Subgroups — AGL(1,ℤ/8)×#10597010 #34061446

Order 19072.

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×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
3	#23750666	C₂	1	2	yes	maximal, complemented
4	#23750664	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#10597010	C₂	1	2	yes	maximal, complemented
6	D₈×#10597010	C₂	1	2	yes	maximal, complemented
7	#23750636	C₂	1	1	yes	maximal, characteristic, complemented
8	#23750617	C₂	1	1	yes	maximal, characteristic, complemented
9	#23750616	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10597010	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₄₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10597010	—	2	1	no	—
13	D₁₄₉⋊M₁₆	C₂²	1	1	yes	characteristic
14	Q₈×#10597010	C₂²	1	1	yes	characteristic, complemented
15	Q₈×#10597010	C₂²	1	1	yes	characteristic, complemented
16	D₄×#10597010	—	2	1	no	—
17	D₄×#10597010	—	2	1	no	—
18	D₄×#10597010	—	2	1	no	—
19	D₄×#10597010	—	2	1	no	—
20	D₄×#10597010	C₂²	1	2	yes	—
21	D₄×#10597010	C₂²	1	2	yes	—
22	D₄×#10597010	C₂²	1	1	yes	characteristic, complemented
23	D₄×#10597010	C₂²	1	1	yes	characteristic, complemented
24	#18011990	—	2	1	no	—
25	#18011990	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10597010	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#10597010	—	2	1	no	—
28	C₂×C₄×#10597010	—	2	1	no	—
29	C₂×C₄×#10597010	C₂²	1	1	yes	characteristic
30	#18011980	C₂²	1	2	yes	complemented
31	#18011979	C₂²	1	2	yes	complemented
32	#18011974	C₂²	1	2	yes	complemented
33	#18011973	C₂²	1	2	yes	—
34	#18011973	C₂²	1	2	yes	—
35	#18011973	C₂²	1	2	yes	complemented
36	#18011965	C₂²	1	2	yes	complemented
37	C₈×#10597010	C₂²	1	2	yes	complemented
38	#41×D₁₄₉	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₄₉	C₂²	1	1	yes	characteristic
40	#18011939	C₄	1	1	yes	characteristic, complemented
41	#18011938	C₄	1	2	yes	complemented
42	#18011937	C₄	1	1	yes	characteristic, complemented
43	#18011936	C₄	1	1	yes	characteristic, complemented
44	#18011935	C₄	1	2	yes	complemented
45	SD₁₆×D₁₄₉	C₂²	1	2	yes	—
46	D₈×D₁₄₉	C₂²	1	2	yes	—
47	M₁₆×D₁₄₉	C₂²	1	1	yes	characteristic
48	AGL(1,ℤ/8)×C₁₄₉	C₄	1	1	yes	characteristic, complemented
49	C₂²×#10597010	—	2	1	no	—
50	C₂²×#10597010	—	2	1	no	—
51	C₂²×#10597010	—	2	2	no	—
52	C₂²×#10597010	—	2	2	no	—
53	C₂²×#10597010	—	2	1	no	—
54	C₂²×#10597010	—	4	4	no	—
55	C₂²×#10597010	D₄	1	1	yes	characteristic
56	C₂²×#10597010	D₄	1	1	yes	characteristic
