Subgroups — C₂²×#11719623 #16809631

Order 3328.

14590 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	C₂×#11719623	C₂	1	48	yes	maximal, direct product factor
2	C₂²×D₄×#261	C₂	1	8	yes	maximal, complemented
3	C₂²×#88237	C₂	1	2	yes	maximal, complemented
4	C₂³×C₂²⋊#261	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂⁵×D₁₃	C₂²	1	2	yes	—
7	C₂⁴×#261	C₂²	1	8	yes	complemented
8	C₂³×D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
9	C₂³×C₂²⋊D₁₃	C₄	1	2	yes	complemented
10	C₂²×D₄×D₁₃	C₄	1	24	yes	complemented
11	C₂²×D₄×D₁₃	C₄	1	4	yes	complemented
12	C₂²×D₄×D₁₃	C₂²	1	4	yes	—
13	C₂²×D₄×D₁₃	C₂²	1	24	yes	—
14	C₂³×D₅₂	C₄	1	1	yes	characteristic, complemented
15	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊#261	C₂²	1	4	yes	—
17	C₂²×C₂²⋊#261	C₂²	1	96	yes	complemented
18	C₂²×C₂²⋊#261	C₂²	1	8	yes	complemented
19	#11719623	C₂²	1	256	yes	direct product factor
20	C₂×D₄×#261	C₂²	1	192	yes	complemented
21	C₂×#88237	C₂²	1	48	yes	complemented
22	C₂²×C₄⋊#261	C₂²	1	4	yes	complemented
23	C₂²×C₄×#261	C₂²	1	4	yes	complemented
24	C₂⁵×C₁₃	C₂×C₄	1	2	yes	complemented
25	C₂⁴×D₁₃	—	4	16	no	—
26	C₂⁴×D₁₃	C₂×C₄	1	24	yes	complemented
27	C₂⁴×D₁₃	C₂×C₄	1	2	yes	complemented
28	C₂⁴×D₁₃	C₂×C₄	1	4	yes	complemented
29	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
30	C₂⁴×D₁₃	C₂³	1	4	yes	—
31	C₂⁴×D₁₃	C₂³	1	24	yes	—
32	C₂³×#261	—	4	32	no	—
33	C₂³×#261	C₂³	1	8	yes	—
34	C₂³×#261	C₂³	1	96	yes	complemented
35	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	complemented
36	C₂²×D₄×C₁₃	C₂×C₄	1	24	yes	complemented
37	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊D₁₃	C₂×C₄	1	8	yes	complemented
39	C₂²×C₂²⋊D₁₃	C₂×C₄	1	48	yes	complemented
40	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂×D₄×D₁₃	C₂×C₄	1	48	yes	complemented
42	C₂×D₄×D₁₃	C₂×C₄	1	192	yes	complemented
43	C₂×D₄×D₁₃	C₂×C₄	1	96	yes	complemented
44	C₂×D₄×D₁₃	C₂³	1	48	yes	—
45	C₂×D₄×D₁₃	C₂³	1	64	yes	—
46	C₂²×D₅₂	C₂×C₄	1	4	yes	complemented
47	C₂²×D₅₂	C₂×C₄	1	24	yes	complemented
48	C₂²×C₄×D₁₃	C₂×C₄	1	12	yes	complemented
49	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	complemented
50	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
51	C₂²×C₄×D₁₃	C₂³	1	12	yes	—
52	C₂×C₂²⋊#261	C₂³	1	48	yes	—
53	C₂×C₂²⋊#261	C₂³	1	256	yes	complemented
54	C₂×C₂²⋊#261	C₂³	1	96	yes	complemented
55	D₄×#261	C₂³	1	512	yes	complemented
56	#88237	C₂³	1	128	yes	complemented
57	C₂×C₄⋊#261	C₂³	1	48	yes	complemented
