Subgroups — C₃×D₄×C₂²⋊D₇ #13061145

Order 1344.

856 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#6516	C₂	1	2	yes	maximal, complemented
5	C₃×#6503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#6502	C₂	1	2	yes	maximal, complemented
7	C₃×#6501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#6500	C₂	1	2	yes	maximal, complemented
9	C₃×D₄×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#6493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×C₂²⋊D₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×C₇	C₂²	1	2	yes	complemented
14	C₂³×C₃×D₇	C₂²	1	2	yes	complemented
15	C₂×C₃×C₇×D₄	—	2	4	no	—
16	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₇×D₄	C₂²	1	2	yes	complemented
18	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₄×C₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₂²⋊D₇	—	2	8	no	—
21	C₂×C₃×C₂²⋊D₇	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
23	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
24	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
25	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
26	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
27	C₂²×C₃×Dic₇	C₂²	1	2	yes	complemented
28	C₃×D₄×D₇	—	2	4	no	—
29	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
33	C₃×C₂²⋊Dic₇	C₂²	1	2	yes	complemented
34	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₃×(C₂×D₇)⋊C₄	C₂²	1	2	yes	complemented
36	C₃×C₄⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
37	C₃×Dic₇⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₄×Dic₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×C₇×D₄	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊D₇	C₂×C₃	1	2	yes	complemented
41	C₂×D₄×D₇	C₂×C₃	1	1	yes	characteristic, complemented
42	#6516	C₂×C₃	1	2	yes	complemented
43	#6503	C₂×C₃	1	1	yes	characteristic, complemented
44	#6502	C₂×C₃	1	2	yes	complemented
45	#6501	C₂×C₃	1	1	yes	characteristic, complemented
46	#6500	C₂×C₃	1	2	yes	complemented
47	D₄×Dic₇	C₂×C₃	1	1	yes	characteristic, complemented
48	#6493	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₂²⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×D₄²	—	7	1	no	maximal, Hall
51	C₂³×C₃×C₇	—	2	4	no	—
52	C₂³×C₃×C₇	—	2	4	no	—
53	C₂³×C₃×C₇	—	4	2	no	—
54	C₂³×C₃×C₇	C₂³	1	2	yes	—
55	C₂³×C₃×C₇	C₂³	1	2	yes	—
56	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
57	C₂²×C₃×D₇	—	2	4	no	—
58	C₂²×C₃×D₇	—	2	4	no	—
59	C₂²×C₃×D₇	—	4	2	no	—
60	C₂²×C₃×D₇	C₂³	1	2	yes	—
61	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
62	C₃×C₇×D₄	—	2	4	no	—
63	C₃×C₇×D₄	—	2	2	no	—
64	C₃×C₇×D₄	D₄	1	4	yes	complemented
65	C₂×C₃×C₄×C₇	—	2	2	no	—
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	C₃×C₂²⋊D₇	—	2	4	no	—
