Subgroups — #28742114

Order 15104.

642 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×#16837832	C₂	1	1	yes	maximal, characteristic
2	#21433014	C₂	1	1	yes	maximal, characteristic, complemented
3	#21425980	C₂	1	4	yes	maximal, complemented
4	#21425975	C₂	1	4	yes	maximal, complemented
5	C₂×#16837231	C₂	1	1	yes	maximal, characteristic, complemented
6	#21425824	C₂	1	1	yes	maximal, characteristic, complemented
7	#21425823	C₂	1	1	yes	maximal, characteristic, complemented
8	#21425693	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14273749	C₂²	1	1	yes	characteristic
11	#16838168	—	2	1	no	—
12	#16837832	C₄	1	2	yes	complemented
13	#16837832	C₄	1	2	yes	complemented
14	#16837832	C₂²	1	2	yes	—
15	#16837832	C₂²	1	2	yes	—
16	C₂×#14273673	C₄	1	1	yes	characteristic, complemented
17	C₂×#14273671	C₄	1	1	yes	characteristic, complemented
18	C₂×#14273670	C₄	1	1	yes	characteristic, complemented
19	C₂×#14273668	C₄	1	1	yes	characteristic, complemented
20	C₂×#14273667	C₂²	1	1	yes	characteristic
21	C₂²×C₅₉⋊C₁₆	C₂²	1	1	yes	characteristic
22	#16837525	—	2	2	no	—
23	#16837520	C₂²	1	4	yes	complemented
24	C₂×#14273663	C₂²	1	1	yes	characteristic
25	#16837420	—	2	1	no	—
26	#16837231	C₂²	1	2	yes	complemented
27	#16837231	C₂²	1	2	yes	complemented
28	#16837209	C₂²	1	4	yes	complemented
29	#16837208	C₂²	1	4	yes	complemented
30	#16837178	C₂²	1	2	yes	complemented
31	C₄×C₅₉⋊C₁₆	C₂²	1	2	yes	complemented
32	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#568	—	2	1	no	—
34	C₅₉×#444	—	2	2	no	—
35	C₅₉×#443	C₂²	1	4	yes	complemented
36	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#421	—	2	1	no	—
38	C₅₉×#405	C₂²	1	1	yes	characteristic
39	C₂×#11745685	—	2	1	no	—
40	#14273749	—	2	1	no	—
41	#14273749	—	2	1	no	—
42	#14273749	C₂×C₄	1	2	yes	—
43	#14273749	C₂³	1	2	yes	—
44	C₂×Dic₂₃₆	C₂×C₄	1	1	yes	characteristic
45	C₂×#11745660	—	2	1	no	—
46	C₂×D₄₇₂	C₂×C₄	1	1	yes	characteristic
47	#14273735	—	4	2	no	—
48	#14273733	—	2	4	no	—
49	C₂×#11745664	—	2	1	no	—
50	M₁₆×D₅₉	—	4	2	no	—
51	#14273673	C₂×C₄	1	2	yes	—
52	#14273673	C₂×C₄	1	2	yes	—
53	#14273671	C₂×C₄	1	2	yes	—
54	#14273671	C₂×C₄	1	2	yes	—
55	#14273670	C₂×C₄	1	2	yes	—
56	#14273670	C₂×C₄	1	2	yes	—
57	#14273668	C₂×C₄	1	2	yes	—
58	#14273668	C₂×C₄	1	2	yes	—
59	#14273667	—	2	1	no	—
60	#14273667	—	2	1	no	—
61	C₂×C₅₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
63	C₂×C₅₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
64	C₂×C₅₉⋊C₁₆	C₂×C₄	1	1	yes	characteristic
65	C₂×C₅₉⋊C₁₆	C₂³	1	2	yes	—
66	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
67	C₂×C₅₉⋊C₁₆	C₂³	1	1	yes	characteristic
68	#14273663	—	2	1	no	—
69	#14273663	C₂³	1	2	yes	—
70	#14273655	—	2	4	no	—
71	C₂×#41×C₅₉	—	2	1	no	—
72	#135×C₅₉	—	2	1	no	—
73	#135×C₅₉	—	2	1	no	—
74	#135×C₅₉	C₂×C₄	1	2	yes	—
75	#135×C₅₉	C₂³	1	2	yes	—
76	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×SD₁₆×C₅₉	—	2	1	no	—
78	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
79	#131×C₅₉	—	2	4	no	—
80	#131×C₅₉	—	4	2	no	—
81	C₂×M₁₆×C₅₉	—	2	1	no	—
82	C₂×M₁₆×C₅₉	—	4	2	no	—
83	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
85	#117×C₅₉	D₄	1	1	yes	characteristic
86	#108×C₅₉	—	2	1	no	—
87	#108×C₅₉	C₂³	1	2	yes	—
