Subgroups — #36710897

Order 22784.

738 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152034	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#15667956	C₂	1	1	yes	maximal, characteristic, complemented
3	#26031995	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022516	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022363	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022336	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022307	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022289	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022181	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022173	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022168	C₂	1	1	yes	maximal, characteristic, complemented
12	#26022164	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	D₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668034	C₂²	1	1	yes	characteristic, complemented
17	C₂²×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
18	#19152257	—	2	1	no	—
19	#19152034	—	2	4	no	—
20	C₂×#15667956	—	2	4	no	—
21	C₂×#15667956	C₂²	1	1	yes	characteristic
22	C₂×#15667956	C₂²	1	1	yes	characteristic
23	C₂×#15667956	C₂²	1	1	yes	characteristic, complemented
24	C₂×#15667956	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15667956	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15667956	C₂²	1	1	yes	characteristic, complemented
27	C₂×#15667953	C₂²	1	1	yes	characteristic
28	C₂×#15667953	C₂²	1	1	yes	characteristic, complemented
29	C₂×#15667953	C₂²	1	1	yes	characteristic, complemented
30	C₂×#15667952	C₂²	1	1	yes	characteristic, complemented
31	C₂²×#13083549	C₂²	1	1	yes	characteristic, complemented
32	#19151982	C₂²	1	1	yes	characteristic, complemented
33	#19151839	C₂²	1	1	yes	characteristic, complemented
34	#19151834	C₂²	1	1	yes	characteristic, complemented
35	#19151821	—	2	1	no	—
36	#19151762	—	2	1	no	—
37	#19151739	—	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	#19151401	C₂²	1	1	yes	characteristic, complemented
42	#19151401	C₂²	1	1	yes	characteristic, complemented
43	#19151399	C₂²	1	1	yes	characteristic
44	#19151399	C₂²	1	1	yes	characteristic, complemented
45	#19151399	C₂²	1	1	yes	characteristic, complemented
46	#19151398	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊#13083549	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊#13083549	C₂²	1	1	yes	characteristic, complemented
49	#19151374	C₂²	1	1	yes	characteristic, complemented
50	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
51	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
52	D₄²×C₈₉	—	2	1	no	—
53	#493×C₈₉	C₂²	1	1	yes	characteristic
54	#466×C₈₉	C₂²	1	1	yes	characteristic
55	#466×C₈₉	C₂²	1	1	yes	characteristic
56	#459×C₈₉	—	2	1	no	—
57	#447×C₈₉	—	2	1	no	—
58	#447×C₈₉	—	2	1	no	—
59	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
60	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#13083574	—	2	1	no	—
62	C₂²×Dic₁₇₈	—	2	1	no	—
