Subgroups — #36710912

Order 22784.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152038	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#15667956	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022524	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022363	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022341	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022311	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022297	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022192	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022185	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022181	C₂	1	1	yes	maximal, characteristic, complemented
12	#26022168	C₂	1	1	yes	maximal, characteristic, complemented
13	#26022116	C₂	1	1	yes	maximal, characteristic, complemented
14	#26022078	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#3280	C₂	1	1	yes	maximal, characteristic
16	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic
17	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
18	D₄×Dic₁₇₈	—	2	1	no	—
19	#19152038	—	2	4	no	—
20	C₂×#15667958	C₂²	1	1	yes	characteristic, complemented
21	C₂×#15667958	C₂²	1	1	yes	characteristic, complemented
22	C₂×#15667958	C₂²	1	1	yes	characteristic, complemented
23	C₂×#15667956	—	2	4	no	—
24	C₂×#15667956	C₂²	1	1	yes	characteristic
25	C₂×#15667956	C₂²	1	1	yes	characteristic
26	C₂×#15667956	C₂²	1	1	yes	characteristic
27	C₂×#15667956	C₂²	1	1	yes	characteristic
28	C₂×#15667956	C₂²	1	1	yes	characteristic
29	C₂×#15667956	C₂²	1	1	yes	characteristic
30	C₂×#15667952	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#13083549	C₂²	1	1	yes	characteristic
32	#19151978	C₂²	1	1	yes	characteristic, complemented
33	#19151839	C₂²	1	1	yes	characteristic
34	#19151839	C₂²	1	1	yes	characteristic, complemented
35	#19151809	—	2	1	no	—
36	#19151756	—	2	1	no	—
37	#19151756	—	2	1	no	—
38	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
39	#19151423	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊#13083549	C₂²	1	1	yes	characteristic, complemented
41	#19151402	C₂²	1	1	yes	characteristic, complemented
42	#19151401	C₂²	1	1	yes	characteristic, complemented
43	#19151401	C₂²	1	1	yes	characteristic, complemented
44	#19151401	C₂²	1	1	yes	characteristic, complemented
45	#19151399	C₂²	1	1	yes	characteristic
46	#19151399	C₂²	1	1	yes	characteristic
47	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
48	C₂²⋊#13083549	C₂²	1	1	yes	characteristic, complemented
49	#19151374	C₂²	1	1	yes	characteristic, complemented
50	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
52	#546×C₈₉	—	2	1	no	—
53	#495×C₈₉	C₂²	1	1	yes	characteristic
54	#467×C₈₉	C₂²	1	1	yes	characteristic
55	#466×C₈₉	C₂²	1	1	yes	characteristic
56	#463×C₈₉	—	2	1	no	—
57	#450×C₈₉	—	2	1	no	—
58	#449×C₈₉	—	2	1	no	—
59	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×Dic₁₇₈	—	2	1	no	—