57	#14558746	—	2	1	no	—
58	#14558745	—	2	1	no	—
59	D₁₄₉⋊C₈	C₂³	1	2	yes	—
60	C₄⋊#10597010	—	2	1	no	—
61	C₄⋊#10597010	—	2	1	no	—
62	C₄⋊#10597010	—	2	1	no	—
63	C₄⋊#10597010	C₂³	1	1	yes	characteristic
64	C₄⋊#10597010	C₂³	1	1	yes	characteristic
65	C₄⋊#10597010	C₂³	1	2	yes	—
66	C₂²⋊#10597010	—	2	2	no	—
67	C₂²⋊#10597010	—	2	2	no	—
68	C₂²⋊#10597010	—	2	1	no	—
69	C₂²⋊#10597010	—	2	1	no	—
70	C₂²⋊#10597010	—	2	1	no	—
71	C₄×#10597010	—	2	1	no	—
72	C₄×#10597010	—	2	1	no	—
73	C₄×#10597010	—	2	1	no	—
74	C₄×#10597010	D₄	1	1	yes	characteristic
75	C₄×#10597010	D₄	1	1	yes	characteristic
76	C₄×#10597010	C₂³	1	1	yes	characteristic
77	C₄×#10597010	C₂³	1	1	yes	characteristic
78	C₂³×D₁₄₉	—	2	1	no	—
79	#14558737	C₂×C₄	1	1	yes	characteristic, complemented
80	#14558736	—	2	1	no	—
81	#14558736	C₂×C₄	1	1	yes	characteristic, complemented
82	#14558735	—	2	1	no	—
83	#14558735	C₂×C₄	1	1	yes	characteristic, complemented
84	Q₈×D₁₄₉	C₂³	1	1	yes	characteristic
85	C₂×D₅₉₆	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₁₄₉	—	2	1	no	—
87	D₄×D₁₄₉	—	2	1	no	—
88	D₄×D₁₄₉	—	2	1	no	—
89	D₄×D₁₄₉	—	2	1	no	—
90	D₄×D₁₄₉	C₂×C₄	1	2	yes	complemented
91	D₄×D₁₄₉	C₂³	1	2	yes	—
92	D₄×D₁₄₉	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₄₉	—	2	1	no	—
94	C₂×C₄×D₁₄₉	C₂³	1	1	yes	characteristic
95	#14558725	C₂×C₄	1	2	yes	complemented
96	#14558724	C₂×C₄	1	2	yes	complemented
97	#14558723	C₂×C₄	1	2	yes	complemented
98	D₁₁₉₂	C₂×C₄	1	2	yes	complemented
99	#14558721	C₂×C₄	1	2	yes	complemented
100	#14558721	C₂×C₄	1	2	yes	complemented
101	#14558720	C₂×C₄	1	1	yes	characteristic, complemented
102	#14558719	C₂×C₄	1	2	yes	complemented
103	C₈×D₁₄₉	C₂³	1	2	yes	—
104	#41×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×D₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
106	SD₁₆×C₁₄₉	C₂×C₄	1	2	yes	complemented
107	D₈×C₁₄₉	C₂×C₄	1	2	yes	complemented
108	M₁₆×C₁₄₉	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂×#10597010	—	2	2	no	—
110	C₂×#10597010	—	2	1	no	—
111	C₂×#10597010	—	2	1	no	—
112	C₂×#10597010	—	2	2	no	—
113	C₂×#10597010	—	4	1	no	—
114	C₂×#10597010	—	4	2	no	—
115	C₂×#10597010	—	4	4	no	—
116	C₂×#10597010	—	4	2	no	—
117	C₂×#10597010	—	4	2	no	—
118	C₂×#10597010	—	4	4	no	—
119	C₂×#10597010	C₂×D₄	1	1	yes	characteristic
120	C₂×#10597010	C₂×D₄	1	1	yes	characteristic
121	C₂×#10597010	C₂×D₄	1	1	yes	characteristic
122	C₂×#10597010	C₂×D₄	1	1	yes	characteristic
123	#11924753	—	2	2	no	—
124	C₂²×D₁₄₉	—	2	1	no	—
125	C₂²×D₁₄₉	—	2	2	no	—
