Subgroups — #26035027

Order 11392.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152433	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152410	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152409	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152408	C₂	1	3	yes	maximal, complemented
6	#19152405	C₂	1	3	yes	maximal, complemented
7	#19152402	C₂	1	3	yes	maximal, complemented
8	#19152401	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152399	C₂	1	3	yes	maximal, complemented
10	#19152395	C₂	1	3	yes	maximal, complemented
11	#19152394	C₂	1	3	yes	maximal, complemented
12	C₂×#15668036	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₈₉	C₂	1	3	yes	maximal, complemented
14	#19152363	C₂	1	1	yes	maximal, characteristic, complemented
15	#576×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#15668059	—	2	1	no	—
17	#15668059	C₂²	1	1	yes	characteristic, complemented
18	#15668059	C₂²	1	3	yes	complemented
19	#15668058	—	2	1	no	—
20	#15668058	C₂²	1	1	yes	characteristic, complemented
21	#15668058	C₂²	1	3	yes	complemented
22	#15668057	—	2	3	no	—
23	#15668057	—	2	3	no	—
24	#15668057	C₂²	1	3	yes	complemented
25	#15668057	C₂²	1	3	yes	complemented
26	C₂×#13083573	—	2	3	no	—
27	C₂×#13083573	C₂²	1	3	yes	complemented
28	#41×D₈₉	—	2	1	no	—
29	#41×D₈₉	—	2	1	no	—
30	#41×D₈₉	C₂²	1	1	yes	characteristic
31	#41×D₈₉	C₂²	1	3	yes	complemented
32	#41×D₈₉	C₂²	1	3	yes	complemented
33	C₂×D₄×D₈₉	—	2	3	no	—
34	C₂×D₄×D₈₉	C₂²	1	3	yes	complemented
35	#15668045	C₂²	1	3	yes	complemented
36	#15668044	C₂²	1	1	yes	characteristic, complemented
37	#15668044	C₂²	1	3	yes	complemented
38	#15668042	C₂²	1	3	yes	complemented
39	#15668041	C₂²	1	3	yes	complemented
40	#15668041	C₂²	1	3	yes	complemented
41	#15668040	C₂²	1	3	yes	complemented
42	#15668039	C₂²	1	3	yes	complemented
43	#15668039	C₂²	1	3	yes	complemented
44	#15668038	C₂²	1	3	yes	complemented
45	#15668038	C₂²	1	3	yes	complemented
46	#15668037	C₂²	1	3	yes	complemented
47	#15668036	C₂²	1	6	yes	complemented
48	#15668036	C₂²	1	3	yes	complemented
49	#15668036	C₂²	1	6	yes	complemented
50	#15668036	C₂²	1	6	yes	complemented
51	#15668036	C₂²	1	3	yes	complemented
52	#15668034	C₂²	1	3	yes	complemented
53	#15668033	C₂²	1	6	yes	complemented
54	#15668032	C₂²	1	3	yes	complemented
