Subgroups — C₃×#90468 #13061119

Order 1344.

524 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#1161	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6512	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6505	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6482	C₂	1	2	yes	maximal, complemented
7	C₃×#6481	C₂	1	2	yes	maximal, complemented
8	C₃×#6479	C₂	1	2	yes	maximal, complemented
9	C₃×#6477	C₂	1	2	yes	maximal, complemented
10	C₃×#6471	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#90468	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
15	C₃×#1161	—	2	1	no	—
16	C₃×#1161	—	2	1	no	—
17	C₃×#1161	C₂²	1	2	yes	—
18	C₃×#1161	C₂²	1	2	yes	complemented
19	C₃×#1161	C₂²	1	1	yes	characteristic, complemented
20	C₃×Q₈×D₇	C₂²	1	1	yes	characteristic, complemented
21	C₃×#1159	—	2	1	no	—
22	C₃×#1159	C₂²	1	1	yes	characteristic, complemented
23	C₃×D₄×D₇	—	2	1	no	—
24	C₃×D₄×D₇	C₂²	1	1	yes	characteristic, complemented
25	C₃×#1157	—	2	1	no	—
26	C₃×#1157	C₂²	1	1	yes	characteristic
27	C₂×C₃×D₂₈	—	2	1	no	—
28	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄×D₇	—	2	1	no	—
30	C₂×C₃×C₄×D₇	—	2	1	no	—
31	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
32	C₃×C₇×Q₁₆	C₂²	1	2	yes	complemented
33	C₃×C₇×SD₁₆	C₂²	1	2	yes	complemented
34	C₃×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
35	C₃×#1144	C₂²	1	2	yes	complemented
36	C₃×#1143	C₂²	1	2	yes	complemented
37	C₃×#1143	C₂²	1	2	yes	complemented
38	C₃×#1141	C₂²	1	2	yes	complemented
39	C₃×#1136	C₂²	1	1	yes	characteristic, complemented
40	C₃×D₅₆	C₂²	1	2	yes	complemented
41	C₃×#1132	C₂²	1	2	yes	complemented
42	C₃×#1131	C₂²	1	2	yes	complemented
43	C₃×C₈×D₇	C₂²	1	2	yes	complemented
44	D₇×#41	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#1161	C₂×C₃	1	1	yes	characteristic, complemented
46	C₇×#137	C₂×C₃	1	1	yes	characteristic, complemented
47	#6512	C₂×C₃	1	1	yes	characteristic, complemented
48	#6505	C₂×C₃	1	1	yes	characteristic, complemented
49	#6482	C₂×C₃	1	2	yes	complemented
50	#6481	C₂×C₃	1	2	yes	complemented
51	#6479	C₂×C₃	1	2	yes	complemented
52	#6477	C₂×C₃	1	2	yes	complemented
53	#6471	C₂×C₃	1	1	yes	characteristic, complemented
54	D₇×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×#575	—	7	1	no	maximal, Hall
56	C₂²×C₃×D₇	—	2	1	no	—
57	C₂²×C₃×D₇	—	2	1	no	—
58	C₂²×C₃×D₇	D₄	1	1	yes	characteristic
59	C₃×C₇×Q₈	—	2	1	no	—
60	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₃×C₇×Q₈	C₂³	1	2	yes	—
62	C₃×C₇×D₄	—	2	1	no	—
63	C₃×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₄×C₇	—	2	1	no	—
