Subgroups — C₂×C₇×#3097 #13237729

Order 1792.

2170 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#520	C₂	1	1	yes	maximal, characteristic
3	C₇×#3097	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#483	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#408	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₇×#536	—	2	4	no	—
18	C₇×#536	C₂²	1	8	yes	—
19	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
20	C₂×C₇×#124	—	2	1	no	—
21	C₂×C₇×#123	—	2	2	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₇×#520	—	2	4	no	—
25	C₇×#520	C₂²	1	8	yes	—
26	C₂×C₄×C₇×Q₈	—	2	1	no	—
27	C₂×C₄×C₇×D₄	—	2	2	no	—
28	C₂×C₄×C₇×D₄	—	2	1	no	—
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₂×C₇×#117	C₂²	1	1	yes	characteristic
31	C₂×C₇×#117	C₂²	1	2	yes	—
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₇×#485	C₂²	1	16	yes	complemented
35	C₇×#485	C₂²	1	16	yes	complemented
36	C₇×#484	C₂²	1	16	yes	complemented
37	C₇×#483	C₂²	1	16	yes	complemented
38	C₇×#428	C₂²	1	8	yes	complemented
39	C₇×#427	C₂²	1	8	yes	complemented
40	C₂×C₇×#107	C₂²	1	1	yes	characteristic
41	C₂×C₇×#107	C₂²	1	1	yes	characteristic
42	C₂×C₇×#107	C₂²	1	2	yes	—
43	C₂×C₇×#106	C₂²	1	1	yes	characteristic
44	C₂×C₇×#106	C₂²	1	1	yes	characteristic
45	C₂×C₇×#106	C₂²	1	2	yes	—
46	C₇×#419	C₂²	1	8	yes	complemented
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×#103	C₂²	1	2	yes	—
51	C₂×C₇×#103	C₂²	1	8	yes	complemented
52	C₇×#408	C₂²	1	8	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
55	C₂×#3097	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	4	no	—
57	C₂×C₇×#41	—	2	4	no	—
58	C₂×C₇×#41	D₄	1	4	yes	—
59	C₂×C₇×#41	C₂³	1	4	yes	—
60	C₂²×C₇×Q₈	—	2	1	no	—
61	C₂²×C₇×Q₈	—	2	2	no	—
62	C₂²×C₇×Q₈	—	2	4	no	—
63	C₂²×C₇×Q₈	—	2	4	no	—
64	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
65	C₂²×C₇×Q₈	C₂³	1	2	yes	—
66	C₂²×C₇×Q₈	C₂³	1	4	yes	—
67	C₂²×C₇×D₄	D₄	1	2	yes	—
68	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	—	2	2	no	—
71	C₂³×C₄×C₇	—	2	1	no	—
72	C₂³×C₄×C₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₂×C₇×M₁₆	—	2	4	no	—
75	C₂×C₇×M₁₆	C₂³	1	4	yes	—
76	C₂²×C₇×C₈	—	2	4	no	—
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	2	yes	—
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	4	yes	—
81	C₇×C₄⋊Q₈	—	2	8	no	—
82	C₇×#124	—	2	8	no	—
83	C₇×#123	—	2	16	no	—
84	C₇×C₂²⋊Q₈	—	2	4	no	—
85	C₇×C₂²⋊Q₈	—	2	4	no	—
86	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
87	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₄×C₇×Q₈	—	2	8	no	—
89	C₄×C₇×D₄	—	2	16	no	—
90	C₄×C₇×D₄	—	2	8	no	—
91	C₇×#117	—	2	4	no	—
92	C₇×#117	—	2	2	no	—
93	C₇×#117	—	2	2	no	—
94	C₇×#117	C₂³	1	8	yes	—
95	C₇×#117	C₂³	1	4	yes	—
96	C₇×#117	C₂³	1	4	yes	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	4	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	2	no	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₄²×C₇	—	2	2	no	—
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	—	2	1	no	—
118	C₇×#107	C₂³	1	4	yes	—
119	C₇×#107	C₂³	1	8	yes	—
120	C₇×#107	C₂³	1	4	yes	—
121	C₇×#106	C₂³	1	4	yes	—
122	C₇×#106	C₂³	1	8	yes	—
