Subgroups — C₂²×#17986835 #32911345

Order 18176.

60366 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17986835	C₂	1	96	yes	maximal, direct product factor
2	C₂²×#14556176	C₂	1	2	yes	maximal, complemented
3	C₂²×#14556175	C₂	1	4	yes	maximal, complemented
4	C₂²×#14556174	C₂	1	4	yes	maximal, complemented
5	C₂²×#14556173	C₂	1	6	yes	maximal, complemented
6	C₂³×#11765865	C₂	1	6	yes	maximal, complemented
7	C₂²×#41×D₇₁	C₂	1	8	yes	maximal, complemented
8	C₂³×#41×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#17986835	C₂²	1	1024	yes	direct product factor
10	C₂×#14556176	C₂²	1	96	yes	complemented
11	C₂×#14556175	C₂²	1	192	yes	complemented
12	C₂×#14556174	C₂²	1	192	yes	complemented
13	C₂×#14556173	C₂²	1	288	yes	complemented
14	C₂²×#11765866	C₂²	1	8	yes	complemented
15	C₂²×#11765865	C₂²	1	12	yes	complemented
16	C₂²×#11765865	C₂²	1	4	yes	complemented
17	C₂²×#11765865	C₂²	1	12	yes	complemented
18	C₂²×#11765865	C₂²	1	12	yes	complemented
19	C₂²×#11765865	C₂²	1	288	yes	complemented
20	C₂²×#11765864	C₂²	1	24	yes	complemented
21	C₂×#41×D₇₁	C₂²	1	384	yes	complemented
22	C₂³×Dic₁₄₂	C₂²	1	6	yes	complemented
23	C₂²×Q₈×D₇₁	C₂²	1	8	yes	complemented
24	C₂³×D₂₈₄	C₂²	1	6	yes	complemented
25	C₂³×C₂²⋊D₇₁	C₂²	1	12	yes	complemented
26	C₂²×D₄×D₇₁	C₂²	1	24	yes	complemented
27	C₂³×C₄×D₇₁	C₂²	1	12	yes	complemented
28	C₂²×#41×C₇₁	C₂²	1	4	yes	complemented
29	C₂²×#41×C₇₁	C₂²	1	4	yes	complemented
30	C₂²×#41×C₇₁	C₂²	1	48	yes	complemented
31	C₂³×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
32	C₂³×D₄×C₇₁	C₂²	1	3	yes	complemented
33	C₂⁴×C₄×C₇₁	C₂²	1	3	yes	complemented
34	C₂⁴×D₇₁	C₂³	1	12	yes	—
35	#14556176	C₂³	1	512	yes	complemented
36	#14556175	C₂³	1	1024	yes	complemented
37	#14556174	C₂³	1	1024	yes	complemented
38	#14556173	C₂³	1	1536	yes	complemented
39	C₂×#11765866	C₂³	1	192	yes	complemented
40	C₂×#11765865	C₂³	1	288	yes	complemented
41	C₂×#11765865	C₂³	1	96	yes	complemented
42	C₂×#11765865	C₂³	1	288	yes	complemented
43	C₂×#11765865	C₂³	1	288	yes	complemented
