Subgroups — #29836678

Order 15616.

718 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840194	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₉₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#21457506	C₂	1	2	yes	maximal, complemented
4	#21448080	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447910	C₂	1	1	yes	maximal, characteristic, complemented
6	#21447905	C₂	1	1	yes	maximal, characteristic, complemented
7	#21447875	C₂	1	2	yes	maximal, complemented
8	#21447750	C₂	1	2	yes	maximal, complemented
9	#21447744	C₂	1	2	yes	maximal, complemented
10	C₄×D₉₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14519799	C₂²	1	2	yes	complemented
13	C₂²×D₄₈₈	C₂²	1	2	yes	—
14	#16840408	—	2	2	no	—
15	#16840194	—	2	4	no	—
16	C₂×Dic₄₈₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×#14519722	C₂²	1	2	yes	complemented
18	C₂×#14519722	C₂²	1	2	yes	complemented
19	C₂×D₉₇₆	—	2	4	no	—
20	C₂×D₉₇₆	C₂²	1	2	yes	—
21	C₂×D₉₇₆	C₂²	1	1	yes	characteristic
22	C₂×D₉₇₆	C₂²	1	1	yes	characteristic
23	#16840146	C₂²	1	2	yes	complemented
24	#16840003	C₂²	1	2	yes	—
25	#16839998	C₂²	1	2	yes	complemented
26	#16839978	—	2	2	no	—
27	#16839915	—	2	2	no	—
28	#16839909	—	2	2	no	—
29	C₄×D₄₈₈	C₂²	1	2	yes	complemented
30	#16839588	C₂²	1	1	yes	characteristic, complemented
31	#16839567	C₂²	1	2	yes	complemented
32	#16839564	C₂²	1	2	yes	complemented
33	#16839564	C₂²	1	2	yes	complemented
34	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
35	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
41	C₂×#11758222	—	2	2	no	—
42	C₂²×D₂₄₄	—	2	2	no	—
43	#14519799	—	2	4	no	—
44	#14519799	—	4	2	no	—
45	C₂×Dic₂₄₄	C₂³	1	2	yes	—
46	C₂×#11758190	—	2	2	no	—
47	C₂×#11758190	—	2	2	no	—
48	C₂×D₄₈₈	—	2	4	no	—
49	C₂×D₄₈₈	—	2	2	no	—
50	C₂×D₄₈₈	—	4	2	no	—
51	C₂×D₄₈₈	C₂³	1	2	yes	—
52	C₂×D₄₈₈	C₂³	1	2	yes	—
53	#14519765	—	2	2	no	—
54	#14519762	—	4	2	no	—
55	#14519756	—	2	2	no	—
56	#14519751	—	2	2	no	—
57	#14519750	—	4	2	no	—
58	#14519745	—	4	2	no	—
59	C₄×D₂₄₄	—	2	2	no	—
60	C₂²⋊C₄×D₆₁	—	4	2	no	—
61	Dic₄₈₈	—	2	2	no	—
62	#14519722	—	2	4	no	—
63	#14519722	—	4	2	no	—
64	D₉₇₆	—	2	4	no	—
65	D₉₇₆	—	2	2	no	—
66	D₉₇₆	D₄	1	4	yes	complemented
67	#14519711	C₂³	1	2	yes	—
68	#14519702	—	2	2	no	—
69	#14519699	—	2	2	no	—
70	#14519699	—	2	2	no	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
74	C₂×C₁₆×C₆₁	—	2	2	no	—
75	C₂×C₁₆×C₆₁	—	2	2	no	—
76	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₆₁	D₄	1	1	yes	characteristic
81	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
82	C₂²⋊C₈×C₆₁	D₄	1	1	yes	characteristic
83	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₂³×D₆₁	—	4	2	no	—
85	C₂×D₄×C₆₁	D₈	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₂²⋊D₆₁	—	4	2	no	—
89	C₂×C₂²⋊D₆₁	—	4	2	no	—
90	#11758222	—	4	4	no	—
91	#11758222	—	8	2	no	—
92	C₂×D₂₄₄	—	2	2	no	—
93	C₂×D₂₄₄	—	2	2	no	—
94	C₂×D₂₄₄	—	4	4	no	—
95	C₂×D₂₄₄	—	4	2	no	—
96	C₂×D₂₄₄	—	8	2	no	—
97	C₂×C₄×D₆₁	—	4	2	no	—
98	C₂×C₄×D₆₁	—	4	2	no	—
99	C₂×Dic₁₂₂	—	2	2	no	—
100	C₂×C₈×C₆₁	—	2	1	no	—
