Subgroups — C₂×#20241509 #26131233

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689097	C₂	1	2	yes	maximal
2	#20241509	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
4	C₂×#13093983	—	2	2	no	—
5	#15689097	—	2	2	no	—
6	#15689097	—	2	2	no	—
7	#15689097	C₄	1	4	yes	complemented
8	#15689097	C₂²	1	4	yes	—
9	C₂×#13093939	—	2	2	no	—
10	C₂×#13093939	C₄	1	4	yes	complemented
11	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
13	C₂³×C₈×C₄₇	C₄	1	1	yes	characteristic, complemented
14	C₄₇×#408	—	2	2	no	—
15	C₄₇×#408	C₄	1	2	yes	complemented
16	C₄₇×#408	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
18	#13093983	—	2	4	no	—
19	#13093983	—	2	4	no	—
20	#13093983	—	4	2	no	—
21	#13093983	—	4	2	no	—
22	C₂×C₄⋊Dic₄₇	—	4	2	no	—
23	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
24	C₂×C₄×Dic₄₇	—	4	2	no	—
25	#13093939	—	2	4	no	—
26	#13093939	—	2	4	no	—
27	#13093939	—	2	4	no	—
28	#13093939	C₂×C₄	1	8	yes	complemented
29	C₂×#41×C₄₇	—	4	1	no	—
30	C₂×#41×C₄₇	—	4	1	no	—
31	C₂×#41×C₄₇	—	4	1	no	—
32	C₂×#41×C₄₇	—	4	1	no	—
33	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
34	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
36	C₂×#41×C₄₇	D₄	1	2	yes	—
37	C₂×#41×C₄₇	Q₈	1	1	yes	characteristic
38	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
40	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂×M₁₆×C₄₇	—	2	1	no	—
45	C₂×M₁₆×C₄₇	—	4	1	no	—
46	C₂×M₁₆×C₄₇	—	4	1	no	—
47	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
48	C₂²×C₈×C₄₇	—	2	1	no	—
49	C₂²×C₈×C₄₇	—	2	1	no	—
50	C₂²×C₈×C₄₇	—	2	1	no	—
51	C₂²×C₈×C₄₇	—	4	1	no	—
52	C₂²×C₈×C₄₇	—	4	1	no	—
53	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
54	C₂²⋊C₈×C₄₇	—	2	4	no	—
55	C₂²⋊C₈×C₄₇	—	2	4	no	—
56	C₂⁴×C₄₇	C₄²	1	1	yes	characteristic
57	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
58	#41×C₄₇	—	4	2	no	—
59	#41×C₄₇	—	4	2	no	—
60	#41×C₄₇	—	4	1	no	—
61	#41×C₄₇	—	4	1	no	—
62	#41×C₄₇	—	4	1	no	—
63	#41×C₄₇	—	4	1	no	—
64	#41×C₄₇	—	4	2	no	—
65	#41×C₄₇	—	4	2	no	—
66	#41×C₄₇	—	4	1	no	—
67	#41×C₄₇	—	4	1	no	—
68	#41×C₄₇	—	4	1	no	—
69	#41×C₄₇	—	4	1	no	—
70	C₂×Q₈×C₄₇	—	4	1	no	—
71	C₂×Q₈×C₄₇	—	4	1	no	—
72	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
73	C₂×Q₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂×Q₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
75	C₂×D₄×C₄₇	—	4	2	no	—
76	C₂×D₄×C₄₇	—	4	2	no	—
77	C₂×D₄×C₄₇	—	4	1	no	—
78	C₂×D₄×C₄₇	—	4	1	no	—
79	C₂×D₄×C₄₇	C₄²	1	2	yes	—
80	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
81	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
83	C₂×D₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×Dic₄₇	—	4	4	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₂×C₈×C₄₇	—	4	1	no	—
112	C₂×C₈×C₄₇	—	4	1	no	—
113	C₂×C₈×C₄₇	—	4	1	no	—
114	C₂×C₈×C₄₇	—	4	1	no	—
115	C₂×C₈×C₄₇	—	4	2	no	—
116	C₂²⋊Dic₄₇	—	2	8	no	—
117	C₂²⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	—	4	4	no	—
119	C₄⋊Dic₄₇	—	4	4	no	—
120	C₄×Dic₄₇	—	4	4	no	—
121	C₄×Dic₄₇	—	4	4	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	1	no	—
124	C₂³×C₄₇	—	2	1	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	4	2	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	#95	1	1	yes	characteristic
129	C₂³×C₄₇	#95	1	2	yes	—
130	C₂³×C₄₇	#95	1	1	yes	characteristic
131	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
