Subgroups — #35310315

Order 21248.

766 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14581728	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14581702	C₂	1	1	yes	maximal, characteristic
3	C₂×#19127465	C₂	1	2	yes	maximal
4	#24907156	C₂	1	2	yes	maximal
5	C₂²×#108×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13050574	C₂²	1	2	yes	—
7	C₂³×C₈₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₈₃	C₂²	1	1	yes	characteristic
9	C₂×#14581728	—	2	2	no	—
10	C₂×#14581728	—	2	2	no	—
11	C₂×#14581728	C₄	1	4	yes	complemented
12	C₂×#14581702	—	2	2	no	—
13	C₂×#14581702	—	2	2	no	—
14	C₂×#14581702	C₄	1	4	yes	—
15	#19127465	—	2	4	no	—
16	#19127455	—	2	4	no	—
17	C₂²×M₁₆×C₈₃	C₂²	1	2	yes	—
18	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
19	C₂×#108×C₈₃	—	2	2	no	—
20	C₂×#108×C₈₃	—	2	2	no	—
21	C₂×#108×C₈₃	C₄	1	4	yes	complemented
22	C₂³×Dic₈₃	Q₈	1	2	yes	—
23	C₂×#13050574	—	2	2	no	—
24	C₂×#13050574	—	2	2	no	—
25	C₂×#13050574	—	2	2	no	—
26	C₂×#13050574	—	2	2	no	—
27	C₂×#13050574	—	2	2	no	—
28	C₂×#13050574	C₂×C₄	1	4	yes	—
29	C₂²×C₈₃⋊C₈	—	2	1	no	—
30	C₂²×C₈₃⋊C₈	—	2	1	no	—
31	C₂²×C₈₃⋊C₈	—	2	2	no	—
32	C₂²×C₈₃⋊C₈	—	2	1	no	—
33	C₂²×C₈₃⋊C₈	—	2	1	no	—
34	C₂²×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
35	C₂²×C₈₃⋊C₈	D₄	1	2	yes	—
36	C₂²×C₈₃⋊C₈	Q₈	1	2	yes	—
37	C₂×C₄×Dic₈₃	—	2	1	no	—
38	C₂×C₄×Dic₈₃	—	2	1	no	—
39	C₂×C₄×Dic₈₃	—	2	1	no	—
40	C₂×C₄×Dic₈₃	—	2	1	no	—
41	C₂×C₄×Dic₈₃	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₈₃	D₄	1	2	yes	—
43	#14581728	—	2	8	no	—
44	#14581702	—	2	8	no	—
45	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₈₃	—	2	2	no	—
47	C₂×M₁₆×C₈₃	—	2	2	no	—
48	C₂×M₁₆×C₈₃	—	2	2	no	—
49	C₂×M₁₆×C₈₃	—	2	2	no	—
50	C₂×M₁₆×C₈₃	—	2	2	no	—
51	C₂×M₁₆×C₈₃	C₂×C₄	1	4	yes	—
52	C₂²×C₈×C₈₃	—	2	2	no	—
53	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
56	C₂²×C₈×C₈₃	D₄	1	2	yes	—
57	C₂²×C₈×C₈₃	D₄	1	2	yes	—
58	C₂²×C₈×C₈₃	D₄	1	2	yes	—
59	C₂²×C₈×C₈₃	Q₈	1	2	yes	—
60	#108×C₈₃	—	2	8	no	—
61	C₂²×Dic₈₃	—	2	2	no	—
62	C₂²×Dic₈₃	—	2	2	no	—
63	C₂²×Dic₈₃	—	4	4	no	—
64	C₂²×Dic₈₃	C₄⋊C₄	1	4	yes	—
65	#13050574	—	2	4	no	—
66	#13050574	—	2	4	no	—
67	#13050574	—	4	2	no	—
68	#13050574	—	4	2	no	—
69	C₂×C₈₃⋊C₈	—	2	2	no	—
70	C₂×C₈₃⋊C₈	—	2	2	no	—
71	C₂×C₈₃⋊C₈	—	2	2	no	—
72	C₂×C₈₃⋊C₈	—	2	2	no	—
73	C₂×C₈₃⋊C₈	—	2	2	no	—
74	C₂×C₈₃⋊C₈	—	2	2	no	—
75	C₂×C₈₃⋊C₈	—	2	4	no	—
76	C₂×C₈₃⋊C₈	—	4	2	no	—
77	C₂×C₈₃⋊C₈	—	4	2	no	—
78	C₂×C₈₃⋊C₈	C₄⋊C₄	1	4	yes	—
79	C₄×Dic₈₃	—	2	2	no	—
80	C₄×Dic₈₃	—	2	2	no	—
81	C₄×Dic₈₃	—	2	2	no	—
82	C₄×Dic₈₃	—	2	2	no	—
83	C₂⁴×C₈₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
94	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
98	M₁₆×C₈₃	—	2	4	no	—
99	M₁₆×C₈₃	—	2	4	no	—
100	M₁₆×C₈₃	—	4	2	no	—
101	M₁₆×C₈₃	—	4	2	no	—
102	C₂×C₈×C₈₃	—	2	4	no	—
103	C₂×C₈×C₈₃	—	4	2	no	—
104	C₂×C₈×C₈₃	—	4	2	no	—
105	C₂×C₈×C₈₃	C₄²	1	4	yes	—
106	C₂×C₈×C₈₃	C₂²⋊C₄	1	4	yes	—
107	C₂×C₈×C₈₃	C₂²⋊C₄	1	4	yes	—
108	C₂×C₈×C₈₃	C₂²⋊C₄	1	4	yes	—
109	C₂×C₈×C₈₃	C₄⋊C₄	1	4	yes	—
