Subgroups — #16854522

Order 3968.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758488	C₂	1	1	yes	maximal, characteristic
2	C₄×#92497	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521159	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521151	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521149	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521140	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521136	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521129	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521088	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521052	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521047	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521001	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#92497	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃₁	—	2	1	no	—
19	C₂×D₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
21	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
23	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×#92480	C₂²	1	1	yes	characteristic
25	C₂×#92479	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₃₁	—	2	1	no	—
27	C₄×C₂²⋊D₃₁	—	2	1	no	—
28	C₂×C₄×Dic₃₁	—	2	1	no	—
29	#11758488	C₄	1	8	yes	complemented
30	C₂×#92470	C₂²	1	1	yes	characteristic
31	C₂×#92469	C₂²	1	1	yes	characteristic
32	C₂×#92469	C₂²	1	1	yes	characteristic
33	#11758470	C₂²	1	1	yes	characteristic
34	#11758469	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
36	#11758464	C₂²	1	1	yes	characteristic, complemented
37	(C₂²⋊D₃₁)⋊C₄	—	2	1	no	—
38	(C₂²⋊D₃₁)⋊C₄	—	2	1	no	—
39	C₂²⋊C₄×D₃₁	—	2	1	no	—
40	#11758454	—	2	1	no	—
41	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
42	C₄²×D₃₁	C₂²	1	1	yes	characteristic
43	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
44	C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#102	C₂²	1	1	yes	characteristic
46	C₃₁×#102	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#97	C₂²	1	1	yes	characteristic, complemented
48	#11758420	C₂²	1	1	yes	characteristic
49	#11758420	C₂²	1	1	yes	characteristic, complemented
50	#11758409	C₂²	1	1	yes	characteristic
51	#11758406	C₂²	1	1	yes	characteristic, complemented
52	#11758404	C₂²	1	1	yes	characteristic, complemented
53	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
54	C₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
55	#11758398	C₂²	1	1	yes	characteristic, complemented
56	#11758397	C₂²	1	1	yes	characteristic
57	#11758396	C₂²	1	1	yes	characteristic, complemented
58	#11758395	C₂²	1	1	yes	characteristic, complemented
