Subgroups — C₂×C₄×Q₈×#261 #16807450

Order 3328.

3966 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×#261	C₂	1	2	yes	maximal
2	C₄×Q₈×#261	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄⋊C₄×#261	C₂	1	6	yes	maximal
4	C₂×C₄×C₄⋊#261	C₂	1	3	yes	maximal
5	C₂×C₄²×#261	C₂	1	3	yes	maximal
6	C₂×C₄×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×Q₈×#261	C₄	1	32	yes	direct product factor
9	C₂×Q₈×#261	C₂²	1	16	yes	—
10	C₂²×C₄⋊#261	C₂²	1	6	yes	—
11	C₂²×C₄×#261	C₂²	1	3	yes	—
12	C₂²×C₄×#261	C₂²	1	6	yes	—
13	C₂²×C₄×#261	C₂²	1	6	yes	—
14	C₂²×C₄×#261	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
16	C₂×Q₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
17	C₄×Q₈×D₁₃	C₄	1	8	yes	complemented
18	C₄×Q₈×D₁₃	C₂²	1	8	yes	—
19	C₂×C₄⋊C₄×D₁₃	C₂²	1	3	yes	—
20	C₂×#88141	C₄	1	3	yes	complemented
21	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
22	C₂×C₄×Dic₂₆	C₄	1	3	yes	complemented
23	C₂×(C₂×#261)⋊C₄	C₂²	1	6	yes	—
24	C₄⋊C₄×#261	C₂²	1	48	yes	—
25	C₄×C₄⋊#261	C₂²	1	24	yes	—
26	C₄²×#261	C₂²	1	24	yes	—
27	C₂³×#261	C₂³	1	6	yes	—
28	C₂³×#261	C₂³	1	2	yes	—
29	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×Q₈×D₁₃	C₂×C₄	1	16	yes	—
31	C₂×Q₈×D₁₃	C₂×C₄	1	4	yes	—
32	C₂×Q₈×D₁₃	C₂³	1	4	yes	—
33	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
34	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
35	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
36	C₂²×Dic₂₆	C₂×C₄	1	3	yes	—
37	Q₈×#261	C₂×C₄	1	128	yes	direct product factor
38	C₂×C₄⋊#261	C₂×C₄	1	48	yes	—
39	C₂×C₄⋊#261	C₂³	1	24	yes	—
40	C₂×C₄×#261	—	2	24	no	—
41	C₂×C₄×#261	—	2	12	no	—
42	C₂×C₄×#261	C₂×C₄	1	48	yes	—
43	C₂×C₄×#261	Q₈	1	8	yes	direct product factor
44	C₂×C₄×#261	C₂³	1	12	yes	—
45	C₂×C₄×#261	C₂³	1	24	yes	—
46	C₂×C₄×#261	C₂³	1	24	yes	—
47	C₂×C₄×#261	C₂³	1	4	yes	—
48	C₄×Q₈×C₁₃	C₂×C₄	1	8	yes	complemented
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	3	yes	—
50	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	—
51	Q₈×Dic₁₃	C₂×C₄	1	8	yes	complemented
52	C₂×C₄⋊Dic₁₃	C₂×C₄	1	3	yes	—
53	C₂×#6101	C₂×C₄	1	6	yes	—
54	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
56	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
57	C₄⋊C₄×D₁₃	C₂×C₄	1	12	yes	—
58	C₄⋊C₄×D₁₃	C₂³	1	12	yes	—
59	#88141	C₂×C₄	1	24	yes	complemented
60	C₄²×D₁₃	C₂×C₄	1	12	yes	—
61	C₄²×D₁₃	C₂³	1	12	yes	—
62	C₄×Dic₂₆	C₂×C₄	1	24	yes	complemented
63	(C₂×#261)⋊C₄	C₂³	1	24	yes	—
64	C₂×C₄²×Q₈	—	13	1	no	maximal, Sylow
65	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
66	C₂²×#261	—	2	12	no	—
