Subgroups — #26034207

Order 11392.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 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	#19152317	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152310	C₂	1	2	yes	maximal, complemented
4	#19152278	C₂	1	2	yes	maximal, complemented
5	#19152274	C₂	1	2	yes	maximal, complemented
6	Q₈×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152259	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152256	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152242	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152238	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152212	C₂	1	2	yes	maximal, complemented
14	#19152186	C₂	1	2	yes	maximal, complemented
15	#19152182	C₂	1	2	yes	maximal, complemented
16	#19152147	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152132	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152071	C₂	1	2	yes	maximal, complemented
22	C₄×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#124×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
26	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	—
29	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
30	#15668010	C₂²	1	1	yes	characteristic, complemented
31	#15668010	C₂²	1	2	yes	complemented
32	#15668008	C₂²	1	1	yes	characteristic
33	#15668006	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	complemented
35	#15668005	C₂²	1	2	yes	complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668004	C₂²	1	1	yes	characteristic, complemented
39	#15668001	C₂²	1	2	yes	complemented
40	#15668001	C₂²	1	1	yes	characteristic, complemented
41	#15668000	C₂²	1	1	yes	characteristic, complemented
42	#15667999	C₂²	1	1	yes	characteristic
43	#15667998	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	complemented
45	#15667998	C₂²	1	2	yes	complemented
46	#15667998	C₂²	1	2	yes	complemented
47	#15667996	C₂²	1	2	yes	complemented
48	#15667995	C₂²	1	2	yes	complemented
49	#15667994	C₂²	1	2	yes	complemented
50	#15667994	C₂²	1	2	yes	complemented
51	#15667994	C₂²	1	2	yes	complemented
52	#15667994	C₂²	1	2	yes	complemented
53	#15667993	C₂²	1	2	yes	complemented
54	#15667991	C₂²	1	1	yes	characteristic, complemented
55	#15667991	C₂²	1	2	yes	complemented
56	#15667989	C₂²	1	2	yes	complemented
57	#15667989	C₂²	1	2	yes	complemented
58	#15667988	C₂²	1	2	yes	complemented
59	#15667988	C₂²	1	2	yes	complemented
60	#15667988	C₂²	1	1	yes	characteristic, complemented
61	#15667988	C₂²	1	1	yes	characteristic, complemented
62	#15667986	C₂²	1	1	yes	characteristic
63	#15667986	C₂²	1	2	yes	complemented
64	#15667985	C₂²	1	2	yes	complemented
65	#15667985	C₂²	1	2	yes	complemented
66	#15667985	C₂²	1	2	yes	complemented
67	#15667985	C₂²	1	2	yes	complemented
68	#15667984	C₂²	1	2	yes	—
69	#15667984	C₂²	1	2	yes	complemented