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	—	2	1	no	—
103	C₂×C₈×C₆₁	—	2	1	no	—
104	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₆₁	D₈	1	1	yes	characteristic
109	C₂²⋊C₄×C₆₁	D₈	1	1	yes	characteristic
110	C₂²⋊C₄×C₆₁	D₈	1	1	yes	characteristic
111	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²⋊Dic₆₁	—	4	2	no	—
113	#11758198	—	4	2	no	—
114	#11758198	—	4	2	no	—
115	#11758198	—	4	2	no	—
116	#11758198	—	4	2	no	—
117	C₄⋊Dic₆₁	—	2	2	no	—
118	#11758196	—	4	2	no	—
119	Dic₂₄₄	—	2	2	no	—
120	Dic₂₄₄	—	2	2	no	—
121	D₄₈₈	—	2	2	no	—
122	D₄₈₈	—	2	2	no	—
123	D₄₈₈	—	2	2	no	—
124	D₄₈₈	—	4	4	no	—
125	D₄₈₈	C₂×D₄	1	4	yes	—
126	#11758190	—	4	4	no	—
127	#11758190	—	8	2	no	—
128	C₁₆×C₆₁	—	2	1	no	—
129	C₁₆×C₆₁	—	2	1	no	—
130	C₁₆×C₆₁	—	2	1	no	—
131	C₁₆×C₆₁	C₂×D₄	1	2	yes	—
132	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
133	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
134	C₂²×D₆₁	—	4	2	no	—
135	C₂²×D₆₁	—	4	2	no	—
136	C₂²×D₆₁	—	8	4	no	—
137	C₂²×D₆₁	—	8	4	no	—
138	C₂²×D₆₁	—	16	2	no	—
139	D₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	1	no	—
141	C₂×C₄×C₆₁	—	2	1	no	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
149	C₂²⋊D₆₁	—	8	4	no	—
150	C₂²⋊D₆₁	—	16	2	no	—
151	C₂×Dic₆₁	—	4	2	no	—
152	C₂×Dic₆₁	—	4	2	no	—
153	D₂₄₄	—	2	4	no	—
154	D₂₄₄	—	4	2	no	—
155	D₂₄₄	—	4	2	no	—
156	D₂₄₄	—	4	2	no	—
157	D₂₄₄	—	8	4	no	—
158	C₄×D₆₁	—	8	4	no	—
159	C₄×D₆₁	—	16	2	no	—
160	Dic₁₂₂	—	4	2	no	—
161	Dic₁₂₂	—	4	2	no	—
162	C₈×C₆₁	—	2	1	no	—
163	C₈×C₆₁	—	2	1	no	—
164	C₈×C₆₁	—	2	1	no	—
165	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
167	#33846	—	61	1	no	maximal, Sylow
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	2	1	no	—
170	C₂²×C₆₁	—	2	1	no	—
171	C₂²×C₆₁	—	2	1	no	—
172	C₂²×C₆₁	—	2	1	no	—
173	C₂²×C₆₁	#508	1	2	yes	complemented
174	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
175	C₂×D₆₁	—	4	4	no	—
176	C₂×D₆₁	—	8	2	no	—
177	C₂×D₆₁	—	8	2	no	—
178	C₂×D₆₁	—	8	2	no	—
179	C₂×D₆₁	—	8	2	no	—
180	C₂×D₆₁	—	8	2	no	—
181	C₂×D₆₁	—	16	8	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	2	1	no	—
186	C₄×C₆₁	D₄²	1	1	yes	characteristic
187	C₄×C₆₁	#576	1	1	yes	characteristic
188	Dic₆₁	—	8	2	no	—
189	Dic₆₁	—	8	2	no	—
190	C₂×#508	—	61	1	no	—
191	C₂²×D₁₆	—	61	1	no	—
192	#3280	—	61	2	no	—
193	#2249	—	61	1	no	—
194	#2216	—	61	1	no	—
195	#2215	—	61	1	no	—
196	#2210	—	61	2	no	—
197	#2187	—	61	2	no	—
198	#2186	—	61	2	no	—
199	C₄×D₁₆	—	61	1	no	—
200	D₄×C₁₆	D₆₁	1	1	yes	characteristic, complemented
201	C₂×C₆₁	—	2	2	no	—
202	C₂×C₆₁	—	4	1	no	—
203	C₂×C₆₁	D₄×D₈	1	1	yes	characteristic
204	C₂×C₆₁	C₂×#508	1	1	yes	characteristic
205	C₂×C₆₁	#3415	1	1	yes	characteristic
206	D₆₁	—	8	4	no	—
207	D₆₁	—	16	2	no	—
208	C₂×#135	—	61	2	no	—
209	C₂²×D₈	—	61	2	no	—
210	#546	—	122	2	no	—
211	#508	—	122	4	no	—
212	C₂×Q₃₂	—	61	1	no	—
213	C₂×SD₃₂	—	61	2	no	—
214	C₂×SD₃₂	—	61	2	no	—
215	C₂×D₁₆	—	61	1	no	—
216	C₂×D₁₆	—	61	2	no	—
217	C₂×D₁₆	—	61	1	no	—
218	C₂×D₁₆	—	122	4	no	—
219	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic
220	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