63	#15668034	—	2	2	no	—
64	#15668034	—	4	1	no	—
65	C₂×Dic₃₅₆	—	2	2	no	—
66	C₂×Dic₃₅₆	—	2	1	no	—
67	C₂×Dic₃₅₆	—	4	1	no	—
68	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
69	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
70	C₂×#13083563	—	2	1	no	—
71	C₂×#13083563	—	2	1	no	—
72	C₂×D₇₁₂	C₂³	1	1	yes	characteristic
73	#15668000	—	2	1	no	—
74	#15667998	—	4	1	no	—
75	#15667991	—	2	1	no	—
76	#15667990	—	4	1	no	—
77	#15667986	—	2	1	no	—
78	#15667984	—	4	1	no	—
79	C₄×Dic₁₇₈	—	2	1	no	—
80	#15667972	—	4	1	no	—
81	#15667956	—	2	2	no	—
82	#15667956	—	2	2	no	—
83	#15667956	—	2	2	no	—
84	#15667956	—	2	2	no	—
85	#15667956	—	4	1	no	—
86	#15667956	D₄	1	4	yes	complemented
87	#15667953	—	2	2	no	—
88	#15667953	—	2	2	no	—
89	#15667953	—	4	1	no	—
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	#15667934	—	2	1	no	—
100	C₂²×D₄×C₈₉	—	2	1	no	—
101	C₂²×D₄×C₈₉	—	2	1	no	—
102	C₂²×D₄×C₈₉	—	4	1	no	—
103	C₂×D₈×C₈₉	—	2	2	no	—
104	C₂×D₈×C₈₉	—	2	2	no	—
105	C₂×D₈×C₈₉	—	2	1	no	—
106	C₂×D₈×C₈₉	—	2	1	no	—
107	C₂×D₈×C₈₉	—	2	1	no	—
108	C₂×D₈×C₈₉	—	4	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	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	#127×C₈₉	—	2	1	no	—
116	#121×C₈₉	—	2	1	no	—
117	#121×C₈₉	—	2	1	no	—
118	#121×C₈₉	—	4	1	no	—
119	#120×C₈₉	—	4	1	no	—
120	#120×C₈₉	—	4	1	no	—
121	C₄×D₄×C₈₉	—	2	1	no	—
122	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
123	#107×C₈₉	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₈₉	D₄	1	1	yes	characteristic
125	#102×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	#13083574	—	4	2	no	—
132	#13083574	—	8	1	no	—
133	C₂×Dic₁₇₈	—	2	1	no	—
134	C₂×Dic₁₇₈	—	2	1	no	—
135	C₂×Dic₁₇₈	—	4	2	no	—
136	C₂×Dic₁₇₈	—	4	1	no	—
137	C₂×Dic₁₇₈	—	8	1	no	—
138	C₂×D₃₅₆	—	2	1	no	—
139	C₂×C₂²⋊D₈₉	—	4	1	no	—
140	C₂×C₂²⋊D₈₉	—	4	1	no	—
141	C₂²×Dic₈₉	—	4	1	no	—
142	C₂×C₄×D₈₉	—	4	1	no	—
143	Dic₃₅₆	—	2	1	no	—
144	Dic₃₅₆	—	2	1	no	—
145	Dic₃₅₆	—	2	1	no	—
146	Dic₃₅₆	—	4	2	no	—
147	Dic₃₅₆	C₂×D₄	1	2	yes	complemented
148	#13083563	—	4	2	no	—
149	#13083563	—	8	1	no	—
150	D₇₁₂	—	2	1	no	—
151	D₇₁₂	—	2	1	no	—
152	C₄⋊Dic₈₉	—	2	1	no	—
153	#13083553	—	4	1	no	—
154	#13083553	—	4	1	no	—
155	C₂²⋊Dic₈₉	—	4	1	no	—
156	#13083551	—	4	1	no	—
157	#13083551	—	4	1	no	—
158	#13083551	—	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	complemented
164	C₂⁴×C₈₉	—	4	1	no	—
165	C₂⁴×C₈₉	—	4	1	no	—
166	C₂×D₄×C₈₉	—	2	1	no	—
167	C₂×D₄×C₈₉	—	2	1	no	—
168	C₂×D₄×C₈₉	—	2	1	no	—
169	C₂×D₄×C₈₉	—	4	2	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	—	4	1	no	—
175	C₂×D₄×C₈₉	—	4	1	no	—
176	C₂×D₄×C₈₉	—	4	1	no	—
177	C₂×D₄×C₈₉	—	8	1	no	—
178	C₂×D₄×C₈₉	—	8	1	no	—
179	C₂×D₄×C₈₉	—	8	4	no	—
180	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	—	4	1	no	—
182	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
184	D₈×C₈₉	—	2	1	no	—
185	D₈×C₈₉	—	2	1	no	—
186	D₈×C₈₉	—	2	1	no	—
187	D₈×C₈₉	—	2	1	no	—
188	D₈×C₈₉	—	2	1	no	—
189	D₈×C₈₉	—	4	2	no	—
190	D₈×C₈₉	—	4	2	no	—
191	D₈×C₈₉	—	8	1	no	—
192	D₈×C₈₉	C₂×D₄	1	2	yes	—
