Subgroups — #29836790

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21458962	C₂	1	2	yes	maximal, complemented
2	#21457624	C₂	1	1	yes	maximal, characteristic, complemented
3	#21457619	C₂	1	1	yes	maximal, characteristic, complemented
4	#21448075	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447950	C₂	1	2	yes	maximal, complemented
6	#21447900	C₂	1	1	yes	maximal, characteristic, complemented
7	#21447895	C₂	1	1	yes	maximal, characteristic, complemented
8	#21447791	C₂	1	2	yes	maximal, complemented
9	#21447784	C₂	1	2	yes	maximal, complemented
10	#21447657	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840579	—	2	1	no	—
13	#16840576	C₂²	1	2	yes	complemented
14	#16840567	—	2	1	no	—
15	#16840564	C₂²	1	2	yes	—
16	#16840204	—	2	2	no	—
17	#16840202	C₂²	1	2	yes	—
18	#16840197	C₂²	1	2	yes	complemented
19	#16840196	—	2	2	no	—
20	#16840193	—	2	2	no	—
21	C₂×#14519722	C₂²	1	2	yes	complemented
22	C₂×#14519722	C₂²	1	2	yes	complemented
23	SD₃₂×D₆₁	—	2	2	no	—
24	#16840178	C₂²	1	2	yes	complemented
25	#16840142	C₂²	1	1	yes	characteristic, complemented
26	#16840139	C₂²	1	1	yes	characteristic
27	#16840038	C₂²	1	2	yes	complemented
28	#16840037	—	2	1	no	—
29	#16840033	C₂²	1	2	yes	—
30	#16840032	—	2	1	no	—
31	#16839946	—	2	2	no	—
32	#16839931	—	2	2	no	—
33	#16839880	C₂²	1	1	yes	characteristic
34	#16839583	C₂²	1	1	yes	characteristic, complemented
35	#16839577	C₂²	1	2	yes	complemented
36	#16839574	C₂²	1	2	yes	complemented
37	#16839545	C₂²	1	2	yes	complemented
38	C₆₁×#508	C₂²	1	1	yes	characteristic
39	C₆₁×#443	C₂²	1	1	yes	characteristic
40	C₆₁×#443	C₂²	1	1	yes	characteristic, complemented
41	C₆₁×#368	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#359	C₂²	1	1	yes	characteristic
43	C₆₁×#359	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
45	#14519824	—	2	2	no	—
46	#14519823	—	2	2	no	—
47	#14519810	—	2	2	no	—
48	#14519810	—	4	2	no	—
49	#14519807	—	2	2	no	—
50	#14519806	—	4	2	no	—
51	#14519805	—	2	2	no	—
52	#14519805	—	4	2	no	—
53	#14519804	—	4	2	no	—
54	#14519802	—	2	2	no	—
55	#14519800	—	2	2	no	—
56	#14519799	—	4	1	no	—
57	#14519799	—	4	1	no	—
58	#14519799	D₄	1	1	yes	characteristic
59	#14519796	—	2	2	no	—
60	C₂×Dic₂₄₄	—	2	1	no	—
61	C₂×Dic₂₄₄	—	4	1	no	—
62	C₂×Dic₂₄₄	C₂³	1	2	yes	—
63	Q₁₆×D₆₁	—	2	2	no	—
64	C₂×D₄₈₈	—	2	1	no	—
65	C₂×D₄₈₈	—	4	1	no	—
66	C₂×D₄₈₈	C₂³	1	2	yes	—
67	D₈×D₆₁	—	2	2	no	—
68	#14519783	C₂³	1	2	yes	—
69	#14519777	—	2	1	no	—
70	#14519774	—	2	1	no	—
71	#14519723	—	2	2	no	—
72	#14519722	—	2	2	no	—
73	#14519722	—	2	2	no	—
74	#14519722	—	4	2	no	—
75	#14519721	—	2	2	no	—
76	#14519720	—	2	2	no	—
77	#14519718	—	2	2	no	—
78	#14519717	C₂³	1	2	yes	—
79	#14519716	—	2	2	no	—
80	C₁₆×D₆₁	—	2	2	no	—
