Subgroups — C₂²×#11719184 #16769600

Order 3328.

8670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719184	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88130	C₂	1	2	yes	maximal, complemented
3	C₂²×#88124	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88129	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#88183	C₂	1	2	yes	maximal, complemented
6	C₂²×#88178	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88184	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
11	C₂²×#88126	C₂	1	2	yes	maximal, complemented
12	C₂³×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
17	C₂³×D₅₂	C₂²	1	1	yes	characteristic
18	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
19	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	24	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
26	C₂×#88184	C₂²	1	24	yes	—
27	C₂×#88183	C₂²	1	48	yes	complemented
28	C₂×C₄×C₂²⋊D₁₃	C₂²	1	48	yes	complemented
29	C₂²×#6103	C₂²	1	2	yes	—
30	C₂²×#6103	C₂²	1	2	yes	—
31	C₂²×#6103	C₂²	1	2	yes	—
32	C₂²×#6103	C₂²	1	2	yes	—
33	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	C₂×#88178	C₂²	1	24	yes	complemented
36	C₂²×#6101	C₂²	1	2	yes	—
37	C₂²×#6101	C₂²	1	2	yes	—
38	C₂²×#6101	C₂²	1	2	yes	—
39	C₂²×#6101	C₂²	1	2	yes	—
40	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
41	#11719184	C₂²	1	256	yes	direct product factor
42	C₂×#88130	C₂²	1	48	yes	complemented
43	C₂×#88129	C₂²	1	24	yes	complemented
44	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
45	C₂×#88126	C₂²	1	48	yes	complemented
46	C₂×#88124	C₂²	1	24	yes	complemented
47	C₂×C₄×Dic₂₆	C₂²	1	24	yes	complemented
48	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
49	C₂⁴×D₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	8	no	—
51	C₂³×C₄×C₁₃	—	2	8	no	—
52	C₂³×C₄×C₁₃	—	2	8	no	—
53	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₂²⋊D₁₃	—	2	16	no	—
63	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
64	C₂³×Dic₁₃	C₂³	1	2	yes	—
65	C₂³×Dic₁₃	C₂³	1	2	yes	—
66	C₂³×Dic₁₃	C₂³	1	2	yes	—
67	C₂²×D₅₂	—	2	8	no	—
68	C₂²×D₅₂	C₂³	1	12	yes	—
69	C₂²×C₄×D₁₃	—	2	16	no	—
70	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
71	C₂²×Dic₂₆	—	2	8	no	—
72	C₂²×Dic₂₆	C₂³	1	12	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
74	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
76	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	64	yes	complemented
78	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
79	#88184	C₂³	1	64	yes	—
80	#88183	C₂³	1	128	yes	complemented
81	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
82	C₂×#6103	C₂³	1	24	yes	—
83	C₂×#6103	C₂³	1	24	yes	—
84	C₂×#6103	C₂³	1	24	yes	—
85	C₂×#6103	C₂³	1	24	yes	—
86	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
87	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
88	#88178	C₂³	1	64	yes	complemented
89	C₂×#6101	C₂³	1	24	yes	—
90	C₂×#6101	C₂³	1	24	yes	—
91	C₂×#6101	C₂³	1	24	yes	—
92	C₂×#6101	C₂³	1	24	yes	—
93	C₂×C₄×Dic₁₃	C₂³	1	24	yes	—
94	#88130	C₂³	1	128	yes	complemented
95	#88129	C₂³	1	64	yes	complemented
96	C₄×D₅₂	C₂³	1	64	yes	complemented