70	#15667983	C₂²	1	1	yes	characteristic
71	#15667983	C₂²	1	1	yes	characteristic
72	#15667982	C₂²	1	2	yes	complemented
73	#15667981	C₂²	1	2	yes	—
74	#15667981	C₂²	1	2	yes	complemented
75	#15667980	C₂²	1	2	yes	—
76	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
77	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
84	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
85	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
93	#15667972	C₂²	1	2	yes	complemented
94	#15667972	C₂²	1	2	yes	complemented
95	#15667972	C₂²	1	2	yes	complemented
96	#15667972	C₂²	1	2	yes	complemented
97	#15667972	C₂²	1	2	yes	complemented
98	#15667972	C₂²	1	2	yes	complemented
99	#15667971	C₂²	1	1	yes	characteristic, complemented
100	#15667969	C₂²	1	2	yes	complemented
101	#15667969	C₂²	1	1	yes	characteristic, complemented
102	#15667969	C₂²	1	1	yes	characteristic, complemented
103	#15667968	C₂²	1	2	yes	complemented
104	#15667968	C₂²	1	2	yes	complemented
105	#15667968	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
110	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
114	#124×C₈₉	C₂²	1	1	yes	characteristic
115	#124×C₈₉	C₂²	1	1	yes	characteristic
116	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#124×C₈₉	C₂²	1	2	yes	complemented
118	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#124×C₈₉	C₂²	1	2	yes	complemented
120	C₂×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄×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	—	4	2	no	—
125	#13083574	—	2	4	no	—
126	#13083573	—	4	2	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	Q₈×D₈₉	—	4	2	no	—
131	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	—	2	8	no	—
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
144	D₄×D₈₉	—	4	2	no	—
145	C₂²×Dic₈₉	C₂³	1	2	yes	—
146	C₂²×Dic₈₉	C₂³	1	2	yes	—
147	C₂²×Dic₈₉	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	1	yes	characteristic
152	C₂×C₄×D₈₉	C₂³	1	2	yes	—
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂³	1	2	yes	—
155	C₂×C₄×D₈₉	C₂³	1	2	yes	—
156	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
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	C₄⋊Dic₈₉	C₂³	1	2	yes	—
163	#13083553	C₂³	1	1	yes	characteristic
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	2	yes	—
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
186	#13083551	C₂³	1	1	yes	characteristic
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	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
195	#13083551	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	2	yes	—
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	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂⁴×C₈₉	C₂³	1	2	yes	—
206	C₂×Q₈×C₈₉	—	4	2	no	—
207	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	—	4	2	no	—
