Subgroups — C₃×D₇×#123 #13060998

Order 1344.

684 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6457	C₂	1	2	yes	maximal, complemented
7	C₃×D₇×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₃×#6449	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#6446	C₂	1	2	yes	maximal, complemented
10	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	D₇×#123	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
14	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
19	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
20	C₃×D₄×D₇	—	2	4	no	—
21	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×D₇	—	2	4	no	—
23	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
24	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
25	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄×D₇	C₂²	1	2	yes	complemented
27	C₃×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
28	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
29	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
31	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
33	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
35	C₃×C₄⋊Dic₇	C₂²	1	2	yes	complemented
36	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
37	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
38	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic
39	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
40	C₇×#123	C₂×C₃	1	1	yes	characteristic, complemented
41	#6498	C₂×C₃	1	1	yes	characteristic, complemented
42	#6492	C₂×C₃	1	1	yes	characteristic, complemented
43	#6457	C₂×C₃	1	2	yes	complemented
44	D₇×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
45	#6449	C₂×C₃	1	1	yes	characteristic, complemented
46	#6446	C₂×C₃	1	2	yes	complemented
47	D₇×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
49	C₂×C₃×#123	—	7	1	no	maximal, Hall
50	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
51	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
52	C₂²×C₃×D₇	—	2	4	no	—
53	C₂²×C₃×D₇	—	2	2	no	—
54	C₂²×C₃×D₇	—	2	4	no	—
55	C₂²×C₃×D₇	D₄	1	4	yes	—
56	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
57	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
58	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
59	C₃×C₇×D₄	—	2	2	no	—
60	C₂×C₃×C₄×C₇	—	2	2	no	—
61	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
63	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
64	C₃×C₂²⋊D₇	—	2	2	no	—
65	C₃×C₂²⋊D₇	—	2	2	no	—
66	C₂×C₃×Dic₇	—	2	2	no	—
67	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
68	C₂×C₃×Dic₇	C₂³	1	2	yes	—
69	C₂×C₃×Dic₇	C₂³	1	2	yes	—
70	C₃×D₂₈	—	2	2	no	—
71	C₃×C₄×D₇	—	2	4	no	—
72	C₃×C₄×D₇	—	2	4	no	—
73	C₃×C₄×D₇	—	2	2	no	—
74	C₃×C₄×D₇	—	2	4	no	—
75	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
76	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
79	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
81	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
82	D₄×D₇	—	2	4	no	—
83	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄×D₇	—	2	4	no	—
85	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
86	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
87	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄×D₇	C₂²×C₃	1	2	yes	complemented
89	C₇×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
90	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
91	C₇×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
93	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