65	C₂×C₃×C₄×C₇	—	2	1	no	—
66	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₃×C₂²⋊D₇	—	2	1	no	—
68	C₃×C₂²⋊D₇	—	2	1	no	—
69	C₃×C₂²⋊D₇	—	2	1	no	—
70	C₂×C₃×Dic₇	—	2	1	no	—
71	C₂×C₃×Dic₇	D₄	1	1	yes	characteristic
72	C₃×D₂₈	—	2	2	no	—
73	C₃×D₂₈	—	2	2	no	—
74	C₃×D₂₈	—	2	1	no	—
75	C₃×D₂₈	—	2	1	no	—
76	C₃×D₂₈	C₂³	1	2	yes	—
77	C₃×D₂₈	C₂³	1	1	yes	characteristic
78	C₃×C₄×D₇	—	2	1	no	—
79	C₃×C₄×D₇	—	2	1	no	—
80	C₃×C₄×D₇	—	2	1	no	—
81	C₃×C₄×D₇	—	2	2	no	—
82	C₃×C₄×D₇	—	2	2	no	—
83	C₃×C₄×D₇	D₄	1	1	yes	characteristic
84	C₃×C₄×D₇	D₄	1	1	yes	characteristic
85	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
86	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
87	C₃×Dic₁₄	—	2	1	no	—
88	C₃×Dic₁₄	C₂³	1	1	yes	characteristic
89	C₃×C₇×C₈	C₂³	1	2	yes	—
90	C₃×C₇⋊C₈	C₂³	1	2	yes	—
91	C₇×#41	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₇×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
93	#1161	—	2	1	no	—
94	#1161	—	2	1	no	—
95	#1161	C₂²×C₃	1	2	yes	—
96	#1161	C₂²×C₃	1	2	yes	complemented
97	#1161	C₂²×C₃	1	1	yes	characteristic, complemented
98	Q₈×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	#1159	—	2	1	no	—
100	#1159	C₂²×C₃	1	1	yes	characteristic, complemented
101	D₄×D₇	—	2	1	no	—
102	D₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
103	#1157	—	2	1	no	—
104	#1157	C₂²×C₃	1	1	yes	characteristic
105	C₂×D₂₈	—	2	1	no	—
106	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂×C₄×D₇	—	2	1	no	—
108	C₂×C₄×D₇	—	2	1	no	—
109	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
110	C₇×Q₁₆	C₂²×C₃	1	2	yes	complemented
111	C₇×SD₁₆	C₂²×C₃	1	2	yes	complemented
112	C₇×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
113	#1144	C₂²×C₃	1	2	yes	complemented
114	#1143	C₂²×C₃	1	2	yes	complemented
115	#1143	C₂²×C₃	1	2	yes	complemented
116	#1141	C₂²×C₃	1	2	yes	complemented
117	#1136	C₂²×C₃	1	1	yes	characteristic, complemented
118	D₅₆	C₂²×C₃	1	2	yes	complemented
119	#1132	C₂²×C₃	1	2	yes	complemented
120	#1131	C₂²×C₃	1	2	yes	complemented
121	C₈×D₇	C₂²×C₃	1	2	yes	complemented
122	C₂×C₃×#41	—	7	1	no	—
123	C₂×C₃×#41	—	7	1	no	—
124	C₃×#137	—	7	1	no	—
125	C₃×#137	—	7	2	no	—
126	C₃×#137	D₇	1	1	yes	characteristic, complemented
127	C₃×AGL(1,ℤ/8)	—	7	1	no	—
128	C₃×AGL(1,ℤ/8)	—	7	2	no	—
129	C₃×AGL(1,ℤ/8)	—	7	1	no	—
130	C₃×#135	—	7	2	no	—
131	C₃×#135	—	7	2	no	—
132	C₂×C₃×M₁₆	—	7	1	no	—
133	C₂²×C₃×C₇	—	2	1	no	—
134	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×D₇	—	2	2	no	—
136	C₂×C₃×D₇	—	2	1	no	—
137	C₂×C₃×D₇	—	4	1	no	—
138	C₂×C₃×D₇	—	4	2	no	—
