Subgroups — #26034609

Order 11392.

1060 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152348	C₂	1	1	yes	maximal, characteristic, complemented
2	#19152342	C₂	1	2	yes	maximal, complemented
3	#19152340	C₂	1	1	yes	maximal, characteristic, complemented
4	#19152310	C₂	1	2	yes	maximal, complemented
5	#19152278	C₂	1	2	yes	maximal, complemented
6	#19152274	C₂	1	4	yes	maximal, complemented
7	#19152238	C₂	1	4	yes	maximal, complemented
8	#19152212	C₂	1	4	yes	maximal, complemented
9	#19152182	C₂	1	4	yes	maximal, complemented
10	#19152172	C₂	1	2	yes	maximal, complemented
11	#19152157	C₂	1	2	yes	maximal, complemented
12	#19152132	C₂	1	2	yes	maximal, complemented
13	C₂×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13083574	C₂²	1	2	yes	—
15	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
16	#15668010	C₂²	1	2	yes	complemented
17	#15668010	C₂²	1	2	yes	complemented
18	#15668006	C₂²	1	4	yes	complemented
19	#15668005	C₂²	1	4	yes	complemented
20	#15668005	C₂²	1	4	yes	complemented
21	#15668004	C₂²	1	2	yes	complemented
22	#15668001	C₂²	1	2	yes	complemented
23	#15668001	C₂²	1	2	yes	complemented
24	#15668000	C₂²	1	2	yes	complemented
25	#15667998	C₂²	1	4	yes	complemented
26	#15667998	C₂²	1	4	yes	complemented
27	#15667996	C₂²	1	4	yes	complemented
28	#15667995	C₂²	1	4	yes	complemented
29	#15667995	C₂²	1	4	yes	complemented
30	#15667994	C₂²	1	4	yes	complemented
31	#15667994	C₂²	1	4	yes	complemented
32	#15667993	C₂²	1	2	yes	—
33	#15667993	C₂²	1	2	yes	complemented
34	#15667991	C₂²	1	2	yes	complemented
35	#15667989	C₂²	1	4	yes	complemented
36	#15667989	C₂²	1	4	yes	complemented
37	#15667988	C₂²	1	4	yes	complemented
38	#15667988	C₂²	1	4	yes	complemented
39	#15667986	C₂²	1	2	yes	—
40	#15667985	C₂²	1	4	yes	complemented
41	#15667985	C₂²	1	4	yes	complemented
42	#15667984	C₂²	1	4	yes	—
43	#15667984	C₂²	1	4	yes	complemented
44	#15667982	C₂²	1	4	yes	complemented
45	#15667981	C₂²	1	4	yes	—
46	#15667980	C₂²	1	2	yes	—
47	#15667980	C₂²	1	2	yes	complemented
48	C₄×Dic₁₇₈	C₂²	1	2	yes	complemented
49	C₄×D₃₅₆	C₂²	1	2	yes	complemented
50	C₄×C₂²⋊D₈₉	C₂²	1	4	yes	complemented
51	#15667972	C₂²	1	4	yes	complemented
52	#15667972	C₂²	1	4	yes	complemented
53	#15667971	C₂²	1	2	yes	complemented
54	#15667969	C₂²	1	4	yes	complemented
55	#15667968	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Dic₈₉	C₂²	1	2	yes	complemented
57	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	complemented
58	C₂²×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
60	#124×C₈₉	C₂²	1	1	yes	characteristic
61	#124×C₈₉	C₂²	1	1	yes	characteristic
62	#124×C₈₉	C₂²	1	4	yes	complemented
