Subgroups — #26033667

Order 11392.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152228	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152219	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152216	C₂	1	2	yes	maximal, complemented
4	#19152213	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152199	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152198	C₂	1	2	yes	maximal, complemented
7	#19152184	C₂	1	2	yes	maximal, complemented
8	#19152180	C₂	1	2	yes	maximal, complemented
9	#19152177	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152161	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152146	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152143	C₂	1	2	yes	maximal, complemented
14	#19152143	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152133	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152129	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152125	C₂	1	2	yes	maximal, complemented
18	#19152108	C₂	1	2	yes	maximal, complemented
19	#19152106	C₂	1	2	yes	maximal, complemented
20	#19152066	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#540×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic
25	C₂×#13083573	C₂²	1	1	yes	characteristic
26	C₂×#13083573	C₂²	1	2	yes	complemented
27	C₂×#13083573	C₂²	1	2	yes	complemented
28	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₈₉	C₂²	1	2	yes	—
30	#15668012	C₂²	1	1	yes	characteristic, complemented
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668011	C₂²	1	2	yes	complemented
33	#15668008	C₂²	1	1	yes	characteristic
34	#15668008	C₂²	1	2	yes	—
35	#15668007	C₂²	1	2	yes	complemented
36	#15668007	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668005	C₂²	1	2	yes	complemented
39	#15668003	C₂²	1	1	yes	characteristic, complemented
40	#15668002	C₂²	1	2	yes	complemented
41	#15668000	C₂²	1	1	yes	characteristic
42	#15667999	C₂²	1	1	yes	characteristic
43	#15667999	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	—
45	#15667998	C₂²	1	2	yes	complemented
46	#15667998	C₂²	1	2	yes	complemented
47	#15667998	C₂²	1	2	yes	complemented
48	#15667997	C₂²	1	2	yes	complemented
49	#15667995	C₂²	1	2	yes	complemented
50	#15667995	C₂²	1	2	yes	complemented
51	#15667994	C₂²	1	2	yes	complemented
52	#15667994	C₂²	1	2	yes	complemented
53	#15667993	C₂²	1	2	yes	complemented
54	#15667992	C₂²	1	2	yes	—
55	#15667992	C₂²	1	1	yes	characteristic, complemented
56	#15667991	C₂²	1	1	yes	characteristic, complemented
57	#15667991	C₂²	1	2	yes	complemented
58	#15667990	C₂²	1	2	yes	—
59	#15667990	C₂²	1	2	yes	complemented
60	#15667989	C₂²	1	2	yes	complemented
61	#15667987	C₂²	1	1	yes	characteristic
62	#15667986	C₂²	1	1	yes	characteristic
63	#15667986	C₂²	1	2	yes	complemented
64	#15667985	C₂²	1	2	yes	—
65	#15667985	C₂²	1	2	yes	complemented
66	#15667984	C₂²	1	2	yes	—
