Subgroups — C₂²×#19128181 #36310992

Order 21248.

12270 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#13050590	C₂	1	1	yes	maximal, characteristic
2	C₂×#19128181	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×Dic₁₆₆	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×D₃₃₂	C₂	1	2	yes	maximal, complemented
5	C₂²×(C₂²⋊D₈₃)⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₂²×#14581750	C₂	1	2	yes	maximal, complemented
7	C₂³×C₄⋊Dic₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄⋊C₄×D₈₃	C₂	1	2	yes	maximal, complemented
9	C₂²×#117×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13050590	C₄	1	32	yes	complemented
11	C₂²×#13050590	C₂²	1	24	yes	—
12	C₂³×Dic₁₆₆	C₂²	1	1	yes	characteristic
13	C₂³×D₃₃₂	C₂²	1	1	yes	characteristic
14	C₂³×C₂²⋊D₈₃	C₂²	1	2	yes	—
15	C₂⁴×Dic₈₃	C₂²	1	2	yes	—
16	C₂³×C₄×D₈₃	C₂²	1	4	yes	—
17	C₂³×C₄×D₈₃	C₂²	1	2	yes	—
18	#19128181	C₂²	1	256	yes	direct product factor
19	C₂×C₄×Dic₁₆₆	C₂²	1	48	yes	complemented
20	C₂×C₄×D₃₃₂	C₂²	1	48	yes	complemented
21	C₂×(C₂²⋊D₈₃)⋊C₄	C₂²	1	96	yes	complemented
22	C₂×#14581750	C₂²	1	48	yes	complemented
23	C₂²×C₄⋊Dic₈₃	C₂²	1	2	yes	—
24	C₂²×C₄⋊Dic₈₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₈₃	C₂²	1	24	yes	complemented
26	C₂²×Dic₈₃⋊C₄	C₂²	1	4	yes	—
27	C₂×C₄⋊C₄×D₈₃	C₂²	1	48	yes	complemented
28	C₂²×(C₂×D₈₃)⋊C₄	C₂²	1	4	yes	—
29	C₂²×C₄×Dic₈₃	C₂²	1	4	yes	—
30	C₂⁴×C₄×C₈₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₃	C₂²	1	24	yes	complemented
32	C₂²×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₈₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₈₃	C₂²	1	2	yes	—
36	C₂⁴×D₈₃	C₂³	1	2	yes	—
37	C₂×#13050590	C₂×C₄	1	384	yes	complemented
38	C₂×#13050590	C₂³	1	64	yes	—
39	C₂²×Dic₁₆₆	C₂×C₄	1	16	yes	complemented
40	C₂²×Dic₁₆₆	C₂³	1	12	yes	—
41	C₂²×D₃₃₂	C₂×C₄	1	16	yes	complemented
42	C₂²×D₃₃₂	C₂³	1	12	yes	—
43	C₂²×C₂²⋊D₈₃	C₂×C₄	1	32	yes	complemented
44	C₂²×C₂²⋊D₈₃	C₂³	1	24	yes	—
45	C₂³×Dic₈₃	—	4	8	no	—
46	C₂³×Dic₈₃	C₂³	1	4	yes	—
47	C₂³×Dic₈₃	C₂³	1	24	yes	—
48	C₂³×Dic₈₃	C₂³	1	2	yes	—
49	C₂²×C₄×D₈₃	—	4	16	no	—
50	C₂²×C₄×D₈₃	C₂×C₄	1	32	yes	complemented
51	C₂²×C₄×D₈₃	C₂³	1	48	yes	—
52	C₂²×C₄×D₈₃	C₂³	1	24	yes	—
53	C₄×Dic₁₆₆	C₂³	1	128	yes	complemented
54	C₄×D₃₃₂	C₂³	1	128	yes	complemented
