Subgroups — #26121658

Order 12032.

1222 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256591	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689090	C₂	1	1	yes	maximal, characteristic
3	#20243104	C₂	1	2	yes	maximal, complemented
4	#20243098	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#410	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	1	yes	characteristic
7	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
8	#15689606	—	2	4	no	—
9	#15689601	C₄	1	2	yes	complemented
10	#15689598	—	2	2	no	—
11	#15689598	C₄	1	2	yes	complemented
12	#41×Dic₄₇	—	2	4	no	—
13	C₂×#13093983	—	2	2	no	—
14	C₂×#13093983	C₂²	1	2	yes	—
15	#15689090	—	2	2	no	—
16	#15689090	C₄	1	4	yes	complemented
17	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
18	#15688885	—	2	4	no	—
19	#15688883	—	2	4	no	—
20	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#410	—	2	2	no	—
23	C₄₇×#410	C₄	1	4	yes	complemented
24	C₂×#99×C₄₇	—	2	2	no	—
25	C₂×#10625329	—	2	1	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	C₂×C₄	1	2	yes	complemented
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	C₂²×C₄₇⋊C₈	—	2	1	no	—
32	C₂²×C₄₇⋊C₈	—	2	2	no	—
33	C₂²×C₄₇⋊C₈	—	2	2	no	—
34	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
35	Q₈×Dic₄₇	—	2	8	no	—
36	D₄×Dic₄₇	—	2	16	no	—
37	D₄×Dic₄₇	—	2	8	no	—
38	#13093983	—	2	4	no	—
39	#13093983	—	2	4	no	—
40	#13093983	—	2	4	no	—
41	#13093983	—	2	2	no	—
42	#13093983	—	2	2	no	—
43	#13093983	C₂×C₄	1	4	yes	—
44	#13093983	D₄	1	4	yes	—
45	C₂×C₄⋊Dic₄₇	—	2	4	no	—
46	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
47	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄×Dic₄₇	—	2	4	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×#41×C₄₇	D₄	1	2	yes	—
59	C₂×#41×C₄₇	Q₈	1	2	yes	—
60	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₄₇	D₄	1	2	yes	—
63	C₂³×C₄×C₄₇	D₄	1	2	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	C₂×C₄	1	4	yes	complemented
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	#99×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
74	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
75	#41×C₄₇	—	2	4	no	—
76	#41×C₄₇	—	2	4	no	—
77	#41×C₄₇	—	2	4	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
86	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	C₄²	1	2	yes	—
92	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
93	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
94	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×Dic₄₇	—	2	8	no	—
114	C₂²×Dic₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	4	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	2	no	—
119	C₄²×C₄₇	—	2	4	no	—
120	C₄²×C₄₇	—	4	2	no	—
121	C₂²⋊Dic₄₇	—	2	8	no	—
122	C₂²⋊Dic₄₇	—	2	4	no	—
123	C₂²⋊Dic₄₇	—	2	4	no	—
124	C₄⋊Dic₄₇	—	2	8	no	—
125	C₄⋊Dic₄₇	—	2	4	no	—
126	C₄⋊Dic₄₇	C₂²⋊C₄	1	8	yes	—
127	C₄×Dic₄₇	—	2	8	no	—
128	C₄×Dic₄₇	—	2	4	no	—
129	C₄×Dic₄₇	—	2	4	no	—
130	#10625329	—	2	4	no	—
131	#10625329	—	4	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	4	1	no	—
137	C₂×C₄₇⋊C₈	—	4	2	no	—
138	C₂×C₄₇⋊C₈	—	4	1	no	—
139	C₂×C₄₇⋊C₈	—	4	1	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	#95	1	4	yes	—
145	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂³×C₄₇	#120	1	2	yes	—
149	C₂³×C₄₇	#123	1	2	yes	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	8	no	—
153	D₄×C₄₇	—	2	8	no	—
154	D₄×C₄₇	—	2	4	no	—
155	D₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	8	4	no	—
164	C₂×C₄×C₄₇	#95	1	4	yes	—
165	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#117	1	2	yes	—
171	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
177	C₂×C₄×C₄₇	#121	1	2	yes	—
178	C₂×C₄×C₄₇	#121	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
