Subgroups — C₃×D₇×#121 #13060948

Order 1344.

852 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	C₂×C₃×D₄×D₇	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#6502	C₂	1	2	yes	maximal, complemented
6	C₃×#6501	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6447	C₂	1	2	yes	maximal, complemented
11	C₃×D₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
12	D₇×#121	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×D₇	C₂²	1	2	yes	—
14	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
19	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
20	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
21	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
22	C₃×D₄×D₇	—	2	8	no	—
23	C₃×D₄×D₇	—	2	4	no	—
24	C₂×C₃×D₂₈	C₂²	1	2	yes	complemented
25	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄×D₇	—	2	4	no	—
27	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄×D₇	C₂²	1	2	yes	—
29	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
36	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
37	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
38	C₃×Dic₇⋊C₄	C₂²	1	2	yes	complemented
39	C₂×D₄×D₇	C₂×C₃	1	2	yes	complemented
40	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂²×C₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
42	C₇×#121	C₂×C₃	1	1	yes	characteristic, complemented
43	#6502	C₂×C₃	1	2	yes	complemented
44	#6501	C₂×C₃	1	1	yes	characteristic, complemented
45	#6493	C₂×C₃	1	1	yes	characteristic, complemented
46	#6458	C₂×C₃	1	1	yes	characteristic, complemented
47	D₇×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
48	#6447	C₂×C₃	1	2	yes	complemented
49	D₇×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
50	C₂×C₃×#121	—	7	1	no	maximal, Hall
51	C₂³×C₃×C₇	C₂³	1	2	yes	—
52	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
53	C₂²×C₃×D₇	—	2	2	no	—
54	C₂²×C₃×D₇	—	2	2	no	—
55	C₂²×C₃×D₇	—	2	4	no	—
56	C₂²×C₃×D₇	—	2	4	no	—
57	C₂²×C₃×D₇	—	2	4	no	—
58	C₂²×C₃×D₇	D₄	1	4	yes	complemented
59	C₂²×C₃×D₇	C₂³	1	2	yes	—
60	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
61	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
62	C₃×C₇×D₄	—	2	4	no	—
63	C₃×C₇×D₄	—	2	2	no	—
64	C₂×C₃×C₄×C₇	—	2	2	no	—
65	C₂×C₃×C₄×C₇	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₃×C₂²⋊D₇	—	2	4	no	—
69	C₃×C₂²⋊D₇	—	2	4	no	—
70	C₃×C₂²⋊D₇	—	2	4	no	—
71	C₂×C₃×Dic₇	—	2	2	no	—
72	C₂×C₃×Dic₇	C₂³	1	2	yes	—
73	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
75	C₃×D₂₈	—	2	4	no	—
76	C₃×D₂₈	—	2	2	no	—
77	C₃×C₄×D₇	—	2	2	no	—
78	C₃×C₄×D₇	—	2	4	no	—
79	C₃×C₄×D₇	—	2	2	no	—
80	C₃×C₄×D₇	—	2	2	no	—
