Subgroups — #26029495

Order 11392.

758 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668044	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15668039	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152111	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151759	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151758	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151757	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151746	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151745	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151744	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151743	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151605	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151560	C₂	1	1	yes	maximal, characteristic, complemented
15	#452×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×#13083575	C₂²	1	1	yes	characteristic
18	C₂×#13083574	—	2	1	no	—
19	C₂×#13083574	C₂²	1	1	yes	characteristic
20	C₂×#13083573	—	2	1	no	—
21	C₂×#13083573	C₂²	1	1	yes	characteristic
22	#41×D₈₉	—	2	4	no	—
23	#41×D₈₉	—	2	4	no	—
24	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
25	C₂×D₄×D₈₉	—	2	1	no	—
26	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₈₉	—	2	1	no	—
28	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
29	#15668044	—	2	4	no	—
30	#15668039	—	2	4	no	—
31	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
32	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₇₁₂	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13083557	C₂²	1	1	yes	characteristic
38	C₂×#13083557	C₂²	1	1	yes	characteristic
39	#15667997	—	2	1	no	—
40	#15667988	C₂²	1	1	yes	characteristic, complemented
41	#15667987	C₂²	1	1	yes	characteristic, complemented
42	#15667986	C₂²	1	1	yes	characteristic, complemented
43	#15667982	—	2	1	no	—
44	#15667974	—	2	1	no	—
45	#15667972	—	2	1	no	—
46	#15667970	C₂²	1	1	yes	characteristic
47	#15667937	C₂²	1	1	yes	characteristic, complemented
48	#15667936	C₂²	1	1	yes	characteristic, complemented
49	#15667935	C₂²	1	1	yes	characteristic, complemented
50	#15667934	C₂²	1	1	yes	characteristic, complemented
51	#15667933	C₂²	1	1	yes	characteristic, complemented
52	#15667932	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊#10623494	C₂²	1	1	yes	characteristic, complemented
54	#15667924	C₂²	1	1	yes	characteristic, complemented
55	#15667924	C₂²	1	1	yes	characteristic, complemented
56	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₈₉	—	2	1	no	—
64	C₂³×D₈₉	D₄	1	1	yes	characteristic
65	#13083575	—	2	2	no	—
66	#13083575	—	2	2	no	—
67	#13083575	—	2	2	no	—
68	#13083575	—	2	2	no	—
69	#13083574	—	2	8	no	—
70	#13083574	—	2	2	no	—
71	#13083574	—	2	2	no	—
72	#13083573	—	2	8	no	—