67	C₂²×#261	—	2	12	no	—
68	C₂²×#261	C₂²×C₄	1	24	yes	—
69	C₂²×#261	C₂²×C₄	1	8	yes	—
70	C₂²×#261	C₂×Q₈	1	8	yes	—
71	C₂²×#261	#41	1	8	yes	—
72	C₂²×#261	C₂⁴	1	12	yes	—
73	C₂²×#261	C₂⁴	1	4	yes	—
74	C₂×Q₈×C₁₃	C₄²	1	8	yes	complemented
75	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
76	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
80	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
81	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
82	Q₈×D₁₃	C₄²	1	32	yes	complemented
83	Q₈×D₁₃	C₂²×C₄	1	32	yes	—
84	C₂×C₄×D₁₃	—	2	12	no	—
85	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
86	C₂×C₄×D₁₃	C₂²×C₄	1	6	yes	—
87	C₂×C₄×D₁₃	C₂²×C₄	1	24	yes	—
88	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
89	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
90	C₂×C₄×D₁₃	#41	1	4	yes	—
91	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
92	C₂×C₄×D₁₃	C₂⁴	1	6	yes	—
93	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
94	C₂×Dic₂₆	C₄²	1	24	yes	complemented
95	C₂×Dic₂₆	C₂²×C₄	1	12	yes	—
96	C₄⋊#261	C₂²×C₄	1	96	yes	—
97	C₄×#261	—	2	48	no	—
98	C₄×#261	—	2	24	no	—
99	C₄×#261	C₂²×C₄	1	96	yes	—
100	C₄×#261	C₂×Q₈	1	16	yes	direct product factor
101	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
102	C₄²×C₁₃	C₂²×C₄	1	12	yes	—
103	C₄⋊Dic₁₃	C₂²×C₄	1	12	yes	—
104	#6101	C₂²×C₄	1	24	yes	—
105	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
106	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
107	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
108	C₂²×C₄×Q₈	—	13	2	no	—
109	C₂²×C₄×Q₈	—	13	1	no	—
110	C₄²×Q₈	—	13	16	no	—
111	C₂×C₄×C₄⋊C₄	—	13	3	no	—
112	C₂×C₄×C₄⋊C₄	—	13	6	no	—
113	C₂×C₄³	—	13	3	no	—
114	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
115	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
116	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
117	C₂²×D₁₃	C₂²×Q₈	1	2	yes	—
118	C₂²×D₁₃	C₂×#41	1	4	yes	—
119	C₂²×D₁₃	C₂×#41	1	2	yes	—
120	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
121	C₂×#261	—	2	48	no	—
122	C₂×#261	—	2	12	no	—
123	C₂×#261	—	2	12	no	—
124	C₂×#261	C₄×Q₈	1	32	yes	direct product factor
125	C₂×#261	C₂³×C₄	1	24	yes	—
126	C₂×#261	C₂³×C₄	1	8	yes	—
127	C₂×#261	C₂²×Q₈	1	8	yes	—
128	C₂×#261	C₂×#41	1	8	yes	—
129	Q₈×C₁₃	C₂×C₄²	1	16	yes	complemented
130	C₂×C₄×C₁₃	—	2	6	no	—
131	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
132	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	complemented
133	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
