Subgroups — C₂²×#41×#6157 #28330803

Order 13568.

12878 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×#6157	C₂	1	48	yes	maximal, direct product factor
2	C₂²×Q₈×#6157	C₂	1	2	yes	maximal, complemented
3	C₂²×D₄×#6157	C₂	1	6	yes	maximal, complemented
4	C₂²×#13133296	C₂	1	3	yes	maximal, complemented
5	C₂³×C₄×#6157	C₂	1	3	yes	maximal, complemented
6	C₂²×#41×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂⁴×#6157	C₂²	1	6	yes	—
8	#41×#6157	C₂²	1	256	yes	direct product factor
9	C₂×Q₈×#6157	C₂²	1	48	yes	complemented
10	C₂×D₄×#6157	C₂²	1	144	yes	complemented
11	C₂×#13133296	C₂²	1	72	yes	complemented
12	C₂²×C₄⋊#6157	C₂²	1	6	yes	—
13	C₂²×C₂²⋊#6157	C₂²	1	6	yes	—
14	C₂²×C₄×#6157	C₂²	1	1	yes	characteristic
15	C₂²×C₄×#6157	C₂²	1	3	yes	—
16	C₂²×C₄×#6157	C₂²	1	6	yes	—
17	C₂²×C₄×#6157	C₂²	1	72	yes	complemented
18	C₂²×#11719949	C₄	1	1	yes	characteristic, complemented
19	C₂²×#11719945	C₄	1	3	yes	complemented
20	C₂²×#11719947	C₄	1	3	yes	complemented
21	C₂×#41×D₅₃	C₄	1	24	yes	complemented
22	C₂×#41×D₅₃	C₂²	1	24	yes	—
23	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
24	C₂²×D₄×D₅₃	C₂²	1	3	yes	—
25	C₂³×C₄×D₅₃	C₂²	1	3	yes	—
26	C₂²×#41×C₅₃	C₄	1	1	yes	characteristic, complemented
27	C₂³×#6157	—	2	48	no	—
28	C₂³×#6157	C₂³	1	6	yes	—
29	C₂³×#6157	C₂³	1	72	yes	—
30	C₂³×#6157	C₂³	1	2	yes	—
31	Q₈×#6157	C₂³	1	128	yes	complemented
32	D₄×#6157	C₂³	1	384	yes	complemented
33	#13133296	C₂³	1	192	yes	complemented
34	C₂×C₄⋊#6157	C₂³	1	72	yes	—
35	C₂×C₂²⋊#6157	C₂³	1	72	yes	—
36	C₂×C₄×#6157	C₂³	1	12	yes	—
37	C₂×C₄×#6157	C₂³	1	36	yes	—
38	C₂×C₄×#6157	C₂³	1	72	yes	—
39	C₂×C₄×#6157	C₂³	1	192	yes	complemented
40	C₂⁴×D₅₃	C₂³	1	3	yes	—
41	C₂×#11719949	C₂×C₄	1	24	yes	complemented
42	C₂×#11719945	C₂×C₄	1	72	yes	complemented
43	C₂×#11719947	C₂×C₄	1	72	yes	complemented
44	#41×D₅₃	C₂×C₄	1	192	yes	complemented
45	#41×D₅₃	C₂³	1	64	yes	—
46	C₂²×Dic₁₀₆	C₂×C₄	1	3	yes	complemented
47	C₂×Q₈×D₅₃	C₂×C₄	1	12	yes	complemented
48	C₂×Q₈×D₅₃	C₂³	1	12	yes	—
49	C₂²×D₂₁₂	C₂×C₄	1	3	yes	complemented
50	C₂²×C₂²⋊D₅₃	C₂×C₄	1	6	yes	complemented
51	C₂×D₄×D₅₃	C₂×C₄	1	36	yes	complemented
52	C₂×D₄×D₅₃	C₂³	1	36	yes	—
53	C₂³×Dic₅₃	C₂×C₄	1	3	yes	complemented
54	C₂²×C₄×D₅₃	C₂×C₄	1	36	yes	complemented
55	C₂²×C₄×D₅₃	C₂×C₄	1	3	yes	complemented
56	C₂²×C₄×D₅₃	C₂×C₄	1	3	yes	complemented
