Subgroups — #26034038

Order 11392.

1540 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668057	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152258	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152257	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152256	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152254	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152243	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152242	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152240	C₂	1	2	yes	maximal, complemented
10	#19152238	C₂	1	2	yes	maximal, complemented
11	#19152237	C₂	1	2	yes	maximal, complemented
12	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152235	C₂	1	2	yes	maximal, complemented
14	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152170	C₂	1	2	yes	maximal, complemented
16	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152163	C₂	1	2	yes	maximal, complemented
18	#19152145	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152143	C₂	1	2	yes	maximal, complemented
20	C₂×#15667998	C₂	1	2	yes	maximal, complemented
21	#124×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#15668059	—	2	8	no	—
25	#15668057	—	2	8	no	—
26	C₂×#13083574	C₂²	1	1	yes	characteristic
27	C₂×#13083574	C₂²	1	1	yes	characteristic
28	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13083574	C₂²	1	2	yes	complemented
30	C₂×#13083573	C₂²	1	2	yes	—
31	C₂×#13083573	C₂²	1	1	yes	characteristic
32	C₂×#13083573	C₂²	1	1	yes	characteristic
33	C₂×#13083573	C₂²	1	2	yes	complemented
34	C₂×#13083573	C₂²	1	2	yes	complemented
35	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Dic₁₇₈	C₂²	1	2	yes	complemented
37	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
38	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	—
41	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	—
42	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
43	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
44	C₂×D₄×D₈₉	C₂²	1	2	yes	—
45	#15668011	C₂²	1	2	yes	complemented
46	#15668011	C₂²	1	1	yes	characteristic, complemented
47	#15668008	C₂²	1	2	yes	complemented
48	#15668008	C₂²	1	1	yes	characteristic, complemented
49	#15668001	C₂²	1	1	yes	characteristic, complemented
50	#15668000	C₂²	1	1	yes	characteristic, complemented
51	#15667999	C₂²	1	1	yes	characteristic, complemented
52	#15667998	C₂²	1	1	yes	characteristic, complemented
53	#15667998	C₂²	1	2	yes	complemented
54	#15667998	C₂²	1	1	yes	characteristic, complemented
55	#15667998	C₂²	1	2	yes	complemented
56	#15667998	C₂²	1	2	yes	complemented
57	#15667998	C₂²	1	2	yes	complemented
58	#15667998	C₂²	1	2	yes	complemented
59	#15667998	C₂²	1	2	yes	complemented
60	#15667998	C₂²	1	2	yes	complemented
61	#15667998	C₂²	1	2	yes	complemented
62	#15667997	C₂²	1	2	yes	complemented
63	#15667996	C₂²	1	2	yes	complemented
64	#15667995	C₂²	1	2	yes	complemented
65	#15667994	C₂²	1	2	yes	complemented
66	#15667993	C₂²	1	2	yes	complemented
67	#15667992	C₂²	1	1	yes	characteristic, complemented
68	#15667991	C₂²	1	1	yes	characteristic, complemented
69	#15667990	C₂²	1	2	yes	complemented
70	#15667990	C₂²	1	2	yes	complemented
71	#15667989	C₂²	1	2	yes	complemented
72	#15667989	C₂²	1	2	yes	complemented
73	#15667988	C₂²	1	1	yes	characteristic, complemented
74	#15667987	C₂²	1	1	yes	characteristic, complemented
