Subgroups — #26034404

Order 11392.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152341	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152338	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152336	C₂	1	2	yes	maximal, complemented
4	#19152276	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152271	C₂	1	2	yes	maximal, complemented
6	#19152245	C₂	1	2	yes	maximal, complemented
7	#19152240	C₂	1	2	yes	maximal, complemented
8	#19152238	C₂	1	2	yes	maximal, complemented
9	D₄×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
10	#19152230	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152184	C₂	1	2	yes	maximal, complemented
12	#19152183	C₂	1	2	yes	maximal, complemented
13	#19152180	C₂	1	2	yes	maximal, complemented
14	#19152165	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152164	C₂	1	2	yes	maximal, complemented
16	#19152158	C₂	1	2	yes	maximal, complemented
17	C₂×#15667980	C₂	1	1	yes	maximal, characteristic, complemented
18	#120×D₈₉	C₂	1	2	yes	maximal, complemented
19	#534×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083574	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
25	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
26	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
27	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
28	#15668008	C₂²	1	1	yes	characteristic, complemented
29	#15668008	C₂²	1	1	yes	characteristic, complemented
30	#15668008	C₂²	1	2	yes	complemented
31	#15668007	C₂²	1	2	yes	complemented
32	#15668007	C₂²	1	2	yes	complemented
33	#15668005	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	complemented
35	#15667999	C₂²	1	1	yes	characteristic, complemented
36	#15667999	C₂²	1	1	yes	characteristic, complemented
37	#15667999	C₂²	1	2	yes	complemented
38	#15667998	C₂²	1	2	yes	complemented
39	#15667998	C₂²	1	2	yes	complemented
40	#15667998	C₂²	1	2	yes	complemented
41	#15667998	C₂²	1	2	yes	complemented
42	#15667997	C₂²	1	2	yes	complemented
43	#15667996	C₂²	1	2	yes	complemented
44	#15667995	C₂²	1	2	yes	complemented
45	#15667994	C₂²	1	2	yes	complemented
46	#15667994	C₂²	1	2	yes	complemented
47	#15667994	C₂²	1	2	yes	complemented
48	#15667993	C₂²	1	2	yes	complemented
49	#15667992	C₂²	1	2	yes	complemented
50	#15667990	C₂²	1	2	yes	complemented
51	#15667989	C₂²	1	2	yes	complemented
52	#15667987	C₂²	1	2	yes	complemented
53	#15667986	C₂²	1	2	yes	complemented
54	#15667986	C₂²	1	2	yes	complemented
55	#15667985	C₂²	1	2	yes	complemented
56	#15667985	C₂²	1	2	yes	complemented
57	#15667985	C₂²	1	2	yes	complemented
58	#15667984	C₂²	1	2	yes	complemented
59	#15667984	C₂²	1	2	yes	complemented
60	#15667984	C₂²	1	2	yes	complemented
61	#15667983	C₂²	1	2	yes	complemented
62	#15667983	C₂²	1	2	yes	complemented
63	#15667983	C₂²	1	2	yes	complemented
64	#15667983	C₂²	1	2	yes	complemented
65	#15667982	C₂²	1	2	yes	complemented
66	#15667982	C₂²	1	2	yes	complemented
67	#15667982	C₂²	1	2	yes	complemented
68	#15667982	C₂²	1	2	yes	complemented
69	#15667981	C₂²	1	2	yes	complemented
