Subgroups — C₂×#20241511 #26131239

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689107	C₂	1	2	yes	maximal
2	#20241511	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10625329	—	2	2	no	—
5	#15689107	—	2	2	no	—
6	#15689107	—	2	2	no	—
7	#15689107	C₄	1	4	yes	—
8	#15689107	C₂²	1	4	yes	—
9	C₂×#13093943	—	2	2	no	—
10	C₂×#13093941	C₄	1	4	yes	—
11	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₄	1	1	yes	characteristic
13	C₂³×C₈×C₄₇	C₄	1	1	yes	characteristic
14	C₄₇×#408	—	2	2	no	—
15	C₄₇×#408	C₄	1	2	yes	—
16	C₄₇×#408	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
18	C₂×#10625329	—	2	4	no	—
19	C₂×#10625329	—	2	4	no	—
20	C₂×#10625329	—	2	4	no	—
21	C₂×#10625329	—	4	2	no	—
22	C₂×#10625329	—	4	2	no	—
23	C₂×#10625329	—	4	2	no	—
24	C₂²×C₄₇⋊C₈	—	4	2	no	—
25	#13093943	—	2	4	no	—
26	#13093943	—	2	4	no	—
27	#13093941	—	2	4	no	—
28	#13093941	C₂×C₄	1	8	yes	—
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	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₄₇	Q₈	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	—
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	—
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	C₄⋊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	C₂²⋊C₄	1	2	yes	—
73	C₂×Q₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
74	C₂×Q₈×C₄₇	C₂×D₄	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	C₄⋊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×Q₈	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	2	yes	—
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
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	M₁₆×C₄₇	—	4	2	no	—
106	M₁₆×C₄₇	—	4	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	4	2	no	—
110	C₂×C₈×C₄₇	—	4	1	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	2	no	—
115	#10625329	—	2	8	no	—
116	#10625329	—	4	4	no	—
117	#10625329	—	4	4	no	—
118	#10625329	—	4	4	no	—
119	C₂×C₄₇⋊C₈	—	4	4	no	—
120	C₂×C₄₇⋊C₈	—	4	4	no	—
121	C₂×C₄₇⋊C₈	—	4	4	no	—
122	C₂³×C₄₇	—	2	1	no	—
123	C₂³×C₄₇	—	2	1	no	—
124	C₂³×C₄₇	—	2	2	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×C₄⋊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	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₈×C₄₇	—	4	2	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₄₇⋊C₈	—	4	8	no	—
176	C₂×#1392	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	#342	1	1	yes	characteristic
191	C₂²×C₄₇	#342	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	#342	1	1	yes	characteristic
198	C₄×C₄₇	#342	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#99	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#99	1	1	yes	characteristic
201	C₂×#413	—	47	2	no	—
202	C₂×#408	D₄₇	1	1	yes	characteristic
203	#1392	—	47	4	no	—
204	C₂×C₄₇	—	2	1	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	4	1	no	—
207	C₂×C₄₇	—	4	1	no	—
208	C₂×C₄₇	—	4	2	no	—
209	C₂×C₄₇	—	4	2	no	—
210	C₂×C₄₇	#1392	1	2	yes	complemented
211	C₂×C₄₇	C₂×#342	1	1	yes	characteristic
212	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
213	C₂²×M₁₆	—	94	2	no	—
214	C₂²×M₁₆	Dic₄₇	1	1	yes	characteristic
215	C₂³×C₈	Dic₄₇	1	1	yes	characteristic
216	#413	—	47	4	no	—
217	#413	—	47	4	no	—
218	#413	—	94	2	no	—
219	#413	—	94	2	no	—
220	C₂×#101	—	94	2	no	—
221	C₂×#100	—	47	4	no	—
222	#408	—	2	2	no	—
223	#408	Dic₄₇	1	2	yes	—
224	#408	C₂×D₄₇	1	2	yes	—
225	C₂×C₂²⋊C₈	—	2	2	no	—
226	C₄₇	C₂×#1392	1	1	yes	characteristic, complemented, Sylow
227	C₂×#41	—	4	1	no	—
228	C₂×#41	—	4	1	no	—
229	C₂×#41	—	4	1	no	—
230	C₂×#41	—	4	1	no	—
231	C₂×#41	Dic₉₄	1	1	yes	characteristic
232	C₂×#41	C₄×D₄₇	1	2	yes	—
233	C₂×#41	D₁₈₈	1	1	yes	characteristic
234	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
235	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
236	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
