Subgroups — C₂×C₄×#13133286 #28318363

Order 13568.

1358 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133286	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊#6157	C₂	1	2	yes	maximal
3	C₄×#13133286	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16811497	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊#6157	C₂²	1	4	yes	—
7	C₂²×C₄×#6157	—	2	2	no	—
8	C₂×#13133286	C₄	1	16	yes	direct product factor
9	C₂×#13133286	C₂²	1	8	yes	—
10	C₄×C₄⋊#6157	—	2	4	no	—
11	C₄×C₄⋊#6157	C₂²	1	8	yes	—
12	C₂×(C₂×#6157)⋊C₄	—	2	2	no	—
13	#16811497	C₂²	1	8	yes	—
14	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×#88322	C₄	1	1	yes	characteristic, complemented
18	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
19	C₂×C₈×Dic₅₃	C₄	1	1	yes	characteristic, complemented
20	C₄×C₈×D₅₃	C₄	1	4	yes	complemented
21	C₄×C₈×D₅₃	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic, complemented
23	C₂³×#6157	—	2	4	no	—
24	C₂×C₄⋊#6157	—	2	4	no	—
25	C₂×C₄⋊#6157	—	2	8	no	—
26	C₂×C₄⋊#6157	C₂×C₄	1	16	yes	—
27	C₂×C₄⋊#6157	C₂³	1	8	yes	—
28	C₂×C₄×#6157	—	2	8	no	—
29	C₂×C₄×#6157	—	4	8	no	—
30	#13133286	C₂×C₄	1	32	yes	direct product factor
31	(C₂×#6157)⋊C₄	—	2	8	no	—
32	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
35	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
36	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
37	C₂×C₈×D₅₃	—	2	4	no	—
38	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
40	C₂×C₈×D₅₃	C₂×C₄	1	8	yes	—
41	C₂×C₈×D₅₃	C₂³	1	2	yes	—
42	C₂×C₈×D₅₃	C₂³	1	2	yes	—
43	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
46	C₄²×D₅₃	C₂×C₄	1	2	yes	—
47	C₄²×D₅₃	D₄	1	2	yes	—
48	C₄²×D₅₃	Q₈	1	2	yes	—
49	C₄²×D₅₃	C₂³	1	2	yes	—
50	C₄×#88322	C₂×C₄	1	4	yes	complemented
51	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
52	C₈×Dic₅₃	C₂×C₄	1	4	yes	complemented
53	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	complemented
57	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×#6157	—	2	16	no	—
59	C₂²×#6157	—	2	8	no	—
60	C₂²×#6157	—	4	8	no	—
61	C₂²×#6157	—	4	8	no	—
62	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₄×D₅₃	—	2	4	no	—
69	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
70	C₂×C₄×D₅₃	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₅₃	D₈	1	4	yes	—
72	C₂×C₄×D₅₃	Q₁₆	1	4	yes	—
73	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
75	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
76	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
77	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
78	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
79	C₂×C₄×D₅₃	#41	1	4	yes	—
80	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
81	C₄⋊#6157	—	2	16	no	—
82	C₄⋊#6157	—	2	8	no	—
83	C₄⋊#6157	C₂²×C₄	1	16	yes	—
84	C₄×#6157	—	4	16	no	—
85	C₂×C₈×C₅₃	—	2	2	no	—
86	C₂×C₈×C₅₃	C₄²	1	4	yes	complemented
87	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
89	C₄²×C₅₃	C₄⋊C₄	1	2	yes	—
90	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