70	#15667981	C₂²	1	2	yes	complemented
71	#15667981	C₂²	1	2	yes	complemented
72	#15667980	C₂²	1	1	yes	characteristic
73	#15667980	C₂²	1	2	yes	—
74	#15667980	C₂²	1	2	yes	complemented
75	#15667980	C₂²	1	2	yes	complemented
76	#15667980	C₂²	1	2	yes	complemented
77	#15667980	C₂²	1	1	yes	characteristic, complemented
78	#15667980	C₂²	1	1	yes	characteristic, complemented
79	#15667980	C₂²	1	2	yes	complemented
80	#15667980	C₂²	1	1	yes	characteristic, complemented
81	#15667980	C₂²	1	2	yes	complemented
82	D₄×Dic₈₉	C₂²	1	2	yes	complemented
83	#15667974	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
86	#15667972	C₂²	1	2	yes	complemented
87	#15667972	C₂²	1	2	yes	complemented
88	#15667971	C₂²	1	1	yes	characteristic, complemented
89	#15667970	C₂²	1	2	yes	complemented
90	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
91	C₂×#13083551	C₂²	1	2	yes	complemented
92	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
96	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
97	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
98	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	#123×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#123×C₈₉	C₂²	1	2	yes	complemented
101	#121×C₈₉	C₂²	1	2	yes	complemented
102	#121×C₈₉	C₂²	1	2	yes	complemented
103	#120×C₈₉	C₂²	1	2	yes	complemented
104	#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
105	#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₈₉	—	4	4	no	—
108	C₂³×D₈₉	—	4	2	no	—
109	C₂³×D₈₉	C₂³	1	1	yes	characteristic
110	C₂³×D₈₉	C₂³	1	2	yes	—
111	C₂³×D₈₉	C₂³	1	2	yes	—
112	C₂³×D₈₉	C₂³	1	2	yes	—
113	C₂³×D₈₉	C₂³	1	1	yes	characteristic
114	#13083574	—	4	4	no	—
115	#13083574	—	4	2	no	—
116	C₂×Dic₁₇₈	C₂³	1	2	yes	complemented
117	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic, complemented
118	C₂×D₃₅₆	C₂³	1	2	yes	—
119	C₂×D₃₅₆	C₂³	1	2	yes	—
120	C₂×D₃₅₆	C₂³	1	2	yes	—
121	C₂×D₃₅₆	C₂³	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊D₈₉	—	4	4	no	—
123	C₂×C₂²⋊D₈₉	—	4	4	no	—
124	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	complemented
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	complemented
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	complemented
137	D₄×D₈₉	—	4	4	no	—
138	D₄×D₈₉	—	4	4	no	—
139	D₄×D₈₉	—	4	4	no	—
140	C₂²×Dic₈₉	C₂³	1	2	yes	—
141	C₂²×Dic₈₉	C₂³	1	2	yes	complemented
142	C₂×C₄×D₈₉	C₂³	1	2	yes	—
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
144	C₂×C₄×D₈₉	C₂³	1	2	yes	—
145	C₂×C₄×D₈₉	C₂³	1	2	yes	complemented
146	C₂×C₄×D₈₉	C₂³	1	2	yes	complemented
147	C₄⋊Dic₈₉	C₂³	1	2	yes	complemented
148	C₄⋊Dic₈₉	C₂³	1	2	yes	complemented
149	C₄⋊Dic₈₉	C₂³	1	2	yes	complemented
150	#13083553	C₂³	1	2	yes	complemented
151	#13083553	C₂³	1	2	yes	complemented
152	#13083553	C₂³	1	2	yes	complemented
153	#13083553	C₂³	1	2	yes	complemented
154	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
156	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
158	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
