Subgroups — C₂²×#11719535 #16769674

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	C₂⁴×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11719535	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#88194	C₂	1	2	yes	maximal, complemented
4	C₂²×#88201	C₂	1	2	yes	maximal, complemented
5	C₂²×#88184	C₂	1	4	yes	maximal, complemented
6	C₂²×#88191	C₂	1	4	yes	maximal, complemented
7	C₂²×#88180	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×#41	—	2	16	no	—
11	C₂²×C₁₃×#41	C₂²	1	24	yes	complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
17	C₂³×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
18	C₂³×D₅₂	—	2	16	no	—
19	C₂³×D₅₂	C₂²	1	2	yes	—
20	C₂³×D₅₂	C₂²	1	2	yes	—
21	C₂³×D₅₂	C₂²	1	24	yes	complemented
22	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
23	#11719535	C₂²	1	256	yes	direct product factor
24	C₂×#88201	C₂²	1	48	yes	complemented
25	C₂×#88194	C₂²	1	48	yes	complemented
26	C₂×#88191	C₂²	1	96	yes	complemented
27	C₂×#88184	C₂²	1	96	yes	complemented
28	C₂²×#6103	C₂²	1	8	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	C₂³	1	2	yes	—
33	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
34	C₂⁴×D₁₃	—	2	16	no	—
35	C₂⁴×D₁₃	—	4	16	no	—
36	C₂⁴×D₁₃	C₂³	1	4	yes	—
37	C₂⁴×D₁₃	C₂³	1	24	yes	—
38	C₂×C₁₃×#41	—	2	192	no	—
39	C₂×C₁₃×#41	C₂³	1	64	yes	complemented
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	C₂³	1	12	yes	complemented
42	C₂²×D₄×C₁₃	—	2	16	no	—
43	C₂²×D₄×C₁₃	—	2	8	no	—
44	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	12	yes	complemented
46	C₂³×C₄×C₁₃	—	2	16	no	—
47	C₂³×C₄×C₁₃	D₄	1	16	yes	complemented
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	12	yes	—
52	C₂³×C₄×C₁₃	C₂³	1	24	yes	complemented
53	C₂²×C₂²⋊D₁₃	—	4	32	no	—
54	C₂²×C₂²⋊D₁₃	C₂³	1	96	yes	complemented
55	C₂³×Dic₁₃	C₂³	1	4	yes	—
56	C₂²×D₅₂	—	2	16	no	—
57	C₂²×D₅₂	—	2	16	no	—
58	C₂²×D₅₂	—	2	192	no	—
59	C₂²×D₅₂	C₂³	1	24	yes	—
60	C₂²×D₅₂	C₂³	1	24	yes	—
61	C₂²×D₅₂	C₂³	1	64	yes	complemented
62	C₂×C₂²⋊Dic₁₃	C₂³	1	24	yes	—
63	#88201	C₂³	1	128	yes	complemented
64	#88194	C₂³	1	128	yes	complemented
65	#88191	C₂³	1	256	yes	complemented
66	#88184	C₂³	1	256	yes	complemented
67	C₂×#6103	C₂³	1	96	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	8	no	—
74	C₂⁴×C₁₃	—	2	16	no	—
75	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
76	C₂⁴×C₁₃	C₂⁴	1	12	yes	—
77	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
78	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
79	C₂³×D₁₃	—	2	96	no	—
80	C₂³×D₁₃	—	2	16	no	—
81	C₂³×D₁₃	—	2	32	no	—
82	C₂³×D₁₃	—	4	96	no	—
83	C₂³×D₁₃	—	4	128	no	—
84	C₂³×D₁₃	C₂⁴	1	24	yes	—
85	C₂³×D₁₃	C₂⁴	1	32	yes	—
86	C₁₃×#41	—	2	256	no	—
87	C₂×Q₈×C₁₃	—	2	48	no	—
88	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	complemented
89	C₂×D₄×C₁₃	—	2	96	no	—
90	C₂×D₄×C₁₃	—	2	48	no	—
91	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
92	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
93	C₂²×C₄×C₁₃	—	2	8	no	—
94	C₂²×C₄×C₁₃	—	2	96	no	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	96	yes	complemented
