Subgroups — C₂×C₇×#3190 #13237948

Order 1792.

2374 conjugacy classes of subgroups.

The subgroup lattice has 666 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	1	yes	maximal, characteristic
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3190	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#467	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂²×C₇×Q₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
18	C₂³×C₇×C₈	C₂²	1	2	yes	—
19	C₇×#525	—	2	4	no	—
20	C₇×#525	C₂²	1	8	yes	—
21	C₂×C₇×#123	—	2	1	no	—
22	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	4	no	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×C₂²⋊Q₈	C₂²	1	8	yes	complemented
30	C₂×C₇×#121	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₂×C₇×#120	—	2	1	no	—
33	C₂×C₄×C₇×D₄	—	2	1	no	—
34	C₂×C₄×C₇×D₄	—	2	1	no	—
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
37	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
39	C₇×#485	C₂²	1	16	yes	complemented
40	C₇×#483	C₂²	1	8	yes	complemented
41	C₇×#480	C₂²	1	8	yes	complemented
42	C₇×#467	C₂²	1	16	yes	complemented
43	C₇×#465	C₂²	1	16	yes	complemented
44	C₇×#452	C₂²	1	16	yes	complemented
45	C₇×#451	C₂²	1	8	yes	complemented
46	C₇×#448	C₂²	1	8	yes	complemented
47	C₂×C₇×#107	C₂²	1	2	yes	complemented
48	C₂×C₇×#106	C₂²	1	2	yes	complemented
49	C₂×C₇×#103	C₂²	1	2	yes	complemented
50	C₂×C₇×#103	C₂²	1	2	yes	complemented
51	C₂×C₇×#103	C₂²	1	2	yes	complemented
52	C₂×C₇×#102	C₂²	1	2	yes	complemented
53	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₇×C₂²⋊C₈	C₂²	1	8	yes	complemented
57	C₂×#3190	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂⁵×C₇	D₄	1	1	yes	characteristic
59	C₂×C₇×#41	—	2	2	no	—
60	C₂×C₇×#41	—	4	4	no	—
61	C₂×C₇×#41	C₂³	1	4	yes	—
62	C₂²×C₇×Q₈	—	2	2	no	—
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	—	4	4	no	—
65	C₂²×C₇×Q₈	C₂³	1	2	yes	—
66	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×Q₈	C₂³	1	4	yes	—
68	C₂²×C₇×D₄	—	2	1	no	—
69	C₂²×C₇×D₄	—	2	1	no	—
70	C₂²×C₇×D₄	—	2	1	no	—
71	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	—	2	1	no	—
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	—	4	4	no	—
76	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
79	C₂³×C₄×C₇	D₄	1	4	yes	—
80	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂³	1	4	yes	—
84	C₂×C₇×Q₁₆	—	4	4	no	—
85	C₂×C₇×Q₁₆	C₂³	1	8	yes	complemented
86	C₂×C₇×SD₁₆	—	4	4	no	—
87	C₂×C₇×SD₁₆	C₂³	1	8	yes	complemented
88	C₂²×C₇×C₈	—	4	4	no	—
89	C₂²×C₇×C₈	C₂³	1	2	yes	—
90	C₂²×C₇×C₈	C₂³	1	2	yes	—
91	C₂²×C₇×C₈	C₂³	1	8	yes	—
92	C₇×#123	—	2	8	no	—
93	C₇×C₂²⋊Q₈	—	2	4	no	—
94	C₇×C₂²⋊Q₈	—	2	4	no	—
95	C₇×C₂²⋊Q₈	—	2	8	no	—
96	C₇×C₂²⋊Q₈	—	2	8	no	—
97	C₇×C₂²⋊Q₈	—	2	2	no	—
98	C₇×C₂²⋊Q₈	—	2	2	no	—
99	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
100	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
101	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
102	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
103	C₇×#121	—	2	2	no	—