75	#15667987	C₂²	1	1	yes	characteristic, complemented
76	#15667986	C₂²	1	2	yes	complemented
77	#15667986	C₂²	1	1	yes	characteristic, complemented
78	#15667985	C₂²	1	1	yes	characteristic, complemented
79	#15667985	C₂²	1	1	yes	characteristic, complemented
80	#15667985	C₂²	1	2	yes	complemented
81	#15667985	C₂²	1	2	yes	complemented
82	#15667984	C₂²	1	2	yes	complemented
83	#15667984	C₂²	1	2	yes	complemented
84	#15667984	C₂²	1	2	yes	complemented
85	#15667984	C₂²	1	2	yes	complemented
86	#15667983	C₂²	1	1	yes	characteristic, complemented
87	#15667983	C₂²	1	1	yes	characteristic, complemented
88	#15667982	C₂²	1	2	yes	complemented
89	#15667982	C₂²	1	2	yes	complemented
90	#15667981	C₂²	1	2	yes	complemented
91	#15667980	C₂²	1	2	yes	complemented
92	#15667980	C₂²	1	2	yes	complemented
93	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
94	#15667977	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₈₉	C₂²	1	2	yes	complemented
97	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
98	#15667974	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
102	#15667972	C₂²	1	2	yes	complemented
103	#15667972	C₂²	1	2	yes	complemented
104	#15667972	C₂²	1	2	yes	complemented
105	#15667970	C₂²	1	1	yes	characteristic, complemented
106	#15667968	C₂²	1	2	yes	complemented
107	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
108	C₂×#13083551	C₂²	1	2	yes	complemented
109	C₂×#13083551	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
112	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
113	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
116	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#123×C₈₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₈₉	C₂²	1	2	yes	complemented
120	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₈₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
125	C₂³×D₈₉	C₂³	1	2	yes	—
126	C₂³×D₈₉	C₂³	1	2	yes	—
127	#13083574	—	2	8	no	—
128	#13083574	—	2	4	no	—
129	#13083574	—	2	4	no	—
130	#13083574	—	2	4	no	—
131	#13083573	—	2	4	no	—
132	#13083573	—	2	8	no	—
133	#13083573	—	2	8	no	—
134	#13083573	—	2	8	no	—
135	#13083573	—	2	4	no	—
136	#13083573	D₄	1	8	yes	complemented
137	C₂×Dic₁₇₈	—	2	8	no	—
138	C₂×Dic₁₇₈	—	2	4	no	—
139	C₂×Dic₁₇₈	C₂³	1	2	yes	—
140	C₂×Dic₁₇₈	C₂³	1	2	yes	—
141	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
142	C₂×Dic₁₇₈	C₂³	1	2	yes	—
143	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
146	Q₈×D₈₉	—	2	4	no	—
147	Q₈×D₈₉	—	2	4	no	—
148	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
149	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
150	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
151	C₂×D₃₅₆	C₂³	1	2	yes	—
152	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊D₈₉	—	2	8	no	—
154	C₂×C₂²⋊D₈₉	—	2	8	no	—
155	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
159	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
161	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
163	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
164	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
165	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
166	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
169	D₄×D₈₉	—	2	4	no	—
170	D₄×D₈₉	—	2	8	no	—
171	D₄×D₈₉	—	2	4	no	—
172	C₂²×Dic₈₉	C₂³	1	2	yes	—
173	C₂²×Dic₈₉	C₂³	1	2	yes	—