72	C₃×C₂²⋊D₇	—	4	2	no	—
73	C₃×C₂²⋊D₇	D₄	1	4	yes	direct product factor
74	C₂×C₃×Dic₇	—	2	4	no	—
75	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
76	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
77	C₂×C₃×Dic₇	C₂³	1	2	yes	—
78	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
79	C₃×D₂₈	—	2	2	no	—
80	C₃×C₄×D₇	—	2	2	no	—
81	C₂⁴×C₇	C₂²×C₃	1	2	yes	complemented
82	C₂³×D₇	C₂²×C₃	1	2	yes	complemented
83	C₂×C₇×D₄	—	2	4	no	—
84	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₇×D₄	C₂²×C₃	1	2	yes	complemented
86	C₂×C₇×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₂²×C₄×C₇	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₂×C₂²⋊D₇	—	2	8	no	—
89	C₂×C₂²⋊D₇	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
91	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
92	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
93	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
94	C₂×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
95	C₂²×Dic₇	C₂²×C₃	1	2	yes	complemented
96	D₄×D₇	—	2	4	no	—
97	C₂×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₂×C₄×D₇	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₂²⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
101	C₂²⋊Dic₇	C₂²×C₃	1	2	yes	complemented
102	(C₂×D₇)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
103	(C₂×D₇)⋊C₄	C₂²×C₃	1	2	yes	complemented
104	C₄⋊Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
105	Dic₇⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₄×Dic₇	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂²×C₃×D₄	—	7	2	no	—
108	C₂²×C₃×D₄	—	7	1	no	—
109	C₂²×C₃×D₄	D₇	1	1	yes	characteristic, complemented
110	C₃×#127	—	7	1	no	—
111	C₃×#121	—	7	1	no	—
112	C₃×#121	—	7	2	no	—
113	C₃×#121	—	7	1	no	—
114	C₃×#120	—	7	2	no	—
115	C₃×#120	—	7	2	no	—
116	C₃×C₄×D₄	—	7	1	no	—
117	C₃×C₄×D₄	—	7	1	no	—
118	C₂²×C₃×C₇	—	2	2	no	—
119	C₂²×C₃×C₇	—	2	1	no	—
120	C₂²×C₃×C₇	—	2	2	no	—
121	C₂²×C₃×C₇	—	2	1	no	—
122	C₂²×C₃×C₇	—	2	2	no	—
123	C₂²×C₃×C₇	—	2	2	no	—
124	C₂²×C₃×C₇	—	2	2	no	—
125	C₂²×C₃×C₇	—	4	8	no	—
126	C₂²×C₃×C₇	C₂×D₄	1	2	yes	complemented
127	C₂²×C₃×C₇	C₂×D₄	1	4	yes	complemented
128	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₃×D₇	—	2	1	no	—
130	C₂×C₃×D₇	—	2	1	no	—
131	C₂×C₃×D₇	—	2	2	no	—
132	C₂×C₃×D₇	—	2	2	no	—
133	C₂×C₃×D₇	—	2	2	no	—
134	C₂×C₃×D₇	—	4	8	no	—
135	C₂×C₃×D₇	C₂×D₄	1	2	yes	complemented
136	C₃×C₄×C₇	—	2	1	no	—
137	C₃×C₄×C₇	C₂×D₄	1	2	yes	complemented
138	C₃×Dic₇	—	2	1	no	—
139	C₃×Dic₇	—	2	2	no	—
140	C₃×Dic₇	—	2	1	no	—
141	C₃×Dic₇	C₂×D₄	1	2	yes	complemented
142	D₄²	—	7	1	no	Sylow
143	C₂³×C₇	—	2	4	no	—
144	C₂³×C₇	—	2	4	no	—
145	C₂³×C₇	—	4	2	no	—
146	C₂³×C₇	C₂³×C₃	1	2	yes	—
147	C₂³×C₇	C₂³×C₃	1	2	yes	—