55	#15668032	C₂²	1	3	yes	complemented
56	#15668031	C₂²	1	6	yes	complemented
57	C₂×#13083563	C₂²	1	3	yes	complemented
58	C₂×#13083562	C₂²	1	3	yes	complemented
59	SD₁₆×D₈₉	C₂²	1	6	yes	complemented
60	C₂×#13083559	C₂²	1	3	yes	complemented
61	D₈×D₈₉	C₂²	1	6	yes	complemented
62	#15668020	C₂²	1	3	yes	complemented
63	#15668019	C₂²	1	1	yes	characteristic, complemented
64	#15668018	C₂²	1	3	yes	complemented
65	C₂×#13083557	C₂²	1	3	yes	complemented
66	M₁₆×D₈₉	C₂²	1	3	yes	complemented
67	H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₈₉	C₂²	1	3	yes	complemented
71	#135×C₈₉	C₂²	1	3	yes	complemented
72	C₂×D₈×C₈₉	C₂²	1	3	yes	complemented
73	#131×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₈₉	—	2	3	no	—
75	#13083575	—	2	1	no	—
76	#13083575	D₄	1	1	yes	characteristic
77	#13083575	C₂³	1	3	yes	—
78	#13083575	C₂³	1	1	yes	characteristic
79	#13083574	—	2	3	no	—
80	#13083574	—	2	3	no	—
81	#13083574	—	2	3	no	—
82	#13083574	—	2	3	no	—
83	#13083574	C₂³	1	3	yes	—
84	#13083574	C₂³	1	3	yes	—
85	#13083574	C₂³	1	3	yes	complemented
86	#13083573	—	2	3	no	—
87	#13083573	—	2	6	no	—
88	#13083573	—	2	3	no	—
89	#13083573	—	2	3	no	—
90	#13083573	—	2	3	no	—
91	#13083573	—	2	3	no	—
92	#13083573	—	2	3	no	—
93	#13083573	—	2	3	no	—
94	#13083573	D₄	1	3	yes	—
95	#13083573	C₂³	1	3	yes	—
96	#13083573	C₂³	1	3	yes	—
97	#13083573	C₂³	1	6	yes	complemented
98	C₂×Dic₁₇₈	—	2	3	no	—
99	C₂×Dic₁₇₈	C₂³	1	3	yes	complemented
100	Q₈×D₈₉	—	2	1	no	—
101	Q₈×D₈₉	D₄	1	1	yes	characteristic
102	Q₈×D₈₉	C₂³	1	1	yes	characteristic
103	Q₈×D₈₉	C₂³	1	3	yes	complemented
104	C₂×D₃₅₆	—	2	3	no	—
105	C₂×D₃₅₆	C₂³	1	3	yes	—
106	C₂×C₂²⋊D₈₉	—	2	3	no	—
107	C₂×C₂²⋊D₈₉	—	2	6	no	—
108	C₂×C₂²⋊D₈₉	—	2	6	no	—
109	C₂×C₂²⋊D₈₉	—	2	3	no	—
110	D₄×D₈₉	—	2	3	no	—
111	D₄×D₈₉	—	2	3	no	—
112	D₄×D₈₉	—	2	3	no	—
113	D₄×D₈₉	—	2	6	no	—
114	D₄×D₈₉	—	2	3	no	—
115	D₄×D₈₉	—	2	3	no	—
116	D₄×D₈₉	—	2	3	no	—
117	D₄×D₈₉	—	2	3	no	—
118	D₄×D₈₉	D₄	1	3	yes	—
119	D₄×D₈₉	C₂³	1	6	yes	—
120	D₄×D₈₉	C₂³	1	3	yes	—
121	D₄×D₈₉	C₂³	1	3	yes	complemented
122	C₂²×Dic₈₉	—	2	3	no	—
123	C₂×C₄×D₈₉	—	2	3	no	—
124	C₂×C₄×D₈₉	—	2	3	no	—
125	C₂×C₄×D₈₉	C₂³	1	3	yes	—
126	Dic₃₅₆	C₂³	1	3	yes	complemented
127	#13083564	C₂³	1	1	yes	characteristic, complemented
128	#13083564	C₂³	1	3	yes	complemented
129	#13083563	C₂³	1	6	yes	complemented
130	#13083563	C₂³	1	3	yes	complemented