67	#15667984	C₂²	1	2	yes	—
68	#15667984	C₂²	1	2	yes	complemented
69	#15667984	C₂²	1	2	yes	complemented
70	#15667983	C₂²	1	1	yes	characteristic
71	#15667983	C₂²	1	2	yes	—
72	#15667983	C₂²	1	1	yes	characteristic, complemented
73	#15667983	C₂²	1	2	yes	complemented
74	#15667982	C₂²	1	2	yes	—
75	#15667980	C₂²	1	2	yes	—
76	#15667980	C₂²	1	2	yes	—
77	#15667980	C₂²	1	2	yes	—
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	#15667977	C₂²	1	1	yes	characteristic, complemented
80	#15667977	C₂²	1	1	yes	characteristic, complemented
81	#15667977	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
83	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
84	D₄×Dic₈₉	C₂²	1	2	yes	complemented
85	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
86	D₄×Dic₈₉	C₂²	1	2	yes	complemented
87	#15667974	C₂²	1	1	yes	characteristic
88	#15667974	C₂²	1	1	yes	characteristic
89	#15667974	C₂²	1	1	yes	characteristic
90	#15667974	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
93	#15667972	C₂²	1	2	yes	—
94	#15667972	C₂²	1	1	yes	characteristic
95	#15667972	C₂²	1	2	yes	—
96	#15667972	C₂²	1	1	yes	characteristic
97	#15667972	C₂²	1	1	yes	characteristic, complemented
98	#15667972	C₂²	1	2	yes	complemented
99	#15667972	C₂²	1	1	yes	characteristic, complemented
100	#15667970	C₂²	1	1	yes	characteristic
101	#15667970	C₂²	1	2	yes	complemented
102	#15667969	C₂²	1	1	yes	characteristic
103	#15667969	C₂²	1	1	yes	characteristic, complemented
104	#15667968	C₂²	1	2	yes	complemented
105	#15667968	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
108	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
110	C₄²×D₈₉	C₂²	1	1	yes	characteristic
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
112	#127×C₈₉	C₂²	1	1	yes	characteristic
113	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#123×C₈₉	C₂²	1	2	yes	complemented
115	#123×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×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	#13083574	—	2	4	no	—
125	#13083573	—	2	4	no	—
126	#13083573	—	4	4	no	—
127	#13083573	—	4	4	no	—
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₇₈	C₂³	1	2	yes	—
131	C₂×Dic₁₇₈	C₂³	1	2	yes	—
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
134	C₂×D₃₅₆	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
143	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
144	D₄×D₈₉	—	2	4	no	—
145	C₂²×Dic₈₉	C₂³	1	2	yes	—
146	C₂²×Dic₈₉	C₂³	1	2	yes	—
147	C₂²×Dic₈₉	C₂³	1	2	yes	—
148	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
149	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	—	4	4	no	—
151	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₈₉	C₂³	1	2	yes	—
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₈₉	C₂³	1	2	yes	—
158	C₂×C₄×D₈₉	C₂³	1	2	yes	—
159	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
161	C₄⋊Dic₈₉	C₂³	1	2	yes	—
