Subgroups — #36537626

Order 22784.

710 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	#26031393	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031190	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151971	C₂	1	1	yes	maximal, characteristic
4	#26019724	C₂	1	4	yes	maximal, complemented
5	#26019600	C₂	1	4	yes	maximal, complemented
6	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018925	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018921	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#13083563	—	2	1	no	—
11	C₂²×#13083563	—	2	1	no	—
12	C₂×#15668012	C₂²	1	1	yes	characteristic
13	C₂×#15668009	C₂²	1	1	yes	characteristic
14	#19151994	—	2	1	no	—
15	#19151972	—	2	1	no	—
16	#19151971	—	2	1	no	—
17	#19151971	—	2	1	no	—
18	#19151971	C₂²	1	2	yes	—
19	#19151971	C₂²	1	2	yes	—
20	#19151948	—	2	1	no	—
21	#19151946	—	2	1	no	—
22	#19151926	—	2	2	no	—
23	#19151883	C₂²	1	4	yes	complemented
24	#19151798	C₂²	1	4	yes	—
25	#19151748	—	2	2	no	—
26	#19151651	C₂²	1	1	yes	characteristic
27	#19151651	C₂²	1	1	yes	characteristic
28	#19151351	C₂²	1	2	yes	complemented
29	#19151349	C₂²	1	2	yes	complemented
30	#19151345	C₂²	1	4	yes	complemented
31	#19151341	C₂²	1	4	yes	—
32	#533×C₈₉	C₂²	1	1	yes	characteristic
33	#446×C₈₉	—	2	1	no	—
34	#446×C₈₉	C₂²	1	2	yes	complemented
35	C₈×Q₈×C₈₉	—	2	1	no	—
36	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
37	#424×C₈₉	—	2	1	no	—
38	#423×C₈₉	C₂²	1	1	yes	characteristic
39	#405×C₈₉	—	2	1	no	—
40	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₇₈	—	2	1	no	—
42	C₂²×D₃₅₆	—	2	1	no	—
43	C₂²×D₃₅₆	—	2	1	no	—
44	C₂²×D₃₅₆	—	2	1	no	—
45	C₂×#13083563	—	2	2	no	—
46	C₂×#13083563	—	2	2	no	—
47	C₂×#13083563	—	2	2	no	—
48	C₂×#13083563	—	2	2	no	—
49	C₂×#13083563	—	4	4	no	—
50	C₂×#13083563	—	4	4	no	—
51	C₂×#13083561	—	2	4	no	—
52	#15668012	—	2	1	no	—
53	#15668012	—	2	1	no	—
54	#15668012	—	2	1	no	—
55	#15668012	C₂³	1	2	yes	—
56	#15668009	—	2	1	no	—
57	#15668009	—	2	1	no	—
58	#15668009	—	2	1	no	—
59	#15668009	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₈₉	—	2	1	no	—
61	C₂×C₄⋊Dic₈₉	—	2	1	no	—
62	#15667943	—	2	4	no	—
63	C₄⋊#10623494	C₂³	1	2	yes	—
64	C₄⋊#10623494	C₂³	1	2	yes	—
65	#15667936	—	2	4	no	—
66	#15667932	—	2	4	no	—
67	C₂²⋊#10623494	—	2	1	no	—
68	C₂²⋊#10623494	—	2	1	no	—
69	C₄×#10623494	—	2	1	no	—
70	C₄×#10623494	—	2	1	no	—
71	C₂×M₁₆×C₈₉	—	2	1	no	—
72	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
76	#125×C₈₉	—	2	1	no	—
77	C₂²⋊Q₈×C₈₉	—	2	1	no	—
78	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
79	C₄×Q₈×C₈₉	—	2	1	no	—
80	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
81	#117×C₈₉	—	2	1	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₈₉	—	2	2	no	—
84	C₄⋊C₈×C₈₉	—	2	2	no	—
85	C₄⋊C₈×C₈₉	—	2	1	no	—
86	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
87	#97×C₈₉	—	2	2	no	—
88	C₄×C₈×C₈₉	—	2	2	no	—
