Subgroups — #36572966

Order 22784.

1108 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#10623494	C₂	1	2	yes	maximal
2	#26020971	C₂	1	2	yes	maximal, complemented
3	#26020432	C₂	1	4	yes	maximal, complemented
4	#26020369	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020232	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#19151353	C₂	1	2	yes	maximal, complemented
8	C₄²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×#10623494	C₂²	1	4	yes	—
10	D₄×#10623494	—	2	8	no	—
11	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
12	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
13	C₂×C₄⋊#10623494	C₂²	1	4	yes	—
14	C₂×C₂²⋊#10623494	C₂²	1	4	yes	—
15	C₂×C₄×#10623494	C₂²	1	2	yes	—
16	#19151353	C₂²	1	1	yes	characteristic
17	#19151353	C₂²	1	1	yes	characteristic
18	#19151353	C₂²	1	2	yes	—
19	#19151353	C₂²	1	2	yes	—
20	#19151353	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₈₉	C₄	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₄	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
29	C₄×C₂²⋊C₄×C₈₉	C₄	1	2	yes	—
30	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
31	C₄³×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×#10623494	—	2	8	no	—
33	C₂²×#10623494	—	2	8	no	—
34	C₂²×#10623494	—	4	4	no	—
35	C₂²×#10623494	C₂³	1	2	yes	—
36	C₂²×#10623494	C₂³	1	4	yes	—
37	C₂²×#10623494	C₂³	1	2	yes	—
38	C₄⋊#10623494	—	2	4	no	—
39	C₄⋊#10623494	—	2	4	no	—
40	C₄⋊#10623494	—	4	4	no	—
41	C₂²⋊#10623494	—	2	8	no	—
42	C₄×#10623494	—	2	4	no	—
43	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
47	C₄×D₄×C₈₉	—	2	4	no	—
48	C₄×D₄×C₈₉	C₈	1	8	yes	complemented
49	C₄×D₄×C₈₉	D₄	1	4	yes	—
50	C₄×D₄×C₈₉	Q₈	1	4	yes	—
51	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₈₉	—	4	4	no	—
58	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
62	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	#95×C₈₉	C₂×C₄	1	2	yes	—
69	#95×C₈₉	C₂×C₄	1	2	yes	—
70	#95×C₈₉	C₂×C₄	1	2	yes	—
71	C₂×#10623494	—	2	2	no	—
72	C₂×#10623494	—	2	2	no	—
73	C₂×#10623494	—	2	4	no	—
74	C₂×#10623494	—	2	2	no	—
75	C₂×#10623494	—	2	4	no	—
76	C₂×#10623494	—	2	2	no	—
77	C₂×#10623494	—	2	4	no	—
78	C₂×#10623494	—	2	2	no	—
79	C₂×#10623494	—	4	16	no	—
80	C₂×#10623494	#41	1	4	yes	—
81	C₂⁴×C₈₉	C₂²×C₄	1	2	yes	—
82	C₂×D₄×C₈₉	C₄⋊C₄	1	4	yes	—
83	C₂×D₄×C₈₉	C₂×C₈	1	4	yes	—
84	C₂×D₄×C₈₉	M₁₆	1	4	yes	—
85	C₂²×C₄×C₈₉	—	2	4	no	—
86	C₂²×C₄×C₈₉	—	2	4	no	—
87	C₂²×C₄×C₈₉	—	2	4	no	—
88	C₂²×C₄×C₈₉	—	2	4	no	—
89	C₂²×C₄×C₈₉	—	4	2	no	—
90	C₂²×C₄×C₈₉	—	4	2	no	—
91	C₂²×C₄×C₈₉	—	4	2	no	—
92	C₂²×C₄×C₈₉	C₂×C₈	1	8	yes	complemented
93	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₈₉	—	2	2	no	—
106	C₄⋊C₄×C₈₉	C₄⋊C₄	1	4	yes	—
107	C₄⋊C₄×C₈₉	C₂×C₈	1	4	yes	complemented
108	C₂²⋊C₄×C₈₉	—	2	4	no	—
109	C₂²⋊C₄×C₈₉	C₄⋊C₄	1	8	yes	—
110	C₂²⋊C₄×C₈₉	C₂×C₈	1	8	yes	complemented
111	C₄²×C₈₉	—	2	2	no	—
112	C₄²×C₈₉	—	2	2	no	—
