Subgroups — #26034211

Order 11392.

1142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152330	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152319	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152314	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152312	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152276	C₂	1	2	yes	maximal, complemented
6	#19152275	C₂	1	2	yes	maximal, complemented
7	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152258	C₂	1	2	yes	maximal, complemented
9	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152240	C₂	1	2	yes	maximal, complemented
11	#19152239	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152232	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152220	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152187	C₂	1	2	yes	maximal, complemented
15	#19152182	C₂	1	2	yes	maximal, complemented
16	#19152145	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152131	C₂	1	2	yes	maximal, complemented
18	#19152126	C₂	1	1	yes	maximal, characteristic, complemented
19	#124×D₈₉	C₂	1	2	yes	maximal, complemented
20	#19152072	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
23	#542×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic
25	C₂×#13083574	C₂²	1	2	yes	complemented
26	C₂×Q₈×D₈₉	C₂²	1	2	yes	complemented
27	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
28	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₈₉	C₂²	1	2	yes	—
30	#15668011	C₂²	1	1	yes	characteristic, complemented
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668008	C₂²	1	1	yes	characteristic
33	#15668007	C₂²	1	2	yes	complemented
34	#15668007	C₂²	1	1	yes	characteristic, complemented
35	#15668006	C₂²	1	2	yes	complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	1	yes	characteristic, complemented
38	#15668002	C₂²	1	1	yes	characteristic, complemented
39	#15668001	C₂²	1	2	yes	complemented
40	#15668001	C₂²	1	1	yes	characteristic, complemented
41	#15668001	C₂²	1	2	yes	complemented
42	#15668000	C₂²	1	2	yes	complemented
43	#15667999	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	—
45	#15667998	C₂²	1	1	yes	characteristic
46	#15667998	C₂²	1	2	yes	complemented
47	#15667998	C₂²	1	2	yes	complemented
48	#15667998	C₂²	1	2	yes	complemented
49	#15667997	C₂²	1	2	yes	complemented
50	#15667997	C₂²	1	1	yes	characteristic, complemented
51	#15667997	C₂²	1	2	yes	complemented
52	#15667996	C₂²	1	2	yes	complemented
53	#15667994	C₂²	1	2	yes	complemented
54	#15667994	C₂²	1	1	yes	characteristic, complemented
55	#15667994	C₂²	1	2	yes	complemented
56	#15667990	C₂²	1	2	yes	complemented
57	#15667990	C₂²	1	2	yes	complemented
58	#15667990	C₂²	1	2	yes	complemented
59	#15667990	C₂²	1	1	yes	characteristic, complemented
60	#15667988	C₂²	1	2	yes	complemented
61	#15667988	C₂²	1	1	yes	characteristic, complemented
62	#15667987	C₂²	1	1	yes	characteristic
63	#15667987	C₂²	1	1	yes	characteristic, complemented
64	#15667987	C₂²	1	2	yes	complemented
65	#15667987	C₂²	1	2	yes	complemented
66	#15667985	C₂²	1	2	yes	—