73	#13083573	—	2	2	no	—
74	#13083573	—	2	2	no	—
75	C₂×Dic₁₇₈	—	2	1	no	—
76	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
77	Q₈×D₈₉	—	2	2	no	—
78	Q₈×D₈₉	D₄	1	4	yes	complemented
79	C₂×D₃₅₆	—	2	1	no	—
80	C₂×D₃₅₆	—	2	1	no	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
83	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
84	C₂×C₂²⋊D₈₉	—	2	1	no	—
85	C₂×C₂²⋊D₈₉	—	2	1	no	—
86	C₂×C₂²⋊D₈₉	—	2	1	no	—
87	C₂×C₂²⋊D₈₉	—	2	1	no	—
88	D₄×D₈₉	—	2	8	no	—
89	D₄×D₈₉	—	2	2	no	—
90	D₄×D₈₉	D₄	1	4	yes	complemented
91	C₂²×Dic₈₉	—	2	1	no	—
92	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
93	C₂×C₄×D₈₉	—	2	8	no	—
94	C₂×C₄×D₈₉	—	2	1	no	—
95	C₂×C₄×D₈₉	—	2	1	no	—
96	C₂×C₄×D₈₉	—	2	1	no	—
97	C₂×C₄×D₈₉	—	2	2	no	—
98	C₂×C₄×D₈₉	—	2	2	no	—
99	C₂×C₄×D₈₉	—	2	1	no	—
100	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
104	#13083564	—	2	2	no	—
105	#13083563	—	2	2	no	—
106	#13083561	—	2	2	no	—
107	#13083561	—	2	2	no	—
108	D₇₁₂	—	2	2	no	—
109	#13083559	—	2	2	no	—
110	#13083557	—	2	2	no	—
111	#13083557	—	2	2	no	—
112	C₂×#10623494	C₂³	1	1	yes	characteristic
113	C₂×#10623494	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
115	#13083553	—	2	1	no	—
116	#13083551	—	2	1	no	—
117	#13083551	—	2	1	no	—
118	#13083551	—	2	1	no	—
119	#13083551	—	2	1	no	—
120	C₄×Dic₈₉	—	2	1	no	—
121	#41×C₈₉	—	2	2	no	—
122	#41×C₈₉	—	2	2	no	—
123	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
129	Q₁₆×C₈₉	—	2	2	no	—
130	SD₁₆×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
135	C₂²⋊C₄×C₈₉	—	2	1	no	—
136	C₂³×C₈₉	—	2	1	no	—
137	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₈₉	—	2	1	no	—
139	C₂²×D₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	2	4	no	—
141	C₂²×D₈₉	—	2	1	no	—
142	C₂²×D₈₉	—	4	1	no	—
143	C₂²×D₈₉	—	4	1	no	—
144	C₂²×D₈₉	—	4	2	no	—
145	C₂²×D₈₉	—	4	2	no	—
146	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
148	Q₈×C₈₉	—	2	1	no	—
149	Q₈×C₈₉	—	2	1	no	—
150	Q₈×C₈₉	—	2	1	no	—
151	Q₈×C₈₉	C₂×D₄	1	2	yes	—
152	D₄×C₈₉	—	2	4	no	—
153	D₄×C₈₉	—	2	1	no	—
154	D₄×C₈₉	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	2	4	no	—
164	C₂²⋊D₈₉	—	2	4	no	—
165	C₂²⋊D₈₉	—	2	4	no	—
166	C₂²⋊D₈₉	—	4	2	no	—
167	C₂×Dic₈₉	—	2	4	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	1	no	—
171	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
173	D₃₅₆	—	2	4	no	—
174	D₃₅₆	—	2	1	no	—
175	D₃₅₆	—	2	1	no	—
176	D₃₅₆	—	2	1	no	—
177	D₃₅₆	—	4	2	no	—
178	D₃₅₆	—	4	2	no	—
179	D₃₅₆	C₂×D₄	1	2	yes	—
180	C₄×D₈₉	—	2	4	no	—
181	C₄×D₈₉	—	2	4	no	—
182	C₄×D₈₉	—	2	2	no	—
183	C₄×D₈₉	—	2	4	no	—
184	C₄×D₈₉	—	2	1	no	—
185	C₄×D₈₉	—	2	1	no	—
186	C₄×D₈₉	—	2	2	no	—
187	C₄×D₈₉	—	4	2	no	—
188	C₄×D₈₉	C₂×D₄	1	2	yes	—
189	C₄×D₈₉	C₂×D₄	1	2	yes	—
190	Dic₁₇₈	—	2	1	no	—
191	Dic₁₇₈	—	2	4	no	—
192	Dic₁₇₈	C₂×D₄	1	2	yes	—
