Subgroups — C₂×C₇×#3191 #13237949

Order 1792.

2394 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
2	C₇×#3191	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#449	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₇×#41	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₇×#525	—	2	8	no	—
19	C₇×#525	C₂²	1	16	yes	complemented
20	C₂×C₇×#123	—	2	2	no	—
21	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#121	C₂²	1	2	yes	—
24	C₂×C₇×#121	C₂²	1	2	yes	—
25	C₂×C₇×#120	—	2	2	no	—
26	C₂×C₄×C₇×D₄	—	2	2	no	—
27	C₂×C₄×C₇×D₄	—	2	2	no	—
28	C₂×C₇×#117	C₂²	1	2	yes	—
29	C₇×#485	C₂²	1	16	yes	complemented
30	C₇×#482	C₂²	1	16	yes	complemented
31	C₇×#467	C₂²	1	8	yes	complemented
32	C₇×#466	C₂²	1	8	yes	complemented
33	C₇×#465	C₂²	1	16	yes	complemented
34	C₇×#452	C₂²	1	16	yes	complemented
35	C₇×#449	C₂²	1	16	yes	complemented
36	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#106	C₂²	1	2	yes	complemented
39	C₂×C₇×#103	C₂²	1	2	yes	complemented
40	C₂×C₇×#103	C₂²	1	2	yes	complemented
41	C₂×C₇×#102	C₂²	1	2	yes	complemented
42	C₂×C₇×#102	C₂²	1	2	yes	complemented
43	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₇×C₂²⋊C₈	C₂²	1	8	yes	complemented
46	C₂×#3191	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁵×C₇	D₄	1	1	yes	characteristic
48	C₂×C₇×#41	—	2	4	no	—
49	C₂×C₇×#41	—	4	4	no	—
50	C₂×C₇×#41	—	4	4	no	—
51	C₂×C₇×#41	C₂³	1	8	yes	—
52	C₂²×C₇×Q₈	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	—	2	2	no	—
55	C₂²×C₇×D₄	—	2	2	no	—
56	C₂²×C₇×D₄	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	—	4	2	no	—
59	C₂³×C₄×C₇	—	4	2	no	—
60	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇	D₄	1	2	yes	—
62	C₂³×C₄×C₇	D₄	1	4	yes	—
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₇	C₂³	1	4	yes	—
66	C₂×C₇×Q₁₆	—	4	2	no	—
67	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
68	C₂×C₇×SD₁₆	—	4	4	no	—
69	C₂×C₇×SD₁₆	C₂³	1	8	yes	complemented
70	C₂×C₇×D₈	—	4	2	no	—
71	C₂×C₇×D₈	C₂³	1	4	yes	complemented
72	C₂²×C₇×C₈	—	4	2	no	—
73	C₂²×C₇×C₈	—	4	2	no	—
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	C₂³	1	2	yes	—
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	4	yes	—
78	C₂²×C₇×C₈	C₂³	1	4	yes	—
79	C₇×#123	—	2	16	no	—
80	C₇×C₂²⋊Q₈	—	2	4	no	—
81	C₇×C₂²⋊Q₈	—	2	4	no	—
82	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
84	C₇×#121	—	2	4	no	—
85	C₇×#121	—	2	4	no	—
86	C₇×#121	C₂³	1	8	yes	—
87	C₇×#121	C₂³	1	8	yes	—
88	C₇×#120	—	2	16	no	—
89	C₄×C₇×D₄	—	2	16	no	—
90	C₄×C₇×D₄	—	2	16	no	—
91	C₇×#117	—	2	4	no	—
92	C₇×#117	C₂³	1	8	yes	—
93	C₂×C₇×C₄⋊C₄	—	2	2	no	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
102	C₂×C₄²×C₇	—	2	2	no	—
103	C₇×#107	C₂³	1	4	yes	complemented
104	C₇×#107	C₂³	1	4	yes	complemented
105	C₇×#106	C₂³	1	8	yes	complemented
106	C₇×#103	C₂³	1	8	yes	complemented
107	C₇×#103	C₂³	1	8	yes	complemented
108	C₇×#102	C₂³	1	8	yes	complemented
109	C₇×#102	C₂³	1	8	yes	complemented
110	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
111	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
112	C₂×#525	C₂×C₇	1	2	yes	complemented
113	#3191	C₂×C₇	1	16	yes	direct product factor
114	C₂×#485	C₂×C₇	1	2	yes	complemented
115	C₂×#482	C₂×C₇	1	2	yes	complemented
116	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
