Subgroups — C₂²×#11719260 #16769864

Order 3328.

12230 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6129	C₂	1	2	yes	maximal, complemented
2	C₂×#11719260	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#88140	C₂	1	4	yes	maximal, complemented
5	C₂²×#88151	C₂	1	2	yes	maximal, complemented
6	C₂²×#88184	C₂	1	2	yes	maximal, complemented
7	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₄⋊Dic₁₃	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	—
13	C₂⁴×Dic₁₃	C₂²	1	4	yes	—
14	C₂²×#6129	—	2	32	no	—
15	C₂²×#6129	C₂²	1	48	yes	complemented
16	C₂³×D₅₂	C₂²	1	1	yes	characteristic
17	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
18	C₂³×Dic₂₆	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	complemented
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88184	C₂²	1	48	yes	complemented
24	C₂²×#6103	C₂²	1	2	yes	—
25	C₂²×#6103	C₂²	1	4	yes	—
26	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
28	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	—
29	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	—
30	C₂²×C₄⋊Dic₁₃	C₂²	1	48	yes	complemented
31	#11719260	C₂²	1	256	yes	direct product factor
32	C₂×#88151	C₂²	1	48	yes	complemented
33	C₂×#88140	C₂²	1	96	yes	complemented
34	C₂×C₄×D₅₂	C₂²	1	24	yes	complemented
35	C₂×#88123	C₂²	1	24	yes	complemented
36	C₂⁵×C₁₃	C₂³	1	2	yes	—
37	C₂⁴×D₁₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₃	D₄	1	16	yes	complemented
39	C₂²×D₄×C₁₃	C₂³	1	12	yes	—
40	C₂³×C₄×C₁₃	—	2	16	no	—
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	24	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₂²⋊D₁₃	—	2	32	no	—
47	C₂²×C₂²⋊D₁₃	C₂³	1	48	yes	—
48	C₂³×Dic₁₃	—	2	32	no	—
49	C₂³×Dic₁₃	C₂³	1	48	yes	—
50	C₂³×Dic₁₃	C₂³	1	4	yes	—
51	C₂³×Dic₁₃	C₂³	1	2	yes	—
52	C₂×#6129	—	2	384	no	—
53	C₂×#6129	C₂³	1	128	yes	complemented
54	C₂²×D₅₂	—	2	8	no	—
55	C₂²×D₅₂	C₂³	1	12	yes	—
56	C₂²×C₄×D₁₃	—	2	16	no	—
57	C₂²×C₄×D₁₃	C₂³	1	24	yes	—
58	C₂²×Dic₂₆	—	2	16	no	—
59	C₂²×Dic₂₆	C₂³	1	24	yes	—
60	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
62	C₂×C₁₃×C₂²⋊C₄	C₂³	1	24	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
64	#88184	C₂³	1	128	yes	complemented
65	C₂×#6103	C₂³	1	24	yes	—
66	C₂×#6103	C₂³	1	48	yes	—
67	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
68	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
69	C₂×C₄⋊Dic₁₃	C₂³	1	12	yes	—
70	C₂×C₄⋊Dic₁₃	C₂³	1	48	yes	—
71	C₂×C₄⋊Dic₁₃	C₂³	1	128	yes	complemented
72	#88151	C₂³	1	128	yes	complemented
73	#88140	C₂³	1	256	yes	complemented
74	C₄×D₅₂	C₂³	1	64	yes	complemented
75	#88123	C₂³	1	64	yes	complemented
76	C₂²×#547	—	13	1	no	maximal, Sylow
77	C₂⁴×C₁₃	—	2	8	no	—
