Subgroups — C₂×#13112726 #15753079

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718586	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
3	#13112726	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×M₁₆	—	2	1	no	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6099	C₄	1	2	yes	—
8	C₄×C₁₃×M₁₆	—	2	1	no	—
9	C₄×C₁₃×M₁₆	—	2	1	no	—
10	C₄×C₁₃×M₁₆	C₄	1	2	yes	—
11	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₂×C₁₃×#97	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	—	2	1	no	—
14	C₂×C₂²⋊#1055	—	2	1	no	—
15	#11718586	—	2	1	no	—
16	#11718586	—	2	1	no	—
17	#11718586	C₄	1	2	yes	—
18	#11718586	C₂²	1	2	yes	—
19	#11718585	—	2	1	no	—
20	#11718585	—	2	1	no	—
21	#11718585	C₄	1	2	yes	—
22	#11718585	C₂²	1	2	yes	—
23	C₂×C₄⋊#1055	—	2	1	no	—
24	C₂×C₄⋊#1055	—	2	1	no	—
25	C₂×C₄⋊#1055	C₄	1	2	yes	—
26	C₂×C₄×#1055	—	2	1	no	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	Q₈	1	1	yes	characteristic
30	C₂×C₁₃×M₁₆	—	2	8	no	—
31	C₂×C₁₃×M₁₆	—	2	2	no	—
32	C₂×C₁₃×M₁₆	—	2	2	no	—
33	C₂²×C₈×C₁₃	—	2	2	no	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×#6099	—	2	2	no	—
47	C₂×#6099	—	4	4	no	—
48	C₂×#6099	C₂×C₄	1	4	yes	—
49	C₂²×#1055	—	2	2	no	—
50	C₂²×#1055	—	2	2	no	—
51	C₁₃×#97	—	2	2	no	—
52	C₁₃×#97	C₂×C₄	1	4	yes	—
53	C₄×C₈×C₁₃	—	2	2	no	—
54	C₄×C₈×C₁₃	—	2	2	no	—
55	C₂²⋊#1055	—	2	2	no	—
56	C₂²⋊#1055	—	2	2	no	—
57	C₄⋊#1055	—	2	2	no	—
58	C₄⋊#1055	—	2	2	no	—
59	C₄⋊#1055	—	2	2	no	—
60	C₄⋊#1055	—	2	2	no	—
61	C₄⋊#1055	—	2	2	no	—
62	C₄⋊#1055	C₂×C₄	1	4	yes	—
63	C₄×#1055	—	2	2	no	—
64	C₄×#1055	—	2	2	no	—
65	C₂×#1299	—	13	1	no	maximal, Sylow
66	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₃	—	2	2	no	—
68	C₂²×C₄×C₁₃	—	2	2	no	—
69	C₂²×C₄×C₁₃	—	2	4	no	—
70	C₂²×C₄×C₁₃	—	2	4	no	—
71	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²⋊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	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
89	C₁₃×M₁₆	—	2	8	no	—
90	C₁₃×M₁₆	—	2	8	no	—
91	C₂×C₈×C₁₃	—	2	8	no	—
92	C₂×C₈×C₁₃	—	2	4	no	—
93	C₄²×C₁₃	C₄²	1	1	yes	characteristic
94	C₄²×C₁₃	C₄²	1	1	yes	characteristic
95	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
109	#6099	—	4	4	no	—
110	#6099	—	4	4	no	—
111	C₂×#1055	—	2	4	no	—
112	C₂×#1055	—	2	4	no	—
113	C₂×#1055	—	4	4	no	—
114	C₂×#1055	—	4	4	no	—
115	C₂×#431	—	13	1	no	—
116	C₂×#423	—	13	1	no	—
117	C₂×C₄×M₁₆	D₁₃	1	1	yes	characteristic
118	#1299	—	13	4	no	—
119	C₂³×C₁₃	—	2	2	no	—
120	C₂³×C₁₃	—	2	2	no	—
121	C₂³×C₁₃	—	2	2	no	—
122	C₂³×C₁₃	#95	1	1	yes	characteristic
123	C₂³×C₁₃	#95	1	1	yes	characteristic
124	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
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	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	1	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	1	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
148	C₂×C₄×C₁₃	#100	1	2	yes	—
149	C₂×C₄×C₁₃	#101	1	2	yes	—
150	C₂×C₄×C₁₃	#104	1	4	yes	—
151	C₂×C₄×C₁₃	#108	1	4	yes	—
152	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₂²⋊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	C₈×C₁₃	—	2	8	no	—
159	#1055	—	4	4	no	—
160	#1055	—	4	4	no	—
161	C₂²×M₁₆	—	2	1	no	—
162	C₂²×M₁₆	—	13	2	no	—
