Subgroups — C₂×D₄×C₃⋊#157 #13181516

Order 1728.

1432 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	C₂³×C₃⋊#157	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#88994	C₂	1	2	yes	maximal, complemented
4	D₄×C₃⋊#157	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊(C₃⋊#157)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₃⋊#157	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×#157	—	3	1	no	maximal
8	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
9	C₂²×C₃⋊#157	—	2	8	no	—
10	C₂²×C₃⋊#157	C₂²	1	2	yes	—
11	C₂²×C₃⋊#157	C₂²	1	1	yes	characteristic
12	C₂²×C₃⋊#157	C₂²	1	1	yes	characteristic
13	C₂²×C₃⋊#157	C₂²	1	8	yes	complemented
14	C₂×C₃³×D₄	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×#638	C₄	1	2	yes	complemented
16	C₃×D₄×C₃⋊D₃	C₄	1	4	yes	complemented
17	C₃×D₄×C₃⋊D₃	C₂²	1	4	yes	—
18	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	1	yes	characteristic, complemented
19	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
20	#88994	C₂²	1	8	yes	complemented
21	C₄⋊(C₃⋊#157)	C₂²	1	4	yes	complemented
22	C₄×C₃⋊#157	C₂²	1	4	yes	complemented
23	C₂³×#157	—	3	2	no	—
24	C₂×D₄×C₃⋊D₃	D₃	1	1	yes	characteristic
25	C₂×C₃×D₃×D₄	—	6	2	no	—
26	C₂×C₂²⋊#157	—	3	2	no	—
27	D₄×#157	—	3	8	no	—
28	C₂×C₄⋊#157	—	3	1	no	—
29	C₂×C₄×#157	—	3	1	no	—
30	C₂³×C₃³	C₂×C₄	1	2	yes	complemented
31	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
32	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
33	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	4	yes	complemented
34	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
35	C₂²×C₃×C₃⋊D₃	C₂³	1	4	yes	—
36	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
37	C₂×C₃⋊#157	—	2	4	no	—
38	C₂×C₃⋊#157	—	2	2	no	—
39	C₂×C₃⋊#157	—	2	16	no	—
40	C₂×C₃⋊#157	D₄	1	4	yes	direct product factor
41	C₂×C₃⋊#157	C₂³	1	4	yes	—
42	C₂×C₃⋊#157	C₂³	1	2	yes	—
43	C₂×C₃⋊#157	C₂³	1	2	yes	—
44	C₃³×D₄	C₂×C₄	1	4	yes	complemented
45	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic, complemented
46	C₃×#638	C₂×C₄	1	8	yes	complemented
47	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic, complemented
48	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
49	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
50	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
51	C₂×D₄×Dic₃	—	9	1	no	maximal
52	C₂³×C₃⋊D₃	C₂×D₃	1	2	yes	—
