Subgroups — #26034614

Order 11392.

1150 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152336	C₂	1	2	yes	maximal, complemented
2	#19152336	C₂	1	2	yes	maximal, complemented
3	#19152319	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152296	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152295	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152267	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152266	C₂	1	2	yes	maximal, complemented
8	#19152249	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152239	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152237	C₂	1	2	yes	maximal, complemented
11	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152232	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152218	C₂	1	2	yes	maximal, complemented
14	#19152188	C₂	1	2	yes	maximal, complemented
15	#19152180	C₂	1	2	yes	maximal, complemented
16	#19152178	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152164	C₂	1	2	yes	maximal, complemented
19	#19152162	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152144	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152143	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152134	C₂	1	1	yes	maximal, characteristic, complemented
23	#537×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13083574	C₂²	1	2	yes	complemented
27	C₂×#13083573	C₂²	1	2	yes	complemented
28	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₈₉	C₂²	1	2	yes	—
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668010	C₂²	1	1	yes	characteristic, complemented
33	#15668008	C₂²	1	1	yes	characteristic
34	#15668008	C₂²	1	1	yes	characteristic
35	#15668008	C₂²	1	2	yes	complemented
36	#15668008	C₂²	1	2	yes	complemented
37	#15668008	C₂²	1	2	yes	complemented
38	#15668007	C₂²	1	2	yes	complemented
39	#15668007	C₂²	1	2	yes	complemented
40	#15668007	C₂²	1	2	yes	complemented
41	#15668005	C₂²	1	2	yes	complemented
42	#15668005	C₂²	1	2	yes	complemented
43	#15668003	C₂²	1	1	yes	characteristic, complemented
44	#15668001	C₂²	1	1	yes	characteristic
45	#15668001	C₂²	1	1	yes	characteristic, complemented
46	#15668001	C₂²	1	2	yes	complemented
47	#15667999	C₂²	1	1	yes	characteristic, complemented
48	#15667998	C₂²	1	2	yes	—
49	#15667998	C₂²	1	2	yes	complemented
50	#15667998	C₂²	1	2	yes	complemented
51	#15667997	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667997	C₂²	1	2	yes	complemented
54	#15667996	C₂²	1	2	yes	complemented
55	#15667995	C₂²	1	2	yes	complemented
56	#15667995	C₂²	1	2	yes	complemented
57	#15667993	C₂²	1	2	yes	complemented
58	#15667990	C₂²	1	2	yes	complemented
59	#15667990	C₂²	1	2	yes	complemented
60	#15667988	C₂²	1	1	yes	characteristic, complemented
61	#15667987	C₂²	1	1	yes	characteristic
62	#15667987	C₂²	1	1	yes	characteristic
