Subgroups — #26033956

Order 11392.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152307	C₂	1	2	yes	maximal, complemented
2	#19152305	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152303	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152300	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152291	C₂	1	2	yes	maximal, complemented
6	#19152287	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152286	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152284	C₂	1	2	yes	maximal, complemented
9	#19152253	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152248	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152246	C₂	1	2	yes	maximal, complemented
12	#19152228	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152191	C₂	1	2	yes	maximal, complemented
14	#19152189	C₂	1	2	yes	maximal, complemented
15	#19152177	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152108	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152108	C₂	1	2	yes	maximal, complemented
18	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152107	C₂	1	2	yes	maximal, complemented
20	#19152078	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152077	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄⋊C₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083574	C₂²	1	1	yes	characteristic
25	C₂×#13083574	C₂²	1	2	yes	—
26	C₂×#13083573	C₂²	1	1	yes	characteristic
27	C₂×#13083573	C₂²	1	2	yes	—
28	C₂²×C₄×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	2	yes	complemented
32	#15668011	C₂²	1	1	yes	characteristic, complemented
33	#15668007	C₂²	1	2	yes	complemented
34	#15668005	C₂²	1	2	yes	complemented
35	#15668005	C₂²	1	2	yes	complemented
36	#15668004	C₂²	1	2	yes	complemented
37	#15668003	C₂²	1	2	yes	complemented
38	#15668003	C₂²	1	2	yes	complemented
39	#15668003	C₂²	1	1	yes	characteristic, complemented
40	#15668002	C₂²	1	2	yes	complemented
41	#15668002	C₂²	1	2	yes	complemented
42	#15667997	C₂²	1	1	yes	characteristic
43	#15667997	C₂²	1	2	yes	—
44	#15667996	C₂²	1	2	yes	complemented
45	#15667994	C₂²	1	2	yes	—
46	#15667994	C₂²	1	1	yes	characteristic
47	#15667994	C₂²	1	2	yes	—
48	#15667994	C₂²	1	2	yes	—
49	#15667994	C₂²	1	2	yes	—
50	#15667994	C₂²	1	2	yes	complemented
51	#15667993	C₂²	1	2	yes	complemented
52	#15667992	C₂²	1	2	yes	—
53	#15667992	C₂²	1	1	yes	characteristic
54	#15667992	C₂²	1	1	yes	characteristic, complemented
55	#15667991	C₂²	1	1	yes	characteristic
56	#15667991	C₂²	1	2	yes	—
57	#15667991	C₂²	1	1	yes	characteristic, complemented
58	#15667991	C₂²	1	2	yes	complemented
59	#15667990	C₂²	1	2	yes	—
60	#15667990	C₂²	1	1	yes	characteristic
61	#15667990	C₂²	1	2	yes	complemented
62	#15667989	C₂²	1	2	yes	—
63	#15667989	C₂²	1	1	yes	characteristic
64	#15667989	C₂²	1	2	yes	complemented
65	#15667989	C₂²	1	2	yes	complemented
66	#15667989	C₂²	1	2	yes	complemented
67	#15667985	C₂²	1	2	yes	—
