Subgroups — C₄×#15689597 #26374515

Order 12032.

4186 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689597	C₂	1	2	yes	maximal
2	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20245750	C₂	1	4	yes	maximal, complemented
4	#20245748	C₂	1	4	yes	maximal, complemented
5	#20245744	C₂	1	2	yes	maximal, complemented
6	#20245740	C₂	1	4	yes	maximal, complemented
7	C₄²×D₁₈₈	C₂	1	4	yes	maximal, complemented
8	C₄×#13093986	C₂	1	4	yes	maximal, complemented
9	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₂²⋊C₄×D₄₇	C₂	1	4	yes	maximal, complemented
11	C₄×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
14	#15689597	C₄	1	32	yes	direct product factor
15	C₂×C₄×D₁₈₈	C₄	1	16	yes	complemented
16	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
17	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
18	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
19	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
20	C₂×C₄×D₁₈₈	C₂²	1	8	yes	—
21	C₂×#13093986	C₂²	1	8	yes	—
22	C₂×#13093983	C₂²	1	2	yes	—
23	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₄×D₄₇	C₂²	1	8	yes	—
26	C₂×C₄²×D₄₇	C₂²	1	8	yes	complemented
27	C₄⋊C₄×Dic₄₇	C₂²	1	8	yes	complemented
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
30	C₄×C₄⋊Dic₄₇	C₂²	1	8	yes	complemented
31	C₂²⋊C₄×Dic₄₇	C₂²	1	8	yes	—
32	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	8	yes	complemented
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	16	yes	complemented
34	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
35	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
36	#15688970	C₂²	1	8	yes	complemented
37	#15688970	C₂²	1	16	yes	complemented
38	#15688969	C₂²	1	2	yes	complemented
39	#95×D₄₇	C₂²	1	8	yes	complemented
40	C₄²×Dic₄₇	C₂²	1	2	yes	complemented
41	C₂×#117×C₄₇	C₂²	1	2	yes	—
42	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
44	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
47	C₄₇×#376	C₂²	1	2	yes	complemented
48	C₄³×C₄₇	C₂²	1	2	yes	complemented
49	C₂⁴×D₄₇	C₂³	1	2	yes	—
50	C₂²×D₁₈₈	C₂×C₄	1	8	yes	—
51	C₂²×D₁₈₈	C₂×C₄	1	16	yes	—
52	C₂²×D₁₈₈	C₂³	1	2	yes	—
53	C₂²×D₁₈₈	C₂³	1	2	yes	—
54	C₂³×Dic₄₇	C₂³	1	2	yes	—
55	C₂²×C₄×D₄₇	—	4	8	no	—
56	C₂²×C₄×D₄₇	C₂×C₄	1	16	yes	complemented
57	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
58	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
59	C₂²×C₄×D₄₇	C₂³	1	16	yes	—
60	C₄×D₁₈₈	C₂×C₄	1	16	yes	complemented
61	C₄×D₁₈₈	C₂×C₄	1	16	yes	complemented
62	C₄×D₁₈₈	C₂×C₄	1	16	yes	complemented
63	C₄×D₁₈₈	C₂×C₄	1	16	yes	complemented
64	C₄×D₁₈₈	C₂×C₄	1	64	yes	complemented
65	#13093986	C₂×C₄	1	64	yes	complemented
66	#13093983	C₂×C₄	1	16	yes	complemented
67	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	complemented
68	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
71	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
72	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	16	yes	complemented
73	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
74	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
75	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
76	C₂²⋊C₄×D₄₇	C₂×C₄	1	64	yes	complemented
77	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
78	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
79	C₂×C₄×Dic₄₇	C₂³	1	16	yes	—
80	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
