Subgroups — C₂×#19143527 #25960960

Order 11008.

1982 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583452	C₂	1	1	yes	maximal, characteristic
2	#19143527	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583027	C₂	1	4	yes	maximal, complemented
4	C₂×C₈×Dic₈₆	C₂	1	4	yes	maximal, complemented
5	C₂×#14582927	C₂	1	1	yes	maximal, characteristic
6	C₂×#14582926	C₂	1	1	yes	maximal, characteristic
7	C₂×#14582922	C₂	1	1	yes	maximal, characteristic
8	C₂×#14582854	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	#14583452	C₄	1	8	yes	—
14	#14583452	C₂²	1	8	yes	—
15	C₂×#13063324	C₄	1	2	yes	—
16	C₂×#13063316	C₄	1	2	yes	—
17	C₂×#13063302	C₄	1	4	yes	—
18	C₂×C₄×Dic₈₆	C₂²	1	4	yes	—
19	C₂×#13063284	C₂²	1	1	yes	characteristic
20	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
21	#14583027	C₂²	1	32	yes	complemented
22	C₈×Dic₈₆	C₂²	1	32	yes	complemented
23	#14582927	C₂²	1	8	yes	—
24	#14582926	C₂²	1	8	yes	—
25	#14582922	C₂²	1	8	yes	—
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
27	C₂×Dic₄₃⋊C₈	C₂²	1	4	yes	—
28	C₂×Dic₄₃⋊C₈	C₂²	1	4	yes	—
29	#14582854	C₂²	1	8	yes	—
30	C₂×#13063235	C₂²	1	2	yes	—
31	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
32	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
33	C₂×C₈×Dic₄₃	C₂²	1	8	yes	—
34	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
35	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#405	C₂²	1	8	yes	—
39	C₂×#97×C₄₃	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
41	C₂²×Dic₈₆	C₂×C₄	1	4	yes	—
42	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
43	C₂×#10621877	—	2	4	no	—
44	C₂×#10621877	C₂³	1	4	yes	—
45	C₂²×C₄₃⋊C₈	—	2	4	no	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
48	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
49	#13063324	C₂×C₄	1	16	yes	—
50	#13063316	C₂×C₄	1	16	yes	—
51	#13063302	C₂×C₄	1	32	yes	—
52	C₄×Dic₈₆	C₂×C₄	1	16	yes	—
53	C₄×Dic₈₆	C₂³	1	16	yes	—
54	#13063284	C₂×C₄	1	4	yes	—
55	#13063284	C₂³	1	4	yes	—
56	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₄⋊Dic₄₃	C₂×C₄	1	4	yes	—
58	C₂×Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×Dic₄₃⋊C₄	C₂×C₄	1	4	yes	—
60	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂×C₄	1	4	yes	—
64	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
66	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
68	Dic₄₃⋊C₈	C₂³	1	16	yes	—
69	Dic₄₃⋊C₈	C₂³	1	16	yes	—
70	#13063235	C₂³	1	8	yes	—
71	C₈×Dic₄₃	C₂³	1	8	yes	—
72	C₈×Dic₄₃	C₂³	1	8	yes	—
73	C₈×Dic₄₃	C₂³	1	8	yes	—
74	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₃	—	2	4	no	—
76	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
77	C₂²×C₈×C₄₃	Q₈	1	8	yes	complemented
78	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	#117×C₄₃	C₂×C₄	1	4	yes	—
83	#117×C₄₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
87	#97×C₄₃	C₂³	1	8	yes	—
88	C₄×C₈×C₄₃	C₂³	1	8	yes	—
89	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
94	C₂²×C₄×C₄₃	#41	1	4	yes	—
95	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
97	C₂²×Dic₄₃	—	2	8	no	—
98	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
