Subgroups — C₂²×D₁₃×C₂²⋊Q₈ #16769558

Order 3328.

14078 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#88151	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88150	C₂	1	2	yes	maximal, complemented
6	C₂²×#88132	C₂	1	2	yes	maximal, complemented
7	C₂²×#88200	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₃×C₂²⋊Q₈	C₂	1	48	yes	maximal, direct product factor
9	C₂²×C₄⋊C₄×D₁₃	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal
12	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×D₁₃	—	2	16	no	—
18	C₂²×Q₈×D₁₃	C₂²	1	24	yes	complemented
19	C₂³×C₄×D₁₃	—	2	16	no	—
20	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
21	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
22	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₁₃	C₂²	1	24	yes	—
24	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
25	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
26	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂³×Dic₂₆	C₂²	1	2	yes	complemented
28	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
30	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
34	C₂×#88200	C₂²	1	24	yes	complemented
35	C₂²×#6103	C₂²	1	2	yes	—
36	C₂²×#6103	C₂²	1	2	yes	—
37	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
39	C₂×#88178	C₂²	1	24	yes	complemented
40	C₂²×#6101	C₂²	1	2	yes	complemented
41	C₂²×#6101	C₂²	1	2	yes	complemented
42	C₂²×#6101	C₂²	1	2	yes	complemented
43	D₁₃×C₂²⋊Q₈	C₂²	1	256	yes	direct product factor
44	C₂×#88151	C₂²	1	24	yes	complemented
45	C₂×#88150	C₂²	1	48	yes	complemented
46	C₂×C₄⋊C₄×D₁₃	C₂²	1	24	yes	complemented
47	C₂×C₄⋊C₄×D₁₃	C₂²	1	48	yes	complemented
48	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	—
49	C₂×#88132	C₂²	1	48	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
51	C₂⁴×D₁₃	—	2	8	no	—
52	C₂⁴×D₁₃	—	2	8	no	—
53	C₂⁴×D₁₃	Q₈	1	16	yes	complemented
54	C₂⁴×D₁₃	C₂³	1	12	yes	—
55	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
56	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	—	2	8	no	—
58	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
59	C₂³×C₄×C₁₃	—	2	8	no	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×Dic₁₃	—	2	8	no	—
66	C₂³×Dic₁₃	C₂³	1	12	yes	—
67	C₂³×Dic₁₃	C₂³	1	2	yes	—
68	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
69	C₂³×Dic₁₃	C₂³	1	2	yes	—
70	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
71	C₂×Q₈×D₁₃	—	2	192	no	—
72	C₂×Q₈×D₁₃	C₂³	1	64	yes	complemented
73	C₂²×C₄×D₁₃	—	2	8	no	—
74	C₂²×C₄×D₁₃	—	2	16	no	—
75	C₂²×C₄×D₁₃	—	2	16	no	—
76	C₂²×C₄×D₁₃	—	2	8	no	—
77	C₂²×C₄×D₁₃	—	2	8	no	—
78	C₂²×C₄×D₁₃	—	2	192	no	—
79	C₂²×C₄×D₁₃	D₄	1	16	yes	—
80	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
81	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
82	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
83	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
84	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
