Subgroups — #36471287

Order 22784.

554 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667951	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151377	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151377	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018330	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1374	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₅₆	C₄	1	1	yes	characteristic
11	C₂×#15667951	—	2	2	no	—
12	C₂×#15667951	—	2	2	no	—
13	C₂×#15667951	—	2	2	no	—
14	C₂²×#13083549	C₂²	1	1	yes	characteristic
15	C₂²×#13083549	C₂²	1	1	yes	characteristic
16	C₈×D₃₅₆	—	2	2	no	—
17	C₈×D₃₅₆	—	2	2	no	—
18	C₂×C₄⋊#10623494	C₄	1	1	yes	characteristic
19	C₂×#15667924	C₄	1	1	yes	characteristic
20	C₂×#15667924	C₄	1	1	yes	characteristic
21	#19151377	—	2	2	no	—
22	#19151377	—	2	2	no	—
23	#19151377	—	2	2	no	—
24	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×D₃₅₆	C₈	1	1	yes	characteristic
28	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
30	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
31	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
32	C₂×C₈×D₈₉	—	2	1	no	—
33	C₂×C₈×D₈₉	—	2	1	no	—
34	C₂×C₈×D₈₉	—	2	1	no	—
35	C₂×C₈×D₈₉	—	2	1	no	—
36	C₂×C₈×D₈₉	—	2	1	no	—
37	C₂×C₈×D₈₉	—	2	1	no	—
38	C₂×C₈×D₈₉	—	2	1	no	—
39	C₂×C₈×D₈₉	—	2	1	no	—
40	C₂×C₈×D₈₉	—	2	1	no	—
41	C₂×C₈×D₈₉	—	2	1	no	—
42	C₂×C₈×D₈₉	D₄	1	2	yes	—
43	C₂×C₈×D₈₉	D₄	1	2	yes	—
44	C₄×D₃₅₆	—	2	2	no	—
45	C₄×D₃₅₆	—	2	2	no	—
46	C₂×C₄⋊Dic₈₉	C₈	1	1	yes	characteristic
47	C₂×#13083551	C₈	1	1	yes	characteristic
48	C₂×#13083551	C₈	1	1	yes	characteristic
49	#15667951	—	2	8	no	—
50	C₂×#13083549	—	2	1	no	—
51	C₂×#13083549	—	2	1	no	—
52	C₂×#13083549	—	2	1	no	—
53	C₂×#13083549	—	2	1	no	—
54	C₂×#13083549	—	2	1	no	—
55	C₂×#13083549	D₄	1	2	yes	complemented
56	C₄⋊#10623494	—	2	2	no	—
57	#15667924	—	2	2	no	—
58	#15667924	—	2	2	no	—
59	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₆×C₈₉	—	2	1	no	—
63	C₂×C₁₆×C₈₉	—	2	1	no	—
64	C₂×C₁₆×C₈₉	—	2	1	no	—
65	C₂×C₁₆×C₈₉	—	2	1	no	—
66	C₂×C₁₆×C₈₉	—	2	1	no	—
67	C₂×C₁₆×C₈₉	D₄	1	2	yes	complemented
68	C₄×C₈×C₈₉	—	2	1	no	—
69	C₄×C₈×C₈₉	—	2	1	no	—
70	C₂³×D₈₉	C₂×C₈	1	1	yes	characteristic
71	C₂³×D₈₉	C₂×C₈	1	1	yes	characteristic
72	C₂×D₃₅₆	—	2	2	no	—
73	C₂×D₃₅₆	—	2	2	no	—
74	C₂×D₃₅₆	—	2	2	no	—
75	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
76	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
77	C₂×C₄×D₈₉	—	2	1	no	—
78	C₂×C₄×D₈₉	—	2	1	no	—
