Subgroups — #36563097

Order 22784.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151727	C₂	1	2	yes	maximal
2	C₄×#15668012	C₂	1	1	yes	maximal, characteristic
3	#26021191	C₂	1	2	yes	maximal
4	#26020973	C₂	1	2	yes	maximal
5	#26020968	C₂	1	1	yes	maximal, characteristic
6	#26020968	C₂	1	1	yes	maximal, characteristic
7	#26020129	C₂	1	2	yes	maximal
8	#26020122	C₂	1	1	yes	maximal, characteristic
9	#26020117	C₂	1	1	yes	maximal, characteristic
10	C₄×#15667923	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1842	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668012	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₇₈	C₂²	1	2	yes	—
14	#19151727	—	2	8	no	—
15	C₂×#15667941	C₂²	1	2	yes	—
16	C₂×#15667941	C₂²	1	2	yes	—
17	C₂×#15667923	C₂²	1	1	yes	characteristic
18	C₂×#15667923	C₂²	1	1	yes	characteristic
19	C₂×#15667923	C₂²	1	1	yes	characteristic
20	C₂×#15667923	C₂²	1	1	yes	characteristic
21	C₂×#15667922	C₂²	1	2	yes	—
22	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
23	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
25	#19151504	C₄	1	2	yes	—
26	#19151496	C₄	1	1	yes	characteristic
27	#19151496	C₄	1	1	yes	characteristic
28	#19151496	C₄	1	2	yes	—
29	#19151468	C₄	1	1	yes	characteristic
30	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
33	#19151352	C₂²	1	2	yes	—
34	#19151352	C₂²	1	2	yes	—
35	#19151352	C₂²	1	2	yes	—
36	#19151352	C₂²	1	2	yes	—
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
41	C₄³×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×Dic₁₇₈	C₂×C₄	1	2	yes	—
43	C₂²×#10623494	C₂³	1	1	yes	characteristic
44	C₂²×#10623494	C₂³	1	1	yes	characteristic
45	C₂²×#10623494	C₂³	1	1	yes	characteristic
46	C₂²×#10623494	C₂³	1	1	yes	characteristic
47	#15668012	—	2	4	no	—
48	C₄×Dic₁₇₈	—	2	4	no	—
49	C₄×Dic₁₇₈	—	2	4	no	—
50	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×#13083553	C₂×C₄	1	2	yes	—
58	C₂×#13083553	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
60	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
61	#15667941	—	2	4	no	—
62	#15667941	—	2	4	no	—
63	#15667923	—	2	2	no	—
64	#15667923	—	2	2	no	—
65	#15667923	D₄	1	4	yes	—
66	#15667923	Q₈	1	4	yes	complemented
67	#15667922	—	2	4	no	—
68	C₄×#10623494	—	2	2	no	—
69	C₄×#10623494	Q₈	1	4	yes	complemented
70	C₈×Dic₈₉	—	2	4	no	—
71	#15667919	C₂×C₄	1	2	yes	—
72	#15667919	C₂×C₄	1	2	yes	—
73	#15667919	C₂×C₄	1	2	yes	—
74	#15667919	C₂×C₄	1	2	yes	—
75	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
76	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₈₉	—	2	4	no	—
85	C₄⋊C₈×C₈₉	—	2	2	no	—
86	C₄⋊C₈×C₈₉	—	2	2	no	—
87	C₄⋊C₈×C₈₉	—	2	4	no	—
88	C₂×Dic₁₇₈	—	2	4	no	—
89	C₂×Dic₁₇₈	—	2	4	no	—
90	C₂×Dic₁₇₈	—	4	2	no	—
91	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
95	C₂×#10623494	—	2	1	no	—
96	C₂×#10623494	—	2	1	no	—
97	C₂×#10623494	—	2	1	no	—
