Subgroups — C₂²×#14583711 #26010417

Order 11008.

11118 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063372	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583711	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#13063358	C₂	1	3	yes	maximal, complemented
5	C₂²×#13063353	C₂	1	3	yes	maximal, complemented
6	C₂²×#13063347	C₂	1	3	yes	maximal, complemented
7	C₂³×#10621873	C₂	1	3	yes	maximal, complemented
8	C₂²×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#13063372	—	2	12	no	—
10	C₂×#13063372	C₂²	1	24	yes	complemented
11	C₂×#13063371	—	2	12	no	—
12	C₂×#13063371	C₂²	1	24	yes	complemented
13	C₂²×#10621902	—	2	1	no	—
14	C₂²×#10621898	C₂²	1	3	yes	—
15	C₂²×#10621898	C₂²	1	3	yes	complemented
16	C₂²×#10621900	—	2	3	no	—
17	C₂³×Dic₈₆	C₂²	1	3	yes	complemented
18	C₂²×Q₈×D₄₃	—	2	1	no	—
19	C₂³×D₁₇₂	C₂²	1	3	yes	—
20	C₂²×D₄×D₄₃	—	2	3	no	—
21	#14583711	C₂²	1	256	yes	direct product factor
22	C₂×#13063358	C₂²	1	72	yes	complemented
23	C₂×#13063353	C₂²	1	72	yes	complemented
24	C₂×#13063347	C₂²	1	72	yes	complemented
25	C₂²×Dic₁₇₂	C₂²	1	3	yes	complemented
26	C₂²×#10621873	C₂²	1	3	yes	complemented
27	C₂²×#10621873	C₂²	1	6	yes	complemented
28	C₂²×#10621873	C₂²	1	1	yes	characteristic, complemented
29	C₂²×#10621873	C₂²	1	72	yes	complemented
30	C₂²×D₃₄₄	C₂²	1	3	yes	complemented
31	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#131×C₄₃	C₂²	1	24	yes	complemented
33	C₂²×M₁₆×C₄₃	C₂²	1	3	yes	complemented
34	C₂³×C₈×C₄₃	C₂²	1	3	yes	complemented
35	C₂⁴×D₄₃	—	2	3	no	—
36	#13063372	—	2	96	no	—
37	#13063372	C₂³	1	64	yes	complemented
38	#13063371	—	2	96	no	—
39	#13063371	C₂³	1	64	yes	complemented
40	C₂×#10621902	—	2	24	no	—
41	C₂×#10621898	—	2	18	no	—
42	C₂×#10621898	—	2	18	no	—
43	C₂×#10621898	C₂³	1	36	yes	—
44	C₂×#10621898	C₂³	1	36	yes	complemented
45	C₂×#10621900	—	2	72	no	—
46	C₂²×Dic₈₆	—	2	3	no	—
47	C₂²×Dic₈₆	—	2	18	no	—
48	C₂²×Dic₈₆	C₂³	1	3	yes	—
49	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
50	C₂²×Dic₈₆	C₂³	1	36	yes	complemented
51	C₂×Q₈×D₄₃	—	2	24	no	—
52	C₂²×D₁₇₂	—	2	3	no	—
53	C₂²×D₁₇₂	—	2	18	no	—
54	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
55	C₂²×D₁₇₂	C₂³	1	3	yes	—
56	C₂²×D₁₇₂	C₂³	1	36	yes	—
57	C₂²×C₂²⋊D₄₃	—	2	3	no	—
58	C₂²×C₂²⋊D₄₃	—	2	3	no	—
59	C₂×D₄×D₄₃	—	2	72	no	—
