Subgroups — #26034201

Order 11392.

1142 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152331	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152320	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152311	C₂	1	2	yes	maximal, complemented
4	#19152272	C₂	1	2	yes	maximal, complemented
5	#19152271	C₂	1	2	yes	maximal, complemented
6	#19152261	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152260	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152254	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152243	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	#19152214	C₂	1	2	yes	maximal, complemented
14	#19152187	C₂	1	2	yes	maximal, complemented
15	#19152181	C₂	1	2	yes	maximal, complemented
16	#19152147	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152133	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152133	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#15668000	C₂	1	1	yes	maximal, characteristic, complemented
20	#124×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152070	C₂	1	2	yes	maximal, complemented
22	C₄×#13083574	C₂	1	1	yes	maximal, characteristic, complemented
23	#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13083574	C₂²	1	1	yes	characteristic
26	C₂×#13083573	C₂²	1	1	yes	characteristic, complemented
27	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₈₉	C₂²	1	2	yes	—
31	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
32	#15668011	C₂²	1	2	yes	complemented
33	#15668010	C₂²	1	1	yes	characteristic, complemented
34	#15668008	C₂²	1	1	yes	characteristic
35	#15668007	C₂²	1	2	yes	complemented
36	#15668007	C₂²	1	2	yes	complemented
37	#15668007	C₂²	1	2	yes	complemented
38	#15668006	C₂²	1	2	yes	complemented
39	#15668001	C₂²	1	1	yes	characteristic
40	#15668000	C₂²	1	1	yes	characteristic
41	#15668000	C₂²	1	1	yes	characteristic
42	#15668000	C₂²	1	1	yes	characteristic, complemented
43	#15668000	C₂²	1	2	yes	complemented
44	#15668000	C₂²	1	2	yes	complemented
45	#15668000	C₂²	1	1	yes	characteristic, complemented
46	#15668000	C₂²	1	2	yes	complemented
47	#15667999	C₂²	1	1	yes	characteristic, complemented
48	#15667998	C₂²	1	2	yes	complemented
49	#15667998	C₂²	1	2	yes	complemented
50	#15667998	C₂²	1	2	yes	complemented
51	#15667998	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	#15667996	C₂²	1	2	yes	complemented
56	#15667995	C₂²	1	2	yes	complemented
57	#15667994	C₂²	1	2	yes	complemented
58	#15667992	C₂²	1	1	yes	characteristic, complemented
59	#15667992	C₂²	1	1	yes	characteristic, complemented
60	#15667992	C₂²	1	2	yes	complemented
61	#15667990	C₂²	1	2	yes	complemented
62	#15667990	C₂²	1	2	yes	complemented
63	#15667989	C₂²	1	2	yes	complemented
64	#15667989	C₂²	1	2	yes	complemented
65	#15667987	C₂²	1	1	yes	characteristic
66	#15667987	C₂²	1	1	yes	characteristic
67	#15667987	C₂²	1	2	yes	complemented
68	#15667987	C₂²	1	2	yes	complemented
69	#15667986	C₂²	1	2	yes	complemented
70	#15667985	C₂²	1	2	yes	—
71	#15667985	C₂²	1	2	yes	complemented
