Subgroups — #36524249

Order 22784.

636 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	#26029369	C₂	1	1	yes	maximal, characteristic
2	#26029337	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019161	C₂	1	2	yes	maximal, complemented
4	#26019155	C₂	1	2	yes	maximal, complemented
5	#26019149	C₂	1	2	yes	maximal, complemented
6	#26019143	C₂	1	2	yes	maximal, complemented
7	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018634	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#137×C₈₉	C₂	1	1	yes	maximal, characteristic
12	#19151729	—	2	1	no	—
13	#19151729	—	2	1	no	—
14	#19151729	C₂²	1	2	yes	—
15	#19151729	C₂²	1	2	yes	—
16	#19151729	C₂²	1	2	yes	—
17	#19151676	C₂²	1	2	yes	—
18	#19151670	—	2	2	no	—
19	#19151655	—	2	1	no	—
20	#19151655	—	2	2	no	—
21	#19151651	C₂²	1	1	yes	characteristic
22	#19151651	C₂²	1	1	yes	characteristic
23	#19151622	—	2	1	no	—
24	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151351	C₂²	1	2	yes	—
27	#19151349	C₂²	1	2	yes	—
28	Q₈⋊#10623494	C₂²	1	2	yes	—
29	Q₈⋊#10623494	C₂²	1	2	yes	—
30	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
32	D₄⋊#10623494	C₂²	1	1	yes	characteristic
33	D₄⋊#10623494	C₂²	1	1	yes	characteristic
34	#19151319	C₂²	1	2	yes	—
35	C₈×#10623494	C₂²	1	2	yes	—
36	C₂×#137×C₈₉	C₄	1	1	yes	characteristic
37	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
39	#441×C₈₉	C₄	1	2	yes	—
40	#440×C₈₉	C₄	1	2	yes	—
41	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
42	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
43	#428×C₈₉	C₄	1	1	yes	characteristic
44	#419×C₈₉	C₄	1	1	yes	characteristic
45	#417×C₈₉	C₄	1	1	yes	characteristic
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083558	—	2	2	no	—
48	C₂²×#10623494	—	2	1	no	—
49	C₂²×#10623494	—	2	1	no	—
50	C₄⋊#10623494	—	2	2	no	—
51	C₄⋊#10623494	—	2	2	no	—
52	C₄⋊#10623494	—	2	2	no	—
53	C₄⋊#10623494	—	2	1	no	—
54	C₄⋊#10623494	D₄	1	1	yes	characteristic
55	C₄⋊#10623494	D₄	1	1	yes	characteristic
56	C₄⋊#10623494	C₂³	1	2	yes	—
57	C₄⋊#10623494	C₂³	1	1	yes	characteristic
58	C₄⋊#10623494	C₂³	1	1	yes	characteristic
59	C₂²⋊#10623494	—	2	2	no	—
60	C₂²⋊#10623494	—	2	1	no	—
61	C₂²⋊#10623494	D₄	1	2	yes	—
62	#15667923	—	2	2	no	—
63	#15667923	—	2	2	no	—
64	#15667923	—	2	2	no	—
65	C₄×#10623494	—	2	1	no	—
66	C₄×#10623494	—	2	1	no	—
67	C₄×#10623494	C₂³	1	1	yes	characteristic
68	C₄×#10623494	C₂³	1	1	yes	characteristic
69	C₄×#10623494	C₂³	1	2	yes	—
70	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
72	#137×C₈₉	—	2	4	no	—
73	C₂×Q₁₆×C₈₉	C₂×C₄	1	2	yes	—
74	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
75	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₄×Q₈×C₈₉	—	2	1	no	—
78	C₄×Q₈×C₈₉	—	2	1	no	—
79	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
82	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₈₉	—	2	1	no	—
84	C₄×D₄×C₈₉	—	2	1	no	—
85	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	#117×C₈₉	—	2	1	no	—
88	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
90	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	#107×C₈₉	C₂×C₄	1	2	yes	—
95	#106×C₈₉	C₂×C₄	1	2	yes	—
96	#103×C₈₉	C₂×C₄	1	2	yes	—
97	#103×C₈₉	C₂×C₄	1	2	yes	—
98	#103×C₈₉	C₂×C₄	1	2	yes	—
99	#102×C₈₉	C₂×C₄	1	2	yes	—
100	#97×C₈₉	C₂×C₄	1	2	yes	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083558	—	8	2	no	—
103	C₂×#10623494	—	2	1	no	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	—	2	1	no	—
106	C₂×#10623494	—	2	1	no	—
107	C₂×#10623494	—	2	1	no	—
108	C₂×#10623494	—	4	2	no	—
109	C₂×#10623494	—	8	1	no	—
110	C₂×#10623494	C₂×D₄	1	2	yes	—
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	#41×C₈₉	—	2	2	no	—
113	#41×C₈₉	—	2	2	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	2	no	—
116	C₂×Q₈×C₈₉	—	2	2	no	—