62	C₂²×Dic₁₇₈	—	2	1	no	—
63	C₂×Dic₃₅₆	—	2	2	no	—
64	C₂×Dic₃₅₆	—	2	2	no	—
65	C₂×Dic₃₅₆	—	2	1	no	—
66	C₂×Dic₃₅₆	—	2	1	no	—
67	C₂×Dic₃₅₆	—	2	1	no	—
68	C₂×Dic₃₅₆	—	4	1	no	—
69	C₂×Dic₃₅₆	—	4	1	no	—
70	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
71	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
72	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
73	#15668012	—	2	1	no	—
74	#15668011	—	4	1	no	—
75	#15667991	—	2	1	no	—
76	#15667991	—	2	1	no	—
77	#15667989	—	4	1	no	—
78	#15667989	—	4	1	no	—
79	C₄×Dic₁₇₈	—	2	1	no	—
80	D₄×Dic₈₉	—	4	1	no	—
81	#15667958	—	2	2	no	—
82	#15667958	—	2	2	no	—
83	#15667958	—	4	1	no	—
84	#15667956	—	2	2	no	—
85	#15667956	—	2	2	no	—
86	#15667956	—	2	2	no	—
87	#15667956	—	2	2	no	—
88	#15667956	—	4	1	no	—
89	#15667956	D₄	1	4	yes	complemented
90	#15667952	—	2	2	no	—
91	C₂×#13083549	—	2	2	no	—
92	C₂×#13083549	C₂³	1	1	yes	characteristic
93	C₂×#13083549	C₂³	1	1	yes	characteristic
94	C₂×#13083549	C₂³	1	1	yes	characteristic
95	C₂×#13083549	C₂³	1	1	yes	characteristic
96	#15667946	C₂³	1	1	yes	characteristic
97	#15667937	—	2	1	no	—
98	#15667937	—	2	1	no	—
99	#15667937	—	2	1	no	—
100	C₂×#41×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	#135×C₈₉	—	2	2	no	—
103	#135×C₈₉	—	4	1	no	—
104	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×SD₁₆×C₈₉	—	2	1	no	—
106	C₂×SD₁₆×C₈₉	—	2	1	no	—
107	C₂×D₈×C₈₉	—	2	2	no	—
108	C₂×D₈×C₈₉	—	2	1	no	—
109	C₂×D₈×C₈₉	—	4	1	no	—
110	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	#124×C₈₉	—	2	1	no	—
115	#123×C₈₉	—	4	1	no	—
116	C₂²⋊Q₈×C₈₉	—	2	1	no	—
117	#121×C₈₉	—	2	1	no	—
118	#121×C₈₉	—	4	1	no	—
119	#120×C₈₉	—	4	1	no	—
120	C₄×D₄×C₈₉	—	2	1	no	—
121	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
123	#107×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
125	#103×C₈₉	—	2	1	no	—
126	#102×C₈₉	—	2	1	no	—
127	#102×C₈₉	—	2	1	no	—
128	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
129	C₂²⋊C₈×C₈₉	D₄	1	1	yes	characteristic
130	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₇₈	—	2	1	no	—
132	C₂×Dic₁₇₈	—	2	1	no	—
133	C₂×Dic₁₇₈	—	2	1	no	—
134	C₂×Dic₁₇₈	—	4	2	no	—
135	C₂×Dic₁₇₈	—	4	2	no	—
136	C₂×Dic₁₇₈	—	4	1	no	—
137	C₂×Dic₁₇₈	—	4	1	no	—
138	C₂×Dic₁₇₈	—	8	1	no	—
139	C₂×Dic₁₇₈	—	8	1	no	—
140	C₂²×Dic₈₉	—	4	1	no	—
141	C₂²×Dic₈₉	—	4	1	no	—
142	Dic₃₅₆	—	2	1	no	—
143	Dic₃₅₆	—	2	1	no	—
144	Dic₃₅₆	—	2	1	no	—
145	Dic₃₅₆	—	2	1	no	—
146	Dic₃₅₆	—	2	1	no	—
147	Dic₃₅₆	—	4	2	no	—
148	Dic₃₅₆	—	4	2	no	—
149	Dic₃₅₆	—	8	1	no	—
150	Dic₃₅₆	C₂×D₄	1	2	yes	—
151	C₄⋊Dic₈₉	—	2	1	no	—
152	C₄⋊Dic₈₉	—	4	1	no	—
153	C₄⋊Dic₈₉	—	4	1	no	—
154	#13083553	—	4	1	no	—
155	#13083553	—	4	1	no	—
156	#13083553	—	4	1	no	—
157	C₂²⋊Dic₈₉	—	4	1	no	—
158	C₂²⋊Dic₈₉	—	4	1	no	—
159	C₄×Dic₈₉	—	4	1	no	—
160	#13083549	—	2	1	no	—
161	#13083549	—	2	1	no	—
162	#13083549	—	2	1	no	—
163	#13083549	C₂×D₄	1	2	yes	—
164	C₂⁴×C₈₉	—	4	1	no	—
165	#41×C₈₉	—	4	2	no	—
166	#41×C₈₉	—	8	1	no	—