63	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
66	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂³×D₈₉	C₂³	1	2	yes	—
68	#13083574	—	4	4	no	—
69	C₂×Dic₁₇₈	C₂³	1	2	yes	—
70	C₂×Dic₁₇₈	C₂³	1	2	yes	—
71	C₂×D₃₅₆	C₂³	1	2	yes	—
72	C₂×D₃₅₆	C₂³	1	2	yes	—
73	C₂×C₂²⋊D₈₉	—	4	4	no	—
74	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
75	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
78	C₂²×Dic₈₉	C₂³	1	4	yes	—
79	C₂²×Dic₈₉	C₂³	1	2	yes	—
80	C₂×C₄×D₈₉	C₂³	1	4	yes	—
81	C₂×C₄×D₈₉	C₂³	1	4	yes	—
82	C₄⋊Dic₈₉	C₂³	1	4	yes	—
83	C₄⋊Dic₈₉	C₂³	1	2	yes	—
84	C₄⋊Dic₈₉	C₂³	1	2	yes	—
85	#13083553	C₂³	1	4	yes	—
86	#13083553	C₂³	1	4	yes	—
87	#13083553	C₂³	1	4	yes	—
88	#13083553	C₂³	1	4	yes	—
89	#13083553	C₂³	1	4	yes	—
90	#13083553	C₂³	1	4	yes	—
91	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
92	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
93	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
94	C₂²⋊Dic₈₉	C₂³	1	2	yes	—
95	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
96	#13083551	C₂³	1	4	yes	—
97	#13083551	C₂³	1	4	yes	—
98	#13083551	C₂³	1	4	yes	—
99	#13083551	C₂³	1	4	yes	—
100	#13083551	C₂³	1	4	yes	—
101	#13083551	C₂³	1	4	yes	—
102	C₄×Dic₈₉	C₂³	1	2	yes	—
103	C₄×Dic₈₉	C₂³	1	4	yes	—
104	C₄×Dic₈₉	C₂³	1	2	yes	—
105	C₂⁴×C₈₉	C₂³	1	2	yes	—
106	C₂×Q₈×C₈₉	—	4	2	no	—
107	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₈₉	C₂³	1	2	yes	—
109	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₈₉	—	4	2	no	—
111	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₈₉	C₂³	1	2	yes	—
113	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
117	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
118	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
119	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	C₄²×C₈₉	C₂³	1	2	yes	—
123	C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂³×C₈₉	—	2	4	no	—
125	C₂³×C₈₉	—	4	4	no	—
126	C₂³×C₈₉	C₂⁴	1	2	yes	—
127	C₂³×C₈₉	C₂⁴	1	2	yes	—
128	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
129	C₂²×D₈₉	—	4	2	no	—
130	C₂²×D₈₉	—	4	4	no	—
131	C₂²×D₈₉	C₂⁴	1	4	yes	—
132	Q₈×C₈₉	—	4	1	no	—
133	Q₈×C₈₉	—	4	2	no	—
134	Q₈×C₈₉	—	4	1	no	—
135	D₄×C₈₉	—	4	1	no	—
136	D₄×C₈₉	—	4	2	no	—
137	D₄×C₈₉	—	4	1	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
143	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
146	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂²⋊D₈₉	—	2	8	no	—
148	C₂²⋊D₈₉	—	4	4	no	—
149	C₂²⋊D₈₉	—	4	4	no	—
150	C₂²⋊D₈₉	—	4	4	no	—
151	C₂×Dic₈₉	—	4	4	no	—
152	C₂×Dic₈₉	—	4	2	no	—
153	C₂×Dic₈₉	C₂⁴	1	4	yes	—
154	C₂×Dic₈₉	C₂⁴	1	4	yes	—
155	C₂×Dic₈₉	C₂⁴	1	4	yes	—
156	D₃₅₆	—	4	2	no	—
157	D₃₅₆	—	4	2	no	—
158	C₄×D₈₉	—	4	4	no	—
