Subgroups — #28743082

Order 15104.

696 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21437230	C₂	1	2	yes	maximal, complemented
2	#21434524	C₂	1	1	yes	maximal, characteristic, complemented
3	#21426177	C₂	1	2	yes	maximal, complemented
4	#21426172	C₂	1	2	yes	maximal, complemented
5	#21426165	C₂	1	4	yes	maximal, complemented
6	C₂×#16837223	C₂	1	1	yes	maximal, characteristic, complemented
7	#21425843	C₂	1	2	yes	maximal, complemented
8	C₂×C₅₉×#443	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14273749	—	2	1	no	—
10	C₂×#14273749	C₂²	1	2	yes	—
11	#16837952	—	2	1	no	—
12	#16837843	—	2	2	no	—
13	#16837842	C₂²	1	4	yes	—
14	#16837838	—	2	2	no	—
15	#16837837	C₂²	1	4	yes	—
16	#16837832	—	2	4	no	—
17	C₂×#14273667	C₂²	1	2	yes	—
18	#16837786	—	2	1	no	—
19	#16837786	C₂²	1	2	yes	complemented
20	#16837782	C₂²	1	1	yes	characteristic, complemented
21	#16837779	C₂²	1	1	yes	characteristic, complemented
22	#16837775	—	2	1	no	—
23	#16837223	C₂²	1	2	yes	complemented
24	#16837223	C₂²	1	2	yes	complemented
25	#16837217	C₂²	1	4	yes	complemented
26	#16837214	C₂²	1	4	yes	complemented
27	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#131×C₅₉	—	2	1	no	—
29	C₅₉×#443	—	2	1	no	—
30	C₅₉×#443	—	2	1	no	—
31	C₅₉×#443	C₂²	1	2	yes	—
32	C₅₉×#443	C₂²	1	2	yes	—
33	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
34	C₂×#104×C₅₉	—	2	1	no	—
35	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#11745685	—	2	2	no	—
37	#14273749	—	2	2	no	—
38	#14273749	—	2	2	no	—
39	#14273749	—	2	2	no	—
40	#14273749	—	2	2	no	—
41	#14273749	—	4	1	no	—
42	#14273749	—	4	1	no	—
43	#14273749	—	4	1	no	—
44	#14273749	—	4	1	no	—
45	C₂×Dic₂₃₆	—	2	1	no	—
46	C₂×Dic₂₃₆	C₂³	1	2	yes	—
47	C₂×#11745660	—	2	2	no	—
48	C₂×#11745660	—	2	2	no	—
49	C₂×D₄₇₂	—	2	1	no	—
50	C₂×D₄₇₂	C₂³	1	2	yes	—
51	#14273727	—	2	1	no	—
52	#14273724	—	2	1	no	—
53	#14273715	—	2	2	no	—
54	#14273701	—	4	2	no	—
55	C₄×D₂₃₆	—	4	2	no	—
56	#14273673	—	2	4	no	—
57	#14273671	—	2	4	no	—
58	#14273670	—	2	4	no	—
59	#14273668	—	2	4	no	—
60	#14273667	—	2	2	no	—
61	#14273667	C₂³	1	4	yes	—
62	C₂×C₅₉⋊C₁₆	—	2	2	no	—
63	C₂×#41×C₅₉	—	2	1	no	—
64	#135×C₅₉	—	2	1	no	—
65	#135×C₅₉	—	2	1	no	—
66	#135×C₅₉	D₄	1	2	yes	complemented
67	#135×C₅₉	C₂³	1	2	yes	—
68	C₂×Q₁₆×C₅₉	D₄	1	1	yes	characteristic, complemented
69	C₂×SD₁₆×C₅₉	—	2	1	no	—
70	C₂×D₈×C₅₉	D₄	1	1	yes	characteristic, complemented
71	#131×C₅₉	—	2	2	no	—
72	#131×C₅₉	—	2	2	no	—
73	#131×C₅₉	—	4	1	no	—
74	#131×C₅₉	—	4	1	no	—
75	C₂×M₁₆×C₅₉	—	2	1	no	—
76	C₂×M₁₆×C₅₉	—	4	1	no	—
77	C₂²×C₈×C₅₉	—	4	1	no	—
78	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
81	#108×C₅₉	—	2	1	no	—
82	#108×C₅₉	C₂³	1	2	yes	—
83	#104×C₅₉	—	2	2	no	—
84	#104×C₅₉	—	2	2	no	—
85	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
86	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	#41×C₅₉	—	2	2	no	—
90	#41×C₅₉	—	2	2	no	—
91	#41×C₅₉	—	4	1	no	—
92	#41×C₅₉	—	4	1	no	—
93	C₂×Q₈×C₅₉	—	2	1	no	—
94	C₂×D₄×C₅₉	—	2	1	no	—
95	C₂×D₄×C₅₉	—	4	1	no	—
96	C₂²×C₄×C₅₉	—	2	1	no	—
97	C₂²×C₄×C₅₉	—	4	1	no	—
98	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₅₉	—	4	2	no	—
100	#11745685	—	4	2	no	—
101	#11745685	—	4	2	no	—
102	#11745685	—	4	2	no	—
103	#11745685	—	4	2	no	—
104	C₂×D₂₃₆	—	2	2	no	—