53	C₂³×C₃×D₃	—	6	4	no	—
54	C₂²×#157	—	3	1	no	—
55	C₂²×#157	—	3	1	no	—
56	C₂²×#157	—	3	2	no	—
57	C₂²×#157	—	3	8	no	—
58	C₂²×#157	—	6	8	no	—
59	C₂×C₃²×D₄	—	2	2	no	—
60	C₂×C₃²×D₄	—	4	2	no	—
61	C₂×C₃²×D₄	Dic₃	1	1	yes	characteristic, complemented
62	C₂×#638	Dic₃	1	2	yes	complemented
63	D₄×C₃⋊D₃	Dic₃	1	4	yes	complemented
64	D₄×C₃⋊D₃	C₂×D₃	1	4	yes	—
65	C₂×C₄⋊(C₃⋊D₃)	Dic₃	1	1	yes	characteristic, complemented
66	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
67	C₂×C₃×#67	—	6	4	no	—
68	C₃×D₃×D₄	—	6	8	no	—
69	C₃×D₃×D₄	—	6	8	no	—
70	C₂×C₃×D₁₂	—	6	2	no	—
71	C₂×C₃×C₄×D₃	—	6	2	no	—
72	C₂²⋊#157	—	3	8	no	—
73	C₄⋊#157	—	3	4	no	—
74	C₄×#157	—	3	4	no	—
75	C₂²×C₃³	—	2	4	no	—
76	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₃³	C₂²×C₄	1	4	yes	complemented
78	C₂×C₃×C₃⋊D₃	—	2	4	no	—
79	C₂×C₃×C₃⋊D₃	—	2	8	no	—
80	C₂×C₃×C₃⋊D₃	—	2	4	no	—
81	C₂×C₃×C₃⋊D₃	—	2	4	no	—
82	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	4	yes	complemented
84	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
85	C₂×C₃×C₃⋊D₃	#41	1	2	yes	—
86	C₂×C₃×C₃⋊D₃	C₂⁴	1	1	yes	characteristic
87	C₃⋊#157	—	2	4	no	—
88	C₃⋊#157	—	2	2	no	—
89	C₃⋊#157	C₂×D₄	1	4	yes	direct product factor
90	C₃³×C₄	C₂²×C₄	1	2	yes	complemented
91	C₃×C₃⋊Dic₃	C₂²×C₄	1	2	yes	complemented
92	C₂²×C₃×D₄	—	9	1	no	—
93	C₂³×Dic₃	—	9	2	no	—
94	C₂×D₃×D₄	—	6	2	no	—
95	C₂×#217	—	9	2	no	—
96	D₄×Dic₃	—	9	8	no	—
97	C₂×C₄⋊Dic₃	—	9	1	no	—
98	C₂×C₄×Dic₃	—	9	1	no	—
99	C₂³×C₃²	—	2	4	no	—
100	C₂³×C₃²	—	4	4	no	—
101	C₂³×C₃²	C₂×Dic₃	1	2	yes	complemented
102	C₂²×C₃⋊D₃	—	2	4	no	—
103	C₂²×C₃⋊D₃	—	2	4	no	—
104	C₂²×C₃⋊D₃	C₂×Dic₃	1	4	yes	complemented
105	C₂²×C₃⋊D₃	C₂×Dic₃	1	2	yes	complemented
106	C₂²×C₃⋊D₃	C₂²×D₃	1	4	yes	—
107	C₂²×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
108	C₂²×C₃×D₃	—	6	2	no	—
109	C₂²×C₃×D₃	—	6	4	no	—
110	C₂²×C₃×D₃	—	6	8	no	—
111	C₂²×C₃×D₃	—	6	8	no	—
112	C₂²×C₃×D₃	—	12	8	no	—
113	C₂²×C₃×D₃	—	12	8	no	—
114	C₂×#157	—	3	4	no	—
115	C₂×#157	—	3	2	no	—
116	C₂×#157	—	3	4	no	—
117	C₂×#157	—	3	2	no	—
118	C₂×#157	—	6	16	no	—
119	C₂×#157	—	6	4	no	—
120	C₂×#157	—	6	2	no	—
121	C₃²×D₄	—	2	8	no	—
122	C₃²×D₄	—	4	8	no	—
123	C₃²×D₄	C₂×Dic₃	1	4	yes	complemented
124	C₂×C₃²×C₄	—	2	2	no	—
125	C₂×C₃²×C₄	—	4	2	no	—
126	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic, complemented
127	#638	C₂×Dic₃	1	8	yes	complemented
128	C₂×C₃⋊Dic₃	C₂×Dic₃	1	1	yes	characteristic, complemented