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	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₄²×C₈₉	C₂³	1	1	yes	characteristic
229	C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₂³×C₈₉	—	2	4	no	—
231	C₂³×C₈₉	—	4	2	no	—
232	C₂³×C₈₉	—	4	2	no	—
233	C₂³×C₈₉	C₂⁴	1	2	yes	—
234	C₂³×C₈₉	C₂⁴	1	2	yes	—
235	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₈₉	—	2	4	no	—
237	C₂²×D₈₉	—	4	2	no	—
238	C₂²×D₈₉	—	4	2	no	—
239	C₂²×D₈₉	C₂⁴	1	2	yes	—
240	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₈₉	—	2	2	no	—
243	Q₈×C₈₉	—	2	2	no	—
244	Q₈×C₈₉	—	4	2	no	—
245	D₄×C₈₉	—	2	2	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	4	2	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	2	no	—
250	C₂×C₄×C₈₉	—	4	1	no	—
251	C₂×C₄×C₈₉	—	4	2	no	—
252	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₈₉	—	2	4	no	—
261	C₂²⋊D₈₉	—	2	2	no	—
262	C₂²⋊D₈₉	—	2	4	no	—
263	C₂²⋊D₈₉	—	2	4	no	—
264	C₂²⋊D₈₉	—	4	2	no	—
265	C₂²⋊D₈₉	—	4	2	no	—
266	C₂²⋊D₈₉	—	4	2	no	—
267	C₂²⋊D₈₉	—	4	2	no	—
268	C₂²⋊D₈₉	#41	1	4	yes	complemented
269	C₂×Dic₈₉	—	2	4	no	—
270	C₂×Dic₈₉	—	4	2	no	—
271	C₂×Dic₈₉	—	4	2	no	—
272	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₈₉	C₂⁴	1	2	yes	—
275	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₈₉	C₂⁴	1	2	yes	—
279	C₂×Dic₈₉	C₂⁴	1	2	yes	—
280	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
281	D₃₅₆	—	2	2	no	—
282	D₃₅₆	—	2	2	no	—
283	D₃₅₆	—	4	2	no	—
284	C₄×D₈₉	—	2	2	no	—
285	C₄×D₈₉	—	2	2	no	—
286	C₄×D₈₉	—	2	2	no	—
287	C₄×D₈₉	—	2	2	no	—
288	C₄×D₈₉	—	4	1	no	—
289	C₄×D₈₉	—	4	2	no	—
290	C₄×D₈₉	—	4	1	no	—
291	C₄×D₈₉	—	4	2	no	—
292	C₄×D₈₉	—	4	2	no	—
293	Dic₁₇₈	—	2	2	no	—
294	Dic₁₇₈	—	2	2	no	—
295	Dic₁₇₈	—	4	2	no	—
296	C₂²×C₈₉	—	2	1	no	—
297	C₂²×C₈₉	—	2	1	no	—
298	C₂²×C₈₉	—	2	2	no	—
299	C₂²×C₈₉	—	2	2	no	—
300	C₂²×C₈₉	—	2	2	no	—
301	C₂²×C₈₉	—	2	2	no	—
302	C₂²×C₈₉	—	2	2	no	—
303	C₂²×C₈₉	—	2	2	no	—
304	C₂²×C₈₉	—	8	4	no	—
305	C₂²×C₈₉	C₂×#41	1	2	yes	—
306	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
307	C₂×D₈₉	—	2	1	no	—
308	C₂×D₈₉	—	2	1	no	—
309	C₂×D₈₉	—	2	1	no	—
310	C₂×D₈₉	—	2	2	no	—
311	C₂×D₈₉	—	2	1	no	—
312	C₂×D₈₉	—	2	2	no	—
313	C₂×D₈₉	—	2	1	no	—
314	C₂×D₈₉	—	2	2	no	—
315	C₂×D₈₉	—	8	4	no	—
316	C₂×D₈₉	C₂×#41	1	2	yes	—
317	C₄×C₈₉	—	2	1	no	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	2	no	—
320	C₄×C₈₉	—	2	2	no	—
321	C₄×C₈₉	—	2	1	no	—
322	C₄×C₈₉	—	2	1	no	—
323	C₄×C₈₉	—	2	1	no	—
324	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
325	Dic₈₉	—	2	1	no	—
326	Dic₈₉	—	2	2	no	—
327	Dic₈₉	—	2	2	no	—
328	Dic₈₉	—	2	1	no	—
329	Dic₈₉	—	2	1	no	—
330	Dic₈₉	—	2	1	no	—
331	Dic₈₉	—	2	2	no	—
332	Dic₈₉	—	2	1	no	—
333	Dic₈₉	C₂×#41	1	2	yes	—
334	C₂×C₈₉	—	2	2	no	—
335	C₂×C₈₉	—	4	2	no	—
336	C₂×C₈₉	—	4	2	no	—
337	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
