Subgroups — #26033989

Order 11392.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152313	C₂	1	2	yes	maximal, complemented
2	#19152294	C₂	1	2	yes	maximal, complemented
3	#19152294	C₂	1	2	yes	maximal, complemented
4	#19152271	C₂	1	4	yes	maximal, complemented
5	#19152252	C₂	1	2	yes	maximal, complemented
6	#19152235	C₂	1	4	yes	maximal, complemented
7	#19152226	C₂	1	1	yes	maximal, characteristic, complemented
8	#19152221	C₂	1	2	yes	maximal, complemented
9	#19152201	C₂	1	2	yes	maximal, complemented
10	#19152162	C₂	1	1	yes	maximal, characteristic, complemented
11	#19152143	C₂	1	2	yes	maximal, complemented
12	#19152134	C₂	1	2	yes	maximal, complemented
13	C₂×#15667986	C₂	1	1	yes	maximal, characteristic, complemented
14	#19152081	C₂	1	1	yes	maximal, characteristic, complemented
15	#19152072	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15667971	C₂	1	1	yes	maximal, characteristic, complemented
17	#525×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13083573	C₂²	1	4	yes	complemented
19	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	—
21	#15668012	C₂²	1	2	yes	complemented
22	#15668011	C₂²	1	2	yes	complemented
23	#15668008	C₂²	1	2	yes	complemented
24	#15668007	C₂²	1	4	yes	complemented
25	#15668007	C₂²	1	4	yes	complemented
26	#15668004	C₂²	1	2	yes	complemented
27	#15668003	C₂²	1	2	yes	complemented
28	#15668001	C₂²	1	2	yes	complemented
29	#15667998	C₂²	1	4	yes	complemented
30	#15667998	C₂²	1	4	yes	complemented
31	#15667996	C₂²	1	4	yes	complemented
32	#15667996	C₂²	1	4	yes	complemented
33	#15667994	C₂²	1	4	yes	complemented
34	#15667994	C₂²	1	4	yes	complemented
35	#15667992	C₂²	1	4	yes	complemented
36	#15667989	C₂²	1	4	yes	—
37	#15667986	C₂²	1	2	yes	—
38	#15667986	C₂²	1	2	yes	—
39	#15667986	C₂²	1	2	yes	—
40	#15667986	C₂²	1	2	yes	—
41	#15667986	C₂²	1	2	yes	complemented
42	#15667986	C₂²	1	2	yes	complemented
43	#15667984	C₂²	1	4	yes	complemented
44	#15667984	C₂²	1	4	yes	complemented
45	#15667983	C₂²	1	4	yes	complemented
46	#15667980	C₂²	1	4	yes	—
47	Q₈×Dic₈₉	C₂²	1	2	yes	complemented
48	C₄×D₃₅₆	C₂²	1	2	yes	complemented
49	C₄×D₃₅₆	C₂²	1	2	yes	complemented
50	D₄×Dic₈₉	C₂²	1	4	yes	—
51	D₄×Dic₈₉	C₂²	1	2	yes	complemented
52	#15667974	C₂²	1	2	yes	complemented
53	#15667974	C₂²	1	2	yes	complemented
54	#15667972	C₂²	1	4	yes	complemented
55	#15667972	C₂²	1	4	yes	complemented
56	#15667971	C₂²	1	1	yes	characteristic
57	#15667971	C₂²	1	2	yes	—
58	#15667971	C₂²	1	1	yes	characteristic
59	#15667971	C₂²	1	2	yes	complemented
60	#15667971	C₂²	1	1	yes	characteristic, complemented
61	#15667971	C₂²	1	2	yes	complemented
62	#15667971	C₂²	1	1	yes	characteristic, complemented
63	#15667970	C₂²	1	4	yes	complemented
64	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄⋊Dic₈₉	C₂²	1	2	yes	complemented
67	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	—
69	C₂×#13083551	C₂²	1	2	yes	—
70	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	—
71	C₂×C₄×Dic₈₉	C₂²	1	2	yes	complemented
72	C₂×#41×C₈₉	C₂²	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	C₂²	1	1	yes	characteristic
74	#123×C₈₉	C₂²	1	2	yes	—
