Subgroups — #32150877

Order 18176.

642 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986429	C₂	1	1	yes	maximal, characteristic
2	#22597258	C₂	1	1	yes	maximal, characteristic, complemented
3	#22590224	C₂	1	4	yes	maximal, complemented
4	#22590219	C₂	1	4	yes	maximal, complemented
5	C₂×#17985828	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590068	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590067	C₂	1	1	yes	maximal, characteristic, complemented
8	#22589937	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14556150	C₂²	1	1	yes	characteristic
11	#17986765	—	2	1	no	—
12	#17986429	C₄	1	2	yes	complemented
13	#17986429	C₄	1	2	yes	complemented
14	#17986429	C₂²	1	2	yes	—
15	#17986429	C₂²	1	2	yes	—
16	C₂×#14556074	C₄	1	1	yes	characteristic, complemented
17	C₂×#14556072	C₄	1	1	yes	characteristic, complemented
18	C₂×#14556071	C₄	1	1	yes	characteristic, complemented
19	C₂×#14556069	C₄	1	1	yes	characteristic, complemented
20	C₂×#14556068	C₂²	1	1	yes	characteristic
21	C₂²×C₇₁⋊C₁₆	C₂²	1	1	yes	characteristic
22	#17986122	—	2	2	no	—
23	#17986117	C₂²	1	4	yes	complemented
24	C₂×#14556064	C₂²	1	1	yes	characteristic
25	#17986017	—	2	1	no	—
26	#17985828	C₂²	1	2	yes	complemented
27	#17985828	C₂²	1	2	yes	complemented
28	#17985806	C₂²	1	4	yes	complemented
29	#17985805	C₂²	1	4	yes	complemented
30	#17985775	C₂²	1	2	yes	complemented
31	C₄×C₇₁⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
33	#568×C₇₁	—	2	1	no	—
34	#444×C₇₁	—	2	2	no	—
35	#443×C₇₁	C₂²	1	4	yes	complemented
36	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
37	#421×C₇₁	—	2	1	no	—
38	#405×C₇₁	C₂²	1	1	yes	characteristic
39	C₂×#11765865	—	2	1	no	—
40	#14556150	—	2	1	no	—
41	#14556150	—	2	1	no	—
42	#14556150	C₂×C₄	1	2	yes	—
43	#14556150	C₂³	1	2	yes	—
44	C₂×Dic₂₈₄	C₂×C₄	1	1	yes	characteristic
45	C₂×#11765854	—	2	1	no	—
46	C₂×D₅₆₈	C₂×C₄	1	1	yes	characteristic
47	#14556136	—	4	2	no	—
48	#14556134	—	2	4	no	—
49	C₂×#11765849	—	2	1	no	—
50	M₁₆×D₇₁	—	4	2	no	—
51	#14556074	C₂×C₄	1	2	yes	—
52	#14556074	C₂×C₄	1	2	yes	—
53	#14556072	C₂×C₄	1	2	yes	—
54	#14556072	C₂×C₄	1	2	yes	—
55	#14556071	C₂×C₄	1	2	yes	—
56	#14556071	C₂×C₄	1	2	yes	—
57	#14556069	C₂×C₄	1	2	yes	—
58	#14556069	C₂×C₄	1	2	yes	—
59	#14556068	—	2	1	no	—
60	#14556068	—	2	1	no	—
61	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
63	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂×C₇₁⋊C₁₆	C₂×C₄	1	1	yes	characteristic
65	C₂×C₇₁⋊C₁₆	C₂³	1	2	yes	—
66	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₇₁⋊C₁₆	C₂³	1	1	yes	characteristic
68	#14556064	—	2	1	no	—
69	#14556064	C₂³	1	2	yes	—
70	#14556056	—	2	4	no	—
71	C₂×#41×C₇₁	—	2	1	no	—
72	#135×C₇₁	—	2	1	no	—
73	#135×C₇₁	—	2	1	no	—
74	#135×C₇₁	C₂×C₄	1	2	yes	—
75	#135×C₇₁	C₂³	1	2	yes	—
76	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₇₁	—	2	1	no	—
78	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic
79	#131×C₇₁	—	2	4	no	—
80	#131×C₇₁	—	4	2	no	—
81	C₂×M₁₆×C₇₁	—	2	1	no	—
82	C₂×M₁₆×C₇₁	—	4	2	no	—
83	C₂×M₁₆×C₇₁	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
85	#117×C₇₁	D₄	1	1	yes	characteristic
86	#108×C₇₁	—	2	1	no	—
87	#108×C₇₁	C₂³	1	2	yes	—
88	#104×C₇₁	—	2	4	no	—
89	#97×C₇₁	D₄	1	2	yes	—
90	C₄×C₈×C₇₁	C₂³	1	2	yes	—