131	#13083563	C₂³	1	1	yes	characteristic, complemented
132	#13083562	C₂³	1	6	yes	complemented
133	#13083562	C₂³	1	3	yes	complemented
134	#13083562	C₂³	1	3	yes	complemented
135	#13083561	C₂³	1	3	yes	complemented
136	#13083561	C₂³	1	1	yes	characteristic, complemented
137	D₇₁₂	C₂³	1	3	yes	complemented
138	#13083559	C₂³	1	3	yes	complemented
139	#13083559	C₂³	1	6	yes	complemented
140	#13083559	C₂³	1	3	yes	complemented
141	#13083558	C₂³	1	3	yes	complemented
142	#13083557	C₂³	1	3	yes	—
143	#13083557	C₂³	1	1	yes	characteristic
144	#13083557	C₂³	1	3	yes	complemented
145	#13083557	C₂³	1	3	yes	complemented
146	C₂×#10623494	C₂³	1	3	yes	complemented
147	C₈×D₈₉	C₂³	1	6	yes	complemented
148	#41×C₈₉	—	2	1	no	—
149	#41×C₈₉	—	2	1	no	—
150	#41×C₈₉	C₂³	1	3	yes	—
151	#41×C₈₉	C₂³	1	1	yes	characteristic
152	#41×C₈₉	C₂³	1	3	yes	complemented
153	C₂×D₄×C₈₉	—	2	3	no	—
154	C₂×D₄×C₈₉	—	2	3	no	—
155	C₂×D₄×C₈₉	C₂³	1	3	yes	—
156	C₂×D₄×C₈₉	C₂³	1	3	yes	complemented
157	Q₁₆×C₈₉	C₂³	1	1	yes	characteristic, complemented
158	SD₁₆×C₈₉	C₂³	1	3	yes	complemented
159	SD₁₆×C₈₉	C₂³	1	3	yes	complemented
160	D₈×C₈₉	C₂³	1	6	yes	complemented
161	D₈×C₈₉	C₂³	1	3	yes	complemented
162	M₁₆×C₈₉	C₂³	1	3	yes	complemented
163	C₂×C₈×C₈₉	C₂³	1	3	yes	complemented
164	C₂³×C₈₉	—	2	3	no	—
165	C₂³×C₈₉	—	2	3	no	—
166	C₂²×D₈₉	—	2	3	no	—
167	C₂²×D₈₉	—	2	3	no	—
168	C₂²×D₈₉	—	2	3	no	—
169	C₂²×D₈₉	—	2	6	no	—
170	C₂²×D₈₉	—	8	6	no	—
171	C₂²×D₈₉	C₂×D₄	1	3	yes	—
172	Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
173	Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
174	Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
175	D₄×C₈₉	—	2	3	no	—
176	D₄×C₈₉	—	2	3	no	—
177	D₄×C₈₉	—	2	3	no	—
178	D₄×C₈₉	—	2	3	no	—
179	D₄×C₈₉	C₂×D₄	1	3	yes	—
180	D₄×C₈₉	C₂⁴	1	3	yes	—
181	D₄×C₈₉	C₂⁴	1	3	yes	—
182	C₂×C₄×C₈₉	—	2	3	no	—
183	C₂×C₄×C₈₉	—	2	3	no	—
184	C₂×C₄×C₈₉	C₂⁴	1	3	yes	—
185	C₂²⋊D₈₉	—	2	3	no	—
186	C₂²⋊D₈₉	—	2	3	no	—
187	C₂²⋊D₈₉	—	2	3	no	—
188	C₂²⋊D₈₉	—	2	3	no	—
189	C₂²⋊D₈₉	—	2	6	no	—
190	C₂²⋊D₈₉	—	2	6	no	—
191	C₂²⋊D₈₉	—	2	3	no	—
192	C₂²⋊D₈₉	—	2	3	no	—
193	C₂²⋊D₈₉	C₂×D₄	1	6	yes	—
194	C₂×Dic₈₉	—	2	3	no	—
195	C₂×Dic₈₉	—	2	3	no	—
196	C₂×Dic₈₉	—	2	3	no	—
197	C₂×Dic₈₉	—	2	6	no	—
198	C₂×Dic₈₉	C₂×D₄	1	3	yes	—
199	D₃₅₆	—	2	3	no	—
200	D₃₅₆	—	2	1	no	—
201	D₃₅₆	—	2	3	no	—