193	C₈×C₈₉	—	2	1	no	—
194	C₈×C₈₉	—	2	1	no	—
195	#10623494	—	2	1	no	—
196	#10623494	—	2	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	2	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×D₈₉	—	2	1	no	—
205	C₂×D₈₉	—	2	1	no	—
206	C₂×D₈₉	—	2	1	no	—
207	C₂×D₈₉	—	2	2	no	—
208	C₂×D₈₉	—	2	1	no	—
209	C₂×D₈₉	—	2	1	no	—
210	C₂×D₈₉	—	4	4	no	—
211	C₂×D₈₉	—	4	8	no	—
212	C₂×D₈₉	—	4	1	no	—
213	C₂×D₈₉	—	4	1	no	—
214	C₂×D₈₉	—	4	1	no	—
215	C₂×D₈₉	—	4	1	no	—
216	C₂×D₈₉	—	4	1	no	—
217	C₂×D₈₉	#120	1	2	yes	—
218	C₄×C₈₉	—	2	2	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	4	1	no	—
221	C₄×C₈₉	—	4	1	no	—
222	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	Dic₈₉	—	2	2	no	—
225	Dic₈₉	—	2	1	no	—
226	Dic₈₉	—	4	1	no	—
227	Dic₈₉	#120	1	2	yes	—
228	C₂×C₈₉	—	4	1	no	—
229	C₂×C₈₉	—	4	2	no	—
230	C₂×C₈₉	C₂×#120	1	1	yes	characteristic
231	C₂×C₈₉	#575	1	1	yes	characteristic
232	C₂×C₈₉	#575	1	1	yes	characteristic
233	D₈₉	—	2	2	no	—
234	D₈₉	—	4	1	no	—
235	D₈₉	—	4	2	no	—
236	D₈₉	—	8	1	no	—
237	#3005	—	89	1	no	maximal, Sylow
238	C₈₉	#3005	1	1	yes	characteristic, complemented, Sylow
239	C₂²×#41	—	89	1	no	—
240	C₂×#137	—	89	1	no	—
241	C₂×AGL(1,ℤ/8)	—	89	1	no	—
242	#525	—	89	1	no	—
243	#452	—	89	1	no	—
244	#452	—	89	1	no	—
245	#452	—	89	1	no	—
246	#452	D₈₉	1	1	yes	characteristic, complemented
247	#449	—	89	1	no	—
248	#449	—	89	1	no	—
249	#449	—	89	1	no	—
250	#449	—	89	1	no	—
251	#419	—	89	1	no	—
252	#418	—	89	1	no	—
253	#407	—	89	1	no	—
254	C₂×#41	—	89	1	no	—
255	C₂×#41	—	89	1	no	—
256	C₂×#41	—	89	1	no	—
257	C₂×#41	—	89	1	no	—
258	C₂×#41	—	178	1	no	—
259	C₂×#41	—	178	1	no	—
260	C₂×#41	—	178	4	no	—
261	C₂×#41	—	178	4	no	—
262	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
263	C₂²×Q₈	—	89	1	no	—
264	C₂²×D₄	—	89	1	no	—
265	C₂²×D₄	—	178	1	no	—
266	C₂³×C₄	—	89	1	no	—
267	C₂³×C₄	—	178	1	no	—
268	#137	—	178	4	no	—
269	AGL(1,ℤ/8)	—	178	4	no	—
270	C₂×Q₁₆	—	89	1	no	—
271	C₂×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	—	89	1	no	—
273	C₂×SD₁₆	—	89	1	no	—
274	C₂×SD₁₆	—	89	1	no	—
275	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
276	C₂×D₈	—	89	1	no	—
277	C₂×D₈	—	89	1	no	—
278	C₂×M₁₆	—	89	1	no	—
279	C₂×M₁₆	—	89	1	no	—
280	#123	—	178	1	no	—
281	C₂²⋊Q₈	—	89	1	no	—
282	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
283	#121	—	89	1	no	—
284	#121	—	89	1	no	—
285	#120	—	178	1	no	—
286	C₄×D₄	—	178	1	no	—
287	C₄×D₄	—	178	1	no	—
288	#117	—	89	1	no	—
289	#103	—	89	1	no	—
290	#103	—	89	1	no	—
291	#103	—	89	1	no	—
292	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
293	#102	—	89	1	no	—
294	#102	—	89	1	no	—
295	#102	—	89	1	no	—
296	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
297	C₂²⋊C₈	—	89	1	no	—
298	C₂²⋊C₈	—	89	1	no	—
299	C₂²⋊C₈	—	89	1	no	—