44	C₂×#11765865	C₂³	1	1536	yes	complemented
45	C₂×#11765864	C₂³	1	576	yes	complemented
46	#41×D₇₁	C₂³	1	2048	yes	complemented
47	C₂²×Dic₁₄₂	C₂³	1	12	yes	—
48	C₂²×Dic₁₄₂	C₂³	1	4	yes	—
49	C₂²×Dic₁₄₂	C₂³	1	144	yes	complemented
50	C₂×Q₈×D₇₁	C₂³	1	192	yes	complemented
51	C₂²×D₂₈₄	C₂³	1	12	yes	—
52	C₂²×D₂₈₄	C₂³	1	4	yes	—
53	C₂²×D₂₈₄	C₂³	1	144	yes	complemented
54	C₂²×C₂²⋊D₇₁	C₂³	1	24	yes	—
55	C₂²×C₂²⋊D₇₁	C₂³	1	8	yes	—
56	C₂²×C₂²⋊D₇₁	C₂³	1	288	yes	complemented
57	C₂×D₄×D₇₁	C₂³	1	576	yes	complemented
58	C₂³×Dic₇₁	C₂³	1	12	yes	—
59	C₂²×C₄×D₇₁	C₂³	1	8	yes	—
60	C₂²×C₄×D₇₁	C₂³	1	24	yes	—
61	C₂²×C₄×D₇₁	C₂³	1	288	yes	complemented
62	C₂⁵×C₇₁	C₂³	1	3	yes	—
63	C₂×#41×C₇₁	C₂³	1	96	yes	complemented
64	C₂×#41×C₇₁	C₂³	1	96	yes	complemented
65	C₂×#41×C₇₁	C₂³	1	256	yes	complemented
66	C₂²×Q₈×C₇₁	C₂³	1	4	yes	—
67	C₂²×Q₈×C₇₁	C₂³	1	24	yes	complemented
68	C₂²×D₄×C₇₁	C₂³	1	12	yes	—
69	C₂²×D₄×C₇₁	C₂³	1	72	yes	complemented
70	C₂³×C₄×C₇₁	C₂³	1	6	yes	—
71	C₂³×C₄×C₇₁	C₂³	1	6	yes	—
72	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇₁	C₂³	1	3	yes	—
74	C₂³×C₄×C₇₁	C₂³	1	72	yes	complemented
75	C₂³×D₇₁	—	4	48	no	—
76	C₂³×D₇₁	C₂⁴	1	8	yes	—
77	C₂³×D₇₁	C₂⁴	1	144	yes	—
78	#11765866	C₂⁴	1	512	yes	complemented
79	#11765865	C₂⁴	1	768	yes	complemented
80	#11765865	C₂⁴	1	256	yes	complemented
81	#11765865	C₂⁴	1	768	yes	complemented
82	#11765865	C₂⁴	1	768	yes	complemented
83	#11765864	C₂⁴	1	1536	yes	complemented
84	C₂×Dic₁₄₂	C₂⁴	1	144	yes	—
85	C₂×Dic₁₄₂	C₂⁴	1	48	yes	—
86	C₂×Dic₁₄₂	C₂⁴	1	384	yes	complemented
87	Q₈×D₇₁	C₂⁴	1	512	yes	complemented
88	C₂×D₂₈₄	C₂⁴	1	144	yes	—
89	C₂×D₂₈₄	C₂⁴	1	48	yes	—
90	C₂×D₂₈₄	C₂⁴	1	384	yes	complemented
91	C₂×C₂²⋊D₇₁	C₂⁴	1	288	yes	—
92	C₂×C₂²⋊D₇₁	C₂⁴	1	96	yes	—
93	C₂×C₂²⋊D₇₁	C₂⁴	1	768	yes	complemented
94	D₄×D₇₁	C₂⁴	1	1536	yes	complemented
95	C₂²×Dic₇₁	C₂⁴	1	8	yes	—
96	C₂²×Dic₇₁	C₂⁴	1	144	yes	—
97	C₂×C₄×D₇₁	C₂⁴	1	96	yes	—
98	C₂×C₄×D₇₁	C₂⁴	1	288	yes	—
99	C₂×C₄×D₇₁	C₂⁴	1	768	yes	complemented
100	C₂⁴×C₇₁	—	4	12	no	—
101	C₂⁴×C₇₁	C₂⁴	1	6	yes	—
102	C₂⁴×C₇₁	C₂⁴	1	1	yes	characteristic
