Subgroups — #36312955

Order 21248.

11346 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19128537	C₂	1	2	yes	maximal, complemented
2	#24921256	C₂	1	8	yes	maximal, complemented
3	#24921248	C₂	1	4	yes	maximal, complemented
4	#24921241	C₂	1	4	yes	maximal, complemented
5	#24921234	C₂	1	4	yes	maximal, complemented
6	#24921227	C₂	1	12	yes	maximal, complemented
7	#41×D₃₃₂	C₂	1	16	yes	maximal, complemented
8	#24920796	C₂	1	6	yes	maximal, complemented
9	C₂×#19128251	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×#41×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#19128537	—	2	32	no	—
12	C₂×#14581840	C₂²	1	4	yes	complemented
13	C₂×#14581839	C₂²	1	8	yes	complemented
14	C₂×#14581838	C₂²	1	8	yes	complemented
15	C₂×#14581837	C₂²	1	12	yes	complemented
16	C₂²×#13050590	C₂²	1	12	yes	complemented
17	C₂×#41×D₈₃	C₂²	1	16	yes	complemented
18	#19128373	C₂²	1	16	yes	complemented
19	Q₈×D₃₃₂	C₂²	1	16	yes	complemented
20	#19128363	C₂²	1	32	yes	complemented
21	#19128355	C₂²	1	48	yes	complemented
22	#19128346	C₂²	1	96	yes	complemented
23	D₄×D₃₃₂	C₂²	1	48	yes	complemented
24	#19128282	C₂²	1	24	yes	complemented
25	#19128277	C₂²	1	24	yes	complemented
26	#19128270	C₂²	1	24	yes	complemented
27	#19128263	C₂²	1	24	yes	complemented
28	#19128251	C₂²	1	24	yes	complemented
29	#19128251	C₂²	1	24	yes	complemented
30	#19128251	C₂²	1	12	yes	complemented
31	#19128251	C₂²	1	12	yes	complemented
32	#19128251	C₂²	1	4	yes	complemented
33	#19128251	C₂²	1	12	yes	complemented
34	C₂×#14581792	C₂²	1	6	yes	complemented
35	C₂×#14581789	C₂²	1	6	yes	complemented
36	C₂×#14581780	C₂²	1	12	yes	complemented
37	#19128213	C₂²	1	48	yes	complemented
38	C₂×#14581766	C₂²	1	24	yes	complemented
39	C₂×C₄×D₃₃₂	C₂²	1	24	yes	complemented
40	C₂²×#41×C₈₃	C₂²	1	1	yes	characteristic
41	C₄×#41×C₈₃	C₂²	1	8	yes	complemented
42	C₄×#41×C₈₃	C₂²	1	4	yes	complemented
43	C₄×#41×C₈₃	C₂²	1	4	yes	complemented
44	C₂×C₄×Q₈×C₈₃	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₈₃	C₂²	1	6	yes	complemented
46	C₂×#117×C₈₃	C₂²	1	3	yes	complemented
47	C₂²×C₄²×C₈₃	C₂²	1	3	yes	complemented
48	#14581840	—	2	32	no	—
49	#14581839	—	2	64	no	—
50	#14581838	—	2	64	no	—
51	#14581837	—	2	96	no	—
52	C₂×#13050591	C₂³	1	16	yes	—
53	C₂×#13050590	—	2	96	no	—
54	C₂×#13050590	C₂³	1	24	yes	—