159	C₄×D₈₉	—	4	4	no	—
160	Dic₁₇₈	—	4	2	no	—
161	Dic₁₇₈	—	4	2	no	—
162	C₂²×C₈₉	—	2	2	no	—
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	4	no	—
166	C₂²×C₈₉	—	2	4	no	—
167	C₂²×C₈₉	—	8	4	no	—
168	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
170	C₂×D₈₉	—	2	4	no	—
171	C₂×D₈₉	—	2	4	no	—
172	C₂×D₈₉	—	2	4	no	—
173	C₂×D₈₉	—	8	4	no	—
174	C₄×C₈₉	—	2	2	no	—
175	C₄×C₈₉	—	2	2	no	—
176	C₄×C₈₉	—	2	1	no	—
177	C₄×C₈₉	—	2	1	no	—
178	C₄×C₈₉	—	2	2	no	—
179	C₄×C₈₉	—	2	2	no	—
180	Dic₈₉	—	2	4	no	—
181	Dic₈₉	—	2	4	no	—
182	Dic₈₉	—	2	4	no	—
183	C₂×C₈₉	—	2	2	no	—
184	C₂×C₈₉	—	4	2	no	—
185	C₂×C₈₉	—	4	2	no	—
186	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₈₉	#585	1	2	yes	—
188	D₈₉	—	4	4	no	—
189	#3545	—	89	1	no	maximal, Sylow
190	C₈₉	#3545	1	1	yes	characteristic, complemented, Sylow
191	#563	—	89	1	no	—
192	#562	—	89	2	no	—
193	H(3,𝔽₄)	—	89	1	no	—
194	#555	—	89	2	no	—
195	#551	—	89	2	no	—
196	#551	—	89	4	no	—
197	#546	—	89	4	no	—
198	#542	—	89	4	no	—
199	#538	—	89	4	no	—
200	#536	—	89	2	no	—
201	#534	—	89	2	no	—
202	#529	—	89	2	no	—
203	C₂×#124	D₈₉	1	1	yes	characteristic, complemented
204	C₂×#41	—	89	2	no	—
205	C₂²×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
206	C₂²×D₄	—	89	2	no	—
207	C₂²×D₄	C₂×D₈₉	1	1	yes	characteristic
208	C₄⋊Q₈	—	89	2	no	—
209	C₄⋊Q₈	—	89	2	no	—
210	#126	—	89	4	no	—
211	#126	—	89	4	no	—
212	#126	—	89	4	no	—
213	#125	—	89	2	no	—
214	#124	—	89	2	no	—
215	#124	—	89	2	no	—
216	#124	—	89	4	no	—
217	#124	—	89	4	no	—
218	#124	—	89	2	no	—
219	#124	C₂×D₈₉	1	1	yes	characteristic
220	#124	C₂×D₈₉	1	1	yes	characteristic
221	#124	C₂×D₈₉	1	4	yes	complemented
222	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
223	#124	C₂×D₈₉	1	1	yes	characteristic, complemented
224	#123	—	89	2	no	—
225	#123	—	89	2	no	—
226	#123	—	89	4	no	—
227	#123	—	89	4	no	—
228	#123	—	89	4	no	—
229	#123	—	89	4	no	—
230	#123	—	89	4	no	—
231	C₂²⋊Q₈	—	89	4	no	—
232	C₂²⋊Q₈	—	89	4	no	—
233	C₂²⋊Q₈	—	89	2	no	—
234	C₂²⋊Q₈	—	89	4	no	—
235	C₂²⋊Q₈	—	89	4	no	—
236	#121	—	89	4	no	—
237	#121	—	89	4	no	—
238	#121	—	89	2	no	—
239	#121	—	89	4	no	—
240	#121	—	89	4	no	—
241	#120	—	89	4	no	—
242	#120	—	89	2	no	—
243	#120	—	89	2	no	—
244	#120	—	89	4	no	—
245	C₄×Q₈	—	89	2	no	—
246	C₄×D₄	—	89	4	no	—
247	C₄×D₄	—	89	4	no	—
248	C₄×D₄	—	89	4	no	—
249	C₄×D₄	—	89	2	no	—
250	#117	—	89	2	no	—
251	#117	—	89	4	no	—
252	#117	—	89	4	no	—
253	C₂×C₂²⋊C₄	—	89	2	no	—
254	C₂×C₂²⋊C₄	—	89	4	no	—
255	C₂×C₂²⋊C₄	C₂×D₈₉	1	4	yes	complemented
256	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic, complemented
257	C₂⁴	—	89	2	no	—
258	C₂⁴	C₂²×D₈₉	1	2	yes	—
259	#41	—	356	4	no	—
260	C₂×Q₈	—	4	2	no	—
261	C₂×Q₈	—	89	2	no	—