117	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
118	C₂×#465	C₂×C₇	1	2	yes	complemented
119	C₂×#452	C₂×C₇	1	2	yes	complemented
120	C₂×#449	C₂×C₇	1	2	yes	complemented
121	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
122	C₂⁴×C₇	—	2	4	no	—
123	C₂⁴×C₇	—	2	2	no	—
124	C₂⁴×C₇	—	4	2	no	—
125	C₂⁴×C₇	—	4	2	no	—
126	C₂⁴×C₇	C₂×D₄	1	2	yes	—
127	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
128	C₂⁴×C₇	C₂×D₄	1	4	yes	—
129	C₇×#41	—	4	8	no	—
130	C₇×#41	—	4	8	no	—
131	C₇×#41	—	4	16	no	—
132	C₂×C₇×Q₈	—	2	2	no	—
133	C₂×C₇×Q₈	—	2	4	no	—
134	C₂×C₇×Q₈	—	2	4	no	—
135	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
136	C₂×C₇×D₄	—	2	8	no	—
137	C₂×C₇×D₄	—	2	8	no	—
138	C₂×C₇×D₄	—	2	8	no	—
139	C₂×C₇×D₄	—	2	2	no	—
140	C₂×C₇×D₄	—	2	4	no	—
141	C₂×C₇×D₄	—	2	4	no	—
142	C₂×C₇×D₄	—	4	8	no	—
143	C₂×C₇×D₄	—	4	8	no	—
144	C₂×C₇×D₄	—	4	8	no	—
145	C₂×C₇×D₄	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₇	—	2	2	no	—
147	C₂²×C₄×C₇	—	2	2	no	—
148	C₂²×C₄×C₇	—	2	4	no	—
149	C₂²×C₄×C₇	—	2	4	no	—
150	C₂²×C₄×C₇	—	2	2	no	—
151	C₂²×C₄×C₇	—	2	2	no	—
152	C₂²×C₄×C₇	—	2	2	no	—
153	C₂²×C₄×C₇	—	2	8	no	—
154	C₂²×C₄×C₇	—	4	8	no	—
155	C₂²×C₄×C₇	—	4	4	no	—
156	C₂²×C₄×C₇	—	4	4	no	—
157	C₂²×C₄×C₇	—	4	2	no	—
158	C₂²×C₄×C₇	—	4	4	no	—
159	C₂²×C₄×C₇	—	4	8	no	—
160	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
166	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
169	C₇×Q₁₆	—	4	4	no	—
170	C₇×SD₁₆	—	4	8	no	—
171	C₇×D₈	—	4	4	no	—
172	C₂×C₇×C₈	—	2	2	no	—
173	C₂×C₇×C₈	—	2	4	no	—
174	C₂×C₇×C₈	—	2	2	no	—
175	C₂×C₇×C₈	—	4	4	no	—
176	C₂×C₇×C₈	—	4	4	no	—
177	C₂×C₇×C₈	C₂⁴	1	2	yes	—
178	C₂×C₇×C₈	C₂⁴	1	4	yes	—
179	C₂×C₇×C₈	C₂⁴	1	2	yes	—
180	C₇×C₄⋊C₄	—	2	8	no	—
181	C₇×C₄⋊C₄	—	2	8	no	—
182	C₇×C₄⋊C₄	—	2	2	no	—
183	C₇×C₄⋊C₄	—	2	2	no	—
184	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
185	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₇×C₂²⋊C₄	—	2	8	no	—
187	C₇×C₂²⋊C₄	—	2	8	no	—
188	C₇×C₂²⋊C₄	—	2	8	no	—
189	C₇×C₂²⋊C₄	—	2	8	no	—
190	C₇×C₂²⋊C₄	—	2	8	no	—
191	C₄²×C₇	—	2	8	no	—
192	C₂²×#41	C₂²×C₇	1	2	yes	—
193	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
194	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
195	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
196	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
197	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
199	#525	—	2	8	no	—
200	#525	C₂²×C₇	1	16	yes	complemented
201	C₂×#123	—	2	2	no	—
202	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
203	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
204	C₂×#121	C₂²×C₇	1	2	yes	—
205	C₂×#121	C₂²×C₇	1	2	yes	—
206	C₂×#120	—	2	2	no	—
207	C₂×C₄×D₄	—	2	2	no	—
208	C₂×C₄×D₄	—	2	2	no	—
209	C₂×#117	C₂²×C₇	1	2	yes	—
210	#485	C₂²×C₇	1	16	yes	complemented
211	#482	C₂²×C₇	1	16	yes	complemented
212	#467	C₂²×C₇	1	8	yes	complemented
213	#466	C₂²×C₇	1	8	yes	complemented
214	#465	C₂²×C₇	1	16	yes	complemented
215	#452	C₂²×C₇	1	16	yes	complemented
216	#449	C₂²×C₇	1	16	yes	complemented
217	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
218	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
219	C₂×#106	C₂²×C₇	1	2	yes	complemented
220	C₂×#103	C₂²×C₇	1	2	yes	complemented
221	C₂×#103	C₂²×C₇	1	2	yes	complemented
