Subgroups — #26029466

Order 11392.

764 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×#15668032	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152105	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151759	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151757	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151752	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151747	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151742	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151740	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151735	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151730	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151595	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151594	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15667924	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083575	C₂²	1	1	yes	characteristic
17	C₂×#13083574	—	2	1	no	—
18	C₂×#13083574	C₂²	1	1	yes	characteristic
19	C₂×#13083573	—	2	1	no	—
20	C₂×#13083573	C₂²	1	1	yes	characteristic
21	#41×D₈₉	—	2	4	no	—
22	#41×D₈₉	—	2	4	no	—
23	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
24	C₂×D₄×D₈₉	—	2	1	no	—
25	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₈₉	—	2	1	no	—
27	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
28	#15668032	—	2	4	no	—
29	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
31	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
32	C₂×#13083559	C₂²	1	1	yes	characteristic, complemented
33	C₂²×#10623494	C₂²	1	1	yes	characteristic, complemented
34	#15667993	—	2	1	no	—
35	#15667988	C₂²	1	1	yes	characteristic
36	#15667988	C₂²	1	1	yes	characteristic, complemented
37	#15667983	C₂²	1	1	yes	characteristic
38	#15667983	C₂²	1	1	yes	characteristic, complemented
39	#15667980	—	2	1	no	—
40	C₄×C₂²⋊D₈₉	—	2	1	no	—
41	C₄×C₂²⋊D₈₉	—	2	1	no	—
42	#15667971	C₂²	1	1	yes	characteristic, complemented
43	#15667937	C₂²	1	1	yes	characteristic, complemented
44	#15667937	C₂²	1	1	yes	characteristic, complemented
45	#15667936	C₂²	1	1	yes	characteristic, complemented
46	#15667936	C₂²	1	1	yes	characteristic, complemented
47	#15667934	C₂²	1	1	yes	characteristic, complemented
48	#15667934	C₂²	1	1	yes	characteristic, complemented
49	#15667933	C₂²	1	1	yes	characteristic, complemented
50	#15667933	C₂²	1	1	yes	characteristic, complemented
51	#15667924	C₂²	1	1	yes	characteristic
52	#15667924	C₂²	1	1	yes	characteristic
53	#15667924	C₂²	1	1	yes	characteristic, complemented
54	#15667924	C₂²	1	1	yes	characteristic, complemented
55	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#135×C₈₉	—	2	4	no	—
58	C₂×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₈×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	#13083574	—	2	8	no	—
68	#13083574	—	2	2	no	—
69	#13083574	D₄	1	4	yes	complemented
70	#13083573	—	2	8	no	—
71	#13083573	—	2	2	no	—
72	#13083573	—	2	2	no	—
73	C₂×Dic₁₇₈	—	2	1	no	—
74	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
75	Q₈×D₈₉	—	2	2	no	—
76	Q₈×D₈₉	—	2	2	no	—
77	C₂×D₃₅₆	—	2	1	no	—
78	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊D₈₉	—	2	1	no	—
80	C₂×C₂²⋊D₈₉	—	2	1	no	—
81	C₂×C₂²⋊D₈₉	—	2	1	no	—
82	C₂×C₂²⋊D₈₉	—	2	1	no	—
83	C₂×C₂²⋊D₈₉	—	2	1	no	—
84	D₄×D₈₉	—	2	8	no	—
85	D₄×D₈₉	—	2	2	no	—
86	D₄×D₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	—	2	1	no	—
