Subgroups — C₂²×#11719339 #16769640

Order 3328.

9310 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719339	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88151	C₂	1	2	yes	maximal, complemented
3	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88150	C₂	1	2	yes	maximal, complemented
5	C₂²×#88150	C₂	1	2	yes	maximal, complemented
6	C₂²×#88132	C₂	1	2	yes	maximal, complemented
7	C₂²×#88200	C₂	1	2	yes	maximal, complemented
8	C₂³×#6103	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₂²⋊C₄×D₁₃	C₂	1	2	yes	maximal
10	C₂²×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
16	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
17	C₂³×Dic₂₆	C₂²	1	2	yes	complemented
18	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
24	C₂×#88200	C₂²	1	48	yes	complemented
25	C₂²×#6103	C₂²	1	24	yes	—
26	C₂²×#6103	C₂²	1	2	yes	—
27	C₂²×#6103	C₂²	1	2	yes	—
28	C₂²×#6103	C₂²	1	2	yes	—
29	C₂²×#6103	C₂²	1	2	yes	—
30	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
31	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#88178	C₂²	1	24	yes	complemented
33	C₂²×#6101	C₂²	1	2	yes	complemented
34	C₂²×#6101	C₂²	1	2	yes	complemented
35	C₂²×#6101	C₂²	1	2	yes	complemented
36	#11719339	C₂²	1	256	yes	direct product factor
37	C₂×#88151	C₂²	1	48	yes	complemented
38	C₂×#88150	C₂²	1	48	yes	complemented
39	C₂×#88150	C₂²	1	48	yes	complemented
40	C₂×C₂²⋊C₄×D₁₃	C₂²	1	48	yes	—
41	C₂×#88132	C₂²	1	48	yes	complemented
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁴×D₁₃	—	4	4	no	—
44	C₂⁴×D₁₃	—	4	4	no	—
45	C₂⁴×D₁₃	Q₈	1	16	yes	complemented
46	C₂⁴×D₁₃	C₂³	1	2	yes	—
47	C₂⁴×D₁₃	C₂³	1	12	yes	—
48	C₂²×Q₈×C₁₃	—	4	4	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
50	C₂³×C₄×C₁₃	—	4	4	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
56	C₂³×Dic₁₃	—	4	4	no	—
57	C₂³×Dic₁₃	C₂³	1	2	yes	—
58	C₂³×Dic₁₃	C₂³	1	2	yes	—
59	C₂³×Dic₁₃	C₂³	1	2	yes	—
60	C₂³×Dic₁₃	C₂³	1	12	yes	—
61	C₂²×C₄×D₁₃	—	4	8	no	—
62	C₂²×C₄×D₁₃	—	4	8	no	—
63	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
64	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
65	C₂²×Dic₂₆	—	4	4	no	—
66	C₂²×Dic₂₆	—	4	8	no	—
67	C₂²×Dic₂₆	C₂³	1	24	yes	complemented
68	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
69	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
73	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
74	#88200	C₂³	1	128	yes	complemented
75	C₂×#6103	C₂³	1	24	yes	—
76	C₂×#6103	C₂³	1	24	yes	—
77	C₂×#6103	C₂³	1	24	yes	—
78	C₂×#6103	C₂³	1	24	yes	—
79	C₂×#6103	C₂³	1	64	yes	—
80	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
81	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
82	#88178	C₂³	1	64	yes	complemented
83	C₂×#6101	C₂³	1	24	yes	complemented
84	C₂×#6101	C₂³	1	24	yes	complemented
85	C₂×#6101	C₂³	1	24	yes	complemented
86	#88151	C₂³	1	128	yes	complemented
87	#88150	C₂³	1	128	yes	complemented
88	#88150	C₂³	1	128	yes	complemented
89	C₂²⋊C₄×D₁₃	C₂³	1	128	yes	—
90	#88132	C₂³	1	128	yes	complemented
91	C₂²×#543	—	13	1	no	maximal, Sylow
92	C₂⁴×C₁₃	—	2	4	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
95	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₂³×D₁₃	—	2	8	no	—
98	C₂³×D₁₃	—	2	8	no	—
99	C₂³×D₁₃	—	4	64	no	—
