Subgroups — AGL(1,ℤ/8)×#10621924 #36370318

Order 22144.

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×#10621924	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#10621924	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012532	C₂	1	2	yes	maximal, complemented
4	#26012530	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#10621924	C₂	1	2	yes	maximal, complemented
6	D₈×#10621924	C₂	1	2	yes	maximal, complemented
7	#26012502	C₂	1	1	yes	maximal, characteristic, complemented
8	#26012483	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012482	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10621924	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂³×#10621924	—	2	1	no	—
13	D₁₇₃⋊M₁₆	C₂²	1	1	yes	characteristic
14	Q₈×#10621924	C₂²	1	1	yes	characteristic, complemented
15	Q₈×#10621924	C₂²	1	1	yes	characteristic, complemented
16	D₄×#10621924	—	2	1	no	—
17	D₄×#10621924	—	2	1	no	—
18	D₄×#10621924	—	2	1	no	—
19	D₄×#10621924	—	2	1	no	—
20	D₄×#10621924	C₂²	1	2	yes	—
21	D₄×#10621924	C₂²	1	2	yes	—
22	D₄×#10621924	C₂²	1	1	yes	characteristic, complemented
23	D₄×#10621924	C₂²	1	1	yes	characteristic, complemented
24	#19149758	—	2	1	no	—
25	#19149758	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10621924	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#10621924	—	2	1	no	—
28	C₂×C₄×#10621924	—	2	1	no	—
29	C₂×C₄×#10621924	C₂²	1	1	yes	characteristic
30	#19149748	C₂²	1	2	yes	complemented
31	#19149747	C₂²	1	2	yes	complemented
32	#19149742	C₂²	1	2	yes	complemented
33	#19149741	C₂²	1	2	yes	—
34	#19149741	C₂²	1	2	yes	—
35	#19149741	C₂²	1	2	yes	complemented
36	#19149733	C₂²	1	2	yes	complemented
37	C₈×#10621924	C₂²	1	2	yes	complemented
38	#41×D₁₇₃	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₇₃	C₂²	1	1	yes	characteristic
40	#19149707	C₄	1	1	yes	characteristic, complemented
41	#19149706	C₄	1	2	yes	complemented
42	#19149705	C₄	1	1	yes	characteristic, complemented
43	#19149704	C₄	1	1	yes	characteristic, complemented
44	#19149703	C₄	1	2	yes	complemented
45	SD₁₆×D₁₇₃	C₂²	1	2	yes	—
46	D₈×D₁₇₃	C₂²	1	2	yes	—
47	M₁₆×D₁₇₃	C₂²	1	1	yes	characteristic
48	AGL(1,ℤ/8)×C₁₇₃	C₄	1	1	yes	characteristic, complemented
49	C₂²×#10621924	—	2	1	no	—
50	C₂²×#10621924	—	2	1	no	—
51	C₂²×#10621924	—	2	2	no	—
52	C₂²×#10621924	—	2	2	no	—
53	C₂²×#10621924	—	2	1	no	—
54	C₂²×#10621924	—	4	4	no	—
55	C₂²×#10621924	D₄	1	1	yes	characteristic
56	C₂²×#10621924	D₄	1	1	yes	characteristic
57	#14583836	—	2	1	no	—
