Subgroups — #36574125

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028918	C₂	1	2	yes	maximal, complemented
2	#26021141	C₂	1	2	yes	maximal
3	#26020902	C₂	1	4	yes	maximal, complemented
4	#26020424	C₂	1	1	yes	maximal, characteristic, complemented
5	#26020272	C₂	1	2	yes	maximal, complemented
6	#26020133	C₂	1	2	yes	maximal, complemented
7	C₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic
9	#19151659	—	2	4	no	—
10	#19151655	—	2	2	no	—
11	#19151651	—	2	2	no	—
12	C₂×#15667948	C₂²	1	2	yes	—
13	C₂×#15667948	C₂²	1	2	yes	—
14	#19151622	C₂²	1	2	yes	—
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×#15667939	C₂²	1	4	yes	—
17	#19151565	C₂²	1	4	yes	—
18	#19151554	C₂²	1	4	yes	—
19	C₂×C₈×Dic₈₉	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
21	#19151357	C₂²	1	4	yes	—
22	#19151352	C₂²	1	2	yes	—
23	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
24	C₄×#41×C₈₉	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
26	C₄×Q₁₆×C₈₉	C₄	1	1	yes	characteristic, complemented
27	C₄×SD₁₆×C₈₉	C₄	1	2	yes	complemented
28	C₄×SD₁₆×C₈₉	C₄	1	2	yes	complemented
29	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
30	C₄×D₈×C₈₉	C₄	1	1	yes	characteristic, complemented
31	#427×C₈₉	C₂²	1	1	yes	characteristic
32	#416×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#13083558	C₂³	1	4	yes	—
35	C₂²×#10623494	C₂³	1	2	yes	—
36	C₂×C₄⋊Dic₈₉	—	2	1	no	—
37	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
38	#15667948	—	2	4	no	—
39	#15667948	—	4	2	no	—
40	C₄⋊#10623494	—	2	2	no	—
41	C₄⋊#10623494	—	2	2	no	—
42	C₄⋊#10623494	D₄	1	1	yes	characteristic
43	C₄⋊#10623494	D₄	1	1	yes	characteristic
44	C₄⋊#10623494	D₄	1	2	yes	—
45	#15667939	—	4	4	no	—
46	C₂²⋊#10623494	—	2	4	no	—
47	C₂²⋊#10623494	—	2	4	no	—
48	#15667923	—	2	4	no	—
49	C₄×#10623494	—	2	4	no	—
50	C₈×Dic₈₉	—	2	4	no	—
51	#15667919	—	2	1	no	—
52	C₂×#41×C₈₉	C₂³	1	2	yes	—
53	#135×C₈₉	—	2	2	no	—
54	#135×C₈₉	—	2	2	no	—
55	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
57	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₈₉	—	2	2	no	—
63	C₄×D₄×C₈₉	—	2	2	no	—
64	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
66	#117×C₈₉	—	2	2	no	—
67	#117×C₈₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₈₉	—	2	2	no	—
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
71	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
72	#106×C₈₉	C₂×C₄	1	2	yes	—
73	#103×C₈₉	C₂×C₄	1	2	yes	—
74	#103×C₈₉	C₂×C₄	1	2	yes	—
75	#102×C₈₉	C₂×C₄	1	2	yes	—
76	#102×C₈₉	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₂²×Dic₈₉	—	2	2	no	—
82	#13083558	—	2	4	no	—
83	#13083558	—	2	4	no	—
84	C₂×#10623494	—	2	2	no	—
85	C₂×#10623494	—	2	2	no	—
86	C₂×#10623494	—	2	4	no	—
87	C₂×#10623494	C₂×D₄	1	2	yes	—
88	C₂×#10623494	C₂×D₄	1	2	yes	—
89	C₄⋊Dic₈₉	—	2	4	no	—
90	C₄×Dic₈₉	—	2	2	no	—
91	C₄×Dic₈₉	—	2	2	no	—
92	#41×C₈₉	—	2	2	no	—
93	#41×C₈₉	—	2	2	no	—
94	#41×C₈₉	—	2	2	no	—
95	#41×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₈₉	—	2	2	no	—
98	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₈₉	—	2	2	no	—
100	C₂²×C₄×C₈₉	—	2	2	no	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
105	Q₁₆×C₈₉	—	2	2	no	—
106	SD₁₆×C₈₉	—	2	4	no	—
107	D₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	—	2	1	no	—
109	C₂×C₈×C₈₉	—	2	1	no	—
110	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	#41	1	2	yes	—
115	C₂×C₈×C₈₉	#41	1	2	yes	—
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
120	C₂²⋊C₄×C₈₉	—	2	2	no	—
121	C₂²⋊C₄×C₈₉	—	2	2	no	—
122	C₂²⋊C₄×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	—	2	2	no	—
126	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂³×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
132	Q₈×C₈₉	—	2	2	no	—
133	Q₈×C₈₉	—	2	2	no	—
134	D₄×C₈₉	—	2	2	no	—
135	D₄×C₈₉	—	2	2	no	—
136	D₄×C₈₉	—	4	2	no	—