123	C₇×#106	C₂³	1	4	yes	—
124	C₇×#103	C₂³	1	8	yes	—
125	C₇×#103	C₂³	1	8	yes	—
126	C₇×#103	C₂³	1	8	yes	—
127	C₇×#103	C₂³	1	8	yes	—
128	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
129	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
130	C₂×#536	C₂×C₇	1	1	yes	characteristic
131	C₂×#520	C₂×C₇	1	1	yes	characteristic
132	#3097	C₂×C₇	1	16	yes	direct product factor
133	C₂×#484	C₂×C₇	1	2	yes	complemented
134	C₂×#485	C₂×C₇	1	2	yes	complemented
135	C₂×#485	C₂×C₇	1	2	yes	complemented
136	C₂×#483	C₂×C₇	1	2	yes	complemented
137	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×#419	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂²×#103	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#408	C₂×C₇	1	1	yes	characteristic
142	C₂⁴×C₇	C₂×D₄	1	2	yes	—
143	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
144	C₇×#41	—	2	16	no	—
145	C₇×#41	—	2	8	no	—
146	C₇×#41	—	2	8	no	—
147	C₂×C₇×Q₈	—	2	4	no	—
148	C₂×C₇×Q₈	—	2	2	no	—
149	C₂×C₇×Q₈	—	2	4	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	2	4	no	—
152	C₂×C₇×Q₈	—	2	8	no	—
153	C₂×C₇×Q₈	—	2	8	no	—
154	C₂×C₇×Q₈	—	4	4	no	—
155	C₂×C₇×Q₈	—	4	8	no	—
156	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
157	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
158	C₂×C₇×D₄	—	2	8	no	—
159	C₂×C₇×D₄	—	2	4	no	—
160	C₂×C₇×D₄	C₂×D₄	1	8	yes	—
161	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₇	—	2	4	no	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	2	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	2	no	—
171	C₂²×C₄×C₇	—	2	8	no	—
172	C₂²×C₄×C₇	—	2	4	no	—
173	C₂²×C₄×C₇	—	4	4	no	—
174	C₂²×C₄×C₇	—	8	2	no	—
175	C₂²×C₄×C₇	—	8	4	no	—
176	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇	#41	1	4	yes	—
181	C₂²×C₄×C₇	#41	1	4	yes	—
182	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₇×M₁₆	—	2	8	no	—
186	C₂×C₇×C₈	—	2	2	no	—
187	C₂×C₇×C₈	—	2	2	no	—
188	C₂×C₇×C₈	—	2	8	no	—
189	C₂×C₇×C₈	—	2	4	no	—
190	C₂×C₇×C₈	C₂⁴	1	2	yes	—
191	C₂×C₇×C₈	C₂⁴	1	4	yes	—
192	C₂×C₇×C₈	C₂⁴	1	2	yes	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	2	no	—
195	C₇×C₄⋊C₄	—	2	8	no	—
196	C₇×C₄⋊C₄	—	2	4	no	—
197	C₇×C₄⋊C₄	—	2	8	no	—
198	C₇×C₄⋊C₄	—	2	8	no	—
199	C₇×C₄⋊C₄	—	2	1	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	—	2	1	no	—
202	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
203	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
204	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
205	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
206	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
207	C₇×C₂²⋊C₄	—	2	8	no	—
208	C₇×C₂²⋊C₄	—	2	4	no	—
209	C₇×C₂²⋊C₄	—	2	4	no	—
210	C₇×C₂²⋊C₄	—	2	8	no	—
211	C₇×C₂²⋊C₄	—	2	8	no	—
212	C₄²×C₇	—	2	8	no	—
213	C₄²×C₇	—	2	4	no	—
214	C₄²×C₇	—	2	4	no	—
215	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
216	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
218	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
219	#536	—	2	4	no	—
220	#536	C₂²×C₇	1	8	yes	—
221	C₂×C₄⋊Q₈	—	2	1	no	—
222	C₂×#124	—	2	1	no	—
223	C₂×#123	—	2	2	no	—
224	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
