Subgroups — #26034528

Order 11392.

1058 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152340	C₂	1	2	yes	maximal, complemented
2	#19152339	C₂	1	2	yes	maximal, complemented
3	#19152333	C₂	1	2	yes	maximal, complemented
4	#19152316	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152314	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152311	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152273	C₂	1	2	yes	maximal, complemented
8	#19152260	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152258	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152244	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152239	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152222	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152220	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152220	C₂	1	2	yes	maximal, complemented
15	#19152214	C₂	1	2	yes	maximal, complemented
16	#19152187	C₂	1	2	yes	maximal, complemented
17	#19152182	C₂	1	2	yes	maximal, complemented
18	#19152171	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152167	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152111	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152110	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic
25	C₂×#13083574	C₂²	1	1	yes	characteristic
26	C₂×#13083574	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
30	#15668011	C₂²	1	2	yes	complemented
31	#15668011	C₂²	1	1	yes	characteristic, complemented
32	#15668009	C₂²	1	2	yes	—
33	#15668007	C₂²	1	2	yes	complemented
34	#15668006	C₂²	1	2	yes	complemented
35	#15668006	C₂²	1	2	yes	complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668001	C₂²	1	2	yes	complemented
38	#15668001	C₂²	1	1	yes	characteristic, complemented
39	#15668001	C₂²	1	2	yes	complemented
40	#15668001	C₂²	1	2	yes	complemented
41	#15668000	C₂²	1	2	yes	complemented
42	#15668000	C₂²	1	2	yes	complemented
43	#15668000	C₂²	1	2	yes	complemented
44	#15668000	C₂²	1	2	yes	complemented
45	#15668000	C₂²	1	1	yes	characteristic, complemented
46	#15667998	C₂²	1	2	yes	—
47	#15667998	C₂²	1	2	yes	—
48	#15667998	C₂²	1	2	yes	complemented
49	#15667998	C₂²	1	2	yes	complemented
50	#15667997	C₂²	1	2	yes	complemented
51	#15667997	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667997	C₂²	1	2	yes	complemented
54	#15667997	C₂²	1	2	yes	complemented
55	#15667997	C₂²	1	2	yes	complemented
56	#15667997	C₂²	1	1	yes	characteristic, complemented
57	#15667996	C₂²	1	2	yes	complemented
58	#15667994	C₂²	1	1	yes	characteristic
59	#15667994	C₂²	1	2	yes	complemented
60	#15667992	C₂²	1	1	yes	characteristic, complemented
61	#15667992	C₂²	1	2	yes	complemented
62	#15667992	C₂²	1	1	yes	characteristic, complemented
63	#15667991	C₂²	1	1	yes	characteristic, complemented
64	#15667990	C₂²	1	2	yes	complemented
65	#15667990	C₂²	1	1	yes	characteristic, complemented
66	#15667990	C₂²	1	2	yes	complemented
67	#15667989	C₂²	1	1	yes	characteristic, complemented
68	#15667988	C₂²	1	1	yes	characteristic, complemented
