Subgroups — D₄×#88059 #15881172

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6099	C₂	1	2	yes	maximal
2	C₂²×#88059	C₂	1	2	yes	maximal, complemented
3	#13115612	C₂	1	2	yes	maximal, complemented
4	#13115043	C₂	1	4	yes	maximal, complemented
5	#13115008	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114874	C₂	1	2	yes	maximal, complemented
7	C₄×#88059	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×#6099	C₂²	1	4	yes	—
12	C₈×D₄×C₁₃	C₄	1	4	yes	—
13	C₈×D₄×C₁₃	C₄	1	2	yes	—
14	C₈×D₄×C₁₃	C₄	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718868	C₂²	1	4	yes	—
19	C₂×#88059	—	2	8	no	—
20	C₂×#88059	C₂²	1	2	yes	—
21	C₂×#88059	C₂²	1	4	yes	—
22	C₂×#88059	C₂²	1	1	yes	characteristic
23	C₂×#88059	C₂²	1	2	yes	—
24	C₂×#88059	C₂²	1	1	yes	characteristic
25	#11718673	—	2	2	no	—
26	#11718672	—	2	4	no	—
27	D₄×#1055	—	2	2	no	—
28	#11718585	C₂²	1	2	yes	—
29	C₄×#6099	C₂²	1	2	yes	—
30	#11718144	C₂²	1	2	yes	—
31	#11718144	C₂²	1	4	yes	—
32	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₃	—	2	4	no	—
35	C₂²×C₈×C₁₃	—	2	4	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
42	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₄×D₄×C₁₃	D₄	1	2	yes	—
46	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
48	C₂×C₁₃×C₂²⋊C₄	Q₈	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×#6099	—	2	4	no	—
51	C₂×#6099	—	2	8	no	—
52	C₂×#6099	—	4	4	no	—
53	C₂×#6099	C₂³	1	2	yes	—
54	C₂×#6099	C₂³	1	4	yes	—
55	C₂×#6099	C₂³	1	2	yes	—
56	C₂²×#1055	—	2	4	no	—
57	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
58	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
59	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
60	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
62	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
63	C₂²⋊#1055	—	2	4	no	—
64	C₂²⋊#1055	—	2	4	no	—
65	#88059	—	2	4	no	—
66	#88059	—	2	2	no	—
67	#88059	—	2	8	no	—
68	#88059	—	4	2	no	—
69	#88059	D₄	1	4	yes	direct product factor
70	C₄⋊#1055	—	2	2	no	—
71	C₄⋊#1055	—	2	2	no	—
72	#88043	—	2	2	no	—
73	C₄×#1055	—	2	2	no	—
74	D₄×#108	—	13	1	no	maximal, Sylow
75	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
76	C₂×D₄×C₁₃	—	2	4	no	—
77	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
78	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	8	no	—
97	C₂×C₈×C₁₃	—	2	8	no	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₃	#41	1	2	yes	—
103	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
104	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
106	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
107	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
108	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
109	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
114	#6099	—	2	2	no	—
115	#6099	—	2	4	no	—
116	#6099	—	2	2	no	—
117	#6099	—	2	4	no	—
118	#6099	—	2	2	no	—
119	#6099	—	4	8	no	—
120	#6099	C₂×D₄	1	4	yes	—
121	C₂×#1055	—	2	2	no	—
122	C₂×#1055	—	2	2	no	—
123	C₂×#1055	—	2	4	no	—
124	C₂×#1055	—	4	8	no	—
125	D₄×M₁₆	—	13	2	no	—
126	C₂×C₈×D₄	D₁₃	1	1	yes	characteristic
127	C₂²×#108	—	13	2	no	—
128	#1950	—	13	2	no	—
129	#1855	—	13	4	no	—
130	#1848	—	13	1	no	—
131	#1810	—	13	2	no	—
132	C₄×#108	—	13	1	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	—	2	2	no	—
135	C₂³×C₁₃	—	2	4	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
140	D₄×C₁₃	—	2	4	no	—
141	D₄×C₁₃	—	2	2	no	—
142	D₄×C₁₃	#108	1	4	yes	complemented
