Subgroups — C₄×Q₈×Dic₂₆ #16022923

Order 3328.

2324 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	#13117925	C₂	1	3	yes	maximal
3	#13117923	C₂	1	6	yes	maximal
4	Q₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×Dic₂₆	C₂	1	3	yes	maximal
6	Q₈×#6101	C₂	1	2	yes	maximal
7	C₄×#88123	C₂	1	3	yes	maximal
8	C₄×#88142	C₂	1	6	yes	maximal
9	C₄×Q₈×Dic₁₃	C₂	1	2	yes	maximal
10	C₄²×Dic₂₆	C₂	1	3	yes	maximal
11	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	—
16	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	—
17	Q₈×Dic₂₆	C₄	1	16	yes	direct product factor
18	C₂×#88142	C₂²	1	6	yes	—
19	C₂×#88123	C₂²	1	3	yes	—
20	C₂×C₄×Dic₂₆	C₂²	1	3	yes	—
21	C₂×C₄×Dic₂₆	C₂²	1	6	yes	—
22	C₂×C₄×Dic₂₆	C₂²	1	3	yes	—
23	C₂×C₄×Dic₂₆	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
25	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
27	C₄³×C₁₃	C₂²	1	3	yes	—
28	#11718646	C₂²	1	6	yes	—
29	#11718637	C₂²	1	6	yes	—
30	C₄⋊C₄×Dic₁₃	C₂²	1	6	yes	—
31	C₄⋊C₄×Dic₁₃	C₂²	1	6	yes	—
32	#11718634	C₂²	1	6	yes	—
33	#11718596	C₂²	1	3	yes	—
34	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
35	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
36	C₄×C₄⋊Dic₁₃	C₂²	1	3	yes	—
37	C₄×C₄⋊Dic₁₃	C₂²	1	6	yes	—
38	C₄×#6101	C₂²	1	6	yes	—
39	C₄×#6101	C₂²	1	6	yes	—
40	C₄×#6101	C₂²	1	6	yes	—
41	C₄²×Dic₁₃	C₂²	1	6	yes	—
42	#11718590	C₂²	1	6	yes	—
43	#11718589	C₂²	1	6	yes	—
44	#11718589	C₂²	1	6	yes	—
45	#11718308	C₂²	1	12	yes	—
46	#11718307	C₂²	1	12	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×Dic₂₆	C₂³	1	6	yes	—
49	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃	—	2	4	no	—
51	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	—
52	C₄×Q₈×C₁₃	Q₈	1	8	yes	complemented
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
56	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
57	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
60	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	Q₈×Dic₁₃	—	2	8	no	—
64	Q₈×Dic₁₃	C₂×C₄	1	16	yes	—
65	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
66	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
67	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
68	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
69	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	—
70	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂×#6101	C₂³	1	6	yes	—
72	C₂×#6101	C₂³	1	12	yes	—
73	C₂×#6101	C₂³	1	6	yes	—
74	C₂×#6101	C₂³	1	2	yes	—
75	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
76	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
77	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
78	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
79	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
80	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
81	#88142	C₂×C₄	1	48	yes	—
82	#88123	C₂×C₄	1	24	yes	—
83	C₄×Dic₂₆	—	2	12	no	—
84	C₄×Dic₂₆	—	4	12	no	—
85	C₄×Dic₂₆	C₂×C₄	1	24	yes	—
86	C₄×Dic₂₆	Q₈	1	8	yes	direct product factor
87	C₁₃×#95	C₂³	1	6	yes	—
88	#88071	C₂³	1	6	yes	—
89	#88071	C₂³	1	6	yes	—
90	#88071	C₂³	1	12	yes	—
91	#88071	C₂³	1	6	yes	—
92	C₄×Q₈²	—	13	1	no	maximal, Sylow
93	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
95	C₂×Q₈×C₁₃	#41	1	4	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
104	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
105	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
106	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
