Subgroups — #31903377

Order 18176.

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×#14556064	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986037	C₂	1	1	yes	maximal, characteristic
3	C₂×#17985770	C₂	1	2	yes	maximal
4	C₂×#17985755	C₂	1	2	yes	maximal
5	C₂×#405×C₇₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#11765849	C₂²	1	2	yes	—
7	C₂×#14556087	C₂²	1	2	yes	—
8	C₂×#14556064	—	2	1	no	—
9	C₂×#14556064	—	2	1	no	—
10	C₂×#14556064	—	2	2	no	—
11	C₂×#14556064	C₄	1	4	yes	complemented
12	#17986037	—	2	2	no	—
13	#17986037	C₄	1	4	yes	complemented
14	C₂×#14556062	—	2	1	no	—
15	C₂×#14556060	—	2	1	no	—
16	#17985770	—	2	4	no	—
17	#17985755	—	2	4	no	—
18	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₁	C₂²	1	1	yes	characteristic
21	#405×C₇₁	—	2	2	no	—
22	#405×C₇₁	—	2	2	no	—
23	C₂×#97×C₇₁	C₄	1	2	yes	complemented
24	C₂×C₄×C₈×C₇₁	C₄	1	2	yes	complemented
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	2	no	—
30	C₂×#11765849	C₂×C₄	1	4	yes	—
31	C₂²×C₇₁⋊C₈	—	2	2	no	—
32	#14556087	—	2	2	no	—
33	#14556087	—	2	2	no	—
34	#14556087	—	2	2	no	—
35	#14556087	C₂×C₄	1	4	yes	—
36	C₂×C₄⋊Dic₇₁	—	2	2	no	—
37	C₂×C₂²⋊Dic₇₁	—	2	2	no	—
38	C₂×C₄×Dic₇₁	—	2	2	no	—
39	#14556064	—	2	4	no	—
40	#14556064	—	2	4	no	—
41	#14556062	—	2	4	no	—
42	#14556060	—	2	4	no	—
43	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₇₁	—	2	1	no	—
45	C₂×M₁₆×C₇₁	—	2	1	no	—
46	C₂×M₁₆×C₇₁	—	2	1	no	—
47	C₂×M₁₆×C₇₁	—	2	1	no	—
48	C₂×M₁₆×C₇₁	D₄	1	2	yes	—
49	C₂×M₁₆×C₇₁	Q₈	1	2	yes	—
50	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
52	C₂²×C₈×C₇₁	C₂×C₄	1	2	yes	—
53	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₁	D₄	1	2	yes	—
58	C₂²×C₈×C₇₁	D₄	1	2	yes	—
59	C₂²×C₈×C₇₁	Q₈	1	1	yes	characteristic
60	C₂²×C₈×C₇₁	Q₈	1	1	yes	characteristic
61	#117×C₇₁	—	2	1	no	—
62	#117×C₇₁	—	2	1	no	—
63	#117×C₇₁	D₄	1	2	yes	—
64	#117×C₇₁	Q₈	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₇₁	—	2	1	no	—
67	C₂×C₄²×C₇₁	C₂×C₄	1	2	yes	—
68	#97×C₇₁	—	2	4	no	—
69	C₄×C₈×C₇₁	—	2	4	no	—
70	C₂²×Dic₇₁	—	4	2	no	—
71	#11765849	—	2	4	no	—
72	#11765849	—	2	4	no	—
73	#11765849	—	4	2	no	—
74	#11765849	—	4	2	no	—
75	C₂×C₇₁⋊C₈	—	2	4	no	—
76	C₂×C₇₁⋊C₈	—	4	2	no	—
77	C₂×C₇₁⋊C₈	—	4	2	no	—
78	C₄⋊Dic₇₁	—	2	4	no	—
79	C₄⋊Dic₇₁	—	4	2	no	—
80	C₂²⋊Dic₇₁	—	2	4	no	—
81	C₂²⋊Dic₇₁	—	4	2	no	—
82	C₄×Dic₇₁	—	2	4	no	—
83	C₄×Dic₇₁	—	4	2	no	—
84	C₂⁴×C₇₁	#41	1	1	yes	characteristic
85	C₂²×C₄×C₇₁	—	2	2	no	—
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	C₂×Q₈	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	2	no	—
101	M₁₆×C₇₁	—	2	2	no	—
102	M₁₆×C₇₁	—	2	2	no	—
103	M₁₆×C₇₁	—	2	2	no	—
104	C₂×C₈×C₇₁	—	2	2	no	—
105	C₂×C₈×C₇₁	—	2	2	no	—
106	C₂×C₈×C₇₁	C₄²	1	2	yes	—
107	C₂×C₈×C₇₁	C₄²	1	2	yes	—
108	C₂×C₈×C₇₁	C₂²⋊C₄	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	2	yes	—
112	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
113	C₂×C₈×C₇₁	C₂²⋊C₄	1	2	yes	—
114	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
115	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
116	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
117	C₂×C₈×C₇₁	C₄⋊C₄	1	2	yes	—
118	C₂×C₈×C₇₁	C₄⋊C₄	1	4	yes	—
