Subgroups — C₃×D₇×#137 #13061118

Order 1344.

516 conjugacy classes of subgroups.

The subgroup lattice has 400 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
2	C₂×C₃×Q₈×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6514	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6505	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6481	C₂	1	2	yes	maximal, complemented
7	C₃×D₇×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₃×#6478	C₂	1	2	yes	maximal, complemented
9	C₃×D₇×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₃×#6472	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	D₇×#137	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	C₂²	1	1	yes	characteristic
16	C₃×Q₈×D₇	—	2	1	no	—
17	C₃×Q₈×D₇	—	2	1	no	—
18	C₃×Q₈×D₇	C₂²	1	2	yes	—
19	C₃×Q₈×D₇	C₂²	1	1	yes	characteristic
20	C₃×Q₈×D₇	C₂²	1	2	yes	complemented
21	C₃×#1159	—	2	1	no	—
22	C₃×#1159	C₂²	1	1	yes	characteristic
23	C₃×D₄×D₇	—	2	1	no	—
24	C₃×D₄×D₇	C₂²	1	1	yes	characteristic
25	C₃×#1157	—	2	1	no	—
26	C₃×#1157	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄×D₇	—	2	1	no	—
28	C₂×C₃×C₄×D₇	—	2	1	no	—
29	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
30	C₂×C₃×Dic₁₄	—	2	1	no	—
31	C₂×C₃×Dic₁₄	C₂²	1	1	yes	characteristic, complemented
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×#1144	C₂²	1	2	yes	complemented
37	C₃×#1143	C₂²	1	2	yes	complemented
38	C₃×#1142	C₂²	1	2	yes	complemented
39	C₃×#1136	C₂²	1	1	yes	characteristic, complemented
40	C₃×Dic₂₈	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	—
44	D₇×#41	C₂×C₃	1	1	yes	characteristic
45	C₂×Q₈×D₇	C₂×C₃	1	1	yes	characteristic, complemented
46	C₇×#137	C₂×C₃	1	1	yes	characteristic, complemented
47	#6514	C₂×C₃	1	1	yes	characteristic, complemented
48	#6505	C₂×C₃	1	1	yes	characteristic, complemented
49	#6481	C₂×C₃	1	2	yes	complemented
50	D₇×Q₁₆	C₂×C₃	1	2	yes	complemented
51	#6478	C₂×C₃	1	2	yes	complemented
52	D₇×SD₁₆	C₂×C₃	1	2	yes	complemented
53	#6472	C₂×C₃	1	1	yes	characteristic, complemented
54	D₇×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₃×#137	—	7	1	no	maximal, Hall
56	C₂²×C₃×D₇	—	2	1	no	—
57	C₂²×C₃×D₇	D₄	1	1	yes	characteristic
58	C₃×C₇×Q₈	—	2	1	no	—
59	C₃×C₇×Q₈	C₂³	1	2	yes	—
60	C₃×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₃×C₇×D₄	—	2	1	no	—