91	#11765865	—	2	2	no	—
92	#11765865	—	2	2	no	—
93	#11765865	—	4	1	no	—
94	#11765865	—	4	1	no	—
95	C₂×Dic₁₄₂	—	2	1	no	—
96	C₂×D₂₈₄	—	2	1	no	—
97	C₂×C₂²⋊D₇₁	—	4	1	no	—
98	C₂×C₄×D₇₁	—	4	1	no	—
99	Dic₂₈₄	—	2	1	no	—
100	Dic₂₈₄	C₂²×C₄	1	2	yes	—
101	#11765854	—	2	2	no	—
102	#11765854	—	2	2	no	—
103	D₅₆₈	—	2	1	no	—
104	D₅₆₈	C₂²×C₄	1	2	yes	—
105	#11765849	—	2	2	no	—
106	#11765849	—	4	1	no	—
107	#11765848	—	4	4	no	—
108	C₂×C₇₁⋊C₈	—	4	1	no	—
109	C₈×D₇₁	—	4	4	no	—
110	C₇₁⋊C₁₆	—	2	2	no	—
111	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
112	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
113	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
114	C₇₁⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
115	#41×C₇₁	—	2	2	no	—
116	#41×C₇₁	—	2	2	no	—
117	#41×C₇₁	—	4	1	no	—
118	#41×C₇₁	—	4	1	no	—
119	C₂×Q₈×C₇₁	—	2	1	no	—
120	C₂×D₄×C₇₁	—	2	1	no	—
121	C₂×D₄×C₇₁	—	4	1	no	—
122	C₂²×C₄×C₇₁	—	4	1	no	—
123	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₇₁	—	2	1	no	—
125	Q₁₆×C₇₁	C₂²×C₄	1	2	yes	—
126	SD₁₆×C₇₁	—	2	2	no	—
127	SD₁₆×C₇₁	—	2	2	no	—
128	D₈×C₇₁	—	2	1	no	—
129	D₈×C₇₁	C₂²×C₄	1	2	yes	—
130	M₁₆×C₇₁	—	2	2	no	—
131	M₁₆×C₇₁	—	4	1	no	—
132	M₁₆×C₇₁	—	4	4	no	—
133	M₁₆×C₇₁	D₈	1	2	yes	—
134	M₁₆×C₇₁	D₈	1	2	yes	—
135	C₂×C₈×C₇₁	—	4	1	no	—
136	C₂×C₈×C₇₁	—	4	4	no	—
137	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₇₁	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
142	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
143	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
144	C₄⋊C₄×C₇₁	—	2	1	no	—
145	C₂²⋊C₄×C₇₁	—	2	1	no	—
146	C₄²×C₇₁	C₂×D₄	1	2	yes	—
147	C₂³×C₇₁	—	4	1	no	—
148	C₂³×C₇₁	#135	1	1	yes	characteristic
149	C₂²×D₇₁	—	4	1	no	—
150	Q₈×C₇₁	—	2	2	no	—
151	Q₈×C₇₁	—	4	1	no	—
152	D₄×C₇₁	—	2	2	no	—
153	D₄×C₇₁	—	4	2	no	—
154	D₄×C₇₁	—	4	2	no	—
155	D₄×C₇₁	—	4	1	no	—
156	C₂×C₄×C₇₁	—	2	2	no	—
157	C₂×C₄×C₇₁	—	4	1	no	—
158	C₂×C₄×C₇₁	—	4	2	no	—
159	C₂×C₄×C₇₁	—	4	2	no	—
160	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₇₁	#135	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₇₁	—	4	2	no	—
167	C₂²⋊D₇₁	—	4	2	no	—
168	C₂×Dic₇₁	—	4	1	no	—
169	D₂₈₄	—	2	2	no	—
170	D₂₈₄	—	4	1	no	—
171	C₄×D₇₁	—	4	2	no	—
172	C₄×D₇₁	—	4	2	no	—
173	Dic₁₄₂	—	2	2	no	—
174	Dic₁₄₂	—	4	1	no	—
175	C₈×C₇₁	—	4	2	no	—
176	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
177	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
178	C₈×C₇₁	C₂×D₈	1	4	yes	—
179	C₈×C₇₁	C₂³×C₄	1	1	yes	characteristic
180	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
181	C₇₁⋊C₈	—	4	2	no	—
182	C₂²×C₇₁	—	4	1	no	—
183	C₂²×C₇₁	—	4	2	no	—
184	C₂²×C₇₁	—	16	1	no	—
185	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
186	C₂²×C₇₁	C₄×D₈	1	1	yes	characteristic
187	C₂²×C₇₁	C₂×#135	1	1	yes	characteristic
188	C₂×D₇₁	—	4	2	no	—
189	C₂×D₇₁	—	16	1	no	—
190	C₄×C₇₁	—	4	2	no	—
191	C₄×C₇₁	—	4	2	no	—
192	C₄×C₇₁	C₄×D₈	1	1	yes	characteristic
193	C₄×C₇₁	C₄×D₈	1	1	yes	characteristic
194	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
195	C₄×C₇₁	C₂²×D₈	1	1	yes	characteristic
196	Dic₇₁	—	4	2	no	—
197	#33465	—	71	1	no	maximal, Sylow
198	C₂×C₇₁	—	2	1	no	—
199	C₂×C₇₁	—	2	1	no	—
200	C₂×C₇₁	—	2	1	no	—
201	C₂×C₇₁	—	8	2	no	—
