Subgroups — #3549×D₇₁ #32905250

Order 18176.

8802 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22602745	C₂	1	3	yes	maximal, complemented
2	#22602744	C₂	1	4	yes	maximal, complemented
3	#22602743	C₂	1	12	yes	maximal, complemented
4	#22602742	C₂	1	6	yes	maximal, complemented
5	#22602741	C₂	1	6	yes	maximal, complemented
6	H(3,𝔽₄)×D₇₁	C₂	1	4	yes	maximal, complemented
7	#555×D₇₁	C₂	1	6	yes	maximal, complemented
8	D₄²×D₇₁	C₂	1	6	yes	maximal, complemented
9	#535×D₇₁	C₂	1	12	yes	maximal, complemented
10	#532×D₇₁	C₂	1	3	yes	maximal, complemented
11	C₇₁×#3549	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₇₁	C₂²	1	6	yes	complemented
13	C₂²×D₄×D₇₁	C₂²	1	12	yes	complemented
14	#17986742	C₂²	1	24	yes	complemented
15	#17986741	C₂²	1	24	yes	complemented
16	#17986741	C₂²	1	12	yes	complemented
17	#17986715	C₂²	1	6	yes	complemented
18	#17986714	C₂²	1	12	yes	complemented
19	#17986713	C₂²	1	24	yes	complemented
20	#17986712	C₂²	1	24	yes	complemented
21	#17986711	C₂²	1	24	yes	complemented
22	D₄×D₂₈₄	C₂²	1	12	yes	complemented
23	#17986634	C₂²	1	6	yes	complemented
24	#17986633	C₂²	1	24	yes	complemented
25	D₄×C₂²⋊D₇₁	C₂²	1	24	yes	complemented
26	#17986631	C₂²	1	24	yes	complemented
27	#17986568	C₂²	1	12	yes	complemented
28	#17986567	C₂²	1	24	yes	complemented
29	#17986566	C₂²	1	12	yes	complemented
30	#17986565	C₂²	1	24	yes	complemented
31	#17986565	C₂²	1	24	yes	complemented
32	#17986564	C₂²	1	24	yes	complemented
33	#17986564	C₂²	1	24	yes	complemented
34	#17986563	C₂²	1	12	yes	complemented
35	#17986562	C₂²	1	24	yes	complemented
36	#17986550	C₂²	1	3	yes	complemented
37	#17986549	C₂²	1	3	yes	complemented
38	#17986548	C₂²	1	6	yes	complemented
39	#17986547	C₂²	1	3	yes	complemented
40	#17986546	C₂²	1	12	yes	complemented
41	#17986545	C₂²	1	6	yes	complemented
42	#17986544	C₂²	1	12	yes	complemented
43	C₄⋊Q₈×D₇₁	C₂²	1	3	yes	complemented
44	#127×D₇₁	C₂²	1	3	yes	—
45	#127×D₇₁	C₂²	1	8	yes	complemented
46	#124×D₇₁	C₂²	1	6	yes	complemented
47	#124×D₇₁	C₂²	1	24	yes	complemented
48	#121×D₇₁	C₂²	1	24	yes	complemented
49	#121×D₇₁	C₂²	1	12	yes	complemented
50	#120×D₇₁	C₂²	1	24	yes	complemented
51	#120×D₇₁	C₂²	1	8	yes	complemented
52	C₄×D₄×D₇₁	C₂²	1	12	yes	complemented
53	#117×D₇₁	C₂²	1	12	yes	complemented
54	C₂×C₄²×D₇₁	C₂²	1	1	yes	characteristic, complemented
55	H(3,𝔽₄)×C₇₁	C₂²	1	4	yes	complemented
56	#555×C₇₁	C₂²	1	6	yes	complemented
57	D₄²×C₇₁	C₂²	1	6	yes	complemented
58	#535×C₇₁	C₂²	1	12	yes	complemented
59	#532×C₇₁	C₂²	1	3	yes	complemented
60	C₂⁴×D₇₁	C₂³	1	8	yes	—
61	C₂×#11765866	C₂³	1	6	yes	complemented
62	C₂×#11765865	C₂³	1	6	yes	complemented
63	C₂×#11765865	C₂³	1	12	yes	complemented
64	C₂×#11765864	C₂³	1	12	yes	complemented
