Subgroups — C₂×#26020971 #36557694

Order 22784.

1246 conjugacy classes of subgroups.

The subgroup lattice has 348 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	C₂²×C₄⋊#10623494	C₂	1	2	yes	maximal
3	C₂²×C₄×#10623494	C₂	1	1	yes	maximal, characteristic
4	#26020971	C₂	1	8	yes	maximal, direct product factor
5	C₂×#19151353	C₂	1	2	yes	maximal
6	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
7	C₂³×#10623494	C₂²	1	2	yes	—
8	C₂³×#10623494	C₂²	1	1	yes	characteristic
9	C₂³×#10623494	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#10623494	—	2	4	no	—
11	C₂×C₄⋊#10623494	—	2	8	no	—
12	C₂×C₄⋊#10623494	C₂²	1	4	yes	—
13	C₂×C₄⋊#10623494	C₂²	1	8	yes	—
14	C₂×C₄×#10623494	—	2	4	no	—
15	C₂×C₄×#10623494	C₂²	1	4	yes	—
16	#19151353	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
20	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₈₉	C₄	1	4	yes	—
22	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
23	C₂×#95×C₈₉	C₄	1	2	yes	—
24	C₂²×#10623494	—	2	2	no	—
25	C₂²×#10623494	—	2	2	no	—
26	C₂²×#10623494	—	2	4	no	—
27	C₂²×#10623494	—	2	4	no	—
28	C₂²×#10623494	—	2	2	no	—
29	C₂²×#10623494	—	2	2	no	—
30	C₂²×#10623494	—	2	4	no	—
31	C₂²×#10623494	D₄	1	4	yes	—
32	C₂²×#10623494	Q₈	1	4	yes	—
33	C₂²×#10623494	C₂³	1	4	yes	—
34	C₂²×#10623494	C₂³	1	2	yes	—
35	C₂²×#10623494	C₂³	1	2	yes	—
36	C₄⋊#10623494	—	2	16	no	—
37	C₄⋊#10623494	—	2	8	no	—
38	C₄×#10623494	—	2	8	no	—
39	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₈₉	C₈	1	8	yes	complemented
46	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₈₉	—	2	4	no	—
49	C₂×C₄²×C₈₉	—	2	4	no	—
50	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
51	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₈₉	D₄	1	4	yes	—
53	C₂×C₄²×C₈₉	Q₈	1	4	yes	—
54	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
55	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
56	#95×C₈₉	C₂×C₄	1	8	yes	—
57	C₂×#10623494	—	2	8	no	—
58	C₂×#10623494	—	2	8	no	—
59	C₂×#10623494	—	2	2	no	—
60	C₂×#10623494	—	2	2	no	—
61	C₂×#10623494	—	2	2	no	—
62	C₂×#10623494	—	2	2	no	—
63	C₂×#10623494	—	2	4	no	—
64	C₂×#10623494	—	2	4	no	—
65	C₂×#10623494	—	2	4	no	—
66	C₂×#10623494	—	4	8	no	—
67	C₂×#10623494	C₂×D₄	1	4	yes	—
68	C₂×#10623494	C₂×Q₈	1	4	yes	—
69	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₈₉	—	2	4	no	—
71	C₂²×C₄×C₈₉	—	2	2	no	—
72	C₂²×C₄×C₈₉	—	2	2	no	—
73	C₂²×C₄×C₈₉	—	2	4	no	—
74	C₂²×C₄×C₈₉	—	2	4	no	—
75	C₂²×C₄×C₈₉	—	2	4	no	—
76	C₂²×C₄×C₈₉	—	2	4	no	—
77	C₂²×C₄×C₈₉	C₄⋊C₄	1	4	yes	—
78	C₂²×C₄×C₈₉	C₄⋊C₄	1	4	yes	—
79	C₂²×C₄×C₈₉	C₂×C₈	1	8	yes	—
80	C₂²×C₄×C₈₉	C₂×C₈	1	4	yes	—
81	C₂²×C₄×C₈₉	M₁₆	1	4	yes	—
82	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₈₉	#41	1	2	yes	—
92	C₂²×C₄×C₈₉	#41	1	2	yes	—
93	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
94	C₄⋊C₄×C₈₉	—	2	8	no	—
95	C₄⋊C₄×C₈₉	C₂×C₈	1	16	yes	complemented
96	C₄²×C₈₉	—	2	8	no	—
97	C₄²×C₈₉	—	2	4	no	—
98	C₄²×C₈₉	—	2	4	no	—
99	C₄²×C₈₉	C₄⋊C₄	1	8	yes	—
100	C₄²×C₈₉	C₂×D₄	1	4	yes	—
101	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
102	C₂³×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
