Subgroups — #36576247

Order 22784.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151883	C₂	1	1	yes	maximal, characteristic
2	#26023308	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic
4	#26021213	C₂	1	1	yes	maximal, characteristic
5	#26021015	C₂	1	1	yes	maximal, characteristic
6	#26020979	C₂	1	2	yes	maximal
7	#26020840	C₂	1	2	yes	maximal
8	#26020518	C₂	1	2	yes	maximal
9	C₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic
10	#103×Dic₈₉	C₂	1	2	yes	maximal
11	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668012	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₈₉	C₂²	1	2	yes	—
14	C₂×C₄×Dic₁₇₈	—	2	1	no	—
15	#19151883	C₄	1	8	yes	complemented
16	C₂×#15667943	C₂²	1	2	yes	—
17	C₂×#15667943	C₂²	1	2	yes	—
18	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
19	C₂×#15667936	C₂²	1	2	yes	—
20	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
21	#19151504	—	2	1	no	—
22	#19151497	—	2	2	no	—
23	#19151497	C₂²	1	2	yes	—
24	#19151494	C₂²	1	2	yes	—
25	#19151481	—	2	2	no	—
26	#19151468	—	2	1	no	—
27	#19151468	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₈₉	—	2	1	no	—
30	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151361	C₂²	1	2	yes	—
32	#19151361	C₂²	1	2	yes	—
33	#19151360	C₂²	1	2	yes	—
34	#19151352	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	1	yes	characteristic
41	#340×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×Dic₁₇₈	—	2	1	no	—
43	C₂²×#10623494	C₂³	1	2	yes	—
44	#15668012	—	2	2	no	—
45	#15668012	C₂×C₄	1	4	yes	—
46	Q₈×Dic₈₉	—	2	4	no	—
47	Q₈×Dic₈₉	—	4	2	no	—
48	C₄×Dic₁₇₈	—	4	4	no	—
49	C₂×C₄⋊Dic₈₉	—	2	2	no	—
50	C₂×C₄⋊Dic₈₉	—	2	2	no	—
51	C₂×C₄⋊Dic₈₉	—	2	1	no	—
52	C₂×C₄⋊Dic₈₉	—	2	1	no	—
53	C₂×C₄⋊Dic₈₉	—	2	1	no	—
54	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
58	C₂×#13083553	—	2	2	no	—
59	C₂×C₄×Dic₈₉	—	2	2	no	—
60	C₂×C₄×Dic₈₉	—	2	2	no	—
61	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
62	#15667943	—	4	2	no	—
63	#15667943	C₂×C₄	1	8	yes	—
64	C₄⋊#10623494	C₂×C₄	1	4	yes	—
65	#15667936	C₂×C₄	1	8	yes	—
66	C₈×Dic₈₉	—	4	2	no	—
67	#15667919	—	2	2	no	—
68	#15667919	—	2	2	no	—
69	#15667919	—	2	2	no	—
70	#15667919	D₄	1	2	yes	—
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₄×Q₈×C₈₉	—	2	2	no	—
75	C₄×Q₈×C₈₉	C₂×C₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	—	2	1	no	—
81	C₂×C₄²×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	#103×C₈₉	—	2	2	no	—
84	#103×C₈₉	Q₈	1	4	yes	complemented
85	C₄×C₈×C₈₉	—	2	2	no	—
86	#95×C₈₉	—	2	1	no	—
87	C₂×Dic₁₇₈	—	2	4	no	—
88	C₂×Dic₁₇₈	—	4	2	no	—
89	C₂×Dic₁₇₈	—	4	2	no	—
90	C₂²×Dic₈₉	—	2	2	no	—
91	C₂²×Dic₈₉	—	2	2	no	—
92	C₂²×Dic₈₉	C₂×D₄	1	2	yes	—
93	C₂²×Dic₈₉	C₂×D₄	1	2	yes	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	C₂²×C₄	1	4	yes	—
97	C₄⋊Dic₈₉	—	2	4	no	—
98	C₄⋊Dic₈₉	—	2	2	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	—	2	2	no	—
102	C₄⋊Dic₈₉	—	4	4	no	—
103	C₄⋊Dic₈₉	—	4	2	no	—
104	C₄⋊Dic₈₉	—	8	2	no	—
105	C₄⋊Dic₈₉	—	8	1	no	—
106	C₄⋊Dic₈₉	SD₁₆	1	4	yes	—
107	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
108	#13083553	—	4	4	no	—
109	C₄×Dic₈₉	—	2	2	no	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₄×Dic₈₉	—	4	4	no	—
112	C₄×Dic₈₉	—	4	4	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
117	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
118	C₂×Q₈×C₈₉	#41	1	2	yes	—
119	C₂²×C₄×C₈₉	—	2	1	no	—
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	—	2	1	no	—
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₈₉	—	2	4	no	—
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	1	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
138	C₄⋊C₄×C₈₉	C₂×Q₈	1	2	yes	—
139	C₄²×C₈₉	—	2	4	no	—
140	C₄²×C₈₉	—	4	2	no	—
141	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₈₉	#41	1	2	yes	—
143	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₈₉	—	2	2	no	—