60	C₂³×Dic₄₃	—	2	3	no	—
61	C₂²×C₄×D₄₃	—	2	3	no	—
62	C₂²×C₄×D₄₃	—	2	3	no	—
63	#13063358	C₂³	1	192	yes	complemented
64	#13063353	C₂³	1	192	yes	complemented
65	#13063347	C₂³	1	192	yes	complemented
66	C₂×Dic₁₇₂	C₂³	1	36	yes	complemented
67	C₂×#10621873	C₂³	1	36	yes	complemented
68	C₂×#10621873	C₂³	1	72	yes	complemented
69	C₂×#10621873	C₂³	1	12	yes	complemented
70	C₂×#10621873	C₂³	1	192	yes	complemented
71	C₂×D₃₄₄	C₂³	1	36	yes	complemented
72	C₂×#41×C₄₃	D₄	1	12	yes	—
73	C₂×#41×C₄₃	C₂³	1	12	yes	—
74	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
75	C₂²×D₄×C₄₃	D₄	1	3	yes	—
76	C₂³×C₄×C₄₃	C₂³	1	3	yes	—
77	#131×C₄₃	C₂³	1	64	yes	complemented
78	C₂×M₁₆×C₄₃	C₂³	1	36	yes	complemented
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
81	C₂²×C₈×C₄₃	C₂³	1	36	yes	complemented
82	C₂⁴×C₄₃	C₂×D₄	1	3	yes	—
83	C₂³×D₄₃	—	2	1	no	—
84	C₂³×D₄₃	—	2	3	no	—
85	C₂³×D₄₃	—	2	36	no	—
86	C₂³×D₄₃	—	8	12	no	—
87	#41×C₄₃	C₂×D₄	1	48	yes	—
88	#41×C₄₃	C₂⁴	1	16	yes	—
89	C₂×Q₈×C₄₃	C₂×D₄	1	12	yes	—
90	C₂×D₄×C₄₃	C₂×D₄	1	36	yes	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	3	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	18	yes	—
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂⁴	1	18	yes	—
95	C₂×C₂²⋊D₄₃	—	2	36	no	—
96	C₂×C₂²⋊D₄₃	—	2	36	no	—
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	—	2	3	no	—
99	C₂²×Dic₄₃	—	2	36	no	—
100	#10621902	—	2	64	no	—
101	Q₈×D₄₃	—	2	64	no	—
102	#10621900	—	2	192	no	—
103	D₄×D₄₃	—	2	192	no	—
104	#10621898	—	2	72	no	—
105	#10621898	—	2	72	no	—
106	#10621898	C₂⁴	1	48	yes	—
107	#10621898	C₂⁴	1	48	yes	complemented
108	C₂×D₁₇₂	—	2	36	no	—
109	C₂×D₁₇₂	—	2	9	no	—
110	C₂×D₁₇₂	—	2	72	no	—
111	C₂×D₁₇₂	—	2	3	no	—
112	C₂×D₁₇₂	C₂⁴	1	6	yes	—
113	C₂×D₁₇₂	C₂⁴	1	18	yes	—
114	C₂×D₁₇₂	C₂⁴	1	48	yes	—
115	C₂×C₄×D₄₃	—	2	36	no	—
116	C₂×C₄×D₄₃	—	2	36	no	—
117	C₂×Dic₈₆	—	2	36	no	—
118	C₂×Dic₈₆	—	2	9	no	—
119	C₂×Dic₈₆	—	2	72	no	—
120	C₂×Dic₈₆	—	2	3	no	—
121	C₂×Dic₈₆	C₂⁴	1	18	yes	—
122	C₂×Dic₈₆	C₂⁴	1	6	yes	—
123	C₂×Dic₈₆	C₂⁴	1	48	yes	complemented
124	M₁₆×C₄₃	C₂⁴	1	48	yes	complemented
125	C₂×C₈×C₄₃	C₂⁴	1	6	yes	—
126	C₂×C₈×C₄₃	C₂⁴	1	18	yes	—
127	C₂×C₈×C₄₃	C₂⁴	1	48	yes	complemented
128	Dic₁₇₂	C₂⁴	1	48	yes	complemented
129	D₃₄₄	C₂⁴	1	48	yes	complemented
130	#10621873	C₂⁴	1	48	yes	complemented
