Subgroups — #36708822

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	#26033388	C₂	1	2	yes	maximal, complemented
2	#26030680	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19151716	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022334	C₂	1	2	yes	maximal, complemented
5	#26022329	C₂	1	2	yes	maximal, complemented
6	#26022322	C₂	1	4	yes	maximal, complemented
7	#26022002	C₂	1	2	yes	maximal, complemented
8	C₂×#364×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15668034	—	2	1	no	—
10	C₂×#15668034	C₂²	1	1	yes	characteristic
11	C₂×#15668034	C₂²	1	2	yes	—
12	C₂×#15668018	—	2	1	no	—
13	#19152148	—	2	1	no	—
14	#19152041	—	2	2	no	—
15	#19152041	C₂²	1	4	yes	—
16	#19152036	—	2	2	no	—
17	#19152036	C₂²	1	4	yes	—
18	#19152030	—	2	4	no	—
19	#19151982	—	2	1	no	—
20	#19151982	C₂²	1	2	yes	complemented
21	#19151978	C₂²	1	1	yes	characteristic, complemented
22	#19151975	C₂²	1	1	yes	characteristic, complemented
23	#19151971	—	2	1	no	—
24	#19151716	—	2	1	no	—
25	#19151716	—	2	1	no	—
26	#19151716	C₂²	1	2	yes	—
27	#19151716	C₂²	1	2	yes	—
28	C₂×#15667948	C₂²	1	1	yes	characteristic
29	C₂×#15667940	—	2	1	no	—
30	#19151415	C₂²	1	4	yes	complemented
31	#19151412	C₂²	1	4	yes	complemented
32	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	#364×C₈₉	C₂²	1	2	yes	complemented
35	#364×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#13083574	—	2	1	no	—
37	C₂×#13083574	—	2	2	no	—
38	#15668034	—	2	1	no	—
39	#15668034	—	2	2	no	—
40	#15668034	—	2	2	no	—
41	#15668034	—	2	1	no	—
42	#15668034	—	2	2	no	—
43	#15668034	—	2	2	no	—
44	#15668034	—	4	1	no	—
45	#15668034	—	4	1	no	—
46	#15668034	—	4	1	no	—
47	#15668034	—	4	1	no	—
48	#15668034	D₄	1	2	yes	complemented
49	#15668034	C₂³	1	2	yes	—
50	C₂×Dic₃₅₆	—	2	1	no	—
51	C₂×Dic₃₅₆	D₄	1	1	yes	characteristic, complemented
52	C₂×Dic₃₅₆	C₂³	1	2	yes	—
53	C₂×#13083563	—	2	2	no	—
54	C₂×#13083563	—	2	2	no	—
55	C₂×#13083563	—	2	1	no	—
56	C₂×D₇₁₂	—	2	1	no	—
57	C₂×D₇₁₂	D₄	1	1	yes	characteristic, complemented
58	C₂×D₇₁₂	C₂³	1	2	yes	—
59	#15668018	—	2	2	no	—
60	#15668018	—	2	2	no	—
61	#15668018	—	4	1	no	—
62	#15668018	—	4	1	no	—
63	C₂×#13083558	—	2	1	no	—
64	C₂×#13083557	—	4	1	no	—
65	C₂×C₈×D₈₉	—	4	1	no	—
66	#15668012	—	2	1	no	—
67	#15668009	—	2	1	no	—
68	#15668000	—	2	2	no	—
69	#15667986	—	4	2	no	—
70	C₄×D₃₅₆	—	4	2	no	—
71	Dic₇₁₂	—	2	4	no	—
72	#15667957	—	2	4	no	—
73	#15667957	—	2	4	no	—
74	D₁₄₂₄	—	2	4	no	—
75	#15667948	—	2	1	no	—
76	#15667948	C₂³	1	2	yes	—
77	#15667940	—	2	2	no	—
78	#15667940	—	2	2	no	—
79	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
82	M₃₂×C₈₉	—	2	2	no	—
83	M₃₂×C₈₉	C₂³	1	4	yes	—
84	C₂×C₁₆×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	—	2	2	no	—
90	#13083574	—	2	2	no	—
91	#13083574	—	4	1	no	—
92	#13083574	—	4	1	no	—
93	#13083574	—	4	2	no	—
94	#13083574	—	4	2	no	—
95	#13083574	—	4	2	no	—
96	#13083574	—	4	2	no	—