68	#15667985	C₂²	1	1	yes	characteristic
69	#15667984	C₂²	1	1	yes	characteristic
70	#15667984	C₂²	1	2	yes	—
71	#15667984	C₂²	1	2	yes	complemented
72	#15667983	C₂²	1	2	yes	—
73	#15667983	C₂²	1	1	yes	characteristic
74	#15667983	C₂²	1	1	yes	characteristic, complemented
75	#15667982	C₂²	1	1	yes	characteristic
76	#15667980	C₂²	1	2	yes	—
77	#15667980	C₂²	1	1	yes	characteristic
78	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
80	#15667977	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₃₅₆	C₂²	1	2	yes	—
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
83	D₄×Dic₈₉	C₂²	1	2	yes	—
84	D₄×Dic₈₉	C₂²	1	2	yes	—
85	D₄×Dic₈₉	C₂²	1	2	yes	—
86	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
87	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
88	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
89	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
91	#15667972	C₂²	1	2	yes	—
92	#15667972	C₂²	1	2	yes	—
93	#15667972	C₂²	1	2	yes	—
94	#15667972	C₂²	1	2	yes	complemented
95	#15667970	C₂²	1	1	yes	characteristic
96	#15667970	C₂²	1	2	yes	—
97	#15667970	C₂²	1	1	yes	characteristic, complemented
98	#15667969	C₂²	1	1	yes	characteristic
99	#15667969	C₂²	1	2	yes	—
100	#15667968	C₂²	1	2	yes	complemented
101	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13083553	C₂²	1	2	yes	—
104	C₂×#13083553	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
107	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
108	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
111	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
112	#126×C₈₉	C₂²	1	2	yes	complemented
113	#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#123×C₈₉	C₂²	1	2	yes	complemented
115	#121×C₈₉	C₂²	1	2	yes	—
116	#121×C₈₉	C₂²	1	1	yes	characteristic
117	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₈₉	C₂²	1	2	yes	—
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₂³×D₈₉	C₂³	1	1	yes	characteristic
124	#13083574	—	2	4	no	—
125	#13083574	—	4	4	no	—
126	#13083573	—	2	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×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
141	C₂²×Dic₈₉	C₂³	1	2	yes	—
142	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
143	C₂²×Dic₈₉	C₂³	1	2	yes	—
144	C₂²×Dic₈₉	C₂³	1	2	yes	—
145	C₂²×Dic₈₉	C₂³	1	2	yes	—
146	C₂×C₄×D₈₉	—	2	4	no	—
147	C₂×C₄×D₈₉	—	4	4	no	—
148	C₂×C₄×D₈₉	C₂³	1	2	yes	—
149	C₂×C₄×D₈₉	C₂³	1	2	yes	—
150	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂³	1	2	yes	—
155	C₂×C₄×D₈₉	C₂³	1	2	yes	—
156	C₂×C₄×D₈₉	C₂³	1	2	yes	—
157	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₉	C₂³	1	2	yes	—
159	C₄⋊Dic₈₉	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	2	yes	—
163	C₄⋊Dic₈₉	C₂³	1	2	yes	—
164	C₄⋊Dic₈₉	C₂³	1	2	yes	—
165	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
166	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
167	C₄⋊Dic₈₉	C₂³	1	2	yes	—
