Subgroups — #36449267

Order 22784.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151804	C₂	1	1	yes	maximal, characteristic
2	#26023203	C₂	1	1	yes	maximal, characteristic
3	#26021212	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021203	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#19151325	C₂	1	1	yes	maximal, characteristic
6	#26018091	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083563	—	2	1	no	—
9	C₂×#15668012	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
11	C₂×#15667970	—	2	1	no	—
12	#19151804	—	2	2	no	—
13	#19151804	C₄	1	4	yes	complemented
14	C₂×#15667937	—	2	1	no	—
15	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
16	#19151499	—	2	1	no	—
17	#19151488	—	2	2	no	—
18	#19151455	—	2	1	no	—
19	C₄⋊C₄×Dic₈₉	—	2	1	no	—
20	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
21	#19151361	—	2	1	no	—
22	#19151361	—	2	1	no	—
23	#19151360	—	2	2	no	—
24	#19151325	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	#384×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₇₈	—	2	1	no	—
29	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₈₉	—	2	1	no	—
31	C₂×#13083563	—	2	4	no	—
32	C₂×#13083563	—	4	2	no	—
33	C₂×#13083563	—	4	2	no	—
34	C₂²×#10623494	—	2	1	no	—
35	#15668012	—	2	1	no	—
36	#15668012	—	2	1	no	—
37	#15668012	—	2	1	no	—
38	#15668012	C₂×C₄	1	2	yes	—
39	C₄×D₃₅₆	—	2	1	no	—
40	C₄×D₃₅₆	—	2	1	no	—
41	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
42	C₄×D₃₅₆	D₄	1	2	yes	—
43	#15667970	—	4	2	no	—
44	#15667970	—	4	2	no	—
45	C₂×C₄⋊Dic₈₉	—	2	1	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
50	C₂×#13083551	—	2	2	no	—
51	C₂×#13083551	—	2	2	no	—
52	C₂×#13083551	—	2	1	no	—
53	C₂×C₄×Dic₈₉	—	2	2	no	—
54	C₂×C₄×Dic₈₉	—	2	1	no	—
55	#15667937	—	2	4	no	—
56	C₄×#10623494	—	2	1	no	—
57	C₄×#10623494	—	2	1	no	—
58	#15667919	—	2	2	no	—
59	#15667919	—	2	1	no	—
60	C₂²×C₈×C₈₉	—	2	1	no	—
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₈₉	—	2	1	no	—
67	C₄⋊C₈×C₈₉	—	2	1	no	—
68	C₄⋊C₈×C₈₉	—	2	1	no	—
69	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
70	C₂³×D₈₉	—	2	1	no	—
71	C₂×Dic₁₇₈	—	2	2	no	—
72	C₂×Dic₁₇₈	—	4	1	no	—
73	C₂×Dic₁₇₈	—	4	1	no	—
74	C₂×Dic₁₇₈	—	4	1	no	—
75	C₂×Dic₁₇₈	—	4	1	no	—
76	C₂×Dic₁₇₈	—	4	1	no	—
77	C₂×D₃₅₆	—	2	1	no	—
78	C₂×D₃₅₆	—	2	1	no	—
79	C₂×D₃₅₆	—	2	1	no	—
80	C₂×D₃₅₆	—	2	1	no	—
81	C₂×D₃₅₆	—	2	1	no	—
82	C₂×D₃₅₆	C₂²⋊C₄	1	2	yes	—
83	C₂²×Dic₈₉	—	2	1	no	—
84	C₂²×Dic₈₉	—	2	1	no	—
85	C₂²×Dic₈₉	—	2	1	no	—
86	C₂²×Dic₈₉	—	4	1	no	—
87	C₂×C₄×D₈₉	—	2	2	no	—
88	C₂×C₄×D₈₉	—	2	2	no	—
89	C₂×C₄×D₈₉	—	4	1	no	—
90	C₂×C₄×D₈₉	—	4	1	no	—
91	C₂×C₄×D₈₉	—	4	1	no	—
92	C₂×C₄×D₈₉	—	4	1	no	—
93	#13083563	—	4	8	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	4	1	no	—
96	C₂×#10623494	—	4	1	no	—
97	C₄⋊Dic₈₉	—	2	1	no	—
98	C₄⋊Dic₈₉	—	2	1	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	—	2	1	no	—
102	C₄⋊Dic₈₉	—	2	1	no	—
103	C₄⋊Dic₈₉	—	4	1	no	—
104	C₄⋊Dic₈₉	—	4	1	no	—
105	C₄⋊Dic₈₉	C₂²⋊C₄	1	2	yes	—
106	C₄⋊Dic₈₉	SD₁₆	1	2	yes	complemented
107	#13083551	—	2	2	no	—
108	#13083551	—	2	2	no	—
109	#13083551	—	4	4	no	—