202	D₃₅₆	C₂×D₄	1	3	yes	—
203	D₃₅₆	C₂⁴	1	1	yes	characteristic
204	D₃₅₆	C₂⁴	1	3	yes	—
205	C₄×D₈₉	—	2	1	no	—
206	C₄×D₈₉	—	2	3	no	—
207	C₄×D₈₉	—	2	3	no	—
208	C₄×D₈₉	—	2	3	no	—
209	C₄×D₈₉	—	2	1	no	—
210	C₄×D₈₉	—	2	3	no	—
211	C₄×D₈₉	C₂×D₄	1	3	yes	—
212	C₄×D₈₉	C₂×D₄	1	3	yes	—
213	C₄×D₈₉	C₂⁴	1	3	yes	—
214	C₄×D₈₉	C₂⁴	1	1	yes	characteristic
215	Dic₁₇₈	—	2	3	no	—
216	Dic₁₇₈	—	2	1	no	—
217	Dic₁₇₈	—	2	3	no	—
218	Dic₁₇₈	C₂×D₄	1	3	yes	—
219	Dic₁₇₈	C₂⁴	1	3	yes	—
220	Dic₁₇₈	C₂⁴	1	1	yes	characteristic
221	C₈×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₈×C₈₉	C₂⁴	1	3	yes	—
223	#10623494	C₂⁴	1	3	yes	—
224	#10623494	C₂⁴	1	1	yes	characteristic
225	C₂²×C₈₉	—	2	3	no	—
226	C₂²×C₈₉	—	2	3	no	—
227	C₂²×C₈₉	—	8	3	no	—
228	C₂²×C₈₉	—	8	3	no	—
229	C₂²×C₈₉	C₂²×D₄	1	3	yes	—
230	C₂×D₈₉	—	2	1	no	—
231	C₂×D₈₉	—	2	3	no	—
232	C₂×D₈₉	—	4	3	no	—
233	C₂×D₈₉	—	4	6	no	—
234	C₂×D₈₉	—	8	3	no	—
235	C₂×D₈₉	—	8	6	no	—
236	C₂×D₈₉	—	8	3	no	—
237	C₂×D₈₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₈₉	C₂²×D₄	1	3	yes	—
239	C₄×C₈₉	—	2	1	no	—
240	C₄×C₈₉	—	2	1	no	—
241	C₄×C₈₉	C₂²×D₄	1	3	yes	—
242	C₄×C₈₉	C₂⁵	1	1	yes	characteristic
243	Dic₈₉	—	2	3	no	—
244	Dic₈₉	—	2	1	no	—
245	Dic₈₉	C₂²×D₄	1	3	yes	—
246	Dic₈₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₈₉	—	2	3	no	—
248	C₂×C₈₉	—	4	3	no	—
249	C₂×C₈₉	—	4	3	no	—
250	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
251	D₈₉	—	2	1	no	—
252	D₈₉	—	2	3	no	—
253	D₈₉	—	4	3	no	—
254	D₈₉	—	4	1	no	—
255	#3585	—	89	1	no	maximal, Sylow
256	C₈₉	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	89	1	no	—
258	C₂×H(5,𝔽₂)	—	89	1	no	—
259	#577	—	89	1	no	—
260	#577	—	89	3	no	—
261	#577	—	89	3	no	—
262	#577	—	89	1	no	—
263	#576	—	89	1	no	—
264	#576	—	89	3	no	—
265	#576	—	89	3	no	—
266	#576	D₈₉	1	1	yes	characteristic, complemented
267	#575	—	89	3	no	—
268	#575	—	89	3	no	—
269	C₂×AGL(1,ℤ/8)	—	89	3	no	—
270	C₂×AGL(1,ℤ/8)	—	89	3	no	—
271	#568	—	89	1	no	—
272	2₋¹⁺⁴	—	89	1	no	—
273	2₋¹⁺⁴	—	89	3	no	—
274	2₋¹⁺⁴	—	178	1	no	—
275	H(5,𝔽₂)	—	89	3	no	—
276	H(5,𝔽₂)	—	89	1	no	—
277	H(5,𝔽₂)	—	89	3	no	—
278	H(5,𝔽₂)	—	89	3	no	—
279	H(5,𝔽₂)	—	178	3	no	—
280	H(5,𝔽₂)	—	178	3	no	—
281	H(5,𝔽₂)	—	178	1	no	—
282	H(5,𝔽₂)	C₂×D₈₉	1	1	yes	characteristic, complemented
283	H(5,𝔽₂)	C₂×D₈₉	1	1	yes	characteristic, complemented
284	C₂×#41	—	89	1	no	—
