Subgroups — AGL(1,ℤ/8)×#261 #13131591

Order 1664.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#261	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#261	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
4	#11719164	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719138	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719106	C₂	1	2	yes	maximal, complemented
7	SD₁₆×#261	C₂	1	2	yes	maximal, complemented
8	#11719102	C₂	1	2	yes	maximal, complemented
9	D₈×#261	C₂	1	2	yes	maximal, complemented
10	#11719098	C₂	1	1	yes	maximal, characteristic, complemented
11	M₁₆×#261	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×#261	—	2	1	no	—
13	#41×D₁₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊#261	—	2	1	no	—
16	Q₈×#261	C₂²	1	1	yes	characteristic, complemented
17	Q₈×#261	C₂²	1	1	yes	characteristic, complemented
18	D₄×#261	—	2	1	no	—
19	D₄×#261	—	2	1	no	—
20	D₄×#261	—	2	1	no	—
21	D₄×#261	—	2	1	no	—
22	D₄×#261	C₂²	1	2	yes	—
23	D₄×#261	C₂²	1	2	yes	—
24	D₄×#261	C₂²	1	1	yes	characteristic, complemented
25	D₄×#261	C₂²	1	1	yes	characteristic, complemented
26	#88237	—	2	1	no	—
27	#88237	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#261	C₂²	1	1	yes	characteristic
29	C₂×C₄×#261	—	2	1	no	—
30	C₂×C₄×#261	C₂²	1	1	yes	characteristic
31	D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
32	C₁₃×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
33	#88203	C₄	1	1	yes	characteristic, complemented
34	#88186	C₄	1	1	yes	characteristic, complemented
35	#88168	C₄	1	2	yes	complemented
36	SD₁₆×D₁₃	C₂²	1	2	yes	—
37	#88165	C₄	1	2	yes	complemented
38	D₈×D₁₃	C₂²	1	2	yes	—
39	#88162	C₄	1	1	yes	characteristic, complemented
40	M₁₆×D₁₃	C₂²	1	1	yes	characteristic
41	#88117	C₂²	1	2	yes	complemented
42	#88115	C₂²	1	2	yes	—
43	#88115	C₂²	1	2	yes	—
44	#88115	C₂²	1	2	yes	complemented
45	#88102	C₂²	1	2	yes	complemented
46	#88101	C₂²	1	2	yes	complemented
47	#88100	C₂²	1	2	yes	complemented
48	C₈×#261	C₂²	1	2	yes	complemented
49	C₂³×D₁₃	—	2	1	no	—
50	C₂²×#261	—	2	1	no	—
51	C₂²×#261	—	2	1	no	—
52	C₂²×#261	—	2	1	no	—
53	C₂²×#261	—	2	2	no	—
54	C₂²×#261	—	2	2	no	—
55	C₂²×#261	—	4	4	no	—
56	C₂²×#261	D₄	1	1	yes	characteristic
57	C₂²×#261	D₄	1	1	yes	characteristic
58	C₁₃×#41	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊D₁₃	—	2	1	no	—
61	#6131	C₂×C₄	1	1	yes	characteristic, complemented
62	Q₈×D₁₃	C₂³	1	1	yes	characteristic
63	#6129	—	2	1	no	—
64	#6129	C₂×C₄	1	1	yes	characteristic, complemented
65	D₄×D₁₃	—	2	1	no	—
66	D₄×D₁₃	—	2	1	no	—
67	D₄×D₁₃	—	2	1	no	—
68	D₄×D₁₃	C₂×C₄	1	2	yes	complemented
69	D₄×D₁₃	C₂³	1	2	yes	—
70	D₄×D₁₃	C₂³	1	1	yes	characteristic
71	#6127	—	2	1	no	—
