Subgroups — AGL(1,ℤ/8)×#90673 #28407329

Order 14464.

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×#90673	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#90673	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299639	C₂	1	2	yes	maximal, complemented
4	#20299637	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#90673	C₂	1	2	yes	maximal, complemented
6	D₈×#90673	C₂	1	2	yes	maximal, complemented
7	#20299609	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299590	C₂	1	1	yes	maximal, characteristic, complemented
9	#20299589	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#90673	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂³×#90673	—	2	1	no	—
13	D₁₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
14	Q₈×#90673	C₂²	1	1	yes	characteristic, complemented
15	Q₈×#90673	C₂²	1	1	yes	characteristic, complemented
16	D₄×#90673	—	2	1	no	—
17	D₄×#90673	—	2	1	no	—
18	D₄×#90673	—	2	1	no	—
19	D₄×#90673	—	2	1	no	—
20	D₄×#90673	C₂²	1	2	yes	—
21	D₄×#90673	C₂²	1	2	yes	—
22	D₄×#90673	C₂²	1	1	yes	characteristic, complemented
23	D₄×#90673	C₂²	1	1	yes	characteristic, complemented
24	#16813701	—	2	1	no	—
25	#16813701	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#90673	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#90673	—	2	1	no	—
28	C₂×C₄×#90673	—	2	1	no	—
29	C₂×C₄×#90673	C₂²	1	1	yes	characteristic
30	#16813691	C₂²	1	2	yes	complemented
31	#16813690	C₂²	1	2	yes	complemented
32	#16813685	C₂²	1	2	yes	complemented
33	#16813684	C₂²	1	2	yes	—
34	#16813684	C₂²	1	2	yes	—
35	#16813684	C₂²	1	2	yes	complemented
36	#16813676	C₂²	1	2	yes	complemented
37	C₈×#90673	C₂²	1	2	yes	complemented
38	#41×D₁₁₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₁₃	C₂²	1	1	yes	characteristic
40	#16813650	C₄	1	1	yes	characteristic, complemented
41	#16813649	C₄	1	2	yes	complemented
42	#16813648	C₄	1	1	yes	characteristic, complemented
43	#16813647	C₄	1	1	yes	characteristic, complemented
44	#16813646	C₄	1	2	yes	complemented
45	SD₁₆×D₁₁₃	C₂²	1	2	yes	—
46	D₈×D₁₁₃	C₂²	1	2	yes	—
47	M₁₆×D₁₁₃	C₂²	1	1	yes	characteristic
48	AGL(1,ℤ/8)×C₁₁₃	C₄	1	1	yes	characteristic, complemented
49	C₂²×#90673	—	2	1	no	—
50	C₂²×#90673	—	2	1	no	—
51	C₂²×#90673	—	2	1	no	—
52	C₂²×#90673	—	2	2	no	—
53	C₂²×#90673	—	2	2	no	—
54	C₂²×#90673	—	4	4	no	—
55	C₂²×#90673	D₄	1	1	yes	characteristic
56	C₂²×#90673	D₄	1	1	yes	characteristic
57	#14268657	—	2	1	no	—
