Subgroups — C₂×C₇×#3367 #13238522

Order 1792.

2070 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3367	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#489	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#477	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#463	C₂	1	2	yes	maximal
9	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
13	C₂³×C₇×Q₈	—	2	1	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
16	C₇×#556	—	2	4	no	—
17	C₇×#556	C₂²	1	8	yes	complemented
18	C₇×D₄×Q₈	—	2	4	no	—
19	C₇×D₄×Q₈	C₂²	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#126	—	2	2	no	—
24	C₂×C₇×#124	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
28	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
33	C₂×C₇×#117	—	2	1	no	—
34	C₇×#489	C₂²	1	16	yes	complemented
35	C₇×#487	C₂²	1	8	yes	complemented
36	C₇×#477	C₂²	1	16	yes	complemented
37	C₇×#474	C₂²	1	8	yes	complemented
38	C₇×#463	C₂²	1	16	yes	—
39	C₇×#461	C₂²	1	8	yes	complemented
40	C₇×#446	C₂²	1	8	yes	complemented
41	C₇×#440	C₂²	1	16	yes	complemented
42	C₄×C₇×D₈	C₂²	1	8	yes	—
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
47	C₂×C₇×#103	C₂²	1	2	yes	—
48	C₂×C₇×#103	C₂²	1	2	yes	—
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	1	yes	characteristic
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3367	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	8	no	—
57	C₂²×C₇×Q₈	—	2	2	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	4	8	no	—
60	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
61	C₂²×C₇×Q₈	C₂³	1	2	yes	—
62	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂³×C₄×C₇	—	2	1	no	—
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂×C₇×SD₁₆	—	2	8	no	—
68	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
69	C₂×C₇×D₈	—	2	4	no	—
70	C₂×C₇×D₈	C₂³	1	4	yes	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₇×C₈	C₂³	1	2	yes	—
74	C₇×C₄⋊Q₈	—	2	2	no	—
75	C₇×C₄⋊Q₈	—	2	4	no	—
76	C₇×C₄⋊Q₈	—	2	2	no	—
77	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
80	C₇×#126	—	2	16	no	—
81	C₇×#124	—	2	4	no	—
82	C₇×#124	C₂³	1	8	yes	—
83	C₇×C₂²⋊Q₈	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	8	no	—
85	C₇×C₂²⋊Q₈	—	2	16	no	—
86	C₄×C₇×Q₈	—	2	4	no	—
87	C₄×C₇×Q₈	D₄	1	4	yes	—
88	C₄×C₇×Q₈	C₂³	1	8	yes	—
89	C₄×C₇×Q₈	C₂³	1	4	yes	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	—	2	4	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	C₂³	1	4	yes	—
94	C₄×C₇×D₄	C₂³	1	4	yes	—
95	C₄×C₇×D₄	C₂³	1	8	yes	—
96	C₇×#117	—	2	8	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₄²×C₇	—	2	2	no	—
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇	C₂³	1	2	yes	—
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×#107	C₂³	1	4	yes	—
117	C₇×C₄⋊C₈	C₂³	1	4	yes	—
118	C₇×C₄⋊C₈	C₂³	1	8	yes	—
119	C₇×#103	C₂³	1	8	yes	—
120	C₇×#103	C₂³	1	8	yes	—
121	C₇×#103	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	4	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×#97	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
129	#3367	C₂×C₇	1	16	yes	direct product factor
130	C₂×#489	C₂×C₇	1	2	yes	complemented
131	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#477	C₂×C₇	1	2	yes	complemented
133	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#463	C₂×C₇	1	2	yes	—
135	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#440	C₂×C₇	1	2	yes	complemented
138	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	4	no	—
142	C₂×C₇×Q₈	—	2	2	no	—
143	C₂×C₇×Q₈	—	2	8	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	2	4	no	—
146	C₂×C₇×Q₈	—	2	4	no	—
147	C₂×C₇×Q₈	—	4	8	no	—
148	C₂×C₇×Q₈	—	4	32	no	—
149	C₂×C₇×Q₈	—	4	4	no	—
