Subgroups — #26034876

Order 11392.

936 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152350	C₂	1	2	yes	maximal, complemented
2	#19152350	C₂	1	2	yes	maximal, complemented
3	#19152315	C₂	1	2	yes	maximal, complemented
4	#19152303	C₂	1	2	yes	maximal, complemented
5	#19152284	C₂	1	2	yes	maximal, complemented
6	#19152283	C₂	1	2	yes	maximal, complemented
7	#19152274	C₂	1	2	yes	maximal, complemented
8	#19152274	C₂	1	2	yes	maximal, complemented
9	#19152229	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152224	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152214	C₂	1	2	yes	maximal, complemented
12	#19152205	C₂	1	2	yes	maximal, complemented
13	#19152205	C₂	1	2	yes	maximal, complemented
14	#19152195	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152189	C₂	1	2	yes	maximal, complemented
16	#19152186	C₂	1	1	yes	maximal, characteristic
17	#19152155	C₂	1	1	yes	maximal, characteristic, complemented
18	#19152132	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#126×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
20	#15668012	C₂²	1	1	yes	characteristic, complemented
21	#15668012	C₂²	1	1	yes	characteristic, complemented
22	#15668011	C₂²	1	2	yes	complemented
23	#15668011	C₂²	1	2	yes	complemented
24	#15668011	C₂²	1	2	yes	complemented
25	#15668007	C₂²	1	2	yes	complemented
26	#15668007	C₂²	1	2	yes	complemented
27	#15668007	C₂²	1	2	yes	complemented
28	#15668006	C₂²	1	2	yes	complemented
29	#15668005	C₂²	1	2	yes	—
30	#15668005	C₂²	1	2	yes	—
31	#15668005	C₂²	1	2	yes	—
32	#15668005	C₂²	1	2	yes	—
33	#15668005	C₂²	1	2	yes	—
34	#15668004	C₂²	1	1	yes	characteristic, complemented
35	#15668004	C₂²	1	2	yes	complemented
36	#15668003	C₂²	1	2	yes	complemented
37	#15668003	C₂²	1	2	yes	complemented
38	#15668003	C₂²	1	2	yes	complemented
39	#15668002	C₂²	1	2	yes	complemented
40	#15668002	C₂²	1	2	yes	complemented
41	#15668002	C₂²	1	2	yes	complemented
42	#15668002	C₂²	1	2	yes	complemented
43	#15668002	C₂²	1	2	yes	complemented
44	#15668000	C₂²	1	1	yes	characteristic, complemented
45	#15667998	C₂²	1	2	yes	—
46	#15667998	C₂²	1	2	yes	—
47	#15667998	C₂²	1	2	yes	—
48	#15667997	C₂²	1	2	yes	complemented
49	#15667996	C₂²	1	2	yes	—
50	#15667996	C₂²	1	2	yes	—
51	#15667995	C₂²	1	2	yes	—
52	#15667995	C₂²	1	2	yes	—
53	#15667994	C₂²	1	2	yes	—
54	#15667994	C₂²	1	2	yes	—
55	#15667994	C₂²	1	2	yes	—
56	#15667992	C₂²	1	2	yes	complemented
57	#15667992	C₂²	1	2	yes	complemented
58	#15667991	C₂²	1	1	yes	characteristic
59	#15667991	C₂²	1	1	yes	characteristic
60	#15667991	C₂²	1	1	yes	characteristic
61	#15667991	C₂²	1	2	yes	—
62	#15667991	C₂²	1	2	yes	—
63	#15667991	C₂²	1	2	yes	—
64	#15667990	C₂²	1	2	yes	complemented
65	#15667990	C₂²	1	2	yes	complemented
66	#15667990	C₂²	1	2	yes	complemented
67	#15667989	C₂²	1	2	yes	—