126	C₂²×D₁₄₉	—	2	1	no	—
127	C₂²×D₁₄₉	—	2	2	no	—
128	C₂²×D₁₄₉	—	4	2	no	—
129	C₂²×D₁₄₉	—	4	2	no	—
130	C₂²×D₁₄₉	C₂×D₄	1	1	yes	characteristic
131	Dic₂₉₈	—	2	1	no	—
132	Dic₂₉₈	C₂²×C₄	1	1	yes	characteristic, complemented
133	D₅₉₆	—	2	1	no	—
134	D₅₉₆	—	2	1	no	—
135	D₅₉₆	C₂²×C₄	1	2	yes	—
136	D₅₉₆	C₂²×C₄	1	1	yes	characteristic, complemented
137	C₂²⋊D₁₄₉	—	2	1	no	—
138	C₂²⋊D₁₄₉	—	2	1	no	—
139	C₂²⋊D₁₄₉	—	2	2	no	—
140	C₂²⋊D₁₄₉	—	2	2	no	—
141	C₂²⋊D₁₄₉	—	2	1	no	—
142	C₂×Dic₁₄₉	—	2	1	no	—
143	C₂×Dic₁₄₉	#41	1	1	yes	characteristic
144	C₄×D₁₄₉	—	2	1	no	—
145	C₄×D₁₄₉	—	2	1	no	—
146	C₄×D₁₄₉	—	2	1	no	—
147	C₄×D₁₄₉	C₂²×C₄	1	1	yes	characteristic
148	C₄×D₁₄₉	C₂×D₄	1	1	yes	characteristic
149	C₄×D₁₄₉	#41	1	1	yes	characteristic
150	C₄×D₁₄₉	C₂⁴	1	1	yes	characteristic
151	#11924746	C₂²×C₄	1	2	yes	complemented
152	C₂³×C₁₄₉	—	2	1	no	—
153	Q₈×C₁₄₉	C₂²×C₄	1	1	yes	characteristic, complemented
154	D₄×C₁₄₉	—	2	1	no	—
155	D₄×C₁₄₉	—	2	1	no	—
156	D₄×C₁₄₉	C₂²×C₄	1	2	yes	—
157	D₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic, complemented
158	C₂×C₄×C₁₄₉	—	2	1	no	—
159	C₂×C₄×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
160	C₈×C₁₄₉	C₂²×C₄	1	2	yes	complemented
161	C₂²×C₁₄₉	—	2	1	no	—
162	C₂²×C₁₄₉	—	2	2	no	—
163	C₂²×C₁₄₉	—	4	2	no	—
164	C₂²×C₁₄₉	C₄×D₄	1	1	yes	characteristic
165	C₂×D₁₄₉	—	2	1	no	—
166	C₂×D₁₄₉	—	2	1	no	—
167	C₂×D₁₄₉	—	2	1	no	—
168	C₂×D₁₄₉	—	2	2	no	—
169	C₂×D₁₄₉	—	4	4	no	—
170	C₂×D₁₄₉	—	4	2	no	—
171	C₂×D₁₄₉	—	4	2	no	—
172	C₂×D₁₄₉	—	4	1	no	—
173	C₂×D₁₄₉	—	4	2	no	—
174	C₂×D₁₄₉	—	4	1	no	—
175	C₂×D₁₄₉	C₄×D₄	1	1	yes	characteristic
176	C₂×D₁₄₉	C₂²×D₄	1	1	yes	characteristic
177	#10597010	—	2	1	no	—
178	#10597010	—	2	1	no	—
179	#10597010	—	2	1	no	—
180	#10597010	—	4	1	no	—
181	#10597010	—	4	2	no	—
182	#10597010	—	4	1	no	—
183	#10597010	AGL(1,ℤ/8)	1	2	yes	direct product factor
184	C₄×C₁₄₉	—	2	1	no	—
185	C₄×C₁₄₉	C₄×D₄	1	1	yes	characteristic
186	C₄×C₁₄₉	C₂³×C₄	1	1	yes	characteristic
187	Dic₁₄₉	—	2	1	no	—
188	Dic₁₄₉	C₄×D₄	1	1	yes	characteristic
189	Dic₁₄₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₁₄₉	—	2	1	no	—
191	C₂×C₁₄₉	—	4	2	no	—
192	C₂×C₁₄₉	—	4	1	no	—
193	C₂×C₁₄₉	C₂×C₄×D₄	1	1	yes	characteristic
194	D₁₄₉	—	2	1	no	—
195	D₁₄₉	—	4	1	no	—
196	D₁₄₉	—	4	2	no	—
197	D₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	D₁₄₉	#575	1	1	yes	characteristic
199	C₁₄₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
200	C₄×AGL(1,ℤ/8)	—	149	1	no	maximal, Sylow
201	C₂×AGL(1,ℤ/8)	—	149	1	no	—