134	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
135	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
136	C₂×Dic₁₃	—	2	6	no	—
137	C₂×Dic₁₃	C₂×C₄²	1	12	yes	—
138	C₂×Dic₁₃	C₄×Q₈	1	4	yes	complemented
139	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
140	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
141	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
142	C₄×D₁₃	—	2	12	no	—
143	C₄×D₁₃	—	2	12	no	—
144	C₄×D₁₃	C₂×C₄²	1	24	yes	—
145	C₄×D₁₃	C₄×Q₈	1	8	yes	complemented
146	C₄×D₁₃	C₂³×C₄	1	24	yes	—
147	C₄×D₁₃	C₂²×Q₈	1	4	yes	—
148	C₄×D₁₃	C₂×#41	1	4	yes	—
149	Dic₂₆	C₂×C₄²	1	48	yes	complemented
150	C₂³×Q₈	—	13	1	no	—
151	C₂×C₄×Q₈	—	13	32	no	—
152	C₂×C₄×Q₈	—	13	16	no	—
153	C₂×C₄×Q₈	—	13	1	no	—
154	C₂×C₄×Q₈	—	13	8	no	—
155	C₂×C₄×Q₈	—	13	8	no	—
156	C₂×C₄×Q₈	—	13	3	no	—
157	C₂×C₄×Q₈	—	13	3	no	—
158	C₂×C₄×Q₈	#261	1	1	yes	characteristic, direct product factor
159	C₂²×C₄⋊C₄	—	13	6	no	—
160	C₂²×C₄⋊C₄	—	13	3	no	—
161	C₂²×C₄²	—	13	6	no	—
162	C₂²×C₄²	—	13	1	no	—
163	C₂²×C₄²	—	13	3	no	—
164	C₂²×C₄²	—	13	6	no	—
165	C₂²×C₄²	—	13	3	no	—
166	C₄×C₄⋊C₄	—	13	24	no	—
167	C₄×C₄⋊C₄	—	13	48	no	—
168	C₂×#95	—	13	6	no	—
169	C₄³	—	13	24	no	—
170	C₂²×C₁₃	C₂²×C₄²	1	2	yes	—
171	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
172	C₂²×C₁₃	C₄×#41	1	2	yes	—
173	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
174	C₂×D₁₃	C₂²×C₄²	1	2	yes	—
175	C₂×D₁₃	C₂×C₄×Q₈	1	8	yes	—
176	C₂×D₁₃	C₂×C₄×Q₈	1	2	yes	—
177	C₂×D₁₃	C₄×#41	1	8	yes	—
178	C₂×D₁₃	C₄×#41	1	2	yes	—
179	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
180	C₂×D₁₃	C₂³×Q₈	1	1	yes	characteristic
181	C₂×D₁₃	C₂²×#41	1	2	yes	—
182	C₂×D₁₃	C₂²×#41	1	1	yes	characteristic
183	#261	—	2	24	no	—
184	#261	C₂×C₄×Q₈	1	16	yes	direct product factor
185	C₄×C₁₃	—	2	6	no	—
186	C₄×C₁₃	C₂²×C₄²	1	12	yes	—
187	C₄×C₁₃	C₂×C₄×Q₈	1	4	yes	complemented
188	Dic₁₃	—	2	6	no	—
189	Dic₁₃	C₂²×C₄²	1	12	yes	—
190	Dic₁₃	C₂×C₄×Q₈	1	4	yes	complemented
191	C₂²×Q₈	—	13	16	no	—
192	C₂²×Q₈	—	13	4	no	—
193	C₂²×Q₈	—	13	4	no	—
194	C₂²×Q₈	—	13	3	no	—
195	C₂²×Q₈	C₂×#261	1	1	yes	characteristic
196	C₂³×C₄	—	13	2	no	—
197	C₂³×C₄	—	13	3	no	—
198	C₂³×C₄	—	13	1	no	—
199	C₂³×C₄	—	13	6	no	—
200	C₂³×C₄	—	13	3	no	—
201	C₄×Q₈	—	13	128	no	—
202	C₄×Q₈	—	13	8	no	—
203	C₄×Q₈	—	13	24	no	—
204	C₄×Q₈	—	13	24	no	—
205	C₄×Q₈	C₂×#261	1	8	yes	direct product factor
206	C₂×C₄⋊C₄	—	13	24	no	—
207	C₂×C₄⋊C₄	—	13	48	no	—
208	C₂×C₄⋊C₄	—	13	6	no	—
209	C₂×C₄⋊C₄	—	13	3	no	—
210	C₂×C₄⋊C₄	—	13	12	no	—
211	C₂×C₄⋊C₄	—	13	12	no	—
212	C₂×C₄⋊C₄	C₂×#261	1	3	yes	—
213	C₂×C₄²	—	13	24	no	—
