Subgroups — #26033808

Order 11392.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152317	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152312	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152293	C₂	1	2	yes	maximal, complemented
5	#19152286	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152284	C₂	1	2	yes	maximal, complemented
7	#19152282	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152276	C₂	1	2	yes	maximal, complemented
9	#19152273	C₂	1	2	yes	maximal, complemented
10	#19152250	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152245	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152152	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152130	C₂	1	2	yes	maximal, complemented
15	#19152130	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152126	C₂	1	2	yes	maximal, complemented
17	#19152107	C₂	1	2	yes	maximal, complemented
18	C₄×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	#117×D₈₉	C₂	1	2	yes	maximal, complemented
23	#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic
25	C₂×#13083574	C₂²	1	1	yes	characteristic
26	C₂×#13083574	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₈₉	C₂²	1	2	yes	—
29	#15668011	C₂²	1	1	yes	characteristic, complemented
30	#15668010	C₂²	1	1	yes	characteristic, complemented
31	#15668007	C₂²	1	2	yes	complemented
32	#15668005	C₂²	1	2	yes	complemented
33	#15668005	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	complemented
35	#15668005	C₂²	1	2	yes	complemented
36	#15668003	C₂²	1	1	yes	characteristic, complemented
37	#15668003	C₂²	1	2	yes	complemented
38	#15668002	C₂²	1	2	yes	complemented
39	#15668002	C₂²	1	2	yes	complemented
40	#15667999	C₂²	1	1	yes	characteristic
41	#15667999	C₂²	1	2	yes	complemented
42	#15667998	C₂²	1	2	yes	complemented
43	#15667997	C₂²	1	2	yes	—
44	#15667997	C₂²	1	2	yes	complemented
45	#15667994	C₂²	1	2	yes	—
46	#15667994	C₂²	1	2	yes	—
47	#15667994	C₂²	1	2	yes	—
48	#15667994	C₂²	1	2	yes	complemented
49	#15667994	C₂²	1	2	yes	complemented
50	#15667992	C₂²	1	1	yes	characteristic
51	#15667992	C₂²	1	1	yes	characteristic, complemented
52	#15667992	C₂²	1	2	yes	complemented
53	#15667990	C₂²	1	2	yes	—
54	#15667990	C₂²	1	2	yes	complemented
55	#15667990	C₂²	1	2	yes	complemented
56	#15667989	C₂²	1	2	yes	complemented
57	#15667988	C₂²	1	1	yes	characteristic
58	#15667985	C₂²	1	2	yes	—
59	#15667985	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	—
63	#15667982	C₂²	1	2	yes	—
64	#15667980	C₂²	1	2	yes	—
65	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
67	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
68	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
69	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
70	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
71	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