68	#15667989	C₂²	1	2	yes	—
69	#15667989	C₂²	1	2	yes	—
70	#15667989	C₂²	1	2	yes	—
71	#15667989	C₂²	1	2	yes	—
72	#15667989	C₂²	1	2	yes	—
73	#15667986	C₂²	1	1	yes	characteristic
74	#15667985	C₂²	1	2	yes	—
75	#15667981	C₂²	1	2	yes	—
76	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
78	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
79	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
80	#15667977	C₂²	1	2	yes	complemented
81	#15667977	C₂²	1	2	yes	complemented
82	C₄×D₃₅₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
85	C₄×C₂²⋊D₈₉	C₂²	1	2	yes	—
86	#15667972	C₂²	1	2	yes	—
87	#15667972	C₂²	1	2	yes	—
88	#15667971	C₂²	1	2	yes	—
89	#15667971	C₂²	1	2	yes	—
90	#15667970	C₂²	1	2	yes	complemented
91	#15667969	C₂²	1	2	yes	complemented
92	#15667968	C₂²	1	2	yes	—
93	#15667968	C₂²	1	2	yes	—
94	C₄⋊C₄×D₈₉	C₂²	1	2	yes	complemented
95	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	—
96	#126×C₈₉	C₂²	1	2	yes	—
97	#126×C₈₉	C₂²	1	2	yes	—
98	#126×C₈₉	C₂²	1	2	yes	—
99	#126×C₈₉	C₂²	1	2	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
107	C₂×Dic₁₇₈	C₂³	1	2	yes	—
108	C₂×Dic₁₇₈	C₂³	1	2	yes	—
109	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
110	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
111	C₂×Dic₁₇₈	C₂³	1	2	yes	—
112	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
113	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₈₉	C₂³	1	2	yes	—
117	C₂²×Dic₈₉	C₂³	1	2	yes	—
118	C₂²×Dic₈₉	C₂³	1	2	yes	—
119	C₂×C₄×D₈₉	C₂³	1	2	yes	—
120	C₂×C₄×D₈₉	C₂³	1	2	yes	—
121	C₂×C₄×D₈₉	C₂³	1	2	yes	—
122	C₄⋊Dic₈₉	C₂³	1	2	yes	—
123	C₄⋊Dic₈₉	C₂³	1	2	yes	—
124	C₄⋊Dic₈₉	C₂³	1	2	yes	—
125	C₄⋊Dic₈₉	C₂³	1	2	yes	—
126	C₄⋊Dic₈₉	C₂³	1	2	yes	—
127	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
128	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
130	C₄⋊Dic₈₉	C₂³	1	2	yes	—
131	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₈₉	C₂³	1	2	yes	—
133	#13083553	C₂³	1	2	yes	—
134	#13083553	C₂³	1	2	yes	—
135	#13083553	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	#13083553	C₂³	1	2	yes	—
145	#13083553	C₂³	1	2	yes	—
146	#13083553	C₂³	1	2	yes	—
147	#13083553	C₂³	1	2	yes	—
148	#13083553	C₂³	1	2	yes	—
149	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
150	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
151	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
152	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
153	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
154	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₈₉	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	C₄×Dic₈₉	C₂³	1	2	yes	—
165	C₄×Dic₈₉	C₂³	1	2	yes	—
166	C₄×Dic₈₉	C₂³	1	2	yes	—
167	C₄×Dic₈₉	C₂³	1	2	yes	—
168	C₄×Dic₈₉	C₂³	1	2	yes	—
169	C₄×Dic₈₉	C₂³	1	2	yes	—
170	C₄×Dic₈₉	C₂³	1	2	yes	—
