Subgroups — #36525436

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030283	C₂	1	1	yes	maximal, characteristic
2	#26028998	C₂	1	1	yes	maximal, characteristic
3	#26019152	C₂	1	2	yes	maximal, complemented
4	#26019130	C₂	1	2	yes	maximal, complemented
5	#26019107	C₂	1	2	yes	maximal, complemented
6	#26019062	C₂	1	2	yes	maximal, complemented
7	#26019028	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018702	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018539	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151916	C₄	1	2	yes	—
15	#19151883	C₄	1	1	yes	characteristic
16	#19151883	C₄	1	1	yes	characteristic
17	#19151798	C₄	1	1	yes	characteristic
18	#19151798	C₄	1	1	yes	characteristic
19	#19151737	C₄	1	2	yes	—
20	C₄×#13083561	C₂²	1	2	yes	—
21	C₄×#13083561	C₂²	1	2	yes	—
22	#19151677	C₂²	1	2	yes	—
23	#19151671	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	#19151566	—	2	1	no	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	2	yes	—
30	#19151350	C₂²	1	2	yes	—
31	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
32	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
33	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
34	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
35	#19151325	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151320	C₂²	1	2	yes	—
38	#19151320	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	—	2	2	no	—
41	#446×C₈₉	C₂²	1	2	yes	—
42	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
43	#423×C₈₉	—	2	1	no	—
44	#423×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083561	C₂×C₄	1	2	yes	—
49	C₂×#13083561	C₂×C₄	1	2	yes	—
50	#15668020	—	4	4	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668009	C₂×C₄	1	1	yes	characteristic
57	#15668000	—	2	1	no	—
58	#15667986	—	2	1	no	—
59	#15667986	C₂×C₄	1	2	yes	—
60	C₄×D₃₅₆	—	2	1	no	—
61	C₄×D₃₅₆	C₂³	1	2	yes	—
62	#15667943	C₂×C₄	1	2	yes	—
63	#15667943	C₂×C₄	1	2	yes	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	#15667936	C₂×C₄	1	2	yes	—
70	#15667936	C₂×C₄	1	2	yes	—
71	#15667932	C₂×C₄	1	2	yes	—
72	#15667932	C₂×C₄	1	2	yes	—
73	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
74	#15667924	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	C₄×#10623494	—	2	1	no	—
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	2	yes	—
80	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂×M₁₆×C₈₉	—	2	1	no	—
82	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
83	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
84	C₄×Q₈×C₈₉	—	2	1	no	—
85	C₄×Q₈×C₈₉	—	2	1	no	—
86	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
91	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	—	2	2	no	—
95	C₄⋊C₈×C₈₉	—	2	2	no	—
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	#97×C₈₉	—	2	2	no	—
99	#97×C₈₉	D₄	1	2	yes	—
100	C₄×C₈×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083574	—	4	2	no	—
103	#13083574	—	4	2	no	—
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×D₃₅₆	—	2	1	no	—
106	C₂×D₃₅₆	—	2	1	no	—
107	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
108	C₂×C₂²⋊D₈₉	—	2	2	no	—
109	C₂×C₄×D₈₉	—	2	2	no	—
110	#13083561	—	2	4	no	—
111	#13083561	—	4	2	no	—
112	#13083557	—	4	4	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	4	2	no	—
118	C₂×#10623494	—	4	2	no	—
119	C₂×#10623494	C₂²×C₄	1	2	yes	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₈×D₈₉	—	4	4	no	—
122	C₄⋊Dic₈₉	—	2	1	no	—
123	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
124	#13083551	—	2	2	no	—
125	#13083551	—	2	2	no	—
126	C₂×Q₈×C₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	2	no	—
128	C₂×Q₈×C₈₉	—	4	1	no	—
129	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	—	2	1	no	—
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
136	M₁₆×C₈₉	—	2	2	no	—
