Subgroups — #36574139

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029054	C₂	1	1	yes	maximal, characteristic
2	#26028917	C₂	1	2	yes	maximal, complemented
3	#26021145	C₂	1	1	yes	maximal, characteristic
4	#26021140	C₂	1	1	yes	maximal, characteristic
5	#26020901	C₂	1	2	yes	maximal, complemented
6	#26020901	C₂	1	2	yes	maximal, complemented
7	#26020427	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020273	C₂	1	2	yes	maximal, complemented
9	#26020136	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₄×#13083574	C₂²	1	2	yes	—
14	#19151711	C₄	1	2	yes	complemented
15	#19151706	C₄	1	2	yes	complemented
16	#19151700	C₄	1	2	yes	complemented
17	#19151700	C₄	1	2	yes	complemented
18	#19151658	—	2	2	no	—
19	#19151658	—	2	2	no	—
20	#19151654	—	2	2	no	—
21	#19151650	—	2	2	no	—
22	C₂×#15667948	C₂²	1	1	yes	characteristic
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667948	C₂²	1	2	yes	—
25	#19151636	C₂²	1	1	yes	characteristic
26	#19151622	C₂²	1	2	yes	—
27	C₂×#15667940	C₂²	1	2	yes	—
28	C₂×#15667940	C₂²	1	2	yes	—
29	#19151595	C₂²	1	2	yes	—
30	#19151564	C₂²	1	2	yes	—
31	#19151564	C₂²	1	2	yes	—
32	#19151553	C₂²	1	2	yes	—
33	#19151553	C₂²	1	2	yes	—
34	#19151358	C₂²	1	2	yes	—
35	#19151358	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	#336×C₈₉	C₂²	1	1	yes	characteristic
42	#336×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083574	C₂³	1	2	yes	—
44	#15668034	—	2	2	no	—
45	#15668034	—	2	2	no	—
46	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083563	C₂×C₄	1	2	yes	—
48	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
49	C₂×#13083558	C₂³	1	2	yes	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
52	C₄×Dic₁₇₈	C₂×C₄	1	2	yes	—
53	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
54	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
55	C₄×C₂²⋊D₈₉	—	2	2	no	—
56	C₄×C₂²⋊D₈₉	—	2	2	no	—
57	#15667971	C₂³	1	2	yes	—
58	#15667969	—	2	2	no	—
59	C₄²×D₈₉	—	2	2	no	—
60	#15667948	—	2	2	no	—
61	#15667948	—	2	2	no	—
62	#15667948	—	4	2	no	—
63	#15667946	C₂×C₄	1	1	yes	characteristic
64	#15667946	C₂×C₄	1	1	yes	characteristic
65	#15667944	C₂×C₄	1	2	yes	—
66	C₄⋊#10623494	—	2	2	no	—
67	C₄⋊#10623494	—	2	2	no	—
68	#15667940	—	4	2	no	—
69	#15667940	—	4	2	no	—
70	#15667937	C₂×C₄	1	2	yes	—
71	#15667937	C₂×C₄	1	2	yes	—
72	#15667934	C₂×C₄	1	2	yes	—
73	#15667934	C₂×C₄	1	2	yes	—
74	#15667924	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	#15667922	—	2	2	no	—
79	#15667922	—	2	2	no	—
80	C₈×Dic₈₉	—	2	2	no	—
81	C₈×Dic₈₉	—	2	2	no	—
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
87	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
91	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
92	#97×C₈₉	—	2	2	no	—
93	#97×C₈₉	C₂×C₄	1	2	yes	—
94	#97×C₈₉	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₈₉	—	2	2	no	—
96	#95×C₈₉	—	2	1	no	—
97	#13083574	—	2	2	no	—
98	#13083574	—	2	2	no	—
99	#13083574	—	2	2	no	—
100	#13083574	—	2	2	no	—
101	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
102	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
103	C₂×C₂²⋊D₈₉	—	2	2	no	—
104	C₂×C₄×D₈₉	—	2	2	no	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	2	2	no	—
107	Dic₃₅₆	—	2	2	no	—
108	#13083563	—	2	4	no	—
109	D₇₁₂	—	2	2	no	—
110	#13083558	—	2	2	no	—
111	#13083558	—	2	2	no	—
112	#13083558	—	2	2	no	—
113	#13083558	—	2	2	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
117	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
118	#13083553	—	2	2	no	—
119	#13083553	—	2	2	no	—
120	C₂²⋊Dic₈₉	—	2	2	no	—
121	#13083551	—	2	2	no	—
122	#13083551	—	2	2	no	—
123	C₄×Dic₈₉	—	2	2	no	—
124	C₄×Dic₈₉	—	2	2	no	—
125	C₄×Dic₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	#41	1	2	yes	—
144	C₂×C₈×C₈₉	#41	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	4	2	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₈₉	C₂×D₄	1	2	yes	—