63	#15667987	C₂²	1	2	yes	complemented
64	#15667987	C₂²	1	2	yes	complemented
65	#15667986	C₂²	1	1	yes	characteristic
66	#15667986	C₂²	1	1	yes	characteristic
67	#15667986	C₂²	1	1	yes	characteristic, complemented
68	#15667986	C₂²	1	1	yes	characteristic, complemented
69	#15667986	C₂²	1	2	yes	complemented
70	#15667986	C₂²	1	2	yes	complemented
71	#15667985	C₂²	1	2	yes	—
72	#15667985	C₂²	1	2	yes	complemented
73	#15667985	C₂²	1	2	yes	complemented
74	#15667984	C₂²	1	1	yes	characteristic
75	#15667984	C₂²	1	2	yes	complemented
76	#15667984	C₂²	1	1	yes	characteristic, complemented
77	#15667984	C₂²	1	1	yes	characteristic, complemented
78	#15667984	C₂²	1	1	yes	characteristic, complemented
79	#15667984	C₂²	1	2	yes	complemented
80	#15667983	C₂²	1	1	yes	characteristic, complemented
81	#15667983	C₂²	1	2	yes	complemented
82	#15667983	C₂²	1	2	yes	complemented
83	#15667982	C₂²	1	2	yes	—
84	#15667982	C₂²	1	2	yes	complemented
85	#15667982	C₂²	1	2	yes	complemented
86	#15667980	C₂²	1	2	yes	—
87	#15667980	C₂²	1	2	yes	complemented
88	#15667980	C₂²	1	2	yes	complemented
89	#15667980	C₂²	1	2	yes	complemented
90	#15667980	C₂²	1	2	yes	complemented
91	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
92	#15667977	C₂²	1	2	yes	complemented
93	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
94	#15667974	C₂²	1	1	yes	characteristic
95	#15667974	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
98	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
100	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	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	#15667971	C₂²	1	1	yes	characteristic, complemented
106	#15667970	C₂²	1	2	yes	complemented
107	#15667970	C₂²	1	1	yes	characteristic, complemented
108	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×#13083551	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₉	C₂²	1	1	yes	characteristic
118	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₈₉	C₂²	1	2	yes	complemented
120	#121×C₈₉	C₂²	1	2	yes	complemented
121	#121×C₈₉	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	C₂³×D₈₉	C₂³	1	2	yes	—
125	#13083575	—	4	2	no	—
126	#13083574	—	4	4	no	—
127	#13083574	—	4	2	no	—
128	#13083573	—	4	4	no	—
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
131	C₂×D₃₅₆	—	4	2	no	—
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
134	C₂×D₃₅₆	C₂³	1	2	yes	—
135	C₂×D₃₅₆	C₂³	1	2	yes	—
136	C₂×D₃₅₆	C₂³	1	2	yes	—
137	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
138	C₂×D₃₅₆	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
146	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
153	D₄×D₈₉	—	4	2	no	—
154	D₄×D₈₉	—	4	4	no	—
155	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
156	C₂²×Dic₈₉	C₂³	1	2	yes	—
157	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂³	1	2	yes	—
