Subgroups — #36447112

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₃₅₆	C₂	1	1	yes	maximal, characteristic
2	#26020404	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151327	C₂	1	2	yes	maximal
4	#26018092	C₂	1	2	yes	maximal, complemented
5	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₃₅₆	C₄	1	1	yes	characteristic
7	C₂×C₄×D₃₅₆	C₄	1	1	yes	characteristic
8	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
9	C₂×C₄²×D₈₉	—	2	1	no	—
10	C₂×C₄⋊#10623494	—	2	1	no	—
11	C₂×C₄⋊#10623494	—	2	1	no	—
12	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
13	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
14	C₄×C₄⋊Dic₈₉	C₄	1	1	yes	characteristic
15	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
16	C₄×#13083551	—	2	1	no	—
17	C₄×#13083551	—	2	1	no	—
18	C₄×#13083551	—	2	1	no	—
19	#19151327	—	2	4	no	—
20	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
21	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
22	C₄³×C₈₉	C₂²	1	1	yes	characteristic
23	#336×C₈₉	—	2	1	no	—
24	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₄×D₈₉	—	2	1	no	—
26	C₂²×C₄×D₈₉	—	2	1	no	—
27	C₂²×C₄×D₈₉	—	2	1	no	—
28	C₂²×#10623494	—	2	2	no	—
29	C₄×D₃₅₆	—	2	2	no	—
30	C₄×D₃₅₆	—	2	2	no	—
31	C₄×D₃₅₆	—	2	2	no	—
32	C₄×D₃₅₆	—	2	1	no	—
33	C₄×D₃₅₆	—	2	1	no	—
34	C₄×D₃₅₆	C₈	1	4	yes	complemented
35	C₄×D₃₅₆	D₄	1	2	yes	—
36	C₄×D₃₅₆	Q₈	1	2	yes	—
37	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂×#13083551	—	2	1	no	—
41	C₂×#13083551	—	2	1	no	—
42	C₂×#13083551	—	2	1	no	—
43	C₂×C₄×Dic₈₉	—	2	1	no	—
44	C₂×C₄×Dic₈₉	—	2	1	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	C₄²×D₈₉	—	4	2	no	—
47	C₄²×D₈₉	—	4	2	no	—
48	C₄⋊#10623494	—	2	2	no	—
49	C₄⋊#10623494	—	2	2	no	—
50	C₄⋊#10623494	—	4	2	no	—
51	C₄⋊#10623494	—	4	2	no	—
52	#15667919	—	2	1	no	—
53	#15667919	—	2	1	no	—
54	#15667919	—	2	1	no	—
55	C₂²×C₈×C₈₉	—	2	2	no	—
56	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₈₉	—	2	4	no	—
64	C₄×C₈×C₈₉	—	2	2	no	—
65	C₄×C₈×C₈₉	—	2	2	no	—
66	C₂³×D₈₉	—	2	1	no	—
67	C₂×D₃₅₆	—	2	1	no	—
68	C₂×D₃₅₆	—	2	1	no	—
69	C₂×D₃₅₆	—	2	1	no	—
70	C₂×D₃₅₆	C₄⋊C₄	1	2	yes	—
71	C₂×D₃₅₆	C₂×C₈	1	2	yes	—
72	C₂×D₃₅₆	M₁₆	1	2	yes	—
73	C₂²×Dic₈₉	—	2	1	no	—
74	C₂²×Dic₈₉	—	2	1	no	—
75	C₂²×Dic₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	2	4	no	—
77	C₂×C₄×D₈₉	—	2	4	no	—
78	C₂×C₄×D₈₉	—	2	2	no	—
79	C₂×C₄×D₈₉	—	2	2	no	—
80	C₂×C₄×D₈₉	—	4	2	no	—
81	C₂×C₄×D₈₉	—	4	2	no	—
82	C₂×C₄×D₈₉	—	4	2	no	—
83	C₂×C₄×D₈₉	—	4	2	no	—
84	C₂×C₄×D₈₉	—	4	1	no	—
