Subgroups — AGL(1,ℤ/8)×#3866 #18011351

Order 4736.

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×#3866	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#3866	C₂	1	1	yes	maximal, characteristic, complemented
3	#14558574	C₂	1	2	yes	maximal, complemented
4	#14558572	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#3866	C₂	1	2	yes	maximal, complemented
6	D₈×#3866	C₂	1	2	yes	maximal, complemented
7	#14558544	C₂	1	1	yes	maximal, characteristic, complemented
8	#14558525	C₂	1	1	yes	maximal, characteristic, complemented
9	#14558524	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#3866	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₃₇	C₂	1	1	yes	maximal, characteristic
12	C₂³×#3866	—	2	1	no	—
13	D₃₇⋊M₁₆	C₂²	1	1	yes	characteristic
14	Q₈×#3866	C₂²	1	1	yes	characteristic, complemented
15	Q₈×#3866	C₂²	1	1	yes	characteristic, complemented
16	D₄×#3866	—	2	1	no	—
17	D₄×#3866	—	2	1	no	—
18	D₄×#3866	—	2	1	no	—
19	D₄×#3866	—	2	1	no	—
20	D₄×#3866	C₂²	1	2	yes	—
21	D₄×#3866	C₂²	1	2	yes	—
22	D₄×#3866	C₂²	1	1	yes	characteristic, complemented
23	D₄×#3866	C₂²	1	1	yes	characteristic, complemented
24	#11924615	—	2	1	no	—
25	#11924615	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#3866	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#3866	—	2	1	no	—
28	C₂×C₄×#3866	—	2	1	no	—
29	C₂×C₄×#3866	C₂²	1	1	yes	characteristic
30	#11924605	C₂²	1	2	yes	complemented
31	#11924604	C₂²	1	2	yes	complemented
32	#11924599	C₂²	1	2	yes	complemented
33	#11924598	C₂²	1	2	yes	—
34	#11924598	C₂²	1	2	yes	—
35	#11924598	C₂²	1	2	yes	complemented
36	#11924590	C₂²	1	2	yes	complemented
37	C₈×#3866	C₂²	1	2	yes	complemented
38	#41×D₃₇	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₃₇	C₂²	1	1	yes	characteristic
40	#11924564	C₄	1	1	yes	characteristic, complemented
41	#11924563	C₄	1	2	yes	complemented
42	#11924562	C₄	1	1	yes	characteristic, complemented
43	#11924561	C₄	1	1	yes	characteristic, complemented
44	#11924560	C₄	1	2	yes	complemented
45	SD₁₆×D₃₇	C₂²	1	2	yes	—
46	D₈×D₃₇	C₂²	1	2	yes	—
47	M₁₆×D₃₇	C₂²	1	1	yes	characteristic
48	AGL(1,ℤ/8)×C₃₇	C₄	1	1	yes	characteristic, complemented
49	C₂³×D₃₇	—	2	1	no	—
50	C₂²×#3866	—	2	1	no	—
51	C₂²×#3866	—	2	1	no	—
52	C₂²×#3866	—	2	1	no	—
53	C₂²×#3866	—	2	2	no	—
54	C₂²×#3866	—	2	2	no	—
55	C₂²×#3866	—	4	4	no	—
56	C₂²×#3866	D₄	1	1	yes	characteristic
