Subgroups — #36553026

Order 22784.

998 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151716	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151714	C₂	1	1	yes	maximal, characteristic
3	#26029023	C₂	1	1	yes	maximal, characteristic
4	#26028679	C₂	1	2	yes	maximal, complemented
5	#108×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020098	C₂	1	2	yes	maximal, complemented
8	#26020093	C₂	1	2	yes	maximal, complemented
9	#26020061	C₂	1	2	yes	maximal, complemented
10	#26019938	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	2	yes	—
15	#19152066	C₂²	1	2	yes	—
16	#19151716	C₄	1	8	yes	complemented
17	#19151714	C₄	1	8	yes	complemented
18	#19151692	C₄	1	2	yes	complemented
19	#19151685	C₄	1	4	yes	complemented
20	#19151680	C₄	1	2	yes	complemented
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667940	C₂²	1	2	yes	—
23	C₂×#15667938	C₂²	1	2	yes	—
24	#19151592	C₂²	1	2	yes	—
25	#19151555	—	2	2	no	—
26	#19151554	C₂²	1	2	yes	—
27	#19151552	—	2	2	no	—
28	M₁₆×Dic₈₉	C₂²	1	2	yes	—
29	C₄×#13083557	—	2	2	no	—
30	C₂×#15667923	C₂²	1	1	yes	characteristic
31	C₂×#15667922	C₂²	1	1	yes	characteristic
32	C₂×#15667922	C₂²	1	1	yes	characteristic
33	#97×D₈₉	—	2	2	no	—
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
36	#19151444	C₂²	1	1	yes	characteristic
37	#19151362	C₂²	1	2	yes	—
38	#19151357	C₂²	1	2	yes	—
39	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#405×C₈₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#339×C₈₉	C₂²	1	2	yes	—
44	C₂×#13083574	C₂³	1	2	yes	—
45	#15668034	C₂×C₄	1	4	yes	—
46	#15668034	C₂×C₄	1	4	yes	—
47	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083563	C₂×C₄	1	2	yes	—
49	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
50	#15668020	—	2	4	no	—
51	#15668020	C₂×C₄	1	8	yes	complemented
52	#15668018	—	2	4	no	—
53	#15668018	C₂×C₄	1	8	yes	complemented
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×#13083557	—	2	2	no	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₂×C₈×D₈₉	—	2	2	no	—
61	#15667977	C₂×C₄	1	4	yes	—
62	#15667974	C₂×C₄	1	4	yes	—
63	#15667972	—	2	4	no	—
64	#15667969	—	2	2	no	—
65	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
67	C₄²×D₈₉	—	2	2	no	—
68	#15667948	C₂×C₄	1	4	yes	complemented
69	#15667940	C₂×C₄	1	8	yes	complemented
70	#15667938	C₂×C₄	1	8	yes	complemented
71	#15667935	C₂×C₄	1	4	yes	—
72	#15667932	C₂×C₄	1	4	yes	—
73	#15667923	—	2	2	no	—
74	#15667923	—	2	2	no	—
75	#15667922	—	2	2	no	—
76	#15667922	—	2	2	no	—
77	#15667922	D₄	1	1	yes	characteristic
78	#15667922	D₄	1	1	yes	characteristic
79	#15667922	D₄	1	1	yes	characteristic
80	#15667922	D₄	1	1	yes	characteristic
81	C₄×#10623494	—	2	2	no	—
82	C₈×Dic₈₉	—	2	2	no	—
83	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
84	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
85	C₈×Dic₈₉	C₂×C₄	1	4	yes	complemented
86	#15667919	—	2	2	no	—
87	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	#117×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	#108×C₈₉	C₂×C₄	1	4	yes	complemented
93	#107×C₈₉	C₂×C₄	1	2	yes	—
94	#106×C₈₉	C₂×C₄	1	2	yes	—