88	#104×C₅₉	—	2	4	no	—
89	#97×C₅₉	D₄	1	2	yes	—
90	C₄×C₈×C₅₉	C₂³	1	2	yes	—
91	#41×C₅₉	—	2	2	no	—
92	#41×C₅₉	—	2	2	no	—
93	#41×C₅₉	—	4	1	no	—
94	#41×C₅₉	—	4	1	no	—
95	C₂×Q₈×C₅₉	—	2	1	no	—
96	C₂×D₄×C₅₉	—	2	1	no	—
97	C₂×D₄×C₅₉	—	4	1	no	—
98	C₂²×C₄×C₅₉	—	4	1	no	—
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂×C₂²⋊D₅₉	—	4	1	no	—
101	#11745685	—	2	2	no	—
102	#11745685	—	2	2	no	—
103	#11745685	—	4	1	no	—
104	#11745685	—	4	1	no	—
105	C₂×D₂₃₆	—	2	1	no	—
106	C₂×C₄×D₅₉	—	4	1	no	—
107	C₂×Dic₁₁₈	—	2	1	no	—
108	Q₁₆×C₅₉	—	2	1	no	—
109	Q₁₆×C₅₉	C₂²×C₄	1	2	yes	—
110	SD₁₆×C₅₉	—	2	2	no	—
111	SD₁₆×C₅₉	—	2	2	no	—
112	D₈×C₅₉	—	2	1	no	—
113	D₈×C₅₉	C₂²×C₄	1	2	yes	—
114	M₁₆×C₅₉	—	2	2	no	—
115	M₁₆×C₅₉	—	4	1	no	—
116	M₁₆×C₅₉	—	4	4	no	—
117	M₁₆×C₅₉	D₈	1	2	yes	—
118	M₁₆×C₅₉	D₈	1	2	yes	—
119	C₂×C₈×C₅₉	—	4	1	no	—
120	C₂×C₈×C₅₉	—	4	4	no	—
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
126	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
127	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₂²⋊C₄×C₅₉	—	2	1	no	—
130	C₄²×C₅₉	C₂×D₄	1	2	yes	—
131	#11745664	—	2	2	no	—
132	#11745664	—	4	1	no	—
133	C₂×C₅₉⋊C₈	—	4	1	no	—
134	Dic₂₃₆	—	2	1	no	—
135	Dic₂₃₆	C₂²×C₄	1	2	yes	—
136	D₄₇₂	—	2	1	no	—
137	D₄₇₂	C₂²×C₄	1	2	yes	—
138	#11745660	—	2	2	no	—
139	#11745660	—	2	2	no	—
140	#11745659	—	4	4	no	—
141	C₈×D₅₉	—	4	4	no	—
142	C₅₉⋊C₁₆	—	2	2	no	—
143	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
144	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
145	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
146	C₅₉⋊C₁₆	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₅₉	—	4	1	no	—
148	C₂³×C₅₉	#135	1	1	yes	characteristic
149	C₂²×D₅₉	—	4	1	no	—
150	Q₈×C₅₉	—	2	2	no	—
151	Q₈×C₅₉	—	4	1	no	—
152	D₄×C₅₉	—	2	2	no	—
153	D₄×C₅₉	—	4	2	no	—
154	D₄×C₅₉	—	4	2	no	—
155	D₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	—	2	2	no	—
157	C₂×C₄×C₅₉	—	4	1	no	—
158	C₂×C₄×C₅₉	—	4	2	no	—
159	C₂×C₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
166	C₂²⋊D₅₉	—	4	2	no	—
167	C₂²⋊D₅₉	—	4	2	no	—
168	C₂×Dic₅₉	—	4	1	no	—
169	D₂₃₆	—	2	2	no	—
170	D₂₃₆	—	4	1	no	—
171	C₄×D₅₉	—	4	2	no	—
172	C₄×D₅₉	—	4	2	no	—
173	Dic₁₁₈	—	2	2	no	—
174	Dic₁₁₈	—	4	1	no	—
175	C₈×C₅₉	—	4	2	no	—
176	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
177	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
178	C₈×C₅₉	C₂×D₈	1	4	yes	—
179	C₈×C₅₉	C₂³×C₄	1	1	yes	characteristic
180	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
181	C₅₉⋊C₈	—	4	2	no	—
182	#33465	—	59	1	no	maximal, Sylow
183	C₂²×C₅₉	—	4	1	no	—
184	C₂²×C₅₉	—	4	2	no	—
185	C₂²×C₅₉	—	16	1	no	—
186	C₂²×C₅₉	C₄×D₈	1	1	yes	characteristic
187	C₂²×C₅₉	C₄×D₈	1	1	yes	characteristic
188	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
189	C₂×D₅₉	—	4	2	no	—
190	C₂×D₅₉	—	16	1	no	—
191	C₄×C₅₉	—	4	2	no	—
192	C₄×C₅₉	—	4	2	no	—
193	C₄×C₅₉	C₄×D₈	1	1	yes	characteristic
194	C₄×C₅₉	C₄×D₈	1	1	yes	characteristic
195	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
197	Dic₅₉	—	4	2	no	—
198	C₂×#508	—	59	1	no	—
199	#2957	—	59	1	no	—
200	#2957	D₅₉	1	1	yes	characteristic, complemented
201	#2179	—	59	4	no	—
202	#2178	—	59	4	no	—
203	C₂×#368	—	59	1	no	—
204	#2143	—	59	1	no	—
205	#2143	—	59	1	no	—
