Subgroups — #26034483

Order 11392.

1270 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152337	C₂	1	2	yes	maximal, complemented
2	#19152336	C₂	1	2	yes	maximal, complemented
3	#19152300	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152298	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152295	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152294	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152233	C₂	1	1	yes	maximal, characteristic, complemented
8	D₄×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152230	C₂	1	2	yes	maximal, complemented
12	#19152202	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152199	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152183	C₂	1	2	yes	maximal, complemented
15	#19152180	C₂	1	2	yes	maximal, complemented
16	#19152165	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152158	C₂	1	2	yes	maximal, complemented
19	#19152157	C₂	1	2	yes	maximal, complemented
20	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15667983	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
28	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
31	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
33	#15668008	C₂²	1	2	yes	complemented
34	#15668008	C₂²	1	2	yes	complemented
35	#15668008	C₂²	1	1	yes	characteristic, complemented
36	#15668007	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668005	C₂²	1	2	yes	complemented
39	#15668005	C₂²	1	2	yes	complemented
40	#15668004	C₂²	1	1	yes	characteristic, complemented
41	#15668003	C₂²	1	1	yes	characteristic, complemented
42	#15667999	C₂²	1	2	yes	complemented
43	#15667998	C₂²	1	2	yes	complemented
44	#15667997	C₂²	1	1	yes	characteristic, complemented
45	#15667996	C₂²	1	2	yes	complemented
46	#15667995	C₂²	1	2	yes	complemented
47	#15667995	C₂²	1	2	yes	complemented
48	#15667994	C₂²	1	2	yes	complemented
49	#15667994	C₂²	1	2	yes	complemented
50	#15667994	C₂²	1	1	yes	characteristic, complemented
51	#15667993	C₂²	1	2	yes	complemented
52	#15667993	C₂²	1	2	yes	complemented
53	#15667993	C₂²	1	2	yes	complemented
54	#15667990	C₂²	1	1	yes	characteristic, complemented
55	#15667989	C₂²	1	1	yes	characteristic, complemented
56	#15667987	C₂²	1	1	yes	characteristic, complemented
57	#15667986	C₂²	1	1	yes	characteristic, complemented
58	#15667986	C₂²	1	2	yes	complemented
59	#15667986	C₂²	1	1	yes	characteristic, complemented
60	#15667985	C₂²	1	1	yes	characteristic, complemented
61	#15667985	C₂²	1	2	yes	complemented
62	#15667985	C₂²	1	2	yes	complemented
63	#15667985	C₂²	1	2	yes	complemented
64	#15667984	C₂²	1	1	yes	characteristic, complemented
65	#15667984	C₂²	1	2	yes	complemented
66	#15667984	C₂²	1	2	yes	complemented
67	#15667984	C₂²	1	2	yes	complemented
68	#15667984	C₂²	1	2	yes	complemented
69	#15667984	C₂²	1	2	yes	complemented
70	#15667984	C₂²	1	2	yes	complemented
71	#15667984	C₂²	1	2	yes	complemented
72	#15667983	C₂²	1	2	yes	complemented
73	#15667983	C₂²	1	2	yes	complemented
74	#15667983	C₂²	1	1	yes	characteristic, complemented
75	#15667983	C₂²	1	1	yes	characteristic, complemented
76	#15667983	C₂²	1	1	yes	characteristic, complemented
