Subgroups — C₄⋊C₄×#10625329 #26214272

Order 12032.

1242 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625329	C₂	1	2	yes	maximal
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
4	#20243263	C₂	1	4	yes	maximal, complemented
5	#20243257	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#20243082	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	2	yes	—
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	#15689147	C₄	1	8	yes	complemented
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₄×#10625329	—	2	8	no	—
16	C₄×#10625329	C₄	1	8	yes	complemented
17	C₂×#13093935	C₂²	1	4	yes	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	4	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
21	#15688878	C₂²	1	4	yes	—
22	#15688878	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
24	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₂×#95×C₄₇	C₄	1	2	yes	—
32	C₂×#10625329	—	2	4	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	4	no	—
36	C₂×#10625329	C₂×C₄	1	4	yes	—
37	C₂×#10625329	C₂×C₄	1	8	yes	—
38	C₂×#10625329	C₂×C₄	1	4	yes	—
39	C₂×#10625329	D₄	1	4	yes	—
40	C₂×#10625329	Q₈	1	4	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
45	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
46	#13093935	—	2	8	no	—
47	#13093935	C₂×C₄	1	8	yes	complemented
48	C₄×C₄₇⋊C₈	—	2	8	no	—
49	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
50	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	—	2	4	no	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	#95×C₄₇	C₂×C₄	1	2	yes	—
70	#95×C₄₇	C₂×C₄	1	4	yes	—
71	#95×C₄₇	C₂×C₄	1	2	yes	—
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	8	no	—
75	C₂²×C₄×C₄₇	—	2	8	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	4	no	—
78	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
79	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₄⋊C₄×C₄₇	—	2	8	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
97	C₄²×C₄₇	—	2	8	no	—
98	C₄²×C₄₇	—	2	2	no	—
99	C₄²×C₄₇	—	2	2	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	2	no	—
102	C₄²×C₄₇	C₄²	1	4	yes	—
103	C₄²×C₄₇	C₄²	1	4	yes	—
104	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
105	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
106	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
107	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
108	#10625329	—	2	8	no	—
109	#10625329	—	2	16	no	—
110	#10625329	C₄⋊C₄	1	16	yes	direct product factor
111	C₂×C₄₇⋊C₈	—	2	4	no	—
112	C₂×C₄₇⋊C₈	—	2	2	no	—
113	C₂×C₄₇⋊C₈	—	2	2	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
117	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
118	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
119	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
123	C₂³×C₄₇	C₄×D₄	1	2	yes	—
124	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
125	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	4	no	—
131	C₂×C₄×C₄₇	—	2	8	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	—	4	16	no	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₄₇	#117	1	4	yes	—
144	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
147	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
149	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₄₇⋊C₈	—	2	4	no	—
157	C₄₇⋊C₈	—	2	8	no	—
158	C₄₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	complemented
159	C₄⋊C₄×M₁₆	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
165	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
166	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
167	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
168	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
169	C₂²×C₄₇	#568	1	2	yes	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	2	8	no	—
174	C₄×C₄₇	—	4	4	no	—
175	C₄×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
176	C₄×C₄₇	C₄×M₁₆	1	4	yes	complemented
177	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
178	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
179	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
181	C₂×#423	—	47	1	no	—
182	C₂×C₄×M₁₆	—	47	1	no	—
183	C₂×C₄×M₁₆	—	47	2	no	—
184	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
185	#1771	—	47	4	no	—
186	#1770	—	47	2	no	—
187	C₈×C₄⋊C₄	—	47	2	no	—
188	#1728	—	47	2	no	—
189	C₂×C₄₇	—	2	4	no	—
190	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
192	C₂×C₄₇	#2873	1	1	yes	characteristic
193	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
194	C₂×C₄₇	Q₈×M₁₆	1	2	yes	—
195	C₂²×M₁₆	—	47	1	no	—
196	C₂²×M₁₆	—	47	2	no	—
197	C₂²×M₁₆	—	47	1	no	—
198	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
199	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
200	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
201	#423	—	47	8	no	—
202	C₂×C₄⋊C₈	—	47	2	no	—
203	C₂×C₄⋊C₈	—	47	2	no	—
204	C₄×M₁₆	—	47	8	no	—
205	C₄×M₁₆	—	94	8	no	—
206	C₂×#97	—	47	2	no	—
207	C₂×#97	—	47	4	no	—
208	C₂×C₄×C₈	—	47	2	no	—
209	C₂×C₄×C₈	—	47	4	no	—
210	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
211	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