99	C₂²×Dic₄₃	C₂²×C₄	1	8	yes	—
100	C₂²×Dic₄₃	C₂²×C₄	1	4	yes	—
101	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
102	C₂×Dic₈₆	—	2	16	no	—
103	C₂×Dic₈₆	C₂²×C₄	1	16	yes	—
104	M₁₆×C₄₃	—	2	8	no	—
105	C₂×C₈×C₄₃	—	2	4	no	—
106	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
107	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
108	C₂×C₈×C₄₃	C₂×Q₈	1	16	yes	complemented
109	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
110	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
111	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
112	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
113	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
114	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₄₃	C₂⁴	1	4	yes	—
116	C₂²⋊Dic₄₃	C₂²×C₄	1	8	yes	—
117	C₄⋊Dic₄₃	C₂²×C₄	1	8	yes	—
118	C₄⋊Dic₄₃	C₂²×C₄	1	16	yes	—
119	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
120	Dic₄₃⋊C₄	C₂²×C₄	1	16	yes	—
121	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
122	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
123	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
124	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
125	C₄×Dic₄₃	C₂⁴	1	4	yes	—
126	C₄×Dic₄₃	C₂⁴	1	4	yes	—
127	#10621877	—	2	8	no	—
128	C₂×C₄₃⋊C₈	—	2	4	no	—
129	C₂×C₄₃⋊C₈	—	2	8	no	—
130	C₂×C₄₃⋊C₈	—	2	4	no	—
131	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
132	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
133	C₂³×C₄₃	—	2	4	no	—
134	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
135	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
136	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₄₃	—	2	8	no	—
138	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
139	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
140	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
144	C₂×C₄×C₄₃	C₂²×Q₈	1	4	yes	—
145	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
146	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
147	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
148	C₂×Dic₄₃	—	2	8	no	—
149	C₂×Dic₄₃	—	2	4	no	—
150	C₂×Dic₄₃	—	2	16	no	—
151	C₂×Dic₄₃	#131	1	8	yes	—
152	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
153	C₂×Dic₄₃	C₂³×C₄	1	8	yes	—
154	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
155	Dic₈₆	—	2	32	no	—
156	C₈×C₄₃	—	2	4	no	—
157	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
158	C₈×C₄₃	C₂²×Q₈	1	4	yes	—
159	C₄₃⋊C₈	—	2	4	no	—
160	C₄₃⋊C₈	—	2	4	no	—
161	C₂×#2960	—	43	1	no	maximal, Sylow
162	C₂²×C₄₃	—	2	8	no	—
163	C₂²×C₄₃	—	2	4	no	—
164	C₂²×C₄₃	C₂×C₄×Q₈	1	4	yes	—
165	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
166	C₂²×C₄₃	C₂×#131	1	4	yes	—
167	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
168	C₄×C₄₃	—	2	8	no	—
169	C₄×C₄₃	C₂×C₄×Q₈	1	2	yes	—
170	C₄×C₄₃	C₂×C₄×Q₈	1	4	yes	—
171	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
172	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
173	Dic₄₃	—	2	8	no	—
174	Dic₄₃	—	2	4	no	—
175	Dic₄₃	C₂×#131	1	8	yes	—
176	C₂×#533	—	43	1	no	—
177	#2960	—	43	16	no	—
178	C₂×#446	—	43	4	no	—