75	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
76	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
77	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
78	#121×C₈₉	C₂²	1	1	yes	characteristic, complemented
79	#120×C₈₉	C₂²	1	2	yes	—
80	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
81	C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
82	#117×C₈₉	C₂²	1	1	yes	characteristic
83	C₂³×D₈₉	C₂³	1	2	yes	—
84	#13083573	—	4	8	no	—
85	C₂×Dic₁₇₈	C₂³	1	4	yes	—
86	C₂×D₃₅₆	—	2	4	no	—
87	C₂×D₃₅₆	C₂³	1	2	yes	—
88	C₂×D₃₅₆	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₈₉	—	4	4	no	—
90	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
94	C₂²×Dic₈₉	C₂³	1	2	yes	—
95	C₂²×Dic₈₉	C₂³	1	2	yes	—
96	C₂²×Dic₈₉	C₂³	1	4	yes	—
97	C₂²×Dic₈₉	C₂³	1	2	yes	—
98	C₂×C₄×D₈₉	C₂³	1	4	yes	—
99	C₂×C₄×D₈₉	C₂³	1	4	yes	—
100	C₄⋊Dic₈₉	C₂³	1	4	yes	—
101	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₈₉	C₂³	1	2	yes	—
106	C₄⋊Dic₈₉	C₂³	1	2	yes	—
107	C₄⋊Dic₈₉	C₂³	1	2	yes	—
108	C₄⋊Dic₈₉	C₂³	1	4	yes	—
109	C₄⋊Dic₈₉	C₂³	1	2	yes	—
110	#13083553	C₂³	1	4	yes	—
111	#13083553	C₂³	1	4	yes	—
112	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
113	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
114	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
115	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
117	#13083551	C₂³	1	4	yes	—
118	#13083551	C₂³	1	4	yes	—
119	#13083551	C₂³	1	4	yes	—
120	#13083551	C₂³	1	4	yes	—
121	#13083551	C₂³	1	4	yes	—
122	#13083551	C₂³	1	4	yes	—
123	C₄×Dic₈₉	C₂³	1	2	yes	—
124	C₄×Dic₈₉	C₂³	1	4	yes	—
125	C₄×Dic₈₉	C₂³	1	2	yes	—
126	C₄×Dic₈₉	C₂³	1	2	yes	—
127	C₄×Dic₈₉	C₂³	1	2	yes	—
128	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
129	#41×C₈₉	—	2	4	no	—
130	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₈₉	C₂³	1	2	yes	—
132	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₈₉	C₂³	1	2	yes	—
134	C₂×D₄×C₈₉	C₂³	1	2	yes	—
135	C₂²×C₄×C₈₉	—	2	4	no	—
136	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
147	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
152	C₄²×C₈₉	C₂³	1	2	yes	—
153	C₂³×C₈₉	—	2	2	no	—
154	C₂³×C₈₉	—	2	2	no	—
155	C₂³×C₈₉	—	4	1	no	—
156	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₂³×C₈₉	C₂⁴	1	2	yes	—
158	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂²×D₈₉	—	2	4	no	—
161	C₂²×D₈₉	—	4	2	no	—
162	C₂²×D₈₉	—	4	2	no	—
163	C₂²×D₈₉	C₂⁴	1	4	yes	—
164	Q₈×C₈₉	—	2	2	no	—
165	D₄×C₈₉	—	2	4	no	—
166	D₄×C₈₉	—	2	4	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	#41	1	4	yes	complemented
176	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
177	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
178	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
181	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²⋊D₈₉	—	2	8	no	—
184	C₂²⋊D₈₉	—	4	4	no	—
185	C₂²⋊D₈₉	—	4	4	no	—
186	C₂²⋊D₈₉	—	4	4	no	—
187	C₂×Dic₈₉	—	2	4	no	—
188	C₂×Dic₈₉	—	4	2	no	—
189	C₂×Dic₈₉	—	4	2	no	—
190	C₂×Dic₈₉	—	4	4	no	—
191	C₂×Dic₈₉	C₂⁴	1	2	yes	—
192	C₂×Dic₈₉	C₂⁴	1	2	yes	—
193	C₂×Dic₈₉	C₂⁴	1	2	yes	—
194	C₂×Dic₈₉	C₂⁴	1	2	yes	—
195	C₂×Dic₈₉	C₂⁴	1	4	yes	—
196	D₃₅₆	—	2	4	no	—
197	D₃₅₆	—	2	4	no	—
198	C₄×D₈₉	—	4	4	no	—