159	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₈₉	C₂³	1	2	yes	—
162	C₂×C₄×D₈₉	C₂³	1	2	yes	—
163	C₂×C₄×D₈₉	C₂³	1	2	yes	—
164	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₈₉	C₂³	1	2	yes	—
166	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₈₉	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	1	yes	characteristic
174	#13083553	C₂³	1	2	yes	—
175	#13083553	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	#13083551	C₂³	1	2	yes	—
184	#13083551	C₂³	1	2	yes	—
185	#13083551	C₂³	1	2	yes	—
186	#13083551	C₂³	1	1	yes	characteristic
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	1	yes	characteristic
194	#13083551	C₂³	1	2	yes	—
195	#13083551	C₂³	1	2	yes	—
196	#13083551	C₂³	1	2	yes	—
197	#13083551	C₂³	1	2	yes	—
198	#13083551	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂³	1	2	yes	—
201	C₄×Dic₈₉	C₂³	1	2	yes	—
202	C₄×Dic₈₉	C₂³	1	2	yes	—
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
206	#41×C₈₉	—	4	2	no	—
207	#41×C₈₉	—	4	2	no	—
208	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₉	C₂³	1	2	yes	—
212	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂×D₄×C₈₉	C₂³	1	2	yes	—
215	C₂×D₄×C₈₉	C₂³	1	2	yes	—
216	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
222	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
229	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
230	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
231	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₈₉	C₂⁴	1	2	yes	—
233	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
234	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₈₉	—	4	2	no	—
236	C₂²×D₈₉	—	4	2	no	—
237	C₂²×D₈₉	—	4	2	no	—
238	C₂²×D₈₉	—	4	2	no	—
239	C₂²×D₈₉	—	4	2	no	—
240	C₂²×D₈₉	—	4	2	no	—
241	C₂²×D₈₉	C₂⁴	1	2	yes	—
242	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₈₉	C₂⁴	1	2	yes	—
244	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
245	Q₈×C₈₉	—	2	2	no	—
246	Q₈×C₈₉	—	4	1	no	—
247	D₄×C₈₉	—	2	2	no	—
248	D₄×C₈₉	—	4	1	no	—
249	D₄×C₈₉	—	4	2	no	—
250	D₄×C₈₉	—	4	1	no	—
251	D₄×C₈₉	—	4	1	no	—
252	D₄×C₈₉	—	4	2	no	—
253	D₄×C₈₉	—	4	2	no	—
254	C₂×C₄×C₈₉	—	2	2	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	2	2	no	—
257	C₂×C₄×C₈₉	—	4	2	no	—
258	C₂×C₄×C₈₉	—	4	2	no	—
259	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
261	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
266	C₂²⋊D₈₉	—	2	2	no	—
267	C₂²⋊D₈₉	—	2	4	no	—
268	C₂²⋊D₈₉	—	2	2	no	—
269	C₂²⋊D₈₉	—	4	2	no	—
270	C₂²⋊D₈₉	—	4	1	no	—
271	C₂²⋊D₈₉	—	4	2	no	—
272	C₂²⋊D₈₉	—	4	1	no	—
273	C₂²⋊D₈₉	—	4	2	no	—
274	C₂²⋊D₈₉	—	4	2	no	—
275	C₂²⋊D₈₉	—	4	2	no	—
276	C₂²⋊D₈₉	—	4	2	no	—
277	C₂²⋊D₈₉	—	4	2	no	—
278	C₂²⋊D₈₉	—	4	1	no	—
279	C₂²⋊D₈₉	—	4	1	no	—
280	C₂×Dic₈₉	—	2	2	no	—
281	C₂×Dic₈₉	—	4	1	no	—
282	C₂×Dic₈₉	—	4	2	no	—
283	C₂×Dic₈₉	C₂⁴	1	2	yes	—
