Subgroups — #32015919

Order 18176.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986116	C₂	1	2	yes	maximal
2	#22596908	C₂	1	2	yes	maximal, complemented
3	#22589089	C₂	1	2	yes	maximal, complemented
4	#22588617	C₂	1	4	yes	maximal, complemented
5	#22588512	C₂	1	1	yes	maximal, characteristic, complemented
6	#22588360	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₇₁	C₂	1	1	yes	maximal, characteristic
9	C₂×#14556135	C₂²	1	4	yes	—
10	#17986116	—	2	8	no	—
11	C₂×#14556064	C₂²	1	2	yes	—
12	C₂×#14556064	C₂²	1	2	yes	—
13	#17986026	—	2	4	no	—
14	#17986026	C₂²	1	4	yes	—
15	#17986023	—	2	2	no	—
16	#17986023	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
18	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#14556055	C₂²	1	4	yes	—
20	C₂×C₈×Dic₇₁	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₇₁	C₂²	1	1	yes	characteristic
22	#17985758	C₂²	1	4	yes	—
23	#17985753	C₂²	1	2	yes	—
24	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
25	C₄×#41×C₇₁	C₂²	1	2	yes	—
26	C₄×Q₁₆×C₇₁	C₄	1	1	yes	characteristic, complemented
27	C₄×Q₁₆×C₇₁	C₄	1	1	yes	characteristic, complemented
28	C₄×SD₁₆×C₇₁	C₄	1	2	yes	complemented
29	C₄×SD₁₆×C₇₁	C₄	1	2	yes	complemented
30	C₄×D₈×C₇₁	C₄	1	1	yes	characteristic, complemented
31	C₄×D₈×C₇₁	C₄	1	1	yes	characteristic, complemented
32	#427×C₇₁	C₂²	1	1	yes	characteristic
33	#416×C₇₁	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
35	#14556135	—	2	8	no	—
36	#14556135	—	4	4	no	—
37	C₂×#11765849	—	2	4	no	—
38	C₂×#11765849	C₂³	1	4	yes	—
39	C₂²×C₇₁⋊C₈	—	2	4	no	—
40	C₂²×C₇₁⋊C₈	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₇₁	—	2	1	no	—
42	C₂×C₄×Dic₇₁	C₂³	1	2	yes	—
43	#14556064	—	2	4	no	—
44	#14556064	—	4	2	no	—
45	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
46	C₄⋊(C₇₁⋊C₈)	—	2	4	no	—
47	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
48	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
50	C₄⋊(C₇₁⋊C₈)	D₄	1	1	yes	characteristic
51	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
52	#14556055	—	2	8	no	—
53	C₈×Dic₇₁	—	2	4	no	—
54	C₇₁⋊#95	—	2	1	no	—
55	C₂×#41×C₇₁	C₂³	1	2	yes	—
56	#135×C₇₁	D₄	1	4	yes	—
57	#135×C₇₁	Q₈	1	4	yes	—
58	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
59	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	—
60	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₇₁	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₇₁	—	2	2	no	—
66	C₄×D₄×C₇₁	—	2	2	no	—
67	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
69	#117×C₇₁	—	2	2	no	—
70	#117×C₇₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₇₁	—	2	2	no	—
72	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
73	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
74	#107×C₇₁	C₂×C₄	1	1	yes	characteristic
75	#106×C₇₁	C₂×C₄	1	2	yes	—
76	#103×C₇₁	C₂×C₄	1	2	yes	—
77	#103×C₇₁	C₂×C₄	1	2	yes	—
78	#102×C₇₁	C₂×C₄	1	2	yes	—
79	#102×C₇₁	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
84	C₂²×Dic₇₁	—	2	2	no	—
85	#11765849	—	2	4	no	—
86	#11765849	—	2	4	no	—
87	#11765849	—	4	8	no	—
88	C₂×C₇₁⋊C₈	—	2	2	no	—
89	C₂×C₇₁⋊C₈	—	2	2	no	—
90	C₂×C₇₁⋊C₈	—	2	4	no	—
91	C₂×C₇₁⋊C₈	—	4	8	no	—
92	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