79	C₂×C₄×D₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	—	2	1	no	—
82	C₂×C₄×D₈₉	—	2	1	no	—
83	C₂×C₄×D₈₉	—	2	1	no	—
84	C₂×C₄×D₈₉	—	2	1	no	—
85	C₂×C₄×D₈₉	—	2	1	no	—
86	C₂×C₄×D₈₉	—	2	1	no	—
87	C₂×C₄×D₈₉	C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×D₈₉	M₁₆	1	2	yes	—
89	C₂×#10623494	—	2	1	no	—
90	C₂×#10623494	—	2	1	no	—
91	C₂×#10623494	—	2	1	no	—
92	C₂×#10623494	—	2	1	no	—
93	C₂×#10623494	—	2	1	no	—
94	C₂×#10623494	C₂²⋊C₄	1	2	yes	—
95	C₈×D₈₉	—	2	2	no	—
96	C₈×D₈₉	—	2	2	no	—
97	C₈×D₈₉	—	2	2	no	—
98	C₈×D₈₉	—	2	2	no	—
99	C₈×D₈₉	—	4	1	no	—
100	C₈×D₈₉	—	4	1	no	—
101	C₈×D₈₉	—	4	1	no	—
102	C₈×D₈₉	—	4	1	no	—
103	C₄⋊Dic₈₉	—	2	2	no	—
104	#13083551	—	2	2	no	—
105	#13083551	—	2	2	no	—
106	#13083549	—	2	2	no	—
107	#13083549	—	4	1	no	—
108	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
119	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
120	C₄²×C₈₉	—	2	1	no	—
121	C₄²×C₈₉	—	2	1	no	—
122	C₁₆×C₈₉	—	2	2	no	—
123	C₁₆×C₈₉	—	4	1	no	—
124	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	—	2	1	no	—
128	C₂²×D₈₉	—	2	1	no	—
129	C₂²×D₈₉	—	2	1	no	—
130	C₂²×D₈₉	—	2	1	no	—
131	C₂²×D₈₉	—	2	1	no	—
132	C₂²×D₈₉	—	2	1	no	—
133	C₂²×D₈₉	—	2	1	no	—
134	C₂²×D₈₉	—	2	1	no	—
135	C₂²×D₈₉	—	2	1	no	—
136	C₂²×D₈₉	—	2	1	no	—
137	C₂²×D₈₉	C₂²⋊C₈	1	2	yes	—
138	C₂²×D₈₉	M₃₂	1	2	yes	complemented
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	M₃₂	1	2	yes	complemented
145	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	2	1	no	—
156	C₂×Dic₈₉	C₂²⋊C₈	1	2	yes	—
157	D₃₅₆	—	2	8	no	—
158	C₄×D₈₉	—	2	2	no	—
159	C₄×D₈₉	—	2	2	no	—
160	C₄×D₈₉	—	2	2	no	—
161	C₄×D₈₉	—	2	2	no	—
162	C₄×D₈₉	—	4	1	no	—
163	C₄×D₈₉	—	4	1	no	—
164	C₄×D₈₉	—	4	1	no	—
165	C₄×D₈₉	—	4	1	no	—
166	C₈×C₈₉	—	4	1	no	—
167	C₈×C₈₉	#120	1	1	yes	characteristic
168	C₈×C₈₉	#121	1	1	yes	characteristic
169	C₈×C₈₉	#121	1	1	yes	characteristic
170	C₈×C₈₉	#123	1	1	yes	characteristic
171	#10623494	—	2	2	no	—
172	#10623494	—	4	1	no	—
173	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
174	C₂²×C₈₉	C₈×D₄	1	1	yes	characteristic
175	C₂²×C₈₉	C₈×D₄	1	1	yes	characteristic
176	C₂²×C₈₉	C₂×M₃₂	1	1	yes	characteristic
177	C₂²×C₈₉	C₂×M₃₂	1	1	yes	characteristic
178	C₂²×C₈₉	#504	1	1	yes	characteristic
179	C₂²×C₈₉	#504	1	1	yes	characteristic
180	C₂×D₈₉	—	2	2	no	—
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	2	no	—
183	C₂×D₈₉	—	2	2	no	—
184	C₂×D₈₉	—	2	2	no	—
185	C₂×D₈₉	—	2	2	no	—
186	C₂×D₈₉	—	4	1	no	—
187	C₂×D₈₉	—	4	1	no	—
188	C₂×D₈₉	—	4	1	no	—
189	C₂×D₈₉	—	4	1	no	—
190	C₂×D₈₉	—	4	1	no	—
