Subgroups — C₄×#11924560 #18003399

Order 4736.

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×#11924560	C₂	1	1	yes	maximal, characteristic
2	C₄×#10596964	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#14557645	C₂	1	1	yes	maximal, characteristic, complemented
5	#14557642	C₂	1	1	yes	maximal, characteristic, complemented
6	#14557632	C₂	1	1	yes	maximal, characteristic, complemented
7	#14557630	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#10596930	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#10596940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#10596939	C₂	1	1	yes	maximal, characteristic, complemented
11	#14557574	C₂	1	1	yes	maximal, characteristic, complemented
12	#14557536	C₂	1	1	yes	maximal, characteristic, complemented
13	#14557531	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#10596929	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₈×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10596964	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₃₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₃₇	—	2	1	no	—
19	#11924560	C₄	1	8	yes	direct product factor
20	C₂×#10596930	C₂²	1	1	yes	characteristic
21	C₂×#10596940	C₂²	1	1	yes	characteristic
22	C₂×#10596939	C₂²	1	1	yes	characteristic
23	C₂×#10596929	C₂²	1	1	yes	characteristic
24	C₂×#10596929	C₂²	1	1	yes	characteristic
25	C₄×Dic₇₄	C₂²	1	1	yes	characteristic, complemented
26	#11924501	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₁₄₈	C₂²	1	1	yes	characteristic
28	D₄×Dic₃₇	C₂²	1	1	yes	characteristic
29	D₄×Dic₃₇	C₂²	1	1	yes	characteristic, complemented
30	#11924498	C₂²	1	1	yes	characteristic
31	C₄×C₂²⋊D₃₇	—	2	1	no	—
32	C₄×C₂²⋊D₃₇	—	2	1	no	—
33	#11924496	—	2	1	no	—
34	#11924496	—	2	1	no	—
35	#11924494	C₂²	1	1	yes	characteristic
36	#11924492	—	2	1	no	—
37	C₄⋊C₄×D₃₇	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₃₇	—	2	1	no	—
39	C₂×C₄×Dic₃₇	—	2	1	no	—
40	C₄²×D₃₇	C₂²	1	1	yes	characteristic
41	#11924469	C₂²	1	1	yes	characteristic, complemented
42	#11924468	C₂²	1	1	yes	characteristic, complemented
43	#11924467	C₂²	1	1	yes	characteristic, complemented
44	#11924461	C₂²	1	1	yes	characteristic, complemented
45	#11924459	C₂²	1	1	yes	characteristic, complemented
46	#11924458	C₂²	1	1	yes	characteristic
47	#11924457	C₂²	1	1	yes	characteristic
48	#11924457	C₂²	1	1	yes	characteristic, complemented
49	#11924456	C₂²	1	1	yes	characteristic
50	#11924446	C₂²	1	1	yes	characteristic, complemented
51	#11924446	C₂²	1	1	yes	characteristic, complemented
52	C₄×#64436	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₃₇	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₃₇	C₂²	1	1	yes	characteristic, complemented
56	#107×C₃₇	C₂²	1	1	yes	characteristic, complemented
