Subgroups — #24918962

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×#14581816	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13050578	C₂	1	1	yes	maximal, characteristic, complemented
3	#19128357	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊D₈₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#19128089	C₂	1	1	yes	maximal, characteristic, complemented
6	#19127946	C₂	1	1	yes	maximal, characteristic, complemented
7	#19127935	C₂	1	1	yes	maximal, characteristic, complemented
8	#19127914	C₂	1	1	yes	maximal, characteristic, complemented
9	#19127900	C₂	1	1	yes	maximal, characteristic, complemented
10	#19127853	C₂	1	1	yes	maximal, characteristic, complemented
11	#19127843	C₂	1	1	yes	maximal, characteristic, complemented
12	#19127842	C₂	1	1	yes	maximal, characteristic, complemented
13	#19127798	C₂	1	1	yes	maximal, characteristic, complemented
14	#19127769	C₂	1	1	yes	maximal, characteristic, complemented
15	#447×C₈₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13050589	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Dic₁₆₆	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₈₃	—	2	1	no	—
19	C₂×D₄×D₈₃	C₂²	1	1	yes	characteristic
20	#14581816	—	2	4	no	—
21	C₂×#13050579	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13050579	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13050578	—	2	4	no	—
24	C₂×#13050578	C₂²	1	1	yes	characteristic
25	C₂×#13050578	C₂²	1	1	yes	characteristic
26	C₂×#13050578	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13050578	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13050575	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13050573	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	#14581788	C₂²	1	1	yes	characteristic
32	#14581779	C₂²	1	1	yes	characteristic, complemented
33	#14581778	—	2	1	no	—
34	#14581772	C₂²	1	1	yes	characteristic, complemented
35	#14581769	—	2	1	no	—
36	#14581766	C₂²	1	1	yes	characteristic
37	#14581764	—	2	1	no	—
38	#14581764	—	2	1	no	—
39	#14581763	C₂²	1	1	yes	characteristic
40	#14581761	—	2	1	no	—
41	#14581760	—	2	1	no	—
42	#14581757	C₂²	1	1	yes	characteristic, complemented
43	D₄×Dic₈₃	—	2	1	no	—
44	D₄×Dic₈₃	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊D₈₃	C₂²	1	1	yes	characteristic
46	#14581725	C₂²	1	1	yes	characteristic, complemented
47	Dic₈₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	#14581717	C₂²	1	1	yes	characteristic, complemented
49	#14581717	C₂²	1	1	yes	characteristic, complemented
50	#14581713	C₂²	1	1	yes	characteristic, complemented
51	#14581712	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	C₂²×D₄×C₈₃	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₈₃	C₂²	1	1	yes	characteristic
56	C₂×D₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
57	#121×C₈₃	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₃	C₂²	1	1	yes	characteristic
59	#102×C₈₃	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊C₈×C₈₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₈₃	—	2	1	no	—
62	#13050589	—	2	2	no	—
63	#13050589	—	4	1	no	—
64	C₂×Dic₁₆₆	—	2	2	no	—
65	C₂×Dic₁₆₆	—	2	1	no	—
66	C₂×Dic₁₆₆	—	4	1	no	—
67	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
68	C₂×Dic₁₆₆	C₂³	1	1	yes	characteristic