91	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
92	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
93	C₄×Dic₅₃	C₄⋊C₄	1	2	yes	—
94	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
95	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
96	C₄×Dic₅₃	C₂×Q₈	1	2	yes	—
97	C₂×#88322	—	2	2	no	—
98	C₂×#88322	C₄²	1	4	yes	complemented
99	C₂×#88322	C₂²×C₄	1	2	yes	—
100	C₂×#88322	C₂²×C₄	1	2	yes	—
101	C₈×D₅₃	—	2	4	no	—
102	C₈×D₅₃	—	2	4	no	—
103	C₈×D₅₃	C₄²	1	8	yes	complemented
104	C₈×D₅₃	C₂²×C₄	1	8	yes	—
105	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂²×D₅₃	C₄×D₄	1	4	yes	—
108	C₂²×D₅₃	C₂×D₈	1	2	yes	—
109	C₂²×D₅₃	C₂×Q₁₆	1	2	yes	—
110	C₂²×D₅₃	#135	1	4	yes	—
111	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
112	C₂×#6157	—	2	16	no	—
113	C₂×#6157	—	4	8	no	—
114	C₂×#6157	—	4	8	no	—
115	C₂×#6157	—	4	32	no	—
116	C₂×C₄×C₅₃	—	2	2	no	—
117	C₂×C₄×C₅₃	#107	1	4	yes	complemented
118	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
119	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₅₃	#117	1	2	yes	—
123	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
124	C₂×Dic₅₃	—	2	2	no	—
125	C₂×Dic₅₃	#107	1	4	yes	complemented
126	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×Dic₅₃	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×Dic₅₃	C₄×Q₈	1	4	yes	—
130	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
131	C₄×D₅₃	—	2	4	no	—
132	C₄×D₅₃	—	2	4	no	—
133	C₄×D₅₃	#107	1	8	yes	complemented
134	C₄×D₅₃	C₂×C₄²	1	2	yes	—
135	C₄×D₅₃	#117	1	2	yes	—
136	C₄×D₅₃	C₄×D₄	1	4	yes	—
137	C₄×D₅₃	C₄×Q₈	1	4	yes	—
138	C₄×D₅₃	C₂×D₈	1	4	yes	—
139	C₄×D₅₃	C₂×Q₁₆	1	4	yes	—
140	C₄×D₅₃	C₂³×C₄	1	2	yes	—
141	C₄×D₅₃	C₂×#41	1	2	yes	—
142	C₈×C₅₃	—	2	2	no	—
143	C₈×C₅₃	C₂×C₄²	1	4	yes	complemented
144	#88322	—	2	2	no	—
145	#88322	C₂×C₄²	1	4	yes	complemented
146	C₂×C₄×#107	—	53	1	no	maximal, Sylow
147	C₂²×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
148	C₂²×C₅₃	C₂×#107	1	2	yes	—
149	C₂²×C₅₃	#427	1	2	yes	—
150	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
151	C₂×D₅₃	C₄×C₄⋊C₄	1	2	yes	—
152	C₂×D₅₃	C₂×#107	1	2	yes	—
153	C₂×D₅₃	#427	1	2	yes	—
154	C₂×D₅₃	C₄×D₈	1	8	yes	—
155	C₂×D₅₃	C₄×Q₁₆	1	8	yes	—
156	C₂×D₅₃	C₂×C₄×D₄	1	2	yes	—
157	C₂×D₅₃	C₂²×D₈	1	1	yes	characteristic
158	C₂×D₅₃	C₂²×Q₁₆	1	1	yes	characteristic
159	C₂×D₅₃	C₂×#135	1	2	yes	—
160	#6157	—	4	16	no	—
161	C₄×C₅₃	—	2	2	no	—
162	C₄×C₅₃	C₄×C₄⋊C₄	1	2	yes	—
163	C₄×C₅₃	C₂×#107	1	4	yes	complemented
164	C₄×C₅₃	C₂²×C₄²	1	1	yes	characteristic
165	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
166	Dic₅₃	—	2	2	no	—
167	Dic₅₃	C₄×C₄⋊C₄	1	2	yes	—
168	Dic₅₃	C₂×#107	1	4	yes	complemented
169	Dic₅₃	C₂×C₄×Q₈	1	2	yes	—
170	C₂²×#107	—	53	2	no	—
171	C₂²×C₄×C₈	—	53	1	no	—
172	C₂×C₄×C₄⋊C₄	—	53	2	no	—
173	C₄×#107	—	53	8	no	—
174	C₂×#340	—	53	2	no	—
175	C₂×C₅₃	C₄×#107	1	4	yes	complemented
176	C₂×C₅₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₅₃	C₂²×#107	1	1	yes	characteristic
178	C₂×C₅₃	C₂×#427	1	1	yes	characteristic
179	D₅₃	C₄×#107	1	4	yes	complemented
180	D₅₃	C₂×C₄×D₈	1	2	yes	—
