Subgroups — #28607214

Order 15104.

808 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433013	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837524	C₂	1	1	yes	maximal, characteristic
3	#21432705	C₂	1	2	yes	maximal, complemented
4	#21424886	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424884	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424336	C₂	1	2	yes	maximal, complemented
7	#21424334	C₂	1	2	yes	maximal, complemented
8	#21424269	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424148	C₂	1	2	yes	maximal, complemented
10	#21423981	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2957	C₂	1	1	yes	maximal, characteristic
12	#16838169	C₂²	1	2	yes	—
13	C₂×#14273734	C₂²	1	2	yes	—
14	#16837524	—	2	2	no	—
15	#16837524	C₄	1	4	yes	complemented
16	#16837524	C₄	1	4	yes	complemented
17	#16837519	—	2	2	no	—
18	#16837450	—	2	4	no	—
19	#16837450	C₂²	1	2	yes	—
20	#16837450	C₂²	1	2	yes	—
21	C₂×#14273663	C₂²	1	1	yes	characteristic
22	C₂×#14273663	C₂²	1	1	yes	characteristic
23	C₂×#14273662	—	2	4	no	—
24	C₂×#14273662	C₂²	1	2	yes	—
25	C₂×#14273662	C₂²	1	1	yes	characteristic
26	#16837438	C₂²	1	1	yes	characteristic
27	#16837425	C₂²	1	2	yes	—
28	#16837419	C₂²	1	2	yes	—
29	C₂×#14273654	C₂²	1	2	yes	—
30	#16837357	C₂²	1	1	yes	characteristic
31	C₂×#14273637	C₂²	1	1	yes	characteristic
32	#16837173	C₂²	1	2	yes	—
33	#16837172	C₂²	1	2	yes	—
34	#16837163	C₂²	1	1	yes	characteristic
35	#16837161	C₂²	1	1	yes	characteristic
36	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#568	C₂²	1	2	yes	—
38	C₅₉×#444	—	2	2	no	—
39	C₅₉×#443	—	2	2	no	—
40	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
41	C₅₉×#421	C₂²	1	2	yes	—
42	C₅₉×#405	C₂²	1	1	yes	characteristic
43	#14273734	—	2	2	no	—
44	#14273734	—	2	2	no	—
45	#14273734	—	2	4	no	—
46	#14273734	—	4	2	no	—
47	#14273734	C₂×C₄	1	4	yes	—
48	#14273734	C₂×C₄	1	4	yes	—
49	C₂×#11745664	—	2	2	no	—
50	C₂×#11745664	—	2	4	no	—
51	C₂×#11745664	C₂³	1	2	yes	—
52	C₂×#11745664	C₂³	1	2	yes	—
53	C₂×#11745664	C₂³	1	1	yes	characteristic
54	C₂²×C₅₉⋊C₈	—	2	2	no	—
55	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
56	#14273686	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
58	#14273663	—	2	1	no	—
59	#14273663	—	2	1	no	—
60	#14273663	C₂×C₄	1	2	yes	—
61	#14273663	C₂×C₄	1	2	yes	—
62	#14273662	—	2	4	no	—
63	#14273662	—	2	4	no	—
64	#14273662	—	2	2	no	—
65	#14273662	—	2	2	no	—
66	#14273662	D₄	1	4	yes	—
67	#14273660	—	2	1	no	—
68	#14273658	—	2	1	no	—
69	Dic₅₉⋊C₈	—	4	2	no	—
70	#14273654	—	2	4	no	—
71	#14273654	C₂×C₄	1	8	yes	—
72	#14273637	—	2	1	no	—
73	#14273637	C₂×C₄	1	2	yes	—
74	#14273637	C₂×C₄	1	2	yes	—
75	C₈×Dic₅₉	—	2	1	no	—
76	C₂×#41×C₅₉	C₂³	1	2	yes	—
77	#135×C₅₉	C₂×C₄	1	2	yes	—
78	#135×C₅₉	C₂×C₄	1	2	yes	—
79	#135×C₅₉	D₄	1	2	yes	—
80	#135×C₅₉	D₄	1	2	yes	—
81	C₂×Q₁₆×C₅₉	Q₈	1	1	yes	characteristic
82	C₂×SD₁₆×C₅₉	Q₈	1	2	yes	—
83	C₂×D₈×C₅₉	Q₈	1	1	yes	characteristic
84	#131×C₅₉	—	2	4	no	—
85	#131×C₅₉	—	4	2	no	—
86	C₂×M₁₆×C₅₉	—	2	4	no	—
87	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
88	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
90	#117×C₅₉	C₂³	1	1	yes	characteristic