129	C₄⋊(C₃⋊D₃)	C₂×Dic₃	1	4	yes	complemented
130	C₄×C₃⋊D₃	C₂×Dic₃	1	2	yes	complemented
131	C₄×C₃⋊D₃	C₂²×D₃	1	2	yes	—
132	C₃×#67	—	6	16	no	—
133	C₂×C₃×Dic₃	—	6	2	no	—
134	C₃×D₁₂	—	6	8	no	—
135	C₃×C₄×D₃	—	6	4	no	—
136	C₃×C₄×D₃	—	6	4	no	—
137	C₂×C₄×D₄	—	27	1	no	Sylow
138	C₂×C₃³	—	2	4	no	—
139	C₂×C₃³	C₄×D₄	1	2	yes	complemented
140	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
141	C₃×C₃⋊D₃	—	2	4	no	—
142	C₃×C₃⋊D₃	C₄×D₄	1	2	yes	complemented
143	C₃×C₃⋊D₃	C₂²×D₄	1	1	yes	characteristic
144	C₃×C₃⋊D₃	C₂×#41	1	1	yes	characteristic
145	C₂⁴×C₃	—	9	2	no	—
146	C₂³×D₃	—	6	4	no	—
147	C₂×C₃×D₄	—	2	2	no	—
148	C₂×C₃×D₄	—	4	2	no	—
149	C₂×C₃×D₄	—	9	2	no	—
150	C₂×C₃×D₄	—	9	4	no	—
151	C₂×C₃×D₄	—	9	4	no	—
152	C₂×C₃×D₄	—	9	1	no	—
153	C₂×C₃×D₄	#157	1	1	yes	characteristic, complemented
154	C₂²×C₃×C₄	—	9	1	no	—
155	C₂×#67	—	6	4	no	—
156	C₂²×Dic₃	—	9	1	no	—
157	C₂²×Dic₃	—	9	1	no	—
158	C₂²×Dic₃	—	9	2	no	—
159	C₂²×Dic₃	—	9	8	no	—
160	C₂²×Dic₃	—	18	8	no	—
161	D₃×D₄	—	6	8	no	—
162	D₃×D₄	—	6	8	no	—
163	C₂×D₁₂	—	6	2	no	—
164	C₂×C₄×D₃	—	6	2	no	—
165	#217	—	9	8	no	—
166	C₄⋊Dic₃	—	9	4	no	—
167	C₄×Dic₃	—	9	4	no	—
168	C₂²×C₃²	—	2	2	no	—
169	C₂²×C₃²	—	2	8	no	—
170	C₂²×C₃²	—	2	4	no	—
171	C₂²×C₃²	—	4	2	no	—
172	C₂²×C₃²	—	4	8	no	—
173	C₂²×C₃²	—	4	8	no	—
174	C₂²×C₃²	—	8	8	no	—
175	C₂²×C₃²	C₂²×Dic₃	1	1	yes	characteristic
176	C₂²×C₃²	C₂²×Dic₃	1	4	yes	complemented
177	C₂×C₃⋊D₃	—	2	4	no	—
178	C₂×C₃⋊D₃	—	2	8	no	—
179	C₂×C₃⋊D₃	—	2	4	no	—
180	C₂×C₃⋊D₃	—	2	4	no	—
181	C₂×C₃⋊D₃	D₃×D₄	1	2	yes	—
182	C₂×C₃⋊D₃	#237	1	2	yes	—
183	C₂×C₃⋊D₃	C₂²×Dic₃	1	1	yes	characteristic
184	C₂×C₃⋊D₃	C₂²×Dic₃	1	4	yes	complemented
185	C₂×C₃⋊D₃	C₂³×D₃	1	1	yes	characteristic
186	C₂×C₃×D₃	—	6	2	no	—
187	C₂×C₃×D₃	—	6	4	no	—
188	C₂×C₃×D₃	—	6	4	no	—
189	C₂×C₃×D₃	—	6	2	no	—
190	C₂×C₃×D₃	—	6	8	no	—
191	C₂×C₃×D₃	—	12	8	no	—
192	C₂×C₃×D₃	—	12	16	no	—
193	C₂×C₃×D₃	—	12	8	no	—
194	C₂×C₃×D₃	—	12	8	no	—
195	#157	—	3	4	no	—
196	#157	—	6	4	no	—
197	#157	—	6	2	no	—
198	C₃²×C₄	—	2	4	no	—
199	C₃²×C₄	—	4	4	no	—
200	C₃²×C₄	C₂²×Dic₃	1	2	yes	complemented
201	C₃⋊Dic₃	C₂²×Dic₃	1	2	yes	complemented
202	C₃×Dic₃	—	6	4	no	—
203	C₂²×D₄	—	9	1	no	—
204	C₂³×C₄	—	27	2	no	—
205	C₄×D₄	—	27	8	no	—
206	C₂×C₄⋊C₄	—	27	1	no	—
207	C₂×C₂²⋊C₄	—	27	2	no	—
208	C₂×C₄²	—	27	1	no	—
209	C₃³	C₂×C₄×D₄	1	1	yes	characteristic, complemented, Sylow
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	4	4	no	—