62	C₃×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×C₇	—	2	1	no	—
64	C₂×C₃×C₄×C₇	—	2	1	no	—
65	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
66	C₃×C₂²⋊D₇	—	2	1	no	—
67	C₃×C₂²⋊D₇	—	2	1	no	—
68	C₃×C₂²⋊D₇	—	2	1	no	—
69	C₂×C₃×Dic₇	—	2	1	no	—
70	C₂×C₃×Dic₇	—	2	1	no	—
71	C₂×C₃×Dic₇	D₄	1	1	yes	characteristic
72	C₃×D₂₈	—	2	1	no	—
73	C₃×D₂₈	C₂³	1	1	yes	characteristic
74	C₃×C₄×D₇	—	2	1	no	—
75	C₃×C₄×D₇	—	2	2	no	—
76	C₃×C₄×D₇	—	2	2	no	—
77	C₃×C₄×D₇	—	2	1	no	—
78	C₃×C₄×D₇	—	2	1	no	—
79	C₃×C₄×D₇	D₄	1	1	yes	characteristic
80	C₃×C₄×D₇	D₄	1	1	yes	characteristic
81	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
82	C₃×C₄×D₇	C₂³	1	1	yes	characteristic
83	C₃×Dic₁₄	—	2	1	no	—
84	C₃×Dic₁₄	—	2	2	no	—
85	C₃×Dic₁₄	—	2	2	no	—
86	C₃×Dic₁₄	—	2	1	no	—
87	C₃×Dic₁₄	C₂³	1	2	yes	—
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	C₂²×C₃	1	1	yes	characteristic
94	Q₈×D₇	—	2	1	no	—
95	Q₈×D₇	—	2	1	no	—
96	Q₈×D₇	C₂²×C₃	1	2	yes	—
97	Q₈×D₇	C₂²×C₃	1	1	yes	characteristic
98	Q₈×D₇	C₂²×C₃	1	2	yes	complemented
99	#1159	—	2	1	no	—
100	#1159	C₂²×C₃	1	1	yes	characteristic
101	D₄×D₇	—	2	1	no	—
102	D₄×D₇	C₂²×C₃	1	1	yes	characteristic
103	#1157	—	2	1	no	—
104	#1157	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄×D₇	—	2	1	no	—
106	C₂×C₄×D₇	—	2	1	no	—
107	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
108	C₂×Dic₁₄	—	2	1	no	—
109	C₂×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
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	#1144	C₂²×C₃	1	2	yes	complemented
115	#1143	C₂²×C₃	1	2	yes	complemented
116	#1142	C₂²×C₃	1	2	yes	complemented
117	#1136	C₂²×C₃	1	1	yes	characteristic, complemented
118	Dic₂₈	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	—
122	C₂×C₃×#41	—	7	1	no	—
123	C₂²×C₃×Q₈	—	7	1	no	—
124	C₃×#137	—	7	1	no	—
125	C₃×#137	—	7	1	no	—
126	C₃×#137	—	7	2	no	—
127	C₃×#137	—	7	2	no	—
128	C₃×#137	—	7	1	no	—
129	C₃×#137	D₇	1	1	yes	characteristic, direct product factor
130	C₂×C₃×Q₁₆	—	7	2	no	—
131	C₂×C₃×SD₁₆	—	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	2	no	—
138	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×D₇	C₂×D₄	1	1	yes	characteristic
140	C₃×C₄×C₇	—	2	2	no	—
141	C₃×C₄×C₇	—	2	1	no	—
142	C₃×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₃×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₃×Dic₇	—	2	2	no	—
