Subgroups — #26034526

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	#19152336	C₂	1	2	yes	maximal, complemented
3	#19152331	C₂	1	2	yes	maximal, complemented
4	#19152321	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152319	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152313	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152312	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152275	C₂	1	2	yes	maximal, complemented
9	#19152259	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152236	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152220	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152218	C₂	1	2	yes	maximal, complemented
14	#19152217	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152212	C₂	1	2	yes	maximal, complemented
16	#19152181	C₂	1	2	yes	maximal, complemented
17	#19152180	C₂	1	2	yes	maximal, complemented
18	#19152172	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152164	C₂	1	1	yes	maximal, characteristic, complemented
20	#19152111	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152105	C₂	1	1	yes	maximal, characteristic, complemented
23	#548×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×D₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
28	#15668012	C₂²	1	1	yes	characteristic, complemented
29	#15668011	C₂²	1	1	yes	characteristic, complemented
30	#15668010	C₂²	1	2	yes	complemented
31	#15668008	C₂²	1	2	yes	—
32	#15668007	C₂²	1	2	yes	complemented
33	#15668007	C₂²	1	2	yes	complemented
34	#15668007	C₂²	1	2	yes	complemented
35	#15668006	C₂²	1	2	yes	complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668001	C₂²	1	2	yes	—
39	#15668001	C₂²	1	2	yes	complemented
40	#15668001	C₂²	1	1	yes	characteristic, complemented
41	#15668000	C₂²	1	2	yes	—
42	#15668000	C₂²	1	2	yes	complemented
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	#15667998	C₂²	1	2	yes	complemented
49	#15667998	C₂²	1	2	yes	complemented
50	#15667997	C₂²	1	1	yes	characteristic
51	#15667997	C₂²	1	2	yes	complemented
52	#15667997	C₂²	1	2	yes	complemented
53	#15667996	C₂²	1	2	yes	complemented
54	#15667995	C₂²	1	2	yes	complemented
55	#15667995	C₂²	1	2	yes	complemented
56	#15667995	C₂²	1	2	yes	complemented
57	#15667994	C₂²	1	2	yes	complemented
58	#15667994	C₂²	1	1	yes	characteristic, complemented
59	#15667993	C₂²	1	2	yes	complemented
60	#15667990	C₂²	1	2	yes	complemented
61	#15667990	C₂²	1	1	yes	characteristic, complemented
62	#15667989	C₂²	1	2	yes	complemented
63	#15667989	C₂²	1	1	yes	characteristic, complemented
64	#15667988	C₂²	1	1	yes	characteristic, complemented
65	#15667988	C₂²	1	1	yes	characteristic, complemented
66	#15667988	C₂²	1	1	yes	characteristic, complemented
67	#15667988	C₂²	1	1	yes	characteristic, complemented
68	#15667988	C₂²	1	2	yes	complemented
69	#15667988	C₂²	1	1	yes	characteristic, complemented
70	#15667987	C₂²	1	1	yes	characteristic
71	#15667986	C₂²	1	1	yes	characteristic
72	#15667986	C₂²	1	1	yes	characteristic, complemented
73	#15667986	C₂²	1	2	yes	complemented
74	#15667985	C₂²	1	1	yes	characteristic
75	#15667985	C₂²	1	2	yes	—
76	#15667984	C₂²	1	1	yes	characteristic
77	#15667984	C₂²	1	2	yes	—
78	#15667984	C₂²	1	2	yes	complemented
79	#15667983	C₂²	1	1	yes	characteristic
80	#15667983	C₂²	1	1	yes	characteristic
81	#15667983	C₂²	1	2	yes	complemented
