Subgroups — #36552993

Order 22784.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151720	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151715	C₂	1	1	yes	maximal, characteristic
3	C₄×#15668019	C₂	1	2	yes	maximal, complemented
4	#26020158	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020099	C₂	1	2	yes	maximal, complemented
8	#26020092	C₂	1	2	yes	maximal, complemented
9	#26020062	C₂	1	2	yes	maximal, complemented
10	#26019940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668019	C₂²	1	2	yes	—
13	C₂×#15668019	C₂²	1	2	yes	—
14	#19151720	C₄	1	8	yes	complemented
15	#19151715	C₄	1	8	yes	complemented
16	C₂×#15667948	C₂²	1	1	yes	characteristic
17	C₂×#15667948	C₂²	1	1	yes	characteristic
18	C₂×#15667939	C₂²	1	2	yes	—
19	C₂×#15667939	C₂²	1	2	yes	—
20	#19151554	—	2	2	no	—
21	#19151554	—	2	2	no	—
22	#19151554	C₂²	1	2	yes	—
23	#19151554	C₂²	1	2	yes	—
24	C₄×#13083558	—	2	2	no	—
25	C₄×#13083558	C₂²	1	2	yes	—
26	C₂×#15667922	C₂²	1	1	yes	characteristic
27	C₂×#15667922	C₂²	1	1	yes	characteristic
28	C₂×C₄×#10623494	—	2	2	no	—
29	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
32	#19151444	C₂²	1	1	yes	characteristic
33	#19151363	C₂²	1	2	yes	—
34	#19151357	C₂²	1	2	yes	—
35	#19151357	C₂²	1	2	yes	—
36	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
37	C₄×#41×C₈₉	C₂²	1	2	yes	—
38	#442×C₈₉	C₄	1	2	yes	complemented
39	#441×C₈₉	C₄	1	2	yes	complemented
40	#440×C₈₉	C₄	1	4	yes	complemented
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#416×C₈₉	C₂²	1	2	yes	—
43	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
44	#15668019	—	2	4	no	—
45	#15668019	—	2	4	no	—
46	#15668019	C₂×C₄	1	8	yes	complemented
47	#15668019	C₂×C₄	1	8	yes	complemented
48	C₂×#13083558	—	2	2	no	—
49	C₂×#13083558	—	2	2	no	—
50	C₂×#13083558	C₂³	1	2	yes	—
51	C₂×#13083558	C₂³	1	2	yes	—
52	C₂²×#10623494	—	2	2	no	—
53	C₂²×#10623494	—	2	2	no	—
54	C₂²×#10623494	C₂³	1	1	yes	characteristic
55	C₂²×#10623494	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
58	#15667948	C₂×C₄	1	4	yes	complemented
59	#15667948	C₂×C₄	1	4	yes	complemented
60	#15667939	C₂×C₄	1	8	yes	complemented
61	#15667939	C₂×C₄	1	8	yes	complemented
62	#15667923	—	2	2	no	—
63	#15667923	—	2	2	no	—
64	#15667923	—	2	2	no	—
65	#15667922	—	2	2	no	—
66	#15667922	C₂×C₄	1	4	yes	complemented
67	C₄×#10623494	—	2	2	no	—
68	C₄×#10623494	—	2	2	no	—
69	C₄×#10623494	—	2	2	no	—
70	C₄×#10623494	D₄	1	2	yes	—
71	C₄×#10623494	D₄	1	2	yes	—
72	C₈×Dic₈₉	—	2	2	no	—
73	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
74	#15667919	—	2	2	no	—
75	C₂×#41×C₈₉	C₂³	1	2	yes	—
76	#135×C₈₉	C₂×C₄	1	4	yes	—
77	#135×C₈₉	C₂×C₄	1	4	yes	—
78	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
80	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₈₉	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₈₉	—	2	4	no	—
85	C₄×D₄×C₈₉	C₂×C₄	1	4	yes	—
86	#117×C₈₉	—	2	2	no	—
