Subgroups — D₈×#13083558 #36525851

Order 22784.

794 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#13083558	C₂	1	2	yes	maximal, complemented
2	#26019137	C₂	1	2	yes	maximal, complemented
3	#26019082	C₂	1	4	yes	maximal, complemented
4	D₈×#10623494	C₂	1	2	yes	maximal, complemented
5	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018677	C₂	1	2	yes	maximal, complemented
7	C₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#13083558	—	2	2	no	—
10	#19151676	C₂²	1	4	yes	complemented
11	#19151670	—	2	4	no	—
12	D₄×#10623494	C₂²	1	4	yes	complemented
13	#19151651	C₂²	1	1	yes	characteristic
14	#19151622	C₂²	1	2	yes	—
15	#19151562	—	2	2	no	—
16	C₄×#13083558	C₂²	1	1	yes	characteristic
17	#19151351	C₂²	1	2	yes	complemented
18	#19151351	C₂²	1	2	yes	complemented
19	D₄⋊#10623494	C₂²	1	4	yes	complemented
20	D₄⋊#10623494	C₂²	1	4	yes	complemented
21	#19151320	C₂²	1	2	yes	complemented
22	C₈×#10623494	C₂²	1	2	yes	complemented
23	C₂²×D₈×C₈₉	C₄	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
25	C₄×D₈×C₈₉	C₄	1	2	yes	—
26	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic
27	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic
28	C₄×D₈×C₈₉	C₂²	1	2	yes	—
29	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#107×C₈₉	C₄	1	1	yes	characteristic
32	C₂×#102×C₈₉	C₄	1	2	yes	—
33	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#13083558	—	2	4	no	—
35	C₂×#13083558	—	2	2	no	—
36	C₂×#13083558	—	4	8	no	—
37	C₂×#13083558	D₄	1	1	yes	characteristic
38	C₂×#13083558	D₄	1	1	yes	characteristic
39	C₂²×#10623494	—	2	4	no	—
40	C₄⋊#10623494	—	2	2	no	—
41	C₄⋊#10623494	—	2	1	no	—
42	C₄⋊#10623494	C₂³	1	4	yes	—
43	C₂²⋊#10623494	—	2	4	no	—
44	C₂²⋊#10623494	—	2	4	no	—
45	C₂²⋊#10623494	—	2	1	no	—
46	#15667923	D₄	1	2	yes	—
47	C₄×#10623494	C₂³	1	2	yes	—
48	C₄×#10623494	C₂³	1	2	yes	—
49	C₂²×D₄×C₈₉	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₈₉	—	2	2	no	—
51	C₂×D₈×C₈₉	—	2	4	no	—
52	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
53	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₄×D₄×C₈₉	—	2	2	no	—
58	C₄×D₄×C₈₉	—	2	2	no	—
59	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
60	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
61	C₄×D₄×C₈₉	C₂³	1	2	yes	—
62	C₄×D₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	#107×C₈₉	C₂×C₄	1	2	yes	—
67	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
68	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
69	#102×C₈₉	C₂×C₄	1	2	yes	—
70	#102×C₈₉	C₂×C₄	1	2	yes	—
71	#102×C₈₉	C₂×C₄	1	2	yes	—
72	#102×C₈₉	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	#13083558	—	2	2	no	—
78	#13083558	—	4	4	no	—
79	#13083558	—	4	8	no	—
80	#13083558	D₈	1	4	yes	direct product factor
81	C₂×#10623494	—	2	4	no	—
82	C₂×#10623494	—	2	2	no	—
83	C₂×#10623494	—	4	8	no	—
84	C₂×#10623494	C₂×D₄	1	2	yes	—
85	C₂×#10623494	C₂×D₄	1	2	yes	—
86	C₂⁴×C₈₉	—	2	2	no	—
87	C₂×D₄×C₈₉	—	2	4	no	—
88	C₂×D₄×C₈₉	—	2	2	no	—
89	C₂×D₄×C₈₉	—	4	2	no	—
90	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
91	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
93	C₂²×C₄×C₈₉	—	2	2	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	2	2	no	—
97	C₂²×C₄×C₈₉	—	4	4	no	—
98	C₂²×C₄×C₈₉	—	4	4	no	—
99	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
102	D₈×C₈₉	—	2	4	no	—
103	D₈×C₈₉	—	2	2	no	—
104	D₈×C₈₉	M₁₆	1	4	yes	complemented
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	—	4	1	no	—
107	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
114	C₂²⋊C₄×C₈₉	—	2	2	no	—
115	C₂²⋊C₄×C₈₉	—	2	2	no	—
116	C₂²⋊C₄×C₈₉	—	2	2	no	—
117	C₂²⋊C₄×C₈₉	—	2	2	no	—
118	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₈₉	#41	1	1	yes	characteristic
121	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
122	C₂³×C₈₉	—	2	2	no	—
123	C₂³×C₈₉	—	2	2	no	—
124	C₂³×C₈₉	—	4	4	no	—
125	C₂³×C₈₉	—	4	4	no	—
126	C₂³×C₈₉	—	8	2	no	—
127	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