67	#15667985	C₂²	1	1	yes	characteristic
68	#15667985	C₂²	1	2	yes	complemented
69	#15667985	C₂²	1	2	yes	complemented
70	#15667984	C₂²	1	2	yes	complemented
71	#15667983	C₂²	1	1	yes	characteristic, complemented
72	#15667982	C₂²	1	2	yes	—
73	#15667982	C₂²	1	2	yes	complemented
74	#15667982	C₂²	1	2	yes	complemented
75	#15667980	C₂²	1	2	yes	—
76	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
78	#15667977	C₂²	1	2	yes	complemented
79	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
80	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
81	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₅₆	C₂²	1	2	yes	complemented
83	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
86	#15667974	C₂²	1	1	yes	characteristic
87	#15667974	C₂²	1	1	yes	characteristic
88	#15667974	C₂²	1	2	yes	complemented
89	#15667974	C₂²	1	2	yes	complemented
90	#15667974	C₂²	1	2	yes	complemented
91	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
93	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
95	#15667972	C₂²	1	2	yes	complemented
96	#15667972	C₂²	1	2	yes	complemented
97	#15667971	C₂²	1	1	yes	characteristic, complemented
98	#15667970	C₂²	1	2	yes	complemented
99	#15667970	C₂²	1	2	yes	complemented
100	#15667970	C₂²	1	1	yes	characteristic, complemented
101	#15667970	C₂²	1	1	yes	characteristic, complemented
102	#15667969	C₂²	1	1	yes	characteristic, complemented
103	#15667968	C₂²	1	2	yes	complemented
104	C₂×#13083551	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
110	C₄²×D₈₉	C₂²	1	2	yes	complemented
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₈₉	C₂²	1	2	yes	complemented
114	#124×C₈₉	C₂²	1	2	yes	complemented
115	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	#123×C₈₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
119	#121×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
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	C₂³×D₈₉	C₂³	1	2	yes	—
125	#13083575	—	2	4	no	—
126	#13083574	—	4	4	no	—
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	Q₈×D₈₉	—	4	4	no	—
131	C₂×D₃₅₆	—	2	4	no	—
132	C₂×D₃₅₆	C₂³	1	2	yes	—
133	C₂×D₃₅₆	C₂³	1	2	yes	—
134	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
135	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
136	C₂×D₃₅₆	C₂³	1	2	yes	—
137	C₂×D₃₅₆	C₂³	1	2	yes	—
138	C₂×D₃₅₆	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	1	yes	characteristic
142	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
145	D₄×D₈₉	—	2	4	no	—
146	D₄×D₈₉	—	4	4	no	—
147	C₂²×Dic₈₉	C₂³	1	2	yes	—
148	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂³	1	2	yes	—
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
152	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₈₉	C₂³	1	2	yes	—
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	2	yes	—
158	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
170	#13083553	C₂³	1	2	yes	—
171	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
178	#13083551	C₂³	1	1	yes	characteristic
179	#13083551	C₂³	1	1	yes	characteristic
180	#13083551	C₂³	1	2	yes	—
181	#13083551	C₂³	1	2	yes	—
