Subgroups — #26034480

Order 11392.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152346	C₂	1	2	yes	maximal, complemented
2	#19152344	C₂	1	2	yes	maximal, complemented
3	#19152303	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152260	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152258	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152251	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152249	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152244	C₂	1	2	yes	maximal, complemented
9	#19152244	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152239	C₂	1	2	yes	maximal, complemented
11	#19152239	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152223	C₂	1	2	yes	maximal, complemented
13	#19152222	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152220	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152196	C₂	1	2	yes	maximal, complemented
16	#19152181	C₂	1	2	yes	maximal, complemented
17	#19152179	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152178	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152178	C₂	1	2	yes	maximal, complemented
20	#19152107	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#15667987	C₂	1	1	yes	maximal, characteristic, complemented
23	#554×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	2	yes	complemented
25	C₂×#13083575	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13083574	C₂²	1	2	yes	complemented
28	C₂×#13083574	C₂²	1	1	yes	characteristic, complemented
29	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
31	C₂²×D₃₅₆	C₂²	1	2	yes	—
32	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
33	#15668011	C₂²	1	1	yes	characteristic, complemented
34	#15668007	C₂²	1	2	yes	complemented
35	#15668006	C₂²	1	2	yes	complemented
36	#15668002	C₂²	1	2	yes	complemented
37	#15668001	C₂²	1	1	yes	characteristic, complemented
38	#15668001	C₂²	1	2	yes	complemented
39	#15668000	C₂²	1	2	yes	complemented
40	#15668000	C₂²	1	2	yes	complemented
41	#15668000	C₂²	1	1	yes	characteristic, complemented
42	#15667998	C₂²	1	2	yes	complemented
43	#15667997	C₂²	1	2	yes	complemented
44	#15667997	C₂²	1	2	yes	complemented
45	#15667997	C₂²	1	2	yes	complemented
46	#15667997	C₂²	1	2	yes	complemented
47	#15667997	C₂²	1	2	yes	complemented
48	#15667997	C₂²	1	2	yes	complemented
49	#15667997	C₂²	1	2	yes	complemented
50	#15667997	C₂²	1	1	yes	characteristic, complemented
51	#15667995	C₂²	1	2	yes	complemented
52	#15667994	C₂²	1	1	yes	characteristic, complemented
53	#15667992	C₂²	1	2	yes	complemented
54	#15667992	C₂²	1	1	yes	characteristic, complemented
55	#15667992	C₂²	1	1	yes	characteristic, complemented
56	#15667992	C₂²	1	2	yes	complemented
57	#15667991	C₂²	1	2	yes	—
58	#15667991	C₂²	1	1	yes	characteristic
59	#15667990	C₂²	1	2	yes	complemented
60	#15667990	C₂²	1	2	yes	complemented
61	#15667990	C₂²	1	2	yes	complemented
62	#15667990	C₂²	1	1	yes	characteristic, complemented
63	#15667990	C₂²	1	2	yes	complemented
64	#15667990	C₂²	1	2	yes	complemented
65	#15667990	C₂²	1	2	yes	complemented
66	#15667989	C₂²	1	2	yes	—
67	#15667989	C₂²	1	1	yes	characteristic
68	#15667988	C₂²	1	1	yes	characteristic, complemented