77	#15667983	C₂²	1	1	yes	characteristic, complemented
78	#15667983	C₂²	1	1	yes	characteristic, complemented
79	#15667983	C₂²	1	2	yes	complemented
80	#15667983	C₂²	1	1	yes	characteristic, complemented
81	#15667983	C₂²	1	1	yes	characteristic, complemented
82	#15667983	C₂²	1	2	yes	complemented
83	#15667982	C₂²	1	2	yes	complemented
84	#15667982	C₂²	1	1	yes	characteristic, complemented
85	#15667981	C₂²	1	2	yes	complemented
86	#15667981	C₂²	1	2	yes	complemented
87	#15667981	C₂²	1	2	yes	complemented
88	#15667981	C₂²	1	2	yes	complemented
89	#15667980	C₂²	1	2	yes	complemented
90	#15667980	C₂²	1	2	yes	complemented
91	#15667980	C₂²	1	2	yes	complemented
92	#15667980	C₂²	1	2	yes	complemented
93	#15667980	C₂²	1	2	yes	complemented
94	#15667980	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₈₉	C₂²	1	2	yes	complemented
98	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
99	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
103	#15667972	C₂²	1	2	yes	complemented
104	#15667972	C₂²	1	2	yes	complemented
105	#15667971	C₂²	1	1	yes	characteristic, complemented
106	#15667970	C₂²	1	1	yes	characteristic, complemented
107	#15667969	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
112	C₂²×D₄×C₈₉	C₂²	1	2	yes	complemented
113	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₉	C₂²	1	2	yes	complemented
118	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#120×C₈₉	C₂²	1	2	yes	complemented
120	#120×C₈₉	C₂²	1	2	yes	complemented
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	1	yes	characteristic
124	C₂³×D₈₉	C₂³	1	2	yes	—
125	C₂³×D₈₉	C₂³	1	2	yes	—
126	#13083574	—	4	2	no	—
127	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
128	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
129	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
130	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
131	C₂×D₃₅₆	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₈₉	—	4	4	no	—
133	C₂×C₂²⋊D₈₉	—	4	4	no	—
134	C₂×C₂²⋊D₈₉	—	4	4	no	—
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
152	D₄×D₈₉	—	4	2	no	—
153	D₄×D₈₉	—	4	2	no	—
154	D₄×D₈₉	—	4	4	no	—
155	D₄×D₈₉	—	4	4	no	—
156	C₂²×Dic₈₉	C₂³	1	2	yes	—
157	C₂²×Dic₈₉	C₂³	1	2	yes	—
158	C₂²×Dic₈₉	C₂³	1	2	yes	—
159	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₈₉	—	4	2	no	—
161	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₈₉	C₂³	1	2	yes	—
165	C₂×C₄×D₈₉	C₂³	1	2	yes	—
166	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₈₉	C₂³	1	2	yes	—
172	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₈₉	C₂³	1	2	yes	—
174	#13083553	C₂³	1	1	yes	characteristic
175	#13083553	C₂³	1	1	yes	characteristic
176	#13083553	C₂³	1	2	yes	—
177	#13083553	C₂³	1	2	yes	—
178	#13083553	C₂³	1	1	yes	characteristic
179	#13083553	C₂³	1	1	yes	characteristic
180	#13083553	C₂³	1	2	yes	—
181	#13083553	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
187	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
189	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
190	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
191	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