88	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
89	C₂×C₄×D₈₉	—	2	8	no	—
90	C₂×C₄×D₈₉	—	2	1	no	—
91	C₂×C₄×D₈₉	—	2	1	no	—
92	C₂×C₄×D₈₉	—	2	2	no	—
93	C₂×C₄×D₈₉	—	2	2	no	—
94	C₂×C₄×D₈₉	—	2	1	no	—
95	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
96	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
99	#13083564	—	2	2	no	—
100	#13083562	—	2	2	no	—
101	#13083561	—	2	2	no	—
102	#13083559	—	2	2	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	C₂³	1	1	yes	characteristic
105	C₂×#10623494	C₂³	1	1	yes	characteristic
106	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
108	#13083553	—	2	1	no	—
109	#13083553	—	2	1	no	—
110	C₂²⋊Dic₈₉	—	2	1	no	—
111	C₂²⋊Dic₈₉	—	2	1	no	—
112	C₂²⋊Dic₈₉	—	2	1	no	—
113	#13083551	—	2	1	no	—
114	#13083551	—	2	1	no	—
115	C₄×Dic₈₉	—	2	1	no	—
116	#41×C₈₉	—	2	2	no	—
117	#41×C₈₉	—	2	2	no	—
118	#41×C₈₉	—	2	2	no	—
119	#41×C₈₉	D₄	1	4	yes	complemented
120	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×D₄×C₈₉	—	2	1	no	—
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	—	2	1	no	—
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	SD₁₆×C₈₉	—	2	2	no	—
132	D₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₂³×C₈₉	—	2	1	no	—
137	C₂³×C₈₉	—	2	1	no	—
138	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₈₉	—	2	4	no	—
140	C₂²×D₈₉	—	2	2	no	—
141	C₂²×D₈₉	—	2	1	no	—
142	C₂²×D₈₉	—	2	2	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	—	2	1	no	—
155	D₄×C₈₉	—	2	1	no	—
156	D₄×C₈₉	—	4	2	no	—
157	D₄×C₈₉	C₂×D₄	1	2	yes	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
163	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
165	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₈₉	—	2	4	no	—
167	C₂²⋊D₈₉	—	2	4	no	—
168	C₂²⋊D₈₉	—	2	4	no	—
169	C₂²⋊D₈₉	—	4	2	no	—
170	C₂²⋊D₈₉	—	4	2	no	—
171	C₂×Dic₈₉	—	2	4	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	2	1	no	—
174	C₂×Dic₈₉	—	2	1	no	—
175	C₂×Dic₈₉	—	2	1	no	—
176	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
178	D₃₅₆	—	2	4	no	—
179	D₃₅₆	—	2	1	no	—
180	D₃₅₆	C₂×D₄	1	2	yes	—
181	C₄×D₈₉	—	2	4	no	—
182	C₄×D₈₉	—	2	4	no	—
183	C₄×D₈₉	—	2	2	no	—
184	C₄×D₈₉	—	2	4	no	—
185	C₄×D₈₉	—	2	2	no	—
186	C₄×D₈₉	—	2	1	no	—
187	C₄×D₈₉	—	2	1	no	—
188	C₄×D₈₉	—	2	1	no	—
189	C₄×D₈₉	—	2	1	no	—
190	Dic₁₇₈	—	2	4	no	—
191	Dic₁₇₈	—	2	1	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	1	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	—	4	1	no	—
204	C₂²×C₈₉	—	4	1	no	—
205	C₂²×C₈₉	#120	1	2	yes	—
206	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×D₈₉	—	2	1	no	—
208	C₂×D₈₉	—	2	1	no	—
209	C₂×D₈₉	—	2	1	no	—
210	C₂×D₈₉	—	2	2	no	—
211	C₂×D₈₉	—	2	1	no	—
212	C₂×D₈₉	—	2	1	no	—
213	C₂×D₈₉	—	4	4	no	—
214	C₂×D₈₉	—	4	8	no	—
215	C₂×D₈₉	—	4	1	no	—
216	C₂×D₈₉	—	4	1	no	—
217	C₂×D₈₉	#135	1	2	yes	complemented
218	C₄×C₈₉	—	2	2	no	—
219	C₄×C₈₉	—	4	1	no	—
220	C₄×C₈₉	#120	1	2	yes	—
221	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	Dic₈₉	—	2	1	no	—
224	Dic₈₉	—	2	2	no	—
225	Dic₈₉	—	2	1	no	—
226	Dic₈₉	—	4	1	no	—
227	Dic₈₉	—	4	1	no	—
228	C₂×C₈₉	—	2	2	no	—
229	C₂×C₈₉	—	4	2	no	—
230	C₂×C₈₉	—	8	1	no	—
231	C₂×C₈₉	C₂×#120	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#135	1	1	yes	characteristic
233	C₂×C₈₉	#575	1	1	yes	characteristic
234	D₈₉	—	2	2	no	—
235	D₈₉	—	4	1	no	—
236	D₈₉	—	4	2	no	—
237	#3002	—	89	1	no	maximal, Sylow
238	C₈₉	#3002	1	1	yes	characteristic, complemented, Sylow
