Subgroups — #26034240

Order 11392.

1012 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152326	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152315	C₂	1	2	yes	maximal, complemented
3	#19152308	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152302	C₂	1	2	yes	maximal, complemented
5	#19152299	C₂	1	2	yes	maximal, complemented
6	#19152298	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152289	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152281	C₂	1	2	yes	maximal, complemented
9	#19152263	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152256	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152256	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152218	C₂	1	2	yes	maximal, complemented
13	#19152217	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152209	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152205	C₂	1	2	yes	maximal, complemented
16	#19152135	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152131	C₂	1	2	yes	maximal, complemented
18	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
19	#19152126	C₂	1	2	yes	maximal, complemented
20	#19152077	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152074	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083573	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
27	#15668012	C₂²	1	1	yes	characteristic
28	#15668011	C₂²	1	2	yes	—
29	#15668010	C₂²	1	2	yes	—
30	#15668007	C₂²	1	1	yes	characteristic
31	#15668007	C₂²	1	1	yes	characteristic
32	#15668007	C₂²	1	2	yes	—
33	#15668007	C₂²	1	2	yes	—
34	#15668006	C₂²	1	2	yes	—
35	#15668005	C₂²	1	2	yes	—
36	#15668005	C₂²	1	2	yes	—
37	#15668005	C₂²	1	2	yes	—
38	#15668004	C₂²	1	2	yes	—
39	#15668004	C₂²	1	1	yes	characteristic
40	#15668004	C₂²	1	1	yes	characteristic
41	#15668003	C₂²	1	1	yes	characteristic
42	#15668002	C₂²	1	2	yes	—
43	#15668002	C₂²	1	2	yes	—
44	#15668002	C₂²	1	2	yes	—
45	#15668002	C₂²	1	2	yes	—
46	#15668002	C₂²	1	2	yes	—
47	#15668001	C₂²	1	1	yes	characteristic
48	#15667998	C₂²	1	2	yes	—
49	#15667998	C₂²	1	2	yes	—
50	#15667998	C₂²	1	2	yes	—
51	#15667997	C₂²	1	1	yes	characteristic
52	#15667997	C₂²	1	1	yes	characteristic
53	#15667997	C₂²	1	2	yes	—
54	#15667996	C₂²	1	2	yes	—
55	#15667995	C₂²	1	2	yes	—
56	#15667994	C₂²	1	2	yes	—
57	#15667990	C₂²	1	2	yes	—
58	#15667990	C₂²	1	2	yes	—
59	#15667990	C₂²	1	2	yes	—
60	#15667990	C₂²	1	2	yes	—
61	#15667989	C₂²	1	2	yes	—
62	#15667989	C₂²	1	2	yes	—
63	#15667989	C₂²	1	2	yes	—
64	#15667988	C₂²	1	1	yes	characteristic
65	#15667988	C₂²	1	1	yes	characteristic
66	#15667988	C₂²	1	1	yes	characteristic
67	#15667988	C₂²	1	1	yes	characteristic
68	#15667988	C₂²	1	1	yes	characteristic
69	#15667987	C₂²	1	1	yes	characteristic
70	#15667985	C₂²	1	2	yes	—
71	#15667985	C₂²	1	2	yes	—
72	#15667985	C₂²	1	2	yes	—
73	#15667983	C₂²	1	1	yes	characteristic
74	#15667983	C₂²	1	1	yes	characteristic
75	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
76	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
77	C₄×Dic₁₇₈	C₂²	1	2	yes	—