222	C₂×#102	C₂²×C₇	1	2	yes	complemented
223	C₂×#102	C₂²×C₇	1	2	yes	complemented
224	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
225	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
226	C₂×C₂²⋊C₈	C₂²×C₇	1	8	yes	complemented
227	C₂³×C₇	—	2	2	no	—
228	C₂³×C₇	—	2	2	no	—
229	C₂³×C₇	—	2	4	no	—
230	C₂³×C₇	—	2	8	no	—
231	C₂³×C₇	—	2	4	no	—
232	C₂³×C₇	—	2	4	no	—
233	C₂³×C₇	—	2	4	no	—
234	C₂³×C₇	—	4	4	no	—
235	C₂³×C₇	—	4	4	no	—
236	C₂³×C₇	—	4	16	no	—
237	C₂³×C₇	—	4	4	no	—
238	C₂³×C₇	—	4	4	no	—
239	C₂³×C₇	—	4	4	no	—
240	C₂³×C₇	#135	1	4	yes	—
241	C₂³×C₇	C₂²×D₄	1	4	yes	—
242	C₂³×C₇	C₂²×D₄	1	2	yes	—
243	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
244	C₇×Q₈	—	2	4	no	—
245	C₇×Q₈	—	2	4	no	—
246	C₇×Q₈	—	4	4	no	—
247	C₇×D₄	—	2	4	no	—
248	C₇×D₄	—	2	4	no	—
249	C₇×D₄	—	4	16	no	—
250	C₇×D₄	—	4	16	no	—
251	C₇×D₄	—	4	16	no	—
252	C₇×D₄	—	4	4	no	—
253	C₂×C₄×C₇	—	2	4	no	—
254	C₂×C₄×C₇	—	2	2	no	—
255	C₂×C₄×C₇	—	2	4	no	—
256	C₂×C₄×C₇	—	2	8	no	—
257	C₂×C₄×C₇	—	2	2	no	—
258	C₂×C₄×C₇	—	2	2	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	4	no	—
261	C₂×C₄×C₇	—	2	4	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	2	4	no	—
264	C₂×C₄×C₇	—	4	4	no	—
265	C₂×C₄×C₇	—	4	8	no	—
266	C₂×C₄×C₇	—	4	16	no	—
267	C₂×C₄×C₇	—	4	4	no	—
268	C₂×C₄×C₇	—	4	4	no	—
269	C₂×C₄×C₇	—	4	4	no	—
270	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
274	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
275	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
276	C₇×C₈	—	2	2	no	—
277	C₇×C₈	—	2	4	no	—
278	C₇×C₈	—	2	2	no	—
279	C₂⁵	C₇×D₄	1	1	yes	characteristic
280	C₂×#41	—	2	4	no	—
281	C₂×#41	—	4	4	no	—
282	C₂×#41	—	4	4	no	—
283	C₂×#41	C₂³×C₇	1	8	yes	—
284	C₂²×Q₈	C₂³×C₇	1	2	yes	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	2	no	—
288	C₂²×D₄	C₂³×C₇	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	4	2	no	—
291	C₂³×C₄	—	4	2	no	—
292	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
293	C₂³×C₄	C₇×D₄	1	2	yes	—
294	C₂³×C₄	C₇×D₄	1	4	yes	—
295	C₂³×C₄	C₂³×C₇	1	2	yes	—
296	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₇	1	4	yes	—
298	C₂×Q₁₆	—	4	2	no	—
299	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
300	C₂×SD₁₆	—	4	4	no	—
301	C₂×SD₁₆	C₂³×C₇	1	8	yes	complemented
302	C₂×D₈	—	4	2	no	—
303	C₂×D₈	C₂³×C₇	1	4	yes	complemented
304	C₂²×C₈	—	4	2	no	—
305	C₂²×C₈	—	4	2	no	—
306	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₇	1	2	yes	—
308	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₇	1	4	yes	—
310	C₂²×C₈	C₂³×C₇	1	4	yes	—
311	#123	—	2	16	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
315	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
316	#121	—	2	4	no	—
317	#121	—	2	4	no	—
318	#121	C₂³×C₇	1	8	yes	—
319	#121	C₂³×C₇	1	8	yes	—
320	#120	—	2	16	no	—
321	C₄×D₄	—	2	16	no	—
322	C₄×D₄	—	2	16	no	—
323	#117	—	2	4	no	—
324	#117	C₂³×C₇	1	8	yes	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	#107	C₂³×C₇	1	4	yes	complemented
336	#107	C₂³×C₇	1	4	yes	complemented
337	#106	C₂³×C₇	1	8	yes	complemented
338	#103	C₂³×C₇	1	8	yes	complemented
339	#103	C₂³×C₇	1	8	yes	complemented
340	#102	C₂³×C₇	1	8	yes	complemented
341	#102	C₂³×C₇	1	8	yes	complemented
342	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
