Subgroups — #26221583

Order 12032.

1430 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244366	C₂	1	2	yes	maximal, complemented
4	#20244217	C₂	1	2	yes	maximal, complemented
5	#20243832	C₂	1	4	yes	maximal, complemented
6	C₄×#13093951	C₂	1	4	yes	maximal, complemented
7	C₄₇×#3444	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×Dic₄₇	—	2	2	no	—
9	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
10	#15689180	—	2	2	no	—
11	#15689176	—	2	2	no	—
12	#15689147	C₂²	1	2	yes	—
13	C₂×#13093951	C₂²	1	8	yes	—
14	#15689087	C₂²	1	2	yes	—
15	C₄×#10625329	C₂²	1	2	yes	—
16	C₄²×Dic₄₇	—	2	2	no	—
17	C₄²×Dic₄₇	C₂²	1	2	yes	—
18	C₄²×Dic₄₇	C₂²	1	2	yes	—
19	#15688882	C₂²	1	8	yes	—
20	C₄₇×#533	C₄	1	2	yes	complemented
21	C₄₇×#533	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₄	1	2	yes	complemented
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₄₇×#529	—	2	2	no	—
25	C₄₇×#529	—	2	2	no	—
26	C₄₇×#529	C₄	1	4	yes	complemented
27	C₄₇×#525	—	2	2	no	—
28	C₄₇×#525	C₂²	1	2	yes	—
29	C₄×#41×C₄₇	—	2	2	no	—
30	C₄×#41×C₄₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Dic₄₇	—	2	2	no	—
33	C₂×#10625329	C₂³	1	4	yes	—
34	C₂×C₄×Dic₄₇	—	2	16	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	4	no	—
37	C₂×C₄×Dic₄₇	—	2	4	no	—
38	C₂×C₄×Dic₄₇	—	2	8	no	—
39	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
40	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
41	#13093951	—	2	16	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
43	#13093935	—	2	2	no	—
44	C₄×C₄₇⋊C₈	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
51	#127×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
52	#126×C₄₇	—	2	4	no	—
53	#125×C₄₇	—	2	2	no	—
54	#125×C₄₇	C₂×C₄	1	2	yes	complemented
55	#124×C₄₇	—	2	2	no	—
56	#124×C₄₇	C₂×C₄	1	2	yes	complemented
57	#123×C₄₇	—	2	4	no	—
58	#123×C₄₇	—	2	2	no	—
59	C₂²⋊Q₈×C₄₇	—	2	2	no	—
60	C₂²⋊Q₈×C₄₇	—	2	2	no	—
61	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
62	#121×C₄₇	—	2	2	no	—
63	#121×C₄₇	—	2	2	no	—
64	#121×C₄₇	C₂×C₄	1	4	yes	—
65	#120×C₄₇	—	2	2	no	—
66	C₄×Q₈×C₄₇	—	2	2	no	—
67	C₄×Q₈×C₄₇	—	2	2	no	—
68	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
69	C₄×D₄×C₄₇	—	2	4	no	—
70	C₄×D₄×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
75	#117×C₄₇	—	2	2	no	—
76	#117×C₄₇	—	2	4	no	—
77	#117×C₄₇	—	2	2	no	—
78	#117×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	D₄	1	2	yes	—
83	C₂×C₄²×C₄₇	D₄	1	2	yes	—
84	C₂×C₄²×C₄₇	D₄	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
88	#41×C₄₇	—	2	8	no	—
89	#41×C₄₇	—	4	8	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂×D₄×C₄₇	—	2	4	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	—	2	16	no	—
111	C₂²×Dic₄₇	—	2	8	no	—
112	C₂²×Dic₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₄₇	—	2	4	no	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	2	4	no	—
123	C₂²⋊C₄×C₄₇	—	2	4	no	—
124	C₄²×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
127	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
128	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₄₇	—	2	16	no	—
137	C₄×Dic₄₇	—	2	16	no	—
138	C₄×Dic₄₇	—	2	8	no	—
139	C₄×Dic₄₇	—	2	4	no	—
140	C₄×Dic₄₇	#41	1	8	yes	complemented
141	#10625329	—	2	8	no	—
142	C₂×C₄₇⋊C₈	—	2	4	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₄₇	—	2	4	no	—
149	Q₈×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	4	4	no	—
152	D₄×C₄₇	—	4	8	no	—
153	D₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	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	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	—	4	8	no	—
