Subgroups — #26223908

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689400	C₂	1	1	yes	maximal, characteristic
2	C₄²×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20244341	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243977	C₂	1	2	yes	maximal, complemented
6	#20243648	C₂	1	2	yes	maximal
7	#20243385	C₂	1	1	yes	maximal, characteristic
8	#20243286	C₂	1	2	yes	maximal, complemented
9	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243216	C₂	1	2	yes	maximal
11	C₄×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×C₄²×D₄₇	—	2	1	no	—
16	#15689400	C₄	1	8	yes	complemented
17	C₂×#13093957	C₂²	1	2	yes	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093944	C₂²	1	2	yes	—
22	C₂×#13093944	C₂²	1	2	yes	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
28	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
29	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
37	C₄₇×#391	—	2	1	no	—
38	C₄₇×#389	—	2	1	no	—
39	C₄₇×#389	C₂²	1	2	yes	—
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	—	2	1	no	—
46	C₂²×C₄×D₄₇	—	2	1	no	—
47	C₂²×C₄×D₄₇	—	2	1	no	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₄×D₁₈₈	—	2	2	no	—
51	C₄×D₁₈₈	—	2	2	no	—
52	C₄×D₁₈₈	—	2	2	no	—
53	C₄×D₁₈₈	—	2	2	no	—
54	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
55	C₄×D₁₈₈	Q₈	1	4	yes	complemented
56	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
61	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
62	C₂×C₄×Dic₄₇	—	2	1	no	—
63	C₂×C₄×Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₄²×D₄₇	—	4	4	no	—
66	#13093957	C₂×C₄	1	8	yes	complemented
67	#13093955	—	2	4	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
69	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
70	#13093944	—	2	4	no	—
71	#13093944	C₂×C₄	1	8	yes	—
72	#13093935	—	2	4	no	—
73	C₄₇⋊#95	—	2	1	no	—
74	C₄₇⋊#95	—	2	1	no	—
75	C₄₇⋊#95	—	2	1	no	—
76	C₂²×Q₈×C₄₇	—	2	1	no	—
77	C₄⋊Q₈×C₄₇	—	2	2	no	—
78	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₄×Q₈×C₄₇	—	4	4	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	2	no	—
96	C₂³×D₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	4	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	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	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂²×Dic₄₇	—	2	1	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	—	2	1	no	—
115	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
116	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
117	C₂×D₁₈₈	#41	1	2	yes	—
118	C₂×C₄×D₄₇	—	2	4	no	—
119	C₂×C₄×D₄₇	—	2	4	no	—
120	C₂×C₄×D₄₇	—	2	4	no	—
121	C₂×C₄×D₄₇	—	4	2	no	—
122	C₂×C₄×D₄₇	—	4	2	no	—
123	C₂×C₄×D₄₇	—	4	2	no	—
124	C₂×C₄×D₄₇	—	4	2	no	—
125	C₂×C₄×D₄₇	—	4	2	no	—
126	C₂×C₄×D₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	2	no	—
132	C₄⋊C₄×C₄₇	—	4	4	no	—
133	C₄⋊C₄×C₄₇	—	4	2	no	—
134	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	—	2	1	no	—
139	C₄²×C₄₇	—	2	1	no	—
140	C₄²×C₄₇	—	4	1	no	—
141	C₄²×C₄₇	—	4	4	no	—
142	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
144	C₄²×C₄₇	#41	1	2	yes	—
