Subgroups — C₂×#26019003 #36523406

Order 22784.

834 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151650	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#13083557	C₂	1	1	yes	maximal, characteristic
4	#26019003	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151350	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#19151349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151348	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#335×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#13083557	C₄	1	1	yes	characteristic
10	C₂²×#13083557	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₈₉	—	2	1	no	—
12	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
13	#19151650	—	2	2	no	—
14	#19151650	C₂²	1	4	yes	—
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
17	C₂×#15667941	—	2	1	no	—
18	C₄⋊C₈×D₈₉	—	2	2	no	—
19	C₄⋊C₈×D₈₉	C₂²	1	4	yes	—
20	C₂×#15667924	—	2	1	no	—
21	C₄×#13083557	C₄	1	4	yes	—
22	C₄×#13083557	C₂²	1	4	yes	—
23	C₂×#15667922	C₄	1	1	yes	characteristic
24	C₂×#15667922	C₄	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₈₉	—	2	1	no	—
27	#19151350	C₂²	1	4	yes	complemented
28	#19151349	C₂²	1	4	yes	complemented
29	#19151348	C₂²	1	4	yes	complemented
30	C₂×C₄⋊C₈×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	#335×C₈₉	C₂²	1	4	yes	complemented
34	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
37	C₂×#13083557	—	2	4	no	—
38	C₂×#13083557	C₈	1	8	yes	complemented
39	C₂×#13083557	C₂×C₄	1	4	yes	—
40	C₂×#13083557	C₂×C₄	1	4	yes	—
41	C₂²×#10623494	—	2	1	no	—
42	C₂²×#10623494	—	2	1	no	—
43	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
44	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₈₉	—	2	4	no	—
46	C₂×C₈×D₈₉	—	4	4	no	—
47	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
50	C₄²×D₈₉	C₂×C₄	1	2	yes	—
51	C₄²×D₈₉	D₄	1	2	yes	—
52	C₄²×D₈₉	Q₈	1	2	yes	—
53	C₄²×D₈₉	C₂³	1	2	yes	—
54	C₄⋊#10623494	—	2	1	no	—
55	C₄⋊#10623494	—	2	1	no	—
56	C₄⋊#10623494	C₂³	1	2	yes	—
57	C₄⋊#10623494	C₂³	1	2	yes	—
58	#15667941	—	2	4	no	—
59	#15667924	—	2	4	no	—
60	#15667922	C₂×C₄	1	4	yes	—
61	#15667922	C₂×C₄	1	4	yes	—
62	C₄×#10623494	C₂×C₄	1	2	yes	—
63	C₄×#10623494	C₂³	1	2	yes	—
64	C₈×Dic₈₉	—	2	4	no	—
65	C₂²×C₈×C₈₉	—	2	1	no	—
66	C₂²×C₈×C₈₉	—	2	1	no	—
67	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₈₉	—	2	1	no	—
71	C₄⋊C₈×C₈₉	—	2	1	no	—
72	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
73	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
74	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
75	C₄×C₈×C₈₉	C₂³	1	2	yes	—
76	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₈₉	—	2	2	no	—
81	C₂×C₄×D₈₉	—	2	2	no	—
82	C₂×C₄×D₈₉	—	4	2	no	—
83	C₂×C₄×D₈₉	C₄⋊C₄	1	2	yes	—
84	C₂×C₄×D₈₉	C₄⋊C₄	1	2	yes	—
85	C₂×C₄×D₈₉	C₄⋊C₄	1	2	yes	—
86	C₂×C₄×D₈₉	C₂×C₈	1	4	yes	—
87	C₂×C₄×D₈₉	M₁₆	1	4	yes	—
88	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
90	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
91	#13083557	—	2	8	no	—
92	#13083557	C₂×C₈	1	16	yes	complemented
