Subgroups — #24918965

Order 10624.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14581820	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128361	C₂	1	1	yes	maximal, characteristic, complemented
4	#19128335	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128087	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127938	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127919	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127900	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127851	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127844	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127841	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127836	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127800	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127770	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050590	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₃₃₂	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₈₃	—	2	1	no	—
20	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
21	#14581820	—	2	4	no	—
22	C₂×#13050579	C₂²	1	1	yes	characteristic
23	C₂×#13050579	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13050578	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13050577	C₂²	1	1	yes	characteristic
26	C₂×#13050577	C₂²	1	1	yes	characteristic, complemented
27	SD₁₆×D₈₃	—	2	4	no	—
28	C₂×D₆₆₄	C₂²	1	1	yes	characteristic
29	C₂×D₆₆₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13050575	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₈×D₈₃	C₂²	1	1	yes	characteristic, complemented
32	#14581788	C₂²	1	1	yes	characteristic
33	#14581781	C₂²	1	1	yes	characteristic, complemented
34	#14581778	—	2	1	no	—
35	#14581770	—	2	1	no	—
36	#14581767	C₂²	1	1	yes	characteristic
37	#14581767	C₂²	1	1	yes	characteristic, complemented
38	#14581765	—	2	1	no	—
39	#14581765	—	2	1	no	—
40	#14581762	—	2	1	no	—
41	#14581760	—	2	1	no	—
42	#14581757	C₂²	1	1	yes	characteristic, complemented
43	#14581754	—	2	1	no	—
44	#14581754	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
46	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	#14581715	C₂²	1	1	yes	characteristic, complemented
48	#14581712	C₂²	1	1	yes	characteristic
49	#14581712	C₂²	1	1	yes	characteristic, complemented
50	#14581712	C₂²	1	1	yes	characteristic, complemented
51	C₂²⋊(C₈₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
52	(C₂×D₈₃)⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	#14581702	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₁₆×C₈₃	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
57	#121×C₈₃	C₂²	1	1	yes	characteristic
58	#107×C₈₃	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₃	—	2	1	no	—
62	C₂³×D₈₃	—	2	1	no	—
63	#13050590	—	2	2	no	—
64	#13050590	—	4	1	no	—
65	C₂×Dic₁₆₆	—	2	1	no	—
