Subgroups — C₂×C₇×#3394 #13238606

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3394	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#495	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#464	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic
10	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₇×D₈	C₂²	1	2	yes	—
18	C₇×#559	—	2	4	no	—
19	C₇×#559	C₂²	1	8	yes	complemented
20	C₇×#556	—	2	4	no	—
21	C₇×#556	C₂²	1	8	yes	complemented
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₇×#126	—	2	2	no	—
25	C₂×C₇×#124	—	2	1	no	—
26	C₂×C₇×#124	C₂²	1	2	yes	—
27	C₂×C₇×#124	C₂²	1	2	yes	—
28	C₂×C₇×#123	—	2	2	no	—
29	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×D₄	—	2	1	no	—
34	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
36	C₂×C₇×#117	—	2	1	no	—
37	C₇×#495	C₂²	1	16	yes	complemented
38	C₇×#492	C₂²	1	8	yes	complemented
39	C₇×#464	C₂²	1	16	yes	complemented
40	C₇×#463	C₂²	1	16	yes	complemented
41	C₇×#462	C₂²	1	8	yes	complemented
42	C₇×#459	C₂²	1	8	yes	—
43	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
44	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
45	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
46	C₂×C₇×#106	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#103	C₂²	1	1	yes	characteristic
51	C₂×C₇×#102	C₂²	1	2	yes	—
52	C₂×C₇×#102	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
55	C₂×#3394	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
57	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×Q₈	C₂³	1	2	yes	—
59	C₂²×C₇×D₄	—	2	1	no	—
60	C₂²×C₇×D₄	—	2	1	no	—
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₇×D₄	C₂³	1	2	yes	—
63	C₂³×C₄×C₇	—	2	1	no	—
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂×C₇×Q₁₆	—	4	4	no	—
66	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
67	C₂×C₇×SD₁₆	—	2	8	no	—
68	C₂×C₇×SD₁₆	—	2	4	no	—
69	C₂×C₇×SD₁₆	—	4	4	no	—
70	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
71	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
72	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₇×D₈	—	4	4	no	—
74	C₂×C₇×D₈	C₂³	1	8	yes	—
75	C₂²×C₇×C₈	C₂³	1	2	yes	—
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₇×C₄⋊Q₈	—	2	2	no	—
79	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₇×#127	—	2	2	no	—
81	C₇×#127	C₂³	1	4	yes	—
82	C₇×#126	—	2	16	no	—
83	C₇×#124	—	2	8	no	—
84	C₇×#124	—	2	4	no	—
85	C₇×#124	—	2	4	no	—
86	C₇×#124	C₂³	1	8	yes	—
87	C₇×#124	C₂³	1	8	yes	—
88	C₇×#123	—	2	16	no	—
89	C₇×C₂²⋊Q₈	—	2	8	no	—
90	C₄×C₇×Q₈	—	2	4	no	—
91	C₄×C₇×Q₈	—	2	2	no	—
92	C₄×C₇×Q₈	D₄	1	4	yes	—
93	C₄×C₇×Q₈	C₂³	1	8	yes	—
94	C₄×C₇×Q₈	C₂³	1	4	yes	—
95	C₄×C₇×Q₈	C₂³	1	4	yes	—
96	C₄×C₇×D₄	—	2	8	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₄×C₇×D₄	—	2	4	no	—
99	C₄×C₇×D₄	C₂³	1	4	yes	—
100	C₄×C₇×D₄	C₂³	1	8	yes	—
101	C₇×#117	—	2	8	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	—	2	2	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	1	no	—
106	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
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	2	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