100	C₂³×D₁₃	—	4	24	no	—
101	C₂³×D₁₃	—	4	24	no	—
102	C₂³×D₁₃	C₂×Q₈	1	16	yes	—
103	C₂³×D₁₃	C₂×Q₈	1	96	yes	complemented
104	C₂³×D₁₃	C₂⁴	1	12	yes	—
105	C₂³×D₁₃	C₂⁴	1	16	yes	—
106	C₂×Q₈×C₁₃	—	4	24	no	—
107	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	8	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	4	24	no	—
113	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
114	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
118	C₂²×Dic₁₃	—	2	8	no	—
119	C₂²×Dic₁₃	—	2	8	no	—
120	C₂²×Dic₁₃	—	2	8	no	—
121	C₂²×Dic₁₃	—	4	24	no	—
122	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
123	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
124	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
125	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
126	C₂×C₄×D₁₃	—	4	48	no	—
127	C₂×C₄×D₁₃	—	4	48	no	—
128	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
129	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
130	C₂×Dic₂₆	—	4	24	no	—
131	C₂×Dic₂₆	—	4	48	no	—
132	C₂×Dic₂₆	C₂⁴	1	32	yes	complemented
133	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
134	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
135	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
136	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
137	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
138	#6103	C₂⁴	1	32	yes	—
139	#6103	C₂⁴	1	32	yes	—
140	#6103	C₂⁴	1	32	yes	—
141	#6103	C₂⁴	1	32	yes	—
142	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
143	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
144	#6101	C₂⁴	1	32	yes	complemented
145	#6101	C₂⁴	1	32	yes	complemented
146	#6101	C₂⁴	1	32	yes	complemented
147	C₂×#543	—	13	48	no	—
148	C₂²×C₂²⋊Q₈	—	13	2	no	—
149	C₂²×C₂²⋊Q₈	—	13	1	no	—
150	C₂²×C₂²⋊Q₈	—	13	2	no	—
151	C₂²×C₂²⋊Q₈	—	13	2	no	—
152	C₂²×C₂²⋊Q₈	—	13	2	no	—
153	C₂²×C₂²⋊Q₈	—	13	2	no	—
154	C₂²×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic, complemented
155	C₂³×C₂²⋊C₄	—	13	1	no	—
156	C₂³×C₂²⋊C₄	—	13	2	no	—
157	C₂³×C₁₃	—	2	32	no	—
158	C₂³×C₁₃	—	2	12	no	—
159	C₂³×C₁₃	—	2	12	no	—
160	C₂³×C₁₃	C₂²×Q₈	1	24	yes	—
161	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
162	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
163	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
164	C₂³×C₁₃	C₂⁵	1	4	yes	—
165	C₂³×C₁₃	C₂⁵	1	3	yes	—
166	C₂²×D₁₃	—	2	64	no	—
167	C₂²×D₁₃	—	2	24	no	—
168	C₂²×D₁₃	—	2	24	no	—
169	C₂²×D₁₃	—	4	192	no	—
170	C₂²×D₁₃	—	4	16	no	—
171	C₂²×D₁₃	—	4	16	no	—
172	C₂²×D₁₃	C₂²×Q₈	1	48	yes	—
173	C₂²×D₁₃	C₂²×Q₈	1	64	yes	complemented
174	C₂²×D₁₃	C₂⁵	1	8	yes	—
175	Q₈×C₁₃	—	4	16	no	—
176	C₂×C₄×C₁₃	—	2	24	no	—
177	C₂×C₄×C₁₃	—	2	12	no	—
178	C₂×C₄×C₁₃	—	2	24	no	—
179	C₂×C₄×C₁₃	—	2	12	no	—
180	C₂×C₄×C₁₃	—	4	16	no	—
181	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
182	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
183	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
184	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
185	C₂×Dic₁₃	—	2	24	no	—
186	C₂×Dic₁₃	—	2	24	no	—
187	C₂×Dic₁₃	—	2	24	no	—
188	C₂×Dic₁₃	—	4	16	no	—
189	C₂×Dic₁₃	C₂⁵	1	8	yes	—
190	C₂×Dic₁₃	C₂⁵	1	8	yes	—
191	C₂×Dic₁₃	C₂⁵	1	8	yes	—
192	C₄×D₁₃	—	4	32	no	—
193	C₄×D₁₃	—	4	32	no	—