117	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
118	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×D₄×C₈₉	—	2	1	no	—
120	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	Q₁₆×C₈₉	—	2	4	no	—
130	SD₁₆×C₈₉	—	2	4	no	—
131	M₁₆×C₈₉	—	2	2	no	—
132	M₁₆×C₈₉	M₁₆	1	4	yes	complemented
133	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	2	2	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₈₉	—	2	1	no	—
144	C₂²⋊C₄×C₈₉	—	2	1	no	—
145	C₂²⋊C₄×C₈₉	—	2	1	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	#41	1	1	yes	characteristic
154	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₈₉	—	2	2	no	—
158	Q₈×C₈₉	—	2	1	no	—
159	Q₈×C₈₉	—	2	2	no	—
160	Q₈×C₈₉	—	2	1	no	—
161	Q₈×C₈₉	—	4	2	no	—
162	D₄×C₈₉	—	2	1	no	—
163	D₄×C₈₉	—	2	1	no	—
164	D₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	1	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	—	8	1	no	—
178	C₂×C₄×C₈₉	—	8	1	no	—
179	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₈₉	#131	1	2	yes	—
184	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	C₂×M₁₆	1	4	yes	—
189	#10623494	—	2	2	no	—
190	#10623494	—	2	2	no	—
191	#10623494	—	2	2	no	—
192	#10623494	—	4	1	no	—
193	#10623494	—	4	1	no	—
194	#10623494	—	4	2	no	—
195	#10623494	—	4	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	#436	1	2	yes	—
202	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	4	1	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	—	4	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	4	2	no	—
211	C₄×C₈₉	#436	1	2	yes	—
212	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
213	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
214	C₄×C₈₉	#577	1	1	yes	characteristic
215	C₄×C₈₉	#578	1	1	yes	characteristic
216	#17894	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	—	8	1	no	—
219	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
220	C₂×C₈₉	#2947	1	1	yes	characteristic
221	C₂×C₈₉	#2956	1	1	yes	characteristic
222	#2989	—	89	1	no	—
223	#2983	—	89	1	no	—
224	C₄×#137	D₈₉	1	1	yes	characteristic
225	#1593	—	89	2	no	—
226	#1592	—	89	2	no	—
227	#1591	—	89	2	no	—
228	#1590	—	89	2	no	—
229	#1565	—	89	1	no	—
230	#1476	—	89	1	no	—
231	C₂×Q₈⋊C₈	—	89	1	no	—
232	C₈×M₁₆	—	89	1	no	—
233	C₈₉	#17894	1	1	yes	characteristic, complemented, Sylow
234	C₂×#137	Dic₈₉	1	1	yes	characteristic
235	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
237	#446	—	89	2	no	—
238	#446	—	89	2	no	—
239	#446	—	89	2	no	—
240	#446	—	178	1	no	—
241	#446	—	178	1	no	—
242	#441	Dic₈₉	1	2	yes	—
243	#440	Dic₈₉	1	2	yes	—
244	C₄×Q₁₆	C₂×D₈₉	1	2	yes	—
245	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
246	#436	—	89	2	no	—
247	#435	—	178	2	no	—
248	#432	—	178	2	no	—
249	#432	—	178	1	no	—
250	#431	—	89	1	no	—
251	#431	—	89	1	no	—
252	#428	Dic₈₉	1	1	yes	characteristic
253	#423	—	178	1	no	—
254	C₂×C₄⋊C₈	—	89	1	no	—
255	#419	Dic₈₉	1	1	yes	characteristic
256	#417	Dic₈₉	1	1	yes	characteristic
257	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	—	89	1	no	—
259	#335	—	89	2	no	—
260	#334	—	89	2	no	—
261	Q₈⋊C₈	—	89	2	no	—
262	Q₈⋊C₈	—	89	1	no	—
263	Q₈⋊C₈	—	89	2	no	—
264	Q₈⋊C₈	—	89	1	no	—
265	D₄⋊C₈	—	89	1	no	—
266	D₄⋊C₈	—	89	1	no	—
267	#322	—	89	2	no	—
268	C₈²	—	89	2	no	—
269	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
270	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
271	#137	—	2	4	no	—
272	C₂×Q₁₆	C₂×Dic₈₉	1	2	yes	—
273	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
274	C₂×M₁₆	—	178	2	no	—
275	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
276	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
277	C₂²×C₈	—	178	1	no	—
278	C₂²×C₈	—	178	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
282	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
