Subgroups — #26034319

Order 11392.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152321	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152308	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152299	C₂	1	2	yes	maximal, complemented
4	#19152298	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152289	C₂	1	1	yes	maximal, characteristic, complemented
6	#19152284	C₂	1	2	yes	maximal, complemented
7	#19152275	C₂	1	2	yes	maximal, complemented
8	#19152272	C₂	1	2	yes	maximal, complemented
9	#19152251	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152241	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152217	C₂	1	1	yes	maximal, characteristic, complemented
13	#19152209	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152194	C₂	1	2	yes	maximal, complemented
15	#19152187	C₂	1	2	yes	maximal, complemented
16	#19152135	C₂	1	1	yes	maximal, characteristic, complemented
17	#19152127	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152126	C₂	1	2	yes	maximal, complemented
19	#126×D₈₉	C₂	1	2	yes	maximal, complemented
20	#19152080	C₂	1	1	yes	maximal, characteristic, complemented
21	#19152070	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13083575	C₂	1	1	yes	maximal, characteristic, complemented
23	#556×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13083575	C₂²	1	1	yes	characteristic
25	C₂×#13083575	C₂²	1	1	yes	characteristic
26	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
27	#15668012	C₂²	1	1	yes	characteristic, complemented
28	#15668007	C₂²	1	1	yes	characteristic
29	#15668007	C₂²	1	2	yes	—
30	#15668007	C₂²	1	2	yes	—
31	#15668007	C₂²	1	2	yes	—
32	#15668007	C₂²	1	1	yes	characteristic, complemented
33	#15668007	C₂²	1	2	yes	complemented
34	#15668006	C₂²	1	2	yes	—
35	#15668005	C₂²	1	2	yes	complemented
36	#15668005	C₂²	1	2	yes	complemented
37	#15668005	C₂²	1	2	yes	complemented
38	#15668004	C₂²	1	1	yes	characteristic, complemented
39	#15668004	C₂²	1	1	yes	characteristic, complemented
40	#15668003	C₂²	1	1	yes	characteristic, complemented
41	#15668002	C₂²	1	2	yes	complemented
42	#15668002	C₂²	1	2	yes	complemented
43	#15668002	C₂²	1	2	yes	complemented
44	#15668001	C₂²	1	1	yes	characteristic
45	#15668000	C₂²	1	2	yes	—
46	#15667998	C₂²	1	2	yes	complemented
47	#15667997	C₂²	1	1	yes	characteristic
48	#15667997	C₂²	1	2	yes	—
49	#15667997	C₂²	1	1	yes	characteristic, complemented
50	#15667997	C₂²	1	2	yes	complemented
51	#15667997	C₂²	1	2	yes	complemented
52	#15667996	C₂²	1	2	yes	complemented
53	#15667995	C₂²	1	2	yes	complemented
54	#15667994	C₂²	1	2	yes	—
55	#15667994	C₂²	1	2	yes	—
56	#15667994	C₂²	1	2	yes	complemented
57	#15667990	C₂²	1	2	yes	complemented
58	#15667990	C₂²	1	2	yes	complemented
59	#15667989	C₂²	1	2	yes	complemented
60	#15667988	C₂²	1	1	yes	characteristic
61	#15667988	C₂²	1	1	yes	characteristic
62	#15667988	C₂²	1	1	yes	characteristic, complemented
63	#15667988	C₂²	1	2	yes	complemented