338	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₈₉	#585	1	1	yes	characteristic
340	D₈₉	—	2	2	no	—
341	D₈₉	—	4	1	no	—
342	D₈₉	—	4	2	no	—
343	#3514	—	89	1	no	maximal, Sylow
344	C₈₉	#3514	1	1	yes	characteristic, complemented, Sylow
345	#559	—	89	1	no	—
346	#556	—	89	1	no	—
347	#555	—	89	2	no	—
348	#551	—	89	2	no	—
349	#551	—	89	2	no	—
350	D₄×Q₈	—	89	1	no	—
351	#548	—	89	1	no	—
352	#548	—	89	1	no	—
353	#546	—	89	1	no	—
354	#546	—	89	1	no	—
355	#546	—	89	2	no	—
356	D₄²	—	89	1	no	—
357	#542	—	89	2	no	—
358	#538	—	89	2	no	—
359	#538	—	89	2	no	—
360	#532	—	89	1	no	—
361	#529	—	89	1	no	—
362	#529	—	89	1	no	—
363	#529	—	89	1	no	—
364	C₂×#124	—	89	1	no	—
365	C₂×#124	D₈₉	1	1	yes	characteristic, complemented
366	#518	—	89	2	no	—
367	C₄×#41	—	89	1	no	—
368	C₂×#41	—	89	1	no	—
369	C₂×#41	—	89	1	no	—
370	C₂×#41	—	89	1	no	—
371	C₂²×Q₈	—	89	1	no	—
372	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
373	C₂²×D₄	—	89	2	no	—
374	C₂²×D₄	—	89	1	no	—
375	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
376	C₄⋊Q₈	—	89	1	no	—
377	C₄⋊Q₈	—	89	2	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	#126	—	89	2	no	—
384	#125	—	89	1	no	—
385	#124	—	89	1	no	—
386	#124	—	89	2	no	—
387	#124	—	89	1	no	—
388	#124	—	89	2	no	—
389	#124	—	89	2	no	—
390	#124	—	89	2	no	—
391	#124	—	89	2	no	—
392	#124	—	89	1	no	—
393	#124	C₂×D₈₉	1	1	yes	characteristic
394	#124	C₂×D₈₉	1	1	yes	characteristic
395	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
396	#124	C₂×D₈₉	1	2	yes	complemented
397	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
398	#124	C₂×D₈₉	1	2	yes	complemented
399	#123	—	89	2	no	—
400	#123	—	89	2	no	—
401	#123	—	89	2	no	—
402	#123	—	89	2	no	—
403	#123	—	89	2	no	—
404	#123	—	89	2	no	—
405	#123	—	89	2	no	—
406	C₂²⋊Q₈	—	89	1	no	—
407	C₂²⋊Q₈	—	89	1	no	—
408	C₂²⋊Q₈	—	89	2	no	—
409	C₂²⋊Q₈	—	89	2	no	—
410	C₂²⋊Q₈	—	89	1	no	—
411	C₂²⋊Q₈	—	89	2	no	—
412	C₂²⋊Q₈	—	89	2	no	—
413	C₂²⋊Q₈	—	89	2	no	—
414	#121	—	89	1	no	—
415	#121	—	89	1	no	—
416	#121	—	89	2	no	—
417	#121	—	89	2	no	—
418	#121	—	89	1	no	—
419	#121	—	89	2	no	—
420	#121	—	89	2	no	—
421	#121	—	89	2	no	—
422	#121	—	89	2	no	—
423	#121	—	89	2	no	—
424	#120	—	89	2	no	—
425	#120	—	89	2	no	—
426	#120	—	89	2	no	—
427	#120	—	89	2	no	—
428	C₄×Q₈	—	89	1	no	—
429	C₄×Q₈	—	89	1	no	—
430	C₄×Q₈	—	89	1	no	—
431	C₄×Q₈	—	89	1	no	—
432	C₄×Q₈	—	89	1	no	—
433	C₄×D₄	—	89	1	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	1	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	2	no	—
447	C₄×D₄	—	89	2	no	—
448	C₄×D₄	—	89	1	no	—
449	C₄×D₄	—	89	1	no	—
450	C₄×D₄	—	89	1	no	—
451	#117	—	89	1	no	—
452	#117	—	89	2	no	—
453	#117	—	89	2	no	—
454	#117	—	89	2	no	—
455	#117	—	89	1	no	—
456	#117	—	89	1	no	—
457	#117	—	89	2	no	—
458	C₂×C₂²⋊C₄	—	89	2	no	—
459	C₂×C₂²⋊C₄	—	89	2	no	—
460	C₂×C₂²⋊C₄	—	89	2	no	—
461	C₂×C₂²⋊C₄	—	89	2	no	—