57	C₂²×#3866	D₄	1	1	yes	characteristic
58	#41×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×D₄×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊D₃₇	—	2	1	no	—
61	#10596966	C₂×C₄	1	1	yes	characteristic, complemented
62	Q₈×D₃₇	C₂³	1	1	yes	characteristic
63	#10596964	—	2	1	no	—
64	#10596964	C₂×C₄	1	1	yes	characteristic, complemented
65	D₄×D₃₇	—	2	1	no	—
66	D₄×D₃₇	—	2	1	no	—
67	D₄×D₃₇	—	2	1	no	—
68	D₄×D₃₇	C₂×C₄	1	2	yes	complemented
69	D₄×D₃₇	C₂³	1	2	yes	—
70	D₄×D₃₇	C₂³	1	1	yes	characteristic
71	#10596962	—	2	1	no	—
72	#10596962	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂×D₁₄₈	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×C₄×D₃₇	—	2	1	no	—
75	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
76	C₂²⋊#3866	—	2	1	no	—
77	C₂²⋊#3866	—	2	2	no	—
78	C₂²⋊#3866	—	2	2	no	—
79	C₂²⋊#3866	—	2	1	no	—
80	C₂²⋊#3866	—	2	1	no	—
81	#10596957	—	2	1	no	—
82	C₄⋊#3866	—	2	1	no	—
83	C₄⋊#3866	—	2	1	no	—
84	C₄⋊#3866	—	2	1	no	—
85	C₄⋊#3866	C₂³	1	1	yes	characteristic
86	C₄⋊#3866	C₂³	1	1	yes	characteristic
87	C₄⋊#3866	C₂³	1	2	yes	—
88	C₄×#3866	—	2	1	no	—
89	C₄×#3866	—	2	1	no	—
90	C₄×#3866	—	2	1	no	—
91	C₄×#3866	D₄	1	1	yes	characteristic
92	C₄×#3866	D₄	1	1	yes	characteristic
93	C₄×#3866	C₂³	1	1	yes	characteristic
94	C₄×#3866	C₂³	1	1	yes	characteristic
95	#10596953	—	2	1	no	—
96	D₃₇⋊C₈	C₂³	1	2	yes	—
97	SD₁₆×C₃₇	C₂×C₄	1	2	yes	complemented
98	D₈×C₃₇	C₂×C₄	1	2	yes	complemented
99	M₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic, complemented
100	#10596941	C₂×C₄	1	2	yes	complemented
101	#10596940	C₂×C₄	1	2	yes	complemented
102	#10596939	C₂×C₄	1	2	yes	complemented
103	#10596939	C₂×C₄	1	2	yes	complemented
104	#10596934	C₂×C₄	1	1	yes	characteristic, complemented
105	D₂₉₆	C₂×C₄	1	2	yes	complemented
106	#10596930	C₂×C₄	1	2	yes	complemented
107	#10596929	C₂×C₄	1	2	yes	complemented
108	C₈×D₃₇	C₂³	1	2	yes	—
109	C₂³×C₃₇	—	2	1	no	—
110	C₂²×D₃₇	—	2	1	no	—
111	C₂²×D₃₇	—	2	2	no	—
112	C₂²×D₃₇	—	2	1	no	—
113	C₂²×D₃₇	—	2	2	no	—
114	C₂²×D₃₇	—	4	2	no	—
115	C₂²×D₃₇	—	4	2	no	—
116	C₂²×D₃₇	C₂×D₄	1	1	yes	characteristic
117	C₂×#3866	—	2	2	no	—
118	C₂×#3866	—	2	1	no	—
119	C₂×#3866	—	2	1	no	—
120	C₂×#3866	—	2	2	no	—
121	C₂×#3866	—	4	1	no	—
122	C₂×#3866	—	4	2	no	—
123	C₂×#3866	—	4	4	no	—
124	C₂×#3866	—	4	2	no	—
125	C₂×#3866	—	4	2	no	—
126	C₂×#3866	—	4	4	no	—