110	C₂×C₈×C₈₃	C₄⋊C₄	1	4	yes	—
111	C₂×C₈×C₈₃	C₄⋊C₄	1	4	yes	—
112	C₂³×C₈₃	—	2	4	no	—
113	C₂³×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂³×C₈₃	C₄×Q₈	1	1	yes	characteristic
115	C₂³×C₈₃	C₄×Q₈	1	1	yes	characteristic
116	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
117	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
118	C₂³×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
119	C₂³×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
120	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
121	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
123	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
129	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
130	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
133	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
134	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
137	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
138	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
139	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
140	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
143	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
144	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
145	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
146	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
148	C₂×Dic₈₃	—	2	4	no	—
149	C₂×Dic₈₃	—	2	8	no	—
150	C₂×Dic₈₃	—	4	4	no	—
151	C₂×Dic₈₃	—	4	4	no	—
152	C₈×C₈₃	—	4	4	no	—
153	C₈×C₈₃	#95	1	8	yes	—
154	C₈₃⋊C₈	—	2	4	no	—
155	C₈₃⋊C₈	—	4	4	no	—
156	C₂²×C₈₃	—	2	2	no	—
157	C₂²×C₈₃	—	2	2	no	—
158	C₂²×C₈₃	—	2	2	no	—
159	C₂²×C₈₃	—	2	2	no	—
160	C₂²×C₈₃	—	2	2	no	—
161	C₂²×C₈₃	—	2	2	no	—
162	C₂²×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×C₈₃	#380	1	1	yes	characteristic
164	C₂²×C₈₃	#384	1	1	yes	characteristic
165	C₂²×C₈₃	#389	1	1	yes	characteristic
166	C₂²×C₈₃	#389	1	1	yes	characteristic
167	C₂²×C₈₃	#391	1	1	yes	characteristic
168	C₂²×C₈₃	#391	1	1	yes	characteristic
169	C₂²×C₈₃	#430	1	4	yes	—
170	C₄×C₈₃	C₂×#95	1	1	yes	characteristic
171	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
172	C₄×C₈₃	#380	1	1	yes	characteristic
173	C₄×C₈₃	#382	1	1	yes	characteristic
174	C₄×C₈₃	#389	1	1	yes	characteristic
175	C₄×C₈₃	#389	1	1	yes	characteristic
176	C₄×C₈₃	#390	1	1	yes	characteristic
177	C₄×C₈₃	#390	1	1	yes	characteristic
178	Dic₈₃	—	4	4	no	—
179	#10865	—	83	1	no	maximal, Sylow
180	C₂×C₈₃	—	2	1	no	—
181	C₂×C₈₃	—	2	1	no	—
182	C₂×C₈₃	—	2	1	no	—
183	C₂×C₈₃	—	2	1	no	—
184	C₂×C₈₃	C₄⋊#95	1	1	yes	characteristic
185	C₂×C₈₃	#1778	1	2	yes	—
186	C₂×C₈₃	#1811	1	2	yes	—
187	C₂×C₈₃	#1849	1	2	yes	—
188	C₂²×#108	—	83	1	no	—
189	C₂²×#108	D₈₃	1	1	yes	characteristic
190	C₂²×#97	—	83	1	no	—
191	C₂×#341	—	83	2	no	—
192	#1728	—	83	2	no	—
193	C₈₃	#10865	1	1	yes	characteristic, complemented, Sylow
194	C₂²×M₁₆	—	83	2	no	—
195	C₂²×M₁₆	C₂×D₈₃	1	2	yes	—
196	C₂³×C₈	—	83	1	no	—
197	C₂³×C₈	C₂×D₈₃	1	1	yes	characteristic
