Subgroups — C₂×#26019092 #36523929

Order 22784.

750 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#13083561	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151675	C₂	1	1	yes	maximal, characteristic
4	#26019092	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151348	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151327	C₂	1	1	yes	maximal, characteristic
7	C₂×#19151320	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13083561	C₄	1	1	yes	characteristic
10	C₂²×#13083557	—	2	1	no	—
11	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
12	Q₈×#10623494	—	2	2	no	—
13	Q₈×#10623494	C₂²	1	4	yes	complemented
14	C₄×#13083561	C₄	1	4	yes	—
15	C₄×#13083561	C₂²	1	4	yes	—
16	#19151675	—	2	2	no	—
17	#19151675	C₂²	1	4	yes	—
18	C₂×#15667943	C₄	1	1	yes	characteristic
19	C₂×C₄⋊#10623494	—	2	1	no	—
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×#15667936	C₄	1	1	yes	characteristic
22	C₂×#15667932	C₄	1	1	yes	characteristic
23	C₂×#15667924	—	2	1	no	—
24	C₂×C₄×#10623494	—	2	1	no	—
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
27	#19151348	C₂²	1	4	yes	complemented
28	#19151327	C₂²	1	4	yes	—
29	#19151320	C₂²	1	4	yes	complemented
30	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
33	Q₈⋊C₈×C₈₉	C₂²	1	4	yes	complemented
34	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₈₉	—	2	1	no	—
36	C₂×#13083561	—	2	4	no	—
37	C₂×#13083561	C₂×C₄	1	4	yes	—
38	C₂×#13083557	—	2	4	no	—
39	C₂×#13083557	—	4	4	no	—
40	C₂²×#10623494	—	2	1	no	—
41	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
42	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
43	C₂²×#10623494	D₄	1	1	yes	characteristic
44	C₂²×#10623494	D₄	1	1	yes	characteristic
45	C₄×D₃₅₆	—	2	1	no	—
46	C₄×D₃₅₆	—	2	1	no	—
47	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
48	C₄×D₃₅₆	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083551	—	2	1	no	—
51	#15667943	C₂×C₄	1	4	yes	—
52	C₄⋊#10623494	—	2	4	no	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	C₂³	1	2	yes	—
55	#15667936	C₂×C₄	1	4	yes	—
56	#15667932	C₂×C₄	1	4	yes	—
57	#15667924	—	2	4	no	—
58	C₄×#10623494	—	2	4	no	—
59	C₄×#10623494	C₂×C₄	1	2	yes	—
60	C₄×#10623494	D₄	1	2	yes	—
61	C₄×#10623494	C₂³	1	2	yes	—
62	C₄×#10623494	C₂³	1	2	yes	—
63	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	—	2	1	no	—
65	C₂²×C₈×C₈₉	—	2	1	no	—
66	C₄×Q₈×C₈₉	—	2	1	no	—
67	C₄×Q₈×C₈₉	—	2	1	no	—
68	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
69	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	—	2	1	no	—
73	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₈₉	—	2	1	no	—
75	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
76	C₄×C₈×C₈₉	—	2	1	no	—
77	C₄×C₈×C₈₉	C₂³	1	2	yes	—
78	C₂³×D₈₉	—	2	1	no	—
79	C₂×D₃₅₆	—	2	2	no	—
80	C₂×D₃₅₆	—	2	2	no	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
83	C₂²×Dic₈₉	—	2	1	no	—
84	C₂×C₄×D₈₉	—	2	2	no	—
85	C₂×C₄×D₈₉	—	2	2	no	—
86	C₂×C₄×D₈₉	—	4	2	no	—
87	C₂×C₄×D₈₉	—	4	2	no	—
88	#13083561	—	2	8	no	—
89	#13083557	—	4	8	no	—
90	C₂×#10623494	—	2	2	no	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	4	2	no	—
95	C₂×#10623494	SD₁₆	1	4	yes	complemented
96	C₂×#10623494	C₂²×C₄	1	2	yes	—
97	C₂×#10623494	C₂²×C₄	1	2	yes	—
98	C₂×#10623494	C₂×D₄	1	2	yes	—
99	C₂×#10623494	C₂×D₄	1	2	yes	—
100	C₄⋊Dic₈₉	—	2	1	no	—
101	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
102	#13083551	—	2	2	no	—
103	#13083551	—	2	2	no	—
104	C₂×Q₈×C₈₉	—	2	1	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×Q₈×C₈₉	M₁₆	1	4	yes	complemented
107	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
113	C₂×C₈×C₈₉	—	2	2	no	—
114	C₂×C₈×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	—	4	2	no	—
116	C₂×C₈×C₈₉	—	4	2	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
121	C₄²×C₈₉	—	2	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₈₉	#41	1	1	yes	characteristic
126	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