103	C₂⁴×C₇₁	C₂⁴	1	36	yes	—
104	#41×C₇₁	C₂⁴	1	256	yes	complemented
105	#41×C₇₁	C₂⁴	1	256	yes	complemented
106	C₂×Q₈×C₇₁	C₂⁴	1	48	yes	—
107	C₂×Q₈×C₇₁	C₂⁴	1	64	yes	complemented
108	C₂×D₄×C₇₁	C₂⁴	1	144	yes	—
109	C₂×D₄×C₇₁	C₂⁴	1	192	yes	complemented
110	C₂²×C₄×C₇₁	C₂⁴	1	6	yes	—
111	C₂²×C₄×C₇₁	C₂⁴	1	72	yes	—
112	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₇₁	C₂⁴	1	72	yes	—
114	C₂²×C₄×C₇₁	C₂⁴	1	12	yes	—
115	C₂²×C₄×C₇₁	C₂⁴	1	36	yes	—
116	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	C₂⁴	1	192	yes	complemented
118	C₂³×C₇₁	—	2	4	no	—
119	C₂³×C₇₁	—	2	24	no	—
120	C₂³×C₇₁	—	4	72	no	—
121	C₂³×C₇₁	C₂⁵	1	6	yes	—
122	C₂³×C₇₁	C₂⁵	1	36	yes	—
123	C₂³×C₇₁	C₂⁵	1	48	yes	—
124	C₂³×C₇₁	C₂⁵	1	1	yes	characteristic
125	C₂²×D₇₁	—	2	32	no	—
126	C₂²×D₇₁	—	4	288	no	—
127	C₂²×D₇₁	C₂⁵	1	48	yes	—
128	C₂²×D₇₁	C₂⁵	1	192	yes	—
129	Q₈×C₇₁	C₂⁵	1	64	yes	—
130	D₄×C₇₁	C₂⁵	1	192	yes	—
131	C₂×C₄×C₇₁	C₂⁵	1	6	yes	—
132	C₂×C₄×C₇₁	C₂⁵	1	6	yes	—
133	C₂×C₄×C₇₁	C₂⁵	1	36	yes	—
134	C₂×C₄×C₇₁	C₂⁵	1	16	yes	—
135	C₂×C₄×C₇₁	C₂⁵	1	48	yes	—
136	C₂×C₄×C₇₁	C₂⁵	1	96	yes	—
137	C₂×C₄×C₇₁	C₂⁵	1	96	yes	—
138	C₂²⋊D₇₁	C₂⁵	1	384	yes	—
139	C₂²⋊D₇₁	C₂⁵	1	128	yes	—
140	C₂×Dic₇₁	C₂⁵	1	48	yes	—
141	C₂×Dic₇₁	C₂⁵	1	192	yes	—
142	D₂₈₄	C₂⁵	1	192	yes	—
143	D₂₈₄	C₂⁵	1	64	yes	—
144	C₄×D₇₁	C₂⁵	1	128	yes	—
145	C₄×D₇₁	C₂⁵	1	384	yes	—
146	Dic₁₄₂	C₂⁵	1	192	yes	—
147	Dic₁₄₂	C₂⁵	1	64	yes	—
148	C₂²×C₇₁	—	2	72	no	—
149	C₂²×C₇₁	—	2	12	no	—
150	C₂²×C₇₁	—	4	48	no	—
151	C₂²×C₇₁	#585	1	4	yes	complemented
152	C₂²×C₇₁	C₂⁶	1	24	yes	—
153	C₂²×C₇₁	C₂⁶	1	4	yes	—
154	C₂²×C₇₁	C₂⁶	1	3	yes	—
155	C₂×D₇₁	—	2	96	no	—
156	C₂×D₇₁	—	4	192	no	—
157	C₂×D₇₁	C₂⁶	1	32	yes	—
158	C₄×C₇₁	C₂⁶	1	4	yes	—
159	C₄×C₇₁	C₂⁶	1	24	yes	—
160	C₄×C₇₁	C₂⁶	1	4	yes	—
161	Dic₇₁	C₂⁶	1	32	yes	—
162	C₂²×#585	—	71	1	no	maximal, Sylow
163	C₂×C₇₁	—	2	24	no	—
164	C₂×C₇₁	—	2	4	no	—
165	C₂×C₇₁	C₂×#585	1	6	yes	complemented
166	C₂×C₇₁	C₂⁷	1	1	yes	characteristic
167	D₇₁	—	2	32	no	—
168	C₂×#585	—	71	96	no	—
169	C₂²×2₋¹⁺⁴	—	71	4	no	—
170	C₂²×2₋¹⁺⁴	—	71	2	no	—
171	C₂²×H(5,𝔽₂)	—	71	4	no	—