181	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
183	C₂×Dic₄₇	—	2	8	no	—
184	C₂×Dic₄₇	—	8	4	no	—
185	C₂×Dic₄₇	—	8	8	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	#10752	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	—	2	4	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	4	1	no	—
193	C₂²×C₄₇	—	4	1	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	—	4	4	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
199	C₂²×C₄₇	#379	1	1	yes	characteristic
200	C₂²×C₄₇	#381	1	1	yes	characteristic
201	C₂²×C₄₇	#385	1	2	yes	—
202	C₂²×C₄₇	#386	1	2	yes	—
203	C₄×C₄₇	—	2	4	no	—
204	C₄×C₄₇	—	8	4	no	—
205	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
206	C₄×C₄₇	#380	1	2	yes	—
207	C₄×C₄₇	#385	1	1	yes	characteristic
208	C₄×C₄₇	#385	1	1	yes	characteristic
209	C₄×C₄₇	#386	1	1	yes	characteristic
210	C₄×C₄₇	#386	1	1	yes	characteristic
211	Dic₄₇	—	4	8	no	—
212	#3428	—	47	1	no	—
213	C₂×#410	D₄₇	1	1	yes	characteristic
214	C₂×#408	—	47	1	no	—
215	#1735	—	47	2	no	—
216	#1733	—	47	2	no	—
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	—	2	1	no	—
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	—	4	4	no	—
222	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
223	C₂×C₄₇	#1794	1	2	yes	—
224	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
225	C₂²×M₁₆	—	47	1	no	—
226	C₂³×C₈	—	47	1	no	—
227	#520	—	94	4	no	—
228	#519	—	47	2	no	—
229	#518	—	47	2	no	—
230	#518	—	94	2	no	—
231	C₄×#41	—	94	4	no	—
232	C₂×#117	—	47	2	no	—
233	C₂×#117	—	94	2	no	—
234	C₂×#117	C₂×D₄₇	1	2	yes	—
235	#410	—	2	2	no	—
236	#410	Dic₄₇	1	4	yes	complemented
237	C₂×#99	—	2	2	no	—
238	#408	—	47	4	no	—
239	#408	—	94	2	no	—
240	C₂×C₂²⋊C₈	—	94	2	no	—
241	#340	—	94	4	no	—
242	#339	—	94	4	no	—
243	C₄₇	#10752	1	1	yes	characteristic, complemented, Sylow
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	2	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	2	no	—
248	C₂×#41	Dic₉₄	1	2	yes	—
249	C₂×#41	C₄×D₄₇	1	2	yes	—
250	C₂×#41	C₂×Dic₄₇	1	2	yes	—
251	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
252	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
253	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
254	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
255	C₂³×C₄	D₁₈₈	1	2	yes	—
256	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
257	C₂×M₁₆	—	47	2	no	—
258	C₂×M₁₆	—	94	1	no	—
259	C₂×M₁₆	—	94	2	no	—
260	C₂×M₁₆	—	94	2	no	—
261	C₂²×C₈	—	47	2	no	—
262	C₂²×C₈	—	94	1	no	—
263	C₂²×C₈	—	94	1	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	—	94	1	no	—
267	C₄×Q₈	—	94	8	no	—
268	C₄×D₄	—	94	8	no	—
269	C₄×D₄	—	94	16	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	—	47	4	no	—
274	#117	—	47	4	no	—
275	#117	—	94	4	no	—
276	#117	—	94	4	no	—
277	#117	—	94	4	no	—
278	#117	—	94	2	no	—
279	#117	—	94	2	no	—
280	#117	C₂×Dic₄₇	1	4	yes	complemented
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	47	4	no	—
283	C₂×C₄⋊C₄	—	94	4	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	94	4	no	—
286	C₂×C₂²⋊C₄	—	94	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	94	4	no	—
289	C₂×C₄²	—	94	2	no	—
290	#99	—	2	8	no	—
291	C₂²⋊C₈	—	94	8	no	—
292	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
293	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
294	#41	—	2	4	no	—
295	#41	—	2	4	no	—
296	#41	—	2	4	no	—
297	#41	—	2	4	no	—
298	#41	—	2	4	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₄×Dic₄₇	1	2	yes	—
305	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₄×Dic₄₇	1	2	yes	—
311	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
312	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
313	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	94	8	no	—
320	C₂²×C₄	—	94	4	no	—
321	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
