Subgroups — #36707630

Order 22784.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152016	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028946	C₂	1	1	yes	maximal, characteristic
3	#26022082	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	#26022075	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
7	#26022012	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021867	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊#13083549	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	1	yes	characteristic
13	#19152109	C₄	1	1	yes	characteristic
14	#19152016	—	2	4	no	—
15	C₂×#15667951	C₂²	1	2	yes	complemented
16	C₂²×#13083549	C₂²	1	1	yes	characteristic
17	C₂²×#13083549	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
19	#19151669	C₄	1	2	yes	—
20	#19151669	C₄	1	2	yes	—
21	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
23	#19151624	C₄	1	1	yes	characteristic
24	#19151564	C₄	1	1	yes	characteristic
25	#19151562	C₄	1	1	yes	characteristic
26	#19151553	C₂²	1	1	yes	characteristic
27	#19151416	C₂²	1	2	yes	complemented
28	#19151416	C₂²	1	2	yes	complemented
29	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
30	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
31	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
32	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
33	#19151377	C₂²	1	2	yes	complemented
34	#19151377	C₂²	1	2	yes	complemented
35	#19151373	C₂²	1	2	yes	complemented
36	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
37	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×M₃₂×C₈₉	—	2	4	no	—
39	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
41	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
43	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
44	#15668018	—	2	2	no	—
45	#15668018	—	2	2	no	—
46	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083557	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₈₉	C₂³	1	2	yes	—
50	#15667995	C₈	1	2	yes	—
51	#15667991	C₈	1	1	yes	characteristic
52	#15667991	C₈	1	1	yes	characteristic
53	#15667986	C₈	1	1	yes	characteristic
54	#15667986	C₈	1	1	yes	characteristic
55	#15667981	C₈	1	2	yes	—
56	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
58	#15667971	C₂×C₄	1	1	yes	characteristic
59	#15667951	—	2	4	no	—
60	C₂×#13083549	—	2	2	no	—
61	C₂×#13083549	—	2	2	no	—
62	C₂×#13083549	C₂³	1	1	yes	characteristic
63	C₂×#13083549	C₂³	1	1	yes	characteristic
64	C₂×#13083549	C₂³	1	1	yes	characteristic
65	C₂×#13083549	C₂³	1	1	yes	characteristic
66	C₁₆×D₈₉	—	2	4	no	—
67	#15667941	C₂×C₄	1	2	yes	—
68	#15667941	C₂×C₄	1	2	yes	—
69	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
70	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
71	#15667924	C₂×C₄	1	2	yes	—
72	#15667924	C₂×C₄	1	2	yes	—
73	#15667922	C₂×C₄	1	2	yes	—
74	C₈×Dic₈₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	—	2	2	no	—
77	C₂²×C₈×C₈₉	—	2	2	no	—
78	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	M₃₂×C₈₉	—	2	2	no	—
85	M₃₂×C₈₉	—	2	4	no	—
86	M₃₂×C₈₉	D₄	1	4	yes	complemented
87	C₂×C₁₆×C₈₉	—	2	4	no	—
88	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
89	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
90	#13083574	—	2	2	no	—
91	#13083574	—	2	2	no	—
92	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
93	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
94	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
95	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
96	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
98	#13083558	—	2	2	no	—
99	#13083558	—	2	2	no	—
100	#13083557	—	2	4	no	—
101	C₂×#10623494	C₂²×C₄	1	2	yes	—
102	C₂×#10623494	C₂²×C₄	1	2	yes	—
103	C₈×D₈₉	—	2	2	no	—
104	C₈×D₈₉	—	2	2	no	—
105	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
106	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
107	#13083553	C₂×C₈	1	2	yes	—
108	#13083553	C₂×C₈	1	2	yes	—
109	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
110	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
111	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