139	C₂×C₃×D₇	—	4	2	no	—
140	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
142	C₃×C₄×C₇	—	2	1	no	—
143	C₃×C₄×C₇	—	2	2	no	—
144	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₃×Dic₇	—	2	1	no	—
147	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
148	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
149	#575	—	7	1	no	Sylow
150	C₂²×D₇	—	2	1	no	—
151	C₂²×D₇	—	2	1	no	—
152	C₂²×D₇	C₃×D₄	1	1	yes	characteristic
153	C₇×Q₈	—	2	1	no	—
154	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
155	C₇×Q₈	C₂³×C₃	1	2	yes	—
156	C₇×D₄	—	2	1	no	—
157	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
158	C₂×C₄×C₇	—	2	1	no	—
159	C₂×C₄×C₇	—	2	1	no	—
160	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
161	C₂²⋊D₇	—	2	1	no	—
162	C₂²⋊D₇	—	2	1	no	—
163	C₂²⋊D₇	—	2	1	no	—
164	C₂×Dic₇	—	2	1	no	—
165	C₂×Dic₇	C₃×D₄	1	1	yes	characteristic
166	D₂₈	—	2	2	no	—
167	D₂₈	—	2	2	no	—
168	D₂₈	—	2	1	no	—
169	D₂₈	—	2	1	no	—
170	D₂₈	C₂³×C₃	1	2	yes	—
171	D₂₈	C₂³×C₃	1	1	yes	characteristic
172	C₄×D₇	—	2	1	no	—
173	C₄×D₇	—	2	1	no	—
174	C₄×D₇	—	2	1	no	—
175	C₄×D₇	—	2	2	no	—
176	C₄×D₇	—	2	2	no	—
177	C₄×D₇	C₃×D₄	1	1	yes	characteristic
178	C₄×D₇	C₃×D₄	1	1	yes	characteristic
179	C₄×D₇	C₂³×C₃	1	1	yes	characteristic
180	C₄×D₇	C₂³×C₃	1	1	yes	characteristic
181	Dic₁₄	—	2	1	no	—
182	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
183	C₇×C₈	C₂³×C₃	1	2	yes	—
184	C₇⋊C₈	C₂³×C₃	1	2	yes	—
185	C₃×#41	—	7	2	no	—
186	C₃×#41	—	7	1	no	—
187	C₃×#41	—	7	2	no	—
188	C₃×#41	—	7	1	no	—
189	C₃×#41	—	7	1	no	—
190	C₃×#41	—	14	1	no	—
191	C₃×#41	—	14	1	no	—
192	C₃×#41	—	14	1	no	—
193	C₃×#41	—	14	1	no	—
194	C₃×#41	C₂×D₇	1	1	yes	characteristic
195	C₂×C₃×Q₈	—	7	1	no	—
196	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
197	C₂×C₃×D₄	—	7	1	no	—
198	C₂×C₃×D₄	—	7	1	no	—
199	C₂×C₃×D₄	—	14	1	no	—
200	C₂×C₃×D₄	—	14	1	no	—
201	C₂²×C₃×C₄	—	7	1	no	—
202	C₂²×C₃×C₄	—	14	1	no	—
203	C₂²×C₃×C₄	—	14	1	no	—
204	C₃×Q₁₆	—	7	2	no	—
205	C₃×Q₁₆	C₂×D₇	1	2	yes	complemented
206	C₃×SD₁₆	—	7	2	no	—
207	C₃×SD₁₆	—	7	2	no	—
208	C₃×SD₁₆	—	7	2	no	—
209	C₃×SD₁₆	C₂×D₇	1	2	yes	complemented
210	C₃×D₈	—	7	2	no	—
211	C₃×D₈	—	7	2	no	—
212	C₃×M₁₆	—	7	1	no	—
213	C₃×M₁₆	—	7	2	no	—
214	C₃×M₁₆	C₂×D₇	1	1	yes	characteristic, complemented
215	C₂×C₃×C₈	—	7	2	no	—
216	C₂×C₃×C₇	—	2	1	no	—
217	C₂×C₃×C₇	—	4	1	no	—
218	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
219	C₃×D₇	—	2	1	no	—
220	C₃×D₇	—	2	1	no	—
221	C₃×D₇	—	4	2	no	—
222	C₃×D₇	—	4	1	no	—
223	C₂×#41	—	7	1	no	—
224	C₂×#41	—	7	1	no	—
225	#137	—	7	1	no	—
226	#137	—	7	2	no	—