104	C₇×#121	—	2	2	no	—
105	C₇×#121	C₂³	1	4	yes	—
106	C₇×#121	C₂³	1	4	yes	—
107	C₇×#120	—	2	8	no	—
108	C₄×C₇×D₄	—	2	8	no	—
109	C₄×C₇×D₄	—	2	8	no	—
110	C₇×#117	—	2	2	no	—
111	C₇×#117	C₂³	1	4	yes	—
112	C₂×C₇×C₄⋊C₄	—	2	2	no	—
113	C₂×C₇×C₄⋊C₄	—	2	2	no	—
114	C₂×C₇×C₄⋊C₄	—	2	8	no	—
115	C₂×C₇×C₄⋊C₄	—	2	2	no	—
116	C₂×C₇×C₄⋊C₄	—	2	1	no	—
117	C₂×C₇×C₄⋊C₄	—	2	1	no	—
118	C₂×C₇×C₄⋊C₄	—	2	1	no	—
119	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
120	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
124	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
126	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
128	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
129	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
130	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
131	C₂×C₄²×C₇	—	2	1	no	—
132	C₇×#107	C₂³	1	8	yes	complemented
133	C₇×#106	C₂³	1	8	yes	complemented
134	C₇×#103	C₂³	1	8	yes	complemented
135	C₇×#103	C₂³	1	8	yes	complemented
136	C₇×#103	C₂³	1	8	yes	complemented
137	C₇×#102	C₂³	1	8	yes	complemented
138	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
139	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
140	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
141	C₂×#525	C₂×C₇	1	1	yes	characteristic
142	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
143	#3190	C₂×C₇	1	16	yes	direct product factor
144	C₂×#485	C₂×C₇	1	2	yes	complemented
145	C₂×#483	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#467	C₂×C₇	1	2	yes	complemented
148	C₂×#465	C₂×C₇	1	2	yes	complemented
149	C₂×#452	C₂×C₇	1	2	yes	complemented
150	C₂×#451	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂×#448	C₂×C₇	1	1	yes	characteristic, complemented
152	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
153	C₂⁴×C₇	—	2	4	no	—
154	C₂⁴×C₇	—	2	4	no	—
155	C₂⁴×C₇	—	2	1	no	—
156	C₂⁴×C₇	—	4	2	no	—
157	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₇	C₂×D₄	1	4	yes	—
159	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
160	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
161	C₇×#41	—	4	8	no	—
162	C₇×#41	—	4	8	no	—
163	C₂×C₇×Q₈	—	2	4	no	—
164	C₂×C₇×Q₈	—	2	2	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	4	no	—
167	C₂×C₇×Q₈	—	2	4	no	—
168	C₂×C₇×Q₈	—	2	4	no	—
169	C₂×C₇×Q₈	—	4	8	no	—
170	C₂×C₇×Q₈	—	4	4	no	—
171	C₂×C₇×Q₈	—	4	8	no	—
172	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
173	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
174	C₂×C₇×D₄	—	2	4	no	—
175	C₂×C₇×D₄	—	2	4	no	—
176	C₂×C₇×D₄	—	2	4	no	—
177	C₂×C₇×D₄	—	2	1	no	—
178	C₂×C₇×D₄	—	2	4	no	—
179	C₂×C₇×D₄	—	4	4	no	—
180	C₂×C₇×D₄	—	4	4	no	—
181	C₂×C₇×D₄	—	4	4	no	—
182	C₂×C₇×D₄	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₇	—	2	4	no	—
184	C₂²×C₄×C₇	—	2	4	no	—
185	C₂²×C₄×C₇	—	2	4	no	—
186	C₂²×C₄×C₇	—	2	4	no	—
187	C₂²×C₄×C₇	—	2	4	no	—
188	C₂²×C₄×C₇	—	2	1	no	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	2	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	2	no	—
