Subgroups — C₂×C₈₃×#3444 #35290492

Order 21248.

8518 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₃×#3444	C₂	1	32	yes	maximal, direct product factor
2	C₂×#533×C₈₃	C₂	1	3	yes	maximal, complemented
3	C₂×#532×C₈₃	C₂	1	3	yes	maximal, complemented
4	C₂×#529×C₈₃	C₂	1	12	yes	maximal, complemented
5	C₂×#525×C₈₃	C₂	1	6	yes	maximal, complemented
6	C₂×C₄×#41×C₈₃	C₂	1	6	yes	maximal, complemented
7	C₂³×C₄²×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₈₃	C₂²	1	6	yes	—
9	C₂⁴×C₄×C₈₃	C₂²	1	3	yes	—
10	#533×C₈₃	C₂²	1	48	yes	complemented
11	#532×C₈₃	C₂²	1	48	yes	complemented
12	C₂×C₄⋊Q₈×C₈₃	C₂²	1	3	yes	complemented
13	C₂×#127×C₈₃	C₂²	1	1	yes	characteristic, complemented
14	#529×C₈₃	C₂²	1	192	yes	complemented
15	C₂×#126×C₈₃	C₂²	1	8	yes	complemented
16	C₂×#125×C₈₃	C₂²	1	6	yes	complemented
17	C₂×#124×C₈₃	C₂²	1	6	yes	complemented
18	#525×C₈₃	C₂²	1	96	yes	complemented
19	C₂×#123×C₈₃	C₂²	1	12	yes	—
20	C₂×C₂²⋊Q₈×C₈₃	C₂²	1	12	yes	—
21	C₂×#121×C₈₃	C₂²	1	12	yes	—
22	C₂×#120×C₈₃	C₂²	1	4	yes	—
23	C₄×#41×C₈₃	C₂²	1	96	yes	complemented
24	C₂×C₄×Q₈×C₈₃	C₂²	1	12	yes	complemented
25	C₂×C₄×D₄×C₈₃	C₂²	1	24	yes	—
26	C₂×C₄×D₄×C₈₃	C₂²	1	12	yes	complemented
27	C₂×#117×C₈₃	C₂²	1	6	yes	—
28	C₂×#117×C₈₃	C₂²	1	12	yes	complemented
29	C₂²×C₄²×C₈₃	C₂²	1	6	yes	—
30	C₂²×C₄²×C₈₃	C₂²	1	3	yes	—
31	C₂²×C₄²×C₈₃	C₂²	1	3	yes	—
32	C₂²×C₄²×C₈₃	C₂²	1	16	yes	complemented
33	C₂²×C₄²×C₈₃	C₂²	1	4	yes	complemented
34	C₂⁵×C₈₃	C₂³	1	1	yes	characteristic
35	C₂×#41×C₈₃	—	2	48	no	—
36	C₂×#41×C₈₃	C₂³	1	48	yes	—
37	C₂²×Q₈×C₈₃	C₂³	1	6	yes	—
38	C₂²×D₄×C₈₃	C₂³	1	12	yes	—
39	C₂²×D₄×C₈₃	C₂³	1	6	yes	—
40	C₂³×C₄×C₈₃	—	2	24	no	—
41	C₂³×C₄×C₈₃	C₂³	1	6	yes	—
42	C₂³×C₄×C₈₃	C₂³	1	6	yes	—
43	C₂³×C₄×C₈₃	C₂³	1	3	yes	—
44	C₂³×C₄×C₈₃	C₂³	1	24	yes	—
45	C₂³×C₄×C₈₃	C₂³	1	12	yes	—
46	C₂³×C₄×C₈₃	C₂³	1	3	yes	—
47	C₄⋊Q₈×C₈₃	C₂³	1	24	yes	complemented
48	#127×C₈₃	C₂³	1	8	yes	complemented
49	#126×C₈₃	C₂³	1	64	yes	complemented
50	#125×C₈₃	C₂³	1	48	yes	complemented
51	#124×C₈₃	C₂³	1	48	yes	complemented
52	#123×C₈₃	C₂³	1	96	yes	—
53	C₂²⋊Q₈×C₈₃	C₂³	1	96	yes	—
54	#121×C₈₃	C₂³	1	96	yes	—
55	#120×C₈₃	C₂³	1	32	yes	—
56	C₄×Q₈×C₈₃	C₂³	1	96	yes	complemented