69	C₂×D₃₃₂	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₃	—	2	1	no	—
71	C₂×C₂²⋊D₈₃	—	2	1	no	—
72	C₂×C₂²⋊D₈₃	—	2	1	no	—
73	C₂×C₂²⋊D₈₃	—	2	1	no	—
74	C₂×C₂²⋊D₈₃	—	2	1	no	—
75	C₂×C₂²⋊D₈₃	—	2	1	no	—
76	C₂×C₂²⋊D₈₃	—	4	4	no	—
77	C₂×C₂²⋊D₈₃	D₄	1	1	yes	characteristic
78	D₄×D₈₃	—	2	2	no	—
79	D₄×D₈₃	—	4	1	no	—
80	C₂²×Dic₈₃	—	2	1	no	—
81	C₂²×Dic₈₃	—	2	1	no	—
82	C₂²×Dic₈₃	—	2	1	no	—
83	C₂×C₄×D₈₃	C₂³	1	1	yes	characteristic
84	#13050579	—	2	2	no	—
85	#13050579	—	4	1	no	—
86	#13050578	—	2	2	no	—
87	#13050578	—	2	2	no	—
88	#13050578	—	2	2	no	—
89	#13050578	D₄	1	4	yes	complemented
90	#13050575	—	2	2	no	—
91	#13050573	—	2	2	no	—
92	C₂×C₈₃⋊C₈	—	2	2	no	—
93	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₂×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₈₃	—	2	1	no	—
96	C₄⋊Dic₈₃	C₂³	1	1	yes	characteristic
97	Dic₈₃⋊C₄	—	2	1	no	—
98	Dic₈₃⋊C₄	D₄	1	1	yes	characteristic
99	C₂²⋊Dic₈₃	—	2	1	no	—
100	C₂²⋊Dic₈₃	—	2	1	no	—
101	C₂²⋊Dic₈₃	—	2	1	no	—
102	C₂²⋊Dic₈₃	—	2	1	no	—
103	C₂²⋊Dic₈₃	D₄	1	1	yes	characteristic
104	(C₂×D₈₃)⋊C₄	—	2	1	no	—
105	(C₂×D₈₃)⋊C₄	—	2	1	no	—
106	(C₂×D₈₃)⋊C₄	D₄	1	1	yes	characteristic
107	C₄×Dic₈₃	—	2	1	no	—
108	C₄×Dic₈₃	C₂³	1	1	yes	characteristic
109	C₂⁴×C₈₃	—	2	1	no	—
110	C₂×D₄×C₈₃	—	2	2	no	—
111	C₂×D₄×C₈₃	—	2	1	no	—
112	C₂×D₄×C₈₃	—	2	1	no	—
113	C₂×D₄×C₈₃	—	4	1	no	—
114	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₈₃	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₈₃	C₂³	1	1	yes	characteristic
118	D₈×C₈₃	—	2	2	no	—
119	D₈×C₈₃	—	4	1	no	—
120	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
121	C₂×C₈×C₈₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₄×C₈₃	C₂³	1	1	yes	characteristic
123	C₂²⋊C₄×C₈₃	—	2	1	no	—
124	C₂³×C₈₃	—	2	1	no	—
125	C₂³×C₈₃	—	2	1	no	—
126	C₂³×C₈₃	—	2	1	no	—
127	C₂³×C₈₃	—	4	2	no	—
128	C₂³×C₈₃	—	4	2	no	—
129	C₂³×C₈₃	—	8	1	no	—
130	C₂³×C₈₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₈₃	—	2	1	no	—
132	C₂²×D₈₃	—	4	2	no	—
133	C₂²×D₈₃	—	4	2	no	—
134	C₂²×D₈₃	—	8	1	no	—
135	C₂²×D₈₃	C₂×D₄	1	1	yes	characteristic
136	D₄×C₈₃	—	2	1	no	—
137	D₄×C₈₃	—	2	1	no	—
138	D₄×C₈₃	—	2	1	no	—
139	D₄×C₈₃	—	2	1	no	—
140	D₄×C₈₃	—	2	1	no	—
141	D₄×C₈₃	—	4	2	no	—
142	D₄×C₈₃	—	4	2	no	—
143	D₄×C₈₃	C₂×D₄	1	2	yes	—
144	C₂×C₄×C₈₃	—	2	1	no	—
145	C₂×C₄×C₈₃	—	2	1	no	—
146	C₂×C₄×C₈₃	—	2	1	no	—
147	C₂×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₈₃	—	2	2	no	—
150	C₂²⋊D₈₃	—	4	2	no	—
151	C₂²⋊D₈₃	—	4	2	no	—
152	C₂²⋊D₈₃	—	4	2	no	—
153	C₂²⋊D₈₃	—	4	2	no	—
154	C₂²⋊D₈₃	—	4	2	no	—
155	C₂²⋊D₈₃	—	8	1	no	—
156	C₂×Dic₈₃	—	2	1	no	—
157	C₂×Dic₈₃	—	2	1	no	—
158	C₂×Dic₈₃	—	2	1	no	—
159	C₂×Dic₈₃	—	4	2	no	—
160	C₂×Dic₈₃	—	4	2	no	—
161	C₂×Dic₈₃	—	4	2	no	—
162	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₈₃	C₂×D₄	1	1	yes	characteristic
165	D₃₃₂	—	2	1	no	—
166	D₃₃₂	—	2	1	no	—
167	C₄×D₈₃	—	2	1	no	—
168	C₄×D₈₃	—	2	1	no	—
169	Dic₁₆₆	—	2	1	no	—
170	Dic₁₆₆	—	2	1	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	—	2	1	no	—
176	C₈₃⋊C₈	—	2	1	no	—
177	C₈₃⋊C₈	C₂×D₄	1	2	yes	complemented
178	C₂²×C₈₃	—	2	1	no	—
179	C₂²×C₈₃	—	2	1	no	—
180	C₂²×C₈₃	—	2	2	no	—
181	C₂²×C₈₃	—	4	1	no	—
182	C₂²×C₈₃	—	4	1	no	—
183	C₂²×C₈₃	—	4	1	no	—
184	C₂²×C₈₃	—	4	1	no	—
185	C₂²×C₈₃	—	4	1	no	—
186	C₂²×C₈₃	—	4	1	no	—
187	C₂²×C₈₃	—	4	1	no	—
188	C₂²×C₈₃	—	4	1	no	—
189	C₂²×C₈₃	—	8	4	no	—