78	C₂⁴×C₁₃	—	2	8	no	—
79	C₂⁴×C₁₃	C₂×D₄	1	16	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
81	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
82	C₂³×D₁₃	—	2	8	no	—
83	C₂³×D₁₃	—	2	8	no	—
84	C₂³×D₁₃	—	2	8	no	—
85	C₂³×D₁₃	C₂⁴	1	12	yes	—
86	C₂×D₄×C₁₃	C₂×D₄	1	96	yes	complemented
87	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	4	no	—
90	C₂²×C₄×C₁₃	—	2	96	no	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
93	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
98	C₂×C₂²⋊D₁₃	—	2	192	no	—
99	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	—
100	C₂²×Dic₁₃	—	2	16	no	—
101	C₂²×Dic₁₃	—	2	8	no	—
102	C₂²×Dic₁₃	—	2	192	no	—
103	C₂²×Dic₁₃	C₂⁴	1	64	yes	—
104	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
105	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
106	#6129	—	2	512	no	—
107	C₂×D₅₂	—	2	48	no	—
108	C₂×D₅₂	C₂⁴	1	16	yes	—
109	C₂×C₄×D₁₃	—	2	96	no	—
110	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
111	C₂×Dic₂₆	—	2	96	no	—
112	C₂×Dic₂₆	C₂⁴	1	32	yes	—
113	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
114	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
115	C₄²×C₁₃	C₂⁴	1	16	yes	—
116	#6103	C₂⁴	1	32	yes	—
117	#6103	C₂⁴	1	64	yes	—
118	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
119	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
120	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
121	C₄⋊Dic₁₃	C₂⁴	1	64	yes	—
122	C₂³×#41	—	13	2	no	—
123	C₂×#547	—	13	48	no	—
124	C₂²×C₄⋊Q₈	—	13	1	no	—
125	C₂²×#123	—	13	4	no	—
126	C₂²×C₂²⋊Q₈	—	13	2	no	—
127	C₂²×#121	—	13	2	no	—
128	C₂²×C₄×D₄	—	13	1	no	—
129	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
130	C₂³×C₄⋊C₄	—	13	2	no	—
131	C₂³×C₁₃	—	2	64	no	—
132	C₂³×C₁₃	—	2	24	no	—
133	C₂³×C₁₃	—	2	24	no	—
134	C₂³×C₁₃	C₂²×D₄	1	48	yes	—
135	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
136	C₂³×C₁₃	C₂×#41	1	4	yes	—
137	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
138	C₂³×C₁₃	C₂⁵	1	8	yes	—
139	C₂³×C₁₃	C₂⁵	1	3	yes	—
140	C₂²×D₁₃	—	2	24	no	—
141	C₂²×D₁₃	—	2	24	no	—
142	C₂²×D₁₃	—	2	24	no	—
143	C₂²×D₁₃	—	4	32	no	—
144	C₂²×D₁₃	C₂⁵	1	8	yes	—
145	D₄×C₁₃	C₂²×D₄	1	64	yes	complemented
146	C₂×C₄×C₁₃	—	2	24	no	—
147	C₂×C₄×C₁₃	—	2	12	no	—
148	C₂×C₄×C₁₃	—	2	64	no	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
150	C₂×C₄×C₁₃	C₂×#41	1	24	yes	complemented
151	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
152	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
153	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
154	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
155	C₂²⋊D₁₃	—	2	128	no	—
156	C₂×Dic₁₃	—	2	48	no	—
157	C₂×Dic₁₃	—	2	24	no	—