221	#495	—	61	2	no	—
222	#467	—	61	2	no	—
223	#466	—	61	2	no	—
224	#463	—	122	2	no	—
225	#450	—	122	2	no	—
226	#449	—	122	2	no	—
227	C₄×D₈	—	61	2	no	—
228	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
229	#366	—	61	1	no	—
230	C₄⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
231	#358	—	61	2	no	—
232	#357	—	61	2	no	—
233	#357	—	61	2	no	—
234	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
235	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
236	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
237	C₆₁	#33846	1	1	yes	characteristic, complemented, Sylow
238	C₂×#41	—	122	2	no	—
239	C₂²×D₄	—	122	2	no	—
240	#135	—	122	4	no	—
241	#135	—	244	2	no	—
242	C₂×Q₁₆	—	61	2	no	—
243	C₂×SD₁₆	—	122	2	no	—
244	C₂×SD₁₆	—	122	2	no	—
245	C₂×D₈	—	61	2	no	—
246	C₂×D₈	—	61	2	no	—
247	C₂×D₈	—	122	4	no	—
248	C₂×D₈	—	122	2	no	—
249	C₂×D₈	—	244	2	no	—
250	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
252	#124	—	122	2	no	—
253	#123	—	244	2	no	—
254	C₂²⋊Q₈	—	122	2	no	—
255	#121	—	122	2	no	—
256	#121	—	244	2	no	—
257	#120	—	244	2	no	—
258	C₄×D₄	—	122	2	no	—
259	C₄×D₄	D₂₄₄	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	244	2	no	—
261	Q₃₂	—	122	2	no	—
262	SD₃₂	—	122	4	no	—
263	SD₃₂	—	244	2	no	—
264	D₁₆	—	61	4	no	—
265	D₁₆	—	122	4	no	—
266	D₁₆	—	122	2	no	—
267	C₂×C₁₆	—	2	2	no	—
268	C₂×C₁₆	—	2	2	no	—
269	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
270	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
271	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
272	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
273	#107	—	61	2	no	—
274	C₄⋊C₈	D₂₄₄	1	1	yes	characteristic
275	#103	—	122	2	no	—
276	#102	—	122	2	no	—
277	#102	—	122	2	no	—
278	C₂²⋊C₈	D₂₄₄	1	1	yes	characteristic
279	C₂²⋊C₈	D₂₄₄	1	1	yes	characteristic
280	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
281	C₂⁴	—	244	2	no	—
282	#41	—	488	2	no	—
283	#41	—	244	4	no	—
284	C₂×Q₈	—	122	2	no	—
285	C₂×D₄	—	122	2	no	—
286	C₂×D₄	—	122	2	no	—
287	C₂×D₄	—	488	2	no	—
288	C₂×D₄	—	244	4	no	—
289	C₂×D₄	—	244	2	no	—
290	C₂×D₄	—	244	2	no	—
291	C₂×D₄	—	244	2	no	—
292	C₂×D₄	D₄₈₈	1	1	yes	characteristic
293	C₂²×C₄	—	244	2	no	—
294	C₂²×C₄	—	244	2	no	—
295	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₂₄₄	1	1	yes	characteristic
297	Q₁₆	—	122	2	no	—
298	Q₁₆	—	122	2	no	—
299	SD₁₆	—	488	2	no	—
300	SD₁₆	—	244	4	no	—
301	D₈	—	61	4	no	—
302	D₈	—	122	2	no	—
303	D₈	—	122	2	no	—
304	D₈	—	122	2	no	—
305	D₈	—	244	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	C₂×D₂₄₄	1	1	yes	characteristic
311	C₂×C₈	C₂×D₂₄₄	1	1	yes	characteristic
312	C₂×C₈	C₂×D₂₄₄	1	1	yes	characteristic
313	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
314	C₄⋊C₄	—	122	2	no	—
315	C₄⋊C₄	—	244	2	no	—
316	C₄⋊C₄	D₄₈₈	1	1	yes	characteristic
317	C₂²⋊C₄	—	244	2	no	—
318	C₂²⋊C₄	—	244	2	no	—
319	C₂²⋊C₄	—	244	2	no	—
320	C₂²⋊C₄	—	244	2	no	—
321	C₂²⋊C₄	—	244	2	no	—
322	C₂²⋊C₄	D₄₈₈	1	1	yes	characteristic
323	C₂²⋊C₄	D₄₈₈	1	1	yes	characteristic
324	C₄²	C₂×D₂₄₄	1	1	yes	characteristic