227	#137	C₃×D₇	1	1	yes	characteristic, complemented
228	AGL(1,ℤ/8)	—	7	1	no	—
229	AGL(1,ℤ/8)	—	7	2	no	—
230	AGL(1,ℤ/8)	—	7	1	no	—
231	#135	—	7	2	no	—
232	#135	—	7	2	no	—
233	C₂×M₁₆	—	7	1	no	—
234	C₂²×C₇	—	2	1	no	—
235	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×D₇	—	2	2	no	—
237	C₂×D₇	—	2	1	no	—
238	C₂×D₇	—	4	1	no	—
239	C₂×D₇	—	4	2	no	—
240	C₂×D₇	—	4	2	no	—
241	C₂×D₇	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×D₇	C₂×C₃×D₄	1	1	yes	characteristic
243	C₄×C₇	—	2	1	no	—
244	C₄×C₇	—	2	2	no	—
245	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
246	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
247	Dic₇	—	2	1	no	—
248	Dic₇	C₂×C₃×D₄	1	1	yes	characteristic
249	Dic₇	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂³×C₃	—	7	1	no	—
251	C₂³×C₃	—	14	1	no	—
252	C₂³×C₃	—	14	1	no	—
253	C₃×Q₈	—	2	1	no	—
254	C₃×Q₈	—	7	1	no	—
255	C₃×Q₈	—	14	1	no	—
256	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
257	C₃×Q₈	C₂²×D₇	1	2	yes	—
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	—	7	2	no	—
260	C₃×D₄	—	7	1	no	—
261	C₃×D₄	—	14	1	no	—
262	C₃×D₄	—	14	2	no	—
263	C₃×D₄	—	14	2	no	—
264	C₃×D₄	—	14	1	no	—
265	C₃×D₄	—	14	1	no	—
266	C₃×D₄	—	14	1	no	—
267	C₃×D₄	—	14	1	no	—
268	C₃×D₄	C₂²×D₇	1	1	yes	characteristic
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	1	no	—
271	C₂×C₃×C₄	—	7	1	no	—
272	C₂×C₃×C₄	—	7	1	no	—
273	C₂×C₃×C₄	—	7	1	no	—
274	C₂×C₃×C₄	—	7	1	no	—
275	C₂×C₃×C₄	—	7	1	no	—
276	C₂×C₃×C₄	—	14	1	no	—
277	C₂×C₃×C₄	—	14	2	no	—
278	C₂×C₃×C₄	—	14	2	no	—
279	C₂×C₃×C₄	—	14	1	no	—
280	C₂×C₃×C₄	—	14	1	no	—
281	C₂×C₃×C₄	—	14	1	no	—
282	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
283	C₃×C₈	—	7	2	no	—
284	C₃×C₈	C₂²×D₇	1	2	yes	—
285	C₃×C₇	#575	1	1	yes	characteristic, complemented, Hall
286	#41	—	7	1	no	—
287	#41	—	7	2	no	—
288	#41	—	7	2	no	—
289	#41	—	7	1	no	—
290	#41	—	7	1	no	—
291	#41	—	14	1	no	—
292	#41	—	14	1	no	—
293	#41	—	14	1	no	—
294	#41	—	14	1	no	—
295	#41	C₂×C₃×D₇	1	1	yes	characteristic
296	C₂×Q₈	—	7	1	no	—
297	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
298	C₂×D₄	—	7	1	no	—
299	C₂×D₄	—	7	1	no	—
300	C₂×D₄	—	14	1	no	—
301	C₂×D₄	—	14	1	no	—
302	C₂²×C₄	—	7	1	no	—
303	C₂²×C₄	—	14	1	no	—
304	C₂²×C₄	—	14	1	no	—
305	Q₁₆	—	7	2	no	—
306	Q₁₆	C₂×C₃×D₇	1	2	yes	complemented
307	SD₁₆	—	7	2	no	—
308	SD₁₆	—	7	2	no	—
309	SD₁₆	—	7	2	no	—
310	SD₁₆	C₂×C₃×D₇	1	2	yes	complemented
311	D₈	—	7	2	no	—
312	D₈	—	7	2	no	—
313	M₁₆	—	7	1	no	—
314	M₁₆	—	7	2	no	—
315	M₁₆	C₂×C₃×D₇	1	1	yes	characteristic, complemented
316	C₂×C₈	—	7	2	no	—