191	C₂×D₈₉	—	4	1	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	4	1	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	#386	1	1	yes	characteristic
197	C₄×C₈₉	#408	1	1	yes	characteristic
198	C₄×C₈₉	#435	1	1	yes	characteristic
199	C₄×C₈₉	#435	1	1	yes	characteristic
200	Dic₈₉	—	2	2	no	—
201	Dic₈₉	—	4	1	no	—
202	#12977	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	#1869	1	1	yes	characteristic
204	C₂×C₈₉	#2112	1	1	yes	characteristic
205	C₂×C₈₉	#2113	1	1	yes	characteristic
206	C₂×C₈₉	#2168	1	1	yes	characteristic
207	C₂×C₈₉	#2168	1	1	yes	characteristic
208	C₂×C₈₉	#2169	1	1	yes	characteristic
209	C₂×C₈₉	#2169	1	1	yes	characteristic
210	D₈₉	—	4	2	no	—
211	D₈₉	—	4	2	no	—
212	C₂²×M₃₂	—	89	1	no	—
213	C₂×C₈×D₄	—	89	1	no	—
214	C₂×C₂²⋊C₁₆	—	89	1	no	—
215	C₂×C₂²⋊C₁₆	—	89	1	no	—
216	C₂×C₂²⋊C₁₆	—	89	1	no	—
217	#1374	—	89	1	no	—
218	#1374	D₈₉	1	1	yes	characteristic, complemented
219	C₈₉	#12977	1	1	yes	characteristic, complemented, Sylow
220	C₂³×C₈	—	89	1	no	—
221	C₂³×C₈	—	89	1	no	—
222	C₂×C₄×D₄	—	89	1	no	—
223	C₂×M₃₂	—	178	2	no	—
224	C₂×M₃₂	—	178	2	no	—
225	C₂×M₃₂	—	178	2	no	—
226	C₂²×C₁₆	—	89	1	no	—
227	C₂²×C₁₆	—	89	1	no	—
228	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
229	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
230	C₈×D₄	—	178	2	no	—
231	C₈×D₄	—	178	2	no	—
232	C₂×C₄⋊C₈	—	89	1	no	—
233	C₂×C₂²⋊C₈	—	89	1	no	—
234	C₂×C₂²⋊C₈	—	89	1	no	—
235	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
236	C₂²⋊C₁₆	—	178	2	no	—
237	C₂²⋊C₁₆	—	178	2	no	—
238	C₂²⋊C₁₆	—	178	2	no	—
239	C₂²×D₄	—	89	1	no	—
240	C₂³×C₄	—	89	1	no	—
241	C₂³×C₄	—	89	1	no	—
242	C₂²×C₈	—	89	1	no	—
243	C₂²×C₈	—	89	2	no	—
244	C₂²×C₈	—	89	2	no	—
245	C₂²×C₈	—	89	1	no	—
246	C₂²×C₈	—	178	1	no	—
247	C₂²×C₈	—	178	1	no	—
248	C₂²×C₈	—	178	1	no	—
249	C₂²×C₈	—	178	1	no	—
250	C₂²×C₈	—	178	1	no	—
251	C₂²×C₈	—	178	1	no	—
252	C₂²×C₈	—	178	1	no	—
253	C₂²×C₈	—	178	1	no	—
254	C₂²×C₈	—	178	1	no	—
255	C₂²×C₈	—	178	1	no	—
256	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
258	C₄×D₄	—	178	2	no	—
259	C₄×D₄	—	178	2	no	—
260	C₂×C₄⋊C₄	—	89	1	no	—
261	C₂×C₂²⋊C₄	—	89	1	no	—
262	C₂×C₂²⋊C₄	—	89	1	no	—
263	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
264	M₃₂	—	178	8	no	—
265	C₂×C₁₆	—	2	1	no	—
266	C₂×C₁₆	—	2	1	no	—
267	C₂×C₁₆	—	2	1	no	—
268	C₂×C₁₆	—	2	1	no	—
269	C₂×C₁₆	—	2	1	no	—
270	C₂×C₁₆	—	89	2	no	—
271	C₂×C₁₆	—	178	1	no	—
272	C₂×C₁₆	—	178	1	no	—
273	C₂×C₁₆	—	178	1	no	—
274	C₂×C₁₆	—	178	1	no	—
275	C₂×C₁₆	—	178	1	no	—
