Subgroups — #26033857

Order 11392.

1242 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152330	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152307	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152306	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152295	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152294	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152291	C₂	1	2	yes	maximal, complemented
7	#19152274	C₂	1	2	yes	maximal, complemented
8	#19152271	C₂	1	2	yes	maximal, complemented
9	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152235	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152143	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152134	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152125	C₂	1	2	yes	maximal, complemented
16	#19152108	C₂	1	2	yes	maximal, complemented
17	#19152104	C₂	1	2	yes	maximal, complemented
18	#41×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₄×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15667972	C₂	1	2	yes	maximal, complemented
22	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#546×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083573	C₂²	1	1	yes	characteristic
25	C₂×#13083573	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	—
27	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
28	C₂³×Dic₈₉	C₂²	1	2	yes	complemented
29	C₂²×C₄×D₈₉	C₂²	1	2	yes	complemented
30	#15668011	C₂²	1	1	yes	characteristic, complemented
31	#15668008	C₂²	1	1	yes	characteristic
32	#15668007	C₂²	1	2	yes	complemented
33	#15668007	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	complemented
35	#15668005	C₂²	1	2	yes	complemented
36	#15668004	C₂²	1	1	yes	characteristic, complemented
37	#15668003	C₂²	1	1	yes	characteristic, complemented
38	#15668002	C₂²	1	2	yes	complemented
39	#15668001	C₂²	1	1	yes	characteristic, complemented
40	#15667998	C₂²	1	2	yes	complemented
41	#15667998	C₂²	1	2	yes	complemented
42	#15667996	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	#15667991	C₂²	1	2	yes	complemented
51	#15667989	C₂²	1	2	yes	complemented
52	#15667989	C₂²	1	2	yes	complemented
53	#15667989	C₂²	1	2	yes	complemented
54	#15667988	C₂²	1	1	yes	characteristic, complemented
55	#15667986	C₂²	1	1	yes	characteristic
56	#15667986	C₂²	1	1	yes	characteristic, complemented
57	#15667984	C₂²	1	2	yes	—
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	1	yes	characteristic
62	#15667983	C₂²	1	2	yes	complemented
63	#15667981	C₂²	1	2	yes	—
64	#15667980	C₂²	1	2	yes	—
65	#15667980	C₂²	1	2	yes	complemented
66	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
67	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
68	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
69	#15667977	C₂²	1	1	yes	characteristic, complemented
70	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
71	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
72	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
73	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