150	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
151	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
152	C₂×C₇×D₄	—	2	1	no	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	—	2	2	no	—
156	C₂×C₇×D₄	—	2	2	no	—
157	C₂×C₇×D₄	#41	1	4	yes	—
158	C₂×C₇×D₄	C₂⁴	1	2	yes	—
159	C₂×C₇×D₄	C₂⁴	1	2	yes	—
160	C₂²×C₄×C₇	—	2	1	no	—
161	C₂²×C₄×C₇	—	2	2	no	—
162	C₂²×C₄×C₇	—	2	2	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	8	no	—
166	C₂²×C₄×C₇	—	2	4	no	—
167	C₂²×C₄×C₇	—	4	8	no	—
168	C₂²×C₄×C₇	—	4	4	no	—
169	C₂²×C₄×C₇	—	4	4	no	—
170	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
173	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
175	C₇×SD₁₆	—	2	16	no	—
176	C₇×D₈	—	2	8	no	—
177	C₂×C₇×C₈	—	2	2	no	—
178	C₂×C₇×C₈	—	2	4	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	C₂⁴	1	2	yes	—
181	C₂×C₇×C₈	C₂⁴	1	2	yes	—
182	C₂×C₇×C₈	C₂⁴	1	4	yes	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	8	no	—
185	C₇×C₄⋊C₄	—	2	8	no	—
186	C₇×C₄⋊C₄	—	2	4	no	—
187	C₇×C₄⋊C₄	—	2	4	no	—
188	C₇×C₄⋊C₄	—	2	1	no	—
189	C₇×C₄⋊C₄	—	2	1	no	—
190	C₇×C₄⋊C₄	—	2	2	no	—
191	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
192	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
194	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₇×C₂²⋊C₄	—	2	8	no	—
197	C₇×C₂²⋊C₄	—	2	8	no	—
198	C₇×C₂²⋊C₄	—	2	4	no	—
199	C₇×C₂²⋊C₄	—	2	4	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₄²×C₇	—	2	8	no	—
202	C₄²×C₇	C₂×D₄	1	2	yes	—
203	C₄²×C₇	C₂×D₄	1	4	yes	—
204	C₄²×C₇	C₂⁴	1	2	yes	—
205	C₄²×C₇	C₂⁴	1	4	yes	—
206	C₂³×Q₈	—	2	1	no	—
207	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
208	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
209	#556	—	2	4	no	—
210	#556	C₂²×C₇	1	8	yes	complemented
211	D₄×Q₈	—	2	4	no	—
212	D₄×Q₈	C₂²×C₇	1	8	yes	complemented
213	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×#126	—	2	2	no	—
217	C₂×#124	C₂²×C₇	1	2	yes	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×C₂²⋊Q₈	—	2	2	no	—
221	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
226	C₂×#117	—	2	1	no	—
227	#489	C₂²×C₇	1	16	yes	complemented
228	#487	C₂²×C₇	1	8	yes	complemented
229	#477	C₂²×C₇	1	16	yes	complemented
230	#474	C₂²×C₇	1	8	yes	complemented
231	#463	C₂²×C₇	1	16	yes	—
232	#461	C₂²×C₇	1	8	yes	complemented
233	#446	C₂²×C₇	1	8	yes	complemented
234	#440	C₂²×C₇	1	16	yes	complemented
235	C₄×D₈	C₂²×C₇	1	8	yes	—
236	C₂×#107	C₂²×C₇	1	1	yes	characteristic
237	C₂×#107	C₂²×C₇	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
240	C₂×#103	C₂²×C₇	1	2	yes	—
241	C₂×#103	C₂²×C₇	1	2	yes	—
242	C₂×#103	C₂²×C₇	1	2	yes	—
243	C₂×#102	C₂²×C₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₇	1	2	yes	—
245	C₂×#102	C₂²×C₇	1	1	yes	characteristic
246	C₂×#97	C₂²×C₇	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
248	C₂³×C₇	—	2	4	no	—
249	C₂³×C₇	—	2	2	no	—
250	C₂³×C₇	—	2	2	no	—
251	C₂³×C₇	—	4	2	no	—
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	—	4	2	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
257	C₇×Q₈	—	2	8	no	—
258	C₇×Q₈	—	2	4	no	—
259	C₇×Q₈	—	2	4	no	—
260	C₇×Q₈	—	4	16	no	—
261	C₇×Q₈	—	4	4	no	—
262	C₇×Q₈	—	4	8	no	—
263	C₇×D₄	—	2	4	no	—
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	2	2	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	—	4	2	no	—
268	C₇×D₄	C₂×#41	1	4	yes	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	4	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	2	2	no	—
276	C₂×C₄×C₇	—	4	16	no	—
277	C₂×C₄×C₇	—	4	4	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	4	no	—
280	C₂×C₄×C₇	—	4	2	no	—
281	C₂×C₄×C₇	—	4	8	no	—
282	C₂×C₄×C₇	—	4	8	no	—
283	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