57	C₄×D₄×C₈₃	C₂³	1	192	yes	—
58	C₄×D₄×C₈₃	C₂³	1	96	yes	complemented
59	#117×C₈₃	C₂³	1	48	yes	—
60	#117×C₈₃	C₂³	1	96	yes	complemented
61	C₂×C₄⋊C₄×C₈₃	C₂³	1	12	yes	—
62	C₂×C₄⋊C₄×C₈₃	C₂³	1	24	yes	—
63	C₂×C₂²⋊C₄×C₈₃	C₂³	1	12	yes	—
64	C₂×C₂²⋊C₄×C₈₃	C₂³	1	24	yes	—
65	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
66	C₂×C₄²×C₈₃	C₂³	1	6	yes	—
67	C₂×C₄²×C₈₃	C₂³	1	3	yes	—
68	C₂×C₄²×C₈₃	C₂³	1	2	yes	—
69	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₈₃	C₂³	1	24	yes	—
71	C₂×C₄²×C₈₃	C₂³	1	48	yes	—
72	C₂×C₄²×C₈₃	C₂³	1	24	yes	—
73	C₂×C₄²×C₈₃	C₂³	1	12	yes	—
74	C₂×C₄²×C₈₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₈₃	C₂³	1	32	yes	complemented
76	C₂⁴×C₈₃	—	2	12	no	—
77	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
78	C₂⁴×C₈₃	C₂⁴	1	4	yes	—
79	C₂⁴×C₈₃	C₂⁴	1	3	yes	—
80	#41×C₈₃	—	2	192	no	—
81	C₂×Q₈×C₈₃	—	2	24	no	—
82	C₂×Q₈×C₈₃	C₂⁴	1	24	yes	—
83	C₂×D₄×C₈₃	—	2	48	no	—
84	C₂×D₄×C₈₃	—	2	24	no	—
85	C₂×D₄×C₈₃	C₂⁴	1	48	yes	—
86	C₂×D₄×C₈₃	C₂⁴	1	24	yes	—
87	C₂²×C₄×C₈₃	—	2	12	no	—
88	C₂²×C₄×C₈₃	—	2	24	no	—
89	C₂²×C₄×C₈₃	—	2	24	no	—
90	C₂²×C₄×C₈₃	—	2	48	no	—
91	C₂²×C₄×C₈₃	—	2	96	no	—
92	C₂²×C₄×C₈₃	#41	1	24	yes	complemented
93	C₂²×C₄×C₈₃	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₈₃	C₂⁴	1	24	yes	—
95	C₂²×C₄×C₈₃	C₂⁴	1	24	yes	—
96	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
97	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₈₃	C₂⁴	1	48	yes	—
99	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₈₃	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₈₃	C₂⁴	1	12	yes	—
102	C₄⋊C₄×C₈₃	C₂⁴	1	48	yes	—
103	C₄⋊C₄×C₈₃	C₂⁴	1	96	yes	—
104	C₂²⋊C₄×C₈₃	C₂⁴	1	48	yes	—
105	C₂²⋊C₄×C₈₃	C₂⁴	1	96	yes	—
106	C₄²×C₈₃	C₂⁴	1	12	yes	—
107	C₄²×C₈₃	C₂⁴	1	24	yes	—
108	C₄²×C₈₃	C₂⁴	1	12	yes	—
109	C₄²×C₈₃	C₂⁴	1	8	yes	—
110	C₄²×C₈₃	C₂⁴	1	4	yes	—
111	C₄²×C₈₃	C₂⁴	1	4	yes	—
112	C₄²×C₈₃	C₂⁴	1	48	yes	—
113	C₂³×C₈₃	—	2	32	no	—
114	C₂³×C₈₃	—	2	24	no	—
115	C₂³×C₈₃	—	2	12	no	—
116	C₂³×C₈₃	—	2	24	no	—
117	C₂³×C₈₃	C₂×#41	1	12	yes	—
118	C₂³×C₈₃	C₂⁵	1	8	yes	—
119	C₂³×C₈₃	C₂⁵	1	6	yes	—
120	C₂³×C₈₃	C₂⁵	1	1	yes	characteristic
121	Q₈×C₈₃	—	2	48	no	—
122	D₄×C₈₃	—	2	96	no	—
123	D₄×C₈₃	—	2	48	no	—
