Subgroups — #36708821

Order 22784.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033386	C₂	1	2	yes	maximal, complemented
2	#26030680	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022333	C₂	1	2	yes	maximal, complemented
4	#26022328	C₂	1	2	yes	maximal, complemented
5	#26022321	C₂	1	4	yes	maximal, complemented
6	C₂×#19151419	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021999	C₂	1	2	yes	maximal, complemented
8	C₂×#443×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15668034	—	2	1	no	—
10	C₂×#15668034	C₂²	1	2	yes	—
11	#19152148	—	2	1	no	—
12	#19152039	—	2	2	no	—
13	#19152038	C₂²	1	4	yes	—
14	#19152034	—	2	2	no	—
15	#19152033	C₂²	1	4	yes	—
16	#19152028	—	2	4	no	—
17	C₂×#15667952	C₂²	1	2	yes	—
18	#19151982	—	2	1	no	—
19	#19151982	C₂²	1	2	yes	complemented
20	#19151978	C₂²	1	1	yes	characteristic, complemented
21	#19151975	C₂²	1	1	yes	characteristic, complemented
22	#19151971	—	2	1	no	—
23	#19151419	C₂²	1	2	yes	complemented
24	#19151419	C₂²	1	2	yes	complemented
25	#19151413	C₂²	1	4	yes	complemented
26	#19151410	C₂²	1	4	yes	complemented
27	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#131×C₈₉	—	2	1	no	—
29	#443×C₈₉	—	2	1	no	—
30	#443×C₈₉	—	2	1	no	—
31	#443×C₈₉	C₂²	1	2	yes	—
32	#443×C₈₉	C₂²	1	2	yes	—
33	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#104×C₈₉	—	2	1	no	—
35	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#13083574	—	2	2	no	—
37	#15668034	—	2	2	no	—
38	#15668034	—	2	2	no	—
39	#15668034	—	2	2	no	—
40	#15668034	—	2	2	no	—
41	#15668034	—	4	1	no	—
42	#15668034	—	4	1	no	—
43	#15668034	—	4	1	no	—
44	#15668034	—	4	1	no	—
45	C₂×Dic₃₅₆	—	2	1	no	—
46	C₂×Dic₃₅₆	C₂³	1	2	yes	—
47	C₂×#13083563	—	2	2	no	—
48	C₂×#13083563	—	2	2	no	—
49	C₂×D₇₁₂	—	2	1	no	—
50	C₂×D₇₁₂	C₂³	1	2	yes	—
51	#15668012	—	2	1	no	—
52	#15668009	—	2	1	no	—
53	#15668000	—	2	2	no	—
54	#15667986	—	4	2	no	—
55	C₄×D₃₅₆	—	4	2	no	—
56	#15667958	—	2	4	no	—
57	#15667956	—	2	4	no	—
58	#15667955	—	2	4	no	—
59	#15667953	—	2	4	no	—
60	#15667952	—	2	2	no	—
61	#15667952	C₂³	1	4	yes	—
62	C₂×#13083549	—	2	2	no	—
63	C₂×#41×C₈₉	—	2	1	no	—
64	#135×C₈₉	—	2	1	no	—
65	#135×C₈₉	—	2	1	no	—
66	#135×C₈₉	D₄	1	2	yes	complemented
67	#135×C₈₉	C₂³	1	2	yes	—
68	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic, complemented
69	C₂×SD₁₆×C₈₉	—	2	1	no	—
70	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic, complemented
71	#131×C₈₉	—	2	2	no	—
72	#131×C₈₉	—	2	2	no	—
73	#131×C₈₉	—	4	1	no	—
74	#131×C₈₉	—	4	1	no	—
75	C₂×M₁₆×C₈₉	—	2	1	no	—
76	C₂×M₁₆×C₈₉	—	4	1	no	—
77	C₂²×C₈×C₈₉	—	4	1	no	—
78	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
81	#108×C₈₉	—	2	1	no	—
82	#108×C₈₉	C₂³	1	2	yes	—
83	#104×C₈₉	—	2	2	no	—
84	#104×C₈₉	—	2	2	no	—
85	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
86	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	#13083574	—	4	2	no	—
90	#13083574	—	4	2	no	—
91	#13083574	—	4	2	no	—
92	#13083574	—	4	2	no	—
93	C₂×Dic₁₇₈	—	2	2	no	—
94	C₂×D₃₅₆	—	2	2	no	—
95	C₂×D₃₅₆	—	4	2	no	—
