Subgroups — #26187206

Order 12032.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253415	C₂	1	1	yes	maximal, characteristic
2	#20252339	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252132	C₂	1	1	yes	maximal, characteristic
4	#20242281	C₂	1	2	yes	maximal, complemented
5	#20242234	C₂	1	2	yes	maximal, complemented
6	#20242221	C₂	1	2	yes	maximal, complemented
7	#20242191	C₂	1	2	yes	maximal, complemented
8	#20242160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15688855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1492	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	#15689439	C₄	1	2	yes	—
15	#15689405	C₄	1	1	yes	characteristic
16	#15689405	C₄	1	1	yes	characteristic
17	#15689320	C₄	1	1	yes	characteristic
18	#15689320	C₄	1	1	yes	characteristic
19	#15689261	C₄	1	2	yes	—
20	#15689252	—	2	2	no	—
21	#15689250	C₂²	1	2	yes	—
22	#15689247	C₂²	1	2	yes	—
23	C₄×#10625335	C₂²	1	2	yes	—
24	C₄×#10625335	C₂²	1	2	yes	—
25	#15689201	C₂²	1	2	yes	—
26	#15689195	—	2	2	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689146	—	2	1	no	—
30	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	#15689090	—	2	1	no	—
32	C₄×#10625329	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₄₇	—	2	1	no	—
34	#15688873	C₂²	1	2	yes	—
35	#15688873	C₂²	1	2	yes	—
36	#15688855	C₂²	1	1	yes	characteristic
37	#15688855	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	1	yes	characteristic
39	#15688855	C₂²	1	1	yes	characteristic
40	#15688845	C₂²	1	2	yes	—
41	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
42	C₄₇×#532	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625335	C₂×C₄	1	2	yes	—
49	C₂×#10625335	C₂×C₄	1	2	yes	—
50	#13094031	—	4	4	no	—
51	C₂×#10625329	—	2	2	no	—
52	C₂×#10625329	D₄	1	1	yes	characteristic
53	C₂×#10625329	D₄	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	2	no	—
56	C₄×Dic₉₄	—	2	1	no	—
57	C₄×Dic₉₄	—	2	1	no	—
58	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×Dic₄₇⋊C₄	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	#13093955	C₂×C₄	1	2	yes	—
66	#13093955	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
70	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
72	Dic₄₇⋊C₈	—	2	2	no	—
73	Dic₄₇⋊C₈	—	2	2	no	—
74	#13093947	C₂×C₄	1	2	yes	—
75	#13093947	C₂×C₄	1	2	yes	—
76	#13093945	C₂×C₄	1	2	yes	—
77	#13093945	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
81	#13093935	D₄	1	2	yes	—
82	#13093934	—	2	2	no	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₇	—	2	2	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
91	#124×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	#121×C₄₇	C₂×C₄	1	2	yes	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	C₂³	1	2	yes	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	—	4	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×Dic₄₇	—	2	1	no	—
114	C₂²×Dic₄₇	—	2	1	no	—
115	C₂×Dic₉₄	—	2	2	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	4	1	no	—
118	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
119	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
120	M₁₆×C₄₇	—	4	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²⋊C₄×C₄₇	—	2	2	no	—
128	C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	#41	1	1	yes	characteristic
132	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
133	#10625335	—	2	4	no	—
134	#10625335	—	4	2	no	—
135	C₄⋊Dic₄₇	—	2	1	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	Dic₄₇⋊C₄	—	2	1	no	—
139	Dic₄₇⋊C₄	—	2	1	no	—
140	Dic₄₇⋊C₄	—	2	1	no	—
141	Dic₄₇⋊C₄	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	#10625329	—	2	2	no	—
147	#10625329	—	4	4	no	—