91	#108×C₅₉	—	2	1	no	—
92	#108×C₅₉	—	2	1	no	—
93	#104×C₅₉	—	2	4	no	—
94	#97×C₅₉	—	2	1	no	—
95	C₄×C₈×C₅₉	—	2	1	no	—
96	#41×C₅₉	—	2	2	no	—
97	#41×C₅₉	—	2	2	no	—
98	#41×C₅₉	C₂²×C₄	1	4	yes	—
99	#41×C₅₉	C₂×D₄	1	4	yes	—
100	C₂×Q₈×C₅₉	C₂×Q₈	1	2	yes	—
101	C₂×D₄×C₅₉	—	2	2	no	—
102	C₂×D₄×C₅₉	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₅₉	—	2	2	no	—
104	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₅₉	—	2	1	no	—
106	Q₁₆×C₅₉	C₄⋊C₄	1	2	yes	—
107	Q₁₆×C₅₉	C₄⋊C₄	1	2	yes	—
108	SD₁₆×C₅₉	C₄⋊C₄	1	4	yes	—
109	SD₁₆×C₅₉	C₄⋊C₄	1	4	yes	—
110	D₈×C₅₉	C₄⋊C₄	1	2	yes	—
111	D₈×C₅₉	C₄⋊C₄	1	2	yes	—
112	M₁₆×C₅₉	—	2	1	no	—
113	M₁₆×C₅₉	—	2	2	no	—
114	M₁₆×C₅₉	—	2	2	no	—
115	M₁₆×C₅₉	—	4	4	no	—
116	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₅₉	—	2	1	no	—
118	C₂×C₈×C₅₉	—	2	2	no	—
119	C₂×C₈×C₅₉	—	4	4	no	—
120	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
126	C₄⋊C₄×C₅₉	—	2	1	no	—
127	C₂²⋊C₄×C₅₉	—	2	1	no	—
128	C₄²×C₅₉	—	2	1	no	—
129	C₂²⋊Dic₅₉	—	2	1	no	—
130	C₄⋊Dic₅₉	—	2	1	no	—
131	C₄×Dic₅₉	—	2	1	no	—
132	C₄×Dic₅₉	—	2	1	no	—
133	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
134	#11745664	—	2	2	no	—
135	#11745664	—	2	1	no	—
136	#11745664	—	2	4	no	—
137	#11745664	—	2	4	no	—
138	#11745664	—	2	2	no	—
139	#11745664	—	2	2	no	—
140	#11745664	—	4	4	no	—
141	#11745664	C₂²×C₄	1	4	yes	—
142	#11745664	C₂×D₄	1	2	yes	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	C₂×C₅₉⋊C₈	—	2	2	no	—
145	C₂×C₅₉⋊C₈	—	2	4	no	—
146	C₂×C₅₉⋊C₈	—	2	4	no	—
147	C₂×C₅₉⋊C₈	—	2	2	no	—
148	C₂×C₅₉⋊C₈	—	4	4	no	—
149	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
150	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
152	C₂×C₅₉⋊C₈	#41	1	1	yes	characteristic
153	C₂³×C₅₉	—	2	2	no	—
154	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
155	Q₈×C₅₉	—	2	2	no	—
156	Q₈×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
157	D₄×C₅₉	—	2	4	no	—
158	D₄×C₅₉	—	2	4	no	—
159	D₄×C₅₉	—	2	2	no	—
160	D₄×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	4	no	—
163	C₂×C₄×C₅₉	—	2	4	no	—
164	C₂×C₄×C₅₉	—	4	1	no	—
165	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×Dic₅₉	—	2	2	no	—
172	C₂×Dic₅₉	—	4	1	no	—
173	C₂×Dic₅₉	—	8	1	no	—
174	C₈×C₅₉	—	2	2	no	—
175	C₈×C₅₉	—	4	2	no	—
176	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₈×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₅₉⋊C₈	—	2	4	no	—
181	C₅₉⋊C₈	—	2	2	no	—
182	C₅₉⋊C₈	—	4	2	no	—
183	C₅₉⋊C₈	C₄×D₄	1	2	yes	—
184	C₅₉⋊C₈	C₄×D₄	1	2	yes	—
185	#22695	—	59	1	no	maximal, Sylow
186	C₂²×C₅₉	—	2	4	no	—
187	C₂²×C₅₉	—	4	1	no	—
188	C₂²×C₅₉	—	8	2	no	—
189	C₂²×C₅₉	#520	1	1	yes	characteristic
190	C₂²×C₅₉	#547	1	1	yes	characteristic
191	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
192	C₄×C₅₉	—	2	4	no	—
193	C₄×C₅₉	—	8	1	no	—
194	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₅₉	D₄²	1	1	yes	characteristic
197	C₄×C₅₉	#554	1	1	yes	characteristic
198	Dic₅₉	—	4	2	no	—
199	Dic₅₉	—	8	1	no	—
200	#2957	—	59	1	no	—
201	#2957	D₅₉	1	1	yes	characteristic
202	C₂×#444	—	59	1	no	—
203	#2916	—	59	2	no	—
204	#1953	—	59	1	no	—
205	#1953	—	59	1	no	—
206	#1861	—	59	2	no	—
207	#1861	—	59	2	no	—