145	C₃×Dic₇	—	2	1	no	—
146	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
147	C₃×Dic₇	C₂×D₄	1	1	yes	characteristic
148	C₂×#137	—	7	1	no	Sylow
149	C₂²×D₇	—	2	1	no	—
150	C₂²×D₇	C₃×D₄	1	1	yes	characteristic
151	C₇×Q₈	—	2	1	no	—
152	C₇×Q₈	C₂³×C₃	1	2	yes	—
153	C₇×Q₈	C₂³×C₃	1	1	yes	characteristic
154	C₇×D₄	—	2	1	no	—
155	C₇×D₄	C₂³×C₃	1	1	yes	characteristic
156	C₂×C₄×C₇	—	2	1	no	—
157	C₂×C₄×C₇	—	2	1	no	—
158	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
159	C₂²⋊D₇	—	2	1	no	—
160	C₂²⋊D₇	—	2	1	no	—
161	C₂²⋊D₇	—	2	1	no	—
162	C₂×Dic₇	—	2	1	no	—
163	C₂×Dic₇	—	2	1	no	—
164	C₂×Dic₇	C₃×D₄	1	1	yes	characteristic
165	D₂₈	—	2	1	no	—
166	D₂₈	C₂³×C₃	1	1	yes	characteristic
167	C₄×D₇	—	2	1	no	—
168	C₄×D₇	—	2	2	no	—
169	C₄×D₇	—	2	2	no	—
170	C₄×D₇	—	2	1	no	—
171	C₄×D₇	—	2	1	no	—
172	C₄×D₇	C₃×D₄	1	1	yes	characteristic
173	C₄×D₇	C₃×D₄	1	1	yes	characteristic
174	C₄×D₇	C₂³×C₃	1	1	yes	characteristic
175	C₄×D₇	C₂³×C₃	1	1	yes	characteristic
176	Dic₁₄	—	2	1	no	—
177	Dic₁₄	—	2	2	no	—
178	Dic₁₄	—	2	2	no	—
179	Dic₁₄	—	2	1	no	—
180	Dic₁₄	C₂³×C₃	1	2	yes	—
181	Dic₁₄	C₂³×C₃	1	1	yes	characteristic
182	C₇×C₈	C₂³×C₃	1	2	yes	—
183	C₇⋊C₈	C₂³×C₃	1	2	yes	—
184	C₃×#41	—	7	1	no	—
185	C₃×#41	—	7	1	no	—
186	C₃×#41	—	7	1	no	—
187	C₃×#41	—	14	1	no	—
188	C₃×#41	—	14	1	no	—
189	C₃×#41	C₂×D₇	1	1	yes	characteristic
190	C₂×C₃×Q₈	—	7	2	no	—
191	C₂×C₃×Q₈	—	7	1	no	—
192	C₂×C₃×Q₈	—	7	2	no	—
193	C₂×C₃×Q₈	—	7	1	no	—
194	C₂×C₃×Q₈	—	14	1	no	—
195	C₂×C₃×Q₈	—	14	1	no	—
196	C₂×C₃×Q₈	—	14	1	no	—
197	C₂×C₃×Q₈	C₂×D₇	1	1	yes	characteristic, complemented
198	C₂×C₃×D₄	—	7	1	no	—
199	C₂×C₃×D₄	—	14	1	no	—
200	C₂²×C₃×C₄	—	7	1	no	—
201	C₂²×C₃×C₄	—	14	1	no	—
202	C₂²×C₃×C₄	—	14	1	no	—
203	C₃×Q₁₆	—	7	2	no	—
204	C₃×Q₁₆	—	7	2	no	—
205	C₃×Q₁₆	—	7	2	no	—
206	C₃×Q₁₆	C₂×D₇	1	2	yes	complemented
207	C₃×SD₁₆	—	7	2	no	—
208	C₃×SD₁₆	—	7	2	no	—
209	C₃×SD₁₆	—	7	2	no	—
210	C₃×SD₁₆	C₂×D₇	1	2	yes	complemented
211	C₃×M₁₆	—	7	1	no	—
212	C₃×M₁₆	—	7	2	no	—
213	C₃×M₁₆	C₂×D₇	1	1	yes	characteristic, complemented
214	C₂×C₃×C₈	—	7	2	no	—
215	C₂×C₃×C₇	—	2	1	no	—
216	C₂×C₃×C₇	—	4	1	no	—
217	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₃×D₇	—	2	1	no	—
219	C₃×D₇	—	4	1	no	—
220	C₃×D₇	#137	1	2	yes	direct product factor
221	C₂×#41	—	7	1	no	—