322	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
323	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
324	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
328	C₂²×C₄	D₄×D₄₇	1	2	yes	—
329	C₂²×C₄	D₄×D₄₇	1	2	yes	—
330	C₂²×C₄	#10625352	1	2	yes	—
331	C₂²×C₄	#10625352	1	2	yes	—
332	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	M₁₆	—	94	4	no	—
335	M₁₆	—	188	2	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	4	no	—
339	C₂×C₈	—	188	1	no	—
340	C₂×C₈	—	188	1	no	—
341	C₂×C₈	—	188	2	no	—
342	C₂×C₈	—	188	1	no	—
343	C₂×C₈	—	188	1	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	47	8	no	—
347	C₄⋊C₄	—	94	8	no	—
348	C₄⋊C₄	—	94	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	94	8	no	—
352	C₂²⋊C₄	—	94	4	no	—
353	C₂²⋊C₄	—	94	4	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	4	2	no	—
356	C₄²	—	94	8	no	—
357	C₄²	—	94	4	no	—
358	C₄²	—	94	4	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	4	no	—
363	C₂³	C₄₇⋊#95	1	4	yes	—
364	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
365	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
366	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
367	C₂³	#13093992	1	2	yes	—
368	C₂³	#13094005	1	2	yes	—
369	Q₈	—	2	4	no	—
370	Q₈	—	2	4	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	8	no	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	8	4	no	—
383	C₂×C₄	—	94	8	no	—
384	C₂×C₄	—	376	4	no	—
385	C₂×C₄	—	376	8	no	—
386	C₂×C₄	C₄₇⋊#95	1	4	yes	—
387	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
389	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	#13093980	1	2	yes	—
393	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
394	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
395	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
396	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
397	C₂×C₄	#13093994	1	1	yes	characteristic
398	C₂×C₄	#13093994	1	1	yes	characteristic
399	C₂×C₄	#13093996	1	2	yes	—
400	C₂×C₄	#13093996	1	2	yes	—
401	C₂×C₄	#13094001	1	2	yes	—
402	C₂×C₄	#13094001	1	2	yes	—
403	C₂×C₄	#13094008	1	1	yes	characteristic
404	C₂×C₄	#13094008	1	1	yes	characteristic
405	C₈	—	188	2	no	—
406	C₈	—	188	2	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	8	2	no	—
416	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
417	C₂²	#15688978	1	1	yes	characteristic
418	C₂²	#15688984	1	1	yes	characteristic
419	C₂²	#15688995	1	2	yes	—
420	C₂²	#15689003	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	8	4	no	—
423	C₄	—	188	8	no	—
424	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
425	C₄	#15688981	1	2	yes	—
426	C₄	#15688998	1	1	yes	characteristic
427	C₄	#15688998	1	1	yes	characteristic
428	C₄	#15689000	1	1	yes	characteristic
429	C₄	#15689000	1	1	yes	characteristic
430	C₂	—	2	2	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	2	2	no	—
434	C₂	—	4	4	no	—
435	C₂	#20241610	1	1	yes	characteristic
436	C₂	#20243354	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#410	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#410	D₄₇
hypocenter	C₄₇	#10752
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#410

Complements

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

N	H ≅ G/N	type
3. #20243104	C₂	semidirect
4. #20243098	C₂	semidirect
9. #15689601	C₄	semidirect
11. #15689598	C₄	semidirect
16. #15689090	C₄	semidirect
23. C₄₇×#410	C₄	semidirect
28. C₂×#10625329	C₂×C₄	semidirect
34. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
68. #117×C₄₇	C₂×C₄	semidirect
236. #410	Dic₄₇	semidirect
243. C₄₇	#10752	semidirect
280. #117	C₂×Dic₄₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20256591	2
C₂×#15689090	2
#20243104	2
#20243098	2
C₂×C₄₇×#410	2
#10752	47