98	C₂×#10623494	—	2	1	no	—
99	C₂×#10623494	—	2	1	no	—
100	C₂×#10623494	—	2	1	no	—
101	C₂×#10623494	C₂×D₄	1	2	yes	—
102	C₂×#10623494	C₂×D₄	1	2	yes	—
103	C₂×#10623494	C₂×Q₈	1	2	yes	—
104	C₂×#10623494	C₂×Q₈	1	2	yes	—
105	C₂×#10623494	C₂×Q₈	1	2	yes	—
106	C₂×#10623494	C₂×Q₈	1	2	yes	—
107	C₄⋊Dic₈₉	—	2	4	no	—
108	C₄⋊Dic₈₉	—	2	2	no	—
109	C₄⋊Dic₈₉	—	2	2	no	—
110	C₄⋊Dic₈₉	—	2	2	no	—
111	C₄⋊Dic₈₉	—	2	4	no	—
112	C₄⋊Dic₈₉	—	4	2	no	—
113	C₄⋊Dic₈₉	M₁₆	1	4	yes	—
114	#13083553	—	2	4	no	—
115	#13083553	—	2	4	no	—
116	C₄×Dic₈₉	—	2	2	no	—
117	C₄×Dic₈₉	—	2	2	no	—
118	C₄×Dic₈₉	—	2	2	no	—
119	C₄×Dic₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₈₉	—	2	2	no	—
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	2	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₄²×C₈₉	—	2	2	no	—
134	C₄²×C₈₉	—	2	2	no	—
135	C₄²×C₈₉	—	4	1	no	—
136	C₄²×C₈₉	—	4	1	no	—
137	C₄²×C₈₉	C₂×D₄	1	2	yes	—
138	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
139	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
140	C₄²×C₈₉	#41	1	2	yes	—
141	C₄²×C₈₉	#41	1	2	yes	—
142	C₄²×C₈₉	#41	1	2	yes	—
143	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	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	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
157	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
158	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
159	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
160	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
161	C₂×C₄×C₈₉	#131	1	2	yes	—
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₈₉	—	2	2	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	C₂×Dic₈₉	—	2	2	no	—
178	C₂×Dic₈₉	—	2	2	no	—
179	C₂×Dic₈₉	C₂×M₁₆	1	4	yes	—
180	Dic₁₇₈	—	4	8	no	—
181	C₈×C₈₉	—	4	2	no	—
182	C₈×C₈₉	—	4	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	2	2	no	—
186	#10623494	C₄⋊Q₈	1	4	yes	complemented
187	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
190	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
192	C₂²×C₈₉	#568	1	1	yes	characteristic
193	C₂²×C₈₉	#568	1	1	yes	characteristic
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	2	2	no	—
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	2	2	no	—
199	C₄×C₈₉	#446	1	4	yes	complemented
200	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	C₄×C₈₉	#532	1	1	yes	characteristic
202	C₄×C₈₉	#533	1	1	yes	characteristic
203	C₄×C₈₉	#533	1	1	yes	characteristic
204	Dic₈₉	—	2	4	no	—
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	4	2	no	—
207	Dic₈₉	—	4	2	no	—
208	#21713	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
210	C₂×C₈₉	D₄×M₁₆	1	1	yes	characteristic
211	C₂×C₈₉	#2935	1	1	yes	characteristic
212	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
213	C₂×C₈₉	#2961	1	1	yes	characteristic
214	C₂×C₈₉	#2962	1	1	yes	characteristic