222	C₂²×Q₈	—	7	1	no	—
223	#137	—	7	1	no	—
224	#137	—	7	1	no	—
225	#137	—	7	2	no	—
226	#137	—	7	2	no	—
227	#137	—	7	1	no	—
228	#137	C₃×D₇	1	1	yes	characteristic, direct product factor
229	C₂×Q₁₆	—	7	2	no	—
230	C₂×SD₁₆	—	7	2	no	—
231	C₂×M₁₆	—	7	1	no	—
232	C₂²×C₇	—	2	1	no	—
233	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×D₇	—	2	2	no	—
235	C₂×D₇	—	2	1	no	—
236	C₂×D₇	—	4	2	no	—
237	C₂×D₇	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×D₇	C₂×C₃×D₄	1	1	yes	characteristic
239	C₄×C₇	—	2	2	no	—
240	C₄×C₇	—	2	1	no	—
241	C₄×C₇	C₂×C₃×D₄	1	1	yes	characteristic
242	C₄×C₇	C₂⁴×C₃	1	1	yes	characteristic
243	Dic₇	—	2	2	no	—
244	Dic₇	—	2	1	no	—
245	Dic₇	C₂×C₃×D₄	1	1	yes	characteristic
246	Dic₇	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂³×C₃	—	7	1	no	—
248	C₂³×C₃	—	14	1	no	—
249	C₃×Q₈	—	2	1	no	—
250	C₃×Q₈	—	7	2	no	—
251	C₃×Q₈	—	7	1	no	—
252	C₃×Q₈	—	14	2	no	—
253	C₃×Q₈	—	14	2	no	—
254	C₃×Q₈	—	14	1	no	—
255	C₃×Q₈	—	14	1	no	—
256	C₃×Q₈	C₂²×D₇	1	2	yes	—
257	C₃×Q₈	C₂²×D₇	1	1	yes	characteristic
258	C₃×D₄	—	2	1	no	—
259	C₃×D₄	—	7	1	no	—
260	C₃×D₄	—	14	1	no	—
261	C₃×D₄	—	14	1	no	—
262	C₃×D₄	—	14	1	no	—
263	C₃×D₄	—	14	1	no	—
264	C₃×D₄	C₂²×D₇	1	1	yes	characteristic
265	C₂×C₃×C₄	—	2	1	no	—
266	C₂×C₃×C₄	—	2	1	no	—
267	C₂×C₃×C₄	—	7	1	no	—
268	C₂×C₃×C₄	—	7	1	no	—
269	C₂×C₃×C₄	—	7	1	no	—
270	C₂×C₃×C₄	—	7	1	no	—
271	C₂×C₃×C₄	—	7	1	no	—
272	C₂×C₃×C₄	—	14	1	no	—
273	C₂×C₃×C₄	—	14	1	no	—
274	C₂×C₃×C₄	—	14	2	no	—
275	C₂×C₃×C₄	—	14	2	no	—
276	C₂×C₃×C₄	—	14	1	no	—
277	C₂×C₃×C₄	—	14	1	no	—
278	C₂×C₃×C₄	—	14	1	no	—
279	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
280	C₃×C₈	—	7	2	no	—
281	C₃×C₈	C₂²×D₇	1	2	yes	—
282	C₃×C₇	C₂×#137	1	1	yes	characteristic, complemented, Hall
283	#41	—	7	1	no	—
284	#41	—	7	1	no	—
285	#41	—	7	1	no	—
286	#41	—	14	1	no	—
287	#41	—	14	1	no	—
288	#41	C₂×C₃×D₇	1	1	yes	characteristic
289	C₂×Q₈	—	7	2	no	—
290	C₂×Q₈	—	7	1	no	—
291	C₂×Q₈	—	7	2	no	—
292	C₂×Q₈	—	7	1	no	—
293	C₂×Q₈	—	14	1	no	—
294	C₂×Q₈	—	14	1	no	—
295	C₂×Q₈	—	14	1	no	—
296	C₂×Q₈	C₂×C₃×D₇	1	1	yes	characteristic, complemented
297	C₂×D₄	—	7	1	no	—
298	C₂×D₄	—	14	1	no	—
299	C₂²×C₄	—	7	1	no	—
300	C₂²×C₄	—	14	1	no	—
301	C₂²×C₄	—	14	1	no	—
302	Q₁₆	—	7	2	no	—
303	Q₁₆	—	7	2	no	—
304	Q₁₆	—	7	2	no	—
305	Q₁₆	C₂×C₃×D₇	1	2	yes	complemented
306	SD₁₆	—	7	2	no	—