202	C₄×#41	—	149	1	no	—
203	C₂×C₄×D₄	—	149	1	no	—
204	#442	—	149	2	no	—
205	#440	—	149	2	no	—
206	C₄×SD₁₆	—	149	2	no	—
207	C₄×D₈	—	149	2	no	—
208	#428	—	149	1	no	—
209	#418	—	149	1	no	—
210	#417	—	149	1	no	—
211	C₄×M₁₆	—	149	1	no	—
212	C₂×#41	—	149	1	no	—
213	C₂²×D₄	—	149	1	no	—
214	C₂³×C₄	—	298	1	no	—
215	AGL(1,ℤ/8)	—	149	1	no	—
216	AGL(1,ℤ/8)	—	149	1	no	—
217	AGL(1,ℤ/8)	—	149	2	no	—
218	AGL(1,ℤ/8)	—	149	2	no	—
219	AGL(1,ℤ/8)	—	149	1	no	—
220	AGL(1,ℤ/8)	#10597010	1	1	yes	characteristic, direct product factor
221	C₂×SD₁₆	—	149	2	no	—
222	C₂×D₈	—	149	2	no	—
223	C₂×M₁₆	—	149	1	no	—
224	C₂×M₁₆	—	149	1	no	—
225	C₄×Q₈	—	149	1	no	—
226	C₄×Q₈	—	149	1	no	—
227	C₄×D₄	—	298	1	no	—
228	C₄×D₄	—	298	1	no	—
229	C₄×D₄	—	298	1	no	—
230	C₄×D₄	—	298	1	no	—
231	C₄×D₄	—	149	2	no	—
232	C₄×D₄	—	149	2	no	—
233	C₄×D₄	—	149	1	no	—
234	C₄×D₄	—	149	1	no	—
235	#117	—	298	1	no	—
236	#117	—	149	1	no	—
237	C₂×C₄⋊C₄	—	149	1	no	—
238	C₂×C₂²⋊C₄	—	298	1	no	—
239	C₂×C₄²	—	298	1	no	—
240	C₂×C₄²	—	149	1	no	—
241	#107	—	149	2	no	—
242	#106	—	149	2	no	—
243	#103	—	149	2	no	—
244	#102	—	149	2	no	—
245	#102	—	149	2	no	—
246	#102	—	149	2	no	—
247	#97	—	149	2	no	—
248	C₄×C₈	—	149	2	no	—
249	C₂⁴	—	298	1	no	—
250	#41	—	298	1	no	—
251	#41	—	298	1	no	—
252	#41	—	149	1	no	—
253	#41	—	149	1	no	—
254	#41	—	149	1	no	—
255	#41	C₂×#10597010	1	1	yes	characteristic, complemented
256	C₂×Q₈	—	149	1	no	—
257	C₂×D₄	—	298	1	no	—
258	C₂×D₄	—	298	1	no	—
259	C₂×D₄	—	298	1	no	—
260	C₂×D₄	—	298	1	no	—
261	C₂×D₄	—	149	2	no	—
262	C₂×D₄	—	149	2	no	—
263	C₂×D₄	—	149	1	no	—
264	C₂×D₄	—	149	1	no	—
265	C₂×D₄	C₂×#10597010	1	1	yes	characteristic, complemented
266	C₂²×C₄	—	298	1	no	—
267	C₂²×C₄	—	298	1	no	—
268	C₂²×C₄	—	298	1	no	—
269	C₂²×C₄	—	298	1	no	—
270	C₂²×C₄	—	298	2	no	—
271	C₂²×C₄	—	298	2	no	—
272	C₂²×C₄	—	596	4	no	—
273	C₂²×C₄	—	149	1	no	—
274	C₂²×C₄	—	149	1	no	—
275	C₂²×C₄	—	149	1	no	—
276	SD₁₆	—	149	2	no	—
277	SD₁₆	—	149	2	no	—
278	SD₁₆	—	149	2	no	—
279	SD₁₆	C₂×#10597010	1	2	yes	complemented
280	D₈	—	149	2	no	—
281	D₈	—	149	2	no	—
282	D₈	—	149	2	no	—
283	D₈	C₂×#10597010	1	2	yes	complemented
284	M₁₆	—	298	1	no	—
285	M₁₆	—	298	1	no	—
286	M₁₆	—	149	1	no	—
287	M₁₆	—	149	2	no	—
288	M₁₆	C₂×#10597010	1	1	yes	characteristic, complemented
289	C₂×C₈	—	149	2	no	—
290	C₂×C₈	—	149	2	no	—
291	C₄⋊C₄	—	298	1	no	—
292	C₄⋊C₄	—	298	1	no	—
293	C₄⋊C₄	—	298	1	no	—
294	C₄⋊C₄	—	149	1	no	—
295	C₄⋊C₄	—	149	1	no	—
296	C₄⋊C₄	—	149	2	no	—