59	#11758391	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₃₁	—	2	1	no	—
61	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	—	2	1	no	—
64	C₂²×C₄×C₃₁	—	2	1	no	—
65	C₂×C₂²⋊D₃₁	—	2	1	no	—
66	C₂×C₂²⋊D₃₁	—	2	1	no	—
67	C₂²×Dic₃₁	—	2	1	no	—
68	C₂²×Dic₃₁	—	2	1	no	—
69	C₂²×Dic₃₁	—	2	1	no	—
70	#92497	—	2	2	no	—
71	#92497	C₂×C₄	1	4	yes	complemented
72	D₄×D₃₁	—	2	2	no	—
73	D₄×D₃₁	C₂×C₄	1	4	yes	complemented
74	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₃₁	—	2	1	no	—
76	C₂×C₄×D₃₁	—	2	1	no	—
77	C₂×C₄×D₃₁	—	2	1	no	—
78	C₂×C₄×D₃₁	—	4	4	no	—
79	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
80	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
81	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
82	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
83	D₈×C₃₁	C₂×C₄	1	4	yes	complemented
84	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₃₁	—	2	1	no	—
89	C₂²⋊C₄×C₃₁	—	2	1	no	—
90	C₄²×C₃₁	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₃₁	—	2	1	no	—
92	C₂²⋊Dic₃₁	—	2	1	no	—
93	#92480	C₂×C₄	1	4	yes	complemented
94	#92479	C₂×C₄	1	4	yes	complemented
95	(C₂×D₃₁)⋊C₄	—	2	1	no	—
96	(C₂×D₃₁)⋊C₄	—	2	1	no	—
97	(C₂×D₃₁)⋊C₄	—	2	1	no	—
98	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
100	Dic₃₁⋊C₄	—	2	1	no	—
101	Dic₃₁⋊C₄	—	2	1	no	—
102	Dic₃₁⋊C₄	—	2	1	no	—
103	C₄×Dic₃₁	—	2	1	no	—
104	C₄×Dic₃₁	—	2	1	no	—
105	C₄×Dic₃₁	—	2	1	no	—
106	C₄×Dic₃₁	D₄	1	1	yes	characteristic
107	C₄×Dic₃₁	D₄	1	1	yes	characteristic
108	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
109	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₃₁⋊C₈	C₂³	1	1	yes	characteristic
111	#92470	C₂×C₄	1	4	yes	complemented
112	#92469	—	2	2	no	—
113	#92469	C₂×C₄	1	4	yes	complemented
114	C₂³×C₃₁	—	2	1	no	—
115	C₂³×C₃₁	—	2	1	no	—
116	C₂²×D₃₁	—	2	1	no	—
117	C₂²×D₃₁	—	2	4	no	—
118	C₂²×D₃₁	—	4	2	no	—
119	C₂²×D₃₁	—	4	2	no	—
120	C₂²×D₃₁	C₂×D₄	1	1	yes	characteristic
121	D₄×C₃₁	—	2	1	no	—
122	D₄×C₃₁	—	2	1	no	—
123	D₄×C₃₁	C₂²×C₄	1	2	yes	—
124	D₄×C₃₁	C₂²×C₄	1	2	yes	complemented
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	4	2	no	—
128	C₂×C₄×C₃₁	—	4	2	no	—
129	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₃₁	—	2	4	no	—
133	C₂²⋊D₃₁	—	2	4	no	—
134	C₂×Dic₃₁	—	2	1	no	—
135	C₂×Dic₃₁	—	2	4	no	—
136	C₂×Dic₃₁	—	2	1	no	—
137	C₂×Dic₃₁	—	2	1	no	—
138	C₂×Dic₃₁	—	4	2	no	—
139	C₂×Dic₃₁	—	4	2	no	—
140	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
142	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
143	D₁₂₄	—	2	1	no	—
144	D₁₂₄	C₂²×C₄	1	2	yes	—
145	C₄×D₃₁	—	2	2	no	—
146	C₄×D₃₁	—	4	1	no	—
147	C₄×D₃₁	—	4	2	no	—