58	#14268656	—	2	1	no	—
59	#14268655	C₂³	1	2	yes	—
60	C₄⋊#90673	—	2	1	no	—
61	C₄⋊#90673	—	2	1	no	—
62	C₄⋊#90673	—	2	1	no	—
63	C₄⋊#90673	C₂³	1	1	yes	characteristic
64	C₄⋊#90673	C₂³	1	1	yes	characteristic
65	C₄⋊#90673	C₂³	1	2	yes	—
66	C₂²⋊#90673	—	2	1	no	—
67	C₂²⋊#90673	—	2	2	no	—
68	C₂²⋊#90673	—	2	2	no	—
69	C₂²⋊#90673	—	2	1	no	—
70	C₂²⋊#90673	—	2	1	no	—
71	C₄×#90673	—	2	1	no	—
72	C₄×#90673	—	2	1	no	—
73	C₄×#90673	—	2	1	no	—
74	C₄×#90673	D₄	1	1	yes	characteristic
75	C₄×#90673	D₄	1	1	yes	characteristic
76	C₄×#90673	C₂³	1	1	yes	characteristic
77	C₄×#90673	C₂³	1	1	yes	characteristic
78	C₂³×D₁₁₃	—	2	1	no	—
79	#14268648	C₂×C₄	1	1	yes	characteristic, complemented
80	#14268647	—	2	1	no	—
81	#14268647	C₂×C₄	1	1	yes	characteristic, complemented
82	#14268646	—	2	1	no	—
83	#14268646	C₂×C₄	1	1	yes	characteristic, complemented
84	Q₈×D₁₁₃	C₂³	1	1	yes	characteristic
85	C₂×D₄₅₂	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₁₁₃	—	2	1	no	—
87	D₄×D₁₁₃	—	2	1	no	—
88	D₄×D₁₁₃	—	2	1	no	—
89	D₄×D₁₁₃	—	2	1	no	—
90	D₄×D₁₁₃	C₂×C₄	1	2	yes	complemented
91	D₄×D₁₁₃	C₂³	1	2	yes	—
92	D₄×D₁₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₁₃	—	2	1	no	—
94	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
95	#14268636	C₂×C₄	1	2	yes	complemented
96	#14268635	C₂×C₄	1	2	yes	complemented
97	#14268634	C₂×C₄	1	2	yes	complemented
98	D₉₀₄	C₂×C₄	1	2	yes	complemented
99	#14268632	C₂×C₄	1	2	yes	complemented
100	#14268632	C₂×C₄	1	2	yes	complemented
101	#14268631	C₂×C₄	1	1	yes	characteristic, complemented
102	#14268630	C₂×C₄	1	2	yes	complemented
103	C₈×D₁₁₃	C₂³	1	2	yes	—
104	#41×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×D₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
106	SD₁₆×C₁₁₃	C₂×C₄	1	2	yes	complemented
107	D₈×C₁₁₃	C₂×C₄	1	2	yes	complemented
108	M₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂³×C₁₁₃	—	2	1	no	—
110	C₂²×D₁₁₃	—	2	1	no	—
111	C₂²×D₁₁₃	—	2	2	no	—
112	C₂²×D₁₁₃	—	2	1	no	—
113	C₂²×D₁₁₃	—	2	2	no	—
114	C₂²×D₁₁₃	—	4	2	no	—
115	C₂²×D₁₁₃	—	4	2	no	—
116	C₂²×D₁₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂×#90673	—	2	2	no	—
118	C₂×#90673	—	2	1	no	—
119	C₂×#90673	—	2	1	no	—
120	C₂×#90673	—	2	2	no	—
121	C₂×#90673	—	4	1	no	—
122	C₂×#90673	—	4	2	no	—
123	C₂×#90673	—	4	4	no	—
124	C₂×#90673	—	4	2	no	—
125	C₂×#90673	—	4	2	no	—
126	C₂×#90673	—	4	4	no	—
127	C₂×#90673	C₂×D₄	1	1	yes	characteristic
128	C₂×#90673	C₂×D₄	1	1	yes	characteristic