193	C₂×C₈×C₈₉	—	2	1	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₄⋊C₄×C₈₉	D₈	1	1	yes	characteristic
203	C₂²⋊C₄×C₈₉	—	4	1	no	—
204	C₂²⋊C₄×C₈₉	—	4	1	no	—
205	C₂²⋊C₄×C₈₉	—	4	1	no	—
206	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
207	C₂²⋊C₄×C₈₉	D₈	1	1	yes	characteristic
208	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
209	C₂³×C₈₉	—	4	1	no	—
210	C₂³×C₈₉	—	4	1	no	—
211	C₂³×C₈₉	—	4	1	no	—
212	C₂³×C₈₉	—	8	2	no	—
213	C₂³×C₈₉	—	8	2	no	—
214	C₂³×C₈₉	—	8	2	no	—
215	C₂³×C₈₉	—	8	2	no	—
216	C₂³×C₈₉	—	16	1	no	—
217	C₂³×C₈₉	—	16	1	no	—
218	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
219	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
220	C₂²×D₈₉	—	4	1	no	—
221	D₄×C₈₉	—	2	2	no	—
222	D₄×C₈₉	—	2	2	no	—
223	D₄×C₈₉	—	4	1	no	—
224	D₄×C₈₉	—	4	1	no	—
225	D₄×C₈₉	—	4	1	no	—
226	D₄×C₈₉	—	4	1	no	—
227	D₄×C₈₉	—	4	1	no	—
228	D₄×C₈₉	—	8	2	no	—
229	D₄×C₈₉	—	8	2	no	—
230	D₄×C₈₉	—	8	2	no	—
231	D₄×C₈₉	—	8	2	no	—
232	D₄×C₈₉	—	8	2	no	—
233	D₄×C₈₉	—	16	1	no	—
234	C₂×C₄×C₈₉	—	2	1	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	1	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	4	1	no	—
239	C₂×C₄×C₈₉	—	8	2	no	—
240	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
241	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
244	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
245	C₂²⋊D₈₉	—	8	2	no	—
246	C₂²⋊D₈₉	—	8	2	no	—
247	C₂×Dic₈₉	—	4	1	no	—
248	C₂×Dic₈₉	—	4	1	no	—
249	C₂×Dic₈₉	—	4	1	no	—
250	C₂×Dic₈₉	—	8	2	no	—
251	D₃₅₆	—	4	1	no	—
252	D₃₅₆	—	4	1	no	—
253	C₄×D₈₉	—	8	2	no	—
254	Dic₁₇₈	—	2	2	no	—
255	Dic₁₇₈	—	4	1	no	—
256	Dic₁₇₈	—	4	1	no	—
257	Dic₁₇₈	—	4	1	no	—
258	Dic₁₇₈	—	8	2	no	—
259	C₈×C₈₉	—	2	1	no	—
260	C₈×C₈₉	—	2	1	no	—
261	C₈×C₈₉	—	2	1	no	—
262	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂²×C₈₉	—	2	1	no	—
265	C₂²×C₈₉	—	2	1	no	—
266	C₂²×C₈₉	—	2	1	no	—
267	C₂²×C₈₉	—	2	1	no	—
268	C₂²×C₈₉	—	2	1	no	—
269	C₂²×C₈₉	—	4	2	no	—
270	C₂²×C₈₉	—	8	1	no	—
271	C₂²×C₈₉	—	8	1	no	—
272	C₂²×C₈₉	—	8	1	no	—
273	C₂²×C₈₉	—	8	1	no	—
274	C₂²×C₈₉	—	8	1	no	—
275	C₂²×C₈₉	—	8	1	no	—
276	C₂²×C₈₉	—	8	1	no	—
277	C₂²×C₈₉	—	8	1	no	—
278	C₂²×C₈₉	—	16	4	no	—
279	C₂²×C₈₉	—	16	4	no	—
280	C₂²×C₈₉	#509	1	2	yes	complemented
281	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
282	C₂×D₈₉	—	8	1	no	—
283	C₂×D₈₉	—	8	1	no	—
284	C₂×D₈₉	—	8	1	no	—
285	C₄×C₈₉	—	2	1	no	—
286	C₄×C₈₉	—	2	1	no	—
287	C₄×C₈₉	—	2	1	no	—
288	C₄×C₈₉	—	2	1	no	—
289	C₄×C₈₉	—	8	1	no	—
290	C₄×C₈₉	D₄²	1	1	yes	characteristic
291	C₄×C₈₉	#576	1	1	yes	characteristic
292	Dic₈₉	—	4	2	no	—
293	Dic₈₉	—	8	1	no	—
294	Dic₈₉	—	8	1	no	—
295	#33831	—	89	1	no	maximal, Sylow
296	C₂×C₈₉	—	2	2	no	—
297	C₂×C₈₉	—	4	1	no	—
298	C₂×C₈₉	—	8	2	no	—
299	C₂×C₈₉	—	16	1	no	—
300	C₂×C₈₉	—	16	1	no	—
301	C₂×C₈₉	D₄×D₈	1	1	yes	characteristic
302	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
303	C₂×C₈₉	#3416	1	1	yes	characteristic
304	D₈₉	—	16	1	no	—
305	C₂×#509	—	89	1	no	—
306	C₂²×SD₃₂	—	89	1	no	—
307	#3285	—	89	1	no	—
