Subgroups — #36573275

Order 22784.

750 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic
2	#26023210	C₂	1	2	yes	maximal
3	#26021020	C₂	1	2	yes	maximal
4	#26021019	C₂	1	2	yes	maximal
5	#26021014	C₂	1	2	yes	maximal
6	#26020416	C₂	1	1	yes	maximal, characteristic
7	#26020415	C₂	1	1	yes	maximal, characteristic
8	#26020410	C₂	1	1	yes	maximal, characteristic
9	#107×Dic₈₉	C₂	1	1	yes	maximal, characteristic
10	#107×Dic₈₉	C₂	1	1	yes	maximal, characteristic
11	C₄×#107×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₇₈	C₄	1	8	yes	complemented
14	C₂×#15667946	C₂²	1	1	yes	characteristic
15	C₂×#15667946	C₂²	1	1	yes	characteristic
16	C₂×#15667945	C₂²	1	2	yes	—
17	C₂×#15667944	C₂²	1	2	yes	—
18	C₂×#15667943	C₂²	1	2	yes	—
19	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
20	C₂×#15667941	C₂²	1	1	yes	characteristic
21	C₂×#15667941	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
24	#19151502	—	2	2	no	—
25	#19151482	—	2	2	no	—
26	#19151481	—	2	2	no	—
27	#19151467	C₂²	1	2	yes	—
28	#19151464	C₂²	1	2	yes	—
29	#19151463	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
32	C₄×#13083553	—	2	2	no	—
33	#19151360	C₂²	1	2	yes	—
34	#19151360	C₂²	1	2	yes	—
35	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	2	yes	—
40	C₂²×Dic₁₇₈	D₄	1	1	yes	characteristic
41	C₂²×#10623494	C₂³	1	1	yes	characteristic
42	C₂²×#10623494	C₂³	1	1	yes	characteristic
43	C₄×Dic₁₇₈	C₂×C₄	1	4	yes	—
44	C₄×Dic₁₇₈	Q₈	1	4	yes	—
45	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
47	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
48	C₂×#13083553	—	2	2	no	—
49	C₂×#13083553	—	2	2	no	—
50	C₂×#13083553	D₄	1	1	yes	characteristic
51	C₂×#13083553	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₈₉	—	2	2	no	—
53	C₂×C₄×Dic₈₉	—	2	2	no	—
54	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
56	#15667946	—	2	2	no	—
57	#15667946	—	2	2	no	—
58	#15667945	—	4	2	no	—
59	#15667944	—	4	2	no	—
60	#15667943	—	4	2	no	—
61	C₄⋊#10623494	C₂×C₄	1	4	yes	—
62	#15667941	C₂×C₄	1	4	yes	—
63	#15667941	C₂×C₄	1	4	yes	—
64	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
65	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
66	#15667919	—	2	2	no	—
67	#15667919	—	2	2	no	—
68	#15667919	—	2	2	no	—
69	#15667919	—	2	2	no	—
70	#15667919	—	2	2	no	—
71	#15667919	—	2	2	no	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₈₉	—	2	2	no	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#107×C₈₉	—	2	2	no	—
79	#107×C₈₉	Q₈	1	4	yes	complemented
80	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
81	#95×C₈₉	—	2	2	no	—
82	C₂×Dic₁₇₈	—	2	2	no	—
83	C₂×Dic₁₇₈	—	2	2	no	—
84	C₂×Dic₁₇₈	C₄⋊C₄	1	4	yes	—
85	C₂²×Dic₈₉	—	2	2	no	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
91	C₂×#10623494	—	2	1	no	—
92	C₂×#10623494	—	2	1	no	—
93	C₂×#10623494	—	2	1	no	—
94	C₂×#10623494	—	2	1	no	—
95	C₂×#10623494	C₂²×C₄	1	2	yes	—
96	C₂×#10623494	C₂²×C₄	1	2	yes	—
97	C₄⋊Dic₈₉	—	2	2	no	—
98	C₄⋊Dic₈₉	—	2	2	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	C₄⋊C₄	1	4	yes	—
102	#13083553	—	4	4	no	—
103	#13083553	—	8	2	no	—
104	#13083553	C₄⋊C₄	1	4	yes	—
105	#13083553	C₄⋊C₄	1	4	yes	—
106	C₄×Dic₈₉	—	4	4	no	—
107	C₄×Dic₈₉	—	8	2	no	—
108	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
109	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
110	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
111	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
122	C₂×C₈×C₈₉	#41	1	2	yes	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
127	C₄²×C₈₉	—	8	2	no	—
128	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
129	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
