Subgroups — C₂×#26018091 #36443951

Order 22784.

974 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#10623494	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	#26018091	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂³×#10623494	—	2	1	no	—
6	C₂²×C₄⋊Dic₈₉	C₄	1	2	yes	—
7	C₂²×C₄×Dic₈₉	—	2	1	no	—
8	C₂×C₄×#10623494	—	2	2	no	—
9	C₂×C₄×#10623494	—	2	1	no	—
10	C₂×C₄×#10623494	C₄	1	4	yes	complemented
11	C₂×C₄×#10623494	C₂²	1	2	yes	—
12	C₄×C₄⋊Dic₈₉	—	2	1	no	—
13	C₄×C₄⋊Dic₈₉	—	2	1	no	—
14	C₄×C₄⋊Dic₈₉	C₄	1	2	yes	—
15	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
16	C₂×#15667919	—	2	1	no	—
17	C₂³×C₈×C₈₉	—	2	1	no	—
18	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
20	C₂×C₄⋊C₈×C₈₉	—	2	2	no	—
21	C₂×C₄⋊C₈×C₈₉	C₄	1	4	yes	complemented
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
23	C₂³×Dic₈₉	—	2	2	no	—
24	C₂²×#10623494	—	2	8	no	—
25	C₂²×#10623494	—	2	4	no	—
26	C₂²×#10623494	—	2	2	no	—
27	C₂×C₄⋊Dic₈₉	—	2	2	no	—
28	C₂×C₄⋊Dic₈₉	—	2	4	no	—
29	C₂×C₄⋊Dic₈₉	C₈	1	8	yes	complemented
30	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
31	C₂×C₄×Dic₈₉	—	2	2	no	—
32	C₂×C₄×Dic₈₉	—	2	2	no	—
33	C₂×C₄×Dic₈₉	—	4	2	no	—
34	C₂×C₄×Dic₈₉	—	4	2	no	—
35	C₄×#10623494	—	2	4	no	—
36	C₄×#10623494	—	2	2	no	—
37	C₄×#10623494	C₂×C₄	1	4	yes	complemented
38	#15667919	—	2	2	no	—
39	#15667919	—	2	2	no	—
40	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₈₉	—	2	4	no	—
44	C₂²×C₈×C₈₉	—	2	2	no	—
45	C₂²×C₈×C₈₉	—	4	2	no	—
46	C₂²×C₈×C₈₉	—	4	2	no	—
47	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	D₄	1	2	yes	—
53	C₂×C₄²×C₈₉	Q₈	1	2	yes	—
54	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₈×C₈₉	—	2	4	no	—
56	C₄⋊C₈×C₈₉	—	2	2	no	—
57	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
58	C₂²×Dic₈₉	—	2	8	no	—
59	C₂²×Dic₈₉	—	2	4	no	—
60	C₂²×Dic₈₉	—	4	4	no	—
61	C₂²×Dic₈₉	—	4	4	no	—
62	C₂×#10623494	—	2	16	no	—
63	C₂×#10623494	—	2	8	no	—
64	C₂×#10623494	—	2	4	no	—
65	C₄⋊Dic₈₉	—	2	8	no	—
66	C₄⋊Dic₈₉	—	2	4	no	—
67	C₄⋊Dic₈₉	C₂×C₈	1	8	yes	complemented
68	C₄×Dic₈₉	—	4	4	no	—
69	C₄×Dic₈₉	—	4	2	no	—
70	C₄×Dic₈₉	—	4	2	no	—
71	C₂⁴×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₈₉	—	2	4	no	—
73	C₂²×C₄×C₈₉	C₄²	1	2	yes	—
74	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₈₉	C₄⋊C₄	1	2	yes	—
82	C₂²×C₄×C₈₉	C₂×C₈	1	4	yes	—
83	C₂²×C₄×C₈₉	M₁₆	1	4	yes	—
84	C₂²×C₄×C₈₉	D₈	1	2	yes	—
85	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
86	C₂²×C₄×C₈₉	SD₁₆	1	2	yes	—
87	C₂²×C₄×C₈₉	Q₁₆	1	2	yes	—
88	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂×C₈×C₈₉	—	2	4	no	—
92	C₂×C₈×C₈₉	—	4	8	no	—
93	C₂×C₈×C₈₉	—	4	2	no	—
94	C₂×C₈×C₈₉	—	4	2	no	—
95	C₄²×C₈₉	C₄²	1	2	yes	—
96	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
97	C₄²×C₈₉	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
99	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
100	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
