Subgroups — C₂²×#11719349 #16769651

Order 3328.

9566 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×#11719349	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#88152	C₂	1	2	yes	maximal, complemented
3	C₂²×#88201	C₂	1	2	yes	maximal, complemented
4	C₂²×#88148	C₂	1	2	yes	maximal, complemented
5	C₂²×#88149	C₂	1	2	yes	maximal, complemented
6	C₂²×#88184	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#88136	C₂	1	2	yes	maximal, complemented
8	C₂²×#88135	C₂	1	2	yes	maximal, complemented
9	C₂³×#6103	C₂	1	1	yes	maximal, characteristic, complemented
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	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
15	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₅₂	C₂²	1	2	yes	—
17	C₂³×D₅₂	C₂²	1	2	yes	—
18	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	24	yes	complemented
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
24	C₂×#88201	C₂²	1	48	yes	complemented
25	C₂×#88184	C₂²	1	24	yes	complemented
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×#6103	C₂²	1	24	yes	complemented
31	C₂²×#6103	C₂²	1	2	yes	complemented
32	C₂²×#6103	C₂²	1	2	yes	complemented
33	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×#6101	C₂²	1	2	yes	complemented
35	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
36	#11719349	C₂²	1	256	yes	direct product factor
37	C₂×#88152	C₂²	1	48	yes	complemented
38	C₂×#88149	C₂²	1	48	yes	complemented
39	C₂×#88148	C₂²	1	48	yes	complemented
40	C₂×#88136	C₂²	1	48	yes	complemented
41	C₂×#88135	C₂²	1	48	yes	complemented
42	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
43	C₂⁴×D₁₃	—	2	8	no	—
44	C₂⁴×D₁₃	—	4	4	no	—
45	C₂⁴×D₁₃	—	4	4	no	—
46	C₂⁴×D₁₃	C₂³	1	2	yes	—
47	C₂⁴×D₁₃	C₂³	1	2	yes	—
48	C₂⁴×D₁₃	C₂³	1	12	yes	—
49	C₂²×Q₈×C₁₃	—	4	4	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
51	C₂³×C₄×C₁₃	—	4	4	no	—
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	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
57	C₂²×C₂²⋊D₁₃	—	2	16	no	—
58	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
59	C₂³×Dic₁₃	—	4	4	no	—
60	C₂³×Dic₁₃	C₂³	1	2	yes	—
61	C₂³×Dic₁₃	C₂³	1	2	yes	—
62	C₂³×Dic₁₃	C₂³	1	12	yes	—
63	C₂²×D₅₂	—	4	8	no	—
64	C₂²×D₅₂	—	4	8	no	—
65	C₂²×D₅₂	—	4	4	no	—
66	C₂²×D₅₂	C₂³	1	24	yes	—
67	C₂²×D₅₂	C₂³	1	24	yes	—
68	C₂²×D₅₂	C₂³	1	12	yes	complemented
69	C₂²×C₄×D₁₃	—	4	8	no	—
70	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
71	C₁₃×C₂²⋊Q₈	C₂³	1	64	yes	complemented
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	complemented
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
75	#88201	C₂³	1	128	yes	complemented
76	#88184	C₂³	1	64	yes	complemented
77	C₂×#6103	C₂³	1	24	yes	—
78	C₂×#6103	C₂³	1	24	yes	—
79	C₂×#6103	C₂³	1	24	yes	—
80	C₂×#6103	C₂³	1	24	yes	—