300	C₂²⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
301	C₂⁴	—	89	1	no	—
302	C₂⁴	—	178	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	178	2	no	—
306	#41	—	178	2	no	—
307	#41	—	178	8	no	—
308	#41	—	178	2	no	—
309	#41	—	178	2	no	—
310	#41	—	178	2	no	—
311	#41	—	178	8	no	—
312	#41	—	178	2	no	—
313	#41	—	178	2	no	—
314	#41	—	178	2	no	—
315	C₂×Q₈	—	89	4	no	—
316	C₂×Q₈	—	89	1	no	—
317	C₂×Q₈	—	178	1	no	—
318	C₂×Q₈	—	178	2	no	—
319	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	89	4	no	—
323	C₂×D₄	—	89	1	no	—
324	C₂×D₄	—	89	1	no	—
325	C₂×D₄	—	178	1	no	—
326	C₂×D₄	—	178	1	no	—
327	C₂×D₄	—	178	1	no	—
328	C₂×D₄	—	178	2	no	—
329	C₂×D₄	—	178	1	no	—
330	C₂×D₄	—	178	8	no	—
331	C₂×D₄	—	178	1	no	—
332	C₂×D₄	—	178	1	no	—
333	C₂×D₄	—	178	1	no	—
334	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	C₂²×C₄	—	89	1	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	—	178	1	no	—
342	C₂²×C₄	—	178	2	no	—
343	C₂²×C₄	—	178	2	no	—
344	C₂²×C₄	—	178	1	no	—
345	C₂²×C₄	—	178	1	no	—
346	C₂²×C₄	—	178	8	no	—
347	C₂²×C₄	—	178	1	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	Q₁₆	—	178	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	178	2	no	—
354	SD₁₆	—	178	2	no	—
355	SD₁₆	—	178	2	no	—
356	D₈	—	178	2	no	—
357	D₈	—	178	2	no	—
358	M₁₆	—	178	2	no	—
359	M₁₆	—	178	2	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
363	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	89	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	178	1	no	—
370	C₂²⋊C₄	—	178	1	no	—
371	C₂²⋊C₄	—	178	1	no	—
372	C₂²⋊C₄	—	178	1	no	—
373	C₄²	—	178	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	89	1	no	—
376	C₂³	—	89	1	no	—
377	C₂³	—	356	1	no	—
378	C₂³	—	356	1	no	—
379	C₂³	—	356	2	no	—
380	C₂³	—	356	2	no	—
381	C₂³	—	178	4	no	—
382	C₂³	—	178	2	no	—
383	C₂³	—	178	1	no	—
384	C₂³	—	178	1	no	—
385	C₂³	D₄×D₈₉	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	—	2	1	no	—
388	Q₈	—	2	1	no	—
389	Q₈	—	89	2	no	—
390	Q₈	—	178	4	no	—
391	Q₈	—	178	1	no	—
392	Q₈	D₄×D₈₉	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	89	2	no	—
396	D₄	—	356	2	no	—
397	D₄	—	356	2	no	—
398	D₄	—	356	2	no	—
399	D₄	—	178	4	no	—
400	D₄	—	178	4	no	—
401	D₄	—	178	4	no	—
402	D₄	—	178	4	no	—
403	D₄	—	178	1	no	—
404	D₄	—	178	1	no	—
405	D₄	—	178	1	no	—
406	D₄	D₄×D₈₉	1	2	yes	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	89	1	no	—
414	C₂×C₄	—	89	2	no	—
415	C₂×C₄	—	89	2	no	—
416	C₂×C₄	—	89	1	no	—
417	C₂×C₄	—	356	2	no	—
418	C₂×C₄	—	178	2	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	178	4	no	—
421	C₂×C₄	—	178	4	no	—
422	C₂×C₄	—	178	4	no	—
423	C₂×C₄	—	178	2	no	—
424	C₂×C₄	—	178	1	no	—
425	C₂×C₄	—	178	4	no	—
426	C₂×C₄	—	178	1	no	—
427	C₂×C₄	—	178	1	no	—
428	C₂×C₄	—	178	1	no	—