69	#15667988	C₂²	1	2	yes	complemented
70	#15667988	C₂²	1	2	yes	complemented
71	#15667987	C₂²	1	2	yes	—
72	#15667987	C₂²	1	1	yes	characteristic
73	#15667987	C₂²	1	1	yes	characteristic
74	#15667987	C₂²	1	1	yes	characteristic
75	#15667987	C₂²	1	1	yes	characteristic
76	#15667987	C₂²	1	2	yes	—
77	#15667987	C₂²	1	2	yes	complemented
78	#15667987	C₂²	1	2	yes	complemented
79	#15667987	C₂²	1	2	yes	complemented
80	#15667987	C₂²	1	1	yes	characteristic, complemented
81	#15667987	C₂²	1	2	yes	complemented
82	#15667986	C₂²	1	2	yes	complemented
83	#15667986	C₂²	1	1	yes	characteristic, complemented
84	#15667986	C₂²	1	2	yes	complemented
85	#15667985	C₂²	1	2	yes	complemented
86	#15667985	C₂²	1	1	yes	characteristic, complemented
87	#15667985	C₂²	1	2	yes	complemented
88	#15667985	C₂²	1	2	yes	complemented
89	#15667985	C₂²	1	2	yes	complemented
90	#15667984	C₂²	1	1	yes	characteristic
91	#15667982	C₂²	1	2	yes	—
92	#15667982	C₂²	1	1	yes	characteristic
93	#15667980	C₂²	1	2	yes	—
94	#15667980	C₂²	1	1	yes	characteristic
95	#15667977	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₃₅₆	C₂²	1	2	yes	complemented
97	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
98	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
99	#15667974	C₂²	1	2	yes	complemented
100	#15667974	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
102	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic, complemented
104	#15667969	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
108	C₂×#13083551	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
111	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#125×C₈₉	C₂²	1	2	yes	complemented
114	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
115	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₈₉	C₂²	1	2	yes	—
120	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₈₉	C₂³	1	1	yes	characteristic
124	C₂³×D₈₉	C₂³	1	2	yes	—
125	#13083575	—	4	4	no	—
126	#13083575	—	4	2	no	—
127	#13083574	—	4	2	no	—
128	#13083574	—	4	2	no	—
129	#13083574	—	4	4	no	—
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	—	4	4	no	—
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	1	yes	characteristic
142	C₂×D₃₅₆	C₂³	1	2	yes	—
143	C₂×D₃₅₆	C₂³	1	2	yes	—
144	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
145	C₂×D₃₅₆	C₂³	1	2	yes	—
146	C₂×D₃₅₆	C₂³	1	2	yes	—
147	C₂×D₃₅₆	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
149	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
154	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₈₉	—	4	2	no	—
156	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₈₉	C₂³	1	2	yes	—
160	C₂×C₄×D₈₉	C₂³	1	2	yes	—
161	C₂×C₄×D₈₉	C₂³	1	2	yes	—
162	C₂×C₄×D₈₉	C₂³	1	2	yes	—
163	C₂×C₄×D₈₉	C₂³	1	2	yes	—
164	C₂×C₄×D₈₉	C₂³	1	2	yes	—
165	C₂×C₄×D₈₉	C₂³	1	2	yes	—
166	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
168	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
169	C₄⋊Dic₈₉	C₂³	1	2	yes	—
170	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₈₉	C₂³	1	2	yes	—
172	#13083553	C₂³	1	1	yes	characteristic
173	#13083553	C₂³	1	1	yes	characteristic
174	#13083553	C₂³	1	1	yes	characteristic
