Subgroups — C₂²×#11718386 #16726748

Order 3328.

3694 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×#1055	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718386	C₂	1	24	yes	maximal, direct product factor
5	C₂²×#88054	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88060	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₂³×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
11	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₂²⋊Dic₁₃	C₄	1	1	yes	characteristic
15	C₂×C₄×C₂²⋊D₁₃	C₄	1	12	yes	—
16	C₂×C₄×C₂²⋊D₁₃	C₂²	1	12	yes	—
17	C₂²×#6103	C₄	1	1	yes	characteristic
18	C₂²×#6101	C₄	1	1	yes	characteristic
19	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
20	C₂³×#1055	—	2	8	no	—
21	C₂³×#1055	C₂²	1	1	yes	characteristic
22	C₂³×#1055	C₂²	1	1	yes	characteristic
23	C₂³×#1055	C₂²	1	12	yes	complemented
24	C₂²×C₈×D₁₃	—	2	8	no	—
25	C₂²×C₈×D₁₃	C₂²	1	12	yes	complemented
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	12	yes	complemented
27	C₂×#88060	C₂²	1	12	yes	complemented
28	C₂×#88054	C₂²	1	12	yes	complemented
29	C₂×C₈×Dic₁₃	C₂²	1	12	yes	complemented
30	#11718386	C₂²	1	64	yes	direct product factor
31	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂⁴×D₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	—	2	4	no	—
34	C₂³×C₄×C₁₃	—	2	4	no	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂×C₄	1	6	yes	—
37	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₂²⋊D₁₃	C₈	1	16	yes	complemented
40	C₂²×C₂²⋊D₁₃	C₂×C₄	1	12	yes	—
41	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₁₃	—	2	4	no	—
45	C₂²×C₄×D₁₃	—	2	4	no	—
46	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
47	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
48	C₂²×C₈×C₁₃	—	2	4	no	—
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
52	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	12	yes	—
53	C₄×C₂²⋊D₁₃	C₂×C₄	1	48	yes	—
54	C₄×C₂²⋊D₁₃	C₂³	1	16	yes	—
55	C₂×#6103	C₂×C₄	1	12	yes	—
56	C₂×#6101	C₂×C₄	1	12	yes	—
57	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
58	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
59	C₂²×#1055	—	2	4	no	—
60	C₂²×#1055	—	2	48	no	—
61	C₂²×#1055	D₄	1	8	yes	complemented
62	C₂²×#1055	C₂³	1	6	yes	—
63	C₂²×#1055	C₂³	1	6	yes	—
64	C₂²×#1055	C₂³	1	16	yes	complemented
65	C₂×C₈×D₁₃	—	2	48	no	—
66	C₂×C₈×D₁₃	C₂³	1	16	yes	complemented
67	C₁₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
68	#88060	C₂³	1	16	yes	complemented
69	#88054	C₂³	1	16	yes	complemented
70	C₈×Dic₁₃	C₂³	1	16	yes	complemented
71	C₂²×C₈×D₄	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	4	no	—
73	C₂⁴×C₁₃	—	2	4	no	—
74	C₂⁴×C₁₃	C₂×C₈	1	8	yes	complemented