130	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	—	2	1	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	—	4	2	no	—
160	C₂×Dic₈₉	—	4	2	no	—
161	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×Dic₈₉	#135	1	2	yes	—
166	C₂×Dic₈₉	#135	1	2	yes	—
167	Dic₁₇₈	—	2	8	no	—
168	C₈×C₈₉	—	2	2	no	—
169	C₈×C₈₉	C₄×Q₈	1	4	yes	—
170	#10623494	—	2	2	no	—
171	#10623494	—	2	2	no	—
172	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
174	C₂²×C₈₉	#550	1	1	yes	characteristic
175	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
176	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
177	C₂²×C₈₉	#576	1	1	yes	characteristic
178	C₂²×C₈₉	#578	1	1	yes	characteristic
179	C₄×C₈₉	—	2	2	no	—
180	C₄×C₈₉	—	2	2	no	—
181	C₄×C₈₉	—	4	4	no	—
182	C₄×C₈₉	—	8	2	no	—
183	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
184	C₄×C₈₉	#520	1	1	yes	characteristic
185	C₄×C₈₉	#557	1	1	yes	characteristic
186	C₄×C₈₉	Q₈²	1	1	yes	characteristic
187	Dic₈₉	—	2	2	no	—
188	Dic₈₉	—	2	2	no	—
189	Dic₈₉	—	2	2	no	—
190	Dic₈₉	—	8	2	no	—
191	Dic₈₉	—	8	2	no	—
192	Dic₈₉	#427	1	4	yes	—
193	#22727	—	89	1	no	maximal, Sylow
194	C₂×C₈₉	Q₈×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
196	C₂×C₈₉	#2913	1	1	yes	characteristic
197	C₂×C₈₉	#3380	1	1	yes	characteristic
198	C₂×C₈₉	#3383	1	1	yes	characteristic
199	C₂×C₈₉	#3393	1	1	yes	characteristic
200	C₂×C₈₉	#3396	1	1	yes	characteristic
201	C₂×C₈×Q₈	—	89	1	no	—
202	#2355	—	89	2	no	—
203	#1949	—	89	2	no	—
204	#1949	—	89	2	no	—
205	#1948	—	89	2	no	—
206	#1846	—	89	1	no	—
207	#1846	—	89	1	no	—
208	#1845	—	89	1	no	—
209	C₄×#107	—	89	1	no	—
210	C₄×#107	—	89	1	no	—
211	C₄×#107	D₈₉	1	1	yes	characteristic
212	C₈₉	#22727	1	1	yes	characteristic, complemented, Sylow
213	C₂×C₄×Q₈	—	89	1	no	—
214	C₈×Q₈	—	89	8	no	—
215	C₂×#107	—	89	2	no	—
216	C₂×#107	—	89	1	no	—
217	C₂×#107	—	89	1	no	—
218	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
219	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
220	C₂×#106	—	89	2	no	—
221	C₂×#106	—	89	2	no	—
222	C₂×C₄⋊C₈	—	89	1	no	—
223	C₂×C₄⋊C₈	—	89	1	no	—
224	C₂×C₄⋊C₈	—	89	1	no	—
225	C₂×C₄×C₈	—	89	1	no	—
226	C₂×C₄×C₈	—	89	1	no	—
227	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
228	#391	—	178	2	no	—
229	#387	—	178	2	no	—
230	#387	—	178	2	no	—
231	#384	—	89	2	no	—
232	#382	—	89	2	no	—
233	#382	—	89	2	no	—
234	C₄×C₄⋊C₄	—	89	2	no	—
235	C₄×C₄⋊C₄	—	89	2	no	—
236	C₄×C₄⋊C₄	—	178	2	no	—
237	C₄×C₄⋊C₄	C₂×D₈₉	1	2	yes	—
238	#340	—	89	2	no	—
239	#340	—	89	2	no	—
240	#340	C₂×D₈₉	1	2	yes	—
241	C₂²×Q₈	—	89	1	no	—
242	C₂²×C₈	—	89	1	no	—
243	C₂²×C₈	—	89	1	no	—
244	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
245	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
246	C₄×Q₈	—	89	4	no	—
247	C₄×Q₈	—	89	4	no	—
248	C₂×C₄⋊C₄	—	89	1	no	—
249	C₂×C₄⋊C₄	—	89	1	no	—
250	C₂×C₄⋊C₄	—	89	1	no	—
251	C₂×C₄⋊C₄	—	89	2	no	—
252	C₂×C₄⋊C₄	—	89	2	no	—
253	C₂×C₄⋊C₄	—	178	2	no	—
254	C₂×C₄⋊C₄	—	178	2	no	—
255	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
256	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	89	1	no	—
259	C₂×C₄²	—	89	1	no	—
260	C₂×C₄²	—	178	2	no	—
261	C₂×C₄²	—	178	2	no	—
262	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
263	#107	—	2	2	no	—
264	#107	—	356	2	no	—
265	#107	—	178	2	no	—
266	#107	—	178	2	no	—
267	#107	Dic₁₇₈	1	4	yes	complemented
268	#106	—	356	2	no	—
269	#106	—	356	2	no	—
270	C₄⋊C₈	—	89	4	no	—
271	C₄⋊C₈	—	89	4	no	—
272	C₄⋊C₈	—	89	4	no	—
273	C₄×C₈	—	89	4	no	—
274	C₄×C₈	—	89	4	no	—
275	C₄×C₈	C₄×D₈₉	1	4	yes	—
276	#95	—	2	2	no	—
277	#95	—	178	2	no	—
278	#95	—	178	2	no	—
279	#95	—	178	2	no	—
280	#95	—	178	2	no	—
281	#95	—	178	2	no	—
282	#95	—	178	2	no	—
283	C₂×Q₈	—	89	4	no	—