285	C₂×#41	—	89	3	no	—
286	C₂×#41	—	89	3	no	—
287	C₂×#41	—	89	3	no	—
288	C₂×#41	—	178	3	no	—
289	C₂×#41	—	178	1	no	—
290	C₂×#41	—	178	1	no	—
291	C₂²×D₄	—	89	3	no	—
292	C₂²×D₄	—	178	3	no	—
293	#137	—	89	3	no	—
294	#137	—	89	1	no	—
295	#137	—	89	3	no	—
296	#137	—	89	3	no	—
297	#137	—	89	3	no	—
298	#137	—	89	3	no	—
299	AGL(1,ℤ/8)	—	89	3	no	—
300	AGL(1,ℤ/8)	—	89	3	no	—
301	AGL(1,ℤ/8)	—	89	3	no	—
302	AGL(1,ℤ/8)	—	89	3	no	—
303	AGL(1,ℤ/8)	—	89	3	no	—
304	AGL(1,ℤ/8)	—	89	6	no	—
305	AGL(1,ℤ/8)	—	89	3	no	—
306	AGL(1,ℤ/8)	—	89	6	no	—
307	AGL(1,ℤ/8)	—	89	6	no	—
308	AGL(1,ℤ/8)	—	89	3	no	—
309	AGL(1,ℤ/8)	—	89	3	no	—
310	AGL(1,ℤ/8)	C₂×D₈₉	1	3	yes	complemented
311	AGL(1,ℤ/8)	C₂×D₈₉	1	3	yes	complemented
312	#135	—	89	3	no	—
313	#135	—	89	3	no	—
314	#135	—	89	6	no	—
315	#135	—	89	6	no	—
316	#135	—	89	3	no	—
317	#135	C₂×D₈₉	1	3	yes	complemented
318	C₂×SD₁₆	—	89	3	no	—
319	C₂×SD₁₆	—	89	6	no	—
320	C₂×SD₁₆	—	89	3	no	—
321	C₂×D₈	—	89	3	no	—
322	C₂×D₈	—	89	6	no	—
323	C₂×D₈	C₂×D₈₉	1	3	yes	complemented
324	#131	—	89	1	no	—
325	#131	—	89	3	no	—
326	#131	—	89	3	no	—
327	#131	C₂×D₈₉	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	89	3	no	—
329	C₂×M₁₆	—	89	3	no	—
330	C₂⁴	—	178	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	89	1	no	—
334	#41	—	89	3	no	—
335	#41	—	89	3	no	—
336	#41	—	89	3	no	—
337	#41	—	89	1	no	—
338	#41	—	89	6	no	—
339	#41	—	89	3	no	—
340	#41	—	89	3	no	—
341	#41	—	89	3	no	—
342	#41	—	89	3	no	—
343	#41	—	178	3	no	—
344	#41	—	178	3	no	—
345	#41	—	178	3	no	—
346	#41	—	178	3	no	—
347	#41	—	178	3	no	—
348	#41	—	178	3	no	—
349	#41	—	178	3	no	—
350	#41	—	178	3	no	—
351	#41	—	178	6	no	—
352	#41	—	178	3	no	—
353	#41	—	178	3	no	—
354	#41	—	178	1	no	—
355	#41	—	178	3	no	—
356	#41	C₂²×D₈₉	1	3	yes	—
357	#41	C₂²×D₈₉	1	1	yes	characteristic
358	#41	C₂²×D₈₉	1	3	yes	complemented
359	C₂×Q₈	—	89	1	no	—
360	C₂×Q₈	—	89	3	no	—
361	C₂×Q₈	—	89	1	no	—
362	C₂×Q₈	—	89	3	no	—
363	C₂×Q₈	—	178	3	no	—
364	C₂×Q₈	—	178	1	no	—
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	89	3	no	—
368	C₂×D₄	—	89	3	no	—
369	C₂×D₄	—	89	6	no	—
370	C₂×D₄	—	89	3	no	—
371	C₂×D₄	—	89	3	no	—
372	C₂×D₄	—	178	3	no	—
373	C₂×D₄	—	178	3	no	—
374	C₂×D₄	—	178	3	no	—
375	C₂×D₄	—	178	3	no	—
376	C₂×D₄	—	178	6	no	—
377	C₂×D₄	—	178	3	no	—
378	C₂×D₄	—	178	3	no	—
379	C₂×D₄	—	178	3	no	—
