Subgroups — C₂×C₇×#3385 #13238575

Order 1792.

1854 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×Q₈²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic
3	C₇×#3385	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#501	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic
9	C₂×C₇×#474	C₂	1	2	yes	maximal
10	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#440	C₂	1	2	yes	maximal
12	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
13	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
14	C₇×Q₈²	—	2	4	no	—
15	C₇×Q₈²	C₂²	1	8	yes	complemented
16	C₇×#554	—	2	4	no	—
17	C₇×#554	C₂²	1	8	yes	—
18	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
19	C₂×C₇×C₄⋊Q₈	—	2	2	no	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#125	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₄×C₇×Q₈	—	2	1	no	—
27	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
33	C₇×#501	C₂²	1	16	yes	complemented
34	C₇×#500	C₂²	1	8	yes	complemented
35	C₇×#479	C₂²	1	16	yes	complemented
36	C₇×#477	C₂²	1	8	yes	complemented
37	C₇×#476	C₂²	1	8	yes	—
38	C₇×#474	C₂²	1	16	yes	—
39	C₇×#446	C₂²	1	8	yes	complemented
40	C₇×#440	C₂²	1	16	yes	—
41	C₄×C₇×SD₁₆	C₂²	1	8	yes	—
42	C₂×C₇×#107	C₂²	1	2	yes	—
43	C₂×C₇×#107	C₂²	1	2	yes	—
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×#106	C₂²	1	1	yes	characteristic
46	C₂×C₇×#106	C₂²	1	2	yes	—
47	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
48	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#103	C₂²	1	1	yes	characteristic
50	C₂×C₇×#103	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3385	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂²×C₇×Q₈	—	2	1	no	—
57	C₂²×C₇×Q₈	—	2	1	no	—
58	C₂²×C₇×Q₈	—	2	2	no	—
59	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₇	—	2	1	no	—
63	C₂³×C₄×C₇	—	2	2	no	—
64	C₂×C₇×SD₁₆	Q₈	1	8	yes	complemented
65	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	2	yes	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₇×C₄⋊Q₈	—	2	8	no	—
70	C₇×C₄⋊Q₈	—	2	16	no	—
71	C₇×C₄⋊Q₈	—	2	2	no	—
72	C₇×C₄⋊Q₈	—	2	4	no	—
73	C₇×C₄⋊Q₈	—	2	2	no	—
74	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
75	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₇×#125	—	2	4	no	—
78	C₇×#125	C₂³	1	8	yes	—
79	C₇×C₂²⋊Q₈	—	2	8	no	—
80	C₇×C₂²⋊Q₈	—	2	16	no	—
81	C₄×C₇×Q₈	—	2	8	no	—
82	C₄×C₇×Q₈	—	2	4	no	—
83	C₄×C₇×Q₈	—	2	2	no	—
84	C₄×C₇×Q₈	D₄	1	4	yes	—
85	C₄×C₇×Q₈	C₂³	1	4	yes	—
86	C₄×C₇×Q₈	C₂³	1	8	yes	—
87	C₄×C₇×Q₈	C₂³	1	4	yes	—
88	C₄×C₇×D₄	—	2	4	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	C₂³	1	8	yes	—
91	C₄×C₇×D₄	C₂³	1	4	yes	—
92	C₂×C₇×C₄⋊C₄	—	2	2	no	—
93	C₂×C₇×C₄⋊C₄	—	2	1	no	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	—	2	1	no	—
96	C₂×C₇×C₄⋊C₄	—	2	1	no	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	2	no	—
99	C₂×C₇×C₄⋊C₄	—	2	8	no	—
100	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
101	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
102	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₄²×C₇	—	2	2	no	—