57	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
58	C₂²×C₄×D₅₃	C₂³	1	3	yes	—
59	C₂²×C₄×D₅₃	C₂³	1	36	yes	—
60	C₂×#41×C₅₃	C₂×C₄	1	24	yes	complemented
61	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
62	C₂²×D₄×C₅₃	C₂×C₄	1	3	yes	complemented
63	C₂³×C₄×C₅₃	C₂×C₄	1	3	yes	complemented
64	C₂⁴×C₅₃	C₂²×C₄	1	3	yes	—
65	C₂³×D₅₃	—	2	24	no	—
66	C₂³×D₅₃	C₂²×C₄	1	18	yes	—
67	C₂³×D₅₃	C₂²×C₄	1	3	yes	—
68	C₂³×D₅₃	C₂⁴	1	18	yes	—
69	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
70	C₂²×#6157	—	2	24	no	—
71	C₂²×#6157	—	2	288	no	—
72	C₂²×#6157	#41	1	16	yes	direct product factor
73	C₂²×#6157	C₂⁴	1	36	yes	—
74	C₂²×#6157	C₂⁴	1	96	yes	—
75	C₂²×#6157	C₂⁴	1	12	yes	—
76	#41×C₅₃	C₂²×C₄	1	64	yes	complemented
77	C₂×Q₈×C₅₃	C₂²×C₄	1	12	yes	complemented
78	C₂×D₄×C₅₃	C₂²×C₄	1	36	yes	complemented
79	C₂²×C₄×C₅₃	C₂²×C₄	1	3	yes	—
80	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	C₂²×C₄	1	36	yes	complemented
82	C₂×C₂²⋊D₅₃	C₂²×C₄	1	72	yes	complemented
83	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×Dic₅₃	C₂²×C₄	1	3	yes	—
85	C₂²×Dic₅₃	C₂²×C₄	1	36	yes	complemented
86	#11719949	C₂²×C₄	1	64	yes	complemented
87	Q₈×D₅₃	C₂²×C₄	1	48	yes	complemented
88	Q₈×D₅₃	C₂⁴	1	16	yes	—
89	#11719947	C₂²×C₄	1	192	yes	complemented
90	D₄×D₅₃	C₂²×C₄	1	144	yes	complemented
91	D₄×D₅₃	C₂⁴	1	48	yes	—
92	#11719945	C₂²×C₄	1	192	yes	complemented
93	C₂×D₂₁₂	C₂²×C₄	1	36	yes	complemented
94	C₂×C₄×D₅₃	C₂²×C₄	1	6	yes	—
95	C₂×C₄×D₅₃	C₂²×C₄	1	18	yes	—
96	C₂×C₄×D₅₃	C₂²×C₄	1	144	yes	complemented
97	C₂×C₄×D₅₃	C₂²×C₄	1	36	yes	complemented
98	C₂×C₄×D₅₃	C₂²×C₄	1	36	yes	complemented
99	C₂×C₄×D₅₃	C₂⁴	1	6	yes	—
100	C₂×C₄×D₅₃	C₂⁴	1	18	yes	—
101	C₂×C₄×D₅₃	C₂⁴	1	48	yes	—
102	C₂×Dic₁₀₆	C₂²×C₄	1	36	yes	complemented
103	C₂²⋊#6157	C₂⁴	1	96	yes	—
104	C₄⋊#6157	C₂⁴	1	96	yes	—
105	C₄×#6157	C₂⁴	1	16	yes	—
106	C₄×#6157	C₂⁴	1	48	yes	—
107	C₄×#6157	C₂⁴	1	96	yes	—
108	C₂³×C₅₃	—	2	12	no	—
109	C₂³×C₅₃	C₂³×C₄	1	18	yes	—
110	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
111	C₂²×D₅₃	—	2	12	no	—
112	C₂²×D₅₃	—	2	72	no	—
113	C₂²×D₅₃	—	2	72	no	—
114	C₂²×D₅₃	C₂³×C₄	1	18	yes	—
115	C₂²×D₅₃	C₂³×C₄	1	36	yes	—
116	C₂²×D₅₃	C₂³×C₄	1	3	yes	—
117	C₂²×D₅₃	C₂×#41	1	8	yes	—
118	C₂²×D₅₃	C₂⁵	1	12	yes	—
119	C₂²×D₅₃	C₂⁵	1	3	yes	—
120	C₂×#6157	—	2	72	no	—
121	C₂×#6157	—	2	192	no	—