74	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
75	D₄×Dic₈₉	C₂²	1	2	yes	complemented
76	D₄×Dic₈₉	C₂²	1	2	yes	complemented
77	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₈₉	C₂²	1	2	yes	complemented
79	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
80	D₄×Dic₈₉	C₂²	1	2	yes	complemented
81	#15667974	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
84	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
85	#15667972	C₂²	1	2	yes	—
86	#15667972	C₂²	1	1	yes	characteristic
87	#15667972	C₂²	1	2	yes	complemented
88	#15667972	C₂²	1	2	yes	complemented
89	#15667972	C₂²	1	2	yes	complemented
90	#15667972	C₂²	1	2	yes	complemented
91	#15667972	C₂²	1	2	yes	complemented
92	#15667972	C₂²	1	2	yes	complemented
93	#15667972	C₂²	1	2	yes	complemented
94	#15667972	C₂²	1	1	yes	characteristic, complemented
95	#15667971	C₂²	1	2	yes	complemented
96	#15667971	C₂²	1	1	yes	characteristic, complemented
97	#15667970	C₂²	1	2	yes	complemented
98	#15667970	C₂²	1	1	yes	characteristic, complemented
99	#15667968	C₂²	1	1	yes	characteristic, complemented
100	#15667968	C₂²	1	1	yes	characteristic, complemented
101	#15667968	C₂²	1	2	yes	complemented
102	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13083553	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
106	C₂×#13083551	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
108	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
114	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₈₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₈₉	C₂²	1	2	yes	complemented
119	#120×C₈₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	#13083573	—	2	4	no	—
125	#13083573	—	4	4	no	—
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₈₉	—	2	8	no	—
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	1	yes	characteristic
134	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
138	D₄×D₈₉	—	2	4	no	—
139	C₂²×Dic₈₉	—	4	4	no	—
140	C₂²×Dic₈₉	C₂³	1	2	yes	—
141	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
142	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
144	C₂²×Dic₈₉	C₂³	1	2	yes	—
145	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
146	C₂²×Dic₈₉	C₂³	1	2	yes	—
147	C₂²×Dic₈₉	C₂³	1	2	yes	—
148	C₂²×Dic₈₉	C₂³	1	2	yes	—
149	C₂²×Dic₈₉	C₂³	1	2	yes	—
150	C₂×C₄×D₈₉	—	4	4	no	—
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
152	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂³	1	2	yes	—
156	C₂×C₄×D₈₉	C₂³	1	2	yes	—
157	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₉	C₂³	1	2	yes	—
159	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₉	C₂³	1	2	yes	—
162	C₄⋊Dic₈₉	C₂³	1	2	yes	—
163	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₈₉	C₂³	1	2	yes	—
165	#13083553	C₂³	1	1	yes	characteristic
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	2	yes	—
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	2	yes	—
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	#13083551	C₂³	1	1	yes	characteristic
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	2	yes	—