145	C₄²×C₄₇	#41	1	2	yes	—
146	(C₂×D₄₇)⋊C₄	—	2	4	no	—
147	(C₂×D₄₇)⋊C₄	—	2	4	no	—
148	(C₂×D₄₇)⋊C₄	—	2	4	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
153	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
154	C₄⋊Dic₄₇	#41	1	2	yes	—
155	C₄×Dic₄₇	—	4	2	no	—
156	C₄×Dic₄₇	—	4	2	no	—
157	C₄×Dic₄₇	—	4	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
164	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂²×D₄₇	—	2	2	no	—
166	C₂²×D₄₇	—	2	2	no	—
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	4	1	no	—
169	C₂²×D₄₇	—	4	1	no	—
170	C₂²×D₄₇	—	4	1	no	—
171	C₂²×D₄₇	—	4	1	no	—
172	Q₈×C₄₇	—	4	8	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
194	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
195	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
196	C₂×C₄×C₄₇	#137	1	2	yes	—
197	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₄₇	—	2	2	no	—
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	2	2	no	—
206	C₂×Dic₄₇	—	4	1	no	—
207	C₂×Dic₄₇	—	4	1	no	—
208	C₂×Dic₄₇	—	4	1	no	—
209	C₂×Dic₄₇	—	4	1	no	—
210	C₂×Dic₄₇	—	4	1	no	—
211	C₂×Dic₄₇	—	4	1	no	—
212	D₁₈₈	—	2	2	no	—
213	D₁₈₈	—	2	2	no	—
214	D₁₈₈	—	2	2	no	—
215	D₁₈₈	C₄×Q₈	1	4	yes	complemented
216	C₄×D₄₇	—	4	8	no	—
217	C₄×D₄₇	—	4	8	no	—
218	C₄×D₄₇	—	4	8	no	—
219	C₄₇⋊C₈	—	2	4	no	—
220	C₄₇⋊C₈	—	4	2	no	—
221	#21613	—	47	1	no	maximal, Sylow
222	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₂²×C₄₇	#525	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
228	C₂²×C₄₇	#575	1	1	yes	characteristic
229	C₂×D₄₇	—	2	4	no	—
230	C₂×D₄₇	—	4	2	no	—
231	C₂×D₄₇	—	4	2	no	—
232	C₂×D₄₇	—	4	2	no	—
233	C₂×D₄₇	—	4	2	no	—
234	C₂×D₄₇	—	4	2	no	—
235	C₂×D₄₇	—	4	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	4	1	no	—
241	C₄×C₄₇	—	4	4	no	—
242	C₄×C₄₇	—	8	2	no	—
243	C₄×C₄₇	#442	1	4	yes	—
244	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
245	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
246	C₄×C₄₇	#529	1	1	yes	characteristic
247	C₄×C₄₇	#533	1	1	yes	characteristic
248	Dic₄₇	—	4	2	no	—
249	Dic₄₇	—	4	2	no	—
250	Dic₄₇	—	4	2	no	—
251	C₂×#474	—	47	1	no	—
252	C₄×C₄⋊Q₈	D₄₇	1	1	yes	characteristic, complemented
253	C₄²×D₄	—	47	1	no	—
254	#1988	—	47	1	no	—
255	#1948	—	47	1	no	—
256	#1921	—	47	2	no	—
257	#1864	—	47	2	no	—
258	#1802	—	47	1	no	—
259	#1776	—	47	2	no	—
260	#1767	—	47	1	no	—
261	#1762	—	47	2	no	—
262	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
264	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
265	C₂×C₄₇	#3077	1	1	yes	characteristic
266	C₂×C₄₇	#3079	1	1	yes	characteristic
267	C₂×C₄₇	#3110	1	1	yes	characteristic
268	C₂×C₄₇	#3115	1	1	yes	characteristic
269	D₄₇	—	4	4	no	—
270	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
271	C₂×C₄×Q₈	—	2	1	no	—
272	C₂×C₄×D₄	—	47	1	no	—
273	C₂×C₄×D₄	—	47	1	no	—
274	C₂×C₄×D₄	—	47	1	no	—
275	C₂²×C₄²	—	94	1	no	—
276	#474	—	47	8	no	—
277	C₂×#107	—	47	2	no	—
278	C₂×#106	—	47	2	no	—
279	C₂×C₄⋊C₈	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	C₂×#102	—	47	2	no	—
282	C₂×#102	—	47	2	no	—
283	C₂×#97	—	47	2	no	—
284	#391	—	2	1	no	—
285	#389	—	2	1	no	—
