Subgroups — C₂×#20242574 #26191958

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689469	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689408	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689333	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242574	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688867	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#559	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625337	—	2	1	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	#15689469	—	2	2	no	—
12	#15689469	C₂²	1	4	yes	—
13	#15689408	—	2	2	no	—
14	#15689408	C₂²	1	4	yes	complemented
15	#15689333	—	2	2	no	—
16	#15689333	C₂²	1	4	yes	complemented
17	C₂×#13093955	—	2	1	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	—	2	1	no	—
21	C₂×#13093947	—	2	1	no	—
22	C₂×#13093945	—	2	2	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15688867	C₂²	1	4	yes	—
25	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
27	C₄₇×#559	—	2	2	no	—
28	C₄₇×#559	—	2	2	no	—
29	C₄₇×#559	—	2	2	no	—
30	C₄₇×#559	C₂²	1	4	yes	—
31	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#124×C₄₇	—	2	1	no	—
33	C₂×#124×C₄₇	—	2	1	no	—
34	C₂×#123×C₄₇	—	2	2	no	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₇	—	2	1	no	—
38	C₂×C₄×D₄×C₄₇	—	2	1	no	—
39	C₂²×Dic₉₄	—	2	1	no	—
40	C₂×#10625337	—	2	4	no	—
41	C₂×#10625337	—	4	4	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	#13093955	—	2	4	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	#13093948	—	2	4	no	—
57	#13093947	—	2	4	no	—
58	#13093945	—	2	8	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	1	yes	characteristic
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	D₄	1	2	yes	—
66	C₂³×C₄×C₄₇	—	2	2	no	—
67	#127×C₄₇	—	2	1	no	—
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	D₄	1	2	yes	—
70	#127×C₄₇	C₂³	1	2	yes	—
71	#124×C₄₇	—	2	4	no	—
72	#124×C₄₇	—	2	4	no	—
73	#124×C₄₇	—	2	4	no	—
74	#124×C₄₇	—	2	4	no	—
75	#123×C₄₇	—	2	8	no	—
76	#123×C₄₇	—	2	8	no	—
77	C₄×Q₈×C₄₇	—	2	1	no	—
78	C₄×Q₈×C₄₇	—	2	1	no	—
79	C₄×Q₈×C₄₇	—	2	1	no	—
80	C₄×Q₈×C₄₇	—	2	1	no	—
81	C₄×Q₈×C₄₇	D₄	1	2	yes	—
82	C₄×Q₈×C₄₇	D₄	1	2	yes	—
83	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
84	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
85	C₄×D₄×C₄₇	—	2	4	no	—
86	C₄×D₄×C₄₇	—	2	4	no	—
87	C₄×D₄×C₄₇	—	2	4	no	—
88	C₄×D₄×C₄₇	—	2	4	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂⁴×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	4	4	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂×D₄×C₄₇	—	4	2	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂×D₄×C₄₇	—	4	2	no	—
118	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	8	no	—
124	C₂²×C₄×C₄₇	—	8	4	no	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×Dic₄₇	—	4	1	no	—
129	C₂×Dic₉₄	—	2	2	no	—
130	C₂×Dic₉₄	—	4	2	no	—
131	C₂×Dic₉₄	—	4	2	no	—
132	C₂×Dic₉₄	—	4	1	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₄₇	—	2	8	no	—
142	C₂²⋊C₄×C₄₇	—	2	8	no	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₄²×C₄₇	—	2	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	2	no	—
148	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
152	#10625337	—	4	8	no	—
153	C₄⋊Dic₄₇	—	2	2	no	—
154	C₄⋊Dic₄₇	—	2	2	no	—
155	C₄⋊Dic₄₇	—	4	1	no	—
156	C₄⋊Dic₄₇	—	4	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	4	2	no	—
161	C₂×C₄₇⋊C₈	—	4	2	no	—
162	C₂×C₄₇⋊C₈	—	4	2	no	—
163	C₂³×C₄₇	—	2	4	no	—
164	C₂³×C₄₇	—	4	4	no	—
165	C₂³×C₄₇	—	4	4	no	—
166	C₂³×C₄₇	—	4	4	no	—
167	C₂³×C₄₇	#120	1	1	yes	characteristic