262	C₂×Q₈	—	89	2	no	—
263	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
264	C₂×Q₈	C₂²×D₈₉	1	2	yes	—
265	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	89	4	no	—
268	C₂×D₄	—	89	4	no	—
269	C₂×D₄	—	89	4	no	—
270	C₂×D₄	—	89	4	no	—
271	C₂×D₄	—	89	2	no	—
272	C₂×D₄	—	89	2	no	—
273	C₂×D₄	—	356	4	no	—
274	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
275	C₂×D₄	C₂²×D₈₉	1	2	yes	—
276	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
277	C₂²×C₄	—	89	4	no	—
278	C₂²×C₄	—	89	2	no	—
279	C₂²×C₄	—	89	4	no	—
280	C₂²×C₄	—	89	4	no	—
281	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
282	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
283	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
284	C₄⋊C₄	—	89	4	no	—
285	C₄⋊C₄	—	89	4	no	—
286	C₄⋊C₄	—	89	4	no	—
287	C₄⋊C₄	—	89	4	no	—
288	C₄⋊C₄	—	89	4	no	—
289	C₄⋊C₄	—	89	4	no	—
290	C₄⋊C₄	—	89	2	no	—
291	C₄⋊C₄	—	89	2	no	—
292	C₄⋊C₄	—	89	4	no	—
293	C₂²⋊C₄	—	89	4	no	—
294	C₂²⋊C₄	—	89	4	no	—
295	C₂²⋊C₄	—	89	2	no	—
296	C₂²⋊C₄	—	89	2	no	—
297	C₂²⋊C₄	—	89	4	no	—
298	C₂²⋊C₄	—	89	4	no	—
299	C₂²⋊C₄	—	89	4	no	—
300	C₂²⋊C₄	—	89	4	no	—
301	C₂²⋊C₄	—	89	4	no	—
302	C₂²⋊C₄	—	89	4	no	—
303	C₂²⋊C₄	—	89	4	no	—
304	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
305	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
306	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
307	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
308	C₄²	—	89	2	no	—
309	C₄²	—	89	4	no	—
310	C₄²	—	89	2	no	—
311	C₄²	C₂²×D₈₉	1	1	yes	characteristic
312	C₄²	C₂²×D₈₉	1	2	yes	—
313	C₄²	C₂²×D₈₉	1	1	yes	characteristic
314	C₂³	—	2	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	89	4	no	—
317	C₂³	—	356	2	no	—
318	C₂³	—	356	4	no	—
319	C₂³	C₂³×D₈₉	1	2	yes	—
320	C₂³	C₂³×D₈₉	1	2	yes	—
321	C₂³	C₂³×D₈₉	1	1	yes	characteristic
322	Q₈	—	4	1	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	356	2	no	—
326	Q₈	—	356	2	no	—
327	D₄	—	4	1	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	1	no	—
330	D₄	—	356	2	no	—
331	D₄	—	356	2	no	—
332	D₄	—	356	4	no	—
333	D₄	—	356	4	no	—
334	D₄	—	356	4	no	—
335	D₄	—	178	8	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	89	4	no	—
340	C₂×C₄	—	89	4	no	—
341	C₂×C₄	—	89	4	no	—
342	C₂×C₄	—	356	4	no	—
343	C₂×C₄	—	356	4	no	—
344	C₂×C₄	—	356	4	no	—
345	C₂×C₄	—	356	2	no	—
346	C₂×C₄	C₂³×D₈₉	1	2	yes	—
347	C₂×C₄	C₂³×D₈₉	1	2	yes	—
348	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
349	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
350	C₂×C₄	C₂³×D₈₉	1	2	yes	—
351	C₂×C₄	C₂³×D₈₉	1	2	yes	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	178	4	no	—
359	C₂²	—	178	4	no	—
360	C₂²	—	178	4	no	—