57	#102×C₃₇	C₂²	1	1	yes	characteristic
58	#102×C₃₇	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₈×C₃₇	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₃₇	—	2	1	no	—
61	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₃₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₃₇	—	2	1	no	—
64	C₂²×C₄×C₃₇	—	2	1	no	—
65	C₂×C₂²⋊D₃₇	—	2	1	no	—
66	C₂×C₂²⋊D₃₇	—	2	1	no	—
67	C₂²×Dic₃₇	—	2	1	no	—
68	C₂²×Dic₃₇	—	2	1	no	—
69	C₂²×Dic₃₇	—	2	1	no	—
70	#10596964	—	2	2	no	—
71	#10596964	C₂×C₄	1	4	yes	complemented
72	D₄×D₃₇	—	2	2	no	—
73	D₄×D₃₇	C₂×C₄	1	4	yes	complemented
74	C₂×D₁₄₈	C₂³	1	1	yes	characteristic
75	C₂×C₄×D₃₇	—	2	1	no	—
76	C₂×C₄×D₃₇	—	2	1	no	—
77	C₂×C₄×D₃₇	—	2	1	no	—
78	C₂×C₄×D₃₇	—	4	4	no	—
79	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
80	C₂×C₄×D₃₇	D₄	1	1	yes	characteristic
81	C₂×C₄×D₃₇	C₂³	1	1	yes	characteristic
82	C₂×Dic₇₄	C₂³	1	1	yes	characteristic
83	D₈×C₃₇	C₂×C₄	1	4	yes	complemented
84	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₄×C₃₇	C₂³	1	1	yes	characteristic
88	C₂²⋊C₄×C₃₇	—	2	1	no	—
89	C₂²⋊C₄×C₃₇	—	2	1	no	—
90	C₄²×C₃₇	C₂³	1	1	yes	characteristic
91	C₂²⋊Dic₃₇	—	2	1	no	—
92	C₂²⋊Dic₃₇	—	2	1	no	—
93	#10596940	C₂×C₄	1	4	yes	complemented
94	#10596939	C₂×C₄	1	4	yes	complemented
95	#10596938	—	2	1	no	—
96	#10596938	—	2	1	no	—
97	#10596938	—	2	1	no	—
98	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
99	C₄⋊Dic₃₇	C₂³	1	1	yes	characteristic
100	#10596936	—	2	1	no	—
101	#10596936	—	2	1	no	—
102	#10596936	—	2	1	no	—
103	C₄×Dic₃₇	—	2	1	no	—
104	C₄×Dic₃₇	—	2	1	no	—
105	C₄×Dic₃₇	—	2	1	no	—
106	C₄×Dic₃₇	D₄	1	1	yes	characteristic
107	C₄×Dic₃₇	D₄	1	1	yes	characteristic
108	C₄×Dic₃₇	C₂³	1	1	yes	characteristic
109	C₂×#64436	C₂³	1	1	yes	characteristic
110	C₂×#64436	C₂³	1	1	yes	characteristic
111	#10596930	C₂×C₄	1	4	yes	complemented
112	#10596929	—	2	2	no	—
113	#10596929	C₂×C₄	1	4	yes	complemented
114	C₂³×C₃₇	—	2	1	no	—
115	C₂³×C₃₇	—	2	1	no	—
116	C₂²×D₃₇	—	2	1	no	—
117	C₂²×D₃₇	—	2	4	no	—
118	C₂²×D₃₇	—	4	2	no	—
119	C₂²×D₃₇	—	4	2	no	—
120	C₂²×D₃₇	C₂×D₄	1	1	yes	characteristic
121	D₄×C₃₇	—	2	1	no	—
122	D₄×C₃₇	—	2	1	no	—
123	D₄×C₃₇	C₂²×C₄	1	2	yes	—
124	D₄×C₃₇	C₂²×C₄	1	2	yes	complemented
125	C₂×C₄×C₃₇	—	2	1	no	—
126	C₂×C₄×C₃₇	—	2	1	no	—
127	C₂×C₄×C₃₇	—	4	2	no	—
128	C₂×C₄×C₃₇	—	4	2	no	—
129	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₃₇	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₃₇	—	2	4	no	—
133	C₂²⋊D₃₇	—	2	4	no	—
134	C₂×Dic₃₇	—	2	1	no	—
135	C₂×Dic₃₇	—	2	4	no	—
136	C₂×Dic₃₇	—	2	1	no	—
137	C₂×Dic₃₇	—	2	1	no	—
138	C₂×Dic₃₇	—	4	2	no	—
139	C₂×Dic₃₇	—	4	2	no	—
140	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
142	C₂×Dic₃₇	C₂×D₄	1	1	yes	characteristic
143	D₁₄₈	—	2	1	no	—
144	D₁₄₈	C₂²×C₄	1	2	yes	—