131	#10621873	C₂⁴	1	96	yes	complemented
132	#10621873	C₂⁴	1	16	yes	complemented
133	C₂³×C₄₃	—	2	12	no	—
134	C₂³×C₄₃	C₂²×D₄	1	18	yes	—
135	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
136	C₂²×D₄₃	—	2	6	no	—
137	C₂²×D₄₃	—	2	18	no	—
138	C₂²×D₄₃	—	2	48	no	—
139	C₂²×D₄₃	—	4	4	no	—
140	C₂²×D₄₃	—	4	12	no	—
141	C₂²×D₄₃	—	8	72	no	—
142	Q₈×C₄₃	C₂²×D₄	1	16	yes	—
143	D₄×C₄₃	C₂²×D₄	1	48	yes	—
144	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
145	C₂×C₄×C₄₃	C₂²×D₄	1	18	yes	—
146	C₂×C₄×C₄₃	C₂²×D₄	1	36	yes	—
147	C₂×C₄×C₄₃	C₂⁵	1	3	yes	—
148	C₂×C₄×C₄₃	C₂⁵	1	12	yes	—
149	C₂²⋊D₄₃	—	2	48	no	—
150	C₂²⋊D₄₃	—	2	48	no	—
151	C₂×Dic₄₃	—	2	18	no	—
152	C₂×Dic₄₃	—	2	48	no	—
153	C₂×Dic₄₃	—	2	6	no	—
154	D₁₇₂	—	2	18	no	—
155	D₁₇₂	—	2	48	no	—
156	D₁₇₂	—	2	6	no	—
157	D₁₇₂	C₂⁵	1	12	yes	—
158	D₁₇₂	C₂⁵	1	4	yes	—
159	C₄×D₄₃	—	2	48	no	—
160	C₄×D₄₃	—	2	48	no	—
161	Dic₈₆	—	2	18	no	—
162	Dic₈₆	—	2	48	no	—
163	Dic₈₆	—	2	6	no	—
164	Dic₈₆	C₂⁵	1	12	yes	—
165	Dic₈₆	C₂⁵	1	4	yes	—
166	C₈×C₄₃	C₂⁵	1	4	yes	—
167	C₈×C₄₃	C₂⁵	1	12	yes	—
168	C₂²×#577	—	43	1	no	maximal, Sylow
169	C₂²×C₄₃	—	2	36	no	—
170	C₂²×C₄₃	#577	1	4	yes	complemented
171	C₂²×C₄₃	C₂³×D₄	1	12	yes	—
172	C₂²×C₄₃	C₂³×D₄	1	3	yes	—
173	C₂×D₄₃	—	2	12	no	—
174	C₂×D₄₃	—	2	4	no	—
175	C₂×D₄₃	—	4	12	no	—
176	C₂×D₄₃	—	4	36	no	—
177	C₂×D₄₃	—	8	48	no	—
178	C₄×C₄₃	C₂³×D₄	1	3	yes	—
179	C₄×C₄₃	C₂³×D₄	1	12	yes	—
180	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
181	Dic₄₃	—	2	12	no	—
182	Dic₄₃	—	2	4	no	—
183	C₂²×2₋¹⁺⁴	—	43	1	no	—
184	C₂²×H(5,𝔽₂)	—	43	1	no	—
185	C₂×#577	—	43	48	no	—
186	C₂²×#137	—	43	3	no	—
187	C₂²×AGL(1,ℤ/8)	—	43	3	no	—
188	C₂²×#135	—	43	3	no	—
189	C₂³×SD₁₆	—	43	3	no	—
190	C₂²×#131	D₄₃	1	1	yes	characteristic, complemented
191	C₂×C₄₃	—	2	12	no	—
192	C₂×C₄₃	C₂×#577	1	6	yes	complemented
193	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
194	D₄₃	—	4	4	no	—
195	D₄₃	—	4	12	no	—
196	C₂×2₋¹⁺⁴	—	43	24	no	—
197	C₂×2₋¹⁺⁴	—	86	12	no	—
198	C₂×H(5,𝔽₂)	—	43	24	no	—
199	C₂×H(5,𝔽₂)	—	86	12	no	—
200	C₂²×#41	—	43	3	no	—
201	C₂²×#41	—	43	3	no	—
202	C₂²×#41	—	86	1	no	—
203	C₂²×#41	—	86	3	no	—
204	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
205	C₂³×Q₈	—	43	3	no	—
206	C₂³×Q₈	—	86	1	no	—
207	C₂³×D₄	—	43	3	no	—
208	C₂³×D₄	—	86	3	no	—
209	#577	—	43	256	no	—
210	C₂×#137	—	43	72	no	—