55	C₂×#13050590	C₂³	1	8	yes	—
56	C₂×#13050590	C₂³	1	24	yes	—
57	C₂×#13050590	C₂³	1	24	yes	—
58	C₂×#13050589	C₂³	1	48	yes	—
59	#41×D₈₃	—	2	128	no	—
60	C₂²×Dic₁₆₆	C₂³	1	12	yes	—
61	C₂×Q₈×D₈₃	C₂³	1	16	yes	—
62	C₂²×D₃₃₂	C₂³	1	12	yes	—
63	C₂²×D₃₃₂	C₂³	1	24	yes	—
64	C₂²×C₂²⋊D₈₃	C₂³	1	24	yes	—
65	C₂×D₄×D₈₃	C₂³	1	48	yes	—
66	C₂²×C₄×D₈₃	C₂³	1	24	yes	—
67	#14581792	C₂³	1	24	yes	—
68	#14581792	C₂³	1	4	yes	—
69	#14581792	C₂³	1	12	yes	—
70	#14581789	C₂³	1	24	yes	—
71	#14581789	C₂³	1	4	yes	—
72	#14581789	C₂³	1	12	yes	—
73	#14581780	C₂³	1	48	yes	—
74	#14581780	C₂³	1	8	yes	—
75	#14581780	C₂³	1	24	yes	—
76	#14581776	C₂³	1	96	yes	—
77	#14581772	C₂³	1	96	yes	—
78	#14581767	C₂³	1	96	yes	—
79	#14581766	C₂³	1	48	yes	—
80	#14581766	C₂³	1	48	yes	—
81	#14581766	C₂³	1	16	yes	—
82	#14581766	C₂³	1	48	yes	—
83	#14581762	C₂³	1	96	yes	—
84	C₄×D₃₃₂	C₂³	1	48	yes	—
85	C₄×D₃₃₂	C₂³	1	48	yes	—
86	C₄×D₃₃₂	C₂³	1	16	yes	—
87	C₄×D₃₃₂	C₂³	1	48	yes	—
88	C₂×C₄⋊Dic₈₃	C₂³	1	24	yes	—
89	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	48	yes	—
90	C₂×#41×C₈₃	D₄	1	16	yes	complemented
91	C₂×#41×C₈₃	C₂³	1	4	yes	—
92	C₂×#41×C₈₃	C₂³	1	4	yes	—
93	C₂²×Q₈×C₈₃	C₂³	1	1	yes	characteristic
94	C₂²×D₄×C₈₃	C₂³	1	3	yes	—
95	C₂³×C₄×C₈₃	C₂³	1	6	yes	—
96	C₂³×C₄×C₈₃	C₂³	1	3	yes	—
97	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
98	C₄×Q₈×C₈₃	C₂³	1	8	yes	—
99	C₄×D₄×C₈₃	C₂³	1	24	yes	—
100	C₄×D₄×C₈₃	C₂³	1	24	yes	—
101	#117×C₈₃	C₂³	1	12	yes	—
102	#117×C₈₃	C₂³	1	12	yes	—
103	C₂×C₄⋊C₄×C₈₃	C₂³	1	6	yes	—
104	C₂×C₂²⋊C₄×C₈₃	C₂³	1	6	yes	—
105	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
107	C₂×C₄²×C₈₃	C₂³	1	6	yes	—
108	C₂×C₄²×C₈₃	C₂³	1	12	yes	—
109	C₂×C₄²×C₈₃	C₂³	1	6	yes	—
110	C₂×C₄²×C₈₃	C₂³	1	6	yes	—
111	C₂³×D₈₃	C₂⁴	1	24	yes	—
112	#13050591	—	2	64	no	—
113	#13050590	—	2	96	no	—
114	#13050590	—	2	32	no	—
115	#13050590	—	2	96	no	—
116	#13050590	—	2	96	no	—
117	#13050589	—	2	192	no	—
118	C₂×Dic₁₆₆	—	2	48	no	—
119	C₂×Dic₁₆₆	C₂⁴	1	24	yes	—
120	C₂×Dic₁₆₆	C₂⁴	1	8	yes	—
121	Q₈×D₈₃	—	2	64	no	—
122	C₂×D₃₃₂	—	2	48	no	—
123	C₂×D₃₃₂	—	4	48	no	—
124	C₂×D₃₃₂	C₂⁴	1	16	yes	—
125	C₂×D₃₃₂	C₂⁴	1	24	yes	—
126	C₂×D₃₃₂	C₂⁴	1	8	yes	—
127	C₂×D₃₃₂	C₂⁴	1	48	yes	—
128	C₂×C₂²⋊D₈₃	—	2	96	no	—
129	C₂×C₂²⋊D₈₃	C₂⁴	1	48	yes	—
130	C₂×C₂²⋊D₈₃	C₂⁴	1	16	yes	—
131	D₄×D₈₃	—	2	192	no	—
132	C₂²×Dic₈₃	C₂⁴	1	24	yes	—
