Subgroups — #26034535

Order 11392.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152351	C₂	1	2	yes	maximal, complemented
2	#19152343	C₂	1	2	yes	maximal, complemented
3	#19152319	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152306	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152303	C₂	1	2	yes	maximal, complemented
6	#19152298	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152293	C₂	1	2	yes	maximal, complemented
8	#19152288	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152255	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152255	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152216	C₂	1	2	yes	maximal, complemented
13	#19152213	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152209	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152195	C₂	1	2	yes	maximal, complemented
16	#19152184	C₂	1	2	yes	maximal, complemented
17	#19152180	C₂	1	2	yes	maximal, complemented
18	#19152176	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152105	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
28	#15668011	C₂²	1	2	yes	complemented
29	#15668011	C₂²	1	1	yes	characteristic, complemented
30	#15668011	C₂²	1	2	yes	complemented
31	#15668007	C₂²	1	2	yes	—
32	#15668007	C₂²	1	2	yes	—
33	#15668007	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	—
35	#15668005	C₂²	1	2	yes	—
36	#15668005	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668004	C₂²	1	1	yes	characteristic, complemented
39	#15668002	C₂²	1	2	yes	complemented
40	#15668002	C₂²	1	2	yes	complemented
41	#15668002	C₂²	1	2	yes	complemented
42	#15668002	C₂²	1	2	yes	complemented
43	#15667999	C₂²	1	2	yes	—
44	#15667999	C₂²	1	1	yes	characteristic, complemented
45	#15667999	C₂²	1	2	yes	complemented
46	#15667998	C₂²	1	2	yes	—
47	#15667998	C₂²	1	2	yes	—
48	#15667998	C₂²	1	2	yes	—
49	#15667997	C₂²	1	2	yes	—
50	#15667997	C₂²	1	1	yes	characteristic
51	#15667995	C₂²	1	2	yes	—
52	#15667995	C₂²	1	2	yes	complemented
53	#15667994	C₂²	1	1	yes	characteristic
54	#15667994	C₂²	1	2	yes	complemented
55	#15667993	C₂²	1	2	yes	—
56	#15667993	C₂²	1	2	yes	—
57	#15667992	C₂²	1	1	yes	characteristic
58	#15667992	C₂²	1	2	yes	—
59	#15667991	C₂²	1	1	yes	characteristic
60	#15667991	C₂²	1	1	yes	characteristic, complemented
61	#15667991	C₂²	1	2	yes	complemented
62	#15667991	C₂²	1	2	yes	complemented
63	#15667991	C₂²	1	2	yes	complemented
64	#15667991	C₂²	1	2	yes	complemented
65	#15667990	C₂²	1	2	yes	—
66	#15667990	C₂²	1	2	yes	—
67	#15667990	C₂²	1	1	yes	characteristic
68	#15667990	C₂²	1	2	yes	complemented
69	#15667989	C₂²	1	2	yes	—
70	#15667989	C₂²	1	1	yes	characteristic
71	#15667989	C₂²	1	2	yes	complemented
72	#15667988	C₂²	1	1	yes	characteristic
73	#15667988	C₂²	1	1	yes	characteristic
74	#15667988	C₂²	1	1	yes	characteristic
75	#15667988	C₂²	1	1	yes	characteristic, complemented
76	#15667986	C₂²	1	2	yes	—
77	#15667985	C₂²	1	2	yes	—
78	#15667985	C₂²	1	1	yes	characteristic
79	#15667984	C₂²	1	2	yes	—
80	#15667984	C₂²	1	1	yes	characteristic
81	#15667984	C₂²	1	2	yes	complemented
82	#15667983	C₂²	1	1	yes	characteristic
