Subgroups — C₂²×C₄×C₄⋊#261 #16807445

Order 3328.

5758 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊#261	C₂	1	2	yes	maximal
2	C₂³×C₄×#261	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊#261	C₂	1	24	yes	maximal, direct product factor
4	C₂²×(C₂×#261)⋊C₄	C₂	1	2	yes	maximal
5	C₂²×C₄²×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂⁴×#261	C₂²	1	4	yes	—
7	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
8	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
9	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊#261	C₄	1	32	yes	direct product factor
11	C₂²×C₄⋊#261	C₂²	1	24	yes	—
12	C₂²×C₄×#261	—	2	16	no	—
13	C₂²×C₄×#261	C₂²	1	24	yes	—
14	C₂²×C₄²×C₁₃	C₄	1	1	yes	characteristic, complemented
15	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄²×D₁₃	C₄	1	12	yes	complemented
19	C₂×C₄²×D₁₃	C₂²	1	12	yes	—
20	C₂×(C₂×#261)⋊C₄	C₂²	1	24	yes	—
21	C₄×C₄⋊#261	C₂²	1	64	yes	direct product factor
22	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
23	C₂³×#261	—	2	16	no	—
24	C₂³×#261	—	2	16	no	—
25	C₂³×#261	C₂×C₄	1	32	yes	—
26	C₂³×#261	C₂³	1	24	yes	—
27	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₁₃	—	2	8	no	—
34	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
35	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
36	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	—
37	C₂²×C₄×D₁₃	C₂×C₄	1	6	yes	—
38	C₂²×C₄×D₁₃	D₄	1	8	yes	—
39	C₂²×C₄×D₁₃	Q₈	1	8	yes	—
40	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
41	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
42	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
43	C₂×C₄⋊#261	C₂×C₄	1	192	yes	direct product factor
44	C₂×C₄⋊#261	C₂³	1	32	yes	—
45	C₂×C₄×#261	—	2	96	no	—
46	C₂×C₄×#261	C₂³	1	32	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	complemented
48	C₂×C₄×Dic₁₃	C₂×C₄	1	12	yes	complemented
49	C₂×C₄×Dic₁₃	C₂×C₄	1	12	yes	complemented
50	C₂×C₄×Dic₁₃	C₂×C₄	1	12	yes	complemented
51	C₄²×D₁₃	C₂×C₄	1	48	yes	complemented
52	C₄²×D₁₃	C₂³	1	16	yes	—
53	(C₂×#261)⋊C₄	C₂³	1	32	yes	—
54	C₂²×C₄×C₄⋊C₄	—	13	1	no	maximal, Sylow
55	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂³×D₁₃	C₂²×C₄	1	3	yes	—
57	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
58	C₂³×D₁₃	C₂×D₄	1	4	yes	—
59	C₂³×D₁₃	C₂×Q₈	1	4	yes	—
60	C₂³×D₁₃	#41	1	8	yes	—
61	C₂³×D₁₃	C₂⁴	1	3	yes	—
62	C₂²×#261	—	2	128	no	—
63	C₂²×#261	—	2	48	no	—
64	C₂²×#261	—	2	48	no	—
65	C₂²×#261	C₂²×C₄	1	96	yes	—
66	C₂²×#261	C₂⁴	1	16	yes	—
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	C₄²	1	8	yes	complemented
69	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	complemented