193	C₂²×C₄×C₇	—	2	4	no	—
194	C₂²×C₄×C₇	—	4	8	no	—
195	C₂²×C₄×C₇	—	4	8	no	—
196	C₂²×C₄×C₇	—	4	2	no	—
197	C₂²×C₄×C₇	—	4	2	no	—
198	C₂²×C₄×C₇	—	4	2	no	—
199	C₂²×C₄×C₇	—	4	4	no	—
200	C₂²×C₄×C₇	—	4	4	no	—
201	C₂²×C₄×C₇	—	4	4	no	—
202	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
203	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
204	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
215	C₇×Q₁₆	—	4	8	no	—
216	C₇×SD₁₆	—	4	8	no	—
217	C₂×C₇×C₈	—	2	4	no	—
218	C₂×C₇×C₈	—	2	4	no	—
219	C₂×C₇×C₈	—	4	8	no	—
220	C₂×C₇×C₈	C₂⁴	1	4	yes	—
221	C₂×C₇×C₈	C₂⁴	1	4	yes	—
222	C₇×C₄⋊C₄	—	2	8	no	—
223	C₇×C₄⋊C₄	—	2	8	no	—
224	C₇×C₄⋊C₄	—	2	4	no	—
225	C₇×C₄⋊C₄	—	2	2	no	—
226	C₇×C₄⋊C₄	—	2	4	no	—
227	C₇×C₄⋊C₄	—	2	4	no	—
228	C₇×C₄⋊C₄	—	2	1	no	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
231	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
232	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
233	C₇×C₂²⋊C₄	—	2	8	no	—
234	C₇×C₂²⋊C₄	—	2	8	no	—
235	C₇×C₂²⋊C₄	—	2	4	no	—
236	C₇×C₂²⋊C₄	—	2	4	no	—
237	C₇×C₂²⋊C₄	—	2	4	no	—
238	C₇×C₂²⋊C₄	—	2	4	no	—
239	C₇×C₂²⋊C₄	—	2	4	no	—
240	C₄²×C₇	—	2	4	no	—
241	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
242	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
243	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
244	C₂²×Q₁₆	C₂²×C₇	1	2	yes	complemented
245	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
246	C₂³×C₈	C₂²×C₇	1	2	yes	—
247	#525	—	2	4	no	—
248	#525	C₂²×C₇	1	8	yes	—
249	C₂×#123	—	2	1	no	—
250	C₂×C₂²⋊Q₈	—	2	1	no	—
251	C₂×C₂²⋊Q₈	—	2	1	no	—
252	C₂×C₂²⋊Q₈	—	2	4	no	—
253	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
256	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₇	1	8	yes	complemented
258	C₂×#121	C₂²×C₇	1	1	yes	characteristic
259	C₂×#121	C₂²×C₇	1	1	yes	characteristic
260	C₂×#120	—	2	1	no	—
261	C₂×C₄×D₄	—	2	1	no	—
262	C₂×C₄×D₄	—	2	1	no	—
263	C₂×#117	C₂²×C₇	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	—	2	1	no	—
265	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	—	2	1	no	—
267	#485	C₂²×C₇	1	16	yes	complemented
268	#483	C₂²×C₇	1	8	yes	complemented
269	#480	C₂²×C₇	1	8	yes	complemented
270	#467	C₂²×C₇	1	16	yes	complemented
271	#465	C₂²×C₇	1	16	yes	complemented
272	#452	C₂²×C₇	1	16	yes	complemented
273	#451	C₂²×C₇	1	8	yes	complemented
274	#448	C₂²×C₇	1	8	yes	complemented
275	C₂×#107	C₂²×C₇	1	2	yes	complemented
276	C₂×#106	C₂²×C₇	1	2	yes	complemented
277	C₂×#103	C₂²×C₇	1	2	yes	complemented
278	C₂×#103	C₂²×C₇	1	2	yes	complemented
279	C₂×#103	C₂²×C₇	1	2	yes	complemented
280	C₂×#102	C₂²×C₇	1	2	yes	complemented
281	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
282	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
283	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₇	1	8	yes	complemented
285	C₂³×C₇	—	2	2	no	—
286	C₂³×C₇	—	2	2	no	—
287	C₂³×C₇	—	2	2	no	—
288	C₂³×C₇	—	2	2	no	—
289	C₂³×C₇	—	2	2	no	—
290	C₂³×C₇	—	2	8	no	—
291	C₂³×C₇	—	2	2	no	—
292	C₂³×C₇	—	2	8	no	—
293	C₂³×C₇	—	2	2	no	—