97	#88126	C₂³	1	128	yes	complemented
98	#88124	C₂³	1	64	yes	complemented
99	C₄×Dic₂₆	C₂³	1	64	yes	complemented
100	C₂²×#529	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	—	2	4	no	—
102	C₂⁴×C₁₃	—	2	4	no	—
103	C₂⁴×C₁₃	#41	1	8	yes	—
104	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
105	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂³×D₁₃	—	2	8	no	—
107	C₂³×D₁₃	—	2	8	no	—
108	C₂³×D₁₃	—	2	8	no	—
109	C₂³×D₁₃	C₂⁴	1	12	yes	—
110	C₂²×C₄×C₁₃	—	2	48	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	48	no	—
116	C₂²×C₄×C₁₃	—	2	48	no	—
117	C₂²×C₄×C₁₃	#41	1	8	yes	—
118	C₂²×C₄×C₁₃	#41	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
123	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
124	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
126	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
128	C₂×C₂²⋊D₁₃	—	2	96	no	—
129	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
130	C₂²×Dic₁₃	—	2	8	no	—
131	C₂²×Dic₁₃	—	2	8	no	—
132	C₂²×Dic₁₃	—	2	8	no	—
133	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
134	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
135	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
136	C₂×D₅₂	—	2	48	no	—
137	C₂×D₅₂	C₂⁴	1	16	yes	—
138	C₂×C₄×D₁₃	—	2	96	no	—
139	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
140	C₂×Dic₂₆	—	2	48	no	—
141	C₂×Dic₂₆	C₂⁴	1	16	yes	—
142	C₄²×C₁₃	C₂⁴	1	16	yes	—
143	C₄²×C₁₃	C₂⁴	1	16	yes	—
144	C₄²×C₁₃	C₂⁴	1	16	yes	—
145	C₄²×C₁₃	C₂⁴	1	16	yes	—
146	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
147	#6103	C₂⁴	1	32	yes	—
148	#6103	C₂⁴	1	32	yes	—
149	#6103	C₂⁴	1	32	yes	—
150	#6103	C₂⁴	1	32	yes	—
151	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
152	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
153	#6101	C₂⁴	1	32	yes	—
154	#6101	C₂⁴	1	32	yes	—
155	#6101	C₂⁴	1	32	yes	—
156	#6101	C₂⁴	1	32	yes	—
157	C₄×Dic₁₃	C₂⁴	1	32	yes	—
158	C₂×#529	—	13	48	no	—
159	C₂²×#126	—	13	2	no	—
160	C₂²×#125	—	13	1	no	—
161	C₂²×#124	—	13	1	no	—
162	C₂²×#123	—	13	2	no	—
163	C₂²×C₂²⋊Q₈	—	13	1	no	—
164	C₂²×#121	—	13	1	no	—
165	C₂²×C₄×Q₈	—	13	1	no	—
166	C₂²×C₄×D₄	—	13	1	no	—
167	C₂²×C₄×D₄	—	13	2	no	—
168	C₂²×#117	—	13	2	no	—
169	C₂³×C₄²	D₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	32	no	—
171	C₂³×C₁₃	—	2	12	no	—
172	C₂³×C₁₃	—	2	12	no	—
173	C₂³×C₁₃	C₂×#41	1	24	yes	—
174	C₂³×C₁₃	C₂×#41	1	4	yes	—
175	C₂³×C₁₃	C₂×#41	1	4	yes	—
176	C₂³×C₁₃	C₂×#41	1	4	yes	—
177	C₂³×C₁₃	C₂⁵	1	4	yes	—
178	C₂³×C₁₃	C₂⁵	1	3	yes	—
179	C₂²×D₁₃	—	2	24	no	—
180	C₂²×D₁₃	—	2	24	no	—
181	C₂²×D₁₃	—	2	24	no	—
182	C₂²×D₁₃	—	4	32	no	—
183	C₂²×D₁₃	C₂⁵	1	8	yes	—
184	C₂×C₄×C₁₃	—	2	32	no	—
185	C₂×C₄×C₁₃	—	2	12	no	—
186	C₂×C₄×C₁₃	—	2	12	no	—
187	C₂×C₄×C₁₃	—	2	12	no	—
188	C₂×C₄×C₁₃	—	2	12	no	—
189	C₂×C₄×C₁₃	—	2	32	no	—
190	C₂×C₄×C₁₃	—	2	32	no	—
191	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
192	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
193	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
194	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
195	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