113	C₄²×C₈₉	—	2	2	no	—
114	C₄²×C₈₉	—	2	2	no	—
115	C₄²×C₈₉	—	2	4	no	—
116	C₄²×C₈₉	—	4	2	no	—
117	C₄²×C₈₉	—	4	2	no	—
118	C₄²×C₈₉	—	4	1	no	—
119	C₄²×C₈₉	C₂×C₈	1	4	yes	complemented
120	C₄²×C₈₉	C₂×D₄	1	2	yes	—
121	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
122	C₂³×C₈₉	—	2	2	no	—
123	C₂³×C₈₉	—	2	2	no	—
124	C₂³×C₈₉	—	2	2	no	—
125	C₂³×C₈₉	—	2	2	no	—
126	C₂³×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
127	C₂³×C₈₉	C₂²×C₈	1	4	yes	—
128	C₂³×C₈₉	C₂×M₁₆	1	4	yes	—
129	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
130	D₄×C₈₉	C₄⋊C₈	1	16	yes	complemented
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	2	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	2	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	2	8	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	4	8	no	—
152	C₂×C₄×C₈₉	—	4	8	no	—
153	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
155	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
157	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
159	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
160	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₈₉	#131	1	2	yes	—
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
165	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
166	#10623494	—	2	4	no	—
167	#10623494	—	4	2	no	—
168	#10623494	—	4	4	no	—
169	C₂²×C₈₉	—	2	4	no	—
170	C₂²×C₈₉	—	2	4	no	—
171	C₂²×C₈₉	—	2	4	no	—
172	C₂²×C₈₉	—	2	4	no	—
173	C₂²×C₈₉	—	2	4	no	—
174	C₂²×C₈₉	—	2	4	no	—
175	C₂²×C₈₉	C₂×C₄⋊C₈	1	8	yes	—
176	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
178	C₂²×C₈₉	#518	1	1	yes	characteristic
179	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
180	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
181	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
182	C₂²×C₈₉	#568	1	1	yes	characteristic
183	C₄×C₈₉	—	2	4	no	—
184	C₄×C₈₉	—	2	2	no	—
185	C₄×C₈₉	—	2	2	no	—
186	C₄×C₈₉	—	2	2	no	—
187	C₄×C₈₉	—	2	4	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	—	4	2	no	—
191	C₄×C₈₉	C₂×C₄⋊C₈	1	4	yes	—
192	C₄×C₈₉	#546	1	2	yes	—
193	C₄×C₈₉	#554	1	2	yes	—
194	#22696	—	89	1	no	maximal, Sylow
195	C₂×C₈₉	—	2	8	no	—
196	C₂×C₈₉	#2349	1	1	yes	characteristic
197	C₂×C₈₉	C₂²×C₄⋊C₈	1	1	yes	characteristic
198	C₂×C₈₉	#2906	1	1	yes	characteristic
199	C₂×C₈₉	C₈×#41	1	1	yes	characteristic
200	C₂×C₈₉	#2970	1	1	yes	characteristic
201	C₂×C₈₉	#2972	1	1	yes	characteristic
202	C₂×C₈₉	#2974	1	1	yes	characteristic
203	C₂×C₈×D₄	—	89	2	no	—
204	C₄²×D₄	D₈₉	1	1	yes	characteristic
205	#1939	—	89	2	no	—
206	#1850	—	89	4	no	—
207	#1831	—	89	1	no	—
208	#1797	—	89	2	no	—
209	C₄×C₄⋊C₈	—	89	1	no	—
210	C₂×#336	—	89	2	no	—
211	C₈₉	#22696	1	1	yes	characteristic, complemented, Sylow
212	C₂³×C₈	—	89	4	no	—
213	C₂×C₄×D₄	Dic₈₉	1	1	yes	characteristic
214	C₂×C₄×D₄	Dic₈₉	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
