Subgroups — C₂²×#11719510 #16769675

Order 3328.

14414 conjugacy classes of subgroups.

The subgroup lattice has 348 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	C₂×#11719510	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88194	C₂	1	2	yes	maximal, complemented
4	C₂²×#88190	C₂	1	2	yes	maximal, complemented
5	C₂²×#88192	C₂	1	4	yes	maximal, complemented
6	C₂²×#88207	C₂	1	4	yes	maximal, complemented
7	C₂²×#88180	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁴×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₁₃	C₂²	1	2	yes	—
10	C₂³×D₄×C₁₃	—	2	16	no	—
11	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂³×D₄×C₁₃	C₂²	1	24	yes	complemented
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
16	C₂³×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
17	C₂²×#6127	—	2	16	no	—
18	C₂²×#6127	C₂²	1	24	yes	complemented
19	C₂³×D₅₂	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂³×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×#88207	C₂²	1	96	yes	complemented
23	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊Dic₁₃	C₂²	1	8	yes	complemented
25	#11719510	C₂²	1	256	yes	direct product factor
26	C₂×#88194	C₂²	1	48	yes	complemented
27	C₂×#88192	C₂²	1	96	yes	complemented
28	C₂×#88190	C₂²	1	48	yes	complemented
29	C₂×#88180	C₂²	1	24	yes	complemented
30	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
31	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	complemented
32	C₂⁵×C₁₃	—	2	16	no	—
33	C₂⁵×C₁₃	—	4	16	no	—
34	C₂⁵×C₁₃	C₂³	1	4	yes	—
35	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
36	C₂⁵×C₁₃	C₂³	1	24	yes	—
37	C₂⁴×D₁₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₃	—	2	16	no	—
39	C₂²×D₄×C₁₃	—	2	16	no	—
40	C₂²×D₄×C₁₃	—	2	192	no	—
41	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
42	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
43	C₂²×D₄×C₁₃	C₂³	1	64	yes	complemented
44	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
48	C₂²×C₂²⋊D₁₃	—	2	16	no	—
49	C₂²×C₂²⋊D₁₃	—	4	32	no	—
50	C₂²×C₂²⋊D₁₃	C₂³	1	24	yes	—
51	C₂²×C₂²⋊D₁₃	C₂³	1	96	yes	complemented
52	C₂³×Dic₁₃	C₂³	1	4	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	8	no	—
57	C₂²×D₅₂	C₂³	1	12	yes	complemented
58	C₂²×C₄×D₁₃	—	2	16	no	—
59	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
60	C₂²×Dic₂₆	—	2	8	no	—
61	C₂²×Dic₂₆	C₂³	1	12	yes	complemented
62	#88207	C₂³	1	256	yes	complemented
63	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
64	C₂×C₂²⋊Dic₁₃	C₂³	1	96	yes	complemented
65	#88194	C₂³	1	128	yes	complemented
66	#88192	C₂³	1	256	yes	complemented
67	#88190	C₂³	1	128	yes	complemented
68	#88180	C₂³	1	64	yes	complemented
69	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	complemented
