Subgroups — #26034695

Order 11392.

1004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152349	C₂	1	2	yes	maximal, complemented
2	#19152347	C₂	1	2	yes	maximal, complemented
3	#19152323	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152320	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152302	C₂	1	2	yes	maximal, complemented
6	#19152297	C₂	1	2	yes	maximal, complemented
7	Q₈×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152259	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152257	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152250	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152225	C₂	1	2	yes	maximal, complemented
13	#19152218	C₂	1	2	yes	maximal, complemented
14	#19152208	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152206	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152197	C₂	1	2	yes	maximal, complemented
17	#19152190	C₂	1	2	yes	maximal, complemented
18	#19152173	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152172	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#15668010	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152134	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152128	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×Q₈×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	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
28	#15668011	C₂²	1	2	yes	—
29	#15668010	C₂²	1	1	yes	characteristic
30	#15668010	C₂²	1	1	yes	characteristic
31	#15668010	C₂²	1	2	yes	—
32	#15668010	C₂²	1	1	yes	characteristic
33	#15668010	C₂²	1	1	yes	characteristic
34	#15668010	C₂²	1	2	yes	—
35	#15668010	C₂²	1	1	yes	characteristic
36	#15668010	C₂²	1	2	yes	—
37	#15668007	C₂²	1	1	yes	characteristic
38	#15668007	C₂²	1	2	yes	—
39	#15668007	C₂²	1	2	yes	—
40	#15668007	C₂²	1	2	yes	—
41	#15668006	C₂²	1	2	yes	—
42	#15668006	C₂²	1	2	yes	—
43	#15668005	C₂²	1	1	yes	characteristic
44	#15668005	C₂²	1	2	yes	—
45	#15668005	C₂²	1	2	yes	—
46	#15668004	C₂²	1	2	yes	—
47	#15668003	C₂²	1	1	yes	characteristic
48	#15668003	C₂²	1	2	yes	—
49	#15668003	C₂²	1	2	yes	—
50	#15668002	C₂²	1	1	yes	characteristic
51	#15668002	C₂²	1	2	yes	—
52	#15668002	C₂²	1	2	yes	—
53	#15668002	C₂²	1	2	yes	—
54	#15668002	C₂²	1	2	yes	—
55	#15668001	C₂²	1	1	yes	characteristic
56	#15668001	C₂²	1	1	yes	characteristic
57	#15668001	C₂²	1	2	yes	—
58	#15668000	C₂²	1	1	yes	characteristic
59	#15667998	C₂²	1	1	yes	characteristic
60	#15667998	C₂²	1	2	yes	—
61	#15667997	C₂²	1	2	yes	—
62	#15667997	C₂²	1	2	yes	—
63	#15667997	C₂²	1	2	yes	—
64	#15667996	C₂²	1	1	yes	characteristic
65	#15667996	C₂²	1	2	yes	—
66	#15667995	C₂²	1	2	yes	—
67	#15667995	C₂²	1	2	yes	—
68	#15667994	C₂²	1	2	yes	—
69	#15667993	C₂²	1	1	yes	characteristic
70	#15667992	C₂²	1	1	yes	characteristic
71	#15667991	C₂²	1	2	yes	—
72	#15667991	C₂²	1	1	yes	characteristic
