Subgroups — #36447214

Order 22784.

684 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15668009	C₂	1	1	yes	maximal, characteristic
2	#26020404	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151341	C₂	1	2	yes	maximal
4	#26018136	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1842	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15668009	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₃₅₆	—	2	1	no	—
8	C₂×C₄×D₃₅₆	—	2	1	no	—
9	C₂×C₄×D₃₅₆	C₄	1	2	yes	—
10	C₂×C₄⋊#10623494	—	2	1	no	—
11	C₂×C₄⋊#10623494	—	2	1	no	—
12	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
13	#19151500	—	2	1	no	—
14	#19151500	—	2	1	no	—
15	#19151500	C₄	1	2	yes	—
16	#19151468	C₂²	1	1	yes	characteristic
17	#19151341	—	2	4	no	—
18	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
19	C₂×C₄⋊C₈×C₈₉	—	2	1	no	—
20	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
21	C₄³×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×D₃₅₆	—	2	1	no	—
23	C₂²×D₃₅₆	—	2	1	no	—
24	C₂²×D₃₅₆	C₂×C₄	1	2	yes	—
25	C₂²×C₄×D₈₉	—	2	2	no	—
26	C₂²×#10623494	—	2	2	no	—
27	#15668009	—	2	1	no	—
28	#15668009	—	2	1	no	—
29	#15668009	D₄	1	2	yes	—
30	#15668009	Q₈	1	2	yes	—
31	C₄×D₃₅₆	—	4	4	no	—
32	C₄×D₃₅₆	—	4	2	no	—
33	C₄×D₃₅₆	—	4	2	no	—
34	C₄×D₃₅₆	—	4	2	no	—
35	C₄×D₃₅₆	—	4	2	no	—
36	C₂×C₄⋊Dic₈₉	—	2	1	no	—
37	C₂×C₄⋊Dic₈₉	—	2	1	no	—
38	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
39	C₂×#13083551	—	2	2	no	—
40	C₂×#13083551	—	2	2	no	—
41	C₂×#13083551	—	2	2	no	—
42	C₄⋊#10623494	—	2	2	no	—
43	C₄⋊#10623494	—	2	2	no	—
44	C₄⋊#10623494	—	4	2	no	—
45	C₄⋊#10623494	—	4	2	no	—
46	C₂²×C₈×C₈₉	—	2	2	no	—
47	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₈₉	—	2	2	no	—
55	C₄⋊C₈×C₈₉	—	2	2	no	—
56	C₄⋊C₈×C₈₉	—	4	2	no	—
57	C₄⋊C₈×C₈₉	—	4	2	no	—
58	C₂³×D₈₉	—	2	2	no	—
59	C₂×D₃₅₆	—	2	2	no	—
60	C₂×D₃₅₆	—	2	2	no	—
61	C₂×D₃₅₆	—	2	2	no	—
62	C₂×D₃₅₆	—	2	2	no	—
63	C₂×D₃₅₆	—	2	2	no	—
64	C₂×D₃₅₆	—	4	2	no	—
65	C₂×D₃₅₆	—	4	2	no	—
66	C₂×D₃₅₆	—	4	1	no	—
67	C₂×D₃₅₆	—	4	1	no	—
68	C₂×D₃₅₆	—	4	1	no	—
69	C₂×D₃₅₆	—	4	1	no	—
70	C₂×D₃₅₆	—	4	1	no	—
71	C₂×D₃₅₆	—	4	1	no	—
72	C₂×D₃₅₆	—	4	1	no	—
73	C₂×D₃₅₆	—	4	1	no	—
74	C₂×D₃₅₆	C₄⋊C₄	1	4	yes	—
75	C₂²×Dic₈₉	—	2	2	no	—
76	C₂×C₄×D₈₉	—	4	4	no	—
77	C₂×C₄×D₈₉	—	4	4	no	—
78	C₂×C₄×D₈₉	—	4	4	no	—
79	C₂×#10623494	—	4	2	no	—
80	C₂×#10623494	—	4	2	no	—
81	C₂×#10623494	—	4	2	no	—
82	C₄⋊Dic₈₉	—	4	1	no	—
83	C₄⋊Dic₈₉	—	4	1	no	—
84	C₄⋊Dic₈₉	—	4	1	no	—
85	C₄⋊Dic₈₉	—	4	1	no	—
86	C₄⋊Dic₈₉	—	4	2	no	—
87	#13083551	—	4	4	no	—
88	#13083551	—	4	4	no	—
89	#13083551	—	4	4	no	—
90	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₈₉	—	4	2	no	—
98	C₂×C₈×C₈₉	—	4	2	no	—
99	C₂×C₈×C₈₉	—	4	2	no	—
100	C₄²×C₈₉	—	2	2	no	—
101	C₄²×C₈₉	—	2	1	no	—
102	C₄²×C₈₉	—	2	1	no	—
103	C₄²×C₈₉	—	2	1	no	—
104	C₄²×C₈₉	—	2	1	no	—
105	C₄²×C₈₉	—	4	1	no	—
106	C₄²×C₈₉	D₈	1	2	yes	—
107	C₄²×C₈₉	D₈	1	2	yes	—
108	C₄²×C₈₉	SD₁₆	1	2	yes	—
109	C₄²×C₈₉	SD₁₆	1	2	yes	—
