Subgroups — #26034900

Order 11392.

930 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152352	C₂	1	2	yes	maximal, complemented
2	#19152345	C₂	1	2	yes	maximal, complemented
3	#19152324	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152319	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152315	C₂	1	2	yes	maximal, complemented
6	#19152311	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152304	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152296	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152294	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152290	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152287	C₂	1	2	yes	maximal, complemented
12	#19152229	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152226	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152221	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152221	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152219	C₂	1	2	yes	maximal, complemented
17	#19152216	C₂	1	2	yes	maximal, complemented
18	#19152211	C₂	1	2	yes	maximal, complemented
19	#19152189	C₂	1	2	yes	maximal, complemented
20	#19152154	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152135	C₂	1	1	yes	maximal, characteristic, complemented
22	#19152130	C₂	1	1	yes	maximal, characteristic, complemented
23	#552×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	#15668012	C₂²	1	2	yes	—
25	#15668011	C₂²	1	1	yes	characteristic
26	#15668011	C₂²	1	1	yes	characteristic
27	#15668011	C₂²	1	2	yes	—
28	#15668011	C₂²	1	1	yes	characteristic
29	#15668011	C₂²	1	1	yes	characteristic
30	#15668011	C₂²	1	2	yes	—
31	#15668007	C₂²	1	2	yes	—
32	#15668007	C₂²	1	2	yes	—
33	#15668007	C₂²	1	2	yes	—
34	#15668007	C₂²	1	2	yes	—
35	#15668007	C₂²	1	2	yes	—
36	#15668007	C₂²	1	2	yes	—
37	#15668007	C₂²	1	2	yes	—
38	#15668005	C₂²	1	1	yes	characteristic
39	#15668005	C₂²	1	1	yes	characteristic
40	#15668005	C₂²	1	2	yes	—
41	#15668004	C₂²	1	1	yes	characteristic
42	#15668004	C₂²	1	2	yes	—
43	#15668004	C₂²	1	2	yes	—
44	#15668003	C₂²	1	1	yes	characteristic
45	#15668003	C₂²	1	1	yes	characteristic
46	#15668003	C₂²	1	2	yes	—
47	#15668003	C₂²	1	2	yes	—
48	#15668003	C₂²	1	2	yes	—
49	#15668003	C₂²	1	1	yes	characteristic
50	#15668003	C₂²	1	1	yes	characteristic
51	#15668001	C₂²	1	1	yes	characteristic
52	#15668000	C₂²	1	2	yes	—
53	#15667999	C₂²	1	1	yes	characteristic
54	#15667998	C₂²	1	2	yes	—
55	#15667998	C₂²	1	2	yes	—
56	#15667998	C₂²	1	2	yes	—
57	#15667998	C₂²	1	2	yes	—
58	#15667997	C₂²	1	2	yes	—
59	#15667997	C₂²	1	2	yes	—
60	#15667996	C₂²	1	2	yes	—
61	#15667994	C₂²	1	1	yes	characteristic
62	#15667994	C₂²	1	1	yes	characteristic
63	#15667994	C₂²	1	2	yes	—
64	#15667994	C₂²	1	2	yes	—
65	#15667994	C₂²	1	2	yes	—
66	#15667992	C₂²	1	1	yes	characteristic
67	#15667992	C₂²	1	2	yes	—
68	#15667992	C₂²	1	2	yes	—
69	#15667992	C₂²	1	2	yes	—
70	#15667991	C₂²	1	2	yes	—
71	#15667991	C₂²	1	2	yes	—
72	#15667990	C₂²	1	2	yes	—
73	#15667990	C₂²	1	2	yes	—
74	#15667990	C₂²	1	2	yes	—