172	C₂²×H(5,𝔽₂)	—	71	6	no	—
173	C₂³×#41	—	71	8	no	—
174	C₂³×#41	—	71	6	no	—
175	C₂³×#41	D₇₁	1	1	yes	characteristic, complemented
176	C₇₁	C₂²×#585	1	1	yes	characteristic, complemented, Sylow
177	#585	—	71	1024	no	—
178	C₂×2₋¹⁺⁴	—	71	192	no	—
179	C₂×2₋¹⁺⁴	—	71	96	no	—
180	C₂×H(5,𝔽₂)	—	71	192	no	—
181	C₂×H(5,𝔽₂)	—	71	288	no	—
182	C₂²×#41	—	71	384	no	—
183	C₂²×#41	—	71	8	no	—
184	C₂²×#41	—	71	24	no	—
185	C₂²×#41	—	71	12	no	—
186	C₂²×#41	—	71	4	no	—
187	C₂²×#41	—	71	12	no	—
188	C₂²×#41	—	71	12	no	—
189	C₂²×#41	—	71	288	no	—
190	C₂²×#41	C₂×D₇₁	1	4	yes	complemented
191	C₂²×#41	C₂×D₇₁	1	4	yes	complemented
192	C₂²×#41	C₂×D₇₁	1	48	yes	complemented
193	C₂³×Q₈	—	71	8	no	—
194	C₂³×Q₈	—	71	6	no	—
195	C₂³×Q₈	C₂×D₇₁	1	1	yes	characteristic, complemented
196	C₂³×D₄	—	71	12	no	—
197	C₂³×D₄	—	71	24	no	—
198	C₂³×D₄	—	71	6	no	—
199	C₂³×D₄	C₂×D₇₁	1	3	yes	complemented
200	C₂⁴×C₄	—	71	12	no	—
201	C₂⁴×C₄	C₂×D₇₁	1	3	yes	complemented
202	C₂⁵	—	71	12	no	—
203	C₂⁵	C₂²×D₇₁	1	3	yes	—
204	2₋¹⁺⁴	—	71	1024	no	—
205	2₋¹⁺⁴	—	71	512	no	—
206	H(5,𝔽₂)	—	71	1024	no	—
207	H(5,𝔽₂)	—	71	1536	no	—
208	C₂×#41	—	71	2048	no	—
209	C₂×#41	—	71	192	no	—
210	C₂×#41	—	71	576	no	—
211	C₂×#41	—	71	288	no	—
212	C₂×#41	—	71	96	no	—
213	C₂×#41	—	71	288	no	—
214	C₂×#41	—	71	288	no	—
215	C₂×#41	—	71	1536	no	—
216	C₂×#41	C₂²×D₇₁	1	96	yes	complemented
217	C₂×#41	C₂²×D₇₁	1	96	yes	complemented
218	C₂×#41	C₂²×D₇₁	1	256	yes	complemented
219	C₂²×Q₈	—	71	192	no	—
220	C₂²×Q₈	—	71	12	no	—
221	C₂²×Q₈	—	71	4	no	—
222	C₂²×Q₈	—	71	144	no	—
223	C₂²×Q₈	C₂²×D₇₁	1	4	yes	—
224	C₂²×Q₈	C₂²×D₇₁	1	24	yes	complemented
225	C₂²×D₄	—	71	24	no	—
226	C₂²×D₄	—	71	8	no	—
227	C₂²×D₄	—	71	288	no	—
228	C₂²×D₄	—	71	576	no	—
229	C₂²×D₄	—	71	12	no	—
230	C₂²×D₄	—	71	4	no	—
231	C₂²×D₄	—	71	144	no	—
232	C₂²×D₄	C₂²×D₇₁	1	12	yes	—
233	C₂²×D₄	C₂²×D₇₁	1	72	yes	complemented
234	C₂³×C₄	—	71	12	no	—
235	C₂³×C₄	—	71	24	no	—
236	C₂³×C₄	—	71	288	no	—
237	C₂³×C₄	—	71	8	no	—
238	C₂³×C₄	C₂²×D₇₁	1	6	yes	—
239	C₂³×C₄	C₂²×D₇₁	1	3	yes	—
240	C₂³×C₄	C₂²×D₇₁	1	6	yes	—