98	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
101	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
103	C₂×C₂²⋊D₁₃	—	4	192	no	—
104	C₂×C₂²⋊D₁₃	C₂⁴	1	128	yes	complemented
105	C₂²×Dic₁₃	—	2	16	no	—
106	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
107	C₂×D₅₂	—	2	96	no	—
108	C₂×D₅₂	—	2	96	no	—
109	C₂×D₅₂	—	2	256	no	—
110	C₂×D₅₂	C₂⁴	1	32	yes	—
111	C₂×D₅₂	C₂⁴	1	32	yes	—
112	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
113	#6103	C₂⁴	1	128	yes	complemented
114	C₄⋊Dic₁₃	C₂⁴	1	32	yes	complemented
115	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
116	C₂³×#41	D₁₃	1	1	yes	characteristic, complemented
117	C₂⁴×D₄	—	13	1	no	—
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	24	no	—
127	C₂³×C₁₃	—	2	48	no	—
128	C₂³×C₁₃	—	4	32	no	—
129	C₂³×C₁₃	C₂²×D₄	1	24	yes	—
130	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
131	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
132	C₂³×C₁₃	C₂⁵	1	8	yes	—
133	C₂³×C₁₃	C₂⁵	1	4	yes	—
134	C₂³×C₁₃	C₂⁵	1	3	yes	—
135	C₂²×D₁₃	—	2	64	no	—
136	C₂²×D₁₃	—	2	48	no	—
137	C₂²×D₁₃	—	2	96	no	—
138	C₂²×D₁₃	—	4	64	no	—
139	C₂²×D₁₃	—	4	384	no	—
140	C₂²×D₁₃	—	4	64	no	—
141	C₂²×D₁₃	C₂⁵	1	16	yes	—
142	Q₈×C₁₃	—	2	32	no	—
143	D₄×C₁₃	—	2	64	no	—
144	D₄×C₁₃	—	2	32	no	—
145	C₂×C₄×C₁₃	—	2	24	no	—
146	C₂×C₄×C₁₃	—	2	64	no	—
147	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	24	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	64	yes	complemented
150	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
151	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
152	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
153	C₂²⋊D₁₃	—	4	128	no	—
154	C₂×Dic₁₃	—	2	48	no	—
155	C₂×Dic₁₃	C₂⁵	1	16	yes	—
156	D₅₂	—	2	64	no	—
157	D₅₂	—	2	64	no	—
158	C₂⁶	—	13	2	no	—
159	C₂²×#41	—	2	16	no	—
160	C₂²×#41	C₂×D₁₃	1	24	yes	complemented
161	C₂³×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
162	C₂³×D₄	—	13	8	no	—
163	C₂³×D₄	—	13	2	no	—
164	C₂³×D₄	—	13	2	no	—
165	C₂³×D₄	—	13	24	no	—
166	C₂³×D₄	—	26	16	no	—
167	C₂³×D₄	C₂×D₁₃	1	2	yes	—
168	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
169	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
170	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
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	8	no	—
184	C₂²×C₁₃	—	2	16	no	—
185	C₂²×C₁₃	—	4	48	no	—
186	C₂²×C₁₃	#535	1	16	yes	complemented
187	C₂²×C₁₃	C₂³×D₄	1	8	yes	—
188	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
189	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
190	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
191	C₂×D₁₃	—	2	16	no	—
192	C₂×D₁₃	—	2	32	no	—
193	C₂×D₁₃	—	4	128	no	—
194	C₂×D₁₃	—	4	96	no	—
195	C₄×C₁₃	—	2	8	no	—
196	C₄×C₁₃	C₂³×D₄	1	8	yes	—
197	C₄×C₁₃	C₂³×D₄	1	8	yes	—
198	Dic₁₃	—	2	16	no	—
199	C₂⁵	—	13	4	no	—
200	C₂⁵	—	13	24	no	—
201	C₂⁵	—	26	16	no	—
202	C₂⁵	—	52	16	no	—
203	C₂⁵	C₂²×D₁₃	1	2	yes	—
204	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
205	C₂×#41	—	2	192	no	—
206	C₂×#41	C₂²×D₁₃	1	64	yes	complemented
207	C₂²×Q₈	—	2	8	no	—