75	#15667990	C₂²	1	2	yes	—
76	#15667989	C₂²	1	2	yes	—
77	#15667989	C₂²	1	2	yes	—
78	#15667988	C₂²	1	1	yes	characteristic
79	#15667987	C₂²	1	1	yes	characteristic
80	#15667986	C₂²	1	2	yes	—
81	#15667986	C₂²	1	1	yes	characteristic
82	#15667986	C₂²	1	1	yes	characteristic
83	#15667985	C₂²	1	2	yes	—
84	#15667984	C₂²	1	2	yes	—
85	#15667983	C₂²	1	1	yes	characteristic
86	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
87	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic
88	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
89	C₄×Dic₁₇₈	C₂²	1	2	yes	—
90	#15667977	C₂²	1	2	yes	—
91	#15667977	C₂²	1	2	yes	—
92	#15667977	C₂²	1	2	yes	—
93	C₄×D₃₅₆	C₂²	1	2	yes	—
94	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
95	#15667974	C₂²	1	1	yes	characteristic
96	#15667974	C₂²	1	1	yes	characteristic
97	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
99	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
100	#15667972	C₂²	1	2	yes	—
101	#15667971	C₂²	1	1	yes	characteristic
102	#15667971	C₂²	1	1	yes	characteristic
103	#15667971	C₂²	1	1	yes	characteristic
104	#15667970	C₂²	1	1	yes	characteristic
105	#15667970	C₂²	1	1	yes	characteristic
106	#15667969	C₂²	1	2	yes	—
107	#15667969	C₂²	1	2	yes	—
108	#15667968	C₂²	1	2	yes	—
109	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₈₉	C₂²	1	2	yes	—
111	C₄²×D₈₉	C₂²	1	1	yes	characteristic
112	#126×C₈₉	C₂²	1	2	yes	—
113	#125×C₈₉	C₂²	1	1	yes	characteristic
114	#125×C₈₉	C₂²	1	2	yes	—
115	#123×C₈₉	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
120	#117×C₈₉	C₂²	1	2	yes	—
121	#117×C₈₉	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
123	C₂×Dic₁₇₈	C₂³	1	2	yes	—
124	C₂×Dic₁₇₈	C₂³	1	2	yes	—
125	C₂×Dic₁₇₈	C₂³	1	2	yes	—
126	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
127	C₂×Dic₁₇₈	C₂³	1	2	yes	—
128	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
129	C₂×D₃₅₆	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
134	C₂²×Dic₈₉	C₂³	1	2	yes	—
135	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₈₉	C₂³	1	2	yes	—
137	C₂×C₄×D₈₉	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	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
146	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
151	C₄⋊Dic₈₉	C₂³	1	2	yes	—
152	C₄⋊Dic₈₉	C₂³	1	2	yes	—
153	C₄⋊Dic₈₉	C₂³	1	2	yes	—
154	C₄⋊Dic₈₉	C₂³	1	2	yes	—
155	#13083553	C₂³	1	2	yes	—
156	#13083553	C₂³	1	2	yes	—
157	#13083553	C₂³	1	1	yes	characteristic
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	2	yes	—
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	1	yes	characteristic
167	#13083553	C₂³	1	1	yes	characteristic
168	#13083553	C₂³	1	2	yes	—
169	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₈₉	C₂³	1	1	yes	characteristic
176	#13083551	C₂³	1	2	yes	—
177	#13083551	C₂³	1	2	yes	—
178	#13083551	C₂³	1	2	yes	—
179	#13083551	C₂³	1	2	yes	—
180	#13083551	C₂³	1	2	yes	—
181	#13083551	C₂³	1	2	yes	—
182	#13083551	C₂³	1	1	yes	characteristic
183	#13083551	C₂³	1	1	yes	characteristic
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	C₄×Dic₈₉	C₂³	1	2	yes	—