127	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
128	C₂²×D₈₉	—	2	2	no	—
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	2	no	—
131	C₂²×D₈₉	—	4	2	no	—
132	Q₈×C₈₉	—	2	2	no	—
133	Q₈×C₈₉	—	2	4	no	—
134	Q₈×C₈₉	C₂×M₁₆	1	4	yes	complemented
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₈₉	#131	1	2	yes	—
145	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
146	C₂×C₄×C₈₉	#135	1	2	yes	—
147	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
150	C₂×Dic₈₉	—	2	2	no	—
151	C₂×Dic₈₉	—	4	2	no	—
152	D₃₅₆	—	2	2	no	—
153	D₃₅₆	—	2	2	no	—
154	D₃₅₆	—	4	2	no	—
155	C₄×D₈₉	—	4	2	no	—
156	C₄×D₈₉	—	4	2	no	—
157	C₄×D₈₉	—	4	4	no	—
158	C₈×C₈₉	—	4	2	no	—
159	C₈×C₈₉	—	4	2	no	—
160	#10623494	—	2	2	no	—
161	#10623494	—	2	2	no	—
162	#10623494	—	2	2	no	—
163	#10623494	—	4	2	no	—
164	#10623494	C₂×SD₁₆	1	4	yes	complemented
165	C₂²×C₈₉	#435	1	2	yes	—
166	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
167	C₂²×C₈₉	#444	1	2	yes	—
168	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂×D₈₉	—	4	2	no	—
170	C₂×D₈₉	—	4	2	no	—
171	C₂×D₈₉	—	4	2	no	—
172	C₂×D₈₉	—	8	4	no	—
173	C₄×C₈₉	—	2	4	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	#435	1	2	yes	—
178	C₄×C₈₉	C₄×SD₁₆	1	2	yes	—
179	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
180	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
181	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
182	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
183	Dic₈₉	—	4	2	no	—
184	C₂×#1583	—	89	1	no	maximal, Sylow
185	C₂×C₈₉	#1583	1	4	yes	complemented
186	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
187	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
188	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
189	D₈₉	—	8	2	no	—
190	C₂×C₈×Q₈	—	89	1	no	—
191	C₂×C₄×SD₁₆	—	89	1	no	—
192	C₂×#436	—	89	1	no	—
193	#1583	—	89	8	no	—
194	C₂×#334	—	89	1	no	—
195	C₂×Q₈⋊C₈	D₈₉	1	1	yes	characteristic, complemented
196	C₂×D₄⋊C₈	—	89	1	no	—
197	C₂×#322	—	89	1	no	—
198	C₈₉	C₂×#1583	1	1	yes	characteristic, complemented, Sylow
199	C₂²×SD₁₆	—	89	1	no	—
200	C₂²×M₁₆	—	178	1	no	—
201	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
202	C₂×C₄×D₄	—	89	1	no	—
203	C₈×Q₈	—	89	4	no	—
204	C₈×Q₈	—	178	2	no	—
205	C₄×SD₁₆	—	89	4	no	—
206	C₄×SD₁₆	—	89	4	no	—
207	#436	—	89	4	no	—
208	#436	—	178	2	no	—
209	C₂×#106	—	89	1	no	—
210	C₂×C₄⋊C₈	—	89	1	no	—
211	C₂×C₄⋊C₈	—	178	1	no	—
212	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
213	C₂×#103	—	89	1	no	—
214	C₂×#102	—	89	1	no	—
215	C₂×C₂²⋊C₈	—	178	1	no	—
216	C₂×C₄×C₈	—	89	1	no	—
217	C₂×C₄×C₈	—	89	1	no	—
218	C₂×C₄×C₈	—	178	1	no	—
219	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
220	#334	—	89	4	no	—
221	Q₈⋊C₈	C₂×D₈₉	1	4	yes	complemented
222	D₄⋊C₈	—	89	4	no	—
223	#322	—	89	4	no	—
224	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
225	C₂²×D₄	—	89	1	no	—
226	C₂³×C₄	—	178	1	no	—
227	C₂×SD₁₆	—	89	4	no	—
228	C₂×SD₁₆	—	178	4	no	—
229	C₂×M₁₆	—	356	4	no	—
230	C₂×M₁₆	—	178	4	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	89	1	no	—
234	C₂²×C₈	—	89	1	no	—
235	C₂²×C₈	—	89	1	no	—
236	C₂²×C₈	—	89	1	no	—
237	C₂²×C₈	—	178	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₄×D₈₉	1	2	yes	—
241	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
242	C₄×D₄	—	89	2	no	—
243	C₄×D₄	—	89	2	no	—
244	C₄×D₄	—	178	1	no	—
245	C₄×D₄	—	178	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	89	1	no	—
248	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	178	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
252	#106	—	89	4	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	89	2	no	—
255	C₄⋊C₈	—	178	4	no	—
256	C₄⋊C₈	—	178	1	no	—
257	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
258	#103	—	89	4	no	—
259	#102	—	89	4	no	—
260	C₂²⋊C₈	—	178	4	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	89	2	no	—
263	C₄×C₈	—	89	2	no	—
264	C₄×C₈	—	89	2	no	—
265	C₄×C₈	—	89	2	no	—
266	C₄×C₈	—	178	4	no	—