116	C₂×C₄²×C₇	—	2	2	no	—
117	C₂×C₄²×C₇	—	2	1	no	—
118	C₂×C₄²×C₇	C₂³	1	2	yes	—
119	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
120	C₇×#106	C₂³	1	4	yes	—
121	C₇×C₄⋊C₈	C₂³	1	4	yes	—
122	C₇×C₄⋊C₈	C₂³	1	8	yes	—
123	C₇×#103	C₂³	1	8	yes	—
124	C₇×#103	C₂³	1	4	yes	—
125	C₇×#102	C₂³	1	8	yes	—
126	C₇×#102	C₂³	1	4	yes	—
127	C₄×C₇×C₈	C₂³	1	4	yes	—
128	C₄×C₇×C₈	C₂³	1	8	yes	—
129	C₂×#559	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#556	C₂×C₇	1	1	yes	characteristic, complemented
131	#3394	C₂×C₇	1	16	yes	direct product factor
132	C₂×#495	C₂×C₇	1	2	yes	complemented
133	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#464	C₂×C₇	1	2	yes	complemented
135	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#463	C₂×C₇	1	2	yes	complemented
137	C₂×#459	C₂×C₇	1	1	yes	characteristic
138	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
141	C₂⁴×C₇	—	2	1	no	—
142	C₂⁴×C₇	—	2	2	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	2	4	no	—
148	C₂×C₇×Q₈	—	2	4	no	—
149	C₂×C₇×Q₈	—	2	2	no	—
150	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
151	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
152	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
153	C₂×C₇×D₄	—	2	1	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	4	no	—
157	C₂×C₇×D₄	—	2	2	no	—
158	C₂×C₇×D₄	—	2	4	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	4	4	no	—
162	C₂×C₇×D₄	—	8	2	no	—
163	C₂×C₇×D₄	C₂⁴	1	2	yes	—
164	C₂×C₇×D₄	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₇	—	2	1	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	2	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	2	8	no	—
171	C₂²×C₄×C₇	—	4	4	no	—
172	C₂²×C₄×C₇	—	8	4	no	—
173	C₂²×C₄×C₇	C₂×D₄	1	2	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	1	yes	characteristic
178	C₇×Q₁₆	—	4	8	no	—
179	C₇×SD₁₆	—	2	16	no	—
180	C₇×SD₁₆	—	2	8	no	—
181	C₇×SD₁₆	—	4	8	no	—
182	C₇×D₈	—	4	8	no	—
183	C₂×C₇×C₈	—	2	4	no	—
184	C₂×C₇×C₈	—	2	2	no	—
185	C₂×C₇×C₈	#41	1	4	yes	—
186	C₂×C₇×C₈	C₂⁴	1	4	yes	—
187	C₂×C₇×C₈	C₂⁴	1	2	yes	—
188	C₂×C₇×C₈	C₂⁴	1	2	yes	—
189	C₇×C₄⋊C₄	—	2	4	no	—
190	C₇×C₄⋊C₄	—	2	8	no	—
191	C₇×C₄⋊C₄	—	2	4	no	—
192	C₇×C₄⋊C₄	—	2	4	no	—
193	C₇×C₄⋊C₄	—	2	1	no	—
194	C₇×C₄⋊C₄	—	2	1	no	—
195	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₇×C₂²⋊C₄	—	2	8	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	8	no	—
202	C₇×C₂²⋊C₄	—	2	4	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	—	2	8	no	—
205	C₄²×C₇	—	2	8	no	—
206	C₄²×C₇	—	2	4	no	—
207	C₄²×C₇	C₂×D₄	1	4	yes	—
208	C₄²×C₇	C₂×D₄	1	2	yes	—
209	C₄²×C₇	C₂⁴	1	4	yes	—
210	C₄²×C₇	C₂⁴	1	2	yes	—
211	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
213	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
214	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
215	C₂²×D₈	C₂²×C₇	1	2	yes	—
216	#559	—	2	4	no	—
217	#559	C₂²×C₇	1	8	yes	complemented
218	#556	—	2	4	no	—
219	#556	C₂²×C₇	1	8	yes	complemented
220	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
221	C₂×#127	C₂²×C₇	1	1	yes	characteristic
222	C₂×#126	—	2	2	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×#124	C₂²×C₇	1	2	yes	—
