Subgroups — C₂²×D₄×Dic₂₆ #16769835

Order 3328.

11798 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×Dic₂₆	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Dic₂₆	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88142	C₂	1	2	yes	maximal, complemented
5	C₂²×#88178	C₂	1	2	yes	maximal, complemented
6	C₂²×#88132	C₂	1	4	yes	maximal, complemented
7	C₂²×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×Dic₁₃	C₂	1	2	yes	maximal
9	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂⁴×Dic₁₃	C₂²	1	4	yes	—
13	C₂³×Dic₂₆	—	2	32	no	—
14	C₂³×Dic₂₆	C₂²	1	4	yes	—
15	C₂³×Dic₂₆	C₂²	1	2	yes	—
16	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
17	C₂³×Dic₂₆	C₂²	1	48	yes	complemented
18	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
23	C₂×D₄×Dic₁₃	C₂²	1	48	yes	—
24	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
25	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
27	C₂×#88178	C₂²	1	48	yes	complemented
28	C₂²×#6101	C₂²	1	2	yes	—
29	C₂²×#6101	C₂²	1	4	yes	—
30	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
31	D₄×Dic₂₆	C₂²	1	256	yes	direct product factor
32	C₂×#88142	C₂²	1	48	yes	complemented
33	C₂×#88132	C₂²	1	96	yes	complemented
34	C₂×#88123	C₂²	1	24	yes	complemented
35	C₂×C₄×Dic₂₆	C₂²	1	24	yes	complemented
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₁₃	Q₈	1	16	yes	complemented
38	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
39	C₂³×C₄×C₁₃	—	2	16	no	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×Dic₁₃	—	2	32	no	—
46	C₂³×Dic₁₃	C₂³	1	48	yes	—
47	C₂³×Dic₁₃	C₂³	1	2	yes	—
48	C₂³×Dic₁₃	C₂³	1	4	yes	—
49	C₂³×Dic₁₃	C₂³	1	2	yes	—
50	C₂²×Dic₂₆	—	2	16	no	—
51	C₂²×Dic₂₆	—	2	32	no	—
52	C₂²×Dic₂₆	—	2	384	no	—
53	C₂²×Dic₂₆	D₄	1	16	yes	direct product factor
54	C₂²×Dic₂₆	C₂³	1	24	yes	—
55	C₂²×Dic₂₆	C₂³	1	48	yes	—
56	C₂²×Dic₂₆	C₂³	1	12	yes	—
57	C₂²×Dic₂₆	C₂³	1	128	yes	complemented
58	C₄×D₄×C₁₃	C₂³	1	64	yes	—
59	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
60	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
62	C₂×C₂²⋊Dic₁₃	C₂³	1	48	yes	—
63	D₄×Dic₁₃	C₂³	1	128	yes	—
64	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
66	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
67	#88178	C₂³	1	128	yes	complemented
68	C₂×#6101	C₂³	1	24	yes	—
69	C₂×#6101	C₂³	1	48	yes	—
70	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
71	#88142	C₂³	1	128	yes	complemented
72	#88132	C₂³	1	256	yes	complemented
73	#88123	C₂³	1	64	yes	complemented
74	C₄×Dic₂₆	C₂³	1	64	yes	complemented
75	C₂²×D₄×Q₈	—	13	1	no	maximal, Sylow
76	C₂⁴×C₁₃	—	2	8	no	—
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	C₂×Q₈	1	16	yes	complemented
79	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₂×D₄×C₁₃	C₂×Q₈	1	96	yes	complemented
82	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
83	C₂²×C₄×C₁₃	—	2	8	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	96	no	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
87	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	complemented
88	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
89	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
93	C₂²×Dic₁₃	—	2	16	no	—
94	C₂²×Dic₁₃	—	2	8	no	—
95	C₂²×Dic₁₃	—	2	192	no	—
96	C₂²×Dic₁₃	C₂×D₄	1	16	yes	—
97	C₂²×Dic₁₃	C₂⁴	1	64	yes	—
