Subgroups — C₂×D₈×Dic₈₆ #25977011

Order 11008.

2286 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Dic₈₆	C₂	1	2	yes	maximal, complemented
2	D₈×Dic₈₆	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14583304	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14583303	C₂	1	2	yes	maximal, complemented
5	C₂×#14583179	C₂	1	2	yes	maximal, complemented
6	C₂×#14583177	C₂	1	4	yes	maximal, complemented
7	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₈×Dic₄₃	C₂	1	2	yes	maximal
9	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Dic₈₆	—	2	2	no	—
11	D₄×Dic₈₆	—	2	8	no	—
12	D₄×Dic₈₆	C₂²	1	16	yes	complemented
13	C₂×#13063325	C₂²	1	2	yes	—
14	C₂×#13063324	C₂²	1	4	yes	—
15	C₂×#13063304	—	2	2	no	—
16	C₂×#13063302	—	2	4	no	—
17	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
18	C₂×D₄×Dic₄₃	C₂²	1	4	yes	—
19	#14583304	C₂²	1	8	yes	complemented
20	#14583303	C₂²	1	16	yes	complemented
21	#14583179	C₂²	1	16	yes	complemented
22	#14583177	C₂²	1	32	yes	complemented
23	C₈×Dic₈₆	C₂²	1	8	yes	complemented
24	D₈×Dic₄₃	C₂²	1	16	yes	—
25	C₂×#13063259	C₂²	1	2	yes	—
26	C₂×#13063259	C₂²	1	2	yes	—
27	C₂×#13063258	C₂²	1	4	yes	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
30	C₂×#13063246	C₂²	1	4	yes	—
31	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
32	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
34	C₄×D₈×C₄₃	C₂²	1	8	yes	—
35	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₃	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂²×Dic₈₆	—	2	2	no	—
39	C₂²×Dic₈₆	—	2	4	no	—
40	C₂²×Dic₈₆	—	2	16	no	—
41	C₂²×Dic₈₆	—	4	16	no	—
42	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
43	C₂³×Dic₄₃	—	2	4	no	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	#13063325	—	2	4	no	—
46	#13063325	C₂³	1	8	yes	—
47	#13063324	—	2	8	no	—
48	#13063324	C₂³	1	16	yes	—
49	#13063304	—	2	16	no	—
50	#13063302	—	2	32	no	—
51	C₄×Dic₈₆	D₄	1	4	yes	—
52	C₄×Dic₈₆	C₂³	1	4	yes	—
53	D₄×Dic₄₃	—	2	8	no	—
54	D₄×Dic₄₃	C₂³	1	16	yes	—
55	C₂×C₄⋊Dic₄₃	—	2	2	no	—
56	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
58	C₂×Dic₄₃⋊C₄	—	2	4	no	—
59	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
61	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
62	#13063259	C₂³	1	8	yes	—
63	#13063259	C₂³	1	8	yes	—
64	#13063258	C₂³	1	16	yes	—
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
66	Dic₄₃⋊C₈	C₂³	1	8	yes	—
67	#13063246	C₂³	1	16	yes	—
68	C₈×Dic₄₃	C₂³	1	8	yes	—
69	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₄₃	—	2	2	no	—
71	C₂×D₈×C₄₃	Q₈	1	8	yes	complemented
72	C₂×D₈×C₄₃	C₂³	1	4	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₄₃	—	2	4	no	—
76	C₄×D₄×C₄₃	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#107×C₄₃	C₂³	1	4	yes	—
81	#102×C₄₃	C₂³	1	8	yes	—
82	C₄×C₈×C₄₃	C₂³	1	4	yes	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂×D₄×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	4	no	—
86	C₂×D₄×C₄₃	C₂×Q₈	1	8	yes	complemented
87	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
88	C₂²×C₄×C₄₃	—	2	8	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	4	8	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	16	no	—
95	C₂²×Dic₄₃	—	2	4	no	—