72	#15667985	C₂²	1	2	yes	complemented
73	#15667984	C₂²	1	2	yes	complemented
74	#15667982	C₂²	1	2	yes	—
75	#15667982	C₂²	1	2	yes	complemented
76	#15667982	C₂²	1	2	yes	complemented
77	#15667980	C₂²	1	2	yes	—
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
80	#15667977	C₂²	1	1	yes	characteristic, complemented
81	#15667977	C₂²	1	1	yes	characteristic, complemented
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₃₅₆	C₂²	1	2	yes	complemented
85	D₄×Dic₈₉	C₂²	1	2	yes	complemented
86	#15667974	C₂²	1	1	yes	characteristic
87	#15667974	C₂²	1	2	yes	complemented
88	#15667974	C₂²	1	1	yes	characteristic, complemented
89	#15667974	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
92	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, 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	—
96	#15667972	C₂²	1	2	yes	complemented
97	#15667972	C₂²	1	2	yes	complemented
98	#15667971	C₂²	1	1	yes	characteristic, complemented
99	#15667970	C₂²	1	2	yes	complemented
100	#15667970	C₂²	1	2	yes	complemented
101	#15667969	C₂²	1	1	yes	characteristic, complemented
102	#15667969	C₂²	1	1	yes	characteristic, complemented
103	#15667969	C₂²	1	2	yes	complemented
104	C₂×#13083551	C₂²	1	2	yes	complemented
105	C₂×#13083551	C₂²	1	2	yes	complemented
106	C₂×#13083551	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	1	yes	characteristic, complemented
111	C₄²×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	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
115	#123×C₈₉	C₂²	1	2	yes	complemented
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	#121×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	#117×C₈₉	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	C₂³×D₈₉	C₂³	1	2	yes	—
125	#13083575	—	4	2	no	—
126	#13083574	—	2	4	no	—
127	#13083573	—	4	2	no	—
128	C₂×Dic₁₇₈	—	4	2	no	—
129	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
130	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
131	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
132	C₂×Dic₁₇₈	C₂³	1	2	yes	—
133	C₂×Dic₁₇₈	C₂³	1	2	yes	—
134	Q₈×D₈₉	—	4	2	no	—
135	C₂×D₃₅₆	—	4	2	no	—
136	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
137	C₂×D₃₅₆	C₂³	1	2	yes	—
138	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
139	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
140	C₂×D₃₅₆	C₂³	1	2	yes	—
141	C₂×D₃₅₆	C₂³	1	2	yes	—
142	C₂×D₃₅₆	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
146	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
147	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
149	D₄×D₈₉	—	2	8	no	—
150	D₄×D₈₉	—	4	2	no	—
151	C₂²×Dic₈₉	C₂³	1	2	yes	—
152	C₂²×Dic₈₉	C₂³	1	2	yes	—
153	C₂×C₄×D₈₉	C₂³	1	2	yes	—
154	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂³	1	2	yes	—
159	C₂×C₄×D₈₉	C₂³	1	2	yes	—
160	C₂×C₄×D₈₉	C₂³	1	2	yes	—
161	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
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	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	2	yes	—
169	#13083553	C₂³	1	1	yes	characteristic
