Subgroups — C₂×#20242484 #26192007

Order 12032.

1030 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×#15689471	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
4	#20242484	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688869	C₂	1	1	yes	maximal, characteristic, complemented
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×#557	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625336	—	2	1	no	—
10	C₂²×#10625336	—	2	1	no	—
11	C₂×#13094021	C₂²	1	1	yes	characteristic
12	#15689471	—	2	2	no	—
13	#15689471	C₂²	1	4	yes	—
14	#15689323	—	2	2	no	—
15	#15689323	—	2	2	no	—
16	#15689323	C₂²	1	4	yes	—
17	#15689323	C₂²	1	4	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093944	—	2	1	no	—
21	C₂×#13093944	—	2	1	no	—
22	C₂×#13093944	—	2	2	no	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15688869	C₂²	1	4	yes	complemented
25	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
27	C₄₇×#557	—	2	2	no	—
28	C₄₇×#557	—	2	2	no	—
29	C₄₇×#557	—	2	2	no	—
30	C₄₇×#557	C₂²	1	4	yes	complemented
31	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
32	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#125×C₄₇	—	2	2	no	—
34	C₂×#125×C₄₇	—	2	1	no	—
35	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×D₁₈₈	—	2	1	no	—
40	C₂²×D₁₈₈	—	2	1	no	—
41	C₂²×D₁₈₈	—	2	1	no	—
42	C₂×#10625336	—	2	4	no	—
43	C₂×#10625336	—	2	4	no	—
44	C₂×#10625336	—	4	4	no	—
45	C₂×#10625336	—	4	4	no	—
46	C₂²×C₄₇⋊C₈	—	2	1	no	—
47	C₂²×C₄₇⋊C₈	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	—	2	1	no	—
49	#13094021	—	2	1	no	—
50	#13094021	—	2	1	no	—
51	#13094021	—	2	1	no	—
52	#13094021	C₂³	1	2	yes	—
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	#13093944	—	2	4	no	—
58	#13093944	—	2	4	no	—
59	#13093944	—	2	8	no	—
60	C₄×C₄₇⋊C₈	—	2	1	no	—
61	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
62	C₂²×Q₈×C₄₇	—	2	1	no	—
63	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₇	—	2	4	no	—
66	C₄⋊Q₈×C₄₇	—	2	4	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	—	2	1	no	—
69	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
70	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
71	#125×C₄₇	—	2	8	no	—
72	#125×C₄₇	—	2	4	no	—
73	#125×C₄₇	—	2	8	no	—
74	#125×C₄₇	—	2	4	no	—
75	C₄×Q₈×C₄₇	—	2	4	no	—
76	C₄×Q₈×C₄₇	—	2	4	no	—
77	C₄×Q₈×C₄₇	—	2	4	no	—
78	C₄×Q₈×C₄₇	—	2	4	no	—
79	C₄×Q₈×C₄₇	—	2	1	no	—
80	C₄×Q₈×C₄₇	—	2	1	no	—
81	C₄×Q₈×C₄₇	—	2	1	no	—
82	C₄×Q₈×C₄₇	—	2	1	no	—
83	C₄×Q₈×C₄₇	D₄	1	2	yes	—
84	C₄×Q₈×C₄₇	D₄	1	2	yes	—
85	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
86	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
96	C₂×C₄²×C₄₇	—	2	2	no	—
97	C₂×C₄²×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	—	2	1	no	—
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	C₂³×D₄₇	—	4	1	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	1	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	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	4	2	no	—
109	C₂×Q₈×C₄₇	—	4	2	no	—
110	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	complemented
111	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×D₁₈₈	—	2	2	no	—
122	C₂×D₁₈₈	—	2	2	no	—
123	C₂×D₁₈₈	—	2	2	no	—
124	C₂×D₁₈₈	—	4	4	no	—
125	C₂×D₁₈₈	—	4	2	no	—
126	C₂×D₁₈₈	—	4	2	no	—
127	C₂×D₁₈₈	—	4	2	no	—
128	C₂×D₁₈₈	—	4	2	no	—
129	C₂×D₁₈₈	—	4	1	no	—
130	C₂×D₁₈₈	—	4	1	no	—
131	C₂×D₁₈₈	—	4	1	no	—
132	C₄⋊C₄×C₄₇	—	2	8	no	—
133	C₄⋊C₄×C₄₇	—	2	8	no	—
134	C₄⋊C₄×C₄₇	—	2	8	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	—	2	1	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
147	C₄²×C₄₇	—	2	8	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	2	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	—	2	2	no	—
152	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
156	#10625336	—	4	8	no	—
157	#10625336	—	4	8	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	4	2	no	—
