Subgroups — C₂×#13115612 #15866440

Order 3328.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	2	yes	maximal
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
4	#13115612	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718144	C₂	1	2	yes	maximal
6	C₂²×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×#6099	C₂²	1	2	yes	—
10	C₂²×#6099	C₂²	1	1	yes	characteristic
11	C₂²×#6099	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
16	C₂×#88059	—	2	8	no	—
17	C₂×#88059	C₂²	1	8	yes	—
18	#11718585	—	2	2	no	—
19	#11718585	C₂²	1	4	yes	—
20	C₂×C₄⋊#1055	—	2	1	no	—
21	C₂×C₄⋊#1055	—	2	1	no	—
22	C₄×#6099	—	2	2	no	—
23	C₄×#6099	C₂²	1	4	yes	—
24	C₂×#88043	—	2	1	no	—
25	C₂×C₄×#1055	—	2	1	no	—
26	#11718144	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	—	2	4	no	—
31	C₂²×C₈×C₁₃	—	2	4	no	—
32	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	2	yes	—
41	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
43	C₂×#6099	—	2	1	no	—
44	C₂×#6099	—	2	1	no	—
45	C₂×#6099	—	2	2	no	—
46	C₂×#6099	—	2	2	no	—
47	C₂×#6099	—	2	2	no	—
48	C₂×#6099	—	2	4	no	—
49	C₂×#6099	—	2	4	no	—
50	C₂×#6099	D₄	1	4	yes	—
51	C₂×#6099	Q₈	1	4	yes	—
52	C₂×#6099	C₂³	1	4	yes	—
53	C₂×#6099	C₂³	1	2	yes	—
54	C₂×#6099	C₂³	1	2	yes	—
55	C₂²×#1055	—	2	1	no	—
56	C₂²×#1055	—	2	1	no	—
57	C₂²×#1055	—	2	2	no	—
58	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
59	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
60	#88059	—	2	16	no	—
61	C₄⋊#1055	—	2	4	no	—
62	C₄⋊#1055	—	2	4	no	—
63	#88043	—	2	4	no	—
64	C₄×#1055	—	2	4	no	—
65	C₂×#1950	—	13	1	no	maximal, Sylow
66	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	—	4	2	no	—
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₁₃	#41	1	2	yes	—
85	C₂²×C₄×C₁₃	#41	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₁₃	—	2	8	no	—
88	C₂×C₈×C₁₃	—	2	8	no	—
89	C₂×C₈×C₁₃	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	4	no	—
91	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
92	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
93	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
94	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
95	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
96	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
97	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
98	C₄²×C₁₃	C₂×D₄	1	2	yes	—
99	C₄²×C₁₃	C₂×D₄	1	2	yes	—
100	#6099	—	2	4	no	—
101	#6099	—	2	4	no	—
102	#6099	—	2	2	no	—
103	#6099	—	2	2	no	—
104	#6099	—	2	4	no	—
105	#6099	—	2	4	no	—
106	#6099	—	4	4	no	—
107	#6099	C₂×D₄	1	4	yes	—
108	#6099	C₂×Q₈	1	4	yes	—
109	C₂×#1055	—	2	4	no	—
110	C₂×#1055	—	2	4	no	—
111	C₂×#1055	—	2	2	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	4	no	—
114	C₂×#1055	—	4	4	no	—
115	C₂²×#108	—	13	2	no	—
116	C₂×#423	—	13	1	no	—
117	C₂²×C₄⋊C₈	D₁₃	1	1	yes	characteristic
118	C₂×C₄×M₁₆	—	13	1	no	—
119	#1950	—	13	8	no	—
120	C₂×#341	—	13	2	no	—
121	C₂³×C₁₃	—	2	2	no	—
122	C₂³×C₁₃	—	2	2	no	—
123	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₃	#125	1	2	yes	—
126	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
127	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	4	no	—
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	4	2	no	—
134	C₂×C₄×C₁₃	—	4	2	no	—
135	C₂×C₄×C₁₃	#108	1	4	yes	complemented
136	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
143	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₁₃	#121	1	2	yes	—