241	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
242	C₂³×C₄	C₂²×D₇₁	1	72	yes	complemented
243	C₂⁴	—	4	12	no	—
244	C₂⁴	—	284	48	no	—
245	C₂⁴	—	71	144	no	—
246	C₂⁴	—	71	8	no	—
247	C₂⁴	C₂³×D₇₁	1	6	yes	—
248	C₂⁴	C₂³×D₇₁	1	1	yes	characteristic
249	C₂⁴	C₂³×D₇₁	1	36	yes	—
250	#41	—	71	512	no	—
251	#41	—	71	1536	no	—
252	#41	—	71	768	no	—
253	#41	—	71	256	no	—
254	#41	—	71	768	no	—
255	#41	—	71	768	no	—
256	#41	C₂³×D₇₁	1	256	yes	complemented
257	#41	C₂³×D₇₁	1	256	yes	complemented
258	C₂×Q₈	—	71	512	no	—
259	C₂×Q₈	—	71	144	no	—
260	C₂×Q₈	—	71	48	no	—
261	C₂×Q₈	—	71	384	no	—
262	C₂×Q₈	C₂³×D₇₁	1	48	yes	—
263	C₂×Q₈	C₂³×D₇₁	1	64	yes	complemented
264	C₂×D₄	—	71	288	no	—
265	C₂×D₄	—	71	96	no	—
266	C₂×D₄	—	71	768	no	—
267	C₂×D₄	—	71	1536	no	—
268	C₂×D₄	—	71	144	no	—
269	C₂×D₄	—	71	48	no	—
270	C₂×D₄	—	71	384	no	—
271	C₂×D₄	C₂³×D₇₁	1	144	yes	—
272	C₂×D₄	C₂³×D₇₁	1	192	yes	complemented
273	C₂²×C₄	—	71	8	no	—
274	C₂²×C₄	—	71	144	no	—
275	C₂²×C₄	—	71	96	no	—
276	C₂²×C₄	—	71	288	no	—
277	C₂²×C₄	—	71	768	no	—
278	C₂²×C₄	C₂³×D₇₁	1	6	yes	—
279	C₂²×C₄	C₂³×D₇₁	1	72	yes	—
280	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
281	C₂²×C₄	C₂³×D₇₁	1	12	yes	—
282	C₂²×C₄	C₂³×D₇₁	1	72	yes	—
283	C₂²×C₄	C₂³×D₇₁	1	36	yes	—
284	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
285	C₂²×C₄	C₂³×D₇₁	1	192	yes	complemented
286	C₂³	—	2	4	no	—
287	C₂³	—	2	24	no	—
288	C₂³	—	4	72	no	—
289	C₂³	—	284	288	no	—
290	C₂³	—	71	192	no	—
291	C₂³	—	71	48	no	—
292	C₂³	—	142	32	no	—
293	C₂³	C₂⁴×D₇₁	1	36	yes	—
294	C₂³	C₂⁴×D₇₁	1	6	yes	—
295	C₂³	C₂⁴×D₇₁	1	48	yes	—
296	C₂³	C₂⁴×D₇₁	1	1	yes	characteristic
297	Q₈	—	71	192	no	—
298	Q₈	—	71	64	no	—
299	Q₈	C₂⁴×D₇₁	1	64	yes	—
300	D₄	—	71	384	no	—
301	D₄	—	71	128	no	—
302	D₄	—	71	192	no	—
303	D₄	—	71	64	no	—
304	D₄	C₂⁴×D₇₁	1	192	yes	—
305	C₂×C₄	—	71	48	no	—
306	C₂×C₄	—	71	192	no	—
307	C₂×C₄	—	71	128	no	—
308	C₂×C₄	—	71	384	no	—
309	C₂×C₄	C₂⁴×D₇₁	1	6	yes	—
310	C₂×C₄	C₂⁴×D₇₁	1	36	yes	—
311	C₂×C₄	C₂⁴×D₇₁	1	96	yes	—
312	C₂×C₄	C₂⁴×D₇₁	1	6	yes	—
313	C₂×C₄	C₂⁴×D₇₁	1	16	yes	—
