Subgroups — #26121655

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×#15689097	C₂	1	1	yes	maximal, characteristic
3	#20243105	C₂	1	2	yes	maximal, complemented
4	#20243099	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
6	#15689606	—	2	4	no	—
7	#15689601	C₄	1	2	yes	complemented
8	#15689598	—	2	2	no	—
9	#15689598	C₄	1	2	yes	complemented
10	#41×Dic₄₇	—	2	4	no	—
11	C₂×#13093983	—	2	2	no	—
12	C₂×#13093983	C₂²	1	2	yes	—
13	C₂×#13093983	C₂²	1	2	yes	—
14	#15689097	—	2	2	no	—
15	#15689097	C₄	1	4	yes	complemented
16	C₂×#13093939	—	2	2	no	—
17	#15688886	—	2	4	no	—
18	#15688884	—	2	4	no	—
19	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#408	—	2	2	no	—
23	C₄₇×#408	C₄	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
25	Q₈×Dic₄₇	—	2	8	no	—
26	D₄×Dic₄₇	—	2	16	no	—
27	D₄×Dic₄₇	—	2	8	no	—
28	#13093983	—	2	4	no	—
29	#13093983	—	2	4	no	—
30	#13093983	—	2	4	no	—
31	#13093983	—	2	2	no	—
32	#13093983	—	2	2	no	—
33	#13093983	—	2	2	no	—
34	#13093983	—	2	2	no	—
35	#13093983	—	2	2	no	—
36	#13093983	C₂×C₄	1	4	yes	—
37	#13093983	C₂×C₄	1	4	yes	complemented
38	#13093983	D₄	1	4	yes	—
39	C₂×C₄⋊Dic₄₇	—	2	4	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
42	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
43	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
44	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
45	C₂×C₄×Dic₄₇	—	2	4	no	—
46	C₂×C₄×Dic₄₇	—	2	2	no	—
47	C₂×C₄×Dic₄₇	—	2	2	no	—
48	#13093939	—	2	8	no	—
49	C₂×#41×C₄₇	—	2	2	no	—
50	C₂×#41×C₄₇	—	2	2	no	—
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	—	2	2	no	—
53	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×#41×C₄₇	D₄	1	2	yes	—
56	C₂×#41×C₄₇	Q₈	1	2	yes	—
57	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×D₄×C₄₇	D₄	1	2	yes	—
60	C₂³×C₄×C₄₇	D₄	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₇	—	2	1	no	—
63	C₂×M₁₆×C₄₇	—	2	2	no	—
64	C₂×M₁₆×C₄₇	—	2	2	no	—
65	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
66	C₂²×C₈×C₄₇	—	2	2	no	—
67	C₂²×C₈×C₄₇	—	2	1	no	—
68	C₂²×C₈×C₄₇	—	2	1	no	—
69	C₂²×C₈×C₄₇	—	2	1	no	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
72	C₂²⋊C₈×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	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×Dic₄₇	—	2	8	no	—
113	C₂²×Dic₄₇	—	2	4	no	—
114	C₂²×Dic₄₇	—	4	2	no	—
115	M₁₆×C₄₇	—	2	4	no	—
116	M₁₆×C₄₇	—	4	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	4	no	—
120	C₂×C₈×C₄₇	—	4	1	no	—
121	C₂×C₈×C₄₇	—	4	1	no	—
122	C₂×C₈×C₄₇	—	4	2	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	—	4	1	no	—
125	C₂²⋊Dic₄₇	—	2	8	no	—
126	C₂²⋊Dic₄₇	—	2	4	no	—
127	C₂²⋊Dic₄₇	—	2	4	no	—
128	C₂²⋊Dic₄₇	—	2	4	no	—
129	C₂²⋊Dic₄₇	—	4	2	no	—
130	C₄⋊Dic₄₇	—	2	8	no	—
131	C₄⋊Dic₄₇	—	2	4	no	—
132	C₄⋊Dic₄₇	—	2	4	no	—
133	C₄⋊Dic₄₇	—	4	2	no	—
134	C₄⋊Dic₄₇	C₂²⋊C₄	1	8	yes	—
135	C₄×Dic₄₇	—	2	8	no	—
136	C₄×Dic₄₇	—	2	4	no	—
137	C₄×Dic₄₇	—	2	4	no	—
138	C₄×Dic₄₇	—	2	4	no	—
139	C₄×Dic₄₇	—	4	2	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	#95	1	4	yes	—
163	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#117	1	2	yes	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	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	#120	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#121	1	2	yes	—
176	C₂×C₄×C₄₇	#121	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
179	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
180	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
181	C₂×Dic₄₇	—	2	8	no	—
182	C₂×Dic₄₇	—	4	4	no	—
183	C₂×Dic₄₇	—	8	4	no	—
184	C₂×Dic₄₇	—	8	8	no	—
185	C₂×Dic₄₇	—	8	4	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₈×C₄₇	—	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	C₄×C₂²⋊C₄	1	2	yes	—
205	C₄×C₄₇	#380	1	2	yes	—
206	C₄×C₄₇	#385	1	1	yes	characteristic
207	C₄×C₄₇	#385	1	1	yes	characteristic
208	C₄×C₄₇	#386	1	1	yes	characteristic
209	C₄×C₄₇	#386	1	1	yes	characteristic
210	Dic₄₇	—	4	8	no	—
211	Dic₄₇	—	8	4	no	—
212	#3428	—	47	1	no	—
213	C₂×#410	—	47	1	no	—
214	C₂×#408	D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic
226	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
234	C₂×#117	—	94	2	no	—