239	C₂²×#41	—	89	1	no	—
240	C₂×#135	—	89	1	no	—
241	C₂×#135	D₈₉	1	1	yes	characteristic, complemented
242	#525	—	89	1	no	—
243	#452	—	89	1	no	—
244	#452	—	89	1	no	—
245	#451	—	89	1	no	—
246	#450	—	89	1	no	—
247	#449	—	89	1	no	—
248	#449	—	89	1	no	—
249	#448	—	89	1	no	—
250	#447	—	89	1	no	—
251	#416	—	89	1	no	—
252	#416	—	89	1	no	—
253	C₂×C₂²⋊C₈	—	89	1	no	—
254	C₂×#41	—	89	1	no	—
255	C₂×#41	—	89	1	no	—
256	C₂×#41	—	89	1	no	—
257	C₂×#41	—	178	1	no	—
258	C₂×#41	—	178	1	no	—
259	C₂×#41	—	178	4	no	—
260	C₂×#41	—	178	4	no	—
261	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
262	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
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	#135	—	2	4	no	—
269	#135	—	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	C₂×D₈₉	1	1	yes	characteristic, complemented
275	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
276	C₂×D₈	—	89	1	no	—
277	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic, complemented
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
280	#123	—	178	1	no	—
281	C₂²⋊Q₈	—	89	1	no	—
282	C₂²⋊Q₈	—	89	1	no	—
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	—	89	1	no	—
293	#102	—	89	1	no	—
294	#102	—	89	1	no	—
295	#102	—	89	1	no	—
296	#102	—	89	1	no	—
297	C₂²⋊C₈	—	89	1	no	—
298	C₂²⋊C₈	—	89	1	no	—
299	C₂²⋊C₈	—	89	1	no	—
300	C₂²⋊C₈	—	89	1	no	—
301	C₂⁴	—	89	1	no	—
302	C₂⁴	—	178	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	89	4	no	—
307	#41	—	178	8	no	—
308	#41	—	178	2	no	—
309	#41	—	178	8	no	—
310	#41	—	178	2	no	—
311	#41	—	178	2	no	—
312	#41	—	178	2	no	—
313	#41	—	178	2	no	—
314	#41	C₂²⋊D₈₉	1	4	yes	complemented
315	C₂×Q₈	—	89	1	no	—
316	C₂×Q₈	—	178	1	no	—
317	C₂×Q₈	—	178	2	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	—	2	1	no	—
323	C₂×D₄	—	89	1	no	—
324	C₂×D₄	—	178	1	no	—
325	C₂×D₄	—	178	1	no	—
326	C₂×D₄	—	178	2	no	—
327	C₂×D₄	—	178	8	no	—
328	C₂×D₄	—	178	1	no	—
329	C₂×D₄	—	178	1	no	—
330	C₂×D₄	—	178	1	no	—
331	C₂×D₄	—	178	1	no	—
332	C₂×D₄	—	178	2	no	—
333	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
334	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	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	—	89	1	no	—
342	C₂²×C₄	—	178	1	no	—
343	C₂²×C₄	—	178	1	no	—
344	C₂²×C₄	—	178	8	no	—
345	C₂²×C₄	—	178	1	no	—
346	C₂²×C₄	—	178	2	no	—
347	C₂²×C₄	—	178	1	no	—
348	C₂²×C₄	—	178	2	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	—	2	2	no	—
354	SD₁₆	—	178	2	no	—
355	SD₁₆	—	178	2	no	—
356	D₈	—	2	2	no	—
357	D₈	—	178	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	89	1	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	178	2	no	—
362	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
363	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
364	C₄⋊C₄	—	89	1	no	—
365	C₄⋊C₄	—	89	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₂²⋊C₄	—	178	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	—	2	1	no	—
376	C₂³	—	89	1	no	—
377	C₂³	—	89	1	no	—
378	C₂³	—	356	1	no	—
379	C₂³	—	356	2	no	—
380	C₂³	—	356	2	no	—
381	C₂³	—	178	2	no	—
382	C₂³	—	178	4	no	—
383	C₂³	—	178	2	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	C₂×C₂²⋊D₈₉	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	2	1	no	—
396	D₄	—	2	1	no	—
397	D₄	—	4	2	no	—
398	D₄	—	89	2	no	—
399	D₄	—	356	2	no	—
400	D₄	—	356	2	no	—
401	D₄	—	178	4	no	—
402	D₄	—	178	4	no	—
403	D₄	—	178	4	no	—