284	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
288	C₂×Dic₈₉	C₂⁴	1	2	yes	—
289	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
291	D₃₅₆	—	2	2	no	—
292	D₃₅₆	—	2	2	no	—
293	D₃₅₆	—	4	2	no	—
294	D₃₅₆	—	4	2	no	—
295	D₃₅₆	—	4	2	no	—
296	D₃₅₆	—	4	1	no	—
297	D₃₅₆	—	4	2	no	—
298	C₄×D₈₉	—	2	2	no	—
299	C₄×D₈₉	—	2	2	no	—
300	C₄×D₈₉	—	2	4	no	—
301	C₄×D₈₉	—	4	2	no	—
302	C₄×D₈₉	—	4	2	no	—
303	C₄×D₈₉	—	4	2	no	—
304	Dic₁₇₈	—	2	4	no	—
305	Dic₁₇₈	—	4	1	no	—
306	C₂²×C₈₉	—	2	1	no	—
307	C₂²×C₈₉	—	2	2	no	—
308	C₂²×C₈₉	—	2	1	no	—
309	C₂²×C₈₉	—	2	1	no	—
310	C₂²×C₈₉	—	2	1	no	—
311	C₂²×C₈₉	—	2	2	no	—
312	C₂²×C₈₉	—	2	1	no	—
313	C₂²×C₈₉	—	2	1	no	—
314	C₂²×C₈₉	—	2	1	no	—
315	C₂²×C₈₉	—	2	1	no	—
316	C₂²×C₈₉	—	2	2	no	—
317	C₂²×C₈₉	—	2	1	no	—
318	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
319	C₂×D₈₉	—	2	1	no	—
320	C₂×D₈₉	—	2	2	no	—
321	C₂×D₈₉	—	2	1	no	—
322	C₂×D₈₉	—	2	1	no	—
323	C₂×D₈₉	—	2	2	no	—
324	C₂×D₈₉	—	2	2	no	—
325	C₂×D₈₉	—	2	2	no	—
326	C₂×D₈₉	—	2	1	no	—
327	C₂×D₈₉	—	2	1	no	—
328	C₂×D₈₉	—	2	2	no	—
329	C₂×D₈₉	—	2	2	no	—
330	C₂×D₈₉	—	2	1	no	—
331	C₂×D₈₉	—	8	4	no	—
332	C₂×D₈₉	—	8	4	no	—
333	C₄×C₈₉	—	2	2	no	—
334	C₄×C₈₉	—	2	1	no	—
335	C₄×C₈₉	—	2	2	no	—
336	C₄×C₈₉	—	2	2	no	—
337	C₄×C₈₉	—	2	1	no	—
338	C₄×C₈₉	—	2	1	no	—
339	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
340	Dic₈₉	—	2	2	no	—
341	Dic₈₉	—	2	1	no	—
342	Dic₈₉	—	2	1	no	—
343	Dic₈₉	—	2	1	no	—
344	Dic₈₉	—	2	1	no	—
345	Dic₈₉	—	2	1	no	—
346	Dic₈₉	—	2	2	no	—
347	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
348	C₂×C₈₉	—	4	1	no	—
349	C₂×C₈₉	—	4	2	no	—
350	C₂×C₈₉	—	4	1	no	—
351	C₂×C₈₉	—	4	1	no	—
352	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₈₉	#585	1	1	yes	characteristic
355	D₈₉	—	4	1	no	—
356	D₈₉	—	4	2	no	—
357	D₈₉	—	4	2	no	—
358	D₈₉	—	4	1	no	—
359	#3546	—	89	1	no	maximal, Sylow
360	C₈₉	#3546	1	1	yes	characteristic, complemented, Sylow
361	#560	—	89	2	no	—
362	#560	—	89	2	no	—
363	#556	—	89	1	no	—
364	#553	—	89	1	no	—
365	#553	—	89	1	no	—
366	#550	—	89	1	no	—
367	#550	—	89	2	no	—
368	#547	—	89	1	no	—
369	#546	—	89	1	no	—
370	#546	—	89	1	no	—
371	#546	—	89	2	no	—
372	D₄²	—	89	1	no	—
373	#542	—	89	2	no	—
374	#538	—	89	2	no	—
375	#538	—	89	2	no	—
376	#537	—	89	1	no	—
377	#537	D₈₉	1	1	yes	characteristic, complemented
378	#535	—	89	1	no	—
379	#535	—	89	2	no	—
380	#535	—	89	1	no	—
381	#532	—	89	1	no	—
382	#532	—	89	1	no	—
383	#529	—	89	1	no	—
384	C₂×#41	—	89	1	no	—
385	C₂×#41	—	89	2	no	—
386	C₂×#41	—	89	1	no	—
387	C₂×#41	—	89	2	no	—
388	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
389	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
390	C₂²×D₄	—	89	1	no	—
391	C₂²×D₄	—	89	2	no	—
392	C₂²×D₄	—	89	1	no	—
393	C₄⋊Q₈	—	89	1	no	—
394	C₄⋊Q₈	—	89	1	no	—
395	#127	—	89	1	no	—
396	#127	—	89	1	no	—
397	#127	—	89	2	no	—