235	#410	—	47	4	no	—
236	#410	—	94	2	no	—
237	C₂×#99	—	94	2	no	—
238	#408	—	2	2	no	—
239	#408	Dic₄₇	1	4	yes	complemented
240	C₂×C₂²⋊C₈	—	2	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	D₁₈₈	1	2	yes	—
255	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
256	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	complemented
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	C₂×Dic₄₇	1	2	yes	complemented
267	C₄×Q₈	—	94	8	no	—
268	C₄×D₄	—	94	8	no	—
269	C₄×D₄	—	94	16	no	—
270	#117	—	47	4	no	—
271	#117	—	47	4	no	—
272	#117	—	47	4	no	—
273	#117	—	94	4	no	—
274	#117	—	94	4	no	—
275	#117	—	94	4	no	—
276	#117	—	94	2	no	—
277	#117	—	94	2	no	—
278	#117	—	94	2	no	—
279	#117	—	94	2	no	—
280	#117	—	94	2	no	—
281	C₂×C₄⋊C₄	—	47	4	no	—
282	C₂×C₄⋊C₄	—	94	4	no	—
283	C₂×C₄⋊C₄	—	94	2	no	—
284	C₂×C₂²⋊C₄	—	94	4	no	—
285	C₂×C₂²⋊C₄	—	94	2	no	—
286	C₂×C₂²⋊C₄	—	94	2	no	—
287	C₂×C₄²	—	94	4	no	—
288	C₂×C₄²	—	94	2	no	—
289	C₂×C₄²	—	94	2	no	—
290	#99	—	94	8	no	—
291	C₂²⋊C₈	—	2	8	no	—
292	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
293	C₂⁴	C₂×D₁₈₈	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	2	yes	—
312	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
313	C₂×D₄	(C₂×D₄₇)⋊C₄	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	—	94	8	no	—
319	C₂²×C₄	—	94	4	no	—
320	C₂²×C₄	—	188	2	no	—
321	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
322	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
323	C₂²×C₄	C₂²⋊Dic₄₇	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	D₄×D₄₇	1	2	yes	—
328	C₂²×C₄	D₄×D₄₇	1	2	yes	—
329	C₂²×C₄	#10625352	1	2	yes	—
330	C₂²×C₄	#10625352	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
334	M₁₆	—	2	4	no	—
335	M₁₆	—	4	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	4	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₄⋊C₄	—	47	8	no	—
345	C₄⋊C₄	—	94	8	no	—
346	C₄⋊C₄	—	94	4	no	—
347	C₄⋊C₄	—	94	4	no	—
348	C₄⋊C₄	—	188	2	no	—
349	C₂²⋊C₄	—	94	8	no	—
350	C₂²⋊C₄	—	94	4	no	—
351	C₂²⋊C₄	—	94	4	no	—
352	C₂²⋊C₄	—	94	4	no	—
353	C₂²⋊C₄	—	188	2	no	—
354	C₄²	—	94	8	no	—
355	C₄²	—	94	4	no	—
356	C₄²	—	94	4	no	—
357	C₄²	—	94	4	no	—
358	C₄²	—	188	2	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×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
366	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
367	C₂³	#13093994	1	2	yes	—
368	C₂³	#13094008	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	—	94	8	no	—
382	C₂×C₄	—	376	4	no	—
383	C₂×C₄	—	376	4	no	—
384	C₂×C₄	—	376	8	no	—
385	C₂×C₄	—	188	4	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×C₂²⋊Dic₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×Dic₄₇⋊C₄	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	#13093992	1	1	yes	characteristic
398	C₂×C₄	#13093992	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	#13094005	1	1	yes	characteristic
404	C₂×C₄	#13094005	1	1	yes	characteristic
405	C₈	—	4	2	no	—
406	C₈	—	4	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	#15688998	1	2	yes	—
420	C₂²	#15689000	1	2	yes	—
421	C₄	—	2	4	no	—
422	C₄	—	376	4	no	—
423	C₄	—	188	8	no	—
424	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
425	C₄	#15688981	1	2	yes	—
426	C₄	#15688995	1	1	yes	characteristic
427	C₄	#15688995	1	1	yes	characteristic
428	C₄	#15689003	1	1	yes	characteristic
429	C₄	#15689003	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	#20243351	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#408	C₂
socle	C₂²×C₄₇	#379
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#408	D₄₇
hypocenter	C₄₇	#10752
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
3. #20243105	C₂	semidirect
4. #20243099	C₂	semidirect
7. #15689601	C₄	semidirect
9. #15689598	C₄	semidirect
15. #15689097	C₄	semidirect
23. C₄₇×#408	C₄	semidirect
37. #13093983	C₂×C₄	semidirect
65. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
71. C₂²×C₈×C₄₇	C₂×C₄	semidirect
239. #408	Dic₄₇	semidirect
243. C₄₇	#10752	semidirect
260. C₂×M₁₆	C₂×Dic₄₇	semidirect
266. C₂²×C₈	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×#15689097	2
#20243105	2
#20243099	2
C₂×C₄₇×#408	2
#10752	47