158	C₂×Dic₁₃	—	2	128	no	—
159	C₂×Dic₁₃	C₂⁵	1	16	yes	—
160	C₂×Dic₁₃	C₂⁵	1	8	yes	—
161	D₅₂	—	2	32	no	—
162	C₄×D₁₃	—	2	64	no	—
163	Dic₂₆	—	2	64	no	—
164	C₂²×#41	—	13	48	no	—
165	C₂²×#41	—	26	32	no	—
166	C₂³×Q₈	—	13	2	no	—
167	C₂³×D₄	—	13	4	no	—
168	C₂³×D₄	—	13	1	no	—
169	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
170	C₂⁴×C₄	—	13	4	no	—
171	C₂⁴×C₄	—	13	2	no	—
172	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
173	#547	—	13	256	no	—
174	C₂×C₄⋊Q₈	—	13	24	no	—
175	C₂×#123	—	13	96	no	—
176	C₂×C₂²⋊Q₈	—	13	48	no	—
177	C₂×#121	—	13	48	no	—
178	C₂×C₄×D₄	—	13	24	no	—
179	C₂×C₄×D₄	C₂×D₁₃	1	24	yes	complemented
180	C₂²×C₄⋊C₄	—	13	1	no	—
181	C₂²×C₄⋊C₄	—	13	2	no	—
182	C₂²×C₄⋊C₄	—	13	4	no	—
183	C₂²×C₄⋊C₄	—	13	2	no	—
184	C₂²×C₄⋊C₄	—	13	48	no	—
185	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
186	C₂²×C₂²⋊C₄	—	13	2	no	—
187	C₂²×C₂²⋊C₄	—	13	4	no	—
188	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
189	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
190	C₂²×C₁₃	—	2	8	no	—
191	C₂²×C₁₃	—	2	8	no	—
192	C₂²×C₁₃	—	2	96	no	—
193	C₂²×C₁₃	#547	1	16	yes	complemented
194	C₂²×C₁₃	C₂³×D₄	1	16	yes	—
195	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
196	C₂²×C₁₃	C₂²×#41	1	6	yes	—
197	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
198	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
199	C₂×D₁₃	—	2	8	no	—
200	C₂×D₁₃	—	2	8	no	—
201	C₂×D₁₃	—	2	8	no	—
202	C₂×D₁₃	—	4	48	no	—
203	C₄×C₁₃	—	2	8	no	—
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	C₂³×D₄	1	8	yes	—
206	C₄×C₁₃	C₂²×#41	1	8	yes	complemented
207	Dic₁₃	—	2	16	no	—
208	Dic₁₃	—	2	8	no	—
209	C₂⁵	—	13	2	no	—
210	C₂⁵	C₂²×D₁₃	1	2	yes	—
211	C₂×#41	—	13	128	no	—
212	C₂×#41	—	26	384	no	—
213	C₂²×Q₈	—	13	24	no	—
214	C₂²×Q₈	—	26	16	no	—
215	C₂²×D₄	—	13	48	no	—
216	C₂²×D₄	—	13	12	no	—
217	C₂²×D₄	—	26	32	no	—
218	C₂²×D₄	—	26	8	no	—
219	C₂²×D₄	D₅₂	1	16	yes	complemented
220	C₂²×D₄	C₂²×D₁₃	1	12	yes	—
221	C₂³×C₄	—	2	16	no	—
222	C₂³×C₄	—	13	48	no	—
223	C₂³×C₄	—	13	2	no	—
224	C₂³×C₄	—	13	4	no	—
225	C₂³×C₄	—	13	24	no	—
226	C₂³×C₄	—	26	32	no	—
227	C₂³×C₄	—	26	16	no	—
228	C₂³×C₄	C₂²×D₁₃	1	24	yes	—
229	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
230	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
231	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
232	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
233	C₄⋊Q₈	—	13	64	no	—
234	#123	—	13	256	no	—
235	C₂²⋊Q₈	—	13	128	no	—
236	#121	—	13	128	no	—
237	C₄×D₄	—	13	64	no	—
238	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
239	C₂×C₄⋊C₄	—	13	12	no	—
240	C₂×C₄⋊C₄	—	13	24	no	—
241	C₂×C₄⋊C₄	—	13	48	no	—
242	C₂×C₄⋊C₄	—	13	128	no	—
243	C₂×C₄⋊C₄	—	13	24	no	—
