Subgroups — D₄×#88055 #15861378

Order 3328.

1274 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×#1055	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88055	C₂	1	2	yes	maximal, complemented
3	C₄×D₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13114706	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114703	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114691	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114615	C₂	1	2	yes	maximal, complemented
8	#13114612	C₂	1	2	yes	maximal, complemented
9	#13114600	C₂	1	2	yes	maximal, complemented
10	C₄×#88055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₁₃	C₄	1	2	yes	—
15	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
16	C₂³×#1055	C₂²	1	2	yes	—
17	C₈×D₄×C₁₃	C₄	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊#1055	C₂²	1	2	yes	—
23	C₂×#88055	—	2	8	no	—
24	C₂×#88055	C₂²	1	2	yes	—
25	C₂×#88055	C₂²	1	2	yes	—
26	C₂×#88055	C₂²	1	2	yes	—
27	C₂×#88055	C₂²	1	1	yes	characteristic
28	C₂×#88055	C₂²	1	1	yes	characteristic
29	C₂×#88055	C₂²	1	1	yes	characteristic
30	C₂×#88055	C₂²	1	1	yes	characteristic
31	D₄×#1055	C₄	1	8	yes	complemented
32	C₄⋊C₄×Dic₁₃	C₄	1	2	yes	—
33	C₂²⋊C₄×Dic₁₃	C₄	1	4	yes	—
34	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
37	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
38	#11718142	C₂²	1	2	yes	—
39	#11718142	C₂²	1	2	yes	—
40	#11718142	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×Dic₁₃	C₂×C₄	1	4	yes	—
44	C₂²×C₈×C₁₃	—	2	4	no	—
45	C₂²×C₈×C₁₃	—	2	4	no	—
46	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	complemented
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
51	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₁₃	C₂×C₄	1	4	yes	—
56	D₄×Dic₁₃	—	2	8	no	—
57	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₁₃	—	2	4	no	—
59	C₂×C₄×Dic₁₃	—	2	4	no	—
60	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
61	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
63	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
64	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂²×#1055	—	2	4	no	—
67	C₂²×#1055	—	2	4	no	—
68	C₂²×#1055	C₂×C₄	1	8	yes	complemented
69	C₂²×#1055	C₂³	1	2	yes	—
70	C₂²×#1055	C₂³	1	1	yes	characteristic
71	C₂²×#1055	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
73	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	complemented
74	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
75	#88071	C₂×C₄	1	2	yes	—
76	#88071	C₂×C₄	1	4	yes	—
77	C₂²⋊#1055	C₂×C₄	1	8	yes	complemented
78	#88055	—	2	4	no	—
79	#88055	—	2	2	no	—
80	#88055	—	2	4	no	—
81	#88055	—	2	2	no	—
82	#88055	—	2	4	no	—
83	#88055	—	2	2	no	—
84	#88055	D₄	1	4	yes	direct product factor
85	C₄⋊#1055	C₂×C₄	1	4	yes	complemented
86	C₄×#1055	C₂×C₄	1	4	yes	complemented
87	D₄×#97	—	13	1	no	maximal, Sylow
88	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	C₄²	1	4	yes	—
90	C₂×D₄×C₁₃	M₁₆	1	8	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	—	2	2	no	—
93	C₂²×C₄×C₁₃	—	2	2	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₁₃	—	2	8	no	—
102	C₂²×Dic₁₃	—	2	8	no	—
103	C₂²×Dic₁₃	—	4	4	no	—
104	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₁₃	C₂²×C₄	1	4	yes	—