65	C₂×#11765864	C₂³	1	6	yes	complemented
66	#41×D₇₁	—	4	24	no	—
67	C₂×Q₈×D₇₁	C₂³	1	6	yes	—
68	C₂²×D₂₈₄	C₂³	1	12	yes	complemented
69	C₂²×C₂²⋊D₇₁	C₂³	1	24	yes	complemented
70	C₂×D₄×D₇₁	—	4	48	no	—
71	C₂×D₄×D₇₁	C₂³	1	12	yes	—
72	C₂×D₄×D₇₁	C₂³	1	24	yes	—
73	C₂×D₄×D₇₁	C₂³	1	6	yes	—
74	C₂×D₄×D₇₁	C₂³	1	12	yes	—
75	C₂×D₄×D₇₁	C₂³	1	24	yes	complemented
76	C₂×D₄×D₇₁	C₂³	1	24	yes	complemented
77	C₂²×C₄×D₇₁	C₂³	1	12	yes	—
78	C₂²×C₄×D₇₁	C₂³	1	3	yes	—
79	#14556128	C₂³	1	3	yes	complemented
80	#14556127	C₂³	1	12	yes	complemented
81	#14556126	C₂³	1	6	yes	complemented
82	#14556125	C₂³	1	3	yes	—
83	#14556125	C₂³	1	8	yes	complemented
84	#14556124	C₂³	1	6	yes	—
85	#14556124	C₂³	1	12	yes	—
86	#14556124	C₂³	1	24	yes	complemented
87	#14556124	C₂³	1	24	yes	complemented
88	#14556117	C₂³	1	24	yes	complemented
89	#14556117	C₂³	1	6	yes	complemented
90	#14556116	C₂³	1	24	yes	complemented
91	#14556116	C₂³	1	6	yes	complemented
92	#14556115	C₂³	1	24	yes	complemented
93	#14556115	C₂³	1	6	yes	complemented
94	#14556114	C₂³	1	48	yes	complemented
95	#14556114	C₂³	1	48	yes	complemented
96	#14556114	C₂³	1	24	yes	complemented
97	#14556103	C₂³	1	12	yes	complemented
98	#14556103	C₂³	1	24	yes	complemented
99	#14556102	C₂³	1	12	yes	complemented
100	#14556102	C₂³	1	24	yes	complemented
101	#14556101	C₂³	1	24	yes	complemented
102	#14556101	C₂³	1	48	yes	complemented
103	#14556100	C₂³	1	24	yes	complemented
104	#14556100	C₂³	1	48	yes	complemented
105	#14556099	C₂³	1	12	yes	complemented
106	#14556099	C₂³	1	24	yes	complemented
107	#14556098	C₂³	1	24	yes	complemented
108	#14556098	C₂³	1	24	yes	complemented
109	#14556098	C₂³	1	48	yes	complemented
110	#14556097	C₂³	1	8	yes	complemented
111	#14556097	C₂³	1	24	yes	complemented
112	#14556096	C₂³	1	24	yes	complemented
113	#14556096	C₂³	1	48	yes	complemented
114	#14556096	C₂³	1	24	yes	complemented
115	C₄×D₂₈₄	C₂³	1	12	yes	complemented
116	D₄×Dic₇₁	C₂³	1	12	yes	complemented
117	#14556090	C₂³	1	12	yes	complemented
118	C₄×C₂²⋊D₇₁	C₂³	1	24	yes	complemented
119	(C₂²⋊D₇₁)⋊C₄	C₂³	1	24	yes	complemented
120	#14556087	C₂³	1	12	yes	complemented
121	#14556086	C₂³	1	24	yes	complemented
122	#14556085	C₂³	1	24	yes	complemented
123	#14556084	C₂³	1	24	yes	complemented
124	C₄⋊C₄×D₇₁	C₂³	1	12	yes	—
125	C₂²⋊C₄×D₇₁	C₂³	1	24	yes	—
126	C₂²⋊C₄×D₇₁	C₂³	1	24	yes	—
127	C₂×C₄×Dic₇₁	C₂³	1	3	yes	complemented
128	C₄²×D₇₁	C₂³	1	3	yes	—
129	C₄²×D₇₁	C₂³	1	1	yes	characteristic
130	C₄²×D₇₁	C₂³	1	8	yes	—
131	C₄²×D₇₁	C₂³	1	3	yes	complemented
132	C₄²×D₇₁	C₂³	1	1	yes	characteristic, complemented
133	C₂×#41×C₇₁	C₂³	1	6	yes	complemented
134	C₂²×D₄×C₇₁	C₂³	1	12	yes	complemented
135	C₄⋊Q₈×C₇₁	C₂³	1	3	yes	complemented
136	#127×C₇₁	C₂³	1	3	yes	—
