Subgroups — #36574141

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028918	C₂	1	2	yes	maximal, complemented
2	#26021146	C₂	1	1	yes	maximal, characteristic
3	#26021141	C₂	1	1	yes	maximal, characteristic
4	#26020902	C₂	1	2	yes	maximal, complemented
5	#26020902	C₂	1	2	yes	maximal, complemented
6	#26020427	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020272	C₂	1	2	yes	maximal, complemented
8	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020124	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2943	C₂	1	1	yes	maximal, characteristic
12	#19151659	—	2	2	no	—
13	#19151659	—	2	2	no	—
14	#19151655	—	2	2	no	—
15	#19151651	—	2	2	no	—
16	C₂×#15667948	C₂²	1	1	yes	characteristic
17	C₂×#15667948	C₂²	1	1	yes	characteristic
18	C₂×#15667948	C₂²	1	2	yes	—
19	#19151622	C₂²	1	2	yes	—
20	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
21	C₂×#15667939	C₂²	1	2	yes	—
22	C₂×#15667939	C₂²	1	2	yes	—
23	#19151565	C₂²	1	2	yes	—
24	#19151565	C₂²	1	2	yes	—
25	#19151554	C₂²	1	2	yes	—
26	#19151554	C₂²	1	2	yes	—
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
30	#19151357	C₂²	1	2	yes	—
31	#19151357	C₂²	1	2	yes	—
32	#19151352	C₂²	1	1	yes	characteristic
33	#19151352	C₂²	1	1	yes	characteristic
34	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₈₉	C₂²	1	2	yes	—
36	#442×C₈₉	C₄	1	2	yes	complemented
37	#441×C₈₉	C₄	1	2	yes	complemented
38	#440×C₈₉	C₄	1	2	yes	complemented
39	#440×C₈₉	C₄	1	2	yes	complemented
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#416×C₈₉	C₂²	1	2	yes	—
42	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083558	C₂³	1	2	yes	—
44	C₂×#13083558	C₂³	1	2	yes	—
45	C₂²×#10623494	C₂³	1	1	yes	characteristic
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
50	#15667948	—	2	2	no	—
51	#15667948	—	2	2	no	—
52	#15667948	—	4	2	no	—
53	C₄⋊#10623494	—	2	2	no	—
54	C₄⋊#10623494	—	2	2	no	—
55	C₄⋊#10623494	D₄	1	2	yes	—
56	C₄⋊#10623494	D₄	1	2	yes	—
57	#15667939	—	4	2	no	—
58	#15667939	—	4	2	no	—
59	C₂²⋊#10623494	—	2	2	no	—
60	C₂²⋊#10623494	—	2	2	no	—
61	C₂²⋊#10623494	—	2	2	no	—
62	C₂²⋊#10623494	—	2	2	no	—
63	#15667923	—	2	2	no	—
64	#15667923	—	2	2	no	—
65	#15667922	—	2	2	no	—
66	C₄×#10623494	—	2	2	no	—
67	C₄×#10623494	—	2	2	no	—
68	C₈×Dic₈₉	—	2	2	no	—
69	#15667919	—	2	1	no	—
70	C₂×#41×C₈₉	C₂³	1	2	yes	—
71	#135×C₈₉	—	2	2	no	—
72	#135×C₈₉	—	2	2	no	—
73	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₈₉	—	2	2	no	—
81	C₄×D₄×C₈₉	—	2	2	no	—
82	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
84	#117×C₈₉	—	2	2	no	—
85	#117×C₈₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₈₉	—	2	2	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
90	#106×C₈₉	C₂×C₄	1	2	yes	—
91	#103×C₈₉	C₂×C₄	1	2	yes	—
92	#103×C₈₉	C₂×C₄	1	2	yes	—
93	#102×C₈₉	C₂×C₄	1	2	yes	—
94	#102×C₈₉	C₂×C₄	1	2	yes	—
95	#97×C₈₉	C₂×C₄	1	2	yes	—
96	#97×C₈₉	C₂×C₄	1	2	yes	—
97	C₂²×Dic₈₉	—	2	1	no	—
98	C₂²×Dic₈₉	—	2	1	no	—
99	#13083558	—	2	2	no	—
100	#13083558	—	2	2	no	—
101	#13083558	—	2	2	no	—
102	#13083558	—	2	2	no	—
103	C₂×#10623494	—	2	1	no	—
104	C₂×#10623494	—	2	1	no	—
105	C₂×#10623494	—	2	1	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	2	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
110	C₂×#10623494	C₂×D₄	1	2	yes	—
111	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
112	C₄⋊Dic₈₉	—	4	2	no	—
113	C₄×Dic₈₉	—	2	1	no	—
114	C₄×Dic₈₉	—	2	1	no	—
115	C₄×Dic₈₉	—	2	1	no	—
116	C₄×Dic₈₉	—	2	1	no	—
117	#41×C₈₉	—	2	2	no	—
118	#41×C₈₉	—	2	2	no	—
119	#41×C₈₉	—	2	2	no	—
120	#41×C₈₉	—	2	2	no	—
121	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₈₉	—	2	2	no	—
123	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₈₉	—	2	2	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₈₉	—	2	2	no	—
