Subgroups — C₂×D₄×#6099 #16726821

Order 3328.

3218 conjugacy classes of subgroups.

The subgroup lattice has 530 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	2	yes	maximal, complemented
2	D₄×#6099	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718673	C₂	1	2	yes	maximal, complemented
4	C₂×#11718672	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×#1055	C₂	1	2	yes	maximal, complemented
6	C₂×#11718585	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718868	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃	C₄	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₄	1	8	yes	—
15	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×#6099	—	2	16	no	—
24	C₂²×#6099	C₂²	1	2	yes	—
25	C₂²×#6099	C₂²	1	1	yes	characteristic
26	C₂²×#6099	C₂²	1	1	yes	characteristic
27	C₂²×#6099	C₂²	1	4	yes	complemented
28	C₂²×#6099	C₂²	1	16	yes	complemented
29	C₂³×#1055	C₂²	1	4	yes	complemented
30	#11718868	C₂²	1	16	yes	complemented
31	C₂×C₂²⋊#1055	C₂²	1	4	yes	complemented
32	C₂×C₂²⋊#1055	C₂²	1	4	yes	complemented
33	#11718673	C₂²	1	16	yes	complemented
34	#11718672	C₂²	1	32	yes	complemented
35	D₄×#1055	C₂²	1	16	yes	complemented
36	#11718585	C₂²	1	8	yes	complemented
37	C₂×C₄⋊#1055	C₂²	1	2	yes	complemented
38	C₂×C₄⋊#1055	C₂²	1	2	yes	complemented
39	C₄×#6099	C₂²	1	8	yes	complemented
40	C₂×#88043	C₂²	1	2	yes	complemented
41	C₂×C₄×#1055	C₂²	1	2	yes	complemented
42	C₂⁵×C₁₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	8	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
46	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	—	2	8	no	—
49	C₂³×C₄×C₁₃	—	2	8	no	—
50	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
54	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
61	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
62	C₄×D₄×C₁₃	C₂×C₄	1	16	yes	—
63	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
64	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
66	C₄×D₄×C₁₃	C₂³	1	4	yes	—
67	C₄×D₄×C₁₃	C₂³	1	8	yes	—
68	C₄×D₄×C₁₃	C₂³	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	—
78	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
84	C₂×#6099	—	2	8	no	—
85	C₂×#6099	—	2	4	no	—
86	C₂×#6099	—	2	64	no	—
87	C₂×#6099	—	2	16	no	—
88	C₂×#6099	D₄	1	8	yes	direct product factor
89	C₂×#6099	C₂³	1	8	yes	—
90	C₂×#6099	C₂³	1	4	yes	—
91	C₂×#6099	C₂³	1	4	yes	—
92	C₂×#6099	C₂³	1	16	yes	complemented
93	C₂²×#1055	—	2	16	no	—
94	C₂²×#1055	C₂³	1	4	yes	—
95	C₂²×#1055	C₂³	1	2	yes	—
96	C₂²×#1055	C₂³	1	2	yes	—
97	C₂²×#1055	C₂³	1	16	yes	complemented
98	C₂²⋊#1055	C₂³	1	16	yes	complemented
99	C₂²⋊#1055	C₂³	1	16	yes	complemented
100	C₄⋊#1055	C₂³	1	8	yes	complemented
101	C₄⋊#1055	C₂³	1	8	yes	complemented
102	#88043	C₂³	1	8	yes	complemented
103	C₄×#1055	C₂³	1	8	yes	complemented
104	C₂×D₄×M₁₆	—	13	1	no	maximal, Sylow
105	C₂⁴×C₁₃	—	2	8	no	—
106	C₂⁴×C₁₃	—	2	8	no	—
107	C₂⁴×C₁₃	—	4	4	no	—
108	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
110	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	32	no	—
114	C₂×D₄×C₁₃	—	2	4	no	—
115	C₂×D₄×C₁₃	M₁₆	1	8	yes	complemented
116	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
118	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	8	no	—
121	C₂²×C₄×C₁₃	—	2	32	no	—
122	C₂²×C₄×C₁₃	—	2	8	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	16	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	16	no	—
130	C₂²×C₄×C₁₃	—	4	2	no	—