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₈×C₁₃	—	2	4	no	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	C₄×D₄	1	4	yes	—
170	#1055	—	2	4	no	—
171	#1055	—	4	4	no	—
172	#1055	—	4	2	no	—
173	C₂²×M₁₆	—	13	4	no	—
174	C₂³×C₈	C₂×D₁₃	1	2	yes	—
175	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
176	#436	—	26	2	no	—
177	#435	—	26	4	no	—
178	C₈×D₄	—	26	2	no	—
179	C₈×D₄	Dic₁₃	1	4	yes	—
180	C₈×D₄	Dic₁₃	1	2	yes	—
181	C₈×D₄	Dic₁₃	1	2	yes	—
182	C₂×#108	—	13	1	no	—
183	C₂×#108	—	13	1	no	—
184	C₂×#108	—	13	2	no	—
185	C₂×#108	—	13	4	no	—
186	C₂×#108	—	13	2	no	—
187	C₂×#108	—	26	8	no	—
188	#423	—	13	2	no	—
189	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
190	#407	—	13	4	no	—
191	C₂×C₂²⋊C₈	C₂×D₁₃	1	2	yes	—
192	C₄×M₁₆	—	13	2	no	—
193	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
194	#341	—	13	4	no	—
195	#341	—	13	2	no	—
196	C₂²×C₁₃	—	2	2	no	—
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	4	4	no	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	C₂×#108	1	4	yes	complemented
206	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
207	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
208	C₂²×C₁₃	#554	1	1	yes	characteristic
209	C₄×C₁₃	—	2	2	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	C₂×#108	1	2	yes	complemented
215	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
216	C₄×C₁₃	#520	1	1	yes	characteristic
217	C₄×C₁₃	D₄²	1	1	yes	characteristic
218	C₄×C₁₃	#547	1	1	yes	characteristic
219	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
220	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
221	C₂×M₁₆	—	13	2	no	—
222	C₂×M₁₆	—	13	4	no	—
223	C₂×M₁₆	—	13	2	no	—
224	C₂×M₁₆	—	26	4	no	—
225	C₂×M₁₆	—	26	8	no	—
226	C₂×M₁₆	—	52	4	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	26	4	no	—
230	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
231	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
232	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
233	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
235	C₄×D₄	D₅₂	1	1	yes	characteristic
236	C₄×D₄	D₅₂	1	2	yes	—
237	C₄×D₄	D₅₂	1	1	yes	characteristic
238	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
239	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
240	C₄×D₄	C₂×Dic₁₃	1	1	yes	characteristic
241	C₂×C₄⋊C₄	Dic₂₆	1	1	yes	characteristic
242	C₂×C₂²⋊C₄	Dic₂₆	1	2	yes	—
243	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
244	#108	—	13	4	no	—
245	#108	—	26	8	no	—
246	#108	—	26	4	no	—
247	#108	—	26	2	no	—
248	#108	—	52	2	no	—
249	C₄⋊C₈	—	26	2	no	—
250	C₄⋊C₈	—	26	2	no	—
251	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
252	C₄⋊C₈	C₂×Dic₁₃	1	2	yes	—
253	C₂²⋊C₈	—	26	4	no	—
254	C₂²⋊C₈	—	26	4	no	—
255	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
256	C₂²⋊C₈	C₂×Dic₁₃	1	4	yes	—
257	#97	—	26	2	no	—
258	C₄×C₈	—	26	2	no	—
259	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
260	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
261	C₂×C₁₃	—	2	1	no	—
262	C₂×C₁₃	—	2	1	no	—
263	C₂×C₁₃	—	2	4	no	—
264	C₂×C₁₃	—	4	2	no	—
265	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
267	C₂×C₁₃	#2916	1	1	yes	characteristic
268	C₂⁴	C₂×Dic₂₆	1	2	yes	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	C₄⋊Dic₁₃	1	2	yes	—
271	C₂×D₄	C₄⋊Dic₁₃	1	1	yes	characteristic
272	C₂×D₄	C₄⋊Dic₁₃	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
278	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
