Subgroups — C₂²×#11719229 #16769577

Order 3328.

14334 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6127	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719229	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#88140	C₂	1	2	yes	maximal, complemented
5	C₂²×#88151	C₂	1	2	yes	maximal, complemented
6	C₂²×#88149	C₂	1	2	yes	maximal, complemented
7	C₂²×#88136	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×D₅₂	C₂	1	4	yes	maximal, complemented
9	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
13	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6127	—	2	16	no	—
15	C₂²×#6127	C₂²	1	24	yes	complemented
16	C₂³×D₅₂	C₂²	1	4	yes	—
17	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₄×D₁₃	—	2	16	no	—
19	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
20	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
21	C₂³×C₄×D₁₃	C₂²	1	24	yes	complemented
22	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
23	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₃×#117	C₂²	1	24	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
28	C₂²×#6103	C₂²	1	4	yes	—
29	C₂²×#6103	C₂²	1	4	yes	complemented
30	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	complemented
31	#11719229	C₂²	1	256	yes	direct product factor
32	C₂×#88151	C₂²	1	48	yes	complemented
33	C₂×#88149	C₂²	1	48	yes	complemented
34	C₂×#88140	C₂²	1	48	yes	complemented
35	C₂×#88136	C₂²	1	48	yes	complemented
36	C₂×C₄×D₅₂	C₂²	1	96	yes	complemented
37	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
38	C₂⁴×D₁₃	—	2	8	no	—
39	C₂⁴×D₁₃	—	2	16	no	—
40	C₂⁴×D₁₃	C₂³	1	12	yes	—
41	C₂⁴×D₁₃	C₂³	1	2	yes	—
42	C₂⁴×D₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
44	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₂²⋊D₁₃	—	2	16	no	—
49	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
50	C₂³×Dic₁₃	—	2	8	no	—
51	C₂³×Dic₁₃	C₂³	1	12	yes	—
52	C₂³×Dic₁₃	C₂³	1	2	yes	—
53	C₂³×Dic₁₃	C₂³	1	2	yes	—
54	C₂×#6127	—	2	192	no	—
55	C₂×#6127	C₂³	1	64	yes	complemented
56	C₂²×D₅₂	—	2	32	no	—
57	C₂²×D₅₂	—	2	8	no	—
58	C₂²×D₅₂	C₂³	1	48	yes	—
59	C₂²×D₅₂	C₂³	1	12	yes	complemented
60	C₂²×C₄×D₁₃	—	2	16	no	—
61	C₂²×C₄×D₁₃	—	2	16	no	—
62	C₂²×C₄×D₁₃	—	2	16	no	—
63	C₂²×C₄×D₁₃	—	2	192	no	—
64	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
65	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
66	C₂²×C₄×D₁₃	C₂³	1	64	yes	complemented
67	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
68	C₂²×Dic₂₆	—	2	8	no	—
69	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
70	C₁₃×#117	C₂³	1	64	yes	complemented
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	complemented
72	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
73	C₂×C₄²×C₁₃	C₂³	1	24	yes	complemented
74	C₂×#6103	C₂³	1	48	yes	—
75	C₂×#6103	C₂³	1	48	yes	complemented
76	C₂×C₄⋊Dic₁₃	C₂³	1	48	yes	complemented
77	#88151	C₂³	1	128	yes	complemented
78	#88149	C₂³	1	128	yes	complemented
79	#88140	C₂³	1	128	yes	complemented
80	#88136	C₂³	1	128	yes	complemented
81	C₄×D₅₂	C₂³	1	256	yes	complemented
82	C₂²×#525	—	13	1	no	maximal, Sylow
