Subgroups — #35310327

Order 21248.

730 conjugacy classes of subgroups.

The subgroup lattice has 416 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	C₂×#19127656	C₂	1	1	yes	maximal, characteristic
3	C₂×#19127471	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	2	yes	—
7	C₂²×#13050574	C₂²	1	1	yes	characteristic
8	C₂×#14581751	C₂²	1	1	yes	characteristic
9	C₂×#14581728	—	2	2	no	—
10	C₂×#14581728	—	2	1	no	—
11	C₂×#14581728	—	2	1	no	—
12	C₂×#14581728	C₄	1	4	yes	complemented
13	#19127656	—	2	2	no	—
14	#19127656	—	2	2	no	—
15	C₂×#14581702	C₄	1	2	yes	complemented
16	C₂×C₈×Dic₈₃	C₄	1	2	yes	complemented
17	#19127471	—	2	4	no	—
18	#19127457	—	2	4	no	—
19	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₈₃	C₂²	1	2	yes	—
21	#427×C₈₃	—	2	2	no	—
22	#427×C₈₃	C₄	1	4	yes	complemented
23	C₂×#107×C₈₃	—	2	1	no	—
24	C₂×#106×C₈₃	—	2	1	no	—
25	C₂×#13050574	—	2	1	no	—
26	C₂×#13050574	—	2	1	no	—
27	C₂×#13050574	—	2	2	no	—
28	C₂×#13050574	—	2	2	no	—
29	C₂×#13050574	—	2	2	no	—
30	C₂×#13050574	—	2	2	no	—
31	C₂×#13050574	—	2	1	no	—
32	C₂×#13050574	—	2	1	no	—
33	C₂×#13050574	—	2	2	no	—
34	C₂×#13050574	C₂×C₄	1	4	yes	—
35	C₂×#13050574	D₄	1	2	yes	—
36	C₂×#13050574	Q₈	1	2	yes	—
37	C₂²×C₈₃⋊C₈	—	2	2	no	—
38	C₂²×C₈₃⋊C₈	C₂×C₄	1	2	yes	—
39	#14581751	—	2	1	no	—
40	#14581751	—	2	1	no	—
41	#14581751	D₄	1	2	yes	—
42	#14581751	Q₈	1	2	yes	—
43	C₂×C₄⋊Dic₈₃	—	2	1	no	—
44	C₂×C₂²⋊Dic₈₃	—	2	1	no	—
45	C₂×C₄×Dic₈₃	C₂×C₄	1	2	yes	—
46	#14581728	—	2	4	no	—
47	#14581728	—	2	4	no	—
48	#14581702	—	2	4	no	—
49	C₈×Dic₈₃	—	2	4	no	—
50	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₈₃	D₄	1	2	yes	—
56	C₂²×C₈×C₈₃	D₄	1	2	yes	—
57	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₈₃	Q₈	1	1	yes	characteristic
60	C₂²×C₈×C₈₃	Q₈	1	1	yes	characteristic
61	#117×C₈₃	—	2	2	no	—
62	#117×C₈₃	—	2	2	no	—
63	#117×C₈₃	—	2	2	no	—
64	#117×C₈₃	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₈₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₈₃	—	2	2	no	—
67	C₂×C₄²×C₈₃	—	2	2	no	—
68	#107×C₈₃	—	2	4	no	—
69	#106×C₈₃	—	2	4	no	—
70	C₂²×Dic₈₃	—	2	2	no	—
71	#13050574	—	2	2	no	—
72	#13050574	—	2	2	no	—
73	#13050574	—	2	2	no	—
74	#13050574	—	2	2	no	—
75	#13050574	—	2	4	no	—
76	#13050574	—	2	4	no	—
77	#13050574	—	4	2	no	—
78	#13050574	—	4	2	no	—
79	C₂×C₈₃⋊C₈	—	2	2	no	—
80	C₂×C₈₃⋊C₈	—	2	2	no	—
81	C₂×C₈₃⋊C₈	—	2	4	no	—
82	C₂×C₈₃⋊C₈	—	4	2	no	—
83	C₂×C₈₃⋊C₈	—	4	2	no	—
84	C₂×C₈₃⋊C₈	C₄⋊C₄	1	4	yes	—
85	C₄⋊Dic₈₃	—	2	2	no	—
86	C₄⋊Dic₈₃	—	2	2	no	—
87	C₂²⋊Dic₈₃	—	2	2	no	—
88	C₂²⋊Dic₈₃	—	2	2	no	—
89	C₄×Dic₈₃	—	2	2	no	—
90	C₄×Dic₈₃	C₄⋊C₄	1	4	yes	—
91	C₂⁴×C₈₃	#41	1	1	yes	characteristic
92	C₂²×C₄×C₈₃	—	4	2	no	—
93	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
104	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
105	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
107	C₂×C₈×C₈₃	C₄²	1	2	yes	—
108	C₂×C₈×C₈₃	C₄²	1	2	yes	—
109	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
110	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
111	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