137	D₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	4	1	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	4	no	—
146	C₂×C₄×C₈₉	—	8	2	no	—
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
156	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
157	C₂×Dic₈₉	—	2	4	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	—	4	2	no	—
160	C₈×C₈₉	—	2	1	no	—
161	C₈×C₈₉	—	2	1	no	—
162	C₈×C₈₉	#117	1	2	yes	—
163	C₈×C₈₉	#117	1	2	yes	—
164	#10623494	—	2	2	no	—
165	#10623494	—	2	2	no	—
166	#10623494	—	4	4	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	4	2	no	—
170	C₂²×C₈₉	—	4	2	no	—
171	C₂²×C₈₉	—	4	2	no	—
172	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
173	C₂²×C₈₉	#555	1	1	yes	characteristic
174	C₂²×C₈₉	#556	1	1	yes	characteristic
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	4	2	no	—
179	C₄×C₈₉	—	4	2	no	—
180	C₄×C₈₉	—	4	2	no	—
181	C₄×C₈₉	#443	1	2	yes	—
182	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
183	C₄×C₈₉	#520	1	1	yes	characteristic
184	C₄×C₈₉	#547	1	1	yes	characteristic
185	C₄×C₈₉	#550	1	1	yes	characteristic
186	Dic₈₉	—	4	4	no	—
187	#22802	—	89	1	no	maximal, Sylow
188	C₂×C₈₉	—	2	1	no	—
189	C₂×C₈₉	—	2	1	no	—
190	C₂×C₈₉	—	8	2	no	—
191	C₂×C₈₉	#2354	1	1	yes	characteristic
192	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
193	C₂×C₈₉	#2957	1	1	yes	characteristic
194	C₄×#135	D₈₉	1	1	yes	characteristic
195	#2925	—	89	2	no	—
196	#1974	—	89	2	no	—
197	#1929	—	89	4	no	—
198	#1848	—	89	1	no	—
199	#1806	—	89	2	no	—
200	#1772	—	89	2	no	—
201	C₈×C₄⋊C₄	—	89	1	no	—
202	C₈₉	#22802	1	1	yes	characteristic, complemented, Sylow
203	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
204	C₄×#41	C₂×D₈₉	1	2	yes	—
205	C₄×Q₁₆	Dic₈₉	1	1	yes	characteristic, complemented
206	C₄×Q₁₆	Dic₈₉	1	1	yes	characteristic, complemented
207	C₄×SD₁₆	Dic₈₉	1	2	yes	complemented
208	C₄×SD₁₆	Dic₈₉	1	2	yes	complemented
209	C₄×D₈	Dic₈₉	1	1	yes	characteristic, complemented
210	C₄×D₈	Dic₈₉	1	1	yes	characteristic, complemented
211	#433	—	178	4	no	—
212	#432	—	178	2	no	—
213	#431	—	178	2	no	—
214	C₂×#108	—	89	2	no	—
215	C₂×#108	—	89	2	no	—
216	#427	C₂×D₈₉	1	1	yes	characteristic
217	#423	—	89	2	no	—
218	C₂×C₄⋊C₈	—	89	1	no	—
219	C₂×#104	—	89	4	no	—
220	#416	C₂×D₈₉	1	2	yes	—
221	#408	—	89	4	no	—
222	#405	—	89	4	no	—
223	C₂×C₄×C₈	—	89	2	no	—
224	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
225	C₄×C₄⋊C₄	—	89	1	no	—
226	#339	—	89	4	no	—
227	#336	—	89	2	no	—
228	C₂×#41	C₂²×D₈₉	1	2	yes	—
229	#135	—	2	2	no	—
230	#135	—	2	2	no	—
231	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic
232	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
233	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic
234	C₂×M₁₆	—	89	4	no	—
235	C₂²×C₈	—	89	2	no	—
236	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
237	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
238	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
239	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
240	C₄×D₄	—	2	2	no	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
243	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
244	#117	—	2	2	no	—
245	#117	C₂²×D₈₉	1	2	yes	—
246	C₂×C₄⋊C₄	—	178	1	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	89	2	no	—
249	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
250	#108	—	356	2	no	—
251	#108	—	178	4	no	—
252	#107	C₂×Dic₈₉	1	1	yes	characteristic
253	#107	C₂×Dic₈₉	1	1	yes	characteristic
254	#106	C₂×Dic₈₉	1	2	yes	—
255	C₄⋊C₈	—	89	1	no	—
256	C₄⋊C₈	—	89	1	no	—
257	C₄⋊C₈	—	89	2	no	—
258	C₄⋊C₈	—	178	2	no	—
259	C₄⋊C₈	—	178	2	no	—
260	#104	—	356	4	no	—
261	#103	C₂×Dic₈₉	1	2	yes	—
262	#103	C₂×Dic₈₉	1	2	yes	—
263	#102	C₂×Dic₈₉	1	2	yes	—
264	#102	C₂×Dic₈₉	1	2	yes	—
265	C₂²⋊C₈	—	178	4	no	—
266	C₂²⋊C₈	—	178	4	no	—
