Subgroups — C₄×#11758491 #16854520

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×#11758491	C₂	1	1	yes	maximal, characteristic
2	C₄×#92499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521160	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521158	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521152	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#92481	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₂₄₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#92479	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	#14521049	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#92469	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#92499	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃₁	—	2	1	no	—
19	C₂×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic
20	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
22	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
23	C₂×#92481	C₂²	1	1	yes	characteristic
24	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
25	C₂×#92479	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊D₃₁	—	2	1	no	—
27	#11758491	C₄	1	8	yes	direct product factor
28	C₂×D₂₄₈	C₂²	1	1	yes	characteristic
29	C₂×#92469	C₂²	1	1	yes	characteristic
30	C₂×#92469	C₂²	1	1	yes	characteristic
31	#11758470	—	2	1	no	—
32	#11758470	C₂²	1	1	yes	characteristic
33	#11758470	C₂²	1	1	yes	characteristic, complemented
34	#11758469	—	2	1	no	—
35	#11758469	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
37	(C₂²⋊D₃₁)⋊C₄	—	2	1	no	—
38	C₂²⋊C₄×D₃₁	—	2	1	no	—
39	C₄×D₁₂₄	—	2	1	no	—
40	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
41	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
42	C₄²×D₃₁	—	2	1	no	—
43	C₄²×D₃₁	C₂²	1	1	yes	characteristic
44	C₃₁×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃₁×#103	C₂²	1	1	yes	characteristic, complemented
46	C₃₁×#102	C₂²	1	1	yes	characteristic
47	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
48	#11758423	C₂²	1	1	yes	characteristic, complemented
49	#11758420	C₂²	1	1	yes	characteristic
50	#11758409	C₂²	1	1	yes	characteristic
51	#11758409	C₂²	1	1	yes	characteristic, complemented
52	#11758406	C₂²	1	1	yes	characteristic, complemented
53	#11758403	C₂²	1	1	yes	characteristic, complemented
54	#11758403	C₂²	1	1	yes	characteristic, complemented
55	#11758397	C₂²	1	1	yes	characteristic
56	#11758397	C₂²	1	1	yes	characteristic, complemented
57	#11758396	C₂²	1	1	yes	characteristic, complemented
58	#11758395	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₃₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₃₁	—	2	1	no	—
61	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	—	2	1	no	—
64	C₂×C₂²⋊D₃₁	—	2	1	no	—
65	C₂²×Dic₃₁	—	2	1	no	—
66	#92499	—	2	2	no	—
67	#92499	C₂×C₄	1	4	yes	complemented
68	D₄×D₃₁	—	2	2	no	—
69	D₄×D₃₁	C₂×C₄	1	4	yes	complemented
70	C₂×D₁₂₄	—	2	1	no	—
71	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
72	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₃₁	—	2	1	no	—
74	C₂×C₄×D₃₁	—	2	1	no	—
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	—	2	1	no	—
79	C₂×C₄×D₃₁	—	4	4	no	—
80	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
81	C₂×C₄×D₃₁	D₄	1	1	yes	characteristic
82	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
83	SD₁₆×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	—	2	1	no	—
87	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
89	C₂²⋊C₄×C₃₁	—	2	1	no	—
90	C₄²×C₃₁	—	2	1	no	—
91	C₄²×C₃₁	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₃₁	—	2	1	no	—
93	#92481	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	(C₂×D₃₁)⋊C₄	—	2	1	no	—
99	(C₂×D₃₁)⋊C₄	—	2	1	no	—
100	C₄⋊Dic₃₁	—	2	1	no	—
