Subgroups — #28481388

Order 15104.

568 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	C₄²×Dic₁₁₈	C₂	1	1	yes	maximal, characteristic
2	#21424213	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837134	C₂	1	2	yes	maximal
4	#21421936	C₂	1	2	yes	maximal
5	C₄×C₄⋊C₈×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₁₁₈	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₁₁₈	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₁₈	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
10	C₄×Dic₅₉⋊C₄	—	2	1	no	—
11	C₄×Dic₅₉⋊C₄	—	2	1	no	—
12	C₄×Dic₅₉⋊C₄	—	2	1	no	—
13	C₄×C₄⋊Dic₅₉	C₄	1	1	yes	characteristic
14	C₄×C₄⋊Dic₅₉	C₄	1	1	yes	characteristic
15	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
16	C₄²×Dic₅₉	—	2	1	no	—
17	#16837157	—	2	1	no	—
18	#16837157	—	2	1	no	—
19	#16837134	—	2	4	no	—
20	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
21	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
22	C₄³×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#336	—	2	1	no	—
24	C₂²×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₅₉⋊C₈	—	2	2	no	—
26	C₄×Dic₁₁₈	—	2	2	no	—
27	C₄×Dic₁₁₈	—	2	2	no	—
28	C₄×Dic₁₁₈	—	2	1	no	—
29	C₄×Dic₁₁₈	—	2	1	no	—
30	C₄×Dic₁₁₈	—	2	2	no	—
31	C₄×Dic₁₁₈	C₈	1	4	yes	complemented
32	C₄×Dic₁₁₈	D₄	1	2	yes	—
33	C₄×Dic₁₁₈	Q₈	1	2	yes	—
34	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
37	C₂×Dic₅₉⋊C₄	—	2	1	no	—
38	C₂×Dic₅₉⋊C₄	—	2	1	no	—
39	C₂×Dic₅₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₅₉	—	2	1	no	—
41	C₂×C₄×Dic₅₉	—	2	1	no	—
42	C₂×C₄×Dic₅₉	—	2	1	no	—
43	C₂×C₄×Dic₅₉	—	2	1	no	—
44	C₂×C₄×Dic₅₉	—	2	1	no	—
45	C₂×C₄×Dic₅₉	—	2	1	no	—
46	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
47	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
48	C₅₉⋊#95	—	2	1	no	—
49	C₅₉⋊#95	—	2	1	no	—
50	C₅₉⋊#95	—	2	1	no	—
51	C₂²×C₈×C₅₉	—	2	2	no	—
52	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₅₉	—	2	4	no	—
60	C₄×C₈×C₅₉	—	2	2	no	—
61	C₄×C₈×C₅₉	—	2	2	no	—
62	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×Dic₅₉	—	2	1	no	—
70	C₂²×Dic₅₉	—	2	1	no	—
71	C₂²×Dic₅₉	—	2	1	no	—
72	C₂²×Dic₅₉	—	2	1	no	—
73	C₂×Dic₁₁₈	—	2	1	no	—
74	C₂×Dic₁₁₈	—	2	1	no	—
75	C₂×Dic₁₁₈	—	2	1	no	—
76	C₂×Dic₁₁₈	C₄⋊C₄	1	2	yes	—
77	C₂×Dic₁₁₈	C₂×C₈	1	2	yes	—
78	C₂×Dic₁₁₈	M₁₆	1	2	yes	—
79	C₂×C₈×C₅₉	—	2	4	no	—
80	C₂×C₈×C₅₉	—	4	2	no	—
81	C₂×C₈×C₅₉	—	4	2	no	—
82	C₄²×C₅₉	—	2	2	no	—
83	C₄²×C₅₉	—	2	1	no	—
84	C₄²×C₅₉	—	2	1	no	—
85	C₄²×C₅₉	—	2	2	no	—
86	C₄²×C₅₉	—	2	2	no	—
87	C₄²×C₅₉	—	4	1	no	—
88	C₄²×C₅₉	C₂×C₈	1	2	yes	—
89	C₄²×C₅₉	M₁₆	1	2	yes	—
90	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
92	C₄²×C₅₉	#41	1	1	yes	characteristic
93	C₄²×C₅₉	#41	1	1	yes	characteristic
94	C₄⋊Dic₅₉	—	2	1	no	—
95	C₄⋊Dic₅₉	—	2	1	no	—
