Subgroups — #26029741

Order 11392.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15668041	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15668036	C₂	1	1	yes	maximal, characteristic
3	#124×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13083573	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151823	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151821	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151819	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151817	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151815	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151813	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151811	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151620	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151605	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151601	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13083573	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	#15668041	—	2	4	no	—
20	#15668036	—	2	4	no	—
21	C₂×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083564	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083563	C₂²	1	1	yes	characteristic
24	C₂×#13083562	C₂²	1	1	yes	characteristic
25	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13083559	C₂²	1	1	yes	characteristic
27	C₂×#13083557	C₂²	1	1	yes	characteristic
28	C₂×#13083557	C₂²	1	1	yes	characteristic
29	#15668001	C₂²	1	1	yes	characteristic
30	#15668000	C₂²	1	1	yes	characteristic
31	#15667999	C₂²	1	1	yes	characteristic
32	#15667998	—	2	1	no	—
33	#15667998	—	2	1	no	—
34	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
35	#15667977	C₂²	1	1	yes	characteristic, complemented
36	D₄×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₂²⋊D₈₉	—	2	1	no	—
38	#15667972	—	2	1	no	—
39	#15667970	C₂²	1	1	yes	characteristic
40	#15667968	—	2	1	no	—
41	C₂²⋊C₄×D₈₉	—	2	1	no	—
42	C₂²⋊C₄×D₈₉	—	2	1	no	—
43	C₂×C₄×Dic₈₉	—	2	1	no	—
44	C₄²×D₈₉	C₂²	1	1	yes	characteristic
45	C₄⋊#10623494	C₂²	1	1	yes	characteristic, complemented
46	#15667941	C₂²	1	1	yes	characteristic, complemented
47	#15667941	C₂²	1	1	yes	characteristic, complemented
48	#15667937	C₂²	1	1	yes	characteristic, complemented
49	#15667936	C₂²	1	1	yes	characteristic, complemented
50	#15667935	C₂²	1	1	yes	characteristic, complemented
51	#15667934	C₂²	1	1	yes	characteristic
52	#15667933	C₂²	1	1	yes	characteristic
53	#15667932	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×C₈₉	C₂²	1	1	yes	characteristic
56	#124×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₈₉	C₂²	1	1	yes	characteristic
61	C₂³×D₈₉	—	2	1	no	—
62	#13083573	—	2	2	no	—
63	#13083573	D₄	1	4	yes	—
64	C₂×Dic₁₇₈	—	2	1	no	—
65	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
67	Q₈×D₈₉	—	2	2	no	—
68	Q₈×D₈₉	—	2	2	no	—
69	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₈₉	—	2	1	no	—
71	C₂×C₂²⋊D₈₉	—	2	1	no	—
72	D₄×D₈₉	—	2	2	no	—
73	D₄×D₈₉	—	2	2	no	—
74	C₂²×Dic₈₉	—	2	1	no	—
75	C₂²×Dic₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	2	1	no	—