73	#15667990	C₂²	1	2	yes	—
74	#15667990	C₂²	1	2	yes	—
75	#15667990	C₂²	1	2	yes	—
76	#15667990	C₂²	1	2	yes	—
77	#15667990	C₂²	1	2	yes	—
78	#15667989	C₂²	1	1	yes	characteristic
79	#15667989	C₂²	1	2	yes	—
80	#15667988	C₂²	1	2	yes	—
81	#15667988	C₂²	1	2	yes	—
82	#15667988	C₂²	1	2	yes	—
83	#15667988	C₂²	1	1	yes	characteristic
84	#15667988	C₂²	1	2	yes	—
85	#15667986	C₂²	1	1	yes	characteristic
86	#15667986	C₂²	1	2	yes	—
87	#15667985	C₂²	1	2	yes	—
88	#15667984	C₂²	1	1	yes	characteristic
89	#15667984	C₂²	1	2	yes	—
90	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
91	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
93	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
94	#15667977	C₂²	1	1	yes	characteristic
95	#15667977	C₂²	1	2	yes	—
96	#15667974	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
100	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
101	#15667972	C₂²	1	2	yes	—
102	#15667972	C₂²	1	2	yes	—
103	#15667972	C₂²	1	2	yes	—
104	#15667971	C₂²	1	1	yes	characteristic
105	#15667970	C₂²	1	2	yes	—
106	#15667969	C₂²	1	1	yes	characteristic
107	#15667969	C₂²	1	2	yes	—
108	C₂×#13083553	C₂²	1	2	yes	—
109	C₂×#13083553	C₂²	1	2	yes	—
110	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
111	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
112	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic
114	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
115	C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₄×D₄×C₈₉	C₂²	1	2	yes	—
123	#13083575	—	4	2	no	—
124	#13083574	—	4	2	no	—
125	C₂×Dic₁₇₈	—	4	2	no	—
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
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×Dic₁₇₈	C₂³	1	2	yes	—
131	Q₈×D₈₉	—	4	2	no	—
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
139	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
140	C₂²×Dic₈₉	C₂³	1	2	yes	—
141	C₂×C₄×D₈₉	C₂³	1	2	yes	—
142	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
144	C₂×C₄×D₈₉	C₂³	1	2	yes	—
145	C₂×C₄×D₈₉	C₂³	1	2	yes	—
146	C₄⋊Dic₈₉	C₂³	1	2	yes	—
147	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₈₉	C₂³	1	2	yes	—
152	C₄⋊Dic₈₉	C₂³	1	2	yes	—
153	C₄⋊Dic₈₉	C₂³	1	2	yes	—
154	#13083553	C₂³	1	1	yes	characteristic
155	#13083553	C₂³	1	2	yes	—
156	#13083553	C₂³	1	1	yes	characteristic
157	#13083553	C₂³	1	1	yes	characteristic
158	#13083553	C₂³	1	2	yes	—
159	#13083553	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	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
180	#13083551	C₂³	1	2	yes	—
181	#13083551	C₂³	1	1	yes	characteristic
182	#13083551	C₂³	1	2	yes	—
183	#13083551	C₂³	1	1	yes	characteristic
184	#13083551	C₂³	1	2	yes	—
185	#13083551	C₂³	1	2	yes	—
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	1	yes	characteristic
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	2	yes	—