127	C₂×#3866	C₂×D₄	1	1	yes	characteristic
128	C₂×#3866	C₂×D₄	1	1	yes	characteristic
129	C₂×#3866	C₂×D₄	1	1	yes	characteristic
130	C₂×#3866	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₃₇	C₂²×C₄	1	1	yes	characteristic, complemented
132	D₄×C₃₇	—	2	1	no	—
133	D₄×C₃₇	—	2	1	no	—
134	D₄×C₃₇	C₂²×C₄	1	2	yes	—
135	D₄×C₃₇	C₂²×C₄	1	1	yes	characteristic, complemented
136	C₂×C₄×C₃₇	—	2	1	no	—
137	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊D₃₇	—	2	1	no	—
139	C₂²⋊D₃₇	—	2	1	no	—
140	C₂²⋊D₃₇	—	2	2	no	—
141	C₂²⋊D₃₇	—	2	1	no	—
142	C₂²⋊D₃₇	—	2	2	no	—
143	C₂×Dic₃₇	—	2	1	no	—
144	C₂×Dic₃₇	#41	1	1	yes	characteristic
145	D₁₄₈	—	2	1	no	—
146	D₁₄₈	—	2	1	no	—
147	D₁₄₈	C₂²×C₄	1	2	yes	—
148	D₁₄₈	C₂²×C₄	1	1	yes	characteristic, complemented
149	C₄×D₃₇	—	2	1	no	—
150	C₄×D₃₇	—	2	1	no	—
151	C₄×D₃₇	—	2	1	no	—
152	C₄×D₃₇	C₂²×C₄	1	1	yes	characteristic
153	C₄×D₃₇	C₂×D₄	1	1	yes	characteristic
154	C₄×D₃₇	#41	1	1	yes	characteristic
155	C₄×D₃₇	C₂⁴	1	1	yes	characteristic
156	Dic₇₄	—	2	1	no	—
157	Dic₇₄	C₂²×C₄	1	1	yes	characteristic, complemented
158	#64438	—	2	2	no	—
159	C₈×C₃₇	C₂²×C₄	1	2	yes	complemented
160	#64436	C₂²×C₄	1	2	yes	complemented
161	C₂²×C₃₇	—	2	1	no	—
162	C₂²×C₃₇	—	2	2	no	—
163	C₂²×C₃₇	—	4	2	no	—
164	C₂²×C₃₇	C₄×D₄	1	1	yes	characteristic
165	C₂×D₃₇	—	2	1	no	—
166	C₂×D₃₇	—	2	1	no	—
167	C₂×D₃₇	—	2	1	no	—
168	C₂×D₃₇	—	2	2	no	—
169	C₂×D₃₇	—	4	4	no	—
170	C₂×D₃₇	—	4	2	no	—
171	C₂×D₃₇	—	4	2	no	—
172	C₂×D₃₇	—	4	1	no	—
173	C₂×D₃₇	—	4	1	no	—
174	C₂×D₃₇	—	4	2	no	—
175	C₂×D₃₇	C₄×D₄	1	1	yes	characteristic
176	C₂×D₃₇	C₂²×D₄	1	1	yes	characteristic
177	#3866	—	2	1	no	—
178	#3866	—	2	1	no	—
179	#3866	—	2	1	no	—
180	#3866	—	4	1	no	—
181	#3866	—	4	2	no	—
182	#3866	—	4	1	no	—
183	#3866	AGL(1,ℤ/8)	1	2	yes	direct product factor
184	C₄×C₃₇	—	2	1	no	—
185	C₄×C₃₇	C₄×D₄	1	1	yes	characteristic
186	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
187	Dic₃₇	—	2	1	no	—
188	Dic₃₇	C₄×D₄	1	1	yes	characteristic
189	Dic₃₇	C₂×#41	1	1	yes	characteristic
190	C₄×AGL(1,ℤ/8)	—	37	1	no	maximal, Sylow
191	C₂×C₃₇	—	2	1	no	—
192	C₂×C₃₇	—	4	2	no	—
193	C₂×C₃₇	—	4	1	no	—
194	C₂×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
195	D₃₇	—	2	1	no	—
196	D₃₇	—	4	1	no	—
197	D₃₇	—	4	2	no	—
198	D₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	D₃₇	#575	1	1	yes	characteristic
200	C₂×AGL(1,ℤ/8)	—	37	1	no	—
201	C₄×#41	—	37	1	no	—