168	Q₈×C₄₇	—	2	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	—	4	2	no	—
173	Q₈×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	4	no	—
175	D₄×C₄₇	—	4	2	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	4	2	no	—
179	D₄×C₄₇	—	4	4	no	—
180	D₄×C₄₇	—	4	4	no	—
181	D₄×C₄₇	—	8	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	8	8	no	—
192	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
193	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
195	C₂×C₄×C₄₇	#135	1	2	yes	—
196	C₂×C₄×C₄₇	#135	1	2	yes	—
197	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
198	C₂×C₄×C₄₇	#137	1	2	yes	—
199	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	8	2	no	—
204	Dic₉₄	—	4	2	no	—
205	Dic₉₄	—	4	2	no	—
206	Dic₉₄	—	8	2	no	—
207	C₄₇⋊C₈	—	4	2	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	C₂×#1640	—	47	1	no	maximal, Sylow
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	4	4	no	—
213	C₂²×C₄₇	—	4	4	no	—
214	C₂²×C₄₇	—	8	8	no	—
215	C₂²×C₄₇	#449	1	2	yes	—
216	C₂²×C₄₇	#452	1	2	yes	—
217	C₂²×C₄₇	#455	1	2	yes	—
218	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
219	C₄×C₄₇	—	2	1	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	#449	1	2	yes	—
226	C₄×C₄₇	#452	1	2	yes	—
227	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
228	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
229	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
231	Dic₄₇	—	8	2	no	—
232	C₂×#559	D₄₇	1	1	yes	characteristic
233	C₂×#486	—	47	1	no	—
234	C₂×#475	—	47	1	no	—
235	C₂×#462	—	47	1	no	—
236	#1640	—	47	8	no	—
237	C₂×#331	—	47	1	no	—
238	C₂×Q₈⋊C₈	—	47	1	no	—
239	C₂×Q₈⋊C₈	—	47	1	no	—
240	C₂×C₄₇	—	8	4	no	—
241	C₂×C₄₇	#1640	1	4	yes	complemented
242	C₂×C₄₇	C₂×#449	1	1	yes	characteristic
243	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
244	C₂×C₄₇	C₂×#455	1	1	yes	characteristic
245	C₂²×Q₁₆	—	94	1	no	—
246	#559	—	2	2	no	—
247	#559	—	2	2	no	—
248	#559	—	2	2	no	—
249	#559	C₂×D₄₇	1	4	yes	—
250	C₂×C₄⋊Q₈	—	47	1	no	—
251	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
252	C₂×#124	—	2	1	no	—
253	C₂×#124	—	2	1	no	—
254	C₂×#123	—	2	2	no	—
255	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
257	C₂×C₄×D₄	—	2	1	no	—
258	C₂×C₄×D₄	—	2	1	no	—
259	#486	—	47	4	no	—
260	#486	—	94	2	no	—
261	#475	—	47	4	no	—
262	#475	—	94	2	no	—
263	#462	—	47	4	no	—
264	#462	—	94	2	no	—
265	C₂×#106	—	94	1	no	—
266	C₂×C₄⋊C₈	—	47	1	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×#103	—	94	1	no	—
269	C₂×#103	—	94	1	no	—
270	C₂×#102	—	94	2	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	#331	—	47	4	no	—
273	Q₈⋊C₈	—	47	4	no	—
274	Q₈⋊C₈	—	47	4	no	—
275	C₄₇	C₂×#1640	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	94	1	no	—
277	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
282	C₂³×C₄	—	2	2	no	—
283	C₂×Q₁₆	—	94	4	no	—
284	C₂×Q₁₆	—	188	4	no	—
285	C₂²×C₈	—	94	1	no	—
286	C₂²×C₈	—	94	1	no	—
287	C₂²×C₈	—	94	1	no	—
288	C₄⋊Q₈	—	47	2	no	—
289	C₄⋊Q₈	—	94	1	no	—
290	C₄⋊Q₈	—	94	1	no	—
291	C₄⋊Q₈	—	94	1	no	—
292	#127	—	2	1	no	—
293	#127	—	2	1	no	—
294	#127	C₂²⋊D₄₇	1	2	yes	—
295	#127	C₂²×D₄₇	1	2	yes	—
296	#124	—	2	4	no	—
297	#124	—	2	4	no	—
298	#124	—	2	4	no	—
299	#124	—	2	4	no	—
300	#123	—	2	8	no	—
301	#123	—	2	8	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
307	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
308	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
309	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
