Subgroups — D₄×#15667946 #36572546

Order 22784.

1126 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667946	C₂	1	2	yes	maximal, complemented
2	D₄×C₄⋊Dic₈₉	C₂	1	2	yes	maximal
3	#26021011	C₂	1	2	yes	maximal, complemented
4	#26020442	C₂	1	4	yes	maximal, complemented
5	#26020412	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020281	C₂	1	2	yes	maximal, complemented
7	C₄×#15667946	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂×D₄×Dic₈₉	—	2	2	no	—
10	C₂²×C₄⋊Dic₈₉	C₂²	1	4	yes	—
11	C₂×#15667946	—	2	8	no	—
12	C₂×#15667946	C₂²	1	2	yes	—
13	C₂×#15667946	C₂²	1	4	yes	—
14	C₂×#15667946	C₂²	1	1	yes	characteristic
15	C₂×#15667946	C₂²	1	2	yes	—
16	C₂×#15667946	C₂²	1	1	yes	characteristic
17	#19151497	—	2	2	no	—
18	#19151473	—	2	4	no	—
19	#19151468	C₂²	1	2	yes	—
20	#19151458	C₂²	1	4	yes	—
21	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
22	#19151361	C₂²	1	2	yes	—
23	#19151361	C₂²	1	4	yes	—
24	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₈×D₄×C₈₉	C₄	1	8	yes	complemented
27	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂³×Dic₈₉	—	2	4	no	—
31	D₄×Dic₈₉	—	4	8	no	—
32	C₂×C₄⋊Dic₈₉	—	2	8	no	—
33	C₂×C₄⋊Dic₈₉	—	2	2	no	—
34	C₂×C₄⋊Dic₈₉	—	2	4	no	—
35	C₂×C₄⋊Dic₈₉	—	2	2	no	—
36	C₂×C₄⋊Dic₈₉	—	4	4	no	—
37	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
38	C₂×C₄⋊Dic₈₉	C₂³	1	4	yes	—
39	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
40	C₂×C₂²⋊Dic₈₉	—	2	4	no	—
41	C₂×C₄×Dic₈₉	—	2	2	no	—
42	#15667946	—	2	8	no	—
43	#15667946	—	2	4	no	—
44	#15667946	—	2	2	no	—
45	#15667946	—	4	2	no	—
46	#15667946	D₄	1	4	yes	direct product factor
47	#15667919	—	2	2	no	—
48	#15667919	—	2	4	no	—
49	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₈₉	—	2	4	no	—
52	C₂²×C₈×C₈₉	—	2	4	no	—
53	C₂²×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
54	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
58	C₄×D₄×C₈₉	Q₈	1	4	yes	—
59	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
61	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	complemented
63	C₂²⋊C₈×C₈₉	C₂×C₄	1	8	yes	complemented
64	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
65	C₂²×Dic₈₉	—	2	2	no	—
66	C₂²×Dic₈₉	—	2	4	no	—
67	C₂²×Dic₈₉	—	2	2	no	—
68	C₂²×Dic₈₉	—	4	8	no	—
69	C₂²×Dic₈₉	—	4	8	no	—
70	C₂²×Dic₈₉	—	8	4	no	—
71	C₄⋊Dic₈₉	—	2	2	no	—
72	C₄⋊Dic₈₉	—	2	4	no	—
73	C₄⋊Dic₈₉	—	2	2	no	—
74	C₄⋊Dic₈₉	—	2	4	no	—
75	C₄⋊Dic₈₉	—	2	2	no	—
76	C₄⋊Dic₈₉	—	4	8	no	—
77	C₄⋊Dic₈₉	—	4	4	no	—
78	C₄⋊Dic₈₉	—	8	2	no	—
79	C₄⋊Dic₈₉	C₂×D₄	1	4	yes	—
80	C₂²⋊Dic₈₉	—	4	8	no	—
81	C₄×Dic₈₉	—	4	4	no	—
82	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
83	C₂×D₄×C₈₉	C₄⋊C₄	1	4	yes	—
84	C₂×D₄×C₈₉	D₈	1	4	yes	—
85	C₂×D₄×C₈₉	Q₁₆	1	4	yes	—
86	C₂²×C₄×C₈₉	—	2	2	no	—
87	C₂²×C₄×C₈₉	—	2	2	no	—
88	C₂²×C₄×C₈₉	—	2	2	no	—
89	C₂²×C₄×C₈₉	—	2	2	no	—
90	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₈₉	—	2	2	no	—
97	C₂×C₈×C₈₉	—	2	2	no	—
98	C₂×C₈×C₈₉	—	2	1	no	—
99	C₂×C₈×C₈₉	—	2	1	no	—
100	C₂×C₈×C₈₉	—	2	16	no	—
101	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₈₉	#41	1	2	yes	—
106	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
