—
57	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
58	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	—	2	12	no	—
61	C₂³×C₄×C₄₇	—	4	8	no	—
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₄₇	—	2	24	no	—
66	C₄×D₄×C₄₇	C₂³	1	16	yes	complemented
67	C₂×C₄⋊C₄×C₄₇	—	2	3	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
70	C₂×C₄²×C₄₇	D₄	1	6	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
72	C₂⁴×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	—	2	6	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	—	4	4	no	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂³×D₄₇	—	2	8	no	—
78	C₂³×D₄₇	—	2	6	no	—
79	C₂³×D₄₇	—	4	4	no	—
80	C₂³×D₄₇	—	4	4	no	—
81	C₂×D₄×C₄₇	—	2	24	no	—
82	C₂×D₄×C₄₇	—	2	6	no	—
83	C₂×D₄×C₄₇	—	2	12	no	—
84	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	complemented
85	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	6	no	—
89	C₂²×C₄×C₄₇	—	2	16	no	—
90	C₂²×C₄×C₄₇	—	4	48	no	—
91	C₂²×C₄×C₄₇	—	4	4	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₄₇	#41	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
98	C₂²×Dic₄₇	—	2	6	no	—
99	C₂²×Dic₄₇	—	4	4	no	—
100	C₂×D₁₈₈	—	2	24	no	—
101	C₂×D₁₈₈	—	2	6	no	—
102	C₂×D₁₈₈	—	2	12	no	—
103	C₂×D₁₈₈	C₂²×C₄	1	24	yes	complemented
104	C₂×D₁₈₈	C₂⁴	1	4	yes	—
105	C₂×C₄×D₄₇	—	2	16	no	—
106	C₂×C₄×D₄₇	—	4	48	no	—
107	C₄⋊C₄×C₄₇	—	2	6	no	—
108	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
109	C₂²⋊C₄×C₄₇	—	2	16	no	—
110	C₄²×C₄₇	C₂×D₄	1	12	yes	—
111	C₄²×C₄₇	C₂⁴	1	4	yes	—
112	#10625334	C₂²×C₄	1	64	yes	complemented
113	(C₂×D₄₇)⋊C₄	—	2	16	no	—
114	C₄⋊Dic₄₇	—	2	6	no	—
115	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
116	C₂×C₄₇⋊C₈	—	2	12	no	—
117	C₂×C₄₇⋊C₈	C₂²×C₄	1	24	yes	complemented
118	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
119	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
120	C₂³×C₄₇	—	2	24	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	4	12	no	—
123	C₂³×C₄₇	—	4	12	no	—
124	C₂³×C₄₇	—	4	32	no	—
125	C₂³×C₄₇	C₄×D₄	1	4	yes	—
126	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
128	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
129	C₂²×D₄₇	—	2	24	no	—
130	C₂²×D₄₇	—	2	4	no	—
131	C₂²×D₄₇	—	4	12	no	—
132	C₂²×D₄₇	—	4	12	no	—
133	C₂²×D₄₇	—	4	32	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	12	no	—
138	C₂×C₄×C₄₇	—	2	12	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	4	32	no	—
141	C₂×C₄×C₄₇	—	4	12	no	—
142	C₂×C₄×C₄₇	C₄×D₄	1	12	yes	—
143	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
144	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
146	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
147	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
148	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
149	C₂×Dic₄₇	—	2	4	no	—
150	C₂×Dic₄₇	—	4	12	no	—
151	D₁₈₈	—	2	24	no	—
152	D₁₈₈	—	2	4	no	—
153	D₁₈₈	C₂³×C₄	1	8	yes	complemented
154	C₄×D₄₇	—	4	32	no	—
155	C₄₇⋊C₈	—	2	4	no	—
156	C₄₇⋊C₈	C₂³×C₄	1	8	yes	complemented
157	C₂²×#442	—	47	1	no	maximal, Sylow
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	#442	1	16	yes	complemented
163	C₂²×C₄₇	C₂×C₄×D₄	1	6	yes	—
164	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
165	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
166	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
167	C₂×D₄₇	—	2	8	no	—
168	C₂×D₄₇	—	4	48	no	—
169	C₂×D₄₇	—	4	4	no	—
170	C₂×D₄₇	—	4	4	no	—
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	—	2	4	no	—
173	C₄×C₄₇	—	4	4	no	—
174	C₄×C₄₇	C₂×C₄×D₄	1	6	yes	—
175	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
176	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
177	Dic₄₇	—	4	4	no	—
178	C₂³×D₈	—	47	1	no	—
