Subgroups — #26034611

Order 11392.

1150 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152336	C₂	1	2	yes	maximal, complemented
2	#19152335	C₂	1	2	yes	maximal, complemented
3	#19152320	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152297	C₂	1	2	yes	maximal, complemented
5	#19152268	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152266	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152247	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152244	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152237	C₂	1	2	yes	maximal, complemented
10	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152232	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152220	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152215	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152181	C₂	1	2	yes	maximal, complemented
15	#19152180	C₂	1	2	yes	maximal, complemented
16	#19152175	C₂	1	2	yes	maximal, complemented
17	#19152162	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152161	C₂	1	2	yes	maximal, complemented
19	#19152161	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152144	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152143	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152128	C₂	1	1	yes	maximal, characteristic, complemented
23	#550×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083573	C₂²	1	2	yes	complemented
26	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13083573	C₂²	1	2	yes	complemented
28	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₈₉	C₂²	1	2	yes	—
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668010	C₂²	1	1	yes	characteristic, complemented
33	#15668008	C₂²	1	1	yes	characteristic
34	#15668008	C₂²	1	1	yes	characteristic
35	#15668008	C₂²	1	2	yes	complemented
36	#15668008	C₂²	1	1	yes	characteristic, complemented
37	#15668007	C₂²	1	1	yes	characteristic, complemented
38	#15668007	C₂²	1	2	yes	complemented
39	#15668006	C₂²	1	2	yes	complemented
40	#15668006	C₂²	1	2	yes	complemented
41	#15668005	C₂²	1	1	yes	characteristic, complemented
42	#15668005	C₂²	1	2	yes	complemented
43	#15668002	C₂²	1	1	yes	characteristic, complemented
44	#15668001	C₂²	1	1	yes	characteristic
45	#15668001	C₂²	1	1	yes	characteristic, complemented
46	#15668000	C₂²	1	1	yes	characteristic
47	#15668000	C₂²	1	2	yes	complemented
48	#15667999	C₂²	1	1	yes	characteristic, complemented
49	#15667999	C₂²	1	2	yes	complemented
50	#15667998	C₂²	1	1	yes	characteristic
51	#15667998	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667997	C₂²	1	2	yes	complemented
54	#15667996	C₂²	1	1	yes	characteristic, complemented
55	#15667995	C₂²	1	2	yes	complemented
56	#15667995	C₂²	1	2	yes	complemented
57	#15667993	C₂²	1	1	yes	characteristic, complemented
58	#15667993	C₂²	1	2	yes	complemented
59	#15667993	C₂²	1	2	yes	complemented