72	#6127	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×D₅₂	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×C₄×D₁₃	—	2	1	no	—
75	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
76	C₂²⋊#261	—	2	1	no	—
77	C₂²⋊#261	—	2	1	no	—
78	C₂²⋊#261	—	2	1	no	—
79	C₂²⋊#261	—	2	2	no	—
80	C₂²⋊#261	—	2	2	no	—
81	#6122	—	2	1	no	—
82	C₄⋊#261	—	2	1	no	—
83	C₄⋊#261	—	2	1	no	—
84	C₄⋊#261	—	2	1	no	—
85	C₄⋊#261	C₂³	1	1	yes	characteristic
86	C₄⋊#261	C₂³	1	2	yes	—
87	C₄⋊#261	C₂³	1	1	yes	characteristic
88	C₄×#261	—	2	1	no	—
89	C₄×#261	—	2	1	no	—
90	C₄×#261	—	2	1	no	—
91	C₄×#261	D₄	1	1	yes	characteristic
92	C₄×#261	D₄	1	1	yes	characteristic
93	C₄×#261	C₂³	1	1	yes	characteristic
94	C₄×#261	C₂³	1	1	yes	characteristic
95	#6118	—	2	1	no	—
96	D₁₃⋊C₈	C₂³	1	2	yes	—
97	C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
98	C₁₃×D₈	C₂×C₄	1	2	yes	complemented
99	C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic, complemented
100	#6106	C₂×C₄	1	2	yes	complemented
101	#6105	C₂×C₄	1	2	yes	complemented
102	#6104	C₂×C₄	1	2	yes	complemented
103	#6104	C₂×C₄	1	2	yes	complemented
104	#6099	C₂×C₄	1	1	yes	characteristic, complemented
105	D₁₀₄	C₂×C₄	1	2	yes	complemented
106	#6095	C₂×C₄	1	2	yes	complemented
107	#6094	C₂×C₄	1	2	yes	complemented
108	C₈×D₁₃	C₂³	1	2	yes	—
109	C₄×AGL(1,ℤ/8)	—	13	1	no	maximal, Sylow
110	C₂³×C₁₃	—	2	1	no	—
111	C₂²×D₁₃	—	2	1	no	—
112	C₂²×D₁₃	—	2	2	no	—
113	C₂²×D₁₃	—	2	1	no	—
114	C₂²×D₁₃	—	2	2	no	—
115	C₂²×D₁₃	—	4	2	no	—
116	C₂²×D₁₃	—	4	2	no	—
117	C₂²×D₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×#261	—	2	2	no	—
119	C₂×#261	—	2	1	no	—
120	C₂×#261	—	2	1	no	—
121	C₂×#261	—	2	2	no	—
122	C₂×#261	—	4	1	no	—
123	C₂×#261	—	4	2	no	—
124	C₂×#261	—	4	4	no	—
125	C₂×#261	—	4	2	no	—
126	C₂×#261	—	4	2	no	—
127	C₂×#261	—	4	4	no	—
128	C₂×#261	C₂×D₄	1	1	yes	characteristic
129	C₂×#261	C₂×D₄	1	1	yes	characteristic
130	C₂×#261	C₂×D₄	1	1	yes	characteristic
131	C₂×#261	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented
133	D₄×C₁₃	—	2	1	no	—
134	D₄×C₁₃	—	2	1	no	—
135	D₄×C₁₃	C₂²×C₄	1	2	yes	—
136	D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²⋊D₁₃	—	2	1	no	—
140	C₂²⋊D₁₃	—	2	1	no	—
141	C₂²⋊D₁₃	—	2	2	no	—
142	C₂²⋊D₁₃	—	2	1	no	—
143	C₂²⋊D₁₃	—	2	2	no	—
144	C₂×Dic₁₃	—	2	1	no	—
145	C₂×Dic₁₃	#41	1	1	yes	characteristic
146	D₅₂	—	2	1	no	—
147	D₅₂	—	2	1	no	—
148	D₅₂	C₂²×C₄	1	2	yes	—
149	D₅₂	C₂²×C₄	1	1	yes	characteristic, complemented
150	C₄×D₁₃	—	2	1	no	—
151	C₄×D₁₃	—	2	1	no	—
152	C₄×D₁₃	—	2	1	no	—
153	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
155	C₄×D₁₃	#41	1	1	yes	characteristic
156	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
157	Dic₂₆	—	2	1	no	—
158	Dic₂₆	C₂²×C₄	1	1	yes	characteristic, complemented
