Subgroups — C₂×C₇×#3116 #13237755

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic
3	C₇×#3116	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#452	C₂	1	2	yes	maximal
10	C₂×C₇×#441	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₇×#533	—	2	4	no	—
17	C₇×#533	C₂²	1	8	yes	complemented
18	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₇×#125	—	2	1	no	—
21	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₄×C₇×#41	—	2	4	no	—
24	C₄×C₇×#41	C₂²	1	8	yes	—
25	C₂×C₄×C₇×Q₈	—	2	1	no	—
26	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	—	2	1	no	—
30	C₂×C₄×C₇×D₄	—	2	1	no	—
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	—	2	1	no	—
34	C₂×C₇×#117	—	2	1	no	—
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	—	2	1	no	—
37	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
38	C₇×#485	C₂²	1	16	yes	complemented
39	C₇×#477	C₂²	1	8	yes	complemented
40	C₇×#476	C₂²	1	8	yes	complemented
41	C₇×#462	C₂²	1	8	yes	complemented
42	C₇×#461	C₂²	1	8	yes	complemented
43	C₇×#452	C₂²	1	16	yes	—
44	C₇×#441	C₂²	1	16	yes	complemented
45	C₇×#440	C₂²	1	16	yes	complemented
46	C₇×#432	C₂²	1	8	yes	complemented
47	C₂×C₇×#107	C₂²	1	2	yes	—
48	C₂×C₇×#106	C₂²	1	2	yes	—
49	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₇×#103	C₂²	1	2	yes	—
52	C₂×C₇×#103	C₂²	1	2	yes	—
53	C₂×C₇×#103	C₂²	1	2	yes	—
54	C₂×C₇×#102	C₂²	1	2	yes	—
55	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
56	C₂×C₇×#97	C₂²	1	2	yes	—
57	C₂×#3116	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
58	C₂×C₇×#41	—	2	4	no	—
59	C₂×C₇×#41	—	2	4	no	—
60	C₂×C₇×#41	—	2	2	no	—
61	C₂×C₇×#41	C₂³	1	4	yes	—
62	C₂²×C₇×Q₈	—	2	1	no	—
63	C₂²×C₇×Q₈	C₂³	1	2	yes	—
64	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₇×Q₁₆	—	2	8	no	—
74	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₇×SD₁₆	—	2	8	no	—
76	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
77	C₂²×C₇×C₈	C₂³	1	2	yes	—
78	C₂²×C₇×C₈	C₂³	1	2	yes	—
79	C₇×C₄⋊Q₈	—	2	2	no	—
80	C₇×C₄⋊Q₈	—	2	2	no	—
81	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
82	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₇×#125	—	2	8	no	—
84	C₇×C₂²⋊Q₈	—	2	8	no	—
85	C₇×C₂²⋊Q₈	—	2	4	no	—
86	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
87	C₄×C₇×Q₈	—	2	8	no	—
88	C₄×C₇×Q₈	—	2	2	no	—
89	C₄×C₇×Q₈	—	2	2	no	—
90	C₄×C₇×Q₈	—	2	4	no	—
91	C₄×C₇×Q₈	C₂³	1	4	yes	—
92	C₄×C₇×Q₈	C₂³	1	4	yes	—
93	C₄×C₇×Q₈	C₂³	1	8	yes	—
94	C₄×C₇×D₄	—	2	8	no	—
95	C₄×C₇×D₄	—	2	8	no	—
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₄×C₇×D₄	C₂³	1	4	yes	—
99	C₄×C₇×D₄	C₂³	1	4	yes	—
100	C₇×#117	—	2	8	no	—
101	C₇×#117	—	2	2	no	—
102	C₇×#117	—	2	8	no	—
103	C₇×#117	C₂³	1	4	yes	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	—	2	1	no	—
108	C₂×C₇×C₄⋊C₄	—	2	1	no	—
109	C₂×C₇×C₄⋊C₄	—	2	2	no	—
110	C₂×C₇×C₄⋊C₄	—	2	2	no	—
111	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₄²×C₇	—	2	1	no	—
119	C₂×C₄²×C₇	—	2	1	no	—
120	C₂×C₄²×C₇	—	2	1	no	—
121	C₂×C₄²×C₇	—	2	2	no	—
122	C₂×C₄²×C₇	—	2	8	no	—
123	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₇	D₄	1	4	yes	—
126	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇	C₂³	1	4	yes	—
129	C₇×#107	C₂³	1	8	yes	—
130	C₇×#106	C₂³	1	8	yes	—
131	C₇×C₄⋊C₈	C₂³	1	4	yes	—
132	C₇×C₄⋊C₈	C₂³	1	4	yes	—
133	C₇×#103	C₂³	1	8	yes	—
134	C₇×#103	C₂³	1	8	yes	—
