Subgroups — C₂×#13127974 #16769428

Order 3328.

2126 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719474	C₂	1	2	yes	maximal, complemented
2	#13127974	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718575	C₂	1	4	yes	maximal, complemented
4	C₂×#11718854	C₂	1	2	yes	maximal, complemented
5	C₂×#11718580	C₂	1	2	yes	maximal, complemented
6	C₂²×D₂₀₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₁₃×D₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×#11718562	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#508	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#88256	—	2	2	no	—
11	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
12	C₂×#88203	—	2	2	no	—
13	#11719474	—	2	8	no	—
14	#11719474	C₂²	1	16	yes	complemented
15	C₂×#88173	C₂²	1	4	yes	complemented
16	C₂×#88168	—	2	4	no	—
17	C₂×D₈×D₁₃	C₂²	1	4	yes	complemented
18	C₂²×D₁₀₄	C₂²	1	2	yes	complemented
19	C₂×#88155	C₂²	1	1	yes	characteristic
20	C₁₃×#508	C₂²	1	8	yes	complemented
21	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
23	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
25	#11718854	C₂²	1	16	yes	complemented
26	C₂×#88068	C₂²	1	4	yes	complemented
27	C₂×#88066	C₂²	1	4	yes	complemented
28	C₂×#88052	C₂²	1	1	yes	characteristic, complemented
29	#11718580	C₂²	1	16	yes	complemented
30	#11718575	C₂²	1	32	yes	complemented
31	D₁₃×D₁₆	C₂²	1	16	yes	complemented
32	C₂×D₂₀₈	C₂²	1	2	yes	complemented
33	C₂×D₂₀₈	C₂²	1	2	yes	complemented
34	C₂×D₂₀₈	C₂²	1	8	yes	complemented
35	#11718562	C₂²	1	8	yes	complemented
36	C₂×#88038	C₂²	1	2	yes	complemented
37	C₂×C₁₆×D₁₃	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#41	—	2	2	no	—
39	#88256	—	2	16	no	—
40	#88256	—	4	8	no	—
41	C₂×#6131	—	2	4	no	—
42	C₂×D₄×D₁₃	—	2	4	no	—
43	C₂×D₄×D₁₃	—	4	4	no	—
44	C₂×#6127	—	4	2	no	—
45	C₂×#6127	D₄	1	1	yes	characteristic
46	C₂²×D₅₂	—	2	2	no	—
47	C₂²×D₅₂	—	4	2	no	—
48	C₁₃×#135	—	2	4	no	—
49	C₁₃×#135	C₂³	1	8	yes	complemented
50	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×D₈	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	#88203	—	2	16	no	—
55	C₂×#6106	—	2	4	no	—
56	C₂×#6104	—	2	4	no	—
57	C₂×#6099	D₄	1	1	yes	characteristic
58	#88173	—	2	8	no	—
59	#88173	C₂³	1	16	yes	complemented
60	#88168	—	2	32	no	—
61	D₈×D₁₃	—	2	8	no	—
62	D₈×D₁₃	C₂³	1	16	yes	complemented
63	C₂×D₁₀₄	—	2	2	no	—
64	C₂×D₁₀₄	—	2	4	no	—
65	C₂×D₁₀₄	C₂³	1	4	yes	—
66	C₂×D₁₀₄	C₂³	1	8	yes	complemented
67	#88155	D₄	1	4	yes	—
68	#88155	C₂³	1	4	yes	—
69	C₂×#6094	D₄	1	2	yes	—
70	C₂×C₈×D₁₃	C₂³	1	2	yes	—
71	C₁₃×Q₃₂	C₂³	1	4	yes	complemented
72	C₁₃×SD₃₂	C₂³	1	8	yes	complemented
73	C₁₃×D₁₆	C₂³	1	4	yes	complemented