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
80	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
81	C₄×Dic₁₇₈	C₂²	1	2	yes	—
82	#15667977	C₂²	1	2	yes	—
83	#15667977	C₂²	1	2	yes	—
84	#15667977	C₂²	1	2	yes	—
85	#15667977	C₂²	1	1	yes	characteristic
86	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
87	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
88	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
89	C₄×D₃₅₆	C₂²	1	2	yes	—
90	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
91	#15667974	C₂²	1	2	yes	—
92	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
93	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
94	#15667972	C₂²	1	2	yes	—
95	#15667972	C₂²	1	2	yes	—
96	#15667972	C₂²	1	2	yes	—
97	#15667972	C₂²	1	2	yes	—
98	#15667970	C₂²	1	2	yes	—
99	#15667970	C₂²	1	1	yes	characteristic
100	#15667969	C₂²	1	1	yes	characteristic
101	#15667969	C₂²	1	1	yes	characteristic
102	#15667969	C₂²	1	2	yes	—
103	#15667969	C₂²	1	2	yes	—
104	#15667968	C₂²	1	2	yes	—
105	#15667968	C₂²	1	2	yes	—
106	C₂×#13083553	C₂²	1	2	yes	—
107	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₄²×D₈₉	C₂²	1	2	yes	—
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
113	#126×C₈₉	C₂²	1	2	yes	—
114	#126×C₈₉	C₂²	1	2	yes	—
115	#124×C₈₉	C₂²	1	1	yes	characteristic
116	#124×C₈₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	#117×C₈₉	C₂²	1	2	yes	—
123	#13083573	—	2	4	no	—
124	C₂×Dic₁₇₈	C₂³	1	2	yes	—
125	C₂×Dic₁₇₈	C₂³	1	2	yes	—
126	C₂×Dic₁₇₈	C₂³	1	2	yes	—
127	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
128	Q₈×D₈₉	—	2	4	no	—
129	Q₈×D₈₉	—	2	4	no	—
130	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
131	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
132	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
136	C₂²×Dic₈₉	C₂³	1	2	yes	—
137	C₂²×Dic₈₉	C₂³	1	2	yes	—
138	C₂×C₄×D₈₉	C₂³	1	2	yes	—
139	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₈₉	C₂³	1	2	yes	—
142	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₈₉	C₂³	1	2	yes	—
145	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₈₉	C₂³	1	2	yes	—
147	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₈₉	C₂³	1	2	yes	—
149	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
151	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
152	C₄⋊Dic₈₉	C₂³	1	2	yes	—
153	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₈₉	C₂³	1	2	yes	—
156	#13083553	C₂³	1	1	yes	characteristic
157	#13083553	C₂³	1	2	yes	—
158	#13083553	C₂³	1	2	yes	—
159	#13083553	C₂³	1	2	yes	—
160	#13083553	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	2	yes	—
165	#13083553	C₂³	1	1	yes	characteristic
166	#13083553	C₂³	1	2	yes	—
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	#13083553	C₂³	1	2	yes	—
172	#13083553	C₂³	1	2	yes	—
173	#13083553	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
175	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
176	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
177	#13083551	C₂³	1	1	yes	characteristic