110	#13083551	—	8	2	no	—
111	C₄×Dic₈₉	—	4	4	no	—
112	C₄×Dic₈₉	—	4	1	no	—
113	C₄×Dic₈₉	—	4	1	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₈₉	—	2	2	no	—
119	C₂×C₈×C₈₉	—	4	1	no	—
120	C₂×C₈×C₈₉	—	4	1	no	—
121	C₂×C₈×C₈₉	—	4	1	no	—
122	C₂×C₈×C₈₉	—	4	1	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₄⋊C₄×C₈₉	—	4	2	no	—
125	C₄⋊C₄×C₈₉	—	4	1	no	—
126	C₄⋊C₄×C₈₉	—	4	1	no	—
127	C₄⋊C₄×C₈₉	—	4	1	no	—
128	C₄⋊C₄×C₈₉	—	4	1	no	—
129	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₈₉	#41	1	1	yes	characteristic
132	C₄²×C₈₉	#41	1	1	yes	characteristic
133	C₂³×C₈₉	#120	1	1	yes	characteristic
134	C₂²×D₈₉	—	2	2	no	—
135	C₂²×D₈₉	—	4	1	no	—
136	C₂²×D₈₉	—	4	1	no	—
137	C₂²×D₈₉	—	4	1	no	—
138	C₂²×D₈₉	—	4	1	no	—
139	C₂²×D₈₉	—	4	1	no	—
140	C₂²×D₈₉	—	4	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
156	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
160	C₂×Dic₈₉	—	2	2	no	—
161	C₂×Dic₈₉	—	2	2	no	—
162	C₂×Dic₈₉	—	4	1	no	—
163	C₂×Dic₈₉	—	4	1	no	—
164	C₂×Dic₈₉	—	4	1	no	—
165	C₂×Dic₈₉	—	4	1	no	—
166	C₂×Dic₈₉	—	4	2	no	—
167	C₂×Dic₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	4	1	no	—
169	C₂×Dic₈₉	—	4	1	no	—
170	C₂×Dic₈₉	—	8	1	no	—
171	C₂×Dic₈₉	—	8	1	no	—
172	D₃₅₆	—	2	2	no	—
173	D₃₅₆	—	2	2	no	—
174	D₃₅₆	—	4	1	no	—
175	D₃₅₆	—	4	1	no	—
176	C₄×D₈₉	—	4	2	no	—
177	C₄×D₈₉	—	4	2	no	—
178	C₄×D₈₉	—	4	2	no	—
179	C₄×D₈₉	—	4	2	no	—
180	Dic₁₇₈	—	4	2	no	—
181	Dic₁₇₈	—	4	2	no	—
182	Dic₁₇₈	—	8	1	no	—
183	Dic₁₇₈	—	8	1	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₈×C₈₉	—	8	1	no	—
186	#10623494	—	4	2	no	—
187	C₂²×C₈₉	#386	1	1	yes	characteristic
188	C₂²×C₈₉	#449	1	1	yes	characteristic
189	C₂²×C₈₉	#449	1	1	yes	characteristic
190	C₂²×C₈₉	#450	1	1	yes	characteristic
191	C₂²×C₈₉	#452	1	1	yes	characteristic
192	C₂²×C₈₉	#455	1	1	yes	characteristic
193	C₂²×C₈₉	#456	1	1	yes	characteristic
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	8	1	no	—
198	C₂×D₈₉	—	8	1	no	—
199	C₂×D₈₉	—	8	1	no	—
200	C₂×D₈₉	—	8	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	8	2	no	—
204	C₄×C₈₉	#416	1	1	yes	characteristic
205	C₄×C₈₉	#418	1	1	yes	characteristic
206	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
207	C₄×C₈₉	#440	1	1	yes	characteristic
208	C₄×C₈₉	#461	1	1	yes	characteristic
209	C₄×C₈₉	#463	1	1	yes	characteristic
210	C₄×C₈₉	#482	1	1	yes	characteristic
211	C₄×C₈₉	#482	1	1	yes	characteristic
212	Dic₈₉	—	4	2	no	—
213	Dic₈₉	—	4	2	no	—
214	Dic₈₉	—	8	2	no	—
215	Dic₈₉	—	8	1	no	—
216	#8988	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	#1642	1	1	yes	characteristic
218	C₂×C₈₉	#1646	1	1	yes	characteristic
219	C₂×C₈₉	#1650	1	1	yes	characteristic
220	C₂×C₈₉	#1654	1	1	yes	characteristic
221	C₂×C₈₉	#1875	1	1	yes	characteristic
222	C₂×C₈₉	#1877	1	1	yes	characteristic
223	C₂×C₈₉	#1882	1	1	yes	characteristic
224	D₈₉	—	8	2	no	—
225	C₂×#461	—	89	1	no	—
226	#2354	—	89	1	no	—
227	#1990	—	89	1	no	—
228	#1988	—	89	1	no	—
229	C₂×D₄⋊C₈	—	89	1	no	—
230	#1296	D₈₉	1	1	yes	characteristic, complemented
231	#1279	—	89	1	no	—
232	C₈₉	#8988	1	1	yes	characteristic, complemented, Sylow