64	#15667988	C₂²	1	1	yes	characteristic, complemented
65	#15667988	C₂²	1	1	yes	characteristic, complemented
66	#15667987	C₂²	1	1	yes	characteristic
67	#15667987	C₂²	1	2	yes	complemented
68	#15667985	C₂²	1	2	yes	—
69	#15667985	C₂²	1	2	yes	—
70	#15667985	C₂²	1	2	yes	complemented
71	#15667983	C₂²	1	1	yes	characteristic
72	#15667983	C₂²	1	1	yes	characteristic
73	#15667982	C₂²	1	2	yes	—
74	#15667982	C₂²	1	2	yes	—
75	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
76	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
78	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
79	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
80	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
81	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
83	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₃₅₆	C₂²	1	2	yes	complemented
85	C₄×D₃₅₆	C₂²	1	2	yes	complemented
86	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
87	#15667974	C₂²	1	1	yes	characteristic
88	#15667974	C₂²	1	2	yes	complemented
89	#15667974	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
92	#15667972	C₂²	1	2	yes	—
93	#15667972	C₂²	1	2	yes	complemented
94	#15667970	C₂²	1	1	yes	characteristic
95	#15667970	C₂²	1	2	yes	complemented
96	#15667970	C₂²	1	1	yes	characteristic, complemented
97	#15667969	C₂²	1	1	yes	characteristic
98	#15667969	C₂²	1	1	yes	characteristic, complemented
99	#15667969	C₂²	1	2	yes	complemented
100	#15667969	C₂²	1	2	yes	complemented
101	#15667968	C₂²	1	2	yes	complemented
102	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
103	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
105	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
106	C₂×#13083551	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₈₉	C₂²	1	2	yes	—
110	C₄²×D₈₉	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₈₉	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
113	#126×C₈₉	C₂²	1	2	yes	complemented
114	#126×C₈₉	C₂²	1	2	yes	complemented
115	#124×C₈₉	C₂²	1	1	yes	characteristic
116	#124×C₈₉	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
118	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
119	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
120	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
122	#117×C₈₉	C₂²	1	2	yes	complemented
123	C₂³×D₈₉	C₂³	1	2	yes	—
124	#13083575	—	2	4	no	—
125	#13083575	—	2	4	no	—
126	C₂×Dic₁₇₈	C₂³	1	2	yes	—
127	C₂×D₃₅₆	C₂³	1	2	yes	—
128	C₂×D₃₅₆	C₂³	1	2	yes	—
129	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
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	D₄×D₈₉	—	2	4	no	—
137	C₂²×Dic₈₉	C₂³	1	2	yes	—
138	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₈₉	C₂³	1	2	yes	—
141	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₈₉	C₂³	1	2	yes	—
143	C₂×C₄×D₈₉	C₂³	1	2	yes	—
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	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₈₉	C₂³	1	2	yes	—