174	C₂²×Dic₈₉	C₂³	1	2	yes	—
175	C₂²×Dic₈₉	C₂³	1	2	yes	—
176	C₂²×Dic₈₉	C₂³	1	2	yes	—
177	C₂×C₄×D₈₉	C₂³	1	2	yes	—
178	C₂×C₄×D₈₉	C₂³	1	2	yes	—
179	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
181	C₂×C₄×D₈₉	C₂³	1	2	yes	—
182	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
183	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₈₉	C₂³	1	2	yes	—
187	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
188	#13083553	C₂³	1	2	yes	—
189	#13083553	C₂³	1	2	yes	—
190	#13083553	C₂³	1	2	yes	—
191	#13083553	C₂³	1	2	yes	—
192	#13083553	C₂³	1	1	yes	characteristic
193	#13083553	C₂³	1	1	yes	characteristic
194	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
195	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
196	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
197	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
198	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
199	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
200	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
201	#13083551	C₂³	1	2	yes	—
202	#13083551	C₂³	1	1	yes	characteristic
203	#13083551	C₂³	1	2	yes	—
204	#13083551	C₂³	1	1	yes	characteristic
205	#13083551	C₂³	1	1	yes	characteristic
206	#13083551	C₂³	1	2	yes	—
207	#13083551	C₂³	1	1	yes	characteristic
208	#13083551	C₂³	1	2	yes	—
209	#13083551	C₂³	1	2	yes	—
210	#13083551	C₂³	1	2	yes	—
211	#13083551	C₂³	1	2	yes	—
212	#13083551	C₂³	1	2	yes	—
213	#13083551	C₂³	1	2	yes	—
214	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
215	C₄×Dic₈₉	C₂³	1	2	yes	—
216	C₄×Dic₈₉	C₂³	1	2	yes	—
217	C₄×Dic₈₉	C₂³	1	2	yes	—
218	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
219	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
220	C₂⁴×C₈₉	C₂³	1	2	yes	—
221	#41×C₈₉	—	2	4	no	—
222	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
223	C₂×D₄×C₈₉	—	2	4	no	—
224	C₂×D₄×C₈₉	C₂³	1	2	yes	—
225	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₂×D₄×C₈₉	C₂³	1	2	yes	—
227	C₂×D₄×C₈₉	C₂³	1	2	yes	—
228	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
233	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
234	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
236	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
237	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
238	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
239	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
240	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
241	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
242	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
243	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
244	C₄²×C₈₉	C₂³	1	1	yes	characteristic
245	C₂³×C₈₉	—	2	4	no	—
246	C₂³×C₈₉	—	4	2	no	—
247	C₂³×C₈₉	—	4	2	no	—
248	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂³×C₈₉	C₂⁴	1	2	yes	—
250	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂³×C₈₉	C₂⁴	1	2	yes	—
252	C₂²×D₈₉	—	2	4	no	—
253	C₂²×D₈₉	—	2	4	no	—
254	C₂²×D₈₉	—	4	2	no	—
255	C₂²×D₈₉	—	4	2	no	—
256	C₂²×D₈₉	—	4	2	no	—
257	C₂²×D₈₉	—	4	2	no	—
258	C₂²×D₈₉	C₂⁴	1	2	yes	—
259	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
261	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
262	Q₈×C₈₉	—	2	2	no	—
263	D₄×C₈₉	—	2	4	no	—
264	D₄×C₈₉	—	2	4	no	—
265	D₄×C₈₉	—	2	2	no	—
266	D₄×C₈₉	—	4	1	no	—