361	C₂²	—	712	4	no	—
362	C₂²	#15668057	1	2	yes	—
363	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	178	4	no	—
371	C₄	—	178	4	no	—
372	C₄	—	178	4	no	—
373	C₂	—	2	2	no	—
374	C₂	—	4	2	no	—
375	C₂	—	4	2	no	—
376	C₂	—	356	4	no	—
377	C₂	C₂×#15668057	1	1	yes	characteristic
378	C₂	#19152434	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	C₂×#124×C₈₉	C₂
hypercenter	C₂×#124	D₈₉
hypocenter	C₈₉	#3545
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. #19152348	C₂	semidirect
2. #19152342	C₂	semidirect
3. #19152340	C₂	semidirect
4. #19152310	C₂	semidirect
5. #19152278	C₂	semidirect
6. #19152274	C₂	semidirect
7. #19152238	C₂	semidirect
8. #19152212	C₂	semidirect
9. #19152182	C₂	semidirect
10. #19152172	C₂	semidirect
11. #19152157	C₂	semidirect
12. #19152132	C₂	semidirect
13. C₂×#124×C₈₉	C₂	semidirect
15. C₂²×C₂²⋊D₈₉	C₂²	semidirect
16. #15668010	C₂²	semidirect
17. #15668010	C₂²	semidirect
18. #15668006	C₂²	semidirect
19. #15668005	C₂²	semidirect
20. #15668005	C₂²	semidirect
21. #15668004	C₂²	semidirect
22. #15668001	C₂²	semidirect
23. #15668001	C₂²	semidirect
24. #15668000	C₂²	semidirect
25. #15667998	C₂²	semidirect
26. #15667998	C₂²	semidirect
27. #15667996	C₂²	semidirect
28. #15667995	C₂²	semidirect
29. #15667995	C₂²	semidirect
30. #15667994	C₂²	semidirect
31. #15667994	C₂²	semidirect
33. #15667993	C₂²	semidirect
34. #15667991	C₂²	semidirect
35. #15667989	C₂²	semidirect
36. #15667989	C₂²	semidirect
37. #15667988	C₂²	semidirect
38. #15667988	C₂²	semidirect
40. #15667985	C₂²	semidirect
41. #15667985	C₂²	semidirect
43. #15667984	C₂²	semidirect
44. #15667982	C₂²	semidirect
47. #15667980	C₂²	semidirect
48. C₄×Dic₁₇₈	C₂²	semidirect
49. C₄×D₃₅₆	C₂²	semidirect
50. C₄×C₂²⋊D₈₉	C₂²	semidirect
51. #15667972	C₂²	semidirect
52. #15667972	C₂²	semidirect
53. #15667971	C₂²	semidirect
54. #15667969	C₂²	semidirect
55. #15667968	C₂²	semidirect
56. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
57. C₂²⋊C₄×D₈₉	C₂²	semidirect
58. C₂²×Q₈×C₈₉	C₂²	semidirect
62. #124×C₈₉	C₂²	semidirect
63. #124×C₈₉	C₂²	semidirect
64. #124×C₈₉	C₂²	semidirect
65. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
66. C₂×C₄²×C₈₉	C₂²	semidirect
190. C₈₉	#3545	semidirect
203. C₂×#124	D₈₉	semidirect
205. C₂²×Q₈	C₂×D₈₉	semidirect
221. #124	C₂×D₈₉	semidirect
222. #124	C₂×D₈₉	semidirect
223. #124	C₂×D₈₉	semidirect
255. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
256. C₂×C₄²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152348	2
#19152342	2
#19152340	2
#19152310	2
#19152278	2
#19152274	2
#19152238	2
#19152212	2
#19152182	2
#19152172	2
#19152157	2
#19152132	2
C₂×#124×C₈₉	2
#3545	89