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₁₃	#41	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×C₄⋊C₄	C₂²×C₄	1	8	yes	—
153	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
154	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
155	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
156	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
157	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
158	C₁₃×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
159	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
161	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
163	C₄²×C₁₃	C₂⁴	1	2	yes	—
164	C₄²×C₁₃	C₂⁴	1	2	yes	—
165	#6099	—	2	16	no	—
166	#6099	—	2	8	no	—
167	#6099	—	2	32	no	—
168	#6099	C₂×D₄	1	16	yes	direct product factor
169	C₂×#1055	—	2	8	no	—
170	C₂×#1055	—	2	4	no	—
171	C₂×#1055	—	2	32	no	—
172	C₂×#1055	C₂×D₄	1	8	yes	complemented
173	C₂×#1055	C₂⁴	1	4	yes	—
174	C₂×#1055	C₂⁴	1	8	yes	—
175	C₂×#1055	C₂⁴	1	4	yes	—
176	C₂³×M₁₆	—	13	2	no	—
177	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic
178	D₄×M₁₆	—	13	16	no	—
179	C₂×#436	—	13	2	no	—
180	C₂×#435	—	13	4	no	—
181	C₂×C₈×D₄	—	13	2	no	—
182	C₂×#423	—	13	1	no	—
183	C₂×#407	—	13	2	no	—
184	C₂×C₄×M₁₆	—	13	1	no	—
185	C₂³×C₁₃	—	2	4	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	4	no	—
189	C₂³×C₁₃	—	2	16	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	4	no	—
192	C₂³×C₁₃	—	2	16	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	4	8	no	—
195	C₂³×C₁₃	—	4	32	no	—
196	C₂³×C₁₃	C₄×D₄	1	4	yes	—
197	C₂³×C₁₃	C₂×M₁₆	1	8	yes	complemented
198	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
200	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
201	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
202	D₄×C₁₃	—	2	16	no	—
203	D₄×C₁₃	—	2	8	no	—
204	D₄×C₁₃	C₂×M₁₆	1	16	yes	complemented
205	C₂×C₄×C₁₃	—	2	16	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	8	no	—
212	C₂×C₄×C₁₃	—	2	16	no	—
213	C₂×C₄×C₁₃	—	2	16	no	—
214	C₂×C₄×C₁₃	—	2	8	no	—
215	C₂×C₄×C₁₃	—	2	8	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	C₄×D₄	1	8	yes	—
222	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
223	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	complemented
224	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
225	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
226	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
227	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
228	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
230	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
235	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
236	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
237	#1055	—	2	8	no	—
238	#1055	—	2	4	no	—
239	#1055	C₂²×D₄	1	8	yes	complemented
240	C₂³×D₄	Dic₁₃	1	1	yes	characteristic
241	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
242	C₂²×M₁₆	—	13	1	no	—
243	C₂²×M₁₆	—	13	1	no	—
244	C₂²×M₁₆	—	13	2	no	—
245	C₂²×M₁₆	—	13	4	no	—
246	C₂²×M₁₆	—	13	16	no	—
247	C₂²×M₁₆	—	26	16	no	—
248	C₂³×C₈	—	13	4	no	—
249	C₂×C₄×D₄	Dic₁₃	1	2	yes	—
250	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
251	C₂×C₄×D₄	Dic₁₃	1	8	yes	—
252	C₂×C₄×D₄	Dic₁₃	1	1	yes	characteristic
253	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	—
255	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂×D₁₃	1	8	yes	—
257	C₂²×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
258	C₂²×C₂²⋊C₄	Dic₁₃	1	2	yes	—
259	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