226	#520	—	2	4	no	—
227	#520	C₂²×C₇	1	8	yes	—
228	C₂×C₄×Q₈	—	2	1	no	—
229	C₂×C₄×D₄	—	2	2	no	—
230	C₂×C₄×D₄	—	2	1	no	—
231	C₂×#117	C₂²×C₇	1	2	yes	—
232	C₂×#117	C₂²×C₇	1	1	yes	characteristic
233	C₂×#117	C₂²×C₇	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
236	#485	C₂²×C₇	1	16	yes	complemented
237	#485	C₂²×C₇	1	16	yes	complemented
238	#484	C₂²×C₇	1	16	yes	complemented
239	#483	C₂²×C₇	1	16	yes	complemented
240	#428	C₂²×C₇	1	8	yes	complemented
241	#427	C₂²×C₇	1	8	yes	complemented
242	C₂×#107	C₂²×C₇	1	1	yes	characteristic
243	C₂×#107	C₂²×C₇	1	2	yes	—
244	C₂×#107	C₂²×C₇	1	1	yes	characteristic
245	C₂×#106	C₂²×C₇	1	1	yes	characteristic
246	C₂×#106	C₂²×C₇	1	2	yes	—
247	C₂×#106	C₂²×C₇	1	1	yes	characteristic
248	#419	C₂²×C₇	1	8	yes	complemented
249	C₂×#103	C₂²×C₇	1	2	yes	—
250	C₂×#103	C₂²×C₇	1	2	yes	—
251	C₂×#103	C₂²×C₇	1	2	yes	—
252	C₂×#103	C₂²×C₇	1	2	yes	—
253	C₂×#103	C₂²×C₇	1	8	yes	complemented
254	#408	C₂²×C₇	1	8	yes	—
255	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
257	C₂³×C₇	—	2	2	no	—
258	C₂³×C₇	—	2	2	no	—
259	C₂³×C₇	—	2	4	no	—
260	C₂³×C₇	—	2	4	no	—
261	C₂³×C₇	—	2	4	no	—
262	C₂³×C₇	#123	1	4	yes	—
263	C₂³×C₇	C₂²×D₄	1	4	yes	—
264	C₂³×C₇	C₂²×D₄	1	2	yes	—
265	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
266	C₇×Q₈	—	2	8	no	—
267	C₇×Q₈	—	2	4	no	—
268	C₇×Q₈	—	2	4	no	—
269	C₇×Q₈	—	4	4	no	—
270	C₇×Q₈	—	4	8	no	—
271	C₇×D₄	—	2	16	no	—
272	C₇×D₄	—	2	8	no	—
273	C₂×C₄×C₇	—	2	4	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	2	no	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	4	8	no	—
284	C₂×C₄×C₇	—	4	4	no	—
285	C₂×C₄×C₇	—	4	2	no	—
286	C₂×C₄×C₇	—	4	4	no	—
287	C₂×C₄×C₇	—	4	2	no	—
288	C₂×C₄×C₇	—	4	2	no	—
289	C₂×C₄×C₇	—	4	2	no	—
290	C₂×C₄×C₇	—	8	4	no	—
291	C₂×C₄×C₇	—	8	8	no	—
292	C₂×C₄×C₇	#123	1	4	yes	—
293	C₂×C₄×C₇	#123	1	8	yes	—
294	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
295	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇	C₂×#41	1	2	yes	—
298	C₂×C₄×C₇	C₂×#41	1	2	yes	—
299	C₂×C₄×C₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₇	C₂×#41	1	4	yes	—
301	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
302	C₇×C₈	—	2	2	no	—
303	C₇×C₈	—	2	2	no	—
304	C₇×C₈	—	2	4	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	4	no	—
307	C₂×#41	C₇×D₄	1	4	yes	—
308	C₂×#41	C₂³×C₇	1	4	yes	—
309	C₂²×Q₈	—	2	1	no	—
310	C₂²×Q₈	—	2	2	no	—
311	C₂²×Q₈	—	2	4	no	—
312	C₂²×Q₈	—	2	4	no	—
313	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
314	C₂²×Q₈	C₂³×C₇	1	2	yes	—
315	C₂²×Q₈	C₂³×C₇	1	4	yes	—
316	C₂²×D₄	C₇×D₄	1	2	yes	—
317	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	2	no	—
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	C₂³×C₇	1	2	yes	—
322	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
323	C₂×M₁₆	—	2	4	no	—
324	C₂×M₁₆	C₂³×C₇	1	4	yes	—
325	C₂²×C₈	—	2	4	no	—
326	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₇	1	4	yes	—
329	C₂²×C₈	C₂³×C₇	1	2	yes	—
330	C₄⋊Q₈	—	2	8	no	—
331	#124	—	2	8	no	—
332	#123	—	2	16	no	—
333	C₂²⋊Q₈	—	2	4	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