81	C₂×#6103	C₂³	1	64	yes	complemented
82	C₂×#6103	C₂³	1	24	yes	complemented
83	C₂×#6103	C₂³	1	24	yes	complemented
84	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	complemented
85	C₂×#6101	C₂³	1	24	yes	complemented
86	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
87	#88152	C₂³	1	128	yes	complemented
88	#88149	C₂³	1	128	yes	complemented
89	#88148	C₂³	1	128	yes	complemented
90	#88136	C₂³	1	128	yes	complemented
91	#88135	C₂³	1	128	yes	complemented
92	C₂²×#538	—	13	1	no	maximal, Sylow
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	4	no	—
95	C₂⁴×C₁₃	#41	1	8	yes	—
96	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
97	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂³×D₁₃	—	2	8	no	—
99	C₂³×D₁₃	—	2	48	no	—
100	C₂³×D₁₃	—	2	8	no	—
101	C₂³×D₁₃	—	2	8	no	—
102	C₂³×D₁₃	—	2	8	no	—
103	C₂³×D₁₃	—	2	8	no	—
104	C₂³×D₁₃	—	2	8	no	—
105	C₂³×D₁₃	—	4	24	no	—
106	C₂³×D₁₃	—	4	24	no	—
107	C₂³×D₁₃	—	4	64	no	—
108	C₂³×D₁₃	C₂⁴	1	12	yes	—
109	C₂³×D₁₃	C₂⁴	1	12	yes	—
110	C₂³×D₁₃	C₂⁴	1	16	yes	—
111	C₂×Q₈×C₁₃	—	4	24	no	—
112	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	8	no	—
116	C₂²×C₄×C₁₃	—	2	4	no	—
117	C₂²×C₄×C₁₃	—	4	24	no	—
118	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
123	C₂×C₂²⋊D₁₃	—	2	96	no	—
124	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
125	C₂²×Dic₁₃	—	2	8	no	—
126	C₂²×Dic₁₃	—	2	8	no	—
127	C₂²×Dic₁₃	—	4	24	no	—
128	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
129	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
130	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
131	C₂×D₅₂	—	4	48	no	—
132	C₂×D₅₂	—	4	48	no	—
133	C₂×D₅₂	—	4	24	no	—
134	C₂×D₅₂	C₂⁴	1	32	yes	—
135	C₂×D₅₂	C₂⁴	1	32	yes	—
136	C₂×D₅₂	C₂⁴	1	16	yes	complemented
137	C₂×C₄×D₁₃	—	4	48	no	—
138	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
139	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
140	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
141	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
142	#6103	C₂⁴	1	32	yes	—
143	#6103	C₂⁴	1	32	yes	—
144	#6103	C₂⁴	1	32	yes	—
145	#6103	C₂⁴	1	32	yes	—
146	#6103	C₂⁴	1	32	yes	complemented
147	#6103	C₂⁴	1	32	yes	complemented
148	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
149	#6101	C₂⁴	1	32	yes	complemented
150	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
151	C₂×#538	—	13	48	no	—
152	C₂²×#126	—	13	2	no	—
153	C₂²×#124	—	13	2	no	—
154	C₂²×#123	—	13	2	no	—
155	C₂²×C₂²⋊Q₈	D₁₃	1	1	yes	characteristic, complemented
156	C₂²×#121	—	13	1	no	—
157	C₂²×#121	—	13	2	no	—
158	C₂²×#120	—	13	2	no	—
159	C₂²×C₄×D₄	—	13	2	no	—
160	C₂³×C₂²⋊C₄	—	13	1	no	—
161	C₂³×C₁₃	—	2	32	no	—
162	C₂³×C₁₃	—	2	12	no	—
163	C₂³×C₁₃	—	2	12	no	—
164	C₂³×C₁₃	C₂×#41	1	24	yes	—
165	C₂³×C₁₃	C₂×#41	1	4	yes	—