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	4	2	no	—
97	C₂×#10623494	—	4	2	no	—
98	C₂×#10623494	C₂×C₈	1	4	yes	complemented
99	C₂×#10623494	C₂²×C₄	1	2	yes	—
100	C₂×#10623494	C₂²×C₄	1	2	yes	—
101	C₈×D₈₉	—	4	8	no	—
102	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
103	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
104	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
105	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
106	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
107	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₈×C₈₉	—	2	2	no	—
112	C₂×C₈×C₈₉	—	2	2	no	—
113	C₂×C₈×C₈₉	—	2	2	no	—
114	C₂×C₈×C₈₉	—	4	2	no	—
115	C₂×C₈×C₈₉	—	4	2	no	—
116	C₂×C₈×C₈₉	C₂×C₈	1	4	yes	complemented
117	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
119	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
123	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₈₉	—	2	2	no	—
125	C₂²×D₈₉	—	2	2	no	—
126	C₂²×D₈₉	C₄⋊C₈	1	4	yes	—
127	C₂²×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
134	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₈₉	#137	1	2	yes	—
136	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
139	C₂×Dic₈₉	—	2	2	no	—
140	C₂×Dic₈₉	—	2	2	no	—
141	C₂×Dic₈₉	C₄⋊C₈	1	4	yes	—
142	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
145	C₄×D₈₉	—	2	2	no	—
146	C₄×D₈₉	—	2	2	no	—
147	C₄×D₈₉	—	2	4	no	—
148	C₄×D₈₉	—	4	2	no	—
149	C₄×D₈₉	—	4	2	no	—
150	C₄×D₈₉	C₄⋊C₈	1	8	yes	—
151	C₄×D₈₉	C₂²×C₈	1	4	yes	—
152	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
153	C₈×C₈₉	—	2	2	no	—
154	C₈×C₈₉	—	4	2	no	—
155	C₈×C₈₉	—	4	2	no	—
156	C₈×C₈₉	C₂²×C₈	1	4	yes	complemented
157	#10623494	—	2	2	no	—
158	#10623494	—	4	2	no	—
159	#10623494	—	4	2	no	—
160	#10623494	C₂²×C₈	1	4	yes	complemented
161	C₂²×C₈₉	C₂×C₄⋊C₈	1	2	yes	—
162	C₂²×C₈₉	#428	1	2	yes	—
163	C₂²×C₈₉	#430	1	2	yes	—
164	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂×D₈₉	—	2	8	no	—
166	C₂×D₈₉	—	2	2	no	—
167	C₂×D₈₉	—	2	2	no	—
168	C₂×D₈₉	C₂×C₄⋊C₈	1	4	yes	—
169	C₄×C₈₉	—	2	1	no	—
170	C₄×C₈₉	—	2	1	no	—
171	C₄×C₈₉	C₂×C₄⋊C₈	1	2	yes	—
172	C₄×C₈₉	#428	1	2	yes	—
173	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
174	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
175	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
176	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
177	Dic₈₉	—	2	2	no	—
178	Dic₈₉	—	2	2	no	—
179	Dic₈₉	C₂×C₄⋊C₈	1	4	yes	—
180	C₂×#1565	—	89	1	no	maximal, Sylow
181	C₂×C₈₉	#1565	1	4	yes	complemented
182	C₂×C₈₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
183	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
184	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
185	D₈₉	—	2	4	no	—
186	C₂×#431	—	89	1	no	—
187	C₂²×C₄⋊C₈	—	89	1	no	—
188	C₂×C₄×M₁₆	—	89	1	no	—
189	#1565	—	89	8	no	—
190	C₂×#335	—	89	1	no	—
191	C₂×#335	D₈₉	1	1	yes	characteristic, complemented
192	C₂×#334	—	89	1	no	—
193	C₂×#334	—	89	1	no	—
194	C₈₉	C₂×#1565	1	1	yes	characteristic, complemented, Sylow