96	C₂²×Dic₄₃	—	4	16	no	—
97	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
98	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
99	C₂×Dic₈₆	—	2	8	no	—
100	C₂×Dic₈₆	—	2	16	no	—
101	C₂×Dic₈₆	—	4	8	no	—
102	C₂×Dic₈₆	—	4	16	no	—
103	C₂×Dic₈₆	—	4	64	no	—
104	C₂×Dic₈₆	D₈	1	8	yes	direct product factor
105	C₂×Dic₈₆	C₂×D₄	1	4	yes	—
106	D₈×C₄₃	C₂×Q₈	1	16	yes	complemented
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
109	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
110	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₄₃	—	2	2	no	—
112	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
113	C₂²⋊C₄×C₄₃	—	2	8	no	—
114	C₄²×C₄₃	C₂×D₄	1	2	yes	—
115	C₄²×C₄₃	C₂⁴	1	2	yes	—
116	C₂²⋊Dic₄₃	—	2	16	no	—
117	C₄⋊Dic₄₃	—	2	8	no	—
118	C₄⋊Dic₄₃	—	2	4	no	—
119	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
120	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
121	Dic₄₃⋊C₄	—	2	16	no	—
122	Dic₄₃⋊C₄	C₂×D₄	1	8	yes	—
123	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
124	C₄×Dic₄₃	C₂⁴	1	4	yes	—
125	C₂×C₄₃⋊C₈	—	2	4	no	—
126	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
127	C₂³×C₄₃	—	2	8	no	—
128	C₂³×C₄₃	—	2	4	no	—
129	C₂³×C₄₃	—	4	4	no	—
130	C₂³×C₄₃	—	4	4	no	—
131	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₄₃	—	2	8	no	—
133	D₄×C₄₃	—	2	4	no	—
134	D₄×C₄₃	C₂²×Q₈	1	8	yes	complemented
135	C₂×C₄×C₄₃	—	2	2	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	4	4	no	—
138	C₂×C₄×C₄₃	—	4	16	no	—
139	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
140	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
144	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
145	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
146	C₂×Dic₄₃	—	2	4	no	—
147	C₂×Dic₄₃	—	2	8	no	—
148	C₂×Dic₄₃	—	4	8	no	—
149	C₂×Dic₄₃	—	4	32	no	—
150	C₂×Dic₄₃	C₂×D₈	1	8	yes	—
151	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
152	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
153	Dic₈₆	—	4	16	no	—
154	Dic₈₆	—	4	32	no	—
155	Dic₈₆	C₂×D₈	1	16	yes	direct product factor
156	C₈×C₄₃	—	2	2	no	—
157	C₈×C₄₃	C₂²×Q₈	1	4	yes	complemented
158	C₄₃⋊C₈	—	2	4	no	—
159	C₂×Q₈×D₈	—	43	1	no	maximal, Sylow
160	C₂²×C₄₃	—	2	8	no	—
161	C₂²×C₄₃	—	4	16	no	—
162	C₂²×C₄₃	—	4	4	no	—
163	C₂²×C₄₃	—	4	4	no	—
164	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
165	C₂²×C₄₃	C₂²×D₈	1	2	yes	—
166	C₂²×C₄₃	#578	1	2	yes	—
167	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
168	C₄×C₄₃	—	2	2	no	—
169	C₄×C₄₃	—	4	4	no	—
170	C₄×C₄₃	D₄×Q₈	1	2	yes	—
171	C₄×C₄₃	C₂²×D₈	1	4	yes	—
172	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
173	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
174	Dic₄₃	—	2	4	no	—
175	Dic₄₃	—	4	8	no	—
176	Dic₄₃	C₂²×D₈	1	8	yes	—
177	C₂×D₄×Q₈	—	43	2	no	—
178	Q₈×D₈	—	43	16	no	—
179	C₂×#500	—	43	2	no	—
180	C₂×#500	—	43	1	no	—
181	C₂×#474	—	43	4	no	—
182	C₂×#474	—	43	2	no	—
183	C₂×C₈×Q₈	—	43	1	no	—
184	C₂×C₄×D₈	—	43	2	no	—
185	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic
186	C₂×C₄₃	—	4	8	no	—
187	C₂×C₄₃	Q₈×D₈	1	4	yes	complemented
188	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
189	C₂×C₄₃	C₂³×D₈	1	1	yes	characteristic