72	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
73	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
74	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
75	C₄×D₃₅₆	C₂²	1	2	yes	complemented
76	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
77	#15667974	C₂²	1	1	yes	characteristic
78	#15667974	C₂²	1	1	yes	characteristic
79	#15667974	C₂²	1	2	yes	complemented
80	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
81	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
83	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
84	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
87	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
88	#15667972	C₂²	1	2	yes	—
89	#15667971	C₂²	1	2	yes	complemented
90	#15667971	C₂²	1	1	yes	characteristic, complemented
91	#15667971	C₂²	1	1	yes	characteristic, complemented
92	#15667970	C₂²	1	2	yes	—
93	#15667970	C₂²	1	2	yes	—
94	#15667970	C₂²	1	2	yes	complemented
95	#15667970	C₂²	1	1	yes	characteristic, complemented
96	#15667969	C₂²	1	2	yes	—
97	#15667969	C₂²	1	1	yes	characteristic
98	#15667969	C₂²	1	2	yes	complemented
99	#15667969	C₂²	1	1	yes	characteristic, complemented
100	#15667968	C₂²	1	2	yes	complemented
101	#15667968	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
103	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
106	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
108	C₄²×D₈₉	C₂²	1	1	yes	characteristic
109	C₄²×D₈₉	C₂²	1	2	yes	complemented
110	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₈₉	C₂²	1	2	yes	complemented
112	#126×C₈₉	C₂²	1	2	yes	complemented
113	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₈₉	C₂²	1	1	yes	characteristic
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
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
121	#117×C₈₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	#13083575	—	2	4	no	—
125	#13083574	—	2	4	no	—
126	#13083574	—	2	4	no	—
127	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	C₂×D₃₅₆	C₂³	1	2	yes	—
131	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	D₄×D₈₉	—	2	4	no	—
139	C₂²×Dic₈₉	C₂³	1	2	yes	—
140	C₂×C₄×D₈₉	—	2	8	no	—
141	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₈₉	C₂³	1	2	yes	—
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
144	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₈₉	C₂³	1	2	yes	—
146	C₂×C₄×D₈₉	C₂³	1	2	yes	—
147	C₂×C₄×D₈₉	C₂³	1	2	yes	—
148	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
152	C₂×C₄×D₈₉	C₂³	1	2	yes	—
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₈₉	C₂³	1	2	yes	—
155	C₄⋊Dic₈₉	C₂³	1	2	yes	—
156	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₉	C₂³	1	2	yes	—
158	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₉	C₂³	1	2	yes	—
162	#13083553	C₂³	1	1	yes	characteristic