82	#15667982	C₂²	1	2	yes	—
83	#15667982	C₂²	1	2	yes	—
84	#15667982	C₂²	1	1	yes	characteristic
85	#15667982	C₂²	1	2	yes	complemented
86	#15667980	C₂²	1	2	yes	—
87	#15667980	C₂²	1	2	yes	complemented
88	#15667980	C₂²	1	1	yes	characteristic, complemented
89	#15667980	C₂²	1	2	yes	complemented
90	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
91	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
92	#15667977	C₂²	1	2	yes	complemented
93	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
94	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
95	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
96	#15667974	C₂²	1	2	yes	complemented
97	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
99	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
100	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
102	#15667972	C₂²	1	2	yes	complemented
103	#15667971	C₂²	1	1	yes	characteristic, complemented
104	#15667971	C₂²	1	1	yes	characteristic, 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	#15667968	C₂²	1	2	yes	complemented
110	C₂×#13083551	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
112	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
113	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
114	#124×C₈₉	C₂²	1	2	yes	complemented
115	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
118	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₈₉	C₂²	1	2	yes	complemented
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
122	C₄×D₄×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	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×Dic₁₇₈	C₂³	1	2	yes	—
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
131	C₂×D₃₅₆	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	2	yes	—
136	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
144	D₄×D₈₉	—	4	2	no	—
145	C₂²×Dic₈₉	C₂³	1	2	yes	—
146	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₈₉	—	4	2	no	—
148	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂³	1	2	yes	—
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	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
156	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
157	C₄⋊Dic₈₉	C₂³	1	2	yes	—
158	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
159	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
160	C₄⋊Dic₈₉	C₂³	1	2	yes	—
161	#13083553	C₂³	1	1	yes	characteristic
162	#13083553	C₂³	1	2	yes	—
163	#13083553	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	2	yes	—
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	2	yes	—
170	#13083553	C₂³	1	2	yes	—
171	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
172	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
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	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	1	yes	characteristic
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	1	yes	characteristic
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
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	2	yes	—
202	C₄×Dic₈₉	C₂³	1	2	yes	—
203	#41×C₈₉	—	4	2	no	—
204	C₂×Q₈×C₈₉	—	4	2	no	—
205	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
206	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
208	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₈₉	C₂³	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