297	C₂²⋊C₄	—	298	1	no	—
298	C₂²⋊C₄	—	298	2	no	—
299	C₂²⋊C₄	—	298	2	no	—
300	C₂²⋊C₄	—	298	1	no	—
301	C₂²⋊C₄	—	298	1	no	—
302	C₄²	—	298	1	no	—
303	C₄²	—	298	1	no	—
304	C₄²	—	298	1	no	—
305	C₄²	—	149	1	no	—
306	C₄²	—	149	1	no	—
307	C₄²	—	149	1	no	—
308	C₄²	—	149	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	298	1	no	—
311	C₂³	—	298	2	no	—
312	C₂³	—	298	2	no	—
313	C₂³	—	298	1	no	—
314	C₂³	—	596	2	no	—
315	C₂³	—	596	2	no	—
316	C₂³	—	149	1	no	—
317	Q₈	—	298	1	no	—
318	Q₈	—	149	1	no	—
319	Q₈	C₂²×#10597010	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	298	1	no	—
323	D₄	—	298	1	no	—
324	D₄	—	298	1	no	—
325	D₄	—	298	2	no	—
326	D₄	—	298	2	no	—
327	D₄	—	298	1	no	—
328	D₄	—	298	1	no	—
329	D₄	—	149	2	no	—
330	D₄	—	149	1	no	—
331	D₄	C₂²×#10597010	1	2	yes	—
332	D₄	C₂²×#10597010	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	298	1	no	—
335	C₂×C₄	—	298	1	no	—
336	C₂×C₄	—	298	1	no	—
337	C₂×C₄	—	298	2	no	—
338	C₂×C₄	—	298	1	no	—
339	C₂×C₄	—	298	1	no	—
340	C₂×C₄	—	298	1	no	—
341	C₂×C₄	—	298	2	no	—
342	C₂×C₄	—	596	1	no	—
343	C₂×C₄	—	596	2	no	—
344	C₂×C₄	—	596	4	no	—
345	C₂×C₄	—	596	2	no	—
346	C₂×C₄	—	596	2	no	—
347	C₂×C₄	—	596	4	no	—
348	C₂×C₄	—	149	1	no	—
349	C₂×C₄	—	149	1	no	—
350	C₂×C₄	—	149	1	no	—
351	C₂×C₄	—	149	1	no	—
352	C₂×C₄	—	149	1	no	—
353	C₂×C₄	—	149	1	no	—
354	C₂×C₄	—	149	1	no	—
355	C₂×C₄	—	149	1	no	—
356	C₂×C₄	—	149	1	no	—
357	C₂×C₄	C₂²×#10597010	1	1	yes	characteristic
358	C₈	—	298	2	no	—
359	C₈	—	149	2	no	—
360	C₈	C₂²×#10597010	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	298	1	no	—
365	C₂²	—	298	1	no	—
366	C₂²	—	298	1	no	—
367	C₂²	—	298	2	no	—
368	C₂²	—	596	2	no	—
369	C₂²	—	596	4	no	—
370	C₂²	—	596	2	no	—
371	C₂²	—	596	1	no	—
372	C₂²	—	596	1	no	—
373	C₂²	—	596	2	no	—
374	C₂²	—	149	1	no	—
375	C₂²	—	149	1	no	—
376	C₂²	D₄×#10597010	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	298	1	no	—
379	C₄	—	298	1	no	—
380	C₄	—	298	1	no	—
381	C₄	—	298	1	no	—
382	C₄	—	596	2	no	—
383	C₄	—	596	1	no	—
384	C₄	—	596	1	no	—
385	C₄	—	149	2	no	—
386	C₄	—	149	1	no	—
387	C₄	—	149	1	no	—
388	C₄	D₄×#10597010	1	1	yes	characteristic
389	C₄	C₂³×#10597010	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	298	1	no	—
394	C₂	—	596	2	no	—
395	C₂	—	596	1	no	—
396	C₂	—	149	1	no	—
397	C₂	—	149	1	no	—
398	C₂	C₂×D₄×#10597010	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#10597010
commutator	C₄×C₁₄₉	C₂³×C₄
Frattini	C₄	C₂³×#10597010
Fitting	AGL(1,ℤ/8)×C₁₄₉	C₄