163	#13083553	C₂³	1	1	yes	characteristic
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	2	yes	—
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	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	#13083551	C₂³	1	1	yes	characteristic
182	#13083551	C₂³	1	1	yes	characteristic
183	#13083551	C₂³	1	2	yes	—
184	#13083551	C₂³	1	2	yes	—
185	#13083551	C₂³	1	2	yes	—
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	1	yes	characteristic
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	2	yes	—
194	C₄×Dic₈₉	C₂³	1	2	yes	—
195	C₄×Dic₈₉	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₈₉	C₂³	1	2	yes	—
207	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₄²×C₈₉	C₂³	1	1	yes	characteristic
223	C₄²×C₈₉	C₂³	1	2	yes	—
224	C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₂³×C₈₉	C₂⁴	1	2	yes	—
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂²×D₈₉	—	2	4	no	—
230	C₂²×D₈₉	—	2	4	no	—
231	C₂²×D₈₉	—	4	2	no	—
232	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
234	C₂²×D₈₉	C₂⁴	1	2	yes	—
235	Q₈×C₈₉	—	2	2	no	—
236	D₄×C₈₉	—	2	2	no	—
237	D₄×C₈₉	—	4	2	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	4	1	no	—
242	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
248	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₈₉	—	2	4	no	—
252	C₂²⋊D₈₉	—	2	2	no	—
253	C₂²⋊D₈₉	—	2	4	no	—
254	C₂²⋊D₈₉	—	2	2	no	—
255	C₂²⋊D₈₉	—	4	2	no	—
256	C₂×Dic₈₉	—	2	4	no	—
257	C₂×Dic₈₉	C₂⁴	1	2	yes	—
258	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₈₉	C₂⁴	1	2	yes	—
262	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₈₉	C₂⁴	1	2	yes	—
264	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
266	D₃₅₆	—	2	2	no	—
267	D₃₅₆	—	2	4	no	—
268	D₃₅₆	#41	1	4	yes	complemented
269	C₄×D₈₉	—	2	4	no	—
270	C₄×D₈₉	—	2	4	no	—
271	C₄×D₈₉	—	2	4	no	—
272	C₄×D₈₉	—	2	4	no	—
273	C₄×D₈₉	—	2	2	no	—
274	C₄×D₈₉	—	2	2	no	—
275	C₄×D₈₉	—	2	2	no	—
276	C₄×D₈₉	—	2	4	no	—
277	C₄×D₈₉	—	4	1	no	—
278	C₄×D₈₉	—	4	2	no	—
279	C₄×D₈₉	—	4	2	no	—
280	C₄×D₈₉	—	4	1	no	—
281	C₄×D₈₉	#41	1	4	yes	complemented
282	Dic₁₇₈	—	2	2	no	—
283	Dic₁₇₈	—	2	2	no	—
284	Dic₁₇₈	—	4	2	no	—
285	C₂²×C₈₉	—	2	2	no	—
286	C₂²×C₈₉	—	2	1	no	—
287	C₂²×C₈₉	—	2	1	no	—
288	C₂²×C₈₉	—	2	2	no	—
289	C₂²×C₈₉	—	2	2	no	—
290	C₂²×C₈₉	—	2	1	no	—
291	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
292	C₂×D₈₉	—	2	2	no	—
293	C₂×D₈₉	—	2	1	no	—
294	C₂×D₈₉	—	2	2	no	—
295	C₂×D₈₉	—	2	1	no	—
296	C₂×D₈₉	—	2	1	no	—
297	C₂×D₈₉	—	2	1	no	—
298	C₂×D₈₉	—	2	1	no	—
299	C₂×D₈₉	—	4	8	no	—
300	C₂×D₈₉	C₂×#41	1	2	yes	—
301	C₂×D₈₉	C₂×#41	1	4	yes	—
302	C₄×C₈₉	—	2	1	no	—
303	C₄×C₈₉	—	2	1	no	—
304	C₄×C₈₉	—	2	2	no	—
305	C₄×C₈₉	—	2	2	no	—
306	C₄×C₈₉	—	2	2	no	—
307	C₄×C₈₉	—	2	1	no	—
308	C₄×C₈₉	—	2	1	no	—
309	C₄×C₈₉	C₂×#41	1	2	yes	—
310	C₄×C₈₉	C₂×#41	1	2	yes	—
311	Dic₈₉	—	2	2	no	—
312	Dic₈₉	—	2	1	no	—
313	Dic₈₉	—	2	1	no	—
314	Dic₈₉	—	2	2	no	—