260	#436	—	13	16	no	—
261	#435	—	13	32	no	—
262	C₈×D₄	—	13	16	no	—
263	#423	—	13	8	no	—
264	C₂×C₄⋊C₈	—	13	2	no	—
265	C₂×C₄⋊C₈	—	13	2	no	—
266	#407	—	13	16	no	—
267	C₂×C₂²⋊C₈	—	13	4	no	—
268	C₂×C₂²⋊C₈	—	13	4	no	—
269	C₄×M₁₆	—	13	8	no	—
270	C₂×#97	—	13	2	no	—
271	C₂×C₄×C₈	—	13	2	no	—
272	C₂²×C₁₃	—	2	4	no	—
273	C₂²×C₁₃	—	2	8	no	—
274	C₂²×C₁₃	—	2	16	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	4	no	—
278	C₂²×C₁₃	—	2	4	no	—
279	C₂²×C₁₃	—	2	4	no	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	4	32	no	—
282	C₂²×C₁₃	—	4	8	no	—
283	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
284	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
285	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
286	C₂²×C₁₃	C₂²×M₁₆	1	8	yes	complemented
287	C₂²×C₁₃	#568	1	2	yes	—
288	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
289	C₄×C₁₃	—	2	4	no	—
290	C₄×C₁₃	—	2	4	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
295	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
296	C₄×C₁₃	C₂²×M₁₆	1	4	yes	complemented
297	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
299	C₂⁵	C₂×Dic₁₃	1	2	yes	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
302	C₂²×D₄	C₂×Dic₁₃	1	8	yes	—
303	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
304	C₂²×D₄	C₂×Dic₁₃	1	1	yes	characteristic
305	C₂³×C₄	—	2	8	no	—
306	C₂³×C₄	—	2	8	no	—
307	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
308	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
309	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
310	C₂³×C₄	C₂×Dic₁₃	1	8	yes	—
311	C₂³×C₄	C₂×Dic₁₃	1	2	yes	—
312	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
313	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
314	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
315	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
316	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×M₁₆	—	13	8	no	—
318	C₂×M₁₆	—	13	4	no	—
319	C₂×M₁₆	—	13	8	no	—
320	C₂×M₁₆	—	13	16	no	—
321	C₂×M₁₆	—	13	4	no	—
322	C₂×M₁₆	—	26	16	no	—
323	C₂×M₁₆	—	26	64	no	—
324	C₂×M₁₆	—	26	8	no	—
325	C₂×M₁₆	—	26	4	no	—
326	C₂²×C₈	—	13	2	no	—
327	C₂²×C₈	—	13	16	no	—
328	C₂²×C₈	—	13	4	no	—
329	C₂²×C₈	—	13	2	no	—
330	C₂²×C₈	—	26	16	no	—
331	C₄×D₄	C₂×Dic₁₃	1	8	yes	—
332	C₄×D₄	C₂×Dic₁₃	1	4	yes	—
333	C₄×D₄	C₂×Dic₁₃	1	16	yes	—
334	C₄×D₄	C₂×Dic₁₃	1	8	yes	—
335	C₄×D₄	C₂×Dic₁₃	1	4	yes	—
336	C₄×D₄	C₂×Dic₁₃	1	8	yes	—
337	C₄×D₄	C₂²×D₁₃	1	4	yes	—
338	C₄×D₄	C₂²×D₁₃	1	8	yes	—
339	C₄×D₄	C₂²×D₁₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
341	C₂×C₄⋊C₄	C₂×Dic₁₃	1	8	yes	—
342	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
345	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
347	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
348	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	16	yes	—
349	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
350	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
351	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
352	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
355	C₄⋊C₈	—	13	8	no	—
356	C₄⋊C₈	—	13	8	no	—
357	C₂²⋊C₈	—	13	16	no	—
358	C₂²⋊C₈	—	13	16	no	—
359	#97	—	13	8	no	—
360	C₄×C₈	—	13	8	no	—
361	C₂×C₁₃	—	2	4	no	—
362	C₂×C₁₃	—	2	8	no	—
363	C₂×C₁₃	—	4	4	no	—
364	C₂×C₁₃	D₄×M₁₆	1	4	yes	complemented
365	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
366	C₂×C₁₃	C₂³×M₁₆	1	1	yes	characteristic
367	C₂×C₁₃	C₂×#568	1	1	yes	characteristic