182	#13083551	C₂³	1	2	yes	—
183	#13083551	C₂³	1	2	yes	—
184	#13083551	C₂³	1	2	yes	—
185	#13083551	C₂³	1	2	yes	—
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	2	yes	—
188	#13083551	C₂³	1	1	yes	characteristic
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
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	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂³	1	2	yes	—
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×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×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	2	yes	—
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊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	2	yes	—
224	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	1	yes	characteristic
227	C₄²×C₈₉	C₂³	1	2	yes	—
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₉	C₂⁴	1	2	yes	—
230	C₂²×D₈₉	—	2	4	no	—
231	C₂²×D₈₉	—	2	4	no	—
232	C₂²×D₈₉	—	4	2	no	—
233	C₂²×D₈₉	—	4	2	no	—
234	C₂²×D₈₉	—	4	2	no	—
235	C₂²×D₈₉	—	4	2	no	—
236	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
237	C₂²×D₈₉	C₂⁴	1	2	yes	—
238	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₈₉	C₂⁴	1	2	yes	—
240	Q₈×C₈₉	—	2	2	no	—
241	Q₈×C₈₉	—	4	2	no	—
242	D₄×C₈₉	—	2	2	no	—
243	D₄×C₈₉	—	4	2	no	—
244	C₂×C₄×C₈₉	—	2	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	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	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₈₉	—	2	4	no	—
256	C₂²⋊D₈₉	—	2	2	no	—
257	C₂²⋊D₈₉	—	2	4	no	—
258	C₂²⋊D₈₉	—	4	2	no	—
259	C₂²⋊D₈₉	—	4	1	no	—
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂×Dic₈₉	—	4	2	no	—
262	C₂×Dic₈₉	C₂⁴	1	2	yes	—
263	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₈₉	C₂⁴	1	2	yes	—
269	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
270	D₃₅₆	—	2	4	no	—
271	D₃₅₆	—	2	4	no	—
272	D₃₅₆	—	2	2	no	—
273	D₃₅₆	—	4	2	no	—
274	D₃₅₆	—	4	1	no	—
275	D₃₅₆	—	4	2	no	—
276	D₃₅₆	#41	1	4	yes	complemented
277	C₄×D₈₉	—	2	4	no	—
278	C₄×D₈₉	—	2	2	no	—
279	C₄×D₈₉	—	2	2	no	—
280	C₄×D₈₉	—	2	4	no	—
281	C₄×D₈₉	—	2	2	no	—
282	C₄×D₈₉	—	4	2	no	—
283	C₄×D₈₉	—	4	2	no	—
284	C₄×D₈₉	—	4	1	no	—
285	C₄×D₈₉	—	4	2	no	—
286	C₄×D₈₉	—	4	2	no	—
287	C₄×D₈₉	—	4	2	no	—
288	Dic₁₇₈	—	2	2	no	—
289	Dic₁₇₈	—	2	4	no	—
290	Dic₁₇₈	—	4	2	no	—
291	C₂²×C₈₉	—	2	2	no	—
292	C₂²×C₈₉	—	2	1	no	—
293	C₂²×C₈₉	—	2	2	no	—
294	C₂²×C₈₉	—	2	1	no	—
295	C₂²×C₈₉	—	2	2	no	—
296	C₂²×C₈₉	—	2	1	no	—
297	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
298	C₂×D₈₉	—	2	2	no	—
299	C₂×D₈₉	—	2	2	no	—
300	C₂×D₈₉	—	2	1	no	—
301	C₂×D₈₉	—	2	1	no	—
302	C₂×D₈₉	—	2	2	no	—
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	2	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	1	no	—
307	C₂×D₈₉	—	2	2	no	—
308	C₂×D₈₉	—	2	1	no	—
309	C₂×D₈₉	—	8	4	no	—
310	C₂×D₈₉	—	8	4	no	—
311	C₂×D₈₉	C₂×#41	1	4	yes	—
312	C₄×C₈₉	—	2	2	no	—
313	C₄×C₈₉	—	2	1	no	—
314	C₄×C₈₉	—	2	1	no	—
315	C₄×C₈₉	—	2	2	no	—
316	C₄×C₈₉	—	2	2	no	—
317	C₄×C₈₉	—	2	1	no	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	1	no	—
320	C₄×C₈₉	C₂×#41	1	2	yes	—
321	Dic₈₉	—	2	1	no	—
