Subgroups — C₂²×#15689778 #27123220

Order 12032.

12230 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×#10625350	C₂	1	2	yes	maximal, complemented
2	C₂×#15689778	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13094006	C₂	1	4	yes	maximal, complemented
5	C₂²×#13094003	C₂	1	2	yes	maximal, complemented
6	C₂²×#13093995	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄⋊C₄×D₄₇	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625350	—	2	32	no	—
11	C₂²×#10625350	C₂²	1	48	yes	complemented
12	C₂³×Dic₉₄	C₂²	1	2	yes	—
13	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₄₇	C₂²	1	4	yes	—
15	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
16	C₂³×C₄×D₄₇	C₂²	1	4	yes	—
17	#15689778	C₂²	1	256	yes	direct product factor
18	C₂×#13094024	C₂²	1	24	yes	complemented
19	C₂×#13094006	C₂²	1	96	yes	complemented
20	C₂×#13094003	C₂²	1	48	yes	complemented
21	C₂×#13093995	C₂²	1	48	yes	complemented
22	C₂×C₄×D₁₈₈	C₂²	1	24	yes	complemented
23	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	—
27	C₂×C₄⋊C₄×D₄₇	C₂²	1	48	yes	complemented
28	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
29	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
30	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₄₇	C₂²	1	24	yes	complemented
33	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
36	C₂⁴×D₄₇	C₂³	1	2	yes	—
37	C₂×#10625350	—	2	384	no	—
38	C₂×#10625350	C₂³	1	128	yes	complemented
39	C₂²×Dic₉₄	—	2	16	no	—
40	C₂²×Dic₉₄	C₂³	1	24	yes	—
41	C₂²×D₁₈₈	D₄	1	16	yes	complemented
42	C₂²×D₁₈₈	C₂³	1	12	yes	—
43	C₂²×C₂²⋊D₄₇	—	2	32	no	—
44	C₂²×C₂²⋊D₄₇	C₂³	1	48	yes	—
45	C₂³×Dic₄₇	C₂³	1	2	yes	—
46	C₂³×Dic₄₇	C₂³	1	4	yes	—
47	C₂²×C₄×D₄₇	—	2	32	no	—
48	C₂²×C₄×D₄₇	—	2	16	no	—
49	C₂²×C₄×D₄₇	C₂³	1	24	yes	—
50	C₂²×C₄×D₄₇	C₂³	1	48	yes	—
51	#13094024	C₂³	1	64	yes	complemented
52	#13094006	C₂³	1	256	yes	complemented
53	#13094003	C₂³	1	128	yes	complemented
54	#13093995	C₂³	1	128	yes	complemented
55	C₄×D₁₈₈	C₂³	1	64	yes	complemented
56	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
57	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
58	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
59	C₂×Dic₄₇⋊C₄	C₂³	1	48	yes	—
60	C₄⋊C₄×D₄₇	C₂³	1	128	yes	complemented
61	C₂×C₂²⋊Dic₄₇	C₂³	1	48	yes	—
62	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
63	C₂⁵×C₄₇	C₂³	1	2	yes	—
64	C₂²×D₄×C₄₇	—	2	8	no	—
65	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
66	C₂³×C₄×C₄₇	—	2	16	no	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	24	yes	—
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₄₇	C₂³	1	64	yes	complemented