83	#15667983	C₂²	1	2	yes	—
84	#15667983	C₂²	1	2	yes	—
85	#15667983	C₂²	1	1	yes	characteristic
86	#15667983	C₂²	1	1	yes	characteristic, complemented
87	#15667982	C₂²	1	1	yes	characteristic
88	#15667980	C₂²	1	1	yes	characteristic
89	#15667980	C₂²	1	2	yes	—
90	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
91	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
93	#15667977	C₂²	1	2	yes	complemented
94	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
95	#15667974	C₂²	1	2	yes	—
96	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
97	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
98	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
103	#15667972	C₂²	1	2	yes	—
104	#15667971	C₂²	1	1	yes	characteristic
105	#15667970	C₂²	1	1	yes	characteristic, complemented
106	#15667969	C₂²	1	1	yes	characteristic
107	#15667968	C₂²	1	2	yes	complemented
108	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
112	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
113	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₈₉	C₂²	1	2	yes	—
116	#123×C₈₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
118	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₈₉	C₂²	1	2	yes	—
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
123	C₂³×D₈₉	C₂³	1	1	yes	characteristic
124	#13083574	—	4	2	no	—
125	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
126	C₂×Dic₁₇₈	C₂³	1	2	yes	—
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	Q₈×D₈₉	—	4	2	no	—
131	Q₈×D₈₉	—	4	2	no	—
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
141	C₂²×Dic₈₉	C₂³	1	2	yes	—
142	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₉	—	4	2	no	—
144	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
152	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
153	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₉	C₂³	1	2	yes	—
156	C₄⋊Dic₈₉	C₂³	1	2	yes	—
157	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₉	C₂³	1	2	yes	—
159	C₄⋊Dic₈₉	C₂³	1	2	yes	—
160	#13083553	C₂³	1	2	yes	—
161	#13083553	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	1	yes	characteristic
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	2	yes	—
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	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
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	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	#13083551	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
191	#13083551	C₂³	1	1	yes	characteristic
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	1	yes	characteristic
195	#13083551	C₂³	1	2	yes	—
196	#13083551	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	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	#41×C₈₉	—	4	2	no	—
204	#41×C₈₉	—	4	2	no	—
205	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₈₉	C₂³	1	2	yes	—
209	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₈₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
227	C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₈₉	C₂⁴	1	2	yes	—