175	#13083553	C₂³	1	2	yes	—
176	#13083553	C₂³	1	1	yes	characteristic
177	#13083553	C₂³	1	2	yes	—
178	#13083553	C₂³	1	2	yes	—
179	#13083553	C₂³	1	2	yes	—
180	#13083553	C₂³	1	2	yes	—
181	#13083553	C₂³	1	2	yes	—
182	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
184	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	1	yes	characteristic
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	1	yes	characteristic
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	2	yes	—
195	#13083551	C₂³	1	1	yes	characteristic
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	#13083551	C₂³	1	2	yes	—
202	#13083551	C₂³	1	2	yes	—
203	#13083551	C₂³	1	2	yes	—
204	#13083551	C₂³	1	2	yes	—
205	#13083551	C₂³	1	2	yes	—
206	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
207	C₄×Dic₈₉	C₂³	1	2	yes	—
208	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
209	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
210	C₂×D₄×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	C₂²×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	1	yes	characteristic
220	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
221	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
222	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
223	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
225	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
227	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
229	C₄²×C₈₉	C₂³	1	1	yes	characteristic
230	C₄²×C₈₉	C₂³	1	2	yes	—
231	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂²×D₈₉	—	2	2	no	—
234	C₂²×D₈₉	—	2	4	no	—
235	C₂²×D₈₉	—	2	2	no	—
236	C₂²×D₈₉	—	4	1	no	—
237	C₂²×D₈₉	—	4	2	no	—
238	C₂²×D₈₉	—	4	2	no	—
239	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²×D₈₉	C₂⁴	1	2	yes	—
241	C₂²×D₈₉	C₂⁴	1	2	yes	—
242	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
243	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
244	Q₈×C₈₉	—	2	2	no	—
245	Q₈×C₈₉	—	4	2	no	—
246	D₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	4	2	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
258	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
259	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
260	C₂²⋊D₈₉	—	2	2	no	—
261	C₂²⋊D₈₉	—	2	2	no	—
262	C₂²⋊D₈₉	—	4	2	no	—
263	C₂²⋊D₈₉	—	4	1	no	—
264	C₂²⋊D₈₉	—	4	2	no	—
265	C₂²⋊D₈₉	—	4	1	no	—
266	C₂×Dic₈₉	—	4	1	no	—
267	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₈₉	C₂⁴	1	2	yes	—
270	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₈₉	C₂⁴	1	2	yes	—
273	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
274	D₃₅₆	—	2	4	no	—
275	D₃₅₆	—	2	4	no	—
276	D₃₅₆	—	2	2	no	—
277	D₃₅₆	—	2	2	no	—
278	D₃₅₆	—	2	2	no	—
279	D₃₅₆	—	4	2	no	—
280	D₃₅₆	—	4	2	no	—
281	D₃₅₆	—	4	2	no	—
282	D₃₅₆	—	4	1	no	—
283	D₃₅₆	—	4	2	no	—
284	D₃₅₆	—	4	2	no	—
285	C₄×D₈₉	—	2	4	no	—
286	C₄×D₈₉	—	2	2	no	—
287	C₄×D₈₉	—	2	2	no	—
288	C₄×D₈₉	—	2	2	no	—
289	C₄×D₈₉	—	4	1	no	—
290	C₄×D₈₉	—	4	1	no	—
291	C₄×D₈₉	—	4	2	no	—
292	C₄×D₈₉	—	4	2	no	—
293	C₄×D₈₉	—	4	2	no	—
294	C₄×D₈₉	—	4	2	no	—
295	C₄×D₈₉	—	4	2	no	—
296	C₄×D₈₉	—	4	2	no	—
297	Dic₁₇₈	—	2	2	no	—
298	Dic₁₇₈	—	4	2	no	—
299	Dic₁₇₈	—	4	2	no	—
300	Dic₁₇₈	—	4	1	no	—