216	C₂²×C₄²	C₂×D₈₉	1	2	yes	—
217	C₈×D₄	—	178	8	no	—
218	C₂×C₄⋊C₈	—	89	4	no	—
219	C₂×C₄⋊C₈	—	89	2	no	—
220	C₂×C₄⋊C₈	—	89	2	no	—
221	C₂×C₂²⋊C₈	—	89	4	no	—
222	C₂×C₄×C₈	—	89	2	no	—
223	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
224	C₄×C₄⋊C₄	Dic₈₉	1	1	yes	characteristic
225	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	Dic₈₉	1	2	yes	—
227	C₄×C₂²⋊C₄	Dic₈₉	1	2	yes	—
228	C₄×C₂²⋊C₄	C₂×D₈₉	1	2	yes	—
229	C₄³	C₂×D₈₉	1	1	yes	characteristic
230	#336	—	89	1	no	—
231	#336	—	89	2	no	—
232	#336	—	89	2	no	—
233	#336	—	89	4	no	—
234	#336	—	89	1	no	—
235	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
236	C₂³×C₄	C₂×Dic₈₉	1	2	yes	—
237	C₂³×C₄	C₂×Dic₈₉	1	2	yes	—
238	C₂³×C₄	C₂²×D₈₉	1	2	yes	—
239	C₂²×C₈	—	89	2	no	—
240	C₂²×C₈	—	89	4	no	—
241	C₂²×C₈	—	89	2	no	—
242	C₂²×C₈	—	356	4	no	—
243	C₂²×C₈	—	178	8	no	—
244	C₂²×C₈	—	178	8	no	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	#10623494	1	8	yes	complemented
247	C₄×D₄	Dic₁₇₈	1	4	yes	—
248	C₄×D₄	D₃₅₆	1	4	yes	—
249	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×Dic₈₉	1	2	yes	—
255	C₂×C₄²	—	4	4	no	—
256	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
257	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
258	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
259	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
260	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
261	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
265	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
266	C₄⋊C₈	—	356	4	no	—
267	C₄⋊C₈	—	178	4	no	—
268	C₄⋊C₈	—	178	4	no	—
269	C₂²⋊C₈	—	178	8	no	—
270	C₄×C₈	—	178	4	no	—
271	#95	C₂×Dic₈₉	1	2	yes	—
272	#95	C₂×Dic₈₉	1	2	yes	—
273	#95	C₂×Dic₈₉	1	2	yes	—
274	C₂⁴	C₂²×Dic₈₉	1	2	yes	—
275	C₂×D₄	C₄⋊Dic₈₉	1	4	yes	—
276	C₂×D₄	C₂×#10623494	1	4	yes	—
277	C₂×D₄	#13083558	1	4	yes	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	C₂×#10623494	1	8	yes	complemented
286	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
288	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
290	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
294	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₃₅₆	1	4	yes	—
296	C₂²×C₄	C₂×Dic₁₇₈	1	4	yes	—
297	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
298	C₂×C₈	—	89	4	no	—
299	C₂×C₈	—	356	16	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	—	178	4	no	—
302	C₂×C₈	—	178	2	no	—
303	C₂×C₈	—	178	4	no	—
304	C₂×C₈	—	178	2	no	—
305	C₂×C₈	—	178	4	no	—
306	C₂×C₈	—	178	2	no	—
307	C₂×C₈	—	178	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	C₄⋊Dic₈₉	1	4	yes	—
310	C₄⋊C₄	C₂×#10623494	1	4	yes	complemented
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	C₄⋊Dic₈₉	1	8	yes	—
313	C₂²⋊C₄	C₂×#10623494	1	8	yes	complemented
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	4	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	—	4	1	no	—