190	C₄×Dic₈₉	C₂³	1	2	yes	—
191	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
192	C₄×Dic₈₉	C₂³	1	2	yes	—
193	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂³	1	2	yes	—
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
200	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
203	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
204	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
205	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
207	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
208	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
209	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
210	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
211	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
213	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
214	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
215	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
217	C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
219	C₄²×C₈₉	C₂³	1	2	yes	—
220	C₄²×C₈₉	C₂³	1	2	yes	—
221	C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
223	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
224	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
225	C₂²×D₈₉	C₂⁴	1	2	yes	—
226	Q₈×C₈₉	—	2	2	no	—
227	D₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	2	no	—
230	C₂×C₄×C₈₉	—	4	2	no	—
231	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
234	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
235	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
236	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
239	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂²⋊D₈₉	—	4	2	no	—
241	C₂²⋊D₈₉	—	4	1	no	—
242	C₂²⋊D₈₉	—	4	2	no	—
243	C₂²⋊D₈₉	—	4	1	no	—
244	C₂×Dic₈₉	—	4	2	no	—
245	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₈₉	C₂⁴	1	2	yes	—
248	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
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	2	yes	—
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
255	D₃₅₆	—	2	2	no	—
256	D₃₅₆	—	4	2	no	—
257	C₄×D₈₉	—	2	2	no	—
258	C₄×D₈₉	—	4	1	no	—
259	C₄×D₈₉	—	4	1	no	—
260	C₄×D₈₉	—	4	2	no	—
261	C₄×D₈₉	—	4	2	no	—
262	C₄×D₈₉	—	4	2	no	—
263	Dic₁₇₈	—	4	2	no	—
264	Dic₁₇₈	—	4	1	no	—
265	Dic₁₇₈	—	4	2	no	—
266	Dic₁₇₈	—	4	2	no	—
267	Dic₁₇₈	—	4	2	no	—
268	C₂²×C₈₉	—	2	1	no	—
269	C₂²×C₈₉	—	2	1	no	—
270	C₂²×C₈₉	—	2	1	no	—
271	C₂²×C₈₉	—	2	1	no	—
272	C₂²×C₈₉	—	2	1	no	—
273	C₂²×C₈₉	—	2	1	no	—
274	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
275	C₂×D₈₉	—	2	1	no	—
276	C₂×D₈₉	—	2	2	no	—
277	C₂×D₈₉	—	2	2	no	—
278	C₂×D₈₉	—	2	1	no	—
279	C₂×D₈₉	—	2	2	no	—
280	C₂×D₈₉	—	2	1	no	—
281	C₄×C₈₉	—	2	1	no	—
282	C₄×C₈₉	—	2	1	no	—
283	C₄×C₈₉	—	2	2	no	—
284	C₄×C₈₉	—	2	2	no	—
285	C₄×C₈₉	—	2	2	no	—
286	C₄×C₈₉	—	2	1	no	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	1	no	—
289	C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
290	Dic₈₉	—	2	1	no	—
291	Dic₈₉	—	2	1	no	—
