Subgroups — C₂×C₇×#3328 #13238364

Order 1792.

2082 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
2	C₂×C₇×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₇×#3328	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#470	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#451	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#419	C₂	1	2	yes	maximal, complemented
13	C₂³×C₇×Q₈	C₂²	1	2	yes	—
14	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
17	C₇×#556	—	2	4	no	—
18	C₇×#556	C₂²	1	8	yes	—
19	C₇×D₄×Q₈	—	2	4	no	—
20	C₇×D₄×Q₈	C₂²	1	8	yes	—
21	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#126	—	2	2	no	—
25	C₂×C₇×#124	—	2	1	no	—
26	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×Q₈	—	2	1	no	—
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
34	C₂×C₇×#117	C₂²	1	2	yes	—
35	C₇×#487	C₂²	1	8	yes	complemented
36	C₇×#485	C₂²	1	16	yes	complemented
37	C₇×#475	C₂²	1	8	yes	complemented
38	C₇×#470	C₂²	1	16	yes	complemented
39	C₇×#462	C₂²	1	8	yes	complemented
40	C₇×#451	C₂²	1	16	yes	complemented
41	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
42	C₇×#436	C₂²	1	8	yes	—
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₇×#419	C₂²	1	16	yes	complemented
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×#103	C₂²	1	2	yes	—
51	C₂×C₇×#103	C₂²	1	2	yes	—
52	C₂×C₇×#103	C₂²	1	2	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3328	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	2	no	—
57	C₂²×C₇×Q₈	—	2	4	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	2	8	no	—
60	C₂²×C₇×Q₈	—	4	4	no	—
61	C₂²×C₇×Q₈	C₂³	1	2	yes	—
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×Q₈	C₂³	1	8	yes	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇	—	2	2	no	—
67	C₂³×C₄×C₇	C₂³	1	2	yes	—
68	C₂×C₇×Q₁₆	—	2	4	no	—
69	C₂×C₇×Q₁₆	—	4	4	no	—
70	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
71	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
72	C₂×C₇×M₁₆	—	4	4	no	—
73	C₂×C₇×M₁₆	C₂³	1	8	yes	—
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	2	yes	—
77	C₇×C₄⋊Q₈	—	2	8	no	—
78	C₇×C₄⋊Q₈	—	2	2	no	—
79	C₇×C₄⋊Q₈	—	2	2	no	—
80	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
81	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₇×#126	—	2	16	no	—
83	C₇×#124	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	4	no	—
85	C₇×C₂²⋊Q₈	—	2	4	no	—
86	C₇×C₂²⋊Q₈	—	2	16	no	—
87	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
89	C₄×C₇×Q₈	—	2	8	no	—
90	C₄×C₇×Q₈	—	2	2	no	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	C₂³	1	4	yes	—
93	C₄×C₇×Q₈	C₂³	1	4	yes	—
94	C₄×C₇×D₄	—	2	8	no	—
95	C₄×C₇×D₄	D₄	1	4	yes	—
96	C₄×C₇×D₄	C₂³	1	4	yes	—
97	C₇×#117	—	2	4	no	—
98	C₇×#117	C₂³	1	8	yes	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	2	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
114	C₂×C₄²×C₇	—	2	2	no	—
115	C₂×C₄²×C₇	—	2	1	no	—
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₇×#107	C₂³	1	4	yes	—
119	C₇×#106	C₂³	1	8	yes	—
120	C₇×C₄⋊C₈	C₂³	1	4	yes	—
121	C₇×#103	C₂³	1	4	yes	—
122	C₇×#103	C₂³	1	8	yes	—
123	C₇×#103	C₂³	1	8	yes	—
124	C₇×#103	C₂³	1	8	yes	—
125	C₇×#103	C₂³	1	8	yes	—
126	C₇×#103	C₂³	1	4	yes	—
127	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₇×C₈	C₂³	1	4	yes	—
129	C₂×#556	C₂×C₇	1	1	yes	characteristic
130	C₂×D₄×Q₈	C₂×C₇	1	1	yes	characteristic
131	#3328	C₂×C₇	1	16	yes	direct product factor
132	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#485	C₂×C₇	1	2	yes	complemented
134	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#470	C₂×C₇	1	2	yes	complemented
136	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#451	C₂×C₇	1	2	yes	complemented
