Subgroups — #35310355

Order 21248.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 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×#19127473	C₂	1	2	yes	maximal
4	#24907190	C₂	1	2	yes	maximal
5	C₂²×#108×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	1	no	—
10	C₂×#14581728	—	2	1	no	—
11	C₂×#14581728	—	2	2	no	—
12	C₂×#14581728	C₄	1	4	yes	complemented
13	#19127656	—	2	2	no	—
14	#19127656	C₄	1	4	yes	—
15	C₂×#14581702	—	2	1	no	—
16	C₂×C₈×Dic₈₃	—	2	1	no	—
17	#19127473	—	2	4	no	—
18	#19127466	—	2	4	no	—
19	C₂²×M₁₆×C₈₃	C₂²	1	2	yes	—
20	C₂³×C₈×C₈₃	C₂²	1	1	yes	characteristic
21	C₂×#108×C₈₃	—	2	2	no	—
22	C₂×#108×C₈₃	—	2	2	no	—
23	C₂×#108×C₈₃	C₄	1	4	yes	complemented
24	C₂×#13050574	—	2	1	no	—
25	C₂×#13050574	—	2	2	no	—
26	C₂×#13050574	—	2	2	no	—
27	C₂×#13050574	—	2	2	no	—
28	C₂×#13050574	—	2	2	no	—
29	C₂×#13050574	—	2	1	no	—
30	C₂×#13050574	—	2	1	no	—
31	C₂×#13050574	—	2	2	no	—
32	C₂×#13050574	C₂×C₄	1	4	yes	—
33	C₂×#13050574	C₂×C₄	1	2	yes	—
34	C₂×#13050574	D₄	1	2	yes	—
35	C₂×#13050574	Q₈	1	2	yes	—
36	C₂²×C₈₃⋊C₈	—	2	1	no	—
37	C₂²×C₈₃⋊C₈	—	2	2	no	—
38	#14581751	—	2	1	no	—
39	#14581751	—	2	1	no	—
40	#14581751	C₂×C₄	1	2	yes	—
41	#14581751	D₄	1	2	yes	—
42	C₂×C₄⋊Dic₈₃	—	2	1	no	—
43	C₂×C₂²⋊Dic₈₃	Q₈	1	2	yes	—
44	C₂×C₄×Dic₈₃	—	2	1	no	—
45	#14581728	—	2	4	no	—
46	#14581728	—	2	4	no	—
47	#14581702	—	2	4	no	—
48	C₈×Dic₈₃	—	2	4	no	—
49	C₂³×C₄×C₈₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₈₃	—	2	2	no	—
51	C₂×M₁₆×C₈₃	—	2	2	no	—
52	C₂×M₁₆×C₈₃	—	2	2	no	—
53	C₂×M₁₆×C₈₃	—	2	2	no	—
54	C₂×M₁₆×C₈₃	—	2	2	no	—
55	C₂×M₁₆×C₈₃	C₂×C₄	1	4	yes	—
56	C₂²×C₈×C₈₃	—	2	2	no	—
57	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₈₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₈₃	D₄	1	2	yes	—
63	C₂²×C₈×C₈₃	D₄	1	2	yes	—
64	C₂²×C₈×C₈₃	Q₈	1	2	yes	—
65	#108×C₈₃	—	2	8	no	—
66	C₂²×Dic₈₃	—	2	2	no	—
67	#13050574	—	2	2	no	—
68	#13050574	—	2	2	no	—
69	#13050574	—	2	2	no	—
70	#13050574	—	2	4	no	—
71	#13050574	—	2	4	no	—
72	#13050574	—	4	2	no	—
73	#13050574	—	4	2	no	—
74	#13050574	C₄⋊C₄	1	4	yes	—
75	C₂×C₈₃⋊C₈	—	2	2	no	—
76	C₂×C₈₃⋊C₈	—	2	2	no	—
77	C₂×C₈₃⋊C₈	—	2	2	no	—
78	C₂×C₈₃⋊C₈	—	2	4	no	—
79	C₂×C₈₃⋊C₈	—	4	2	no	—
80	C₂×C₈₃⋊C₈	—	4	2	no	—
81	C₄⋊Dic₈₃	—	2	2	no	—
82	C₄⋊Dic₈₃	—	2	2	no	—
83	C₂²⋊Dic₈₃	—	2	2	no	—
84	C₂²⋊Dic₈₃	C₄⋊C₄	1	4	yes	—
85	C₄×Dic₈₃	—	2	2	no	—
86	C₄×Dic₈₃	—	2	2	no	—
87	C₂⁴×C₈₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
97	C₂²×C₄×C₈₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
99	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
100	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₈₃	#41	1	1	yes	characteristic
102	M₁₆×C₈₃	—	2	4	no	—
103	M₁₆×C₈₃	—	2	4	no	—
104	M₁₆×C₈₃	—	4	2	no	—
105	M₁₆×C₈₃	—	4	2	no	—
106	C₂×C₈×C₈₃	—	2	4	no	—
107	C₂×C₈×C₈₃	—	4	2	no	—
108	C₂×C₈×C₈₃	—	4	2	no	—
109	C₂×C₈×C₈₃	C₄²	1	4	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	4	yes	—
115	C₂×C₈×C₈₃	C₄⋊C₄	1	4	yes	—
116	C₂×C₈×C₈₃	C₄⋊C₄	1	4	yes	—
