Subgroups — #36449201

Order 22784.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151798	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#26021178	C₂	1	1	yes	maximal, characteristic
4	#26021058	C₂	1	1	yes	maximal, characteristic
5	#26018136	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018092	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Q₈⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083561	—	2	1	no	—
9	C₂×#15668009	C₂²	1	1	yes	characteristic
10	C₂×Q₈×Dic₈₉	—	2	1	no	—
11	#19151798	—	2	2	no	—
12	#19151798	C₄	1	4	yes	complemented
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×#15667934	—	2	1	no	—
15	C₂×#15667934	—	2	1	no	—
16	C₂×#15667934	—	2	2	no	—
17	C₂×#15667932	—	2	1	no	—
18	#19151497	—	2	2	no	—
19	#19151497	—	2	1	no	—
20	#19151468	—	2	1	no	—
21	#19151468	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₈₉	—	2	1	no	—
23	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	Q₈⋊C₈×C₈₉	—	2	2	no	—
28	C₂²×D₃₅₆	—	2	1	no	—
29	C₂²×D₃₅₆	—	2	1	no	—
30	C₂²×D₃₅₆	—	2	1	no	—
31	C₂×#13083561	—	2	4	no	—
32	C₂×#13083561	—	4	2	no	—
33	C₂×#13083561	—	4	2	no	—
34	C₂²×#10623494	—	2	1	no	—
35	#15668009	—	2	1	no	—
36	#15668009	—	2	1	no	—
37	#15668009	—	2	1	no	—
38	#15668009	C₂×C₄	1	2	yes	—
39	Q₈×Dic₈₉	—	4	2	no	—
40	Q₈×Dic₈₉	—	4	2	no	—
41	C₂×C₄⋊Dic₈₉	—	2	2	no	—
42	C₂×C₄⋊Dic₈₉	—	2	2	no	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	—	2	1	no	—
45	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
48	C₂×C₄×Dic₈₉	—	2	2	no	—
49	C₂×C₄×Dic₈₉	—	2	1	no	—
50	C₄⋊#10623494	—	2	1	no	—
51	C₄⋊#10623494	C₂×C₄	1	2	yes	—
52	#15667934	—	4	4	no	—
53	#15667934	—	4	2	no	—
54	#15667934	—	4	2	no	—
55	#15667932	—	2	4	no	—
56	#15667919	—	2	2	no	—
57	#15667919	—	2	1	no	—
58	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₄×Q₈×C₈₉	—	2	1	no	—
62	C₄×Q₈×C₈₉	—	2	1	no	—
63	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
64	C₄×Q₈×C₈₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	—	2	1	no	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₈₉	—	2	1	no	—
70	C₄⋊C₈×C₈₉	—	2	1	no	—
71	C₄×C₈×C₈₉	—	2	1	no	—
72	C₄×C₈×C₈₉	—	2	1	no	—
73	C₂³×D₈₉	—	4	1	no	—
74	C₂×D₃₅₆	—	2	2	no	—
75	C₂×D₃₅₆	—	2	2	no	—
76	C₂×D₃₅₆	—	2	2	no	—
77	C₂×D₃₅₆	—	4	2	no	—
78	C₂×D₃₅₆	—	4	2	no	—
79	C₂×D₃₅₆	—	4	1	no	—
80	C₂×D₃₅₆	—	4	1	no	—
81	C₂×D₃₅₆	—	4	1	no	—
82	C₂×D₃₅₆	—	4	1	no	—
83	C₂×D₃₅₆	—	4	1	no	—
84	C₂×D₃₅₆	—	4	1	no	—
85	C₂×D₃₅₆	—	4	1	no	—
86	C₂×D₃₅₆	—	4	1	no	—
87	C₂×D₃₅₆	—	4	1	no	—
88	C₂×D₃₅₆	—	4	1	no	—