137	#127×C₇₁	C₂³	1	8	yes	complemented
138	#124×C₇₁	C₂³	1	24	yes	complemented
139	#124×C₇₁	C₂³	1	6	yes	complemented
140	#121×C₇₁	C₂³	1	12	yes	complemented
141	#121×C₇₁	C₂³	1	24	yes	complemented
142	#120×C₇₁	C₂³	1	8	yes	complemented
143	#120×C₇₁	C₂³	1	24	yes	complemented
144	C₄×D₄×C₇₁	C₂³	1	12	yes	complemented
145	#117×C₇₁	C₂³	1	12	yes	complemented
146	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic, complemented
147	C₂³×D₇₁	—	4	48	no	—
148	C₂³×D₇₁	C₂⁴	1	1	yes	characteristic
149	C₂³×D₇₁	C₂⁴	1	12	yes	—
150	C₂³×D₇₁	C₂⁴	1	24	yes	—
151	#11765866	—	4	12	no	—
152	#11765865	—	4	12	no	—
153	#11765865	—	4	24	no	—
154	#11765864	—	4	24	no	—
155	#11765864	—	4	12	no	—
156	C₂×Dic₁₄₂	C₂⁴	1	6	yes	—
157	C₂×Dic₁₄₂	C₂⁴	1	12	yes	—
158	Q₈×D₇₁	—	4	12	no	—
159	C₂×D₂₈₄	—	4	24	no	—
160	C₂×D₂₈₄	C₂⁴	1	12	yes	—
161	C₂×D₂₈₄	C₂⁴	1	24	yes	—
162	C₂×D₂₈₄	C₂⁴	1	6	yes	—
163	C₂×D₂₈₄	C₂⁴	1	12	yes	—
164	C₂×C₂²⋊D₇₁	—	4	48	no	—
165	C₂×C₂²⋊D₇₁	C₂⁴	1	24	yes	—
166	C₂×C₂²⋊D₇₁	C₂⁴	1	48	yes	—
167	C₂×C₂²⋊D₇₁	C₂⁴	1	12	yes	—
168	C₂×C₂²⋊D₇₁	C₂⁴	1	12	yes	—
169	C₂×C₂²⋊D₇₁	C₂⁴	1	12	yes	—
170	D₄×D₇₁	—	2	48	no	—
171	D₄×D₇₁	—	4	48	no	—
172	D₄×D₇₁	—	4	48	no	—
173	D₄×D₇₁	—	4	48	no	—
174	D₄×D₇₁	—	4	24	no	—
175	D₄×D₇₁	—	4	12	no	—
176	C₂²×Dic₇₁	C₂⁴	1	12	yes	—
177	C₂²×Dic₇₁	C₂⁴	1	3	yes	—
178	C₂×C₄×D₇₁	—	2	48	no	—
179	C₂×C₄×D₇₁	—	2	12	no	—
180	C₂×C₄×D₇₁	C₂⁴	1	12	yes	—
181	C₂×C₄×D₇₁	C₂⁴	1	3	yes	—
182	C₂×C₄×D₇₁	C₂⁴	1	12	yes	—
183	C₂×C₄×D₇₁	C₂⁴	1	12	yes	—
184	C₂×C₄×D₇₁	C₂⁴	1	3	yes	—
185	C₂×C₄×D₇₁	C₂⁴	1	3	yes	—
186	C₂×C₄×D₇₁	C₂⁴	1	3	yes	—
187	C₄⋊Dic₇₁	C₂⁴	1	12	yes	—
188	Dic₇₁⋊C₄	C₂⁴	1	24	yes	—
189	C₂²⋊Dic₇₁	C₂⁴	1	24	yes	—
190	C₂²⋊Dic₇₁	C₂⁴	1	24	yes	—
191	(C₂×D₇₁)⋊C₄	C₂⁴	1	48	yes	—
192	(C₂×D₇₁)⋊C₄	C₂⁴	1	24	yes	—
193	(C₂×D₇₁)⋊C₄	C₂⁴	1	24	yes	—
194	C₄×Dic₇₁	C₂⁴	1	3	yes	—
195	C₄×Dic₇₁	C₂⁴	1	6	yes	—
196	C₄×Dic₇₁	C₂⁴	1	3	yes	—
197	C₄×Dic₇₁	C₂⁴	1	24	yes	—
198	C₂⁴×C₇₁	C₂⁴	1	8	yes	—
199	#41×C₇₁	—	4	12	no	—
200	C₂×Q₈×C₇₁	C₂⁴	1	6	yes	—
201	C₂×D₄×C₇₁	—	4	24	no	—
202	C₂×D₄×C₇₁	C₂⁴	1	12	yes	—
203	C₂×D₄×C₇₁	C₂⁴	1	24	yes	—
204	C₂×D₄×C₇₁	C₂⁴	1	6	yes	—
205	C₂×D₄×C₇₁	C₂⁴	1	12	yes	—
206	C₂²×C₄×C₇₁	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₇₁	C₂⁴	1	3	yes	—
208	C₄⋊C₄×C₇₁	C₂⁴	1	12	yes	—
209	C₂²⋊C₄×C₇₁	C₂⁴	1	24	yes	—
210	C₂²⋊C₄×C₇₁	C₂⁴	1	24	yes	—
211	C₄²×C₇₁	C₂⁴	1	3	yes	—
212	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
213	C₄²×C₇₁	C₂⁴	1	8	yes	—
214	C₂³×C₇₁	—	4	24	no	—
215	C₂³×C₇₁	C₂⁵	1	12	yes	—
216	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
217	C₂²×D₇₁	—	2	6	no	—
218	C₂²×D₇₁	—	2	24	no	—
219	C₂²×D₇₁	—	2	48	no	—
220	C₂²×D₇₁	—	4	48	no	—
221	C₂²×D₇₁	—	4	24	no	—
222	C₂²×D₇₁	—	8	64	no	—
223	C₂²×D₇₁	C₂⁵	1	12	yes	—
224	C₂²×D₇₁	C₂⁵	1	1	yes	characteristic