159	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₈₉	C₂³	1	2	yes	complemented
161	C₂²⋊Dic₈₉	C₂³	1	2	yes	complemented
162	C₂²⋊Dic₈₉	C₂³	1	2	yes	complemented
163	C₂²⋊Dic₈₉	C₂³	1	2	yes	complemented
164	#13083551	C₂³	1	2	yes	—
165	#13083551	C₂³	1	2	yes	—
166	#13083551	C₂³	1	2	yes	—
167	#13083551	C₂³	1	2	yes	—
168	#13083551	C₂³	1	2	yes	—
169	#13083551	C₂³	1	2	yes	—
170	#13083551	C₂³	1	2	yes	—
171	#13083551	C₂³	1	2	yes	—
172	#13083551	C₂³	1	2	yes	—
173	#13083551	C₂³	1	2	yes	—
174	#13083551	C₂³	1	2	yes	complemented
175	#13083551	C₂³	1	2	yes	complemented
176	C₄×Dic₈₉	C₂³	1	1	yes	characteristic, complemented
177	C₄×Dic₈₉	C₂³	1	2	yes	complemented
178	C₄×Dic₈₉	C₂³	1	1	yes	characteristic, complemented
179	C₄×Dic₈₉	C₂³	1	2	yes	complemented
180	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
181	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
182	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic, complemented
183	C₂×D₄×C₈₉	—	4	2	no	—
184	C₂×D₄×C₈₉	—	4	2	no	—
185	C₂×D₄×C₈₉	C₂³	1	2	yes	—
186	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
187	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
188	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₈₉	C₂³	1	2	yes	—
191	C₂×D₄×C₈₉	C₂³	1	2	yes	—
192	C₂×D₄×C₈₉	C₂³	1	2	yes	complemented
193	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
195	C₂²×C₄×C₈₉	C₂³	1	2	yes	complemented
196	C₄⋊C₄×C₈₉	C₂³	1	2	yes	complemented
197	C₄⋊C₄×C₈₉	C₂³	1	2	yes	complemented
198	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
199	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
200	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
201	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	complemented
202	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
203	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic, complemented
204	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	complemented
205	C₂³×C₈₉	—	2	2	no	—
206	C₂³×C₈₉	—	2	2	no	—
207	C₂³×C₈₉	—	4	2	no	—
208	C₂³×C₈₉	—	4	1	no	—
209	C₂³×C₈₉	—	4	2	no	—
210	C₂³×C₈₉	—	4	2	no	—
211	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂³×C₈₉	C₂⁴	1	2	yes	—
215	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
216	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₂²×D₈₉	—	2	4	no	—
218	C₂²×D₈₉	—	2	4	no	—
219	C₂²×D₈₉	—	2	4	no	—
220	C₂²×D₈₉	—	2	4	no	—
221	C₂²×D₈₉	—	2	4	no	—
222	C₂²×D₈₉	—	4	1	no	—
223	C₂²×D₈₉	—	4	2	no	—
224	C₂²×D₈₉	—	4	2	no	—
225	C₂²×D₈₉	—	4	2	no	—
226	C₂²×D₈₉	—	4	1	no	—
227	C₂²×D₈₉	—	4	2	no	—
228	C₂²×D₈₉	—	4	2	no	—
229	C₂²×D₈₉	—	4	2	no	—
230	C₂²×D₈₉	—	4	16	no	—
231	C₂²×D₈₉	C₂⁴	1	2	yes	—
232	C₂²×D₈₉	C₂⁴	1	2	yes	—
233	C₂²×D₈₉	C₂⁴	1	2	yes	—
234	D₄×C₈₉	—	2	4	no	—
235	D₄×C₈₉	—	4	1	no	—
236	D₄×C₈₉	—	4	1	no	—
237	D₄×C₈₉	—	4	1	no	—
238	D₄×C₈₉	—	4	1	no	—
239	D₄×C₈₉	—	4	2	no	—
240	D₄×C₈₉	—	4	2	no	—
241	D₄×C₈₉	—	4	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	4	1	no	—
244	C₂×C₄×C₈₉	—	4	2	no	—
245	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂²⋊D₈₉	—	2	4	no	—
251	C₂²⋊D₈₉	—	2	4	no	—