198	C₂²×C₄²	—	83	1	no	—
199	C₂×#108	—	2	2	no	—
200	C₂×#108	—	2	2	no	—
201	C₂×#108	—	83	4	no	—
202	C₂×#108	—	166	2	no	—
203	C₂×#108	—	166	2	no	—
204	C₂×#108	Dic₈₃	1	4	yes	complemented
205	C₂×#97	—	83	4	no	—
206	C₂×#97	—	166	2	no	—
207	C₂×#97	—	166	2	no	—
208	#341	—	166	4	no	—
209	#336	—	166	4	no	—
210	C₂³×C₄	—	83	2	no	—
211	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	83	4	no	—
218	C₂×M₁₆	—	166	2	no	—
219	C₂×M₁₆	—	166	2	no	—
220	C₂×M₁₆	—	166	2	no	—
221	C₂×M₁₆	—	166	2	no	—
222	C₂×M₁₆	—	166	2	no	—
223	C₂×M₁₆	C₂×Dic₈₃	1	4	yes	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	83	2	no	—
226	C₂²×C₈	—	83	2	no	—
227	C₂²×C₈	—	83	2	no	—
228	C₂²×C₈	—	166	2	no	—
229	C₂²×C₈	—	166	1	no	—
230	C₂²×C₈	—	166	1	no	—
231	C₂²×C₈	—	166	1	no	—
232	C₂²×C₈	—	166	1	no	—
233	C₂²×C₈	Dic₁₆₆	1	2	yes	—
234	C₂²×C₈	C₄×D₈₃	1	2	yes	—
235	C₂²×C₈	C₄×D₈₃	1	2	yes	—
236	C₂²×C₈	D₃₃₂	1	2	yes	—
237	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
238	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
239	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
240	C₂×C₄²	—	83	2	no	—
241	C₂×C₄²	—	83	2	no	—
242	C₂×C₄²	—	166	1	no	—
243	C₂×C₄²	—	166	1	no	—
244	C₂×C₄²	—	166	1	no	—
245	C₂×C₄²	—	166	1	no	—
246	#108	—	2	8	no	—
247	#108	—	166	8	no	—
248	#97	—	166	8	no	—
249	C₂⁴	Q₈×D₈₃	1	1	yes	characteristic
250	C₂²×C₄	—	332	4	no	—
251	C₂²×C₄	—	83	4	no	—
252	C₂²×C₄	—	166	2	no	—
253	C₂²×C₄	—	166	2	no	—
254	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
257	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
258	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
262	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
264	C₂²×C₄	#13050589	1	1	yes	characteristic
265	C₂²×C₄	#13050589	1	1	yes	characteristic
266	C₂²×C₄	#13050591	1	1	yes	characteristic
267	C₂²×C₄	#13050591	1	1	yes	characteristic
268	M₁₆	—	2	4	no	—
269	M₁₆	—	2	4	no	—
270	M₁₆	—	4	2	no	—
271	M₁₆	—	4	2	no	—
272	M₁₆	—	332	2	no	—
273	M₁₆	—	332	2	no	—
274	M₁₆	—	166	4	no	—
275	M₁₆	—	166	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	4	2	no	—
278	C₂×C₈	—	4	2	no	—
279	C₂×C₈	—	332	2	no	—
280	C₂×C₈	—	332	2	no	—
281	C₂×C₈	—	83	4	no	—
282	C₂×C₈	—	166	4	no	—
283	C₂×C₈	—	166	2	no	—
284	C₂×C₈	—	166	2	no	—
285	C₂×C₈	—	166	2	no	—
286	C₂×C₈	—	166	2	no	—
287	C₂×C₈	—	166	2	no	—
288	C₂×C₈	—	166	2	no	—
289	C₂×C₈	C₄×Dic₈₃	1	4	yes	—
290	C₂×C₈	(C₂×D₈₃)⋊C₄	1	4	yes	—
291	C₂×C₈	(C₂×D₈₃)⋊C₄	1	4	yes	—
292	C₂×C₈	C₂²⋊Dic₈₃	1	4	yes	—
293	C₂×C₈	Dic₈₃⋊C₄	1	4	yes	—
294	C₂×C₈	Dic₈₃⋊C₄	1	4	yes	—
295	C₂×C₈	C₄⋊Dic₈₃	1	4	yes	—
296	C₄²	—	166	2	no	—
297	C₄²	—	166	2	no	—
298	C₄²	—	166	2	no	—
299	C₄²	—	166	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	C₄⋊C₄×D₈₃	1	1	yes	characteristic
302	C₂³	#14581757	1	1	yes	characteristic
303	C₂³	Q₈×Dic₈₃	1	1	yes	characteristic
304	C₂³	#14581768	1	1	yes	characteristic
305	C₂³	#14581772	1	1	yes	characteristic
306	C₂³	#14581790	1	1	yes	characteristic
307	C₂³	#14581791	1	1	yes	characteristic
