Subgroups — #36708091

Order 22784.

444 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029181	C₂	1	1	yes	maximal, characteristic
2	#26022161	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022160	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022159	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022159	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022158	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022158	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022157	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022060	C₂	1	1	yes	maximal, characteristic
10	#26022058	C₂	1	1	yes	maximal, characteristic
11	#26022058	C₂	1	1	yes	maximal, characteristic
12	#26022057	C₂	1	1	yes	maximal, characteristic
13	#26022054	C₂	1	1	yes	maximal, characteristic
14	#26022053	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2183	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₄	1	1	yes	characteristic
17	#19151729	C₄	1	1	yes	characteristic
18	#19151727	C₄	1	1	yes	characteristic
19	#19151727	C₄	1	1	yes	characteristic
20	#19151725	C₄	1	1	yes	characteristic
21	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
23	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	#19151623	C₄	1	1	yes	characteristic
25	#19151623	C₄	1	1	yes	characteristic
26	#19151620	C₄	1	1	yes	characteristic
27	#19151552	C₂²	1	1	yes	characteristic
28	#19151552	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	C₄⋊#13083549	C₂²	1	1	yes	characteristic
31	C₄⋊#13083549	C₂²	1	1	yes	characteristic
32	C₄⋊#13083549	C₂²	1	1	yes	characteristic
33	#19151416	C₂²	1	1	yes	characteristic
34	#19151416	C₂²	1	1	yes	characteristic
35	#19151416	C₂²	1	1	yes	characteristic
36	#19151416	C₂²	1	1	yes	characteristic
37	#19151416	C₂²	1	1	yes	characteristic
38	#19151416	C₂²	1	1	yes	characteristic
39	#19151377	C₂²	1	1	yes	characteristic
40	#19151377	C₂²	1	1	yes	characteristic
41	#19151377	C₂²	1	1	yes	characteristic
42	#19151377	C₂²	1	1	yes	characteristic
43	#19151374	C₂²	1	1	yes	characteristic
44	#19151374	C₂²	1	1	yes	characteristic
45	#19151373	C₂²	1	1	yes	characteristic
46	#19151373	C₂²	1	1	yes	characteristic
47	#19151373	C₂²	1	1	yes	characteristic
48	#19151373	C₂²	1	1	yes	characteristic
49	C₄×#13083549	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
52	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	#346×C₈₉	C₂²	1	1	yes	characteristic
57	#346×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
60	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
63	#15668011	C₈	1	1	yes	characteristic
64	#15668010	C₈	1	1	yes	characteristic
65	#15668002	C₈	1	1	yes	characteristic
66	#15668002	C₈	1	1	yes	characteristic
67	#15667992	C₈	1	1	yes	characteristic
68	#15667990	C₈	1	1	yes	characteristic
69	#15667990	C₈	1	1	yes	characteristic
70	#15667988	C₈	1	1	yes	characteristic
71	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
74	#15667969	C₂×C₄	1	1	yes	characteristic
75	#15667969	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×#13083549	C₂³	1	1	yes	characteristic
78	C₂×#13083549	C₂³	1	1	yes	characteristic
79	C₂×#13083549	C₂³	1	1	yes	characteristic