124	C₂×C₄×C₈₃	—	2	24	no	—
125	C₂×C₄×C₈₃	—	2	12	no	—
126	C₂×C₄×C₈₃	—	2	24	no	—
127	C₂×C₄×C₈₃	—	2	48	no	—
128	C₂×C₄×C₈₃	—	2	48	no	—
129	C₂×C₄×C₈₃	—	2	96	no	—
130	C₂×C₄×C₈₃	C₂×#41	1	12	yes	—
131	C₂×C₄×C₈₃	C₂×#41	1	12	yes	—
132	C₂×C₄×C₈₃	C₂×#41	1	48	yes	complemented
133	C₂×C₄×C₈₃	C₂⁵	1	12	yes	—
134	C₂×C₄×C₈₃	C₂⁵	1	24	yes	—
135	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
136	C₂×C₄×C₈₃	C₂⁵	1	6	yes	—
137	C₂²×C₈₃	—	2	32	no	—
138	C₂²×C₈₃	—	2	12	no	—
139	C₂²×C₈₃	—	2	24	no	—
140	C₂²×C₈₃	—	2	24	no	—
141	C₂²×C₈₃	—	4	16	no	—
142	C₂²×C₈₃	C₂²×#41	1	12	yes	—
143	C₂²×C₈₃	C₂²×#41	1	6	yes	—
144	C₂²×C₈₃	C₂⁶	1	1	yes	characteristic
145	C₄×C₈₃	—	2	12	no	—
146	C₄×C₈₃	—	2	24	no	—
147	C₄×C₈₃	C₂²×#41	1	12	yes	—
148	C₄×C₈₃	C₂²×#41	1	12	yes	—
149	C₂×#3444	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂×C₈₃	—	2	12	no	—
151	C₂×C₈₃	—	4	8	no	—
152	C₂×C₈₃	#3444	1	4	yes	direct product factor
153	C₂×C₈₃	C₂³×#41	1	3	yes	—
154	#3444	C₂×C₈₃	1	32	yes	direct product factor
155	C₂×#533	C₂×C₈₃	1	3	yes	complemented
156	C₂×#532	C₂×C₈₃	1	3	yes	complemented
157	C₂×#529	C₂×C₈₃	1	12	yes	complemented
158	C₂×#525	C₂×C₈₃	1	6	yes	complemented
159	C₂×C₄×#41	C₂×C₈₃	1	6	yes	complemented
160	C₂³×C₄²	C₂×C₈₃	1	1	yes	characteristic, complemented
161	C₈₃	C₂×#3444	1	1	yes	characteristic, direct product factor, Sylow
162	C₂²×#41	C₂²×C₈₃	1	6	yes	—
163	C₂⁴×C₄	C₂²×C₈₃	1	3	yes	—
164	#533	C₂²×C₈₃	1	48	yes	complemented
165	#532	C₂²×C₈₃	1	48	yes	complemented
166	C₂×C₄⋊Q₈	C₂²×C₈₃	1	3	yes	complemented
167	C₂×#127	C₂²×C₈₃	1	1	yes	characteristic, complemented
168	#529	C₂²×C₈₃	1	192	yes	complemented
169	C₂×#126	C₂²×C₈₃	1	8	yes	complemented
170	C₂×#125	C₂²×C₈₃	1	6	yes	complemented
171	C₂×#124	C₂²×C₈₃	1	6	yes	complemented
172	#525	C₂²×C₈₃	1	96	yes	complemented
173	C₂×#123	C₂²×C₈₃	1	12	yes	—
174	C₂×C₂²⋊Q₈	C₂²×C₈₃	1	12	yes	—
175	C₂×#121	C₂²×C₈₃	1	12	yes	—
176	C₂×#120	C₂²×C₈₃	1	4	yes	—
177	C₄×#41	C₂²×C₈₃	1	96	yes	complemented
178	C₂×C₄×Q₈	C₂²×C₈₃	1	12	yes	complemented
179	C₂×C₄×D₄	C₂²×C₈₃	1	24	yes	—
180	C₂×C₄×D₄	C₂²×C₈₃	1	12	yes	complemented
181	C₂×#117	C₂²×C₈₃	1	6	yes	—
182	C₂×#117	C₂²×C₈₃	1	12	yes	complemented
