Subgroups — #26034606

Order 11392.

1060 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152347	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152344	C₂	1	2	yes	maximal, complemented
3	#19152340	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152314	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152310	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152275	C₂	1	2	yes	maximal, complemented
7	#19152272	C₂	1	2	yes	maximal, complemented
8	#19152271	C₂	1	2	yes	maximal, complemented
9	#19152240	C₂	1	2	yes	maximal, complemented
10	#19152236	C₂	1	2	yes	maximal, complemented
11	#19152222	C₂	1	2	yes	maximal, complemented
12	#19152218	C₂	1	2	yes	maximal, complemented
13	#19152188	C₂	1	2	yes	maximal, complemented
14	#19152182	C₂	1	2	yes	maximal, complemented
15	#19152172	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152159	C₂	1	2	yes	maximal, complemented
17	#19152125	C₂	1	2	yes	maximal, complemented
18	C₂×#15668001	C₂	1	1	yes	maximal, characteristic, complemented
19	#536×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13083574	C₂²	1	1	yes	characteristic
21	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
22	C₂×D₄×D₈₉	C₂²	1	2	yes	complemented
23	#15668010	C₂²	1	1	yes	characteristic, complemented
24	#15668010	C₂²	1	1	yes	characteristic, complemented
25	#15668007	C₂²	1	2	yes	complemented
26	#15668007	C₂²	1	2	yes	complemented
27	#15668007	C₂²	1	2	yes	complemented
28	#15668007	C₂²	1	2	yes	complemented
29	#15668006	C₂²	1	2	yes	complemented
30	#15668005	C₂²	1	2	yes	complemented
31	#15668002	C₂²	1	2	yes	complemented
32	#15668001	C₂²	1	1	yes	characteristic
33	#15668001	C₂²	1	1	yes	characteristic
34	#15668001	C₂²	1	1	yes	characteristic, complemented
35	#15668001	C₂²	1	1	yes	characteristic, complemented
36	#15668001	C₂²	1	2	yes	complemented
37	#15668001	C₂²	1	2	yes	complemented
38	#15668001	C₂²	1	2	yes	complemented
39	#15668001	C₂²	1	1	yes	characteristic, complemented
40	#15668001	C₂²	1	1	yes	characteristic, complemented
41	#15668000	C₂²	1	2	yes	complemented
42	#15667998	C₂²	1	2	yes	complemented
43	#15667998	C₂²	1	2	yes	complemented
44	#15667998	C₂²	1	2	yes	complemented
45	#15667997	C₂²	1	2	yes	—
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	#15667996	C₂²	1	2	yes	complemented
51	#15667995	C₂²	1	2	yes	complemented
52	#15667995	C₂²	1	2	yes	complemented
53	#15667995	C₂²	1	2	yes	complemented
54	#15667994	C₂²	1	2	yes	complemented
55	#15667992	C₂²	1	2	yes	complemented
56	#15667990	C₂²	1	2	yes	complemented
57	#15667990	C₂²	1	2	yes	complemented
58	#15667989	C₂²	1	2	yes	complemented
59	#15667988	C₂²	1	2	yes	complemented
60	#15667988	C₂²	1	2	yes	complemented
61	#15667988	C₂²	1	2	yes	complemented
62	#15667987	C₂²	1	2	yes	—
63	#15667987	C₂²	1	2	yes	complemented
64	#15667987	C₂²	1	2	yes	complemented
65	#15667986	C₂²	1	2	yes	complemented
66	#15667985	C₂²	1	2	yes	—
67	#15667985	C₂²	1	2	yes	complemented
