Subgroups — #26234737

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689246	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689241	C₂	1	1	yes	maximal, characteristic
3	#20252190	C₂	1	1	yes	maximal, characteristic
4	#20251953	C₂	1	2	yes	maximal, complemented
5	#20244141	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243666	C₂	1	2	yes	maximal, complemented
8	#20243666	C₂	1	2	yes	maximal, complemented
9	#20243563	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243409	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	2	yes	—
14	C₂×#13094030	C₂²	1	2	yes	—
15	C₄×#10625350	C₂²	1	2	yes	—
16	#15689246	—	2	4	no	—
17	#15689241	—	2	4	no	—
18	#15689236	C₄	1	2	yes	complemented
19	#15689231	C₄	1	2	yes	complemented
20	#15689225	C₄	1	2	yes	complemented
21	#15689225	C₄	1	2	yes	complemented
22	C₂×#13093960	C₂²	1	1	yes	characteristic
23	C₂×#13093960	C₂²	1	1	yes	characteristic
24	C₂×#13093960	C₂²	1	2	yes	—
25	#15689161	C₂²	1	1	yes	characteristic
26	#15689149	C₂²	1	2	yes	—
27	#15689149	C₂²	1	2	yes	—
28	#15689148	—	2	2	no	—
29	#15689148	—	2	2	no	—
30	#15689147	C₂²	1	2	yes	—
31	#15689145	—	2	2	no	—
32	C₄⋊C₈×D₄₇	—	2	2	no	—
33	C₂×#13093952	C₂²	1	2	yes	—
34	C₂×#13093952	C₂²	1	2	yes	—
35	#15689120	C₂²	1	2	yes	—
36	#15688883	C₂²	1	2	yes	—
37	#15688883	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	1	yes	characteristic
45	C₂×#10625350	C₂³	1	2	yes	—
46	#13094046	D₄	1	4	yes	—
47	#13094046	Q₈	1	4	yes	—
48	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
51	#13094030	—	2	4	no	—
52	#13094030	—	2	4	no	—
53	#13094030	—	4	2	no	—
54	#13094030	—	4	2	no	—
55	C₂×#10625329	C₂³	1	2	yes	—
56	C₂×#10625329	C₂³	1	2	yes	—
57	C₂×#10625324	—	2	2	no	—
58	C₂×#10625324	—	2	2	no	—
59	C₂×C₈×D₄₇	—	2	2	no	—
60	C₂×C₈×D₄₇	—	2	2	no	—
61	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
62	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
63	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
64	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
65	C₄×C₂²⋊D₄₇	—	2	2	no	—
66	C₄×C₂²⋊D₄₇	—	2	2	no	—
67	#13093983	C₂³	1	2	yes	—
68	#13093981	—	2	2	no	—
69	C₄²×D₄₇	—	2	2	no	—
70	#13093960	—	2	2	no	—
71	#13093960	—	2	2	no	—
72	#13093960	—	4	2	no	—
73	#13093958	C₂×C₄	1	1	yes	characteristic
74	#13093958	C₂×C₄	1	1	yes	characteristic
75	#13093956	C₂×C₄	1	2	yes	—
76	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	2	no	—
81	Dic₄₇⋊C₈	—	2	2	no	—
82	#13093952	—	2	4	no	—
83	#13093952	—	2	4	no	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093949	C₂×C₄	1	2	yes	—
86	#13093946	C₂×C₄	1	2	yes	—
87	#13093946	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
97	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
98	#97×C₄₇	—	2	2	no	—
99	#97×C₄₇	C₂×C₄	1	2	yes	—
100	#97×C₄₇	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₄₇	—	2	2	no	—
102	#95×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₇	—	2	2	no	—
109	#10625350	—	2	2	no	—
110	#10625350	—	2	2	no	—
111	#10625350	C₂×D₄	1	4	yes	—
112	#10625350	C₂×Q₈	1	4	yes	—
113	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₇	—	2	2	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	2	2	no	—
117	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
138	C₄²×C₄₇	C₂×D₄	1	2	yes	—
139	C₂²⋊Dic₄₇	—	2	2	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
144	Dic₄₇⋊C₄	—	2	2	no	—
145	Dic₄₇⋊C₄	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	#10625329	—	2	2	no	—
150	#10625329	—	2	2	no	—
151	#10625329	—	2	2	no	—
152	#10625329	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	Dic₁₈₈	C₄⋊C₄	1	4	yes	complemented
156	D₃₇₆	C₄⋊C₄	1	4	yes	complemented
157	#10625325	C₄⋊C₄	1	8	yes	complemented