244	C₂×C₄⋊C₄	C₂²×D₁₃	1	12	yes	—
245	C₂×C₂²⋊C₄	—	13	24	no	—
246	C₂×C₂²⋊C₄	—	13	48	no	—
247	C₂×C₂²⋊C₄	C₂²×D₁₃	1	24	yes	—
248	C₂×C₄²	C₂²×D₁₃	1	12	yes	—
249	C₂×C₁₃	—	2	16	no	—
250	C₂×C₁₃	C₂×#547	1	12	yes	complemented
251	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
252	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
253	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
254	D₁₃	—	4	8	no	—
255	C₂⁴	—	2	8	no	—
256	C₂⁴	—	2	8	no	—
257	C₂⁴	—	13	12	no	—
258	C₂⁴	—	26	8	no	—
259	C₂⁴	—	26	8	no	—
260	C₂⁴	—	26	8	no	—
261	C₂⁴	C₂×D₅₂	1	16	yes	—
262	C₂⁴	C₂³×D₁₃	1	12	yes	—
263	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
264	#41	—	26	512	no	—
265	C₂×Q₈	—	13	32	no	—
266	C₂×Q₈	—	26	96	no	—
267	C₂×D₄	—	13	64	no	—
268	C₂×D₄	—	13	16	no	—
269	C₂×D₄	—	26	192	no	—
270	C₂×D₄	—	26	48	no	—
271	C₂×D₄	C₂×D₅₂	1	96	yes	complemented
272	C₂×D₄	C₂³×D₁₃	1	16	yes	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	96	no	—
276	C₂²×C₄	—	13	12	no	—
277	C₂²×C₄	—	13	24	no	—
278	C₂²×C₄	—	13	64	no	—
279	C₂²×C₄	—	13	32	no	—
280	C₂²×C₄	—	26	8	no	—
281	C₂²×C₄	—	26	16	no	—
282	C₂²×C₄	—	26	192	no	—
283	C₂²×C₄	—	26	96	no	—
284	C₂²×C₄	C₂×D₅₂	1	8	yes	—
285	C₂²×C₄	#6129	1	8	yes	complemented
286	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
287	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
288	C₂²×C₄	C₂³×D₁₃	1	32	yes	—
289	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
290	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
291	C₄⋊C₄	—	13	16	no	—
292	C₄⋊C₄	—	13	32	no	—
293	C₄⋊C₄	—	13	64	no	—
294	C₄⋊C₄	—	13	32	no	—
295	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
296	C₂²⋊C₄	—	13	32	no	—
297	C₂²⋊C₄	—	13	64	no	—
298	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
299	C₄²	C₂³×D₁₃	1	16	yes	—
300	C₁₃	C₂²×#547	1	1	yes	characteristic, complemented, Sylow
301	C₂³	—	2	64	no	—
302	C₂³	—	2	24	no	—
303	C₂³	—	2	24	no	—
304	C₂³	—	13	8	no	—
305	C₂³	—	26	24	no	—
306	C₂³	—	26	24	no	—
307	C₂³	—	26	24	no	—
308	C₂³	—	52	32	no	—
309	C₂³	C₂²×D₅₂	1	48	yes	—
310	C₂³	C₂²×D₅₂	1	4	yes	—
311	C₂³	C₂×#6129	1	4	yes	—
312	C₂³	#88257	1	4	yes	—
313	C₂³	C₂⁴×D₁₃	1	8	yes	—
314	C₂³	C₂⁴×D₁₃	1	3	yes	—
315	Q₈	—	26	64	no	—
316	D₄	—	26	128	no	—
317	D₄	—	26	32	no	—
318	D₄	C₂²×D₅₂	1	64	yes	complemented
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	64	no	—
322	C₂×C₄	—	13	8	no	—
323	C₂×C₄	—	13	16	no	—
324	C₂×C₄	—	26	24	no	—
325	C₂×C₄	—	26	48	no	—
326	C₂×C₄	—	26	128	no	—
327	C₂×C₄	—	26	64	no	—
328	C₂×C₄	C₂²×D₅₂	1	24	yes	—
329	C₂×C₄	C₂×#6129	1	24	yes	complemented
330	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
331	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