58	C₂×C₄×#261	C₂³	1	48	yes	complemented
59	C₂²×#518	—	13	1	no	maximal, Sylow
60	C₂⁴×C₁₃	—	4	8	no	—
61	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
63	C₂⁴×C₁₃	C₂²×C₄	1	24	yes	complemented
64	C₂³×D₁₃	—	2	32	no	—
65	C₂³×D₁₃	—	2	8	no	—
66	C₂³×D₁₃	—	4	96	no	—
67	C₂³×D₁₃	—	4	96	no	—
68	C₂³×D₁₃	—	4	16	no	—
69	C₂³×D₁₃	—	4	8	no	—
70	C₂³×D₁₃	C₂²×C₄	1	6	yes	—
71	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
72	C₂³×D₁₃	C₂²×C₄	1	4	yes	—
73	C₂³×D₁₃	C₂²×C₄	1	24	yes	—
74	C₂³×D₁₃	C₂²×C₄	1	96	yes	complemented
75	C₂³×D₁₃	C₂²×C₄	1	24	yes	complemented
76	C₂³×D₁₃	C₂²×C₄	1	48	yes	complemented
77	C₂³×D₁₃	C₂⁴	1	6	yes	—
78	C₂³×D₁₃	C₂⁴	1	24	yes	—
79	C₂³×D₁₃	C₂⁴	1	32	yes	—
80	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
81	C₂²×#261	—	2	32	no	—
82	C₂²×#261	—	4	192	no	—
83	C₂²×#261	C₂⁴	1	48	yes	—
84	C₂²×#261	C₂⁴	1	128	yes	complemented
85	C₂×D₄×C₁₃	C₂²×C₄	1	48	yes	complemented
86	C₂×D₄×C₁₃	C₂²×C₄	1	64	yes	complemented
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	complemented
89	C₂×C₂²⋊D₁₃	C₂²×C₄	1	96	yes	complemented
90	C₂×C₂²⋊D₁₃	C₂²×C₄	1	128	yes	complemented
91	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₁₃	C₂²×C₄	1	12	yes	complemented
93	D₄×D₁₃	C₂²×C₄	1	192	yes	complemented
94	D₄×D₁₃	C₂²×C₄	1	256	yes	complemented
95	D₄×D₁₃	C₂⁴	1	64	yes	—
96	C₂×D₅₂	C₂²×C₄	1	48	yes	complemented
97	C₂×D₅₂	C₂²×C₄	1	64	yes	complemented
98	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
99	C₂×C₄×D₁₃	C₂²×C₄	1	48	yes	complemented
100	C₂×C₄×D₁₃	C₂²×C₄	1	24	yes	complemented
101	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
102	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
103	C₂²⋊#261	C₂⁴	1	64	yes	—
104	C₂²⋊#261	C₂⁴	1	128	yes	complemented
105	C₄⋊#261	C₂⁴	1	64	yes	complemented
106	C₄×#261	C₂⁴	1	64	yes	complemented
107	C₂⁴×D₄	—	13	1	no	—
108	C₂×#518	—	13	48	no	—
109	C₂²×C₄×D₄	—	13	8	no	—
110	C₂²×#117	—	13	2	no	—
111	C₂³×C₂²⋊C₄	—	13	4	no	—
112	C₂³×C₁₃	—	2	4	no	—
113	C₂³×C₁₃	—	2	16	no	—
114	C₂³×C₁₃	—	4	48	no	—
115	C₂³×C₁₃	C₂³×C₄	1	6	yes	—
116	C₂³×C₁₃	C₂³×C₄	1	24	yes	—
117	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
118	C₂³×C₁₃	C₂³×C₄	1	32	yes	complemented
119	C₂²×D₁₃	—	2	4	no	—
120	C₂²×D₁₃	—	2	16	no	—
121	C₂²×D₁₃	—	2	24	no	—
122	C₂²×D₁₃	—	2	96	no	—
123	C₂²×D₁₃	—	2	96	no	—
124	C₂²×D₁₃	—	2	24	no	—
125	C₂²×D₁₃	—	4	192	no	—
126	C₂²×D₁₃	—	4	64	no	—
127	C₂²×D₁₃	—	4	96	no	—
128	C₂²×D₁₃	—	4	48	no	—
