Subgroups — #26031053

Order 11392.

462 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#121×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#19151935	C₂	1	1	yes	maximal, characteristic, complemented
4	#19151932	C₂	1	1	yes	maximal, characteristic, complemented
5	#19151913	C₂	1	1	yes	maximal, characteristic, complemented
6	#19151910	C₂	1	1	yes	maximal, characteristic, complemented
7	#19151846	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151844	C₂	1	1	yes	maximal, characteristic, complemented
9	#19151842	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151750	C₂	1	1	yes	maximal, characteristic, complemented
11	#19151747	C₂	1	1	yes	maximal, characteristic, complemented
12	#19151738	C₂	1	1	yes	maximal, characteristic, complemented
13	#19151735	C₂	1	1	yes	maximal, characteristic, complemented
14	#19151561	C₂	1	1	yes	maximal, characteristic, complemented
15	#468×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×D₄×D₈₉	—	2	1	no	—
18	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×#13083563	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13083562	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13083561	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13083558	C₂²	1	1	yes	characteristic, complemented
24	#15667992	C₂²	1	1	yes	characteristic
25	#15667991	C₂²	1	1	yes	characteristic, complemented
26	#15667990	—	2	1	no	—
27	#15667989	—	2	1	no	—
28	#15667988	C₂²	1	1	yes	characteristic
29	#15667987	C₂²	1	1	yes	characteristic
30	#15667986	C₂²	1	1	yes	characteristic
31	#15667985	—	2	1	no	—
32	#15667984	—	2	1	no	—
33	#15667983	C₂²	1	1	yes	characteristic
34	C₄⋊C₄×D₈₉	—	2	1	no	—
35	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²⋊C₄×D₈₉	—	2	1	no	—
38	C₂²⋊C₄×D₈₉	—	2	1	no	—
39	#15667946	C₂²	1	1	yes	characteristic, complemented
40	#15667945	C₂²	1	1	yes	characteristic, complemented
41	#15667945	C₂²	1	1	yes	characteristic, complemented
42	#15667937	C₂²	1	1	yes	characteristic, complemented
43	#15667936	C₂²	1	1	yes	characteristic, complemented
44	#15667935	C₂²	1	1	yes	characteristic, complemented
45	#15667934	C₂²	1	1	yes	characteristic, complemented
46	#15667933	C₂²	1	1	yes	characteristic, complemented
47	#15667932	C₂²	1	1	yes	characteristic, complemented
48	#15667924	C₂²	1	1	yes	characteristic
49	#15667924	C₂²	1	1	yes	characteristic
50	#15667924	C₂²	1	1	yes	characteristic, complemented
51	#15667924	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×M₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	#121×C₈₉	C₂²	1	1	yes	characteristic
56	#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₈₉	—	2	1	no	—
60	C₂³×D₈₉	D₄	1	1	yes	characteristic
61	C₂×Dic₁₇₈	—	2	1	no	—
62	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	Q₈×D₈₉	—	4	1	no	—
64	Q₈×D₈₉	—	4	1	no	—
65	C₂×D₃₅₆	—	2	1	no	—
66	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₈₉	—	2	1	no	—
68	C₂×C₂²⋊D₈₉	—	2	1	no	—
69	C₂×C₂²⋊D₈₉	—	2	1	no	—
70	D₄×D₈₉	—	4	1	no	—
71	D₄×D₈₉	—	4	1	no	—
72	D₄×D₈₉	—	4	4	no	—
73	C₂²×Dic₈₉	D₄	1	1	yes	characteristic
74	C₂×C₄×D₈₉	—	2	1	no	—
75	C₂×C₄×D₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	2	1	no	—
77	C₂×C₄×D₈₉	—	4	1	no	—
78	C₂×C₄×D₈₉	—	4	1	no	—
79	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
80	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