231	C₂²×D₈₉	—	2	2	no	—
232	C₂²×D₈₉	—	4	1	no	—
233	C₂²×D₈₉	—	4	1	no	—
234	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
237	Q₈×C₈₉	—	2	2	no	—
238	Q₈×C₈₉	—	2	2	no	—
239	D₄×C₈₉	—	2	2	no	—
240	D₄×C₈₉	—	4	1	no	—
241	D₄×C₈₉	—	4	2	no	—
242	D₄×C₈₉	—	4	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	4	2	no	—
246	C₂×C₄×C₈₉	—	4	2	no	—
247	C₂×C₄×C₈₉	—	4	2	no	—
248	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
251	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₈₉	—	2	2	no	—
257	C₂²⋊D₈₉	—	2	4	no	—
258	C₂²⋊D₈₉	—	4	1	no	—
259	C₂²⋊D₈₉	—	4	2	no	—
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂²⋊D₈₉	—	4	1	no	—
262	C₂²⋊D₈₉	—	4	1	no	—
263	C₂×Dic₈₉	—	4	1	no	—
264	C₂×Dic₈₉	—	4	2	no	—
265	C₂×Dic₈₉	C₂⁴	1	2	yes	—
266	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₈₉	C₂⁴	1	2	yes	—
269	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₈₉	C₂⁴	1	2	yes	—
271	C₂×Dic₈₉	C₂⁴	1	2	yes	—
272	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	D₃₅₆	—	2	2	no	—
275	D₃₅₆	—	4	1	no	—
276	C₄×D₈₉	—	2	2	no	—
277	C₄×D₈₉	—	2	2	no	—
278	C₄×D₈₉	—	2	2	no	—
279	C₄×D₈₉	—	4	1	no	—
280	C₄×D₈₉	—	4	1	no	—
281	C₄×D₈₉	—	4	2	no	—
282	C₄×D₈₉	—	4	2	no	—
283	C₄×D₈₉	—	4	2	no	—
284	Dic₁₇₈	—	2	2	no	—
285	Dic₁₇₈	—	4	2	no	—
286	Dic₁₇₈	—	4	2	no	—
287	Dic₁₇₈	—	4	2	no	—
288	Dic₁₇₈	—	4	1	no	—
289	C₂²×C₈₉	—	2	1	no	—
290	C₂²×C₈₉	—	2	1	no	—
291	C₂²×C₈₉	—	2	2	no	—
292	C₂²×C₈₉	—	2	1	no	—
293	C₂²×C₈₉	—	2	2	no	—
294	C₂²×C₈₉	—	2	1	no	—
295	C₂²×C₈₉	—	2	1	no	—
296	C₂²×C₈₉	—	2	2	no	—
297	C₂²×C₈₉	—	2	1	no	—
298	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
299	C₂×D₈₉	—	2	1	no	—
300	C₂×D₈₉	—	2	1	no	—
301	C₂×D₈₉	—	2	1	no	—
302	C₂×D₈₉	—	2	1	no	—
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	1	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	1	no	—
307	C₂×D₈₉	—	4	4	no	—
308	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	—
309	C₄×C₈₉	—	2	2	no	—
310	C₄×C₈₉	—	2	2	no	—
311	C₄×C₈₉	—	2	1	no	—
312	C₄×C₈₉	—	2	1	no	—
313	C₄×C₈₉	—	2	1	no	—
314	C₄×C₈₉	—	2	2	no	—
315	C₄×C₈₉	—	2	1	no	—
316	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
317	Dic₈₉	—	2	2	no	—
318	Dic₈₉	—	2	1	no	—
319	Dic₈₉	—	2	1	no	—
320	Dic₈₉	—	2	1	no	—
321	Dic₈₉	—	2	2	no	—
322	Dic₈₉	—	2	1	no	—
323	Dic₈₉	—	2	1	no	—
324	Dic₈₉	—	2	2	no	—
325	Dic₈₉	—	2	2	no	—
326	C₂×C₈₉	—	4	1	no	—
327	C₂×C₈₉	—	4	1	no	—
328	C₂×C₈₉	—	4	2	no	—
329	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
331	C₂×C₈₉	#585	1	1	yes	characteristic
332	D₈₉	—	2	2	no	—
333	D₈₉	—	4	1	no	—
334	D₈₉	—	4	1	no	—
335	#3541	—	89	1	no	maximal, Sylow
336	C₈₉	#3541	1	1	yes	characteristic, complemented, Sylow
337	#563	—	89	2	no	—
338	#562	—	89	2	no	—
339	#556	—	89	1	no	—
340	#554	—	89	1	no	—
341	#554	—	89	2	no	—
342	#553	—	89	2	no	—
343	#553	—	89	1	no	—
344	#552	—	89	1	no	—
345	D₄×Q₈	—	89	1	no	—
346	#548	—	89	1	no	—
347	#548	—	89	1	no	—
348	#547	D₈₉	1	1	yes	characteristic, complemented
349	#542	—	89	2	no	—
350	#542	—	89	1	no	—
351	#541	—	89	1	no	—
352	#539	—	89	2	no	—
353	#538	—	89	2	no	—
354	#538	—	89	2	no	—
355	#537	—	89	1	no	—
356	#536	—	89	1	no	—
357	#525	—	89	1	no	—