129	C₂×#90673	C₂×D₄	1	1	yes	characteristic
130	C₂×#90673	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₁₁₃	C₂²×C₄	1	1	yes	characteristic, complemented
132	D₄×C₁₁₃	—	2	1	no	—
133	D₄×C₁₁₃	—	2	1	no	—
134	D₄×C₁₁₃	C₂²×C₄	1	2	yes	—
135	D₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic, complemented
136	C₂×C₄×C₁₁₃	—	2	1	no	—
137	C₂×C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊D₁₁₃	—	2	1	no	—
139	C₂²⋊D₁₁₃	—	2	1	no	—
140	C₂²⋊D₁₁₃	—	2	2	no	—
141	C₂²⋊D₁₁₃	—	2	2	no	—
142	C₂²⋊D₁₁₃	—	2	1	no	—
143	C₂×Dic₁₁₃	—	2	1	no	—
144	C₂×Dic₁₁₃	#41	1	1	yes	characteristic
145	D₄₅₂	—	2	1	no	—
146	D₄₅₂	—	2	1	no	—
147	D₄₅₂	C₂²×C₄	1	2	yes	—
148	D₄₅₂	C₂²×C₄	1	1	yes	characteristic, complemented
149	C₄×D₁₁₃	—	2	1	no	—
150	C₄×D₁₁₃	—	2	1	no	—
151	C₄×D₁₁₃	—	2	1	no	—
152	C₄×D₁₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×D₁₁₃	C₂×D₄	1	1	yes	characteristic
154	C₄×D₁₁₃	#41	1	1	yes	characteristic
155	C₄×D₁₁₃	C₂⁴	1	1	yes	characteristic
156	Dic₂₂₆	—	2	1	no	—
157	Dic₂₂₆	C₂²×C₄	1	1	yes	characteristic, complemented
158	#11744753	—	2	2	no	—
159	C₈×C₁₁₃	C₂²×C₄	1	2	yes	complemented
160	#11744751	C₂²×C₄	1	2	yes	complemented
161	C₂²×C₁₁₃	—	2	1	no	—
162	C₂²×C₁₁₃	—	2	2	no	—
163	C₂²×C₁₁₃	—	4	2	no	—
164	C₂²×C₁₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂×D₁₁₃	—	2	1	no	—
166	C₂×D₁₁₃	—	2	1	no	—
167	C₂×D₁₁₃	—	2	1	no	—
168	C₂×D₁₁₃	—	2	2	no	—
169	C₂×D₁₁₃	—	4	4	no	—
170	C₂×D₁₁₃	—	4	2	no	—
171	C₂×D₁₁₃	—	4	2	no	—
172	C₂×D₁₁₃	—	4	1	no	—
173	C₂×D₁₁₃	—	4	1	no	—
174	C₂×D₁₁₃	—	4	2	no	—
175	C₂×D₁₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×D₁₁₃	C₂²×D₄	1	1	yes	characteristic
177	#90673	—	2	1	no	—
178	#90673	—	2	1	no	—
179	#90673	—	2	1	no	—
180	#90673	—	4	1	no	—
181	#90673	—	4	2	no	—
182	#90673	—	4	1	no	—
183	#90673	AGL(1,ℤ/8)	1	2	yes	direct product factor
184	C₄×C₁₁₃	—	2	1	no	—
185	C₄×C₁₁₃	C₄×D₄	1	1	yes	characteristic
186	C₄×C₁₁₃	C₂³×C₄	1	1	yes	characteristic
187	Dic₁₁₃	—	2	1	no	—
188	Dic₁₁₃	C₄×D₄	1	1	yes	characteristic
189	Dic₁₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₁₁₃	—	2	1	no	—
191	C₂×C₁₁₃	—	4	2	no	—
192	C₂×C₁₁₃	—	4	1	no	—
193	C₂×C₁₁₃	C₂×C₄×D₄	1	1	yes	characteristic
194	D₁₁₃	—	2	1	no	—
195	D₁₁₃	—	4	1	no	—
196	D₁₁₃	—	4	2	no	—
197	D₁₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	D₁₁₃	#575	1	1	yes	characteristic
199	C₄×AGL(1,ℤ/8)	—	113	1	no	maximal, Sylow
200	C₁₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