192	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
193	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
194	#13083551	C₂³	1	1	yes	characteristic
195	#13083551	C₂³	1	1	yes	characteristic
196	#13083551	C₂³	1	2	yes	—
197	#13083551	C₂³	1	1	yes	characteristic
198	#13083551	C₂³	1	2	yes	—
199	#13083551	C₂³	1	1	yes	characteristic
200	#13083551	C₂³	1	1	yes	characteristic
201	#13083551	C₂³	1	2	yes	—
202	#13083551	C₂³	1	1	yes	characteristic
203	#13083551	C₂³	1	2	yes	—
204	#13083551	C₂³	1	2	yes	—
205	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
206	C₄×Dic₈₉	C₂³	1	2	yes	—
207	C₄×Dic₈₉	C₂³	1	2	yes	—
208	C₂⁴×C₈₉	C₂³	1	2	yes	—
209	C₂⁴×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	—	4	2	no	—
211	C₂×D₄×C₈₉	—	4	2	no	—
212	C₂×D₄×C₈₉	—	4	4	no	—
213	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂×D₄×C₈₉	C₂³	1	2	yes	—
216	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₂×D₄×C₈₉	C₂³	1	2	yes	—
219	C₂×D₄×C₈₉	C₂³	1	2	yes	—
220	C₂×D₄×C₈₉	C₂³	1	2	yes	—
221	C₂×D₄×C₈₉	C₂³	1	2	yes	—
222	C₂×D₄×C₈₉	C₂³	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
226	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
231	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
232	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
233	C₄²×C₈₉	C₂³	1	1	yes	characteristic
234	C₂³×C₈₉	—	2	4	no	—
235	C₂³×C₈₉	—	4	2	no	—
236	C₂³×C₈₉	—	4	2	no	—
237	C₂³×C₈₉	—	4	2	no	—
238	C₂³×C₈₉	—	4	2	no	—
239	C₂³×C₈₉	—	4	2	no	—
240	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂³×C₈₉	C₂⁴	1	2	yes	—
242	C₂³×C₈₉	C₂⁴	1	2	yes	—
243	C₂³×C₈₉	C₂⁴	1	2	yes	—
244	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂²×D₈₉	—	2	2	no	—
246	C₂²×D₈₉	—	2	2	no	—
247	C₂²×D₈₉	—	2	4	no	—
248	C₂²×D₈₉	—	4	1	no	—
249	C₂²×D₈₉	—	4	2	no	—
250	C₂²×D₈₉	—	4	2	no	—
251	C₂²×D₈₉	—	4	2	no	—
252	C₂²×D₈₉	—	4	2	no	—
253	C₂²×D₈₉	—	4	2	no	—
254	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²×D₈₉	C₂⁴	1	2	yes	—
256	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
257	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
258	D₄×C₈₉	—	2	2	no	—
259	D₄×C₈₉	—	2	4	no	—
260	D₄×C₈₉	—	2	2	no	—
261	D₄×C₈₉	—	2	2	no	—
262	D₄×C₈₉	—	2	2	no	—
263	D₄×C₈₉	—	4	2	no	—
264	D₄×C₈₉	—	4	2	no	—
265	D₄×C₈₉	—	4	2	no	—
266	D₄×C₈₉	—	4	2	no	—
267	D₄×C₈₉	—	4	2	no	—
268	C₂×C₄×C₈₉	—	2	2	no	—
269	C₂×C₄×C₈₉	—	2	2	no	—
270	C₂×C₄×C₈₉	—	4	2	no	—
271	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
275	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂²⋊D₈₉	—	2	4	no	—
278	C₂²⋊D₈₉	—	2	2	no	—
279	C₂²⋊D₈₉	—	2	4	no	—
280	C₂²⋊D₈₉	—	2	4	no	—
281	C₂²⋊D₈₉	—	2	2	no	—
282	C₂²⋊D₈₉	—	4	2	no	—
283	C₂²⋊D₈₉	—	4	2	no	—
284	C₂²⋊D₈₉	—	4	2	no	—
285	C₂²⋊D₈₉	—	4	2	no	—
286	C₂²⋊D₈₉	—	4	2	no	—
287	C₂²⋊D₈₉	—	4	2	no	—
288	C₂²⋊D₈₉	—	4	2	no	—
289	C₂²⋊D₈₉	—	4	2	no	—
290	C₂²⋊D₈₉	—	4	2	no	—
291	C₂²⋊D₈₉	—	4	2	no	—
292	C₂²⋊D₈₉	—	4	1	no	—
293	C₂²⋊D₈₉	—	4	1	no	—
294	C₂×Dic₈₉	—	4	1	no	—
295	C₂×Dic₈₉	—	4	2	no	—
296	C₂×Dic₈₉	—	4	2	no	—
297	C₂×Dic₈₉	—	4	2	no	—
298	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
299	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