159	#1057	—	2	2	no	—
160	C₈×C₁₃	C₂²×C₄	1	2	yes	complemented
161	#1055	C₂²×C₄	1	2	yes	complemented
162	C₂×AGL(1,ℤ/8)	—	13	1	no	—
163	C₄×#41	—	13	1	no	—
164	C₂×C₄×D₄	—	13	1	no	—
165	#442	—	13	2	no	—
166	#440	—	13	2	no	—
167	C₄×SD₁₆	—	13	2	no	—
168	C₄×D₈	—	13	2	no	—
169	#428	—	13	1	no	—
170	#418	—	13	1	no	—
171	#417	—	13	1	no	—
172	C₄×M₁₆	—	13	1	no	—
173	C₂²×C₁₃	—	2	1	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	—	4	2	no	—
176	C₂²×C₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×D₁₃	—	2	1	no	—
178	C₂×D₁₃	—	2	1	no	—
179	C₂×D₁₃	—	2	1	no	—
180	C₂×D₁₃	—	2	2	no	—
181	C₂×D₁₃	—	4	4	no	—
182	C₂×D₁₃	—	4	2	no	—
183	C₂×D₁₃	—	4	2	no	—
184	C₂×D₁₃	—	4	1	no	—
185	C₂×D₁₃	—	4	1	no	—
186	C₂×D₁₃	—	4	2	no	—
187	C₂×D₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂×D₁₃	C₂²×D₄	1	1	yes	characteristic
189	#261	—	2	1	no	—
190	#261	—	2	1	no	—
191	#261	—	2	1	no	—
192	#261	—	4	1	no	—
193	#261	—	4	2	no	—
194	#261	—	4	1	no	—
195	#261	AGL(1,ℤ/8)	1	2	yes	direct product factor
196	C₄×C₁₃	—	2	1	no	—
197	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
199	Dic₁₃	—	2	1	no	—
200	Dic₁₃	C₄×D₄	1	1	yes	characteristic
201	Dic₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×#41	—	13	1	no	—
203	C₂²×D₄	—	13	1	no	—
204	C₂³×C₄	—	26	1	no	—
205	AGL(1,ℤ/8)	—	13	1	no	—
206	AGL(1,ℤ/8)	—	13	1	no	—
207	AGL(1,ℤ/8)	—	13	2	no	—
208	AGL(1,ℤ/8)	—	13	2	no	—
209	AGL(1,ℤ/8)	—	13	1	no	—
210	AGL(1,ℤ/8)	#261	1	1	yes	characteristic, direct product factor
211	C₂×SD₁₆	—	13	2	no	—
212	C₂×D₈	—	13	2	no	—
213	C₂×M₁₆	—	13	1	no	—
214	C₂×M₁₆	—	13	1	no	—
215	C₄×Q₈	—	13	1	no	—
216	C₄×Q₈	—	13	1	no	—
217	C₄×D₄	—	13	2	no	—
218	C₄×D₄	—	13	2	no	—
219	C₄×D₄	—	13	1	no	—
220	C₄×D₄	—	13	1	no	—
221	C₄×D₄	—	26	1	no	—
222	C₄×D₄	—	26	1	no	—
223	C₄×D₄	—	26	1	no	—
224	C₄×D₄	—	26	1	no	—
225	#117	—	13	1	no	—
226	#117	—	26	1	no	—
227	C₂×C₄⋊C₄	—	13	1	no	—
228	C₂×C₂²⋊C₄	—	26	1	no	—
229	C₂×C₄²	—	13	1	no	—
230	C₂×C₄²	—	26	1	no	—
231	#107	—	13	2	no	—
232	#106	—	13	2	no	—
233	#103	—	13	2	no	—
234	#102	—	13	2	no	—
235	#102	—	13	2	no	—
236	#102	—	13	2	no	—
237	#97	—	13	2	no	—
238	C₄×C₈	—	13	2	no	—
239	C₂×C₁₃	—	2	1	no	—
240	C₂×C₁₃	—	4	2	no	—
241	C₂×C₁₃	—	4	1	no	—
242	C₂×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	D₁₃	—	2	1	no	—
244	D₁₃	—	4	1	no	—
245	D₁₃	—	4	2	no	—
246	D₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	D₁₃	#575	1	1	yes	characteristic
248	C₂⁴	—	26	1	no	—
249	#41	—	13	1	no	—
250	#41	—	13	1	no	—
251	#41	—	13	1	no	—
252	#41	—	26	1	no	—
253	#41	—	26	1	no	—
254	#41	C₂×#261	1	1	yes	characteristic, complemented
255	C₂×Q₈	—	13	1	no	—
256	C₂×D₄	—	13	2	no	—
257	C₂×D₄	—	13	2	no	—
258	C₂×D₄	—	13	1	no	—
259	C₂×D₄	—	13	1	no	—
260	C₂×D₄	—	26	1	no	—