201	C₂×AGL(1,ℤ/8)	—	113	1	no	—
202	C₄×#41	—	113	1	no	—
203	C₂×C₄×D₄	—	113	1	no	—
204	#442	—	113	2	no	—
205	#440	—	113	2	no	—
206	C₄×SD₁₆	—	113	2	no	—
207	C₄×D₈	—	113	2	no	—
208	#428	—	113	1	no	—
209	#418	—	113	1	no	—
210	#417	—	113	1	no	—
211	C₄×M₁₆	—	113	1	no	—
212	C₂×#41	—	113	1	no	—
213	C₂²×D₄	—	113	1	no	—
214	C₂³×C₄	—	226	1	no	—
215	AGL(1,ℤ/8)	—	113	1	no	—
216	AGL(1,ℤ/8)	—	113	1	no	—
217	AGL(1,ℤ/8)	—	113	2	no	—
218	AGL(1,ℤ/8)	—	113	2	no	—
219	AGL(1,ℤ/8)	—	113	1	no	—
220	AGL(1,ℤ/8)	#90673	1	1	yes	characteristic, direct product factor
221	C₂×SD₁₆	—	113	2	no	—
222	C₂×D₈	—	113	2	no	—
223	C₂×M₁₆	—	113	1	no	—
224	C₂×M₁₆	—	113	1	no	—
225	C₄×Q₈	—	113	1	no	—
226	C₄×Q₈	—	113	1	no	—
227	C₄×D₄	—	113	2	no	—
228	C₄×D₄	—	113	2	no	—
229	C₄×D₄	—	113	1	no	—
230	C₄×D₄	—	113	1	no	—
231	C₄×D₄	—	226	1	no	—
232	C₄×D₄	—	226	1	no	—
233	C₄×D₄	—	226	1	no	—
234	C₄×D₄	—	226	1	no	—
235	#117	—	113	1	no	—
236	#117	—	226	1	no	—
237	C₂×C₄⋊C₄	—	113	1	no	—
238	C₂×C₂²⋊C₄	—	226	1	no	—
239	C₂×C₄²	—	113	1	no	—
240	C₂×C₄²	—	226	1	no	—
241	#107	—	113	2	no	—
242	#106	—	113	2	no	—
243	#103	—	113	2	no	—
244	#102	—	113	2	no	—
245	#102	—	113	2	no	—
246	#102	—	113	2	no	—
247	#97	—	113	2	no	—
248	C₄×C₈	—	113	2	no	—
249	C₂⁴	—	226	1	no	—
250	#41	—	113	1	no	—
251	#41	—	113	1	no	—
252	#41	—	113	1	no	—
253	#41	—	226	1	no	—
254	#41	—	226	1	no	—
255	#41	C₂×#90673	1	1	yes	characteristic, complemented
256	C₂×Q₈	—	113	1	no	—
257	C₂×D₄	—	113	2	no	—
258	C₂×D₄	—	113	2	no	—
259	C₂×D₄	—	113	1	no	—
260	C₂×D₄	—	113	1	no	—
261	C₂×D₄	—	226	1	no	—
262	C₂×D₄	—	226	1	no	—
263	C₂×D₄	—	226	1	no	—
264	C₂×D₄	—	226	1	no	—
265	C₂×D₄	C₂×#90673	1	1	yes	characteristic, complemented
266	C₂²×C₄	—	113	1	no	—
267	C₂²×C₄	—	113	1	no	—
268	C₂²×C₄	—	113	1	no	—
269	C₂²×C₄	—	452	4	no	—
270	C₂²×C₄	—	226	1	no	—
271	C₂²×C₄	—	226	1	no	—
272	C₂²×C₄	—	226	1	no	—
273	C₂²×C₄	—	226	2	no	—
274	C₂²×C₄	—	226	2	no	—
275	C₂²×C₄	—	226	1	no	—
276	SD₁₆	—	113	2	no	—
277	SD₁₆	—	113	2	no	—
278	SD₁₆	—	113	2	no	—
279	SD₁₆	C₂×#90673	1	2	yes	complemented
280	D₈	—	113	2	no	—
281	D₈	—	113	2	no	—
282	D₈	—	113	2	no	—
283	D₈	C₂×#90673	1	2	yes	complemented
284	M₁₆	—	113	1	no	—
285	M₁₆	—	113	2	no	—
286	M₁₆	—	226	1	no	—
287	M₁₆	—	226	1	no	—
288	M₁₆	C₂×#90673	1	1	yes	characteristic, complemented
289	C₂×C₈	—	113	2	no	—
290	C₂×C₈	—	113	2	no	—
291	C₄⋊C₄	—	113	1	no	—
292	C₄⋊C₄	—	113	1	no	—
293	C₄⋊C₄	—	113	2	no	—
294	C₄⋊C₄	—	226	1	no	—