96	C₂×C₂²⋊D₈₉	—	4	2	no	—
97	C₂×C₄×D₈₉	—	4	2	no	—
98	Dic₃₅₆	—	2	2	no	—
99	Dic₃₅₆	—	2	2	no	—
100	Dic₃₅₆	—	4	1	no	—
101	Dic₃₅₆	—	4	1	no	—
102	#13083563	—	4	2	no	—
103	#13083563	—	4	2	no	—
104	#13083563	—	4	2	no	—
105	#13083563	—	4	2	no	—
106	D₇₁₂	—	2	2	no	—
107	D₇₁₂	—	2	2	no	—
108	D₇₁₂	—	4	1	no	—
109	D₇₁₂	—	4	1	no	—
110	C₄⋊Dic₈₉	—	4	2	no	—
111	#13083551	—	4	4	no	—
112	#13083549	—	2	4	no	—
113	#41×C₈₉	—	2	2	no	—
114	#41×C₈₉	—	2	2	no	—
115	#41×C₈₉	—	4	1	no	—
116	#41×C₈₉	—	4	1	no	—
117	C₂×Q₈×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	—	2	1	no	—
119	C₂×D₄×C₈₉	—	4	1	no	—
120	C₂²×C₄×C₈₉	—	2	1	no	—
121	C₂²×C₄×C₈₉	—	4	1	no	—
122	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
123	Q₁₆×C₈₉	—	2	1	no	—
124	Q₁₆×C₈₉	C₂×D₄	1	2	yes	—
125	SD₁₆×C₈₉	—	2	2	no	—
126	SD₁₆×C₈₉	—	2	2	no	—
127	D₈×C₈₉	—	2	1	no	—
128	D₈×C₈₉	C₂×D₄	1	2	yes	—
129	M₁₆×C₈₉	—	2	2	no	—
130	M₁₆×C₈₉	—	4	1	no	—
131	M₁₆×C₈₉	—	4	2	no	—
132	M₁₆×C₈₉	—	4	2	no	—
133	C₂×C₈×C₈₉	—	4	1	no	—
134	C₂×C₈×C₈₉	—	4	2	no	—
135	C₂×C₈×C₈₉	—	4	2	no	—
136	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
137	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
138	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
139	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₄²×C₈₉	—	2	1	no	—
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂³×C₈₉	—	4	1	no	—
152	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂²×D₈₉	—	4	2	no	—
154	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	4	1	no	—
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	—	4	2	no	—
158	D₄×C₈₉	—	4	2	no	—
159	D₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₈₉	—	8	2	no	—
173	C₂²⋊D₈₉	—	8	2	no	—
174	C₂×Dic₈₉	—	4	2	no	—
175	D₃₅₆	—	4	2	no	—
176	D₃₅₆	—	4	2	no	—
177	D₃₅₆	—	8	4	no	—
178	C₄×D₈₉	—	8	2	no	—
179	C₄×D₈₉	—	8	2	no	—
180	Dic₁₇₈	—	4	2	no	—
181	Dic₁₇₈	—	4	2	no	—
182	C₈×C₈₉	—	4	2	no	—
183	C₈×C₈₉	#121	1	1	yes	characteristic
184	C₈×C₈₉	#121	1	1	yes	characteristic
185	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
186	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
187	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
188	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
189	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	—	4	2	no	—
193	C₂²×C₈₉	—	8	2	no	—
194	C₂²×C₈₉	#459	1	1	yes	characteristic
195	C₂²×C₈₉	#459	1	1	yes	characteristic
196	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×D₈₉	—	8	4	no	—
198	C₂×D₈₉	—	8	2	no	—
199	C₄×C₈₉	—	2	2	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	#459	1	1	yes	characteristic
203	C₄×C₈₉	#459	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
205	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
206	Dic₈₉	—	8	2	no	—
207	#33594	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	2	1	no	—
209	C₂×C₈₉	—	2	1	no	—
210	C₂×C₈₉	—	2	1	no	—
211	C₂×C₈₉	—	8	2	no	—
212	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
213	D₈₉	—	16	2	no	—
214	#3414	—	89	2	no	—
215	#3147	—	89	1	no	—
