Subgroups — C₂×#11719475 #13129592

Order 1664.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#88257	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#88256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88205	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88203	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719475	C₂	1	16	yes	maximal, direct product factor
7	C₂×#88172	C₂	1	2	yes	maximal, complemented
8	C₂×#88170	C₂	1	2	yes	maximal, complemented
9	C₂×SD₁₆×D₁₃	C₂	1	2	yes	maximal, complemented
10	C₂×#88165	C₂	1	2	yes	maximal, complemented
11	C₂²×#6095	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88155	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
15	#88257	—	2	4	no	—
16	#88257	C₂²	1	8	yes	complemented
17	#88256	—	2	4	no	—
18	#88256	C₂²	1	8	yes	complemented
19	C₂×#6131	C₂²	1	2	yes	—
20	C₂×Q₈×D₁₃	C₂²	1	2	yes	complemented
21	C₂×#6129	—	2	2	no	—
22	C₂×#6129	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₃	—	2	2	no	—
24	C₂×D₄×D₁₃	C₂²	1	2	yes	—
25	C₂×#6127	—	2	1	no	—
26	C₂×#6127	—	2	1	no	—
27	C₂×#6127	C₂²	1	1	yes	characteristic
28	C₂²×D₅₂	—	2	1	no	—
29	C₂²×D₅₂	C₂²	1	1	yes	characteristic
30	C₂²×Dic₂₆	—	2	1	no	—
31	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#135	C₂²	1	8	yes	complemented
33	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	#88205	C₂²	1	8	yes	complemented
39	#88203	C₂²	1	8	yes	complemented
40	C₂×#6107	C₂²	1	2	yes	complemented
41	C₂×#6106	C₂²	1	2	yes	complemented
42	C₂×#6105	C₂²	1	2	yes	complemented
43	C₂×#6104	C₂²	1	2	yes	complemented
44	C₂×#6099	C₂²	1	1	yes	characteristic, complemented
45	#88172	C₂²	1	16	yes	complemented
46	#88170	C₂²	1	16	yes	complemented
47	SD₁₆×D₁₃	C₂²	1	16	yes	complemented
48	#88165	C₂²	1	16	yes	complemented
49	C₂×#6095	C₂²	1	2	yes	complemented
50	C₂×#6095	C₂²	1	2	yes	complemented
51	C₂×#6095	C₂²	1	8	yes	complemented
52	#88155	C₂²	1	8	yes	complemented
53	C₂×#6094	C₂²	1	2	yes	complemented
54	C₂×C₈×D₁₃	C₂²	1	2	yes	complemented
55	C₂³×D₁₃	—	2	1	no	—
56	C₂³×D₁₃	—	2	2	no	—
57	C₁₃×#41	—	2	2	no	—
58	C₁₃×#41	—	2	2	no	—
59	C₁₃×#41	C₂³	1	4	yes	—
60	C₁₃×#41	C₂³	1	4	yes	complemented
61	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₃	—	2	1	no	—
64	C₂×D₄×C₁₃	—	2	1	no	—
65	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₃	—	2	2	no	—
71	C₂×C₂²⋊D₁₃	—	2	2	no	—
72	C₂×C₂²⋊D₁₃	D₄	1	2	yes	—
73	C₂²×Dic₁₃	—	2	1	no	—
74	C₂²×Dic₁₃	—	2	2	no	—
75	#6131	—	2	4	no	—
76	#6131	C₂³	1	8	yes	—
77	Q₈×D₁₃	—	2	4	no	—
78	Q₈×D₁₃	C₂³	1	8	yes	complemented
79	#6129	—	2	16	no	—
80	#6129	—	2	4	no	—
81	#6129	C₂³	1	8	yes	complemented
82	D₄×D₁₃	—	2	16	no	—
83	D₄×D₁₃	—	2	4	no	—
84	D₄×D₁₃	C₂³	1	8	yes	—