128	D₄×C₈₉	—	2	2	no	—
129	D₄×C₈₉	—	2	2	no	—
130	D₄×C₈₉	—	2	2	no	—
131	D₄×C₈₉	—	4	4	no	—
132	D₄×C₈₉	C₂×M₁₆	1	4	yes	complemented
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	4	4	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	—	4	2	no	—
142	C₂×C₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	4	4	no	—
144	C₂×C₄×C₈₉	—	4	4	no	—
145	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₈₉	#135	1	2	yes	—
150	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₈×C₈₉	—	2	1	no	—
154	C₈×C₈₉	—	2	1	no	—
155	C₈×C₈₉	—	2	1	no	—
156	C₈×C₈₉	C₂×M₁₆	1	2	yes	complemented
157	#10623494	—	2	2	no	—
158	#10623494	—	4	2	no	—
159	#10623494	—	4	4	no	—
160	#10623494	C₂×D₈	1	4	yes	complemented
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	2	4	no	—
164	C₂²×C₈₉	—	4	2	no	—
165	C₂²×C₈₉	—	4	2	no	—
166	C₂²×C₈₉	—	4	2	no	—
167	C₂²×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	—	4	2	no	—
169	C₂²×C₈₉	—	8	8	no	—
170	C₂²×C₈₉	C₄×D₈	1	2	yes	—
171	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
172	C₄×C₈₉	—	2	1	no	—
173	C₄×C₈₉	—	2	1	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	4	2	no	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	C₄×D₈	1	2	yes	—
178	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
179	C₄×C₈₉	#568	1	1	yes	characteristic
180	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
181	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
182	M₁₆×D₈	—	89	1	no	maximal, Sylow
183	C₂×C₈₉	—	2	2	no	—
184	C₂×C₈₉	—	4	4	no	—
185	C₂×C₈₉	—	8	2	no	—
186	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
187	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
188	C₂×C₈₉	#2957	1	1	yes	characteristic
189	C₂×C₄×D₈	D₈₉	1	1	yes	characteristic
190	D₄×M₁₆	—	89	2	no	—
191	#1589	—	89	2	no	—
192	#1581	—	89	4	no	—
193	C₈×D₈	—	89	2	no	—
194	#1567	—	89	1	no	—
195	#1486	—	89	2	no	—
196	C₈×M₁₆	—	89	1	no	—
197	C₈₉	M₁₆×D₈	1	1	yes	characteristic, complemented, Sylow
198	C₂²×D₈	Dic₈₉	1	1	yes	characteristic
199	C₂²×M₁₆	—	178	2	no	—
200	C₂×C₄×D₄	C₂×D₈₉	1	2	yes	—
201	C₄×D₈	Dic₈₉	1	2	yes	—
202	C₄×D₈	Dic₈₉	1	1	yes	characteristic
203	C₄×D₈	Dic₈₉	1	1	yes	characteristic
204	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
205	C₄×D₈	C₂×D₈₉	1	2	yes	—
206	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
207	#436	—	89	4	no	—
208	#435	—	178	4	no	—
209	C₈×D₄	—	89	4	no	—
210	#431	—	89	1	no	—
211	C₂×#107	Dic₈₉	1	1	yes	characteristic
212	#423	—	89	2	no	—
213	C₂×#102	Dic₈₉	1	2	yes	—
214	#407	—	178	2	no	—
215	C₄×M₁₆	—	89	1	no	—
216	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
217	#335	—	89	2	no	—
218	#335	—	89	2	no	—
219	D₄⋊C₈	—	89	4	no	—
220	D₄⋊C₈	—	89	4	no	—
221	#322	—	89	2	no	—
222	C₈²	—	89	2	no	—
223	C₂²×D₄	C₂×Dic₈₉	1	2	yes	—
224	C₂³×C₄	—	2	2	no	—
225	C₂×D₈	—	2	4	no	—
226	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
227	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
228	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
229	C₂×M₁₆	—	89	1	no	—
230	C₂×M₁₆	—	89	1	no	—
231	C₂×M₁₆	—	356	8	no	—
232	C₂×M₁₆	—	178	4	no	—
233	C₂×M₁₆	—	178	2	no	—
234	C₂²×C₈	—	178	4	no	—
235	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	—	2	2	no	—
239	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
240	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
241	C₄×D₄	C₂²×D₈₉	1	2	yes	—
242	C₄×D₄	C₂²×D₈₉	1	2	yes	—
243	C₂×C₄⋊C₄	C₂×Dic₈₉	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
246	#107	C₂×Dic₈₉	1	2	yes	—
247	#107	C₂×Dic₈₉	1	1	yes	characteristic
248	#107	C₂×Dic₈₉	1	1	yes	characteristic
249	C₄⋊C₈	—	89	4	no	—
250	C₄⋊C₈	—	178	2	no	—
251	C₄⋊C₈	—	178	1	no	—
252	#102	C₂×Dic₈₉	1	2	yes	—
253	#102	C₂×Dic₈₉	1	2	yes	—
254	#102	C₂×Dic₈₉	1	2	yes	—
255	#102	C₂×Dic₈₉	1	2	yes	—
256	C₂²⋊C₈	—	178	4	no	—
257	C₂²⋊C₈	—	178	4	no	—
258	C₂²⋊C₈	—	178	1	no	—
259	#97	—	89	2	no	—
260	C₄×C₈	—	89	2	no	—
261	C₄×C₈	—	89	2	no	—