196	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
197	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
198	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
199	C₂²⋊D₁₃	—	2	64	no	—
200	C₂×Dic₁₃	—	2	24	no	—
201	C₂×Dic₁₃	—	2	24	no	—
202	C₂×Dic₁₃	—	2	24	no	—
203	C₂×Dic₁₃	C₂⁵	1	8	yes	—
204	C₂×Dic₁₃	C₂⁵	1	8	yes	—
205	C₂×Dic₁₃	C₂⁵	1	8	yes	—
206	D₅₂	—	2	32	no	—
207	C₄×D₁₃	—	2	64	no	—
208	Dic₂₆	—	2	32	no	—
209	C₂³×Q₈	—	13	1	no	—
210	C₂³×D₄	—	13	2	no	—
211	C₂³×D₄	—	13	1	no	—
212	C₂⁴×C₄	—	13	2	no	—
213	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
214	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
215	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
216	#529	—	13	256	no	—
217	C₂×#126	—	13	48	no	—
218	C₂×#125	—	13	24	no	—
219	C₂×#124	—	13	24	no	—
220	C₂×#123	—	13	48	no	—
221	C₂×C₂²⋊Q₈	—	13	24	no	—
222	C₂×#121	—	13	24	no	—
223	C₂×C₄×Q₈	—	13	24	no	—
224	C₂×C₄×D₄	—	13	48	no	—
225	C₂×C₄×D₄	—	13	24	no	—
226	C₂×#117	—	13	48	no	—
227	C₂²×C₄⋊C₄	—	13	2	no	—
228	C₂²×C₄⋊C₄	—	13	2	no	—
229	C₂²×C₄⋊C₄	—	13	2	no	—
230	C₂²×C₄⋊C₄	—	13	2	no	—
231	C₂²×C₄⋊C₄	—	13	1	no	—
232	C₂²×C₄⋊C₄	—	13	1	no	—
233	C₂²×C₂²⋊C₄	—	13	2	no	—
234	C₂²×C₂²⋊C₄	—	13	2	no	—
235	C₂²×C₂²⋊C₄	—	13	2	no	—
236	C₂²×C₂²⋊C₄	—	13	2	no	—
237	C₂²×C₂²⋊C₄	—	13	2	no	—
238	C₂²×C₄²	—	13	2	no	—
239	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
240	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
241	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
243	C₂²×C₄²	C₂×D₁₃	1	24	yes	complemented
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	4	no	—
246	C₂²×C₁₃	—	2	48	no	—
247	C₂²×C₁₃	#529	1	16	yes	complemented
248	C₂²×C₁₃	C₂²×#41	1	8	yes	—
249	C₂²×C₁₃	C₂²×#41	1	6	yes	—
250	C₂²×C₁₃	C₂²×#41	1	6	yes	—
251	C₂²×C₁₃	C₂²×#41	1	6	yes	—
252	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
253	C₂×D₁₃	—	2	8	no	—
254	C₂×D₁₃	—	2	8	no	—
255	C₂×D₁₃	—	2	8	no	—
256	C₂×D₁₃	—	4	48	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	2	4	no	—
260	C₄×C₁₃	—	2	4	no	—
261	C₄×C₁₃	C₂²×#41	1	8	yes	—
262	C₄×C₁₃	C₂²×#41	1	8	yes	—
263	Dic₁₃	—	2	8	no	—
264	Dic₁₃	—	2	8	no	—
265	Dic₁₃	—	2	8	no	—
266	C₂⁵	—	13	2	no	—
267	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
268	C₂²×Q₈	—	13	12	no	—
269	C₂²×Q₈	—	26	8	no	—
270	C₂²×D₄	—	13	24	no	—
271	C₂²×D₄	—	13	12	no	—
272	C₂²×D₄	—	26	16	no	—
273	C₂²×D₄	—	26	8	no	—
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	2	8	no	—
276	C₂³×C₄	—	2	8	no	—
277	C₂³×C₄	—	13	2	no	—
278	C₂³×C₄	—	13	2	no	—
279	C₂³×C₄	—	13	2	no	—
280	C₂³×C₄	—	13	24	no	—
281	C₂³×C₄	—	26	16	no	—
282	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
285	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
287	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
288	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
289	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
291	#126	—	13	128	no	—
292	#125	—	13	64	no	—
293	#124	—	13	64	no	—
294	#123	—	13	128	no	—
295	C₂²⋊Q₈	—	13	64	no	—
296	#121	—	13	64	no	—
297	C₄×Q₈	—	13	64	no	—
298	C₄×D₄	—	13	128	no	—
299	C₄×D₄	—	13	64	no	—
