Subgroups — #36552999

Order 22784.

1022 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	C₂×#19151721	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151719	C₂	1	1	yes	maximal, characteristic
3	#26029023	C₂	1	1	yes	maximal, characteristic
4	#26028674	C₂	1	2	yes	maximal, complemented
5	#108×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020138	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020098	C₂	1	2	yes	maximal, complemented
8	#26020093	C₂	1	2	yes	maximal, complemented
9	#26020056	C₂	1	2	yes	maximal, complemented
10	#97×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668034	C₂²	1	1	yes	characteristic
13	C₂×#15668020	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	2	yes	—
15	#19152066	C₂²	1	2	yes	—
16	#19151721	C₄	1	8	yes	complemented
17	#19151719	C₄	1	8	yes	complemented
18	#19151692	C₄	1	2	yes	complemented
19	#19151685	C₄	1	4	yes	complemented
20	#19151680	C₄	1	2	yes	complemented
21	C₂×#15667948	C₂²	1	1	yes	characteristic
22	C₂×#15667940	C₂²	1	2	yes	—
23	C₂×#15667938	C₂²	1	2	yes	—
24	#19151592	C₂²	1	2	yes	—
25	#19151555	—	2	2	no	—
26	#19151554	C₂²	1	2	yes	—
27	#19151552	—	2	2	no	—
28	#19151550	—	2	2	no	—
29	M₁₆×Dic₈₉	C₂²	1	2	yes	—
30	C₂×#15667923	C₂²	1	1	yes	characteristic
31	C₂×#15667922	C₂²	1	1	yes	characteristic
32	C₂×#15667922	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	—	2	2	no	—
36	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
37	#19151362	C₂²	1	2	yes	—
38	#19151357	C₂²	1	2	yes	—
39	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
40	#427×C₈₉	C₂²	1	1	yes	characteristic
41	#405×C₈₉	C₂²	1	2	yes	—
42	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
43	#339×C₈₉	C₂²	1	2	yes	—
44	C₂×#13083574	C₂³	1	2	yes	—
45	#15668034	C₂×C₄	1	4	yes	—
46	#15668034	C₂×C₄	1	4	yes	—
47	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083563	C₂×C₄	1	2	yes	—
49	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
50	#15668020	—	2	4	no	—
51	#15668020	C₂×C₄	1	8	yes	complemented
52	#15668018	—	2	4	no	—
53	#15668018	C₂×C₄	1	8	yes	complemented
54	C₂×#13083558	C₂³	1	2	yes	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×#13083557	—	2	2	no	—
57	C₂²×#10623494	C₂³	1	1	yes	characteristic
58	C₂²×#10623494	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₈₉	—	2	2	no	—
60	C₂×C₈×D₈₉	—	2	2	no	—
61	#15667977	C₂×C₄	1	4	yes	—
62	#15667974	C₂×C₄	1	4	yes	—
63	#15667972	—	2	4	no	—
64	#15667969	—	2	2	no	—
65	C₂×C₄×Dic₈₉	—	2	2	no	—
66	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
68	C₄²×D₈₉	—	2	2	no	—
69	#15667948	C₂×C₄	1	4	yes	complemented
70	#15667940	C₂×C₄	1	8	yes	complemented
71	#15667938	C₂×C₄	1	8	yes	complemented
72	#15667935	C₂×C₄	1	4	yes	—
73	#15667932	C₂×C₄	1	4	yes	—
74	#15667923	—	2	2	no	—
75	#15667923	—	2	2	no	—
76	#15667922	—	2	2	no	—
77	#15667922	—	2	2	no	—
78	#15667922	C₂×C₄	1	4	yes	complemented
79	C₄×#10623494	—	2	2	no	—
80	C₈×Dic₈₉	—	2	2	no	—
81	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
82	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
83	C₈×Dic₈₉	D₄	1	2	yes	—
84	C₈×Dic₈₉	D₄	1	2	yes	—