358	#525	—	89	1	no	—
359	C₂×C₂²⋊Q₈	—	89	1	no	—
360	C₂×#41	—	89	1	no	—
361	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
362	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
363	C₂²×Q₈	—	89	1	no	—
364	C₂²×Q₈	—	89	1	no	—
365	C₂³×C₄	—	89	1	no	—
366	C₄⋊Q₈	—	89	2	no	—
367	C₄⋊Q₈	—	89	2	no	—
368	C₄⋊Q₈	—	89	1	no	—
369	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
370	#126	—	89	2	no	—
371	#126	—	89	2	no	—
372	#126	—	89	2	no	—
373	#126	—	89	2	no	—
374	#126	—	89	2	no	—
375	#126	—	89	2	no	—
376	#126	—	89	2	no	—
377	#125	—	89	2	no	—
378	#125	—	89	2	no	—
379	#125	—	89	2	no	—
380	#125	—	89	2	no	—
381	#125	—	89	1	no	—
382	#124	—	89	2	no	—
383	#124	—	89	1	no	—
384	#124	—	89	2	no	—
385	#124	—	89	2	no	—
386	#124	—	89	2	no	—
387	#124	—	89	2	no	—
388	#123	—	89	2	no	—
389	#123	—	89	2	no	—
390	#123	—	89	2	no	—
391	#123	—	89	2	no	—
392	#123	—	89	1	no	—
393	#123	—	89	2	no	—
394	#123	—	89	1	no	—
395	#123	—	89	2	no	—
396	#123	C₂×D₈₉	1	2	yes	—
397	#123	C₂×D₈₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	89	1	no	—
399	C₂²⋊Q₈	—	89	1	no	—
400	C₂²⋊Q₈	—	89	1	no	—
401	C₂²⋊Q₈	—	89	1	no	—
402	C₂²⋊Q₈	—	89	1	no	—
403	C₂²⋊Q₈	—	89	1	no	—
404	C₂²⋊Q₈	—	89	2	no	—
405	C₂²⋊Q₈	—	89	2	no	—
406	C₂²⋊Q₈	—	89	2	no	—
407	C₂²⋊Q₈	—	89	2	no	—
408	C₂²⋊Q₈	—	89	2	no	—
409	C₂²⋊Q₈	—	89	1	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	C₂²⋊Q₈	—	89	2	no	—
415	C₂²⋊Q₈	—	89	1	no	—
416	C₂²⋊Q₈	—	89	2	no	—
417	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
418	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
419	#121	—	89	1	no	—
420	#121	—	89	1	no	—
421	#121	—	89	1	no	—
422	#121	—	89	2	no	—
423	#121	—	89	2	no	—
424	#121	—	89	1	no	—
425	#121	—	89	2	no	—
426	#121	—	89	2	no	—
427	#121	—	89	2	no	—
428	#121	—	89	1	no	—
429	#121	—	89	2	no	—
430	#121	C₂×D₈₉	1	2	yes	—
431	#120	—	89	2	no	—
432	#120	—	89	1	no	—
433	#120	—	89	1	no	—
434	C₄×Q₈	—	89	1	no	—
435	C₄×Q₈	—	89	1	no	—
436	C₄×Q₈	—	89	2	no	—
437	C₄×Q₈	—	89	1	no	—
438	C₄×D₄	—	89	2	no	—
439	C₄×D₄	—	89	1	no	—
440	C₄×D₄	—	89	1	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	1	no	—
448	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
450	#117	—	89	1	no	—
451	#117	—	89	1	no	—
452	#117	—	89	2	no	—
453	#117	—	89	1	no	—
454	C₂×C₄⋊C₄	—	89	1	no	—
455	C₂×C₄⋊C₄	—	89	1	no	—
456	C₂×C₄⋊C₄	—	89	2	no	—
457	C₂×C₄⋊C₄	C₂×D₈₉	1	2	yes	complemented
458	C₂×C₂²⋊C₄	—	89	2	no	—
459	C₂⁴	—	89	1	no	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	356	2	no	—
463	C₂×Q₈	—	89	2	no	—
464	C₂×Q₈	—	89	2	no	—
465	C₂×Q₈	—	89	1	no	—
466	C₂×Q₈	—	89	2	no	—
467	C₂×Q₈	—	89	1	no	—
468	C₂×Q₈	—	356	2	no	—
469	C₂×Q₈	—	356	2	no	—
470	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
472	C₂×D₄	—	89	2	no	—
473	C₂×D₄	—	89	1	no	—
474	C₂×D₄	—	89	2	no	—
475	C₂×D₄	—	89	1	no	—
476	C₂×D₄	—	89	1	no	—
477	C₂×D₄	—	89	2	no	—
478	C₂×D₄	—	89	1	no	—
479	C₂×D₄	—	89	1	no	—
480	C₂×D₄	—	89	1	no	—
481	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₈₉	1	2	yes	—
484	C₂×D₄	C₂²×D₈₉	1	2	yes	—
485	C₂²×C₄	—	89	2	no	—
486	C₂²×C₄	—	89	1	no	—
487	C₂²×C₄	—	89	2	no	—
488	C₂²×C₄	—	89	2	no	—