310	C₄×D₄	—	2	4	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	2	4	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	94	1	no	—
317	C₂×C₄⋊C₄	—	94	1	no	—
318	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	#106	—	94	4	no	—
327	C₄⋊C₈	—	47	2	no	—
328	C₄⋊C₈	—	47	2	no	—
329	C₄⋊C₈	—	94	1	no	—
330	C₄⋊C₈	—	94	1	no	—
331	#103	—	94	4	no	—
332	#103	—	94	4	no	—
333	#102	—	94	8	no	—
334	C₄×C₈	—	47	2	no	—
335	C₄×C₈	—	94	1	no	—
336	C₂⁴	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	94	2	no	—
344	C₂×Q₈	—	188	2	no	—
345	C₂×Q₈	—	188	2	no	—
346	C₂×Q₈	—	188	1	no	—
347	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
348	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	C₂×C₂²⋊D₄₇	1	4	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	8	4	no	—
366	C₂²×C₄	—	188	1	no	—
367	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
370	Q₁₆	—	188	8	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	188	2	no	—
375	C₂×C₈	—	188	2	no	—
376	C₂×C₈	—	188	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₄⋊C₄	—	188	1	no	—
386	C₄⋊C₄	—	188	1	no	—
387	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
388	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₄²	C₂³×D₄₇	1	1	yes	characteristic
400	C₂³	—	2	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	4	no	—
404	C₂³	#13093993	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	376	2	no	—
412	Q₈	—	188	2	no	—
413	Q₈	—	188	2	no	—
414	D₄	—	4	4	no	—
415	D₄	—	4	4	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	—	376	2	no	—
433	C₂×C₄	—	188	2	no	—
434	C₂×C₄	#13093993	1	1	yes	characteristic
435	C₂×C₄	#13093993	1	1	yes	characteristic
436	C₂×C₄	#13093993	1	1	yes	characteristic
437	C₂×C₄	#13094044	1	2	yes	—
438	C₂×C₄	#13094044	1	2	yes	—
439	C₂×C₄	#13094049	1	2	yes	—
440	C₂×C₄	#13094054	1	2	yes	—
441	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
444	C₈	—	188	2	no	—
445	C₈	—	188	2	no	—
446	C₈	—	188	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	8	no	—
451	C₂²	#15689268	1	2	yes	—
452	C₂²	#15689285	1	2	yes	—
453	C₂²	#15689301	1	2	yes	—
454	C₂²	C₂×#13093993	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	376	2	no	—
462	C₄	#15689268	1	2	yes	—
463	C₄	#15689285	1	2	yes	—
464	C₄	C₂×#13094044	1	1	yes	characteristic
465	C₄	C₂×#13094044	1	1	yes	characteristic
466	C₄	C₂×#13094049	1	1	yes	characteristic
467	C₄	C₂×#13094054	1	1	yes	characteristic
468	C₂	—	8	4	no	—
469	C₂	#20242574	1	4	yes	direct product factor
470	C₂	C₂×#15689268	1	1	yes	characteristic
471	C₂	C₂×#15689285	1	1	yes	characteristic
472	C₂	C₂×#15689301	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#559	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	C₂×#559	D₄₇
hypocenter	C₄₇	C₂×#1640
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#559

Complements

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

N	H ≅ G/N	type
2. C₂×#15689408	C₂	semidirect
3. C₂×#15689333	C₂	semidirect
4. #20242574	C₂	direct (N × H)
6. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
14. #15689408	C₂²	semidirect
16. #15689333	C₂²	semidirect
25. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
26. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
241. C₂×C₄₇	#1640	semidirect
275. C₄₇	C₂×#1640	semidirect
469. C₂	#20242574	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×#15689469	2
C₂×#15689408	2
C₂×#15689333	2
#20242574	2
C₂×#15688867	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#559	2
C₂×#1640	47

Subgroups — C2×#20242574 #26191958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242574 #26191958