276	C₂×C₁₆	D₃₅₆	1	2	yes	complemented
277	C₄⋊C₈	—	178	2	no	—
278	C₂²⋊C₈	—	178	2	no	—
279	C₂²⋊C₈	—	178	2	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	2	1	no	—
282	C₂⁴	—	89	1	no	—
283	C₂⁴	—	89	1	no	—
284	C₂×D₄	—	178	2	no	—
285	C₂×D₄	—	178	2	no	—
286	C₂×D₄	—	178	2	no	—
287	C₂²×C₄	—	89	1	no	—
288	C₂²×C₄	—	89	2	no	—
289	C₂²×C₄	—	89	2	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	178	1	no	—
292	C₂²×C₄	—	178	1	no	—
293	C₂²×C₄	—	178	1	no	—
294	C₂²×C₄	—	178	1	no	—
295	C₂²×C₄	—	178	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	—	178	1	no	—
298	C₂²×C₄	—	178	1	no	—
299	C₂²×C₄	—	178	1	no	—
300	C₂²×C₄	—	178	1	no	—
301	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
302	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	89	2	no	—
308	C₂×C₈	—	356	1	no	—
309	C₂×C₈	—	356	1	no	—
310	C₂×C₈	—	356	1	no	—
311	C₂×C₈	—	356	1	no	—
312	C₂×C₈	—	178	1	no	—
313	C₂×C₈	—	178	1	no	—
314	C₂×C₈	—	178	1	no	—
315	C₂×C₈	—	178	1	no	—
316	C₂×C₈	—	178	1	no	—
317	C₂×C₈	—	178	2	no	—
318	C₂×C₈	—	178	2	no	—
319	C₂×C₈	—	178	2	no	—
320	C₂×C₈	—	178	2	no	—
321	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
322	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
323	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
324	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
325	C₂×C₈	#13083574	1	1	yes	characteristic
326	C₂×C₈	#13083575	1	1	yes	characteristic
327	C₄⋊C₄	—	178	2	no	—
328	C₂²⋊C₄	—	178	2	no	—
329	C₂²⋊C₄	—	178	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₁₆	—	2	2	no	—
333	C₁₆	—	4	1	no	—
334	C₁₆	—	356	1	no	—
335	C₁₆	—	178	2	no	—
336	C₂³	—	89	2	no	—
337	C₂³	—	89	2	no	—
338	C₂³	—	178	1	no	—
339	C₂³	—	178	1	no	—
340	C₂³	—	178	1	no	—
341	C₂³	—	178	1	no	—
342	C₂³	—	178	1	no	—
343	C₂³	—	178	1	no	—
344	C₂³	—	178	1	no	—
345	C₂³	—	178	1	no	—
346	C₂³	—	178	1	no	—
347	C₂³	—	178	1	no	—
348	C₂³	—	178	1	no	—
349	C₂³	—	178	1	no	—
350	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
351	D₄	—	178	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	89	2	no	—
358	C₂×C₄	—	356	1	no	—
359	C₂×C₄	—	356	1	no	—
360	C₂×C₄	—	356	1	no	—
361	C₂×C₄	—	356	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	—	178	1	no	—
366	C₂×C₄	—	178	1	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	178	2	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	#15667951	1	2	yes	complemented
372	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
373	C₂×C₄	#15667974	1	1	yes	characteristic
