Subgroups — #32011385

Order 18176.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597257	C₂	1	1	yes	maximal, characteristic, complemented
2	#22597192	C₂	1	1	yes	maximal, characteristic, complemented
3	#22589251	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589239	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588873	C₂	1	2	yes	maximal, complemented
6	#22588868	C₂	1	2	yes	maximal, complemented
7	#22588829	C₂	1	2	yes	maximal, complemented
8	#22588822	C₂	1	2	yes	maximal, complemented
9	#22588464	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3155	C₂	1	1	yes	maximal, characteristic
12	#17986766	C₂²	1	2	yes	—
13	#17986474	C₂²	1	2	yes	—
14	#17986121	—	2	2	no	—
15	#17986116	—	2	2	no	—
16	#17986111	—	2	2	no	—
17	D₈×Dic₇₁	—	2	2	no	—
18	C₂×#14556064	C₂²	1	1	yes	characteristic
19	#17986037	C₂²	1	1	yes	characteristic
20	#17986016	C₂²	1	2	yes	—
21	#17986016	C₂²	1	2	yes	—
22	#17986004	C₂²	1	2	yes	—
23	#17986004	C₂²	1	2	yes	—
24	C₂×#14556045	C₂²	1	2	yes	—
25	#17985973	C₂²	1	2	yes	—
26	#17985954	C₂²	1	1	yes	characteristic
27	#17985954	C₂²	1	1	yes	characteristic
28	#17985770	C₂²	1	2	yes	—
29	C₇₁⋊#338	C₂²	1	1	yes	characteristic
30	#17985756	C₂²	1	1	yes	characteristic
31	#17985755	C₂²	1	2	yes	—
32	#17985755	C₂²	1	1	yes	characteristic
33	#17985755	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×C₇₁	C₂²	1	2	yes	—
35	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
36	C₂²×D₈×C₇₁	C₂²	1	1	yes	characteristic
37	#535×C₇₁	C₂²	1	2	yes	—
38	#496×C₇₁	C₄	1	4	yes	complemented
39	#495×C₇₁	C₄	1	2	yes	complemented
40	#493×C₇₁	C₄	1	2	yes	complemented
41	#405×C₇₁	C₂²	1	1	yes	characteristic
42	#14556135	—	2	4	no	—
43	#14556135	—	4	2	no	—
44	C₂×#11765849	—	4	2	no	—
45	C₂×#11765849	C₂³	1	1	yes	characteristic
46	C₂×#11765849	C₂³	1	2	yes	—
47	C₂×#11765849	C₂³	1	1	yes	characteristic
48	D₄×Dic₇₁	—	2	4	no	—
49	D₄×Dic₇₁	—	4	2	no	—
50	#14556087	C₂³	1	1	yes	characteristic
51	#14556087	C₂³	1	2	yes	—
52	#14556087	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₇₁	—	4	2	no	—
54	#14556064	—	2	1	no	—
55	#14556064	—	2	1	no	—
56	#14556062	—	2	1	no	—
57	#14556060	—	2	1	no	—
58	#14556055	—	2	4	no	—
59	#14556055	—	4	2	no	—
60	#14556049	—	2	4	no	—
61	#14556049	—	4	2	no	—
62	#14556045	—	4	2	no	—
63	#14556043	—	4	2	no	—
64	#14556038	—	2	1	no	—
65	#14556038	D₄	1	2	yes	complemented
66	C₈×Dic₇₁	—	2	1	no	—
67	C₈×Dic₇₁	D₄	1	2	yes	complemented
68	C₂×#41×C₇₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₇₁	C₂³	1	2	yes	—
70	AGL(1,ℤ/8)×C₇₁	—	4	2	no	—
71	AGL(1,ℤ/8)×C₇₁	—	4	2	no	—
72	#135×C₇₁	—	2	1	no	—
73	#135×C₇₁	—	2	1	no	—
74	#135×C₇₁	—	2	1	no	—
75	#135×C₇₁	—	2	1	no	—