133	Q₈×C₄₇	—	4	2	no	—
134	Q₈×C₄₇	—	4	1	no	—
135	Q₈×C₄₇	—	4	1	no	—
136	D₄×C₄₇	—	4	2	no	—
137	D₄×C₄₇	—	4	2	no	—
138	D₄×C₄₇	—	4	2	no	—
139	D₄×C₄₇	—	4	2	no	—
140	D₄×C₄₇	—	4	1	no	—
141	D₄×C₄₇	—	4	2	no	—
142	D₄×C₄₇	—	4	1	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#95	1	2	yes	—
165	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#99	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#99	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#99	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#99	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₄₇	—	4	8	no	—
174	C₂×Dic₄₇	—	8	8	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₂×#1391	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	#342	1	1	yes	characteristic
192	C₂²×C₄₇	#342	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	#342	1	1	yes	characteristic
199	C₄×C₄₇	#342	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#99	1	1	yes	characteristic
201	C₄×C₄₇	C₂×#99	1	1	yes	characteristic
202	Dic₄₇	—	8	8	no	—
203	C₂×#410	—	47	2	no	—
204	C₂×#408	D₄₇	1	1	yes	characteristic
205	#1391	—	47	4	no	—
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	—	2	1	no	—
208	C₂×C₄₇	—	4	2	no	—
209	C₂×C₄₇	—	4	1	no	—
210	C₂×C₄₇	—	4	1	no	—
211	C₂×C₄₇	—	4	2	no	—
212	C₂×C₄₇	#1391	1	2	yes	complemented
213	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
214	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
215	C₂²×M₁₆	Dic₄₇	1	1	yes	characteristic, complemented
216	C₂³×C₈	Dic₄₇	1	1	yes	characteristic, complemented
217	C₂×#117	—	94	2	no	—
218	#410	—	47	4	no	—
219	#410	—	47	4	no	—
220	#410	—	94	2	no	—
221	#410	—	94	2	no	—
222	C₂×#99	—	47	4	no	—
223	C₂×#99	—	94	2	no	—
224	#408	—	2	2	no	—
225	#408	Dic₄₇	1	2	yes	complemented
226	#408	C₂×D₄₇	1	2	yes	—
227	C₂×C₂²⋊C₈	—	2	2	no	—
228	C₄₇	C₂×#1391	1	1	yes	characteristic, complemented, Sylow
229	C₂×#41	—	4	1	no	—
230	C₂×#41	—	4	1	no	—
231	C₂×#41	—	4	1	no	—
232	C₂×#41	—	4	1	no	—
233	C₂×#41	Dic₉₄	1	1	yes	characteristic
234	C₂×#41	C₄×D₄₇	1	2	yes	—
235	C₂×#41	D₁₈₈	1	1	yes	characteristic
236	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
237	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
238	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
240	C₂²×D₄	C₄×D₄₇	1	2	yes	—
241	C₂²×D₄	D₁₈₈	1	1	yes	characteristic
242	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	4	1	no	—
246	C₂×M₁₆	—	4	1	no	—
247	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	complemented
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	4	1	no	—
252	C₂²×C₈	—	4	1	no	—
253	C₂²×C₈	C₂×Dic₄₇	1	2	yes	complemented
254	#117	—	94	4	no	—
255	#117	—	94	4	no	—
256	#117	—	188	2	no	—
257	#117	—	188	2	no	—
258	C₂×C₄⋊C₄	—	188	2	no	—
259	C₂×C₂²⋊C₄	—	94	4	no	—
260	C₂×C₄²	—	188	2	no	—
261	#99	—	47	8	no	—
262	#99	—	94	4	no	—
263	#99	—	94	4	no	—
264	#99	—	94	4	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	C₂²⋊C₈	—	2	4	no	—
267	C₂⁴	C₄×Dic₄₇	1	1	yes	characteristic
268	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
269	#41	—	4	1	no	—
270	#41	—	4	1	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	1	no	—
276	#41	—	4	1	no	—
277	#41	—	4	2	no	—
278	#41	—	4	2	no	—
279	#41	—	4	1	no	—
280	#41	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
284	C₂×Q₈	C₄⋊Dic₄₇	1	1	yes	characteristic
285	C₂×Q₈	C₂×Dic₉₄	1	1	yes	characteristic