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂⁴×C₈₉	C₂³	1	2	yes	—
206	#41×C₈₉	—	2	4	no	—
207	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₈₉	—	2	4	no	—
209	C₂×D₄×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	C₂³	1	2	yes	—
211	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂³	1	2	yes	—
214	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
228	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
229	C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₂³×C₈₉	—	2	4	no	—
231	C₂³×C₈₉	—	2	4	no	—
232	C₂³×C₈₉	—	4	2	no	—
233	C₂³×C₈₉	C₂⁴	1	2	yes	—
234	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂³×C₈₉	C₂⁴	1	2	yes	—
237	C₂²×D₈₉	—	2	4	no	—
238	C₂²×D₈₉	—	2	4	no	—
239	C₂²×D₈₉	—	4	2	no	—
240	C₂²×D₈₉	C₂⁴	1	2	yes	—
241	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₈₉	—	2	2	no	—
243	D₄×C₈₉	—	2	4	no	—
244	D₄×C₈₉	—	2	4	no	—
245	D₄×C₈₉	—	2	2	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	4	2	no	—
248	D₄×C₈₉	#41	1	4	yes	complemented
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	2	2	no	—
251	C₂×C₄×C₈₉	—	2	2	no	—
252	C₂×C₄×C₈₉	—	4	2	no	—
253	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₈₉	—	2	4	no	—
261	C₂²⋊D₈₉	—	2	4	no	—
262	C₂²⋊D₈₉	—	2	4	no	—
263	C₂²⋊D₈₉	—	2	2	no	—
264	C₂²⋊D₈₉	—	2	4	no	—
265	C₂²⋊D₈₉	—	4	2	no	—
266	C₂²⋊D₈₉	—	4	2	no	—
267	C₂²⋊D₈₉	#41	1	4	yes	complemented
268	C₂×Dic₈₉	—	2	2	no	—
269	C₂×Dic₈₉	—	2	4	no	—
270	C₂×Dic₈₉	—	2	2	no	—
271	C₂×Dic₈₉	—	2	4	no	—
272	C₂×Dic₈₉	—	2	2	no	—
273	C₂×Dic₈₉	—	2	4	no	—
274	C₂×Dic₈₉	—	2	2	no	—
275	C₂×Dic₈₉	—	4	2	no	—
276	C₂×Dic₈₉	—	4	2	no	—
277	C₂×Dic₈₉	—	4	2	no	—
278	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
279	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₈₉	C₂⁴	1	2	yes	—
282	C₂×Dic₈₉	C₂⁴	1	2	yes	—
283	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₈₉	C₂⁴	1	2	yes	—
286	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
288	D₃₅₆	—	2	2	no	—
289	C₄×D₈₉	—	2	2	no	—
290	C₄×D₈₉	—	2	2	no	—
291	C₄×D₈₉	—	2	2	no	—
292	C₄×D₈₉	—	2	4	no	—
293	C₄×D₈₉	—	4	2	no	—
294	C₄×D₈₉	—	4	2	no	—
295	Dic₁₇₈	—	2	2	no	—
296	Dic₁₇₈	—	4	2	no	—
297	C₂²×C₈₉	—	2	2	no	—
298	C₂²×C₈₉	—	2	1	no	—
299	C₂²×C₈₉	—	2	1	no	—
300	C₂²×C₈₉	—	2	2	no	—
301	C₂²×C₈₉	—	2	1	no	—
302	C₂²×C₈₉	—	2	2	no	—
303	C₂²×C₈₉	—	2	1	no	—
304	C₂²×C₈₉	—	2	2	no	—
305	C₂²×C₈₉	—	2	2	no	—
306	C₂²×C₈₉	—	2	1	no	—
307	C₂²×C₈₉	—	4	8	no	—
308	C₂²×C₈₉	C₂×#41	1	2	yes	—
309	C₂²×C₈₉	C₂×#41	1	4	yes	—
310	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
311	C₂×D₈₉	—	2	1	no	—
312	C₂×D₈₉	—	2	1	no	—
313	C₂×D₈₉	—	2	2	no	—
314	C₂×D₈₉	—	2	2	no	—
315	C₂×D₈₉	—	2	2	no	—
316	C₂×D₈₉	—	4	8	no	—
317	C₂×D₈₉	C₂×#41	1	2	yes	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	1	no	—
320	C₄×C₈₉	—	2	1	no	—
321	C₄×C₈₉	—	2	2	no	—
322	C₄×C₈₉	—	2	2	no	—
323	C₄×C₈₉	—	2	1	no	—
324	C₄×C₈₉	C₂×#41	1	2	yes	—
325	Dic₈₉	—	2	1	no	—
326	Dic₈₉	—	2	1	no	—
327	Dic₈₉	—	2	1	no	—
328	Dic₈₉	—	2	2	no	—
329	Dic₈₉	—	2	1	no	—
330	Dic₈₉	—	2	2	no	—
331	Dic₈₉	—	2	2	no	—
332	Dic₈₉	—	2	1	no	—