81	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
83	#13083563	—	4	1	no	—
84	#13083562	—	4	1	no	—
85	#13083561	—	4	1	no	—
86	#13083558	—	4	1	no	—
87	C₂×#10623494	C₂³	1	1	yes	characteristic
88	C₂×#10623494	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₈₉	—	2	1	no	—
90	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
92	#13083553	—	2	1	no	—
93	#13083553	—	2	1	no	—
94	#13083553	—	2	1	no	—
95	#13083553	—	2	1	no	—
96	C₂²⋊Dic₈₉	—	2	1	no	—
97	C₂²⋊Dic₈₉	—	2	1	no	—
98	#13083551	—	2	1	no	—
99	#13083551	—	2	1	no	—
100	#13083551	—	2	1	no	—
101	#13083551	—	2	1	no	—
102	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
106	SD₁₆×C₈₉	—	4	1	no	—
107	M₁₆×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₈₉	—	2	1	no	—
111	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²⋊C₄×C₈₉	—	2	1	no	—
114	C₂²⋊C₄×C₈₉	—	2	1	no	—
115	C₂³×C₈₉	—	2	1	no	—
116	C₂³×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×D₈₉	—	2	2	no	—
118	C₂²×D₈₉	—	2	2	no	—
119	C₂²×D₈₉	—	2	1	no	—
120	C₂²×D₈₉	—	4	1	no	—
121	C₂²×D₈₉	—	4	2	no	—
122	C₂²×D₈₉	—	4	2	no	—
123	C₂²×D₈₉	—	4	2	no	—
124	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
126	Q₈×C₈₉	—	2	1	no	—
127	Q₈×C₈₉	—	2	1	no	—
128	D₄×C₈₉	—	2	1	no	—
129	D₄×C₈₉	—	2	1	no	—
130	D₄×C₈₉	—	4	2	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	1	no	—
136	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₈₉	—	4	2	no	—
139	C₂²⋊D₈₉	—	4	2	no	—
140	C₂²⋊D₈₉	—	4	2	no	—
141	C₂×Dic₈₉	—	2	1	no	—
142	C₂×Dic₈₉	—	2	1	no	—
143	C₂×Dic₈₉	—	2	1	no	—
144	C₂×Dic₈₉	—	4	1	no	—
145	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
147	D₃₅₆	—	2	1	no	—
148	D₃₅₆	—	2	1	no	—
149	D₃₅₆	—	4	2	no	—
150	C₄×D₈₉	—	2	1	no	—
151	C₄×D₈₉	—	2	1	no	—
152	C₄×D₈₉	—	2	1	no	—
153	C₄×D₈₉	—	2	1	no	—
154	C₄×D₈₉	—	4	1	no	—
155	C₄×D₈₉	—	4	1	no	—
156	C₄×D₈₉	—	4	2	no	—
157	C₄×D₈₉	—	4	2	no	—
158	C₄×D₈₉	—	4	2	no	—
159	Dic₁₇₈	—	2	1	no	—
160	Dic₁₇₈	—	2	1	no	—
161	Dic₁₇₈	—	4	2	no	—
162	C₈×C₈₉	—	2	1	no	—
163	C₈×C₈₉	—	2	1	no	—
164	#10623494	—	2	1	no	—
165	#10623494	—	2	1	no	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	4	1	no	—
170	C₂²×C₈₉	—	4	1	no	—
171	C₂²×C₈₉	—	4	1	no	—
172	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×D₈₉	—	2	1	no	—
174	C₂×D₈₉	—	2	1	no	—
175	C₂×D₈₉	—	2	1	no	—
176	C₂×D₈₉	—	2	1	no	—
177	C₂×D₈₉	—	4	4	no	—
178	C₂×D₈₉	—	4	1	no	—
179	C₂×D₈₉	—	4	1	no	—
180	C₂×D₈₉	—	4	1	no	—
181	C₂×D₈₉	—	8	4	no	—
182	C₂×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×D₈₉	#137	1	2	yes	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	4	1	no	—
186	C₄×C₈₉	—	4	1	no	—
187	C₄×C₈₉	—	4	1	no	—
188	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
189	C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
190	Dic₈₉	—	2	1	no	—
191	Dic₈₉	—	2	1	no	—
192	Dic₈₉	—	4	1	no	—
193	Dic₈₉	—	4	1	no	—
194	Dic₈₉	—	4	1	no	—
195	C₂×C₈₉	—	4	1	no	—
196	C₂×C₈₉	—	8	1	no	—
197	C₂×C₈₉	#534	1	1	yes	characteristic
198	C₂×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂×C₈₉	C₂×#137	1	1	yes	characteristic
200	D₈₉	—	2	2	no	—
201	D₈₉	—	2	2	no	—
202	D₈₉	—	8	1	no	—
203	#3193	—	89	1	no	maximal, Sylow
204	C₈₉	#3193	1	1	yes	characteristic, complemented, Sylow
205	C₂×C₂²⋊Q₈	—	89	1	no	—
206	C₂×#121	—	89	1	no	—
207	#484	—	89	1	no	—
208	#484	—	89	1	no	—
209	#480	—	89	1	no	—
210	#480	—	89	1	no	—