216	C₂×#443	D₈₉	1	1	yes	characteristic, complemented
217	#2214	—	89	2	no	—
218	#2213	—	89	2	no	—
219	#2212	—	89	4	no	—
220	C₂×#364	—	89	1	no	—
221	#2148	—	89	2	no	—
222	C₈₉	#33594	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	89	2	no	—
224	C₂×#135	—	178	1	no	—
225	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
226	C₂×#131	—	2	1	no	—
227	#532	—	178	1	no	—
228	#510	—	89	4	no	—
229	#510	—	178	2	no	—
230	#509	—	89	4	no	—
231	#509	—	178	2	no	—
232	#508	—	178	4	no	—
233	C₂×M₃₂	—	89	2	no	—
234	#495	—	89	2	no	—
235	#495	—	178	1	no	—
236	#494	—	89	1	no	—
237	#493	—	89	1	no	—
238	#492	—	178	1	no	—
239	#443	—	2	1	no	—
240	#443	—	2	1	no	—
241	#443	C₂×D₈₉	1	2	yes	—
242	#443	C₂×D₈₉	1	2	yes	—
243	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
244	C₂×#104	—	2	1	no	—
245	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
246	#364	—	89	2	no	—
247	#364	—	89	2	no	—
248	#362	—	89	4	no	—
249	#361	—	89	4	no	—
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	178	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	356	1	no	—
255	#135	—	356	1	no	—
256	#135	—	356	1	no	—
257	#135	—	356	1	no	—
258	#135	—	178	2	no	—
259	#135	—	178	2	no	—
260	#135	—	178	2	no	—
261	#135	—	178	2	no	—
262	#135	D₃₅₆	1	2	yes	complemented
263	#135	C₂²×D₈₉	1	2	yes	—
264	C₂×Q₁₆	—	89	2	no	—
265	C₂×Q₁₆	—	178	1	no	—
266	C₂×Q₁₆	D₃₅₆	1	1	yes	characteristic, complemented
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	178	2	no	—
269	C₂×SD₁₆	—	178	2	no	—
270	C₂×D₈	—	89	2	no	—
271	C₂×D₈	—	178	1	no	—
272	C₂×D₈	D₃₅₆	1	1	yes	characteristic, complemented
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	4	1	no	—
279	C₂²×C₈	—	4	1	no	—
280	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₄⋊Q₈	—	178	1	no	—
283	#127	—	178	1	no	—
284	#124	—	178	2	no	—
285	#121	—	356	2	no	—
286	C₄×D₄	—	356	2	no	—
287	C₂×C₄²	C₂²⋊D₈₉	1	1	yes	characteristic
288	Q₃₂	—	178	4	no	—
289	SD₃₂	—	178	4	no	—
290	SD₃₂	—	178	4	no	—
291	D₁₆	—	178	4	no	—
292	M₃₂	—	89	4	no	—
293	M₃₂	—	178	2	no	—
294	C₂×C₁₆	—	178	2	no	—
295	#108	—	2	1	no	—
296	#108	C₂²×D₈₉	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	356	2	no	—
308	#41	—	356	2	no	—
309	#41	—	356	2	no	—
310	#41	—	356	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	178	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	356	2	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	356	2	no	—
321	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	356	1	no	—
324	Q₁₆	—	356	1	no	—
325	Q₁₆	—	178	2	no	—
326	Q₁₆	—	178	2	no	—
327	Q₁₆	C₂×D₃₅₆	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	356	2	no	—
331	SD₁₆	—	356	2	no	—
332	SD₁₆	—	356	2	no	—
333	SD₁₆	—	356	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	356	1	no	—
336	D₈	—	356	1	no	—
337	D₈	—	178	2	no	—
338	D₈	—	178	2	no	—
339	D₈	C₂×D₃₅₆	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	#13083559	1	1	yes	characteristic
348	C₂×C₈	#13083559	1	1	yes	characteristic
349	C₂×C₈	#13083559	1	1	yes	characteristic