109	C₂×C₄²×C₇	—	2	1	no	—
110	C₂×C₄²×C₇	C₂³	1	2	yes	—
111	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
112	C₇×#107	C₂³	1	8	yes	—
113	C₇×#107	C₂³	1	8	yes	—
114	C₇×#107	C₂³	1	8	yes	—
115	C₇×#106	C₂³	1	8	yes	—
116	C₇×#106	C₂³	1	4	yes	—
117	C₇×C₄⋊C₈	C₂³	1	8	yes	—
118	C₇×C₄⋊C₈	C₂³	1	4	yes	—
119	C₇×#103	C₂³	1	8	yes	—
120	C₇×#103	C₂³	1	4	yes	—
121	C₇×#102	C₂³	1	4	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#97	C₂³	1	8	yes	—
124	C₄×C₇×C₈	C₂³	1	4	yes	—
125	C₂×Q₈²	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#554	C₂×C₇	1	1	yes	characteristic
127	#3385	C₂×C₇	1	16	yes	direct product factor
128	C₂×#501	C₂×C₇	1	2	yes	complemented
129	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#479	C₂×C₇	1	2	yes	complemented
131	C₂×#477	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#476	C₂×C₇	1	1	yes	characteristic
133	C₂×#474	C₂×C₇	1	2	yes	—
134	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#440	C₂×C₇	1	2	yes	—
136	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
137	C₂⁴×C₇	—	2	1	no	—
138	C₂×C₇×Q₈	—	2	4	no	—
139	C₂×C₇×Q₈	—	2	1	no	—
140	C₂×C₇×Q₈	—	2	4	no	—
141	C₂×C₇×Q₈	—	2	4	no	—
142	C₂×C₇×Q₈	—	2	8	no	—
143	C₂×C₇×Q₈	—	2	2	no	—
144	C₂×C₇×Q₈	—	8	4	no	—
145	C₂×C₇×Q₈	—	8	2	no	—
146	C₂×C₇×Q₈	—	8	2	no	—
147	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
148	C₂×C₇×Q₈	C₂×Q₈	1	4	yes	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	—	2	2	no	—
152	C₂×C₇×D₄	C₂×Q₈	1	4	yes	—
153	C₂×C₇×D₄	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₇	—	2	1	no	—
155	C₂²×C₄×C₇	—	2	2	no	—
156	C₂²×C₄×C₇	—	2	1	no	—
157	C₂²×C₄×C₇	—	2	1	no	—
158	C₂²×C₄×C₇	—	2	2	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	8	no	—
161	C₂²×C₄×C₇	—	4	4	no	—
162	C₂²×C₄×C₇	—	8	4	no	—
163	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
168	C₇×SD₁₆	C₂×Q₈	1	16	yes	complemented
169	C₂×C₇×C₈	—	2	2	no	—
170	C₂×C₇×C₈	—	2	4	no	—
171	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
172	C₂×C₇×C₈	C₂⁴	1	2	yes	—
173	C₂×C₇×C₈	C₂⁴	1	4	yes	—
174	C₂×C₇×C₈	C₂⁴	1	2	yes	—
175	C₇×C₄⋊C₄	—	2	8	no	—
176	C₇×C₄⋊C₄	—	2	4	no	—
177	C₇×C₄⋊C₄	—	2	8	no	—
178	C₇×C₄⋊C₄	—	2	4	no	—
179	C₇×C₄⋊C₄	—	2	4	no	—
180	C₇×C₄⋊C₄	—	2	8	no	—
181	C₇×C₄⋊C₄	—	2	8	no	—
182	C₇×C₄⋊C₄	—	2	1	no	—
183	C₇×C₄⋊C₄	—	2	2	no	—
184	C₇×C₄⋊C₄	—	2	1	no	—
185	C₇×C₄⋊C₄	—	2	2	no	—
186	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
187	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
188	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
189	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
191	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
192	C₇×C₂²⋊C₄	—	2	4	no	—
193	C₇×C₂²⋊C₄	—	2	8	no	—
194	C₄²×C₇	—	2	8	no	—
195	C₄²×C₇	—	2	4	no	—
196	C₄²×C₇	C₂×D₄	1	4	yes	—
197	C₄²×C₇	C₂×D₄	1	2	yes	—
198	C₄²×C₇	C₂⁴	1	2	yes	—
199	C₄²×C₇	C₂⁴	1	4	yes	—
200	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
201	Q₈²	—	2	4	no	—
202	Q₈²	C₂²×C₇	1	8	yes	complemented
203	#554	—	2	4	no	—
204	#554	C₂²×C₇	1	8	yes	—
205	C₂×C₄⋊Q₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	—	2	2	no	—
