Subgroups — #36524451

Order 22784.

624 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	#26030328	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019100	C₂	1	2	yes	maximal, complemented
4	#26019093	C₂	1	2	yes	maximal, complemented
5	#26019069	C₂	1	2	yes	maximal, complemented
6	#26019064	C₂	1	2	yes	maximal, complemented
7	#26019038	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018698	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018665	C₂	1	1	yes	maximal, characteristic
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	#19151926	C₄	1	1	yes	characteristic
14	#19151909	C₄	1	1	yes	characteristic
15	#19151902	C₄	1	2	yes	—
16	#19151817	C₄	1	2	yes	—
17	#19151753	C₄	1	1	yes	characteristic
18	#19151736	C₄	1	1	yes	characteristic
19	C₈×Dic₁₇₈	—	2	1	no	—
20	C₈×Dic₁₇₈	—	2	1	no	—
21	C₈×Dic₁₇₈	C₂²	1	2	yes	—
22	C₈×Dic₁₇₈	C₂²	1	2	yes	—
23	C₄×#13083564	C₂²	1	2	yes	—
24	C₄×#13083562	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	C₂×#15667941	—	2	1	no	—
28	C₄×#13083558	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	—	2	1	no	—
30	#19151350	C₂²	1	2	yes	—
31	#19151348	C₂²	1	2	yes	—
32	Q₈⋊#10623494	C₂²	1	2	yes	—
33	#19151328	C₂²	1	2	yes	—
34	#19151328	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	—
36	#19151320	C₂²	1	2	yes	—
37	#19151319	C₂²	1	2	yes	—
38	#529×C₈₉	C₂²	1	1	yes	characteristic
39	#446×C₈₉	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#436×C₈₉	C₂²	1	1	yes	characteristic
42	#435×C₈₉	—	2	1	no	—
43	C₈×D₄×C₈₉	—	2	1	no	—
44	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	#433×C₈₉	—	2	1	no	—
46	#432×C₈₉	C₂²	1	1	yes	characteristic
47	#405×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083564	C₂×C₄	1	2	yes	—
51	C₂×#13083562	C₂×C₄	1	2	yes	—
52	C₂×#13083558	—	2	1	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₄×Dic₁₇₈	—	2	1	no	—
55	C₄×Dic₁₇₈	—	2	1	no	—
56	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₇₈	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×#13083553	—	2	1	no	—
60	C₂×C₄×Dic₈₉	—	2	1	no	—
61	#15667945	C₂×C₄	1	2	yes	—
62	#15667943	C₂×C₄	1	2	yes	—
63	C₄⋊#10623494	—	2	1	no	—
64	C₄⋊#10623494	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	#15667941	—	2	2	no	—
67	#15667941	—	2	2	no	—
68	#15667936	C₂×C₄	1	2	yes	—
69	#15667935	C₂×C₄	1	2	yes	—
70	#15667935	C₂×C₄	1	2	yes	—
71	#15667933	C₂×C₄	1	2	yes	—
72	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
74	#15667923	—	2	1	no	—
75	C₄×#10623494	C₂³	1	2	yes	—
76	C₄×#10623494	C₂³	1	2	yes	—
77	C₈×Dic₈₉	—	2	2	no	—
78	C₈×Dic₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	—	2	1	no	—
80	C₂²×C₈×C₈₉	—	2	1	no	—
81	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
83	#126×C₈₉	—	2	1	no	—
84	#125×C₈₉	C₂×C₄	1	1	yes	characteristic
85	#124×C₈₉	C₂×C₄	1	1	yes	characteristic
86	#123×C₈₉	—	2	1	no	—
87	C₂²⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	#121×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
92	#117×C₈₉	—	2	1	no	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	—	2	1	no	—
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₈₉	—	2	1	no	—
99	C₂²⋊C₈×C₈₉	—	2	1	no	—
100	C₂²⋊C₈×C₈₉	—	2	1	no	—
101	#97×C₈₉	—	2	1	no	—
102	#97×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	—	2	1	no	—
104	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
105	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
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	2	yes	—
111	C₂²×Dic₈₉	—	2	1	no	—
112	C₂²×Dic₈₉	—	2	1	no	—
113	#13083564	—	2	4	no	—
114	#13083562	—	2	4	no	—
115	#13083558	—	4	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	4	2	no	—