85	C₂²×C₄×D₁₃	C₂³	1	64	yes	—
86	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
87	C₂²×Dic₂₆	—	2	8	no	—
88	C₂²×Dic₂₆	—	2	16	no	—
89	C₂²×Dic₂₆	C₂³	1	24	yes	complemented
90	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
91	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
95	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
96	#88200	C₂³	1	64	yes	complemented
97	C₂×#6103	C₂³	1	24	yes	—
98	C₂×#6103	C₂³	1	24	yes	—
99	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
100	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
101	#88178	C₂³	1	64	yes	complemented
102	C₂×#6101	C₂³	1	24	yes	complemented
103	C₂×#6101	C₂³	1	24	yes	complemented
104	C₂×#6101	C₂³	1	24	yes	complemented
105	#88151	C₂³	1	64	yes	complemented
106	#88150	C₂³	1	128	yes	complemented
107	C₄⋊C₄×D₁₃	C₂³	1	64	yes	complemented
108	C₄⋊C₄×D₁₃	C₂³	1	128	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	—
110	#88132	C₂³	1	128	yes	complemented
111	C₂³×C₂²⋊Q₈	—	13	1	no	maximal, Sylow
112	C₂⁴×C₁₃	—	2	4	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	complemented
115	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
116	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂³×D₁₃	—	2	4	no	—
118	C₂³×D₁₃	—	2	4	no	—
119	C₂³×D₁₃	—	2	128	no	—
120	C₂³×D₁₃	—	2	48	no	—
121	C₂³×D₁₃	—	2	48	no	—
122	C₂³×D₁₃	C₂×D₄	1	8	yes	—
123	C₂³×D₁₃	C₂×Q₈	1	8	yes	—
124	C₂³×D₁₃	C₂×Q₈	1	96	yes	complemented
125	C₂³×D₁₃	C₂×Q₈	1	8	yes	complemented
126	C₂³×D₁₃	#41	1	8	yes	—
127	C₂³×D₁₃	C₂⁴	1	16	yes	—
128	C₂³×D₁₃	C₂⁴	1	6	yes	—
129	C₂³×D₁₃	C₂⁴	1	6	yes	—
130	C₂×Q₈×C₁₃	—	2	48	no	—
131	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	8	no	—
135	C₂²×C₄×C₁₃	—	2	48	no	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
142	C₂²×Dic₁₃	—	2	8	no	—
143	C₂²×Dic₁₃	—	2	4	no	—
144	C₂²×Dic₁₃	—	2	8	no	—
145	C₂²×Dic₁₃	—	2	48	no	—
146	C₂²×Dic₁₃	C₂×D₄	1	8	yes	—
147	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
148	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
149	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
150	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
151	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
152	Q₈×D₁₃	—	2	256	no	—
153	C₂×C₄×D₁₃	—	2	48	no	—
154	C₂×C₄×D₁₃	—	2	96	no	—
155	C₂×C₄×D₁₃	—	2	96	no	—
156	C₂×C₄×D₁₃	—	2	48	no	—
157	C₂×C₄×D₁₃	—	2	48	no	—
158	C₂×C₄×D₁₃	—	2	256	no	—
159	C₂×C₄×D₁₃	C₂×D₄	1	96	yes	—
160	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
161	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
162	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
163	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
164	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
165	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
166	C₂×Dic₂₆	—	2	48	no	—
167	C₂×Dic₂₆	—	2	96	no	—
168	C₂×Dic₂₆	C₂⁴	1	32	yes	complemented
169	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