148	C₂³×C₇	C₂³×C₃	1	1	yes	characteristic
149	C₂²×D₇	—	2	4	no	—
150	C₂²×D₇	—	2	4	no	—
151	C₂²×D₇	—	4	2	no	—
152	C₂²×D₇	C₂³×C₃	1	2	yes	—
153	C₂²×D₇	C₂³×C₃	1	1	yes	characteristic
154	C₇×D₄	—	2	4	no	—
155	C₇×D₄	—	2	2	no	—
156	C₇×D₄	C₃×D₄	1	4	yes	complemented
157	C₂×C₄×C₇	—	2	2	no	—
158	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
159	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
160	C₂²⋊D₇	—	2	4	no	—
161	C₂²⋊D₇	—	2	4	no	—
162	C₂²⋊D₇	—	2	4	no	—
163	C₂²⋊D₇	—	2	4	no	—
164	C₂²⋊D₇	—	4	2	no	—
165	C₂²⋊D₇	C₃×D₄	1	4	yes	direct product factor
166	C₂×Dic₇	—	2	4	no	—
167	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
168	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
169	C₂×Dic₇	C₂³×C₃	1	2	yes	—
170	C₂×Dic₇	C₂³×C₃	1	1	yes	characteristic
171	D₂₈	—	2	2	no	—
172	C₄×D₇	—	2	2	no	—
173	C₂⁴×C₃	—	7	2	no	—
174	C₂⁴×C₃	C₂×D₇	1	2	yes	complemented
175	C₂×C₃×D₄	—	2	4	no	—
176	C₂×C₃×D₄	—	7	1	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	2	no	—
182	C₂×C₃×D₄	—	7	1	no	—
183	C₂×C₃×D₄	—	14	8	no	—
184	C₂×C₃×D₄	—	14	4	no	—
185	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic
186	C₂×C₃×D₄	C₂×D₇	1	2	yes	complemented
187	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
188	C₂²×C₃×C₄	—	7	2	no	—
189	C₂²×C₃×C₄	—	7	1	no	—
190	C₂²×C₃×C₄	C₂×D₇	1	1	yes	characteristic, complemented
191	C₃×C₄⋊C₄	—	7	1	no	—
192	C₃×C₄⋊C₄	—	7	1	no	—
193	C₃×C₂²⋊C₄	—	7	1	no	—
194	C₃×C₂²⋊C₄	—	7	2	no	—
195	C₃×C₂²⋊C₄	—	7	2	no	—
196	C₃×C₂²⋊C₄	—	7	1	no	—
197	C₃×C₂²⋊C₄	—	7	2	no	—
198	C₃×C₄²	—	7	1	no	—
199	C₂×C₃×C₇	—	2	4	no	—
200	C₂×C₃×C₇	—	2	2	no	—
201	C₂×C₃×C₇	—	4	2	no	—
202	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₃×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₃×C₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₃×D₇	—	2	2	no	—
206	C₃×D₇	—	4	2	no	—
207	C₂²×D₄	—	7	2	no	—
208	C₂²×D₄	—	7	1	no	—
209	C₂²×D₄	C₃×D₇	1	1	yes	characteristic, complemented
210	#127	—	7	1	no	—
211	#121	—	7	1	no	—
212	#121	—	7	2	no	—
213	#121	—	7	1	no	—
214	#120	—	7	2	no	—
215	#120	—	7	2	no	—
216	C₄×D₄	—	7	1	no	—
217	C₄×D₄	—	7	1	no	—
218	C₂²×C₇	—	2	2	no	—
219	C₂²×C₇	—	2	1	no	—
220	C₂²×C₇	—	2	2	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	—	4	8	no	—
226	C₂²×C₇	C₂×C₃×D₄	1	2	yes	complemented
227	C₂²×C₇	C₂×C₃×D₄	1	4	yes	complemented
228	C₂²×C₇	C₂⁴×C₃	1	1	yes	characteristic
229	C₂×D₇	—	2	1	no	—
230	C₂×D₇	—	2	1	no	—
231	C₂×D₇	—	2	2	no	—
232	C₂×D₇	—	2	2	no	—
233	C₂×D₇	—	2	2	no	—
234	C₂×D₇	—	4	8	no	—
235	C₂×D₇	C₂×C₃×D₄	1	2	yes	complemented
236	C₄×C₇	—	2	1	no	—
237	C₄×C₇	C₂×C₃×D₄	1	2	yes	complemented
238	Dic₇	—	2	1	no	—
239	Dic₇	—	2	2	no	—
240	Dic₇	—	2	1	no	—
241	Dic₇	C₂×C₃×D₄	1	2	yes	complemented
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	2	4	no	—
