Subgroups — C₂²×#11718672 #16726758

Order 3328.

3350 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6099	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718672	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₄	1	12	yes	—
13	C₂×C₄×D₄×C₁₃	C₂²	1	12	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
16	C₂²×C₁₃×C₂²⋊C₄	C₄	1	1	yes	characteristic
17	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×#6099	—	2	8	no	—
19	C₂²×#6099	C₂²	1	12	yes	complemented
20	C₂³×#1055	—	2	8	no	—
21	C₂³×#1055	C₂²	1	1	yes	characteristic
22	C₂³×#1055	C₂²	1	1	yes	characteristic
23	C₂³×#1055	C₂²	1	1	yes	characteristic
24	C₂³×#1055	C₂²	1	1	yes	characteristic
25	C₂³×#1055	C₂²	1	12	yes	complemented
26	C₂×C₂²⋊#1055	C₂²	1	12	yes	complemented
27	C₂×C₂²⋊#1055	C₂²	1	12	yes	complemented
28	#11718672	C₂²	1	64	yes	direct product factor
29	C₂×C₄⋊#1055	C₂²	1	12	yes	complemented
30	C₂×#88043	C₂²	1	12	yes	complemented
31	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₁₃	—	2	8	no	—
34	C₂²×D₄×C₁₃	C₂×C₄	1	12	yes	—
35	C₂³×C₄×C₁₃	—	2	4	no	—
36	C₂³×C₄×C₁₃	—	2	4	no	—
37	C₂³×C₄×C₁₃	—	2	4	no	—
38	C₂³×C₄×C₁₃	—	2	4	no	—
39	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	C₂×C₄	1	6	yes	—
44	C₂³×C₄×C₁₃	C₂×C₄	1	6	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₄×D₄×C₁₃	C₂×C₄	1	48	yes	—
49	C₄×D₄×C₁₃	C₂³	1	16	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	12	yes	—
51	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	12	yes	—
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	12	yes	—
53	C₂×C₄²×C₁₃	C₂×C₄	1	6	yes	—
54	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
55	C₂×#6099	—	2	48	no	—
56	C₂×#6099	C₂³	1	16	yes	complemented
57	C₂²×#1055	—	2	4	no	—
58	C₂²×#1055	—	2	4	no	—
59	C₂²×#1055	—	2	4	no	—
60	C₂²×#1055	—	2	48	no	—
61	C₂²×#1055	D₄	1	8	yes	complemented
62	C₂²×#1055	C₂³	1	6	yes	—
63	C₂²×#1055	C₂³	1	6	yes	—
64	C₂²×#1055	C₂³	1	6	yes	—
65	C₂²×#1055	C₂³	1	6	yes	—
66	C₂²×#1055	C₂³	1	16	yes	complemented
67	C₂²⋊#1055	C₂³	1	16	yes	complemented
68	C₂²⋊#1055	C₂³	1	16	yes	complemented
69	C₄⋊#1055	C₂³	1	16	yes	complemented
70	#88043	C₂³	1	16	yes	complemented
71	C₂²×#435	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	4	no	—
73	C₂⁴×C₁₃	—	2	4	no	—
74	C₂⁴×C₁₃	—	2	4	no	—
75	C₂⁴×C₁₃	—	2	4	no	—
76	C₂⁴×C₁₃	—	2	4	no	—
77	C₂⁴×C₁₃	M₁₆	1	8	yes	complemented
78	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
79	C₂⁴×C₁₃	C₂²×C₄	1	6	yes	—
80	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×D₄×C₁₃	—	2	48	no	—
82	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	4	no	—
85	C₂²×C₄×C₁₃	—	2	4	no	—
86	C₂²×C₄×C₁₃	—	2	4	no	—
87	C₂²×C₄×C₁₃	—	2	24	no	—
88	C₂²×C₄×C₁₃	—	2	24	no	—
89	C₂²×C₄×C₁₃	—	2	12	no	—
90	C₂²×C₄×C₁₃	—	2	12	no	—
91	C₂²×C₄×C₁₃	—	2	12	no	—
92	C₂²×C₄×C₁₃	—	2	12	no	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃	#41	1	4	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
105	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	—
106	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
107	C₁₃×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
108	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