429	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	178	1	no	—
434	C₈	—	178	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	89	2	no	—
442	C₂²	—	356	4	no	—
443	C₂²	—	356	8	no	—
444	C₂²	—	356	1	no	—
445	C₂²	—	356	1	no	—
446	C₂²	—	356	1	no	—
447	C₂²	—	356	1	no	—
448	C₂²	—	356	1	no	—
449	C₂²	—	178	1	no	—
450	C₂²	—	178	1	no	—
451	C₂²	—	178	2	no	—
452	C₂²	—	178	1	no	—
453	C₂²	—	178	1	no	—
454	C₂²	—	178	1	no	—
455	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	89	2	no	—
461	C₄	—	356	1	no	—
462	C₄	—	178	1	no	—
463	C₄	—	178	2	no	—
464	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
465	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
466	C₂	—	4	1	no	—
467	C₂	—	4	2	no	—
468	C₂	—	356	2	no	—
469	C₂	—	356	1	no	—
470	C₂	—	178	2	no	—
471	C₂	—	712	1	no	—
472	C₂	#120×D₈₉	1	1	yes	characteristic
473	C₂	#19152395	1	1	yes	characteristic
474	C₂	#19152397	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#452×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	#452	D₈₉
hypocenter	C₈₉	#3005
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₈₉	C₂	semidirect
2. C₂×#15668044	C₂	semidirect
3. C₂×#15668039	C₂	semidirect
4. #19152111	C₂	semidirect
5. #19151759	C₂	semidirect
6. #19151758	C₂	semidirect
7. #19151757	C₂	semidirect
8. #19151746	C₂	semidirect
9. #19151745	C₂	semidirect
10. #19151744	C₂	semidirect
11. #19151743	C₂	semidirect
12. #19151605	C₂	semidirect
13. #19151601	C₂	semidirect
14. #19151560	C₂	semidirect
15. #452×C₈₉	C₂	semidirect
31. C₂×#13083564	C₂²	semidirect
32. C₂×#13083563	C₂²	semidirect
33. C₂×#13083561	C₂²	semidirect
34. C₂×#13083561	C₂²	semidirect
35. C₂×D₇₁₂	C₂²	semidirect
36. C₂×#13083559	C₂²	semidirect
40. #15667988	C₂²	semidirect
41. #15667987	C₂²	semidirect
42. #15667986	C₂²	semidirect
47. #15667937	C₂²	semidirect
48. #15667936	C₂²	semidirect
49. #15667935	C₂²	semidirect
50. #15667934	C₂²	semidirect
51. #15667933	C₂²	semidirect
52. #15667932	C₂²	semidirect
53. C₂²⋊#10623494	C₂²	semidirect
54. #15667924	C₂²	semidirect
55. #15667924	C₂²	semidirect
57. C₂×Q₁₆×C₈₉	C₂²	semidirect
58. C₂×SD₁₆×C₈₉	C₂²	semidirect
59. C₂²⋊Q₈×C₈₉	C₂²	semidirect
60. #103×C₈₉	C₂²	semidirect
61. #102×C₈₉	C₂²	semidirect
62. C₂²⋊C₈×C₈₉	C₂²	semidirect
78. Q₈×D₈₉	D₄	semidirect
90. D₄×D₈₉	D₄	semidirect
238. C₈₉	#3005	semidirect
246. #452	D₈₉	semidirect
271. C₂×Q₁₆	C₂×D₈₉	semidirect
275. C₂×SD₁₆	C₂×D₈₉	semidirect
282. C₂²⋊Q₈	C₂×D₈₉	semidirect
292. #103	C₂×D₈₉	semidirect
296. #102	C₂×D₈₉	semidirect
300. C₂²⋊C₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₈₉	2
C₂×#15668044	2
C₂×#15668039	2
#19152111	2
#19151759	2
#19151758	2
#19151757	2
#19151746	2
#19151745	2
#19151744	2
#19151743	2
#19151605	2
#19151601	2
#19151560	2
#452×C₈₉	2
#3005	89