148	#10625329	SD₁₆	1	4	yes	complemented
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	4	2	no	—
152	C₂×C₄₇⋊C₈	—	4	4	no	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
159	Q₈×C₄₇	—	4	2	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	4	4	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	8	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	#135	1	2	yes	—
176	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	8	1	no	—
185	Dic₉₄	—	2	1	no	—
186	Dic₉₄	—	2	1	no	—
187	Dic₉₄	—	2	1	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	#131	1	2	yes	complemented
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₄₇⋊C₈	—	2	2	no	—
194	C₄₇⋊C₈	—	2	2	no	—
195	C₄₇⋊C₈	—	2	2	no	—
196	C₄₇⋊C₈	—	4	1	no	—
197	C₄₇⋊C₈	—	4	1	no	—
198	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	—
199	#17997	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	2	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
212	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
213	C₄×C₄₇	#568	1	1	yes	characteristic
214	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
216	Dic₄₇	—	2	2	no	—
217	Dic₄₇	—	4	1	no	—
218	Dic₄₇	—	4	1	no	—
219	Dic₄₇	—	4	1	no	—
220	#3103	—	47	1	no	—
221	Q₈×M₁₆	—	47	1	no	—
222	#2935	—	47	1	no	—
223	#1590	—	47	2	no	—
224	#1583	—	47	2	no	—
225	#1582	—	47	2	no	—
226	C₈×SD₁₆	—	47	2	no	—
227	#1570	—	47	1	no	—
228	#1492	D₄₇	1	1	yes	characteristic
229	C₂×Q₈⋊C₈	—	47	1	no	—
230	C₈×M₁₆	—	47	1	no	—
231	C₂×C₄₇	—	2	2	no	—
232	C₂×C₄₇	—	8	2	no	—
233	C₂×C₄₇	#2933	1	1	yes	characteristic
234	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
235	C₂×C₄₇	#2956	1	1	yes	characteristic
236	C₂×#131	—	94	1	no	—
237	#532	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₄×Q₈	—	47	1	no	—
239	#481	—	47	2	no	—
240	#475	—	47	1	no	—
241	#475	—	47	1	no	—
242	#460	—	47	1	no	—
243	#460	—	47	1	no	—
244	#448	—	47	2	no	—
245	#446	—	47	2	no	—
246	#446	—	94	2	no	—
247	C₈×Q₈	—	47	2	no	—
248	C₄×SD₁₆	—	47	2	no	—
249	C₄×SD₁₆	—	47	2	no	—
250	#436	—	47	2	no	—
251	#435	—	94	2	no	—
252	C₈×D₄	—	47	2	no	—
253	#431	—	47	1	no	—
254	#423	—	94	1	no	—
255	#423	C₂×D₄₇	1	1	yes	characteristic
256	C₂×C₄⋊C₈	—	47	1	no	—
257	#408	—	94	1	no	—
258	C₄×M₁₆	—	47	1	no	—
259	C₄×M₁₆	—	94	1	no	—
260	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
261	#334	—	47	2	no	—
262	#334	—	47	2	no	—
263	Q₈⋊C₈	—	47	1	no	—
264	Q₈⋊C₈	—	47	1	no	—
265	Q₈⋊C₈	—	47	1	no	—
266	Q₈⋊C₈	—	47	1	no	—
267	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
268	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
269	#322	—	47	2	no	—
270	C₈²	—	47	2	no	—
271	C₄₇	#17997	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	—	2	1	no	—
273	C₂²×Q₈	—	47	1	no	—
274	C₂×SD₁₆	—	47	2	no	—
275	C₂×SD₁₆	—	47	2	no	—
276	#131	—	188	4	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	47	1	no	—
279	C₂×M₁₆	—	47	1	no	—
280	C₂×M₁₆	—	94	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	94	2	no	—
283	C₂²×C₈	—	94	1	no	—
284	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
285	#127	C₄×D₄₇	1	1	yes	characteristic
286	#124	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	C₄×D₄₇	1	2	yes	—
289	C₄×Q₈	—	47	1	no	—
290	C₄×Q₈	—	47	1	no	—
291	C₄×Q₈	—	47	1	no	—
292	C₄×Q₈	—	47	1	no	—
293	C₄×Q₈	—	94	1	no	—
294	C₄×Q₈	—	94	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂²×D₄₇	1	2	yes	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	94	1	no	—
299	C₂×C₄²	—	94	1	no	—
300	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
301	#106	—	47	2	no	—
302	#106	—	47	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	47	1	no	—
305	C₄⋊C₈	—	47	1	no	—