208	C₂²×Q₈	C₂²×D₁₃	1	12	yes	complemented
209	C₂²×D₄	—	2	16	no	—
210	C₂²×D₄	—	2	8	no	—
211	C₂²×D₄	—	13	96	no	—
212	C₂²×D₄	—	13	24	no	—
213	C₂²×D₄	—	13	24	no	—
214	C₂²×D₄	—	13	64	no	—
215	C₂²×D₄	—	26	16	no	—
216	C₂²×D₄	—	26	16	no	—
217	C₂²×D₄	—	26	192	no	—
218	C₂²×D₄	—	52	32	no	—
219	C₂²×D₄	C₂²×D₁₃	1	24	yes	—
220	C₂²×D₄	C₂²×D₁₃	1	12	yes	complemented
221	C₂³×C₄	—	2	16	no	—
222	C₂³×C₄	—	13	4	no	—
223	C₂³×C₄	C₂²⋊D₁₃	1	16	yes	complemented
224	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
225	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
227	C₂³×C₄	C₂²×D₁₃	1	12	yes	—
228	C₂³×C₄	C₂²×D₁₃	1	24	yes	complemented
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	8	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	16	no	—
244	C₂⁴	—	2	8	no	—
245	C₂⁴	—	2	16	no	—
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	13	24	no	—
248	C₂⁴	—	13	32	no	—
249	C₂⁴	—	26	32	no	—
250	C₂⁴	—	26	96	no	—
251	C₂⁴	—	26	16	no	—
252	C₂⁴	—	52	96	no	—
253	C₂⁴	—	52	128	no	—
254	C₂⁴	C₂×C₂²⋊D₁₃	1	8	yes	—
255	C₂⁴	C₂³×D₁₃	1	12	yes	—
256	C₂⁴	C₂³×D₁₃	1	6	yes	—
257	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
258	#41	—	2	256	no	—
259	C₂×Q₈	—	2	48	no	—
260	C₂×Q₈	C₂³×D₁₃	1	16	yes	complemented
261	C₂×D₄	—	2	96	no	—
262	C₂×D₄	—	2	48	no	—
263	C₂×D₄	—	13	128	no	—
264	C₂×D₄	—	13	32	no	—
265	C₂×D₄	—	13	32	no	—
266	C₂×D₄	—	26	96	no	—
267	C₂×D₄	—	26	96	no	—
268	C₂×D₄	—	26	256	no	—
269	C₂×D₄	—	52	192	no	—
270	C₂×D₄	C₂³×D₁₃	1	32	yes	—
271	C₂×D₄	C₂³×D₁₃	1	16	yes	complemented
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	96	no	—
274	C₂²×C₄	—	13	24	no	—
275	C₂²×C₄	—	26	16	no	—
276	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
277	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
278	C₂²×C₄	C₂×C₂²⋊D₁₃	1	96	yes	complemented
279	C₂²×C₄	C₂³×D₁₃	1	12	yes	—
280	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
281	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
282	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
283	C₂²×C₄	C₂³×D₁₃	1	32	yes	complemented
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	48	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	13	16	no	—
295	C₂³	—	26	96	no	—
296	C₂³	—	26	64	no	—
297	C₂³	—	26	48	no	—
298	C₂³	—	52	64	no	—
299	C₂³	—	52	384	no	—
300	C₂³	—	52	64	no	—
301	C₂³	#88256	1	8	yes	—
302	C₂³	C₂²×C₂²⋊D₁₃	1	24	yes	—
303	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
304	C₂³	C₂⁴×D₁₃	1	8	yes	—
305	C₂³	C₂⁴×D₁₃	1	4	yes	—
306	C₂³	C₂⁴×D₁₃	1	3	yes	—
307	Q₈	—	2	32	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	32	no	—
310	D₄	—	26	64	no	—
311	D₄	—	26	64	no	—
312	D₄	—	52	128	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	64	no	—
315	C₂×C₄	—	13	16	no	—
316	C₂×C₄	—	26	48	no	—
317	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
318	C₂×C₄	C₂²×C₂²⋊D₁₃	1	24	yes	—
319	C₂×C₄	C₂²×C₂²⋊D₁₃	1	64	yes	complemented
320	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
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	8	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	4	48	no	—