68	#15667985	C₂²	1	2	yes	complemented
69	#15667984	C₂²	1	2	yes	—
70	#15667984	C₂²	1	2	yes	complemented
71	#15667982	C₂²	1	2	yes	—
72	#15667982	C₂²	1	2	yes	—
73	#15667982	C₂²	1	2	yes	complemented
74	#15667982	C₂²	1	2	yes	complemented
75	#15667980	C₂²	1	2	yes	—
76	#15667980	C₂²	1	2	yes	complemented
77	#15667977	C₂²	1	2	yes	complemented
78	C₄×D₃₅₆	C₂²	1	2	yes	complemented
79	D₄×Dic₈₉	C₂²	1	2	yes	complemented
80	#15667974	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
82	#15667972	C₂²	1	2	yes	complemented
83	#15667972	C₂²	1	2	yes	complemented
84	#15667972	C₂²	1	2	yes	complemented
85	#15667971	C₂²	1	1	yes	characteristic, complemented
86	#15667970	C₂²	1	2	yes	complemented
87	#15667970	C₂²	1	2	yes	complemented
88	#15667969	C₂²	1	2	yes	complemented
89	#15667968	C₂²	1	2	yes	complemented
90	C₂×#13083551	C₂²	1	2	yes	complemented
91	C₂×#13083551	C₂²	1	2	yes	complemented
92	C₂×#13083551	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	complemented
95	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
97	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
98	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
99	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
100	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
101	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
102	#123×C₈₉	C₂²	1	2	yes	complemented
103	#123×C₈₉	C₂²	1	2	yes	complemented
104	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
105	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
106	#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
107	C₂³×D₈₉	C₂³	1	2	yes	—
108	C₂³×D₈₉	C₂³	1	2	yes	—
109	#13083574	—	4	2	no	—
110	C₂×Dic₁₇₈	C₂³	1	2	yes	—
111	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
112	C₂×D₃₅₆	—	4	2	no	—
113	C₂×D₃₅₆	C₂³	1	2	yes	—
114	C₂×D₃₅₆	C₂³	1	2	yes	—
115	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
116	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
117	C₂×D₃₅₆	C₂³	1	2	yes	—
118	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
119	C₂×D₃₅₆	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
125	D₄×D₈₉	—	4	4	no	—
126	C₂²×Dic₈₉	C₂³	1	2	yes	—
127	C₂²×Dic₈₉	C₂³	1	2	yes	—
128	C₂×C₄×D₈₉	C₂³	1	2	yes	—
129	C₂×C₄×D₈₉	C₂³	1	2	yes	—
130	C₂×C₄×D₈₉	C₂³	1	2	yes	—
131	C₂×C₄×D₈₉	C₂³	1	2	yes	—
132	C₂×C₄×D₈₉	C₂³	1	2	yes	—
133	C₄⋊Dic₈₉	C₂³	1	2	yes	—
134	C₄⋊Dic₈₉	C₂³	1	2	yes	—
135	C₄⋊Dic₈₉	C₂³	1	2	yes	—
136	#13083553	C₂³	1	2	yes	—
137	#13083553	C₂³	1	2	yes	—
138	#13083553	C₂³	1	2	yes	—
139	#13083553	C₂³	1	2	yes	—
140	#13083553	C₂³	1	2	yes	—
141	#13083553	C₂³	1	2	yes	—
142	#13083553	C₂³	1	2	yes	—
143	#13083553	C₂³	1	2	yes	—
144	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
145	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
146	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
147	#13083551	C₂³	1	2	yes	—
148	#13083551	C₂³	1	2	yes	—
149	#13083551	C₂³	1	2	yes	—
150	#13083551	C₂³	1	2	yes	—
151	#13083551	C₂³	1	2	yes	—