343	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
344	C₂²×C₇	—	2	2	no	—
345	C₂²×C₇	—	2	8	no	—
346	C₂²×C₇	—	2	2	no	—
347	C₂²×C₇	—	2	4	no	—
348	C₂²×C₇	—	2	4	no	—
349	C₂²×C₇	—	2	4	no	—
350	C₂²×C₇	—	4	16	no	—
351	C₂²×C₇	—	4	8	no	—
352	C₂²×C₇	—	4	4	no	—
353	C₂²×C₇	—	4	4	no	—
354	C₂²×C₇	—	4	4	no	—
355	C₂²×C₇	—	8	8	no	—
356	C₂²×C₇	#534	1	2	yes	—
357	C₂²×C₇	C₂×#135	1	4	yes	—
358	C₂²×C₇	C₂×#135	1	2	yes	—
359	C₂²×C₇	#575	1	2	yes	—
360	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₇	—	2	4	no	—
362	C₄×C₇	—	2	2	no	—
363	C₄×C₇	—	4	4	no	—
364	C₄×C₇	—	4	4	no	—
365	C₄×C₇	—	4	4	no	—
366	C₄×C₇	#534	1	2	yes	—
367	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
369	C₂⁴	—	2	4	no	—
370	C₂⁴	—	2	2	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	2	no	—
373	C₂⁴	C₂×C₇×D₄	1	2	yes	—
374	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
375	C₂⁴	C₂×C₇×D₄	1	4	yes	—
376	#41	—	4	8	no	—
377	#41	—	4	8	no	—
378	#41	—	4	16	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	8	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	8	no	—
392	C₂×D₄	C₂⁴×C₇	1	4	yes	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	4	8	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	4	no	—
406	C₂²×C₄	—	4	8	no	—
407	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
408	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
410	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
411	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
412	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
413	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
416	Q₁₆	—	4	4	no	—
417	SD₁₆	—	4	8	no	—
418	D₈	—	4	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	4	4	no	—
423	C₂×C₈	—	4	4	no	—
424	C₂×C₈	C₂⁴×C₇	1	2	yes	—
425	C₂×C₈	C₂⁴×C₇	1	4	yes	—
426	C₂×C₈	C₂⁴×C₇	1	2	yes	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₄²	—	2	8	no	—
439	C₂×C₇	—	2	4	no	—
440	C₂×C₇	—	4	4	no	—
441	C₂×C₇	—	8	4	no	—
442	C₂×C₇	#3191	1	4	yes	direct product factor
443	C₂×C₇	C₂×#534	1	1	yes	characteristic
444	C₂×C₇	C₂²×#135	1	1	yes	characteristic
445	C₂×C₇	C₂×#575	1	1	yes	characteristic
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	8	no	—
450	C₂³	—	2	4	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	16	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	C₇×#135	1	4	yes	—
460	C₂³	C₂²×C₇×D₄	1	4	yes	—
461	C₂³	C₂²×C₇×D₄	1	2	yes	—
462	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	4	4	no	—
466	D₄	—	2	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	4	16	no	—
469	D₄	—	4	16	no	—
470	D₄	—	4	16	no	—
471	D₄	—	4	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	4	4	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
490	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
491	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
492	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
493	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	4	no	—
497	C₈	—	2	2	no	—
498	C₇	C₂×#3191	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	2	2	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₇×#534	1	2	yes	—
512	C₂²	C₂×C₇×#135	1	4	yes	—
513	C₂²	C₂×C₇×#135	1	2	yes	—
514	C₂²	C₇×#575	1	2	yes	—
515	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	C₇×#534	1	2	yes	—
