Subgroups — C₂×C₇×#3375 #13238527

Order 1792.

1906 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3375	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#489	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic
6	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic
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×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₇×#559	—	2	4	no	—
16	C₇×#559	C₂²	1	8	yes	—
17	C₇×Q₈²	—	2	4	no	—
18	C₇×Q₈²	C₂²	1	8	yes	complemented
19	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₇×C₄⋊Q₈	—	2	2	no	—
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₇×#124	—	2	1	no	—
25	C₂×C₇×#124	C₂²	1	2	yes	—
26	C₂×C₇×#123	—	2	2	no	—
27	C₂×C₄×C₇×Q₈	—	2	1	no	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
31	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	—	2	1	no	—
33	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
34	C₇×#489	C₂²	1	16	yes	complemented
35	C₇×#486	C₂²	1	8	yes	—
36	C₇×#477	C₂²	1	8	yes	complemented
37	C₇×#474	C₂²	1	16	yes	complemented
38	C₇×#464	C₂²	1	16	yes	complemented
39	C₇×#460	C₂²	1	8	yes	—
40	C₇×#446	C₂²	1	8	yes	complemented
41	C₇×#440	C₂²	1	16	yes	complemented
42	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
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	1	yes	characteristic
48	C₂×C₇×#103	C₂²	1	1	yes	characteristic
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	2	yes	—
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×#3375	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	2	no	—
57	C₂²×C₇×Q₈	—	2	1	no	—
58	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
59	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	—	2	1	no	—
62	C₂²×C₇×D₄	—	2	1	no	—
63	C₂²×C₇×D₄	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂×C₇×Q₁₆	—	2	4	no	—
66	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
67	C₂×C₇×SD₁₆	—	2	8	no	—
68	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	2	yes	—
72	C₇×C₄⋊Q₈	—	2	8	no	—
73	C₇×C₄⋊Q₈	—	2	16	no	—
74	C₇×C₄⋊Q₈	—	2	4	no	—
75	C₇×C₄⋊Q₈	—	2	2	no	—
76	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
77	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₇×#127	—	2	2	no	—
79	C₇×#127	C₂³	1	4	yes	—
80	C₇×#124	—	2	8	no	—
81	C₇×#124	—	2	4	no	—
82	C₇×#124	C₂³	1	8	yes	—
83	C₇×#123	—	2	16	no	—
84	C₄×C₇×Q₈	—	2	8	no	—
85	C₄×C₇×Q₈	—	2	4	no	—
86	C₄×C₇×Q₈	—	2	2	no	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	D₄	1	4	yes	—
89	C₄×C₇×Q₈	C₂³	1	4	yes	—
90	C₄×C₇×Q₈	C₂³	1	4	yes	—
91	C₄×C₇×Q₈	C₂³	1	8	yes	—
92	C₄×C₇×Q₈	C₂³	1	4	yes	—
93	C₄×C₇×D₄	—	2	8	no	—
94	C₄×C₇×D₄	—	2	4	no	—
95	C₄×C₇×D₄	C₂³	1	8	yes	—
96	C₂×C₇×C₄⋊C₄	—	2	2	no	—
97	C₂×C₇×C₄⋊C₄	—	2	1	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	2	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	—	2	2	no	—
111	C₂×C₄²×C₇	—	2	1	no	—
112	C₂×C₄²×C₇	C₂³	1	2	yes	—
113	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
114	C₇×#107	C₂³	1	4	yes	—
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×C₄⋊C₈	C₂³	1	8	yes	—
117	C₇×C₄⋊C₈	C₂³	1	4	yes	—
118	C₇×#103	C₂³	1	8	yes	—
119	C₇×#103	C₂³	1	4	yes	—
120	C₇×#103	C₂³	1	4	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	8	yes	—
124	C₇×#97	C₂³	1	8	yes	—
125	C₄×C₇×C₈	C₂³	1	4	yes	—
126	C₂×#559	C₂×C₇	1	1	yes	characteristic
127	C₂×Q₈²	C₂×C₇	1	1	yes	characteristic, complemented
128	#3375	C₂×C₇	1	16	yes	direct product factor
129	C₂×#489	C₂×C₇	1	2	yes	complemented
130	C₂×#486	C₂×C₇	1	1	yes	characteristic
131	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#474	C₂×C₇	1	2	yes	complemented
133	C₂×#464	C₂×C₇	1	2	yes	complemented