166	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
167	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
168	C₂³×C₁₃	C₂⁵	1	4	yes	—
169	C₂³×C₁₃	C₂⁵	1	3	yes	—
170	C₂²×D₁₃	—	2	24	no	—
171	C₂²×D₁₃	—	2	32	no	—
172	C₂²×D₁₃	—	2	24	no	—
173	C₂²×D₁₃	—	2	24	no	—
174	C₂²×D₁₃	—	2	24	no	—
175	C₂²×D₁₃	—	2	24	no	—
176	C₂²×D₁₃	—	2	24	no	—
177	C₂²×D₁₃	—	4	16	no	—
178	C₂²×D₁₃	—	4	16	no	—
179	C₂²×D₁₃	—	4	192	no	—
180	C₂²×D₁₃	—	4	32	no	—
181	C₂²×D₁₃	—	4	32	no	—
182	C₂²×D₁₃	C₂⁵	1	8	yes	—
183	C₂²×D₁₃	C₂⁵	1	8	yes	—
184	Q₈×C₁₃	—	4	16	no	—
185	C₂×C₄×C₁₃	—	2	24	no	—
186	C₂×C₄×C₁₃	—	2	12	no	—
187	C₂×C₄×C₁₃	—	2	24	no	—
188	C₂×C₄×C₁₃	—	2	12	no	—
189	C₂×C₄×C₁₃	—	4	16	no	—
190	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
191	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
192	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
193	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
194	C₂²⋊D₁₃	—	2	64	no	—
195	C₂×Dic₁₃	—	2	24	no	—
196	C₂×Dic₁₃	—	2	24	no	—
197	C₂×Dic₁₃	—	4	16	no	—
198	C₂×Dic₁₃	C₂⁵	1	8	yes	—
199	C₂×Dic₁₃	C₂⁵	1	8	yes	—
200	D₅₂	—	4	32	no	—
201	D₅₂	—	4	32	no	—
202	D₅₂	—	4	16	no	—
203	C₄×D₁₃	—	4	32	no	—
204	C₂⁶	—	13	1	no	—
205	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
206	C₂³×D₄	—	13	2	no	—
207	C₂³×D₄	—	13	2	no	—
208	C₂³×D₄	—	13	2	no	—
209	C₂³×D₄	—	13	1	no	—
210	C₂⁴×C₄	—	13	1	no	—
211	C₂⁴×C₄	—	13	2	no	—
212	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
213	#538	—	13	256	no	—
214	C₂×#126	—	13	48	no	—
215	C₂×#124	—	13	48	no	—
216	C₂×#123	—	13	48	no	—
217	C₂×C₂²⋊Q₈	C₂×D₁₃	1	24	yes	complemented
218	C₂×#121	—	13	24	no	—
219	C₂×#121	—	13	48	no	—
220	C₂×#120	—	13	48	no	—
221	C₂×C₄×D₄	—	13	48	no	—
222	C₂²×C₄⋊C₄	—	13	2	no	—
223	C₂²×C₄⋊C₄	—	13	1	no	—
224	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
225	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
226	C₂²×C₂²⋊C₄	—	13	2	no	—
227	C₂²×C₂²⋊C₄	—	13	2	no	—
228	C₂²×C₂²⋊C₄	—	13	2	no	—
229	C₂²×C₂²⋊C₄	—	13	2	no	—
230	C₂²×C₂²⋊C₄	—	13	24	no	—
231	C₂²×C₂²⋊C₄	—	13	2	no	—
232	C₂²×C₂²⋊C₄	—	13	2	no	—
233	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
234	C₂²×C₄²	—	13	2	no	—
235	C₂²×C₁₃	—	2	4	no	—
236	C₂²×C₁₃	—	2	4	no	—
237	C₂²×C₁₃	—	2	48	no	—
238	C₂²×C₁₃	#538	1	16	yes	complemented
239	C₂²×C₁₃	C₂²×#41	1	8	yes	—
240	C₂²×C₁₃	C₂²×#41	1	6	yes	—
241	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
242	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
243	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
244	C₂×D₁₃	—	2	8	no	—
245	C₂×D₁₃	—	2	8	no	—
246	C₂×D₁₃	—	2	8	no	—
247	C₂×D₁₃	—	2	8	no	—
248	C₂×D₁₃	—	2	8	no	—
249	C₂×D₁₃	—	2	8	no	—
250	C₂×D₁₃	—	4	64	no	—
251	C₂×D₁₃	—	4	48	no	—
252	C₂×D₁₃	—	4	48	no	—
253	C₄×C₁₃	—	2	8	no	—
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	8	no	—