77	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
80	Dic₃₅₆	—	2	2	no	—
81	#13083564	—	2	2	no	—
82	#13083563	—	2	2	no	—
83	#13083562	—	2	2	no	—
84	#13083562	—	2	2	no	—
85	#13083559	—	2	2	no	—
86	#13083557	—	2	2	no	—
87	#13083557	—	2	2	no	—
88	C₂×#10623494	C₂³	1	1	yes	characteristic
89	C₂×#10623494	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
91	#13083553	—	2	1	no	—
92	#13083553	—	2	1	no	—
93	C₂²⋊Dic₈₉	—	2	1	no	—
94	C₂²⋊Dic₈₉	—	2	1	no	—
95	C₂²⋊Dic₈₉	—	2	1	no	—
96	#13083551	—	2	1	no	—
97	#13083551	—	2	1	no	—
98	#13083551	—	2	1	no	—
99	#13083551	—	2	1	no	—
100	#13083551	—	2	1	no	—
101	C₄×Dic₈₉	—	2	1	no	—
102	C₄×Dic₈₉	—	2	1	no	—
103	C₄×Dic₈₉	—	2	1	no	—
104	C₄×Dic₈₉	D₄	1	1	yes	characteristic
105	C₄×Dic₈₉	D₄	1	1	yes	characteristic
106	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	SD₁₆×C₈₉	—	2	2	no	—
112	D₈×C₈₉	—	2	2	no	—
113	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₈₉	—	2	1	no	—
117	C₂²⋊C₄×C₈₉	—	2	1	no	—
118	C₂²⋊C₄×C₈₉	—	2	1	no	—
119	C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂²×D₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	4	2	no	—
124	C₂²×D₈₉	—	4	2	no	—
125	C₂²×D₈₉	—	4	2	no	—
126	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₈₉	—	2	1	no	—
128	Q₈×C₈₉	—	2	1	no	—
129	D₄×C₈₉	—	2	1	no	—
130	D₄×C₈₉	—	2	1	no	—
131	D₄×C₈₉	—	2	1	no	—
132	D₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂²⋊D₈₉	—	2	4	no	—
140	C₂²⋊D₈₉	—	4	2	no	—
141	C₂×Dic₈₉	—	2	1	no	—
142	C₂×Dic₈₉	—	2	4	no	—
143	C₂×Dic₈₉	—	2	1	no	—
144	C₂×Dic₈₉	—	2	1	no	—
145	C₂×Dic₈₉	—	4	2	no	—
146	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
149	D₃₅₆	—	2	1	no	—
150	D₃₅₆	—	2	1	no	—
151	C₄×D₈₉	—	4	1	no	—
152	C₄×D₈₉	—	4	1	no	—
153	C₄×D₈₉	—	4	2	no	—
154	C₄×D₈₉	C₂×D₄	1	2	yes	—
155	C₄×D₈₉	#41	1	2	yes	—
156	Dic₁₇₈	—	2	1	no	—
157	Dic₁₇₈	—	2	1	no	—
158	Dic₁₇₈	—	2	1	no	—
159	Dic₁₇₈	—	4	2	no	—
160	Dic₁₇₈	C₂×D₄	1	2	yes	—
161	C₈×C₈₉	—	2	1	no	—
162	C₈×C₈₉	—	2	1	no	—
163	#10623494	—	2	1	no	—
164	#10623494	—	2	1	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	4	1	no	—
167	C₂²×C₈₉	—	4	1	no	—
168	C₂²×C₈₉	—	4	1	no	—
169	C₂²×C₈₉	—	4	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₈₉	—	2	1	no	—
173	C₂×D₈₉	—	2	1	no	—
174	C₂×D₈₉	—	4	1	no	—
175	C₂×D₈₉	—	4	1	no	—
176	C₂×D₈₉	—	4	1	no	—
177	C₂×D₈₉	—	8	4	no	—
178	C₂×D₈₉	#121	1	2	yes	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	4	1	no	—
182	C₄×C₈₉	—	4	1	no	—
183	C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
185	Dic₈₉	—	2	2	no	—
186	Dic₈₉	—	2	1	no	—
187	Dic₈₉	—	2	1	no	—
188	Dic₈₉	—	4	1	no	—
189	Dic₈₉	—	4	1	no	—
190	Dic₈₉	#121	1	2	yes	—
191	C₂×C₈₉	—	4	2	no	—
192	C₂×C₈₉	—	8	1	no	—
193	C₂×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂×C₈₉	#575	1	1	yes	characteristic
195	C₂×C₈₉	#575	1	1	yes	characteristic
196	D₈₉	—	2	2	no	—
197	D₈₉	—	8	1	no	—
198	#3040	—	89	1	no	maximal, Sylow
199	C₈₉	#3040	1	1	yes	characteristic, complemented, Sylow
200	C₂×#137	—	89	1	no	—
201	C₂×AGL(1,ℤ/8)	—	89	1	no	—
202	C₂×#124	—	89	1	no	—
203	C₄×#41	—	89	1	no	—