162	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₈₉	C₂³	1	2	yes	—
164	C₄⋊Dic₈₉	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	2	yes	—
167	#13083553	C₂³	1	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
178	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
180	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
181	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
182	#13083551	C₂³	1	1	yes	characteristic
183	#13083551	C₂³	1	1	yes	characteristic
184	#13083551	C₂³	1	1	yes	characteristic
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
199	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₉	C₂³	1	2	yes	—
203	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×D₄×C₈₉	C₂³	1	2	yes	—
208	C₂×D₄×C₈₉	C₂³	1	2	yes	—
209	C₂×D₄×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	C₂³	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂³×C₈₉	C₂⁴	1	2	yes	—
229	C₂³×C₈₉	C₂⁴	1	2	yes	—
230	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	—	2	4	no	—
232	C₂²×D₈₉	—	4	2	no	—
233	C₂²×D₈₉	—	4	2	no	—
234	C₂²×D₈₉	C₂⁴	1	2	yes	—
235	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
237	D₄×C₈₉	—	2	2	no	—
238	D₄×C₈₉	—	2	2	no	—
239	D₄×C₈₉	—	4	2	no	—
240	D₄×C₈₉	—	4	2	no	—
241	D₄×C₈₉	—	4	2	no	—
242	D₄×C₈₉	—	4	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	4	2	no	—
245	C₂×C₄×C₈₉	—	4	2	no	—
246	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
252	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₈₉	—	2	4	no	—
255	C₂²⋊D₈₉	—	2	2	no	—
256	C₂²⋊D₈₉	—	2	4	no	—
257	C₂²⋊D₈₉	—	2	2	no	—
258	C₂²⋊D₈₉	—	4	2	no	—
259	C₂²⋊D₈₉	—	4	2	no	—
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂²⋊D₈₉	—	4	2	no	—
262	C₂²⋊D₈₉	—	4	2	no	—
263	C₂×Dic₈₉	—	2	4	no	—
264	C₂×Dic₈₉	—	2	4	no	—
265	C₂×Dic₈₉	—	2	4	no	—
266	C₂×Dic₈₉	—	2	2	no	—
267	C₂×Dic₈₉	—	4	1	no	—
268	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₈₉	C₂⁴	1	2	yes	—
270	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₈₉	C₂⁴	1	2	yes	—
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₈₉	C₂⁴	1	2	yes	—
275	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
277	D₃₅₆	—	2	2	no	—
278	D₃₅₆	—	2	2	no	—
279	D₃₅₆	—	4	2	no	—
280	C₄×D₈₉	—	2	2	no	—
281	C₄×D₈₉	—	2	2	no	—
282	C₄×D₈₉	—	2	4	no	—
283	C₄×D₈₉	—	2	2	no	—
284	C₄×D₈₉	—	4	2	no	—
285	C₄×D₈₉	—	4	2	no	—
286	C₄×D₈₉	—	4	1	no	—
287	C₄×D₈₉	—	4	1	no	—
288	C₄×D₈₉	#41	1	4	yes	complemented
289	Dic₁₇₈	—	2	2	no	—
290	Dic₁₇₈	—	2	2	no	—
291	Dic₁₇₈	—	4	2	no	—
292	Dic₁₇₈	—	4	2	no	—
293	C₂²×C₈₉	—	2	2	no	—
294	C₂²×C₈₉	—	2	1	no	—
295	C₂²×C₈₉	—	2	2	no	—
296	C₂²×C₈₉	—	2	2	no	—
297	C₂²×C₈₉	—	2	1	no	—
298	C₂²×C₈₉	—	2	2	no	—
299	C₂²×C₈₉	—	2	1	no	—
300	C₂²×C₈₉	—	2	2	no	—
301	C₂²×C₈₉	—	2	2	no	—
302	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	1	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	2	no	—
307	C₂×D₈₉	—	2	2	no	—