256	C₄×C₁₃	—	2	4	no	—
257	Dic₁₃	—	2	8	no	—
258	Dic₁₃	—	2	8	no	—
259	C₂⁵	—	13	2	no	—
260	C₂⁵	—	13	2	no	—
261	C₂⁵	—	13	12	no	—
262	C₂⁵	—	26	8	no	—
263	C₂⁵	—	52	4	no	—
264	C₂⁵	—	52	4	no	—
265	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
266	C₂²×Q₈	—	4	4	no	—
267	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
268	C₂²×D₄	—	13	24	no	—
269	C₂²×D₄	—	13	24	no	—
270	C₂²×D₄	—	13	24	no	—
271	C₂²×D₄	—	13	12	no	—
272	C₂²×D₄	—	26	16	no	—
273	C₂²×D₄	—	52	4	no	—
274	C₂²×D₄	—	52	8	no	—
275	C₂²×D₄	—	52	8	no	—
276	C₂³×C₄	—	4	4	no	—
277	C₂³×C₄	—	13	2	no	—
278	C₂³×C₄	—	13	2	no	—
279	C₂³×C₄	—	13	12	no	—
280	C₂³×C₄	—	13	24	no	—
281	C₂³×C₄	—	52	8	no	—
282	C₂³×C₄	—	52	4	no	—
283	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
284	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
285	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
287	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
288	#126	—	13	128	no	—
289	#124	—	13	128	no	—
290	#123	—	13	128	no	—
291	C₂²⋊Q₈	C₂²×D₁₃	1	64	yes	complemented
292	#121	—	13	64	no	—
293	#121	—	13	128	no	—
294	#120	—	13	128	no	—
295	C₄×D₄	—	13	128	no	—
296	C₂×C₄⋊C₄	—	13	24	no	—
297	C₂×C₄⋊C₄	—	13	12	no	—
298	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
299	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	complemented
300	C₂×C₂²⋊C₄	—	13	24	no	—
301	C₂×C₂²⋊C₄	—	13	24	no	—
302	C₂×C₂²⋊C₄	—	13	64	no	—
303	C₂×C₂²⋊C₄	—	13	24	no	—
304	C₂×C₂²⋊C₄	—	13	24	no	—
305	C₂×C₂²⋊C₄	—	13	24	no	—
306	C₂×C₂²⋊C₄	—	13	24	no	—
307	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
308	C₂×C₄²	—	13	24	no	—
309	C₂×C₁₃	—	2	8	no	—
310	C₂×C₁₃	C₂×#538	1	12	yes	complemented
311	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
312	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
314	D₁₃	—	4	8	no	—
315	D₁₃	—	4	8	no	—
316	C₂⁴	—	2	4	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	13	12	no	—
319	C₂⁴	—	13	12	no	—
320	C₂⁴	—	13	16	no	—
321	C₂⁴	—	26	8	no	—
322	C₂⁴	—	26	8	no	—
323	C₂⁴	—	26	8	no	—
324	C₂⁴	—	26	48	no	—
325	C₂⁴	—	26	8	no	—
326	C₂⁴	—	26	8	no	—
327	C₂⁴	—	26	8	no	—
328	C₂⁴	—	52	24	no	—
329	C₂⁴	—	52	24	no	—
330	C₂⁴	—	52	64	no	—
331	C₂⁴	#6131	1	8	yes	—
332	C₂⁴	C₂³×D₁₃	1	6	yes	—
333	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
334	C₂×Q₈	—	4	24	no	—
335	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
336	C₂×D₄	—	13	32	no	—
337	C₂×D₄	—	13	32	no	—
338	C₂×D₄	—	13	32	no	—
339	C₂×D₄	—	13	16	no	—
340	C₂×D₄	—	26	96	no	—
341	C₂×D₄	—	52	24	no	—
342	C₂×D₄	—	52	48	no	—
343	C₂×D₄	—	52	48	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	4	24	no	—
349	C₂²×C₄	—	13	12	no	—
350	C₂²×C₄	—	13	12	no	—
351	C₂²×C₄	—	13	16	no	—
352	C₂²×C₄	—	13	32	no	—
353	C₂²×C₄	—	26	8	no	—
354	C₂²×C₄	—	26	8	no	—
355	C₂²×C₄	—	52	48	no	—