119	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₇₁	—	2	2	no	—
124	C₄⋊C₄×C₇₁	—	2	2	no	—
125	C₂²⋊C₄×C₇₁	—	2	2	no	—
126	C₂²⋊C₄×C₇₁	—	2	2	no	—
127	C₄²×C₇₁	—	2	2	no	—
128	C₄²×C₇₁	C₄⋊C₄	1	4	yes	—
129	C₂³×C₇₁	—	4	2	no	—
130	C₂³×C₇₁	#117	1	1	yes	characteristic
131	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
132	C₂³×C₇₁	C₄×Q₈	1	1	yes	characteristic
133	C₂³×C₇₁	#121	1	1	yes	characteristic
134	C₂³×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₇₁	#124	1	1	yes	characteristic
136	C₂³×C₇₁	#125	1	1	yes	characteristic
137	C₂×C₄×C₇₁	—	2	4	no	—
138	C₂×C₄×C₇₁	—	4	4	no	—
139	C₂×C₄×C₇₁	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₇₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	#117	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₄×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₇₁	#121	1	1	yes	characteristic
158	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₇₁	#124	1	1	yes	characteristic
162	C₂×C₄×C₇₁	#125	1	1	yes	characteristic
163	C₂×C₄×C₇₁	#127	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₇₁	C₄⋊Q₈	1	1	yes	characteristic
167	C₂×Dic₇₁	—	4	4	no	—
168	C₂×Dic₇₁	—	8	4	no	—
169	C₈×C₇₁	—	2	4	no	—
170	C₈×C₇₁	#95	1	2	yes	—
171	C₈×C₇₁	#95	1	2	yes	—
172	C₈×C₇₁	#95	1	2	yes	—
173	C₈×C₇₁	#95	1	2	yes	—
174	C₇₁⋊C₈	—	4	4	no	—
175	C₂²×C₇₁	—	2	2	no	—
176	C₂²×C₇₁	—	2	2	no	—
177	C₂²×C₇₁	—	2	2	no	—
178	C₂²×C₇₁	—	4	1	no	—
179	C₂²×C₇₁	—	4	1	no	—
180	C₂²×C₇₁	—	4	1	no	—
181	C₂²×C₇₁	—	4	1	no	—
182	C₂²×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₇₁	#380	1	1	yes	characteristic
184	C₂²×C₇₁	#382	1	1	yes	characteristic
185	C₂²×C₇₁	#389	1	1	yes	characteristic
186	C₂²×C₇₁	#389	1	1	yes	characteristic
187	C₂²×C₇₁	#390	1	1	yes	characteristic
188	C₂²×C₇₁	#391	1	1	yes	characteristic
189	C₄×C₇₁	—	4	4	no	—
190	C₄×C₇₁	C₂×#95	1	1	yes	characteristic
191	C₄×C₇₁	C₄×C₄⋊C₄	1	1	yes	characteristic
192	C₄×C₇₁	#380	1	1	yes	characteristic
193	C₄×C₇₁	#384	1	1	yes	characteristic
194	C₄×C₇₁	#389	1	1	yes	characteristic
195	C₄×C₇₁	#389	1	1	yes	characteristic
196	C₄×C₇₁	#390	1	1	yes	characteristic
197	C₄×C₇₁	#391	1	1	yes	characteristic
198	Dic₇₁	—	8	4	no	—
199	#10868	—	71	1	no	maximal, Sylow
200	C₂×C₇₁	—	2	1	no	—
201	C₂×C₇₁	—	2	1	no	—
202	C₂×C₇₁	—	2	1	no	—
203	C₂×C₇₁	—	2	1	no	—
204	C₂×C₇₁	—	2	1	no	—
205	C₂×C₇₁	—	2	1	no	—
206	C₂×C₇₁	C₄⋊#95	1	1	yes	characteristic
207	C₂×C₇₁	#1833	1	2	yes	—
208	C₂²×#108	—	71	1	no	—
209	C₂×#427	—	71	1	no	—
210	C₂×#405	D₇₁	1	1	yes	characteristic
211	C₂×#344	—	71	2	no	—
212	C₂×H(3,ℤ/4)	—	71	2	no	—
213	C₇₁	#10868	1	1	yes	characteristic, complemented, Sylow
214	C₂²×M₁₆	—	71	2	no	—
215	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
216	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic
217	C₂×#117	—	71	2	no	—
218	C₂×#117	C₂×D₇₁	1	1	yes	characteristic
219	C₂×#108	—	71	4	no	—
220	C₂×#108	—	142	1	no	—
221	C₂×#108	—	142	1	no	—
222	C₂×#108	—	142	2	no	—
223	#427	—	71	4	no	—
224	#427	—	142	2	no	—
225	C₂×#107	—	142	1	no	—
226	C₂×#106	—	142	1	no	—
227	#405	—	2	2	no	—
228	#405	—	2	2	no	—
229	C₂×#97	Dic₇₁	1	2	yes	complemented
230	C₂×C₄×C₈	Dic₇₁	1	2	yes	complemented
231	#344	—	142	4	no	—