socle	C₂×C₁₄₉	C₂×C₄×D₄
prime radical	AGL(1,ℤ/8)×D₁₄₉	C₂
cosocle	C₄×D₁₄₉	C₂⁴
hypercenter	AGL(1,ℤ/8)	#10597010
hypocenter	C₁₄₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₄₉ ▷ C₂×C₁₄₉ ▷ C₁₄₉
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×#10597010	C₂	semidirect
2. C₂×D₄×#10597010	C₂	semidirect
3. #23750666	C₂	semidirect
4. #23750664	C₂	semidirect
5. SD₁₆×#10597010	C₂	semidirect
6. D₈×#10597010	C₂	semidirect
7. #23750636	C₂	semidirect
8. #23750617	C₂	semidirect
9. #23750616	C₂	semidirect
10. M₁₆×#10597010	C₂	semidirect
14. Q₈×#10597010	C₂²	semidirect
15. Q₈×#10597010	C₂²	semidirect
22. D₄×#10597010	C₂²	semidirect
23. D₄×#10597010	C₂²	semidirect
30. #18011980	C₂²	semidirect
31. #18011979	C₂²	semidirect
32. #18011974	C₂²	semidirect
35. #18011973	C₂²	semidirect
36. #18011965	C₂²	semidirect
37. C₈×#10597010	C₂²	semidirect
40. #18011939	C₄	semidirect
41. #18011938	C₄	semidirect
42. #18011937	C₄	semidirect
43. #18011936	C₄	semidirect
44. #18011935	C₄	semidirect
48. AGL(1,ℤ/8)×C₁₄₉	C₄	semidirect
79. #14558737	C₂×C₄	semidirect
81. #14558736	C₂×C₄	semidirect
83. #14558735	C₂×C₄	semidirect
85. C₂×D₅₉₆	C₂×C₄	semidirect
90. D₄×D₁₄₉	C₂×C₄	semidirect
95. #14558725	C₂×C₄	semidirect
96. #14558724	C₂×C₄	semidirect
97. #14558723	C₂×C₄	semidirect
98. D₁₁₉₂	C₂×C₄	semidirect
99. #14558721	C₂×C₄	semidirect
100. #14558721	C₂×C₄	semidirect
101. #14558720	C₂×C₄	semidirect
102. #14558719	C₂×C₄	semidirect
104. #41×C₁₄₉	C₂×C₄	semidirect
105. C₂×D₄×C₁₄₉	C₂×C₄	semidirect
106. SD₁₆×C₁₄₉	C₂×C₄	semidirect
107. D₈×C₁₄₉	C₂×C₄	semidirect
108. M₁₆×C₁₄₉	C₂×C₄	semidirect
132. Dic₂₉₈	C₂²×C₄	semidirect
136. D₅₉₆	C₂²×C₄	semidirect
151. #11924746	C₂²×C₄	semidirect
153. Q₈×C₁₄₉	C₂²×C₄	semidirect
157. D₄×C₁₄₉	C₂²×C₄	semidirect
160. C₈×C₁₄₉	C₂²×C₄	semidirect
183. #10597010	AGL(1,ℤ/8)	direct (N × H)
199. C₁₄₉	C₄×AGL(1,ℤ/8)	semidirect
220. AGL(1,ℤ/8)	#10597010	direct (N × H)
255. #41	C₂×#10597010	semidirect
265. C₂×D₄	C₂×#10597010	semidirect
279. SD₁₆	C₂×#10597010	semidirect
283. D₈	C₂×#10597010	semidirect
288. M₁₆	C₂×#10597010	semidirect
319. Q₈	C₂²×#10597010	semidirect
332. D₄	C₂²×#10597010	semidirect
360. C₈	C₂²×#10597010	semidirect

Maximal subgroups

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

subgroup	index
#41×#10597010	2
C₂×D₄×#10597010	2
#23750666	2
#23750664	2
SD₁₆×#10597010	2
D₈×#10597010	2
#23750636	2
#23750617	2
#23750616	2
M₁₆×#10597010	2
AGL(1,ℤ/8)×D₁₄₉	2
C₄×AGL(1,ℤ/8)	149