308	C₂×C₄	—	332	4	no	—
309	C₂×C₄	—	332	4	no	—
310	C₂×C₄	—	166	4	no	—
311	C₂×C₄	—	166	8	no	—
312	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
313	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
314	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
315	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
316	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
317	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
320	C₂×C₄	#14581750	1	1	yes	characteristic
321	C₂×C₄	#14581750	1	1	yes	characteristic
322	C₂×C₄	#14581754	1	1	yes	characteristic
323	C₂×C₄	#14581754	1	1	yes	characteristic
324	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
325	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
326	C₂×C₄	#14581757	1	1	yes	characteristic
327	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
328	C₂×C₄	#14581763	1	1	yes	characteristic
329	C₂×C₄	#14581763	1	1	yes	characteristic
330	C₂×C₄	#14581767	1	1	yes	characteristic
331	C₂×C₄	#14581767	1	1	yes	characteristic
332	C₂×C₄	#14581768	1	1	yes	characteristic
333	C₂×C₄	#14581772	1	1	yes	characteristic
334	C₂×C₄	#14581779	1	1	yes	characteristic
335	C₂×C₄	#14581781	1	1	yes	characteristic
336	C₂×C₄	#14581783	1	1	yes	characteristic
337	C₂×C₄	#14581783	1	1	yes	characteristic
338	C₂×C₄	#14581788	1	1	yes	characteristic
339	C₂×C₄	#14581791	1	1	yes	characteristic
340	C₈	—	4	4	no	—
341	C₈	—	332	4	no	—
342	C₈	—	166	4	no	—
343	C₈	C₈₃⋊#95	1	8	yes	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
351	C₂²	#19127558	1	1	yes	characteristic
352	C₂²	#19127570	1	1	yes	characteristic
353	C₂²	#19127597	1	1	yes	characteristic
354	C₂²	#19127600	1	1	yes	characteristic
355	C₂²	#19127606	1	1	yes	characteristic
356	C₂²	#19127608	1	1	yes	characteristic
357	C₂²	#19127748	1	4	yes	—
358	C₄	—	332	4	no	—
359	C₄	C₂×C₈₃⋊#95	1	1	yes	characteristic
360	C₄	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
361	C₄	#19127558	1	1	yes	characteristic
362	C₄	#19127566	1	1	yes	characteristic
363	C₄	#19127597	1	1	yes	characteristic
364	C₄	#19127600	1	1	yes	characteristic
365	C₄	#19127602	1	1	yes	characteristic
366	C₄	#19127604	1	1	yes	characteristic
367	C₂	—	2	1	no	—
368	C₂	—	2	1	no	—
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	#24905692	1	1	yes	characteristic
372	C₂	#24907371	1	2	yes	—
373	C₂	#24907502	1	2	yes	—
374	C₂	#24907636	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₃
commutator	C₂×C₄×C₈₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₃
Fitting	C₂²×#108×C₈₃	C₂
socle	C₂³×C₈₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₈₃	C₂×Q₈
cosocle	C₂³×C₄×C₈₃	C₂³
hypercenter	C₂²×#108	D₈₃
hypocenter	C₈₃	#10865
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
11. C₂×#14581728	C₄	semidirect
21. C₂×#108×C₈₃	C₄	semidirect
193. C₈₃	#10865	semidirect
204. C₂×#108	Dic₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14581728	2
C₂²×#14581702	2
C₂×#19127465	2
#24907156	2
C₂²×#108×C₈₃	2
#10865	83