103	C₂³×C₈₉	C₄×D₄	1	2	yes	—
104	C₂³×C₈₉	C₄×Q₈	1	2	yes	—
105	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
106	C₂³×C₈₉	C₂×M₁₆	1	2	yes	—
107	C₂³×C₈₉	#131	1	2	yes	—
108	C₂³×C₈₉	#131	1	2	yes	—
109	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
110	C₂×C₄×C₈₉	—	2	4	no	—
111	C₂×C₄×C₈₉	—	2	2	no	—
112	C₂×C₄×C₈₉	—	2	2	no	—
113	C₂×C₄×C₈₉	—	2	4	no	—
114	C₂×C₄×C₈₉	—	2	8	no	—
115	C₂×C₄×C₈₉	—	2	16	no	—
116	C₂×C₄×C₈₉	—	2	4	no	—
117	C₂×C₄×C₈₉	—	2	4	no	—
118	C₂×C₄×C₈₉	—	2	4	no	—
119	C₂×C₄×C₈₉	—	4	8	no	—
120	C₂×C₄×C₈₉	C₄⋊C₈	1	16	yes	complemented
121	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
122	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
124	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
125	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
126	C₂×C₄×C₈₉	#121	1	4	yes	—
127	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
128	C₂×C₄×C₈₉	#125	1	4	yes	—
129	C₂×C₄×C₈₉	C₄⋊Q₈	1	4	yes	—
130	C₂×C₄×C₈₉	C₂²×C₈	1	8	yes	—
131	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
132	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
133	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
136	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
139	#10623494	—	2	4	no	—
140	#10623494	—	2	4	no	—
141	#10623494	—	4	4	no	—
142	C₂²×C₈₉	#389	1	4	yes	—
143	C₂²×C₈₉	C₂×C₄⋊C₈	1	4	yes	—
144	C₂²×C₈₉	#424	1	4	yes	—
145	C₂²×C₈₉	C₈×D₄	1	4	yes	—
146	C₂²×C₈₉	#436	1	4	yes	—
147	C₂²×C₈₉	C₈×Q₈	1	4	yes	—
148	C₂²×C₈₉	#446	1	4	yes	—
149	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
151	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
152	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
153	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
154	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
155	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
156	C₄×C₈₉	—	2	4	no	—
157	C₄×C₈₉	—	2	8	no	—
158	C₄×C₈₉	—	4	4	no	—
159	C₄×C₈₉	#389	1	4	yes	—
160	C₄×C₈₉	C₂×C₄⋊C₈	1	8	yes	complemented
161	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
162	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
163	C₄×C₈₉	C₂×#125	1	1	yes	characteristic
164	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
165	C₂×#1939	—	89	1	no	maximal, Sylow
166	C₂×C₈₉	#1939	1	8	yes	complemented
167	C₂×C₈₉	C₂×#389	1	1	yes	characteristic
168	C₂×C₈₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
169	C₂×C₈₉	C₂×#424	1	1	yes	characteristic
170	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
171	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
172	C₂×C₈₉	C₂×C₈×Q₈	1	1	yes	characteristic
173	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
174	C₂²×C₄⋊C₈	—	89	2	no	—
175	C₂²×C₄⋊C₈	—	89	1	no	—
176	C₂²×C₄×C₈	—	89	1	no	—
177	C₂×C₄×C₄⋊C₄	D₈₉	1	1	yes	characteristic
178	#1939	—	89	8	no	—
179	C₂×#336	—	89	2	no	—
180	C₈₉	C₂×#1939	1	1	yes	characteristic, complemented, Sylow
181	C₂³×C₈	—	89	1	no	—
182	C₂³×C₈	—	89	1	no	—
183	C₂³×C₈	—	89	2	no	—
184	C₂²×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
185	C₂²×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