380	C₂×D₄	—	178	3	no	—
381	C₂×D₄	—	178	6	no	—
382	C₂×D₄	—	178	6	no	—
383	C₂×D₄	—	178	3	no	—
384	C₂×D₄	—	178	3	no	—
385	C₂×D₄	C₂²×D₈₉	1	3	yes	—
386	C₂×D₄	C₂²×D₈₉	1	3	yes	complemented
387	C₂²×C₄	—	89	3	no	—
388	C₂²×C₄	—	178	3	no	—
389	C₂²×C₄	—	178	3	no	—
390	C₂²×C₄	—	178	3	no	—
391	Q₁₆	—	89	3	no	—
392	Q₁₆	—	89	1	no	—
393	Q₁₆	—	89	3	no	—
394	Q₁₆	C₂²×D₈₉	1	1	yes	characteristic, complemented
395	SD₁₆	—	89	3	no	—
396	SD₁₆	—	89	1	no	—
397	SD₁₆	—	89	3	no	—
398	SD₁₆	—	89	6	no	—
399	SD₁₆	—	89	3	no	—
400	SD₁₆	—	89	6	no	—
401	SD₁₆	—	89	3	no	—
402	SD₁₆	—	89	1	no	—
403	SD₁₆	C₂²×D₈₉	1	3	yes	complemented
404	SD₁₆	C₂²×D₈₉	1	3	yes	complemented
405	D₈	—	89	3	no	—
406	D₈	—	89	3	no	—
407	D₈	—	89	6	no	—
408	D₈	—	89	3	no	—
409	D₈	C₂²×D₈₉	1	6	yes	complemented
410	D₈	C₂²×D₈₉	1	3	yes	complemented
411	M₁₆	—	89	3	no	—
412	M₁₆	—	89	3	no	—
413	M₁₆	—	89	1	no	—
414	M₁₆	—	89	3	no	—
415	M₁₆	—	89	3	no	—
416	M₁₆	C₂²×D₈₉	1	3	yes	complemented
417	C₂×C₈	—	89	3	no	—
418	C₂×C₈	—	89	6	no	—
419	C₂×C₈	C₂²×D₈₉	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	89	3	no	—
423	C₂³	—	178	3	no	—
424	C₂³	—	178	3	no	—
425	C₂³	—	178	6	no	—
426	C₂³	—	178	3	no	—
427	C₂³	—	712	6	no	—
428	Q₈	—	89	3	no	—
429	Q₈	—	89	3	no	—
430	Q₈	—	89	1	no	—
431	Q₈	—	178	3	no	—
432	Q₈	—	178	1	no	—
433	Q₈	—	178	3	no	—
434	Q₈	D₄×D₈₉	1	1	yes	characteristic
435	Q₈	C₂³×D₈₉	1	1	yes	characteristic
436	Q₈	C₂³×D₈₉	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	2	3	no	—
441	D₄	—	89	6	no	—
442	D₄	—	89	3	no	—
443	D₄	—	89	1	no	—
444	D₄	—	89	3	no	—
445	D₄	—	178	3	no	—
446	D₄	—	178	1	no	—
447	D₄	—	178	3	no	—
448	D₄	—	178	6	no	—
449	D₄	—	178	3	no	—
450	D₄	—	178	3	no	—
451	D₄	—	178	3	no	—
452	D₄	—	178	6	no	—
453	D₄	—	178	3	no	—
454	D₄	—	178	3	no	—
455	D₄	—	178	3	no	—
456	D₄	D₄×D₈₉	1	3	yes	—
457	D₄	C₂³×D₈₉	1	3	yes	—
458	D₄	C₂³×D₈₉	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	89	3	no	—
462	C₂×C₄	—	89	3	no	—
463	C₂×C₄	—	89	3	no	—
464	C₂×C₄	—	89	3	no	—
465	C₂×C₄	—	89	1	no	—
466	C₂×C₄	—	178	1	no	—
467	C₂×C₄	—	178	3	no	—
468	C₂×C₄	—	178	1	no	—
469	C₂×C₄	—	178	3	no	—
470	C₂×C₄	—	178	3	no	—
471	C₂×C₄	—	178	3	no	—
472	C₂×C₄	—	178	6	no	—
473	C₂×C₄	—	178	3	no	—
474	C₂×C₄	—	178	3	no	—
475	C₂×C₄	—	178	3	no	—
476	C₂×C₄	C₂³×D₈₉	1	3	yes	—
477	C₈	—	89	3	no	—
478	C₈	—	89	1	no	—
479	C₈	C₂³×D₈₉	1	3	yes	—