112	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
113	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
114	C₂×C₈×C₈₃	C₂²⋊C₄	1	2	yes	—
115	C₂×C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₈×C₈₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
120	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
121	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
122	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
123	C₄⋊C₄×C₈₃	—	2	4	no	—
124	C₄⋊C₄×C₈₃	—	4	2	no	—
125	C₂²⋊C₄×C₈₃	—	2	4	no	—
126	C₂²⋊C₄×C₈₃	—	4	2	no	—
127	C₄²×C₈₃	—	2	4	no	—
128	C₄²×C₈₃	—	4	2	no	—
129	C₂³×C₈₃	—	4	2	no	—
130	C₂³×C₈₃	#117	1	1	yes	characteristic
131	C₂³×C₈₃	C₄×D₄	1	1	yes	characteristic
132	C₂³×C₈₃	C₄×Q₈	1	1	yes	characteristic
133	C₂³×C₈₃	#121	1	1	yes	characteristic
134	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₈₃	#124	1	1	yes	characteristic
136	C₂³×C₈₃	#125	1	1	yes	characteristic
137	C₂×C₄×C₈₃	—	4	4	no	—
138	C₂×C₄×C₈₃	—	8	4	no	—
139	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
149	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
156	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
162	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
163	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
167	C₂×Dic₈₃	—	2	4	no	—
168	C₂×Dic₈₃	—	4	4	no	—
169	C₈×C₈₃	#95	1	2	yes	—
170	C₈×C₈₃	#95	1	2	yes	—
171	C₈×C₈₃	#95	1	2	yes	—
172	C₈×C₈₃	#95	1	2	yes	—
173	C₈₃⋊C₈	—	2	4	no	—
174	C₈₃⋊C₈	—	4	4	no	—
175	C₂²×C₈₃	—	2	2	no	—
176	C₂²×C₈₃	—	2	2	no	—
177	C₂²×C₈₃	—	2	2	no	—
178	C₂²×C₈₃	—	4	1	no	—
179	C₂²×C₈₃	—	4	1	no	—
180	C₂²×C₈₃	—	4	1	no	—
181	C₂²×C₈₃	—	4	1	no	—
182	C₂²×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₈₃	#380	1	1	yes	characteristic
184	C₂²×C₈₃	#382	1	1	yes	characteristic
185	C₂²×C₈₃	#389	1	1	yes	characteristic
186	C₂²×C₈₃	#389	1	1	yes	characteristic
187	C₂²×C₈₃	#390	1	1	yes	characteristic
188	C₂²×C₈₃	#391	1	1	yes	characteristic
189	C₄×C₈₃	—	8	4	no	—
190	C₄×C₈₃	C₂×#95	1	1	yes	characteristic
191	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₈₃	#380	1	1	yes	characteristic
193	C₄×C₈₃	#384	1	1	yes	characteristic
194	C₄×C₈₃	#389	1	1	yes	characteristic
195	C₄×C₈₃	#389	1	1	yes	characteristic
196	C₄×C₈₃	#390	1	1	yes	characteristic
197	C₄×C₈₃	#391	1	1	yes	characteristic
198	Dic₈₃	—	4	4	no	—
199	#10868	—	83	1	no	maximal, Sylow
200	C₂×C₈₃	—	2	1	no	—
201	C₂×C₈₃	—	2	1	no	—
202	C₂×C₈₃	—	2	1	no	—
203	C₂×C₈₃	—	2	1	no	—
204	C₂×C₈₃	—	2	1	no	—
205	C₂×C₈₃	—	2	1	no	—
206	C₂×C₈₃	C₄⋊#95	1	1	yes	characteristic
207	C₂×C₈₃	#1833	1	2	yes	—
208	C₂²×#108	—	83	1	no	—
209	C₂×#427	D₈₃	1	1	yes	characteristic
210	C₂×#405	—	83	1	no	—
211	C₂×#344	—	83	2	no	—
212	C₂×H(3,ℤ/4)	—	83	2	no	—
213	C₈₃	#10868	1	1	yes	characteristic, complemented, Sylow
214	C₂²×M₁₆	—	83	1	no	—
215	C₂²×M₁₆	—	83	2	no	—
216	C₂³×C₈	C₂×D₈₃	1	1	yes	characteristic
217	C₂×#117	—	83	1	no	—
218	C₂×#117	C₂×D₈₃	1	2	yes	—
219	C₂×#108	—	83	4	no	—
220	C₂×#108	—	166	2	no	—
221	C₂×#108	—	166	1	no	—
222	C₂×#108	—	166	1	no	—
223	#427	—	2	2	no	—
224	#427	Dic₈₃	1	4	yes	complemented
225	C₂×#107	—	2	1	no	—
226	C₂×#106	—	2	1	no	—