81	C₃×C₄×D₇	D₄	1	4	yes	complemented
82	C₂³×D₇	C₂²×C₃	1	2	yes	—
83	C₂³×D₇	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
85	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
86	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
88	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
89	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
90	C₂²×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
91	D₄×D₇	—	2	8	no	—
92	D₄×D₇	—	2	4	no	—
93	C₂×D₂₈	C₂²×C₃	1	2	yes	complemented
94	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×C₄×D₇	—	2	4	no	—
96	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄×D₇	C₂²×C₃	1	2	yes	—
98	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₇×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₇×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
103	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
104	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
105	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
106	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
107	Dic₇⋊C₄	C₂²×C₃	1	2	yes	complemented
108	C₂²×C₃×D₄	—	7	1	no	—
109	C₂²×C₃×D₄	—	7	2	no	—
110	C₂³×C₃×C₄	—	7	1	no	—
111	C₃×#121	—	7	1	no	—
112	C₃×#121	—	7	2	no	—
113	C₃×#121	—	7	1	no	—
114	C₃×#121	—	7	1	no	—
115	C₃×#121	—	7	2	no	—
116	C₃×#121	D₇	1	1	yes	characteristic, direct product factor
117	C₂×C₃×C₄⋊C₄	—	7	1	no	—
118	C₂×C₃×C₂²⋊C₄	—	7	2	no	—
119	C₂²×C₃×C₇	—	2	1	no	—
120	C₂²×C₃×C₇	—	2	1	no	—
121	C₂²×C₃×C₇	—	2	2	no	—
122	C₂²×C₃×C₇	—	2	2	no	—
123	C₂²×C₃×C₇	—	2	2	no	—
124	C₂²×C₃×C₇	C₂×D₄	1	2	yes	complemented
125	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
126	C₂×C₃×D₇	—	2	1	no	—
127	C₂×C₃×D₇	—	2	1	no	—
128	C₂×C₃×D₇	—	2	8	no	—
129	C₂×C₃×D₇	—	2	2	no	—
130	C₂×C₃×D₇	—	2	2	no	—
131	C₂×C₃×D₇	—	2	2	no	—
132	C₂×C₃×D₇	—	4	8	no	—
133	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
134	C₂×C₃×D₇	C₂×D₄	1	2	yes	—
135	C₂×C₃×D₇	C₂×D₄	1	2	yes	complemented
136	C₂×C₃×D₇	#41	1	2	yes	—
137	C₃×C₄×C₇	—	2	1	no	—
138	C₃×C₄×C₇	—	2	2	no	—
139	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
140	C₃×Dic₇	—	2	1	no	—
141	C₃×Dic₇	—	2	2	no	—
142	C₃×Dic₇	C₂×D₄	1	2	yes	complemented
143	C₂×#121	—	7	1	no	Sylow
144	C₂³×C₇	C₂³×C₃	1	2	yes	—
145	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
146	C₂²×D₇	—	2	2	no	—
147	C₂²×D₇	—	2	2	no	—
148	C₂²×D₇	—	2	4	no	—
149	C₂²×D₇	—	2	4	no	—
150	C₂²×D₇	—	2	4	no	—
151	C₂²×D₇	C₃×D₄	1	4	yes	complemented
152	C₂²×D₇	C₂³×C₃	1	2	yes	—
153	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
154	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