308	C₂×D₈₉	—	2	1	no	—
309	C₂×D₈₉	—	2	1	no	—
310	C₂×D₈₉	—	2	2	no	—
311	C₂×D₈₉	—	4	8	no	—
312	C₂×D₈₉	C₂×#41	1	2	yes	—
313	C₄×C₈₉	—	2	1	no	—
314	C₄×C₈₉	—	2	1	no	—
315	C₄×C₈₉	—	2	2	no	—
316	C₄×C₈₉	—	2	1	no	—
317	C₄×C₈₉	—	2	1	no	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	2	no	—
320	C₄×C₈₉	C₂×#41	1	2	yes	—
321	Dic₈₉	—	2	1	no	—
322	Dic₈₉	—	2	2	no	—
323	Dic₈₉	—	2	1	no	—
324	Dic₈₉	—	2	2	no	—
325	Dic₈₉	—	2	2	no	—
326	Dic₈₉	—	2	1	no	—
327	Dic₈₉	—	2	1	no	—
328	Dic₈₉	C₂×#41	1	2	yes	—
329	Dic₈₉	H(5,𝔽₂)	1	2	yes	—
330	C₂×C₈₉	—	4	2	no	—
331	C₂×C₈₉	—	4	2	no	—
332	C₂×C₈₉	—	4	1	no	—
333	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
334	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₈₉	#585	1	1	yes	characteristic
336	D₈₉	—	2	2	no	—
337	D₈₉	—	4	1	no	—
338	D₈₉	—	4	2	no	—
339	#3460	—	89	1	no	maximal, Sylow
340	C₈₉	#3460	1	1	yes	characteristic, complemented, Sylow
341	#544	—	89	1	no	—
342	#542	—	89	2	no	—
343	#542	—	89	1	no	—
344	#542	—	89	1	no	—
345	#540	—	89	2	no	—
346	#540	—	89	1	no	—
347	#540	D₈₉	1	1	yes	characteristic, complemented
348	#538	—	89	2	no	—
349	#538	—	89	2	no	—
350	#537	—	89	1	no	—
351	#535	—	89	1	no	—
352	#535	—	89	1	no	—
353	#532	—	89	1	no	—
354	#532	—	89	1	no	—
355	#532	—	89	2	no	—
356	#529	—	89	1	no	—
357	#529	—	89	2	no	—
358	#529	—	89	1	no	—
359	#525	—	89	2	no	—
360	#525	—	89	2	no	—
361	C₄×#41	—	89	1	no	—
362	C₄×#41	—	89	1	no	—
363	C₂×C₄×D₄	—	89	1	no	—
364	C₂×#41	—	89	2	no	—
365	C₂×#41	—	89	2	no	—
366	C₂×#41	—	89	1	no	—
367	C₂×#41	—	89	1	no	—
368	C₂²×D₄	—	89	1	no	—
369	C₂³×C₄	—	89	2	no	—
370	C₄⋊Q₈	—	89	2	no	—
371	C₄⋊Q₈	—	89	1	no	—
372	C₄⋊Q₈	—	89	1	no	—
373	#127	—	89	1	no	—
374	#127	—	89	2	no	—
375	#127	C₂×D₈₉	1	1	yes	characteristic
376	#126	—	89	2	no	—
377	#126	—	89	2	no	—
378	#126	—	89	2	no	—
379	#126	—	89	2	no	—
380	#125	—	89	2	no	—
381	#125	—	89	1	no	—
382	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
383	#124	—	89	1	no	—
384	#124	—	89	2	no	—
385	#124	—	89	2	no	—
386	#124	—	89	2	no	—
387	#124	—	89	2	no	—
388	#124	—	89	2	no	—
389	#124	—	89	1	no	—
390	#123	—	89	2	no	—
391	#123	—	89	2	no	—
392	#123	—	89	2	no	—
393	#123	—	89	2	no	—
394	#123	—	89	2	no	—
395	#123	—	89	2	no	—
396	#123	C₂×D₈₉	1	2	yes	complemented
397	#123	C₂×D₈₉	1	2	yes	complemented
398	C₂²⋊Q₈	—	89	2	no	—
399	C₂²⋊Q₈	—	89	1	no	—
400	C₂²⋊Q₈	—	89	2	no	—
401	C₂²⋊Q₈	—	89	2	no	—
402	C₂²⋊Q₈	—	89	2	no	—
403	C₂²⋊Q₈	—	89	1	no	—
404	C₂²⋊Q₈	—	89	2	no	—
405	#121	—	89	2	no	—
406	#121	—	89	1	no	—
407	#121	—	89	1	no	—
408	#121	—	89	2	no	—
409	#121	—	89	2	no	—
410	#121	—	89	2	no	—
411	#121	—	89	2	no	—
412	#121	—	89	2	no	—
413	#121	—	89	1	no	—
414	#121	—	89	2	no	—
415	#121	—	89	1	no	—
416	#121	—	89	2	no	—
417	#121	—	89	2	no	—
418	#121	C₂×D₈₉	1	1	yes	characteristic
419	#121	C₂×D₈₉	1	2	yes	complemented
420	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