94	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
95	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
96	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
97	C₄⋊Dic₇	C₂²×C₃	1	2	yes	complemented
98	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
99	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
100	C₂²×C₃×D₄	—	7	1	no	—
101	C₂³×C₃×C₄	—	7	1	no	—
102	C₃×#123	—	7	1	no	—
103	C₃×#123	—	7	1	no	—
104	C₃×#123	—	7	2	no	—
105	C₃×#123	—	7	2	no	—
106	C₃×#123	—	7	1	no	—
107	C₃×#123	D₇	1	1	yes	characteristic, direct product factor
108	C₂×C₃×C₄⋊C₄	—	7	2	no	—
109	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
110	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
111	C₂²×C₃×C₇	—	2	2	no	—
112	C₂²×C₃×C₇	—	2	1	no	—
113	C₂²×C₃×C₇	—	2	2	no	—
114	C₂²×C₃×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₃×D₇	—	2	2	no	—
117	C₂×C₃×D₇	—	2	8	no	—
118	C₂×C₃×D₇	—	2	1	no	—
119	C₂×C₃×D₇	—	2	2	no	—
120	C₂×C₃×D₇	—	4	4	no	—
121	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
122	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
123	C₂×C₃×D₇	#41	1	4	yes	—
124	C₃×C₄×C₇	—	2	2	no	—
125	C₃×C₄×C₇	—	2	1	no	—
126	C₃×C₄×C₇	—	2	2	no	—
127	C₃×Dic₇	—	2	2	no	—
128	C₃×Dic₇	—	2	1	no	—
129	C₃×Dic₇	—	2	2	no	—
130	C₂×#123	—	7	1	no	Sylow
131	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
132	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
133	C₂²×D₇	—	2	4	no	—
134	C₂²×D₇	—	2	2	no	—
135	C₂²×D₇	—	2	4	no	—
136	C₂²×D₇	C₃×D₄	1	4	yes	—
137	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
138	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
139	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
140	C₇×D₄	—	2	2	no	—
141	C₂×C₄×C₇	—	2	2	no	—
142	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
144	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
145	C₂²⋊D₇	—	2	2	no	—
146	C₂²⋊D₇	—	2	2	no	—
147	C₂×Dic₇	—	2	2	no	—
148	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
149	C₂×Dic₇	C₂³×C₃	1	2	yes	—
150	C₂×Dic₇	C₂³×C₃	1	2	yes	—
151	D₂₈	—	2	2	no	—
152	C₄×D₇	—	2	4	no	—
153	C₄×D₇	—	2	4	no	—
154	C₄×D₇	—	2	2	no	—
155	C₄×D₇	—	2	4	no	—
156	C₂⁴×C₃	—	7	1	no	—
157	C₂⁴×C₃	—	7	1	no	—
158	C₂×C₃×D₄	—	7	1	no	—
159	C₂×C₃×D₄	—	7	1	no	—
160	C₂×C₃×D₄	—	7	1	no	—
161	C₂×C₃×D₄	—	14	4	no	—
162	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
163	C₂²×C₃×C₄	—	7	1	no	—
164	C₂²×C₃×C₄	—	7	2	no	—
165	C₂²×C₃×C₄	—	7	2	no	—
166	C₂²×C₃×C₄	—	7	1	no	—
167	C₂²×C₃×C₄	—	7	2	no	—
168	C₂²×C₃×C₄	—	14	4	no	—
169	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
170	C₃×C₄⋊C₄	—	7	2	no	—
171	C₃×C₄⋊C₄	—	7	2	no	—
172	C₃×C₄⋊C₄	—	7	2	no	—
173	C₃×C₄⋊C₄	C₂×D₇	1	2	yes	complemented
174	C₃×C₂²⋊C₄	—	7	1	no	—
175	C₃×C₂²⋊C₄	—	7	2	no	—
176	C₃×C₂²⋊C₄	—	7	2	no	—
177	C₃×C₂²⋊C₄	—	7	2	no	—
178	C₃×C₂²⋊C₄	—	7	2	no	—
179	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
180	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
181	C₂×C₃×C₇	—	2	2	no	—
182	C₂×C₃×C₇	—	4	1	no	—
183	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₃×C₇	C₂×#41	1	2	yes	—
185	C₃×D₇	—	2	2	no	—
186	C₃×D₇	—	4	1	no	—
187	C₃×D₇	#123	1	4	yes	direct product factor
188	C₂²×D₄	—	7	1	no	—
189	C₂³×C₄	—	7	1	no	—
190	#123	—	7	1	no	—
191	#123	—	7	1	no	—
192	#123	—	7	2	no	—
193	#123	—	7	2	no	—
194	#123	—	7	1	no	—
195	#123	C₃×D₇	1	1	yes	characteristic, direct product factor
196	C₂×C₄⋊C₄	—	7	2	no	—
197	C₂×C₂²⋊C₄	—	7	1	no	—
198	C₂×C₂²⋊C₄	—	7	2	no	—
199	C₂²×C₇	—	2	2	no	—
200	C₂²×C₇	—	2	1	no	—