168	#13083553	C₂³	1	1	yes	characteristic
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	2	yes	—
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	#13083553	C₂³	1	2	yes	—
176	#13083553	C₂³	1	2	yes	—
177	#13083553	C₂³	1	1	yes	characteristic
178	#13083553	C₂³	1	2	yes	—
179	#13083553	C₂³	1	1	yes	characteristic
180	#13083553	C₂³	1	2	yes	—
181	#13083553	C₂³	1	2	yes	—
182	#13083553	C₂³	1	2	yes	—
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
185	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
187	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
188	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
189	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
190	#13083551	C₂³	1	1	yes	characteristic
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
199	#13083551	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂³	1	2	yes	—
201	C₄×Dic₈₉	C₂³	1	2	yes	—
202	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	2	yes	—
204	C₄×Dic₈₉	C₂³	1	2	yes	—
205	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×D₄×C₈₉	C₂³	1	2	yes	—
207	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₈₉	C₂³	1	2	yes	—
209	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
220	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	2	yes	—
227	C₄²×C₈₉	C₂³	1	1	yes	characteristic
228	C₂³×C₈₉	C₂⁴	1	2	yes	—
229	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	—	2	2	no	—
232	C₂²×D₈₉	—	2	2	no	—
233	C₂²×D₈₉	—	2	2	no	—
234	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
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	4	no	—
239	D₄×C₈₉	—	2	2	no	—
240	D₄×C₈₉	—	4	2	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	4	2	no	—
244	C₂×C₄×C₈₉	—	4	2	no	—
245	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
247	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
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	1	yes	characteristic
253	C₂²⋊D₈₉	—	2	2	no	—
254	C₂²⋊D₈₉	—	2	4	no	—
255	C₂²⋊D₈₉	—	2	2	no	—
256	C₂²⋊D₈₉	—	2	2	no	—
257	C₂²⋊D₈₉	—	2	4	no	—
258	C₂²⋊D₈₉	—	2	2	no	—
259	C₂²⋊D₈₉	—	4	2	no	—
260	C₂×Dic₈₉	—	2	2	no	—
261	C₂×Dic₈₉	—	2	4	no	—
262	C₂×Dic₈₉	—	4	2	no	—
263	C₂×Dic₈₉	—	4	2	no	—
264	C₂×Dic₈₉	—	4	2	no	—
265	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₈₉	C₂⁴	1	2	yes	—
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₈₉	C₂⁴	1	2	yes	—
269	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₈₉	C₂⁴	1	2	yes	—
271	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₈₉	C₂⁴	1	2	yes	—
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	D₃₅₆	—	2	2	no	—
275	D₃₅₆	—	2	2	no	—
276	C₄×D₈₉	—	2	2	no	—
277	C₄×D₈₉	—	2	4	no	—
278	C₄×D₈₉	—	2	4	no	—
279	C₄×D₈₉	—	2	2	no	—
280	C₄×D₈₉	—	2	2	no	—
281	C₄×D₈₉	—	2	2	no	—
282	C₄×D₈₉	—	4	2	no	—
283	C₄×D₈₉	—	4	2	no	—
284	C₄×D₈₉	—	4	2	no	—
285	C₄×D₈₉	#41	1	4	yes	complemented
286	Dic₁₇₈	—	2	2	no	—
287	Dic₁₇₈	—	2	2	no	—
288	Dic₁₇₈	—	4	2	no	—