225	C₂²×D₇₁	C₂⁵	1	1	yes	characteristic
226	Q₈×C₇₁	—	4	6	no	—
227	D₄×C₇₁	—	2	24	no	—
228	D₄×C₇₁	—	4	24	no	—
229	D₄×C₇₁	—	4	6	no	—
230	D₄×C₇₁	—	4	12	no	—
231	C₂×C₄×C₇₁	—	2	24	no	—
232	C₂×C₄×C₇₁	—	2	6	no	—
233	C₂×C₄×C₇₁	C₂⁵	1	3	yes	—
234	C₂×C₄×C₇₁	C₂⁵	1	12	yes	—
235	C₂×C₄×C₇₁	C₂⁵	1	3	yes	—
236	C₂²⋊D₇₁	—	2	48	no	—
237	C₂²⋊D₇₁	—	4	48	no	—
238	C₂²⋊D₇₁	—	4	12	no	—
239	C₂²⋊D₇₁	—	4	12	no	—
240	C₂²⋊D₇₁	—	4	12	no	—
241	C₂×Dic₇₁	—	2	24	no	—
242	C₂×Dic₇₁	—	2	6	no	—
243	C₂×Dic₇₁	C₂⁵	1	3	yes	—
244	C₂×Dic₇₁	C₂⁵	1	12	yes	—
245	C₂×Dic₇₁	C₂⁵	1	3	yes	—
246	D₂₈₄	—	2	24	no	—
247	D₂₈₄	—	4	24	no	—
248	D₂₈₄	—	4	6	no	—
249	D₂₈₄	—	4	12	no	—
250	C₄×D₇₁	—	2	24	no	—
251	C₄×D₇₁	—	2	6	no	—
252	C₄×D₇₁	—	2	24	no	—
253	C₄×D₇₁	—	2	6	no	—
254	C₄×D₇₁	—	2	24	no	—
255	C₄×D₇₁	—	2	6	no	—
256	C₄×D₇₁	H(5,𝔽₂)	1	12	yes	—
257	Dic₁₄₂	—	4	12	no	—
258	Dic₁₄₂	—	4	6	no	—
259	C₂²×C₇₁	—	2	3	no	—
260	C₂²×C₇₁	—	2	12	no	—
261	C₂²×C₇₁	—	2	24	no	—
262	C₂²×C₇₁	—	8	16	no	—
263	C₂²×C₇₁	C₂⁶	1	1	yes	characteristic
264	C₂×D₇₁	—	2	3	no	—
265	C₂×D₇₁	—	2	12	no	—
266	C₂×D₇₁	—	2	24	no	—
267	C₂×D₇₁	—	4	4	no	—
268	C₂×D₇₁	—	4	48	no	—
269	C₂×D₇₁	—	8	48	no	—
270	C₂×D₇₁	C₂×H(5,𝔽₂)	1	6	yes	—
271	C₄×C₇₁	—	2	3	no	—
272	C₄×C₇₁	—	2	12	no	—
273	C₄×C₇₁	C₂×H(5,𝔽₂)	1	6	yes	—
274	Dic₇₁	—	2	3	no	—
275	Dic₇₁	—	2	12	no	—
276	Dic₇₁	C₂×H(5,𝔽₂)	1	6	yes	—
277	C₂×#3549	—	71	1	no	maximal, Sylow
278	C₂×C₇₁	—	4	12	no	—
279	C₂×C₇₁	—	4	1	no	—
280	C₂×C₇₁	C₂²×H(5,𝔽₂)	1	3	yes	—
281	D₇₁	—	4	1	no	—
282	D₇₁	—	4	12	no	—
283	D₇₁	#3549	1	4	yes	direct product factor
284	#3549	—	71	4	no	—
285	#3549	—	71	6	no	—
286	#3549	—	71	6	no	—
287	#3549	—	71	12	no	—
288	#3549	—	71	3	no	—
289	#3549	D₇₁	1	1	yes	characteristic, direct product factor
290	C₂×H(3,𝔽₄)	—	71	4	no	—
291	C₂×#555	—	71	6	no	—
292	C₂×D₄²	—	71	6	no	—
293	C₂×#535	—	71	12	no	—
294	C₂×#532	—	71	3	no	—
295	C₇₁	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
296	C₂²×#41	—	71	6	no	—
297	C₂³×D₄	—	71	12	no	—
298	H(3,𝔽₄)	—	71	24	no	—
299	H(3,𝔽₄)	—	71	12	no	—
300	H(3,𝔽₄)	—	71	24	no	—
301	H(3,𝔽₄)	C₂×D₇₁	1	4	yes	complemented
302	#555	—	71	6	no	—
303	#555	—	71	24	no	—
304	#555	—	71	24	no	—
305	#555	—	71	12	no	—
306	#555	—	71	24	no	—
307	#555	C₂×D₇₁	1	6	yes	complemented
308	D₄²	—	71	24	no	—
309	D₄²	—	71	6	no	—
310	D₄²	—	71	24	no	—
311	D₄²	—	71	24	no	—
312	D₄²	—	71	12	no	—
313	D₄²	C₂×D₇₁	1	6	yes	complemented
314	#535	—	71	12	no	—
315	#535	—	71	12	no	—
316	#535	—	71	24	no	—
317	#535	—	71	24	no	—
318	#535	—	71	24	no	—
319	#535	—	71	24	no	—
320	#535	—	71	24	no	—
321	#535	—	71	24	no	—
322	#535	—	71	12	no	—
323	#535	C₂×D₇₁	1	12	yes	complemented
324	#532	—	71	6	no	—
325	#532	—	71	3	no	—
326	#532	—	71	3	no	—
327	#532	—	71	6	no	—
328	#532	—	71	12	no	—
329	#532	—	71	12	no	—