58	#14583835	—	2	1	no	—
59	D₁₇₃⋊C₈	C₂³	1	2	yes	—
60	C₄⋊#10621924	—	2	1	no	—
61	C₄⋊#10621924	—	2	1	no	—
62	C₄⋊#10621924	—	2	1	no	—
63	C₄⋊#10621924	C₂³	1	1	yes	characteristic
64	C₄⋊#10621924	C₂³	1	1	yes	characteristic
65	C₄⋊#10621924	C₂³	1	2	yes	—
66	C₂²⋊#10621924	—	2	2	no	—
67	C₂²⋊#10621924	—	2	2	no	—
68	C₂²⋊#10621924	—	2	1	no	—
69	C₂²⋊#10621924	—	2	1	no	—
70	C₂²⋊#10621924	—	2	1	no	—
71	C₄×#10621924	—	2	1	no	—
72	C₄×#10621924	—	2	1	no	—
73	C₄×#10621924	—	2	1	no	—
74	C₄×#10621924	D₄	1	1	yes	characteristic
75	C₄×#10621924	D₄	1	1	yes	characteristic
76	C₄×#10621924	C₂³	1	1	yes	characteristic
77	C₄×#10621924	C₂³	1	1	yes	characteristic
78	C₂³×D₁₇₃	—	2	1	no	—
79	#14583827	C₂×C₄	1	1	yes	characteristic, complemented
80	#14583826	—	2	1	no	—
81	#14583826	C₂×C₄	1	1	yes	characteristic, complemented
82	#14583825	—	2	1	no	—
83	#14583825	C₂×C₄	1	1	yes	characteristic, complemented
84	Q₈×D₁₇₃	C₂³	1	1	yes	characteristic
85	C₂×D₆₉₂	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₁₇₃	—	2	1	no	—
87	D₄×D₁₇₃	—	2	1	no	—
88	D₄×D₁₇₃	—	2	1	no	—
89	D₄×D₁₇₃	—	2	1	no	—
90	D₄×D₁₇₃	C₂×C₄	1	2	yes	complemented
91	D₄×D₁₇₃	C₂³	1	2	yes	—
92	D₄×D₁₇₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₇₃	—	2	1	no	—
94	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
95	#14583815	C₂×C₄	1	2	yes	complemented
96	#14583814	C₂×C₄	1	2	yes	complemented
97	#14583813	C₂×C₄	1	2	yes	complemented
98	D₁₃₈₄	C₂×C₄	1	2	yes	complemented
99	#14583811	C₂×C₄	1	2	yes	complemented
100	#14583811	C₂×C₄	1	2	yes	complemented
101	#14583810	C₂×C₄	1	1	yes	characteristic, complemented
102	#14583809	C₂×C₄	1	2	yes	complemented
103	C₈×D₁₇₃	C₂³	1	2	yes	—
104	#41×C₁₇₃	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×D₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic, complemented
106	SD₁₆×C₁₇₃	C₂×C₄	1	2	yes	complemented
107	D₈×C₁₇₃	C₂×C₄	1	2	yes	complemented
108	M₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂×#10621924	—	2	2	no	—
110	C₂×#10621924	—	2	1	no	—
111	C₂×#10621924	—	2	1	no	—
112	C₂×#10621924	—	2	2	no	—
113	C₂×#10621924	—	4	1	no	—
114	C₂×#10621924	—	4	2	no	—
115	C₂×#10621924	—	4	4	no	—
116	C₂×#10621924	—	4	2	no	—
117	C₂×#10621924	—	4	2	no	—
118	C₂×#10621924	—	4	4	no	—
119	C₂×#10621924	C₂×D₄	1	1	yes	characteristic
120	C₂×#10621924	C₂×D₄	1	1	yes	characteristic
121	C₂×#10621924	C₂×D₄	1	1	yes	characteristic
122	C₂×#10621924	C₂×D₄	1	1	yes	characteristic
123	#13063443	—	2	2	no	—
124	C₂²×D₁₇₃	—	2	1	no	—