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	2	yes	—
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	C₂×Q₈×C₈₉	—	4	2	no	—
204	C₂×Q₈×C₈₉	—	4	2	no	—
205	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
209	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
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	C₄⋊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	1	yes	characteristic
219	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₄²×C₈₉	C₂³	1	2	yes	—
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	C₂⁴	1	2	yes	—
232	Q₈×C₈₉	—	2	2	no	—
233	Q₈×C₈₉	—	2	2	no	—
234	Q₈×C₈₉	—	2	2	no	—
235	Q₈×C₈₉	—	4	2	no	—
236	Q₈×C₈₉	—	4	2	no	—
237	D₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	4	2	no	—
241	C₂×C₄×C₈₉	—	4	2	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	2	yes	—
245	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
246	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
254	C₂²⋊D₈₉	—	4	2	no	—
255	C₂×Dic₈₉	—	2	2	no	—
256	C₂×Dic₈₉	—	2	2	no	—
257	C₂×Dic₈₉	—	4	2	no	—
258	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₈₉	C₂⁴	1	2	yes	—
261	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₈₉	C₂⁴	1	2	yes	—
265	C₂×Dic₈₉	C₂⁴	1	2	yes	—
266	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	D₃₅₆	—	2	2	no	—
269	D₃₅₆	—	4	2	no	—
270	C₄×D₈₉	—	2	2	no	—
271	C₄×D₈₉	—	2	4	no	—
272	C₄×D₈₉	—	4	2	no	—
273	C₄×D₈₉	—	4	2	no	—
274	C₄×D₈₉	—	4	2	no	—
275	Dic₁₇₈	—	2	2	no	—
276	Dic₁₇₈	—	2	2	no	—
277	Dic₁₇₈	—	2	2	no	—
278	Dic₁₇₈	—	4	2	no	—
279	Dic₁₇₈	—	4	2	no	—
280	C₂²×C₈₉	—	2	1	no	—
281	C₂²×C₈₉	—	2	1	no	—
282	C₂²×C₈₉	—	2	1	no	—
283	C₂²×C₈₉	—	2	1	no	—
284	C₂²×C₈₉	—	2	1	no	—
285	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
286	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
287	C₂×D₈₉	—	2	1	no	—
288	C₂×D₈₉	—	2	2	no	—
289	C₂×D₈₉	—	2	2	no	—
290	C₂×D₈₉	—	2	1	no	—
291	C₂×D₈₉	—	2	1	no	—
292	C₂×D₈₉	—	2	2	no	—
293	C₄×C₈₉	—	2	1	no	—
294	C₄×C₈₉	—	2	2	no	—
295	C₄×C₈₉	—	2	1	no	—
296	C₄×C₈₉	—	2	2	no	—
297	C₄×C₈₉	—	2	2	no	—
298	C₄×C₈₉	—	2	1	no	—
299	C₄×C₈₉	—	2	2	no	—
300	C₄×C₈₉	—	2	1	no	—
301	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
302	Dic₈₉	—	2	2	no	—
303	Dic₈₉	—	2	2	no	—
304	Dic₈₉	—	2	1	no	—
305	Dic₈₉	—	2	1	no	—
306	Dic₈₉	—	2	1	no	—
307	Dic₈₉	—	2	1	no	—
308	Dic₈₉	—	2	1	no	—
309	Dic₈₉	—	2	1	no	—
310	Dic₈₉	—	2	2	no	—
311	Dic₈₉	2₋¹⁺⁴	1	2	yes	—
312	C₂×C₈₉	—	2	2	no	—
313	C₂×C₈₉	—	4	1	no	—
314	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	D₈₉	—	4	1	no	—
318	D₈₉	—	4	2	no	—
319	#3552	—	89	1	no	maximal, Sylow
320	C₈₉	#3552	1	1	yes	characteristic, complemented, Sylow
321	#563	—	89	2	no	—
322	#563	—	89	2	no	—
323	#557	—	89	1	no	—
324	#556	—	89	1	no	—
325	#554	—	89	2	no	—
326	#553	—	89	2	no	—
327	D₄×Q₈	—	89	1	no	—
328	D₄×Q₈	—	89	1	no	—
329	D₄×Q₈	D₈₉	1	1	yes	characteristic, complemented
330	#548	—	89	1	no	—