306	C₄⋊C₈	—	47	1	no	—
307	C₄⋊C₈	—	47	1	no	—
308	C₄⋊C₈	—	94	2	no	—
309	C₄⋊C₈	—	94	2	no	—
310	C₄⋊C₈	—	94	1	no	—
311	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
312	#103	—	47	2	no	—
313	#103	—	47	2	no	—
314	#102	—	47	2	no	—
315	#102	—	47	2	no	—
316	C₂²⋊C₈	—	47	2	no	—
317	C₂²⋊C₈	—	94	2	no	—
318	C₂²⋊C₈	—	94	2	no	—
319	#97	—	47	2	no	—
320	#97	—	94	2	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	47	2	no	—
323	C₄×C₈	—	47	2	no	—
324	C₄×C₈	—	94	2	no	—
325	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	47	1	no	—
331	C₂×Q₈	—	47	1	no	—
332	C₂×Q₈	—	94	2	no	—
333	C₂×Q₈	—	94	1	no	—
334	C₂×Q₈	—	188	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	94	1	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
344	C₂²×C₄	#10625352	1	1	yes	characteristic
345	SD₁₆	—	94	4	no	—
346	SD₁₆	—	188	2	no	—
347	M₁₆	—	4	2	no	—
348	M₁₆	—	47	4	no	—
349	M₁₆	—	94	2	no	—
350	M₁₆	—	188	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	47	2	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	188	4	no	—
362	C₂×C₈	—	188	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	47	1	no	—
365	C₄⋊C₄	—	47	1	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	1	no	—
369	C₄⋊C₄	—	94	1	no	—
370	C₄⋊C₄	—	94	1	no	—
371	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₄²	—	94	1	no	—
377	C₄²	—	94	1	no	—
378	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₄²	D₄×D₄₇	1	1	yes	characteristic
380	C₄²	#10625352	1	1	yes	characteristic
381	C₄²	C₂³×D₄₇	1	1	yes	characteristic
382	C₂³	—	2	2	no	—
383	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
384	Q₈	—	4	2	no	—
385	Q₈	—	47	2	no	—
386	Q₈	—	94	1	no	—
387	Q₈	—	94	1	no	—
388	Q₈	—	94	1	no	—
389	Q₈	—	188	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	376	1	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
408	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
409	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
411	C₂×C₄	#13094043	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	2	no	—
418	C₈	—	47	4	no	—
419	C₈	—	94	2	no	—
420	C₈	—	94	2	no	—
421	C₈	—	94	2	no	—
422	C₈	—	188	1	no	—
423	C₈	—	188	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	#15689214	1	2	yes	—
430	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	2	no	—
435	C₄	—	94	2	no	—
436	C₄	—	188	1	no	—
437	C₄	—	188	1	no	—
438	C₄	—	188	1	no	—
439	C₄	#15689214	1	2	yes	—
440	C₄	#131×D₄₇	1	1	yes	characteristic
441	C₄	#15689888	1	1	yes	characteristic
442	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
443	C₄	C₂×#13094043	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	8	2	no	—
446	C₂	#20252118	1	1	yes	characteristic
447	C₂	C₂×#15689214	1	1	yes	characteristic
448	C₂	#20252294	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1492	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#532	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1492	D₄₇
hypocenter	C₄₇	#17997
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1492

Complements

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

N	H ≅ G/N	type
2. #20252339	C₂	semidirect
4. #20242281	C₂	semidirect
5. #20242234	C₂	semidirect
6. #20242221	C₂	semidirect
7. #20242191	C₂	semidirect
8. #20242160	C₂	semidirect
9. C₂×#15688855	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
148. #10625329	SD₁₆	semidirect
189. Dic₉₄	#131	semidirect
271. C₄₇	#17997	semidirect

Maximal subgroups

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

subgroup	index
#20253415	2
#20252339	2
#20252132	2
#20242281	2
#20242234	2
#20242221	2
#20242191	2
#20242160	2
C₂×#15688855	2
C₈×#10625329	2
C₄₇×#1492	2
#17997	47