Subgroups — #28587260

Order 15104.

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×#16837525	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837523	C₂	1	1	yes	maximal, characteristic
3	#21432867	C₂	1	1	yes	maximal, characteristic
4	#21432518	C₂	1	2	yes	maximal, complemented
5	#108×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#21423982	C₂	1	1	yes	maximal, characteristic, complemented
7	#21423942	C₂	1	2	yes	maximal, complemented
8	#21423937	C₂	1	2	yes	maximal, complemented
9	#21423900	C₂	1	2	yes	maximal, complemented
10	#97×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273749	C₂²	1	1	yes	characteristic
13	C₂×#14273735	C₂²	1	2	yes	—
14	C₂×#14273733	C₂²	1	2	yes	—
15	#16837870	C₂²	1	2	yes	—
16	#16837525	C₄	1	8	yes	complemented
17	#16837523	C₄	1	8	yes	complemented
18	#16837496	C₄	1	2	yes	complemented
19	#16837489	C₄	1	4	yes	complemented
20	#16837484	C₄	1	2	yes	complemented
21	C₂×#14273663	C₂²	1	1	yes	characteristic
22	C₂×#14273655	C₂²	1	2	yes	—
23	C₂×#14273653	C₂²	1	2	yes	—
24	#16837396	C₂²	1	2	yes	—
25	#16837359	—	2	2	no	—
26	#16837358	C₂²	1	2	yes	—
27	#16837356	—	2	2	no	—
28	#16837354	—	2	2	no	—
29	M₁₆×Dic₅₉	C₂²	1	2	yes	—
30	C₂×#14273638	C₂²	1	1	yes	characteristic
31	C₂×#14273637	C₂²	1	1	yes	characteristic
32	C₂×#14273637	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₅₉	—	2	2	no	—
36	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
37	#16837166	C₂²	1	2	yes	—
38	#16837161	C₂²	1	2	yes	—
39	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#427	C₂²	1	1	yes	characteristic
41	C₅₉×#405	C₂²	1	2	yes	—
42	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#339	C₂²	1	2	yes	—
44	C₂×#11745685	C₂³	1	2	yes	—
45	#14273749	C₂×C₄	1	4	yes	—
46	#14273749	C₂×C₄	1	4	yes	—
47	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#11745660	C₂×C₄	1	2	yes	—
49	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
50	#14273735	—	2	4	no	—
51	#14273735	C₂×C₄	1	8	yes	complemented
52	#14273733	—	2	4	no	—
53	#14273733	C₂×C₄	1	8	yes	complemented
54	C₂×#11745664	C₂³	1	2	yes	—
55	C₂×#11745659	—	2	2	no	—
56	C₂×#11745659	—	2	2	no	—
57	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₅₉	—	2	2	no	—
60	C₂×C₈×D₅₉	—	2	2	no	—
61	#14273692	C₂×C₄	1	4	yes	—
62	#14273689	C₂×C₄	1	4	yes	—
63	(C₂²⋊D₅₉)⋊C₄	—	2	4	no	—
64	#14273684	—	2	2	no	—
65	C₂×C₄×Dic₅₉	—	2	2	no	—
66	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
68	C₄²×D₅₉	—	2	2	no	—
69	#14273663	C₂×C₄	1	4	yes	complemented
70	#14273655	C₂×C₄	1	8	yes	complemented
71	#14273653	C₂×C₄	1	8	yes	complemented
72	#14273650	C₂×C₄	1	4	yes	—
73	#14273647	C₂×C₄	1	4	yes	—
74	#14273638	—	2	2	no	—
75	#14273638	—	2	2	no	—
76	#14273637	—	2	2	no	—
77	#14273637	—	2	2	no	—
78	#14273637	C₂×C₄	1	4	yes	complemented
79	C₄×C₅₉⋊C₈	—	2	2	no	—
80	C₈×Dic₅₉	—	2	2	no	—
81	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
82	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
83	C₈×Dic₅₉	D₄	1	2	yes	—
84	C₈×Dic₅₉	D₄	1	2	yes	—
85	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
86	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	#117×C₅₉	C₂³	1	2	yes	—
89	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
90	#108×C₅₉	C₂×C₄	1	4	yes	complemented