70	C₂×C₄×Dic₁₃	C₂³	1	24	yes	complemented
71	C₂²×#535	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	—	2	8	no	—
73	C₂⁴×C₁₃	—	2	96	no	—
74	C₂⁴×C₁₃	—	2	16	no	—
75	C₂⁴×C₁₃	—	2	32	no	—
76	C₂⁴×C₁₃	—	4	96	no	—
77	C₂⁴×C₁₃	—	4	128	no	—
78	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
79	C₂⁴×C₁₃	C₂⁴	1	24	yes	—
80	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
81	C₂⁴×C₁₃	C₂⁴	1	32	yes	—
82	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₂³×D₁₃	—	2	8	no	—
84	C₂³×D₁₃	—	2	16	no	—
85	C₂³×D₁₃	C₂⁴	1	12	yes	—
86	C₂×D₄×C₁₃	—	2	96	no	—
87	C₂×D₄×C₁₃	—	2	96	no	—
88	C₂×D₄×C₁₃	—	2	256	no	—
89	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
90	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
91	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
92	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
94	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
97	C₂×C₂²⋊D₁₃	—	2	96	no	—
98	C₂×C₂²⋊D₁₃	—	4	192	no	—
99	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
100	C₂×C₂²⋊D₁₃	C₂⁴	1	128	yes	complemented
101	C₂²×Dic₁₃	—	2	8	no	—
102	C₂²×Dic₁₃	—	2	16	no	—
103	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
104	C₂²×Dic₁₃	C₂⁴	1	12	yes	—
105	#6127	—	2	256	no	—
106	C₂×D₅₂	—	2	48	no	—
107	C₂×D₅₂	C₂⁴	1	16	yes	complemented
108	C₂×C₄×D₁₃	—	2	96	no	—
109	C₂×C₄×D₁₃	C₂⁴	1	32	yes	complemented
110	C₂×Dic₂₆	—	2	48	no	—
111	C₂×Dic₂₆	C₂⁴	1	16	yes	complemented
112	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
113	C₂²⋊Dic₁₃	C₂⁴	1	128	yes	complemented
114	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
115	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
116	C₂³×#41	—	13	1	no	—
117	C₂⁴×D₄	D₁₃	1	1	yes	characteristic, complemented
118	C₂×#535	—	13	48	no	—
119	C₂²×#127	—	13	2	no	—
120	C₂²×#124	—	13	2	no	—
121	C₂²×#121	—	13	4	no	—
122	C₂²×#120	—	13	4	no	—
123	C₂²×#117	—	13	1	no	—
124	C₂³×C₁₃	—	2	32	no	—
125	C₂³×C₁₃	—	2	24	no	—
126	C₂³×C₁₃	—	2	64	no	—
127	C₂³×C₁₃	—	2	48	no	—
128	C₂³×C₁₃	—	2	96	no	—
129	C₂³×C₁₃	—	4	64	no	—
130	C₂³×C₁₃	—	4	384	no	—
131	C₂³×C₁₃	—	4	64	no	—
132	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
133	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
134	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
135	C₂³×C₁₃	C₂⁵	1	16	yes	—
136	C₂³×C₁₃	C₂⁵	1	4	yes	—
137	C₂³×C₁₃	C₂⁵	1	3	yes	—
138	C₂²×D₁₃	—	2	24	no	—
139	C₂²×D₁₃	—	2	48	no	—
140	C₂²×D₁₃	—	4	32	no	—
141	C₂²×D₁₃	C₂⁵	1	8	yes	—
142	D₄×C₁₃	—	2	64	no	—
143	D₄×C₁₃	—	2	64	no	—
144	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
145	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
146	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
147	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