202	C₂×C₄×D₄	—	37	1	no	—
203	#442	—	37	2	no	—
204	#440	—	37	2	no	—
205	C₄×SD₁₆	—	37	2	no	—
206	C₄×D₈	—	37	2	no	—
207	#428	—	37	1	no	—
208	#418	—	37	1	no	—
209	#417	—	37	1	no	—
210	C₄×M₁₆	—	37	1	no	—
211	C₃₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
212	C₂×#41	—	37	1	no	—
213	C₂²×D₄	—	37	1	no	—
214	C₂³×C₄	—	74	1	no	—
215	AGL(1,ℤ/8)	—	37	1	no	—
216	AGL(1,ℤ/8)	—	37	1	no	—
217	AGL(1,ℤ/8)	—	37	2	no	—
218	AGL(1,ℤ/8)	—	37	2	no	—
219	AGL(1,ℤ/8)	—	37	1	no	—
220	AGL(1,ℤ/8)	#3866	1	1	yes	characteristic, direct product factor
221	C₂×SD₁₆	—	37	2	no	—
222	C₂×D₈	—	37	2	no	—
223	C₂×M₁₆	—	37	1	no	—
224	C₂×M₁₆	—	37	1	no	—
225	C₄×Q₈	—	37	1	no	—
226	C₄×Q₈	—	37	1	no	—
227	C₄×D₄	—	37	2	no	—
228	C₄×D₄	—	37	2	no	—
229	C₄×D₄	—	37	1	no	—
230	C₄×D₄	—	37	1	no	—
231	C₄×D₄	—	74	1	no	—
232	C₄×D₄	—	74	1	no	—
233	C₄×D₄	—	74	1	no	—
234	C₄×D₄	—	74	1	no	—
235	#117	—	37	1	no	—
236	#117	—	74	1	no	—
237	C₂×C₄⋊C₄	—	37	1	no	—
238	C₂×C₂²⋊C₄	—	74	1	no	—
239	C₂×C₄²	—	37	1	no	—
240	C₂×C₄²	—	74	1	no	—
241	#107	—	37	2	no	—
242	#106	—	37	2	no	—
243	#103	—	37	2	no	—
244	#102	—	37	2	no	—
245	#102	—	37	2	no	—
246	#102	—	37	2	no	—
247	#97	—	37	2	no	—
248	C₄×C₈	—	37	2	no	—
249	C₂⁴	—	74	1	no	—
250	#41	—	37	1	no	—
251	#41	—	37	1	no	—
252	#41	—	37	1	no	—
253	#41	—	74	1	no	—
254	#41	—	74	1	no	—
255	#41	C₂×#3866	1	1	yes	characteristic, complemented
256	C₂×Q₈	—	37	1	no	—
257	C₂×D₄	—	37	2	no	—
258	C₂×D₄	—	37	2	no	—
259	C₂×D₄	—	37	1	no	—
260	C₂×D₄	—	37	1	no	—
261	C₂×D₄	—	74	1	no	—
262	C₂×D₄	—	74	1	no	—
263	C₂×D₄	—	74	1	no	—
264	C₂×D₄	—	74	1	no	—
265	C₂×D₄	C₂×#3866	1	1	yes	characteristic, complemented
266	C₂²×C₄	—	37	1	no	—
267	C₂²×C₄	—	37	1	no	—
268	C₂²×C₄	—	37	1	no	—
269	C₂²×C₄	—	74	1	no	—
270	C₂²×C₄	—	74	1	no	—
271	C₂²×C₄	—	74	1	no	—
272	C₂²×C₄	—	74	2	no	—
273	C₂²×C₄	—	74	2	no	—
274	C₂²×C₄	—	74	1	no	—
275	C₂²×C₄	—	148	4	no	—
276	SD₁₆	—	37	2	no	—
277	SD₁₆	—	37	2	no	—
278	SD₁₆	—	37	2	no	—
279	SD₁₆	C₂×#3866	1	2	yes	complemented
280	D₈	—	37	2	no	—
281	D₈	—	37	2	no	—
282	D₈	—	37	2	no	—
283	D₈	C₂×#3866	1	2	yes	complemented
284	M₁₆	—	37	1	no	—
285	M₁₆	—	37	2	no	—
286	M₁₆	—	74	1	no	—
287	M₁₆	—	74	1	no	—
288	M₁₆	C₂×#3866	1	1	yes	characteristic, complemented
289	C₂×C₈	—	37	2	no	—
290	C₂×C₈	—	37	2	no	—
291	C₄⋊C₄	—	37	1	no	—
292	C₄⋊C₄	—	37	1	no	—
293	C₄⋊C₄	—	37	2	no	—
294	C₄⋊C₄	—	74	1	no	—
295	C₄⋊C₄	—	74	1	no	—