97	C₂×Dic₁₇₈	—	2	1	no	—
98	C₂×Dic₁₇₈	—	2	2	no	—
99	C₂×D₃₅₆	—	2	1	no	—
100	C₂×D₃₅₆	—	2	2	no	—
101	C₂×D₃₅₆	—	4	2	no	—
102	C₂×C₂²⋊D₈₉	—	4	1	no	—
103	C₂×C₂²⋊D₈₉	—	4	2	no	—
104	C₂×C₄×D₈₉	—	4	1	no	—
105	C₂×C₄×D₈₉	—	4	2	no	—
106	Dic₃₅₆	—	2	1	no	—
107	Dic₃₅₆	—	2	2	no	—
108	Dic₃₅₆	—	2	2	no	—
109	Dic₃₅₆	—	4	1	no	—
110	Dic₃₅₆	—	4	1	no	—
111	Dic₃₅₆	C₂×D₄	1	2	yes	—
112	#13083563	—	2	2	no	—
113	#13083563	—	2	2	no	—
114	#13083563	—	4	2	no	—
115	#13083563	—	4	2	no	—
116	#13083563	—	4	2	no	—
117	#13083563	—	4	2	no	—
118	D₇₁₂	—	2	1	no	—
119	D₇₁₂	—	2	2	no	—
120	D₇₁₂	—	2	2	no	—
121	D₇₁₂	—	4	1	no	—
122	D₇₁₂	—	4	1	no	—
123	D₇₁₂	C₂×D₄	1	2	yes	—
124	#13083558	—	2	2	no	—
125	#13083558	—	4	1	no	—
126	#13083557	—	4	2	no	—
127	#13083557	—	4	2	no	—
128	C₂×#10623494	—	4	1	no	—
129	C₈×D₈₉	—	4	2	no	—
130	C₈×D₈₉	—	4	2	no	—
131	C₄⋊Dic₈₉	—	4	2	no	—
132	#13083551	—	4	4	no	—
133	C₂²×C₄×C₈₉	—	2	1	no	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
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	C₂×D₄	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	#41	1	1	yes	characteristic
145	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₁₆×C₈₉	—	2	4	no	—
151	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂²×D₈₉	—	4	1	no	—
153	C₂²×D₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	4	2	no	—
164	C₂²⋊D₈₉	—	4	2	no	—
165	C₂²⋊D₈₉	—	8	2	no	—
166	C₂²⋊D₈₉	—	8	2	no	—
167	C₂×Dic₈₉	—	4	1	no	—
168	C₂×Dic₈₉	—	4	2	no	—
169	D₃₅₆	—	2	2	no	—
170	D₃₅₆	—	4	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	4	1	no	—
173	D₃₅₆	—	8	4	no	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	2	no	—
176	C₄×D₈₉	—	8	2	no	—
177	C₄×D₈₉	—	8	2	no	—
178	Dic₁₇₈	—	2	2	no	—
179	Dic₁₇₈	—	4	1	no	—
180	Dic₁₇₈	—	4	2	no	—
181	Dic₁₇₈	—	4	2	no	—
182	C₈×C₈₉	#121	1	1	yes	characteristic
183	C₈×C₈₉	#121	1	1	yes	characteristic
184	C₈×C₈₉	C₂×D₈	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	C₂²×D₄	1	1	yes	characteristic
189	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
190	#10623494	—	4	2	no	—
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	#459	1	1	yes	characteristic
193	C₂²×C₈₉	#459	1	1	yes	characteristic
194	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	8	2	no	—
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	#459	1	1	yes	characteristic
202	C₄×C₈₉	#459	1	1	yes	characteristic
203	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
204	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
205	Dic₈₉	—	4	2	no	—
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	C₂×#459	1	1	yes	characteristic
212	D₈₉	—	8	2	no	—
213	D₈₉	—	16	2	no	—
214	#3414	—	89	2	no	—
215	#3147	—	89	1	no	—
216	C₂×#443	—	89	1	no	—
217	#2214	—	89	2	no	—
218	#2213	—	89	2	no	—
219	#2212	—	89	4	no	—
220	C₂×#364	D₈₉	1	1	yes	characteristic, complemented
221	#2148	—	89	2	no	—
222	C₈₉	#33594	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	89	1	no	—