70	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
71	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
72	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
73	C₂²×Dic₁₃	—	2	4	no	—
74	C₂²×Dic₁₃	C₄²	1	8	yes	complemented
75	C₂²×Dic₁₃	C₄⋊C₄	1	8	yes	complemented
76	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
77	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
78	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
79	C₂×C₄×D₁₃	—	2	24	no	—
80	C₂×C₄×D₁₃	—	2	24	no	—
81	C₂×C₄×D₁₃	C₄²	1	48	yes	complemented
82	C₂×C₄×D₁₃	C₄⋊C₄	1	48	yes	complemented
83	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
84	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
85	C₂×C₄×D₁₃	C₂²×C₄	1	48	yes	—
86	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
87	C₂×C₄×D₁₃	C₂×D₄	1	24	yes	—
88	C₂×C₄×D₁₃	C₂×Q₈	1	24	yes	—
89	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
90	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
91	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
92	C₄⋊#261	C₂²×C₄	1	128	yes	direct product factor
93	C₄×#261	—	2	64	no	—
94	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
95	C₄×Dic₁₃	C₂²×C₄	1	16	yes	complemented
96	C₄×Dic₁₃	C₂²×C₄	1	16	yes	complemented
97	C₄×Dic₁₃	C₂²×C₄	1	16	yes	complemented
98	C₂³×C₄⋊C₄	—	13	2	no	—
99	C₂³×C₄²	—	13	1	no	—
100	C₂³×C₄²	—	13	2	no	—
101	C₂×C₄×C₄⋊C₄	—	13	24	no	—
102	C₂²×#95	—	13	2	no	—
103	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
104	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
105	C₂³×C₁₃	#117	1	4	yes	—
106	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
107	C₂²×D₁₃	C₂×C₄²	1	12	yes	—
108	C₂²×D₁₃	C₂×C₄⋊C₄	1	12	yes	—
109	C₂²×D₁₃	#117	1	12	yes	—
110	C₂²×D₁₃	C₄×D₄	1	32	yes	—
111	C₂²×D₁₃	C₄×Q₈	1	32	yes	—
112	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
113	C₂²×D₁₃	C₂³×C₄	1	12	yes	—
114	C₂²×D₁₃	C₂²×D₄	1	6	yes	—
115	C₂²×D₁₃	C₂²×Q₈	1	6	yes	—
116	C₂²×D₁₃	C₂×#41	1	12	yes	—
117	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
118	C₂×#261	—	2	192	no	—
119	C₂×#261	—	2	16	no	—
120	C₂×#261	—	2	16	no	—
121	C₂×#261	C₂³×C₄	1	32	yes	—
122	C₂×C₄×C₁₃	—	2	12	no	—
123	C₂×C₄×C₁₃	C₂×C₄²	1	24	yes	complemented
124	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	24	yes	complemented
125	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
126	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
127	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
128	C₂×Dic₁₃	—	2	12	no	—
129	C₂×Dic₁₃	C₂×C₄²	1	24	yes	complemented
130	C₂×Dic₁₃	C₂×C₄⋊C₄	1	24	yes	complemented
131	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