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	—	4	2	no	—
259	C₂²⋊D₈₉	—	4	2	no	—
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂²⋊D₈₉	—	4	2	no	—
262	C₂²⋊D₈₉	—	4	2	no	—
263	C₂×Dic₈₉	—	4	2	no	—
264	C₂×Dic₈₉	—	4	2	no	—
265	C₂×Dic₈₉	C₂⁴	1	2	yes	—
266	C₂×Dic₈₉	C₂⁴	1	2	yes	—
267	C₂×Dic₈₉	C₂⁴	1	2	yes	—
268	C₂×Dic₈₉	C₂⁴	1	2	yes	—
269	C₂×Dic₈₉	C₂⁴	1	2	yes	—
270	D₃₅₆	—	2	4	no	—
271	D₃₅₆	—	4	2	no	—
272	D₃₅₆	—	4	2	no	—
273	D₃₅₆	—	4	1	no	—
274	C₄×D₈₉	—	2	4	no	—
275	C₄×D₈₉	—	4	2	no	—
276	C₄×D₈₉	—	4	2	no	—
277	C₄×D₈₉	—	4	2	no	—
278	C₄×D₈₉	—	4	2	no	—
279	Dic₁₇₈	—	4	2	no	—
280	Dic₁₇₈	—	4	1	no	—
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	—	2	2	no	—
283	C₂²×C₈₉	—	2	2	no	—
284	C₂²×C₈₉	—	2	2	no	—
285	C₂²×C₈₉	—	2	2	no	—
286	C₂²×C₈₉	—	2	2	no	—
287	C₂²×C₈₉	—	2	2	no	—
288	C₂²×C₈₉	—	2	2	no	—
289	C₂²×C₈₉	—	2	1	no	—
290	C₂²×C₈₉	—	2	1	no	—
291	C₂²×C₈₉	—	2	1	no	—
292	C₂²×C₈₉	—	2	1	no	—
293	C₂²×C₈₉	—	4	4	no	—
294	C₂²×C₈₉	—	8	2	no	—
295	C₂²×C₈₉	—	8	2	no	—
296	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
297	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
298	C₂×D₈₉	—	2	2	no	—
299	C₂×D₈₉	—	2	2	no	—
300	C₂×D₈₉	—	2	2	no	—
301	C₂×D₈₉	—	2	2	no	—
302	C₂×D₈₉	—	2	2	no	—
303	C₂×D₈₉	—	2	2	no	—
304	C₂×D₈₉	—	2	2	no	—
305	C₂×D₈₉	—	2	2	no	—
306	C₂×D₈₉	—	4	4	no	—
307	C₂×D₈₉	—	4	8	no	—
308	C₂×D₈₉	—	4	8	no	—
309	C₂×D₈₉	—	4	4	no	—
310	C₂×D₈₉	—	8	4	no	—
311	C₂×D₈₉	H(5,𝔽₂)	1	4	yes	—
312	C₄×C₈₉	—	2	2	no	—
313	C₄×C₈₉	—	2	1	no	—
314	C₄×C₈₉	—	2	2	no	—
315	C₄×C₈₉	—	2	1	no	—
316	C₄×C₈₉	—	2	2	no	—
317	Dic₈₉	—	2	2	no	—
318	Dic₈₉	—	2	2	no	—
319	Dic₈₉	—	2	2	no	—
320	Dic₈₉	—	2	2	no	—
321	Dic₈₉	—	2	2	no	—
322	C₂×C₈₉	—	2	2	no	—
323	C₂×C₈₉	—	4	1	no	—
324	C₂×C₈₉	—	4	1	no	—
325	C₂×C₈₉	—	4	2	no	—
326	C₂×C₈₉	—	4	1	no	—
327	C₂×C₈₉	—	4	1	no	—
328	C₂×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
329	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	D₈₉	—	2	4	no	—
331	D₈₉	—	4	2	no	—
332	D₈₉	—	4	2	no	—
333	#3532	—	89	1	no	maximal, Sylow
334	C₈₉	#3532	1	1	yes	characteristic, complemented, Sylow
335	H(3,𝔽₄)	—	89	1	no	—
336	#560	—	89	1	no	—
337	#560	—	89	2	no	—
338	#551	—	89	2	no	—
339	#551	—	89	1	no	—
340	#546	—	89	2	no	—
341	#546	—	89	2	no	—
342	#546	—	89	2	no	—
343	D₄²	—	89	2	no	—
344	D₄²	—	89	1	no	—
345	#538	—	89	2	no	—
346	#538	—	89	2	no	—
347	#538	—	89	2	no	—
348	#535	—	89	1	no	—
349	#535	—	89	2	no	—
350	#534	—	89	2	no	—
351	#534	D₈₉	1	1	yes	characteristic, complemented
352	C₂×#120	—	89	1	no	—
353	C₂×#120	—	89	2	no	—
354	C₂⁵	—	89	1	no	—
355	C₂×#41	—	89	1	no	—
356	C₂×#41	—	89	2	no	—
357	C₂²×D₄	—	89	2	no	—
358	C₂²×D₄	—	89	2	no	—
359	C₂²×D₄	—	89	2	no	—
360	C₂²×D₄	—	89	2	no	—
361	C₂²×D₄	—	89	2	no	—
362	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
363	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
364	#127	—	89	1	no	—
365	#127	—	89	1	no	—
366	#127	—	89	2	no	—
367	#126	—	89	2	no	—
368	#126	—	89	2	no	—
369	#126	—	89	2	no	—
370	#126	—	89	2	no	—
371	#124	—	89	1	no	—
372	#124	—	89	1	no	—
373	#124	—	89	2	no	—
374	#124	—	89	2	no	—