227	#405	—	166	2	no	—
228	#405	—	166	2	no	—
229	C₂×#97	—	83	2	no	—
230	C₂×C₄×C₈	—	83	2	no	—
231	#344	—	166	4	no	—
232	H(3,ℤ/4)	—	166	4	no	—
233	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
234	C₂×M₁₆	—	83	2	no	—
235	C₂×M₁₆	—	83	2	no	—
236	C₂×M₁₆	—	83	4	no	—
237	C₂×M₁₆	—	166	2	no	—
238	C₂×M₁₆	—	166	2	no	—
239	C₂×M₁₆	—	166	2	no	—
240	C₂×M₁₆	—	166	2	no	—
241	C₂×M₁₆	—	166	2	no	—
242	C₂×M₁₆	—	166	1	no	—
243	C₂×M₁₆	—	166	1	no	—
244	C₂×M₁₆	—	166	1	no	—
245	C₂×M₁₆	—	166	1	no	—
246	C₂²×C₈	—	83	2	no	—
247	C₂²×C₈	—	166	2	no	—
248	C₂²×C₈	Dic₁₆₆	1	1	yes	characteristic
249	C₂²×C₈	Dic₁₆₆	1	1	yes	characteristic
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	2	yes	—
254	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
255	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
256	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
257	C₂²×C₈	C₂²⋊D₈₃	1	1	yes	characteristic
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	—	83	2	no	—
262	#117	—	83	2	no	—
263	#117	—	166	1	no	—
264	#117	—	166	1	no	—
265	#117	C₂×Dic₈₃	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	166	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	166	1	no	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	83	2	no	—
272	#108	—	166	4	no	—
273	#108	—	166	4	no	—
274	#107	—	2	4	no	—
275	#106	—	2	4	no	—
276	#97	—	166	4	no	—
277	C₄×C₈	—	166	4	no	—
278	C₂⁴	#13050589	1	1	yes	characteristic
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	166	2	no	—
281	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
284	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
289	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
290	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
292	C₂²×C₄	#13050589	1	1	yes	characteristic
293	C₂²×C₄	#13050591	1	1	yes	characteristic
294	C₂²×C₄	#13050591	1	1	yes	characteristic
295	M₁₆	—	332	2	no	—
296	M₁₆	—	332	2	no	—
297	M₁₆	—	166	4	no	—
298	M₁₆	—	166	4	no	—
299	M₁₆	—	166	2	no	—
300	M₁₆	—	166	2	no	—
301	M₁₆	—	166	2	no	—
302	M₁₆	—	166	2	no	—
303	C₂×C₈	—	332	2	no	—
304	C₂×C₈	—	332	2	no	—
305	C₂×C₈	—	83	4	no	—
306	C₂×C₈	—	166	4	no	—
307	C₂×C₈	—	166	2	no	—
308	C₂×C₈	—	166	2	no	—
309	C₂×C₈	C₄×Dic₈₃	1	2	yes	—
310	C₂×C₈	C₄×Dic₈₃	1	2	yes	—
311	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
312	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
313	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
314	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
315	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
316	C₂×C₈	C₂²⋊Dic₈₃	1	2	yes	—
317	C₂×C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
318	C₂×C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
319	C₂×C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
320	C₂×C₈	Dic₈₃⋊C₄	1	1	yes	characteristic
321	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
322	C₂×C₈	Dic₈₃⋊C₄	1	2	yes	—
323	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
324	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	166	2	no	—
328	C₄⋊C₄	—	166	2	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	166	2	no	—