66	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
67	Q₈×D₈₃	—	2	2	no	—
68	Q₈×D₈₃	—	4	1	no	—
69	C₂×D₃₃₂	—	2	2	no	—
70	C₂×D₃₃₂	—	2	1	no	—
71	C₂×D₃₃₂	—	2	1	no	—
72	C₂×D₃₃₂	—	2	1	no	—
73	C₂×D₃₃₂	—	4	1	no	—
74	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
75	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
76	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
77	C₂×C₂²⋊D₈₃	—	2	1	no	—
78	C₂×C₂²⋊D₈₃	—	2	1	no	—
79	C₂×C₂²⋊D₈₃	—	2	1	no	—
80	C₂×C₂²⋊D₈₃	—	2	1	no	—
81	C₂×C₂²⋊D₈₃	D₄	1	1	yes	characteristic
82	D₄×D₈₃	—	2	2	no	—
83	D₄×D₈₃	—	4	1	no	—
84	D₄×D₈₃	—	4	4	no	—
85	C₂×C₄×D₈₃	—	2	1	no	—
86	C₂×C₄×D₈₃	—	2	1	no	—
87	C₂×C₄×D₈₃	—	2	1	no	—
88	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
89	#13050579	—	2	2	no	—
90	#13050579	D₄	1	4	yes	complemented
91	#13050578	—	2	2	no	—
92	#13050577	—	2	2	no	—
93	#13050577	—	4	1	no	—
94	D₆₆₄	—	2	2	no	—
95	D₆₆₄	—	2	2	no	—
96	#13050575	—	4	1	no	—
97	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
98	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
99	C₈×D₈₃	—	2	2	no	—
100	Dic₈₃⋊C₄	—	2	1	no	—
101	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
102	C₂²⋊Dic₈₃	D₄	1	1	yes	characteristic
103	(C₂×D₈₃)⋊C₄	—	2	1	no	—
104	(C₂×D₈₃)⋊C₄	—	2	1	no	—
105	(C₂×D₈₃)⋊C₄	—	2	1	no	—
106	(C₂×D₈₃)⋊C₄	—	2	1	no	—
107	(C₂×D₈₃)⋊C₄	—	2	1	no	—
108	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
109	C₄×Dic₈₃	—	2	1	no	—
110	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₈₃	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₈₃	—	2	1	no	—
113	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
115	SD₁₆×C₈₃	—	2	2	no	—
116	M₁₆×C₈₃	—	2	2	no	—
117	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₈₃	—	2	1	no	—
120	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
121	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
122	C₂²⋊C₄×C₈₃	—	2	1	no	—
123	C₂²⋊C₄×C₈₃	—	2	1	no	—
124	C₂³×C₈₃	—	2	1	no	—
125	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₈₃	—	2	1	no	—
127	C₂²×D₈₃	—	2	1	no	—
128	C₂²×D₈₃	—	2	1	no	—
129	C₂²×D₈₃	—	4	2	no	—
130	C₂²×D₈₃	—	4	2	no	—
131	C₂²×D₈₃	—	4	2	no	—
132	C₂²×D₈₃	—	4	2	no	—
133	C₂²×D₈₃	—	8	1	no	—
134	C₂²×D₈₃	—	8	1	no	—
135	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₈₃	—	2	1	no	—
137	Q₈×C₈₃	—	2	1	no	—
138	D₄×C₈₃	—	2	1	no	—
139	D₄×C₈₃	—	2	1	no	—
140	D₄×C₈₃	—	4	2	no	—
141	C₂×C₄×C₈₃	—	2	1	no	—
142	C₂×C₄×C₈₃	—	2	1	no	—
143	C₂×C₄×C₈₃	—	2	1	no	—
144	C₂×C₄×C₈₃	—	2	1	no	—
145	C₂×C₄×C₈₃	—	2	1	no	—
146	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
148	C₂²⋊D₈₃	—	2	2	no	—
149	C₂²⋊D₈₃	—	4	2	no	—
150	C₂²⋊D₈₃	—	4	2	no	—
151	C₂²⋊D₈₃	—	4	2	no	—
152	C₂²⋊D₈₃	—	8	1	no	—
153	C₂×Dic₈₃	—	2	1	no	—
154	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
155	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
156	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
157	D₃₃₂	—	2	1	no	—
158	D₃₃₂	—	2	1	no	—