129	C₂²×D₁₃	C₂³×C₄	1	6	yes	—
130	C₂²×D₁₃	C₂³×C₄	1	12	yes	—
131	C₂²×D₁₃	C₂³×C₄	1	24	yes	—
132	C₂²×D₁₃	C₂³×C₄	1	48	yes	—
133	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
134	C₂²×D₁₃	C₂³×C₄	1	32	yes	complemented
135	C₂²×D₁₃	C₂³×C₄	1	64	yes	complemented
136	C₂²×D₁₃	H(5,𝔽₂)	1	8	yes	—
137	C₂²×D₁₃	C₂⁵	1	4	yes	—
138	C₂²×D₁₃	C₂⁵	1	16	yes	—
139	C₂²×D₁₃	C₂⁵	1	3	yes	—
140	C₂×#261	—	2	96	no	—
141	C₂×#261	—	4	128	no	—
142	C₂×#261	C₂⁵	1	32	yes	—
143	D₄×C₁₃	C₂³×C₄	1	64	yes	complemented
144	C₂×C₄×C₁₃	C₂³×C₄	1	12	yes	—
145	C₂×C₄×C₁₃	C₂³×C₄	1	16	yes	complemented
146	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
147	C₂×Dic₁₃	C₂³×C₄	1	12	yes	—
148	C₂×Dic₁₃	C₂³×C₄	1	16	yes	complemented
149	D₅₂	C₂³×C₄	1	64	yes	complemented
150	C₄×D₁₃	C₂³×C₄	1	24	yes	—
151	C₄×D₁₃	C₂³×C₄	1	32	yes	complemented
152	C₄×D₁₃	C₂⁵	1	8	yes	—
153	C₂⁶	—	13	2	no	—
154	C₂³×D₄	—	13	2	no	—
155	C₂³×D₄	—	13	4	no	—
156	C₂³×D₄	—	13	24	no	—
157	C₂³×D₄	—	13	4	no	—
158	C₂³×D₄	—	13	24	no	—
159	C₂³×D₄	—	13	1	no	—
160	C₂³×D₄	#261	1	1	yes	characteristic, complemented
161	C₂⁴×C₄	—	13	1	no	—
162	C₂⁴×C₄	—	13	8	no	—
163	#518	—	13	256	no	—
164	C₂×C₄×D₄	—	13	192	no	—
165	C₂×#117	—	13	48	no	—
166	C₂²×C₄⋊C₄	—	13	4	no	—
167	C₂²×C₂²⋊C₄	—	13	4	no	—
168	C₂²×C₂²⋊C₄	—	13	8	no	—
169	C₂²×C₂²⋊C₄	—	13	96	no	—
170	C₂²×C₄²	—	13	4	no	—
171	C₂²×C₁₃	—	2	12	no	—
172	C₂²×C₁₃	—	2	48	no	—
173	C₂²×C₁₃	—	4	32	no	—
174	C₂²×C₁₃	#518	1	4	yes	complemented
175	C₂²×C₁₃	C₂⁴×C₄	1	4	yes	—
176	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
177	C₂²×C₁₃	C₂⁴×C₄	1	3	yes	—
178	C₂×D₁₃	—	2	12	no	—
179	C₂×D₁₃	—	2	48	no	—
180	C₂×D₁₃	—	2	32	no	—
181	C₂×D₁₃	—	2	8	no	—
182	C₂×D₁₃	—	2	24	no	—
183	C₂×D₁₃	—	2	96	no	—
184	C₂×D₁₃	—	4	64	no	—
185	C₂×D₁₃	—	4	32	no	—
186	C₂×D₁₃	#518	1	12	yes	complemented
187	C₂×D₁₃	C₂⁴×C₄	1	4	yes	—
188	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
189	C₂×D₁₃	C₂⁴×C₄	1	3	yes	—
190	C₂×D₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
191	C₂×D₁₃	C₂⁶	1	1	yes	characteristic
192	#261	—	2	32	no	—
193	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
194	Dic₁₃	C₂⁴×C₄	1	8	yes	—
195	C₂⁵	—	13	1	no	—
196	C₂⁵	—	13	4	no	—
197	C₂⁵	—	13	4	no	—
198	C₂⁵	—	13	2	no	—
199	C₂⁵	—	13	24	no	—
200	C₂⁵	—	13	24	no	—
201	C₂⁵	—	52	16	no	—
202	C₂⁵	C₂×#261	1	2	yes	complemented
203	C₂²×D₄	—	13	8	no	—
204	C₂²×D₄	—	13	48	no	—
205	C₂²×D₄	—	13	48	no	—
206	C₂²×D₄	—	13	64	no	—
207	C₂²×D₄	—	13	48	no	—
208	C₂²×D₄	—	13	96	no	—