300	#117	—	13	128	no	—
301	C₂×C₄⋊C₄	—	13	24	no	—
302	C₂×C₄⋊C₄	—	13	24	no	—
303	C₂×C₄⋊C₄	—	13	12	no	—
304	C₂×C₄⋊C₄	—	13	24	no	—
305	C₂×C₄⋊C₄	—	13	12	no	—
306	C₂×C₄⋊C₄	—	13	24	no	—
307	C₂×C₂²⋊C₄	—	13	24	no	—
308	C₂×C₂²⋊C₄	—	13	24	no	—
309	C₂×C₂²⋊C₄	—	13	24	no	—
310	C₂×C₂²⋊C₄	—	13	24	no	—
311	C₂×C₂²⋊C₄	—	13	24	no	—
312	C₂×C₄²	—	13	24	no	—
313	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
314	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
315	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
316	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
317	C₂×C₄²	C₂²×D₁₃	1	64	yes	complemented
318	C₂×C₁₃	—	2	8	no	—
319	C₂×C₁₃	C₂×#529	1	12	yes	complemented
320	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
321	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
322	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
323	D₁₃	—	4	8	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	4	no	—
326	C₂⁴	—	13	12	no	—
327	C₂⁴	—	26	8	no	—
328	C₂⁴	—	26	8	no	—
329	C₂⁴	—	26	8	no	—
330	C₂⁴	#6127	1	8	yes	—
331	C₂⁴	C₂³×D₁₃	1	6	yes	—
332	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
333	C₂×Q₈	—	13	16	no	—
334	C₂×Q₈	—	26	48	no	—
335	C₂×D₄	—	13	32	no	—
336	C₂×D₄	—	13	16	no	—
337	C₂×D₄	—	26	96	no	—
338	C₂×D₄	—	26	48	no	—
339	C₂²×C₄	—	2	48	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	48	no	—
345	C₂²×C₄	—	2	48	no	—
346	C₂²×C₄	—	13	12	no	—
347	C₂²×C₄	—	13	12	no	—
348	C₂²×C₄	—	13	12	no	—
349	C₂²×C₄	—	13	32	no	—
350	C₂²×C₄	—	26	8	no	—
351	C₂²×C₄	—	26	8	no	—
352	C₂²×C₄	—	26	8	no	—
353	C₂²×C₄	—	26	96	no	—
354	C₂²×C₄	#6127	1	8	yes	—
355	C₂²×C₄	#6127	1	8	yes	—
356	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
357	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
358	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
359	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
360	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
361	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
362	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
363	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
364	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
365	C₄⋊C₄	—	13	32	no	—
366	C₄⋊C₄	—	13	32	no	—
367	C₄⋊C₄	—	13	16	no	—
368	C₄⋊C₄	—	13	32	no	—
369	C₄⋊C₄	—	13	16	no	—
370	C₄⋊C₄	—	13	32	no	—
371	C₂²⋊C₄	—	13	32	no	—
372	C₂²⋊C₄	—	13	32	no	—
373	C₂²⋊C₄	—	13	32	no	—
374	C₂²⋊C₄	—	13	32	no	—
375	C₂²⋊C₄	—	13	32	no	—
376	C₄²	—	13	32	no	—
377	C₄²	C₂³×D₁₃	1	16	yes	—
378	C₄²	C₂³×D₁₃	1	16	yes	—
379	C₄²	C₂³×D₁₃	1	16	yes	—
380	C₄²	C₂³×D₁₃	1	16	yes	—
381	C₁₃	C₂²×#529	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	2	32	no	—
383	C₂³	—	2	12	no	—
384	C₂³	—	2	12	no	—
385	C₂³	—	13	8	no	—
386	C₂³	—	26	24	no	—
387	C₂³	—	26	24	no	—
388	C₂³	—	26	24	no	—
389	C₂³	—	52	32	no	—
390	C₂³	C₂×#6127	1	24	yes	—
391	C₂³	C₂×#6127	1	4	yes	—
392	C₂³	C₂×#6127	1	4	yes	—
393	C₂³	C₂×#6127	1	4	yes	—
394	C₂³	C₂⁴×D₁₃	1	4	yes	—
395	C₂³	C₂⁴×D₁₃	1	3	yes	—
396	Q₈	—	26	32	no	—
397	D₄	—	26	64	no	—
398	D₄	—	26	32	no	—
399	C₂×C₄	—	2	32	no	—
400	C₂×C₄	—	2	12	no	—
401	C₂×C₄	—	2	12	no	—