167	C₂×Q₈×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	4	2	no	—
171	C₂×D₄×C₈₉	—	4	1	no	—
172	C₂×D₄×C₈₉	—	4	1	no	—
173	C₂×D₄×C₈₉	—	4	1	no	—
174	C₂×D₄×C₈₉	—	8	1	no	—
175	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	—	4	1	no	—
177	C₂²×C₄×C₈₉	—	4	1	no	—
178	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
180	Q₁₆×C₈₉	—	2	1	no	—
181	Q₁₆×C₈₉	—	2	1	no	—
182	SD₁₆×C₈₉	—	4	2	no	—
183	SD₁₆×C₈₉	—	8	1	no	—
184	D₈×C₈₉	—	2	1	no	—
185	D₈×C₈₉	—	2	1	no	—
186	D₈×C₈₉	—	2	1	no	—
187	D₈×C₈₉	—	4	2	no	—
188	D₈×C₈₉	C₂×D₄	1	2	yes	—
189	C₂×C₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	—	2	1	no	—
193	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄⋊C₄×C₈₉	—	4	1	no	—
199	C₄⋊C₄×C₈₉	D₈	1	1	yes	characteristic
200	C₂²⋊C₄×C₈₉	—	4	1	no	—
201	C₂²⋊C₄×C₈₉	—	4	1	no	—
202	C₂²⋊C₄×C₈₉	—	4	1	no	—
203	C₂²⋊C₄×C₈₉	—	4	1	no	—
204	C₂²⋊C₄×C₈₉	—	4	1	no	—
205	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
206	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
207	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
208	C₂³×C₈₉	—	4	1	no	—
209	C₂³×C₈₉	—	4	1	no	—
210	C₂³×C₈₉	—	8	2	no	—
211	C₂³×C₈₉	—	8	2	no	—
212	C₂³×C₈₉	—	16	1	no	—
213	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
214	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
215	Q₈×C₈₉	—	4	1	no	—
216	Q₈×C₈₉	—	4	1	no	—
217	D₄×C₈₉	—	2	2	no	—
218	D₄×C₈₉	—	2	2	no	—
219	D₄×C₈₉	—	4	1	no	—
220	D₄×C₈₉	—	4	1	no	—
221	D₄×C₈₉	—	4	1	no	—
222	D₄×C₈₉	—	8	2	no	—
223	D₄×C₈₉	—	8	2	no	—
224	D₄×C₈₉	—	16	1	no	—
225	C₂×C₄×C₈₉	—	2	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	1	no	—
228	C₂×C₄×C₈₉	—	2	1	no	—
229	C₂×C₄×C₈₉	—	4	1	no	—
230	C₂×C₄×C₈₉	—	4	1	no	—
231	C₂×C₄×C₈₉	—	8	2	no	—
232	C₂×C₄×C₈₉	—	16	1	no	—
233	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
234	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×Dic₈₉	—	4	1	no	—
239	C₂×Dic₈₉	—	4	1	no	—
240	C₂×Dic₈₉	—	4	1	no	—
241	C₂×Dic₈₉	—	4	1	no	—
242	C₂×Dic₈₉	—	8	2	no	—
243	C₂×Dic₈₉	—	8	2	no	—
244	Dic₁₇₈	—	2	2	no	—
245	Dic₁₇₈	—	4	1	no	—
246	Dic₁₇₈	—	4	1	no	—
247	Dic₁₇₈	—	4	1	no	—
248	Dic₁₇₈	—	4	1	no	—
249	Dic₁₇₈	—	4	1	no	—
250	Dic₁₇₈	—	8	2	no	—
251	Dic₁₇₈	—	8	2	no	—
252	C₈×C₈₉	—	2	1	no	—
253	C₈×C₈₉	—	2	1	no	—
254	C₈×C₈₉	—	2	1	no	—
255	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂²×C₈₉	—	2	1	no	—
258	C₂²×C₈₉	—	2	1	no	—
259	C₂²×C₈₉	—	2	1	no	—
260	C₂²×C₈₉	—	2	1	no	—
261	C₂²×C₈₉	—	2	1	no	—
262	C₂²×C₈₉	—	4	2	no	—
263	C₂²×C₈₉	—	8	1	no	—
264	C₂²×C₈₉	—	8	1	no	—
265	C₂²×C₈₉	—	8	1	no	—
266	C₂²×C₈₉	—	8	1	no	—
267	C₂²×C₈₉	—	8	1	no	—
268	C₂²×C₈₉	—	16	4	no	—
269	C₂²×C₈₉	#510	1	2	yes	complemented
270	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	2	1	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	—	2	1	no	—
275	C₄×C₈₉	—	8	1	no	—
276	C₄×C₈₉	—	8	1	no	—
277	C₄×C₈₉	D₄²	1	1	yes	characteristic
278	C₄×C₈₉	#576	1	1	yes	characteristic
279	Dic₈₉	—	4	2	no	—
280	Dic₈₉	—	8	1	no	—
281	Dic₈₉	—	8	1	no	—
