Subgroups — #26034283

Order 11392.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152313	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152308	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152298	C₂	1	2	yes	maximal, complemented
4	#19152295	C₂	1	2	yes	maximal, complemented
5	#19152237	C₂	1	4	yes	maximal, complemented
6	#19152236	C₂	1	2	yes	maximal, complemented
7	#19152233	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152233	C₂	1	2	yes	maximal, complemented
9	#19152202	C₂	1	2	yes	maximal, complemented
10	#19152180	C₂	1	4	yes	maximal, complemented
11	#19152146	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152135	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152105	C₂	1	2	yes	maximal, complemented
14	#121×D₈₉	C₂	1	2	yes	maximal, complemented
15	#19152070	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#550×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083573	C₂²	1	2	yes	complemented
19	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₈₉	C₂²	1	2	yes	—
21	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
22	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₈₉	C₂²	1	2	yes	complemented
24	#15668012	C₂²	1	1	yes	characteristic, complemented
25	#15668007	C₂²	1	2	yes	complemented
26	#15668005	C₂²	1	4	yes	complemented
27	#15668004	C₂²	1	2	yes	complemented
28	#15668003	C₂²	1	1	yes	characteristic, complemented
29	#15668001	C₂²	1	1	yes	characteristic, complemented
30	#15667999	C₂²	1	2	yes	complemented
31	#15667998	C₂²	1	4	yes	complemented
32	#15667997	C₂²	1	2	yes	complemented
33	#15667995	C₂²	1	4	yes	complemented
34	#15667993	C₂²	1	4	yes	complemented
35	#15667993	C₂²	1	4	yes	complemented
36	#15667990	C₂²	1	4	yes	complemented
37	#15667988	C₂²	1	1	yes	characteristic, complemented
38	#15667988	C₂²	1	2	yes	complemented
39	#15667987	C₂²	1	1	yes	characteristic
40	#15667986	C₂²	1	2	yes	complemented
41	#15667985	C₂²	1	4	yes	complemented
42	#15667984	C₂²	1	4	yes	complemented
43	#15667984	C₂²	1	4	yes	complemented
44	#15667983	C₂²	1	2	yes	complemented
45	#15667983	C₂²	1	2	yes	complemented
46	#15667983	C₂²	1	4	yes	complemented
47	#15667983	C₂²	1	2	yes	complemented
48	#15667983	C₂²	1	2	yes	complemented
49	#15667983	C₂²	1	2	yes	complemented
50	#15667980	C₂²	1	4	yes	complemented
51	#15667980	C₂²	1	4	yes	complemented
52	#15667980	C₂²	1	4	yes	complemented
53	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
54	C₄×D₃₅₆	C₂²	1	2	yes	—
55	C₄×D₃₅₆	C₂²	1	2	yes	complemented
56	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
57	D₄×Dic₈₉	C₂²	1	2	yes	complemented
58	D₄×Dic₈₉	C₂²	1	2	yes	complemented
59	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
60	#15667974	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	complemented