85	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	#117×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	#108×C₈₉	C₂×C₄	1	4	yes	complemented
91	#107×C₈₉	C₂×C₄	1	2	yes	—
92	#106×C₈₉	C₂×C₄	1	2	yes	—
93	#97×C₈₉	—	2	2	no	—
94	#97×C₈₉	C₂×C₄	1	4	yes	complemented
95	C₄×C₈×C₈₉	—	2	2	no	—
96	#13083574	—	2	2	no	—
97	#13083574	—	2	2	no	—
98	#13083574	C₂²×C₄	1	4	yes	—
99	#13083574	C₂²×C₄	1	4	yes	—
100	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
101	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
102	C₂×C₂²⋊D₈₉	—	2	2	no	—
103	C₂²×Dic₈₉	—	2	1	no	—
104	C₂²×Dic₈₉	#41	1	2	yes	—
105	C₂×C₄×D₈₉	—	2	2	no	—
106	C₂×C₄×D₈₉	—	2	4	no	—
107	Dic₃₅₆	C₄²	1	4	yes	complemented
108	#13083563	C₄²	1	8	yes	complemented
109	D₇₁₂	C₄²	1	4	yes	complemented
110	#13083558	—	2	2	no	—
111	#13083558	C₂²×C₄	1	4	yes	—
112	#13083557	—	2	8	no	—
113	#13083557	—	2	8	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	C₂²×C₄	1	2	yes	—
118	C₂×#10623494	C₂²×C₄	1	2	yes	—
119	C₂×#10623494	C₂×D₄	1	2	yes	—
120	C₂×#10623494	#41	1	2	yes	—
121	C₈×D₈₉	—	2	8	no	—
122	C₈×D₈₉	—	2	8	no	—
123	#13083553	—	2	4	no	—
124	#13083551	—	2	4	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	4	no	—
127	C₄×Dic₈₉	—	4	4	no	—
128	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
129	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
130	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	—	2	1	no	—
133	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₈₉	—	2	2	no	—
135	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₈₉	#41	1	2	yes	—
144	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	1	no	—
148	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
149	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
150	C₂²×D₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	4	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
160	C₂²⋊D₈₉	—	2	4	no	—
161	C₂²⋊D₈₉	—	2	4	no	—
162	C₂×Dic₈₉	—	2	2	no	—
163	C₂×Dic₈₉	—	2	4	no	—
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	4	2	no	—
166	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
167	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
168	D₃₅₆	—	2	2	no	—
169	D₃₅₆	C₂×C₄²	1	4	yes	—
170	C₄×D₈₉	—	2	4	no	—
171	C₄×D₈₉	—	2	4	no	—
172	C₄×D₈₉	—	4	8	no	—
173	Dic₁₇₈	—	2	2	no	—
174	Dic₁₇₈	C₂×C₄²	1	4	yes	—
175	C₈×C₈₉	—	2	4	no	—
176	C₈×C₈₉	C₂×C₄²	1	2	yes	—
177	C₈×C₈₉	C₂×C₄²	1	2	yes	—
178	C₈×C₈₉	C₄×D₄	1	4	yes	—
179	#10623494	—	2	4	no	—
180	#10623494	—	2	2	no	—
181	#10623494	C₄×D₄	1	4	yes	—
182	C₂²×C₈₉	—	2	2	no	—
183	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
185	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
186	C₂×D₈₉	—	2	4	no	—
187	C₂×D₈₉	—	4	4	no	—
188	C₄×C₈₉	—	4	2	no	—
189	C₄×C₈₉	—	4	4	no	—
190	C₄×C₈₉	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
194	Dic₈₉	—	2	2	no	—
195	Dic₈₉	—	2	4	no	—
196	Dic₈₉	—	4	2	no	—
197	Dic₈₉	#444	1	4	yes	complemented
198	C₄×#444	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	—	2	1	no	—
200	C₂×C₈₉	—	2	1	no	—
201	C₂×C₈₉	C₄²×D₄	1	1	yes	characteristic
202	C₂×C₈₉	C₂×#444	1	2	yes	—
203	D₈₉	—	4	4	no	—
204	C₂×#444	—	89	1	no	—