331	#548	—	89	1	no	—
332	#547	—	89	1	no	—
333	#544	—	89	2	no	—
334	#542	—	89	2	no	—
335	#541	—	89	1	no	—
336	#541	—	89	1	no	—
337	#539	—	89	2	no	—
338	#539	—	89	2	no	—
339	#536	—	89	1	no	—
340	#536	—	89	1	no	—
341	C₂×C₄⋊Q₈	—	89	1	no	—
342	#529	—	89	1	no	—
343	#529	—	89	1	no	—
344	C₂×#41	—	89	1	no	—
345	C₂×#41	—	89	1	no	—
346	C₂²×Q₈	—	89	1	no	—
347	C₂²×Q₈	—	89	1	no	—
348	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic
349	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic
350	C₄⋊Q₈	—	89	1	no	—
351	C₄⋊Q₈	—	89	1	no	—
352	C₄⋊Q₈	—	89	2	no	—
353	C₄⋊Q₈	—	89	1	no	—
354	C₄⋊Q₈	—	89	1	no	—
355	C₄⋊Q₈	—	89	2	no	—
356	C₄⋊Q₈	—	89	1	no	—
357	C₄⋊Q₈	—	89	2	no	—
358	C₄⋊Q₈	—	89	2	no	—
359	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
360	C₄⋊Q₈	C₂×D₈₉	1	2	yes	—
361	#126	—	89	2	no	—
362	#126	—	89	1	no	—
363	#126	—	89	2	no	—
364	#126	—	89	2	no	—
365	#126	—	89	1	no	—
366	#126	—	89	2	no	—
367	#126	—	89	2	no	—
368	#126	—	89	2	no	—
369	#126	—	89	2	no	—
370	#125	—	89	1	no	—
371	#125	—	89	1	no	—
372	#125	—	89	2	no	—
373	#125	—	89	2	no	—
374	#125	—	89	2	no	—
375	#125	—	89	2	no	—
376	#125	—	89	2	no	—
377	#125	—	89	2	no	—
378	#125	—	89	2	no	—
379	#124	—	89	1	no	—
380	#124	—	89	1	no	—
381	#124	—	89	2	no	—
382	#124	—	89	1	no	—
383	#124	—	89	2	no	—
384	#124	—	89	1	no	—
385	#123	—	89	1	no	—
386	#123	—	89	2	no	—
387	#123	—	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	C₂²⋊Q₈	—	89	2	no	—
395	C₂²⋊Q₈	—	89	2	no	—
396	C₂²⋊Q₈	—	89	2	no	—
397	C₂²⋊Q₈	—	89	1	no	—
398	C₂²⋊Q₈	—	89	2	no	—
399	C₂²⋊Q₈	—	89	2	no	—
400	C₂²⋊Q₈	—	89	1	no	—
401	C₂²⋊Q₈	—	89	2	no	—
402	C₂²⋊Q₈	—	89	2	no	—
403	C₂²⋊Q₈	—	89	2	no	—
404	C₂²⋊Q₈	—	89	2	no	—
405	C₂²⋊Q₈	—	89	2	no	—
406	C₂²⋊Q₈	—	89	1	no	—
407	C₂²⋊Q₈	—	89	1	no	—
408	C₂²⋊Q₈	—	89	2	no	—
409	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
410	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
411	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
413	#121	—	89	1	no	—
414	#121	—	89	2	no	—
415	#121	—	89	1	no	—
416	#121	—	89	2	no	—
417	#121	—	89	2	no	—
418	C₄×Q₈	—	89	1	no	—
419	C₄×Q₈	—	89	1	no	—
420	C₄×Q₈	—	89	1	no	—
421	C₄×Q₈	—	89	2	no	—
422	C₄×Q₈	—	89	1	no	—
423	C₄×Q₈	—	89	1	no	—
424	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
425	C₄×D₄	—	89	1	no	—
426	C₄×D₄	—	89	1	no	—
427	C₄×D₄	—	89	2	no	—
428	C₄×D₄	—	89	2	no	—
429	C₄×D₄	—	89	1	no	—
430	C₄×D₄	—	89	2	no	—
431	C₄×D₄	—	89	2	no	—
432	C₄×D₄	—	89	2	no	—
433	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
434	C₄×D₄	C₂×D₈₉	1	2	yes	—
435	#117	—	89	1	no	—
436	#117	—	89	2	no	—
437	#117	—	89	1	no	—
438	#117	—	89	2	no	—
439	C₂×C₄⋊C₄	—	89	2	no	—
440	C₂×C₄⋊C₄	—	89	2	no	—
441	C₂×C₄⋊C₄	—	89	2	no	—
442	C₂×C₄²	—	89	1	no	—
443	#41	—	356	2	no	—
444	#41	—	356	2	no	—
445	C₂×Q₈	—	4	2	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	—	89	2	no	—
448	C₂×Q₈	—	89	2	no	—