308	D₄×D₈	D₈₉	1	1	yes	characteristic, complemented
309	#2250	—	89	1	no	—
310	#2220	—	89	1	no	—
311	#2215	—	89	1	no	—
312	#2210	—	89	1	no	—
313	#2207	—	89	1	no	—
314	#2187	—	89	1	no	—
315	#2186	—	89	1	no	—
316	#2185	—	89	1	no	—
317	#2184	—	89	1	no	—
318	#2175	—	89	1	no	—
319	#2168	—	89	1	no	—
320	C₈₉	#33831	1	1	yes	characteristic, complemented, Sylow
321	C₂×#135	—	89	1	no	—
322	C₂²×Q₁₆	—	89	1	no	—
323	C₂²×D₈	C₂×D₈₉	1	1	yes	characteristic
324	C₂²×D₈	C₂×D₈₉	1	1	yes	characteristic
325	#548	—	178	1	no	—
326	D₄²	—	2	1	no	—
327	#509	—	178	4	no	—
328	C₂×SD₃₂	—	89	1	no	—
329	C₂×SD₃₂	—	89	1	no	—
330	C₂×SD₃₂	—	89	1	no	—
331	C₂×SD₃₂	—	89	1	no	—
332	C₂×SD₃₂	—	89	1	no	—
333	C₂×SD₃₂	—	89	1	no	—
334	C₂×SD₃₂	—	178	4	no	—
335	C₂×D₁₆	—	89	1	no	—
336	C₂×D₁₆	—	89	1	no	—
337	C₂×D₁₆	—	89	1	no	—
338	C₂×M₃₂	—	89	1	no	—
339	C₂²×C₁₆	—	89	1	no	—
340	#495	—	89	1	no	—
341	#493	C₂×D₈₉	1	1	yes	characteristic
342	#467	—	89	1	no	—
343	#466	—	89	1	no	—
344	#466	C₂×D₈₉	1	1	yes	characteristic
345	#466	C₂×D₈₉	1	1	yes	characteristic
346	#464	—	178	1	no	—
347	#459	—	2	1	no	—
348	#452	—	178	1	no	—
349	#448	—	178	1	no	—
350	#447	—	2	1	no	—
351	#447	—	2	1	no	—
352	C₄×Q₁₆	—	89	1	no	—
353	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
354	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
355	#366	—	89	1	no	—
356	C₄⋊C₁₆	—	89	1	no	—
357	#358	—	89	1	no	—
358	#358	—	89	1	no	—
359	#357	—	89	1	no	—
360	#357	—	89	1	no	—
361	#357	—	89	1	no	—
362	#357	—	89	1	no	—
363	C₂²⋊C₁₆	—	89	1	no	—
364	C₂²⋊C₁₆	—	89	1	no	—
365	#346	—	89	1	no	—
366	C₂×#41	—	178	1	no	—
367	C₂²×Q₈	—	178	1	no	—
368	C₂²×D₄	—	2	1	no	—
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	—	4	1	no	—
371	#135	—	356	1	no	—
372	#135	—	178	2	no	—
373	C₂×Q₁₆	—	89	1	no	—
374	C₂×Q₁₆	—	89	1	no	—
375	C₂×Q₁₆	—	356	1	no	—
376	C₂×Q₁₆	—	178	2	no	—
377	C₂×Q₁₆	—	178	1	no	—
378	C₂×SD₁₆	—	178	1	no	—
379	C₂×SD₁₆	—	178	1	no	—
380	C₂×D₈	—	2	2	no	—
381	C₂×D₈	—	2	2	no	—
382	C₂×D₈	—	2	1	no	—
383	C₂×D₈	—	2	1	no	—
384	C₂×D₈	—	2	1	no	—
385	C₂×D₈	—	4	1	no	—
386	C₂×D₈	—	4	1	no	—
387	C₂×D₈	—	89	1	no	—
388	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
389	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
390	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
391	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
392	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
393	#127	—	2	1	no	—
394	#124	—	356	1	no	—
395	#124	—	178	1	no	—
396	C₂²⋊Q₈	—	356	1	no	—
397	C₂²⋊Q₈	—	178	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	4	1	no	—
401	#121	—	356	1	no	—
402	#121	—	178	1	no	—
403	#120	—	4	1	no	—
404	#120	—	4	1	no	—
405	C₄×Q₈	—	178	1	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	356	1	no	—
408	C₄×D₄	C₂²⋊D₈₉	1	1	yes	characteristic
409	SD₃₂	—	89	4	no	—
410	SD₃₂	—	356	1	no	—
411	SD₃₂	—	178	2	no	—
412	SD₃₂	—	178	2	no	—
413	SD₃₂	—	178	2	no	—
414	SD₃₂	—	178	2	no	—
415	D₁₆	—	356	1	no	—
416	D₁₆	—	178	2	no	—
417	D₁₆	—	178	2	no	—
418	M₃₂	—	178	2	no	—