158	#10625324	—	4	4	no	—
159	#10625324	—	4	4	no	—
160	C₈×D₄₇	—	4	4	no	—
161	C₈×D₄₇	—	4	4	no	—
162	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	2	4	no	—
181	C₂²⋊D₄₇	—	2	4	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
187	C₄×D₄₇	—	2	4	no	—
188	C₄×D₄₇	—	2	4	no	—
189	C₄×D₄₇	—	4	4	no	—
190	C₄×D₄₇	—	8	2	no	—
191	Dic₉₄	—	2	2	no	—
192	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	2	1	no	—
195	C₈×C₄₇	—	2	2	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
198	C₈×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
199	C₄₇⋊C₈	—	4	2	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	#22687	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₇	#547	1	1	yes	characteristic
206	C₂²×C₄₇	#554	1	1	yes	characteristic
207	C₂×D₄₇	—	2	4	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	4	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	8	1	no	—
214	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₄×C₄₇	#520	1	1	yes	characteristic
216	C₄×C₄₇	D₄²	1	1	yes	characteristic
217	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
218	Dic₄₇	—	2	4	no	—
219	Dic₄₇	—	4	2	no	—
220	Dic₄₇	—	4	2	no	—
221	C₂×#444	—	47	1	no	—
222	C₂×#443	—	47	1	no	—
223	#2943	—	47	1	no	—
224	#2906	—	47	2	no	—
225	#1946	—	47	1	no	—
226	#1945	—	47	1	no	—
227	#1866	—	47	2	no	—
228	#1866	—	47	2	no	—
229	#1849	—	47	1	no	—
230	#1806	—	47	2	no	—
231	#1771	D₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄₇	#2955	1	1	yes	characteristic
236	C₂×C₄₇	#2956	1	1	yes	characteristic
237	D₄₇	—	4	4	no	—
238	C₂×#135	—	47	1	no	—
239	C₂×#131	—	47	2	no	—
240	C₂×#131	—	47	2	no	—
241	C₄×#41	—	47	2	no	—
242	#444	—	94	4	no	—
243	#443	—	94	4	no	—
244	#442	—	47	2	no	—
245	#441	—	47	2	no	—
246	#440	—	47	2	no	—
247	#440	—	47	2	no	—
248	C₂×#108	—	47	1	no	—
249	C₂×#108	—	47	1	no	—
250	C₂×#108	—	47	2	no	—
251	#427	—	47	1	no	—
252	#424	—	47	2	no	—
253	#424	—	47	2	no	—
254	#424	—	94	2	no	—
255	#424	—	94	2	no	—
256	#423	—	47	2	no	—
257	#423	—	94	2	no	—
258	C₂×C₄⋊C₈	—	94	2	no	—
259	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂×#104	—	47	2	no	—
261	C₂×#104	—	47	2	no	—
262	#416	—	47	2	no	—
263	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
264	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
266	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
267	#339	—	47	2	no	—
268	#339	—	47	2	no	—
269	#336	C₂×D₄₇	1	1	yes	characteristic
270	#336	C₂×D₄₇	1	1	yes	characteristic
271	C₄₇	#22687	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	47	2	no	—
273	#135	—	47	4	no	—
274	#135	—	47	4	no	—
275	C₂×Q₁₆	—	47	1	no	—
276	C₂×SD₁₆	—	47	2	no	—
277	C₂×D₈	—	47	1	no	—
278	#131	—	94	4	no	—
279	#131	—	94	4	no	—
280	#131	—	188	2	no	—
281	#131	—	188	2	no	—
282	C₂×M₁₆	—	47	2	no	—
283	C₂×M₁₆	—	47	2	no	—
284	C₂×M₁₆	—	94	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂²×C₈	—	94	2	no	—
287	C₂²×C₈	—	94	2	no	—
288	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₄×Q₈	—	47	2	no	—
293	C₄×Q₈	—	47	2	no	—
294	C₄×D₄	—	47	2	no	—
295	C₄×D₄	—	47	2	no	—
296	C₄×D₄	—	94	2	no	—
297	C₄×D₄	—	94	2	no	—
298	#117	—	47	2	no	—
299	#117	—	94	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#108	—	94	2	no	—
306	#108	—	94	2	no	—
307	#108	—	188	2	no	—
308	#107	—	47	1	no	—
309	#107	—	47	1	no	—
310	#106	—	47	2	no	—
311	C₄⋊C₈	—	94	2	no	—
312	C₄⋊C₈	—	94	2	no	—
313	C₄⋊C₈	—	94	2	no	—
314	C₄⋊C₈	—	94	2	no	—
315	C₄⋊C₈	—	94	2	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	D₁₈₈	1	2	yes	—
318	C₄⋊C₈	D₁₈₈	1	2	yes	—
319	#104	—	94	4	no	—
320	#104	—	94	4	no	—
321	#103	—	47	2	no	—
322	#103	—	47	2	no	—
323	#102	—	47	2	no	—
324	#102	—	47	2	no	—
325	#97	—	2	2	no	—
