Subgroups — C₂²×#15688890 #26213706

Order 12032.

4334 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
2	C₂×#15688890	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×Dic₄₇	—	2	2	no	—
5	C₂²×C₂²⋊Dic₄₇	—	2	8	no	—
6	C₂²×C₂²⋊Dic₄₇	—	2	6	no	—
7	C₂²×C₂²⋊Dic₄₇	C₄	1	16	yes	complemented
8	C₂²×C₂²⋊Dic₄₇	C₂²	1	12	yes	—
9	#15688890	C₂²	1	16	yes	direct product factor
10	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₇	C₄	1	2	yes	complemented
12	C₂²×C₂²⋊C₄×C₄₇	—	2	2	no	—
13	C₂²×C₂²⋊C₄×C₄₇	—	2	6	no	—
14	C₂²×C₂²⋊C₄×C₄₇	C₄	1	6	yes	complemented
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	6	yes	—
16	C₂³×Dic₄₇	—	2	16	no	—
17	C₂³×Dic₄₇	—	2	12	no	—
18	C₂³×Dic₄₇	—	4	16	no	—
19	C₂×C₂²⋊Dic₄₇	—	2	48	no	—
20	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
21	C₂×C₂²⋊Dic₄₇	—	2	24	no	—
22	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	48	yes	complemented
23	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
24	C₂⁵×C₄₇	—	4	8	no	—
25	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂⁵×C₄₇	C₂×C₄	1	8	yes	—
27	C₂⁵×C₄₇	C₂×C₄	1	3	yes	—
28	C₂⁵×C₄₇	D₄	1	2	yes	—
29	C₂⁵×C₄₇	D₄	1	4	yes	—
30	C₂⁵×C₄₇	D₄	1	6	yes	—
31	C₂⁵×C₄₇	Q₈	1	4	yes	—
32	C₂⁵×C₄₇	C₂³	1	3	yes	—
33	C₂³×C₄×C₄₇	—	2	6	no	—
34	C₂³×C₄×C₄₇	—	2	2	no	—
35	C₂³×C₄×C₄₇	—	4	8	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	12	yes	complemented
37	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
38	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
39	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
41	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	12	yes	complemented
42	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
43	C₂⁴×C₄₇	—	2	8	no	—
44	C₂⁴×C₄₇	—	2	16	no	—
45	C₂⁴×C₄₇	—	4	32	no	—
46	C₂⁴×C₄₇	—	4	12	no	—
47	C₂⁴×C₄₇	—	4	16	no	—
48	C₂⁴×C₄₇	—	4	24	no	—
49	C₂⁴×C₄₇	—	4	16	no	—
50	C₂⁴×C₄₇	—	4	12	no	—
51	C₂⁴×C₄₇	C₄²	1	4	yes	—
52	C₂⁴×C₄₇	C₄²	1	12	yes	—
53	C₂⁴×C₄₇	C₂²⋊C₄	1	8	yes	—
54	C₂⁴×C₄₇	C₂²⋊C₄	1	6	yes	—
55	C₂⁴×C₄₇	C₂²⋊C₄	1	3	yes	—
56	C₂⁴×C₄₇	C₂²⋊C₄	1	24	yes	—
57	C₂⁴×C₄₇	C₂²⋊C₄	1	6	yes	—
58	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
59	C₂⁴×C₄₇	C₄⋊C₄	1	8	yes	—
60	C₂⁴×C₄₇	C₄⋊C₄	1	4	yes	—
61	C₂⁴×C₄₇	C₄⋊C₄	1	24	yes	—
62	C₂⁴×C₄₇	C₄⋊C₄	1	12	yes	—
63	C₂⁴×C₄₇	C₂²×C₄	1	3	yes	—
64	C₂⁴×C₄₇	C₂²×C₄	1	12	yes	—
65	C₂⁴×C₄₇	C₂²×C₄	1	3	yes	—
66	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