91	#107×C₅₉	C₂×C₄	1	2	yes	—
92	#106×C₅₉	C₂×C₄	1	2	yes	—
93	#97×C₅₉	—	2	2	no	—
94	#97×C₅₉	C₂×C₄	1	4	yes	complemented
95	C₄×C₈×C₅₉	—	2	2	no	—
96	C₂²×C₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₅₉	—	2	2	no	—
99	C₂²×Dic₅₉	—	2	1	no	—
100	C₂²×Dic₅₉	#41	1	2	yes	—
101	#11745685	—	2	2	no	—
102	#11745685	—	2	2	no	—
103	#11745685	C₂²×C₄	1	4	yes	—
104	#11745685	C₂²×C₄	1	4	yes	—
105	C₂×D₂₃₆	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₅₉	—	2	2	no	—
107	C₂×C₄×D₅₉	—	2	4	no	—
108	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
109	M₁₆×C₅₉	—	2	2	no	—
110	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₅₉	—	2	2	no	—
112	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₅₉	#41	1	2	yes	—
119	C₄⋊C₄×C₅₉	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₅₉	—	2	2	no	—
121	C₄²×C₅₉	—	2	2	no	—
122	C₄²×C₅₉	—	2	1	no	—
123	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
124	(C₂×D₅₉)⋊C₄	—	2	4	no	—
125	Dic₅₉⋊C₄	—	2	4	no	—
126	C₄×Dic₅₉	—	2	1	no	—
127	C₄×Dic₅₉	—	2	4	no	—
128	C₄×Dic₅₉	—	4	4	no	—
129	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
130	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
131	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
133	#11745664	—	2	2	no	—
134	#11745664	C₂²×C₄	1	4	yes	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	1	no	—
137	C₂×C₅₉⋊C₈	—	2	1	no	—
138	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
141	C₂×C₅₉⋊C₈	#41	1	2	yes	—
142	Dic₂₃₆	C₄²	1	4	yes	complemented
143	D₄₇₂	C₄²	1	4	yes	complemented
144	#11745660	C₄²	1	8	yes	complemented
145	#11745659	—	2	8	no	—
146	#11745659	—	2	8	no	—
147	C₈×D₅₉	—	2	8	no	—
148	C₈×D₅₉	—	2	8	no	—
149	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
150	C₂²×D₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	2	4	no	—
152	C₂×C₄×C₅₉	—	2	2	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
160	C₂²⋊D₅₉	—	2	4	no	—
161	C₂²⋊D₅₉	—	2	4	no	—
162	C₂×Dic₅₉	—	2	2	no	—
163	C₂×Dic₅₉	—	2	4	no	—
164	C₂×Dic₅₉	—	2	2	no	—
165	C₂×Dic₅₉	—	4	2	no	—
166	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
167	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
168	D₂₃₆	—	2	2	no	—
169	D₂₃₆	C₂×C₄²	1	4	yes	—
170	C₄×D₅₉	—	2	4	no	—
171	C₄×D₅₉	—	2	4	no	—
172	C₄×D₅₉	—	4	8	no	—
173	Dic₁₁₈	—	2	2	no	—
174	Dic₁₁₈	C₂×C₄²	1	4	yes	—
175	C₈×C₅₉	—	2	4	no	—
176	C₈×C₅₉	C₂×C₄²	1	2	yes	—
177	C₈×C₅₉	C₂×C₄²	1	2	yes	—
178	C₈×C₅₉	C₄×D₄	1	4	yes	—
179	C₅₉⋊C₈	—	2	4	no	—
180	C₅₉⋊C₈	—	2	2	no	—
181	C₅₉⋊C₈	C₄×D₄	1	4	yes	—
182	C₄×#444	—	59	1	no	maximal, Sylow
183	C₂²×C₅₉	—	2	2	no	—
184	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
186	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
187	C₂×D₅₉	—	2	4	no	—
188	C₂×D₅₉	—	4	4	no	—
189	C₄×C₅₉	—	4	2	no	—
190	C₄×C₅₉	—	4	4	no	—
191	C₄×C₅₉	C₂²×C₄²	1	1	yes	characteristic
192	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
195	Dic₅₉	—	2	2	no	—
196	Dic₅₉	—	2	4	no	—
197	Dic₅₉	—	4	2	no	—
198	Dic₅₉	#444	1	4	yes	complemented
199	C₂×#444	—	59	1	no	—
200	C₂×#444	—	59	1	no	—
201	C₄×#135	—	59	1	no	—
202	C₄×#131	—	59	2	no	—
203	C₄×#108	—	59	1	no	—
204	#1773	—	59	1	no	—
205	#1773	D₅₉	1	1	yes	characteristic, complemented
206	#1765	—	59	2	no	—
207	#1765	—	59	2	no	—