315	Dic₈₉	—	2	1	no	—
316	Dic₈₉	—	2	1	no	—
317	Dic₈₉	—	2	2	no	—
318	Dic₈₉	—	2	1	no	—
319	Dic₈₉	C₂×#41	1	2	yes	—
320	C₂×C₈₉	—	4	2	no	—
321	C₂×C₈₉	—	4	1	no	—
322	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
323	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
324	C₂×C₈₉	#585	1	1	yes	characteristic
325	D₈₉	—	2	2	no	—
326	D₈₉	—	2	4	no	—
327	D₈₉	—	4	1	no	—
328	#3475	—	89	1	no	maximal, Sylow
329	C₈₉	#3475	1	1	yes	characteristic, complemented, Sylow
330	#556	—	89	1	no	—
331	#555	—	89	1	no	—
332	#554	—	89	1	no	—
333	#553	—	89	2	no	—
334	#552	—	89	2	no	—
335	#552	—	89	1	no	—
336	#552	—	89	1	no	—
337	#551	—	89	2	no	—
338	#551	—	89	2	no	—
339	#547	—	89	1	no	—
340	#546	—	89	1	no	—
341	#546	—	89	1	no	—
342	#533	—	89	1	no	—
343	#529	—	89	1	no	—
344	#529	—	89	2	no	—
345	#529	—	89	2	no	—
346	#529	D₈₉	1	1	yes	characteristic, complemented
347	#525	—	89	2	no	—
348	C₄×#41	—	89	1	no	—
349	C₄×#41	—	89	1	no	—
350	C₄×#41	—	89	1	no	—
351	C₂×C₄×D₄	—	89	1	no	—
352	C₂×#117	—	89	2	no	—
353	C₂×#41	—	89	1	no	—
354	C₂×#41	—	89	1	no	—
355	C₂×#41	—	89	1	no	—
356	C₂²×D₄	—	89	1	no	—
357	C₂³×C₄	—	89	2	no	—
358	C₄⋊Q₈	—	89	1	no	—
359	C₄⋊Q₈	—	89	1	no	—
360	#126	—	89	2	no	—
361	#126	—	89	2	no	—
362	#126	—	89	2	no	—
363	#126	—	89	2	no	—
364	#126	—	89	2	no	—
365	#126	C₂×D₈₉	1	2	yes	complemented
366	#125	—	89	2	no	—
367	#125	—	89	2	no	—
368	#125	—	89	1	no	—
369	#125	—	89	2	no	—
370	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
371	#124	—	89	1	no	—
372	#124	—	89	2	no	—
373	#124	—	89	2	no	—
374	#124	C₂×D₈₉	1	1	yes	characteristic
375	#123	—	89	2	no	—
376	#123	—	89	2	no	—
377	#123	—	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	C₂×D₈₉	1	2	yes	complemented
383	C₂²⋊Q₈	—	89	1	no	—
384	C₂²⋊Q₈	—	89	2	no	—
385	C₂²⋊Q₈	—	89	2	no	—
386	C₂²⋊Q₈	—	89	1	no	—
387	C₂²⋊Q₈	—	89	2	no	—
388	C₂²⋊Q₈	—	89	2	no	—
389	C₂²⋊Q₈	—	89	1	no	—
390	C₂²⋊Q₈	—	89	2	no	—
391	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
392	#121	—	89	2	no	—
393	#121	—	89	2	no	—
394	#121	—	89	1	no	—
395	#121	—	89	2	no	—
396	#121	—	89	2	no	—
397	#121	C₂×D₈₉	1	1	yes	characteristic
398	#120	—	89	2	no	—
399	#120	—	89	2	no	—
400	C₄×Q₈	—	89	1	no	—
401	C₄×Q₈	—	89	1	no	—
402	C₄×Q₈	—	89	1	no	—
403	C₄×Q₈	—	89	1	no	—
404	C₄×Q₈	—	89	1	no	—
405	C₄×Q₈	—	89	2	no	—
406	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
407	C₄×D₄	—	89	1	no	—
408	C₄×D₄	—	89	2	no	—
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	1	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	1	no	—
413	C₄×D₄	—	89	2	no	—
414	C₄×D₄	—	89	1	no	—
415	C₄×D₄	—	89	2	no	—
416	C₄×D₄	—	89	1	no	—
417	C₄×D₄	—	89	1	no	—
418	C₄×D₄	—	89	2	no	—
419	C₄×D₄	—	89	2	no	—
420	C₄×D₄	—	89	1	no	—
421	C₄×D₄	—	89	1	no	—
422	C₄×D₄	—	89	1	no	—
423	C₄×D₄	—	89	1	no	—
424	C₄×D₄	—	89	2	no	—
425	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