211	C₂×AGL(1,ℤ/8)	—	43	72	no	—
212	C₂×#135	—	43	72	no	—
213	C₂²×Q₁₆	—	43	3	no	—
214	C₂²×SD₁₆	—	43	3	no	—
215	C₂²×SD₁₆	—	43	6	no	—
216	C₂²×SD₁₆	—	43	1	no	—
217	C₂²×SD₁₆	—	43	72	no	—
218	C₂²×D₈	—	43	3	no	—
219	C₂×#131	C₂×D₄₃	1	24	yes	complemented
220	C₂²×M₁₆	C₂×D₄₃	1	3	yes	complemented
221	C₂³×C₈	C₂×D₄₃	1	3	yes	complemented
222	C₄₃	C₂²×#577	1	1	yes	characteristic, complemented, Sylow
223	C₂⁵	—	86	3	no	—
224	2₋¹⁺⁴	—	43	64	no	—
225	2₋¹⁺⁴	—	86	96	no	—
226	H(5,𝔽₂)	—	43	64	no	—
227	H(5,𝔽₂)	—	86	96	no	—
228	C₂×#41	—	43	36	no	—
229	C₂×#41	—	43	36	no	—
230	C₂×#41	—	86	24	no	—
231	C₂×#41	—	86	72	no	—
232	C₂×#41	—	86	18	no	—
233	C₂×#41	—	86	18	no	—
234	C₂×#41	D₁₇₂	1	12	yes	—
235	C₂×#41	C₂²×D₄₃	1	12	yes	—
236	C₂²×Q₈	—	43	3	no	—
237	C₂²×Q₈	—	43	36	no	—
238	C₂²×Q₈	—	43	1	no	—
239	C₂²×Q₈	—	86	24	no	—
240	C₂²×Q₈	—	86	3	no	—
241	C₂²×Q₈	—	86	18	no	—
242	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
243	C₂²×D₄	—	43	1	no	—
244	C₂²×D₄	—	43	3	no	—
245	C₂²×D₄	—	43	36	no	—
246	C₂²×D₄	—	86	3	no	—
247	C₂²×D₄	—	86	3	no	—
248	C₂²×D₄	—	86	72	no	—
249	C₂²×D₄	—	86	3	no	—
250	C₂²×D₄	—	86	18	no	—
251	C₂²×D₄	D₁₇₂	1	3	yes	—
252	C₂³×C₄	—	86	3	no	—
253	C₂³×C₄	—	86	3	no	—
254	C₂³×C₄	—	86	3	no	—
255	C₂³×C₄	C₂²×D₄₃	1	3	yes	—
256	#137	—	43	192	no	—
257	AGL(1,ℤ/8)	—	43	192	no	—
258	#135	—	43	192	no	—
259	C₂×Q₁₆	—	43	36	no	—
260	C₂×SD₁₆	—	43	36	no	—
261	C₂×SD₁₆	—	43	72	no	—
262	C₂×SD₁₆	—	43	12	no	—
263	C₂×SD₁₆	—	43	192	no	—
264	C₂×D₈	—	43	36	no	—
265	#131	C₂²×D₄₃	1	64	yes	complemented
266	C₂×M₁₆	C₂²×D₄₃	1	36	yes	complemented
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
269	C₂²×C₈	C₂²×D₄₃	1	36	yes	complemented
270	C₂⁴	—	86	36	no	—
271	C₂⁴	—	86	1	no	—
272	C₂⁴	—	86	3	no	—
273	C₂⁴	—	344	12	no	—
274	C₂⁴	C₂×D₁₇₂	1	3	yes	—
275	#41	—	43	48	no	—
276	#41	—	43	48	no	—
277	#41	—	86	64	no	—
278	#41	—	86	192	no	—
279	#41	—	86	72	no	—
280	#41	—	86	72	no	—
281	#41	C₂×D₁₇₂	1	48	yes	—
282	#41	C₂³×D₄₃	1	16	yes	—
283	C₂×Q₈	—	43	18	no	—
284	C₂×Q₈	—	43	48	no	—
285	C₂×Q₈	—	43	6	no	—
286	C₂×Q₈	—	86	64	no	—
287	C₂×Q₈	—	86	36	no	—
288	C₂×Q₈	—	86	9	no	—
289	C₂×Q₈	—	86	72	no	—
290	C₂×Q₈	—	86	3	no	—
291	C₂×Q₈	C₂×D₁₇₂	1	12	yes	—
292	C₂×D₄	—	43	6	no	—
293	C₂×D₄	—	43	18	no	—
294	C₂×D₄	—	43	48	no	—
295	C₂×D₄	—	86	36	no	—
296	C₂×D₄	—	86	36	no	—
297	C₂×D₄	—	86	192	no	—
