Subgroups — C₂×#13123549 #16726794

Order 3328.

2894 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88155	C₂	1	2	yes	maximal, complemented
2	C₂×#11719182	C₂	1	1	yes	maximal, characteristic
3	#13123549	C₂	1	16	yes	maximal, direct product factor
4	C₂×#11718349	C₂	1	4	yes	maximal, complemented
5	C₂×C₈×D₅₂	C₂	1	4	yes	maximal, complemented
6	C₂×#11718585	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718771	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	2	yes	—
10	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88184	C₄	1	4	yes	—
14	C₂²×#6099	C₂²	1	2	yes	—
15	C₂×#88155	—	2	16	no	—
16	C₂×#88155	C₂²	1	16	yes	complemented
17	C₂²×#6094	C₂²	1	4	yes	—
18	C₂²×C₈×D₁₃	C₂²	1	4	yes	—
19	#11719182	C₄	1	8	yes	—
20	#11719182	C₂²	1	8	yes	—
21	C₂×#88129	C₄	1	2	yes	—
22	C₂×#88128	C₄	1	1	yes	characteristic
23	C₂×C₄×D₅₂	C₂²	1	4	yes	—
24	C₂×#88123	C₄	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	8	yes	complemented
28	#11718771	C₂²	1	16	yes	complemented
29	C₂×#88060	C₂²	1	8	yes	—
30	#11718585	C₂²	1	8	yes	complemented
31	C₂×C₄⋊#1055	C₂²	1	4	yes	—
32	#11718349	C₂²	1	32	yes	complemented
33	C₈×D₅₂	C₂²	1	32	yes	complemented
34	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₂²⋊D₁₃	C₂×C₄	1	4	yes	—
37	C₂×#6127	—	2	8	no	—
38	C₂×#6127	—	2	8	no	—
39	C₂×#6127	C₂×C₄	1	8	yes	—
40	C₂×#6127	C₂³	1	8	yes	—
41	C₂²×D₅₂	C₂×C₄	1	4	yes	—
42	C₂²×D₅₂	C₂×C₄	1	2	yes	—
43	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
44	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	D₄	1	8	yes	complemented
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
57	#88184	C₂×C₄	1	32	yes	—
58	C₂×#6103	C₂×C₄	1	8	yes	—
59	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
60	C₂×#6099	—	2	8	no	—
61	C₂×#6099	C₂³	1	8	yes	—
62	C₂²×#1055	C₂³	1	4	yes	—
63	#88155	—	2	64	no	—
64	C₂×#6094	—	2	16	no	—
65	C₂×#6094	C₂³	1	16	yes	—
66	C₂×C₈×D₁₃	—	2	16	no	—
67	C₂×C₈×D₁₃	C₂³	1	16	yes	—
68	#88129	C₂×C₄	1	16	yes	—
69	#88128	C₂×C₄	1	8	yes	—
70	C₄×D₅₂	C₂×C₄	1	16	yes	—
71	C₄×D₅₂	C₂³	1	16	yes	—
72	#88123	C₂×C₄	1	8	yes	—
73	C₄×C₈×C₁₃	C₂³	1	8	yes	—
74	C₄×C₈×C₁₃	C₂³	1	8	yes	—
75	#88060	C₂³	1	32	yes	—
76	C₄⋊#1055	C₂³	1	16	yes	—
77	C₂×#2931	—	13	1	no	maximal, Sylow
78	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂³×D₁₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	—	2	8	no	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₁₃	#41	1	4	yes	—
88	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
90	C₂×C₂²⋊D₁₃	—	2	16	no	—
91	C₂×C₂²⋊D₁₃	C₂²×C₄	1	16	yes	—
92	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
93	#6127	—	2	32	no	—
94	#6127	—	2	16	no	—
95	#6127	—	2	16	no	—
96	C₂×D₅₂	—	2	8	no	—
97	C₂×D₅₂	—	2	16	no	—
98	C₂×D₅₂	C₂²×C₄	1	16	yes	—
99	C₂×D₅₂	C₂²×C₄	1	8	yes	—
100	C₂×C₄×D₁₃	—	2	8	no	—
101	C₂×C₄×D₁₃	—	2	8	no	—
102	C₂×C₄×D₁₃	C₂²×C₄	1	8	yes	—
103	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
104	C₂×Dic₂₆	—	2	8	no	—
105	C₂×Dic₂₆	C₂²×C₄	1	8	yes	—
106	C₂×C₈×C₁₃	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	8	no	—