85	#6127	—	2	8	no	—
86	#6127	—	2	8	no	—
87	#6127	D₄	1	4	yes	—
88	#6127	C₂³	1	4	yes	—
89	C₂×D₅₂	—	2	2	no	—
90	C₂×D₅₂	—	2	1	no	—
91	C₂×D₅₂	—	2	2	no	—
92	C₂×D₅₂	—	2	8	no	—
93	C₂×D₅₂	D₄	1	1	yes	characteristic
94	C₂×D₅₂	C₂³	1	2	yes	—
95	C₂×D₅₂	C₂³	1	4	yes	—
96	C₂×C₄×D₁₃	—	2	2	no	—
97	C₂×C₄×D₁₃	—	2	2	no	—
98	C₂×C₄×D₁₃	C₂³	1	2	yes	—
99	C₂×Dic₂₆	—	2	1	no	—
100	C₂×Dic₂₆	—	2	2	no	—
101	C₂×Dic₂₆	—	2	2	no	—
102	C₂×Dic₂₆	—	2	8	no	—
103	C₂×Dic₂₆	D₄	1	1	yes	characteristic
104	C₂×Dic₂₆	C₂³	1	2	yes	—
105	C₂×Dic₂₆	C₂³	1	4	yes	complemented
106	C₁₃×Q₁₆	C₂³	1	4	yes	complemented
107	C₁₃×SD₁₆	C₂³	1	4	yes	complemented
108	C₁₃×SD₁₆	C₂³	1	4	yes	complemented
109	C₁₃×D₈	C₂³	1	4	yes	complemented
110	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂³	1	4	yes	complemented
113	#6107	C₂³	1	8	yes	complemented
114	#6106	C₂³	1	8	yes	complemented
115	#6105	C₂³	1	8	yes	complemented
116	#6104	C₂³	1	8	yes	complemented
117	#6099	C₂³	1	4	yes	complemented
118	C₂×#1055	C₂³	1	2	yes	—
119	#6095	C₂³	1	8	yes	complemented
120	#6095	C₂³	1	8	yes	complemented
121	#6094	C₂³	1	8	yes	complemented
122	C₈×D₁₃	C₂³	1	8	yes	complemented
123	C₂×#577	—	13	1	no	maximal, Sylow
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	1	no	—
126	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₁₃	—	2	2	no	—
128	C₂²×D₁₃	—	2	4	no	—
129	C₂²×D₁₃	—	2	8	no	—
130	C₂²×D₁₃	—	8	4	no	—
131	C₂²×D₁₃	—	8	2	no	—
132	C₂²×D₁₃	C₂×D₄	1	2	yes	—
133	Q₈×C₁₃	—	2	1	no	—
134	Q₈×C₁₃	—	2	1	no	—
135	Q₈×C₁₃	C₂⁴	1	2	yes	—
136	Q₈×C₁₃	C₂⁴	1	2	yes	—
137	D₄×C₁₃	—	2	4	no	—
138	D₄×C₁₃	—	2	4	no	—
139	D₄×C₁₃	—	2	1	no	—
140	D₄×C₁₃	—	2	1	no	—
141	D₄×C₁₃	C₂⁴	1	2	yes	—
142	D₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²⋊D₁₃	—	2	8	no	—
152	C₂²⋊D₁₃	—	2	8	no	—
153	C₂²⋊D₁₃	C₂×D₄	1	8	yes	—
154	C₂×Dic₁₃	—	2	2	no	—
155	C₂×Dic₁₃	—	2	4	no	—
156	C₂×Dic₁₃	—	2	8	no	—
157	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
158	D₅₂	—	2	8	no	—
159	D₅₂	—	2	4	no	—
160	D₅₂	—	2	2	no	—
161	D₅₂	C₂×D₄	1	4	yes	—
162	D₅₂	C₂⁴	1	4	yes	—
163	C₄×D₁₃	—	2	8	no	—
164	C₄×D₁₃	—	2	8	no	—
165	C₄×D₁₃	C₂×D₄	1	4	yes	—
166	C₄×D₁₃	C₂⁴	1	4	yes	—
167	Dic₂₆	—	2	4	no	—
168	Dic₂₆	—	2	2	no	—
169	Dic₂₆	—	2	8	no	—
170	Dic₂₆	C₂×D₄	1	4	yes	—
171	Dic₂₆	C₂⁴	1	4	yes	—
172	C₈×C₁₃	C₂⁴	1	2	yes	—
173	C₈×C₁₃	C₂⁴	1	2	yes	—
174	#1055	C₂⁴	1	4	yes	—
175	C₂×2₋¹⁺⁴	—	13	1	no	—
176	C₂×H(5,𝔽₂)	—	13	1	no	—
177	#577	—	13	16	no	—
178	C₂×#137	—	13	1	no	—
179	C₂×#137	—	13	2	no	—
180	C₂×AGL(1,ℤ/8)	—	13	1	no	—
181	C₂×AGL(1,ℤ/8)	—	13	2	no	—
182	C₂×#135	—	13	2	no	—
183	C₂×#135	D₁₃	1	1	yes	characteristic, complemented
184	C₂²×SD₁₆	—	13	2	no	—
185	C₂²×SD₁₆	—	13	1	no	—
186	C₂×#131	—	13	1	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	4	2	no	—