282	Dic₈₉	—	8	1	no	—
283	#33832	—	89	1	no	maximal, Sylow
284	C₂×C₈₉	—	2	2	no	—
285	C₂×C₈₉	—	4	1	no	—
286	C₂×C₈₉	—	8	2	no	—
287	C₂×C₈₉	—	16	1	no	—
288	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
289	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
290	C₂×C₈₉	#3416	1	1	yes	characteristic
291	C₂×#510	—	89	1	no	—
292	C₂²×SD₃₂	—	89	1	no	—
293	D₄×Q₁₆	—	89	1	no	—
294	#3280	D₈₉	1	1	yes	characteristic
295	#2251	—	89	1	no	—
296	#2220	—	89	1	no	—
297	#2216	—	89	1	no	—
298	#2211	—	89	1	no	—
299	#2208	—	89	1	no	—
300	#2189	—	89	1	no	—
301	#2188	—	89	1	no	—
302	#2187	—	89	1	no	—
303	#2185	—	89	1	no	—
304	#2175	—	89	1	no	—
305	#2168	—	89	1	no	—
306	C₈₉	#33832	1	1	yes	characteristic, complemented, Sylow
307	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
308	C₂²×Q₁₆	—	89	1	no	—
309	C₂²×Q₁₆	—	89	1	no	—
310	C₂²×D₈	C₂×D₈₉	1	1	yes	characteristic
311	D₄×Q₈	—	178	1	no	—
312	#546	—	2	1	no	—
313	#510	—	178	4	no	—
314	C₂×Q₃₂	—	89	1	no	—
315	C₂×Q₃₂	—	89	1	no	—
316	C₂×Q₃₂	—	89	1	no	—
317	C₂×SD₃₂	—	89	1	no	—
318	C₂×SD₃₂	—	89	1	no	—
319	C₂×SD₃₂	—	89	1	no	—
320	C₂×SD₃₂	—	89	1	no	—
321	C₂×SD₃₂	—	89	1	no	—
322	C₂×SD₃₂	—	89	1	no	—
323	C₂×SD₃₂	—	178	4	no	—
324	C₂×M₃₂	—	89	1	no	—
325	C₂²×C₁₆	—	89	1	no	—
326	#495	C₂×D₈₉	1	1	yes	characteristic
327	#494	—	89	1	no	—
328	#467	—	89	1	no	—
329	#467	—	89	1	no	—
330	#467	C₂×D₈₉	1	1	yes	characteristic
331	#466	C₂×D₈₉	1	1	yes	characteristic
332	#463	—	2	1	no	—
333	#462	—	178	1	no	—
334	#451	—	178	1	no	—
335	#451	—	178	1	no	—
336	#450	—	2	1	no	—
337	#449	—	2	1	no	—
338	C₄×Q₁₆	—	89	1	no	—
339	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
340	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
341	#366	—	89	1	no	—
342	C₄⋊C₁₆	—	89	1	no	—
343	#358	—	89	1	no	—
344	#358	—	89	1	no	—
345	#358	—	89	1	no	—
346	#358	—	89	1	no	—
347	#357	—	89	1	no	—
348	#357	—	89	1	no	—
349	C₂²⋊C₁₆	—	89	1	no	—
350	C₂²⋊C₁₆	—	89	1	no	—
351	#346	—	89	1	no	—
352	C₂×#41	—	2	1	no	—
353	C₂²×Q₈	—	178	1	no	—
354	C₂²×Q₈	—	178	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	#135	—	2	2	no	—
357	#135	—	4	1	no	—
358	C₂×Q₁₆	—	89	1	no	—
359	C₂×Q₁₆	—	89	1	no	—
360	C₂×Q₁₆	—	89	1	no	—
361	C₂×Q₁₆	—	356	1	no	—
362	C₂×Q₁₆	—	356	1	no	—
363	C₂×Q₁₆	—	178	2	no	—
364	C₂×Q₁₆	—	178	2	no	—
365	C₂×Q₁₆	—	178	1	no	—
366	C₂×Q₁₆	—	178	1	no	—
367	C₂×Q₁₆	—	178	1	no	—
368	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
369	C₂×SD₁₆	—	2	1	no	—
370	C₂×SD₁₆	—	2	1	no	—
371	C₂×D₈	—	2	2	no	—
372	C₂×D₈	—	2	1	no	—
373	C₂×D₈	—	4	1	no	—
374	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
375	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
376	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
377	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄⋊Q₈	—	356	1	no	—
379	C₄⋊Q₈	—	178	1	no	—
380	#124	—	2	1	no	—
381	#123	—	4	1	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	—	356	1	no	—
384	C₂²⋊Q₈	—	356	1	no	—