267	D₄×C₈₉	—	4	2	no	—
268	D₄×C₈₉	C₂×D₄	1	4	yes	—
269	C₂×C₄×C₈₉	—	2	4	no	—
270	C₂×C₄×C₈₉	—	2	2	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	4	2	no	—
273	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
276	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
278	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
279	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
280	C₂²⋊D₈₉	—	2	4	no	—
281	C₂²⋊D₈₉	—	2	4	no	—
282	C₂²⋊D₈₉	—	2	2	no	—
283	C₂²⋊D₈₉	—	2	2	no	—
284	C₂²⋊D₈₉	—	2	4	no	—
285	C₂²⋊D₈₉	—	2	4	no	—
286	C₂²⋊D₈₉	—	2	2	no	—
287	C₂²⋊D₈₉	—	2	4	no	—
288	C₂²⋊D₈₉	—	2	2	no	—
289	C₂²⋊D₈₉	—	4	1	no	—
290	C₂²⋊D₈₉	—	4	1	no	—
291	C₂²⋊D₈₉	—	4	2	no	—
292	C₂²⋊D₈₉	—	4	2	no	—
293	C₂²⋊D₈₉	C₂×D₄	1	8	yes	—
294	C₂×Dic₈₉	—	2	4	no	—
295	C₂×Dic₈₉	—	2	4	no	—
296	C₂×Dic₈₉	—	2	4	no	—
297	C₂×Dic₈₉	—	4	2	no	—
298	C₂×Dic₈₉	C₂×D₄	1	8	yes	—
299	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
300	C₂×Dic₈₉	C₂⁴	1	2	yes	—
301	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
302	C₂×Dic₈₉	C₂⁴	1	2	yes	—
303	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
304	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
305	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
306	C₂×Dic₈₉	C₂⁴	1	2	yes	—
307	D₃₅₆	—	2	2	no	—
308	D₃₅₆	—	2	2	no	—
309	D₃₅₆	—	2	2	no	—
310	D₃₅₆	—	4	1	no	—
311	D₃₅₆	—	4	2	no	—
312	C₄×D₈₉	—	2	4	no	—
313	C₄×D₈₉	—	2	2	no	—
314	C₄×D₈₉	—	2	2	no	—
315	C₄×D₈₉	—	2	4	no	—
316	C₄×D₈₉	—	2	4	no	—
317	C₄×D₈₉	—	4	1	no	—
318	C₄×D₈₉	—	4	1	no	—
319	C₄×D₈₉	C₂×D₄	1	4	yes	—
320	Dic₁₇₈	—	2	2	no	—
321	Dic₁₇₈	—	2	4	no	—
322	Dic₁₇₈	—	2	4	no	—
323	Dic₁₇₈	—	2	2	no	—
324	Dic₁₇₈	—	2	4	no	—
325	Dic₁₇₈	—	2	2	no	—
326	Dic₁₇₈	C₂×D₄	1	4	yes	—
327	C₂²×C₈₉	—	2	2	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	1	no	—
330	C₂²×C₈₉	—	2	2	no	—
331	C₂²×C₈₉	—	2	1	no	—
332	C₂²×C₈₉	—	2	1	no	—
333	C₂²×C₈₉	—	2	1	no	—
334	C₂²×C₈₉	—	2	2	no	—
335	C₂²×C₈₉	—	2	1	no	—
336	C₂²×C₈₉	—	2	2	no	—
337	C₂²×C₈₉	—	2	1	no	—
338	C₂²×C₈₉	—	8	4	no	—
339	C₂²×C₈₉	C₂²×D₄	1	4	yes	—
340	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
341	C₂×D₈₉	—	2	1	no	—
342	C₂×D₈₉	—	2	1	no	—
343	C₂×D₈₉	—	2	1	no	—
344	C₂×D₈₉	—	2	1	no	—
345	C₂×D₈₉	—	2	2	no	—
346	C₂×D₈₉	—	2	1	no	—
347	C₂×D₈₉	—	2	1	no	—
348	C₂×D₈₉	—	2	2	no	—
349	C₂×D₈₉	—	2	1	no	—
350	C₂×D₈₉	—	2	1	no	—
351	C₂×D₈₉	—	2	2	no	—
352	C₂×D₈₉	—	8	4	no	—
353	C₂×D₈₉	—	8	4	no	—
354	C₂×D₈₉	C₂²×D₄	1	2	yes	—
355	C₄×C₈₉	—	2	1	no	—
356	C₄×C₈₉	—	2	2	no	—
357	C₄×C₈₉	—	2	1	no	—
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	2	1	no	—
360	C₄×C₈₉	—	2	2	no	—
361	C₄×C₈₉	C₂²×D₄	1	2	yes	—
362	Dic₈₉	—	2	2	no	—
363	Dic₈₉	—	2	1	no	—
364	Dic₈₉	—	2	1	no	—
365	Dic₈₉	—	2	1	no	—
366	Dic₈₉	—	2	1	no	—
367	Dic₈₉	—	2	2	no	—
368	Dic₈₉	C₂²×D₄	1	2	yes	—
369	Dic₈₉	C₂²×D₄	1	4	yes	—
370	C₂×C₈₉	—	2	4	no	—
371	C₂×C₈₉	—	4	2	no	—
372	C₂×C₈₉	—	4	1	no	—
373	C₂×C₈₉	—	4	1	no	—
374	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
375	C₂×C₈₉	#585	1	1	yes	characteristic
376	C₂×C₈₉	#585	1	1	yes	characteristic
377	D₈₉	—	2	2	no	—
378	D₈₉	—	4	1	no	—
379	D₈₉	—	4	2	no	—
380	D₈₉	—	4	1	no	—
381	#3500	—	89	1	no	maximal, Sylow
382	C₈₉	#3500	1	1	yes	characteristic, complemented, Sylow
383	C₂×2₋¹⁺⁴	—	89	1	no	—
384	C₂×H(5,𝔽₂)	—	89	1	no	—
385	#548	—	89	1	no	—
386	#548	—	89	1	no	—
387	#548	—	89	1	no	—
388	#548	—	89	1	no	—
389	#546	—	89	1	no	—
390	#546	—	89	1	no	—