155	C₇×D₄	—	2	4	no	—
156	C₇×D₄	—	2	2	no	—
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	C₂³×C₃	1	2	yes	—
159	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
161	C₂²⋊D₇	—	2	4	no	—
162	C₂²⋊D₇	—	2	4	no	—
163	C₂²⋊D₇	—	2	4	no	—
164	C₂×Dic₇	—	2	2	no	—
165	C₂×Dic₇	C₂³×C₃	1	2	yes	—
166	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
167	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
168	D₂₈	—	2	4	no	—
169	D₂₈	—	2	2	no	—
170	C₄×D₇	—	2	2	no	—
171	C₄×D₇	—	2	4	no	—
172	C₄×D₇	—	2	2	no	—
173	C₄×D₇	—	2	2	no	—
174	C₄×D₇	C₃×D₄	1	4	yes	complemented
175	C₂⁴×C₃	—	7	1	no	—
176	C₂⁴×C₃	—	7	2	no	—
177	C₂×C₃×D₄	—	7	2	no	—
178	C₂×C₃×D₄	—	7	2	no	—
179	C₂×C₃×D₄	—	7	2	no	—
180	C₂×C₃×D₄	—	7	2	no	—
181	C₂×C₃×D₄	—	7	1	no	—
182	C₂×C₃×D₄	—	14	4	no	—
183	C₂×C₃×D₄	—	14	8	no	—
184	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
185	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
186	C₂²×C₃×C₄	—	7	1	no	—
187	C₂²×C₃×C₄	—	7	1	no	—
188	C₂²×C₃×C₄	—	7	1	no	—
189	C₂²×C₃×C₄	—	7	2	no	—
190	C₂²×C₃×C₄	—	7	1	no	—
191	C₂²×C₃×C₄	—	7	1	no	—
192	C₂²×C₃×C₄	—	14	4	no	—
193	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
194	C₃×C₄⋊C₄	—	7	2	no	—
195	C₃×C₄⋊C₄	—	7	1	no	—
196	C₃×C₄⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
197	C₃×C₂²⋊C₄	—	7	2	no	—
198	C₃×C₂²⋊C₄	—	7	2	no	—
199	C₃×C₂²⋊C₄	—	7	2	no	—
200	C₃×C₂²⋊C₄	C₂×D₇	1	2	yes	complemented
201	C₂×C₃×C₇	—	2	2	no	—
202	C₂×C₃×C₇	—	4	2	no	—
203	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
206	C₃×D₇	—	2	2	no	—
207	C₃×D₇	—	4	2	no	—
208	C₃×D₇	#121	1	4	yes	direct product factor
209	C₂²×D₄	—	7	1	no	—
210	C₂²×D₄	—	7	2	no	—
211	C₂³×C₄	—	7	1	no	—
212	#121	—	7	1	no	—
213	#121	—	7	2	no	—
214	#121	—	7	1	no	—
215	#121	—	7	1	no	—
216	#121	—	7	2	no	—
217	#121	C₃×D₇	1	1	yes	characteristic, direct product factor
218	C₂×C₄⋊C₄	—	7	1	no	—
219	C₂×C₂²⋊C₄	—	7	2	no	—
220	C₂²×C₇	—	2	1	no	—
221	C₂²×C₇	—	2	1	no	—
222	C₂²×C₇	—	2	2	no	—
223	C₂²×C₇	—	2	2	no	—
224	C₂²×C₇	—	2	2	no	—
225	C₂²×C₇	C₂×C₃×D₄	1	2	yes	complemented
226	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
227	C₂×D₇	—	2	1	no	—
228	C₂×D₇	—	2	1	no	—
229	C₂×D₇	—	2	8	no	—
230	C₂×D₇	—	2	2	no	—
231	C₂×D₇	—	2	2	no	—
232	C₂×D₇	—	2	2	no	—
233	C₂×D₇	—	4	8	no	—
234	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
235	C₂×D₇	C₂×C₃×D₄	1	2	yes	—
236	C₂×D₇	C₂×C₃×D₄	1	2	yes	complemented
237	C₂×D₇	C₃×#41	1	2	yes	—
238	C₄×C₇	—	2	1	no	—
239	C₄×C₇	—	2	2	no	—
240	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
241	Dic₇	—	2	1	no	—
242	Dic₇	—	2	2	no	—
243	Dic₇	C₂×C₃×D₄	1	2	yes	complemented
244	C₂³×C₃	—	7	1	no	—
245	C₂³×C₃	—	7	4	no	—