112	#13083551	C₂×C₈	1	2	yes	—
113	#13083551	C₂×C₈	1	2	yes	—
114	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
115	#13083549	—	2	1	no	—
116	#13083549	—	2	1	no	—
117	#13083549	—	2	1	no	—
118	#13083549	—	2	1	no	—
119	C₂⁴×C₈₉	C₂×C₈	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	—	2	2	no	—
121	C₂²×C₄×C₈₉	—	2	2	no	—
122	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₈₉	—	2	2	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₈₉	#41	1	2	yes	—
140	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₁₆×C₈₉	—	2	2	no	—
142	C₁₆×C₈₉	C₂×D₄	1	4	yes	—
143	C₂³×C₈₉	—	2	2	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	—	4	1	no	—
146	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
148	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#131	1	2	yes	—
162	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	2	4	no	—
164	C₂²⋊D₈₉	—	2	4	no	—
165	C₂²⋊D₈₉	—	4	2	no	—
166	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
167	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
168	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
169	D₃₅₆	—	2	2	no	—
170	C₄×D₈₉	—	2	2	no	—
171	C₄×D₈₉	—	2	2	no	—
172	Dic₁₇₈	—	2	2	no	—
173	C₈×C₈₉	—	2	1	no	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	C₄×D₄	1	2	yes	—
176	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
178	#10623494	—	2	2	no	—
179	#10623494	—	2	2	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	—	2	1	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	C₈×D₄	1	2	yes	—
189	C₂²×C₈₉	#504	1	2	yes	complemented
190	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
191	C₂×D₈₉	—	2	2	no	—
192	C₂×D₈₉	—	2	2	no	—
193	C₂×D₈₉	—	2	2	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	C₈×D₄	1	2	yes	—
197	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
199	Dic₈₉	—	2	2	no	—
200	Dic₈₉	—	2	2	no	—
201	Dic₈₉	—	2	2	no	—
202	#33436	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	—	2	2	no	—
204	C₂×C₈₉	—	2	2	no	—
205	C₂×C₈₉	—	4	1	no	—
206	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
208	C₂×C₈₉	#3407	1	1	yes	characteristic
209	D₈₉	—	4	2	no	—
210	C₂×#504	—	89	1	no	—
211	C₂²×M₃₂	D₈₉	1	1	yes	characteristic, complemented
212	#2929	—	89	1	no	—
213	#2169	—	89	2	no	—
214	#2168	—	89	2	no	—
215	#2168	—	89	2	no	—
216	D₄×C₁₆	—	89	2	no	—
217	#2151	—	89	1	no	—
218	#2113	—	89	1	no	—
219	C₂×C₂²⋊C₁₆	—	89	1	no	—
220	#2108	—	89	1	no	—
221	C₈₉	#33436	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	—	89	1	no	—
223	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
224	#525	—	89	1	no	—
225	#504	—	178	4	no	—
226	C₂×M₃₂	—	2	4	no	—
227	C₂×M₃₂	—	89	2	no	—
228	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
229	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
230	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
231	C₂²×C₁₆	—	89	1	no	—
232	C₂²×C₁₆	—	89	1	no	—
233	C₂²×C₁₆	—	89	2	no	—
234	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
235	#435	—	89	2	no	—
236	#435	—	89	2	no	—
237	C₈×D₄	—	89	2	no	—
238	C₈×D₄	—	89	2	no	—
239	#424	—	89	1	no	—
240	#408	—	89	1	no	—
241	#407	—	89	1	no	—
242	#405	—	89	1	no	—
243	C₄⋊C₁₆	—	89	2	no	—
244	C₄⋊C₁₆	—	89	2	no	—
245	C₂²⋊C₁₆	—	89	1	no	—
246	C₂²⋊C₁₆	—	89	1	no	—
247	C₂²⋊C₁₆	—	89	1	no	—
248	C₂²⋊C₁₆	—	89	1	no	—
249	C₂²⋊C₁₆	—	89	2	no	—
250	C₂²⋊C₁₆	—	89	2	no	—
251	#346	—	89	2	no	—
252	C₄×C₁₆	—	89	2	no	—
253	C₂×#41	—	89	1	no	—
254	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
255	#131	—	178	2	no	—
256	#131	—	178	2	no	—
257	C₂×M₁₆	—	89	1	no	—
258	C₂×M₁₆	—	89	1	no	—
259	C₂×M₁₆	—	89	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	89	2	no	—
263	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
269	#123	—	89	2	no	—
270	C₂²⋊Q₈	—	89	1	no	—
271	C₂²⋊Q₈	—	89	1	no	—
272	#121	—	89	1	no	—
273	#121	—	89	1	no	—
274	#120	—	89	2	no	—
275	C₄×D₄	—	89	2	no	—
276	C₄×D₄	—	89	2	no	—
277	#117	—	89	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	2	4	no	—
280	M₃₂	—	178	4	no	—
281	M₃₂	C₂²⋊D₈₉	1	4	yes	complemented
282	C₂×C₁₆	—	2	4	no	—
283	C₂×C₁₆	—	89	1	no	—
284	C₂×C₁₆	—	89	1	no	—