55	(C₂²⋊D₈₃)⋊C₄	C₂³	1	256	yes	complemented
56	#14581750	C₂³	1	128	yes	complemented
57	C₂×C₄⋊Dic₈₃	C₂³	1	24	yes	—
58	C₂×C₄⋊Dic₈₃	C₂³	1	24	yes	—
59	C₂×C₄⋊Dic₈₃	C₂³	1	64	yes	complemented
60	C₂×Dic₈₃⋊C₄	C₂³	1	48	yes	—
61	C₄⋊C₄×D₈₃	C₂³	1	128	yes	complemented
62	C₂×(C₂×D₈₃)⋊C₄	C₂³	1	48	yes	—
63	C₂×C₄×Dic₈₃	C₂³	1	48	yes	—
64	C₂⁵×C₈₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₃	C₂×C₄	1	16	yes	complemented
66	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₈₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₈₃	C₂³	1	12	yes	—
71	#117×C₈₃	C₂³	1	64	yes	complemented
72	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	—
73	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	—
74	C₂×C₂²⋊C₄×C₈₃	C₂³	1	24	yes	—
75	C₂×C₄²×C₈₃	C₂³	1	24	yes	—
76	C₂³×D₈₃	—	2	8	no	—
77	C₂³×D₈₃	—	2	8	no	—
78	C₂³×D₈₃	C₂²×C₄	1	16	yes	—
79	C₂³×D₈₃	C₂⁴	1	12	yes	—
80	#13050590	C₂²×C₄	1	512	yes	complemented
81	C₂×Dic₁₆₆	C₂²×C₄	1	96	yes	complemented
82	C₂×Dic₁₆₆	C₂⁴	1	16	yes	—
83	C₂×D₃₃₂	C₂²×C₄	1	96	yes	complemented
84	C₂×D₃₃₂	C₂⁴	1	16	yes	—
85	C₂×C₂²⋊D₈₃	C₂²×C₄	1	192	yes	complemented
86	C₂×C₂²⋊D₈₃	C₂⁴	1	32	yes	—
87	C₂²×Dic₈₃	—	2	16	no	—
88	C₂²×Dic₈₃	—	4	48	no	—
89	C₂²×Dic₈₃	C₂²×C₄	1	16	yes	—
90	C₂²×Dic₈₃	C₂⁴	1	24	yes	—
91	C₂²×Dic₈₃	C₂⁴	1	32	yes	—
92	C₂²×Dic₈₃	C₂⁴	1	12	yes	—
93	C₂×C₄×D₈₃	—	4	96	no	—
94	C₂×C₄×D₈₃	C₂²×C₄	1	192	yes	complemented
95	C₂×C₄×D₈₃	C₂⁴	1	64	yes	—
96	C₂×C₄×D₈₃	C₂⁴	1	32	yes	—
97	C₄⋊Dic₈₃	C₂⁴	1	32	yes	—
98	C₄⋊Dic₈₃	C₂⁴	1	32	yes	—
99	Dic₈₃⋊C₄	C₂⁴	1	64	yes	—
100	(C₂×D₈₃)⋊C₄	C₂⁴	1	64	yes	—
101	C₄×Dic₈₃	C₂⁴	1	64	yes	—
102	C₂⁴×C₈₃	—	2	4	no	—
103	C₂⁴×C₈₃	—	2	4	no	—
104	C₂⁴×C₈₃	C₂²×C₄	1	8	yes	—
105	C₂⁴×C₈₃	C₂⁴	1	6	yes	—
106	C₂⁴×C₈₃	C₂⁴	1	1	yes	characteristic
107	C₂²×C₄×C₈₃	—	2	8	no	—
108	C₂²×C₄×C₈₃	—	2	8	no	—
109	C₂²×C₄×C₈₃	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₈₃	C₂²×C₄	1	8	yes	—
111	C₂²×C₄×C₈₃	C₂²×C₄	1	96	yes	complemented
112	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
113	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
114	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
116	C₂²×C₄×C₈₃	C₂⁴	1	16	yes	—
117	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
118	C₄⋊C₄×C₈₃	C₂⁴	1	16	yes	—
119	C₂²⋊C₄×C₈₃	C₂⁴	1	32	yes	—
120	C₄²×C₈₃	C₂⁴	1	32	yes	—
121	C₂³×C₈₃	—	2	32	no	—