170	#13083553	C₂³	1	1	yes	characteristic
171	#13083553	C₂³	1	1	yes	characteristic
172	#13083553	C₂³	1	2	yes	—
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	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
179	#13083551	C₂³	1	1	yes	characteristic
180	#13083551	C₂³	1	1	yes	characteristic
181	#13083551	C₂³	1	1	yes	characteristic
182	#13083551	C₂³	1	1	yes	characteristic
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	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	2	yes	—
191	#13083551	C₂³	1	2	yes	—
192	#13083551	C₂³	1	2	yes	—
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
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	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	1	yes	characteristic
203	C₄×Dic₈₉	C₂³	1	2	yes	—
204	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
205	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
206	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
207	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
208	C₂×D₄×C₈₉	C₂³	1	2	yes	—
209	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₈₉	C₂³	1	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	2	yes	—
224	C₂²⋊C₄×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	1	yes	characteristic
228	C₄²×C₈₉	C₂³	1	1	yes	characteristic
229	C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₂³×C₈₉	C₂⁴	1	2	yes	—
231	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₈₉	—	2	4	no	—
233	C₂²×D₈₉	—	2	4	no	—
234	C₂²×D₈₉	—	4	2	no	—
235	C₂²×D₈₉	—	4	2	no	—
236	C₂²×D₈₉	—	4	2	no	—
237	C₂²×D₈₉	—	4	2	no	—
238	C₂²×D₈₉	C₂⁴	1	2	yes	—
239	C₂²×D₈₉	C₂⁴	1	2	yes	—
240	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
241	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
242	Q₈×C₈₉	—	2	2	no	—
243	D₄×C₈₉	—	2	4	no	—
244	D₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	4	2	no	—
249	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
257	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
258	C₂²⋊D₈₉	—	2	2	no	—
259	C₂²⋊D₈₉	—	2	4	no	—
260	C₂²⋊D₈₉	—	4	2	no	—
261	C₂²⋊D₈₉	—	4	2	no	—
262	C₂²⋊D₈₉	—	4	2	no	—
263	C₂²⋊D₈₉	#41	1	4	yes	complemented
264	C₂×Dic₈₉	—	4	2	no	—
265	C₂×Dic₈₉	—	4	2	no	—
266	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₈₉	C₂⁴	1	2	yes	—
272	C₂×Dic₈₉	C₂⁴	1	2	yes	—
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	D₃₅₆	—	2	4	no	—
275	D₃₅₆	—	2	2	no	—
276	D₃₅₆	—	2	2	no	—
277	D₃₅₆	—	2	2	no	—
278	D₃₅₆	—	4	2	no	—
279	D₃₅₆	—	4	2	no	—
280	D₃₅₆	—	4	2	no	—
281	C₄×D₈₉	—	2	2	no	—
282	C₄×D₈₉	—	2	2	no	—
283	C₄×D₈₉	—	2	2	no	—
284	C₄×D₈₉	—	2	4	no	—
285	C₄×D₈₉	—	2	2	no	—
286	C₄×D₈₉	—	4	1	no	—
287	C₄×D₈₉	—	4	2	no	—
288	C₄×D₈₉	—	4	1	no	—
289	C₄×D₈₉	—	4	2	no	—
290	C₄×D₈₉	—	4	2	no	—
291	Dic₁₇₈	—	2	2	no	—
292	Dic₁₇₈	—	2	2	no	—
293	Dic₁₇₈	—	2	2	no	—
294	Dic₁₇₈	—	4	2	no	—
295	Dic₁₇₈	—	4	2	no	—
296	C₂²×C₈₉	—	2	1	no	—
297	C₂²×C₈₉	—	2	1	no	—
298	C₂²×C₈₉	—	2	2	no	—
299	C₂²×C₈₉	—	2	2	no	—
300	C₂²×C₈₉	—	2	2	no	—
301	C₂²×C₈₉	C₂×#41	1	2	yes	—
302	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
