Subgroups — #26220771

Order 12032.

1106 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256793	C₂	1	1	yes	maximal, characteristic
2	#20251806	C₂	1	1	yes	maximal, characteristic
3	#20245870	C₂	1	1	yes	maximal, characteristic
4	#20244330	C₂	1	8	yes	maximal, complemented
5	#20243098	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688884	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688882	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#1733	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	#15689754	C₄	1	4	yes	complemented
11	#15689751	—	2	2	no	—
12	#15689751	C₄	1	4	yes	complemented
13	#15689749	—	2	2	no	—
14	#15689680	—	2	2	no	—
15	#15689676	—	2	2	no	—
16	#15689676	C₂²	1	4	yes	—
17	C₂×#13093983	C₂²	1	1	yes	characteristic
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	#15689081	—	2	2	no	—
21	#15689078	—	2	2	no	—
22	M₁₆×Dic₄₇	C₂²	1	4	yes	—
23	#15689019	—	2	2	no	—
24	#15688995	—	2	2	no	—
25	C₄×Dic₄₇⋊C₄	C₂²	1	4	yes	—
26	#15688884	C₂²	1	4	yes	—
27	#15688883	C₂²	1	4	yes	—
28	#15688882	C₂²	1	4	yes	—
29	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#339	C₂²	1	4	yes	—
33	C₂³×Dic₄₇	—	2	1	no	—
34	C₂×#10625329	—	2	1	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	Q₈	1	4	yes	complemented
37	C₂×#10625329	C₂³	1	2	yes	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	#13094024	—	2	4	no	—
40	#13094023	—	2	4	no	—
41	#13094023	C₂×C₄	1	8	yes	complemented
42	#13094016	—	2	4	no	—
43	#13094015	—	2	4	no	—
44	#13094015	C₂×C₄	1	8	yes	complemented
45	#13094003	—	2	8	no	—
46	#13094001	—	2	8	no	—
47	#13094001	—	2	8	no	—
48	C₄×Dic₉₄	—	2	8	no	—
49	#13093983	—	2	1	no	—
50	#13093983	—	2	1	no	—
51	#13093983	C₂×C₄	1	2	yes	—
52	#13093983	C₂×C₄	1	2	yes	—
53	#13093983	C₂×C₄	1	2	yes	—
54	#13093983	D₄	1	2	yes	—
55	#13093983	D₄	1	2	yes	—
56	#13093983	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
59	C₂×Dic₄₇⋊C₄	—	2	4	no	—
60	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
61	C₂×C₂²⋊Dic₄₇	D₄	1	2	yes	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	#13093934	—	2	4	no	—
69	C₈×Dic₄₇	—	2	4	no	—
70	C₄₇⋊#95	—	2	4	no	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂×M₁₆×C₄₇	—	2	2	no	—
74	C₂×M₁₆×C₄₇	Q₈	1	4	yes	complemented
75	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₇	—	2	1	no	—
77	#117×C₄₇	—	2	1	no	—
78	#117×C₄₇	—	2	1	no	—
79	#117×C₄₇	—	2	2	no	—
80	#117×C₄₇	—	2	2	no	—
81	#117×C₄₇	C₂×C₄	1	2	yes	—
82	#117×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₇	—	2	2	no	—
103	C₂²×Dic₄₇	—	2	2	no	—
104	C₂²×Dic₄₇	—	4	4	no	—
105	C₂²×Dic₄₇	—	4	2	no	—
106	C₂²×Dic₄₇	C₂×D₄	1	4	yes	—
107	C₂×Dic₉₄	—	2	8	no	—
108	M₁₆×C₄₇	—	2	4	no	—
109	M₁₆×C₄₇	—	2	2	no	—
110	M₁₆×C₄₇	C₂×Q₈	1	4	yes	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	4	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₂²⋊Dic₄₇	—	2	2	no	—
124	C₂²⋊Dic₄₇	—	2	2	no	—
125	C₂²⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
126	C₂²⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	8	no	—
129	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
130	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
131	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
132	Dic₄₇⋊C₄	—	2	8	no	—
133	Dic₄₇⋊C₄	—	2	8	no	—
134	Dic₄₇⋊C₄	—	4	8	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	4	2	no	—
140	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
141	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
142	#10625329	—	2	4	no	—
143	#10625329	—	2	2	no	—
144	#10625329	C₂×Q₈	1	4	yes	—