67	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
68	C₂⁴×C₄₇	C₂×D₄	1	6	yes	—
69	C₂⁴×C₄₇	C₂×Q₈	1	6	yes	—
70	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	—	2	12	no	—
72	C₂²×C₄×C₄₇	—	2	12	no	—
73	C₂²×C₄×C₄₇	—	4	24	no	—
74	C₂²×C₄×C₄₇	—	4	8	no	—
75	C₂²×C₄×C₄₇	—	4	24	no	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	complemented
77	C₂²×Dic₄₇	—	2	48	no	—
78	C₂²×Dic₄₇	—	2	8	no	—
79	C₂²×Dic₄₇	—	4	64	no	—
80	C₂²×Dic₄₇	—	4	48	no	—
81	C₂²⋊C₄×C₄₇	—	2	24	no	—
82	C₂²⋊C₄×C₄₇	—	2	8	no	—
83	C₂²⋊Dic₄₇	—	2	48	no	—
84	C₂²⋊Dic₄₇	—	2	8	no	—
85	C₂²⋊Dic₄₇	C₂²×C₄	1	16	yes	complemented
86	C₂³×C₄₇	—	2	32	no	—
87	C₂³×C₄₇	—	2	16	no	—
88	C₂³×C₄₇	—	2	32	no	—
89	C₂³×C₄₇	—	2	16	no	—
90	C₂³×C₄₇	—	2	24	no	—
91	C₂³×C₄₇	—	2	12	no	—
92	C₂³×C₄₇	—	2	12	no	—
93	C₂³×C₄₇	—	2	24	no	—
94	C₂³×C₄₇	—	4	24	no	—
95	C₂³×C₄₇	—	4	48	no	—
96	C₂³×C₄₇	—	4	12	no	—
97	C₂³×C₄₇	—	4	48	no	—
98	C₂³×C₄₇	—	4	24	no	—
99	C₂³×C₄₇	—	4	24	no	—
100	C₂³×C₄₇	—	4	6	no	—
101	C₂³×C₄₇	—	4	12	no	—
102	C₂³×C₄₇	—	4	12	no	—
103	C₂³×C₄₇	—	4	12	no	—
104	C₂³×C₄₇	—	4	2	no	—
105	C₂³×C₄₇	#95	1	12	yes	—
106	C₂³×C₄₇	#95	1	24	yes	—
107	C₂³×C₄₇	#95	1	24	yes	—
108	C₂³×C₄₇	#95	1	4	yes	—
109	C₂³×C₄₇	#99	1	8	yes	—
110	C₂³×C₄₇	C₂×C₄²	1	6	yes	—
111	C₂³×C₄₇	C₂×C₄²	1	6	yes	—
112	C₂³×C₄₇	C₂×C₂²⋊C₄	1	12	yes	—
113	C₂³×C₄₇	C₂×C₂²⋊C₄	1	12	yes	—
114	C₂³×C₄₇	C₂×C₂²⋊C₄	1	6	yes	—
115	C₂³×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
116	C₂³×C₄₇	C₂×C₂²⋊C₄	1	3	yes	—
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	12	yes	—
118	C₂³×C₄₇	C₂×C₄⋊C₄	1	12	yes	—
119	C₂³×C₄₇	C₂×C₄⋊C₄	1	6	yes	—
120	C₂³×C₄₇	C₂×C₄⋊C₄	1	6	yes	—
121	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
122	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
123	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
124	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
125	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	4	24	no	—
128	C₂×C₄×C₄₇	—	4	24	no	—
129	C₂×C₄×C₄₇	—	4	8	no	—
130	C₂×Dic₄₇	—	2	16	no	—
131	C₂×Dic₄₇	—	4	16	no	—
132	C₂×Dic₄₇	—	4	96	no	—
133	C₂²×#342	—	47	1	no	maximal, Sylow
134	C₂²×C₄₇	—	2	4	no	—
135	C₂²×C₄₇	—	2	6	no	—
136	C₂²×C₄₇	—	2	2	no	—
137	C₂²×C₄₇	—	2	12	no	—
138	C₂²×C₄₇	—	2	24	no	—
139	C₂²×C₄₇	—	2	48	no	—
140	C₂²×C₄₇	—	2	24	no	—
141	C₂²×C₄₇	—	2	12	no	—
142	C₂²×C₄₇	—	2	24	no	—
143	C₂²×C₄₇	—	2	12	no	—
144	C₂²×C₄₇	—	4	24	no	—
145	C₂²×C₄₇	—	4	6	no	—
146	C₂²×C₄₇	—	4	12	no	—
147	C₂²×C₄₇	—	4	12	no	—
