Subgroups — #25113257

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	#19137552	C₂	1	1	yes	maximal, characteristic
3	#19135568	C₂	1	2	yes	maximal
4	#19135556	C₂	1	1	yes	maximal, characteristic
5	#19135546	C₂	1	2	yes	maximal
6	#19135542	C₂	1	1	yes	maximal, characteristic
7	#19134611	C₂	1	2	yes	maximal
8	#19134601	C₂	1	1	yes	maximal, characteristic
9	#19134426	C₂	1	2	yes	maximal
10	C₄×#13063250	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₃×#446	C₂	1	1	yes	maximal, characteristic
12	Q₈×Dic₈₆	—	2	4	no	—
13	Q₈×Dic₈₆	C₄	1	8	yes	complemented
14	C₂×#13063325	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	2	yes	—
16	C₂×#13063324	—	2	2	no	—
17	C₂×#13063324	—	2	1	no	—
18	C₂×Q₈×Dic₄₃	—	2	1	no	—
19	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
20	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
21	C₂×#13063250	C₂²	1	2	yes	—
22	C₂×#13063250	C₂²	1	1	yes	characteristic
23	C₂×#13063250	C₂²	1	1	yes	characteristic
24	#14582806	—	2	1	no	—
25	#14582785	—	2	2	no	—
26	#14582769	C₂²	1	1	yes	characteristic
27	#14582765	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₃	—	2	1	no	—
29	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
31	#14582662	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	1	yes	characteristic
34	#14582662	C₂²	1	2	yes	—
35	#14582662	C₂²	1	2	yes	—
36	#14582662	C₂²	1	2	yes	—
37	#14582662	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#446	—	2	4	no	—
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
42	C₂×#97×C₄₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₂²×Dic₈₆	—	2	2	no	—
45	C₂²×Dic₈₆	—	2	1	no	—
46	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
47	#13063325	—	2	2	no	—
48	#13063325	—	2	4	no	—
49	#13063325	C₂×C₄	1	4	yes	—
50	#13063325	C₂×C₄	1	8	yes	—
51	#13063324	—	2	16	no	—
52	#13063324	—	2	8	no	—
53	Q₈×Dic₄₃	—	2	8	no	—
54	C₄×Dic₈₆	—	2	2	no	—
55	C₄×Dic₈₆	—	2	4	no	—
56	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
57	C₄×Dic₈₆	C₂×C₄	1	8	yes	—
58	C₂×C₄⋊Dic₄₃	—	2	2	no	—
59	C₂×C₄⋊Dic₄₃	—	2	1	no	—
60	C₂×C₄⋊Dic₄₃	—	2	1	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂×Dic₄₃⋊C₄	—	2	2	no	—
68	C₂×Dic₄₃⋊C₄	—	2	1	no	—
69	C₂×C₄×Dic₄₃	—	2	2	no	—
70	C₂×C₄×Dic₄₃	—	2	1	no	—
71	C₂×C₄×Dic₄₃	—	2	1	no	—
72	C₂×C₄×Dic₄₃	—	2	2	no	—
73	#13063250	—	2	4	no	—
74	#13063250	—	2	2	no	—
75	#13063250	Q₈	1	4	yes	complemented
76	C₄₃⋊#95	—	2	1	no	—
77	C₄₃⋊#95	—	2	2	no	—
78	C₄₃⋊#95	—	2	2	no	—
79	C₄₃⋊#95	—	2	2	no	—
80	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
85	C₄×Q₈×C₄₃	D₄	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	—	2	4	no	—
92	#97×C₄₃	—	2	4	no	—
93	C₄×C₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
102	C₂²×Dic₄₃	—	2	1	no	—
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	C₂²×Dic₄₃	—	2	1	no	—
106	C₂²×Dic₄₃	—	2	1	no	—
107	C₂²×Dic₄₃	—	2	2	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	—	2	4	no	—
112	C₂×Dic₈₆	—	2	8	no	—
113	C₂×Dic₈₆	—	8	2	no	—
114	C₂×Dic₈₆	—	8	1	no	—
115	C₂×Dic₈₆	—	8	2	no	—
116	C₂×Dic₈₆	—	8	1	no	—
117	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