75	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
76	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂³×D₁₃	—	2	4	no	—
78	C₂³×D₁₃	—	2	4	no	—
79	C₂³×D₁₃	C₂×C₈	1	8	yes	complemented
80	C₂³×D₁₃	C₂²×C₄	1	6	yes	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	24	no	—
83	C₂²×C₄×C₁₃	—	2	12	no	—
84	C₂²×C₄×C₁₃	—	2	12	no	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
89	C₂²×C₄×C₁₃	#41	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
92	C₂×C₂²⋊D₁₃	C₂×C₈	1	96	yes	complemented
93	C₂×C₂²⋊D₁₃	C₂²×C₄	1	16	yes	—
94	C₂²×Dic₁₃	—	2	4	no	—
95	C₂²×Dic₁₃	—	2	4	no	—
96	C₂²×Dic₁₃	C₂×C₈	1	8	yes	complemented
97	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
98	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
99	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
100	C₂×C₄×D₁₃	—	2	24	no	—
101	C₂×C₄×D₁₃	—	2	12	no	—
102	C₂×C₄×D₁₃	—	2	12	no	—
103	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
104	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
105	C₂×C₈×C₁₃	—	2	12	no	—
106	C₂×C₈×C₁₃	—	2	12	no	—
107	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
108	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
109	C₂²⋊Dic₁₃	C₂²×C₄	1	16	yes	—
110	#6103	C₂²×C₄	1	16	yes	—
111	#6101	C₂²×C₄	1	16	yes	—
112	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
113	C₄×Dic₁₃	C₂⁴	1	4	yes	—
114	C₂×#1055	—	2	12	no	—
115	C₂×#1055	—	2	32	no	—
116	C₂×#1055	C₂×D₄	1	24	yes	complemented
117	C₂×#1055	C₂⁴	1	4	yes	—
118	C₂×#1055	C₂⁴	1	4	yes	—
119	C₈×D₁₃	—	2	32	no	—
120	C₂⁴×C₈	—	13	1	no	—
121	C₂⁴×C₈	—	13	1	no	—
122	C₂²×C₄×D₄	—	13	1	no	—
123	C₂×C₈×D₄	—	13	24	no	—
124	C₂²×C₄⋊C₈	—	13	1	no	—
125	C₂²×C₂²⋊C₈	—	13	1	no	—
126	C₂²×C₂²⋊C₈	D₁₃	1	1	yes	characteristic, complemented
127	C₂²×C₄×C₈	—	13	1	no	—
128	C₂³×C₁₃	—	2	12	no	—
129	C₂³×C₁₃	—	2	12	no	—
130	C₂³×C₁₃	—	2	32	no	—
131	C₂³×C₁₃	C₄×D₄	1	4	yes	—
132	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
133	C₂³×C₁₃	C₂²×C₈	1	24	yes	complemented
134	C₂³×C₁₃	#131	1	4	yes	—
135	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
136	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
137	C₂²×D₁₃	—	2	12	no	—
138	C₂²×D₁₃	—	2	12	no	—
139	C₂²×D₁₃	—	2	32	no	—
140	C₂²×D₁₃	C₂²×C₈	1	24	yes	complemented
141	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
142	C₂×C₄×C₁₃	—	2	12	no	—
143	C₂×C₄×C₁₃	—	2	24	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	C₄×D₄	1	12	yes	—
147	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
150	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
151	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
152	C₂²⋊D₁₃	C₂²×C₈	1	64	yes	complemented
153	C₂×Dic₁₃	—	2	12	no	—
154	C₂×Dic₁₃	—	2	12	no	—
