Subgroups — #36574326

Order 22784.

656 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022729	C₂	1	1	yes	maximal, characteristic
2	#26021188	C₂	1	1	yes	maximal, characteristic
3	#26021188	C₂	1	1	yes	maximal, characteristic
4	#26020819	C₂	1	2	yes	maximal
5	#26020812	C₂	1	2	yes	maximal
6	#26020404	C₂	1	1	yes	maximal, characteristic
7	#26020371	C₂	1	2	yes	maximal
8	#26020119	C₂	1	1	yes	maximal, characteristic
9	C₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic
10	#26020111	C₂	1	2	yes	maximal
11	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
17	C₂×#15667922	C₂²	1	2	yes	—
18	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
19	#19151504	C₄	1	1	yes	characteristic
20	#19151504	C₄	1	1	yes	characteristic
21	#19151496	C₄	1	1	yes	characteristic
22	#19151496	C₄	1	1	yes	characteristic
23	#19151482	C₄	1	2	yes	—
24	#19151482	C₄	1	2	yes	—
25	C₄×#13083553	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
27	#19151444	C₂²	1	2	yes	—
28	#19151352	C₂²	1	2	yes	—
29	#19151352	C₂²	1	2	yes	—
30	#19151352	C₂²	1	2	yes	—
31	#19151352	C₂²	1	2	yes	—
32	#19151352	C₂²	1	2	yes	—
33	#19151352	C₂²	1	2	yes	—
34	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄³×C₈₉	C₂²	1	1	yes	characteristic
39	#336×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×#10623494	C₂³	1	2	yes	—
43	C₂²×#10623494	C₂³	1	2	yes	—
44	C₄×Dic₁₇₈	—	2	2	no	—
45	C₄×Dic₁₇₈	—	2	2	no	—
46	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083553	C₂×C₄	1	2	yes	—
50	C₂×#13083553	C₂×C₄	1	2	yes	—
51	C₂×#13083553	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
53	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
54	C₄⋊#10623494	—	2	4	no	—
55	C₄⋊#10623494	—	2	2	no	—
56	C₄⋊#10623494	—	2	2	no	—
57	C₄⋊#10623494	—	4	2	no	—
58	#15667922	—	4	2	no	—
59	C₈×Dic₈₉	—	4	2	no	—
60	#15667919	C₂×C₄	1	2	yes	—
61	#15667919	C₂×C₄	1	2	yes	—
62	#15667919	C₂×C₄	1	2	yes	—
63	#15667919	C₂×C₄	1	2	yes	—
64	#15667919	C₂×C₄	1	2	yes	—
65	#15667919	C₂×C₄	1	2	yes	—
66	#15667919	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₈₉	—	2	2	no	—
79	C₄⋊C₈×C₈₉	Q₈	1	4	yes	complemented
80	C₄×C₈×C₈₉	—	2	2	no	—
81	C₄×C₈×C₈₉	—	2	2	no	—
82	C₂×Dic₁₇₈	—	2	2	no	—
83	C₂×Dic₁₇₈	—	2	2	no	—
84	C₂×Dic₁₇₈	—	2	2	no	—
85	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
86	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
87	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
88	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
89	C₂×#10623494	—	2	2	no	—
90	C₂×#10623494	—	2	2	no	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₄⋊Dic₈₉	—	2	2	no	—
96	C₄⋊Dic₈₉	—	2	2	no	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	#13083553	—	2	4	no	—
99	#13083553	—	2	4	no	—
100	#13083553	—	4	2	no	—
101	C₄×Dic₈₉	—	2	2	no	—
102	C₄×Dic₈₉	—	2	2	no	—
103	C₄×Dic₈₉	—	2	2	no	—
104	C₄×Dic₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	—	2	1	no	—
115	C₂×C₈×C₈₉	—	2	1	no	—
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
123	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	—	2	2	no	—
126	C₄²×C₈₉	—	2	2	no	—
127	C₄²×C₈₉	—	2	1	no	—
128	C₄²×C₈₉	—	2	1	no	—
129	C₄²×C₈₉	—	4	1	no	—
130	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
131	C₄²×C₈₉	#41	1	2	yes	—
132	C₄²×C₈₉	#41	1	2	yes	—
133	C₄²×C₈₉	#41	1	2	yes	—
134	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	1	no	—
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	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	#117	1	2	yes	—
147	C₂×C₄×C₈₉	#117	1	2	yes	—
148	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
149	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₈₉	#131	1	2	yes	—
