Subgroups — #35310319

Order 21248.

746 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19127739	C₂	1	1	yes	maximal, characteristic
2	C₂×#19127656	C₂	1	1	yes	maximal, characteristic
3	#24907195	C₂	1	2	yes	maximal
4	C₂×#19127457	C₂	1	2	yes	maximal
5	C₂×#427×C₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#13050574	C₂²	1	1	yes	characteristic
7	C₂×#14581751	C₂²	1	2	yes	—
8	C₂×#14581751	C₂²	1	1	yes	characteristic
9	#19127739	—	2	2	no	—
10	#19127739	C₄	1	4	yes	complemented
11	C₂×#14581726	—	2	1	no	—
12	C₂×#14581724	—	2	1	no	—
13	#19127656	—	2	1	no	—
14	#19127656	—	2	1	no	—
15	#19127656	—	2	1	no	—
16	#19127656	—	2	1	no	—
17	C₂×#14581702	C₄	1	2	yes	complemented
18	C₂×C₈×Dic₈₃	C₄	1	2	yes	complemented
19	#19127467	—	2	4	no	—
20	#19127457	—	2	4	no	—
21	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
22	C₂×#117×C₈₃	C₂²	1	2	yes	—
23	#427×C₈₃	—	2	2	no	—
24	#427×C₈₃	C₄	1	4	yes	complemented
25	C₂×#107×C₈₃	—	2	1	no	—
26	C₂×#106×C₈₃	—	2	1	no	—
27	C₂×#13050574	—	2	1	no	—
28	C₂×#13050574	—	2	1	no	—
29	C₂×#13050574	—	2	1	no	—
30	C₂×#13050574	—	2	1	no	—
31	C₂×#13050574	D₄	1	2	yes	—
32	C₂×#13050574	Q₈	1	2	yes	—
33	C₂²×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
34	#14581751	—	2	1	no	—
35	#14581751	—	2	1	no	—
36	#14581751	—	2	2	no	—
37	#14581751	—	2	2	no	—
38	#14581751	—	2	1	no	—
39	#14581751	—	2	1	no	—
40	#14581751	—	2	2	no	—
41	#14581751	C₂×C₄	1	4	yes	—
42	C₂×C₄⋊Dic₈₃	—	2	2	no	—
43	C₂×C₄⋊Dic₈₃	Q₈	1	2	yes	—
44	C₂×C₂²⋊Dic₈₃	—	2	2	no	—
45	C₂×C₂²⋊Dic₈₃	D₄	1	2	yes	—
46	C₂×C₄×Dic₈₃	—	2	2	no	—
47	C₂×C₄×Dic₈₃	C₂×C₄	1	2	yes	—
48	#14581726	—	2	4	no	—
49	#14581724	—	2	4	no	—
50	#14581702	—	2	2	no	—
51	#14581702	—	2	2	no	—
52	C₈×Dic₈₃	—	2	2	no	—
53	C₈×Dic₈₃	—	2	2	no	—
54	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₈₃	D₄	1	2	yes	—
64	C₂²×C₈×C₈₃	Q₈	1	2	yes	—
65	#117×C₈₃	—	2	2	no	—
66	#117×C₈₃	—	2	2	no	—
67	#117×C₈₃	—	2	2	no	—
68	#117×C₈₃	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
71	C₂×C₄²×C₈₃	—	2	2	no	—
72	#107×C₈₃	—	2	4	no	—
73	#106×C₈₃	—	2	4	no	—
74	C₂²×Dic₈₃	—	4	2	no	—
75	C₂²×Dic₈₃	C₄⋊C₄	1	4	yes	—
76	#13050574	—	2	2	no	—
77	#13050574	—	2	2	no	—
78	#13050574	—	2	2	no	—
79	#13050574	—	2	2	no	—
80	C₂×C₈₃⋊C₈	—	2	2	no	—
81	C₂×C₈₃⋊C₈	—	2	2	no	—
82	C₂×C₈₃⋊C₈	C₄⋊C₄	1	4	yes	—
83	C₄⋊Dic₈₃	—	2	2	no	—
84	C₄⋊Dic₈₃	—	2	2	no	—
85	C₄⋊Dic₈₃	—	2	4	no	—
86	C₄⋊Dic₈₃	—	4	2	no	—
87	C₂²⋊Dic₈₃	—	2	2	no	—
88	C₂²⋊Dic₈₃	—	2	2	no	—
89	C₂²⋊Dic₈₃	—	2	4	no	—
90	C₂²⋊Dic₈₃	—	4	2	no	—
91	C₄×Dic₈₃	—	2	2	no	—
92	C₄×Dic₈₃	—	2	2	no	—
93	C₄×Dic₈₃	—	2	4	no	—
94	C₄×Dic₈₃	—	4	2	no	—
95	C₂⁴×C₈₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₃	—	4	2	no	—
97	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
111	C₂×C₈×C₈₃	C₄²	1	2	yes	—
112	C₂×C₈×C₈₃	C₄²	1	2	yes	—
113	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×C₈×C₈₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
118	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
119	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
120	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
121	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
122	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
123	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
