Subgroups — #25118429

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583194	C₂	1	1	yes	maximal, characteristic
2	#19137684	C₂	1	1	yes	maximal, characteristic
3	#19135555	C₂	1	1	yes	maximal, characteristic
4	#19135351	C₂	1	1	yes	maximal, characteristic
5	#19135325	C₂	1	2	yes	maximal
6	#19135184	C₂	1	2	yes	maximal
7	#19134849	C₂	1	2	yes	maximal
8	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₄×#13063249	C₂	1	2	yes	maximal
10	C₄×#13063249	C₂	1	1	yes	maximal, characteristic
11	Q₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	#14583194	C₄	1	8	yes	complemented
14	C₂×#13063258	C₂²	1	2	yes	—
15	C₂×#13063258	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13063249	C₂²	1	1	yes	characteristic
18	C₂×#13063249	C₂²	1	2	yes	—
19	C₂×#13063249	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
22	#14582803	—	2	2	no	—
23	#14582797	C₂²	1	2	yes	—
24	#14582795	—	2	1	no	—
25	C₄⋊C₄×Dic₄₃	—	2	1	no	—
26	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
28	#14582661	C₂²	1	2	yes	—
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	1	yes	characteristic
31	#14582661	C₂²	1	2	yes	—
32	#14582661	C₂²	1	1	yes	characteristic
33	#14582654	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#389	—	2	2	no	—
37	C₄₃×#389	C₂²	1	2	yes	—
38	C₄₃×#384	—	2	1	no	—
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×Dic₈₆	—	2	1	no	—
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
46	#13063325	—	2	2	no	—
47	#13063325	C₂×C₄	1	4	yes	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×Dic₄₃⋊C₄	—	2	2	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	C₂×C₄×Dic₄₃	—	2	2	no	—
55	#13063258	—	4	2	no	—
56	#13063258	C₂×C₄	1	8	yes	—
57	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
58	#13063249	—	2	2	no	—
59	#13063249	C₂×C₄	1	8	yes	—
60	#13063249	Q₈	1	4	yes	complemented
61	C₄×C₄₃⋊C₈	—	2	2	no	—
62	C₄×C₄₃⋊C₈	—	4	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	—	2	1	no	—
66	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₄₃	—	2	2	no	—
68	C₄×Q₈×C₄₃	—	2	4	no	—
69	C₄×Q₈×C₄₃	—	4	2	no	—
70	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	—	2	2	no	—
82	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	D₄	1	2	yes	—
86	C₂×Q₈×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	—	2	1	no	—
88	C₂×Q₈×C₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
90	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂×Q₈×C₄₃	#41	1	2	yes	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₃	—	2	1	no	—
101	C₂²×Dic₄₃	—	2	2	no	—
102	C₂²×Dic₄₃	—	2	1	no	—
103	C₂×Dic₈₆	—	2	4	no	—
104	C₂×Dic₈₆	—	8	1	no	—
105	C₂×Dic₈₆	—	8	1	no	—
106	C₄⋊C₄×C₄₃	—	2	4	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₄⋊C₄×C₄₃	—	2	2	no	—
110	C₄⋊C₄×C₄₃	—	2	2	no	—
111	C₄⋊C₄×C₄₃	—	4	4	no	—
112	C₄⋊C₄×C₄₃	—	4	2	no	—
113	C₄⋊C₄×C₄₃	—	8	1	no	—
114	C₄⋊C₄×C₄₃	—	8	2	no	—
115	C₄⋊C₄×C₄₃	Q₁₆	1	4	yes	—
116	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₃	—	2	4	no	—
118	C₄²×C₄₃	—	2	2	no	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	—	4	4	no	—
121	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₃	#41	1	2	yes	—
123	C₄⋊Dic₄₃	—	2	4	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	2	1	no	—
127	C₄⋊Dic₄₃	—	2	1	no	—
128	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
129	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
130	Dic₄₃⋊C₄	—	8	2	no	—
131	C₄×Dic₄₃	—	4	2	no	—
132	C₄×Dic₄₃	—	8	2	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	2	no	—