314	C₂×C₄	C₂⁴×D₇₁	1	96	yes	—
315	C₂×C₄	C₂⁴×D₇₁	1	48	yes	—
316	C₂²	—	2	12	no	—
317	C₂²	—	2	72	no	—
318	C₂²	—	4	48	no	—
319	C₂²	—	284	192	no	—
320	C₂²	—	71	32	no	—
321	C₂²	—	142	96	no	—
322	C₂²	#17986835	1	4	yes	direct product factor
323	C₂²	C₂⁵×D₇₁	1	24	yes	—
324	C₂²	C₂⁵×D₇₁	1	4	yes	—
325	C₂²	C₂⁵×D₇₁	1	3	yes	—
326	C₄	—	71	32	no	—
327	C₄	C₂⁵×D₇₁	1	4	yes	—
328	C₄	C₂⁵×D₇₁	1	24	yes	—
329	C₄	C₂⁵×D₇₁	1	4	yes	—
330	C₂	—	2	4	no	—
331	C₂	—	2	24	no	—
332	C₂	—	142	32	no	—
333	C₂	C₂×#17986835	1	6	yes	direct product factor
334	C₂	C₂⁶×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₇₁
commutator, cosocle	C₂×C₇₁	C₂⁷
Frattini	C₂	C₂⁶×D₇₁
Fitting	C₂³×#41×C₇₁	C₂
socle	C₂³×C₇₁	C₂⁵
hypercenter	C₂³×#41	D₇₁
hypocenter	C₇₁	C₂²×#585
LCS	G ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#17986835	C₂	direct (N × H)
2. C₂²×#14556176	C₂	semidirect
3. C₂²×#14556175	C₂	semidirect
4. C₂²×#14556174	C₂	semidirect
5. C₂²×#14556173	C₂	semidirect
6. C₂³×#11765865	C₂	semidirect
7. C₂²×#41×D₇₁	C₂	semidirect
8. C₂³×#41×C₇₁	C₂	semidirect
9. #17986835	C₂²	direct (N × H)
10. C₂×#14556176	C₂²	semidirect
11. C₂×#14556175	C₂²	semidirect
12. C₂×#14556174	C₂²	semidirect
13. C₂×#14556173	C₂²	semidirect
14. C₂²×#11765866	C₂²	semidirect
15. C₂²×#11765865	C₂²	semidirect
16. C₂²×#11765865	C₂²	semidirect
17. C₂²×#11765865	C₂²	semidirect
18. C₂²×#11765865	C₂²	semidirect
19. C₂²×#11765865	C₂²	semidirect
20. C₂²×#11765864	C₂²	semidirect
21. C₂×#41×D₇₁	C₂²	semidirect
22. C₂³×Dic₁₄₂	C₂²	semidirect
23. C₂²×Q₈×D₇₁	C₂²	semidirect
24. C₂³×D₂₈₄	C₂²	semidirect
25. C₂³×C₂²⋊D₇₁	C₂²	semidirect
26. C₂²×D₄×D₇₁	C₂²	semidirect
27. C₂³×C₄×D₇₁	C₂²	semidirect
28. C₂²×#41×C₇₁	C₂²	semidirect
29. C₂²×#41×C₇₁	C₂²	semidirect
30. C₂²×#41×C₇₁	C₂²	semidirect
31. C₂³×Q₈×C₇₁	C₂²	semidirect
32. C₂³×D₄×C₇₁	C₂²	semidirect
33. C₂⁴×C₄×C₇₁	C₂²	semidirect
35. #14556176	C₂³	semidirect
36. #14556175	C₂³	semidirect
37. #14556174	C₂³	semidirect
38. #14556173	C₂³	semidirect
39. C₂×#11765866	C₂³	semidirect
40. C₂×#11765865	C₂³	semidirect
41. C₂×#11765865	C₂³	semidirect