295	C₄⋊C₄	—	226	1	no	—
296	C₄⋊C₄	—	226	1	no	—
297	C₂²⋊C₄	—	226	2	no	—
298	C₂²⋊C₄	—	226	2	no	—
299	C₂²⋊C₄	—	226	1	no	—
300	C₂²⋊C₄	—	226	1	no	—
301	C₂²⋊C₄	—	226	1	no	—
302	C₄²	—	113	1	no	—
303	C₄²	—	113	1	no	—
304	C₄²	—	113	1	no	—
305	C₄²	—	113	1	no	—
306	C₄²	—	226	1	no	—
307	C₄²	—	226	1	no	—
308	C₄²	—	226	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	113	1	no	—
311	C₂³	—	452	2	no	—
312	C₂³	—	452	2	no	—
313	C₂³	—	226	1	no	—
314	C₂³	—	226	2	no	—
315	C₂³	—	226	2	no	—
316	C₂³	—	226	1	no	—
317	Q₈	—	113	1	no	—
318	Q₈	—	226	1	no	—
319	Q₈	C₂²×#90673	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	113	1	no	—
323	D₄	—	113	2	no	—
324	D₄	—	226	1	no	—
325	D₄	—	226	2	no	—
326	D₄	—	226	2	no	—
327	D₄	—	226	1	no	—
328	D₄	—	226	1	no	—
329	D₄	—	226	1	no	—
330	D₄	—	226	1	no	—
331	D₄	C₂²×#90673	1	2	yes	—
332	D₄	C₂²×#90673	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	113	1	no	—
335	C₂×C₄	—	113	1	no	—
336	C₂×C₄	—	113	1	no	—
337	C₂×C₄	—	113	1	no	—
338	C₂×C₄	—	113	1	no	—
339	C₂×C₄	—	113	1	no	—
340	C₂×C₄	—	113	1	no	—
341	C₂×C₄	—	113	1	no	—
342	C₂×C₄	—	113	1	no	—
343	C₂×C₄	—	452	4	no	—
344	C₂×C₄	—	452	2	no	—
345	C₂×C₄	—	452	2	no	—
346	C₂×C₄	—	452	4	no	—
347	C₂×C₄	—	452	2	no	—
348	C₂×C₄	—	452	1	no	—
349	C₂×C₄	—	226	1	no	—
350	C₂×C₄	—	226	1	no	—
351	C₂×C₄	—	226	1	no	—
352	C₂×C₄	—	226	2	no	—
353	C₂×C₄	—	226	1	no	—
354	C₂×C₄	—	226	1	no	—
355	C₂×C₄	—	226	2	no	—
356	C₂×C₄	—	226	1	no	—
357	C₂×C₄	C₂²×#90673	1	1	yes	characteristic
358	C₈	—	113	2	no	—
359	C₈	—	226	2	no	—
360	C₈	C₂²×#90673	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	113	1	no	—
365	C₂²	—	113	1	no	—
366	C₂²	—	452	2	no	—
367	C₂²	—	452	2	no	—
368	C₂²	—	452	1	no	—
369	C₂²	—	452	1	no	—
370	C₂²	—	452	2	no	—
371	C₂²	—	452	4	no	—
372	C₂²	—	226	1	no	—
373	C₂²	—	226	1	no	—
374	C₂²	—	226	1	no	—
375	C₂²	—	226	2	no	—
376	C₂²	D₄×#90673	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	113	2	no	—
379	C₄	—	113	1	no	—
380	C₄	—	113	1	no	—
381	C₄	—	452	2	no	—
382	C₄	—	452	1	no	—
383	C₄	—	452	1	no	—
384	C₄	—	226	1	no	—
385	C₄	—	226	1	no	—
386	C₄	—	226	1	no	—
387	C₄	—	226	1	no	—
388	C₄	D₄×#90673	1	1	yes	characteristic
389	C₄	C₂³×#90673	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	113	1	no	—
394	C₂	—	113	1	no	—
395	C₂	—	452	2	no	—
396	C₂	—	452	1	no	—
397	C₂	—	226	1	no	—
398	C₂	C₂×D₄×#90673	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#90673
commutator	C₄×C₁₁₃	C₂³×C₄