85	C₂×C₄×D₈₉	—	4	1	no	—
86	C₂×C₄×D₈₉	—	4	1	no	—
87	C₂×C₄×D₈₉	—	4	1	no	—
88	C₂×#10623494	—	4	2	no	—
89	C₂×#10623494	—	4	2	no	—
90	C₂×#10623494	—	4	2	no	—
91	C₄⋊Dic₈₉	—	2	1	no	—
92	C₄⋊Dic₈₉	—	2	1	no	—
93	C₄⋊Dic₈₉	—	2	1	no	—
94	C₄⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
95	C₄⋊Dic₈₉	C₂×C₈	1	2	yes	—
96	C₄⋊Dic₈₉	M₁₆	1	2	yes	—
97	#13083551	—	2	4	no	—
98	#13083551	—	2	4	no	—
99	#13083551	—	2	2	no	—
100	#13083551	—	2	2	no	—
101	C₄×Dic₈₉	—	4	2	no	—
102	C₄×Dic₈₉	—	4	2	no	—
103	C₄×Dic₈₉	—	4	1	no	—
104	C₄×Dic₈₉	—	4	1	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	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₈₉	—	2	4	no	—
113	C₂×C₈×C₈₉	—	4	2	no	—
114	C₂×C₈×C₈₉	—	4	2	no	—
115	C₄²×C₈₉	—	2	2	no	—
116	C₄²×C₈₉	—	2	1	no	—
117	C₄²×C₈₉	—	2	1	no	—
118	C₄²×C₈₉	—	2	1	no	—
119	C₄²×C₈₉	—	2	1	no	—
120	C₄²×C₈₉	—	4	1	no	—
121	C₄²×C₈₉	C₂×C₈	1	2	yes	—
122	C₄²×C₈₉	M₁₆	1	2	yes	—
123	C₄²×C₈₉	D₈	1	2	yes	—
124	C₄²×C₈₉	SD₁₆	1	2	yes	—
125	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₈₉	#41	1	1	yes	characteristic
128	C₄²×C₈₉	#41	1	1	yes	characteristic
129	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×D₈₉	—	2	2	no	—
131	C₂²×D₈₉	—	2	2	no	—
132	C₂²×D₈₉	—	2	2	no	—
133	C₂²×D₈₉	—	4	1	no	—
134	C₂²×D₈₉	—	4	1	no	—
135	C₂²×D₈₉	—	4	1	no	—
136	C₂²×D₈₉	—	4	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	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₈₉	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₈₉	#102	1	2	yes	—
149	C₂×C₄×C₈₉	#102	1	2	yes	—
150	C₂×C₄×C₈₉	#104	1	2	yes	—
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
163	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	4	1	no	—
170	C₂×Dic₈₉	—	4	1	no	—
171	C₂×Dic₈₉	—	4	1	no	—
172	C₂×Dic₈₉	—	4	1	no	—
173	C₂×Dic₈₉	—	4	1	no	—
174	D₃₅₆	—	2	2	no	—
175	D₃₅₆	—	2	2	no	—
176	D₃₅₆	—	2	2	no	—
177	D₃₅₆	C₄⋊C₈	1	4	yes	complemented
178	C₄×D₈₉	—	4	8	no	—
179	C₄×D₈₉	—	4	8	no	—
180	C₄×D₈₉	—	4	2	no	—
181	C₄×D₈₉	—	4	2	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	C₈×C₈₉	—	4	4	no	—
185	#10623494	—	8	2	no	—
186	C₂²×C₈₉	#380	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
188	C₂²×C₈₉	#407	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
190	C₂²×C₈₉	#417	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#104	1	1	yes	characteristic
192	C₂²×C₈₉	#421	1	1	yes	characteristic
193	C₂×D₈₉	—	2	4	no	—
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	4	2	no	—
198	C₂×D₈₉	—	4	2	no	—
199	C₂×D₈₉	—	4	2	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	2	no	—