69	#15667988	C₂²	1	2	yes	complemented
70	#15667987	C₂²	1	1	yes	characteristic
71	#15667987	C₂²	1	1	yes	characteristic
72	#15667987	C₂²	1	2	yes	—
73	#15667987	C₂²	1	1	yes	characteristic
74	#15667987	C₂²	1	1	yes	characteristic, complemented
75	#15667987	C₂²	1	1	yes	characteristic, complemented
76	#15667987	C₂²	1	2	yes	complemented
77	#15667987	C₂²	1	2	yes	complemented
78	#15667986	C₂²	1	1	yes	characteristic
79	#15667985	C₂²	1	1	yes	characteristic
80	#15667985	C₂²	1	2	yes	—
81	#15667985	C₂²	1	2	yes	complemented
82	#15667985	C₂²	1	2	yes	complemented
83	#15667984	C₂²	1	1	yes	characteristic
84	#15667982	C₂²	1	2	yes	—
85	#15667982	C₂²	1	2	yes	—
86	#15667982	C₂²	1	2	yes	complemented
87	#15667982	C₂²	1	1	yes	characteristic, complemented
88	#15667982	C₂²	1	2	yes	complemented
89	#15667982	C₂²	1	2	yes	complemented
90	#15667980	C₂²	1	2	yes	—
91	#15667980	C₂²	1	1	yes	characteristic
92	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
93	#15667977	C₂²	1	1	yes	characteristic, complemented
94	C₄×D₃₅₆	C₂²	1	2	yes	complemented
95	C₄×D₃₅₆	C₂²	1	2	yes	complemented
96	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
97	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₃₅₆	C₂²	1	2	yes	complemented
99	#15667974	C₂²	1	2	yes	complemented
100	#15667974	C₂²	1	1	yes	characteristic, complemented
101	#15667974	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
104	#15667972	C₂²	1	2	yes	complemented
105	#15667970	C₂²	1	1	yes	characteristic, complemented
106	#15667970	C₂²	1	2	yes	complemented
107	#15667970	C₂²	1	1	yes	characteristic, complemented
108	#15667969	C₂²	1	1	yes	characteristic, complemented
109	#15667969	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₈₉	C₂²	1	2	yes	complemented
114	#126×C₈₉	C₂²	1	2	yes	complemented
115	#124×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	#117×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	1	yes	characteristic
125	#13083575	—	4	2	no	—
126	#13083574	—	4	2	no	—
127	#13083574	—	4	2	no	—
128	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
129	C₂×Dic₁₇₈	C₂³	1	2	yes	—
130	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₇₈	C₂³	1	2	yes	—
132	Q₈×D₈₉	—	4	2	no	—
133	C₂×D₃₅₆	—	4	2	no	—
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	2	yes	—
139	C₂×D₃₅₆	C₂³	1	2	yes	—
140	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
141	C₂×D₃₅₆	C₂³	1	2	yes	—
142	C₂×D₃₅₆	C₂³	1	2	yes	—
143	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
144	C₂×D₃₅₆	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
151	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₈₉	—	4	2	no	—
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	2	yes	—
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	C₂×C₄×D₈₉	C₂³	1	2	yes	—
161	C₂×C₄×D₈₉	C₂³	1	2	yes	—
162	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
163	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
164	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
165	C₄⋊Dic₈₉	C₂³	1	2	yes	—
166	C₄⋊Dic₈₉	C₂³	1	2	yes	—