155	C₂×Dic₁₃	C₂²×C₈	1	24	yes	complemented
156	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
157	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
158	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
159	C₄×D₁₃	—	2	24	no	—
160	C₄×D₁₃	—	2	4	no	—
161	C₄×D₁₃	—	2	4	no	—
162	C₈×C₁₃	—	2	4	no	—
163	C₈×C₁₃	—	2	4	no	—
164	#1055	—	2	4	no	—
165	#1055	C₂²×D₄	1	8	yes	complemented
166	C₂³×D₄	—	13	1	no	—
167	C₂⁴×C₄	—	13	1	no	—
168	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
169	C₂³×C₈	—	13	1	no	—
170	C₂³×C₈	—	13	12	no	—
171	C₂³×C₈	—	13	1	no	—
172	C₂³×C₈	—	13	12	no	—
173	C₂³×C₈	—	26	8	no	—
174	C₂³×C₈	—	26	8	no	—
175	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
176	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
177	C₂×C₄×D₄	—	13	12	no	—
178	C₂×C₄×D₄	—	13	12	no	—
179	C₂²×C₄⋊C₄	—	13	1	no	—
180	C₂²×C₂²⋊C₄	—	13	1	no	—
181	C₂²×C₂²⋊C₄	—	13	1	no	—
182	C₂²×C₄²	—	13	1	no	—
183	C₈×D₄	—	13	64	no	—
184	C₂×C₄⋊C₈	—	13	12	no	—
185	C₂×C₂²⋊C₈	—	13	12	no	—
186	C₂×C₂²⋊C₈	C₂×D₁₃	1	12	yes	complemented
187	C₂×C₄×C₈	—	13	12	no	—
188	C₂²×C₁₃	—	2	4	no	—
189	C₂²×C₁₃	—	2	48	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	C₈×D₄	1	16	yes	complemented
192	C₂²×C₁₃	C₂×C₄×D₄	1	6	yes	—
193	C₂²×C₁₃	C₂³×C₈	1	6	yes	—
194	C₂²×C₁₃	C₂³×C₈	1	8	yes	complemented
195	C₂²×C₁₃	C₂×#131	1	6	yes	—
196	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
197	C₂×D₁₃	—	2	4	no	—
198	C₂×D₁₃	—	2	48	no	—
199	C₂×D₁₃	—	2	4	no	—
200	C₂×D₁₃	C₂³×C₈	1	8	yes	complemented
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	C₂×C₄×D₄	1	6	yes	—
203	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
205	Dic₁₃	—	2	4	no	—
206	Dic₁₃	—	2	4	no	—
207	Dic₁₃	C₂³×C₈	1	8	yes	complemented
208	C₂⁵	—	13	1	no	—
209	C₂⁵	C₄×D₁₃	1	1	yes	characteristic
210	C₂²×D₄	—	13	16	no	—
211	C₂²×D₄	—	13	12	no	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	4	no	—
214	C₂³×C₄	—	13	1	no	—
215	C₂³×C₄	—	13	1	no	—
216	C₂³×C₄	—	13	1	no	—
217	C₂³×C₄	—	13	6	no	—
218	C₂³×C₄	—	13	6	no	—
219	C₂³×C₄	—	26	4	no	—
220	C₂³×C₄	—	26	4	no	—
221	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₄×D₁₃	1	6	yes	—
223	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
224	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	—	13	8	no	—
228	C₂²×C₈	—	13	6	no	—
229	C₂²×C₈	—	13	6	no	—
230	C₂²×C₈	—	13	16	no	—
231	C₂²×C₈	—	13	16	no	—
232	C₂²×C₈	—	26	48	no	—
233	C₂²×C₈	—	26	48	no	—
234	C₂²×C₈	—	26	4	no	—
235	C₂²×C₈	C₂²×D₁₃	1	6	yes	—
236	C₂²×C₈	C₂²×D₁₃	1	6	yes	—
237	C₄×D₄	—	13	48	no	—
238	C₄×D₄	—	13	16	no	—
239	C₂×C₄⋊C₄	—	13	12	no	—
240	C₂×C₂²⋊C₄	—	13	12	no	—
241	C₂×C₂²⋊C₄	—	13	12	no	—
242	C₂×C₄²	—	13	6	no	—
243	C₂×C₄²	—	13	6	no	—