149	C₂×C₄×D₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
156	C₄⋊Dic₈₉	C₂³	1	2	yes	—
157	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
158	C₄⋊Dic₈₉	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	1	yes	characteristic
163	#13083553	C₂³	1	1	yes	characteristic
164	#13083553	C₂³	1	2	yes	—
165	#13083553	C₂³	1	2	yes	—
166	#13083553	C₂³	1	1	yes	characteristic
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	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
173	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
174	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
175	#13083551	C₂³	1	1	yes	characteristic
176	#13083551	C₂³	1	1	yes	characteristic
177	#13083551	C₂³	1	1	yes	characteristic
178	#13083551	C₂³	1	2	yes	—
179	#13083551	C₂³	1	1	yes	characteristic
180	#13083551	C₂³	1	2	yes	—
181	#13083551	C₂³	1	1	yes	characteristic
182	#13083551	C₂³	1	2	yes	—
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	1	yes	characteristic
189	#13083551	C₂³	1	1	yes	characteristic
190	#13083551	C₂³	1	1	yes	characteristic
191	#13083551	C₂³	1	1	yes	characteristic
192	#13083551	C₂³	1	1	yes	characteristic
193	#13083551	C₂³	1	2	yes	—
194	#13083551	C₂³	1	2	yes	—
195	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
196	C₄×Dic₈₉	C₂³	1	2	yes	—
197	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₉	C₂³	1	2	yes	—
199	C₄×Dic₈₉	C₂³	1	2	yes	—
200	C₄×Dic₈₉	C₂³	1	2	yes	—
201	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
208	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	1	yes	characteristic
221	C₄²×C₈₉	C₂³	1	1	yes	characteristic
222	C₄²×C₈₉	C₂³	1	2	yes	—
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	—	2	4	no	—
227	C₂²×D₈₉	—	4	2	no	—
228	C₂²×D₈₉	—	4	2	no	—
229	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
230	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×D₈₉	C₂⁴	1	2	yes	—
233	Q₈×C₈₉	—	2	2	no	—
234	Q₈×C₈₉	—	2	2	no	—
235	Q₈×C₈₉	—	4	1	no	—
236	D₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	4	2	no	—
238	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
241	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
243	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
244	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₈₉	—	2	4	no	—
249	C₂²⋊D₈₉	—	4	2	no	—
250	C₂²⋊D₈₉	—	4	2	no	—
251	C₂×Dic₈₉	—	4	2	no	—
252	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₈₉	C₂⁴	1	2	yes	—
256	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₈₉	C₂⁴	1	2	yes	—
258	C₂×Dic₈₉	C₂⁴	1	2	yes	—
259	C₂×Dic₈₉	C₂⁴	1	1	yes	characteristic
260	D₃₅₆	—	2	4	no	—
261	D₃₅₆	—	2	4	no	—
262	D₃₅₆	—	4	1	no	—
263	D₃₅₆	—	4	1	no	—
264	D₃₅₆	—	4	1	no	—
265	D₃₅₆	#41	1	4	yes	—
266	C₄×D₈₉	—	2	4	no	—
267	C₄×D₈₉	—	2	4	no	—
268	C₄×D₈₉	—	2	2	no	—
269	C₄×D₈₉	—	2	2	no	—
270	C₄×D₈₉	—	2	2	no	—
271	C₄×D₈₉	—	4	2	no	—
272	C₄×D₈₉	—	4	2	no	—
273	C₄×D₈₉	—	4	2	no	—
274	C₄×D₈₉	—	4	1	no	—
275	C₄×D₈₉	—	4	2	no	—
276	C₄×D₈₉	—	4	2	no	—
277	C₄×D₈₉	—	4	1	no	—