122	C₂³×C₈₃	—	2	12	no	—
123	C₂³×C₈₃	—	2	12	no	—
124	C₂³×C₈₃	C₂³×C₄	1	24	yes	—
125	C₂³×C₈₃	C₂³×C₄	1	4	yes	—
126	C₂³×C₈₃	H(5,𝔽₂)	1	4	yes	—
127	C₂³×C₈₃	2₋¹⁺⁴	1	4	yes	—
128	C₂³×C₈₃	C₂⁵	1	4	yes	—
129	C₂³×C₈₃	C₂⁵	1	3	yes	—
130	C₂²×D₈₃	—	2	64	no	—
131	C₂²×D₈₃	—	2	24	no	—
132	C₂²×D₈₃	—	2	24	no	—
133	C₂²×D₈₃	C₂³×C₄	1	48	yes	—
134	C₂²×D₈₃	C₂⁵	1	8	yes	—
135	C₂×C₄×C₈₃	—	2	24	no	—
136	C₂×C₄×C₈₃	—	2	24	no	—
137	C₂×C₄×C₈₃	C₂³×C₄	1	24	yes	—
138	C₂×C₄×C₈₃	C₂³×C₄	1	24	yes	—
139	C₂×C₄×C₈₃	C₂³×C₄	1	64	yes	complemented
140	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
141	C₂×C₄×C₈₃	C₂⁵	1	8	yes	—
142	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
143	C₂×C₄×C₈₃	C₂⁵	1	4	yes	—
144	C₂²⋊D₈₃	C₂³×C₄	1	128	yes	complemented
145	C₂×Dic₈₃	—	2	48	no	—
146	C₂×Dic₈₃	—	4	32	no	—
147	C₂×Dic₈₃	C₂³×C₄	1	48	yes	—
148	C₂×Dic₈₃	C₂⁵	1	16	yes	—
149	C₂×Dic₈₃	C₂⁵	1	8	yes	—
150	D₃₃₂	C₂³×C₄	1	64	yes	complemented
151	C₄×D₈₃	—	4	64	no	—
152	C₄×D₈₃	C₂³×C₄	1	128	yes	complemented
153	Dic₁₆₆	C₂³×C₄	1	64	yes	complemented
154	C₂²×C₈₃	—	2	4	no	—
155	C₂²×C₈₃	—	2	4	no	—
156	C₂²×C₈₃	—	2	48	no	—
157	C₂²×C₈₃	#520	1	16	yes	complemented
158	C₂²×C₈₃	C₂⁴×C₄	1	8	yes	—
159	C₂²×C₈₃	C₂⁴×C₄	1	6	yes	—
160	C₂²×C₈₃	C₂×H(5,𝔽₂)	1	6	yes	—
161	C₂²×C₈₃	C₂×2₋¹⁺⁴	1	6	yes	—
162	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
163	C₂×D₈₃	—	2	8	no	—
164	C₂×D₈₃	—	2	8	no	—
165	C₂×D₈₃	—	2	96	no	—
166	C₂×D₈₃	C₂⁴×C₄	1	16	yes	—
167	C₄×C₈₃	—	2	8	no	—
168	C₄×C₈₃	—	2	8	no	—
169	C₄×C₈₃	C₂⁴×C₄	1	8	yes	—
170	C₄×C₈₃	C₂⁴×C₄	1	8	yes	—
171	Dic₈₃	—	2	16	no	—
172	Dic₈₃	C₂⁴×C₄	1	16	yes	—
173	C₂²×#520	—	83	1	no	maximal, Sylow
174	C₂×C₈₃	—	2	8	no	—
175	C₂×C₈₃	C₂×#520	1	12	yes	complemented
176	C₂×C₈₃	C₂⁵×C₄	1	1	yes	characteristic
177	C₂×C₈₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₈₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
179	D₈₃	—	2	16	no	—
180	C₂³×#41	—	83	1	no	—
181	C₂×#520	—	83	48	no	—
182	C₂²×C₄×Q₈	—	83	2	no	—
183	C₂²×C₄×D₄	—	83	2	no	—
184	C₂²×C₄×D₄	—	83	4	no	—
185	C₂²×#117	—	83	2	no	—
186	C₂²×#117	D₈₃	1	1	yes	characteristic, complemented
187	C₂³×C₄⋊C₄	—	83	1	no	—
188	C₂³×C₄⋊C₄	—	83	2	no	—
189	C₈₃	C₂²×#520	1	1	yes	characteristic, complemented, Sylow
190	C₂²×#41	—	83	32	no	—
191	C₂²×#41	—	83	24	no	—
192	C₂³×Q₈	—	83	1	no	—
193	C₂³×D₄	—	83	2	no	—