195	C₂²×M₁₆	—	89	1	no	—
196	C₂²×M₁₆	—	89	1	no	—
197	C₂³×C₈	—	178	1	no	—
198	C₂²×C₄²	—	89	1	no	—
199	#431	—	89	4	no	—
200	#431	—	178	2	no	—
201	C₂×C₄⋊C₈	—	89	1	no	—
202	C₂×C₄⋊C₈	—	89	1	no	—
203	C₂×C₄⋊C₈	—	89	4	no	—
204	C₂×C₄⋊C₈	—	178	2	no	—
205	C₂×C₄⋊C₈	—	178	1	no	—
206	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
208	C₂×C₂²⋊C₈	—	178	1	no	—
209	C₄×M₁₆	—	89	4	no	—
210	C₄×M₁₆	—	89	4	no	—
211	C₂×#97	—	89	1	no	—
212	C₂×#97	—	89	1	no	—
213	C₂×C₄×C₈	—	89	1	no	—
214	C₂×C₄×C₈	—	178	1	no	—
215	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
216	#335	—	89	4	no	—
217	#335	C₂×D₈₉	1	4	yes	complemented
218	#334	—	89	4	no	—
219	#334	—	89	4	no	—
220	C₂³×C₄	—	89	1	no	—
221	C₂³×C₄	—	89	1	no	—
222	C₂³×C₄	—	89	1	no	—
223	C₂×M₁₆	—	89	8	no	—
224	C₂×M₁₆	—	89	4	no	—
225	C₂×M₁₆	—	89	4	no	—
226	C₂×M₁₆	—	178	4	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	89	1	no	—
230	C₂²×C₈	—	89	1	no	—
231	C₂²×C₈	—	356	4	no	—
232	C₂²×C₈	—	178	4	no	—
233	C₂²×C₈	—	178	1	no	—
234	C₂²×C₈	—	178	1	no	—
235	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
237	C₂×C₄²	—	89	1	no	—
238	C₂×C₄²	—	89	1	no	—
239	C₂×C₄²	—	89	1	no	—
240	C₂×C₄²	—	89	2	no	—
241	C₂×C₄²	—	89	2	no	—
242	C₂×C₄²	—	89	2	no	—
243	C₂×C₄²	—	89	2	no	—
244	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
245	C₄⋊C₈	—	2	1	no	—
246	C₄⋊C₈	—	2	1	no	—
247	C₄⋊C₈	—	89	2	no	—
248	C₄⋊C₈	—	89	2	no	—
249	C₄⋊C₈	—	178	4	no	—
250	C₄⋊C₈	—	178	1	no	—
251	C₄⋊C₈	—	178	1	no	—
252	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
253	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
254	C₂²⋊C₈	—	178	4	no	—
255	#97	—	89	4	no	—
256	#97	—	89	4	no	—
257	C₄×C₈	—	89	2	no	—
258	C₄×C₈	—	89	2	no	—
259	C₄×C₈	—	178	4	no	—
260	C₄×C₈	C₄×D₈₉	1	2	yes	—
261	C₄×C₈	C₂²×D₈₉	1	2	yes	—
262	C₂⁴	—	89	1	no	—
263	C₂²×C₄	—	89	1	no	—
264	C₂²×C₄	—	89	4	no	—
265	C₂²×C₄	—	89	4	no	—
266	C₂²×C₄	—	89	2	no	—
267	C₂²×C₄	—	89	2	no	—
268	C₂²×C₄	—	89	1	no	—
269	C₂²×C₄	—	89	1	no	—
270	C₂²×C₄	—	89	2	no	—
271	C₂²×C₄	—	89	2	no	—
272	C₂²×C₄	—	89	2	no	—
273	C₂²×C₄	—	89	2	no	—
274	C₂²×C₄	—	356	2	no	—
275	C₂²×C₄	—	178	2	no	—
276	C₂²×C₄	—	178	2	no	—
277	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
278	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
279	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
280	M₁₆	—	89	16	no	—
281	M₁₆	—	178	8	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	2	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	89	4	no	—
288	C₂×C₈	—	89	2	no	—
289	C₂×C₈	—	89	2	no	—
290	C₂×C₈	—	356	8	no	—
291	C₂×C₈	—	356	2	no	—
292	C₂×C₈	—	356	2	no	—
293	C₂×C₈	—	178	2	no	—
294	C₂×C₈	—	178	2	no	—
295	C₂×C₈	—	178	2	no	—
296	C₂×C₈	C₈×D₈₉	1	4	yes	complemented
297	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
298	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
299	C₄²	—	89	2	no	—
300	C₄²	—	89	2	no	—
301	C₄²	—	89	2	no	—
302	C₄²	—	89	2	no	—
303	C₄²	—	89	2	no	—
304	C₄²	—	89	2	no	—
305	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
