Subgroups — #36561257

Order 22784.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029858	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151712	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028956	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021142	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021004	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020957	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020953	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020695	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020292	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020130	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020097	C₂	1	1	yes	maximal, characteristic, complemented
14	#26020093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668032	C₂²	1	1	yes	characteristic
17	C₂×#15668020	C₂²	1	1	yes	characteristic
18	C₂×#15668019	C₂²	1	1	yes	characteristic
19	C₂²×#13083558	C₂²	1	1	yes	characteristic
20	C₂²×#13083558	C₂²	1	1	yes	characteristic
21	#19152109	C₂²	1	1	yes	characteristic
22	#19151854	C₄	1	2	yes	complemented
23	#19151849	C₄	1	2	yes	complemented
24	#19151846	C₄	1	2	yes	complemented
25	#19151842	C₄	1	2	yes	complemented
26	#19151712	—	2	4	no	—
27	#19151676	—	2	2	no	—
28	#19151673	—	2	2	no	—
29	#19151672	—	2	2	no	—
30	#19151670	—	2	2	no	—
31	C₂×#15667947	C₂²	1	1	yes	characteristic
32	C₂×#15667947	C₂²	1	1	yes	characteristic
33	#19151634	C₂²	1	1	yes	characteristic
34	#19151626	C₂²	1	1	yes	characteristic
35	#19151625	C₂²	1	1	yes	characteristic
36	C₂×#15667940	C₂²	1	1	yes	characteristic
37	C₂×#15667940	C₂²	1	1	yes	characteristic
38	#19151594	C₂²	1	1	yes	characteristic
39	#19151592	C₂²	1	1	yes	characteristic
40	#19151566	C₂²	1	1	yes	characteristic
41	#19151565	C₂²	1	1	yes	characteristic
42	#19151562	C₂²	1	1	yes	characteristic
43	#19151556	C₂²	1	1	yes	characteristic
44	#19151554	C₂²	1	1	yes	characteristic
45	C₄×#13083558	—	2	4	no	—
46	C₂×#15667923	C₂²	1	1	yes	characteristic
47	C₂×#15667923	C₂²	1	1	yes	characteristic
48	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
49	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
50	#19151362	C₂²	1	1	yes	characteristic
51	#19151362	C₂²	1	1	yes	characteristic
52	#19151358	C₂²	1	1	yes	characteristic
53	#19151358	C₂²	1	1	yes	characteristic
54	#525×C₈₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
58	#407×C₈₉	C₂²	1	1	yes	characteristic
59	#339×C₈₉	C₂²	1	1	yes	characteristic
60	#339×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×#13083574	C₂³	1	1	yes	characteristic
62	#15668032	—	2	2	no	—
63	#15668032	—	2	2	no	—
64	C₂×#13083564	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#13083562	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×#13083561	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#13083559	C₂×C₄	1	1	yes	characteristic, complemented
68	#15668020	—	2	2	no	—
69	#15668020	—	2	2	no	—
70	#15668019	—	2	2	no	—
71	#15668019	—	2	2	no	—
