Subgroups — #28560462

Order 15104.

586 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434678	C₂	1	1	yes	maximal, characteristic
2	#21433045	C₂	1	1	yes	maximal, characteristic
3	#21433039	C₂	1	1	yes	maximal, characteristic
4	#21422990	C₂	1	2	yes	maximal, complemented
5	#21422949	C₂	1	2	yes	maximal, complemented
6	#21422943	C₂	1	2	yes	maximal, complemented
7	#21422900	C₂	1	2	yes	maximal, complemented
8	C₂×#16837154	C₂	1	1	yes	maximal, characteristic
9	#21422500	C₂	1	1	yes	maximal, characteristic
10	#21422377	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#1481	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837805	C₄	1	1	yes	characteristic
14	#16837781	C₄	1	1	yes	characteristic
15	#16837754	C₄	1	1	yes	characteristic
16	#16837752	C₄	1	1	yes	characteristic
17	#16837641	C₄	1	2	yes	—
18	#16837641	C₄	1	2	yes	—
19	#16837533	—	2	2	no	—
20	#16837533	C₂²	1	2	yes	—
21	#16837531	—	2	2	no	—
22	#16837529	C₂²	1	2	yes	—
23	Q₈×C₅₉⋊C₈	C₂²	1	2	yes	—
24	#16837526	C₂²	1	2	yes	—
25	C₄×#11745672	C₂²	1	2	yes	—
26	C₄×#11745672	C₂²	1	2	yes	—
27	#16837429	—	2	1	no	—
28	#16837428	—	2	1	no	—
29	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
30	#16837358	—	2	1	no	—
31	#16837357	—	2	1	no	—
32	C₄×#11745664	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
34	#16837154	C₂²	1	1	yes	characteristic
35	#16837154	C₂²	1	1	yes	characteristic
36	#16837154	C₂²	1	1	yes	characteristic
37	#16837154	C₂²	1	1	yes	characteristic
38	#16837134	C₂²	1	2	yes	—
39	#16837134	C₂²	1	2	yes	—
40	#16837124	C₂²	1	2	yes	—
41	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
42	C₅₉×#533	C₂²	1	1	yes	characteristic
43	C₅₉×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅₉×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₂×#11745672	C₂×C₄	1	2	yes	—
48	C₂×#11745672	C₂×C₄	1	2	yes	—
49	C₂×#11745664	D₄	1	1	yes	characteristic
50	C₂×#11745664	D₄	1	1	yes	characteristic
51	C₂²×C₅₉⋊C₈	—	2	1	no	—
52	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
54	#14273727	C₂×C₄	1	1	yes	characteristic
55	#14273727	C₂×C₄	1	1	yes	characteristic
56	#14273719	—	2	1	no	—
57	#14273706	—	2	1	no	—
58	#14273706	C₂×C₄	1	2	yes	—
59	C₄×Dic₁₁₈	—	2	1	no	—
60	C₄×Dic₁₁₈	C₂³	1	2	yes	—
61	#14273686	—	2	1	no	—
62	#14273660	C₂×C₄	1	2	yes	—
63	#14273660	C₂×C₄	1	2	yes	—
64	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
66	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
67	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₅₉⋊C₈)	C₂³	1	1	yes	characteristic
69	Dic₅₉⋊C₈	—	2	2	no	—
70	Dic₅₉⋊C₈	—	2	2	no	—
71	#14273651	C₂×C₄	1	2	yes	—
72	#14273651	C₂×C₄	1	2	yes	—
73	#14273650	C₂×C₄	1	2	yes	—
74	#14273650	C₂×C₄	1	2	yes	—
75	#14273638	—	2	2	no	—
76	#14273638	D₄	1	2	yes	—
77	#14273637	—	2	2	no	—
78	C₄×C₅₉⋊C₈	—	2	2	no	—
79	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
84	C₈×Dic₅₉	—	2	2	no	—
85	C₂²×C₈×C₅₉	—	2	1	no	—