118	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
119	C₂×Dic₈₆	#41	1	2	yes	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
130	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
132	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₃	C₂×D₄	1	2	yes	—
134	C₄²×C₄₃	C₂×D₄	1	4	yes	—
135	C₄⋊Dic₄₃	—	2	8	no	—
136	C₄⋊Dic₄₃	—	2	4	no	—
137	C₄⋊Dic₄₃	—	2	1	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	1	no	—
140	C₄⋊Dic₄₃	—	2	1	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	C₄⋊Dic₄₃	—	4	2	no	—
145	C₄⋊Dic₄₃	—	8	1	no	—
146	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
147	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
148	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
149	Dic₄₃⋊C₄	—	2	4	no	—
150	Dic₄₃⋊C₄	—	2	8	no	—
151	C₄×Dic₄₃	—	2	8	no	—
152	C₄×Dic₄₃	—	2	4	no	—
153	C₄×Dic₄₃	—	4	2	no	—
154	C₄×Dic₄₃	—	8	2	no	—
155	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₄₃	—	2	8	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
164	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₃	#137	1	2	yes	—
168	C₂×C₄×C₄₃	#137	1	2	yes	—
169	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	C₂×Dic₄₃	—	2	4	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	1	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	C₂×Dic₄₃	—	4	1	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	Dic₈₆	—	2	2	no	—
194	Dic₈₆	—	2	2	no	—
195	Dic₈₆	—	2	2	no	—
196	Dic₈₆	—	8	8	no	—
197	Dic₈₆	—	8	4	no	—
198	Dic₈₆	C₄×Q₈	1	4	yes	—
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	4	1	no	—
201	C₈×C₄₃	—	4	2	no	—
202	#22525	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₄₃	#548	1	1	yes	characteristic
205	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
206	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
207	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₃	#576	1	1	yes	characteristic
209	C₂²×C₄₃	#577	1	1	yes	characteristic
210	C₄×C₄₃	—	2	4	no	—
211	C₄×C₄₃	—	2	4	no	—
212	C₄×C₄₃	—	2	2	no	—
213	C₄×C₄₃	#419	1	4	yes	—
214	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
215	C₄×C₄₃	#519	1	1	yes	characteristic
216	C₄×C₄₃	#548	1	1	yes	characteristic
217	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
218	Dic₄₃	—	2	4	no	—
219	Dic₄₃	—	4	2	no	—
220	Dic₄₃	—	4	2	no	—
221	Dic₄₃	—	4	4	no	—
222	Dic₄₃	—	8	1	no	—
223	Dic₄₃	—	8	2	no	—
224	C₂×Q₈²	—	43	1	no	—
225	C₂×#446	D₄₃	1	1	yes	characteristic
226	#2355	—	43	1	no	—
227	#1993	—	43	2	no	—
228	#1990	—	43	1	no	—
229	#1988	—	43	2	no	—
230	#1987	—	43	1	no	—
231	#1805	—	43	2	no	—
232	#1803	—	43	1	no	—
233	#1763	—	43	2	no	—
234	C₄×#103	—	43	1	no	—
235	C₂×C₄₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄₃	C₂×#419	1	1	yes	characteristic
237	C₂×C₄₃	#2897	1	1	yes	characteristic
238	C₂×C₄₃	#3369	1	1	yes	characteristic
239	C₂×C₄₃	#3375	1	1	yes	characteristic
240	C₂×C₄₃	#3385	1	1	yes	characteristic
241	C₂×C₄₃	#3387	1	1	yes	characteristic
242	Q₈²	—	43	8	no	—
243	Q₈²	—	86	4	no	—
244	C₂×C₄⋊Q₈	—	43	1	no	—
245	C₂×C₄⋊Q₈	—	43	2	no	—
246	C₂×C₄⋊Q₈	—	86	1	no	—
247	C₂×C₄⋊Q₈	—	86	2	no	—
248	C₂×C₄×Q₈	—	43	1	no	—
249	C₂×C₄×Q₈	—	43	2	no	—