152	#13083551	C₂³	1	2	yes	—
153	#13083551	C₂³	1	2	yes	—
154	#13083551	C₂³	1	2	yes	—
155	#13083551	C₂³	1	2	yes	—
156	#13083551	C₂³	1	2	yes	—
157	#13083551	C₂³	1	2	yes	—
158	#13083551	C₂³	1	2	yes	—
159	#13083551	C₂³	1	2	yes	—
160	#13083551	C₂³	1	2	yes	—
161	#13083551	C₂³	1	2	yes	—
162	#13083551	C₂³	1	2	yes	—
163	#13083551	C₂³	1	2	yes	—
164	#13083551	C₂³	1	2	yes	—
165	#13083551	C₂³	1	2	yes	—
166	#13083551	C₂³	1	2	yes	—
167	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
168	C₄×Dic₈₉	C₂³	1	2	yes	—
169	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
170	C₄×Dic₈₉	C₂³	1	2	yes	—
171	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
172	C₄×Dic₈₉	C₂³	1	2	yes	—
173	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
174	#41×C₈₉	—	4	2	no	—
175	C₂×Q₈×C₈₉	—	4	2	no	—
176	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
177	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
178	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
179	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
180	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₈₉	C₂³	1	2	yes	—
182	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
187	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
191	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
195	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
197	C₄²×C₈₉	C₂³	1	1	yes	characteristic
198	C₄²×C₈₉	C₂³	1	1	yes	characteristic
199	C₂³×C₈₉	C₂⁴	1	2	yes	—
200	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₂²×D₈₉	—	2	4	no	—
202	C₂²×D₈₉	—	4	2	no	—
203	C₂²×D₈₉	—	4	2	no	—
204	C₂²×D₈₉	—	4	2	no	—
205	C₂²×D₈₉	—	4	2	no	—
206	C₂²×D₈₉	—	4	2	no	—
207	C₂²×D₈₉	C₂⁴	1	2	yes	—
208	C₂²×D₈₉	C₂⁴	1	2	yes	—
209	C₂²×D₈₉	C₂⁴	1	2	yes	—
210	Q₈×C₈₉	—	4	1	no	—
211	Q₈×C₈₉	—	4	1	no	—
212	Q₈×C₈₉	—	4	1	no	—
213	Q₈×C₈₉	—	4	1	no	—
214	Q₈×C₈₉	—	4	1	no	—
215	D₄×C₈₉	—	2	4	no	—
216	D₄×C₈₉	—	4	1	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	4	2	no	—
221	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
223	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
225	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
226	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
229	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²⋊D₈₉	—	2	4	no	—
231	C₂²⋊D₈₉	—	4	2	no	—
232	C₂²⋊D₈₉	—	4	2	no	—
233	C₂²⋊D₈₉	—	4	2	no	—
234	C₂²⋊D₈₉	—	4	2	no	—
235	C₂×Dic₈₉	—	4	2	no	—
236	C₂×Dic₈₉	—	4	2	no	—
237	C₂×Dic₈₉	C₂⁴	1	2	yes	—
238	C₂×Dic₈₉	C₂⁴	1	2	yes	—
239	C₂×Dic₈₉	C₂⁴	1	2	yes	—
240	C₂×Dic₈₉	C₂⁴	1	2	yes	—
241	C₂×Dic₈₉	C₂⁴	1	2	yes	—
242	D₃₅₆	—	4	2	no	—
243	D₃₅₆	—	4	1	no	—
244	D₃₅₆	—	4	2	no	—
245	D₃₅₆	—	4	1	no	—
246	D₃₅₆	—	4	2	no	—
247	D₃₅₆	—	4	2	no	—
248	D₃₅₆	—	4	1	no	—
249	C₄×D₈₉	—	4	2	no	—
250	C₄×D₈₉	—	4	2	no	—
251	C₄×D₈₉	—	4	2	no	—
252	C₄×D₈₉	—	4	2	no	—
253	C₄×D₈₉	—	4	2	no	—
254	Dic₁₇₈	—	4	2	no	—
255	Dic₁₇₈	—	4	1	no	—
256	C₂²×C₈₉	—	2	2	no	—
257	C₂²×C₈₉	—	2	2	no	—
258	C₂²×C₈₉	—	2	2	no	—
259	C₂²×C₈₉	—	2	2	no	—