109	C₄²×C₁₃	C₂⁴	1	4	yes	—
110	#6099	—	2	32	no	—
111	C₂×#1055	—	2	12	no	—
112	C₂×#1055	—	2	12	no	—
113	C₂×#1055	—	2	12	no	—
114	C₂×#1055	—	2	32	no	—
115	C₂×#1055	C₂×D₄	1	24	yes	complemented
116	C₂×#1055	C₂⁴	1	4	yes	—
117	C₂×#1055	C₂⁴	1	4	yes	—
118	C₂×#1055	C₂⁴	1	4	yes	—
119	C₂×#1055	C₂⁴	1	4	yes	—
120	C₂³×M₁₆	—	13	1	no	—
121	C₂⁴×C₈	—	13	1	no	—
122	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic
123	C₂×#435	—	13	24	no	—
124	C₂²×C₄⋊C₈	—	13	1	no	—
125	C₂²×C₂²⋊C₈	—	13	1	no	—
126	C₂²×C₂²⋊C₈	—	13	1	no	—
127	C₂²×#97	—	13	1	no	—
128	C₂³×C₁₃	—	2	12	no	—
129	C₂³×C₁₃	—	2	12	no	—
130	C₂³×C₁₃	—	2	32	no	—
131	C₂³×C₁₃	—	2	12	no	—
132	C₂³×C₁₃	—	2	12	no	—
133	C₂³×C₁₃	—	2	12	no	—
134	C₂³×C₁₃	—	4	16	no	—
135	C₂³×C₁₃	C₄×D₄	1	4	yes	—
136	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
137	C₂³×C₁₃	C₂×M₁₆	1	24	yes	complemented
138	C₂³×C₁₃	#131	1	4	yes	—
139	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
140	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
141	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
142	D₄×C₁₃	—	2	32	no	—
143	C₂×C₄×C₁₃	—	2	12	no	—
144	C₂×C₄×C₁₃	—	2	12	no	—
145	C₂×C₄×C₁₃	—	2	12	no	—
146	C₂×C₄×C₁₃	—	2	12	no	—
147	C₂×C₄×C₁₃	—	2	24	no	—
148	C₂×C₄×C₁₃	—	2	24	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	—	2	4	no	—
152	C₂×C₄×C₁₃	—	2	4	no	—
153	C₂×C₄×C₁₃	C₄×D₄	1	12	yes	—
154	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
155	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
156	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
157	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
158	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
159	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
161	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
162	#1055	—	2	4	no	—
163	#1055	—	2	4	no	—
164	#1055	—	2	4	no	—
165	#1055	C₂²×D₄	1	8	yes	complemented
166	C₂³×D₄	Dic₁₃	1	1	yes	characteristic
167	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
168	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
169	C₂²×M₁₆	—	13	12	no	—
170	C₂²×M₁₆	—	26	8	no	—
171	C₂³×C₈	—	13	1	no	—
172	C₂³×C₈	—	13	12	no	—
173	C₂³×C₈	—	13	1	no	—
174	C₂³×C₈	—	13	1	no	—
175	C₂³×C₈	—	13	1	no	—
176	C₂³×C₈	—	26	8	no	—
177	C₂×C₄×D₄	Dic₁₃	1	12	yes	—
178	C₂×C₄×D₄	C₂×D₁₃	1	12	yes	—
179	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
180	C₂²×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
181	C₂²×C₂²⋊C₄	Dic₁₃	1	1	yes	characteristic
182	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
183	#435	—	13	64	no	—
184	C₂×C₄⋊C₈	—	13	12	no	—
185	C₂×C₂²⋊C₈	—	13	12	no	—
186	C₂×C₂²⋊C₈	—	13	12	no	—
187	C₂×#97	—	13	12	no	—
188	C₂²×C₁₃	—	2	4	no	—
189	C₂²×C₁₃	—	2	48	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	2	4	no	—
193	C₂²×C₁₃	—	2	4	no	—
194	C₂²×C₁₃	—	4	24	no	—
195	C₂²×C₁₃	#435	1	16	yes	complemented
196	C₂²×C₁₃	C₂×C₄×D₄	1	6	yes	—
197	C₂²×C₁₃	C₂²×M₁₆	1	6	yes	—
198	C₂²×C₁₃	C₂²×M₁₆	1	8	yes	complemented
199	C₂²×C₁₃	C₂×#131	1	6	yes	—
200	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
201	C₄×C₁₃	—	2	4	no	—
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	C₂×C₄×D₄	1	6	yes	—