170	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
171	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
172	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
173	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
174	#6103	C₂⁴	1	32	yes	—
175	#6103	C₂⁴	1	32	yes	—
176	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
177	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
178	#6101	C₂⁴	1	32	yes	complemented
179	#6101	C₂⁴	1	32	yes	complemented
180	#6101	C₂⁴	1	32	yes	complemented
181	C₂⁴×Q₈	—	13	1	no	—
182	C₂⁵×C₄	—	13	1	no	—
183	C₂²×C₂²⋊Q₈	—	13	1	no	—
184	C₂²×C₂²⋊Q₈	—	13	1	no	—
185	C₂²×C₂²⋊Q₈	—	13	48	no	—
186	C₂²×C₂²⋊Q₈	—	13	2	no	—
187	C₂²×C₂²⋊Q₈	—	13	1	no	—
188	C₂²×C₂²⋊Q₈	—	13	2	no	—
189	C₂²×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic, direct product factor
190	C₂³×C₄⋊C₄	—	13	1	no	—
191	C₂³×C₄⋊C₄	—	13	2	no	—
192	C₂³×C₂²⋊C₄	—	13	2	no	—
193	C₂³×C₁₃	—	2	32	no	—
194	C₂³×C₁₃	—	2	12	no	—
195	C₂³×C₁₃	—	2	12	no	—
196	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
197	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
198	C₂³×C₁₃	C₂²×Q₈	1	24	yes	complemented
199	C₂³×C₁₃	C₂×#41	1	4	yes	—
200	C₂³×C₁₃	C₂⁵	1	4	yes	—
201	C₂³×C₁₃	C₂⁵	1	3	yes	—
202	C₂²×D₁₃	—	2	32	no	—
203	C₂²×D₁₃	—	2	12	no	—
204	C₂²×D₁₃	—	2	12	no	—
205	C₂²×D₁₃	—	2	384	no	—
206	C₂²×D₁₃	—	2	32	no	—
207	C₂²×D₁₃	—	2	32	no	—
208	C₂²×D₁₃	C₂²⋊Q₈	1	64	yes	direct product factor
209	C₂²×D₁₃	C₂²×D₄	1	24	yes	—
210	C₂²×D₁₃	C₂²×Q₈	1	24	yes	—
211	C₂²×D₁₃	C₂²×Q₈	1	64	yes	complemented
212	C₂²×D₁₃	C₂²×Q₈	1	24	yes	complemented
213	C₂²×D₁₃	C₂×#41	1	24	yes	—
214	C₂²×D₁₃	C₂⁵	1	4	yes	—
215	C₂²×D₁₃	C₂⁵	1	4	yes	—
216	Q₈×C₁₃	—	2	32	no	—
217	C₂×C₄×C₁₃	—	2	24	no	—
218	C₂×C₄×C₁₃	—	2	12	no	—
219	C₂×C₄×C₁₃	—	2	24	no	—
220	C₂×C₄×C₁₃	—	2	32	no	—
221	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
222	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
224	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
225	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
226	C₂×Dic₁₃	—	2	24	no	—
227	C₂×Dic₁₃	—	2	12	no	—
228	C₂×Dic₁₃	—	2	24	no	—
229	C₂×Dic₁₃	—	2	32	no	—
230	C₂×Dic₁₃	C₂²×D₄	1	24	yes	—
231	C₂×Dic₁₃	C₂⁵	1	8	yes	—
232	C₂×Dic₁₃	C₂⁵	1	4	yes	—
233	C₂×Dic₁₃	C₂⁵	1	8	yes	—
234	C₂×Dic₁₃	C₂⁵	1	4	yes	—
235	C₄×D₁₃	—	2	32	no	—
236	C₄×D₁₃	—	2	64	no	—
237	C₄×D₁₃	—	2	64	no	—
238	C₄×D₁₃	—	2	32	no	—
239	C₄×D₁₃	—	2	32	no	—
240	C₄×D₁₃	C₂²×D₄	1	64	yes	—
241	Dic₂₆	—	2	32	no	—
242	Dic₂₆	—	2	64	no	—
243	C₂⁶	—	13	1	no	—
244	C₂³×Q₈	—	13	24	no	—
245	C₂³×Q₈	—	13	2	no	—
246	C₂³×Q₈	—	13	1	no	—
247	C₂³×Q₈	—	26	16	no	—
248	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
249	C₂⁴×C₄	—	13	1	no	—
250	C₂⁴×C₄	—	13	1	no	—
251	C₂⁴×C₄	—	13	1	no	—
252	C₂⁴×C₄	—	13	1	no	—
253	C₂⁴×C₄	—	13	24	no	—
254	C₂⁴×C₄	—	13	1	no	—
255	C₂⁴×C₄	—	13	2	no	—
256	C₂⁴×C₄	—	13	2	no	—
257	C₂⁴×C₄	—	26	16	no	—
258	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
