Subgroups — #36450622

Order 22784.

546 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151889	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151677	C₂	1	1	yes	maximal, characteristic
3	#26021213	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020253	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151346	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018136	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#13083557	—	2	1	no	—
9	C₂×#15668012	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
11	#19151889	—	2	2	no	—
12	#19151889	C₄	1	4	yes	complemented
13	#19151677	—	2	2	no	—
14	#19151677	—	2	2	no	—
15	C₂×#15667944	—	2	1	no	—
16	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
17	C₂×#15667934	—	2	1	no	—
18	C₂×#15667934	—	2	1	no	—
19	C₂×#15667924	—	2	1	no	—
20	#19151468	C₂²	1	1	yes	characteristic
21	#19151361	—	2	1	no	—
22	#19151361	—	2	1	no	—
23	#19151361	—	2	1	no	—
24	#19151346	—	2	2	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×Dic₁₇₈	—	2	1	no	—
29	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₈₉	—	2	1	no	—
31	C₂×#13083557	—	2	4	no	—
32	C₂×#13083557	—	4	2	no	—
33	C₂×#13083557	—	4	2	no	—
34	C₂²×#10623494	—	2	1	no	—
35	#15668012	—	2	1	no	—
36	#15668012	—	2	1	no	—
37	#15668012	—	2	1	no	—
38	#15668012	C₂×C₄	1	2	yes	—
39	C₄×D₃₅₆	—	2	1	no	—
40	C₄×D₃₅₆	—	2	1	no	—
41	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
42	C₄×D₃₅₆	D₄	1	2	yes	—
43	C₂×C₄⋊Dic₈₉	—	2	1	no	—
44	C₂×C₄⋊Dic₈₉	—	2	1	no	—
45	C₂×C₄⋊Dic₈₉	—	2	1	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
49	C₂×#13083551	—	2	1	no	—
50	#15667944	—	2	4	no	—
51	C₄⋊#10623494	—	2	1	no	—
52	C₄⋊#10623494	D₄	1	2	yes	—
53	#15667934	—	2	4	no	—
54	#15667934	—	4	2	no	—
55	#15667924	—	2	4	no	—
56	C₂²×C₈×C₈₉	—	2	1	no	—
57	C₂²×C₈×C₈₉	—	2	1	no	—
58	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₈₉	—	2	1	no	—
62	C₄⋊C₈×C₈₉	—	2	1	no	—
63	C₄⋊C₈×C₈₉	—	2	1	no	—
64	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₈₉	—	2	1	no	—
66	C₄×C₈×C₈₉	—	2	1	no	—
67	C₂³×D₈₉	—	2	1	no	—
68	C₂×Dic₁₇₈	—	2	2	no	—
69	C₂×Dic₁₇₈	—	4	1	no	—
70	C₂×Dic₁₇₈	—	8	1	no	—
71	C₂×Dic₁₇₈	—	8	1	no	—
72	C₂×D₃₅₆	—	2	1	no	—
73	C₂×D₃₅₆	—	2	1	no	—
74	C₂×D₃₅₆	—	2	1	no	—
75	C₂×D₃₅₆	—	2	1	no	—
76	C₂×D₃₅₆	—	2	1	no	—
77	C₂×D₃₅₆	C₂²⋊C₄	1	2	yes	—
78	C₂²×Dic₈₉	—	2	1	no	—
79	C₂²×Dic₈₉	—	4	1	no	—
80	C₂²×Dic₈₉	—	4	1	no	—
81	C₂×C₄×D₈₉	—	2	2	no	—
82	C₂×C₄×D₈₉	—	2	2	no	—
83	C₂×C₄×D₈₉	—	4	1	no	—
84	C₂×C₄×D₈₉	—	4	1	no	—
85	C₂×C₄×D₈₉	—	4	1	no	—
86	C₂×C₄×D₈₉	—	4	1	no	—
87	#13083557	—	4	8	no	—
88	C₂×#10623494	—	2	2	no	—
89	C₂×#10623494	—	4	1	no	—
90	C₂×#10623494	—	4	1	no	—
91	C₄⋊Dic₈₉	—	2	1	no	—
92	C₄⋊Dic₈₉	—	2	2	no	—
93	C₄⋊Dic₈₉	—	2	2	no	—
94	C₄⋊Dic₈₉	—	4	1	no	—
95	C₄⋊Dic₈₉	—	4	1	no	—
96	C₄⋊Dic₈₉	—	4	1	no	—
97	C₄⋊Dic₈₉	—	4	1	no	—
98	C₄⋊Dic₈₉	—	4	1	no	—
99	C₄⋊Dic₈₉	—	4	1	no	—
100	C₄⋊Dic₈₉	—	8	1	no	—
101	C₄⋊Dic₈₉	C₂²⋊C₄	1	2	yes	—
102	#13083551	—	2	2	no	—
103	#13083551	—	2	2	no	—
104	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