62	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	complemented
64	#15667972	C₂²	1	2	yes	complemented
65	#15667972	C₂²	1	4	yes	complemented
66	#15667971	C₂²	1	2	yes	complemented
67	#15667970	C₂²	1	2	yes	complemented
68	#15667969	C₂²	1	2	yes	complemented
69	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
70	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
71	C₂×#13083551	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
74	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
75	C₂×#41×C₈₉	C₂²	1	2	yes	complemented
76	#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#127×C₈₉	C₂²	1	2	yes	complemented
78	#121×C₈₉	C₂²	1	4	yes	complemented
79	#121×C₈₉	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
82	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₈₉	C₂³	1	2	yes	—
84	C₂³×D₈₉	C₂³	1	4	yes	—
85	#13083573	—	4	4	no	—
86	C₂×Dic₁₇₈	C₂³	1	2	yes	—
87	C₂×D₃₅₆	C₂³	1	2	yes	—
88	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
89	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
95	D₄×D₈₉	—	2	4	no	—
96	D₄×D₈₉	—	2	8	no	—
97	D₄×D₈₉	—	4	4	no	—
98	D₄×D₈₉	—	4	8	no	—
99	C₂²×Dic₈₉	C₂³	1	4	yes	—
100	C₂²×Dic₈₉	C₂³	1	2	yes	—
101	C₂×C₄×D₈₉	—	4	4	no	—
102	C₂×C₄×D₈₉	C₂³	1	2	yes	—
103	C₂×C₄×D₈₉	C₂³	1	2	yes	—
104	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₂³	1	2	yes	—
108	C₂×C₄×D₈₉	C₂³	1	4	yes	—
109	C₂×C₄×D₈₉	C₂³	1	2	yes	—
110	C₄⋊Dic₈₉	C₂³	1	2	yes	—
111	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₈₉	C₂³	1	2	yes	—
113	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₈₉	C₂³	1	2	yes	—
115	#13083553	C₂³	1	2	yes	—
116	#13083553	C₂³	1	2	yes	—
117	#13083553	C₂³	1	2	yes	—
118	#13083553	C₂³	1	4	yes	—
119	#13083553	C₂³	1	4	yes	—
120	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
121	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
122	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
123	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
124	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
125	#13083551	C₂³	1	2	yes	—
126	#13083551	C₂³	1	2	yes	—
127	#13083551	C₂³	1	4	yes	—
128	#13083551	C₂³	1	2	yes	—
129	#13083551	C₂³	1	2	yes	—
130	#13083551	C₂³	1	2	yes	—
131	#13083551	C₂³	1	4	yes	—
132	#13083551	C₂³	1	2	yes	—
133	#13083551	C₂³	1	2	yes	—
134	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂³	1	4	yes	—
136	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
138	#41×C₈₉	—	4	4	no	—
139	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
140	C₂×D₄×C₈₉	C₂³	1	2	yes	—
141	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×D₄×C₈₉	C₂³	1	2	yes	—
143	C₂×D₄×C₈₉	C₂³	1	4	yes	—
144	C₂×D₄×C₈₉	C₂³	1	2	yes	—
145	C₂×D₄×C₈₉	C₂³	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
147	C₂²×C₄×C₈₉	C₂³	1	4	yes	—
148	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