131	SD₁₆×C₈₉	—	2	4	no	—
132	D₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	#41	1	2	yes	—
139	C₂×C₈×C₈₉	#41	1	2	yes	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₈₉	—	2	2	no	—
145	C₂²⋊C₄×C₈₉	—	2	2	no	—
146	C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₈₉	C₂×D₄	1	2	yes	—
152	C₂³×C₈₉	—	2	2	no	—
153	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
154	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	2	2	no	—
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	2	2	no	—
158	D₄×C₈₉	—	4	2	no	—
159	D₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	4	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	8	2	no	—
169	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₈₉	—	2	2	no	—
178	C₂×Dic₈₉	—	4	1	no	—
179	C₂×Dic₈₉	—	4	1	no	—
180	C₂×Dic₈₉	—	4	1	no	—
181	C₂×Dic₈₉	—	4	1	no	—
182	C₂×Dic₈₉	—	4	1	no	—
183	C₈×C₈₉	—	2	2	no	—
184	C₈×C₈₉	#117	1	2	yes	—
185	C₈×C₈₉	#117	1	2	yes	—
186	#10623494	—	2	1	no	—
187	#10623494	—	2	1	no	—
188	#10623494	—	2	2	no	—
189	#10623494	—	4	2	no	—
190	#10623494	—	4	2	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	4	2	no	—
194	C₂²×C₈₉	—	4	2	no	—
195	C₂²×C₈₉	—	4	2	no	—
196	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₈₉	#555	1	1	yes	characteristic
198	C₂²×C₈₉	#556	1	1	yes	characteristic
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	—	4	2	no	—
204	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
205	C₄×C₈₉	#520	1	1	yes	characteristic
206	C₄×C₈₉	#547	1	1	yes	characteristic
207	C₄×C₈₉	#550	1	1	yes	characteristic
208	Dic₈₉	—	4	2	no	—
209	Dic₈₉	—	8	1	no	—
210	#22804	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	—	8	2	no	—
214	C₂×C₈₉	#2354	1	1	yes	characteristic
215	C₂×C₈₉	#2955	1	1	yes	characteristic
216	C₂×C₈₉	#2956	1	1	yes	characteristic
217	#2943	D₈₉	1	1	yes	characteristic
218	#2925	—	89	2	no	—
219	#1975	—	89	1	no	—
220	#1974	—	89	1	no	—
221	#1929	—	89	2	no	—
222	#1929	—	89	2	no	—
223	#1849	—	89	1	no	—
224	#1806	—	89	2	no	—
225	#1773	—	89	1	no	—
226	#1772	—	89	1	no	—
227	#1771	—	89	1	no	—
228	C₈₉	#22804	1	1	yes	characteristic, complemented, Sylow
229	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
230	C₄×#41	C₂×D₈₉	1	2	yes	—
231	#442	Dic₈₉	1	2	yes	complemented
232	#441	Dic₈₉	1	2	yes	complemented
233	#440	Dic₈₉	1	2	yes	complemented
234	#440	Dic₈₉	1	2	yes	complemented
235	#433	—	178	2	no	—
236	#433	—	178	2	no	—
237	#432	—	178	2	no	—
238	#431	—	178	2	no	—
239	C₂×#108	—	89	2	no	—
240	C₂×#108	—	89	1	no	—
241	C₂×#108	—	89	1	no	—
242	#427	C₂×D₈₉	1	1	yes	characteristic
243	#423	—	89	2	no	—
244	C₂×C₄⋊C₈	—	89	1	no	—
245	C₂×#104	—	89	2	no	—
246	C₂×#104	—	89	2	no	—
247	#416	C₂×D₈₉	1	2	yes	—
248	#408	—	89	2	no	—
249	#408	—	89	2	no	—
250	#405	—	89	2	no	—
251	#405	—	89	2	no	—
252	C₂×#97	—	89	1	no	—
253	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
254	C₂×C₄×C₈	—	89	1	no	—
255	C₄×C₄⋊C₄	—	89	1	no	—
256	#339	—	89	2	no	—
257	#339	—	89	2	no	—
258	#336	—	89	1	no	—
259	#336	—	89	1	no	—
260	C₂×#41	C₂²×D₈₉	1	2	yes	—
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
265	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
266	C₂×M₁₆	—	89	2	no	—
267	C₂×M₁₆	—	89	2	no	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	89	1	no	—
270	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
273	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
277	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	C₂²×D₈₉	1	2	yes	—
280	C₂×C₄⋊C₄	—	178	1	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	89	1	no	—
283	C₂×C₄²	—	89	1	no	—
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	#108	—	356	2	no	—
286	#108	—	178	2	no	—
287	#108	—	178	2	no	—