76	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
78	C₂×SD₁₆×C₇₁	C₂×C₄	1	4	yes	complemented
79	C₂×D₈×C₇₁	—	2	1	no	—
80	C₂×D₈×C₇₁	—	2	1	no	—
81	C₂×D₈×C₇₁	—	2	1	no	—
82	C₂×D₈×C₇₁	—	2	1	no	—
83	C₂×D₈×C₇₁	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₇₁	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×D₈×C₇₁	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
89	#127×C₇₁	C₂×C₄	1	4	yes	complemented
90	#124×C₇₁	C₂×C₄	1	4	yes	complemented
91	#121×C₇₁	—	4	2	no	—
92	#120×C₇₁	—	4	2	no	—
93	#117×C₇₁	C₂³	1	1	yes	characteristic
94	#97×C₇₁	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	complemented
96	C₂²×Dic₇₁	—	4	4	no	—
97	#11765849	—	2	1	no	—
98	#11765849	—	2	1	no	—
99	#11765849	—	2	2	no	—
100	#11765849	—	2	1	no	—
101	#11765849	—	2	2	no	—
102	#11765849	—	2	1	no	—
103	#11765849	—	4	4	no	—
104	C₂×C₇₁⋊C₈	—	2	1	no	—
105	C₂×C₇₁⋊C₈	—	2	2	no	—
106	C₂×C₇₁⋊C₈	—	4	4	no	—
107	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
108	C₄⋊Dic₇₁	—	2	1	no	—
109	C₄⋊Dic₇₁	—	2	2	no	—
110	C₄⋊Dic₇₁	—	2	1	no	—
111	C₂²⋊Dic₇₁	—	2	1	no	—
112	C₂²⋊Dic₇₁	—	2	1	no	—
113	C₂²⋊Dic₇₁	—	2	2	no	—
114	C₂²⋊Dic₇₁	—	4	4	no	—
115	C₄×Dic₇₁	—	2	1	no	—
116	C₄×Dic₇₁	—	2	2	no	—
117	C₄×Dic₇₁	C₂×D₄	1	2	yes	—
118	C₂⁴×C₇₁	—	2	2	no	—
119	#41×C₇₁	—	2	2	no	—
120	#41×C₇₁	—	2	2	no	—
121	#41×C₇₁	—	2	2	no	—
122	#41×C₇₁	—	2	2	no	—
123	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
124	C₂×D₄×C₇₁	—	2	2	no	—
125	C₂×D₄×C₇₁	—	2	2	no	—
126	C₂×D₄×C₇₁	—	2	2	no	—
127	C₂×D₄×C₇₁	—	2	2	no	—
128	C₂×D₄×C₇₁	—	2	2	no	—
129	C₂×D₄×C₇₁	—	2	2	no	—
130	C₂×D₄×C₇₁	—	4	4	no	—
131	C₂×D₄×C₇₁	C₂²×C₄	1	4	yes	—
132	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₇₁	—	2	2	no	—
134	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₇₁	—	2	1	no	—
136	Q₁₆×C₇₁	—	2	1	no	—
137	SD₁₆×C₇₁	—	2	2	no	—
138	SD₁₆×C₇₁	—	2	2	no	—
139	SD₁₆×C₇₁	—	4	4	no	—
140	D₈×C₇₁	—	2	2	no	—
141	D₈×C₇₁	—	2	2	no	—
142	D₈×C₇₁	—	2	2	no	—
143	D₈×C₇₁	—	2	2	no	—
144	D₈×C₇₁	—	2	1	no	—
145	D₈×C₇₁	—	2	1	no	—
146	D₈×C₇₁	—	4	4	no	—
147	M₁₆×C₇₁	—	2	1	no	—
148	M₁₆×C₇₁	—	2	1	no	—
149	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
155	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
156	C₄⋊C₄×C₇₁	—	2	1	no	—
157	C₂²⋊C₄×C₇₁	—	2	1	no	—
158	C₂²⋊C₄×C₇₁	—	4	4	no	—
159	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
160	C₂³×C₇₁	—	2	4	no	—
161	C₂³×C₇₁	—	2	2	no	—
162	C₂³×C₇₁	—	4	2	no	—
163	C₂³×C₇₁	—	4	2	no	—
164	C₂³×C₇₁	—	16	2	no	—
165	C₂³×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
166	Q₈×C₇₁	—	2	2	no	—
167	Q₈×C₇₁	—	2	2	no	—
168	D₄×C₇₁	—	2	4	no	—
169	D₄×C₇₁	—	2	2	no	—
170	D₄×C₇₁	—	2	2	no	—
171	D₄×C₇₁	—	2	4	no	—
172	D₄×C₇₁	—	4	2	no	—