89	C₂×D₃₅₆	—	4	1	no	—
90	C₂²×Dic₈₉	—	2	1	no	—
91	C₂²×Dic₈₉	—	2	1	no	—
92	C₂²×Dic₈₉	—	2	2	no	—
93	#13083561	—	4	8	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	4	1	no	—
96	C₂×#10623494	—	4	1	no	—
97	C₄⋊Dic₈₉	—	2	1	no	—
98	C₄⋊Dic₈₉	—	2	1	no	—
99	C₄⋊Dic₈₉	—	2	1	no	—
100	C₄⋊Dic₈₉	—	4	4	no	—
101	C₄⋊Dic₈₉	—	4	1	no	—
102	C₄⋊Dic₈₉	—	4	1	no	—
103	C₄⋊Dic₈₉	—	4	1	no	—
104	C₄⋊Dic₈₉	—	4	1	no	—
105	C₄⋊Dic₈₉	—	4	2	no	—
106	C₄⋊Dic₈₉	—	8	2	no	—
107	C₄⋊Dic₈₉	SD₁₆	1	2	yes	complemented
108	C₄×Dic₈₉	—	4	4	no	—
109	C₄×Dic₈₉	—	4	1	no	—
110	C₄×Dic₈₉	—	4	1	no	—
111	C₂×Q₈×C₈₉	—	2	1	no	—
112	C₂×Q₈×C₈₉	—	2	1	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	C₂²⋊C₄	1	2	yes	—
115	C₂×Q₈×C₈₉	D₈	1	2	yes	—
116	C₂×Q₈×C₈₉	SD₁₆	1	2	yes	—
117	C₂²×C₄×C₈₉	—	2	1	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₂×C₈×C₈₉	—	4	1	no	—
125	C₂×C₈×C₈₉	—	4	1	no	—
126	C₂×C₈×C₈₉	—	4	1	no	—
127	C₂×C₈×C₈₉	—	4	1	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₈₉	—	2	2	no	—
133	C₄²×C₈₉	—	2	2	no	—
134	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₈₉	#41	1	1	yes	characteristic
137	C₄²×C₈₉	#41	1	1	yes	characteristic
138	C₂³×C₈₉	#120	1	1	yes	characteristic
139	C₂²×D₈₉	—	4	2	no	—
140	C₂²×D₈₉	—	8	1	no	—
141	C₂²×D₈₉	—	8	1	no	—
142	C₂²×D₈₉	—	8	1	no	—
143	C₂²×D₈₉	—	8	1	no	—
144	C₂²×D₈₉	—	8	1	no	—
145	C₂²×D₈₉	—	8	1	no	—
146	Q₈×C₈₉	—	2	2	no	—
147	Q₈×C₈₉	—	2	2	no	—
148	Q₈×C₈₉	—	2	2	no	—
149	Q₈×C₈₉	#102	1	4	yes	complemented
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	2	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	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	4	1	no	—
174	C₂×Dic₈₉	—	4	1	no	—
175	C₂×Dic₈₉	—	4	2	no	—
176	C₂×Dic₈₉	—	4	1	no	—
177	C₂×Dic₈₉	—	4	1	no	—
178	C₂×Dic₈₉	—	4	2	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	C₂×Dic₈₉	—	4	1	no	—
181	D₃₅₆	—	4	4	no	—
182	D₃₅₆	—	4	2	no	—
183	D₃₅₆	—	4	2	no	—
184	D₃₅₆	—	4	2	no	—
185	D₃₅₆	—	4	2	no	—
186	D₃₅₆	—	8	2	no	—
187	D₃₅₆	—	8	1	no	—
188	D₃₅₆	—	8	1	no	—
189	D₃₅₆	—	8	1	no	—
190	D₃₅₆	—	8	1	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₈×C₈₉	—	8	1	no	—
193	#10623494	—	4	2	no	—
194	C₂²×C₈₉	#386	1	1	yes	characteristic
195	C₂²×C₈₉	#447	1	1	yes	characteristic
196	C₂²×C₈₉	#448	1	1	yes	characteristic
197	C₂²×C₈₉	#448	1	1	yes	characteristic
198	C₂²×C₈₉	#449	1	1	yes	characteristic
199	C₂²×C₈₉	#453	1	1	yes	characteristic
200	C₂²×C₈₉	#454	1	1	yes	characteristic
201	C₂×D₈₉	—	8	2	no	—
202	C₂×D₈₉	—	8	2	no	—
203	C₂×D₈₉	—	8	2	no	—
204	C₂×D₈₉	—	16	1	no	—