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	#13083553	C₂³	1	2	yes	—
174	#13083553	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
178	#13083551	C₂³	1	2	yes	—
179	#13083551	C₂³	1	1	yes	characteristic
180	#13083551	C₂³	1	2	yes	—
181	#13083551	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
188	#13083551	C₂³	1	1	yes	characteristic
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	1	yes	characteristic
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	#13083551	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×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	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₄⋊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	2	yes	—
217	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
222	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₄²×C₈₉	C₂³	1	2	yes	—
225	C₄²×C₈₉	C₂³	1	1	yes	characteristic
226	C₄²×C₈₉	C₂³	1	2	yes	—
227	C₄²×C₈₉	C₂³	1	2	yes	—
228	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
229	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₈₉	—	4	1	no	—
231	C₂²×D₈₉	—	4	1	no	—
232	C₂²×D₈₉	—	4	1	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	1	yes	characteristic
238	C₂²×D₈₉	C₂⁴	1	2	yes	—
239	C₂²×D₈₉	C₂⁴	1	2	yes	—
240	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
241	Q₈×C₈₉	—	2	2	no	—
242	Q₈×C₈₉	—	4	2	no	—
243	D₄×C₈₉	—	4	1	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
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	2	yes	—
254	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
255	C₂²⋊D₈₉	—	4	1	no	—
256	C₂²⋊D₈₉	—	4	2	no	—
257	C₂²⋊D₈₉	—	4	1	no	—
258	C₂²⋊D₈₉	—	4	2	no	—
259	C₂²⋊D₈₉	—	4	1	no	—
260	C₂²⋊D₈₉	—	4	1	no	—
261	C₂×Dic₈₉	—	4	1	no	—
262	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₈₉	C₂⁴	1	2	yes	—
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	2	yes	—
268	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
269	D₃₅₆	—	2	2	no	—
270	D₃₅₆	—	2	2	no	—
271	D₃₅₆	—	4	2	no	—
272	D₃₅₆	—	4	2	no	—
273	D₃₅₆	—	4	2	no	—
274	D₃₅₆	—	4	1	no	—
275	D₃₅₆	—	4	2	no	—
276	D₃₅₆	—	4	2	no	—
277	D₃₅₆	—	4	2	no	—
278	D₃₅₆	—	4	1	no	—
279	D₃₅₆	—	4	2	no	—
280	C₄×D₈₉	—	2	2	no	—
281	C₄×D₈₉	—	2	2	no	—
282	C₄×D₈₉	—	2	2	no	—
283	C₄×D₈₉	—	4	1	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	C₄×D₈₉	—	4	2	no	—
289	C₄×D₈₉	—	4	2	no	—
290	Dic₁₇₈	—	2	2	no	—
291	Dic₁₇₈	—	4	2	no	—
292	Dic₁₇₈	—	4	2	no	—
293	Dic₁₇₈	—	4	1	no	—
294	C₂²×C₈₉	—	2	1	no	—
295	C₂²×C₈₉	—	2	1	no	—
296	C₂²×C₈₉	—	2	1	no	—
297	C₂²×C₈₉	—	2	1	no	—
298	C₂²×C₈₉	—	2	1	no	—
299	C₂²×C₈₉	—	2	1	no	—
300	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
301	C₂×D₈₉	—	2	1	no	—
302	C₂×D₈₉	—	2	1	no	—
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	2	no	—
305	C₂×D₈₉	—	2	2	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	1	no	—
311	C₂×D₈₉	—	2	1	no	—
312	C₂×D₈₉	—	2	1	no	—
313	C₂×D₈₉	—	2	2	no	—
314	C₂×D₈₉	—	2	1	no	—
315	C₂×D₈₉	—	2	2	no	—
316	C₂×D₈₉	—	4	4	no	—
317	C₂×D₈₉	—	8	4	no	—
318	C₄×C₈₉	—	2	2	no	—
319	C₄×C₈₉	—	2	1	no	—