171	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
178	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
179	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
180	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
181	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
182	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
183	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
190	C₄²×C₈₉	C₂³	1	1	yes	characteristic
191	C₄²×C₈₉	C₂³	1	1	yes	characteristic
192	C₄²×C₈₉	C₂³	1	1	yes	characteristic
193	C₄²×C₈₉	C₂³	1	1	yes	characteristic
194	C₂³×C₈₉	—	2	2	no	—
195	C₂³×C₈₉	—	4	1	no	—
196	C₂³×C₈₉	—	4	1	no	—
197	C₂³×C₈₉	C₂⁴	1	2	yes	—
198	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
199	C₂²×D₈₉	C₂⁴	1	2	yes	—
200	C₂×C₄×C₈₉	—	2	2	no	—
201	C₂×C₄×C₈₉	—	2	2	no	—
202	C₂×C₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	4	1	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²⋊D₈₉	—	2	4	no	—
216	C₂²⋊D₈₉	—	4	2	no	—
217	C₂²⋊D₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	4	2	no	—
219	C₂×Dic₈₉	—	4	2	no	—
220	C₂×Dic₈₉	C₂⁴	1	2	yes	—
221	C₂×Dic₈₉	C₂⁴	1	2	yes	—
222	C₂×Dic₈₉	C₂⁴	1	2	yes	—
223	C₂×Dic₈₉	C₂⁴	1	2	yes	—
224	C₂×Dic₈₉	C₂⁴	1	2	yes	—
225	C₂×Dic₈₉	C₂⁴	1	2	yes	—
226	C₂×Dic₈₉	C₂⁴	1	2	yes	—
227	D₃₅₆	—	4	1	no	—
228	C₄×D₈₉	—	4	2	no	—
229	C₄×D₈₉	—	4	2	no	—
230	C₄×D₈₉	—	4	2	no	—
231	Dic₁₇₈	—	4	1	no	—
232	Dic₁₇₈	—	4	2	no	—
233	Dic₁₇₈	—	4	2	no	—
234	Dic₁₇₈	—	4	2	no	—
235	Dic₁₇₈	—	4	1	no	—
236	Dic₁₇₈	—	4	1	no	—
237	C₂²×C₈₉	—	2	1	no	—
238	C₂²×C₈₉	—	2	1	no	—
239	C₂²×C₈₉	—	2	2	no	—
240	C₂²×C₈₉	—	2	2	no	—
241	C₂²×C₈₉	—	2	2	no	—
242	C₂²×C₈₉	—	8	2	no	—
243	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
244	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
245	C₂×D₈₉	—	2	2	no	—
246	C₂×D₈₉	—	2	2	no	—
247	C₂×D₈₉	—	2	2	no	—
248	C₄×C₈₉	—	2	1	no	—
249	C₄×C₈₉	—	2	1	no	—
250	C₄×C₈₉	—	2	2	no	—
251	C₄×C₈₉	—	2	1	no	—
252	C₄×C₈₉	—	2	1	no	—
253	C₄×C₈₉	—	2	2	no	—
254	C₄×C₈₉	—	2	2	no	—
255	C₄×C₈₉	—	2	1	no	—
256	C₄×C₈₉	—	2	1	no	—
257	Dic₈₉	—	2	2	no	—
258	Dic₈₉	—	2	2	no	—
259	Dic₈₉	—	2	2	no	—
260	Dic₈₉	—	2	2	no	—
261	Dic₈₉	—	2	2	no	—
262	Dic₈₉	—	2	2	no	—
263	Dic₈₉	—	2	2	no	—
264	C₂×C₈₉	—	2	2	no	—
265	C₂×C₈₉	—	4	2	no	—
266	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₈₉	#585	1	1	yes	characteristic
268	C₂×C₈₉	#585	1	1	yes	characteristic
269	D₈₉	—	4	2	no	—
270	#3564	—	89	1	no	maximal, Sylow
271	C₈₉	#3564	1	1	yes	characteristic, complemented, Sylow
272	#563	—	89	2	no	—
273	#563	—	89	2	no	—
274	#556	—	89	2	no	—
275	#554	—	89	2	no	—
276	#552	—	89	2	no	—
277	#552	—	89	2	no	—
278	#551	—	89	2	no	—
279	#551	—	89	2	no	—
280	#544	—	89	1	no	—
281	#543	—	89	1	no	—
282	#542	—	89	2	no	—
283	#541	—	89	2	no	—
284	#541	—	89	2	no	—
285	#539	—	89	2	no	—
286	#539	—	89	1	no	—