89	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
90	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×D₈₉	—	4	1	no	—
94	C₂×Dic₁₇₈	—	2	2	no	—
95	C₂×Dic₁₇₈	—	4	2	no	—
96	C₂×Dic₁₇₈	—	4	2	no	—
97	C₂×Dic₁₇₈	—	4	1	no	—
98	C₂×D₃₅₆	—	2	2	no	—
99	C₂×D₃₅₆	—	2	2	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	4	2	no	—
102	C₂×D₃₅₆	—	4	2	no	—
103	C₂×D₃₅₆	—	4	1	no	—
104	C₂×D₃₅₆	—	4	1	no	—
105	C₂×D₃₅₆	—	4	1	no	—
106	C₂×D₃₅₆	—	8	2	no	—
107	C₂×D₃₅₆	—	8	2	no	—
108	C₂²×Dic₈₉	—	4	1	no	—
109	#13083563	—	4	4	no	—
110	#13083563	—	4	4	no	—
111	#13083563	—	4	4	no	—
112	#13083563	—	4	4	no	—
113	#13083561	—	8	4	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₄⋊Dic₈₉	—	2	2	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	C₄⋊Dic₈₉	—	4	1	no	—
119	C₄⋊Dic₈₉	—	4	1	no	—
120	C₂×Q₈×C₈₉	—	2	1	no	—
121	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
125	M₁₆×C₈₉	—	4	2	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	SD₁₆	1	4	yes	complemented
129	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	1	no	—
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	—	2	2	no	—
141	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₈₉	#41	1	1	yes	characteristic
144	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂³×C₈₉	#121	1	1	yes	characteristic
146	C₂²×D₈₉	—	4	2	no	—
147	C₂²×D₈₉	—	8	2	no	—
148	C₂²×D₈₉	—	8	2	no	—
149	C₂²×D₈₉	—	8	2	no	—
150	Q₈×C₈₉	—	2	4	no	—
151	Q₈×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₈₉	—	4	2	no	—
165	C₂×Dic₈₉	—	8	2	no	—
166	D₃₅₆	—	4	2	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	4	4	no	—
169	D₃₅₆	—	8	2	no	—
170	D₃₅₆	—	8	2	no	—
171	D₃₅₆	—	8	2	no	—
172	D₃₅₆	—	8	2	no	—
173	Dic₁₇₈	—	4	2	no	—
174	Dic₁₇₈	—	4	2	no	—
175	Dic₁₇₈	—	8	2	no	—
176	C₈×C₈₉	—	2	1	no	—
177	C₈×C₈₉	—	2	1	no	—
178	C₈×C₈₉	—	4	2	no	—
179	C₈×C₈₉	C₂×SD₁₆	1	2	yes	—
180	C₈×C₈₉	C₂×SD₁₆	1	2	yes	—
181	#10623494	—	4	2	no	—
182	#10623494	—	4	2	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	#460	1	2	yes	—
186	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
187	C₂×D₈₉	—	8	2	no	—
188	C₂×D₈₉	—	8	2	no	—
189	C₂×D₈₉	—	8	2	no	—
190	C₂×D₈₉	—	16	4	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	4	2	no	—
194	C₄×C₈₉	—	4	2	no	—
195	C₄×C₈₉	#460	1	2	yes	—
196	C₄×C₈₉	#471	1	2	yes	—
197	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
198	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₈₉	#577	1	2	yes	—
200	Dic₈₉	—	8	2	no	—
201	#19202	—	89	1	no	maximal, Sylow
202	C₂×C₈₉	—	2	2	no	—
203	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
204	C₂×C₈₉	#3057	1	1	yes	characteristic
205	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
206	D₈₉	—	16	2	no	—
207	#3229	—	89	1	no	—
208	#3208	—	89	1	no	—
209	C₂×#492	—	89	1	no	—
210	#2960	D₈₉	1	1	yes	characteristic, complemented
211	#1686	—	89	4	no	—
212	#1666	—	89	4	no	—
213	#1564	—	89	1	no	—
214	#1546	—	89	1	no	—
215	#1545	—	89	1	no	—
