Subgroups — #36552994

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×#19151719	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151716	C₂	1	1	yes	maximal, characteristic
3	#26029052	C₂	1	1	yes	maximal, characteristic
4	#26028674	C₂	1	2	yes	maximal, complemented
5	#26020160	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020093	C₂	1	2	yes	maximal, complemented
8	#26020091	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	#19151719	C₄	1	8	yes	complemented
17	#19151716	C₄	1	8	yes	complemented
18	#19151709	C₄	1	2	yes	complemented
19	#19151704	C₄	1	2	yes	complemented
20	#19151697	C₄	1	4	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	#19151550	—	2	2	no	—
29	M₁₆×Dic₈₉	C₂²	1	2	yes	—
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	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	—	2	2	no	—
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	C₂×C₄	1	2	yes	—
77	#15667922	C₂×C₄	1	2	yes	—
78	#15667922	C₂×C₄	1	4	yes	complemented
79	C₄×#10623494	—	2	2	no	—
80	C₈×Dic₈₉	—	2	2	no	—
81	C₈×Dic₈₉	—	2	2	no	—
82	C₈×Dic₈₉	D₄	1	2	yes	—
83	C₈×Dic₈₉	D₄	1	2	yes	—
84	#15667919	—	2	2	no	—
85	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	#117×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	#108×C₈₉	C₂×C₄	1	4	yes	complemented
91	#107×C₈₉	C₂×C₄	1	2	yes	—
92	#106×C₈₉	C₂×C₄	1	2	yes	—
93	#97×C₈₉	—	2	2	no	—
94	C₄×C₈×C₈₉	—	2	2	no	—
95	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	complemented
96	#13083574	—	2	2	no	—
97	#13083574	—	2	2	no	—
98	#13083574	C₂²×C₄	1	4	yes	—
99	#13083574	C₂²×C₄	1	4	yes	—
100	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
101	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₈₉	—	2	2	no	—
103	C₂²×Dic₈₉	—	2	1	no	—
104	C₂²×Dic₈₉	#41	1	2	yes	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	2	4	no	—
107	Dic₃₅₆	C₄²	1	4	yes	—
108	#13083563	C₄²	1	8	yes	—
109	D₇₁₂	C₄²	1	4	yes	—
110	#13083558	—	2	2	no	—
111	#13083558	C₂²×C₄	1	4	yes	—
112	#13083557	—	2	8	no	—
113	#13083557	—	2	8	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	C₂²×C₄	1	2	yes	—
118	C₂×#10623494	C₂²×C₄	1	2	yes	—
119	C₂×#10623494	C₂×D₄	1	2	yes	—
120	C₂×#10623494	#41	1	2	yes	—
121	C₈×D₈₉	—	2	8	no	—
122	C₈×D₈₉	—	2	8	no	—
123	#13083553	—	2	4	no	—
124	#13083551	—	2	4	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	4	no	—
127	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
128	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
129	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₈₉	—	2	1	no	—
131	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₈₉	—	2	2	no	—
133	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	#41	1	2	yes	—
143	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
144	C₂²⋊C₄×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	1	no	—
147	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
148	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
149	C₂²×D₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	4	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
159	C₂²⋊D₈₉	—	2	4	no	—
160	C₂²⋊D₈₉	—	2	4	no	—
161	C₂×Dic₈₉	—	2	2	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	—	4	2	no	—
164	C₂×Dic₈₉	—	4	2	no	—
165	C₂×Dic₈₉	C₄×D₄	1	4	yes	—
166	D₃₅₆	—	2	2	no	—