260	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
261	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
262	C₂×D₈₉	—	2	2	no	—
263	C₂×D₈₉	—	2	2	no	—
264	C₂×D₈₉	—	2	2	no	—
265	C₂×D₈₉	—	2	2	no	—
266	C₂×D₈₉	—	2	2	no	—
267	C₂×D₈₉	—	2	2	no	—
268	C₂×D₈₉	—	2	2	no	—
269	C₂×D₈₉	—	2	2	no	—
270	C₂×D₈₉	—	2	2	no	—
271	C₂×D₈₉	—	8	4	no	—
272	C₂×D₈₉	—	8	4	no	—
273	C₄×C₈₉	—	2	1	no	—
274	C₄×C₈₉	—	2	1	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	1	no	—
277	C₄×C₈₉	—	2	1	no	—
278	C₄×C₈₉	—	2	1	no	—
279	C₄×C₈₉	—	2	1	no	—
280	C₄×C₈₉	—	2	2	no	—
281	C₄×C₈₉	—	2	2	no	—
282	Dic₈₉	—	2	2	no	—
283	Dic₈₉	—	2	2	no	—
284	Dic₈₉	—	2	2	no	—
285	Dic₈₉	—	2	2	no	—
286	Dic₈₉	—	2	2	no	—
287	C₂×C₈₉	—	2	2	no	—
288	C₂×C₈₉	—	4	2	no	—
289	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₈₉	#585	1	2	yes	—
291	D₈₉	—	4	2	no	—
292	D₈₉	—	4	2	no	—
293	D₈₉	—	4	2	no	—
294	#3545	—	89	1	no	maximal, Sylow
295	C₈₉	#3545	1	1	yes	characteristic, complemented, Sylow
296	#563	—	89	1	no	—
297	#562	—	89	2	no	—
298	H(3,𝔽₄)	—	89	1	no	—
299	#555	—	89	1	no	—
300	#555	—	89	1	no	—
301	#551	—	89	2	no	—
302	#551	—	89	2	no	—
303	#551	—	89	2	no	—
304	#546	—	89	2	no	—
305	#546	—	89	2	no	—
306	#542	—	89	2	no	—
307	#542	—	89	2	no	—
308	#538	—	89	2	no	—
309	#538	—	89	2	no	—
310	#536	—	89	1	no	—
311	#536	D₈₉	1	1	yes	characteristic, complemented
312	#534	—	89	2	no	—
313	#529	—	89	2	no	—
314	C₂×#124	—	89	1	no	—
315	C₂×#41	—	89	1	no	—
316	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
317	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
318	C₂²×D₄	—	89	2	no	—
319	C₂²×D₄	—	89	1	no	—
320	C₄⋊Q₈	—	89	1	no	—
321	C₄⋊Q₈	—	89	1	no	—
322	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
323	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
324	#126	—	89	2	no	—
325	#126	—	89	2	no	—
326	#126	—	89	2	no	—
327	#126	—	89	2	no	—
328	#126	—	89	2	no	—
329	#126	—	89	2	no	—
330	#125	—	89	2	no	—
331	#124	—	89	2	no	—
332	#124	—	89	2	no	—
333	#124	—	89	1	no	—
334	#124	—	89	1	no	—
335	#124	—	89	1	no	—
336	#124	—	89	1	no	—
337	#124	—	89	1	no	—
338	#124	—	89	1	no	—
339	#124	—	89	2	no	—
340	#124	—	89	2	no	—
341	#124	—	89	2	no	—
342	#124	—	89	2	no	—
343	#124	—	89	2	no	—
344	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
345	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
346	#123	—	89	2	no	—
347	#123	—	89	2	no	—
348	#123	—	89	2	no	—
349	#123	—	89	2	no	—
350	#123	—	89	2	no	—
351	#123	—	89	2	no	—
352	#123	—	89	2	no	—
353	#123	—	89	2	no	—
354	#123	—	89	2	no	—
355	#123	—	89	2	no	—
356	#123	C₂×D₈₉	1	2	yes	complemented
357	#123	C₂×D₈₉	1	2	yes	complemented
358	C₂²⋊Q₈	—	89	2	no	—
359	C₂²⋊Q₈	—	89	2	no	—
360	C₂²⋊Q₈	—	89	2	no	—
361	C₂²⋊Q₈	—	89	2	no	—
362	C₂²⋊Q₈	—	89	2	no	—
363	C₂²⋊Q₈	—	89	2	no	—
364	C₂²⋊Q₈	—	89	2	no	—
365	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
366	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
367	#121	—	89	2	no	—
368	#121	—	89	2	no	—
369	#121	—	89	2	no	—
370	#121	—	89	2	no	—
371	#121	—	89	2	no	—
