Subgroups — #26121681

Order 12032.

1168 conjugacy classes of subgroups.

The subgroup lattice has 420 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	1	yes	maximal, characteristic
2	#20251833	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688895	C₂	1	2	yes	maximal, complemented
4	#20243126	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#568	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	1	yes	characteristic
7	C₂²×#10625329	C₂²	1	1	yes	characteristic
8	C₂×#13093983	C₂²	1	2	yes	—
9	#15689097	—	2	2	no	—
10	#15689097	—	2	2	no	—
11	C₂×#13093939	C₄	1	4	yes	—
12	#15689090	—	2	2	no	—
13	#15689090	C₄	1	4	yes	complemented
14	#15689087	—	2	2	no	—
15	#15688895	—	2	4	no	—
16	#15688891	—	2	4	no	—
17	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#568	—	2	2	no	—
19	C₄₇×#568	—	2	4	no	—
20	C₄₇×#568	C₄	1	4	yes	complemented
21	C₂×#131×C₄₇	—	2	4	no	—
22	C₂²×M₁₆×C₄₇	—	2	2	no	—
23	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
24	C₂×#10625329	—	2	1	no	—
25	C₂×#10625329	—	2	1	no	—
26	C₂×#10625329	—	2	1	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	C₂×C₄	1	2	yes	—
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
34	#13093983	—	2	2	no	—
35	#13093983	—	2	2	no	—
36	#13093983	—	2	2	no	—
37	#13093983	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	2	no	—
39	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	#13093939	—	2	8	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
49	C₂×#41×C₄₇	D₄	1	2	yes	—
50	C₂×#41×C₄₇	D₄	1	2	yes	—
51	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
52	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	#131×C₄₇	—	2	16	no	—
57	#131×C₄₇	—	2	16	no	—
58	C₂×M₁₆×C₄₇	—	2	4	no	—
59	C₂×M₁₆×C₄₇	—	2	8	no	—
60	C₂×M₁₆×C₄₇	—	2	8	no	—
61	C₂×M₁₆×C₄₇	—	2	2	no	—
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	2	no	—
64	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
66	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
67	C₂²×C₈×C₄₇	—	2	4	no	—
68	C₂²×C₈×C₄₇	—	2	2	no	—
69	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	#41×C₄₇	—	2	4	no	—
72	#41×C₄₇	—	2	4	no	—
73	#41×C₄₇	—	2	4	no	—
74	#41×C₄₇	—	2	4	no	—
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	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
82	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	4	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	C₄²	1	4	yes	—
88	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
90	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
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	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	2	yes	—
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×Dic₄₇	—	2	4	no	—
109	M₁₆×C₄₇	—	2	16	no	—
110	M₁₆×C₄₇	—	2	4	no	—
111	M₁₆×C₄₇	—	2	4	no	—
112	M₁₆×C₄₇	—	2	4	no	—
113	M₁₆×C₄₇	C₂²⋊C₄	1	8	yes	—
114	C₂×C₈×C₄₇	—	2	16	no	—
115	C₂×C₈×C₄₇	—	2	4	no	—
116	C₂×C₈×C₄₇	—	2	4	no	—
117	C₂×C₈×C₄₇	—	2	4	no	—
118	C₂²⋊Dic₄₇	—	2	4	no	—
119	C₂²⋊Dic₄₇	—	2	4	no	—
120	C₄⋊Dic₄₇	—	4	2	no	—
121	C₄⋊Dic₄₇	—	4	2	no	—
122	C₄×Dic₄₇	—	4	2	no	—
123	C₄×Dic₄₇	—	4	2	no	—
124	#10625329	—	2	4	no	—
125	#10625329	—	4	1	no	—
126	#10625329	—	4	1	no	—
127	#10625329	—	4	2	no	—
128	#10625329	—	4	1	no	—
129	#10625329	—	4	1	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	4	no	—
133	C₂×C₄₇⋊C₈	—	4	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	8	1	no	—
137	C₂³×C₄₇	—	8	2	no	—
138	C₂³×C₄₇	#95	1	4	yes	—
139	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
140	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂³×C₄₇	C₄×D₄	1	2	yes	—