107	C₂×C₈×C₈₉	—	2	1	no	—
108	C₂×C₈×C₈₉	—	2	1	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	—	4	1	no	—
114	C₂×C₈×C₈₉	—	4	1	no	—
115	C₂×C₈×C₈₉	—	4	1	no	—
116	C₂×C₈×C₈₉	—	4	1	no	—
117	C₂×C₈×C₈₉	—	4	1	no	—
118	C₂×C₈×C₈₉	SD₁₆	1	2	yes	—
119	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₈₉	#41	1	1	yes	characteristic
123	C₂³×C₈₉	#121	1	1	yes	characteristic
124	C₂²×D₈₉	—	2	2	no	—
125	C₂²×D₈₉	—	4	1	no	—
126	C₂²×D₈₉	—	4	1	no	—
127	C₂²×D₈₉	—	4	1	no	—
128	C₂²×D₈₉	—	4	1	no	—
129	C₂²×D₈₉	—	4	1	no	—
130	C₂²×D₈₉	—	4	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
136	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
137	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
138	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
140	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
141	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
142	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
144	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
147	C₂×Dic₈₉	—	2	2	no	—
148	C₂×Dic₈₉	—	4	1	no	—
149	C₂×Dic₈₉	—	4	1	no	—
150	C₂×Dic₈₉	—	4	2	no	—
151	C₂×Dic₈₉	—	8	1	no	—
152	C₂×Dic₈₉	—	8	1	no	—
153	C₂×Dic₈₉	—	8	1	no	—
154	C₂×Dic₈₉	—	8	1	no	—
155	C₂×Dic₈₉	—	8	1	no	—
156	D₃₅₆	—	2	2	no	—
157	D₃₅₆	—	2	2	no	—
158	D₃₅₆	—	4	1	no	—
159	D₃₅₆	—	4	1	no	—
160	C₄×D₈₉	—	4	2	no	—
161	C₄×D₈₉	—	4	2	no	—
162	C₄×D₈₉	—	4	2	no	—
163	C₄×D₈₉	—	4	2	no	—
164	Dic₁₇₈	—	8	2	no	—
165	Dic₁₇₈	—	8	2	no	—
166	C₈×C₈₉	—	2	2	no	—
167	C₈×C₈₉	—	4	2	no	—
168	C₈×C₈₉	—	4	1	no	—
169	C₈×C₈₉	—	8	1	no	—
170	#10623494	—	4	2	no	—
171	C₂²×C₈₉	#386	1	1	yes	characteristic
172	C₂²×C₈₉	#461	1	1	yes	characteristic
173	C₂²×C₈₉	#463	1	1	yes	characteristic
174	C₂²×C₈₉	#468	1	1	yes	characteristic
175	C₂²×C₈₉	#470	1	1	yes	characteristic
176	C₂²×C₈₉	#471	1	1	yes	characteristic
177	C₂²×C₈₉	#472	1	1	yes	characteristic
178	C₂×D₈₉	—	4	2	no	—
179	C₂×D₈₉	—	4	2	no	—
180	C₂×D₈₉	—	4	2	no	—
181	C₂×D₈₉	—	8	1	no	—
182	C₂×D₈₉	—	8	1	no	—
183	C₂×D₈₉	—	8	1	no	—
184	C₂×D₈₉	—	8	1	no	—
185	C₄×C₈₉	—	2	1	no	—
186	C₄×C₈₉	—	2	1	no	—
187	C₄×C₈₉	#417	1	1	yes	characteristic
188	C₄×C₈₉	#419	1	1	yes	characteristic
189	C₄×C₈₉	C₄×SD₁₆	1	1	yes	characteristic
190	C₄×C₈₉	#440	1	1	yes	characteristic
191	C₄×C₈₉	#450	1	1	yes	characteristic
192	C₄×C₈₉	#452	1	1	yes	characteristic
193	C₄×C₈₉	#468	1	1	yes	characteristic
194	C₄×C₈₉	#470	1	1	yes	characteristic
195	Dic₈₉	—	4	2	no	—
196	Dic₈₉	—	8	2	no	—
197	Dic₈₉	—	16	1	no	—
198	#9223	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	#1691	1	1	yes	characteristic
200	C₂×C₈₉	#1695	1	1	yes	characteristic
201	C₂×C₈₉	#1697	1	1	yes	characteristic
202	C₂×C₈₉	#1703	1	1	yes	characteristic
203	C₂×C₈₉	#1877	1	1	yes	characteristic
204	C₂×C₈₉	#1894	1	1	yes	characteristic
205	C₂×C₈₉	#1907	1	1	yes	characteristic
206	D₈₉	—	8	2	no	—
207	C₂×#476	—	89	1	no	—
208	C₂×#436	—	89	1	no	—
209	#1990	—	89	1	no	—
210	#1802	—	89	1	no	—
211	C₂×#333	—	89	1	no	—
212	#1296	—	89	1	no	—