186	C₂²×C₄²	C₂×D₈₉	1	2	yes	—
187	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
188	C₂×C₄⋊C₈	—	89	8	no	—
189	C₂×C₄⋊C₈	—	89	4	no	—
190	C₂×C₄⋊C₈	—	178	8	no	—
191	C₂×C₄⋊C₈	—	178	4	no	—
192	C₂×C₄×C₈	—	89	4	no	—
193	C₂×C₄×C₈	—	178	4	no	—
194	C₄×C₄⋊C₄	Dic₈₉	1	4	yes	—
195	C₄×C₄⋊C₄	C₂×D₈₉	1	4	yes	—
196	C₂×#95	Dic₈₉	1	2	yes	—
197	#336	—	89	8	no	—
198	C₂³×C₄	C₂×Dic₈₉	1	2	yes	—
199	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
200	C₂³×C₄	C₂×Dic₈₉	1	2	yes	—
201	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
202	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
203	C₂²×C₈	—	89	4	no	—
204	C₂²×C₈	—	89	4	no	—
205	C₂²×C₈	—	89	2	no	—
206	C₂²×C₈	—	89	2	no	—
207	C₂²×C₈	—	89	4	no	—
208	C₂²×C₈	—	178	4	no	—
209	C₂²×C₈	—	178	4	no	—
210	C₂²×C₈	—	178	4	no	—
211	C₂²×C₈	—	178	2	no	—
212	C₂²×C₈	—	178	2	no	—
213	C₂²×C₈	—	178	2	no	—
214	C₂²×C₈	—	178	2	no	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	#10623494	1	8	yes	complemented
217	C₂×C₄⋊C₄	C₂×Dic₈₉	1	4	yes	—
218	C₂×C₄⋊C₄	C₂×Dic₈₉	1	4	yes	—
219	C₂×C₄²	—	2	4	no	—
220	C₂×C₄²	—	2	4	no	—
221	C₂×C₄²	Dic₁₇₈	1	4	yes	—
222	C₂×C₄²	D₃₅₆	1	4	yes	—
223	C₂×C₄²	C₂×Dic₈₉	1	4	yes	—
224	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
225	C₂×C₄²	C₂²×D₈₉	1	4	yes	—
226	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
227	C₄⋊C₈	—	178	16	no	—
228	C₄⋊C₈	—	178	8	no	—
229	C₄×C₈	—	178	8	no	—
230	#95	C₂×Dic₈₉	1	8	yes	—
231	C₂⁴	C₂²×Dic₈₉	1	1	yes	characteristic
232	C₂²×C₄	—	2	4	no	—
233	C₂²×C₄	—	2	2	no	—
234	C₂²×C₄	—	2	2	no	—
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	C₄⋊Dic₈₉	1	4	yes	—
240	C₂²×C₄	C₄⋊Dic₈₉	1	4	yes	—
241	C₂²×C₄	C₂×#10623494	1	8	yes	—
242	C₂²×C₄	C₂×#10623494	1	4	yes	—
243	C₂²×C₄	#13083558	1	4	yes	—
244	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
245	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
246	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
247	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
248	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
249	C₂²×C₄	D₄×D₈₉	1	2	yes	—
250	C₂²×C₄	C₂×D₃₅₆	1	2	yes	—
251	C₂²×C₄	Q₈×D₈₉	1	2	yes	—
252	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
253	C₂²×C₄	#13083573	1	2	yes	—
254	C₂²×C₄	#13083575	1	2	yes	—
255	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
256	C₂×C₈	—	89	4	no	—
257	C₂×C₈	—	89	4	no	—
258	C₂×C₈	—	356	8	no	—
259	C₂×C₈	—	178	4	no	—
260	C₂×C₈	—	178	4	no	—
261	C₂×C₈	—	178	4	no	—
262	C₂×C₈	—	178	8	no	—
263	C₂×C₈	—	178	8	no	—
264	C₂×C₈	—	178	2	no	—
265	C₂×C₈	—	178	2	no	—
266	C₂×C₈	—	178	2	no	—
267	C₂×C₈	—	178	2	no	—
268	C₄⋊C₄	—	2	8	no	—
269	C₄⋊C₄	C₂×#10623494	1	16	yes	complemented
270	C₄²	—	2	8	no	—
271	C₄²	—	2	4	no	—
272	C₄²	—	2	4	no	—
273	C₄²	C₄⋊Dic₈₉	1	8	yes	—
274	C₄²	C₂×D₃₅₆	1	4	yes	—
275	C₄²	C₂×Dic₁₇₈	1	4	yes	—
276	C₂³	C₂×C₄⋊Dic₈₉	1	2	yes	—
277	C₂³	D₄×Dic₈₉	1	2	yes	—
278	C₂³	Q₈×Dic₈₉	1	2	yes	—
279	C₂³	C₂²×#10623494	1	2	yes	—
280	C₂³	C₂×#13083558	1	2	yes	—
281	C₂³	#15668019	1	2	yes	—
282	C₂³	#15668019	1	2	yes	—
283	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
284	C₂×C₄	—	2	8	no	—