426	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
427	#117	—	89	2	no	—
428	#117	—	89	1	no	—
429	#117	—	89	1	no	—
430	#117	—	89	2	no	—
431	#117	—	89	2	no	—
432	#117	—	89	2	no	—
433	#117	—	89	1	no	—
434	#117	—	89	2	no	—
435	#117	—	89	2	no	—
436	#117	—	89	1	no	—
437	#117	—	89	2	no	—
438	#117	—	89	1	no	—
439	#117	—	89	2	no	—
440	#117	C₂×D₈₉	1	2	yes	complemented
441	C₂×C₄⋊C₄	—	89	2	no	—
442	C₂×C₄⋊C₄	—	89	2	no	—
443	C₂×C₄⋊C₄	—	89	1	no	—
444	C₂×C₂²⋊C₄	—	89	2	no	—
445	C₂×C₂²⋊C₄	—	89	2	no	—
446	C₂×C₂²⋊C₄	—	89	2	no	—
447	C₂×C₄²	—	89	2	no	—
448	C₂×C₄²	—	89	2	no	—
449	C₂×C₄²	—	89	1	no	—
450	C₂×C₄²	—	89	1	no	—
451	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic, complemented
452	C₂⁴	—	89	2	no	—
453	#41	—	178	4	no	—
454	#41	—	178	4	no	—
455	#41	—	178	4	no	—
456	C₂×Q₈	—	89	2	no	—
457	C₂×Q₈	—	89	1	no	—
458	C₂×Q₈	—	89	1	no	—
459	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
460	C₂×D₄	—	89	2	no	—
461	C₂×D₄	—	89	1	no	—
462	C₂×D₄	—	89	2	no	—
463	C₂×D₄	—	89	1	no	—
464	C₂×D₄	—	89	2	no	—
465	C₂×D₄	—	89	1	no	—
466	C₂×D₄	—	89	1	no	—
467	C₂×D₄	—	89	2	no	—
468	C₂×D₄	—	178	4	no	—
469	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
470	C₂×D₄	C₂²×D₈₉	1	2	yes	—
471	C₂²×C₄	—	89	1	no	—
472	C₂²×C₄	—	89	2	no	—
473	C₂²×C₄	—	89	1	no	—
474	C₂²×C₄	—	89	2	no	—
475	C₂²×C₄	—	89	2	no	—
476	C₂²×C₄	—	89	1	no	—
477	C₂²×C₄	—	89	2	no	—
478	C₂²×C₄	—	89	2	no	—
479	C₂²×C₄	—	89	1	no	—
480	C₂²×C₄	—	89	1	no	—
481	C₂²×C₄	—	89	2	no	—
482	C₂²×C₄	—	89	2	no	—
483	C₂²×C₄	—	89	2	no	—
484	C₂²×C₄	—	89	1	no	—
485	C₂²×C₄	—	178	8	no	—
486	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
489	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
490	C₄⋊C₄	—	89	1	no	—
491	C₄⋊C₄	—	89	1	no	—
492	C₄⋊C₄	—	89	1	no	—
493	C₄⋊C₄	—	89	2	no	—
494	C₄⋊C₄	—	89	2	no	—
495	C₄⋊C₄	—	89	2	no	—
496	C₄⋊C₄	—	89	2	no	—
497	C₄⋊C₄	—	89	2	no	—
498	C₄⋊C₄	—	89	1	no	—
499	C₄⋊C₄	—	89	1	no	—
500	C₄⋊C₄	—	89	1	no	—
501	C₄⋊C₄	—	89	2	no	—
502	C₄⋊C₄	—	89	2	no	—
503	C₄⋊C₄	—	89	2	no	—
504	C₄⋊C₄	—	89	1	no	—
505	C₄⋊C₄	—	89	1	no	—
506	C₄⋊C₄	—	89	2	no	—
507	C₄⋊C₄	—	89	2	no	—
508	C₄⋊C₄	—	89	2	no	—
509	C₄⋊C₄	—	89	2	no	—
510	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
511	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
512	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
515	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
516	C₂²⋊C₄	—	89	2	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	2	no	—
519	C₂²⋊C₄	—	89	1	no	—
520	C₂²⋊C₄	—	89	2	no	—
521	C₂²⋊C₄	—	89	1	no	—
522	C₂²⋊C₄	—	89	2	no	—
523	C₂²⋊C₄	—	89	1	no	—
524	C₂²⋊C₄	—	89	1	no	—
525	C₂²⋊C₄	—	89	2	no	—
526	C₂²⋊C₄	—	89	2	no	—
527	C₂²⋊C₄	—	89	2	no	—
528	C₂²⋊C₄	—	89	2	no	—
529	C₂²⋊C₄	—	89	2	no	—
530	C₂²⋊C₄	—	89	2	no	—
531	C₂²⋊C₄	—	89	1	no	—
532	C₂²⋊C₄	—	89	2	no	—
533	C₂²⋊C₄	—	89	1	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