101	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
103	Dic₃₁⋊C₄	—	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	D₂₄₈	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	C₂²×D₃₁	—	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	Q₈×C₃₁	—	2	1	no	—
122	Q₈×C₃₁	C₂²×C₄	1	2	yes	complemented
123	D₄×C₃₁	—	2	1	no	—
124	D₄×C₃₁	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₃₁	—	2	1	no	—
126	C₂×C₄×C₃₁	—	2	1	no	—
127	C₂×C₄×C₃₁	—	2	1	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	C₂×Dic₃₁	—	2	1	no	—
134	C₂×Dic₃₁	—	2	1	no	—
135	C₂×Dic₃₁	—	4	2	no	—
136	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₃₁	C₂×D₄	1	1	yes	characteristic
139	D₁₂₄	—	2	4	no	—
140	D₁₂₄	—	2	1	no	—
141	D₁₂₄	—	2	1	no	—
142	D₁₂₄	C₂²×C₄	1	2	yes	—
143	D₁₂₄	C₂²×C₄	1	2	yes	complemented
144	C₄×D₃₁	—	2	2	no	—
145	C₄×D₃₁	—	2	4	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	—	4	2	no	—
151	C₄×D₃₁	—	4	2	no	—
152	C₄×D₃₁	C₂²×C₄	1	2	yes	—
153	C₄×D₃₁	#41	1	2	yes	—
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	—	4	1	no	—
161	C₂²×C₃₁	—	4	1	no	—
162	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×D₃₁	—	2	1	no	—
164	C₂×D₃₁	—	2	1	no	—
165	C₂×D₃₁	—	2	2	no	—
166	C₂×D₃₁	—	2	2	no	—
167	C₂×D₃₁	—	4	8	no	—
168	C₂×D₃₁	—	4	1	no	—
169	C₂×D₃₁	—	4	1	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	2	no	—
174	C₄×C₃₁	—	2	1	no	—
175	C₄×C₃₁	—	4	1	no	—
176	C₄×C₃₁	—	4	1	no	—
177	C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	complemented
178	C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
179	C₄×C₃₁	C₂×#41	1	1	yes	characteristic
180	Dic₃₁	—	2	1	no	—
181	Dic₃₁	—	2	1	no	—
182	Dic₃₁	—	4	1	no	—
183	Dic₃₁	—	4	1	no	—
184	Dic₃₁	C₄×D₄	1	2	yes	—
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	—	31	1	no	—
190	#440	—	31	1	no	—
191	#440	—	31	1	no	—
192	C₄×SD₁₆	—	31	1	no	—
193	C₄×SD₁₆	D₃₁	1	1	yes	characteristic, complemented
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	C₂×C₄×D₄	1	1	yes	characteristic
202	C₂×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂×C₃₁	#575	1	1	yes	characteristic
204	D₃₁	—	2	2	no	—
205	D₃₁	—	4	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	C₂×D₃₁	1	1	yes	characteristic
213	C₂×D₈	—	31	1	no	—
214	C₂×D₈	—	31	1	no	—
215	C₂×M₁₆	—	31	1	no	—
216	C₂×M₁₆	—	31	1	no	—
217	C₄×Q₈	—	31	1	no	—
218	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
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	—	31	1	no	—
224	C₄×D₄	—	62	1	no	—
225	C₄×D₄	—	62	1	no	—
226	C₄×D₄	—	62	1	no	—
227	C₄×D₄	—	62	1	no	—
228	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
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	C₂×D₃₁	1	1	yes	characteristic, complemented
241	#102	—	31	1	no	—
242	#102	—	31	1	no	—
243	#102	—	31	1	no	—
244	#102	—	31	1	no	—
245	#102	—	31	1	no	—
246	#102	C₂×D₃₁	1	1	yes	characteristic
247	#97	—	31	1	no	—
248	#97	—	31	1	no	—
249	C₄×C₈	—	31	1	no	—
250	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic, complemented
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	C₂²×D₃₁	1	1	yes	characteristic
256	C₂×D₄	—	31	4	no	—
257	C₂×D₄	—	31	1	no	—
258	C₂×D₄	—	31	1	no	—
259	C₂×D₄	—	62	1	no	—
260	C₂×D₄	—	62	2	no	—
261	C₂×D₄	—	62	1	no	—
262	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	31	1	no	—
265	C₂²×C₄	—	31	1	no	—
266	C₂²×C₄	—	31	1	no	—
267	C₂²×C₄	—	62	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	C₄×D₃₁	1	4	yes	complemented
277	D₈	—	31	4	no	—
278	D₈	—	31	4	no	—
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	—	2	1	no	—
286	C₄⋊C₄	—	31	1	no	—
287	C₄⋊C₄	—	31	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	—	62	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	—	2	1	no	—
300	C₄²	—	31	1	no	—
301	C₄²	—	31	1	no	—