178	#13083551	C₂³	1	1	yes	characteristic
179	#13083551	C₂³	1	2	yes	—
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	1	yes	characteristic
185	#13083551	C₂³	1	1	yes	characteristic
186	#13083551	C₂³	1	2	yes	—
187	#13083551	C₂³	1	1	yes	characteristic
188	#13083551	C₂³	1	2	yes	—
189	#13083551	C₂³	1	2	yes	—
190	#13083551	C₂³	1	1	yes	characteristic
191	#13083551	C₂³	1	1	yes	characteristic
192	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
193	C₄×Dic₈₉	C₂³	1	2	yes	—
194	C₄×Dic₈₉	C₂³	1	2	yes	—
195	C₄×Dic₈₉	C₂³	1	2	yes	—
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	2	yes	—
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₉	C₂³	1	2	yes	—
202	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
203	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
204	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
205	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
209	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
210	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
211	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
212	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
216	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
218	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
220	C₄²×C₈₉	C₂³	1	2	yes	—
221	C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₄²×C₈₉	C₂³	1	1	yes	characteristic
223	C₄²×C₈₉	C₂³	1	2	yes	—
224	C₄²×C₈₉	C₂³	1	1	yes	characteristic
225	C₂³×C₈₉	C₂⁴	1	2	yes	—
226	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
228	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
229	Q₈×C₈₉	—	2	2	no	—
230	Q₈×C₈₉	—	2	2	no	—
231	Q₈×C₈₉	—	4	1	no	—
232	D₄×C₈₉	—	2	2	no	—
233	C₂×C₄×C₈₉	—	4	2	no	—
234	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
237	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
240	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂²⋊D₈₉	—	2	4	no	—
245	C₂²⋊D₈₉	—	2	4	no	—
246	C₂²⋊D₈₉	—	4	2	no	—
247	C₂×Dic₈₉	—	2	4	no	—
248	C₂×Dic₈₉	—	4	2	no	—
249	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₈₉	C₂⁴	1	2	yes	—
252	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	2	yes	—
255	C₂×Dic₈₉	C₂⁴	1	2	yes	—
256	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₈₉	C₂⁴	1	2	yes	—
258	D₃₅₆	—	2	2	no	—
259	D₃₅₆	—	2	2	no	—
260	D₃₅₆	—	4	1	no	—
261	C₄×D₈₉	—	2	2	no	—
262	C₄×D₈₉	—	2	2	no	—
263	C₄×D₈₉	—	2	2	no	—
264	C₄×D₈₉	—	2	2	no	—
265	C₄×D₈₉	—	2	4	no	—
266	C₄×D₈₉	—	2	4	no	—
267	C₄×D₈₉	—	4	2	no	—
268	C₄×D₈₉	—	4	2	no	—
269	C₄×D₈₉	—	4	1	no	—
270	Dic₁₇₈	—	2	4	no	—
271	Dic₁₇₈	—	2	4	no	—
272	Dic₁₇₈	—	4	2	no	—
273	Dic₁₇₈	#41	1	4	yes	—
274	C₂²×C₈₉	—	2	2	no	—
275	C₂²×C₈₉	—	2	2	no	—
276	C₂²×C₈₉	—	2	2	no	—
277	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
278	C₂×D₈₉	—	2	1	no	—
279	C₂×D₈₉	—	2	1	no	—
280	C₂×D₈₉	—	2	1	no	—
281	C₂×D₈₉	—	2	1	no	—
282	C₂×D₈₉	—	2	1	no	—
283	C₂×D₈₉	—	2	1	no	—
284	C₂×D₈₉	—	2	1	no	—
285	C₂×D₈₉	—	2	1	no	—
286	C₂×D₈₉	2₋¹⁺⁴	1	2	yes	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	2	no	—
289	C₄×C₈₉	—	2	1	no	—