163	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
164	#431	—	13	2	no	—
165	#431	—	13	2	no	—
166	#431	—	26	1	no	—
167	#431	—	26	1	no	—
168	#423	—	13	2	no	—
169	#423	—	13	2	no	—
170	#423	—	26	1	no	—
171	#423	—	26	1	no	—
172	C₂×C₄⋊C₈	—	13	2	no	—
173	C₂×C₄⋊C₈	—	26	1	no	—
174	C₂×C₄⋊C₈	—	26	1	no	—
175	C₂×C₂²⋊C₈	—	26	1	no	—
176	C₄×M₁₆	—	2	1	no	—
177	C₄×M₁₆	—	2	1	no	—
178	C₄×M₁₆	Dic₁₃	1	2	yes	—
179	C₄×M₁₆	C₂×D₁₃	1	2	yes	—
180	C₂×#97	Dic₁₃	1	2	yes	—
181	C₂×C₄×C₈	—	2	1	no	—
182	C₂×C₄×C₈	—	26	1	no	—
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	—	2	1	no	—
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	4	4	no	—
190	C₂²×C₁₃	#339	1	2	yes	—
191	C₂²×C₁₃	#341	1	2	yes	—
192	C₂²×C₁₃	#343	1	2	yes	—
193	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
194	C₄×C₁₃	—	2	1	no	—
195	C₄×C₁₃	—	2	1	no	—
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	—	2	1	no	—
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	1	no	—
200	C₄×C₁₃	#339	1	2	yes	—
201	C₄×C₁₃	#341	1	2	yes	—
202	C₄×C₁₃	#343	1	2	yes	—
203	C₄×C₁₃	C₂×#100	1	1	yes	characteristic
204	C₄×C₁₃	C₂×#101	1	1	yes	characteristic
205	C₄×C₁₃	C₂×#104	1	2	yes	—
206	C₄×C₁₃	C₂×#108	1	2	yes	—
207	C₂³×C₄	Dic₂₆	1	1	yes	characteristic
208	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
209	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
210	C₂×M₁₆	—	2	8	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	13	4	no	—
214	C₂×M₁₆	—	26	2	no	—
215	C₂×M₁₆	—	52	4	no	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	26	2	no	—
218	C₂²×C₈	—	26	2	no	—
219	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
220	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
221	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
223	C₂×C₄²	D₅₂	1	1	yes	characteristic
224	C₂×C₄²	D₅₂	1	1	yes	characteristic
225	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
226	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
231	C₄⋊C₈	—	13	4	no	—
232	C₄⋊C₈	—	26	2	no	—
233	C₄⋊C₈	—	26	2	no	—
234	C₄⋊C₈	—	26	2	no	—
235	C₄⋊C₈	—	26	2	no	—
236	C₄⋊C₈	—	26	2	no	—
237	C₂²⋊C₈	—	26	2	no	—
238	C₂²⋊C₈	—	26	2	no	—
239	#97	—	2	2	no	—
240	#97	C₂×Dic₁₃	1	4	yes	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	—	2	2	no	—
243	C₄×C₈	—	26	2	no	—
244	C₄×C₈	—	26	2	no	—
245	C₂×C₁₃	—	4	1	no	—
246	C₂×C₁₃	—	4	1	no	—
247	C₂×C₁₃	#1299	1	4	yes	complemented
248	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
249	C₂×C₁₃	C₂×#341	1	1	yes	characteristic
250	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
251	C₂⁴	#6101	1	1	yes	characteristic
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
258	C₂²×C₄	#6101	1	1	yes	characteristic
259	C₂²×C₄	#6101	1	1	yes	characteristic
260	C₂²×C₄	#6101	1	1	yes	characteristic
261	C₂²×C₄	#6101	1	1	yes	characteristic
262	C₂²×C₄	#6101	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
265	C₂²×C₄	#6103	1	1	yes	characteristic
266	C₂²×C₄	#6103	1	1	yes	characteristic
267	C₂²×C₄	#6103	1	1	yes	characteristic
268	C₂²×C₄	#6103	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
274	M₁₆	—	2	8	no	—
275	M₁₆	—	2	8	no	—
276	M₁₆	—	52	4	no	—
277	M₁₆	—	52	4	no	—