208	#1849	—	59	1	no	—
209	#1814	—	59	2	no	—
210	#1773	—	59	1	no	—
211	C₂×C₅₉	—	2	1	no	—
212	C₂×C₅₉	—	2	1	no	—
213	C₂×C₅₉	—	2	1	no	—
214	C₂×C₅₉	—	4	4	no	—
215	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
217	#568	—	59	2	no	—
218	#568	C₂×D₅₉	1	2	yes	—
219	C₂×#131	—	59	2	no	—
220	#444	—	2	2	no	—
221	#444	—	59	4	no	—
222	#444	—	59	4	no	—
223	#444	—	118	2	no	—
224	#443	—	2	2	no	—
225	#443	—	118	2	no	—
226	#430	—	59	2	no	—
227	#430	—	59	2	no	—
228	#430	—	118	4	no	—
229	C₂×#108	—	59	1	no	—
230	C₂×#108	—	59	1	no	—
231	C₂×#108	—	59	2	no	—
232	C₂×#108	—	59	1	no	—
233	C₂×#108	—	118	4	no	—
234	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
235	#427	—	59	1	no	—
236	#423	—	59	2	no	—
237	#421	—	59	2	no	—
238	#421	C₂×D₅₉	1	2	yes	—
239	C₂×#104	—	59	2	no	—
240	#405	—	59	1	no	—
241	#405	C₂×D₅₉	1	1	yes	characteristic
242	C₂×#97	—	59	1	no	—
243	#344	—	59	2	no	—
244	#344	—	59	2	no	—
245	#339	—	59	1	no	—
246	#339	—	59	1	no	—
247	C₅₉	#22695	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	C₂²×D₅₉	1	2	yes	—
249	#135	C₄×D₅₉	1	2	yes	—
250	#135	C₄×D₅₉	1	2	yes	—
251	#135	C₂²⋊D₅₉	1	2	yes	—
252	#135	C₂²⋊D₅₉	1	2	yes	—
253	C₂×Q₁₆	Dic₁₁₈	1	1	yes	characteristic
254	C₂×SD₁₆	Dic₁₁₈	1	2	yes	—
255	C₂×D₈	Dic₁₁₈	1	1	yes	characteristic
256	#131	—	2	4	no	—
257	#131	—	4	2	no	—
258	#131	—	59	4	no	—
259	#131	—	59	4	no	—
260	#131	—	118	2	no	—
261	#131	—	118	2	no	—
262	#131	—	118	4	no	—
263	#131	—	236	2	no	—
264	C₂×M₁₆	—	2	4	no	—
265	C₂×M₁₆	—	59	2	no	—
266	C₂×M₁₆	—	59	1	no	—
267	C₂×M₁₆	—	59	2	no	—
268	C₂×M₁₆	—	118	2	no	—
269	C₂×M₁₆	—	118	4	no	—
270	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
271	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
272	C₂²×C₈	—	59	1	no	—
273	C₂²×C₈	—	118	2	no	—
274	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
275	#117	—	59	1	no	—
276	#117	C₂²×D₅₉	1	1	yes	characteristic
277	C₂×C₄²	—	59	1	no	—
278	#108	—	2	1	no	—
279	#108	—	2	1	no	—
280	#108	—	59	4	no	—
281	#108	—	59	2	no	—
282	#108	—	59	2	no	—
283	#108	—	118	2	no	—
284	#108	—	118	2	no	—
285	#108	—	118	4	no	—
286	#108	—	118	4	no	—
287	#108	—	118	1	no	—
288	#108	—	118	1	no	—
289	#107	—	118	1	no	—
290	#106	—	118	1	no	—
291	C₄⋊C₈	—	236	2	no	—
292	#104	—	2	4	no	—
293	#104	—	59	8	no	—
294	#104	—	118	4	no	—
295	#97	—	2	1	no	—
296	#97	—	59	2	no	—
297	#97	—	59	2	no	—
298	#97	—	118	1	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	118	1	no	—
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	#41	C₂×C₄×D₅₉	1	4	yes	—
304	#41	C₂×C₂²⋊D₅₉	1	4	yes	—
305	C₂×Q₈	C₂×Dic₁₁₈	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₂×Dic₁₁₈	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	118	1	no	—
310	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
311	Q₁₆	Dic₅₉⋊C₄	1	2	yes	—
312	Q₁₆	Dic₅₉⋊C₄	1	2	yes	—
313	SD₁₆	Dic₅₉⋊C₄	1	4	yes	—
314	SD₁₆	Dic₅₉⋊C₄	1	4	yes	—
315	D₈	Dic₅₉⋊C₄	1	2	yes	—
316	D₈	Dic₅₉⋊C₄	1	2	yes	—
317	M₁₆	—	2	1	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	4	4	no	—
321	M₁₆	—	59	4	no	—
322	M₁₆	—	59	2	no	—
323	M₁₆	—	118	4	no	—
324	M₁₆	—	118	4	no	—
325	M₁₆	—	118	2	no	—
326	M₁₆	—	118	1	no	—
327	M₁₆	—	118	2	no	—