278	Dic₁₇₈	—	4	2	no	—
279	C₂²×C₈₉	—	2	2	no	—
280	C₂²×C₈₉	—	2	2	no	—
281	C₂²×C₈₉	—	2	2	no	—
282	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
283	C₂×D₈₉	—	2	2	no	—
284	C₂×D₈₉	—	2	2	no	—
285	C₂×D₈₉	—	2	1	no	—
286	C₂×D₈₉	—	2	1	no	—
287	C₂×D₈₉	—	2	1	no	—
288	C₂×D₈₉	—	2	1	no	—
289	C₂×D₈₉	—	2	1	no	—
290	C₂×D₈₉	—	2	1	no	—
291	C₂×D₈₉	—	2	1	no	—
292	C₂×D₈₉	—	2	1	no	—
293	C₂×D₈₉	—	2	1	no	—
294	C₂×D₈₉	—	8	4	no	—
295	C₂×D₈₉	C₂×#41	1	4	yes	—
296	C₄×C₈₉	—	2	2	no	—
297	C₄×C₈₉	—	2	2	no	—
298	C₄×C₈₉	—	2	1	no	—
299	C₄×C₈₉	—	2	1	no	—
300	C₄×C₈₉	—	2	1	no	—
301	C₄×C₈₉	—	2	2	no	—
302	C₄×C₈₉	—	2	1	no	—
303	C₄×C₈₉	—	2	1	no	—
304	C₄×C₈₉	—	2	1	no	—
305	C₄×C₈₉	C₂×#41	1	2	yes	—
306	Dic₈₉	—	2	1	no	—
307	Dic₈₉	—	2	1	no	—
308	Dic₈₉	—	2	1	no	—
309	Dic₈₉	—	2	2	no	—
310	Dic₈₉	—	2	2	no	—
311	Dic₈₉	—	2	1	no	—
312	Dic₈₉	—	2	2	no	—
313	Dic₈₉	—	2	1	no	—
314	C₂×C₈₉	—	4	2	no	—
315	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
316	C₂×C₈₉	#585	1	1	yes	characteristic
317	C₂×C₈₉	#585	1	1	yes	characteristic
318	D₈₉	—	2	4	no	—
319	D₈₉	—	4	1	no	—
320	D₈₉	—	4	1	no	—
321	D₈₉	—	4	1	no	—
322	#3521	—	89	1	no	maximal, Sylow
323	C₈₉	#3521	1	1	yes	characteristic, complemented, Sylow
324	#556	—	89	1	no	—
325	#556	D₈₉	1	1	yes	characteristic, complemented
326	#554	—	89	1	no	—
327	#553	—	89	2	no	—
328	#553	—	89	1	no	—
329	#552	—	89	2	no	—
330	#552	—	89	1	no	—
331	#551	—	89	2	no	—
332	#551	—	89	2	no	—
333	#547	—	89	1	no	—
334	#546	—	89	1	no	—
335	#546	—	89	1	no	—
336	#542	—	89	1	no	—
337	#541	—	89	1	no	—
338	#539	—	89	2	no	—
339	#538	—	89	2	no	—
340	#529	—	89	1	no	—
341	#529	—	89	1	no	—
342	#529	—	89	2	no	—
343	C₂×#126	—	89	2	no	—
344	#520	—	89	1	no	—
345	#518	—	89	1	no	—
346	C₄×#41	—	89	1	no	—
347	C₂×#41	—	89	1	no	—
348	C₂×#41	—	89	1	no	—
349	C₂²×D₄	—	89	1	no	—
350	C₄⋊Q₈	—	89	1	no	—
351	C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
352	#126	—	89	1	no	—
353	#126	—	89	2	no	—
354	#126	—	89	2	no	—
355	#126	—	89	1	no	—
356	#126	—	89	2	no	—
357	#126	—	89	2	no	—
358	#126	—	89	2	no	—
359	#126	—	89	2	no	—
360	#126	—	89	2	no	—
361	#126	—	89	2	no	—
362	#126	C₂×D₈₉	1	2	yes	complemented
363	#126	C₂×D₈₉	1	2	yes	complemented
364	#125	—	89	2	no	—
365	#125	—	89	1	no	—
366	#125	—	89	2	no	—
367	#125	—	89	2	no	—
368	#125	—	89	1	no	—
369	#125	—	89	1	no	—
370	#124	—	89	1	no	—
371	#124	—	89	2	no	—
372	#124	—	89	2	no	—
373	#124	C₂×D₈₉	1	1	yes	characteristic
374	#124	C₂×D₈₉	1	1	yes	characteristic
375	#123	—	89	2	no	—
376	#123	—	89	1	no	—
377	#123	—	89	2	no	—
378	#123	—	89	1	no	—
379	#123	—	89	2	no	—
380	#123	—	89	2	no	—
381	#123	—	89	2	no	—
382	#123	—	89	2	no	—
383	#123	—	89	2	no	—
384	#123	—	89	2	no	—
385	C₂²⋊Q₈	—	89	1	no	—
386	C₂²⋊Q₈	—	89	1	no	—
387	C₂²⋊Q₈	—	89	1	no	—
388	C₂²⋊Q₈	—	89	1	no	—
389	C₂²⋊Q₈	—	89	2	no	—
390	C₂²⋊Q₈	—	89	1	no	—
391	C₂²⋊Q₈	—	89	2	no	—
392	C₂²⋊Q₈	—	89	2	no	—
393	C₂²⋊Q₈	—	89	2	no	—
394	C₂²⋊Q₈	C₂×D₈₉	1	2	yes	complemented
395	#121	—	89	1	no	—
396	#121	—	89	1	no	—