205	C₂×#444	—	89	1	no	—
206	C₄×#135	—	89	1	no	—
207	C₄×#131	—	89	2	no	—
208	C₄×#108	—	89	1	no	—
209	#1773	—	89	1	no	—
210	#1773	D₈₉	1	1	yes	characteristic, complemented
211	#1765	—	89	2	no	—
212	#1765	—	89	2	no	—
213	C₄×#104	—	89	2	no	—
214	C₄×#97	—	89	1	no	—
215	C₈₉	C₄×#444	1	1	yes	characteristic, complemented, Sylow
216	C₂×#135	—	89	1	no	—
217	C₂×#131	—	89	2	no	—
218	C₂×#131	—	89	2	no	—
219	C₄×#41	—	89	2	no	—
220	#444	—	89	8	no	—
221	#444	—	89	8	no	—
222	C₄×Q₁₆	—	89	2	no	—
223	C₄×SD₁₆	—	89	4	no	—
224	C₄×D₈	—	89	2	no	—
225	C₂×#108	—	89	1	no	—
226	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
227	#427	C₂×D₈₉	1	1	yes	characteristic
228	C₂×#104	—	89	2	no	—
229	C₂×#104	—	89	2	no	—
230	#416	—	89	2	no	—
231	#405	—	89	2	no	—
232	#405	—	178	2	no	—
233	#405	—	178	2	no	—
234	#405	C₂×D₈₉	1	2	yes	—
235	C₄×M₁₆	—	89	2	no	—
236	C₄×M₁₆	—	178	2	no	—
237	C₂×#97	—	89	1	no	—
238	C₂×#97	—	89	1	no	—
239	C₂×#97	—	89	1	no	—
240	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
241	C₂×C₄×C₈	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	178	2	no	—
244	C₄³	—	89	1	no	—
245	#341	—	89	2	no	—
246	#339	—	89	2	no	—
247	#339	C₂×D₈₉	1	2	yes	—
248	C₂×#41	—	89	2	no	—
249	#135	—	89	4	no	—
250	#135	—	89	4	no	—
251	C₂×Q₁₆	—	89	1	no	—
252	C₂×SD₁₆	—	89	2	no	—
253	C₂×D₈	—	89	1	no	—
254	#131	—	89	8	no	—
255	#131	—	89	8	no	—
256	#131	—	178	4	no	—
257	#131	—	178	4	no	—
258	C₂×M₁₆	—	89	2	no	—
259	C₂×M₁₆	—	178	2	no	—
260	C₂×M₁₆	—	178	2	no	—
261	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	—	178	2	no	—
265	C₂²×C₈	—	178	2	no	—
266	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
268	C₄×Q₈	—	89	4	no	—
269	C₄×D₄	—	89	4	no	—
270	C₄×D₄	—	178	4	no	—
271	#117	—	178	2	no	—
272	#117	C₂²×D₈₉	1	2	yes	—
273	C₂×C₄²	—	89	1	no	—
274	C₂×C₄²	—	89	1	no	—
275	C₂×C₄²	—	178	2	no	—
276	C₂×C₄²	—	178	2	no	—
277	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
278	#108	—	89	4	no	—
279	#108	C₄×D₈₉	1	4	yes	complemented
280	#107	C₄×D₈₉	1	2	yes	—
281	#106	C₄×D₈₉	1	2	yes	—
282	#104	—	89	8	no	—
283	#104	—	89	8	no	—
284	#103	—	89	4	no	—
285	#102	—	89	4	no	—
286	#97	—	2	2	no	—
287	#97	—	89	4	no	—
288	#97	—	178	2	no	—
289	#97	—	178	2	no	—
290	#97	—	178	2	no	—
291	#97	—	178	2	no	—
292	#97	C₄×D₈₉	1	4	yes	complemented
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	89	2	no	—
295	C₄×C₈	—	89	2	no	—
296	C₄×C₈	—	89	2	no	—
297	C₄×C₈	—	89	2	no	—
298	C₄×C₈	—	178	2	no	—
299	C₄×C₈	—	178	2	no	—
300	#41	—	89	4	no	—
301	#41	—	89	4	no	—
302	#41	—	178	2	no	—
303	#41	—	178	2	no	—
304	C₂×Q₈	—	89	2	no	—
305	C₂×D₄	—	89	2	no	—
306	C₂×D₄	—	178	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	89	2	no	—
309	C₂²×C₄	—	178	4	no	—
310	C₂²×C₄	—	178	1	no	—
311	C₂²×C₄	—	178	2	no	—
312	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
313	Q₁₆	—	89	4	no	—
314	SD₁₆	—	89	8	no	—
315	D₈	—	89	4	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	89	4	no	—
318	M₁₆	—	178	8	no	—
319	M₁₆	—	178	2	no	—
320	M₁₆	—	178	8	no	—
321	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	89	2	no	—
326	C₂×C₈	—	89	2	no	—
327	C₂×C₈	—	178	8	no	—