80	C₂×#13083549	C₂³	1	1	yes	characteristic
81	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
82	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
83	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
84	#15667941	C₂×C₄	1	1	yes	characteristic
85	#15667941	C₂×C₄	1	1	yes	characteristic
86	#15667941	C₂×C₄	1	1	yes	characteristic
87	#15667941	C₂×C₄	1	1	yes	characteristic
88	#15667941	C₂×C₄	1	1	yes	characteristic
89	#15667941	C₂×C₄	1	1	yes	characteristic
90	#15667923	C₂×C₄	1	1	yes	characteristic
91	#15667923	C₂×C₄	1	1	yes	characteristic
92	#15667922	C₂×C₄	1	1	yes	characteristic
93	#15667922	C₂×C₄	1	1	yes	characteristic
94	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
97	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
98	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
111	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
112	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
116	#13083557	—	4	1	no	—
117	#13083557	—	4	1	no	—
118	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₈₉	—	2	1	no	—
123	C₈×D₈₉	—	2	1	no	—
124	C₈×D₈₉	—	4	1	no	—
125	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
128	#13083553	C₂×C₈	1	1	yes	characteristic
129	#13083553	C₂×C₈	1	1	yes	characteristic
130	#13083553	C₂×C₈	1	1	yes	characteristic
131	#13083553	C₂×C₈	1	1	yes	characteristic
132	#13083553	C₂×C₈	1	1	yes	characteristic
133	#13083553	C₂×C₈	1	1	yes	characteristic
134	#13083553	C₂×C₈	1	1	yes	characteristic
135	#13083553	C₂×C₈	1	1	yes	characteristic
136	#13083553	C₂×C₈	1	1	yes	characteristic
137	#13083553	C₂×C₈	1	1	yes	characteristic
138	#13083551	C₂×C₈	1	1	yes	characteristic
139	#13083551	C₂×C₈	1	1	yes	characteristic
140	#13083551	C₂×C₈	1	1	yes	characteristic
141	#13083551	C₂×C₈	1	1	yes	characteristic
142	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
147	#13083549	—	2	1	no	—
148	#13083549	—	2	1	no	—
149	#13083549	—	2	1	no	—
150	#13083549	—	2	1	no	—
151	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
157	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
158	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
159	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
162	C₁₆×C₈₉	—	2	1	no	—
163	C₁₆×C₈₉	—	2	1	no	—
164	C₁₆×C₈₉	—	2	1	no	—
165	C₁₆×C₈₉	—	2	1	no	—
166	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
167	Q₈×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
182	C₄×D₈₉	—	2	1	no	—
183	C₄×D₈₉	—	2	1	no	—
184	C₄×D₈₉	—	4	1	no	—
185	C₄×D₈₉	—	4	1	no	—
186	Dic₁₇₈	—	4	1	no	—
187	Dic₁₇₈	—	4	1	no	—
188	Dic₁₇₈	—	4	1	no	—
189	C₈×C₈₉	—	2	1	no	—
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	—	2	1	no	—
192	C₈×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
194	#10623494	—	2	1	no	—
195	#10623494	—	2	1	no	—
196	#10623494	—	2	1	no	—
197	#10623494	—	2	1	no	—
198	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
199	C₂×D₈₉	—	2	1	no	—
200	C₂×D₈₉	—	2	1	no	—
201	C₂×D₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	#519	1	1	yes	characteristic
209	C₄×C₈₉	#568	1	1	yes	characteristic
210	Dic₈₉	—	2	1	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	2	1	no	—