87	#117×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄²×C₈₉	—	2	2	no	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	#107×C₈₉	C₂×C₄	1	2	yes	—
91	#106×C₈₉	C₂×C₄	1	2	yes	—
92	#103×C₈₉	C₂×C₄	1	4	yes	—
93	#102×C₈₉	C₂×C₄	1	4	yes	—
94	#97×C₈₉	C₂×C₄	1	2	yes	—
95	#97×C₈₉	C₂×C₄	1	2	yes	—
96	C₂²×Dic₈₉	—	2	1	no	—
97	C₂²×Dic₈₉	—	2	1	no	—
98	#13083558	—	2	2	no	—
99	#13083558	—	2	2	no	—
100	#13083558	—	2	8	no	—
101	#13083558	—	2	8	no	—
102	#13083558	C₂²×C₄	1	4	yes	—
103	#13083558	C₂²×C₄	1	4	yes	—
104	C₂×#10623494	—	2	2	no	—
105	C₂×#10623494	—	2	2	no	—
106	C₂×#10623494	—	2	8	no	—
107	C₂×#10623494	—	2	8	no	—
108	C₂×#10623494	C₂²×C₄	1	2	yes	—
109	C₂×#10623494	C₂²×C₄	1	2	yes	—
110	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
111	C₂×#10623494	C₂×D₄	1	2	yes	—
112	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
113	C₂×#10623494	#41	1	2	yes	—
114	C₂×#10623494	#41	1	2	yes	—
115	C₄×Dic₈₉	—	2	1	no	—
116	C₄×Dic₈₉	—	2	1	no	—
117	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
118	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
119	#41×C₈₉	—	2	2	no	—
120	#41×C₈₉	—	2	2	no	—
121	#41×C₈₉	C₂²×C₄	1	4	yes	—
122	#41×C₈₉	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
124	C₂×D₄×C₈₉	—	2	2	no	—
125	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	#41	1	2	yes	—
129	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₈₉	C₄²	1	4	yes	—
131	SD₁₆×C₈₉	C₄²	1	8	yes	—
132	D₈×C₈₉	C₄²	1	4	yes	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
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	C₄⋊C₄×C₈₉	—	2	4	no	—
141	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₂²⋊C₄×C₈₉	—	2	4	no	—
144	C₄²×C₈₉	—	2	4	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
147	C₄²×C₈₉	C₂×D₄	1	2	yes	—
148	C₂³×C₈₉	—	2	2	no	—
149	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
150	Q₈×C₈₉	—	2	2	no	—
151	Q₈×C₈₉	C₂×C₄²	1	4	yes	—
152	D₄×C₈₉	—	2	4	no	—
153	D₄×C₈₉	—	2	4	no	—
154	D₄×C₈₉	—	2	2	no	—
155	D₄×C₈₉	C₂×C₄²	1	4	yes	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	8	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	4	2	no	—
173	C₈×C₈₉	—	2	2	no	—
174	C₈×C₈₉	C₂×C₄²	1	2	yes	—
175	C₈×C₈₉	C₂×C₄²	1	2	yes	—
176	#10623494	—	2	4	no	—
177	#10623494	—	2	4	no	—
178	#10623494	C₄×D₄	1	2	yes	—
179	#10623494	C₄×D₄	1	4	yes	—
180	#10623494	C₄×D₄	1	2	yes	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	2	4	no	—
183	C₂²×C₈₉	—	4	4	no	—
184	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
186	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
187	C₄×C₈₉	—	2	4	no	—
188	C₄×C₈₉	—	2	4	no	—
189	C₄×C₈₉	—	4	4	no	—
190	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
194	Dic₈₉	—	4	2	no	—
195	Dic₈₉	—	4	2	no	—
196	#20510	—	89	1	no	maximal, Sylow
197	C₂×C₈₉	—	2	1	no	—
198	C₂×C₈₉	—	2	1	no	—
199	C₂×C₈₉	—	4	4	no	—
200	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
201	C₂×C₈₉	#2955	1	2	yes	—
202	C₂×#444	—	89	1	no	—
203	C₂×#443	—	89	1	no	—
204	#2943	D₈₉	1	1	yes	characteristic
205	C₄×#131	—	89	2	no	—
206	#1778	—	89	1	no	—