110	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
112	C₄²×C₈₉	#41	1	1	yes	characteristic
113	C₄²×C₈₉	#41	1	1	yes	characteristic
114	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂²×D₈₉	—	2	4	no	—
116	C₂²×D₈₉	—	4	2	no	—
117	C₂²×D₈₉	—	4	2	no	—
118	C₂²×D₈₉	—	4	2	no	—
119	C₂²×D₈₉	—	4	2	no	—
120	C₂²×D₈₉	—	4	2	no	—
121	C₂²×D₈₉	—	4	2	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	1	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	#100	1	2	yes	—
132	C₂×C₄×C₈₉	#102	1	2	yes	—
133	C₂×C₄×C₈₉	#102	1	2	yes	—
134	C₂×C₄×C₈₉	#102	1	2	yes	—
135	C₂×C₄×C₈₉	#102	1	2	yes	—
136	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
138	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
139	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
149	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
150	C₂×Dic₈₉	—	4	2	no	—
151	C₂×Dic₈₉	—	4	2	no	—
152	C₂×Dic₈₉	—	4	2	no	—
153	D₃₅₆	—	4	4	no	—
154	D₃₅₆	—	4	4	no	—
155	D₃₅₆	—	4	2	no	—
156	D₃₅₆	—	4	2	no	—
157	D₃₅₆	—	4	2	no	—
158	D₃₅₆	—	4	2	no	—
159	D₃₅₆	—	4	2	no	—
160	D₃₅₆	—	4	2	no	—
161	D₃₅₆	—	4	2	no	—
162	D₃₅₆	—	4	2	no	—
163	C₄×D₈₉	—	8	8	no	—
164	C₈×C₈₉	—	8	2	no	—
165	#10623494	—	8	2	no	—
166	C₂²×C₈₉	#380	1	1	yes	characteristic
167	C₂²×C₈₉	C₂×#100	1	1	yes	characteristic
168	C₂²×C₈₉	#413	1	1	yes	characteristic
169	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
170	C₂²×C₈₉	C₂×#102	1	1	yes	characteristic
171	C₂²×C₈₉	#417	1	1	yes	characteristic
172	C₂²×C₈₉	#417	1	1	yes	characteristic
173	C₂×D₈₉	—	4	4	no	—
174	C₂×D₈₉	—	4	4	no	—
175	C₂×D₈₉	—	4	4	no	—
176	C₂×D₈₉	—	8	2	no	—
177	C₂×D₈₉	—	8	2	no	—
178	C₂×D₈₉	—	8	2	no	—
179	C₂×D₈₉	—	8	2	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	2	1	no	—
182	C₄×C₈₉	—	2	2	no	—
183	C₄×C₈₉	—	2	2	no	—
184	C₄×C₈₉	—	4	1	no	—
185	C₄×C₈₉	#331	1	4	yes	complemented
186	C₄×C₈₉	#459	1	1	yes	characteristic
187	C₄×C₈₉	#459	1	1	yes	characteristic
188	C₄×C₈₉	#461	1	1	yes	characteristic
189	C₄×C₈₉	#461	1	1	yes	characteristic
190	C₄×C₈₉	#474	1	1	yes	characteristic
191	C₄×C₈₉	#474	1	1	yes	characteristic
192	C₄×C₈₉	#476	1	1	yes	characteristic
193	C₄×C₈₉	#476	1	1	yes	characteristic
194	Dic₈₉	—	8	2	no	—
195	#8585	—	89	1	no	maximal, Sylow
196	C₂×C₈₉	C₂×#331	1	1	yes	characteristic
197	C₂×C₈₉	#1547	1	1	yes	characteristic
198	C₂×C₈₉	#1547	1	1	yes	characteristic
199	C₂×C₈₉	#1560	1	1	yes	characteristic
200	C₂×C₈₉	#1800	1	1	yes	characteristic
201	C₂×C₈₉	#1802	1	1	yes	characteristic
202	C₂×C₈₉	#1802	1	1	yes	characteristic
203	D₈₉	—	8	4	no	—
204	C₄×#127	—	89	1	no	—
205	#1842	—	89	1	no	—
206	#1842	D₈₉	1	1	yes	characteristic, complemented
207	C₂×#331	—	89	2	no	—
208	#1296	—	89	2	no	—
209	C₈₉	#8585	1	1	yes	characteristic, complemented, Sylow
210	C₂×#127	—	89	1	no	—
211	C₂×C₄×D₄	—	89	2	no	—
212	C₂×C₄×D₄	—	178	1	no	—
213	C₂×C₄×D₄	—	178	1	no	—
214	C₂×C₄⋊C₈	—	2	1	no	—
215	C₂×C₄⋊C₈	—	2	1	no	—
216	C₂×C₄⋊C₈	—	89	2	no	—