124	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
125	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
126	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
127	C₄⋊C₄×C₈₃	—	2	4	no	—
128	C₄⋊C₄×C₈₃	—	4	2	no	—
129	C₂²⋊C₄×C₈₃	—	2	4	no	—
130	C₂²⋊C₄×C₈₃	—	4	2	no	—
131	C₄²×C₈₃	—	2	4	no	—
132	C₄²×C₈₃	—	4	2	no	—
133	C₂³×C₈₃	—	4	2	no	—
134	C₂³×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
136	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
137	C₂³×C₈₃	#121	1	1	yes	characteristic
138	C₂³×C₈₃	#121	1	1	yes	characteristic
139	C₂³×C₈₃	#127	1	1	yes	characteristic
140	C₂³×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₈₃	—	4	4	no	—
142	C₂×C₄×C₈₃	—	8	4	no	—
143	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
152	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
153	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
166	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
167	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
168	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
169	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
171	C₂×Dic₈₃	—	2	4	no	—
172	C₂×Dic₈₃	—	4	4	no	—
173	C₂×Dic₈₃	—	4	4	no	—
174	C₂×Dic₈₃	—	8	4	no	—
175	C₈×C₈₃	#95	1	2	yes	—
176	C₈×C₈₃	#95	1	2	yes	—
177	C₈×C₈₃	#95	1	2	yes	—
178	C₈×C₈₃	#95	1	2	yes	—
179	C₈₃⋊C₈	—	2	4	no	—
180	C₂²×C₈₃	—	2	2	no	—
181	C₂²×C₈₃	—	2	2	no	—
182	C₂²×C₈₃	—	2	2	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	C₄×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₈₃	#380	1	1	yes	characteristic
189	C₂²×C₈₃	#384	1	1	yes	characteristic
190	C₂²×C₈₃	#389	1	1	yes	characteristic
191	C₂²×C₈₃	#389	1	1	yes	characteristic
192	C₂²×C₈₃	#390	1	1	yes	characteristic
193	C₂²×C₈₃	#390	1	1	yes	characteristic
194	C₄×C₈₃	—	8	4	no	—
195	C₄×C₈₃	C₂×#95	1	1	yes	characteristic
196	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
197	C₄×C₈₃	#380	1	1	yes	characteristic
198	C₄×C₈₃	#382	1	1	yes	characteristic
199	C₄×C₈₃	#389	1	1	yes	characteristic
200	C₄×C₈₃	#389	1	1	yes	characteristic
201	C₄×C₈₃	#391	1	1	yes	characteristic
202	C₄×C₈₃	#391	1	1	yes	characteristic
203	Dic₈₃	—	4	4	no	—
204	Dic₈₃	—	8	4	no	—
205	#10866	—	83	1	no	maximal, Sylow
206	C₂×C₈₃	—	2	1	no	—
207	C₂×C₈₃	—	2	1	no	—
208	C₂×C₈₃	—	2	1	no	—
209	C₂×C₈₃	—	2	1	no	—
210	C₂×C₈₃	—	2	1	no	—
211	C₂×C₈₃	—	2	1	no	—
212	C₂×C₈₃	C₄⋊#95	1	1	yes	characteristic
213	C₂×C₈₃	#1812	1	2	yes	—
214	C₂×#427	—	83	1	no	—
215	C₂×#427	D₈₃	1	1	yes	characteristic
216	C₂×#405	—	83	1	no	—
217	#1740	—	83	2	no	—
218	C₂×H(3,ℤ/4)	—	83	2	no	—
219	C₈₃	#10866	1	1	yes	characteristic, complemented, Sylow
220	C₂²×M₁₆	—	83	1	no	—
221	C₂³×C₈	C₂×D₈₃	1	1	yes	characteristic
222	C₂×#117	—	83	1	no	—
223	C₂×#117	—	83	2	no	—
224	C₂×#117	C₂×D₈₃	1	2	yes	—
225	#427	—	2	2	no	—
226	#427	—	83	4	no	—
227	#427	—	166	2	no	—
228	#427	Dic₈₃	1	4	yes	complemented
229	C₂×#107	—	2	1	no	—
230	C₂×#107	—	166	1	no	—
231	C₂×#106	—	2	1	no	—
232	C₂×#106	—	166	1	no	—
233	#405	—	166	1	no	—
234	#405	—	166	1	no	—
235	#405	—	166	1	no	—
236	#405	—	166	1	no	—
237	C₂×#97	—	83	2	no	—
238	C₂×C₄×C₈	—	83	2	no	—
239	#342	—	166	4	no	—
240	H(3,ℤ/4)	—	166	4	no	—
241	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
242	C₂×M₁₆	—	83	2	no	—
243	C₂×M₁₆	—	83	2	no	—