205	C₂×D₈₉	—	16	1	no	—
206	C₂×D₈₉	—	16	1	no	—
207	C₂×D₈₉	—	16	1	no	—
208	C₄×C₈₉	—	2	4	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	4	2	no	—
212	C₄×C₈₉	C₂×#102	1	1	yes	characteristic
213	C₄×C₈₉	#417	1	1	yes	characteristic
214	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
215	C₄×C₈₉	#440	1	1	yes	characteristic
216	C₄×C₈₉	#460	1	1	yes	characteristic
217	C₄×C₈₉	#464	1	1	yes	characteristic
218	C₄×C₈₉	#480	1	1	yes	characteristic
219	C₄×C₈₉	#481	1	1	yes	characteristic
220	Dic₈₉	—	4	2	no	—
221	Dic₈₉	—	8	1	no	—
222	Dic₈₉	—	8	2	no	—
223	#8979	—	89	1	no	maximal, Sylow
224	C₂×C₈₉	#1621	1	1	yes	characteristic
225	C₂×C₈₉	#1623	1	1	yes	characteristic
226	C₂×C₈₉	#1626	1	1	yes	characteristic
227	C₂×C₈₉	#1627	1	1	yes	characteristic
228	C₂×C₈₉	#1874	1	1	yes	characteristic
229	C₂×C₈₉	#1880	1	1	yes	characteristic
230	C₂×C₈₉	#1883	1	1	yes	characteristic
231	D₈₉	—	16	2	no	—
232	C₂×#460	—	89	1	no	—
233	Q₈×C₄⋊C₄	—	89	1	no	—
234	#1982	—	89	1	no	—
235	#1957	—	89	1	no	—
236	C₂×Q₈⋊C₈	D₈₉	1	1	yes	characteristic, complemented
237	#1296	—	89	1	no	—
238	#1279	—	89	1	no	—
239	C₈₉	#8979	1	1	yes	characteristic, complemented, Sylow
240	C₂²×SD₁₆	—	178	1	no	—
241	C₂×#127	—	89	1	no	—
242	C₂×C₄×Q₈	—	178	1	no	—
243	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
244	#460	—	89	4	no	—
245	#460	—	178	2	no	—
246	C₂×C₄⋊C₈	—	89	1	no	—
247	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
248	C₂×#102	—	178	2	no	—
249	C₂×#102	—	178	1	no	—
250	C₂×#102	—	178	1	no	—
251	C₂×#102	—	178	1	no	—
252	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
253	#389	—	178	2	no	—
254	#389	—	178	1	no	—
255	#384	—	89	1	no	—
256	#384	—	178	1	no	—
257	C₄×C₄⋊C₄	—	89	1	no	—
258	C₄×C₄⋊C₄	—	178	1	no	—
259	Q₈⋊C₈	—	2	2	no	—
260	C₂²×Q₈	D₃₅₆	1	1	yes	characteristic
261	C₂²×D₄	—	178	1	no	—
262	C₂²×D₄	—	178	1	no	—
263	C₂²×D₄	—	178	1	no	—
264	C₂×SD₁₆	—	356	2	no	—
265	C₂×SD₁₆	—	356	2	no	—
266	C₂×SD₁₆	—	178	4	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	178	1	no	—
270	#127	—	89	2	no	—
271	#127	—	178	1	no	—
272	#127	—	178	1	no	—
273	#127	—	178	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	—	356	2	no	—
277	C₄×Q₈	—	356	2	no	—
278	C₄×Q₈	C₄×D₈₉	1	2	yes	—
279	C₄×Q₈	C₂²⋊D₈₉	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	89	1	no	—
282	C₂×C₄⋊C₄	—	89	2	no	—
283	C₂×C₄⋊C₄	—	89	1	no	—
284	C₂×C₄⋊C₄	—	178	2	no	—
285	C₂×C₄⋊C₄	—	178	1	no	—
286	C₂×C₄⋊C₄	—	178	1	no	—
287	C₂×C₄⋊C₄	—	178	2	no	—
288	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	178	2	no	—