540	C₄²	—	89	2	no	—
541	C₄²	—	89	2	no	—
542	C₄²	—	89	2	no	—
543	C₄²	—	89	2	no	—
544	C₄²	—	89	1	no	—
545	C₄²	—	89	1	no	—
546	C₄²	—	89	1	no	—
547	C₄²	—	89	1	no	—
548	C₄²	—	89	1	no	—
549	C₄²	—	89	1	no	—
550	C₄²	—	89	2	no	—
551	C₄²	C₂²×D₈₉	1	1	yes	characteristic
552	C₄²	C₂²×D₈₉	1	1	yes	characteristic
553	C₄²	C₂²×D₈₉	1	1	yes	characteristic
554	C₄²	C₂²×D₈₉	1	1	yes	characteristic
555	C₄²	C₂²×D₈₉	1	2	yes	—
556	C₂³	—	89	1	no	—
557	C₂³	—	89	2	no	—
558	C₂³	—	89	1	no	—
559	C₂³	—	356	2	no	—
560	C₂³	—	178	4	no	—
561	C₂³	—	178	4	no	—
562	C₂³	C₂³×D₈₉	1	2	yes	—
563	C₂³	C₂³×D₈₉	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	356	2	no	—
566	Q₈	—	178	2	no	—
567	Q₈	—	178	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	4	2	no	—
570	D₄	—	89	4	no	—
571	D₄	—	356	2	no	—
572	D₄	—	178	2	no	—
573	D₄	—	178	4	no	—
574	D₄	—	178	2	no	—
575	D₄	—	178	4	no	—
576	D₄	—	178	2	no	—
577	D₄	—	178	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	89	1	no	—
583	C₂×C₄	—	89	4	no	—
584	C₂×C₄	—	89	2	no	—
585	C₂×C₄	—	89	1	no	—
586	C₂×C₄	—	89	1	no	—
587	C₂×C₄	—	89	1	no	—
588	C₂×C₄	—	89	1	no	—
589	C₂×C₄	—	89	2	no	—
590	C₂×C₄	—	89	2	no	—
591	C₂×C₄	—	89	1	no	—
592	C₂×C₄	—	356	1	no	—
593	C₂×C₄	—	356	2	no	—
594	C₂×C₄	—	356	1	no	—
595	C₂×C₄	—	356	2	no	—
596	C₂×C₄	—	178	4	no	—
597	C₂×C₄	—	178	4	no	—
598	C₂×C₄	—	178	4	no	—
599	C₂×C₄	—	178	4	no	—
600	C₂×C₄	—	178	4	no	—
601	C₂×C₄	—	178	4	no	—
602	C₂×C₄	—	178	2	no	—
603	C₂×C₄	—	178	2	no	—
604	C₂×C₄	—	178	2	no	—
605	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₈₉	1	2	yes	—
609	C₂×C₄	C₂³×D₈₉	1	2	yes	—
610	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₈₉	1	2	yes	—
612	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	89	2	no	—
621	C₂²	—	89	4	no	—
622	C₂²	—	356	8	no	—
623	C₂²	—	178	1	no	—
624	C₂²	—	178	1	no	—
625	C₂²	—	178	1	no	—
626	C₂²	—	178	2	no	—
627	C₂²	—	178	1	no	—
628	C₂²	—	178	2	no	—
629	C₂²	—	178	1	no	—
630	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	2	no	—
638	C₄	—	89	2	no	—
639	C₄	—	178	2	no	—
640	C₄	—	178	1	no	—
641	C₄	—	178	1	no	—
642	C₄	—	178	1	no	—
643	C₄	—	178	2	no	—
644	C₄	—	178	1	no	—
645	C₄	—	178	2	no	—
646	C₄	—	178	1	no	—
647	C₄	#41×D₈₉	1	2	yes	—
648	C₄	#41×D₈₉	1	2	yes	—
649	C₂	—	4	1	no	—
650	C₂	—	4	2	no	—
651	C₂	—	356	1	no	—
652	C₂	—	178	2	no	—
653	C₂	—	178	4	no	—
654	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
655	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
656	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Frattini	C₂²	C₂⁴×D₈₉
Fitting	#529×C₈₉	C₂
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3475
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19152317	C₂	semidirect
2. #19152312	C₂	semidirect
3. #19152304	C₂	semidirect
4. #19152293	C₂	semidirect
5. #19152286	C₂	semidirect
6. #19152284	C₂	semidirect
7. #19152282	C₂	semidirect