330	#532	—	71	3	no	—
331	#532	C₂×D₇₁	1	3	yes	complemented
332	C₂×C₄⋊Q₈	—	71	3	no	—
333	C₂×#127	—	71	3	no	—
334	C₂×#127	—	71	8	no	—
335	C₂×#124	—	71	6	no	—
336	C₂×#124	—	71	24	no	—
337	C₂×#121	—	71	12	no	—
338	C₂×#121	—	71	24	no	—
339	C₂×#120	—	71	8	no	—
340	C₂×#120	—	71	24	no	—
341	C₂×C₄×D₄	—	71	12	no	—
342	C₂×#117	—	71	12	no	—
343	C₂²×C₄²	—	71	1	no	—
344	C₂⁵	—	71	8	no	—
345	C₂×#41	—	284	24	no	—
346	C₂×#41	—	71	6	no	—
347	C₂×#41	—	71	12	no	—
348	C₂×#41	—	71	6	no	—
349	C₂×#41	—	71	12	no	—
350	C₂×#41	—	71	6	no	—
351	C₂×#41	C₂²×D₇₁	1	6	yes	complemented
352	C₂²×Q₈	—	71	6	no	—
353	C₂²×D₄	—	284	48	no	—
354	C₂²×D₄	—	71	24	no	—
355	C₂²×D₄	—	71	6	no	—
356	C₂²×D₄	—	71	24	no	—
357	C₂²×D₄	—	71	12	no	—
358	C₂²×D₄	—	71	24	no	—
359	C₂²×D₄	—	71	24	no	—
360	C₂²×D₄	—	71	12	no	—
361	C₂²×D₄	—	71	12	no	—
362	C₂²×D₄	C₂²×D₇₁	1	12	yes	complemented
363	C₂³×C₄	—	71	12	no	—
364	C₂³×C₄	—	71	3	no	—
365	C₄⋊Q₈	—	71	6	no	—
366	C₄⋊Q₈	—	71	12	no	—
367	C₄⋊Q₈	—	71	3	no	—
368	C₄⋊Q₈	C₂²×D₇₁	1	3	yes	complemented
369	#127	—	71	12	no	—
370	#127	—	71	6	no	—
371	#127	—	71	24	no	—
372	#127	—	71	24	no	—
373	#127	—	71	3	no	—
374	#127	—	71	8	no	—
375	#127	C₂²×D₇₁	1	3	yes	—
376	#127	C₂²×D₇₁	1	8	yes	complemented
377	#124	—	71	6	no	—
378	#124	—	71	24	no	—
379	#124	—	71	6	no	—
380	#124	—	71	24	no	—
381	#124	—	71	24	no	—
382	#124	—	71	48	no	—
383	#124	—	71	48	no	—
384	#124	—	71	6	no	—
385	#124	—	71	24	no	—
386	#124	C₂²×D₇₁	1	6	yes	complemented
387	#124	C₂²×D₇₁	1	24	yes	complemented
388	#121	—	71	12	no	—
389	#121	—	71	24	no	—
390	#121	—	71	24	no	—
391	#121	—	71	48	no	—
392	#121	—	71	12	no	—
393	#121	—	71	24	no	—
394	#121	—	71	12	no	—
395	#121	—	71	24	no	—
396	#121	—	71	24	no	—
397	#121	—	71	48	no	—
398	#121	C₂²×D₇₁	1	12	yes	complemented
399	#121	C₂²×D₇₁	1	24	yes	complemented
400	#120	—	71	8	no	—
401	#120	—	71	24	no	—
402	#120	—	71	24	no	—
403	#120	—	71	24	no	—
404	#120	—	71	48	no	—
405	#120	—	71	24	no	—
406	#120	—	71	48	no	—
407	#120	—	71	24	no	—
408	#120	C₂²×D₇₁	1	8	yes	complemented
409	#120	C₂²×D₇₁	1	24	yes	complemented
410	C₄×D₄	—	71	12	no	—
411	C₄×D₄	—	71	24	no	—
412	C₄×D₄	—	71	12	no	—
413	C₄×D₄	—	71	24	no	—
414	C₄×D₄	—	71	12	no	—
415	C₄×D₄	C₂²×D₇₁	1	12	yes	complemented
416	#117	—	71	12	no	—
417	#117	—	71	24	no	—
418	#117	—	71	24	no	—
419	#117	—	71	24	no	—
420	#117	C₂²×D₇₁	1	12	yes	complemented
421	C₂×C₄⋊C₄	—	71	12	no	—
422	C₂×C₂²⋊C₄	—	71	24	no	—
423	C₂×C₂²⋊C₄	—	71	24	no	—
424	C₂×C₄²	—	71	3	no	—
425	C₂×C₄²	—	71	8	no	—
426	C₂×C₄²	—	71	3	no	—
427	C₂×C₄²	—	71	1	no	—
428	C₂×C₄²	—	71	1	no	—
429	C₂×C₄²	—	71	3	no	—
430	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic, complemented
431	C₂⁴	—	284	48	no	—
432	C₂⁴	—	71	24	no	—
433	C₂⁴	—	71	12	no	—