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	2	4	no	—
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	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	8	no	—
294	C₂×C₄	C₄⋊#10623494	1	16	yes	complemented
295	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
296	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
297	C₂×C₄	C₂×C₄⋊Dic₈₉	1	2	yes	—
298	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
299	C₂×C₄	Q₈×Dic₈₉	1	2	yes	—
300	C₂×C₄	#15667987	1	4	yes	—
301	C₂×C₄	#15667992	1	4	yes	—
302	C₂×C₄	#15668003	1	4	yes	—
303	C₂×C₄	#15668011	1	4	yes	—
304	C₂×C₄	C₂²×#10623494	1	8	yes	—
305	C₂×C₄	C₂²×#10623494	1	4	yes	—
306	C₂×C₄	C₂×#13083558	1	4	yes	—
307	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
309	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
310	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
311	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
312	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
313	C₈	—	356	4	no	—
314	C₈	—	178	4	no	—
315	C₈	—	178	4	no	—
316	C₂²	#19151497	1	4	yes	—
317	C₂²	C₂×C₄⋊#10623494	1	4	yes	—
318	C₂²	#19151625	1	4	yes	—
319	C₂²	D₄×#10623494	1	4	yes	—
320	C₂²	#19151676	1	4	yes	—
321	C₂²	Q₈×#10623494	1	4	yes	—
322	C₂²	#19151729	1	4	yes	—
323	C₂²	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
324	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
325	C₂²	C₂×Q₈×Dic₈₉	1	1	yes	characteristic
326	C₂²	C₂³×#10623494	1	1	yes	characteristic
327	C₂²	C₂²×#13083558	1	1	yes	characteristic
328	C₂²	C₂×#15668019	1	1	yes	characteristic
329	C₂²	C₂×#15668019	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	8	no	—
332	C₄	—	4	4	no	—
333	C₄	#19151497	1	4	yes	—
334	C₄	C₂×C₄⋊#10623494	1	8	yes	complemented
335	C₄	C₂×#15667987	1	1	yes	characteristic
336	C₄	C₂×#15667992	1	1	yes	characteristic
337	C₄	C₂×#15668003	1	1	yes	characteristic
338	C₄	C₂×#15668011	1	1	yes	characteristic
339	C₂	#26020971	1	8	yes	direct product factor
340	C₂	C₂×#19151497	1	1	yes	characteristic
341	C₂	C₂²×C₄⋊#10623494	1	1	yes	characteristic
342	C₂	C₂×#19151625	1	1	yes	characteristic
343	C₂	C₂×D₄×#10623494	1	1	yes	characteristic
344	C₂	C₂×#19151676	1	1	yes	characteristic
345	C₂	C₂×Q₈×#10623494	1	1	yes	characteristic
346	C₂	C₂×#19151729	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×C₄×C₄⋊C₄×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₈₉
hypocenter	C₈₉	C₂×#1939
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #26020971	C₂	direct (N × H)
45. C₂×C₄⋊C₄×C₈₉	C₈	semidirect
95. C₄⋊C₄×C₈₉	C₂×C₈	semidirect
120. C₂×C₄×C₈₉	C₄⋊C₈	semidirect
160. C₄×C₈₉	C₂×C₄⋊C₈	semidirect
166. C₂×C₈₉	#1939	semidirect
180. C₈₉	C₂×#1939	semidirect
216. C₂×C₄⋊C₄	#10623494	semidirect
269. C₄⋊C₄	C₂×#10623494	semidirect
294. C₂×C₄	C₄⋊#10623494	semidirect
334. C₄	C₂×C₄⋊#10623494	semidirect
339. C₂	#26020971	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
C₂²×C₄×#10623494	2
#26020971	2
C₂×#19151353	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₂×#1939	89

Subgroups — C2×#26020971 #36557694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26020971 #36557694