292	Dic₈₉	—	2	1	no	—
293	Dic₈₉	—	2	1	no	—
294	Dic₈₉	—	2	2	no	—
295	Dic₈₉	—	2	1	no	—
296	Dic₈₉	—	2	1	no	—
297	Dic₈₉	—	2	2	no	—
298	Dic₈₉	—	2	2	no	—
299	Dic₈₉	—	2	1	no	—
300	C₂×C₈₉	—	4	1	no	—
301	C₂×C₈₉	—	4	1	no	—
302	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
303	C₂×C₈₉	#585	1	1	yes	characteristic
304	C₂×C₈₉	#585	1	1	yes	characteristic
305	D₈₉	—	4	1	no	—
306	D₈₉	—	4	2	no	—
307	#3565	—	89	1	no	maximal, Sylow
308	C₈₉	#3565	1	1	yes	characteristic, complemented, Sylow
309	#563	—	89	2	no	—
310	#562	—	89	2	no	—
311	#557	—	89	1	no	—
312	#556	—	89	2	no	—
313	#556	—	89	1	no	—
314	#555	—	89	1	no	—
315	#554	—	89	1	no	—
316	#553	—	89	1	no	—
317	#553	—	89	1	no	—
318	#552	—	89	1	no	—
319	#552	—	89	2	no	—
320	#552	D₈₉	1	1	yes	characteristic, complemented
321	#544	—	89	1	no	—
322	#544	—	89	1	no	—
323	#542	—	89	2	no	—
324	#542	—	89	1	no	—
325	#542	—	89	1	no	—
326	#542	—	89	2	no	—
327	#541	—	89	2	no	—
328	#539	—	89	2	no	—
329	#533	—	89	1	no	—
330	#529	—	89	1	no	—
331	#529	—	89	1	no	—
332	C₄⋊Q₈	—	89	1	no	—
333	C₄⋊Q₈	—	89	1	no	—
334	C₄⋊Q₈	—	89	2	no	—
335	C₄⋊Q₈	—	89	1	no	—
336	C₄⋊Q₈	—	89	1	no	—
337	C₄⋊Q₈	—	89	2	no	—
338	C₄⋊Q₈	—	89	2	no	—
339	#126	—	89	2	no	—
340	#126	—	89	2	no	—
341	#126	—	89	2	no	—
342	#126	—	89	2	no	—
343	#126	—	89	2	no	—
344	#126	—	89	2	no	—
345	#126	—	89	2	no	—
346	#126	—	89	1	no	—
347	#126	—	89	1	no	—
348	#126	—	89	2	no	—
349	#126	C₂×D₈₉	1	2	yes	—
350	#125	—	89	1	no	—
351	#125	—	89	1	no	—
352	#125	—	89	2	no	—
353	#125	—	89	2	no	—
354	#125	—	89	2	no	—
355	#125	—	89	1	no	—
356	#125	—	89	1	no	—
357	#125	—	89	1	no	—
358	#125	—	89	2	no	—
359	#125	—	89	2	no	—
360	#125	C₂×D₈₉	1	1	yes	characteristic
361	#125	C₂×D₈₉	1	2	yes	—
362	#124	—	89	1	no	—
363	#124	—	89	1	no	—
364	#124	—	89	2	no	—
365	#124	—	89	2	no	—
366	#124	—	89	2	no	—
367	#124	—	89	2	no	—
368	#124	—	89	2	no	—
369	#123	—	89	2	no	—
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	#123	—	89	2	no	—
377	#123	C₂×D₈₉	1	2	yes	—
378	C₂²⋊Q₈	—	89	1	no	—
379	C₂²⋊Q₈	—	89	2	no	—
380	C₂²⋊Q₈	—	89	2	no	—
381	C₂²⋊Q₈	—	89	1	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	—	89	2	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	2	no	—
391	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
392	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
393	#121	—	89	1	no	—
394	#121	—	89	2	no	—
395	#121	—	89	1	no	—
396	#121	—	89	1	no	—
397	#121	—	89	2	no	—
398	#121	—	89	1	no	—
399	#121	—	89	2	no	—
400	C₄×Q₈	—	89	1	no	—
401	C₄×Q₈	—	89	1	no	—
402	C₄×Q₈	—	89	2	no	—
403	C₄×Q₈	—	89	2	no	—
404	C₄×Q₈	—	89	2	no	—
405	C₄×Q₈	—	89	1	no	—
406	C₄×Q₈	—	89	2	no	—
407	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
408	C₄×D₄	—	89	1	no	—
409	C₄×D₄	—	89	1	no	—
410	C₄×D₄	—	89	2	no	—
411	C₄×D₄	—	89	1	no	—
412	C₄×D₄	—	89	1	no	—
413	C₄×D₄	—	89	2	no	—
414	C₄×D₄	—	89	2	no	—
415	C₄×D₄	—	89	1	no	—
416	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
417	#117	—	89	1	no	—
418	#117	—	89	1	no	—
419	#117	—	89	1	no	—
420	#117	—	89	1	no	—
421	#117	—	89	1	no	—
422	#117	—	89	2	no	—