74	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₁₆	C₂³	1	4	yes	complemented
77	#88068	C₂³	1	16	yes	complemented
78	#88066	C₂³	1	16	yes	complemented
79	#88052	C₂³	1	4	yes	complemented
80	C₂×#6090	C₂³	1	2	yes	—
81	D₂₀₈	C₂³	1	8	yes	complemented
82	D₂₀₈	C₂³	1	8	yes	complemented
83	#88038	C₂³	1	8	yes	complemented
84	C₁₆×D₁₃	C₂³	1	8	yes	complemented
85	C₂×#3415	—	13	1	no	maximal, Sylow
86	C₂³×D₁₃	—	4	2	no	—
87	C₂³×D₁₃	—	4	4	no	—
88	C₁₃×#41	—	2	8	no	—
89	C₁₃×#41	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂²×C₄×C₁₃	—	4	2	no	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₂²⋊D₁₃	—	4	4	no	—
96	C₂×C₂²⋊D₁₃	D₈	1	2	yes	—
97	#6131	—	2	16	no	—
98	#6131	—	4	8	no	—
99	D₄×D₁₃	—	2	16	no	—
100	D₄×D₁₃	—	4	32	no	—
101	D₄×D₁₃	—	4	8	no	—
102	#6127	—	4	16	no	—
103	#6127	D₈	1	4	yes	—
104	#6127	C₂×D₄	1	4	yes	—
105	C₂×D₅₂	—	2	4	no	—
106	C₂×D₅₂	—	2	8	no	—
107	C₂×D₅₂	—	4	4	no	—
108	C₂×D₅₂	—	4	2	no	—
109	C₂×D₅₂	—	4	4	no	—
110	C₂×D₅₂	—	4	16	no	—
111	C₂×D₅₂	D₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	—	4	4	no	—
113	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
114	C₂×Dic₂₆	D₈	1	1	yes	characteristic
115	C₁₃×Q₁₆	—	2	2	no	—
116	C₁₃×Q₁₆	C₂⁴	1	4	yes	—
117	C₁₃×SD₁₆	—	2	8	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×D₈	C₂⁴	1	4	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
124	#6106	—	2	16	no	—
125	#6104	—	2	16	no	—
126	#6099	C₂×D₄	1	4	yes	—
127	C₂×#1055	C₂×D₄	1	2	yes	—
128	D₁₀₄	—	2	4	no	—
129	D₁₀₄	—	2	8	no	—
130	D₁₀₄	C₂⁴	1	8	yes	—
131	#6094	C₂×D₄	1	8	yes	—
132	C₈×D₁₃	C₂×D₄	1	4	yes	—
133	C₈×D₁₃	C₂⁴	1	4	yes	—
134	C₁₃×C₁₆	C₂⁴	1	2	yes	—
135	C₁₃×C₁₆	C₂⁴	1	2	yes	—
136	#6090	C₂⁴	1	4	yes	—
137	C₂×#576	—	13	2	no	—
138	#3415	—	13	16	no	—
139	C₂×#509	—	13	4	no	—
140	C₂×#509	—	13	2	no	—
141	C₂×#508	—	13	2	no	—
142	C₂×#508	D₁₃	1	1	yes	characteristic, complemented
143	C₂²×D₁₆	—	13	2	no	—
144	C₂²×D₁₆	—	13	1	no	—
145	C₂×#504	—	13	1	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
148	C₂²×D₁₃	—	4	4	no	—
149	C₂²×D₁₃	—	4	8	no	—
150	C₂²×D₁₃	—	4	16	no	—
151	C₂²×D₁₃	—	16	8	no	—
152	C₂²×D₁₃	—	16	4	no	—
153	C₂²×D₁₃	C₂×D₈	1	2	yes	—
154	Q₈×C₁₃	—	2	4	no	—
155	Q₈×C₁₃	—	4	2	no	—
156	D₄×C₁₃	—	2	4	no	—
157	D₄×C₁₃	—	4	8	no	—
158	D₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
165	C₂²⋊D₁₃	—	4	16	no	—
166	C₂²⋊D₁₃	C₂×D₈	1	8	yes	—
167	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
168	D₅₂	—	2	8	no	—
169	D₅₂	—	4	16	no	—
170	D₅₂	—	4	8	no	—
171	D₅₂	—	4	4	no	—
172	D₅₂	C₂×D₈	1	4	yes	—
173	C₄×D₁₃	—	4	16	no	—
174	C₄×D₁₃	C₂×D₈	1	4	yes	—
175	C₄×D₁₃	C₂²×D₄	1	4	yes	—
176	Dic₂₆	C₂×D₈	1	4	yes	—
177	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃	C₂²×D₄	1	2	yes	—