199	C₄×D₈₉	—	4	4	no	—
200	Dic₁₇₈	—	4	4	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	2	1	no	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	2	1	no	—
209	C₂²×C₈₉	—	2	2	no	—
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	—	4	4	no	—
212	C₂²×C₈₉	C₂×#41	1	2	yes	—
213	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
214	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
215	C₂×D₈₉	—	2	4	no	—
216	C₂×D₈₉	—	2	4	no	—
217	C₂×D₈₉	—	2	4	no	—
218	C₂×D₈₉	—	8	4	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	2	1	no	—
221	C₄×C₈₉	—	2	2	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	C₂×#41	1	2	yes	—
225	C₄×C₈₉	C₂×#41	1	2	yes	—
226	Dic₈₉	—	2	2	no	—
227	Dic₈₉	—	2	4	no	—
228	Dic₈₉	—	2	2	no	—
229	Dic₈₉	—	2	2	no	—
230	Dic₈₉	—	2	2	no	—
231	C₂×C₈₉	—	2	2	no	—
232	C₂×C₈₉	—	2	2	no	—
233	C₂×C₈₉	—	4	2	no	—
234	C₂×C₈₉	—	4	1	no	—
235	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
236	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
237	C₂×C₈₉	#585	1	1	yes	characteristic
238	D₈₉	—	4	4	no	—
239	#3494	—	89	1	no	maximal, Sylow
240	C₈₉	#3494	1	1	yes	characteristic, complemented, Sylow
241	#555	—	89	2	no	—
242	#553	—	89	2	no	—
243	#553	—	89	2	no	—
244	#551	—	89	4	no	—
245	#547	—	89	2	no	—
246	#546	—	89	4	no	—
247	#544	—	89	1	no	—
248	#542	—	89	2	no	—
249	#540	—	89	2	no	—
250	#535	—	89	1	no	—
251	#532	—	89	2	no	—
252	#529	—	89	2	no	—
253	#525	D₈₉	1	1	yes	characteristic, complemented
254	C₂×#121	—	89	1	no	—
255	#520	—	89	1	no	—
256	#518	—	89	1	no	—
257	C₂×#117	—	89	1	no	—
258	C₂×#41	—	89	4	no	—
259	C₂×#41	C₂×D₈₉	1	1	yes	characteristic
260	C₂²×D₄	—	89	2	no	—
261	C₂²×D₄	—	89	1	no	—
262	C₂³×C₄	C₂×D₈₉	1	1	yes	characteristic
263	C₄⋊Q₈	—	89	2	no	—
264	C₄⋊Q₈	—	89	2	no	—
265	#127	—	89	2	no	—
266	#126	—	89	4	no	—
267	#126	—	89	4	no	—
268	#125	—	89	2	no	—
269	#125	—	89	2	no	—
270	#124	—	89	2	no	—
271	#124	—	89	4	no	—
272	#124	—	89	4	no	—
273	#123	—	89	4	no	—
274	#123	—	89	4	no	—
275	#123	—	89	4	no	—
276	#123	—	89	4	no	—
277	#123	C₂×D₈₉	1	2	yes	—
278	C₂²⋊Q₈	—	89	4	no	—
279	C₂²⋊Q₈	—	89	4	no	—
280	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
281	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
282	#121	—	89	4	no	—
283	#121	—	89	4	no	—
284	#121	—	89	4	no	—
285	#121	—	89	2	no	—
286	#121	—	89	2	no	—
287	#121	—	89	2	no	—
288	#121	—	89	2	no	—
289	#121	—	89	2	no	—
290	#121	—	89	2	no	—
291	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
292	#121	C₂×D₈₉	1	1	yes	characteristic, complemented
293	#120	—	89	4	no	—
294	#120	C₂×D₈₉	1	2	yes	—
295	C₄×Q₈	—	89	2	no	—
296	C₄×D₄	—	89	4	no	—
297	C₄×D₄	—	89	2	no	—
298	C₄×D₄	—	89	2	no	—
299	C₄×D₄	—	89	2	no	—
300	C₄×D₄	—	89	4	no	—
301	C₄×D₄	—	89	4	no	—
302	C₄×D₄	—	89	2	no	—
303	C₄×D₄	—	89	2	no	—
304	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
305	C₄×D₄	C₂×D₈₉	1	2	yes	complemented
306	#117	—	89	1	no	—
307	#117	—	89	1	no	—
308	#117	—	89	2	no	—
309	#117	—	89	2	no	—
310	#117	—	89	1	no	—
311	#117	—	89	1	no	—
312	#117	—	89	2	no	—
313	#117	—	89	4	no	—
314	#117	C₂×D₈₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	89	1	no	—
316	C₂×C₄⋊C₄	—	89	1	no	—
