Subgroups — #36524413

Order 22784.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030334	C₂	1	1	yes	maximal, characteristic
2	#26029227	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019132	C₂	1	2	yes	maximal, complemented
5	#26019125	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₃₅₆	C₂	1	2	yes	maximal, complemented
7	C₈×#13083563	C₂	1	2	yes	maximal, complemented
8	#26019037	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018700	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018666	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152132	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
14	#19151929	C₄	1	1	yes	characteristic
15	#19151912	C₄	1	1	yes	characteristic
16	#19151906	C₄	1	2	yes	—
17	#19151821	C₄	1	2	yes	—
18	#19151756	C₄	1	1	yes	characteristic
19	#19151739	C₄	1	1	yes	characteristic
20	#19151728	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₇₈	—	2	1	no	—
22	C₈×Dic₁₇₈	—	2	1	no	—
23	C₈×Dic₁₇₈	C₂²	1	2	yes	—
24	C₈×Dic₁₇₈	C₂²	1	2	yes	—
25	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₅₆	C₂²	1	2	yes	—
27	C₄×#13083563	C₂²	1	2	yes	—
28	#19151677	C₂²	1	1	yes	characteristic
29	#19151669	—	2	1	no	—
30	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₈₉	—	2	1	no	—
32	#19151657	—	2	1	no	—
33	#19151655	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
35	C₂×#15667941	—	2	1	no	—
36	#19151552	—	2	1	no	—
37	C₂×C₈×Dic₈₉	—	2	1	no	—
38	#19151351	C₂²	1	2	yes	—
39	#19151349	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151330	C₂²	1	2	yes	—
42	#19151330	C₂²	1	2	yes	—
43	#19151327	C₂²	1	2	yes	—
44	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	#322×C₈₉	C₂²	1	2	yes	—
48	C₈²×C₈₉	C₂²	1	2	yes	—
49	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₃₅₆	C₂×C₄	1	2	yes	—
51	C₂×#13083563	C₂×C₄	1	2	yes	—
52	C₂×#13083557	—	2	1	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	1	no	—
55	#15668006	—	2	1	no	—
56	#15668004	C₂×C₄	1	1	yes	characteristic
57	#15668000	C₂×C₄	1	1	yes	characteristic
58	#15667995	—	2	1	no	—
59	#15667991	C₂×C₄	1	1	yes	characteristic
60	#15667986	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₇₈	—	2	1	no	—
62	C₄×Dic₁₇₈	—	2	1	no	—
63	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
64	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
65	C₄×Dic₁₇₈	C₂³	1	2	yes	—
66	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₈₉	—	2	1	no	—
68	#15667969	—	2	1	no	—
69	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083553	—	2	1	no	—
71	C₂×C₄×Dic₈₉	—	2	1	no	—
72	#15667946	C₂×C₄	1	2	yes	—
73	#15667944	C₂×C₄	1	2	yes	—
74	C₄⋊#10623494	—	2	1	no	—
75	C₄⋊#10623494	C₂³	1	2	yes	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	#15667941	—	2	2	no	—
79	#15667941	—	2	2	no	—
80	#15667941	—	2	1	no	—
81	#15667941	—	2	1	no	—
82	#15667937	C₂×C₄	1	2	yes	—
83	#15667937	C₂×C₄	1	2	yes	—
84	#15667937	C₂×C₄	1	2	yes	—
85	#15667934	C₂×C₄	1	2	yes	—
86	C₂²⋊#10623494	—	2	1	no	—
87	#15667924	—	2	1	no	—
88	#15667924	—	2	1	no	—
89	#15667923	—	2	1	no	—
90	#15667922	—	2	1	no	—
91	C₈×Dic₈₉	—	2	1	no	—
92	C₈×Dic₈₉	—	2	2	no	—
93	C₈×Dic₈₉	—	2	2	no	—
94	C₂×M₁₆×C₈₉	—	2	1	no	—
95	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
101	#97×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
103	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₈₉	C₂³	1	2	yes	—
105	C₄×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₇₈	—	2	1	no	—
109	C₂×Dic₁₇₈	—	2	4	no	—
110	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
112	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₈₉	—	2	1	no	—
114	C₂²×Dic₈₉	—	2	1	no	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	Dic₃₅₆	—	2	4	no	—
118	#13083563	—	2	4	no	—
119	#13083557	—	4	2	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	4	2	no	—
124	C₈×D₈₉	—	4	2	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
128	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	#13083553	—	2	1	no	—
130	#13083553	—	2	1	no	—
131	#13083553	—	2	1	no	—
132	#13083553	—	2	2	no	—
133	#13083553	—	2	2	no	—
134	#13083553	—	2	1	no	—