207	#1773	—	89	1	no	—
208	#1772	—	89	1	no	—
209	#1765	—	89	2	no	—
210	#1764	—	89	2	no	—
211	#1759	—	89	2	no	—
212	#1726	—	89	1	no	—
213	C₈₉	#20510	1	1	yes	characteristic, complemented, Sylow
214	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
215	C₂×#131	—	89	2	no	—
216	C₂×#131	—	89	2	no	—
217	C₄×#41	C₂×D₈₉	1	2	yes	—
218	#444	—	89	8	no	—
219	#443	—	89	8	no	—
220	#442	Dic₈₉	1	2	yes	complemented
221	#441	Dic₈₉	1	2	yes	complemented
222	#440	Dic₈₉	1	4	yes	complemented
223	C₂×#108	—	89	1	no	—
224	C₂×#108	—	89	1	no	—
225	#427	C₂×D₈₉	1	1	yes	characteristic
226	C₂×#104	—	89	2	no	—
227	C₂×#104	—	89	2	no	—
228	#416	C₂×D₈₉	1	2	yes	—
229	#405	—	89	2	no	—
230	#405	—	89	2	no	—
231	#405	—	178	2	no	—
232	#405	—	178	2	no	—
233	C₄×M₁₆	—	89	2	no	—
234	C₄×M₁₆	—	178	2	no	—
235	C₂×#97	—	89	1	no	—
236	C₂×#97	—	89	1	no	—
237	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	C₂×C₄×C₈	—	89	1	no	—
241	C₂×C₄×C₈	—	178	2	no	—
242	#376	—	89	1	no	—
243	#341	—	89	2	no	—
244	#339	—	89	2	no	—
245	#339	—	89	2	no	—
246	C₂×#41	C₂²×D₈₉	1	2	yes	—
247	#135	C₄×D₈₉	1	4	yes	—
248	#135	C₄×D₈₉	1	4	yes	—
249	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
250	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
251	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
252	#131	—	89	8	no	—
253	#131	—	89	8	no	—
254	#131	—	178	4	no	—
255	#131	—	178	4	no	—
256	C₂×M₁₆	—	89	2	no	—
257	C₂×M₁₆	—	89	2	no	—
258	C₂×M₁₆	—	178	2	no	—
259	C₂×M₁₆	—	178	2	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₂²×C₈	—	89	1	no	—
262	C₂²×C₈	—	178	2	no	—
263	C₂²×C₈	—	178	2	no	—
264	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
266	C₄×Q₈	C₂×Dic₈₉	1	4	yes	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	C₂×Dic₈₉	1	4	yes	—
269	#117	—	2	2	no	—
270	#117	C₂²×D₈₉	1	2	yes	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	89	1	no	—
273	C₂×C₄²	—	89	1	no	—
274	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
275	#108	—	89	4	no	—
276	#108	—	89	4	no	—
277	#107	C₂×Dic₈₉	1	2	yes	—
278	#106	C₂×Dic₈₉	1	2	yes	—
279	#104	—	89	8	no	—
280	#104	—	89	8	no	—
281	#103	C₂×Dic₈₉	1	4	yes	—
282	#102	C₂×Dic₈₉	1	4	yes	—
283	#97	—	89	4	no	—
284	#97	—	178	2	no	—
285	#97	—	178	2	no	—
286	#97	—	178	2	no	—
287	#97	—	178	2	no	—
288	#97	C₂×Dic₈₉	1	2	yes	—
289	#97	C₂×Dic₈₉	1	2	yes	—
290	C₄×C₈	—	89	4	no	—
291	C₄×C₈	—	89	2	no	—
292	C₄×C₈	—	89	2	no	—
293	C₄×C₈	—	178	2	no	—
294	C₄×C₈	—	178	2	no	—
295	C₄×C₈	—	178	2	no	—
296	C₄×C₈	—	178	2	no	—
297	#95	—	178	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	C₂×C₄×D₈₉	1	4	yes	—
301	#41	C₂×C₄×D₈₉	1	4	yes	—
302	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	178	1	no	—
308	C₂²×C₄	—	178	1	no	—
309	C₂²×C₄	#13083573	1	2	yes	—
310	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
311	Q₁₆	C₄×Dic₈₉	1	4	yes	—
312	SD₁₆	C₄×Dic₈₉	1	8	yes	—
313	D₈	C₄×Dic₈₉	1	4	yes	—
314	M₁₆	—	89	4	no	—
315	M₁₆	—	89	4	no	—
316	M₁₆	—	178	8	no	—
317	M₁₆	—	178	8	no	—
318	M₁₆	—	178	2	no	—