152	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
153	C₄²×C₈₉	C₂³	1	2	yes	—
154	C₄²×C₈₉	C₂³	1	1	yes	characteristic
155	C₂³×C₈₉	C₂⁴	1	4	yes	—
156	C₂³×C₈₉	C₂⁴	1	2	yes	—
157	C₂²×D₈₉	—	2	4	no	—
158	C₂²×D₈₉	—	2	4	no	—
159	C₂²×D₈₉	—	2	8	no	—
160	C₂²×D₈₉	—	4	2	no	—
161	C₂²×D₈₉	—	4	4	no	—
162	C₂²×D₈₉	—	4	4	no	—
163	C₂²×D₈₉	C₂⁴	1	2	yes	—
164	C₂²×D₈₉	C₂⁴	1	2	yes	—
165	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
166	Q₈×C₈₉	—	2	2	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	2	4	no	—
169	D₄×C₈₉	—	2	4	no	—
170	D₄×C₈₉	—	4	4	no	—
171	D₄×C₈₉	—	4	4	no	—
172	D₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	2	4	no	—
174	C₂×C₄×C₈₉	—	4	4	no	—
175	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
177	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
179	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂²⋊D₈₉	—	2	4	no	—
182	C₂²⋊D₈₉	—	2	8	no	—
183	C₂²⋊D₈₉	—	2	8	no	—
184	C₂²⋊D₈₉	—	4	4	no	—
185	C₂²⋊D₈₉	—	4	4	no	—
186	C₂×Dic₈₉	—	4	2	no	—
187	C₂×Dic₈₉	—	4	4	no	—
188	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂⁴	1	2	yes	—
190	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₈₉	C₂⁴	1	4	yes	—
193	C₂×Dic₈₉	C₂⁴	1	2	yes	—
194	D₃₅₆	—	2	4	no	—
195	D₃₅₆	—	2	2	no	—
196	D₃₅₆	#41	1	4	yes	complemented
197	C₄×D₈₉	—	2	2	no	—
198	C₄×D₈₉	—	2	2	no	—
199	C₄×D₈₉	—	2	4	no	—
200	C₄×D₈₉	—	2	2	no	—
201	C₄×D₈₉	—	2	4	no	—
202	C₄×D₈₉	—	4	2	no	—
203	C₄×D₈₉	—	4	2	no	—
204	C₄×D₈₉	—	4	4	no	—
205	Dic₁₇₈	—	4	2	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	4	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	2	2	no	—
211	C₂²×C₈₉	—	2	4	no	—
212	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
213	C₂×D₈₉	—	2	1	no	—
214	C₂×D₈₉	—	2	1	no	—
215	C₂×D₈₉	—	2	2	no	—
216	C₂×D₈₉	—	2	2	no	—
217	C₂×D₈₉	—	2	2	no	—
218	C₂×D₈₉	—	2	2	no	—
219	C₂×D₈₉	—	2	2	no	—
220	C₂×D₈₉	—	4	8	no	—
221	C₂×D₈₉	—	8	8	no	—
222	C₂×D₈₉	C₂×#41	1	4	yes	—
223	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	2	no	—
226	C₄×C₈₉	—	2	2	no	—
227	C₄×C₈₉	—	2	2	no	—
228	C₄×C₈₉	C₂×#41	1	2	yes	—
229	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
230	Dic₈₉	—	2	1	no	—
231	Dic₈₉	—	2	2	no	—
232	Dic₈₉	—	2	4	no	—
233	Dic₈₉	—	2	1	no	—
234	Dic₈₉	—	2	2	no	—
235	Dic₈₉	—	2	1	no	—
236	C₂×C₈₉	—	4	2	no	—
237	C₂×C₈₉	—	4	4	no	—
238	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
239	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	D₈₉	—	2	2	no	—
242	D₈₉	—	2	4	no	—
243	D₈₉	—	4	2	no	—
244	#3519	—	89	1	no	maximal, Sylow
245	C₈₉	#3519	1	1	yes	characteristic, complemented, Sylow
246	#555	—	89	1	no	—
247	#554	—	89	1	no	—
248	#553	—	89	2	no	—
249	#553	—	89	2	no	—
250	#550	D₈₉	1	1	yes	characteristic, complemented
251	#546	—	89	2	no	—
252	#546	—	89	4	no	—
253	D₄²	—	89	1	no	—
254	D₄²	—	89	2	no	—
255	#540	—	89	2	no	—
256	#538	—	89	4	no	—
257	#532	—	89	1	no	—