397	#121	—	89	1	no	—
398	#121	—	89	2	no	—
399	#121	—	89	2	no	—
400	#121	—	89	2	no	—
401	#121	—	89	2	no	—
402	#120	—	89	2	no	—
403	#120	—	89	2	no	—
404	C₄×Q₈	—	89	1	no	—
405	C₄×Q₈	—	89	1	no	—
406	C₄×Q₈	—	89	2	no	—
407	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
408	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
410	C₄×D₄	—	89	1	no	—
411	C₄×D₄	—	89	2	no	—
412	C₄×D₄	—	89	2	no	—
413	C₄×D₄	—	89	1	no	—
414	C₄×D₄	—	89	2	no	—
415	C₄×D₄	—	89	2	no	—
416	C₄×D₄	—	89	2	no	—
417	C₄×D₄	—	89	2	no	—
418	C₄×D₄	—	89	1	no	—
419	C₄×D₄	—	89	2	no	—
420	C₄×D₄	—	89	1	no	—
421	C₄×D₄	—	89	1	no	—
422	C₄×D₄	—	89	2	no	—
423	C₄×D₄	—	89	1	no	—
424	C₄×D₄	—	89	1	no	—
425	C₄×D₄	—	89	1	no	—
426	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
427	#117	—	89	1	no	—
428	#117	—	89	2	no	—
429	#117	—	89	1	no	—
430	#117	—	89	2	no	—
431	#117	—	89	1	no	—
432	#117	—	89	1	no	—
433	#117	—	89	2	no	—
434	#117	—	89	2	no	—
435	#117	C₂×D₈₉	1	2	yes	complemented
436	C₂×C₄⋊C₄	—	89	2	no	—
437	C₂×C₄⋊C₄	—	89	1	no	—
438	C₂×C₄⋊C₄	—	89	2	no	—
439	C₂×C₄⋊C₄	—	89	2	no	—
440	C₂×C₂²⋊C₄	—	89	2	no	—
441	C₂×C₂²⋊C₄	—	89	2	no	—
442	C₂×C₂²⋊C₄	—	89	2	no	—
443	C₂×C₂²⋊C₄	—	89	2	no	—
444	C₂×C₄²	—	89	2	no	—
445	C₂×C₄²	—	89	1	no	—
446	C₂⁴	—	89	2	no	—
447	#41	—	178	4	no	—
448	#41	—	178	4	no	—
449	C₂×Q₈	—	89	2	no	—
450	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
451	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
453	C₂×D₄	—	89	2	no	—
454	C₂×D₄	—	89	2	no	—
455	C₂×D₄	—	89	2	no	—
456	C₂×D₄	—	89	1	no	—
457	C₂×D₄	—	89	1	no	—
458	C₂×D₄	—	89	1	no	—
459	C₂×D₄	—	89	1	no	—
460	C₂×D₄	—	89	2	no	—
461	C₂×D₄	—	89	2	no	—
462	C₂×D₄	—	178	4	no	—
463	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
464	C₂²×C₄	—	89	2	no	—
465	C₂²×C₄	—	89	2	no	—
466	C₂²×C₄	—	89	2	no	—
467	C₂²×C₄	—	89	1	no	—
468	C₂²×C₄	—	89	1	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	1	no	—
474	C₂²×C₄	—	89	2	no	—
475	C₂²×C₄	—	89	1	no	—
476	C₂²×C₄	—	89	1	no	—
477	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
478	C₄⋊C₄	—	89	1	no	—
479	C₄⋊C₄	—	89	2	no	—
480	C₄⋊C₄	—	89	1	no	—
481	C₄⋊C₄	—	89	2	no	—
482	C₄⋊C₄	—	89	2	no	—
483	C₄⋊C₄	—	89	1	no	—
484	C₄⋊C₄	—	89	2	no	—
485	C₄⋊C₄	—	89	2	no	—
486	C₄⋊C₄	—	89	2	no	—
487	C₄⋊C₄	—	89	2	no	—
488	C₄⋊C₄	—	89	1	no	—
489	C₄⋊C₄	—	89	1	no	—
490	C₄⋊C₄	—	89	1	no	—
491	C₄⋊C₄	—	89	1	no	—
492	C₄⋊C₄	—	89	1	no	—
493	C₄⋊C₄	—	89	2	no	—
494	C₄⋊C₄	—	89	2	no	—
495	C₄⋊C₄	—	89	2	no	—
496	C₄⋊C₄	—	89	1	no	—
497	C₄⋊C₄	—	89	2	no	—
498	C₄⋊C₄	—	89	1	no	—
499	C₄⋊C₄	—	89	2	no	—
500	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
503	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
504	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
505	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
507	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
508	C₂²⋊C₄	—	89	2	no	—
509	C₂²⋊C₄	—	89	2	no	—
510	C₂²⋊C₄	—	89	2	no	—
511	C₂²⋊C₄	—	89	1	no	—
512	C₂²⋊C₄	—	89	1	no	—
513	C₂²⋊C₄	—	89	2	no	—