122	C₂×#6157	C₂×#41	1	48	yes	direct product factor
123	C₂×#6157	C₂⁵	1	24	yes	—
124	C₂×#6157	C₂⁵	1	8	yes	—
125	Q₈×C₅₃	C₂³×C₄	1	16	yes	complemented
126	D₄×C₅₃	C₂³×C₄	1	48	yes	complemented
127	C₂×C₄×C₅₃	C₂³×C₄	1	18	yes	—
128	C₂×C₄×C₅₃	C₂³×C₄	1	6	yes	—
129	C₂×C₄×C₅₃	C₂³×C₄	1	48	yes	complemented
130	C₂²⋊D₅₃	C₂³×C₄	1	96	yes	complemented
131	C₂×Dic₅₃	C₂³×C₄	1	18	yes	—
132	C₂×Dic₅₃	C₂³×C₄	1	6	yes	—
133	C₂×Dic₅₃	C₂³×C₄	1	48	yes	complemented
134	D₂₁₂	C₂³×C₄	1	48	yes	complemented
135	C₄×D₅₃	C₂³×C₄	1	12	yes	—
136	C₄×D₅₃	C₂³×C₄	1	36	yes	—
137	C₄×D₅₃	C₂³×C₄	1	48	yes	complemented
138	C₄×D₅₃	C₂³×C₄	1	48	yes	complemented
139	C₄×D₅₃	C₂⁵	1	4	yes	—
140	C₄×D₅₃	C₂⁵	1	12	yes	—
141	Dic₁₀₆	C₂³×C₄	1	48	yes	complemented
142	C₂²×C₄×#41	—	53	1	no	maximal, Sylow
143	C₂²×C₅₃	—	2	36	no	—
144	C₂²×C₅₃	C₄×#41	1	4	yes	complemented
145	C₂²×C₅₃	C₂⁴×C₄	1	12	yes	—
146	C₂²×C₅₃	C₂⁴×C₄	1	3	yes	—
147	C₂×D₅₃	—	2	36	no	—
148	C₂×D₅₃	—	2	24	no	—
149	C₂×D₅₃	—	2	72	no	—
150	C₂×D₅₃	C₄×#41	1	12	yes	complemented
151	C₂×D₅₃	C₂⁴×C₄	1	12	yes	—
152	C₂×D₅₃	C₂⁴×C₄	1	3	yes	—
153	C₂×D₅₃	C₂²×#41	1	12	yes	—
154	C₂×D₅₃	C₂⁶	1	1	yes	characteristic
155	#6157	—	2	24	no	—
156	#6157	C₂²×#41	1	16	yes	direct product factor
157	C₄×C₅₃	C₂⁴×C₄	1	12	yes	—
158	C₄×C₅₃	C₂⁴×C₄	1	4	yes	—
159	Dic₅₃	C₂⁴×C₄	1	12	yes	—
160	Dic₅₃	C₂⁴×C₄	1	4	yes	—
161	C₂³×#41	—	53	1	no	—
162	C₂×C₄×#41	—	53	48	no	—
163	C₂²×C₄×Q₈	—	53	2	no	—
164	C₂²×C₄×D₄	—	53	6	no	—
165	C₂²×#117	—	53	3	no	—
166	C₂³×C₄²	—	53	3	no	—
167	C₂×C₅₃	—	2	12	no	—
168	C₂×C₅₃	C₂×C₄×#41	1	6	yes	complemented
169	C₂×C₅₃	C₂⁵×C₄	1	1	yes	characteristic
170	D₅₃	—	2	12	no	—
171	D₅₃	C₂×C₄×#41	1	6	yes	complemented
172	D₅₃	C₂³×#41	1	2	yes	—
173	C₂²×#41	—	53	24	no	—
174	C₂²×#41	—	53	24	no	—
175	C₂²×#41	—	53	1	no	—
176	C₂²×#41	—	53	3	no	—
177	C₂²×#41	—	53	3	no	—
178	C₂²×#41	#6157	1	1	yes	characteristic, direct product factor
179	C₂³×Q₈	—	53	1	no	—
180	C₂³×D₄	—	53	3	no	—
181	C₂⁴×C₄	—	53	3	no	—
182	C₂⁴×C₄	—	53	6	no	—
183	C₄×#41	—	53	256	no	—
184	C₂×C₄×Q₈	—	53	48	no	—
185	C₂×C₄×D₄	—	53	144	no	—
186	C₂×#117	—	53	72	no	—
187	C₂²×C₄⋊C₄	—	53	6	no	—
188	C₂²×C₂²⋊C₄	—	53	6	no	—
189	C₂²×C₄²	—	53	1	no	—
190	C₂²×C₄²	—	53	3	no	—
191	C₂²×C₄²	—	53	6	no	—
192	C₂²×C₄²	—	53	72	no	—
193	C₅₃	C₂²×C₄×#41	1	1	yes	characteristic, complemented, Sylow
194	C₂⁵	—	53	3	no	—