194	Dic₂₆	—	4	16	no	—
195	Dic₂₆	—	4	32	no	—
196	C₂⁶	—	13	1	no	—
197	C₂³×Q₈	—	13	1	no	—
198	C₂³×Q₈	—	13	2	no	—
199	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
200	C₂⁴×C₄	—	13	1	no	—
201	C₂⁴×C₄	—	13	2	no	—
202	C₂⁴×C₄	—	13	2	no	—
203	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
204	#543	—	13	256	no	—
205	C₂×C₂²⋊Q₈	—	13	48	no	—
206	C₂×C₂²⋊Q₈	—	13	24	no	—
207	C₂×C₂²⋊Q₈	—	13	48	no	—
208	C₂×C₂²⋊Q₈	—	13	48	no	—
209	C₂×C₂²⋊Q₈	—	13	48	no	—
210	C₂×C₂²⋊Q₈	—	13	48	no	—
211	C₂×C₂²⋊Q₈	C₂×D₁₃	1	24	yes	complemented
212	C₂²×C₄⋊C₄	—	13	2	no	—
213	C₂²×C₄⋊C₄	—	13	2	no	—
214	C₂²×C₄⋊C₄	—	13	2	no	—
215	C₂²×C₄⋊C₄	—	13	1	no	—
216	C₂²×C₄⋊C₄	—	13	2	no	—
217	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
218	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
219	C₂²×C₂²⋊C₄	—	13	2	no	—
220	C₂²×C₂²⋊C₄	—	13	2	no	—
221	C₂²×C₂²⋊C₄	—	13	2	no	—
222	C₂²×C₂²⋊C₄	—	13	2	no	—
223	C₂²×C₂²⋊C₄	—	13	2	no	—
224	C₂²×C₂²⋊C₄	—	13	24	no	—
225	C₂²×C₂²⋊C₄	—	13	48	no	—
226	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	—	2	4	no	—
229	C₂²×C₁₃	—	2	48	no	—
230	C₂²×C₁₃	#543	1	16	yes	complemented
231	C₂²×C₁₃	C₂³×Q₈	1	8	yes	—
232	C₂²×C₁₃	C₂³×Q₈	1	6	yes	—
233	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
234	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
235	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
236	C₂×D₁₃	—	2	8	no	—
237	C₂×D₁₃	—	2	8	no	—
238	C₂×D₁₃	—	2	96	no	—
239	C₂×D₁₃	—	4	64	no	—
240	C₂×D₁₃	C₂³×Q₈	1	16	yes	—
241	C₄×C₁₃	—	2	8	no	—
242	C₄×C₁₃	—	2	4	no	—
243	C₄×C₁₃	—	2	8	no	—
244	C₄×C₁₃	—	2	4	no	—
245	Dic₁₃	—	2	8	no	—
246	Dic₁₃	—	2	8	no	—
247	Dic₁₃	—	2	8	no	—
248	C₂⁵	—	13	2	no	—
249	C₂⁵	—	13	16	no	—
250	C₂⁵	—	13	12	no	—
251	C₂⁵	—	52	4	no	—
252	C₂⁵	—	52	4	no	—
253	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
254	C₂²×Q₈	—	4	4	no	—
255	C₂²×Q₈	—	13	12	no	—
256	C₂²×Q₈	—	13	24	no	—
257	C₂²×Q₈	—	52	4	no	—
258	C₂²×Q₈	—	52	8	no	—
259	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
260	C₂³×C₄	—	4	4	no	—
261	C₂³×C₄	—	13	2	no	—
262	C₂³×C₄	—	13	2	no	—
263	C₂³×C₄	—	13	2	no	—
264	C₂³×C₄	—	13	12	no	—
265	C₂³×C₄	—	13	24	no	—
266	C₂³×C₄	—	13	24	no	—
267	C₂³×C₄	—	52	8	no	—
268	C₂³×C₄	—	52	8	no	—
269	C₂³×C₄	—	52	4	no	—
270	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
271	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
272	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
273	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
274	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
275	C₂²⋊Q₈	—	13	128	no	—
276	C₂²⋊Q₈	—	13	64	no	—
277	C₂²⋊Q₈	—	13	128	no	—
278	C₂²⋊Q₈	—	13	128	no	—
279	C₂²⋊Q₈	—	13	128	no	—
280	C₂²⋊Q₈	—	13	128	no	—
281	C₂²⋊Q₈	C₂²×D₁₃	1	64	yes	complemented
282	C₂×C₄⋊C₄	—	13	24	no	—
283	C₂×C₄⋊C₄	—	13	24	no	—
284	C₂×C₄⋊C₄	—	13	24	no	—
285	C₂×C₄⋊C₄	—	13	12	no	—
286	C₂×C₄⋊C₄	—	13	24	no	—
287	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
288	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
289	C₂×C₂²⋊C₄	—	13	24	no	—
290	C₂×C₂²⋊C₄	—	13	24	no	—
291	C₂×C₂²⋊C₄	—	13	24	no	—
292	C₂×C₂²⋊C₄	—	13	24	no	—
293	C₂×C₂²⋊C₄	—	13	24	no	—
294	C₂×C₂²⋊C₄	—	13	64	no	—
295	C₂×C₂²⋊C₄	—	13	128	no	—
296	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
297	C₂×C₁₃	—	2	8	no	—