385	C₂²⋊Q₈	—	178	1	no	—
386	C₂²⋊Q₈	—	178	1	no	—
387	#121	—	2	1	no	—
388	#121	—	4	1	no	—
389	#120	—	4	1	no	—
390	C₄×Q₈	—	178	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	356	1	no	—
393	C₄×D₄	C₂²⋊D₈₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	4	1	no	—
395	Q₃₂	—	356	1	no	—
396	Q₃₂	—	178	2	no	—
397	Q₃₂	—	178	2	no	—
398	SD₃₂	—	89	4	no	—
399	SD₃₂	—	356	1	no	—
400	SD₃₂	—	178	2	no	—
401	SD₃₂	—	178	2	no	—
402	SD₃₂	—	178	2	no	—
403	SD₃₂	—	178	2	no	—
404	M₃₂	—	178	2	no	—
405	C₂×C₁₆	—	89	1	no	—
406	C₂×C₁₆	—	89	1	no	—
407	C₂×C₁₆	—	89	1	no	—
408	C₂×C₁₆	—	89	1	no	—
409	C₂×C₁₆	—	178	2	no	—
410	#107	—	89	1	no	—
411	#107	C₂²×D₈₉	1	1	yes	characteristic
412	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
413	#103	—	2	1	no	—
414	#103	—	178	1	no	—
415	#103	—	178	1	no	—
416	#103	—	178	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
420	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
421	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
422	C₂⁴	—	4	1	no	—
423	#41	—	4	2	no	—
424	#41	—	8	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	356	2	no	—
427	C₂×Q₈	—	356	2	no	—
428	C₂×Q₈	—	356	1	no	—
429	C₂×Q₈	—	356	1	no	—
430	C₂×Q₈	—	178	1	no	—
431	C₂×Q₈	—	178	1	no	—
432	C₂×Q₈	—	178	1	no	—
433	C₂×Q₈	—	712	1	no	—
434	C₂×Q₈	—	712	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	4	2	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	8	1	no	—
442	C₂×D₄	#13083559	1	1	yes	characteristic
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	356	1	no	—
446	C₂²×C₄	—	356	1	no	—
447	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
449	Q₁₆	—	2	1	no	—
450	Q₁₆	—	2	1	no	—
451	Q₁₆	—	89	2	no	—
452	Q₁₆	—	356	2	no	—
453	Q₁₆	—	356	2	no	—
454	Q₁₆	—	178	1	no	—
455	Q₁₆	—	178	1	no	—
456	Q₁₆	—	178	1	no	—
457	Q₁₆	—	178	1	no	—
458	Q₁₆	—	178	1	no	—
459	Q₁₆	—	712	1	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	8	1	no	—
462	D₈	—	2	1	no	—
463	D₈	—	2	1	no	—
464	D₈	—	2	1	no	—
465	D₈	—	4	2	no	—
466	D₈	D₄×D₈₉	1	2	yes	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
473	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
474	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	—	356	1	no	—
478	C₄⋊C₄	—	356	1	no	—
479	C₄⋊C₄	—	356	1	no	—
480	C₄⋊C₄	—	356	1	no	—
481	C₄⋊C₄	—	356	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₄⋊C₄	#13083559	1	1	yes	characteristic
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	356	1	no	—
490	C₂²⋊C₄	—	356	1	no	—
491	C₂²⋊C₄	#13083559	1	1	yes	characteristic
492	C₂²⋊C₄	#13083559	1	1	yes	characteristic
493	C₄²	—	356	1	no	—
494	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
495	C₁₆	—	89	2	no	—
496	C₁₆	—	178	1	no	—
497	C₁₆	—	178	1	no	—
498	C₁₆	—	178	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	16	1	no	—
504	C₂³	C₂×#13083559	1	1	yes	characteristic
505	C₂³	C₂×#13083559	1	1	yes	characteristic
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	356	1	no	—