119	C₂×#10623494	C₂²×C₄	1	2	yes	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₄⋊Dic₈₉	—	2	1	no	—
122	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
123	#13083553	—	2	2	no	—
124	#13083553	—	2	2	no	—
125	C₄×Dic₈₉	—	2	2	no	—
126	C₄×Dic₈₉	—	2	2	no	—
127	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₈₉	—	2	1	no	—
129	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	M₁₆×C₈₉	—	4	2	no	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	4	1	no	—
139	C₂×C₈×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂²⋊C₄×C₈₉	—	2	1	no	—
152	C₂²⋊C₄×C₈₉	—	2	1	no	—
153	C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₂²⋊C₄×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	—	2	1	no	—
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	—	2	1	no	—
161	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
162	Q₈×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	2	no	—
164	D₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂×Dic₈₉	—	2	4	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	C₂×Dic₈₉	—	2	2	no	—
183	C₂×Dic₈₉	—	4	2	no	—
184	Dic₁₇₈	—	2	4	no	—
185	Dic₁₇₈	—	2	2	no	—
186	Dic₁₇₈	#131	1	4	yes	—
187	C₈×C₈₉	—	2	1	no	—
188	C₈×C₈₉	—	2	1	no	—
189	C₈×C₈₉	—	2	1	no	—
190	C₈×C₈₉	—	4	1	no	—
191	C₈×C₈₉	—	4	1	no	—
192	C₈×C₈₉	#137	1	2	yes	—
193	#10623494	—	2	2	no	—
194	#10623494	—	2	2	no	—
195	#10623494	—	4	2	no	—
196	#10623494	—	4	2	no	—
197	C₂²×C₈₉	—	2	1	no	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	#444	1	2	yes	—
203	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
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	—	4	1	no	—
209	C₄×C₈₉	—	4	1	no	—
210	C₄×C₈₉	—	4	1	no	—
211	C₄×C₈₉	C₂×#131	1	2	yes	—
212	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
213	C₄×C₈₉	#575	1	1	yes	characteristic
214	Dic₈₉	—	2	4	no	—
215	Dic₈₉	—	4	2	no	—
216	#17915	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	—	8	1	no	—
219	C₂×C₈₉	#2929	1	1	yes	characteristic
220	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
221	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
222	#3108	—	89	1	no	—
223	#2966	D₈₉	1	1	yes	characteristic
224	C₂×C₈×Q₈	—	89	1	no	—
225	#1584	—	89	2	no	—
226	#1583	—	89	2	no	—
227	#1579	—	89	2	no	—
228	SD₁₆⋊C₈	—	89	2	no	—
229	#1573	—	89	1	no	—
230	#1491	—	89	1	no	—
231	#1483	—	89	1	no	—
232	#1451	—	89	1	no	—
233	C₈₉	#17915	1	1	yes	characteristic, complemented, Sylow
234	#529	C₂×D₈₉	1	1	yes	characteristic
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	C₂×D₈₉	1	1	yes	characteristic
243	C₈×Q₈	—	89	2	no	—
244	C₈×Q₈	—	89	2	no	—
245	C₈×Q₈	—	178	1	no	—
246	C₈×Q₈	—	178	1	no	—
247	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
248	C₄×Q₁₆	—	89	2	no	—
249	C₄×SD₁₆	—	89	2	no	—
250	#436	C₂×D₈₉	1	1	yes	characteristic
251	#435	—	2	1	no	—
252	C₈×D₄	—	2	1	no	—
253	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
254	#433	—	2	1	no	—
255	#432	C₂×D₈₉	1	1	yes	characteristic
256	#431	—	89	1	no	—
257	C₂×C₄⋊C₈	—	89	1	no	—
258	C₂×C₄⋊C₈	—	178	1	no	—
259	#405	—	2	1	no	—
260	C₄×M₁₆	—	89	1	no	—
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	—	89	2	no	—
270	#322	—	89	2	no	—
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	—	2	1	no	—
277	C₂²×C₈	—	178	1	no	—
278	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
280	#126	—	2	1	no	—
281	#125	C₄×D₈₉	1	1	yes	characteristic
282	#124	C₄×D₈₉	1	1	yes	characteristic
283	#123	—	2	1	no	—
284	C₂²⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
285	#121	C₄×D₈₉	1	1	yes	characteristic
286	C₄×Q₈	—	89	2	no	—
287	C₄×Q₈	—	89	2	no	—
288	C₄×Q₈	—	178	1	no	—
289	C₄×Q₈	—	178	1	no	—
290	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