208	C₄×#104	—	59	2	no	—
209	C₄×#97	—	59	1	no	—
210	C₂×C₅₉	—	2	1	no	—
211	C₂×C₅₉	—	2	1	no	—
212	C₂×C₅₉	C₄²×D₄	1	1	yes	characteristic
213	C₂×C₅₉	C₂×#444	1	2	yes	—
214	D₅₉	—	4	4	no	—
215	C₂×#135	—	59	1	no	—
216	C₂×#131	—	59	2	no	—
217	C₂×#131	—	59	2	no	—
218	C₄×#41	—	59	2	no	—
219	#444	—	59	8	no	—
220	#444	—	59	8	no	—
221	C₄×Q₁₆	—	59	2	no	—
222	C₄×SD₁₆	—	59	4	no	—
223	C₄×D₈	—	59	2	no	—
224	C₂×#108	—	59	1	no	—
225	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
226	#427	C₂×D₅₉	1	1	yes	characteristic
227	C₂×#104	—	59	2	no	—
228	C₂×#104	—	59	2	no	—
229	#416	—	59	2	no	—
230	#405	—	59	2	no	—
231	#405	—	118	2	no	—
232	#405	—	118	2	no	—
233	#405	C₂×D₅₉	1	2	yes	—
234	C₄×M₁₆	—	59	2	no	—
235	C₄×M₁₆	—	118	2	no	—
236	C₂×#97	—	59	1	no	—
237	C₂×#97	—	59	1	no	—
238	C₂×#97	—	59	1	no	—
239	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
240	C₂×C₄×C₈	—	59	1	no	—
241	C₂×C₄×C₈	—	59	1	no	—
242	C₂×C₄×C₈	—	118	2	no	—
243	C₄³	—	59	1	no	—
244	#341	—	59	2	no	—
245	#339	—	59	2	no	—
246	#339	C₂×D₅₉	1	2	yes	—
247	C₅₉	C₄×#444	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	59	2	no	—
249	#135	—	59	4	no	—
250	#135	—	59	4	no	—
251	C₂×Q₁₆	—	59	1	no	—
252	C₂×SD₁₆	—	59	2	no	—
253	C₂×D₈	—	59	1	no	—
254	#131	—	59	8	no	—
255	#131	—	59	8	no	—
256	#131	—	118	4	no	—
257	#131	—	118	4	no	—
258	C₂×M₁₆	—	59	2	no	—
259	C₂×M₁₆	—	118	2	no	—
260	C₂×M₁₆	—	118	2	no	—
261	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
262	C₂²×C₈	—	59	1	no	—
263	C₂²×C₈	—	59	1	no	—
264	C₂²×C₈	—	118	2	no	—
265	C₂²×C₈	—	118	2	no	—
266	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
268	C₄×Q₈	—	59	4	no	—
269	C₄×D₄	—	59	4	no	—
270	C₄×D₄	—	118	4	no	—
271	#117	—	118	2	no	—
272	#117	C₂²×D₅₉	1	2	yes	—
273	C₂×C₄²	—	59	1	no	—
274	C₂×C₄²	—	59	1	no	—
275	C₂×C₄²	—	118	2	no	—
276	C₂×C₄²	—	118	2	no	—
277	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
278	#108	—	59	4	no	—
279	#108	C₄×D₅₉	1	4	yes	complemented
280	#107	C₄×D₅₉	1	2	yes	—
281	#106	C₄×D₅₉	1	2	yes	—
282	#104	—	59	8	no	—
283	#104	—	59	8	no	—
284	#103	—	59	4	no	—
285	#102	—	59	4	no	—
286	#97	—	2	2	no	—
287	#97	—	59	4	no	—
288	#97	—	118	2	no	—
289	#97	—	118	2	no	—
290	#97	—	118	2	no	—
291	#97	—	118	2	no	—
292	#97	C₄×D₅₉	1	4	yes	complemented
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	59	2	no	—
295	C₄×C₈	—	59	2	no	—
296	C₄×C₈	—	59	2	no	—
297	C₄×C₈	—	59	2	no	—
298	C₄×C₈	—	118	2	no	—
299	C₄×C₈	—	118	2	no	—
300	#41	—	59	4	no	—
301	#41	—	59	4	no	—
302	#41	—	118	2	no	—
303	#41	—	118	2	no	—
304	C₂×Q₈	—	59	2	no	—
305	C₂×D₄	—	59	2	no	—
306	C₂×D₄	—	118	2	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	59	2	no	—
309	C₂²×C₄	—	118	4	no	—
310	C₂²×C₄	—	118	2	no	—
311	C₂²×C₄	—	118	1	no	—
312	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
313	Q₁₆	—	59	4	no	—
314	SD₁₆	—	59	8	no	—
315	D₈	—	59	4	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	59	4	no	—
318	M₁₆	—	118	8	no	—
319	M₁₆	—	118	2	no	—
320	M₁₆	—	118	8	no	—
321	M₁₆	C₂×C₄×D₅₉	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	59	2	no	—
324	C₂×C₈	—	59	2	no	—
325	C₂×C₈	—	59	2	no	—
326	C₂×C₈	—	59	2	no	—
327	C₂×C₈	—	118	8	no	—
328	C₂×C₈	—	118	2	no	—
329	C₂×C₈	—	118	1	no	—
330	C₂×C₈	—	118	1	no	—
331	C₂×C₈	—	118	8	no	—