244	C₄⋊C₈	—	13	16	no	—
245	C₂²⋊C₈	—	13	16	no	—
246	C₂²⋊C₈	C₂²×D₁₃	1	16	yes	complemented
247	C₄×C₈	—	13	16	no	—
248	C₂×C₁₃	—	2	8	no	—
249	C₂×C₁₃	C₂×C₈×D₄	1	12	yes	complemented
250	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
251	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
252	C₂×C₁₃	C₂²×#131	1	1	yes	characteristic
253	D₁₃	—	2	8	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	13	8	no	—
257	C₂⁴	—	13	6	no	—
258	C₂⁴	—	26	4	no	—
259	C₂⁴	—	26	4	no	—
260	C₂⁴	C₈×D₁₃	1	8	yes	complemented
261	C₂⁴	C₂×C₄×D₁₃	1	6	yes	—
262	C₂⁴	C₂×C₄×D₁₃	1	1	yes	characteristic
263	C₂×D₄	—	13	96	no	—
264	C₂×D₄	—	13	16	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	24	no	—
267	C₂²×C₄	—	2	12	no	—
268	C₂²×C₄	—	2	12	no	—
269	C₂²×C₄	—	13	8	no	—
270	C₂²×C₄	—	13	6	no	—
271	C₂²×C₄	—	13	6	no	—
272	C₂²×C₄	—	13	6	no	—
273	C₂²×C₄	—	13	12	no	—
274	C₂²×C₄	—	13	4	no	—
275	C₂²×C₄	—	26	4	no	—
276	C₂²×C₄	—	26	4	no	—
277	C₂²×C₄	—	26	24	no	—
278	C₂²×C₄	—	26	12	no	—
279	C₂²×C₄	—	26	12	no	—
280	C₂²×C₄	C₂×C₄×D₁₃	1	6	yes	—
281	C₂²×C₄	C₂×C₄×D₁₃	1	12	yes	—
282	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
283	C₂²×C₄	D₄×D₁₃	1	4	yes	—
284	C₂²×C₄	#6129	1	4	yes	—
285	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
286	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
287	C₂×C₈	—	2	12	no	—
288	C₂×C₈	—	2	12	no	—
289	C₂×C₈	—	13	24	no	—
290	C₂×C₈	—	13	4	no	—
291	C₂×C₈	—	13	4	no	—
292	C₂×C₈	—	26	32	no	—
293	C₂×C₈	—	26	32	no	—
294	C₂×C₈	—	26	12	no	—
295	C₂×C₈	C₂³×D₁₃	1	4	yes	—
296	C₂×C₈	C₂³×D₁₃	1	4	yes	—
297	C₄⋊C₄	—	13	16	no	—
298	C₂²⋊C₄	—	13	16	no	—
299	C₂²⋊C₄	—	13	16	no	—
300	C₄²	—	13	12	no	—
301	C₄²	—	13	4	no	—
302	C₁₃	C₂²×C₈×D₄	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	32	no	—
306	C₂³	—	13	24	no	—
307	C₂³	—	13	4	no	—
308	C₂³	—	26	12	no	—
309	C₂³	—	26	12	no	—
310	C₂³	—	26	32	no	—
311	C₂³	#88135	1	4	yes	—
312	C₂³	C₂×C₈×D₁₃	1	4	yes	—
313	C₂³	C₂×C₈×D₁₃	1	24	yes	complemented
314	C₂³	#88161	1	4	yes	—
315	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
316	C₂³	C₂²×C₄×D₁₃	1	3	yes	—
317	D₄	—	13	64	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	13	24	no	—
323	C₂×C₄	—	13	4	no	—
324	C₂×C₄	—	13	4	no	—
325	C₂×C₄	—	13	4	no	—
326	C₂×C₄	—	26	12	no	—
327	C₂×C₄	—	26	12	no	—
328	C₂×C₄	—	26	24	no	—
329	C₂×C₄	—	26	4	no	—
330	C₂×C₄	—	26	4	no	—
331	C₂×C₄	#88135	1	12	yes	—
332	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
333	C₂×C₄	C₂²×C₄×D₁₃	1	3	yes	—
334	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
335	C₂×C₄	C₂×#6129	1	6	yes	—
336	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	4	no	—
339	C₈	—	13	8	no	—
340	C₈	—	26	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	13	8	no	—