278	C₂×C₈	—	2	8	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	26	4	no	—
281	C₂×C₈	—	26	4	no	—
282	C₂×C₈	—	52	4	no	—
283	C₂×C₈	—	52	4	no	—
284	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
285	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
286	C₄²	#6101	1	1	yes	characteristic
287	C₄²	#6101	1	1	yes	characteristic
288	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
289	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
290	C₄²	#6103	1	1	yes	characteristic
291	C₄²	#6103	1	1	yes	characteristic
292	C₄²	#6103	1	1	yes	characteristic
293	C₄²	#6103	1	1	yes	characteristic
294	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
295	C₄²	C₂²⋊Dic₁₃	1	1	yes	characteristic
296	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
297	C₄²	C₂×D₅₂	1	1	yes	characteristic
298	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
299	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
300	C₁₃	C₂×#1299	1	1	yes	characteristic, complemented, Sylow
301	C₂³	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	#88071	1	1	yes	characteristic
305	C₂³	#88071	1	1	yes	characteristic
306	C₂³	C₂×#6101	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	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	#88045	1	4	yes	—
325	C₂×C₄	#88062	1	4	yes	—
326	C₂×C₄	#88063	1	2	yes	—
327	C₂×C₄	#88064	1	2	yes	—
328	C₂×C₄	#88071	1	1	yes	characteristic
329	C₂×C₄	#88071	1	1	yes	characteristic
330	C₂×C₄	#88071	1	1	yes	characteristic
331	C₂×C₄	#88071	1	1	yes	characteristic
332	C₂×C₄	#88071	1	1	yes	characteristic
333	C₂×C₄	#88071	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂×#6101	1	1	yes	characteristic
336	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
337	C₂×C₄	C₂×#6103	1	1	yes	characteristic
338	C₂×C₄	C₂×#6103	1	1	yes	characteristic
339	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
340	C₈	—	2	8	no	—
341	C₈	—	52	4	no	—
342	C₈	—	52	4	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	4	4	no	—
350	C₂²	#11718115	1	2	yes	—
351	C₂²	#11718146	1	2	yes	—
352	C₂²	#11718150	1	2	yes	—
353	C₂²	C₂×#88071	1	1	yes	characteristic
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	#11718115	1	2	yes	—
361	C₄	#11718146	1	2	yes	—
362	C₄	#11718150	1	2	yes	—
363	C₄	C₂×#88045	1	2	yes	—
364	C₄	C₂×#88062	1	2	yes	—
365	C₄	C₂×#88063	1	1	yes	characteristic
366	C₄	C₂×#88064	1	1	yes	characteristic
367	C₂	—	4	1	no	—
368	C₂	—	4	1	no	—
369	C₂	#13112726	1	4	yes	direct product factor
370	C₂	C₂×#11718115	1	1	yes	characteristic
371	C₂	C₂×#11718150	1	1	yes	characteristic
372	C₂	C₂×#11718146	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	#6103
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×M₁₆	C₂
socle	C₂³×C₁₃	#95
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₂×#1299
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13112726	C₂	direct (N × H)
247. C₂×C₁₃	#1299	semidirect
300. C₁₃	C₂×#1299	semidirect
369. C₂	#13112726	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×#11718586	2
C₂×#11718585	2
#13112726	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#1299	13

Subgroups — C2×#13112726 #15753079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112726 #15753079