107	C₂×Dic₂₆	—	4	6	no	—
108	C₂×Dic₂₆	—	4	6	no	—
109	C₂×Dic₂₆	C₂²×C₄	1	24	yes	—
110	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
111	C₂×Dic₂₆	C₂×Q₈	1	4	yes	—
112	C₂×Dic₂₆	#41	1	4	yes	—
113	C₁₃×C₄⋊C₄	—	2	6	no	—
114	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
115	C₁₃×C₄⋊C₄	C₂×Q₈	1	12	yes	—
116	C₄²×C₁₃	—	2	6	no	—
117	C₄²×C₁₃	—	2	6	no	—
118	C₄²×C₁₃	—	2	6	no	—
119	C₄²×C₁₃	—	4	3	no	—
120	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
121	C₄²×C₁₃	C₂×Q₈	1	12	yes	—
122	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
123	C₄⋊Dic₁₃	—	2	6	no	—
124	C₄⋊Dic₁₃	—	2	12	no	—
125	C₄⋊Dic₁₃	—	4	6	no	—
126	C₄⋊Dic₁₃	C₂²×C₄	1	12	yes	—
127	C₄⋊Dic₁₃	C₂²×C₄	1	24	yes	—
128	C₄⋊Dic₁₃	C₂×Q₈	1	4	yes	—
129	#6101	—	2	12	no	—
130	#6101	—	4	12	no	—
131	#6101	C₂²×C₄	1	24	yes	—
132	#6101	C₂×Q₈	1	8	yes	—
133	C₄×Dic₁₃	—	2	12	no	—
134	C₄×Dic₁₃	—	2	12	no	—
135	C₄×Dic₁₃	—	2	12	no	—
136	C₄×Dic₁₃	—	4	6	no	—
137	C₄×Dic₁₃	C₂²×C₄	1	24	yes	—
138	C₄×Dic₁₃	C₂×Q₈	1	8	yes	—
139	C₂×Q₈²	—	13	1	no	—
140	#2369	—	13	6	no	—
141	#2369	—	13	3	no	—
142	Q₈×C₄⋊C₄	—	13	3	no	—
143	Q₈×C₄⋊C₄	—	13	2	no	—
144	Q₈×C₄⋊C₄	—	13	1	no	—
145	C₄×C₄⋊Q₈	—	13	6	no	—
146	C₄×C₄⋊Q₈	—	13	3	no	—
147	C₄²×Q₈	—	13	3	no	—
148	C₄²×Q₈	—	13	2	no	—
149	C₄²×Q₈	D₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
151	Q₈×C₁₃	C₄×Q₈	1	16	yes	complemented
152	C₂×C₄×C₁₃	—	2	3	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	3	no	—
155	C₂×C₄×C₁₃	—	2	3	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	3	no	—
158	C₂×C₄×C₁₃	—	2	3	no	—
159	C₂×C₄×C₁₃	—	2	3	no	—
160	C₂×C₄×C₁₃	—	2	3	no	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
162	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
163	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₁₃	C₂²×Q₈	1	6	yes	—
165	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
166	C₂×C₄×C₁₃	C₂²×Q₈	1	6	yes	—
167	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
168	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
169	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
171	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
172	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
173	C₂×Dic₁₃	—	2	2	no	—
174	C₂×Dic₁₃	—	2	6	no	—
175	C₂×Dic₁₃	—	2	2	no	—
176	C₂×Dic₁₃	—	2	6	no	—
177	C₂×Dic₁₃	—	2	6	no	—
178	C₂×Dic₁₃	—	2	6	no	—
179	C₂×Dic₁₃	—	2	6	no	—
180	C₂×Dic₁₃	C₂³×C₄	1	12	yes	—
181	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
182	C₂×Dic₁₃	C₂²×Q₈	1	4	yes	—
183	C₂×Dic₁₃	C₂²×Q₈	1	4	yes	—
184	C₂×Dic₁₃	C₂×#41	1	4	yes	—
185	Dic₂₆	—	4	24	no	—
186	Dic₂₆	C₄×Q₈	1	16	yes	direct product factor
187	Q₈²	—	13	16	no	—
188	C₂×C₄⋊Q₈	—	13	6	no	—
189	C₂×C₄⋊Q₈	—	13	3	no	—
190	C₂×C₄×Q₈	—	13	2	no	—
191	C₂×C₄×Q₈	—	13	2	no	—
192	C₂×C₄×Q₈	—	13	3	no	—
193	C₂×C₄×Q₈	—	13	1	no	—
194	C₂×C₄×Q₈	—	13	3	no	—
195	C₂×C₄×Q₈	—	13	6	no	—
196	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
198	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
199	#391	—	13	6	no	—
200	#391	—	13	12	no	—
201	#389	—	13	6	no	—
202	#389	—	13	6	no	—
203	#389	—	13	6	no	—
204	#389	—	13	6	no	—
205	#389	—	13	12	no	—
206	#384	—	13	6	no	—
207	#384	—	13	3	no	—
208	C₄×C₄⋊C₄	—	13	6	no	—
209	C₄×C₄⋊C₄	—	13	6	no	—
210	C₄×C₄⋊C₄	—	13	6	no	—
211	C₄×C₄⋊C₄	—	13	6	no	—
212	C₄×C₄⋊C₄	—	13	3	no	—
213	C₄×C₄⋊C₄	—	13	6	no	—
214	C₄×C₄⋊C₄	—	13	3	no	—
215	C₄×C₄⋊C₄	—	13	6	no	—
216	C₄×C₄⋊C₄	—	13	3	no	—
217	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
218	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