134	C₂×#460	C₂×C₇	1	1	yes	characteristic
135	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#440	C₂×C₇	1	2	yes	complemented
137	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂⁴×C₇	—	2	2	no	—
139	C₂×C₇×Q₈	—	2	4	no	—
140	C₂×C₇×Q₈	—	2	1	no	—
141	C₂×C₇×Q₈	—	2	1	no	—
142	C₂×C₇×Q₈	—	2	8	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	2	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	8	4	no	—
148	C₂×C₇×Q₈	—	8	2	no	—
149	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
150	C₂×C₇×Q₈	#41	1	4	yes	—
151	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
152	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
153	C₂×C₇×D₄	—	2	2	no	—
154	C₂×C₇×D₄	—	2	4	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	4	no	—
157	C₂×C₇×D₄	—	2	4	no	—
158	C₂×C₇×D₄	—	4	4	no	—
159	C₂×C₇×D₄	—	8	2	no	—
160	C₂×C₇×D₄	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	2	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	8	no	—
167	C₂²×C₄×C₇	—	8	4	no	—
168	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
173	C₇×Q₁₆	—	2	8	no	—
174	C₇×SD₁₆	—	2	16	no	—
175	C₂×C₇×C₈	—	2	4	no	—
176	C₂×C₇×C₈	—	2	2	no	—
177	C₂×C₇×C₈	—	2	2	no	—
178	C₂×C₇×C₈	C₂⁴	1	2	yes	—
179	C₂×C₇×C₈	C₂⁴	1	2	yes	—
180	C₂×C₇×C₈	C₂⁴	1	4	yes	—
181	C₇×C₄⋊C₄	—	2	8	no	—
182	C₇×C₄⋊C₄	—	2	4	no	—
183	C₇×C₄⋊C₄	—	2	4	no	—
184	C₇×C₄⋊C₄	—	2	8	no	—
185	C₇×C₄⋊C₄	—	2	4	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
190	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
193	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
194	C₇×C₂²⋊C₄	—	2	8	no	—
195	C₇×C₂²⋊C₄	—	2	8	no	—
196	C₇×C₂²⋊C₄	—	2	8	no	—
197	C₄²×C₇	—	2	4	no	—
198	C₄²×C₇	—	2	8	no	—
199	C₄²×C₇	—	2	4	no	—
200	C₄²×C₇	C₂×D₄	1	4	yes	—
201	C₄²×C₇	C₂×D₄	1	2	yes	—
202	C₄²×C₇	C₂⁴	1	2	yes	—
203	C₄²×C₇	C₂⁴	1	4	yes	—
204	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
205	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
206	#559	—	2	4	no	—
207	#559	C₂²×C₇	1	8	yes	—
208	Q₈²	—	2	4	no	—
209	Q₈²	C₂²×C₇	1	8	yes	complemented
210	C₂×C₄⋊Q₈	—	2	1	no	—
211	C₂×C₄⋊Q₈	—	2	2	no	—
212	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
214	C₂×#127	C₂²×C₇	1	1	yes	characteristic
215	C₂×#124	—	2	1	no	—
216	C₂×#124	C₂²×C₇	1	2	yes	—
217	C₂×#123	—	2	2	no	—
218	C₂×C₄×Q₈	—	2	1	no	—
219	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
225	#489	C₂²×C₇	1	16	yes	complemented
226	#486	C₂²×C₇	1	8	yes	—
227	#477	C₂²×C₇	1	8	yes	complemented
228	#474	C₂²×C₇	1	16	yes	complemented
229	#464	C₂²×C₇	1	16	yes	complemented
230	#460	C₂²×C₇	1	8	yes	—
231	#446	C₂²×C₇	1	8	yes	complemented
232	#440	C₂²×C₇	1	16	yes	complemented
233	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
234	C₂×#107	C₂²×C₇	1	2	yes	—
235	C₂×#107	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
238	C₂×#103	C₂²×C₇	1	2	yes	—
239	C₂×#103	C₂²×C₇	1	1	yes	characteristic
240	C₂×#103	C₂²×C₇	1	1	yes	characteristic
241	C₂×#102	C₂²×C₇	1	2	yes	—
242	C₂×#102	C₂²×C₇	1	2	yes	—
243	C₂×#102	C₂²×C₇	1	2	yes	—
244	C₂×#97	C₂²×C₇	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
246	C₂³×C₇	—	2	4	no	—
247	C₂³×C₇	—	4	4	no	—
248	C₂³×C₇	—	4	4	no	—
249	C₂³×C₇	—	4	4	no	—
250	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
251	C₇×Q₈	—	2	4	no	—
252	C₇×Q₈	—	2	8	no	—
253	C₇×Q₈	—	2	2	no	—
254	C₇×Q₈	—	2	2	no	—
255	C₇×Q₈	—	2	2	no	—
256	C₇×Q₈	—	4	2	no	—
257	C₇×Q₈	—	8	8	no	—
258	C₇×Q₈	—	8	4	no	—
259	C₇×Q₈	C₂×#41	1	4	yes	—
260	C₇×D₄	—	2	4	no	—
261	C₇×D₄	—	2	4	no	—
262	C₇×D₄	—	4	4	no	—
263	C₇×D₄	—	4	8	no	—
264	C₇×D₄	—	8	4	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	2	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	2	no	—