262	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
263	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
264	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
265	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
266	C₂⁴	—	2	2	no	—
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
271	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	4	no	—
279	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
280	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
281	C₂²×C₄	#13083573	1	1	yes	characteristic
282	D₈	—	2	4	no	—
283	D₈	—	2	2	no	—
284	D₈	#13083558	1	4	yes	direct product factor
285	M₁₆	—	89	4	no	—
286	M₁₆	—	356	8	no	—
287	M₁₆	—	356	4	no	—
288	M₁₆	—	178	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	89	2	no	—
292	C₂×C₈	—	89	2	no	—
293	C₂×C₈	—	356	8	no	—
294	C₂×C₈	—	178	4	no	—
295	C₂×C₈	—	178	2	no	—
296	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
297	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
298	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
299	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
302	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
308	C₄²	D₄×D₈₉	1	1	yes	characteristic
309	C₄²	#13083573	1	1	yes	characteristic
310	C₄²	C₂³×D₈₉	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	4	4	no	—
314	C₂³	—	4	4	no	—
315	C₂³	—	8	2	no	—
316	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
317	D₄	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	D₄	C₂×#13083558	1	4	yes	complemented
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
335	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
336	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
337	C₂×C₄	D₈×D₈₉	1	2	yes	—
338	C₂×C₄	#15668031	1	2	yes	—
339	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
340	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
341	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
342	C₈	—	2	1	no	—
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	—	89	4	no	—
346	C₈	—	356	2	no	—
347	C₈	—	356	4	no	—
348	C₈	—	178	2	no	—
349	C₈	C₂×#13083558	1	2	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	4	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	D₈×Dic₈₉	1	2	yes	—
360	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	D₈×Dic₈₉	1	2	yes	—
367	C₄	C₂²×#13083558	1	1	yes	characteristic
368	C₄	#19152365	1	1	yes	characteristic
369	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
370	C₄	C₂×#15668031	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	4	no	—
373	C₂	—	8	2	no	—
374	C₂	D₄×#13083558	1	1	yes	characteristic
375	C₂	C₂×D₈×Dic₈₉	1	1	yes	characteristic
376	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×C₄×D₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×C₄×D₈	D₈₉
hypocenter	C₈₉	M₁₆×D₈
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#13083558	C₂	semidirect
2. #26019137	C₂	semidirect
3. #26019082	C₂	semidirect
4. D₈×#10623494	C₂	semidirect
5. #26019011	C₂	semidirect
6. #26018677	C₂	semidirect
7. C₈×#13083558	C₂	semidirect
10. #19151676	C₂²	semidirect
12. D₄×#10623494	C₂²	semidirect
17. #19151351	C₂²	semidirect
18. #19151351	C₂²	semidirect
19. D₄⋊#10623494	C₂²	semidirect
20. D₄⋊#10623494	C₂²	semidirect
21. #19151320	C₂²	semidirect
22. C₈×#10623494	C₂²	semidirect
80. #13083558	D₈	direct (N × H)
104. D₈×C₈₉	M₁₆	semidirect
132. D₄×C₈₉	C₂×M₁₆	semidirect
156. C₈×C₈₉	C₂×M₁₆	semidirect
160. #10623494	C₂×D₈	semidirect
197. C₈₉	M₁₆×D₈	semidirect
284. D₈	#13083558	direct (N × H)
321. D₄	C₂×#13083558	semidirect
349. C₈	C₂×#13083558	semidirect

Maximal subgroups

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

subgroup	index
D₄×#13083558	2
#26019137	2
#26019082	2
D₈×#10623494	2
#26019011	2
#26018677	2
C₈×#13083558	2
C₂×C₄×D₈×C₈₉	2
M₁₆×D₈	89

Subgroups — D8×#13083558 #36525851

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#13083558 #36525851