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
291	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
292	C₂×D₄	C₄⋊Dic₄₇	1	1	yes	characteristic
293	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
294	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
295	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
296	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	188	4	no	—
306	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
308	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
309	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
311	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
312	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
313	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	2	no	—
327	C₄⋊C₄	—	188	4	no	—
328	C₄⋊C₄	—	188	4	no	—
329	C₂²⋊C₄	—	94	8	no	—
330	C₂²⋊C₄	—	188	4	no	—
331	C₄²	—	188	4	no	—
332	C₄²	—	188	4	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	4	no	—
339	C₂³	C₄₇⋊#95	1	1	yes	characteristic
340	C₂³	C₄₇⋊#95	1	2	yes	—
341	C₂³	C₄₇⋊#95	1	1	yes	characteristic
342	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
343	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	1	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	376	8	no	—
375	C₂×C₄	—	188	8	no	—
376	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
377	C₂×C₄	C₄₇⋊#95	1	2	yes	—
378	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
379	C₂×C₄	#13093939	1	1	yes	characteristic
380	C₂×C₄	#13093939	1	1	yes	characteristic
381	C₂×C₄	#13093939	1	1	yes	characteristic
382	C₂×C₄	#13093939	1	1	yes	characteristic
383	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
385	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	#15688890	1	1	yes	characteristic
402	C₂²	#15688890	1	1	yes	characteristic
403	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	376	8	no	—
409	C₄	#15688890	1	1	yes	characteristic
410	C₄	#15688890	1	1	yes	characteristic
411	C₄	C₂×#13093939	1	1	yes	characteristic
412	C₄	C₂×#13093939	1	1	yes	characteristic
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	4	2	no	—
416	C₂	—	4	1	no	—
417	C₂	—	4	1	no	—
418	C₂	—	4	2	no	—
419	C₂	#20241509	1	2	yes	direct product factor
420	C₂	C₂×#15688890	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093939
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂×#41	C₂²×D₄₇
Fitting	C₂×C₄₇×#408	C₂
socle	C₂²×C₄₇	#342
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂×#41×C₄₇	C₂³
hypercenter	C₂×#408	D₄₇
hypocenter	C₄₇	C₂×#1391
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
2. #20241509	C₂	direct (N × H)
7. #15689097	C₄	semidirect
10. C₂×#13093939	C₄	semidirect
12. C₂²×M₁₆×C₄₇	C₄	semidirect
13. C₂³×C₈×C₄₇	C₄	semidirect
15. C₄₇×#408	C₄	semidirect
28. #13093939	C₂×C₄	semidirect
47. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
53. C₂²×C₈×C₄₇	C₂×C₄	semidirect
212. C₂×C₄₇	#1391	semidirect
215. C₂²×M₁₆	Dic₄₇	semidirect
216. C₂³×C₈	Dic₄₇	semidirect
225. #408	Dic₄₇	semidirect
228. C₄₇	C₂×#1391	semidirect
247. C₂×M₁₆	C₂×Dic₄₇	semidirect
253. C₂²×C₈	C₂×Dic₄₇	semidirect
419. C₂	#20241509	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×#15689097	2
#20241509	2
C₂×C₄₇×#408	2
C₂×#1391	47

Subgroups — C2×#20241509 #26131233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241509 #26131233