179	C₂×C₈×Q₈	—	43	4	no	—
180	C₂×#424	—	43	1	no	—
181	C₂×#424	—	43	1	no	—
182	C₂×#423	—	43	1	no	—
183	C₂×#405	—	43	1	no	—
184	C₂×#405	D₄₃	1	1	yes	characteristic
185	C₂²×C₄×C₈	—	43	1	no	—
186	C₂×C₄₃	—	2	4	no	—
187	C₂×C₄₃	#2960	1	4	yes	complemented
188	C₂×C₄₃	C₂²×C₄×Q₈	1	1	yes	characteristic
189	C₂×C₄₃	C₂²×#131	1	2	yes	—
190	C₂²×M₁₆	—	43	1	no	—
191	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
192	C₂³×C₈	—	43	1	no	—
193	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
194	#533	—	43	8	no	—
195	#533	—	43	8	no	—
196	C₂×C₄⋊Q₈	—	43	2	no	—
197	C₂×#125	—	43	2	no	—
198	C₂×C₂²⋊Q₈	—	43	4	no	—
199	C₂×C₄×Q₈	—	43	4	no	—
200	C₂×#117	—	43	1	no	—
201	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
202	C₂²×C₄²	—	43	1	no	—
203	#446	—	43	32	no	—
204	C₈×Q₈	—	43	32	no	—
205	#424	—	43	8	no	—
206	#424	—	43	8	no	—
207	#423	—	43	8	no	—
208	C₂×C₄⋊C₈	—	43	4	no	—
209	C₂×C₄⋊C₈	—	43	4	no	—
210	C₂×C₄⋊C₈	—	43	4	no	—
211	#405	—	43	8	no	—
212	#405	C₂×D₄₃	1	8	yes	—
213	C₂×#97	—	43	2	no	—
214	C₂×#97	C₂×D₄₃	1	2	yes	—
215	C₂×C₄×C₈	—	43	2	no	—
216	C₂×C₄×C₈	—	43	8	no	—
217	C₂×C₄×C₈	—	43	2	no	—
218	C₂×C₄×C₈	—	43	2	no	—
219	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
220	C₄₃	C₂×#2960	1	1	yes	characteristic, complemented, Sylow
221	C₂²×Q₈	—	43	4	no	—
222	C₂³×C₄	—	43	2	no	—
223	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
224	C₂×M₁₆	—	2	4	no	—
225	C₂×M₁₆	—	43	4	no	—
226	C₂×M₁₆	—	86	4	no	—
227	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
228	C₂²×C₈	—	43	2	no	—
229	C₂²×C₈	—	43	4	no	—
230	C₂²×C₈	—	43	2	no	—
231	C₂²×C₈	—	86	4	no	—
232	C₂²×C₈	Dic₈₆	1	8	yes	complemented
233	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
234	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
235	C₂²×C₈	C₂²×D₄₃	1	4	yes	—
236	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
237	C₄⋊Q₈	—	43	16	no	—
238	#125	—	43	16	no	—
239	C₂²⋊Q₈	—	43	32	no	—
240	C₄×Q₈	—	43	16	no	—
241	C₄×Q₈	—	43	16	no	—
242	#117	—	43	4	no	—
243	#117	—	43	4	no	—
244	#117	C₄×D₄₃	1	4	yes	—
245	#117	C₂²×D₄₃	1	4	yes	—
246	C₂×C₄⋊C₄	—	43	2	no	—
247	C₂×C₄⋊C₄	—	43	4	no	—
248	C₂×C₄⋊C₄	—	43	4	no	—
249	C₂×C₄⋊C₄	—	43	4	no	—
250	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
251	C₂×C₂²⋊C₄	—	43	2	no	—
252	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
253	C₂×C₄²	—	43	1	no	—
254	C₂×C₄²	—	43	1	no	—
255	C₂×C₄²	—	43	4	no	—
256	C₂×C₄²	—	43	2	no	—
257	C₂×C₄²	—	43	2	no	—
258	C₂×C₄²	—	43	4	no	—
259	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
260	C₄⋊C₈	—	43	16	no	—
261	C₄⋊C₈	—	43	16	no	—
262	C₄⋊C₈	—	43	16	no	—
263	#97	—	43	8	no	—
264	#97	C₂²×D₄₃	1	8	yes	—
265	C₄×C₈	—	43	8	no	—
266	C₄×C₈	—	43	8	no	—
267	C₄×C₈	—	43	8	no	—
268	C₄×C₈	C₂²×D₄₃	1	8	yes	—
269	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
270	C₂×Q₈	—	43	16	no	—
271	C₂×Q₈	—	86	16	no	—
272	C₂²×C₄	—	43	2	no	—
273	C₂²×C₄	—	43	2	no	—
274	C₂²×C₄	—	43	8	no	—
275	C₂²×C₄	—	43	4	no	—
276	C₂²×C₄	—	86	8	no	—
277	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
278	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
279	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