224	C₂×#135	—	89	2	no	—
225	C₂×#135	—	178	1	no	—
226	C₂×#131	—	178	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	C₂×D₈₉	1	2	yes	—
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	—	89	2	no	—
240	#443	—	89	2	no	—
241	#443	—	178	1	no	—
242	#443	—	178	1	no	—
243	C₂×#108	—	89	1	no	—
244	C₂×#104	—	178	1	no	—
245	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
246	#364	C₂×D₈₉	1	2	yes	complemented
247	#364	C₂×D₈₉	1	2	yes	complemented
248	#362	—	89	4	no	—
249	#361	—	89	4	no	—
250	C₂×#41	—	178	2	no	—
251	C₂×#41	—	178	1	no	—
252	#135	—	89	2	no	—
253	#135	—	89	2	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	1	no	—
261	#135	—	178	2	no	—
262	#135	—	178	2	no	—
263	#135	—	178	1	no	—
264	C₂×Q₁₆	—	89	1	no	—
265	C₂×Q₁₆	—	89	2	no	—
266	C₂×Q₁₆	—	178	1	no	—
267	C₂×SD₁₆	—	178	2	no	—
268	C₂×SD₁₆	—	178	2	no	—
269	C₂×SD₁₆	—	178	1	no	—
270	C₂×D₈	—	89	1	no	—
271	C₂×D₈	—	89	2	no	—
272	C₂×D₈	—	178	1	no	—
273	#131	—	356	1	no	—
274	#131	—	356	1	no	—
275	#131	—	178	2	no	—
276	#131	—	178	2	no	—
277	C₂×M₁₆	—	356	1	no	—
278	C₂×M₁₆	—	178	1	no	—
279	C₂²×C₈	—	356	1	no	—
280	C₂²×C₈	D₃₅₆	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	D₃₅₆	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	—	2	2	no	—
293	M₃₂	C₂²×D₈₉	1	4	yes	—
294	C₂×C₁₆	—	2	2	no	—
295	#108	—	89	2	no	—
296	#108	—	178	1	no	—
297	#104	—	178	2	no	—
298	#104	—	178	2	no	—
299	C₄×C₈	D₃₅₆	1	1	yes	characteristic
300	C₄×C₈	D₃₅₆	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
303	#41	—	356	1	no	—
304	#41	—	356	1	no	—
305	#41	—	356	2	no	—
306	#41	—	356	2	no	—
307	#41	—	356	2	no	—
308	#41	—	356	2	no	—
309	#41	—	178	2	no	—
310	#41	—	178	2	no	—
311	C₂×Q₈	—	178	1	no	—
312	C₂×Q₈	—	178	2	no	—
313	C₂×D₄	—	356	2	no	—
314	C₂×D₄	—	356	1	no	—
315	C₂×D₄	—	356	2	no	—
316	C₂×D₄	—	178	1	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	356	1	no	—
320	C₂²×C₄	—	356	2	no	—
321	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
322	Q₁₆	—	89	2	no	—
323	Q₁₆	—	356	1	no	—
324	Q₁₆	—	356	1	no	—
325	Q₁₆	—	178	1	no	—
326	Q₁₆	—	178	2	no	—
327	Q₁₆	—	178	2	no	—
328	SD₁₆	—	356	2	no	—
329	SD₁₆	—	356	2	no	—
330	SD₁₆	—	356	2	no	—
331	SD₁₆	—	356	2	no	—
332	SD₁₆	—	178	2	no	—
333	SD₁₆	—	178	2	no	—
334	D₈	—	89	2	no	—
335	D₈	—	356	1	no	—
336	D₈	—	356	1	no	—
337	D₈	—	178	1	no	—
338	D₈	—	178	2	no	—
339	D₈	—	178	2	no	—
340	M₁₆	—	356	1	no	—
341	M₁₆	—	356	2	no	—
342	M₁₆	—	356	2	no	—
343	M₁₆	—	178	2	no	—
344	C₂×C₈	—	356	1	no	—
345	C₂×C₈	—	356	2	no	—
346	C₂×C₈	—	356	2	no	—
347	C₂×C₈	D₇₁₂	1	1	yes	characteristic
348	C₂×C₈	D₇₁₂	1	1	yes	characteristic
349	C₂×C₈	D₇₁₂	1	1	yes	characteristic
350	C₂×C₈	D₇₁₂	1	1	yes	characteristic
351	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
352	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
353	C₂×C₈	C₂×D₃₅₆	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	#13083575	1	1	yes	characteristic