125	C₂²×D₁₇₃	—	2	2	no	—
126	C₂²×D₁₇₃	—	2	1	no	—
127	C₂²×D₁₇₃	—	2	2	no	—
128	C₂²×D₁₇₃	—	4	2	no	—
129	C₂²×D₁₇₃	—	4	2	no	—
130	C₂²×D₁₇₃	C₂×D₄	1	1	yes	characteristic
131	Dic₃₄₆	—	2	1	no	—
132	Dic₃₄₆	C₂²×C₄	1	1	yes	characteristic, complemented
133	D₆₉₂	—	2	1	no	—
134	D₆₉₂	—	2	1	no	—
135	D₆₉₂	C₂²×C₄	1	2	yes	—
136	D₆₉₂	C₂²×C₄	1	1	yes	characteristic, complemented
137	C₂²⋊D₁₇₃	—	2	1	no	—
138	C₂²⋊D₁₇₃	—	2	1	no	—
139	C₂²⋊D₁₇₃	—	2	2	no	—
140	C₂²⋊D₁₇₃	—	2	2	no	—
141	C₂²⋊D₁₇₃	—	2	1	no	—
142	C₂×Dic₁₇₃	—	2	1	no	—
143	C₂×Dic₁₇₃	#41	1	1	yes	characteristic
144	C₄×D₁₇₃	—	2	1	no	—
145	C₄×D₁₇₃	—	2	1	no	—
146	C₄×D₁₇₃	—	2	1	no	—
147	C₄×D₁₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×D₁₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄×D₁₇₃	#41	1	1	yes	characteristic
150	C₄×D₁₇₃	C₂⁴	1	1	yes	characteristic
151	#13063436	C₂²×C₄	1	2	yes	complemented
152	C₂³×C₁₇₃	—	2	1	no	—
153	Q₈×C₁₇₃	C₂²×C₄	1	1	yes	characteristic, complemented
154	D₄×C₁₇₃	—	2	1	no	—
155	D₄×C₁₇₃	—	2	1	no	—
156	D₄×C₁₇₃	C₂²×C₄	1	2	yes	—
157	D₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic, complemented
158	C₂×C₄×C₁₇₃	—	2	1	no	—
159	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₈×C₁₇₃	C₂²×C₄	1	2	yes	complemented
161	C₂²×C₁₇₃	—	2	1	no	—
162	C₂²×C₁₇₃	—	2	2	no	—
163	C₂²×C₁₇₃	—	4	2	no	—
164	C₂²×C₁₇₃	C₄×D₄	1	1	yes	characteristic
165	C₂×D₁₇₃	—	2	1	no	—
166	C₂×D₁₇₃	—	2	1	no	—
167	C₂×D₁₇₃	—	2	1	no	—
168	C₂×D₁₇₃	—	2	2	no	—
169	C₂×D₁₇₃	—	4	4	no	—
170	C₂×D₁₇₃	—	4	2	no	—
171	C₂×D₁₇₃	—	4	2	no	—
172	C₂×D₁₇₃	—	4	1	no	—
173	C₂×D₁₇₃	—	4	2	no	—
174	C₂×D₁₇₃	—	4	1	no	—
175	C₂×D₁₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×D₁₇₃	C₂²×D₄	1	1	yes	characteristic
177	#10621924	—	2	1	no	—
178	#10621924	—	2	1	no	—
179	#10621924	—	2	1	no	—
180	#10621924	—	4	1	no	—
181	#10621924	—	4	2	no	—
182	#10621924	—	4	1	no	—
183	#10621924	AGL(1,ℤ/8)	1	2	yes	direct product factor
184	C₄×C₁₇₃	—	2	1	no	—
185	C₄×C₁₇₃	C₄×D₄	1	1	yes	characteristic
186	C₄×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
187	Dic₁₇₃	—	2	1	no	—
188	Dic₁₇₃	C₄×D₄	1	1	yes	characteristic
189	Dic₁₇₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₁₇₃	—	2	1	no	—
191	C₂×C₁₇₃	—	4	2	no	—
192	C₂×C₁₇₃	—	4	1	no	—
193	C₂×C₁₇₃	C₂×C₄×D₄	1	1	yes	characteristic
194	D₁₇₃	—	2	1	no	—
195	D₁₇₃	—	4	1	no	—
196	D₁₇₃	—	4	2	no	—
197	D₁₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	D₁₇₃	#575	1	1	yes	characteristic
199	C₁₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