279	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₅₂	1	2	yes	—
281	C₂²×C₄	C₂×D₅₂	1	2	yes	—
282	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
284	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
285	M₁₆	—	13	4	no	—
286	M₁₆	—	26	2	no	—
287	M₁₆	—	26	4	no	—
288	M₁₆	—	26	2	no	—
289	M₁₆	—	26	4	no	—
290	M₁₆	—	26	2	no	—
291	M₁₆	—	52	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	2	8	no	—
298	C₂×C₈	—	26	2	no	—
299	C₂×C₈	—	26	2	no	—
300	C₂×C₈	—	26	4	no	—
301	C₂×C₈	—	52	8	no	—
302	C₂×C₈	D₄×D₁₃	1	2	yes	—
303	C₂×C₈	#6129	1	2	yes	—
304	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
305	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
306	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
307	C₄⋊C₄	C₄⋊Dic₁₃	1	2	yes	—
308	C₄⋊C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
309	C₄⋊C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
310	C₂²⋊C₄	C₄⋊Dic₁₃	1	2	yes	—
311	C₂²⋊C₄	C₄⋊Dic₁₃	1	2	yes	—
312	C₂²⋊C₄	C₄⋊Dic₁₃	1	2	yes	—
313	C₂²⋊C₄	C₄⋊Dic₁₃	1	2	yes	—
314	C₄²	C₂×D₅₂	1	1	yes	characteristic
315	C₄²	C₂×D₅₂	1	1	yes	characteristic
316	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
317	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
318	C₁₃	D₄×#108	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
324	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
325	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	#88059	1	4	yes	direct product factor
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
345	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
346	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
348	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
349	C₂×C₄	C₂×#6129	1	1	yes	characteristic
350	C₂×C₄	#88256	1	1	yes	characteristic
351	C₂×C₄	#88257	1	1	yes	characteristic
352	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	2	2	no	—
355	C₈	—	26	4	no	—
356	C₈	—	52	4	no	—
357	C₈	—	52	2	no	—
358	C₈	D₄×Dic₁₃	1	4	yes	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	C₂×#88059	1	4	yes	complemented
369	C₂²	D₄×Dic₂₆	1	1	yes	characteristic
370	C₂²	#11719248	1	1	yes	characteristic
371	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	C₂×#88059	1	2	yes	complemented
378	C₄	D₄×D₅₂	1	1	yes	characteristic
379	C₄	#11719260	1	1	yes	characteristic
380	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
381	C₄	#11719532	1	1	yes	characteristic
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	4	no	—
385	C₂	—	4	2	no	—
386	C₂	D₄×C₄⋊Dic₁₃	1	1	yes	characteristic
387	C₂	C₂²×#88059	1	1	yes	characteristic
388	C₂	#13123447	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₈×D₄×C₁₃	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₈×D₄	D₁₃
hypocenter	C₁₃	D₄×#108
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#88059	C₂	semidirect
3. #13115612	C₂	semidirect
4. #13115043	C₂	semidirect
5. #13115008	C₂	semidirect
6. #13114874	C₂	semidirect
7. C₄×#88059	C₂	semidirect
69. #88059	D₄	direct (N × H)
142. D₄×C₁₃	#108	semidirect
205. C₂²×C₁₃	C₂×#108	semidirect
214. C₄×C₁₃	C₂×#108	semidirect
318. C₁₃	D₄×#108	semidirect
328. D₄	#88059	direct (N × H)
368. C₂²	C₂×#88059	semidirect
377. C₄	C₂×#88059	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6099	2
C₂²×#88059	2
#13115612	2
#13115043	2
#13115008	2
#13114874	2
C₄×#88059	2
C₂×C₈×D₄×C₁₃	2
D₄×#108	13

Subgroups — D4×#88059 #15881172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#88059 #15881172