173	D₄×C₇₁	—	4	2	no	—
174	D₄×C₇₁	—	4	2	no	—
175	D₄×C₇₁	—	4	2	no	—
176	D₄×C₇₁	—	16	4	no	—
177	C₂×C₄×C₇₁	—	2	2	no	—
178	C₂×C₄×C₇₁	—	2	2	no	—
179	C₂×C₄×C₇₁	—	4	2	no	—
180	C₂×C₄×C₇₁	—	4	2	no	—
181	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×Dic₇₁	—	2	2	no	—
188	C₂×Dic₇₁	—	4	2	no	—
189	C₂×Dic₇₁	—	4	1	no	—
190	C₂×Dic₇₁	—	16	4	no	—
191	C₈×C₇₁	—	2	2	no	—
192	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
193	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
194	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
195	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
196	C₇₁⋊C₈	—	2	2	no	—
197	C₇₁⋊C₈	—	4	2	no	—
198	C₇₁⋊C₈	—	4	1	no	—
199	C₂²×C₇₁	—	4	1	no	—
200	C₂²×C₇₁	—	4	2	no	—
201	C₂²×C₇₁	—	4	4	no	—
202	C₂²×C₇₁	—	8	2	no	—
203	C₂²×C₇₁	—	8	4	no	—
204	C₂²×C₇₁	—	8	4	no	—
205	C₂²×C₇₁	—	16	2	no	—
206	C₂²×C₇₁	#518	1	1	yes	characteristic
207	C₂²×C₇₁	#535	1	1	yes	characteristic
208	C₂²×C₇₁	#540	1	1	yes	characteristic
209	C₄×C₇₁	—	4	2	no	—
210	C₄×C₇₁	—	4	2	no	—
211	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₇₁	#518	1	1	yes	characteristic
213	C₄×C₇₁	#535	1	1	yes	characteristic
214	C₄×C₇₁	#540	1	1	yes	characteristic
215	Dic₇₁	—	4	2	no	—
216	Dic₇₁	—	8	1	no	—
217	Dic₇₁	—	8	2	no	—
218	#22286	—	71	1	no	maximal, Sylow
219	C₂×C₇₁	—	2	1	no	—
220	C₂×C₇₁	—	2	1	no	—
221	C₂×C₇₁	—	2	1	no	—
222	C₂×C₇₁	—	8	2	no	—
223	C₂×C₇₁	—	8	4	no	—
224	C₂×C₇₁	#2328	1	1	yes	characteristic
225	#3155	D₇₁	1	1	yes	characteristic
226	#2957	—	71	1	no	—
227	#2948	—	71	1	no	—
228	#1978	—	71	1	no	—
229	#1976	—	71	1	no	—
230	#1911	—	71	2	no	—
231	#1910	—	71	2	no	—
232	#1904	—	71	2	no	—
233	#1903	—	71	2	no	—
234	#1833	—	71	1	no	—
235	#1747	—	71	1	no	—
236	C₇₁	#22286	1	1	yes	characteristic, complemented, Sylow
237	C₂×AGL(1,ℤ/8)	C₂×D₇₁	1	2	yes	—
238	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
239	C₂²×D₈	C₂×D₇₁	1	1	yes	characteristic
240	#568	—	71	2	no	—
241	#535	C₂×D₇₁	1	2	yes	—
242	#518	—	71	2	no	—
243	#496	Dic₇₁	1	4	yes	complemented
244	#495	Dic₇₁	1	2	yes	complemented
245	#493	Dic₇₁	1	2	yes	complemented
246	#444	—	142	2	no	—
247	#443	—	142	2	no	—
248	#442	—	142	2	no	—
249	C₄×D₈	—	142	2	no	—
250	C₂×#108	—	71	1	no	—
251	#427	—	71	1	no	—
252	#421	—	71	2	no	—
253	#421	—	71	2	no	—
254	#418	—	71	2	no	—
255	#418	—	71	2	no	—
256	C₂×#100	—	71	2	no	—
257	#410	—	71	2	no	—
258	#405	—	71	1	no	—
259	#405	—	71	1	no	—
260	#405	C₂×D₇₁	1	1	yes	characteristic
261	#344	—	71	2	no	—
262	#338	—	71	1	no	—
263	H(3,ℤ/4)	—	71	1	no	—
264	H(3,ℤ/4)	—	71	2	no	—
265	H(3,ℤ/4)	—	71	1	no	—
266	H(3,ℤ/4)	—	71	1	no	—
267	C₂×#41	C₂²×D₇₁	1	2	yes	—