60	#15667991	C₂²	1	1	yes	characteristic, complemented
61	#15667990	C₂²	1	2	yes	complemented
62	#15667990	C₂²	1	2	yes	complemented
63	#15667989	C₂²	1	1	yes	characteristic, complemented
64	#15667989	C₂²	1	2	yes	complemented
65	#15667988	C₂²	1	1	yes	characteristic, complemented
66	#15667987	C₂²	1	1	yes	characteristic
67	#15667986	C₂²	1	1	yes	characteristic
68	#15667986	C₂²	1	2	yes	complemented
69	#15667986	C₂²	1	2	yes	complemented
70	#15667985	C₂²	1	2	yes	—
71	#15667985	C₂²	1	2	yes	complemented
72	#15667985	C₂²	1	2	yes	complemented
73	#15667984	C₂²	1	1	yes	characteristic
74	#15667984	C₂²	1	2	yes	—
75	#15667984	C₂²	1	2	yes	complemented
76	#15667984	C₂²	1	2	yes	complemented
77	#15667984	C₂²	1	2	yes	complemented
78	#15667984	C₂²	1	2	yes	complemented
79	#15667984	C₂²	1	2	yes	complemented
80	#15667984	C₂²	1	2	yes	complemented
81	#15667984	C₂²	1	2	yes	complemented
82	#15667984	C₂²	1	2	yes	complemented
83	#15667984	C₂²	1	2	yes	complemented
84	#15667983	C₂²	1	2	yes	complemented
85	#15667982	C₂²	1	2	yes	—
86	#15667980	C₂²	1	2	yes	—
87	#15667980	C₂²	1	2	yes	complemented
88	#15667980	C₂²	1	2	yes	complemented
89	#15667980	C₂²	1	2	yes	complemented
90	#15667980	C₂²	1	2	yes	complemented
91	#15667980	C₂²	1	2	yes	complemented
92	#15667980	C₂²	1	2	yes	complemented
93	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
94	#15667977	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
96	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
97	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
98	#15667974	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
100	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
103	#15667972	C₂²	1	2	yes	complemented
104	#15667972	C₂²	1	2	yes	complemented
105	#15667971	C₂²	1	1	yes	characteristic, complemented
106	#15667969	C₂²	1	1	yes	characteristic, complemented
107	#15667969	C₂²	1	2	yes	complemented
108	C₂×#13083553	C₂²	1	2	yes	complemented
109	C₂×#13083551	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#127×C₈₉	C₂²	1	2	yes	complemented
116	#121×C₈₉	C₂²	1	1	yes	characteristic
117	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₈₉	C₂²	1	2	yes	complemented
119	#121×C₈₉	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	C₂³×D₈₉	C₂³	1	2	yes	—
125	#13083574	—	4	2	no	—
126	#13083573	—	4	2	no	—
127	#13083573	—	4	4	no	—
128	#13083573	—	4	4	no	—
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₇₈	C₂³	1	2	yes	—
132	C₂×D₃₅₆	—	4	2	no	—
133	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
134	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
135	C₂×D₃₅₆	C₂³	1	2	yes	—
136	C₂×D₃₅₆	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
149	D₄×D₈₉	—	4	2	no	—
150	D₄×D₈₉	—	4	4	no	—
151	C₂²×Dic₈₉	C₂³	1	2	yes	—
152	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
153	C₂²×Dic₈₉	C₂³	1	2	yes	—
154	C₂²×Dic₈₉	C₂³	1	2	yes	—