325	C₁₆	—	2	1	no	—
326	C₁₆	—	2	1	no	—
327	C₁₆	—	2	1	no	—
328	C₁₆	D₄×D₆₁	1	2	yes	—
329	C₂³	—	976	2	no	—
330	C₂³	—	488	4	no	—
331	C₂³	—	488	4	no	—
332	C₂³	—	244	2	no	—
333	C₂³	—	244	2	no	—
334	C₂³	C₂×D₄₈₈	1	1	yes	characteristic
335	C₂³	C₂×D₄₈₈	1	1	yes	characteristic
336	Q₈	—	244	2	no	—
337	Q₈	—	244	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	122	4	no	—
340	D₄	—	976	2	no	—
341	D₄	—	488	4	no	—
342	D₄	—	488	4	no	—
343	D₄	—	244	2	no	—
344	D₄	—	244	2	no	—
345	D₄	—	244	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	976	2	no	—
351	C₂×C₄	—	488	4	no	—
352	C₂×C₄	—	244	2	no	—
353	C₂×C₄	—	244	2	no	—
354	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
357	C₂×C₄	C₂×D₄₈₈	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	C₂×D₄×D₆₁	1	1	yes	characteristic
363	C₈	#14519823	1	1	yes	characteristic
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	976	8	no	—
370	C₂²	—	488	2	no	—
371	C₂²	—	488	2	no	—
372	C₂²	—	488	2	no	—
373	C₂²	—	488	2	no	—
374	C₂²	—	488	2	no	—
375	C₂²	—	244	4	no	—
376	C₂²	#16840194	1	2	yes	complemented
377	C₂²	C₂²×D₄₈₈	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	488	2	no	—
383	C₄	—	488	2	no	—
384	C₄	D₄×D₂₄₄	1	1	yes	characteristic
385	C₄	#16840567	1	1	yes	characteristic
386	C₂	—	2	2	no	—
387	C₂	—	4	1	no	—
388	C₂	—	976	2	no	—
389	C₂	—	488	4	no	—
390	C₂	D₄×D₄₈₈	1	1	yes	characteristic
391	C₂	C₂×#16840194	1	1	yes	characteristic
392	C₂	#21458960	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄₈₈
commutator, cosocle	C₂×C₈×C₆₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₁
Fitting	D₄×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×D₈
hypercenter	D₄×C₁₆	D₆₁
hypocenter	C₆₁	#33846
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ C₈×D₄ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16840194	C₂	semidirect
2. C₂²×D₉₇₆	C₂	semidirect
3. #21457506	C₂	semidirect
4. #21448080	C₂	semidirect
5. #21447910	C₂	semidirect
6. #21447905	C₂	semidirect
7. #21447875	C₂	semidirect
8. #21447750	C₂	semidirect
9. #21447744	C₂	semidirect
10. C₄×D₉₇₆	C₂	semidirect
11. D₄×C₁₆×C₆₁	C₂	semidirect
12. C₂×#14519799	C₂²	semidirect
16. C₂×Dic₄₈₈	C₂²	semidirect
17. C₂×#14519722	C₂²	semidirect
18. C₂×#14519722	C₂²	semidirect
23. #16840146	C₂²	semidirect
25. #16839998	C₂²	semidirect
29. C₄×D₄₈₈	C₂²	semidirect
30. #16839588	C₂²	semidirect
31. #16839567	C₂²	semidirect
32. #16839564	C₂²	semidirect
33. #16839564	C₂²	semidirect
35. C₂²×C₁₆×C₆₁	C₂²	semidirect
37. C₆₁×C₄⋊C₁₆	C₂²	semidirect
39. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₆₁	C₂²	semidirect
66. D₉₇₆	D₄	semidirect
173. C₂²×C₆₁	#508	semidirect
200. D₄×C₁₆	D₆₁	semidirect
220. C₂²×C₁₆	C₂×D₆₁	semidirect
230. C₄⋊C₁₆	C₂×D₆₁	semidirect
235. C₂²⋊C₁₆	C₂×D₆₁	semidirect
236. C₄×C₁₆	C₂×D₆₁	semidirect
237. C₆₁	#33846	semidirect
376. C₂²	#16840194	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16840194	2
C₂²×D₉₇₆	2
#21457506	2
#21448080	2
#21447910	2
#21447905	2
#21447875	2
#21447750	2
#21447744	2
C₄×D₉₇₆	2
D₄×C₁₆×C₆₁	2
#33846	61