514	C₂²⋊C₄	—	89	1	no	—
515	C₂²⋊C₄	—	89	1	no	—
516	C₂²⋊C₄	—	89	2	no	—
517	C₂²⋊C₄	—	89	2	no	—
518	C₂²⋊C₄	—	89	2	no	—
519	C₂²⋊C₄	—	89	2	no	—
520	C₂²⋊C₄	—	89	1	no	—
521	C₂²⋊C₄	—	89	2	no	—
522	C₂²⋊C₄	—	89	2	no	—
523	C₂²⋊C₄	—	89	2	no	—
524	C₂²⋊C₄	—	89	1	no	—
525	C₂²⋊C₄	—	89	1	no	—
526	C₂²⋊C₄	—	89	2	no	—
527	C₂²⋊C₄	—	89	1	no	—
528	C₂²⋊C₄	—	89	1	no	—
529	C₂²⋊C₄	—	89	2	no	—
530	C₂²⋊C₄	—	89	1	no	—
531	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
536	C₄²	—	89	1	no	—
537	C₄²	—	89	1	no	—
538	C₄²	—	89	1	no	—
539	C₄²	—	89	2	no	—
540	C₄²	—	89	2	no	—
541	C₄²	—	89	2	no	—
542	C₄²	—	89	2	no	—
543	C₄²	C₂²×D₈₉	1	2	yes	—
544	C₄²	C₂²×D₈₉	1	1	yes	characteristic
545	C₄²	C₂²×D₈₉	1	2	yes	—
546	C₄²	C₂²×D₈₉	1	1	yes	characteristic
547	C₄²	C₂²×D₈₉	1	1	yes	characteristic
548	C₂³	—	89	2	no	—
549	C₂³	—	89	1	no	—
550	C₂³	—	89	1	no	—
551	C₂³	—	89	1	no	—
552	C₂³	—	356	2	no	—
553	C₂³	—	356	2	no	—
554	C₂³	—	178	4	no	—
555	C₂³	C₂³×D₈₉	1	2	yes	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	4	1	no	—
559	Q₈	—	356	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	89	4	no	—
562	D₄	—	356	1	no	—
563	D₄	—	356	1	no	—
564	D₄	—	356	1	no	—
565	D₄	—	356	2	no	—
566	D₄	—	356	2	no	—
567	D₄	—	178	4	no	—
568	D₄	—	178	4	no	—
569	D₄	—	178	4	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	89	1	no	—
572	C₂×C₄	—	89	1	no	—
573	C₂×C₄	—	89	1	no	—
574	C₂×C₄	—	89	2	no	—
575	C₂×C₄	—	89	1	no	—
576	C₂×C₄	—	89	2	no	—
577	C₂×C₄	—	89	2	no	—
578	C₂×C₄	—	89	1	no	—
579	C₂×C₄	—	356	2	no	—
580	C₂×C₄	—	356	2	no	—
581	C₂×C₄	—	356	2	no	—
582	C₂×C₄	—	356	1	no	—
583	C₂×C₄	—	356	1	no	—
584	C₂×C₄	—	356	2	no	—
585	C₂×C₄	—	356	2	no	—
586	C₂×C₄	—	356	2	no	—
587	C₂×C₄	—	178	4	no	—
588	C₂×C₄	—	178	4	no	—
589	C₂×C₄	—	178	2	no	—
590	C₂×C₄	—	178	2	no	—
591	C₂×C₄	—	178	2	no	—
592	C₂×C₄	C₂³×D₈₉	1	2	yes	—
593	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₈₉	1	2	yes	—
595	C₂×C₄	C₂³×D₈₉	1	2	yes	—
596	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
600	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
602	C₂²	—	2	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	89	4	no	—
606	C₂²	—	178	1	no	—
607	C₂²	—	178	1	no	—
608	C₂²	—	178	1	no	—
609	C₂²	—	178	1	no	—
610	C₂²	—	178	1	no	—
611	C₂²	—	178	1	no	—
612	C₂²	—	178	1	no	—
613	C₂²	—	178	1	no	—
614	C₂²	—	178	1	no	—
615	C₂²	—	178	2	no	—
616	C₂²	—	178	2	no	—
617	C₂²	—	712	4	no	—
618	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	178	1	no	—
629	C₄	—	178	1	no	—
630	C₄	—	178	1	no	—
631	C₄	—	178	1	no	—
632	C₄	—	178	2	no	—
633	C₄	—	178	1	no	—
634	C₄	—	178	2	no	—
635	C₄	—	178	2	no	—
636	C₄	#41×D₈₉	1	2	yes	—
637	C₂	—	4	2	no	—
638	C₂	—	356	1	no	—
639	C₂	—	356	1	no	—
640	C₂	—	356	1	no	—
641	C₂	—	178	4	no	—
642	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
643	C₂	#19152434	1	1	yes	characteristic
644	C₂	#19152435	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	#3521
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. #19152321	C₂	semidirect