133	C₂×C₄×D₈₃	—	2	96	no	—
134	C₂×C₄×D₈₃	C₂⁴	1	48	yes	—
135	C₂×C₄×D₈₃	C₂⁴	1	16	yes	—
136	C₄⋊Dic₈₃	C₂⁴	1	16	yes	—
137	C₄⋊Dic₈₃	C₂⁴	1	48	yes	—
138	(C₂×D₈₃)⋊C₄	C₂⁴	1	96	yes	—
139	(C₂×D₈₃)⋊C₄	C₂⁴	1	32	yes	—
140	C₂⁴×C₈₃	C₂⁴	1	3	yes	—
141	#41×C₈₃	C₂×D₄	1	32	yes	complemented
142	#41×C₈₃	C₂×D₄	1	32	yes	complemented
143	C₂×Q₈×C₈₃	C₂×D₄	1	8	yes	complemented
144	C₂×Q₈×C₈₃	C₂⁴	1	4	yes	—
145	C₂×D₄×C₈₃	C₂×D₄	1	24	yes	complemented
146	C₂×D₄×C₈₃	C₂⁴	1	12	yes	—
147	C₂²×C₄×C₈₃	—	4	12	no	—
148	C₂²×C₄×C₈₃	C₂×D₄	1	24	yes	complemented
149	C₂²×C₄×C₈₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
151	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
152	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
153	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
154	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
155	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
157	C₄⋊C₄×C₈₃	C₂⁴	1	24	yes	—
158	C₂²⋊C₄×C₈₃	C₂⁴	1	24	yes	—
159	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
160	C₄²×C₈₃	C₂⁴	1	6	yes	—
161	C₄²×C₈₃	C₂⁴	1	12	yes	—
162	C₄²×C₈₃	C₂⁴	1	1	yes	characteristic
163	C₄²×C₈₃	C₂⁴	1	12	yes	—
164	C₄²×C₈₃	C₂⁴	1	2	yes	—
165	C₄²×C₈₃	C₂⁴	1	6	yes	—
166	C₂³×C₈₃	—	4	6	no	—
167	C₂³×C₈₃	C₂²×D₄	1	12	yes	—
168	C₂³×C₈₃	C₂⁵	1	6	yes	—
169	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
170	C₂²×D₈₃	—	2	48	no	—
171	C₂²×D₈₃	—	4	48	no	—
172	C₂²×D₈₃	C₂⁵	1	16	yes	—
173	Q₈×C₈₃	C₂²×D₄	1	16	yes	—
174	D₄×C₈₃	C₂²×D₄	1	48	yes	—
175	C₂×C₄×C₈₃	—	2	4	no	—
176	C₂×C₄×C₈₃	—	2	24	no	—
177	C₂×C₄×C₈₃	—	4	6	no	—
178	C₂×C₄×C₈₃	—	4	12	no	—
179	C₂×C₄×C₈₃	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₈₃	C₂²×D₄	1	12	yes	—
181	C₂×C₄×C₈₃	C₂²×D₄	1	24	yes	—
182	C₂×C₄×C₈₃	C₂²×D₄	1	24	yes	—
183	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
184	C₂×C₄×C₈₃	C₂⁵	1	12	yes	—
185	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
186	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
187	C₂×C₄×C₈₃	C₂⁵	1	2	yes	—
188	C₂×C₄×C₈₃	C₂⁵	1	1	yes	characteristic
189	C₂²⋊D₈₃	—	2	96	no	—
190	C₂²⋊D₈₃	—	2	32	no	—
191	C₂×Dic₈₃	—	2	48	no	—
192	C₂×Dic₈₃	C₂⁵	1	16	yes	—
193	D₃₃₂	—	2	48	no	—
194	D₃₃₂	—	2	16	no	—
195	D₃₃₂	—	2	32	no	—
196	D₃₃₂	—	4	48	no	—
197	C₄×D₈₃	—	2	32	no	—
198	C₄×D₈₃	—	2	96	no	—
199	Dic₁₆₆	—	2	48	no	—
200	Dic₁₆₆	—	2	16	no	—