225	C₂×#124	C₂²×C₇	1	2	yes	—
226	C₂×#123	—	2	2	no	—
227	C₂×C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
229	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
230	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₄×D₄	—	2	1	no	—
232	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
233	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
234	C₂×#117	—	2	1	no	—
235	#495	C₂²×C₇	1	16	yes	complemented
236	#492	C₂²×C₇	1	8	yes	complemented
237	#464	C₂²×C₇	1	16	yes	complemented
238	#463	C₂²×C₇	1	16	yes	complemented
239	#462	C₂²×C₇	1	8	yes	complemented
240	#459	C₂²×C₇	1	8	yes	—
241	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
242	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
243	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
244	C₂×#106	C₂²×C₇	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
247	C₂×#103	C₂²×C₇	1	2	yes	—
248	C₂×#103	C₂²×C₇	1	1	yes	characteristic
249	C₂×#102	C₂²×C₇	1	2	yes	—
250	C₂×#102	C₂²×C₇	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
253	C₂³×C₇	—	2	2	no	—
254	C₂³×C₇	—	2	4	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	—	4	4	no	—
257	C₂³×C₇	—	4	2	no	—
258	C₂³×C₇	—	4	4	no	—
259	C₂³×C₇	—	4	4	no	—
260	C₂³×C₇	—	4	2	no	—
261	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
262	C₇×Q₈	—	2	8	no	—
263	C₇×Q₈	—	2	2	no	—
264	C₇×Q₈	—	2	4	no	—
265	C₇×Q₈	—	2	4	no	—
266	C₇×Q₈	—	2	2	no	—
267	C₇×Q₈	—	4	2	no	—
268	C₇×Q₈	—	4	4	no	—
269	C₇×D₄	—	2	2	no	—
270	C₇×D₄	—	2	4	no	—
271	C₇×D₄	—	2	2	no	—
272	C₇×D₄	—	2	4	no	—
273	C₇×D₄	—	4	2	no	—
274	C₇×D₄	—	4	4	no	—
275	C₇×D₄	—	4	8	no	—
276	C₇×D₄	—	8	4	no	—
277	C₂×C₄×C₇	—	2	4	no	—
278	C₂×C₄×C₇	—	2	4	no	—
279	C₂×C₄×C₇	—	2	2	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	2	2	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	—	4	8	no	—
289	C₂×C₄×C₇	—	8	8	no	—
290	C₂×C₄×C₇	#135	1	4	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
293	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₇	C₂×#41	1	2	yes	—
297	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
299	C₇×C₈	—	2	4	no	—
300	C₇×C₈	—	2	2	no	—
301	C₇×C₈	C₂×#41	1	4	yes	—
302	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
303	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
304	C₂²×Q₈	C₂³×C₇	1	2	yes	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₇	1	2	yes	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	—	2	2	no	—
311	C₂×Q₁₆	—	4	4	no	—
312	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
313	C₂×SD₁₆	—	2	8	no	—
314	C₂×SD₁₆	—	2	4	no	—
315	C₂×SD₁₆	—	4	4	no	—
316	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
317	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
318	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
319	C₂×D₈	—	4	4	no	—
320	C₂×D₈	C₂³×C₇	1	8	yes	—
321	C₂²×C₈	C₂³×C₇	1	2	yes	—
322	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
326	#127	—	2	2	no	—
327	#127	C₂³×C₇	1	4	yes	—
328	#126	—	2	16	no	—
329	#124	—	2	8	no	—
330	#124	—	2	4	no	—
331	#124	—	2	4	no	—
332	#124	C₂³×C₇	1	8	yes	—
333	#124	C₂³×C₇	1	8	yes	—