203	C₄×C₈₉	—	2	2	no	—
204	C₄×C₈₉	—	4	1	no	—
205	C₄×C₈₉	D₄⋊C₈	1	4	yes	complemented
206	C₄×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
207	C₄×C₈₉	#423	1	1	yes	characteristic
208	C₄×C₈₉	#431	1	1	yes	characteristic
209	C₄×C₈₉	#432	1	1	yes	characteristic
210	C₄×C₈₉	#459	1	1	yes	characteristic
211	C₄×C₈₉	#461	1	1	yes	characteristic
212	C₄×C₈₉	#474	1	1	yes	characteristic
213	C₄×C₈₉	#476	1	1	yes	characteristic
214	Dic₈₉	—	4	2	no	—
215	Dic₈₉	—	4	2	no	—
216	Dic₈₉	—	4	2	no	—
217	#8563	—	89	1	no	maximal, Sylow
218	C₂×C₈₉	C₂×D₄⋊C₈	1	1	yes	characteristic
219	C₂×C₈₉	#1477	1	1	yes	characteristic
220	C₂×C₈₉	#1486	1	1	yes	characteristic
221	C₂×C₈₉	#1489	1	1	yes	characteristic
222	C₂×C₈₉	#1797	1	1	yes	characteristic
223	C₂×C₈₉	#1802	1	1	yes	characteristic
224	C₂×C₈₉	#1806	1	1	yes	characteristic
225	D₈₉	—	4	4	no	—
226	C₄²×D₄	—	89	1	no	—
227	#1842	—	89	1	no	—
228	C₄×C₄⋊C₈	D₈₉	1	1	yes	characteristic, complemented
229	C₂×D₄⋊C₈	—	89	2	no	—
230	#1279	—	89	2	no	—
231	C₈₉	#8563	1	1	yes	characteristic, complemented, Sylow
232	C₂×C₄×D₄	—	89	1	no	—
233	C₂×C₄×D₄	—	89	1	no	—
234	C₂×C₄×D₄	—	89	1	no	—
235	C₂²×C₄²	—	178	1	no	—
236	C₂×C₄⋊C₈	—	2	1	no	—
237	C₂×C₄⋊C₈	—	89	2	no	—
238	C₂×C₄⋊C₈	—	178	1	no	—
239	C₂×C₄⋊C₈	—	178	1	no	—
240	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
241	C₄×C₄⋊C₄	—	89	1	no	—
242	C₄×C₄⋊C₄	—	89	1	no	—
243	C₄×C₄⋊C₄	—	89	1	no	—
244	C₄×C₂²⋊C₄	—	178	1	no	—
245	C₄×C₂²⋊C₄	—	178	1	no	—
246	C₄×C₂²⋊C₄	—	178	1	no	—
247	C₄³	C₂×D₈₉	1	1	yes	characteristic
248	#336	—	2	1	no	—
249	D₄⋊C₈	—	178	4	no	—
250	C₂²×D₄	—	89	1	no	—
251	C₂³×C₄	—	178	1	no	—
252	C₂³×C₄	—	178	1	no	—
253	C₂³×C₄	—	178	1	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	178	2	no	—
256	C₄×D₄	—	89	4	no	—
257	C₄×D₄	—	89	2	no	—
258	C₄×D₄	—	89	2	no	—
259	C₄×D₄	—	178	2	no	—
260	C₄×D₄	—	178	2	no	—
261	C₄×D₄	—	178	2	no	—
262	C₄×D₄	—	178	1	no	—
263	C₄×D₄	—	178	1	no	—
264	C₂×C₄⋊C₄	—	89	1	no	—
265	C₂×C₄⋊C₄	—	89	1	no	—
266	C₂×C₄⋊C₄	—	89	1	no	—
267	C₂×C₂²⋊C₄	—	178	1	no	—
268	C₂×C₂²⋊C₄	—	178	1	no	—
269	C₂×C₂²⋊C₄	—	178	1	no	—
270	C₂×C₄²	—	356	2	no	—
271	C₂×C₄²	—	356	2	no	—
272	C₂×C₄²	—	178	1	no	—
273	C₂×C₄²	—	178	1	no	—
274	C₂×C₄²	—	178	1	no	—
275	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
276	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
277	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
278	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
279	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