81	C₄²×D₄₇	—	4	16	no	—
82	C₄₇⋊#95	C₂³	1	4	yes	—
83	C₄₇⋊#95	C₂³	1	16	yes	—
84	C₄₇⋊#95	C₂³	1	4	yes	—
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
88	#117×C₄₇	C₂×C₄	1	16	yes	complemented
89	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
91	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
92	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
99	#95×C₄₇	C₂³	1	4	yes	—
100	#95×C₄₇	C₂³	1	4	yes	—
101	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂³×D₄₇	—	4	4	no	—
103	C₂³×D₄₇	—	4	4	no	—
104	C₂³×D₄₇	C₂²×C₄	1	16	yes	—
105	C₂³×D₄₇	C₂²×C₄	1	8	yes	—
106	C₂³×D₄₇	C₂⁴	1	4	yes	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	4	2	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₇	—	4	4	no	—
121	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
122	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
123	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
124	C₂×D₁₈₈	C₄²	1	64	yes	complemented
125	C₂×D₁₈₈	C₂²×C₄	1	16	yes	—
126	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
127	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
128	C₂×D₁₈₈	C₂²×C₄	1	16	yes	—
129	C₂×C₄×D₄₇	—	2	16	no	—
130	C₂×C₄×D₄₇	—	4	32	no	—
131	C₂×C₄×D₄₇	—	4	16	no	—
132	C₂×C₄×D₄₇	—	4	8	no	—
133	C₂×C₄×D₄₇	—	4	16	no	—
134	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
135	C₂×C₄×D₄₇	C₂²×C₄	1	16	yes	—
136	C₂×C₄×D₄₇	C₂²×C₄	1	64	yes	complemented
137	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
138	C₂²⋊C₄×C₄₇	C₂²×C₄	1	16	yes	—
139	C₄²×C₄₇	—	2	8	no	—
140	C₄²×C₄₇	—	4	4	no	—
141	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
142	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
143	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
144	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
145	C₄²×C₄₇	C₂²×C₄	1	16	yes	complemented
146	C₂²⋊Dic₄₇	C₂²×C₄	1	16	yes	—
147	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
148	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
149	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	64	yes	complemented
150	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
151	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
152	C₄⋊Dic₄₇	C₂²×C₄	1	16	yes	complemented
153	C₄×Dic₄₇	—	2	8	no	—
154	C₄×Dic₄₇	—	4	16	no	—
155	C₄×Dic₄₇	—	4	4	no	—
156	C₄×Dic₄₇	C₂²×C₄	1	16	yes	complemented
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
160	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
161	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	8	no	—
163	C₂²×D₄₇	—	2	8	no	—
164	C₂²×D₄₇	—	4	8	no	—
165	C₂²×D₄₇	—	4	8	no	—
166	C₂²×D₄₇	—	4	32	no	—
167	C₂²×D₄₇	C₂×C₄²	1	32	yes	complemented
168	C₂²×D₄₇	C₂³×C₄	1	8	yes	—
169	C₂²×D₄₇	C₂³×C₄	1	16	yes	—
170	C₂×C₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	8	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	complemented
178	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂³×C₄	1	16	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
187	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
188	C₂×Dic₄₇	—	2	8	no	—
189	C₂×Dic₄₇	—	2	8	no	—
190	C₂×Dic₄₇	—	2	8	no	—
191	C₂×Dic₄₇	—	4	8	no	—
192	C₂×Dic₄₇	C₂³×C₄	1	16	yes	—
193	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
194	D₁₈₈	C₂×C₄²	1	32	yes	complemented
195	D₁₈₈	C₂×C₄²	1	32	yes	complemented
196	C₄×D₄₇	—	2	32	no	—