294	C₂³×C₇	—	2	2	no	—
295	C₂³×C₇	—	4	4	no	—
296	C₂³×C₇	—	4	16	no	—
297	C₂³×C₇	—	4	2	no	—
298	C₂³×C₇	—	4	2	no	—
299	C₂³×C₇	—	4	2	no	—
300	C₂³×C₇	#135	1	4	yes	—
301	C₂³×C₇	#137	1	4	yes	—
302	C₂³×C₇	C₂²×D₄	1	2	yes	—
303	C₂³×C₇	C₂²×D₄	1	2	yes	—
304	C₂³×C₇	C₂²×D₄	1	2	yes	—
305	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
306	C₇×Q₈	—	2	4	no	—
307	C₇×Q₈	—	2	4	no	—
308	C₇×Q₈	—	2	4	no	—
309	C₇×Q₈	—	4	8	no	—
310	C₇×Q₈	—	4	4	no	—
311	C₇×Q₈	—	4	2	no	—
312	C₇×D₄	—	2	4	no	—
313	C₇×D₄	—	4	8	no	—
314	C₇×D₄	—	4	8	no	—
315	C₇×D₄	—	4	8	no	—
316	C₇×D₄	—	4	2	no	—
317	C₂×C₄×C₇	—	2	2	no	—
318	C₂×C₄×C₇	—	2	2	no	—
319	C₂×C₄×C₇	—	2	2	no	—
320	C₂×C₄×C₇	—	2	4	no	—
321	C₂×C₄×C₇	—	2	4	no	—
322	C₂×C₄×C₇	—	2	4	no	—
323	C₂×C₄×C₇	—	2	4	no	—
324	C₂×C₄×C₇	—	2	4	no	—
325	C₂×C₄×C₇	—	2	4	no	—
326	C₂×C₄×C₇	—	2	2	no	—
327	C₂×C₄×C₇	—	2	2	no	—
328	C₂×C₄×C₇	—	2	4	no	—
329	C₂×C₄×C₇	—	2	2	no	—
330	C₂×C₄×C₇	—	2	4	no	—
331	C₂×C₄×C₇	—	4	4	no	—
332	C₂×C₄×C₇	—	4	4	no	—
333	C₂×C₄×C₇	—	4	4	no	—
334	C₂×C₄×C₇	—	4	8	no	—
335	C₂×C₄×C₇	—	4	8	no	—
336	C₂×C₄×C₇	—	4	2	no	—
337	C₂×C₄×C₇	—	4	4	no	—
338	C₂×C₄×C₇	—	4	8	no	—
339	C₂×C₄×C₇	—	4	4	no	—
340	C₂×C₄×C₇	—	4	2	no	—
341	C₂×C₄×C₇	—	4	2	no	—
342	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
344	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
345	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
346	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
347	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
348	C₇×C₈	—	2	4	no	—
349	C₇×C₈	—	2	4	no	—
350	C₂⁵	C₇×D₄	1	1	yes	characteristic
351	C₂×#41	—	2	2	no	—
352	C₂×#41	—	4	4	no	—
353	C₂×#41	C₂³×C₇	1	4	yes	—
354	C₂²×Q₈	—	2	1	no	—
355	C₂²×Q₈	—	2	2	no	—
356	C₂²×Q₈	—	4	4	no	—
357	C₂²×Q₈	C₂³×C₇	1	2	yes	—
358	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₇	1	4	yes	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	—	2	1	no	—
362	C₂²×D₄	—	2	1	no	—
363	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	1	no	—
366	C₂³×C₄	—	2	1	no	—
367	C₂³×C₄	—	4	4	no	—
368	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
369	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
370	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
371	C₂³×C₄	C₇×D₄	1	4	yes	—
372	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
374	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₇	1	4	yes	—
376	C₂×Q₁₆	—	4	4	no	—
377	C₂×Q₁₆	C₂³×C₇	1	8	yes	complemented
378	C₂×SD₁₆	—	4	4	no	—
379	C₂×SD₁₆	C₂³×C₇	1	8	yes	complemented
380	C₂²×C₈	—	4	4	no	—
381	C₂²×C₈	C₂³×C₇	1	2	yes	—
382	C₂²×C₈	C₂³×C₇	1	2	yes	—
383	C₂²×C₈	C₂³×C₇	1	8	yes	—
384	#123	—	2	8	no	—
385	C₂²⋊Q₈	—	2	4	no	—
386	C₂²⋊Q₈	—	2	4	no	—
387	C₂²⋊Q₈	—	2	8	no	—
388	C₂²⋊Q₈	—	2	8	no	—
389	C₂²⋊Q₈	—	2	2	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
392	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
393	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
394	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
395	#121	—	2	2	no	—
396	#121	—	2	2	no	—
397	#121	C₂³×C₇	1	4	yes	—