72	C₂×#13083558	—	2	2	no	—
73	C₂×#13083558	—	2	2	no	—
74	C₂×#13083558	—	2	1	no	—
75	C₂×#13083558	—	2	2	no	—
76	C₂×#13083558	—	2	2	no	—
77	C₂×#13083558	C₂×C₄	1	2	yes	—
78	C₂×#13083558	C₂×C₄	1	2	yes	—
79	C₂×#13083558	D₄	1	2	yes	—
80	C₂×#13083558	D₄	1	2	yes	—
81	C₂×#13083558	C₂³	1	1	yes	characteristic
82	C₂×#13083558	C₂³	1	1	yes	characteristic
83	C₂×#13083557	—	2	1	no	—
84	C₂²×#10623494	—	2	1	no	—
85	C₂²×#10623494	C₂³	1	1	yes	characteristic
86	C₂²×#10623494	C₂³	1	1	yes	characteristic
87	C₂²×#10623494	C₂³	1	1	yes	characteristic
88	C₂²×#10623494	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₈₉	—	2	1	no	—
90	#15667995	—	2	1	no	—
91	#15667991	C₂×C₄	1	2	yes	—
92	#15667986	C₂×C₄	1	2	yes	—
93	#15667981	—	2	1	no	—
94	C₄×C₂²⋊D₈₉	—	2	2	no	—
95	#15667971	C₂³	1	1	yes	characteristic
96	#15667947	—	2	2	no	—
97	#15667947	—	2	2	no	—
98	#15667945	C₂×C₄	1	2	yes	complemented
99	#15667943	C₂×C₄	1	2	yes	complemented
100	C₄⋊#10623494	—	2	2	no	—
101	#15667941	—	2	2	no	—
102	#15667940	—	2	2	no	—
103	#15667940	—	2	2	no	—
104	#15667936	C₂×C₄	1	2	yes	complemented
105	#15667935	C₂×C₄	1	2	yes	complemented
106	#15667933	C₂×C₄	1	2	yes	complemented
107	#15667932	C₂×C₄	1	2	yes	complemented
108	C₂²⋊#10623494	—	2	2	no	—
109	C₂²⋊#10623494	—	2	2	no	—
110	#15667924	—	2	2	no	—
111	#15667923	—	2	1	no	—
112	#15667923	—	2	2	no	—
113	#15667923	—	2	2	no	—
114	#15667922	—	2	1	no	—
115	C₄×#10623494	—	2	1	no	—
116	C₄×#10623494	—	2	2	no	—
117	C₄×#10623494	D₄	1	4	yes	complemented
118	C₈×Dic₈₉	—	2	1	no	—
119	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₈₉	—	2	1	no	—
121	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
124	#123×C₈₉	—	2	1	no	—
125	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
126	#121×C₈₉	C₂×C₄	1	2	yes	—
127	#120×C₈₉	—	2	1	no	—
128	C₄×D₄×C₈₉	—	2	2	no	—
129	#117×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	—	2	1	no	—
131	C₂×C₄²×C₈₉	—	2	2	no	—
132	C₂×C₄²×C₈₉	—	2	2	no	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	#104×C₈₉	—	2	2	no	—
136	#104×C₈₉	—	2	2	no	—
137	C₂²⋊C₈×C₈₉	—	2	2	no	—
138	#13083574	—	2	1	no	—
139	#13083574	—	2	1	no	—
140	#13083574	—	2	1	no	—
141	#13083574	—	2	1	no	—
142	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊D₈₉	—	2	1	no	—
145	C₂×C₂²⋊D₈₉	—	2	2	no	—
146	C₂×C₄×D₈₉	—	2	1	no	—
147	#13083564	—	2	2	no	—
148	#13083562	—	2	2	no	—
149	#13083561	—	2	2	no	—
150	#13083559	—	2	2	no	—
151	#13083558	—	2	4	no	—
152	#13083558	—	2	4	no	—
153	#13083558	—	2	4	no	—
154	#13083558	—	2	4	no	—
155	#13083558	—	2	1	no	—
156	#13083558	—	2	1	no	—
157	#13083558	—	2	1	no	—
158	#13083558	—	2	1	no	—
159	#13083558	—	4	2	no	—
160	#13083557	—	4	2	no	—
161	C₂×#10623494	—	2	1	no	—
162	C₂×#10623494	—	2	1	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	—	2	1	no	—
167	C₂×#10623494	—	4	2	no	—
168	C₂×#10623494	C₂²×C₄	1	2	yes	—
169	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
170	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
171	C₂×#10623494	C₂×D₄	1	2	yes	—