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	4	2	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	1	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	#41	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	2	1	no	—
160	Q₈×C₈₉	—	2	1	no	—
161	Q₈×C₈₉	—	2	1	no	—
162	Q₈×C₈₉	—	4	2	no	—
163	Q₈×C₈₉	#131	1	2	yes	complemented
164	C₂×C₄×C₈₉	—	2	1	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	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	8	1	no	—
173	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₈₉	#137	1	2	yes	—
178	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₈₉	—	4	4	no	—
182	C₂×Dic₈₉	—	2	2	no	—
183	D₃₅₆	—	2	2	no	—
184	D₃₅₆	—	2	2	no	—
185	D₃₅₆	—	4	2	no	—
186	D₃₅₆	—	8	1	no	—
187	C₄×D₈₉	—	4	2	no	—
188	C₄×D₈₉	—	4	2	no	—
189	Dic₁₇₈	—	4	2	no	—
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	4	2	no	—
193	#10623494	—	2	2	no	—
194	#10623494	—	2	2	no	—
195	#10623494	—	2	2	no	—
196	#10623494	—	4	1	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	1	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	#440	1	2	yes	—
202	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₈₉	—	4	2	no	—
204	C₂×D₈₉	—	4	2	no	—
205	C₂×D₈₉	—	4	2	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	2	no	—
208	C₄×C₈₉	—	2	1	no	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	—	4	1	no	—
212	C₄×C₈₉	—	4	1	no	—
213	C₄×C₈₉	#440	1	2	yes	—
214	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
215	C₄×C₈₉	#568	1	1	yes	characteristic
216	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
218	Dic₈₉	—	4	2	no	—
219	#18004	—	89	1	no	maximal, Sylow
220	C₂×C₈₉	—	2	2	no	—
221	C₂×C₈₉	#2933	1	1	yes	characteristic
222	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
223	C₂×C₈₉	#2956	1	1	yes	characteristic
224	D₈₉	—	8	2	no	—
225	#3103	—	89	1	no	—
226	Q₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
227	#2935	—	89	1	no	—
228	#1592	—	89	2	no	—
229	#1588	—	89	2	no	—
230	#1585	—	89	2	no	—
231	SD₁₆⋊C₈	—	89	2	no	—
232	#1571	—	89	1	no	—
233	#1492	—	89	1	no	—
234	C₂×Q₈⋊C₈	—	89	1	no	—
235	#1451	—	89	1	no	—
236	C₈₉	#18004	1	1	yes	characteristic, complemented, Sylow
237	C₂×#131	—	178	1	no	—
238	#532	—	89	1	no	—
239	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
240	#481	—	89	2	no	—
241	#475	—	89	1	no	—
242	#475	—	89	1	no	—
243	#460	—	89	1	no	—
244	#460	—	89	1	no	—
245	#448	—	89	2	no	—
246	#446	—	2	2	no	—
247	#446	C₂×D₈₉	1	2	yes	—
248	C₈×Q₈	C₂×D₈₉	1	2	yes	—
249	C₄×SD₁₆	—	89	2	no	—
250	C₄×SD₁₆	—	89	2	no	—
251	#436	—	89	2	no	—
252	#435	—	178	2	no	—
253	C₈×D₄	—	89	2	no	—
254	#431	—	89	1	no	—
255	#423	—	2	1	no	—
256	#423	C₂×D₈₉	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	89	1	no	—
258	#408	—	178	1	no	—
259	C₄×M₁₆	—	2	1	no	—
260	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
261	C₂×C₄×C₈	—	89	1	no	—
262	#335	—	89	2	no	—
263	#335	—	89	2	no	—
264	Q₈⋊C₈	—	89	1	no	—
265	Q₈⋊C₈	—	89	1	no	—
266	Q₈⋊C₈	—	89	1	no	—
267	Q₈⋊C₈	—	89	1	no	—
268	D₄⋊C₈	—	89	2	no	—
269	D₄⋊C₈	—	89	2	no	—
270	#322	—	89	2	no	—
271	#322	—	89	2	no	—
272	C₂×#41	—	178	1	no	—
273	C₂²×Q₈	C₄×D₈₉	1	1	yes	characteristic
274	C₂×SD₁₆	—	89	2	no	—
275	C₂×SD₁₆	—	89	2	no	—
276	#131	—	356	4	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	178	2	no	—
279	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
280	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
281	C₂²×C₈	—	178	1	no	—
282	C₂²×C₈	—	178	1	no	—
283	C₂²×C₈	—	178	2	no	—
284	C₄⋊Q₈	—	89	1	no	—
285	#127	—	89	1	no	—
286	#124	—	178	1	no	—
287	#121	—	89	2	no	—
288	#121	—	178	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
292	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
295	C₄×D₄	—	89	2	no	—
296	C₄×D₄	—	178	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
301	#106	—	89	2	no	—
302	#106	—	89	2	no	—
303	C₄⋊C₈	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	89	1	no	—