202	C₂×C₇₁	C₂×C₄×D₈	1	1	yes	characteristic
203	D₇₁	—	8	2	no	—
204	C₂×#508	—	71	1	no	—
205	#2957	—	71	1	no	—
206	#2957	D₇₁	1	1	yes	characteristic, complemented
207	#2179	—	71	4	no	—
208	#2178	—	71	4	no	—
209	C₂×#368	—	71	1	no	—
210	#2143	—	71	1	no	—
211	#2143	—	71	1	no	—
212	#2108	—	71	1	no	—
213	C₇₁	#33465	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	—	71	1	no	—
215	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
216	#568	—	2	1	no	—
217	#568	—	142	1	no	—
218	#508	—	71	2	no	—
219	#508	—	71	2	no	—
220	#508	—	71	2	no	—
221	#508	—	71	2	no	—
222	C₂×Q₃₂	—	71	1	no	—
223	C₂×SD₃₂	—	71	1	no	—
224	C₂×SD₃₂	—	71	1	no	—
225	C₂×D₁₆	—	71	1	no	—
226	C₂×M₃₂	—	71	1	no	—
227	C₂²×C₁₆	—	71	1	no	—
228	#444	—	2	2	no	—
229	#444	—	142	2	no	—
230	#443	—	71	4	no	—
231	#443	C₂×D₇₁	1	4	yes	complemented
232	C₂×#108	—	71	1	no	—
233	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
234	#421	—	2	1	no	—
235	#421	—	142	1	no	—
236	#405	C₂×D₇₁	1	1	yes	characteristic
237	#368	—	71	2	no	—
238	#368	—	71	2	no	—
239	#359	—	71	4	no	—
240	#359	—	71	4	no	—
241	#346	—	71	2	no	—
242	C₄×C₁₆	—	71	2	no	—
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	142	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	71	2	no	—
248	#135	—	71	2	no	—
249	#135	—	142	1	no	—
250	#135	—	142	1	no	—
251	#135	C₄×D₇₁	1	2	yes	—
252	#135	C₂²×D₇₁	1	2	yes	—
253	C₂×Q₁₆	—	71	1	no	—
254	C₂×Q₁₆	C₄×D₇₁	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	142	1	no	—
257	C₂×D₈	—	71	1	no	—
258	C₂×D₈	C₄×D₇₁	1	1	yes	characteristic
259	#131	—	2	4	no	—
260	#131	—	4	2	no	—
261	#131	—	284	2	no	—
262	#131	—	142	4	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	4	2	no	—
265	C₂×M₁₆	—	284	2	no	—
266	C₂×M₁₆	—	142	1	no	—
267	C₂×M₁₆	C₂²⋊D₇₁	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
269	#117	C₂²⋊D₇₁	1	1	yes	characteristic
270	Q₃₂	—	71	2	no	—
271	Q₃₂	—	71	2	no	—
272	SD₃₂	—	71	2	no	—
273	SD₃₂	—	71	2	no	—
274	SD₃₂	—	71	2	no	—
275	SD₃₂	—	71	2	no	—
276	D₁₆	—	71	2	no	—
277	D₁₆	—	71	2	no	—
278	M₃₂	—	142	1	no	—
279	M₃₂	—	142	1	no	—
280	C₂×C₁₆	—	71	1	no	—
281	C₂×C₁₆	—	71	1	no	—
282	C₂×C₁₆	—	71	1	no	—
283	C₂×C₁₆	—	71	1	no	—
284	C₂×C₁₆	—	71	1	no	—
285	C₂×C₁₆	—	71	1	no	—
286	C₂×C₁₆	—	71	2	no	—
287	#108	—	2	1	no	—
288	#108	—	71	2	no	—
289	#108	—	142	1	no	—
290	#108	C₂²×D₇₁	1	2	yes	—
291	#104	—	2	4	no	—
292	#104	—	142	4	no	—
293	#97	C₂²⋊D₇₁	1	2	yes	—
294	C₄×C₈	C₂²×D₇₁	1	2	yes	—
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	284	1	no	—
300	#41	—	284	1	no	—
301	#41	—	142	2	no	—
302	#41	—	142	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	142	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	284	1	no	—
308	C₂×D₄	—	142	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	284	1	no	—
311	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
312	Q₁₆	—	2	1	no	—
313	Q₁₆	—	71	2	no	—
314	Q₁₆	—	142	1	no	—
315	Q₁₆	C₂×C₄×D₇₁	1	2	yes	—
316	SD₁₆	—	2	2	no	—
317	SD₁₆	—	2	2	no	—
318	SD₁₆	—	142	2	no	—
319	SD₁₆	—	142	2	no	—
320	D₈	—	2	1	no	—
321	D₈	—	71	2	no	—
322	D₈	—	142	1	no	—
323	D₈	C₂×C₄×D₇₁	1	2	yes	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	4	no	—
327	M₁₆	—	284	1	no	—
328	M₁₆	—	284	4	no	—
329	M₁₆	—	142	2	no	—
330	M₁₆	#11765850	1	2	yes	—