402	C₂×C₄	—	2	12	no	—
403	C₂×C₄	—	2	12	no	—
404	C₂×C₄	—	2	32	no	—
405	C₂×C₄	—	2	32	no	—
406	C₂×C₄	—	13	8	no	—
407	C₂×C₄	—	13	8	no	—
408	C₂×C₄	—	13	8	no	—
409	C₂×C₄	—	26	24	no	—
410	C₂×C₄	—	26	24	no	—
411	C₂×C₄	—	26	24	no	—
412	C₂×C₄	—	26	64	no	—
413	C₂×C₄	C₂×#6127	1	24	yes	—
414	C₂×C₄	C₂×#6127	1	24	yes	—
415	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
416	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
417	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
418	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
419	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
420	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	48	no	—
424	C₂²	—	26	8	no	—
425	C₂²	—	26	8	no	—
426	C₂²	—	26	8	no	—
427	C₂²	—	52	48	no	—
428	C₂²	#11719184	1	16	yes	direct product factor
429	C₂²	C₂²×#6127	1	8	yes	—
430	C₂²	C₂²×#6127	1	6	yes	—
431	C₂²	C₂²×#6127	1	6	yes	—
432	C₂²	C₂²×#6127	1	6	yes	—
433	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	26	8	no	—
439	C₄	—	26	8	no	—
440	C₄	—	26	8	no	—
441	C₄	C₂²×#6127	1	8	yes	—
442	C₄	C₂²×#6127	1	8	yes	—
443	C₂	—	2	8	no	—
444	C₂	—	52	8	no	—
445	C₂	C₂×#11719184	1	12	yes	direct product factor
446	C₂	C₂³×#6127	1	1	yes	characteristic
447	C₂	C₂³×#6127	1	1	yes	characteristic
448	C₂	C₂³×#6127	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₄²×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂²×#88184	C₂
hypercenter	C₂³×C₄²	D₁₃
hypocenter	C₁₃	C₂²×#529
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#11719184	C₂	direct (N × H)
2. C₂²×#88130	C₂	semidirect
3. C₂²×#88124	C₂	semidirect
4. C₂²×#88129	C₂	semidirect
5. C₂²×#88183	C₂	semidirect
6. C₂²×#88178	C₂	semidirect
8. C₂²×C₄×Dic₂₆	C₂	semidirect
9. C₂²×C₄×D₅₂	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
11. C₂²×#88126	C₂	semidirect
12. C₂³×C₄²×C₁₃	C₂	semidirect
24. C₂²×C₄²×C₁₃	C₂²	semidirect
27. C₂×#88183	C₂²	semidirect
28. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
35. C₂×#88178	C₂²	semidirect
41. #11719184	C₂²	direct (N × H)
42. C₂×#88130	C₂²	semidirect
43. C₂×#88129	C₂²	semidirect
44. C₂×C₄×D₅₂	C₂²	semidirect
45. C₂×#88126	C₂²	semidirect
46. C₂×#88124	C₂²	semidirect
47. C₂×C₄×Dic₂₆	C₂²	semidirect
77. C₂×C₄²×C₁₃	C₂³	semidirect
80. #88183	C₂³	semidirect
81. C₄×C₂²⋊D₁₃	C₂³	semidirect
88. #88178	C₂³	semidirect
94. #88130	C₂³	semidirect
95. #88129	C₂³	semidirect
96. C₄×D₅₂	C₂³	semidirect
97. #88126	C₂³	semidirect
98. #88124	C₂³	semidirect
99. C₄×Dic₂₆	C₂³	semidirect
169. C₂³×C₄²	D₁₃	semidirect
243. C₂²×C₄²	C₂×D₁₃	semidirect
247. C₂²×C₁₃	#529	semidirect
317. C₂×C₄²	C₂²×D₁₃	semidirect
319. C₂×C₁₃	C₂×#529	semidirect
381. C₁₃	C₂²×#529	semidirect
428. C₂²	#11719184	direct (N × H)
445. C₂	C₂×#11719184	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×#11719184	2
C₂²×#88130	2
C₂²×#88124	2
C₂²×#88129	2
C₂²×#88183	2
C₂²×#88178	2
C₂²×#88184	2
C₂²×C₄×Dic₂₆	2
C₂²×C₄×D₅₂	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂²×#88126	2
C₂³×C₄²×C₁₃	2
C₂²×#529	13

Subgroups — C22×#11719184 #16769600

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719184 #16769600