372	#121	—	89	2	no	—
373	#121	—	89	2	no	—
374	#121	—	89	2	no	—
375	#121	—	89	2	no	—
376	#120	—	89	2	no	—
377	#120	—	89	2	no	—
378	#120	—	89	2	no	—
379	#120	—	89	2	no	—
380	#120	—	89	2	no	—
381	#120	—	89	2	no	—
382	C₄×Q₈	—	89	2	no	—
383	C₄×D₄	—	89	2	no	—
384	C₄×D₄	—	89	2	no	—
385	C₄×D₄	—	89	2	no	—
386	C₄×D₄	—	89	2	no	—
387	C₄×D₄	—	89	2	no	—
388	C₄×D₄	—	89	2	no	—
389	C₄×D₄	—	89	2	no	—
390	#117	—	89	1	no	—
391	#117	—	89	2	no	—
392	#117	—	89	2	no	—
393	#117	—	89	2	no	—
394	#117	—	89	2	no	—
395	#117	C₂×D₈₉	1	1	yes	characteristic, complemented
396	C₂×C₂²⋊C₄	—	89	2	no	—
397	C₂×C₂²⋊C₄	—	89	2	no	—
398	C₂×C₂²⋊C₄	—	89	2	no	—
399	C₂×C₂²⋊C₄	—	89	2	no	—
400	C₂×C₂²⋊C₄	—	89	2	no	—
401	C₂×C₄²	—	89	1	no	—
402	C₂⁴	—	89	2	no	—
403	C₂⁴	—	89	2	no	—
404	#41	—	4	2	no	—
405	#41	—	356	2	no	—
406	C₂×Q₈	—	4	2	no	—
407	C₂×Q₈	—	89	2	no	—
408	C₂×Q₈	—	89	1	no	—
409	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
410	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
411	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
412	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
413	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
414	C₂×D₄	—	89	2	no	—
415	C₂×D₄	—	89	2	no	—
416	C₂×D₄	—	89	2	no	—
417	C₂×D₄	—	89	2	no	—
418	C₂×D₄	—	89	2	no	—
419	C₂×D₄	—	89	2	no	—
420	C₂×D₄	—	89	2	no	—
421	C₂×D₄	—	89	1	no	—
422	C₂×D₄	—	89	1	no	—
423	C₂×D₄	—	89	2	no	—
424	C₂×D₄	—	89	2	no	—
425	C₂×D₄	—	89	1	no	—
426	C₂×D₄	—	356	2	no	—
427	C₂×D₄	—	356	4	no	—
428	C₂×D₄	C₂²×D₈₉	1	2	yes	—
429	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
430	C₂²×C₄	—	89	2	no	—
431	C₂²×C₄	—	89	2	no	—
432	C₂²×C₄	—	89	2	no	—
433	C₂²×C₄	—	89	2	no	—
434	C₂²×C₄	—	89	2	no	—
435	C₂²×C₄	—	89	2	no	—
436	C₂²×C₄	—	89	2	no	—
437	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
438	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
440	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
441	C₄⋊C₄	—	89	2	no	—
442	C₄⋊C₄	—	89	2	no	—
443	C₄⋊C₄	—	89	2	no	—
444	C₄⋊C₄	—	89	2	no	—
445	C₄⋊C₄	—	89	2	no	—
446	C₄⋊C₄	—	89	2	no	—
447	C₄⋊C₄	—	89	2	no	—
448	C₄⋊C₄	—	89	2	no	—
449	C₄⋊C₄	—	89	2	no	—
450	C₄⋊C₄	—	89	2	no	—
451	C₄⋊C₄	—	89	2	no	—
452	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
453	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
454	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
455	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
456	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
457	C₂²⋊C₄	—	89	2	no	—
458	C₂²⋊C₄	—	89	2	no	—
459	C₂²⋊C₄	—	89	2	no	—
460	C₂²⋊C₄	—	89	2	no	—
461	C₂²⋊C₄	—	89	2	no	—
462	C₂²⋊C₄	—	89	2	no	—
463	C₂²⋊C₄	—	89	2	no	—
464	C₂²⋊C₄	—	89	2	no	—
465	C₂²⋊C₄	—	89	2	no	—
466	C₂²⋊C₄	—	89	2	no	—
467	C₂²⋊C₄	—	89	2	no	—
468	C₂²⋊C₄	—	89	2	no	—
469	C₂²⋊C₄	—	89	2	no	—
470	C₂²⋊C₄	—	89	2	no	—
471	C₂²⋊C₄	—	89	2	no	—
472	C₂²⋊C₄	—	89	2	no	—
473	C₂²⋊C₄	—	89	2	no	—
474	C₂²⋊C₄	—	89	2	no	—
475	C₂²⋊C₄	—	89	2	no	—
476	C₂²⋊C₄	—	89	2	no	—
477	C₂²⋊C₄	—	89	2	no	—