136	C₂×C₄₃⋊C₈	—	2	2	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	—	2	1	no	—
140	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
142	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	2	2	no	—
144	Q₈×C₄₃	—	2	2	no	—
145	Q₈×C₄₃	—	2	2	no	—
146	Q₈×C₄₃	C₄×Q₈	1	4	yes	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
166	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
167	C₂×C₄×C₄₃	#135	1	2	yes	—
168	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×Dic₄₃	—	2	4	no	—
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	2	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	Dic₈₆	—	8	4	no	—
184	C₄₃⋊C₈	—	2	4	no	—
185	C₄₃⋊C₈	—	2	2	no	—
186	C₄₃⋊C₈	—	4	1	no	—
187	#22965	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₃	#546	1	1	yes	characteristic
190	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
191	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
193	C₂²×C₄₃	#576	1	1	yes	characteristic
194	C₂²×C₄₃	#577	1	1	yes	characteristic
195	C₄×C₄₃	—	2	4	no	—
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	—	2	4	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	C₄×Q₁₆	1	4	yes	—
202	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₄×C₄₃	#520	1	1	yes	characteristic
204	C₄×C₄₃	#552	1	1	yes	characteristic
205	C₄×C₄₃	#554	1	1	yes	characteristic
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	4	4	no	—
208	Dic₄₃	—	8	1	no	—
209	C₂×#477	—	43	1	no	—
210	#2369	—	43	1	no	—
211	Q₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic
212	#1990	—	43	1	no	—
213	#1947	—	43	1	no	—
214	#1942	—	43	2	no	—
215	#1921	—	43	2	no	—
216	#1863	—	43	2	no	—
217	C₈×C₄⋊C₄	—	43	1	no	—
218	C₄×#103	—	43	2	no	—
219	C₄×#103	—	43	1	no	—
220	C₂×C₄₃	#2360	1	1	yes	characteristic
221	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₄₃	#2946	1	1	yes	characteristic
223	C₂×C₄₃	#3299	1	1	yes	characteristic
224	C₂×C₄₃	#3305	1	1	yes	characteristic
225	C₂×C₄₃	#3381	1	1	yes	characteristic
226	C₂×C₄₃	Q₈×Q₁₆	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	—	43	1	no	—
228	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
229	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
230	#477	—	43	8	no	—
231	C₂×#107	—	43	2	no	—
232	C₂×#107	—	43	2	no	—
233	C₂×C₄⋊C₈	—	43	1	no	—
234	C₂×#103	—	43	2	no	—
235	C₂×#103	—	43	1	no	—
236	C₂×#103	—	43	1	no	—
237	C₂×C₄×C₈	—	43	1	no	—
238	C₂×C₄×C₈	—	43	2	no	—
239	#391	—	86	2	no	—
240	#389	—	2	2	no	—
241	#389	—	43	2	no	—
242	#389	—	86	1	no	—
243	#389	C₂×D₄₃	1	2	yes	—
244	#384	—	2	1	no	—
245	#384	C₂×D₄₃	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	2	1	no	—
247	C₄×C₄⋊C₄	—	43	2	no	—
248	C₄×C₄⋊C₄	—	43	1	no	—
249	C₄×C₄⋊C₄	—	86	1	no	—
250	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
251	#340	—	43	2	no	—
252	#340	—	43	1	no	—
253	#340	—	43	2	no	—
254	#340	—	43	1	no	—
255	#340	—	43	2	no	—
256	#336	—	43	2	no	—
257	C₄₃	#22965	1	1	yes	characteristic, complemented, Sylow
258	C₂²×Q₈	—	86	1	no	—
259	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
260	C₂²×C₈	—	43	2	no	—
261	C₂²×C₈	—	43	1	no	—
262	C₂²×C₈	—	43	1	no	—
263	C₄⋊Q₈	—	43	4	no	—
264	C₄⋊Q₈	—	86	2	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	4	2	no	—
268	C₄×Q₈	C₄×D₄₃	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	43	2	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	86	1	no	—
278	C₂×C₄⋊C₄	—	86	2	no	—
279	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	86	2	no	—
286	C₂×C₄²	—	86	1	no	—
287	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	#107	—	43	8	no	—
290	#107	—	172	2	no	—