83	C₂⁴×C₁₃	—	2	8	no	—
84	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
85	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
86	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
87	C₂³×D₁₃	—	2	128	no	—
88	C₂³×D₁₃	—	2	48	no	—
89	C₂³×D₁₃	—	2	8	no	—
90	C₂³×D₁₃	—	2	8	no	—
91	C₂³×D₁₃	—	2	96	no	—
92	C₂³×D₁₃	—	2	8	no	—
93	C₂³×D₁₃	—	2	16	no	—
94	C₂³×D₁₃	#41	1	16	yes	complemented
95	C₂³×D₁₃	C₂⁴	1	16	yes	—
96	C₂³×D₁₃	C₂⁴	1	12	yes	—
97	C₂³×D₁₃	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₁₃	—	2	16	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
102	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
103	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
104	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
105	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
106	C₂×C₂²⋊D₁₃	—	2	96	no	—
107	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
108	C₂²×Dic₁₃	—	2	8	no	—
109	C₂²×Dic₁₃	—	2	48	no	—
110	C₂²×Dic₁₃	—	2	8	no	—
111	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
112	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
113	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
114	#6127	—	2	256	no	—
115	C₂×D₅₂	—	2	192	no	—
116	C₂×D₅₂	—	2	48	no	—
117	C₂×D₅₂	C₂⁴	1	64	yes	—
118	C₂×D₅₂	C₂⁴	1	16	yes	complemented
119	C₂×C₄×D₁₃	—	2	96	no	—
120	C₂×C₄×D₁₃	—	2	96	no	—
121	C₂×C₄×D₁₃	—	2	96	no	—
122	C₂×C₄×D₁₃	—	2	256	no	—
123	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
124	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
125	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
126	C₂×Dic₂₆	—	2	48	no	—
127	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
128	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	complemented
129	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
130	C₄²×C₁₃	C₂⁴	1	32	yes	complemented
131	#6103	C₂⁴	1	64	yes	—
132	#6103	C₂⁴	1	64	yes	complemented
133	C₄⋊Dic₁₃	C₂⁴	1	64	yes	complemented
134	C₂³×#41	—	13	1	no	—
135	C₂⁵×C₄	—	13	1	no	—
136	C₂×#525	—	13	48	no	—
137	C₂²×#123	—	13	2	no	—
138	C₂²×C₂²⋊Q₈	—	13	2	no	—
139	C₂²×#121	—	13	2	no	—
140	C₂²×#120	—	13	2	no	—
141	C₂²×C₄×D₄	—	13	4	no	—
142	C₂²×#117	D₁₃	1	1	yes	characteristic, complemented
143	C₂³×C₁₃	—	2	32	no	—
144	C₂³×C₁₃	—	2	24	no	—
145	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
146	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
147	C₂³×C₁₃	C₂×#41	1	8	yes	—
148	C₂³×C₁₃	C₂⁵	1	4	yes	—
149	C₂³×C₁₃	C₂⁵	1	3	yes	—
150	C₂²×D₁₃	—	2	384	no	—
151	C₂²×D₁₃	—	2	64	no	—
152	C₂²×D₁₃	—	2	32	no	—
153	C₂²×D₁₃	—	2	24	no	—
154	C₂²×D₁₃	—	2	24	no	—
155	C₂²×D₁₃	—	2	64	no	—
156	C₂²×D₁₃	—	2	24	no	—
157	C₂²×D₁₃	—	2	48	no	—
158	C₂²×D₁₃	—	4	32	no	—
159	C₂²×D₁₃	C₂×#41	1	48	yes	complemented
160	C₂²×D₁₃	C₂⁵	1	8	yes	—
161	C₂²×D₁₃	C₂⁵	1	8	yes	—
162	C₂×C₄×C₁₃	—	2	48	no	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
165	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
166	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
167	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
168	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