287	#538	—	89	1	no	—
288	#533	—	89	1	no	—
289	#529	—	89	1	no	—
290	C₂×#126	D₈₉	1	1	yes	characteristic, complemented
291	C₄⋊Q₈	—	89	2	no	—
292	C₄⋊Q₈	—	89	2	no	—
293	C₄⋊Q₈	—	89	2	no	—
294	C₄⋊Q₈	—	89	1	no	—
295	C₄⋊Q₈	—	89	1	no	—
296	#126	—	89	2	no	—
297	#126	—	89	2	no	—
298	#126	—	89	2	no	—
299	#126	—	89	2	no	—
300	#126	—	89	2	no	—
301	#126	—	89	2	no	—
302	#126	—	89	2	no	—
303	#126	—	89	2	no	—
304	#126	—	89	2	no	—
305	#126	C₂×D₈₉	1	2	yes	—
306	#126	C₂×D₈₉	1	2	yes	—
307	#126	C₂×D₈₉	1	2	yes	—
308	#126	C₂×D₈₉	1	2	yes	—
309	#125	—	89	2	no	—
310	#125	—	89	2	no	—
311	#125	—	89	2	no	—
312	#125	—	89	2	no	—
313	#125	—	89	2	no	—
314	#125	—	89	2	no	—
315	#125	—	89	2	no	—
316	#125	—	89	2	no	—
317	#125	—	89	1	no	—
318	#125	—	89	2	no	—
319	#124	—	89	2	no	—
320	#124	—	89	2	no	—
321	#124	—	89	2	no	—
322	#124	—	89	1	no	—
323	#123	—	89	2	no	—
324	#123	—	89	2	no	—
325	#123	—	89	2	no	—
326	#123	—	89	2	no	—
327	#123	—	89	2	no	—
328	#123	—	89	2	no	—
329	#123	—	89	2	no	—
330	#123	—	89	2	no	—
331	C₂²⋊Q₈	—	89	1	no	—
332	C₂²⋊Q₈	—	89	1	no	—
333	C₂²⋊Q₈	—	89	1	no	—
334	C₂²⋊Q₈	—	89	2	no	—
335	C₂²⋊Q₈	—	89	2	no	—
336	C₂²⋊Q₈	—	89	2	no	—
337	C₂²⋊Q₈	—	89	2	no	—
338	C₂²⋊Q₈	—	89	2	no	—
339	C₂²⋊Q₈	—	89	2	no	—
340	C₂²⋊Q₈	—	89	2	no	—
341	C₂²⋊Q₈	—	89	2	no	—
342	C₂²⋊Q₈	—	89	2	no	—
343	C₂²⋊Q₈	—	89	2	no	—
344	C₂²⋊Q₈	—	89	2	no	—
345	C₂²⋊Q₈	—	89	2	no	—
346	C₂²⋊Q₈	—	89	2	no	—
347	C₂²⋊Q₈	—	89	2	no	—
348	#121	—	89	1	no	—
349	#121	—	89	2	no	—
350	#120	—	89	2	no	—
351	C₄×Q₈	—	89	2	no	—
352	C₄×Q₈	—	89	2	no	—
353	C₄×Q₈	—	89	1	no	—
354	C₄×Q₈	—	89	2	no	—
355	C₄×Q₈	—	89	1	no	—
356	C₄×Q₈	—	89	1	no	—
357	C₄×D₄	—	89	2	no	—
358	C₄×D₄	—	89	2	no	—
359	C₄×D₄	—	89	2	no	—
360	C₄×D₄	—	89	2	no	—
361	C₄×D₄	—	89	2	no	—
362	C₄×D₄	—	89	1	no	—
363	#117	—	89	2	no	—
364	#117	—	89	2	no	—
365	#117	—	89	2	no	—
366	#117	—	89	2	no	—
367	#117	—	89	2	no	—
368	#117	—	89	2	no	—
369	C₂×C₄⋊C₄	—	89	2	no	—
370	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	89	2	no	—
374	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
377	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
378	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
379	C₂×Q₈	—	89	2	no	—
380	C₂×Q₈	—	89	1	no	—
381	C₂×Q₈	—	89	2	no	—
382	C₂×Q₈	—	89	1	no	—
383	C₂×Q₈	—	89	2	no	—
384	C₂×Q₈	—	89	1	no	—
385	C₂×D₄	—	89	2	no	—
386	C₂×D₄	—	89	2	no	—
387	C₂×D₄	—	89	2	no	—
388	C₂×D₄	—	89	1	no	—
389	C₂²×C₄	—	89	2	no	—
390	C₂²×C₄	—	89	2	no	—
391	C₂²×C₄	—	89	2	no	—
392	C₂²×C₄	—	89	2	no	—
393	C₂²×C₄	—	89	2	no	—
394	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
395	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
396	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
398	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
399	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