132	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
133	C₂×Dic₁₃	C₂³×C₄	1	4	yes	—
134	C₄×D₁₃	—	2	24	no	—
135	C₄×D₁₃	—	2	8	no	—
136	C₄×D₁₃	C₂×C₄²	1	48	yes	complemented
137	C₄×D₁₃	C₂×C₄⋊C₄	1	48	yes	complemented
138	C₄×D₁₃	C₂³×C₄	1	16	yes	—
139	C₄×D₁₃	C₂²×D₄	1	8	yes	—
140	C₄×D₁₃	C₂²×Q₈	1	8	yes	—
141	C₂⁴×C₄	—	13	1	no	—
142	C₂⁴×C₄	—	13	1	no	—
143	C₂⁴×C₄	—	13	4	no	—
144	C₂⁴×C₄	—	13	1	no	—
145	C₂²×C₄⋊C₄	—	13	32	no	—
146	C₂²×C₄⋊C₄	—	13	24	no	—
147	C₂²×C₄²	—	13	1	no	—
148	C₂²×C₄²	—	13	1	no	—
149	C₂²×C₄²	—	13	1	no	—
150	C₂²×C₄²	—	13	12	no	—
151	C₂²×C₄²	—	13	12	no	—
152	C₂²×C₄²	—	13	24	no	—
153	C₂²×C₄²	—	26	16	no	—
154	C₂²×C₄²	#261	1	1	yes	characteristic, complemented
155	C₄×C₄⋊C₄	—	13	64	no	—
156	C₂×#95	—	13	24	no	—
157	C₂²×C₁₃	C₄×C₄⋊C₄	1	16	yes	complemented
158	C₂²×C₁₃	C₂²×C₄²	1	6	yes	—
159	C₂²×C₁₃	C₂²×C₄⋊C₄	1	6	yes	—
160	C₂²×C₁₃	C₂×#117	1	6	yes	—
161	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
162	C₂×D₁₃	C₄×C₄⋊C₄	1	48	yes	complemented
163	C₂×D₁₃	C₂²×C₄²	1	6	yes	—
164	C₂×D₁₃	C₂²×C₄⋊C₄	1	6	yes	—
165	C₂×D₁₃	C₂×#117	1	6	yes	—
166	C₂×D₁₃	C₂×C₄×D₄	1	24	yes	—
167	C₂×D₁₃	C₂×C₄×Q₈	1	24	yes	—
168	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
169	C₂×D₁₃	C₂³×D₄	1	1	yes	characteristic
170	C₂×D₁₃	C₂³×Q₈	1	1	yes	characteristic
171	C₂×D₁₃	C₂²×#41	1	2	yes	—
172	#261	—	2	32	no	—
173	C₄×C₁₃	—	2	4	no	—
174	C₄×C₁₃	C₂²×C₄²	1	8	yes	complemented
175	C₄×C₁₃	C₂²×C₄⋊C₄	1	8	yes	complemented
176	Dic₁₃	—	2	4	no	—
177	Dic₁₃	C₂²×C₄²	1	8	yes	complemented
178	Dic₁₃	C₂²×C₄⋊C₄	1	8	yes	complemented
179	C₂⁵	—	13	1	no	—
180	C₂³×C₄	—	13	1	no	—
181	C₂³×C₄	—	13	1	no	—
182	C₂³×C₄	—	13	16	no	—
183	C₂³×C₄	—	13	8	no	—
184	C₂³×C₄	—	13	8	no	—
185	C₂³×C₄	—	13	6	no	—
186	C₂³×C₄	—	13	6	no	—
187	C₂³×C₄	—	13	6	no	—
188	C₂³×C₄	—	13	6	no	—
189	C₂³×C₄	—	13	24	no	—
190	C₂³×C₄	—	13	32	no	—
191	C₂³×C₄	—	13	1	no	—
192	C₂³×C₄	—	13	6	no	—
193	C₂³×C₄	—	13	6	no	—
194	C₂³×C₄	—	26	8	no	—
195	C₂³×C₄	—	26	16	no	—
196	C₂³×C₄	—	26	16	no	—
197	C₂³×C₄	C₂×#261	1	1	yes	characteristic
198	C₂³×C₄	C₂×#261	1	1	yes	characteristic
199	C₂³×C₄	C₂×#261	1	1	yes	characteristic
200	C₂×C₄⋊C₄	—	13	32	no	—
201	C₂×C₄⋊C₄	—	13	192	no	—
202	C₂×C₄²	—	13	12	no	—
203	C₂×C₄²	—	13	12	no	—
204	C₂×C₄²	—	13	12	no	—
205	C₂×C₄²	—	13	48	no	—
206	C₂×C₄²	—	13	16	no	—
207	C₂×C₄²	—	13	32	no	—
208	C₂×C₄²	—	26	96	no	—
209	C₂×C₄²	C₂×#261	1	12	yes	complemented
210	#95	—	13	32	no	—
211	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	12	yes	complemented
212	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
213	C₂×C₁₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₁₃	C₂²×#117	1	1	yes	characteristic