181	D₅₃	C₂×C₄×Q₁₆	1	2	yes	—
182	C₂³×C₈	—	53	1	no	—
183	C₂³×C₈	—	53	1	no	—
184	C₂²×C₄⋊C₄	—	53	4	no	—
185	C₂²×C₄²	—	53	1	no	—
186	C₂²×C₄²	—	106	2	no	—
187	C₂×#107	—	53	16	no	—
188	C₂×#107	—	53	8	no	—
189	C₂×C₄×C₈	—	53	1	no	—
190	C₂×C₄×C₈	—	53	1	no	—
191	C₂×C₄×C₈	—	53	1	no	—
192	C₂×C₄×C₈	—	53	4	no	—
193	C₂×C₄×C₈	—	53	4	no	—
194	C₂×C₄×C₈	#6157	1	1	yes	characteristic, complemented
195	C₄×C₄⋊C₄	—	53	8	no	—
196	C₄×C₄⋊C₄	—	106	4	no	—
197	C₂×#95	—	106	2	no	—
198	#340	—	53	8	no	—
199	C₅₃	C₂×C₄×#107	1	1	yes	characteristic, complemented, Sylow
200	C₂³×C₄	—	53	1	no	—
201	C₂³×C₄	—	53	1	no	—
202	C₂³×C₄	—	53	1	no	—
203	C₂³×C₄	—	106	4	no	—
204	C₂²×C₈	—	53	1	no	—
205	C₂²×C₈	—	53	8	no	—
206	C₂²×C₈	—	53	2	no	—
207	C₂²×C₈	—	53	2	no	—
208	C₂²×C₈	—	53	1	no	—
209	C₂²×C₈	—	53	2	no	—
210	C₂²×C₈	—	53	2	no	—
211	C₂²×C₈	—	106	4	no	—
212	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
213	C₂²×C₈	C₂×#6157	1	1	yes	characteristic
214	C₂×C₄⋊C₄	—	53	8	no	—
215	C₂×C₄⋊C₄	—	53	16	no	—
216	C₂×C₄⋊C₄	—	106	4	no	—
217	C₂×C₄⋊C₄	—	106	8	no	—
218	C₂×C₄²	—	53	1	no	—
219	C₂×C₄²	—	53	1	no	—
220	C₂×C₄²	—	53	1	no	—
221	C₂×C₄²	—	53	2	no	—
222	C₂×C₄²	—	53	2	no	—
223	C₂×C₄²	—	53	2	no	—
224	C₂×C₄²	—	53	2	no	—
225	C₂×C₄²	—	106	8	no	—
226	C₂×C₄²	—	212	8	no	—
227	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
228	#107	—	53	32	no	—
229	C₄×C₈	—	53	4	no	—
230	C₄×C₈	—	53	4	no	—
231	C₄×C₈	—	53	4	no	—
232	C₄×C₈	C₂×#6157	1	4	yes	complemented
233	#95	—	106	8	no	—
234	C₂⁴	—	53	1	no	—
235	C₂²×C₄	—	53	1	no	—
236	C₂²×C₄	—	53	1	no	—
237	C₂²×C₄	—	53	4	no	—
238	C₂²×C₄	—	53	4	no	—
239	C₂²×C₄	—	53	4	no	—
240	C₂²×C₄	—	53	2	no	—
241	C₂²×C₄	—	53	2	no	—
242	C₂²×C₄	—	53	1	no	—
243	C₂²×C₄	—	53	1	no	—
244	C₂²×C₄	—	53	4	no	—
245	C₂²×C₄	—	53	1	no	—
246	C₂²×C₄	—	53	1	no	—
247	C₂²×C₄	—	53	1	no	—
248	C₂²×C₄	—	53	2	no	—
249	C₂²×C₄	—	53	2	no	—
250	C₂²×C₄	—	106	4	no	—
251	C₂²×C₄	—	106	8	no	—
252	C₂²×C₄	—	106	16	no	—
253	C₂²×C₄	—	212	8	no	—
254	C₂²×C₄	—	212	8	no	—
255	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
257	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	53	4	no	—
260	C₂×C₈	—	53	2	no	—
261	C₂×C₈	—	53	8	no	—
262	C₂×C₈	—	53	8	no	—
263	C₂×C₈	—	53	2	no	—
264	C₂×C₈	—	106	4	no	—
265	C₂×C₈	—	106	4	no	—
266	C₂×C₈	—	106	2	no	—
267	C₂×C₈	C₄×#6157	1	4	yes	complemented
268	C₂×C₈	C₂²×#6157	1	2	yes	—
269	C₂×C₈	C₂²×#6157	1	2	yes	—
270	C₄⋊C₄	—	53	16	no	—
271	C₄⋊C₄	—	106	16	no	—
272	C₄⋊C₄	—	106	8	no	—
273	C₄²	—	53	2	no	—
274	C₄²	—	53	2	no	—
275	C₄²	—	53	2	no	—
276	C₄²	—	53	2	no	—
277	C₄²	—	53	2	no	—
278	C₄²	—	53	2	no	—
279	C₄²	—	212	16	no	—
280	C₄²	C₄⋊#6157	1	2	yes	—
281	C₄²	C₂²×#6157	1	2	yes	—
282	C₂³	—	53	4	no	—
283	C₂³	—	53	2	no	—
284	C₂³	—	53	2	no	—
285	C₂³	—	53	4	no	—
286	C₂³	—	53	1	no	—
287	C₂³	—	53	1	no	—
288	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	53	4	no	—
291	C₂×C₄	—	53	4	no	—
292	C₂×C₄	—	53	2	no	—
293	C₂×C₄	—	53	1	no	—
294	C₂×C₄	—	53	1	no	—
295	C₂×C₄	—	53	4	no	—
296	C₂×C₄	—	53	4	no	—
297	C₂×C₄	—	53	8	no	—
298	C₂×C₄	—	53	4	no	—
299	C₂×C₄	—	53	4	no	—