267	C₄×C₈	C₂²×D₈₉	1	2	yes	—
268	C₂⁴	—	178	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	#13083557	1	4	yes	complemented
272	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
273	C₂×D₄	—	89	2	no	—
274	C₂×D₄	—	178	1	no	—
275	C₂×D₄	—	178	2	no	—
276	C₂×D₄	—	178	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	356	2	no	—
280	C₂²×C₄	—	356	2	no	—
281	C₂²×C₄	—	178	1	no	—
282	C₂²×C₄	—	178	2	no	—
283	C₂²×C₄	—	178	2	no	—
284	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
286	C₂²×C₄	#13083573	1	1	yes	characteristic
287	SD₁₆	—	178	8	no	—
288	M₁₆	—	356	8	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	89	4	no	—
294	C₂×C₈	—	89	2	no	—
295	C₂×C₈	—	89	2	no	—
296	C₂×C₈	—	89	2	no	—
297	C₂×C₈	—	89	2	no	—
298	C₂×C₈	—	356	2	no	—
299	C₂×C₈	—	178	2	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	—	178	2	no	—
302	C₂×C₈	—	178	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	89	2	no	—
307	C₄⋊C₄	—	178	1	no	—
308	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
309	C₂²⋊C₄	—	178	2	no	—
310	C₂²⋊C₄	—	178	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
314	C₄²	D₄×D₈₉	1	1	yes	characteristic
315	C₄²	#13083573	1	1	yes	characteristic
316	C₄²	C₂³×D₈₉	1	1	yes	characteristic
317	C₂³	—	356	2	no	—
318	C₂³	—	356	2	no	—
319	C₂³	—	356	2	no	—
320	C₂³	—	178	2	no	—
321	C₂³	#15667972	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	2	no	—
324	Q₈	C₂×#13083557	1	4	yes	complemented
325	D₄	—	356	2	no	—
326	D₄	—	178	2	no	—
327	D₄	—	178	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	356	2	no	—
334	C₂×C₄	—	356	4	no	—
335	C₂×C₄	—	356	2	no	—
336	C₂×C₄	—	356	2	no	—
337	C₂×C₄	—	178	2	no	—
338	C₂×C₄	#15667972	1	1	yes	characteristic
339	C₂×C₄	#15667972	1	1	yes	characteristic
340	C₂×C₄	#15667972	1	1	yes	characteristic
341	C₂×C₄	C₂×#13083557	1	2	yes	—
342	C₂×C₄	#15668020	1	2	yes	—
343	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
344	C₂×C₄	#15668035	1	2	yes	—
345	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	89	4	no	—
351	C₈	—	356	2	no	—
352	C₈	—	178	2	no	—
353	C₈	—	178	2	no	—
354	C₈	—	178	2	no	—
355	C₂²	—	356	2	no	—
356	C₂²	—	356	2	no	—
357	C₂²	—	356	2	no	—
358	C₂²	—	712	4	no	—
359	C₂²	#19151666	1	2	yes	—
360	C₂²	#19151683	1	2	yes	—
361	C₂²	#19151717	1	2	yes	—
362	C₂²	C₂×#15667972	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	356	2	no	—
368	C₄	#19151666	1	2	yes	—
369	C₄	#19151683	1	2	yes	—
370	C₄	C₂²×#13083557	1	1	yes	characteristic
371	C₄	C₂×#15668020	1	1	yes	characteristic
372	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
373	C₄	C₂×#15668035	1	1	yes	characteristic
374	C₂	—	712	2	no	—
375	C₂	#26019092	1	4	yes	direct product factor
376	C₂	C₂×#19151666	1	1	yes	characteristic
377	C₂	C₂×#19151683	1	1	yes	characteristic
378	C₂	C₂×#19151717	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×Q₈⋊C₈×C₈₉	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂²×D₃₅₆	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₈₉
hypocenter	C₈₉	C₂×#1583
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×#10623494	C₂	semidirect
4. #26019092	C₂	direct (N × H)
5. C₂×#19151348	C₂	semidirect
7. C₂×#19151320	C₂	semidirect
8. C₂×Q₈⋊C₈×C₈₉	C₂	semidirect
13. Q₈×#10623494	C₂²	semidirect
27. #19151348	C₂²	semidirect
29. #19151320	C₂²	semidirect
33. Q₈⋊C₈×C₈₉	C₂²	semidirect
95. C₂×#10623494	SD₁₆	semidirect
106. C₂×Q₈×C₈₉	M₁₆	semidirect
134. Q₈×C₈₉	C₂×M₁₆	semidirect
164. #10623494	C₂×SD₁₆	semidirect
185. C₂×C₈₉	#1583	semidirect
195. C₂×Q₈⋊C₈	D₈₉	semidirect
198. C₈₉	C₂×#1583	semidirect
221. Q₈⋊C₈	C₂×D₈₉	semidirect
271. C₂×Q₈	#13083557	semidirect
324. Q₈	C₂×#13083557	semidirect
375. C₂	#26019092	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×Q₈×#10623494	2
C₂×C₄×#13083561	2
C₂×#19151675	2
#26019092	2
C₂×#19151348	2
C₂×#19151327	2
C₂×#19151320	2
C₂×Q₈⋊C₈×C₈₉	2
C₂×#1583	89

Subgroups — C2×#26019092 #36523929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26019092 #36523929