138	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×#436	C₂×C₇	1	1	yes	characteristic
140	C₂×#419	C₂×C₇	1	2	yes	complemented
141	C₂⁴×C₇	C₂×D₄	1	2	yes	—
142	C₂×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	2	8	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	2	2	no	—
148	C₂×C₇×Q₈	—	2	16	no	—
149	C₂×C₇×Q₈	—	2	2	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	2	2	no	—
152	C₂×C₇×Q₈	—	2	4	no	—
153	C₂×C₇×Q₈	—	4	8	no	—
154	C₂×C₇×Q₈	—	4	8	no	—
155	C₂×C₇×Q₈	—	4	16	no	—
156	C₂×C₇×Q₈	—	4	4	no	—
157	C₂×C₇×Q₈	#41	1	4	yes	—
158	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
159	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
160	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₇	—	2	1	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	4	no	—
166	C₂²×C₄×C₇	—	2	8	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	2	no	—
171	C₂²×C₄×C₇	—	2	2	no	—
172	C₂²×C₄×C₇	—	4	8	no	—
173	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
179	C₇×Q₁₆	—	2	8	no	—
180	C₇×Q₁₆	—	4	8	no	—
181	C₇×M₁₆	—	4	8	no	—
182	C₂×C₇×C₈	—	2	2	no	—
183	C₂×C₇×C₈	—	2	2	no	—
184	C₂×C₇×C₈	—	2	4	no	—
185	C₂×C₇×C₈	C₂⁴	1	2	yes	—
186	C₂×C₇×C₈	C₂⁴	1	2	yes	—
187	C₂×C₇×C₈	C₂⁴	1	4	yes	—
188	C₇×C₄⋊C₄	—	2	4	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	4	no	—
191	C₇×C₄⋊C₄	—	2	4	no	—
192	C₇×C₄⋊C₄	—	2	4	no	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	1	no	—
196	C₇×C₄⋊C₄	—	2	2	no	—
197	C₇×C₄⋊C₄	—	2	1	no	—
198	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
201	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
206	C₄²×C₇	—	2	8	no	—
207	C₄²×C₇	—	2	4	no	—
208	C₄²×C₇	—	2	4	no	—
209	C₄²×C₇	C₂×D₄	1	2	yes	—
210	C₄²×C₇	C₂⁴	1	2	yes	—
211	C₂³×Q₈	C₂²×C₇	1	2	yes	—
212	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
214	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
215	#556	—	2	4	no	—
216	#556	C₂²×C₇	1	8	yes	—
217	D₄×Q₈	—	2	4	no	—
218	D₄×Q₈	C₂²×C₇	1	8	yes	—
219	C₂×C₄⋊Q₈	—	2	1	no	—
220	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
222	C₂×#126	—	2	2	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
227	C₂×C₄×Q₈	—	2	1	no	—
228	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
232	C₂×#117	C₂²×C₇	1	2	yes	—
233	#487	C₂²×C₇	1	8	yes	complemented
234	#485	C₂²×C₇	1	16	yes	complemented
235	#475	C₂²×C₇	1	8	yes	complemented
236	#470	C₂²×C₇	1	16	yes	complemented
237	#462	C₂²×C₇	1	8	yes	complemented
238	#451	C₂²×C₇	1	16	yes	complemented
239	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
240	#436	C₂²×C₇	1	8	yes	—
241	C₂×#107	C₂²×C₇	1	1	yes	characteristic
242	C₂×#106	C₂²×C₇	1	2	yes	—
243	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
244	#419	C₂²×C₇	1	16	yes	complemented
245	C₂×#103	C₂²×C₇	1	2	yes	—
246	C₂×#103	C₂²×C₇	1	2	yes	—
247	C₂×#103	C₂²×C₇	1	2	yes	—
248	C₂×#103	C₂²×C₇	1	2	yes	—
249	C₂×#103	C₂²×C₇	1	1	yes	characteristic
250	C₂×#103	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
253	C₂³×C₇	—	2	4	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	2	4	no	—
256	C₂³×C₇	C₂²×D₄	1	4	yes	—
257	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
258	C₇×Q₈	—	2	4	no	—
259	C₇×Q₈	—	2	2	no	—
260	C₇×Q₈	—	2	2	no	—
261	C₇×Q₈	—	2	4	no	—
262	C₇×Q₈	—	2	2	no	—
263	C₇×Q₈	—	2	4	no	—
264	C₇×Q₈	—	4	16	no	—
265	C₇×Q₈	—	4	2	no	—
266	C₇×Q₈	—	4	4	no	—
267	C₇×Q₈	—	4	8	no	—
268	C₇×Q₈	C₂×#41	1	4	yes	—
269	C₇×D₄	—	2	8	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	4	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	8	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	2	4	no	—
277	C₂×C₄×C₇	—	2	2	no	—
278	C₂×C₄×C₇	—	2	2	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	4	no	—