258	#529	—	89	1	no	—
259	#525	—	89	2	no	—
260	C₂×#121	—	89	2	no	—
261	#518	—	89	2	no	—
262	C₂×C₄×D₄	—	89	1	no	—
263	C₂×#41	—	89	2	no	—
264	C₂×#41	C₂×D₈₉	1	2	yes	complemented
265	C₂²×D₄	—	89	4	no	—
266	C₂²×D₄	—	89	2	no	—
267	C₂²×D₄	—	89	1	no	—
268	C₂²×D₄	—	89	2	no	—
269	C₂³×C₄	—	89	2	no	—
270	C₄⋊Q₈	—	89	1	no	—
271	#127	C₂×D₈₉	1	1	yes	characteristic, complemented
272	#127	C₂×D₈₉	1	2	yes	complemented
273	#126	—	89	2	no	—
274	#126	—	89	4	no	—
275	#125	—	89	1	no	—
276	#125	—	89	2	no	—
277	#124	—	89	1	no	—
278	#124	—	89	2	no	—
279	#124	—	89	4	no	—
280	#123	—	89	4	no	—
281	#123	—	89	4	no	—
282	#123	—	89	4	no	—
283	#123	—	89	2	no	—
284	C₂²⋊Q₈	—	89	1	no	—
285	C₂²⋊Q₈	—	89	2	no	—
286	C₂²⋊Q₈	—	89	4	no	—
287	#121	—	89	2	no	—
288	#121	—	89	4	no	—
289	#121	—	89	2	no	—
290	#121	—	89	2	no	—
291	#121	—	89	4	no	—
292	#121	—	89	2	no	—
293	#121	—	89	2	no	—
294	#121	—	89	4	no	—
295	#121	—	89	2	no	—
296	#121	—	89	1	no	—
297	#121	—	89	4	no	—
298	#121	C₂×D₈₉	1	2	yes	complemented
299	#121	C₂×D₈₉	1	4	yes	complemented
300	#120	—	89	4	no	—
301	#120	—	89	4	no	—
302	#120	—	89	4	no	—
303	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
304	C₄×D₄	—	89	1	no	—
305	C₄×D₄	—	89	2	no	—
306	C₄×D₄	—	89	2	no	—
307	C₄×D₄	—	89	2	no	—
308	C₄×D₄	—	89	4	no	—
309	C₄×D₄	—	89	4	no	—
310	C₄×D₄	—	89	1	no	—
311	C₄×D₄	—	89	2	no	—
312	C₄×D₄	—	89	4	no	—
313	C₄×D₄	—	89	1	no	—
314	C₄×D₄	—	89	2	no	—
315	C₄×D₄	—	89	2	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
318	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
319	#117	—	89	2	no	—
320	#117	—	89	2	no	—
321	#117	—	89	2	no	—
322	C₂×C₄⋊C₄	—	89	1	no	—
323	C₂×C₄⋊C₄	—	89	2	no	—
324	C₂×C₂²⋊C₄	—	89	4	no	—
325	C₂×C₂²⋊C₄	—	89	2	no	—
326	C₂×C₂²⋊C₄	—	89	4	no	—
327	C₂×C₄²	—	89	1	no	—
328	C₂⁴	—	89	4	no	—
329	C₂⁴	—	89	2	no	—
330	#41	—	4	4	no	—
331	#41	—	356	4	no	—
332	C₂×Q₈	—	89	2	no	—
333	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₂×D₄	—	89	4	no	—
335	C₂×D₄	—	89	4	no	—
336	C₂×D₄	—	89	2	no	—
337	C₂×D₄	—	89	4	no	—
338	C₂×D₄	—	89	4	no	—
339	C₂×D₄	—	89	1	no	—
340	C₂×D₄	—	89	2	no	—
341	C₂×D₄	—	89	1	no	—
342	C₂×D₄	—	356	8	no	—
343	C₂×D₄	—	356	4	no	—
344	C₂×D₄	—	178	4	no	—
345	C₂×D₄	—	178	8	no	—
346	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
347	C₂×D₄	C₂²×D₈₉	1	2	yes	—
348	C₂×D₄	C₂²×D₈₉	1	2	yes	—
349	C₂×D₄	C₂²×D₈₉	1	4	yes	—
350	C₂×D₄	C₂²×D₈₉	1	2	yes	—
351	C₂×D₄	C₂²×D₈₉	1	4	yes	—
352	C₂²×C₄	—	89	4	no	—
353	C₂²×C₄	—	89	2	no	—
354	C₂²×C₄	—	89	2	no	—
355	C₂²×C₄	—	89	2	no	—
356	C₂²×C₄	—	89	4	no	—
357	C₂²×C₄	—	89	1	no	—
358	C₂²×C₄	—	89	1	no	—
359	C₂²×C₄	—	89	1	no	—
360	C₂²×C₄	—	89	2	no	—
361	C₂²×C₄	—	89	2	no	—
362	C₂²×C₄	—	356	4	no	—
363	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
364	C₂²×C₄	C₂²×D₈₉	1	4	yes	—
365	C₄⋊C₄	—	89	2	no	—
366	C₄⋊C₄	—	89	1	no	—
367	C₄⋊C₄	—	89	2	no	—
368	C₄⋊C₄	—	89	4	no	—