246	C₂³×C₃	—	7	1	no	—
247	C₂³×C₃	—	7	2	no	—
248	C₂³×C₃	—	14	2	no	—
249	C₂³×C₃	—	14	2	no	—
250	C₂³×C₃	—	14	4	no	—
251	C₂³×C₃	—	14	4	no	—
252	C₂³×C₃	—	14	4	no	—
253	C₂³×C₃	C₂²×D₇	1	2	yes	—
254	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
255	C₃×D₄	—	2	4	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	14	4	no	—
258	C₃×D₄	—	14	4	no	—
259	C₃×D₄	—	14	4	no	—
260	C₃×D₄	—	14	4	no	—
261	C₃×D₄	—	14	2	no	—
262	C₂×C₃×C₄	—	2	2	no	—
263	C₂×C₃×C₄	—	7	1	no	—
264	C₂×C₃×C₄	—	7	4	no	—
265	C₂×C₃×C₄	—	7	1	no	—
266	C₂×C₃×C₄	—	7	2	no	—
267	C₂×C₃×C₄	—	14	2	no	—
268	C₂×C₃×C₄	—	14	2	no	—
269	C₂×C₃×C₄	—	14	4	no	—
270	C₂×C₃×C₄	—	14	2	no	—
271	C₂×C₃×C₄	—	14	2	no	—
272	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂²×D₇	1	2	yes	—
274	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
275	C₃×C₇	C₂×#121	1	1	yes	characteristic, complemented, Hall
276	C₂⁴	—	7	1	no	—
277	C₂⁴	—	7	2	no	—
278	C₂×D₄	—	7	2	no	—
279	C₂×D₄	—	7	2	no	—
280	C₂×D₄	—	7	2	no	—
281	C₂×D₄	—	7	2	no	—
282	C₂×D₄	—	7	1	no	—
283	C₂×D₄	—	14	4	no	—
284	C₂×D₄	—	14	8	no	—
285	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
286	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
287	C₂²×C₄	—	7	1	no	—
288	C₂²×C₄	—	7	1	no	—
289	C₂²×C₄	—	7	1	no	—
290	C₂²×C₄	—	7	2	no	—
291	C₂²×C₄	—	7	1	no	—
292	C₂²×C₄	—	7	1	no	—
293	C₂²×C₄	—	14	4	no	—
294	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
295	C₄⋊C₄	—	7	2	no	—
296	C₄⋊C₄	—	7	1	no	—
297	C₄⋊C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
298	C₂²⋊C₄	—	7	2	no	—
299	C₂²⋊C₄	—	7	2	no	—
300	C₂²⋊C₄	—	7	2	no	—
301	C₂²⋊C₄	C₂×C₃×D₇	1	2	yes	complemented
302	C₂×C₇	—	2	2	no	—
303	C₂×C₇	—	4	2	no	—
304	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
305	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
306	C₂×C₇	C₂×C₃×#41	1	1	yes	characteristic
307	D₇	—	2	2	no	—
308	D₇	—	4	2	no	—
309	D₇	C₃×#121	1	4	yes	direct product factor
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	2	2	no	—
315	C₂²×C₃	—	7	2	no	—
316	C₂²×C₃	—	7	2	no	—
317	C₂²×C₃	—	7	2	no	—
318	C₂²×C₃	—	7	2	no	—
319	C₂²×C₃	—	14	8	no	—
320	C₂²×C₃	—	14	1	no	—
321	C₂²×C₃	—	14	1	no	—
322	C₂²×C₃	—	14	2	no	—
323	C₂²×C₃	—	14	2	no	—
324	C₂²×C₃	—	14	2	no	—
325	C₂²×C₃	—	28	8	no	—
326	C₂²×C₃	D₄×D₇	1	2	yes	complemented
327	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	2	2	no	—
330	C₃×C₄	—	7	2	no	—
331	C₃×C₄	—	14	1	no	—
332	C₃×C₄	—	14	2	no	—
333	C₃×C₄	D₄×D₇	1	2	yes	complemented
334	C₂³	—	7	1	no	—
335	C₂³	—	7	4	no	—
336	C₂³	—	7	1	no	—
337	C₂³	—	7	2	no	—
338	C₂³	—	14	2	no	—
339	C₂³	—	14	2	no	—
340	C₂³	—	14	4	no	—
341	C₂³	—	14	4	no	—