145	Q₈×C₈₉	—	2	2	no	—
146	Q₈×C₈₉	—	2	2	no	—
147	Q₈×C₈₉	C₄×Q₈	1	4	yes	complemented
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
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	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	1	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₈₉	#135	1	2	yes	—
166	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	—	2	4	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	2	no	—
177	C₂×Dic₈₉	—	2	2	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	4	2	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	C₂×Dic₈₉	—	4	2	no	—
183	C₂×Dic₈₉	C₂×SD₁₆	1	4	yes	—
184	Dic₁₇₈	—	4	8	no	—
185	C₈×C₈₉	—	2	2	no	—
186	C₈×C₈₉	—	4	1	no	—
187	#10623494	—	2	4	no	—
188	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₈₉	#546	1	1	yes	characteristic
190	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
191	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
192	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
193	C₂²×C₈₉	#577	1	1	yes	characteristic
194	C₂²×C₈₉	#578	1	1	yes	characteristic
195	C₄×C₈₉	—	2	4	no	—
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	8	1	no	—
200	C₄×C₈₉	C₄×SD₁₆	1	4	yes	—
201	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₄×C₈₉	#520	1	1	yes	characteristic
203	C₄×C₈₉	#552	1	1	yes	characteristic
204	C₄×C₈₉	#554	1	1	yes	characteristic
205	Dic₈₉	—	2	4	no	—
206	Dic₈₉	—	4	4	no	—
207	Dic₈₉	—	4	2	no	—
208	Dic₈₉	—	8	2	no	—
209	#22964	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	#2360	1	1	yes	characteristic
211	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
212	C₂×C₈₉	#2947	1	1	yes	characteristic
213	C₂×C₈₉	#3298	1	1	yes	characteristic
214	C₂×C₈₉	#3304	1	1	yes	characteristic
215	C₂×C₈₉	Q₈×SD₁₆	1	1	yes	characteristic
216	C₂×C₈₉	#3383	1	1	yes	characteristic
217	C₂×#475	—	89	1	no	—
218	#2365	—	89	1	no	—
219	Q₈×C₄⋊C₄	—	89	1	no	—
220	#1990	—	89	1	no	—
221	#1948	—	89	1	no	—
222	#1941	—	89	2	no	—
223	#1920	—	89	2	no	—
224	#1865	—	89	2	no	—
225	C₈×C₄⋊C₄	—	89	1	no	—
226	C₄×#103	—	89	2	no	—
227	C₄×#103	D₈₉	1	1	yes	characteristic
228	C₈₉	#22964	1	1	yes	characteristic, complemented, Sylow
229	C₂×C₄⋊Q₈	—	89	1	no	—
230	C₂×C₄×Q₈	—	89	2	no	—
231	C₂×C₄×Q₈	—	178	1	no	—
232	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
233	#475	—	89	8	no	—
234	C₂×#106	—	89	2	no	—
235	C₂×#106	—	89	2	no	—
236	C₂×C₄⋊C₈	—	89	1	no	—
237	C₂×#103	—	89	2	no	—
238	C₂×#103	C₂×D₈₉	1	1	yes	characteristic
239	C₂×#103	C₂×D₈₉	1	1	yes	characteristic
240	C₂×C₄×C₈	—	89	2	no	—
241	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
242	#391	—	178	1	no	—
243	#389	—	89	2	no	—
244	#389	—	89	2	no	—
245	#389	—	178	2	no	—
246	#387	—	178	2	no	—
247	#384	—	89	1	no	—
248	#384	—	178	1	no	—
249	C₄×C₄⋊C₄	—	89	1	no	—
250	C₄×C₄⋊C₄	—	89	2	no	—
251	C₄×C₄⋊C₄	—	178	1	no	—
252	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
253	#340	—	89	2	no	—
254	#340	—	89	2	no	—
255	#340	—	89	2	no	—
256	#340	C₂×D₈₉	1	1	yes	characteristic
257	#340	C₂×D₈₉	1	1	yes	characteristic
258	#336	—	89	2	no	—
259	C₂²×Q₈	—	178	1	no	—
260	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
261	C₂²×C₈	—	89	2	no	—
262	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
263	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
264	C₄⋊Q₈	—	89	4	no	—
265	C₄⋊Q₈	—	178	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	356	4	no	—
268	C₄×Q₈	—	356	2	no	—
269	C₄×Q₈	—	178	4	no	—
270	C₄×Q₈	C₄×D₈₉	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	89	1	no	—
273	C₂×C₄⋊C₄	—	89	2	no	—
274	C₂×C₄⋊C₄	—	89	1	no	—
275	C₂×C₄⋊C₄	—	89	2	no	—
276	C₂×C₄⋊C₄	—	178	2	no	—
277	C₂×C₄⋊C₄	—	178	2	no	—
278	C₂×C₄⋊C₄	—	178	1	no	—
279	C₂×C₄⋊C₄	—	178	1	no	—
280	C₂×C₄⋊C₄	—	178	2	no	—
281	C₂×C₄⋊C₄	—	178	1	no	—
282	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	89	2	no	—
288	C₂×C₄²	—	178	2	no	—