190	C₂²×C₈₃	AGL(1,ℤ/8)	1	2	yes	complemented
191	C₂²×C₈₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×D₈₃	—	2	1	no	—
193	C₂×D₈₃	—	2	1	no	—
194	C₂×D₈₃	—	2	1	no	—
195	C₂×D₈₃	—	4	1	no	—
196	C₂×D₈₃	—	4	1	no	—
197	C₂×D₈₃	—	4	1	no	—
198	C₂×D₈₃	—	8	4	no	—
199	C₄×C₈₃	—	2	1	no	—
200	C₄×C₈₃	—	4	1	no	—
201	C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
202	C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
203	Dic₈₃	—	2	2	no	—
204	Dic₈₃	—	2	1	no	—
205	Dic₈₃	—	2	1	no	—
206	Dic₈₃	—	2	1	no	—
207	Dic₈₃	—	4	1	no	—
208	Dic₈₃	—	4	1	no	—
209	C₂×C₈₃	—	2	2	no	—
210	C₂×C₈₃	—	4	2	no	—
211	C₂×C₈₃	—	8	1	no	—
212	C₂×C₈₃	—	8	1	no	—
213	C₂×C₈₃	D₄²	1	1	yes	characteristic
214	C₂×C₈₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₈₃	#577	1	1	yes	characteristic
216	D₈₃	—	4	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	—	83	1	no	—
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	D₈₃	1	1	yes	characteristic, complemented
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	—	166	1	no	—
239	C₂²×D₄	C₂×D₈₃	1	1	yes	characteristic
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	—	83	1	no	—
247	C₂×SD₁₆	—	166	4	no	—
248	C₂×D₈	—	83	1	no	—
249	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic
250	C₂×D₈	C₂×D₈₃	1	1	yes	characteristic, complemented
251	C₂×M₁₆	—	83	1	no	—
252	C₂²×C₈	—	83	1	no	—
253	#127	—	83	1	no	—
254	#124	—	83	1	no	—
255	#124	—	166	1	no	—
256	C₂²⋊Q₈	—	83	1	no	—
257	C₂²⋊Q₈	—	166	1	no	—
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, complemented
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	—	83	1	no	—
270	C₄⋊C₈	—	83	1	no	—
271	#103	—	83	1	no	—
272	#103	—	83	1	no	—
273	#102	—	83	1	no	—
274	#102	—	83	1	no	—
275	#102	C₂×D₈₃	1	1	yes	characteristic
276	#102	C₂×D₈₃	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	83	1	no	—
278	C₂²⋊C₈	C₂×D₈₃	1	1	yes	characteristic, complemented
279	#97	—	83	1	no	—
280	C₂⁴	—	2	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	—	83	1	no	—
287	C₂×Q₈	—	166	2	no	—
288	C₂×Q₈	—	166	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	332	4	no	—
294	C₂×D₄	—	332	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	1	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	C₂²×D₈₃	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₈₃	1	1	yes	characteristic
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	—	332	1	no	—
313	SD₁₆	—	83	4	no	—
314	SD₁₆	—	166	2	no	—
315	SD₁₆	—	166	2	no	—
316	SD₁₆	—	166	2	no	—
317	SD₁₆	—	166	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	1	no	—
320	D₈	—	166	2	no	—
321	M₁₆	—	166	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	—	83	1	no	—
328	C₄⋊C₄	—	83	1	no	—
329	C₄⋊C₄	—	166	1	no	—
330	C₄⋊C₄	—	166	1	no	—
331	C₄⋊C₄	C₂²×D₈₃	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	83	1	no	—
334	C₂²⋊C₄	—	83	1	no	—
335	C₂²⋊C₄	—	166	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	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	332	2	no	—
350	C₂³	—	332	2	no	—
351	C₂³	—	83	1	no	—
352	C₂³	—	664	1	no	—
353	C₂³	—	166	1	no	—
354	C₂³	D₄×D₈₃	1	1	yes	characteristic
355	Q₈	—	332	2	no	—
356	Q₈	—	83	2	no	—
357	Q₈	—	166	1	no	—
358	Q₈	—	166	1	no	—
359	Q₈	—	166	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	332	2	no	—
368	D₄	—	332	2	no	—
369	D₄	—	332	2	no	—