215	C₂²×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	2	yes	—
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	2	yes	—
223	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
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	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	—	4	1	no	—
232	C₂²×D₈₉	—	4	1	no	—
233	C₂²×D₈₉	—	4	1	no	—
234	C₂²×D₈₉	—	4	2	no	—
235	C₂²×D₈₉	—	4	2	no	—
236	C₂²×D₈₉	—	4	2	no	—
237	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
238	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
239	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×D₈₉	C₂⁴	1	2	yes	—
241	Q₈×C₈₉	—	2	2	no	—
242	Q₈×C₈₉	—	2	2	no	—
243	Q₈×C₈₉	—	4	2	no	—
244	D₄×C₈₉	—	2	2	no	—
245	D₄×C₈₉	—	4	2	no	—
246	D₄×C₈₉	—	4	1	no	—
247	D₄×C₈₉	—	4	2	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	2	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	—	4	2	no	—
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	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂²⋊D₈₉	—	4	1	no	—
262	C₂²⋊D₈₉	—	4	2	no	—
263	C₂²⋊D₈₉	—	4	2	no	—
264	C₂²⋊D₈₉	—	4	2	no	—
265	C₂²⋊D₈₉	—	4	2	no	—
266	C₂²⋊D₈₉	—	4	1	no	—
267	C₂²⋊D₈₉	—	4	1	no	—
268	C₂²⋊D₈₉	—	4	1	no	—
269	C₂×Dic₈₉	—	4	1	no	—
270	C₂×Dic₈₉	—	4	2	no	—
271	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₈₉	C₂⁴	1	2	yes	—
273	C₂×Dic₈₉	C₂⁴	1	2	yes	—
274	C₂×Dic₈₉	C₂⁴	1	2	yes	—
275	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
279	D₃₅₆	—	2	2	no	—
280	D₃₅₆	—	4	1	no	—
281	D₃₅₆	—	4	2	no	—
282	D₃₅₆	—	4	1	no	—
283	D₃₅₆	—	4	2	no	—
284	C₄×D₈₉	—	2	2	no	—
285	C₄×D₈₉	—	2	2	no	—
286	C₄×D₈₉	—	2	2	no	—
287	C₄×D₈₉	—	4	1	no	—
288	C₄×D₈₉	—	4	1	no	—
289	C₄×D₈₉	—	4	2	no	—
290	C₄×D₈₉	—	4	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	2	no	—
297	C₂²×C₈₉	—	2	2	no	—
298	C₂²×C₈₉	—	2	1	no	—
299	C₂²×C₈₉	—	2	1	no	—
300	C₂²×C₈₉	—	2	1	no	—
301	C₂²×C₈₉	—	2	2	no	—
302	C₂²×C₈₉	—	2	1	no	—
303	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
304	C₂×D₈₉	—	2	1	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	1	no	—
307	C₂×D₈₉	—	2	2	no	—
308	C₂×D₈₉	—	2	2	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	1	no	—
314	C₂×D₈₉	—	2	2	no	—
315	C₂×D₈₉	—	2	1	no	—
316	C₂×D₈₉	—	4	4	no	—
317	C₂×D₈₉	—	8	4	no	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	1	no	—
320	C₄×C₈₉	—	2	2	no	—
321	C₄×C₈₉	—	2	2	no	—
322	C₄×C₈₉	—	2	1	no	—
323	C₄×C₈₉	—	2	2	no	—
324	C₄×C₈₉	—	2	1	no	—
325	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
326	Dic₈₉	—	2	1	no	—
327	Dic₈₉	—	2	1	no	—
328	Dic₈₉	—	2	1	no	—
329	Dic₈₉	—	2	1	no	—
330	Dic₈₉	—	2	2	no	—
331	Dic₈₉	—	2	2	no	—
332	Dic₈₉	—	2	2	no	—
333	Dic₈₉	—	2	1	no	—
334	C₂×C₈₉	—	4	1	no	—
335	C₂×C₈₉	—	4	2	no	—
336	C₂×C₈₉	—	4	1	no	—
337	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₈₉	#585	1	1	yes	characteristic
339	C₂×C₈₉	#585	1	1	yes	characteristic
340	D₈₉	—	4	1	no	—
341	D₈₉	—	4	1	no	—
342	D₈₉	—	4	2	no	—
343	D₈₉	—	4	1	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	—	89	1	no	—
351	#555	—	89	1	no	—
352	#555	—	89	1	no	—
353	#551	—	89	2	no	—
354	#548	—	89	1	no	—
355	#548	D₈₉	1	1	yes	characteristic, complemented
356	#546	—	89	1	no	—
357	#546	—	89	1	no	—
358	#542	—	89	2	no	—
359	#542	—	89	1	no	—
360	#542	—	89	2	no	—
361	#542	—	89	1	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	C₂×D₈₉	1	1	yes	characteristic