135	C₂²⋊Dic₈₉	—	2	1	no	—
136	#13083551	—	2	1	no	—
137	#13083551	—	2	1	no	—
138	#13083551	—	2	1	no	—
139	#13083551	—	2	1	no	—
140	C₄×Dic₈₉	—	2	2	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	—	2	2	no	—
143	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
146	M₁₆×C₈₉	—	2	4	no	—
147	C₂×C₈×C₈₉	—	2	2	no	—
148	C₂×C₈×C₈₉	—	2	2	no	—
149	C₂×C₈×C₈₉	—	4	1	no	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	#41	1	1	yes	characteristic
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	2	4	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	C₂×Dic₈₉	—	2	2	no	—
176	C₂×Dic₈₉	—	2	1	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	C₂×Dic₈₉	—	4	2	no	—
180	D₃₅₆	—	2	2	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	Dic₁₇₈	—	2	4	no	—
184	Dic₁₇₈	—	2	2	no	—
185	Dic₁₇₈	—	2	2	no	—
186	Dic₁₇₈	#131	1	4	yes	—
187	C₈×C₈₉	—	2	4	no	—
188	C₈×C₈₉	—	2	2	no	—
189	C₈×C₈₉	—	2	2	no	—
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	—	2	1	no	—
192	C₈×C₈₉	—	2	1	no	—
193	C₈×C₈₉	#137	1	2	yes	—
194	#10623494	—	4	1	no	—
195	#10623494	—	4	2	no	—
196	#10623494	—	4	1	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	#443	1	2	yes	—
200	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₈₉	—	4	1	no	—
202	C₂×D₈₉	—	4	1	no	—
203	C₂×D₈₉	—	4	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	2	1	no	—
206	C₄×C₈₉	—	2	1	no	—
207	C₄×C₈₉	—	2	1	no	—
208	C₄×C₈₉	C₂×#131	1	2	yes	—
209	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
210	C₄×C₈₉	#575	1	1	yes	characteristic
211	Dic₈₉	—	2	4	no	—
212	Dic₈₉	—	4	1	no	—
213	Dic₈₉	—	4	1	no	—
214	Dic₈₉	—	4	2	no	—
215	Dic₈₉	—	4	1	no	—
216	#17911	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	#2929	1	1	yes	characteristic
219	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
221	D₈₉	—	8	1	no	—
222	#3108	—	89	1	no	—
223	#2966	—	89	1	no	—
224	C₂×C₈×Q₈	—	89	1	no	—
225	#1588	—	89	2	no	—
226	#1587	—	89	2	no	—
227	C₈×Q₁₆	—	89	2	no	—
228	C₈×SD₁₆	—	89	2	no	—
229	#1573	—	89	1	no	—
230	#1491	—	89	1	no	—
231	#1483	—	89	1	no	—
232	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
233	C₈₉	#17911	1	1	yes	characteristic, complemented, Sylow
234	#529	—	89	1	no	—
235	C₂×C₄×Q₈	—	89	1	no	—
236	#483	—	89	1	no	—
237	#480	—	89	1	no	—
238	#479	—	89	2	no	—
239	#464	—	89	2	no	—
240	#451	—	89	1	no	—
241	#448	—	89	1	no	—
242	#446	—	89	1	no	—
243	C₈×Q₈	—	89	2	no	—
244	C₈×Q₈	—	89	1	no	—
245	C₈×Q₈	—	89	2	no	—
246	C₈×Q₈	—	178	1	no	—
247	C₈×Q₈	—	178	1	no	—
248	C₄×Q₁₆	—	89	2	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	#436	—	89	1	no	—
251	#435	—	178	1	no	—
252	C₈×D₄	—	89	1	no	—
253	C₈×D₄	—	178	1	no	—
254	#433	—	178	1	no	—
255	#432	—	89	1	no	—
256	#431	C₂×D₈₉	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	89	1	no	—
258	C₂×C₄⋊C₈	—	178	1	no	—
259	#405	—	178	1	no	—
260	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
261	C₂×C₄×C₈	—	178	1	no	—
262	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
263	#335	—	89	2	no	—
264	#334	—	89	2	no	—
265	Q₈⋊C₈	—	89	2	no	—
266	Q₈⋊C₈	—	89	2	no	—
267	Q₈⋊C₈	—	89	2	no	—
268	D₄⋊C₈	—	89	2	no	—
269	#322	C₂×D₈₉	1	2	yes	—
270	C₈²	C₂×D₈₉	1	2	yes	—
271	C₂²×Q₈	—	89	1	no	—
272	C₂×Q₁₆	—	89	2	no	—
273	C₂×SD₁₆	—	89	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	178	1	no	—
276	C₂²×C₈	—	178	1	no	—
277	C₂²×C₈	—	178	1	no	—
278	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
279	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
280	#126	—	178	1	no	—
281	#125	—	89	1	no	—
282	#124	—	89	1	no	—
283	#123	—	178	1	no	—
284	C₂²⋊Q₈	—	89	1	no	—
285	#121	—	89	1	no	—
286	C₄×Q₈	—	89	2	no	—
287	C₄×Q₈	—	89	2	no	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	—	178	1	no	—
290	C₄×Q₈	—	178	1	no	—
291	C₄×D₄	—	89	1	no	—
292	C₄×D₄	—	178	1	no	—
293	#117	—	178	1	no	—
294	C₂×C₄⋊C₄	—	89	1	no	—
295	C₂×C₄⋊C₄	—	178	1	no	—
296	C₂×C₄²	—	178	1	no	—
297	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
298	#107	—	89	2	no	—
299	#106	—	89	2	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	89	1	no	—