280	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	356	2	no	—
284	C₄⋊C₈	—	356	2	no	—
285	C₄⋊C₈	—	178	2	no	—
286	C₄⋊C₈	—	178	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	178	1	no	—
290	#95	—	178	1	no	—
291	#95	—	178	1	no	—
292	C₂⁴	—	178	1	no	—
293	C₂×D₄	—	89	2	no	—
294	C₂×D₄	—	89	2	no	—
295	C₂×D₄	—	89	2	no	—
296	C₂×D₄	—	178	1	no	—
297	C₂×D₄	—	178	1	no	—
298	C₂×D₄	—	178	1	no	—
299	C₂²×C₄	—	356	2	no	—
300	C₂²×C₄	—	356	1	no	—
301	C₂²×C₄	—	356	1	no	—
302	C₂²×C₄	—	356	1	no	—
303	C₂²×C₄	—	356	1	no	—
304	C₂²×C₄	—	356	2	no	—
305	C₂²×C₄	—	356	2	no	—
306	C₂²×C₄	—	356	2	no	—
307	C₂²×C₄	—	178	4	no	—
308	C₂²×C₄	—	178	1	no	—
309	C₂²×C₄	—	178	1	no	—
310	C₂²×C₄	—	178	1	no	—
311	C₂²×C₄	—	178	2	no	—
312	C₂²×C₄	—	178	2	no	—
313	C₂²×C₄	—	178	4	no	—
314	C₂²×C₄	#13083551	1	1	yes	characteristic
315	C₂²×C₄	#13083551	1	1	yes	characteristic
316	C₂²×C₄	#13083551	1	1	yes	characteristic
317	C₂²×C₄	#13083551	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	356	2	no	—
325	C₂×C₈	—	356	2	no	—
326	C₂×C₈	—	356	2	no	—
327	C₄⋊C₄	—	89	2	no	—
328	C₄⋊C₄	—	89	2	no	—
329	C₄⋊C₄	—	89	2	no	—
330	C₄⋊C₄	—	178	1	no	—
331	C₄⋊C₄	—	178	1	no	—
332	C₄⋊C₄	—	178	1	no	—
333	C₂²⋊C₄	—	178	4	no	—
334	C₂²⋊C₄	—	178	2	no	—
335	C₂²⋊C₄	—	178	2	no	—
336	C₂²⋊C₄	—	178	4	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	356	1	no	—
344	C₄²	—	356	1	no	—
345	C₄²	—	356	2	no	—
346	C₄²	—	356	2	no	—
347	C₄²	C₈×D₈₉	1	2	yes	—
348	C₄²	#13083557	1	2	yes	—
349	C₄²	D₇₁₂	1	2	yes	—
350	C₄²	#13083563	1	2	yes	—
351	C₄²	D₄×D₈₉	1	1	yes	characteristic
352	C₄²	Q₈×D₈₉	1	1	yes	characteristic
353	C₄²	#13083573	1	1	yes	characteristic
354	C₄²	#13083575	1	1	yes	characteristic
355	C₂³	—	356	1	no	—
356	C₂³	—	356	1	no	—
357	C₂³	—	356	1	no	—
358	C₂³	—	356	1	no	—
359	C₂³	—	178	2	no	—
360	C₂³	—	178	2	no	—
361	C₂³	—	178	2	no	—
362	C₂³	C₂×#13083551	1	1	yes	characteristic
363	D₄	—	89	4	no	—
364	D₄	—	178	2	no	—
365	D₄	—	178	2	no	—
366	D₄	—	178	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	356	8	no	—
377	C₂×C₄	—	356	1	no	—
378	C₂×C₄	—	356	1	no	—
379	C₂×C₄	—	356	1	no	—
380	C₂×C₄	—	356	1	no	—
381	C₂×C₄	—	356	1	no	—
382	C₂×C₄	—	356	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	8	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	#15667924	1	2	yes	—
392	C₂×C₄	#15667924	1	2	yes	—
393	C₂×C₄	#15667934	1	2	yes	—
394	C₂×C₄	#15667934	1	2	yes	—
395	C₂×C₄	#15667940	1	2	yes	—
396	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
397	C₂×C₄	#15667970	1	1	yes	characteristic