301	C₂²×C₈₉	—	2	1	no	—
302	C₂²×C₈₉	—	2	1	no	—
303	C₂²×C₈₉	—	2	1	no	—
304	C₂²×C₈₉	—	2	1	no	—
305	C₂²×C₈₉	—	2	1	no	—
306	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
307	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
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	2	no	—
315	C₂×D₈₉	—	2	2	no	—
316	C₂×D₈₉	—	2	2	no	—
317	C₂×D₈₉	—	2	1	no	—
318	C₂×D₈₉	—	2	1	no	—
319	C₂×D₈₉	—	2	1	no	—
320	C₂×D₈₉	—	2	2	no	—
321	C₂×D₈₉	—	2	2	no	—
322	C₂×D₈₉	—	4	4	no	—
323	C₂×D₈₉	—	8	4	no	—
324	C₂×D₈₉	H(5,𝔽₂)	1	2	yes	—
325	C₄×C₈₉	—	2	1	no	—
326	C₄×C₈₉	—	2	2	no	—
327	C₄×C₈₉	—	2	2	no	—
328	C₄×C₈₉	—	2	2	no	—
329	C₄×C₈₉	—	2	1	no	—
330	C₄×C₈₉	—	2	1	no	—
331	C₄×C₈₉	—	2	2	no	—
332	C₄×C₈₉	—	2	1	no	—
333	C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
334	Dic₈₉	—	2	2	no	—
335	Dic₈₉	—	2	1	no	—
336	Dic₈₉	—	2	1	no	—
337	Dic₈₉	—	2	2	no	—
338	Dic₈₉	—	2	1	no	—
339	Dic₈₉	—	2	1	no	—
340	Dic₈₉	—	2	1	no	—
341	C₂×C₈₉	—	2	2	no	—
342	C₂×C₈₉	—	4	1	no	—
343	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
346	D₈₉	—	2	2	no	—
347	D₈₉	—	4	1	no	—
348	D₈₉	—	4	1	no	—
349	D₈₉	—	4	2	no	—
350	D₈₉	—	4	2	no	—
351	#3536	—	89	1	no	maximal, Sylow
352	C₈₉	#3536	1	1	yes	characteristic, complemented, Sylow
353	#562	—	89	2	no	—
354	#562	—	89	2	no	—
355	#554	—	89	1	no	—
356	#554	D₈₉	1	1	yes	characteristic, complemented
357	#548	—	89	1	no	—
358	#548	—	89	1	no	—
359	#547	—	89	1	no	—
360	#547	—	89	1	no	—
361	#546	—	89	2	no	—
362	#546	—	89	1	no	—
363	#546	—	89	2	no	—
364	#546	—	89	1	no	—
365	#543	—	89	2	no	—
366	#542	—	89	1	no	—
367	#542	—	89	1	no	—
368	#539	—	89	2	no	—
369	#538	—	89	2	no	—
370	#537	—	89	2	no	—
371	#537	—	89	1	no	—
372	#537	—	89	1	no	—
373	#525	—	89	1	no	—
374	C₂×C₂²⋊Q₈	—	89	1	no	—
375	C₂×#121	—	89	1	no	—
376	C₂×#41	—	89	2	no	—
377	C₂×#41	—	89	1	no	—
378	C₂×#41	—	89	1	no	—
379	C₂×#41	—	89	2	no	—
380	C₂×#41	—	89	1	no	—
381	C₂²×Q₈	—	89	1	no	—
382	C₂²×D₄	—	89	1	no	—
383	C₂²×D₄	—	89	2	no	—
384	C₂³×C₄	—	89	1	no	—
385	C₄⋊Q₈	—	89	1	no	—
386	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
387	#126	—	89	2	no	—
388	#126	—	89	2	no	—
389	#125	—	89	2	no	—
390	#125	C₂×D₈₉	1	2	yes	complemented
391	#124	—	89	1	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	#123	—	89	2	no	—
398	#123	—	89	1	no	—
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	—	89	2	no	—
406	#123	—	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	1	no	—
411	C₂²⋊Q₈	—	89	2	no	—
412	C₂²⋊Q₈	—	89	2	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	2	no	—
419	C₂²⋊Q₈	—	89	2	no	—
420	C₂²⋊Q₈	—	89	2	no	—
421	C₂²⋊Q₈	—	89	1	no	—
422	C₂²⋊Q₈	—	89	2	no	—
423	C₂²⋊Q₈	—	89	2	no	—
424	C₂²⋊Q₈	—	89	1	no	—
425	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
426	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
427	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
428	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
429	#121	—	89	1	no	—
430	#121	—	89	2	no	—
431	#121	—	89	1	no	—
432	#121	—	89	2	no	—
433	#121	—	89	2	no	—
434	#121	—	89	1	no	—
435	#121	—	89	1	no	—
436	#121	—	89	1	no	—
437	#121	—	89	1	no	—
438	#121	—	89	2	no	—
439	#121	—	89	1	no	—
440	#121	—	89	2	no	—
441	#121	—	89	2	no	—