250	C₂×C₄×Q₈	—	86	1	no	—
251	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
252	#446	—	2	4	no	—
253	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
255	C₂×#103	—	43	1	no	—
256	C₂×#103	—	43	2	no	—
257	C₂×#103	—	43	1	no	—
258	C₂×#97	C₂×D₄₃	1	2	yes	—
259	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
260	#391	—	86	1	no	—
261	#387	—	86	2	no	—
262	#384	—	43	1	no	—
263	#382	—	43	2	no	—
264	C₄×C₄⋊C₄	—	43	1	no	—
265	C₄×C₄⋊C₄	—	43	2	no	—
266	C₄×C₄⋊C₄	—	86	1	no	—
267	#340	—	43	2	no	—
268	#340	—	43	2	no	—
269	#340	—	43	2	no	—
270	#340	—	43	2	no	—
271	#340	—	43	1	no	—
272	#340	—	43	2	no	—
273	#340	—	43	1	no	—
274	C₄₃	#22525	1	1	yes	characteristic, complemented, Sylow
275	C₂²×Q₈	—	43	1	no	—
276	C₂²×Q₈	—	86	2	no	—
277	C₂²×Q₈	—	86	1	no	—
278	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
279	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
280	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
281	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
282	C₄⋊Q₈	—	43	4	no	—
283	C₄⋊Q₈	—	43	8	no	—
284	C₄⋊Q₈	—	86	16	no	—
285	C₄⋊Q₈	—	86	8	no	—
286	C₄⋊Q₈	—	86	2	no	—
287	C₄⋊Q₈	—	86	4	no	—
288	C₄×Q₈	—	43	4	no	—
289	C₄×Q₈	—	43	8	no	—
290	C₄×Q₈	—	86	8	no	—
291	C₄×Q₈	—	86	2	no	—
292	C₄×Q₈	—	86	4	no	—
293	C₄×Q₈	C₄×D₄₃	1	4	yes	—
294	C₄×Q₈	C₂²⋊D₄₃	1	4	yes	—
295	C₂×C₄⋊C₄	—	43	1	no	—
296	C₂×C₄⋊C₄	—	43	2	no	—
297	C₂×C₄⋊C₄	—	43	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₄⋊C₄	—	43	2	no	—
300	C₂×C₄⋊C₄	—	86	2	no	—
301	C₂×C₄⋊C₄	—	86	1	no	—
302	C₂×C₄⋊C₄	—	86	2	no	—
303	C₂×C₄⋊C₄	—	86	1	no	—
304	C₂×C₄⋊C₄	—	86	1	no	—
305	C₂×C₄⋊C₄	—	86	1	no	—
306	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
307	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
308	C₂×C₄²	—	86	2	no	—
309	C₂×C₄²	—	86	1	no	—
310	C₂×C₄²	—	86	2	no	—
311	C₂×C₄²	—	86	1	no	—
312	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
313	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	—	2	4	no	—
316	#103	—	43	4	no	—
317	#103	—	86	4	no	—
318	#103	—	86	2	no	—
319	#97	—	2	4	no	—
320	C₄×C₈	—	2	2	no	—
321	#95	—	86	1	no	—
322	#95	—	86	2	no	—
323	#95	—	86	2	no	—
324	#95	—	86	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	43	2	no	—
328	C₂×Q₈	—	43	2	no	—
329	C₂×Q₈	—	43	2	no	—
330	C₂×Q₈	—	86	4	no	—
331	C₂×Q₈	—	86	8	no	—
332	C₂×Q₈	—	86	1	no	—
333	C₂×Q₈	—	86	1	no	—
334	C₂×Q₈	—	86	1	no	—
335	C₂×Q₈	—	344	2	no	—
336	C₂×Q₈	—	344	1	no	—
337	C₂×Q₈	—	344	2	no	—
338	C₂×Q₈	—	344	1	no	—
339	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	2	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	86	1	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
347	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
348	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
350	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	Q₈×D₄₃	1	2	yes	—
360	C₄⋊C₄	—	43	2	no	—
361	C₄⋊C₄	—	43	4	no	—
362	C₄⋊C₄	—	43	2	no	—
363	C₄⋊C₄	—	86	4	no	—
364	C₄⋊C₄	—	86	8	no	—
365	C₄⋊C₄	—	86	8	no	—
366	C₄⋊C₄	—	86	4	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	—	344	1	no	—
375	C₄⋊C₄	—	172	2	no	—