215	D₁₃	C₂×C₄×C₄⋊C₄	1	12	yes	complemented
216	D₁₃	C₂²×C₄×D₄	1	2	yes	—
217	D₁₃	C₂²×C₄×Q₈	1	2	yes	—
218	C₂⁴	—	13	8	no	—
219	C₂⁴	—	13	4	no	—
220	C₂⁴	—	13	4	no	—
221	C₂⁴	—	13	8	no	—
222	C₂⁴	—	13	3	no	—
223	C₂⁴	—	13	3	no	—
224	C₂⁴	C₂²×#261	1	1	yes	characteristic
225	C₂²×C₄	—	2	4	no	—
226	C₂²×C₄	—	13	8	no	—
227	C₂²×C₄	—	13	8	no	—
228	C₂²×C₄	—	13	6	no	—
229	C₂²×C₄	—	13	6	no	—
230	C₂²×C₄	—	13	48	no	—
231	C₂²×C₄	—	13	48	no	—
232	C₂²×C₄	—	13	24	no	—
233	C₂²×C₄	—	13	48	no	—
234	C₂²×C₄	—	13	24	no	—
235	C₂²×C₄	—	13	4	no	—
236	C₂²×C₄	—	13	4	no	—
237	C₂²×C₄	—	13	12	no	—
238	C₂²×C₄	—	13	12	no	—
239	C₂²×C₄	—	13	16	no	—
240	C₂²×C₄	—	13	96	no	—
241	C₂²×C₄	—	13	6	no	—
242	C₂²×C₄	—	13	4	no	—
243	C₂²×C₄	—	13	12	no	—
244	C₂²×C₄	—	26	24	no	—
245	C₂²×C₄	—	26	24	no	—
246	C₂²×C₄	—	26	48	no	—
247	C₂²×C₄	—	26	128	no	—
248	C₂²×C₄	—	26	48	no	—
249	C₂²×C₄	—	26	4	no	—
250	C₂²×C₄	C₄×#261	1	8	yes	complemented
251	C₂²×C₄	C₄⋊#261	1	8	yes	direct product factor
252	C₂²×C₄	C₂²×#261	1	6	yes	—
253	C₂²×C₄	C₂²×#261	1	6	yes	—
254	C₂²×C₄	C₂²×#261	1	6	yes	—
255	C₄⋊C₄	—	13	128	no	—
256	C₄²	—	13	16	no	—
257	C₄²	—	13	16	no	—
258	C₄²	—	13	16	no	—
259	C₄²	—	26	64	no	—
260	C₄²	C₂²×#261	1	16	yes	complemented
261	C₁₃	C₂²×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
262	C₂³	—	13	32	no	—
263	C₂³	—	13	32	no	—
264	C₂³	—	13	12	no	—
265	C₂³	—	13	12	no	—
266	C₂³	—	13	6	no	—
267	C₂³	—	13	12	no	—
268	C₂³	—	13	6	no	—
269	C₂³	—	13	12	no	—
270	C₂³	—	13	12	no	—
271	C₂³	—	13	1	no	—
272	C₂³	—	13	3	no	—
273	C₂³	C₂×C₄×#261	1	4	yes	—
274	C₂³	C₂×C₄⋊#261	1	4	yes	—
275	C₂³	#88237	1	4	yes	—
276	C₂³	C₂³×#261	1	3	yes	—
277	C₂×C₄	—	2	12	no	—
278	C₂×C₄	—	13	24	no	—
279	C₂×C₄	—	13	24	no	—
280	C₂×C₄	—	13	4	no	—
281	C₂×C₄	—	13	4	no	—
282	C₂×C₄	—	13	16	no	—
283	C₂×C₄	—	13	48	no	—
284	C₂×C₄	—	13	8	no	—
285	C₂×C₄	—	13	48	no	—
286	C₂×C₄	—	13	8	no	—
287	C₂×C₄	—	13	32	no	—
288	C₂×C₄	—	13	4	no	—
289	C₂×C₄	—	26	24	no	—
290	C₂×C₄	—	26	8	no	—
291	C₂×C₄	—	26	16	no	—
292	C₂×C₄	—	26	192	no	—
293	C₂×C₄	—	26	16	no	—
294	C₂×C₄	—	26	12	no	—
295	C₂×C₄	C₂×C₄×#261	1	24	yes	complemented
296	C₂×C₄	C₂×C₄⋊#261	1	24	yes	direct product factor
297	C₂×C₄	C₂³×#261	1	4	yes	—
298	C₂×C₄	C₂³×#261	1	4	yes	—
299	C₂×C₄	C₂³×#261	1	4	yes	—
300	C₂²	—	13	24	no	—
301	C₂²	—	13	24	no	—
302	C₂²	—	13	48	no	—
303	C₂²	—	13	2	no	—
304	C₂²	—	13	6	no	—
305	C₂²	—	13	6	no	—
306	C₂²	—	13	1	no	—
307	C₂²	—	13	1	no	—
308	C₂²	—	13	6	no	—
309	C₂²	—	13	2	no	—
310	C₂²	C₄×C₄⋊#261	1	16	yes	direct product factor
311	C₂²	C₂²×C₄×#261	1	6	yes	—
312	C₂²	C₂²×C₄⋊#261	1	6	yes	—
313	C₂²	C₂×#88237	1	6	yes	—
314	C₂²	C₂⁴×#261	1	1	yes	characteristic
315	C₄	—	2	4	no	—