232	H(3,ℤ/4)	—	142	4	no	—
233	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
234	C₂×M₁₆	—	2	1	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	1	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂×M₁₆	—	71	4	no	—
239	C₂×M₁₆	—	142	2	no	—
240	C₂×M₁₆	—	142	2	no	—
241	C₂×M₁₆	—	142	2	no	—
242	C₂×M₁₆	—	142	2	no	—
243	C₂×M₁₆	—	142	2	no	—
244	C₂×M₁₆	Dic₁₄₂	1	2	yes	—
245	C₂×M₁₆	D₂₈₄	1	2	yes	—
246	C₂²×C₈	—	142	2	no	—
247	C₂²×C₈	Dic₁₄₂	1	1	yes	characteristic
248	C₂²×C₈	Dic₁₄₂	1	1	yes	characteristic
249	C₂²×C₈	C₄×D₇₁	1	2	yes	—
250	C₂²×C₈	C₄×D₇₁	1	2	yes	—
251	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
252	C₂²×C₈	D₂₈₄	1	1	yes	characteristic
253	C₂²×C₈	C₂×Dic₇₁	1	2	yes	—
254	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
255	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
257	C₂²×C₈	C₂²⋊D₇₁	1	2	yes	—
258	#117	—	2	1	no	—
259	#117	—	2	1	no	—
260	#117	—	71	4	no	—
261	#117	—	142	2	no	—
262	#117	—	142	2	no	—
263	#117	—	142	2	no	—
264	#117	Dic₁₄₂	1	2	yes	—
265	#117	D₂₈₄	1	2	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	142	2	no	—
268	C₂×C₂²⋊C₄	—	2	1	no	—
269	C₂×C₂²⋊C₄	—	142	2	no	—
270	C₂×C₄²	—	142	2	no	—
271	C₂×C₄²	C₂×Dic₇₁	1	2	yes	—
272	#108	—	142	4	no	—
273	#108	—	142	4	no	—
274	#107	—	142	4	no	—
275	#106	—	142	4	no	—
276	#97	—	2	4	no	—
277	C₄×C₈	—	2	4	no	—
278	C₂⁴	#11765865	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	284	2	no	—
281	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
283	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
290	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
291	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
292	C₂²×C₄	#11765865	1	1	yes	characteristic
293	C₂²×C₄	#11765865	1	1	yes	characteristic
294	C₂²×C₄	#11765865	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	2	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	—	2	2	no	—
299	M₁₆	—	284	2	no	—
300	M₁₆	—	284	2	no	—
301	M₁₆	—	142	4	no	—
302	M₁₆	—	142	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	284	2	no	—
306	C₂×C₈	—	284	2	no	—
307	C₂×C₈	—	142	4	no	—
308	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
309	C₂×C₈	C₄×Dic₇₁	1	2	yes	—
310	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
311	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
312	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
313	C₂×C₈	(C₂×D₇₁)⋊C₄	1	2	yes	—
314	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
315	C₂×C₈	C₂²⋊Dic₇₁	1	2	yes	—
316	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
317	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
318	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
319	C₂×C₈	Dic₇₁⋊C₄	1	2	yes	—
320	C₂×C₈	C₄⋊Dic₇₁	1	4	yes	—
321	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
322	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
323	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
324	C₂×C₈	C₄⋊Dic₇₁	1	1	yes	characteristic
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	284	2	no	—
328	C₄⋊C₄	—	142	4	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	284	2	no	—
332	C₂²⋊C₄	—	142	4	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	284	2	no	—