108	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
109	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₃	C₂×D₄	1	16	yes	complemented
111	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
112	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
113	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
114	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
116	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
117	C₄²×C₁₃	C₂⁴	1	4	yes	—
118	#6103	C₂²×C₄	1	32	yes	—
119	C₄⋊Dic₁₃	C₂²×C₄	1	16	yes	—
120	#6099	—	2	16	no	—
121	C₂×#1055	—	2	8	no	—
122	C₂×#1055	C₂⁴	1	8	yes	—
123	#6094	—	2	32	no	—
124	C₈×D₁₃	—	2	32	no	—
125	C₂²×#131	—	13	2	no	—
126	C₂×#532	—	13	1	no	—
127	#2931	—	13	16	no	—
128	C₂×#436	—	13	4	no	—
129	C₂×C₈×D₄	—	13	4	no	—
130	C₂×#423	—	13	1	no	—
131	C₂×#408	—	13	2	no	—
132	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic, complemented
133	C₂³×C₁₃	—	2	4	no	—
134	C₂³×C₁₃	C₄×D₄	1	4	yes	—
135	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
136	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
137	C₂²×D₁₃	—	2	8	no	—
138	C₂²×D₁₃	—	2	16	no	—
139	C₂²×D₁₃	C₂³×C₄	1	8	yes	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	2	16	no	—
142	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
143	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
144	C₂×C₄×C₁₃	#131	1	8	yes	complemented
145	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
146	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
153	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
154	C₂²⋊D₁₃	—	2	32	no	—
155	C₂×Dic₁₃	—	2	8	no	—
156	C₂×Dic₁₃	C₂³×C₄	1	8	yes	—
157	D₅₂	—	2	16	no	—
158	D₅₂	—	2	32	no	—
159	C₄×D₁₃	—	2	16	no	—
160	C₄×D₁₃	—	2	8	no	—
161	C₄×D₁₃	—	2	8	no	—
162	Dic₂₆	—	2	16	no	—
163	C₈×C₁₃	—	2	4	no	—
164	C₈×C₁₃	C₂²×D₄	1	4	yes	—
165	C₈×C₁₃	C₂²×D₄	1	4	yes	—
166	#1055	—	2	8	no	—
167	C₂²×#41	—	13	2	no	—
168	C₂×#131	—	13	16	no	—
169	C₂×#131	—	26	16	no	—
170	C₂²×M₁₆	—	13	2	no	—
171	C₂²×M₁₆	—	13	4	no	—
172	C₂³×C₈	—	13	4	no	—
173	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
174	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
175	#532	—	13	8	no	—
176	#532	—	13	8	no	—
177	C₂×C₄⋊Q₈	—	13	1	no	—
178	C₂×#127	—	13	1	no	—
179	C₂×#124	—	13	2	no	—
180	C₂×#121	—	13	4	no	—
181	C₂×C₄×D₄	—	13	4	no	—
182	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
183	#436	—	13	32	no	—
184	C₈×D₄	—	13	32	no	—
185	#423	—	13	8	no	—
186	C₂×C₄⋊C₈	—	13	4	no	—
187	#408	—	13	16	no	—
188	C₂×C₂²⋊C₈	—	13	8	no	—
189	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
190	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
191	C₂×C₄×C₈	C₂×D₁₃	1	8	yes	complemented
192	C₂²×C₁₃	—	2	8	no	—
193	C₂²×C₁₃	—	2	4	no	—
194	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
195	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
196	C₂²×C₁₃	C₂×#131	1	4	yes	—
197	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
198	C₂×D₁₃	—	2	8	no	—
199	C₂×D₁₃	—	2	16	no	—
200	C₂×D₁₃	—	4	16	no	—
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