398	#121	C₂³×C₇	1	4	yes	—
399	#120	—	2	8	no	—
400	C₄×D₄	—	2	8	no	—
401	C₄×D₄	—	2	8	no	—
402	#117	—	2	2	no	—
403	#117	C₂³×C₇	1	4	yes	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	—	2	2	no	—
406	C₂×C₄⋊C₄	—	2	8	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	2	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	—	2	2	no	—
416	C₂×C₂²⋊C₄	—	2	2	no	—
417	C₂×C₂²⋊C₄	—	2	8	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	#107	C₂³×C₇	1	8	yes	complemented
425	#106	C₂³×C₇	1	8	yes	complemented
426	#103	C₂³×C₇	1	8	yes	complemented
427	#103	C₂³×C₇	1	8	yes	complemented
428	#103	C₂³×C₇	1	8	yes	complemented
429	#102	C₂³×C₇	1	8	yes	complemented
430	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
431	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
432	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
433	C₂²×C₇	—	2	2	no	—
434	C₂²×C₇	—	2	2	no	—
435	C₂²×C₇	—	2	8	no	—
436	C₂²×C₇	—	2	8	no	—
437	C₂²×C₇	—	2	2	no	—
438	C₂²×C₇	—	2	2	no	—
439	C₂²×C₇	—	2	2	no	—
440	C₂²×C₇	—	2	2	no	—
441	C₂²×C₇	—	2	2	no	—
442	C₂²×C₇	—	4	16	no	—
443	C₂²×C₇	—	4	4	no	—
444	C₂²×C₇	—	4	2	no	—
445	C₂²×C₇	—	4	2	no	—
446	C₂²×C₇	—	4	2	no	—
447	C₂²×C₇	—	8	4	no	—
448	C₂²×C₇	#534	1	2	yes	—
449	C₂²×C₇	C₂×#135	1	4	yes	—
450	C₂²×C₇	C₂×#135	1	2	yes	—
451	C₂²×C₇	C₂×#137	1	4	yes	—
452	C₂²×C₇	C₂×#137	1	2	yes	—
453	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
454	C₄×C₇	—	2	2	no	—
455	C₄×C₇	—	2	2	no	—
456	C₄×C₇	—	2	2	no	—
457	C₄×C₇	—	4	2	no	—
458	C₄×C₇	—	4	4	no	—
459	C₄×C₇	—	4	4	no	—
460	C₄×C₇	—	4	2	no	—
461	C₄×C₇	—	4	2	no	—
462	C₄×C₇	#534	1	2	yes	—
463	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
464	C₂⁴	—	2	4	no	—
465	C₂⁴	—	2	4	no	—
466	C₂⁴	—	2	1	no	—
467	C₂⁴	—	4	2	no	—
468	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
469	C₂⁴	C₂×C₇×D₄	1	4	yes	—
470	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
472	#41	—	4	8	no	—
473	#41	—	4	8	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	4	no	—
478	C₂×Q₈	—	2	4	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	4	8	no	—
481	C₂×Q₈	—	4	4	no	—
482	C₂×Q₈	—	4	8	no	—
483	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
484	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
485	C₂×D₄	—	2	4	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	4	no	—
492	C₂×D₄	—	4	4	no	—
493	C₂×D₄	C₂⁴×C₇	1	2	yes	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	4	no	—
505	C₂²×C₄	—	4	8	no	—
506	C₂²×C₄	—	4	8	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	2	no	—
510	C₂²×C₄	—	4	4	no	—
511	C₂²×C₄	—	4	4	no	—
512	C₂²×C₄	—	4	4	no	—
513	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
517	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
518	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
519	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
520	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
521	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
523	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