335	C₄²	—	142	4	no	—
336	C₄²	C₄⋊Dic₇₁	1	4	yes	—
337	C₂³	—	4	2	no	—
338	C₂³	#14556087	1	1	yes	characteristic
339	C₂³	C₄×D₂₈₄	1	1	yes	characteristic
340	C₂³	C₄×Dic₁₄₂	1	1	yes	characteristic
341	C₂³	#14556102	1	1	yes	characteristic
342	C₂³	#14556107	1	1	yes	characteristic
343	C₂³	#14556116	1	1	yes	characteristic
344	C₂³	#14556120	1	1	yes	characteristic
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	284	4	no	—
348	C₂×C₄	—	568	4	no	—
349	C₂×C₄	C₂×C₄×Dic₇₁	1	1	yes	characteristic
350	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
351	C₂×C₄	C₂×(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₂²⋊Dic₇₁	1	1	yes	characteristic
353	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
358	C₂×C₄	#14556087	1	1	yes	characteristic
359	C₂×C₄	C₄×D₂₈₄	1	1	yes	characteristic
360	C₂×C₄	C₄×D₂₈₄	1	1	yes	characteristic
361	C₂×C₄	C₄×D₂₈₄	1	1	yes	characteristic
362	C₂×C₄	C₄×Dic₁₄₂	1	1	yes	characteristic
363	C₂×C₄	C₄×Dic₁₄₂	1	1	yes	characteristic
364	C₂×C₄	C₄×Dic₁₄₂	1	1	yes	characteristic
365	C₂×C₄	#14556102	1	1	yes	characteristic
366	C₂×C₄	#14556102	1	1	yes	characteristic
367	C₂×C₄	#14556102	1	1	yes	characteristic
368	C₂×C₄	#14556107	1	1	yes	characteristic
369	C₂×C₄	#14556107	1	1	yes	characteristic
370	C₂×C₄	#14556107	1	1	yes	characteristic
371	C₂×C₄	#14556116	1	1	yes	characteristic
372	C₂×C₄	#14556120	1	1	yes	characteristic
373	C₂×C₄	#14556125	1	1	yes	characteristic
374	C₂×C₄	#14556128	1	1	yes	characteristic
375	C₂×C₄	#14556128	1	1	yes	characteristic
376	C₂×C₄	#14556128	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	284	4	no	—
379	C₈	C₇₁⋊#95	1	2	yes	—
380	C₈	C₇₁⋊#95	1	2	yes	—
381	C₈	C₇₁⋊#95	1	2	yes	—
382	C₈	C₇₁⋊#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⋊Dic₇₁	1	1	yes	characteristic
391	C₂²	#17985859	1	1	yes	characteristic
392	C₂²	#17985865	1	1	yes	characteristic
393	C₂²	#17985897	1	1	yes	characteristic
394	C₂²	#17985897	1	1	yes	characteristic
395	C₂²	#17985901	1	1	yes	characteristic
396	C₂²	#17985905	1	1	yes	characteristic
397	C₄	—	4	4	no	—
398	C₄	—	568	4	no	—
399	C₄	C₂×C₇₁⋊#95	1	1	yes	characteristic
400	C₄	C₄×C₄⋊Dic₇₁	1	1	yes	characteristic
401	C₄	#17985859	1	1	yes	characteristic
402	C₄	#17985869	1	1	yes	characteristic
403	C₄	#17985897	1	1	yes	characteristic
404	C₄	#17985897	1	1	yes	characteristic
405	C₄	#17985901	1	1	yes	characteristic
406	C₄	#17985905	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	#22586570	1	1	yes	characteristic
414	C₂	#22588464	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#14556087
commutator	C₂×C₄×C₇₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₁
Fitting	C₂×#405×C₇₁	C₂
socle	C₂²×C₇₁	#382
prime radical	C₂⁴×C₇₁	#41
cosocle	C₂³×C₄×C₇₁	C₂³
hypercenter	C₂×#405	D₇₁
hypocenter	C₇₁	#10868
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
11. C₂×#14556064	C₄	semidirect
13. #17986037	C₄	semidirect
23. C₂×#97×C₇₁	C₄	semidirect
24. C₂×C₄×C₈×C₇₁	C₄	semidirect
213. C₇₁	#10868	semidirect
229. C₂×#97	Dic₇₁	semidirect
230. C₂×C₄×C₈	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×#17986037	2
C₂×#17985770	2
C₂×#17985755	2
C₂×#405×C₇₁	2
#10868	71