213	Dic₈₉	—	2	1	no	—
214	Dic₈₉	—	2	1	no	—
215	Dic₈₉	—	2	1	no	—
216	Dic₈₉	—	2	1	no	—
217	#33501	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	#2982	1	1	yes	characteristic
219	C₂×C₈₉	#3407	1	1	yes	characteristic
220	C₂×C₈₉	#3407	1	1	yes	characteristic
221	D₈₉	—	4	1	no	—
222	#2960	—	89	1	no	—
223	#2183	—	89	1	no	—
224	#2183	—	89	1	no	—
225	#2183	—	89	1	no	—
226	#2183	—	89	1	no	—
227	#2183	—	89	1	no	—
228	#2183	—	89	1	no	—
229	#2183	—	89	1	no	—
230	#2183	D₈₉	1	1	yes	characteristic, complemented
231	#2164	—	89	1	no	—
232	#2164	—	89	1	no	—
233	#2164	—	89	1	no	—
234	#2164	—	89	1	no	—
235	#2163	—	89	1	no	—
236	#2163	—	89	1	no	—
237	C₈₉	#33501	1	1	yes	characteristic, complemented, Sylow
238	#533	—	89	1	no	—
239	#446	—	89	1	no	—
240	#446	—	89	1	no	—
241	#446	—	89	1	no	—
242	#446	—	89	1	no	—
243	C₈×Q₈	—	89	1	no	—
244	C₈×Q₈	—	89	1	no	—
245	C₈×Q₈	—	89	1	no	—
246	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
247	#424	—	89	1	no	—
248	#424	—	89	1	no	—
249	#423	—	89	1	no	—
250	#405	—	89	1	no	—
251	#405	—	89	1	no	—
252	C₂×C₄×C₈	—	89	1	no	—
253	C₄⋊C₁₆	—	89	1	no	—
254	C₄⋊C₁₆	—	89	1	no	—
255	C₄⋊C₁₆	—	89	1	no	—
256	C₄⋊C₁₆	—	89	1	no	—
257	C₄⋊C₁₆	—	89	1	no	—
258	C₄⋊C₁₆	—	89	1	no	—
259	C₄⋊C₁₆	—	89	1	no	—
260	C₄⋊C₁₆	—	89	1	no	—
261	C₄⋊C₁₆	—	89	1	no	—
262	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
264	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
265	C₂²⋊C₁₆	—	89	1	no	—
266	C₂²⋊C₁₆	—	89	1	no	—
267	C₂²⋊C₁₆	—	89	1	no	—
268	C₂²⋊C₁₆	—	89	1	no	—
269	#346	—	89	1	no	—
270	#346	—	89	1	no	—
271	#346	—	89	1	no	—
272	#346	—	89	1	no	—
273	#346	—	89	1	no	—
274	#346	—	89	1	no	—
275	#346	C₂×D₈₉	1	1	yes	characteristic
276	#346	C₂×D₈₉	1	1	yes	characteristic
277	C₄×C₁₆	—	89	1	no	—
278	C₄×C₁₆	—	89	1	no	—
279	C₄×C₁₆	—	89	1	no	—
280	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
281	C₂×M₁₆	—	89	1	no	—
282	C₂×M₁₆	—	89	1	no	—
283	C₂²×C₈	—	89	1	no	—
284	C₂²×C₈	—	89	1	no	—
285	C₄⋊Q₈	—	89	1	no	—
286	C₄⋊Q₈	—	89	1	no	—
287	#125	—	89	1	no	—
288	#125	—	89	1	no	—
289	C₂²⋊Q₈	—	89	1	no	—
290	C₂²⋊Q₈	—	89	1	no	—
291	C₂²⋊Q₈	—	89	1	no	—
292	C₂²⋊Q₈	—	89	1	no	—
293	C₄×Q₈	—	89	1	no	—
294	C₄×Q₈	—	89	1	no	—
295	C₄×Q₈	—	89	1	no	—
296	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
297	#117	—	89	1	no	—
298	#117	—	89	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₁₆	—	89	1	no	—
301	C₂×C₁₆	—	89	1	no	—
302	C₂×C₁₆	—	89	1	no	—
303	C₂×C₁₆	—	89	1	no	—
304	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
306	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
307	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₈	—	89	1	no	—
309	C₄⋊C₈	—	89	1	no	—
310	C₄⋊C₈	—	89	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	1	no	—
313	C₄⋊C₈	—	89	1	no	—
314	C₄⋊C₈	—	89	1	no	—
315	C₄⋊C₈	—	89	1	no	—
316	C₄⋊C₈	—	89	1	no	—
317	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
318	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
319	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
320	#97	—	89	1	no	—
321	#97	—	89	1	no	—
322	#97	—	89	1	no	—
323	#97	—	89	1	no	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	89	1	no	—
326	C₄×C₈	—	89	1	no	—