271	C₂×C₄×C₇	—	2	2	no	—
272	C₂×C₄×C₇	—	2	4	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	4	2	no	—
275	C₂×C₄×C₇	—	4	2	no	—
276	C₂×C₄×C₇	—	4	2	no	—
277	C₂×C₄×C₇	—	4	4	no	—
278	C₂×C₄×C₇	—	8	8	no	—
279	C₂×C₄×C₇	#137	1	4	yes	—
280	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
281	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
282	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₇	C₂×#41	1	2	yes	—
286	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
287	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
288	C₇×C₈	—	2	4	no	—
289	C₇×C₈	—	2	2	no	—
290	C₇×C₈	—	2	2	no	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂³×C₇	1	2	yes	—
299	C₂³×C₄	—	2	2	no	—
300	C₂×Q₁₆	—	2	4	no	—
301	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
302	C₂×SD₁₆	—	2	8	no	—
303	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
304	C₂²×C₈	C₂³×C₇	1	2	yes	—
305	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
307	C₄⋊Q₈	—	2	8	no	—
308	C₄⋊Q₈	—	2	16	no	—
309	C₄⋊Q₈	—	2	4	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
312	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
313	#127	—	2	2	no	—
314	#127	C₂³×C₇	1	4	yes	—
315	#124	—	2	8	no	—
316	#124	—	2	4	no	—
317	#124	C₂³×C₇	1	8	yes	—
318	#123	—	2	16	no	—
319	C₄×Q₈	—	2	8	no	—
320	C₄×Q₈	—	2	4	no	—
321	C₄×Q₈	—	2	2	no	—
322	C₄×Q₈	—	2	2	no	—
323	C₄×Q₈	C₇×D₄	1	4	yes	—
324	C₄×Q₈	C₂³×C₇	1	4	yes	—
325	C₄×Q₈	C₂³×C₇	1	8	yes	—
326	C₄×Q₈	C₂³×C₇	1	4	yes	—
327	C₄×Q₈	C₂³×C₇	1	4	yes	—
328	C₄×D₄	—	2	8	no	—
329	C₄×D₄	—	2	4	no	—
330	C₄×D₄	C₂³×C₇	1	8	yes	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₇	1	2	yes	—
348	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
349	#107	C₂³×C₇	1	4	yes	—
350	#107	C₂³×C₇	1	8	yes	—
351	C₄⋊C₈	C₂³×C₇	1	4	yes	—
352	C₄⋊C₈	C₂³×C₇	1	8	yes	—
353	#103	C₂³×C₇	1	4	yes	—
354	#103	C₂³×C₇	1	4	yes	—
355	#103	C₂³×C₇	1	8	yes	—
356	#102	C₂³×C₇	1	8	yes	—
357	#102	C₂³×C₇	1	8	yes	—
358	#102	C₂³×C₇	1	8	yes	—
359	#97	C₂³×C₇	1	8	yes	—
360	C₄×C₈	C₂³×C₇	1	4	yes	—
361	C₂²×C₇	—	4	4	no	—
362	C₂²×C₇	—	4	4	no	—
363	C₂²×C₇	—	4	4	no	—
364	C₂²×C₇	—	8	8	no	—
365	C₂²×C₇	#548	1	2	yes	—
366	C₂²×C₇	C₂×#137	1	2	yes	—
367	C₂²×C₇	#576	1	2	yes	—
368	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
369	C₄×C₇	—	2	4	no	—
370	C₄×C₇	—	2	4	no	—
371	C₄×C₇	—	2	4	no	—
372	C₄×C₇	—	2	2	no	—
373	C₄×C₇	—	4	2	no	—
374	C₄×C₇	—	4	2	no	—
375	C₄×C₇	—	4	2	no	—
376	C₄×C₇	—	4	4	no	—
377	C₄×C₇	#548	1	2	yes	—
378	C₄×C₇	C₂×#137	1	4	yes	—
379	C₄×C₇	C₂²×#41	1	1	yes	characteristic
380	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	C₂⁴	—	2	2	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	8	4	no	—
391	C₂×Q₈	—	8	2	no	—
392	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
393	C₂×Q₈	C₇×#41	1	4	yes	—
394	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
395	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	8	2	no	—
403	C₂×D₄	C₂⁴×C₇	1	4	yes	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	8	4	no	—
411	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
412	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
413	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
415	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
416	Q₁₆	—	2	8	no	—
417	SD₁₆	—	2	16	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	C₂⁴×C₇	1	2	yes	—
422	C₂×C₈	C₂⁴×C₇	1	2	yes	—
423	C₂×C₈	C₂⁴×C₇	1	4	yes	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
433	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
434	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