195	C₂×#41	—	53	64	no	—
196	C₂×#41	—	53	192	no	—
197	C₂×#41	—	53	24	no	—
198	C₂×#41	—	53	72	no	—
199	C₂×#41	—	53	72	no	—
200	C₂×#41	C₂×#6157	1	24	yes	direct product factor
201	C₂²×Q₈	—	53	12	no	—
202	C₂²×Q₈	—	53	12	no	—
203	C₂²×Q₈	—	53	3	no	—
204	C₂²×Q₈	C₂×#6157	1	1	yes	characteristic, complemented
205	C₂²×D₄	—	53	6	no	—
206	C₂²×D₄	—	53	36	no	—
207	C₂²×D₄	—	53	36	no	—
208	C₂²×D₄	—	53	3	no	—
209	C₂²×D₄	C₂×#6157	1	3	yes	complemented
210	C₂³×C₄	—	53	2	no	—
211	C₂³×C₄	—	53	3	no	—
212	C₂³×C₄	—	53	3	no	—
213	C₂³×C₄	—	53	3	no	—
214	C₂³×C₄	—	53	1	no	—
215	C₂³×C₄	—	53	3	no	—
216	C₂³×C₄	—	53	36	no	—
217	C₂³×C₄	—	53	36	no	—
218	C₂³×C₄	—	53	6	no	—
219	C₂³×C₄	—	53	72	no	—
220	C₂³×C₄	—	106	48	no	—
221	C₂³×C₄	C₂×#6157	1	3	yes	complemented
222	C₄×Q₈	—	53	128	no	—
223	C₄×D₄	—	53	384	no	—
224	#117	—	53	192	no	—
225	C₂×C₄⋊C₄	—	53	72	no	—
226	C₂×C₂²⋊C₄	—	53	72	no	—
227	C₂×C₄²	—	53	36	no	—
228	C₂×C₄²	—	53	72	no	—
229	C₂×C₄²	—	53	192	no	—
230	C₂×C₄²	—	53	12	no	—
231	C₂⁴	—	53	1	no	—
232	C₂⁴	—	53	18	no	—
233	C₂⁴	—	53	3	no	—
234	C₂⁴	—	53	18	no	—
235	C₂⁴	—	106	24	no	—
236	C₂⁴	C₂²×#6157	1	3	yes	—
237	#41	—	53	64	no	—
238	#41	—	53	192	no	—
239	#41	—	53	192	no	—
240	#41	C₂²×#6157	1	64	yes	direct product factor
241	C₂×Q₈	—	53	48	no	—
242	C₂×Q₈	—	53	16	no	—
243	C₂×Q₈	—	53	36	no	—
244	C₂×Q₈	C₂²×#6157	1	12	yes	complemented
245	C₂×D₄	—	53	72	no	—
246	C₂×D₄	—	53	144	no	—
247	C₂×D₄	—	53	48	no	—
248	C₂×D₄	—	53	36	no	—
249	C₂×D₄	C₂²×#6157	1	36	yes	complemented
250	C₂²×C₄	—	53	16	no	—
251	C₂²×C₄	—	53	12	no	—
252	C₂²×C₄	—	53	1	no	—
253	C₂²×C₄	—	53	3	no	—
254	C₂²×C₄	—	53	36	no	—
255	C₂²×C₄	—	53	6	no	—
256	C₂²×C₄	—	53	18	no	—
257	C₂²×C₄	—	53	36	no	—
258	C₂²×C₄	—	53	36	no	—
259	C₂²×C₄	—	53	6	no	—
260	C₂²×C₄	—	53	18	no	—
261	C₂²×C₄	—	53	144	no	—
262	C₂²×C₄	—	53	48	no	—
263	C₂²×C₄	—	53	36	no	—
264	C₂²×C₄	—	53	96	no	—
265	C₂²×C₄	—	106	288	no	—
266	C₂²×C₄	—	106	24	no	—
267	C₂²×C₄	C₂²×#6157	1	3	yes	—
268	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
269	C₂²×C₄	C₂²×#6157	1	36	yes	complemented
270	C₄⋊C₄	—	53	96	no	—
271	C₂²⋊C₄	—	53	96	no	—
272	C₄²	—	53	16	no	—
273	C₄²	—	53	48	no	—
274	C₄²	—	53	96	no	—
275	C₂³	—	2	12	no	—
276	C₂³	—	53	8	no	—
277	C₂³	—	53	3	no	—
278	C₂³	—	53	3	no	—
279	C₂³	—	53	36	no	—
280	C₂³	—	53	18	no	—
281	C₂³	—	53	12	no	—