298	C₂×C₁₃	C₂×#543	1	12	yes	complemented
299	C₂×C₁₃	C₂⁴×Q₈	1	1	yes	characteristic
300	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
302	D₁₃	—	2	16	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	—	13	16	no	—
306	C₂⁴	—	13	12	no	—
307	C₂⁴	—	13	96	no	—
308	C₂⁴	—	13	16	no	—
309	C₂⁴	—	26	8	no	—
310	C₂⁴	—	26	8	no	—
311	C₂⁴	—	52	64	no	—
312	C₂⁴	—	52	24	no	—
313	C₂⁴	—	52	24	no	—
314	C₂⁴	Q₈×D₁₃	1	8	yes	—
315	C₂⁴	C₂³×D₁₃	1	6	yes	—
316	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
317	C₂×Q₈	—	4	24	no	—
318	C₂×Q₈	—	13	16	no	—
319	C₂×Q₈	—	13	32	no	—
320	C₂×Q₈	—	52	24	no	—
321	C₂×Q₈	—	52	48	no	—
322	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	4	24	no	—
328	C₂²×C₄	—	13	12	no	—
329	C₂²×C₄	—	13	12	no	—
330	C₂²×C₄	—	13	12	no	—
331	C₂²×C₄	—	13	16	no	—
332	C₂²×C₄	—	13	32	no	—
333	C₂²×C₄	—	13	32	no	—
334	C₂²×C₄	—	26	8	no	—
335	C₂²×C₄	—	26	8	no	—
336	C₂²×C₄	—	26	8	no	—
337	C₂²×C₄	—	52	48	no	—
338	C₂²×C₄	—	52	48	no	—
339	C₂²×C₄	—	52	24	no	—
340	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
341	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
342	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
343	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
344	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
345	C₄⋊C₄	—	13	32	no	—
346	C₄⋊C₄	—	13	32	no	—
347	C₄⋊C₄	—	13	32	no	—
348	C₄⋊C₄	—	13	16	no	—
349	C₄⋊C₄	—	13	32	no	—
350	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
351	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
352	C₂²⋊C₄	—	13	32	no	—
353	C₂²⋊C₄	—	13	32	no	—
354	C₂²⋊C₄	—	13	32	no	—
355	C₂²⋊C₄	—	13	32	no	—
356	C₂²⋊C₄	—	13	32	no	—
357	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
358	C₁₃	C₂²×#543	1	1	yes	characteristic, complemented, Sylow
359	C₂³	—	2	32	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	2	12	no	—
362	C₂³	—	13	48	no	—
363	C₂³	—	13	8	no	—
364	C₂³	—	13	64	no	—
365	C₂³	—	26	64	no	—
366	C₂³	—	26	24	no	—
367	C₂³	—	26	24	no	—
368	C₂³	—	52	192	no	—
369	C₂³	—	52	16	no	—
370	C₂³	—	52	16	no	—
371	C₂³	#88251	1	4	yes	—
372	C₂³	C₂×Q₈×D₁₃	1	24	yes	—
373	C₂³	C₂×Q₈×D₁₃	1	4	yes	—
374	C₂³	#88256	1	4	yes	—
375	C₂³	C₂⁴×D₁₃	1	4	yes	—
376	C₂³	C₂⁴×D₁₃	1	3	yes	—
377	Q₈	—	4	16	no	—
378	Q₈	—	52	16	no	—
379	Q₈	—	52	32	no	—
380	C₂×C₄	—	2	12	no	—
381	C₂×C₄	—	2	12	no	—
382	C₂×C₄	—	2	24	no	—
383	C₂×C₄	—	2	24	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	13	8	no	—
386	C₂×C₄	—	13	8	no	—
387	C₂×C₄	—	13	8	no	—
388	C₂×C₄	—	26	24	no	—
389	C₂×C₄	—	26	24	no	—
390	C₂×C₄	—	26	24	no	—
391	C₂×C₄	—	52	32	no	—
392	C₂×C₄	—	52	32	no	—
393	C₂×C₄	—	52	16	no	—
394	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
395	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
396	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
397	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
398	C₂²	—	2	48	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	13	16	no	—
402	C₂²	—	26	96	no	—
403	C₂²	—	26	8	no	—
404	C₂²	—	26	8	no	—
405	C₂²	—	52	64	no	—
406	C₂²	#11719339	1	16	yes	direct product factor
407	C₂²	C₂×#88251	1	6	yes	—
408	C₂²	C₂²×Q₈×D₁₃	1	8	yes	—
409	C₂²	C₂²×Q₈×D₁₃	1	6	yes	—
410	C₂²	C₂×#88256	1	6	yes	—
411	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	8	no	—