317	C₂×C₇	—	2	1	no	—
318	C₂×C₇	—	4	1	no	—
319	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
320	D₇	—	2	1	no	—
321	D₇	—	2	1	no	—
322	D₇	—	4	2	no	—
323	D₇	—	4	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	7	1	no	—
326	C₂²×C₃	—	7	1	no	—
327	C₂²×C₃	—	14	2	no	—
328	C₂²×C₃	—	14	1	no	—
329	C₂²×C₃	—	28	1	no	—
330	C₂²×C₃	—	28	2	no	—
331	C₂²×C₃	—	28	2	no	—
332	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
333	C₃×C₄	—	2	1	no	—
334	C₃×C₄	—	2	2	no	—
335	C₃×C₄	—	7	1	no	—
336	C₃×C₄	—	7	1	no	—
337	C₃×C₄	—	14	1	no	—
338	C₃×C₄	D₄×D₇	1	1	yes	characteristic
339	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
340	C₂³	—	7	1	no	—
341	C₂³	—	14	1	no	—
342	C₂³	—	14	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	7	1	no	—
345	Q₈	—	14	1	no	—
346	Q₈	C₂²×C₃×D₇	1	1	yes	characteristic
347	Q₈	C₂²×C₃×D₇	1	2	yes	—
348	D₄	—	2	1	no	—
349	D₄	—	7	2	no	—
350	D₄	—	7	1	no	—
351	D₄	—	14	1	no	—
352	D₄	—	14	2	no	—
353	D₄	—	14	2	no	—
354	D₄	—	14	1	no	—
355	D₄	—	14	1	no	—
356	D₄	—	14	1	no	—
357	D₄	—	14	1	no	—
358	D₄	C₂²×C₃×D₇	1	1	yes	characteristic
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	7	1	no	—
362	C₂×C₄	—	7	1	no	—
363	C₂×C₄	—	7	1	no	—
364	C₂×C₄	—	7	1	no	—
365	C₂×C₄	—	7	1	no	—
366	C₂×C₄	—	14	1	no	—
367	C₂×C₄	—	14	2	no	—
368	C₂×C₄	—	14	2	no	—
369	C₂×C₄	—	14	1	no	—
370	C₂×C₄	—	14	1	no	—
371	C₂×C₄	—	14	1	no	—
372	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
373	C₈	—	7	2	no	—
374	C₈	C₂²×C₃×D₇	1	2	yes	—
375	C₇	C₃×#575	1	1	yes	characteristic, complemented, Sylow
376	C₂×C₃	—	2	1	no	—
377	C₂×C₃	—	4	1	no	—
378	C₂×C₃	—	14	1	no	—
379	C₂×C₃	—	14	1	no	—
380	C₂×C₃	—	28	2	no	—
381	C₂×C₃	—	28	1	no	—
382	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
383	C₂²	—	2	1	no	—
384	C₂²	—	7	1	no	—
385	C₂²	—	7	1	no	—
386	C₂²	—	14	2	no	—
387	C₂²	—	14	1	no	—
388	C₂²	—	28	1	no	—
389	C₂²	—	28	2	no	—
390	C₂²	—	28	2	no	—
391	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	7	1	no	—
395	C₄	—	7	1	no	—
396	C₄	—	14	1	no	—
397	C₄	C₃×D₄×D₇	1	1	yes	characteristic
398	C₄	C₂³×C₃×D₇	1	1	yes	characteristic
399	C₃	#90468	1	1	yes	characteristic, direct product factor, Sylow
400	C₂	—	2	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	14	1	no	—
403	C₂	—	14	1	no	—
404	C₂	—	28	2	no	—
405	C₂	—	28	1	no	—
406	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₇
commutator, cosocle	C₄×C₇	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×D₇
Fitting	C₃×C₇×#137	C₂
socle	C₂×C₃×C₇	C₂²×D₄
hypercenter	C₃×#137	D₇
hypocenter	C₇	C₃×#575
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#137