81	#14519713	D₄	1	1	yes	characteristic
82	#14519705	D₄	1	2	yes	—
83	#14519695	—	2	2	no	—
84	#14519693	—	2	2	no	—
85	#135×C₆₁	C₂³	1	1	yes	characteristic
86	#135×C₆₁	C₂³	1	1	yes	characteristic
87	#131×C₆₁	—	2	1	no	—
88	#131×C₆₁	—	2	1	no	—
89	Q₃₂×C₆₁	D₄	1	1	yes	characteristic, complemented
90	SD₃₂×C₆₁	D₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₆₁	D₄	1	1	yes	characteristic, complemented
92	D₁₆×C₆₁	D₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
95	#108×C₆₁	C₂³	1	1	yes	characteristic
96	#108×C₆₁	C₂³	1	1	yes	characteristic
97	#104×C₆₁	—	2	1	no	—
98	#104×C₆₁	—	2	1	no	—
99	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	#41×C₆₁	—	2	1	no	—
101	#41×C₆₁	—	2	1	no	—
102	#11758226	—	4	2	no	—
103	Q₈×D₆₁	—	4	2	no	—
104	#11758224	—	4	2	no	—
105	#11758224	—	8	2	no	—
106	D₄×D₆₁	—	4	2	no	—
107	D₄×D₆₁	—	8	2	no	—
108	#11758222	—	4	2	no	—
109	#11758222	—	4	2	no	—
110	#11758222	C₂×D₄	1	2	yes	—
111	C₂×D₂₄₄	—	2	2	no	—
112	C₂×D₂₄₄	—	4	2	no	—
113	C₂×D₂₄₄	—	8	1	no	—
114	C₂×Dic₁₂₂	—	2	2	no	—
115	C₂×Dic₁₂₂	—	4	2	no	—
116	Q₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
117	Q₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
118	SD₁₆×C₆₁	—	2	1	no	—
119	SD₁₆×C₆₁	—	2	1	no	—
120	D₈×C₆₁	C₂×D₄	1	1	yes	characteristic
121	D₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	M₁₆×C₆₁	—	2	1	no	—
123	M₁₆×C₆₁	—	2	1	no	—
124	M₁₆×C₆₁	—	4	1	no	—
125	M₁₆×C₆₁	—	4	1	no	—
126	C₂×C₈×C₆₁	—	4	1	no	—
127	C₂×C₈×C₆₁	—	4	1	no	—
128	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
130	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
131	#11758202	—	4	2	no	—
132	#11758201	—	4	2	no	—
133	#11758200	—	4	2	no	—
134	#11758199	—	4	2	no	—
135	C₄⋊Dic₆₁	—	8	1	no	—
136	#11758194	C₂×D₄	1	2	yes	—
137	Dic₂₄₄	—	2	2	no	—
138	Dic₂₄₄	—	2	2	no	—
139	Dic₂₄₄	—	4	2	no	—
140	Dic₂₄₄	—	4	1	no	—
141	Dic₂₄₄	—	4	1	no	—
142	Dic₂₄₄	D₈	1	1	yes	characteristic
143	D₄₈₈	—	2	2	no	—
144	D₄₈₈	—	2	2	no	—
145	D₄₈₈	—	4	2	no	—
146	D₄₈₈	—	4	1	no	—
147	D₄₈₈	—	4	1	no	—
148	D₄₈₈	D₈	1	1	yes	characteristic
149	#11758190	—	4	2	no	—
150	#11758190	—	4	2	no	—
151	#11758190	D₈	1	2	yes	—
152	#11758189	—	2	2	no	—
153	C₈×D₆₁	—	2	2	no	—
154	C₁₆×C₆₁	—	2	1	no	—
155	C₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₆₁	C₂×D₄	1	1	yes	characteristic
157	#11758185	—	2	2	no	—
158	C₂²×D₆₁	—	4	2	no	—
159	C₂²×D₆₁	—	8	2	no	—
160	Q₈×C₆₁	—	2	1	no	—
161	Q₈×C₆₁	—	2	1	no	—
162	D₄×C₆₁	—	2	1	no	—
163	D₄×C₆₁	—	2	1	no	—
164	D₄×C₆₁	—	4	1	no	—
165	D₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	4	1	no	—
168	C₂×C₄×C₆₁	—	4	1	no	—
169	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	C₂²⋊D₆₁	—	2	2	no	—
171	C₂²⋊D₆₁	—	8	2	no	—
172	C₂²⋊D₆₁	—	8	2	no	—
173	C₂×Dic₆₁	—	4	2	no	—