284	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
285	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
286	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₇	C₂×#41	1	2	yes	—
290	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
291	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
292	C₇×C₈	—	2	2	no	—
293	C₇×C₈	—	2	4	no	—
294	C₇×C₈	—	2	2	no	—
295	C₂²×Q₈	—	2	8	no	—
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	—	4	8	no	—
299	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₇	1	2	yes	—
301	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
302	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂×SD₁₆	—	2	8	no	—
307	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
308	C₂×D₈	—	2	4	no	—
309	C₂×D₈	C₂³×C₇	1	4	yes	—
310	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₇	1	2	yes	—
312	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	4	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
317	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
318	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
319	#126	—	2	16	no	—
320	#124	—	2	4	no	—
321	#124	C₂³×C₇	1	8	yes	—
322	C₂²⋊Q₈	—	2	8	no	—
323	C₂²⋊Q₈	—	2	8	no	—
324	C₂²⋊Q₈	—	2	16	no	—
325	C₄×Q₈	—	2	4	no	—
326	C₄×Q₈	C₇×D₄	1	4	yes	—
327	C₄×Q₈	C₂³×C₇	1	8	yes	—
328	C₄×Q₈	C₂³×C₇	1	4	yes	—
329	C₄×D₄	—	2	2	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	C₂³×C₇	1	4	yes	—
333	C₄×D₄	C₂³×C₇	1	8	yes	—
334	C₄×D₄	C₂³×C₇	1	4	yes	—
335	#117	—	2	8	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₇	1	2	yes	—
354	#107	C₂³×C₇	1	4	yes	—
355	#107	C₂³×C₇	1	8	yes	—
356	C₄⋊C₈	C₂³×C₇	1	4	yes	—
357	C₄⋊C₈	C₂³×C₇	1	8	yes	—
358	#103	C₂³×C₇	1	8	yes	—
359	#103	C₂³×C₇	1	8	yes	—
360	#103	C₂³×C₇	1	8	yes	—
361	#102	C₂³×C₇	1	4	yes	—
362	#102	C₂³×C₇	1	4	yes	—
363	#102	C₂³×C₇	1	8	yes	—
364	#97	C₂³×C₇	1	8	yes	—
365	C₄×C₈	C₂³×C₇	1	4	yes	—
366	C₂²×C₇	—	2	4	no	—
367	C₂²×C₇	—	4	8	no	—
368	C₂²×C₇	—	4	2	no	—
369	C₂²×C₇	—	4	2	no	—
370	C₂²×C₇	—	4	2	no	—
371	C₂²×C₇	—	4	2	no	—
372	C₂²×C₇	—	4	2	no	—
373	C₂²×C₇	—	8	4	no	—
374	C₂²×C₇	#548	1	2	yes	—
375	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
376	C₂²×C₇	#578	1	2	yes	—
377	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
378	C₄×C₇	—	2	4	no	—
379	C₄×C₇	—	2	4	no	—
380	C₄×C₇	—	2	2	no	—
381	C₄×C₇	—	4	4	no	—
382	C₄×C₇	—	4	2	no	—
383	C₄×C₇	—	4	4	no	—
384	C₄×C₇	—	4	2	no	—
385	C₄×C₇	#548	1	2	yes	—
386	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
387	C₄×C₇	C₂²×#41	1	1	yes	characteristic
388	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂⁴	—	2	1	no	—
390	C₂⁴	—	2	1	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	4	8	no	—
398	C₂×Q₈	—	4	32	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
401	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	C₇×#41	1	4	yes	—
408	C₂×D₄	C₂⁴×C₇	1	2	yes	—
409	C₂×D₄	C₂⁴×C₇	1	2	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	4	8	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
421	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
422	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
423	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
424	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
425	SD₁₆	—	2	16	no	—
426	D₈	—	2	8	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	4	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	C₂⁴×C₇	1	2	yes	—
431	C₂×C₈	C₂⁴×C₇	1	2	yes	—
432	C₂×C₈	C₂⁴×C₇	1	4	yes	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
442	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
443	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