147	C₂×C₄×C₁₃	#121	1	2	yes	—
148	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
150	C₂×C₄×C₁₃	#125	1	2	yes	—
151	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
158	C₈×C₁₃	—	2	8	no	—
159	#1055	—	2	4	no	—
160	#1055	—	2	4	no	—
161	#1055	—	4	4	no	—
162	C₂²×M₁₆	—	13	1	no	—
163	C₂²×M₁₆	—	13	1	no	—
164	C₂²×M₁₆	—	13	2	no	—
165	C₂³×C₈	C₂×D₁₃	1	2	yes	—
166	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
167	C₂×#108	—	13	8	no	—
168	C₂×#108	—	26	8	no	—
169	#423	—	13	4	no	—
170	#423	—	26	2	no	—
171	C₂×C₄⋊C₈	—	26	1	no	—
172	C₂×C₄⋊C₈	—	26	1	no	—
173	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
174	C₂×C₄⋊C₈	Dic₁₃	1	4	yes	—
175	C₂×C₄⋊C₈	Dic₁₃	1	2	yes	—
176	C₂×C₄⋊C₈	C₂×D₁₃	1	4	yes	—
177	C₄×M₁₆	—	13	4	no	—
178	C₄×M₁₆	—	26	2	no	—
179	C₂×#97	—	26	1	no	—
180	C₂×C₄×C₈	—	26	1	no	—
181	#341	—	13	8	no	—
182	C₂²×C₁₃	—	2	1	no	—
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	4	no	—
187	C₂²×C₁₃	—	2	4	no	—
188	C₂²×C₁₃	#389	1	2	yes	—
189	C₂²×C₁₃	#389	1	2	yes	—
190	C₂²×C₁₃	C₂×#108	1	2	yes	—
191	C₂²×C₁₃	#430	1	2	yes	—
192	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	#389	1	2	yes	—
199	C₄×C₁₃	#389	1	2	yes	—
200	C₄×C₁₃	C₂×#108	1	4	yes	complemented
201	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
203	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
204	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
206	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
207	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
208	C₂×M₁₆	—	13	4	no	—
209	C₂×M₁₆	—	13	4	no	—
210	C₂×M₁₆	—	13	2	no	—
211	C₂×M₁₆	—	13	2	no	—
212	C₂×M₁₆	—	13	4	no	—
213	C₂×M₁₆	—	26	1	no	—
214	C₂×M₁₆	—	26	1	no	—
215	C₂×M₁₆	—	26	2	no	—
216	C₂×M₁₆	—	26	2	no	—
217	C₂×M₁₆	—	26	2	no	—
218	C₂×M₁₆	—	26	4	no	—
219	C₂×M₁₆	—	26	4	no	—
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	4	no	—
222	C₂²×C₈	—	26	1	no	—
223	C₂²×C₈	—	26	1	no	—
224	C₂²×C₈	—	26	2	no	—
225	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
226	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
227	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
228	C₂×C₄²	Dic₂₆	1	2	yes	—
229	C₂×C₄²	D₅₂	1	2	yes	—
230	C₂×C₄²	D₅₂	1	1	yes	characteristic
231	C₂×C₄²	D₅₂	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
234	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
236	#108	—	26	16	no	—
237	C₄⋊C₈	—	26	4	no	—
238	C₄⋊C₈	—	26	4	no	—
239	C₄⋊C₈	C₂×Dic₁₃	1	8	yes	—
240	C₄⋊C₈	C₂×Dic₁₃	1	8	yes	—
241	#97	—	26	4	no	—
242	C₄×C₈	—	26	4	no	—
243	C₂×C₁₃	—	2	1	no	—
244	C₂×C₁₃	—	2	1	no	—
245	C₂×C₁₃	—	2	2	no	—
246	C₂×C₁₃	#1950	1	4	yes	complemented
247	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
248	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
249	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
250	C₂⁴	C₂×Dic₂₆	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
257	C₂²×C₄	C₄⋊Dic₁₃	1	2	yes	—
258	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
260	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
261	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
262	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
264	C₂²×C₄	D₄×D₁₃	1	2	yes	—
265	C₂²×C₄	#6129	1	2	yes	—
266	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
267	C₂²×C₄	#6131	1	2	yes	—
268	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
271	M₁₆	—	13	4	no	—
272	M₁₆	—	13	4	no	—
273	M₁₆	—	26	4	no	—
274	M₁₆	—	26	4	no	—