152	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₂²×D₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	1	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂²⋊D₈₉	—	4	2	no	—
171	C₂²⋊D₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	—	2	2	no	—
175	D₃₅₆	—	2	2	no	—
176	D₃₅₆	—	2	2	no	—
177	C₄×D₈₉	—	4	4	no	—
178	C₄×D₈₉	—	4	2	no	—
179	C₄×D₈₉	—	4	2	no	—
180	C₄×D₈₉	—	8	2	no	—
181	Dic₁₇₈	—	2	2	no	—
182	Dic₁₇₈	—	2	2	no	—
183	C₈×C₈₉	—	2	2	no	—
184	C₈×C₈₉	—	2	1	no	—
185	C₈×C₈₉	—	2	1	no	—
186	C₈×C₈₉	—	2	2	no	—
187	C₈×C₈₉	#117	1	2	yes	—
188	C₈×C₈₉	#117	1	2	yes	—
189	#10623494	—	4	2	no	—
190	#10623494	—	4	2	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂²×C₈₉	#555	1	1	yes	characteristic
195	C₂²×C₈₉	#556	1	1	yes	characteristic
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	4	2	no	—
198	C₂×D₈₉	—	4	2	no	—
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	—	8	1	no	—
203	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
204	C₄×C₈₉	#520	1	1	yes	characteristic
205	C₄×C₈₉	#547	1	1	yes	characteristic
206	C₄×C₈₉	#550	1	1	yes	characteristic
207	Dic₈₉	—	4	2	no	—
208	Dic₈₉	—	4	2	no	—
209	Dic₈₉	—	4	2	no	—
210	#22804	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	—	2	1	no	—
212	C₂×C₈₉	—	2	1	no	—
213	C₂×C₈₉	#2354	1	1	yes	characteristic
214	C₂×C₈₉	#2955	1	1	yes	characteristic
215	C₂×C₈₉	#2956	1	1	yes	characteristic
216	D₈₉	—	8	2	no	—
217	#2943	—	89	1	no	—
218	#2925	—	89	2	no	—
219	#1975	—	89	1	no	—
220	#1974	—	89	1	no	—
221	#1929	—	89	2	no	—
222	#1929	—	89	2	no	—
223	#1849	—	89	1	no	—
224	#1806	—	89	2	no	—
225	#1773	—	89	1	no	—
226	#1772	—	89	1	no	—
227	#1771	D₈₉	1	1	yes	characteristic, complemented
228	C₈₉	#22804	1	1	yes	characteristic, complemented, Sylow
229	C₂×#135	—	89	1	no	—
230	C₄×#41	—	89	2	no	—
231	#442	—	89	2	no	—
232	#441	—	89	2	no	—
233	#440	—	89	2	no	—
234	#440	—	89	2	no	—
235	#433	—	178	2	no	—
236	#433	—	178	2	no	—
237	#432	—	178	2	no	—
238	#431	—	178	2	no	—
239	C₂×#108	—	89	2	no	—
240	C₂×#108	—	89	1	no	—
241	C₂×#108	—	89	1	no	—
242	#427	—	89	1	no	—
243	#423	—	89	2	no	—
244	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
245	C₂×#104	—	89	2	no	—
246	C₂×#104	—	89	2	no	—
247	#416	—	89	2	no	—
248	#408	—	89	2	no	—
249	#408	—	89	2	no	—
250	#405	—	89	2	no	—
251	#405	—	89	2	no	—
252	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
253	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
256	#339	—	89	2	no	—
257	#339	—	89	2	no	—
258	#336	C₂×D₈₉	1	1	yes	characteristic
259	#336	C₂×D₈₉	1	1	yes	characteristic
260	C₂×#41	—	89	2	no	—
261	#135	—	178	2	no	—
262	#135	—	178	2	no	—
263	C₂×Q₁₆	—	89	1	no	—
264	C₂×SD₁₆	—	89	2	no	—
265	C₂×D₈	—	89	1	no	—
266	C₂×M₁₆	—	89	2	no	—
267	C₂×M₁₆	—	89	2	no	—
268	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₄×Q₈	—	89	2	no	—
273	C₄×Q₈	—	89	2	no	—
274	C₄×D₄	—	89	2	no	—
275	C₄×D₄	—	89	2	no	—
276	C₄×D₄	—	178	2	no	—
277	C₄×D₄	—	178	2	no	—
278	#117	—	89	2	no	—
279	#117	—	178	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄²	—	178	2	no	—
282	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
283	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
284	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
285	#108	—	356	2	no	—
286	#108	—	178	2	no	—
287	#108	—	178	2	no	—
288	#107	—	89	1	no	—
289	#107	—	89	1	no	—
290	#106	—	89	2	no	—
291	C₄⋊C₈	—	178	2	no	—
292	C₄⋊C₈	—	178	2	no	—
293	C₄⋊C₈	D₃₅₆	1	2	yes	—
294	C₄⋊C₈	D₃₅₆	1	2	yes	—
295	#104	—	356	2	no	—
296	#104	—	356	2	no	—
297	#103	—	89	2	no	—
298	#103	—	89	2	no	—
299	#102	—	89	2	no	—
300	#102	—	89	2	no	—
301	C₂²⋊C₈	—	178	2	no	—
302	C₂²⋊C₈	—	178	2	no	—
303	C₂²⋊C₈	—	178	2	no	—
304	C₂²⋊C₈	—	178	2	no	—
305	#97	—	2	2	no	—
306	#97	—	178	2	no	—
307	#97	—	178	2	no	—
308	#97	C₄×D₈₉	1	2	yes	—