261	C₂×D₄	—	26	1	no	—
262	C₂×D₄	—	26	1	no	—
263	C₂×D₄	—	26	1	no	—
264	C₂×D₄	C₂×#261	1	1	yes	characteristic, complemented
265	C₂²×C₄	—	13	1	no	—
266	C₂²×C₄	—	13	1	no	—
267	C₂²×C₄	—	13	1	no	—
268	C₂²×C₄	—	26	1	no	—
269	C₂²×C₄	—	26	1	no	—
270	C₂²×C₄	—	26	1	no	—
271	C₂²×C₄	—	26	2	no	—
272	C₂²×C₄	—	26	2	no	—
273	C₂²×C₄	—	26	1	no	—
274	C₂²×C₄	—	52	4	no	—
275	SD₁₆	—	13	2	no	—
276	SD₁₆	—	13	2	no	—
277	SD₁₆	—	13	2	no	—
278	SD₁₆	C₂×#261	1	2	yes	complemented
279	D₈	—	13	2	no	—
280	D₈	—	13	2	no	—
281	D₈	—	13	2	no	—
282	D₈	C₂×#261	1	2	yes	complemented
283	M₁₆	—	13	1	no	—
284	M₁₆	—	13	2	no	—
285	M₁₆	—	26	1	no	—
286	M₁₆	—	26	1	no	—
287	M₁₆	C₂×#261	1	1	yes	characteristic, complemented
288	C₂×C₈	—	13	2	no	—
289	C₂×C₈	—	13	2	no	—
290	C₄⋊C₄	—	13	1	no	—
291	C₄⋊C₄	—	13	1	no	—
292	C₄⋊C₄	—	13	2	no	—
293	C₄⋊C₄	—	26	1	no	—
294	C₄⋊C₄	—	26	1	no	—
295	C₄⋊C₄	—	26	1	no	—
296	C₂²⋊C₄	—	26	2	no	—
297	C₂²⋊C₄	—	26	2	no	—
298	C₂²⋊C₄	—	26	1	no	—
299	C₂²⋊C₄	—	26	1	no	—
300	C₂²⋊C₄	—	26	1	no	—
301	C₄²	—	13	1	no	—
302	C₄²	—	13	1	no	—
303	C₄²	—	13	1	no	—
304	C₄²	—	13	1	no	—
305	C₄²	—	26	1	no	—
306	C₄²	—	26	1	no	—
307	C₄²	—	26	1	no	—
308	C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
309	C₂³	—	2	1	no	—
310	C₂³	—	13	1	no	—
311	C₂³	—	26	1	no	—
312	C₂³	—	26	2	no	—
313	C₂³	—	26	2	no	—
314	C₂³	—	26	1	no	—
315	C₂³	—	52	2	no	—
316	C₂³	—	52	2	no	—
317	Q₈	—	13	1	no	—
318	Q₈	—	26	1	no	—
319	Q₈	C₂²×#261	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	13	1	no	—
323	D₄	—	13	2	no	—
324	D₄	—	26	1	no	—
325	D₄	—	26	2	no	—
326	D₄	—	26	2	no	—
327	D₄	—	26	1	no	—
328	D₄	—	26	1	no	—
329	D₄	—	26	1	no	—
330	D₄	—	26	1	no	—
331	D₄	C₂²×#261	1	2	yes	—
332	D₄	C₂²×#261	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	13	1	no	—
335	C₂×C₄	—	13	1	no	—
336	C₂×C₄	—	13	1	no	—
337	C₂×C₄	—	13	1	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	13	1	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	no	—
343	C₂×C₄	—	26	1	no	—
344	C₂×C₄	—	26	1	no	—
345	C₂×C₄	—	26	1	no	—
346	C₂×C₄	—	26	2	no	—
347	C₂×C₄	—	26	1	no	—
348	C₂×C₄	—	26	1	no	—
349	C₂×C₄	—	26	1	no	—
350	C₂×C₄	—	26	2	no	—
351	C₂×C₄	—	52	4	no	—
352	C₂×C₄	—	52	2	no	—
353	C₂×C₄	—	52	1	no	—
354	C₂×C₄	—	52	4	no	—
355	C₂×C₄	—	52	2	no	—
356	C₂×C₄	—	52	2	no	—
357	C₂×C₄	C₂²×#261	1	1	yes	characteristic
358	C₈	—	13	2	no	—
359	C₈	—	26	2	no	—
360	C₈	C₂²×#261	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	13	1	no	—
365	C₂²	—	13	1	no	—
366	C₂²	—	26	1	no	—
367	C₂²	—	26	1	no	—
368	C₂²	—	26	1	no	—
369	C₂²	—	26	2	no	—
370	C₂²	—	52	2	no	—
371	C₂²	—	52	2	no	—
372	C₂²	—	52	1	no	—
373	C₂²	—	52	1	no	—
374	C₂²	—	52	2	no	—
375	C₂²	—	52	4	no	—
376	C₂²	D₄×#261	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	13	2	no	—