509	Q₈	—	356	1	no	—
510	Q₈	—	356	1	no	—
511	Q₈	—	356	1	no	—
512	Q₈	—	356	1	no	—
513	Q₈	—	178	2	no	—
514	Q₈	—	712	2	no	—
515	Q₈	—	712	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	2	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	16	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	16	1	no	—
532	C₂×C₄	—	356	1	no	—
533	C₂×C₄	—	356	1	no	—
534	C₂×C₄	—	356	1	no	—
535	C₂×C₄	—	356	1	no	—
536	C₂×C₄	—	712	2	no	—
537	C₂×C₄	—	712	2	no	—
538	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
539	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
540	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
541	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
542	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
547	C₈	#15668057	1	1	yes	characteristic
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	—	16	4	no	—
560	C₂²	#19152038	1	2	yes	complemented
561	C₂²	C₂²×#13083559	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	356	2	no	—
569	C₄	—	712	1	no	—
570	C₄	—	712	1	no	—
571	C₄	—	712	1	no	—
572	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
573	C₄	#19152401	1	1	yes	characteristic
574	C₂	—	2	2	no	—
575	C₂	—	4	1	no	—
576	C₂	—	8	2	no	—
577	C₂	—	16	1	no	—
578	C₂	D₄×#13083559	1	1	yes	characteristic
579	C₂	C₂×#19152038	1	1	yes	characteristic
580	C₂	#26033399	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#13083559
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3280	C₂
socle	C₂²×C₈₉	C₂²×D₈
hypercenter	#3280	D₈₉
hypocenter	C₈₉	#33832
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ #3280

Complements

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

N	H ≅ G/N	type
1. C₂×#19152038	C₂	semidirect
2. C₂²×#15667956	C₂	semidirect
3. D₄×Dic₃₅₆	C₂	semidirect
4. #26022524	C₂	semidirect
5. #26022363	C₂	semidirect
6. #26022341	C₂	semidirect
7. #26022311	C₂	semidirect
8. #26022297	C₂	semidirect
9. #26022192	C₂	semidirect
10. #26022185	C₂	semidirect
11. #26022181	C₂	semidirect
12. #26022168	C₂	semidirect
13. #26022116	C₂	semidirect
14. #26022078	C₂	semidirect
17. C₂²×Dic₃₅₆	C₂²	semidirect
20. C₂×#15667958	C₂²	semidirect
21. C₂×#15667958	C₂²	semidirect
22. C₂×#15667958	C₂²	semidirect
30. C₂×#15667952	C₂²	semidirect
32. #19151978	C₂²	semidirect
34. #19151839	C₂²	semidirect
38. C₄×Dic₃₅₆	C₂²	semidirect
39. #19151423	C₂²	semidirect
40. C₄⋊#13083549	C₂²	semidirect
41. #19151402	C₂²	semidirect
42. #19151401	C₂²	semidirect
43. #19151401	C₂²	semidirect
44. #19151401	C₂²	semidirect
48. C₂²⋊#13083549	C₂²	semidirect
49. #19151374	C₂²	semidirect
89. #15667956	D₄	semidirect
269. C₂²×C₈₉	#510	semidirect
306. C₈₉	#33832	semidirect
560. C₂²	#19152038	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152038	2
C₂²×#15667956	2
D₄×Dic₃₅₆	2
#26022524	2
#26022363	2
#26022341	2
#26022311	2
#26022297	2
#26022192	2
#26022185	2
#26022181	2
#26022168	2
#26022116	2
#26022078	2
C₈₉×#3280	2
#33832	89