400	C₄⋊C₄	—	89	2	no	—
401	C₄⋊C₄	—	89	2	no	—
402	C₄⋊C₄	—	89	2	no	—
403	C₄⋊C₄	—	89	2	no	—
404	C₄⋊C₄	—	89	2	no	—
405	C₄⋊C₄	—	89	2	no	—
406	C₄⋊C₄	—	89	2	no	—
407	C₄⋊C₄	—	89	2	no	—
408	C₄⋊C₄	—	89	2	no	—
409	C₄⋊C₄	—	89	2	no	—
410	C₄⋊C₄	—	89	2	no	—
411	C₄⋊C₄	—	89	2	no	—
412	C₄⋊C₄	—	89	2	no	—
413	C₄⋊C₄	—	89	1	no	—
414	C₄⋊C₄	—	89	2	no	—
415	C₄⋊C₄	—	89	2	no	—
416	C₄⋊C₄	—	89	2	no	—
417	C₄⋊C₄	—	89	2	no	—
418	C₄⋊C₄	—	89	2	no	—
419	C₄⋊C₄	—	89	1	no	—
420	C₄⋊C₄	—	89	2	no	—
421	C₄⋊C₄	—	89	2	no	—
422	C₄⋊C₄	—	89	1	no	—
423	C₄⋊C₄	—	89	2	no	—
424	C₄⋊C₄	—	89	1	no	—
425	C₄⋊C₄	—	89	2	no	—
426	C₄⋊C₄	—	89	2	no	—
427	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
428	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
429	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
430	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
431	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
432	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
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	—	89	2	no	—
438	C₂²⋊C₄	—	89	2	no	—
439	C₂²⋊C₄	—	89	2	no	—
440	C₂²⋊C₄	—	89	2	no	—
441	C₂²⋊C₄	—	89	2	no	—
442	C₂²⋊C₄	—	89	2	no	—
443	C₂²⋊C₄	—	89	2	no	—
444	C₂²⋊C₄	—	89	2	no	—
445	C₂²⋊C₄	—	89	2	no	—
446	C₂²⋊C₄	—	89	2	no	—
447	C₂²⋊C₄	—	89	2	no	—
448	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
449	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
450	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
451	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
452	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
453	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
454	C₄²	—	89	2	no	—
455	C₄²	—	89	2	no	—
456	C₄²	—	89	2	no	—
457	C₄²	—	89	2	no	—
458	C₄²	—	89	2	no	—
459	C₄²	—	89	2	no	—
460	C₄²	—	89	2	no	—
461	C₄²	C₂²×D₈₉	1	1	yes	characteristic
462	C₄²	C₂²×D₈₉	1	1	yes	characteristic
463	C₄²	C₂²×D₈₉	1	1	yes	characteristic
464	C₄²	C₂²×D₈₉	1	1	yes	characteristic
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	89	2	no	—
469	C₂³	C₂³×D₈₉	1	2	yes	—
470	C₂³	C₂³×D₈₉	1	1	yes	characteristic
471	Q₈	—	356	2	no	—
472	Q₈	—	356	2	no	—
473	Q₈	—	356	1	no	—
474	Q₈	—	356	1	no	—
475	Q₈	—	356	2	no	—
476	Q₈	—	356	1	no	—
477	D₄	—	356	1	no	—
478	D₄	—	356	2	no	—
479	D₄	—	356	2	no	—
480	D₄	—	178	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	89	2	no	—
488	C₂×C₄	—	89	2	no	—
489	C₂×C₄	—	89	2	no	—
490	C₂×C₄	—	89	2	no	—
491	C₂×C₄	—	89	2	no	—
492	C₂×C₄	—	89	2	no	—
493	C₂×C₄	—	89	2	no	—
494	C₂×C₄	—	356	2	no	—
495	C₂×C₄	—	356	2	no	—
496	C₂×C₄	—	356	2	no	—
497	C₂×C₄	—	356	2	no	—
498	C₂×C₄	—	356	2	no	—
499	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
500	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
501	C₂×C₄	C₂³×D₈₉	1	2	yes	—
502	C₂×C₄	C₂³×D₈₉	1	2	yes	—
503	C₂×C₄	C₂³×D₈₉	1	2	yes	—