282	C₂³	—	106	72	no	—
283	C₂³	—	106	72	no	—
284	C₂³	—	106	12	no	—
285	C₂³	C₂³×#6157	1	18	yes	—
286	C₂³	C₂³×#6157	1	1	yes	characteristic
287	Q₈	—	53	48	no	—
288	Q₈	C₂³×#6157	1	16	yes	complemented
289	D₄	—	53	96	no	—
290	D₄	—	53	48	no	—
291	D₄	C₂³×#6157	1	48	yes	complemented
292	C₂×C₄	—	53	48	no	—
293	C₂×C₄	—	53	8	no	—
294	C₂×C₄	—	53	6	no	—
295	C₂×C₄	—	53	18	no	—
296	C₂×C₄	—	53	48	no	—
297	C₂×C₄	—	53	12	no	—
298	C₂×C₄	—	53	36	no	—
299	C₂×C₄	—	53	48	no	—
300	C₂×C₄	—	53	48	no	—
301	C₂×C₄	—	53	4	no	—
302	C₂×C₄	—	53	12	no	—
303	C₂×C₄	—	53	24	no	—
304	C₂×C₄	—	106	192	no	—
305	C₂×C₄	—	106	72	no	—
306	C₂×C₄	C₂³×#6157	1	6	yes	—
307	C₂×C₄	C₂³×#6157	1	18	yes	—
308	C₂×C₄	C₂³×#6157	1	48	yes	complemented
309	C₂²	—	2	36	no	—
310	C₂²	—	53	12	no	—
311	C₂²	—	53	12	no	—
312	C₂²	—	53	1	no	—
313	C₂²	—	53	3	no	—
314	C₂²	—	53	12	no	—
315	C₂²	—	106	24	no	—
316	C₂²	—	106	72	no	—
317	C₂²	—	106	36	no	—
318	C₂²	#41×#6157	1	4	yes	direct product factor
319	C₂²	C₂⁴×#6157	1	12	yes	—
320	C₂²	C₂⁴×#6157	1	3	yes	—
321	C₄	—	53	16	no	—
322	C₄	—	53	4	no	—
323	C₄	—	53	12	no	—
324	C₄	—	106	24	no	—
325	C₄	C₂⁴×#6157	1	4	yes	—
326	C₄	C₂⁴×#6157	1	12	yes	—
327	C₂	—	2	12	no	—
328	C₂	—	53	2	no	—
329	C₂	—	53	6	no	—
330	C₂	—	106	12	no	—
331	C₂	C₂×#41×#6157	1	6	yes	direct product factor
332	C₂	C₂⁵×#6157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#6157
commutator	C₂×C₅₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#6157
Fitting	C₂²×#41×C₅₃	C₄
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂²×#41×D₅₃	C₂
cosocle	C₂×D₅₃	C₂⁶
hypercenter	C₂²×#41	#6157
hypocenter	C₅₃	C₂²×C₄×#41
LCS	G ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×#6157	C₂	direct (N × H)
2. C₂²×Q₈×#6157	C₂	semidirect
3. C₂²×D₄×#6157	C₂	semidirect
4. C₂²×#13133296	C₂	semidirect
5. C₂³×C₄×#6157	C₂	semidirect
8. #41×#6157	C₂²	direct (N × H)
9. C₂×Q₈×#6157	C₂²	semidirect
10. C₂×D₄×#6157	C₂²	semidirect
11. C₂×#13133296	C₂²	semidirect
17. C₂²×C₄×#6157	C₂²	semidirect
18. C₂²×#11719949	C₄	semidirect
19. C₂²×#11719945	C₄	semidirect
20. C₂²×#11719947	C₄	semidirect
21. C₂×#41×D₅₃	C₄	semidirect
26. C₂²×#41×C₅₃	C₄	semidirect
31. Q₈×#6157	C₂³	semidirect
32. D₄×#6157	C₂³	semidirect
33. #13133296	C₂³	semidirect
39. C₂×C₄×#6157	C₂³	semidirect
41. C₂×#11719949	C₂×C₄	semidirect