289	Dic₁₇₈	—	4	2	no	—
290	C₂²×C₈₉	—	2	1	no	—
291	C₂²×C₈₉	—	2	1	no	—
292	C₂²×C₈₉	—	2	2	no	—
293	C₂²×C₈₉	—	2	1	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	2₋¹⁺⁴	1	2	yes	—
299	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
300	C₂×D₈₉	—	2	8	no	—
301	C₂×D₈₉	—	2	1	no	—
302	C₂×D₈₉	—	2	1	no	—
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	1	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	1	no	—
307	C₂×D₈₉	—	2	1	no	—
308	C₂×D₈₉	C₂×#41	1	2	yes	—
309	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
310	C₄×C₈₉	—	2	1	no	—
311	C₄×C₈₉	—	2	1	no	—
312	C₄×C₈₉	—	2	1	no	—
313	C₄×C₈₉	—	2	2	no	—
314	C₄×C₈₉	—	2	2	no	—
315	C₄×C₈₉	—	2	2	no	—
316	C₄×C₈₉	—	2	1	no	—
317	C₄×C₈₉	C₂×#41	1	2	yes	—
318	Dic₈₉	—	2	1	no	—
319	Dic₈₉	—	2	2	no	—
320	Dic₈₉	—	2	1	no	—
321	Dic₈₉	—	2	2	no	—
322	Dic₈₉	—	2	1	no	—
323	Dic₈₉	—	2	2	no	—
324	Dic₈₉	—	2	2	no	—
325	Dic₈₉	—	2	1	no	—
326	Dic₈₉	C₂×#41	1	2	yes	—
327	C₂×C₈₉	—	2	2	no	—
328	C₂×C₈₉	—	4	2	no	—
329	C₂×C₈₉	—	4	1	no	—
330	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
331	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
332	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
333	D₈₉	—	2	2	no	—
334	D₈₉	—	2	2	no	—
335	D₈₉	—	4	1	no	—
336	#3492	—	89	1	no	maximal, Sylow
337	C₈₉	#3492	1	1	yes	characteristic, complemented, Sylow
338	#554	—	89	1	no	—
339	#554	—	89	2	no	—
340	#554	—	89	1	no	—
341	#553	—	89	2	no	—
342	#553	—	89	1	no	—
343	#553	D₈₉	1	1	yes	characteristic, complemented
344	#552	—	89	2	no	—
345	#552	—	89	1	no	—
346	#552	—	89	1	no	—
347	#547	—	89	2	no	—
348	#547	—	89	1	no	—
349	#547	—	89	1	no	—
350	#544	—	89	1	no	—
351	#539	—	89	2	no	—
352	#539	—	89	2	no	—
353	#537	—	89	1	no	—
354	#525	—	89	1	no	—
355	#525	—	89	2	no	—
356	#525	—	89	1	no	—
357	#525	—	89	2	no	—
358	#520	—	89	1	no	—
359	#520	—	89	1	no	—
360	C₂²×C₄⋊C₄	—	89	1	no	—
361	C₂×#41	—	89	2	no	—
362	C₂×#41	—	89	1	no	—
363	C₂×#41	—	89	2	no	—
364	C₂×#41	—	89	1	no	—
365	C₂³×C₄	—	89	2	no	—
366	C₂³×C₄	—	89	1	no	—
367	C₄⋊Q₈	—	89	2	no	—
368	C₄⋊Q₈	—	89	1	no	—
369	C₄⋊Q₈	—	89	1	no	—
370	#126	—	89	2	no	—
371	#126	—	89	2	no	—
372	#126	—	89	2	no	—
373	#126	C₂×D₈₉	1	2	yes	complemented
374	#125	—	89	2	no	—
375	#125	—	89	2	no	—
376	#125	—	89	2	no	—
377	#125	—	89	2	no	—
378	#125	—	89	1	no	—
379	#125	—	89	2	no	—
380	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
381	#123	—	89	2	no	—
382	#123	—	89	1	no	—
383	#123	—	89	2	no	—
384	#123	—	89	2	no	—
385	#123	—	89	1	no	—
386	#123	—	89	2	no	—
387	#123	—	89	2	no	—
388	#123	—	89	2	no	—
389	#123	—	89	2	no	—
390	#123	—	89	2	no	—
391	#123	C₂×D₈₉	1	2	yes	complemented
392	C₂²⋊Q₈	—	89	1	no	—
393	C₂²⋊Q₈	—	89	2	no	—
394	C₂²⋊Q₈	—	89	1	no	—
395	C₂²⋊Q₈	—	89	2	no	—
396	C₂²⋊Q₈	—	89	2	no	—
397	C₂²⋊Q₈	—	89	1	no	—
398	C₂²⋊Q₈	—	89	2	no	—
399	C₂²⋊Q₈	—	89	1	no	—
400	C₂²⋊Q₈	—	89	2	no	—
401	C₂²⋊Q₈	—	89	1	no	—
402	C₂²⋊Q₈	—	89	1	no	—
403	C₂²⋊Q₈	—	89	2	no	—