322	Dic₈₉	—	2	1	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	H(5,𝔽₂)	1	2	yes	—
329	C₂×C₈₉	—	4	1	no	—
330	C₂×C₈₉	—	4	2	no	—
331	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
332	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×C₈₉	#585	1	1	yes	characteristic
334	D₈₉	—	2	4	no	—
335	D₈₉	—	4	1	no	—
336	D₈₉	—	4	2	no	—
337	D₈₉	—	4	1	no	—
338	#3514	—	89	1	no	maximal, Sylow
339	C₈₉	#3514	1	1	yes	characteristic, complemented, Sylow
340	#559	—	89	1	no	—
341	#556	—	89	1	no	—
342	#555	—	89	1	no	—
343	#555	—	89	1	no	—
344	#551	—	89	2	no	—
345	#551	—	89	2	no	—
346	D₄×Q₈	—	89	1	no	—
347	#548	—	89	2	no	—
348	#546	—	89	1	no	—
349	#546	—	89	2	no	—
350	#546	—	89	1	no	—
351	D₄²	—	89	1	no	—
352	#542	—	89	1	no	—
353	#542	D₈₉	1	1	yes	characteristic, complemented
354	#538	—	89	2	no	—
355	#538	—	89	2	no	—
356	#532	—	89	1	no	—
357	#529	—	89	2	no	—
358	#529	—	89	1	no	—
359	C₂×#124	—	89	2	no	—
360	#518	—	89	1	no	—
361	#518	—	89	1	no	—
362	C₄×#41	—	89	1	no	—
363	C₂×#41	—	89	1	no	—
364	C₂×#41	—	89	2	no	—
365	C₂²×Q₈	—	89	2	no	—
366	C₂²×D₄	—	89	2	no	—
367	C₂²×D₄	—	89	1	no	—
368	C₂²×D₄	—	89	1	no	—
369	C₄⋊Q₈	—	89	1	no	—
370	C₄⋊Q₈	—	89	1	no	—
371	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
372	#127	—	89	1	no	—
373	#126	—	89	1	no	—
374	#126	—	89	2	no	—
375	#126	—	89	1	no	—
376	#126	—	89	2	no	—
377	#126	—	89	2	no	—
378	#126	C₂×D₈₉	1	2	yes	complemented
379	#125	—	89	1	no	—
380	#124	—	89	2	no	—
381	#124	—	89	2	no	—
382	#124	—	89	1	no	—
383	#124	—	89	2	no	—
384	#124	—	89	1	no	—
385	#124	—	89	2	no	—
386	#124	—	89	2	no	—
387	#124	—	89	2	no	—
388	#124	—	89	2	no	—
389	#124	—	89	2	no	—
390	#124	C₂×D₈₉	1	2	yes	complemented
391	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
392	#123	—	89	1	no	—
393	#123	—	89	2	no	—
394	#123	—	89	2	no	—
395	#123	—	89	1	no	—
396	#123	—	89	2	no	—
397	#123	—	89	2	no	—
398	#123	—	89	2	no	—
399	#123	C₂×D₈₉	1	2	yes	complemented
400	C₂²⋊Q₈	—	89	2	no	—
401	C₂²⋊Q₈	—	89	1	no	—
402	C₂²⋊Q₈	—	89	2	no	—
403	C₂²⋊Q₈	—	89	1	no	—
404	C₂²⋊Q₈	—	89	2	no	—
405	C₂²⋊Q₈	—	89	2	no	—
406	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
407	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
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	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	#120	—	89	2	no	—
420	#120	—	89	2	no	—
421	#120	—	89	2	no	—
422	#120	—	89	2	no	—
423	C₄×Q₈	—	89	1	no	—
424	C₄×Q₈	—	89	2	no	—
425	C₄×Q₈	—	89	1	no	—
426	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
427	C₄×D₄	—	89	1	no	—
428	C₄×D₄	—	89	1	no	—
429	C₄×D₄	—	89	2	no	—
430	C₄×D₄	—	89	1	no	—
431	C₄×D₄	—	89	2	no	—
432	C₄×D₄	—	89	1	no	—
433	C₄×D₄	—	89	2	no	—
434	C₄×D₄	—	89	1	no	—
435	C₄×D₄	—	89	2	no	—
436	C₄×D₄	—	89	2	no	—
437	C₄×D₄	—	89	2	no	—
438	C₄×D₄	—	89	2	no	—
439	C₄×D₄	—	89	1	no	—
440	C₄×D₄	—	89	2	no	—
441	C₄×D₄	—	89	1	no	—
442	C₄×D₄	—	89	1	no	—
443	C₄×D₄	—	89	1	no	—
444	C₄×D₄	—	89	1	no	—
445	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
446	#117	—	89	1	no	—
447	#117	—	89	2	no	—
448	#117	—	89	1	no	—
449	#117	—	89	1	no	—
450	#117	—	89	2	no	—