204	#464	—	89	1	no	—
205	#464	—	89	1	no	—
206	#464	—	89	1	no	—
207	#464	—	89	1	no	—
208	#463	—	89	1	no	—
209	#463	—	89	1	no	—
210	#463	—	89	1	no	—
211	#463	D₈₉	1	1	yes	characteristic, complemented
212	#423	—	89	1	no	—
213	#419	—	89	1	no	—
214	#418	—	89	1	no	—
215	C₂×#41	—	89	1	no	—
216	C₂²×Q₈	—	89	1	no	—
217	C₂²×D₄	—	89	1	no	—
218	#137	—	178	4	no	—
219	AGL(1,ℤ/8)	—	178	4	no	—
220	C₂×Q₁₆	—	89	1	no	—
221	C₂×Q₁₆	—	89	1	no	—
222	C₂×SD₁₆	—	89	1	no	—
223	C₂×SD₁₆	—	89	1	no	—
224	C₂×SD₁₆	—	89	1	no	—
225	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
226	C₂×D₈	—	89	1	no	—
227	C₂×D₈	C₂×D₈₉	1	1	yes	characteristic
228	C₂×M₁₆	—	89	1	no	—
229	C₂×M₁₆	—	89	1	no	—
230	#124	—	89	1	no	—
231	#124	—	89	1	no	—
232	#124	—	89	1	no	—
233	#124	—	178	1	no	—
234	#124	—	178	1	no	—
235	#124	C₂×D₈₉	1	1	yes	characteristic
236	C₄×Q₈	—	89	1	no	—
237	C₄×Q₈	—	89	1	no	—
238	C₄×D₄	—	89	1	no	—
239	C₄×D₄	—	178	1	no	—
240	C₄×D₄	—	178	1	no	—
241	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic, complemented
242	#117	—	89	1	no	—
243	#117	—	178	1	no	—
244	C₂×C₂²⋊C₄	—	178	1	no	—
245	C₂×C₂²⋊C₄	—	178	1	no	—
246	C₂×C₄²	—	89	1	no	—
247	C₂×C₄²	—	178	1	no	—
248	C₄⋊C₈	—	89	1	no	—
249	C₄⋊C₈	—	89	1	no	—
250	C₄⋊C₈	—	89	1	no	—
251	C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
252	#103	—	89	1	no	—
253	#103	—	89	1	no	—
254	#103	—	89	1	no	—
255	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
256	#102	—	89	1	no	—
257	#102	—	89	1	no	—
258	#102	—	89	1	no	—
259	#102	C₂×D₈₉	1	1	yes	characteristic
260	C₂⁴	—	178	1	no	—
261	#41	—	89	4	no	—
262	#41	—	178	2	no	—
263	C₂×Q₈	—	89	1	no	—
264	C₂×Q₈	—	89	1	no	—
265	C₂×Q₈	—	178	1	no	—
266	C₂×Q₈	—	178	2	no	—
267	C₂×Q₈	—	178	2	no	—
268	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
269	C₂×D₄	—	89	1	no	—
270	C₂×D₄	—	178	2	no	—
271	C₂×D₄	—	178	2	no	—
272	C₂×D₄	—	178	1	no	—
273	C₂×D₄	—	178	1	no	—
274	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
275	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	89	1	no	—
278	C₂²×C₄	—	89	1	no	—
279	C₂²×C₄	—	89	1	no	—
280	C₂²×C₄	—	178	1	no	—
281	C₂²×C₄	—	178	1	no	—
282	C₂²×C₄	—	178	1	no	—
283	Q₁₆	—	178	2	no	—
284	Q₁₆	—	178	2	no	—
285	SD₁₆	—	2	2	no	—
286	SD₁₆	—	178	2	no	—
287	SD₁₆	—	178	2	no	—
288	SD₁₆	—	178	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	178	2	no	—
291	M₁₆	—	178	2	no	—
292	M₁₆	—	178	2	no	—
293	C₂×C₈	—	89	1	no	—
294	C₂×C₈	—	89	1	no	—
295	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
296	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄⋊C₄	—	89	1	no	—
298	C₄⋊C₄	—	178	1	no	—
299	C₄⋊C₄	—	178	1	no	—
300	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	178	1	no	—
305	C₂²⋊C₄	—	178	1	no	—
306	C₂²⋊C₄	—	178	1	no	—
307	C₂²⋊C₄	—	178	1	no	—
308	C₂²⋊C₄	—	178	1	no	—
309	C₂²⋊C₄	—	178	1	no	—
310	C₂²⋊C₄	—	178	1	no	—
311	C₂²⋊C₄	—	178	1	no	—
312	C₄²	—	89	1	no	—
313	C₄²	—	89	1	no	—
314	C₄²	—	89	1	no	—
315	C₄²	—	178	1	no	—
316	C₄²	—	178	1	no	—
317	C₄²	—	178	1	no	—
318	C₄²	C₂²×D₈₉	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	89	1	no	—