206	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
207	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
208	C₂⁵	C₂×Dic₁₃	1	1	yes	characteristic
209	C₂⁵	C₂×Dic₁₃	1	1	yes	characteristic
210	C₂²×D₄	—	2	8	no	—
211	C₂²×D₄	C₂×Dic₁₃	1	12	yes	—
212	C₂³×C₄	—	2	4	no	—
213	C₂³×C₄	—	2	4	no	—
214	C₂³×C₄	—	2	4	no	—
215	C₂³×C₄	—	2	4	no	—
216	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
218	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
219	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
220	C₂³×C₄	C₂×Dic₁₃	1	6	yes	—
221	C₂³×C₄	C₂×Dic₁₃	1	6	yes	—
222	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
223	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
224	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
225	C₂×M₁₆	—	13	16	no	—
226	C₂×M₁₆	—	26	48	no	—
227	C₂²×C₈	—	13	8	no	—
228	C₂²×C₈	—	13	6	no	—
229	C₂²×C₈	—	13	6	no	—
230	C₂²×C₈	—	13	16	no	—
231	C₂²×C₈	—	13	6	no	—
232	C₂²×C₈	—	13	6	no	—
233	C₂²×C₈	—	26	48	no	—
234	C₂²×C₈	—	26	4	no	—
235	C₂²×C₈	—	26	4	no	—
236	C₂²×C₈	—	26	4	no	—
237	C₄×D₄	C₂×Dic₁₃	1	48	yes	—
238	C₄×D₄	C₂²×D₁₃	1	16	yes	—
239	C₂×C₄⋊C₄	C₂×Dic₁₃	1	12	yes	—
240	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	12	yes	—
241	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	12	yes	—
242	C₂×C₄²	C₂×Dic₁₃	1	6	yes	—
243	C₂×C₄²	C₂²×D₁₃	1	6	yes	—
244	C₄⋊C₈	—	13	16	no	—
245	C₂²⋊C₈	—	13	16	no	—
246	C₂²⋊C₈	—	13	16	no	—
247	#97	—	13	16	no	—
248	C₂×C₁₃	—	2	8	no	—
249	C₂×C₁₃	—	4	4	no	—
250	C₂×C₁₃	C₂×#435	1	12	yes	complemented
251	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
252	C₂×C₁₃	C₂³×M₁₆	1	1	yes	characteristic
253	C₂×C₁₃	C₂²×#131	1	1	yes	characteristic
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	2	4	no	—
259	C₂⁴	#6099	1	8	yes	complemented
260	C₂⁴	C₂²×Dic₁₃	1	6	yes	—
261	C₂⁴	C₂²×Dic₁₃	1	6	yes	—
262	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
263	C₂×D₄	—	2	48	no	—
264	C₂×D₄	C₂²×Dic₁₃	1	16	yes	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	24	no	—
270	C₂²×C₄	—	2	24	no	—
271	C₂²×C₄	—	2	12	no	—
272	C₂²×C₄	—	2	12	no	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	12	no	—
275	C₂²×C₄	D₄×D₁₃	1	4	yes	—
276	C₂²×C₄	#6129	1	4	yes	—
277	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
278	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
279	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
280	C₂²×C₄	C₂²×Dic₁₃	1	6	yes	—
281	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
282	C₂²×C₄	C₂²×Dic₁₃	1	12	yes	—
283	C₂²×C₄	C₂²×Dic₁₃	1	3	yes	—
284	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
285	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
286	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
287	M₁₆	—	26	32	no	—
288	C₂×C₈	—	13	24	no	—
289	C₂×C₈	—	13	4	no	—
290	C₂×C₈	—	13	4	no	—
291	C₂×C₈	—	13	4	no	—
292	C₂×C₈	—	13	4	no	—
293	C₂×C₈	—	26	32	no	—
294	C₂×C₈	—	26	12	no	—
295	C₂×C₈	—	26	12	no	—
296	C₂×C₈	—	26	12	no	—
297	C₄⋊C₄	C₂²×Dic₁₃	1	16	yes	—
298	C₂²⋊C₄	C₂²×Dic₁₃	1	16	yes	—
299	C₂²⋊C₄	C₂²×Dic₁₃	1	16	yes	—
300	C₄²	C₂²×Dic₁₃	1	12	yes	—
301	C₄²	C₂³×D₁₃	1	4	yes	—
302	C₁₃	C₂²×#435	1	1	yes	characteristic, complemented, Sylow