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	—	4	4	no	—
371	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
372	C₂⁴	C₂²×Dic₁₃	1	8	yes	—
373	C₂⁴	C₂²×Dic₁₃	1	2	yes	—
374	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	32	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	#6099	1	8	yes	direct product factor
379	C₂×D₄	C₂²×Dic₁₃	1	8	yes	—
380	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
381	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	32	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	16	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	16	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	D₄×D₁₃	1	4	yes	—
395	C₂²×C₄	#6129	1	4	yes	—
396	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
400	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
401	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
402	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
403	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
404	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
405	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
406	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
407	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
408	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
410	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
411	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
412	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
413	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
414	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
415	M₁₆	—	13	16	no	—
416	M₁₆	—	26	32	no	—
417	M₁₆	—	26	16	no	—
418	M₁₆	—	26	8	no	—
419	C₂×C₈	—	13	8	no	—
420	C₂×C₈	—	13	4	no	—
421	C₂×C₈	—	13	4	no	—
422	C₂×C₈	—	13	8	no	—
423	C₂×C₈	—	26	32	no	—
424	C₂×C₈	—	26	8	no	—
425	C₂×C₈	—	26	4	no	—
426	C₄⋊C₄	C₂²×Dic₁₃	1	8	yes	—
427	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
428	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
429	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
430	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
431	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
432	C₂²⋊C₄	C₂²×Dic₁₃	1	8	yes	—
433	C₄²	C₂²×Dic₁₃	1	4	yes	—
434	C₄²	C₂²×Dic₁₃	1	2	yes	—
435	C₄²	C₂²×Dic₁₃	1	4	yes	—
436	C₄²	C₂²×Dic₁₃	1	2	yes	—
437	C₄²	C₂³×D₁₃	1	2	yes	—
438	C₄²	C₂³×D₁₃	1	2	yes	—
439	C₁₃	C₂×D₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
440	C₂³	—	2	2	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	4	no	—
445	C₂³	—	2	16	no	—
446	C₂³	—	2	16	no	—
447	C₂³	—	2	4	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	4	8	no	—
450	C₂³	—	4	32	no	—
451	C₂³	C₂×#6099	1	8	yes	complemented
452	C₂³	D₄×Dic₁₃	1	4	yes	—
453	C₂³	C₂³×Dic₁₃	1	4	yes	—
454	C₂³	C₂³×Dic₁₃	1	4	yes	—
455	C₂³	C₂³×Dic₁₃	1	2	yes	—
456	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
457	D₄	—	2	16	no	—
458	D₄	—	2	8	no	—
459	D₄	C₂×#6099	1	16	yes	direct product factor
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	16	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	16	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	C₂×#6099	1	4	yes	complemented
477	C₂×C₄	D₄×Dic₁₃	1	8	yes	—
478	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
479	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
480	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
481	C₂×C₄	C₂×#6129	1	2	yes	—
482	C₂×C₄	C₂×#6129	1	4	yes	—
483	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