320	C₄×C₈₉	—	2	1	no	—
321	C₄×C₈₉	—	2	2	no	—
322	C₄×C₈₉	—	2	1	no	—
323	C₄×C₈₉	—	2	2	no	—
324	C₄×C₈₉	—	2	2	no	—
325	C₄×C₈₉	—	2	1	no	—
326	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
327	Dic₈₉	—	2	2	no	—
328	Dic₈₉	—	2	1	no	—
329	Dic₈₉	—	2	1	no	—
330	Dic₈₉	—	2	1	no	—
331	Dic₈₉	—	2	1	no	—
332	Dic₈₉	—	2	2	no	—
333	Dic₈₉	—	2	1	no	—
334	C₂×C₈₉	—	4	1	no	—
335	C₂×C₈₉	—	4	1	no	—
336	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₈₉	#585	1	1	yes	characteristic
338	C₂×C₈₉	#585	1	1	yes	characteristic
339	D₈₉	—	4	1	no	—
340	D₈₉	—	4	1	no	—
341	D₈₉	—	4	1	no	—
342	D₈₉	—	4	2	no	—
343	D₈₉	—	4	2	no	—
344	#3540	—	89	1	no	maximal, Sylow
345	C₈₉	#3540	1	1	yes	characteristic, complemented, Sylow
346	H(3,𝔽₄)	—	89	2	no	—
347	#560	—	89	2	no	—
348	#559	—	89	2	no	—
349	#556	—	89	1	no	—
350	#556	D₈₉	1	1	yes	characteristic, complemented
351	#555	—	89	1	no	—
352	#555	—	89	1	no	—
353	#551	—	89	2	no	—
354	#548	—	89	1	no	—
355	#548	—	89	1	no	—
356	#546	—	89	1	no	—
357	#546	—	89	1	no	—
358	#542	—	89	1	no	—
359	#542	—	89	2	no	—
360	#542	—	89	1	no	—
361	#542	—	89	2	no	—
362	#538	—	89	2	no	—
363	#538	—	89	2	no	—
364	#536	—	89	1	no	—
365	#535	—	89	1	no	—
366	#525	—	89	1	no	—
367	#525	—	89	1	no	—
368	#525	—	89	1	no	—
369	C₂×#41	—	89	1	no	—
370	C₂×#41	—	89	1	no	—
371	C₂×#41	—	89	1	no	—
372	C₂²×Q₈	—	89	1	no	—
373	C₂²×D₄	—	89	1	no	—
374	C₂³×C₄	—	89	1	no	—
375	C₄⋊Q₈	—	89	2	no	—
376	C₄⋊Q₈	—	89	1	no	—
377	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
378	#127	—	89	2	no	—
379	#126	—	89	2	no	—
380	#126	—	89	2	no	—
381	#126	—	89	2	no	—
382	#126	—	89	2	no	—
383	#126	C₂×D₈₉	1	2	yes	complemented
384	#126	C₂×D₈₉	1	2	yes	complemented
385	#124	—	89	2	no	—
386	#124	—	89	1	no	—
387	#124	—	89	2	no	—
388	#124	—	89	2	no	—
389	#124	—	89	2	no	—
390	#124	—	89	2	no	—
391	#124	—	89	2	no	—
392	#124	—	89	2	no	—
393	#124	—	89	2	no	—
394	#124	—	89	2	no	—
395	#124	—	89	1	no	—
396	#124	—	89	2	no	—
397	#124	—	89	2	no	—
398	#124	C₂×D₈₉	1	2	yes	—
399	#123	—	89	2	no	—
400	#123	—	89	1	no	—
401	#123	—	89	2	no	—
402	#123	—	89	2	no	—
403	#123	—	89	2	no	—
404	#123	—	89	2	no	—
405	#123	—	89	2	no	—
406	#123	—	89	2	no	—
407	#123	—	89	1	no	—
408	#123	—	89	2	no	—
409	C₂²⋊Q₈	—	89	1	no	—
410	C₂²⋊Q₈	—	89	2	no	—
411	C₂²⋊Q₈	—	89	1	no	—
412	C₂²⋊Q₈	—	89	1	no	—
413	C₂²⋊Q₈	—	89	1	no	—
414	C₂²⋊Q₈	—	89	1	no	—
415	C₂²⋊Q₈	—	89	2	no	—
416	C₂²⋊Q₈	—	89	2	no	—
417	C₂²⋊Q₈	—	89	2	no	—
418	C₂²⋊Q₈	—	89	1	no	—
419	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
421	#121	—	89	1	no	—
422	#121	—	89	1	no	—
423	#121	—	89	1	no	—
424	#121	—	89	1	no	—
425	#121	—	89	1	no	—
426	#121	—	89	2	no	—
427	#121	—	89	1	no	—
428	#121	—	89	1	no	—
429	#121	—	89	2	no	—
430	#121	—	89	2	no	—
431	#121	—	89	1	no	—
432	#121	—	89	2	no	—
433	#121	—	89	2	no	—
434	#121	—	89	2	no	—
435	#120	—	89	1	no	—
436	#120	—	89	2	no	—
437	#120	—	89	1	no	—
438	#120	—	89	2	no	—
439	#120	—	89	2	no	—
440	#120	—	89	2	no	—
441	#120	—	89	2	no	—
442	#120	—	89	2	no	—
443	C₄×Q₈	—	89	1	no	—
444	C₄×Q₈	—	89	2	no	—