201	C₂²×C₈₃	—	2	2	no	—
202	C₂²×C₈₃	—	2	12	no	—
203	C₂²×C₈₃	—	4	12	no	—
204	C₂²×C₈₃	C₂³×D₄	1	12	yes	—
205	C₂²×C₈₃	C₂³×D₄	1	2	yes	—
206	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
207	C₂×D₈₃	—	2	16	no	—
208	C₂×D₈₃	—	2	32	no	—
209	C₂×D₈₃	—	8	48	no	—
210	C₄×C₈₃	—	2	12	no	—
211	C₄×C₈₃	—	2	2	no	—
212	C₄×C₈₃	C₂³×D₄	1	2	yes	—
213	C₄×C₈₃	C₂³×D₄	1	12	yes	—
214	C₄×C₈₃	C₂³×D₄	1	2	yes	—
215	C₄×C₈₃	#585	1	4	yes	complemented
216	Dic₈₃	—	2	16	no	—
217	#62812	—	83	1	no	maximal, Sylow
218	C₂×C₈₃	—	2	12	no	—
219	C₂×C₈₃	—	2	2	no	—
220	C₂×C₈₃	C₂⁴×D₄	1	1	yes	characteristic
221	C₂×C₈₃	C₂×#585	1	2	yes	—
222	D₈₃	—	4	16	no	—
223	C₂×#585	—	83	2	no	—
224	#3500	—	83	8	no	—
225	#3499	—	83	4	no	—
226	#3498	—	83	4	no	—
227	#3497	—	83	4	no	—
228	#3496	—	83	12	no	—
229	D₄×#41	—	83	16	no	—
230	#3449	—	83	6	no	—
231	C₂×#532	—	83	6	no	—
232	C₂×C₄×#41	D₈₃	1	1	yes	characteristic, complemented
233	C₈₃	#62812	1	1	yes	characteristic, complemented, Sylow
234	#585	—	166	32	no	—
235	C₂×2₋¹⁺⁴	—	83	8	no	—
236	C₂×2₋¹⁺⁴	—	83	4	no	—
237	C₂×H(5,𝔽₂)	—	83	8	no	—
238	C₂×H(5,𝔽₂)	—	83	12	no	—
239	C₂²×#41	—	83	16	no	—
240	C₂²×#41	—	83	12	no	—
241	C₂²×#41	C₂×D₈₃	1	1	yes	characteristic
242	#550	—	83	16	no	—
243	D₄×Q₈	—	83	16	no	—
244	#548	—	83	32	no	—
245	#547	—	83	48	no	—
246	#546	—	83	96	no	—
247	D₄²	—	83	48	no	—
248	#537	—	83	24	no	—
249	#536	—	83	24	no	—
250	#535	—	83	24	no	—
251	#534	—	83	24	no	—
252	#532	—	83	4	no	—
253	#532	—	83	12	no	—
254	#532	—	83	24	no	—
255	#532	—	83	24	no	—
256	#532	—	83	12	no	—
257	#532	—	83	12	no	—
258	C₂×C₄⋊Q₈	—	83	6	no	—
259	C₂×#127	—	83	6	no	—
260	C₂×#124	—	83	12	no	—
261	#525	—	83	48	no	—
262	C₂×#121	—	83	24	no	—
263	C₄×#41	C₂×D₈₃	1	8	yes	complemented
264	C₄×#41	C₂×D₈₃	1	4	yes	complemented
265	C₄×#41	C₂×D₈₃	1	4	yes	complemented
266	C₂×C₄×Q₈	C₂×D₈₃	1	2	yes	complemented
267	C₂×C₄×D₄	—	83	24	no	—
268	C₂×C₄×D₄	C₂×D₈₃	1	6	yes	complemented
269	C₂×#117	C₂×D₈₃	1	3	yes	complemented
270	C₂²×C₄²	C₂×D₈₃	1	3	yes	complemented
271	2₋¹⁺⁴	—	166	64	no	—
272	2₋¹⁺⁴	—	166	32	no	—
273	H(5,𝔽₂)	—	166	64	no	—
274	H(5,𝔽₂)	—	166	96	no	—
275	C₂×#41	—	83	16	no	—
276	C₂×#41	—	83	48	no	—
277	C₂×#41	—	83	24	no	—
278	C₂×#41	—	83	8	no	—
279	C₂×#41	—	83	24	no	—
280	C₂×#41	—	83	24	no	—
281	C₂×#41	—	166	128	no	—
282	C₂×#41	—	166	96	no	—
283	C₂×#41	D₃₃₂	1	16	yes	complemented