201	C₂²×C₇	—	2	2	no	—
202	C₂²×C₇	C₂×C₃×D₄	1	2	yes	—
203	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
204	C₂×D₇	—	2	2	no	—
205	C₂×D₇	—	2	8	no	—
206	C₂×D₇	—	2	1	no	—
207	C₂×D₇	—	2	2	no	—
208	C₂×D₇	—	4	4	no	—
209	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
210	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
211	C₂×D₇	C₃×#41	1	4	yes	—
212	C₄×C₇	—	2	2	no	—
213	C₄×C₇	—	2	1	no	—
214	C₄×C₇	—	2	2	no	—
215	Dic₇	—	2	2	no	—
216	Dic₇	—	2	1	no	—
217	Dic₇	—	2	2	no	—
218	C₂³×C₃	—	7	1	no	—
219	C₂³×C₃	—	7	4	no	—
220	C₂³×C₃	—	7	1	no	—
221	C₂³×C₃	—	7	1	no	—
222	C₂³×C₃	—	14	4	no	—
223	C₂³×C₃	—	14	2	no	—
224	C₂³×C₃	—	14	4	no	—
225	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
226	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
227	C₃×D₄	—	2	2	no	—
228	C₃×D₄	—	14	2	no	—
229	C₃×D₄	—	14	2	no	—
230	C₃×D₄	—	14	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	7	2	no	—
233	C₂×C₃×C₄	—	7	2	no	—
234	C₂×C₃×C₄	—	7	1	no	—
235	C₂×C₃×C₄	—	14	4	no	—
236	C₂×C₃×C₄	—	14	4	no	—
237	C₂×C₃×C₄	—	14	4	no	—
238	C₂×C₃×C₄	—	14	2	no	—
239	C₂×C₃×C₄	—	14	2	no	—
240	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
241	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
242	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
243	C₃×C₇	C₂×#123	1	1	yes	characteristic, complemented, Hall
244	C₂⁴	—	7	1	no	—
245	C₂⁴	—	7	1	no	—
246	C₂×D₄	—	7	1	no	—
247	C₂×D₄	—	7	1	no	—
248	C₂×D₄	—	7	1	no	—
249	C₂×D₄	—	14	4	no	—
250	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
251	C₂²×C₄	—	7	1	no	—
252	C₂²×C₄	—	7	2	no	—
253	C₂²×C₄	—	7	2	no	—
254	C₂²×C₄	—	7	1	no	—
255	C₂²×C₄	—	7	2	no	—
256	C₂²×C₄	—	14	4	no	—
257	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
258	C₄⋊C₄	—	7	2	no	—
259	C₄⋊C₄	—	7	2	no	—
260	C₄⋊C₄	—	7	2	no	—
261	C₄⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
262	C₂²⋊C₄	—	7	1	no	—
263	C₂²⋊C₄	—	7	2	no	—
264	C₂²⋊C₄	—	7	2	no	—
265	C₂²⋊C₄	—	7	2	no	—
266	C₂²⋊C₄	—	7	2	no	—
267	C₂²⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
268	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
269	C₂×C₇	—	2	2	no	—
270	C₂×C₇	—	4	1	no	—
271	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₂×C₇	C₂×C₃×#41	1	2	yes	—
273	D₇	—	2	2	no	—
274	D₇	—	4	1	no	—
275	D₇	C₃×#123	1	4	yes	direct product factor
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	7	2	no	—
280	C₂²×C₃	—	7	4	no	—
281	C₂²×C₃	—	7	2	no	—
282	C₂²×C₃	—	14	8	no	—
283	C₂²×C₃	—	14	2	no	—
284	C₂²×C₃	—	14	1	no	—
285	C₂²×C₃	—	14	2	no	—
286	C₂²×C₃	—	28	4	no	—
287	C₂²×C₃	D₄×D₇	1	2	yes	—
288	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	1	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	14	2	no	—
293	C₃×C₄	—	14	1	no	—
294	C₃×C₄	—	14	2	no	—
295	C₂³	—	7	1	no	—
296	C₂³	—	7	4	no	—
297	C₂³	—	7	1	no	—
298	C₂³	—	7	1	no	—
299	C₂³	—	14	4	no	—
300	C₂³	—	14	2	no	—
301	C₂³	—	14	4	no	—
302	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
303	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
304	D₄	—	2	2	no	—
305	D₄	—	14	2	no	—
306	D₄	—	14	2	no	—
307	D₄	—	14	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	7	2	no	—
310	C₂×C₄	—	7	2	no	—
311	C₂×C₄	—	7	1	no	—
312	C₂×C₄	—	14	4	no	—
313	C₂×C₄	—	14	4	no	—
314	C₂×C₄	—	14	2	no	—
315	C₂×C₄	—	14	4	no	—
316	C₂×C₄	—	14	2	no	—
317	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
318	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
319	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
320	C₇	C₂×C₃×#123	1	1	yes	characteristic, complemented, Sylow