209	C₂²×D₄	—	13	192	no	—
210	C₂²×D₄	—	13	4	no	—
211	C₂²×D₄	—	13	24	no	—
212	C₂²×D₄	C₂×#261	1	4	yes	complemented
213	C₂²×D₄	C₂×#261	1	24	yes	complemented
214	C₂³×C₄	—	13	1	no	—
215	C₂³×C₄	—	13	2	no	—
216	C₂³×C₄	—	13	2	no	—
217	C₂³×C₄	—	13	12	no	—
218	C₂³×C₄	—	13	12	no	—
219	C₂³×C₄	—	13	8	no	—
220	C₂³×C₄	—	13	96	no	—
221	C₂³×C₄	—	52	32	no	—
222	C₂³×C₄	C₂×#261	1	1	yes	characteristic, complemented
223	C₄×D₄	—	13	512	no	—
224	#117	—	13	128	no	—
225	C₂×C₄⋊C₄	—	13	48	no	—
226	C₂×C₂²⋊C₄	—	13	48	no	—
227	C₂×C₂²⋊C₄	—	13	96	no	—
228	C₂×C₂²⋊C₄	—	13	256	no	—
229	C₂×C₄²	—	13	48	no	—
230	C₂×C₁₃	—	2	4	no	—
231	C₂×C₁₃	—	2	16	no	—
232	C₂×C₁₃	C₂×#518	1	6	yes	complemented
233	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
234	D₁₃	—	2	4	no	—
235	D₁₃	—	2	16	no	—
236	D₁₃	C₂×#518	1	6	yes	complemented
237	D₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
238	C₂⁴	—	4	8	no	—
239	C₂⁴	—	13	1	no	—
240	C₂⁴	—	13	6	no	—
241	C₂⁴	—	13	24	no	—
242	C₂⁴	—	13	6	no	—
243	C₂⁴	—	13	24	no	—
244	C₂⁴	—	13	1	no	—
245	C₂⁴	—	13	4	no	—
246	C₂⁴	—	13	48	no	—
247	C₂⁴	—	13	24	no	—
248	C₂⁴	—	13	32	no	—
249	C₂⁴	—	13	96	no	—
250	C₂⁴	—	26	32	no	—
251	C₂⁴	—	26	8	no	—
252	C₂⁴	—	52	8	no	—
253	C₂⁴	—	52	16	no	—
254	C₂⁴	—	52	96	no	—
255	C₂⁴	—	52	96	no	—
256	C₂⁴	C₂²×#261	1	1	yes	characteristic
257	C₂⁴	C₂²×#261	1	4	yes	—
258	C₂⁴	C₂²×#261	1	24	yes	complemented
259	C₂×D₄	—	13	96	no	—
260	C₂×D₄	—	13	128	no	—
261	C₂×D₄	—	13	64	no	—
262	C₂×D₄	—	13	192	no	—
263	C₂×D₄	—	13	256	no	—
264	C₂×D₄	—	13	48	no	—
265	C₂×D₄	—	13	64	no	—
266	C₂×D₄	C₂²×#261	1	48	yes	complemented
267	C₂×D₄	C₂²×#261	1	64	yes	complemented
268	C₂²×C₄	—	13	12	no	—
269	C₂²×C₄	—	13	2	no	—
270	C₂²×C₄	—	13	12	no	—
271	C₂²×C₄	—	13	12	no	—
272	C₂²×C₄	—	13	24	no	—
273	C₂²×C₄	—	13	16	no	—
274	C₂²×C₄	—	13	48	no	—
275	C₂²×C₄	—	13	48	no	—
276	C₂²×C₄	—	13	128	no	—
277	C₂²×C₄	—	26	32	no	—
278	C₂²×C₄	—	52	192	no	—
279	C₂²×C₄	C₂²×#261	1	2	yes	—
280	C₂²×C₄	C₂²×#261	1	12	yes	complemented
281	C₄⋊C₄	—	13	64	no	—
282	C₂²⋊C₄	—	13	64	no	—
283	C₂²⋊C₄	—	13	128	no	—
284	C₄²	—	13	64	no	—
285	C₁₃	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
286	C₂³	—	2	4	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	4	48	no	—
289	C₂³	—	13	8	no	—
290	C₂³	—	13	3	no	—
291	C₂³	—	13	3	no	—
292	C₂³	—	13	4	no	—
293	C₂³	—	13	16	no	—
294	C₂³	—	13	12	no	—
295	C₂³	—	13	6	no	—
296	C₂³	—	13	48	no	—
297	C₂³	—	13	24	no	—
298	C₂³	—	13	64	no	—
299	C₂³	—	13	32	no	—