Complements

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

N	H ≅ G/N	type
1. C₃×D₇×#41	C₂	semidirect
2. C₂×C₃×#1161	C₂	semidirect
3. C₃×C₇×#137	C₂	semidirect
4. C₃×#6512	C₂	semidirect
5. C₃×#6505	C₂	semidirect
6. C₃×#6482	C₂	semidirect
7. C₃×#6481	C₂	semidirect
8. C₃×#6479	C₂	semidirect
9. C₃×#6477	C₂	semidirect
10. C₃×#6471	C₂	semidirect
11. C₃×D₇×M₁₆	C₂	semidirect
12. #90468	C₃	direct (N × H)
14. C₂×C₃×C₇×Q₈	C₂²	semidirect
18. C₃×#1161	C₂²	semidirect
19. C₃×#1161	C₂²	semidirect
20. C₃×Q₈×D₇	C₂²	semidirect
22. C₃×#1159	C₂²	semidirect
24. C₃×D₄×D₇	C₂²	semidirect
28. C₂×C₃×D₂₈	C₂²	semidirect
32. C₃×C₇×Q₁₆	C₂²	semidirect
33. C₃×C₇×SD₁₆	C₂²	semidirect
34. C₃×C₇×M₁₆	C₂²	semidirect
35. C₃×#1144	C₂²	semidirect
36. C₃×#1143	C₂²	semidirect
37. C₃×#1143	C₂²	semidirect
38. C₃×#1141	C₂²	semidirect
39. C₃×#1136	C₂²	semidirect
40. C₃×D₅₆	C₂²	semidirect
41. C₃×#1132	C₂²	semidirect
42. C₃×#1131	C₂²	semidirect
43. C₃×C₈×D₇	C₂²	semidirect
44. D₇×#41	C₂×C₃	semidirect
45. C₂×#1161	C₂×C₃	semidirect
46. C₇×#137	C₂×C₃	semidirect
47. #6512	C₂×C₃	semidirect
48. #6505	C₂×C₃	semidirect
49. #6482	C₂×C₃	semidirect
50. #6481	C₂×C₃	semidirect
51. #6479	C₂×C₃	semidirect
52. #6477	C₂×C₃	semidirect
53. #6471	C₂×C₃	semidirect
54. D₇×M₁₆	C₂×C₃	semidirect
92. C₂×C₇×Q₈	C₂²×C₃	semidirect
96. #1161	C₂²×C₃	semidirect
97. #1161	C₂²×C₃	semidirect
98. Q₈×D₇	C₂²×C₃	semidirect
100. #1159	C₂²×C₃	semidirect
102. D₄×D₇	C₂²×C₃	semidirect
106. C₂×D₂₈	C₂²×C₃	semidirect
110. C₇×Q₁₆	C₂²×C₃	semidirect
111. C₇×SD₁₆	C₂²×C₃	semidirect
112. C₇×M₁₆	C₂²×C₃	semidirect
113. #1144	C₂²×C₃	semidirect
114. #1143	C₂²×C₃	semidirect
115. #1143	C₂²×C₃	semidirect
116. #1141	C₂²×C₃	semidirect
117. #1136	C₂²×C₃	semidirect
118. D₅₆	C₂²×C₃	semidirect
119. #1132	C₂²×C₃	semidirect
120. #1131	C₂²×C₃	semidirect
121. C₈×D₇	C₂²×C₃	semidirect
126. C₃×#137	D₇	semidirect
196. C₂×C₃×Q₈	C₂×D₇	semidirect
205. C₃×Q₁₆	C₂×D₇	semidirect
209. C₃×SD₁₆	C₂×D₇	semidirect
214. C₃×M₁₆	C₂×D₇	semidirect
227. #137	C₃×D₇	semidirect
285. C₃×C₇	#575	semidirect
297. C₂×Q₈	C₂×C₃×D₇	semidirect
306. Q₁₆	C₂×C₃×D₇	semidirect
310. SD₁₆	C₂×C₃×D₇	semidirect
315. M₁₆	C₂×C₃×D₇	semidirect
375. C₇	C₃×#575	semidirect
399. C₃	#90468	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₇×#41	2
C₂×C₃×#1161	2
C₃×C₇×#137	2
C₃×#6512	2
C₃×#6505	2
C₃×#6482	2
C₃×#6481	2
C₃×#6479	2
C₃×#6477	2
C₃×#6471	2
C₃×D₇×M₁₆	2
#90468	3
C₃×#575	7

Subgroups — C3×#90468 #13061119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#90468 #13061119