306	C₄²	D₄×D₈₉	1	1	yes	characteristic
307	C₄²	Q₈×D₈₉	1	1	yes	characteristic
308	C₄²	C₂³×D₈₉	1	1	yes	characteristic
309	C₂³	—	89	4	no	—
310	C₂³	—	89	2	no	—
311	C₂³	—	178	2	no	—
312	C₂³	—	178	2	no	—
313	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	89	4	no	—
316	C₂×C₄	—	89	2	no	—
317	C₂×C₄	—	89	8	no	—
318	C₂×C₄	—	89	4	no	—
319	C₂×C₄	—	89	4	no	—
320	C₂×C₄	—	89	2	no	—
321	C₂×C₄	—	89	2	no	—
322	C₂×C₄	—	356	2	no	—
323	C₂×C₄	—	356	2	no	—
324	C₂×C₄	—	178	2	no	—
325	C₂×C₄	—	178	2	no	—
326	C₂×C₄	—	178	2	no	—
327	C₂×C₄	—	178	4	no	—
328	C₂×C₄	—	178	2	no	—
329	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
330	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
331	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
333	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
334	C₂×C₄	#15668036	1	2	yes	—
335	C₂×C₄	#15668044	1	2	yes	—
336	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
338	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₈	—	89	4	no	—
343	C₈	—	356	2	no	—
344	C₈	—	356	2	no	—
345	C₈	—	178	2	no	—
346	C₈	C₂×C₈×D₈₉	1	4	yes	complemented
347	C₂²	—	89	4	no	—
348	C₂²	—	178	2	no	—
349	C₂²	—	178	2	no	—
350	C₂²	—	178	8	no	—
351	C₂²	C₄⋊C₈×D₈₉	1	2	yes	—
352	C₂²	#19151639	1	2	yes	—
353	C₂²	#19151645	1	2	yes	—
354	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	89	4	no	—
358	C₄	—	178	2	no	—
359	C₄	—	178	2	no	—
360	C₄	C₄⋊C₈×D₈₉	1	2	yes	—
361	C₄	#19151639	1	2	yes	—
362	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
363	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
364	C₄	C₂×#15668036	1	1	yes	characteristic
365	C₄	C₂×#15668044	1	1	yes	characteristic
366	C₂	—	178	4	no	—
367	C₂	#26019003	1	4	yes	direct product factor
368	C₂	C₂×C₄⋊C₈×D₈₉	1	1	yes	characteristic
369	C₂	C₂×#19151639	1	1	yes	characteristic
370	C₂	C₂×#19151645	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#335×C₈₉	C₂
socle	C₂³×C₈₉	C₂×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#335	D₈₉
hypocenter	C₈₉	C₂×#1565
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
4. #26019003	C₂	direct (N × H)
5. C₂×#19151350	C₂	semidirect
6. C₂×#19151349	C₂	semidirect
7. C₂×#19151348	C₂	semidirect
8. C₂×#335×C₈₉	C₂	semidirect
27. #19151350	C₂²	semidirect
28. #19151349	C₂²	semidirect
29. #19151348	C₂²	semidirect
33. #335×C₈₉	C₂²	semidirect
38. C₂×#13083557	C₈	semidirect
92. #13083557	C₂×C₈	semidirect
98. C₂×#10623494	C₂×C₈	semidirect
116. C₂×C₈×C₈₉	C₂×C₈	semidirect
156. C₈×C₈₉	C₂²×C₈	semidirect
160. #10623494	C₂²×C₈	semidirect
181. C₂×C₈₉	#1565	semidirect
191. C₂×#335	D₈₉	semidirect
194. C₈₉	C₂×#1565	semidirect
217. #335	C₂×D₈₉	semidirect
296. C₂×C₈	C₈×D₈₉	semidirect
346. C₈	C₂×C₈×D₈₉	semidirect
367. C₂	#26019003	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×#19151650	2
C₂×C₄⋊C₈×D₈₉	2
C₂×C₄×#13083557	2
#26019003	2
C₂×#19151350	2
C₂×#19151349	2
C₂×#19151348	2
C₂×#335×C₈₉	2
C₂×#1565	89

Subgroups — C2×#26019003 #36523406

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26019003 #36523406