159	D₃₃₂	—	2	1	no	—
160	D₃₃₂	—	2	1	no	—
161	D₃₃₂	—	2	1	no	—
162	D₃₃₂	—	4	2	no	—
163	D₃₃₂	—	4	2	no	—
164	D₃₃₂	—	4	2	no	—
165	D₃₃₂	C₂×D₄	1	2	yes	—
166	C₄×D₈₃	—	2	1	no	—
167	C₄×D₈₃	—	2	1	no	—
168	C₄×D₈₃	—	4	2	no	—
169	C₄×D₈₃	—	4	2	no	—
170	C₄×D₈₃	—	4	2	no	—
171	Dic₁₆₆	—	2	1	no	—
172	Dic₁₆₆	—	4	2	no	—
173	Dic₁₆₆	C₂×D₄	1	2	yes	complemented
174	C₈×C₈₃	—	2	1	no	—
175	C₈×C₈₃	C₂×D₄	1	2	yes	complemented
176	C₈₃⋊C₈	—	2	1	no	—
177	C₈₃⋊C₈	—	2	1	no	—
178	C₂²×C₈₃	—	2	1	no	—
179	C₂²×C₈₃	—	2	1	no	—
180	C₂²×C₈₃	—	2	1	no	—
181	C₂²×C₈₃	—	4	1	no	—
182	C₂²×C₈₃	—	4	1	no	—
183	C₂²×C₈₃	—	4	1	no	—
184	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×D₈₃	—	2	1	no	—
186	C₂×D₈₃	—	2	1	no	—
187	C₂×D₈₃	—	2	2	no	—
188	C₂×D₈₃	—	4	1	no	—
189	C₂×D₈₃	—	4	1	no	—
190	C₂×D₈₃	—	4	1	no	—
191	C₂×D₈₃	—	4	1	no	—
192	C₂×D₈₃	—	4	1	no	—
193	C₂×D₈₃	—	4	1	no	—
194	C₂×D₈₃	—	4	1	no	—
195	C₂×D₈₃	—	4	1	no	—
196	C₂×D₈₃	—	8	4	no	—
197	C₂×D₈₃	—	8	4	no	—
198	C₂×D₈₃	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₈₃	—	2	1	no	—
200	C₄×C₈₃	—	4	1	no	—
201	C₄×C₈₃	—	4	1	no	—
202	C₄×C₈₃	—	4	1	no	—
203	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
205	Dic₈₃	—	2	2	no	—
206	Dic₈₃	—	2	1	no	—
207	Dic₈₃	—	2	1	no	—
208	Dic₈₃	—	2	1	no	—
209	C₂×C₈₃	—	4	1	no	—
210	C₂×C₈₃	—	8	1	no	—
211	C₂×C₈₃	D₄²	1	1	yes	characteristic
212	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂×C₈₃	#577	1	1	yes	characteristic
214	D₈₃	—	2	2	no	—
215	D₈₃	—	4	2	no	—
216	D₈₃	—	8	1	no	—
217	D₈₃	—	8	1	no	—
218	#3265	—	83	1	no	maximal, Sylow
219	C₈₃	#3265	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	83	1	no	—
221	C₂²×SD₁₆	—	83	1	no	—
222	#548	—	83	1	no	—
223	D₄²	—	83	1	no	—
224	#496	—	83	1	no	—
225	#468	D₈₃	1	1	yes	characteristic, complemented
226	#466	—	83	1	no	—
227	#463	—	83	1	no	—
228	#460	—	83	1	no	—
229	#450	—	83	1	no	—
230	#449	—	83	1	no	—
231	#448	—	83	1	no	—
232	#447	—	83	1	no	—
233	#440	—	83	1	no	—
234	#435	—	83	1	no	—
235	C₂×#41	—	83	1	no	—
236	C₂²×Q₈	—	83	1	no	—
237	C₂²×D₄	—	83	1	no	—
238	C₂²×D₄	—	83	1	no	—
239	C₂²×D₄	—	166	1	no	—
240	AGL(1,ℤ/8)	—	166	4	no	—
241	C₂×SD₁₆	—	83	1	no	—
242	C₂×SD₁₆	—	83	1	no	—
243	C₂×SD₁₆	—	83	1	no	—
244	C₂×SD₁₆	—	83	1	no	—
245	C₂×SD₁₆	—	83	1	no	—
246	C₂×SD₁₆	—	166	4	no	—
247	C₂×SD₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
248	C₂×D₈	—	83	1	no	—
249	C₂×D₈	—	83	1	no	—
250	C₂×D₈	—	83	1	no	—
251	C₂×M₁₆	C₂×D₈₃	1	1	yes	characteristic, complemented
252	C₂²×C₈	—	83	1	no	—
253	#127	—	83	1	no	—
254	#124	—	83	1	no	—
255	#124	—	166	1	no	—
256	C₂²⋊Q₈	—	166	1	no	—
257	C₂²⋊Q₈	C₂×D₈₃	1	1	yes	characteristic, complemented
258	#121	—	83	1	no	—
259	#121	—	83	1	no	—
260	#121	—	166	1	no	—
261	#121	—	166	1	no	—
262	#121	C₂×D₈₃	1	1	yes	characteristic
263	#120	—	166	1	no	—
264	#120	—	166	1	no	—
265	C₄×Q₈	—	83	1	no	—
266	C₄×D₄	—	83	1	no	—
267	C₄×D₄	—	83	1	no	—
268	C₄×D₄	—	166	1	no	—