42. C₂×#11719945	C₂×C₄	semidirect
43. C₂×#11719947	C₂×C₄	semidirect
44. #41×D₅₃	C₂×C₄	semidirect
46. C₂²×Dic₁₀₆	C₂×C₄	semidirect
47. C₂×Q₈×D₅₃	C₂×C₄	semidirect
49. C₂²×D₂₁₂	C₂×C₄	semidirect
50. C₂²×C₂²⋊D₅₃	C₂×C₄	semidirect
51. C₂×D₄×D₅₃	C₂×C₄	semidirect
53. C₂³×Dic₅₃	C₂×C₄	semidirect
54. C₂²×C₄×D₅₃	C₂×C₄	semidirect
55. C₂²×C₄×D₅₃	C₂×C₄	semidirect
56. C₂²×C₄×D₅₃	C₂×C₄	semidirect
60. C₂×#41×C₅₃	C₂×C₄	semidirect
61. C₂²×Q₈×C₅₃	C₂×C₄	semidirect
62. C₂²×D₄×C₅₃	C₂×C₄	semidirect
63. C₂³×C₄×C₅₃	C₂×C₄	semidirect
72. C₂²×#6157	#41	direct (N × H)
76. #41×C₅₃	C₂²×C₄	semidirect
77. C₂×Q₈×C₅₃	C₂²×C₄	semidirect
78. C₂×D₄×C₅₃	C₂²×C₄	semidirect
81. C₂²×C₄×C₅₃	C₂²×C₄	semidirect
82. C₂×C₂²⋊D₅₃	C₂²×C₄	semidirect
85. C₂²×Dic₅₃	C₂²×C₄	semidirect
86. #11719949	C₂²×C₄	semidirect
87. Q₈×D₅₃	C₂²×C₄	semidirect
89. #11719947	C₂²×C₄	semidirect
90. D₄×D₅₃	C₂²×C₄	semidirect
92. #11719945	C₂²×C₄	semidirect
93. C₂×D₂₁₂	C₂²×C₄	semidirect
96. C₂×C₄×D₅₃	C₂²×C₄	semidirect
97. C₂×C₄×D₅₃	C₂²×C₄	semidirect
98. C₂×C₄×D₅₃	C₂²×C₄	semidirect
102. C₂×Dic₁₀₆	C₂²×C₄	semidirect
122. C₂×#6157	C₂×#41	direct (N × H)
125. Q₈×C₅₃	C₂³×C₄	semidirect
126. D₄×C₅₃	C₂³×C₄	semidirect
129. C₂×C₄×C₅₃	C₂³×C₄	semidirect
130. C₂²⋊D₅₃	C₂³×C₄	semidirect
133. C₂×Dic₅₃	C₂³×C₄	semidirect
134. D₂₁₂	C₂³×C₄	semidirect
137. C₄×D₅₃	C₂³×C₄	semidirect
138. C₄×D₅₃	C₂³×C₄	semidirect
141. Dic₁₀₆	C₂³×C₄	semidirect
144. C₂²×C₅₃	C₄×#41	semidirect
150. C₂×D₅₃	C₄×#41	semidirect
156. #6157	C₂²×#41	direct (N × H)
168. C₂×C₅₃	C₂×C₄×#41	semidirect
171. D₅₃	C₂×C₄×#41	semidirect
178. C₂²×#41	#6157	direct (N × H)
193. C₅₃	C₂²×C₄×#41	semidirect
200. C₂×#41	C₂×#6157	direct (N × H)
204. C₂²×Q₈	C₂×#6157	semidirect
209. C₂²×D₄	C₂×#6157	semidirect
221. C₂³×C₄	C₂×#6157	semidirect
240. #41	C₂²×#6157	direct (N × H)
244. C₂×Q₈	C₂²×#6157	semidirect
249. C₂×D₄	C₂²×#6157	semidirect
269. C₂²×C₄	C₂²×#6157	semidirect
288. Q₈	C₂³×#6157	semidirect
291. D₄	C₂³×#6157	semidirect
308. C₂×C₄	C₂³×#6157	semidirect
318. C₂²	#41×#6157	direct (N × H)
331. C₂	C₂×#41×#6157	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×#6157	2
C₂²×Q₈×#6157	2
C₂²×D₄×#6157	2
C₂²×#13133296	2
C₂³×C₄×#6157	2
C₂²×#41×D₅₃	2
C₂²×C₄×#41	53

Subgroups — C22×#41×#6157 #28330803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#41×#6157 #28330803