332	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
335	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
337	C₂×C₈	D₄×D₅₉	1	2	yes	—
338	C₂×C₈	#11745689	1	2	yes	—
339	C₄⋊C₄	—	118	4	no	—
340	C₄⋊C₄	C₂×C₄×D₅₉	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	118	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	59	2	no	—
346	C₄²	—	59	1	no	—
347	C₄²	—	59	1	no	—
348	C₄²	—	59	2	no	—
349	C₄²	—	118	4	no	—
350	C₄²	—	118	1	no	—
351	C₄²	—	236	4	no	—
352	C₄²	C₂×C₄×D₅₉	1	2	yes	—
353	C₂³	—	118	2	no	—
354	C₂³	#41×D₅₉	1	1	yes	characteristic
355	Q₈	—	59	4	no	—
356	Q₈	—	118	2	no	—
357	D₄	—	59	4	no	—
358	D₄	—	118	4	no	—
359	D₄	—	118	4	no	—
360	D₄	—	118	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	59	2	no	—
365	C₂×C₄	—	59	2	no	—
366	C₂×C₄	—	118	4	no	—
367	C₂×C₄	—	118	2	no	—
368	C₂×C₄	—	118	4	no	—
369	C₂×C₄	—	118	4	no	—
370	C₂×C₄	—	118	2	no	—
371	C₂×C₄	—	236	8	no	—
372	C₂×C₄	—	236	2	no	—
373	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
377	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	59	4	no	—
381	C₈	—	118	4	no	—
382	C₈	—	118	2	no	—
383	C₈	C₄²×D₅₉	1	2	yes	—
384	C₈	C₄²×D₅₉	1	2	yes	—
385	C₈	#14273689	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	118	4	no	—
388	C₂²	—	236	4	no	—
389	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
390	C₂²	#16837870	1	1	yes	characteristic
391	C₂²	C₄×#11745689	1	1	yes	characteristic
392	C₄	—	4	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	59	4	no	—
395	C₄	—	118	4	no	—
396	C₄	—	118	2	no	—
397	C₄	—	236	2	no	—
398	C₄	C₂×C₄²×D₅₉	1	1	yes	characteristic
399	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
400	C₄	C₂×#14273689	1	1	yes	characteristic
401	C₄	C₄×#11745689	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	236	4	no	—
405	C₂	C₄×#14273689	1	1	yes	characteristic
406	C₂	#444×D₅₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1773	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273749	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1773	D₅₉
hypocenter	C₅₉	C₄×#444
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1773

Complements

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

N	H ≅ G/N	type
4. #21432518	C₂	semidirect
5. #108×Dic₅₉	C₂	semidirect
6. #21423982	C₂	semidirect
7. #21423942	C₂	semidirect
8. #21423937	C₂	semidirect
9. #21423900	C₂	semidirect
10. #97×Dic₅₉	C₂	semidirect
11. C₅₉×#1773	C₂	semidirect
16. #16837525	C₄	semidirect
17. #16837523	C₄	semidirect
18. #16837496	C₄	semidirect
19. #16837489	C₄	semidirect
20. #16837484	C₄	semidirect
51. #14273735	C₂×C₄	semidirect
53. #14273733	C₂×C₄	semidirect
69. #14273663	C₂×C₄	semidirect
70. #14273655	C₂×C₄	semidirect
71. #14273653	C₂×C₄	semidirect
78. #14273637	C₂×C₄	semidirect
90. #108×C₅₉	C₂×C₄	semidirect
94. #97×C₅₉	C₂×C₄	semidirect
142. Dic₂₃₆	C₄²	semidirect
143. D₄₇₂	C₄²	semidirect
144. #11745660	C₄²	semidirect
198. Dic₅₉	#444	semidirect
205. #1773	D₅₉	semidirect
247. C₅₉	C₄×#444	semidirect
279. #108	C₄×D₅₉	semidirect
292. #97	C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837525	2
C₂×#16837523	2
#21432867	2
#21432518	2
#108×Dic₅₉	2
#21423982	2
#21423942	2
#21423937	2
#21423900	2
#97×Dic₅₉	2
C₅₉×#1773	2
C₄×#444	59