219	C₄×C₄⋊C₄	C₂×D₁₃	1	3	yes	—
220	C₄³	—	13	6	no	—
221	C₄³	C₂×D₁₃	1	3	yes	—
222	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
223	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
224	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
225	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
226	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
227	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂²×C₁₃	#585	1	1	yes	characteristic
229	C₄×C₁₃	—	2	6	no	—
230	C₄×C₁₃	—	2	6	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	4	3	no	—
233	C₄×C₁₃	C₂×C₄×Q₈	1	12	yes	—
234	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	—
235	C₄×C₁₃	Q₈²	1	4	yes	complemented
236	Dic₁₃	—	2	12	no	—
237	Dic₁₃	—	2	4	no	—
238	Dic₁₃	—	4	6	no	—
239	Dic₁₃	C₂×C₄×Q₈	1	8	yes	—
240	C₂²×Q₈	—	13	1	no	—
241	C₂²×Q₈	—	13	6	no	—
242	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
243	C₄⋊Q₈	—	13	48	no	—
244	C₄⋊Q₈	—	13	24	no	—
245	C₄×Q₈	—	2	4	no	—
246	C₄×Q₈	—	13	16	no	—
247	C₄×Q₈	—	13	24	no	—
248	C₄×Q₈	—	13	8	no	—
249	C₄×Q₈	—	26	12	no	—
250	C₄×Q₈	—	26	8	no	—
251	C₄×Q₈	—	52	12	no	—
252	C₄×Q₈	Dic₂₆	1	8	yes	direct product factor
253	C₄×Q₈	C₄×D₁₃	1	8	yes	—
254	C₂×C₄⋊C₄	—	13	6	no	—
255	C₂×C₄⋊C₄	—	13	6	no	—
256	C₂×C₄⋊C₄	—	13	3	no	—
257	C₂×C₄⋊C₄	—	13	2	no	—
258	C₂×C₄⋊C₄	—	13	1	no	—
259	C₂×C₄⋊C₄	—	13	6	no	—
260	C₂×C₄⋊C₄	—	13	6	no	—
261	C₂×C₄⋊C₄	—	13	3	no	—
262	C₂×C₄⋊C₄	—	13	12	no	—
263	C₂×C₄⋊C₄	—	13	6	no	—
264	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
265	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
266	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
267	C₂×C₄²	—	13	6	no	—
268	C₂×C₄²	—	13	2	no	—
269	C₂×C₄²	—	13	6	no	—
270	C₂×C₄²	—	13	6	no	—
271	C₂×C₄²	—	13	6	no	—
272	C₂×C₄²	—	13	6	no	—
273	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
274	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
275	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
276	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
277	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
278	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
279	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
280	#95	—	13	6	no	—
281	#95	—	13	6	no	—
282	#95	—	13	12	no	—
283	#95	—	13	6	no	—
284	#95	C₂²×D₁₃	1	6	yes	—
285	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
286	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
287	C₂×C₁₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₁₃	C₂×Q₈²	1	1	yes	characteristic
289	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
290	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
291	C₂×C₁₃	#3483	1	1	yes	characteristic
292	C₂×Q₈	—	13	4	no	—
293	C₂×Q₈	—	13	24	no	—
294	C₂×Q₈	—	13	4	no	—
295	C₂×Q₈	—	13	4	no	—
296	C₂×Q₈	—	52	6	no	—
297	C₂×Q₈	—	52	6	no	—
298	C₂×Q₈	C₂×Dic₂₆	1	4	yes	—
299	C₂×Q₈	C₂×C₄×D₁₃	1	4	yes	—
300	C₂×Q₈	#6127	1	4	yes	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	13	2	no	—
303	C₂²×C₄	—	13	6	no	—
304	C₂²×C₄	—	13	6	no	—
305	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
306	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
307	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
308	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
310	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
312	C₄⋊C₄	—	2	6	no	—
313	C₄⋊C₄	—	13	24	no	—
314	C₄⋊C₄	—	13	24	no	—
315	C₄⋊C₄	—	13	12	no	—
316	C₄⋊C₄	—	13	8	no	—
317	C₄⋊C₄	—	13	4	no	—