404	C₂²⋊Q₈	—	89	2	no	—
405	C₂²⋊Q₈	—	89	2	no	—
406	C₂²⋊Q₈	—	89	2	no	—
407	#121	—	89	2	no	—
408	#121	—	89	1	no	—
409	#121	—	89	2	no	—
410	#121	—	89	1	no	—
411	#121	—	89	1	no	—
412	#121	—	89	2	no	—
413	#121	—	89	2	no	—
414	#121	—	89	1	no	—
415	#121	C₂×D₈₉	1	2	yes	—
416	#121	C₂×D₈₉	1	1	yes	characteristic
417	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
418	#120	—	89	1	no	—
419	#120	—	89	2	no	—
420	#120	—	89	1	no	—
421	C₄×Q₈	—	89	1	no	—
422	C₄×Q₈	—	89	1	no	—
423	C₄×Q₈	—	89	2	no	—
424	C₄×D₄	—	89	2	no	—
425	C₄×D₄	—	89	2	no	—
426	C₄×D₄	—	89	2	no	—
427	C₄×D₄	—	89	1	no	—
428	C₄×D₄	—	89	2	no	—
429	C₄×D₄	—	89	1	no	—
430	C₄×D₄	—	89	2	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	2	no	—
437	C₄×D₄	—	89	1	no	—
438	C₄×D₄	C₂×D₈₉	1	2	yes	—
439	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
440	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
441	#117	—	89	1	no	—
442	#117	—	89	2	no	—
443	#117	—	89	1	no	—
444	#117	—	89	2	no	—
445	#117	—	89	1	no	—
446	#117	—	89	2	no	—
447	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₄	—	89	2	no	—
449	C₂×C₄⋊C₄	—	89	1	no	—
450	C₂×C₄⋊C₄	—	89	2	no	—
451	C₂×C₄⋊C₄	—	89	1	no	—
452	C₂×C₄⋊C₄	—	89	1	no	—
453	C₂×C₄⋊C₄	—	89	1	no	—
454	C₂×C₄⋊C₄	—	89	2	no	—
455	C₂×C₄⋊C₄	—	89	2	no	—
456	C₂×C₄⋊C₄	—	89	1	no	—
457	C₂×C₄⋊C₄	—	89	1	no	—
458	C₂×C₄⋊C₄	—	89	1	no	—
459	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
460	C₂⁴	—	89	1	no	—
461	#41	—	356	4	no	—
462	#41	—	356	4	no	—
463	#41	—	178	4	no	—
464	#41	—	178	4	no	—
465	C₂×Q₈	—	89	2	no	—
466	C₂×Q₈	—	89	2	no	—
467	C₂×Q₈	—	89	1	no	—
468	C₂×Q₈	—	89	1	no	—
469	C₂×D₄	—	89	2	no	—
470	C₂×D₄	—	89	1	no	—
471	C₂×D₄	—	89	2	no	—
472	C₂×D₄	—	89	1	no	—
473	C₂×D₄	—	89	1	no	—
474	C₂×D₄	—	89	1	no	—
475	C₂×D₄	—	89	2	no	—
476	C₂×D₄	—	89	1	no	—
477	C₂×D₄	—	89	1	no	—
478	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
479	C₂×D₄	C₂²×D₈₉	1	2	yes	—
480	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₈₉	1	2	yes	—
482	C₂²×C₄	—	89	1	no	—
483	C₂²×C₄	—	89	2	no	—
484	C₂²×C₄	—	89	2	no	—
485	C₂²×C₄	—	89	2	no	—
486	C₂²×C₄	—	89	1	no	—
487	C₂²×C₄	—	89	2	no	—
488	C₂²×C₄	—	89	2	no	—
489	C₂²×C₄	—	89	2	no	—
490	C₂²×C₄	—	89	2	no	—
491	C₂²×C₄	—	89	2	no	—
492	C₂²×C₄	—	89	2	no	—
493	C₂²×C₄	—	89	1	no	—
494	C₂²×C₄	—	89	1	no	—
495	C₂²×C₄	—	89	1	no	—
496	C₂²×C₄	—	89	1	no	—
497	C₂²×C₄	—	356	4	no	—
498	C₂²×C₄	—	178	4	no	—
499	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
501	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
502	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
503	C₄⋊C₄	—	89	2	no	—
504	C₄⋊C₄	—	89	1	no	—
505	C₄⋊C₄	—	89	2	no	—
506	C₄⋊C₄	—	89	1	no	—
507	C₄⋊C₄	—	89	2	no	—
508	C₄⋊C₄	—	89	2	no	—
509	C₄⋊C₄	—	89	2	no	—
510	C₄⋊C₄	—	89	1	no	—
511	C₄⋊C₄	—	89	1	no	—
512	C₄⋊C₄	—	89	2	no	—
513	C₄⋊C₄	—	89	2	no	—
514	C₄⋊C₄	—	89	2	no	—
515	C₄⋊C₄	—	89	2	no	—
516	C₄⋊C₄	—	89	1	no	—
517	C₄⋊C₄	—	89	2	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	2	no	—