197	C₄×D₄₇	—	4	16	no	—
198	C₄×D₄₇	—	4	64	no	—
199	C₄×#518	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	8	no	—
203	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
204	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
205	C₂²×C₄₇	C₂⁴×C₄	1	2	yes	—
206	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
207	C₂²×C₄₇	#585	1	2	yes	—
208	C₂×D₄₇	—	2	8	no	—
209	C₂×D₄₇	—	2	8	no	—
210	C₂×D₄₇	—	2	32	no	—
211	C₂×D₄₇	—	4	32	no	—
212	C₂×D₄₇	C₂²×C₄²	1	16	yes	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	16	no	—
217	C₄×C₄₇	C₂²×C₄²	1	4	yes	—
218	C₄×C₄₇	C₂²×C₄²	1	4	yes	—
219	C₄×C₄₇	#518	1	4	yes	complemented
220	Dic₄₇	—	2	8	no	—
221	Dic₄₇	—	2	16	no	—
222	C₂×#518	—	47	2	no	—
223	C₂²×C₄×D₄	—	47	1	no	—
224	#2275	—	47	4	no	—
225	#2275	—	47	4	no	—
226	#2274	—	47	2	no	—
227	#2273	—	47	4	no	—
228	C₄²×D₄	—	47	4	no	—
229	C₄²×D₄	—	47	4	no	—
230	C₄×#117	—	47	1	no	—
231	C₄×#117	D₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄×C₂²⋊C₄	—	47	4	no	—
233	C₂×C₄₇	—	2	4	no	—
234	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
235	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
236	C₂×C₄₇	#3428	1	1	yes	characteristic
237	C₂×C₄₇	C₄×H(5,𝔽₂)	1	4	yes	—
238	D₄₇	—	2	16	no	—
239	C₂³×D₄	—	47	1	no	—
240	C₂⁴×C₄	—	47	2	no	—
241	#518	—	47	32	no	—
242	C₂×C₄×D₄	—	47	8	no	—
243	C₂×C₄×D₄	—	47	16	no	—
244	C₂×C₄×D₄	—	47	2	no	—
245	C₂×C₄×D₄	—	47	2	no	—
246	C₂×C₄×D₄	—	47	2	no	—
247	C₂×C₄×D₄	—	47	2	no	—
248	C₂×C₄×D₄	—	47	8	no	—
249	C₂×#117	—	47	2	no	—
250	C₂×#117	C₂×D₄₇	1	2	yes	—
251	C₂²×C₄⋊C₄	—	47	1	no	—
252	C₂²×C₂²⋊C₄	—	47	2	no	—
253	C₂²×C₂²⋊C₄	—	47	8	no	—
254	C₂²×C₄²	—	47	8	no	—
255	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
256	C₄×C₄⋊C₄	—	47	8	no	—
257	C₄×C₄⋊C₄	—	47	2	no	—
258	C₄×C₄⋊C₄	—	47	2	no	—
259	C₄×C₄⋊C₄	—	47	8	no	—
260	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
261	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
262	C₄×C₂²⋊C₄	—	47	2	no	—
263	C₄×C₂²⋊C₄	—	47	2	no	—
264	C₄×C₂²⋊C₄	—	47	8	no	—
265	C₄×C₂²⋊C₄	—	47	8	no	—
266	C₄×C₂²⋊C₄	—	47	16	no	—
267	C₄×C₂²⋊C₄	—	47	8	no	—
268	C₄×C₂²⋊C₄	—	47	16	no	—
269	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
270	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
271	#376	—	47	2	no	—
272	#376	C₂×D₄₇	1	2	yes	complemented
273	C₂×#95	—	47	8	no	—
274	C₄³	—	47	2	no	—
275	C₄³	C₂×D₄₇	1	2	yes	complemented
276	C₄₇	C₄×#518	1	1	yes	characteristic, complemented, Sylow
277	C₂⁵	—	47	2	no	—
278	C₂²×D₄	—	47	8	no	—
279	C₂²×D₄	—	47	16	no	—
280	C₂²×D₄	—	47	2	no	—
281	C₂²×D₄	—	47	2	no	—
282	C₂³×C₄	—	47	2	no	—
283	C₂³×C₄	—	47	4	no	—
284	C₂³×C₄	—	47	16	no	—
285	C₂³×C₄	—	47	16	no	—
286	C₂³×C₄	—	47	4	no	—
287	C₂³×C₄	—	188	8	no	—
288	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₄×D₄	—	47	64	no	—
292	C₄×D₄	—	47	16	no	—
293	C₄×D₄	—	47	16	no	—
294	C₄×D₄	—	47	16	no	—
295	C₄×D₄	—	47	16	no	—
296	C₄×D₄	—	47	64	no	—
297	#117	—	47	16	no	—
298	#117	C₄×D₄₇	1	16	yes	complemented
299	C₂×C₄⋊C₄	—	47	8	no	—
300	C₂×C₄⋊C₄	—	47	2	no	—
301	C₂×C₄⋊C₄	—	47	2	no	—
302	C₂×C₄⋊C₄	—	47	4	no	—
303	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
304	C₂×C₂²⋊C₄	—	47	4	no	—
305	C₂×C₂²⋊C₄	—	47	16	no	—
306	C₂×C₂²⋊C₄	—	47	4	no	—
307	C₂×C₂²⋊C₄	—	47	4	no	—
308	C₂×C₂²⋊C₄	—	47	16	no	—
309	C₂×C₂²⋊C₄	—	47	64	no	—
310	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