419	C₂×C₁₆	—	89	1	no	—
420	C₂×C₁₆	—	89	1	no	—
421	C₂×C₁₆	—	89	1	no	—
422	C₂×C₁₆	—	89	1	no	—
423	C₂×C₁₆	—	178	2	no	—
424	#107	—	89	1	no	—
425	#107	C₂²×D₈₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
427	#103	—	178	1	no	—
428	#103	—	178	1	no	—
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	178	1	no	—
433	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
434	C₂²⋊C₈	C₂²⋊D₈₉	1	1	yes	characteristic
435	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
436	C₂⁴	—	4	1	no	—
437	C₂⁴	—	4	1	no	—
438	#41	—	356	2	no	—
439	#41	—	712	1	no	—
440	C₂×Q₈	—	356	2	no	—
441	C₂×Q₈	—	356	1	no	—
442	C₂×Q₈	—	178	1	no	—
443	C₂×Q₈	—	178	1	no	—
444	C₂×Q₈	—	712	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	—	4	1	no	—
456	C₂×D₄	—	8	1	no	—
457	C₂×D₄	—	8	1	no	—
458	C₂×D₄	—	8	4	no	—
459	C₂×D₄	—	356	1	no	—
460	C₂×D₄	—	356	1	no	—
461	C₂×D₄	—	178	1	no	—
462	C₂×D₄	#13083559	1	1	yes	characteristic
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	356	1	no	—
465	C₂²×C₄	—	356	1	no	—
466	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
468	Q₁₆	—	89	2	no	—
469	Q₁₆	—	356	2	no	—
470	Q₁₆	—	178	1	no	—
471	Q₁₆	—	178	1	no	—
472	Q₁₆	—	178	1	no	—
473	SD₁₆	—	356	2	no	—
474	SD₁₆	—	712	1	no	—
475	D₈	—	2	1	no	—
476	D₈	—	2	1	no	—
477	D₈	—	2	1	no	—
478	D₈	—	2	1	no	—
479	D₈	—	2	1	no	—
480	D₈	—	4	2	no	—
481	D₈	—	4	2	no	—
482	D₈	—	8	1	no	—
483	D₈	—	178	1	no	—
484	D₈	—	178	1	no	—
485	D₈	D₄×D₈₉	1	2	yes	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
491	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
492	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
493	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	356	1	no	—
496	C₄⋊C₄	—	356	1	no	—
497	C₄⋊C₄	—	178	1	no	—
498	C₄⋊C₄	#13083559	1	1	yes	characteristic
499	C₂²⋊C₄	—	4	1	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₂²⋊C₄	—	356	1	no	—
503	C₂²⋊C₄	—	356	1	no	—
504	C₂²⋊C₄	—	356	1	no	—
505	C₂²⋊C₄	—	356	1	no	—
506	C₂²⋊C₄	#13083559	1	1	yes	characteristic
507	C₂²⋊C₄	#13083559	1	1	yes	characteristic
508	C₄²	—	356	1	no	—
509	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
510	C₁₆	—	89	2	no	—
511	C₁₆	—	178	1	no	—
512	C₁₆	—	178	1	no	—
513	C₁₆	—	178	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	8	2	no	—
518	C₂³	—	8	2	no	—
519	C₂³	—	8	2	no	—
520	C₂³	—	8	2	no	—
521	C₂³	—	16	1	no	—
522	C₂³	—	16	1	no	—
523	C₂³	—	356	1	no	—
524	C₂³	C₂×#13083559	1	1	yes	characteristic
525	C₂³	C₂×#13083559	1	1	yes	characteristic
526	Q₈	—	356	1	no	—
527	Q₈	—	356	1	no	—
528	Q₈	—	356	1	no	—
529	Q₈	—	178	2	no	—
530	Q₈	—	712	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	2	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	8	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	2	no	—
541	D₄	—	8	2	no	—
542	D₄	—	8	2	no	—
543	D₄	—	16	1	no	—
544	D₄	—	356	1	no	—
545	D₄	—	356	1	no	—
546	D₄	—	712	2	no	—
547	D₄	—	712	2	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	2	no	—
554	C₂×C₄	—	356	1	no	—
555	C₂×C₄	—	356	1	no	—
556	C₂×C₄	—	356	1	no	—