302	C₄⋊C₈	—	89	1	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	—	178	2	no	—
305	C₄⋊C₈	—	178	1	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	—	178	1	no	—
308	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
309	#103	—	89	2	no	—
310	#103	—	89	2	no	—
311	#103	—	89	2	no	—
312	#102	—	89	2	no	—
313	C₂²⋊C₈	—	178	1	no	—
314	C₂²⋊C₈	—	178	1	no	—
315	C₂²⋊C₈	—	178	1	no	—
316	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
317	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
318	#97	—	2	1	no	—
319	#97	—	178	1	no	—
320	#97	—	178	1	no	—
321	C₄×C₈	—	178	2	no	—
322	C₄×C₈	—	178	2	no	—
323	C₄×C₈	—	178	1	no	—
324	C₄×C₈	D₃₅₆	1	1	yes	characteristic
325	C₄×C₈	D₃₅₆	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₈₉	1	2	yes	—
327	C₄×C₈	C₂²×D₈₉	1	2	yes	—
328	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₂×Q₈	—	89	2	no	—
331	C₂×Q₈	—	89	1	no	—
332	C₂×Q₈	—	178	4	no	—
333	C₂×Q₈	—	178	1	no	—
334	C₂×D₄	—	89	1	no	—
335	C₂×D₄	—	178	1	no	—
336	C₂²×C₄	—	178	1	no	—
337	C₂²×C₄	—	178	1	no	—
338	C₂²×C₄	—	178	1	no	—
339	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
341	C₂²×C₄	#13083574	1	1	yes	characteristic
342	Q₁₆	—	178	4	no	—
343	SD₁₆	—	178	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	356	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	356	2	no	—
350	C₂×C₈	—	356	2	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	—	178	1	no	—
353	C₂×C₈	—	178	1	no	—
354	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
356	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
357	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
358	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
359	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
360	C₄⋊C₄	—	89	2	no	—
361	C₄⋊C₄	—	89	1	no	—
362	C₄⋊C₄	—	89	1	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₄⋊C₄	—	178	2	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	2	no	—
369	C₄⋊C₄	—	178	1	no	—
370	C₂²⋊C₄	—	178	1	no	—
371	C₂²⋊C₄	—	178	1	no	—
372	C₂²⋊C₄	—	178	1	no	—
373	C₂²⋊C₄	—	178	1	no	—
374	C₂²⋊C₄	—	178	1	no	—
375	C₄²	—	178	2	no	—
376	C₄²	—	178	2	no	—
377	C₄²	—	178	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
380	C₄²	#13083574	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	178	1	no	—
383	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
384	Q₈	—	89	4	no	—
385	Q₈	—	178	4	no	—
386	Q₈	—	178	2	no	—
387	Q₈	—	178	2	no	—
388	D₄	—	356	2	no	—
389	D₄	—	178	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	356	1	no	—
396	C₂×C₄	—	356	1	no	—
397	C₂×C₄	—	178	2	no	—
398	C₂×C₄	—	178	1	no	—
399	C₂×C₄	—	178	1	no	—
400	C₂×C₄	—	178	1	no	—
401	C₂×C₄	—	178	4	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
404	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
405	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	356	1	no	—
416	C₈	—	356	2	no	—
417	C₈	—	356	1	no	—
418	C₈	#15668045	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	356	1	no	—
422	C₂²	—	356	1	no	—
423	C₂²	—	356	1	no	—
424	C₂²	#19151716	1	2	yes	—
425	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	356	1	no	—
431	C₄	—	356	2	no	—
432	C₄	—	356	1	no	—
433	C₄	—	356	1	no	—
434	C₄	—	178	4	no	—
435	C₄	#131×D₈₉	1	2	yes	—
436	C₄	C₂×#15668045	1	1	yes	characteristic
437	C₄	#19152398	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	712	1	no	—
440	C₂	#26028948	1	1	yes	characteristic
441	C₂	C₄×#15668045	1	1	yes	characteristic
442	C₂	C₂×#19151716	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17911
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₈×Dic₁₇₈	C₂	semidirect
4. #26019132	C₂	semidirect
5. #26019125	C₂	semidirect
6. C₈×Dic₃₅₆	C₂	semidirect
7. C₈×#13083563	C₂	semidirect
8. #26019037	C₂	semidirect
9. #26018700	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
232. C₈×M₁₆	D₈₉	semidirect
233. C₈₉	#17911	semidirect

Maximal subgroups

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

subgroup	index
#26030334	2
#26029227	2
C₂×C₈×Dic₁₇₈	2
#26019132	2
#26019125	2
C₈×Dic₃₅₆	2
C₈×#13083563	2
#26019037	2
#26018700	2
#26018666	2
C₈×M₁₆×C₈₉	2
#17911	89