322	C₂³	—	356	2	no	—
323	C₂³	—	356	2	no	—
324	C₂³	—	356	2	no	—
325	C₂³	—	178	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	89	2	no	—
329	Q₈	—	356	2	no	—
330	Q₈	—	178	1	no	—
331	Q₈	—	178	1	no	—
332	Q₈	—	178	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	356	2	no	—
337	D₄	—	178	4	no	—
338	D₄	—	178	1	no	—
339	D₄	—	178	1	no	—
340	D₄	D₄×D₈₉	1	2	yes	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	89	1	no	—
345	C₂×C₄	—	89	2	no	—
346	C₂×C₄	—	89	2	no	—
347	C₂×C₄	—	89	1	no	—
348	C₂×C₄	—	89	1	no	—
349	C₂×C₄	—	356	1	no	—
350	C₂×C₄	—	356	1	no	—
351	C₂×C₄	—	356	2	no	—
352	C₂×C₄	—	356	2	no	—
353	C₂×C₄	—	178	4	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	—	178	1	no	—
356	C₂×C₄	—	178	1	no	—
357	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
359	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	178	1	no	—
363	C₈	—	178	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	89	2	no	—
371	C₂²	—	356	1	no	—
372	C₂²	—	356	1	no	—
373	C₂²	—	356	1	no	—
374	C₂²	—	178	1	no	—
375	C₂²	—	178	1	no	—
376	C₂²	—	712	4	no	—
377	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	89	2	no	—
383	C₄	—	356	1	no	—
384	C₄	—	356	1	no	—
385	C₄	—	178	1	no	—
386	C₄	—	178	1	no	—
387	C₄	—	178	2	no	—
388	C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
389	C₄	#41×D₈₉	1	1	yes	characteristic
390	C₂	—	4	2	no	—
391	C₂	—	8	1	no	—
392	C₂	—	178	2	no	—
393	C₂	—	712	1	no	—
394	C₂	#121×D₈₉	1	1	yes	characteristic
395	C₂	#19152394	1	1	yes	characteristic
396	C₂	#19152395	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#463×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	C₂×#15668036	C₂
hypercenter	#463	D₈₉
hypocenter	C₈₉	#3040
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
1. C₂×#15668041	C₂	semidirect
3. #124×D₈₉	C₂	semidirect
4. C₄×#13083573	C₂	semidirect
5. #19151823	C₂	semidirect
6. #19151821	C₂	semidirect
7. #19151819	C₂	semidirect
8. #19151817	C₂	semidirect
9. #19151815	C₂	semidirect
10. #19151813	C₂	semidirect
11. #19151811	C₂	semidirect
12. #19151620	C₂	semidirect
13. #19151605	C₂	semidirect
14. #19151601	C₂	semidirect
15. #463×C₈₉	C₂	semidirect
21. C₂×Dic₃₅₆	C₂²	semidirect
22. C₂×#13083564	C₂²	semidirect
25. C₂×#13083562	C₂²	semidirect
34. C₄×Dic₁₇₈	C₂²	semidirect
35. #15667977	C₂²	semidirect
36. D₄×Dic₈₉	C₂²	semidirect
45. C₄⋊#10623494	C₂²	semidirect
46. #15667941	C₂²	semidirect
47. #15667941	C₂²	semidirect
48. #15667937	C₂²	semidirect
49. #15667936	C₂²	semidirect
50. #15667935	C₂²	semidirect
54. C₂×SD₁₆×C₈₉	C₂²	semidirect
57. C₄×D₄×C₈₉	C₂²	semidirect
58. C₄⋊C₈×C₈₉	C₂²	semidirect
59. #103×C₈₉	C₂²	semidirect
199. C₈₉	#3040	semidirect
211. #463	D₈₉	semidirect
225. C₂×SD₁₆	C₂×D₈₉	semidirect
241. C₄×D₄	C₂×D₈₉	semidirect
251. C₄⋊C₈	C₂×D₈₉	semidirect
255. #103	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×#15668041	2
C₂×#15668036	2
#124×D₈₉	2
C₄×#13083573	2
#19151823	2
#19151821	2
#19151819	2
#19151817	2
#19151815	2
#19151813	2
#19151811	2
#19151620	2
#19151605	2
#19151601	2
#463×C₈₉	2
#3040	89