268	C₂²×D₄	C₂²×D₇₁	1	2	yes	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	AGL(1,ℤ/8)	—	4	2	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	#135	—	2	1	no	—
275	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	complemented
277	C₂×SD₁₆	C₂×Dic₇₁	1	4	yes	complemented
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	C₂×Dic₇₁	1	2	yes	—
283	C₂×D₈	C₂×Dic₇₁	1	2	yes	—
284	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic, complemented
285	C₂×D₈	C₂×Dic₇₁	1	4	yes	complemented
286	#131	—	284	2	no	—
287	#131	—	142	4	no	—
288	C₂×M₁₆	—	284	2	no	—
289	C₂×M₁₆	—	71	1	no	—
290	C₂×M₁₆	—	71	2	no	—
291	C₂×M₁₆	—	71	1	no	—
292	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
294	#127	C₂×Dic₇₁	1	4	yes	complemented
295	#124	C₂×Dic₇₁	1	4	yes	complemented
296	#121	—	4	2	no	—
297	#120	—	4	2	no	—
298	C₄×D₄	—	284	2	no	—
299	C₄×D₄	—	142	4	no	—
300	#117	—	71	1	no	—
301	#117	—	71	2	no	—
302	#117	—	71	1	no	—
303	#117	C₂²×D₇₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	284	2	no	—
305	#108	—	142	1	no	—
306	#108	—	142	1	no	—
307	#107	—	142	1	no	—
308	#106	—	142	1	no	—
309	#104	—	284	2	no	—
310	#104	—	142	4	no	—
311	#102	—	284	2	no	—
312	#102	—	142	4	no	—
313	#100	—	284	2	no	—
314	#99	—	284	2	no	—
315	#97	—	71	2	no	—
316	#97	—	142	1	no	—
317	#97	C₂×Dic₇₁	1	2	yes	complemented
318	C₄×C₈	—	71	2	no	—
319	C₄×C₈	—	142	1	no	—
320	C₄×C₈	C₂×Dic₇₁	1	2	yes	complemented
321	C₂⁴	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	C₂²×Dic₇₁	1	4	yes	—
335	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	284	4	no	—
338	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	2	1	no	—
349	D₈	—	2	1	no	—
350	D₈	—	4	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	284	4	no	—
354	M₁₆	—	142	2	no	—
355	M₁₆	—	142	1	no	—
356	M₁₆	—	142	2	no	—
357	M₁₆	—	142	1	no	—
358	M₁₆	—	142	1	no	—
359	M₁₆	—	142	1	no	—
360	C₂×C₈	—	284	4	no	—
361	C₂×C₈	—	71	2	no	—
362	C₂×C₈	—	142	1	no	—
363	C₂×C₈	—	142	2	no	—
364	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
365	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
366	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
367	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
368	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
369	C₂×C₈	#11765864	1	1	yes	characteristic
370	C₂×C₈	#11765864	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	142	2	no	—
373	C₄⋊C₄	—	142	1	no	—
374	C₄⋊C₄	—	142	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	284	4	no	—
378	C₂²⋊C₄	—	142	1	no	—
379	C₂²⋊C₄	—	142	2	no	—
380	C₂²⋊C₄	—	142	1	no	—
381	C₄²	—	71	2	no	—
382	C₄²	—	142	1	no	—
383	C₄²	—	142	2	no	—
384	C₄²	C₂²×Dic₇₁	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	#14556173	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	284	2	no	—