95	#97×C₈₉	—	2	2	no	—
96	C₄×C₈×C₈₉	—	2	2	no	—
97	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
98	#13083574	—	2	2	no	—
99	#13083574	—	2	2	no	—
100	#13083574	C₂²×C₄	1	4	yes	—
101	#13083574	C₂²×C₄	1	4	yes	—
102	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
103	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
104	C₂×C₂²⋊D₈₉	—	2	2	no	—
105	C₂²×Dic₈₉	—	2	1	no	—
106	C₂²×Dic₈₉	#41	1	2	yes	—
107	C₂×C₄×D₈₉	—	2	2	no	—
108	C₂×C₄×D₈₉	—	2	4	no	—
109	Dic₃₅₆	C₄²	1	4	yes	—
110	#13083563	C₄²	1	8	yes	—
111	D₇₁₂	C₄²	1	4	yes	—
112	#13083558	—	2	2	no	—
113	#13083558	C₂²×C₄	1	4	yes	—
114	#13083557	—	2	8	no	—
115	#13083557	—	2	8	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	C₂²×C₄	1	2	yes	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	#41	1	2	yes	—
124	C₈×D₈₉	—	2	8	no	—
125	C₈×D₈₉	—	2	8	no	—
126	#13083553	—	2	4	no	—
127	#13083551	—	2	4	no	—
128	C₄×Dic₈₉	—	2	1	no	—
129	C₄×Dic₈₉	—	2	4	no	—
130	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
131	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
132	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	—	2	1	no	—
135	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₈₉	—	2	2	no	—
137	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	#41	1	2	yes	—
147	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
148	C₂²⋊C₄×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
152	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₂²×D₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	2	4	no	—
164	C₂²⋊D₈₉	—	2	4	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	4	2	no	—
168	C₂×Dic₈₉	—	4	2	no	—
169	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
170	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
171	D₃₅₆	—	2	2	no	—
172	D₃₅₆	C₂×C₄²	1	4	yes	—
173	C₄×D₈₉	—	2	4	no	—
174	C₄×D₈₉	—	2	4	no	—
175	C₄×D₈₉	—	8	4	no	—
176	Dic₁₇₈	—	2	2	no	—
177	Dic₁₇₈	C₂×C₄²	1	4	yes	—
178	C₈×C₈₉	—	2	4	no	—
179	C₈×C₈₉	C₂×C₄²	1	2	yes	—
180	C₈×C₈₉	C₂×C₄²	1	2	yes	—
181	C₈×C₈₉	C₄×D₄	1	2	yes	—
182	C₈×C₈₉	C₄×D₄	1	2	yes	—
183	#10623494	—	2	4	no	—
184	#10623494	—	2	2	no	—
185	#10623494	C₄×D₄	1	2	yes	—
186	#10623494	C₄×D₄	1	2	yes	—
187	C₂²×C₈₉	—	2	2	no	—
188	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
190	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
191	C₂×D₈₉	—	2	4	no	—
192	C₂×D₈₉	—	4	4	no	—
193	C₄×C₈₉	—	4	2	no	—
194	C₄×C₈₉	—	4	4	no	—
195	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
196	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
199	Dic₈₉	—	2	2	no	—
200	Dic₈₉	—	2	2	no	—
201	Dic₈₉	—	2	4	no	—
202	Dic₈₉	—	4	2	no	—
203	#20514	—	89	1	no	maximal, Sylow
204	C₂×C₈₉	—	2	1	no	—
205	C₂×C₈₉	—	2	1	no	—
206	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
207	C₂×C₈₉	#2957	1	2	yes	—
208	D₈₉	—	4	4	no	—
209	C₂×#443	—	89	1	no	—
210	C₂×#443	—	89	1	no	—
211	C₄×#135	—	89	1	no	—
212	#2875	—	89	2	no	—
213	C₄×#108	—	89	1	no	—
214	#1772	—	89	1	no	—
215	#1772	D₈₉	1	1	yes	characteristic, complemented
216	#1765	—	89	2	no	—
217	#1765	—	89	2	no	—
218	#1759	—	89	2	no	—