93	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
94	C₄⋊Dic₇₁	—	2	4	no	—
95	C₄×Dic₇₁	—	2	2	no	—
96	C₄×Dic₇₁	—	2	2	no	—
97	#41×C₇₁	—	2	2	no	—
98	#41×C₇₁	—	2	2	no	—
99	#41×C₇₁	C₂×D₄	1	4	yes	—
100	#41×C₇₁	C₂×Q₈	1	4	yes	—
101	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₇₁	—	2	2	no	—
103	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₇₁	—	2	2	no	—
105	C₂²×C₄×C₇₁	—	2	2	no	—
106	C₂²×C₄×C₇₁	—	2	2	no	—
107	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
108	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
109	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₇₁	C₄⋊C₄	1	4	yes	complemented
111	SD₁₆×C₇₁	C₄⋊C₄	1	8	yes	complemented
112	D₈×C₇₁	C₄⋊C₄	1	4	yes	complemented
113	C₂×C₈×C₇₁	—	2	1	no	—
114	C₂×C₈×C₇₁	—	2	1	no	—
115	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₇₁	C₂×Q₈	1	2	yes	—
121	C₄⋊C₄×C₇₁	—	2	2	no	—
122	C₄⋊C₄×C₇₁	—	2	2	no	—
123	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₇₁	—	2	2	no	—
126	C₂²⋊C₄×C₇₁	—	2	2	no	—
127	C₂²⋊C₄×C₇₁	—	2	2	no	—
128	C₄²×C₇₁	—	2	2	no	—
129	C₄²×C₇₁	—	2	2	no	—
130	C₄²×C₇₁	—	2	2	no	—
131	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₇₁	—	2	2	no	—
136	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
137	Q₈×C₇₁	—	2	2	no	—
138	Q₈×C₇₁	C₂×C₄⋊C₄	1	4	yes	—
139	D₄×C₇₁	—	2	4	no	—
140	D₄×C₇₁	—	2	4	no	—
141	D₄×C₇₁	—	2	2	no	—
142	D₄×C₇₁	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₇₁	—	2	2	no	—
144	C₂×C₄×C₇₁	—	2	4	no	—
145	C₂×C₄×C₇₁	—	2	4	no	—
146	C₂×C₄×C₇₁	—	2	2	no	—
147	C₂×C₄×C₇₁	—	2	2	no	—
148	C₂×C₄×C₇₁	—	2	2	no	—
149	C₂×C₄×C₇₁	—	4	1	no	—
150	C₂×C₄×C₇₁	—	4	4	no	—
151	C₂×C₄×C₇₁	—	8	2	no	—
152	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₇₁	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×Dic₇₁	—	2	4	no	—
163	C₂×Dic₇₁	—	4	2	no	—
164	C₂×Dic₇₁	—	4	2	no	—
165	C₈×C₇₁	—	2	1	no	—
166	C₈×C₇₁	—	2	1	no	—
167	C₈×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
168	C₈×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
169	C₇₁⋊C₈	—	2	2	no	—
170	C₇₁⋊C₈	—	2	2	no	—
171	C₇₁⋊C₈	—	4	4	no	—
172	C₂²×C₇₁	—	2	1	no	—
173	C₂²×C₇₁	—	2	1	no	—
174	C₂²×C₇₁	—	2	4	no	—
175	C₂²×C₇₁	—	4	2	no	—
176	C₂²×C₇₁	—	4	2	no	—
177	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂²×C₇₁	#547	1	1	yes	characteristic
179	C₂²×C₇₁	#554	1	1	yes	characteristic
180	C₄×C₇₁	—	2	4	no	—
181	C₄×C₇₁	—	2	1	no	—
182	C₄×C₇₁	—	2	1	no	—
183	C₄×C₇₁	—	2	1	no	—
184	C₄×C₇₁	—	4	2	no	—
185	C₄×C₇₁	—	4	2	no	—
186	C₄×C₇₁	#443	1	2	yes	complemented
187	C₄×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₄×C₇₁	#520	1	1	yes	characteristic
189	C₄×C₇₁	D₄²	1	1	yes	characteristic
190	C₄×C₇₁	D₄×Q₈	1	1	yes	characteristic
191	Dic₇₁	—	4	4	no	—
192	#22688	—	71	1	no	maximal, Sylow
193	C₂×C₇₁	—	2	1	no	—
194	C₂×C₇₁	—	2	1	no	—
195	C₂×C₇₁	—	4	4	no	—
196	C₂×C₇₁	D₄×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₇₁	C₂×#443	1	1	yes	characteristic
198	C₂×C₇₁	#2957	1	1	yes	characteristic
199	C₂×#443	—	71	2	no	—
200	C₄×#135	D₇₁	1	1	yes	characteristic
201	#2906	—	71	2	no	—
202	#1945	—	71	2	no	—
203	#1866	—	71	4	no	—
204	#1848	—	71	1	no	—
205	#1806	—	71	2	no	—
206	C₈×C₄⋊C₄	—	71	1	no	—
207	C₇₁	#22688	1	1	yes	characteristic, complemented, Sylow
208	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