451	#117	—	89	2	no	—
452	#117	—	89	1	no	—
453	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
454	C₂×C₂²⋊C₄	—	89	2	no	—
455	C₂×C₂²⋊C₄	—	89	2	no	—
456	C₂×C₂²⋊C₄	—	89	2	no	—
457	C₂×C₂²⋊C₄	—	89	2	no	—
458	C₂×C₂²⋊C₄	—	89	2	no	—
459	C₂×C₂²⋊C₄	—	89	2	no	—
460	C₂×C₄²	—	89	2	no	—
461	C₂×C₄²	—	89	1	no	—
462	C₂⁴	—	89	2	no	—
463	C₂⁴	—	89	2	no	—
464	#41	—	356	4	no	—
465	#41	—	178	4	no	—
466	C₂×Q₈	—	89	2	no	—
467	C₂×Q₈	—	89	1	no	—
468	C₂×Q₈	—	89	2	no	—
469	C₂×Q₈	—	356	4	no	—
470	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
471	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
472	C₂×D₄	—	89	1	no	—
473	C₂×D₄	—	89	2	no	—
474	C₂×D₄	—	89	2	no	—
475	C₂×D₄	—	89	2	no	—
476	C₂×D₄	—	89	1	no	—
477	C₂×D₄	—	89	2	no	—
478	C₂×D₄	—	89	1	no	—
479	C₂×D₄	—	89	1	no	—
480	C₂×D₄	—	89	2	no	—
481	C₂×D₄	—	89	2	no	—
482	C₂×D₄	—	89	2	no	—
483	C₂×D₄	—	89	2	no	—
484	C₂×D₄	—	89	1	no	—
485	C₂×D₄	—	356	4	no	—
486	C₂×D₄	—	178	4	no	—
487	C₂×D₄	—	178	4	no	—
488	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
489	C₂×D₄	C₂²×D₈₉	1	2	yes	—
490	C₂²×C₄	—	89	2	no	—
491	C₂²×C₄	—	89	2	no	—
492	C₂²×C₄	—	89	1	no	—
493	C₂²×C₄	—	89	2	no	—
494	C₂²×C₄	—	89	2	no	—
495	C₂²×C₄	—	89	2	no	—
496	C₂²×C₄	—	89	2	no	—
497	C₂²×C₄	—	89	2	no	—
498	C₂²×C₄	—	89	1	no	—
499	C₂²×C₄	—	89	2	no	—
500	C₂²×C₄	—	89	1	no	—
501	C₂²×C₄	—	89	1	no	—
502	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
503	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
504	C₄⋊C₄	—	89	1	no	—
505	C₄⋊C₄	—	89	1	no	—
506	C₄⋊C₄	—	89	1	no	—
507	C₄⋊C₄	—	89	1	no	—
508	C₄⋊C₄	—	89	1	no	—
509	C₄⋊C₄	—	89	1	no	—
510	C₄⋊C₄	—	89	2	no	—
511	C₄⋊C₄	—	89	2	no	—
512	C₄⋊C₄	—	89	1	no	—
513	C₄⋊C₄	—	89	1	no	—
514	C₄⋊C₄	—	89	2	no	—
515	C₄⋊C₄	—	89	2	no	—
516	C₄⋊C₄	—	89	1	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
519	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
521	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
522	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
525	C₂²⋊C₄	—	89	2	no	—
526	C₂²⋊C₄	—	89	1	no	—
527	C₂²⋊C₄	—	89	2	no	—
528	C₂²⋊C₄	—	89	2	no	—
529	C₂²⋊C₄	—	89	1	no	—
530	C₂²⋊C₄	—	89	2	no	—
531	C₂²⋊C₄	—	89	1	no	—
532	C₂²⋊C₄	—	89	2	no	—
533	C₂²⋊C₄	—	89	1	no	—
534	C₂²⋊C₄	—	89	1	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	2	no	—
540	C₂²⋊C₄	—	89	2	no	—
541	C₂²⋊C₄	—	89	2	no	—
542	C₂²⋊C₄	—	89	2	no	—
543	C₂²⋊C₄	—	89	2	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	1	no	—
549	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
550	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
551	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
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	2	yes	—
556	C₄²	—	89	1	no	—
557	C₄²	—	89	2	no	—
558	C₄²	—	89	1	no	—
559	C₄²	—	89	2	no	—
560	C₄²	—	89	1	no	—
561	C₄²	—	89	2	no	—
562	C₄²	—	89	2	no	—
563	C₄²	—	89	1	no	—
564	C₄²	C₂²×D₈₉	1	1	yes	characteristic
565	C₄²	C₂²×D₈₉	1	2	yes	—
566	C₄²	C₂²×D₈₉	1	1	yes	characteristic
567	C₂³	—	89	2	no	—
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	—	356	2	no	—
574	C₂³	—	356	2	no	—
575	C₂³	—	178	4	no	—