290	C₄×C₈₉	—	2	1	no	—
291	C₄×C₈₉	—	2	1	no	—
292	C₄×C₈₉	—	2	1	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	2	1	no	—
295	C₄×C₈₉	—	2	1	no	—
296	C₄×C₈₉	C₂×#41	1	2	yes	—
297	Dic₈₉	—	2	1	no	—
298	Dic₈₉	—	2	1	no	—
299	Dic₈₉	—	2	1	no	—
300	Dic₈₉	—	2	1	no	—
301	Dic₈₉	—	2	2	no	—
302	Dic₈₉	—	2	2	no	—
303	Dic₈₉	—	2	2	no	—
304	Dic₈₉	—	2	1	no	—
305	Dic₈₉	C₂×#41	1	4	yes	—
306	C₂×C₈₉	—	4	2	no	—
307	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
308	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
309	C₂×C₈₉	#585	1	1	yes	characteristic
310	D₈₉	—	2	2	no	—
311	D₈₉	—	4	1	no	—
312	D₈₉	—	4	1	no	—
313	#3516	—	89	1	no	maximal, Sylow
314	C₈₉	#3516	1	1	yes	characteristic, complemented, Sylow
315	#557	—	89	1	no	—
316	#556	—	89	2	no	—
317	#556	D₈₉	1	1	yes	characteristic, complemented
318	#554	—	89	2	no	—
319	#554	—	89	1	no	—
320	#553	—	89	2	no	—
321	#553	—	89	1	no	—
322	#552	—	89	1	no	—
323	#552	—	89	2	no	—
324	D₄×Q₈	—	89	1	no	—
325	#548	—	89	1	no	—
326	#548	—	89	1	no	—
327	#542	—	89	1	no	—
328	#542	—	89	2	no	—
329	#541	—	89	1	no	—
330	#541	—	89	2	no	—
331	#529	—	89	2	no	—
332	#529	—	89	1	no	—
333	#529	—	89	1	no	—
334	#529	—	89	2	no	—
335	#520	—	89	1	no	—
336	#519	—	89	1	no	—
337	C₂×C₄×Q₈	—	89	1	no	—
338	C₂×#41	—	89	1	no	—
339	C₂²×Q₈	—	89	1	no	—
340	C₂²×Q₈	—	89	1	no	—
341	C₄⋊Q₈	—	89	2	no	—
342	C₄⋊Q₈	—	89	2	no	—
343	C₄⋊Q₈	—	89	1	no	—
344	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
345	#126	—	89	2	no	—
346	#126	—	89	1	no	—
347	#126	—	89	1	no	—
348	#126	—	89	2	no	—
349	#126	—	89	2	no	—
350	#126	—	89	2	no	—
351	#126	—	89	2	no	—
352	#126	—	89	2	no	—
353	#126	C₂×D₈₉	1	2	yes	—
354	#126	C₂×D₈₉	1	2	yes	—
355	#125	—	89	2	no	—
356	#125	—	89	1	no	—
357	#125	—	89	2	no	—
358	#125	—	89	2	no	—
359	#125	—	89	2	no	—
360	#125	—	89	2	no	—
361	#125	—	89	1	no	—
362	#125	—	89	2	no	—
363	#125	—	89	1	no	—
364	#124	—	89	1	no	—
365	#124	—	89	2	no	—
366	#124	—	89	2	no	—
367	#124	—	89	2	no	—
368	#124	C₂×D₈₉	1	1	yes	characteristic
369	#124	C₂×D₈₉	1	1	yes	characteristic
370	#123	—	89	2	no	—
371	#123	—	89	1	no	—
372	#123	—	89	1	no	—
373	#123	—	89	2	no	—
374	#123	—	89	2	no	—
375	#123	—	89	2	no	—
376	C₂²⋊Q₈	—	89	1	no	—
377	C₂²⋊Q₈	—	89	1	no	—
378	C₂²⋊Q₈	—	89	1	no	—
379	C₂²⋊Q₈	—	89	1	no	—
380	C₂²⋊Q₈	—	89	1	no	—
381	C₂²⋊Q₈	—	89	2	no	—
382	C₂²⋊Q₈	—	89	2	no	—
383	C₂²⋊Q₈	—	89	2	no	—
384	C₂²⋊Q₈	—	89	2	no	—
385	C₂²⋊Q₈	—	89	2	no	—
386	C₂²⋊Q₈	—	89	2	no	—
387	C₂²⋊Q₈	—	89	2	no	—
388	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	—
389	#121	—	89	1	no	—
390	#121	—	89	1	no	—
391	#121	—	89	1	no	—
392	#121	—	89	2	no	—
393	#121	—	89	2	no	—
394	#121	—	89	2	no	—
395	C₄×Q₈	—	89	1	no	—
396	C₄×Q₈	—	89	1	no	—
397	C₄×Q₈	—	89	1	no	—
398	C₄×Q₈	—	89	2	no	—
399	C₄×Q₈	—	89	2	no	—
400	C₄×Q₈	—	89	2	no	—
401	C₄×Q₈	—	89	1	no	—
402	C₄×Q₈	—	89	2	no	—
403	C₄×Q₈	—	89	2	no	—
404	C₄×Q₈	—	89	1	no	—
405	C₄×Q₈	—	89	1	no	—
406	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
407	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