209	C₂×#131	—	71	4	no	—
210	C₄×#41	C₂×D₇₁	1	2	yes	—
211	#443	—	142	8	no	—
212	C₄×Q₁₆	Dic₇₁	1	1	yes	characteristic, complemented
213	C₄×Q₁₆	Dic₇₁	1	1	yes	characteristic, complemented
214	C₄×SD₁₆	Dic₇₁	1	2	yes	complemented
215	C₄×SD₁₆	Dic₇₁	1	2	yes	complemented
216	C₄×D₈	Dic₇₁	1	1	yes	characteristic, complemented
217	C₄×D₈	Dic₇₁	1	1	yes	characteristic, complemented
218	C₂×#108	—	71	2	no	—
219	C₂×#108	—	71	2	no	—
220	#427	C₂×D₇₁	1	1	yes	characteristic
221	#424	—	71	4	no	—
222	#424	—	142	4	no	—
223	#423	—	71	2	no	—
224	#423	—	142	2	no	—
225	C₂×C₄⋊C₈	—	71	1	no	—
226	C₂×C₄⋊C₈	—	142	2	no	—
227	C₂×#104	—	71	4	no	—
228	#416	C₂×D₇₁	1	2	yes	—
229	C₂×C₄×C₈	—	71	2	no	—
230	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
231	C₄×C₄⋊C₄	—	71	1	no	—
232	#339	—	71	4	no	—
233	#336	—	71	2	no	—
234	C₂×#41	C₂²×D₇₁	1	2	yes	—
235	#135	Dic₁₄₂	1	4	yes	—
236	#135	D₂₈₄	1	4	yes	—
237	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic
238	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	—
239	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic
240	#131	—	284	4	no	—
241	#131	—	142	8	no	—
242	C₂×M₁₆	—	71	4	no	—
243	C₂×M₁₆	—	142	4	no	—
244	C₂²×C₈	—	71	2	no	—
245	C₂²×C₈	—	142	4	no	—
246	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
248	C₄×Q₈	C₂×Dic₇₁	1	2	yes	—
249	C₄×Q₈	C₂×Dic₇₁	1	2	yes	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
253	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
254	#117	—	2	2	no	—
255	#117	C₂²×D₇₁	1	2	yes	—
256	C₂×C₄⋊C₄	—	142	1	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	71	2	no	—
259	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
260	#108	—	284	2	no	—
261	#108	—	142	4	no	—
262	#107	C₂×Dic₇₁	1	1	yes	characteristic
263	#107	C₂×Dic₇₁	1	1	yes	characteristic
264	#106	C₂×Dic₇₁	1	2	yes	—
265	C₄⋊C₈	—	71	1	no	—
266	C₄⋊C₈	—	71	1	no	—
267	C₄⋊C₈	—	71	2	no	—
268	C₄⋊C₈	—	142	4	no	—
269	C₄⋊C₈	—	142	4	no	—
270	C₄⋊C₈	—	142	2	no	—
271	C₄⋊C₈	—	142	2	no	—
272	#104	—	142	8	no	—
273	#103	C₂×Dic₇₁	1	2	yes	—
274	#103	C₂×Dic₇₁	1	2	yes	—
275	#102	C₂×Dic₇₁	1	2	yes	—
276	#102	C₂×Dic₇₁	1	2	yes	—
277	C₄×C₈	—	142	4	no	—
278	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
279	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
280	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
281	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
282	#95	—	142	1	no	—
283	#41	—	2	2	no	—
284	#41	—	2	2	no	—
285	#41	C₂×D₂₈₄	1	4	yes	—
286	#41	C₂×Dic₁₄₂	1	4	yes	—
287	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	142	2	no	—
294	C₂²×C₄	#11765864	1	1	yes	characteristic
295	C₂²×C₄	#11765864	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
297	Q₁₆	C₄⋊Dic₇₁	1	4	yes	complemented
298	SD₁₆	C₄⋊Dic₇₁	1	8	yes	complemented
299	D₈	C₄⋊Dic₇₁	1	4	yes	complemented
300	M₁₆	—	284	8	no	—
301	M₁₆	—	142	4	no	—
302	M₁₆	—	142	4	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	284	8	no	—
306	C₂×C₈	—	71	2	no	—
307	C₂×C₈	—	71	2	no	—
308	C₂×C₈	—	142	4	no	—
309	C₂×C₈	—	142	2	no	—
310	C₂×C₈	—	142	2	no	—
311	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
312	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
313	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