183	C₂²×C₄²	C₂²×C₈₃	1	3	yes	—
184	C₂²×C₄²	C₂²×C₈₃	1	6	yes	—
185	C₂²×C₄²	C₂²×C₈₃	1	3	yes	—
186	C₂²×C₄²	C₂²×C₈₃	1	16	yes	complemented
187	C₂²×C₄²	C₂²×C₈₃	1	4	yes	complemented
188	C₂⁵	C₂³×C₈₃	1	1	yes	characteristic
189	C₂×#41	—	2	48	no	—
190	C₂×#41	C₂³×C₈₃	1	48	yes	—
191	C₂²×Q₈	C₂³×C₈₃	1	6	yes	—
192	C₂²×D₄	C₂³×C₈₃	1	12	yes	—
193	C₂²×D₄	C₂³×C₈₃	1	6	yes	—
194	C₂³×C₄	—	2	24	no	—
195	C₂³×C₄	C₂³×C₈₃	1	12	yes	—
196	C₂³×C₄	C₂³×C₈₃	1	6	yes	—
197	C₂³×C₄	C₂³×C₈₃	1	6	yes	—
198	C₂³×C₄	C₂³×C₈₃	1	3	yes	—
199	C₂³×C₄	C₂³×C₈₃	1	24	yes	—
200	C₂³×C₄	C₂³×C₈₃	1	3	yes	—
201	C₄⋊Q₈	C₂³×C₈₃	1	24	yes	complemented
202	#127	C₂³×C₈₃	1	8	yes	complemented
203	#126	C₂³×C₈₃	1	64	yes	complemented
204	#125	C₂³×C₈₃	1	48	yes	complemented
205	#124	C₂³×C₈₃	1	48	yes	complemented
206	#123	C₂³×C₈₃	1	96	yes	—
207	C₂²⋊Q₈	C₂³×C₈₃	1	96	yes	—
208	#121	C₂³×C₈₃	1	96	yes	—
209	#120	C₂³×C₈₃	1	32	yes	—
210	C₄×Q₈	C₂³×C₈₃	1	96	yes	complemented
211	C₄×D₄	C₂³×C₈₃	1	192	yes	—
212	C₄×D₄	C₂³×C₈₃	1	96	yes	complemented
213	#117	C₂³×C₈₃	1	48	yes	—
214	#117	C₂³×C₈₃	1	96	yes	complemented
215	C₂×C₄⋊C₄	C₂³×C₈₃	1	12	yes	—
216	C₂×C₄⋊C₄	C₂³×C₈₃	1	24	yes	—
217	C₂×C₂²⋊C₄	C₂³×C₈₃	1	12	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₈₃	1	24	yes	—
219	C₂×C₄²	C₂³×C₈₃	1	12	yes	—
220	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
221	C₂×C₄²	C₂³×C₈₃	1	6	yes	—
222	C₂×C₄²	C₂³×C₈₃	1	24	yes	—
223	C₂×C₄²	C₂³×C₈₃	1	3	yes	—
224	C₂×C₄²	C₂³×C₈₃	1	2	yes	—
225	C₂×C₄²	C₂³×C₈₃	1	48	yes	—
226	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₈₃	1	24	yes	—
228	C₂×C₄²	C₂³×C₈₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₈₃	1	32	yes	complemented
230	C₂⁴	—	2	12	no	—
231	C₂⁴	C₂⁴×C₈₃	1	4	yes	—
232	C₂⁴	C₂⁴×C₈₃	1	4	yes	—
233	C₂⁴	C₂⁴×C₈₃	1	3	yes	—
234	#41	—	2	192	no	—
235	C₂×Q₈	—	2	24	no	—
236	C₂×Q₈	C₂⁴×C₈₃	1	24	yes	—
237	C₂×D₄	—	2	48	no	—
238	C₂×D₄	—	2	24	no	—
239	C₂×D₄	C₂⁴×C₈₃	1	48	yes	—
240	C₂×D₄	C₂⁴×C₈₃	1	24	yes	—
241	C₂²×C₄	—	2	12	no	—
242	C₂²×C₄	—	2	24	no	—
243	C₂²×C₄	—	2	24	no	—
244	C₂²×C₄	—	2	48	no	—
245	C₂²×C₄	—	2	96	no	—
246	C₂²×C₄	#41×C₈₃	1	24	yes	complemented
247	C₂²×C₄	C₂⁴×C₈₃	1	6	yes	—
248	C₂²×C₄	C₂⁴×C₈₃	1	24	yes	—
249	C₂²×C₄	C₂⁴×C₈₃	1	24	yes	—
