Subgroups — C₂×#20242522 #26191903

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689418	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689413	C₂	1	1	yes	maximal, characteristic
4	#20242522	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688872	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#554	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625337	—	2	2	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689502	—	2	2	no	—
12	#15689502	C₂²	1	4	yes	complemented
13	#15689418	—	2	2	no	—
14	#15689418	C₂²	1	4	yes	complemented
15	#15689413	—	2	2	no	—
16	#15689413	C₂²	1	4	yes	—
17	C₂×#13093957	—	2	1	no	—
18	C₂×#13093955	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093948	—	2	1	no	—
22	C₂×#13093945	—	2	1	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15688872	C₂²	1	4	yes	complemented
25	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
26	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
27	C₄₇×#554	—	2	2	no	—
28	C₄₇×#554	—	2	2	no	—
29	C₄₇×#554	—	2	2	no	—
30	C₄₇×#554	C₂²	1	4	yes	—
31	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#125×C₄₇	—	2	1	no	—
33	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
34	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₇	—	2	1	no	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₂²×Dic₉₄	—	2	1	no	—
40	C₂×#10625337	—	2	8	no	—
41	C₂×#10625337	—	4	8	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	#13094024	—	2	1	no	—
46	#13094024	—	2	1	no	—
47	#13094024	—	2	1	no	—
48	#13094024	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	#13093957	—	2	4	no	—
52	#13093955	—	2	4	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093948	—	2	4	no	—
58	#13093945	—	2	4	no	—
59	C₄×C₄₇⋊C₈	—	2	1	no	—
60	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
62	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
63	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	—	2	2	no	—
65	C₂³×C₄×C₄₇	—	2	1	no	—
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
69	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
70	#125×C₄₇	—	2	4	no	—
71	#125×C₄₇	—	2	4	no	—
72	C₂²⋊Q₈×C₄₇	—	2	4	no	—
73	C₂²⋊Q₈×C₄₇	—	2	8	no	—
74	C₂²⋊Q₈×C₄₇	—	2	4	no	—
75	C₂²⋊Q₈×C₄₇	—	2	8	no	—
76	C₄×Q₈×C₄₇	—	2	1	no	—
77	C₄×Q₈×C₄₇	—	2	1	no	—
78	C₄×Q₈×C₄₇	D₄	1	2	yes	—
79	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₄×D₄×C₄₇	—	2	4	no	—
81	C₄×D₄×C₄₇	—	2	4	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	D₄	1	2	yes	—
85	C₄×D₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
93	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂⁴×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	4	4	no	—
105	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	Q₁₆	1	4	yes	complemented
110	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	8	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	—	8	4	no	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×Dic₄₇	—	4	1	no	—
125	C₂×Dic₉₄	—	2	2	no	—
126	C₂×Dic₉₄	—	4	4	no	—
127	C₂×Dic₉₄	—	4	1	no	—
128	C₄⋊C₄×C₄₇	—	2	8	no	—
129	C₄⋊C₄×C₄₇	—	2	8	no	—
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₇	—	2	8	no	—
141	C₂²⋊C₄×C₄₇	—	2	2	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
149	#10625337	—	4	16	no	—
150	C₄⋊Dic₄₇	—	2	2	no	—
151	C₄⋊Dic₄₇	—	2	2	no	—
152	C₄⋊Dic₄₇	—	4	1	no	—
153	C₄⋊Dic₄₇	—	4	1	no	—
154	C₂×C₄₇⋊C₈	—	2	4	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	4	2	no	—
159	C₂×C₄₇⋊C₈	—	4	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	4	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	#120	1	1	yes	characteristic