350	C₂×C₈	#13083559	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
354	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
355	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
356	C₂×C₈	#13083574	1	1	yes	characteristic
357	C₂×C₈	#13083574	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
359	C₄⋊C₄	—	356	2	no	—
360	C₂²⋊C₄	—	356	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
364	C₁₆	—	178	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	356	2	no	—
367	C₂³	#15668037	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	356	2	no	—
371	Q₈	—	356	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	356	2	no	—
377	D₄	—	356	2	no	—
378	D₄	—	712	4	no	—
379	D₄	—	712	2	no	—
380	D₄	—	712	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	712	2	no	—
389	C₂×C₄	—	712	2	no	—
390	C₂×C₄	#15667986	1	1	yes	characteristic
391	C₂×C₄	#15667986	1	1	yes	characteristic
392	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
393	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
394	C₂×C₄	#15668037	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	#15667986	1	1	yes	characteristic
398	C₈	#15667986	1	1	yes	characteristic
399	C₈	C₂×#13083559	1	1	yes	characteristic
400	C₈	C₂×#13083559	1	1	yes	characteristic
401	C₈	C₂×#13083559	1	1	yes	characteristic
402	C₈	C₂×#13083559	1	1	yes	characteristic
403	C₈	C₂²×D₃₅₆	1	1	yes	characteristic
404	C₈	C₂×#13083574	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	712	4	no	—
409	C₂²	—	712	2	no	—
410	C₂²	#19151793	1	1	yes	characteristic
411	C₂²	#19151793	1	1	yes	characteristic
412	C₂²	C₂×#15668037	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	712	2	no	—
417	C₄	#19151793	1	1	yes	characteristic
418	C₄	#19151793	1	1	yes	characteristic
419	C₄	C₂×#15667986	1	1	yes	characteristic
420	C₄	C₂²×#13083559	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	1424	2	no	—
426	C₂	C₂×#19151793	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19151793
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#443×C₈₉	C₂
socle	C₂×C₈₉	C₂×#459
hypercenter	C₂×#443	D₈₉
hypocenter	C₈₉	#33594
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #26033386	C₂	semidirect
2. #26030680	C₂	semidirect
3. #26022333	C₂	semidirect
4. #26022328	C₂	semidirect
5. #26022321	C₂	semidirect
6. C₂×#19151419	C₂	semidirect
7. #26021999	C₂	semidirect
8. C₂×#443×C₈₉	C₂	semidirect
19. #19151982	C₂²	semidirect
20. #19151978	C₂²	semidirect
21. #19151975	C₂²	semidirect
23. #19151419	C₂²	semidirect
24. #19151419	C₂²	semidirect
25. #19151413	C₂²	semidirect
26. #19151410	C₂²	semidirect
66. #135×C₈₉	D₄	semidirect
68. C₂×Q₁₆×C₈₉	D₄	semidirect
70. C₂×D₈×C₈₉	D₄	semidirect
216. C₂×#443	D₈₉	semidirect
222. C₈₉	#33594	semidirect
262. #135	D₃₅₆	semidirect
266. C₂×Q₁₆	D₃₅₆	semidirect
272. C₂×D₈	D₃₅₆	semidirect

Maximal subgroups

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

subgroup	index
#26033386	2
#26030680	2
#26022333	2
#26022328	2
#26022321	2
C₂×#19151419	2
#26021999	2
C₂×#443×C₈₉	2
#33594	89