332	C₂²⋊C₄	—	166	2	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	4	2	no	—
335	C₄²	—	83	4	no	—
336	C₄²	—	166	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	#14581750	1	1	yes	characteristic
339	C₂³	D₄×Dic₈₃	1	1	yes	characteristic
340	C₂³	#14581757	1	1	yes	characteristic
341	C₂³	#14581763	1	1	yes	characteristic
342	C₂³	#14581772	1	1	yes	characteristic
343	C₂³	#14581779	1	1	yes	characteristic
344	C₂³	#14581783	1	1	yes	characteristic
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	332	4	no	—
348	C₂×C₄	—	166	4	no	—
349	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
350	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
353	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
354	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
358	C₂×C₄	#14581750	1	1	yes	characteristic
359	C₂×C₄	#14581754	1	1	yes	characteristic
360	C₂×C₄	#14581754	1	1	yes	characteristic
361	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
362	C₂×C₄	#14581757	1	1	yes	characteristic
363	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
364	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
365	C₂×C₄	#14581763	1	1	yes	characteristic
366	C₂×C₄	#14581767	1	1	yes	characteristic
367	C₂×C₄	#14581767	1	1	yes	characteristic
368	C₂×C₄	#14581768	1	1	yes	characteristic
369	C₂×C₄	#14581768	1	1	yes	characteristic
370	C₂×C₄	#14581772	1	1	yes	characteristic
371	C₂×C₄	#14581781	1	1	yes	characteristic
372	C₂×C₄	#14581783	1	1	yes	characteristic
373	C₂×C₄	#14581788	1	1	yes	characteristic
374	C₂×C₄	#14581790	1	1	yes	characteristic
375	C₂×C₄	#14581791	1	1	yes	characteristic
376	C₂×C₄	#14581791	1	1	yes	characteristic
377	C₈	—	332	4	no	—
378	C₈	—	166	4	no	—
379	C₈	C₈₃⋊#95	1	2	yes	—
380	C₈	C₈₃⋊#95	1	2	yes	—
381	C₈	C₈₃⋊#95	1	2	yes	—
382	C₈	C₈₃⋊#95	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
391	C₂²	#19127558	1	1	yes	characteristic
392	C₂²	#19127566	1	1	yes	characteristic
393	C₂²	#19127597	1	1	yes	characteristic
394	C₂²	#19127600	1	1	yes	characteristic
395	C₂²	#19127604	1	1	yes	characteristic
396	C₂²	#19127606	1	1	yes	characteristic
397	C₄	—	8	4	no	—
398	C₄	—	332	4	no	—
399	C₄	C₂×C₈₃⋊#95	1	1	yes	characteristic
400	C₄	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
401	C₄	#19127558	1	1	yes	characteristic
402	C₄	#19127570	1	1	yes	characteristic
403	C₄	#19127597	1	1	yes	characteristic
404	C₄	#19127600	1	1	yes	characteristic
405	C₄	#19127602	1	1	yes	characteristic
406	C₄	#19127608	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	#24905692	1	1	yes	characteristic
414	C₂	#24907586	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	#382
prime radical	C₂⁴×C₈₃	#41
cosocle	C₂³×C₄×C₈₃	C₂³
hypercenter	C₂×#427	D₈₃
hypocenter	C₈₃	#10868
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
12. C₂×#14581728	C₄	semidirect
15. C₂×#14581702	C₄	semidirect
16. C₂×C₈×Dic₈₃	C₄	semidirect
22. #427×C₈₃	C₄	semidirect
213. C₈₃	#10868	semidirect
224. #427	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
C₂×#19127656	2
C₂×#19127471	2
C₂×#19127457	2
C₂×#427×C₈₃	2
#10868	83