200	C₄×AGL(1,ℤ/8)	—	173	1	no	maximal, Sylow
201	C₂×AGL(1,ℤ/8)	—	173	1	no	—
202	C₄×#41	—	173	1	no	—
203	C₂×C₄×D₄	—	173	1	no	—
204	#442	—	173	2	no	—
205	#440	—	173	2	no	—
206	C₄×SD₁₆	—	173	2	no	—
207	C₄×D₈	—	173	2	no	—
208	#428	—	173	1	no	—
209	#418	—	173	1	no	—
210	#417	—	173	1	no	—
211	C₄×M₁₆	—	173	1	no	—
212	C₂×#41	—	173	1	no	—
213	C₂²×D₄	—	173	1	no	—
214	C₂³×C₄	—	346	1	no	—
215	AGL(1,ℤ/8)	—	173	1	no	—
216	AGL(1,ℤ/8)	—	173	1	no	—
217	AGL(1,ℤ/8)	—	173	2	no	—
218	AGL(1,ℤ/8)	—	173	2	no	—
219	AGL(1,ℤ/8)	—	173	1	no	—
220	AGL(1,ℤ/8)	#10621924	1	1	yes	characteristic, direct product factor
221	C₂×SD₁₆	—	173	2	no	—
222	C₂×D₈	—	173	2	no	—
223	C₂×M₁₆	—	173	1	no	—
224	C₂×M₁₆	—	173	1	no	—
225	C₄×Q₈	—	173	1	no	—
226	C₄×Q₈	—	173	1	no	—
227	C₄×D₄	—	346	1	no	—
228	C₄×D₄	—	346	1	no	—
229	C₄×D₄	—	346	1	no	—
230	C₄×D₄	—	346	1	no	—
231	C₄×D₄	—	173	2	no	—
232	C₄×D₄	—	173	2	no	—
233	C₄×D₄	—	173	1	no	—
234	C₄×D₄	—	173	1	no	—
235	#117	—	346	1	no	—
236	#117	—	173	1	no	—
237	C₂×C₄⋊C₄	—	173	1	no	—
238	C₂×C₂²⋊C₄	—	346	1	no	—
239	C₂×C₄²	—	346	1	no	—
240	C₂×C₄²	—	173	1	no	—
241	#107	—	173	2	no	—
242	#106	—	173	2	no	—
243	#103	—	173	2	no	—
244	#102	—	173	2	no	—
245	#102	—	173	2	no	—
246	#102	—	173	2	no	—
247	#97	—	173	2	no	—
248	C₄×C₈	—	173	2	no	—
249	C₂⁴	—	346	1	no	—
250	#41	—	346	1	no	—
251	#41	—	346	1	no	—
252	#41	—	173	1	no	—
253	#41	—	173	1	no	—
254	#41	—	173	1	no	—
255	#41	C₂×#10621924	1	1	yes	characteristic, complemented
256	C₂×Q₈	—	173	1	no	—
257	C₂×D₄	—	346	1	no	—
258	C₂×D₄	—	346	1	no	—
259	C₂×D₄	—	346	1	no	—
260	C₂×D₄	—	346	1	no	—
261	C₂×D₄	—	173	2	no	—
262	C₂×D₄	—	173	2	no	—
263	C₂×D₄	—	173	1	no	—
264	C₂×D₄	—	173	1	no	—
265	C₂×D₄	C₂×#10621924	1	1	yes	characteristic, complemented
266	C₂²×C₄	—	346	1	no	—
267	C₂²×C₄	—	346	1	no	—
268	C₂²×C₄	—	346	1	no	—
269	C₂²×C₄	—	346	1	no	—
270	C₂²×C₄	—	346	2	no	—
271	C₂²×C₄	—	346	2	no	—
272	C₂²×C₄	—	173	1	no	—
273	C₂²×C₄	—	173	1	no	—
274	C₂²×C₄	—	173	1	no	—
275	C₂²×C₄	—	692	4	no	—
276	SD₁₆	—	173	2	no	—
277	SD₁₆	—	173	2	no	—
278	SD₁₆	—	173	2	no	—
279	SD₁₆	C₂×#10621924	1	2	yes	complemented
280	D₈	—	173	2	no	—
281	D₈	—	173	2	no	—
282	D₈	—	173	2	no	—
283	D₈	C₂×#10621924	1	2	yes	complemented
284	M₁₆	—	346	1	no	—
285	M₁₆	—	346	1	no	—
286	M₁₆	—	173	1	no	—
287	M₁₆	—	173	2	no	—
288	M₁₆	C₂×#10621924	1	1	yes	characteristic, complemented
289	C₂×C₈	—	173	2	no	—
290	C₂×C₈	—	173	2	no	—
291	C₄⋊C₄	—	346	1	no	—
292	C₄⋊C₄	—	346	1	no	—
293	C₄⋊C₄	—	346	1	no	—
294	C₄⋊C₄	—	173	1	no	—