576	C₂³	—	178	4	no	—
577	C₂³	C₂³×D₈₉	1	1	yes	characteristic
578	C₂³	C₂³×D₈₉	1	2	yes	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	2	no	—
581	Q₈	—	356	2	no	—
582	Q₈	—	178	2	no	—
583	Q₈	—	178	4	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	89	4	no	—
587	D₄	—	356	1	no	—
588	D₄	—	356	2	no	—
589	D₄	—	356	2	no	—
590	D₄	—	356	1	no	—
591	D₄	—	356	2	no	—
592	D₄	—	356	2	no	—
593	D₄	—	178	4	no	—
594	D₄	—	178	4	no	—
595	D₄	—	178	2	no	—
596	D₄	—	178	4	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	—	89	1	no	—
602	C₂×C₄	—	89	1	no	—
603	C₂×C₄	—	89	2	no	—
604	C₂×C₄	—	89	1	no	—
605	C₂×C₄	—	89	1	no	—
606	C₂×C₄	—	89	1	no	—
607	C₂×C₄	—	89	1	no	—
608	C₂×C₄	—	89	2	no	—
609	C₂×C₄	—	356	2	no	—
610	C₂×C₄	—	356	1	no	—
611	C₂×C₄	—	356	2	no	—
612	C₂×C₄	—	356	2	no	—
613	C₂×C₄	—	356	2	no	—
614	C₂×C₄	—	356	2	no	—
615	C₂×C₄	—	356	2	no	—
616	C₂×C₄	—	178	4	no	—
617	C₂×C₄	—	178	2	no	—
618	C₂×C₄	—	178	4	no	—
619	C₂×C₄	—	178	2	no	—
620	C₂×C₄	—	178	2	no	—
621	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
622	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₈₉	1	2	yes	—
624	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₈₉	1	2	yes	—
626	C₂×C₄	C₂³×D₈₉	1	2	yes	—
627	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
628	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	89	4	no	—
637	C₂²	—	178	1	no	—
638	C₂²	—	178	1	no	—
639	C₂²	—	178	2	no	—
640	C₂²	—	178	2	no	—
641	C₂²	—	178	1	no	—
642	C₂²	—	178	1	no	—
643	C₂²	—	178	1	no	—
644	C₂²	—	178	2	no	—
645	C₂²	—	178	1	no	—
646	C₂²	—	178	2	no	—
647	C₂²	—	178	2	no	—
648	C₂²	—	712	4	no	—
649	C₂²	—	712	4	no	—
650	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
651	C₄	—	2	1	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	1	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	89	2	no	—
660	C₄	—	178	1	no	—
661	C₄	—	178	1	no	—
662	C₄	—	178	2	no	—
663	C₄	—	178	1	no	—
664	C₄	—	178	2	no	—
665	C₄	—	178	1	no	—
666	C₄	—	178	1	no	—
667	C₄	#41×D₈₉	1	2	yes	—
668	C₂	—	4	2	no	—
669	C₂	—	4	1	no	—
670	C₂	—	356	1	no	—
671	C₂	—	356	2	no	—
672	C₂	—	356	1	no	—
673	C₂	—	178	4	no	—
674	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
675	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
676	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#542×C₈₉	C₂
hypercenter	#542	D₈₉
hypocenter	C₈₉	#3514
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. #19152330	C₂	semidirect
2. #19152319	C₂	semidirect
3. #19152314	C₂	semidirect
4. #19152312	C₂	semidirect
5. #19152276	C₂	semidirect
6. #19152275	C₂	semidirect
7. #19152263	C₂	semidirect
8. #19152258	C₂	semidirect
9. #19152241	C₂	semidirect
10. #19152240	C₂	semidirect
11. #19152239	C₂	semidirect
12. #19152232	C₂	semidirect
13. #19152220	C₂	semidirect
14. #19152187	C₂	semidirect
15. #19152182	C₂	semidirect
16. #19152145	C₂	semidirect
17. #19152131	C₂	semidirect
18. #19152126	C₂	semidirect
19. #124×D₈₉	C₂	semidirect
20. #19152072	C₂	semidirect
21. #19152070	C₂	semidirect
22. C₄×#13083575	C₂	semidirect
23. #542×C₈₉	C₂	semidirect
25. C₂×#13083574	C₂²	semidirect