107	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	8	yes	—
108	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
109	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
110	C₂³×C₈₉	—	2	2	no	—
111	C₂³×C₈₉	—	2	2	no	—
112	C₂³×C₈₉	—	2	2	no	—
113	C₂³×C₈₉	—	2	2	no	—
114	C₂³×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
115	C₂³×C₈₉	C₂×D₈	1	4	yes	—
116	C₂³×C₈₉	C₂×Q₁₆	1	4	yes	—
117	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
118	D₄×C₈₉	#107	1	16	yes	complemented
119	C₂×C₄×C₈₉	—	2	2	no	—
120	C₂×C₄×C₈₉	—	2	2	no	—
121	C₂×C₄×C₈₉	—	2	1	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	4	no	—
124	C₂×C₄×C₈₉	—	2	4	no	—
125	C₂×C₄×C₈₉	—	2	4	no	—
126	C₂×C₄×C₈₉	—	2	4	no	—
127	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
129	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
131	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
132	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
136	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
137	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
138	C₂×Dic₈₉	—	2	4	no	—
139	C₂×Dic₈₉	—	4	2	no	—
140	C₂×Dic₈₉	—	4	2	no	—
141	C₂×Dic₈₉	—	4	4	no	—
142	C₂×Dic₈₉	—	4	2	no	—
143	C₂×Dic₈₉	—	4	2	no	—
144	C₂×Dic₈₉	—	4	4	no	—
145	C₂×Dic₈₉	—	4	4	no	—
146	C₂×Dic₈₉	—	4	2	no	—
147	C₂×Dic₈₉	—	8	16	no	—
148	C₈×C₈₉	—	2	4	no	—
149	C₈×C₈₉	—	2	2	no	—
150	C₈×C₈₉	C₄×D₄	1	4	yes	complemented
151	C₂²×C₈₉	—	2	4	no	—
152	C₂²×C₈₉	—	2	4	no	—
153	C₂²×C₈₉	—	2	4	no	—
154	C₂²×C₈₉	—	2	4	no	—
155	C₂²×C₈₉	—	2	4	no	—
156	C₂²×C₈₉	—	2	4	no	—
157	C₂²×C₈₉	C₂×#107	1	8	yes	complemented
158	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
159	C₂²×C₈₉	D₄²	1	1	yes	characteristic
160	C₂²×C₈₉	#547	1	1	yes	characteristic
161	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
162	C₂²×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
163	C₂²×C₈₉	#576	1	1	yes	characteristic
164	C₂²×C₈₉	#578	1	1	yes	characteristic
165	C₄×C₈₉	—	2	4	no	—
166	C₄×C₈₉	—	2	2	no	—
167	C₄×C₈₉	C₂×#107	1	4	yes	complemented
168	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₈₉	#520	1	1	yes	characteristic
170	C₄×C₈₉	D₄×Q₈	1	1	yes	characteristic
171	C₄×C₈₉	#554	1	1	yes	characteristic
172	Dic₈₉	—	4	4	no	—
173	Dic₈₉	—	8	2	no	—
174	Dic₈₉	—	8	4	no	—
175	D₄×#107	—	89	1	no	maximal, Sylow
176	C₂×C₈₉	—	2	8	no	—
177	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₈₉	C₂²×#107	1	1	yes	characteristic
179	C₂×C₈₉	#2913	1	1	yes	characteristic
180	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
181	C₂×C₈₉	D₄×Q₁₆	1	1	yes	characteristic
182	C₂×C₈₉	#3334	1	1	yes	characteristic
183	C₂×C₈₉	#3338	1	1	yes	characteristic
184	C₂×C₈×D₄	D₈₉	1	1	yes	characteristic
185	C₂²×#107	—	89	2	no	—
186	D₄×C₄⋊C₄	—	89	2	no	—
187	#1947	—	89	2	no	—
188	#1852	—	89	4	no	—
189	#1845	—	89	1	no	—
190	#1808	—	89	2	no	—
191	C₄×#107	—	89	1	no	—
192	C₈₉	D₄×#107	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₈	C₂×D₈₉	1	2	yes	—
194	C₂×C₄×D₄	—	178	2	no	—
195	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
196	C₂²×C₄⋊C₄	—	89	4	no	—
197	C₈×D₄	Dic₈₉	1	8	yes	complemented
198	C₂×#107	—	89	1	no	—