415	C₄	—	2	8	no	—
416	C₄	—	26	8	no	—
417	C₄	—	26	8	no	—
418	C₄	—	26	8	no	—
419	C₂	—	2	8	no	—
420	C₂	—	26	16	no	—
421	C₂	C₂×#11719339	1	12	yes	direct product factor
422	C₂	C₂³×Q₈×D₁₃	1	1	yes	characteristic
423	C₂	C₂²×#88251	1	1	yes	characteristic
424	C₂	C₂²×#88256	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	C₂²×#543
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. C₂×#11719339	C₂	direct (N × H)
2. C₂²×#88151	C₂	semidirect
3. C₂²×#88178	C₂	semidirect
4. C₂²×#88150	C₂	semidirect
5. C₂²×#88150	C₂	semidirect
6. C₂²×#88132	C₂	semidirect
7. C₂²×#88200	C₂	semidirect
10. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
17. C₂³×Dic₂₆	C₂²	semidirect
18. C₂³×Dic₂₆	C₂²	semidirect
19. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
20. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
21. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂×#88200	C₂²	semidirect
30. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
31. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
32. C₂×#88178	C₂²	semidirect
33. C₂²×#6101	C₂²	semidirect
34. C₂²×#6101	C₂²	semidirect
35. C₂²×#6101	C₂²	semidirect
36. #11719339	C₂²	direct (N × H)
37. C₂×#88151	C₂²	semidirect
38. C₂×#88150	C₂²	semidirect
39. C₂×#88150	C₂²	semidirect
41. C₂×#88132	C₂²	semidirect
45. C₂⁴×D₁₃	Q₈	semidirect
49. C₂²×Q₈×C₁₃	C₂³	semidirect
67. C₂²×Dic₂₆	C₂³	semidirect
68. C₂²×Dic₂₆	C₂³	semidirect
69. C₁₃×C₂²⋊Q₈	C₂³	semidirect
70. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
71. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
74. #88200	C₂³	semidirect
80. C₂×C₄⋊Dic₁₃	C₂³	semidirect
81. C₂×C₄⋊Dic₁₃	C₂³	semidirect
82. #88178	C₂³	semidirect
83. C₂×#6101	C₂³	semidirect
84. C₂×#6101	C₂³	semidirect
85. C₂×#6101	C₂³	semidirect
86. #88151	C₂³	semidirect
87. #88150	C₂³	semidirect
88. #88150	C₂³	semidirect
90. #88132	C₂³	semidirect
103. C₂³×D₁₃	C₂×Q₈	semidirect
107. C₂×Q₈×C₁₃	C₂⁴	semidirect
132. C₂×Dic₂₆	C₂⁴	semidirect
133. C₂×Dic₂₆	C₂⁴	semidirect
134. C₁₃×C₄⋊C₄	C₂⁴	semidirect
135. C₁₃×C₄⋊C₄	C₂⁴	semidirect
142. C₄⋊Dic₁₃	C₂⁴	semidirect
143. C₄⋊Dic₁₃	C₂⁴	semidirect
144. #6101	C₂⁴	semidirect
145. #6101	C₂⁴	semidirect
146. #6101	C₂⁴	semidirect
154. C₂²×C₂²⋊Q₈	D₁₃	semidirect
173. C₂²×D₁₃	C₂²×Q₈	semidirect
199. C₂³×Q₈	C₂×D₁₃	semidirect
211. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
217. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
218. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
230. C₂²×C₁₃	#543	semidirect
259. C₂²×Q₈	C₂²×D₁₃	semidirect
281. C₂²⋊Q₈	C₂²×D₁₃	semidirect
287. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
288. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
298. C₂×C₁₃	C₂×#543	semidirect
322. C₂×Q₈	C₂³×D₁₃	semidirect
350. C₄⋊C₄	C₂³×D₁₃	semidirect
351. C₄⋊C₄	C₂³×D₁₃	semidirect
358. C₁₃	C₂²×#543	semidirect
406. C₂²	#11719339	direct (N × H)
421. C₂	C₂×#11719339	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×#11719339	2
C₂²×#88151	2
C₂²×#88178	2
C₂²×#88150	2
C₂²×#88132	2
C₂²×#88200	2
C₂³×#6103	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×#543	13

Subgroups — C22×#11719339 #16769640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719339 #16769640