155	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₈₉	C₂³	1	2	yes	—
157	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂³	1	2	yes	—
159	C₂×C₄×D₈₉	C₂³	1	2	yes	—
160	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
162	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
164	#13083553	C₂³	1	1	yes	characteristic
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	2	yes	—
173	#13083553	C₂³	1	1	yes	characteristic
174	#13083553	C₂³	1	2	yes	—
175	#13083553	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	1	yes	characteristic
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	1	yes	characteristic
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	1	yes	characteristic
195	#13083551	C₂³	1	2	yes	—
196	#13083551	C₂³	1	2	yes	—
197	#13083551	C₂³	1	2	yes	—
198	#13083551	C₂³	1	2	yes	—
199	#13083551	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	2	yes	—
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
206	#41×C₈₉	—	4	2	no	—
207	#41×C₈₉	—	4	2	no	—
208	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₉	C₂³	1	2	yes	—
212	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂×D₄×C₈₉	C₂³	1	2	yes	—
214	C₂×D₄×C₈₉	C₂³	1	2	yes	—
215	C₂×D₄×C₈₉	C₂³	1	2	yes	—
216	C₂×D₄×C₈₉	C₂³	1	2	yes	—
217	C₂×D₄×C₈₉	C₂³	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
222	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
224	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
229	C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₄²×C₈₉	C₂³	1	2	yes	—
231	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₈₉	C₂⁴	1	2	yes	—
233	C₂³×C₈₉	C₂⁴	1	2	yes	—
234	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂²×D₈₉	—	4	2	no	—
236	C₂²×D₈₉	—	4	2	no	—
237	C₂²×D₈₉	—	4	2	no	—
238	C₂²×D₈₉	—	4	2	no	—
239	C₂²×D₈₉	—	4	2	no	—
240	C₂²×D₈₉	—	4	2	no	—
241	C₂²×D₈₉	C₂⁴	1	2	yes	—
242	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₈₉	C₂⁴	1	2	yes	—
244	Q₈×C₈₉	—	2	2	no	—
245	D₄×C₈₉	—	2	2	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	4	1	no	—
248	D₄×C₈₉	—	4	2	no	—
249	D₄×C₈₉	—	4	2	no	—
250	D₄×C₈₉	—	4	2	no	—
251	D₄×C₈₉	—	4	2	no	—
252	D₄×C₈₉	—	4	2	no	—
253	D₄×C₈₉	—	4	2	no	—
254	C₂×C₄×C₈₉	—	2	2	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	4	2	no	—
257	C₂×C₄×C₈₉	—	4	2	no	—
258	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
261	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
264	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
265	C₂²⋊D₈₉	—	2	2	no	—
266	C₂²⋊D₈₉	—	2	4	no	—
267	C₂²⋊D₈₉	—	4	2	no	—
268	C₂²⋊D₈₉	—	4	2	no	—
269	C₂²⋊D₈₉	—	4	2	no	—
270	C₂²⋊D₈₉	—	4	2	no	—
271	C₂²⋊D₈₉	—	4	1	no	—
272	C₂²⋊D₈₉	—	4	2	no	—
273	C₂²⋊D₈₉	—	4	2	no	—
274	C₂²⋊D₈₉	—	4	2	no	—
275	C₂²⋊D₈₉	—	4	2	no	—
276	C₂²⋊D₈₉	—	4	2	no	—
277	C₂×Dic₈₉	—	2	2	no	—
278	C₂×Dic₈₉	—	2	4	no	—
279	C₂×Dic₈₉	—	4	1	no	—
280	C₂×Dic₈₉	—	4	2	no	—
281	C₂×Dic₈₉	—	4	2	no	—