214	C₂×C₄²	—	13	48	no	—
215	C₂×C₄²	—	13	4	no	—
216	C₂×C₄²	—	13	8	no	—
217	C₂×C₄²	—	13	3	no	—
218	C₂×C₄²	—	13	3	no	—
219	C₂×C₄²	—	13	3	no	—
220	C₂×C₄²	—	13	12	no	—
221	C₂×C₄²	—	13	12	no	—
222	C₂×C₄²	—	13	24	no	—
223	C₂×C₄²	—	13	12	no	—
224	C₂×C₄²	—	26	24	no	—
225	C₂×C₄²	—	26	12	no	—
226	C₂×C₄²	C₂×#261	1	3	yes	—
227	#95	—	13	24	no	—
228	C₂×C₁₃	C₄²×Q₈	1	4	yes	complemented
229	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
230	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
231	C₂×C₁₃	C₂×C₄×#41	1	1	yes	characteristic
232	D₁₃	C₄²×Q₈	1	4	yes	complemented
233	D₁₃	C₂²×C₄×Q₈	1	2	yes	—
234	D₁₃	C₂×C₄×#41	1	2	yes	—
235	C₂⁴	—	13	1	no	—
236	C₂×Q₈	—	13	32	no	—
237	C₂×Q₈	—	13	32	no	—
238	C₂×Q₈	—	13	24	no	—
239	C₂×Q₈	—	13	12	no	—
240	C₂×Q₈	C₄×#261	1	8	yes	direct product factor
241	C₂×Q₈	C₂²×#261	1	4	yes	—
242	C₂²×C₄	—	13	4	no	—
243	C₂²×C₄	—	13	8	no	—
244	C₂²×C₄	—	13	8	no	—
245	C₂²×C₄	—	13	8	no	—
246	C₂²×C₄	—	13	1	no	—
247	C₂²×C₄	—	13	3	no	—
248	C₂²×C₄	—	13	24	no	—
249	C₂²×C₄	—	13	4	no	—
250	C₂²×C₄	—	13	4	no	—
251	C₂²×C₄	—	13	2	no	—
252	C₂²×C₄	—	13	6	no	—
253	C₂²×C₄	—	13	2	no	—
254	C₂²×C₄	—	13	6	no	—
255	C₂²×C₄	—	13	12	no	—
256	C₂²×C₄	—	13	24	no	—
257	C₂²×C₄	—	13	3	no	—
258	C₂²×C₄	—	13	6	no	—
259	C₂²×C₄	—	13	6	no	—
260	C₂²×C₄	—	26	12	no	—
261	C₂²×C₄	—	26	12	no	—
262	C₂²×C₄	—	26	12	no	—
263	C₂²×C₄	C₂²×#261	1	3	yes	—
264	C₂²×C₄	C₂²×#261	1	3	yes	—
265	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
266	C₄⋊C₄	—	13	96	no	—
267	C₄⋊C₄	—	13	24	no	—
268	C₄⋊C₄	—	13	12	no	—
269	C₄⋊C₄	C₂²×#261	1	12	yes	—
270	C₄²	—	13	96	no	—
271	C₄²	—	13	16	no	—
272	C₄²	—	13	12	no	—
273	C₄²	—	13	12	no	—
274	C₄²	—	13	12	no	—
275	C₄²	—	26	48	no	—
276	C₄²	—	26	24	no	—
277	C₄²	C₂²×#261	1	12	yes	—
278	C₁₃	C₂×C₄²×Q₈	1	1	yes	characteristic, complemented, Sylow
279	C₂³	—	13	4	no	—
280	C₂³	—	13	2	no	—
281	C₂³	—	13	2	no	—
282	C₂³	—	13	4	no	—
283	C₂³	—	13	1	no	—
284	C₂³	—	13	1	no	—
285	C₂³	C₂³×#261	1	1	yes	characteristic
286	Q₈	—	13	48	no	—
287	Q₈	C₂×C₄×#261	1	16	yes	direct product factor
288	C₂×C₄	—	2	6	no	—
289	C₂×C₄	—	13	8	no	—
290	C₂×C₄	—	13	8	no	—
291	C₂×C₄	—	13	8	no	—
292	C₂×C₄	—	13	32	no	—
293	C₂×C₄	—	13	12	no	—
294	C₂×C₄	—	13	4	no	—
295	C₂×C₄	—	13	2	no	—
296	C₂×C₄	—	13	6	no	—
297	C₂×C₄	—	13	24	no	—
298	C₂×C₄	—	13	24	no	—
299	C₂×C₄	—	13	4	no	—
300	C₂×C₄	—	13	4	no	—
301	C₂×C₄	—	13	8	no	—
302	C₂×C₄	—	13	24	no	—
303	C₂×C₄	—	13	6	no	—
304	C₂×C₄	—	26	12	no	—
305	C₂×C₄	—	26	12	no	—
306	C₂×C₄	—	26	12	no	—
307	C₂×C₄	—	26	12	no	—
308	C₂×C₄	—	26	48	no	—
309	C₂×C₄	—	26	6	no	—