391	#546	—	89	2	no	—
392	#546	—	89	2	no	—
393	#546	—	89	2	no	—
394	#546	—	89	1	no	—
395	#546	—	89	2	no	—
396	#546	D₈₉	1	1	yes	characteristic, complemented
397	#536	—	89	2	no	—
398	#536	—	89	1	no	—
399	#535	—	89	1	no	—
400	#535	—	89	2	no	—
401	#532	—	89	2	no	—
402	#532	—	89	1	no	—
403	C₂×#124	—	89	1	no	—
404	C₂×#124	—	89	2	no	—
405	C₄×#41	—	89	1	no	—
406	2₋¹⁺⁴	—	178	8	no	—
407	H(5,𝔽₂)	—	178	8	no	—
408	C₂×#41	—	89	1	no	—
409	C₂×#41	—	89	2	no	—
410	C₂×#41	—	89	2	no	—
411	C₂×#41	—	89	1	no	—
412	C₂×#41	—	89	2	no	—
413	C₂×#41	—	89	1	no	—
414	C₂×#41	—	89	1	no	—
415	C₂×#41	—	89	1	no	—
416	C₂×#41	—	89	2	no	—
417	C₂×#41	—	89	1	no	—
418	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
419	C₂²×Q₈	—	89	1	no	—
420	C₂²×Q₈	—	89	1	no	—
421	C₂²×Q₈	—	89	2	no	—
422	C₂²×Q₈	—	89	1	no	—
423	C₂²×D₄	—	89	2	no	—
424	C₂²×D₄	—	89	2	no	—
425	C₂²×D₄	—	89	1	no	—
426	C₂²×D₄	—	89	2	no	—
427	C₂²×D₄	—	89	1	no	—
428	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
429	C₄⋊Q₈	—	89	2	no	—
430	C₄⋊Q₈	—	89	1	no	—
431	#127	—	89	2	no	—
432	#127	—	89	1	no	—
433	#124	—	89	1	no	—
434	#124	—	89	1	no	—
435	#124	—	89	2	no	—
436	#124	—	89	1	no	—
437	#124	—	89	2	no	—
438	#124	—	89	2	no	—
439	#124	—	89	2	no	—
440	#124	—	89	2	no	—
441	#124	—	89	2	no	—
442	#124	—	89	2	no	—
443	#124	—	89	2	no	—
444	#124	—	89	1	no	—
445	#124	—	89	1	no	—
446	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
447	#123	—	89	2	no	—
448	#123	—	89	2	no	—
449	#123	—	89	2	no	—
450	#123	—	89	2	no	—
451	#123	—	89	2	no	—
452	#123	C₂×D₈₉	1	2	yes	complemented
453	C₂²⋊Q₈	—	89	1	no	—
454	C₂²⋊Q₈	—	89	1	no	—
455	C₂²⋊Q₈	—	89	2	no	—
456	C₂²⋊Q₈	—	89	2	no	—
457	C₂²⋊Q₈	—	89	1	no	—
458	C₂²⋊Q₈	—	89	2	no	—
459	C₂²⋊Q₈	—	89	2	no	—
460	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
461	#121	—	89	1	no	—
462	#121	—	89	1	no	—
463	#121	—	89	2	no	—
464	#121	—	89	2	no	—
465	#121	—	89	2	no	—
466	#121	—	89	2	no	—
467	#121	—	89	2	no	—
468	#121	—	89	1	no	—
469	#121	—	89	1	no	—
470	#121	—	89	1	no	—
471	#121	—	89	1	no	—
472	#121	—	89	1	no	—
473	#121	—	89	2	no	—
474	#121	—	89	2	no	—
475	#121	C₂×D₈₉	1	2	yes	complemented
476	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
477	#120	—	89	2	no	—
478	#120	—	89	2	no	—
479	#120	—	89	2	no	—
480	#120	—	89	2	no	—
481	#120	—	89	2	no	—
482	#120	C₂×D₈₉	1	2	yes	complemented
483	C₄×Q₈	—	89	1	no	—
484	C₄×Q₈	—	89	1	no	—
485	C₄×D₄	—	89	1	no	—
486	C₄×D₄	—	89	2	no	—
487	C₄×D₄	—	89	2	no	—
488	C₄×D₄	—	89	1	no	—
489	C₄×D₄	—	89	1	no	—
490	C₄×D₄	—	89	2	no	—
491	C₄×D₄	—	89	2	no	—
492	C₄×D₄	—	89	2	no	—
493	C₄×D₄	—	89	2	no	—
494	C₄×D₄	—	89	1	no	—
495	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
496	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
497	#117	—	89	1	no	—
498	#117	—	89	2	no	—
499	C₂×C₂²⋊C₄	—	89	2	no	—
500	C₂×C₂²⋊C₄	—	89	2	no	—
501	C₂×C₂²⋊C₄	—	89	2	no	—
502	C₂×C₂²⋊C₄	—	89	2	no	—
503	C₂×C₂²⋊C₄	—	89	2	no	—
504	C₂×C₂²⋊C₄	C₂×D₈₉	1	2	yes	complemented
505	C₂×C₄²	—	89	2	no	—
506	C₂×C₄²	—	89	1	no	—
507	C₂⁴	—	89	2	no	—
508	C₂⁴	—	89	2	no	—
509	C₂⁴	C₂²×D₈₉	1	2	yes	—
510	#41	—	2	4	no	—
511	#41	—	89	8	no	—
512	#41	—	178	4	no	—
513	#41	—	178	4	no	—
514	#41	—	178	8	no	—
515	#41	—	178	4	no	—
516	#41	—	178	8	no	—
517	#41	—	178	8	no	—
518	#41	—	178	8	no	—
519	#41	—	178	4	no	—
520	#41	—	178	4	no	—
521	C₂×Q₈	—	89	1	no	—
522	C₂×Q₈	—	89	2	no	—
523	C₂×Q₈	—	89	2	no	—