282	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
283	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
284	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
285	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
286	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
287	C₂×Dic₈₉	C₂⁴	1	2	yes	—
288	C₂×Dic₈₉	C₂⁴	1	2	yes	—
289	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
290	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
291	D₃₅₆	—	2	2	no	—
292	D₃₅₆	—	2	2	no	—
293	D₃₅₆	—	4	2	no	—
294	D₃₅₆	—	4	2	no	—
295	C₄×D₈₉	—	2	2	no	—
296	C₄×D₈₉	—	2	4	no	—
297	C₄×D₈₉	—	4	2	no	—
298	C₄×D₈₉	—	4	2	no	—
299	Dic₁₇₈	—	2	2	no	—
300	Dic₁₇₈	—	2	2	no	—
301	Dic₁₇₈	—	4	2	no	—
302	C₂²×C₈₉	—	2	2	no	—
303	C₂²×C₈₉	—	2	1	no	—
304	C₂²×C₈₉	—	2	2	no	—
305	C₂²×C₈₉	—	2	2	no	—
306	C₂²×C₈₉	—	2	1	no	—
307	C₂²×C₈₉	—	2	1	no	—
308	C₂²×C₈₉	—	2	2	no	—
309	C₂²×C₈₉	—	2	1	no	—
310	C₂²×C₈₉	—	2	1	no	—
311	C₂²×C₈₉	—	2	2	no	—
312	C₂²×C₈₉	—	2	2	no	—
313	C₂²×C₈₉	—	2	1	no	—
314	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
315	C₂×D₈₉	—	2	2	no	—
316	C₂×D₈₉	—	2	1	no	—
317	C₂×D₈₉	—	2	2	no	—
318	C₂×D₈₉	—	2	2	no	—
319	C₂×D₈₉	—	2	2	no	—
320	C₂×D₈₉	—	2	1	no	—
321	C₂×D₈₉	—	2	2	no	—
322	C₂×D₈₉	—	2	2	no	—
323	C₂×D₈₉	—	2	1	no	—
324	C₂×D₈₉	—	8	4	no	—
325	C₂×D₈₉	—	8	4	no	—
326	C₄×C₈₉	—	2	1	no	—
327	C₄×C₈₉	—	2	2	no	—
328	C₄×C₈₉	—	2	1	no	—
329	C₄×C₈₉	—	2	1	no	—
330	C₄×C₈₉	—	2	2	no	—
331	C₄×C₈₉	—	2	1	no	—
332	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
333	Dic₈₉	—	2	2	no	—
334	Dic₈₉	—	2	1	no	—
335	Dic₈₉	—	2	1	no	—
336	Dic₈₉	—	2	2	no	—
337	Dic₈₉	—	2	1	no	—
338	Dic₈₉	—	2	1	no	—
339	Dic₈₉	—	2	1	no	—
340	Dic₈₉	—	2	1	no	—
341	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
342	C₂×C₈₉	—	4	1	no	—
343	C₂×C₈₉	—	4	2	no	—
344	C₂×C₈₉	—	4	2	no	—
345	C₂×C₈₉	—	4	1	no	—
346	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
347	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
348	C₂×C₈₉	#585	1	1	yes	characteristic
349	D₈₉	—	4	2	no	—
350	D₈₉	—	4	2	no	—
351	D₈₉	—	4	1	no	—
352	#3546	—	89	1	no	maximal, Sylow
353	C₈₉	#3546	1	1	yes	characteristic, complemented, Sylow
354	#560	—	89	2	no	—
355	#560	—	89	2	no	—
356	#556	—	89	1	no	—
357	#553	—	89	2	no	—
358	#550	—	89	1	no	—
359	#550	—	89	1	no	—
360	#550	D₈₉	1	1	yes	characteristic, complemented
361	#547	—	89	1	no	—
362	#546	—	89	1	no	—
363	#546	—	89	2	no	—
364	#546	—	89	1	no	—
365	D₄²	—	89	1	no	—
366	#542	—	89	1	no	—
367	#542	—	89	1	no	—
368	#538	—	89	2	no	—
369	#538	—	89	2	no	—
370	#537	—	89	2	no	—
371	#535	—	89	1	no	—
372	#535	—	89	1	no	—
373	#535	—	89	2	no	—
374	#532	—	89	1	no	—
375	#532	—	89	1	no	—
376	#529	—	89	1	no	—
377	C₂×#41	—	89	2	no	—
378	C₂×#41	—	89	1	no	—
379	C₂×#41	—	89	2	no	—
380	C₂×#41	—	89	1	no	—
381	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
382	C₂×#41	C₂×D₈₉	1	1	yes	characteristic, complemented
383	C₂²×D₄	—	89	1	no	—