216	C₈₉	#19202	1	1	yes	characteristic, complemented, Sylow
217	C₂²×SD₁₆	—	178	1	no	—
218	C₂²×SD₁₆	—	178	1	no	—
219	#533	C₂×D₈₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	—	89	1	no	—
221	C₂×#127	—	89	1	no	—
222	#498	—	178	1	no	—
223	#492	—	89	2	no	—
224	#492	—	89	2	no	—
225	#492	—	178	1	no	—
226	#492	—	178	1	no	—
227	#492	—	178	1	no	—
228	#487	—	178	1	no	—
229	#486	—	178	1	no	—
230	#483	—	178	2	no	—
231	#475	—	89	4	no	—
232	#460	—	89	4	no	—
233	#450	—	178	2	no	—
234	#446	—	2	1	no	—
235	#446	C₂×D₈₉	1	2	yes	complemented
236	C₈×Q₈	—	2	1	no	—
237	C₈×Q₈	C₂×D₈₉	1	2	yes	complemented
238	#431	—	89	1	no	—
239	#431	—	89	1	no	—
240	#424	—	2	1	no	—
241	#423	C₂×D₈₉	1	1	yes	characteristic
242	#405	—	2	1	no	—
243	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
244	#335	—	89	2	no	—
245	#334	—	89	2	no	—
246	#332	—	89	4	no	—
247	#331	—	89	4	no	—
248	C₂²×Q₈	—	178	1	no	—
249	C₂²×D₄	—	178	1	no	—
250	C₂²×D₄	—	178	1	no	—
251	C₂²×D₄	—	178	1	no	—
252	C₂×SD₁₆	—	356	4	no	—
253	C₂×SD₁₆	—	356	4	no	—
254	C₂×SD₁₆	—	178	4	no	—
255	C₂×SD₁₆	—	178	2	no	—
256	C₂×SD₁₆	—	178	2	no	—
257	C₂×SD₁₆	—	178	2	no	—
258	C₂×SD₁₆	—	178	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
261	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
262	C₄⋊Q₈	—	89	2	no	—
263	C₄⋊Q₈	—	178	1	no	—
264	C₄⋊Q₈	—	178	1	no	—
265	C₄⋊Q₈	—	178	1	no	—
266	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
267	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
268	#127	—	89	2	no	—
269	#127	—	178	1	no	—
270	#127	—	178	1	no	—
271	#127	—	178	1	no	—
272	#125	—	2	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	D₃₅₆	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
277	#117	—	2	1	no	—
278	C₂×C₄⋊C₄	—	178	1	no	—
279	C₂×C₄⋊C₄	—	178	1	no	—
280	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
281	#106	—	178	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	89	2	no	—
286	C₄⋊C₈	—	89	2	no	—
287	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
288	#103	—	178	4	no	—
289	#102	—	178	4	no	—
290	C₂²⋊C₈	—	178	1	no	—
291	C₂²⋊C₈	—	178	1	no	—
292	#97	—	2	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	178	1	no	—
295	C₄×C₈	—	178	1	no	—
296	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
297	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₂⁴	—	356	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	356	1	no	—
303	C₂×Q₈	—	356	2	no	—
304	C₂×Q₈	—	356	2	no	—
305	C₂×Q₈	—	178	2	no	—
306	C₂×Q₈	C₂×D₃₅₆	1	2	yes	—
307	C₂×D₄	—	356	1	no	—
308	C₂×D₄	—	356	1	no	—
309	C₂×D₄	—	356	1	no	—
310	C₂×D₄	—	356	2	no	—
311	C₂×D₄	—	356	2	no	—
312	C₂×D₄	—	178	2	no	—
313	C₂×D₄	—	178	2	no	—
314	C₂×D₄	—	178	2	no	—
315	C₂×D₄	—	712	2	no	—
316	C₂×D₄	—	712	2	no	—
317	C₂²×C₄	—	356	1	no	—
318	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
320	C₂²×C₄	#13083574	1	1	yes	characteristic
321	SD₁₆	—	356	4	no	—
322	SD₁₆	—	356	4	no	—
323	SD₁₆	—	356	4	no	—
324	SD₁₆	—	356	4	no	—