444	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
445	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₄²	—	2	8	no	—
452	C₄²	C₂×C₇×D₄	1	2	yes	—
453	C₄²	C₂×C₇×D₄	1	4	yes	—
454	C₄²	C₂⁴×C₇	1	2	yes	—
455	C₄²	C₂⁴×C₇	1	4	yes	—
456	C₂×C₇	—	4	4	no	—
457	C₂×C₇	—	8	2	no	—
458	C₂×C₇	#3367	1	4	yes	direct product factor
459	C₂×C₇	C₂×#548	1	1	yes	characteristic
460	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂×C₇	C₂×#578	1	1	yes	characteristic
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
471	Q₈	—	2	8	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	4	16	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	8	no	—
477	D₄	—	2	2	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	2	no	—
482	D₄	C₂×C₇×#41	1	4	yes	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
498	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
499	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
500	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
501	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
503	C₂×C₄	C₂×C₇×#41	1	2	yes	—
504	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
505	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	4	no	—
508	C₈	—	2	2	no	—
509	C₇	C₂×#3367	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²	—	2	4	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	8	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	4	no	—
518	C₂²	C₇×#548	1	2	yes	—
519	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
520	C₂²	C₇×#578	1	2	yes	—
521	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
522	C₄	—	2	4	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	C₇×#548	1	2	yes	—
530	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
531	C₄	C₂²×C₇×#41	1	1	yes	characteristic
532	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
533	C₂	—	4	4	no	—
534	C₂	—	8	2	no	—
535	C₂	C₇×#3367	1	4	yes	direct product factor
536	C₂	C₂×C₇×#548	1	1	yes	characteristic
537	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
538	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#556	C₂	semidirect
2. C₂×C₇×D₄×Q₈	C₂	semidirect
3. C₇×#3367	C₂	direct (N × H)
4. C₂×C₇×#489	C₂	semidirect
5. C₂×C₇×#487	C₂	semidirect
6. C₂×C₇×#477	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
9. C₂×C₇×#461	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
11. C₂×C₇×#440	C₂	semidirect
17. C₇×#556	C₂²	semidirect
19. C₇×D₄×Q₈	C₂²	semidirect
34. C₇×#489	C₂²	semidirect
35. C₇×#487	C₂²	semidirect
36. C₇×#477	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
39. C₇×#461	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#440	C₂²	semidirect
55. C₂×#3367	C₇	direct (N × H)
127. C₂×#556	C₂×C₇	semidirect
128. C₂×D₄×Q₈	C₂×C₇	semidirect
129. #3367	C₂×C₇	direct (N × H)
130. C₂×#489	C₂×C₇	semidirect
131. C₂×#487	C₂×C₇	semidirect
132. C₂×#477	C₂×C₇	semidirect
133. C₂×#474	C₂×C₇	semidirect
135. C₂×#461	C₂×C₇	semidirect
136. C₂×#446	C₂×C₇	semidirect
137. C₂×#440	C₂×C₇	semidirect
210. #556	C₂²×C₇	semidirect
212. D₄×Q₈	C₂²×C₇	semidirect
227. #489	C₂²×C₇	semidirect
228. #487	C₂²×C₇	semidirect
229. #477	C₂²×C₇	semidirect
230. #474	C₂²×C₇	semidirect
232. #461	C₂²×C₇	semidirect
233. #446	C₂²×C₇	semidirect
234. #440	C₂²×C₇	semidirect
458. C₂×C₇	#3367	direct (N × H)
509. C₇	C₂×#3367	direct (N × H)
535. C₂	C₇×#3367	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×C₇×#556	2
C₂×C₇×D₄×Q₈	2
C₇×#3367	2
C₂×C₇×#489	2
C₂×C₇×#487	2
C₂×C₇×#477	2
C₂×C₇×#474	2
C₂×C₇×#463	2
C₂×C₇×#461	2
C₂×C₇×#446	2
C₂×C₇×#440	2
C₂×C₄×C₇×D₈	2
C₂×#3367	7

Subgroups — C2×C7×#3367 #13238522

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3367 #13238522