86	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
88	#125×C₅₉	—	2	1	no	—
89	C₂²⋊Q₈×C₅₉	—	2	1	no	—
90	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
91	C₄×Q₈×C₅₉	—	2	1	no	—
92	C₄×Q₈×C₅₉	C₂³	1	2	yes	—
93	#117×C₅₉	—	2	1	no	—
94	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₅₉	—	2	1	no	—
96	C₄⋊C₈×C₅₉	—	2	1	no	—
97	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₅₉	—	2	1	no	—
100	C₄×C₈×C₅₉	C₂³	1	2	yes	—
101	C₂×Q₈×C₅₉	—	2	1	no	—
102	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
106	C₂×Dic₁₁₈	—	2	1	no	—
107	C₂×Dic₁₁₈	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₅₉	—	2	1	no	—
109	C₂×C₈×C₅₉	—	2	1	no	—
110	C₂×C₈×C₅₉	—	2	2	no	—
111	C₂×C₈×C₅₉	—	4	2	no	—
112	C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₄⋊C₄×C₅₉	—	2	1	no	—
114	C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₄⋊C₄×C₅₉	—	2	2	no	—
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₅₉	—	2	2	no	—
119	C₄²×C₅₉	—	2	2	no	—
120	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₅₉	#41	1	1	yes	characteristic
123	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₅₉	—	2	2	no	—
125	#11745672	—	2	4	no	—
126	#11745672	—	4	2	no	—
127	C₄⋊Dic₅₉	—	2	1	no	—
128	C₄⋊Dic₅₉	—	2	1	no	—
129	C₄⋊Dic₅₉	—	2	1	no	—
130	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
131	Dic₅₉⋊C₄	—	2	2	no	—
132	Dic₅₉⋊C₄	—	2	2	no	—
133	C₄×Dic₅₉	—	2	2	no	—
134	#11745664	—	2	2	no	—
135	#11745664	Q₁₆	1	4	yes	complemented
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	1	no	—
138	C₂×C₅₉⋊C₈	—	2	1	no	—
139	C₂×C₅₉⋊C₈	—	4	1	no	—
140	C₂×C₅₉⋊C₈	—	4	2	no	—
141	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
147	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
148	Q₈×C₅₉	—	2	2	no	—
149	Q₈×C₅₉	—	2	2	no	—
150	Q₈×C₅₉	—	8	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	1	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	—	4	1	no	—
156	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₅₉	#135	1	2	yes	—
161	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₅₉	—	2	2	no	—
165	C₂×Dic₅₉	—	2	2	no	—
166	Dic₁₁₈	—	2	2	no	—
167	Dic₁₁₈	—	2	2	no	—
168	Dic₁₁₈	—	8	1	no	—
169	C₈×C₅₉	—	4	2	no	—
170	C₈×C₅₉	—	4	1	no	—
171	C₈×C₅₉	—	4	1	no	—
172	C₅₉⋊C₈	—	2	1	no	—
173	C₅₉⋊C₈	—	2	1	no	—
174	C₅₉⋊C₈	—	2	1	no	—
175	C₅₉⋊C₈	—	2	2	no	—
176	C₅₉⋊C₈	—	4	1	no	—
177	C₅₉⋊C₈	—	4	1	no	—
178	C₅₉⋊C₈	#131	1	2	yes	—
179	C₅₉⋊C₈	C₂×Q₁₆	1	4	yes	—
180	#18068	—	59	1	no	maximal, Sylow
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	C₄×Q₁₆	1	2	yes	—
184	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₅₉	—	2	1	no	—
186	C₄×C₅₉	—	2	1	no	—
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	4	2	no	—
189	C₄×C₅₉	—	4	2	no	—
190	C₄×C₅₉	C₄×Q₁₆	1	2	yes	—
191	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
192	C₄×C₅₉	#568	1	1	yes	characteristic
193	C₄×C₅₉	C₂²×Q₁₆	1	1	yes	characteristic
194	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
195	Dic₅₉	—	4	2	no	—