259	C₂×C₂²⋊Q₈	—	13	24	no	—
260	C₂×C₂²⋊Q₈	—	13	24	no	—
261	C₂×C₂²⋊Q₈	—	13	256	no	—
262	C₂×C₂²⋊Q₈	—	13	48	no	—
263	C₂×C₂²⋊Q₈	—	13	24	no	—
264	C₂×C₂²⋊Q₈	—	13	48	no	—
265	C₂×C₂²⋊Q₈	C₂×D₁₃	1	24	yes	direct product factor
266	C₂²×C₄⋊C₄	—	13	2	no	—
267	C₂²×C₄⋊C₄	—	13	2	no	—
268	C₂²×C₄⋊C₄	—	13	2	no	—
269	C₂²×C₄⋊C₄	—	13	1	no	—
270	C₂²×C₄⋊C₄	—	13	2	no	—
271	C₂²×C₄⋊C₄	—	13	24	no	—
272	C₂²×C₄⋊C₄	—	13	48	no	—
273	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
274	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
275	C₂²×C₂²⋊C₄	—	13	2	no	—
276	C₂²×C₂²⋊C₄	—	13	2	no	—
277	C₂²×C₂²⋊C₄	—	13	2	no	—
278	C₂²×C₂²⋊C₄	—	13	48	no	—
279	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	48	no	—
283	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	16	yes	complemented
284	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
285	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
286	C₂²×C₁₃	C₂³×Q₈	1	8	yes	complemented
287	C₂²×C₁₃	C₂²×#41	1	6	yes	—
288	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
289	C₂×D₁₃	—	2	4	no	—
290	C₂×D₁₃	—	2	4	no	—
291	C₂×D₁₃	—	2	48	no	—
292	C₂×D₁₃	—	2	128	no	—
293	C₂×D₁₃	C₂×C₂²⋊Q₈	1	96	yes	direct product factor
294	C₂×D₁₃	C₂³×D₄	1	8	yes	—
295	C₂×D₁₃	C₂³×Q₈	1	8	yes	—
296	C₂×D₁₃	C₂³×Q₈	1	8	yes	complemented
297	C₂×D₁₃	C₂²×#41	1	8	yes	—
298	C₄×C₁₃	—	2	8	no	—
299	C₄×C₁₃	—	2	4	no	—
300	C₄×C₁₃	—	2	8	no	—
301	C₄×C₁₃	C₂³×D₄	1	8	yes	—
302	Dic₁₃	—	2	8	no	—
303	Dic₁₃	—	2	4	no	—
304	Dic₁₃	—	2	8	no	—
305	Dic₁₃	C₂³×D₄	1	8	yes	—
306	C₂⁵	—	13	1	no	—
307	C₂⁵	—	13	16	no	—
308	C₂⁵	—	13	12	no	—
309	C₂⁵	—	13	1	no	—
310	C₂⁵	—	26	8	no	—
311	C₂⁵	—	26	8	no	—
312	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
313	C₂²×Q₈	—	2	8	no	—
314	C₂²×Q₈	—	13	64	no	—
315	C₂²×Q₈	—	13	24	no	—
316	C₂²×Q₈	—	13	12	no	—
317	C₂²×Q₈	—	26	16	no	—
318	C₂²×Q₈	—	26	192	no	—
319	C₂²×Q₈	—	26	8	no	—
320	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
321	C₂³×C₄	—	2	8	no	—
322	C₂³×C₄	—	13	1	no	—
323	C₂³×C₄	—	13	16	no	—
324	C₂³×C₄	—	13	12	no	—
325	C₂³×C₄	—	13	12	no	—
326	C₂³×C₄	—	13	2	no	—
327	C₂³×C₄	—	13	2	no	—
328	C₂³×C₄	—	13	1	no	—
329	C₂³×C₄	—	13	24	no	—
330	C₂³×C₄	—	13	24	no	—
331	C₂³×C₄	—	13	12	no	—
332	C₂³×C₄	—	13	12	no	—
333	C₂³×C₄	—	13	64	no	—
334	C₂³×C₄	—	13	12	no	—
335	C₂³×C₄	—	26	8	no	—
336	C₂³×C₄	—	26	192	no	—
337	C₂³×C₄	—	26	8	no	—
338	C₂³×C₄	—	26	16	no	—
339	C₂³×C₄	—	26	16	no	—
340	C₂³×C₄	—	26	8	no	—
341	C₂³×C₄	—	26	8	no	—
342	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
343	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
344	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
345	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
346	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
347	C₂²⋊Q₈	—	13	64	no	—
348	C₂²⋊Q₈	—	13	64	no	—
349	C₂²⋊Q₈	—	13	128	no	—
350	C₂²⋊Q₈	—	13	64	no	—
351	C₂²⋊Q₈	—	13	128	no	—
352	C₂²⋊Q₈	C₂²×D₁₃	1	64	yes	direct product factor
353	C₂×C₄⋊C₄	—	13	24	no	—