212	C₂³×C₃	—	9	1	no	—
213	C₂³×C₃	—	9	2	no	—
214	C₂³×C₃	—	9	4	no	—
215	C₂³×C₃	—	9	4	no	—
216	C₂³×C₃	—	18	4	no	—
217	C₂³×C₃	—	18	4	no	—
218	C₂³×C₃	C₂×#157	1	2	yes	complemented
219	C₂²×D₃	—	6	2	no	—
220	C₂²×D₃	—	6	4	no	—
221	C₂²×D₃	—	6	8	no	—
222	C₂²×D₃	—	6	8	no	—
223	C₂²×D₃	—	12	8	no	—
224	C₂²×D₃	—	12	8	no	—
225	C₃×D₄	—	2	8	no	—
226	C₃×D₄	—	4	8	no	—
227	C₃×D₄	—	9	8	no	—
228	C₃×D₄	—	9	4	no	—
229	C₃×D₄	C₂×#157	1	4	yes	complemented
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	9	1	no	—
233	C₂×C₃×C₄	—	9	2	no	—
234	C₂×C₃×C₄	—	9	2	no	—
235	C₂×C₃×C₄	C₂×#157	1	1	yes	characteristic, complemented
236	#67	—	6	16	no	—
237	C₂×Dic₃	—	6	2	no	—
238	C₂×Dic₃	—	9	4	no	—
239	C₂×Dic₃	—	9	2	no	—
240	C₂×Dic₃	—	9	2	no	—
241	C₂×Dic₃	—	9	4	no	—
242	C₂×Dic₃	—	18	16	no	—
243	C₂×Dic₃	—	18	2	no	—
244	C₂×Dic₃	—	18	4	no	—
245	D₁₂	—	6	8	no	—
246	C₄×D₃	—	6	4	no	—
247	C₄×D₃	—	6	4	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	2	no	—
250	C₂×C₃²	—	2	4	no	—
251	C₂×C₃²	—	4	4	no	—
252	C₂×C₃²	—	4	2	no	—
253	C₂×C₃²	—	4	8	no	—
254	C₂×C₃²	—	8	8	no	—
255	C₂×C₃²	D₄×Dic₃	1	2	yes	complemented
256	C₂×C₃²	C₂³×Dic₃	1	1	yes	characteristic
257	C₃⋊D₃	—	2	4	no	—
258	C₃⋊D₃	D₄×Dic₃	1	2	yes	complemented
259	C₃⋊D₃	C₂×D₃×D₄	1	1	yes	characteristic
260	C₃⋊D₃	C₂×#237	1	1	yes	characteristic
261	C₃×D₃	—	6	4	no	—
262	C₃×D₃	—	6	2	no	—
263	C₃×D₃	—	6	2	no	—
264	C₃×D₃	—	12	8	no	—
265	C₂⁴	—	9	2	no	—
266	C₂×D₄	—	9	2	no	—
267	C₂×D₄	—	9	4	no	—
268	C₂×D₄	—	9	4	no	—
269	C₂×D₄	—	9	1	no	—
270	C₂×D₄	C₃⋊#157	1	1	yes	characteristic, direct product factor
271	C₂²×C₄	—	9	1	no	—
272	C₂²×C₄	—	27	1	no	—
273	C₂²×C₄	—	27	1	no	—
274	C₂²×C₄	—	27	2	no	—
275	C₂²×C₄	—	27	8	no	—
276	C₂²×C₄	—	54	8	no	—
277	C₄⋊C₄	—	27	4	no	—
278	C₂²⋊C₄	—	27	8	no	—
279	C₄²	—	27	4	no	—
280	C₂²×C₃	—	2	4	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	8	no	—
283	C₂²×C₃	—	4	8	no	—
284	C₂²×C₃	—	4	2	no	—
285	C₂²×C₃	—	4	8	no	—
286	C₂²×C₃	—	8	8	no	—
287	C₂²×C₃	—	9	2	no	—
288	C₂²×C₃	—	9	2	no	—
289	C₂²×C₃	—	9	1	no	—
290	C₂²×C₃	—	9	1	no	—
291	C₂²×C₃	—	9	4	no	—
292	C₂²×C₃	—	18	4	no	—
293	C₂²×C₃	—	18	4	no	—
294	C₂²×C₃	—	18	8	no	—
295	C₂²×C₃	—	18	4	no	—
296	C₂²×C₃	C₂²×#157	1	1	yes	characteristic
297	C₂²×C₃	C₂²×#157	1	4	yes	complemented
298	C₂×D₃	—	6	2	no	—
299	C₂×D₃	—	6	2	no	—
300	C₂×D₃	—	6	4	no	—
301	C₂×D₃	—	6	4	no	—
302	C₂×D₃	—	6	8	no	—
303	C₂×D₃	—	12	8	no	—
304	C₂×D₃	—	12	16	no	—