445	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
446	C₄×Q₈	C₂×D₈₉	1	2	yes	complemented
447	C₄×D₄	—	89	1	no	—
448	C₄×D₄	—	89	1	no	—
449	C₄×D₄	—	89	2	no	—
450	C₄×D₄	—	89	2	no	—
451	C₄×D₄	—	89	1	no	—
452	C₄×D₄	—	89	2	no	—
453	C₄×D₄	—	89	2	no	—
454	C₄×D₄	—	89	1	no	—
455	C₄×D₄	—	89	2	no	—
456	C₄×D₄	—	89	2	no	—
457	C₄×D₄	—	89	1	no	—
458	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
459	#117	—	89	1	no	—
460	#117	—	89	1	no	—
461	#117	—	89	2	no	—
462	#117	—	89	1	no	—
463	#117	—	89	2	no	—
464	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
465	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
466	C₂×C₂²⋊C₄	—	89	2	no	—
467	C₂×C₂²⋊C₄	—	89	2	no	—
468	C₂⁴	—	89	2	no	—
469	C₂⁴	—	89	1	no	—
470	#41	—	356	2	no	—
471	#41	—	356	2	no	—
472	#41	—	356	2	no	—
473	C₂×Q₈	—	89	2	no	—
474	C₂×Q₈	—	89	2	no	—
475	C₂×Q₈	—	89	1	no	—
476	C₂×Q₈	—	89	1	no	—
477	C₂×Q₈	—	356	2	no	—
478	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
479	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
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	—	89	1	no	—
485	C₂×D₄	—	89	2	no	—
486	C₂×D₄	—	89	2	no	—
487	C₂×D₄	—	89	2	no	—
488	C₂×D₄	—	89	2	no	—
489	C₂×D₄	—	89	1	no	—
490	C₂×D₄	—	89	2	no	—
491	C₂×D₄	—	89	2	no	—
492	C₂×D₄	—	89	2	no	—
493	C₂×D₄	—	89	1	no	—
494	C₂×D₄	—	89	2	no	—
495	C₂×D₄	—	89	1	no	—
496	C₂×D₄	—	89	1	no	—
497	C₂×D₄	—	356	2	no	—
498	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
499	C₂²×C₄	—	89	1	no	—
500	C₂²×C₄	—	89	2	no	—
501	C₂²×C₄	—	89	2	no	—
502	C₂²×C₄	—	89	2	no	—
503	C₂²×C₄	—	89	2	no	—
504	C₂²×C₄	—	89	1	no	—
505	C₂²×C₄	—	89	2	no	—
506	C₂²×C₄	—	89	1	no	—
507	C₂²×C₄	—	89	1	no	—
508	C₂²×C₄	—	89	1	no	—
509	C₂²×C₄	—	89	1	no	—
510	C₂²×C₄	—	356	2	no	—
511	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
513	C₄⋊C₄	—	89	1	no	—
514	C₄⋊C₄	—	89	1	no	—
515	C₄⋊C₄	—	89	1	no	—
516	C₄⋊C₄	—	89	1	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	89	2	no	—
519	C₄⋊C₄	—	89	2	no	—
520	C₄⋊C₄	—	89	1	no	—
521	C₄⋊C₄	—	89	2	no	—
522	C₄⋊C₄	—	89	2	no	—
523	C₄⋊C₄	—	89	2	no	—
524	C₄⋊C₄	—	89	2	no	—
525	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
530	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
532	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
533	C₂²⋊C₄	—	89	1	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	1	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	1	no	—
544	C₂²⋊C₄	—	89	1	no	—
545	C₂²⋊C₄	—	89	2	no	—
546	C₂²⋊C₄	—	89	1	no	—
547	C₂²⋊C₄	—	89	1	no	—
548	C₂²⋊C₄	—	89	1	no	—
549	C₂²⋊C₄	—	89	2	no	—
550	C₂²⋊C₄	—	89	2	no	—
551	C₂²⋊C₄	—	89	2	no	—
552	C₂²⋊C₄	—	89	2	no	—
553	C₂²⋊C₄	—	89	2	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	—	89	2	no	—
556	C₂²⋊C₄	—	89	1	no	—
557	C₂²⋊C₄	—	89	2	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
563	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
564	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
565	C₄²	—	89	2	no	—
566	C₄²	—	89	2	no	—
567	C₄²	—	89	1	no	—
568	C₄²	—	89	2	no	—
569	C₄²	C₂²×D₈₉	1	2	yes	—
570	C₄²	C₂²×D₈₉	1	1	yes	characteristic