303	C₂×D₈₉	—	2	1	no	—
304	C₂×D₈₉	—	2	1	no	—
305	C₂×D₈₉	—	2	1	no	—
306	C₂×D₈₉	—	2	2	no	—
307	C₂×D₈₉	—	2	2	no	—
308	C₂×D₈₉	—	2	1	no	—
309	C₂×D₈₉	—	2	2	no	—
310	C₂×D₈₉	—	2	2	no	—
311	C₂×D₈₉	—	2	1	no	—
312	C₂×D₈₉	—	2	2	no	—
313	C₂×D₈₉	—	2	2	no	—
314	C₂×D₈₉	—	8	4	no	—
315	C₂×D₈₉	—	8	4	no	—
316	C₂×D₈₉	C₂×#41	1	2	yes	—
317	C₄×C₈₉	—	2	1	no	—
318	C₄×C₈₉	—	2	1	no	—
319	C₄×C₈₉	—	2	2	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	1	no	—
325	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
326	Dic₈₉	—	2	1	no	—
327	Dic₈₉	—	2	2	no	—
328	Dic₈₉	—	2	2	no	—
329	Dic₈₉	—	2	1	no	—
330	Dic₈₉	—	2	1	no	—
331	Dic₈₉	—	2	1	no	—
332	Dic₈₉	—	2	1	no	—
333	Dic₈₉	C₂×#41	1	2	yes	—
334	C₂×C₈₉	—	2	2	no	—
335	C₂×C₈₉	—	4	2	no	—
336	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
337	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₈₉	#585	1	1	yes	characteristic
339	D₈₉	—	2	2	no	—
340	D₈₉	—	4	1	no	—
341	D₈₉	—	4	2	no	—
342	D₈₉	—	4	2	no	—
343	#3514	—	89	1	no	maximal, Sylow
344	C₈₉	#3514	1	1	yes	characteristic, complemented, Sylow
345	#559	—	89	1	no	—
346	#556	—	89	1	no	—
347	#555	—	89	2	no	—
348	#551	—	89	2	no	—
349	#551	—	89	2	no	—
350	D₄×Q₈	—	89	1	no	—
351	#548	—	89	1	no	—
352	#548	—	89	1	no	—
353	#546	—	89	2	no	—
354	#546	—	89	1	no	—
355	#546	—	89	1	no	—
356	D₄²	—	89	1	no	—
357	#542	—	89	2	no	—
358	#538	—	89	2	no	—
359	#538	—	89	2	no	—
360	#532	—	89	1	no	—
361	#529	—	89	1	no	—
362	#529	—	89	1	no	—
363	#529	D₈₉	1	1	yes	characteristic, complemented
364	C₂×#124	—	89	1	no	—
365	C₂×#124	—	89	1	no	—
366	#518	—	89	2	no	—
367	C₄×#41	—	89	1	no	—
368	C₂×#41	—	89	1	no	—
369	C₂×#41	—	89	1	no	—
370	C₂×#41	—	89	1	no	—
371	C₂²×Q₈	—	89	1	no	—
372	C₂²×Q₈	—	89	1	no	—
373	C₂²×D₄	—	89	1	no	—
374	C₂²×D₄	—	89	2	no	—
375	C₂²×D₄	—	89	1	no	—
376	C₄⋊Q₈	—	89	1	no	—
377	C₄⋊Q₈	—	89	2	no	—
378	#127	—	89	1	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	#125	C₂×D₈₉	1	1	yes	characteristic, complemented
385	#124	—	89	1	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	1	no	—
392	#124	—	89	1	no	—
393	#124	—	89	2	no	—
394	#124	—	89	1	no	—
395	#124	—	89	1	no	—
396	#124	—	89	2	no	—
397	#124	—	89	2	no	—
398	#124	C₂×D₈₉	1	1	yes	characteristic, 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	2	no	—
405	#123	C₂×D₈₉	1	2	yes	complemented
406	C₂²⋊Q₈	—	89	1	no	—
407	C₂²⋊Q₈	—	89	1	no	—
408	C₂²⋊Q₈	—	89	2	no	—
409	C₂²⋊Q₈	—	89	2	no	—
410	C₂²⋊Q₈	—	89	2	no	—
411	C₂²⋊Q₈	—	89	2	no	—
412	C₂²⋊Q₈	—	89	2	no	—
413	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
414	#121	—	89	2	no	—
415	#121	—	89	2	no	—
416	#121	—	89	1	no	—
417	#121	—	89	1	no	—
418	#121	—	89	2	no	—
419	#121	—	89	2	no	—
420	#121	—	89	2	no	—
421	#121	—	89	2	no	—
422	#121	—	89	2	no	—
423	#121	C₂×D₈₉	1	1	yes	characteristic
424	#120	—	89	2	no	—
425	#120	—	89	2	no	—
426	#120	—	89	2	no	—
427	#120	—	89	2	no	—
428	C₄×Q₈	—	89	1	no	—
429	C₄×Q₈	—	89	1	no	—
430	C₄×Q₈	—	89	1	no	—
431	C₄×Q₈	—	89	1	no	—
432	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
433	C₄×D₄	—	89	2	no	—