284	C₂×#41	C₂²×D₈₃	1	4	yes	—
285	C₂×#41	C₂²×D₈₃	1	4	yes	—
286	C₂²×Q₈	—	83	16	no	—
287	C₂²×Q₈	—	83	12	no	—
288	C₂²×Q₈	C₂²×D₈₃	1	1	yes	characteristic
289	C₂²×D₄	—	83	24	no	—
290	C₂²×D₄	—	83	48	no	—
291	C₂²×D₄	—	83	24	no	—
292	C₂²×D₄	—	83	12	no	—
293	C₂²×D₄	C₂²×D₈₃	1	3	yes	—
294	C₂³×C₄	—	83	24	no	—
295	C₂³×C₄	C₂²×D₈₃	1	6	yes	—
296	C₂³×C₄	C₂²×D₈₃	1	3	yes	—
297	C₄⋊Q₈	—	83	4	no	—
298	C₄⋊Q₈	—	83	12	no	—
299	C₄⋊Q₈	—	83	24	no	—
300	#127	—	83	4	no	—
301	#127	—	83	12	no	—
302	#127	—	83	24	no	—
303	#124	—	83	8	no	—
304	#124	—	83	24	no	—
305	#124	—	83	48	no	—
306	#123	—	83	96	no	—
307	C₂²⋊Q₈	—	83	96	no	—
308	#121	—	83	16	no	—
309	#121	—	83	48	no	—
310	#121	—	83	48	no	—
311	#121	—	83	48	no	—
312	#121	—	83	96	no	—
313	#120	—	83	96	no	—
314	C₄×Q₈	C₂²×D₈₃	1	8	yes	—
315	C₄×Q₈	C₂²×D₈₃	1	8	yes	—
316	C₄×D₄	—	83	16	no	—
317	C₄×D₄	—	83	48	no	—
318	C₄×D₄	—	83	48	no	—
319	C₄×D₄	—	83	48	no	—
320	C₄×D₄	C₂²×D₈₃	1	24	yes	—
321	C₄×D₄	C₂²×D₈₃	1	24	yes	—
322	#117	C₂²×D₈₃	1	12	yes	—
323	#117	C₂²×D₈₃	1	12	yes	—
324	C₂×C₄⋊C₄	—	83	24	no	—
325	C₂×C₄⋊C₄	C₂²×D₈₃	1	6	yes	—
326	C₂×C₂²⋊C₄	—	83	48	no	—
327	C₂×C₂²⋊C₄	C₂²×D₈₃	1	6	yes	—
328	C₂×C₄²	C₂²×D₈₃	1	3	yes	—
329	C₂×C₄²	C₂²×D₈₃	1	12	yes	—
330	C₂×C₄²	C₂²×D₈₃	1	6	yes	—
331	C₂×C₄²	C₂²×D₈₃	1	6	yes	—
332	C₂×C₄²	C₂²×D₈₃	1	6	yes	—
333	C₂×C₄²	C₂²×D₈₃	1	1	yes	characteristic
334	C₂⁴	—	83	24	no	—
335	C₂⁴	C₂³×D₈₃	1	3	yes	—
336	#41	—	166	64	no	—
337	#41	—	166	192	no	—
338	#41	—	166	96	no	—
339	#41	—	166	32	no	—
340	#41	—	166	96	no	—
341	#41	—	166	96	no	—
342	#41	C₂×D₃₃₂	1	32	yes	complemented
343	#41	C₂×D₃₃₂	1	32	yes	complemented
344	C₂×Q₈	—	83	24	no	—
345	C₂×Q₈	—	83	8	no	—
346	C₂×Q₈	—	166	64	no	—
347	C₂×Q₈	—	166	48	no	—
348	C₂×Q₈	C₂×D₃₃₂	1	8	yes	complemented
349	C₂×Q₈	C₂³×D₈₃	1	4	yes	—
350	C₂×D₄	—	332	48	no	—
351	C₂×D₄	—	83	48	no	—
352	C₂×D₄	—	83	16	no	—
353	C₂×D₄	—	83	48	no	—
354	C₂×D₄	—	83	16	no	—
355	C₂×D₄	—	83	24	no	—
356	C₂×D₄	—	83	8	no	—
357	C₂×D₄	—	166	96	no	—
358	C₂×D₄	—	166	192	no	—
359	C₂×D₄	—	166	48	no	—
360	C₂×D₄	C₂×D₃₃₂	1	24	yes	complemented
361	C₂×D₄	C₂³×D₈₃	1	12	yes	—
362	C₂²×C₄	—	4	12	no	—
363	C₂²×C₄	—	83	24	no	—
364	C₂²×C₄	—	83	48	no	—
365	C₂²×C₄	—	83	16	no	—
366	C₂²×C₄	—	166	96	no	—
367	C₂²×C₄	C₂×D₃₃₂	1	24	yes	complemented
368	C₂²×C₄	C₂³×D₈₃	1	2	yes	—
369	C₂²×C₄	C₂³×D₈₃	1	12	yes	—