375	#124	—	89	2	no	—
376	#124	—	89	2	no	—
377	#124	—	89	2	no	—
378	#123	—	89	2	no	—
379	#123	—	89	2	no	—
380	#123	—	89	2	no	—
381	#123	—	89	2	no	—
382	#123	—	89	2	no	—
383	#123	—	89	2	no	—
384	#123	—	89	2	no	—
385	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
386	#123	C₂×D₈₉	1	1	yes	characteristic, complemented
387	#123	C₂×D₈₉	1	2	yes	complemented
388	C₂²⋊Q₈	—	89	2	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	2	no	—
391	#121	—	89	2	no	—
392	#121	—	89	2	no	—
393	#121	—	89	2	no	—
394	#121	—	89	2	no	—
395	#121	—	89	2	no	—
396	#121	—	89	2	no	—
397	#121	—	89	2	no	—
398	#121	—	89	2	no	—
399	#121	—	89	2	no	—
400	#121	—	89	2	no	—
401	#121	—	89	2	no	—
402	#121	—	89	2	no	—
403	#121	—	89	2	no	—
404	#121	C₂×D₈₉	1	2	yes	complemented
405	#121	C₂×D₈₉	1	2	yes	complemented
406	#120	—	89	2	no	—
407	#120	—	89	2	no	—
408	#120	—	89	2	no	—
409	#120	—	89	2	no	—
410	#120	—	89	1	no	—
411	#120	—	89	2	no	—
412	#120	—	89	2	no	—
413	#120	—	89	2	no	—
414	#120	—	89	1	no	—
415	#120	—	89	1	no	—
416	#120	—	89	2	no	—
417	#120	—	89	1	no	—
418	#120	—	89	2	no	—
419	#120	—	89	2	no	—
420	#120	—	89	2	no	—
421	#120	—	89	2	no	—
422	#120	—	89	2	no	—
423	#120	C₂×D₈₉	1	2	yes	complemented
424	#120	C₂×D₈₉	1	1	yes	characteristic, complemented
425	#120	C₂×D₈₉	1	1	yes	characteristic, complemented
426	C₄×D₄	—	89	2	no	—
427	C₄×D₄	—	89	2	no	—
428	C₄×D₄	—	89	2	no	—
429	C₄×D₄	—	89	2	no	—
430	C₄×D₄	—	89	2	no	—
431	C₄×D₄	—	89	2	no	—
432	#117	—	89	1	no	—
433	#117	—	89	2	no	—
434	C₂×C₂²⋊C₄	—	89	1	no	—
435	C₂×C₂²⋊C₄	—	89	2	no	—
436	C₂×C₂²⋊C₄	—	89	2	no	—
437	C₂×C₂²⋊C₄	—	89	2	no	—
438	C₂×C₂²⋊C₄	—	89	2	no	—
439	C₂×C₂²⋊C₄	—	89	2	no	—
440	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
441	C₂⁴	—	89	1	no	—
442	C₂⁴	—	89	2	no	—
443	C₂⁴	—	89	2	no	—
444	C₂⁴	—	89	1	no	—
445	C₂⁴	—	89	2	no	—
446	C₂⁴	—	356	2	no	—
447	C₂⁴	—	356	4	no	—
448	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
449	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
450	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic, complemented
451	#41	—	356	2	no	—
452	#41	—	356	4	no	—
453	C₂×Q₈	—	89	2	no	—
454	C₂×Q₈	—	89	1	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	2	no	—
457	C₂×D₄	—	89	2	no	—
458	C₂×D₄	—	89	2	no	—
459	C₂×D₄	—	89	2	no	—
460	C₂×D₄	—	89	2	no	—
461	C₂×D₄	—	89	2	no	—
462	C₂×D₄	—	89	2	no	—
463	C₂×D₄	—	89	2	no	—
464	C₂×D₄	—	89	2	no	—
465	C₂×D₄	—	89	2	no	—
466	C₂×D₄	—	89	2	no	—
467	C₂×D₄	—	89	2	no	—
468	C₂×D₄	—	89	2	no	—
469	C₂×D₄	—	89	2	no	—
470	C₂×D₄	—	89	2	no	—
471	C₂×D₄	—	89	2	no	—
472	C₂×D₄	—	89	1	no	—
473	C₂×D₄	—	89	2	no	—
474	C₂×D₄	—	356	4	no	—
475	C₂×D₄	—	356	4	no	—
476	C₂×D₄	—	356	4	no	—
477	C₂×D₄	—	356	4	no	—
478	C₂×D₄	—	356	4	no	—
479	C₂×D₄	C₂²×D₈₉	1	2	yes	—
480	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
484	C₂×D₄	C₂²×D₈₉	1	2	yes	—
485	C₂×D₄	C₂²×D₈₉	1	2	yes	—
486	C₂×D₄	C₂²×D₈₉	1	2	yes	complemented
487	C₂²×C₄	—	89	2	no	—
488	C₂²×C₄	—	89	2	no	—
489	C₂²×C₄	—	89	2	no	—
490	C₂²×C₄	—	89	2	no	—
491	C₂²×C₄	—	89	2	no	—
492	C₂²×C₄	—	89	2	no	—