408	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	2	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	2	no	—
413	C₄×D₄	—	89	2	no	—
414	C₄×D₄	—	89	2	no	—
415	C₄×D₄	—	89	2	no	—
416	C₄×D₄	—	89	2	no	—
417	C₄×D₄	—	89	1	no	—
418	C₄×D₄	—	89	1	no	—
419	C₄×D₄	—	89	1	no	—
420	C₄×D₄	—	89	2	no	—
421	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
422	#117	—	89	2	no	—
423	#117	—	89	1	no	—
424	#117	—	89	2	no	—
425	#117	—	89	2	no	—
426	#117	—	89	1	no	—
427	#117	—	89	2	no	—
428	#117	—	89	1	no	—
429	#117	—	89	2	no	—
430	#117	C₂×D₈₉	1	2	yes	—
431	C₂×C₄⋊C₄	—	89	2	no	—
432	C₂×C₄⋊C₄	—	89	2	no	—
433	C₂×C₄⋊C₄	—	89	1	no	—
434	C₂×C₄⋊C₄	—	89	1	no	—
435	C₂×C₄²	—	89	1	no	—
436	C₂×C₄²	—	89	2	no	—
437	#41	—	178	4	no	—
438	C₂×Q₈	—	89	1	no	—
439	C₂×Q₈	—	89	2	no	—
440	C₂×Q₈	—	89	2	no	—
441	C₂×Q₈	—	89	2	no	—
442	C₂×Q₈	—	178	4	no	—
443	C₂×Q₈	—	178	4	no	—
444	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
445	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
446	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
447	C₂×D₄	—	89	2	no	—
448	C₂×D₄	—	89	2	no	—
449	C₂×D₄	—	89	2	no	—
450	C₂×D₄	—	89	1	no	—
451	C₂×D₄	—	89	1	no	—
452	C₂×D₄	—	89	1	no	—
453	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
454	C₂²×C₄	—	89	2	no	—
455	C₂²×C₄	—	89	2	no	—
456	C₂²×C₄	—	89	1	no	—
457	C₂²×C₄	—	89	2	no	—
458	C₂²×C₄	—	89	2	no	—
459	C₂²×C₄	—	89	1	no	—
460	C₂²×C₄	—	89	2	no	—
461	C₂²×C₄	—	89	1	no	—
462	C₂²×C₄	—	89	1	no	—
463	C₂²×C₄	—	89	2	no	—
464	C₂²×C₄	—	89	1	no	—
465	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
466	C₄⋊C₄	—	89	2	no	—
467	C₄⋊C₄	—	89	1	no	—
468	C₄⋊C₄	—	89	2	no	—
469	C₄⋊C₄	—	89	2	no	—
470	C₄⋊C₄	—	89	1	no	—
471	C₄⋊C₄	—	89	2	no	—
472	C₄⋊C₄	—	89	1	no	—
473	C₄⋊C₄	—	89	2	no	—
474	C₄⋊C₄	—	89	2	no	—
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	2	no	—
477	C₄⋊C₄	—	89	2	no	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	89	1	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	2	no	—
482	C₄⋊C₄	—	89	2	no	—
483	C₄⋊C₄	—	89	2	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	—	89	1	no	—
486	C₄⋊C₄	—	89	2	no	—
487	C₄⋊C₄	—	89	1	no	—
488	C₄⋊C₄	—	89	2	no	—
489	C₄⋊C₄	—	89	2	no	—
490	C₄⋊C₄	—	89	2	no	—
491	C₄⋊C₄	—	89	1	no	—
492	C₄⋊C₄	—	89	2	no	—
493	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
495	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
496	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
498	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
499	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	89	2	no	—
511	C₂²⋊C₄	—	89	1	no	—
512	C₂²⋊C₄	—	89	2	no	—
513	C₂²⋊C₄	—	89	1	no	—
514	C₂²⋊C₄	—	89	1	no	—
515	C₂²⋊C₄	—	89	2	no	—
516	C₂²⋊C₄	—	89	1	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	1	no	—
519	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
524	C₄²	—	89	2	no	—
525	C₄²	—	89	1	no	—
526	C₄²	—	89	1	no	—
527	C₄²	—	89	2	no	—
528	C₄²	—	89	1	no	—
529	C₄²	—	89	2	no	—
530	C₄²	—	89	2	no	—
531	C₄²	—	89	2	no	—
532	C₄²	—	89	2	no	—
533	C₄²	—	89	2	no	—
534	C₄²	C₂²×D₈₉	1	2	yes	—