319	M₁₆	—	178	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	1	no	—
325	C₂×C₈	—	89	2	no	—
326	C₂×C₈	—	89	1	no	—
327	C₂×C₈	—	89	2	no	—
328	C₂×C₈	—	89	2	no	—
329	C₂×C₈	—	178	8	no	—
330	C₂×C₈	—	178	8	no	—
331	C₂×C₈	—	178	2	no	—
332	C₂×C₈	—	178	2	no	—
333	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
334	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
335	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
336	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
337	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	C₂²×Dic₈₉	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	89	2	no	—
345	C₄²	—	89	2	no	—
346	C₄²	—	178	1	no	—
347	C₄²	—	178	1	no	—
348	C₄²	C₂²×Dic₈₉	1	2	yes	—
349	C₄²	D₄×D₈₉	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	C₂×#13083573	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	C₂×C₄×Dic₈₉	1	4	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂×C₄×Dic₈₉	1	4	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	D₄×Dic₈₉	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
373	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
374	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	89	2	no	—
377	C₈	—	89	4	no	—
378	C₈	—	89	2	no	—
379	C₈	—	178	4	no	—
380	C₈	—	178	4	no	—
381	C₈	C₂×C₄×Dic₈₉	1	2	yes	—
382	C₈	C₂×C₄×Dic₈₉	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
387	C₂²	C₄×#13083573	1	1	yes	characteristic
388	C₂²	C₄×#13083573	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	4	no	—
392	C₄	—	356	2	no	—
393	C₄	—	356	2	no	—
394	C₄	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
395	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
396	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
397	C₄	#41×Dic₈₉	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	C₄×D₄×Dic₈₉	1	1	yes	characteristic
402	C₂	#26029155	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2943	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2943	D₈₉
hypocenter	C₈₉	#20510
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. C₄×#15668019	C₂	semidirect
4. #26020158	C₂	semidirect
5. #26020138	C₂	semidirect
6. #26020133	C₂	semidirect
7. #26020099	C₂	semidirect
8. #26020092	C₂	semidirect
9. #26020062	C₂	semidirect
10. #26019940	C₂	semidirect
14. #19151720	C₄	semidirect
15. #19151715	C₄	semidirect
38. #442×C₈₉	C₄	semidirect
39. #441×C₈₉	C₄	semidirect
40. #440×C₈₉	C₄	semidirect
46. #15668019	C₂×C₄	semidirect
47. #15668019	C₂×C₄	semidirect
58. #15667948	C₂×C₄	semidirect
59. #15667948	C₂×C₄	semidirect
60. #15667939	C₂×C₄	semidirect
61. #15667939	C₂×C₄	semidirect
66. #15667922	C₂×C₄	semidirect
73. C₈×Dic₈₉	C₂×C₄	semidirect
213. C₈₉	#20510	semidirect
220. #442	Dic₈₉	semidirect
221. #441	Dic₈₉	semidirect
222. #440	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151720	2
C₂×#19151715	2
C₄×#15668019	2
#26020158	2
#26020138	2
#26020133	2
#26020099	2
#26020092	2
#26020062	2
#26019940	2
C₈₉×#2943	2
#20510	89