174	C₂×Dic₆₁	—	8	2	no	—
175	D₂₄₄	—	4	2	no	—
176	D₂₄₄	—	4	2	no	—
177	D₂₄₄	—	8	2	no	—
178	D₂₄₄	—	16	2	no	—
179	D₂₄₄	C₂×D₈	1	2	yes	—
180	C₄×D₆₁	—	2	2	no	—
181	C₄×D₆₁	—	8	2	no	—
182	C₄×D₆₁	—	8	2	no	—
183	Dic₁₂₂	—	4	2	no	—
184	Dic₁₂₂	—	4	2	no	—
185	Dic₁₂₂	—	8	2	no	—
186	Dic₁₂₂	C₂×D₈	1	2	yes	—
187	C₈×C₆₁	—	4	1	no	—
188	C₈×C₆₁	—	4	1	no	—
189	C₈×C₆₁	C₂×D₈	1	1	yes	characteristic
190	C₈×C₆₁	C₂×D₈	1	1	yes	characteristic
191	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
193	#92418	—	2	2	no	—
194	#33856	—	61	1	no	maximal, Sylow
195	C₂²×C₆₁	—	4	1	no	—
196	C₂²×C₆₁	—	4	1	no	—
197	C₂²×C₆₁	#576	1	1	yes	characteristic
198	C₂×D₆₁	—	2	2	no	—
199	C₂×D₆₁	—	8	2	no	—
200	C₂×D₆₁	—	16	2	no	—
201	C₂×D₆₁	—	32	2	no	—
202	C₄×C₆₁	—	2	2	no	—
203	C₄×C₆₁	—	4	1	no	—
204	C₄×C₆₁	—	4	1	no	—
205	C₄×C₆₁	D₄²	1	1	yes	characteristic
206	C₄×C₆₁	C₂²×D₈	1	1	yes	characteristic
207	Dic₆₁	—	2	2	no	—
208	Dic₆₁	—	8	2	no	—
209	#3416	—	61	2	no	—
210	#3293	—	61	1	no	—
211	#3292	—	61	1	no	—
212	#2248	—	61	1	no	—
213	#2223	—	61	2	no	—
214	#2214	—	61	1	no	—
215	#2213	—	61	1	no	—
216	#2194	—	61	2	no	—
217	#2193	—	61	2	no	—
218	#2178	D₆₁	1	1	yes	characteristic, complemented
219	#2170	—	61	1	no	—
220	C₂×C₆₁	—	2	1	no	—
221	C₂×C₆₁	—	8	1	no	—
222	C₂×C₆₁	—	8	1	no	—
223	C₂×C₆₁	D₄×D₈	1	1	yes	characteristic
224	D₆₁	—	4	2	no	—
225	D₆₁	—	16	2	no	—
226	#578	—	61	2	no	—
227	#578	—	122	1	no	—
228	#576	—	61	2	no	—
229	#576	—	122	1	no	—
230	#510	—	61	2	no	—
231	#510	—	122	2	no	—
232	#509	—	61	2	no	—
233	#509	—	122	2	no	—
234	#508	—	122	2	no	—
235	#508	C₂×D₆₁	1	1	yes	characteristic
236	C₂×SD₃₂	—	61	2	no	—
237	C₂×SD₃₂	—	61	2	no	—
238	C₂×SD₃₂	—	122	2	no	—
239	#504	—	61	2	no	—
240	#494	—	61	1	no	—
241	#493	—	61	1	no	—
242	#473	—	61	2	no	—
243	#473	—	122	1	no	—
244	#472	—	61	2	no	—
245	#472	—	122	1	no	—
246	#456	—	122	2	no	—
247	#453	—	122	2	no	—
248	#443	—	61	1	no	—
249	#443	C₂×D₆₁	1	1	yes	characteristic
250	#443	C₂×D₆₁	1	1	yes	characteristic, complemented
251	#368	C₂×D₆₁	1	1	yes	characteristic, complemented
252	#364	—	61	1	no	—
253	#362	—	61	2	no	—
254	#361	—	61	2	no	—
255	#359	C₂×D₆₁	1	1	yes	characteristic
256	#359	C₂×D₆₁	1	1	yes	characteristic, complemented
257	#350	—	61	2	no	—
258	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
259	C₆₁	#33856	1	1	yes	characteristic, complemented, Sylow
260	2₋¹⁺⁴	—	122	2	no	—
261	H(5,𝔽₂)	—	122	2	no	—
262	#137	—	122	2	no	—
263	#137	—	122	2	no	—
264	#137	—	244	2	no	—
265	#137	—	244	2	no	—
266	AGL(1,ℤ/8)	—	122	2	no	—
267	AGL(1,ℤ/8)	—	122	2	no	—
268	AGL(1,ℤ/8)	—	244	2	no	—
269	AGL(1,ℤ/8)	—	244	2	no	—
270	#135	—	61	1	no	—
271	#135	—	122	2	no	—
272	#135	—	122	2	no	—
273	#135	—	244	1	no	—
274	#135	—	244	1	no	—