331	M₁₆	#11765850	1	2	yes	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	4	no	—
334	C₂×C₈	—	284	1	no	—
335	C₂×C₈	—	284	4	no	—
336	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₇₁	1	2	yes	—
340	C₂×C₈	#11765865	1	1	yes	characteristic
341	C₂×C₈	#11765865	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₄²	C₂×C₂²⋊D₇₁	1	2	yes	—
346	C₁₆	—	71	1	no	—
347	C₁₆	—	71	1	no	—
348	C₁₆	—	71	1	no	—
349	C₁₆	—	71	1	no	—
350	C₁₆	—	142	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	284	1	no	—
353	C₂³	#14556148	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	284	1	no	—
357	Q₈	—	142	2	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	284	2	no	—
363	D₄	—	284	2	no	—
364	D₄	—	284	1	no	—
365	D₄	—	142	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	284	1	no	—
371	C₂×C₄	—	284	2	no	—
372	C₂×C₄	—	284	2	no	—
373	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
374	C₂×C₄	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
375	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
376	C₂×C₄	C₂×#11765850	1	1	yes	characteristic
377	C₂×C₄	#14556148	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
379	C₈	—	4	2	no	—
380	C₈	—	284	2	no	—
381	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
382	C₈	C₄×C₂²⋊D₇₁	1	1	yes	characteristic
383	C₈	C₂×#11765850	1	4	yes	—
384	C₈	C₂²×C₄×D₇₁	1	1	yes	characteristic
385	C₈	C₂×#11765865	1	1	yes	characteristic
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	16	1	no	—
389	C₂²	—	284	2	no	—
390	C₂²	—	1136	1	no	—
391	C₂²	C₄×#11765850	1	1	yes	characteristic
392	C₂²	C₄×#11765850	1	1	yes	characteristic
393	C₂²	C₂×#14556148	1	1	yes	characteristic
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	284	2	no	—
397	C₄	C₄×#11765850	1	1	yes	characteristic
398	C₄	C₄×#11765850	1	1	yes	characteristic
399	C₄	C₂×C₄×C₂²⋊D₇₁	1	1	yes	characteristic
400	C₄	C₂²×#11765850	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	568	2	no	—
406	C₂	C₂×C₄×#11765850	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#11765850
commutator	C₈×C₇₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×#2957	C₂
socle	C₂×C₇₁	C₂×C₄×D₈
prime radical	C₂×#17986429	C₂
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	#2957	D₇₁
hypocenter	C₇₁	#33465
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405 ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #22597258	C₂	semidirect
3. #22590224	C₂	semidirect
4. #22590219	C₂	semidirect
5. C₂×#17985828	C₂	semidirect
6. #22590068	C₂	semidirect
7. #22590067	C₂	semidirect
8. #22589937	C₂	semidirect
9. C₇₁×#2957	C₂	semidirect
12. #17986429	C₄	semidirect
13. #17986429	C₄	semidirect
16. C₂×#14556074	C₄	semidirect
17. C₂×#14556072	C₄	semidirect
18. C₂×#14556071	C₄	semidirect
19. C₂×#14556069	C₄	semidirect
23. #17986117	C₂²	semidirect
26. #17985828	C₂²	semidirect
27. #17985828	C₂²	semidirect
28. #17985806	C₂²	semidirect
29. #17985805	C₂²	semidirect
30. #17985775	C₂²	semidirect
31. C₄×C₇₁⋊C₁₆	C₂²	semidirect
35. #443×C₇₁	C₂²	semidirect
206. #2957	D₇₁	semidirect
213. C₇₁	#33465	semidirect
231. #443	C₂×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17986429	2
#22597258	2
#22590224	2
#22590219	2
C₂×#17985828	2
#22590068	2
#22590067	2
#22589937	2
C₇₁×#2957	2
#33465	71