101	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
105	C₂³×C₈₉	#95	1	2	yes	—
106	C₂³×C₈₉	C₂²⋊C₈	1	4	yes	—
107	C₂³×C₈₉	#102	1	2	yes	—
108	C₂³×C₈₉	#103	1	2	yes	—
109	C₂³×C₈₉	#104	1	4	yes	—
110	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₈₉	—	2	4	no	—
112	C₂×C₄×C₈₉	—	2	4	no	—
113	C₂×C₄×C₈₉	—	2	2	no	—
114	C₂×C₄×C₈₉	—	2	2	no	—
115	C₂×C₄×C₈₉	#95	1	2	yes	—
116	C₂×C₄×C₈₉	#95	1	2	yes	—
117	C₂×C₄×C₈₉	#95	1	2	yes	—
118	C₂×C₄×C₈₉	C₄×C₈	1	4	yes	—
119	C₂×C₄×C₈₉	#97	1	4	yes	—
120	C₂×C₄×C₈₉	C₂²⋊C₈	1	4	yes	—
121	C₂×C₄×C₈₉	#102	1	2	yes	—
122	C₂×C₄×C₈₉	#102	1	4	yes	—
123	C₂×C₄×C₈₉	#103	1	2	yes	—
124	C₂×C₄×C₈₉	#103	1	4	yes	—
125	C₂×C₄×C₈₉	C₄⋊C₈	1	8	yes	—
126	C₂×C₄×C₈₉	#106	1	4	yes	—
127	C₂×C₄×C₈₉	#107	1	4	yes	—
128	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
129	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
136	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
140	C₂×Dic₈₉	—	2	8	no	—
141	C₂×Dic₈₉	—	4	16	no	—
142	C₂×Dic₈₉	—	4	4	no	—
143	C₂×Dic₈₉	—	4	4	no	—
144	C₈×C₈₉	—	4	4	no	—
145	#10623494	—	2	8	no	—
146	C₂²×C₈₉	D₄⋊C₈	1	8	yes	—
147	C₂²×C₈₉	Q₈⋊C₈	1	8	yes	—
148	C₂²×C₈₉	#336	1	4	yes	—
149	C₂²×C₈₉	#339	1	4	yes	—
150	C₂²×C₈₉	#340	1	4	yes	—
151	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
152	C₂²×C₈₉	C₂×C₂²⋊C₈	1	2	yes	—
153	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
154	C₂²×C₈₉	C₂×#103	1	1	yes	characteristic
155	C₂²×C₈₉	C₂×#104	1	2	yes	—
156	C₄×C₈₉	—	2	1	no	—
157	C₄×C₈₉	—	2	2	no	—
158	C₄×C₈₉	—	2	1	no	—
159	C₄×C₈₉	#336	1	4	yes	—
160	C₄×C₈₉	#340	1	4	yes	—
161	C₄×C₈₉	C₂×C₄×C₈	1	1	yes	characteristic
162	C₄×C₈₉	C₂×#97	1	1	yes	characteristic
163	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
164	C₄×C₈₉	C₂×#103	1	1	yes	characteristic
165	C₄×C₈₉	C₂×C₄⋊C₈	1	2	yes	—
166	C₄×C₈₉	C₂×#106	1	1	yes	characteristic
167	C₄×C₈₉	C₂×#107	1	1	yes	characteristic
168	Dic₈₉	—	4	8	no	—
169	C₂×#1279	—	89	1	no	maximal, Sylow
170	C₂×C₈₉	#1279	1	8	yes	complemented
171	C₂×C₈₉	C₂×D₄⋊C₈	1	2	yes	—
172	C₂×C₈₉	C₂×Q₈⋊C₈	1	2	yes	—
173	C₂×C₈₉	C₂×#336	1	1	yes	characteristic
174	C₂×C₈₉	C₂×#339	1	1	yes	characteristic
175	C₂×C₈₉	C₂×#340	1	1	yes	characteristic
176	C₂²×C₄⋊C₈	D₈₉	1	1	yes	characteristic
177	C₂²×C₄×C₈	—	89	1	no	—
178	C₂×C₄×C₄⋊C₄	—	89	1	no	—
179	#1279	—	89	4	no	—
180	C₈₉	C₂×#1279	1	1	yes	characteristic, complemented, Sylow
181	C₂³×C₈	—	2	1	no	—
182	C₂³×C₈	—	178	1	no	—
183	C₂²×C₄⋊C₄	—	89	2	no	—
184	C₂²×C₄²	—	178	1	no	—
185	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
186	C₂×C₄⋊C₈	—	2	1	no	—
187	C₂×C₄⋊C₈	—	2	2	no	—
188	C₂×C₄⋊C₈	Dic₈₉	1	4	yes	complemented
189	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
190	C₂×C₄×C₈	—	89	4	no	—
191	C₂×C₄×C₈	—	89	2	no	—
192	C₂×C₄×C₈	—	178	1	no	—
193	C₂×C₄×C₈	—	178	2	no	—
194	C₄×C₄⋊C₄	—	89	2	no	—
195	C₄×C₄⋊C₄	—	89	2	no	—
196	C₄×C₄⋊C₄	—	178	1	no	—
197	C₄×C₄⋊C₄	—	178	1	no	—
198	C₂×#95	—	178	1	no	—
199	C₂³×C₄	—	178	2	no	—