267	#97	—	178	4	no	—
268	C₄×C₈	—	178	4	no	—
269	C₄×C₈	—	178	4	no	—
270	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
271	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
272	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
273	C₄×C₈	C₂×Dic₈₉	1	1	yes	characteristic
274	#95	—	178	1	no	—
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	#41	—	2	2	no	—
278	#41	—	2	2	no	—
279	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	178	2	no	—
286	C₂²×C₄	#13083573	1	1	yes	characteristic
287	C₂²×C₄	#13083573	1	1	yes	characteristic
288	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	SD₁₆	—	2	4	no	—
291	D₈	—	2	2	no	—
292	M₁₆	—	178	4	no	—
293	M₁₆	—	178	4	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	89	2	no	—
297	C₂×C₈	—	89	2	no	—
298	C₂×C₈	—	178	4	no	—
299	C₂×C₈	—	178	2	no	—
300	C₂×C₈	—	178	2	no	—
301	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
302	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
305	C₂×C₈	#13083574	1	2	yes	—
306	C₂×C₈	#13083574	1	2	yes	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	178	4	no	—
310	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
311	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	178	2	no	—
319	C₄²	—	178	2	no	—
320	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
321	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
322	C₄²	D₄×D₈₉	1	1	yes	characteristic
323	C₄²	D₄×D₈₉	1	1	yes	characteristic
324	C₂³	—	2	2	no	—
325	C₂³	C₂×#13083573	1	1	yes	characteristic
326	Q₈	—	2	2	no	—
327	Q₈	—	2	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	—	356	2	no	—
342	C₂×C₄	—	356	2	no	—
343	C₂×C₄	—	178	4	no	—
344	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
345	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
346	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
347	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
348	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
350	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
351	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
352	C₂×C₄	#15668058	1	1	yes	characteristic
353	C₂×C₄	#15668059	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	356	4	no	—
357	C₈	—	178	2	no	—
358	C₈	—	178	2	no	—
359	C₈	#15667971	1	2	yes	—
360	C₈	#15667971	1	2	yes	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
367	C₂²	#19152313	1	1	yes	characteristic
368	C₂²	#19152318	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	—	356	4	no	—
376	C₄	#19151715	1	2	yes	—
377	C₄	C₂×#15667971	1	1	yes	characteristic
378	C₄	#19152081	1	1	yes	characteristic
379	C₄	#19152253	1	1	yes	characteristic
380	C₄	#19152269	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	8	2	no	—
384	C₂	#26023201	1	1	yes	characteristic
385	C₂	C₂×#19151715	1	1	yes	characteristic
386	C₂	#26029169	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#135×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#135×C₈₉	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₄×#135	D₈₉
hypocenter	C₈₉	#22802
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #26028918	C₂	semidirect
3. #26020902	C₂	semidirect
4. #26020424	C₂	semidirect
5. #26020272	C₂	semidirect
6. #26020133	C₂	semidirect
7. C₈×C₄⋊Dic₈₉	C₂	semidirect
25. C₄×Q₁₆×C₈₉	C₄	semidirect
26. C₄×Q₁₆×C₈₉	C₄	semidirect
27. C₄×SD₁₆×C₈₉	C₄	semidirect
28. C₄×SD₁₆×C₈₉	C₄	semidirect
29. C₄×D₈×C₈₉	C₄	semidirect
30. C₄×D₈×C₈₉	C₄	semidirect
202. C₈₉	#22802	semidirect
205. C₄×Q₁₆	Dic₈₉	semidirect
206. C₄×Q₁₆	Dic₈₉	semidirect
207. C₄×SD₁₆	Dic₈₉	semidirect
208. C₄×SD₁₆	Dic₈₉	semidirect
209. C₄×D₈	Dic₈₉	semidirect
210. C₄×D₈	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028918	2
#26021141	2
#26020902	2
#26020424	2
#26020272	2
#26020133	2
C₈×C₄⋊Dic₈₉	2
C₄×#135×C₈₉	2
#22802	89