215	C₂×C₈₉	Q₈×M₁₆	1	1	yes	characteristic
216	C₂×#446	—	89	2	no	—
217	C₄×C₄⋊Q₈	—	89	1	no	—
218	#1985	—	89	2	no	—
219	#1940	—	89	2	no	—
220	#1939	—	89	1	no	—
221	#1939	—	89	1	no	—
222	#1842	D₈₉	1	1	yes	characteristic
223	#1771	—	89	2	no	—
224	#1770	—	89	1	no	—
225	C₈×C₄⋊C₄	—	89	1	no	—
226	C₄×#97	—	89	1	no	—
227	C₈₉	#21713	1	1	yes	characteristic, complemented, Sylow
228	C₂×C₄⋊Q₈	—	89	1	no	—
229	C₂×C₄×Q₈	—	89	2	no	—
230	#446	—	178	8	no	—
231	C₂×C₄⋊C₈	—	89	2	no	—
232	C₂×C₄⋊C₈	—	89	2	no	—
233	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
234	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
237	C₂×#97	—	89	1	no	—
238	C₂×#97	—	89	1	no	—
239	C₂×#97	—	89	2	no	—
240	C₂×#97	—	89	1	no	—
241	C₂×#97	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	89	2	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	#391	—	89	2	no	—
246	#389	—	89	1	no	—
247	#389	—	89	1	no	—
248	#389	—	89	2	no	—
249	#384	—	89	1	no	—
250	C₄×C₄⋊C₄	—	89	1	no	—
251	C₄×C₄⋊C₄	—	89	1	no	—
252	C₄×C₄⋊C₄	—	89	2	no	—
253	C₄³	C₂×D₈₉	1	1	yes	characteristic
254	#336	—	89	2	no	—
255	#336	—	89	2	no	—
256	#336	—	89	2	no	—
257	#336	—	89	2	no	—
258	C₂²×Q₈	—	89	2	no	—
259	C₂²×C₈	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
264	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
265	C₄⋊Q₈	—	178	4	no	—
266	C₄×Q₈	—	178	4	no	—
267	C₄×Q₈	—	178	4	no	—
268	C₂×C₄⋊C₄	—	89	1	no	—
269	C₂×C₄⋊C₄	—	89	2	no	—
270	C₂×C₄⋊C₄	—	89	2	no	—
271	C₂×C₄⋊C₄	—	89	2	no	—
272	C₂×C₄⋊C₄	—	89	2	no	—
273	C₂×C₄⋊C₄	—	89	2	no	—
274	C₂×C₄⋊C₄	—	89	1	no	—
275	C₂×C₄⋊C₄	—	89	1	no	—
276	C₂×C₄⋊C₄	—	89	1	no	—
277	C₂×C₄²	—	89	2	no	—
278	C₂×C₄²	—	89	2	no	—
279	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
280	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
281	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
282	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	4	no	—
287	C₄⋊C₈	—	2	2	no	—
288	C₄⋊C₈	—	2	2	no	—
289	C₄⋊C₈	—	2	4	no	—
290	C₄⋊C₈	—	178	4	no	—
291	C₄⋊C₈	—	178	4	no	—
292	#97	—	89	4	no	—
293	#97	—	89	4	no	—
294	#97	—	178	4	no	—
295	#97	—	178	2	no	—
296	#97	—	178	2	no	—
297	C₄×C₈	—	89	4	no	—
298	C₄×C₈	—	178	4	no	—
299	C₄×C₈	—	178	2	no	—
300	#95	—	89	2	no	—
301	#95	—	89	2	no	—
302	#95	—	89	2	no	—
303	#95	—	89	2	no	—
304	C₂×Q₈	—	356	2	no	—
305	C₂×Q₈	—	178	4	no	—
306	C₂×Q₈	—	178	4	no	—
307	C₂²×C₄	—	89	2	no	—
308	C₂²×C₄	—	89	2	no	—
309	C₂²×C₄	—	89	2	no	—
310	C₂²×C₄	—	89	2	no	—
311	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×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	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	89	2	no	—
326	C₂×C₈	—	89	2	no	—
327	C₂×C₈	—	89	2	no	—
328	C₂×C₈	—	89	2	no	—
329	C₂×C₈	—	89	2	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	1	no	—
332	C₂×C₈	—	178	1	no	—
333	C₂×C₈	—	178	1	no	—
334	C₂×C₈	—	178	1	no	—
335	C₂×C₈	—	178	1	no	—
336	C₄⋊C₄	—	89	4	no	—