301	C₂×Dic₈₉	C₂⁴	1	2	yes	—
302	C₂×Dic₈₉	C₂⁴	1	2	yes	—
303	C₂×Dic₈₉	C₂⁴	1	2	yes	—
304	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
306	D₃₅₆	—	2	2	no	—
307	D₃₅₆	—	2	2	no	—
308	D₃₅₆	—	4	2	no	—
309	D₃₅₆	—	4	1	no	—
310	C₄×D₈₉	—	2	2	no	—
311	C₄×D₈₉	—	2	2	no	—
312	C₄×D₈₉	—	2	2	no	—
313	C₄×D₈₉	—	4	1	no	—
314	C₄×D₈₉	—	4	1	no	—
315	C₄×D₈₉	—	4	2	no	—
316	C₄×D₈₉	—	4	2	no	—
317	Dic₁₇₈	—	4	1	no	—
318	C₂²×C₈₉	—	2	1	no	—
319	C₂²×C₈₉	—	2	1	no	—
320	C₂²×C₈₉	—	2	2	no	—
321	C₂²×C₈₉	—	2	2	no	—
322	C₂²×C₈₉	—	2	1	no	—
323	C₂²×C₈₉	—	2	2	no	—
324	C₂²×C₈₉	—	2	2	no	—
325	C₂²×C₈₉	—	2	1	no	—
326	C₂²×C₈₉	—	2	2	no	—
327	C₂²×C₈₉	—	2	2	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	2	no	—
330	C₂²×C₈₉	—	2	1	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	8	4	no	—
333	C₂²×C₈₉	—	8	4	no	—
334	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
335	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
336	C₂×D₈₉	—	2	1	no	—
337	C₂×D₈₉	—	2	1	no	—
338	C₂×D₈₉	—	2	1	no	—
339	C₂×D₈₉	—	2	1	no	—
340	C₂×D₈₉	—	2	2	no	—
341	C₂×D₈₉	—	2	1	no	—
342	C₂×D₈₉	—	2	2	no	—
343	C₂×D₈₉	—	2	1	no	—
344	C₂×D₈₉	—	2	2	no	—
345	C₂×D₈₉	—	2	1	no	—
346	C₂×D₈₉	—	2	1	no	—
347	C₂×D₈₉	—	4	4	no	—
348	C₂×D₈₉	—	8	4	no	—
349	C₂×D₈₉	—	8	4	no	—
350	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
351	C₄×C₈₉	—	2	1	no	—
352	C₄×C₈₉	—	2	1	no	—
353	C₄×C₈₉	—	2	1	no	—
354	C₄×C₈₉	—	2	2	no	—
355	C₄×C₈₉	—	2	1	no	—
356	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
357	Dic₈₉	—	2	1	no	—
358	Dic₈₉	—	2	1	no	—
359	Dic₈₉	—	2	1	no	—
360	Dic₈₉	—	2	2	no	—
361	Dic₈₉	—	2	2	no	—
362	Dic₈₉	—	2	2	no	—
363	Dic₈₉	—	2	1	no	—
364	Dic₈₉	—	2	1	no	—
365	C₂×C₈₉	—	2	2	no	—
366	C₂×C₈₉	—	4	2	no	—
367	C₂×C₈₉	—	4	2	no	—
368	C₂×C₈₉	—	4	1	no	—
369	C₂×C₈₉	—	4	2	no	—
370	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
371	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
373	D₈₉	—	2	2	no	—
374	D₈₉	—	4	1	no	—
375	D₈₉	—	4	1	no	—
376	D₈₉	—	4	2	no	—
377	#3537	—	89	1	no	maximal, Sylow
378	C₈₉	#3537	1	1	yes	characteristic, complemented, Sylow
379	#560	—	89	2	no	—
380	#560	—	89	2	no	—
381	#553	—	89	1	no	—
382	#553	—	89	1	no	—
383	#553	—	89	1	no	—
384	#553	—	89	1	no	—
385	D₄²	—	89	2	no	—
386	D₄²	—	89	1	no	—
387	D₄²	—	89	1	no	—
388	D₄²	—	89	1	no	—
389	D₄²	—	89	2	no	—
390	D₄²	D₈₉	1	1	yes	characteristic, complemented
391	#540	—	89	1	no	—
392	#540	—	89	1	no	—
393	#538	—	89	2	no	—
394	#538	—	89	2	no	—
395	#535	—	89	1	no	—
396	#535	—	89	1	no	—
397	#534	—	89	2	no	—
398	#534	—	89	2	no	—
399	#525	—	89	1	no	—
400	C₂×#121	—	89	1	no	—
401	C₂×#121	—	89	1	no	—
402	C₂×#41	—	89	1	no	—
403	C₂²×D₄	—	89	2	no	—
404	C₂²×D₄	—	89	2	no	—
405	C₂²×D₄	—	89	2	no	—
406	C₂²×D₄	—	89	2	no	—
407	C₂²×D₄	—	89	1	no	—
408	C₂²×D₄	—	89	2	no	—
409	C₂²×D₄	—	89	1	no	—
410	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
411	C₂²×D₄	C₂×D₈₉	1	2	yes	complemented
412	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
413	C₂³×C₄	—	89	1	no	—
414	#127	—	89	2	no	—
415	#127	—	89	2	no	—
416	#127	—	89	1	no	—
417	#127	C₂×D₈₉	1	1	yes	characteristic, complemented
418	#126	—	89	2	no	—
419	#126	—	89	2	no	—
420	#126	—	89	2	no	—