398	#127	—	89	2	no	—
399	#127	—	89	2	no	—
400	#126	—	89	2	no	—
401	#126	—	89	2	no	—
402	#126	—	89	2	no	—
403	#126	—	89	2	no	—
404	#126	—	89	2	no	—
405	#125	—	89	1	no	—
406	#124	—	89	1	no	—
407	#124	—	89	1	no	—
408	#124	—	89	2	no	—
409	#124	—	89	1	no	—
410	#124	—	89	2	no	—
411	#124	—	89	2	no	—
412	#124	—	89	2	no	—
413	#123	—	89	2	no	—
414	#123	—	89	2	no	—
415	#123	—	89	2	no	—
416	#123	—	89	2	no	—
417	#123	—	89	2	no	—
418	#123	—	89	2	no	—
419	#123	—	89	2	no	—
420	C₂²⋊Q₈	—	89	1	no	—
421	C₂²⋊Q₈	—	89	2	no	—
422	C₂²⋊Q₈	—	89	2	no	—
423	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
424	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
425	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
426	#121	—	89	1	no	—
427	#121	—	89	2	no	—
428	#121	—	89	2	no	—
429	#121	—	89	1	no	—
430	#121	—	89	1	no	—
431	#121	—	89	1	no	—
432	#121	—	89	2	no	—
433	#121	—	89	1	no	—
434	#121	—	89	2	no	—
435	#121	—	89	1	no	—
436	#121	—	89	1	no	—
437	#121	—	89	1	no	—
438	#121	—	89	1	no	—
439	#121	—	89	2	no	—
440	#121	—	89	2	no	—
441	#121	—	89	1	no	—
442	#121	—	89	1	no	—
443	#121	—	89	2	no	—
444	#121	—	89	2	no	—
445	#121	—	89	2	no	—
446	#121	—	89	2	no	—
447	#121	—	89	2	no	—
448	#121	C₂×D₈₉	1	1	yes	characteristic
449	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
450	#121	C₂×D₈₉	1	2	yes	complemented
451	#121	C₂×D₈₉	1	2	yes	complemented
452	#121	C₂×D₈₉	1	2	yes	complemented
453	#120	—	89	2	no	—
454	#120	—	89	2	no	—
455	#120	—	89	2	no	—
456	#120	—	89	2	no	—
457	#120	—	89	2	no	—
458	#120	—	89	2	no	—
459	#120	—	89	2	no	—
460	#120	—	89	2	no	—
461	C₄×Q₈	—	89	1	no	—
462	C₄×Q₈	—	89	2	no	—
463	C₄×D₄	—	89	1	no	—
464	C₄×D₄	—	89	1	no	—
465	C₄×D₄	—	89	1	no	—
466	C₄×D₄	—	89	1	no	—
467	C₄×D₄	—	89	1	no	—
468	C₄×D₄	—	89	2	no	—
469	C₄×D₄	—	89	2	no	—
470	C₄×D₄	—	89	1	no	—
471	C₄×D₄	—	89	1	no	—
472	C₄×D₄	—	89	2	no	—
473	C₄×D₄	—	89	2	no	—
474	C₄×D₄	—	89	2	no	—
475	#117	—	89	1	no	—
476	#117	—	89	2	no	—
477	#117	—	89	1	no	—
478	C₂×C₄⋊C₄	—	89	1	no	—
479	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
480	C₂×C₂²⋊C₄	—	89	2	no	—
481	C₂×C₂²⋊C₄	—	89	2	no	—
482	C₂×C₄²	—	89	1	no	—
483	C₂⁴	—	89	2	no	—
484	C₂⁴	—	89	2	no	—
485	#41	—	4	2	no	—
486	#41	—	4	2	no	—
487	#41	—	356	2	no	—
488	#41	—	356	4	no	—
489	#41	—	356	4	no	—
490	#41	—	356	2	no	—
491	C₂×Q₈	—	89	1	no	—
492	C₂×Q₈	—	89	2	no	—
493	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
494	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
495	C₂×D₄	—	89	1	no	—
496	C₂×D₄	—	89	2	no	—
497	C₂×D₄	—	89	1	no	—
498	C₂×D₄	—	89	2	no	—
499	C₂×D₄	—	89	2	no	—
500	C₂×D₄	—	89	2	no	—
501	C₂×D₄	—	89	1	no	—
502	C₂×D₄	—	89	2	no	—
503	C₂×D₄	—	89	2	no	—
504	C₂×D₄	—	89	2	no	—
505	C₂×D₄	—	89	1	no	—
506	C₂×D₄	—	89	1	no	—
507	C₂×D₄	—	89	2	no	—
508	C₂×D₄	—	89	1	no	—
509	C₂×D₄	—	89	2	no	—
510	C₂×D₄	—	89	1	no	—