194	C₂³×D₄	—	83	1	no	—
195	C₂⁴×C₄	—	83	2	no	—
196	C₂⁴×C₄	—	83	4	no	—
197	C₂⁴×C₄	—	83	2	no	—
198	C₂⁴×C₄	C₂×D₈₃	1	1	yes	characteristic
199	#520	—	83	256	no	—
200	C₂×C₄×Q₈	—	83	48	no	—
201	C₂×C₄×D₄	—	83	96	no	—
202	C₂×C₄×D₄	—	83	48	no	—
203	C₂×#117	—	83	48	no	—
204	C₂×#117	C₂×D₈₃	1	24	yes	complemented
205	C₂²×C₄⋊C₄	—	83	4	no	—
206	C₂²×C₄⋊C₄	—	83	2	no	—
207	C₂²×C₄⋊C₄	—	83	2	no	—
208	C₂²×C₄⋊C₄	—	83	24	no	—
209	C₂²×C₄⋊C₄	—	83	48	no	—
210	C₂²×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂×D₈₃	1	1	yes	characteristic
212	C₂²×C₂²⋊C₄	—	83	4	no	—
213	C₂²×C₂²⋊C₄	C₂×D₈₃	1	2	yes	—
214	C₂²×C₄²	—	83	4	no	—
215	C₂²×C₄²	C₂×D₈₃	1	2	yes	—
216	C₂⁵	—	83	2	no	—
217	C₂⁵	C₂²×D₈₃	1	1	yes	characteristic
218	C₂×#41	—	83	384	no	—
219	C₂×#41	—	83	64	no	—
220	C₂²×Q₈	—	83	16	no	—
221	C₂²×Q₈	—	83	12	no	—
222	C₂²×D₄	—	83	32	no	—
223	C₂²×D₄	—	83	24	no	—
224	C₂²×D₄	—	83	16	no	—
225	C₂²×D₄	—	83	12	no	—
226	C₂³×C₄	—	332	16	no	—
227	C₂³×C₄	—	332	8	no	—
228	C₂³×C₄	—	83	24	no	—
229	C₂³×C₄	—	83	48	no	—
230	C₂³×C₄	—	83	2	no	—
231	C₂³×C₄	—	83	32	no	—
232	C₂³×C₄	—	83	24	no	—
233	C₂³×C₄	—	83	4	no	—
234	C₂³×C₄	C₄×D₈₃	1	16	yes	complemented
235	C₂³×C₄	C₂²×D₈₃	1	2	yes	—
236	C₂³×C₄	C₂²×D₈₃	1	2	yes	—
237	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
239	C₂³×C₄	C₂²×D₈₃	1	12	yes	—
240	C₄×Q₈	—	83	128	no	—
241	C₄×D₄	—	83	256	no	—
242	C₄×D₄	—	83	128	no	—
243	#117	—	83	128	no	—
244	#117	C₂²×D₈₃	1	64	yes	complemented
245	C₂×C₄⋊C₄	—	83	24	no	—
246	C₂×C₄⋊C₄	—	83	48	no	—
247	C₂×C₄⋊C₄	—	83	24	no	—
248	C₂×C₄⋊C₄	—	83	64	no	—
249	C₂×C₄⋊C₄	—	83	128	no	—
250	C₂×C₄⋊C₄	C₂²×D₈₃	1	12	yes	—
251	C₂×C₄⋊C₄	C₂²×D₈₃	1	12	yes	—
252	C₂×C₂²⋊C₄	—	83	48	no	—
253	C₂×C₂²⋊C₄	C₂²×D₈₃	1	24	yes	—
254	C₂×C₄²	—	83	48	no	—
255	C₂×C₄²	C₂²×D₈₃	1	24	yes	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	83	16	no	—
259	C₂⁴	—	83	12	no	—
260	C₂⁴	—	166	8	no	—
261	C₂⁴	—	166	8	no	—
262	C₂⁴	C₂×C₄×D₈₃	1	8	yes	—
263	C₂⁴	C₂³×D₈₃	1	6	yes	—
264	C₂⁴	C₂³×D₈₃	1	1	yes	characteristic
265	#41	—	83	512	no	—
266	C₂×Q₈	—	83	96	no	—
267	C₂×Q₈	—	83	16	no	—
268	C₂×D₄	—	83	192	no	—
269	C₂×D₄	—	83	32	no	—
270	C₂×D₄	—	83	96	no	—
271	C₂×D₄	—	83	16	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	332	96	no	—
275	C₂²×C₄	—	332	48	no	—
276	C₂²×C₄	—	83	32	no	—
277	C₂²×C₄	—	83	64	no	—