302	C₄²	—	31	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	—	31	1	no	—
308	C₂³	—	62	4	no	—
309	C₂³	—	62	1	no	—
310	C₂³	—	62	1	no	—
311	C₂³	—	124	2	no	—
312	C₂³	—	124	2	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₃₁	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	31	2	no	—
317	D₄	—	31	2	no	—
318	D₄	—	62	4	no	—
319	D₄	—	62	4	no	—
320	D₄	—	62	1	no	—
321	D₄	—	62	1	no	—
322	D₄	C₂×C₄×D₃₁	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	31	1	no	—
328	C₂×C₄	—	31	2	no	—
329	C₂×C₄	—	31	2	no	—
330	C₂×C₄	—	31	1	no	—
331	C₂×C₄	—	31	1	no	—
332	C₂×C₄	—	62	4	no	—
333	C₂×C₄	—	62	2	no	—
334	C₂×C₄	—	62	1	no	—
335	C₂×C₄	—	62	1	no	—
336	C₂×C₄	—	124	1	no	—
337	C₂×C₄	—	124	2	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	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	31	2	no	—
354	C₂²	—	62	1	no	—
355	C₂²	—	62	1	no	—
356	C₂²	—	62	2	no	—
357	C₂²	—	62	2	no	—
358	C₂²	—	124	8	no	—
359	C₂²	—	124	1	no	—
360	C₂²	—	124	1	no	—
361	C₂²	—	124	1	no	—
362	C₂²	—	124	1	no	—
363	C₂²	C₂×D₄×D₃₁	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	31	2	no	—
369	C₄	—	62	1	no	—
370	C₄	—	62	1	no	—
371	C₄	—	124	1	no	—
372	C₄	—	124	1	no	—
373	C₄	#11758491	1	2	yes	direct product factor
374	C₄	C₂²×C₄×D₃₁	1	1	yes	characteristic
375	C₄	#41×D₃₁	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	62	2	no	—
378	C₂	—	124	2	no	—
379	C₂	—	124	2	no	—
380	C₂	C₄×D₄×D₃₁	1	1	yes	characteristic
381	C₂	C₂×#11758491	1	1	yes	characteristic
382	C₂	#14521846	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₃₁
commutator	C₄×C₃₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₁
Fitting	C₄×SD₁₆×C₃₁	C₂
socle	C₂²×C₃₁	C₂²×D₄
prime radical	C₂×#11758491	C₂
cosocle	C₂×C₄×C₃₁	C₂⁴
hypercenter	C₄×SD₁₆	D₃₁
hypocenter	C₃₁	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#92499	C₂	semidirect
3. C₄×D₄×D₃₁	C₂	semidirect
4. #14521160	C₂	semidirect
5. #14521158	C₂	semidirect
6. #14521152	C₂	semidirect
7. #14521150	C₂	semidirect
8. C₄×#92481	C₂	semidirect
9. C₄×D₂₄₈	C₂	semidirect
10. C₄×#92479	C₂	semidirect
11. #14521088	C₂	semidirect
12. #14521052	C₂	semidirect
13. #14521049	C₂	semidirect
14. C₄×#92469	C₂	semidirect
15. C₄×SD₁₆×C₃₁	C₂	semidirect
20. C₄×Q₈×C₃₁	C₂²	semidirect
22. Q₈×Dic₃₁	C₂²	semidirect
27. #11758491	C₄	direct (N × H)
33. #11758470	C₂²	semidirect
41. C₄×D₁₂₄	C₂²	semidirect
44. C₃₁×#106	C₂²	semidirect
45. C₃₁×#103	C₂²	semidirect
47. C₄×C₈×C₃₁	C₂²	semidirect
48. #11758423	C₂²	semidirect
51. #11758409	C₂²	semidirect
52. #11758406	C₂²	semidirect
53. #11758403	C₂²	semidirect
54. #11758403	C₂²	semidirect
56. #11758397	C₂²	semidirect
57. #11758396	C₂²	semidirect
58. #11758395	C₂²	semidirect
59. C₄×C₃₁⋊C₈	C₂²	semidirect
67. #92499	C₂×C₄	semidirect
69. D₄×D₃₁	C₂×C₄	semidirect
83. SD₁₆×C₃₁	C₂×C₄	semidirect
93. #92481	C₂×C₄	semidirect
94. #92479	C₂×C₄	semidirect
111. D₂₄₈	C₂×C₄	semidirect
113. #92469	C₂×C₄	semidirect
122. Q₈×C₃₁	C₂²×C₄	semidirect
143. D₁₂₄	C₂²×C₄	semidirect
155. C₈×C₃₁	C₂²×C₄	semidirect
157. C₃₁⋊C₈	C₂²×C₄	semidirect
177. C₄×C₃₁	AGL(1,ℤ/8)	semidirect
193. C₄×SD₁₆	D₃₁	semidirect
218. C₄×Q₈	C₂×D₃₁	semidirect
238. #106	C₂×D₃₁	semidirect
240. #103	C₂×D₃₁	semidirect
250. C₄×C₈	C₂×D₃₁	semidirect
251. C₃₁	C₄×AGL(1,ℤ/8)	semidirect
276. SD₁₆	C₄×D₃₁	semidirect
314. Q₈	C₂×C₄×D₃₁	semidirect
349. C₈	C₂×C₄×D₃₁	semidirect
373. C₄	#11758491	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11758491	2
C₄×#92499	2
C₄×D₄×D₃₁	2
#14521160	2
#14521158	2
#14521152	2
#14521150	2
C₄×#92481	2
C₄×D₂₄₈	2
C₄×#92479	2
#14521088	2
#14521052	2
#14521049	2
C₄×#92469	2
C₄×SD₁₆×C₃₁	2
C₄×AGL(1,ℤ/8)	31

Subgroups — C4×#11758491 #16854520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11758491 #16854520