148	C₂²×C₄₇	—	4	6	no	—
149	C₂²×C₄₇	—	4	2	no	—
150	C₂²×C₄₇	—	4	1	no	—
151	C₂²×C₄₇	—	4	1	no	—
152	C₂²×C₄₇	#342	1	16	yes	complemented
153	C₂²×C₄₇	C₂×#95	1	6	yes	—
154	C₂²×C₄₇	C₂×#95	1	12	yes	—
155	C₂²×C₄₇	C₂×#95	1	6	yes	—
156	C₂²×C₄₇	C₂×#99	1	12	yes	—
157	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
158	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
159	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄₇	C₂²×C₄⋊C₄	1	2	yes	—
161	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
162	C₄×C₄₇	—	4	8	no	—
163	Dic₄₇	—	4	16	no	—
164	C₂³×C₂²⋊C₄	—	47	2	no	—
165	C₂³×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
166	C₂×#342	—	47	12	no	—
167	C₂×C₄₇	—	2	2	no	—
168	C₂×C₄₇	—	2	2	no	—
169	C₂×C₄₇	—	2	1	no	—
170	C₂×C₄₇	—	2	6	no	—
171	C₂×C₄₇	—	2	12	no	—
172	C₂×C₄₇	—	2	1	no	—
173	C₂×C₄₇	C₂×#342	1	12	yes	complemented
174	C₂×C₄₇	C₂²×#95	1	1	yes	characteristic
175	C₂×C₄₇	C₂²×#99	1	2	yes	—
176	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
177	C₂⁴×C₄	—	94	2	no	—
178	C₂⁴×C₄	Dic₄₇	1	2	yes	complemented
179	C₂²×C₂²⋊C₄	—	2	6	no	—
180	C₂²×C₂²⋊C₄	—	2	2	no	—
181	C₂²×C₂²⋊C₄	—	47	16	no	—
182	C₂²×C₂²⋊C₄	—	47	12	no	—
183	C₂²×C₂²⋊C₄	—	94	8	no	—
184	C₂²×C₂²⋊C₄	—	94	6	no	—
185	C₂²×C₂²⋊C₄	Dic₄₇	1	6	yes	complemented
186	C₂²×C₂²⋊C₄	C₂×D₄₇	1	6	yes	—
187	#342	—	47	16	no	—
188	C₄₇	C₂²×#342	1	1	yes	characteristic, complemented, Sylow
189	C₂⁵	—	4	8	no	—
190	C₂⁵	Dic₉₄	1	4	yes	—
191	C₂⁵	C₄×D₄₇	1	8	yes	—
192	C₂⁵	D₁₈₈	1	4	yes	—
193	C₂⁵	C₂×Dic₄₇	1	1	yes	characteristic
194	C₂⁵	C₂×Dic₄₇	1	3	yes	—
195	C₂⁵	C₂²⋊D₄₇	1	2	yes	—
196	C₂⁵	C₂²⋊D₄₇	1	6	yes	—
197	C₂⁵	C₂²×D₄₇	1	3	yes	—
198	C₂³×C₄	—	2	6	no	—
199	C₂³×C₄	—	2	2	no	—
200	C₂³×C₄	—	4	8	no	—
201	C₂³×C₄	—	94	16	no	—
202	C₂³×C₄	—	94	12	no	—
203	C₂³×C₄	—	188	16	no	—
204	C₂³×C₄	C₂×Dic₄₇	1	12	yes	complemented
205	C₂×C₂²⋊C₄	—	2	12	no	—
206	C₂×C₂²⋊C₄	—	2	12	no	—
207	C₂×C₂²⋊C₄	—	2	12	no	—
208	C₂×C₂²⋊C₄	—	2	12	no	—
209	C₂×C₂²⋊C₄	—	47	48	no	—
210	C₂×C₂²⋊C₄	—	47	8	no	—
211	C₂×C₂²⋊C₄	—	94	48	no	—
212	C₂×C₂²⋊C₄	—	94	24	no	—
213	C₂×C₂²⋊C₄	—	94	12	no	—
214	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	12	yes	complemented
215	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
216	C₂⁴	—	2	8	no	—
217	C₂⁴	—	2	16	no	—
218	C₂⁴	—	4	16	no	—
219	C₂⁴	—	4	32	no	—
220	C₂⁴	—	4	16	no	—
221	C₂⁴	—	4	12	no	—
222	C₂⁴	—	4	24	no	—
223	C₂⁴	—	4	12	no	—
224	C₂⁴	C₄×Dic₄₇	1	4	yes	—
225	C₂⁴	C₄×Dic₄₇	1	12	yes	—
