Subgroups — #36707667

Order 22784.

646 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152014	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029153	C₂	1	1	yes	maximal, characteristic
3	#26022092	C₂	1	4	yes	maximal, complemented
4	#26022087	C₂	1	4	yes	maximal, complemented
5	#26022017	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021881	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021880	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021848	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#504×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#19152396	C₄	1	1	yes	characteristic
11	C₂×#15668018	C₂²	1	1	yes	characteristic
12	#19152014	—	2	1	no	—
13	#19152014	—	2	1	no	—
14	#19152014	C₂²	1	2	yes	complemented
15	#19152014	C₂²	1	2	yes	complemented
16	C₂×#15667952	C₂²	1	1	yes	characteristic
17	C₂×#15667952	C₂²	1	1	yes	characteristic
18	C₂×#15667951	—	2	1	no	—
19	C₂×C₁₆×D₈₉	—	2	1	no	—
20	#19151718	C₄	1	4	yes	—
21	#19151713	C₂²	1	4	yes	—
22	#19151646	C₄	1	1	yes	characteristic
23	#19151615	C₄	1	1	yes	characteristic
24	#19151614	C₄	1	1	yes	characteristic
25	#19151553	C₂²	1	1	yes	characteristic
26	#19151418	C₂²	1	4	yes	complemented
27	#19151383	C₂²	1	4	yes	complemented
28	#19151382	C₂²	1	4	yes	complemented
29	#19151373	C₂²	1	2	yes	complemented
30	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
31	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
32	#504×C₈₉	—	2	1	no	—
33	#504×C₈₉	—	2	1	no	—
34	#504×C₈₉	C₂²	1	2	yes	complemented
35	#504×C₈₉	C₂²	1	2	yes	complemented
36	C₂×M₃₂×C₈₉	—	2	1	no	—
37	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₁₆×C₈₉	—	2	1	no	—
39	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
41	#15668043	C₈	1	2	yes	—
42	#15668042	C₈	1	2	yes	—
43	#15668038	C₈	1	2	yes	—
44	#15668037	C₈	1	2	yes	—
45	#15668032	C₂×C₄	1	4	yes	—
46	#15668018	—	2	1	no	—
47	#15668018	—	2	1	no	—
48	#15668018	C₂×C₄	1	2	yes	—
49	#15668018	C₂³	1	2	yes	—
50	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
51	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
52	C₂×#13083557	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	1	no	—
54	#15667971	C₂×C₄	1	1	yes	characteristic
55	#15667952	—	2	1	no	—
56	#15667952	—	2	1	no	—
57	#15667952	—	2	1	no	—
58	#15667952	C₂³	1	2	yes	—
59	#15667951	—	2	2	no	—
60	#15667951	—	2	2	no	—
61	C₂×#13083549	—	2	1	no	—
62	C₂×#13083549	C₂³	1	2	yes	—
63	C₁₆×D₈₉	—	2	2	no	—
64	C₁₆×D₈₉	—	2	2	no	—
65	#15667947	C₂×C₄	1	4	yes	—
66	#15667939	C₂×C₄	1	4	yes	—
67	#15667938	C₂×C₄	1	4	yes	—
68	#15667922	C₂×C₄	1	2	yes	—
69	C₈×Dic₈₉	C₂³	1	2	yes	—
70	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
71	#131×C₈₉	—	2	1	no	—
72	#131×C₈₉	—	2	1	no	—
73	#131×C₈₉	C₂×C₄	1	2	yes	—
74	#131×C₈₉	C₂³	1	2	yes	—
75	C₂×M₁₆×C₈₉	—	2	1	no	—
76	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	—	2	1	no	—
78	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
79	M₃₂×C₈₉	—	2	1	no	—
80	M₃₂×C₈₉	—	2	2	no	—
81	M₃₂×C₈₉	—	2	2	no	—
82	M₃₂×C₈₉	C₂³	1	2	yes	—
83	C₂×C₁₆×C₈₉	—	2	1	no	—
84	C₂×C₁₆×C₈₉	—	2	2	no	—
85	C₂×C₁₆×C₈₉	—	2	2	no	—
86	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
87	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