305	C₂×D₃	—	12	8	no	—
306	C₂×D₃	—	12	8	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	4	4	no	—
309	C₃×C₄	—	9	2	no	—
310	C₃×C₄	C₂²×#157	1	2	yes	complemented
311	Dic₃	—	6	4	no	—
312	Dic₃	—	9	4	no	—
313	Dic₃	—	18	4	no	—
314	Dic₃	—	18	2	no	—
315	C₃²	—	2	2	no	—
316	C₃²	—	4	2	no	—
317	C₃²	C₂×D₄×Dic₃	1	1	yes	characteristic, complemented
318	C₂³	—	9	1	no	—
319	C₂³	—	9	2	no	—
320	C₂³	—	9	4	no	—
321	C₂³	—	9	4	no	—
322	C₂³	—	18	4	no	—
323	C₂³	—	18	4	no	—
324	C₂³	C₂×C₃⋊#157	1	2	yes	complemented
325	D₄	—	9	8	no	—
326	D₄	—	9	4	no	—
327	D₄	C₂×C₃⋊#157	1	4	yes	direct product factor
328	C₂×C₄	—	9	1	no	—
329	C₂×C₄	—	9	2	no	—
330	C₂×C₄	—	9	2	no	—
331	C₂×C₄	—	27	2	no	—
332	C₂×C₄	—	27	4	no	—
333	C₂×C₄	—	27	2	no	—
334	C₂×C₄	—	27	4	no	—
335	C₂×C₄	—	54	16	no	—
336	C₂×C₄	—	54	4	no	—
337	C₂×C₄	—	54	2	no	—
338	C₂×C₄	C₂×C₃⋊#157	1	1	yes	characteristic, complemented
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	4	no	—
342	C₂×C₃	—	4	8	no	—
343	C₂×C₃	—	4	2	no	—
344	C₂×C₃	—	4	4	no	—
345	C₂×C₃	—	8	8	no	—
346	C₂×C₃	—	9	1	no	—
347	C₂×C₃	—	9	1	no	—
348	C₂×C₃	—	9	2	no	—
349	C₂×C₃	—	18	4	no	—
350	C₂×C₃	D₄×#157	1	2	yes	complemented
351	C₂×C₃	C₂³×#157	1	1	yes	characteristic
352	D₃	—	6	4	no	—
353	D₃	—	6	2	no	—
354	D₃	—	6	2	no	—
355	D₃	—	12	8	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	9	1	no	—
358	C₂²	—	9	1	no	—
359	C₂²	—	9	2	no	—
360	C₂²	—	9	2	no	—
361	C₂²	—	9	4	no	—
362	C₂²	—	18	4	no	—
363	C₂²	—	18	4	no	—
364	C₂²	—	18	8	no	—
365	C₂²	—	18	4	no	—
366	C₂²	C₂²×C₃⋊#157	1	1	yes	characteristic
367	C₂²	C₂²×C₃⋊#157	1	4	yes	complemented
368	C₄	—	9	2	no	—
369	C₄	—	27	4	no	—
370	C₄	—	54	4	no	—
371	C₄	—	54	2	no	—
372	C₄	C₂²×C₃⋊#157	1	2	yes	complemented
373	C₃	—	2	2	no	—
374	C₃	—	4	2	no	—
375	C₃	C₂×D₄×#157	1	1	yes	characteristic, complemented
376	C₂	—	2	4	no	—
377	C₂	—	9	1	no	—
378	C₂	—	9	1	no	—
379	C₂	—	9	2	no	—
380	C₂	—	18	4	no	—
381	C₂	D₄×C₃⋊#157	1	2	yes	direct product factor
382	C₂	C₂³×C₃⋊#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₃⋊#157
commutator	C₂×C₃³	C₂³×C₄
Frattini	C₂	C₂³×C₃⋊#157
Fitting	C₂×C₃³×D₄	C₄
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃×D₄×C₃⋊D₃	C₂
cosocle	C₂×C₃×C₃⋊D₃	C₂⁴
hypercenter	C₂×D₄	C₃⋊#157
hypocenter	C₃³	C₂×C₄×D₄
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃⋊#157	C₂	semidirect
3. C₂×#88994	C₂	semidirect
4. D₄×C₃⋊#157	C₂	direct (N × H)