480	C₈	C₂³×D₈₉	1	1	yes	characteristic
481	C₂²	—	2	3	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	8	3	no	—
485	C₂²	—	89	1	no	—
486	C₂²	—	89	3	no	—
487	C₂²	—	356	3	no	—
488	C₂²	—	356	6	no	—
489	C₂²	—	178	1	no	—
490	C₂²	—	178	3	no	—
491	C₂²	—	712	3	no	—
492	C₂²	—	712	6	no	—
493	C₂²	—	712	3	no	—
494	C₂²	C₂×D₄×D₈₉	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	89	1	no	—
498	C₄	—	89	3	no	—
499	C₄	—	178	1	no	—
500	C₄	—	178	3	no	—
501	C₄	C₂×D₄×D₈₉	1	3	yes	—
502	C₄	C₂⁴×D₈₉	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	3	no	—
506	C₂	—	356	3	no	—
507	C₂	—	356	1	no	—
508	C₂	—	178	1	no	—
509	C₂	—	178	3	no	—
510	C₂	C₂²×D₄×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₈₉
commutator, cosocle	C₄×C₈₉	C₂⁵
Frattini	C₄	C₂⁴×D₈₉
Fitting	#576×C₈₉	C₂
socle	C₂×C₈₉	C₂³×D₄
hypercenter	#576	D₈₉
hypocenter	C₈₉	#3585
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #19152433	C₂	semidirect
2. H(5,𝔽₂)×D₈₉	C₂	semidirect
3. #19152410	C₂	semidirect
4. #19152409	C₂	semidirect
5. #19152408	C₂	semidirect
6. #19152405	C₂	semidirect
7. #19152402	C₂	semidirect
8. #19152401	C₂	semidirect
9. #19152399	C₂	semidirect
10. #19152395	C₂	semidirect
11. #19152394	C₂	semidirect
12. C₂×#15668036	C₂	semidirect
13. AGL(1,ℤ/8)×D₈₉	C₂	semidirect
14. #19152363	C₂	semidirect
15. #576×C₈₉	C₂	semidirect
17. #15668059	C₂²	semidirect
18. #15668059	C₂²	semidirect
20. #15668058	C₂²	semidirect
21. #15668058	C₂²	semidirect
24. #15668057	C₂²	semidirect
25. #15668057	C₂²	semidirect
27. C₂×#13083573	C₂²	semidirect
31. #41×D₈₉	C₂²	semidirect
32. #41×D₈₉	C₂²	semidirect
34. C₂×D₄×D₈₉	C₂²	semidirect
35. #15668045	C₂²	semidirect
36. #15668044	C₂²	semidirect
37. #15668044	C₂²	semidirect
38. #15668042	C₂²	semidirect
39. #15668041	C₂²	semidirect
40. #15668041	C₂²	semidirect
41. #15668040	C₂²	semidirect
42. #15668039	C₂²	semidirect
43. #15668039	C₂²	semidirect
44. #15668038	C₂²	semidirect
45. #15668038	C₂²	semidirect
46. #15668037	C₂²	semidirect
47. #15668036	C₂²	semidirect
48. #15668036	C₂²	semidirect
49. #15668036	C₂²	semidirect
50. #15668036	C₂²	semidirect
51. #15668036	C₂²	semidirect
52. #15668034	C₂²	semidirect
53. #15668033	C₂²	semidirect
54. #15668032	C₂²	semidirect
55. #15668032	C₂²	semidirect
56. #15668031	C₂²	semidirect
57. C₂×#13083563	C₂²	semidirect