524	C₂×Q₈	—	89	1	no	—
525	C₂×Q₈	—	89	2	no	—
526	C₂×Q₈	—	89	1	no	—
527	C₂×Q₈	—	89	1	no	—
528	C₂×Q₈	—	178	8	no	—
529	C₂×Q₈	—	178	4	no	—
530	C₂×Q₈	—	178	4	no	—
531	C₂×Q₈	—	178	4	no	—
532	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	89	2	no	—
535	C₂×D₄	—	89	1	no	—
536	C₂×D₄	—	89	2	no	—
537	C₂×D₄	—	89	2	no	—
538	C₂×D₄	—	89	1	no	—
539	C₂×D₄	—	89	1	no	—
540	C₂×D₄	—	89	2	no	—
541	C₂×D₄	—	89	1	no	—
542	C₂×D₄	—	89	2	no	—
543	C₂×D₄	—	89	2	no	—
544	C₂×D₄	—	89	2	no	—
545	C₂×D₄	—	89	2	no	—
546	C₂×D₄	—	89	1	no	—
547	C₂×D₄	—	89	1	no	—
548	C₂×D₄	—	89	2	no	—
549	C₂×D₄	—	89	1	no	—
550	C₂×D₄	—	89	1	no	—
551	C₂×D₄	—	89	1	no	—
552	C₂×D₄	—	89	1	no	—
553	C₂×D₄	—	178	4	no	—
554	C₂×D₄	—	178	8	no	—
555	C₂×D₄	—	178	8	no	—
556	C₂×D₄	—	178	8	no	—
557	C₂×D₄	—	178	4	no	—
558	C₂×D₄	C₂²×D₈₉	1	2	yes	—
559	C₂×D₄	C₂²×D₈₉	1	2	yes	—
560	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
561	C₂×D₄	C₂²×D₈₉	1	2	yes	—
562	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
563	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
564	C₂²×C₄	—	89	2	no	—
565	C₂²×C₄	—	89	1	no	—
566	C₂²×C₄	—	89	2	no	—
567	C₂²×C₄	—	89	2	no	—
568	C₂²×C₄	—	89	2	no	—
569	C₂²×C₄	—	89	2	no	—
570	C₂²×C₄	—	89	1	no	—
571	C₂²×C₄	—	89	1	no	—
572	C₂²×C₄	—	89	2	no	—
573	C₂²×C₄	—	89	2	no	—
574	C₂²×C₄	—	89	1	no	—
575	C₂²×C₄	—	89	2	no	—
576	C₂²×C₄	—	89	1	no	—
577	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
578	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
579	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
580	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
581	C₄⋊C₄	—	89	2	no	—
582	C₄⋊C₄	—	89	2	no	—
583	C₄⋊C₄	—	89	1	no	—
584	C₄⋊C₄	—	89	1	no	—
585	C₄⋊C₄	—	89	2	no	—
586	C₄⋊C₄	—	89	2	no	—
587	C₄⋊C₄	—	89	1	no	—
588	C₄⋊C₄	—	89	2	no	—
589	C₄⋊C₄	—	89	1	no	—
590	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
591	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
592	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
593	C₂²⋊C₄	—	89	2	no	—
594	C₂²⋊C₄	—	89	1	no	—
595	C₂²⋊C₄	—	89	2	no	—
596	C₂²⋊C₄	—	89	2	no	—
597	C₂²⋊C₄	—	89	2	no	—
598	C₂²⋊C₄	—	89	2	no	—
599	C₂²⋊C₄	—	89	1	no	—
600	C₂²⋊C₄	—	89	2	no	—
601	C₂²⋊C₄	—	89	1	no	—
602	C₂²⋊C₄	—	89	1	no	—
603	C₂²⋊C₄	—	89	2	no	—
604	C₂²⋊C₄	—	89	2	no	—
605	C₂²⋊C₄	—	89	2	no	—
606	C₂²⋊C₄	—	89	2	no	—
607	C₂²⋊C₄	—	89	2	no	—
608	C₂²⋊C₄	—	89	2	no	—
609	C₂²⋊C₄	—	89	2	no	—
610	C₂²⋊C₄	—	89	2	no	—
611	C₂²⋊C₄	—	89	1	no	—
612	C₂²⋊C₄	—	89	1	no	—
613	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
614	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
615	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
616	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
617	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
618	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
619	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
620	C₄²	—	89	1	no	—
621	C₄²	—	89	2	no	—
622	C₄²	—	89	1	no	—
623	C₄²	—	89	2	no	—
624	C₄²	—	89	2	no	—
625	C₄²	—	89	1	no	—
626	C₄²	C₂²×D₈₉	1	1	yes	characteristic
627	C₂³	—	2	4	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	2	no	—
630	C₂³	—	89	1	no	—
631	C₂³	—	89	2	no	—
632	C₂³	—	89	1	no	—
633	C₂³	—	89	1	no	—
634	C₂³	—	356	2	no	—
635	C₂³	—	356	2	no	—
636	C₂³	—	356	2	no	—
637	C₂³	—	356	2	no	—
638	C₂³	—	178	4	no	—
639	C₂³	—	178	4	no	—
640	C₂³	C₂³×D₈₉	1	2	yes	—