135	C₇×#103	C₂³	1	8	yes	—
136	C₇×#102	C₂³	1	8	yes	—
137	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
138	C₇×#97	C₂³	1	8	yes	—
139	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic
141	#3116	C₂×C₇	1	16	yes	direct product factor
142	C₂×#485	C₂×C₇	1	2	yes	complemented
143	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
144	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
145	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
147	C₂×#452	C₂×C₇	1	2	yes	—
148	C₂×#441	C₂×C₇	1	2	yes	complemented
149	C₂×#440	C₂×C₇	1	2	yes	complemented
150	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
151	C₂⁴×C₇	—	2	1	no	—
152	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
153	C₇×#41	—	2	16	no	—
154	C₇×#41	—	2	8	no	—
155	C₇×#41	—	2	8	no	—
156	C₂×C₇×Q₈	—	2	1	no	—
157	C₂×C₇×Q₈	—	2	2	no	—
158	C₂×C₇×Q₈	—	2	4	no	—
159	C₂×C₇×Q₈	—	2	2	no	—
160	C₂×C₇×Q₈	—	2	4	no	—
161	C₂×C₇×Q₈	—	2	4	no	—
162	C₂×C₇×Q₈	—	4	4	no	—
163	C₂×C₇×Q₈	#41	1	4	yes	—
164	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
165	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
166	C₂×C₇×D₄	—	2	8	no	—
167	C₂×C₇×D₄	—	2	4	no	—
168	C₂×C₇×D₄	—	2	1	no	—
169	C₂×C₇×D₄	—	2	2	no	—
170	C₂×C₇×D₄	#41	1	4	yes	—
171	C₂×C₇×D₄	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₇	—	2	8	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	4	no	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	2	2	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	1	no	—
179	C₂²×C₄×C₇	—	2	1	no	—
180	C₂²×C₄×C₇	—	2	2	no	—
181	C₂²×C₄×C₇	—	2	2	no	—
182	C₂²×C₄×C₇	—	2	4	no	—
183	C₂²×C₄×C₇	—	2	4	no	—
184	C₂²×C₄×C₇	—	4	2	no	—
185	C₂²×C₄×C₇	—	4	4	no	—
186	C₂²×C₄×C₇	—	4	4	no	—
187	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
194	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
197	C₇×Q₁₆	—	2	16	no	—
198	C₇×SD₁₆	—	2	16	no	—
199	C₂×C₇×C₈	—	2	4	no	—
200	C₂×C₇×C₈	—	2	4	no	—
201	C₂×C₇×C₈	C₂⁴	1	4	yes	—
202	C₂×C₇×C₈	C₂⁴	1	4	yes	—
203	C₇×C₄⋊C₄	—	2	4	no	—
204	C₇×C₄⋊C₄	—	2	4	no	—
205	C₇×C₄⋊C₄	—	2	4	no	—
206	C₇×C₄⋊C₄	—	2	4	no	—
207	C₇×C₄⋊C₄	—	2	4	no	—
208	C₇×C₄⋊C₄	—	2	8	no	—
209	C₇×C₄⋊C₄	—	2	8	no	—
210	C₇×C₄⋊C₄	—	2	1	no	—
211	C₇×C₄⋊C₄	—	2	1	no	—
212	C₇×C₄⋊C₄	—	2	2	no	—
213	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
214	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
215	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₇×C₂²⋊C₄	—	2	8	no	—
217	C₇×C₂²⋊C₄	—	2	4	no	—
218	C₇×C₂²⋊C₄	—	2	4	no	—
219	C₇×C₂²⋊C₄	—	2	4	no	—
220	C₄²×C₇	—	2	4	no	—
221	C₄²×C₇	—	2	4	no	—
222	C₄²×C₇	—	2	4	no	—
223	C₄²×C₇	—	2	8	no	—
224	C₄²×C₇	C₂×D₄	1	4	yes	—
225	C₄²×C₇	C₂×D₄	1	4	yes	—
226	C₄²×C₇	C₂×D₄	1	2	yes	—
227	C₄²×C₇	C₂×D₄	1	2	yes	—
228	C₄²×C₇	C₂⁴	1	2	yes	—
229	C₄²×C₇	C₂⁴	1	2	yes	—
230	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
231	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
232	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
233	#533	—	2	4	no	—
234	#533	C₂²×C₇	1	8	yes	complemented
235	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
237	C₂×#125	—	2	1	no	—
238	C₂×C₂²⋊Q₈	—	2	1	no	—
239	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
240	C₄×#41	—	2	4	no	—
241	C₄×#41	C₂²×C₇	1	8	yes	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
246	C₂×C₄×D₄	—	2	1	no	—
247	C₂×C₄×D₄	—	2	1	no	—