233	C₂²×SD₁₆	—	178	1	no	—
234	C₂×C₄⋊Q₈	—	89	1	no	—
235	C₂×C₄×D₄	—	89	1	no	—
236	C₂×#117	—	178	1	no	—
237	#461	—	89	4	no	—
238	#461	—	178	2	no	—
239	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
241	C₂×#103	—	178	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	#390	—	178	1	no	—
244	#388	—	178	2	no	—
245	#384	C₂×D₈₉	1	1	yes	characteristic
246	#380	—	178	1	no	—
247	C₄×C₄⋊C₄	—	89	1	no	—
248	C₄×C₄⋊C₄	—	178	1	no	—
249	#340	—	178	1	no	—
250	#340	—	178	1	no	—
251	#340	—	178	2	no	—
252	D₄⋊C₈	—	178	2	no	—
253	C₂²×Q₈	—	178	1	no	—
254	C₂²×D₄	—	89	1	no	—
255	C₂³×C₄	—	178	1	no	—
256	C₂×SD₁₆	—	356	2	no	—
257	C₂×SD₁₆	—	356	2	no	—
258	C₂×SD₁₆	—	178	4	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	178	1	no	—
262	C₄⋊Q₈	—	89	2	no	—
263	C₄⋊Q₈	—	178	1	no	—
264	C₄⋊Q₈	—	178	1	no	—
265	C₄⋊Q₈	—	178	1	no	—
266	C₄×D₄	—	89	2	no	—
267	C₄×D₄	—	89	2	no	—
268	C₄×D₄	—	178	1	no	—
269	C₄×D₄	—	178	1	no	—
270	#117	—	356	2	no	—
271	#117	—	356	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	89	1	no	—
275	C₂×C₄⋊C₄	—	89	1	no	—
276	C₂×C₄⋊C₄	—	89	1	no	—
277	C₂×C₄⋊C₄	—	178	1	no	—
278	C₂×C₄⋊C₄	—	178	1	no	—
279	C₂×C₄⋊C₄	D₃₅₆	1	2	yes	—
280	C₂×C₂²⋊C₄	—	178	2	no	—
281	C₂×C₂²⋊C₄	—	178	1	no	—
282	C₂×C₂²⋊C₄	—	178	2	no	—
283	C₂×C₄²	—	178	2	no	—
284	C₂×C₄²	—	178	1	no	—
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
290	#103	—	178	4	no	—
291	C₄×C₈	—	178	1	no	—
292	C₄×C₈	—	178	1	no	—
293	#95	—	178	2	no	—
294	#95	—	178	1	no	—
295	C₂⁴	—	178	1	no	—
296	C₂×Q₈	—	356	1	no	—
297	C₂×Q₈	—	356	1	no	—
298	C₂×Q₈	—	356	1	no	—
299	C₂×Q₈	—	356	1	no	—
300	C₂×Q₈	—	356	1	no	—
301	C₂×Q₈	—	178	2	no	—
302	C₂×D₄	—	89	2	no	—
303	C₂×D₄	—	178	1	no	—
304	C₂×D₄	—	178	1	no	—
305	C₂×D₄	—	178	1	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	356	1	no	—
310	C₂²×C₄	—	356	1	no	—
311	C₂²×C₄	—	356	1	no	—
312	C₂²×C₄	—	356	1	no	—
313	C₂²×C₄	—	356	1	no	—
314	C₂²×C₄	—	178	1	no	—
315	C₂²×C₄	—	178	1	no	—
316	C₂²×C₄	—	178	1	no	—
317	C₂²×C₄	—	178	2	no	—
318	C₂²×C₄	—	178	2	no	—
319	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
322	SD₁₆	—	356	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	356	1	no	—
330	C₂×C₈	—	356	1	no	—
331	C₂×C₈	—	178	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	89	2	no	—
338	C₄⋊C₄	—	89	2	no	—
339	C₄⋊C₄	—	356	1	no	—
340	C₄⋊C₄	—	356	1	no	—
341	C₄⋊C₄	—	178	2	no	—
342	C₄⋊C₄	—	178	2	no	—
343	C₄⋊C₄	—	178	1	no	—
344	C₄⋊C₄	—	178	1	no	—
345	C₄⋊C₄	—	178	1	no	—
346	C₄⋊C₄	—	178	1	no	—
347	C₂²⋊C₄	—	356	4	no	—
348	C₂²⋊C₄	—	178	2	no	—
349	C₂²⋊C₄	—	178	2	no	—
350	C₂²⋊C₄	—	712	2	no	—
351	C₄²	—	356	4	no	—
352	C₄²	—	356	1	no	—
353	C₄²	—	356	1	no	—
354	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
355	C₄²	D₄×D₈₉	1	1	yes	characteristic
356	C₄²	#13083574	1	1	yes	characteristic
357	C₄²	#13083575	1	1	yes	characteristic
358	C₂³	—	356	1	no	—
359	C₂³	—	356	1	no	—
360	C₂³	—	356	1	no	—
361	C₂³	—	356	1	no	—
362	C₂³	—	356	1	no	—
363	C₂³	—	356	1	no	—
364	C₂³	—	178	2	no	—
365	C₂³	#15667982	1	1	yes	characteristic
366	Q₈	—	356	2	no	—
367	Q₈	—	356	2	no	—