318	C₄⋊C₄	—	26	12	no	—
319	C₄⋊C₄	—	26	12	no	—
320	C₄⋊C₄	—	26	6	no	—
321	C₄⋊C₄	—	52	12	no	—
322	C₄⋊C₄	—	52	6	no	—
323	C₄⋊C₄	C₂×Dic₂₆	1	12	yes	—
324	C₄⋊C₄	C₂×C₄×D₁₃	1	12	yes	—
325	C₄²	—	2	6	no	—
326	C₄²	—	2	6	no	—
327	C₄²	—	2	6	no	—
328	C₄²	—	4	3	no	—
329	C₄²	—	13	24	no	—
330	C₄²	—	13	8	no	—
331	C₄²	—	26	12	no	—
332	C₄²	—	26	12	no	—
333	C₄²	—	26	12	no	—
334	C₄²	—	52	6	no	—
335	C₄²	C₂×Dic₂₆	1	12	yes	—
336	C₄²	C₂×C₄×D₁₃	1	12	yes	—
337	C₄²	Q₈×D₁₃	1	4	yes	—
338	C₁₃	C₄×Q₈²	1	1	yes	characteristic, complemented, Sylow
339	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
340	Q₈	—	13	16	no	—
341	Q₈	—	52	24	no	—
342	Q₈	C₄×Dic₂₆	1	16	yes	direct product factor
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	3	no	—
345	C₂×C₄	—	2	3	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	3	no	—
348	C₂×C₄	—	2	3	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	3	no	—
352	C₂×C₄	—	13	4	no	—
353	C₂×C₄	—	13	4	no	—
354	C₂×C₄	—	13	4	no	—
355	C₂×C₄	—	13	12	no	—
356	C₂×C₄	—	13	4	no	—
357	C₂×C₄	—	26	2	no	—
358	C₂×C₄	—	26	6	no	—
359	C₂×C₄	—	26	2	no	—
360	C₂×C₄	—	26	6	no	—
361	C₂×C₄	—	26	6	no	—
362	C₂×C₄	—	26	6	no	—
363	C₂×C₄	—	26	6	no	—
364	C₂×C₄	C₂²×Dic₂₆	1	6	yes	—
365	C₂×C₄	C₂²×Dic₂₆	1	6	yes	—
366	C₂×C₄	C₂²×Dic₂₆	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
368	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
369	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
370	C₂×C₄	C₂×#6127	1	6	yes	—
371	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
372	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
373	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
374	C₂×C₄	#41×D₁₃	1	2	yes	—
375	C₂×C₄	#88256	1	2	yes	—
376	C₂²	C₂³×Dic₂₆	1	1	yes	characteristic
377	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
378	C₂²	C₂²×#6127	1	1	yes	characteristic
379	C₂²	C₂²×Q₈×D₁₃	1	1	yes	characteristic
380	C₂²	C₂×#41×D₁₃	1	1	yes	characteristic
381	C₂²	C₂×#88256	1	1	yes	characteristic
382	C₂²	#11719648	1	1	yes	characteristic
383	C₄	—	2	6	no	—
384	C₄	—	2	6	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	3	no	—
387	C₄	—	13	8	no	—
388	C₄	—	26	12	no	—
389	C₄	—	26	4	no	—
390	C₄	—	52	6	no	—
391	C₄	C₂×C₄×Dic₂₆	1	12	yes	—
392	C₄	Q₈×Dic₂₆	1	4	yes	direct product factor
393	C₄	C₄×Q₈×D₁₃	1	4	yes	—
394	C₂	C₂×C₄×Q₈×D₁₃	1	1	yes	characteristic
395	C₂	C₂²×C₄×Dic₂₆	1	1	yes	characteristic
396	C₂	C₄×#88256	1	1	yes	characteristic
397	C₂	C₂×Q₈×Dic₂₆	1	1	yes	characteristic
398	C₂	#41×Dic₂₆	1	1	yes	characteristic
399	C₂	Q₈×#6127	1	1	yes	characteristic
400	C₂	#13128462	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₄²×Q₈×C₁₃	C₂
socle, prime radical, cosocle	C₂³×C₁₃	C₂⁵
hypercenter	C₄²×Q₈	D₁₃
hypocenter	C₁₃	C₄×Q₈²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×Q₈

Complements

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

N	H ≅ G/N	type
17. Q₈×Dic₂₆	C₄	direct (N × H)
52. C₄×Q₈×C₁₃	Q₈	semidirect
86. C₄×Dic₂₆	Q₈	direct (N × H)
151. Q₈×C₁₃	C₄×Q₈	semidirect
186. Dic₂₆	C₄×Q₈	direct (N × H)
235. C₄×C₁₃	Q₈²	semidirect
252. C₄×Q₈	Dic₂₆	direct (N × H)
338. C₁₃	C₄×Q₈²	semidirect
342. Q₈	C₄×Dic₂₆	direct (N × H)
392. C₄	Q₈×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
C₂×Q₈×Dic₂₆	2
#13117925	2
#13117923	2
Q₈×C₄⋊Dic₁₃	2
C₄⋊C₄×Dic₂₆	2
Q₈×#6101	2
C₄×#88123	2
C₄×#88142	2
C₄×Q₈×Dic₁₃	2
C₄²×Dic₂₆	2
C₄²×Q₈×C₁₃	2
C₄×Q₈²	13

Subgroups — C4×Q8×Dic26 #16022923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₈×Dic₂₆ #16022923