421	#126	—	89	2	no	—
422	#125	—	89	1	no	—
423	#125	—	89	1	no	—
424	#124	—	89	2	no	—
425	#124	—	89	2	no	—
426	#123	—	89	2	no	—
427	#123	—	89	2	no	—
428	#123	—	89	2	no	—
429	#123	—	89	2	no	—
430	#123	—	89	2	no	—
431	#123	—	89	1	no	—
432	#123	—	89	1	no	—
433	#123	—	89	2	no	—
434	#123	—	89	2	no	—
435	#123	—	89	2	no	—
436	C₂²⋊Q₈	—	89	1	no	—
437	C₂²⋊Q₈	—	89	1	no	—
438	#121	—	89	2	no	—
439	#121	—	89	1	no	—
440	#121	—	89	1	no	—
441	#121	—	89	1	no	—
442	#121	—	89	1	no	—
443	#121	—	89	1	no	—
444	#121	—	89	2	no	—
445	#121	—	89	2	no	—
446	#121	—	89	1	no	—
447	#121	—	89	2	no	—
448	#121	—	89	1	no	—
449	#121	—	89	1	no	—
450	#121	—	89	2	no	—
451	#121	—	89	2	no	—
452	#121	—	89	2	no	—
453	#121	—	89	2	no	—
454	#121	—	89	2	no	—
455	#121	—	89	2	no	—
456	#121	—	89	2	no	—
457	#121	—	89	1	no	—
458	#121	—	89	1	no	—
459	#121	—	89	2	no	—
460	#121	—	89	1	no	—
461	#121	—	89	2	no	—
462	#121	—	89	1	no	—
463	#121	—	89	2	no	—
464	#121	—	89	2	no	—
465	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
466	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
467	#121	C₂×D₈₉	1	2	yes	complemented
468	#120	—	89	2	no	—
469	#120	—	89	2	no	—
470	#120	—	89	2	no	—
471	#120	—	89	2	no	—
472	#120	—	89	1	no	—
473	#120	—	89	2	no	—
474	#120	—	89	2	no	—
475	#120	—	89	2	no	—
476	#120	—	89	2	no	—
477	#120	—	89	2	no	—
478	#120	—	89	1	no	—
479	#120	—	89	2	no	—
480	#120	C₂×D₈₉	1	2	yes	complemented
481	#120	C₂×D₈₉	1	2	yes	complemented
482	C₄×D₄	—	89	2	no	—
483	C₄×D₄	—	89	1	no	—
484	C₄×D₄	—	89	1	no	—
485	C₄×D₄	—	89	1	no	—
486	C₄×D₄	—	89	1	no	—
487	C₄×D₄	—	89	2	no	—
488	C₄×D₄	—	89	2	no	—
489	C₄×D₄	—	89	2	no	—
490	C₄×D₄	—	89	1	no	—
491	C₄×D₄	—	89	1	no	—
492	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
493	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
494	#117	—	89	1	no	—
495	#117	—	89	1	no	—
496	#117	—	89	1	no	—
497	C₂×C₄⋊C₄	—	89	1	no	—
498	C₂×C₄⋊C₄	—	89	1	no	—
499	C₂×C₂²⋊C₄	—	89	2	no	—
500	C₂×C₂²⋊C₄	—	89	2	no	—
501	C₂⁴	—	89	2	no	—
502	C₂⁴	—	89	2	no	—
503	C₂⁴	—	89	1	no	—
504	C₂⁴	C₂²×D₈₉	1	2	yes	—
505	C₂⁴	C₂²×D₈₉	1	2	yes	—
506	#41	—	356	2	no	—
507	C₂×Q₈	—	89	1	no	—
508	C₂×D₄	—	4	2	no	—
509	C₂×D₄	—	4	2	no	—
510	C₂×D₄	—	4	4	no	—
511	C₂×D₄	—	89	1	no	—
512	C₂×D₄	—	89	1	no	—
513	C₂×D₄	—	89	2	no	—
514	C₂×D₄	—	89	2	no	—
515	C₂×D₄	—	89	2	no	—
516	C₂×D₄	—	89	2	no	—
517	C₂×D₄	—	89	2	no	—
518	C₂×D₄	—	89	2	no	—
519	C₂×D₄	—	89	2	no	—
520	C₂×D₄	—	89	2	no	—
521	C₂×D₄	—	89	2	no	—
522	C₂×D₄	—	89	2	no	—
523	C₂×D₄	—	89	2	no	—
524	C₂×D₄	—	89	1	no	—
525	C₂×D₄	—	89	2	no	—
526	C₂×D₄	—	89	1	no	—
527	C₂×D₄	—	89	2	no	—
528	C₂×D₄	—	89	1	no	—
529	C₂×D₄	—	89	2	no	—
530	C₂×D₄	—	89	1	no	—
531	C₂×D₄	—	89	1	no	—
532	C₂×D₄	—	356	4	no	—
533	C₂×D₄	—	356	4	no	—
534	C₂×D₄	—	356	4	no	—
535	C₂×D₄	—	356	4	no	—
536	C₂×D₄	—	356	4	no	—
537	C₂×D₄	—	356	2	no	—
538	C₂×D₄	—	356	2	no	—
539	C₂×D₄	C₂²×D₈₉	1	2	yes	—
540	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
541	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
542	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
543	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
544	C₂×D₄	C₂²×D₈₉	1	2	yes	—
545	C₂×D₄	C₂²×D₈₉	1	2	yes	—