384	C₂²×D₄	—	89	2	no	—
385	C₂²×D₄	—	89	1	no	—
386	C₄⋊Q₈	—	89	1	no	—
387	C₄⋊Q₈	—	89	1	no	—
388	#127	—	89	1	no	—
389	#127	—	89	1	no	—
390	#127	—	89	1	no	—
391	#127	—	89	2	no	—
392	#127	C₂×D₈₉	1	1	yes	characteristic, complemented
393	#127	C₂×D₈₉	1	2	yes	complemented
394	#126	—	89	1	no	—
395	#126	—	89	2	no	—
396	#126	—	89	1	no	—
397	#126	—	89	2	no	—
398	#126	—	89	2	no	—
399	#126	—	89	2	no	—
400	#125	—	89	1	no	—
401	#124	—	89	1	no	—
402	#124	—	89	1	no	—
403	#124	—	89	1	no	—
404	#124	—	89	2	no	—
405	#124	—	89	1	no	—
406	#124	—	89	2	no	—
407	#124	—	89	2	no	—
408	#124	—	89	1	no	—
409	#123	—	89	1	no	—
410	#123	—	89	2	no	—
411	#123	—	89	2	no	—
412	#123	—	89	2	no	—
413	#123	—	89	2	no	—
414	#123	—	89	2	no	—
415	#123	—	89	2	no	—
416	#123	—	89	1	no	—
417	C₂²⋊Q₈	—	89	1	no	—
418	C₂²⋊Q₈	—	89	1	no	—
419	C₂²⋊Q₈	—	89	2	no	—
420	C₂²⋊Q₈	—	89	2	no	—
421	C₂²⋊Q₈	—	89	1	no	—
422	C₂²⋊Q₈	—	89	2	no	—
423	#121	—	89	2	no	—
424	#121	—	89	1	no	—
425	#121	—	89	2	no	—
426	#121	—	89	2	no	—
427	#121	—	89	2	no	—
428	#121	—	89	2	no	—
429	#121	—	89	2	no	—
430	#121	—	89	2	no	—
431	#121	—	89	2	no	—
432	#121	—	89	2	no	—
433	#121	—	89	2	no	—
434	#121	—	89	2	no	—
435	#121	—	89	1	no	—
436	#121	—	89	2	no	—
437	#121	—	89	2	no	—
438	#121	—	89	1	no	—
439	#121	—	89	2	no	—
440	#121	—	89	2	no	—
441	#121	—	89	2	no	—
442	#121	C₂×D₈₉	1	1	yes	characteristic
443	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
444	#121	C₂×D₈₉	1	2	yes	complemented
445	#121	C₂×D₈₉	1	2	yes	complemented
446	#120	—	89	2	no	—
447	#120	—	89	2	no	—
448	#120	—	89	2	no	—
449	#120	—	89	2	no	—
450	#120	—	89	2	no	—
451	#120	—	89	2	no	—
452	#120	—	89	2	no	—
453	#120	—	89	2	no	—
454	C₄×Q₈	—	89	1	no	—
455	C₄×Q₈	—	89	1	no	—
456	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
457	C₄×D₄	—	89	1	no	—
458	C₄×D₄	—	89	1	no	—
459	C₄×D₄	—	89	1	no	—
460	C₄×D₄	—	89	1	no	—
461	C₄×D₄	—	89	2	no	—
462	C₄×D₄	—	89	2	no	—
463	C₄×D₄	—	89	1	no	—
464	C₄×D₄	—	89	2	no	—
465	C₄×D₄	—	89	2	no	—
466	C₄×D₄	—	89	1	no	—
467	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
468	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
469	#117	—	89	1	no	—
470	#117	—	89	1	no	—
471	#117	—	89	2	no	—
472	C₂×C₄⋊C₄	—	89	2	no	—
473	C₂×C₂²⋊C₄	—	89	2	no	—
474	C₂×C₂²⋊C₄	—	89	2	no	—
475	C₂×C₄²	—	89	1	no	—
476	C₂⁴	—	89	2	no	—
477	C₂⁴	—	89	2	no	—
478	#41	—	4	2	no	—
479	#41	—	4	2	no	—
480	#41	—	356	2	no	—
481	#41	—	356	2	no	—
482	#41	—	356	4	no	—
483	#41	—	356	4	no	—
484	C₂×Q₈	—	89	2	no	—
485	C₂×Q₈	—	89	1	no	—
486	C₂×Q₈	—	89	1	no	—
487	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
488	C₂×D₄	—	89	2	no	—
489	C₂×D₄	—	89	2	no	—
490	C₂×D₄	—	89	1	no	—
491	C₂×D₄	—	89	2	no	—
492	C₂×D₄	—	89	2	no	—
493	C₂×D₄	—	89	2	no	—
494	C₂×D₄	—	89	2	no	—
495	C₂×D₄	—	89	2	no	—
496	C₂×D₄	—	89	2	no	—
497	C₂×D₄	—	89	2	no	—
498	C₂×D₄	—	89	1	no	—
499	C₂×D₄	—	89	2	no	—
500	C₂×D₄	—	89	2	no	—