278	C₂²×C₄	—	83	16	no	—
279	C₂²×C₄	—	83	12	no	—
280	C₂²×C₄	—	83	192	no	—
281	C₂²×C₄	—	83	32	no	—
282	C₂²×C₄	—	83	24	no	—
283	C₂²×C₄	—	166	16	no	—
284	C₂²×C₄	C₂×C₄×D₈₃	1	8	yes	—
285	C₂²×C₄	C₂×C₄×D₈₃	1	8	yes	—
286	C₂²×C₄	C₂×C₄×D₈₃	1	96	yes	complemented
287	C₂²×C₄	C₂³×D₈₃	1	12	yes	—
288	C₂²×C₄	C₂³×D₈₃	1	12	yes	—
289	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
290	C₂²×C₄	C₂³×D₈₃	1	6	yes	—
291	C₂²×C₄	C₂³×D₈₃	1	16	yes	—
292	C₄⋊C₄	—	83	32	no	—
293	C₄⋊C₄	—	83	64	no	—
294	C₄⋊C₄	—	83	32	no	—
295	C₄⋊C₄	C₂³×D₈₃	1	16	yes	—
296	C₄⋊C₄	C₂³×D₈₃	1	16	yes	—
297	C₂²⋊C₄	—	83	64	no	—
298	C₂²⋊C₄	C₂³×D₈₃	1	32	yes	—
299	C₄²	—	83	64	no	—
300	C₄²	C₂³×D₈₃	1	32	yes	—
301	C₂³	—	2	32	no	—
302	C₂³	—	2	12	no	—
303	C₂³	—	2	12	no	—
304	C₂³	—	83	48	no	—
305	C₂³	—	83	8	no	—
306	C₂³	—	166	64	no	—
307	C₂³	—	166	24	no	—
308	C₂³	—	166	24	no	—
309	C₂³	C₂²×C₄×D₈₃	1	24	yes	—
310	C₂³	C₂²×C₄×D₈₃	1	4	yes	—
311	C₂³	#14581838	1	4	yes	—
312	C₂³	#14581839	1	4	yes	—
313	C₂³	C₂⁴×D₈₃	1	4	yes	—
314	C₂³	C₂⁴×D₈₃	1	3	yes	—
315	Q₈	—	83	64	no	—
316	D₄	—	83	128	no	—
317	D₄	—	83	64	no	—
318	C₂×C₄	—	2	24	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	332	64	no	—
321	C₂×C₄	—	332	32	no	—
322	C₂×C₄	—	83	48	no	—
323	C₂×C₄	—	83	8	no	—
324	C₂×C₄	—	83	128	no	—
325	C₂×C₄	—	83	16	no	—
326	C₂×C₄	—	166	48	no	—
327	C₂×C₄	C₂²×C₄×D₈₃	1	24	yes	—
328	C₂×C₄	C₂²×C₄×D₈₃	1	24	yes	—
329	C₂×C₄	C₂²×C₄×D₈₃	1	64	yes	complemented
330	C₂×C₄	C₂⁴×D₈₃	1	8	yes	—
331	C₂×C₄	C₂⁴×D₈₃	1	8	yes	—
332	C₂×C₄	C₂⁴×D₈₃	1	4	yes	—
333	C₂×C₄	C₂⁴×D₈₃	1	4	yes	—
334	C₂²	—	2	48	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	83	16	no	—
338	C₂²	—	166	96	no	—
339	C₂²	—	166	8	no	—
340	C₂²	—	166	8	no	—
341	C₂²	#19128181	1	16	yes	direct product factor
342	C₂²	C₂³×C₄×D₈₃	1	8	yes	—
343	C₂²	C₂³×C₄×D₈₃	1	6	yes	—
344	C₂²	C₂×#14581838	1	6	yes	—
345	C₂²	C₂×#14581839	1	6	yes	—
346	C₂²	C₂⁵×D₈₃	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	8	no	—
349	C₄	—	83	16	no	—
350	C₄	—	166	16	no	—
351	C₄	C₂³×C₄×D₈₃	1	8	yes	—
352	C₄	C₂³×C₄×D₈₃	1	8	yes	—
353	C₂	—	2	8	no	—
354	C₂	—	166	16	no	—
355	C₂	C₂×#19128181	1	12	yes	direct product factor
356	C₂	C₂⁴×C₄×D₈₃	1	1	yes	characteristic
357	C₂	C₂²×#14581838	1	1	yes	characteristic
358	C₂	C₂²×#14581839	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₈₃