199	C₂×#107	—	89	2	no	—
200	C₂×#107	—	89	1	no	—
201	C₂×#107	—	89	2	no	—
202	C₂×#107	—	89	4	no	—
203	C₂×#107	—	178	8	no	—
204	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂×D₈₉	1	2	yes	—
206	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
207	#389	—	178	2	no	—
208	#385	—	178	4	no	—
209	#384	—	89	2	no	—
210	#380	—	89	4	no	—
211	C₄×C₄⋊C₄	—	89	2	no	—
212	#340	—	89	4	no	—
213	#340	—	89	2	no	—
214	C₂²×D₄	D₃₅₆	1	1	yes	characteristic
215	C₂³×C₄	—	178	4	no	—
216	C₂³×C₄	C₂²×D₈₉	1	2	yes	—
217	C₂²×C₈	—	2	4	no	—
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	C₂×Dic₈₉	1	8	yes	complemented
220	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
221	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
222	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
223	C₄×D₄	—	356	8	no	—
224	C₄×D₄	Dic₁₇₈	1	4	yes	—
225	C₄×D₄	C₂×Dic₈₉	1	4	yes	—
226	C₂×C₄⋊C₄	—	89	2	no	—
227	C₂×C₄⋊C₄	—	89	4	no	—
228	C₂×C₄⋊C₄	—	89	2	no	—
229	C₂×C₄⋊C₄	—	356	4	no	—
230	C₂×C₄⋊C₄	—	178	8	no	—
231	C₂×C₄⋊C₄	—	178	4	no	—
232	C₂×C₄⋊C₄	—	178	2	no	—
233	C₂×C₄⋊C₄	—	178	2	no	—
234	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
235	C₂×C₂²⋊C₄	—	178	4	no	—
236	C₂×C₂²⋊C₄	D₃₅₆	1	2	yes	—
237	C₂×C₄²	—	178	2	no	—
238	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
239	#107	—	89	4	no	—
240	#107	—	356	2	no	—
241	#107	—	178	8	no	—
242	#107	—	178	4	no	—
243	#107	—	178	2	no	—
244	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	complemented
245	C₂²⋊C₈	C₂×Dic₈₉	1	8	yes	complemented
246	C₄×C₈	C₂×Dic₈₉	1	4	yes	complemented
247	#95	—	178	2	no	—
248	#95	—	178	4	no	—
249	C₂⁴	C₂×D₃₅₆	1	2	yes	—
250	C₂×D₄	C₄⋊Dic₈₉	1	4	yes	—
251	C₂×D₄	D₇₁₂	1	4	yes	—
252	C₂×D₄	Dic₃₅₆	1	4	yes	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	356	8	no	—
258	C₂²×C₄	—	356	8	no	—
259	C₂²×C₄	—	178	2	no	—
260	C₂²×C₄	—	178	4	no	—
261	C₂²×C₄	—	178	2	no	—
262	C₂²×C₄	—	712	4	no	—
263	C₂²×C₄	C₂²×Dic₈₉	1	4	yes	—
264	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₃₅₆	1	2	yes	—
266	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
267	C₂²×C₄	C₂×Dic₁₇₈	1	4	yes	—
268	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	16	no	—
274	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
275	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
276	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
277	C₂×C₈	D₄×D₈₉	1	2	yes	—
278	C₂×C₈	#13083573	1	2	yes	—
279	C₄⋊C₄	—	89	4	no	—
280	C₄⋊C₄	—	356	8	no	—
281	C₄⋊C₄	—	356	4	no	—
282	C₄⋊C₄	—	178	4	no	—
283	C₄⋊C₄	—	178	2	no	—
284	C₄⋊C₄	—	178	4	no	—
285	C₄⋊C₄	—	178	2	no	—
286	C₄⋊C₄	—	178	2	no	—
287	C₄⋊C₄	—	712	2	no	—
288	C₄⋊C₄	C₄⋊Dic₈₉	1	4	yes	—
289	C₂²⋊C₄	—	356	8	no	—
290	C₂²⋊C₄	C₄⋊Dic₈₉	1	8	yes	—
291	C₄²	—	356	4	no	—
292	C₄²	C₂²×Dic₈₉	1	2	yes	—
293	C₄²	C₂×Dic₁₇₈	1	2	yes	—
294	C₂³	—	2	2	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₄⋊Dic₈₉	1	4	yes	—
299	C₂³	C₂×D₇₁₂	1	4	yes	—
300	C₂³	C₂×Dic₃₅₆	1	4	yes	—
301	C₂³	C₂²×D₃₅₆	1	1	yes	characteristic
302	D₄	#15667946	1	16	yes	direct product factor
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	356	2	no	—
312	C₂×C₄	—	356	2	no	—
313	C₂×C₄	—	356	4	no	—