370	D₄	—	332	2	no	—
371	D₄	—	332	2	no	—
372	D₄	—	664	1	no	—
373	D₄	—	166	2	no	—
374	D₄	—	166	1	no	—
375	D₄	—	166	1	no	—
376	D₄	D₄×D₈₃	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	332	2	no	—
381	C₂×C₄	—	332	2	no	—
382	C₂×C₄	—	332	2	no	—
383	C₂×C₄	—	83	1	no	—
384	C₂×C₄	—	83	1	no	—
385	C₂×C₄	—	83	1	no	—
386	C₂×C₄	—	166	1	no	—
387	C₂×C₄	—	166	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	—	2	1	no	—
395	C₈	—	83	2	no	—
396	C₈	—	166	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	8	4	no	—
409	C₂²	—	332	1	no	—
410	C₂²	—	332	1	no	—
411	C₂²	—	332	1	no	—
412	C₂²	—	664	4	no	—
413	C₂²	—	166	1	no	—
414	C₂²	—	166	1	no	—
415	C₂²	—	166	1	no	—
416	C₂²	#14581816	1	2	yes	complemented
417	C₂²	C₂×D₄×D₈₃	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	332	1	no	—
421	C₄	—	332	1	no	—
422	C₄	—	166	1	no	—
423	C₄	—	166	2	no	—
424	C₄	—	166	1	no	—
425	C₄	—	166	1	no	—
426	C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
427	C₄	#14581837	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	8	1	no	—
432	C₂	—	332	1	no	—
433	C₂	—	664	1	no	—
434	C₂	#19128333	1	1	yes	characteristic
435	C₂	C₂×#14581816	1	1	yes	characteristic
436	C₂	#19128511	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₃
commutator, cosocle	C₂×C₄×C₈₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₃
Fitting	#447×C₈₃	C₂
socle	C₂²×C₈₃	C₂²×D₄
hypercenter	#447	D₈₃
hypocenter	C₈₃	#3265
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #447

Complements

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

N	H ≅ G/N	type
1. C₂×#14581816	C₂	semidirect
2. C₂²×#13050578	C₂	semidirect
3. #19128357	C₂	semidirect
4. D₄×C₂²⋊D₈₃	C₂	semidirect
5. #19128089	C₂	semidirect
6. #19127946	C₂	semidirect
7. #19127935	C₂	semidirect
8. #19127914	C₂	semidirect
9. #19127900	C₂	semidirect
10. #19127853	C₂	semidirect
11. #19127843	C₂	semidirect
12. #19127842	C₂	semidirect
13. #19127798	C₂	semidirect
14. #19127769	C₂	semidirect
15. #447×C₈₃	C₂	semidirect
16. C₂×#13050589	C₂²	semidirect
17. C₂²×Dic₁₆₆	C₂²	semidirect
21. C₂×#13050579	C₂²	semidirect
22. C₂×#13050579	C₂²	semidirect
26. C₂×#13050578	C₂²	semidirect
27. C₂×#13050578	C₂²	semidirect
28. C₂×#13050575	C₂²	semidirect
29. C₂×#13050573	C₂²	semidirect
30. C₂²×C₈₃⋊C₈	C₂²	semidirect
32. #14581779	C₂²	semidirect
34. #14581772	C₂²	semidirect
42. #14581757	C₂²	semidirect
46. #14581725	C₂²	semidirect
47. Dic₈₃⋊C₈	C₂²	semidirect
48. #14581717	C₂²	semidirect
49. #14581717	C₂²	semidirect
50. #14581713	C₂²	semidirect
51. #14581712	C₂²	semidirect
52. (C₂×D₈₃)⋊C₈	C₂²	semidirect
53. #14581702	C₂²	semidirect
56. C₂×D₈×C₈₃	C₂²	semidirect
57. #121×C₈₃	C₂²	semidirect
59. #102×C₈₃	C₂²	semidirect
60. C₂²⋊C₈×C₈₃	C₂²	semidirect
89. #13050578	D₄	semidirect
173. Dic₁₆₆	C₂×D₄	semidirect
177. C₈₃⋊C₈	C₂×D₄	semidirect
190. C₂²×C₈₃	AGL(1,ℤ/8)	semidirect
219. C₈₃	#3265	semidirect
232. #447	D₈₃	semidirect
250. C₂×D₈	C₂×D₈₃	semidirect
262. #121	C₂×D₈₃	semidirect
276. #102	C₂×D₈₃	semidirect
278. C₂²⋊C₈	C₂×D₈₃	semidirect
416. C₂²	#14581816	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14581816	2
C₂²×#13050578	2
#19128357	2
D₄×C₂²⋊D₈₃	2
#19128089	2
#19127946	2
#19127935	2
#19127914	2
#19127900	2
#19127853	2
#19127843	2
#19127842	2
#19127798	2
#19127769	2
#447×C₈₃	2
#3265	83