307	SD₁₆	—	7	2	no	—
308	SD₁₆	—	7	2	no	—
309	SD₁₆	C₂×C₃×D₇	1	2	yes	complemented
310	M₁₆	—	7	1	no	—
311	M₁₆	—	7	2	no	—
312	M₁₆	C₂×C₃×D₇	1	1	yes	characteristic, complemented
313	C₂×C₈	—	7	2	no	—
314	C₂×C₇	—	2	1	no	—
315	C₂×C₇	—	4	1	no	—
316	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
317	D₇	—	2	1	no	—
318	D₇	—	4	1	no	—
319	D₇	C₃×#137	1	2	yes	direct product factor
320	C₂²×C₃	—	2	1	no	—
321	C₂²×C₃	—	7	1	no	—
322	C₂²×C₃	—	7	1	no	—
323	C₂²×C₃	—	14	2	no	—
324	C₂²×C₃	—	14	1	no	—
325	C₂²×C₃	—	28	2	no	—
326	C₂²×C₃	D₄×D₇	1	1	yes	characteristic
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	2	no	—
329	C₃×C₄	—	7	1	no	—
330	C₃×C₄	—	7	1	no	—
331	C₃×C₄	—	14	1	no	—
332	C₃×C₄	—	14	2	no	—
333	C₃×C₄	D₄×D₇	1	1	yes	characteristic
334	C₃×C₄	C₂³×D₇	1	1	yes	characteristic
335	C₂³	—	7	1	no	—
336	C₂³	—	14	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	7	2	no	—
339	Q₈	—	7	1	no	—
340	Q₈	—	14	2	no	—
341	Q₈	—	14	2	no	—
342	Q₈	—	14	1	no	—
343	Q₈	—	14	1	no	—
344	Q₈	C₂²×C₃×D₇	1	2	yes	—
345	Q₈	C₂²×C₃×D₇	1	1	yes	characteristic
346	D₄	—	2	1	no	—
347	D₄	—	7	1	no	—
348	D₄	—	14	1	no	—
349	D₄	—	14	1	no	—
350	D₄	—	14	1	no	—
351	D₄	—	14	1	no	—
352	D₄	C₂²×C₃×D₇	1	1	yes	characteristic
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	7	1	no	—
356	C₂×C₄	—	7	1	no	—
357	C₂×C₄	—	7	1	no	—
358	C₂×C₄	—	7	1	no	—
359	C₂×C₄	—	7	1	no	—
360	C₂×C₄	—	14	1	no	—
361	C₂×C₄	—	14	1	no	—
362	C₂×C₄	—	14	2	no	—
363	C₂×C₄	—	14	2	no	—
364	C₂×C₄	—	14	1	no	—
365	C₂×C₄	—	14	1	no	—
366	C₂×C₄	—	14	1	no	—
367	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
368	C₈	—	7	2	no	—
369	C₈	C₂²×C₃×D₇	1	2	yes	—
370	C₇	C₂×C₃×#137	1	1	yes	characteristic, complemented, Sylow
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	4	1	no	—
373	C₂×C₃	—	7	2	no	—
374	C₂×C₃	—	14	1	no	—
375	C₂×C₃	—	28	1	no	—
376	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
377	C₂²	—	2	1	no	—
378	C₂²	—	7	1	no	—
379	C₂²	—	7	1	no	—
380	C₂²	—	14	2	no	—
381	C₂²	—	14	1	no	—
382	C₂²	—	28	2	no	—
383	C₂²	C₃×D₄×D₇	1	1	yes	characteristic
384	C₄	—	2	1	no	—
385	C₄	—	2	2	no	—
386	C₄	—	7	1	no	—
387	C₄	—	7	1	no	—
388	C₄	—	14	1	no	—
389	C₄	—	14	2	no	—
390	C₄	C₃×D₄×D₇	1	1	yes	characteristic
391	C₄	C₂³×C₃×D₇	1	1	yes	characteristic
392	C₃	D₇×#137	1	1	yes	characteristic, direct product factor, Sylow