106	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	—	2	2	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	16	no	—
112	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₁₃	#41	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
118	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
121	C₂²⋊Dic₁₃	—	2	8	no	—
122	C₄⋊Dic₁₃	—	2	4	no	—
123	C₄×Dic₁₃	—	2	4	no	—
124	C₄×Dic₁₃	—	2	2	no	—
125	C₄×Dic₁₃	—	2	2	no	—
126	C₄×Dic₁₃	—	2	1	no	—
127	C₄×Dic₁₃	—	2	1	no	—
128	C₄×Dic₁₃	—	2	8	no	—
129	C₄×Dic₁₃	—	4	2	no	—
130	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
131	C₄×Dic₁₃	#41	1	2	yes	—
132	C₂×#1055	—	2	2	no	—
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	—	2	1	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	16	no	—
137	C₂×#1055	C₂²×C₄	1	2	yes	—
138	C₂×#1055	C₂²×C₄	1	4	yes	—
139	C₂×#1055	C₂²×C₄	1	2	yes	—
140	C₂×#1055	C₂×D₄	1	2	yes	—
141	C₂×#1055	#41	1	2	yes	—
142	C₂×C₈×D₄	—	13	1	no	—
143	C₂×C₈×D₄	D₁₃	1	1	yes	characteristic
144	C₂²×#97	—	13	2	no	—
145	C₄²×D₄	—	13	1	no	—
146	#1770	—	13	1	no	—
147	#1770	—	13	1	no	—
148	#1767	—	13	1	no	—
149	#1752	—	13	2	no	—
150	#1752	—	13	2	no	—
151	#1749	—	13	2	no	—
152	C₄×#97	—	13	1	no	—
153	C₂³×C₁₃	—	2	2	no	—
154	C₂³×C₁₃	—	2	2	no	—
155	C₂³×C₁₃	—	2	4	no	—
156	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
157	C₂³×C₁₃	C₂×M₁₆	1	8	yes	—
158	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	D₄×C₁₃	#97	1	16	yes	complemented
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
169	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	4	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	4	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	4	no	—
185	C₂×Dic₁₃	—	4	16	no	—
186	C₂×Dic₁₃	C₄×D₄	1	4	yes	—
187	C₈×C₁₃	—	2	4	no	—
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	C₄×D₄	1	4	yes	complemented
190	#1055	—	2	4	no	—
191	#1055	—	2	2	no	—
192	#1055	C₄×D₄	1	4	yes	complemented
193	C₂³×C₈	—	13	2	no	—
194	C₂³×C₈	C₂×D₁₃	1	2	yes	—
195	C₂×C₄×D₄	—	13	2	no	—
196	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
197	C₂²×C₄²	—	13	2	no	—
198	C₈×D₄	—	13	8	no	—
199	C₈×D₄	Dic₁₃	1	8	yes	complemented
200	C₂×C₄⋊C₈	—	13	1	no	—
201	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
202	C₂×C₂²⋊C₈	—	13	2	no	—
203	C₂×C₂²⋊C₈	C₂×D₁₃	1	2	yes	—
204	C₂×#97	—	13	1	no	—
205	C₂×#97	—	13	2	no	—
206	C₂×#97	—	13	2	no	—
207	C₂×#97	—	13	2	no	—
208	C₂×#97	—	13	1	no	—
209	C₂×#97	—	13	1	no	—
210	C₂×#97	—	13	1	no	—
211	C₂×#97	—	26	8	no	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
214	C₄×C₄⋊C₄	—	13	2	no	—
215	C₄×C₄⋊C₄	—	13	1	no	—
216	C₄×C₂²⋊C₄	—	13	2	no	—
217	C₄×C₂²⋊C₄	—	13	4	no	—
218	C₄³	—	13	1	no	—
219	#336	—	13	2	no	—
220	#336	—	13	2	no	—
221	#336	—	13	2	no	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	2	8	no	—
224	C₂²×C₁₃	—	2	8	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	C₂×#97	1	8	yes	complemented
227	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
230	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
231	C₂²×C₁₃	#568	1	2	yes	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	4	no	—
234	C₄×C₁₃	C₂×#97	1	4	yes	complemented
235	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