449	C₂×Q₈	—	89	1	no	—
450	C₂×Q₈	—	89	1	no	—
451	C₂×Q₈	—	89	1	no	—
452	C₂×Q₈	—	356	2	no	—
453	C₂×Q₈	—	356	2	no	—
454	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
455	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
456	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
457	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
458	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
459	C₂×D₄	—	89	2	no	—
460	C₂×D₄	—	89	1	no	—
461	C₂×D₄	—	89	2	no	—
462	C₂×D₄	—	89	1	no	—
463	C₂×D₄	—	89	2	no	—
464	C₂×D₄	—	89	1	no	—
465	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
466	C₂²×C₄	—	89	2	no	—
467	C₂²×C₄	—	89	1	no	—
468	C₂²×C₄	—	89	1	no	—
469	C₂²×C₄	—	89	2	no	—
470	C₂²×C₄	—	89	2	no	—
471	C₂²×C₄	—	89	2	no	—
472	C₂²×C₄	—	89	2	no	—
473	C₂²×C₄	—	89	1	no	—
474	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
475	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
476	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
477	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	2	no	—
481	C₄⋊C₄	—	89	2	no	—
482	C₄⋊C₄	—	89	2	no	—
483	C₄⋊C₄	—	89	2	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	—	89	2	no	—
486	C₄⋊C₄	—	89	2	no	—
487	C₄⋊C₄	—	89	2	no	—
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	—	89	1	no	—
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	1	no	—
497	C₄⋊C₄	—	89	2	no	—
498	C₄⋊C₄	—	89	2	no	—
499	C₄⋊C₄	—	89	1	no	—
500	C₄⋊C₄	—	89	2	no	—
501	C₄⋊C₄	—	89	2	no	—
502	C₄⋊C₄	—	89	2	no	—
503	C₄⋊C₄	—	89	2	no	—
504	C₄⋊C₄	—	89	2	no	—
505	C₄⋊C₄	—	89	1	no	—
506	C₄⋊C₄	—	89	1	no	—
507	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
508	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
509	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
511	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
512	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
513	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
514	C₂²⋊C₄	—	89	1	no	—
515	C₂²⋊C₄	—	89	1	no	—
516	C₂²⋊C₄	—	89	1	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	1	no	—
519	C₂²⋊C₄	—	89	2	no	—
520	C₂²⋊C₄	—	89	2	no	—
521	C₂²⋊C₄	—	89	2	no	—
522	C₂²⋊C₄	—	89	1	no	—
523	C₂²⋊C₄	—	89	2	no	—
524	C₂²⋊C₄	—	89	1	no	—
525	C₂²⋊C₄	—	89	2	no	—
526	C₂²⋊C₄	—	89	2	no	—
527	C₂²⋊C₄	—	89	1	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	C₂²×D₈₉	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
537	C₄²	—	89	1	no	—
538	C₄²	—	89	1	no	—
539	C₄²	—	89	1	no	—
540	C₄²	—	89	1	no	—
541	C₄²	—	89	2	no	—
542	C₄²	—	89	1	no	—
543	C₄²	—	89	2	no	—
544	C₄²	—	89	2	no	—
545	C₄²	—	89	2	no	—
546	C₄²	C₂²×D₈₉	1	1	yes	characteristic
547	C₄²	C₂²×D₈₉	1	2	yes	—
548	C₂³	—	89	1	no	—
549	C₂³	—	89	2	no	—
550	C₂³	C₂³×D₈₉	1	1	yes	characteristic
551	C₂³	C₂³×D₈₉	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	2	no	—
555	Q₈	—	4	2	no	—
556	Q₈	—	4	2	no	—
557	Q₈	—	356	2	no	—