283	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
284	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
288	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
289	#117	—	2	1	no	—
290	#117	C₂×Dic₈₉	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
296	#107	C₂×Dic₈₉	1	2	yes	—
297	#106	C₂×Dic₈₉	1	2	yes	—
298	C₄⋊C₈	—	89	1	no	—
299	C₄⋊C₈	—	89	1	no	—
300	C₄⋊C₈	—	89	1	no	—
301	C₄⋊C₈	—	89	1	no	—
302	C₄⋊C₈	—	89	2	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	—	178	2	no	—
305	C₄⋊C₈	—	178	2	no	—
306	C₄⋊C₈	—	178	1	no	—
307	#103	C₂×Dic₈₉	1	2	yes	—
308	#103	C₂×Dic₈₉	1	2	yes	—
309	#103	C₂×Dic₈₉	1	2	yes	—
310	#102	C₂×Dic₈₉	1	2	yes	—
311	C₂²⋊C₈	—	89	2	no	—
312	C₂²⋊C₈	—	178	2	no	—
313	C₂²⋊C₈	—	178	1	no	—
314	#97	—	178	2	no	—
315	#97	—	178	2	no	—
316	#97	—	178	2	no	—
317	#97	C₂×Dic₈₉	1	2	yes	—
318	C₄×C₈	—	89	2	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	1	no	—
321	C₄×C₈	—	178	1	no	—
322	C₄×C₈	—	178	1	no	—
323	C₄×C₈	C₂²×D₈₉	1	2	yes	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
330	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	#13083573	1	1	yes	characteristic
341	Q₁₆	—	2	4	no	—
342	SD₁₆	—	2	4	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	712	2	no	—
345	M₁₆	#13083558	1	4	yes	complemented
346	C₂×C₈	—	89	2	no	—
347	C₂×C₈	—	89	2	no	—
348	C₂×C₈	—	356	2	no	—
349	C₂×C₈	—	178	1	no	—
350	C₂×C₈	—	178	1	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	—	178	1	no	—
353	C₂×C₈	—	178	1	no	—
354	C₂×C₈	—	712	1	no	—
355	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
356	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
363	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
364	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
374	C₄²	D₄×D₈₉	1	1	yes	characteristic
375	C₄²	#13083573	1	1	yes	characteristic
376	C₄²	C₂³×D₈₉	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	1	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	1	no	—
385	D₄	—	2	1	no	—
386	D₄	—	4	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	—	8	1	no	—
401	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
402	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
403	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
404	C₂×C₄	C₂×#13083558	1	2	yes	—
405	C₂×C₄	#15668019	1	2	yes	—
406	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	356	1	no	—
411	C₈	—	356	1	no	—
412	C₈	—	356	2	no	—
413	C₈	—	356	1	no	—
414	C₈	—	178	2	no	—
415	C₈	—	178	2	no	—
416	C₈	—	178	2	no	—
417	C₈	C₂×#13083558	1	4	yes	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	#19151676	1	2	yes	—
424	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	2	no	—
433	C₄	#19151676	1	2	yes	—
434	C₄	C₂²×#13083558	1	1	yes	characteristic
435	C₄	C₂×#15668019	1	1	yes	characteristic
436	C₄	#19152407	1	1	yes	characteristic
437	C₄	#19152414	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	C₂×#19151676	1	1	yes	characteristic
441	C₂	#26029096	1	1	yes	characteristic
442	C₂	#26029162	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₄×#137×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#41×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×#137	D₈₉
hypocenter	C₈₉	#17894
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
2. #26029337	C₂	semidirect
3. #26019161	C₂	semidirect
4. #26019155	C₂	semidirect
5. #26019149	C₂	semidirect
6. #26019143	C₂	semidirect
7. #26019004	C₂	semidirect
9. C₂×Q₈⋊#10623494	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
132. M₁₆×C₈₉	M₁₆	semidirect
233. C₈₉	#17894	semidirect
345. M₁₆	#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26029369	2
#26029337	2
#26019161	2
#26019155	2
#26019149	2
#26019143	2
#26019004	2
#26018634	2
C₂×Q₈⋊#10623494	2
M₁₆×#10623494	2
C₄×#137×C₈₉	2
#17894	89