211	#468	—	89	1	no	—
212	#468	—	89	1	no	—
213	#468	—	89	1	no	—
214	#468	D₈₉	1	1	yes	characteristic, complemented
215	#450	—	89	1	no	—
216	#450	—	89	1	no	—
217	#448	—	89	1	no	—
218	#448	—	89	1	no	—
219	#407	—	89	1	no	—
220	C₂²×Q₈	—	89	1	no	—
221	C₂²×D₄	—	89	1	no	—
222	C₂²×D₄	—	178	1	no	—
223	C₂³×C₄	—	89	1	no	—
224	C₂×SD₁₆	—	89	1	no	—
225	C₂×SD₁₆	—	89	1	no	—
226	C₂×SD₁₆	—	89	1	no	—
227	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
228	C₂×M₁₆	—	89	1	no	—
229	C₂×M₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
230	C₂²⋊Q₈	—	89	1	no	—
231	C₂²⋊Q₈	—	89	1	no	—
232	C₂²⋊Q₈	—	89	1	no	—
233	C₂²⋊Q₈	—	178	1	no	—
234	C₂²⋊Q₈	—	178	1	no	—
235	C₂²⋊Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
236	#121	—	89	1	no	—
237	#121	—	89	1	no	—
238	#121	—	89	1	no	—
239	#121	—	178	1	no	—
240	#121	—	178	1	no	—
241	#121	C₂×D₈₉	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	89	1	no	—
243	C₂×C₄⋊C₄	—	89	1	no	—
244	C₂×C₄⋊C₄	—	178	1	no	—
245	C₂×C₂²⋊C₄	—	178	1	no	—
246	C₂×C₂²⋊C₄	—	178	1	no	—
247	#107	—	89	1	no	—
248	#107	—	89	1	no	—
249	#107	—	89	1	no	—
250	#107	C₂×D₈₉	1	1	yes	characteristic, complemented
251	#103	—	89	1	no	—
252	#103	—	89	1	no	—
253	#103	—	89	1	no	—
254	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#102	—	89	1	no	—
256	#102	—	89	1	no	—
257	#102	—	89	1	no	—
258	#102	C₂×D₈₉	1	1	yes	characteristic, complemented
259	C₂²⋊C₈	—	89	1	no	—
260	C₂²⋊C₈	—	89	1	no	—
261	C₂²⋊C₈	—	89	1	no	—
262	C₂²⋊C₈	—	89	1	no	—
263	C₂⁴	—	89	1	no	—
264	C₂⁴	—	178	1	no	—
265	C₂×Q₈	—	89	1	no	—
266	C₂×Q₈	—	356	1	no	—
267	C₂×Q₈	—	356	1	no	—
268	C₂×Q₈	—	178	1	no	—
269	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	89	1	no	—
272	C₂×D₄	—	356	4	no	—
273	C₂×D₄	—	356	1	no	—
274	C₂×D₄	—	356	1	no	—
275	C₂×D₄	—	178	1	no	—
276	C₂×D₄	—	178	1	no	—
277	C₂×D₄	—	178	1	no	—
278	C₂×D₄	—	178	1	no	—
279	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
280	C₂²×C₄	—	89	1	no	—
281	C₂²×C₄	—	89	1	no	—
282	C₂²×C₄	—	89	1	no	—
283	C₂²×C₄	—	89	1	no	—
284	C₂²×C₄	—	89	1	no	—
285	C₂²×C₄	—	356	1	no	—
286	C₂²×C₄	—	356	1	no	—
287	C₂²×C₄	—	178	1	no	—
288	C₂²×C₄	—	178	1	no	—
289	C₂²×C₄	—	178	1	no	—
290	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
291	SD₁₆	—	4	1	no	—
292	SD₁₆	—	356	1	no	—
293	SD₁₆	—	356	1	no	—
294	SD₁₆	—	356	1	no	—
295	M₁₆	—	4	1	no	—
296	M₁₆	—	356	1	no	—
297	C₂×C₈	—	89	1	no	—
298	C₂×C₈	—	89	1	no	—
299	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	89	1	no	—
303	C₄⋊C₄	—	89	1	no	—
304	C₄⋊C₄	—	178	1	no	—
305	C₄⋊C₄	—	178	1	no	—
306	C₄⋊C₄	—	178	1	no	—
307	C₄⋊C₄	—	178	1	no	—
308	C₄⋊C₄	—	178	1	no	—
309	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
310	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	178	1	no	—
314	C₂²⋊C₄	—	178	1	no	—
315	C₂²⋊C₄	—	178	1	no	—
316	C₂²⋊C₄	—	178	1	no	—
317	C₂²⋊C₄	—	178	1	no	—
318	C₂²⋊C₄	—	178	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	89	1	no	—
321	C₂³	—	89	1	no	—
322	C₂³	—	356	1	no	—
323	C₂³	—	356	2	no	—
324	C₂³	—	356	2	no	—
325	C₂³	—	356	2	no	—
326	C₂³	—	178	2	no	—
327	C₂³	—	178	2	no	—
328	C₂³	—	178	1	no	—
329	C₂³	D₄×D₈₉	1	1	yes	characteristic
330	Q₈	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	356	2	no	—
333	Q₈	—	178	1	no	—
334	Q₈	—	178	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	2	1	no	—
337	D₄	—	4	2	no	—
