Subgroups — #26274357

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246335	C₂	1	1	yes	maximal, characteristic
2	#20244773	C₂	1	2	yes	maximal
3	#20244521	C₂	1	2	yes	maximal
4	#20244341	C₂	1	2	yes	maximal, complemented
5	#20244146	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243956	C₂	1	2	yes	maximal, complemented
8	#20243515	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243385	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093944	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#2551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	C₂×#13093982	—	2	1	no	—
14	C₂×#13093957	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093944	C₂²	1	1	yes	characteristic
18	C₂×#13093944	C₂²	1	1	yes	characteristic
19	C₂×#13093944	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	#15689025	C₂²	1	2	yes	—
22	#15689015	—	2	2	no	—
23	#15688993	C₂²	1	1	yes	characteristic
24	#15688980	—	2	1	no	—
25	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
26	#15688885	C₂²	1	1	yes	characteristic
27	#15688885	C₂²	1	1	yes	characteristic
28	#15688885	C₂²	1	2	yes	—
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
35	C₄₇×#395	—	2	2	no	—
36	C₄₇×#389	—	2	1	no	—
37	C₄₇×#389	C₂²	1	2	yes	—
38	C₄₇×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₄×D₁₈₈	—	2	2	no	—
47	C₄×D₁₈₈	Q₈	1	4	yes	complemented
48	#13093982	—	4	4	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
54	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	#13093957	—	2	4	no	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
60	#13093944	—	2	2	no	—
61	#13093944	—	2	2	no	—
62	#13093944	—	4	2	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄₇⋊#95	—	2	2	no	—
65	C₂²×Q₈×C₄₇	—	2	2	no	—
66	C₄⋊Q₈×C₄₇	—	2	4	no	—
67	C₄⋊Q₈×C₄₇	—	4	2	no	—
68	C₄⋊Q₈×C₄₇	—	4	4	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	#95×C₄₇	—	2	1	no	—
82	#95×C₄₇	—	2	2	no	—
83	#95×C₄₇	D₄	1	2	yes	—
84	C₂³×D₄₇	—	2	1	no	—
85	C₂×Q₈×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	—	4	4	no	—
87	C₂×Q₈×C₄₇	—	8	2	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	1	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂×D₁₈₈	—	2	1	no	—
99	C₂×D₁₈₈	—	2	1	no	—
100	C₂×D₁₈₈	—	2	1	no	—
101	C₂×D₁₈₈	—	2	1	no	—
102	C₂×D₁₈₈	—	2	1	no	—
103	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
104	C₂×C₄×D₄₇	—	2	4	no	—
105	C₂×C₄×D₄₇	—	4	2	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	2	no	—
108	C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	4	4	no	—
113	C₄⋊C₄×C₄₇	—	4	4	no	—
114	C₄⋊C₄×C₄₇	—	4	2	no	—
115	C₄⋊C₄×C₄₇	—	8	1	no	—
116	C₄⋊C₄×C₄₇	D₈	1	4	yes	—
117	C₄⋊C₄×C₄₇	#41	1	2	yes	—
118	C₄⋊C₄×C₄₇	#41	1	2	yes	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	4	2	no	—
122	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
123	C₄²×C₄₇	#41	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	—	2	4	no	—
125	(C₂×D₄₇)⋊C₄	—	4	4	no	—
126	(C₂×D₄₇)⋊C₄	—	8	2	no	—
127	C₄⋊Dic₄₇	—	2	1	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	—	4	2	no	—
131	C₄⋊Dic₄₇	—	8	1	no	—
132	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
133	C₄×Dic₄₇	—	4	4	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	4	1	no	—
146	C₂²×D₄₇	—	4	1	no	—
147	C₂²×D₄₇	—	4	1	no	—
148	C₂²×D₄₇	—	4	1	no	—
149	C₂²×D₄₇	—	4	1	no	—
150	C₂²×D₄₇	—	4	1	no	—
151	Q₈×C₄₇	—	8	8	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
171	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
172	C₂×C₄×C₄₇	#137	1	2	yes	—
173	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×Dic₄₇	—	2	2	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	—	2	2	no	—