321	C₂×C₃	—	2	2	no	—
322	C₂×C₃	—	4	1	no	—
323	C₂×C₃	—	7	4	no	—
324	C₂×C₃	—	14	2	no	—
325	C₂×C₃	—	28	1	no	—
326	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
327	C₂×C₃	D₇×#41	1	2	yes	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	7	2	no	—
332	C₂²	—	7	4	no	—
333	C₂²	—	7	2	no	—
334	C₂²	—	14	8	no	—
335	C₂²	—	14	2	no	—
336	C₂²	—	14	1	no	—
337	C₂²	—	14	2	no	—
338	C₂²	—	28	4	no	—
339	C₂²	C₃×D₄×D₇	1	2	yes	—
340	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	2	no	—
344	C₄	—	14	2	no	—
345	C₄	—	14	1	no	—
346	C₄	—	14	2	no	—
347	C₃	D₇×#123	1	1	yes	characteristic, direct product factor, Sylow
348	C₂	—	2	2	no	—
349	C₂	—	4	1	no	—
350	C₂	—	7	4	no	—
351	C₂	—	14	2	no	—
352	C₂	—	28	1	no	—
353	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
354	C₂	C₃×D₇×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×#123	C₂
socle	C₂²×C₃×C₇	C₂⁴
prime radical	C₂×C₃×D₄×D₇	C₂
hypercenter	C₃×#123	D₇
hypocenter	C₇	C₂×C₃×#123
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄×D₇	C₂	semidirect
3. C₃×C₇×#123	C₂	semidirect
4. C₃×#6498	C₂	semidirect
5. C₃×#6492	C₂	semidirect
6. C₃×#6457	C₂	semidirect
7. C₃×D₇×C₄⋊C₄	C₂	semidirect
8. C₃×#6449	C₂	semidirect
9. C₃×#6446	C₂	semidirect
10. C₃×D₇×C₂²⋊C₄	C₂	semidirect
11. C₃×D₇×C₂²⋊C₄	C₂	semidirect
12. D₇×#123	C₃	direct (N × H)
16. C₂²×C₃×C₄×C₇	C₂²	semidirect
19. C₂²×C₃×Dic₇	C₂²	semidirect
26. C₂×C₃×C₄×D₇	C₂²	semidirect
27. C₃×C₇×C₄⋊C₄	C₂²	semidirect
28. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
29. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
30. C₃×C₂²⋊Dic₇	C₂²	semidirect
31. C₃×C₂²⋊Dic₇	C₂²	semidirect
32. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
33. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×C₄⋊Dic₇	C₂²	semidirect
36. C₃×Dic₇⋊C₄	C₂²	semidirect
37. C₃×Dic₇⋊C₄	C₂²	semidirect
39. C₂²×C₄×D₇	C₂×C₃	semidirect
40. C₇×#123	C₂×C₃	semidirect
41. #6498	C₂×C₃	semidirect
42. #6492	C₂×C₃	semidirect
43. #6457	C₂×C₃	semidirect
44. D₇×C₄⋊C₄	C₂×C₃	semidirect
45. #6449	C₂×C₃	semidirect
46. #6446	C₂×C₃	semidirect
47. D₇×C₂²⋊C₄	C₂×C₃	semidirect
48. D₇×C₂²⋊C₄	C₂×C₃	semidirect
78. C₂²×C₄×C₇	C₂²×C₃	semidirect
81. C₂²×Dic₇	C₂²×C₃	semidirect
88. C₂×C₄×D₇	C₂²×C₃	semidirect
89. C₇×C₄⋊C₄	C₂²×C₃	semidirect
90. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
91. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
92. C₂²⋊Dic₇	C₂²×C₃	semidirect
93. C₂²⋊Dic₇	C₂²×C₃	semidirect
94. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
95. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
96. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
97. C₄⋊Dic₇	C₂²×C₃	semidirect
98. Dic₇⋊C₄	C₂²×C₃	semidirect
99. Dic₇⋊C₄	C₂²×C₃	semidirect
107. C₃×#123	D₇	direct (N × H)
169. C₂²×C₃×C₄	C₂×D₇	semidirect
173. C₃×C₄⋊C₄	C₂×D₇	semidirect
179. C₃×C₂²⋊C₄	C₂×D₇	semidirect
180. C₃×C₂²⋊C₄	C₂×D₇	semidirect
187. C₃×D₇	#123	direct (N × H)
195. #123	C₃×D₇	direct (N × H)
243. C₃×C₇	C₂×#123	semidirect
257. C₂²×C₄	C₂×C₃×D₇	semidirect
261. C₄⋊C₄	C₂×C₃×D₇	semidirect
267. C₂²⋊C₄	C₂×C₃×D₇	semidirect
268. C₂²⋊C₄	C₂×C₃×D₇	semidirect
275. D₇	C₃×#123	direct (N × H)
320. C₇	C₂×C₃×#123	semidirect
347. C₃	D₇×#123	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×C₃×D₄×D₇	2
C₂²×C₃×C₄×D₇	2
C₃×C₇×#123	2
C₃×#6498	2
C₃×#6492	2
C₃×#6457	2
C₃×D₇×C₄⋊C₄	2
C₃×#6449	2
C₃×#6446	2
C₃×D₇×C₂²⋊C₄	2
D₇×#123	3
C₂×C₃×#123	7

Subgroups — C3×D7×#123 #13060998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×#123 #13060998