190	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
191	C₂³×Q₈	—	86	2	no	—
192	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
193	D₄×Q₈	—	43	16	no	—
194	D₄×Q₈	—	86	8	no	—
195	C₂×C₄⋊Q₈	—	43	4	no	—
196	C₂×C₄⋊Q₈	—	43	2	no	—
197	C₂×C₂²⋊Q₈	—	86	4	no	—
198	C₂×C₂²⋊Q₈	—	86	2	no	—
199	C₂×C₄×Q₈	—	43	1	no	—
200	C₂×C₄×D₄	—	43	4	no	—
201	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
202	#500	—	43	16	no	—
203	#500	—	43	8	no	—
204	#474	—	43	16	no	—
205	#474	—	43	32	no	—
206	C₈×Q₈	—	43	8	no	—
207	C₄×D₈	—	43	16	no	—
208	C₄×D₈	C₂×D₄₃	1	8	yes	—
209	C₂×#107	—	43	2	no	—
210	C₂×#107	—	43	2	no	—
211	C₂×#107	—	43	4	no	—
212	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	43	2	no	—
214	C₂×C₄⋊C₈	—	43	1	no	—
215	C₂×#102	—	43	4	no	—
216	C₂×#102	C₂×D₄₃	1	2	yes	—
217	C₂×C₄×C₈	—	43	2	no	—
218	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
219	C₄₃	C₂×Q₈×D₈	1	1	yes	characteristic, complemented, Sylow
220	C₂²×Q₈	—	43	1	no	—
221	C₂²×Q₈	—	86	4	no	—
222	C₂²×Q₈	—	86	16	no	—
223	C₂²×Q₈	—	86	2	no	—
224	C₂²×Q₈	—	172	16	no	—
225	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	—	86	4	no	—
228	C₂×D₈	Dic₈₆	1	8	yes	direct product factor
229	C₂×D₈	C₂²×D₄₃	1	4	yes	—
230	C₂²×C₈	—	43	2	no	—
231	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
232	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
233	C₄⋊Q₈	—	43	16	no	—
234	C₄⋊Q₈	—	43	8	no	—
235	C₄⋊Q₈	—	86	8	no	—
236	C₄⋊Q₈	—	86	4	no	—
237	C₂²⋊Q₈	—	86	32	no	—
238	C₂²⋊Q₈	—	86	16	no	—
239	C₄×Q₈	—	43	4	no	—
240	C₄×Q₈	—	43	4	no	—
241	C₄×D₄	—	2	4	no	—
242	C₄×D₄	—	43	16	no	—
243	C₄×D₄	—	86	8	no	—
244	C₄×D₄	C₂²×D₄₃	1	8	yes	—
245	C₂×C₄⋊C₄	—	43	2	no	—
246	C₂×C₄⋊C₄	—	43	1	no	—
247	C₂×C₄⋊C₄	—	43	4	no	—
248	C₂×C₄⋊C₄	—	86	4	no	—
249	C₂×C₄⋊C₄	—	86	2	no	—
250	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	—	86	4	no	—
253	C₂×C₄²	—	43	2	no	—
254	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
255	#107	—	43	8	no	—
256	#107	—	43	8	no	—
257	#107	—	43	16	no	—
258	#107	C₂²×D₄₃	1	4	yes	—
259	C₄⋊C₈	—	43	8	no	—
260	C₄⋊C₈	—	43	4	no	—
261	#102	—	43	16	no	—
262	#102	C₂²×D₄₃	1	8	yes	—
263	C₄×C₈	—	43	8	no	—
264	C₄×C₈	C₂²×D₄₃	1	4	yes	—
265	C₂⁴	—	2	2	no	—
266	C₂×Q₈	—	43	8	no	—
267	C₂×Q₈	—	43	4	no	—
268	C₂×Q₈	—	86	16	no	—
269	C₂×Q₈	—	86	8	no	—
270	C₂×Q₈	—	172	16	no	—
271	C₂×Q₈	—	172	64	no	—
272	C₂×Q₈	—	172	8	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	C₂×Dic₈₆	1	8	yes	complemented
276	C₂×D₄	C₂³×D₄₃	1	4	yes	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	8	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	43	2	no	—
281	C₂²×C₄	—	43	2	no	—
282	C₂²×C₄	—	86	16	no	—
283	C₂²×C₄	—	86	4	no	—
284	C₂²×C₄	—	172	16	no	—
285	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
286	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
288	D₈	C₂×Dic₈₆	1	16	yes	direct product factor
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	43	4	no	—
291	C₂×C₈	—	86	4	no	—
292	C₂×C₈	C₂×Dic₈₆	1	4	yes	complemented
293	C₂×C₈	C₂³×D₄₃	1	2	yes	—
294	C₂×C₈	C₂³×D₄₃	1	2	yes	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	43	8	no	—
297	C₄⋊C₄	—	43	4	no	—
298	C₄⋊C₄	—	43	8	no	—
299	C₄⋊C₄	—	86	16	no	—
300	C₄⋊C₄	—	86	4	no	—