288	#107	C₂×Dic₈₉	1	1	yes	characteristic
289	#107	C₂×Dic₈₉	1	1	yes	characteristic
290	#106	C₂×Dic₈₉	1	2	yes	—
291	C₄⋊C₈	—	89	2	no	—
292	C₄⋊C₈	—	89	2	no	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	2	no	—
295	#104	—	356	2	no	—
296	#104	—	356	2	no	—
297	#103	C₂×Dic₈₉	1	2	yes	—
298	#103	C₂×Dic₈₉	1	2	yes	—
299	#102	C₂×Dic₈₉	1	2	yes	—
300	#102	C₂×Dic₈₉	1	2	yes	—
301	C₂²⋊C₈	—	178	2	no	—
302	C₂²⋊C₈	—	178	2	no	—
303	C₂²⋊C₈	—	178	2	no	—
304	C₂²⋊C₈	—	178	2	no	—
305	#97	—	178	2	no	—
306	#97	—	178	2	no	—
307	#97	—	178	2	no	—
308	#97	C₂×Dic₈₉	1	2	yes	—
309	#97	C₂×Dic₈₉	1	2	yes	—
310	C₄×C₈	—	178	2	no	—
311	C₄×C₈	—	178	2	no	—
312	C₄×C₈	—	178	2	no	—
313	#95	—	178	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	178	1	no	—
325	C₂²×C₄	—	178	1	no	—
326	C₂²×C₄	#13083573	1	1	yes	characteristic
327	C₂²×C₄	#13083573	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	178	2	no	—
333	M₁₆	—	178	2	no	—
334	M₁₆	—	178	2	no	—
335	M₁₆	—	178	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	89	2	no	—
340	C₂×C₈	—	89	1	no	—
341	C₂×C₈	—	178	2	no	—
342	C₂×C₈	—	178	2	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	—	178	1	no	—
345	C₂×C₈	—	178	1	no	—
346	C₂×C₈	—	178	1	no	—
347	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
348	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
349	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
350	C₂×C₈	#13083574	1	2	yes	—
351	C₂×C₈	#13083574	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	356	2	no	—
355	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	178	1	no	—
364	C₄²	—	178	1	no	—
365	C₄²	—	178	1	no	—
366	C₄²	—	178	1	no	—
367	C₄²	C₂²×Dic₈₉	1	2	yes	—
368	C₄²	D₄×D₈₉	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×#13083573	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	356	1	no	—
387	C₂×C₄	—	356	1	no	—
388	C₂×C₄	—	356	1	no	—
389	C₂×C₄	—	356	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
393	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
394	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
397	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
398	C₂×C₄	#15668058	1	1	yes	characteristic
399	C₂×C₄	#15668059	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	356	2	no	—
402	C₈	—	356	2	no	—
403	C₈	—	178	1	no	—
404	C₈	—	178	2	no	—
405	C₈	—	178	1	no	—
406	C₈	#15667971	1	2	yes	—
407	C₈	#15667971	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
414	C₂²	#19152313	1	1	yes	characteristic
415	C₂²	#19152318	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	356	2	no	—
422	C₄	—	712	1	no	—
423	C₄	C₂×#15667971	1	1	yes	characteristic
424	C₄	#19152081	1	1	yes	characteristic
425	C₄	#19152253	1	1	yes	characteristic
426	C₄	#19152269	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#26023201	1	1	yes	characteristic
431	C₂	#26029155	1	1	yes	characteristic
432	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2943	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2943	D₈₉
hypocenter	C₈₉	#22804
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #26028918	C₂	semidirect
4. #26020902	C₂	semidirect
5. #26020902	C₂	semidirect
6. #26020427	C₂	semidirect
7. #26020272	C₂	semidirect
8. #26020138	C₂	semidirect
9. #26020133	C₂	semidirect
10. #26020124	C₂	semidirect
36. #442×C₈₉	C₄	semidirect
37. #441×C₈₉	C₄	semidirect
38. #440×C₈₉	C₄	semidirect
39. #440×C₈₉	C₄	semidirect
228. C₈₉	#22804	semidirect
231. #442	Dic₈₉	semidirect
232. #441	Dic₈₉	semidirect
233. #440	Dic₈₉	semidirect
234. #440	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028918	2
#26021146	2
#26021141	2
#26020902	2
#26020427	2
#26020272	2
#26020138	2
#26020133	2
#26020124	2
C₈₉×#2943	2
#22804	89