187	D₁₈₈	—	4	1	no	—
188	D₁₈₈	—	4	1	no	—
189	C₄×D₄₇	—	4	8	no	—
190	C₄₇⋊C₈	—	4	1	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	C₄₇⋊C₈	—	4	1	no	—
193	#26020	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₄₇	#546	1	1	yes	characteristic
196	C₂²×C₄₇	#548	1	1	yes	characteristic
197	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
199	C₂²×C₄₇	#577	1	1	yes	characteristic
200	C₂²×C₄₇	#577	1	1	yes	characteristic
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	4	2	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	8	1	no	—
205	C₂×D₄₇	—	8	1	no	—
206	C₂×D₄₇	—	8	1	no	—
207	C₂×D₄₇	—	8	1	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	8	2	no	—
214	C₄×C₄₇	#474	1	4	yes	—
215	C₄×C₄₇	#533	1	1	yes	characteristic
216	C₄×C₄₇	#544	1	1	yes	characteristic
217	C₄×C₄₇	#555	1	1	yes	characteristic
218	C₄×C₄₇	#556	1	1	yes	characteristic
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	8	2	no	—
221	#2551	D₄₇	1	1	yes	characteristic, complemented
222	#2354	—	47	1	no	—
223	#2067	—	47	2	no	—
224	#2023	—	47	2	no	—
225	#1988	—	47	2	no	—
226	#1947	—	47	1	no	—
227	#1939	—	47	1	no	—
228	#1918	—	47	2	no	—
229	#1834	—	47	1	no	—
230	#1802	—	47	1	no	—
231	C₄×#102	—	47	1	no	—
232	C₂×C₄₇	#2439	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#474	1	1	yes	characteristic
234	C₂×C₄₇	#3084	1	1	yes	characteristic
235	C₂×C₄₇	#3294	1	1	yes	characteristic
236	C₂×C₄₇	#3329	1	1	yes	characteristic
237	C₂×C₄₇	#3358	1	1	yes	characteristic
238	C₂×C₄₇	#3369	1	1	yes	characteristic
239	D₄₇	—	8	2	no	—
240	C₂×C₄⋊Q₈	—	2	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
242	C₂×C₄×D₄	—	47	1	no	—
243	C₂×#117	—	94	1	no	—
244	C₂×#107	—	47	2	no	—
245	C₂×C₄⋊C₈	—	47	1	no	—
246	C₂×C₄⋊C₈	—	47	2	no	—
247	C₂×#102	—	47	1	no	—
248	C₂×#102	—	47	1	no	—
249	C₂×#102	—	47	2	no	—
250	C₂×C₄×C₈	—	47	1	no	—
251	#395	—	2	2	no	—
252	#390	—	47	2	no	—
253	#389	—	2	1	no	—
254	#389	C₂×D₄₇	1	2	yes	—
255	#388	—	94	2	no	—
256	#384	—	47	1	no	—
257	#384	C₂×D₄₇	1	1	yes	characteristic
258	#380	—	94	1	no	—
259	C₄×C₄⋊C₄	—	47	2	no	—
260	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
262	#340	—	47	2	no	—
263	#340	—	47	2	no	—
264	#340	—	47	2	no	—
265	#340	—	47	1	no	—
266	#340	—	47	2	no	—
267	#340	—	47	1	no	—
268	#336	—	47	2	no	—
269	C₄₇	#26020	1	1	yes	characteristic, complemented, Sylow
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×D₄	—	47	1	no	—
272	C₂³×C₄	—	94	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	—	47	1	no	—
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	—	4	2	no	—
278	C₄⋊Q₈	—	4	4	no	—
279	C₄×D₄	—	47	4	no	—
280	C₄×D₄	—	94	2	no	—
281	#117	—	188	4	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	47	1	no	—
287	C₂×C₄⋊C₄	—	47	2	no	—
288	C₂×C₄⋊C₄	—	94	1	no	—
289	C₂×C₄⋊C₄	—	94	1	no	—
290	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	—	94	1	no	—
296	C₂×C₂²⋊C₄	—	94	2	no	—
297	C₂×C₂²⋊C₄	—	94	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	94	2	no	—
300	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
301	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
302	#107	—	94	4	no	—
303	C₄⋊C₈	—	94	2	no	—
304	C₄⋊C₈	—	188	2	no	—
305	#102	—	94	2	no	—
306	#102	—	94	2	no	—
307	#102	—	188	2	no	—
308	C₄×C₈	—	94	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	#95	—	94	2	no	—
312	#95	C₂²⋊D₄₇	1	2	yes	—
313	C₂⁴	—	94	1	no	—
314	C₂×Q₈	—	4	4	no	—
315	C₂×Q₈	—	4	4	no	—
316	C₂×Q₈	—	8	2	no	—
317	C₂×D₄	—	47	2	no	—
318	C₂×D₄	—	94	1	no	—
319	C₂×D₄	—	94	1	no	—
320	C₂×D₄	—	94	1	no	—
321	C₂×D₄	—	94	1	no	—