148	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
149	C₂²⋊D₁₃	—	2	64	no	—
150	C₂²⋊D₁₃	—	4	128	no	—
151	C₂×Dic₁₃	—	2	24	no	—
152	C₂×Dic₁₃	—	2	48	no	—
153	C₂×Dic₁₃	C₂⁵	1	16	yes	—
154	C₂×Dic₁₃	C₂⁵	1	8	yes	—
155	D₅₂	—	2	32	no	—
156	C₄×D₁₃	—	2	64	no	—
157	Dic₂₆	—	2	32	no	—
158	C₂⁶	C₂×D₁₃	1	2	yes	—
159	C₂²×#41	—	13	24	no	—
160	C₂²×#41	—	26	16	no	—
161	C₂³×Q₈	—	13	1	no	—
162	C₂³×D₄	—	2	16	no	—
163	C₂³×D₄	—	13	2	no	—
164	C₂³×D₄	—	13	8	no	—
165	C₂³×D₄	—	13	1	no	—
166	C₂³×D₄	C₂×D₁₃	1	2	yes	—
167	C₂³×D₄	C₂×D₁₃	1	2	yes	—
168	C₂³×D₄	C₂×D₁₃	1	24	yes	complemented
169	C₂⁴×C₄	—	13	2	no	—
170	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
171	#535	—	13	256	no	—
172	C₂×#127	—	13	48	no	—
173	C₂×#124	—	13	48	no	—
174	C₂×#121	—	13	96	no	—
175	C₂×#120	—	13	96	no	—
176	C₂×#117	—	13	24	no	—
177	C₂²×C₄⋊C₄	—	13	2	no	—
178	C₂²×C₂²⋊C₄	—	13	2	no	—
179	C₂²×C₂²⋊C₄	—	13	8	no	—
180	C₂²×C₄²	—	13	2	no	—
181	C₂²×C₁₃	—	2	8	no	—
182	C₂²×C₁₃	—	2	48	no	—
183	C₂²×C₁₃	—	2	16	no	—
184	C₂²×C₁₃	—	2	32	no	—
185	C₂²×C₁₃	—	4	128	no	—
186	C₂²×C₁₃	—	4	96	no	—
187	C₂²×C₁₃	#535	1	16	yes	complemented
188	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
189	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
190	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
191	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
192	C₂×D₁₃	—	2	8	no	—
193	C₂×D₁₃	—	2	16	no	—
194	C₂×D₁₃	—	4	48	no	—
195	C₄×C₁₃	C₂³×D₄	1	8	yes	—
196	C₄×C₁₃	C₂³×D₄	1	8	yes	—
197	Dic₁₃	—	2	8	no	—
198	Dic₁₃	—	2	16	no	—
199	C₂⁵	—	2	16	no	—
200	C₂⁵	—	4	16	no	—
201	C₂⁵	—	13	2	no	—
202	C₂⁵	C₂²×D₁₃	1	4	yes	—
203	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
204	C₂⁵	C₂²×D₁₃	1	24	yes	—
205	C₂×#41	—	13	64	no	—
206	C₂×#41	—	26	192	no	—
207	C₂²×Q₈	—	13	12	no	—
208	C₂²×Q₈	—	26	8	no	—
209	C₂²×D₄	—	2	16	no	—
210	C₂²×D₄	—	2	16	no	—
211	C₂²×D₄	—	2	192	no	—
212	C₂²×D₄	—	13	24	no	—
213	C₂²×D₄	—	13	96	no	—
214	C₂²×D₄	—	13	12	no	—
215	C₂²×D₄	—	26	16	no	—
216	C₂²×D₄	—	26	8	no	—
217	C₂²×D₄	—	52	32	no	—
218	C₂²×D₄	C₂²×D₁₃	1	24	yes	—
219	C₂²×D₄	C₂²×D₁₃	1	24	yes	—
220	C₂²×D₄	C₂²×D₁₃	1	64	yes	complemented
221	C₂³×C₄	—	13	2	no	—
222	C₂³×C₄	—	13	4	no	—
223	C₂³×C₄	—	13	24	no	—
224	C₂³×C₄	—	26	16	no	—
225	C₂³×C₄	C₂²⋊D₁₃	1	16	yes	complemented
226	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
229	#127	—	13	128	no	—
230	#124	—	13	128	no	—
231	#121	—	13	256	no	—
232	#120	—	13	256	no	—
233	#117	—	13	64	no	—
234	C₂×C₄⋊C₄	—	13	24	no	—
235	C₂×C₂²⋊C₄	—	13	24	no	—
236	C₂×C₂²⋊C₄	—	13	96	no	—
237	C₂×C₄²	—	13	24	no	—
238	C₂×C₁₃	—	2	8	no	—
239	C₂×C₁₃	—	4	16	no	—
240	C₂×C₁₃	C₂×#535	1	12	yes	complemented
241	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