289	C₂×C₄²	—	178	2	no	—
290	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
291	#106	—	89	8	no	—
292	#106	—	356	2	no	—
293	C₄⋊C₈	—	89	4	no	—
294	#103	—	2	2	no	—
295	#103	—	89	8	no	—
296	#103	Dic₁₇₈	1	4	yes	complemented
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	356	2	no	—
299	#95	—	2	1	no	—
300	#95	—	89	2	no	—
301	#95	—	178	2	no	—
302	#95	—	178	2	no	—
303	#95	—	178	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	356	2	no	—
308	C₂×Q₈	—	356	2	no	—
309	C₂×Q₈	—	178	4	no	—
310	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
311	C₂×Q₈	C₂×Dic₁₇₈	1	2	yes	—
312	C₂×Q₈	#13083574	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	89	2	no	—
318	C₂²×C₄	—	89	2	no	—
319	C₂²×C₄	—	178	2	no	—
320	C₂²×C₄	—	178	2	no	—
321	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
323	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	89	4	no	—
330	C₂×C₈	—	178	2	no	—
331	C₂×C₈	—	178	2	no	—
332	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	89	4	no	—
339	C₄⋊C₄	—	89	4	no	—
340	C₄⋊C₄	—	356	4	no	—
341	C₄⋊C₄	—	356	4	no	—
342	C₄⋊C₄	—	356	2	no	—
343	C₄⋊C₄	—	178	2	no	—
344	C₄⋊C₄	—	178	2	no	—
345	C₄⋊C₄	—	178	4	no	—
346	C₄⋊C₄	—	178	2	no	—
347	C₄⋊C₄	—	178	2	no	—
348	C₄⋊C₄	—	712	1	no	—
349	C₄⋊C₄	—	712	2	no	—
350	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
351	C₄⋊C₄	C₂×Dic₁₇₈	1	2	yes	—
352	C₄²	—	2	4	no	—
353	C₄²	—	4	2	no	—
354	C₄²	—	356	4	no	—
355	C₄²	—	356	4	no	—
356	C₄²	—	178	2	no	—
357	C₄²	—	178	2	no	—
358	C₄²	C₂×C₄×D₈₉	1	2	yes	—
359	C₄²	#13083573	1	2	yes	—
360	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	356	8	no	—
365	Q₈	C₄×Dic₁₇₈	1	4	yes	complemented
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	89	4	no	—
381	C₂×C₄	—	356	2	no	—
382	C₂×C₄	—	356	2	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	178	2	no	—
387	C₂×C₄	—	178	2	no	—
388	C₂×C₄	—	178	4	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	#15667972	1	2	yes	—
393	C₂×C₄	#15667972	1	2	yes	—
394	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
395	C₂×C₄	#15668035	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
398	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
399	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
400	C₂×C₄	#15668058	1	1	yes	characteristic
401	C₂×C₄	#15668059	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	1	no	—
404	C₈	—	178	4	no	—
405	C₂²	C₂×#15667972	1	1	yes	characteristic
406	C₂²	#19152244	1	1	yes	characteristic
407	C₂²	D₄×Dic₁₇₈	1	1	yes	characteristic
408	C₂²	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
409	C₂²	C₂×#15668035	1	1	yes	characteristic
410	C₂²	#19152405	1	1	yes	characteristic
411	C₂²	#19152412	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	356	2	no	—
418	C₄	—	356	4	no	—
419	C₄	—	178	4	no	—
420	C₄	—	712	2	no	—
421	C₄	#19151683	1	4	yes	—
422	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
423	C₄	#19152078	1	1	yes	characteristic
424	C₄	#19152288	1	1	yes	characteristic
425	C₄	#19152305	1	1	yes	characteristic
426	C₂	#26023255	1	1	yes	characteristic
427	C₂	C₂×#19151683	1	1	yes	characteristic
428	C₂	#26029098	1	1	yes	characteristic
429	C₂	#26032119	1	1	yes	characteristic
430	C₂	#26032193	1	1	yes	characteristic
431	C₂	SD₁₆×Dic₁₇₈	1	1	yes	characteristic
432	C₂	#26033141	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#103×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#103	D₈₉
hypocenter	C₈₉	#22964
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
15. #19151883	C₄	semidirect
84. #103×C₈₉	Q₈	semidirect
147. Q₈×C₈₉	C₄×Q₈	semidirect
228. C₈₉	#22964	semidirect
296. #103	Dic₁₇₈	semidirect
365. Q₈	C₄×Dic₁₇₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151883	2
#26023308	2
Q₈×C₄⋊Dic₈₉	2
#26021213	2
#26021015	2
#26020979	2
#26020840	2
#26020518	2
C₈×C₄⋊Dic₈₉	2
#103×Dic₈₉	2
C₄×#103×C₈₉	2
#22964	89