105	C₂×D₂₃₆	—	4	2	no	—
106	C₂×C₄×D₅₉	—	4	2	no	—
107	C₂×Dic₁₁₈	—	2	2	no	—
108	Q₁₆×C₅₉	—	2	1	no	—
109	Q₁₆×C₅₉	C₂×D₄	1	2	yes	—
110	SD₁₆×C₅₉	—	2	2	no	—
111	SD₁₆×C₅₉	—	2	2	no	—
112	D₈×C₅₉	—	2	1	no	—
113	D₈×C₅₉	C₂×D₄	1	2	yes	—
114	M₁₆×C₅₉	—	2	2	no	—
115	M₁₆×C₅₉	—	4	1	no	—
116	M₁₆×C₅₉	—	4	2	no	—
117	M₁₆×C₅₉	—	4	2	no	—
118	C₂×C₈×C₅₉	—	4	1	no	—
119	C₂×C₈×C₅₉	—	4	2	no	—
120	C₂×C₈×C₅₉	—	4	2	no	—
121	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
122	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
123	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
124	C₂×C₈×C₅₉	D₈	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
131	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
132	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₄²×C₅₉	—	2	1	no	—
134	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
136	(C₂×D₅₉)⋊C₄	—	4	4	no	—
137	C₄⋊Dic₅₉	—	4	2	no	—
138	Dic₂₃₆	—	2	2	no	—
139	Dic₂₃₆	—	2	2	no	—
140	Dic₂₃₆	—	4	1	no	—
141	Dic₂₃₆	—	4	1	no	—
142	D₄₇₂	—	2	2	no	—
143	D₄₇₂	—	2	2	no	—
144	D₄₇₂	—	4	1	no	—
145	D₄₇₂	—	4	1	no	—
146	#11745660	—	4	2	no	—
147	#11745660	—	4	2	no	—
148	#11745660	—	4	2	no	—
149	#11745660	—	4	2	no	—
150	C₅₉⋊C₁₆	—	2	4	no	—
151	C₂³×C₅₉	—	4	1	no	—
152	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
153	C₂²×D₅₉	—	4	2	no	—
154	Q₈×C₅₉	—	2	2	no	—
155	Q₈×C₅₉	—	4	1	no	—
156	D₄×C₅₉	—	2	2	no	—
157	D₄×C₅₉	—	4	2	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	4	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	4	2	no	—
163	C₂×C₄×C₅₉	—	4	1	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
172	C₂²⋊D₅₉	—	8	2	no	—
173	C₂²⋊D₅₉	—	8	2	no	—
174	C₂×Dic₅₉	—	4	2	no	—
175	D₂₃₆	—	4	2	no	—
176	D₂₃₆	—	4	2	no	—
177	D₂₃₆	—	8	4	no	—
178	C₄×D₅₉	—	8	2	no	—
179	C₄×D₅₉	—	8	2	no	—
180	Dic₁₁₈	—	4	2	no	—
181	Dic₁₁₈	—	4	2	no	—
182	C₈×C₅₉	—	4	2	no	—
183	C₈×C₅₉	#121	1	1	yes	characteristic
184	C₈×C₅₉	#121	1	1	yes	characteristic
185	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
186	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
187	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
188	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
189	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
191	#33594	—	59	1	no	maximal, Sylow
192	C₂²×C₅₉	—	4	1	no	—
193	C₂²×C₅₉	—	4	2	no	—
194	C₂²×C₅₉	—	8	2	no	—
195	C₂²×C₅₉	#459	1	1	yes	characteristic
196	C₂²×C₅₉	#459	1	1	yes	characteristic
197	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂×D₅₉	—	8	4	no	—
199	C₂×D₅₉	—	8	2	no	—
200	C₄×C₅₉	—	2	2	no	—
201	C₄×C₅₉	—	4	1	no	—
202	C₄×C₅₉	—	4	2	no	—
203	C₄×C₅₉	#459	1	1	yes	characteristic
204	C₄×C₅₉	#459	1	1	yes	characteristic
205	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
206	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
207	Dic₅₉	—	8	2	no	—
208	#3414	—	59	2	no	—
209	#3147	—	59	1	no	—
210	C₂×#443	D₅₉	1	1	yes	characteristic, complemented
211	#2214	—	59	2	no	—
212	#2213	—	59	2	no	—
213	#2212	—	59	4	no	—
214	C₂×#364	—	59	1	no	—
215	#2148	—	59	2	no	—
216	C₂×C₅₉	—	2	1	no	—
217	C₂×C₅₉	—	2	1	no	—
218	C₂×C₅₉	—	2	1	no	—
219	C₂×C₅₉	—	8	2	no	—
220	C₂×C₅₉	C₂×#459	1	1	yes	characteristic
221	D₅₉	—	16	2	no	—
222	C₂×#135	—	59	2	no	—
223	C₂×#135	—	118	1	no	—
224	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