407	C₂×C₄	—	284	1	no	—
408	C₂×C₄	—	1136	4	no	—
409	C₂×C₄	—	142	2	no	—
410	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
412	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
413	C₂×C₄	#14556173	1	1	yes	characteristic
414	C₂×C₄	#14556173	1	1	yes	characteristic
415	C₂×C₄	#14556173	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	284	2	no	—
418	C₈	—	284	1	no	—
419	C₈	—	142	2	no	—
420	C₈	D₄×Dic₇₁	1	1	yes	characteristic
421	C₈	D₄×Dic₇₁	1	1	yes	characteristic
422	C₈	D₄×Dic₇₁	1	1	yes	characteristic
423	C₈	D₄×Dic₇₁	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	#17986474	1	1	yes	characteristic
432	C₂²	#17986562	1	1	yes	characteristic
433	C₂²	#17986603	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	284	2	no	—
437	C₄	—	568	2	no	—
438	C₄	—	568	1	no	—
439	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
440	C₄	#17986474	1	1	yes	characteristic
441	C₄	#17986562	1	1	yes	characteristic
442	C₄	#17986603	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	#22591066	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22591066
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting, prime radical	C₇₁×#3155	C₂
socle	C₂×C₇₁	#2328
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	#3155	D₇₁
hypocenter	C₇₁	#22286
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #22597257	C₂	semidirect
2. #22597192	C₂	semidirect
3. #22589251	C₂	semidirect
4. #22589239	C₂	semidirect
5. #22588873	C₂	semidirect
6. #22588868	C₂	semidirect
7. #22588829	C₂	semidirect
8. #22588822	C₂	semidirect
9. #22588464	C₂	semidirect
10. #22588095	C₂	semidirect
38. #496×C₇₁	C₄	semidirect
39. #495×C₇₁	C₄	semidirect
40. #493×C₇₁	C₄	semidirect
65. #14556038	D₄	semidirect
67. C₈×Dic₇₁	D₄	semidirect
76. C₂×Q₁₆×C₇₁	C₂×C₄	semidirect
77. C₂×SD₁₆×C₇₁	C₂×C₄	semidirect
78. C₂×SD₁₆×C₇₁	C₂×C₄	semidirect
85. C₂×D₈×C₇₁	C₂×C₄	semidirect
86. C₂×D₈×C₇₁	C₂×C₄	semidirect
89. #127×C₇₁	C₂×C₄	semidirect
90. #124×C₇₁	C₂×C₄	semidirect
94. #97×C₇₁	C₂×C₄	semidirect
95. C₄×C₈×C₇₁	C₂×C₄	semidirect
236. C₇₁	#22286	semidirect
243. #496	Dic₇₁	semidirect
244. #495	Dic₇₁	semidirect
245. #493	Dic₇₁	semidirect
275. C₂×Q₁₆	C₂×Dic₇₁	semidirect
276. C₂×SD₁₆	C₂×Dic₇₁	semidirect
277. C₂×SD₁₆	C₂×Dic₇₁	semidirect
284. C₂×D₈	C₂×Dic₇₁	semidirect
285. C₂×D₈	C₂×Dic₇₁	semidirect
294. #127	C₂×Dic₇₁	semidirect
295. #124	C₂×Dic₇₁	semidirect
317. #97	C₂×Dic₇₁	semidirect
320. C₄×C₈	C₂×Dic₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22597257	2
#22597192	2
#22589251	2
#22589239	2
#22588873	2
#22588868	2
#22588829	2
#22588822	2
#22588464	2
#22588095	2
C₇₁×#3155	2
#22286	71