Subgroups — C₂×#20244957 #26246179

Order 12032.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689021	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688989	C₂	1	1	yes	maximal, characteristic
3	#20244957	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688886	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
14	#15689021	—	2	2	no	—
15	#15689021	C₂²	1	4	yes	—
16	#15688989	—	2	2	no	—
17	#15688989	C₂²	1	4	yes	—
18	C₂×C₄₇⋊#95	—	2	1	no	—
19	C₂×C₄₇⋊#95	—	2	1	no	—
20	C₂×C₄₇⋊#95	—	2	1	no	—
21	#15688886	C₂²	1	4	yes	—
22	#15688886	C₂²	1	4	yes	—
23	#15688886	C₂²	1	4	yes	—
24	#15688886	C₂²	1	4	yes	—
25	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#336	C₂²	1	4	yes	—
29	C₂³×Dic₄₇	—	2	1	no	—
30	C₂³×Dic₄₇	—	2	1	no	—
31	C₂³×Dic₄₇	—	2	1	no	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	1	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	Q₈	1	4	yes	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	—	2	4	no	—
50	C₂×Dic₄₇⋊C₄	—	4	4	no	—
51	C₄₇⋊#95	—	2	4	no	—
52	C₄₇⋊#95	—	2	4	no	—
53	C₄₇⋊#95	—	2	4	no	—
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	—	2	2	no	—
58	C₂²×C₈×C₄₇	—	2	2	no	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	2	no	—
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	D₄	1	2	yes	—
68	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
69	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₄₇	#41	1	2	yes	—
81	C₂²×C₄×C₄₇	#41	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×C₄×C₄₇	#41	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₄₇	—	2	4	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	—	2	2	no	—
90	C₂²×Dic₄₇	—	2	2	no	—
91	C₂²×Dic₄₇	—	4	2	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₂²×Dic₄₇	—	4	2	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₂²×Dic₄₇	—	4	2	no	—
97	C₂²×Dic₄₇	—	4	2	no	—
98	C₂²×Dic₄₇	—	4	2	no	—
99	C₂²×Dic₄₇	—	4	2	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	—	4	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	4	4	no	—
109	C₂×C₈×C₄₇	—	4	4	no	—
110	C₄²×C₄₇	—	2	4	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	4	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	2	2	no	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	4	2	no	—
122	C₄⋊Dic₄₇	—	4	2	no	—
123	C₄⋊Dic₄₇	—	4	2	no	—
124	C₄⋊Dic₄₇	C₂×Q₈	1	4	yes	—
125	Dic₄₇⋊C₄	—	4	8	no	—
126	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
127	C₂³×C₄₇	#123	1	2	yes	—
128	C₂³×C₄₇	#124	1	2	yes	—
129	C₂³×C₄₇	#135	1	2	yes	—
130	C₂³×C₄₇	#135	1	2	yes	—
131	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
132	C₂³×C₄₇	#137	1	2	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	#123	1	2	yes	—
144	C₂×C₄×C₄₇	#124	1	2	yes	—
145	C₂×C₄×C₄₇	#125	1	4	yes	—
146	C₂×C₄×C₄₇	#125	1	4	yes	—
147	C₂×C₄×C₄₇	#126	1	4	yes	—
148	C₂×C₄×C₄₇	#126	1	4	yes	—
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	8	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	8	4	no	—
169	C₂×Dic₄₇	—	8	4	no	—
170	C₂×Dic₄₇	—	8	4	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₈×C₄₇	—	4	2	no	—
173	C₂×#2101	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	#400	1	4	yes	—
175	C₂²×C₄₇	#478	1	4	yes	—
176	C₂²×C₄₇	#479	1	4	yes	—
177	C₂²×C₄₇	#482	1	4	yes	—
178	C₂²×C₄₇	#485	1	4	yes	—
179	C₂²×C₄₇	#488	1	4	yes	—
180	C₂²×C₄₇	#489	1	4	yes	—
181	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	#400	1	4	yes	—
191	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
192	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
195	Dic₄₇	—	4	4	no	—
196	Dic₄₇	—	8	2	no	—
197	Dic₄₇	—	8	2	no	—
198	Dic₄₇	—	8	2	no	—
199	C₂×#389	—	47	1	no	—
200	C₂×#382	—	47	1	no	—
201	#2101	—	47	8	no	—
202	C₂×#340	—	47	1	no	—
203	C₂×#340	—	47	1	no	—
204	C₂×#340	—	47	1	no	—
205	C₂×#340	—	47	1	no	—
206	C₂×#336	D₄₇	1	1	yes	characteristic
207	C₂×C₄₇	#2101	1	8	yes	complemented
208	C₂×C₄₇	C₂×#400	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#478	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#479	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#482	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#485	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#488	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#489	1	1	yes	characteristic
215	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
216	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
217	C₂²×C₄⋊C₄	—	47	1	no	—
218	C₂²×C₄⋊C₄	—	47	1	no	—
219	C₂²×C₄⋊C₄	—	47	1	no	—
220	C₂²×C₄⋊C₄	—	47	1	no	—
221	C₂²×C₄⋊C₄	—	94	1	no	—
222	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
223	#389	—	47	4	no	—