372	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
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	—	89	2	no	—
384	#126	—	89	2	no	—
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	2	no	—
396	#124	—	89	2	no	—
397	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
398	#124	C₂×D₈₉	1	2	yes	complemented
399	#123	—	89	2	no	—
400	#123	—	89	2	no	—
401	#123	—	89	2	no	—
402	#123	—	89	2	no	—
403	#123	—	89	2	no	—
404	#123	—	89	1	no	—
405	#123	—	89	2	no	—
406	#123	—	89	1	no	—
407	#123	—	89	2	no	—
408	#123	—	89	2	no	—
409	C₂²⋊Q₈	—	89	1	no	—
410	C₂²⋊Q₈	—	89	1	no	—
411	C₂²⋊Q₈	—	89	1	no	—
412	C₂²⋊Q₈	—	89	1	no	—
413	C₂²⋊Q₈	—	89	1	no	—
414	C₂²⋊Q₈	—	89	2	no	—
415	C₂²⋊Q₈	—	89	1	no	—
416	C₂²⋊Q₈	—	89	2	no	—
417	C₂²⋊Q₈	—	89	1	no	—
418	C₂²⋊Q₈	—	89	2	no	—
419	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
420	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
421	#121	—	89	1	no	—
422	#121	—	89	1	no	—
423	#121	—	89	1	no	—
424	#121	—	89	2	no	—
425	#121	—	89	2	no	—
426	#121	—	89	2	no	—
427	#121	—	89	1	no	—
428	#121	—	89	1	no	—
429	#121	—	89	2	no	—
430	#121	—	89	1	no	—
431	#121	—	89	1	no	—
432	#121	—	89	2	no	—
433	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
434	#121	C₂×D₈₉	1	2	yes	complemented
435	#120	—	89	2	no	—
436	#120	—	89	1	no	—
437	#120	—	89	2	no	—
438	#120	—	89	2	no	—
439	#120	—	89	1	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	—	89	2	no	—
446	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
447	C₄×D₄	—	89	1	no	—
448	C₄×D₄	—	89	1	no	—
449	C₄×D₄	—	89	2	no	—
450	C₄×D₄	—	89	1	no	—
451	C₄×D₄	—	89	2	no	—
452	C₄×D₄	—	89	2	no	—
453	C₄×D₄	—	89	2	no	—
454	C₄×D₄	—	89	2	no	—
455	C₄×D₄	—	89	1	no	—
456	C₄×D₄	—	89	1	no	—
457	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
458	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
459	#117	—	89	1	no	—
460	#117	—	89	1	no	—
461	#117	—	89	1	no	—
462	#117	—	89	1	no	—
463	#117	—	89	2	no	—
464	#117	—	89	2	no	—
465	#117	—	89	1	no	—
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	—	4	2	no	—
471	#41	—	356	2	no	—
472	#41	—	356	2	no	—
473	C₂×Q₈	—	4	2	no	—
474	C₂×Q₈	—	89	2	no	—
475	C₂×Q₈	—	89	2	no	—
476	C₂×Q₈	—	89	1	no	—
477	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
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	2	no	—
483	C₂×D₄	—	89	2	no	—
484	C₂×D₄	—	89	1	no	—
485	C₂×D₄	—	89	2	no	—
486	C₂×D₄	—	89	1	no	—
487	C₂×D₄	—	89	1	no	—
488	C₂×D₄	—	89	2	no	—
489	C₂×D₄	—	89	1	no	—
490	C₂×D₄	—	89	2	no	—
491	C₂×D₄	—	89	1	no	—
492	C₂×D₄	—	89	2	no	—
493	C₂×D₄	—	89	1	no	—
494	C₂×D₄	—	356	2	no	—
495	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
497	C₂×D₄	C₂²×D₈₉	1	2	yes	—
498	C₂×D₄	C₂²×D₈₉	1	2	yes	—
499	C₂²×C₄	—	89	2	no	—
500	C₂²×C₄	—	89	1	no	—
501	C₂²×C₄	—	89	2	no	—
502	C₂²×C₄	—	89	2	no	—
503	C₂²×C₄	—	89	1	no	—
504	C₂²×C₄	—	89	1	no	—
505	C₂²×C₄	—	89	1	no	—
506	C₂²×C₄	—	89	1	no	—
507	C₂²×C₄	—	89	1	no	—
508	C₂²×C₄	—	356	2	no	—
509	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
512	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
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	1	no	—
519	C₄⋊C₄	—	89	2	no	—
520	C₄⋊C₄	—	89	2	no	—
521	C₄⋊C₄	—	89	2	no	—
522	C₄⋊C₄	—	89	1	no	—
523	C₄⋊C₄	—	89	1	no	—
524	C₄⋊C₄	—	89	2	no	—
525	C₄⋊C₄	—	89	2	no	—
526	C₄⋊C₄	—	89	2	no	—
527	C₄⋊C₄	—	89	2	no	—
528	C₄⋊C₄	—	89	2	no	—