281	C₂×C₄×C₇	—	2	4	no	—
282	C₂×C₄×C₇	—	4	16	no	—
283	C₂×C₄×C₇	—	4	4	no	—
284	C₂×C₄×C₇	—	4	2	no	—
285	C₂×C₄×C₇	—	4	4	no	—
286	C₂×C₄×C₇	—	4	2	no	—
287	C₂×C₄×C₇	—	4	2	no	—
288	C₂×C₄×C₇	#137	1	4	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
290	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇	C₂×#41	1	2	yes	—
294	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
295	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
296	C₇×C₈	—	2	2	no	—
297	C₇×C₈	—	2	2	no	—
298	C₇×C₈	—	2	4	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	2	4	no	—
302	C₂²×Q₈	—	2	8	no	—
303	C₂²×Q₈	—	4	4	no	—
304	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₇	1	2	yes	—
306	C₂²×Q₈	C₂³×C₇	1	8	yes	—
307	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
308	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	C₂³×C₇	1	2	yes	—
311	C₂×Q₁₆	—	2	4	no	—
312	C₂×Q₁₆	—	4	4	no	—
313	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
314	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
315	C₂×M₁₆	—	4	4	no	—
316	C₂×M₁₆	C₂³×C₇	1	8	yes	—
317	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₇	1	2	yes	—
319	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
320	C₄⋊Q₈	—	2	8	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
324	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
325	#126	—	2	16	no	—
326	#124	—	2	8	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	16	no	—
330	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
331	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
332	C₄×Q₈	—	2	8	no	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	C₂³×C₇	1	4	yes	—
336	C₄×Q₈	C₂³×C₇	1	4	yes	—
337	C₄×D₄	—	2	8	no	—
338	C₄×D₄	C₇×D₄	1	4	yes	—
339	C₄×D₄	C₂³×C₇	1	4	yes	—
340	#117	—	2	4	no	—
341	#117	C₂³×C₇	1	8	yes	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
357	C₂×C₄²	—	2	2	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
361	#107	C₂³×C₇	1	4	yes	—
362	#106	C₂³×C₇	1	8	yes	—
363	C₄⋊C₈	C₂³×C₇	1	4	yes	—
364	#103	C₂³×C₇	1	4	yes	—
365	#103	C₂³×C₇	1	8	yes	—
366	#103	C₂³×C₇	1	8	yes	—
367	#103	C₂³×C₇	1	8	yes	—
368	#103	C₂³×C₇	1	4	yes	—
369	#103	C₂³×C₇	1	8	yes	—
370	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
371	C₄×C₈	C₂³×C₇	1	4	yes	—
372	C₂²×C₇	—	2	4	no	—
373	C₂²×C₇	—	2	4	no	—
374	C₂²×C₇	—	2	4	no	—
375	C₂²×C₇	—	4	8	no	—
376	C₂²×C₇	#546	1	2	yes	—
377	C₂²×C₇	C₂×#137	1	2	yes	—
378	C₂²×C₇	#578	1	2	yes	—
379	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₇	—	2	4	no	—
381	C₄×C₇	—	2	4	no	—
382	C₄×C₇	—	2	2	no	—
383	C₄×C₇	—	4	4	no	—
384	C₄×C₇	—	4	2	no	—
385	C₄×C₇	—	4	4	no	—
386	C₄×C₇	—	4	2	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	#546	1	2	yes	—
389	C₄×C₇	C₂×#137	1	4	yes	—
390	C₄×C₇	C₂²×#41	1	1	yes	characteristic
391	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂⁴	C₂×C₇×D₄	1	2	yes	—
393	C₂×Q₈	—	2	1	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	8	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	16	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	4	8	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	—	4	16	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	C₇×#41	1	4	yes	—
409	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
410	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
411	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	4	8	no	—
424	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
425	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
427	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
430	Q₁₆	—	2	8	no	—
431	Q₁₆	—	4	8	no	—
432	M₁₆	—	4	8	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	C₂⁴×C₇	1	2	yes	—