219	#1726	—	89	1	no	—
220	C₈₉	#20514	1	1	yes	characteristic, complemented, Sylow
221	C₂×#135	—	89	1	no	—
222	C₂×#131	—	89	2	no	—
223	C₂×#131	—	89	2	no	—
224	C₄×#41	—	89	2	no	—
225	#443	—	89	8	no	—
226	#443	—	89	8	no	—
227	C₄×Q₁₆	—	89	2	no	—
228	C₄×SD₁₆	—	89	4	no	—
229	C₄×D₈	—	89	2	no	—
230	C₂×#108	—	89	1	no	—
231	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
232	#427	C₂×D₈₉	1	1	yes	characteristic
233	C₂×#104	—	89	2	no	—
234	C₂×#104	—	89	2	no	—
235	#416	—	89	2	no	—
236	#405	—	89	2	no	—
237	#405	—	178	2	no	—
238	#405	—	178	2	no	—
239	#405	C₂×D₈₉	1	2	yes	—
240	C₄×M₁₆	—	89	2	no	—
241	C₄×M₁₆	—	178	2	no	—
242	C₂×#97	—	89	1	no	—
243	C₂×#97	—	89	1	no	—
244	C₂×#97	—	89	1	no	—
245	C₂×#97	—	178	2	no	—
246	C₂×C₄×C₈	—	89	1	no	—
247	C₂×C₄×C₈	—	89	1	no	—
248	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
249	#376	—	89	1	no	—
250	#341	—	89	2	no	—
251	#339	—	89	2	no	—
252	#339	C₂×D₈₉	1	2	yes	—
253	C₂×#41	—	89	2	no	—
254	#135	—	89	4	no	—
255	#135	—	89	4	no	—
256	C₂×Q₁₆	—	89	1	no	—
257	C₂×SD₁₆	—	89	2	no	—
258	C₂×D₈	—	89	1	no	—
259	#131	—	89	8	no	—
260	#131	—	89	8	no	—
261	#131	—	178	4	no	—
262	#131	—	178	4	no	—
263	C₂×M₁₆	—	89	2	no	—
264	C₂×M₁₆	—	178	2	no	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	178	2	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
272	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
273	C₄×Q₈	—	89	4	no	—
274	C₄×D₄	—	89	4	no	—
275	C₄×D₄	—	178	4	no	—
276	#117	—	178	2	no	—
277	#117	C₂²×D₈₉	1	2	yes	—
278	C₂×C₄²	—	89	1	no	—
279	C₂×C₄²	—	89	1	no	—
280	C₂×C₄²	—	178	2	no	—
281	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
282	#108	—	89	4	no	—
283	#108	C₄×D₈₉	1	4	yes	complemented
284	#107	C₄×D₈₉	1	2	yes	—
285	#106	C₄×D₈₉	1	2	yes	—
286	#104	—	89	8	no	—
287	#104	—	89	8	no	—
288	#103	—	89	4	no	—
289	#102	—	89	4	no	—
290	#97	—	2	2	no	—
291	#97	—	89	1	no	—
292	#97	—	89	1	no	—
293	#97	—	89	1	no	—
294	#97	—	89	1	no	—
295	#97	—	178	2	no	—
296	#97	—	178	2	no	—
297	#97	—	178	2	no	—
298	#97	—	178	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	89	2	no	—
301	C₄×C₈	—	89	2	no	—
302	C₄×C₈	—	89	4	no	—
303	C₄×C₈	—	178	2	no	—
304	C₄×C₈	—	178	2	no	—
305	C₄×C₈	C₄×D₈₉	1	4	yes	complemented
306	#95	—	178	2	no	—
307	#41	—	89	4	no	—
308	#41	—	89	4	no	—
309	#41	—	178	2	no	—
310	#41	—	178	2	no	—
311	C₂×Q₈	—	89	2	no	—
312	C₂×D₄	—	89	2	no	—
313	C₂×D₄	—	178	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	89	2	no	—
316	C₂²×C₄	—	178	4	no	—
317	C₂²×C₄	—	178	1	no	—
318	C₂²×C₄	—	178	2	no	—
319	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
320	Q₁₆	—	89	4	no	—
321	SD₁₆	—	89	8	no	—
322	D₈	—	89	4	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	89	4	no	—
325	M₁₆	—	178	8	no	—
326	M₁₆	—	178	2	no	—
327	M₁₆	—	178	8	no	—
328	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	89	2	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	89	2	no	—
334	C₂×C₈	—	89	2	no	—
335	C₂×C₈	—	178	8	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	1	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	—	178	8	no	—