314	C₂×C₄	—	356	2	no	—
315	C₂×C₄	—	356	4	no	—
316	C₂×C₄	—	356	2	no	—
317	C₂×C₄	—	356	2	no	—
318	C₂×C₄	—	356	4	no	—
319	C₂×C₄	—	178	4	no	—
320	C₂×C₄	—	712	16	no	—
321	C₂×C₄	C₂×C₄⋊Dic₈₉	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
323	C₂×C₄	C₂×C₄⋊Dic₈₉	1	2	yes	—
324	C₂×C₄	C₂×D₇₁₂	1	2	yes	—
325	C₂×C₄	C₂×Dic₃₅₆	1	2	yes	—
326	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
328	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
329	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
330	C₂×C₄	#15668058	1	1	yes	characteristic
331	C₂×C₄	#15668059	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	—	2	2	no	—
334	C₈	D₄×Dic₈₉	1	4	yes	complemented
335	C₂²	—	2	4	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	4	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	C₂×#15667946	1	8	yes	complemented
342	C₂²	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
343	C₂²	D₄×D₃₅₆	1	1	yes	characteristic
344	C₂²	#19152252	1	1	yes	characteristic
345	C₂²	C₂²×D₇₁₂	1	1	yes	characteristic
346	C₂²	C₂²×Dic₃₅₆	1	1	yes	characteristic
347	C₂²	#19152403	1	1	yes	characteristic
348	C₂²	#19152415	1	1	yes	characteristic
349	C₄	—	2	2	no	—
350	C₄	—	2	4	no	—
351	C₄	—	356	4	no	—
352	C₄	—	712	4	no	—
353	C₄	—	712	2	no	—
354	C₄	C₂×#15667946	1	4	yes	complemented
355	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
356	C₄	#19152081	1	1	yes	characteristic
357	C₄	D₄×Dic₁₇₈	1	1	yes	characteristic
358	C₄	#19152305	1	1	yes	characteristic
359	C₂	—	2	8	no	—
360	C₂	D₄×C₄⋊Dic₈₉	1	1	yes	characteristic
361	C₂	C₂²×#15667946	1	1	yes	characteristic
362	C₂	#26028852	1	1	yes	characteristic
363	C₂	D₄×D₇₁₂	1	1	yes	characteristic
364	C₂	D₄×Dic₃₅₆	1	1	yes	characteristic
365	C₂	#26032600	1	1	yes	characteristic
366	C₂	#26032645	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₂×C₈×D₄×C₈₉	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×D₄×C₈₉	D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×C₈×D₄	D₈₉
hypocenter	C₈₉	D₄×#107
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#15667946	C₂	semidirect
3. #26021011	C₂	semidirect
4. #26020442	C₂	semidirect
5. #26020412	C₂	semidirect
6. #26020281	C₂	semidirect
7. C₄×#15667946	C₂	semidirect
26. C₈×D₄×C₈₉	C₄	semidirect
46. #15667946	D₄	direct (N × H)
53. C₂²×C₈×C₈₉	C₂×C₄	semidirect
62. C₄⋊C₈×C₈₉	C₂×C₄	semidirect
63. C₂²⋊C₈×C₈₉	C₂×C₄	semidirect
64. C₄×C₈×C₈₉	C₂×C₄	semidirect
118. D₄×C₈₉	#107	semidirect
150. C₈×C₈₉	C₄×D₄	semidirect
157. C₂²×C₈₉	C₂×#107	semidirect
167. C₄×C₈₉	C₂×#107	semidirect
192. C₈₉	D₄×#107	semidirect
197. C₈×D₄	Dic₈₉	semidirect
219. C₂²×C₈	C₂×Dic₈₉	semidirect
244. C₄⋊C₈	C₂×Dic₈₉	semidirect
245. C₂²⋊C₈	C₂×Dic₈₉	semidirect
246. C₄×C₈	C₂×Dic₈₉	semidirect
302. D₄	#15667946	direct (N × H)
334. C₈	D₄×Dic₈₉	semidirect
341. C₂²	C₂×#15667946	semidirect
354. C₄	C₂×#15667946	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15667946	2
D₄×C₄⋊Dic₈₉	2
#26021011	2
#26020442	2
#26020412	2
#26020281	2
C₄×#15667946	2
C₂×C₈×D₄×C₈₉	2
D₄×#107	89

Subgroups — D4×#15667946 #36572546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#15667946 #36572546