322	C₄²	C₂×#10623494	1	4	yes	complemented
323	C₄²	C₂×D₃₅₆	1	2	yes	—
324	C₄²	C₂×Dic₁₇₈	1	2	yes	—
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	2	no	—
329	C₂³	C₂×C₄⋊Dic₈₉	1	4	yes	—
330	C₂³	C₂²×#10623494	1	4	yes	—
331	C₂³	C₂×#13083558	1	4	yes	—
332	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
333	D₄	C₄⋊#10623494	1	16	yes	complemented
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	8	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	C₂×C₄⋊Dic₈₉	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
358	C₂×C₄	C₂×C₄⋊Dic₈₉	1	2	yes	—
359	C₂×C₄	C₂²×#10623494	1	2	yes	—
360	C₂×C₄	C₂²×#10623494	1	2	yes	—
361	C₂×C₄	C₂²×#10623494	1	4	yes	—
362	C₂×C₄	C₂²×#10623494	1	2	yes	—
363	C₂×C₄	C₂×#13083558	1	2	yes	—
364	C₂×C₄	#15668019	1	2	yes	—
365	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
366	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
367	C₂×C₄	#41×D₈₉	1	2	yes	—
368	C₂×C₄	#15668057	1	2	yes	—
369	C₈	—	356	4	no	—
370	C₈	—	356	2	no	—
371	C₈	—	178	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	4	no	—
378	C₂²	C₂×C₄⋊#10623494	1	8	yes	—
379	C₂²	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
380	C₂²	#41×Dic₈₉	1	1	yes	characteristic
381	C₂²	#19152073	1	1	yes	characteristic
382	C₂²	C₂³×#10623494	1	1	yes	characteristic
383	C₂²	C₂²×#13083558	1	1	yes	characteristic
384	C₂²	C₂×#15668019	1	1	yes	characteristic
385	C₂²	#19152365	1	1	yes	characteristic
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	C₂×C₄⋊#10623494	1	4	yes	—
395	C₄	#19152243	1	2	yes	—
396	C₄	#19152307	1	2	yes	—
397	C₂	—	2	8	no	—
398	C₂	#26023162	1	1	yes	characteristic
399	C₂	C₂²×C₄⋊#10623494	1	1	yes	characteristic
400	C₂	#26028820	1	1	yes	characteristic
401	C₂	#41×#10623494	1	1	yes	characteristic
402	C₂	#26029266	1	1	yes	characteristic
403	C₂	#26029276	1	1	yes	characteristic
404	C₂	#26029287	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂³×C₈
Fitting	C₄²×D₄×C₈₉	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄²×D₄	D₈₉
hypocenter	C₈₉	#22696
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. #26020971	C₂	semidirect
3. #26020432	C₂	semidirect
4. #26020369	C₂	semidirect
5. #26020232	C₂	semidirect
6. C₄×C₄⋊#10623494	C₂	semidirect
7. C₂×#19151353	C₂	semidirect
48. C₄×D₄×C₈₉	C₈	semidirect
92. C₂²×C₄×C₈₉	C₂×C₈	semidirect
107. C₄⋊C₄×C₈₉	C₂×C₈	semidirect
110. C₂²⋊C₄×C₈₉	C₂×C₈	semidirect
119. C₄²×C₈₉	C₂×C₈	semidirect
130. D₄×C₈₉	C₄⋊C₈	semidirect
211. C₈₉	#22696	semidirect
246. C₄×D₄	#10623494	semidirect
285. C₂²×C₄	C₂×#10623494	semidirect
310. C₄⋊C₄	C₂×#10623494	semidirect
313. C₂²⋊C₄	C₂×#10623494	semidirect
322. C₄²	C₂×#10623494	semidirect
333. D₄	C₄⋊#10623494	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×#10623494	2
#26020971	2
#26020432	2
#26020369	2
#26020232	2
C₄×C₄⋊#10623494	2
C₂×#19151353	2
C₄²×D₄×C₈₉	2
#22696	89