434	C₄×D₄	—	89	1	no	—
435	C₄×D₄	—	89	1	no	—
436	C₄×D₄	—	89	1	no	—
437	C₄×D₄	—	89	1	no	—
438	C₄×D₄	—	89	2	no	—
439	C₄×D₄	—	89	2	no	—
440	C₄×D₄	—	89	1	no	—
441	C₄×D₄	—	89	2	no	—
442	C₄×D₄	—	89	1	no	—
443	C₄×D₄	—	89	2	no	—
444	C₄×D₄	—	89	2	no	—
445	C₄×D₄	—	89	2	no	—
446	C₄×D₄	—	89	1	no	—
447	C₄×D₄	—	89	1	no	—
448	C₄×D₄	—	89	2	no	—
449	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
450	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
451	#117	—	89	1	no	—
452	#117	—	89	2	no	—
453	#117	—	89	2	no	—
454	#117	—	89	1	no	—
455	#117	—	89	1	no	—
456	#117	—	89	2	no	—
457	#117	C₂×D₈₉	1	2	yes	complemented
458	C₂×C₂²⋊C₄	—	89	2	no	—
459	C₂×C₂²⋊C₄	—	89	2	no	—
460	C₂×C₂²⋊C₄	—	89	2	no	—
461	C₂×C₂²⋊C₄	—	89	2	no	—
462	C₂×C₂²⋊C₄	—	89	2	no	—
463	C₂×C₂²⋊C₄	—	89	2	no	—
464	C₂×C₄²	—	89	1	no	—
465	C₂×C₄²	—	89	1	no	—
466	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic, complemented
467	C₂⁴	—	89	2	no	—
468	C₂⁴	—	89	2	no	—
469	#41	—	356	2	no	—
470	#41	—	356	2	no	—
471	#41	—	178	4	no	—
472	C₂×Q₈	—	89	2	no	—
473	C₂×Q₈	—	89	2	no	—
474	C₂×Q₈	—	89	1	no	—
475	C₂×Q₈	—	89	1	no	—
476	C₂×Q₈	—	89	1	no	—
477	C₂×Q₈	—	356	2	no	—
478	C₂×Q₈	—	356	2	no	—
479	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
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	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	1	no	—
492	C₂×D₄	—	89	1	no	—
493	C₂×D₄	—	356	2	no	—
494	C₂×D₄	—	356	2	no	—
495	C₂×D₄	—	178	8	no	—
496	C₂×D₄	C₂²×D₈₉	1	2	yes	—
497	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
498	C₂²×C₄	—	89	2	no	—
499	C₂²×C₄	—	89	2	no	—
500	C₂²×C₄	—	89	1	no	—
501	C₂²×C₄	—	89	1	no	—
502	C₂²×C₄	—	89	2	no	—
503	C₂²×C₄	—	89	2	no	—
504	C₂²×C₄	—	89	2	no	—
505	C₂²×C₄	—	89	1	no	—
506	C₂²×C₄	—	89	1	no	—
507	C₂²×C₄	—	89	1	no	—
508	C₂²×C₄	—	89	1	no	—
509	C₂²×C₄	—	89	2	no	—
510	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
511	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
514	C₄⋊C₄	—	89	1	no	—
515	C₄⋊C₄	—	89	2	no	—
516	C₄⋊C₄	—	89	2	no	—
517	C₄⋊C₄	—	89	1	no	—
518	C₄⋊C₄	—	89	1	no	—
519	C₄⋊C₄	—	89	1	no	—
520	C₄⋊C₄	—	89	1	no	—
521	C₄⋊C₄	—	89	1	no	—
522	C₄⋊C₄	—	89	2	no	—
523	C₄⋊C₄	—	89	2	no	—
524	C₄⋊C₄	—	89	2	no	—
525	C₄⋊C₄	—	89	2	no	—
526	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
527	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
528	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
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	C₂²⋊C₄	—	89	1	no	—
533	C₂²⋊C₄	—	89	2	no	—
534	C₂²⋊C₄	—	89	2	no	—
535	C₂²⋊C₄	—	89	1	no	—
536	C₂²⋊C₄	—	89	1	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	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	C₂²×D₈₉	1	2	yes	—
557	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
561	C₄²	—	89	1	no	—
562	C₄²	—	89	1	no	—
563	C₄²	—	89	1	no	—
564	C₄²	—	89	1	no	—
565	C₄²	—	89	1	no	—
566	C₄²	—	89	1	no	—
567	C₄²	—	89	2	no	—
568	C₄²	—	89	2	no	—
569	C₄²	C₂²×D₈₉	1	1	yes	characteristic
570	C₄²	C₂²×D₈₉	1	1	yes	characteristic
571	C₄²	C₂²×D₈₉	1	1	yes	characteristic