217	C₂×C₄⋊C₈	—	178	1	no	—
218	C₂×C₄⋊C₈	—	178	1	no	—
219	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
220	#390	—	89	2	no	—
221	#390	—	178	1	no	—
222	#390	—	178	1	no	—
223	#384	—	89	1	no	—
224	C₄³	C₂×D₈₉	1	1	yes	characteristic
225	#331	—	178	4	no	—
226	C₂²×D₄	—	89	2	no	—
227	C₂²×D₄	—	178	1	no	—
228	C₂²×D₄	—	178	1	no	—
229	C₂³×C₄	—	178	2	no	—
230	C₂²×C₈	—	2	2	no	—
231	C₂²×C₈	—	178	2	no	—
232	#127	—	89	2	no	—
233	#127	—	89	2	no	—
234	#127	—	178	1	no	—
235	#127	—	178	1	no	—
236	C₄×D₄	—	356	4	no	—
237	C₄×D₄	—	356	2	no	—
238	C₄×D₄	—	356	2	no	—
239	C₄×D₄	—	356	2	no	—
240	C₄×D₄	—	356	2	no	—
241	C₂×C₄⋊C₄	—	89	2	no	—
242	C₂×C₄⋊C₄	—	178	1	no	—
243	C₂×C₄⋊C₄	—	178	1	no	—
244	C₂×C₂²⋊C₄	—	178	2	no	—
245	C₂×C₂²⋊C₄	—	178	2	no	—
246	C₂×C₂²⋊C₄	—	178	2	no	—
247	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
249	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
250	C₂×C₄²	D₃₅₆	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
253	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
254	C₄⋊C₈	—	2	2	no	—
255	C₄⋊C₈	—	2	2	no	—
256	C₄⋊C₈	—	4	2	no	—
257	C₄⋊C₈	—	4	2	no	—
258	C₄⋊C₈	—	356	2	no	—
259	C₄⋊C₈	—	356	2	no	—
260	C₄⋊C₈	—	178	2	no	—
261	C₄⋊C₈	—	178	2	no	—
262	C₂⁴	—	178	2	no	—
263	C₂×D₄	—	89	4	no	—
264	C₂×D₄	—	356	2	no	—
265	C₂×D₄	—	356	2	no	—
266	C₂×D₄	—	356	1	no	—
267	C₂×D₄	—	356	1	no	—
268	C₂×D₄	—	356	1	no	—
269	C₂×D₄	—	356	1	no	—
270	C₂×D₄	—	356	1	no	—
271	C₂×D₄	—	356	1	no	—
272	C₂×D₄	—	356	1	no	—
273	C₂×D₄	—	356	1	no	—
274	C₂×D₄	—	178	2	no	—
275	C₂×D₄	—	178	2	no	—
276	C₂×D₄	—	178	2	no	—
277	C₂×D₄	—	178	2	no	—
278	C₂×D₄	—	178	2	no	—
279	C₂²×C₄	—	356	4	no	—
280	C₂²×C₄	—	356	4	no	—
281	C₂²×C₄	—	356	4	no	—
282	C₂²×C₄	—	178	2	no	—
283	C₂²×C₄	#13083551	1	1	yes	characteristic
284	C₂²×C₄	#13083551	1	1	yes	characteristic
285	C₂²×C₄	#13083551	1	1	yes	characteristic
286	C₂²×C₄	#13083551	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	4	2	no	—
293	C₂×C₈	—	356	2	no	—
294	C₂×C₈	—	356	2	no	—
295	C₂×C₈	—	356	2	no	—
296	C₄⋊C₄	—	356	2	no	—
297	C₄⋊C₄	—	356	1	no	—
298	C₄⋊C₄	—	356	1	no	—
299	C₄⋊C₄	—	356	1	no	—
300	C₄⋊C₄	—	356	1	no	—
301	C₂²⋊C₄	—	356	4	no	—
302	C₂²⋊C₄	—	356	4	no	—
303	C₂²⋊C₄	—	356	4	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	1	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	4	1	no	—
310	C₄²	#13083559	1	2	yes	—
311	C₄²	D₇₁₂	1	2	yes	—
312	C₄²	#13083561	1	2	yes	—
313	C₄²	#13083563	1	2	yes	—
314	C₄²	D₄×D₈₉	1	1	yes	characteristic
315	C₄²	Q₈×D₈₉	1	1	yes	characteristic
316	C₄²	#13083573	1	1	yes	characteristic
317	C₄²	#13083575	1	1	yes	characteristic
318	C₂³	—	356	2	no	—
319	C₂³	—	356	2	no	—
320	C₂³	—	356	2	no	—
321	C₂³	—	356	2	no	—
322	C₂³	—	356	2	no	—
323	C₂³	—	356	2	no	—
324	C₂³	—	178	4	no	—
325	C₂³	C₂×#13083551	1	1	yes	characteristic
326	D₄	—	356	4	no	—
327	D₄	—	356	4	no	—
328	D₄	—	356	2	no	—
329	D₄	—	356	2	no	—
330	D₄	—	356	2	no	—