226	C₂⁴	Dic₄₇⋊C₄	1	8	yes	—
227	C₂⁴	Dic₄₇⋊C₄	1	24	yes	—
228	C₂⁴	C₄⋊Dic₄₇	1	4	yes	—
229	C₂⁴	C₄⋊Dic₄₇	1	12	yes	—
230	C₂⁴	(C₂×D₄₇)⋊C₄	1	8	yes	—
231	C₂⁴	(C₂×D₄₇)⋊C₄	1	24	yes	—
232	C₂⁴	C₂²⋊Dic₄₇	1	6	yes	—
233	C₂⁴	C₂²⋊Dic₄₇	1	3	yes	—
234	C₂⁴	C₂²⋊Dic₄₇	1	6	yes	—
235	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
236	C₂⁴	C₂×Dic₉₄	1	6	yes	—
237	C₂⁴	C₂×C₄×D₄₇	1	12	yes	—
238	C₂⁴	C₂×D₁₈₈	1	6	yes	—
239	C₂⁴	C₂²×Dic₄₇	1	3	yes	—
240	C₂⁴	C₂²×Dic₄₇	1	3	yes	—
241	C₂⁴	C₂×C₂²⋊D₄₇	1	6	yes	—
242	C₂⁴	C₂×C₂²⋊D₄₇	1	6	yes	—
243	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
244	C₂²×C₄	—	2	12	no	—
245	C₂²×C₄	—	2	12	no	—
246	C₂²×C₄	—	4	24	no	—
247	C₂²×C₄	—	4	8	no	—
248	C₂²×C₄	—	4	24	no	—
249	C₂²×C₄	—	94	48	no	—
250	C₂²×C₄	—	94	8	no	—
251	C₂²×C₄	—	188	48	no	—
252	C₂²×C₄	—	188	64	no	—
253	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	complemented
254	C₂²⋊C₄	—	2	24	no	—
255	C₂²⋊C₄	—	2	8	no	—
256	C₂²⋊C₄	—	47	16	no	—
257	C₂²⋊C₄	—	94	48	no	—
258	C₂²⋊C₄	—	94	8	no	—
259	C₂³	—	2	12	no	—
260	C₂³	—	2	12	no	—
261	C₂³	—	2	24	no	—
262	C₂³	—	2	24	no	—
263	C₂³	—	2	32	no	—
264	C₂³	—	2	16	no	—
265	C₂³	—	2	32	no	—
266	C₂³	—	2	16	no	—
267	C₂³	—	4	24	no	—
268	C₂³	—	4	48	no	—
269	C₂³	—	4	24	no	—
270	C₂³	—	4	48	no	—
271	C₂³	—	4	12	no	—
272	C₂³	—	4	12	no	—
273	C₂³	—	4	24	no	—
274	C₂³	—	4	12	no	—
275	C₂³	—	4	6	no	—
276	C₂³	—	4	12	no	—
277	C₂³	—	4	2	no	—
278	C₂³	C₄₇⋊#95	1	12	yes	—
279	C₂³	C₄₇⋊#95	1	24	yes	—
280	C₂³	C₄₇⋊#95	1	24	yes	—
281	C₂³	C₄₇⋊#95	1	4	yes	—
282	C₂³	#13093939	1	8	yes	—
283	C₂³	C₂×C₄×Dic₄₇	1	6	yes	—
284	C₂³	C₂×C₄×Dic₄₇	1	6	yes	—
285	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	12	yes	—
286	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	12	yes	—
287	C₂³	C₂×C₂²⋊Dic₄₇	1	6	yes	—
288	C₂³	C₂×C₂²⋊Dic₄₇	1	3	yes	—
289	C₂³	C₂×C₂²⋊Dic₄₇	1	3	yes	—
290	C₂³	C₂×Dic₄₇⋊C₄	1	12	yes	—
291	C₂³	C₂×Dic₄₇⋊C₄	1	12	yes	—
292	C₂³	C₂×C₄⋊Dic₄₇	1	6	yes	—
293	C₂³	C₂×C₄⋊Dic₄₇	1	6	yes	—
294	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
295	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
296	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
297	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
298	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
299	C₂×C₄	—	2	8	no	—
300	C₂×C₄	—	4	24	no	—
301	C₂×C₄	—	4	24	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	94	16	no	—
304	C₂×C₄	—	188	96	no	—
305	C₂×C₄	—	188	16	no	—