307	C₄⋊C₈	—	89	1	no	—
308	C₄⋊C₈	—	89	1	no	—
309	C₄⋊C₈	—	89	1	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
312	#103	—	89	2	no	—
313	#103	—	89	2	no	—
314	#102	—	89	2	no	—
315	#102	—	89	2	no	—
316	C₂²⋊C₈	—	89	2	no	—
317	C₂²⋊C₈	—	178	2	no	—
318	C₂²⋊C₈	—	178	2	no	—
319	#97	—	2	2	no	—
320	#97	C₂²⋊D₈₉	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	89	2	no	—
323	C₄×C₈	—	89	1	no	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	178	1	no	—
326	C₄×C₈	C₂²×D₈₉	1	2	yes	—
327	#41	—	356	2	no	—
328	#41	—	356	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	1	no	—
332	C₂×Q₈	—	178	1	no	—
333	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
335	C₂×D₄	—	89	2	no	—
336	C₂×D₄	—	178	2	no	—
337	C₂×D₄	—	178	1	no	—
338	C₂×D₄	—	178	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	178	2	no	—
342	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
344	C₂²×C₄	#13083574	1	1	yes	characteristic
345	SD₁₆	—	356	2	no	—
346	SD₁₆	—	178	4	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	2	2	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	356	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	89	2	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	356	4	no	—
355	C₂×C₈	—	356	2	no	—
356	C₂×C₈	—	356	2	no	—
357	C₂×C₈	—	178	1	no	—
358	C₂×C₈	—	178	1	no	—
359	C₂×C₈	—	178	1	no	—
360	C₂×C₈	—	178	1	no	—
361	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
362	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	89	2	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
371	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
372	C₂²⋊C₄	—	178	2	no	—
373	C₂²⋊C₄	—	178	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
380	C₄²	#13083574	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	178	2	no	—
383	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	356	2	no	—
389	Q₈	#15668020	1	2	yes	complemented
390	D₄	—	356	4	no	—
391	D₄	—	356	2	no	—
392	D₄	—	178	2	no	—
393	D₄	—	178	2	no	—
394	D₄	—	712	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	356	2	no	—
405	C₂×C₄	—	356	2	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
410	C₂×C₄	#15668037	1	2	yes	—
411	C₂×C₄	#15668043	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
414	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	356	1	no	—
419	C₈	—	356	1	no	—
420	C₈	—	356	1	no	—
421	C₈	—	178	2	no	—
422	C₈	—	178	2	no	—
423	C₈	—	178	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	356	2	no	—
427	C₂²	—	356	2	no	—
428	C₂²	—	356	2	no	—
429	C₂²	#19151696	1	2	yes	—
430	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	356	2	no	—
439	C₄	#19151696	1	2	yes	—
440	C₄	C₂×#15668020	1	1	yes	characteristic
441	C₄	#19152364	1	1	yes	characteristic
442	C₄	C₂×#15668037	1	1	yes	characteristic
443	C₄	C₂×#15668043	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	712	2	no	—
446	C₂	#26028977	1	1	yes	characteristic
447	C₂	C₂×#19151696	1	1	yes	characteristic
448	C₂	#26029159	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	Q₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152148	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	Q₈×M₁₆	D₈₉
hypocenter	C₈₉	#18004
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ Q₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #26019152	C₂	semidirect
4. #26019130	C₂	semidirect
5. #26019107	C₂	semidirect
6. #26019062	C₂	semidirect
7. #26019028	C₂	semidirect
9. C₂×Q₈⋊#10623494	C₂	semidirect
10. #26018539	C₂	semidirect
11. Q₈×M₁₆×C₈₉	C₂	semidirect
163. Q₈×C₈₉	#131	semidirect
226. Q₈×M₁₆	D₈₉	semidirect
236. C₈₉	#18004	semidirect
389. Q₈	#15668020	semidirect

Maximal subgroups

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

subgroup	index
#26030283	2
#26028998	2
#26019152	2
#26019130	2
#26019107	2
#26019062	2
#26019028	2
#26018702	2
C₂×Q₈⋊#10623494	2
#26018539	2
Q₈×M₁₆×C₈₉	2
#18004	89