333	Dic₈₉	C₂×#41	1	2	yes	—
334	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
335	C₂×C₈₉	—	2	4	no	—
336	C₂×C₈₉	—	2	2	no	—
337	C₂×C₈₉	—	4	1	no	—
338	C₂×C₈₉	—	4	2	no	—
339	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
340	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
341	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
342	D₈₉	—	2	2	no	—
343	D₈₉	—	4	2	no	—
344	#3481	—	89	1	no	maximal, Sylow
345	C₈₉	#3481	1	1	yes	characteristic, complemented, Sylow
346	#559	—	89	1	no	—
347	#554	—	89	1	no	—
348	#554	—	89	1	no	—
349	#553	—	89	2	no	—
350	#553	—	89	1	no	—
351	#553	—	89	1	no	—
352	#551	—	89	2	no	—
353	#551	—	89	2	no	—
354	#546	—	89	1	no	—
355	#546	—	89	2	no	—
356	#546	D₈₉	1	1	yes	characteristic, complemented
357	D₄²	—	89	1	no	—
358	#532	—	89	1	no	—
359	#529	—	89	1	no	—
360	#529	—	89	2	no	—
361	#529	—	89	1	no	—
362	#525	—	89	2	no	—
363	#525	—	89	2	no	—
364	C₄×#41	—	89	1	no	—
365	C₄×#41	—	89	1	no	—
366	C₂×C₄×D₄	—	89	1	no	—
367	C₂×C₄×D₄	—	89	1	no	—
368	C₂×C₄×D₄	—	89	2	no	—
369	C₂×#41	—	89	2	no	—
370	C₂×#41	—	89	1	no	—
371	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
372	C₂²×D₄	—	89	2	no	—
373	C₂²×D₄	—	89	1	no	—
374	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
375	C₂³×C₄	—	89	2	no	—
376	C₂³×C₄	—	89	2	no	—
377	C₄⋊Q₈	—	89	1	no	—
378	#127	—	89	1	no	—
379	#126	—	89	2	no	—
380	#126	—	89	2	no	—
381	#126	—	89	2	no	—
382	#126	—	89	2	no	—
383	#125	—	89	2	no	—
384	#125	—	89	1	no	—
385	#125	—	89	1	no	—
386	#124	—	89	1	no	—
387	#124	—	89	2	no	—
388	#124	—	89	2	no	—
389	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
390	#123	—	89	2	no	—
391	#123	—	89	2	no	—
392	#123	—	89	2	no	—
393	#123	—	89	2	no	—
394	#123	—	89	2	no	—
395	#123	—	89	2	no	—
396	#123	—	89	2	no	—
397	#123	C₂×D₈₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	89	1	no	—
399	C₂²⋊Q₈	—	89	2	no	—
400	C₂²⋊Q₈	—	89	2	no	—
401	C₂²⋊Q₈	—	89	2	no	—
402	C₂²⋊Q₈	—	89	2	no	—
403	C₂²⋊Q₈	—	89	2	no	—
404	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
405	#121	—	89	2	no	—
406	#121	—	89	2	no	—
407	#121	—	89	2	no	—
408	#121	—	89	1	no	—
409	#121	—	89	2	no	—
410	#121	—	89	2	no	—
411	#121	—	89	1	no	—
412	#121	—	89	1	no	—
413	#121	C₂×D₈₉	1	2	yes	complemented
414	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
415	#120	—	89	2	no	—
416	#120	—	89	2	no	—
417	#120	—	89	2	no	—
418	#120	C₂×D₈₉	1	2	yes	complemented
419	C₄×Q₈	—	89	1	no	—
420	C₄×Q₈	—	89	1	no	—
421	C₄×Q₈	—	89	1	no	—
422	C₄×Q₈	—	89	1	no	—
423	C₄×D₄	—	89	1	no	—
424	C₄×D₄	—	89	1	no	—
425	C₄×D₄	—	89	2	no	—
426	C₄×D₄	—	89	1	no	—
427	C₄×D₄	—	89	2	no	—
428	C₄×D₄	—	89	1	no	—
429	C₄×D₄	—	89	1	no	—
430	C₄×D₄	—	89	2	no	—
431	C₄×D₄	—	89	1	no	—
432	C₄×D₄	—	89	2	no	—
433	C₄×D₄	—	89	2	no	—
434	C₄×D₄	—	89	1	no	—
435	C₄×D₄	—	89	1	no	—
436	C₄×D₄	—	89	1	no	—
437	C₄×D₄	—	89	1	no	—
438	C₄×D₄	—	89	2	no	—
439	C₄×D₄	—	89	2	no	—
440	C₄×D₄	—	89	2	no	—
441	C₄×D₄	—	89	2	no	—
442	C₄×D₄	—	89	2	no	—
443	C₄×D₄	—	89	2	no	—
444	C₄×D₄	—	89	2	no	—
445	C₄×D₄	—	89	2	no	—
446	C₄×D₄	—	89	1	no	—
447	C₄×D₄	—	89	1	no	—