298	C₂×D₄	—	86	36	no	—
299	C₂×D₄	—	86	9	no	—
300	C₂×D₄	—	86	72	no	—
301	C₂×D₄	—	86	3	no	—
302	C₂×D₄	C₂×D₁₇₂	1	36	yes	—
303	C₂²×C₄	—	86	36	no	—
304	C₂²×C₄	—	86	1	no	—
305	C₂²×C₄	—	86	3	no	—
306	C₂²×C₄	—	86	36	no	—
307	C₂²×C₄	—	86	36	no	—
308	C₂²×C₄	C₂×D₁₇₂	1	18	yes	—
309	C₂²×C₄	C₂×D₁₇₂	1	3	yes	—
310	C₂²×C₄	C₂³×D₄₃	1	18	yes	—
311	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
312	Q₁₆	—	43	48	no	—
313	SD₁₆	—	43	48	no	—
314	SD₁₆	—	43	96	no	—
315	SD₁₆	—	43	16	no	—
316	D₈	—	43	48	no	—
317	M₁₆	C₂³×D₄₃	1	48	yes	complemented
318	C₂×C₈	C₂³×D₄₃	1	6	yes	—
319	C₂×C₈	C₂³×D₄₃	1	18	yes	—
320	C₂×C₈	C₂³×D₄₃	1	48	yes	complemented
321	C₂³	—	2	12	no	—
322	C₂³	—	86	48	no	—
323	C₂³	—	86	6	no	—
324	C₂³	—	86	18	no	—
325	C₂³	—	344	72	no	—
326	C₂³	—	172	4	no	—
327	C₂³	—	172	12	no	—
328	C₂³	C₂²×D₁₇₂	1	18	yes	—
329	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
330	Q₈	—	43	12	no	—
331	Q₈	—	43	4	no	—
332	Q₈	—	86	48	no	—
333	Q₈	—	86	18	no	—
334	Q₈	—	86	6	no	—
335	Q₈	C₂²×D₁₇₂	1	16	yes	—
336	D₄	—	43	4	no	—
337	D₄	—	43	12	no	—
338	D₄	—	86	48	no	—
339	D₄	—	86	48	no	—
340	D₄	—	86	48	no	—
341	D₄	—	86	18	no	—
342	D₄	—	86	6	no	—
343	D₄	C₂²×D₁₇₂	1	48	yes	—
344	C₂×C₄	—	86	6	no	—
345	C₂×C₄	—	86	18	no	—
346	C₂×C₄	—	86	48	no	—
347	C₂×C₄	—	86	48	no	—
348	C₂×C₄	—	86	48	no	—
349	C₂×C₄	C₂²×D₁₇₂	1	18	yes	—
350	C₂×C₄	C₂²×D₁₇₂	1	3	yes	—
351	C₂×C₄	C₂²×D₁₇₂	1	36	yes	—
352	C₂×C₄	C₂⁴×D₄₃	1	3	yes	—
353	C₂×C₄	C₂⁴×D₄₃	1	12	yes	—
354	C₈	C₂⁴×D₄₃	1	4	yes	—
355	C₈	C₂⁴×D₄₃	1	12	yes	—
356	C₂²	—	2	36	no	—
357	C₂²	—	86	4	no	—
358	C₂²	—	86	12	no	—
359	C₂²	—	344	48	no	—
360	C₂²	—	172	36	no	—
361	C₂²	—	172	12	no	—
362	C₂²	#14583711	1	4	yes	direct product factor
363	C₂²	C₂³×D₁₇₂	1	12	yes	—
364	C₂²	C₂³×D₁₇₂	1	3	yes	—
365	C₄	—	86	4	no	—
366	C₄	—	86	12	no	—
367	C₄	C₂³×D₁₇₂	1	12	yes	—
368	C₄	C₂³×D₁₇₂	1	3	yes	—
369	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
370	C₂	—	2	12	no	—
371	C₂	—	172	12	no	—
372	C₂	—	172	4	no	—
373	C₂	C₂×#14583711	1	6	yes	direct product factor
374	C₂	C₂⁴×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₂²×#131×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
hypercenter	C₂²×#131	D₄₃
hypocenter	C₄₃	C₂²×#577
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#41 ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063372	C₂	semidirect