557	C₂×C₄	—	712	2	no	—
558	C₂×C₄	—	712	2	no	—
559	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
560	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
561	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
562	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	2	1	no	—
567	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
568	C₈	#15668057	1	1	yes	characteristic
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	16	4	no	—
584	C₂²	—	16	4	no	—
585	C₂²	—	712	1	no	—
586	C₂²	—	712	1	no	—
587	C₂²	—	712	1	no	—
588	C₂²	#19152034	1	2	yes	complemented
589	C₂²	C₂²×#13083559	1	1	yes	characteristic
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	356	2	no	—
596	C₄	—	712	1	no	—
597	C₄	—	712	1	no	—
598	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
599	C₄	#19152401	1	1	yes	characteristic
600	C₂	—	2	2	no	—
601	C₂	—	4	1	no	—
602	C₂	—	8	2	no	—
603	C₂	—	16	1	no	—
604	C₂	—	16	1	no	—
605	C₂	—	1424	1	no	—
606	C₂	D₄×#13083559	1	1	yes	characteristic
607	C₂	C₂×#19152034	1	1	yes	characteristic
608	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	D₄×D₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
hypercenter	D₄×D₈	D₈₉
hypocenter	C₈₉	#33831
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×D₈

Complements

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

N	H ≅ G/N	type
1. C₂×#19152034	C₂	semidirect
2. C₂²×#15667956	C₂	semidirect
3. #26031995	C₂	semidirect
4. #26022516	C₂	semidirect
5. #26022363	C₂	semidirect
6. #26022336	C₂	semidirect
7. #26022307	C₂	semidirect
8. #26022289	C₂	semidirect
9. #26022181	C₂	semidirect
10. #26022173	C₂	semidirect
11. #26022168	C₂	semidirect
12. #26022164	C₂	semidirect
13. #26022116	C₂	semidirect
14. #26022078	C₂	semidirect
15. D₄×D₈×C₈₉	C₂	semidirect
16. C₂×#15668034	C₂²	semidirect
17. C₂²×Dic₃₅₆	C₂²	semidirect
23. C₂×#15667956	C₂²	semidirect
24. C₂×#15667956	C₂²	semidirect
25. C₂×#15667956	C₂²	semidirect
26. C₂×#15667956	C₂²	semidirect
28. C₂×#15667953	C₂²	semidirect
29. C₂×#15667953	C₂²	semidirect
30. C₂×#15667952	C₂²	semidirect
31. C₂²×#13083549	C₂²	semidirect
32. #19151982	C₂²	semidirect
33. #19151839	C₂²	semidirect
34. #19151834	C₂²	semidirect
38. C₄×Dic₃₅₆	C₂²	semidirect
39. #19151423	C₂²	semidirect
40. C₄⋊#13083549	C₂²	semidirect
41. #19151401	C₂²	semidirect
42. #19151401	C₂²	semidirect
44. #19151399	C₂²	semidirect
45. #19151399	C₂²	semidirect
46. #19151398	C₂²	semidirect
47. C₂²⋊#13083549	C₂²	semidirect
48. C₂²⋊#13083549	C₂²	semidirect
49. #19151374	C₂²	semidirect
86. #15667956	D₄	semidirect
147. Dic₃₅₆	C₂×D₄	semidirect
163. #13083549	C₂×D₄	semidirect
280. C₂²×C₈₉	#509	semidirect
308. D₄×D₈	D₈₉	semidirect
320. C₈₉	#33831	semidirect
588. C₂²	#19152034	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152034	2
C₂²×#15667956	2
#26031995	2
#26022516	2
#26022363	2
#26022336	2
#26022307	2
#26022289	2
#26022181	2
#26022173	2
#26022168	2
#26022164	2
#26022116	2
#26022078	2
D₄×D₈×C₈₉	2
#33831	89