26. C₂×Q₈×D₈₉	C₂²	semidirect
30. #15668011	C₂²	semidirect
31. #15668011	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668007	C₂²	semidirect
35. #15668006	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668002	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15668001	C₂²	semidirect
41. #15668001	C₂²	semidirect
42. #15668000	C₂²	semidirect
43. #15667999	C₂²	semidirect
46. #15667998	C₂²	semidirect
47. #15667998	C₂²	semidirect
48. #15667998	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667997	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667996	C₂²	semidirect
53. #15667994	C₂²	semidirect
54. #15667994	C₂²	semidirect
55. #15667994	C₂²	semidirect
56. #15667990	C₂²	semidirect
57. #15667990	C₂²	semidirect
58. #15667990	C₂²	semidirect
59. #15667990	C₂²	semidirect
60. #15667988	C₂²	semidirect
61. #15667988	C₂²	semidirect
63. #15667987	C₂²	semidirect
64. #15667987	C₂²	semidirect
65. #15667987	C₂²	semidirect
68. #15667985	C₂²	semidirect
69. #15667985	C₂²	semidirect
70. #15667984	C₂²	semidirect
71. #15667983	C₂²	semidirect
73. #15667982	C₂²	semidirect
74. #15667982	C₂²	semidirect
76. Q₈×Dic₈₉	C₂²	semidirect
77. C₄×Dic₁₇₈	C₂²	semidirect
78. #15667977	C₂²	semidirect
81. C₄×D₃₅₆	C₂²	semidirect
82. C₄×D₃₅₆	C₂²	semidirect
83. C₄×D₃₅₆	C₂²	semidirect
84. C₄×D₃₅₆	C₂²	semidirect
85. D₄×Dic₈₉	C₂²	semidirect
88. #15667974	C₂²	semidirect
89. #15667974	C₂²	semidirect
90. #15667974	C₂²	semidirect
92. C₄×C₂²⋊D₈₉	C₂²	semidirect
93. C₄×C₂²⋊D₈₉	C₂²	semidirect
94. C₄×C₂²⋊D₈₉	C₂²	semidirect
95. #15667972	C₂²	semidirect
96. #15667972	C₂²	semidirect
97. #15667971	C₂²	semidirect
98. #15667970	C₂²	semidirect
99. #15667970	C₂²	semidirect
100. #15667970	C₂²	semidirect
101. #15667970	C₂²	semidirect
102. #15667969	C₂²	semidirect
103. #15667968	C₂²	semidirect
104. C₂×#13083551	C₂²	semidirect
105. C₂²⋊C₄×D₈₉	C₂²	semidirect
106. C₂²⋊C₄×D₈₉	C₂²	semidirect
107. C₂²⋊C₄×D₈₉	C₂²	semidirect
108. C₂²⋊C₄×D₈₉	C₂²	semidirect
109. C₂²⋊C₄×D₈₉	C₂²	semidirect
110. C₄²×D₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
112. C₄⋊Q₈×C₈₉	C₂²	semidirect
113. #126×C₈₉	C₂²	semidirect
114. #124×C₈₉	C₂²	semidirect
115. #124×C₈₉	C₂²	semidirect
116. #123×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₂²⋊Q₈×C₈₉	C₂²	semidirect
120. C₄×Q₈×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. #117×C₈₉	C₂²	semidirect
276. D₃₅₆	#41	semidirect
339. C₈₉	#3514	semidirect
353. #542	D₈₉	semidirect
371. C₄⋊Q₈	C₂×D₈₉	semidirect
378. #126	C₂×D₈₉	semidirect
390. #124	C₂×D₈₉	semidirect
391. #124	C₂×D₈₉	semidirect
399. #123	C₂×D₈₉	semidirect
406. C₂²⋊Q₈	C₂×D₈₉	semidirect
407. C₂²⋊Q₈	C₂×D₈₉	semidirect
426. C₄×Q₈	C₂×D₈₉	semidirect
445. C₄×D₄	C₂×D₈₉	semidirect
453. #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
#19152330	2
#19152319	2
#19152314	2
#19152312	2
#19152276	2
#19152275	2
#19152263	2
#19152258	2
#19152241	2
#19152240	2
#19152239	2
#19152232	2
#19152220	2
#19152187	2
#19152182	2
#19152145	2
#19152131	2
#19152126	2
#124×D₈₉	2
#19152072	2
#19152070	2
C₄×#13083575	2
#542×C₈₉	2
#3514	89