250	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
251	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
252	C₂²×C₄	C₂⁴×C₈₃	1	48	yes	—
253	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
254	C₂²×C₄	C₂⁴×C₈₃	1	3	yes	—
255	C₂²×C₄	C₂⁴×C₈₃	1	12	yes	—
256	C₄⋊C₄	C₂⁴×C₈₃	1	48	yes	—
257	C₄⋊C₄	C₂⁴×C₈₃	1	96	yes	—
258	C₂²⋊C₄	C₂⁴×C₈₃	1	48	yes	—
259	C₂²⋊C₄	C₂⁴×C₈₃	1	96	yes	—
260	C₄²	C₂⁴×C₈₃	1	4	yes	—
261	C₄²	C₂⁴×C₈₃	1	12	yes	—
262	C₄²	C₂⁴×C₈₃	1	24	yes	—
263	C₄²	C₂⁴×C₈₃	1	12	yes	—
264	C₄²	C₂⁴×C₈₃	1	8	yes	—
265	C₄²	C₂⁴×C₈₃	1	4	yes	—
266	C₄²	C₂⁴×C₈₃	1	48	yes	—
267	C₂³	—	2	32	no	—
268	C₂³	—	2	24	no	—
269	C₂³	—	2	12	no	—
270	C₂³	—	2	24	no	—
271	C₂³	C₂×#41×C₈₃	1	12	yes	—
272	C₂³	C₂⁵×C₈₃	1	8	yes	—
273	C₂³	C₂⁵×C₈₃	1	6	yes	—
274	C₂³	C₂⁵×C₈₃	1	1	yes	characteristic
275	Q₈	—	2	48	no	—
276	D₄	—	2	96	no	—
277	D₄	—	2	48	no	—
278	C₂×C₄	—	2	24	no	—
279	C₂×C₄	—	2	12	no	—
280	C₂×C₄	—	2	24	no	—
281	C₂×C₄	—	2	48	no	—
282	C₂×C₄	—	2	48	no	—
283	C₂×C₄	—	2	96	no	—
284	C₂×C₄	C₂×#41×C₈₃	1	12	yes	—
285	C₂×C₄	C₂×#41×C₈₃	1	12	yes	—
286	C₂×C₄	C₂×#41×C₈₃	1	48	yes	complemented
287	C₂×C₄	C₂⁵×C₈₃	1	12	yes	—
288	C₂×C₄	C₂⁵×C₈₃	1	24	yes	—
289	C₂×C₄	C₂⁵×C₈₃	1	6	yes	—
290	C₂×C₄	C₂⁵×C₈₃	1	6	yes	—
291	C₂²	—	2	32	no	—
292	C₂²	—	2	12	no	—
293	C₂²	—	2	24	no	—
294	C₂²	—	2	24	no	—
295	C₂²	—	4	16	no	—
296	C₂²	C₂²×#41×C₈₃	1	12	yes	—
297	C₂²	C₂²×#41×C₈₃	1	6	yes	—
298	C₂²	C₂⁶×C₈₃	1	1	yes	characteristic
299	C₄	—	2	12	no	—
300	C₄	—	2	24	no	—
301	C₄	C₂²×#41×C₈₃	1	12	yes	—
302	C₄	C₂²×#41×C₈₃	1	12	yes	—
303	C₂	—	2	12	no	—
304	C₂	—	4	8	no	—
305	C₂	C₈₃×#3444	1	4	yes	direct product factor
306	C₂	C₂³×#41×C₈₃	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₈₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₃
socle	C₂³×C₈₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₈₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₃×#3444	C₂	direct (N × H)
2. C₂×#533×C₈₃	C₂	semidirect
3. C₂×#532×C₈₃	C₂	semidirect
4. C₂×#529×C₈₃	C₂	semidirect
5. C₂×#525×C₈₃	C₂	semidirect
6. C₂×C₄×#41×C₈₃	C₂	semidirect
7. C₂³×C₄²×C₈₃	C₂	semidirect
10. #533×C₈₃	C₂²	semidirect
11. #532×C₈₃	C₂²	semidirect
12. C₂×C₄⋊Q₈×C₈₃	C₂²	semidirect