511	C₂×D₄	—	89	2	no	—
512	C₂×D₄	—	89	2	no	—
513	C₂×D₄	—	89	2	no	—
514	C₂×D₄	—	89	1	no	—
515	C₂×D₄	—	89	1	no	—
516	C₂×D₄	—	356	2	no	—
517	C₂×D₄	—	356	2	no	—
518	C₂×D₄	—	356	4	no	—
519	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
521	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₈₉	1	2	yes	—
523	C₂×D₄	C₂²×D₈₉	1	2	yes	—
524	C₂×D₄	C₂²×D₈₉	1	2	yes	—
525	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₂²×C₄	—	89	1	no	—
527	C₂²×C₄	—	89	2	no	—
528	C₂²×C₄	—	89	1	no	—
529	C₂²×C₄	—	89	2	no	—
530	C₂²×C₄	—	89	2	no	—
531	C₂²×C₄	—	89	2	no	—
532	C₂²×C₄	—	89	1	no	—
533	C₂²×C₄	—	89	2	no	—
534	C₂²×C₄	—	89	1	no	—
535	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
538	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
539	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
540	C₄⋊C₄	—	89	1	no	—
541	C₄⋊C₄	—	89	2	no	—
542	C₄⋊C₄	—	89	1	no	—
543	C₄⋊C₄	—	89	2	no	—
544	C₄⋊C₄	—	89	1	no	—
545	C₄⋊C₄	—	89	2	no	—
546	C₄⋊C₄	—	89	1	no	—
547	C₄⋊C₄	—	89	1	no	—
548	C₄⋊C₄	—	89	2	no	—
549	C₄⋊C₄	—	89	1	no	—
550	C₄⋊C₄	—	89	2	no	—
551	C₄⋊C₄	—	89	2	no	—
552	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
554	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
555	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
556	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
557	C₂²⋊C₄	—	89	1	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	—	89	1	no	—
560	C₂²⋊C₄	—	89	1	no	—
561	C₂²⋊C₄	—	89	2	no	—
562	C₂²⋊C₄	—	89	2	no	—
563	C₂²⋊C₄	—	89	1	no	—
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	2	no	—
571	C₂²⋊C₄	—	89	2	no	—
572	C₂²⋊C₄	—	89	1	no	—
573	C₂²⋊C₄	—	89	1	no	—
574	C₂²⋊C₄	—	89	2	no	—
575	C₂²⋊C₄	—	89	2	no	—
576	C₂²⋊C₄	—	89	2	no	—
577	C₂²⋊C₄	—	89	2	no	—
578	C₂²⋊C₄	—	89	2	no	—
579	C₂²⋊C₄	—	89	1	no	—
580	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
581	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
584	C₄²	—	89	1	no	—
585	C₄²	—	89	1	no	—
586	C₄²	—	89	1	no	—
587	C₄²	—	89	1	no	—
588	C₄²	—	89	2	no	—
589	C₄²	—	89	2	no	—
590	C₄²	—	89	2	no	—
591	C₂³	—	89	2	no	—
592	C₂³	—	89	1	no	—
593	C₂³	—	89	2	no	—
594	C₂³	—	89	1	no	—
595	C₂³	—	356	2	no	—
596	C₂³	—	356	2	no	—
597	C₂³	—	356	2	no	—
598	C₂³	—	356	2	no	—
599	C₂³	—	356	2	no	—
600	C₂³	—	356	2	no	—
601	C₂³	C₂³×D₈₉	1	1	yes	characteristic
602	C₂³	C₂³×D₈₉	1	2	yes	—
603	C₂³	C₂³×D₈₉	1	1	yes	characteristic
604	C₂³	C₂³×D₈₉	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	4	1	no	—
607	Q₈	—	356	1	no	—
608	Q₈	—	178	4	no	—
609	D₄	—	2	2	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	1	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	2	no	—
616	D₄	—	356	2	no	—
617	D₄	—	356	2	no	—
618	D₄	—	356	2	no	—
619	D₄	—	356	1	no	—
620	D₄	—	356	2	no	—
621	D₄	—	356	1	no	—
622	D₄	—	356	2	no	—
623	D₄	—	356	1	no	—
624	D₄	—	356	2	no	—
625	D₄	—	356	2	no	—