88	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
89	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
91	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
92	#13083574	—	2	1	no	—
93	#13083574	—	2	1	no	—
94	#13083574	C₂×C₈	1	2	yes	—
95	#13083574	C₂²×C₄	1	2	yes	—
96	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
97	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
98	C₂×C₂²⋊D₈₉	—	2	1	no	—
99	C₂×C₄×D₈₉	—	2	1	no	—
100	#13083564	C₂×C₈	1	4	yes	—
101	#13083562	C₂×C₈	1	4	yes	—
102	#13083561	C₂×C₈	1	4	yes	—
103	#13083559	C₂×C₈	1	4	yes	—
104	#13083558	—	2	1	no	—
105	#13083558	C₂×C₈	1	2	yes	—
106	#13083558	C₂×C₈	1	2	yes	—
107	#13083558	C₂²×C₄	1	2	yes	—
108	#13083557	—	2	2	no	—
109	#13083557	—	2	2	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	C₂²×C₄	1	2	yes	—
112	C₈×D₈₉	—	2	2	no	—
113	C₈×D₈₉	—	2	2	no	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₂²⋊Dic₈₉	—	2	1	no	—
116	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
117	#13083549	—	2	2	no	—
118	#13083549	—	2	2	no	—
119	#41×C₈₉	—	2	1	no	—
120	#41×C₈₉	—	2	1	no	—
121	#41×C₈₉	C₂×C₈	1	2	yes	—
122	#41×C₈₉	C₂²×C₄	1	2	yes	—
123	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
124	C₂×D₄×C₈₉	—	2	1	no	—
125	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	—	2	1	no	—
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	M₁₆×C₈₉	—	2	1	no	—
129	M₁₆×C₈₉	—	2	2	no	—
130	M₁₆×C₈₉	—	2	2	no	—
131	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
139	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₁₆×C₈₉	—	2	2	no	—
142	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₈₉	—	2	1	no	—
147	C₂³×C₈₉	#131	1	1	yes	characteristic
148	C₂²×D₈₉	—	2	1	no	—
149	Q₈×C₈₉	—	2	1	no	—
150	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
151	D₄×C₈₉	—	2	2	no	—
152	D₄×C₈₉	—	2	2	no	—
153	D₄×C₈₉	—	2	1	no	—
154	D₄×C₈₉	C₂²×C₈	1	2	yes	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#131	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
164	C₂²⋊D₈₉	—	2	2	no	—
165	C₂²⋊D₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	D₃₅₆	—	2	1	no	—
169	D₃₅₆	C₂²×C₈	1	2	yes	—
170	C₄×D₈₉	—	2	2	no	—
171	C₄×D₈₉	—	2	2	no	—
172	Dic₁₇₈	—	2	1	no	—
173	Dic₁₇₈	C₂²×C₈	1	2	yes	—
174	C₈×C₈₉	—	2	2	no	—
175	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
176	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
177	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
179	#10623494	—	2	2	no	—
180	#10623494	C₂²×C₈	1	4	yes	—
181	C₂²×C₈₉	—	2	2	no	—
182	C₂²×C₈₉	—	4	1	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	C₈×D₄	1	1	yes	characteristic
185	C₂²×C₈₉	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
187	C₂×D₈₉	—	2	2	no	—
188	C₂×D₈₉	—	4	2	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	C₈×D₄	1	1	yes	characteristic
191	C₄×C₈₉	C₈×D₄	1	1	yes	characteristic
192	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
194	Dic₈₉	—	2	2	no	—
195	Dic₈₉	—	4	2	no	—
196	#33441	—	89	1	no	maximal, Sylow
197	C₂×C₈₉	—	2	1	no	—
198	C₂×C₈₉	—	2	1	no	—
199	C₂×C₈₉	—	2	1	no	—
200	C₂×C₈₉	—	4	2	no	—
201	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
202	D₈₉	—	4	2	no	—
203	C₂×#504	—	89	1	no	—
204	C₂×#504	D₈₉	1	1	yes	characteristic, complemented