167	D₃₅₆	C₂×C₄²	1	4	yes	—
168	C₄×D₈₉	—	2	4	no	—
169	C₄×D₈₉	—	2	4	no	—
170	C₄×D₈₉	—	4	8	no	—
171	Dic₁₇₈	—	2	2	no	—
172	Dic₁₇₈	C₂×C₄²	1	4	yes	—
173	C₈×C₈₉	—	2	4	no	—
174	C₈×C₈₉	C₂×C₄²	1	2	yes	—
175	C₈×C₈₉	C₂×C₄²	1	2	yes	—
176	C₈×C₈₉	C₄×D₄	1	2	yes	—
177	C₈×C₈₉	C₄×D₄	1	2	yes	—
178	#10623494	—	2	4	no	—
179	#10623494	—	2	2	no	—
180	#10623494	C₄×D₄	1	4	yes	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
184	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
185	C₂×D₈₉	—	2	4	no	—
186	C₂×D₈₉	—	4	4	no	—
187	C₄×C₈₉	—	4	2	no	—
188	C₄×C₈₉	—	4	4	no	—
189	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
191	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
193	Dic₈₉	—	2	4	no	—
194	Dic₈₉	—	2	4	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	C₄²×D₄	1	1	yes	characteristic
200	C₂×C₈₉	#2955	1	2	yes	—
201	D₈₉	—	4	4	no	—
202	C₂×#444	—	89	1	no	—
203	C₂×#443	—	89	1	no	—
204	#2943	—	89	1	no	—
205	C₄×#131	—	89	2	no	—
206	#1778	—	89	1	no	—
207	#1773	—	89	1	no	—
208	#1772	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
215	C₂×#131	—	89	2	no	—
216	C₂×#131	—	89	2	no	—
217	C₄×#41	—	89	2	no	—
218	#444	—	89	8	no	—
219	#443	—	89	8	no	—
220	#442	—	89	2	no	—
221	#441	—	89	2	no	—
222	#440	—	89	4	no	—
223	C₂×#108	—	89	1	no	—
224	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
225	#427	C₂×D₈₉	1	1	yes	characteristic
226	C₂×#104	—	89	2	no	—
227	C₂×#104	—	89	2	no	—
228	#416	—	89	2	no	—
229	#405	—	89	2	no	—
230	#405	—	178	2	no	—
231	#405	—	178	2	no	—
232	#405	C₂×D₈₉	1	2	yes	—
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	—	89	1	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	C₂×C₄×C₈	—	178	2	no	—
241	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
242	#376	—	89	1	no	—
243	#341	—	89	2	no	—
244	#339	—	89	2	no	—
245	#339	C₂×D₈₉	1	2	yes	—
246	C₂×#41	—	89	2	no	—
247	#135	—	89	4	no	—
248	#135	—	89	4	no	—
249	C₂×Q₁₆	—	89	1	no	—
250	C₂×SD₁₆	—	89	2	no	—
251	C₂×D₈	—	89	1	no	—
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	—	178	2	no	—
258	C₂×M₁₆	—	178	2	no	—
259	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
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	—	89	4	no	—
267	C₄×D₄	—	89	4	no	—
268	C₄×D₄	—	178	4	no	—
269	#117	—	178	2	no	—
270	#117	C₂²×D₈₉	1	2	yes	—
271	C₂×C₄²	—	89	1	no	—
272	C₂×C₄²	—	89	1	no	—
273	C₂×C₄²	—	178	2	no	—
274	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
275	#108	—	89	4	no	—
276	#108	C₄×D₈₉	1	4	yes	complemented
277	#107	C₄×D₈₉	1	2	yes	—
278	#106	C₄×D₈₉	1	2	yes	—
279	#104	—	89	8	no	—
280	#104	—	89	8	no	—
281	#103	—	89	4	no	—
282	#102	—	89	4	no	—
283	#97	—	2	2	no	—
284	#97	—	89	2	no	—
285	#97	—	89	2	no	—
286	#97	—	89	4	no	—
287	#97	—	178	2	no	—
288	#97	—	178	2	no	—
289	#97	—	178	2	no	—
290	C₄×C₈	—	2	2	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	C₄×D₈₉	1	4	yes	complemented
297	#95	—	178	2	no	—
298	#41	—	89	4	no	—
299	#41	—	89	4	no	—
300	#41	—	178	2	no	—
301	#41	—	178	2	no	—
302	C₂×Q₈	—	89	2	no	—
303	C₂×D₄	—	89	2	no	—
304	C₂×D₄	—	178	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	89	2	no	—
307	C₂²×C₄	—	178	4	no	—
308	C₂²×C₄	—	178	1	no	—
309	C₂²×C₄	—	178	2	no	—
310	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
311	Q₁₆	—	89	4	no	—
312	SD₁₆	—	89	8	no	—