462	C₂×C₂²⋊C₄	C₂×D₈₉	1	2	yes	complemented
463	C₂×C₂²⋊C₄	C₂×D₈₉	1	2	yes	complemented
464	C₂×C₄²	—	89	1	no	—
465	C₂×C₄²	—	89	1	no	—
466	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic, complemented
467	C₂⁴	—	89	2	no	—
468	C₂⁴	C₂²×D₈₉	1	2	yes	—
469	#41	—	356	2	no	—
470	#41	—	356	2	no	—
471	#41	—	178	4	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	89	2	no	—
474	C₂×Q₈	—	89	1	no	—
475	C₂×Q₈	—	89	1	no	—
476	C₂×Q₈	—	356	2	no	—
477	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
478	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
480	C₂×D₄	—	4	2	no	—
481	C₂×D₄	—	89	1	no	—
482	C₂×D₄	—	89	2	no	—
483	C₂×D₄	—	89	2	no	—
484	C₂×D₄	—	89	2	no	—
485	C₂×D₄	—	89	2	no	—
486	C₂×D₄	—	89	1	no	—
487	C₂×D₄	—	89	2	no	—
488	C₂×D₄	—	89	2	no	—
489	C₂×D₄	—	89	2	no	—
490	C₂×D₄	—	89	2	no	—
491	C₂×D₄	—	89	1	no	—
492	C₂×D₄	—	89	1	no	—
493	C₂×D₄	—	356	2	no	—
494	C₂×D₄	—	178	8	no	—
495	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₈₉	1	2	yes	—
498	C₂²×C₄	—	89	2	no	—
499	C₂²×C₄	—	89	2	no	—
500	C₂²×C₄	—	89	2	no	—
501	C₂²×C₄	—	89	1	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	1	no	—
510	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
514	C₄⋊C₄	—	89	1	no	—
515	C₄⋊C₄	—	89	2	no	—
516	C₄⋊C₄	—	89	2	no	—
517	C₄⋊C₄	—	89	2	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	1	no	—
520	C₄⋊C₄	—	89	1	no	—
521	C₄⋊C₄	—	89	1	no	—
522	C₄⋊C₄	—	89	1	no	—
523	C₄⋊C₄	—	89	1	no	—
524	C₄⋊C₄	—	89	2	no	—
525	C₄⋊C₄	—	89	2	no	—
526	C₄⋊C₄	—	89	1	no	—
527	C₄⋊C₄	—	89	1	no	—
528	C₄⋊C₄	—	89	2	no	—
529	C₄⋊C₄	—	89	2	no	—
530	C₄⋊C₄	—	89	2	no	—
531	C₄⋊C₄	—	89	2	no	—
532	C₂²⋊C₄	—	89	1	no	—
533	C₂²⋊C₄	—	89	2	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	2	no	—
536	C₂²⋊C₄	—	89	2	no	—
537	C₂²⋊C₄	—	89	1	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	2	no	—
545	C₂²⋊C₄	—	89	2	no	—
546	C₂²⋊C₄	—	89	2	no	—
547	C₂²⋊C₄	—	89	1	no	—
548	C₂²⋊C₄	—	89	1	no	—
549	C₂²⋊C₄	—	89	1	no	—
550	C₂²⋊C₄	—	89	2	no	—
551	C₂²⋊C₄	—	89	2	no	—
552	C₂²⋊C₄	—	89	2	no	—
553	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
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	2	yes	—
561	C₄²	—	89	1	no	—
562	C₄²	—	89	1	no	—
563	C₄²	—	89	1	no	—
564	C₄²	—	89	1	no	—
565	C₄²	—	89	1	no	—
566	C₄²	—	89	1	no	—
567	C₄²	—	89	2	no	—
568	C₄²	—	89	2	no	—
569	C₄²	—	89	2	no	—
570	C₄²	C₂²×D₈₉	1	1	yes	characteristic
571	C₄²	C₂²×D₈₉	1	1	yes	characteristic
572	C₄²	C₂²×D₈₉	1	1	yes	characteristic
573	C₄²	C₂²×D₈₉	1	1	yes	characteristic
574	C₂³	—	2	4	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	4	2	no	—
577	C₂³	—	89	1	no	—
578	C₂³	—	89	2	no	—
579	C₂³	—	89	1	no	—
580	C₂³	—	356	2	no	—
581	C₂³	—	356	2	no	—
582	C₂³	—	178	4	no	—
583	C₂³	C₂³×D₈₉	1	2	yes	—
584	C₂³	C₂³×D₈₉	1	2	yes	—
585	C₂³	C₂³×D₈₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	356	2	no	—