326	#97	C₄×D₄₇	1	2	yes	—
327	#97	C₄×D₄₇	1	2	yes	—
328	C₄×C₈	—	2	2	no	—
329	#95	—	2	1	no	—
330	#41	—	47	4	no	—
331	#41	—	47	4	no	—
332	#41	—	94	2	no	—
333	#41	—	94	2	no	—
334	C₂×Q₈	—	47	2	no	—
335	C₂×D₄	—	47	2	no	—
336	C₂×D₄	—	94	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	#10625350	1	1	yes	characteristic
343	C₂²×C₄	#10625350	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
345	Q₁₆	—	47	4	no	—
346	SD₁₆	—	47	8	no	—
347	D₈	—	47	4	no	—
348	M₁₆	—	94	2	no	—
349	M₁₆	—	94	2	no	—
350	M₁₆	—	94	2	no	—
351	M₁₆	—	94	2	no	—
352	M₁₆	—	188	4	no	—
353	M₁₆	—	188	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	188	4	no	—
363	C₂×C₈	—	188	4	no	—
364	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
368	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
369	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
370	C₂×C₈	D₄×D₄₇	1	2	yes	—
371	C₂×C₈	Q₈×D₄₇	1	2	yes	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	47	2	no	—
374	C₄⋊C₄	—	47	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	94	2	no	—
377	C₂²⋊C₄	—	94	2	no	—
378	C₂²⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	94	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	94	2	no	—
385	C₄²	—	94	2	no	—
386	C₄²	—	94	2	no	—
387	C₄²	C₂×C₄×D₄₇	1	2	yes	—
388	C₄²	C₂×D₁₈₈	1	2	yes	—
389	C₂³	—	94	2	no	—
390	C₂³	C₂×#10625350	1	1	yes	characteristic
391	Q₈	—	47	4	no	—
392	Q₈	—	94	2	no	—
393	D₄	—	47	4	no	—
394	D₄	—	94	4	no	—
395	D₄	—	94	4	no	—
396	D₄	—	94	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	94	4	no	—
407	C₂×C₄	—	94	4	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	376	2	no	—
411	C₂×C₄	—	188	4	no	—
412	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
413	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
414	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
417	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
418	C₂×C₄	#13094070	1	1	yes	characteristic
419	C₂×C₄	#13094071	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	2	no	—
424	C₈	—	188	2	no	—
425	C₈	—	188	2	no	—
426	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
427	C₈	C₄⋊C₄×D₄₇	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	94	4	no	—
431	C₂²	—	188	2	no	—
432	C₂²	—	188	2	no	—
433	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
434	C₂²	#15689778	1	1	yes	characteristic
435	C₂²	#15689833	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	94	4	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
444	C₄	#15689603	1	1	yes	characteristic
445	C₄	D₄×D₁₈₈	1	1	yes	characteristic
446	C₄	Q₈×D₁₈₈	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	188	4	no	—
450	C₂	C₄⋊C₄×D₁₈₈	1	1	yes	characteristic
451	C₂	#20252292	1	1	yes	characteristic
452	C₂	#20252299	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1771	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094046	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1771	D₄₇
hypocenter	C₄₇	#22687
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. #20251953	C₂	semidirect
5. #20244141	C₂	semidirect
6. #20244136	C₂	semidirect
7. #20243666	C₂	semidirect
8. #20243666	C₂	semidirect
9. #20243563	C₂	semidirect
10. #20243409	C₂	semidirect
11. C₄₇×#1771	C₂	semidirect
18. #15689236	C₄	semidirect
19. #15689231	C₄	semidirect
20. #15689225	C₄	semidirect
21. #15689225	C₄	semidirect
155. Dic₁₈₈	C₄⋊C₄	semidirect
156. D₃₇₆	C₄⋊C₄	semidirect
157. #10625325	C₄⋊C₄	semidirect
231. #1771	D₄₇	semidirect
271. C₄₇	#22687	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689246	2
C₂×#15689241	2
#20252190	2
#20251953	2
#20244141	2
#20244136	2
#20243666	2
#20243563	2
#20243409	2
C₄₇×#1771	2
#22687	47