191	C₂²×C₁₃	—	4	2	no	—
192	C₂²×C₁₃	C₂²×D₄	1	2	yes	—
193	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×D₁₃	—	2	4	no	—
195	C₂×D₁₃	—	2	4	no	—
196	C₂×D₁₃	—	4	4	no	—
197	C₂×D₁₃	—	8	8	no	—
198	C₂×D₁₃	—	8	4	no	—
199	C₂×D₁₃	C₂²×D₄	1	4	yes	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	C₂²×D₄	1	2	yes	—
203	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₁₃	C₂⁵	1	1	yes	characteristic
205	Dic₁₃	—	2	4	no	—
206	Dic₁₃	C₂²×D₄	1	4	yes	—
207	2₋¹⁺⁴	—	13	8	no	—
208	2₋¹⁺⁴	—	26	4	no	—
209	H(5,𝔽₂)	—	13	8	no	—
210	H(5,𝔽₂)	—	26	4	no	—
211	C₂×#41	—	13	1	no	—
212	C₂×#41	—	13	2	no	—
213	C₂×#41	—	13	2	no	—
214	C₂×#41	—	26	1	no	—
215	C₂×#41	—	26	1	no	—
216	C₂×#41	—	26	2	no	—
217	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
218	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
219	C₂²×Q₈	—	13	2	no	—
220	C₂²×Q₈	—	13	1	no	—
221	C₂²×Q₈	—	26	1	no	—
222	C₂²×D₄	—	13	2	no	—
223	C₂²×D₄	—	13	1	no	—
224	C₂²×D₄	—	26	1	no	—
225	C₂²×D₄	—	26	2	no	—
226	#137	—	13	8	no	—
227	#137	—	13	16	no	—
228	AGL(1,ℤ/8)	—	13	8	no	—
229	AGL(1,ℤ/8)	—	13	16	no	—
230	#135	—	13	16	no	—
231	#135	C₂×D₁₃	1	8	yes	complemented
232	C₂×Q₁₆	—	13	2	no	—
233	C₂×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
234	C₂×SD₁₆	—	13	2	no	—
235	C₂×SD₁₆	—	13	2	no	—
236	C₂×SD₁₆	—	13	16	no	—
237	C₂×SD₁₆	—	13	2	no	—
238	C₂×SD₁₆	—	13	2	no	—
239	C₂×SD₁₆	—	13	8	no	—
240	C₂×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
241	C₂×SD₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
242	C₂×D₈	—	13	2	no	—
243	C₂×D₈	C₂×D₁₃	1	1	yes	characteristic, complemented
244	#131	—	13	8	no	—
245	C₂×M₁₆	—	13	1	no	—
246	C₂×M₁₆	—	13	2	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
249	C₂×C₁₃	—	2	2	no	—
250	C₂×C₁₃	—	4	2	no	—
251	C₂×C₁₃	—	4	2	no	—
252	C₂×C₁₃	#577	1	2	yes	complemented
253	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
254	D₁₃	—	2	4	no	—
255	D₁₃	—	4	4	no	—
256	C₂⁴	—	26	2	no	—
257	C₂⁴	—	26	1	no	—
258	#41	—	2	2	no	—
259	#41	—	2	2	no	—
260	#41	—	13	4	no	—
261	#41	—	13	4	no	—
262	#41	—	13	8	no	—
263	#41	—	13	8	no	—
264	#41	—	26	8	no	—
265	#41	—	26	8	no	—
266	#41	—	26	4	no	—
267	#41	—	26	4	no	—
268	#41	—	26	16	no	—
269	#41	C₂²×D₁₃	1	4	yes	—
270	#41	C₂²×D₁₃	1	4	yes	complemented
271	C₂×Q₈	—	13	1	no	—
272	C₂×Q₈	—	13	8	no	—
273	C₂×Q₈	—	13	2	no	—
274	C₂×Q₈	—	13	4	no	—
275	C₂×Q₈	—	26	2	no	—
276	C₂×Q₈	—	26	8	no	—
277	C₂×Q₈	—	26	4	no	—
278	C₂×Q₈	—	26	1	no	—
279	C₂×Q₈	—	26	2	no	—
280	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
281	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	13	2	no	—
285	C₂×D₄	—	13	8	no	—
286	C₂×D₄	—	13	1	no	—