172	C₂×#10623494	C₂×D₄	1	2	yes	—
173	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
174	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
175	C₂×#10623494	C₂×D₄	1	2	yes	—
176	C₂×#10623494	#41	1	2	yes	—
177	C₂×#10623494	#41	1	2	yes	—
178	C₈×D₈₉	—	4	2	no	—
179	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
180	#13083553	—	2	2	no	—
181	C₂²⋊Dic₈₉	—	2	2	no	—
182	C₂²⋊Dic₈₉	—	2	1	no	—
183	#13083551	—	2	2	no	—
184	C₄×Dic₈₉	—	2	1	no	—
185	C₂⁴×C₈₉	#41	1	1	yes	characteristic
186	#41×C₈₉	—	2	1	no	—
187	#41×C₈₉	—	2	1	no	—
188	#41×C₈₉	—	2	1	no	—
189	#41×C₈₉	—	2	1	no	—
190	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	C₂²×C₄×C₈₉	—	2	1	no	—
196	C₂²×C₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	2	1	no	—
198	C₂²×C₄×C₈₉	—	2	1	no	—
199	C₂²×C₄×C₈₉	—	2	4	no	—
200	C₂²×C₄×C₈₉	—	2	1	no	—
201	C₂²×C₄×C₈₉	—	2	1	no	—
202	C₂²×C₄×C₈₉	—	4	4	no	—
203	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
207	M₁₆×C₈₉	—	2	1	no	—
208	M₁₆×C₈₉	—	2	1	no	—
209	M₁₆×C₈₉	—	2	1	no	—
210	M₁₆×C₈₉	—	2	1	no	—
211	C₂×C₈×C₈₉	—	2	1	no	—
212	C₂×C₈×C₈₉	—	2	1	no	—
213	C₄⋊C₄×C₈₉	—	2	2	no	—
214	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
215	C₂²⋊C₄×C₈₉	—	2	2	no	—
216	C₂²⋊C₄×C₈₉	—	2	1	no	—
217	C₂²⋊C₄×C₈₉	—	2	2	no	—
218	C₄²×C₈₉	—	2	4	no	—
219	C₄²×C₈₉	—	2	1	no	—
220	C₄²×C₈₉	—	2	1	no	—
221	C₄²×C₈₉	—	2	1	no	—
222	C₄²×C₈₉	C₂×D₄	1	2	yes	—
223	C₄²×C₈₉	#41	1	2	yes	—
224	C₂³×C₈₉	—	2	1	no	—
225	C₂³×C₈₉	—	2	1	no	—
226	C₂³×C₈₉	—	2	1	no	—
227	C₂³×C₈₉	—	4	2	no	—
228	C₂³×C₈₉	C₄×D₄	1	2	yes	—
229	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
230	C₂²×D₈₉	—	2	1	no	—
231	Q₈×C₈₉	—	2	1	no	—
232	Q₈×C₈₉	—	2	1	no	—
233	D₄×C₈₉	—	2	1	no	—
234	D₄×C₈₉	—	2	1	no	—
235	D₄×C₈₉	—	4	1	no	—
236	D₄×C₈₉	—	4	1	no	—
237	D₄×C₈₉	—	8	2	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	1	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	1	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	1	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	4	8	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	—	4	1	no	—
252	C₂×C₄×C₈₉	—	4	1	no	—
253	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₈₉	—	4	1	no	—
261	C₂²⋊D₈₉	—	4	1	no	—
262	C₂²⋊D₈₉	—	8	2	no	—
263	C₂×Dic₈₉	—	2	2	no	—
264	C₂×Dic₈₉	—	2	1	no	—
265	D₃₅₆	—	2	1	no	—
266	D₃₅₆	—	2	1	no	—
267	C₄×D₈₉	—	4	1	no	—
268	C₄×D₈₉	—	4	1	no	—
269	Dic₁₇₈	—	2	1	no	—
270	Dic₁₇₈	—	2	1	no	—
271	C₈×C₈₉	—	4	1	no	—
272	C₈×C₈₉	—	4	1	no	—
273	#10623494	—	2	2	no	—
274	#10623494	—	2	2	no	—
275	#10623494	—	4	1	no	—
276	#10623494	—	4	1	no	—
277	#10623494	C₄×D₄	1	2	yes	—
278	#10623494	C₄×D₄	1	2	yes	—
279	#10623494	#121	1	2	yes	—
280	#10623494	#121	1	2	yes	—
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	—	2	2	no	—
283	C₂²×C₈₉	—	2	2	no	—
284	C₂²×C₈₉	—	2	2	no	—
285	C₂²×C₈₉	—	4	2	no	—
286	C₂²×C₈₉	—	4	2	no	—
287	C₂²×C₈₉	—	4	2	no	—
288	C₂²×C₈₉	—	4	1	no	—
289	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₈₉	#525	1	1	yes	characteristic
291	C₂²×C₈₉	#529	1	1	yes	characteristic