179	C₂²×C₄×D₄	—	47	1	no	—
180	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
181	C₂×#442	—	47	24	no	—
182	C₂²×#106	—	47	1	no	—
183	C₂²×#102	—	47	1	no	—
184	C₂²×#102	—	47	1	no	—
185	C₂²×#97	—	47	1	no	—
186	C₂×C₄₇	—	4	8	no	—
187	C₂×C₄₇	C₂×#442	1	12	yes	complemented
188	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
189	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂×C₄₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
191	D₄₇	—	4	8	no	—
192	C₂³×D₄	—	47	1	no	—
193	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
194	C₂⁴×C₄	—	2	1	no	—
195	C₂⁴×C₄	—	94	1	no	—
196	C₂²×D₈	—	47	16	no	—
197	C₂²×D₈	—	47	12	no	—
198	C₂³×C₈	—	47	1	no	—
199	C₂³×C₈	—	47	1	no	—
200	C₂×C₄×D₄	—	2	6	no	—
201	C₂×C₄×D₄	—	47	12	no	—
202	C₂×C₄×D₄	—	94	6	no	—
203	C₂×C₄×D₄	C₂×D₄₇	1	12	yes	complemented
204	C₂²×C₄⋊C₄	—	47	1	no	—
205	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	—	2	1	no	—
207	C₂²×C₂²⋊C₄	—	94	1	no	—
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	#442	—	47	64	no	—
210	C₂×#106	—	47	12	no	—
211	C₂×#102	—	47	12	no	—
212	C₂×#102	—	47	12	no	—
213	C₂×#97	—	47	12	no	—
214	C₄₇	C₂²×#442	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	—	2	1	no	—
216	C₂⁵	—	94	1	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	2	3	no	—
219	C₂²×D₄	—	47	8	no	—
220	C₂²×D₄	—	47	6	no	—
221	C₂²×D₄	—	94	4	no	—
222	C₂²×D₄	—	94	3	no	—
223	C₂²×D₄	C₄×D₄₇	1	8	yes	complemented
224	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	—	2	12	no	—
227	C₂³×C₄	—	4	8	no	—
228	C₂³×C₄	—	94	1	no	—
229	C₂³×C₄	—	94	12	no	—
230	C₂³×C₄	—	188	8	no	—
231	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
234	C₂×D₈	—	47	96	no	—
235	C₂×D₈	—	47	16	no	—
236	C₂²×C₈	—	47	8	no	—
237	C₂²×C₈	—	47	6	no	—
238	C₂²×C₈	—	47	6	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₄×D₄	—	2	24	no	—
241	C₄×D₄	—	47	16	no	—
242	C₄×D₄	—	94	24	no	—
243	C₄×D₄	C₂²×D₄₇	1	16	yes	complemented
244	C₂×C₄⋊C₄	—	2	3	no	—
245	C₂×C₄⋊C₄	—	47	6	no	—
246	C₂×C₄⋊C₄	—	94	3	no	—
247	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
248	C₂×C₂²⋊C₄	—	2	12	no	—
249	C₂×C₂²⋊C₄	—	94	12	no	—
250	C₂×C₄²	C₂²⋊D₄₇	1	6	yes	—
251	C₂×C₄²	C₂²×D₄₇	1	6	yes	—
252	#106	—	47	16	no	—
253	#102	—	47	16	no	—
254	#102	—	47	16	no	—
255	#97	—	47	16	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	6	no	—
258	C₂⁴	—	4	4	no	—
259	C₂⁴	—	4	4	no	—
260	C₂⁴	—	94	8	no	—
261	C₂⁴	—	94	6	no	—
262	C₂⁴	—	188	4	no	—
263	C₂⁴	—	188	4	no	—
264	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×D₄	—	2	24	no	—
266	C₂×D₄	—	2	6	no	—
267	C₂×D₄	—	2	12	no	—
268	C₂×D₄	—	47	24	no	—
269	C₂×D₄	—	47	4	no	—
270	C₂×D₄	—	94	24	no	—
271	C₂×D₄	—	94	6	no	—
272	C₂×D₄	—	94	12	no	—
273	C₂×D₄	C₂×C₄×D₄₇	1	24	yes	complemented
274	C₂×D₄	C₂³×D₄₇	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	—	4	48	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	94	6	no	—
282	C₂²×C₄	—	94	16	no	—
283	C₂²×C₄	—	188	48	no	—
284	C₂²×C₄	—	188	4	no	—
285	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
286	C₂²×C₄	#10625350	1	4	yes	—
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
288	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
289	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
290	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
291	D₈	—	47	64	no	—
292	C₂×C₈	—	47	24	no	—
293	C₂×C₈	—	47	4	no	—
294	C₂×C₈	—	47	4	no	—
295	C₂×C₈	—	94	12	no	—
296	C₄⋊C₄	—	2	6	no	—
297	C₄⋊C₄	—	47	4	no	—
298	C₄⋊C₄	—	94	6	no	—
299	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂²⋊C₄	—	94	16	no	—
302	C₄²	C₂×C₂²⋊D₄₇	1	12	yes	—
303	C₄²	C₂³×D₄₇	1	4	yes	—
304	C₂³	—	2	24	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	4	32	no	—
307	C₂³	—	4	12	no	—
308	C₂³	—	4	12	no	—