145	C₄×D₃₇	—	2	2	no	—
146	C₄×D₃₇	—	4	1	no	—
147	C₄×D₃₇	—	4	2	no	—
148	C₄×D₃₇	—	4	2	no	—
149	C₄×D₃₇	—	4	2	no	—
150	C₄×D₃₇	C₂²×C₄	1	2	yes	—
151	C₄×D₃₇	#41	1	2	yes	—
152	Dic₇₄	—	2	1	no	—
153	Dic₇₄	C₂²×C₄	1	2	yes	complemented
154	C₈×C₃₇	—	2	1	no	—
155	C₈×C₃₇	C₂²×C₄	1	2	yes	complemented
156	#64436	—	2	1	no	—
157	#64436	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₃₇	—	2	2	no	—
159	C₂²×C₃₇	—	2	2	no	—
160	C₂²×C₃₇	—	4	1	no	—
161	C₂²×C₃₇	—	4	1	no	—
162	C₂²×C₃₇	—	4	1	no	—
163	C₂²×C₃₇	—	4	1	no	—
164	C₂²×C₃₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₃₇	—	2	1	no	—
166	C₂×D₃₇	—	2	1	no	—
167	C₂×D₃₇	—	2	2	no	—
168	C₂×D₃₇	—	4	8	no	—
169	C₂×D₃₇	—	4	1	no	—
170	C₂×D₃₇	—	4	1	no	—
171	C₂×D₃₇	C₄×D₄	1	2	yes	—
172	C₄×C₃₇	—	2	1	no	—
173	C₄×C₃₇	—	4	1	no	—
174	C₄×C₃₇	—	4	1	no	—
175	C₄×C₃₇	AGL(1,ℤ/8)	1	2	yes	complemented
176	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
177	C₄×C₃₇	C₂×#41	1	1	yes	characteristic
178	Dic₃₇	—	2	2	no	—
179	Dic₃₇	—	2	1	no	—
180	Dic₃₇	—	2	1	no	—
181	Dic₃₇	—	4	1	no	—
182	Dic₃₇	—	4	1	no	—
183	Dic₃₇	C₄×D₄	1	2	yes	—
184	C₄×AGL(1,ℤ/8)	—	37	1	no	maximal, Sylow
185	C₂×C₃₇	—	4	2	no	—
186	C₂×C₃₇	—	4	2	no	—
187	C₂×C₃₇	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂×C₃₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×C₃₇	#575	1	1	yes	characteristic
190	D₃₇	—	2	2	no	—
191	D₃₇	—	4	2	no	—
192	C₂×AGL(1,ℤ/8)	—	37	1	no	—
193	C₄×#41	—	37	1	no	—
194	C₂×C₄×D₄	—	37	1	no	—
195	#442	—	37	1	no	—
196	#442	—	37	1	no	—
197	#440	—	37	1	no	—
198	#440	—	37	1	no	—
199	C₄×SD₁₆	—	37	1	no	—
200	C₄×SD₁₆	—	37	1	no	—
201	C₄×D₈	—	37	1	no	—
202	C₄×D₈	D₃₇	1	1	yes	characteristic, complemented
203	#428	—	37	1	no	—
204	#418	—	37	1	no	—
205	#417	—	37	1	no	—
206	C₄×M₁₆	—	37	1	no	—
207	C₃₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
208	C₂×#41	—	37	1	no	—
209	C₂²×D₄	—	37	1	no	—
210	C₂³×C₄	—	74	1	no	—
211	AGL(1,ℤ/8)	—	37	8	no	—
212	C₂×SD₁₆	—	37	1	no	—
213	C₂×SD₁₆	—	37	1	no	—
214	C₂×D₈	—	37	1	no	—
215	C₂×D₈	C₂×D₃₇	1	1	yes	characteristic
216	C₂×M₁₆	—	37	1	no	—
217	C₂×M₁₆	—	37	1	no	—
218	C₄×Q₈	—	37	1	no	—
219	C₄×Q₈	—	37	1	no	—
220	C₄×D₄	—	37	1	no	—
221	C₄×D₄	—	37	1	no	—
222	C₄×D₄	—	37	1	no	—
223	C₄×D₄	—	37	1	no	—
224	C₄×D₄	—	74	1	no	—
225	C₄×D₄	—	74	1	no	—
226	C₄×D₄	—	74	1	no	—
227	C₄×D₄	—	74	1	no	—
228	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic
229	C₄×D₄	C₂×D₃₇	1	1	yes	characteristic, complemented
230	#117	—	37	1	no	—
231	#117	—	74	1	no	—
232	C₂×C₄⋊C₄	—	37	1	no	—
233	C₂×C₂²⋊C₄	—	74	1	no	—
234	C₂×C₄²	—	37	1	no	—
235	C₂×C₄²	—	74	1	no	—
236	#107	—	37	1	no	—
237	#107	C₂×D₃₇	1	1	yes	characteristic, complemented
238	#106	—	37	1	no	—
239	#106	—	37	1	no	—
240	#103	—	37	1	no	—
241	#103	—	37	1	no	—
242	#102	—	37	1	no	—