293	#117	—	2	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	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	89	2	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	—	178	2	no	—
305	C₄⋊C₈	—	178	2	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#103	—	89	2	no	—
310	#103	—	89	2	no	—
311	#103	—	89	2	no	—
312	#102	—	89	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	89	1	no	—
317	C₂²⋊C₈	—	89	1	no	—
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	#97	—	178	1	no	—
321	C₄×C₈	—	2	1	no	—
322	C₄×C₈	—	89	2	no	—
323	C₄×C₈	—	89	2	no	—
324	C₄×C₈	—	178	2	no	—
325	C₄×C₈	—	178	2	no	—
326	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
327	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
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	—	178	4	no	—
332	C₂×Q₈	—	178	1	no	—
333	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
336	C₂²×C₄	—	2	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×C₂²⋊D₈₉	1	1	yes	characteristic
341	C₂²×C₄	#13083574	1	1	yes	characteristic
342	Q₁₆	—	178	4	no	—
343	SD₁₆	—	178	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	356	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	89	2	no	—
352	C₂×C₈	—	89	2	no	—
353	C₂×C₈	—	356	2	no	—
354	C₂×C₈	—	178	2	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
358	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
359	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	89	2	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₄⋊C₄	—	178	2	no	—
367	C₄⋊C₄	—	178	2	no	—
368	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
369	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	178	2	no	—
377	C₄²	—	178	2	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
380	C₄²	#13083574	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	2	1	no	—
383	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	89	4	no	—
386	Q₈	—	178	4	no	—
387	Q₈	—	178	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	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	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	356	2	no	—
400	C₂×C₄	—	178	2	no	—
401	C₂×C₄	—	178	4	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
404	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
405	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	356	2	no	—
415	C₈	—	356	2	no	—
416	C₈	—	178	2	no	—
417	C₈	—	178	2	no	—
418	C₈	#15668042	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	#19151718	1	2	yes	—
425	C₂²	C₂×C₄×C₂²⋊D₈₉	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	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	356	2	no	—
434	C₄	—	178	4	no	—
435	C₄	#131×D₈₉	1	2	yes	—
436	C₄	C₂×#15668042	1	1	yes	characteristic
437	C₄	#19152396	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	8	1	no	—
440	C₂	#26028944	1	1	yes	characteristic
441	C₂	C₄×#15668042	1	1	yes	characteristic
442	C₂	C₂×#19151718	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2966	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#121×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2966	D₈₉
hypocenter	C₈₉	#17915
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Dic₁₇₈	C₂	semidirect
3. #26019100	C₂	semidirect
4. #26019093	C₂	semidirect
5. #26019069	C₂	semidirect
6. #26019064	C₂	semidirect
7. #26019038	C₂	semidirect
8. #26018698	C₂	semidirect
10. #26018541	C₂	semidirect
233. C₈₉	#17915	semidirect

Maximal subgroups

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

subgroup	index
#26030328	2
C₂×C₈×Dic₁₇₈	2
#26019100	2
#26019093	2
#26019069	2
#26019064	2
#26019038	2
#26018698	2
#26018665	2
#26018541	2
C₈₉×#2966	2
#17915	89