Subgroups — #31903371

Order 18176.

714 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556064	C₂	1	1	yes	maximal, characteristic
2	C₂×#17985954	C₂	1	1	yes	maximal, characteristic
3	#22588078	C₂	1	2	yes	maximal
4	C₂×C₇₁⋊#338	C₂	1	2	yes	maximal
5	C₂²×#108×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11765849	C₂²	1	2	yes	—
7	C₂²×#11765849	C₂²	1	1	yes	characteristic
8	C₂×#14556087	C₂²	1	1	yes	characteristic
9	C₂×#14556064	—	2	2	no	—
10	C₂×#14556064	—	2	2	no	—
11	C₂×#14556064	C₄	1	4	yes	complemented
12	#17985954	—	2	2	no	—
13	#17985954	—	2	2	no	—
14	C₂×#14556038	C₄	1	2	yes	—
15	C₂×C₈×Dic₇₁	C₄	1	2	yes	—
16	#17985767	—	2	4	no	—
17	C₇₁⋊#338	—	2	4	no	—
18	C₂²×M₁₆×C₇₁	C₂²	1	2	yes	—
19	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#108×C₇₁	—	2	2	no	—
21	C₂×#108×C₇₁	—	2	2	no	—
22	C₂×#108×C₇₁	C₄	1	4	yes	complemented
23	C₂×#11765849	—	2	1	no	—
24	C₂×#11765849	—	2	1	no	—
25	C₂×#11765849	—	2	2	no	—
26	C₂×#11765849	—	2	2	no	—
27	C₂×#11765849	—	2	2	no	—
28	C₂×#11765849	—	2	2	no	—
29	C₂×#11765849	—	2	1	no	—
30	C₂×#11765849	—	2	1	no	—
31	C₂×#11765849	—	2	2	no	—
32	C₂×#11765849	C₂×C₄	1	4	yes	—
33	C₂×#11765849	D₄	1	2	yes	—
34	C₂×#11765849	Q₈	1	2	yes	—
35	C₂²×C₇₁⋊C₈	—	2	2	no	—
36	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
37	#14556087	—	2	1	no	—
38	#14556087	—	2	1	no	—
39	#14556087	—	2	1	no	—
40	#14556087	—	2	1	no	—
41	C₂×C₄⋊Dic₇₁	D₄	1	2	yes	—
42	C₂×C₂²⋊Dic₇₁	Q₈	1	2	yes	—
43	C₂×C₄×Dic₇₁	C₂×C₄	1	2	yes	—
44	#14556064	—	2	8	no	—
45	#14556038	—	2	4	no	—
46	C₈×Dic₇₁	—	2	4	no	—
47	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₇₁	—	2	2	no	—
49	C₂×M₁₆×C₇₁	—	2	2	no	—
50	C₂×M₁₆×C₇₁	—	2	2	no	—
51	C₂×M₁₆×C₇₁	—	2	2	no	—
52	C₂×M₁₆×C₇₁	—	2	2	no	—
53	C₂×M₁₆×C₇₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₇₁	—	2	2	no	—
55	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
58	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₇₁	D₄	1	2	yes	—
60	C₂²×C₈×C₇₁	D₄	1	2	yes	—
61	C₂²×C₈×C₇₁	D₄	1	2	yes	—
62	C₂²×C₈×C₇₁	Q₈	1	2	yes	—
63	#108×C₇₁	—	2	8	no	—
64	C₂²×Dic₇₁	C₄⋊C₄	1	4	yes	—
65	#11765849	—	2	2	no	—
66	#11765849	—	2	2	no	—
67	#11765849	—	2	2	no	—
68	#11765849	—	2	2	no	—
69	#11765849	—	2	4	no	—
70	#11765849	—	2	4	no	—
71	#11765849	—	4	2	no	—
72	#11765849	—	4	2	no	—
73	C₂×C₇₁⋊C₈	—	2	2	no	—
74	C₂×C₇₁⋊C₈	—	2	2	no	—
75	C₂×C₇₁⋊C₈	—	2	4	no	—
76	C₂×C₇₁⋊C₈	—	4	2	no	—
77	C₂×C₇₁⋊C₈	—	4	2	no	—
78	C₂×C₇₁⋊C₈	C₄⋊C₄	1	4	yes	—
79	C₄⋊Dic₇₁	—	2	2	no	—
80	C₄⋊Dic₇₁	—	2	2	no	—
81	C₂²⋊Dic₇₁	—	2	2	no	—
82	C₂²⋊Dic₇₁	—	2	2	no	—
83	C₄×Dic₇₁	—	2	2	no	—
84	C₄×Dic₇₁	—	2	2	no	—
85	C₂⁴×C₇₁	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
95	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
96	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
99	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
100	M₁₆×C₇₁	—	2	4	no	—
101	M₁₆×C₇₁	—	2	4	no	—
102	M₁₆×C₇₁	—	4	2	no	—
103	M₁₆×C₇₁	—	4	2	no	—
104	C₂×C₈×C₇₁	—	2	4	no	—
105	C₂×C₈×C₇₁	—	4	2	no	—
106	C₂×C₈×C₇₁	—	4	2	no	—
107	C₂×C₈×C₇₁	C₄²	1	2	yes	—
108	C₂×C₈×C₇₁	C₄²	1	2	yes	—
109	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
110	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