337	C₄⋊C₄	—	356	2	no	—
338	C₄⋊C₄	—	178	4	no	—
339	C₄⋊C₄	—	178	4	no	—
340	C₄⋊C₄	—	178	4	no	—
341	C₄⋊C₄	—	178	4	no	—
342	C₄⋊C₄	—	178	2	no	—
343	C₄⋊C₄	—	178	2	no	—
344	C₄⋊C₄	—	178	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	178	2	no	—
350	C₄²	—	178	2	no	—
351	C₄²	—	178	2	no	—
352	C₄²	—	178	2	no	—
353	C₄²	D₄×D₈₉	1	2	yes	—
354	C₄²	Q₈×D₈₉	1	2	yes	—
355	C₄²	Q₈×D₈₉	1	2	yes	—
356	C₄²	#13083573	1	2	yes	—
357	C₄²	#13083573	1	2	yes	—
358	C₄²	#13083575	1	2	yes	—
359	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
360	Q₈	—	356	8	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	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	—	89	4	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	178	2	no	—
375	C₂×C₄	—	178	2	no	—
376	C₂×C₄	—	178	2	no	—
377	C₂×C₄	—	178	2	no	—
378	C₂×C₄	—	178	2	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	2	no	—
381	C₂×C₄	—	178	2	no	—
382	C₂×C₄	—	178	2	no	—
383	C₂×C₄	#15667974	1	2	yes	—
384	C₂×C₄	#15667974	1	2	yes	—
385	C₂×C₄	#15667977	1	2	yes	—
386	C₂×C₄	#15667977	1	2	yes	—
387	C₂×C₄	#15667977	1	2	yes	—
388	C₂×C₄	#15667977	1	2	yes	—
389	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
390	C₂×C₄	#15668018	1	2	yes	—
391	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
395	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₈	—	89	4	no	—
400	C₈	—	178	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₂²	C₂×#15667974	1	1	yes	characteristic
404	C₂²	C₂×#15667977	1	1	yes	characteristic
405	C₂²	C₂×#15667977	1	1	yes	characteristic
406	C₂²	C₂×M₁₆×D₈₉	1	1	yes	characteristic
407	C₂²	C₂×#15668018	1	1	yes	characteristic
408	C₂²	#19152364	1	1	yes	characteristic
409	C₂²	#19152364	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	356	2	no	—
416	C₄	—	356	2	no	—
417	C₄	—	356	2	no	—
418	C₄	—	178	4	no	—
419	C₄	#19151727	1	4	yes	complemented
420	C₄	C₄⋊Q₈×D₈₉	1	1	yes	characteristic
421	C₄	#19152146	1	1	yes	characteristic
422	C₄	#19152153	1	1	yes	characteristic
423	C₄	#19152153	1	1	yes	characteristic
424	C₂	#26022819	1	1	yes	characteristic
425	C₂	#26028987	1	1	yes	characteristic
426	C₂	#26028995	1	1	yes	characteristic
427	C₂	C₂×#19151727	1	1	yes	characteristic
428	C₂	#26029189	1	1	yes	characteristic
429	C₂	#26029195	1	1	yes	characteristic
430	C₂	#26029203	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1842	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1842	D₈₉
hypocenter	C₈₉	#21713
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
66. #15667923	Q₈	semidirect
69. C₄×#10623494	Q₈	semidirect
186. #10623494	C₄⋊Q₈	semidirect
199. C₄×C₈₉	#446	semidirect
227. C₈₉	#21713	semidirect
419. C₄	#19151727	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151727	2
C₄×#15668012	2
#26021191	2
#26020973	2
#26020968	2
#26020129	2
#26020122	2
#26020117	2
C₄×#15667923	2
C₈₉×#1842	2
#21713	89