442	#121	—	89	2	no	—
443	#121	—	89	2	no	—
444	#121	—	89	1	no	—
445	#121	—	89	2	no	—
446	#121	—	89	2	no	—
447	#121	—	89	2	no	—
448	#121	—	89	2	no	—
449	#120	—	89	1	no	—
450	#120	—	89	2	no	—
451	#120	—	89	1	no	—
452	#120	—	89	2	no	—
453	C₄×Q₈	—	89	1	no	—
454	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
455	C₄×D₄	—	89	1	no	—
456	C₄×D₄	—	89	2	no	—
457	C₄×D₄	—	89	1	no	—
458	C₄×D₄	—	89	2	no	—
459	C₄×D₄	—	89	1	no	—
460	C₄×D₄	—	89	1	no	—
461	C₄×D₄	—	89	2	no	—
462	C₄×D₄	—	89	1	no	—
463	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
464	C₄×D₄	C₂×D₈₉	1	2	yes	—
465	#117	—	89	1	no	—
466	C₂×C₄⋊C₄	—	89	2	no	—
467	C₂×C₄⋊C₄	—	89	1	no	—
468	C₂×C₄⋊C₄	—	89	1	no	—
469	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
471	C₂×C₂²⋊C₄	—	89	2	no	—
472	C₂×C₂²⋊C₄	—	89	2	no	—
473	C₂×C₂²⋊C₄	—	89	2	no	—
474	C₂×C₂²⋊C₄	—	89	2	no	—
475	C₂⁴	—	89	2	no	—
476	C₂⁴	—	89	1	no	—
477	#41	—	356	2	no	—
478	#41	—	356	2	no	—
479	#41	—	356	4	no	—
480	#41	—	356	2	no	—
481	#41	—	356	4	no	—
482	C₂×Q₈	—	89	1	no	—
483	C₂×Q₈	—	89	2	no	—
484	C₂×Q₈	—	89	2	no	—
485	C₂×Q₈	—	89	1	no	—
486	C₂×Q₈	—	356	2	no	—
487	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
488	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
489	C₂×D₄	—	89	1	no	—
490	C₂×D₄	—	89	2	no	—
491	C₂×D₄	—	89	2	no	—
492	C₂×D₄	—	89	1	no	—
493	C₂×D₄	—	89	1	no	—
494	C₂×D₄	—	89	1	no	—
495	C₂×D₄	—	89	2	no	—
496	C₂×D₄	—	89	1	no	—
497	C₂×D₄	—	89	2	no	—
498	C₂×D₄	—	89	2	no	—
499	C₂×D₄	—	89	2	no	—
500	C₂×D₄	—	89	2	no	—
501	C₂×D₄	—	89	1	no	—
502	C₂×D₄	—	89	2	no	—
503	C₂×D₄	—	89	2	no	—
504	C₂×D₄	—	89	1	no	—
505	C₂×D₄	—	89	1	no	—
506	C₂×D₄	—	356	2	no	—
507	C₂×D₄	—	356	4	no	—
508	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
509	C₂²×C₄	—	89	1	no	—
510	C₂²×C₄	—	89	2	no	—
511	C₂²×C₄	—	89	2	no	—
512	C₂²×C₄	—	89	2	no	—
513	C₂²×C₄	—	89	2	no	—
514	C₂²×C₄	—	89	2	no	—
515	C₂²×C₄	—	89	1	no	—
516	C₂²×C₄	—	89	2	no	—
517	C₂²×C₄	—	89	1	no	—
518	C₂²×C₄	—	89	2	no	—
519	C₂²×C₄	—	89	1	no	—
520	C₂²×C₄	—	89	1	no	—
521	C₂²×C₄	—	89	1	no	—
522	C₂²×C₄	—	356	2	no	—
523	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
526	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
527	C₄⋊C₄	—	89	1	no	—
528	C₄⋊C₄	—	89	2	no	—
529	C₄⋊C₄	—	89	2	no	—
530	C₄⋊C₄	—	89	2	no	—
531	C₄⋊C₄	—	89	2	no	—
532	C₄⋊C₄	—	89	2	no	—
533	C₄⋊C₄	—	89	1	no	—
534	C₄⋊C₄	—	89	1	no	—
535	C₄⋊C₄	—	89	2	no	—
536	C₄⋊C₄	—	89	1	no	—
537	C₄⋊C₄	—	89	1	no	—
538	C₄⋊C₄	—	89	1	no	—
539	C₄⋊C₄	—	89	2	no	—
540	C₄⋊C₄	—	89	2	no	—
541	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
542	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
543	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
544	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
546	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
547	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
548	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
550	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
551	C₂²⋊C₄	—	89	2	no	—
552	C₂²⋊C₄	—	89	1	no	—
553	C₂²⋊C₄	—	89	1	no	—
554	C₂²⋊C₄	—	89	2	no	—
555	C₂²⋊C₄	—	89	2	no	—
556	C₂²⋊C₄	—	89	2	no	—
557	C₂²⋊C₄	—	89	2	no	—
558	C₂²⋊C₄	—	89	2	no	—