291	C₂×C₄²	—	178	1	no	—
292	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	89	2	no	—
296	C₄⋊C₈	—	178	1	no	—
297	#102	—	356	2	no	—
298	#102	—	356	4	no	—
299	#102	—	356	2	no	—
300	#102	—	178	4	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	2	1	no	—
303	#95	—	178	2	no	—
304	#95	—	178	1	no	—
305	C₂⁴	—	356	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	#13083551	1	2	yes	—
310	C₂×Q₈	D₇₁₂	1	2	yes	—
311	C₂×Q₈	#13083563	1	2	yes	—
312	C₂×D₄	—	356	2	no	—
313	C₂×D₄	—	356	2	no	—
314	C₂×D₄	—	356	1	no	—
315	C₂×D₄	—	356	1	no	—
316	C₂×D₄	—	356	1	no	—
317	C₂×D₄	—	356	1	no	—
318	C₂×D₄	—	356	1	no	—
319	C₂×D₄	—	356	1	no	—
320	C₂×D₄	—	356	1	no	—
321	C₂×D₄	—	356	1	no	—
322	C₂×D₄	—	356	1	no	—
323	C₂×D₄	—	356	1	no	—
324	C₂×D₄	—	356	1	no	—
325	C₂×D₄	—	178	2	no	—
326	C₂×D₄	—	178	2	no	—
327	C₂×D₄	—	178	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	178	2	no	—
331	C₂²×C₄	—	178	1	no	—
332	C₂²×C₄	—	178	1	no	—
333	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
336	SD₁₆	—	356	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	356	1	no	—
344	C₂×C₈	—	356	1	no	—
345	C₂×C₈	—	178	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	89	2	no	—
350	C₄⋊C₄	—	356	2	no	—
351	C₄⋊C₄	—	356	4	no	—
352	C₄⋊C₄	—	356	1	no	—
353	C₄⋊C₄	—	356	1	no	—
354	C₄⋊C₄	—	356	1	no	—
355	C₄⋊C₄	—	356	1	no	—
356	C₄⋊C₄	—	178	1	no	—
357	C₄⋊C₄	—	178	1	no	—
358	C₄⋊C₄	—	178	1	no	—
359	C₄⋊C₄	—	712	2	no	—
360	C₄⋊C₄	#13083551	1	2	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	356	4	no	—
364	C₄²	—	356	1	no	—
365	C₄²	—	356	1	no	—
366	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
367	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
368	C₄²	#13083573	1	1	yes	characteristic
369	C₄²	#13083573	1	1	yes	characteristic
370	C₂³	—	356	2	no	—
371	C₂³	—	712	1	no	—
372	C₂³	—	712	1	no	—
373	C₂³	—	712	1	no	—
374	C₂³	—	712	1	no	—
375	C₂³	—	712	1	no	—
376	C₂³	—	712	1	no	—
377	C₂³	#15667982	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	#15667934	1	4	yes	complemented
382	D₄	—	356	4	no	—
383	D₄	—	356	2	no	—
384	D₄	—	356	2	no	—
385	D₄	—	356	2	no	—
386	D₄	—	356	2	no	—
387	D₄	—	712	2	no	—
388	D₄	—	712	1	no	—
389	D₄	—	712	1	no	—
390	D₄	—	712	1	no	—
391	D₄	—	712	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	356	1	no	—
401	C₂×C₄	—	356	1	no	—
402	C₂×C₄	—	356	2	no	—
403	C₂×C₄	—	356	1	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	356	1	no	—
406	C₂×C₄	—	356	2	no	—
407	C₂×C₄	—	356	1	no	—
408	C₂×C₄	—	178	2	no	—