242	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
243	D₁₃	—	4	8	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	32	no	—
246	C₂⁴	—	2	96	no	—
247	C₂⁴	—	2	16	no	—
248	C₂⁴	—	4	96	no	—
249	C₂⁴	—	4	128	no	—
250	C₂⁴	—	13	12	no	—
251	C₂⁴	—	26	16	no	—
252	C₂⁴	—	26	8	no	—
253	C₂⁴	C₂×C₂²⋊D₁₃	1	8	yes	—
254	C₂⁴	C₂³×D₁₃	1	24	yes	—
255	C₂⁴	C₂³×D₁₃	1	6	yes	—
256	C₂⁴	C₂³×D₁₃	1	32	yes	—
257	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
258	#41	—	26	256	no	—
259	C₂×Q₈	—	13	16	no	—
260	C₂×Q₈	—	26	48	no	—
261	C₂×D₄	—	2	96	no	—
262	C₂×D₄	—	2	96	no	—
263	C₂×D₄	—	2	256	no	—
264	C₂×D₄	—	13	32	no	—
265	C₂×D₄	—	13	128	no	—
266	C₂×D₄	—	13	16	no	—
267	C₂×D₄	—	26	96	no	—
268	C₂×D₄	—	26	48	no	—
269	C₂×D₄	—	52	192	no	—
270	C₂×D₄	C₂³×D₁₃	1	32	yes	—
271	C₂×D₄	C₂³×D₁₃	1	32	yes	—
272	C₂²×C₄	—	13	24	no	—
273	C₂²×C₄	—	13	12	no	—
274	C₂²×C₄	—	13	32	no	—
275	C₂²×C₄	—	26	16	no	—
276	C₂²×C₄	—	26	8	no	—
277	C₂²×C₄	—	26	96	no	—
278	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
279	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
280	C₂²×C₄	C₂×C₂²⋊D₁₃	1	96	yes	complemented
281	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
282	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
283	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
284	C₄⋊C₄	—	13	32	no	—
285	C₂²⋊C₄	—	13	32	no	—
286	C₂²⋊C₄	—	13	128	no	—
287	C₄²	—	13	32	no	—
288	C₁₃	C₂²×#535	1	1	yes	characteristic, complemented, Sylow
289	C₂³	—	2	32	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	96	no	—
292	C₂³	—	2	64	no	—
293	C₂³	—	2	48	no	—
294	C₂³	—	4	64	no	—
295	C₂³	—	4	384	no	—
296	C₂³	—	4	64	no	—
297	C₂³	—	13	8	no	—
298	C₂³	—	26	48	no	—
299	C₂³	—	26	24	no	—
300	C₂³	—	52	32	no	—
301	C₂³	#88251	1	8	yes	—
302	C₂³	C₂²×C₂²⋊D₁₃	1	24	yes	—
303	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
304	C₂³	C₂⁴×D₁₃	1	16	yes	—
305	C₂³	C₂⁴×D₁₃	1	4	yes	—
306	C₂³	C₂⁴×D₁₃	1	3	yes	—
307	Q₈	—	26	32	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	64	no	—
310	D₄	—	26	64	no	—
311	D₄	—	26	32	no	—
312	D₄	—	52	128	no	—
313	C₂×C₄	—	13	16	no	—
314	C₂×C₄	—	13	8	no	—
315	C₂×C₄	—	26	48	no	—
316	C₂×C₄	—	26	24	no	—
317	C₂×C₄	—	26	64	no	—
318	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
319	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
320	C₂×C₄	C₂²×C₂²⋊D₁₃	1	64	yes	complemented
321	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
322	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	2	32	no	—
327	C₂²	—	4	128	no	—
328	C₂²	—	4	96	no	—
329	C₂²	—	26	8	no	—
330	C₂²	—	26	16	no	—
331	C₂²	—	52	48	no	—
332	C₂²	#11719510	1	16	yes	direct product factor
333	C₂²	C₂×#88251	1	12	yes	—
334	C₂²	C₂³×C₂²⋊D₁₃	1	8	yes	—
335	C₂²	C₂³×C₂²⋊D₁₃	1	6	yes	—