354	C₂×C₄⋊C₄	—	13	24	no	—
355	C₂×C₄⋊C₄	—	13	24	no	—
356	C₂×C₄⋊C₄	—	13	12	no	—
357	C₂×C₄⋊C₄	—	13	24	no	—
358	C₂×C₄⋊C₄	—	13	64	no	—
359	C₂×C₄⋊C₄	—	13	128	no	—
360	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
361	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
362	C₂×C₂²⋊C₄	—	13	24	no	—
363	C₂×C₂²⋊C₄	—	13	24	no	—
364	C₂×C₂²⋊C₄	—	13	24	no	—
365	C₂×C₂²⋊C₄	—	13	128	no	—
366	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
367	C₂×C₁₃	—	2	8	no	—
368	C₂×C₁₃	C₂²×C₂²⋊Q₈	1	12	yes	complemented
369	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
370	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
371	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
372	D₁₃	—	2	8	no	—
373	D₁₃	C₂²×C₂²⋊Q₈	1	16	yes	direct product factor
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	13	8	no	—
377	C₂⁴	—	13	8	no	—
378	C₂⁴	—	13	8	no	—
379	C₂⁴	—	13	6	no	—
380	C₂⁴	—	13	8	no	—
381	C₂⁴	—	13	96	no	—
382	C₂⁴	—	13	16	no	—
383	C₂⁴	—	13	6	no	—
384	C₂⁴	—	26	48	no	—
385	C₂⁴	—	26	128	no	—
386	C₂⁴	—	26	48	no	—
387	C₂⁴	—	26	4	no	—
388	C₂⁴	—	26	4	no	—
389	C₂⁴	Q₈×D₁₃	1	8	yes	complemented
390	C₂⁴	C₂³×D₁₃	1	6	yes	—
391	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
392	C₂×Q₈	—	2	48	no	—
393	C₂×Q₈	—	13	32	no	—
394	C₂×Q₈	—	13	16	no	—
395	C₂×Q₈	—	26	96	no	—
396	C₂×Q₈	—	26	256	no	—
397	C₂×Q₈	—	26	48	no	—
398	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	2	8	no	—
402	C₂²×C₄	—	2	48	no	—
403	C₂²×C₄	—	13	8	no	—
404	C₂²×C₄	—	13	6	no	—
405	C₂²×C₄	—	13	96	no	—
406	C₂²×C₄	—	13	16	no	—
407	C₂²×C₄	—	13	12	no	—
408	C₂²×C₄	—	13	12	no	—
409	C₂²×C₄	—	13	6	no	—
410	C₂²×C₄	—	13	16	no	—
411	C₂²×C₄	—	13	32	no	—
412	C₂²×C₄	—	13	32	no	—
413	C₂²×C₄	—	13	16	no	—
414	C₂²×C₄	—	13	16	no	—
415	C₂²×C₄	—	13	16	no	—
416	C₂²×C₄	—	26	48	no	—
417	C₂²×C₄	—	26	256	no	—
418	C₂²×C₄	—	26	48	no	—
419	C₂²×C₄	—	26	96	no	—
420	C₂²×C₄	—	26	96	no	—
421	C₂²×C₄	—	26	48	no	—
422	C₂²×C₄	—	26	4	no	—
423	C₂²×C₄	—	26	8	no	—
424	C₂²×C₄	—	26	8	no	—
425	C₂²×C₄	—	26	48	no	—
426	C₂²×C₄	D₄×D₁₃	1	8	yes	—
427	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
428	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
429	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
430	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
431	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
432	C₄⋊C₄	—	13	32	no	—
433	C₄⋊C₄	—	13	32	no	—
434	C₄⋊C₄	—	13	32	no	—
435	C₄⋊C₄	—	13	16	no	—
436	C₄⋊C₄	—	13	32	no	—
437	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
438	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
439	C₂²⋊C₄	—	13	32	no	—
440	C₂²⋊C₄	—	13	32	no	—
441	C₂²⋊C₄	—	13	32	no	—
442	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
443	C₁₃	C₂³×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
444	C₂³	—	2	32	no	—
445	C₂³	—	2	12	no	—
446	C₂³	—	2	12	no	—
447	C₂³	—	13	64	no	—
448	C₂³	—	13	24	no	—
449	C₂³	—	13	24	no	—