317	C₂×C₄⋊C₄	—	89	1	no	—
318	C₂×C₄⋊C₄	—	89	2	no	—
319	C₂×C₂²⋊C₄	—	89	2	no	—
320	C₂×C₂²⋊C₄	—	89	2	no	—
321	C₂×C₂²⋊C₄	—	89	4	no	—
322	C₂×C₄²	—	89	2	no	—
323	C₂⁴	—	89	2	no	—
324	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
325	#41	—	2	4	no	—
326	#41	—	356	8	no	—
327	C₂×Q₈	—	89	4	no	—
328	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
329	C₂×D₄	—	89	4	no	—
330	C₂×D₄	—	89	4	no	—
331	C₂×D₄	—	89	4	no	—
332	C₂×D₄	—	89	4	no	—
333	C₂×D₄	—	89	2	no	—
334	C₂×D₄	—	89	2	no	—
335	C₂×D₄	—	356	4	no	—
336	C₂×D₄	—	178	4	no	—
337	C₂×D₄	C₂²×D₈₉	1	2	yes	—
338	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
339	C₂×D₄	C₂²×D₈₉	1	2	yes	—
340	C₂×D₄	C₂²×D₈₉	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	89	2	no	—
343	C₂²×C₄	—	89	2	no	—
344	C₂²×C₄	—	89	4	no	—
345	C₂²×C₄	—	89	2	no	—
346	C₂²×C₄	—	89	4	no	—
347	C₂²×C₄	—	89	4	no	—
348	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
350	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
352	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
353	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
355	C₄⋊C₄	—	89	1	no	—
356	C₄⋊C₄	—	89	2	no	—
357	C₄⋊C₄	—	89	1	no	—
358	C₄⋊C₄	—	89	1	no	—
359	C₄⋊C₄	—	89	1	no	—
360	C₄⋊C₄	—	89	2	no	—
361	C₄⋊C₄	—	89	2	no	—
362	C₄⋊C₄	—	89	2	no	—
363	C₄⋊C₄	—	89	4	no	—
364	C₄⋊C₄	—	89	4	no	—
365	C₄⋊C₄	—	89	4	no	—
366	C₄⋊C₄	—	89	4	no	—
367	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
368	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
371	C₂²⋊C₄	—	89	2	no	—
372	C₂²⋊C₄	—	89	2	no	—
373	C₂²⋊C₄	—	89	2	no	—
374	C₂²⋊C₄	—	89	2	no	—
375	C₂²⋊C₄	—	89	4	no	—
376	C₂²⋊C₄	—	89	4	no	—
377	C₂²⋊C₄	—	89	4	no	—
378	C₂²⋊C₄	—	89	4	no	—
379	C₂²⋊C₄	—	89	4	no	—
380	C₂²⋊C₄	—	89	4	no	—
381	C₂²⋊C₄	—	89	4	no	—
382	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
383	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
385	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
386	C₂²⋊C₄	C₂²×D₈₉	1	2	yes	—
387	C₄²	—	89	2	no	—
388	C₄²	—	89	2	no	—
389	C₄²	—	89	2	no	—
390	C₄²	—	89	2	no	—
391	C₄²	—	89	4	no	—
392	C₄²	C₂²×D₈₉	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	89	4	no	—
397	C₂³	—	356	2	no	—
398	C₂³	—	356	2	no	—
399	C₂³	—	178	4	no	—
400	C₂³	C₂³×D₈₉	1	1	yes	characteristic
401	C₂³	C₂³×D₈₉	1	2	yes	—
402	C₂³	C₂³×D₈₉	1	1	yes	characteristic
403	C₂³	C₂³×D₈₉	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	356	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	356	4	no	—
411	D₄	—	356	4	no	—
412	D₄	—	356	4	no	—
413	D₄	—	178	8	no	—
414	D₄	—	178	4	no	—
415	D₄	—	178	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	89	2	no	—
423	C₂×C₄	—	89	2	no	—
424	C₂×C₄	—	89	2	no	—
425	C₂×C₄	—	89	2	no	—
426	C₂×C₄	—	89	4	no	—
427	C₂×C₄	—	356	4	no	—
428	C₂×C₄	—	356	4	no	—
429	C₂×C₄	—	356	2	no	—
430	C₂×C₄	—	356	2	no	—
431	C₂×C₄	—	356	4	no	—
432	C₂×C₄	—	178	4	no	—
433	C₂×C₄	#13083573	1	4	yes	complemented
434	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₈₉	1	2	yes	—
436	C₂×C₄	C₂³×D₈₉	1	2	yes	—
437	C₂×C₄	C₂³×D₈₉	1	2	yes	—
438	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	178	4	no	—
453	C₂²	—	178	4	no	—
454	C₂²	—	178	4	no	—