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
74	C₂×C₂²⋊C₄×C₄₇	C₂³	1	24	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
76	C₂⁴×C₄₇	—	2	8	no	—
77	C₂⁴×C₄₇	—	2	8	no	—
78	C₂⁴×C₄₇	—	2	8	no	—
79	C₂⁴×C₄₇	C₂⁴	1	12	yes	—
80	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
81	C₂³×D₄₇	—	2	8	no	—
82	C₂³×D₄₇	—	2	8	no	—
83	C₂³×D₄₇	C₂×D₄	1	16	yes	—
84	C₂³×D₄₇	C₂⁴	1	12	yes	—
85	C₂×D₄×C₄₇	—	2	48	no	—
86	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	96	no	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
91	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
92	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
94	C₂²×C₄×C₄₇	C₂⁴	1	32	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
97	C₂×C₂²⋊D₄₇	—	2	192	no	—
98	C₂×C₂²⋊D₄₇	C₂⁴	1	64	yes	—
99	C₂²×Dic₄₇	—	2	16	no	—
100	C₂²×Dic₄₇	—	2	8	no	—
101	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
102	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
103	#10625350	—	2	512	no	—
104	C₂×D₁₈₈	C₂×D₄	1	96	yes	complemented
105	C₂×D₁₈₈	C₂⁴	1	16	yes	—
106	C₂×C₄×D₄₇	—	2	192	no	—
107	C₂×C₄×D₄₇	—	2	96	no	—
108	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
109	C₂×C₄×D₄₇	C₂⁴	1	64	yes	—
110	C₂×Dic₉₄	—	2	96	no	—
111	C₂×Dic₉₄	C₂⁴	1	32	yes	—
112	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
113	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
114	C₄²×C₄₇	C₂⁴	1	16	yes	—
115	C₂²⋊Dic₄₇	C₂⁴	1	64	yes	—
116	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
117	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
118	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
119	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
120	Dic₄₇⋊C₄	C₂⁴	1	64	yes	—
121	C₂³×C₄₇	—	2	24	no	—
122	C₂³×C₄₇	—	2	24	no	—
123	C₂³×C₄₇	—	2	24	no	—
124	C₂³×C₄₇	—	4	32	no	—
125	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
126	C₂³×C₄₇	C₂×#41	1	4	yes	—
127	C₂³×C₄₇	2₋¹⁺⁴	1	4	yes	—
128	C₂³×C₄₇	C₂⁵	1	8	yes	—
129	C₂³×C₄₇	C₂⁵	1	3	yes	—
130	C₂²×D₄₇	—	2	64	no	—
131	C₂²×D₄₇	—	2	24	no	—
132	C₂²×D₄₇	—	2	24	no	—
133	C₂²×D₄₇	C₂²×D₄	1	48	yes	—
134	C₂²×D₄₇	C₂⁵	1	8	yes	—
135	D₄×C₄₇	—	2	32	no	—
136	C₂×C₄×C₄₇	—	2	24	no	—
137	C₂×C₄×C₄₇	—	2	12	no	—
138	C₂×C₄×C₄₇	—	2	64	no	—
139	C₂×C₄×C₄₇	C₂²×D₄	1	24	yes	—
140	C₂×C₄×C₄₇	C₂×#41	1	24	yes	complemented
141	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
142	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
143	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
144	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
145	C₂²⋊D₄₇	—	2	128	no	—
146	C₂×Dic₄₇	—	2	48	no	—
147	C₂×Dic₄₇	—	2	24	no	—
148	C₂×Dic₄₇	C₂⁵	1	8	yes	—
149	C₂×Dic₄₇	C₂⁵	1	16	yes	—