248	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
250	C₂×#117	—	2	1	no	—
251	C₂×#117	—	2	1	no	—
252	C₂×#117	C₂²×C₇	1	1	yes	characteristic
253	C₂²×C₄²	—	2	1	no	—
254	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
255	#485	C₂²×C₇	1	16	yes	complemented
256	#477	C₂²×C₇	1	8	yes	complemented
257	#476	C₂²×C₇	1	8	yes	complemented
258	#462	C₂²×C₇	1	8	yes	complemented
259	#461	C₂²×C₇	1	8	yes	complemented
260	#452	C₂²×C₇	1	16	yes	—
261	#441	C₂²×C₇	1	16	yes	complemented
262	#440	C₂²×C₇	1	16	yes	complemented
263	#432	C₂²×C₇	1	8	yes	complemented
264	C₂×#107	C₂²×C₇	1	2	yes	—
265	C₂×#106	C₂²×C₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
268	C₂×#103	C₂²×C₇	1	2	yes	—
269	C₂×#103	C₂²×C₇	1	2	yes	—
270	C₂×#103	C₂²×C₇	1	2	yes	—
271	C₂×#102	C₂²×C₇	1	2	yes	—
272	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
273	C₂×#97	C₂²×C₇	1	2	yes	—
274	C₂³×C₇	—	2	2	no	—
275	C₂³×C₇	—	2	4	no	—
276	C₂³×C₇	—	2	2	no	—
277	C₂³×C₇	—	2	2	no	—
278	C₂³×C₇	—	2	2	no	—
279	C₂³×C₇	—	4	2	no	—
280	C₂³×C₇	—	4	2	no	—
281	C₂³×C₇	C₂²×D₄	1	2	yes	—
282	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
283	C₇×Q₈	—	2	4	no	—
284	C₇×Q₈	—	2	2	no	—
285	C₇×Q₈	—	2	4	no	—
286	C₇×Q₈	—	2	4	no	—
287	C₇×Q₈	—	4	8	no	—
288	C₇×Q₈	—	4	4	no	—
289	C₇×Q₈	C₂×#41	1	4	yes	—
290	C₇×D₄	—	2	16	no	—
291	C₇×D₄	—	2	4	no	—
292	C₇×D₄	—	2	2	no	—
293	C₇×D₄	C₂×#41	1	4	yes	—
294	C₂×C₄×C₇	—	2	16	no	—
295	C₂×C₄×C₇	—	2	2	no	—
296	C₂×C₄×C₇	—	2	4	no	—
297	C₂×C₄×C₇	—	2	2	no	—
298	C₂×C₄×C₇	—	2	2	no	—
299	C₂×C₄×C₇	—	2	2	no	—
300	C₂×C₄×C₇	—	2	2	no	—
301	C₂×C₄×C₇	—	2	4	no	—
302	C₂×C₄×C₇	—	2	8	no	—
303	C₂×C₄×C₇	—	2	2	no	—
304	C₂×C₄×C₇	—	2	2	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	2	no	—
307	C₂×C₄×C₇	—	2	4	no	—
308	C₂×C₄×C₇	—	2	4	no	—
309	C₂×C₄×C₇	—	4	4	no	—
310	C₂×C₄×C₇	—	4	8	no	—
311	C₂×C₄×C₇	—	4	4	no	—
312	C₂×C₄×C₇	—	4	2	no	—
313	C₂×C₄×C₇	—	4	2	no	—
314	C₂×C₄×C₇	—	4	4	no	—
315	C₂×C₄×C₇	—	4	8	no	—
316	C₂×C₄×C₇	#137	1	4	yes	—
317	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
319	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
320	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
321	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₇	C₂×#41	1	2	yes	—
324	C₂×C₄×C₇	C₂×#41	1	2	yes	—
325	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
326	C₇×C₈	—	2	4	no	—
327	C₇×C₈	—	2	4	no	—
328	C₂×#41	—	2	4	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	—	2	2	no	—
331	C₂×#41	C₂³×C₇	1	4	yes	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×Q₈	C₂³×C₇	1	2	yes	—
334	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
341	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
342	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
343	C₂×Q₁₆	—	2	8	no	—
344	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
345	C₂×SD₁₆	—	2	8	no	—
346	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
347	C₂²×C₈	C₂³×C₇	1	2	yes	—
348	C₂²×C₈	C₂³×C₇	1	2	yes	—
349	C₄⋊Q₈	—	2	2	no	—
350	C₄⋊Q₈	—	2	2	no	—
351	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
352	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
353	#125	—	2	8	no	—
354	C₂²⋊Q₈	—	2	8	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
357	C₄×Q₈	—	2	8	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	C₂³×C₇	1	4	yes	—
362	C₄×Q₈	C₂³×C₇	1	4	yes	—