244	C₂³×C₃	—	4	2	no	—
245	C₂³×C₃	—	7	1	no	—
246	C₂³×C₃	—	7	2	no	—
247	C₂³×C₃	—	14	4	no	—
248	C₂³×C₃	—	14	4	no	—
249	C₂³×C₃	—	28	2	no	—
250	C₂³×C₃	C₂²×D₇	1	2	yes	—
251	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
252	C₂³×C₃	C₂²×D₇	1	2	yes	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	7	4	no	—
256	C₃×D₄	—	14	4	no	—
257	C₃×D₄	—	14	4	no	—
258	C₃×D₄	—	14	4	no	—
259	C₃×D₄	—	14	4	no	—
260	C₃×D₄	—	14	2	no	—
261	C₃×D₄	—	28	2	no	—
262	C₃×D₄	C₂²⋊D₇	1	4	yes	direct product factor
263	C₂×C₃×C₄	—	2	2	no	—
264	C₂×C₃×C₄	—	7	1	no	—
265	C₂×C₃×C₄	—	7	1	no	—
266	C₂×C₃×C₄	—	7	2	no	—
267	C₂×C₃×C₄	—	7	1	no	—
268	C₂×C₃×C₄	—	14	4	no	—
269	C₂×C₃×C₄	—	14	2	no	—
270	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
271	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
272	C₃×C₇	D₄²	1	1	yes	characteristic, complemented, Hall
273	C₂⁴	—	7	2	no	—
274	C₂⁴	C₂×C₃×D₇	1	2	yes	complemented
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	7	1	no	—
277	C₂×D₄	—	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	8	no	—
284	C₂×D₄	—	14	4	no	—
285	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic
286	C₂×D₄	C₂×C₃×D₇	1	2	yes	complemented
287	C₂×D₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
288	C₂²×C₄	—	7	2	no	—
289	C₂²×C₄	—	7	1	no	—
290	C₂²×C₄	C₂×C₃×D₇	1	1	yes	characteristic, complemented
291	C₄⋊C₄	—	7	1	no	—
292	C₄⋊C₄	—	7	1	no	—
293	C₂²⋊C₄	—	7	1	no	—
294	C₂²⋊C₄	—	7	2	no	—
295	C₂²⋊C₄	—	7	2	no	—
296	C₂²⋊C₄	—	7	1	no	—
297	C₂²⋊C₄	—	7	2	no	—
298	C₄²	—	7	1	no	—
299	C₂×C₇	—	2	4	no	—
300	C₂×C₇	—	2	2	no	—
301	C₂×C₇	—	4	2	no	—
302	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
303	C₂×C₇	C₂²×C₃×D₄	1	1	yes	characteristic
304	C₂×C₇	C₃×H(5,𝔽₂)	1	1	yes	characteristic
305	D₇	—	2	2	no	—
306	D₇	—	4	2	no	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	2	2	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	2	no	—
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	—	2	2	no	—
314	C₂²×C₃	—	4	8	no	—
315	C₂²×C₃	—	7	2	no	—
316	C₂²×C₃	—	14	1	no	—
317	C₂²×C₃	—	14	1	no	—
318	C₂²×C₃	—	14	2	no	—
319	C₂²×C₃	—	14	2	no	—
320	C₂²×C₃	—	14	2	no	—
321	C₂²×C₃	—	28	8	no	—
322	C₂²×C₃	D₄×D₇	1	2	yes	complemented
323	C₂²×C₃	C₂×C₂²⋊D₇	1	4	yes	complemented
324	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	7	2	no	—
327	C₃×C₄	—	14	2	no	—
328	C₃×C₄	—	14	1	no	—
329	C₃×C₄	—	14	1	no	—
330	C₃×C₄	C₂×C₂²⋊D₇	1	2	yes	complemented
331	C₂³	—	2	4	no	—
332	C₂³	—	2	4	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	7	1	no	—
335	C₂³	—	7	2	no	—
336	C₂³	—	14	4	no	—
337	C₂³	—	14	4	no	—
338	C₂³	—	28	2	no	—
339	C₂³	C₂²×C₃×D₇	1	2	yes	—
340	C₂³	C₂²×C₃×D₇	1	1	yes	characteristic
341	C₂³	C₂²×C₃×D₇	1	2	yes	—
342	D₄	—	2	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	7	4	no	—