296	C₄⋊C₄	—	74	1	no	—
297	C₂²⋊C₄	—	74	2	no	—
298	C₂²⋊C₄	—	74	2	no	—
299	C₂²⋊C₄	—	74	1	no	—
300	C₂²⋊C₄	—	74	1	no	—
301	C₂²⋊C₄	—	74	1	no	—
302	C₄²	—	37	1	no	—
303	C₄²	—	37	1	no	—
304	C₄²	—	37	1	no	—
305	C₄²	—	37	1	no	—
306	C₄²	—	74	1	no	—
307	C₄²	—	74	1	no	—
308	C₄²	—	74	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	37	1	no	—
311	C₂³	—	74	1	no	—
312	C₂³	—	74	2	no	—
313	C₂³	—	74	2	no	—
314	C₂³	—	74	1	no	—
315	C₂³	—	148	2	no	—
316	C₂³	—	148	2	no	—
317	Q₈	—	37	1	no	—
318	Q₈	—	74	1	no	—
319	Q₈	C₂²×#3866	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	37	1	no	—
323	D₄	—	37	2	no	—
324	D₄	—	74	1	no	—
325	D₄	—	74	2	no	—
326	D₄	—	74	2	no	—
327	D₄	—	74	1	no	—
328	D₄	—	74	1	no	—
329	D₄	—	74	1	no	—
330	D₄	—	74	1	no	—
331	D₄	C₂²×#3866	1	2	yes	—
332	D₄	C₂²×#3866	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	37	1	no	—
335	C₂×C₄	—	37	1	no	—
336	C₂×C₄	—	37	1	no	—
337	C₂×C₄	—	37	1	no	—
338	C₂×C₄	—	37	1	no	—
339	C₂×C₄	—	37	1	no	—
340	C₂×C₄	—	37	1	no	—
341	C₂×C₄	—	37	1	no	—
342	C₂×C₄	—	37	1	no	—
343	C₂×C₄	—	74	1	no	—
344	C₂×C₄	—	74	1	no	—
345	C₂×C₄	—	74	1	no	—
346	C₂×C₄	—	74	2	no	—
347	C₂×C₄	—	74	1	no	—
348	C₂×C₄	—	74	1	no	—
349	C₂×C₄	—	74	1	no	—
350	C₂×C₄	—	74	2	no	—
351	C₂×C₄	—	148	4	no	—
352	C₂×C₄	—	148	2	no	—
353	C₂×C₄	—	148	1	no	—
354	C₂×C₄	—	148	4	no	—
355	C₂×C₄	—	148	2	no	—
356	C₂×C₄	—	148	2	no	—
357	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
358	C₈	—	37	2	no	—
359	C₈	—	74	2	no	—
360	C₈	C₂²×#3866	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	37	1	no	—
365	C₂²	—	37	1	no	—
366	C₂²	—	74	1	no	—
367	C₂²	—	74	1	no	—
368	C₂²	—	74	1	no	—
369	C₂²	—	74	2	no	—
370	C₂²	—	148	2	no	—
371	C₂²	—	148	2	no	—
372	C₂²	—	148	1	no	—
373	C₂²	—	148	1	no	—
374	C₂²	—	148	2	no	—
375	C₂²	—	148	4	no	—
376	C₂²	D₄×#3866	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	37	2	no	—
379	C₄	—	37	1	no	—
380	C₄	—	37	1	no	—
381	C₄	—	74	1	no	—
382	C₄	—	74	1	no	—
383	C₄	—	74	1	no	—
384	C₄	—	74	1	no	—
385	C₄	—	148	2	no	—
386	C₄	—	148	1	no	—
387	C₄	—	148	1	no	—
388	C₄	D₄×#3866	1	1	yes	characteristic
389	C₄	C₂³×#3866	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	37	1	no	—
394	C₂	—	37	1	no	—
395	C₂	—	74	1	no	—
396	C₂	—	148	2	no	—
397	C₂	—	148	1	no	—
398	C₂	C₂×D₄×#3866	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#3866
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₄	C₂³×#3866