421	#121	C₂×D₈₉	1	2	yes	complemented
422	#120	—	89	2	no	—
423	#120	—	89	2	no	—
424	#120	—	89	2	no	—
425	#120	—	89	2	no	—
426	C₄×Q₈	—	89	1	no	—
427	C₄×Q₈	—	89	1	no	—
428	C₄×Q₈	—	89	1	no	—
429	C₄×Q₈	—	89	1	no	—
430	C₄×D₄	—	89	1	no	—
431	C₄×D₄	—	89	1	no	—
432	C₄×D₄	—	89	2	no	—
433	C₄×D₄	—	89	2	no	—
434	C₄×D₄	—	89	2	no	—
435	C₄×D₄	—	89	2	no	—
436	C₄×D₄	—	89	1	no	—
437	C₄×D₄	—	89	1	no	—
438	C₄×D₄	—	89	1	no	—
439	C₄×D₄	—	89	2	no	—
440	C₄×D₄	—	89	2	no	—
441	C₄×D₄	—	89	2	no	—
442	C₄×D₄	—	89	1	no	—
443	C₄×D₄	—	89	1	no	—
444	C₄×D₄	—	89	1	no	—
445	C₄×D₄	—	89	1	no	—
446	C₄×D₄	—	89	2	no	—
447	C₄×D₄	—	89	1	no	—
448	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
449	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
450	#117	—	89	1	no	—
451	#117	—	89	2	no	—
452	#117	—	89	2	no	—
453	#117	—	89	2	no	—
454	#117	—	89	1	no	—
455	#117	—	89	1	no	—
456	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
457	C₂×C₄⋊C₄	—	89	1	no	—
458	C₂×C₂²⋊C₄	—	89	2	no	—
459	C₂×C₄²	—	89	1	no	—
460	C₂×C₄²	—	89	2	no	—
461	C₂×C₄²	—	89	1	no	—
462	C₂×C₄²	—	89	1	no	—
463	C₂⁴	—	89	2	no	—
464	#41	—	356	4	no	—
465	#41	—	356	4	no	—
466	#41	—	178	4	no	—
467	#41	—	178	4	no	—
468	C₂×Q₈	—	89	2	no	—
469	C₂×Q₈	—	89	2	no	—
470	C₂×Q₈	—	89	1	no	—
471	C₂×Q₈	—	89	1	no	—
472	C₂×D₄	—	89	2	no	—
473	C₂×D₄	—	89	2	no	—
474	C₂×D₄	—	89	2	no	—
475	C₂×D₄	—	89	2	no	—
476	C₂×D₄	—	89	2	no	—
477	C₂×D₄	—	89	2	no	—
478	C₂×D₄	—	89	1	no	—
479	C₂×D₄	—	89	2	no	—
480	C₂×D₄	—	89	1	no	—
481	C₂×D₄	—	89	2	no	—
482	C₂×D₄	—	89	1	no	—
483	C₂×D₄	—	89	1	no	—
484	C₂×D₄	—	178	4	no	—
485	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₈₉	1	2	yes	—
488	C₂×D₄	C₂²×D₈₉	1	2	yes	—
489	C₂×D₄	C₂²×D₈₉	1	2	yes	—
490	C₂×D₄	C₂²×D₈₉	1	2	yes	—
491	C₂²×C₄	—	89	1	no	—
492	C₂²×C₄	—	89	1	no	—
493	C₂²×C₄	—	89	2	no	—
494	C₂²×C₄	—	89	2	no	—
495	C₂²×C₄	—	89	1	no	—
496	C₂²×C₄	—	89	2	no	—
497	C₂²×C₄	—	89	1	no	—
498	C₂²×C₄	—	89	1	no	—
499	C₂²×C₄	—	89	2	no	—
500	C₂²×C₄	—	89	2	no	—
501	C₂²×C₄	—	89	1	no	—
502	C₂²×C₄	—	89	1	no	—
503	C₂²×C₄	—	89	1	no	—
504	C₂²×C₄	—	89	2	no	—
505	C₂²×C₄	—	356	4	no	—
506	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
508	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
509	C₄⋊C₄	—	89	2	no	—
510	C₄⋊C₄	—	89	1	no	—
511	C₄⋊C₄	—	89	1	no	—
512	C₄⋊C₄	—	89	1	no	—
513	C₄⋊C₄	—	89	1	no	—
514	C₄⋊C₄	—	89	2	no	—
515	C₄⋊C₄	—	89	1	no	—
516	C₄⋊C₄	—	89	2	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	2	no	—
520	C₄⋊C₄	—	89	2	no	—
521	C₄⋊C₄	—	89	2	no	—
522	C₄⋊C₄	—	89	2	no	—
523	C₄⋊C₄	—	89	2	no	—
524	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
530	C₂²⋊C₄	—	89	2	no	—
531	C₂²⋊C₄	—	89	2	no	—
532	C₂²⋊C₄	—	89	2	no	—
533	C₂²⋊C₄	—	89	2	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	2	no	—
536	C₂²⋊C₄	—	89	2	no	—
537	C₂²⋊C₄	—	89	2	no	—
538	C₂²⋊C₄	—	89	2	no	—
539	C₂²⋊C₄	—	89	1	no	—
540	C₂²⋊C₄	—	89	2	no	—