572	C₄²	C₂²×D₈₉	1	1	yes	characteristic
573	C₄²	C₂²×D₈₉	1	2	yes	—
574	C₂³	—	89	1	no	—
575	C₂³	—	89	2	no	—
576	C₂³	—	89	2	no	—
577	C₂³	—	89	1	no	—
578	C₂³	—	356	2	no	—
579	C₂³	—	356	2	no	—
580	C₂³	—	356	2	no	—
581	C₂³	—	356	2	no	—
582	C₂³	—	178	4	no	—
583	C₂³	—	178	4	no	—
584	C₂³	C₂³×D₈₉	1	2	yes	—
585	C₂³	C₂³×D₈₉	1	1	yes	characteristic
586	Q₈	—	2	2	no	—
587	Q₈	—	356	2	no	—
588	Q₈	—	356	2	no	—
589	Q₈	—	178	2	no	—
590	Q₈	—	178	2	no	—
591	Q₈	—	178	2	no	—
592	D₄	—	2	4	no	—
593	D₄	—	2	2	no	—
594	D₄	—	89	4	no	—
595	D₄	—	356	2	no	—
596	D₄	—	356	2	no	—
597	D₄	—	356	2	no	—
598	D₄	—	356	2	no	—
599	D₄	—	356	2	no	—
600	D₄	—	356	2	no	—
601	D₄	—	178	4	no	—
602	D₄	—	178	2	no	—
603	D₄	—	178	4	no	—
604	D₄	—	178	2	no	—
605	D₄	—	178	2	no	—
606	D₄	—	178	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	89	1	no	—
612	C₂×C₄	—	89	1	no	—
613	C₂×C₄	—	89	1	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	2	no	—
619	C₂×C₄	—	356	1	no	—
620	C₂×C₄	—	356	1	no	—
621	C₂×C₄	—	356	2	no	—
622	C₂×C₄	—	356	2	no	—
623	C₂×C₄	—	356	2	no	—
624	C₂×C₄	—	356	2	no	—
625	C₂×C₄	—	356	2	no	—
626	C₂×C₄	—	178	4	no	—
627	C₂×C₄	—	178	2	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	1	yes	characteristic
632	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
633	C₂×C₄	C₂³×D₈₉	1	2	yes	—
634	C₂×C₄	C₂³×D₈₉	1	2	yes	—
635	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
638	C₂×C₄	C₂³×D₈₉	1	2	yes	—
639	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	89	2	no	—
646	C₂²	—	178	1	no	—
647	C₂²	—	178	2	no	—
648	C₂²	—	178	2	no	—
649	C₂²	—	178	2	no	—
650	C₂²	—	178	1	no	—
651	C₂²	—	178	2	no	—
652	C₂²	—	178	1	no	—
653	C₂²	—	178	2	no	—
654	C₂²	—	178	2	no	—
655	C₂²	—	178	1	no	—
656	C₂²	—	178	1	no	—
657	C₂²	—	712	4	no	—
658	C₂²	—	712	4	no	—
659	C₂²	#41×D₈₉	1	2	yes	—
660	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	89	2	no	—
670	C₄	—	178	1	no	—
671	C₄	—	178	1	no	—
672	C₄	—	178	2	no	—
673	C₄	—	178	2	no	—
674	C₄	—	178	1	no	—
675	C₄	—	178	1	no	—
676	C₄	—	178	1	no	—
677	C₄	#15668058	1	2	yes	—
678	C₂	—	2	2	no	—
679	C₂	—	4	2	no	—
680	C₂	—	356	1	no	—
681	C₂	—	356	2	no	—
682	C₂	—	356	2	no	—
683	C₂	—	178	2	no	—
684	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
685	C₂	C₂×#15668058	1	1	yes	characteristic
686	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#529×C₈₉	C₂
hypercenter	#529	D₈₉
hypocenter	C₈₉	#3514
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19152331	C₂	semidirect
2. #19152320	C₂	semidirect
3. #19152311	C₂	semidirect
4. #19152272	C₂	semidirect
5. #19152271	C₂	semidirect
6. #19152261	C₂	semidirect
7. #19152260	C₂	semidirect
8. #19152254	C₂	semidirect
9. #19152243	C₂	semidirect
10. #19152240	C₂	semidirect
11. #19152239	C₂	semidirect
12. #19152232	C₂	semidirect
13. #19152214	C₂	semidirect
14. #19152187	C₂	semidirect
15. #19152181	C₂	semidirect
16. #19152147	C₂	semidirect
17. #19152133	C₂	semidirect
18. #19152133	C₂	semidirect
19. C₂×#15668000	C₂	semidirect
20. #124×D₈₉	C₂	semidirect
21. #19152070	C₂	semidirect
22. C₄×#13083574	C₂	semidirect