340	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
341	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
344	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
345	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	#13083575	1	2	yes	—
348	C₄⋊C₄	—	178	4	no	—
349	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	178	4	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	89	2	no	—
355	C₄²	—	89	1	no	—
356	C₄²	—	89	1	no	—
357	C₄²	—	89	2	no	—
358	C₄²	—	178	4	no	—
359	C₄²	—	178	1	no	—
360	C₄²	C₂×C₄×D₈₉	1	2	yes	—
361	C₂³	—	178	2	no	—
362	C₂³	#41×D₈₉	1	1	yes	characteristic
363	Q₈	—	89	4	no	—
364	Q₈	—	178	2	no	—
365	D₄	—	89	4	no	—
366	D₄	—	178	4	no	—
367	D₄	—	178	4	no	—
368	D₄	—	178	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	89	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	356	2	no	—
375	C₂×C₄	—	356	2	no	—
376	C₂×C₄	—	178	2	no	—
377	C₂×C₄	—	178	2	no	—
378	C₂×C₄	—	178	4	no	—
379	C₂×C₄	—	178	4	no	—
380	C₂×C₄	—	712	4	no	—
381	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
385	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
387	C₈	—	2	4	no	—
388	C₈	—	89	2	no	—
389	C₈	—	89	2	no	—
390	C₈	—	178	4	no	—
391	C₈	—	178	2	no	—
392	C₈	C₄²×D₈₉	1	2	yes	—
393	C₈	C₄²×D₈₉	1	2	yes	—
394	C₈	#15667974	1	2	yes	—
395	C₈	#15667974	1	2	yes	—
396	C₂²	—	2	2	no	—
397	C₂²	—	356	4	no	—
398	C₂²	—	178	4	no	—
399	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
400	C₂²	#19152066	1	1	yes	characteristic
401	C₂²	C₄×#13083575	1	1	yes	characteristic
402	C₄	—	4	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	356	2	no	—
405	C₄	—	178	2	no	—
406	C₄	—	178	2	no	—
407	C₄	—	178	4	no	—
408	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
409	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
410	C₄	C₂×#15667974	1	1	yes	characteristic
411	C₄	C₄×#13083575	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	1	no	—
414	C₂	—	356	4	no	—
415	C₂	C₄×#15667974	1	1	yes	characteristic
416	C₂	#26029164	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1772	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1772	D₈₉
hypocenter	C₈₉	#20514
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. #26028679	C₂	semidirect
5. #108×Dic₈₉	C₂	semidirect
6. #26020133	C₂	semidirect
7. #26020098	C₂	semidirect
8. #26020093	C₂	semidirect
9. #26020061	C₂	semidirect
10. #26019938	C₂	semidirect
11. C₈₉×#1772	C₂	semidirect
16. #19151716	C₄	semidirect
17. #19151714	C₄	semidirect
18. #19151692	C₄	semidirect
19. #19151685	C₄	semidirect
20. #19151680	C₄	semidirect
51. #15668020	C₂×C₄	semidirect
53. #15668018	C₂×C₄	semidirect
68. #15667948	C₂×C₄	semidirect
69. #15667940	C₂×C₄	semidirect
70. #15667938	C₂×C₄	semidirect
85. C₈×Dic₈₉	C₂×C₄	semidirect
92. #108×C₈₉	C₂×C₄	semidirect
97. C₄×C₈×C₈₉	C₂×C₄	semidirect
215. #1772	D₈₉	semidirect
220. C₈₉	#20514	semidirect
283. #108	C₄×D₈₉	semidirect
305. C₄×C₈	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151716	2
C₂×#19151714	2
#26029023	2
#26028679	2
#108×Dic₈₉	2
#26020133	2
#26020098	2
#26020093	2
#26020061	2
#26019938	2
C₈₉×#1772	2
#20514	89