541	C₂²⋊C₄	—	89	1	no	—
542	C₂²⋊C₄	—	89	1	no	—
543	C₂²⋊C₄	—	89	1	no	—
544	C₂²⋊C₄	—	89	2	no	—
545	C₂²⋊C₄	—	89	2	no	—
546	C₂²⋊C₄	—	89	2	no	—
547	C₂²⋊C₄	—	89	2	no	—
548	C₂²⋊C₄	—	89	2	no	—
549	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
555	C₄²	—	89	1	no	—
556	C₄²	—	89	1	no	—
557	C₄²	—	89	2	no	—
558	C₄²	—	89	1	no	—
559	C₄²	—	89	1	no	—
560	C₄²	—	89	1	no	—
561	C₄²	—	89	2	no	—
562	C₄²	—	89	1	no	—
563	C₄²	—	89	1	no	—
564	C₄²	—	89	1	no	—
565	C₄²	—	89	2	no	—
566	C₄²	C₂²×D₈₉	1	1	yes	characteristic
567	C₄²	C₂²×D₈₉	1	1	yes	characteristic
568	C₂³	—	89	1	no	—
569	C₂³	—	89	2	no	—
570	C₂³	—	89	1	no	—
571	C₂³	—	356	2	no	—
572	C₂³	—	356	2	no	—
573	C₂³	—	178	4	no	—
574	C₂³	C₂³×D₈₉	1	2	yes	—
575	C₂³	C₂³×D₈₉	1	1	yes	characteristic
576	C₂³	C₂³×D₈₉	1	2	yes	—
577	Q₈	—	356	2	no	—
578	Q₈	—	356	2	no	—
579	Q₈	—	178	2	no	—
580	Q₈	—	178	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	356	2	no	—
588	D₄	—	356	2	no	—
589	D₄	—	356	2	no	—
590	D₄	—	356	2	no	—
591	D₄	—	356	2	no	—
592	D₄	—	356	2	no	—
593	D₄	—	178	2	no	—
594	D₄	—	178	4	no	—
595	D₄	—	178	2	no	—
596	D₄	—	178	2	no	—
597	D₄	—	178	4	no	—
598	D₄	—	178	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	89	1	no	—
603	C₂×C₄	—	89	1	no	—
604	C₂×C₄	—	89	4	no	—
605	C₂×C₄	—	89	1	no	—
606	C₂×C₄	—	89	2	no	—
607	C₂×C₄	—	89	1	no	—
608	C₂×C₄	—	89	1	no	—
609	C₂×C₄	—	89	2	no	—
610	C₂×C₄	—	89	1	no	—
611	C₂×C₄	—	89	2	no	—
612	C₂×C₄	—	356	1	no	—
613	C₂×C₄	—	356	1	no	—
614	C₂×C₄	—	356	2	no	—
615	C₂×C₄	—	356	2	no	—
616	C₂×C₄	—	356	1	no	—
617	C₂×C₄	—	178	2	no	—
618	C₂×C₄	—	178	4	no	—
619	C₂×C₄	—	178	2	no	—
620	C₂×C₄	—	178	4	no	—
621	C₂×C₄	—	178	4	no	—
622	C₂×C₄	—	178	2	no	—
623	C₂×C₄	—	178	4	no	—
624	C₂×C₄	—	178	2	no	—
625	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₈₉	1	2	yes	—
628	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₈₉	1	2	yes	—
632	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	89	2	no	—
643	C₂²	—	356	8	no	—
644	C₂²	—	178	1	no	—
645	C₂²	—	178	2	no	—
646	C₂²	—	178	2	no	—
647	C₂²	—	178	1	no	—
648	C₂²	—	178	1	no	—
649	C₂²	—	178	2	no	—
650	C₂²	—	178	1	no	—
651	C₂²	—	178	1	no	—
652	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	89	2	no	—
661	C₄	—	89	2	no	—
662	C₄	—	178	2	no	—
663	C₄	—	178	1	no	—
664	C₄	—	178	2	no	—
665	C₄	—	178	2	no	—
666	C₄	—	178	1	no	—
667	C₄	—	178	1	no	—
668	C₄	—	178	1	no	—
669	C₄	#41×D₈₉	1	2	yes	—
670	C₂	—	4	1	no	—
671	C₂	—	4	2	no	—
672	C₂	—	4	2	no	—
673	C₂	—	356	2	no	—
674	C₂	—	356	1	no	—
675	C₂	—	178	2	no	—
676	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
678	C₂	#19152433	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#540×C₈₉	C₂
hypercenter	#540	D₈₉
hypocenter	C₈₉	#3460
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #19152228	C₂	semidirect
2. #19152219	C₂	semidirect
3. #19152216	C₂	semidirect
4. #19152213	C₂	semidirect