493	C₂²×C₄	—	89	2	no	—
494	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₈₉	1	2	yes	complemented
496	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic, complemented
497	C₄⋊C₄	—	89	2	no	—
498	C₄⋊C₄	—	89	2	no	—
499	C₄⋊C₄	—	89	2	no	—
500	C₄⋊C₄	—	89	2	no	—
501	C₄⋊C₄	—	89	2	no	—
502	C₄⋊C₄	—	89	2	no	—
503	C₄⋊C₄	—	89	2	no	—
504	C₄⋊C₄	C₂²×D₈₉	1	2	yes	complemented
505	C₄⋊C₄	C₂²×D₈₉	1	2	yes	complemented
506	C₂²⋊C₄	—	89	2	no	—
507	C₂²⋊C₄	—	89	1	no	—
508	C₂²⋊C₄	—	89	2	no	—
509	C₂²⋊C₄	—	89	2	no	—
510	C₂²⋊C₄	—	89	2	no	—
511	C₂²⋊C₄	—	89	1	no	—
512	C₂²⋊C₄	—	89	2	no	—
513	C₂²⋊C₄	—	89	2	no	—
514	C₂²⋊C₄	—	89	2	no	—
515	C₂²⋊C₄	—	89	2	no	—
516	C₂²⋊C₄	—	89	2	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	2	no	—
519	C₂²⋊C₄	—	89	2	no	—
520	C₂²⋊C₄	—	89	2	no	—
521	C₂²⋊C₄	—	89	2	no	—
522	C₂²⋊C₄	—	89	2	no	—
523	C₂²⋊C₄	—	89	2	no	—
524	C₂²⋊C₄	—	89	2	no	—
525	C₂²⋊C₄	—	89	2	no	—
526	C₂²⋊C₄	—	89	2	no	—
527	C₂²⋊C₄	—	89	2	no	—
528	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
529	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	complemented
532	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic, complemented
533	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic, complemented
534	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	complemented
535	C₄²	—	89	1	no	—
536	C₄²	—	89	2	no	—
537	C₄²	—	89	1	no	—
538	C₄²	—	89	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	89	2	no	—
546	C₂³	—	89	2	no	—
547	C₂³	—	89	2	no	—
548	C₂³	—	356	2	no	—
549	C₂³	—	356	2	no	—
550	C₂³	—	356	2	no	—
551	C₂³	—	356	1	no	—
552	C₂³	—	356	2	no	—
553	C₂³	—	356	1	no	—
554	C₂³	—	356	2	no	—
555	C₂³	—	356	2	no	—
556	C₂³	—	356	16	no	—
557	C₂³	—	178	4	no	—
558	C₂³	—	178	4	no	—
559	C₂³	—	178	4	no	—
560	C₂³	—	178	4	no	—
561	C₂³	—	178	4	no	—
562	C₂³	C₂³×D₈₉	1	1	yes	characteristic
563	C₂³	C₂³×D₈₉	1	1	yes	characteristic
564	C₂³	C₂³×D₈₉	1	2	yes	—
565	C₂³	C₂³×D₈₉	1	1	yes	characteristic
566	C₂³	C₂³×D₈₉	1	1	yes	characteristic
567	C₂³	C₂³×D₈₉	1	1	yes	characteristic
568	Q₈	—	356	2	no	—
569	Q₈	—	356	1	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	356	2	no	—
579	D₄	—	356	2	no	—
580	D₄	—	356	1	no	—
581	D₄	—	356	2	no	—
582	D₄	—	356	2	no	—
583	D₄	—	356	2	no	—
584	D₄	—	356	2	no	—
585	D₄	—	356	2	no	—
586	D₄	—	356	2	no	—
587	D₄	—	356	2	no	—
588	D₄	—	356	2	no	—
589	D₄	—	356	2	no	—
590	D₄	—	178	4	no	—
591	D₄	—	178	4	no	—
592	D₄	—	178	4	no	—
593	D₄	—	178	4	no	—
594	D₄	—	178	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	89	2	no	—
599	C₂×C₄	—	89	2	no	—
600	C₂×C₄	—	89	2	no	—
601	C₂×C₄	—	89	2	no	—
602	C₂×C₄	—	89	2	no	—
603	C₂×C₄	—	356	2	no	—
604	C₂×C₄	—	356	2	no	—
605	C₂×C₄	—	356	2	no	—
606	C₂×C₄	—	356	2	no	—
607	C₂×C₄	—	356	2	no	—
608	C₂×C₄	—	356	2	no	—
609	C₂×C₄	—	178	4	no	—
610	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₈₉	1	2	yes	—
612	C₂×C₄	C₂³×D₈₉	1	2	yes	—
613	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₈₉	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	2	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	89	4	no	—