356	C₂²×C₄	—	52	24	no	—
357	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
358	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
359	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
360	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
361	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
362	C₄⋊C₄	—	13	32	no	—
363	C₄⋊C₄	—	13	16	no	—
364	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
365	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
366	C₂²⋊C₄	—	13	32	no	—
367	C₂²⋊C₄	—	13	32	no	—
368	C₂²⋊C₄	—	13	32	no	—
369	C₂²⋊C₄	—	13	32	no	—
370	C₂²⋊C₄	—	13	32	no	—
371	C₂²⋊C₄	—	13	32	no	—
372	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
373	C₄²	—	13	32	no	—
374	C₁₃	C₂²×#538	1	1	yes	characteristic, complemented, Sylow
375	C₂³	—	2	32	no	—
376	C₂³	—	2	12	no	—
377	C₂³	—	2	12	no	—
378	C₂³	—	13	8	no	—
379	C₂³	—	13	8	no	—
380	C₂³	—	26	24	no	—
381	C₂³	—	26	24	no	—
382	C₂³	—	26	24	no	—
383	C₂³	—	26	32	no	—
384	C₂³	—	26	24	no	—
385	C₂³	—	26	24	no	—
386	C₂³	—	26	24	no	—
387	C₂³	—	52	16	no	—
388	C₂³	—	52	16	no	—
389	C₂³	—	52	192	no	—
390	C₂³	—	52	32	no	—
391	C₂³	—	52	32	no	—
392	C₂³	#88251	1	4	yes	—
393	C₂³	C₂×#6131	1	24	yes	—
394	C₂³	C₂×#6131	1	4	yes	—
395	C₂³	#88256	1	4	yes	—
396	C₂³	C₂⁴×D₁₃	1	4	yes	—
397	C₂³	C₂⁴×D₁₃	1	3	yes	—
398	Q₈	—	4	16	no	—
399	D₄	—	26	64	no	—
400	D₄	—	52	16	no	—
401	D₄	—	52	32	no	—
402	D₄	—	52	32	no	—
403	C₂×C₄	—	2	12	no	—
404	C₂×C₄	—	2	12	no	—
405	C₂×C₄	—	2	24	no	—
406	C₂×C₄	—	2	24	no	—
407	C₂×C₄	—	4	16	no	—
408	C₂×C₄	—	13	8	no	—
409	C₂×C₄	—	13	8	no	—
410	C₂×C₄	—	26	24	no	—
411	C₂×C₄	—	26	24	no	—
412	C₂×C₄	—	52	32	no	—
413	C₂×C₄	—	52	16	no	—
414	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
415	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
416	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
417	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	48	no	—
421	C₂²	—	26	8	no	—
422	C₂²	—	26	8	no	—
423	C₂²	—	26	8	no	—
424	C₂²	—	26	8	no	—
425	C₂²	—	26	8	no	—
426	C₂²	—	26	8	no	—
427	C₂²	—	52	64	no	—
428	C₂²	—	52	48	no	—
429	C₂²	—	52	48	no	—
430	C₂²	#11719349	1	16	yes	direct product factor
431	C₂²	C₂×#88251	1	6	yes	—
432	C₂²	C₂²×#6131	1	8	yes	—
433	C₂²	C₂²×#6131	1	6	yes	—
434	C₂²	C₂×#88256	1	6	yes	—
435	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	8	no	—
440	C₄	—	26	8	no	—
441	C₄	—	26	8	no	—
442	C₂	—	2	8	no	—
443	C₂	—	52	8	no	—
444	C₂	—	52	8	no	—
445	C₂	C₂×#11719349	1	12	yes	direct product factor
446	C₂	C₂³×#6131	1	1	yes	characteristic
447	C₂	C₂²×#88251	1	1	yes	characteristic
448	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
hypercenter	C₂²×C₂²⋊Q₈	D₁₃
hypocenter	C₁₃	C₂²×#538
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×#11719349	C₂	direct (N × H)
2. C₂²×#88152	C₂	semidirect