5. #19152199	C₂	semidirect
6. #19152198	C₂	semidirect
7. #19152184	C₂	semidirect
8. #19152180	C₂	semidirect
9. #19152177	C₂	semidirect
10. #19152164	C₂	semidirect
11. #19152161	C₂	semidirect
12. #19152146	C₂	semidirect
13. #19152143	C₂	semidirect
14. #19152143	C₂	semidirect
15. #19152133	C₂	semidirect
16. #19152129	C₂	semidirect
17. #19152125	C₂	semidirect
18. #19152108	C₂	semidirect
19. #19152106	C₂	semidirect
20. #19152066	C₂	semidirect
21. C₄×#13083573	C₂	semidirect
22. C₄×D₄×D₈₉	C₂	semidirect
23. #540×C₈₉	C₂	semidirect
26. C₂×#13083573	C₂²	semidirect
27. C₂×#13083573	C₂²	semidirect
30. #15668012	C₂²	semidirect
31. #15668011	C₂²	semidirect
32. #15668011	C₂²	semidirect
35. #15668007	C₂²	semidirect
36. #15668007	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668005	C₂²	semidirect
39. #15668003	C₂²	semidirect
40. #15668002	C₂²	semidirect
43. #15667999	C₂²	semidirect
45. #15667998	C₂²	semidirect
46. #15667998	C₂²	semidirect
47. #15667998	C₂²	semidirect
48. #15667997	C₂²	semidirect
49. #15667995	C₂²	semidirect
50. #15667995	C₂²	semidirect
51. #15667994	C₂²	semidirect
52. #15667994	C₂²	semidirect
53. #15667993	C₂²	semidirect
55. #15667992	C₂²	semidirect
56. #15667991	C₂²	semidirect
57. #15667991	C₂²	semidirect
59. #15667990	C₂²	semidirect
60. #15667989	C₂²	semidirect
63. #15667986	C₂²	semidirect
65. #15667985	C₂²	semidirect
68. #15667984	C₂²	semidirect
69. #15667984	C₂²	semidirect
72. #15667983	C₂²	semidirect
73. #15667983	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. #15667977	C₂²	semidirect
80. #15667977	C₂²	semidirect
81. #15667977	C₂²	semidirect
84. D₄×Dic₈₉	C₂²	semidirect
85. D₄×Dic₈₉	C₂²	semidirect
86. D₄×Dic₈₉	C₂²	semidirect
90. #15667974	C₂²	semidirect
97. #15667972	C₂²	semidirect
98. #15667972	C₂²	semidirect
99. #15667972	C₂²	semidirect
101. #15667970	C₂²	semidirect
103. #15667969	C₂²	semidirect
104. #15667968	C₂²	semidirect
105. #15667968	C₂²	semidirect
108. C₂×C₄×Dic₈₉	C₂²	semidirect
109. C₂×C₄×Dic₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
114. #123×C₈₉	C₂²	semidirect
115. #123×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #121×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. #117×C₈₉	C₂²	semidirect
288. C₄×D₈₉	#41	semidirect
340. C₈₉	#3460	semidirect
347. #540	D₈₉	semidirect
382. #125	C₂×D₈₉	semidirect
396. #123	C₂×D₈₉	semidirect
397. #123	C₂×D₈₉	semidirect
419. #121	C₂×D₈₉	semidirect
420. #121	C₂×D₈₉	semidirect
421. #121	C₂×D₈₉	semidirect
449. C₄×D₄	C₂×D₈₉	semidirect
456. #117	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152228	2
#19152219	2
#19152216	2
#19152213	2
#19152199	2
#19152198	2
#19152184	2
#19152180	2
#19152177	2
#19152164	2
#19152161	2
#19152146	2
#19152143	2
#19152133	2
#19152129	2
#19152125	2
#19152108	2
#19152106	2
#19152066	2
C₄×#13083573	2
C₄×D₄×D₈₉	2
#540×C₈₉	2
#3460	89