322	C₂×D₄	—	94	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	4	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	188	2	no	—
330	C₂²×C₄	—	188	2	no	—
331	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
332	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
334	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	1	no	—
344	C₂×C₈	—	94	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	4	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	8	1	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	—	94	2	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₄⋊C₄	—	376	1	no	—
359	C₄⋊C₄	—	188	2	no	—
360	C₄⋊C₄	#10625334	1	4	yes	—
361	C₄⋊C₄	#10625352	1	2	yes	—
362	C₄⋊C₄	#10625354	1	2	yes	—
363	C₂²⋊C₄	—	94	4	no	—
364	C₂²⋊C₄	—	376	2	no	—
365	C₂²⋊C₄	—	188	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	188	4	no	—
370	C₄²	Q₈×D₄₇	1	2	yes	—
371	C₄²	#10625354	1	2	yes	—
372	C₂³	—	94	2	no	—
373	C₂³	—	188	1	no	—
374	C₂³	—	188	1	no	—
375	C₂³	—	188	1	no	—
376	C₂³	—	188	1	no	—
377	C₂³	—	188	1	no	—
378	C₂³	—	188	1	no	—
379	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
380	Q₈	—	8	8	no	—
381	D₄	—	94	2	no	—
382	D₄	—	94	2	no	—
383	D₄	—	188	1	no	—
384	D₄	—	188	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	—	188	2	no	—
405	C₂×C₄	—	188	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	8	no	—
408	C₂×C₄	#13094000	1	2	yes	—
409	C₂×C₄	#13094000	1	2	yes	—
410	C₂×C₄	C₂×#10625334	1	4	yes	—
411	C₂×C₄	C₂×#10625334	1	2	yes	—
412	C₂×C₄	#13094055	1	2	yes	—
413	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
416	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
417	C₂×C₄	#13094069	1	1	yes	characteristic
418	C₂×C₄	#13094072	1	1	yes	characteristic
419	C₈	—	188	1	no	—
420	C₈	—	188	2	no	—
421	C₈	—	188	1	no	—
422	C₂²	—	376	1	no	—
423	C₂²	—	376	1	no	—
424	C₂²	—	376	1	no	—
425	C₂²	—	376	1	no	—
426	C₂²	—	188	2	no	—
427	C₂²	—	188	2	no	—
428	C₂²	—	188	2	no	—
429	C₂²	C₂×#13094000	1	1	yes	characteristic
430	C₂²	#15689767	1	1	yes	characteristic
431	C₂²	#15689784	1	1	yes	characteristic
432	C₂²	C₂²×#10625334	1	1	yes	characteristic
433	C₂²	C₂×#13094055	1	1	yes	characteristic
434	C₂²	#15689931	1	1	yes	characteristic
435	C₂²	#15689934	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	376	2	no	—
443	C₄	—	188	2	no	—
444	C₄	#15689400	1	4	yes	—
445	C₄	#15689678	1	1	yes	characteristic
446	C₄	#15689750	1	1	yes	characteristic
447	C₄	#15689839	1	1	yes	characteristic
448	C₄	#15689847	1	1	yes	characteristic
449	C₂	—	376	2	no	—
450	C₂	#20247075	1	1	yes	characteristic
451	C₂	C₂×#15689400	1	1	yes	characteristic
452	C₂	#20253246	1	1	yes	characteristic
453	C₂	#20255201	1	1	yes	characteristic
454	C₂	#20255682	1	1	yes	characteristic
455	C₂	#20256023	1	1	yes	characteristic
456	C₂	#20256128	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2551	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	C₂³
hypercenter	#2551	D₄₇
hypocenter	C₄₇	#26020
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2551

Complements

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

N	H ≅ G/N	type
4. #20244341	C₂	semidirect
5. #20244146	C₂	semidirect
6. #20244107	C₂	semidirect
7. #20243956	C₂	semidirect
8. #20243515	C₂	semidirect
11. C₄₇×#2551	C₂	semidirect
47. C₄×D₁₈₈	Q₈	semidirect
221. #2551	D₄₇	semidirect
269. C₄₇	#26020	semidirect

Maximal subgroups

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

subgroup	index
#20246335	2
#20244773	2
#20244521	2
#20244341	2
#20244146	2
#20244107	2
#20243956	2
#20243515	2
#20243385	2
C₄×#13093944	2
C₄₇×#2551	2
#26020	47