546	C₂×D₄	C₂²×D₈₉	1	2	yes	—
547	C₂×D₄	C₂²×D₈₉	1	2	yes	—
548	C₂×D₄	C₂²×D₈₉	1	2	yes	—
549	C₂²×C₄	—	89	1	no	—
550	C₂²×C₄	—	89	2	no	—
551	C₂²×C₄	—	89	2	no	—
552	C₂²×C₄	—	89	2	no	—
553	C₂²×C₄	—	89	1	no	—
554	C₂²×C₄	—	89	2	no	—
555	C₂²×C₄	—	89	2	no	—
556	C₂²×C₄	—	89	1	no	—
557	C₂²×C₄	—	89	1	no	—
558	C₂²×C₄	—	89	1	no	—
559	C₂²×C₄	—	89	1	no	—
560	C₂²×C₄	—	356	2	no	—
561	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
562	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
563	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
564	C₄⋊C₄	—	89	1	no	—
565	C₄⋊C₄	—	89	1	no	—
566	C₄⋊C₄	—	89	1	no	—
567	C₄⋊C₄	—	89	2	no	—
568	C₄⋊C₄	—	89	2	no	—
569	C₄⋊C₄	—	89	1	no	—
570	C₄⋊C₄	—	89	1	no	—
571	C₄⋊C₄	—	89	1	no	—
572	C₄⋊C₄	—	89	1	no	—
573	C₄⋊C₄	—	89	1	no	—
574	C₄⋊C₄	—	89	2	no	—
575	C₄⋊C₄	—	89	2	no	—
576	C₄⋊C₄	—	89	2	no	—
577	C₄⋊C₄	—	89	2	no	—
578	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
579	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
580	C₂²⋊C₄	—	89	2	no	—
581	C₂²⋊C₄	—	89	2	no	—
582	C₂²⋊C₄	—	89	2	no	—
583	C₂²⋊C₄	—	89	2	no	—
584	C₂²⋊C₄	—	89	2	no	—
585	C₂²⋊C₄	—	89	2	no	—
586	C₂²⋊C₄	—	89	1	no	—
587	C₂²⋊C₄	—	89	2	no	—
588	C₂²⋊C₄	—	89	2	no	—
589	C₂²⋊C₄	—	89	2	no	—
590	C₂²⋊C₄	—	89	2	no	—
591	C₂²⋊C₄	—	89	1	no	—
592	C₂²⋊C₄	—	89	2	no	—
593	C₂²⋊C₄	—	89	2	no	—
594	C₂²⋊C₄	—	89	2	no	—
595	C₂²⋊C₄	—	89	1	no	—
596	C₂²⋊C₄	—	89	1	no	—
597	C₂²⋊C₄	—	89	1	no	—
598	C₂²⋊C₄	—	89	1	no	—
599	C₂²⋊C₄	—	89	2	no	—
600	C₂²⋊C₄	—	89	2	no	—
601	C₂²⋊C₄	—	89	1	no	—
602	C₂²⋊C₄	—	89	1	no	—
603	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
604	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
605	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
606	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
607	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
608	C₄²	—	89	1	no	—
609	C₄²	—	89	2	no	—
610	C₄²	—	89	2	no	—
611	C₄²	C₂²×D₈₉	1	1	yes	characteristic
612	C₂³	—	2	4	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	4	2	no	—
616	C₂³	—	4	2	no	—
617	C₂³	—	4	2	no	—
618	C₂³	—	89	1	no	—
619	C₂³	—	89	2	no	—
620	C₂³	—	89	1	no	—
621	C₂³	—	89	1	no	—
622	C₂³	—	356	1	no	—
623	C₂³	—	356	2	no	—
624	C₂³	—	356	2	no	—
625	C₂³	—	356	2	no	—
626	C₂³	—	356	2	no	—
627	C₂³	—	356	2	no	—
628	C₂³	—	178	2	no	—
629	C₂³	—	178	4	no	—
630	C₂³	—	178	2	no	—
631	C₂³	C₂³×D₈₉	1	2	yes	—
632	C₂³	C₂³×D₈₉	1	2	yes	—
633	C₂³	C₂³×D₈₉	1	1	yes	characteristic
634	C₂³	C₂³×D₈₉	1	2	yes	—
635	C₂³	C₂³×D₈₉	1	1	yes	characteristic
636	Q₈	—	356	1	no	—
637	D₄	—	2	2	no	—
638	D₄	—	2	4	no	—
639	D₄	—	2	2	no	—
640	D₄	—	2	2	no	—
641	D₄	—	2	2	no	—
642	D₄	—	4	2	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	2	no	—
646	D₄	—	4	2	no	—
647	D₄	—	356	2	no	—
648	D₄	—	356	1	no	—
649	D₄	—	356	2	no	—
650	D₄	—	356	2	no	—
651	D₄	—	356	2	no	—
652	D₄	—	356	2	no	—
653	D₄	—	356	2	no	—
654	D₄	—	356	2	no	—
655	D₄	—	356	2	no	—
656	D₄	—	356	2	no	—
657	D₄	—	356	2	no	—
658	D₄	—	356	2	no	—
659	D₄	—	356	1	no	—
660	D₄	—	356	1	no	—
661	D₄	—	178	2	no	—
662	D₄	—	178	4	no	—
663	D₄	—	178	2	no	—
664	D₄	—	178	4	no	—
665	D₄	—	178	4	no	—
666	D₄	—	178	2	no	—