196	Dic₅₉	—	4	2	no	—
197	#3170	—	59	1	no	—
198	#2962	—	59	1	no	—
199	#2962	—	59	1	no	—
200	#1591	—	59	2	no	—
201	#1584	—	59	2	no	—
202	#1584	—	59	2	no	—
203	C₈×Q₁₆	—	59	2	no	—
204	C₂×#335	—	59	1	no	—
205	#1481	—	59	1	no	—
206	#1481	D₅₉	1	1	yes	characteristic
207	C₈×M₁₆	—	59	1	no	—
208	C₂×C₅₉	—	2	2	no	—
209	C₂×C₅₉	#2935	1	1	yes	characteristic
210	C₂×C₅₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
211	C₂×C₅₉	#2957	1	1	yes	characteristic
212	#533	—	59	1	no	—
213	#533	C₂×D₅₉	1	1	yes	characteristic
214	#500	—	59	1	no	—
215	#494	—	59	1	no	—
216	#487	—	59	1	no	—
217	#487	—	59	1	no	—
218	#467	—	59	2	no	—
219	#467	—	59	2	no	—
220	#446	—	59	2	no	—
221	#446	—	59	2	no	—
222	#446	—	118	2	no	—
223	#446	—	118	2	no	—
224	C₈×Q₈	—	59	2	no	—
225	C₈×Q₈	—	59	2	no	—
226	C₄×Q₁₆	—	59	2	no	—
227	C₄×Q₁₆	—	59	2	no	—
228	#431	C₂×D₅₉	1	1	yes	characteristic
229	#424	—	118	1	no	—
230	#424	—	118	1	no	—
231	C₂×C₄⋊C₈	—	59	1	no	—
232	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
233	#405	—	118	1	no	—
234	#405	—	118	1	no	—
235	C₄×M₁₆	—	59	1	no	—
236	C₂×C₄×C₈	—	59	1	no	—
237	#335	—	59	1	no	—
238	#335	—	59	1	no	—
239	#335	—	59	1	no	—
240	#335	—	59	1	no	—
241	Q₈⋊C₈	—	59	2	no	—
242	Q₈⋊C₈	—	59	2	no	—
243	Q₈⋊C₈	C₂×D₅₉	1	2	yes	—
244	Q₈⋊C₈	C₂×D₅₉	1	2	yes	—
245	#322	—	59	2	no	—
246	C₈²	—	59	2	no	—
247	C₅₉	#18068	1	1	yes	characteristic, complemented, Sylow
248	C₂×Q₁₆	—	59	2	no	—
249	C₂×Q₁₆	—	59	2	no	—
250	C₂×M₁₆	—	59	1	no	—
251	C₂×M₁₆	—	59	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	59	1	no	—
254	C₂²×C₈	—	59	1	no	—
255	C₂²×C₈	—	118	1	no	—
256	C₄⋊Q₈	—	59	1	no	—
257	C₄⋊Q₈	—	59	1	no	—
258	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
259	C₄⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#125	—	118	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	59	2	no	—
264	C₂²⋊Q₈	—	118	1	no	—
265	C₂²⋊Q₈	C₄×D₅₉	1	2	yes	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	59	2	no	—
268	C₄×Q₈	—	118	1	no	—
269	C₄×Q₈	C₂²×D₅₉	1	2	yes	—
270	#117	—	2	1	no	—
271	#117	—	118	1	no	—
272	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
273	#107	—	59	2	no	—
274	#107	—	59	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	59	1	no	—
278	C₄⋊C₈	—	59	1	no	—
279	C₄⋊C₈	—	118	2	no	—
280	C₄⋊C₈	—	118	2	no	—
281	C₄⋊C₈	—	118	2	no	—
282	C₄⋊C₈	—	118	2	no	—
283	C₄⋊C₈	—	118	1	no	—
284	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
285	C₄⋊C₈	C₂²×D₅₉	1	1	yes	characteristic
286	#103	—	59	2	no	—
287	#103	—	59	2	no	—
288	#103	—	59	2	no	—
289	#103	—	59	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	59	2	no	—
292	#97	—	118	2	no	—
293	#97	—	118	2	no	—
294	C₄×C₈	—	59	1	no	—
295	C₄×C₈	—	59	1	no	—
296	C₄×C₈	—	59	1	no	—
297	C₄×C₈	—	59	2	no	—
298	C₄×C₈	—	59	1	no	—
299	C₄×C₈	—	118	2	no	—
300	C₄×C₈	—	118	2	no	—
301	C₄×C₈	C₂²×D₅₉	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	59	2	no	—
304	C₂×Q₈	—	118	1	no	—