244	C₂×M₁₆	—	166	1	no	—
245	C₂×M₁₆	—	166	1	no	—
246	C₂×M₁₆	—	166	1	no	—
247	C₂×M₁₆	—	166	1	no	—
248	C₂²×C₈	—	83	2	no	—
249	C₂²×C₈	Dic₁₆₆	1	2	yes	—
250	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
251	C₂²×C₈	C₄×D₈₃	1	1	yes	characteristic
252	C₂²×C₈	C₄×D₈₃	1	2	yes	—
253	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
254	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
255	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
256	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
257	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
258	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	83	4	no	—
263	#117	—	166	2	no	—
264	#117	—	166	2	no	—
265	#117	—	166	2	no	—
266	#117	—	166	1	no	—
267	#117	—	166	1	no	—
268	#117	—	166	1	no	—
269	#117	—	166	1	no	—
270	#117	C₂×Dic₈₃	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	83	2	no	—
273	C₂×C₄⋊C₄	—	166	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	83	2	no	—
276	C₂×C₂²⋊C₄	—	166	2	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	83	2	no	—
279	C₂×C₄²	—	166	2	no	—
280	#107	—	2	4	no	—
281	#107	—	166	4	no	—
282	#106	—	2	4	no	—
283	#106	—	166	4	no	—
284	#97	—	166	2	no	—
285	#97	—	166	2	no	—
286	C₄×C₈	—	166	2	no	—
287	C₄×C₈	—	166	2	no	—
288	C₂⁴	D₄×D₈₃	1	1	yes	characteristic
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	332	2	no	—
291	C₂²×C₄	—	83	4	no	—
292	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
299	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
300	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
301	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
302	C₂²×C₄	#13050589	1	1	yes	characteristic
303	C₂²×C₄	#13050589	1	1	yes	characteristic
304	C₂²×C₄	#13050591	1	1	yes	characteristic
305	C₂²×C₄	#13050591	1	1	yes	characteristic
306	M₁₆	—	166	2	no	—
307	M₁₆	—	166	2	no	—
308	M₁₆	—	166	2	no	—
309	M₁₆	—	166	2	no	—
310	C₂×C₈	—	83	4	no	—
311	C₂×C₈	—	166	2	no	—
312	C₂×C₈	—	166	2	no	—
313	C₂×C₈	C₄×Dic₈₃	1	2	yes	—
314	C₂×C₈	C₄×Dic₈₃	1	2	yes	—
315	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
316	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
317	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
318	C₂×C₈	(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
319	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
320	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
321	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
322	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
323	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
324	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
325	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
326	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
327	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
328	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	332	2	no	—
332	C₄⋊C₄	—	166	4	no	—
333	C₄⋊C₄	—	166	2	no	—
334	C₄⋊C₄	—	166	2	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	332	2	no	—
338	C₂²⋊C₄	—	166	4	no	—
339	C₂²⋊C₄	—	166	2	no	—
340	C₂²⋊C₄	—	166	2	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	4	2	no	—
343	C₄²	—	332	2	no	—
344	C₄²	—	166	4	no	—
345	C₄²	—	166	2	no	—