338	D₄	—	356	2	no	—
339	D₄	—	356	2	no	—
340	D₄	—	356	2	no	—
341	D₄	—	356	2	no	—
342	D₄	—	178	1	no	—
343	D₄	—	178	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	89	1	no	—
350	C₂×C₄	—	89	1	no	—
351	C₂×C₄	—	356	1	no	—
352	C₂×C₄	—	356	1	no	—
353	C₂×C₄	—	356	2	no	—
354	C₂×C₄	—	356	2	no	—
355	C₂×C₄	—	356	2	no	—
356	C₂×C₄	—	356	1	no	—
357	C₂×C₄	—	178	1	no	—
358	C₂×C₄	—	178	1	no	—
359	C₂×C₄	—	178	1	no	—
360	C₂×C₄	—	178	1	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
365	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	178	1	no	—
369	C₈	—	178	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	89	2	no	—
377	C₂²	—	89	2	no	—
378	C₂²	—	356	4	no	—
379	C₂²	—	356	1	no	—
380	C₂²	—	356	1	no	—
381	C₂²	—	356	1	no	—
382	C₂²	—	178	1	no	—
383	C₂²	—	178	1	no	—
384	C₂²	—	178	1	no	—
385	C₂²	—	178	1	no	—
386	C₂²	—	712	4	no	—
387	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	356	1	no	—
393	C₄	—	356	1	no	—
394	C₄	—	356	1	no	—
395	C₄	—	178	1	no	—
396	C₄	—	178	1	no	—
397	C₄	#15668057	1	1	yes	characteristic
398	C₄	#15668058	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	8	1	no	—
401	C₂	—	178	2	no	—
402	C₂	—	178	2	no	—
403	C₂	—	712	1	no	—
404	C₂	#19152156	1	1	yes	characteristic
405	C₂	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
406	C₂	#137×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₈₉
commutator, cosocle	C₂×C₄×C₈₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₈₉
Fitting	#468×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₄
prime radical	#121×D₈₉	C₂
hypercenter	#468	D₈₉
hypocenter	C₈₉	#3193
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #468

Complements

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

N	H ≅ G/N	type
1. C₂²⋊Q₈×D₈₉	C₂	semidirect
3. #19151935	C₂	semidirect
4. #19151932	C₂	semidirect
5. #19151913	C₂	semidirect
6. #19151910	C₂	semidirect
7. #19151846	C₂	semidirect
8. #19151844	C₂	semidirect
9. #19151842	C₂	semidirect
10. #19151750	C₂	semidirect
11. #19151747	C₂	semidirect
12. #19151738	C₂	semidirect
13. #19151735	C₂	semidirect
14. #19151561	C₂	semidirect
15. #468×C₈₉	C₂	semidirect
16. C₂×Q₈×D₈₉	C₂²	semidirect
20. C₂×#13083563	C₂²	semidirect
21. C₂×#13083562	C₂²	semidirect
22. C₂×#13083561	C₂²	semidirect
23. C₂×#13083558	C₂²	semidirect
25. #15667991	C₂²	semidirect
36. C₄⋊C₄×D₈₉	C₂²	semidirect
39. #15667946	C₂²	semidirect
40. #15667945	C₂²	semidirect
41. #15667945	C₂²	semidirect
42. #15667937	C₂²	semidirect
43. #15667936	C₂²	semidirect
44. #15667935	C₂²	semidirect
45. #15667934	C₂²	semidirect
46. #15667933	C₂²	semidirect
47. #15667932	C₂²	semidirect
50. #15667924	C₂²	semidirect
51. #15667924	C₂²	semidirect
52. C₂×SD₁₆×C₈₉	C₂²	semidirect
53. C₂×M₁₆×C₈₉	C₂²	semidirect
54. C₂²⋊Q₈×C₈₉	C₂²	semidirect
56. #107×C₈₉	C₂²	semidirect
57. #103×C₈₉	C₂²	semidirect
58. #102×C₈₉	C₂²	semidirect
204. C₈₉	#3193	semidirect
214. #468	D₈₉	semidirect
227. C₂×SD₁₆	C₂×D₈₉	semidirect
229. C₂×M₁₆	C₂×D₈₉	semidirect
235. C₂²⋊Q₈	C₂×D₈₉	semidirect
250. #107	C₂×D₈₉	semidirect
254. #103	C₂×D₈₉	semidirect
258. #102	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊Q₈×D₈₉	2
#121×D₈₉	2
#19151935	2
#19151932	2
#19151913	2
#19151910	2
#19151846	2
#19151844	2
#19151842	2
#19151750	2
#19151747	2
#19151738	2
#19151735	2
#19151561	2
#468×C₈₉	2
#3193	89