369	C₄⋊C₄	—	89	1	no	—
370	C₄⋊C₄	—	89	2	no	—
371	C₄⋊C₄	—	89	2	no	—
372	C₄⋊C₄	—	89	2	no	—
373	C₄⋊C₄	—	89	2	no	—
374	C₄⋊C₄	—	89	4	no	—
375	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
377	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
378	C₂²⋊C₄	—	89	2	no	—
379	C₂²⋊C₄	—	89	4	no	—
380	C₂²⋊C₄	—	89	4	no	—
381	C₂²⋊C₄	—	89	4	no	—
382	C₂²⋊C₄	—	89	4	no	—
383	C₂²⋊C₄	—	89	2	no	—
384	C₂²⋊C₄	—	89	2	no	—
385	C₂²⋊C₄	—	89	2	no	—
386	C₂²⋊C₄	—	89	4	no	—
387	C₂²⋊C₄	—	89	4	no	—
388	C₂²⋊C₄	—	89	2	no	—
389	C₂²⋊C₄	—	89	2	no	—
390	C₂²⋊C₄	—	89	2	no	—
391	C₂²⋊C₄	—	89	2	no	—
392	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
393	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
394	C₄²	—	89	1	no	—
395	C₄²	—	89	1	no	—
396	C₄²	—	89	1	no	—
397	C₄²	—	89	4	no	—
398	C₄²	C₂²×D₈₉	1	1	yes	characteristic
399	C₄²	C₂²×D₈₉	1	2	yes	—
400	C₂³	—	89	2	no	—
401	C₂³	—	89	1	no	—
402	C₂³	—	89	2	no	—
403	C₂³	—	356	2	no	—
404	C₂³	—	356	4	no	—
405	C₂³	—	356	4	no	—
406	C₂³	—	178	4	no	—
407	C₂³	—	178	4	no	—
408	C₂³	—	178	8	no	—
409	C₂³	C₂³×D₈₉	1	4	yes	—
410	C₂³	C₂³×D₈₉	1	2	yes	—
411	Q₈	—	2	2	no	—
412	Q₈	—	356	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	4	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	89	4	no	—
420	D₄	—	356	4	no	—
421	D₄	—	356	4	no	—
422	D₄	—	178	4	no	—
423	D₄	—	178	8	no	—
424	D₄	—	178	4	no	—
425	D₄	—	178	8	no	—
426	D₄	—	178	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	89	1	no	—
430	C₂×C₄	—	89	2	no	—
431	C₂×C₄	—	89	1	no	—
432	C₂×C₄	—	89	1	no	—
433	C₂×C₄	—	89	4	no	—
434	C₂×C₄	—	89	2	no	—
435	C₂×C₄	—	356	2	no	—
436	C₂×C₄	—	356	2	no	—
437	C₂×C₄	—	356	4	no	—
438	C₂×C₄	—	356	2	no	—
439	C₂×C₄	—	356	4	no	—
440	C₂×C₄	—	178	2	no	—
441	C₂×C₄	—	178	4	no	—
442	C₂×C₄	—	178	2	no	—
443	C₂×C₄	—	178	2	no	—
444	C₂×C₄	—	178	4	no	—
445	C₂×C₄	C₂³×D₈₉	1	2	yes	—
446	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×D₈₉	1	2	yes	—
448	C₂×C₄	C₂³×D₈₉	1	2	yes	—
449	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	89	4	no	—
458	C₂²	—	89	2	no	—
459	C₂²	—	356	8	no	—
460	C₂²	—	178	2	no	—
461	C₂²	—	178	2	no	—
462	C₂²	—	178	2	no	—
463	C₂²	—	178	1	no	—
464	C₂²	—	178	2	no	—
465	C₂²	—	178	1	no	—
466	C₂²	—	178	2	no	—
467	C₂²	—	712	8	no	—
468	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	178	1	no	—
474	C₄	—	178	2	no	—
475	C₄	—	178	1	no	—
476	C₄	—	178	4	no	—
477	C₄	—	178	1	no	—
478	C₄	—	178	2	no	—
479	C₄	#41×D₈₉	1	2	yes	—
480	C₄	#15668057	1	2	yes	—
481	C₂	—	4	2	no	—
482	C₂	—	4	4	no	—
483	C₂	—	356	2	no	—
484	C₂	—	178	2	no	—
485	C₂	—	178	4	no	—
486	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
487	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
488	C₂	C₂×#15668057	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#550×C₈₉	C₂
hypercenter	#550	D₈₉
hypocenter	C₈₉	#3519