448	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
450	#117	—	89	2	no	—
451	#117	—	89	1	no	—
452	#117	—	89	1	no	—
453	#117	—	89	2	no	—
454	#117	—	89	1	no	—
455	#117	—	89	1	no	—
456	#117	—	89	2	no	—
457	C₂×C₄⋊C₄	—	89	2	no	—
458	C₂×C₄⋊C₄	—	89	1	no	—
459	C₂×C₄⋊C₄	—	89	1	no	—
460	C₂×C₂²⋊C₄	—	89	2	no	—
461	C₂×C₂²⋊C₄	—	89	2	no	—
462	C₂×C₂²⋊C₄	—	89	2	no	—
463	C₂×C₂²⋊C₄	C₂×D₈₉	1	2	yes	complemented
464	C₂×C₄²	—	89	1	no	—
465	C₂×C₄²	—	89	2	no	—
466	C₂×C₄²	—	89	1	no	—
467	C₂×C₄²	—	89	1	no	—
468	C₂⁴	—	89	2	no	—
469	C₂⁴	C₂²×D₈₉	1	2	yes	—
470	#41	—	2	4	no	—
471	#41	—	356	4	no	—
472	#41	—	178	4	no	—
473	C₂×Q₈	—	89	2	no	—
474	C₂×Q₈	—	89	1	no	—
475	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	89	1	no	—
478	C₂×D₄	—	89	2	no	—
479	C₂×D₄	—	89	2	no	—
480	C₂×D₄	—	89	1	no	—
481	C₂×D₄	—	89	2	no	—
482	C₂×D₄	—	89	2	no	—
483	C₂×D₄	—	89	2	no	—
484	C₂×D₄	—	89	2	no	—
485	C₂×D₄	—	89	1	no	—
486	C₂×D₄	—	178	8	no	—
487	C₂×D₄	—	178	4	no	—
488	C₂×D₄	C₂²×D₈₉	1	2	yes	—
489	C₂×D₄	C₂²×D₈₉	1	2	yes	—
490	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
491	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
492	C₂×D₄	C₂²×D₈₉	1	2	yes	—
493	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
494	C₂²×C₄	—	89	2	no	—
495	C₂²×C₄	—	89	2	no	—
496	C₂²×C₄	—	89	2	no	—
497	C₂²×C₄	—	89	1	no	—
498	C₂²×C₄	—	89	2	no	—
499	C₂²×C₄	—	89	1	no	—
500	C₂²×C₄	—	89	1	no	—
501	C₂²×C₄	—	89	2	no	—
502	C₂²×C₄	—	89	1	no	—
503	C₂²×C₄	—	89	2	no	—
504	C₂²×C₄	—	89	2	no	—
505	C₂²×C₄	—	89	2	no	—
506	C₂²×C₄	—	89	1	no	—
507	C₂²×C₄	—	89	1	no	—
508	C₂²×C₄	—	89	1	no	—
509	C₂²×C₄	—	89	2	no	—
510	C₂²×C₄	—	356	4	no	—
511	C₂²×C₄	—	356	4	no	—
512	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
513	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
515	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
516	C₄⋊C₄	—	89	1	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	1	no	—
520	C₄⋊C₄	—	89	2	no	—
521	C₄⋊C₄	—	89	2	no	—
522	C₄⋊C₄	—	89	2	no	—
523	C₄⋊C₄	—	89	2	no	—
524	C₄⋊C₄	—	89	1	no	—
525	C₄⋊C₄	—	89	1	no	—
526	C₄⋊C₄	—	89	1	no	—
527	C₄⋊C₄	—	89	2	no	—
528	C₄⋊C₄	—	89	1	no	—
529	C₄⋊C₄	—	89	1	no	—
530	C₄⋊C₄	—	89	2	no	—
531	C₄⋊C₄	—	89	2	no	—
532	C₄⋊C₄	—	89	2	no	—
533	C₄⋊C₄	—	89	2	no	—
534	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
537	C₂²⋊C₄	—	89	2	no	—
538	C₂²⋊C₄	—	89	2	no	—
539	C₂²⋊C₄	—	89	2	no	—
540	C₂²⋊C₄	—	89	2	no	—
541	C₂²⋊C₄	—	89	1	no	—
542	C₂²⋊C₄	—	89	2	no	—
543	C₂²⋊C₄	—	89	2	no	—
544	C₂²⋊C₄	—	89	1	no	—
545	C₂²⋊C₄	—	89	2	no	—
546	C₂²⋊C₄	—	89	1	no	—
547	C₂²⋊C₄	—	89	2	no	—
548	C₂²⋊C₄	—	89	2	no	—
549	C₂²⋊C₄	—	89	2	no	—
550	C₂²⋊C₄	—	89	2	no	—
551	C₂²⋊C₄	—	89	2	no	—
552	C₂²⋊C₄	—	89	1	no	—
553	C₂²⋊C₄	—	89	2	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
557	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
562	C₄²	—	89	1	no	—
563	C₄²	—	89	1	no	—
564	C₄²	—	89	1	no	—
565	C₄²	—	89	1	no	—
566	C₄²	—	89	2	no	—
567	C₄²	—	89	1	no	—
568	C₄²	—	89	1	no	—
569	C₄²	—	89	1	no	—
570	C₄²	—	89	2	no	—
571	C₄²	—	89	2	no	—
572	C₄²	—	89	1	no	—
573	C₄²	—	89	1	no	—