150	D₁₈₈	C₂²×D₄	1	64	yes	complemented
151	C₄×D₄₇	—	2	128	no	—
152	C₄×D₄₇	—	2	64	no	—
153	Dic₉₄	—	2	64	no	—
154	C₂²×#547	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	8	no	—
156	C₂²×C₄₇	—	2	8	no	—
157	C₂²×C₄₇	—	2	8	no	—
158	C₂²×C₄₇	—	4	48	no	—
159	C₂²×C₄₇	#547	1	16	yes	complemented
160	C₂²×C₄₇	C₂³×D₄	1	6	yes	—
161	C₂²×C₄₇	C₂²×#41	1	6	yes	—
162	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	6	yes	—
163	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
164	C₂×D₄₇	—	2	8	no	—
165	C₂×D₄₇	—	2	8	no	—
166	C₂×D₄₇	—	2	96	no	—
167	C₂×D₄₇	C₂³×D₄	1	16	yes	—
168	C₄×C₄₇	—	2	8	no	—
169	C₄×C₄₇	—	2	4	no	—
170	C₄×C₄₇	C₂³×D₄	1	8	yes	—
171	C₄×C₄₇	C₂²×#41	1	8	yes	complemented
172	Dic₄₇	—	2	16	no	—
173	Dic₄₇	—	2	8	no	—
174	C₂³×#41	—	47	2	no	—
175	C₂×#547	—	47	48	no	—
176	C₂²×C₄⋊Q₈	—	47	1	no	—
177	C₂²×#123	—	47	4	no	—
178	C₂²×C₂²⋊Q₈	—	47	2	no	—
179	C₂²×#121	—	47	2	no	—
180	C₂²×C₄×D₄	—	47	1	no	—
181	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
182	C₂³×C₄⋊C₄	—	47	2	no	—
183	C₂×C₄₇	—	4	8	no	—
184	C₂×C₄₇	C₂×#547	1	12	yes	complemented
185	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
186	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
187	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
188	D₄₇	—	2	16	no	—
189	C₂²×#41	—	47	48	no	—
190	C₂²×#41	—	94	32	no	—
191	C₂³×Q₈	—	47	2	no	—
192	C₂³×D₄	—	47	4	no	—
193	C₂³×D₄	—	47	1	no	—
194	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
195	C₂⁴×C₄	—	47	4	no	—
196	C₂⁴×C₄	—	47	2	no	—
197	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
198	#547	—	47	256	no	—
199	C₂×C₄⋊Q₈	—	47	24	no	—
200	C₂×#123	—	47	96	no	—
201	C₂×C₂²⋊Q₈	—	47	48	no	—
202	C₂×#121	—	47	48	no	—
203	C₂×C₄×D₄	—	47	24	no	—
204	C₂×C₄×D₄	C₂×D₄₇	1	24	yes	complemented
205	C₂²×C₄⋊C₄	—	47	4	no	—
206	C₂²×C₄⋊C₄	—	47	2	no	—
207	C₂²×C₄⋊C₄	—	47	1	no	—
208	C₂²×C₄⋊C₄	—	47	2	no	—
209	C₂²×C₄⋊C₄	—	47	48	no	—
210	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
211	C₂²×C₂²⋊C₄	—	47	4	no	—
212	C₂²×C₂²⋊C₄	—	47	2	no	—
213	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
214	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
215	C₄₇	C₂²×#547	1	1	yes	characteristic, complemented, Sylow
216	C₂⁵	—	47	2	no	—
217	C₂⁵	C₂²×D₄₇	1	2	yes	—
218	C₂×#41	—	47	128	no	—
219	C₂×#41	—	94	384	no	—
220	C₂²×Q₈	—	47	24	no	—
221	C₂²×Q₈	—	94	16	no	—
222	C₂²×D₄	—	2	8	no	—
223	C₂²×D₄	—	47	48	no	—
224	C₂²×D₄	—	47	16	no	—
225	C₂²×D₄	—	47	12	no	—
226	C₂²×D₄	—	94	32	no	—
227	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
228	C₂³×C₄	—	2	16	no	—
229	C₂³×C₄	—	47	2	no	—
230	C₂³×C₄	—	47	4	no	—
231	C₂³×C₄	—	47	24	no	—
232	C₂³×C₄	—	47	48	no	—