328	M₁₆	—	118	2	no	—
329	M₁₆	—	236	4	no	—
330	M₁₆	D₄×D₅₉	1	2	yes	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	4	no	—
334	C₂×C₈	—	59	2	no	—
335	C₂×C₈	—	59	2	no	—
336	C₂×C₈	—	59	1	no	—
337	C₂×C₈	—	59	1	no	—
338	C₂×C₈	—	118	4	no	—
339	C₂×C₈	—	118	4	no	—
340	C₂×C₈	—	118	2	no	—
341	C₂×C₈	—	118	1	no	—
342	C₂×C₈	—	118	2	no	—
343	C₂×C₈	—	236	4	no	—
344	C₂×C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
345	C₂×C₈	C₂×Dic₁₁₈	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
349	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	118	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	118	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	59	2	no	—
356	C₄²	—	118	1	no	—
357	C₄²	—	118	1	no	—
358	C₂³	—	2	2	no	—
359	C₂³	#14273774	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	C₂×Dic₅₉⋊C₄	1	4	yes	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	2	no	—
365	D₄	C₂×Dic₅₉⋊C₄	1	4	yes	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	118	2	no	—
371	C₂×C₄	—	472	1	no	—
372	C₂×C₄	—	236	1	no	—
373	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
376	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
377	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
378	C₂×C₄	#14273772	1	1	yes	characteristic
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	59	2	no	—
382	C₈	—	59	2	no	—
383	C₈	—	118	2	no	—
384	C₈	—	118	4	no	—
385	C₈	—	236	2	no	—
386	C₈	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
387	C₈	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
388	C₈	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
389	C₈	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
390	C₂²	—	2	4	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	#16837881	1	1	yes	characteristic
394	C₂²	#16838051	1	1	yes	characteristic
395	C₂²	D₄×Dic₁₁₈	1	1	yes	characteristic
396	C₄	—	2	4	no	—
397	C₄	—	8	1	no	—
398	C₄	—	472	1	no	—
399	C₄	—	236	2	no	—
400	C₄	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
401	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
402	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
403	C₄	#16838111	1	1	yes	characteristic
404	C₂	—	2	1	no	—
405	C₂	—	2	1	no	—
406	C₂	—	2	1	no	—
407	C₂	—	4	4	no	—
408	C₂	D₄×Dic₅₉⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2957	C₂
socle	C₂×C₅₉	D₄×C₄⋊C₄
prime radical	C₂×#135×C₅₉	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2957	D₅₉
hypocenter	C₅₉	#22695
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2957

Complements

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

N	H ≅ G/N	type
3. #21432705	C₂	semidirect
4. #21424886	C₂	semidirect
5. #21424884	C₂	semidirect
6. #21424336	C₂	semidirect
7. #21424334	C₂	semidirect
8. #21424269	C₂	semidirect
9. #21424148	C₂	semidirect
10. #21423981	C₂	semidirect
15. #16837524	C₄	semidirect
16. #16837524	C₄	semidirect
247. C₅₉	#22695	semidirect

Maximal subgroups

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

subgroup	index
#21433013	2
C₂×#16837524	2
#21432705	2
#21424886	2
#21424884	2
#21424336	2
#21424334	2
#21424269	2
#21424148	2
#21423981	2
C₅₉×#2957	2
#22695	59