206	#2108	—	59	1	no	—
207	C₂×C₅₉	—	2	1	no	—
208	C₂×C₅₉	—	2	1	no	—
209	C₂×C₅₉	—	2	1	no	—
210	C₂×C₅₉	—	8	2	no	—
211	C₂×C₅₉	C₂×C₄×D₈	1	1	yes	characteristic
212	D₅₉	—	8	2	no	—
213	C₂×#135	—	59	1	no	—
214	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
215	#568	—	2	1	no	—
216	#568	—	118	1	no	—
217	#508	—	59	2	no	—
218	#508	—	59	2	no	—
219	#508	—	59	2	no	—
220	#508	—	59	2	no	—
221	C₂×Q₃₂	—	59	1	no	—
222	C₂×SD₃₂	—	59	1	no	—
223	C₂×SD₃₂	—	59	1	no	—
224	C₂×D₁₆	—	59	1	no	—
225	C₂×M₃₂	—	59	1	no	—
226	C₂²×C₁₆	—	59	1	no	—
227	#444	—	2	2	no	—
228	#444	—	118	2	no	—
229	#443	—	59	4	no	—
230	#443	C₂×D₅₉	1	4	yes	complemented
231	C₂×#108	—	59	1	no	—
232	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
233	#421	—	2	1	no	—
234	#421	—	118	1	no	—
235	#405	C₂×D₅₉	1	1	yes	characteristic
236	#368	—	59	2	no	—
237	#368	—	59	2	no	—
238	#359	—	59	4	no	—
239	#359	—	59	4	no	—
240	#346	—	59	2	no	—
241	C₄×C₁₆	—	59	2	no	—
242	C₅₉	#33465	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	2	1	no	—
244	C₂×#41	—	118	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	59	2	no	—
248	#135	—	59	2	no	—
249	#135	—	118	1	no	—
250	#135	—	118	1	no	—
251	#135	C₄×D₅₉	1	2	yes	—
252	#135	C₂²×D₅₉	1	2	yes	—
253	C₂×Q₁₆	—	59	1	no	—
254	C₂×Q₁₆	C₄×D₅₉	1	1	yes	characteristic
255	C₂×SD₁₆	—	2	1	no	—
256	C₂×SD₁₆	—	118	1	no	—
257	C₂×D₈	—	59	1	no	—
258	C₂×D₈	C₄×D₅₉	1	1	yes	characteristic
259	#131	—	2	4	no	—
260	#131	—	4	2	no	—
261	#131	—	118	4	no	—
262	#131	—	236	2	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	4	2	no	—
265	C₂×M₁₆	—	118	1	no	—
266	C₂×M₁₆	—	236	2	no	—
267	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
269	#117	C₂²⋊D₅₉	1	1	yes	characteristic
270	Q₃₂	—	59	2	no	—
271	Q₃₂	—	59	2	no	—
272	SD₃₂	—	59	2	no	—
273	SD₃₂	—	59	2	no	—
274	SD₃₂	—	59	2	no	—
275	SD₃₂	—	59	2	no	—
276	D₁₆	—	59	2	no	—
277	D₁₆	—	59	2	no	—
278	M₃₂	—	118	1	no	—
279	M₃₂	—	118	1	no	—
280	C₂×C₁₆	—	59	1	no	—
281	C₂×C₁₆	—	59	1	no	—
282	C₂×C₁₆	—	59	1	no	—
283	C₂×C₁₆	—	59	1	no	—
284	C₂×C₁₆	—	59	1	no	—
285	C₂×C₁₆	—	59	1	no	—
286	C₂×C₁₆	—	59	2	no	—
287	#108	—	2	1	no	—
288	#108	—	59	2	no	—
289	#108	—	118	1	no	—
290	#108	C₂²×D₅₉	1	2	yes	—
291	#104	—	2	4	no	—
292	#104	—	118	4	no	—
293	#97	C₂²⋊D₅₉	1	2	yes	—
294	C₄×C₈	C₂²×D₅₉	1	2	yes	—
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	#41	—	4	1	no	—
298	#41	—	4	1	no	—
299	#41	—	118	2	no	—
300	#41	—	118	2	no	—
301	#41	—	236	1	no	—
302	#41	—	236	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	118	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	118	1	no	—
308	C₂×D₄	—	236	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	236	1	no	—
311	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
312	Q₁₆	—	2	1	no	—
313	Q₁₆	—	59	2	no	—
314	Q₁₆	—	118	1	no	—
315	Q₁₆	C₂×C₄×D₅₉	1	2	yes	—
316	SD₁₆	—	2	2	no	—
317	SD₁₆	—	2	2	no	—
318	SD₁₆	—	118	2	no	—
319	SD₁₆	—	118	2	no	—
320	D₈	—	2	1	no	—
321	D₈	—	59	2	no	—
322	D₈	—	118	1	no	—
323	D₈	C₂×C₄×D₅₉	1	2	yes	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	4	4	no	—
327	M₁₆	—	118	2	no	—
328	M₁₆	—	236	1	no	—
329	M₁₆	—	236	4	no	—
330	M₁₆	#11745669	1	2	yes	—
331	M₁₆	#11745669	1	2	yes	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	4	no	—