363	C₄×Q₈	C₂³×C₇	1	8	yes	—
364	C₄×D₄	—	2	8	no	—
365	C₄×D₄	—	2	8	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	C₂³×C₇	1	4	yes	—
369	C₄×D₄	C₂³×C₇	1	4	yes	—
370	#117	—	2	8	no	—
371	#117	—	2	2	no	—
372	#117	—	2	8	no	—
373	#117	C₂³×C₇	1	4	yes	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	8	no	—
393	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
394	C₂×C₄²	C₇×D₄	1	4	yes	—
395	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
396	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
397	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
398	C₂×C₄²	C₂³×C₇	1	4	yes	—
399	#107	C₂³×C₇	1	8	yes	—
400	#106	C₂³×C₇	1	8	yes	—
401	C₄⋊C₈	C₂³×C₇	1	4	yes	—
402	C₄⋊C₈	C₂³×C₇	1	4	yes	—
403	#103	C₂³×C₇	1	8	yes	—
404	#103	C₂³×C₇	1	8	yes	—
405	#103	C₂³×C₇	1	8	yes	—
406	#102	C₂³×C₇	1	8	yes	—
407	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
408	#97	C₂³×C₇	1	8	yes	—
409	C₂²×C₇	—	2	2	no	—
410	C₂²×C₇	—	2	4	no	—
411	C₂²×C₇	—	2	2	no	—
412	C₂²×C₇	—	2	2	no	—
413	C₂²×C₇	—	4	4	no	—
414	C₂²×C₇	—	4	8	no	—
415	C₂²×C₇	—	4	2	no	—
416	C₂²×C₇	—	4	2	no	—
417	C₂²×C₇	#525	1	2	yes	—
418	C₂²×C₇	C₂×#137	1	2	yes	—
419	C₂²×C₇	#575	1	2	yes	—
420	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
421	C₄×C₇	—	2	2	no	—
422	C₄×C₇	—	2	4	no	—
423	C₄×C₇	—	2	2	no	—
424	C₄×C₇	—	2	2	no	—
425	C₄×C₇	—	2	2	no	—
426	C₄×C₇	—	4	4	no	—
427	C₄×C₇	—	4	2	no	—
428	C₄×C₇	—	4	2	no	—
429	C₄×C₇	—	4	4	no	—
430	C₄×C₇	#525	1	2	yes	—
431	C₄×C₇	C₂×#137	1	4	yes	—
432	C₄×C₇	C₂²×#41	1	1	yes	characteristic
433	C₄×C₇	C₂²×#41	1	1	yes	characteristic
434	C₂⁴	—	2	1	no	—
435	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
436	#41	—	2	16	no	—
437	#41	—	2	8	no	—
438	#41	—	2	8	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	4	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	4	no	—
445	C₂×Q₈	—	4	4	no	—
446	C₂×Q₈	C₇×#41	1	4	yes	—
447	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
448	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
449	C₂×D₄	—	2	8	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	C₇×#41	1	4	yes	—
454	C₂×D₄	C₂⁴×C₇	1	2	yes	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	4	2	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	—	4	4	no	—
470	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
474	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
476	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
477	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
479	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
480	Q₁₆	—	2	16	no	—
481	SD₁₆	—	2	16	no	—
482	C₂×C₈	—	2	4	no	—
483	C₂×C₈	—	2	4	no	—
484	C₂×C₈	C₂⁴×C₇	1	4	yes	—
485	C₂×C₈	C₂⁴×C₇	1	4	yes	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	8	no	—
492	C₄⋊C₄	—	2	8	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
497	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
498	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	4	no	—
505	C₄²	—	2	4	no	—
506	C₄²	—	2	8	no	—
507	C₄²	C₂×C₇×D₄	1	4	yes	—
508	C₄²	C₂×C₇×D₄	1	4	yes	—
509	C₄²	C₂×C₇×D₄	1	2	yes	—
510	C₄²	C₂×C₇×D₄	1	2	yes	—
511	C₄²	C₂⁴×C₇	1	2	yes	—
512	C₄²	C₂⁴×C₇	1	2	yes	—
513	C₂×C₇	—	4	2	no	—
514	C₂×C₇	—	4	4	no	—
515	C₂×C₇	#3116	1	4	yes	direct product factor
516	C₂×C₇	C₂×#525	1	1	yes	characteristic
517	C₂×C₇	C₂²×#137	1	1	yes	characteristic