626	D₄	—	356	2	no	—
627	D₄	—	356	2	no	—
628	D₄	—	356	2	no	—
629	D₄	—	356	2	no	—
630	D₄	—	356	1	no	—
631	D₄	—	356	1	no	—
632	D₄	—	178	2	no	—
633	D₄	—	178	4	no	—
634	D₄	—	178	2	no	—
635	D₄	—	178	2	no	—
636	D₄	—	178	2	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	—	89	1	no	—
643	C₂×C₄	—	89	2	no	—
644	C₂×C₄	—	89	1	no	—
645	C₂×C₄	—	89	1	no	—
646	C₂×C₄	—	89	1	no	—
647	C₂×C₄	—	89	1	no	—
648	C₂×C₄	—	89	2	no	—
649	C₂×C₄	—	89	1	no	—
650	C₂×C₄	—	356	2	no	—
651	C₂×C₄	—	356	2	no	—
652	C₂×C₄	—	356	2	no	—
653	C₂×C₄	—	356	1	no	—
654	C₂×C₄	—	356	2	no	—
655	C₂×C₄	—	178	4	no	—
656	C₂×C₄	—	178	2	no	—
657	C₂×C₄	—	178	2	no	—
658	C₂×C₄	—	178	2	no	—
659	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
661	C₂×C₄	C₂³×D₈₉	1	2	yes	—
662	C₂×C₄	C₂³×D₈₉	1	2	yes	—
663	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₈₉	1	2	yes	—
665	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
666	C₂²	—	2	1	no	—
667	C₂²	—	2	2	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	178	1	no	—
679	C₂²	—	178	2	no	—
680	C₂²	—	178	2	no	—
681	C₂²	—	178	1	no	—
682	C₂²	—	178	2	no	—
683	C₂²	—	178	1	no	—
684	C₂²	—	178	1	no	—
685	C₂²	—	178	2	no	—
686	C₂²	—	178	1	no	—
687	C₂²	—	178	2	no	—
688	C₂²	—	178	2	no	—
689	C₂²	—	178	1	no	—
690	C₂²	—	712	4	no	—
691	C₂²	—	712	4	no	—
692	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
693	C₄	—	2	2	no	—
694	C₄	—	2	2	no	—
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	89	2	no	—
700	C₄	—	178	1	no	—
701	C₄	—	178	2	no	—
702	C₄	—	178	1	no	—
703	C₄	—	178	1	no	—
704	C₄	—	178	1	no	—
705	C₄	—	178	1	no	—
706	C₄	—	178	2	no	—
707	C₄	#15668057	1	2	yes	—
708	C₂	—	4	1	no	—
709	C₂	—	4	1	no	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	356	1	no	—
713	C₂	—	356	2	no	—
714	C₂	—	356	2	no	—
715	C₂	—	356	1	no	—
716	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
717	C₂	C₂×#15668057	1	1	yes	characteristic
718	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#537×C₈₉	C₂
hypercenter	#537	D₈₉
hypocenter	C₈₉	#3546
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. #19152336	C₂	semidirect
2. #19152336	C₂	semidirect
3. #19152319	C₂	semidirect
4. #19152296	C₂	semidirect
5. #19152295	C₂	semidirect
6. #19152267	C₂	semidirect
7. #19152266	C₂	semidirect
8. #19152249	C₂	semidirect
9. #19152239	C₂	semidirect
10. #19152237	C₂	semidirect
11. #19152236	C₂	semidirect
12. #19152232	C₂	semidirect
13. #19152218	C₂	semidirect
14. #19152188	C₂	semidirect
15. #19152180	C₂	semidirect
16. #19152178	C₂	semidirect
17. #19152164	C₂	semidirect
18. #19152164	C₂	semidirect
19. #19152162	C₂	semidirect
20. #19152144	C₂	semidirect
21. #19152143	C₂	semidirect
22. #19152134	C₂	semidirect
23. #537×C₈₉	C₂	semidirect
24. C₂×#13083575	C₂²	semidirect
25. C₂×#13083574	C₂²	semidirect
26. C₂×#13083574	C₂²	semidirect