450	C₂³	—	13	24	no	—
451	C₂³	—	13	4	no	—
452	C₂³	—	13	24	no	—
453	C₂³	—	13	64	no	—
454	C₂³	—	13	4	no	—
455	C₂³	—	26	32	no	—
456	C₂³	—	26	384	no	—
457	C₂³	—	26	32	no	—
458	C₂³	—	26	32	no	—
459	C₂³	—	26	12	no	—
460	C₂³	—	26	12	no	—
461	C₂³	C₂×D₄×D₁₃	1	4	yes	—
462	C₂³	C₂×Q₈×D₁₃	1	4	yes	—
463	C₂³	C₂×Q₈×D₁₃	1	24	yes	complemented
464	C₂³	#41×D₁₃	1	4	yes	—
465	C₂³	C₂⁴×D₁₃	1	4	yes	—
466	C₂³	C₂⁴×D₁₃	1	3	yes	—
467	Q₈	—	2	32	no	—
468	Q₈	—	26	64	no	—
469	Q₈	—	26	32	no	—
470	C₂×C₄	—	2	12	no	—
471	C₂×C₄	—	2	24	no	—
472	C₂×C₄	—	2	24	no	—
473	C₂×C₄	—	2	32	no	—
474	C₂×C₄	—	13	24	no	—
475	C₂×C₄	—	13	4	no	—
476	C₂×C₄	—	13	64	no	—
477	C₂×C₄	—	13	8	no	—
478	C₂×C₄	—	13	8	no	—
479	C₂×C₄	—	13	4	no	—
480	C₂×C₄	—	26	32	no	—
481	C₂×C₄	—	26	64	no	—
482	C₂×C₄	—	26	32	no	—
483	C₂×C₄	—	26	64	no	—
484	C₂×C₄	—	26	32	no	—
485	C₂×C₄	—	26	12	no	—
486	C₂×C₄	—	26	24	no	—
487	C₂×C₄	—	26	24	no	—
488	C₂×C₄	—	26	32	no	—
489	C₂×C₄	C₂×D₄×D₁₃	1	24	yes	—
490	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
491	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
492	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
493	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
494	C₂²	—	2	48	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	13	96	no	—
498	C₂²	—	13	8	no	—
499	C₂²	—	13	8	no	—
500	C₂²	—	13	8	no	—
501	C₂²	—	13	8	no	—
502	C₂²	—	26	128	no	—
503	C₂²	—	26	48	no	—
504	C₂²	—	26	4	no	—
505	C₂²	—	26	4	no	—
506	C₂²	D₁₃×C₂²⋊Q₈	1	16	yes	direct product factor
507	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
508	C₂²	C₂²×Q₈×D₁₃	1	6	yes	—
509	C₂²	C₂²×Q₈×D₁₃	1	8	yes	complemented
510	C₂²	C₂×#41×D₁₃	1	6	yes	—
511	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
512	C₄	—	2	4	no	—
513	C₄	—	2	8	no	—
514	C₄	—	2	8	no	—
515	C₄	—	13	8	no	—
516	C₄	—	26	4	no	—
517	C₄	—	26	8	no	—
518	C₄	—	26	8	no	—
519	C₄	C₂²×D₄×D₁₃	1	8	yes	—
520	C₂	—	2	8	no	—
521	C₂	—	13	16	no	—
522	C₂	—	26	8	no	—
523	C₂	C₂×D₁₃×C₂²⋊Q₈	1	12	yes	direct product factor
524	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
525	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
526	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×C₂²⋊Q₈	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁵×D₁₃	C₂²
hypercenter	C₂²×C₂²⋊Q₈	D₁₃
hypocenter	C₁₃	C₂³×C₂²⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₁₃	C₂	semidirect
3. C₂²×#88151	C₂	semidirect
4. C₂²×#88178	C₂	semidirect
5. C₂²×#88150	C₂	semidirect
6. C₂²×#88132	C₂	semidirect
7. C₂²×#88200	C₂	semidirect
8. C₂×D₁₃×C₂²⋊Q₈	C₂	direct (N × H)
9. C₂²×C₄⋊C₄×D₁₃	C₂	semidirect
10. C₂²×C₄⋊C₄×D₁₃	C₂	semidirect
12. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
14. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂²×Q₈×D₁₃	C₂²	semidirect
27. C₂³×Dic₂₆	C₂²	semidirect
28. C₂³×Dic₂₆	C₂²	semidirect
29. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
30. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