3. C₂²×#88201	C₂	semidirect
4. C₂²×#88148	C₂	semidirect
5. C₂²×#88149	C₂	semidirect
6. C₂²×#88184	C₂	semidirect
7. C₂²×#88136	C₂	semidirect
8. C₂²×#88135	C₂	semidirect
9. C₂³×#6103	C₂	semidirect
10. C₂²×C₁₃×C₂²⋊Q₈	C₂	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
18. C₂³×D₅₂	C₂²	semidirect
19. C₂³×C₄×D₁₃	C₂²	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
22. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
24. C₂×#88201	C₂²	semidirect
25. C₂×#88184	C₂²	semidirect
30. C₂²×#6103	C₂²	semidirect
31. C₂²×#6103	C₂²	semidirect
32. C₂²×#6103	C₂²	semidirect
33. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
34. C₂²×#6101	C₂²	semidirect
35. C₂²×C₄×Dic₁₃	C₂²	semidirect
36. #11719349	C₂²	direct (N × H)
37. C₂×#88152	C₂²	semidirect
38. C₂×#88149	C₂²	semidirect
39. C₂×#88148	C₂²	semidirect
40. C₂×#88136	C₂²	semidirect
41. C₂×#88135	C₂²	semidirect
50. C₂²×Q₈×C₁₃	C₂³	semidirect
68. C₂²×D₅₂	C₂³	semidirect
70. C₂²×C₄×D₁₃	C₂³	semidirect
71. C₁₃×C₂²⋊Q₈	C₂³	semidirect
72. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
73. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
75. #88201	C₂³	semidirect
76. #88184	C₂³	semidirect
81. C₂×#6103	C₂³	semidirect
82. C₂×#6103	C₂³	semidirect
83. C₂×#6103	C₂³	semidirect
84. C₂×C₄⋊Dic₁₃	C₂³	semidirect
85. C₂×#6101	C₂³	semidirect
86. C₂×C₄×Dic₁₃	C₂³	semidirect
87. #88152	C₂³	semidirect
88. #88149	C₂³	semidirect
89. #88148	C₂³	semidirect
90. #88136	C₂³	semidirect
91. #88135	C₂³	semidirect
112. C₂×Q₈×C₁₃	C₂⁴	semidirect
136. C₂×D₅₂	C₂⁴	semidirect
138. C₂×C₄×D₁₃	C₂⁴	semidirect
139. C₁₃×C₄⋊C₄	C₂⁴	semidirect
140. C₁₃×C₄⋊C₄	C₂⁴	semidirect
146. #6103	C₂⁴	semidirect
147. #6103	C₂⁴	semidirect
148. C₄⋊Dic₁₃	C₂⁴	semidirect
149. #6101	C₂⁴	semidirect
150. C₄×Dic₁₃	C₂⁴	semidirect
155. C₂²×C₂²⋊Q₈	D₁₃	semidirect
205. C₂³×Q₈	C₂×D₁₃	semidirect
217. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
224. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
225. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
238. C₂²×C₁₃	#538	semidirect
267. C₂²×Q₈	C₂²×D₁₃	semidirect
291. C₂²⋊Q₈	C₂²×D₁₃	semidirect
298. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
299. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
310. C₂×C₁₃	C₂×#538	semidirect
335. C₂×Q₈	C₂³×D₁₃	semidirect
364. C₄⋊C₄	C₂³×D₁₃	semidirect
365. C₄⋊C₄	C₂³×D₁₃	semidirect
374. C₁₃	C₂²×#538	semidirect
430. C₂²	#11719349	direct (N × H)
445. C₂	C₂×#11719349	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×#11719349	2
C₂²×#88152	2
C₂²×#88201	2
C₂²×#88148	2
C₂²×#88149	2
C₂²×#88184	2
C₂²×#88136	2
C₂²×#88135	2
C₂³×#6103	2
C₂²×C₁₃×C₂²⋊Q₈	2
C₂²×#538	13

Subgroups — C22×#11719349 #16769651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719349 #16769651