284	C₂×Q₈	—	178	2	no	—
285	C₂×Q₈	—	178	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	89	1	no	—
289	C₂²×C₄	—	89	1	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	89	1	no	—
292	C₂²×C₄	—	178	2	no	—
293	C₂²×C₄	—	178	2	no	—
294	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	89	2	no	—
300	C₂×C₈	—	89	2	no	—
301	C₂×C₈	—	178	1	no	—
302	C₂×C₈	—	178	1	no	—
303	C₂×C₈	—	178	1	no	—
304	C₂×C₈	—	178	1	no	—
305	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
306	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
307	C₂×C₈	C₂×Dic₁₇₈	1	2	yes	—
308	C₂×C₈	#13083574	1	2	yes	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	89	4	no	—
313	C₄⋊C₄	—	89	4	no	—
314	C₄⋊C₄	—	89	4	no	—
315	C₄⋊C₄	—	356	4	no	—
316	C₄⋊C₄	—	178	2	no	—
317	C₄⋊C₄	—	178	2	no	—
318	C₄⋊C₄	—	178	2	no	—
319	C₄⋊C₄	—	178	2	no	—
320	C₄⋊C₄	—	712	2	no	—
321	C₄⋊C₄	C₂×Dic₁₇₈	1	4	yes	—
322	C₄²	—	8	2	no	—
323	C₄²	—	89	2	no	—
324	C₄²	—	89	2	no	—
325	C₄²	—	89	2	no	—
326	C₄²	—	89	2	no	—
327	C₄²	—	356	4	no	—
328	C₄²	—	712	2	no	—
329	C₄²	C₂×C₄×D₈₉	1	2	yes	—
330	C₄²	Q₈×D₈₉	1	2	yes	—
331	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
332	Q₈	—	178	8	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	89	2	no	—
344	C₂×C₄	—	89	2	no	—
345	C₂×C₄	—	89	2	no	—
346	C₂×C₄	—	89	2	no	—
347	C₂×C₄	—	89	2	no	—
348	C₂×C₄	—	89	2	no	—
349	C₂×C₄	—	356	2	no	—
350	C₂×C₄	—	356	2	no	—
351	C₂×C₄	—	356	2	no	—
352	C₂×C₄	—	356	2	no	—
353	C₂×C₄	—	356	2	no	—
354	C₂×C₄	—	356	2	no	—
355	C₂×C₄	—	178	1	no	—
356	C₂×C₄	—	178	1	no	—
357	C₂×C₄	—	178	1	no	—
358	C₂×C₄	—	178	1	no	—
359	C₂×C₄	—	178	1	no	—
360	C₂×C₄	—	178	1	no	—
361	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
362	C₂×C₄	C₄⋊C₄×D₈₉	1	2	yes	—
363	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
364	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
365	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
366	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
367	C₂×C₄	#15668058	1	1	yes	characteristic
368	C₂×C₄	#15668059	1	1	yes	characteristic
369	C₈	—	2	2	no	—
370	C₈	—	178	2	no	—
371	C₈	—	178	2	no	—
372	C₈	C₄×Dic₁₇₈	1	4	yes	—
373	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
374	C₂²	D₄×Dic₁₇₈	1	1	yes	characteristic
375	C₂²	#19152269	1	1	yes	characteristic
376	C₂²	#135×D₈₉	1	1	yes	characteristic
377	C₂²	#135×D₈₉	1	1	yes	characteristic
378	C₂²	#19152399	1	1	yes	characteristic
379	C₂²	#19152411	1	1	yes	characteristic
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	4	no	—
383	C₄	—	8	2	no	—
384	C₄	—	89	4	no	—
385	C₄	—	178	2	no	—
386	C₄	—	178	2	no	—
387	C₄	—	178	2	no	—
388	C₄	—	712	2	no	—
389	C₄	—	712	2	no	—
390	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
391	C₄	#19152078	1	1	yes	characteristic
392	C₄	#19152326	1	1	yes	characteristic
393	C₄	Q₈×Dic₁₇₈	1	1	yes	characteristic
394	C₂	C₄⋊C₄×Dic₁₇₈	1	1	yes	characteristic
395	C₂	#427×D₈₉	1	1	yes	characteristic
396	C₂	#26028848	1	1	yes	characteristic
397	C₂	#26033119	1	1	yes	characteristic
398	C₂	#26033143	1	1	yes	characteristic
399	C₂	#26033240	1	1	yes	characteristic
400	C₂	#26033264	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#107×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#107	D₈₉
hypocenter	C₈₉	#22727
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#107

Complements

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

N	H ≅ G/N	type
13. C₈×Dic₁₇₈	C₄	semidirect
79. #107×C₈₉	Q₈	semidirect
212. C₈₉	#22727	semidirect
267. #107	Dic₁₇₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₁₇₈	2
#26023210	2
#26021020	2
#26021019	2
#26021014	2
#26020416	2
#26020415	2
#26020410	2
#107×Dic₈₉	2
C₄×#107×C₈₉	2
#22727	89