571	C₄²	C₂²×D₈₉	1	2	yes	—
572	C₄²	C₂²×D₈₉	1	2	yes	—
573	C₂³	—	89	1	no	—
574	C₂³	—	89	1	no	—
575	C₂³	—	89	2	no	—
576	C₂³	—	89	2	no	—
577	C₂³	—	89	1	no	—
578	C₂³	—	356	1	no	—
579	C₂³	—	356	1	no	—
580	C₂³	—	356	1	no	—
581	C₂³	—	356	2	no	—
582	C₂³	—	356	2	no	—
583	C₂³	—	356	2	no	—
584	C₂³	C₂³×D₈₉	1	1	yes	characteristic
585	C₂³	C₂³×D₈₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	356	2	no	—
589	Q₈	—	356	2	no	—
590	Q₈	—	356	1	no	—
591	Q₈	—	178	2	no	—
592	D₄	—	4	1	no	—
593	D₄	—	356	2	no	—
594	D₄	—	356	2	no	—
595	D₄	—	356	2	no	—
596	D₄	—	356	1	no	—
597	D₄	—	356	2	no	—
598	D₄	—	356	2	no	—
599	D₄	—	356	2	no	—
600	D₄	—	356	1	no	—
601	D₄	—	356	2	no	—
602	D₄	—	356	1	no	—
603	D₄	—	356	2	no	—
604	D₄	—	356	1	no	—
605	D₄	—	356	1	no	—
606	D₄	—	356	2	no	—
607	D₄	—	356	1	no	—
608	D₄	—	178	2	no	—
609	D₄	—	178	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	89	1	no	—
613	C₂×C₄	—	89	2	no	—
614	C₂×C₄	—	89	1	no	—
615	C₂×C₄	—	89	1	no	—
616	C₂×C₄	—	89	1	no	—
617	C₂×C₄	—	89	2	no	—
618	C₂×C₄	—	89	1	no	—
619	C₂×C₄	—	356	2	no	—
620	C₂×C₄	—	356	2	no	—
621	C₂×C₄	—	356	1	no	—
622	C₂×C₄	—	356	1	no	—
623	C₂×C₄	—	356	2	no	—
624	C₂×C₄	—	356	2	no	—
625	C₂×C₄	—	356	2	no	—
626	C₂×C₄	—	356	1	no	—
627	C₂×C₄	—	178	2	no	—
628	C₂×C₄	—	178	2	no	—
629	C₂×C₄	—	178	2	no	—
630	C₂×C₄	C₂³×D₈₉	1	2	yes	—
631	C₂×C₄	C₂³×D₈₉	1	2	yes	—
632	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₈₉	1	2	yes	—
634	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₈₉	1	2	yes	—
638	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	356	4	no	—
646	C₂²	—	178	1	no	—
647	C₂²	—	178	1	no	—
648	C₂²	—	178	1	no	—
649	C₂²	—	178	2	no	—
650	C₂²	—	178	2	no	—
651	C₂²	—	178	2	no	—
652	C₂²	—	178	1	no	—
653	C₂²	—	178	1	no	—
654	C₂²	—	178	1	no	—
655	C₂²	—	178	2	no	—
656	C₂²	—	178	2	no	—
657	C₂²	—	178	1	no	—
658	C₂²	—	178	1	no	—
659	C₂²	—	178	1	no	—
660	C₂²	—	178	2	no	—
661	C₂²	—	712	4	no	—
662	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	2	no	—
671	C₄	—	178	1	no	—
672	C₄	—	178	1	no	—
673	C₄	—	178	2	no	—
674	C₄	—	178	1	no	—
675	C₄	—	178	1	no	—
676	C₄	—	178	2	no	—
677	C₄	—	178	1	no	—
678	C₄	#15668058	1	2	yes	—
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	356	1	no	—
682	C₂	—	356	1	no	—
683	C₂	—	356	1	no	—
684	C₂	—	356	2	no	—
685	C₂	—	356	2	no	—
686	C₂	C₂×#15668058	1	1	yes	characteristic
687	C₂	#19152434	1	1	yes	characteristic
688	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#556×C₈₉	C₂
hypercenter	#556	D₈₉
hypocenter	C₈₉	#3540
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #19152340	C₂	semidirect
2. #19152339	C₂	semidirect
3. #19152333	C₂	semidirect
4. #19152316	C₂	semidirect
5. #19152314	C₂	semidirect
6. #19152311	C₂	semidirect
7. #19152273	C₂	semidirect
8. #19152260	C₂	semidirect
9. #19152258	C₂	semidirect
10. #19152244	C₂	semidirect
11. #19152239	C₂	semidirect
12. #19152222	C₂	semidirect
13. #19152220	C₂	semidirect
14. #19152220	C₂	semidirect
15. #19152214	C₂	semidirect
16. #19152187	C₂	semidirect
17. #19152182	C₂	semidirect