27. C₂×#13083573	C₂²	semidirect
31. #15668011	C₂²	semidirect
32. #15668010	C₂²	semidirect
35. #15668008	C₂²	semidirect
36. #15668008	C₂²	semidirect
37. #15668008	C₂²	semidirect
38. #15668007	C₂²	semidirect
39. #15668007	C₂²	semidirect
40. #15668007	C₂²	semidirect
41. #15668005	C₂²	semidirect
42. #15668005	C₂²	semidirect
43. #15668003	C₂²	semidirect
45. #15668001	C₂²	semidirect
46. #15668001	C₂²	semidirect
47. #15667999	C₂²	semidirect
49. #15667998	C₂²	semidirect
50. #15667998	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667997	C₂²	semidirect
54. #15667996	C₂²	semidirect
55. #15667995	C₂²	semidirect
56. #15667995	C₂²	semidirect
57. #15667993	C₂²	semidirect
58. #15667990	C₂²	semidirect
59. #15667990	C₂²	semidirect
60. #15667988	C₂²	semidirect
63. #15667987	C₂²	semidirect
64. #15667987	C₂²	semidirect
67. #15667986	C₂²	semidirect
68. #15667986	C₂²	semidirect
69. #15667986	C₂²	semidirect
70. #15667986	C₂²	semidirect
72. #15667985	C₂²	semidirect
73. #15667985	C₂²	semidirect
75. #15667984	C₂²	semidirect
76. #15667984	C₂²	semidirect
77. #15667984	C₂²	semidirect
78. #15667984	C₂²	semidirect
79. #15667984	C₂²	semidirect
80. #15667983	C₂²	semidirect
81. #15667983	C₂²	semidirect
82. #15667983	C₂²	semidirect
84. #15667982	C₂²	semidirect
85. #15667982	C₂²	semidirect
87. #15667980	C₂²	semidirect
88. #15667980	C₂²	semidirect
89. #15667980	C₂²	semidirect
90. #15667980	C₂²	semidirect
91. Q₈×Dic₈₉	C₂²	semidirect
92. #15667977	C₂²	semidirect
93. D₄×Dic₈₉	C₂²	semidirect
95. #15667974	C₂²	semidirect
97. C₄×C₂²⋊D₈₉	C₂²	semidirect
98. C₄×C₂²⋊D₈₉	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. #15667971	C₂²	semidirect
106. #15667970	C₂²	semidirect
107. #15667970	C₂²	semidirect
108. C₄⋊C₄×D₈₉	C₂²	semidirect
109. C₂×#13083551	C₂²	semidirect
110. C₂²⋊C₄×D₈₉	C₂²	semidirect
111. C₂×C₄×Dic₈₉	C₂²	semidirect
112. C₂×#41×C₈₉	C₂²	semidirect
113. C₂×#41×C₈₉	C₂²	semidirect
114. C₂²⋊Q₈×C₈₉	C₂²	semidirect
115. C₂²⋊Q₈×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #121×C₈₉	C₂²	semidirect
120. #121×C₈₉	C₂²	semidirect
121. #121×C₈₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
360. C₈₉	#3546	semidirect
377. #537	D₈₉	semidirect
388. C₂×#41	C₂×D₈₉	semidirect
389. C₂×#41	C₂×D₈₉	semidirect
423. C₂²⋊Q₈	C₂×D₈₉	semidirect
424. C₂²⋊Q₈	C₂×D₈₉	semidirect
425. C₂²⋊Q₈	C₂×D₈₉	semidirect
449. #121	C₂×D₈₉	semidirect
450. #121	C₂×D₈₉	semidirect
451. #121	C₂×D₈₉	semidirect
452. #121	C₂×D₈₉	semidirect
479. C₂×C₄⋊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
#19152336	2
#19152319	2
#19152296	2
#19152295	2
#19152267	2
#19152266	2
#19152249	2
#19152239	2
#19152237	2
#19152236	2
#19152232	2
#19152218	2
#19152188	2
#19152180	2
#19152178	2
#19152164	2
#19152162	2
#19152144	2
#19152143	2
#19152134	2
#537×C₈₉	2
#3546	89