590	Q₈	—	178	2	no	—
591	Q₈	—	178	2	no	—
592	D₄	—	2	2	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	—	356	2	no	—
599	D₄	—	356	2	no	—
600	D₄	—	356	2	no	—
601	D₄	—	178	2	no	—
602	D₄	—	178	4	no	—
603	D₄	—	178	4	no	—
604	D₄	—	178	4	no	—
605	D₄	—	178	2	no	—
606	D₄	—	178	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	89	1	no	—
612	C₂×C₄	—	89	1	no	—
613	C₂×C₄	—	89	1	no	—
614	C₂×C₄	—	89	2	no	—
615	C₂×C₄	—	89	1	no	—
616	C₂×C₄	—	89	1	no	—
617	C₂×C₄	—	89	1	no	—
618	C₂×C₄	—	89	2	no	—
619	C₂×C₄	—	89	2	no	—
620	C₂×C₄	—	356	1	no	—
621	C₂×C₄	—	356	2	no	—
622	C₂×C₄	—	356	1	no	—
623	C₂×C₄	—	356	2	no	—
624	C₂×C₄	—	356	2	no	—
625	C₂×C₄	—	356	2	no	—
626	C₂×C₄	—	356	2	no	—
627	C₂×C₄	—	178	2	no	—
628	C₂×C₄	—	178	2	no	—
629	C₂×C₄	—	178	4	no	—
630	C₂×C₄	—	178	2	no	—
631	C₂×C₄	—	178	2	no	—
632	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₈₉	1	2	yes	—
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	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	8	4	no	—
649	C₂²	—	89	2	no	—
650	C₂²	—	178	1	no	—
651	C₂²	—	178	2	no	—
652	C₂²	—	178	2	no	—
653	C₂²	—	178	1	no	—
654	C₂²	—	178	1	no	—
655	C₂²	—	178	2	no	—
656	C₂²	—	178	1	no	—
657	C₂²	—	178	1	no	—
658	C₂²	—	712	4	no	—
659	C₂²	#41×D₈₉	1	2	yes	—
660	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	89	2	no	—
669	C₄	—	178	2	no	—
670	C₄	—	178	1	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	#15668057	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	4	2	no	—
681	C₂	—	356	1	no	—
682	C₂	—	356	2	no	—
683	C₂	—	178	2	no	—
684	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
685	C₂	C₂×#15668057	1	1	yes	characteristic
686	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	C₂×#124×C₈₉	C₂
hypercenter	C₂×#124	D₈₉
hypocenter	C₈₉	#3514
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #19152330	C₂	semidirect
2. #19152317	C₂	semidirect
3. #19152310	C₂	semidirect
4. #19152278	C₂	semidirect
5. #19152274	C₂	semidirect
6. Q₈×C₂²⋊D₈₉	C₂	semidirect
7. #19152259	C₂	semidirect
8. #19152256	C₂	semidirect
9. #19152242	C₂	semidirect
10. #19152241	C₂	semidirect
11. #19152238	C₂	semidirect
12. D₄×C₂²⋊D₈₉	C₂	semidirect
13. #19152212	C₂	semidirect
14. #19152186	C₂	semidirect
15. #19152182	C₂	semidirect
16. #19152147	C₂	semidirect
17. #19152132	C₂	semidirect
18. #19152127	C₂	semidirect
19. #19152127	C₂	semidirect
20. #124×D₈₉	C₂	semidirect
21. #19152071	C₂	semidirect
22. C₄×#13083574	C₂	semidirect
23. C₂×#124×C₈₉	C₂	semidirect
24. C₂×#13083575	C₂²	semidirect
26. C₂×#13083573	C₂²	semidirect
27. C₂×Q₈×D₈₉	C₂²	semidirect
30. #15668010	C₂²	semidirect
31. #15668010	C₂²	semidirect
33. #15668006	C₂²	semidirect
34. #15668005	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668004	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15668001	C₂²	semidirect