423	#117	—	89	2	no	—
424	#117	—	89	2	no	—
425	#117	C₂×D₈₉	1	2	yes	—
426	#117	C₂×D₈₉	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	89	1	no	—
428	C₂×C₄⋊C₄	—	89	2	no	—
429	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
430	C₂×C₄²	—	89	1	no	—
431	C₂×Q₈	—	89	1	no	—
432	C₂×Q₈	—	89	2	no	—
433	C₂×Q₈	—	89	2	no	—
434	C₂×Q₈	—	89	2	no	—
435	C₂×Q₈	—	89	2	no	—
436	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
437	C₂×D₄	—	89	1	no	—
438	C₂×D₄	—	89	2	no	—
439	C₂×D₄	—	89	1	no	—
440	C₂×D₄	—	89	2	no	—
441	C₂×D₄	—	89	2	no	—
442	C₂×D₄	—	89	1	no	—
443	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
444	C₂²×C₄	—	89	2	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	—	89	1	no	—
447	C₂²×C₄	—	89	2	no	—
448	C₂²×C₄	—	89	2	no	—
449	C₂²×C₄	—	89	2	no	—
450	C₂²×C₄	—	89	1	no	—
451	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
452	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
453	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
454	C₄⋊C₄	—	89	1	no	—
455	C₄⋊C₄	—	89	1	no	—
456	C₄⋊C₄	—	89	1	no	—
457	C₄⋊C₄	—	89	2	no	—
458	C₄⋊C₄	—	89	2	no	—
459	C₄⋊C₄	—	89	2	no	—
460	C₄⋊C₄	—	89	1	no	—
461	C₄⋊C₄	—	89	1	no	—
462	C₄⋊C₄	—	89	2	no	—
463	C₄⋊C₄	—	89	2	no	—
464	C₄⋊C₄	—	89	1	no	—
465	C₄⋊C₄	—	89	2	no	—
466	C₄⋊C₄	—	89	1	no	—
467	C₄⋊C₄	—	89	2	no	—
468	C₄⋊C₄	—	89	1	no	—
469	C₄⋊C₄	—	89	1	no	—
470	C₄⋊C₄	—	89	2	no	—
471	C₄⋊C₄	—	89	1	no	—
472	C₄⋊C₄	—	89	2	no	—
473	C₄⋊C₄	—	89	2	no	—
474	C₄⋊C₄	—	89	1	no	—
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	2	no	—
477	C₄⋊C₄	—	89	2	no	—
478	C₄⋊C₄	—	89	2	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	2	no	—
481	C₄⋊C₄	—	89	2	no	—
482	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
483	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
486	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
487	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
488	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
490	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
491	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
492	C₂²⋊C₄	—	89	1	no	—
493	C₂²⋊C₄	—	89	1	no	—
494	C₂²⋊C₄	—	89	2	no	—
495	C₂²⋊C₄	—	89	1	no	—
496	C₂²⋊C₄	—	89	1	no	—
497	C₂²⋊C₄	—	89	1	no	—
498	C₂²⋊C₄	—	89	1	no	—
499	C₂²⋊C₄	—	89	2	no	—
500	C₂²⋊C₄	—	89	2	no	—
501	C₂²⋊C₄	—	89	2	no	—
502	C₂²⋊C₄	—	89	2	no	—
503	C₂²⋊C₄	—	89	2	no	—
504	C₂²⋊C₄	—	89	2	no	—
505	C₂²⋊C₄	—	89	2	no	—
506	C₂²⋊C₄	—	89	2	no	—
507	C₂²⋊C₄	—	89	2	no	—
508	C₂²⋊C₄	—	89	1	no	—
509	C₂²⋊C₄	—	89	2	no	—
510	C₂²⋊C₄	—	89	1	no	—
511	C₂²⋊C₄	—	89	2	no	—
512	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
513	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
514	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
515	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
517	C₄²	—	89	1	no	—
518	C₄²	—	89	1	no	—
519	C₄²	—	89	1	no	—
520	C₄²	—	89	2	no	—
521	C₄²	—	89	2	no	—
522	C₄²	—	89	1	no	—
523	C₄²	—	89	1	no	—
524	C₄²	—	89	2	no	—
525	C₄²	—	89	2	no	—
526	C₄²	—	89	2	no	—
527	C₄²	C₂²×D₈₉	1	1	yes	characteristic