455	C₂²	—	712	4	no	—
456	C₂²	C₂×#13083573	1	2	yes	—
457	C₂²	#15668058	1	2	yes	—
458	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	178	2	no	—
465	C₄	—	178	4	no	—
466	C₄	—	178	2	no	—
467	C₄	—	178	2	no	—
468	C₄	—	178	2	no	—
469	C₄	C₂×#13083573	1	2	yes	—
470	C₄	C₂×#13083573	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	2	no	—
474	C₂	—	4	1	no	—
475	C₂	—	356	4	no	—
476	C₂	C₂²×#13083573	1	1	yes	characteristic
477	C₂	C₂×#15668058	1	1	yes	characteristic
478	C₂	#19152434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#525×C₈₉	C₂
hypercenter	#525	D₈₉
hypocenter	C₈₉	#3494
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #525

Complements

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

N	H ≅ G/N	type
1. #19152313	C₂	semidirect
2. #19152294	C₂	semidirect
3. #19152294	C₂	semidirect
4. #19152271	C₂	semidirect
5. #19152252	C₂	semidirect
6. #19152235	C₂	semidirect
7. #19152226	C₂	semidirect
8. #19152221	C₂	semidirect
9. #19152201	C₂	semidirect
10. #19152162	C₂	semidirect
11. #19152143	C₂	semidirect
12. #19152134	C₂	semidirect
13. C₂×#15667986	C₂	semidirect
14. #19152081	C₂	semidirect
15. #19152072	C₂	semidirect
16. C₂×#15667971	C₂	semidirect
17. #525×C₈₉	C₂	semidirect
18. C₂×#13083573	C₂²	semidirect
21. #15668012	C₂²	semidirect
22. #15668011	C₂²	semidirect
23. #15668008	C₂²	semidirect
24. #15668007	C₂²	semidirect
25. #15668007	C₂²	semidirect
26. #15668004	C₂²	semidirect
27. #15668003	C₂²	semidirect
28. #15668001	C₂²	semidirect
29. #15667998	C₂²	semidirect
30. #15667998	C₂²	semidirect
31. #15667996	C₂²	semidirect
32. #15667996	C₂²	semidirect
33. #15667994	C₂²	semidirect
34. #15667994	C₂²	semidirect
35. #15667992	C₂²	semidirect
41. #15667986	C₂²	semidirect
42. #15667986	C₂²	semidirect
43. #15667984	C₂²	semidirect
44. #15667984	C₂²	semidirect
45. #15667983	C₂²	semidirect
47. Q₈×Dic₈₉	C₂²	semidirect
48. C₄×D₃₅₆	C₂²	semidirect
49. C₄×D₃₅₆	C₂²	semidirect
51. D₄×Dic₈₉	C₂²	semidirect
52. #15667974	C₂²	semidirect
53. #15667974	C₂²	semidirect
54. #15667972	C₂²	semidirect
55. #15667972	C₂²	semidirect
59. #15667971	C₂²	semidirect
60. #15667971	C₂²	semidirect
61. #15667971	C₂²	semidirect
62. #15667971	C₂²	semidirect
63. #15667970	C₂²	semidirect
65. C₂×C₄⋊Dic₈₉	C₂²	semidirect
66. C₂×C₄⋊Dic₈₉	C₂²	semidirect
67. C₂×C₄⋊Dic₈₉	C₂²	semidirect
71. C₂×C₄×Dic₈₉	C₂²	semidirect
75. C₂²⋊Q₈×C₈₉	C₂²	semidirect
76. C₂²⋊Q₈×C₈₉	C₂²	semidirect
77. #121×C₈₉	C₂²	semidirect
78. #121×C₈₉	C₂²	semidirect
80. C₄×D₄×C₈₉	C₂²	semidirect
81. C₄×D₄×C₈₉	C₂²	semidirect
175. C₂×C₄×C₈₉	#41	semidirect
240. C₈₉	#3494	semidirect
253. #525	D₈₉	semidirect
280. C₂²⋊Q₈	C₂×D₈₉	semidirect
281. C₂²⋊Q₈	C₂×D₈₉	semidirect
291. #121	C₂×D₈₉	semidirect
292. #121	C₂×D₈₉	semidirect
304. C₄×D₄	C₂×D₈₉	semidirect
305. C₄×D₄	C₂×D₈₉	semidirect
433. C₂×C₄	#13083573	semidirect

Maximal subgroups

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

subgroup	index
#19152313	2
#19152294	2
#19152271	2
#19152252	2
#19152235	2
#19152226	2
#19152221	2
#19152201	2
#19152162	2
#19152143	2
#19152134	2
C₂×#15667986	2
#19152081	2
#19152072	2
C₂×#15667971	2
#525×C₈₉	2
#3494	89