518	C₂×C₇	C₂×#575	1	1	yes	characteristic
519	C₂³	—	2	2	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	C₂²×C₇×D₄	1	2	yes	—
527	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
528	Q₈	—	2	2	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	Q₈	—	2	4	no	—
532	Q₈	—	4	8	no	—
533	Q₈	—	4	4	no	—
534	Q₈	C₂×C₇×#41	1	4	yes	—
535	D₄	—	2	16	no	—
536	D₄	—	2	2	no	—
537	D₄	—	2	4	no	—
538	D₄	C₂×C₇×#41	1	4	yes	—
539	C₂×C₄	—	2	16	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	8	no	—
561	C₂×C₄	C₇×#137	1	4	yes	—
562	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
563	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
564	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
565	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
566	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
568	C₂×C₄	C₂×C₇×#41	1	2	yes	—
569	C₂×C₄	C₂×C₇×#41	1	2	yes	—
570	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	—	2	4	no	—
573	C₇	C₂×#3116	1	1	yes	characteristic, direct product factor, Sylow
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	8	no	—
582	C₂²	C₇×#525	1	2	yes	—
583	C₂²	C₂×C₇×#137	1	2	yes	—
584	C₂²	C₇×#575	1	2	yes	—
585	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	4	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	4	no	—
594	C₄	—	4	4	no	—
595	C₄	C₇×#525	1	2	yes	—
596	C₄	C₂×C₇×#137	1	4	yes	—
597	C₄	C₂²×C₇×#41	1	1	yes	characteristic
598	C₄	C₂²×C₇×#41	1	1	yes	characteristic
599	C₂	—	4	2	no	—
600	C₂	—	4	4	no	—
601	C₂	C₇×#3116	1	4	yes	direct product factor
602	C₂	C₂×C₇×#525	1	1	yes	characteristic
603	C₂	C₂²×C₇×#137	1	1	yes	characteristic
604	C₂	C₂×C₇×#575	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×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3116	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
5. C₂×C₇×#477	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#462	C₂	semidirect
8. C₂×C₇×#461	C₂	semidirect
10. C₂×C₇×#441	C₂	semidirect
11. C₂×C₇×#440	C₂	semidirect
12. C₂×C₇×#432	C₂	semidirect
17. C₇×#533	C₂²	semidirect
38. C₇×#485	C₂²	semidirect
39. C₇×#477	C₂²	semidirect
40. C₇×#476	C₂²	semidirect
41. C₇×#462	C₂²	semidirect
42. C₇×#461	C₂²	semidirect
44. C₇×#441	C₂²	semidirect
45. C₇×#440	C₂²	semidirect
46. C₇×#432	C₂²	semidirect
57. C₂×#3116	C₇	direct (N × H)
139. C₂×#533	C₂×C₇	semidirect
141. #3116	C₂×C₇	direct (N × H)
142. C₂×#485	C₂×C₇	semidirect
143. C₂×#477	C₂×C₇	semidirect
144. C₂×#476	C₂×C₇	semidirect
145. C₂×#462	C₂×C₇	semidirect
146. C₂×#461	C₂×C₇	semidirect
148. C₂×#441	C₂×C₇	semidirect
149. C₂×#440	C₂×C₇	semidirect
150. C₂×#432	C₂×C₇	semidirect
234. #533	C₂²×C₇	semidirect
255. #485	C₂²×C₇	semidirect
256. #477	C₂²×C₇	semidirect
257. #476	C₂²×C₇	semidirect
258. #462	C₂²×C₇	semidirect
259. #461	C₂²×C₇	semidirect
261. #441	C₂²×C₇	semidirect
262. #440	C₂²×C₇	semidirect
263. #432	C₂²×C₇	semidirect
515. C₂×C₇	#3116	direct (N × H)
573. C₇	C₂×#3116	direct (N × H)
601. C₂	C₇×#3116	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×#533	2
C₂×C₄×C₇×#41	2
C₇×#3116	2
C₂×C₇×#485	2
C₂×C₇×#477	2
C₂×C₇×#476	2
C₂×C₇×#462	2
C₂×C₇×#461	2
C₂×C₇×#452	2
C₂×C₇×#441	2
C₂×C₇×#440	2
C₂×C₇×#432	2
C₂×#3116	7

Subgroups — C2×C7×#3116 #13237755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3116 #13237755