169	C₂²⋊D₁₃	—	2	64	no	—
170	C₂×Dic₁₃	—	2	24	no	—
171	C₂×Dic₁₃	—	2	32	no	—
172	C₂×Dic₁₃	—	2	24	no	—
173	C₂×Dic₁₃	C₂⁵	1	8	yes	—
174	C₂×Dic₁₃	C₂⁵	1	8	yes	—
175	D₅₂	—	2	128	no	—
176	D₅₂	—	2	32	no	—
177	C₄×D₁₃	—	2	64	no	—
178	C₄×D₁₃	—	2	64	no	—
179	C₄×D₁₃	—	2	64	no	—
180	Dic₂₆	—	2	32	no	—
181	C₂⁶	—	13	1	no	—
182	C₂²×#41	—	13	24	no	—
183	C₂²×#41	—	26	16	no	—
184	C₂³×Q₈	—	13	1	no	—
185	C₂³×D₄	—	13	2	no	—
186	C₂³×D₄	—	13	1	no	—
187	C₂³×D₄	—	13	4	no	—
188	C₂⁴×C₄	—	13	1	no	—
189	C₂⁴×C₄	—	13	2	no	—
190	C₂⁴×C₄	—	13	24	no	—
191	C₂⁴×C₄	—	13	2	no	—
192	C₂⁴×C₄	—	13	2	no	—
193	C₂⁴×C₄	—	26	16	no	—
194	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
195	#525	—	13	256	no	—
196	C₂×#123	—	13	48	no	—
197	C₂×C₂²⋊Q₈	—	13	48	no	—
198	C₂×#121	—	13	48	no	—
199	C₂×#120	—	13	48	no	—
200	C₂×C₄×D₄	—	13	96	no	—
201	C₂×#117	C₂×D₁₃	1	24	yes	complemented
202	C₂²×C₄⋊C₄	—	13	4	no	—
203	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
204	C₂²×C₂²⋊C₄	—	13	4	no	—
205	C₂²×C₂²⋊C₄	—	13	4	no	—
206	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
207	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
208	C₂²×C₁₃	—	2	8	no	—
209	C₂²×C₁₃	—	2	48	no	—
210	C₂²×C₁₃	#525	1	16	yes	complemented
211	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
212	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
213	C₂²×C₁₃	C₂²×#41	1	12	yes	—
214	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
215	C₂×D₁₃	—	2	128	no	—
216	C₂×D₁₃	—	2	8	no	—
217	C₂×D₁₃	—	2	8	no	—
218	C₂×D₁₃	—	2	96	no	—
219	C₂×D₁₃	—	2	8	no	—
220	C₂×D₁₃	—	2	16	no	—
221	C₂×D₁₃	—	4	48	no	—
222	C₂×D₁₃	C₂²×#41	1	16	yes	complemented
223	C₄×C₁₃	—	2	16	no	—
224	C₄×C₁₃	C₂³×D₄	1	8	yes	—
225	C₄×C₁₃	C₂³×D₄	1	8	yes	—
226	Dic₁₃	—	2	8	no	—
227	Dic₁₃	—	2	8	no	—
228	C₂⁵	—	13	2	no	—
229	C₂⁵	—	13	2	no	—
230	C₂⁵	—	13	12	no	—
231	C₂⁵	—	26	16	no	—
232	C₂⁵	—	26	8	no	—
233	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
234	C₂×#41	—	13	64	no	—
235	C₂×#41	—	26	192	no	—
236	C₂²×Q₈	—	13	12	no	—
237	C₂²×Q₈	—	26	8	no	—
238	C₂²×D₄	—	13	24	no	—
239	C₂²×D₄	—	13	48	no	—
240	C₂²×D₄	—	13	12	no	—
241	C₂²×D₄	—	26	32	no	—
242	C₂²×D₄	—	26	16	no	—
243	C₂²×D₄	—	26	8	no	—
244	C₂³×C₄	—	13	2	no	—
245	C₂³×C₄	—	13	2	no	—
246	C₂³×C₄	—	13	12	no	—
247	C₂³×C₄	—	13	24	no	—
248	C₂³×C₄	—	13	24	no	—
249	C₂³×C₄	—	13	24	no	—
250	C₂³×C₄	—	13	64	no	—
251	C₂³×C₄	—	26	8	no	—
252	C₂³×C₄	—	26	16	no	—
253	C₂³×C₄	—	26	16	no	—
254	C₂³×C₄	—	26	16	no	—
255	C₂³×C₄	—	26	192	no	—
256	C₂³×C₄	D₅₂	1	16	yes	complemented
257	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
258	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
259	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
260	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
261	#123	—	13	128	no	—
262	C₂²⋊Q₈	—	13	128	no	—
263	#121	—	13	128	no	—
264	#120	—	13	128	no	—
265	C₄×D₄	—	13	256	no	—
266	#117	C₂²×D₁₃	1	64	yes	complemented
267	C₂×C₄⋊C₄	—	13	48	no	—
268	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	complemented
269	C₂×C₂²⋊C₄	—	13	48	no	—
270	C₂×C₂²⋊C₄	—	13	48	no	—