501	C₂×D₄	—	89	2	no	—
502	C₂×D₄	—	89	1	no	—
503	C₂×D₄	—	89	1	no	—
504	C₂×D₄	—	356	2	no	—
505	C₂×D₄	—	356	2	no	—
506	C₂×D₄	—	356	4	no	—
507	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
508	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
509	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
510	C₂×D₄	C₂²×D₈₉	1	2	yes	—
511	C₂×D₄	C₂²×D₈₉	1	2	yes	—
512	C₂×D₄	C₂²×D₈₉	1	2	yes	—
513	C₂×D₄	C₂²×D₈₉	1	2	yes	—
514	C₂×D₄	C₂²×D₈₉	1	2	yes	—
515	C₂×D₄	C₂²×D₈₉	1	2	yes	—
516	C₂²×C₄	—	89	1	no	—
517	C₂²×C₄	—	89	2	no	—
518	C₂²×C₄	—	89	2	no	—
519	C₂²×C₄	—	89	1	no	—
520	C₂²×C₄	—	89	2	no	—
521	C₂²×C₄	—	89	2	no	—
522	C₂²×C₄	—	89	2	no	—
523	C₂²×C₄	—	89	2	no	—
524	C₂²×C₄	—	89	1	no	—
525	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
527	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
528	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
529	C₄⋊C₄	—	89	1	no	—
530	C₄⋊C₄	—	89	2	no	—
531	C₄⋊C₄	—	89	2	no	—
532	C₄⋊C₄	—	89	2	no	—
533	C₄⋊C₄	—	89	1	no	—
534	C₄⋊C₄	—	89	1	no	—
535	C₄⋊C₄	—	89	1	no	—
536	C₄⋊C₄	—	89	1	no	—
537	C₄⋊C₄	—	89	1	no	—
538	C₄⋊C₄	—	89	1	no	—
539	C₄⋊C₄	—	89	1	no	—
540	C₄⋊C₄	—	89	2	no	—
541	C₄⋊C₄	—	89	2	no	—
542	C₄⋊C₄	—	89	2	no	—
543	C₄⋊C₄	—	89	1	no	—
544	C₄⋊C₄	—	89	1	no	—
545	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
547	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
548	C₂²⋊C₄	—	89	2	no	—
549	C₂²⋊C₄	—	89	1	no	—
550	C₂²⋊C₄	—	89	1	no	—
551	C₂²⋊C₄	—	89	1	no	—
552	C₂²⋊C₄	—	89	2	no	—
553	C₂²⋊C₄	—	89	2	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	—	89	1	no	—
556	C₂²⋊C₄	—	89	2	no	—
557	C₂²⋊C₄	—	89	1	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	—	89	2	no	—
560	C₂²⋊C₄	—	89	2	no	—
561	C₂²⋊C₄	—	89	2	no	—
562	C₂²⋊C₄	—	89	2	no	—
563	C₂²⋊C₄	—	89	2	no	—
564	C₂²⋊C₄	—	89	1	no	—
565	C₂²⋊C₄	—	89	1	no	—
566	C₂²⋊C₄	—	89	2	no	—
567	C₂²⋊C₄	—	89	1	no	—
568	C₂²⋊C₄	—	89	2	no	—
569	C₂²⋊C₄	—	89	2	no	—
570	C₂²⋊C₄	—	89	2	no	—
571	C₂²⋊C₄	—	89	2	no	—
572	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
573	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
576	C₄²	—	89	1	no	—
577	C₄²	—	89	1	no	—
578	C₄²	—	89	1	no	—
579	C₄²	—	89	1	no	—
580	C₄²	—	89	1	no	—
581	C₄²	—	89	2	no	—
582	C₄²	C₂²×D₈₉	1	1	yes	characteristic
583	C₄²	C₂²×D₈₉	1	2	yes	—
584	C₂³	—	89	2	no	—
585	C₂³	—	89	1	no	—
586	C₂³	—	89	2	no	—
587	C₂³	—	356	2	no	—
588	C₂³	—	356	2	no	—
589	C₂³	—	356	2	no	—
590	C₂³	—	356	2	no	—
591	C₂³	—	356	2	no	—
592	C₂³	—	356	2	no	—
593	C₂³	C₂³×D₈₉	1	1	yes	characteristic
594	C₂³	C₂³×D₈₉	1	2	yes	—
595	C₂³	C₂³×D₈₉	1	1	yes	characteristic
596	C₂³	C₂³×D₈₉	1	2	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	356	2	no	—
599	Q₈	—	178	2	no	—
600	Q₈	—	178	2	no	—
601	D₄	—	2	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	2	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	2	no	—
610	D₄	—	356	2	no	—
611	D₄	—	356	2	no	—
612	D₄	—	356	2	no	—