162	C₂×C₄₇⋊C₈	—	4	2	no	—
163	C₂×C₄₇⋊C₈	—	4	2	no	—
164	C₂³×C₄₇	#120	1	1	yes	characteristic
165	C₂²×D₄₇	—	4	2	no	—
166	C₂²×D₄₇	—	8	2	no	—
167	C₂²×D₄₇	—	8	2	no	—
168	C₂²×D₄₇	—	8	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	4	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	—	2	2	no	—
173	Q₈×C₄₇	—	4	2	no	—
174	Q₈×C₄₇	—	4	2	no	—
175	Q₈×C₄₇	—	4	2	no	—
176	Q₈×C₄₇	—	4	4	no	—
177	Q₈×C₄₇	C₂×SD₁₆	1	4	yes	complemented
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	4	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
190	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
191	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
193	C₂×C₄×C₄₇	#135	1	2	yes	—
194	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₄₇	#137	1	2	yes	—
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	D₁₈₈	—	4	4	no	—
200	D₁₈₈	—	4	2	no	—
201	D₁₈₈	—	4	2	no	—
202	D₁₈₈	—	4	2	no	—
203	D₁₈₈	—	4	2	no	—
204	D₁₈₈	—	8	2	no	—
205	D₁₈₈	—	8	2	no	—
206	D₁₈₈	—	8	2	no	—
207	C₄₇⋊C₈	—	4	2	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	C₂×#1626	—	47	1	no	maximal, Sylow
211	C₂²×C₄₇	#448	1	2	yes	—
212	C₂²×C₄₇	#449	1	2	yes	—
213	C₂²×C₄₇	#454	1	2	yes	—
214	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
215	C₂×D₄₇	—	8	2	no	—
216	C₂×D₄₇	—	8	2	no	—
217	C₂×D₄₇	—	8	2	no	—
218	C₂×D₄₇	—	16	4	no	—
219	C₄×C₄₇	—	2	4	no	—
220	C₄×C₄₇	—	2	1	no	—
221	C₄×C₄₇	—	2	1	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	—	4	4	no	—
224	C₄×C₄₇	—	4	2	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	#448	1	2	yes	—
227	C₄×C₄₇	#449	1	2	yes	—
228	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
229	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
230	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
232	C₂×#557	D₄₇	1	1	yes	characteristic, complemented
233	C₂×#486	—	47	1	no	—
234	C₂×#460	—	47	1	no	—
235	C₂×#460	—	47	1	no	—
236	#1626	—	47	8	no	—
237	C₂×#332	—	47	1	no	—
238	C₂×Q₈⋊C₈	—	47	1	no	—
239	C₂×Q₈⋊C₈	—	47	1	no	—
240	C₂×C₄₇	#1626	1	4	yes	complemented
241	C₂×C₄₇	C₂×#448	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#449	1	1	yes	characteristic
243	C₂×C₄₇	C₂×#454	1	1	yes	characteristic
244	D₄₇	—	16	2	no	—
245	C₂²×SD₁₆	—	94	1	no	—
246	C₂²×SD₁₆	—	94	1	no	—
247	#557	—	2	2	no	—
248	#557	—	2	2	no	—
249	#557	—	2	2	no	—
250	#557	C₂×D₄₇	1	4	yes	complemented
251	C₂×C₄⋊Q₈	—	2	1	no	—
252	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
253	C₂×#127	—	47	1	no	—
254	C₂×#125	—	2	2	no	—
255	C₂×#125	—	2	1	no	—
256	C₂×C₄×Q₈	—	2	1	no	—
257	C₂×C₄×Q₈	—	2	1	no	—
258	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
259	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
260	#486	—	47	4	no	—
261	#486	—	94	2	no	—
262	#460	—	47	4	no	—
263	#460	—	47	4	no	—
264	#460	—	94	2	no	—
265	#460	—	94	2	no	—
266	C₂×C₄⋊C₈	—	47	1	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×#102	—	94	2	no	—
269	C₂×#102	—	94	1	no	—
270	C₂×#102	—	94	1	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	#332	—	47	4	no	—
273	Q₈⋊C₈	—	47	4	no	—
274	Q₈⋊C₈	—	47	4	no	—
275	C₄₇	C₂×#1626	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂²×D₄	—	94	1	no	—
280	C₂²×D₄	—	94	1	no	—
281	C₂²×D₄	—	94	1	no	—
282	C₂×SD₁₆	—	94	4	no	—
283	C₂×SD₁₆	—	94	4	no	—
284	C₂×SD₁₆	—	188	4	no	—
285	C₂×SD₁₆	—	188	4	no	—
286	C₂²×C₈	—	94	1	no	—
287	C₂²×C₈	—	94	1	no	—
288	C₂²×C₈	—	94	1	no	—
289	C₄⋊Q₈	—	2	4	no	—
290	C₄⋊Q₈	—	2	4	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
294	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
295	#127	—	47	2	no	—
296	#127	—	94	1	no	—
297	#127	—	94	1	no	—
298	#127	—	94	1	no	—
299	#125	—	2	8	no	—
300	#125	—	2	4	no	—
301	#125	—	2	8	no	—
302	#125	—	2	4	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	2	4	no	—
305	C₄×Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
312	C₄×Q₈	C₂²⋊D₄₇	1	2	yes	—