404	D₄	—	178	4	no	—
405	D₄	—	178	1	no	—
406	D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	89	1	no	—
412	C₂×C₄	—	89	1	no	—
413	C₂×C₄	—	178	4	no	—
414	C₂×C₄	—	178	4	no	—
415	C₂×C₄	—	178	1	no	—
416	C₂×C₄	—	178	1	no	—
417	C₂×C₄	—	178	4	no	—
418	C₂×C₄	—	178	2	no	—
419	C₂×C₄	—	178	1	no	—
420	C₂×C₄	—	178	2	no	—
421	C₂×C₄	—	178	2	no	—
422	C₂×C₄	—	178	4	no	—
423	C₂×C₄	—	178	1	no	—
424	C₂×C₄	—	178	1	no	—
425	C₂×C₄	—	178	1	no	—
426	C₂×C₄	—	178	1	no	—
427	C₂×C₄	D₄×D₈₉	1	2	yes	—
428	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊D₈₉	1	2	yes	—
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	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	89	2	no	—
444	C₂²	—	356	4	no	—
445	C₂²	—	356	8	no	—
446	C₂²	—	356	1	no	—
447	C₂²	—	356	1	no	—
448	C₂²	—	178	1	no	—
449	C₂²	—	178	2	no	—
450	C₂²	—	178	1	no	—
451	C₂²	—	178	1	no	—
452	C₂²	—	178	1	no	—
453	C₂²	—	178	1	no	—
454	C₂²	#15667980	1	2	yes	—
455	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	4	1	no	—
458	C₄	—	356	1	no	—
459	C₄	—	356	1	no	—
460	C₄	—	178	1	no	—
461	C₄	—	178	1	no	—
462	C₄	—	178	2	no	—
463	C₄	#15667980	1	2	yes	—
464	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
465	C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	4	2	no	—
468	C₂	—	8	1	no	—
469	C₂	—	356	2	no	—
470	C₂	—	356	1	no	—
471	C₂	—	178	2	no	—
472	C₂	C₂×#15667980	1	1	yes	characteristic
473	C₂	#135×D₈₉	1	1	yes	characteristic
474	C₂	#19152395	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	C₂×#135×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
hypercenter	C₂×#135	D₈₉
hypocenter	C₈₉	#3002
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₈₉	C₂	semidirect
2. C₂×#15668032	C₂	semidirect
3. #19152105	C₂	semidirect
4. #19151759	C₂	semidirect
5. #19151757	C₂	semidirect
6. #19151752	C₂	semidirect
7. #19151747	C₂	semidirect
8. #19151742	C₂	semidirect
9. #19151740	C₂	semidirect
10. #19151735	C₂	semidirect
11. #19151730	C₂	semidirect
12. #19151595	C₂	semidirect
13. #19151594	C₂	semidirect
14. C₂×#15667924	C₂	semidirect
15. C₂×#135×C₈₉	C₂	semidirect
29. C₂×#13083564	C₂²	semidirect
30. C₂×#13083562	C₂²	semidirect
31. C₂×#13083561	C₂²	semidirect
32. C₂×#13083559	C₂²	semidirect
33. C₂²×#10623494	C₂²	semidirect
36. #15667988	C₂²	semidirect
38. #15667983	C₂²	semidirect
42. #15667971	C₂²	semidirect
43. #15667937	C₂²	semidirect
44. #15667937	C₂²	semidirect
45. #15667936	C₂²	semidirect
46. #15667936	C₂²	semidirect
47. #15667934	C₂²	semidirect
48. #15667934	C₂²	semidirect
49. #15667933	C₂²	semidirect
50. #15667933	C₂²	semidirect
53. #15667924	C₂²	semidirect
54. #15667924	C₂²	semidirect
56. C₂×#41×C₈₉	C₂²	semidirect
58. C₂×Q₁₆×C₈₉	C₂²	semidirect
59. C₂×SD₁₆×C₈₉	C₂²	semidirect
60. C₂×SD₁₆×C₈₉	C₂²	semidirect
61. C₂×D₈×C₈₉	C₂²	semidirect
62. C₂²×C₈×C₈₉	C₂²	semidirect
69. #13083574	D₄	semidirect
119. #41×C₈₉	D₄	semidirect
217. C₂×D₈₉	#135	semidirect
238. C₈₉	#3002	semidirect
241. C₂×#135	D₈₉	semidirect
262. C₂×#41	C₂×D₈₉	semidirect
271. C₂×Q₁₆	C₂×D₈₉	semidirect
274. C₂×SD₁₆	C₂×D₈₉	semidirect
275. C₂×SD₁₆	C₂×D₈₉	semidirect
277. C₂×D₈	C₂×D₈₉	semidirect
279. C₂²×C₈	C₂×D₈₉	semidirect
314. #41	C₂²⋊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×#15668032	2
#19152105	2
#19151759	2
#19151757	2
#19151752	2
#19151747	2
#19151742	2
#19151740	2
#19151735	2
#19151730	2
#19151595	2
#19151594	2
C₂×#15667924	2
C₂×#135×C₈₉	2
#3002	89