529	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	2	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	2	no	—
536	C₂²⋊C₄	—	89	1	no	—
537	C₂²⋊C₄	—	89	1	no	—
538	C₂²⋊C₄	—	89	2	no	—
539	C₂²⋊C₄	—	89	2	no	—
540	C₂²⋊C₄	—	89	1	no	—
541	C₂²⋊C₄	—	89	1	no	—
542	C₂²⋊C₄	—	89	2	no	—
543	C₂²⋊C₄	—	89	2	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	—	89	1	no	—
550	C₂²⋊C₄	—	89	1	no	—
551	C₂²⋊C₄	—	89	1	no	—
552	C₂²⋊C₄	—	89	2	no	—
553	C₂²⋊C₄	—	89	2	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	—	89	2	no	—
556	C₂²⋊C₄	—	89	2	no	—
557	C₂²⋊C₄	—	89	1	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	2	no	—
568	C₄²	—	89	1	no	—
569	C₄²	—	89	2	no	—
570	C₄²	—	89	2	no	—
571	C₄²	C₂²×D₈₉	1	1	yes	characteristic
572	C₄²	C₂²×D₈₉	1	2	yes	—
573	C₂³	—	89	1	no	—
574	C₂³	—	89	1	no	—
575	C₂³	—	89	1	no	—
576	C₂³	—	89	2	no	—
577	C₂³	—	356	1	no	—
578	C₂³	—	356	1	no	—
579	C₂³	—	356	1	no	—
580	C₂³	—	356	2	no	—
581	C₂³	—	356	2	no	—
582	C₂³	—	356	2	no	—
583	C₂³	C₂³×D₈₉	1	1	yes	characteristic
584	C₂³	C₂³×D₈₉	1	2	yes	—
585	C₂³	C₂³×D₈₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	2	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	356	2	no	—
590	Q₈	—	356	2	no	—
591	Q₈	—	356	1	no	—
592	D₄	—	2	2	no	—
593	D₄	—	4	1	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	356	2	no	—
597	D₄	—	356	1	no	—
598	D₄	—	356	1	no	—
599	D₄	—	356	2	no	—
600	D₄	—	356	2	no	—
601	D₄	—	356	1	no	—
602	D₄	—	356	1	no	—
603	D₄	—	356	2	no	—
604	D₄	—	356	2	no	—
605	D₄	—	356	2	no	—
606	D₄	—	356	2	no	—
607	D₄	—	356	1	no	—
608	D₄	—	356	1	no	—
609	D₄	—	178	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	89	1	no	—
615	C₂×C₄	—	89	2	no	—
616	C₂×C₄	—	89	2	no	—
617	C₂×C₄	—	89	2	no	—
618	C₂×C₄	—	89	1	no	—
619	C₂×C₄	—	89	1	no	—
620	C₂×C₄	—	89	1	no	—
621	C₂×C₄	—	89	1	no	—
622	C₂×C₄	—	356	2	no	—
623	C₂×C₄	—	356	1	no	—
624	C₂×C₄	—	356	1	no	—
625	C₂×C₄	—	356	2	no	—
626	C₂×C₄	—	356	2	no	—
627	C₂×C₄	—	356	1	no	—
628	C₂×C₄	—	178	2	no	—
629	C₂×C₄	—	178	2	no	—
630	C₂×C₄	—	178	2	no	—
631	C₂×C₄	C₂³×D₈₉	1	2	yes	—
632	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₈₉	1	2	yes	—
635	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₈₉	1	2	yes	—
637	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	356	4	no	—
649	C₂²	—	178	1	no	—
650	C₂²	—	178	1	no	—
651	C₂²	—	178	2	no	—
652	C₂²	—	178	1	no	—
653	C₂²	—	178	2	no	—
654	C₂²	—	178	1	no	—
655	C₂²	—	178	1	no	—
656	C₂²	—	178	1	no	—
657	C₂²	—	178	1	no	—
658	C₂²	—	178	1	no	—
659	C₂²	—	178	2	no	—
660	C₂²	—	178	1	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	—	178	1	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	2	no	—
678	C₄	#15668057	1	2	yes	—
679	C₂	—	4	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	2	no	—
682	C₂	—	356	1	no	—
683	C₂	—	356	1	no	—
684	C₂	—	356	2	no	—
685	C₂	—	356	1	no	—
686	C₂	C₂×#15668057	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	#548×C₈₉	C₂
hypercenter	#548	D₈₉
hypocenter	C₈₉	#3540
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #548

Complements

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

N	H ≅ G/N	type
1. #19152340	C₂	semidirect
2. #19152336	C₂	semidirect
3. #19152331	C₂	semidirect
4. #19152321	C₂	semidirect
5. #19152319	C₂	semidirect
6. #19152313	C₂	semidirect
7. #19152312	C₂	semidirect
8. #19152275	C₂	semidirect
9. #19152259	C₂	semidirect