13. C₂×#127×C₈₃	C₂²	semidirect
14. #529×C₈₃	C₂²	semidirect
15. C₂×#126×C₈₃	C₂²	semidirect
16. C₂×#125×C₈₃	C₂²	semidirect
17. C₂×#124×C₈₃	C₂²	semidirect
18. #525×C₈₃	C₂²	semidirect
23. C₄×#41×C₈₃	C₂²	semidirect
24. C₂×C₄×Q₈×C₈₃	C₂²	semidirect
26. C₂×C₄×D₄×C₈₃	C₂²	semidirect
28. C₂×#117×C₈₃	C₂²	semidirect
32. C₂²×C₄²×C₈₃	C₂²	semidirect
33. C₂²×C₄²×C₈₃	C₂²	semidirect
47. C₄⋊Q₈×C₈₃	C₂³	semidirect
48. #127×C₈₃	C₂³	semidirect
49. #126×C₈₃	C₂³	semidirect
50. #125×C₈₃	C₂³	semidirect
51. #124×C₈₃	C₂³	semidirect
56. C₄×Q₈×C₈₃	C₂³	semidirect
58. C₄×D₄×C₈₃	C₂³	semidirect
60. #117×C₈₃	C₂³	semidirect
75. C₂×C₄²×C₈₃	C₂³	semidirect
92. C₂²×C₄×C₈₃	#41	semidirect
132. C₂×C₄×C₈₃	C₂×#41	semidirect
149. C₂×#3444	C₈₃	direct (N × H)
152. C₂×C₈₃	#3444	direct (N × H)
154. #3444	C₂×C₈₃	direct (N × H)
155. C₂×#533	C₂×C₈₃	semidirect
156. C₂×#532	C₂×C₈₃	semidirect
157. C₂×#529	C₂×C₈₃	semidirect
158. C₂×#525	C₂×C₈₃	semidirect
159. C₂×C₄×#41	C₂×C₈₃	semidirect
160. C₂³×C₄²	C₂×C₈₃	semidirect
161. C₈₃	C₂×#3444	direct (N × H)
164. #533	C₂²×C₈₃	semidirect
165. #532	C₂²×C₈₃	semidirect
166. C₂×C₄⋊Q₈	C₂²×C₈₃	semidirect
167. C₂×#127	C₂²×C₈₃	semidirect
168. #529	C₂²×C₈₃	semidirect
169. C₂×#126	C₂²×C₈₃	semidirect
170. C₂×#125	C₂²×C₈₃	semidirect
171. C₂×#124	C₂²×C₈₃	semidirect
172. #525	C₂²×C₈₃	semidirect
177. C₄×#41	C₂²×C₈₃	semidirect
178. C₂×C₄×Q₈	C₂²×C₈₃	semidirect
180. C₂×C₄×D₄	C₂²×C₈₃	semidirect
182. C₂×#117	C₂²×C₈₃	semidirect
186. C₂²×C₄²	C₂²×C₈₃	semidirect
187. C₂²×C₄²	C₂²×C₈₃	semidirect
201. C₄⋊Q₈	C₂³×C₈₃	semidirect
202. #127	C₂³×C₈₃	semidirect
203. #126	C₂³×C₈₃	semidirect
204. #125	C₂³×C₈₃	semidirect
205. #124	C₂³×C₈₃	semidirect
210. C₄×Q₈	C₂³×C₈₃	semidirect
212. C₄×D₄	C₂³×C₈₃	semidirect
214. #117	C₂³×C₈₃	semidirect
229. C₂×C₄²	C₂³×C₈₃	semidirect
246. C₂²×C₄	#41×C₈₃	semidirect
286. C₂×C₄	C₂×#41×C₈₃	semidirect
305. C₂	C₈₃×#3444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₃×#3444	2
C₂×#533×C₈₃	2
C₂×#532×C₈₃	2
C₂×#529×C₈₃	2
C₂×#525×C₈₃	2
C₂×C₄×#41×C₈₃	2
C₂³×C₄²×C₈₃	2
C₂×#3444	83

Subgroups — C2×C83×#3444 #35290492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₃×#3444 #35290492