478	C₂²⋊C₄	—	89	2	no	—
479	C₂²⋊C₄	—	89	2	no	—
480	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
484	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
485	C₄²	—	89	1	no	—
486	C₄²	—	89	2	no	—
487	C₄²	—	89	1	no	—
488	C₄²	—	89	1	no	—
489	C₄²	—	89	2	no	—
490	C₄²	—	89	2	no	—
491	C₄²	—	89	1	no	—
492	C₄²	C₂²×D₈₉	1	1	yes	characteristic
493	C₄²	C₂²×D₈₉	1	1	yes	characteristic
494	C₂³	—	89	2	no	—
495	C₂³	—	89	2	no	—
496	C₂³	—	89	2	no	—
497	C₂³	—	356	2	no	—
498	C₂³	—	356	2	no	—
499	C₂³	—	356	2	no	—
500	C₂³	—	356	2	no	—
501	C₂³	—	356	2	no	—
502	C₂³	—	178	4	no	—
503	C₂³	C₂³×D₈₉	1	2	yes	—
504	C₂³	C₂³×D₈₉	1	1	yes	characteristic
505	Q₈	—	4	1	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	1	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	356	2	no	—
511	Q₈	—	356	1	no	—
512	D₄	—	2	4	no	—
513	D₄	—	4	1	no	—
514	D₄	—	356	2	no	—
515	D₄	—	356	2	no	—
516	D₄	—	356	1	no	—
517	D₄	—	356	2	no	—
518	D₄	—	356	1	no	—
519	D₄	—	356	2	no	—
520	D₄	—	356	1	no	—
521	D₄	—	356	2	no	—
522	D₄	—	356	2	no	—
523	D₄	—	356	2	no	—
524	D₄	—	356	2	no	—
525	D₄	—	178	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	89	2	no	—
531	C₂×C₄	—	89	2	no	—
532	C₂×C₄	—	89	2	no	—
533	C₂×C₄	—	89	2	no	—
534	C₂×C₄	—	89	2	no	—
535	C₂×C₄	—	356	2	no	—
536	C₂×C₄	—	356	2	no	—
537	C₂×C₄	—	356	2	no	—
538	C₂×C₄	—	356	2	no	—
539	C₂×C₄	—	356	2	no	—
540	C₂×C₄	—	356	2	no	—
541	C₂×C₄	—	356	2	no	—
542	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
543	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
544	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
545	C₂×C₄	C₂³×D₈₉	1	2	yes	—
546	C₂×C₄	C₂³×D₈₉	1	2	yes	—
547	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
548	C₂×C₄	C₂³×D₈₉	1	2	yes	—
549	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	178	2	no	—
556	C₂²	—	178	2	no	—
557	C₂²	—	178	2	no	—
558	C₂²	—	178	2	no	—
559	C₂²	—	178	2	no	—
560	C₂²	—	178	2	no	—
561	C₂²	—	178	2	no	—
562	C₂²	—	178	2	no	—
563	C₂²	—	178	2	no	—
564	C₂²	—	712	4	no	—
565	C₂²	—	712	4	no	—
566	C₂²	#15668057	1	2	yes	—
567	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	178	2	no	—
578	C₄	—	178	2	no	—
579	C₄	—	178	2	no	—
580	C₄	—	178	2	no	—
581	C₄	—	178	2	no	—
582	C₂	—	2	2	no	—
583	C₂	—	4	2	no	—
584	C₂	—	356	2	no	—
585	C₂	—	356	2	no	—
586	C₂	—	356	2	no	—
587	C₂	C₂×#15668057	1	1	yes	characteristic
588	C₂	#19152435	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#536×C₈₉	C₂
hypercenter	#536	D₈₉
hypocenter	C₈₉	#3545
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #19152347	C₂	semidirect
2. #19152344	C₂	semidirect
3. #19152340	C₂	semidirect
4. #19152314	C₂	semidirect
5. #19152310	C₂	semidirect
6. #19152275	C₂	semidirect
7. #19152272	C₂	semidirect
8. #19152271	C₂	semidirect
9. #19152240	C₂	semidirect
10. #19152236	C₂	semidirect
11. #19152222	C₂	semidirect
12. #19152218	C₂	semidirect
13. #19152188	C₂	semidirect
14. #19152182	C₂	semidirect
15. #19152172	C₂	semidirect
16. #19152159	C₂	semidirect