313	D₈	—	89	4	no	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	89	4	no	—
316	M₁₆	—	178	8	no	—
317	M₁₆	—	178	2	no	—
318	M₁₆	—	178	8	no	—
319	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	178	8	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	—	178	1	no	—
328	C₂×C₈	—	178	1	no	—
329	C₂×C₈	—	178	8	no	—
330	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
331	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
335	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
336	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
337	C₂×C₈	#13083575	1	2	yes	—
338	C₄⋊C₄	—	178	4	no	—
339	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	178	4	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	89	2	no	—
345	C₄²	—	89	2	no	—
346	C₄²	—	89	2	no	—
347	C₄²	—	178	4	no	—
348	C₄²	—	178	1	no	—
349	C₄²	C₂×C₄×D₈₉	1	2	yes	—
350	C₂³	—	178	2	no	—
351	C₂³	#41×D₈₉	1	1	yes	characteristic
352	Q₈	—	89	4	no	—
353	Q₈	—	178	2	no	—
354	D₄	—	89	4	no	—
355	D₄	—	178	4	no	—
356	D₄	—	178	4	no	—
357	D₄	—	178	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	89	4	no	—
362	C₂×C₄	—	356	8	no	—
363	C₂×C₄	—	356	2	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	178	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	4	no	—
368	C₂×C₄	—	178	4	no	—
369	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₄×D₈₉	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	C₂×#13083575	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	89	4	no	—
377	C₈	—	178	4	no	—
378	C₈	—	178	2	no	—
379	C₈	C₄²×D₈₉	1	2	yes	—
380	C₈	C₄²×D₈₉	1	2	yes	—
381	C₈	#15667974	1	2	yes	—
382	C₈	#15667974	1	2	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	356	4	no	—
385	C₂²	—	178	4	no	—
386	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
387	C₂²	#19152066	1	1	yes	characteristic
388	C₂²	C₄×#13083575	1	1	yes	characteristic
389	C₄	—	4	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	356	2	no	—
392	C₄	—	178	4	no	—
393	C₄	—	178	4	no	—
394	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
395	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
396	C₄	C₂×#15667974	1	1	yes	characteristic
397	C₄	C₄×#13083575	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	356	4	no	—
401	C₂	C₄×#15667974	1	1	yes	characteristic
402	C₂	#26029150	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	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	#20510
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. #26028674	C₂	semidirect
5. #26020160	C₂	semidirect
6. #26020138	C₂	semidirect
7. #26020093	C₂	semidirect
8. #26020091	C₂	semidirect
9. #26020061	C₂	semidirect
10. #26019938	C₂	semidirect
11. C₈₉×#1772	C₂	semidirect
16. #19151719	C₄	semidirect
17. #19151716	C₄	semidirect
18. #19151709	C₄	semidirect
19. #19151704	C₄	semidirect
20. #19151697	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
78. #15667922	C₂×C₄	semidirect
90. #108×C₈₉	C₂×C₄	semidirect
95. C₄×C₈×C₈₉	C₂×C₄	semidirect
208. #1772	D₈₉	semidirect
213. C₈₉	#20510	semidirect
276. #108	C₄×D₈₉	semidirect
296. 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×#19151719	2
C₂×#19151716	2
#26029052	2
#26028674	2
#26020160	2
#26020138	2
#26020093	2
#26020091	2
#26020061	2
#26019938	2
C₈₉×#1772	2
#20510	89