489	C₂²×C₄	—	89	1	no	—
490	C₂²×C₄	—	89	2	no	—
491	C₂²×C₄	—	89	1	no	—
492	C₂²×C₄	—	89	1	no	—
493	C₂²×C₄	—	89	1	no	—
494	C₂²×C₄	—	89	1	no	—
495	C₂²×C₄	—	356	2	no	—
496	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
499	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
500	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
501	C₄⋊C₄	—	89	1	no	—
502	C₄⋊C₄	—	89	2	no	—
503	C₄⋊C₄	—	89	1	no	—
504	C₄⋊C₄	—	89	2	no	—
505	C₄⋊C₄	—	89	2	no	—
506	C₄⋊C₄	—	89	2	no	—
507	C₄⋊C₄	—	89	2	no	—
508	C₄⋊C₄	—	89	1	no	—
509	C₄⋊C₄	—	89	1	no	—
510	C₄⋊C₄	—	89	1	no	—
511	C₄⋊C₄	—	89	2	no	—
512	C₄⋊C₄	—	89	1	no	—
513	C₄⋊C₄	—	89	1	no	—
514	C₄⋊C₄	—	89	2	no	—
515	C₄⋊C₄	—	89	2	no	—
516	C₄⋊C₄	—	89	2	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	2	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	C₂²×D₈₉	1	2	yes	—
525	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
529	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
530	C₂²⋊C₄	—	89	2	no	—
531	C₂²⋊C₄	—	89	2	no	—
532	C₂²⋊C₄	—	89	2	no	—
533	C₂²⋊C₄	—	89	1	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	2	no	—
536	C₂²⋊C₄	—	89	1	no	—
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	2	no	—
542	C₂²⋊C₄	—	89	1	no	—
543	C₂²⋊C₄	—	89	1	no	—
544	C₂²⋊C₄	—	89	2	no	—
545	C₂²⋊C₄	—	89	1	no	—
546	C₂²⋊C₄	—	89	2	no	—
547	C₂²⋊C₄	—	89	1	no	—
548	C₂²⋊C₄	—	89	1	no	—
549	C₂²⋊C₄	—	89	2	no	—
550	C₂²⋊C₄	—	89	2	no	—
551	C₂²⋊C₄	—	89	1	no	—
552	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
557	C₄²	—	89	2	no	—
558	C₄²	—	89	1	no	—
559	C₄²	—	89	2	no	—
560	C₄²	—	89	2	no	—
561	C₄²	—	89	2	no	—
562	C₄²	—	89	2	no	—
563	C₄²	C₂²×D₈₉	1	1	yes	characteristic
564	C₂³	—	89	1	no	—
565	C₂³	—	89	1	no	—
566	C₂³	—	89	1	no	—
567	C₂³	—	356	1	no	—
568	C₂³	—	356	1	no	—
569	C₂³	—	178	2	no	—
570	C₂³	C₂³×D₈₉	1	1	yes	characteristic
571	C₂³	C₂³×D₈₉	1	2	yes	—
572	C₂³	C₂³×D₈₉	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	356	2	no	—
576	Q₈	—	356	2	no	—
577	Q₈	—	356	2	no	—
578	Q₈	—	356	1	no	—
579	Q₈	—	178	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	356	1	no	—
585	D₄	—	356	2	no	—
586	D₄	—	356	2	no	—
587	D₄	—	356	1	no	—
588	D₄	—	356	1	no	—
589	D₄	—	356	1	no	—
590	D₄	—	178	2	no	—
591	D₄	—	178	4	no	—
592	D₄	—	178	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	89	2	no	—
599	C₂×C₄	—	89	1	no	—
600	C₂×C₄	—	89	1	no	—
601	C₂×C₄	—	89	2	no	—
602	C₂×C₄	—	89	1	no	—
603	C₂×C₄	—	89	2	no	—
604	C₂×C₄	—	89	2	no	—
605	C₂×C₄	—	89	1	no	—
606	C₂×C₄	—	89	1	no	—
607	C₂×C₄	—	356	2	no	—
608	C₂×C₄	—	356	1	no	—
609	C₂×C₄	—	356	1	no	—
610	C₂×C₄	—	356	2	no	—
611	C₂×C₄	—	356	2	no	—
612	C₂×C₄	—	356	2	no	—
613	C₂×C₄	—	356	1	no	—
614	C₂×C₄	—	178	2	no	—
615	C₂×C₄	—	178	2	no	—
616	C₂×C₄	—	178	2	no	—
617	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
618	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
619	C₂×C₄	C₂³×D₈₉	1	2	yes	—
620	C₂×C₄	C₂³×D₈₉	1	2	yes	—
621	C₂×C₄	C₂³×D₈₉	1	2	yes	—
622	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	89	2	no	—
635	C₂²	—	356	4	no	—
636	C₂²	—	178	1	no	—
637	C₂²	—	178	1	no	—
638	C₂²	—	178	1	no	—
639	C₂²	—	178	1	no	—