314	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₂₈₄	1	2	yes	—
316	C₂×C₈	C₂×Dic₁₄₂	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	142	4	no	—
320	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
321	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	142	2	no	—
329	C₄²	—	142	2	no	—
330	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
331	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
332	C₄²	D₄×D₇₁	1	1	yes	characteristic
333	C₄²	D₄×D₇₁	1	1	yes	characteristic
334	C₂³	—	2	2	no	—
335	C₂³	C₂×#11765864	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	C₂×C₄⋊Dic₇₁	1	4	yes	—
338	D₄	—	2	4	no	—
339	D₄	—	2	4	no	—
340	D₄	—	2	2	no	—
341	D₄	C₂×C₄⋊Dic₇₁	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	284	2	no	—
352	C₂×C₄	—	284	2	no	—
353	C₂×C₄	—	142	4	no	—
354	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
355	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
356	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
357	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
358	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
361	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
362	C₂×C₄	#14556174	1	1	yes	characteristic
363	C₂×C₄	#14556175	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	284	4	no	—
367	C₈	—	142	2	no	—
368	C₈	—	142	2	no	—
369	C₈	C₂×C₄⋊Dic₇₁	1	2	yes	—
370	C₈	C₂×C₄⋊Dic₇₁	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
377	C₂²	#17986653	1	1	yes	characteristic
378	C₂²	#17986706	1	1	yes	characteristic
379	C₄	—	2	4	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	284	4	no	—
386	C₄	#17986116	1	2	yes	complemented
387	C₄	C₂²×C₄⋊Dic₇₁	1	1	yes	characteristic
388	C₄	#17986482	1	1	yes	characteristic
389	C₄	D₄×D₂₈₄	1	1	yes	characteristic
390	C₄	D₄×Dic₁₄₂	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	4	4	no	—
394	C₂	D₄×C₄⋊Dic₇₁	1	1	yes	characteristic
395	C₂	C₂×#17986116	1	1	yes	characteristic
396	C₂	#22597257	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₄×#135×C₇₁	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	C₂×#135×C₇₁	C₂²
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	C₄×#135	D₇₁
hypocenter	C₇₁	#22688
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. #22596908	C₂	semidirect
3. #22589089	C₂	semidirect
4. #22588617	C₂	semidirect
5. #22588512	C₂	semidirect
6. #22588360	C₂	semidirect
7. C₈×C₄⋊Dic₇₁	C₂	semidirect
26. C₄×Q₁₆×C₇₁	C₄	semidirect
27. C₄×Q₁₆×C₇₁	C₄	semidirect
28. C₄×SD₁₆×C₇₁	C₄	semidirect
29. C₄×SD₁₆×C₇₁	C₄	semidirect
30. C₄×D₈×C₇₁	C₄	semidirect
31. C₄×D₈×C₇₁	C₄	semidirect
110. Q₁₆×C₇₁	C₄⋊C₄	semidirect
111. SD₁₆×C₇₁	C₄⋊C₄	semidirect
112. D₈×C₇₁	C₄⋊C₄	semidirect
186. C₄×C₇₁	#443	semidirect
207. C₇₁	#22688	semidirect
212. C₄×Q₁₆	Dic₇₁	semidirect
213. C₄×Q₁₆	Dic₇₁	semidirect
214. C₄×SD₁₆	Dic₇₁	semidirect
215. C₄×SD₁₆	Dic₇₁	semidirect
216. C₄×D₈	Dic₇₁	semidirect
217. C₄×D₈	Dic₇₁	semidirect
297. Q₁₆	C₄⋊Dic₇₁	semidirect
298. SD₁₆	C₄⋊Dic₇₁	semidirect
299. D₈	C₄⋊Dic₇₁	semidirect
386. C₄	#17986116	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986116	2
#22596908	2
#22589089	2
#22588617	2
#22588512	2
#22588360	2
C₈×C₄⋊Dic₇₁	2
C₄×#135×C₇₁	2
#22688	71