151	C₂×C₄×C₈₉	#131	1	2	yes	—
152	C₂×C₄×C₈₉	#131	1	2	yes	—
153	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×Dic₈₉	—	2	2	no	—
160	C₂×Dic₈₉	—	2	2	no	—
161	C₂×Dic₈₉	—	2	2	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	—	2	2	no	—
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	2	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	Dic₁₇₈	—	4	4	no	—
172	C₈×C₈₉	—	2	2	no	—
173	C₈×C₈₉	—	2	2	no	—
174	C₈×C₈₉	—	4	1	no	—
175	C₈×C₈₉	—	4	1	no	—
176	#10623494	—	4	2	no	—
177	#10623494	—	4	2	no	—
178	C₂²×C₈₉	C₂×#117	1	1	yes	characteristic
179	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
180	C₂²×C₈₉	#520	1	1	yes	characteristic
181	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
182	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
183	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
184	C₂²×C₈₉	#568	1	1	yes	characteristic
185	C₄×C₈₉	—	2	2	no	—
186	C₄×C₈₉	—	2	2	no	—
187	C₄×C₈₉	—	2	2	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	#433	1	4	yes	—
191	C₄×C₈₉	#554	1	1	yes	characteristic
192	C₄×C₈₉	#556	1	1	yes	characteristic
193	C₄×C₈₉	#557	1	1	yes	characteristic
194	C₄×C₈₉	#559	1	1	yes	characteristic
195	Dic₈₉	—	4	2	no	—
196	Dic₈₉	—	4	2	no	—
197	Dic₈₉	—	4	2	no	—
198	Dic₈₉	—	4	2	no	—
199	#22822	—	89	1	no	maximal, Sylow
200	C₂×C₈₉	#2355	1	1	yes	characteristic
201	C₂×C₈₉	C₂×#433	1	1	yes	characteristic
202	C₂×C₈₉	#2925	1	1	yes	characteristic
203	C₂×C₈₉	#2960	1	1	yes	characteristic
204	C₂×C₈₉	#2962	1	1	yes	characteristic
205	C₂×C₈₉	#2993	1	1	yes	characteristic
206	C₂×C₈₉	#2994	1	1	yes	characteristic
207	#2295	—	89	1	no	—
208	#1984	—	89	1	no	—
209	#1984	—	89	1	no	—
210	#1917	—	89	2	no	—
211	#1916	—	89	2	no	—
212	#1842	—	89	1	no	—
213	#1832	—	89	2	no	—
214	#1770	—	89	1	no	—
215	C₈×C₄⋊C₄	—	89	1	no	—
216	#1768	—	89	2	no	—
217	C₄×C₄⋊C₈	D₈₉	1	1	yes	characteristic
218	C₈₉	#22822	1	1	yes	characteristic, complemented, Sylow
219	C₂×C₄×Q₈	—	89	1	no	—
220	C₂×C₄⋊C₈	—	89	2	no	—
221	C₂×C₄⋊C₈	—	89	2	no	—
222	C₂×C₄⋊C₈	—	89	1	no	—
223	C₂×C₄⋊C₈	—	89	1	no	—
224	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
226	C₂×#97	—	89	2	no	—
227	C₂×C₄×C₈	—	89	2	no	—
228	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
229	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
230	#391	—	89	1	no	—
231	#391	—	89	1	no	—
232	#389	—	89	1	no	—
233	#389	—	89	1	no	—
234	#387	—	89	2	no	—
235	#387	—	89	2	no	—
236	C₄×C₄⋊C₄	—	89	1	no	—
237	C₄×C₄⋊C₄	—	89	2	no	—
238	#376	—	89	2	no	—
239	C₄³	C₂×D₈₉	1	1	yes	characteristic
240	#336	—	89	2	no	—
241	#336	—	89	2	no	—
242	#336	—	89	2	no	—
243	#336	—	89	2	no	—
244	#336	—	89	2	no	—
245	#336	—	89	2	no	—
246	#336	C₂×D₈₉	1	1	yes	characteristic
247	#336	C₂×D₈₉	1	1	yes	characteristic
248	C₂²×Q₈	—	89	1	no	—
249	C₂²×C₈	—	89	2	no	—
250	C₂²×C₈	—	89	2	no	—
251	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
253	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
255	C₄×Q₈	—	178	2	no	—
256	C₄×Q₈	—	178	2	no	—
257	C₂×C₄⋊C₄	—	89	2	no	—
258	C₂×C₄⋊C₄	—	89	2	no	—
259	C₂×C₄⋊C₄	—	89	1	no	—
260	C₂×C₄⋊C₄	—	89	2	no	—
261	C₂×C₄⋊C₄	—	89	1	no	—
262	C₂×C₄⋊C₄	—	89	1	no	—
263	C₂×C₄²	—	89	2	no	—
264	C₂×C₄²	—	89	2	no	—
265	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
266	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
267	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
268	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
271	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	356	2	no	—
274	C₄⋊C₈	—	178	4	no	—
275	C₄⋊C₈	—	178	2	no	—
276	C₄⋊C₈	—	178	2	no	—
277	C₄⋊C₈	Dic₁₇₈	1	4	yes	complemented