212	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
213	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
215	C₂×#95	Dic₄₇	1	2	yes	—
216	#336	—	47	4	no	—
217	#336	—	47	4	no	—
218	C₄₇	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
220	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	47	4	no	—
224	C₂×M₁₆	—	47	4	no	—
225	C₂×M₁₆	—	47	4	no	—
226	C₂×M₁₆	—	47	4	no	—
227	C₂×M₁₆	—	47	8	no	—
228	C₂×M₁₆	—	94	4	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂×M₁₆	—	94	4	no	—
232	C₂²×C₈	—	47	2	no	—
233	C₂²×C₈	—	47	2	no	—
234	C₂²×C₈	—	47	4	no	—
235	C₂×C₄⋊C₄	—	2	8	no	—
236	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
239	C₂×C₄²	—	2	4	no	—
240	C₂×C₄²	—	2	4	no	—
241	C₂×C₄²	C₄×D₄₇	1	4	yes	—
242	C₂×C₄²	C₄×D₄₇	1	4	yes	—
243	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
244	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
247	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
248	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
250	C₄⋊C₈	—	47	8	no	—
251	C₄⋊C₈	—	47	8	no	—
252	#97	—	47	8	no	—
253	#97	—	94	8	no	—
254	C₄×C₈	—	47	8	no	—
255	C₄×C₈	—	94	8	no	—
256	#95	C₂×Dic₄₇	1	2	yes	—
257	#95	C₂×Dic₄₇	1	4	yes	—
258	#95	C₂×Dic₄₇	1	2	yes	—
259	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
266	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
267	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
268	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
269	C₂²×C₄	D₄×D₄₇	1	2	yes	—
270	C₂²×C₄	#10625352	1	2	yes	—
271	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
272	C₂²×C₄	#10625354	1	2	yes	—
273	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
278	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
279	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
281	M₁₆	—	47	16	no	—
282	M₁₆	—	94	8	no	—
283	M₁₆	—	94	16	no	—
284	C₂×C₈	—	47	4	no	—
285	C₂×C₈	—	47	4	no	—
286	C₂×C₈	—	47	4	no	—
287	C₂×C₈	—	47	4	no	—
288	C₂×C₈	—	47	8	no	—
289	C₂×C₈	—	94	4	no	—
290	C₂×C₈	—	94	2	no	—
291	C₂×C₈	—	94	2	no	—
292	C₂×C₈	—	94	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	#10625329	1	8	yes	direct product factor
296	C₄²	—	2	8	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	C₄×Dic₄₇	1	4	yes	—
302	C₄²	C₄×Dic₄₇	1	4	yes	—
303	C₄²	C₂×C₄×D₄₇	1	2	yes	—
304	C₄²	C₂×C₄×D₄₇	1	2	yes	—
305	C₄²	C₂×C₄×D₄₇	1	2	yes	—
306	C₄²	C₂×C₄×D₄₇	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
310	C₂³	D₄×Dic₄₇	1	2	yes	—
311	C₂³	Q₈×Dic₄₇	1	2	yes	—
312	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
325	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
326	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
327	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
328	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
329	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
330	C₂×C₄	#13093982	1	4	yes	—
331	C₂×C₄	#13093986	1	4	yes	—
332	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
333	C₂×C₄	#13093989	1	4	yes	—
334	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
335	C₂×C₄	C₂×#10625329	1	8	yes	—
336	C₂×C₄	C₂×#10625329	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
341	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
342	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
343	C₈	—	47	8	no	—
344	C₈	—	94	4	no	—
345	C₈	—	94	8	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	C₄⋊C₄×Dic₄₇	1	4	yes	—
351	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
352	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
353	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
354	C₂²	C₂²×#10625329	1	2	yes	—
355	C₂²	#15689890	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	8	no	—
360	C₄	—	4	4	no	—
361	C₄	C₄⋊C₄×Dic₄₇	1	4	yes	—
362	C₄	C₄×#10625329	1	4	yes	complemented
363	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
364	C₄	C₂×#13093982	1	1	yes	characteristic
365	C₄	C₂×#13093986	1	1	yes	characteristic
366	C₄	C₂×#13093989	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
369	C₂	C₂×C₄×#10625329	1	1	yes	characteristic
370	C₂	#20251807	1	1	yes	characteristic
371	C₂	D₄×#10625329	1	2	yes	—
372	C₂	Q₈×#10625329	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20243263	C₂	semidirect
5. #20243257	C₂	semidirect
6. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
12. #15689147	C₄	semidirect
16. C₄×#10625329	C₄	semidirect
44. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
45. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
47. #13093935	C₂×C₄	semidirect
49. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
96. C₄⋊C₄×C₄₇	M₁₆	semidirect
110. #10625329	C₄⋊C₄	direct (N × H)
158. C₄₇⋊C₈	C₂×C₄⋊C₄	semidirect
176. C₄×C₄₇	C₄×M₁₆	semidirect
218. C₄₇	C₄⋊C₄×M₁₆	semidirect
295. C₄⋊C₄	#10625329	direct (N × H)
362. C₄	C₄×#10625329	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×C₄×#10625329	2
#20243263	2
#20243257	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243082	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄⋊C₄×M₁₆	47

Subgroups — C4⋊C4×#10625329 #26214272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#10625329 #26214272