370	C₂²×C₄	C₂³×D₈₃	1	12	yes	—
371	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
372	C₂²×C₄	C₂³×D₈₃	1	3	yes	—
373	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
374	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
376	C₄⋊C₄	—	83	16	no	—
377	C₄⋊C₄	—	83	48	no	—
378	C₄⋊C₄	C₂³×D₈₃	1	24	yes	—
379	C₂²⋊C₄	—	83	32	no	—
380	C₂²⋊C₄	—	83	96	no	—
381	C₂²⋊C₄	C₂³×D₈₃	1	24	yes	—
382	C₄²	C₂³×D₈₃	1	1	yes	characteristic
383	C₄²	C₂³×D₈₃	1	1	yes	characteristic
384	C₄²	C₂³×D₈₃	1	6	yes	—
385	C₄²	C₂³×D₈₃	1	12	yes	—
386	C₄²	C₂³×D₈₃	1	12	yes	—
387	C₄²	C₂³×D₈₃	1	2	yes	—
388	C₄²	C₂³×D₈₃	1	6	yes	—
389	C₂³	—	4	6	no	—
390	C₂³	—	332	48	no	—
391	C₂³	—	83	16	no	—
392	C₂³	—	166	48	no	—
393	C₂³	C₂²×D₃₃₂	1	12	yes	—
394	C₂³	C₂⁴×D₈₃	1	6	yes	—
395	C₂³	C₂⁴×D₈₃	1	1	yes	characteristic
396	Q₈	—	166	48	no	—
397	Q₈	—	166	16	no	—
398	Q₈	C₂²×D₃₃₂	1	16	yes	—
399	D₄	—	332	48	no	—
400	D₄	—	166	96	no	—
401	D₄	—	166	32	no	—
402	D₄	—	166	48	no	—
403	D₄	—	166	16	no	—
404	D₄	—	166	32	no	—
405	D₄	C₂²×D₃₃₂	1	48	yes	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	24	no	—
408	C₂×C₄	—	4	12	no	—
409	C₂×C₄	—	4	6	no	—
410	C₂×C₄	—	83	16	no	—
411	C₂×C₄	—	166	48	no	—
412	C₂×C₄	—	166	32	no	—
413	C₂×C₄	—	166	96	no	—
414	C₂×C₄	C₂²×D₃₃₂	1	24	yes	—
415	C₂×C₄	C₂²×D₃₃₂	1	4	yes	—
416	C₂×C₄	C₂²×D₃₃₂	1	24	yes	—
417	C₂×C₄	C₂²×D₃₃₂	1	12	yes	—
418	C₂×C₄	C₂⁴×D₈₃	1	2	yes	—
419	C₂×C₄	C₂⁴×D₈₃	1	12	yes	—
420	C₂×C₄	C₂⁴×D₈₃	1	1	yes	characteristic
421	C₂×C₄	C₂⁴×D₈₃	1	6	yes	—
422	C₂×C₄	C₂⁴×D₈₃	1	2	yes	—
423	C₂×C₄	C₂⁴×D₈₃	1	1	yes	characteristic
424	C₂²	—	2	2	no	—
425	C₂²	—	2	12	no	—
426	C₂²	—	4	12	no	—
427	C₂²	—	664	48	no	—
428	C₂²	—	166	16	no	—
429	C₂²	—	166	32	no	—
430	C₂²	C₂³×D₃₃₂	1	12	yes	—
431	C₂²	C₂³×D₃₃₂	1	2	yes	—
432	C₂²	C₂⁵×D₈₃	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	12	no	—
435	C₄	—	166	16	no	—
436	C₄	C₂³×D₃₃₂	1	2	yes	—
437	C₄	C₂³×D₃₃₂	1	12	yes	—
438	C₄	C₂³×D₃₃₂	1	2	yes	—
439	C₄	#19128537	1	4	yes	complemented
440	C₂	—	2	2	no	—
441	C₂	—	2	12	no	—
442	C₂	—	332	16	no	—
443	C₂	C₂⁴×D₃₃₂	1	1	yes	characteristic
444	C₂	C₂×#19128537	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₈₃
commutator, socle, cosocle	C₂²×C₈₃	C₂⁶
Frattini	C₂²	C₂⁵×D₈₃
Fitting	C₂×C₄×#41×C₈₃	C₂
hypercenter	C₂×C₄×#41	D₈₃
hypocenter	C₈₃	#62812