179	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
180	#1055	C₂²×D₄	1	4	yes	—
181	C₂×H(5,𝔽₂)	—	26	2	no	—
182	#576	—	13	16	no	—
183	#576	—	26	8	no	—
184	C₂×AGL(1,ℤ/8)	—	26	4	no	—
185	C₂×AGL(1,ℤ/8)	—	26	2	no	—
186	C₂×#135	—	13	4	no	—
187	C₂×#135	C₂×D₁₃	1	2	yes	complemented
188	C₂²×D₈	—	13	4	no	—
189	C₂²×D₈	—	13	2	no	—
190	C₂×#131	—	13	1	no	—
191	#509	—	13	16	no	—
192	#509	—	13	32	no	—
193	#508	—	13	16	no	—
194	#508	C₂×D₁₃	1	8	yes	complemented
195	C₂×Q₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
196	C₂×SD₃₂	—	13	4	no	—
197	C₂×SD₃₂	C₂×D₁₃	1	2	yes	complemented
198	C₂×D₁₆	—	13	4	no	—
199	C₂×D₁₆	—	13	16	no	—
200	C₂×D₁₆	—	13	2	no	—
201	C₂×D₁₆	—	13	2	no	—
202	C₂×D₁₆	—	13	8	no	—
203	C₂×D₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
204	#504	—	13	8	no	—
205	C₂×M₃₂	—	13	1	no	—
206	C₂×M₃₂	—	13	2	no	—
207	C₂²×C₁₆	—	13	2	no	—
208	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	4	4	no	—
211	C₂²×C₁₃	—	8	4	no	—
212	C₂²×C₁₃	C₂²×D₈	1	2	yes	—
213	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
214	C₂×D₁₃	—	2	4	no	—
215	C₂×D₁₃	—	4	8	no	—
216	C₂×D₁₃	—	8	8	no	—
217	C₂×D₁₃	—	16	16	no	—
218	C₂×D₁₃	—	16	8	no	—
219	C₂×D₁₃	C₂²×D₈	1	4	yes	—
220	C₄×C₁₃	—	4	4	no	—
221	C₄×C₁₃	C₂²×D₈	1	2	yes	—
222	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
223	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
224	Dic₁₃	C₂²×D₈	1	4	yes	—
225	H(5,𝔽₂)	—	26	16	no	—
226	H(5,𝔽₂)	—	52	8	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	13	1	no	—
229	C₂×#41	—	26	4	no	—
230	C₂×#41	—	52	2	no	—
231	C₂²×D₄	—	26	4	no	—
232	C₂²×D₄	—	26	2	no	—
233	C₂²×D₄	—	52	2	no	—
234	C₂²×D₄	—	52	4	no	—
235	AGL(1,ℤ/8)	—	26	32	no	—
236	AGL(1,ℤ/8)	—	26	16	no	—
237	#135	—	2	4	no	—
238	#135	—	13	16	no	—
239	#135	—	26	8	no	—
240	#135	C₂²×D₁₃	1	8	yes	complemented
241	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	26	4	no	—
244	C₂×D₈	—	13	16	no	—
245	C₂×D₈	—	13	4	no	—
246	C₂×D₈	—	13	8	no	—
247	C₂×D₈	—	26	8	no	—
248	C₂×D₈	—	26	4	no	—
249	C₂×D₈	—	26	2	no	—
250	C₂×D₈	—	26	4	no	—
251	C₂×D₈	C₂²×D₁₃	1	2	yes	—
252	#131	—	13	4	no	—
253	#131	—	13	4	no	—
254	C₂×M₁₆	—	13	1	no	—
255	C₂×M₁₆	—	13	2	no	—
256	C₂²×C₈	—	13	2	no	—
257	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
258	Q₃₂	C₂²×D₁₃	1	4	yes	complemented
259	SD₃₂	—	13	16	no	—
260	SD₃₂	C₂²×D₁₃	1	8	yes	complemented
261	D₁₆	—	13	16	no	—
262	D₁₆	—	13	8	no	—
263	D₁₆	—	13	8	no	—
264	D₁₆	C₂²×D₁₃	1	4	yes	complemented
265	M₃₂	—	13	4	no	—
266	M₃₂	—	13	8	no	—
267	C₂×C₁₆	—	13	2	no	—
268	C₂×C₁₆	—	13	8	no	—
269	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
270	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
271	C₂×C₁₆	C₂²×D₁₃	1	4	yes	complemented