166	C₂×C₄×C₄₇	#104	1	8	yes	complemented
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
175	C₂×Dic₄₇	—	2	16	no	—
176	C₂×Dic₄₇	—	2	32	no	—
177	C₂×Dic₄₇	—	2	8	no	—
178	C₄₇⋊C₈	—	4	4	no	—
179	#21415	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	C₂×#104	1	4	yes	—
187	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₇	#525	1	2	yes	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	4	4	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	C₂×#104	1	4	yes	—
195	C₄×C₄₇	C₂×#104	1	4	yes	—
196	C₄×C₄₇	C₄×#41	1	2	yes	—
197	C₄×C₄₇	#532	1	2	yes	—
198	Dic₄₇	—	2	16	no	—
199	#3444	D₄₇	1	1	yes	characteristic
200	#2920	—	47	1	no	—
201	C₂×C₄³	—	47	1	no	—
202	#1994	—	47	2	no	—
203	#1962	—	47	2	no	—
204	#1896	—	47	4	no	—
205	C₄×#104	—	47	4	no	—
206	C₂×C₄₇	—	2	2	no	—
207	C₂×C₄₇	—	2	4	no	—
208	C₂×C₄₇	—	8	2	no	—
209	C₂×C₄₇	#2297	1	1	yes	characteristic
210	C₂×C₄₇	C₂²×#104	1	2	yes	—
211	#533	Dic₄₇	1	2	yes	complemented
212	#533	C₂×D₄₇	1	1	yes	characteristic
213	#532	Dic₄₇	1	2	yes	complemented
214	#532	C₂×D₄₇	1	1	yes	characteristic
215	#529	—	2	2	no	—
216	#529	—	2	2	no	—
217	#529	Dic₄₇	1	4	yes	complemented
218	#525	—	2	2	no	—
219	#525	C₂×D₄₇	1	2	yes	—
220	C₄×#41	—	2	2	no	—
221	C₄×#41	C₂×D₄₇	1	2	yes	—
222	C₂²×C₄²	—	47	2	no	—
223	C₂²×C₄²	—	94	2	no	—
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	#432	—	94	2	no	—
226	#431	—	94	2	no	—
227	#423	—	47	2	no	—
228	C₂×#104	—	47	8	no	—
229	#407	—	47	2	no	—
230	C₄×M₁₆	—	47	2	no	—
231	C₄³	—	47	2	no	—
232	C₄³	—	47	2	no	—
233	C₄³	—	94	2	no	—
234	#339	—	47	8	no	—
235	C₄₇	#21415	1	1	yes	characteristic, complemented, Sylow
236	C₂×#41	—	2	2	no	—
237	C₂×#41	C₂²×D₄₇	1	2	yes	—
238	C₂³×C₄	—	94	2	no	—
239	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
240	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
241	C₂×M₁₆	—	47	4	no	—
242	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
243	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
244	#127	C₂×Dic₄₇	1	1	yes	characteristic, complemented
245	#126	—	2	4	no	—
246	#125	—	2	2	no	—
247	#125	C₂×Dic₄₇	1	2	yes	complemented
248	#124	—	2	2	no	—
249	#124	C₂×Dic₄₇	1	2	yes	complemented
250	#123	—	2	4	no	—
251	#123	—	2	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
255	#121	—	2	2	no	—
256	#121	—	2	2	no	—
257	#121	C₂×Dic₄₇	1	4	yes	—
258	#120	—	2	2	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
262	C₄×D₄	—	2	4	no	—
263	C₄×D₄	—	2	4	no	—
264	C₄×D₄	—	2	4	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
268	#117	—	2	2	no	—
269	#117	—	2	4	no	—
270	#117	—	2	2	no	—
271	#117	C₂²×D₄₇	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	47	4	no	—
274	C₂×C₄²	—	94	8	no	—
275	C₂×C₄²	—	94	16	no	—
276	C₂×C₄²	—	94	4	no	—
277	C₂×C₄²	—	94	4	no	—
278	C₂×C₄²	—	94	2	no	—
279	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
280	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
281	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
282	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
283	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
286	C₄⋊C₈	—	94	4	no	—
287	#104	—	94	16	no	—
288	C₂²⋊C₈	—	94	4	no	—
289	#97	—	94	2	no	—
290	C₄×C₈	—	94	2	no	—
291	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
292	#41	—	2	8	no	—
293	#41	—	4	8	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	94	16	no	—
305	C₂²×C₄	—	94	8	no	—
306	C₂²×C₄	—	94	4	no	—
307	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
308	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