Frattini	C₄	C₂³×#90673
Fitting	AGL(1,ℤ/8)×C₁₁₃	C₄
socle	C₂×C₁₁₃	C₂×C₄×D₄
prime radical	AGL(1,ℤ/8)×D₁₁₃	C₂
cosocle	C₄×D₁₁₃	C₂⁴
hypercenter	AGL(1,ℤ/8)	#90673
hypocenter	C₁₁₃	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
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×#90673	C₂	semidirect
2. C₂×D₄×#90673	C₂	semidirect
3. #20299639	C₂	semidirect
4. #20299637	C₂	semidirect
5. SD₁₆×#90673	C₂	semidirect
6. D₈×#90673	C₂	semidirect
7. #20299609	C₂	semidirect
8. #20299590	C₂	semidirect
9. #20299589	C₂	semidirect
10. M₁₆×#90673	C₂	semidirect
14. Q₈×#90673	C₂²	semidirect
15. Q₈×#90673	C₂²	semidirect
22. D₄×#90673	C₂²	semidirect
23. D₄×#90673	C₂²	semidirect
30. #16813691	C₂²	semidirect
31. #16813690	C₂²	semidirect
32. #16813685	C₂²	semidirect
35. #16813684	C₂²	semidirect
36. #16813676	C₂²	semidirect
37. C₈×#90673	C₂²	semidirect
40. #16813650	C₄	semidirect
41. #16813649	C₄	semidirect
42. #16813648	C₄	semidirect
43. #16813647	C₄	semidirect
44. #16813646	C₄	semidirect
48. AGL(1,ℤ/8)×C₁₁₃	C₄	semidirect
79. #14268648	C₂×C₄	semidirect
81. #14268647	C₂×C₄	semidirect
83. #14268646	C₂×C₄	semidirect
85. C₂×D₄₅₂	C₂×C₄	semidirect
90. D₄×D₁₁₃	C₂×C₄	semidirect
95. #14268636	C₂×C₄	semidirect
96. #14268635	C₂×C₄	semidirect
97. #14268634	C₂×C₄	semidirect
98. D₉₀₄	C₂×C₄	semidirect
99. #14268632	C₂×C₄	semidirect
100. #14268632	C₂×C₄	semidirect
101. #14268631	C₂×C₄	semidirect
102. #14268630	C₂×C₄	semidirect
104. #41×C₁₁₃	C₂×C₄	semidirect
105. C₂×D₄×C₁₁₃	C₂×C₄	semidirect
106. SD₁₆×C₁₁₃	C₂×C₄	semidirect
107. D₈×C₁₁₃	C₂×C₄	semidirect
108. M₁₆×C₁₁₃	C₂×C₄	semidirect
131. Q₈×C₁₁₃	C₂²×C₄	semidirect
135. D₄×C₁₁₃	C₂²×C₄	semidirect
148. D₄₅₂	C₂²×C₄	semidirect
157. Dic₂₂₆	C₂²×C₄	semidirect
159. C₈×C₁₁₃	C₂²×C₄	semidirect
160. #11744751	C₂²×C₄	semidirect
183. #90673	AGL(1,ℤ/8)	direct (N × H)
200. C₁₁₃	C₄×AGL(1,ℤ/8)	semidirect
220. AGL(1,ℤ/8)	#90673	direct (N × H)
255. #41	C₂×#90673	semidirect
265. C₂×D₄	C₂×#90673	semidirect
279. SD₁₆	C₂×#90673	semidirect
283. D₈	C₂×#90673	semidirect
288. M₁₆	C₂×#90673	semidirect
319. Q₈	C₂²×#90673	semidirect
332. D₄	C₂²×#90673	semidirect
360. C₈	C₂²×#90673	semidirect

Maximal subgroups

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

subgroup	index
#41×#90673	2
C₂×D₄×#90673	2
#20299639	2
#20299637	2
SD₁₆×#90673	2
D₈×#90673	2
#20299609	2
#20299590	2
#20299589	2
M₁₆×#90673	2
AGL(1,ℤ/8)×D₁₁₃	2
C₄×AGL(1,ℤ/8)	113