272	C₂×C₁₃	—	2	2	no	—
273	C₂×C₁₃	—	8	4	no	—
274	C₂×C₁₃	#3415	1	2	yes	complemented
275	C₂×C₁₃	C₂³×D₈	1	1	yes	characteristic
276	D₁₃	—	2	4	no	—
277	D₁₃	—	8	8	no	—
278	C₂⁴	—	52	4	no	—
279	C₂⁴	—	52	2	no	—
280	#41	—	2	8	no	—
281	#41	—	4	4	no	—
282	#41	—	13	4	no	—
283	#41	—	13	4	no	—
284	#41	—	26	16	no	—
285	#41	—	52	16	no	—
286	#41	—	52	8	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	13	1	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	13	2	no	—
292	C₂×D₄	—	13	1	no	—
293	C₂×D₄	—	26	16	no	—
294	C₂×D₄	—	26	4	no	—
295	C₂×D₄	—	26	8	no	—
296	C₂×D₄	—	52	16	no	—
297	C₂×D₄	—	52	4	no	—
298	C₂×D₄	—	52	8	no	—
299	C₂×D₄	—	52	4	no	—
300	C₂×D₄	—	52	32	no	—
301	C₂×D₄	—	52	2	no	—
302	C₂×D₄	—	52	4	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	13	2	no	—
305	C₂²×C₄	—	52	4	no	—
306	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
307	Q₁₆	—	2	2	no	—
308	Q₁₆	C₂³×D₁₃	1	4	yes	—
309	SD₁₆	—	2	8	no	—
310	SD₁₆	—	26	16	no	—
311	D₈	—	2	2	no	—
312	D₈	—	13	8	no	—
313	D₈	—	26	16	no	—
314	D₈	—	26	4	no	—
315	D₈	—	26	8	no	—
316	D₈	C₂³×D₁₃	1	4	yes	—
317	M₁₆	—	13	4	no	—
318	M₁₆	—	13	8	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	4	no	—
321	C₂×C₈	—	13	4	no	—
322	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
323	C₂×C₈	D₄×D₁₃	1	2	yes	—
324	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
325	C₂×C₈	C₂³×D₁₃	1	2	yes	—
326	C₁₆	—	13	4	no	—
327	C₁₆	C₂³×D₁₃	1	2	yes	—
328	C₁₆	C₂³×D₁₃	1	2	yes	—
329	C₁₃	C₂×#3415	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	4	2	no	—
331	C₂³	—	13	2	no	—
332	C₂³	—	52	16	no	—
333	C₂³	—	52	4	no	—
334	C₂³	—	52	8	no	—
335	C₂³	—	208	4	no	—
336	C₂³	—	208	8	no	—
337	C₂³	D₈×D₁₃	1	1	yes	characteristic
338	Q₈	—	2	4	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	13	4	no	—
341	D₄	—	2	4	no	—
342	D₄	—	4	8	no	—
343	D₄	—	4	2	no	—
344	D₄	—	13	8	no	—
345	D₄	—	13	4	no	—
346	D₄	—	26	8	no	—
347	D₄	—	52	16	no	—
348	D₄	—	52	16	no	—
349	D₄	—	52	8	no	—
350	D₄	—	52	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	4	no	—
355	C₂×C₄	—	13	4	no	—
356	C₂×C₄	—	52	16	no	—
357	C₂×C₄	D₈×D₁₃	1	2	yes	—
358	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
360	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
361	C₈	—	13	4	no	—
362	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
363	C₈	C₂×D₄×D₁₃	1	2	yes	—
364	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	13	4	no	—
369	C₂²	—	26	4	no	—
370	C₂²	—	52	8	no	—
371	C₂²	—	104	8	no	—
372	C₂²	—	208	8	no	—
373	C₂²	—	208	16	no	—
374	C₂²	C₂×D₈×D₁₃	1	2	yes	—
375	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
376	C₄	—	4	4	no	—
377	C₄	—	13	4	no	—
378	C₄	C₂×D₈×D₁₃	1	2	yes	—