213	#1277	D₈₉	1	1	yes	characteristic, complemented
214	C₈₉	#9223	1	1	yes	characteristic, complemented, Sylow
215	C₂²×M₁₆	—	178	1	no	—
216	C₂×C₄⋊Q₈	—	89	1	no	—
217	C₂×C₄×D₄	—	89	1	no	—
218	#476	—	89	4	no	—
219	#476	—	178	2	no	—
220	#436	—	178	2	no	—
221	#436	—	178	2	no	—
222	C₂×#106	—	178	1	no	—
223	C₂×C₄⋊C₈	—	89	1	no	—
224	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
226	C₂×#102	—	178	1	no	—
227	C₂×#102	—	178	1	no	—
228	C₂×C₂²⋊C₈	—	178	1	no	—
229	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
230	#384	—	89	1	no	—
231	#340	—	178	1	no	—
232	#340	—	178	1	no	—
233	#340	—	178	1	no	—
234	#333	—	178	2	no	—
235	C₂²×Q₈	—	178	1	no	—
236	C₂²×D₄	—	89	1	no	—
237	C₂³×C₄	—	178	1	no	—
238	C₂×M₁₆	—	356	2	no	—
239	C₂×M₁₆	—	356	2	no	—
240	C₂×M₁₆	—	178	4	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	178	1	no	—
244	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
245	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
246	C₄⋊Q₈	—	89	2	no	—
247	C₄⋊Q₈	—	178	1	no	—
248	C₄⋊Q₈	—	178	1	no	—
249	C₄⋊Q₈	—	178	1	no	—
250	C₄×D₄	—	89	2	no	—
251	C₄×D₄	—	89	2	no	—
252	C₄×D₄	—	178	1	no	—
253	C₄×D₄	—	178	1	no	—
254	C₂×C₄⋊C₄	—	89	1	no	—
255	C₂×C₄⋊C₄	—	178	1	no	—
256	C₂×C₄⋊C₄	—	178	1	no	—
257	C₂×C₄⋊C₄	—	178	1	no	—
258	C₂×C₄⋊C₄	—	178	1	no	—
259	C₂×C₄⋊C₄	—	178	1	no	—
260	C₂×C₂²⋊C₄	—	178	1	no	—
261	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
262	#106	—	178	4	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	89	2	no	—
267	C₄⋊C₈	—	178	1	no	—
268	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
269	#102	—	356	2	no	—
270	#102	—	178	4	no	—
271	C₂²⋊C₈	—	178	4	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	1	no	—
274	C₂⁴	—	178	1	no	—
275	C₂×Q₈	—	356	1	no	—
276	C₂×Q₈	—	178	2	no	—
277	C₂×Q₈	—	712	1	no	—
278	C₂×Q₈	—	712	1	no	—
279	C₂×D₄	—	89	2	no	—
280	C₂×D₄	—	178	1	no	—
281	C₂×D₄	—	178	1	no	—
282	C₂×D₄	—	178	1	no	—
283	C₂×D₄	—	178	1	no	—
284	C₂×D₄	—	178	1	no	—
285	C₂²×C₄	—	356	1	no	—
286	C₂²×C₄	—	356	1	no	—
287	C₂²×C₄	—	356	1	no	—
288	C₂²×C₄	—	356	1	no	—
289	C₂²×C₄	—	356	1	no	—
290	C₂²×C₄	—	356	1	no	—
291	C₂²×C₄	—	178	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	C₂×D₃₅₆	1	1	yes	characteristic
296	C₂²×C₄	#13083575	1	1	yes	characteristic
297	M₁₆	—	356	8	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	356	1	no	—
310	C₂×C₈	—	356	1	no	—
311	C₂×C₈	—	178	2	no	—
312	C₂×C₈	#13083563	1	2	yes	—
313	C₄⋊C₄	—	89	2	no	—
314	C₄⋊C₄	—	356	1	no	—
315	C₄⋊C₄	—	356	1	no	—
316	C₄⋊C₄	—	356	1	no	—
317	C₄⋊C₄	—	356	1	no	—
318	C₄⋊C₄	—	356	1	no	—
319	C₄⋊C₄	—	356	1	no	—
320	C₄⋊C₄	—	178	2	no	—
321	C₄⋊C₄	—	178	2	no	—
322	C₄⋊C₄	—	178	1	no	—
323	C₄⋊C₄	—	712	1	no	—
324	C₂²⋊C₄	—	178	2	no	—
325	C₂²⋊C₄	—	178	2	no	—
326	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₄²	D₄×D₈₉	1	1	yes	characteristic
328	C₄²	D₄×D₈₉	1	1	yes	characteristic
329	C₄²	#13083574	1	1	yes	characteristic
330	C₂³	—	356	1	no	—
331	C₂³	—	356	1	no	—
332	C₂³	—	356	1	no	—
333	C₂³	—	356	1	no	—
334	C₂³	—	356	1	no	—
335	C₂³	—	356	1	no	—