613	D₄	—	356	2	no	—
614	D₄	—	356	1	no	—
615	D₄	—	356	2	no	—
616	D₄	—	356	2	no	—
617	D₄	—	356	2	no	—
618	D₄	—	356	2	no	—
619	D₄	—	356	2	no	—
620	D₄	—	356	2	no	—
621	D₄	—	356	2	no	—
622	D₄	—	178	2	no	—
623	D₄	—	178	4	no	—
624	D₄	—	178	2	no	—
625	D₄	—	178	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	4	2	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	89	1	no	—
631	C₂×C₄	—	89	1	no	—
632	C₂×C₄	—	89	1	no	—
633	C₂×C₄	—	89	1	no	—
634	C₂×C₄	—	89	1	no	—
635	C₂×C₄	—	89	1	no	—
636	C₂×C₄	—	89	2	no	—
637	C₂×C₄	—	89	2	no	—
638	C₂×C₄	—	89	1	no	—
639	C₂×C₄	—	356	2	no	—
640	C₂×C₄	—	356	2	no	—
641	C₂×C₄	—	356	1	no	—
642	C₂×C₄	—	356	2	no	—
643	C₂×C₄	—	356	2	no	—
644	C₂×C₄	—	178	4	no	—
645	C₂×C₄	—	178	4	no	—
646	C₂×C₄	—	178	2	no	—
647	C₂×C₄	—	178	2	no	—
648	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₈₉	1	2	yes	—
650	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₈₉	1	2	yes	—
652	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
653	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
654	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
655	C₂²	—	2	2	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	178	2	no	—
668	C₂²	—	178	2	no	—
669	C₂²	—	178	1	no	—
670	C₂²	—	178	2	no	—
671	C₂²	—	178	1	no	—
672	C₂²	—	178	2	no	—
673	C₂²	—	178	2	no	—
674	C₂²	—	178	2	no	—
675	C₂²	—	178	1	no	—
676	C₂²	—	712	4	no	—
677	C₂²	—	712	4	no	—
678	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	89	2	no	—
686	C₄	—	178	2	no	—
687	C₄	—	178	1	no	—
688	C₄	—	178	1	no	—
689	C₄	—	178	1	no	—
690	C₄	—	178	2	no	—
691	C₄	—	178	1	no	—
692	C₄	—	178	1	no	—
693	C₄	—	178	1	no	—
694	C₄	#15668057	1	2	yes	—
695	C₂	—	4	1	no	—
696	C₂	—	4	2	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	356	2	no	—
700	C₂	—	356	2	no	—
701	C₂	—	356	1	no	—
702	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
703	C₂	C₂×#15668057	1	1	yes	characteristic
704	C₂	#19152434	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	#3546
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. #19152336	C₂	semidirect
2. #19152335	C₂	semidirect
3. #19152320	C₂	semidirect
4. #19152297	C₂	semidirect
5. #19152268	C₂	semidirect
6. #19152266	C₂	semidirect
7. #19152247	C₂	semidirect
8. #19152244	C₂	semidirect
9. #19152237	C₂	semidirect
10. #19152236	C₂	semidirect
11. #19152232	C₂	semidirect
12. #19152220	C₂	semidirect
13. #19152215	C₂	semidirect
14. #19152181	C₂	semidirect
15. #19152180	C₂	semidirect
16. #19152175	C₂	semidirect
17. #19152162	C₂	semidirect
18. #19152161	C₂	semidirect
19. #19152161	C₂	semidirect
20. #19152144	C₂	semidirect
21. #19152143	C₂	semidirect
22. #19152128	C₂	semidirect
23. #550×C₈₉	C₂	semidirect
24. C₂×#13083574	C₂²	semidirect
25. C₂×#13083573	C₂²	semidirect
26. C₂×#13083573	C₂²	semidirect
27. C₂×#13083573	C₂²	semidirect
31. #15668011	C₂²	semidirect
32. #15668010	C₂²	semidirect