98	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
99	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
100	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
101	C₂×Dic₂₆	—	2	96	no	—
102	C₂×Dic₂₆	—	2	192	no	—
103	C₂×Dic₂₆	—	2	512	no	—
104	C₂×Dic₂₆	C₂×D₄	1	96	yes	direct product factor
105	C₂×Dic₂₆	C₂⁴	1	32	yes	—
106	C₂×Dic₂₆	C₂⁴	1	64	yes	—
107	C₂×Dic₂₆	C₂⁴	1	16	yes	—
108	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
109	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
110	C₄²×C₁₃	C₂⁴	1	16	yes	—
111	C₂²⋊Dic₁₃	C₂⁴	1	64	yes	—
112	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
113	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
114	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
115	#6101	C₂⁴	1	32	yes	—
116	#6101	C₂⁴	1	64	yes	—
117	C₄×Dic₁₃	C₂⁴	1	32	yes	—
118	C₂⁴×Q₈	—	13	2	no	—
119	C₂×D₄×Q₈	—	13	48	no	—
120	C₂²×C₄⋊Q₈	—	13	1	no	—
121	C₂²×C₄⋊Q₈	—	13	2	no	—
122	C₂²×C₂²⋊Q₈	—	13	2	no	—
123	C₂²×C₂²⋊Q₈	—	13	4	no	—
124	C₂²×C₄×Q₈	—	13	1	no	—
125	C₂²×C₄×D₄	—	13	2	no	—
126	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic
127	C₂³×C₁₃	—	2	64	no	—
128	C₂³×C₁₃	—	2	24	no	—
129	C₂³×C₁₃	—	2	24	no	—
130	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
131	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
132	C₂³×C₁₃	C₂²×Q₈	1	48	yes	complemented
133	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
134	C₂³×C₁₃	C₂⁵	1	8	yes	—
135	C₂³×C₁₃	C₂⁵	1	3	yes	—
136	D₄×C₁₃	C₂²×Q₈	1	64	yes	complemented
137	C₂×C₄×C₁₃	—	2	24	no	—
138	C₂×C₄×C₁₃	—	2	12	no	—
139	C₂×C₄×C₁₃	—	2	64	no	—
140	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₁₃	C₂²×Q₈	1	24	yes	complemented
142	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
143	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
144	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
145	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
146	C₂×Dic₁₃	—	2	48	no	—
147	C₂×Dic₁₃	—	2	24	no	—
148	C₂×Dic₁₃	—	2	128	no	—
149	C₂×Dic₁₃	C₂²×D₄	1	48	yes	—
150	C₂×Dic₁₃	C₂⁵	1	8	yes	—
151	C₂×Dic₁₃	C₂⁵	1	16	yes	—
152	C₂×Dic₁₃	C₂⁵	1	8	yes	—
153	Dic₂₆	—	2	64	no	—
154	Dic₂₆	—	2	128	no	—
155	Dic₂₆	C₂²×D₄	1	64	yes	direct product factor
156	C₂³×Q₈	—	13	1	no	—
157	C₂³×Q₈	—	13	4	no	—
158	C₂³×Q₈	—	13	2	no	—
159	C₂³×Q₈	—	13	48	no	—
160	C₂³×Q₈	—	26	32	no	—
161	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
162	C₂⁴×C₄	—	13	4	no	—
163	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
164	D₄×Q₈	—	13	256	no	—
165	C₂×C₄⋊Q₈	—	13	48	no	—
166	C₂×C₄⋊Q₈	—	13	24	no	—
167	C₂×C₂²⋊Q₈	—	13	48	no	—
168	C₂×C₂²⋊Q₈	—	13	96	no	—
169	C₂×C₄×Q₈	—	13	24	no	—
170	C₂×C₄×D₄	—	13	48	no	—
171	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	—
172	C₂²×C₄⋊C₄	—	13	2	no	—
173	C₂²×C₄⋊C₄	—	13	4	no	—
174	C₂²×C₄⋊C₄	—	13	2	no	—
175	C₂²×C₄⋊C₄	—	13	1	no	—
176	C₂²×C₄⋊C₄	—	13	2	no	—
177	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
178	C₂²×C₂²⋊C₄	—	13	4	no	—
179	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
180	C₂²×C₄²	—	13	2	no	—
181	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
182	C₂²×C₁₃	—	2	8	no	—
183	C₂²×C₁₃	—	2	8	no	—
184	C₂²×C₁₃	—	2	96	no	—
185	C₂²×C₁₃	D₄×Q₈	1	16	yes	complemented
186	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
187	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
188	C₂²×C₁₃	C₂³×Q₈	1	16	yes	complemented