23. #529×C₈₉	C₂	semidirect
24. C₂×#13083575	C₂²	semidirect
26. C₂×#13083573	C₂²	semidirect
27. C₂²×Dic₁₇₈	C₂²	semidirect
28. C₂×Q₈×D₈₉	C₂²	semidirect
32. #15668011	C₂²	semidirect
33. #15668010	C₂²	semidirect
35. #15668007	C₂²	semidirect
36. #15668007	C₂²	semidirect
37. #15668007	C₂²	semidirect
38. #15668006	C₂²	semidirect
42. #15668000	C₂²	semidirect
43. #15668000	C₂²	semidirect
44. #15668000	C₂²	semidirect
45. #15668000	C₂²	semidirect
46. #15668000	C₂²	semidirect
47. #15667999	C₂²	semidirect
48. #15667998	C₂²	semidirect
49. #15667998	C₂²	semidirect
50. #15667998	C₂²	semidirect
51. #15667998	C₂²	semidirect
52. #15667997	C₂²	semidirect
53. #15667997	C₂²	semidirect
54. #15667997	C₂²	semidirect
55. #15667996	C₂²	semidirect
56. #15667995	C₂²	semidirect
57. #15667994	C₂²	semidirect
58. #15667992	C₂²	semidirect
59. #15667992	C₂²	semidirect
60. #15667992	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667990	C₂²	semidirect
63. #15667989	C₂²	semidirect
64. #15667989	C₂²	semidirect
67. #15667987	C₂²	semidirect
68. #15667987	C₂²	semidirect
69. #15667986	C₂²	semidirect
71. #15667985	C₂²	semidirect
72. #15667985	C₂²	semidirect
73. #15667984	C₂²	semidirect
75. #15667982	C₂²	semidirect
76. #15667982	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. C₄×Dic₁₇₈	C₂²	semidirect
80. #15667977	C₂²	semidirect
81. #15667977	C₂²	semidirect
82. C₄×D₃₅₆	C₂²	semidirect
83. C₄×D₃₅₆	C₂²	semidirect
84. C₄×D₃₅₆	C₂²	semidirect
85. D₄×Dic₈₉	C₂²	semidirect
87. #15667974	C₂²	semidirect
88. #15667974	C₂²	semidirect
89. #15667974	C₂²	semidirect
92. C₄×C₂²⋊D₈₉	C₂²	semidirect
93. C₄×C₂²⋊D₈₉	C₂²	semidirect
94. C₄×C₂²⋊D₈₉	C₂²	semidirect
96. #15667972	C₂²	semidirect
97. #15667972	C₂²	semidirect
98. #15667971	C₂²	semidirect
99. #15667970	C₂²	semidirect
100. #15667970	C₂²	semidirect
101. #15667969	C₂²	semidirect
102. #15667969	C₂²	semidirect
103. #15667969	C₂²	semidirect
104. C₂×#13083551	C₂²	semidirect
105. C₂×#13083551	C₂²	semidirect
106. C₂×#13083551	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. #126×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
114. #124×C₈₉	C₂²	semidirect
115. #123×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
119. C₄×D₄×C₈₉	C₂²	semidirect
120. C₄×D₄×C₈₉	C₂²	semidirect
121. #117×C₈₉	C₂²	semidirect
122. C₂×C₄²×C₈₉	C₂²	semidirect
263. C₂²⋊D₈₉	#41	semidirect
344. C₈₉	#3514	semidirect
363. #529	D₈₉	semidirect
383. #126	C₂×D₈₉	semidirect
384. #125	C₂×D₈₉	semidirect
398. #124	C₂×D₈₉	semidirect
405. #123	C₂×D₈₉	semidirect
413. C₂²⋊Q₈	C₂×D₈₉	semidirect
432. C₄×Q₈	C₂×D₈₉	semidirect
449. C₄×D₄	C₂×D₈₉	semidirect
450. C₄×D₄	C₂×D₈₉	semidirect
457. #117	C₂×D₈₉	semidirect
466. C₂×C₄²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152331	2
#19152320	2
#19152311	2
#19152272	2
#19152271	2
#19152261	2
#19152260	2
#19152254	2
#19152243	2
#19152240	2
#19152239	2
#19152232	2
#19152214	2
#19152187	2
#19152181	2
#19152147	2
#19152133	2
C₂×#15668000	2
#124×D₈₉	2
#19152070	2
C₄×#13083574	2
#529×C₈₉	2
#3514	89