309	C₂³	—	94	24	no	—
310	C₂³	—	94	4	no	—
311	C₂³	—	188	32	no	—
312	C₂³	—	188	12	no	—
313	C₂³	—	188	12	no	—
314	C₂³	C₄×C₂²⋊D₄₇	1	4	yes	—
315	C₂³	#13094049	1	4	yes	—
316	C₂³	#13094050	1	4	yes	—
317	C₂³	C₂²×C₂²⋊D₄₇	1	3	yes	—
318	D₄	—	2	24	no	—
319	D₄	—	2	4	no	—
320	D₄	—	47	8	no	—
321	D₄	—	94	24	no	—
322	D₄	—	94	4	no	—
323	D₄	C₂²×C₄×D₄₇	1	8	yes	complemented
324	C₂×C₄	—	2	12	no	—
325	C₂×C₄	—	2	12	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	32	no	—
328	C₂×C₄	—	4	12	no	—
329	C₂×C₄	—	94	4	no	—
330	C₂×C₄	—	188	32	no	—
331	C₂×C₄	—	188	12	no	—
332	C₂×C₄	C₄×C₂²⋊D₄₇	1	12	yes	—
333	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
334	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
335	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
336	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
337	C₂×C₄	C₂×#10625350	1	6	yes	—
338	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
339	C₈	—	47	8	no	—
340	C₈	—	94	4	no	—
341	C₂²	—	2	8	no	—
342	C₂²	—	4	48	no	—
343	C₂²	—	4	4	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	94	8	no	—
346	C₂²	—	188	48	no	—
347	C₂²	—	188	4	no	—
348	C₂²	—	188	4	no	—
349	C₂²	#15689233	1	16	yes	direct product factor
350	C₂²	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
351	C₂²	C₂×#13094049	1	6	yes	—
352	C₂²	C₂×#13094050	1	6	yes	—
353	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	4	4	no	—
357	C₄	—	188	4	no	—
358	C₄	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
359	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
360	C₄	C₂²×#10625350	1	1	yes	characteristic
361	C₂	—	4	8	no	—
362	C₂	—	188	8	no	—
363	C₂	C₂×#15689233	1	12	yes	direct product factor
364	C₂	C₂²×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂	C₂²×#13094049	1	1	yes	characteristic
366	C₂	C₂²×#13094050	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂³×#10625334	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#442
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₁₈₈	C₂	semidirect
3. C₂×#15689233	C₂	direct (N × H)
4. C₂²×#13093955	C₂	semidirect
5. C₂²×#13093945	C₂	semidirect
6. C₂²×#13093944	C₂	semidirect
7. C₂²×#13093935	C₂	semidirect
8. C₂²×C₄×D₄×C₄₇	C₂	semidirect
11. C₂²×#10625334	C₄	semidirect
16. C₂×C₄×D₁₈₈	C₂²	semidirect
19. #15689233	C₂²	direct (N × H)
20. C₂×#13093955	C₂²	semidirect
21. C₂×#13093945	C₂²	semidirect
22. C₂×#13093944	C₂²	semidirect
23. C₂×#13093935	C₂²	semidirect
27. C₂×C₄×D₄×C₄₇	C₂²	semidirect
34. C₂²×D₁₈₈	C₂×C₄	semidirect
39. C₂×#10625334	C₂×C₄	semidirect
42. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
46. C₄×D₁₈₈	C₂³	semidirect
50. #13093955	C₂³	semidirect
51. #13093945	C₂³	semidirect
52. #13093944	C₂³	semidirect
53. #13093935	C₂³	semidirect
57. C₂²×D₄×C₄₇	C₂×C₄	semidirect
66. C₄×D₄×C₄₇	C₂³	semidirect
84. C₂×D₄×C₄₇	C₂²×C₄	semidirect
103. C₂×D₁₈₈	C₂²×C₄	semidirect
112. #10625334	C₂²×C₄	semidirect
117. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
136. D₄×C₄₇	C₂³×C₄	semidirect
153. D₁₈₈	C₂³×C₄	semidirect
156. C₄₇⋊C₈	C₂³×C₄	semidirect
162. C₂²×C₄₇	#442	semidirect
180. C₂²×C₄×D₄	D₄₇	semidirect
187. C₂×C₄₇	C₂×#442	semidirect
203. C₂×C₄×D₄	C₂×D₄₇	semidirect
214. C₄₇	C₂²×#442	semidirect
223. C₂²×D₄	C₄×D₄₇	semidirect
243. C₄×D₄	C₂²×D₄₇	semidirect
273. C₂×D₄	C₂×C₄×D₄₇	semidirect
323. D₄	C₂²×C₄×D₄₇	semidirect
349. C₂²	#15689233	direct (N × H)
363. C₂	C₂×#15689233	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×#10625334	2
C₂²×C₄×D₁₈₈	2
C₂×#15689233	2
C₂²×#13093955	2
C₂²×#13093945	2
C₂²×#13093944	2
C₂²×#13093935	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#442	47

Subgroups — C22×#15689233 #27080321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689233 #27080321