300	C₂×C₄	—	53	2	no	—
301	C₂×C₄	—	53	2	no	—
302	C₂×C₄	—	53	2	no	—
303	C₂×C₄	—	53	2	no	—
304	C₂×C₄	—	53	2	no	—
305	C₂×C₄	—	106	4	no	—
306	C₂×C₄	—	106	4	no	—
307	C₂×C₄	—	106	2	no	—
308	C₂×C₄	—	106	16	no	—
309	C₂×C₄	—	212	8	no	—
310	C₂×C₄	—	212	8	no	—
311	C₂×C₄	—	212	32	no	—
312	C₂×C₄	#13133286	1	4	yes	direct product factor
313	C₂×C₄	C₂×C₄×#6157	1	2	yes	—
314	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
315	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄⋊#6157	1	2	yes	—
317	C₂×C₄	#13133296	1	2	yes	—
318	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	—	53	4	no	—
321	C₈	—	106	2	no	—
322	C₈	C₂×C₄×#6157	1	4	yes	complemented
323	C₂²	—	53	1	no	—
324	C₂²	—	53	1	no	—
325	C₂²	—	53	2	no	—
326	C₂²	—	53	2	no	—
327	C₂²	—	53	2	no	—
328	C₂²	—	53	2	no	—
329	C₂²	—	53	2	no	—
330	C₂²	—	53	8	no	—
331	C₂²	—	53	8	no	—
332	C₂²	C₄×C₄⋊#6157	1	2	yes	—
333	C₂²	C₂×#13133286	1	2	yes	—
334	C₂²	#16811633	1	2	yes	—
335	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	53	4	no	—
338	C₄	—	53	2	no	—
339	C₄	—	53	2	no	—
340	C₄	—	106	2	no	—
341	C₄	—	212	16	no	—
342	C₄	C₄×C₄⋊#6157	1	2	yes	—
343	C₄	C₂×#13133286	1	4	yes	direct product factor
344	C₄	C₂²×C₄×#6157	1	1	yes	characteristic
345	C₄	C₂×#13133296	1	1	yes	characteristic
346	C₂	—	53	2	no	—
347	C₂	—	53	2	no	—
348	C₂	—	53	4	no	—
349	C₂	C₄×#13133286	1	4	yes	direct product factor
350	C₂	C₂×C₄×C₄⋊#6157	1	1	yes	characteristic
351	C₂	C₂²×#13133286	1	1	yes	characteristic
352	C₂	C₂×#16811633	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄⋊#6157
commutator	C₄×C₅₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂³×D₅₃	C₂×D₄
cosocle	C₂×C₄×D₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	C₂×C₄×#107
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#13133286	C₂	direct (N × H)
8. C₂×#13133286	C₄	direct (N × H)
17. C₂×C₄×#88322	C₄	semidirect
18. C₂×C₈×Dic₅₃	C₄	semidirect
19. C₂×C₈×Dic₅₃	C₄	semidirect
20. C₄×C₈×D₅₃	C₄	semidirect
22. C₂×C₄×C₈×C₅₃	C₄	semidirect
30. #13133286	C₂×C₄	direct (N × H)
50. C₄×#88322	C₂×C₄	semidirect
51. C₈×Dic₅₃	C₂×C₄	semidirect
52. C₈×Dic₅₃	C₂×C₄	semidirect
56. C₄×C₈×C₅₃	C₂×C₄	semidirect
86. C₂×C₈×C₅₃	C₄²	semidirect
98. C₂×#88322	C₄²	semidirect
103. C₈×D₅₃	C₄²	semidirect
117. C₂×C₄×C₅₃	#107	semidirect
125. C₂×Dic₅₃	#107	semidirect
133. C₄×D₅₃	#107	semidirect
143. C₈×C₅₃	C₂×C₄²	semidirect
145. #88322	C₂×C₄²	semidirect
163. C₄×C₅₃	C₂×#107	semidirect
168. Dic₅₃	C₂×#107	semidirect
175. C₂×C₅₃	C₄×#107	semidirect
179. D₅₃	C₄×#107	semidirect
194. C₂×C₄×C₈	#6157	semidirect
199. C₅₃	C₂×C₄×#107	semidirect
232. C₄×C₈	C₂×#6157	semidirect
267. C₂×C₈	C₄×#6157	semidirect
312. C₂×C₄	#13133286	direct (N × H)
322. C₈	C₂×C₄×#6157	semidirect
343. C₄	C₂×#13133286	direct (N × H)
349. C₂	C₄×#13133286	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13133286	2
C₂×C₄×C₄⋊#6157	2
C₄×#13133286	2
C₂×#16811497	2
C₂×C₄×C₈×D₅₃	2
C₂×C₄×#107	53

Subgroups — C2×C4×#13133286 #28318363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13133286 #28318363