398	C₂×C₄	#15667983	1	1	yes	characteristic
399	C₂×C₄	#15667987	1	1	yes	characteristic
400	C₂×C₄	#15667988	1	1	yes	characteristic
401	C₂×C₄	#15667992	1	1	yes	characteristic
402	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
403	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
404	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#13083557	1	1	yes	characteristic
406	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
407	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
408	C₂×C₄	#15668040	1	1	yes	characteristic
409	C₂×C₄	#15668045	1	1	yes	characteristic
410	C₈	—	4	4	no	—
411	C₈	—	712	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	356	2	no	—
414	C₂²	—	356	2	no	—
415	C₂²	—	356	2	no	—
416	C₂²	—	356	2	no	—
417	C₂²	—	356	2	no	—
418	C₂²	—	178	4	no	—
419	C₂²	#19151455	1	1	yes	characteristic
420	C₂²	C₂×#15667924	1	1	yes	characteristic
421	C₂²	#19151561	1	1	yes	characteristic
422	C₂²	C₂×#15667934	1	1	yes	characteristic
423	C₂²	#19151600	1	1	yes	characteristic
424	C₂²	C₂×#15667940	1	1	yes	characteristic
425	C₂²	#19151616	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	356	2	no	—
432	C₄	—	356	2	no	—
433	C₄	—	356	2	no	—
434	C₄	#19151327	1	4	yes	complemented
435	C₄	C₄⋊C₈×D₈₉	1	1	yes	characteristic
436	C₄	#19151620	1	1	yes	characteristic
437	C₄	#19151650	1	1	yes	characteristic
438	C₄	#19151654	1	1	yes	characteristic
439	C₄	#19151794	1	1	yes	characteristic
440	C₄	#19151804	1	1	yes	characteristic
441	C₄	#19151879	1	1	yes	characteristic
442	C₄	#19151889	1	1	yes	characteristic
443	C₂	—	356	4	no	—
444	C₂	C₂×#19151327	1	1	yes	characteristic
445	C₂	#26018640	1	1	yes	characteristic
446	C₂	#26018678	1	1	yes	characteristic
447	C₂	#26018692	1	1	yes	characteristic
448	C₂	#26020229	1	1	yes	characteristic
449	C₂	#26020253	1	1	yes	characteristic
450	C₂	#26020273	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄×C₄⋊C₈×C₈₉	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂²×D₃₅₆	C₂×C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₈₉
hypocenter	C₈₉	#8563
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. #26020404	C₂	semidirect
4. #26018092	C₂	semidirect
5. C₄×C₄⋊C₈×C₈₉	C₂	semidirect
34. C₄×D₃₅₆	C₈	semidirect
177. D₃₅₆	C₄⋊C₈	semidirect
205. C₄×C₈₉	D₄⋊C₈	semidirect
228. C₄×C₄⋊C₈	D₈₉	semidirect
231. C₈₉	#8563	semidirect
434. C₄	#19151327	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₃₅₆	2
#26020404	2
C₂×#19151327	2
#26018092	2
C₄×C₄⋊C₈×C₈₉	2
#8563	89