286	#389	C₂×D₄₇	1	2	yes	—
287	#384	C₂×D₄₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	—	2	1	no	—
289	C₄×C₄⋊C₄	—	47	1	no	—
290	C₄×C₄⋊C₄	—	47	1	no	—
291	C₄×C₄⋊C₄	—	47	1	no	—
292	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
293	C₄×C₂²⋊C₄	—	94	1	no	—
294	C₄×C₂²⋊C₄	—	94	1	no	—
295	C₄×C₂²⋊C₄	—	94	1	no	—
296	C₄³	C₂×D₄₇	1	1	yes	characteristic
297	#340	—	47	2	no	—
298	#340	—	47	2	no	—
299	#340	—	47	2	no	—
300	#340	—	47	2	no	—
301	#336	—	47	2	no	—
302	C₄₇	#21613	1	1	yes	characteristic, complemented, Sylow
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	—	47	1	no	—
305	C₂³×C₄	—	94	1	no	—
306	C₂³×C₄	—	94	1	no	—
307	C₂³×C₄	—	94	1	no	—
308	C₂²×C₈	—	47	2	no	—
309	C₂²×C₈	—	47	2	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	C₄×D₄₇	1	4	yes	complemented
312	C₄×Q₈	—	4	4	no	—
313	C₄×D₄	—	47	4	no	—
314	C₄×D₄	—	47	4	no	—
315	C₄×D₄	—	94	2	no	—
316	C₄×D₄	—	94	2	no	—
317	C₄×D₄	—	94	2	no	—
318	C₄×D₄	—	94	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	47	1	no	—
324	C₂×C₄⋊C₄	—	47	1	no	—
325	C₂×C₄⋊C₄	—	47	1	no	—
326	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
328	C₂×C₂²⋊C₄	—	94	1	no	—
329	C₂×C₂²⋊C₄	—	94	1	no	—
330	C₂×C₂²⋊C₄	—	94	1	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	94	1	no	—
333	C₂×C₄²	—	94	1	no	—
334	C₂×C₄²	—	94	1	no	—
335	C₂×C₄²	—	188	4	no	—
336	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
337	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
338	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
339	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
343	#107	—	47	8	no	—
344	#106	—	94	4	no	—
345	C₄⋊C₈	—	47	4	no	—
346	C₄⋊C₈	—	94	2	no	—
347	#102	—	47	8	no	—
348	#102	—	94	4	no	—
349	#97	—	94	4	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	94	1	no	—
353	#95	—	94	1	no	—
354	#95	—	94	1	no	—
355	C₂⁴	—	94	1	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×D₄	—	47	2	no	—
360	C₂×D₄	—	47	2	no	—
361	C₂×D₄	—	47	2	no	—
362	C₂×D₄	—	94	1	no	—
363	C₂×D₄	—	94	1	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	94	4	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	1	no	—
370	C₂²×C₄	—	94	1	no	—
371	C₂²×C₄	—	94	4	no	—
372	C₂²×C₄	—	94	4	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	—	188	2	no	—
376	C₂²×C₄	—	188	2	no	—
377	C₂²×C₄	—	188	2	no	—
378	C₂²×C₄	—	188	2	no	—
379	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
386	C₂×C₈	—	47	4	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	94	2	no	—
389	C₂×C₈	—	94	2	no	—
390	C₂×C₈	—	94	2	no	—
391	C₂×C₈	—	94	2	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	4	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	47	2	no	—
400	C₄⋊C₄	—	47	2	no	—
401	C₄⋊C₄	—	47	2	no	—
402	C₄⋊C₄	—	94	1	no	—
403	C₄⋊C₄	—	94	1	no	—
404	C₄⋊C₄	—	94	1	no	—
405	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
406	C₂²⋊C₄	—	94	4	no	—
407	C₂²⋊C₄	—	94	4	no	—
408	C₂²⋊C₄	—	94	4	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	4	4	no	—
416	C₄²	—	188	2	no	—
417	C₄²	—	188	2	no	—
418	C₄²	—	188	2	no	—
419	C₄²	C₂×C₄×D₄₇	1	2	yes	—
420	C₄²	#10625350	1	2	yes	—
421	C₄²	Q₈×D₄₇	1	2	yes	—