111	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
112	C₂×C₈×C₇₁	C₂²⋊C₄	1	4	yes	—
113	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
114	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
115	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
116	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
117	C₂³×C₇₁	—	4	2	no	—
118	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
120	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
121	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
123	C₂³×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
124	C₂³×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
125	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
126	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
134	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
135	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
137	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
140	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
141	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
142	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
143	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
144	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
147	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
148	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
149	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
150	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
151	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
153	C₂×Dic₇₁	—	2	4	no	—
154	C₂×Dic₇₁	—	4	4	no	—
155	C₈×C₇₁	—	4	4	no	—
156	C₈×C₇₁	#95	1	4	yes	—
157	C₈×C₇₁	#95	1	4	yes	—
158	C₇₁⋊C₈	—	2	4	no	—
159	C₇₁⋊C₈	—	4	4	no	—
160	C₂²×C₇₁	—	2	2	no	—
161	C₂²×C₇₁	—	2	2	no	—
162	C₂²×C₇₁	—	2	2	no	—
163	C₂²×C₇₁	—	4	1	no	—
164	C₂²×C₇₁	—	4	1	no	—
165	C₂²×C₇₁	—	4	1	no	—
166	C₂²×C₇₁	—	4	1	no	—
167	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₇₁	#380	1	1	yes	characteristic
169	C₂²×C₇₁	#384	1	1	yes	characteristic
170	C₂²×C₇₁	#389	1	1	yes	characteristic
171	C₂²×C₇₁	#389	1	1	yes	characteristic
172	C₂²×C₇₁	#391	1	1	yes	characteristic
173	C₂²×C₇₁	#391	1	1	yes	characteristic
174	C₄×C₇₁	C₂×#95	1	1	yes	characteristic
175	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
176	C₄×C₇₁	#380	1	1	yes	characteristic
177	C₄×C₇₁	#382	1	1	yes	characteristic
178	C₄×C₇₁	#389	1	1	yes	characteristic
179	C₄×C₇₁	#389	1	1	yes	characteristic
180	C₄×C₇₁	#390	1	1	yes	characteristic
181	C₄×C₇₁	#390	1	1	yes	characteristic
182	Dic₇₁	—	4	4	no	—
183	#10867	—	71	1	no	maximal, Sylow
184	C₂×C₇₁	—	2	1	no	—
185	C₂×C₇₁	—	2	1	no	—
186	C₂×C₇₁	—	2	1	no	—
187	C₂×C₇₁	—	2	1	no	—
188	C₂×C₇₁	—	2	1	no	—
189	C₂×C₇₁	—	2	1	no	—
190	C₂×C₇₁	C₄⋊#95	1	1	yes	characteristic
191	C₂×C₇₁	#1813	1	2	yes	—
192	C₂²×#108	—	71	1	no	—
193	C₂²×#108	D₇₁	1	1	yes	characteristic
194	C₂×#405	—	71	1	no	—
195	#1742	—	71	2	no	—
196	C₂×#338	—	71	2	no	—
197	C₇₁	#10867	1	1	yes	characteristic, complemented, Sylow
198	C₂²×M₁₆	—	71	1	no	—
199	C₂²×M₁₆	—	71	2	no	—
200	C₂²×M₁₆	C₂×D₇₁	1	2	yes	—
201	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
202	C₂×#117	—	71	1	no	—