640	C₂²	—	178	1	no	—
641	C₂²	—	178	1	no	—
642	C₂²	—	178	1	no	—
643	C₂²	—	178	1	no	—
644	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	178	1	no	—
653	C₄	—	178	1	no	—
654	C₄	—	178	2	no	—
655	C₄	—	178	1	no	—
656	C₄	—	178	2	no	—
657	C₄	—	178	1	no	—
658	C₄	—	178	2	no	—
659	C₄	—	178	2	no	—
660	C₄	—	178	1	no	—
661	C₄	#15668057	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	2	no	—
664	C₂	—	4	1	no	—
665	C₂	—	356	1	no	—
666	C₂	—	356	1	no	—
667	C₂	—	178	2	no	—
668	C₂	C₂×#15668057	1	1	yes	characteristic
669	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
670	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#547×C₈₉	C₂
hypercenter	#547	D₈₉
hypocenter	C₈₉	#3541
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. #19152351	C₂	semidirect
2. #19152343	C₂	semidirect
3. #19152319	C₂	semidirect
4. #19152306	C₂	semidirect
5. #19152303	C₂	semidirect
6. #19152298	C₂	semidirect
7. #19152293	C₂	semidirect
8. #19152288	C₂	semidirect
9. #19152263	C₂	semidirect
10. #19152255	C₂	semidirect
11. #19152255	C₂	semidirect
12. #19152216	C₂	semidirect
13. #19152213	C₂	semidirect
14. #19152209	C₂	semidirect
15. #19152195	C₂	semidirect
16. #19152184	C₂	semidirect
17. #19152180	C₂	semidirect
18. #19152176	C₂	semidirect
19. #19152171	C₂	semidirect
20. #19152107	C₂	semidirect
21. #19152105	C₂	semidirect
22. C₂²⋊Q₈×D₈₉	C₂	semidirect
23. #547×C₈₉	C₂	semidirect
26. C₂×Q₈×D₈₉	C₂²	semidirect
28. #15668011	C₂²	semidirect
29. #15668011	C₂²	semidirect
30. #15668011	C₂²	semidirect
33. #15668007	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668004	C₂²	semidirect
39. #15668002	C₂²	semidirect
40. #15668002	C₂²	semidirect
41. #15668002	C₂²	semidirect
42. #15668002	C₂²	semidirect
44. #15667999	C₂²	semidirect
45. #15667999	C₂²	semidirect
52. #15667995	C₂²	semidirect
54. #15667994	C₂²	semidirect
60. #15667991	C₂²	semidirect
61. #15667991	C₂²	semidirect
62. #15667991	C₂²	semidirect
63. #15667991	C₂²	semidirect
64. #15667991	C₂²	semidirect
68. #15667990	C₂²	semidirect
71. #15667989	C₂²	semidirect
75. #15667988	C₂²	semidirect
81. #15667984	C₂²	semidirect
86. #15667983	C₂²	semidirect
90. Q₈×Dic₈₉	C₂²	semidirect
91. Q₈×Dic₈₉	C₂²	semidirect
92. C₄×Dic₁₇₈	C₂²	semidirect
93. #15667977	C₂²	semidirect
102. C₄×C₂²⋊D₈₉	C₂²	semidirect
105. #15667970	C₂²	semidirect
107. #15667968	C₂²	semidirect
108. C₂×C₄⋊Dic₈₉	C₂²	semidirect
113. C₂×#41×C₈₉	C₂²	semidirect
114. C₄⋊Q₈×C₈₉	C₂²	semidirect
116. #123×C₈₉	C₂²	semidirect
118. C₂²⋊Q₈×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
336. C₈₉	#3541	semidirect
348. #547	D₈₉	semidirect
362. C₂×#41	C₂×D₈₉	semidirect
369. C₄⋊Q₈	C₂×D₈₉	semidirect
397. #123	C₂×D₈₉	semidirect
418. C₂²⋊Q₈	C₂×D₈₉	semidirect
449. C₄×D₄	C₂×D₈₉	semidirect
457. 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
#19152351	2
#19152343	2
#19152319	2
#19152306	2
#19152303	2
#19152298	2
#19152293	2
#19152288	2
#19152263	2
#19152255	2
#19152216	2
#19152213	2
#19152209	2
#19152195	2
#19152184	2
#19152180	2
#19152176	2
#19152171	2
#19152107	2
#19152105	2
C₂²⋊Q₈×D₈₉	2
#547×C₈₉	2
#3541	89