379	C₄	—	13	1	no	—
380	C₄	—	13	1	no	—
381	C₄	—	26	1	no	—
382	C₄	—	26	1	no	—
383	C₄	—	26	1	no	—
384	C₄	—	26	1	no	—
385	C₄	—	52	1	no	—
386	C₄	—	52	1	no	—
387	C₄	—	52	2	no	—
388	C₄	D₄×#261	1	1	yes	characteristic
389	C₄	C₂³×#261	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	13	1	no	—
394	C₂	—	13	1	no	—
395	C₂	—	26	1	no	—
396	C₂	—	52	2	no	—
397	C₂	—	52	1	no	—
398	C₂	C₂×D₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#261
commutator	C₄×C₁₃	C₂³×C₄
Frattini	C₄	C₂³×#261
Fitting	C₁₃×AGL(1,ℤ/8)	C₄
socle	C₂×C₁₃	C₂×C₄×D₄
prime radical	D₁₃×AGL(1,ℤ/8)	C₂
cosocle	C₄×D₁₃	C₂⁴
hypercenter	AGL(1,ℤ/8)	#261
hypocenter	C₁₃	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #41×#261	C₂	semidirect
2. C₂×D₄×#261	C₂	semidirect
4. #11719164	C₂	semidirect
5. #11719138	C₂	semidirect
6. #11719106	C₂	semidirect
7. SD₁₆×#261	C₂	semidirect
8. #11719102	C₂	semidirect
9. D₈×#261	C₂	semidirect
10. #11719098	C₂	semidirect
11. M₁₆×#261	C₂	semidirect
16. Q₈×#261	C₂²	semidirect
17. Q₈×#261	C₂²	semidirect
24. D₄×#261	C₂²	semidirect
25. D₄×#261	C₂²	semidirect
32. C₁₃×AGL(1,ℤ/8)	C₄	semidirect
33. #88203	C₄	semidirect
34. #88186	C₄	semidirect
35. #88168	C₄	semidirect
37. #88165	C₄	semidirect
39. #88162	C₄	semidirect
41. #88117	C₂²	semidirect
44. #88115	C₂²	semidirect
45. #88102	C₂²	semidirect
46. #88101	C₂²	semidirect
47. #88100	C₂²	semidirect
48. C₈×#261	C₂²	semidirect
58. C₁₃×#41	C₂×C₄	semidirect
59. C₂×D₄×C₁₃	C₂×C₄	semidirect
61. #6131	C₂×C₄	semidirect
64. #6129	C₂×C₄	semidirect
68. D₄×D₁₃	C₂×C₄	semidirect
72. #6127	C₂×C₄	semidirect
73. C₂×D₅₂	C₂×C₄	semidirect
97. C₁₃×SD₁₆	C₂×C₄	semidirect
98. C₁₃×D₈	C₂×C₄	semidirect
99. C₁₃×M₁₆	C₂×C₄	semidirect
100. #6106	C₂×C₄	semidirect
101. #6105	C₂×C₄	semidirect
102. #6104	C₂×C₄	semidirect
103. #6104	C₂×C₄	semidirect
104. #6099	C₂×C₄	semidirect
105. D₁₀₄	C₂×C₄	semidirect
106. #6095	C₂×C₄	semidirect
107. #6094	C₂×C₄	semidirect
132. Q₈×C₁₃	C₂²×C₄	semidirect
136. D₄×C₁₃	C₂²×C₄	semidirect
149. D₅₂	C₂²×C₄	semidirect
158. Dic₂₆	C₂²×C₄	semidirect
160. C₈×C₁₃	C₂²×C₄	semidirect
161. #1055	C₂²×C₄	semidirect
195. #261	AGL(1,ℤ/8)	direct (N × H)
210. AGL(1,ℤ/8)	#261	direct (N × H)
254. #41	C₂×#261	semidirect
264. C₂×D₄	C₂×#261	semidirect
278. SD₁₆	C₂×#261	semidirect
282. D₈	C₂×#261	semidirect
287. M₁₆	C₂×#261	semidirect
308. C₁₃	C₄×AGL(1,ℤ/8)	semidirect
319. Q₈	C₂²×#261	semidirect
332. D₄	C₂²×#261	semidirect
360. C₈	C₂²×#261	semidirect

Maximal subgroups

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

subgroup	index
#41×#261	2
C₂×D₄×#261	2
D₁₃×AGL(1,ℤ/8)	2
#11719164	2
#11719138	2
#11719106	2
SD₁₆×#261	2
#11719102	2
D₈×#261	2
#11719098	2
M₁₆×#261	2
C₄×AGL(1,ℤ/8)	13