528	C₄²	C₂²×D₈₉	1	2	yes	—
529	C₄²	C₂²×D₈₉	1	2	yes	—
530	C₂³	—	89	1	no	—
531	C₂³	—	89	2	no	—
532	C₂³	C₂³×D₈₉	1	1	yes	characteristic
533	C₂³	C₂³×D₈₉	1	1	yes	characteristic
534	Q₈	—	2	2	no	—
535	Q₈	—	356	2	no	—
536	Q₈	—	356	2	no	—
537	Q₈	—	356	1	no	—
538	Q₈	—	356	2	no	—
539	Q₈	—	356	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	356	2	no	—
542	D₄	—	356	2	no	—
543	D₄	—	356	1	no	—
544	D₄	—	356	2	no	—
545	D₄	—	356	1	no	—
546	D₄	—	178	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	89	1	no	—
551	C₂×C₄	—	89	1	no	—
552	C₂×C₄	—	89	2	no	—
553	C₂×C₄	—	89	1	no	—
554	C₂×C₄	—	89	1	no	—
555	C₂×C₄	—	89	1	no	—
556	C₂×C₄	—	89	2	no	—
557	C₂×C₄	—	89	1	no	—
558	C₂×C₄	—	89	2	no	—
559	C₂×C₄	—	89	1	no	—
560	C₂×C₄	—	356	2	no	—
561	C₂×C₄	—	356	1	no	—
562	C₂×C₄	—	356	2	no	—
563	C₂×C₄	—	356	1	no	—
564	C₂×C₄	—	356	2	no	—
565	C₂×C₄	—	356	2	no	—
566	C₂×C₄	—	178	2	no	—
567	C₂×C₄	C₂³×D₈₉	1	2	yes	—
568	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
569	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₈₉	1	2	yes	—
571	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
572	C₂×C₄	C₂³×D₈₉	1	2	yes	—
573	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
574	C₂×C₄	C₂³×D₈₉	1	2	yes	—
575	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	178	1	no	—
583	C₂²	—	178	2	no	—
584	C₂²	—	178	1	no	—
585	C₂²	—	178	2	no	—
586	C₂²	—	178	2	no	—
587	C₂²	—	178	1	no	—
588	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	178	1	no	—
598	C₄	—	178	1	no	—
599	C₄	—	178	1	no	—
600	C₄	—	178	2	no	—
601	C₄	—	178	1	no	—
602	C₄	—	178	1	no	—
603	C₄	—	178	2	no	—
604	C₄	—	178	2	no	—
605	C₄	—	178	1	no	—
606	C₄	—	178	1	no	—
607	C₄	#15668059	1	2	yes	—
608	C₂	—	4	1	no	—
609	C₂	—	4	1	no	—
610	C₂	—	356	1	no	—
611	C₂	—	356	2	no	—
612	C₂	C₂×#15668059	1	1	yes	characteristic
613	C₂	#19152434	1	1	yes	characteristic
614	C₂	#19152435	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#552×C₈₉	C₂
hypercenter	#552	D₈₉
hypocenter	C₈₉	#3565
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #19152352	C₂	semidirect
2. #19152345	C₂	semidirect
3. #19152324	C₂	semidirect
4. #19152319	C₂	semidirect
5. #19152315	C₂	semidirect
6. #19152311	C₂	semidirect
7. #19152304	C₂	semidirect
8. #19152296	C₂	semidirect
9. #19152294	C₂	semidirect
10. #19152290	C₂	semidirect
11. #19152287	C₂	semidirect
12. #19152229	C₂	semidirect
13. #19152226	C₂	semidirect
14. #19152221	C₂	semidirect
15. #19152221	C₂	semidirect
16. #19152219	C₂	semidirect
17. #19152216	C₂	semidirect
18. #19152211	C₂	semidirect
19. #19152189	C₂	semidirect
20. #19152154	C₂	semidirect
21. #19152135	C₂	semidirect
22. #19152130	C₂	semidirect
23. #552×C₈₉	C₂	semidirect
308. C₈₉	#3565	semidirect
320. #552	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152352	2
#19152345	2
#19152324	2
#19152319	2
#19152315	2
#19152311	2
#19152304	2
#19152296	2
#19152294	2
#19152290	2
#19152287	2
#19152229	2
#19152226	2
#19152221	2
#19152219	2
#19152216	2
#19152211	2
#19152189	2
#19152154	2
#19152135	2
#19152130	2
#552×C₈₉	2
#3565	89