311	C₂×C₄²	—	47	4	no	—
312	C₂×C₄²	—	47	4	no	—
313	C₂×C₄²	—	47	4	no	—
314	C₂×C₄²	—	47	16	no	—
315	C₂×C₄²	—	188	16	no	—
316	C₂×C₄²	C₄×D₄₇	1	8	yes	complemented
317	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
318	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
322	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
323	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
324	#95	—	47	4	no	—
325	#95	—	47	16	no	—
326	#95	—	47	4	no	—
327	#95	C₂²×D₄₇	1	4	yes	—
328	#95	C₂²×D₄₇	1	4	yes	—
329	C₂⁴	—	47	4	no	—
330	C₂⁴	—	47	16	no	—
331	C₂⁴	—	47	8	no	—
332	C₂⁴	—	188	4	no	—
333	C₂⁴	—	188	4	no	—
334	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
335	C₂×D₄	—	47	64	no	—
336	C₂×D₄	—	47	16	no	—
337	C₂×D₄	—	47	8	no	—
338	C₂×D₄	—	47	8	no	—
339	C₂×D₄	—	47	16	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	47	8	no	—
343	C₂²×C₄	—	47	4	no	—
344	C₂²×C₄	—	47	8	no	—
345	C₂²×C₄	—	47	16	no	—
346	C₂²×C₄	—	47	16	no	—
347	C₂²×C₄	—	47	64	no	—
348	C₂²×C₄	—	94	16	no	—
349	C₂²×C₄	—	188	32	no	—
350	C₂²×C₄	—	188	16	no	—
351	C₂²×C₄	—	188	16	no	—
352	C₂²×C₄	—	188	8	no	—
353	C₂²×C₄	—	188	4	no	—
354	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
355	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
356	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
357	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
358	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
359	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
360	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
361	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
365	C₄⋊C₄	—	47	8	no	—
366	C₄⋊C₄	—	47	8	no	—
367	C₄⋊C₄	—	47	16	no	—
368	C₄⋊C₄	C₂×C₄×D₄₇	1	16	yes	complemented
369	C₂²⋊C₄	—	47	16	no	—
370	C₂²⋊C₄	—	47	16	no	—
371	C₂²⋊C₄	—	47	16	no	—
372	C₂²⋊C₄	—	47	64	no	—
373	C₂²⋊C₄	C₂×C₄×D₄₇	1	16	yes	—
374	C₄²	—	2	8	no	—
375	C₄²	—	4	4	no	—
376	C₄²	—	47	16	no	—
377	C₄²	—	94	8	no	—
378	C₄²	—	188	4	no	—
379	C₄²	—	188	16	no	—
380	C₄²	C₂×C₄×D₄₇	1	4	yes	—
381	C₄²	C₂×C₄×D₄₇	1	4	yes	—
382	C₄²	C₂×C₄×D₄₇	1	4	yes	—
383	C₄²	C₂×C₄×D₄₇	1	4	yes	—
384	C₄²	C₂×C₄×D₄₇	1	16	yes	complemented
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	47	8	no	—
388	C₂³	—	47	16	no	—
389	C₂³	—	47	32	no	—
390	C₂³	—	94	8	no	—
391	C₂³	—	94	8	no	—
392	C₂³	—	188	8	no	—
393	C₂³	—	188	8	no	—
394	C₂³	—	188	32	no	—
395	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
396	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
397	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
398	D₄	—	47	32	no	—
399	D₄	—	47	32	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	47	16	no	—
408	C₂×C₄	—	47	8	no	—
409	C₂×C₄	—	94	8	no	—
410	C₂×C₄	—	94	8	no	—
411	C₂×C₄	—	94	8	no	—
412	C₂×C₄	—	94	32	no	—
413	C₂×C₄	—	188	64	no	—
414	C₂×C₄	—	188	16	no	—
415	C₂×C₄	—	188	8	no	—
416	C₂×C₄	C₄²×D₄₇	1	16	yes	complemented
417	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
418	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
419	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₄₇	1	16	yes	—
421	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
422	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
423	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
425	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
426	C₂×C₄	#13094070	1	4	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	47	16	no	—