334	#123	—	2	16	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₄×Q₈	—	2	4	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	C₇×D₄	1	4	yes	—
339	C₄×Q₈	C₂³×C₇	1	8	yes	—
340	C₄×Q₈	C₂³×C₇	1	4	yes	—
341	C₄×Q₈	C₂³×C₇	1	4	yes	—
342	C₄×D₄	—	2	8	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	C₂³×C₇	1	4	yes	—
346	C₄×D₄	C₂³×C₇	1	8	yes	—
347	#117	—	2	8	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	C₂³×C₇	1	2	yes	—
365	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
366	#106	C₂³×C₇	1	4	yes	—
367	C₄⋊C₈	C₂³×C₇	1	4	yes	—
368	C₄⋊C₈	C₂³×C₇	1	8	yes	—
369	#103	C₂³×C₇	1	8	yes	—
370	#103	C₂³×C₇	1	4	yes	—
371	#102	C₂³×C₇	1	8	yes	—
372	#102	C₂³×C₇	1	4	yes	—
373	C₄×C₈	C₂³×C₇	1	4	yes	—
374	C₄×C₈	C₂³×C₇	1	8	yes	—
375	C₂²×C₇	—	4	2	no	—
376	C₂²×C₇	—	4	4	no	—
377	C₂²×C₇	—	4	2	no	—
378	C₂²×C₇	—	4	4	no	—
379	C₂²×C₇	—	4	4	no	—
380	C₂²×C₇	—	4	2	no	—
381	C₂²×C₇	—	8	4	no	—
382	C₂²×C₇	—	8	8	no	—
383	C₂²×C₇	#550	1	2	yes	—
384	C₂²×C₇	C₂×#135	1	2	yes	—
385	C₂²×C₇	#577	1	2	yes	—
386	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
387	C₄×C₇	—	2	4	no	—
388	C₄×C₇	—	2	4	no	—
389	C₄×C₇	—	2	2	no	—
390	C₄×C₇	—	4	2	no	—
391	C₄×C₇	—	4	4	no	—
392	C₄×C₇	—	4	2	no	—
393	C₄×C₇	—	4	2	no	—
394	C₄×C₇	#550	1	2	yes	—
395	C₄×C₇	C₂×#135	1	4	yes	—
396	C₄×C₇	C₂²×#41	1	1	yes	characteristic
397	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	2	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
408	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
409	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	—	8	2	no	—
420	C₂×D₄	C₂⁴×C₇	1	2	yes	—
421	C₂×D₄	C₂⁴×C₇	1	4	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	8	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	8	4	no	—
430	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
431	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
432	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
435	Q₁₆	—	4	8	no	—
436	SD₁₆	—	2	16	no	—
437	SD₁₆	—	2	8	no	—
438	SD₁₆	—	4	8	no	—
439	D₈	—	4	8	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	C₇×#41	1	4	yes	—
443	C₂×C₈	C₂⁴×C₇	1	4	yes	—
444	C₂×C₈	C₂⁴×C₇	1	2	yes	—
445	C₂×C₈	C₂⁴×C₇	1	2	yes	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
453	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
454	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
455	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	8	no	—
461	C₂²⋊C₄	—	2	8	no	—
462	C₄²	—	2	8	no	—
463	C₄²	—	2	4	no	—
464	C₄²	C₂×C₇×D₄	1	4	yes	—
465	C₄²	C₂×C₇×D₄	1	2	yes	—
466	C₄²	C₂⁴×C₇	1	4	yes	—
467	C₄²	C₂⁴×C₇	1	2	yes	—
468	C₂×C₇	—	8	2	no	—
469	C₂×C₇	—	8	4	no	—
470	C₂×C₇	#3394	1	4	yes	direct product factor
471	C₂×C₇	C₂×#550	1	1	yes	characteristic
472	C₂×C₇	C₂²×#135	1	1	yes	characteristic
473	C₂×C₇	C₂×#577	1	1	yes	characteristic
474	C₂³	—	2	2	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	2	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	2	no	—
482	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
483	Q₈	—	2	8	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	4	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	4	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	4	no	—
494	D₄	—	4	2	no	—