96	C₄⋊Dic₅₉	—	2	1	no	—
97	C₄⋊Dic₅₉	C₄⋊C₄	1	2	yes	—
98	C₄⋊Dic₅₉	C₂×C₈	1	2	yes	—
99	C₄⋊Dic₅₉	M₁₆	1	2	yes	—
100	Dic₅₉⋊C₄	—	2	4	no	—
101	Dic₅₉⋊C₄	—	2	4	no	—
102	Dic₅₉⋊C₄	—	2	2	no	—
103	Dic₅₉⋊C₄	—	2	2	no	—
104	C₄×Dic₅₉	—	2	4	no	—
105	C₄×Dic₅₉	—	2	4	no	—
106	C₄×Dic₅₉	—	2	2	no	—
107	C₄×Dic₅₉	—	2	2	no	—
108	C₄×Dic₅₉	—	4	2	no	—
109	C₄×Dic₅₉	—	4	2	no	—
110	C₄×Dic₅₉	—	4	2	no	—
111	C₂×C₅₉⋊C₈	—	4	2	no	—
112	C₂×C₅₉⋊C₈	—	4	2	no	—
113	C₂×C₅₉⋊C₈	—	4	2	no	—
114	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₅₉	—	2	1	no	—
116	C₂×C₄×C₅₉	—	2	1	no	—
117	C₂×C₄×C₅₉	—	2	1	no	—
118	C₂×C₄×C₅₉	—	2	1	no	—
119	C₂×C₄×C₅₉	—	2	1	no	—
120	C₂×C₄×C₅₉	—	2	1	no	—
121	C₂×C₄×C₅₉	—	2	1	no	—
122	C₂×C₄×C₅₉	—	2	1	no	—
123	C₂×C₄×C₅₉	—	2	1	no	—
124	C₂×C₄×C₅₉	—	2	1	no	—
125	C₂×C₄×C₅₉	—	2	1	no	—
126	C₂×C₄×C₅₉	C₂²⋊C₈	1	2	yes	—
127	C₂×C₄×C₅₉	C₂²⋊C₈	1	2	yes	—
128	C₂×C₄×C₅₉	#104	1	2	yes	—
129	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
131	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
132	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
133	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₅₉	C₂²×C₈	1	1	yes	characteristic
136	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
137	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
139	C₂×C₄×C₅₉	#135	1	2	yes	—
140	C₂×C₄×C₅₉	#137	1	2	yes	—
141	C₂×Dic₅₉	—	2	2	no	—
142	C₂×Dic₅₉	—	2	2	no	—
143	C₂×Dic₅₉	—	2	2	no	—
144	C₂×Dic₅₉	—	2	2	no	—
145	C₂×Dic₅₉	—	2	2	no	—
146	C₂×Dic₅₉	—	2	2	no	—
147	C₂×Dic₅₉	—	4	1	no	—
148	C₂×Dic₅₉	—	4	1	no	—
149	C₂×Dic₅₉	—	4	1	no	—
150	C₂×Dic₅₉	—	4	1	no	—
151	C₂×Dic₅₉	—	4	1	no	—
152	C₂×Dic₅₉	—	4	1	no	—
153	Dic₁₁₈	—	2	2	no	—
154	Dic₁₁₈	—	2	2	no	—
155	Dic₁₁₈	—	2	2	no	—
156	Dic₁₁₈	C₄⋊C₈	1	4	yes	complemented
157	C₈×C₅₉	—	4	4	no	—
158	C₅₉⋊C₈	—	8	2	no	—
159	#8566	—	59	1	no	maximal, Sylow
160	C₂²×C₅₉	#380	1	1	yes	characteristic
161	C₂²×C₅₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
162	C₂²×C₅₉	#407	1	1	yes	characteristic
163	C₂²×C₅₉	#416	1	1	yes	characteristic
164	C₂²×C₅₉	#419	1	1	yes	characteristic
165	C₂²×C₅₉	C₂×#104	1	1	yes	characteristic
166	C₂²×C₅₉	#421	1	1	yes	characteristic
167	C₄×C₅₉	—	2	1	no	—
168	C₄×C₅₉	—	2	1	no	—
169	C₄×C₅₉	—	2	2	no	—
170	C₄×C₅₉	—	2	2	no	—
171	C₄×C₅₉	—	2	2	no	—
172	C₄×C₅₉	—	4	1	no	—
173	C₄×C₅₉	C₂×C₄⋊C₈	1	1	yes	characteristic
174	C₄×C₅₉	#423	1	1	yes	characteristic
175	C₄×C₅₉	#431	1	1	yes	characteristic
176	C₄×C₅₉	#432	1	1	yes	characteristic
177	C₄×C₅₉	#464	1	2	yes	—
178	C₄×C₅₉	#479	1	2	yes	—
179	Dic₅₉	—	2	4	no	—
180	Dic₅₉	—	4	2	no	—
181	Dic₅₉	—	4	2	no	—
182	Dic₅₉	—	4	2	no	—
183	C₄²×Q₈	—	59	1	no	—
184	#1831	—	59	1	no	—
185	C₄×C₄⋊C₈	D₅₉	1	1	yes	characteristic
186	C₂×Q₈⋊C₈	—	59	2	no	—
187	#1279	—	59	2	no	—
188	C₂×C₅₉	#1476	1	1	yes	characteristic