409	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
410	C₂×C₄	#15667972	1	1	yes	characteristic
411	C₂×C₄	#15667972	1	1	yes	characteristic
412	C₂×C₄	#15667984	1	1	yes	characteristic
413	C₂×C₄	#15667984	1	1	yes	characteristic
414	C₂×C₄	#15667996	1	1	yes	characteristic
415	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
416	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
418	C₂×C₄	#15668035	1	1	yes	characteristic
419	C₂×C₄	#15668039	1	1	yes	characteristic
420	C₂×C₄	#15668040	1	1	yes	characteristic
421	C₂×C₄	#15668044	1	1	yes	characteristic
422	C₂×C₄	#15668045	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	8	1	no	—
425	C₈	—	356	2	no	—
426	C₂²	—	1424	1	no	—
427	C₂²	—	1424	1	no	—
428	C₂²	—	1424	1	no	—
429	C₂²	—	1424	1	no	—
430	C₂²	—	712	2	no	—
431	C₂²	—	712	2	no	—
432	C₂²	—	712	2	no	—
433	C₂²	#19151475	1	1	yes	characteristic
434	C₂²	#19151734	1	1	yes	characteristic
435	C₂²	#19151738	1	1	yes	characteristic
436	C₂²	#19151739	1	1	yes	characteristic
437	C₂²	#19151746	1	1	yes	characteristic
438	C₂²	#19151767	1	1	yes	characteristic
439	C₂²	#19151772	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	4	no	—
443	C₄	—	4	2	no	—
444	C₄	—	356	2	no	—
445	C₄	—	712	2	no	—
446	C₄	—	712	1	no	—
447	C₄	C₂×#15667934	1	1	yes	characteristic
448	C₄	#19151600	1	1	yes	characteristic
449	C₄	#19151683	1	1	yes	characteristic
450	C₄	#19151701	1	1	yes	characteristic
451	C₄	#19151796	1	1	yes	characteristic
452	C₄	#19151822	1	1	yes	characteristic
453	C₄	#19151912	1	1	yes	characteristic
454	C₄	#19151917	1	1	yes	characteristic
455	C₂	—	1424	2	no	—
456	C₂	#26019319	1	1	yes	characteristic
457	C₂	#26019332	1	1	yes	characteristic
458	C₂	#26019351	1	1	yes	characteristic
459	C₂	#26019357	1	1	yes	characteristic
460	C₂	#26020567	1	1	yes	characteristic
461	C₂	#26020605	1	1	yes	characteristic
462	C₂	#26020626	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×Q₈⋊C₈×C₈₉	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₈₉
hypocenter	C₈₉	#8979
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊Dic₈₉	C₂	semidirect
5. #26018136	C₂	semidirect
6. #26018092	C₂	semidirect
7. C₂×Q₈⋊C₈×C₈₉	C₂	semidirect
12. #19151798	C₄	semidirect
107. C₄⋊Dic₈₉	SD₁₆	semidirect
149. Q₈×C₈₉	#102	semidirect
236. C₂×Q₈⋊C₈	D₈₉	semidirect
239. C₈₉	#8979	semidirect
381. Q₈	#15667934	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151798	2
Q₈×C₄⋊Dic₈₉	2
#26021178	2
#26021058	2
#26018136	2
#26018092	2
C₂×Q₈⋊C₈×C₈₉	2
#8979	89