345	D₄	—	14	4	no	—
346	D₄	—	14	4	no	—
347	D₄	—	14	4	no	—
348	D₄	—	14	4	no	—
349	D₄	—	14	2	no	—
350	D₄	—	28	2	no	—
351	D₄	C₃×C₂²⋊D₇	1	4	yes	direct product factor
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	7	1	no	—
354	C₂×C₄	—	7	1	no	—
355	C₂×C₄	—	7	2	no	—
356	C₂×C₄	—	7	1	no	—
357	C₂×C₄	—	14	4	no	—
358	C₂×C₄	—	14	2	no	—
359	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
361	C₇	C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
362	C₂×C₃	—	2	2	no	—
363	C₂×C₃	—	2	4	no	—
364	C₂×C₃	—	4	2	no	—
365	C₂×C₃	—	14	2	no	—
366	C₂×C₃	—	28	2	no	—
367	C₂×C₃	C₂×D₄×D₇	1	1	yes	characteristic
368	C₂×C₃	#6548	1	1	yes	characteristic
369	C₂×C₃	C₂²×C₂²⋊D₇	1	1	yes	characteristic
370	C₂²	—	2	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	4	8	no	—
378	C₂²	—	7	2	no	—
379	C₂²	—	14	1	no	—
380	C₂²	—	14	1	no	—
381	C₂²	—	14	2	no	—
382	C₂²	—	14	2	no	—
383	C₂²	—	14	2	no	—
384	C₂²	—	28	8	no	—
385	C₂²	C₃×D₄×D₇	1	2	yes	complemented
386	C₂²	C₂×C₃×C₂²⋊D₇	1	4	yes	complemented
387	C₂²	C₂³×C₃×D₇	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	7	2	no	—
390	C₄	—	14	2	no	—
391	C₄	—	14	1	no	—
392	C₄	—	14	1	no	—
393	C₄	C₂×C₃×C₂²⋊D₇	1	2	yes	complemented
394	C₃	D₄×C₂²⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
395	C₂	—	2	2	no	—
396	C₂	—	2	4	no	—
397	C₂	—	4	2	no	—
398	C₂	—	14	2	no	—
399	C₂	—	28	2	no	—
400	C₂	C₂×C₃×D₄×D₇	1	1	yes	characteristic
401	C₂	C₃×#6548	1	1	yes	characteristic
402	C₂	C₂²×C₃×C₂²⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₇
commutator, cosocle	C₂²×C₇	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₇
Fitting	C₂²×C₃×C₇×D₄	C₂
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₂²×C₃×D₄	D₇
hypocenter	C₇	C₃×D₄²
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₇×D₄	C₂	semidirect
2. C₂²×C₃×C₂²⋊D₇	C₂	semidirect
3. C₂×C₃×D₄×D₇	C₂	semidirect
4. C₃×#6516	C₂	semidirect
5. C₃×#6503	C₂	semidirect
6. C₃×#6502	C₂	semidirect
7. C₃×#6501	C₂	semidirect
8. C₃×#6500	C₂	semidirect
9. C₃×D₄×Dic₇	C₂	semidirect
10. C₃×#6493	C₂	semidirect
11. C₃×C₄×C₂²⋊D₇	C₂	semidirect
12. D₄×C₂²⋊D₇	C₃	direct (N × H)
13. C₂⁴×C₃×C₇	C₂²	semidirect
14. C₂³×C₃×D₇	C₂²	semidirect
17. C₂×C₃×C₇×D₄	C₂²	semidirect
18. C₂×C₃×C₇×D₄	C₂²	semidirect
19. C₂²×C₃×C₄×C₇	C₂²	semidirect
22. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
23. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
24. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
25. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
26. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
27. C₂²×C₃×Dic₇	C₂²	semidirect
29. C₂×C₃×D₂₈	C₂²	semidirect
30. C₂×C₃×C₄×D₇	C₂²	semidirect
31. C₃×C₂²⋊Dic₇	C₂²	semidirect
32. C₃×C₂²⋊Dic₇	C₂²	semidirect