526	Q₁₆	—	4	8	no	—
527	SD₁₆	—	4	8	no	—
528	C₂×C₈	—	2	4	no	—
529	C₂×C₈	—	2	4	no	—
530	C₂×C₈	—	4	8	no	—
531	C₂×C₈	C₂⁴×C₇	1	4	yes	—
532	C₂×C₈	C₂⁴×C₇	1	4	yes	—
533	C₄⋊C₄	—	2	8	no	—
534	C₄⋊C₄	—	2	8	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
542	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
543	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	8	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	4	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	4	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₄²	—	2	4	no	—
552	C₂×C₇	—	2	4	no	—
553	C₂×C₇	—	2	4	no	—
554	C₂×C₇	—	4	2	no	—
555	C₂×C₇	—	8	2	no	—
556	C₂×C₇	#3190	1	4	yes	direct product factor
557	C₂×C₇	C₂×#534	1	1	yes	characteristic
558	C₂×C₇	C₂²×#135	1	1	yes	characteristic
559	C₂×C₇	C₂²×#137	1	1	yes	characteristic
560	C₂³	—	2	2	no	—
561	C₂³	—	2	2	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	2	8	no	—
566	C₂³	—	2	2	no	—
567	C₂³	—	2	8	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	4	4	no	—
571	C₂³	—	4	16	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	C₇×#135	1	4	yes	—
576	C₂³	C₇×#137	1	4	yes	—
577	C₂³	C₂²×C₇×D₄	1	2	yes	—
578	C₂³	C₂²×C₇×D₄	1	2	yes	—
579	C₂³	C₂²×C₇×D₄	1	2	yes	—
580	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
581	Q₈	—	2	4	no	—
582	Q₈	—	2	4	no	—
583	Q₈	—	2	4	no	—
584	Q₈	—	4	8	no	—
585	Q₈	—	4	4	no	—
586	Q₈	—	4	2	no	—
587	D₄	—	2	4	no	—
588	D₄	—	4	8	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	8	no	—
591	D₄	—	4	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	4	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	4	no	—
608	C₂×C₄	—	4	4	no	—
609	C₂×C₄	—	4	8	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	4	4	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
618	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
619	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
620	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
621	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
622	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
623	C₈	—	2	4	no	—
624	C₈	—	2	4	no	—
625	C₇	C₂×#3190	1	1	yes	characteristic, direct product factor, Sylow
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	8	no	—
629	C₂²	—	2	8	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	4	16	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	8	4	no	—
641	C₂²	C₇×#534	1	2	yes	—
642	C₂²	C₂×C₇×#135	1	4	yes	—
643	C₂²	C₂×C₇×#135	1	2	yes	—
644	C₂²	C₂×C₇×#137	1	4	yes	—
645	C₂²	C₂×C₇×#137	1	2	yes	—
646	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	4	no	—
651	C₄	—	4	2	no	—
652	C₄	—	4	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	4	no	—
655	C₄	C₇×#534	1	2	yes	—
656	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
657	C₂	—	2	4	no	—
658	C₂	—	2	4	no	—
659	C₂	—	4	2	no	—
660	C₂	—	8	2	no	—
661	C₂	C₇×#3190	1	4	yes	direct product factor
662	C₂	C₂×C₇×#534	1	1	yes	characteristic
663	C₂	C₂²×C₇×#135	1	1	yes	characteristic