203	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
204	C₄×C₁₃	C₂×#131	1	8	yes	complemented
205	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
206	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
207	Dic₁₃	—	2	8	no	—
208	C₂×#41	—	13	8	no	—
209	C₂×#41	—	13	8	no	—
210	C₂×#41	—	26	8	no	—
211	C₂×#41	—	26	8	no	—
212	C₂²×Q₈	—	13	2	no	—
213	C₂²×D₄	—	13	4	no	—
214	C₂²×D₄	—	13	4	no	—
215	C₂²×D₄	—	13	2	no	—
216	C₂³×C₄	—	13	4	no	—
217	C₂³×C₄	C₄×D₁₃	1	2	yes	—
218	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
219	#131	—	26	64	no	—
220	C₂×M₁₆	—	13	8	no	—
221	C₂×M₁₆	—	13	16	no	—
222	C₂×M₁₆	—	26	8	no	—
223	C₂×M₁₆	—	26	16	no	—
224	C₂²×C₈	—	2	4	no	—
225	C₂²×C₈	—	13	4	no	—
226	C₂²×C₈	—	13	16	no	—
227	C₂²×C₈	—	26	16	no	—
228	C₂²×C₈	D₅₂	1	8	yes	complemented
229	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
230	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
231	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
232	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
233	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
234	C₄⋊Q₈	—	13	8	no	—
235	#127	—	13	8	no	—
236	#124	—	13	16	no	—
237	#121	—	13	32	no	—
238	C₄×D₄	—	13	16	no	—
239	C₄×D₄	—	13	16	no	—
240	C₂×C₄⋊C₄	—	13	4	no	—
241	C₂×C₂²⋊C₄	—	13	8	no	—
242	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
243	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
244	C₂×C₄²	C₄×D₁₃	1	4	yes	—
245	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
246	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
247	C₄⋊C₈	—	13	16	no	—
248	C₂²⋊C₈	—	13	32	no	—
249	C₄×C₈	C₂²×D₁₃	1	8	yes	—
250	C₄×C₈	C₂²×D₁₃	1	8	yes	—
251	C₂×C₁₃	—	2	4	no	—
252	C₂×C₁₃	#2931	1	4	yes	complemented
253	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
254	C₂×C₁₃	C₂²×#131	1	2	yes	—
255	D₁₃	—	4	8	no	—
256	C₂⁴	—	13	4	no	—
257	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
258	#41	—	26	32	no	—
259	#41	—	26	16	no	—
260	#41	—	26	16	no	—
261	C₂×Q₈	—	13	8	no	—
262	C₂×Q₈	—	26	8	no	—
263	C₂×D₄	—	13	16	no	—
264	C₂×D₄	—	13	16	no	—
265	C₂×D₄	—	13	8	no	—
266	C₂×D₄	—	26	16	no	—
267	C₂×D₄	—	26	8	no	—
268	C₂×D₄	—	26	16	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	13	4	no	—
271	C₂²×C₄	—	13	8	no	—
272	C₂²×C₄	—	13	8	no	—
273	C₂²×C₄	—	26	8	no	—
274	C₂²×C₄	—	26	8	no	—
275	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
276	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	—
277	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
279	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
280	C₂²×C₄	C₂×D₅₂	1	4	yes	—
281	C₂²×C₄	#6127	1	4	yes	—
282	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
284	M₁₆	—	26	16	no	—
285	M₁₆	—	26	32	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	8	no	—
288	C₂×C₈	—	13	8	no	—
289	C₂×C₈	—	26	8	no	—
290	C₂×C₈	—	26	32	no	—
291	C₂×C₈	C₂×D₅₂	1	4	yes	—
292	C₂×C₈	C₂×D₅₂	1	4	yes	—
293	C₂×C₈	C₂×D₅₂	1	16	yes	complemented
294	C₂×C₈	C₂³×D₁₃	1	4	yes	—
295	C₂×C₈	C₂³×D₁₃	1	2	yes	—
296	C₂×C₈	C₂³×D₁₃	1	2	yes	—
297	C₄⋊C₄	—	13	16	no	—