301	C₄⋊C₄	—	86	8	no	—
302	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
303	C₂²⋊C₄	—	2	8	no	—
304	C₂²⋊C₄	—	86	16	no	—
305	C₄²	—	43	4	no	—
306	C₄²	—	43	4	no	—
307	C₄²	D₄×D₄₃	1	2	yes	—
308	C₄²	C₂³×D₄₃	1	2	yes	—
309	C₂³	—	2	8	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	4	no	—
313	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
314	Q₈	—	43	16	no	—
315	Q₈	—	172	32	no	—
316	Q₈	—	172	16	no	—
317	D₄	—	2	8	no	—
318	D₄	—	2	4	no	—
319	D₄	C₂²×Dic₈₆	1	8	yes	complemented
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	—	43	8	no	—
325	C₂×C₄	—	43	4	no	—
326	C₂×C₄	—	43	4	no	—
327	C₂×C₄	—	86	4	no	—
328	C₂×C₄	—	86	8	no	—
329	C₂×C₄	—	172	32	no	—
330	C₂×C₄	—	172	8	no	—
331	C₂×C₄	D₈×D₄₃	1	4	yes	—
332	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
333	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
334	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
335	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
336	C₂×C₄	#13063372	1	2	yes	—
337	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
338	C₈	—	2	2	no	—
339	C₈	—	86	4	no	—
340	C₈	C₂²×Dic₈₆	1	4	yes	complemented
341	C₂²	—	2	8	no	—
342	C₂²	—	4	4	no	—
343	C₂²	—	4	16	no	—
344	C₂²	—	4	4	no	—
345	C₂²	D₄×Dic₈₆	1	2	yes	—
346	C₂²	C₂×D₈×D₄₃	1	2	yes	—
347	C₂²	#14583713	1	2	yes	—
348	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	4	4	no	—
351	C₄	—	43	8	no	—
352	C₄	—	86	4	no	—
353	C₄	—	172	8	no	—
354	C₄	D₄×Dic₈₆	1	2	yes	—
355	C₄	C₂×D₈×D₄₃	1	4	yes	—
356	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
357	C₄	C₂×#13063372	1	1	yes	characteristic
358	C₂	—	4	8	no	—
359	C₂	D₈×Dic₈₆	1	4	yes	direct product factor
360	C₂	C₂×D₄×Dic₈₆	1	1	yes	characteristic
361	C₂	C₂²×D₈×D₄₃	1	1	yes	characteristic
362	C₂	C₂×#14583713	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×D₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₈×C₄₃	C₂²
hypercenter	C₂×C₄×D₈	D₄₃
hypocenter	C₄₃	C₂×Q₈×D₈
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Dic₈₆	C₂	semidirect
2. D₈×Dic₈₆	C₂	direct (N × H)
3. C₂×#14583304	C₂	semidirect
4. C₂×#14583303	C₂	semidirect
5. C₂×#14583179	C₂	semidirect
6. C₂×#14583177	C₂	semidirect
7. C₂×C₈×Dic₈₆	C₂	semidirect
12. D₄×Dic₈₆	C₂²	semidirect
19. #14583304	C₂²	semidirect
20. #14583303	C₂²	semidirect
21. #14583179	C₂²	semidirect
22. #14583177	C₂²	semidirect
23. C₈×Dic₈₆	C₂²	semidirect
71. C₂×D₈×C₄₃	Q₈	semidirect
86. C₂×D₄×C₄₃	C₂×Q₈	semidirect
104. C₂×Dic₈₆	D₈	direct (N × H)
106. D₈×C₄₃	C₂×Q₈	semidirect
108. C₂×C₈×C₄₃	C₂×Q₈	semidirect
134. D₄×C₄₃	C₂²×Q₈	semidirect
155. Dic₈₆	C₂×D₈	direct (N × H)
157. C₈×C₄₃	C₂²×Q₈	semidirect
187. C₂×C₄₃	Q₈×D₈	semidirect
219. C₄₃	C₂×Q₈×D₈	semidirect
228. C₂×D₈	Dic₈₆	direct (N × H)
275. C₂×D₄	C₂×Dic₈₆	semidirect
288. D₈	C₂×Dic₈₆	direct (N × H)
292. C₂×C₈	C₂×Dic₈₆	semidirect
319. D₄	C₂²×Dic₈₆	semidirect
340. C₈	C₂²×Dic₈₆	semidirect
359. C₂	D₈×Dic₈₆	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×D₄×Dic₈₆	2
D₈×Dic₈₆	2
C₂×#14583304	2
C₂×#14583303	2
C₂×#14583179	2
C₂×#14583177	2
C₂×C₈×Dic₈₆	2
C₂×D₈×Dic₄₃	2
C₂×C₄×D₈×C₄₃	2
C₂×Q₈×D₈	43

Subgroups — C2×D8×Dic86 #25977011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₈×Dic₈₆ #25977011