117	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
118	C₂×C₈×C₈₃	C₄⋊C₄	1	2	yes	—
119	C₂³×C₈₃	—	4	2	no	—
120	C₂³×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₈₃	C₄×Q₈	1	1	yes	characteristic
122	C₂³×C₈₃	C₄×Q₈	1	1	yes	characteristic
123	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
124	C₂³×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
125	C₂³×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂³×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
127	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
128	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₈₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
136	C₂×C₄×C₈₃	#117	1	1	yes	characteristic
137	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₃	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₈₃	C₄×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
144	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
145	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
146	C₂×C₄×C₈₃	#121	1	1	yes	characteristic
147	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
150	C₂×C₄×C₈₃	#124	1	1	yes	characteristic
151	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
152	C₂×C₄×C₈₃	#125	1	1	yes	characteristic
153	C₂×C₄×C₈₃	#127	1	1	yes	characteristic
154	C₂×C₄×C₈₃	C₄⋊Q₈	1	1	yes	characteristic
155	C₂×Dic₈₃	—	2	4	no	—
156	C₂×Dic₈₃	—	4	4	no	—
157	C₈×C₈₃	—	4	4	no	—
158	C₈×C₈₃	#95	1	4	yes	—
159	C₈×C₈₃	#95	1	4	yes	—
160	C₈₃⋊C₈	—	2	4	no	—
161	C₈₃⋊C₈	—	4	4	no	—
162	C₂²×C₈₃	—	2	2	no	—
163	C₂²×C₈₃	—	2	2	no	—
164	C₂²×C₈₃	—	2	2	no	—
165	C₂²×C₈₃	—	4	1	no	—
166	C₂²×C₈₃	—	4	1	no	—
167	C₂²×C₈₃	—	4	1	no	—
168	C₂²×C₈₃	—	4	1	no	—
169	C₂²×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₈₃	#380	1	1	yes	characteristic
171	C₂²×C₈₃	#384	1	1	yes	characteristic
172	C₂²×C₈₃	#389	1	1	yes	characteristic
173	C₂²×C₈₃	#389	1	1	yes	characteristic
174	C₂²×C₈₃	#391	1	1	yes	characteristic
175	C₂²×C₈₃	#391	1	1	yes	characteristic
176	C₄×C₈₃	C₂×#95	1	1	yes	characteristic
177	C₄×C₈₃	C₄×C₄⋊C₄	1	1	yes	characteristic
178	C₄×C₈₃	#380	1	1	yes	characteristic
179	C₄×C₈₃	#382	1	1	yes	characteristic
180	C₄×C₈₃	#389	1	1	yes	characteristic
181	C₄×C₈₃	#389	1	1	yes	characteristic
182	C₄×C₈₃	#390	1	1	yes	characteristic
183	C₄×C₈₃	#390	1	1	yes	characteristic
184	Dic₈₃	—	4	4	no	—
185	#10873	—	83	1	no	maximal, Sylow
186	C₂×C₈₃	—	2	1	no	—
187	C₂×C₈₃	—	2	1	no	—
188	C₂×C₈₃	—	2	1	no	—
189	C₂×C₈₃	—	2	1	no	—
190	C₂×C₈₃	—	2	1	no	—
191	C₂×C₈₃	—	2	1	no	—
192	C₂×C₈₃	C₄⋊#95	1	1	yes	characteristic
193	C₂×C₈₃	#1953	1	2	yes	—
194	C₂²×#108	—	83	1	no	—
195	C₂²×#108	D₈₃	1	1	yes	characteristic
196	C₂×#405	—	83	1	no	—
197	C₂×#344	—	83	2	no	—
198	#1738	—	83	2	no	—
199	C₈₃	#10873	1	1	yes	characteristic, complemented, Sylow
200	C₂²×M₁₆	—	83	1	no	—
201	C₂²×M₁₆	—	83	2	no	—
202	C₂²×M₁₆	C₂×D₈₃	1	2	yes	—
203	C₂³×C₈	C₂×D₈₃	1	1	yes	characteristic
204	C₂×#117	—	83	1	no	—
205	C₂×#108	—	2	2	no	—
206	C₂×#108	—	2	2	no	—
207	C₂×#108	—	83	4	no	—