345	C₂²	—	26	4	no	—
346	C₂²	—	26	4	no	—
347	C₂²	—	26	48	no	—
348	C₂²	#11718386	1	16	yes	direct product factor
349	C₂²	C₂×#88135	1	6	yes	—
350	C₂²	C₂²×C₈×D₁₃	1	6	yes	—
351	C₂²	C₂²×C₈×D₁₃	1	8	yes	complemented
352	C₂²	C₂×#88161	1	6	yes	—
353	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	13	8	no	—
356	C₄	—	26	4	no	—
357	C₄	—	26	4	no	—
358	C₄	C₂×#88135	1	6	yes	—
359	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
360	C₄	C₂²×#6129	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	26	8	no	—
363	C₂	C₂×#11718386	1	12	yes	direct product factor
364	C₂	C₂²×#88135	1	1	yes	characteristic
365	C₂	C₂³×C₈×D₁₃	1	1	yes	characteristic
366	C₂	C₂²×#88161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₁₃×C₂²⋊C₈	C₂
socle	C₂⁴×C₁₃	C₂²×C₄
prime radical	C₂³×C₂²⋊D₁₃	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×C₂²⋊C₈	D₁₃
hypocenter	C₁₃	C₂²×C₈×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂⁴×#1055	C₂	semidirect
2. C₂³×C₈×D₁₃	C₂	semidirect
4. C₂×#11718386	C₂	direct (N × H)
5. C₂²×#88054	C₂	semidirect
6. C₂²×#88060	C₂	semidirect
7. C₂²×C₈×Dic₁₃	C₂	semidirect
8. C₂²×C₁₃×C₂²⋊C₈	C₂	semidirect
23. C₂³×#1055	C₂²	semidirect
25. C₂²×C₈×D₁₃	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
27. C₂×#88060	C₂²	semidirect
28. C₂×#88054	C₂²	semidirect
29. C₂×C₈×Dic₁₃	C₂²	semidirect
30. #11718386	C₂²	direct (N × H)
39. C₂²×C₂²⋊D₁₃	C₈	semidirect
61. C₂²×#1055	D₄	semidirect
64. C₂²×#1055	C₂³	semidirect
66. C₂×C₈×D₁₃	C₂³	semidirect
67. C₁₃×C₂²⋊C₈	C₂³	semidirect
68. #88060	C₂³	semidirect
69. #88054	C₂³	semidirect
70. C₈×Dic₁₃	C₂³	semidirect
74. C₂⁴×C₁₃	C₂×C₈	semidirect
79. C₂³×D₁₃	C₂×C₈	semidirect
92. C₂×C₂²⋊D₁₃	C₂×C₈	semidirect
96. C₂²×Dic₁₃	C₂×C₈	semidirect
116. C₂×#1055	C₂×D₄	semidirect
126. C₂²×C₂²⋊C₈	D₁₃	semidirect
133. C₂³×C₁₃	C₂²×C₈	semidirect
140. C₂²×D₁₃	C₂²×C₈	semidirect
152. C₂²⋊D₁₃	C₂²×C₈	semidirect
155. C₂×Dic₁₃	C₂²×C₈	semidirect
165. #1055	C₂²×D₄	semidirect
186. C₂×C₂²⋊C₈	C₂×D₁₃	semidirect
191. C₂²×C₁₃	C₈×D₄	semidirect
194. C₂²×C₁₃	C₂³×C₈	semidirect
200. C₂×D₁₃	C₂³×C₈	semidirect
207. Dic₁₃	C₂³×C₈	semidirect
246. C₂²⋊C₈	C₂²×D₁₃	semidirect
249. C₂×C₁₃	C₂×C₈×D₄	semidirect
260. C₂⁴	C₈×D₁₃	semidirect
302. C₁₃	C₂²×C₈×D₄	semidirect
313. C₂³	C₂×C₈×D₁₃	semidirect
348. C₂²	#11718386	direct (N × H)
351. C₂²	C₂²×C₈×D₁₃	semidirect
363. C₂	C₂×#11718386	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×#1055	2
C₂³×C₈×D₁₃	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂×#11718386	2
C₂²×#88054	2
C₂²×#88060	2
C₂²×C₈×Dic₁₃	2
C₂²×C₁₃×C₂²⋊C₈	2
C₂²×C₈×D₄	13

Subgroups — C22×#11718386 #16726748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718386 #16726748