224	#389	—	94	2	no	—
225	#382	—	47	4	no	—
226	#382	—	94	2	no	—
227	C₂×#95	—	94	1	no	—
228	C₂×#95	—	94	1	no	—
229	C₂×#95	—	94	1	no	—
230	#340	—	47	4	no	—
231	#340	—	47	4	no	—
232	#340	—	47	4	no	—
233	#340	—	47	4	no	—
234	#336	C₂×D₄₇	1	4	yes	—
235	C₄₇	C₂×#2101	1	1	yes	characteristic, complemented, Sylow
236	C₂³×C₄	—	94	1	no	—
237	C₂³×C₄	—	94	1	no	—
238	C₂³×C₄	—	94	1	no	—
239	C₂³×C₄	—	94	1	no	—
240	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
241	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
250	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
251	C₂×C₄⋊C₄	—	47	4	no	—
252	C₂×C₄⋊C₄	—	47	2	no	—
253	C₂×C₄⋊C₄	—	47	2	no	—
254	C₂×C₄⋊C₄	—	47	2	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	94	1	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	—	94	1	no	—
265	C₂×C₄⋊C₄	—	94	1	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	—	94	4	no	—
268	C₂×C₄⋊C₄	—	188	4	no	—
269	C₂×C₄²	—	2	2	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	D₁₈₈	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
273	#95	—	94	4	no	—
274	#95	—	94	4	no	—
275	#95	—	94	4	no	—
276	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	94	4	no	—
284	C₂²×C₄	—	94	2	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	188	2	no	—
289	C₂²×C₄	—	188	2	no	—
290	C₂²×C₄	—	188	2	no	—
291	C₂²×C₄	—	188	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	—	188	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	—	188	2	no	—
299	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
300	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
301	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
302	C₂²×C₄	#10625350	1	2	yes	—
303	C₂²×C₄	#10625350	1	2	yes	—
304	C₂²×C₄	#10625352	1	2	yes	—
305	C₂²×C₄	#10625352	1	2	yes	—
306	C₂²×C₄	#10625352	1	2	yes	—
307	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	4	4	no	—
317	C₄⋊C₄	—	47	4	no	—
318	C₄⋊C₄	—	94	4	no	—
319	C₄⋊C₄	—	94	2	no	—
320	C₄⋊C₄	—	94	2	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	188	8	no	—
327	C₄⋊C₄	—	188	2	no	—
328	C₄⋊C₄	—	188	2	no	—
329	C₄⋊C₄	—	188	2	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₂³	#13094004	1	2	yes	—
334	C₂³	#13094008	1	2	yes	—
335	C₂³	#13094012	1	2	yes	—
336	C₂³	#13094046	1	2	yes	—
337	C₂³	#13094046	1	2	yes	—
338	C₂³	#13094052	1	2	yes	—
339	C₂³	#13094057	1	2	yes	—
340	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	376	4	no	—
351	C₂×C₄	—	376	4	no	—
352	C₂×C₄	—	376	4	no	—
353	C₂×C₄	—	188	2	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	8	no	—
365	C₂×C₄	#13094004	1	2	yes	—
366	C₂×C₄	#13094008	1	2	yes	—
367	C₂×C₄	#13094012	1	2	yes	—
368	C₂×C₄	#13094014	1	4	yes	—
369	C₂×C₄	#13094014	1	4	yes	—
370	C₂×C₄	#13094017	1	4	yes	—
371	C₂×C₄	#13094017	1	4	yes	—
372	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
377	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₂²	#15689063	1	4	yes	—
381	C₂²	#15689424	1	4	yes	—
382	C₂²	#15689431	1	4	yes	—
383	C₂²	#15689448	1	4	yes	—
384	C₂²	#15689465	1	4	yes	—
385	C₂²	#15689478	1	4	yes	—
386	C₂²	#15689483	1	4	yes	—
387	C₂²	C₂×#13094004	1	1	yes	characteristic
388	C₂²	C₂×#13094008	1	1	yes	characteristic
389	C₂²	C₂×#13094012	1	1	yes	characteristic
390	C₂²	C₂×#13094046	1	1	yes	characteristic
391	C₂²	C₂×#13094046	1	1	yes	characteristic
392	C₂²	C₂×#13094052	1	1	yes	characteristic
393	C₂²	C₂×#13094057	1	1	yes	characteristic
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	376	2	no	—
397	C₄	—	376	2	no	—
398	C₄	—	376	2	no	—
399	C₄	—	188	4	no	—
400	C₄	#15689063	1	4	yes	—
401	C₄	C₂×#13094014	1	1	yes	characteristic
402	C₄	C₂×#13094014	1	1	yes	characteristic
403	C₄	C₂×#13094017	1	1	yes	characteristic
404	C₄	C₂×#13094017	1	1	yes	characteristic
405	C₂	#20244957	1	8	yes	direct product factor
406	C₂	C₂×#15689063	1	1	yes	characteristic
407	C₂	C₂×#15689424	1	1	yes	characteristic
408	C₂	C₂×#15689431	1	1	yes	characteristic
409	C₂	C₂×#15689448	1	1	yes	characteristic
410	C₂	C₂×#15689465	1	1	yes	characteristic
411	C₂	C₂×#15689478	1	1	yes	characteristic
412	C₂	C₂×#15689483	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₈₈
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	C₂×#2101
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
3. #20244957	C₂	direct (N × H)
207. C₂×C₄₇	#2101	semidirect
235. C₄₇	C₂×#2101	semidirect
405. C₂	#20244957	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×#15689021	2
C₂×#15688989	2
#20244957	2
C₂×#15688886	2
C₂×C₄₇×#336	2
C₂×#2101	47

Subgroups — C2×#20244957 #26246179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244957 #26246179