295	C₄⋊C₄	—	173	1	no	—
296	C₄⋊C₄	—	173	2	no	—
297	C₂²⋊C₄	—	346	1	no	—
298	C₂²⋊C₄	—	346	2	no	—
299	C₂²⋊C₄	—	346	2	no	—
300	C₂²⋊C₄	—	346	1	no	—
301	C₂²⋊C₄	—	346	1	no	—
302	C₄²	—	346	1	no	—
303	C₄²	—	346	1	no	—
304	C₄²	—	346	1	no	—
305	C₄²	—	173	1	no	—
306	C₄²	—	173	1	no	—
307	C₄²	—	173	1	no	—
308	C₄²	—	173	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	346	1	no	—
311	C₂³	—	346	2	no	—
312	C₂³	—	346	2	no	—
313	C₂³	—	346	1	no	—
314	C₂³	—	173	1	no	—
315	C₂³	—	692	2	no	—
316	C₂³	—	692	2	no	—
317	Q₈	—	346	1	no	—
318	Q₈	—	173	1	no	—
319	Q₈	C₂²×#10621924	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	346	1	no	—
323	D₄	—	346	1	no	—
324	D₄	—	346	1	no	—
325	D₄	—	346	2	no	—
326	D₄	—	346	2	no	—
327	D₄	—	346	1	no	—
328	D₄	—	346	1	no	—
329	D₄	—	173	2	no	—
330	D₄	—	173	1	no	—
331	D₄	C₂²×#10621924	1	2	yes	—
332	D₄	C₂²×#10621924	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	346	1	no	—
335	C₂×C₄	—	346	1	no	—
336	C₂×C₄	—	346	1	no	—
337	C₂×C₄	—	346	2	no	—
338	C₂×C₄	—	346	1	no	—
339	C₂×C₄	—	346	1	no	—
340	C₂×C₄	—	346	1	no	—
341	C₂×C₄	—	346	2	no	—
342	C₂×C₄	—	173	1	no	—
343	C₂×C₄	—	173	1	no	—
344	C₂×C₄	—	173	1	no	—
345	C₂×C₄	—	173	1	no	—
346	C₂×C₄	—	173	1	no	—
347	C₂×C₄	—	173	1	no	—
348	C₂×C₄	—	173	1	no	—
349	C₂×C₄	—	173	1	no	—
350	C₂×C₄	—	173	1	no	—
351	C₂×C₄	—	692	1	no	—
352	C₂×C₄	—	692	2	no	—
353	C₂×C₄	—	692	4	no	—
354	C₂×C₄	—	692	2	no	—
355	C₂×C₄	—	692	4	no	—
356	C₂×C₄	—	692	2	no	—
357	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
358	C₈	—	346	2	no	—
359	C₈	—	173	2	no	—
360	C₈	C₂²×#10621924	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	346	1	no	—
365	C₂²	—	346	1	no	—
366	C₂²	—	346	1	no	—
367	C₂²	—	346	2	no	—
368	C₂²	—	173	1	no	—
369	C₂²	—	173	1	no	—
370	C₂²	—	692	2	no	—
371	C₂²	—	692	4	no	—
372	C₂²	—	692	2	no	—
373	C₂²	—	692	1	no	—
374	C₂²	—	692	1	no	—
375	C₂²	—	692	2	no	—
376	C₂²	D₄×#10621924	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	346	1	no	—
379	C₄	—	346	1	no	—
380	C₄	—	346	1	no	—
381	C₄	—	346	1	no	—
382	C₄	—	173	2	no	—
383	C₄	—	173	1	no	—
384	C₄	—	173	1	no	—
385	C₄	—	692	2	no	—
386	C₄	—	692	1	no	—
387	C₄	—	692	1	no	—
388	C₄	D₄×#10621924	1	1	yes	characteristic
389	C₄	C₂³×#10621924	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	346	1	no	—
394	C₂	—	173	1	no	—
395	C₂	—	173	1	no	—
396	C₂	—	692	1	no	—
397	C₂	—	692	2	no	—
398	C₂	C₂×D₄×#10621924	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#10621924
commutator	C₄×C₁₇₃	C₂³×C₄
Frattini	C₄	C₂³×#10621924