17. #19152125	C₂	semidirect
18. C₂×#15668001	C₂	semidirect
19. #536×C₈₉	C₂	semidirect
22. C₂×D₄×D₈₉	C₂²	semidirect
23. #15668010	C₂²	semidirect
24. #15668010	C₂²	semidirect
25. #15668007	C₂²	semidirect
26. #15668007	C₂²	semidirect
27. #15668007	C₂²	semidirect
28. #15668007	C₂²	semidirect
29. #15668006	C₂²	semidirect
30. #15668005	C₂²	semidirect
31. #15668002	C₂²	semidirect
34. #15668001	C₂²	semidirect
35. #15668001	C₂²	semidirect
36. #15668001	C₂²	semidirect
37. #15668001	C₂²	semidirect
38. #15668001	C₂²	semidirect
39. #15668001	C₂²	semidirect
40. #15668001	C₂²	semidirect
41. #15668000	C₂²	semidirect
42. #15667998	C₂²	semidirect
43. #15667998	C₂²	semidirect
44. #15667998	C₂²	semidirect
46. #15667997	C₂²	semidirect
47. #15667997	C₂²	semidirect
48. #15667997	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667996	C₂²	semidirect
51. #15667995	C₂²	semidirect
52. #15667995	C₂²	semidirect
53. #15667995	C₂²	semidirect
54. #15667994	C₂²	semidirect
55. #15667992	C₂²	semidirect
56. #15667990	C₂²	semidirect
57. #15667990	C₂²	semidirect
58. #15667989	C₂²	semidirect
59. #15667988	C₂²	semidirect
60. #15667988	C₂²	semidirect
61. #15667988	C₂²	semidirect
63. #15667987	C₂²	semidirect
64. #15667987	C₂²	semidirect
65. #15667986	C₂²	semidirect
67. #15667985	C₂²	semidirect
68. #15667985	C₂²	semidirect
70. #15667984	C₂²	semidirect
73. #15667982	C₂²	semidirect
74. #15667982	C₂²	semidirect
76. #15667980	C₂²	semidirect
77. #15667977	C₂²	semidirect
78. C₄×D₃₅₆	C₂²	semidirect
79. D₄×Dic₈₉	C₂²	semidirect
80. #15667974	C₂²	semidirect
81. C₄×C₂²⋊D₈₉	C₂²	semidirect
82. #15667972	C₂²	semidirect
83. #15667972	C₂²	semidirect
84. #15667972	C₂²	semidirect
85. #15667971	C₂²	semidirect
86. #15667970	C₂²	semidirect
87. #15667970	C₂²	semidirect
88. #15667969	C₂²	semidirect
89. #15667968	C₂²	semidirect
90. C₂×#13083551	C₂²	semidirect
91. C₂×#13083551	C₂²	semidirect
92. C₂×#13083551	C₂²	semidirect
93. C₂²⋊C₄×D₈₉	C₂²	semidirect
94. C₂²⋊C₄×D₈₉	C₂²	semidirect
95. C₂×C₄×Dic₈₉	C₂²	semidirect
97. C₂²×Q₈×C₈₉	C₂²	semidirect
98. C₄⋊Q₈×C₈₉	C₂²	semidirect
99. C₄⋊Q₈×C₈₉	C₂²	semidirect
100. #124×C₈₉	C₂²	semidirect
101. #124×C₈₉	C₂²	semidirect
102. #123×C₈₉	C₂²	semidirect
103. #123×C₈₉	C₂²	semidirect
104. C₂²⋊Q₈×C₈₉	C₂²	semidirect
105. C₂²⋊Q₈×C₈₉	C₂²	semidirect
106. #117×C₈₉	C₂²	semidirect
295. C₈₉	#3545	semidirect
311. #536	D₈₉	semidirect
317. C₂²×Q₈	C₂×D₈₉	semidirect
322. C₄⋊Q₈	C₂×D₈₉	semidirect
323. C₄⋊Q₈	C₂×D₈₉	semidirect
344. #124	C₂×D₈₉	semidirect
345. #124	C₂×D₈₉	semidirect
356. #123	C₂×D₈₉	semidirect
357. #123	C₂×D₈₉	semidirect
365. C₂²⋊Q₈	C₂×D₈₉	semidirect
366. C₂²⋊Q₈	C₂×D₈₉	semidirect
395. #117	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152347	2
#19152344	2
#19152340	2
#19152314	2
#19152310	2
#19152275	2
#19152272	2
#19152271	2
#19152240	2
#19152236	2
#19152222	2
#19152218	2
#19152188	2
#19152182	2
#19152172	2
#19152159	2
#19152125	2
C₂×#15668001	2
#536×C₈₉	2
#3545	89