574	C₄²	C₂²×D₈₉	1	1	yes	characteristic
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	89	1	no	—
579	C₂³	—	89	2	no	—
580	C₂³	—	356	2	no	—
581	C₂³	—	178	4	no	—
582	C₂³	—	178	4	no	—
583	C₂³	C₂³×D₈₉	1	2	yes	—
584	C₂³	C₂³×D₈₉	1	1	yes	characteristic
585	C₂³	C₂³×D₈₉	1	1	yes	characteristic
586	C₂³	C₂³×D₈₉	1	2	yes	—
587	Q₈	—	2	2	no	—
588	Q₈	—	356	2	no	—
589	Q₈	—	178	2	no	—
590	D₄	—	2	2	no	—
591	D₄	—	2	4	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	89	4	no	—
596	D₄	—	356	2	no	—
597	D₄	—	356	2	no	—
598	D₄	—	178	4	no	—
599	D₄	—	178	4	no	—
600	D₄	—	178	2	no	—
601	D₄	—	178	4	no	—
602	D₄	—	178	4	no	—
603	D₄	—	178	2	no	—
604	D₄	#13083573	1	4	yes	complemented
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	89	1	no	—
610	C₂×C₄	—	89	1	no	—
611	C₂×C₄	—	89	1	no	—
612	C₂×C₄	—	89	1	no	—
613	C₂×C₄	—	89	2	no	—
614	C₂×C₄	—	89	1	no	—
615	C₂×C₄	—	89	1	no	—
616	C₂×C₄	—	89	2	no	—
617	C₂×C₄	—	89	1	no	—
618	C₂×C₄	—	89	2	no	—
619	C₂×C₄	—	356	2	no	—
620	C₂×C₄	—	356	2	no	—
621	C₂×C₄	—	356	2	no	—
622	C₂×C₄	—	356	2	no	—
623	C₂×C₄	—	356	2	no	—
624	C₂×C₄	—	178	2	no	—
625	C₂×C₄	—	178	4	no	—
626	C₂×C₄	—	178	2	no	—
627	C₂×C₄	—	178	4	no	—
628	C₂×C₄	—	178	2	no	—
629	C₂×C₄	—	178	4	no	—
630	C₂×C₄	—	178	4	no	—
631	C₂×C₄	—	178	2	no	—
632	C₂×C₄	—	178	2	no	—
633	C₂×C₄	—	178	2	no	—
634	C₂×C₄	—	178	2	no	—
635	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₈₉	1	2	yes	—
637	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
640	C₂×C₄	C₂³×D₈₉	1	2	yes	—
641	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	4	8	no	—
653	C₂²	—	89	2	no	—
654	C₂²	—	356	8	no	—
655	C₂²	—	178	2	no	—
656	C₂²	—	178	2	no	—
657	C₂²	—	178	2	no	—
658	C₂²	—	178	1	no	—
659	C₂²	—	178	1	no	—
660	C₂²	#41×D₈₉	1	2	yes	—
661	C₂²	C₂×#13083573	1	4	yes	—
662	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	89	2	no	—
670	C₄	—	89	2	no	—
671	C₄	—	178	1	no	—
672	C₄	—	178	2	no	—
673	C₄	—	178	1	no	—
674	C₄	—	178	1	no	—
675	C₄	—	178	2	no	—
676	C₄	—	178	1	no	—
677	C₄	—	178	2	no	—
678	C₄	—	178	1	no	—
679	C₄	C₂×#13083573	1	2	yes	—
680	C₂	—	2	2	no	—
681	C₂	—	2	4	no	—
682	C₂	—	4	1	no	—
683	C₂	—	4	2	no	—
684	C₂	—	356	2	no	—
685	C₂	—	178	2	no	—
686	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
687	C₂	C₂²×#13083573	1	1	yes	characteristic
688	C₂	H(5,𝔽₂)×D₈₉	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	#3481
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. #19152330	C₂	semidirect
2. #19152307	C₂	semidirect
3. #19152306	C₂	semidirect
4. #19152295	C₂	semidirect
5. #19152294	C₂	semidirect
6. #19152291	C₂	semidirect
7. #19152274	C₂	semidirect
8. #19152271	C₂	semidirect
9. #19152236	C₂	semidirect
10. #19152235	C₂	semidirect
11. D₄×C₂²⋊D₈₉	C₂	semidirect
12. #19152143	C₂	semidirect
13. #19152134	C₂	semidirect
14. #19152127	C₂	semidirect
15. #19152125	C₂	semidirect
16. #19152108	C₂	semidirect
17. #19152104	C₂	semidirect
18. #41×Dic₈₉	C₂	semidirect
19. C₄×#13083573	C₂	semidirect
20. C₂×D₄×Dic₈₉	C₂	semidirect
21. C₂×#15667972	C₂	semidirect
22. C₄×D₄×D₈₉	C₂	semidirect