41. #15668000	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667998	C₂²	semidirect
45. #15667998	C₂²	semidirect
46. #15667998	C₂²	semidirect
47. #15667996	C₂²	semidirect
48. #15667995	C₂²	semidirect
49. #15667994	C₂²	semidirect
50. #15667994	C₂²	semidirect
51. #15667994	C₂²	semidirect
52. #15667994	C₂²	semidirect
53. #15667993	C₂²	semidirect
54. #15667991	C₂²	semidirect
55. #15667991	C₂²	semidirect
56. #15667989	C₂²	semidirect
57. #15667989	C₂²	semidirect
58. #15667988	C₂²	semidirect
59. #15667988	C₂²	semidirect
60. #15667988	C₂²	semidirect
61. #15667988	C₂²	semidirect
63. #15667986	C₂²	semidirect
64. #15667985	C₂²	semidirect
65. #15667985	C₂²	semidirect
66. #15667985	C₂²	semidirect
67. #15667985	C₂²	semidirect
69. #15667984	C₂²	semidirect
72. #15667982	C₂²	semidirect
74. #15667981	C₂²	semidirect
76. Q₈×Dic₈₉	C₂²	semidirect
77. Q₈×Dic₈₉	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. C₄×Dic₁₇₈	C₂²	semidirect
80. C₄×Dic₁₇₈	C₂²	semidirect
81. C₄×D₃₅₆	C₂²	semidirect
82. C₄×D₃₅₆	C₂²	semidirect
83. C₄×D₃₅₆	C₂²	semidirect
85. D₄×Dic₈₉	C₂²	semidirect
89. C₄×C₂²⋊D₈₉	C₂²	semidirect
90. C₄×C₂²⋊D₈₉	C₂²	semidirect
91. C₄×C₂²⋊D₈₉	C₂²	semidirect
92. C₄×C₂²⋊D₈₉	C₂²	semidirect
93. #15667972	C₂²	semidirect
94. #15667972	C₂²	semidirect
95. #15667972	C₂²	semidirect
96. #15667972	C₂²	semidirect
97. #15667972	C₂²	semidirect
98. #15667972	C₂²	semidirect
99. #15667971	C₂²	semidirect
100. #15667969	C₂²	semidirect
101. #15667969	C₂²	semidirect
102. #15667969	C₂²	semidirect
103. #15667968	C₂²	semidirect
104. #15667968	C₂²	semidirect
105. #15667968	C₂²	semidirect
106. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
107. C₂²⋊C₄×D₈₉	C₂²	semidirect
108. C₂²⋊C₄×D₈₉	C₂²	semidirect
109. C₂²⋊C₄×D₈₉	C₂²	semidirect
110. C₄²×D₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
112. C₂²×Q₈×C₈₉	C₂²	semidirect
116. #124×C₈₉	C₂²	semidirect
117. #124×C₈₉	C₂²	semidirect
118. #124×C₈₉	C₂²	semidirect
119. #124×C₈₉	C₂²	semidirect
120. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
121. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
122. C₂×C₄²×C₈₉	C₂²	semidirect
268. C₂²⋊D₈₉	#41	semidirect
344. C₈₉	#3514	semidirect
365. C₂×#124	D₈₉	semidirect
372. C₂²×Q₈	C₂×D₈₉	semidirect
395. #124	C₂×D₈₉	semidirect
396. #124	C₂×D₈₉	semidirect
397. #124	C₂×D₈₉	semidirect
398. #124	C₂×D₈₉	semidirect
462. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
463. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
466. 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
#19152330	2
#19152317	2
#19152310	2
#19152278	2
#19152274	2
Q₈×C₂²⋊D₈₉	2
#19152259	2
#19152256	2
#19152242	2
#19152241	2
#19152238	2
D₄×C₂²⋊D₈₉	2
#19152212	2
#19152186	2
#19152182	2
#19152147	2
#19152132	2
#19152127	2
#124×D₈₉	2
#19152071	2
C₄×#13083574	2
C₂×#124×C₈₉	2
#3514	89