316	C₄	—	13	8	no	—
317	C₄	—	13	8	no	—
318	C₄	—	26	32	no	—
319	C₄	—	26	4	no	—
320	C₄	C₂²×C₄×#261	1	8	yes	complemented
321	C₄	C₂²×C₄⋊#261	1	8	yes	direct product factor
322	C₂	—	13	2	no	—
323	C₂	—	13	2	no	—
324	C₂	—	13	12	no	—
325	C₂	C₂×C₄×C₄⋊#261	1	12	yes	direct product factor
326	C₂	C₂³×C₄×#261	1	1	yes	characteristic
327	C₂	C₂³×C₄⋊#261	1	1	yes	characteristic
328	C₂	C₂²×#88237	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₂²×C₄²×C₁₃	C₄
socle	C₂⁴×C₁₃	C₂²×C₄
prime radical	C₂⁴×D₁₃	C₂³
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₂²×C₄²	#261
hypocenter	C₁₃	C₂²×C₄×C₄⋊C₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊#261	C₂	direct (N × H)
10. C₂²×C₄⋊#261	C₄	direct (N × H)
14. C₂²×C₄²×C₁₃	C₄	semidirect
15. C₂²×C₄×Dic₁₃	C₄	semidirect
16. C₂²×C₄×Dic₁₃	C₄	semidirect
17. C₂²×C₄×Dic₁₃	C₄	semidirect
18. C₂×C₄²×D₁₃	C₄	semidirect
21. C₄×C₄⋊#261	C₂²	direct (N × H)
43. C₂×C₄⋊#261	C₂×C₄	direct (N × H)
47. C₂×C₄²×C₁₃	C₂×C₄	semidirect
48. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
49. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
50. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
51. C₄²×D₁₃	C₂×C₄	semidirect
68. C₂²×C₄×C₁₃	C₄²	semidirect
69. C₂²×C₄×C₁₃	C₄⋊C₄	semidirect
74. C₂²×Dic₁₃	C₄²	semidirect
75. C₂²×Dic₁₃	C₄⋊C₄	semidirect
81. C₂×C₄×D₁₃	C₄²	semidirect
82. C₂×C₄×D₁₃	C₄⋊C₄	semidirect
92. C₄⋊#261	C₂²×C₄	direct (N × H)
94. C₄²×C₁₃	C₂²×C₄	semidirect
95. C₄×Dic₁₃	C₂²×C₄	semidirect
96. C₄×Dic₁₃	C₂²×C₄	semidirect
97. C₄×Dic₁₃	C₂²×C₄	semidirect
123. C₂×C₄×C₁₃	C₂×C₄²	semidirect
124. C₂×C₄×C₁₃	C₂×C₄⋊C₄	semidirect
129. C₂×Dic₁₃	C₂×C₄²	semidirect
130. C₂×Dic₁₃	C₂×C₄⋊C₄	semidirect
136. C₄×D₁₃	C₂×C₄²	semidirect
137. C₄×D₁₃	C₂×C₄⋊C₄	semidirect
154. C₂²×C₄²	#261	semidirect
157. C₂²×C₁₃	C₄×C₄⋊C₄	semidirect
162. C₂×D₁₃	C₄×C₄⋊C₄	semidirect
174. C₄×C₁₃	C₂²×C₄²	semidirect
175. C₄×C₁₃	C₂²×C₄⋊C₄	semidirect
177. Dic₁₃	C₂²×C₄²	semidirect
178. Dic₁₃	C₂²×C₄⋊C₄	semidirect
209. C₂×C₄²	C₂×#261	semidirect
211. C₂×C₁₃	C₂×C₄×C₄⋊C₄	semidirect
215. D₁₃	C₂×C₄×C₄⋊C₄	semidirect
250. C₂²×C₄	C₄×#261	semidirect
251. C₂²×C₄	C₄⋊#261	direct (N × H)
260. C₄²	C₂²×#261	semidirect
261. C₁₃	C₂²×C₄×C₄⋊C₄	semidirect
295. C₂×C₄	C₂×C₄×#261	semidirect
296. C₂×C₄	C₂×C₄⋊#261	direct (N × H)
310. C₂²	C₄×C₄⋊#261	direct (N × H)
320. C₄	C₂²×C₄×#261	semidirect
321. C₄	C₂²×C₄⋊#261	direct (N × H)
325. C₂	C₂×C₄×C₄⋊#261	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×C₄⋊#261	2
C₂³×C₄×#261	2
C₂×C₄×C₄⋊#261	2
C₂²×(C₂×#261)⋊C₄	2
C₂²×C₄²×D₁₃	2
C₂²×C₄×C₄⋊C₄	13

Subgroups — C22×C4×C4⋊#261 #16807445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₄⋊#261 #16807445