298	C₂²⋊C₄	—	13	32	no	—
299	C₄²	C₂×C₄×D₁₃	1	4	yes	—
300	C₄²	C₂×C₄×D₁₃	1	4	yes	—
301	C₄²	C₂×C₄×D₁₃	1	4	yes	—
302	C₄²	C₂³×D₁₃	1	4	yes	—
303	C₁₃	C₂×#2931	1	1	yes	characteristic, complemented, Sylow
304	C₂³	—	2	4	no	—
305	C₂³	—	13	8	no	—
306	C₂³	—	26	8	no	—
307	C₂³	—	26	16	no	—
308	C₂³	C₄×D₅₂	1	4	yes	—
309	C₂³	C₂²×C₄×D₁₃	1	2	yes	—
310	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
311	Q₈	—	26	16	no	—
312	D₄	—	26	32	no	—
313	D₄	—	26	16	no	—
314	D₄	—	26	32	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	16	no	—
317	C₂×C₄	—	13	8	no	—
318	C₂×C₄	—	26	8	no	—
319	C₂×C₄	—	26	16	no	—
320	C₂×C₄	—	26	8	no	—
321	C₂×C₄	—	26	8	no	—
322	C₂×C₄	C₄×D₅₂	1	4	yes	—
323	C₂×C₄	C₄×D₅₂	1	8	yes	—
324	C₂×C₄	#88155	1	8	yes	complemented
325	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
326	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
328	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
329	C₂×C₄	C₂²×D₅₂	1	2	yes	—
330	C₂×C₄	C₂²×D₅₂	1	4	yes	—
331	C₂×C₄	C₂×#6127	1	2	yes	—
332	C₂×C₄	C₂×#6127	1	4	yes	—
333	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
334	C₈	—	2	4	no	—
335	C₈	—	26	8	no	—
336	C₈	C₂²×D₅₂	1	4	yes	—
337	C₈	C₂²×D₅₂	1	4	yes	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	8	no	—
340	C₂²	—	26	16	no	—
341	C₂²	—	26	8	no	—
342	C₂²	—	52	16	no	—
343	C₂²	C₂×C₄×D₅₂	1	4	yes	—
344	C₂²	C₂×C₄×D₅₂	1	2	yes	—
345	C₂²	C₂×#88155	1	4	yes	—
346	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	26	8	no	—
349	C₄	C₂×C₄×D₅₂	1	2	yes	—
350	C₄	C₂×C₄×D₅₂	1	4	yes	—
351	C₄	C₂×#88155	1	8	yes	complemented
352	C₄	C₂³×D₅₂	1	1	yes	characteristic
353	C₄	C₂²×#6127	1	1	yes	characteristic
354	C₂	—	2	4	no	—
355	C₂	—	52	8	no	—
356	C₂	#13123549	1	4	yes	direct product factor
357	C₂	C₂²×C₄×D₅₂	1	1	yes	characteristic
358	C₂	C₂²×#88155	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂×#11719182	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	C₂×#2931
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
1. C₂²×#88155	C₂	semidirect
3. #13123549	C₂	direct (N × H)
4. C₂×#11718349	C₂	semidirect
5. C₂×C₈×D₅₂	C₂	semidirect
6. C₂×#11718585	C₂	semidirect
7. C₂×#11718771	C₂	semidirect
8. C₂²×C₄×C₈×C₁₃	C₂	semidirect
16. C₂×#88155	C₂²	semidirect
27. C₂×C₄×C₈×C₁₃	C₂²	semidirect
28. #11718771	C₂²	semidirect
30. #11718585	C₂²	semidirect
32. #11718349	C₂²	semidirect
33. C₈×D₅₂	C₂²	semidirect
46. C₂²×C₈×C₁₃	D₄	semidirect
110. C₂×C₈×C₁₃	C₂×D₄	semidirect
132. C₂²×C₄×C₈	D₁₃	semidirect
144. C₂×C₄×C₁₃	#131	semidirect
191. C₂×C₄×C₈	C₂×D₁₃	semidirect
204. C₄×C₁₃	C₂×#131	semidirect
228. C₂²×C₈	D₅₂	semidirect
252. C₂×C₁₃	#2931	semidirect
293. C₂×C₈	C₂×D₅₂	semidirect
303. C₁₃	C₂×#2931	semidirect
324. C₂×C₄	#88155	semidirect
351. C₄	C₂×#88155	semidirect
356. C₂	#13123549	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×#88155	2
C₂×#11719182	2
#13123549	2
C₂×#11718349	2
C₂×C₈×D₅₂	2
C₂×#11718585	2
C₂×#11718771	2
C₂²×C₄×C₈×C₁₃	2
C₂×#2931	13

Subgroups — C2×#13123549 #16726794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123549 #16726794