334	C₂×C₈	—	236	1	no	—
335	C₂×C₈	—	236	4	no	—
336	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
338	C₂×C₈	#11745685	1	1	yes	characteristic
339	C₂×C₈	#11745685	1	1	yes	characteristic
340	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
342	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₄²	C₂×C₂²⋊D₅₉	1	2	yes	—
346	C₁₆	—	59	1	no	—
347	C₁₆	—	59	1	no	—
348	C₁₆	—	59	1	no	—
349	C₁₆	—	59	1	no	—
350	C₁₆	—	118	2	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	236	1	no	—
353	C₂³	#14273747	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	4	1	no	—
356	Q₈	—	118	2	no	—
357	Q₈	—	236	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	1	no	—
362	D₄	—	118	2	no	—
363	D₄	—	236	2	no	—
364	D₄	—	236	2	no	—
365	D₄	—	236	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	236	1	no	—
371	C₂×C₄	—	236	2	no	—
372	C₂×C₄	—	236	2	no	—
373	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
376	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
377	C₂×C₄	#14273747	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
379	C₈	—	4	2	no	—
380	C₈	—	236	2	no	—
381	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
382	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
383	C₈	C₂×#11745669	1	4	yes	—
384	C₈	C₂²×C₄×D₅₉	1	1	yes	characteristic
385	C₈	C₂×#11745685	1	1	yes	characteristic
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	16	1	no	—
389	C₂²	—	944	1	no	—
390	C₂²	—	236	2	no	—
391	C₂²	C₄×#11745669	1	1	yes	characteristic
392	C₂²	C₄×#11745669	1	1	yes	characteristic
393	C₂²	C₂×#14273747	1	1	yes	characteristic
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	236	2	no	—
397	C₄	C₄×#11745669	1	1	yes	characteristic
398	C₄	C₄×#11745669	1	1	yes	characteristic
399	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
400	C₄	C₂²×#11745669	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	8	2	no	—
405	C₂	—	472	2	no	—
406	C₂	C₂×C₄×#11745669	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×#11745669
commutator	C₈×C₅₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₅₉×#2957	C₂
socle	C₂×C₅₉	C₂×C₄×D₈
prime radical	C₂×#16837832	C₂
cosocle	C₂×C₈×C₅₉	C₂⁴
hypercenter	#2957	D₅₉
hypocenter	C₅₉	#33465
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405 ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #21433014	C₂	semidirect
3. #21425980	C₂	semidirect
4. #21425975	C₂	semidirect
5. C₂×#16837231	C₂	semidirect
6. #21425824	C₂	semidirect
7. #21425823	C₂	semidirect
8. #21425693	C₂	semidirect
9. C₅₉×#2957	C₂	semidirect
12. #16837832	C₄	semidirect
13. #16837832	C₄	semidirect
16. C₂×#14273673	C₄	semidirect
17. C₂×#14273671	C₄	semidirect
18. C₂×#14273670	C₄	semidirect
19. C₂×#14273668	C₄	semidirect
23. #16837520	C₂²	semidirect
26. #16837231	C₂²	semidirect
27. #16837231	C₂²	semidirect
28. #16837209	C₂²	semidirect
29. #16837208	C₂²	semidirect
30. #16837178	C₂²	semidirect
31. C₄×C₅₉⋊C₁₆	C₂²	semidirect
35. C₅₉×#443	C₂²	semidirect
200. #2957	D₅₉	semidirect
230. #443	C₂×D₅₉	semidirect
242. C₅₉	#33465	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837832	2
#21433014	2
#21425980	2
#21425975	2
C₂×#16837231	2
#21425824	2
#21425823	2
#21425693	2
C₅₉×#2957	2
#33465	59