42. C₂×#11765865	C₂³	semidirect
43. C₂×#11765865	C₂³	semidirect
44. C₂×#11765865	C₂³	semidirect
45. C₂×#11765864	C₂³	semidirect
46. #41×D₇₁	C₂³	semidirect
49. C₂²×Dic₁₄₂	C₂³	semidirect
50. C₂×Q₈×D₇₁	C₂³	semidirect
53. C₂²×D₂₈₄	C₂³	semidirect
56. C₂²×C₂²⋊D₇₁	C₂³	semidirect
57. C₂×D₄×D₇₁	C₂³	semidirect
61. C₂²×C₄×D₇₁	C₂³	semidirect
63. C₂×#41×C₇₁	C₂³	semidirect
64. C₂×#41×C₇₁	C₂³	semidirect
65. C₂×#41×C₇₁	C₂³	semidirect
67. C₂²×Q₈×C₇₁	C₂³	semidirect
69. C₂²×D₄×C₇₁	C₂³	semidirect
74. C₂³×C₄×C₇₁	C₂³	semidirect
78. #11765866	C₂⁴	semidirect
79. #11765865	C₂⁴	semidirect
80. #11765865	C₂⁴	semidirect
81. #11765865	C₂⁴	semidirect
82. #11765865	C₂⁴	semidirect
83. #11765864	C₂⁴	semidirect
86. C₂×Dic₁₄₂	C₂⁴	semidirect
87. Q₈×D₇₁	C₂⁴	semidirect
90. C₂×D₂₈₄	C₂⁴	semidirect
93. C₂×C₂²⋊D₇₁	C₂⁴	semidirect
94. D₄×D₇₁	C₂⁴	semidirect
99. C₂×C₄×D₇₁	C₂⁴	semidirect
104. #41×C₇₁	C₂⁴	semidirect
105. #41×C₇₁	C₂⁴	semidirect
107. C₂×Q₈×C₇₁	C₂⁴	semidirect
109. C₂×D₄×C₇₁	C₂⁴	semidirect
117. C₂²×C₄×C₇₁	C₂⁴	semidirect
151. C₂²×C₇₁	#585	semidirect
165. C₂×C₇₁	C₂×#585	semidirect
175. C₂³×#41	D₇₁	semidirect
176. C₇₁	C₂²×#585	semidirect
190. C₂²×#41	C₂×D₇₁	semidirect
191. C₂²×#41	C₂×D₇₁	semidirect
192. C₂²×#41	C₂×D₇₁	semidirect
195. C₂³×Q₈	C₂×D₇₁	semidirect
199. C₂³×D₄	C₂×D₇₁	semidirect
201. C₂⁴×C₄	C₂×D₇₁	semidirect
216. C₂×#41	C₂²×D₇₁	semidirect
217. C₂×#41	C₂²×D₇₁	semidirect
218. C₂×#41	C₂²×D₇₁	semidirect
224. C₂²×Q₈	C₂²×D₇₁	semidirect
233. C₂²×D₄	C₂²×D₇₁	semidirect
242. C₂³×C₄	C₂²×D₇₁	semidirect
256. #41	C₂³×D₇₁	semidirect
257. #41	C₂³×D₇₁	semidirect
263. C₂×Q₈	C₂³×D₇₁	semidirect
272. C₂×D₄	C₂³×D₇₁	semidirect
285. C₂²×C₄	C₂³×D₇₁	semidirect
322. C₂²	#17986835	direct (N × H)
333. C₂	C₂×#17986835	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17986835	2
C₂²×#14556176	2
C₂²×#14556175	2
C₂²×#14556174	2
C₂²×#14556173	2
C₂³×#11765865	2
C₂²×#41×D₇₁	2
C₂³×#41×C₇₁	2
C₂²×#585	71

Subgroups — C22×#17986835 #32911345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17986835 #32911345