325	SD₁₆	—	712	4	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	178	2	no	—
330	C₂×C₈	—	178	2	no	—
331	C₂×C₈	#13083561	1	4	yes	complemented
332	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	356	1	no	—
342	C₄⋊C₄	—	356	1	no	—
343	C₄⋊C₄	—	178	2	no	—
344	C₄⋊C₄	—	178	2	no	—
345	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
349	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
350	C₄²	#13083574	1	1	yes	characteristic
351	C₄²	C₂³×D₈₉	1	1	yes	characteristic
352	C₂³	—	356	2	no	—
353	C₂³	—	712	2	no	—
354	C₂³	—	712	2	no	—
355	C₂³	—	712	2	no	—
356	C₂³	#15667986	1	1	yes	characteristic
357	Q₈	—	2	4	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	356	2	no	—
360	Q₈	—	356	2	no	—
361	Q₈	—	712	2	no	—
362	D₄	—	356	2	no	—
363	D₄	—	356	4	no	—
364	D₄	—	356	2	no	—
365	D₄	—	712	2	no	—
366	D₄	—	712	2	no	—
367	D₄	—	712	2	no	—
368	D₄	—	712	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	356	2	no	—
374	C₂×C₄	—	712	2	no	—
375	C₂×C₄	#15667986	1	1	yes	characteristic
376	C₂×C₄	#15667986	1	1	yes	characteristic
377	C₂×C₄	#15667986	1	1	yes	characteristic
378	C₂×C₄	C₂×#13083561	1	2	yes	—
379	C₂×C₄	#15668037	1	2	yes	—
380	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
382	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	356	2	no	—
387	C₈	—	356	2	no	—
388	C₈	C₂×#13083561	1	2	yes	—
389	C₈	C₂×#13083561	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	1424	4	no	—
393	C₂²	—	712	2	no	—
394	C₂²	—	712	2	no	—
395	C₂²	—	712	2	no	—
396	C₂²	#19151798	1	2	yes	—
397	C₂²	C₂×#15667986	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	712	2	no	—
403	C₄	#19151798	1	2	yes	—
404	C₄	#19151861	1	2	yes	—
405	C₄	C₂²×#13083561	1	1	yes	characteristic
406	C₄	C₂×#15668037	1	1	yes	characteristic
407	C₄	#19152410	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	1424	2	no	—
410	C₂	C₂×#19151798	1	1	yes	characteristic
411	C₂	#26029891	1	1	yes	characteristic
412	C₂	C₂×#19151861	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2960	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#15668009	C₂²
hypercenter	#2960	D₈₉
hypocenter	C₈₉	#19202
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #26031393	C₂	semidirect
4. #26019724	C₂	semidirect
5. #26019600	C₂	semidirect
6. #26019000	C₂	semidirect
7. #26018925	C₂	semidirect
9. C₈₉×#2960	C₂	semidirect
23. #19151883	C₂²	semidirect
28. #19151351	C₂²	semidirect
29. #19151349	C₂²	semidirect
30. #19151345	C₂²	semidirect
34. #446×C₈₉	C₂²	semidirect
36. C₈×Q₈×C₈₉	C₂²	semidirect
128. C₂×C₈×C₈₉	SD₁₆	semidirect
210. #2960	D₈₉	semidirect
216. C₈₉	#19202	semidirect
235. #446	C₂×D₈₉	semidirect
237. C₈×Q₈	C₂×D₈₉	semidirect
331. C₂×C₈	#13083561	semidirect

Maximal subgroups

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

subgroup	index
#26031393	2
#26031190	2
C₂×#19151971	2
#26019724	2
#26019600	2
#26019000	2
#26018925	2
#26018921	2
C₈₉×#2960	2
#19202	89