327	C₄×C₈	—	89	1	no	—
328	C₄×C₈	—	89	1	no	—
329	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
332	C₂×Q₈	—	89	1	no	—
333	C₂×Q₈	—	89	1	no	—
334	C₂×Q₈	—	89	1	no	—
335	C₂×Q₈	C₈×D₈₉	1	1	yes	characteristic
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	M₁₆	—	356	1	no	—
340	M₁₆	—	356	1	no	—
341	C₂×C₈	—	89	1	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	89	1	no	—
344	C₂×C₈	—	89	1	no	—
345	C₂×C₈	—	356	1	no	—
346	C₂×C₈	—	178	1	no	—
347	C₂×C₈	—	178	1	no	—
348	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
352	C₄⋊C₄	—	89	1	no	—
353	C₄⋊C₄	—	89	1	no	—
354	C₄⋊C₄	—	89	1	no	—
355	C₄⋊C₄	—	89	1	no	—
356	C₄⋊C₄	—	89	1	no	—
357	C₄⋊C₄	—	89	1	no	—
358	C₄⋊C₄	—	89	1	no	—
359	C₄⋊C₄	—	89	1	no	—
360	C₄⋊C₄	—	89	1	no	—
361	C₄⋊C₄	—	89	1	no	—
362	C₄⋊C₄	—	89	1	no	—
363	C₄⋊C₄	—	89	1	no	—
364	C₄⋊C₄	—	89	1	no	—
365	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
366	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
367	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
368	C₂²⋊C₄	—	89	1	no	—
369	C₂²⋊C₄	—	89	1	no	—
370	C₂²⋊C₄	—	89	1	no	—
371	C₂²⋊C₄	—	89	1	no	—
372	C₄²	—	89	1	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	89	1	no	—
375	C₄²	—	89	1	no	—
376	C₄²	—	89	1	no	—
377	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	2	1	no	—
384	C₁₆	—	178	1	no	—
385	C₁₆	—	178	1	no	—
386	C₁₆	—	178	1	no	—
387	C₁₆	—	178	1	no	—
388	C₂³	—	89	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	356	1	no	—
391	Q₈	—	356	1	no	—
392	Q₈	—	356	1	no	—
393	C₂×C₄	—	89	1	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	89	1	no	—
398	C₂×C₄	—	89	1	no	—
399	C₂×C₄	—	89	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	1	no	—
402	C₂×C₄	—	178	1	no	—
403	C₂×C₄	—	178	1	no	—
404	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	178	1	no	—
415	C₈	—	178	1	no	—
416	C₈	—	178	1	no	—
417	C₈	—	178	1	no	—
418	C₈	#15668059	1	1	yes	characteristic
419	C₈	#15668060	1	1	yes	characteristic
420	C₂²	—	178	1	no	—
421	C₂²	—	178	1	no	—
422	C₂²	—	178	1	no	—
423	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	178	1	no	—
431	C₄	—	178	1	no	—
432	C₄	—	178	1	no	—
433	C₄	—	178	1	no	—
434	C₄	—	178	1	no	—
435	C₄	—	178	1	no	—
436	C₄	—	178	1	no	—
437	C₄	#19152074	1	1	yes	characteristic
438	C₄	#19152363	1	1	yes	characteristic
439	C₂	—	356	1	no	—
440	C₂	#26029331	1	1	yes	characteristic
441	C₂	#26033353	1	1	yes	characteristic
442	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2183	C₂
prime radical	C₂²×D₈₉	C₂²×C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2183	D₈₉
hypocenter	C₈₉	#33501
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #26022161	C₂	semidirect
3. #26022160	C₂	semidirect
4. #26022159	C₂	semidirect
5. #26022159	C₂	semidirect
6. #26022158	C₂	semidirect
7. #26022158	C₂	semidirect
8. #26022157	C₂	semidirect
15. C₈₉×#2183	C₂	semidirect
230. #2183	D₈₉	semidirect
237. C₈₉	#33501	semidirect

Maximal subgroups

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

subgroup	index
#26029181	2
#26022161	2
#26022160	2
#26022159	2
#26022158	2
#26022157	2
#26022060	2
#26022058	2
#26022057	2
#26022054	2
#26022053	2
C₈₉×#2183	2
#33501	89