237	C₂²×Q₈	D₁₈₈	1	1	yes	characteristic
238	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
239	C₂²×D₄	C₄×D₄₇	1	2	yes	—
240	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
242	C₂×M₁₆	—	2	1	no	—
243	C₂×M₁₆	—	4	1	no	—
244	C₂×M₁₆	—	4	1	no	—
245	C₂×M₁₆	—	94	4	no	—
246	C₂×M₁₆	—	94	4	no	—
247	C₂×M₁₆	—	94	4	no	—
248	C₂×M₁₆	—	188	2	no	—
249	C₂×M₁₆	—	188	2	no	—
250	C₂×M₁₆	—	188	2	no	—
251	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	4	1	no	—
256	C₂²×C₈	—	4	1	no	—
257	C₂²×C₈	—	188	2	no	—
258	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
259	#101	—	94	4	no	—
260	#101	—	94	4	no	—
261	#100	—	47	8	no	—
262	#100	—	94	4	no	—
263	C₂²⋊C₈	—	2	4	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	C₂⁴	C₄×Dic₄₇	1	1	yes	characteristic
266	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
267	#41	—	4	1	no	—
268	#41	—	4	1	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	1	no	—
272	#41	—	4	1	no	—
273	#41	—	4	1	no	—
274	#41	—	4	1	no	—
275	#41	—	4	2	no	—
276	#41	—	4	2	no	—
277	#41	—	4	1	no	—
278	#41	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	C₄⋊Dic₄₇	1	1	yes	characteristic
282	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
283	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	1	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
289	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
290	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
291	C₂×D₄	C₄⋊Dic₄₇	1	1	yes	characteristic
292	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
293	C₂×D₄	C₂×Dic₉₄	1	1	yes	characteristic
294	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
305	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
308	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
309	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
310	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
314	M₁₆	—	4	2	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	94	8	no	—
317	M₁₆	—	188	4	no	—
318	M₁₆	—	188	4	no	—
319	M₁₆	—	188	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	188	4	no	—
329	C₂×C₈	—	188	4	no	—
330	C₂×C₈	—	188	4	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	C₄₇⋊#95	1	1	yes	characteristic
338	C₂³	C₄₇⋊#95	1	1	yes	characteristic
339	C₂³	C₄₇⋊#95	1	2	yes	—
340	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
341	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	1	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
373	C₂×C₄	C₄₇⋊#95	1	2	yes	—
374	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
375	C₂×C₄	#13093939	1	1	yes	characteristic
376	C₂×C₄	#13093939	1	1	yes	characteristic
377	C₂×C₄	#13093939	1	1	yes	characteristic
378	C₂×C₄	#13093939	1	1	yes	characteristic
379	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	188	8	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	#15688890	1	1	yes	characteristic
399	C₂²	#15688890	1	1	yes	characteristic
400	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
401	C₄	—	2	2	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	#15688890	1	1	yes	characteristic
406	C₄	#15688890	1	1	yes	characteristic
407	C₄	C₂×#13093939	1	1	yes	characteristic
408	C₄	C₂×#13093939	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	4	1	no	—
412	C₂	—	4	1	no	—
413	C₂	—	4	2	no	—
414	C₂	—	4	2	no	—
415	C₂	#20241511	1	2	yes	direct product factor
416	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×#1392
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. #20241511	C₂	direct (N × H)
210. C₂×C₄₇	#1392	semidirect
226. C₄₇	C₂×#1392	semidirect
415. C₂	#20241511	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×#15689107	2
#20241511	2
C₂×C₄₇×#408	2
C₂×#1392	47

Subgroups — C2×#20241511 #26131239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241511 #26131239