33. C₃×C₂²⋊Dic₇	C₂²	semidirect
34. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
35. C₃×(C₂×D₇)⋊C₄	C₂²	semidirect
36. C₃×C₄⋊Dic₇	C₂²	semidirect
37. C₃×Dic₇⋊C₄	C₂²	semidirect
38. C₃×C₄×Dic₇	C₂²	semidirect
39. C₂²×C₇×D₄	C₂×C₃	semidirect
40. C₂²×C₂²⋊D₇	C₂×C₃	semidirect
41. C₂×D₄×D₇	C₂×C₃	semidirect
42. #6516	C₂×C₃	semidirect
43. #6503	C₂×C₃	semidirect
44. #6502	C₂×C₃	semidirect
45. #6501	C₂×C₃	semidirect
46. #6500	C₂×C₃	semidirect
47. D₄×Dic₇	C₂×C₃	semidirect
48. #6493	C₂×C₃	semidirect
49. C₄×C₂²⋊D₇	C₂×C₃	semidirect
64. C₃×C₇×D₄	D₄	semidirect
73. C₃×C₂²⋊D₇	D₄	direct (N × H)
81. C₂⁴×C₇	C₂²×C₃	semidirect
82. C₂³×D₇	C₂²×C₃	semidirect
85. C₂×C₇×D₄	C₂²×C₃	semidirect
86. C₂×C₇×D₄	C₂²×C₃	semidirect
87. C₂²×C₄×C₇	C₂²×C₃	semidirect
90. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
91. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
92. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
93. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
94. C₂×C₂²⋊D₇	C₂²×C₃	semidirect
95. C₂²×Dic₇	C₂²×C₃	semidirect
97. C₂×D₂₈	C₂²×C₃	semidirect
98. C₂×C₄×D₇	C₂²×C₃	semidirect
99. C₂²⋊Dic₇	C₂²×C₃	semidirect
100. C₂²⋊Dic₇	C₂²×C₃	semidirect
101. C₂²⋊Dic₇	C₂²×C₃	semidirect
102. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
103. (C₂×D₇)⋊C₄	C₂²×C₃	semidirect
104. C₄⋊Dic₇	C₂²×C₃	semidirect
105. Dic₇⋊C₄	C₂²×C₃	semidirect
106. C₄×Dic₇	C₂²×C₃	semidirect
109. C₂²×C₃×D₄	D₇	semidirect
126. C₂²×C₃×C₇	C₂×D₄	semidirect
127. C₂²×C₃×C₇	C₂×D₄	semidirect
135. C₂×C₃×D₇	C₂×D₄	semidirect
137. C₃×C₄×C₇	C₂×D₄	semidirect
141. C₃×Dic₇	C₂×D₄	semidirect
156. C₇×D₄	C₃×D₄	semidirect
165. C₂²⋊D₇	C₃×D₄	direct (N × H)
174. C₂⁴×C₃	C₂×D₇	semidirect
186. C₂×C₃×D₄	C₂×D₇	semidirect
187. C₂×C₃×D₄	C₂×D₇	semidirect
190. C₂²×C₃×C₄	C₂×D₇	semidirect
209. C₂²×D₄	C₃×D₇	semidirect
226. C₂²×C₇	C₂×C₃×D₄	semidirect
227. C₂²×C₇	C₂×C₃×D₄	semidirect
235. C₂×D₇	C₂×C₃×D₄	semidirect
237. C₄×C₇	C₂×C₃×D₄	semidirect
241. Dic₇	C₂×C₃×D₄	semidirect
262. C₃×D₄	C₂²⋊D₇	direct (N × H)
272. C₃×C₇	D₄²	semidirect
274. C₂⁴	C₂×C₃×D₇	semidirect
286. C₂×D₄	C₂×C₃×D₇	semidirect
287. C₂×D₄	C₂×C₃×D₇	semidirect
290. C₂²×C₄	C₂×C₃×D₇	semidirect
322. C₂²×C₃	D₄×D₇	semidirect
323. C₂²×C₃	C₂×C₂²⋊D₇	semidirect
330. C₃×C₄	C₂×C₂²⋊D₇	semidirect
351. D₄	C₃×C₂²⋊D₇	direct (N × H)
361. C₇	C₃×D₄²	semidirect
385. C₂²	C₃×D₄×D₇	semidirect
386. C₂²	C₂×C₃×C₂²⋊D₇	semidirect
393. C₄	C₂×C₃×C₂²⋊D₇	semidirect
394. C₃	D₄×C₂²⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₇×D₄	2
C₂²×C₃×C₂²⋊D₇	2
C₂×C₃×D₄×D₇	2
C₃×#6516	2
C₃×#6503	2
C₃×#6502	2
C₃×#6501	2
C₃×#6500	2
C₃×D₄×Dic₇	2
C₃×#6493	2
C₃×C₄×C₂²⋊D₇	2
D₄×C₂²⋊D₇	3
C₃×D₄²	7

Subgroups — C3×D4×C22⋊D7 #13061145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×C₂²⋊D₇ #13061145