225	C₂×#131	—	2	1	no	—
226	#532	—	118	1	no	—
227	#510	—	59	4	no	—
228	#510	—	118	2	no	—
229	#509	—	59	4	no	—
230	#509	—	118	2	no	—
231	#508	—	118	4	no	—
232	C₂×M₃₂	—	59	2	no	—
233	#495	—	59	2	no	—
234	#495	—	118	1	no	—
235	#494	—	59	1	no	—
236	#493	—	59	1	no	—
237	#492	—	118	1	no	—
238	#443	—	2	1	no	—
239	#443	—	2	1	no	—
240	#443	C₂×D₅₉	1	2	yes	—
241	#443	C₂×D₅₉	1	2	yes	—
242	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
243	C₂×#104	—	2	1	no	—
244	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
245	#364	—	59	2	no	—
246	#364	—	59	2	no	—
247	#362	—	59	4	no	—
248	#361	—	59	4	no	—
249	C₅₉	#33594	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	2	1	no	—
251	C₂×#41	—	118	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	118	2	no	—
255	#135	—	118	2	no	—
256	#135	—	118	2	no	—
257	#135	—	118	2	no	—
258	#135	—	236	1	no	—
259	#135	—	236	1	no	—
260	#135	—	236	1	no	—
261	#135	—	236	1	no	—
262	#135	D₂₃₆	1	2	yes	complemented
263	#135	C₂²×D₅₉	1	2	yes	—
264	C₂×Q₁₆	—	59	2	no	—
265	C₂×Q₁₆	—	118	1	no	—
266	C₂×Q₁₆	D₂₃₆	1	1	yes	characteristic, complemented
267	C₂×SD₁₆	—	2	1	no	—
268	C₂×SD₁₆	—	118	2	no	—
269	C₂×SD₁₆	—	118	2	no	—
270	C₂×D₈	—	59	2	no	—
271	C₂×D₈	—	118	1	no	—
272	C₂×D₈	D₂₃₆	1	1	yes	characteristic, complemented
273	#131	—	2	2	no	—
274	#131	—	2	2	no	—
275	#131	—	4	1	no	—
276	#131	—	4	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	4	1	no	—
279	C₂²×C₈	—	4	1	no	—
280	C₂²×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
281	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
282	C₄⋊Q₈	—	118	1	no	—
283	#127	—	118	1	no	—
284	#124	—	118	2	no	—
285	#121	—	236	2	no	—
286	C₄×D₄	—	236	2	no	—
287	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
288	Q₃₂	—	118	4	no	—
289	SD₃₂	—	118	4	no	—
290	SD₃₂	—	118	4	no	—
291	D₁₆	—	118	4	no	—
292	M₃₂	—	59	4	no	—
293	M₃₂	—	118	2	no	—
294	C₂×C₁₆	—	118	2	no	—
295	#108	—	2	1	no	—
296	#108	C₂²×D₅₉	1	2	yes	—
297	#104	—	2	2	no	—
298	#104	—	2	2	no	—
299	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
301	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	4	1	no	—
306	#41	—	4	1	no	—
307	#41	—	236	2	no	—
308	#41	—	236	2	no	—
309	#41	—	236	2	no	—
310	#41	—	236	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	118	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	118	2	no	—
316	C₂×D₄	—	236	2	no	—
317	C₂×D₄	—	236	2	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	236	2	no	—
321	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	118	2	no	—
324	Q₁₆	—	118	2	no	—
325	Q₁₆	—	236	1	no	—
326	Q₁₆	—	236	1	no	—
327	Q₁₆	C₂×D₂₃₆	1	2	yes	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	236	2	no	—
331	SD₁₆	—	236	2	no	—
332	SD₁₆	—	236	2	no	—
333	SD₁₆	—	236	2	no	—
334	D₈	—	2	1	no	—
335	D₈	—	118	2	no	—
336	D₈	—	118	2	no	—
337	D₈	—	236	1	no	—
338	D₈	—	236	1	no	—
339	D₈	C₂×D₂₃₆	1	2	yes	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	4	2	no	—
343	M₁₆	—	4	2	no	—
344	C₂×C₈	—	4	1	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	#11745669	1	1	yes	characteristic
348	C₂×C₈	#11745669	1	1	yes	characteristic
349	C₂×C₈	#11745669	1	1	yes	characteristic
350	C₂×C₈	#11745669	1	1	yes	characteristic
351	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