667	D₄	—	178	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	4	2	no	—
671	C₂×C₄	—	89	1	no	—
672	C₂×C₄	—	89	1	no	—
673	C₂×C₄	—	89	2	no	—
674	C₂×C₄	—	89	2	no	—
675	C₂×C₄	—	89	1	no	—
676	C₂×C₄	—	89	2	no	—
677	C₂×C₄	—	89	1	no	—
678	C₂×C₄	—	89	1	no	—
679	C₂×C₄	—	356	1	no	—
680	C₂×C₄	—	356	1	no	—
681	C₂×C₄	—	356	2	no	—
682	C₂×C₄	—	356	2	no	—
683	C₂×C₄	—	356	1	no	—
684	C₂×C₄	—	356	2	no	—
685	C₂×C₄	—	356	2	no	—
686	C₂×C₄	—	356	2	no	—
687	C₂×C₄	—	178	2	no	—
688	C₂×C₄	—	178	2	no	—
689	C₂×C₄	—	178	2	no	—
690	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
691	C₂×C₄	C₂³×D₈₉	1	2	yes	—
692	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
693	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
694	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
695	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	2	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	8	4	no	—
711	C₂²	—	8	4	no	—
712	C₂²	—	89	2	no	—
713	C₂²	—	356	4	no	—
714	C₂²	—	178	2	no	—
715	C₂²	—	178	1	no	—
716	C₂²	—	178	1	no	—
717	C₂²	—	178	1	no	—
718	C₂²	—	178	1	no	—
719	C₂²	—	178	1	no	—
720	C₂²	—	178	2	no	—
721	C₂²	—	178	1	no	—
722	C₂²	—	178	2	no	—
723	C₂²	—	178	1	no	—
724	C₂²	—	178	1	no	—
725	C₂²	—	712	4	no	—
726	C₂²	—	712	4	no	—
727	C₂²	#15668057	1	2	yes	—
728	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	2	2	no	—
734	C₄	—	178	2	no	—
735	C₄	—	178	1	no	—
736	C₄	—	178	2	no	—
737	C₄	—	178	1	no	—
738	C₄	—	178	1	no	—
739	C₄	—	178	2	no	—
740	C₄	—	178	1	no	—
741	C₄	—	178	1	no	—
742	C₄	#15668057	1	2	yes	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	4	2	no	—
746	C₂	—	4	2	no	—
747	C₂	—	4	2	no	—
748	C₂	—	356	1	no	—
749	C₂	—	356	2	no	—
750	C₂	—	356	1	no	—
751	C₂	—	178	2	no	—
752	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
753	C₂	C₂×#15668057	1	1	yes	characteristic
754	C₂	C₂×#15668057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	D₄²×C₈₉	C₂
hypercenter	D₄²	D₈₉
hypocenter	C₈₉	#3537
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. #19152337	C₂	semidirect
2. #19152336	C₂	semidirect
3. #19152300	C₂	semidirect
4. #19152298	C₂	semidirect
5. #19152295	C₂	semidirect
6. #19152294	C₂	semidirect
7. #19152233	C₂	semidirect
8. D₄×C₂²⋊D₈₉	C₂	semidirect
9. D₄×C₂²⋊D₈₉	C₂	semidirect
10. D₄×C₂²⋊D₈₉	C₂	semidirect
11. #19152230	C₂	semidirect
12. #19152202	C₂	semidirect
13. #19152199	C₂	semidirect
14. #19152183	C₂	semidirect
15. #19152180	C₂	semidirect
16. #19152165	C₂	semidirect
17. #19152164	C₂	semidirect
18. #19152158	C₂	semidirect
19. #19152157	C₂	semidirect
20. #19152107	C₂	semidirect
21. C₂×#15667983	C₂	semidirect
22. #121×D₈₉	C₂	semidirect
23. D₄²×C₈₉	C₂	semidirect
24. C₂×#13083574	C₂²	semidirect
25. C₂²×C₂²⋊D₈₉	C₂²	semidirect
26. C₂²×C₂²⋊D₈₉	C₂²	semidirect
27. C₂²×C₂²⋊D₈₉	C₂²	semidirect
28. C₂×D₄×D₈₉	C₂²	semidirect
29. C₂×D₄×D₈₉	C₂²	semidirect
30. C₂×D₄×D₈₉	C₂²	semidirect
31. C₂×D₄×D₈₉	C₂²	semidirect
32. C₂²×C₄×D₈₉	C₂²	semidirect
33. #15668008	C₂²	semidirect
34. #15668008	C₂²	semidirect
35. #15668008	C₂²	semidirect
36. #15668007	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668005	C₂²	semidirect
39. #15668005	C₂²	semidirect