300	C₂³	—	26	96	no	—
301	C₂³	—	26	24	no	—
302	C₂³	—	26	24	no	—
303	C₂³	—	26	96	no	—
304	C₂³	—	26	4	no	—
305	C₂³	—	26	16	no	—
306	C₂³	—	52	48	no	—
307	C₂³	—	52	96	no	—
308	C₂³	—	52	64	no	—
309	C₂³	—	52	192	no	—
310	C₂³	C₂³×#261	1	6	yes	—
311	C₂³	C₂³×#261	1	24	yes	—
312	C₂³	C₂³×#261	1	1	yes	characteristic
313	C₂³	C₂³×#261	1	32	yes	complemented
314	D₄	—	13	128	no	—
315	D₄	—	13	64	no	—
316	D₄	C₂³×#261	1	64	yes	complemented
317	C₂×C₄	—	13	12	no	—
318	C₂×C₄	—	13	16	no	—
319	C₂×C₄	—	13	8	no	—
320	C₂×C₄	—	13	24	no	—
321	C₂×C₄	—	13	32	no	—
322	C₂×C₄	—	13	32	no	—
323	C₂×C₄	—	26	96	no	—
324	C₂×C₄	—	52	128	no	—
325	C₂×C₄	C₂³×#261	1	12	yes	—
326	C₂×C₄	C₂³×#261	1	16	yes	complemented
327	C₂²	—	2	12	no	—
328	C₂²	—	2	48	no	—
329	C₂²	—	4	32	no	—
330	C₂²	—	13	12	no	—
331	C₂²	—	13	12	no	—
332	C₂²	—	13	3	no	—
333	C₂²	—	13	1	no	—
334	C₂²	—	13	4	no	—
335	C₂²	—	13	16	no	—
336	C₂²	—	26	32	no	—
337	C₂²	—	26	96	no	—
338	C₂²	—	26	8	no	—
339	C₂²	—	26	24	no	—
340	C₂²	—	26	48	no	—
341	C₂²	—	26	12	no	—
342	C₂²	—	52	32	no	—
343	C₂²	—	52	64	no	—
344	C₂²	#11719623	1	4	yes	direct product factor
345	C₂²	C₂⁴×#261	1	4	yes	—
346	C₂²	C₂⁴×#261	1	16	yes	—
347	C₂²	C₂⁴×#261	1	3	yes	—
348	C₄	—	13	8	no	—
349	C₄	—	26	32	no	—
350	C₄	C₂⁴×#261	1	8	yes	—
351	C₂	—	2	4	no	—
352	C₂	—	2	16	no	—
353	C₂	—	13	2	no	—
354	C₂	—	13	6	no	—
355	C₂	—	26	4	no	—
356	C₂	—	26	16	no	—
357	C₂	C₂×#11719623	1	6	yes	direct product factor
358	C₂	C₂⁵×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×#261
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×#261
Fitting	C₂³×D₄×C₁₃	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₄×D₁₃	C₂
cosocle	C₂×D₁₃	C₂⁶
hypercenter	C₂³×D₄	#261
hypocenter	C₁₃	C₂²×#518
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11719623	C₂	direct (N × H)
2. C₂²×D₄×#261	C₂	semidirect
3. C₂²×#88237	C₂	semidirect
4. C₂³×C₂²⋊#261	C₂	semidirect
7. C₂⁴×#261	C₂²	semidirect
8. C₂³×D₄×C₁₃	C₄	semidirect
9. C₂³×C₂²⋊D₁₃	C₄	semidirect
10. C₂²×D₄×D₁₃	C₄	semidirect
11. C₂²×D₄×D₁₃	C₄	semidirect
14. C₂³×D₅₂	C₄	semidirect
17. C₂²×C₂²⋊#261	C₂²	semidirect
18. C₂²×C₂²⋊#261	C₂²	semidirect
19. #11719623	C₂²	direct (N × H)
20. C₂×D₄×#261	C₂²	semidirect
21. C₂×#88237	C₂²	semidirect
22. C₂²×C₄⋊#261	C₂²	semidirect
23. C₂²×C₄×#261	C₂²	semidirect
24. C₂⁵×C₁₃	C₂×C₄	semidirect
26. C₂⁴×D₁₃	C₂×C₄	semidirect
27. C₂⁴×D₁₃	C₂×C₄	semidirect
28. C₂⁴×D₁₃	C₂×C₄	semidirect
34. C₂³×#261	C₂³	semidirect