535	C₄²	C₂²×D₈₉	1	1	yes	characteristic
536	C₄²	C₂²×D₈₉	1	2	yes	—
537	C₄²	C₂²×D₈₉	1	1	yes	characteristic
538	C₄²	C₂²×D₈₉	1	1	yes	characteristic
539	C₂³	—	89	1	no	—
540	C₂³	—	89	1	no	—
541	C₂³	—	89	1	no	—
542	C₂³	C₂³×D₈₉	1	2	yes	—
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	89	4	no	—
547	Q₈	—	356	2	no	—
548	Q₈	—	178	4	no	—
549	Q₈	—	178	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	356	1	no	—
552	D₄	—	356	2	no	—
553	D₄	—	178	2	no	—
554	D₄	—	178	2	no	—
555	D₄	—	178	4	no	—
556	D₄	—	178	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	89	2	no	—
559	C₂×C₄	—	89	1	no	—
560	C₂×C₄	—	89	1	no	—
561	C₂×C₄	—	89	2	no	—
562	C₂×C₄	—	89	1	no	—
563	C₂×C₄	—	89	1	no	—
564	C₂×C₄	—	89	2	no	—
565	C₂×C₄	—	89	2	no	—
566	C₂×C₄	—	89	1	no	—
567	C₂×C₄	—	356	2	no	—
568	C₂×C₄	—	356	2	no	—
569	C₂×C₄	—	356	1	no	—
570	C₂×C₄	—	356	2	no	—
571	C₂×C₄	—	178	4	no	—
572	C₂×C₄	—	178	4	no	—
573	C₂×C₄	—	178	2	no	—
574	C₂×C₄	—	178	4	no	—
575	C₂×C₄	—	178	2	no	—
576	C₂×C₄	—	178	2	no	—
577	C₂×C₄	—	178	2	no	—
578	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₈₉	1	2	yes	—
580	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₈₉	1	2	yes	—
583	C₂×C₄	C₂³×D₈₉	1	2	yes	—
584	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	2	no	—
591	C₂²	—	89	2	no	—
592	C₂²	—	178	1	no	—
593	C₂²	—	178	1	no	—
594	C₂²	—	178	1	no	—
595	C₂²	—	178	1	no	—
596	C₂²	—	178	1	no	—
597	C₂²	—	178	1	no	—
598	C₂²	—	178	1	no	—
599	C₂²	—	178	1	no	—
600	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	89	4	no	—
611	C₄	—	178	1	no	—
612	C₄	—	178	1	no	—
613	C₄	—	178	1	no	—
614	C₄	—	178	1	no	—
615	C₄	—	178	2	no	—
616	C₄	—	178	1	no	—
617	C₄	—	178	2	no	—
618	C₄	—	178	2	no	—
619	C₄	#41×D₈₉	1	2	yes	—
620	C₂	—	4	2	no	—
621	C₂	—	356	1	no	—
622	C₂	—	356	1	no	—
623	C₂	—	178	2	no	—
624	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
625	C₂	2₋¹⁺⁴×D₈₉	1	1	yes	characteristic
626	C₂	#19152434	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	#3516
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. #19152326	C₂	semidirect
2. #19152315	C₂	semidirect
3. #19152308	C₂	semidirect
4. #19152302	C₂	semidirect
5. #19152299	C₂	semidirect
6. #19152298	C₂	semidirect
7. #19152289	C₂	semidirect
8. #19152281	C₂	semidirect
9. #19152263	C₂	semidirect
10. #19152256	C₂	semidirect
11. #19152256	C₂	semidirect
12. #19152218	C₂	semidirect
13. #19152217	C₂	semidirect
14. #19152209	C₂	semidirect
15. #19152205	C₂	semidirect
16. #19152135	C₂	semidirect
17. #19152131	C₂	semidirect
18. #19152127	C₂	semidirect
19. #19152126	C₂	semidirect
20. #19152077	C₂	semidirect
21. #19152074	C₂	semidirect
22. C₄×Q₈×D₈₉	C₂	semidirect
23. #556×C₈₉	C₂	semidirect
314. C₈₉	#3516	semidirect
317. #556	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152326	2
#19152315	2
#19152308	2
#19152302	2
#19152299	2
#19152298	2
#19152289	2
#19152281	2
#19152263	2
#19152256	2
#19152218	2
#19152217	2
#19152209	2
#19152205	2
#19152135	2
#19152131	2
#19152127	2
#19152126	2
#19152077	2
#19152074	2
C₄×Q₈×D₈₉	2
#556×C₈₉	2
#3516	89