Fitting	AGL(1,ℤ/8)×C₃₇	C₄
socle	C₂×C₃₇	C₂×C₄×D₄
prime radical	AGL(1,ℤ/8)×D₃₇	C₂
cosocle	C₄×D₃₇	C₂⁴
hypercenter	AGL(1,ℤ/8)	#3866
hypocenter	C₃₇	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
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×#3866	C₂	semidirect
2. C₂×D₄×#3866	C₂	semidirect
3. #14558574	C₂	semidirect
4. #14558572	C₂	semidirect
5. SD₁₆×#3866	C₂	semidirect
6. D₈×#3866	C₂	semidirect
7. #14558544	C₂	semidirect
8. #14558525	C₂	semidirect
9. #14558524	C₂	semidirect
10. M₁₆×#3866	C₂	semidirect
14. Q₈×#3866	C₂²	semidirect
15. Q₈×#3866	C₂²	semidirect
22. D₄×#3866	C₂²	semidirect
23. D₄×#3866	C₂²	semidirect
30. #11924605	C₂²	semidirect
31. #11924604	C₂²	semidirect
32. #11924599	C₂²	semidirect
35. #11924598	C₂²	semidirect
36. #11924590	C₂²	semidirect
37. C₈×#3866	C₂²	semidirect
40. #11924564	C₄	semidirect
41. #11924563	C₄	semidirect
42. #11924562	C₄	semidirect
43. #11924561	C₄	semidirect
44. #11924560	C₄	semidirect
48. AGL(1,ℤ/8)×C₃₇	C₄	semidirect
58. #41×C₃₇	C₂×C₄	semidirect
59. C₂×D₄×C₃₇	C₂×C₄	semidirect
61. #10596966	C₂×C₄	semidirect
64. #10596964	C₂×C₄	semidirect
68. D₄×D₃₇	C₂×C₄	semidirect
72. #10596962	C₂×C₄	semidirect
73. C₂×D₁₄₈	C₂×C₄	semidirect
97. SD₁₆×C₃₇	C₂×C₄	semidirect
98. D₈×C₃₇	C₂×C₄	semidirect
99. M₁₆×C₃₇	C₂×C₄	semidirect
100. #10596941	C₂×C₄	semidirect
101. #10596940	C₂×C₄	semidirect
102. #10596939	C₂×C₄	semidirect
103. #10596939	C₂×C₄	semidirect
104. #10596934	C₂×C₄	semidirect
105. D₂₉₆	C₂×C₄	semidirect
106. #10596930	C₂×C₄	semidirect
107. #10596929	C₂×C₄	semidirect
131. Q₈×C₃₇	C₂²×C₄	semidirect
135. D₄×C₃₇	C₂²×C₄	semidirect
148. D₁₄₈	C₂²×C₄	semidirect
157. Dic₇₄	C₂²×C₄	semidirect
159. C₈×C₃₇	C₂²×C₄	semidirect
160. #64436	C₂²×C₄	semidirect
183. #3866	AGL(1,ℤ/8)	direct (N × H)
211. C₃₇	C₄×AGL(1,ℤ/8)	semidirect
220. AGL(1,ℤ/8)	#3866	direct (N × H)
255. #41	C₂×#3866	semidirect
265. C₂×D₄	C₂×#3866	semidirect
279. SD₁₆	C₂×#3866	semidirect
283. D₈	C₂×#3866	semidirect
288. M₁₆	C₂×#3866	semidirect
319. Q₈	C₂²×#3866	semidirect
332. D₄	C₂²×#3866	semidirect
360. C₈	C₂²×#3866	semidirect

Maximal subgroups

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

subgroup	index
#41×#3866	2
C₂×D₄×#3866	2
#14558574	2
#14558572	2
SD₁₆×#3866	2
D₈×#3866	2
#14558544	2
#14558525	2
#14558524	2
M₁₆×#3866	2
AGL(1,ℤ/8)×D₃₇	2
C₄×AGL(1,ℤ/8)	37