271	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
272	C₂×C₄²	C₂²×D₁₃	1	24	yes	complemented
273	C₂×C₁₃	—	2	8	no	—
274	C₂×C₁₃	C₂×#525	1	12	yes	complemented
275	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
276	C₂×C₁₃	C₂³×#41	1	2	yes	—
277	D₁₃	—	2	16	no	—
278	D₁₃	—	4	8	no	—
279	C₂⁴	—	2	8	no	—
280	C₂⁴	—	13	16	no	—
281	C₂⁴	—	13	12	no	—
282	C₂⁴	—	13	12	no	—
283	C₂⁴	—	13	16	no	—
284	C₂⁴	—	26	96	no	—
285	C₂⁴	—	26	128	no	—
286	C₂⁴	—	26	48	no	—
287	C₂⁴	—	26	8	no	—
288	C₂⁴	—	26	8	no	—
289	C₂⁴	—	26	8	no	—
290	C₂⁴	—	26	16	no	—
291	C₂⁴	C₂×D₅₂	1	8	yes	—
292	C₂⁴	C₂³×D₁₃	1	6	yes	—
293	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
294	#41	—	26	256	no	—
295	C₂×Q₈	—	13	16	no	—
296	C₂×Q₈	—	26	48	no	—
297	C₂×D₄	—	13	32	no	—
298	C₂×D₄	—	13	64	no	—
299	C₂×D₄	—	13	16	no	—
300	C₂×D₄	—	26	192	no	—
301	C₂×D₄	—	26	96	no	—
302	C₂×D₄	—	26	48	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	13	12	no	—
305	C₂²×C₄	—	13	12	no	—
306	C₂²×C₄	—	13	16	no	—
307	C₂²×C₄	—	13	32	no	—
308	C₂²×C₄	—	13	32	no	—
309	C₂²×C₄	—	13	32	no	—
310	C₂²×C₄	—	26	48	no	—
311	C₂²×C₄	—	26	8	no	—
312	C₂²×C₄	—	26	8	no	—
313	C₂²×C₄	—	26	96	no	—
314	C₂²×C₄	—	26	96	no	—
315	C₂²×C₄	—	26	96	no	—
316	C₂²×C₄	—	26	256	no	—
317	C₂²×C₄	C₂×D₅₂	1	8	yes	—
318	C₂²×C₄	C₂×D₅₂	1	8	yes	—
319	C₂²×C₄	C₂×D₅₂	1	96	yes	complemented
320	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
321	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
322	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
323	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
324	C₄⋊C₄	—	13	64	no	—
325	C₄⋊C₄	C₂³×D₁₃	1	32	yes	complemented
326	C₂²⋊C₄	—	13	64	no	—
327	C₂²⋊C₄	—	13	64	no	—
328	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
329	C₄²	C₂³×D₁₃	1	32	yes	complemented
330	C₁₃	C₂²×#525	1	1	yes	characteristic, complemented, Sylow
331	C₂³	—	2	32	no	—
332	C₂³	—	2	24	no	—
333	C₂³	—	13	48	no	—
334	C₂³	—	13	8	no	—
335	C₂³	—	13	8	no	—
336	C₂³	—	26	64	no	—
337	C₂³	—	26	384	no	—
338	C₂³	—	26	64	no	—
339	C₂³	—	26	32	no	—
340	C₂³	—	26	24	no	—
341	C₂³	—	26	24	no	—
342	C₂³	—	26	24	no	—
343	C₂³	—	26	48	no	—
344	C₂³	—	52	32	no	—
345	C₂³	C₂²×D₅₂	1	24	yes	—
346	C₂³	C₂²×D₅₂	1	4	yes	—
347	C₂³	#41×D₁₃	1	8	yes	—
348	C₂³	C₂⁴×D₁₃	1	4	yes	—
349	C₂³	C₂⁴×D₁₃	1	3	yes	—
350	Q₈	—	26	32	no	—
351	D₄	—	26	128	no	—
352	D₄	—	26	64	no	—
353	D₄	—	26	32	no	—
354	C₂×C₄	—	2	48	no	—
355	C₂×C₄	—	13	8	no	—
356	C₂×C₄	—	13	8	no	—
357	C₂×C₄	—	26	32	no	—
358	C₂×C₄	—	26	24	no	—
359	C₂×C₄	—	26	24	no	—
360	C₂×C₄	—	26	64	no	—
361	C₂×C₄	—	26	64	no	—
362	C₂×C₄	—	26	64	no	—
363	C₂×C₄	C₂²×D₅₂	1	24	yes	—
364	C₂×C₄	C₂²×D₅₂	1	24	yes	—
365	C₂×C₄	C₂²×D₅₂	1	64	yes	complemented
366	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
367	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
368	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
369	C₂²	—	2	48	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	13	16	no	—
372	C₂²	—	26	128	no	—
373	C₂²	—	26	96	no	—
374	C₂²	—	26	8	no	—
375	C₂²	—	26	8	no	—
376	C₂²	—	26	8	no	—
377	C₂²	—	26	16	no	—
378	C₂²	—	52	48	no	—