275	#135	C₂²×D₆₁	1	1	yes	characteristic
276	#135	C₂²×D₆₁	1	1	yes	characteristic
277	C₂×Q₁₆	—	61	2	no	—
278	C₂×Q₁₆	—	122	2	no	—
279	C₂×Q₁₆	—	122	1	no	—
280	C₂×Q₁₆	—	244	1	no	—
281	C₂×D₈	—	61	2	no	—
282	C₂×D₈	—	122	2	no	—
283	C₂×D₈	—	122	1	no	—
284	C₂×D₈	—	244	1	no	—
285	#131	—	2	1	no	—
286	#131	—	2	1	no	—
287	#131	—	61	2	no	—
288	C₄⋊Q₈	—	122	1	no	—
289	#127	—	122	1	no	—
290	Q₃₂	—	122	2	no	—
291	Q₃₂	D₂₄₄	1	1	yes	characteristic, complemented
292	SD₃₂	—	122	2	no	—
293	SD₃₂	—	122	2	no	—
294	SD₃₂	—	122	2	no	—
295	SD₃₂	—	122	2	no	—
296	SD₃₂	—	244	2	no	—
297	SD₃₂	D₂₄₄	1	1	yes	characteristic, complemented
298	SD₃₂	D₂₄₄	1	1	yes	characteristic, complemented
299	D₁₆	—	122	2	no	—
300	D₁₆	D₂₄₄	1	1	yes	characteristic, complemented
301	M₃₂	—	61	2	no	—
302	M₃₂	—	122	2	no	—
303	C₂×C₁₆	—	122	2	no	—
304	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
306	#108	—	61	1	no	—
307	#108	C₂²×D₆₁	1	1	yes	characteristic
308	#108	C₂²×D₆₁	1	1	yes	characteristic
309	#104	—	2	1	no	—
310	#104	—	2	1	no	—
311	#104	—	61	2	no	—
312	#101	—	122	2	no	—
313	#100	—	122	2	no	—
314	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	—	61	2	no	—
318	#41	—	488	2	no	—
319	#41	—	244	2	no	—
320	#41	—	244	2	no	—
321	#41	—	244	2	no	—
322	#41	—	244	2	no	—
323	C₂×Q₈	—	122	2	no	—
324	C₂×Q₈	—	244	2	no	—
325	C₂×Q₈	—	244	2	no	—
326	C₂×D₄	—	122	2	no	—
327	C₂×D₄	—	488	1	no	—
328	C₂×D₄	—	488	2	no	—
329	C₂×D₄	—	244	2	no	—
330	C₂×D₄	—	244	2	no	—
331	Q₁₆	—	61	1	no	—
332	Q₁₆	—	122	2	no	—
333	Q₁₆	—	122	2	no	—
334	Q₁₆	—	244	2	no	—
335	Q₁₆	—	244	2	no	—
336	Q₁₆	—	244	1	no	—
337	Q₁₆	—	244	1	no	—
338	Q₁₆	C₂×D₂₄₄	1	1	yes	characteristic
339	Q₁₆	C₂×D₂₄₄	1	1	yes	characteristic
340	SD₁₆	—	2	1	no	—
341	SD₁₆	—	2	1	no	—
342	SD₁₆	—	61	2	no	—
343	SD₁₆	—	244	2	no	—
344	SD₁₆	—	244	2	no	—
345	SD₁₆	—	244	2	no	—
346	SD₁₆	—	244	2	no	—
347	D₈	—	61	1	no	—
348	D₈	—	122	2	no	—
349	D₈	—	122	2	no	—
350	D₈	—	244	2	no	—
351	D₈	—	244	2	no	—
352	D₈	—	244	1	no	—
353	D₈	—	244	1	no	—
354	D₈	C₂×D₂₄₄	1	1	yes	characteristic
355	D₈	C₂×D₂₄₄	1	1	yes	characteristic
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	4	1	no	—
360	M₁₆	—	61	2	no	—
361	M₁₆	—	122	2	no	—
362	C₂×C₈	—	4	1	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	122	2	no	—
365	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
366	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
367	C₄⋊C₄	—	488	1	no	—
368	C₄²	D₄×D₆₁	1	1	yes	characteristic
369	C₁₆	—	2	1	no	—
370	C₁₆	—	122	2	no	—
371	C₁₆	C₂×D₂₄₄	1	1	yes	characteristic
372	C₁₆	C₂×D₂₄₄	1	1	yes	characteristic
373	C₂³	—	488	2	no	—
374	C₂³	—	244	2	no	—
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	61	2	no	—
378	Q₈	—	488	2	no	—
379	Q₈	—	244	2	no	—