641	C₂³	C₂³×D₈₉	1	1	yes	characteristic
642	C₂³	C₂³×D₈₉	1	1	yes	characteristic
643	C₂³	C₂³×D₈₉	1	2	yes	—
644	Q₈	—	2	2	no	—
645	Q₈	—	89	4	no	—
646	Q₈	—	178	2	no	—
647	Q₈	—	178	4	no	—
648	Q₈	—	178	4	no	—
649	Q₈	—	178	4	no	—
650	Q₈	—	178	2	no	—
651	Q₈	—	178	2	no	—
652	D₄	—	2	4	no	—
653	D₄	—	2	4	no	—
654	D₄	—	2	2	no	—
655	D₄	—	4	2	no	—
656	D₄	—	4	1	no	—
657	D₄	—	89	8	no	—
658	D₄	—	356	2	no	—
659	D₄	—	356	1	no	—
660	D₄	—	356	1	no	—
661	D₄	—	356	1	no	—
662	D₄	—	356	2	no	—
663	D₄	—	356	2	no	—
664	D₄	—	178	2	no	—
665	D₄	—	178	2	no	—
666	D₄	—	178	2	no	—
667	D₄	—	178	4	no	—
668	D₄	—	178	4	no	—
669	D₄	—	178	4	no	—
670	D₄	—	178	2	no	—
671	D₄	—	178	2	no	—
672	D₄	—	178	2	no	—
673	D₄	—	178	4	no	—
674	D₄	—	178	4	no	—
675	D₄	—	178	2	no	—
676	D₄	D₄×D₈₉	1	4	yes	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	89	8	no	—
682	C₂×C₄	—	89	1	no	—
683	C₂×C₄	—	89	2	no	—
684	C₂×C₄	—	89	4	no	—
685	C₂×C₄	—	89	1	no	—
686	C₂×C₄	—	89	1	no	—
687	C₂×C₄	—	89	2	no	—
688	C₂×C₄	—	89	1	no	—
689	C₂×C₄	—	89	2	no	—
690	C₂×C₄	—	89	1	no	—
691	C₂×C₄	—	356	1	no	—
692	C₂×C₄	—	356	1	no	—
693	C₂×C₄	—	356	2	no	—
694	C₂×C₄	—	178	4	no	—
695	C₂×C₄	—	178	4	no	—
696	C₂×C₄	—	178	4	no	—
697	C₂×C₄	—	178	4	no	—
698	C₂×C₄	—	178	4	no	—
699	C₂×C₄	—	178	4	no	—
700	C₂×C₄	—	178	2	no	—
701	C₂×C₄	—	178	2	no	—
702	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
703	C₂×C₄	C₂³×D₈₉	1	2	yes	—
704	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
705	C₂×C₄	C₂³×D₈₉	1	2	yes	—
706	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
709	C₂²	—	2	2	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	8	4	no	—
721	C₂²	—	89	2	no	—
722	C₂²	—	178	1	no	—
723	C₂²	—	178	2	no	—
724	C₂²	—	178	1	no	—
725	C₂²	—	178	1	no	—
726	C₂²	—	178	2	no	—
727	C₂²	—	178	1	no	—
728	C₂²	—	178	1	no	—
729	C₂²	—	178	1	no	—
730	C₂²	—	178	2	no	—
731	C₂²	—	178	1	no	—
732	C₂²	—	178	1	no	—
733	C₂²	—	712	4	no	—
734	C₂²	—	712	4	no	—
735	C₂²	C₂×D₄×D₈₉	1	4	yes	—
736	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	1	no	—
741	C₄	—	2	2	no	—
742	C₄	—	2	1	no	—
743	C₄	—	89	2	no	—
744	C₄	—	89	4	no	—
745	C₄	—	178	1	no	—
746	C₄	—	178	2	no	—
747	C₄	—	178	1	no	—
748	C₄	—	178	1	no	—
749	C₄	—	178	1	no	—
750	C₄	—	178	2	no	—
751	C₄	C₂×D₄×D₈₉	1	2	yes	—
752	C₂	—	2	4	no	—
753	C₂	—	4	1	no	—
754	C₂	—	4	1	no	—
755	C₂	—	4	2	no	—
756	C₂	—	356	1	no	—
757	C₂	—	356	1	no	—
758	C₂	—	356	2	no	—
759	C₂	—	178	2	no	—
760	C₂	C₂²×D₄×D₈₉	1	1	yes	characteristic
761	C₂	#19152433	1	1	yes	characteristic
762	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#546×C₈₉	C₂
hypercenter	#546	D₈₉
hypocenter	C₈₉	#3500
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#15668059	C₂	semidirect
2. C₂×#15668057	C₂	semidirect
3. #19152258	C₂	semidirect
4. #19152257	C₂	semidirect
5. #19152256	C₂	semidirect
6. #19152254	C₂	semidirect
7. #19152243	C₂	semidirect
8. #19152242	C₂	semidirect
9. #19152240	C₂	semidirect
10. #19152238	C₂	semidirect
11. #19152237	C₂	semidirect
12. #19152236	C₂	semidirect
13. #19152235	C₂	semidirect
14. #19152171	C₂	semidirect
15. #19152170	C₂	semidirect
16. #19152164	C₂	semidirect
17. #19152163	C₂	semidirect
18. #19152145	C₂	semidirect
19. #19152143	C₂	semidirect
20. C₂×#15667998	C₂	semidirect
21. #124×D₈₉	C₂	semidirect
22. C₄×#13083573	C₂	semidirect
23. #546×C₈₉	C₂	semidirect
28. C₂×#13083574	C₂²	semidirect
29. C₂×#13083574	C₂²	semidirect