332	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
333	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
334	C₂²	—	2	96	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	26	8	no	—
338	C₂²	—	26	8	no	—
339	C₂²	—	26	8	no	—
340	C₂²	—	52	48	no	—
341	C₂²	#11719260	1	16	yes	direct product factor
342	C₂²	C₂³×D₅₂	1	16	yes	—
343	C₂²	C₂³×D₅₂	1	6	yes	—
344	C₂²	C₂²×#6129	1	6	yes	—
345	C₂²	C₂×#88257	1	6	yes	—
346	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
347	C₄	—	2	8	no	—
348	C₄	—	2	4	no	—
349	C₄	—	26	8	no	—
350	C₄	—	26	16	no	—
351	C₄	C₂³×D₅₂	1	8	yes	—
352	C₄	C₂²×#6129	1	8	yes	complemented
353	C₂	—	2	16	no	—
354	C₂	—	52	8	no	—
355	C₂	C₂×#11719260	1	12	yes	direct product factor
356	C₂	C₂⁴×D₅₂	1	1	yes	characteristic
357	C₂	C₂³×#6129	1	1	yes	characteristic
358	C₂	C₂²×#88257	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂²×#547
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6129	C₂	semidirect
2. C₂×#11719260	C₂	direct (N × H)
3. C₂²×#88123	C₂	semidirect
4. C₂²×#88140	C₂	semidirect
5. C₂²×#88151	C₂	semidirect
6. C₂²×#88184	C₂	semidirect
7. C₂²×C₄×D₅₂	C₂	semidirect
8. C₂³×C₄⋊Dic₁₃	C₂	semidirect
9. C₂²×C₄×D₄×C₁₃	C₂	semidirect
15. C₂²×#6129	C₂²	semidirect
19. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂×#88184	C₂²	semidirect
30. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
31. #11719260	C₂²	direct (N × H)
32. C₂×#88151	C₂²	semidirect
33. C₂×#88140	C₂²	semidirect
34. C₂×C₄×D₅₂	C₂²	semidirect
35. C₂×#88123	C₂²	semidirect
38. C₂²×D₄×C₁₃	D₄	semidirect
53. C₂×#6129	C₂³	semidirect
60. C₄×D₄×C₁₃	C₂³	semidirect
64. #88184	C₂³	semidirect
71. C₂×C₄⋊Dic₁₃	C₂³	semidirect
72. #88151	C₂³	semidirect
73. #88140	C₂³	semidirect
74. C₄×D₅₂	C₂³	semidirect
75. #88123	C₂³	semidirect
86. C₂×D₄×C₁₃	C₂×D₄	semidirect
92. C₂²×C₄×C₁₃	#41	semidirect
129. C₂²×C₄×D₄	D₁₃	semidirect
145. D₄×C₁₃	C₂²×D₄	semidirect
150. C₂×C₄×C₁₃	C₂×#41	semidirect
179. C₂×C₄×D₄	C₂×D₁₃	semidirect
193. C₂²×C₁₃	#547	semidirect
206. C₄×C₁₃	C₂²×#41	semidirect
219. C₂²×D₄	D₅₂	semidirect
238. C₄×D₄	C₂²×D₁₃	semidirect
250. C₂×C₁₃	C₂×#547	semidirect
271. C₂×D₄	C₂×D₅₂	semidirect
285. C₂²×C₄	#6129	semidirect
300. C₁₃	C₂²×#547	semidirect
318. D₄	C₂²×D₅₂	semidirect
329. C₂×C₄	C₂×#6129	semidirect
341. C₂²	#11719260	direct (N × H)
352. C₄	C₂²×#6129	semidirect
355. C₂	C₂×#11719260	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×#6129	2
C₂×#11719260	2
C₂²×#88123	2
C₂²×#88140	2
C₂²×#88151	2
C₂²×#88184	2
C₂²×C₄×D₅₂	2
C₂³×C₄⋊Dic₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂²×#547	13

Subgroups — C22×#11719260 #16769864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719260 #16769864