148	C₄×D₃₁	—	4	2	no	—
149	C₄×D₃₁	—	4	2	no	—
150	C₄×D₃₁	C₂²×C₄	1	2	yes	—
151	C₄×D₃₁	#41	1	2	yes	—
152	Dic₆₂	—	2	1	no	—
153	Dic₆₂	C₂²×C₄	1	2	yes	complemented
154	C₈×C₃₁	—	2	1	no	—
155	C₈×C₃₁	C₂²×C₄	1	2	yes	complemented
156	C₃₁⋊C₈	—	2	1	no	—
157	C₃₁⋊C₈	C₂²×C₄	1	2	yes	complemented
158	C₄×AGL(1,ℤ/8)	—	31	1	no	maximal, Sylow
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	—	4	1	no	—
162	C₂²×C₃₁	—	4	1	no	—
163	C₂²×C₃₁	—	4	1	no	—
164	C₂²×C₃₁	—	4	1	no	—
165	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×D₃₁	—	2	1	no	—
167	C₂×D₃₁	—	2	1	no	—
168	C₂×D₃₁	—	2	2	no	—
169	C₂×D₃₁	—	4	8	no	—
170	C₂×D₃₁	—	4	1	no	—
171	C₂×D₃₁	—	4	1	no	—
172	C₂×D₃₁	C₄×D₄	1	2	yes	—
173	C₄×C₃₁	—	2	1	no	—
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	4	1	no	—
176	C₄×C₃₁	—	4	1	no	—
177	C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
178	C₄×C₃₁	C₂×#41	1	1	yes	characteristic
179	Dic₃₁	—	2	2	no	—
180	Dic₃₁	—	2	1	no	—
181	Dic₃₁	—	4	1	no	—
182	Dic₃₁	—	4	1	no	—
183	Dic₃₁	C₄×D₄	1	2	yes	—
184	Dic₃₁	AGL(1,ℤ/8)	1	2	yes	complemented
185	C₂×AGL(1,ℤ/8)	—	31	1	no	—
186	C₄×#41	—	31	1	no	—
187	C₂×C₄×D₄	—	31	1	no	—
188	#442	—	31	1	no	—
189	#442	D₃₁	1	1	yes	characteristic, complemented
190	#440	—	31	1	no	—
191	#440	—	31	1	no	—
192	C₄×SD₁₆	—	31	1	no	—
193	C₄×SD₁₆	—	31	1	no	—
194	C₄×D₈	—	31	1	no	—
195	C₄×D₈	—	31	1	no	—
196	#428	—	31	1	no	—
197	#418	—	31	1	no	—
198	#417	—	31	1	no	—
199	C₄×M₁₆	—	31	1	no	—
200	C₂×C₃₁	—	4	2	no	—
201	C₂×C₃₁	—	4	2	no	—
202	C₂×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₂×C₃₁	#575	1	1	yes	characteristic
205	D₃₁	—	2	2	no	—
206	D₃₁	—	4	2	no	—
207	C₂×#41	—	31	1	no	—
208	C₂²×D₄	—	31	1	no	—
209	C₂³×C₄	—	62	1	no	—
210	AGL(1,ℤ/8)	—	31	8	no	—
211	C₂×SD₁₆	—	31	1	no	—
212	C₂×SD₁₆	—	31	1	no	—
213	C₂×D₈	—	31	1	no	—
214	C₂×D₈	C₂×D₃₁	1	1	yes	characteristic
215	C₂×M₁₆	—	31	1	no	—
216	C₂×M₁₆	—	31	1	no	—
217	C₄×Q₈	—	31	1	no	—
218	C₄×Q₈	—	31	1	no	—
219	C₄×D₄	—	31	1	no	—
220	C₄×D₄	—	31	1	no	—
221	C₄×D₄	—	31	1	no	—
222	C₄×D₄	—	31	1	no	—
223	C₄×D₄	—	62	1	no	—
224	C₄×D₄	—	62	1	no	—
225	C₄×D₄	—	62	1	no	—
226	C₄×D₄	—	62	1	no	—
227	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
228	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
229	#117	—	31	1	no	—
230	#117	—	62	1	no	—
231	C₂×C₄⋊C₄	—	31	1	no	—
232	C₂×C₂²⋊C₄	—	62	1	no	—
233	C₂×C₄²	—	31	1	no	—
234	C₂×C₄²	—	62	1	no	—
235	#107	—	31	1	no	—
236	#107	—	31	1	no	—
237	#106	—	31	1	no	—
238	#106	C₂×D₃₁	1	1	yes	characteristic, complemented
239	#103	—	31	1	no	—
240	#103	—	31	1	no	—
241	#102	—	31	1	no	—
242	#102	—	31	1	no	—
243	#102	—	31	1	no	—
244	#102	—	31	1	no	—