437	C₂×C₈	C₂⁴×C₇	1	2	yes	—
438	C₂×C₈	C₂⁴×C₇	1	4	yes	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
450	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
452	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
457	C₄²	—	2	8	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	4	no	—
460	C₄²	C₂×C₇×D₄	1	2	yes	—
461	C₄²	C₂⁴×C₇	1	2	yes	—
462	C₂×C₇	—	4	4	no	—
463	C₂×C₇	#3328	1	4	yes	direct product factor
464	C₂×C₇	C₂×#546	1	1	yes	characteristic
465	C₂×C₇	C₂²×#137	1	1	yes	characteristic
466	C₂×C₇	C₂×#578	1	1	yes	characteristic
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	4	no	—
470	C₂³	C₂²×C₇×D₄	1	4	yes	—
471	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
472	Q₈	—	2	2	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	4	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	2	4	no	—
478	Q₈	—	4	16	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	4	no	—
481	Q₈	—	4	8	no	—
482	Q₈	C₂×C₇×#41	1	4	yes	—
483	D₄	—	2	8	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	4	16	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	C₇×#137	1	4	yes	—
503	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
504	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
505	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
507	C₂×C₄	C₂×C₇×#41	1	2	yes	—
508	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
509	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	2	2	no	—
512	C₈	—	2	4	no	—
513	C₇	C₂×#3328	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	4	8	no	—
518	C₂²	C₇×#546	1	2	yes	—
519	C₂²	C₂×C₇×#137	1	2	yes	—
520	C₂²	C₇×#578	1	2	yes	—
521	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	4	no	—
524	C₄	—	2	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	4	no	—
529	C₄	—	4	2	no	—
530	C₄	C₇×#546	1	2	yes	—
531	C₄	C₂×C₇×#137	1	4	yes	—
532	C₄	C₂²×C₇×#41	1	1	yes	characteristic
533	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂	—	4	4	no	—
535	C₂	C₇×#3328	1	4	yes	direct product factor
536	C₂	C₂×C₇×#546	1	1	yes	characteristic
537	C₂	C₂²×C₇×#137	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×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#3328	C₂	direct (N × H)
4. C₂×C₇×#487	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#475	C₂	semidirect
7. C₂×C₇×#470	C₂	semidirect
8. C₂×C₇×#462	C₂	semidirect
9. C₂×C₇×#451	C₂	semidirect
10. C₂×C₄×C₇×Q₁₆	C₂	semidirect
12. C₂×C₇×#419	C₂	semidirect
35. C₇×#487	C₂²	semidirect
36. C₇×#485	C₂²	semidirect
37. C₇×#475	C₂²	semidirect
38. C₇×#470	C₂²	semidirect
39. C₇×#462	C₂²	semidirect
40. C₇×#451	C₂²	semidirect
41. C₄×C₇×Q₁₆	C₂²	semidirect
46. C₇×#419	C₂²	semidirect
55. C₂×#3328	C₇	direct (N × H)
131. #3328	C₂×C₇	direct (N × H)
132. C₂×#487	C₂×C₇	semidirect
133. C₂×#485	C₂×C₇	semidirect
134. C₂×#475	C₂×C₇	semidirect
135. C₂×#470	C₂×C₇	semidirect
136. C₂×#462	C₂×C₇	semidirect
137. C₂×#451	C₂×C₇	semidirect
138. C₂×C₄×Q₁₆	C₂×C₇	semidirect
140. C₂×#419	C₂×C₇	semidirect
233. #487	C₂²×C₇	semidirect
234. #485	C₂²×C₇	semidirect
235. #475	C₂²×C₇	semidirect
236. #470	C₂²×C₇	semidirect
237. #462	C₂²×C₇	semidirect
238. #451	C₂²×C₇	semidirect
239. C₄×Q₁₆	C₂²×C₇	semidirect
244. #419	C₂²×C₇	semidirect
463. C₂×C₇	#3328	direct (N × H)
513. C₇	C₂×#3328	direct (N × H)
535. C₂	C₇×#3328	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×#3328	2
C₂×C₇×#487	2
C₂×C₇×#485	2
C₂×C₇×#475	2
C₂×C₇×#470	2
C₂×C₇×#462	2
C₂×C₇×#451	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×#436	2
C₂×C₇×#419	2
C₂×#3328	7

Subgroups — C2×C7×#3328 #13238364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3328 #13238364