368	Q₈	—	712	1	no	—
369	Q₈	—	712	1	no	—
370	D₄	—	356	1	no	—
371	D₄	—	356	1	no	—
372	D₄	—	178	2	no	—
373	D₄	—	178	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	356	1	no	—
380	C₂×C₄	—	356	1	no	—
381	C₂×C₄	—	356	1	no	—
382	C₂×C₄	—	356	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	356	2	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	356	1	no	—
389	C₂×C₄	—	356	1	no	—
390	C₂×C₄	—	356	1	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	—	178	2	no	—
393	C₂×C₄	—	712	1	no	—
394	C₂×C₄	—	712	1	no	—
395	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
396	C₂×C₄	#15667974	1	1	yes	characteristic
397	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
398	C₂×C₄	#15667985	1	1	yes	characteristic
399	C₂×C₄	#15667987	1	1	yes	characteristic
400	C₂×C₄	#15667997	1	1	yes	characteristic
401	C₂×C₄	SD₁₆×D₈₉	1	1	yes	characteristic
402	C₂×C₄	#15668033	1	1	yes	characteristic
403	C₂×C₄	#15668033	1	1	yes	characteristic
404	C₂×C₄	#15668035	1	1	yes	characteristic
405	C₂×C₄	#15668036	1	1	yes	characteristic
406	C₂×C₄	#15668036	1	1	yes	characteristic
407	C₂×C₄	#15668039	1	1	yes	characteristic
408	C₂×C₄	#15668044	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	8	1	no	—
411	C₈	—	356	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	356	2	no	—
414	C₂²	—	356	2	no	—
415	C₂²	—	712	1	no	—
416	C₂²	—	712	1	no	—
417	C₂²	—	712	1	no	—
418	C₂²	—	712	1	no	—
419	C₂²	#19151476	1	1	yes	characteristic
420	C₂²	#19151744	1	1	yes	characteristic
421	C₂²	#19151746	1	1	yes	characteristic
422	C₂²	#19151750	1	1	yes	characteristic
423	C₂²	#19151763	1	1	yes	characteristic
424	C₂²	#19151778	1	1	yes	characteristic
425	C₂²	#19151783	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	356	2	no	—
430	C₄	—	356	2	no	—
431	C₄	—	712	1	no	—
432	C₄	—	712	2	no	—
433	C₄	#19151593	1	1	yes	characteristic
434	C₄	#19151601	1	1	yes	characteristic
435	C₄	#19151685	1	1	yes	characteristic
436	C₄	#19151697	1	1	yes	characteristic
437	C₄	#19151802	1	1	yes	characteristic
438	C₄	#19151812	1	1	yes	characteristic
439	C₄	#19151924	1	1	yes	characteristic
440	C₄	#19151925	1	1	yes	characteristic
441	C₂	—	712	2	no	—
442	C₂	#26019453	1	1	yes	characteristic
443	C₂	#26019481	1	1	yes	characteristic
444	C₂	#26019509	1	1	yes	characteristic
445	C₂	#26019537	1	1	yes	characteristic
446	C₂	#26020573	1	1	yes	characteristic
447	C₂	#26020587	1	1	yes	characteristic
448	C₂	#26020620	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667982
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1296	C₂
socle	C₂³×C₈₉	#120
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1296	D₈₉
hypocenter	C₈₉	#8988
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
3. #26021212	C₂	semidirect
4. #26021203	C₂	semidirect
6. #26018091	C₂	semidirect
7. C₈₉×#1296	C₂	semidirect
13. #19151804	C₄	semidirect
106. C₄⋊Dic₈₉	SD₁₆	semidirect
230. #1296	D₈₉	semidirect
232. C₈₉	#8988	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151804	2
#26023203	2
#26021212	2
#26021203	2
C₂×#19151325	2
#26018091	2
C₈₉×#1296	2
#8988	89