336	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
337	C₄×Q₈	—	2	8	no	—
338	C₄×D₄	—	2	16	no	—
339	C₄×D₄	—	2	8	no	—
340	#117	—	2	4	no	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	#117	C₂³×C₇	1	4	yes	—
344	#117	C₂³×C₇	1	8	yes	—
345	#117	C₂³×C₇	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
356	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	#107	C₂³×C₇	1	4	yes	—
368	#107	C₂³×C₇	1	4	yes	—
369	#107	C₂³×C₇	1	8	yes	—
370	#106	C₂³×C₇	1	4	yes	—
371	#106	C₂³×C₇	1	4	yes	—
372	#106	C₂³×C₇	1	8	yes	—
373	#103	C₂³×C₇	1	8	yes	—
374	#103	C₂³×C₇	1	8	yes	—
375	#103	C₂³×C₇	1	8	yes	—
376	#103	C₂³×C₇	1	8	yes	—
377	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
378	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
379	C₂²×C₇	—	2	8	no	—
380	C₂²×C₇	—	2	2	no	—
381	C₂²×C₇	—	2	2	no	—
382	C₂²×C₇	—	2	4	no	—
383	C₂²×C₇	—	2	4	no	—
384	C₂²×C₇	—	2	4	no	—
385	C₂²×C₇	—	4	8	no	—
386	C₂²×C₇	C₂×#123	1	4	yes	—
387	C₂²×C₇	C₂×#123	1	2	yes	—
388	C₂²×C₇	#577	1	2	yes	—
389	C₂²×C₇	#578	1	2	yes	—
390	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
391	C₄×C₇	—	2	4	no	—
392	C₄×C₇	—	4	4	no	—
393	C₄×C₇	—	4	2	no	—
394	C₄×C₇	—	4	4	no	—
395	C₄×C₇	—	4	2	no	—
396	C₄×C₇	—	4	2	no	—
397	C₄×C₇	—	4	2	no	—
398	C₄×C₇	C₂×#123	1	2	yes	—
399	C₄×C₇	C₂×#123	1	4	yes	—
400	C₄×C₇	C₂²×#41	1	1	yes	characteristic
401	C₄×C₇	C₂²×#41	1	1	yes	characteristic
402	C₂⁴	C₂×C₇×D₄	1	2	yes	—
403	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
404	#41	—	2	16	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	C₂×Q₈	—	2	4	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	2	8	no	—
413	C₂×Q₈	—	2	8	no	—
414	C₂×Q₈	—	4	4	no	—
415	C₂×Q₈	—	4	8	no	—
416	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
417	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	C₂×C₇×D₄	1	8	yes	—
421	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	8	2	no	—
435	C₂²×C₄	—	8	4	no	—
436	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
437	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
438	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
440	C₂²×C₄	C₇×#41	1	4	yes	—
441	C₂²×C₄	C₇×#41	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
445	M₁₆	—	2	8	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	8	no	—
449	C₂×C₈	—	2	4	no	—
450	C₂×C₈	C₂⁴×C₇	1	2	yes	—
451	C₂×C₈	C₂⁴×C₇	1	4	yes	—
452	C₂×C₈	C₂⁴×C₇	1	2	yes	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
463	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
464	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
465	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
466	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₄²	—	2	8	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	4	no	—
475	C₂×C₇	—	2	4	no	—
476	C₂×C₇	—	4	4	no	—
477	C₂×C₇	#3097	1	4	yes	direct product factor
478	C₂×C₇	C₂²×#123	1	1	yes	characteristic
479	C₂×C₇	C₂×#577	1	1	yes	characteristic
480	C₂×C₇	C₂×#578	1	1	yes	characteristic
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	4	no	—
485	C₂³	—	2	4	no	—
486	C₂³	C₇×#123	1	4	yes	—
487	C₂³	C₂²×C₇×D₄	1	4	yes	—
488	C₂³	C₂²×C₇×D₄	1	2	yes	—