10. #19152241	C₂	semidirect
11. #19152236	C₂	semidirect
12. #19152220	C₂	semidirect
13. #19152218	C₂	semidirect
14. #19152217	C₂	semidirect
15. #19152212	C₂	semidirect
16. #19152181	C₂	semidirect
17. #19152180	C₂	semidirect
18. #19152172	C₂	semidirect
19. #19152164	C₂	semidirect
20. #19152111	C₂	semidirect
21. #19152107	C₂	semidirect
22. #19152105	C₂	semidirect
23. #548×C₈₉	C₂	semidirect
26. C₂×D₄×D₈₉	C₂²	semidirect
27. C₂²×C₄×D₈₉	C₂²	semidirect
28. #15668012	C₂²	semidirect
29. #15668011	C₂²	semidirect
30. #15668010	C₂²	semidirect
32. #15668007	C₂²	semidirect
33. #15668007	C₂²	semidirect
34. #15668007	C₂²	semidirect
35. #15668006	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668005	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15668001	C₂²	semidirect
42. #15668000	C₂²	semidirect
43. #15667999	C₂²	semidirect
45. #15667998	C₂²	semidirect
46. #15667998	C₂²	semidirect
47. #15667998	C₂²	semidirect
48. #15667998	C₂²	semidirect
49. #15667998	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667996	C₂²	semidirect
54. #15667995	C₂²	semidirect
55. #15667995	C₂²	semidirect
56. #15667995	C₂²	semidirect
57. #15667994	C₂²	semidirect
58. #15667994	C₂²	semidirect
59. #15667993	C₂²	semidirect
60. #15667990	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667989	C₂²	semidirect
63. #15667989	C₂²	semidirect
64. #15667988	C₂²	semidirect
65. #15667988	C₂²	semidirect
66. #15667988	C₂²	semidirect
67. #15667988	C₂²	semidirect
68. #15667988	C₂²	semidirect
69. #15667988	C₂²	semidirect
72. #15667986	C₂²	semidirect
73. #15667986	C₂²	semidirect
78. #15667984	C₂²	semidirect
81. #15667983	C₂²	semidirect
85. #15667982	C₂²	semidirect
87. #15667980	C₂²	semidirect
88. #15667980	C₂²	semidirect
89. #15667980	C₂²	semidirect
90. Q₈×Dic₈₉	C₂²	semidirect
91. C₄×Dic₁₇₈	C₂²	semidirect
92. #15667977	C₂²	semidirect
94. C₄×D₃₅₆	C₂²	semidirect
95. D₄×Dic₈₉	C₂²	semidirect
96. #15667974	C₂²	semidirect
98. C₄×C₂²⋊D₈₉	C₂²	semidirect
99. C₄×C₂²⋊D₈₉	C₂²	semidirect
100. C₄×C₂²⋊D₈₉	C₂²	semidirect
101. C₄×C₂²⋊D₈₉	C₂²	semidirect
102. #15667972	C₂²	semidirect
103. #15667971	C₂²	semidirect
104. #15667971	C₂²	semidirect
105. #15667970	C₂²	semidirect
106. #15667970	C₂²	semidirect
107. #15667970	C₂²	semidirect
108. #15667969	C₂²	semidirect
109. #15667968	C₂²	semidirect
110. C₂×#13083551	C₂²	semidirect
111. C₂²⋊C₄×D₈₉	C₂²	semidirect
113. C₂²×Q₈×C₈₉	C₂²	semidirect
114. #124×C₈₉	C₂²	semidirect
115. #124×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. #121×C₈₉	C₂²	semidirect
119. #121×C₈₉	C₂²	semidirect
120. C₄×Q₈×C₈₉	C₂²	semidirect
121. C₄×D₄×C₈₉	C₂²	semidirect
122. C₄×D₄×C₈₉	C₂²	semidirect
345. C₈₉	#3540	semidirect
355. #548	D₈₉	semidirect
372. C₂²×Q₈	C₂×D₈₉	semidirect
397. #124	C₂×D₈₉	semidirect
398. #124	C₂×D₈₉	semidirect
419. C₂²⋊Q₈	C₂×D₈₉	semidirect
420. C₂²⋊Q₈	C₂×D₈₉	semidirect
433. #121	C₂×D₈₉	semidirect
434. #121	C₂×D₈₉	semidirect
446. C₄×Q₈	C₂×D₈₉	semidirect
457. C₄×D₄	C₂×D₈₉	semidirect
458. C₄×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152340	2
#19152336	2
#19152331	2
#19152321	2
#19152319	2
#19152313	2
#19152312	2
#19152275	2
#19152259	2
#19152241	2
#19152236	2
#19152220	2
#19152218	2
#19152217	2
#19152212	2
#19152181	2
#19152180	2
#19152172	2
#19152164	2
#19152111	2
#19152107	2
#19152105	2
#548×C₈₉	2
#3540	89