292	C₂×D₈₉	—	4	2	no	—
293	C₂×D₈₉	—	4	1	no	—
294	C₄×C₈₉	—	2	4	no	—
295	C₄×C₈₉	—	2	2	no	—
296	C₄×C₈₉	—	4	2	no	—
297	C₄×C₈₉	—	4	2	no	—
298	C₄×C₈₉	—	4	1	no	—
299	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
300	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
301	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
302	C₄×C₈₉	#532	1	1	yes	characteristic
303	Dic₈₉	—	4	2	no	—
304	Dic₈₉	—	4	1	no	—
305	#21549	—	89	1	no	maximal, Sylow
306	C₂×C₈₉	—	2	1	no	—
307	C₂×C₈₉	—	2	1	no	—
308	C₂×C₈₉	—	4	2	no	—
309	C₂×C₈₉	—	8	1	no	—
310	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
311	C₂×C₈₉	#2956	1	2	yes	—
312	D₈₉	—	8	1	no	—
313	#3054	—	89	1	no	—
314	C₂×#443	—	89	1	no	—
315	#2930	—	89	1	no	—
316	#2930	—	89	1	no	—
317	C₂×C₄×M₁₆	—	89	1	no	—
318	#1975	—	89	1	no	—
319	#1946	—	89	1	no	—
320	#1937	—	89	1	no	—
321	#1937	—	89	1	no	—
322	#1896	—	89	1	no	—
323	#1896	D₈₉	1	1	yes	characteristic, complemented
324	#1811	—	89	1	no	—
325	#1772	—	89	1	no	—
326	#1765	—	89	1	no	—
327	#1765	—	89	1	no	—
328	C₈₉	#21549	1	1	yes	characteristic, complemented, Sylow
329	C₂×#135	—	89	1	no	—
330	C₂×#131	—	89	1	no	—
331	C₂×#131	—	89	1	no	—
332	C₂²×M₁₆	—	89	1	no	—
333	C₂²×M₁₆	—	89	1	no	—
334	#525	—	89	1	no	—
335	#525	C₂×D₈₉	1	1	yes	characteristic
336	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
337	#470	—	89	2	no	—
338	#469	—	89	2	no	—
339	#468	—	89	2	no	—
340	#468	—	89	2	no	—
341	#443	—	178	4	no	—
342	#436	—	178	2	no	—
343	#436	—	178	2	no	—
344	#435	—	178	2	no	—
345	#435	—	178	2	no	—
346	C₂×#108	—	89	1	no	—
347	C₂×#108	—	89	1	no	—
348	#427	—	89	1	no	—
349	#424	—	89	1	no	—
350	#424	—	89	1	no	—
351	C₂×#104	—	89	1	no	—
352	C₂×#104	—	89	1	no	—
353	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
354	C₂×#104	C₂×D₈₉	1	1	yes	characteristic
355	#416	—	89	1	no	—
356	#416	—	89	1	no	—
357	#408	—	89	1	no	—
358	#408	—	89	1	no	—
359	#407	—	89	1	no	—
360	#407	C₂×D₈₉	1	1	yes	characteristic
361	#405	—	89	1	no	—
362	#405	—	89	1	no	—
363	C₄×M₁₆	—	178	4	no	—
364	C₂×#97	—	89	1	no	—
365	C₂×#97	—	89	1	no	—
366	C₂×C₄×C₈	—	89	1	no	—
367	C₂×C₄×C₈	—	89	1	no	—
368	#341	—	89	1	no	—
369	#341	—	89	1	no	—
370	#339	—	89	1	no	—
371	#339	—	89	1	no	—
372	#339	C₂×D₈₉	1	1	yes	characteristic
373	#339	C₂×D₈₉	1	1	yes	characteristic
374	C₂×#41	—	89	1	no	—
375	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
378	#135	—	178	2	no	—
379	#135	—	178	2	no	—
380	C₂×Q₁₆	—	89	1	no	—
381	C₂×SD₁₆	—	89	1	no	—
382	C₂×SD₁₆	—	89	1	no	—
383	C₂×D₈	—	89	1	no	—
384	#131	—	178	2	no	—
385	#131	—	178	2	no	—
386	#131	—	178	2	no	—
387	#131	—	178	2	no	—
388	C₂×M₁₆	—	89	2	no	—
389	C₂×M₁₆	—	89	2	no	—
390	C₂×M₁₆	—	89	2	no	—
391	C₂×M₁₆	—	89	2	no	—
392	C₂×M₁₆	—	89	1	no	—
393	C₂×M₁₆	—	89	1	no	—
394	C₂×M₁₆	—	178	1	no	—
395	C₂×M₁₆	—	178	1	no	—
396	C₂×M₁₆	—	178	2	no	—
397	C₂×M₁₆	—	178	2	no	—
398	C₂×M₁₆	—	178	2	no	—
399	C₂×M₁₆	—	178	2	no	—
400	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
401	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