484	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
485	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
486	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
487	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
488	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
489	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
490	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
491	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
492	C₈	—	13	8	no	—
493	C₈	—	26	8	no	—
494	C₈	—	26	4	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	8	no	—
500	C₂²	—	2	16	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	32	no	—
505	C₂²	—	4	8	no	—
506	C₂²	C₂²×#6099	1	2	yes	—
507	C₂²	C₂²×#6099	1	8	yes	complemented
508	C₂²	C₂×D₄×Dic₁₃	1	4	yes	—
509	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
510	C₂²	#11719524	1	2	yes	—
511	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	4	no	—
514	C₄	—	2	4	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	C₂²×#6099	1	4	yes	complemented
518	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
519	C₄	C₂×D₄×Dic₁₃	1	4	yes	—
520	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
521	C₄	C₂²×#6129	1	1	yes	characteristic
522	C₂	—	2	4	no	—
523	C₂	—	2	8	no	—
524	C₂	—	4	4	no	—
525	C₂	D₄×#6099	1	4	yes	direct product factor
526	C₂	C₂²×D₄×Dic₁₃	1	1	yes	characteristic
527	C₂	C₂³×#6099	1	1	yes	characteristic
528	C₂	C₂×#11719524	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₄×C₁₃	C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂×D₄×M₁₆
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×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. D₄×#6099	C₂	direct (N × H)
3. C₂×#11718673	C₂	semidirect
4. C₂×#11718672	C₂	semidirect
5. C₂×D₄×#1055	C₂	semidirect
6. C₂×#11718585	C₂	semidirect
7. C₂×#11718868	C₂	semidirect
8. C₂×C₄×#6099	C₂	semidirect
27. C₂²×#6099	C₂²	semidirect
28. C₂²×#6099	C₂²	semidirect
29. C₂³×#1055	C₂²	semidirect
30. #11718868	C₂²	semidirect
31. C₂×C₂²⋊#1055	C₂²	semidirect
32. C₂×C₂²⋊#1055	C₂²	semidirect
33. #11718673	C₂²	semidirect
34. #11718672	C₂²	semidirect
35. D₄×#1055	C₂²	semidirect
36. #11718585	C₂²	semidirect
37. C₂×C₄⋊#1055	C₂²	semidirect
38. C₂×C₄⋊#1055	C₂²	semidirect
39. C₄×#6099	C₂²	semidirect
40. C₂×#88043	C₂²	semidirect
41. C₂×C₄×#1055	C₂²	semidirect
88. C₂×#6099	D₄	direct (N × H)
92. C₂×#6099	C₂³	semidirect
97. C₂²×#1055	C₂³	semidirect
98. C₂²⋊#1055	C₂³	semidirect
99. C₂²⋊#1055	C₂³	semidirect
100. C₄⋊#1055	C₂³	semidirect
101. C₄⋊#1055	C₂³	semidirect
102. #88043	C₂³	semidirect
103. C₄×#1055	C₂³	semidirect
115. C₂×D₄×C₁₃	M₁₆	semidirect
168. #6099	C₂×D₄	direct (N × H)
172. C₂×#1055	C₂×D₄	semidirect
197. C₂³×C₁₃	C₂×M₁₆	semidirect
204. D₄×C₁₃	C₂×M₁₆	semidirect
223. C₂×C₄×C₁₃	C₂×M₁₆	semidirect
239. #1055	C₂²×D₄	semidirect
286. C₂²×C₁₃	C₂²×M₁₆	semidirect
296. C₄×C₁₃	C₂²×M₁₆	semidirect
364. C₂×C₁₃	D₄×M₁₆	semidirect
378. C₂×D₄	#6099	direct (N × H)
439. C₁₃	C₂×D₄×M₁₆	semidirect
451. C₂³	C₂×#6099	semidirect
459. D₄	C₂×#6099	direct (N × H)
476. C₂×C₄	C₂×#6099	semidirect
507. C₂²	C₂²×#6099	semidirect
517. C₄	C₂²×#6099	semidirect
525. C₂	D₄×#6099	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
D₄×#6099	2
C₂×#11718673	2
C₂×#11718672	2
C₂×D₄×#1055	2
C₂×#11718585	2
C₂×#11718868	2
C₂×C₄×#6099	2
C₂²×C₄×D₄×C₁₃	2
C₂×D₄×M₁₆	13

Subgroups — C2×D4×#6099 #16726821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×#6099 #16726821