189	C₂×C₅₉	#1479	1	1	yes	characteristic
190	C₂×C₅₉	#1488	1	1	yes	characteristic
191	C₂×C₅₉	#1491	1	1	yes	characteristic
192	C₂×C₅₉	#1797	1	1	yes	characteristic
193	C₂×C₅₉	#1805	1	1	yes	characteristic
194	C₂×C₅₉	#1806	1	1	yes	characteristic
195	C₂×C₄×Q₈	—	59	1	no	—
196	C₂×C₄×Q₈	—	59	1	no	—
197	C₂×C₄×Q₈	—	59	1	no	—
198	C₂×C₄⋊C₈	—	2	1	no	—
199	C₂×C₄⋊C₈	—	59	2	no	—
200	C₂×C₄×C₈	C₂×D₅₉	1	2	yes	—
201	C₄×C₄⋊C₄	—	59	1	no	—
202	C₄×C₄⋊C₄	—	59	1	no	—
203	C₄×C₄⋊C₄	—	59	1	no	—
204	C₄×C₄⋊C₄	—	118	1	no	—
205	C₄×C₄⋊C₄	—	118	1	no	—
206	C₄×C₄⋊C₄	—	118	1	no	—
207	C₄³	—	118	1	no	—
208	C₄³	C₂×D₅₉	1	1	yes	characteristic
209	#336	—	2	1	no	—
210	#336	—	118	1	no	—
211	#336	—	118	1	no	—
212	Q₈⋊C₈	—	118	4	no	—
213	C₅₉	#8566	1	1	yes	characteristic, complemented, Sylow
214	C₂²×Q₈	—	59	1	no	—
215	C₂²×C₈	—	2	2	no	—
216	C₂²×C₈	—	118	2	no	—
217	C₄×Q₈	—	59	4	no	—
218	C₄×Q₈	—	59	2	no	—
219	C₄×Q₈	—	59	2	no	—
220	C₄×Q₈	—	118	2	no	—
221	C₄×Q₈	—	118	2	no	—
222	C₄×Q₈	—	118	2	no	—
223	C₄×Q₈	—	118	1	no	—
224	C₄×Q₈	—	118	1	no	—
225	C₂×C₄⋊C₄	—	59	1	no	—
226	C₂×C₄⋊C₄	—	59	1	no	—
227	C₂×C₄⋊C₄	—	59	1	no	—
228	C₂×C₄⋊C₄	—	118	1	no	—
229	C₂×C₄⋊C₄	—	118	1	no	—
230	C₂×C₄⋊C₄	—	118	1	no	—
231	C₂×C₄²	—	118	1	no	—
232	C₂×C₄²	—	118	1	no	—
233	C₂×C₄²	—	118	1	no	—
234	C₂×C₄²	—	118	1	no	—
235	C₂×C₄²	—	118	1	no	—
236	C₂×C₄²	—	118	1	no	—
237	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
239	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
240	C₂×C₄²	D₂₃₆	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
244	C₄⋊C₈	—	2	4	no	—
245	C₄⋊C₈	—	118	2	no	—
246	C₄⋊C₈	—	118	2	no	—
247	C₄×C₈	—	2	2	no	—
248	C₄×C₈	—	2	2	no	—
249	#95	—	118	1	no	—
250	#95	—	118	1	no	—
251	#95	—	118	1	no	—
252	C₂×Q₈	—	59	2	no	—
253	C₂×Q₈	—	59	2	no	—
254	C₂×Q₈	—	59	2	no	—
255	C₂×Q₈	—	118	1	no	—
256	C₂×Q₈	—	118	1	no	—
257	C₂×Q₈	—	118	1	no	—
258	C₂²×C₄	—	118	1	no	—
259	C₂²×C₄	—	118	1	no	—
260	C₂²×C₄	—	118	1	no	—
261	C₂²×C₄	—	118	1	no	—
262	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₂₃₆	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	4	2	no	—
271	C₂×C₈	—	4	2	no	—
272	C₂×C₈	—	236	2	no	—
273	C₂×C₈	—	236	2	no	—
274	C₂×C₈	—	236	2	no	—
275	C₄⋊C₄	—	59	2	no	—
276	C₄⋊C₄	—	59	2	no	—
277	C₄⋊C₄	—	59	2	no	—
278	C₄⋊C₄	—	118	4	no	—
279	C₄⋊C₄	—	118	4	no	—
280	C₄⋊C₄	—	118	1	no	—
281	C₄⋊C₄	—	118	2	no	—
282	C₄⋊C₄	—	118	2	no	—
283	C₄⋊C₄	—	118	1	no	—
284	C₄⋊C₄	—	118	1	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	1	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	4	1	no	—
291	C₄²	—	118	4	no	—
292	C₄²	—	118	4	no	—
293	C₄²	—	118	2	no	—
294	C₄²	—	118	2	no	—
295	C₄²	—	236	2	no	—
296	C₄²	—	236	2	no	—
297	C₄²	—	236	2	no	—
298	C₄²	C₈×D₅₉	1	2	yes	—
299	C₄²	#11745659	1	2	yes	—