203	C₂×#108	—	2	2	no	—
204	C₂×#108	—	2	2	no	—
205	C₂×#108	—	71	4	no	—
206	C₂×#108	—	142	2	no	—
207	C₂×#108	—	142	2	no	—
208	C₂×#108	Dic₇₁	1	4	yes	complemented
209	#405	—	142	2	no	—
210	#405	—	142	2	no	—
211	C₂×#97	—	71	2	no	—
212	C₂×C₄×C₈	—	71	2	no	—
213	#343	—	142	4	no	—
214	#338	—	142	4	no	—
215	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	71	2	no	—
222	C₂×M₁₆	—	71	2	no	—
223	C₂×M₁₆	—	71	4	no	—
224	C₂×M₁₆	—	142	2	no	—
225	C₂×M₁₆	—	142	2	no	—
226	C₂×M₁₆	—	142	2	no	—
227	C₂×M₁₆	—	142	2	no	—
228	C₂×M₁₆	—	142	2	no	—
229	C₂×M₁₆	—	142	1	no	—
230	C₂×M₁₆	—	142	1	no	—
231	C₂×M₁₆	—	142	1	no	—
232	C₂×M₁₆	—	142	1	no	—
233	C₂×M₁₆	C₂×Dic₇₁	1	4	yes	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	71	2	no	—
236	C₂²×C₈	—	142	2	no	—
237	C₂²×C₈	Dic₁₄₂	1	2	yes	—
238	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
239	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
240	C₂²×C₈	C₄×D₇₁	1	2	yes	—
241	C₂²×C₈	D₂₈₄	1	2	yes	—
242	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
243	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
244	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
245	#117	—	142	1	no	—
246	#117	—	142	1	no	—
247	#117	—	142	1	no	—
248	#117	—	142	1	no	—
249	C₂×C₄⋊C₄	—	71	2	no	—
250	C₂×C₂²⋊C₄	—	71	2	no	—
251	C₂×C₄²	—	71	2	no	—
252	#108	—	2	8	no	—
253	#108	—	142	8	no	—
254	#97	—	142	4	no	—
255	C₄×C₈	—	142	4	no	—
256	C₂⁴	Q₈×D₇₁	1	1	yes	characteristic
257	C₂²×C₄	—	71	4	no	—
258	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
260	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
261	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
262	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
266	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
268	C₂²×C₄	#11765864	1	1	yes	characteristic
269	C₂²×C₄	#11765864	1	1	yes	characteristic
270	C₂²×C₄	#11765866	1	1	yes	characteristic
271	C₂²×C₄	#11765866	1	1	yes	characteristic
272	M₁₆	—	2	4	no	—
273	M₁₆	—	2	4	no	—
274	M₁₆	—	4	2	no	—
275	M₁₆	—	4	2	no	—
276	M₁₆	—	284	2	no	—
277	M₁₆	—	284	2	no	—
278	M₁₆	—	142	4	no	—
279	M₁₆	—	142	4	no	—
280	M₁₆	—	142	2	no	—
281	M₁₆	—	142	2	no	—
282	M₁₆	—	142	2	no	—
283	M₁₆	—	142	2	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	284	2	no	—
288	C₂×C₈	—	284	2	no	—
289	C₂×C₈	—	71	4	no	—
290	C₂×C₈	—	142	4	no	—
291	C₂×C₈	—	142	2	no	—
292	C₂×C₈	—	142	2	no	—
293	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
294	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
295	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
296	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
297	C₂×C₈	(C₂×D₇₁)⋊C₄	1	4	yes	—
298	C₂×C₈	C₂²⋊Dic₇₁	1	4	yes	—
299	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
300	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
301	C₂×C₈	Dic₇₁⋊C₄	1	4	yes	—
302	C₂×C₈	C₄⋊Dic₇₁	1	4	yes	—
303	C₄⋊C₄	—	142	2	no	—
304	C₄⋊C₄	—	142	2	no	—
305	C₂²⋊C₄	—	142	2	no	—
306	C₂²⋊C₄	—	142	2	no	—
307	C₄²	—	142	2	no	—
308	C₄²	—	142	2	no	—
309	C₂³	—	4	2	no	—
310	C₂³	C₄⋊C₄×D₇₁	1	1	yes	characteristic
311	C₂³	#14556093	1	1	yes	characteristic
312	C₂³	Q₈×Dic₇₁	1	1	yes	characteristic