33. C₂×#13083573	C₂²	semidirect
34. C₂×#13083573	C₂²	semidirect
35. C₂×#13083573	C₂²	semidirect
36. C₂²×Dic₁₇₈	C₂²	semidirect
37. C₂²×Dic₁₇₈	C₂²	semidirect
38. C₂×Q₈×D₈₉	C₂²	semidirect
39. C₂×Q₈×D₈₉	C₂²	semidirect
45. #15668011	C₂²	semidirect
46. #15668011	C₂²	semidirect
47. #15668008	C₂²	semidirect
48. #15668008	C₂²	semidirect
49. #15668001	C₂²	semidirect
50. #15668000	C₂²	semidirect
51. #15667999	C₂²	semidirect
52. #15667998	C₂²	semidirect
53. #15667998	C₂²	semidirect
54. #15667998	C₂²	semidirect
55. #15667998	C₂²	semidirect
56. #15667998	C₂²	semidirect
57. #15667998	C₂²	semidirect
58. #15667998	C₂²	semidirect
59. #15667998	C₂²	semidirect
60. #15667998	C₂²	semidirect
61. #15667998	C₂²	semidirect
62. #15667997	C₂²	semidirect
63. #15667996	C₂²	semidirect
64. #15667995	C₂²	semidirect
65. #15667994	C₂²	semidirect
66. #15667993	C₂²	semidirect
67. #15667992	C₂²	semidirect
68. #15667991	C₂²	semidirect
69. #15667990	C₂²	semidirect
70. #15667990	C₂²	semidirect
71. #15667989	C₂²	semidirect
72. #15667989	C₂²	semidirect
73. #15667988	C₂²	semidirect
74. #15667987	C₂²	semidirect
75. #15667987	C₂²	semidirect
76. #15667986	C₂²	semidirect
77. #15667986	C₂²	semidirect
78. #15667985	C₂²	semidirect
79. #15667985	C₂²	semidirect
80. #15667985	C₂²	semidirect
81. #15667985	C₂²	semidirect
82. #15667984	C₂²	semidirect
83. #15667984	C₂²	semidirect
84. #15667984	C₂²	semidirect
85. #15667984	C₂²	semidirect
86. #15667983	C₂²	semidirect
87. #15667983	C₂²	semidirect
88. #15667982	C₂²	semidirect
89. #15667982	C₂²	semidirect
90. #15667981	C₂²	semidirect
91. #15667980	C₂²	semidirect
92. #15667980	C₂²	semidirect
93. C₄×Dic₁₇₈	C₂²	semidirect
94. #15667977	C₂²	semidirect
95. C₄×D₃₅₆	C₂²	semidirect
96. D₄×Dic₈₉	C₂²	semidirect
97. D₄×Dic₈₉	C₂²	semidirect
98. #15667974	C₂²	semidirect
99. C₄×C₂²⋊D₈₉	C₂²	semidirect
100. C₄×C₂²⋊D₈₉	C₂²	semidirect
101. C₄×C₂²⋊D₈₉	C₂²	semidirect
102. #15667972	C₂²	semidirect
103. #15667972	C₂²	semidirect
104. #15667972	C₂²	semidirect
105. #15667970	C₂²	semidirect
106. #15667968	C₂²	semidirect
107. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
108. C₂×#13083551	C₂²	semidirect
109. C₂×#13083551	C₂²	semidirect
110. C₂²⋊C₄×D₈₉	C₂²	semidirect
111. C₂²⋊C₄×D₈₉	C₂²	semidirect
112. C₂×C₄×Dic₈₉	C₂²	semidirect
113. C₄²×D₈₉	C₂²	semidirect
114. C₂×#41×C₈₉	C₂²	semidirect
116. #124×C₈₉	C₂²	semidirect
117. #123×C₈₉	C₂²	semidirect
118. C₂²⋊Q₈×C₈₉	C₂²	semidirect
119. #121×C₈₉	C₂²	semidirect
120. #121×C₈₉	C₂²	semidirect
121. #120×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
123. C₄×D₄×C₈₉	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
136. #13083573	D₄	semidirect
382. C₈₉	#3500	semidirect
396. #546	D₈₉	semidirect
418. C₂×#41	C₂×D₈₉	semidirect
446. #124	C₂×D₈₉	semidirect
452. #123	C₂×D₈₉	semidirect
460. C₂²⋊Q₈	C₂×D₈₉	semidirect
475. #121	C₂×D₈₉	semidirect
476. #121	C₂×D₈₉	semidirect
482. #120	C₂×D₈₉	semidirect
495. C₄×D₄	C₂×D₈₉	semidirect
496. C₄×D₄	C₂×D₈₉	semidirect
504. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15668059	2
C₂×#15668057	2
#19152258	2
#19152257	2
#19152256	2
#19152254	2
#19152243	2
#19152242	2
#19152240	2
#19152238	2
#19152237	2
#19152236	2
#19152235	2
#19152171	2
#19152170	2
#19152164	2
#19152163	2
#19152145	2
#19152143	2
C₂×#15667998	2
#124×D₈₉	2
C₄×#13083573	2
#546×C₈₉	2
#3500	89