380	Q₈	—	244	2	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	61	2	no	—
386	D₄	—	122	2	no	—
387	D₄	—	976	2	no	—
388	D₄	—	488	2	no	—
389	D₄	—	488	2	no	—
390	D₄	—	488	2	no	—
391	D₄	—	244	2	no	—
392	D₄	—	244	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	122	2	no	—
397	C₂×C₄	—	488	2	no	—
398	C₂×C₄	—	488	2	no	—
399	C₂×C₄	—	488	2	no	—
400	C₂×C₄	—	244	2	no	—
401	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
402	C₈	—	4	1	no	—
403	C₈	—	4	1	no	—
404	C₈	—	122	2	no	—
405	C₈	D₈×D₆₁	1	1	yes	characteristic
406	C₈	D₈×D₆₁	1	1	yes	characteristic
407	C₈	C₂²×D₂₄₄	1	1	yes	characteristic
408	C₈	#14519823	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	122	2	no	—
412	C₂²	—	1952	2	no	—
413	C₂²	—	976	2	no	—
414	C₂²	—	488	2	no	—
415	C₂²	#16840564	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	122	2	no	—
420	C₄	—	488	2	no	—
421	C₄	D₄×D₂₄₄	1	1	yes	characteristic
422	C₄	C₂×D₈×D₆₁	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	8	1	no	—
425	C₂	—	8	1	no	—
426	C₂	—	976	2	no	—
427	C₂	—	244	2	no	—
428	C₂	D₈×D₂₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₂₄₄
commutator, cosocle	C₂×C₈×C₆₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₁
Fitting	C₆₁×#2178	C₂
socle	C₂×C₆₁	D₄×D₈
hypercenter	#2178	D₆₁
hypocenter	C₆₁	#33856
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
1. #21458962	C₂	semidirect
2. #21457624	C₂	semidirect
3. #21457619	C₂	semidirect
4. #21448075	C₂	semidirect
5. #21447950	C₂	semidirect
6. #21447900	C₂	semidirect
7. #21447895	C₂	semidirect
8. #21447791	C₂	semidirect
9. #21447784	C₂	semidirect
10. #21447657	C₂	semidirect
11. C₆₁×#2178	C₂	semidirect
13. #16840576	C₂²	semidirect
18. #16840197	C₂²	semidirect
21. C₂×#14519722	C₂²	semidirect
22. C₂×#14519722	C₂²	semidirect
24. #16840178	C₂²	semidirect
25. #16840142	C₂²	semidirect
27. #16840038	C₂²	semidirect
34. #16839583	C₂²	semidirect
35. #16839577	C₂²	semidirect
36. #16839574	C₂²	semidirect
37. #16839545	C₂²	semidirect
40. C₆₁×#443	C₂²	semidirect
41. C₆₁×#368	C₂²	semidirect
43. C₆₁×#359	C₂²	semidirect
44. C₄×C₁₆×C₆₁	C₂²	semidirect
89. Q₃₂×C₆₁	D₄	semidirect
90. SD₃₂×C₆₁	D₄	semidirect
91. SD₃₂×C₆₁	D₄	semidirect
92. D₁₆×C₆₁	D₄	semidirect
218. #2178	D₆₁	semidirect
250. #443	C₂×D₆₁	semidirect
251. #368	C₂×D₆₁	semidirect
256. #359	C₂×D₆₁	semidirect
258. C₄×C₁₆	C₂×D₆₁	semidirect
259. C₆₁	#33856	semidirect
291. Q₃₂	D₂₄₄	semidirect
297. SD₃₂	D₂₄₄	semidirect
298. SD₃₂	D₂₄₄	semidirect
300. D₁₆	D₂₄₄	semidirect

Maximal subgroups

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

subgroup	index
#21458962	2
#21457624	2
#21457619	2
#21448075	2
#21447950	2
#21447900	2
#21447895	2
#21447791	2
#21447784	2
#21447657	2
C₆₁×#2178	2
#33856	61