313	C₂³	#14556104	1	1	yes	characteristic
314	C₂³	#14556108	1	1	yes	characteristic
315	C₂³	#14556126	1	1	yes	characteristic
316	C₂³	#14556127	1	1	yes	characteristic
317	C₂×C₄	—	284	4	no	—
318	C₂×C₄	—	142	4	no	—
319	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
320	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
321	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
322	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
323	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
324	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
325	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
327	C₂×C₄	#14556086	1	1	yes	characteristic
328	C₂×C₄	#14556086	1	1	yes	characteristic
329	C₂×C₄	#14556090	1	1	yes	characteristic
330	C₂×C₄	#14556090	1	1	yes	characteristic
331	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
332	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
333	C₂×C₄	#14556093	1	1	yes	characteristic
334	C₂×C₄	Q₈×Dic₇₁	1	1	yes	characteristic
335	C₂×C₄	#14556099	1	1	yes	characteristic
336	C₂×C₄	#14556099	1	1	yes	characteristic
337	C₂×C₄	#14556103	1	1	yes	characteristic
338	C₂×C₄	#14556103	1	1	yes	characteristic
339	C₂×C₄	#14556104	1	1	yes	characteristic
340	C₂×C₄	#14556108	1	1	yes	characteristic
341	C₂×C₄	#14556115	1	1	yes	characteristic
342	C₂×C₄	#14556117	1	1	yes	characteristic
343	C₂×C₄	#14556119	1	1	yes	characteristic
344	C₂×C₄	#14556119	1	1	yes	characteristic
345	C₂×C₄	#14556124	1	1	yes	characteristic
346	C₂×C₄	#14556127	1	1	yes	characteristic
347	C₈	—	4	4	no	—
348	C₈	—	284	4	no	—
349	C₈	—	142	4	no	—
350	C₈	C₇₁⋊#95	1	4	yes	—
351	C₈	C₇₁⋊#95	1	4	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	1	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	C₄⋊C₄×Dic₇₁	1	1	yes	characteristic
360	C₂²	#17985856	1	1	yes	characteristic
361	C₂²	#17985868	1	1	yes	characteristic
362	C₂²	#17985895	1	1	yes	characteristic
363	C₂²	#17985898	1	1	yes	characteristic
364	C₂²	#17985904	1	1	yes	characteristic
365	C₂²	#17985906	1	1	yes	characteristic
366	C₄	—	284	4	no	—
367	C₄	C₂×C₇₁⋊#95	1	1	yes	characteristic
368	C₄	C₄⋊C₄×Dic₇₁	1	1	yes	characteristic
369	C₄	#17985856	1	1	yes	characteristic
370	C₄	#17985864	1	1	yes	characteristic
371	C₄	#17985895	1	1	yes	characteristic
372	C₄	#17985898	1	1	yes	characteristic
373	C₄	#17985900	1	1	yes	characteristic
374	C₄	#17985902	1	1	yes	characteristic
375	C₂	—	2	1	no	—
376	C₂	—	2	1	no	—
377	C₂	—	2	1	no	—
378	C₂	—	2	1	no	—
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	#22586569	1	1	yes	characteristic
382	C₂	#22588387	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14556086
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₂²×#108×C₇₁	C₂
socle	C₂²×C₇₁	#380
prime radical	C₂⁴×C₇₁	C₂×Q₈
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	C₂²×#108	D₇₁
hypocenter	C₇₁	#10867
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
11. C₂×#14556064	C₄	semidirect
22. C₂×#108×C₇₁	C₄	semidirect
197. C₇₁	#10867	semidirect
208. C₂×#108	Dic₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556064	2
C₂×#17985954	2
#22588078	2
C₂×C₇₁⋊#338	2
C₂²×#108×C₇₁	2
#10867	71