431	C₂²	—	94	8	no	—
432	C₂²	—	94	8	no	—
433	C₂²	—	94	32	no	—
434	C₂²	—	188	32	no	—
435	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
436	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
437	C₂²	C₂³×C₄×D₄₇	1	2	yes	—
438	C₂²	C₂×#13094070	1	2	yes	—
439	C₂²	#15689959	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	16	no	—
444	C₄	—	94	8	no	—
445	C₄	—	94	16	no	—
446	C₄	C₂×C₄²×D₄₇	1	4	yes	—
447	C₄	C₂×C₄²×D₄₇	1	4	yes	—
448	C₄	#15689597	1	4	yes	direct product factor
449	C₂	—	2	4	no	—
450	C₂	—	94	16	no	—
451	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
452	C₂	C₂×#15689597	1	1	yes	characteristic
453	C₂	#20256589	1	1	yes	characteristic
454	C₂	C₄×#13094070	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₄×#117×C₄₇	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂³×D₁₈₈	C₂²
hypercenter	C₄×#117	D₄₇
hypocenter	C₄₇	C₄×#518
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #20245750	C₂	semidirect
4. #20245748	C₂	semidirect
5. #20245744	C₂	semidirect
6. #20245740	C₂	semidirect
7. C₄²×D₁₈₈	C₂	semidirect
8. C₄×#13093986	C₂	semidirect
9. C₄×#13093983	C₂	semidirect
10. C₄×C₂²⋊C₄×D₄₇	C₂	semidirect
11. C₄×#117×C₄₇	C₂	semidirect
14. #15689597	C₄	direct (N × H)
15. C₂×C₄×D₁₈₈	C₄	semidirect
26. C₂×C₄²×D₄₇	C₂²	semidirect
27. C₄⋊C₄×Dic₄₇	C₂²	semidirect
28. C₄×C₄⋊Dic₄₇	C₂²	semidirect
29. C₄×C₄⋊Dic₄₇	C₂²	semidirect
30. C₄×C₄⋊Dic₄₇	C₂²	semidirect
32. C₄×(C₂×D₄₇)⋊C₄	C₂²	semidirect
33. C₄×(C₂×D₄₇)⋊C₄	C₂²	semidirect
36. #15688970	C₂²	semidirect
37. #15688970	C₂²	semidirect
38. #15688969	C₂²	semidirect
39. #95×D₄₇	C₂²	semidirect
40. C₄²×Dic₄₇	C₂²	semidirect
43. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
44. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
47. C₄₇×#376	C₂²	semidirect
48. C₄³×C₄₇	C₂²	semidirect
56. C₂²×C₄×D₄₇	C₂×C₄	semidirect
60. C₄×D₁₈₈	C₂×C₄	semidirect
61. C₄×D₁₈₈	C₂×C₄	semidirect
62. C₄×D₁₈₈	C₂×C₄	semidirect
63. C₄×D₁₈₈	C₂×C₄	semidirect
64. C₄×D₁₈₈	C₂×C₄	semidirect
65. #13093986	C₂×C₄	semidirect
66. #13093983	C₂×C₄	semidirect
67. C₂×C₄⋊Dic₄₇	C₂×C₄	semidirect
72. C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	semidirect
76. C₂²⋊C₄×D₄₇	C₂×C₄	semidirect
88. #117×C₄₇	C₂×C₄	semidirect
91. C₂×C₄²×C₄₇	C₂×C₄	semidirect
124. C₂×D₁₈₈	C₄²	semidirect
136. C₂×C₄×D₄₇	C₂²×C₄	semidirect
137. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
145. C₄²×C₄₇	C₂²×C₄	semidirect
149. (C₂×D₄₇)⋊C₄	C₂²×C₄	semidirect
152. C₄⋊Dic₄₇	C₂²×C₄	semidirect
156. C₄×Dic₄₇	C₂²×C₄	semidirect
167. C₂²×D₄₇	C₂×C₄²	semidirect
177. C₂×C₄×C₄₇	C₂×C₄²	semidirect
194. D₁₈₈	C₂×C₄²	semidirect
195. D₁₈₈	C₂×C₄²	semidirect
219. C₄×C₄₇	#518	semidirect
231. C₄×#117	D₄₇	semidirect
260. C₄×C₄⋊C₄	C₂×D₄₇	semidirect
261. C₄×C₄⋊C₄	C₂×D₄₇	semidirect
272. #376	C₂×D₄₇	semidirect
275. C₄³	C₂×D₄₇	semidirect
276. C₄₇	C₄×#518	semidirect
298. #117	C₄×D₄₇	semidirect
316. C₂×C₄²	C₄×D₄₇	semidirect
368. C₄⋊C₄	C₂×C₄×D₄₇	semidirect
384. C₄²	C₂×C₄×D₄₇	semidirect
416. C₂×C₄	C₄²×D₄₇	semidirect
448. C₄	#15689597	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689597	2
C₂²×C₄×D₁₈₈	2
#20245750	2
#20245748	2
#20245744	2
#20245740	2
C₄²×D₁₈₈	2
C₄×#13093986	2
C₄×#13093983	2
C₄×C₂²⋊C₄×D₄₇	2
C₄×#117×C₄₇	2
C₄×#518	47

Subgroups — C4×#15689597 #26374515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689597 #26374515