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	2	2	no	—
167	Q₈×C₄₇	—	4	4	no	—
168	Q₈×C₄₇	—	4	2	no	—
169	Q₈×C₄₇	—	8	2	no	—
170	D₄×C₄₇	—	2	2	no	—
171	D₄×C₄₇	—	2	4	no	—
172	D₄×C₄₇	C₂×Q₁₆	1	4	yes	complemented
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	4	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	—	8	8	no	—
186	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
187	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
190	C₂×C₄×C₄₇	#135	1	2	yes	—
191	C₂×C₄×C₄₇	#137	1	2	yes	—
192	C₂×C₄×C₄₇	#137	1	2	yes	—
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	—	8	2	no	—
198	Dic₉₄	—	4	4	no	—
199	Dic₉₄	—	8	2	no	—
200	C₄₇⋊C₈	—	2	4	no	—
201	C₄₇⋊C₈	—	4	2	no	—
202	C₄₇⋊C₈	—	4	2	no	—
203	C₂×#1632	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	4	8	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	#451	1	2	yes	—
209	C₂²×C₄₇	#452	1	2	yes	—
210	C₂²×C₄₇	#453	1	2	yes	—
211	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	—	4	2	no	—
217	C₄×C₄₇	—	4	4	no	—
218	C₄×C₄₇	#451	1	2	yes	—
219	C₄×C₄₇	#452	1	2	yes	—
220	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
221	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
222	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
223	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
224	Dic₄₇	—	8	2	no	—
225	C₂×#554	D₄₇	1	1	yes	characteristic
226	C₂×#494	—	47	1	no	—
227	C₂×#477	—	47	1	no	—
228	C₂×#476	—	47	1	no	—
229	#1632	—	47	8	no	—
230	C₂×#333	—	47	1	no	—
231	C₂×Q₈⋊C₈	—	47	1	no	—
232	C₂×D₄⋊C₈	—	47	1	no	—
233	C₂×C₄₇	—	4	4	no	—
234	C₂×C₄₇	#1632	1	4	yes	complemented
235	C₂×C₄₇	C₂×#451	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
238	C₂²×Q₁₆	—	94	2	no	—
239	#554	—	2	2	no	—
240	#554	—	2	2	no	—
241	#554	—	2	2	no	—
242	#554	C₂×D₄₇	1	4	yes	—
243	C₂×C₄⋊Q₈	—	47	1	no	—
244	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#125	—	2	1	no	—
246	C₂×C₂²⋊Q₈	—	2	1	no	—
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄×D₄	—	2	1	no	—
250	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
251	C₂²×C₄⋊C₄	—	2	1	no	—
252	#494	—	47	4	no	—
253	#494	—	94	2	no	—
254	#477	—	47	4	no	—
255	#477	—	94	2	no	—
256	#476	—	47	4	no	—
257	#476	—	94	2	no	—
258	C₂×#107	—	94	1	no	—
259	C₂×#106	—	94	1	no	—
260	C₂×C₄⋊C₈	—	47	1	no	—
261	C₂×C₄⋊C₈	—	47	1	no	—
262	C₂×#103	—	94	1	no	—
263	C₂×#102	—	94	1	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	#333	—	47	4	no	—
266	Q₈⋊C₈	—	47	4	no	—
267	D₄⋊C₈	—	47	4	no	—
268	C₄₇	C₂×#1632	1	1	yes	characteristic, complemented, Sylow
269	C₂²×Q₈	—	94	1	no	—
270	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
271	C₂²×Q₈	C₂²⋊D₄₇	1	2	yes	—
272	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂×Q₁₆	—	94	8	no	—
276	C₂×Q₁₆	—	188	8	no	—
277	C₂²×C₈	—	94	1	no	—
278	C₂²×C₈	—	94	1	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	47	2	no	—
283	C₄⋊Q₈	—	94	1	no	—
284	C₄⋊Q₈	—	94	1	no	—
285	C₄⋊Q₈	—	94	1	no	—
286	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
287	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
288	#125	—	2	4	no	—
289	#125	—	2	4	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
297	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
303	C₄×D₄	C₂²×D₄₇	1	2	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	4	no	—
311	C₂×C₄⋊C₄	—	94	1	no	—
312	C₂×C₄⋊C₄	—	94	1	no	—
313	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	#107	—	94	4	no	—
320	#106	—	94	4	no	—
321	C₄⋊C₈	—	47	2	no	—
322	C₄⋊C₈	—	47	2	no	—
323	C₄⋊C₈	—	94	1	no	—
324	C₄⋊C₈	—	94	1	no	—
325	#103	—	94	4	no	—
326	#102	—	94	4	no	—
327	C₄×C₈	—	47	2	no	—