303	C₂³	—	2	32	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	2	12	no	—
307	C₂³	—	2	12	no	—
308	C₂³	—	2	12	no	—
309	C₂³	—	4	16	no	—
310	C₂³	C₂×#6099	1	4	yes	—
311	C₂³	C₂×#6099	1	24	yes	complemented
312	C₂³	D₄×Dic₁₃	1	4	yes	—
313	C₂³	#88202	1	4	yes	—
314	C₂³	C₂³×Dic₁₃	1	4	yes	—
315	C₂³	C₂³×Dic₁₃	1	4	yes	—
316	C₂³	C₂³×Dic₁₃	1	3	yes	—
317	D₄	—	2	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	12	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	24	no	—
323	C₂×C₄	—	2	24	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	D₄×Dic₁₃	1	12	yes	—
329	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
330	C₂×C₄	C₂×#6129	1	6	yes	—
331	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
332	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
333	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
334	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
335	C₂×C₄	C₂³×Dic₁₃	1	3	yes	—
336	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
337	C₈	—	13	8	no	—
338	C₈	—	26	4	no	—
339	C₈	—	26	4	no	—
340	C₈	—	26	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	24	no	—
348	C₂²	#11718672	1	16	yes	direct product factor
349	C₂²	C₂²×#6099	1	6	yes	—
350	C₂²	C₂²×#6099	1	8	yes	complemented
351	C₂²	C₂×D₄×Dic₁₃	1	6	yes	—
352	C₂²	C₂×#88202	1	6	yes	—
353	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	4	no	—
358	C₄	C₂×D₄×Dic₁₃	1	6	yes	—
359	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
360	C₄	C₂²×#6129	1	1	yes	characteristic
361	C₂	—	2	8	no	—
362	C₂	—	4	4	no	—
363	C₂	C₂×#11718672	1	12	yes	direct product factor
364	C₂	C₂²×D₄×Dic₁₃	1	1	yes	characteristic
365	C₂	C₂³×#6099	1	1	yes	characteristic
366	C₂	C₂²×#88202	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂²×C₄
prime radical	C₂³×D₄×C₁₃	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×#435
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6099	C₂	semidirect
2. C₂⁴×#1055	C₂	semidirect
3. C₂×#11718672	C₂	direct (N × H)
4. C₂²×C₄⋊#1055	C₂	semidirect
5. C₂²×C₂²⋊#1055	C₂	semidirect
6. C₂²×C₂²⋊#1055	C₂	semidirect
7. C₂²×#88043	C₂	semidirect
19. C₂²×#6099	C₂²	semidirect
25. C₂³×#1055	C₂²	semidirect
26. C₂×C₂²⋊#1055	C₂²	semidirect
27. C₂×C₂²⋊#1055	C₂²	semidirect
28. #11718672	C₂²	direct (N × H)
29. C₂×C₄⋊#1055	C₂²	semidirect
30. C₂×#88043	C₂²	semidirect
56. C₂×#6099	C₂³	semidirect
61. C₂²×#1055	D₄	semidirect
66. C₂²×#1055	C₂³	semidirect
67. C₂²⋊#1055	C₂³	semidirect
68. C₂²⋊#1055	C₂³	semidirect
69. C₄⋊#1055	C₂³	semidirect
70. #88043	C₂³	semidirect
77. C₂⁴×C₁₃	M₁₆	semidirect
115. C₂×#1055	C₂×D₄	semidirect
137. C₂³×C₁₃	C₂×M₁₆	semidirect
165. #1055	C₂²×D₄	semidirect
195. C₂²×C₁₃	#435	semidirect
198. C₂²×C₁₃	C₂²×M₁₆	semidirect
250. C₂×C₁₃	C₂×#435	semidirect
259. C₂⁴	#6099	semidirect
302. C₁₃	C₂²×#435	semidirect
311. C₂³	C₂×#6099	semidirect
348. C₂²	#11718672	direct (N × H)
350. C₂²	C₂²×#6099	semidirect
363. C₂	C₂×#11718672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#6099	2
C₂⁴×#1055	2
C₂×#11718672	2
C₂²×C₄⋊#1055	2
C₂²×C₂²⋊#1055	2
C₂²×#88043	2
C₂²×C₄×D₄×C₁₃	2
C₂²×#435	13

Subgroups — C22×#11718672 #16726758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718672 #16726758