357	C₂×C₈	#13083575	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×D₃₅₆	1	1	yes	characteristic
363	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
364	C₁₆	—	2	4	no	—
365	C₂³	—	356	1	no	—
366	C₂³	—	356	2	no	—
367	C₂³	#15668040	1	1	yes	characteristic
368	Q₈	—	356	1	no	—
369	Q₈	—	356	2	no	—
370	Q₈	—	356	2	no	—
371	Q₈	—	178	2	no	—
372	D₄	—	356	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	356	1	no	—
375	D₄	—	356	2	no	—
376	D₄	—	356	2	no	—
377	D₄	—	178	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	—	356	1	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	712	2	no	—
389	C₂×C₄	—	712	2	no	—
390	C₂×C₄	#15667987	1	1	yes	characteristic
391	C₂×C₄	#15667987	1	1	yes	characteristic
392	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
393	C₂×C₄	C₂×D₇₁₂	1	1	yes	characteristic
394	C₂×C₄	#15668040	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
396	C₈	—	356	2	no	—
397	C₈	#15667987	1	1	yes	characteristic
398	C₈	#15667987	1	1	yes	characteristic
399	C₈	C₂×D₇₁₂	1	1	yes	characteristic
400	C₈	C₂×D₇₁₂	1	1	yes	characteristic
401	C₈	C₂×D₇₁₂	1	1	yes	characteristic
402	C₈	C₂×D₇₁₂	1	1	yes	characteristic
403	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
404	C₈	C₂×#13083575	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	356	2	no	—
407	C₂²	—	712	4	no	—
408	C₂²	—	712	2	no	—
409	C₂²	—	712	2	no	—
410	C₂²	#19151794	1	1	yes	characteristic
411	C₂²	#19151794	1	1	yes	characteristic
412	C₂²	C₂×#15668040	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	356	2	no	—
416	C₄	—	712	2	no	—
417	C₄	#19151794	1	1	yes	characteristic
418	C₄	#19151794	1	1	yes	characteristic
419	C₄	C₂×#15667987	1	1	yes	characteristic
420	C₄	C₂²×D₇₁₂	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	1424	2	no	—
425	C₂	—	712	2	no	—
426	C₂	C₂×#19151794	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19151794
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₂×#364×C₈₉	C₂
socle	C₂×C₈₉	C₂×#459
hypercenter	C₂×#364	D₈₉
hypocenter	C₈₉	#33594
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
1. #26033388	C₂	semidirect
2. #26030680	C₂	semidirect
3. C₂×#19151716	C₂	semidirect
4. #26022334	C₂	semidirect
5. #26022329	C₂	semidirect
6. #26022322	C₂	semidirect
7. #26022002	C₂	semidirect
8. C₂×#364×C₈₉	C₂	semidirect
20. #19151982	C₂²	semidirect
21. #19151978	C₂²	semidirect
22. #19151975	C₂²	semidirect
30. #19151415	C₂²	semidirect
31. #19151412	C₂²	semidirect
34. #364×C₈₉	C₂²	semidirect
35. #364×C₈₉	C₂²	semidirect
48. #15668034	D₄	semidirect
51. C₂×Dic₃₅₆	D₄	semidirect
57. C₂×D₇₁₂	D₄	semidirect
220. C₂×#364	D₈₉	semidirect
222. C₈₉	#33594	semidirect
246. #364	C₂×D₈₉	semidirect
247. #364	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033388	2
#26030680	2
C₂×#19151716	2
#26022334	2
#26022329	2
#26022322	2
#26022002	2
C₂×#364×C₈₉	2
#33594	89