208	C₂×#108	—	166	1	no	—
209	C₂×#108	—	166	1	no	—
210	C₂×#108	—	166	2	no	—
211	C₂×#108	Dic₈₃	1	4	yes	complemented
212	#405	—	83	4	no	—
213	#405	—	166	2	no	—
214	C₂×#97	—	166	1	no	—
215	C₂×C₄×C₈	—	166	1	no	—
216	#344	—	166	4	no	—
217	#341	—	166	4	no	—
218	C₂³×C₄	C₂²×D₈₃	1	1	yes	characteristic
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	83	2	no	—
225	C₂×M₁₆	—	83	2	no	—
226	C₂×M₁₆	—	83	2	no	—
227	C₂×M₁₆	—	83	4	no	—
228	C₂×M₁₆	—	166	2	no	—
229	C₂×M₁₆	—	166	2	no	—
230	C₂×M₁₆	—	166	2	no	—
231	C₂×M₁₆	—	166	2	no	—
232	C₂×M₁₆	—	166	2	no	—
233	C₂×M₁₆	—	166	1	no	—
234	C₂×M₁₆	—	166	1	no	—
235	C₂×M₁₆	—	166	1	no	—
236	C₂×M₁₆	C₂×Dic₈₃	1	4	yes	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	166	2	no	—
239	C₂²×C₈	—	166	1	no	—
240	C₂²×C₈	Dic₁₆₆	1	2	yes	—
241	C₂²×C₈	C₄×D₈₃	1	2	yes	—
242	C₂²×C₈	C₄×D₈₃	1	2	yes	—
243	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
244	C₂²×C₈	D₃₃₂	1	1	yes	characteristic
245	C₂²×C₈	C₂×Dic₈₃	1	2	yes	—
246	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
247	C₂²×C₈	C₂²⋊D₈₃	1	2	yes	—
248	#117	—	83	2	no	—
249	#117	—	83	2	no	—
250	#117	—	166	1	no	—
251	#117	—	166	1	no	—
252	C₂×C₄⋊C₄	—	166	1	no	—
253	C₂×C₂²⋊C₄	—	83	2	no	—
254	C₂×C₄²	—	166	1	no	—
255	#108	—	2	8	no	—
256	#108	—	166	4	no	—
257	#108	—	166	4	no	—
258	#97	—	166	4	no	—
259	C₄×C₈	—	166	4	no	—
260	C₂⁴	Q₈×D₈₃	1	1	yes	characteristic
261	C₂²×C₄	—	166	2	no	—
262	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
266	C₂²×C₄	D₄×D₈₃	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₈₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₃₃₂	1	1	yes	characteristic
270	C₂²×C₄	Q₈×D₈₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₁₆₆	1	1	yes	characteristic
272	C₂²×C₄	#13050589	1	1	yes	characteristic
273	C₂²×C₄	#13050589	1	1	yes	characteristic
274	C₂²×C₄	#13050591	1	1	yes	characteristic
275	C₂²×C₄	#13050591	1	1	yes	characteristic
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	4	2	no	—
280	M₁₆	—	332	2	no	—
281	M₁₆	—	332	2	no	—
282	M₁₆	—	83	4	no	—
283	M₁₆	—	166	4	no	—
284	M₁₆	—	166	4	no	—
285	M₁₆	—	166	2	no	—
286	M₁₆	—	166	2	no	—
287	M₁₆	—	166	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	332	2	no	—
292	C₂×C₈	—	332	2	no	—
293	C₂×C₈	—	166	4	no	—
294	C₂×C₈	—	166	2	no	—
295	C₂×C₈	—	166	2	no	—
296	C₂×C₈	—	166	2	no	—
297	C₂×C₈	C₄×Dic₈₃	1	4	yes	—
298	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
299	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
300	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
301	C₂×C₈	(C₂×D₈₃)⋊C₄	1	2	yes	—
302	C₂×C₈	C₂²⋊Dic₈₃	1	4	yes	—
303	C₂×C₈	Dic₈₃⋊C₄	1	4	yes	—
304	C₂×C₈	Dic₈₃⋊C₄	1	4	yes	—
305	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
306	C₂×C₈	C₄⋊Dic₈₃	1	2	yes	—
307	C₄⋊C₄	—	166	2	no	—
308	C₄⋊C₄	—	166	2	no	—
309	C₂²⋊C₄	—	83	4	no	—
310	C₂²⋊C₄	—	166	2	no	—
311	C₄²	—	166	2	no	—
312	C₄²	—	166	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₄⋊C₄×D₈₃	1	1	yes	characteristic
315	C₂³	#14581757	1	1	yes	characteristic