2. C₂²×#13063371	C₂	semidirect
3. C₂×#14583711	C₂	direct (N × H)
4. C₂²×#13063358	C₂	semidirect
5. C₂²×#13063353	C₂	semidirect
6. C₂²×#13063347	C₂	semidirect
7. C₂³×#10621873	C₂	semidirect
8. C₂²×#131×C₄₃	C₂	semidirect
10. C₂×#13063372	C₂²	semidirect
12. C₂×#13063371	C₂²	semidirect
15. C₂²×#10621898	C₂²	semidirect
17. C₂³×Dic₈₆	C₂²	semidirect
21. #14583711	C₂²	direct (N × H)
22. C₂×#13063358	C₂²	semidirect
23. C₂×#13063353	C₂²	semidirect
24. C₂×#13063347	C₂²	semidirect
25. C₂²×Dic₁₇₂	C₂²	semidirect
26. C₂²×#10621873	C₂²	semidirect
27. C₂²×#10621873	C₂²	semidirect
28. C₂²×#10621873	C₂²	semidirect
29. C₂²×#10621873	C₂²	semidirect
30. C₂²×D₃₄₄	C₂²	semidirect
32. C₂×#131×C₄₃	C₂²	semidirect
33. C₂²×M₁₆×C₄₃	C₂²	semidirect
34. C₂³×C₈×C₄₃	C₂²	semidirect
37. #13063372	C₂³	semidirect
39. #13063371	C₂³	semidirect
44. C₂×#10621898	C₂³	semidirect
50. C₂²×Dic₈₆	C₂³	semidirect
63. #13063358	C₂³	semidirect
64. #13063353	C₂³	semidirect
65. #13063347	C₂³	semidirect
66. C₂×Dic₁₇₂	C₂³	semidirect
67. C₂×#10621873	C₂³	semidirect
68. C₂×#10621873	C₂³	semidirect
69. C₂×#10621873	C₂³	semidirect
70. C₂×#10621873	C₂³	semidirect
71. C₂×D₃₄₄	C₂³	semidirect
77. #131×C₄₃	C₂³	semidirect
78. C₂×M₁₆×C₄₃	C₂³	semidirect
81. C₂²×C₈×C₄₃	C₂³	semidirect
107. #10621898	C₂⁴	semidirect
123. C₂×Dic₈₆	C₂⁴	semidirect
124. M₁₆×C₄₃	C₂⁴	semidirect
127. C₂×C₈×C₄₃	C₂⁴	semidirect
128. Dic₁₇₂	C₂⁴	semidirect
129. D₃₄₄	C₂⁴	semidirect
130. #10621873	C₂⁴	semidirect
131. #10621873	C₂⁴	semidirect
132. #10621873	C₂⁴	semidirect
170. C₂²×C₄₃	#577	semidirect
190. C₂²×#131	D₄₃	semidirect
192. C₂×C₄₃	C₂×#577	semidirect
219. C₂×#131	C₂×D₄₃	semidirect
220. C₂²×M₁₆	C₂×D₄₃	semidirect
221. C₂³×C₈	C₂×D₄₃	semidirect
222. C₄₃	C₂²×#577	semidirect
265. #131	C₂²×D₄₃	semidirect
266. C₂×M₁₆	C₂²×D₄₃	semidirect
269. C₂²×C₈	C₂²×D₄₃	semidirect
317. M₁₆	C₂³×D₄₃	semidirect
320. C₂×C₈	C₂³×D₄₃	semidirect
362. C₂²	#14583711	direct (N × H)
373. C₂	C₂×#14583711	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063372	2
C₂²×#13063371	2
C₂×#14583711	2
C₂²×#13063358	2
C₂²×#13063353	2
C₂²×#13063347	2
C₂³×#10621873	2
C₂²×#131×C₄₃	2
C₂²×#577	43

Subgroups — C22×#14583711 #26010417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#14583711 #26010417