379	C₂²	#11719229	1	16	yes	direct product factor
380	C₂²	C₂³×D₅₂	1	8	yes	—
381	C₂²	C₂³×D₅₂	1	6	yes	—
382	C₂²	C₂×#41×D₁₃	1	12	yes	—
383	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
384	C₄	—	2	16	no	—
385	C₄	—	26	8	no	—
386	C₄	—	26	8	no	—
387	C₄	C₂³×D₅₂	1	8	yes	—
388	C₄	C₂³×D₅₂	1	8	yes	—
389	C₂	—	2	8	no	—
390	C₂	—	26	16	no	—
391	C₂	—	52	8	no	—
392	C₂	C₂×#11719229	1	12	yes	direct product factor
393	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
394	C₂	C₂²×#41×D₁₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂²×#525
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. C₂⁴×C₄×D₁₃	C₂	semidirect
3. C₂×#11719229	C₂	direct (N × H)
4. C₂²×#88140	C₂	semidirect
5. C₂²×#88151	C₂	semidirect
6. C₂²×#88149	C₂	semidirect
7. C₂²×#88136	C₂	semidirect
8. C₂²×C₄×D₅₂	C₂	semidirect
9. C₂²×C₁₃×#117	C₂	semidirect
15. C₂²×#6127	C₂²	semidirect
17. C₂³×D₅₂	C₂²	semidirect
21. C₂³×C₄×D₁₃	C₂²	semidirect
22. C₂³×C₄×D₁₃	C₂²	semidirect
23. C₂³×Dic₂₆	C₂²	semidirect
24. C₂×C₁₃×#117	C₂²	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₁₃	C₂²	semidirect
29. C₂²×#6103	C₂²	semidirect
30. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
31. #11719229	C₂²	direct (N × H)
32. C₂×#88151	C₂²	semidirect
33. C₂×#88149	C₂²	semidirect
34. C₂×#88140	C₂²	semidirect
35. C₂×#88136	C₂²	semidirect
36. C₂×C₄×D₅₂	C₂²	semidirect
43. C₂³×C₄×C₁₃	D₄	semidirect
55. C₂×#6127	C₂³	semidirect
59. C₂²×D₅₂	C₂³	semidirect
66. C₂²×C₄×D₁₃	C₂³	semidirect
67. C₂²×C₄×D₁₃	C₂³	semidirect
69. C₂²×Dic₂₆	C₂³	semidirect
70. C₁₃×#117	C₂³	semidirect
71. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
73. C₂×C₄²×C₁₃	C₂³	semidirect
75. C₂×#6103	C₂³	semidirect
76. C₂×C₄⋊Dic₁₃	C₂³	semidirect
77. #88151	C₂³	semidirect
78. #88149	C₂³	semidirect
79. #88140	C₂³	semidirect
80. #88136	C₂³	semidirect
81. C₄×D₅₂	C₂³	semidirect
94. C₂³×D₁₃	#41	semidirect
101. C₂²×C₄×C₁₃	C₂×D₄	semidirect
118. C₂×D₅₂	C₂⁴	semidirect
125. C₂×C₄×D₁₃	C₂⁴	semidirect
127. C₂×Dic₂₆	C₂⁴	semidirect
128. C₁₃×C₄⋊C₄	C₂⁴	semidirect
130. C₄²×C₁₃	C₂⁴	semidirect
132. #6103	C₂⁴	semidirect
133. C₄⋊Dic₁₃	C₂⁴	semidirect
142. C₂²×#117	D₁₃	semidirect
159. C₂²×D₁₃	C₂×#41	semidirect
165. C₂×C₄×C₁₃	C₂²×D₄	semidirect
201. C₂×#117	C₂×D₁₃	semidirect
203. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
207. C₂²×C₄²	C₂×D₁₃	semidirect
210. C₂²×C₁₃	#525	semidirect
222. C₂×D₁₃	C₂²×#41	semidirect
256. C₂³×C₄	D₅₂	semidirect
266. #117	C₂²×D₁₃	semidirect
268. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
272. C₂×C₄²	C₂²×D₁₃	semidirect
274. C₂×C₁₃	C₂×#525	semidirect
319. C₂²×C₄	C₂×D₅₂	semidirect
325. C₄⋊C₄	C₂³×D₁₃	semidirect
329. C₄²	C₂³×D₁₃	semidirect
330. C₁₃	C₂²×#525	semidirect
365. C₂×C₄	C₂²×D₅₂	semidirect
379. C₂²	#11719229	direct (N × H)
392. C₂	C₂×#11719229	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×#6127	2
C₂⁴×C₄×D₁₃	2
C₂×#11719229	2
C₂²×#88140	2
C₂²×#88151	2
C₂²×#88149	2
C₂²×#88136	2
C₂²×C₄×D₅₂	2
C₂²×C₁₃×#117	2
C₂²×#525	13

Subgroups — C22×#11719229 #16769577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719229 #16769577