245	#102	C₂×D₃₁	1	1	yes	characteristic
246	#102	C₂×D₃₁	1	1	yes	characteristic, complemented
247	#97	—	31	1	no	—
248	#97	C₂×D₃₁	1	1	yes	characteristic, complemented
249	C₄×C₈	—	31	1	no	—
250	C₄×C₈	—	31	1	no	—
251	C₃₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
252	C₂⁴	—	62	1	no	—
253	#41	—	31	4	no	—
254	#41	—	62	2	no	—
255	C₂×Q₈	—	31	1	no	—
256	C₂×D₄	—	31	4	no	—
257	C₂×D₄	—	31	1	no	—
258	C₂×D₄	—	62	2	no	—
259	C₂×D₄	—	62	1	no	—
260	C₂×D₄	—	62	1	no	—
261	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
262	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	31	1	no	—
266	C₂²×C₄	—	31	1	no	—
267	C₂²×C₄	—	31	1	no	—
268	C₂²×C₄	—	62	1	no	—
269	C₂²×C₄	—	62	1	no	—
270	C₂²×C₄	—	62	1	no	—
271	C₂²×C₄	—	62	1	no	—
272	C₂²×C₄	—	62	1	no	—
273	C₂²×C₄	—	62	1	no	—
274	C₂²×C₄	—	124	4	no	—
275	SD₁₆	—	31	4	no	—
276	SD₁₆	—	31	4	no	—
277	D₈	—	31	4	no	—
278	D₈	C₄×D₃₁	1	4	yes	complemented
279	M₁₆	—	31	4	no	—
280	M₁₆	—	62	2	no	—
281	C₂×C₈	—	31	1	no	—
282	C₂×C₈	—	31	1	no	—
283	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
285	C₄⋊C₄	—	31	1	no	—
286	C₄⋊C₄	—	31	1	no	—
287	C₄⋊C₄	—	62	1	no	—
288	C₄⋊C₄	—	62	1	no	—
289	C₄⋊C₄	—	62	1	no	—
290	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	62	1	no	—
295	C₂²⋊C₄	—	62	1	no	—
296	C₂²⋊C₄	—	62	1	no	—
297	C₂²⋊C₄	—	62	1	no	—
298	C₂²⋊C₄	—	62	1	no	—
299	C₄²	—	31	1	no	—
300	C₄²	—	31	1	no	—
301	C₄²	—	31	1	no	—
302	C₄²	—	62	1	no	—
303	C₄²	—	62	1	no	—
304	C₄²	—	62	1	no	—
305	C₄²	C₂²×D₃₁	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	31	1	no	—
309	C₂³	—	62	4	no	—
310	C₂³	—	62	1	no	—
311	C₂³	—	124	2	no	—
312	C₂³	—	124	2	no	—
313	Q₈	—	31	2	no	—
314	Q₈	—	62	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	2	1	no	—
317	D₄	—	31	2	no	—
318	D₄	—	62	4	no	—
319	D₄	—	62	4	no	—
320	D₄	—	62	1	no	—
321	D₄	C₂×C₄×D₃₁	1	2	yes	—
322	D₄	C₂×C₄×D₃₁	1	2	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	31	1	no	—
328	C₂×C₄	—	31	1	no	—
329	C₂×C₄	—	31	2	no	—
330	C₂×C₄	—	31	2	no	—
331	C₂×C₄	—	31	1	no	—
332	C₂×C₄	—	62	2	no	—
333	C₂×C₄	—	62	4	no	—
334	C₂×C₄	—	62	1	no	—
335	C₂×C₄	—	62	1	no	—
336	C₂×C₄	—	62	1	no	—
337	C₂×C₄	—	124	1	no	—
338	C₂×C₄	—	124	2	no	—
339	C₂×C₄	—	124	2	no	—
340	C₂×C₄	—	124	2	no	—
341	C₂×C₄	—	124	2	no	—
342	C₂×C₄	—	124	2	no	—
343	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
344	C₂×C₄	D₄×D₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	31	2	no	—
348	C₈	—	62	1	no	—
349	C₈	C₂×C₄×D₃₁	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	31	2	no	—
357	C₂²	—	62	1	no	—
358	C₂²	—	62	1	no	—
359	C₂²	—	62	2	no	—
360	C₂²	—	124	8	no	—
361	C₂²	—	124	1	no	—