434	C₂⁴	—	71	1	no	—
435	C₂⁴	C₂³×D₇₁	1	8	yes	—
436	#41	—	4	12	no	—
437	#41	—	284	24	no	—
438	#41	—	284	12	no	—
439	#41	—	284	24	no	—
440	#41	—	284	12	no	—
441	#41	—	284	12	no	—
442	C₂×Q₈	—	284	12	no	—
443	C₂×Q₈	—	71	12	no	—
444	C₂×Q₈	—	71	6	no	—
445	C₂×Q₈	C₂³×D₇₁	1	6	yes	—
446	C₂×D₄	—	4	24	no	—
447	C₂×D₄	—	284	24	no	—
448	C₂×D₄	—	284	48	no	—
449	C₂×D₄	—	284	48	no	—
450	C₂×D₄	—	284	24	no	—
451	C₂×D₄	—	284	12	no	—
452	C₂×D₄	—	284	48	no	—
453	C₂×D₄	—	284	48	no	—
454	C₂×D₄	—	71	12	no	—
455	C₂×D₄	—	71	48	no	—
456	C₂×D₄	—	71	12	no	—
457	C₂×D₄	—	71	12	no	—
458	C₂×D₄	—	71	24	no	—
459	C₂×D₄	—	71	6	no	—
460	C₂×D₄	—	71	24	no	—
461	C₂×D₄	—	71	12	no	—
462	C₂×D₄	—	71	12	no	—
463	C₂×D₄	—	142	48	no	—
464	C₂×D₄	C₂³×D₇₁	1	12	yes	—
465	C₂×D₄	C₂³×D₇₁	1	6	yes	—
466	C₂×D₄	C₂³×D₇₁	1	24	yes	—
467	C₂×D₄	C₂³×D₇₁	1	12	yes	—
468	C₂²×C₄	—	71	3	no	—
469	C₂²×C₄	—	71	3	no	—
470	C₂²×C₄	—	71	12	no	—
471	C₂²×C₄	—	71	3	no	—
472	C₂²×C₄	—	71	12	no	—
473	C₂²×C₄	—	71	3	no	—
474	C₂²×C₄	—	71	3	no	—
475	C₂²×C₄	—	71	12	no	—
476	C₂²×C₄	—	71	12	no	—
477	C₂²×C₄	—	142	48	no	—
478	C₂²×C₄	—	142	12	no	—
479	C₂²×C₄	C₂³×D₇₁	1	3	yes	—
480	C₂²×C₄	C₂³×D₇₁	1	12	yes	—
481	C₄⋊C₄	—	71	24	no	—
482	C₄⋊C₄	—	71	12	no	—
483	C₄⋊C₄	C₂³×D₇₁	1	12	yes	—
484	C₂²⋊C₄	—	71	24	no	—
485	C₂²⋊C₄	—	71	24	no	—
486	C₂²⋊C₄	—	71	48	no	—
487	C₂²⋊C₄	—	71	24	no	—
488	C₂²⋊C₄	—	71	24	no	—
489	C₂²⋊C₄	C₂³×D₇₁	1	24	yes	—
490	C₂²⋊C₄	C₂³×D₇₁	1	24	yes	—
491	C₄²	—	71	3	no	—
492	C₄²	—	71	6	no	—
493	C₄²	—	71	3	no	—
494	C₄²	—	71	24	no	—
495	C₄²	C₂³×D₇₁	1	3	yes	—
496	C₄²	C₂³×D₇₁	1	1	yes	characteristic
497	C₄²	C₂³×D₇₁	1	8	yes	—
498	C₂³	—	4	24	no	—
499	C₂³	—	284	24	no	—
500	C₂³	—	284	48	no	—
501	C₂³	—	568	64	no	—
502	C₂³	—	71	1	no	—
503	C₂³	—	71	12	no	—
504	C₂³	—	71	1	no	—
505	C₂³	—	142	6	no	—
506	C₂³	—	142	24	no	—
507	C₂³	—	142	48	no	—
508	C₂³	C₂⁴×D₇₁	1	12	yes	—
509	C₂³	C₂⁴×D₇₁	1	1	yes	characteristic
510	Q₈	—	4	6	no	—
511	Q₈	—	284	12	no	—
512	Q₈	—	284	6	no	—
513	D₄	—	2	24	no	—
514	D₄	—	4	24	no	—
515	D₄	—	4	12	no	—
516	D₄	—	4	6	no	—
517	D₄	—	284	24	no	—
518	D₄	—	284	12	no	—
519	D₄	—	284	6	no	—
520	D₄	—	284	48	no	—
521	D₄	—	284	12	no	—
522	D₄	—	284	12	no	—
523	D₄	—	284	12	no	—
524	D₄	—	142	48	no	—
525	D₄	—	142	24	no	—
526	C₂×C₄	—	2	24	no	—
527	C₂×C₄	—	2	6	no	—
528	C₂×C₄	—	71	3	no	—
529	C₂×C₄	—	71	12	no	—
530	C₂×C₄	—	71	3	no	—
531	C₂×C₄	—	71	12	no	—
532	C₂×C₄	—	142	24	no	—
533	C₂×C₄	—	142	6	no	—
534	C₂×C₄	—	142	24	no	—
535	C₂×C₄	—	142	6	no	—
536	C₂×C₄	—	142	24	no	—
537	C₂×C₄	—	142	6	no	—
538	C₂×C₄	—	142	24	no	—
539	C₂×C₄	—	142	6	no	—
540	C₂×C₄	C₂⁴×D₇₁	1	3	yes	—
541	C₂×C₄	C₂⁴×D₇₁	1	12	yes	—
542	C₂×C₄	C₂⁴×D₇₁	1	3	yes	—
543	C₂²	—	2	3	no	—
544	C₂²	—	2	12	no	—
545	C₂²	—	2	24	no	—
546	C₂²	—	8	16	no	—