393	C₂	—	2	1	no	—
394	C₂	—	4	1	no	—
395	C₂	—	7	2	no	—
396	C₂	—	14	1	no	—
397	C₂	—	28	1	no	—
398	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
prime radical	C₃×D₇×#41	C₂
hypercenter	C₃×#137	D₇
hypocenter	C₇	C₂×C₃×#137
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
2. C₂×C₃×Q₈×D₇	C₂	semidirect
3. C₃×C₇×#137	C₂	semidirect
4. C₃×#6514	C₂	semidirect
5. C₃×#6505	C₂	semidirect
6. C₃×#6481	C₂	semidirect
7. C₃×D₇×Q₁₆	C₂	semidirect
8. C₃×#6478	C₂	semidirect
9. C₃×D₇×SD₁₆	C₂	semidirect
10. C₃×#6472	C₂	semidirect
11. C₃×D₇×M₁₆	C₂	semidirect
12. D₇×#137	C₃	direct (N × H)
14. C₂×C₃×C₇×Q₈	C₂²	semidirect
20. C₃×Q₈×D₇	C₂²	semidirect
31. C₂×C₃×Dic₁₄	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×#1144	C₂²	semidirect
37. C₃×#1143	C₂²	semidirect
38. C₃×#1142	C₂²	semidirect
39. C₃×#1136	C₂²	semidirect
40. C₃×Dic₂₈	C₂²	semidirect
41. C₃×#1132	C₂²	semidirect
42. C₃×#1131	C₂²	semidirect
45. C₂×Q₈×D₇	C₂×C₃	semidirect
46. C₇×#137	C₂×C₃	semidirect
47. #6514	C₂×C₃	semidirect
48. #6505	C₂×C₃	semidirect
49. #6481	C₂×C₃	semidirect
50. D₇×Q₁₆	C₂×C₃	semidirect
51. #6478	C₂×C₃	semidirect
52. D₇×SD₁₆	C₂×C₃	semidirect
53. #6472	C₂×C₃	semidirect
54. D₇×M₁₆	C₂×C₃	semidirect
92. C₂×C₇×Q₈	C₂²×C₃	semidirect
98. Q₈×D₇	C₂²×C₃	semidirect
109. C₂×Dic₁₄	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. #1144	C₂²×C₃	semidirect
115. #1143	C₂²×C₃	semidirect
116. #1142	C₂²×C₃	semidirect
117. #1136	C₂²×C₃	semidirect
118. Dic₂₈	C₂²×C₃	semidirect
119. #1132	C₂²×C₃	semidirect
120. #1131	C₂²×C₃	semidirect
129. C₃×#137	D₇	direct (N × H)
197. C₂×C₃×Q₈	C₂×D₇	semidirect
206. C₃×Q₁₆	C₂×D₇	semidirect
210. C₃×SD₁₆	C₂×D₇	semidirect
213. C₃×M₁₆	C₂×D₇	semidirect
220. C₃×D₇	#137	direct (N × H)
228. #137	C₃×D₇	direct (N × H)
282. C₃×C₇	C₂×#137	semidirect
296. C₂×Q₈	C₂×C₃×D₇	semidirect
305. Q₁₆	C₂×C₃×D₇	semidirect
309. SD₁₆	C₂×C₃×D₇	semidirect
312. M₁₆	C₂×C₃×D₇	semidirect
319. D₇	C₃×#137	direct (N × H)
370. C₇	C₂×C₃×#137	semidirect
392. C₃	D₇×#137	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×Q₈×D₇	2
C₃×C₇×#137	2
C₃×#6514	2
C₃×#6505	2
C₃×#6481	2
C₃×D₇×Q₁₆	2
C₃×#6478	2
C₃×D₇×SD₁₆	2
C₃×#6472	2
C₃×D₇×M₁₆	2
D₇×#137	3
C₂×C₃×#137	7

Subgroups — C3×D7×#137 #13061118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×#137 #13061118