331	D₄	—	356	2	no	—
332	D₄	—	356	2	no	—
333	D₄	—	356	2	no	—
334	D₄	—	356	2	no	—
335	D₄	—	356	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	356	2	no	—
346	C₂×C₄	—	356	2	no	—
347	C₂×C₄	—	356	2	no	—
348	C₂×C₄	—	712	8	no	—
349	C₂×C₄	#15667928	1	2	yes	—
350	C₂×C₄	#15667932	1	2	yes	—
351	C₂×C₄	#15667932	1	2	yes	—
352	C₂×C₄	#15667934	1	2	yes	—
353	C₂×C₄	#15667934	1	2	yes	—
354	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
355	C₂×C₄	#15667970	1	1	yes	characteristic
356	C₂×C₄	#15667983	1	1	yes	characteristic
357	C₂×C₄	#15667987	1	1	yes	characteristic
358	C₂×C₄	#15667988	1	1	yes	characteristic
359	C₂×C₄	#15667992	1	1	yes	characteristic
360	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
361	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
362	C₂×C₄	C₂×#13083561	1	1	yes	characteristic
363	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
364	C₂×C₄	#15668038	1	1	yes	characteristic
365	C₂×C₄	#15668040	1	1	yes	characteristic
366	C₂×C₄	#15668043	1	1	yes	characteristic
367	C₂×C₄	#15668045	1	1	yes	characteristic
368	C₈	—	8	2	no	—
369	C₈	—	712	2	no	—
370	C₂²	—	356	4	no	—
371	C₂²	—	356	4	no	—
372	C₂²	—	356	4	no	—
373	C₂²	—	712	2	no	—
374	C₂²	—	712	2	no	—
375	C₂²	—	712	2	no	—
376	C₂²	—	712	2	no	—
377	C₂²	#19151455	1	1	yes	characteristic
378	C₂²	C₂×#15667928	1	1	yes	characteristic
379	C₂²	#19151580	1	1	yes	characteristic
380	C₂²	C₂×#15667932	1	1	yes	characteristic
381	C₂²	C₂×#15667934	1	1	yes	characteristic
382	C₂²	#19151597	1	1	yes	characteristic
383	C₂²	#19151600	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	712	2	no	—
390	C₄	#19151341	1	4	yes	complemented
391	C₄	#19151790	1	1	yes	characteristic
392	C₄	#19151794	1	1	yes	characteristic
393	C₄	#19151800	1	1	yes	characteristic
394	C₄	#19151804	1	1	yes	characteristic
395	C₄	#19151875	1	1	yes	characteristic
396	C₄	#19151879	1	1	yes	characteristic
397	C₄	#19151885	1	1	yes	characteristic
398	C₄	#19151889	1	1	yes	characteristic
399	C₂	—	712	4	no	—
400	C₂	C₂×#19151341	1	1	yes	characteristic
401	C₂	#26018927	1	1	yes	characteristic
402	C₂	#26018930	1	1	yes	characteristic
403	C₂	#26018985	1	1	yes	characteristic
404	C₂	#26020241	1	1	yes	characteristic
405	C₂	#26020249	1	1	yes	characteristic
406	C₂	#26020253	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#13083551
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1842	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂×#15668009	C₂²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1842	D₈₉
hypocenter	C₈₉	#8585
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
2. #26020404	C₂	semidirect
4. #26018136	C₂	semidirect
5. C₈₉×#1842	C₂	semidirect
185. C₄×C₈₉	#331	semidirect
206. #1842	D₈₉	semidirect
209. C₈₉	#8585	semidirect
390. C₄	#19151341	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668009	2
#26020404	2
C₂×#19151341	2
#26018136	2
C₈₉×#1842	2
#8585	89