336	C₂³	—	178	2	no	—
337	C₂³	#15667987	1	1	yes	characteristic
338	Q₈	—	712	2	no	—
339	Q₈	—	712	2	no	—
340	D₄	—	356	1	no	—
341	D₄	—	356	1	no	—
342	D₄	—	178	2	no	—
343	D₄	—	178	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	356	1	no	—
347	C₂×C₄	—	356	1	no	—
348	C₂×C₄	—	356	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	—	178	2	no	—
354	C₂×C₄	—	712	1	no	—
355	C₂×C₄	—	712	1	no	—
356	C₂×C₄	—	712	1	no	—
357	C₂×C₄	—	712	1	no	—
358	C₂×C₄	—	712	1	no	—
359	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
360	C₂×C₄	#15667974	1	1	yes	characteristic
361	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
362	C₂×C₄	#15667982	1	1	yes	characteristic
363	C₂×C₄	#15667985	1	1	yes	characteristic
364	C₂×C₄	#15667997	1	1	yes	characteristic
365	C₂×C₄	C₂×#13083563	1	1	yes	characteristic
366	C₂×C₄	#15668034	1	1	yes	characteristic
367	C₂×C₄	#15668036	1	1	yes	characteristic
368	C₂×C₄	#15668040	1	1	yes	characteristic
369	C₂×C₄	#15668041	1	1	yes	characteristic
370	C₂×C₄	#15668041	1	1	yes	characteristic
371	C₂×C₄	#15668044	1	1	yes	characteristic
372	C₂×C₄	#15668045	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	8	1	no	—
377	C₈	—	356	2	no	—
378	C₂²	—	356	2	no	—
379	C₂²	—	356	2	no	—
380	C₂²	—	356	2	no	—
381	C₂²	—	712	1	no	—
382	C₂²	—	712	1	no	—
383	C₂²	—	712	1	no	—
384	C₂²	—	712	1	no	—
385	C₂²	#19151476	1	1	yes	characteristic
386	C₂²	#19151804	1	1	yes	characteristic
387	C₂²	#19151814	1	1	yes	characteristic
388	C₂²	#19151845	1	1	yes	characteristic
389	C₂²	#19151857	1	1	yes	characteristic
390	C₂²	#19151862	1	1	yes	characteristic
391	C₂²	#19151869	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	356	2	no	—
395	C₄	—	1424	1	no	—
396	C₄	—	712	2	no	—
397	C₄	#19151596	1	1	yes	characteristic
398	C₄	#19151605	1	1	yes	characteristic
399	C₄	C₄×#13083563	1	1	yes	characteristic
400	C₄	#19151700	1	1	yes	characteristic
401	C₄	#19151751	1	1	yes	characteristic
402	C₄	#19151762	1	1	yes	characteristic
403	C₄	#19151843	1	1	yes	characteristic
404	C₄	#19151855	1	1	yes	characteristic
405	C₂	—	712	2	no	—
406	C₂	#26019752	1	1	yes	characteristic
407	C₂	#26019776	1	1	yes	characteristic
408	C₂	#26019786	1	1	yes	characteristic
409	C₂	#26019828	1	1	yes	characteristic
410	C₂	#26020585	1	1	yes	characteristic
411	C₂	#26020684	1	1	yes	characteristic
412	C₂	#26020759	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#15667987
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1277	C₂
socle	C₂³×C₈₉	#121
prime radical	C₂²×D₃₅₆	D₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1277	D₈₉
hypocenter	C₈₉	#9223
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. #26021213	C₂	semidirect
5. C₂×#19151346	C₂	semidirect
6. #26018136	C₂	semidirect
7. C₈₉×#1277	C₂	semidirect
12. #19151889	C₄	semidirect
213. #1277	D₈₉	semidirect
214. C₈₉	#9223	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151889	2
C₂×#19151677	2
#26021213	2
#26020253	2
C₂×#19151346	2
#26018136	2
C₈₉×#1277	2
#9223	89