504	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
505	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
506	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
507	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	178	2	no	—
515	C₂²	—	178	2	no	—
516	C₂²	—	178	2	no	—
517	C₂²	#15668059	1	2	yes	—
518	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	1	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	178	2	no	—
529	C₄	—	178	2	no	—
530	C₄	—	178	2	no	—
531	C₄	—	178	2	no	—
532	C₄	—	178	2	no	—
533	C₄	—	178	2	no	—
534	C₄	—	178	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	4	2	no	—
537	C₂	—	356	2	no	—
538	C₂	C₂×#15668059	1	1	yes	characteristic
539	C₂	#19152434	1	1	yes	characteristic
540	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	C₂×#126×C₈₉	C₂
prime radical	#19152186	C₂
hypercenter	C₂×#126	D₈₉
hypocenter	C₈₉	#3564
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #19152350	C₂	semidirect
2. #19152350	C₂	semidirect
3. #19152315	C₂	semidirect
4. #19152303	C₂	semidirect
5. #19152284	C₂	semidirect
6. #19152283	C₂	semidirect
7. #19152274	C₂	semidirect
8. #19152274	C₂	semidirect
9. #19152229	C₂	semidirect
10. #19152224	C₂	semidirect
11. #19152214	C₂	semidirect
12. #19152205	C₂	semidirect
13. #19152205	C₂	semidirect
14. #19152195	C₂	semidirect
15. #19152189	C₂	semidirect
17. #19152155	C₂	semidirect
18. #19152132	C₂	semidirect
19. C₂×#126×C₈₉	C₂	semidirect
20. #15668012	C₂²	semidirect
21. #15668012	C₂²	semidirect
22. #15668011	C₂²	semidirect
23. #15668011	C₂²	semidirect
24. #15668011	C₂²	semidirect
25. #15668007	C₂²	semidirect
26. #15668007	C₂²	semidirect
27. #15668007	C₂²	semidirect
28. #15668006	C₂²	semidirect
34. #15668004	C₂²	semidirect
35. #15668004	C₂²	semidirect
36. #15668003	C₂²	semidirect
37. #15668003	C₂²	semidirect
38. #15668003	C₂²	semidirect
39. #15668002	C₂²	semidirect
40. #15668002	C₂²	semidirect
41. #15668002	C₂²	semidirect
42. #15668002	C₂²	semidirect
43. #15668002	C₂²	semidirect
44. #15668000	C₂²	semidirect
48. #15667997	C₂²	semidirect
56. #15667992	C₂²	semidirect
57. #15667992	C₂²	semidirect
64. #15667990	C₂²	semidirect
65. #15667990	C₂²	semidirect
66. #15667990	C₂²	semidirect
76. C₄×Dic₁₇₈	C₂²	semidirect
77. C₄×Dic₁₇₈	C₂²	semidirect
78. C₄×Dic₁₇₈	C₂²	semidirect
79. C₄×Dic₁₇₈	C₂²	semidirect
80. #15667977	C₂²	semidirect
81. #15667977	C₂²	semidirect
82. C₄×D₃₅₆	C₂²	semidirect
90. #15667970	C₂²	semidirect
91. #15667969	C₂²	semidirect
94. C₄⋊C₄×D₈₉	C₂²	semidirect
271. C₈₉	#3564	semidirect
290. C₂×#126	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152350	2
#19152315	2
#19152303	2
#19152284	2
#19152283	2
#19152274	2
#19152229	2
#19152224	2
#19152214	2
#19152205	2
#19152195	2
#19152189	2
#19152186	2
#19152155	2
#19152132	2
C₂×#126×C₈₉	2
#3564	89