205	#2955	—	89	1	no	—
206	#2171	—	89	4	no	—
207	#2170	—	89	4	no	—
208	#2153	—	89	1	no	—
209	#2117	—	89	1	no	—
210	#2117	—	89	1	no	—
211	#2108	—	89	1	no	—
212	C₈₉	#33441	1	1	yes	characteristic, complemented, Sylow
213	#575	—	89	1	no	—
214	C₂×#131	—	89	1	no	—
215	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
216	#504	—	2	1	no	—
217	#504	—	2	1	no	—
218	#504	—	89	2	no	—
219	#504	—	89	2	no	—
220	#504	—	178	1	no	—
221	#504	—	178	1	no	—
222	#504	C₂×D₈₉	1	2	yes	complemented
223	#504	C₂×D₈₉	1	2	yes	complemented
224	C₂×M₃₂	—	2	1	no	—
225	C₂×M₃₂	—	89	1	no	—
226	C₂×M₃₂	—	89	1	no	—
227	C₂×M₃₂	—	178	1	no	—
228	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
229	C₂²×C₁₆	—	2	1	no	—
230	C₂²×C₁₆	—	178	1	no	—
231	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
232	#444	—	89	4	no	—
233	#443	—	89	4	no	—
234	#430	—	89	1	no	—
235	#421	—	89	1	no	—
236	#421	—	89	1	no	—
237	#405	—	89	1	no	—
238	#364	—	89	4	no	—
239	#350	—	89	4	no	—
240	#350	—	89	4	no	—
241	#346	—	89	2	no	—
242	C₄×C₁₆	—	89	2	no	—
243	C₂×#41	—	89	1	no	—
244	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
245	#137	—	89	2	no	—
246	#137	—	89	2	no	—
247	AGL(1,ℤ/8)	—	89	2	no	—
248	AGL(1,ℤ/8)	—	89	2	no	—
249	#135	—	89	4	no	—
250	#131	—	2	1	no	—
251	#131	—	2	1	no	—
252	#131	—	89	2	no	—
253	#131	—	89	2	no	—
254	#131	—	178	1	no	—
255	#131	—	178	1	no	—
256	#131	C₄×D₈₉	1	2	yes	—
257	#131	C₂²×D₈₉	1	2	yes	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	89	1	no	—
260	C₂×M₁₆	—	89	1	no	—
261	C₂×M₁₆	—	178	1	no	—
262	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	178	1	no	—
265	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
266	#117	—	89	1	no	—
267	M₃₂	—	2	1	no	—
268	M₃₂	—	2	2	no	—
269	M₃₂	—	2	2	no	—
270	M₃₂	—	89	2	no	—
271	M₃₂	—	178	1	no	—
272	M₃₂	—	178	1	no	—
273	M₃₂	—	178	1	no	—
274	M₃₂	—	178	2	no	—
275	M₃₂	—	178	2	no	—
276	M₃₂	C₂²×D₈₉	1	2	yes	—
277	C₂×C₁₆	—	2	1	no	—
278	C₂×C₁₆	—	2	2	no	—
279	C₂×C₁₆	—	2	2	no	—
280	C₂×C₁₆	—	89	2	no	—
281	C₂×C₁₆	—	178	1	no	—
282	C₂×C₁₆	—	178	2	no	—
283	C₂×C₁₆	—	178	2	no	—
284	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
285	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
286	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
287	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
288	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
289	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
290	#108	—	89	4	no	—
291	#104	—	89	4	no	—
292	#104	—	89	4	no	—
293	#97	—	89	2	no	—
294	C₄×C₈	—	89	2	no	—
295	#41	—	2	1	no	—
296	#41	—	2	1	no	—
297	#41	—	89	2	no	—
298	#41	—	89	2	no	—
299	#41	—	178	1	no	—
300	#41	—	178	1	no	—
301	#41	C₈×D₈₉	1	2	yes	—
302	#41	C₂×C₄×D₈₉	1	2	yes	—
303	C₂×Q₈	—	89	1	no	—
304	C₂×Q₈	C₈×D₈₉	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	89	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	178	1	no	—
311	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
312	Q₁₆	—	89	4	no	—
313	SD₁₆	—	89	4	no	—
314	SD₁₆	—	89	4	no	—
315	D₈	—	89	4	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	89	2	no	—
320	M₁₆	—	89	2	no	—
321	M₁₆	—	89	2	no	—
322	M₁₆	—	178	1	no	—
323	M₁₆	—	178	2	no	—
324	M₁₆	—	178	2	no	—