362	C₂²	—	124	1	no	—
363	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	31	2	no	—
369	C₄	—	31	2	no	—
370	C₄	—	62	2	no	—
371	C₄	—	62	1	no	—
372	C₄	—	124	1	no	—
373	C₄	—	124	1	no	—
374	C₄	C₂²×C₄×D₃₁	1	1	yes	characteristic
375	C₄	#41×D₃₁	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	—	62	2	no	—
379	C₂	—	124	2	no	—
380	C₂	C₄×D₄×D₃₁	1	1	yes	characteristic
381	C₂	AGL(1,ℤ/8)×D₃₁	1	1	yes	characteristic
382	C₂	#14521845	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₃₁
commutator	C₄×C₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₃₁×#442	C₂
socle	C₂²×C₃₁	C₂²×D₄
prime radical	C₂×#11758488	C₂
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	#442	D₃₁
hypocenter	C₃₁	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #442

Complements

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

N	H ≅ G/N	type
2. C₄×#92497	C₂	semidirect
3. C₄×D₄×D₃₁	C₂	semidirect
4. #14521159	C₂	semidirect
5. #14521151	C₂	semidirect
6. #14521149	C₂	semidirect
7. #14521140	C₂	semidirect
8. #14521136	C₂	semidirect
9. D₈×Dic₃₁	C₂	semidirect
10. #14521129	C₂	semidirect
11. #14521088	C₂	semidirect
12. #14521052	C₂	semidirect
13. #14521047	C₂	semidirect
14. #14521001	C₂	semidirect
15. C₃₁×#442	C₂	semidirect
21. C₄×D₄×C₃₁	C₂²	semidirect
23. D₄×Dic₃₁	C₂²	semidirect
29. #11758488	C₄	semidirect
36. #11758464	C₂²	semidirect
43. C₄×Dic₆₂	C₂²	semidirect
44. C₃₁×#106	C₂²	semidirect
46. C₃₁×#102	C₂²	semidirect
47. C₃₁×#97	C₂²	semidirect
49. #11758420	C₂²	semidirect
51. #11758406	C₂²	semidirect
52. #11758404	C₂²	semidirect
53. C₈×Dic₃₁	C₂²	semidirect
54. C₈×Dic₃₁	C₂²	semidirect
55. #11758398	C₂²	semidirect
57. #11758396	C₂²	semidirect
58. #11758395	C₂²	semidirect
59. #11758391	C₂²	semidirect
71. #92497	C₂×C₄	semidirect
73. D₄×D₃₁	C₂×C₄	semidirect
83. D₈×C₃₁	C₂×C₄	semidirect
93. #92480	C₂×C₄	semidirect
94. #92479	C₂×C₄	semidirect
111. #92470	C₂×C₄	semidirect
113. #92469	C₂×C₄	semidirect
124. D₄×C₃₁	C₂²×C₄	semidirect
153. Dic₆₂	C₂²×C₄	semidirect
155. C₈×C₃₁	C₂²×C₄	semidirect
157. C₃₁⋊C₈	C₂²×C₄	semidirect
184. Dic₃₁	AGL(1,ℤ/8)	semidirect
189. #442	D₃₁	semidirect
228. C₄×D₄	C₂×D₃₁	semidirect
238. #106	C₂×D₃₁	semidirect
246. #102	C₂×D₃₁	semidirect
248. #97	C₂×D₃₁	semidirect
251. C₃₁	C₄×AGL(1,ℤ/8)	semidirect
278. D₈	C₄×D₃₁	semidirect
322. D₄	C₂×C₄×D₃₁	semidirect
349. C₈	C₂×C₄×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758488	2
C₄×#92497	2
C₄×D₄×D₃₁	2
#14521159	2
#14521151	2
#14521149	2
#14521140	2
#14521136	2
D₈×Dic₃₁	2
#14521129	2
#14521088	2
#14521052	2
#14521047	2
#14521001	2
C₃₁×#442	2
C₄×AGL(1,ℤ/8)	31