18. #19152171	C₂	semidirect
19. #19152167	C₂	semidirect
20. #19152111	C₂	semidirect
21. #19152110	C₂	semidirect
22. #19152107	C₂	semidirect
23. #556×C₈₉	C₂	semidirect
27. C₂×Q₈×D₈₉	C₂²	semidirect
28. C₂²×D₃₅₆	C₂²	semidirect
29. C₂²×C₄×D₈₉	C₂²	semidirect
30. #15668011	C₂²	semidirect
31. #15668011	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668006	C₂²	semidirect
35. #15668006	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668001	C₂²	semidirect
38. #15668001	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15668001	C₂²	semidirect
41. #15668000	C₂²	semidirect
42. #15668000	C₂²	semidirect
43. #15668000	C₂²	semidirect
44. #15668000	C₂²	semidirect
45. #15668000	C₂²	semidirect
48. #15667998	C₂²	semidirect
49. #15667998	C₂²	semidirect
50. #15667997	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667997	C₂²	semidirect
54. #15667997	C₂²	semidirect
55. #15667997	C₂²	semidirect
56. #15667997	C₂²	semidirect
57. #15667996	C₂²	semidirect
59. #15667994	C₂²	semidirect
60. #15667992	C₂²	semidirect
61. #15667992	C₂²	semidirect
62. #15667992	C₂²	semidirect
63. #15667991	C₂²	semidirect
64. #15667990	C₂²	semidirect
65. #15667990	C₂²	semidirect
66. #15667990	C₂²	semidirect
67. #15667989	C₂²	semidirect
68. #15667988	C₂²	semidirect
69. #15667988	C₂²	semidirect
74. #15667987	C₂²	semidirect
75. #15667987	C₂²	semidirect
76. #15667987	C₂²	semidirect
77. #15667987	C₂²	semidirect
81. #15667985	C₂²	semidirect
82. #15667985	C₂²	semidirect
86. #15667982	C₂²	semidirect
87. #15667982	C₂²	semidirect
88. #15667982	C₂²	semidirect
89. #15667982	C₂²	semidirect
92. C₄×Dic₁₇₈	C₂²	semidirect
93. #15667977	C₂²	semidirect
94. C₄×D₃₅₆	C₂²	semidirect
95. C₄×D₃₅₆	C₂²	semidirect
96. C₄×D₃₅₆	C₂²	semidirect
97. C₄×D₃₅₆	C₂²	semidirect
98. C₄×D₃₅₆	C₂²	semidirect
99. #15667974	C₂²	semidirect
100. #15667974	C₂²	semidirect
101. #15667974	C₂²	semidirect
103. C₄×C₂²⋊D₈₉	C₂²	semidirect
104. #15667972	C₂²	semidirect
105. #15667970	C₂²	semidirect
106. #15667970	C₂²	semidirect
107. #15667970	C₂²	semidirect
108. #15667969	C₂²	semidirect
109. #15667969	C₂²	semidirect
110. C₂²⋊C₄×D₈₉	C₂²	semidirect
111. C₂²⋊C₄×D₈₉	C₂²	semidirect
112. C₄⋊Q₈×C₈₉	C₂²	semidirect
113. #126×C₈₉	C₂²	semidirect
114. #126×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
119. C₄×Q₈×C₈₉	C₂²	semidirect
121. #117×C₈₉	C₂²	semidirect
122. #117×C₈₉	C₂²	semidirect
345. C₈₉	#3540	semidirect
350. #556	D₈₉	semidirect
377. C₄⋊Q₈	C₂×D₈₉	semidirect
383. #126	C₂×D₈₉	semidirect
384. #126	C₂×D₈₉	semidirect
419. C₂²⋊Q₈	C₂×D₈₉	semidirect
420. C₂²⋊Q₈	C₂×D₈₉	semidirect
445. C₄×Q₈	C₂×D₈₉	semidirect
446. C₄×Q₈	C₂×D₈₉	semidirect
464. #117	C₂×D₈₉	semidirect
465. #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
#19152340	2
#19152339	2
#19152333	2
#19152316	2
#19152314	2
#19152311	2
#19152273	2
#19152260	2
#19152258	2
#19152244	2
#19152239	2
#19152222	2
#19152220	2
#19152214	2
#19152187	2
#19152182	2
#19152171	2
#19152167	2
#19152111	2
#19152110	2
#19152107	2
#556×C₈₉	2
#3540	89