23. #546×C₈₉	C₂	semidirect
25. C₂×#13083573	C₂²	semidirect
28. C₂³×Dic₈₉	C₂²	semidirect
29. C₂²×C₄×D₈₉	C₂²	semidirect
30. #15668011	C₂²	semidirect
32. #15668007	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668005	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668004	C₂²	semidirect
37. #15668003	C₂²	semidirect
38. #15668002	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15667998	C₂²	semidirect
41. #15667998	C₂²	semidirect
42. #15667996	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. #15667991	C₂²	semidirect
51. #15667989	C₂²	semidirect
52. #15667989	C₂²	semidirect
53. #15667989	C₂²	semidirect
54. #15667988	C₂²	semidirect
56. #15667986	C₂²	semidirect
58. #15667984	C₂²	semidirect
59. #15667984	C₂²	semidirect
60. #15667984	C₂²	semidirect
62. #15667983	C₂²	semidirect
65. #15667980	C₂²	semidirect
66. Q₈×Dic₈₉	C₂²	semidirect
67. Q₈×Dic₈₉	C₂²	semidirect
68. C₄×Dic₁₇₈	C₂²	semidirect
69. #15667977	C₂²	semidirect
70. C₄×D₃₅₆	C₂²	semidirect
74. D₄×Dic₈₉	C₂²	semidirect
75. D₄×Dic₈₉	C₂²	semidirect
76. D₄×Dic₈₉	C₂²	semidirect
77. D₄×Dic₈₉	C₂²	semidirect
78. D₄×Dic₈₉	C₂²	semidirect
79. D₄×Dic₈₉	C₂²	semidirect
80. D₄×Dic₈₉	C₂²	semidirect
81. #15667974	C₂²	semidirect
83. C₄×C₂²⋊D₈₉	C₂²	semidirect
84. C₄×C₂²⋊D₈₉	C₂²	semidirect
87. #15667972	C₂²	semidirect
88. #15667972	C₂²	semidirect
89. #15667972	C₂²	semidirect
90. #15667972	C₂²	semidirect
91. #15667972	C₂²	semidirect
92. #15667972	C₂²	semidirect
93. #15667972	C₂²	semidirect
94. #15667972	C₂²	semidirect
95. #15667971	C₂²	semidirect
96. #15667971	C₂²	semidirect
97. #15667970	C₂²	semidirect
98. #15667970	C₂²	semidirect
99. #15667968	C₂²	semidirect
100. #15667968	C₂²	semidirect
101. #15667968	C₂²	semidirect
102. C₂×C₄⋊Dic₈₉	C₂²	semidirect
103. C₂×#13083553	C₂²	semidirect
104. C₄⋊C₄×D₈₉	C₂²	semidirect
105. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
106. C₂×#13083551	C₂²	semidirect
107. C₂²⋊C₄×D₈₉	C₂²	semidirect
108. C₂×C₄×Dic₈₉	C₂²	semidirect
109. C₂×C₄×Dic₈₉	C₂²	semidirect
110. C₂×C₄×Dic₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
114. #124×C₈₉	C₂²	semidirect
115. #123×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #120×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
248. D₄×C₈₉	#41	semidirect
267. C₂²⋊D₈₉	#41	semidirect
345. C₈₉	#3481	semidirect
356. #546	D₈₉	semidirect
389. #124	C₂×D₈₉	semidirect
397. #123	C₂×D₈₉	semidirect
404. C₂²⋊Q₈	C₂×D₈₉	semidirect
413. #121	C₂×D₈₉	semidirect
414. #121	C₂×D₈₉	semidirect
418. #120	C₂×D₈₉	semidirect
449. C₄×D₄	C₂×D₈₉	semidirect
463. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
604. D₄	#13083573	semidirect

Maximal subgroups

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

subgroup	index
#19152330	2
#19152307	2
#19152306	2
#19152295	2
#19152294	2
#19152291	2
#19152274	2
#19152271	2
#19152236	2
#19152235	2
D₄×C₂²⋊D₈₉	2
#19152143	2
#19152134	2
#19152127	2
#19152125	2
#19152108	2
#19152104	2
#41×Dic₈₉	2
C₄×#13083573	2
C₂×D₄×Dic₈₉	2
C₂×#15667972	2
C₄×D₄×D₈₉	2
#546×C₈₉	2
#3481	89