275	M₁₆	—	26	2	no	—
276	M₁₆	—	26	2	no	—
277	M₁₆	—	26	4	no	—
278	M₁₆	—	26	4	no	—
279	M₁₆	—	52	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	26	4	no	—
285	C₂×C₈	—	26	4	no	—
286	C₂×C₈	—	26	2	no	—
287	C₂×C₈	—	26	2	no	—
288	C₂×C₈	—	26	4	no	—
289	C₂×C₈	—	52	4	no	—
290	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
291	C₄²	C₄⋊Dic₁₃	1	2	yes	—
292	C₄²	C₄⋊Dic₁₃	1	2	yes	—
293	C₄²	C₄⋊Dic₁₃	1	2	yes	—
294	C₄²	C₄⋊Dic₁₃	1	2	yes	—
295	C₄²	C₂×D₅₂	1	2	yes	—
296	C₄²	C₂×D₅₂	1	2	yes	—
297	C₄²	C₂²×Dic₁₃	1	2	yes	—
298	C₄²	C₂²×Dic₁₃	1	2	yes	—
299	C₁₃	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	#88142	1	2	yes	—
303	C₂³	#88144	1	2	yes	—
304	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
305	C₂³	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
306	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	#88059	1	4	yes	complemented
315	C₂×C₄	#88142	1	2	yes	—
316	C₂×C₄	#88144	1	2	yes	—
317	C₂×C₄	#88149	1	2	yes	—
318	C₂×C₄	#88149	1	2	yes	—
319	C₂×C₄	#88151	1	2	yes	—
320	C₂×C₄	#88151	1	2	yes	—
321	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
322	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
323	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
324	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
325	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
326	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
327	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
328	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
329	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
330	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
331	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
333	C₂×C₄	C₂×#6129	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂×#6131	1	1	yes	characteristic
336	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	26	4	no	—
339	C₈	—	26	4	no	—
340	C₈	—	52	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	#11718646	1	2	yes	—
348	C₂²	#11718646	1	2	yes	—
349	C₂²	C₂×#88059	1	2	yes	—
350	C₂²	#11718786	1	2	yes	—
351	C₂²	C₂×#88142	1	1	yes	characteristic
352	C₂²	C₂×#88144	1	1	yes	characteristic
353	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	#11718646	1	2	yes	—
358	C₄	#11718646	1	2	yes	—
359	C₄	C₂×#88059	1	4	yes	complemented
360	C₄	C₂×#88149	1	1	yes	characteristic
361	C₄	C₂×#88151	1	1	yes	characteristic
362	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
363	C₄	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
364	C₂	—	2	1	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	2	no	—
367	C₂	#13115612	1	4	yes	direct product factor
368	C₂	C₂×#11718646	1	1	yes	characteristic
369	C₂	C₂²×#88059	1	1	yes	characteristic
370	C₂	C₂×#11718786	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₄⋊C₈	C₂
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₁₃
hypocenter	C₁₃	C₂×#1950
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #13115612	C₂	direct (N × H)
135. C₂×C₄×C₁₃	#108	semidirect
200. C₄×C₁₃	C₂×#108	semidirect
246. C₂×C₁₃	#1950	semidirect
299. C₁₃	C₂×#1950	semidirect
314. C₂×C₄	#88059	semidirect
359. C₄	C₂×#88059	semidirect
367. C₂	#13115612	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88059	2
C₂×#11718585	2
C₂×C₄×#6099	2
#13115612	2
C₂×#11718144	2
C₂²×C₁₃×C₄⋊C₈	2
C₂×#1950	13

Subgroups — C2×#13115612 #15866440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13115612 #15866440