287	C₂×D₄	—	13	2	no	—
288	C₂×D₄	—	13	4	no	—
289	C₂×D₄	—	26	8	no	—
290	C₂×D₄	—	26	2	no	—
291	C₂×D₄	—	26	4	no	—
292	C₂×D₄	—	26	2	no	—
293	C₂×D₄	—	26	16	no	—
294	C₂×D₄	—	26	2	no	—
295	C₂×D₄	—	26	1	no	—
296	C₂×D₄	—	26	2	no	—
297	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	26	2	no	—
303	C₂²×C₄	—	26	2	no	—
304	C₂²×C₄	—	26	2	no	—
305	C₂²×C₄	—	26	1	no	—
306	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
307	Q₁₆	—	13	8	no	—
308	Q₁₆	C₂²×D₁₃	1	4	yes	complemented
309	SD₁₆	—	13	8	no	—
310	SD₁₆	—	13	8	no	—
311	SD₁₆	—	13	8	no	—
312	SD₁₆	—	13	8	no	—
313	SD₁₆	C₂²×D₁₃	1	4	yes	complemented
314	SD₁₆	C₂²×D₁₃	1	4	yes	complemented
315	D₈	—	13	8	no	—
316	D₈	C₂²×D₁₃	1	4	yes	complemented
317	M₁₆	—	13	4	no	—
318	M₁₆	—	13	8	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	8	no	—
321	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
322	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
323	C₂×C₈	C₂²×D₁₃	1	4	yes	complemented
324	C₁₃	C₂×#577	1	1	yes	characteristic, complemented, Sylow
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	13	2	no	—
328	C₂³	—	26	8	no	—
329	C₂³	—	26	2	no	—
330	C₂³	—	26	4	no	—
331	C₂³	—	104	2	no	—
332	C₂³	—	104	4	no	—
333	C₂³	D₄×D₁₃	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	13	4	no	—
337	Q₈	—	13	4	no	—
338	Q₈	—	26	8	no	—
339	Q₈	—	26	4	no	—
340	Q₈	—	26	2	no	—
341	Q₈	C₂³×D₁₃	1	2	yes	—
342	Q₈	C₂³×D₁₃	1	2	yes	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	13	8	no	—
348	D₄	—	13	4	no	—
349	D₄	—	13	4	no	—
350	D₄	—	26	8	no	—
351	D₄	—	26	8	no	—
352	D₄	—	26	8	no	—
353	D₄	—	26	4	no	—
354	D₄	—	26	2	no	—
355	D₄	C₂³×D₁₃	1	2	yes	—
356	D₄	C₂³×D₁₃	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	13	2	no	—
362	C₂×C₄	—	13	4	no	—
363	C₂×C₄	—	13	4	no	—
364	C₂×C₄	—	26	8	no	—
365	C₂×C₄	—	26	8	no	—
366	C₂×C₄	—	26	8	no	—
367	C₂×C₄	—	26	4	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	D₄×D₁₃	1	2	yes	—
370	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₁₃	1	2	yes	—
372	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
373	C₈	—	13	4	no	—
374	C₈	C₂³×D₁₃	1	2	yes	—
375	C₈	C₂³×D₁₃	1	2	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	13	4	no	—
382	C₂²	—	26	4	no	—
383	C₂²	—	26	4	no	—
384	C₂²	—	52	4	no	—
385	C₂²	—	104	4	no	—
386	C₂²	—	104	8	no	—
387	C₂²	C₂×D₄×D₁₃	1	2	yes	—
388	C₂²	C₂×D₄×D₁₃	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	13	4	no	—
392	C₄	—	26	4	no	—
393	C₄	C₂×D₄×D₁₃	1	2	yes	—
394	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
395	C₄	C₂⁴×D₁₃	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	26	4	no	—
400	C₂	—	52	4	no	—
401	C₂	#11719475	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁵
Frattini	C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂²×D₄
hypercenter	C₂×#135	D₁₃
hypocenter	C₁₃	C₂×#577
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#88257	C₂	semidirect
2. C₂×#88256	C₂	semidirect
3. C₂×C₁₃×#135	C₂	semidirect
4. C₂×#88205	C₂	semidirect
5. C₂×#88203	C₂	semidirect
6. #11719475	C₂	direct (N × H)
7. C₂×#88172	C₂	semidirect
8. C₂×#88170	C₂	semidirect
9. C₂×SD₁₆×D₁₃	C₂	semidirect
10. C₂×#88165	C₂	semidirect
11. C₂²×#6095	C₂	semidirect
12. C₂×#88155	C₂	semidirect
14. C₂×C₁₃×#41	C₂²	semidirect
16. #88257	C₂²	semidirect
18. #88256	C₂²	semidirect
20. C₂×Q₈×D₁₃	C₂²	semidirect
22. C₂×#6129	C₂²	semidirect
31. C₂²×Dic₂₆	C₂²	semidirect
32. C₁₃×#135	C₂²	semidirect
33. C₂×C₁₃×Q₁₆	C₂²	semidirect
34. C₂×C₁₃×SD₁₆	C₂²	semidirect
35. C₂×C₁₃×SD₁₆	C₂²	semidirect
36. C₂×C₁₃×D₈	C₂²	semidirect
37. C₂²×C₈×C₁₃	C₂²	semidirect
38. #88205	C₂²	semidirect
39. #88203	C₂²	semidirect
40. C₂×#6107	C₂²	semidirect
41. C₂×#6106	C₂²	semidirect
42. C₂×#6105	C₂²	semidirect
43. C₂×#6104	C₂²	semidirect
44. C₂×#6099	C₂²	semidirect
45. #88172	C₂²	semidirect
46. #88170	C₂²	semidirect
47. SD₁₆×D₁₃	C₂²	semidirect
48. #88165	C₂²	semidirect
49. C₂×#6095	C₂²	semidirect
50. C₂×#6095	C₂²	semidirect
51. C₂×#6095	C₂²	semidirect
52. #88155	C₂²	semidirect
53. C₂×#6094	C₂²	semidirect
54. C₂×C₈×D₁₃	C₂²	semidirect
60. C₁₃×#41	C₂³	semidirect
78. Q₈×D₁₃	C₂³	semidirect
81. #6129	C₂³	semidirect
105. C₂×Dic₂₆	C₂³	semidirect
106. C₁₃×Q₁₆	C₂³	semidirect
107. C₁₃×SD₁₆	C₂³	semidirect
108. C₁₃×SD₁₆	C₂³	semidirect
109. C₁₃×D₈	C₂³	semidirect
112. C₂×C₈×C₁₃	C₂³	semidirect
113. #6107	C₂³	semidirect
114. #6106	C₂³	semidirect
115. #6105	C₂³	semidirect
116. #6104	C₂³	semidirect
117. #6099	C₂³	semidirect
119. #6095	C₂³	semidirect
120. #6095	C₂³	semidirect
121. #6094	C₂³	semidirect
122. C₈×D₁₃	C₂³	semidirect
183. C₂×#135	D₁₃	semidirect
218. C₂×#41	C₂×D₁₃	semidirect
231. #135	C₂×D₁₃	semidirect
233. C₂×Q₁₆	C₂×D₁₃	semidirect
240. C₂×SD₁₆	C₂×D₁₃	semidirect
241. C₂×SD₁₆	C₂×D₁₃	semidirect
243. C₂×D₈	C₂×D₁₃	semidirect
248. C₂²×C₈	C₂×D₁₃	semidirect
252. C₂×C₁₃	#577	semidirect
270. #41	C₂²×D₁₃	semidirect
308. Q₁₆	C₂²×D₁₃	semidirect
313. SD₁₆	C₂²×D₁₃	semidirect
314. SD₁₆	C₂²×D₁₃	semidirect
316. D₈	C₂²×D₁₃	semidirect
323. C₂×C₈	C₂²×D₁₃	semidirect
324. C₁₃	C₂×#577	semidirect
401. C₂	#11719475	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×#88257	2
C₂×#88256	2
C₂×C₁₃×#135	2
C₂×#88205	2
C₂×#88203	2
#11719475	2
C₂×#88172	2
C₂×#88170	2
C₂×SD₁₆×D₁₃	2
C₂×#88165	2
C₂²×#6095	2
C₂×#88155	2
C₂×#577	13

Subgroups — C2×#11719475 #13129592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719475 #13129592