143	C₂³×C₄₇	C₄×D₄	1	2	yes	—
144	Q₈×C₄₇	—	2	4	no	—
145	Q₈×C₄₇	—	2	4	no	—
146	D₄×C₄₇	—	2	8	no	—
147	D₄×C₄₇	—	2	8	no	—
148	D₄×C₄₇	—	2	4	no	—
149	D₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	#95	1	4	yes	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#117	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	#120	1	2	yes	—
166	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#121	1	2	yes	—
169	C₂×C₄×C₄₇	#121	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₄₇	#123	1	2	yes	—
173	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	8	4	no	—
177	C₈×C₄₇	—	2	8	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	C₄₇⋊C₈	—	4	2	no	—
180	#10757	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	4	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
191	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
192	C₂²×C₄₇	#385	1	1	yes	characteristic
193	C₂²×C₄₇	#385	1	1	yes	characteristic
194	C₂²×C₄₇	#386	1	2	yes	—
195	C₄×C₄₇	—	2	4	no	—
196	C₄×C₄₇	#379	1	1	yes	characteristic
197	C₄×C₄₇	#380	1	2	yes	—
198	C₄×C₄₇	#381	1	1	yes	characteristic
199	C₄×C₄₇	#385	1	2	yes	—
200	C₄×C₄₇	#386	1	1	yes	characteristic
201	C₄×C₄₇	#386	1	1	yes	characteristic
202	Dic₄₇	—	8	4	no	—
203	C₂×#568	D₄₇	1	1	yes	characteristic
204	C₂×#410	—	47	1	no	—
205	#2879	—	47	1	no	—
206	C₂×#344	—	47	2	no	—
207	#1742	—	47	2	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	4	4	no	—
214	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
215	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
216	#568	—	2	2	no	—
217	#568	—	2	4	no	—
218	#568	Dic₄₇	1	4	yes	complemented
219	C₂×#131	—	2	4	no	—
220	C₂²×M₁₆	—	2	2	no	—
221	C₂²×M₁₆	—	47	1	no	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
224	C₂×#117	—	47	2	no	—
225	#410	—	94	2	no	—
226	#410	—	94	2	no	—
227	C₂×#99	—	47	4	no	—
228	#408	—	47	4	no	—
229	#408	—	94	2	no	—
230	#407	—	94	2	no	—
231	#344	—	94	4	no	—
232	#343	—	94	4	no	—
233	C₄₇	#10757	1	1	yes	characteristic, complemented, Sylow
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	C₄×D₄₇	1	2	yes	—
239	C₂×#41	D₁₈₈	1	2	yes	—
240	C₂×#41	C₂×Dic₄₇	1	2	yes	—
241	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
242	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
243	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
244	C₂²×D₄	C₄×D₄₇	1	2	yes	—
245	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
246	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
247	#131	—	2	16	no	—
248	#131	—	2	16	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	—	2	8	no	—
251	C₂×M₁₆	—	2	8	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	47	2	no	—
256	C₂×M₁₆	—	94	1	no	—
257	C₂×M₁₆	—	94	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	—	94	1	no	—
260	C₂×M₁₆	—	94	1	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
264	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
265	C₂×M₁₆	C₂²⋊D₄₇	1	4	yes	—
266	C₂²×C₈	—	2	4	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	47	2	no	—
269	C₂²×C₈	—	94	1	no	—
270	#117	—	94	2	no	—
271	#117	—	94	2	no	—
272	#117	—	94	2	no	—
273	#117	—	94	2	no	—
274	C₂×C₄⋊C₄	—	94	2	no	—
275	C₂×C₂²⋊C₄	—	47	4	no	—
276	C₂×C₄²	—	94	2	no	—
277	#99	—	94	8	no	—
278	C₂²⋊C₈	—	94	8	no	—
279	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
280	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
281	#41	—	2	4	no	—
282	#41	—	2	4	no	—
283	#41	—	2	4	no	—
284	#41	—	2	4	no	—
285	#41	—	2	4	no	—
286	#41	—	2	4	no	—
287	#41	—	2	4	no	—
288	#41	—	2	4	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