559	C₂²⋊C₄	—	89	2	no	—
560	C₂²⋊C₄	—	89	2	no	—
561	C₂²⋊C₄	—	89	2	no	—
562	C₂²⋊C₄	—	89	2	no	—
563	C₂²⋊C₄	—	89	2	no	—
564	C₂²⋊C₄	—	89	1	no	—
565	C₂²⋊C₄	—	89	1	no	—
566	C₂²⋊C₄	—	89	1	no	—
567	C₂²⋊C₄	—	89	1	no	—
568	C₂²⋊C₄	—	89	2	no	—
569	C₂²⋊C₄	—	89	2	no	—
570	C₂²⋊C₄	—	89	2	no	—
571	C₂²⋊C₄	—	89	2	no	—
572	C₂²⋊C₄	—	89	1	no	—
573	C₂²⋊C₄	—	89	2	no	—
574	C₂²⋊C₄	—	89	1	no	—
575	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
578	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
579	C₄²	—	89	1	no	—
580	C₄²	—	89	2	no	—
581	C₄²	C₂²×D₈₉	1	1	yes	characteristic
582	C₄²	C₂²×D₈₉	1	2	yes	—
583	C₂³	—	89	1	no	—
584	C₂³	—	89	2	no	—
585	C₂³	—	89	2	no	—
586	C₂³	—	89	1	no	—
587	C₂³	—	89	1	no	—
588	C₂³	—	356	1	no	—
589	C₂³	—	356	2	no	—
590	C₂³	—	356	2	no	—
591	C₂³	—	178	2	no	—
592	C₂³	—	178	2	no	—
593	C₂³	—	178	4	no	—
594	C₂³	C₂³×D₈₉	1	1	yes	characteristic
595	C₂³	C₂³×D₈₉	1	1	yes	characteristic
596	Q₈	—	2	2	no	—
597	Q₈	—	4	2	no	—
598	Q₈	—	356	2	no	—
599	Q₈	—	356	2	no	—
600	Q₈	—	356	1	no	—
601	Q₈	—	178	2	no	—
602	D₄	—	2	2	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	2	no	—
609	D₄	—	356	2	no	—
610	D₄	—	356	1	no	—
611	D₄	—	356	1	no	—
612	D₄	—	356	2	no	—
613	D₄	—	178	4	no	—
614	D₄	—	178	4	no	—
615	D₄	—	178	2	no	—
616	D₄	—	178	2	no	—
617	D₄	—	178	2	no	—
618	D₄	—	178	2	no	—
619	D₄	—	178	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	89	1	no	—
625	C₂×C₄	—	89	1	no	—
626	C₂×C₄	—	89	2	no	—
627	C₂×C₄	—	89	1	no	—
628	C₂×C₄	—	89	2	no	—
629	C₂×C₄	—	89	1	no	—
630	C₂×C₄	—	89	1	no	—
631	C₂×C₄	—	356	1	no	—
632	C₂×C₄	—	356	1	no	—
633	C₂×C₄	—	356	2	no	—
634	C₂×C₄	—	356	2	no	—
635	C₂×C₄	—	356	2	no	—
636	C₂×C₄	—	356	2	no	—
637	C₂×C₄	—	356	2	no	—
638	C₂×C₄	—	356	2	no	—
639	C₂×C₄	—	356	1	no	—
640	C₂×C₄	—	178	4	no	—
641	C₂×C₄	—	178	2	no	—
642	C₂×C₄	—	178	2	no	—
643	C₂×C₄	—	178	2	no	—
644	C₂×C₄	C₂³×D₈₉	1	2	yes	—
645	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
647	C₂×C₄	C₂³×D₈₉	1	2	yes	—
648	C₂×C₄	C₂³×D₈₉	1	2	yes	—
649	C₂×C₄	C₂³×D₈₉	1	2	yes	—
650	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
651	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	89	2	no	—
659	C₂²	—	356	4	no	—
660	C₂²	—	178	1	no	—
661	C₂²	—	178	2	no	—
662	C₂²	—	178	2	no	—
663	C₂²	—	178	1	no	—
664	C₂²	—	178	1	no	—
665	C₂²	—	178	2	no	—
666	C₂²	—	178	2	no	—
667	C₂²	—	178	1	no	—
668	C₂²	—	178	1	no	—
669	C₂²	—	178	1	no	—
670	C₂²	—	178	2	no	—
671	C₂²	—	178	2	no	—
672	C₂²	—	178	1	no	—
673	C₂²	—	178	1	no	—
674	C₂²	—	712	4	no	—
675	C₂²	#15668060	1	2	yes	—
676	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	1	no	—
685	C₄	—	178	2	no	—
686	C₄	—	178	1	no	—
687	C₄	—	178	1	no	—
688	C₄	—	178	1	no	—
689	C₄	—	178	1	no	—
690	C₄	—	178	2	no	—
691	C₄	—	178	1	no	—
692	C₄	#15668058	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	356	1	no	—
696	C₂	—	356	1	no	—
697	C₂	—	356	2	no	—
698	C₂	—	356	2	no	—
699	C₂	—	178	2	no	—
700	C₂	H(5,𝔽₂)×D₈₉	1	1	yes	characteristic
701	C₂	C₂×#15668058	1	1	yes	characteristic
702	C₂	C₂×#15668060	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#554×C₈₉	C₂
hypercenter	#554	D₈₉
hypocenter	C₈₉	#3536
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #19152346	C₂	semidirect