269	#107	C₂×D₈₃	1	1	yes	characteristic, complemented
270	C₄⋊C₈	—	83	1	no	—
271	#103	—	83	1	no	—
272	#103	C₂×D₈₃	1	1	yes	characteristic, complemented
273	#102	—	83	1	no	—
274	#102	—	83	1	no	—
275	#102	—	83	1	no	—
276	#102	C₂×D₈₃	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	83	1	no	—
278	C₂²⋊C₈	—	83	1	no	—
279	#97	—	83	1	no	—
280	C₂⁴	—	166	1	no	—
281	C₂⁴	—	166	1	no	—
282	#41	—	332	1	no	—
283	#41	—	166	2	no	—
284	C₂×Q₈	—	332	1	no	—
285	C₂×Q₈	—	83	1	no	—
286	C₂×Q₈	—	166	1	no	—
287	C₂×Q₈	—	166	2	no	—
288	C₂×Q₈	C₂²×D₈₃	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	332	1	no	—
291	C₂×D₄	—	332	4	no	—
292	C₂×D₄	—	332	1	no	—
293	C₂×D₄	—	83	1	no	—
294	C₂×D₄	—	83	1	no	—
295	C₂×D₄	—	83	1	no	—
296	C₂×D₄	—	83	1	no	—
297	C₂×D₄	—	166	1	no	—
298	C₂×D₄	—	166	1	no	—
299	C₂×D₄	—	166	2	no	—
300	C₂×D₄	—	166	1	no	—
301	C₂×D₄	—	166	1	no	—
302	C₂×D₄	—	166	1	no	—
303	C₂×D₄	—	166	2	no	—
304	C₂×D₄	—	166	1	no	—
305	C₂×D₄	—	166	1	no	—
306	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
307	C₂²×C₄	—	83	1	no	—
308	C₂²×C₄	—	166	1	no	—
309	C₂²×C₄	—	166	1	no	—
310	C₂²×C₄	—	166	1	no	—
311	C₂²×C₄	C₂²×D₈₃	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	332	1	no	—
314	SD₁₆	—	83	4	no	—
315	SD₁₆	—	166	2	no	—
316	SD₁₆	—	166	2	no	—
317	SD₁₆	—	166	2	no	—
318	D₈	—	332	1	no	—
319	D₈	—	166	2	no	—
320	D₈	—	166	2	no	—
321	M₁₆	—	2	2	no	—
322	C₂×C₈	—	83	1	no	—
323	C₂×C₈	—	83	1	no	—
324	C₂×C₈	—	166	2	no	—
325	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₈₃	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	83	1	no	—
329	C₄⋊C₄	—	166	1	no	—
330	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	83	1	no	—
335	C₂²⋊C₄	—	83	1	no	—
336	C₂²⋊C₄	—	166	1	no	—
337	C₂²⋊C₄	—	166	1	no	—
338	C₂²⋊C₄	—	166	1	no	—
339	C₂²⋊C₄	—	166	1	no	—
340	C₂²⋊C₄	—	166	1	no	—
341	C₄²	—	83	1	no	—
342	C₄²	—	166	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	332	2	no	—
345	C₂³	—	332	2	no	—
346	C₂³	—	332	2	no	—
347	C₂³	—	332	2	no	—
348	C₂³	—	83	1	no	—
349	C₂³	—	664	1	no	—
350	C₂³	—	664	1	no	—
351	C₂³	—	166	1	no	—
352	C₂³	—	166	1	no	—
353	C₂³	—	166	1	no	—
354	C₂³	D₄×D₈₃	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	332	2	no	—
358	Q₈	—	83	2	no	—
359	Q₈	—	166	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	332	2	no	—
364	D₄	—	332	2	no	—
365	D₄	—	332	2	no	—
366	D₄	—	332	2	no	—
367	D₄	—	332	2	no	—
368	D₄	—	332	2	no	—
369	D₄	—	83	2	no	—
370	D₄	—	664	1	no	—
371	D₄	—	166	2	no	—
372	D₄	—	166	1	no	—
373	D₄	—	166	1	no	—
374	D₄	—	166	1	no	—
375	D₄	—	166	1	no	—
376	D₄	—	166	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	332	2	no	—
383	C₂×C₄	—	332	2	no	—
384	C₂×C₄	—	332	2	no	—
385	C₂×C₄	—	83	1	no	—
386	C₂×C₄	—	83	1	no	—
387	C₂×C₄	—	83	1	no	—
388	C₂×C₄	—	166	1	no	—
389	C₂×C₄	—	166	1	no	—
390	C₂×C₄	—	166	1	no	—
391	C₂×C₄	D₄×D₈₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₈₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	166	1	no	—