200	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
201	C₂³×C₄	D₃₅₆	1	1	yes	characteristic
202	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	—	4	2	no	—
206	C₂²×C₈	—	4	2	no	—
207	C₂²×C₈	—	178	8	no	—
208	C₂²×C₈	—	178	4	no	—
209	C₂²×C₈	—	178	2	no	—
210	C₂×C₄⋊C₄	—	89	8	no	—
211	C₂×C₄⋊C₄	—	89	4	no	—
212	C₂×C₄⋊C₄	—	178	2	no	—
213	C₂×C₄⋊C₄	—	178	4	no	—
214	C₂×C₄²	—	356	2	no	—
215	C₂×C₄²	—	356	2	no	—
216	C₂×C₄²	—	178	2	no	—
217	C₂×C₄²	—	178	2	no	—
218	C₂×C₄²	Dic₁₇₈	1	2	yes	—
219	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₈₉	1	2	yes	—
221	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
222	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
223	C₂×C₄²	C₂²⋊D₈₉	1	2	yes	—
224	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
225	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
226	C₄⋊C₈	—	2	4	no	—
227	C₄⋊C₈	—	2	2	no	—
228	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	complemented
229	C₄×C₈	—	89	4	no	—
230	C₄×C₈	—	178	4	no	—
231	C₄×C₈	—	178	2	no	—
232	#95	—	178	2	no	—
233	#95	—	178	2	no	—
234	C₂⁴	#13083551	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	356	4	no	—
237	C₂²×C₄	—	356	4	no	—
238	C₂²×C₄	—	178	8	no	—
239	C₂²×C₄	—	178	4	no	—
240	C₂²×C₄	C₄×Dic₈₉	1	2	yes	—
241	C₂²×C₄	#13083551	1	1	yes	characteristic
242	C₂²×C₄	#13083551	1	2	yes	—
243	C₂²×C₄	#13083551	1	1	yes	characteristic
244	C₂²×C₄	#13083551	1	1	yes	characteristic
245	C₂²×C₄	C₂²⋊Dic₈₉	1	2	yes	—
246	C₂²×C₄	#13083553	1	2	yes	—
247	C₂²×C₄	#13083553	1	2	yes	—
248	C₂²×C₄	C₄⋊Dic₈₉	1	2	yes	—
249	C₂²×C₄	C₈×D₈₉	1	4	yes	—
250	C₂²×C₄	#13083557	1	4	yes	—
251	C₂²×C₄	#13083559	1	2	yes	—
252	C₂²×C₄	#13083561	1	2	yes	—
253	C₂²×C₄	#13083562	1	2	yes	—
254	C₂²×C₄	#13083564	1	2	yes	—
255	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	4	2	no	—
260	C₂×C₈	—	4	2	no	—
261	C₂×C₈	—	4	8	no	—
262	C₂×C₈	—	178	8	no	—
263	C₂×C₈	—	178	16	no	—
264	C₂×C₈	—	178	4	no	—
265	C₄⋊C₄	—	89	8	no	—
266	C₄⋊C₄	—	178	4	no	—
267	C₄⋊C₄	—	178	8	no	—
268	C₄²	—	356	2	no	—
269	C₄²	—	356	2	no	—
270	C₄²	—	356	4	no	—
271	C₄²	C₄×Dic₈₉	1	2	yes	—
272	C₄²	#13083551	1	2	yes	—
273	C₄²	C₂²⋊Dic₈₉	1	2	yes	—
274	C₄²	#13083553	1	2	yes	—
275	C₄²	#13083553	1	2	yes	—
276	C₄²	C₄⋊Dic₈₉	1	2	yes	—
277	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
278	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
279	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
280	C₄²	C₂×Dic₁₇₈	1	1	yes	characteristic
281	C₂³	#15667919	1	2	yes	—
282	C₂³	#15667924	1	4	yes	—
283	C₂³	#15667932	1	2	yes	—
284	C₂³	#15667935	1	2	yes	—
285	C₂³	#15667938	1	4	yes	—
286	C₂³	C₂×#13083551	1	1	yes	characteristic
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	356	16	no	—
292	C₂×C₄	—	356	4	no	—
293	C₂×C₄	—	356	4	no	—
294	C₂×C₄	—	178	8	no	—
295	C₂×C₄	#15667919	1	2	yes	—
296	C₂×C₄	#15667919	1	2	yes	—
297	C₂×C₄	#15667919	1	2	yes	—
298	C₂×C₄	C₈×Dic₈₉	1	4	yes	—