292	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
298	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
299	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
300	C₂×D₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	94	4	no	—
306	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
307	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
308	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
309	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
312	C₂²×C₄	#10625350	1	2	yes	—
313	C₂²×C₄	#10625350	1	2	yes	—
314	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
319	M₁₆	—	2	16	no	—
320	M₁₆	—	2	4	no	—
321	M₁₆	—	2	4	no	—
322	M₁₆	—	2	4	no	—
323	M₁₆	—	94	4	no	—
324	M₁₆	—	188	1	no	—
325	M₁₆	—	188	1	no	—
326	M₁₆	—	188	2	no	—
327	M₁₆	—	188	1	no	—
328	M₁₆	—	188	1	no	—
329	M₁₆	C₂²⋊Dic₄₇	1	8	yes	—
330	C₂×C₈	—	2	16	no	—
331	C₂×C₈	—	2	4	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	4	no	—
337	C₂×C₈	—	188	2	no	—
338	C₄⋊C₄	—	188	2	no	—
339	C₄⋊C₄	—	188	2	no	—
340	C₂²⋊C₄	—	94	4	no	—
341	C₂²⋊C₄	—	94	4	no	—
342	C₄²	—	188	2	no	—
343	C₄²	—	188	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	C₄₇⋊#95	1	4	yes	—
349	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
350	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
351	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
352	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
353	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
354	Q₈	—	2	4	no	—
355	Q₈	—	2	4	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	376	4	no	—
367	C₂×C₄	—	188	4	no	—
368	C₂×C₄	C₄₇⋊#95	1	4	yes	—
369	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
374	C₂×C₄	#13093983	1	2	yes	—
375	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
376	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
377	C₂×C₄	#13093993	1	2	yes	—
378	C₂×C₄	#13093993	1	1	yes	characteristic
379	C₂×C₄	#13093993	1	1	yes	characteristic
380	C₂×C₄	#13093998	1	2	yes	—
381	C₂×C₄	#13093998	1	2	yes	—
382	C₂×C₄	#13094003	1	2	yes	—
383	C₂×C₄	#13094003	1	2	yes	—
384	C₂×C₄	#13094007	1	2	yes	—
385	C₂×C₄	#13094007	1	1	yes	characteristic
386	C₂×C₄	#13094007	1	1	yes	characteristic
387	C₈	—	2	8	no	—
388	C₈	—	188	2	no	—
389	C₈	—	188	2	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	8	2	no	—
399	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
400	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
401	C₂²	#15688996	1	1	yes	characteristic
402	C₂²	#15688996	1	1	yes	characteristic
403	C₂²	#15689002	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	376	4	no	—
406	C₄	#15688979	1	1	yes	characteristic
407	C₄	#15688983	1	2	yes	—
408	C₄	#15688986	1	1	yes	characteristic
409	C₄	#15688996	1	2	yes	—
410	C₄	#15689002	1	1	yes	characteristic
411	C₄	#15689002	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	1	no	—
416	C₂	—	2	2	no	—
417	C₂	—	4	4	no	—
418	C₂	#20241611	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689002
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#568	C₂
socle	C₂×C₄₇	C₂²⋊#95
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#568	D₄₇
hypocenter	C₄₇	#10757
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#568

Complements

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

N	H ≅ G/N	type
3. C₂×#15688895	C₂	semidirect
4. #20243126	C₂	semidirect
13. #15689090	C₄	semidirect
20. C₄₇×#568	C₄	semidirect
218. #568	Dic₄₇	semidirect
233. C₄₇	#10757	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689097	2
#20251833	2
C₂×#15688895	2
#20243126	2
C₂×C₄₇×#568	2
#10757	47