547	C₂²	—	284	48	no	—
548	C₂²	—	284	4	no	—
549	C₂²	—	568	48	no	—
550	C₂²	—	71	6	no	—
551	C₂²	—	142	3	no	—
552	C₂²	—	142	12	no	—
553	C₂²	—	142	24	no	—
554	C₂²	C₂⁵×D₇₁	1	1	yes	characteristic
555	C₄	—	2	12	no	—
556	C₄	—	2	3	no	—
557	C₄	—	71	6	no	—
558	C₄	—	142	12	no	—
559	C₄	—	142	3	no	—
560	C₄	H(5,𝔽₂)×D₇₁	1	6	yes	—
561	C₂	—	4	12	no	—
562	C₂	—	4	1	no	—
563	C₂	—	284	12	no	—
564	C₂	—	284	1	no	—
565	C₂	—	71	4	no	—
566	C₂	C₂×H(5,𝔽₂)×D₇₁	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₁
commutator, socle, cosocle	C₂²×C₇₁	C₂⁶
Fitting	C₇₁×#3549	C₂
hypercenter	#3549	D₇₁
hypocenter	C₇₁	C₂×#3549
LCS	G ▷ C₂²×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂² ◁ #3549

Complements

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

N	H ≅ G/N	type
1. #22602745	C₂	semidirect
2. #22602744	C₂	semidirect
3. #22602743	C₂	semidirect
4. #22602742	C₂	semidirect
5. #22602741	C₂	semidirect
6. H(3,𝔽₄)×D₇₁	C₂	semidirect
7. #555×D₇₁	C₂	semidirect
8. D₄²×D₇₁	C₂	semidirect
9. #535×D₇₁	C₂	semidirect
10. #532×D₇₁	C₂	semidirect
11. C₇₁×#3549	C₂	semidirect
12. C₂×#41×D₇₁	C₂²	semidirect
13. C₂²×D₄×D₇₁	C₂²	semidirect
14. #17986742	C₂²	semidirect
15. #17986741	C₂²	semidirect
16. #17986741	C₂²	semidirect
17. #17986715	C₂²	semidirect
18. #17986714	C₂²	semidirect
19. #17986713	C₂²	semidirect
20. #17986712	C₂²	semidirect
21. #17986711	C₂²	semidirect
22. D₄×D₂₈₄	C₂²	semidirect
23. #17986634	C₂²	semidirect
24. #17986633	C₂²	semidirect
25. D₄×C₂²⋊D₇₁	C₂²	semidirect
26. #17986631	C₂²	semidirect
27. #17986568	C₂²	semidirect
28. #17986567	C₂²	semidirect
29. #17986566	C₂²	semidirect
30. #17986565	C₂²	semidirect
31. #17986565	C₂²	semidirect
32. #17986564	C₂²	semidirect
33. #17986564	C₂²	semidirect
34. #17986563	C₂²	semidirect
35. #17986562	C₂²	semidirect
36. #17986550	C₂²	semidirect
37. #17986549	C₂²	semidirect
38. #17986548	C₂²	semidirect
39. #17986547	C₂²	semidirect
40. #17986546	C₂²	semidirect
41. #17986545	C₂²	semidirect
42. #17986544	C₂²	semidirect
43. C₄⋊Q₈×D₇₁	C₂²	semidirect
45. #127×D₇₁	C₂²	semidirect
46. #124×D₇₁	C₂²	semidirect
47. #124×D₇₁	C₂²	semidirect
48. #121×D₇₁	C₂²	semidirect
49. #121×D₇₁	C₂²	semidirect
50. #120×D₇₁	C₂²	semidirect
51. #120×D₇₁	C₂²	semidirect
52. C₄×D₄×D₇₁	C₂²	semidirect
53. #117×D₇₁	C₂²	semidirect
54. C₂×C₄²×D₇₁	C₂²	semidirect
55. H(3,𝔽₄)×C₇₁	C₂²	semidirect
56. #555×C₇₁	C₂²	semidirect
57. D₄²×C₇₁	C₂²	semidirect
58. #535×C₇₁	C₂²	semidirect
59. #532×C₇₁	C₂²	semidirect
61. C₂×#11765866	C₂³	semidirect
62. C₂×#11765865	C₂³	semidirect
63. C₂×#11765865	C₂³	semidirect
64. C₂×#11765864	C₂³	semidirect
65. C₂×#11765864	C₂³	semidirect
68. C₂²×D₂₈₄	C₂³	semidirect
69. C₂²×C₂²⋊D₇₁	C₂³	semidirect
75. C₂×D₄×D₇₁	C₂³	semidirect