299	C₂×C₄	#15667922	1	4	yes	—
300	C₂×C₄	#15667924	1	4	yes	—
301	C₂×C₄	#15667932	1	2	yes	—
302	C₂×C₄	#15667933	1	4	yes	—
303	C₂×C₄	#15667935	1	2	yes	—
304	C₂×C₄	#15667936	1	4	yes	—
305	C₂×C₄	#15667941	1	8	yes	—
306	C₂×C₄	#15667943	1	4	yes	—
307	C₂×C₄	#15667945	1	4	yes	—
308	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
309	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
310	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
311	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
312	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
313	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
314	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
315	C₂×C₄	C₂×#13083557	1	2	yes	—
316	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
317	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
318	C₂×C₄	C₂×#13083562	1	1	yes	characteristic
319	C₂×C₄	C₂×#13083564	1	1	yes	characteristic
320	C₈	—	4	4	no	—
321	C₈	—	178	8	no	—
322	C₂²	#19151325	1	8	yes	—
323	C₂²	#19151328	1	8	yes	—
324	C₂²	#19151352	1	4	yes	—
325	C₂²	#19151359	1	4	yes	—
326	C₂²	#19151360	1	4	yes	—
327	C₂²	C₂×#15667919	1	1	yes	characteristic
328	C₂²	C₂×#15667924	1	2	yes	—
329	C₂²	C₂×#15667932	1	1	yes	characteristic
330	C₂²	C₂×#15667935	1	1	yes	characteristic
331	C₂²	C₂×#15667938	1	2	yes	—
332	C₄	—	2	1	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	1	no	—
335	C₄	—	356	8	no	—
336	C₄	#19151352	1	4	yes	—
337	C₄	#19151360	1	4	yes	—
338	C₄	C₂×C₈×Dic₈₉	1	1	yes	characteristic
339	C₄	C₂×#15667922	1	1	yes	characteristic
340	C₄	C₂×#15667933	1	1	yes	characteristic
341	C₄	C₂×#15667936	1	1	yes	characteristic
342	C₄	C₂×#15667941	1	2	yes	—
343	C₄	C₂×#15667943	1	1	yes	characteristic
344	C₄	C₂×#15667945	1	1	yes	characteristic
345	C₂	#26018091	1	8	yes	direct product factor
346	C₂	C₂×#19151325	1	2	yes	—
347	C₂	C₂×#19151328	1	2	yes	—
348	C₂	C₂×#19151352	1	1	yes	characteristic
349	C₂	C₂×#19151359	1	1	yes	characteristic
350	C₂	C₂×#19151360	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₈₉
commutator	C₄×C₈₉	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂²×C₄⋊C₈×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂²×C₄⋊C₈	D₈₉
hypocenter	C₈₉	C₂×#1279
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #26018091	C₂	direct (N × H)
10. C₂×C₄×#10623494	C₄	semidirect
21. C₂×C₄⋊C₈×C₈₉	C₄	semidirect
29. C₂×C₄⋊Dic₈₉	C₈	semidirect
37. C₄×#10623494	C₂×C₄	semidirect
57. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
67. C₄⋊Dic₈₉	C₂×C₈	semidirect
170. C₂×C₈₉	#1279	semidirect
180. C₈₉	C₂×#1279	semidirect
188. C₂×C₄⋊C₈	Dic₈₉	semidirect
228. C₄⋊C₈	C₂×Dic₈₉	semidirect
345. C₂	#26018091	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×#10623494	2
C₂×C₄×C₄⋊Dic₈₉	2
#26018091	2
C₂²×C₄⋊C₈×C₈₉	2
C₂×#1279	89

Subgroups — C2×#26018091 #36443951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26018091 #36443951