LCS	G ▷ C₂²×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#19128537	C₂	semidirect
2. #24921256	C₂	semidirect
3. #24921248	C₂	semidirect
4. #24921241	C₂	semidirect
5. #24921234	C₂	semidirect
6. #24921227	C₂	semidirect
7. #41×D₃₃₂	C₂	semidirect
8. #24920796	C₂	semidirect
9. C₂×#19128251	C₂	semidirect
10. C₂×C₄×#41×C₈₃	C₂	semidirect
12. C₂×#14581840	C₂²	semidirect
13. C₂×#14581839	C₂²	semidirect
14. C₂×#14581838	C₂²	semidirect
15. C₂×#14581837	C₂²	semidirect
16. C₂²×#13050590	C₂²	semidirect
17. C₂×#41×D₈₃	C₂²	semidirect
18. #19128373	C₂²	semidirect
19. Q₈×D₃₃₂	C₂²	semidirect
20. #19128363	C₂²	semidirect
21. #19128355	C₂²	semidirect
22. #19128346	C₂²	semidirect
23. D₄×D₃₃₂	C₂²	semidirect
24. #19128282	C₂²	semidirect
25. #19128277	C₂²	semidirect
26. #19128270	C₂²	semidirect
27. #19128263	C₂²	semidirect
28. #19128251	C₂²	semidirect
29. #19128251	C₂²	semidirect
30. #19128251	C₂²	semidirect
31. #19128251	C₂²	semidirect
32. #19128251	C₂²	semidirect
33. #19128251	C₂²	semidirect
34. C₂×#14581792	C₂²	semidirect
35. C₂×#14581789	C₂²	semidirect
36. C₂×#14581780	C₂²	semidirect
37. #19128213	C₂²	semidirect
38. C₂×#14581766	C₂²	semidirect
39. C₂×C₄×D₃₃₂	C₂²	semidirect
41. C₄×#41×C₈₃	C₂²	semidirect
42. C₄×#41×C₈₃	C₂²	semidirect
43. C₄×#41×C₈₃	C₂²	semidirect
44. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
45. C₂×C₄×D₄×C₈₃	C₂²	semidirect
46. C₂×#117×C₈₃	C₂²	semidirect
47. C₂²×C₄²×C₈₃	C₂²	semidirect
90. C₂×#41×C₈₃	D₄	semidirect
141. #41×C₈₃	C₂×D₄	semidirect
142. #41×C₈₃	C₂×D₄	semidirect
143. C₂×Q₈×C₈₃	C₂×D₄	semidirect
145. C₂×D₄×C₈₃	C₂×D₄	semidirect
148. C₂²×C₄×C₈₃	C₂×D₄	semidirect
215. C₄×C₈₃	#585	semidirect
232. C₂×C₄×#41	D₈₃	semidirect
233. C₈₃	#62812	semidirect
263. C₄×#41	C₂×D₈₃	semidirect
264. C₄×#41	C₂×D₈₃	semidirect
265. C₄×#41	C₂×D₈₃	semidirect
266. C₂×C₄×Q₈	C₂×D₈₃	semidirect
268. C₂×C₄×D₄	C₂×D₈₃	semidirect
269. C₂×#117	C₂×D₈₃	semidirect
270. C₂²×C₄²	C₂×D₈₃	semidirect
283. C₂×#41	D₃₃₂	semidirect
342. #41	C₂×D₃₃₂	semidirect
343. #41	C₂×D₃₃₂	semidirect
348. C₂×Q₈	C₂×D₃₃₂	semidirect
360. C₂×D₄	C₂×D₃₃₂	semidirect
367. C₂²×C₄	C₂×D₃₃₂	semidirect
439. C₄	#19128537	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19128537	2
#24921256	2
#24921248	2
#24921241	2
#24921234	2
#24921227	2
#41×D₃₃₂	2
#24920796	2
C₂×#19128251	2
C₂×C₄×#41×C₈₃	2
#62812	83