328	C₂×C₈	—	178	2	no	—
329	C₂×C₈	—	178	1	no	—
330	C₂×C₈	—	178	1	no	—
331	C₂×C₈	—	178	8	no	—
332	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
337	C₂×C₈	D₄×D₈₉	1	2	yes	—
338	C₂×C₈	#13083575	1	2	yes	—
339	C₄⋊C₄	—	178	4	no	—
340	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	178	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	89	2	no	—
346	C₄²	—	89	1	no	—
347	C₄²	—	89	1	no	—
348	C₄²	—	89	2	no	—
349	C₄²	—	356	4	no	—
350	C₄²	—	178	4	no	—
351	C₄²	—	178	1	no	—
352	C₄²	C₂×C₄×D₈₉	1	2	yes	—
353	C₂³	—	178	2	no	—
354	C₂³	#41×D₈₉	1	1	yes	characteristic
355	Q₈	—	89	4	no	—
356	Q₈	—	178	2	no	—
357	D₄	—	89	4	no	—
358	D₄	—	178	4	no	—
359	D₄	—	178	4	no	—
360	D₄	—	178	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	89	2	no	—
365	C₂×C₄	—	89	2	no	—
366	C₂×C₄	—	356	8	no	—
367	C₂×C₄	—	356	2	no	—
368	C₂×C₄	—	178	4	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	4	no	—
372	C₂×C₄	—	178	4	no	—
373	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
377	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	89	4	no	—
381	C₈	—	178	4	no	—
382	C₈	—	178	2	no	—
383	C₈	C₄²×D₈₉	1	2	yes	—
384	C₈	C₄²×D₈₉	1	2	yes	—
385	C₈	#15667974	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	356	4	no	—
388	C₂²	—	178	4	no	—
389	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
390	C₂²	#19152066	1	1	yes	characteristic
391	C₂²	C₄×#13083575	1	1	yes	characteristic
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	89	4	no	—
395	C₄	—	356	2	no	—
396	C₄	—	178	2	no	—
397	C₄	—	178	4	no	—
398	C₄	C₂×C₄²×D₈₉	1	1	yes	characteristic
399	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
400	C₄	C₂×#15667974	1	1	yes	characteristic
401	C₄	C₄×#13083575	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	356	4	no	—
405	C₂	C₄×#15667974	1	1	yes	characteristic
406	C₂	#444×D₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1773	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668034	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1773	D₈₉
hypocenter	C₈₉	C₄×#444
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
4. #26028674	C₂	semidirect
5. #108×Dic₈₉	C₂	semidirect
6. #26020138	C₂	semidirect
7. #26020098	C₂	semidirect
8. #26020093	C₂	semidirect
9. #26020056	C₂	semidirect
10. #97×Dic₈₉	C₂	semidirect
11. C₈₉×#1773	C₂	semidirect
16. #19151721	C₄	semidirect
17. #19151719	C₄	semidirect
18. #19151692	C₄	semidirect
19. #19151685	C₄	semidirect
20. #19151680	C₄	semidirect
51. #15668020	C₂×C₄	semidirect
53. #15668018	C₂×C₄	semidirect
69. #15667948	C₂×C₄	semidirect
70. #15667940	C₂×C₄	semidirect
71. #15667938	C₂×C₄	semidirect
78. #15667922	C₂×C₄	semidirect
90. #108×C₈₉	C₂×C₄	semidirect
94. #97×C₈₉	C₂×C₄	semidirect
107. Dic₃₅₆	C₄²	semidirect
108. #13083563	C₄²	semidirect
109. D₇₁₂	C₄²	semidirect
197. Dic₈₉	#444	semidirect
210. #1773	D₈₉	semidirect
215. C₈₉	C₄×#444	semidirect
279. #108	C₄×D₈₉	semidirect
292. #97	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151721	2
C₂×#19151719	2
#26029023	2
#26028674	2
#108×Dic₈₉	2
#26020138	2
#26020098	2
#26020093	2
#26020056	2
#97×Dic₈₉	2
C₈₉×#1773	2
C₄×#444	89