495	D₄	—	4	4	no	—
496	D₄	—	4	8	no	—
497	D₄	—	8	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	8	8	no	—
511	C₂×C₄	C₇×#135	1	4	yes	—
512	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
513	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
514	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
515	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
517	C₂×C₄	C₂×C₇×#41	1	2	yes	—
518	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
519	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
520	C₈	—	2	4	no	—
521	C₈	—	2	2	no	—
522	C₈	C₂×C₇×#41	1	4	yes	—
523	C₇	C₂×#3394	1	1	yes	characteristic, direct product factor, Sylow
524	C₂²	—	4	2	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	8	4	no	—
531	C₂²	—	8	8	no	—
532	C₂²	C₇×#550	1	2	yes	—
533	C₂²	C₂×C₇×#135	1	2	yes	—
534	C₂²	C₇×#577	1	2	yes	—
535	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
536	C₄	—	2	4	no	—
537	C₄	—	2	4	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	C₇×#550	1	2	yes	—
544	C₄	C₂×C₇×#135	1	4	yes	—
545	C₄	C₂²×C₇×#41	1	1	yes	characteristic
546	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂	—	8	2	no	—
548	C₂	—	8	4	no	—
549	C₂	C₇×#3394	1	4	yes	direct product factor
550	C₂	C₂×C₇×#550	1	1	yes	characteristic
551	C₂	C₂²×C₇×#135	1	1	yes	characteristic
552	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#459	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#559	C₂	semidirect
2. C₂×C₇×#556	C₂	semidirect
3. C₇×#3394	C₂	direct (N × H)
4. C₂×C₇×#495	C₂	semidirect
5. C₂×C₇×#492	C₂	semidirect
6. C₂×C₇×#464	C₂	semidirect
7. C₂×C₇×#462	C₂	semidirect
8. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×C₈×Q₈	C₂	semidirect
11. C₂×C₄×C₇×SD₁₆	C₂	semidirect
12. C₂×C₄×C₇×SD₁₆	C₂	semidirect
19. C₇×#559	C₂²	semidirect
21. C₇×#556	C₂²	semidirect
37. C₇×#495	C₂²	semidirect
38. C₇×#492	C₂²	semidirect
39. C₇×#464	C₂²	semidirect
40. C₇×#463	C₂²	semidirect
41. C₇×#462	C₂²	semidirect
43. C₇×C₈×Q₈	C₂²	semidirect
44. C₄×C₇×SD₁₆	C₂²	semidirect
45. C₄×C₇×SD₁₆	C₂²	semidirect
55. C₂×#3394	C₇	direct (N × H)
129. C₂×#559	C₂×C₇	semidirect
130. C₂×#556	C₂×C₇	semidirect
131. #3394	C₂×C₇	direct (N × H)
132. C₂×#495	C₂×C₇	semidirect
133. C₂×#492	C₂×C₇	semidirect
134. C₂×#464	C₂×C₇	semidirect
135. C₂×#462	C₂×C₇	semidirect
136. C₂×#463	C₂×C₇	semidirect
138. C₂×C₈×Q₈	C₂×C₇	semidirect
139. C₂×C₄×SD₁₆	C₂×C₇	semidirect
140. C₂×C₄×SD₁₆	C₂×C₇	semidirect
217. #559	C₂²×C₇	semidirect
219. #556	C₂²×C₇	semidirect
235. #495	C₂²×C₇	semidirect
236. #492	C₂²×C₇	semidirect
237. #464	C₂²×C₇	semidirect
238. #463	C₂²×C₇	semidirect
239. #462	C₂²×C₇	semidirect
241. C₈×Q₈	C₂²×C₇	semidirect
242. C₄×SD₁₆	C₂²×C₇	semidirect
243. C₄×SD₁₆	C₂²×C₇	semidirect
470. C₂×C₇	#3394	direct (N × H)
523. C₇	C₂×#3394	direct (N × H)
549. C₂	C₇×#3394	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×#559	2
C₂×C₇×#556	2
C₇×#3394	2
C₂×C₇×#495	2
C₂×C₇×#492	2
C₂×C₇×#464	2
C₂×C₇×#462	2
C₂×C₇×#463	2
C₂×C₇×#459	2
C₂×C₇×C₈×Q₈	2
C₂×C₄×C₇×SD₁₆	2
C₂×#3394	7

Subgroups — C2×C7×#3394 #13238606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3394 #13238606