2. #19152308	C₂	semidirect
3. #19152299	C₂	semidirect
4. #19152298	C₂	semidirect
5. #19152289	C₂	semidirect
6. #19152284	C₂	semidirect
7. #19152275	C₂	semidirect
8. #19152272	C₂	semidirect
9. #19152251	C₂	semidirect
10. #19152241	C₂	semidirect
11. #19152241	C₂	semidirect
12. #19152217	C₂	semidirect
13. #19152209	C₂	semidirect
14. #19152194	C₂	semidirect
15. #19152187	C₂	semidirect
16. #19152135	C₂	semidirect
17. #19152127	C₂	semidirect
18. #19152126	C₂	semidirect
19. #126×D₈₉	C₂	semidirect
20. #19152080	C₂	semidirect
21. #19152070	C₂	semidirect
22. C₄×#13083575	C₂	semidirect
23. #556×C₈₉	C₂	semidirect
27. #15668012	C₂²	semidirect
32. #15668007	C₂²	semidirect
33. #15668007	C₂²	semidirect
35. #15668005	C₂²	semidirect
36. #15668005	C₂²	semidirect
37. #15668005	C₂²	semidirect
38. #15668004	C₂²	semidirect
39. #15668004	C₂²	semidirect
40. #15668003	C₂²	semidirect
41. #15668002	C₂²	semidirect
42. #15668002	C₂²	semidirect
43. #15668002	C₂²	semidirect
46. #15667998	C₂²	semidirect
49. #15667997	C₂²	semidirect
50. #15667997	C₂²	semidirect
51. #15667997	C₂²	semidirect
52. #15667996	C₂²	semidirect
53. #15667995	C₂²	semidirect
56. #15667994	C₂²	semidirect
57. #15667990	C₂²	semidirect
58. #15667990	C₂²	semidirect
59. #15667989	C₂²	semidirect
62. #15667988	C₂²	semidirect
63. #15667988	C₂²	semidirect
64. #15667988	C₂²	semidirect
65. #15667988	C₂²	semidirect
67. #15667987	C₂²	semidirect
70. #15667985	C₂²	semidirect
75. Q₈×Dic₈₉	C₂²	semidirect
76. Q₈×Dic₈₉	C₂²	semidirect
77. C₄×Dic₁₇₈	C₂²	semidirect
83. C₄×D₃₅₆	C₂²	semidirect
84. C₄×D₃₅₆	C₂²	semidirect
85. C₄×D₃₅₆	C₂²	semidirect
88. #15667974	C₂²	semidirect
89. #15667974	C₂²	semidirect
91. C₄×C₂²⋊D₈₉	C₂²	semidirect
93. #15667972	C₂²	semidirect
95. #15667970	C₂²	semidirect
96. #15667970	C₂²	semidirect
98. #15667969	C₂²	semidirect
99. #15667969	C₂²	semidirect
100. #15667969	C₂²	semidirect
101. #15667968	C₂²	semidirect
102. C₄⋊C₄×D₈₉	C₂²	semidirect
103. C₄⋊C₄×D₈₉	C₂²	semidirect
104. C₄⋊C₄×D₈₉	C₂²	semidirect
105. C₄⋊C₄×D₈₉	C₂²	semidirect
110. C₄²×D₈₉	C₂²	semidirect
111. C₄²×D₈₉	C₂²	semidirect
112. C₄⋊Q₈×C₈₉	C₂²	semidirect
113. #126×C₈₉	C₂²	semidirect
114. #126×C₈₉	C₂²	semidirect
117. C₂²⋊Q₈×C₈₉	C₂²	semidirect
118. C₄×Q₈×C₈₉	C₂²	semidirect
119. C₄×Q₈×C₈₉	C₂²	semidirect
120. C₄×Q₈×C₈₉	C₂²	semidirect
122. #117×C₈₉	C₂²	semidirect
323. C₈₉	#3521	semidirect
325. #556	D₈₉	semidirect
351. C₄⋊Q₈	C₂×D₈₉	semidirect
362. #126	C₂×D₈₉	semidirect
363. #126	C₂×D₈₉	semidirect
394. C₂²⋊Q₈	C₂×D₈₉	semidirect
407. C₄×Q₈	C₂×D₈₉	semidirect
408. C₄×Q₈	C₂×D₈₉	semidirect
409. C₄×Q₈	C₂×D₈₉	semidirect
435. #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
#19152321	2
#19152308	2
#19152299	2
#19152298	2
#19152289	2
#19152284	2
#19152275	2
#19152272	2
#19152251	2
#19152241	2
#19152217	2
#19152209	2
#19152194	2
#19152187	2
#19152135	2
#19152127	2
#19152126	2
#126×D₈₉	2
#19152080	2
#19152070	2
C₄×#13083575	2
#556×C₈₉	2
#3521	89