189	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
190	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
191	C₄×C₁₃	—	2	8	no	—
192	C₄×C₁₃	—	2	4	no	—
193	C₄×C₁₃	C₂³×D₄	1	8	yes	—
194	C₄×C₁₃	C₂³×Q₈	1	8	yes	complemented
195	Dic₁₃	—	2	16	no	—
196	Dic₁₃	—	2	8	no	—
197	Dic₁₃	C₂³×D₄	1	16	yes	—
198	C₂⁵	C₂²×D₁₃	1	2	yes	—
199	C₂²×Q₈	—	13	16	no	—
200	C₂²×Q₈	—	13	12	no	—
201	C₂²×Q₈	—	13	48	no	—
202	C₂²×Q₈	—	13	24	no	—
203	C₂²×Q₈	—	13	128	no	—
204	C₂²×Q₈	—	26	32	no	—
205	C₂²×Q₈	—	26	384	no	—
206	C₂²×Q₈	—	26	16	no	—
207	C₂²×D₄	Dic₂₆	1	16	yes	direct product factor
208	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
209	C₂³×C₄	—	2	16	no	—
210	C₂³×C₄	—	13	2	no	—
211	C₂³×C₄	—	13	48	no	—
212	C₂³×C₄	—	13	2	no	—
213	C₂³×C₄	—	13	4	no	—
214	C₂³×C₄	—	26	32	no	—
215	C₂³×C₄	C₂²×D₁₃	1	24	yes	—
216	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
218	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
220	C₄⋊Q₈	—	13	128	no	—
221	C₄⋊Q₈	—	13	64	no	—
222	C₂²⋊Q₈	—	13	128	no	—
223	C₂²⋊Q₈	—	13	256	no	—
224	C₄×Q₈	—	13	64	no	—
225	C₄×D₄	—	13	128	no	—
226	C₄×D₄	C₂²×D₁₃	1	64	yes	—
227	C₂×C₄⋊C₄	—	13	24	no	—
228	C₂×C₄⋊C₄	—	13	24	no	—
229	C₂×C₄⋊C₄	—	13	12	no	—
230	C₂×C₄⋊C₄	—	13	48	no	—
231	C₂×C₄⋊C₄	—	13	24	no	—
232	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
233	C₂×C₂²⋊C₄	—	13	48	no	—
234	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
235	C₂×C₄²	—	13	24	no	—
236	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
237	C₂×C₁₃	—	2	16	no	—
238	C₂×C₁₃	C₂×D₄×Q₈	1	12	yes	complemented
239	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
240	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
241	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
242	C₂⁴	—	2	8	no	—
243	C₂⁴	—	2	8	no	—
244	C₂⁴	C₂×Dic₂₆	1	16	yes	complemented
245	C₂⁴	C₂³×D₁₃	1	12	yes	—
246	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
247	C₂×Q₈	—	13	96	no	—
248	C₂×Q₈	—	13	16	no	—
249	C₂×Q₈	—	13	64	no	—
250	C₂×Q₈	—	13	32	no	—
251	C₂×Q₈	—	26	192	no	—
252	C₂×Q₈	—	26	512	no	—
253	C₂×Q₈	—	26	96	no	—
254	C₂×D₄	C₂×Dic₂₆	1	96	yes	direct product factor
255	C₂×D₄	C₂³×D₁₃	1	16	yes	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	96	no	—
259	C₂²×C₄	—	13	16	no	—
260	C₂²×C₄	—	13	12	no	—
261	C₂²×C₄	—	13	12	no	—
262	C₂²×C₄	—	13	24	no	—
263	C₂²×C₄	—	13	64	no	—
264	C₂²×C₄	—	26	192	no	—
265	C₂²×C₄	—	26	16	no	—
266	C₂²×C₄	—	26	8	no	—
267	C₂²×C₄	C₂×Dic₂₆	1	8	yes	complemented
268	C₂²×C₄	D₄×D₁₃	1	8	yes	—
269	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
270	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
271	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
272	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
273	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
274	C₄⋊C₄	—	13	32	no	—
275	C₄⋊C₄	—	13	32	no	—
276	C₄⋊C₄	—	13	16	no	—
277	C₄⋊C₄	—	13	64	no	—
278	C₄⋊C₄	—	13	32	no	—
279	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
280	C₂²⋊C₄	—	13	64	no	—
281	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
282	C₄²	—	13	32	no	—
283	C₄²	C₂³×D₁₃	1	16	yes	—
284	C₁₃	C₂²×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
285	C₂³	—	2	64	no	—
286	C₂³	—	2	24	no	—
287	C₂³	—	2	24	no	—
288	C₂³	C₂²×Dic₂₆	1	4	yes	—
289	C₂³	C₂²×Dic₂₆	1	48	yes	complemented
290	C₂³	C₂×D₄×D₁₃	1	4	yes	—