145	C₂×C₄₇⋊C₈	—	2	4	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	#124	1	2	yes	—
151	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	8	2	no	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₄₇	#124	1	2	yes	—
168	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×Dic₄₇	—	2	4	no	—
176	C₂×Dic₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	C₂×Dic₄₇	—	4	8	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	8	2	no	—
182	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	8	yes	—
183	Dic₉₄	—	8	8	no	—
184	C₈×C₄₇	—	2	4	no	—
185	C₄₇⋊C₈	—	2	4	no	—
186	#21307	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	#391	1	2	yes	—
193	C₂²×C₄₇	#391	1	2	yes	—
194	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	#391	1	2	yes	—
200	C₄×C₄₇	#391	1	2	yes	—
201	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
204	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	Dic₄₇	—	2	8	no	—
206	Dic₄₇	—	4	4	no	—
207	Dic₄₇	—	4	4	no	—
208	#3458	—	47	1	no	—
209	#2873	—	47	1	no	—
210	#2296	—	47	1	no	—
211	#1986	—	47	8	no	—
212	#1733	—	47	1	no	—
213	#1733	D₄₇	1	1	yes	characteristic
214	C₂×#339	—	47	1	no	—
215	C₂×#339	—	47	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	—	2	1	no	—
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	2	2	no	—
220	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
221	C₂×C₄₇	#2901	1	2	yes	—
222	C₂²×M₁₆	—	47	1	no	—
223	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
224	#544	—	47	4	no	—
225	#544	—	47	4	no	—
226	#544	—	94	2	no	—
227	#543	—	94	2	no	—
228	#533	—	47	4	no	—
229	#533	—	94	2	no	—
230	#533	—	94	2	no	—
231	C₂×#117	—	47	1	no	—
232	C₂×#117	—	47	1	no	—
233	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
234	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
235	C₂²×C₄²	—	47	1	no	—
236	#405	—	94	2	no	—
237	#405	—	94	2	no	—
238	C₄×M₁₆	—	47	4	no	—
239	#389	—	94	2	no	—
240	#385	—	94	2	no	—
241	C₄×C₄⋊C₄	—	47	4	no	—
242	#339	—	47	4	no	—
243	#339	—	47	4	no	—
244	#339	—	47	4	no	—
245	#339	C₂×D₄₇	1	4	yes	—
246	C₄₇	#21307	1	1	yes	characteristic, complemented, Sylow
247	C₂³×C₄	—	94	1	no	—
248	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	47	4	no	—
252	C₂×M₁₆	—	47	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	1	no	—
255	C₂×M₁₆	Dic₉₄	1	4	yes	complemented
256	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	94	1	no	—
259	C₄⋊Q₈	—	47	8	no	—
260	C₄⋊Q₈	—	94	4	no	—
261	C₄⋊Q₈	—	94	4	no	—
262	#125	—	47	8	no	—
263	#125	—	94	4	no	—
264	#125	—	94	4	no	—
265	C₂²⋊Q₈	—	94	8	no	—
266	C₂²⋊Q₈	—	94	8	no	—
267	C₂²⋊Q₈	—	94	8	no	—
268	C₄×Q₈	—	94	8	no	—
269	#117	—	2	1	no	—
270	#117	—	2	1	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	#117	—	47	2	no	—
274	#117	—	47	2	no	—
275	#117	—	47	2	no	—
276	#117	—	47	2	no	—
277	#117	—	47	2	no	—
278	#117	—	47	2	no	—
279	#117	—	94	1	no	—
280	#117	—	94	1	no	—
281	#117	C₄×D₄₇	1	2	yes	—
282	#117	C₂²×D₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	47	2	no	—
285	C₂×C₄⋊C₄	—	47	2	no	—
286	C₂×C₄⋊C₄	—	94	4	no	—
287	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	47	2	no	—
291	C₂×C₂²⋊C₄	—	94	1	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	47	2	no	—
294	C₂×C₄²	—	47	2	no	—
295	C₂×C₄²	—	94	1	no	—
296	C₂×C₄²	—	94	2	no	—
297	C₂×C₄²	—	94	2	no	—
298	C₂×C₄²	—	94	1	no	—
299	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
300	#97	—	94	4	no	—
301	C₄×C₈	—	94	4	no	—
302	#95	—	94	4	no	—
303	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
304	C₂×Q₈	—	94	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	47	4	no	—