395	C₈	—	166	1	no	—
396	C₈	D₄×D₈₃	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	332	1	no	—
404	C₂²	—	332	1	no	—
405	C₂²	—	332	1	no	—
406	C₂²	—	332	1	no	—
407	C₂²	—	332	1	no	—
408	C₂²	—	332	1	no	—
409	C₂²	—	332	1	no	—
410	C₂²	—	332	1	no	—
411	C₂²	—	83	2	no	—
412	C₂²	—	664	4	no	—
413	C₂²	—	664	4	no	—
414	C₂²	—	166	2	no	—
415	C₂²	—	166	1	no	—
416	C₂²	—	166	1	no	—
417	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	166	2	no	—
423	C₄	—	166	1	no	—
424	C₄	—	166	1	no	—
425	C₄	—	166	1	no	—
426	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
427	C₄	#14581838	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	8	1	no	—
430	C₂	—	332	2	no	—
431	C₂	—	664	1	no	—
432	C₂	—	664	1	no	—
433	C₂	—	166	2	no	—
434	C₂	#19128335	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₈₃	1	1	yes	characteristic
436	C₂	#19128510	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#468×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	#468	D₈₃
hypocenter	C₈₃	#3265
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂×#14581820	C₂	semidirect
2. C₂×SD₁₆×D₈₃	C₂	semidirect
3. #19128361	C₂	semidirect
4. #19128335	C₂	semidirect
5. #19128087	C₂	semidirect
6. #19127938	C₂	semidirect
7. #19127919	C₂	semidirect
8. #19127900	C₂	semidirect
9. #19127851	C₂	semidirect
10. #19127844	C₂	semidirect
11. #19127841	C₂	semidirect
12. #19127836	C₂	semidirect
13. #19127800	C₂	semidirect
14. #19127770	C₂	semidirect
15. #468×C₈₃	C₂	semidirect
16. C₂×#13050590	C₂²	semidirect
17. C₂×Q₈×D₈₃	C₂²	semidirect
23. C₂×#13050579	C₂²	semidirect
24. C₂×#13050578	C₂²	semidirect
26. C₂×#13050577	C₂²	semidirect
29. C₂×D₆₆₄	C₂²	semidirect
30. C₂×#13050575	C₂²	semidirect
31. C₂×C₈×D₈₃	C₂²	semidirect
33. #14581781	C₂²	semidirect
37. #14581767	C₂²	semidirect
42. #14581757	C₂²	semidirect
46. Dic₈₃⋊C₈	C₂²	semidirect
47. #14581715	C₂²	semidirect
49. #14581712	C₂²	semidirect
50. #14581712	C₂²	semidirect
51. C₂²⋊(C₈₃⋊C₈)	C₂²	semidirect
52. (C₂×D₈₃)⋊C₈	C₂²	semidirect
53. #14581702	C₂²	semidirect
54. C₂×SD₁₆×C₈₃	C₂²	semidirect
55. C₂×M₁₆×C₈₃	C₂²	semidirect
56. C₂²⋊Q₈×C₈₃	C₂²	semidirect
58. #107×C₈₃	C₂²	semidirect
59. #103×C₈₃	C₂²	semidirect
60. #102×C₈₃	C₂²	semidirect
90. #13050579	D₄	semidirect
173. Dic₁₆₆	C₂×D₄	semidirect
175. C₈×C₈₃	C₂×D₄	semidirect
198. C₂×D₈₃	AGL(1,ℤ/8)	semidirect
219. C₈₃	#3265	semidirect
225. #468	D₈₃	semidirect
247. C₂×SD₁₆	C₂×D₈₃	semidirect
251. C₂×M₁₆	C₂×D₈₃	semidirect
257. C₂²⋊Q₈	C₂×D₈₃	semidirect
269. #107	C₂×D₈₃	semidirect
272. #103	C₂×D₈₃	semidirect
276. #102	C₂×D₈₃	semidirect
396. C₈	D₄×D₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581820	2
C₂×SD₁₆×D₈₃	2
#19128361	2
#19128335	2
#19128087	2
#19127938	2
#19127919	2
#19127900	2
#19127851	2
#19127844	2
#19127841	2
#19127836	2
#19127800	2
#19127770	2
#468×C₈₃	2
#3265	83