328	C₂²	—	26	16	no	—
329	C₂²	—	26	32	no	—
330	C₂²	—	52	128	no	—
331	C₂²	—	52	96	no	—
332	C₂²	#11719535	1	16	yes	direct product factor
333	C₂²	C₂×#88256	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	—	2	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	8	no	—
343	C₂	—	52	16	no	—
344	C₂	C₂×#11719535	1	12	yes	direct product factor
345	C₂	C₂⁴×C₂²⋊D₁₃	1	1	yes	characteristic
346	C₂	C₂²×#88256	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂³×C₁₃×#41	C₂
socle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂³×#41	D₁₃
hypocenter	C₁₃	C₂²×#535
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×#41

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₅₂	C₂	semidirect
2. C₂×#11719535	C₂	direct (N × H)
3. C₂²×#88194	C₂	semidirect
4. C₂²×#88201	C₂	semidirect
5. C₂²×#88184	C₂	semidirect
6. C₂²×#88191	C₂	semidirect
7. C₂²×#88180	C₂	semidirect
8. C₂³×C₁₃×#41	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂³×Q₈×C₁₃	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
16. C₂⁴×C₄×C₁₃	C₂²	semidirect
17. C₂³×C₂²⋊D₁₃	C₂²	semidirect
21. C₂³×D₅₂	C₂²	semidirect
23. #11719535	C₂²	direct (N × H)
24. C₂×#88201	C₂²	semidirect
25. C₂×#88194	C₂²	semidirect
26. C₂×#88191	C₂²	semidirect
27. C₂×#88184	C₂²	semidirect
28. C₂²×#6103	C₂²	semidirect
29. C₂×#88180	C₂²	semidirect
30. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
31. C₂²×C₄×Dic₁₃	C₂²	semidirect
39. C₂×C₁₃×#41	C₂³	semidirect
41. C₂²×Q₈×C₁₃	C₂³	semidirect
45. C₂²×D₄×C₁₃	C₂³	semidirect
47. C₂³×C₄×C₁₃	D₄	semidirect
52. C₂³×C₄×C₁₃	C₂³	semidirect
54. C₂²×C₂²⋊D₁₃	C₂³	semidirect
61. C₂²×D₅₂	C₂³	semidirect
63. #88201	C₂³	semidirect
64. #88194	C₂³	semidirect
65. #88191	C₂³	semidirect
66. #88184	C₂³	semidirect
67. C₂×#6103	C₂³	semidirect
68. #88180	C₂³	semidirect
69. C₂×C₄⋊Dic₁₃	C₂³	semidirect
70. C₂×C₄×Dic₁₃	C₂³	semidirect
88. C₂×Q₈×C₁₃	C₂⁴	semidirect
92. C₂×D₄×C₁₃	C₂⁴	semidirect
97. C₂²×C₄×C₁₃	C₂×D₄	semidirect
102. C₂²×C₄×C₁₃	C₂⁴	semidirect
104. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
113. #6103	C₂⁴	semidirect
114. C₄⋊Dic₁₃	C₂⁴	semidirect
115. C₄×Dic₁₃	C₂⁴	semidirect
116. C₂³×#41	D₁₃	semidirect
149. C₂×C₄×C₁₃	C₂²×D₄	semidirect
160. C₂²×#41	C₂×D₁₃	semidirect
161. C₂³×Q₈	C₂×D₁₃	semidirect
168. C₂³×D₄	C₂×D₁₃	semidirect
170. C₂⁴×C₄	C₂×D₁₃	semidirect
186. C₂²×C₁₃	#535	semidirect
206. C₂×#41	C₂²×D₁₃	semidirect
208. C₂²×Q₈	C₂²×D₁₃	semidirect
220. C₂²×D₄	C₂²×D₁₃	semidirect
223. C₂³×C₄	C₂²⋊D₁₃	semidirect
228. C₂³×C₄	C₂²×D₁₃	semidirect
240. C₂×C₁₃	C₂×#535	semidirect
260. C₂×Q₈	C₂³×D₁₃	semidirect
271. C₂×D₄	C₂³×D₁₃	semidirect
278. C₂²×C₄	C₂×C₂²⋊D₁₃	semidirect
283. C₂²×C₄	C₂³×D₁₃	semidirect
288. C₁₃	C₂²×#535	semidirect
319. C₂×C₄	C₂²×C₂²⋊D₁₃	semidirect
332. C₂²	#11719535	direct (N × H)
344. C₂	C₂×#11719535	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×D₅₂	2
C₂×#11719535	2
C₂²×#88194	2
C₂²×#88201	2
C₂²×#88184	2
C₂²×#88191	2
C₂²×#88180	2
C₂³×C₁₃×#41	2
C₂²×#535	13

Subgroups — C22×#11719535 #16769674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719535 #16769674