278	#97	—	356	2	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	356	2	no	—
282	#95	—	89	2	no	—
283	#95	—	89	2	no	—
284	#95	—	89	2	no	—
285	#95	—	89	2	no	—
286	#95	—	89	2	no	—
287	#95	—	89	2	no	—
288	#95	—	89	2	no	—
289	C₂×Q₈	—	178	2	no	—
290	C₂×Q₈	—	178	2	no	—
291	C₂×Q₈	—	178	2	no	—
292	C₂²×C₄	—	89	2	no	—
293	C₂²×C₄	—	89	2	no	—
294	C₂²×C₄	—	89	2	no	—
295	C₂²×C₄	—	89	2	no	—
296	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
302	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	178	2	no	—
314	C₂×C₈	—	178	2	no	—
315	C₂×C₈	—	178	2	no	—
316	C₂×C₈	—	178	2	no	—
317	C₂×C₈	—	178	2	no	—
318	C₂×C₈	—	178	2	no	—
319	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
320	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
321	C₄⋊C₄	—	356	2	no	—
322	C₄⋊C₄	—	178	4	no	—
323	C₄⋊C₄	—	178	2	no	—
324	C₄⋊C₄	—	178	4	no	—
325	C₄⋊C₄	—	178	2	no	—
326	C₄⋊C₄	—	178	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	178	2	no	—
334	C₄²	—	178	2	no	—
335	C₄²	—	178	2	no	—
336	C₄²	—	178	2	no	—
337	C₄²	C₂×Dic₁₇₈	1	2	yes	—
338	C₄²	#13083573	1	2	yes	—
339	C₄²	#13083574	1	2	yes	—
340	C₄²	#13083575	1	2	yes	—
341	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
342	Q₈	—	356	4	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	178	2	no	—
355	C₂×C₄	—	178	2	no	—
356	C₂×C₄	—	178	2	no	—
357	C₂×C₄	—	178	2	no	—
358	C₂×C₄	—	178	2	no	—
359	C₂×C₄	—	178	2	no	—
360	C₂×C₄	—	178	2	no	—
361	C₂×C₄	—	178	2	no	—
362	C₂×C₄	—	178	2	no	—
363	C₂×C₄	—	178	2	no	—
364	C₂×C₄	—	178	2	no	—
365	C₂×C₄	—	178	2	no	—
366	C₂×C₄	#15667970	1	2	yes	—
367	C₂×C₄	#15667970	1	2	yes	—
368	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
369	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
370	C₂×C₄	#15668018	1	2	yes	—
371	C₂×C₄	#15668018	1	2	yes	—
372	C₂×C₄	#15668020	1	2	yes	—
373	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
374	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
375	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
376	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
377	C₂×C₄	#15668058	1	1	yes	characteristic
378	C₂×C₄	#15668059	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	356	2	no	—
384	C₈	—	356	2	no	—
385	C₂²	C₂×#15667970	1	1	yes	characteristic
386	C₂²	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
387	C₂²	#19152078	1	1	yes	characteristic
388	C₂²	C₂×#15668018	1	1	yes	characteristic
389	C₂²	C₂×#15668018	1	1	yes	characteristic
390	C₂²	C₂×#15668020	1	1	yes	characteristic
391	C₂²	#19152364	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	356	2	no	—
398	C₄	—	356	2	no	—
399	C₄	—	356	2	no	—
400	C₄	—	356	2	no	—
401	C₄	#19151658	1	4	yes	—
402	C₄	#19152305	1	1	yes	characteristic
403	C₄	#19152318	1	1	yes	characteristic
404	C₄	#19152327	1	1	yes	characteristic
405	C₄	#19152333	1	1	yes	characteristic
406	C₂	#26023207	1	1	yes	characteristic
407	C₂	C₂×#19151658	1	1	yes	characteristic
408	C₂	#26028917	1	1	yes	characteristic
409	C₂	#26029186	1	1	yes	characteristic
410	C₂	#26029199	1	1	yes	characteristic
411	C₂	#26029403	1	1	yes	characteristic
412	C₂	#26029414	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₄×C₄⋊C₈×C₈₉	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×C₄⋊C₈	D₈₉
hypocenter	C₈₉	#22822
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
79. C₄⋊C₈×C₈₉	Q₈	semidirect
218. C₈₉	#22822	semidirect
277. C₄⋊C₈	Dic₁₇₈	semidirect

Maximal subgroups

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

subgroup	index
#26022729	2
#26021188	2
#26020819	2
#26020812	2
#26020404	2
#26020371	2
#26020119	2
C₈×C₄⋊Dic₈₉	2
#26020111	2
C₄×C₄⋊C₈×C₈₉	2
#22822	89