243	#102	—	37	1	no	—
244	#102	—	37	1	no	—
245	#102	—	37	1	no	—
246	#102	C₂×D₃₇	1	1	yes	characteristic
247	#102	C₂×D₃₇	1	1	yes	characteristic, complemented
248	#97	—	37	1	no	—
249	#97	—	37	1	no	—
250	C₄×C₈	—	37	1	no	—
251	C₄×C₈	C₂×D₃₇	1	1	yes	characteristic, complemented
252	C₂⁴	—	74	1	no	—
253	#41	—	37	4	no	—
254	#41	—	74	2	no	—
255	C₂×Q₈	—	37	1	no	—
256	C₂×D₄	—	37	4	no	—
257	C₂×D₄	—	37	1	no	—
258	C₂×D₄	—	74	2	no	—
259	C₂×D₄	—	74	1	no	—
260	C₂×D₄	—	74	1	no	—
261	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
262	C₂×D₄	C₂²×D₃₇	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	37	1	no	—
266	C₂²×C₄	—	37	1	no	—
267	C₂²×C₄	—	37	1	no	—
268	C₂²×C₄	—	74	1	no	—
269	C₂²×C₄	—	74	1	no	—
270	C₂²×C₄	—	74	1	no	—
271	C₂²×C₄	—	74	1	no	—
272	C₂²×C₄	—	74	1	no	—
273	C₂²×C₄	—	74	1	no	—
274	C₂²×C₄	—	148	4	no	—
275	SD₁₆	—	37	4	no	—
276	SD₁₆	—	37	4	no	—
277	D₈	—	37	4	no	—
278	D₈	C₄×D₃₇	1	4	yes	complemented
279	M₁₆	—	37	4	no	—
280	M₁₆	—	74	2	no	—
281	C₂×C₈	—	37	1	no	—
282	C₂×C₈	—	37	1	no	—
283	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
285	C₄⋊C₄	—	37	1	no	—
286	C₄⋊C₄	—	37	1	no	—
287	C₄⋊C₄	—	74	1	no	—
288	C₄⋊C₄	—	74	1	no	—
289	C₄⋊C₄	—	74	1	no	—
290	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₃₇	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	74	1	no	—
295	C₂²⋊C₄	—	74	1	no	—
296	C₂²⋊C₄	—	74	1	no	—
297	C₂²⋊C₄	—	74	1	no	—
298	C₂²⋊C₄	—	74	1	no	—
299	C₄²	—	37	1	no	—
300	C₄²	—	37	1	no	—
301	C₄²	—	37	1	no	—
302	C₄²	—	74	1	no	—
303	C₄²	—	74	1	no	—
304	C₄²	—	74	1	no	—
305	C₄²	C₂²×D₃₇	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	37	1	no	—
309	C₂³	—	74	4	no	—
310	C₂³	—	74	1	no	—
311	C₂³	—	148	2	no	—
312	C₂³	—	148	2	no	—
313	Q₈	—	37	2	no	—
314	Q₈	—	74	1	no	—
315	D₄	—	2	1	no	—
316	D₄	—	2	1	no	—
317	D₄	—	37	2	no	—
318	D₄	—	74	4	no	—
319	D₄	—	74	4	no	—
320	D₄	—	74	1	no	—
321	D₄	C₂×C₄×D₃₇	1	2	yes	—
322	D₄	C₂×C₄×D₃₇	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	—	37	1	no	—
328	C₂×C₄	—	37	2	no	—
329	C₂×C₄	—	37	2	no	—
330	C₂×C₄	—	37	1	no	—
331	C₂×C₄	—	37	1	no	—
332	C₂×C₄	—	74	4	no	—
333	C₂×C₄	—	74	1	no	—
334	C₂×C₄	—	74	2	no	—
335	C₂×C₄	—	74	1	no	—
336	C₂×C₄	—	74	1	no	—
337	C₂×C₄	—	148	1	no	—
338	C₂×C₄	—	148	2	no	—
339	C₂×C₄	—	148	2	no	—
340	C₂×C₄	—	148	2	no	—
341	C₂×C₄	—	148	2	no	—
342	C₂×C₄	—	148	2	no	—
343	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
344	C₂×C₄	D₄×D₃₇	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₃₇	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	37	2	no	—
348	C₈	—	74	1	no	—
349	C₈	C₂×C₄×D₃₇	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	—	37	2	no	—
357	C₂²	—	74	1	no	—
358	C₂²	—	74	1	no	—
359	C₂²	—	74	2	no	—
360	C₂²	—	148	8	no	—
361	C₂²	—	148	1	no	—
362	C₂²	—	148	1	no	—