35. C₂²×D₄×C₁₃	C₂×C₄	semidirect
36. C₂²×D₄×C₁₃	C₂×C₄	semidirect
37. C₂³×C₄×C₁₃	C₂×C₄	semidirect
38. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
39. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
40. C₂³×Dic₁₃	C₂×C₄	semidirect
41. C₂×D₄×D₁₃	C₂×C₄	semidirect
42. C₂×D₄×D₁₃	C₂×C₄	semidirect
43. C₂×D₄×D₁₃	C₂×C₄	semidirect
46. C₂²×D₅₂	C₂×C₄	semidirect
47. C₂²×D₅₂	C₂×C₄	semidirect
48. C₂²×C₄×D₁₃	C₂×C₄	semidirect
49. C₂²×C₄×D₁₃	C₂×C₄	semidirect
53. C₂×C₂²⋊#261	C₂³	semidirect
54. C₂×C₂²⋊#261	C₂³	semidirect
55. D₄×#261	C₂³	semidirect
56. #88237	C₂³	semidirect
57. C₂×C₄⋊#261	C₂³	semidirect
58. C₂×C₄×#261	C₂³	semidirect
63. C₂⁴×C₁₃	C₂²×C₄	semidirect
74. C₂³×D₁₃	C₂²×C₄	semidirect
75. C₂³×D₁₃	C₂²×C₄	semidirect
76. C₂³×D₁₃	C₂²×C₄	semidirect
84. C₂²×#261	C₂⁴	semidirect
85. C₂×D₄×C₁₃	C₂²×C₄	semidirect
86. C₂×D₄×C₁₃	C₂²×C₄	semidirect
88. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
89. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
90. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
92. C₂²×Dic₁₃	C₂²×C₄	semidirect
93. D₄×D₁₃	C₂²×C₄	semidirect
94. D₄×D₁₃	C₂²×C₄	semidirect
96. C₂×D₅₂	C₂²×C₄	semidirect
97. C₂×D₅₂	C₂²×C₄	semidirect
99. C₂×C₄×D₁₃	C₂²×C₄	semidirect
100. C₂×C₄×D₁₃	C₂²×C₄	semidirect
104. C₂²⋊#261	C₂⁴	semidirect
105. C₄⋊#261	C₂⁴	semidirect
106. C₄×#261	C₂⁴	semidirect
118. C₂³×C₁₃	C₂³×C₄	semidirect
134. C₂²×D₁₃	C₂³×C₄	semidirect
135. C₂²×D₁₃	C₂³×C₄	semidirect
143. D₄×C₁₃	C₂³×C₄	semidirect
145. C₂×C₄×C₁₃	C₂³×C₄	semidirect
146. C₂²⋊D₁₃	C₂³×C₄	semidirect
148. C₂×Dic₁₃	C₂³×C₄	semidirect
149. D₅₂	C₂³×C₄	semidirect
151. C₄×D₁₃	C₂³×C₄	semidirect
160. C₂³×D₄	#261	semidirect
174. C₂²×C₁₃	#518	semidirect
186. C₂×D₁₃	#518	semidirect
202. C₂⁵	C₂×#261	semidirect
212. C₂²×D₄	C₂×#261	semidirect
213. C₂²×D₄	C₂×#261	semidirect
222. C₂³×C₄	C₂×#261	semidirect
232. C₂×C₁₃	C₂×#518	semidirect
236. D₁₃	C₂×#518	semidirect
258. C₂⁴	C₂²×#261	semidirect
266. C₂×D₄	C₂²×#261	semidirect
267. C₂×D₄	C₂²×#261	semidirect
280. C₂²×C₄	C₂²×#261	semidirect
285. C₁₃	C₂²×#518	semidirect
313. C₂³	C₂³×#261	semidirect
316. D₄	C₂³×#261	semidirect
326. C₂×C₄	C₂³×#261	semidirect
344. C₂²	#11719623	direct (N × H)
357. C₂	C₂×#11719623	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×#11719623	2
C₂²×D₄×#261	2
C₂²×#88237	2
C₂³×C₂²⋊#261	2
C₂³×D₄×D₁₃	2
C₂²×#518	13

Subgroups — C22×#11719623 #16809631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11719623 #16809631