308	C₂²×C₄	—	94	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	—	188	4	no	—
311	C₂²×C₄	—	188	2	no	—
312	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
313	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	#10625350	1	2	yes	—
316	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	#10625352	1	2	yes	—
320	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
321	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	47	4	no	—
325	M₁₆	—	94	4	no	—
326	M₁₆	—	94	2	no	—
327	M₁₆	C₂×Dic₉₄	1	4	yes	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	94	4	no	—
331	C₂×C₈	—	94	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	47	4	no	—
335	C₄⋊C₄	—	47	4	no	—
336	C₄⋊C₄	—	47	4	no	—
337	C₄⋊C₄	—	94	8	no	—
338	C₄⋊C₄	—	94	8	no	—
339	C₄⋊C₄	—	94	8	no	—
340	C₄⋊C₄	—	94	2	no	—
341	C₄⋊C₄	—	188	8	no	—
342	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	47	4	no	—
347	C₂²⋊C₄	—	47	4	no	—
348	C₂²⋊C₄	—	94	2	no	—
349	C₂²⋊C₄	—	94	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	47	4	no	—
355	C₄²	—	47	4	no	—
356	C₄²	—	94	2	no	—
357	C₄²	—	94	2	no	—
358	C₄²	—	94	2	no	—
359	C₄²	—	94	2	no	—
360	C₄²	—	188	2	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
363	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
364	C₂³	#13094010	1	2	yes	—
365	C₂³	#13094023	1	2	yes	—
366	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
367	Q₈	—	376	8	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	2	no	—
372	C₂×C₄	—	47	8	no	—
373	C₂×C₄	—	94	4	no	—
374	C₂×C₄	—	94	4	no	—
375	C₂×C₄	—	376	2	no	—
376	C₂×C₄	—	188	4	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	8	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	#13093989	1	2	yes	—
383	C₂×C₄	#13093989	1	2	yes	—
384	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
385	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
386	C₂×C₄	#13094001	1	2	yes	—
387	C₂×C₄	#13094001	1	2	yes	—
388	C₂×C₄	#13094002	1	2	yes	—
389	C₂×C₄	#13094002	1	2	yes	—
390	C₂×C₄	#13094010	1	2	yes	—
391	C₂×C₄	#13094023	1	2	yes	—
392	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
396	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
397	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
398	C₈	—	2	4	no	—
399	C₈	—	94	4	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	#15689027	1	2	yes	—
406	C₂²	#15689027	1	2	yes	—
407	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
408	C₂²	C₂×#13094010	1	1	yes	characteristic
409	C₂²	C₂×#13094023	1	1	yes	characteristic
410	C₄	—	4	4	no	—
411	C₄	—	8	2	no	—
412	C₄	—	94	8	no	—
413	C₄	—	188	4	no	—
414	C₄	—	188	4	no	—
415	C₄	#15689027	1	2	yes	—
416	C₄	#15689027	1	2	yes	—
417	C₄	C₂×#13093989	1	1	yes	characteristic
418	C₄	C₂×C₄×Dic₉₄	1	1	yes	characteristic
419	C₄	C₂×#13094001	1	1	yes	characteristic
420	C₄	C₂×#13094002	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	—	2	1	no	—
425	C₂	C₂×#15689027	1	1	yes	characteristic
426	C₂	#20251934	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1733	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1733	D₄₇
hypocenter	C₄₇	#21307
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
4. #20244330	C₂	semidirect
10. #15689754	C₄	semidirect
12. #15689751	C₄	semidirect
36. C₂×#10625329	Q₈	semidirect
41. #13094023	C₂×C₄	semidirect
44. #13094015	C₂×C₄	semidirect
74. C₂×M₁₆×C₄₇	Q₈	semidirect
246. C₄₇	#21307	semidirect
255. C₂×M₁₆	Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
#20256793	2
#20251806	2
#20245870	2
#20244330	2
#20243098	2
C₂×#15688884	2
C₂×#15688882	2
C₄₇×#1733	2
#21307	47