Fitting	AGL(1,ℤ/8)×C₁₇₃	C₄
socle	C₂×C₁₇₃	C₂×C₄×D₄
prime radical	AGL(1,ℤ/8)×D₁₇₃	C₂
cosocle	C₄×D₁₇₃	C₂⁴
hypercenter	AGL(1,ℤ/8)	#10621924
hypocenter	C₁₇₃	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
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×#10621924	C₂	semidirect
2. C₂×D₄×#10621924	C₂	semidirect
3. #26012532	C₂	semidirect
4. #26012530	C₂	semidirect
5. SD₁₆×#10621924	C₂	semidirect
6. D₈×#10621924	C₂	semidirect
7. #26012502	C₂	semidirect
8. #26012483	C₂	semidirect
9. #26012482	C₂	semidirect
10. M₁₆×#10621924	C₂	semidirect
14. Q₈×#10621924	C₂²	semidirect
15. Q₈×#10621924	C₂²	semidirect
22. D₄×#10621924	C₂²	semidirect
23. D₄×#10621924	C₂²	semidirect
30. #19149748	C₂²	semidirect
31. #19149747	C₂²	semidirect
32. #19149742	C₂²	semidirect
35. #19149741	C₂²	semidirect
36. #19149733	C₂²	semidirect
37. C₈×#10621924	C₂²	semidirect
40. #19149707	C₄	semidirect
41. #19149706	C₄	semidirect
42. #19149705	C₄	semidirect
43. #19149704	C₄	semidirect
44. #19149703	C₄	semidirect
48. AGL(1,ℤ/8)×C₁₇₃	C₄	semidirect
79. #14583827	C₂×C₄	semidirect
81. #14583826	C₂×C₄	semidirect
83. #14583825	C₂×C₄	semidirect
85. C₂×D₆₉₂	C₂×C₄	semidirect
90. D₄×D₁₇₃	C₂×C₄	semidirect
95. #14583815	C₂×C₄	semidirect
96. #14583814	C₂×C₄	semidirect
97. #14583813	C₂×C₄	semidirect
98. D₁₃₈₄	C₂×C₄	semidirect
99. #14583811	C₂×C₄	semidirect
100. #14583811	C₂×C₄	semidirect
101. #14583810	C₂×C₄	semidirect
102. #14583809	C₂×C₄	semidirect
104. #41×C₁₇₃	C₂×C₄	semidirect
105. C₂×D₄×C₁₇₃	C₂×C₄	semidirect
106. SD₁₆×C₁₇₃	C₂×C₄	semidirect
107. D₈×C₁₇₃	C₂×C₄	semidirect
108. M₁₆×C₁₇₃	C₂×C₄	semidirect
132. Dic₃₄₆	C₂²×C₄	semidirect
136. D₆₉₂	C₂²×C₄	semidirect
151. #13063436	C₂²×C₄	semidirect
153. Q₈×C₁₇₃	C₂²×C₄	semidirect
157. D₄×C₁₇₃	C₂²×C₄	semidirect
160. C₈×C₁₇₃	C₂²×C₄	semidirect
183. #10621924	AGL(1,ℤ/8)	direct (N × H)
199. C₁₇₃	C₄×AGL(1,ℤ/8)	semidirect
220. AGL(1,ℤ/8)	#10621924	direct (N × H)
255. #41	C₂×#10621924	semidirect
265. C₂×D₄	C₂×#10621924	semidirect
279. SD₁₆	C₂×#10621924	semidirect
283. D₈	C₂×#10621924	semidirect
288. M₁₆	C₂×#10621924	semidirect
319. Q₈	C₂²×#10621924	semidirect
332. D₄	C₂²×#10621924	semidirect
360. C₈	C₂²×#10621924	semidirect

Maximal subgroups

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

subgroup	index
#41×#10621924	2
C₂×D₄×#10621924	2
#26012532	2
#26012530	2
SD₁₆×#10621924	2
D₈×#10621924	2
#26012502	2
#26012483	2
#26012482	2
M₁₆×#10621924	2
AGL(1,ℤ/8)×D₁₇₃	2
C₄×AGL(1,ℤ/8)	173