631	C₂²	—	356	8	no	—
632	C₂²	—	356	4	no	—
633	C₂²	—	356	8	no	—
634	C₂²	—	356	4	no	—
635	C₂²	—	178	2	no	—
636	C₂²	—	178	2	no	—
637	C₂²	—	178	2	no	—
638	C₂²	—	178	2	no	—
639	C₂²	—	178	2	no	—
640	C₂²	—	178	2	no	—
641	C₂²	—	178	2	no	—
642	C₂²	—	178	2	no	—
643	C₂²	—	712	4	no	—
644	C₂²	#15668057	1	2	yes	—
645	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	178	2	no	—
652	C₄	—	178	2	no	—
653	C₄	—	178	2	no	—
654	C₄	—	178	2	no	—
655	C₄	—	178	2	no	—
656	C₂	—	2	2	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	4	1	no	—
660	C₂	—	4	1	no	—
661	C₂	—	4	2	no	—
662	C₂	—	356	2	no	—
663	C₂	—	356	2	no	—
664	C₂	—	178	4	no	—
665	C₂	H(5,𝔽₂)×D₈₉	1	2	yes	—
666	C₂	C₂×#15668057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#534×C₈₉	C₂
hypercenter	#534	D₈₉
hypocenter	C₈₉	#3532
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. #19152341	C₂	semidirect
2. #19152338	C₂	semidirect
3. #19152336	C₂	semidirect
4. #19152276	C₂	semidirect
5. #19152271	C₂	semidirect
6. #19152245	C₂	semidirect
7. #19152240	C₂	semidirect
8. #19152238	C₂	semidirect
9. D₄×C₂²⋊D₈₉	C₂	semidirect
10. #19152230	C₂	semidirect
11. #19152184	C₂	semidirect
12. #19152183	C₂	semidirect
13. #19152180	C₂	semidirect
14. #19152165	C₂	semidirect
15. #19152164	C₂	semidirect
16. #19152158	C₂	semidirect
17. C₂×#15667980	C₂	semidirect
18. #120×D₈₉	C₂	semidirect
19. #534×C₈₉	C₂	semidirect
20. C₂⁴×D₈₉	C₂²	semidirect
21. C₂×#13083574	C₂²	semidirect
22. C₂×#13083574	C₂²	semidirect
23. C₂²×C₂²⋊D₈₉	C₂²	semidirect
24. C₂²×C₂²⋊D₈₉	C₂²	semidirect
25. C₂×D₄×D₈₉	C₂²	semidirect
26. C₂×D₄×D₈₉	C₂²	semidirect
27. C₂×D₄×D₈₉	C₂²	semidirect
28. #15668008	C₂²	semidirect
29. #15668008	C₂²	semidirect
30. #15668008	C₂²	semidirect
31. #15668007	C₂²	semidirect
32. #15668007	C₂²	semidirect
33. #15668005	C₂²	semidirect
34. #15668005	C₂²	semidirect
35. #15667999	C₂²	semidirect
36. #15667999	C₂²	semidirect
37. #15667999	C₂²	semidirect
38. #15667998	C₂²	semidirect
39. #15667998	C₂²	semidirect
40. #15667998	C₂²	semidirect
41. #15667998	C₂²	semidirect
42. #15667997	C₂²	semidirect
43. #15667996	C₂²	semidirect
44. #15667995	C₂²	semidirect
45. #15667994	C₂²	semidirect
46. #15667994	C₂²	semidirect
47. #15667994	C₂²	semidirect
48. #15667993	C₂²	semidirect
49. #15667992	C₂²	semidirect
50. #15667990	C₂²	semidirect
51. #15667989	C₂²	semidirect
52. #15667987	C₂²	semidirect
53. #15667986	C₂²	semidirect
54. #15667986	C₂²	semidirect
55. #15667985	C₂²	semidirect
56. #15667985	C₂²	semidirect
57. #15667985	C₂²	semidirect
58. #15667984	C₂²	semidirect
59. #15667984	C₂²	semidirect
60. #15667984	C₂²	semidirect
61. #15667983	C₂²	semidirect
62. #15667983	C₂²	semidirect
63. #15667983	C₂²	semidirect
64. #15667983	C₂²	semidirect
65. #15667982	C₂²	semidirect
66. #15667982	C₂²	semidirect
67. #15667982	C₂²	semidirect
68. #15667982	C₂²	semidirect
69. #15667981	C₂²	semidirect
70. #15667981	C₂²	semidirect
71. #15667981	C₂²	semidirect
74. #15667980	C₂²	semidirect
75. #15667980	C₂²	semidirect
76. #15667980	C₂²	semidirect