305	C₂×Q₈	C₂×C₄×D₅₉	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
308	C₂²×C₄	#11745687	1	1	yes	characteristic
309	Q₁₆	—	118	4	no	—
310	Q₁₆	—	236	2	no	—
311	M₁₆	—	59	4	no	—
312	M₁₆	—	118	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	59	1	no	—
318	C₂×C₈	—	59	2	no	—
319	C₂×C₈	—	59	1	no	—
320	C₂×C₈	—	59	1	no	—
321	C₂×C₈	—	59	1	no	—
322	C₂×C₈	—	59	2	no	—
323	C₂×C₈	—	118	2	no	—
324	C₂×C₈	—	118	1	no	—
325	C₂×C₈	—	118	1	no	—
326	C₂×C₈	—	236	1	no	—
327	C₂×C₈	—	236	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	59	2	no	—
334	C₄⋊C₄	—	118	1	no	—
335	C₄⋊C₄	—	118	1	no	—
336	C₄⋊C₄	—	118	2	no	—
337	C₄⋊C₄	—	118	1	no	—
338	C₄⋊C₄	—	118	2	no	—
339	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₂²⋊C₄	—	118	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	118	2	no	—
344	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
345	C₄²	D₄×D₅₉	1	1	yes	characteristic
346	C₄²	#11745687	1	1	yes	characteristic
347	C₄²	C₂³×D₅₉	1	1	yes	characteristic
348	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
349	Q₈	—	2	2	no	—
350	Q₈	—	2	2	no	—
351	Q₈	—	8	1	no	—
352	Q₈	—	118	2	no	—
353	Q₈	—	118	2	no	—
354	Q₈	—	472	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	118	2	no	—
361	C₂×C₄	—	118	2	no	—
362	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
363	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
365	C₂×C₄	Q₁₆×D₅₉	1	2	yes	—
366	C₂×C₄	#14273748	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
369	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	59	2	no	—
374	C₈	—	59	4	no	—
375	C₈	—	118	1	no	—
376	C₈	—	118	1	no	—
377	C₈	—	118	1	no	—
378	C₈	—	118	2	no	—
379	C₈	—	236	1	no	—
380	C₈	—	236	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	#16837494	1	2	yes	—
384	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	236	2	no	—
391	C₄	—	236	2	no	—
392	C₄	#16837494	1	2	yes	—
393	C₄	#131×D₅₉	1	1	yes	characteristic
394	C₄	#16838167	1	1	yes	characteristic
395	C₄	C₂×Q₁₆×D₅₉	1	1	yes	characteristic
396	C₄	C₂×#14273748	1	1	yes	characteristic
397	C₂	—	2	2	no	—
398	C₂	#21432836	1	1	yes	characteristic
399	C₂	C₂×#16837494	1	1	yes	characteristic
400	C₂	#21433009	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1481	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂³×C₅₉	C₄×D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1481	D₅₉
hypocenter	C₅₉	#18068
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1481

Complements

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

N	H ≅ G/N	type
4. #21422990	C₂	semidirect
5. #21422949	C₂	semidirect
6. #21422943	C₂	semidirect
7. #21422900	C₂	semidirect
135. #11745664	Q₁₆	semidirect
247. C₅₉	#18068	semidirect

Maximal subgroups

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

subgroup	index
#21434678	2
#21433045	2
#21433039	2
#21422990	2
#21422949	2
#21422943	2
#21422900	2
C₂×#16837154	2
#21422500	2
#21422377	2
C₅₉×#1481	2
#18068	59