285	C₂×C₁₆	—	89	1	no	—
286	C₂×C₁₆	—	89	1	no	—
287	C₂×C₁₆	—	178	2	no	—
288	C₂×C₁₆	—	178	2	no	—
289	C₂×C₁₆	—	178	4	no	—
290	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
291	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
292	C₄⋊C₈	—	89	2	no	—
293	C₄⋊C₈	—	89	2	no	—
294	C₂²⋊C₈	—	89	2	no	—
295	C₂²⋊C₈	—	89	2	no	—
296	C₂²⋊C₈	—	89	2	no	—
297	C₂²⋊C₈	—	89	2	no	—
298	#97	—	89	2	no	—
299	C₄×C₈	—	89	2	no	—
300	C₂⁴	C₈×D₈₉	1	1	yes	characteristic
301	#41	—	178	2	no	—
302	#41	—	178	2	no	—
303	C₂×Q₈	—	89	1	no	—
304	C₂×D₄	—	89	2	no	—
305	C₂×D₄	—	89	2	no	—
306	C₂×D₄	—	89	2	no	—
307	C₂×D₄	—	89	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	89	2	no	—
311	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
317	M₁₆	—	178	2	no	—
318	M₁₆	—	178	2	no	—
319	M₁₆	—	178	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	89	2	no	—
328	C₂×C₈	—	89	2	no	—
329	C₂×C₈	—	178	2	no	—
330	C₂×C₈	—	178	2	no	—
331	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
335	C₂×C₈	#13083574	1	2	yes	—
336	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
337	C₄⋊C₄	—	89	1	no	—
338	C₄⋊C₄	—	89	1	no	—
339	C₄⋊C₄	—	89	2	no	—
340	C₄⋊C₄	—	89	2	no	—
341	C₂²⋊C₄	—	89	2	no	—
342	C₂²⋊C₄	—	89	2	no	—
343	C₂²⋊C₄	—	89	2	no	—
344	C₂²⋊C₄	—	89	2	no	—
345	C₂²⋊C₄	—	89	2	no	—
346	C₄²	—	89	2	no	—
347	C₁₆	—	2	2	no	—
348	C₁₆	—	178	1	no	—
349	C₁₆	—	178	1	no	—
350	C₁₆	—	178	1	no	—
351	C₁₆	—	178	1	no	—
352	C₁₆	C₂×C₂²⋊D₈₉	1	4	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	89	2	no	—
357	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
359	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
360	Q₈	—	178	2	no	—
361	D₄	—	356	2	no	—
362	D₄	—	178	4	no	—
363	D₄	—	178	4	no	—
364	D₄	—	178	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	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	—	89	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	89	2	no	—
375	C₂×C₄	—	178	2	no	—
376	C₂×C₄	—	178	2	no	—
377	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
379	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
380	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
381	C₂×C₄	#15668018	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	178	2	no	—
386	C₈	—	178	2	no	—
387	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
388	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
389	C₈	C₂×#13083574	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	178	2	no	—
399	C₂²	—	178	2	no	—
400	C₂²	—	178	2	no	—
401	C₂²	C₈×C₂²⋊D₈₉	1	2	yes	—
402	C₂²	#19152016	1	2	yes	complemented
403	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	178	2	no	—
407	C₄	—	178	2	no	—
408	C₄	—	178	2	no	—
409	C₄	C₈×C₂²⋊D₈₉	1	2	yes	—
410	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
411	C₄	C₂×#15668018	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	356	2	no	—
416	C₂	C₂×C₈×C₂²⋊D₈₉	1	1	yes	characteristic
417	C₂	C₂×#19152016	1	1	yes	characteristic
418	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₂²×M₃₂×C₈₉	C₂
prime radical	#19152109	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂²×M₃₂	D₈₉
hypocenter	C₈₉	#33436
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×#19152016	C₂	semidirect
3. #26022082	C₂	semidirect
4. #26022077	C₂	semidirect
5. #26022075	C₂	semidirect
6. C₁₆×C₂²⋊D₈₉	C₂	semidirect
7. #26022012	C₂	semidirect
8. #26021867	C₂	semidirect
9. C₂×C₂²⋊#13083549	C₂	semidirect
10. #26021851	C₂	semidirect
11. C₂²×M₃₂×C₈₉	C₂	semidirect
15. C₂×#15667951	C₂²	semidirect
18. C₂×C₁₆×D₈₉	C₂²	semidirect
27. #19151416	C₂²	semidirect
28. #19151416	C₂²	semidirect
33. #19151377	C₂²	semidirect
34. #19151377	C₂²	semidirect
35. #19151373	C₂²	semidirect
36. C₁₆×Dic₈₉	C₂²	semidirect
86. M₃₂×C₈₉	D₄	semidirect
189. C₂²×C₈₉	#504	semidirect
211. C₂²×M₃₂	D₈₉	semidirect
221. C₈₉	#33436	semidirect
281. M₃₂	C₂²⋊D₈₉	semidirect
402. C₂²	#19152016	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152016	2
#26028946	2
#26022082	2
#26022077	2
#26022075	2
C₁₆×C₂²⋊D₈₉	2
#26022012	2
#26021867	2
C₂×C₂²⋊#13083549	2
#26021851	2
C₂²×M₃₂×C₈₉	2
#33436	89