379	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
380	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
381	C₂	—	2	2	no	—
382	C₂	—	8	4	no	—
383	C₂	—	26	4	no	—
384	C₂	—	104	8	no	—
385	C₂	#13127974	1	2	yes	direct product factor
386	C₂	C₂²×D₈×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₁₃
commutator, cosocle	C₈×C₁₃	C₂⁵
Frattini	C₈	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#508	C₂
socle	C₂²×C₁₃	C₂²×D₈
hypercenter	C₂×#508	D₁₃
hypocenter	C₁₃	C₂×#3415
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. C₂×#11719474	C₂	semidirect
2. #13127974	C₂	direct (N × H)
3. C₂×#11718575	C₂	semidirect
4. C₂×#11718854	C₂	semidirect
5. C₂×#11718580	C₂	semidirect
6. C₂²×D₂₀₈	C₂	semidirect
7. C₂×D₁₃×D₁₆	C₂	semidirect
8. C₂×#11718562	C₂	semidirect
9. C₂×C₁₃×#508	C₂	semidirect
11. C₂×C₁₃×#135	C₂²	semidirect
14. #11719474	C₂²	semidirect
15. C₂×#88173	C₂²	semidirect
17. C₂×D₈×D₁₃	C₂²	semidirect
18. C₂²×D₁₀₄	C₂²	semidirect
20. C₁₃×#508	C₂²	semidirect
21. C₂×C₁₃×Q₃₂	C₂²	semidirect
22. C₂×C₁₃×SD₃₂	C₂²	semidirect
23. C₂×C₁₃×D₁₆	C₂²	semidirect
24. C₂²×C₁₃×C₁₆	C₂²	semidirect
25. #11718854	C₂²	semidirect
26. C₂×#88068	C₂²	semidirect
27. C₂×#88066	C₂²	semidirect
28. C₂×#88052	C₂²	semidirect
29. #11718580	C₂²	semidirect
30. #11718575	C₂²	semidirect
31. D₁₃×D₁₆	C₂²	semidirect
32. C₂×D₂₀₈	C₂²	semidirect
33. C₂×D₂₀₈	C₂²	semidirect
34. C₂×D₂₀₈	C₂²	semidirect
35. #11718562	C₂²	semidirect
36. C₂×#88038	C₂²	semidirect
37. C₂×C₁₆×D₁₃	C₂²	semidirect
49. C₁₃×#135	C₂³	semidirect
59. #88173	C₂³	semidirect
62. D₈×D₁₃	C₂³	semidirect
66. C₂×D₁₀₄	C₂³	semidirect
71. C₁₃×Q₃₂	C₂³	semidirect
72. C₁₃×SD₃₂	C₂³	semidirect
73. C₁₃×D₁₆	C₂³	semidirect
76. C₂×C₁₃×C₁₆	C₂³	semidirect
77. #88068	C₂³	semidirect
78. #88066	C₂³	semidirect
79. #88052	C₂³	semidirect
81. D₂₀₈	C₂³	semidirect
82. D₂₀₈	C₂³	semidirect
83. #88038	C₂³	semidirect
84. C₁₆×D₁₃	C₂³	semidirect
142. C₂×#508	D₁₃	semidirect
187. C₂×#135	C₂×D₁₃	semidirect
194. #508	C₂×D₁₃	semidirect
195. C₂×Q₃₂	C₂×D₁₃	semidirect
197. C₂×SD₃₂	C₂×D₁₃	semidirect
203. C₂×D₁₆	C₂×D₁₃	semidirect
208. C₂²×C₁₆	C₂×D₁₃	semidirect
240. #135	C₂²×D₁₃	semidirect
258. Q₃₂	C₂²×D₁₃	semidirect
260. SD₃₂	C₂²×D₁₃	semidirect
264. D₁₆	C₂²×D₁₃	semidirect
271. C₂×C₁₆	C₂²×D₁₃	semidirect
274. C₂×C₁₃	#3415	semidirect
329. C₁₃	C₂×#3415	semidirect
385. C₂	#13127974	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×#11719474	2
#13127974	2
C₂×#11718575	2
C₂×#11718854	2
C₂×#11718580	2
C₂²×D₂₀₈	2
C₂×D₁₃×D₁₆	2
C₂×#11718562	2
C₂×C₁₃×#508	2
C₂×#3415	13

Subgroups — C2×#13127974 #16769428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13127974 #16769428