291	C₂³	#88257	1	4	yes	—
292	C₂³	C₂⁴×D₁₃	1	8	yes	—
293	C₂³	C₂⁴×D₁₃	1	3	yes	—
294	Q₈	—	13	64	no	—
295	Q₈	—	26	128	no	—
296	Q₈	—	26	64	no	—
297	D₄	C₂²×Dic₂₆	1	64	yes	direct product factor
298	C₂×C₄	—	2	24	no	—
299	C₂×C₄	—	2	12	no	—
300	C₂×C₄	—	2	64	no	—
301	C₂×C₄	—	13	48	no	—
302	C₂×C₄	—	13	8	no	—
303	C₂×C₄	—	13	8	no	—
304	C₂×C₄	—	13	16	no	—
305	C₂×C₄	—	26	128	no	—
306	C₂×C₄	—	26	48	no	—
307	C₂×C₄	—	26	24	no	—
308	C₂×C₄	C₂²×Dic₂₆	1	24	yes	complemented
309	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
310	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
311	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
312	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
313	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
314	C₂²	—	2	96	no	—
315	C₂²	—	2	8	no	—
316	C₂²	—	2	8	no	—
317	C₂²	D₄×Dic₂₆	1	16	yes	direct product factor
318	C₂²	C₂³×Dic₂₆	1	6	yes	—
319	C₂²	C₂³×Dic₂₆	1	16	yes	complemented
320	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
321	C₂²	C₂×#88257	1	6	yes	—
322	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
323	C₄	—	2	8	no	—
324	C₄	—	2	4	no	—
325	C₄	—	13	16	no	—
326	C₄	—	26	16	no	—
327	C₄	—	26	8	no	—
328	C₄	C₂³×Dic₂₆	1	8	yes	complemented
329	C₄	C₂²×D₄×D₁₃	1	8	yes	—
330	C₂	—	2	16	no	—
331	C₂	C₂×D₄×Dic₂₆	1	12	yes	direct product factor
332	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
333	C₂	C₂⁴×Dic₂₆	1	1	yes	characteristic
334	C₂	C₂²×#88257	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂³×D₄×C₁₃	C₂²
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×Dic₂₆	C₂	semidirect
2. C₂×D₄×Dic₂₆	C₂	direct (N × H)
3. C₂²×#88123	C₂	semidirect
4. C₂²×#88142	C₂	semidirect
5. C₂²×#88178	C₂	semidirect
6. C₂²×#88132	C₂	semidirect
7. C₂²×C₄×Dic₂₆	C₂	semidirect
17. C₂³×Dic₂₆	C₂²	semidirect
27. C₂×#88178	C₂²	semidirect
31. D₄×Dic₂₆	C₂²	direct (N × H)
32. C₂×#88142	C₂²	semidirect
33. C₂×#88132	C₂²	semidirect
34. C₂×#88123	C₂²	semidirect
35. C₂×C₄×Dic₂₆	C₂²	semidirect
37. C₂²×D₄×C₁₃	Q₈	semidirect
53. C₂²×Dic₂₆	D₄	direct (N × H)
57. C₂²×Dic₂₆	C₂³	semidirect
67. #88178	C₂³	semidirect
71. #88142	C₂³	semidirect
72. #88132	C₂³	semidirect
73. #88123	C₂³	semidirect
74. C₄×Dic₂₆	C₂³	semidirect
78. C₂⁴×C₁₃	C₂×Q₈	semidirect
81. C₂×D₄×C₁₃	C₂×Q₈	semidirect
87. C₂²×C₄×C₁₃	C₂×Q₈	semidirect
104. C₂×Dic₂₆	C₂×D₄	direct (N × H)
132. C₂³×C₁₃	C₂²×Q₈	semidirect
136. D₄×C₁₃	C₂²×Q₈	semidirect
141. C₂×C₄×C₁₃	C₂²×Q₈	semidirect
155. Dic₂₆	C₂²×D₄	direct (N × H)
185. C₂²×C₁₃	D₄×Q₈	semidirect
188. C₂²×C₁₃	C₂³×Q₈	semidirect
194. C₄×C₁₃	C₂³×Q₈	semidirect
207. C₂²×D₄	Dic₂₆	direct (N × H)
238. C₂×C₁₃	C₂×D₄×Q₈	semidirect
244. C₂⁴	C₂×Dic₂₆	semidirect
254. C₂×D₄	C₂×Dic₂₆	direct (N × H)
267. C₂²×C₄	C₂×Dic₂₆	semidirect
284. C₁₃	C₂²×D₄×Q₈	semidirect
289. C₂³	C₂²×Dic₂₆	semidirect
297. D₄	C₂²×Dic₂₆	direct (N × H)
308. C₂×C₄	C₂²×Dic₂₆	semidirect
317. C₂²	D₄×Dic₂₆	direct (N × H)
319. C₂²	C₂³×Dic₂₆	semidirect
328. C₄	C₂³×Dic₂₆	semidirect
331. C₂	C₂×D₄×Dic₂₆	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×Dic₂₆	2
C₂×D₄×Dic₂₆	2
C₂²×#88123	2
C₂²×#88142	2
C₂²×#88178	2
C₂²×#88132	2
C₂²×C₄×Dic₂₆	2
C₂²×D₄×Dic₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×D₄×Q₈	13

Subgroups — C22×D4×Dic26 #16769835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄×Dic₂₆ #16769835