2. #19152344	C₂	semidirect
3. #19152303	C₂	semidirect
4. #19152260	C₂	semidirect
5. #19152258	C₂	semidirect
6. #19152251	C₂	semidirect
7. #19152249	C₂	semidirect
8. #19152244	C₂	semidirect
9. #19152244	C₂	semidirect
10. #19152239	C₂	semidirect
11. #19152239	C₂	semidirect
12. #19152223	C₂	semidirect
13. #19152222	C₂	semidirect
14. #19152220	C₂	semidirect
15. #19152196	C₂	semidirect
16. #19152181	C₂	semidirect
17. #19152179	C₂	semidirect
18. #19152178	C₂	semidirect
19. #19152178	C₂	semidirect
20. #19152107	C₂	semidirect
21. C₂²⋊Q₈×D₈₉	C₂	semidirect
22. C₂×#15667987	C₂	semidirect
23. #554×C₈₉	C₂	semidirect
24. C₂×#13083575	C₂²	semidirect
25. C₂×#13083575	C₂²	semidirect
26. C₂×#13083574	C₂²	semidirect
27. C₂×#13083574	C₂²	semidirect
28. C₂×#13083574	C₂²	semidirect
29. C₂×Q₈×D₈₉	C₂²	semidirect
33. #15668011	C₂²	semidirect
34. #15668007	C₂²	semidirect
35. #15668006	C₂²	semidirect
36. #15668002	C₂²	semidirect
37. #15668001	C₂²	semidirect
38. #15668001	C₂²	semidirect
39. #15668000	C₂²	semidirect
40. #15668000	C₂²	semidirect
41. #15668000	C₂²	semidirect
42. #15667998	C₂²	semidirect
43. #15667997	C₂²	semidirect
44. #15667997	C₂²	semidirect
45. #15667997	C₂²	semidirect
46. #15667997	C₂²	semidirect
47. #15667997	C₂²	semidirect
48. #15667997	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667997	C₂²	semidirect
51. #15667995	C₂²	semidirect
52. #15667994	C₂²	semidirect
53. #15667992	C₂²	semidirect
54. #15667992	C₂²	semidirect
55. #15667992	C₂²	semidirect
56. #15667992	C₂²	semidirect
59. #15667990	C₂²	semidirect
60. #15667990	C₂²	semidirect
61. #15667990	C₂²	semidirect
62. #15667990	C₂²	semidirect
63. #15667990	C₂²	semidirect
64. #15667990	C₂²	semidirect
65. #15667990	C₂²	semidirect
68. #15667988	C₂²	semidirect
69. #15667988	C₂²	semidirect
70. #15667988	C₂²	semidirect
77. #15667987	C₂²	semidirect
78. #15667987	C₂²	semidirect
79. #15667987	C₂²	semidirect
80. #15667987	C₂²	semidirect
81. #15667987	C₂²	semidirect
82. #15667986	C₂²	semidirect
83. #15667986	C₂²	semidirect
84. #15667986	C₂²	semidirect
85. #15667985	C₂²	semidirect
86. #15667985	C₂²	semidirect
87. #15667985	C₂²	semidirect
88. #15667985	C₂²	semidirect
89. #15667985	C₂²	semidirect
95. #15667977	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
103. C₄×C₂²⋊D₈₉	C₂²	semidirect
104. #15667969	C₂²	semidirect
105. C₄⋊C₄×D₈₉	C₂²	semidirect
106. C₄⋊C₄×D₈₉	C₂²	semidirect
107. C₄⋊C₄×D₈₉	C₂²	semidirect
112. C₄⋊Q₈×C₈₉	C₂²	semidirect
113. #125×C₈₉	C₂²	semidirect
116. C₂²⋊Q₈×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
122. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
352. C₈₉	#3536	semidirect
356. #554	D₈₉	semidirect
386. C₄⋊Q₈	C₂×D₈₉	semidirect
390. #125	C₂×D₈₉	semidirect
427. C₂²⋊Q₈	C₂×D₈₉	semidirect
428. C₂²⋊Q₈	C₂×D₈₉	semidirect
454. C₄×Q₈	C₂×D₈₉	semidirect
470. C₂×C₄⋊C₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152346	2
#19152344	2
#19152303	2
#19152260	2
#19152258	2
#19152251	2
#19152249	2
#19152244	2
#19152239	2
#19152223	2
#19152222	2
#19152220	2
#19152196	2
#19152181	2
#19152179	2
#19152178	2
#19152107	2
C₂²⋊Q₈×D₈₉	2
C₂×#15667987	2
#554×C₈₉	2
#3536	89