34. C₂×#88200	C₂²	semidirect
37. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
38. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
39. C₂×#88178	C₂²	semidirect
40. C₂²×#6101	C₂²	semidirect
41. C₂²×#6101	C₂²	semidirect
42. C₂²×#6101	C₂²	semidirect
43. D₁₃×C₂²⋊Q₈	C₂²	direct (N × H)
44. C₂×#88151	C₂²	semidirect
45. C₂×#88150	C₂²	semidirect
46. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
47. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
49. C₂×#88132	C₂²	semidirect
53. C₂⁴×D₁₃	Q₈	semidirect
58. C₂²×Q₈×C₁₃	C₂³	semidirect
72. C₂×Q₈×D₁₃	C₂³	semidirect
89. C₂²×Dic₂₆	C₂³	semidirect
90. C₂²×Dic₂₆	C₂³	semidirect
91. C₁₃×C₂²⋊Q₈	C₂³	semidirect
92. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
93. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
96. #88200	C₂³	semidirect
99. C₂×C₄⋊Dic₁₃	C₂³	semidirect
100. C₂×C₄⋊Dic₁₃	C₂³	semidirect
101. #88178	C₂³	semidirect
102. C₂×#6101	C₂³	semidirect
103. C₂×#6101	C₂³	semidirect
104. C₂×#6101	C₂³	semidirect
105. #88151	C₂³	semidirect
106. #88150	C₂³	semidirect
107. C₄⋊C₄×D₁₃	C₂³	semidirect
108. C₄⋊C₄×D₁₃	C₂³	semidirect
110. #88132	C₂³	semidirect
114. C₂⁴×C₁₃	C₂×Q₈	semidirect
124. C₂³×D₁₃	C₂×Q₈	semidirect
125. C₂³×D₁₃	C₂×Q₈	semidirect
131. C₂×Q₈×C₁₃	C₂⁴	semidirect
168. C₂×Dic₂₆	C₂⁴	semidirect
169. C₂×Dic₂₆	C₂⁴	semidirect
170. C₁₃×C₄⋊C₄	C₂⁴	semidirect
171. C₁₃×C₄⋊C₄	C₂⁴	semidirect
176. C₄⋊Dic₁₃	C₂⁴	semidirect
177. C₄⋊Dic₁₃	C₂⁴	semidirect
178. #6101	C₂⁴	semidirect
179. #6101	C₂⁴	semidirect
180. #6101	C₂⁴	semidirect
189. C₂²×C₂²⋊Q₈	D₁₃	direct (N × H)
198. C₂³×C₁₃	C₂²×Q₈	semidirect
208. C₂²×D₁₃	C₂²⋊Q₈	direct (N × H)
211. C₂²×D₁₃	C₂²×Q₈	semidirect
212. C₂²×D₁₃	C₂²×Q₈	semidirect
248. C₂³×Q₈	C₂×D₁₃	semidirect
265. C₂×C₂²⋊Q₈	C₂×D₁₃	direct (N × H)
273. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
274. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
283. C₂²×C₁₃	C₂×C₂²⋊Q₈	semidirect
286. C₂²×C₁₃	C₂³×Q₈	semidirect
293. C₂×D₁₃	C₂×C₂²⋊Q₈	direct (N × H)
296. C₂×D₁₃	C₂³×Q₈	semidirect
320. C₂²×Q₈	C₂²×D₁₃	semidirect
352. C₂²⋊Q₈	C₂²×D₁₃	direct (N × H)
360. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
361. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
368. C₂×C₁₃	C₂²×C₂²⋊Q₈	semidirect
373. D₁₃	C₂²×C₂²⋊Q₈	direct (N × H)
389. C₂⁴	Q₈×D₁₃	semidirect
398. C₂×Q₈	C₂³×D₁₃	semidirect
437. C₄⋊C₄	C₂³×D₁₃	semidirect
438. C₄⋊C₄	C₂³×D₁₃	semidirect
443. C₁₃	C₂³×C₂²⋊Q₈	semidirect
463. C₂³	C₂×Q₈×D₁₃	semidirect
506. C₂²	D₁₃×C₂²⋊Q₈	direct (N × H)
509. C₂²	C₂²×Q₈×D₁₃	semidirect
523. C₂	C₂×D₁₃×C₂²⋊Q₈	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×Q₈×D₁₃	2
C₂⁴×C₄×D₁₃	2
C₂²×#88151	2
C₂²×#88178	2
C₂²×#88150	2
C₂²×#88132	2
C₂²×#88200	2
C₂×D₁₃×C₂²⋊Q₈	2
C₂²×C₄⋊C₄×D₁₃	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂³×C₂²⋊Q₈	13

Subgroups — C22×D13×C22⋊Q8 #16769558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₁₃×C₂²⋊Q₈ #16769558