376	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	8	yes	—
377	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
378	C₄²	—	86	8	no	—
379	C₄²	—	86	4	no	—
380	C₄²	—	344	2	no	—
381	C₄²	—	172	2	no	—
382	C₄²	C₂×C₄×D₄₃	1	4	yes	—
383	C₄²	C₂×C₄×D₄₃	1	2	yes	—
384	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
385	C₄²	C₂×C₂²⋊D₄₃	1	4	yes	—
386	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
387	Q₈	—	2	8	no	—
388	Q₈	—	43	4	no	—
389	Q₈	—	86	2	no	—
390	Q₈	—	86	2	no	—
391	Q₈	—	86	2	no	—
392	Q₈	—	344	8	no	—
393	Q₈	—	344	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	86	2	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	86	2	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	86	4	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	172	1	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	1	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	—	172	2	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	—	172	1	no	—
418	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	4	yes	—
419	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
420	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	4	yes	—
421	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
422	C₂×C₄	#13063358	1	2	yes	—
423	C₂×C₄	#13063358	1	2	yes	—
424	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
427	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
428	C₂×C₄	#13063372	1	1	yes	characteristic
429	C₂×C₄	#13063373	1	1	yes	characteristic
430	C₈	—	2	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	2	no	—
433	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
434	C₂²	#14583561	1	1	yes	characteristic
435	C₂²	Q₈×D₁₇₂	1	1	yes	characteristic
436	C₂²	C₂×#13063358	1	1	yes	characteristic
437	C₂²	C₂×#13063358	1	1	yes	characteristic
438	C₂²	#14583704	1	1	yes	characteristic
439	C₂²	#14583711	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	86	4	no	—
444	C₄	—	344	1	no	—
445	C₄	—	344	2	no	—
446	C₄	—	172	4	no	—
447	C₄	—	172	2	no	—
448	C₄	—	172	2	no	—
449	C₄	#14582909	1	4	yes	—
450	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
451	C₄	#14583375	1	1	yes	characteristic
452	C₄	#14583556	1	1	yes	characteristic
453	C₄	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
454	C₂	Q₈×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
455	C₂	C₂×#14582909	1	1	yes	characteristic
456	C₂	#19143122	1	1	yes	characteristic
457	C₂	#19147337	1	1	yes	characteristic
458	C₂	#19147411	1	1	yes	characteristic
459	C₂	#19147507	1	1	yes	characteristic
460	C₂	#19147529	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#446	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#446	D₄₃
hypocenter	C₄₃	#22525
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ C₂×#446

Complements

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

N	H ≅ G/N	type
13. Q₈×Dic₈₆	C₄	semidirect
75. #13063250	Q₈	semidirect
274. C₄₃	#22525	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×Dic₈₆	2
#19137552	2
#19135568	2
#19135556	2
#19135546	2
#19135542	2
#19134611	2
#19134601	2
#19134426	2
C₄×#13063250	2
C₂×C₄₃×#446	2
#22525	43