363	C₂²	C₂×D₄×D₃₇	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	37	2	no	—
368	C₄	—	74	2	no	—
369	C₄	—	74	1	no	—
370	C₄	—	74	1	no	—
371	C₄	—	148	1	no	—
372	C₄	—	148	1	no	—
373	C₄	#11924560	1	2	yes	direct product factor
374	C₄	C₂²×C₄×D₃₇	1	1	yes	characteristic
375	C₄	#41×D₃₇	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	4	2	no	—
378	C₂	—	74	2	no	—
379	C₂	—	148	2	no	—
380	C₂	C₄×D₄×D₃₇	1	1	yes	characteristic
381	C₂	C₂×#11924560	1	1	yes	characteristic
382	C₂	#14558330	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₃₇
commutator	C₄×C₃₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₃₇
Fitting	C₄×D₈×C₃₇	C₂
socle	C₂²×C₃₇	C₂²×D₄
prime radical	C₂×#11924560	C₂
cosocle	C₂×C₄×C₃₇	C₂⁴
hypercenter	C₄×D₈	D₃₇
hypocenter	C₃₇	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
2. C₄×#10596964	C₂	semidirect
3. C₄×D₄×D₃₇	C₂	semidirect
4. #14557645	C₂	semidirect
5. #14557642	C₂	semidirect
6. #14557632	C₂	semidirect
7. #14557630	C₂	semidirect
8. C₄×#10596930	C₂	semidirect
9. C₄×#10596940	C₂	semidirect
10. C₄×#10596939	C₂	semidirect
11. #14557574	C₂	semidirect
12. #14557536	C₂	semidirect
13. #14557531	C₂	semidirect
14. C₄×#10596929	C₂	semidirect
15. C₄×D₈×C₃₇	C₂	semidirect
19. #11924560	C₄	direct (N × H)
25. C₄×Dic₇₄	C₂²	semidirect
26. #11924501	C₂²	semidirect
29. D₄×Dic₃₇	C₂²	semidirect
41. #11924469	C₂²	semidirect
42. #11924468	C₂²	semidirect
43. #11924467	C₂²	semidirect
44. #11924461	C₂²	semidirect
45. #11924459	C₂²	semidirect
48. #11924457	C₂²	semidirect
50. #11924446	C₂²	semidirect
51. #11924446	C₂²	semidirect
52. C₄×#64436	C₂²	semidirect
55. C₄×D₄×C₃₇	C₂²	semidirect
56. #107×C₃₇	C₂²	semidirect
58. #102×C₃₇	C₂²	semidirect
59. C₄×C₈×C₃₇	C₂²	semidirect
71. #10596964	C₂×C₄	semidirect
73. D₄×D₃₇	C₂×C₄	semidirect
83. D₈×C₃₇	C₂×C₄	semidirect
93. #10596940	C₂×C₄	semidirect
94. #10596939	C₂×C₄	semidirect
111. #10596930	C₂×C₄	semidirect
113. #10596929	C₂×C₄	semidirect
124. D₄×C₃₇	C₂²×C₄	semidirect
153. Dic₇₄	C₂²×C₄	semidirect
155. C₈×C₃₇	C₂²×C₄	semidirect
157. #64436	C₂²×C₄	semidirect
175. C₄×C₃₇	AGL(1,ℤ/8)	semidirect
202. C₄×D₈	D₃₇	semidirect
207. C₃₇	C₄×AGL(1,ℤ/8)	semidirect
229. C₄×D₄	C₂×D₃₇	semidirect
237. #107	C₂×D₃₇	semidirect
247. #102	C₂×D₃₇	semidirect
251. C₄×C₈	C₂×D₃₇	semidirect
278. D₈	C₄×D₃₇	semidirect
322. D₄	C₂×C₄×D₃₇	semidirect
349. C₈	C₂×C₄×D₃₇	semidirect
373. C₄	#11924560	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×#11924560	2
C₄×#10596964	2
C₄×D₄×D₃₇	2
#14557645	2
#14557642	2
#14557632	2
#14557630	2
C₄×#10596930	2
C₄×#10596940	2
C₄×#10596939	2
#14557574	2
#14557536	2
#14557531	2
C₄×#10596929	2
C₄×D₈×C₃₇	2
C₄×AGL(1,ℤ/8)	37

Subgroups — C4×#11924560 #18003399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11924560 #18003399