489	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
490	Q₈	—	2	8	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	2	4	no	—
493	Q₈	—	4	4	no	—
494	Q₈	—	4	8	no	—
495	D₄	—	2	16	no	—
496	D₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	8	4	no	—
515	C₂×C₄	—	8	8	no	—
516	C₂×C₄	C₇×#123	1	4	yes	—
517	C₂×C₄	C₇×#123	1	8	yes	—
518	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
519	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
520	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
521	C₂×C₄	C₂×C₇×#41	1	2	yes	—
522	C₂×C₄	C₂×C₇×#41	1	2	yes	—
523	C₂×C₄	C₂×C₇×#41	1	4	yes	—
524	C₂×C₄	C₂×C₇×#41	1	4	yes	—
525	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
526	C₈	—	2	2	no	—
527	C₈	—	2	2	no	—
528	C₈	—	2	4	no	—
529	C₇	C₂×#3097	1	1	yes	characteristic, direct product factor, Sylow
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	8	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	4	no	—
535	C₂²	—	2	4	no	—
536	C₂²	—	4	8	no	—
537	C₂²	C₂×C₇×#123	1	4	yes	—
538	C₂²	C₂×C₇×#123	1	2	yes	—
539	C₂²	C₇×#577	1	2	yes	—
540	C₂²	C₇×#578	1	2	yes	—
541	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
542	C₄	—	2	4	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	4	no	—
549	C₄	C₂×C₇×#123	1	2	yes	—
550	C₄	C₂×C₇×#123	1	4	yes	—
551	C₄	C₂²×C₇×#41	1	1	yes	characteristic
552	C₄	C₂²×C₇×#41	1	1	yes	characteristic
553	C₂	—	2	4	no	—
554	C₂	—	4	4	no	—
555	C₂	C₇×#3097	1	4	yes	direct product factor
556	C₂	C₂²×C₇×#123	1	1	yes	characteristic
557	C₂	C₂×C₇×#577	1	1	yes	characteristic
558	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×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#3097	C₂	direct (N × H)
4. C₂×C₇×#484	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#485	C₂	semidirect
7. C₂×C₇×#483	C₂	semidirect
8. C₂×C₇×#428	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
10. C₂×C₇×#419	C₂	semidirect
11. C₂²×C₇×#103	C₂	semidirect
34. C₇×#485	C₂²	semidirect
35. C₇×#485	C₂²	semidirect
36. C₇×#484	C₂²	semidirect
37. C₇×#483	C₂²	semidirect
38. C₇×#428	C₂²	semidirect
39. C₇×#427	C₂²	semidirect
46. C₇×#419	C₂²	semidirect
51. C₂×C₇×#103	C₂²	semidirect
55. C₂×#3097	C₇	direct (N × H)
132. #3097	C₂×C₇	direct (N × H)
133. C₂×#484	C₂×C₇	semidirect
134. C₂×#485	C₂×C₇	semidirect
135. C₂×#485	C₂×C₇	semidirect
136. C₂×#483	C₂×C₇	semidirect
137. C₂×#428	C₂×C₇	semidirect
138. C₂×#427	C₂×C₇	semidirect
139. C₂×#419	C₂×C₇	semidirect
140. C₂²×#103	C₂×C₇	semidirect
236. #485	C₂²×C₇	semidirect
237. #485	C₂²×C₇	semidirect
238. #484	C₂²×C₇	semidirect
239. #483	C₂²×C₇	semidirect
240. #428	C₂²×C₇	semidirect
241. #427	C₂²×C₇	semidirect
248. #419	C₂²×C₇	semidirect
253. C₂×#103	C₂²×C₇	semidirect
477. C₂×C₇	#3097	direct (N × H)
529. C₇	C₂×#3097	direct (N × H)
555. C₂	C₇×#3097	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×#536	2
C₂×C₇×#520	2
C₇×#3097	2
C₂×C₇×#484	2
C₂×C₇×#485	2
C₂×C₇×#483	2
C₂×C₇×#428	2
C₂×C₇×#427	2
C₂×C₇×#419	2
C₂²×C₇×#103	2
C₂×C₇×#408	2
C₂×#3097	7

Subgroups — C2×C7×#3097 #13237729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3097 #13237729