342	C₂³	—	14	4	no	—
343	C₂³	C₂²×C₃×D₇	1	2	yes	—
344	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
345	D₄	—	2	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	14	4	no	—
348	D₄	—	14	4	no	—
349	D₄	—	14	4	no	—
350	D₄	—	14	4	no	—
351	D₄	—	14	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	7	1	no	—
354	C₂×C₄	—	7	4	no	—
355	C₂×C₄	—	7	1	no	—
356	C₂×C₄	—	7	2	no	—
357	C₂×C₄	—	14	2	no	—
358	C₂×C₄	—	14	2	no	—
359	C₂×C₄	—	14	4	no	—
360	C₂×C₄	—	14	2	no	—
361	C₂×C₄	—	14	2	no	—
362	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₃×D₇	1	2	yes	—
364	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
365	C₇	C₂×C₃×#121	1	1	yes	characteristic, complemented, Sylow
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	4	2	no	—
368	C₂×C₃	—	7	4	no	—
369	C₂×C₃	—	14	2	no	—
370	C₂×C₃	—	28	2	no	—
371	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
372	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
373	C₂×C₃	D₇×#41	1	1	yes	characteristic
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	7	2	no	—
380	C₂²	—	7	2	no	—
381	C₂²	—	7	2	no	—
382	C₂²	—	7	2	no	—
383	C₂²	—	14	8	no	—
384	C₂²	—	14	1	no	—
385	C₂²	—	14	1	no	—
386	C₂²	—	14	2	no	—
387	C₂²	—	14	2	no	—
388	C₂²	—	14	2	no	—
389	C₂²	—	28	8	no	—
390	C₂²	C₃×D₄×D₇	1	2	yes	complemented
391	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	7	2	no	—
395	C₄	—	14	1	no	—
396	C₄	—	14	2	no	—
397	C₄	C₃×D₄×D₇	1	2	yes	complemented
398	C₃	D₇×#121	1	1	yes	characteristic, direct product factor, Sylow
399	C₂	—	2	2	no	—
400	C₂	—	4	2	no	—
401	C₂	—	7	4	no	—
402	C₂	—	14	2	no	—
403	C₂	—	28	2	no	—
404	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
405	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
406	C₂	C₃×D₇×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₃×C₇×#121	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₃×#121	D₇
hypocenter	C₇	C₂×C₃×#121
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₄×D₇	C₂	semidirect
2. C₂×C₃×D₄×D₇	C₂	semidirect
3. C₂²×C₃×C₄×D₇	C₂	semidirect
4. C₃×C₇×#121	C₂	semidirect
5. C₃×#6502	C₂	semidirect
6. C₃×#6501	C₂	semidirect
7. C₃×#6493	C₂	semidirect
8. C₃×#6458	C₂	semidirect
9. C₃×D₇×C₄⋊C₄	C₂	semidirect
10. C₃×#6447	C₂	semidirect
11. C₃×D₇×C₂²⋊C₄	C₂	semidirect
12. D₇×#121	C₃	direct (N × H)
15. C₂×C₃×C₇×D₄	C₂²	semidirect
16. C₂×C₃×C₇×D₄	C₂²	semidirect
17. C₂²×C₃×C₄×C₇	C₂²	semidirect
18. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
19. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
20. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
21. C₂²×C₃×Dic₇	C₂²	semidirect
24. C₂×C₃×D₂₈	C₂²	semidirect