commutator	C₂×C₈₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₈₃
Fitting	C₂²×#117×C₈₃	C₂
socle	C₂⁴×C₈₃	C₂⁴
prime radical	C₂³×#13050590	C₂
cosocle	C₂²×C₈₃	C₂⁶
hypercenter	C₂²×#117	D₈₃
hypocenter	C₈₃	C₂²×#520
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
2. C₂×#19128181	C₂	direct (N × H)
3. C₂²×C₄×Dic₁₆₆	C₂	semidirect
4. C₂²×C₄×D₃₃₂	C₂	semidirect
5. C₂²×(C₂²⋊D₈₃)⋊C₄	C₂	semidirect
6. C₂²×#14581750	C₂	semidirect
7. C₂³×C₄⋊Dic₈₃	C₂	semidirect
8. C₂²×C₄⋊C₄×D₈₃	C₂	semidirect
9. C₂²×#117×C₈₃	C₂	semidirect
10. C₂²×#13050590	C₄	semidirect
18. #19128181	C₂²	direct (N × H)
19. C₂×C₄×Dic₁₆₆	C₂²	semidirect
20. C₂×C₄×D₃₃₂	C₂²	semidirect
21. C₂×(C₂²⋊D₈₃)⋊C₄	C₂²	semidirect
22. C₂×#14581750	C₂²	semidirect
25. C₂²×C₄⋊Dic₈₃	C₂²	semidirect
27. C₂×C₄⋊C₄×D₈₃	C₂²	semidirect
31. C₂×#117×C₈₃	C₂²	semidirect
37. C₂×#13050590	C₂×C₄	semidirect
39. C₂²×Dic₁₆₆	C₂×C₄	semidirect
41. C₂²×D₃₃₂	C₂×C₄	semidirect
43. C₂²×C₂²⋊D₈₃	C₂×C₄	semidirect
50. C₂²×C₄×D₈₃	C₂×C₄	semidirect
53. C₄×Dic₁₆₆	C₂³	semidirect
54. C₄×D₃₃₂	C₂³	semidirect
55. (C₂²⋊D₈₃)⋊C₄	C₂³	semidirect
56. #14581750	C₂³	semidirect
59. C₂×C₄⋊Dic₈₃	C₂³	semidirect
61. C₄⋊C₄×D₈₃	C₂³	semidirect
65. C₂³×C₄×C₈₃	C₂×C₄	semidirect
71. #117×C₈₃	C₂³	semidirect
80. #13050590	C₂²×C₄	semidirect
81. C₂×Dic₁₆₆	C₂²×C₄	semidirect
83. C₂×D₃₃₂	C₂²×C₄	semidirect
85. C₂×C₂²⋊D₈₃	C₂²×C₄	semidirect
94. C₂×C₄×D₈₃	C₂²×C₄	semidirect
111. C₂²×C₄×C₈₃	C₂²×C₄	semidirect
139. C₂×C₄×C₈₃	C₂³×C₄	semidirect
144. C₂²⋊D₈₃	C₂³×C₄	semidirect
150. D₃₃₂	C₂³×C₄	semidirect
152. C₄×D₈₃	C₂³×C₄	semidirect
153. Dic₁₆₆	C₂³×C₄	semidirect
157. C₂²×C₈₃	#520	semidirect
175. C₂×C₈₃	C₂×#520	semidirect
186. C₂²×#117	D₈₃	semidirect
189. C₈₃	C₂²×#520	semidirect
204. C₂×#117	C₂×D₈₃	semidirect
234. C₂³×C₄	C₄×D₈₃	semidirect
244. #117	C₂²×D₈₃	semidirect
286. C₂²×C₄	C₂×C₄×D₈₃	semidirect
329. C₂×C₄	C₂²×C₄×D₈₃	semidirect
341. C₂²	#19128181	direct (N × H)
355. C₂	C₂×#19128181	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#13050590	2
C₂×#19128181	2
C₂²×C₄×Dic₁₆₆	2
C₂²×C₄×D₃₃₂	2
C₂²×(C₂²⋊D₈₃)⋊C₄	2
C₂²×#14581750	2
C₂³×C₄⋊Dic₈₃	2
C₂²×C₄⋊C₄×D₈₃	2
C₂²×#117×C₈₃	2
C₂²×#520	83

Subgroups — C22×#19128181 #36310992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19128181 #36310992