35. #15668008	C₂²	semidirect
36. #15668008	C₂²	semidirect
37. #15668007	C₂²	semidirect
38. #15668007	C₂²	semidirect
39. #15668006	C₂²	semidirect
40. #15668006	C₂²	semidirect
41. #15668005	C₂²	semidirect
42. #15668005	C₂²	semidirect
43. #15668002	C₂²	semidirect
45. #15668001	C₂²	semidirect
47. #15668000	C₂²	semidirect
48. #15667999	C₂²	semidirect
49. #15667999	C₂²	semidirect
51. #15667998	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667997	C₂²	semidirect
54. #15667996	C₂²	semidirect
55. #15667995	C₂²	semidirect
56. #15667995	C₂²	semidirect
57. #15667993	C₂²	semidirect
58. #15667993	C₂²	semidirect
59. #15667993	C₂²	semidirect
60. #15667991	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667990	C₂²	semidirect
63. #15667989	C₂²	semidirect
64. #15667989	C₂²	semidirect
65. #15667988	C₂²	semidirect
68. #15667986	C₂²	semidirect
69. #15667986	C₂²	semidirect
71. #15667985	C₂²	semidirect
72. #15667985	C₂²	semidirect
75. #15667984	C₂²	semidirect
76. #15667984	C₂²	semidirect
77. #15667984	C₂²	semidirect
78. #15667984	C₂²	semidirect
79. #15667984	C₂²	semidirect
80. #15667984	C₂²	semidirect
81. #15667984	C₂²	semidirect
82. #15667984	C₂²	semidirect
83. #15667984	C₂²	semidirect
84. #15667983	C₂²	semidirect
87. #15667980	C₂²	semidirect
88. #15667980	C₂²	semidirect
89. #15667980	C₂²	semidirect
90. #15667980	C₂²	semidirect
91. #15667980	C₂²	semidirect
92. #15667980	C₂²	semidirect
93. C₄×Dic₁₇₈	C₂²	semidirect
94. #15667977	C₂²	semidirect
95. C₄×D₃₅₆	C₂²	semidirect
96. D₄×Dic₈₉	C₂²	semidirect
97. D₄×Dic₈₉	C₂²	semidirect
100. C₄×C₂²⋊D₈₉	C₂²	semidirect
101. C₄×C₂²⋊D₈₉	C₂²	semidirect
102. C₄×C₂²⋊D₈₉	C₂²	semidirect
103. #15667972	C₂²	semidirect
104. #15667972	C₂²	semidirect
105. #15667971	C₂²	semidirect
106. #15667969	C₂²	semidirect
107. #15667969	C₂²	semidirect
108. C₂×#13083553	C₂²	semidirect
109. C₂×#13083551	C₂²	semidirect
110. C₂²⋊C₄×D₈₉	C₂²	semidirect
111. C₂×C₄×Dic₈₉	C₂²	semidirect
112. C₂×#41×C₈₉	C₂²	semidirect
113. C₂×#41×C₈₉	C₂²	semidirect
114. #127×C₈₉	C₂²	semidirect
115. #127×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #121×C₈₉	C₂²	semidirect
120. C₄×Q₈×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
353. C₈₉	#3546	semidirect
360. #550	D₈₉	semidirect
381. C₂×#41	C₂×D₈₉	semidirect
382. C₂×#41	C₂×D₈₉	semidirect
392. #127	C₂×D₈₉	semidirect
393. #127	C₂×D₈₉	semidirect
443. #121	C₂×D₈₉	semidirect
444. #121	C₂×D₈₉	semidirect
445. #121	C₂×D₈₉	semidirect
456. C₄×Q₈	C₂×D₈₉	semidirect
467. C₄×D₄	C₂×D₈₉	semidirect
468. 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
#19152336	2
#19152335	2
#19152320	2
#19152297	2
#19152268	2
#19152266	2
#19152247	2
#19152244	2
#19152237	2
#19152236	2
#19152232	2
#19152220	2
#19152215	2
#19152181	2
#19152180	2
#19152175	2
#19152162	2
#19152161	2
#19152144	2
#19152143	2
#19152128	2
#550×C₈₉	2
#3546	89