310	C₂×C₄	C₂×C₄×#261	1	12	yes	—
311	C₂×C₄	Q₈×#261	1	4	yes	direct product factor
312	C₂×C₄	C₂³×#261	1	6	yes	—
313	C₂×C₄	C₂³×#261	1	6	yes	—
314	C₂×C₄	C₂³×#261	1	2	yes	—
315	C₂²	—	13	8	no	—
316	C₂²	—	13	8	no	—
317	C₂²	—	13	2	no	—
318	C₂²	—	13	2	no	—
319	C₂²	—	13	2	no	—
320	C₂²	—	13	1	no	—
321	C₂²	—	13	1	no	—
322	C₂²	—	13	2	no	—
323	C₂²	—	13	2	no	—
324	C₂²	C₂²×C₄×#261	1	2	yes	—
325	C₂²	C₂×Q₈×#261	1	2	yes	—
326	C₂²	#41×#261	1	2	yes	—
327	C₂²	C₂⁴×#261	1	1	yes	characteristic
328	C₄	—	2	6	no	—
329	C₄	—	13	16	no	—
330	C₄	—	13	12	no	—
331	C₄	—	13	4	no	—
332	C₄	—	26	24	no	—
333	C₄	—	26	6	no	—
334	C₄	C₂²×C₄×#261	1	12	yes	—
335	C₄	C₂×Q₈×#261	1	4	yes	direct product factor
336	C₂	—	13	2	no	—
337	C₂	—	13	2	no	—
338	C₂	—	13	4	no	—
339	C₂	C₄×Q₈×#261	1	4	yes	direct product factor
340	C₂	C₂³×C₄×#261	1	1	yes	characteristic
341	C₂	C₂²×Q₈×#261	1	1	yes	characteristic
342	C₂	C₂×#41×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₂×C₄×Q₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂⁴
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₂×C₄×Q₈	#261
hypocenter	C₁₃	C₂×C₄²×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×#261	C₂	direct (N × H)
8. C₂×Q₈×#261	C₄	direct (N × H)
15. C₂×C₄×Q₈×C₁₃	C₄	semidirect
16. C₂×Q₈×Dic₁₃	C₄	semidirect
17. C₄×Q₈×D₁₃	C₄	semidirect
20. C₂×#88141	C₄	semidirect
22. C₂×C₄×Dic₂₆	C₄	semidirect
37. Q₈×#261	C₂×C₄	direct (N × H)
43. C₂×C₄×#261	Q₈	direct (N × H)
48. C₄×Q₈×C₁₃	C₂×C₄	semidirect
51. Q₈×Dic₁₃	C₂×C₄	semidirect
59. #88141	C₂×C₄	semidirect
62. C₄×Dic₂₆	C₂×C₄	semidirect
74. C₂×Q₈×C₁₃	C₄²	semidirect
82. Q₈×D₁₃	C₄²	semidirect
94. C₂×Dic₂₆	C₄²	semidirect
100. C₄×#261	C₂×Q₈	direct (N × H)
124. C₂×#261	C₄×Q₈	direct (N × H)
129. Q₈×C₁₃	C₂×C₄²	semidirect
132. C₂×C₄×C₁₃	C₄×Q₈	semidirect
138. C₂×Dic₁₃	C₄×Q₈	semidirect
145. C₄×D₁₃	C₄×Q₈	semidirect
149. Dic₂₆	C₂×C₄²	semidirect
158. C₂×C₄×Q₈	#261	direct (N × H)
184. #261	C₂×C₄×Q₈	direct (N × H)
187. C₄×C₁₃	C₂×C₄×Q₈	semidirect
190. Dic₁₃	C₂×C₄×Q₈	semidirect
205. C₄×Q₈	C₂×#261	direct (N × H)
228. C₂×C₁₃	C₄²×Q₈	semidirect
232. D₁₃	C₄²×Q₈	semidirect
240. C₂×Q₈	C₄×#261	direct (N × H)
278. C₁₃	C₂×C₄²×Q₈	semidirect
287. Q₈	C₂×C₄×#261	direct (N × H)
311. C₂×C₄	Q₈×#261	direct (N × H)
335. C₄	C₂×Q₈×#261	direct (N × H)
339. C₂	C₄×Q₈×#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
C₂²×Q₈×#261	2
C₄×Q₈×#261	2
C₂×C₄⋊C₄×#261	2
C₂×C₄×C₄⋊#261	2
C₂×C₄²×#261	2
C₂×C₄×Q₈×D₁₃	2
C₂×C₄²×Q₈	13

Subgroups — C2×C4×Q8×#261 #16807450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×Q₈×#261 #16807450