25. C₂×C₃×D₂₈	C₂²	semidirect
30. C₂×C₃×C₄×D₇	C₂²	semidirect
31. C₂×C₃×C₄×D₇	C₂²	semidirect
32. C₃×C₇×C₄⋊C₄	C₂²	semidirect
33. C₃×C₇×C₂²⋊C₄	C₂²	semidirect
34. C₃×C₂²⋊Dic₇	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
37. C₃×C₄⋊Dic₇	C₂²	semidirect
38. C₃×Dic₇⋊C₄	C₂²	semidirect
39. C₂×D₄×D₇	C₂×C₃	semidirect
40. C₂×D₄×D₇	C₂×C₃	semidirect
41. C₂²×C₄×D₇	C₂×C₃	semidirect
42. C₇×#121	C₂×C₃	semidirect
43. #6502	C₂×C₃	semidirect
44. #6501	C₂×C₃	semidirect
45. #6493	C₂×C₃	semidirect
46. #6458	C₂×C₃	semidirect
47. D₇×C₄⋊C₄	C₂×C₃	semidirect
48. #6447	C₂×C₃	semidirect
49. D₇×C₂²⋊C₄	C₂×C₃	semidirect
58. C₂²×C₃×D₇	D₄	semidirect
81. C₃×C₄×D₇	D₄	semidirect
84. C₂×C₇×D₄	C₂²×C₃	semidirect
85. C₂×C₇×D₄	C₂²×C₃	semidirect
86. C₂²×C₄×C₇	C₂²×C₃	semidirect
87. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
88. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
89. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
90. C₂²×Dic₇	C₂²×C₃	semidirect
93. C₂×D₂₈	C₂²×C₃	semidirect
94. C₂×D₂₈	C₂²×C₃	semidirect
99. C₂×C₄×D₇	C₂²×C₃	semidirect
100. C₂×C₄×D₇	C₂²×C₃	semidirect
101. C₇×C₄⋊C₄	C₂²×C₃	semidirect
102. C₇×C₂²⋊C₄	C₂²×C₃	semidirect
103. C₂²⋊Dic₇	C₂²×C₃	semidirect
104. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
105. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
106. C₄⋊Dic₇	C₂²×C₃	semidirect
107. Dic₇⋊C₄	C₂²×C₃	semidirect
116. C₃×#121	D₇	direct (N × H)
124. C₂²×C₃×C₇	C₂×D₄	semidirect
135. C₂×C₃×D₇	C₂×D₄	semidirect
139. C₃×C₄×C₇	C₂×D₄	semidirect
142. C₃×Dic₇	C₂×D₄	semidirect
151. C₂²×D₇	C₃×D₄	semidirect
174. C₄×D₇	C₃×D₄	semidirect
184. C₂×C₃×D₄	C₂×D₇	semidirect
185. C₂×C₃×D₄	C₂×D₇	semidirect
193. C₂²×C₃×C₄	C₂×D₇	semidirect
196. C₃×C₄⋊C₄	C₂×D₇	semidirect
200. C₃×C₂²⋊C₄	C₂×D₇	semidirect
208. C₃×D₇	#121	direct (N × H)
217. #121	C₃×D₇	direct (N × H)
225. C₂²×C₇	C₂×C₃×D₄	semidirect
236. C₂×D₇	C₂×C₃×D₄	semidirect
240. C₄×C₇	C₂×C₃×D₄	semidirect
243. Dic₇	C₂×C₃×D₄	semidirect
275. C₃×C₇	C₂×#121	semidirect
285. C₂×D₄	C₂×C₃×D₇	semidirect
286. C₂×D₄	C₂×C₃×D₇	semidirect
294. C₂²×C₄	C₂×C₃×D₇	semidirect
297. C₄⋊C₄	C₂×C₃×D₇	semidirect
301. C₂²⋊C₄	C₂×C₃×D₇	semidirect
309. D₇	C₃×#121	direct (N × H)
326. C₂²×C₃	D₄×D₇	semidirect
333. C₃×C₄	D₄×D₇	semidirect
365. C₇	C₂×C₃×#121	semidirect
390. C₂²	C₃×D₄×D₇	semidirect
397. C₄	C₃×D₄×D₇	semidirect
398. C₃	D₇×#121	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×#121	2
C₃×#6502	2
C₃×#6501	2
C₃×#6493	2
C₃×#6458	2
C₃×D₇×C₄⋊C₄	2
C₃×#6447	2
C₃×D₇×C₂²⋊C₄	2
D₇×#121	3
C₂×C₃×#121	7

Subgroups — C3×D7×#121 #13060948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₇×#121 #13060948