233	C₂³×C₄	—	94	32	no	—
234	C₂³×C₄	—	94	16	no	—
235	C₂³×C₄	C₂²×D₄₇	1	24	yes	—
236	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
240	C₄⋊Q₈	—	47	64	no	—
241	#123	—	47	256	no	—
242	C₂²⋊Q₈	—	47	128	no	—
243	#121	—	47	128	no	—
244	C₄×D₄	—	47	64	no	—
245	C₄×D₄	C₂²×D₄₇	1	64	yes	complemented
246	C₂×C₄⋊C₄	—	47	24	no	—
247	C₂×C₄⋊C₄	—	47	48	no	—
248	C₂×C₄⋊C₄	—	47	12	no	—
249	C₂×C₄⋊C₄	—	47	24	no	—
250	C₂×C₄⋊C₄	—	47	128	no	—
251	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
252	C₂×C₂²⋊C₄	—	47	48	no	—
253	C₂×C₂²⋊C₄	—	47	24	no	—
254	C₂×C₂²⋊C₄	C₂²×D₄₇	1	24	yes	—
255	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	2	8	no	—
258	C₂⁴	—	2	8	no	—
259	C₂⁴	—	47	16	no	—
260	C₂⁴	—	47	12	no	—
261	C₂⁴	—	94	8	no	—
262	C₂⁴	—	94	8	no	—
263	C₂⁴	C₂³×D₄₇	1	12	yes	—
264	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
265	#41	—	94	512	no	—
266	C₂×Q₈	—	47	32	no	—
267	C₂×Q₈	—	94	96	no	—
268	C₂×D₄	—	2	48	no	—
269	C₂×D₄	—	47	64	no	—
270	C₂×D₄	—	47	96	no	—
271	C₂×D₄	—	47	16	no	—
272	C₂×D₄	—	94	192	no	—
273	C₂×D₄	C₂³×D₄₇	1	16	yes	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	96	no	—
277	C₂²×C₄	—	47	12	no	—
278	C₂²×C₄	—	47	24	no	—
279	C₂²×C₄	—	47	32	no	—
280	C₂²×C₄	—	47	64	no	—
281	C₂²×C₄	—	94	192	no	—
282	C₂²×C₄	—	94	16	no	—
283	C₂²×C₄	—	94	8	no	—
284	C₂²×C₄	—	94	96	no	—
285	C₂²×C₄	#10625350	1	8	yes	complemented
286	C₂²×C₄	D₄×D₄₇	1	8	yes	—
287	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
289	C₂²×C₄	C₂³×D₄₇	1	32	yes	—
290	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
291	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
292	C₄⋊C₄	—	47	64	no	—
293	C₄⋊C₄	—	47	32	no	—
294	C₄⋊C₄	—	47	16	no	—
295	C₄⋊C₄	—	47	32	no	—
296	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
297	C₂²⋊C₄	—	47	64	no	—
298	C₂²⋊C₄	—	47	32	no	—
299	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
300	C₄²	C₂³×D₄₇	1	16	yes	—
301	C₂³	—	2	24	no	—
302	C₂³	—	2	24	no	—
303	C₂³	—	2	24	no	—
304	C₂³	—	4	32	no	—
305	C₂³	—	47	48	no	—
306	C₂³	—	47	8	no	—
307	C₂³	—	94	64	no	—
308	C₂³	—	94	24	no	—
309	C₂³	—	94	24	no	—
310	C₂³	C₂×D₄×D₄₇	1	4	yes	—
311	C₂³	C₂×#10625350	1	4	yes	—
312	C₂³	#13094071	1	4	yes	—
313	C₂³	C₂⁴×D₄₇	1	8	yes	—
314	C₂³	C₂⁴×D₄₇	1	3	yes	—
315	Q₈	—	94	64	no	—
316	D₄	—	2	32	no	—
317	D₄	—	47	64	no	—
318	D₄	—	94	128	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	64	no	—
322	C₂×C₄	—	47	8	no	—
323	C₂×C₄	—	47	16	no	—
324	C₂×C₄	—	94	128	no	—
325	C₂×C₄	—	94	48	no	—
326	C₂×C₄	—	94	24	no	—
327	C₂×C₄	—	94	64	no	—
328	C₂×C₄	C₂×D₄×D₄₇	1	24	yes	—
329	C₂×C₄	C₂×#10625350	1	24	yes	complemented
330	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