306	C₂²	—	2	24	no	—
307	C₂²	—	2	24	no	—
308	C₂²	—	2	48	no	—
309	C₂²	—	2	12	no	—
310	C₂²	—	2	24	no	—
311	C₂²	—	2	12	no	—
312	C₂²	—	2	6	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	12	no	—
316	C₂²	—	4	24	no	—
317	C₂²	—	4	6	no	—
318	C₂²	—	4	12	no	—
319	C₂²	—	4	12	no	—
320	C₂²	—	4	6	no	—
321	C₂²	—	4	2	no	—
322	C₂²	—	4	1	no	—
323	C₂²	—	4	1	no	—
324	C₂²	#15688890	1	16	yes	direct product factor
325	C₂²	C₂×C₄₇⋊#95	1	6	yes	—
326	C₂²	C₂×C₄₇⋊#95	1	12	yes	—
327	C₂²	C₂×C₄₇⋊#95	1	6	yes	—
328	C₂²	C₂×#13093939	1	12	yes	—
329	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
330	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	2	yes	—
331	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂²	C₂²×Dic₄₇⋊C₄	1	2	yes	—
333	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
334	C₄	—	4	8	no	—
335	C₄	—	188	16	no	—
336	C₂	—	2	2	no	—
337	C₂	—	2	12	no	—
338	C₂	—	2	6	no	—
339	C₂	—	2	1	no	—
340	C₂	—	2	2	no	—
341	C₂	—	2	1	no	—
342	C₂	C₂×#15688890	1	12	yes	direct product factor
343	C₂	C₂²×C₄₇⋊#95	1	1	yes	characteristic
344	C₂	C₂²×#13093939	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂²⋊Dic₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₂³×C₂²⋊C₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²⋊C₄
prime radical	C₂⁶×C₄₇	C₂²
cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	C₂²×#342
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁶ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×#15688890	C₂	direct (N × H)
7. C₂²×C₂²⋊Dic₄₇	C₄	semidirect
9. #15688890	C₂²	direct (N × H)
11. C₂⁴×C₄×C₄₇	C₄	semidirect
14. C₂²×C₂²⋊C₄×C₄₇	C₄	semidirect
22. C₂×C₂²⋊Dic₄₇	C₂×C₄	semidirect
36. C₂³×C₄×C₄₇	C₂×C₄	semidirect
41. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
76. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
85. C₂²⋊Dic₄₇	C₂²×C₄	semidirect
152. C₂²×C₄₇	#342	semidirect
173. C₂×C₄₇	C₂×#342	semidirect
178. C₂⁴×C₄	Dic₄₇	semidirect
185. C₂²×C₂²⋊C₄	Dic₄₇	semidirect
188. C₄₇	C₂²×#342	semidirect
204. C₂³×C₄	C₂×Dic₄₇	semidirect
214. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
253. C₂²×C₄	C₂²×Dic₄₇	semidirect
324. C₂²	#15688890	direct (N × H)
342. C₂	C₂×#15688890	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×C₂²⋊Dic₄₇	2
C₂×#15688890	2
C₂³×C₂²⋊C₄×C₄₇	2
C₂²×#342	47

Subgroups — C22×#15688890 #26213706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15688890 #26213706