316	C₂³	Q₈×Dic₈₃	1	1	yes	characteristic
317	C₂³	#14581768	1	1	yes	characteristic
318	C₂³	#14581772	1	1	yes	characteristic
319	C₂³	#14581790	1	1	yes	characteristic
320	C₂³	#14581791	1	1	yes	characteristic
321	C₂×C₄	—	332	4	no	—
322	C₂×C₄	—	166	4	no	—
323	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
324	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×(C₂×D₈₃)⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₂²⋊Dic₈₃	1	1	yes	characteristic
327	C₂×C₄	C₄⋊C₄×D₈₃	1	1	yes	characteristic
328	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₈₃⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₈₃	1	1	yes	characteristic
331	C₂×C₄	#14581750	1	1	yes	characteristic
332	C₂×C₄	#14581750	1	1	yes	characteristic
333	C₂×C₄	#14581754	1	1	yes	characteristic
334	C₂×C₄	#14581754	1	1	yes	characteristic
335	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
336	C₂×C₄	D₄×Dic₈₃	1	1	yes	characteristic
337	C₂×C₄	#14581757	1	1	yes	characteristic
338	C₂×C₄	Q₈×Dic₈₃	1	1	yes	characteristic
339	C₂×C₄	#14581763	1	1	yes	characteristic
340	C₂×C₄	#14581763	1	1	yes	characteristic
341	C₂×C₄	#14581767	1	1	yes	characteristic
342	C₂×C₄	#14581767	1	1	yes	characteristic
343	C₂×C₄	#14581768	1	1	yes	characteristic
344	C₂×C₄	#14581772	1	1	yes	characteristic
345	C₂×C₄	#14581779	1	1	yes	characteristic
346	C₂×C₄	#14581781	1	1	yes	characteristic
347	C₂×C₄	#14581783	1	1	yes	characteristic
348	C₂×C₄	#14581783	1	1	yes	characteristic
349	C₂×C₄	#14581788	1	1	yes	characteristic
350	C₂×C₄	#14581791	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₈	—	332	4	no	—
353	C₈	—	166	4	no	—
354	C₈	C₈₃⋊#95	1	4	yes	—
355	C₈	C₈₃⋊#95	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
364	C₂²	#19127558	1	1	yes	characteristic
365	C₂²	#19127570	1	1	yes	characteristic
366	C₂²	#19127597	1	1	yes	characteristic
367	C₂²	#19127600	1	1	yes	characteristic
368	C₂²	#19127606	1	1	yes	characteristic
369	C₂²	#19127608	1	1	yes	characteristic
370	C₄	—	332	4	no	—
371	C₄	C₂×C₈₃⋊#95	1	1	yes	characteristic
372	C₄	C₄⋊C₄×Dic₈₃	1	1	yes	characteristic
373	C₄	#19127558	1	1	yes	characteristic
374	C₄	#19127566	1	1	yes	characteristic
375	C₄	#19127597	1	1	yes	characteristic
376	C₄	#19127600	1	1	yes	characteristic
377	C₄	#19127602	1	1	yes	characteristic
378	C₄	#19127604	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	#24905692	1	1	yes	characteristic
386	C₂	#24908254	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14581767
commutator	C₂×C₄×C₈₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₈₃
Fitting	C₂²×#108×C₈₃	C₂
socle	C₂²×C₈₃	#389
prime radical	C₂⁴×C₈₃	C₂×Q₈
cosocle	C₂³×C₄×C₈₃	C₂³
hypercenter	C₂²×#108	D₈₃
hypocenter	C₈₃	#10873
LCS	G ▷ C₂×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
12. C₂×#14581728	C₄	semidirect
23. C₂×#108×C₈₃	C₄	semidirect
199. C₈₃	#10873	semidirect
211. 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
C₂×#19127656	2
C₂×#19127473	2
#24907190	2
C₂²×#108×C₈₃	2
#10873	83