309	#97	C₄×D₈₉	1	2	yes	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	178	2	no	—
312	C₄×C₈	—	178	2	no	—
313	#95	—	2	1	no	—
314	#41	—	178	2	no	—
315	#41	—	178	2	no	—
316	#41	—	178	2	no	—
317	#41	—	178	2	no	—
318	C₂×Q₈	—	89	2	no	—
319	C₂×D₄	—	89	2	no	—
320	C₂×D₄	—	178	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	178	2	no	—
324	C₂²×C₄	—	178	2	no	—
325	C₂²×C₄	—	178	2	no	—
326	C₂²×C₄	#13083574	1	1	yes	characteristic
327	C₂²×C₄	#13083574	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
329	Q₁₆	—	178	2	no	—
330	SD₁₆	—	178	4	no	—
331	D₈	—	178	2	no	—
332	M₁₆	—	178	2	no	—
333	M₁₆	—	178	2	no	—
334	M₁₆	—	178	2	no	—
335	M₁₆	—	178	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	178	2	no	—
343	C₂×C₈	—	178	2	no	—
344	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
345	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
348	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
349	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
350	C₂×C₈	#13083573	1	2	yes	—
351	C₂×C₈	#13083575	1	2	yes	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	89	2	no	—
354	C₄⋊C₄	—	89	2	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	—	178	2	no	—
357	C₂²⋊C₄	—	178	2	no	—
358	C₂²⋊C₄	—	178	2	no	—
359	C₂²⋊C₄	—	178	2	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	178	2	no	—
365	C₄²	—	178	2	no	—
366	C₄²	—	178	2	no	—
367	C₄²	C₂×C₄×D₈₉	1	2	yes	—
368	C₄²	C₂×D₃₅₆	1	2	yes	—
369	C₂³	—	178	2	no	—
370	C₂³	C₂×#13083574	1	1	yes	characteristic
371	Q₈	—	178	2	no	—
372	Q₈	—	178	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	2	no	—
375	D₄	—	178	2	no	—
376	D₄	—	178	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	356	4	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	2	no	—
391	C₂×C₄	—	712	2	no	—
392	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
393	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
394	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
396	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
397	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
398	C₂×C₄	#15668058	1	1	yes	characteristic
399	C₂×C₄	#15668059	1	1	yes	characteristic
400	C₈	—	2	1	no	—
401	C₈	—	2	1	no	—
402	C₈	—	2	2	no	—
403	C₈	—	2	2	no	—
404	C₈	—	356	2	no	—
405	C₈	—	356	2	no	—
406	C₈	#15667970	1	2	yes	—
407	C₈	#15667970	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	356	2	no	—
411	C₂²	—	356	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
414	C₂²	#19152313	1	1	yes	characteristic
415	C₂²	#19152321	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	356	2	no	—
421	C₄	—	356	2	no	—
422	C₄	—	356	2	no	—
423	C₄	C₂×#15667970	1	1	yes	characteristic
424	C₄	#19152078	1	1	yes	characteristic
425	C₄	#19152252	1	1	yes	characteristic
426	C₄	#19152270	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	712	2	no	—
430	C₂	#26023199	1	1	yes	characteristic
431	C₂	#26029156	1	1	yes	characteristic
432	C₂	#26029163	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1771	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1771	D₈₉
hypocenter	C₈₉	#22804
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #1771

Complements

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

N	H ≅ G/N	type
2. #26028917	C₂	semidirect
5. #26020901	C₂	semidirect
6. #26020901	C₂	semidirect
7. #26020427	C₂	semidirect
8. #26020273	C₂	semidirect
9. #26020136	C₂	semidirect
10. #26020131	C₂	semidirect
11. C₈₉×#1771	C₂	semidirect
14. #19151711	C₄	semidirect
15. #19151706	C₄	semidirect
16. #19151700	C₄	semidirect
17. #19151700	C₄	semidirect
227. #1771	D₈₉	semidirect
228. C₈₉	#22804	semidirect

Maximal subgroups

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

subgroup	index
#26029054	2
#26028917	2
#26021145	2
#26021140	2
#26020901	2
#26020427	2
#26020273	2
#26020136	2
#26020131	2
C₈₉×#1771	2
#22804	89