522	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
523	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂	—	2	4	no	—
525	C₂	—	4	4	no	—
526	C₂	—	8	4	no	—
527	C₂	C₇×#3191	1	4	yes	direct product factor
528	C₂	C₂×C₇×#534	1	1	yes	characteristic
529	C₂	C₂²×C₇×#135	1	1	yes	characteristic
530	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#525	C₂	semidirect
2. C₇×#3191	C₂	direct (N × H)
3. C₂×C₇×#485	C₂	semidirect
4. C₂×C₇×#482	C₂	semidirect
5. C₂×C₇×#467	C₂	semidirect
6. C₂×C₇×#466	C₂	semidirect
7. C₂×C₇×#465	C₂	semidirect
8. C₂×C₇×#452	C₂	semidirect
9. C₂×C₇×#449	C₂	semidirect
10. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
13. C₂²×C₇×Q₁₆	C₂²	semidirect
14. C₂²×C₇×SD₁₆	C₂²	semidirect
15. C₂²×C₇×D₈	C₂²	semidirect
19. C₇×#525	C₂²	semidirect
29. C₇×#485	C₂²	semidirect
30. C₇×#482	C₂²	semidirect
31. C₇×#467	C₂²	semidirect
32. C₇×#466	C₂²	semidirect
33. C₇×#465	C₂²	semidirect
34. C₇×#452	C₂²	semidirect
35. C₇×#449	C₂²	semidirect
36. C₂×C₇×#107	C₂²	semidirect
37. C₂×C₇×#107	C₂²	semidirect
38. C₂×C₇×#106	C₂²	semidirect
39. C₂×C₇×#103	C₂²	semidirect
40. C₂×C₇×#103	C₂²	semidirect
41. C₂×C₇×#102	C₂²	semidirect
42. C₂×C₇×#102	C₂²	semidirect
45. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
46. C₂×#3191	C₇	direct (N × H)
67. C₂×C₇×Q₁₆	C₂³	semidirect
69. C₂×C₇×SD₁₆	C₂³	semidirect
71. C₂×C₇×D₈	C₂³	semidirect
103. C₇×#107	C₂³	semidirect
104. C₇×#107	C₂³	semidirect
105. C₇×#106	C₂³	semidirect
106. C₇×#103	C₂³	semidirect
107. C₇×#103	C₂³	semidirect
108. C₇×#102	C₂³	semidirect
109. C₇×#102	C₂³	semidirect
112. C₂×#525	C₂×C₇	semidirect
113. #3191	C₂×C₇	direct (N × H)
114. C₂×#485	C₂×C₇	semidirect
115. C₂×#482	C₂×C₇	semidirect
116. C₂×#467	C₂×C₇	semidirect
117. C₂×#466	C₂×C₇	semidirect
118. C₂×#465	C₂×C₇	semidirect
119. C₂×#452	C₂×C₇	semidirect
120. C₂×#449	C₂×C₇	semidirect
121. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
194. C₂²×Q₁₆	C₂²×C₇	semidirect
195. C₂²×SD₁₆	C₂²×C₇	semidirect
196. C₂²×D₈	C₂²×C₇	semidirect
200. #525	C₂²×C₇	semidirect
210. #485	C₂²×C₇	semidirect
211. #482	C₂²×C₇	semidirect
212. #467	C₂²×C₇	semidirect
213. #466	C₂²×C₇	semidirect
214. #465	C₂²×C₇	semidirect
215. #452	C₂²×C₇	semidirect
216. #449	C₂²×C₇	semidirect
217. C₂×#107	C₂²×C₇	semidirect
218. C₂×#107	C₂²×C₇	semidirect
219. C₂×#106	C₂²×C₇	semidirect
220. C₂×#103	C₂²×C₇	semidirect
221. C₂×#103	C₂²×C₇	semidirect
222. C₂×#102	C₂²×C₇	semidirect
223. C₂×#102	C₂²×C₇	semidirect
226. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
299. C₂×Q₁₆	C₂³×C₇	semidirect
301. C₂×SD₁₆	C₂³×C₇	semidirect
303. C₂×D₈	C₂³×C₇	semidirect
335. #107	C₂³×C₇	semidirect
336. #107	C₂³×C₇	semidirect
337. #106	C₂³×C₇	semidirect
338. #103	C₂³×C₇	semidirect
339. #103	C₂³×C₇	semidirect
340. #102	C₂³×C₇	semidirect
341. #102	C₂³×C₇	semidirect
442. C₂×C₇	#3191	direct (N × H)
498. C₇	C₂×#3191	direct (N × H)
527. C₂	C₇×#3191	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×#525	2
C₇×#3191	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#467	2
C₂×C₇×#466	2
C₂×C₇×#465	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂²×C₇×C₂²⋊C₈	2
C₂×#3191	7

Subgroups — C2×C7×#3191 #13237949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3191 #13237949