520	C₄⋊C₄	—	89	2	no	—
521	C₄⋊C₄	—	89	1	no	—
522	C₄⋊C₄	—	89	1	no	—
523	C₄⋊C₄	—	89	2	no	—
524	C₄⋊C₄	—	89	2	no	—
525	C₄⋊C₄	—	89	2	no	—
526	C₄⋊C₄	—	89	1	no	—
527	C₄⋊C₄	—	89	2	no	—
528	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
531	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
533	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
534	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
535	C₂²⋊C₄	—	89	2	no	—
536	C₂²⋊C₄	—	89	2	no	—
537	C₂²⋊C₄	—	89	1	no	—
538	C₂²⋊C₄	—	89	2	no	—
539	C₂²⋊C₄	—	89	2	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	1	no	—
546	C₂²⋊C₄	—	89	2	no	—
547	C₂²⋊C₄	—	89	1	no	—
548	C₂²⋊C₄	—	89	2	no	—
549	C₂²⋊C₄	—	89	2	no	—
550	C₂²⋊C₄	—	89	1	no	—
551	C₂²⋊C₄	—	89	1	no	—
552	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
556	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
558	C₄²	—	89	2	no	—
559	C₄²	—	89	2	no	—
560	C₄²	—	89	2	no	—
561	C₄²	—	89	2	no	—
562	C₄²	—	89	1	no	—
563	C₄²	C₂²×D₈₉	1	2	yes	—
564	C₄²	C₂²×D₈₉	1	1	yes	characteristic
565	C₂³	—	89	1	no	—
566	C₂³	—	89	1	no	—
567	C₂³	—	89	1	no	—
568	C₂³	—	178	2	no	—
569	C₂³	—	178	2	no	—
570	C₂³	—	178	2	no	—
571	C₂³	C₂³×D₈₉	1	1	yes	characteristic
572	C₂³	C₂³×D₈₉	1	2	yes	—
573	C₂³	C₂³×D₈₉	1	1	yes	characteristic
574	Q₈	—	356	2	no	—
575	Q₈	—	356	2	no	—
576	Q₈	—	178	2	no	—
577	Q₈	—	178	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	356	2	no	—
583	D₄	—	178	2	no	—
584	D₄	—	178	2	no	—
585	D₄	—	178	2	no	—
586	D₄	—	178	4	no	—
587	D₄	—	178	2	no	—
588	D₄	—	178	2	no	—
589	D₄	—	178	4	no	—
590	D₄	—	178	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	89	1	no	—
596	C₂×C₄	—	89	4	no	—
597	C₂×C₄	—	89	1	no	—
598	C₂×C₄	—	89	2	no	—
599	C₂×C₄	—	89	1	no	—
600	C₂×C₄	—	89	2	no	—
601	C₂×C₄	—	89	1	no	—
602	C₂×C₄	—	89	2	no	—
603	C₂×C₄	—	89	1	no	—
604	C₂×C₄	—	89	2	no	—
605	C₂×C₄	—	356	2	no	—
606	C₂×C₄	—	356	2	no	—
607	C₂×C₄	—	356	2	no	—
608	C₂×C₄	—	356	2	no	—
609	C₂×C₄	—	356	2	no	—
610	C₂×C₄	—	356	2	no	—
611	C₂×C₄	—	178	2	no	—
612	C₂×C₄	—	178	4	no	—
613	C₂×C₄	—	178	4	no	—
614	C₂×C₄	—	178	2	no	—
615	C₂×C₄	—	178	2	no	—
616	C₂×C₄	—	178	4	no	—
617	C₂×C₄	—	178	2	no	—
618	C₂×C₄	—	178	2	no	—
619	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₈₉	1	2	yes	—
621	C₂×C₄	C₂³×D₈₉	1	2	yes	—
622	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₈₉	1	2	yes	—
626	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	89	2	no	—
636	C₂²	—	89	2	no	—
637	C₂²	—	178	8	no	—
638	C₂²	—	178	1	no	—
639	C₂²	—	178	1	no	—
640	C₂²	—	178	1	no	—
641	C₂²	—	178	1	no	—
642	C₂²	—	178	1	no	—
643	C₂²	—	178	1	no	—
644	C₂²	—	178	1	no	—
645	C₂²	#15668059	1	2	yes	—
646	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	1	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	2	no	—
654	C₄	—	89	2	no	—
655	C₄	—	178	1	no	—
656	C₄	—	178	2	no	—
657	C₄	—	178	1	no	—
658	C₄	—	178	2	no	—
659	C₄	—	178	2	no	—