291	C₄⋊C₈	—	43	4	no	—
292	#103	—	43	8	no	—
293	#103	—	43	4	no	—
294	#103	—	86	2	no	—
295	C₄×C₈	—	86	2	no	—
296	C₄×C₈	—	172	2	no	—
297	#95	—	2	2	no	—
298	#95	—	86	2	no	—
299	#95	—	86	1	no	—
300	#95	—	86	2	no	—
301	#95	C₂²⋊D₄₃	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	86	4	no	—
306	C₂×Q₈	—	344	1	no	—
307	C₂×Q₈	—	344	1	no	—
308	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
309	C₂×Q₈	#10621900	1	2	yes	—
310	C₂×Q₈	Q₈×D₄₃	1	2	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	86	1	no	—
315	C₂²×C₄	—	86	2	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
318	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
320	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
322	C₂×C₈	—	43	4	no	—
323	C₂×C₈	—	43	2	no	—
324	C₂×C₈	—	86	1	no	—
325	C₂×C₈	—	86	1	no	—
326	C₂×C₈	—	86	2	no	—
327	C₂×C₈	—	86	2	no	—
328	C₂×C₈	—	86	1	no	—
329	C₂×C₈	—	86	1	no	—
330	C₂×C₈	—	86	1	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	8	1	no	—
339	C₄⋊C₄	—	8	2	no	—
340	C₄⋊C₄	—	43	4	no	—
341	C₄⋊C₄	—	43	2	no	—
342	C₄⋊C₄	—	86	4	no	—
343	C₄⋊C₄	—	86	2	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	344	2	no	—
348	C₄⋊C₄	#10621885	1	4	yes	—
349	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	4	no	—
354	C₄²	—	344	2	no	—
355	C₄²	—	172	2	no	—
356	C₄²	C₂×C₄×D₄₃	1	2	yes	—
357	C₄²	#10621898	1	2	yes	—
358	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	344	4	no	—
363	Q₈	#13063290	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	4	no	—
382	C₂×C₄	—	172	1	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	1	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	2	no	—
389	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
390	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
391	C₂×C₄	C₂×#10621885	1	4	yes	—
392	C₂×C₄	C₂×#10621885	1	2	yes	—
393	C₂×C₄	#13063345	1	2	yes	—
394	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
398	C₂×C₄	#13063370	1	1	yes	characteristic
399	C₂×C₄	#13063373	1	1	yes	characteristic
400	C₈	—	86	2	no	—
401	C₈	—	86	4	no	—
402	C₈	—	172	1	no	—
403	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
404	C₂²	#14583543	1	1	yes	characteristic
405	C₂²	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂²	C₂²×#10621885	1	1	yes	characteristic
407	C₂²	C₂×#13063345	1	1	yes	characteristic
408	C₂²	#14583702	1	1	yes	characteristic
409	C₂²	#14583707	1	1	yes	characteristic
410	C₄	—	2	4	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	8	2	no	—
416	C₄	—	344	1	no	—
417	C₄	—	172	2	no	—
418	C₄	—	172	4	no	—
419	C₄	C₄×#10621885	1	4	yes	—
420	C₄	C₂×#13063290	1	1	yes	characteristic
421	C₄	#14583380	1	1	yes	characteristic
422	C₄	#14583584	1	1	yes	characteristic
423	C₄	#14583604	1	1	yes	characteristic
424	C₂	#19137600	1	1	yes	characteristic
425	C₂	C₂×C₄×#10621885	1	1	yes	characteristic
426	C₂	#19143423	1	1	yes	characteristic
427	C₂	#19146471	1	1	yes	characteristic
428	C₂	#19146545	1	1	yes	characteristic
429	C₂	#19147466	1	1	yes	characteristic
430	C₂	Q₈×#10621885	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	Q₈×C₄⋊C₄×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	Q₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#22965
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
13. #14583194	C₄	semidirect
60. #13063249	Q₈	semidirect
257. C₄₃	#22965	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583194	2
#19137684	2
#19135555	2
#19135351	2
#19135325	2
#19135184	2
#19134849	2
C₄⋊C₄×C₄₃⋊C₈	2
C₄×#13063249	2
Q₈×C₄⋊C₄×C₄₃	2
#22965	43