402	C₂²×C₈	—	89	1	no	—
403	C₂²×C₈	—	89	1	no	—
404	C₂²×C₈	—	89	1	no	—
405	C₂²×C₈	—	89	1	no	—
406	C₂²×C₈	—	178	1	no	—
407	C₂²×C₈	—	178	1	no	—
408	#123	—	2	1	no	—
409	#123	—	178	1	no	—
410	C₂²⋊Q₈	—	89	2	no	—
411	C₂²⋊Q₈	C₄×D₈₉	1	2	yes	—
412	#121	—	89	2	no	—
413	#121	C₄×D₈₉	1	2	yes	—
414	#120	—	2	1	no	—
415	#120	—	178	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	178	2	no	—
418	#117	—	89	1	no	—
419	#117	C₂²×D₈₉	1	1	yes	characteristic
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
425	#108	—	178	2	no	—
426	#108	—	178	2	no	—
427	#107	—	89	2	no	—
428	#106	—	89	2	no	—
429	C₄⋊C₈	—	178	2	no	—
430	C₄⋊C₈	—	178	2	no	—
431	#104	—	2	2	no	—
432	#104	—	2	2	no	—
433	#104	—	178	2	no	—
434	#104	—	178	2	no	—
435	#103	—	89	2	no	—
436	#103	—	89	2	no	—
437	#102	—	89	2	no	—
438	#102	—	89	2	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	178	2	no	—
441	C₂²⋊C₈	—	178	2	no	—
442	C₂²⋊C₈	—	178	2	no	—
443	#97	—	178	2	no	—
444	#97	—	178	2	no	—
445	#97	—	178	1	no	—
446	#97	—	178	1	no	—
447	C₄×C₈	—	89	4	no	—
448	C₄×C₈	—	178	1	no	—
449	C₄×C₈	—	178	1	no	—
450	C₄×C₈	—	178	2	no	—
451	C₂⁴	#13083573	1	1	yes	characteristic
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	178	1	no	—
457	#41	—	178	1	no	—
458	#41	—	178	1	no	—
459	#41	—	178	1	no	—
460	C₂×Q₈	—	89	1	no	—
461	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	89	1	no	—
465	C₂×D₄	—	178	1	no	—
466	C₂×D₄	—	178	2	no	—
467	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	178	1	no	—
478	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
479	C₂²×C₄	D₄×D₈₉	1	2	yes	—
480	C₂²×C₄	#13083573	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
482	Q₁₆	—	178	2	no	—
483	SD₁₆	—	178	2	no	—
484	SD₁₆	—	178	2	no	—
485	D₈	—	178	2	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	356	2	no	—
491	M₁₆	—	356	2	no	—
492	M₁₆	—	178	4	no	—
493	M₁₆	—	178	4	no	—
494	M₁₆	—	178	4	no	—
495	M₁₆	—	178	4	no	—
496	M₁₆	—	178	1	no	—
497	M₁₆	—	178	1	no	—
498	M₁₆	—	178	1	no	—
499	M₁₆	—	178	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	89	1	no	—
503	C₂×C₈	—	89	1	no	—
504	C₂×C₈	—	89	2	no	—
505	C₂×C₈	—	89	2	no	—
506	C₂×C₈	—	89	1	no	—
507	C₂×C₈	—	89	1	no	—
508	C₂×C₈	—	89	2	no	—
509	C₂×C₈	—	89	2	no	—
510	C₂×C₈	—	89	2	no	—
511	C₂×C₈	—	89	2	no	—
512	C₂×C₈	—	356	2	no	—
513	C₂×C₈	—	356	2	no	—
514	C₂×C₈	—	178	1	no	—
515	C₂×C₈	—	178	1	no	—
516	C₂×C₈	—	178	1	no	—
517	C₂×C₈	—	178	1	no	—
518	C₂×C₈	—	178	1	no	—
519	C₂×C₈	—	178	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	89	2	no	—
522	C₄⋊C₄	—	178	2	no	—
523	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	178	2	no	—
528	C₂²⋊C₄	—	178	1	no	—
529	C₂²⋊C₄	—	178	2	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	178	1	no	—
535	C₄²	D₄×D₈₉	1	2	yes	—
536	C₄²	#13083573	1	2	yes	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	178	1	no	—
542	C₂³	#15667972	1	2	yes	—
543	C₂³	C₂×#13083573	1	1	yes	characteristic
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	178	1	no	—