58. C₂×#13083562	C₂²	semidirect
59. SD₁₆×D₈₉	C₂²	semidirect
60. C₂×#13083559	C₂²	semidirect
61. D₈×D₈₉	C₂²	semidirect
62. #15668020	C₂²	semidirect
63. #15668019	C₂²	semidirect
64. #15668018	C₂²	semidirect
65. C₂×#13083557	C₂²	semidirect
66. M₁₆×D₈₉	C₂²	semidirect
67. H(5,𝔽₂)×C₈₉	C₂²	semidirect
68. H(5,𝔽₂)×C₈₉	C₂²	semidirect
69. AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
70. AGL(1,ℤ/8)×C₈₉	C₂²	semidirect
71. #135×C₈₉	C₂²	semidirect
72. C₂×D₈×C₈₉	C₂²	semidirect
73. #131×C₈₉	C₂²	semidirect
85. #13083574	C₂³	semidirect
97. #13083573	C₂³	semidirect
99. C₂×Dic₁₇₈	C₂³	semidirect
103. Q₈×D₈₉	C₂³	semidirect
121. D₄×D₈₉	C₂³	semidirect
126. Dic₃₅₆	C₂³	semidirect
127. #13083564	C₂³	semidirect
128. #13083564	C₂³	semidirect
129. #13083563	C₂³	semidirect
130. #13083563	C₂³	semidirect
131. #13083563	C₂³	semidirect
132. #13083562	C₂³	semidirect
133. #13083562	C₂³	semidirect
134. #13083562	C₂³	semidirect
135. #13083561	C₂³	semidirect
136. #13083561	C₂³	semidirect
137. D₇₁₂	C₂³	semidirect
138. #13083559	C₂³	semidirect
139. #13083559	C₂³	semidirect
140. #13083559	C₂³	semidirect
141. #13083558	C₂³	semidirect
144. #13083557	C₂³	semidirect
145. #13083557	C₂³	semidirect
146. C₂×#10623494	C₂³	semidirect
147. C₈×D₈₉	C₂³	semidirect
152. #41×C₈₉	C₂³	semidirect
156. C₂×D₄×C₈₉	C₂³	semidirect
157. Q₁₆×C₈₉	C₂³	semidirect
158. SD₁₆×C₈₉	C₂³	semidirect
159. SD₁₆×C₈₉	C₂³	semidirect
160. D₈×C₈₉	C₂³	semidirect
161. D₈×C₈₉	C₂³	semidirect
162. M₁₆×C₈₉	C₂³	semidirect
163. C₂×C₈×C₈₉	C₂³	semidirect
256. C₈₉	#3585	semidirect
266. #576	D₈₉	semidirect
282. H(5,𝔽₂)	C₂×D₈₉	semidirect
283. H(5,𝔽₂)	C₂×D₈₉	semidirect
310. AGL(1,ℤ/8)	C₂×D₈₉	semidirect
311. AGL(1,ℤ/8)	C₂×D₈₉	semidirect
317. #135	C₂×D₈₉	semidirect
323. C₂×D₈	C₂×D₈₉	semidirect
327. #131	C₂×D₈₉	semidirect
358. #41	C₂²×D₈₉	semidirect
386. C₂×D₄	C₂²×D₈₉	semidirect
394. Q₁₆	C₂²×D₈₉	semidirect
403. SD₁₆	C₂²×D₈₉	semidirect
404. SD₁₆	C₂²×D₈₉	semidirect
409. D₈	C₂²×D₈₉	semidirect
410. D₈	C₂²×D₈₉	semidirect
416. M₁₆	C₂²×D₈₉	semidirect
419. C₂×C₈	C₂²×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152433	2
H(5,𝔽₂)×D₈₉	2
#19152410	2
#19152409	2
#19152408	2
#19152405	2
#19152402	2
#19152401	2
#19152399	2
#19152395	2
#19152394	2
C₂×#15668036	2
AGL(1,ℤ/8)×D₈₉	2
#19152363	2
#576×C₈₉	2
#3585	89