281	C₂²×C₄	#10621898	1	4	yes	—
282	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
284	M₁₆	—	2	8	no	—
285	M₁₆	—	86	8	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	43	4	no	—
288	C₂×C₈	—	43	4	no	—
289	C₂×C₈	—	86	4	no	—
290	C₂×C₈	—	86	8	no	—
291	C₂×C₈	—	86	4	no	—
292	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
293	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
294	C₂×C₈	C₂×Dic₈₆	1	16	yes	complemented
295	C₂×C₈	C₂³×D₄₃	1	4	yes	—
296	C₂×C₈	C₂³×D₄₃	1	2	yes	—
297	C₂×C₈	C₂³×D₄₃	1	2	yes	—
298	C₄⋊C₄	—	43	8	no	—
299	C₄⋊C₄	—	43	16	no	—
300	C₄⋊C₄	—	43	16	no	—
301	C₄⋊C₄	—	43	16	no	—
302	C₄⋊C₄	C₂×C₄×D₄₃	1	8	yes	—
303	C₂²⋊C₄	—	43	8	no	—
304	C₂²⋊C₄	C₂×C₄×D₄₃	1	8	yes	—
305	C₄²	—	43	4	no	—
306	C₄²	—	43	4	no	—
307	C₄²	—	43	4	no	—
308	C₄²	—	43	4	no	—
309	C₄²	—	43	4	no	—
310	C₄²	—	43	4	no	—
311	C₄²	C₂×C₄×D₄₃	1	4	yes	—
312	C₄²	C₂³×D₄₃	1	4	yes	—
313	C₂³	—	2	4	no	—
314	C₂³	C₄×Dic₈₆	1	4	yes	—
315	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
316	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
317	Q₈	—	86	32	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	43	8	no	—
320	C₂×C₄	—	43	4	no	—
321	C₂×C₄	—	43	4	no	—
322	C₂×C₄	—	43	8	no	—
323	C₂×C₄	—	86	16	no	—
324	C₂×C₄	—	86	4	no	—
325	C₂×C₄	—	86	8	no	—
326	C₂×C₄	C₄×Dic₈₆	1	8	yes	—
327	C₂×C₄	C₄×Dic₈₆	1	4	yes	—
328	C₂×C₄	C₂²×C₄×D₄₃	1	8	yes	—
329	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
331	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
332	C₂×C₄	C₂²×Dic₈₆	1	4	yes	—
333	C₂×C₄	C₂×#10621898	1	2	yes	—
334	C₂×C₄	C₂×#10621898	1	4	yes	—
335	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
336	C₈	—	2	4	no	—
337	C₈	—	86	4	no	—
338	C₈	—	86	4	no	—
339	C₈	C₂²×Dic₈₆	1	4	yes	—
340	C₈	C₂²×Dic₈₆	1	4	yes	—
341	C₂²	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	C₂×C₄×Dic₈₆	1	4	yes	—
344	C₂²	C₂×C₄×Dic₈₆	1	2	yes	—
345	C₂²	#131×D₄₃	1	4	yes	—
346	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	43	8	no	—
349	C₄	—	86	4	no	—
350	C₄	—	86	8	no	—
351	C₄	C₂×C₄×Dic₈₆	1	2	yes	—
352	C₄	C₂×C₄×Dic₈₆	1	4	yes	—
353	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
354	C₄	C₂²×#10621898	1	1	yes	characteristic
355	C₂	—	2	4	no	—
356	C₂	#19143527	1	4	yes	direct product factor
357	C₂	C₂²×C₄×Dic₈₆	1	1	yes	characteristic
358	C₂	C₂×#131×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	C₂×#2960
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #19143527	C₂	direct (N × H)
3. C₂×#14583027	C₂	semidirect
4. C₂×C₈×Dic₈₆	C₂	semidirect
21. #14583027	C₂²	semidirect
22. C₈×Dic₈₆	C₂²	semidirect
77. C₂²×C₈×C₄₃	Q₈	semidirect
108. C₂×C₈×C₄₃	C₂×Q₈	semidirect
187. C₂×C₄₃	#2960	semidirect
220. C₄₃	C₂×#2960	semidirect
232. C₂²×C₈	Dic₈₆	semidirect
294. C₂×C₈	C₂×Dic₈₆	semidirect
356. C₂	#19143527	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×#14583452	2
#19143527	2
C₂×#14583027	2
C₂×C₈×Dic₈₆	2
C₂×#14582927	2
C₂×#14582926	2
C₂×#14582922	2
C₂×#14582854	2
C₂²×C₈×Dic₄₃	2
C₂×C₄₃×#405	2
C₂×#2960	43

Subgroups — C2×#19143527 #25960960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143527 #25960960