309	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
310	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
312	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
314	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
315	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
316	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
317	M₁₆	—	94	8	no	—
318	C₂×C₈	—	94	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	47	8	no	—
333	C₄²	—	94	8	no	—
334	C₄²	—	94	16	no	—
335	C₄²	—	94	16	no	—
336	C₄²	—	94	4	no	—
337	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
338	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
339	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
340	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
341	C₄²	C₂²×Dic₄₇	1	2	yes	—
342	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
343	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
344	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	2	no	—
350	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
351	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	4	4	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	4	no	—
356	D₄	—	4	8	no	—
357	D₄	—	4	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	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	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	94	16	no	—
371	C₂×C₄	—	94	32	no	—
372	C₂×C₄	—	94	8	no	—
373	C₂×C₄	#13093951	1	8	yes	complemented
374	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
376	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
377	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
378	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
379	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂×C₄	#41×D₄₇	1	4	yes	—
382	C₈	—	188	4	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	2	no	—
389	C₂²	C₂×#13093951	1	4	yes	—
390	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
391	C₂²	#15689630	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	94	16	no	—
398	C₄	C₂×#13093951	1	4	yes	—
399	C₄	C₂×#13093951	1	4	yes	—
400	C₄	#41×Dic₄₇	1	2	yes	—
401	C₄	#15689669	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	2	4	no	—
404	C₂	—	8	2	no	—
405	C₂	#20245879	1	1	yes	characteristic
406	C₂	C₂²×#13093951	1	2	yes	—

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3444	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3444	D₄₇
hypocenter	C₄₇	#21415
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. C₂×C₄²×Dic₄₇	C₂	semidirect
3. #20244366	C₂	semidirect
4. #20244217	C₂	semidirect
5. #20243832	C₂	semidirect
6. C₄×#13093951	C₂	semidirect
20. C₄₇×#533	C₄	semidirect
22. C₄₇×#532	C₄	semidirect
26. C₄₇×#529	C₄	semidirect
49. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
50. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
51. #127×C₄₇	C₂×C₄	semidirect
54. #125×C₄₇	C₂×C₄	semidirect
56. #124×C₄₇	C₂×C₄	semidirect
68. C₄×Q₈×C₄₇	C₂×C₄	semidirect
74. C₄×D₄×C₄₇	C₂×C₄	semidirect
140. C₄×Dic₄₇	#41	semidirect
166. C₂×C₄×C₄₇	#104	semidirect
211. #533	Dic₄₇	semidirect
213. #532	Dic₄₇	semidirect
217. #529	Dic₄₇	semidirect
235. C₄₇	#21415	semidirect
242. C₄⋊Q₈	C₂×Dic₄₇	semidirect
243. C₄⋊Q₈	C₂×Dic₄₇	semidirect
244. #127	C₂×Dic₄₇	semidirect
247. #125	C₂×Dic₄₇	semidirect
249. #124	C₂×Dic₄₇	semidirect
261. C₄×Q₈	C₂×Dic₄₇	semidirect
267. C₄×D₄	C₂×Dic₄₇	semidirect
373. C₂×C₄	#13093951	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
C₂×C₄²×Dic₄₇	2
#20244366	2
#20244217	2
#20243832	2
C₄×#13093951	2
C₄₇×#3444	2
#21415	47