313	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
314	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	C₄⋊C₈	—	47	2	no	—
329	C₄⋊C₈	—	47	2	no	—
330	C₄⋊C₈	—	94	1	no	—
331	C₄⋊C₈	—	94	1	no	—
332	#102	—	94	4	no	—
333	#102	—	94	4	no	—
334	#102	—	94	8	no	—
335	C₄×C₈	—	47	2	no	—
336	C₄×C₈	—	94	1	no	—
337	C₂⁴	—	188	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	#10625336	1	4	yes	complemented
348	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
349	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
350	C₂×D₄	—	94	2	no	—
351	C₂×D₄	—	94	2	no	—
352	C₂×D₄	—	94	2	no	—
353	C₂×D₄	—	188	4	no	—
354	C₂×D₄	—	188	1	no	—
355	C₂×D₄	—	188	1	no	—
356	C₂×D₄	—	188	1	no	—
357	C₂×D₄	—	188	2	no	—
358	C₂×D₄	—	188	2	no	—
359	C₂×D₄	—	188	2	no	—
360	C₂×D₄	—	188	2	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	SD₁₆	—	188	8	no	—
370	SD₁₆	—	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	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	8	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
390	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
391	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
392	C₄²	—	2	8	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
399	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₄²	C₂³×D₄₇	1	1	yes	characteristic
401	C₂³	—	376	2	no	—
402	C₂³	—	376	2	no	—
403	C₂³	—	376	2	no	—
404	C₂³	—	188	2	no	—
405	C₂³	#13093993	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	4	no	—
412	Q₈	—	4	2	no	—
413	Q₈	—	4	2	no	—
414	Q₈	C₂×#10625336	1	4	yes	complemented
415	D₄	—	376	2	no	—
416	D₄	—	376	2	no	—
417	D₄	—	376	2	no	—
418	D₄	—	188	4	no	—
419	D₄	—	188	2	no	—
420	D₄	—	188	2	no	—
421	D₄	—	188	2	no	—
422	D₄	—	188	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	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	C₂×#10625336	1	2	yes	—
438	C₂×C₄	#13094044	1	2	yes	—
439	C₂×C₄	#13094049	1	2	yes	—
440	C₂×C₄	#13094055	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	—	376	2	no	—
448	C₂²	—	376	2	no	—
449	C₂²	—	376	2	no	—
450	C₂²	—	752	4	no	—
451	C₂²	#15689262	1	2	yes	—
452	C₂²	#15689268	1	2	yes	—
453	C₂²	#15689296	1	2	yes	—
454	C₂²	C₂×#13093993	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	4	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	#15689262	1	2	yes	—
463	C₄	#15689268	1	2	yes	—
464	C₄	C₂²×#10625336	1	1	yes	characteristic
465	C₄	C₂×#13094044	1	1	yes	characteristic
466	C₄	C₂×#13094049	1	1	yes	characteristic
467	C₄	C₂×#13094055	1	1	yes	characteristic
468	C₂	—	752	2	no	—
469	C₂	#20242484	1	4	yes	direct product factor
470	C₂	C₂×#15689262	1	1	yes	characteristic
471	C₂	C₂×#15689268	1	1	yes	characteristic
472	C₂	C₂×#15689296	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#557	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂×#13094021	C₂²
hypercenter	C₂×#557	D₄₇
hypocenter	C₄₇	C₂×#1626
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#557

Complements

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

N	H ≅ G/N	type
4. #20242484	C₂	direct (N × H)
5. C₂×#15688869	C₂	semidirect
6. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
8. C₂×C₄₇×#557	C₂	semidirect
24. #15688869	C₂²	semidirect
25. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
26. Q₈⋊(C₄₇⋊C₈)	C₂²	semidirect
30. C₄₇×#557	C₂²	semidirect
110. C₂×Q₈×C₄₇	SD₁₆	semidirect
177. Q₈×C₄₇	C₂×SD₁₆	semidirect
232. C₂×#557	D₄₇	semidirect
240. C₂×C₄₇	#1626	semidirect
250. #557	C₂×D₄₇	semidirect
275. C₄₇	C₂×#1626	semidirect
347. C₂×Q₈	#10625336	semidirect
414. Q₈	C₂×#10625336	semidirect
469. C₂	#20242484	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×#15689471	2
C₂×#15689323	2
#20242484	2
C₂×#15688869	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×C₄₇×#557	2
C₂×#1626	47

Subgroups — C2×#20242484 #26192007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242484 #26192007