5. C₂×C₄⋊(C₃⋊#157)	C₂	semidirect
6. C₂×C₄×C₃⋊#157	C₂	semidirect
13. C₂²×C₃⋊#157	C₂²	semidirect
14. C₂×C₃³×D₄	C₄	semidirect
15. C₂×C₃×#638	C₄	semidirect
16. C₃×D₄×C₃⋊D₃	C₄	semidirect
18. C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	semidirect
20. #88994	C₂²	semidirect
21. C₄⋊(C₃⋊#157)	C₂²	semidirect
22. C₄×C₃⋊#157	C₂²	semidirect
30. C₂³×C₃³	C₂×C₄	semidirect
33. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
34. C₂²×C₃×C₃⋊D₃	C₂×C₄	semidirect
40. C₂×C₃⋊#157	D₄	direct (N × H)
44. C₃³×D₄	C₂×C₄	semidirect
45. C₂×C₃³×C₄	C₂×C₄	semidirect
46. C₃×#638	C₂×C₄	semidirect
47. C₂×C₃×C₃⋊Dic₃	C₂×C₄	semidirect
48. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
49. C₃×C₄×C₃⋊D₃	C₂×C₄	semidirect
61. C₂×C₃²×D₄	Dic₃	semidirect
62. C₂×#638	Dic₃	semidirect
63. D₄×C₃⋊D₃	Dic₃	semidirect
65. C₂×C₄⋊(C₃⋊D₃)	Dic₃	semidirect
77. C₂²×C₃³	C₂²×C₄	semidirect
83. C₂×C₃×C₃⋊D₃	C₂²×C₄	semidirect
89. C₃⋊#157	C₂×D₄	direct (N × H)
90. C₃³×C₄	C₂²×C₄	semidirect
91. C₃×C₃⋊Dic₃	C₂²×C₄	semidirect
101. C₂³×C₃²	C₂×Dic₃	semidirect
104. C₂²×C₃⋊D₃	C₂×Dic₃	semidirect
105. C₂²×C₃⋊D₃	C₂×Dic₃	semidirect
123. C₃²×D₄	C₂×Dic₃	semidirect
126. C₂×C₃²×C₄	C₂×Dic₃	semidirect
127. #638	C₂×Dic₃	semidirect
128. C₂×C₃⋊Dic₃	C₂×Dic₃	semidirect
129. C₄⋊(C₃⋊D₃)	C₂×Dic₃	semidirect
130. C₄×C₃⋊D₃	C₂×Dic₃	semidirect
139. C₂×C₃³	C₄×D₄	semidirect
142. C₃×C₃⋊D₃	C₄×D₄	semidirect
153. C₂×C₃×D₄	#157	semidirect
176. C₂²×C₃²	C₂²×Dic₃	semidirect
184. C₂×C₃⋊D₃	C₂²×Dic₃	semidirect
200. C₃²×C₄	C₂²×Dic₃	semidirect
201. C₃⋊Dic₃	C₂²×Dic₃	semidirect
209. C₃³	C₂×C₄×D₄	semidirect
218. C₂³×C₃	C₂×#157	semidirect
229. C₃×D₄	C₂×#157	semidirect
235. C₂×C₃×C₄	C₂×#157	semidirect
255. C₂×C₃²	D₄×Dic₃	semidirect
258. C₃⋊D₃	D₄×Dic₃	semidirect
270. C₂×D₄	C₃⋊#157	direct (N × H)
297. C₂²×C₃	C₂²×#157	semidirect
310. C₃×C₄	C₂²×#157	semidirect
317. C₃²	C₂×D₄×Dic₃	semidirect
324. C₂³	C₂×C₃⋊#157	semidirect
327. D₄	C₂×C₃⋊#157	direct (N × H)
338. C₂×C₄	C₂×C₃⋊#157	semidirect
350. C₂×C₃	D₄×#157	semidirect
367. C₂²	C₂²×C₃⋊#157	semidirect
372. C₄	C₂²×C₃⋊#157	semidirect
375. C₃	C₂×D₄×#157	semidirect
381. C₂	D₄×C₃⋊#157	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃⋊#157	2
C₂×C₃×D₄×C₃⋊D₃	2
C₂×#88994	2
D₄×C₃⋊#157	2
C₂×C₄⋊(C₃⋊#157)	2
C₂×C₄×C₃⋊#157	2
C₂×D₄×#157	3
C₂×D₄×Dic₃	9

Subgroups — C2×D4×C3⋊#157 #13181516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₃⋊#157 #13181516