331	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
332	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
333	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	4	48	no	—
338	C₂²	—	47	16	no	—
339	C₂²	—	94	96	no	—
340	C₂²	—	94	8	no	—
341	C₂²	—	94	8	no	—
342	C₂²	#15689778	1	16	yes	direct product factor
343	C₂²	C₂²×D₄×D₄₇	1	6	yes	—
344	C₂²	C₂²×#10625350	1	6	yes	—
345	C₂²	C₂×#13094071	1	6	yes	—
346	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	4	no	—
349	C₄	—	94	16	no	—
350	C₄	—	94	8	no	—
351	C₄	C₂²×D₄×D₄₇	1	8	yes	—
352	C₄	C₂²×#10625350	1	8	yes	complemented
353	C₂	—	4	8	no	—
354	C₂	—	94	16	no	—
355	C₂	C₂×#15689778	1	12	yes	direct product factor
356	C₂	C₂³×D₄×D₄₇	1	1	yes	characteristic
357	C₂	C₂³×#10625350	1	1	yes	characteristic
358	C₂	C₂²×#13094071	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#547
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625350	C₂	semidirect
2. C₂×#15689778	C₂	direct (N × H)
3. C₂²×#13094024	C₂	semidirect
4. C₂²×#13094006	C₂	semidirect
5. C₂²×#13094003	C₂	semidirect
6. C₂²×#13093995	C₂	semidirect
7. C₂²×C₄×D₁₈₈	C₂	semidirect
8. C₂²×C₄⋊C₄×D₄₇	C₂	semidirect
9. C₂²×C₄×D₄×C₄₇	C₂	semidirect
11. C₂²×#10625350	C₂²	semidirect
17. #15689778	C₂²	direct (N × H)
18. C₂×#13094024	C₂²	semidirect
19. C₂×#13094006	C₂²	semidirect
20. C₂×#13094003	C₂²	semidirect
21. C₂×#13093995	C₂²	semidirect
22. C₂×C₄×D₁₈₈	C₂²	semidirect
27. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
32. C₂×C₄×D₄×C₄₇	C₂²	semidirect
38. C₂×#10625350	C₂³	semidirect
41. C₂²×D₁₈₈	D₄	semidirect
51. #13094024	C₂³	semidirect
52. #13094006	C₂³	semidirect
53. #13094003	C₂³	semidirect
54. #13093995	C₂³	semidirect
55. C₄×D₁₈₈	C₂³	semidirect
60. C₄⋊C₄×D₄₇	C₂³	semidirect
72. C₄×D₄×C₄₇	C₂³	semidirect
91. C₂²×C₄×C₄₇	#41	semidirect
104. C₂×D₁₈₈	C₂×D₄	semidirect
140. C₂×C₄×C₄₇	C₂×#41	semidirect
150. D₁₈₈	C₂²×D₄	semidirect
159. C₂²×C₄₇	#547	semidirect
171. C₄×C₄₇	C₂²×#41	semidirect
181. C₂²×C₄×D₄	D₄₇	semidirect
184. C₂×C₄₇	C₂×#547	semidirect
204. C₂×C₄×D₄	C₂×D₄₇	semidirect
215. C₄₇	C₂²×#547	semidirect
245. C₄×D₄	C₂²×D₄₇	semidirect
285. C₂²×C₄	#10625350	semidirect
329. C₂×C₄	C₂×#10625350	semidirect
342. C₂²	#15689778	direct (N × H)
352. C₄	C₂²×#10625350	semidirect
355. C₂	C₂×#15689778	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×#10625350	2
C₂×#15689778	2
C₂²×#13094024	2
C₂²×#13094006	2
C₂²×#13094003	2
C₂²×#13093995	2
C₂²×C₄×D₁₈₈	2
C₂²×C₄⋊C₄×D₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#547	47

Subgroups — C22×#15689778 #27123220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689778 #27123220