422	C₄²	#10625354	1	2	yes	—
423	C₂³	—	94	2	no	—
424	C₂³	—	94	2	no	—
425	C₂³	—	94	2	no	—
426	C₂³	—	188	1	no	—
427	C₂³	—	188	1	no	—
428	C₂³	—	188	1	no	—
429	C₂³	—	188	1	no	—
430	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
431	Q₈	—	4	8	no	—
432	D₄	—	47	4	no	—
433	D₄	—	94	2	no	—
434	D₄	—	94	2	no	—
435	D₄	—	94	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	94	2	no	—
454	C₂×C₄	—	94	2	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	188	8	no	—
457	C₂×C₄	—	188	8	no	—
458	C₂×C₄	—	188	1	no	—
459	C₂×C₄	—	188	1	no	—
460	C₂×C₄	—	188	1	no	—
461	C₂×C₄	—	188	1	no	—
462	C₂×C₄	—	188	1	no	—
463	C₂×C₄	—	188	1	no	—
464	C₂×C₄	—	188	8	no	—
465	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
466	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
467	C₂×C₄	#13094000	1	2	yes	—
468	C₂×C₄	#13094000	1	2	yes	—
469	C₂×C₄	#13094049	1	2	yes	—
470	C₂×C₄	#13094050	1	2	yes	—
471	C₂×C₄	#13094055	1	2	yes	—
472	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
474	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
475	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
477	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
478	C₈	—	94	4	no	—
479	C₈	—	188	2	no	—
480	C₂²	—	94	4	no	—
481	C₂²	—	188	2	no	—
482	C₂²	—	188	2	no	—
483	C₂²	—	188	2	no	—
484	C₂²	—	188	2	no	—
485	C₂²	—	188	2	no	—
486	C₂²	—	188	2	no	—
487	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
488	C₂²	C₂×#13094000	1	1	yes	characteristic
489	C₂²	#15689630	1	1	yes	characteristic
490	C₂²	C₂×#13094049	1	1	yes	characteristic
491	C₂²	C₂×#13094050	1	1	yes	characteristic
492	C₂²	C₂×#13094055	1	1	yes	characteristic
493	C₂²	#15689921	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	1	no	—
500	C₄	—	8	2	no	—
501	C₄	—	188	2	no	—
502	C₄	—	188	2	no	—
503	C₄	—	188	2	no	—
504	C₄	#15689233	1	4	yes	—
505	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
506	C₄	C₄×#10625354	1	1	yes	characteristic
507	C₄	#15689660	1	1	yes	characteristic
508	C₄	#15689677	1	1	yes	characteristic
509	C₂	—	188	4	no	—
510	C₂	C₄×#13094000	1	1	yes	characteristic
511	C₂	C₂×#15689233	1	1	yes	characteristic
512	C₂	C₄×#13094055	1	1	yes	characteristic
513	C₂	#20253181	1	1	yes	characteristic
514	C₂	#20253197	1	1	yes	characteristic
515	C₂	#20253483	1	1	yes	characteristic
516	C₂	#20253533	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	#21613
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #20244341	C₂	semidirect
4. #20244149	C₂	semidirect
5. #20243977	C₂	semidirect
8. #20243286	C₂	semidirect
9. #20243241	C₂	semidirect
11. C₄×C₄⋊Q₈×C₄₇	C₂	semidirect
16. #15689400	C₄	semidirect
55. C₄×D₁₈₈	Q₈	semidirect
66. #13093957	C₂×C₄	semidirect
69. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
78. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
215. D₁₈₈	C₄×Q₈	semidirect
252. C₄×C₄⋊Q₈	D₄₇	semidirect
302. C₄₇	#21613	semidirect
311. C₄⋊Q₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689400	2
C₄²×D₁₈₈	2
#20244341	2
#20244149	2
#20243977	2
#20243648	2
#20243385	2
#20243286	2
#20243241	2
#20243216	2
C₄×C₄⋊Q₈×C₄₇	2
#21613	47