325	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	89	2	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	2	no	—
332	C₂×C₈	—	178	2	no	—
333	C₂×C₈	C₂×C₄×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	C₂×C₈	#13083574	1	1	yes	characteristic
337	C₂×C₈	#13083574	1	1	yes	characteristic
338	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
339	C₄⋊C₄	—	178	1	no	—
340	C₂²⋊C₄	—	178	1	no	—
341	C₄²	—	89	2	no	—
342	C₁₆	—	2	2	no	—
343	C₁₆	—	178	2	no	—
344	C₁₆	—	178	2	no	—
345	C₁₆	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
346	C₁₆	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
347	C₁₆	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
348	C₁₆	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
349	C₂³	—	2	1	no	—
350	C₂³	—	178	1	no	—
351	C₂³	#15668018	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	89	2	no	—
354	Q₈	—	178	1	no	—
355	Q₈	C₂×C₈×D₈₉	1	2	yes	—
356	D₄	—	2	2	no	—
357	D₄	—	2	2	no	—
358	D₄	—	2	1	no	—
359	D₄	—	89	2	no	—
360	D₄	—	178	2	no	—
361	D₄	—	178	2	no	—
362	D₄	—	178	1	no	—
363	D₄	C₂×C₈×D₈₉	1	2	yes	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	178	1	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
372	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
373	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
375	C₂×C₄	#15668018	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	89	4	no	—
379	C₈	—	178	2	no	—
380	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
382	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
383	C₈	C₂×#13083574	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	356	2	no	—
388	C₂²	—	178	2	no	—
389	C₂²	C₈×C₂²⋊D₈₉	1	1	yes	characteristic
390	C₂²	C₈×C₂²⋊D₈₉	1	1	yes	characteristic
391	C₂²	C₂×#15668018	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	356	2	no	—
394	C₄	—	178	2	no	—
395	C₄	C₈×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₄	C₈×C₂²⋊D₈₉	1	1	yes	characteristic
397	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
398	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	2	no	—
403	C₂	—	356	2	no	—
404	C₂	C₂×C₈×C₂²⋊D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂×C₂²⋊D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#504×C₈₉	C₂
socle	C₂×C₈₉	C₂×C₈×D₄
prime radical	#19152396	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#504	D₈₉
hypocenter	C₈₉	#33441
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₁₆ ◁ C₂²×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#19152014	C₂	semidirect
3. #26022092	C₂	semidirect
4. #26022087	C₂	semidirect
5. #26022017	C₂	semidirect
6. #26021881	C₂	semidirect
7. #26021880	C₂	semidirect
8. #26021848	C₂	semidirect
9. C₂×#504×C₈₉	C₂	semidirect
14. #19152014	C₂²	semidirect
15. #19152014	C₂²	semidirect
26. #19151418	C₂²	semidirect
27. #19151383	C₂²	semidirect
28. #19151382	C₂²	semidirect
29. #19151373	C₂²	semidirect
30. C₁₆×Dic₈₉	C₂²	semidirect
34. #504×C₈₉	C₂²	semidirect
35. #504×C₈₉	C₂²	semidirect
204. C₂×#504	D₈₉	semidirect
212. C₈₉	#33441	semidirect
222. #504	C₂×D₈₉	semidirect
223. #504	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152014	2
#26029153	2
#26022092	2
#26022087	2
#26022017	2
#26021881	2
#26021880	2
#26021848	2
C₂×#504×C₈₉	2
#33441	89