77. #15667980	C₂²	semidirect
78. #15667980	C₂²	semidirect
79. #15667980	C₂²	semidirect
80. #15667980	C₂²	semidirect
81. #15667980	C₂²	semidirect
82. D₄×Dic₈₉	C₂²	semidirect
83. #15667974	C₂²	semidirect
84. C₄×C₂²⋊D₈₉	C₂²	semidirect
85. C₄×C₂²⋊D₈₉	C₂²	semidirect
86. #15667972	C₂²	semidirect
87. #15667972	C₂²	semidirect
88. #15667971	C₂²	semidirect
89. #15667970	C₂²	semidirect
90. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
91. C₂×#13083551	C₂²	semidirect
92. C₂²⋊C₄×D₈₉	C₂²	semidirect
93. C₂²⋊C₄×D₈₉	C₂²	semidirect
94. C₂²⋊C₄×D₈₉	C₂²	semidirect
95. C₂²⋊C₄×D₈₉	C₂²	semidirect
96. C₂²×D₄×C₈₉	C₂²	semidirect
97. C₂²×D₄×C₈₉	C₂²	semidirect
98. #123×C₈₉	C₂²	semidirect
99. #123×C₈₉	C₂²	semidirect
100. #123×C₈₉	C₂²	semidirect
101. #121×C₈₉	C₂²	semidirect
102. #121×C₈₉	C₂²	semidirect
103. #120×C₈₉	C₂²	semidirect
104. #120×C₈₉	C₂²	semidirect
105. #120×C₈₉	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
116. C₂×Dic₁₇₈	C₂³	semidirect
117. C₂×Dic₁₇₈	C₂³	semidirect
121. C₂×D₃₅₆	C₂³	semidirect
134. C₂×C₂²⋊D₈₉	C₂³	semidirect
135. C₂×C₂²⋊D₈₉	C₂³	semidirect
136. C₂×C₂²⋊D₈₉	C₂³	semidirect
141. C₂²×Dic₈₉	C₂³	semidirect
145. C₂×C₄×D₈₉	C₂³	semidirect
146. C₂×C₄×D₈₉	C₂³	semidirect
147. C₄⋊Dic₈₉	C₂³	semidirect
148. C₄⋊Dic₈₉	C₂³	semidirect
149. C₄⋊Dic₈₉	C₂³	semidirect
150. #13083553	C₂³	semidirect
151. #13083553	C₂³	semidirect
152. #13083553	C₂³	semidirect
153. #13083553	C₂³	semidirect
160. C₂²⋊Dic₈₉	C₂³	semidirect
161. C₂²⋊Dic₈₉	C₂³	semidirect
162. C₂²⋊Dic₈₉	C₂³	semidirect
163. C₂²⋊Dic₈₉	C₂³	semidirect
174. #13083551	C₂³	semidirect
175. #13083551	C₂³	semidirect
176. C₄×Dic₈₉	C₂³	semidirect
177. C₄×Dic₈₉	C₂³	semidirect
178. C₄×Dic₈₉	C₂³	semidirect
179. C₄×Dic₈₉	C₂³	semidirect
182. C₂⁴×C₈₉	C₂³	semidirect
192. C₂×D₄×C₈₉	C₂³	semidirect
194. C₂²×C₄×C₈₉	C₂³	semidirect
195. C₂²×C₄×C₈₉	C₂³	semidirect
196. C₄⋊C₄×C₈₉	C₂³	semidirect
197. C₄⋊C₄×C₈₉	C₂³	semidirect
201. C₂²⋊C₄×C₈₉	C₂³	semidirect
202. C₂²⋊C₄×C₈₉	C₂³	semidirect
203. C₂²⋊C₄×C₈₉	C₂³	semidirect
204. C₂²⋊C₄×C₈₉	C₂³	semidirect
334. C₈₉	#3532	semidirect
351. #534	D₈₉	semidirect
362. C₂²×D₄	C₂×D₈₉	semidirect
363. C₂²×D₄	C₂×D₈₉	semidirect
385. #123	C₂×D₈₉	semidirect
386. #123	C₂×D₈₉	semidirect
387. #123	C₂×D₈₉	semidirect
404. #121	C₂×D₈₉	semidirect
405. #121	C₂×D₈₉	semidirect
423. #120	C₂×D₈₉	semidirect
424. #120	C₂×D₈₉	semidirect
425. #120	C₂×D₈₉	semidirect
440. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
450. C₂⁴	C₂²×D₈₉	semidirect
486. C₂×D₄	C₂²×D₈₉	semidirect
495. C₂²×C₄	C₂²×D₈₉	semidirect
496. C₂²×C₄	C₂²×D₈₉	semidirect
504. C₄⋊C₄	C₂²×D₈₉	semidirect
505. C₄⋊C₄	C₂²×D₈₉	semidirect
531. C₂²⋊C₄	C₂²×D₈₉	semidirect
532. C₂²⋊C₄	C₂²×D₈₉	semidirect
533. C₂²⋊C₄	C₂²×D₈₉	semidirect
534. C₂²⋊C₄	C₂²×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152341	2
#19152338	2
#19152336	2
#19152276	2
#19152271	2
#19152245	2
#19152240	2
#19152238	2
D₄×C₂²⋊D₈₉	2
#19152230	2
#19152184	2
#19152183	2
#19152180	2
#19152165	2
#19152164	2
#19152158	2
C₂×#15667980	2
#120×D₈₉	2
#534×C₈₉	2
#3532	89