328	C₄×C₈	—	94	1	no	—
329	C₂⁴	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂×Q₈	—	94	2	no	—
336	C₂×Q₈	—	188	4	no	—
337	C₂×Q₈	—	188	1	no	—
338	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
339	C₂×Q₈	C₂×C₂²⋊D₄₇	1	4	yes	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	#10625337	1	4	yes	complemented
343	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	—	8	4	no	—
354	C₂²×C₄	—	188	1	no	—
355	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
358	Q₁₆	—	188	16	no	—
359	C₂×C₈	—	94	4	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	2	no	—
363	C₂×C₈	—	188	2	no	—
364	C₂×C₈	—	188	2	no	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	94	2	no	—
377	C₄⋊C₄	—	188	1	no	—
378	C₄⋊C₄	—	188	1	no	—
379	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
380	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₄²	C₂³×D₄₇	1	1	yes	characteristic
390	C₂³	—	2	4	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	#13093993	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	4	4	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	8	2	no	—
400	Q₈	—	376	2	no	—
401	Q₈	—	188	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	C₂×#10625337	1	4	yes	complemented
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	8	no	—
418	C₂×C₄	—	376	2	no	—
419	C₂×C₄	—	188	2	no	—
420	C₂×C₄	#13093993	1	1	yes	characteristic
421	C₂×C₄	#13093993	1	1	yes	characteristic
422	C₂×C₄	#13093993	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625337	1	2	yes	—
424	C₂×C₄	#13094044	1	2	yes	—
425	C₂×C₄	#13094054	1	2	yes	—
426	C₂×C₄	#13094055	1	2	yes	—
427	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
430	C₈	—	94	4	no	—
431	C₈	—	188	2	no	—
432	C₈	—	188	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	2	no	—
437	C₂²	#15689279	1	2	yes	—
438	C₂²	#15689285	1	2	yes	—
439	C₂²	#15689291	1	2	yes	—
440	C₂²	C₂×#13093993	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	376	2	no	—
448	C₄	#15689279	1	2	yes	—
449	C₄	#15689285	1	2	yes	—
450	C₄	C₂²×#10625337	1	1	yes	characteristic
451	C₄	C₂×#13094044	1	1	yes	characteristic
452	C₄	C₂×#13094054	1	1	yes	characteristic
453	C₄	C₂×#13094055	1	1	yes	characteristic
454	C₂	—	4	4	no	—
455	C₂	#20242522	1	4	yes	direct product factor
456	C₂	C₂×#15689279	1	1	yes	characteristic
457	C₂	C₂×#15689285	1	1	yes	characteristic
458	C₂	C₂×#15689291	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#554	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂²×D₄×C₄₇	D₄
hypercenter	C₂×#554	D₄₇
hypocenter	C₄₇	C₂×#1632
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#554

Complements

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

N	H ≅ G/N	type
1. C₂×#15689502	C₂	semidirect
2. C₂×#15689418	C₂	semidirect
4. #20242522	C₂	direct (N × H)
5. C₂×#15688872	C₂	semidirect
6. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
12. #15689502	C₂²	semidirect
14. #15689418	C₂²	semidirect
24. #15688872	C₂²	semidirect
25. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
109. C₂×D₄×C₄₇	Q₁₆	semidirect
172. D₄×C₄₇	C₂×Q₁₆	semidirect
234. C₂×C₄₇	#1632	semidirect
268. C₄₇	C₂×#1632	semidirect
342. C₂×D₄	#10625337	semidirect
404. D₄	C₂×#10625337	semidirect
455. C₂	#20242522	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×#15689502	2
C₂×#15689418	2
C₂×#15689413	2
#20242522	2
C₂×#15688872	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×D₄⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#554	2
C₂×#1632	47

Subgroups — C2×#20242522 #26191903

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242522 #26191903