664	C₂	C₂²×C₇×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#525	C₂
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
2. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
3. C₇×#3190	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
5. C₂×C₇×#483	C₂	semidirect
6. C₂×C₇×#480	C₂	semidirect
7. C₂×C₇×#467	C₂	semidirect
8. C₂×C₇×#465	C₂	semidirect
9. C₂×C₇×#452	C₂	semidirect
10. C₂×C₇×#451	C₂	semidirect
11. C₂×C₇×#448	C₂	semidirect
12. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
16. C₂²×C₇×Q₁₆	C₂²	semidirect
17. C₂²×C₇×SD₁₆	C₂²	semidirect
29. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
39. C₇×#485	C₂²	semidirect
40. C₇×#483	C₂²	semidirect
41. C₇×#480	C₂²	semidirect
42. C₇×#467	C₂²	semidirect
43. C₇×#465	C₂²	semidirect
44. C₇×#452	C₂²	semidirect
45. C₇×#451	C₂²	semidirect
46. C₇×#448	C₂²	semidirect
47. C₂×C₇×#107	C₂²	semidirect
48. C₂×C₇×#106	C₂²	semidirect
49. C₂×C₇×#103	C₂²	semidirect
50. C₂×C₇×#103	C₂²	semidirect
51. C₂×C₇×#103	C₂²	semidirect
52. C₂×C₇×#102	C₂²	semidirect
56. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
57. C₂×#3190	C₇	direct (N × H)
85. C₂×C₇×Q₁₆	C₂³	semidirect
87. C₂×C₇×SD₁₆	C₂³	semidirect
132. C₇×#107	C₂³	semidirect
133. C₇×#106	C₂³	semidirect
134. C₇×#103	C₂³	semidirect
135. C₇×#103	C₂³	semidirect
136. C₇×#103	C₂³	semidirect
137. C₇×#102	C₂³	semidirect
142. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
143. #3190	C₂×C₇	direct (N × H)
144. C₂×#485	C₂×C₇	semidirect
145. C₂×#483	C₂×C₇	semidirect
146. C₂×#480	C₂×C₇	semidirect
147. C₂×#467	C₂×C₇	semidirect
148. C₂×#465	C₂×C₇	semidirect
149. C₂×#452	C₂×C₇	semidirect
150. C₂×#451	C₂×C₇	semidirect
151. C₂×#448	C₂×C₇	semidirect
152. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
244. C₂²×Q₁₆	C₂²×C₇	semidirect
245. C₂²×SD₁₆	C₂²×C₇	semidirect
257. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
267. #485	C₂²×C₇	semidirect
268. #483	C₂²×C₇	semidirect
269. #480	C₂²×C₇	semidirect
270. #467	C₂²×C₇	semidirect
271. #465	C₂²×C₇	semidirect
272. #452	C₂²×C₇	semidirect
273. #451	C₂²×C₇	semidirect
274. #448	C₂²×C₇	semidirect
275. C₂×#107	C₂²×C₇	semidirect
276. C₂×#106	C₂²×C₇	semidirect
277. C₂×#103	C₂²×C₇	semidirect
278. C₂×#103	C₂²×C₇	semidirect
279. C₂×#103	C₂²×C₇	semidirect
280. C₂×#102	C₂²×C₇	semidirect
284. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
377. C₂×Q₁₆	C₂³×C₇	semidirect
379. C₂×SD₁₆	C₂³×C₇	semidirect
424. #107	C₂³×C₇	semidirect
425. #106	C₂³×C₇	semidirect
426. #103	C₂³×C₇	semidirect
427. #103	C₂³×C₇	semidirect
428. #103	C₂³×C₇	semidirect
429. #102	C₂³×C₇	semidirect
556. C₂×C₇	#3190	direct (N × H)
625. C₇	C₂×#3190	direct (N × H)
661. C₂	C₇×#3190	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
C₂²×C₇×C₂²⋊Q₈	2
C₇×#3190	2
C₂×C₇×#485	2
C₂×C₇×#483	2
C₂×C₇×#480	2
C₂×C₇×#467	2
C₂×C₇×#465	2
C₂×C₇×#452	2
C₂×C₇×#451	2
C₂×C₇×#448	2
C₂²×C₇×C₂²⋊C₈	2
C₂×#3190	7

Subgroups — C2×C7×#3190 #13237948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3190 #13237948