8. #19152276	C₂	semidirect
9. #19152273	C₂	semidirect
10. #19152250	C₂	semidirect
11. #19152245	C₂	semidirect
12. #19152241	C₂	semidirect
13. #19152152	C₂	semidirect
14. #19152130	C₂	semidirect
15. #19152130	C₂	semidirect
16. #19152126	C₂	semidirect
17. #19152107	C₂	semidirect
18. C₄×#13083575	C₂	semidirect
19. C₄×#13083574	C₂	semidirect
20. C₄×#13083574	C₂	semidirect
21. C₄×D₄×D₈₉	C₂	semidirect
22. #117×D₈₉	C₂	semidirect
23. #529×C₈₉	C₂	semidirect
29. #15668011	C₂²	semidirect
30. #15668010	C₂²	semidirect
31. #15668007	C₂²	semidirect
32. #15668005	C₂²	semidirect
33. #15668005	C₂²	semidirect
34. #15668005	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668003	C₂²	semidirect
37. #15668003	C₂²	semidirect
38. #15668002	C₂²	semidirect
39. #15668002	C₂²	semidirect
41. #15667999	C₂²	semidirect
42. #15667998	C₂²	semidirect
44. #15667997	C₂²	semidirect
48. #15667994	C₂²	semidirect
49. #15667994	C₂²	semidirect
51. #15667992	C₂²	semidirect
52. #15667992	C₂²	semidirect
54. #15667990	C₂²	semidirect
55. #15667990	C₂²	semidirect
56. #15667989	C₂²	semidirect
59. #15667985	C₂²	semidirect
60. #15667984	C₂²	semidirect
65. Q₈×Dic₈₉	C₂²	semidirect
66. C₄×Dic₁₇₈	C₂²	semidirect
67. C₄×Dic₁₇₈	C₂²	semidirect
68. C₄×Dic₁₇₈	C₂²	semidirect
69. C₄×Dic₁₇₈	C₂²	semidirect
70. C₄×Dic₁₇₈	C₂²	semidirect
75. C₄×D₃₅₆	C₂²	semidirect
79. #15667974	C₂²	semidirect
83. C₄×C₂²⋊D₈₉	C₂²	semidirect
84. C₄×C₂²⋊D₈₉	C₂²	semidirect
85. C₄×C₂²⋊D₈₉	C₂²	semidirect
86. C₄×C₂²⋊D₈₉	C₂²	semidirect
87. C₄×C₂²⋊D₈₉	C₂²	semidirect
89. #15667971	C₂²	semidirect
90. #15667971	C₂²	semidirect
91. #15667971	C₂²	semidirect
94. #15667970	C₂²	semidirect
95. #15667970	C₂²	semidirect
98. #15667969	C₂²	semidirect
99. #15667969	C₂²	semidirect
100. #15667968	C₂²	semidirect
101. #15667968	C₂²	semidirect
103. C₄⋊C₄×D₈₉	C₂²	semidirect
104. C₄⋊C₄×D₈₉	C₂²	semidirect
109. C₄²×D₈₉	C₂²	semidirect
110. C₄²×D₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
112. #126×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
115. #123×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
120. C₄×D₄×C₈₉	C₂²	semidirect
121. #117×C₈₉	C₂²	semidirect
122. C₂×C₄²×C₈₉	C₂²	semidirect
268. D₃₅₆	#41	semidirect
281. C₄×D₈₉	#41	semidirect
329. C₈₉	#3475	semidirect
346. #529	D₈₉	semidirect
365. #126	C₂×D₈₉	semidirect
370. #125	C₂×D₈₉	semidirect
382. #123	C₂×D₈₉	semidirect
391. C₂²⋊Q₈	C₂×D₈₉	semidirect
406. C₄×Q₈	C₂×D₈₉	semidirect
426. C₄×D₄	C₂×D₈₉	semidirect
440. #117	C₂×D₈₉	semidirect
451. C₂×C₄²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152317	2
#19152312	2
#19152304	2
#19152293	2
#19152286	2
#19152284	2
#19152282	2
#19152276	2
#19152273	2
#19152250	2
#19152245	2
#19152241	2
#19152152	2
#19152130	2
#19152126	2
#19152107	2
C₄×#13083575	2
C₄×#13083574	2
C₄×D₄×D₈₉	2
#117×D₈₉	2
#529×C₈₉	2
#3475	89