374	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
375	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
376	C₂×C₄	#15668018	1	1	yes	characteristic
377	C₂×C₄	#15668020	1	1	yes	characteristic
378	C₈	—	4	1	no	—
379	C₈	—	356	1	no	—
380	C₈	—	178	2	no	—
381	C₈	#15667982	1	1	yes	characteristic
382	C₈	#15667985	1	1	yes	characteristic
383	C₈	#15667987	1	1	yes	characteristic
384	C₈	#15667997	1	1	yes	characteristic
385	C₂²	—	356	1	no	—
386	C₂²	—	356	1	no	—
387	C₂²	—	356	1	no	—
388	C₂²	—	356	1	no	—
389	C₂²	—	356	1	no	—
390	C₂²	—	356	1	no	—
391	C₂²	—	356	1	no	—
392	C₂²	—	356	1	no	—
393	C₂²	—	178	2	no	—
394	C₂²	—	178	2	no	—
395	C₂²	—	178	2	no	—
396	C₂²	—	178	2	no	—
397	C₂²	—	178	2	no	—
398	C₂²	—	178	2	no	—
399	C₂²	C₂²⋊C₈×D₈₉	1	1	yes	characteristic
400	C₂²	#19151663	1	1	yes	characteristic
401	C₂²	C₈×D₃₅₆	1	1	yes	characteristic
402	C₂²	M₃₂×D₈₉	1	1	yes	characteristic
403	C₂²	C₂×#15667951	1	1	yes	characteristic
404	C₂²	#19152014	1	1	yes	characteristic
405	C₂²	#19152016	1	1	yes	characteristic
406	C₄	—	2	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	356	1	no	—
409	C₄	—	178	2	no	—
410	C₄	#19151476	1	1	yes	characteristic
411	C₄	#19151563	1	1	yes	characteristic
412	C₄	#19151668	1	1	yes	characteristic
413	C₄	#19151671	1	1	yes	characteristic
414	C₂	—	356	2	no	—
415	C₂	—	356	2	no	—
416	C₂	#26020543	1	1	yes	characteristic
417	C₂	#26021861	1	1	yes	characteristic
418	C₂	#26021864	1	1	yes	characteristic
419	C₂	#26022076	1	1	yes	characteristic
420	C₂	#26022079	1	1	yes	characteristic
421	C₂	#26022083	1	1	yes	characteristic
422	C₂	#26022085	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₈₉
commutator, socle	C₂³×C₈₉	C₂²×C₈
Fitting	C₈₉×#1374	C₂
prime radical	C₂²×D₃₅₆	C₈
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	#1374	D₈₉
hypocenter	C₈₉	#12977
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₈ ◁ #1374

Complements

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

N	H ≅ G/N	type
1. C₂²×#15667951	C₂	semidirect
3. C₂×#19151377	C₂	semidirect
4. C₂×#19151377	C₂	semidirect
5. C₂×#19151377	C₂	semidirect
6. #26018330	C₂	semidirect
7. C₈₉×#1374	C₂	semidirect
55. C₂×#13083549	D₄	semidirect
67. C₂×C₁₆×C₈₉	D₄	semidirect
138. C₂²×D₈₉	M₃₂	semidirect
144. C₂×C₄×C₈₉	M₃₂	semidirect
218. #1374	D₈₉	semidirect
219. C₈₉	#12977	semidirect
276. C₂×C₁₆	D₃₅₆	semidirect
371. C₂×C₄	#15667951	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15667951	2
C₂×C₈×D₃₅₆	2
C₂×#19151377	2
#26018330	2
C₈₉×#1374	2
#12977	89