238	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
239	Dic₁₃	—	2	4	no	—
240	Dic₁₃	—	4	4	no	—
241	Dic₁₃	—	4	2	no	—
242	C₂²×D₄	C₄×D₁₃	1	1	yes	characteristic
243	C₂³×C₄	—	13	4	no	—
244	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
245	C₂²×C₈	—	2	4	no	—
246	C₂²×C₈	—	2	4	no	—
247	C₂²×C₈	—	13	1	no	—
248	C₂²×C₈	—	13	8	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	26	4	no	—
252	C₂²×C₈	—	26	4	no	—
253	C₂²×C₈	C₂×Dic₁₃	1	8	yes	complemented
254	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
255	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
257	C₄×D₄	—	26	8	no	—
258	C₄×D₄	C₄×D₁₃	1	4	yes	—
259	C₄×D₄	C₂×Dic₁₃	1	4	yes	—
260	C₂×C₄⋊C₄	—	13	2	no	—
261	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	13	4	no	—
263	C₂×C₂²⋊C₄	C₄×D₁₃	1	2	yes	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	—	13	2	no	—
266	C₂×C₄²	—	13	4	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	2	no	—
269	C₂×C₄²	—	13	2	no	—
270	C₂×C₄²	—	26	4	no	—
271	C₂×C₄²	—	26	4	no	—
272	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
273	C₄⋊C₈	—	13	4	no	—
274	C₄⋊C₈	C₂×Dic₁₃	1	4	yes	complemented
275	C₂²⋊C₈	—	13	8	no	—
276	C₂²⋊C₈	C₂×Dic₁₃	1	8	yes	complemented
277	#97	—	13	4	no	—
278	#97	—	26	4	no	—
279	#97	—	26	2	no	—
280	#97	—	26	4	no	—
281	#97	—	26	2	no	—
282	#97	—	26	4	no	—
283	#97	—	26	2	no	—
284	C₄×C₈	—	13	4	no	—
285	C₄×C₈	C₂×Dic₁₃	1	4	yes	complemented
286	#95	—	13	4	no	—
287	#95	—	13	2	no	—
288	C₂×C₁₃	—	2	8	no	—
289	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
290	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
291	C₂×C₁₃	#2875	1	1	yes	characteristic
292	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
293	C₂×C₁₃	#2970	1	2	yes	—
294	C₂⁴	C₂×C₄×D₁₃	1	2	yes	—
295	C₂×D₄	#6094	1	8	yes	—
296	C₂×D₄	C₄×Dic₁₃	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	13	2	no	—
302	C₂²×C₄	—	13	2	no	—
303	C₂²×C₄	—	13	4	no	—
304	C₂²×C₄	—	26	8	no	—
305	C₂²×C₄	—	26	8	no	—
306	C₂²×C₄	—	52	4	no	—
307	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
309	C₂²×C₄	C₂×C₄×D₁₃	1	4	yes	—
310	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
312	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	16	no	—
318	C₂×C₈	—	13	2	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	13	4	no	—
323	C₂×C₈	—	26	16	no	—
324	C₂×C₈	—	26	2	no	—
325	C₂×C₈	—	26	1	no	—
326	C₂×C₈	—	26	1	no	—
327	C₂×C₈	—	26	2	no	—
328	C₂×C₈	D₄×D₁₃	1	2	yes	—
329	C₂×C₈	#6129	1	2	yes	—
330	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
331	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
332	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
333	C₄⋊C₄	—	26	4	no	—
334	C₄⋊C₄	C₄×Dic₁₃	1	4	yes	—
335	C₂²⋊C₄	—	26	8	no	—
336	C₂²⋊C₄	C₄×Dic₁₃	1	8	yes	—
337	C₄²	—	13	2	no	—
338	C₄²	—	13	2	no	—
339	C₄²	—	26	8	no	—
340	C₄²	—	26	4	no	—
341	C₄²	—	26	2	no	—
342	C₄²	—	26	1	no	—
343	C₄²	—	26	1	no	—
344	C₄²	—	26	2	no	—
345	C₄²	—	52	2	no	—
346	C₄²	C₂×C₄×D₁₃	1	2	yes	—
347	C₄²	C₂²×Dic₁₃	1	2	yes	—
348	C₁₃	D₄×#97	1	1	yes	characteristic, complemented, Sylow
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	C₂×#6094	1	8	yes	—
353	C₂³	C₂×C₄×Dic₁₃	1	4	yes	—
354	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