435	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
436	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₄²	—	2	4	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	4	no	—
443	C₄²	C₂×C₇×D₄	1	4	yes	—
444	C₄²	C₂×C₇×D₄	1	2	yes	—
445	C₄²	C₂⁴×C₇	1	2	yes	—
446	C₄²	C₂⁴×C₇	1	4	yes	—
447	C₂×C₇	—	8	4	no	—
448	C₂×C₇	#3375	1	4	yes	direct product factor
449	C₂×C₇	C₂×#548	1	1	yes	characteristic
450	C₂×C₇	C₂²×#137	1	1	yes	characteristic
451	C₂×C₇	C₂×#576	1	1	yes	characteristic
452	C₂³	—	2	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
457	Q₈	—	2	2	no	—
458	Q₈	—	2	4	no	—
459	Q₈	—	2	8	no	—
460	Q₈	—	2	2	no	—
461	Q₈	—	2	2	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	8	8	no	—
464	Q₈	—	8	4	no	—
465	Q₈	C₂×C₇×#41	1	4	yes	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	4	no	—
469	D₄	—	4	8	no	—
470	D₄	—	8	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	8	8	no	—
485	C₂×C₄	C₇×#137	1	4	yes	—
486	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
487	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
488	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
489	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
490	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
491	C₂×C₄	C₂×C₇×#41	1	2	yes	—
492	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
493	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₇	C₂×#3375	1	1	yes	characteristic, direct product factor, Sylow
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	8	8	no	—
502	C₂²	C₇×#548	1	2	yes	—
503	C₂²	C₂×C₇×#137	1	2	yes	—
504	C₂²	C₇×#576	1	2	yes	—
505	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
506	C₄	—	2	4	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	4	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	4	no	—
513	C₄	—	4	2	no	—
514	C₄	C₇×#548	1	2	yes	—
515	C₄	C₂×C₇×#137	1	4	yes	—
516	C₄	C₂²×C₇×#41	1	1	yes	characteristic
517	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
518	C₂	—	8	4	no	—
519	C₂	C₇×#3375	1	4	yes	direct product factor
520	C₂	C₂×C₇×#548	1	1	yes	characteristic
521	C₂	C₂²×C₇×#137	1	1	yes	characteristic
522	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#127	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
2. C₂×C₇×Q₈²	C₂	semidirect
3. C₇×#3375	C₂	direct (N × H)
4. C₂×C₇×#489	C₂	semidirect
6. C₂×C₇×#477	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
11. C₂×C₇×#440	C₂	semidirect
12. C₂×C₄×C₇×Q₁₆	C₂	semidirect
18. C₇×Q₈²	C₂²	semidirect
34. C₇×#489	C₂²	semidirect
36. C₇×#477	C₂²	semidirect
37. C₇×#474	C₂²	semidirect
38. C₇×#464	C₂²	semidirect
40. C₇×#446	C₂²	semidirect
41. C₇×#440	C₂²	semidirect
42. C₄×C₇×Q₁₆	C₂²	semidirect
55. C₂×#3375	C₇	direct (N × H)
127. C₂×Q₈²	C₂×C₇	semidirect
128. #3375	C₂×C₇	direct (N × H)
129. C₂×#489	C₂×C₇	semidirect
131. C₂×#477	C₂×C₇	semidirect
132. C₂×#474	C₂×C₇	semidirect
133. C₂×#464	C₂×C₇	semidirect
135. C₂×#446	C₂×C₇	semidirect
136. C₂×#440	C₂×C₇	semidirect
137. C₂×C₄×Q₁₆	C₂×C₇	semidirect
209. Q₈²	C₂²×C₇	semidirect
225. #489	C₂²×C₇	semidirect
227. #477	C₂²×C₇	semidirect
228. #474	C₂²×C₇	semidirect
229. #464	C₂²×C₇	semidirect
231. #446	C₂²×C₇	semidirect
232. #440	C₂²×C₇	semidirect
233. C₄×Q₁₆	C₂²×C₇	semidirect
448. C₂×C₇	#3375	direct (N × H)
497. C₇	C₂×#3375	direct (N × H)
519. C₂	C₇×#3375	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×#559	2
C₂×C₇×Q₈²	2
C₇×#3375	2
C₂×C₇×#489	2
C₂×C₇×#486	2
C₂×C₇×#477	2
C₂×C₇×#474	2
C₂×C₇×#464	2
C₂×C₇×#460	2
C₂×C₇×#446	2
C₂×C₇×#440	2
C₂×C₄×C₇×Q₁₆	2
C₂×#3375	7

Subgroups — C2×C7×#3375 #13238527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3375 #13238527