76. C₂×D₄×D₇₁	C₂³	semidirect
79. #14556128	C₂³	semidirect
80. #14556127	C₂³	semidirect
81. #14556126	C₂³	semidirect
83. #14556125	C₂³	semidirect
86. #14556124	C₂³	semidirect
87. #14556124	C₂³	semidirect
88. #14556117	C₂³	semidirect
89. #14556117	C₂³	semidirect
90. #14556116	C₂³	semidirect
91. #14556116	C₂³	semidirect
92. #14556115	C₂³	semidirect
93. #14556115	C₂³	semidirect
94. #14556114	C₂³	semidirect
95. #14556114	C₂³	semidirect
96. #14556114	C₂³	semidirect
97. #14556103	C₂³	semidirect
98. #14556103	C₂³	semidirect
99. #14556102	C₂³	semidirect
100. #14556102	C₂³	semidirect
101. #14556101	C₂³	semidirect
102. #14556101	C₂³	semidirect
103. #14556100	C₂³	semidirect
104. #14556100	C₂³	semidirect
105. #14556099	C₂³	semidirect
106. #14556099	C₂³	semidirect
107. #14556098	C₂³	semidirect
108. #14556098	C₂³	semidirect
109. #14556098	C₂³	semidirect
110. #14556097	C₂³	semidirect
111. #14556097	C₂³	semidirect
112. #14556096	C₂³	semidirect
113. #14556096	C₂³	semidirect
114. #14556096	C₂³	semidirect
115. C₄×D₂₈₄	C₂³	semidirect
116. D₄×Dic₇₁	C₂³	semidirect
117. #14556090	C₂³	semidirect
118. C₄×C₂²⋊D₇₁	C₂³	semidirect
119. (C₂²⋊D₇₁)⋊C₄	C₂³	semidirect
120. #14556087	C₂³	semidirect
121. #14556086	C₂³	semidirect
122. #14556085	C₂³	semidirect
123. #14556084	C₂³	semidirect
127. C₂×C₄×Dic₇₁	C₂³	semidirect
131. C₄²×D₇₁	C₂³	semidirect
132. C₄²×D₇₁	C₂³	semidirect
133. C₂×#41×C₇₁	C₂³	semidirect
134. C₂²×D₄×C₇₁	C₂³	semidirect
135. C₄⋊Q₈×C₇₁	C₂³	semidirect
137. #127×C₇₁	C₂³	semidirect
138. #124×C₇₁	C₂³	semidirect
139. #124×C₇₁	C₂³	semidirect
140. #121×C₇₁	C₂³	semidirect
141. #121×C₇₁	C₂³	semidirect
142. #120×C₇₁	C₂³	semidirect
143. #120×C₇₁	C₂³	semidirect
144. C₄×D₄×C₇₁	C₂³	semidirect
145. #117×C₇₁	C₂³	semidirect
146. C₂×C₄²×C₇₁	C₂³	semidirect
283. D₇₁	#3549	direct (N × H)
289. #3549	D₇₁	direct (N × H)
295. C₇₁	C₂×#3549	semidirect
301. H(3,𝔽₄)	C₂×D₇₁	semidirect
307. #555	C₂×D₇₁	semidirect
313. D₄²	C₂×D₇₁	semidirect
323. #535	C₂×D₇₁	semidirect
331. #532	C₂×D₇₁	semidirect
351. C₂×#41	C₂²×D₇₁	semidirect
362. C₂²×D₄	C₂²×D₇₁	semidirect
368. C₄⋊Q₈	C₂²×D₇₁	semidirect
376. #127	C₂²×D₇₁	semidirect
386. #124	C₂²×D₇₁	semidirect
387. #124	C₂²×D₇₁	semidirect
398. #121	C₂²×D₇₁	semidirect
399. #121	C₂²×D₇₁	semidirect
408. #120	C₂²×D₇₁	semidirect
409. #120	C₂²×D₇₁	semidirect
415. C₄×D₄	C₂²×D₇₁	semidirect
420. #117	C₂²×D₇₁	semidirect
430. C₂×C₄²	C₂²×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22602745	2
#22602744	2
#22602743	2
#22602742	2
#22602741	2
H(3,𝔽₄)×D₇₁	2
#555×D₇₁	2
D₄²×D₇₁	2
#535×D₇₁	2
#532×D₇₁	2
C₇₁×#3549	2
C₂×#3549	71

Subgroups — #3549×D71 #32905250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3549×D₇₁ #32905250