300	C₄²	D₄×D₅₉	1	1	yes	characteristic
301	C₄²	#11745687	1	1	yes	characteristic
302	C₄²	Q₈×D₅₉	1	1	yes	characteristic
303	C₄²	#11745689	1	1	yes	characteristic
304	C₂³	C₂×(C₂×D₅₉)⋊C₄	1	1	yes	characteristic
305	Q₈	—	59	4	no	—
306	Q₈	—	118	2	no	—
307	Q₈	—	118	2	no	—
308	Q₈	—	118	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	118	2	no	—
321	C₂×C₄	—	118	2	no	—
322	C₂×C₄	—	118	2	no	—
323	C₂×C₄	—	118	2	no	—
324	C₂×C₄	—	118	2	no	—
325	C₂×C₄	—	118	2	no	—
326	C₂×C₄	—	236	1	no	—
327	C₂×C₄	—	236	1	no	—
328	C₂×C₄	—	236	1	no	—
329	C₂×C₄	—	236	1	no	—
330	C₂×C₄	—	236	1	no	—
331	C₂×C₄	—	236	1	no	—
332	C₂×C₄	(C₂×D₅₉)⋊C₈	1	2	yes	—
333	C₂×C₄	(C₂×D₅₉)⋊C₈	1	2	yes	—
334	C₂×C₄	#14273655	1	2	yes	—
335	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
336	C₂×C₄	#14273685	1	1	yes	characteristic
337	C₂×C₄	#14273698	1	1	yes	characteristic
338	C₂×C₄	#14273702	1	1	yes	characteristic
339	C₂×C₄	#14273703	1	1	yes	characteristic
340	C₂×C₄	#14273707	1	1	yes	characteristic
341	C₂×C₄	C₂×C₈×D₅₉	1	1	yes	characteristic
342	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
343	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
344	C₂×C₄	C₂×#11745659	1	1	yes	characteristic
345	C₂×C₄	#14273749	1	2	yes	—
346	C₂×C₄	#14273760	1	2	yes	—
347	C₈	—	4	4	no	—
348	C₈	—	472	2	no	—
349	C₂²	#16837259	1	1	yes	characteristic
350	C₂²	C₂×(C₂×D₅₉)⋊C₈	1	1	yes	characteristic
351	C₂²	#16837365	1	1	yes	characteristic
352	C₂²	#16837399	1	1	yes	characteristic
353	C₂²	#16837412	1	1	yes	characteristic
354	C₂²	C₂×#14273655	1	1	yes	characteristic
355	C₂²	#16837420	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	118	4	no	—
363	C₄	—	236	2	no	—
364	C₄	—	236	2	no	—
365	C₄	—	236	2	no	—
366	C₄	C₄⋊C₈×D₅₉	1	1	yes	characteristic
367	C₄	#16837424	1	1	yes	characteristic
368	C₄	#16837454	1	1	yes	characteristic
369	C₄	#16837458	1	1	yes	characteristic
370	C₄	#16837625	1	2	yes	—
371	C₄	#16837710	1	2	yes	—
372	C₂	#21422479	1	1	yes	characteristic
373	C₂	#21422492	1	1	yes	characteristic
374	C₂	#21422531	1	1	yes	characteristic
375	C₂	#21422544	1	1	yes	characteristic
376	C₂	#21424073	1	1	yes	characteristic
377	C₂	#21424112	1	1	yes	characteristic
378	C₂	#21424117	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₃₆
commutator	C₂×C₄×C₅₉	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₄×C₄⋊C₈×C₅₉	C₂
socle, prime radical	C₂³×C₅₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₅₉
hypocenter	C₅₉	#8566
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
31. C₄×Dic₁₁₈	C₈	semidirect
156. Dic₁₁₈	C₄⋊C₈	semidirect
213. C₅₉	#8566	semidirect

Maximal subgroups

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

subgroup	index
C₄²×Dic₁₁₈	2
#21424213	2
C₂×#16837134	2
#21421936	2
C₄×C₄⋊C₈×C₅₉	2
#8566	59