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. #19152313	C₂	semidirect
2. #19152308	C₂	semidirect
3. #19152298	C₂	semidirect
4. #19152295	C₂	semidirect
5. #19152237	C₂	semidirect
6. #19152236	C₂	semidirect
7. #19152233	C₂	semidirect
8. #19152233	C₂	semidirect
9. #19152202	C₂	semidirect
10. #19152180	C₂	semidirect
11. #19152146	C₂	semidirect
12. #19152135	C₂	semidirect
13. #19152105	C₂	semidirect
14. #121×D₈₉	C₂	semidirect
15. #19152070	C₂	semidirect
16. C₄×D₄×D₈₉	C₂	semidirect
17. #550×C₈₉	C₂	semidirect
18. C₂×#13083573	C₂²	semidirect
21. C₂×D₄×D₈₉	C₂²	semidirect
22. C₂×D₄×D₈₉	C₂²	semidirect
23. C₂²×C₄×D₈₉	C₂²	semidirect
24. #15668012	C₂²	semidirect
25. #15668007	C₂²	semidirect
26. #15668005	C₂²	semidirect
27. #15668004	C₂²	semidirect
28. #15668003	C₂²	semidirect
29. #15668001	C₂²	semidirect
30. #15667999	C₂²	semidirect
31. #15667998	C₂²	semidirect
32. #15667997	C₂²	semidirect
33. #15667995	C₂²	semidirect
34. #15667993	C₂²	semidirect
35. #15667993	C₂²	semidirect
36. #15667990	C₂²	semidirect
37. #15667988	C₂²	semidirect
38. #15667988	C₂²	semidirect
40. #15667986	C₂²	semidirect
41. #15667985	C₂²	semidirect
42. #15667984	C₂²	semidirect
43. #15667984	C₂²	semidirect
44. #15667983	C₂²	semidirect
45. #15667983	C₂²	semidirect
46. #15667983	C₂²	semidirect
47. #15667983	C₂²	semidirect
48. #15667983	C₂²	semidirect
49. #15667983	C₂²	semidirect
50. #15667980	C₂²	semidirect
51. #15667980	C₂²	semidirect
52. #15667980	C₂²	semidirect
55. C₄×D₃₅₆	C₂²	semidirect
56. C₄×D₃₅₆	C₂²	semidirect
57. D₄×Dic₈₉	C₂²	semidirect
58. D₄×Dic₈₉	C₂²	semidirect
59. D₄×Dic₈₉	C₂²	semidirect
61. C₄×C₂²⋊D₈₉	C₂²	semidirect
62. C₄×C₂²⋊D₈₉	C₂²	semidirect
63. C₄×C₂²⋊D₈₉	C₂²	semidirect
64. #15667972	C₂²	semidirect
65. #15667972	C₂²	semidirect
66. #15667971	C₂²	semidirect
67. #15667970	C₂²	semidirect
68. #15667969	C₂²	semidirect
69. C₄⋊C₄×D₈₉	C₂²	semidirect
70. C₄⋊C₄×D₈₉	C₂²	semidirect
71. C₂×#13083551	C₂²	semidirect
72. C₂²⋊C₄×D₈₉	C₂²	semidirect
73. C₂²⋊C₄×D₈₉	C₂²	semidirect
74. C₄²×D₈₉	C₂²	semidirect
75. C₂×#41×C₈₉	C₂²	semidirect
76. #127×C₈₉	C₂²	semidirect
77. #127×C₈₉	C₂²	semidirect
78. #121×C₈₉	C₂²	semidirect
79. #121×C₈₉	C₂²	semidirect
80. C₄×Q₈×C₈₉	C₂²	semidirect
81. C₄×D₄×C₈₉	C₂²	semidirect
82. C₄×D₄×C₈₉	C₂²	semidirect
196. D₃₅₆	#41	semidirect
245. C₈₉	#3519	semidirect
250. #550	D₈₉	semidirect
264. C₂×#41	C₂×D₈₉	semidirect
271. #127	C₂×D₈₉	semidirect
272. #127	C₂×D₈₉	semidirect
298. #121	C₂×D₈₉	semidirect
299. #121	C₂×D₈₉	semidirect
303. C₄×Q₈	C₂×D₈₉	semidirect
317. C₄×D₄	C₂×D₈₉	semidirect
318. C₄×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152313	2
#19152308	2
#19152298	2
#19152295	2
#19152237	2
#19152236	2
#19152233	2
#19152202	2
#19152180	2
#19152146	2
#19152135	2
#19152105	2
#121×D₈₉	2
#19152070	2
C₄×D₄×D₈₉	2
#550×C₈₉	2
#3519	89