355	D₄	#88055	1	16	yes	direct product factor
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	13	4	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	4	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	4	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	4	no	—
372	C₂×C₄	—	52	16	no	—
373	C₂×C₄	C₂×#6094	1	4	yes	—
374	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
375	C₂×C₄	C₂×C₄×Dic₁₃	1	4	yes	—
376	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
377	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂×#6129	1	1	yes	characteristic
380	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
381	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
383	C₈	—	2	4	no	—
384	C₈	—	2	2	no	—
385	C₈	—	13	4	no	—
386	C₈	—	26	2	no	—
387	C₈	—	26	4	no	—
388	C₈	D₄×Dic₁₃	1	4	yes	complemented
389	C₂²	—	2	8	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	8	no	—
392	C₂²	—	2	4	no	—
393	C₂²	C₂×#88055	1	8	yes	complemented
394	C₂²	C₄×#6129	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
396	C₂²	C₂²×#6094	1	2	yes	—
397	C₂²	#11719455	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	2	4	no	—
401	C₄	—	26	4	no	—
402	C₄	—	52	2	no	—
403	C₄	—	52	4	no	—
404	C₄	C₂×#88055	1	4	yes	complemented
405	C₄	C₄×#6129	1	1	yes	characteristic
406	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
407	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
408	C₄	#41×Dic₁₃	1	1	yes	characteristic
409	C₂	—	2	8	no	—
410	C₂	C₄×D₄×Dic₁₃	1	1	yes	characteristic
411	C₂	C₂²×#88055	1	1	yes	characteristic
412	C₂	#13123262	1	1	yes	characteristic
413	C₂	D₄×#6094	1	2	yes	—
414	C₂	#13123844	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₈×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₁₃
hypocenter	C₁₃	D₄×#97
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#88055	C₂	semidirect
4. #13114706	C₂	semidirect
5. #13114703	C₂	semidirect
6. #13114691	C₂	semidirect
7. #13114615	C₂	semidirect
8. #13114612	C₂	semidirect
9. #13114600	C₂	semidirect
10. C₄×#88055	C₂	semidirect
17. C₈×D₄×C₁₃	C₄	semidirect
31. D₄×#1055	C₄	semidirect
46. C₂²×C₈×C₁₃	C₂×C₄	semidirect
68. C₂²×#1055	C₂×C₄	semidirect
72. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
73. C₁₃×C₂²⋊C₈	C₂×C₄	semidirect
74. C₄×C₈×C₁₃	C₂×C₄	semidirect
77. C₂²⋊#1055	C₂×C₄	semidirect
84. #88055	D₄	direct (N × H)
85. C₄⋊#1055	C₂×C₄	semidirect
86. C₄×#1055	C₂×C₄	semidirect
159. D₄×C₁₃	#97	semidirect
189. C₈×C₁₃	C₄×D₄	semidirect
192. #1055	C₄×D₄	semidirect
199. C₈×D₄	Dic₁₃	semidirect
226. C₂²×C₁₃	C₂×#97	semidirect
234. C₄×C₁₃	C₂×#97	semidirect
253. C₂²×C₈	C₂×Dic₁₃	semidirect
274. C₄⋊C₈	C₂×Dic₁₃	semidirect
276. C₂²⋊C₈	C₂×Dic₁₃	semidirect
285. C₄×C₈	C₂×Dic₁₃	semidirect
348. C₁₃	D₄×#97	semidirect
355. D₄	#88055	direct (N × H)
388. C₈	D₄×Dic₁₃	semidirect
393. C₂²	C₂×#88055	semidirect
404. C₄	C₂×#88055	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×#1055	2
C₂²×#88055	2
C₄×D₄×Dic₁₃	2
#13114706	2
#13114703	2
#13114691	2
#13114615	2
#13114612	2
#13114600	2
C₄×#88055	2
C₂×C₈×D₄×C₁₃	2
D₄×#97	13

Subgroups — D4×#88055 #15861378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#88055 #15861378