547	Q₈	—	178	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	356	1	no	—
554	D₄	—	356	1	no	—
555	D₄	—	178	1	no	—
556	D₄	—	178	1	no	—
557	D₄	—	712	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	356	1	no	—
574	C₂×C₄	—	356	1	no	—
575	C₂×C₄	—	178	2	no	—
576	C₂×C₄	—	178	1	no	—
577	C₂×C₄	#15667972	1	2	yes	—
578	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
580	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
581	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
582	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
583	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	89	2	no	—
587	C₈	—	89	2	no	—
588	C₈	—	89	2	no	—
589	C₈	—	89	2	no	—
590	C₈	—	356	1	no	—
591	C₈	—	356	1	no	—
592	C₈	—	178	2	no	—
593	C₈	—	178	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	356	2	no	—
603	C₂²	—	356	1	no	—
604	C₂²	C₂×#15667972	1	1	yes	characteristic
605	C₂²	#19152104	1	1	yes	characteristic
606	C₂²	#19152125	1	1	yes	characteristic
607	C₄	—	2	4	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	356	2	no	—
613	C₄	—	356	1	no	—
614	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
615	C₄	C₄×#13083573	1	1	yes	characteristic
616	C₄	#121×D₈₉	1	1	yes	characteristic
617	C₄	#19152143	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	4	2	no	—
621	C₂	—	8	1	no	—
622	C₂	—	712	1	no	—
623	C₂	#26022762	1	1	yes	characteristic
624	C₂	#26029158	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1896	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26029858	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1896	D₈₉
hypocenter	C₈₉	#21549
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1896

Complements

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

N	H ≅ G/N	type
2. C₂×#19151712	C₂	semidirect
3. #26028956	C₂	semidirect
4. #26028951	C₂	semidirect
5. C₂×C₄×#13083558	C₂	semidirect
6. #26021142	C₂	semidirect
7. #26021004	C₂	semidirect
8. #26020957	C₂	semidirect
9. #26020953	C₂	semidirect
10. #26020695	C₂	semidirect
11. #26020292	C₂	semidirect
12. #26020130	C₂	semidirect
13. #26020097	C₂	semidirect
14. #26020093	C₂	semidirect
15. C₈₉×#1896	C₂	semidirect
22. #19151854	C₄	semidirect
23. #19151849	C₄	semidirect
24. #19151846	C₄	semidirect
25. #19151842	C₄	semidirect
64. C₂×#13083564	C₂×C₄	semidirect
65. C₂×#13083562	C₂×C₄	semidirect
66. C₂×#13083561	C₂×C₄	semidirect
67. C₂×#13083559	C₂×C₄	semidirect
98. #15667945	C₂×C₄	semidirect
99. #15667943	C₂×C₄	semidirect
104. #15667936	C₂×C₄	semidirect
105. #15667935	C₂×C₄	semidirect
106. #15667933	C₂×C₄	semidirect
107. #15667932	C₂×C₄	semidirect
117. C₄×#10623494	D₄	semidirect
323. #1896	D₈₉	semidirect
328. C₈₉	#21549	semidirect

Maximal subgroups

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

subgroup	index
#26029858	2
C₂×#19151712	2
#26028956	2
#26028951	2
C₂×C₄×#13083558	2
#26021142	2
#26021004	2
#26020957	2
#26020953	2
#26020695	2
#26020292	2
#26020130	2
#26020097	2
#26020093	2
C₈₉×#1896	2
#21549	89