352	C₂×C₈	C₂×D₂₃₆	1	1	yes	characteristic
353	C₂×C₈	#11745685	1	1	yes	characteristic
354	C₂×C₈	#11745685	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
357	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
358	C₂×C₈	C₂³×D₅₉	1	1	yes	characteristic
359	C₄⋊C₄	—	236	2	no	—
360	C₂²⋊C₄	—	236	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
364	C₁₆	—	118	4	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	236	2	no	—
367	C₂³	#14273752	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	4	1	no	—
370	Q₈	—	236	2	no	—
371	Q₈	—	236	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	472	4	no	—
377	D₄	—	472	2	no	—
378	D₄	—	472	2	no	—
379	D₄	—	236	2	no	—
380	D₄	—	236	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	472	2	no	—
388	C₂×C₄	—	472	2	no	—
389	C₂×C₄	—	236	2	no	—
390	C₂×C₄	#14273701	1	1	yes	characteristic
391	C₂×C₄	#14273701	1	1	yes	characteristic
392	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
393	C₂×C₄	C₂×#11745669	1	1	yes	characteristic
394	C₂×C₄	#14273752	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
396	C₈	—	4	2	no	—
397	C₈	#14273701	1	1	yes	characteristic
398	C₈	#14273701	1	1	yes	characteristic
399	C₈	C₂×#11745669	1	1	yes	characteristic
400	C₈	C₂×#11745669	1	1	yes	characteristic
401	C₈	C₂×#11745669	1	1	yes	characteristic
402	C₈	C₂×#11745669	1	1	yes	characteristic
403	C₈	C₂²×D₂₃₆	1	1	yes	characteristic
404	C₈	C₂×#11745685	1	1	yes	characteristic
405	C₂²	—	4	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	472	4	no	—
409	C₂²	—	472	2	no	—
410	C₂²	#16837597	1	1	yes	characteristic
411	C₂²	#16837597	1	1	yes	characteristic
412	C₂²	C₂×#14273752	1	1	yes	characteristic
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	472	2	no	—
417	C₄	#16837597	1	1	yes	characteristic
418	C₄	#16837597	1	1	yes	characteristic
419	C₄	C₂×#14273701	1	1	yes	characteristic
420	C₄	C₂²×#11745669	1	1	yes	characteristic
421	C₂	—	2	1	no	—
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	8	2	no	—
425	C₂	—	944	2	no	—
426	C₂	C₂×#16837597	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16837597
commutator, cosocle	C₂×C₈×C₅₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₉
Fitting	C₂×C₅₉×#443	C₂
socle	C₂×C₅₉	C₂×#459
hypercenter	C₂×#443	D₅₉
hypocenter	C₅₉	#33594
LCS	G ▷ C₂×C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. #21437230	C₂	semidirect
2. #21434524	C₂	semidirect
3. #21426177	C₂	semidirect
4. #21426172	C₂	semidirect
5. #21426165	C₂	semidirect
6. C₂×#16837223	C₂	semidirect
7. #21425843	C₂	semidirect
8. C₂×C₅₉×#443	C₂	semidirect
19. #16837786	C₂²	semidirect
20. #16837782	C₂²	semidirect
21. #16837779	C₂²	semidirect
23. #16837223	C₂²	semidirect
24. #16837223	C₂²	semidirect
25. #16837217	C₂²	semidirect
26. #16837214	C₂²	semidirect
66. #135×C₅₉	D₄	semidirect
68. C₂×Q₁₆×C₅₉	D₄	semidirect
70. C₂×D₈×C₅₉	D₄	semidirect
210. C₂×#443	D₅₉	semidirect
249. C₅₉	#33594	semidirect
262. #135	D₂₃₆	semidirect
266. C₂×Q₁₆	D₂₃₆	semidirect
272. C₂×D₈	D₂₃₆	semidirect

Maximal subgroups

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

subgroup	index
#21437230	2
#21434524	2
#21426177	2
#21426172	2
#21426165	2
C₂×#16837223	2
#21425843	2
C₂×C₅₉×#443	2
#33594	59