40. #15668004	C₂²	semidirect
41. #15668003	C₂²	semidirect
42. #15667999	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667997	C₂²	semidirect
45. #15667996	C₂²	semidirect
46. #15667995	C₂²	semidirect
47. #15667995	C₂²	semidirect
48. #15667994	C₂²	semidirect
49. #15667994	C₂²	semidirect
50. #15667994	C₂²	semidirect
51. #15667993	C₂²	semidirect
52. #15667993	C₂²	semidirect
53. #15667993	C₂²	semidirect
54. #15667990	C₂²	semidirect
55. #15667989	C₂²	semidirect
56. #15667987	C₂²	semidirect
57. #15667986	C₂²	semidirect
58. #15667986	C₂²	semidirect
59. #15667986	C₂²	semidirect
60. #15667985	C₂²	semidirect
61. #15667985	C₂²	semidirect
62. #15667985	C₂²	semidirect
63. #15667985	C₂²	semidirect
64. #15667984	C₂²	semidirect
65. #15667984	C₂²	semidirect
66. #15667984	C₂²	semidirect
67. #15667984	C₂²	semidirect
68. #15667984	C₂²	semidirect
69. #15667984	C₂²	semidirect
70. #15667984	C₂²	semidirect
71. #15667984	C₂²	semidirect
72. #15667983	C₂²	semidirect
73. #15667983	C₂²	semidirect
74. #15667983	C₂²	semidirect
75. #15667983	C₂²	semidirect
76. #15667983	C₂²	semidirect
77. #15667983	C₂²	semidirect
78. #15667983	C₂²	semidirect
79. #15667983	C₂²	semidirect
80. #15667983	C₂²	semidirect
81. #15667983	C₂²	semidirect
82. #15667983	C₂²	semidirect
83. #15667982	C₂²	semidirect
84. #15667982	C₂²	semidirect
85. #15667981	C₂²	semidirect
86. #15667981	C₂²	semidirect
87. #15667981	C₂²	semidirect
88. #15667981	C₂²	semidirect
89. #15667980	C₂²	semidirect
90. #15667980	C₂²	semidirect
91. #15667980	C₂²	semidirect
92. #15667980	C₂²	semidirect
93. #15667980	C₂²	semidirect
94. #15667980	C₂²	semidirect
95. C₄×D₃₅₆	C₂²	semidirect
96. C₄×D₃₅₆	C₂²	semidirect
97. D₄×Dic₈₉	C₂²	semidirect
98. D₄×Dic₈₉	C₂²	semidirect
99. D₄×Dic₈₉	C₂²	semidirect
100. C₄×C₂²⋊D₈₉	C₂²	semidirect
101. C₄×C₂²⋊D₈₉	C₂²	semidirect
102. C₄×C₂²⋊D₈₉	C₂²	semidirect
103. #15667972	C₂²	semidirect
104. #15667972	C₂²	semidirect
105. #15667971	C₂²	semidirect
106. #15667970	C₂²	semidirect
107. #15667969	C₂²	semidirect
108. C₂×C₄⋊Dic₈₉	C₂²	semidirect
109. C₄⋊C₄×D₈₉	C₂²	semidirect
110. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
111. C₂²⋊C₄×D₈₉	C₂²	semidirect
112. C₂²×D₄×C₈₉	C₂²	semidirect
113. C₂²×D₄×C₈₉	C₂²	semidirect
114. C₂²×D₄×C₈₉	C₂²	semidirect
115. #127×C₈₉	C₂²	semidirect
116. #121×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #120×C₈₉	C₂²	semidirect
120. #120×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
378. C₈₉	#3537	semidirect
390. D₄²	D₈₉	semidirect
410. C₂²×D₄	C₂×D₈₉	semidirect
411. C₂²×D₄	C₂×D₈₉	semidirect
412. C₂²×D₄	C₂×D₈₉	semidirect
417. #127	C₂×D₈₉	semidirect
465. #121	C₂×D₈₉	semidirect
466. #121	C₂×D₈₉	semidirect
467. #121	C₂×D₈₉	semidirect
480. #120	C₂×D₈₉	semidirect
481. #120	C₂×D₈₉	semidirect
492. C₄×D₄	C₂×D₈₉	semidirect
493. C₄×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152337	2
#19152336	2
#19152300	2
#19152298	2
#19152295	2
#19152294	2
#19152233	2
D₄×C₂²⋊D₈₉	2
#19152230	2
#19152202	2
#19152199	2
#19152183	2
#19152180	2
#19152165	2
#19152164	2
#19152158	2
#19152157	2
#19152107	2
C₂×#15667983	2
#121×D₈₉	2
D₄²×C₈₉	2
#3537	89