336	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
337	C₄	—	26	8	no	—
338	C₄	—	26	16	no	—
339	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
340	C₄	C₂³×C₂²⋊D₁₃	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	—	52	8	no	—
344	C₂	C₂×#11719510	1	12	yes	direct product factor
345	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
346	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂⁴×D₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂⁴×D₄	D₁₃
hypocenter	C₁₃	C₂²×#535
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#6127	C₂	semidirect
2. C₂×#11719510	C₂	direct (N × H)
3. C₂²×#88194	C₂	semidirect
4. C₂²×#88190	C₂	semidirect
5. C₂²×#88192	C₂	semidirect
6. C₂²×#88207	C₂	semidirect
7. C₂²×#88180	C₂	semidirect
8. C₂⁴×D₄×C₁₃	C₂	semidirect
13. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂³×C₂²⋊D₁₃	C₂²	semidirect
18. C₂²×#6127	C₂²	semidirect
19. C₂³×D₅₂	C₂²	semidirect
20. C₂³×C₄×D₁₃	C₂²	semidirect
21. C₂³×Dic₂₆	C₂²	semidirect
22. C₂×#88207	C₂²	semidirect
24. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
25. #11719510	C₂²	direct (N × H)
26. C₂×#88194	C₂²	semidirect
27. C₂×#88192	C₂²	semidirect
28. C₂×#88190	C₂²	semidirect
29. C₂×#88180	C₂²	semidirect
30. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
31. C₂²×C₄×Dic₁₃	C₂²	semidirect
43. C₂²×D₄×C₁₃	C₂³	semidirect
44. C₂³×C₄×C₁₃	D₄	semidirect
51. C₂²×C₂²⋊D₁₃	C₂³	semidirect
55. C₂×#6127	C₂³	semidirect
57. C₂²×D₅₂	C₂³	semidirect
59. C₂²×C₄×D₁₃	C₂³	semidirect
61. C₂²×Dic₂₆	C₂³	semidirect
62. #88207	C₂³	semidirect
64. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
65. #88194	C₂³	semidirect
66. #88192	C₂³	semidirect
67. #88190	C₂³	semidirect
68. #88180	C₂³	semidirect
69. C₂×C₄⋊Dic₁₃	C₂³	semidirect
70. C₂×C₄×Dic₁₃	C₂³	semidirect
93. C₂²×C₄×C₁₃	C₂×D₄	semidirect
100. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
107. C₂×D₅₂	C₂⁴	semidirect
109. C₂×C₄×D₁₃	C₂⁴	semidirect
111. C₂×Dic₂₆	C₂⁴	semidirect
113. C₂²⋊Dic₁₃	C₂⁴	semidirect
114. C₄⋊Dic₁₃	C₂⁴	semidirect
115. C₄×Dic₁₃	C₂⁴	semidirect
117. C₂⁴×D₄	D₁₃	semidirect
146. C₂×C₄×C₁₃	C₂²×D₄	semidirect
168. C₂³×D₄	C₂×D₁₃	semidirect
187. C₂²×C₁₃	#535	semidirect
220. C₂²×D₄	C₂²×D₁₃	semidirect
225. C₂³×C₄	C₂²⋊D₁₃	semidirect
240. C₂×C₁₃	C₂×#535	semidirect
280. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
288. C₁₃	C₂²×#535	semidirect
320. C₂×C₄	C₂²×C₂²⋊D₁₃	semidirect
332. C₂²	#11719510	direct (N × H)
344. C₂	C₂×#11719510	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
C₂×#11719510	2
C₂²×#88194	2
C₂²×#88190	2
C₂²×#88192	2
C₂²×#88207	2
C₂²×#88180	2
C₂⁴×D₄×C₁₃	2
C₂²×#535	13

Subgroups — C22×#11719510 #16769675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719510 #16769675