558	Q₈	—	356	2	no	—
559	Q₈	—	178	2	no	—
560	Q₈	—	178	2	no	—
561	Q₈	—	178	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	356	2	no	—
564	D₄	—	356	2	no	—
565	D₄	—	178	2	no	—
566	D₄	—	178	2	no	—
567	D₄	—	178	4	no	—
568	D₄	—	178	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	89	1	no	—
574	C₂×C₄	—	89	1	no	—
575	C₂×C₄	—	89	2	no	—
576	C₂×C₄	—	89	1	no	—
577	C₂×C₄	—	89	1	no	—
578	C₂×C₄	—	89	1	no	—
579	C₂×C₄	—	89	1	no	—
580	C₂×C₄	—	89	2	no	—
581	C₂×C₄	—	89	2	no	—
582	C₂×C₄	—	89	1	no	—
583	C₂×C₄	—	356	2	no	—
584	C₂×C₄	—	356	2	no	—
585	C₂×C₄	—	356	2	no	—
586	C₂×C₄	—	356	2	no	—
587	C₂×C₄	—	178	4	no	—
588	C₂×C₄	—	178	2	no	—
589	C₂×C₄	—	178	2	no	—
590	C₂×C₄	—	178	2	no	—
591	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₈₉	1	2	yes	—
594	C₂×C₄	C₂³×D₈₉	1	2	yes	—
595	C₂×C₄	C₂³×D₈₉	1	2	yes	—
596	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₈₉	1	2	yes	—
598	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	178	1	no	—
606	C₂²	—	178	2	no	—
607	C₂²	—	178	2	no	—
608	C₂²	—	178	1	no	—
609	C₂²	—	178	1	no	—
610	C₂²	—	178	2	no	—
611	C₂²	#15668060	1	2	yes	—
612	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	89	2	no	—
622	C₄	—	178	1	no	—
623	C₄	—	178	2	no	—
624	C₄	—	178	2	no	—
625	C₄	—	178	1	no	—
626	C₄	—	178	1	no	—
627	C₄	—	178	1	no	—
628	C₄	—	178	1	no	—
629	C₄	—	178	2	no	—
630	C₄	—	178	1	no	—
631	C₄	#15668057	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	356	1	no	—
635	C₂	—	356	2	no	—
636	C₂	C₂×#15668057	1	1	yes	characteristic
637	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
638	C₂	C₂×#15668060	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	D₄×Q₈×C₈₉	C₂
hypercenter	D₄×Q₈	D₈₉
hypocenter	C₈₉	#3552
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ D₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #19152349	C₂	semidirect
2. #19152347	C₂	semidirect
3. #19152323	C₂	semidirect
4. #19152320	C₂	semidirect
5. #19152302	C₂	semidirect
6. #19152297	C₂	semidirect
7. Q₈×C₂²⋊D₈₉	C₂	semidirect
8. #19152261	C₂	semidirect
9. #19152259	C₂	semidirect
10. #19152257	C₂	semidirect
11. #19152250	C₂	semidirect
12. #19152225	C₂	semidirect
13. #19152218	C₂	semidirect
14. #19152208	C₂	semidirect
15. #19152206	C₂	semidirect
16. #19152197	C₂	semidirect
17. #19152190	C₂	semidirect
18. #19152173	C₂	semidirect
19. #19152172	C₂	semidirect
20. C₂×#15668010	C₂	semidirect
21. #19152134	C₂	semidirect
22. #19152128	C₂	semidirect
23. D₄×Q₈×C₈₉	C₂	semidirect
320. C₈₉	#3552	semidirect
329. D₄×Q₈	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152349	2
#19152347	2
#19152323	2
#19152320	2
#19152302	2
#19152297	2
Q₈×C₂²⋊D₈₉	2
#19152261	2
#19152259	2
#19152257	2
#19152250	2
#19152225	2
#19152218	2
#19152208	2
#19152206	2
#19152197	2
#19152190	2
#19152173	2
#19152172	2
C₂×#15668010	2
#19152134	2
#19152128	2
D₄×Q₈×C₈₉	2
#3552	89