346	C₄²	—	166	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	C₄⋊C₄×D₈₃	1	1	yes	characteristic
349	C₂³	#14581754	1	1	yes	characteristic
350	C₂³	D₄×Dic₈₃	1	1	yes	characteristic
351	C₂³	#14581763	1	1	yes	characteristic
352	C₂³	#14581767	1	1	yes	characteristic
353	C₂³	#14581788	1	1	yes	characteristic
354	C₂³	#14581791	1	1	yes	characteristic
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	—	332	4	no	—
358	C₂×C₄	—	332	4	no	—
359	C₂×C₄	—	664	4	no	—
360	C₂×C₄	—	166	4	no	—
361	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
362	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
365	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
367	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
369	C₂×C₄	#14581750	1	1	yes	characteristic
370	C₂×C₄	#14581750	1	1	yes	characteristic
371	C₂×C₄	#14581754	1	1	yes	characteristic
372	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
373	C₂×C₄	#14581757	1	1	yes	characteristic
374	C₂×C₄	#14581757	1	1	yes	characteristic
375	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
376	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
377	C₂×C₄	#14581763	1	1	yes	characteristic
378	C₂×C₄	#14581767	1	1	yes	characteristic
379	C₂×C₄	#14581768	1	1	yes	characteristic
380	C₂×C₄	#14581768	1	1	yes	characteristic
381	C₂×C₄	#14581772	1	1	yes	characteristic
382	C₂×C₄	#14581772	1	1	yes	characteristic
383	C₂×C₄	#14581779	1	1	yes	characteristic
384	C₂×C₄	#14581781	1	1	yes	characteristic
385	C₂×C₄	#14581783	1	1	yes	characteristic
386	C₂×C₄	#14581783	1	1	yes	characteristic
387	C₂×C₄	#14581790	1	1	yes	characteristic
388	C₂×C₄	#14581791	1	1	yes	characteristic
389	C₈	—	166	4	no	—
390	C₈	C₈₃⋊#95	1	2	yes	—
391	C₈	C₈₃⋊#95	1	2	yes	—
392	C₈	C₈₃⋊#95	1	2	yes	—
393	C₈	C₈₃⋊#95	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
402	C₂²	#19127558	1	1	yes	characteristic
403	C₂²	#19127570	1	1	yes	characteristic
404	C₂²	#19127597	1	1	yes	characteristic
405	C₂²	#19127600	1	1	yes	characteristic
406	C₂²	#19127602	1	1	yes	characteristic
407	C₂²	#19127604	1	1	yes	characteristic
408	C₄	—	8	4	no	—
409	C₄	—	332	4	no	—
410	C₄	—	664	4	no	—
411	C₄	C₂×C₈₃⋊#95	1	1	yes	characteristic
412	C₄	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
413	C₄	#19127558	1	1	yes	characteristic
414	C₄	#19127566	1	1	yes	characteristic
415	C₄	#19127597	1	1	yes	characteristic
416	C₄	#19127600	1	1	yes	characteristic
417	C₄	#19127606	1	1	yes	characteristic
418	C₄	#19127608	1	1	yes	characteristic
419	C₂	—	2	1	no	—
420	C₂	—	2	1	no	—
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	#24905692	1	1	yes	characteristic
426	C₂	#24907506	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14581750
commutator	C₂×C₄×C₈₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₃
Fitting	C₂×#427×C₈₃	C₂
socle	C₂²×C₈₃	#380
prime radical	C₂⁴×C₈₃	C₂×D₄
cosocle	C₂³×C₄×C₈₃	C₂³
hypercenter	C₂×#427	D₈₃
hypocenter	C₈₃	#10866
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
10. #19127739	C₄	semidirect
17. C₂×#14581702	C₄	semidirect
18. C₂×C₈×Dic₈₃	C₄	semidirect
24. #427×C₈₃	C₄	semidirect
219. C₈₃	#10866	semidirect
228. #427	Dic₈₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19127739	2
C₂×#19127656	2
#24907195	2
C₂×#19127457	2
C₂×#427×C₈₃	2
#10866	83