660	C₄	—	178	2	no	—
661	C₄	—	178	1	no	—
662	C₄	—	178	1	no	—
663	C₄	#41×D₈₉	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	356	1	no	—
668	C₂	—	178	2	no	—
669	C₂	—	178	2	no	—
670	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
671	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
672	C₂	C₂×#15668059	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#553×C₈₉	C₂
hypercenter	#553	D₈₉
hypocenter	C₈₉	#3492
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #19152307	C₂	semidirect
2. #19152305	C₂	semidirect
3. #19152303	C₂	semidirect
4. #19152300	C₂	semidirect
5. #19152291	C₂	semidirect
6. #19152287	C₂	semidirect
7. #19152286	C₂	semidirect
8. #19152284	C₂	semidirect
9. #19152253	C₂	semidirect
10. #19152248	C₂	semidirect
11. #19152246	C₂	semidirect
12. #19152228	C₂	semidirect
13. #19152191	C₂	semidirect
14. #19152189	C₂	semidirect
15. #19152177	C₂	semidirect
16. #19152108	C₂	semidirect
17. #19152108	C₂	semidirect
18. #19152107	C₂	semidirect
19. #19152107	C₂	semidirect
20. #19152078	C₂	semidirect
21. #19152077	C₂	semidirect
22. C₂×C₄⋊C₄×D₈₉	C₂	semidirect
23. #553×C₈₉	C₂	semidirect
30. #15668012	C₂²	semidirect
31. #15668011	C₂²	semidirect
32. #15668011	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668005	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668004	C₂²	semidirect
37. #15668003	C₂²	semidirect
38. #15668003	C₂²	semidirect
39. #15668003	C₂²	semidirect
40. #15668002	C₂²	semidirect
41. #15668002	C₂²	semidirect
44. #15667996	C₂²	semidirect
50. #15667994	C₂²	semidirect
51. #15667993	C₂²	semidirect
54. #15667992	C₂²	semidirect
57. #15667991	C₂²	semidirect
58. #15667991	C₂²	semidirect
61. #15667990	C₂²	semidirect
64. #15667989	C₂²	semidirect
65. #15667989	C₂²	semidirect
66. #15667989	C₂²	semidirect
71. #15667984	C₂²	semidirect
74. #15667983	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. C₄×Dic₁₇₈	C₂²	semidirect
80. #15667977	C₂²	semidirect
86. D₄×Dic₈₉	C₂²	semidirect
94. #15667972	C₂²	semidirect
97. #15667970	C₂²	semidirect
100. #15667968	C₂²	semidirect
102. C₂×C₄⋊Dic₈₉	C₂²	semidirect
104. C₂×#13083553	C₂²	semidirect
111. C₄⋊C₄×D₈₉	C₂²	semidirect
112. #126×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
114. #123×C₈₉	C₂²	semidirect
117. #121×C₈₉	C₂²	semidirect
120. C₄×D₄×C₈₉	C₂²	semidirect
121. #117×C₈₉	C₂²	semidirect
285. C₄×D₈₉	#41	semidirect
337. C₈₉	#3492	semidirect
343. #553	D₈₉	semidirect
373. #126	C₂×D₈₉	semidirect
380. #125	C₂×D₈₉	semidirect
391. #123	C₂×D₈₉	semidirect
417. #121	C₂×D₈₉	semidirect
440. C₄×D₄	C₂×D₈₉	semidirect
447. #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
#19152307	2
#19152305	2
#19152303	2
#19152300	2
#19152291	2
#19152287	2
#19152286	2
#19152284	2
#19152253	2
#19152248	2
#19152246	2
#19152228	2
#19152191	2
#19152189	2
#19152177	2
#19152108	2
#19152107	2
#19152078	2
#19152077	2
C₂×C₄⋊C₄×D₈₉	2
#553×C₈₉	2
#3492	89