207	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
208	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
209	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
210	C₂×#125	C₂²×C₇	1	2	yes	—
211	C₂×C₂²⋊Q₈	—	2	1	no	—
212	C₂×C₂²⋊Q₈	—	2	2	no	—
213	C₂×C₄×Q₈	—	2	1	no	—
214	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
216	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
219	C₂²×C₄⋊C₄	—	2	1	no	—
220	#501	C₂²×C₇	1	16	yes	complemented
221	#500	C₂²×C₇	1	8	yes	complemented
222	#479	C₂²×C₇	1	16	yes	complemented
223	#477	C₂²×C₇	1	8	yes	complemented
224	#476	C₂²×C₇	1	8	yes	—
225	#474	C₂²×C₇	1	16	yes	—
226	#446	C₂²×C₇	1	8	yes	complemented
227	#440	C₂²×C₇	1	16	yes	—
228	C₄×SD₁₆	C₂²×C₇	1	8	yes	—
229	C₂×#107	C₂²×C₇	1	2	yes	—
230	C₂×#107	C₂²×C₇	1	2	yes	—
231	C₂×#107	C₂²×C₇	1	2	yes	—
232	C₂×#106	C₂²×C₇	1	2	yes	—
233	C₂×#106	C₂²×C₇	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
236	C₂×#103	C₂²×C₇	1	2	yes	—
237	C₂×#103	C₂²×C₇	1	1	yes	characteristic
238	C₂×#102	C₂²×C₇	1	1	yes	characteristic
239	C₂×#102	C₂²×C₇	1	2	yes	—
240	C₂×#97	C₂²×C₇	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
242	C₂³×C₇	—	2	4	no	—
243	C₂³×C₇	—	2	2	no	—
244	C₂³×C₇	—	4	2	no	—
245	C₂³×C₇	—	4	2	no	—
246	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₇×Q₈	—	2	4	no	—
248	C₇×Q₈	—	2	8	no	—
249	C₇×Q₈	—	2	2	no	—
250	C₇×Q₈	—	8	8	no	—
251	C₇×Q₈	—	8	4	no	—
252	C₇×Q₈	—	8	4	no	—
253	C₇×Q₈	C₂²×Q₈	1	4	yes	—
254	C₇×D₄	—	2	4	no	—
255	C₇×D₄	—	2	2	no	—
256	C₇×D₄	C₂²×Q₈	1	4	yes	—
257	C₂×C₄×C₇	—	2	4	no	—
258	C₂×C₄×C₇	—	2	4	no	—
259	C₂×C₄×C₇	—	2	4	no	—
260	C₂×C₄×C₇	—	2	2	no	—
261	C₂×C₄×C₇	—	2	2	no	—
262	C₂×C₄×C₇	—	2	4	no	—
263	C₂×C₄×C₇	—	2	2	no	—
264	C₂×C₄×C₇	—	2	2	no	—
265	C₂×C₄×C₇	—	2	4	no	—
266	C₂×C₄×C₇	—	4	2	no	—
267	C₂×C₄×C₇	—	4	4	no	—
268	C₂×C₄×C₇	—	4	2	no	—
269	C₂×C₄×C₇	—	4	4	no	—
270	C₂×C₄×C₇	—	4	8	no	—
271	C₂×C₄×C₇	—	8	8	no	—
272	C₂×C₄×C₇	#137	1	4	yes	—
273	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
279	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
280	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
281	C₇×C₈	—	2	2	no	—
282	C₇×C₈	—	2	4	no	—
283	C₇×C₈	C₂²×Q₈	1	4	yes	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
289	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	2	2	no	—
292	C₂×SD₁₆	C₇×Q₈	1	8	yes	complemented
293	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
294	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₇	1	2	yes	—
296	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	8	no	—
298	C₄⋊Q₈	—	2	16	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	4	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
303	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
304	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
305	#125	—	2	4	no	—
306	#125	C₂³×C₇	1	8	yes	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	—	2	16	no	—
309	C₄×Q₈	—	2	8	no	—
310	C₄×Q₈	—	2	4	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	C₇×D₄	1	4	yes	—
313	C₄×Q₈	C₂³×C₇	1	4	yes	—
314	C₄×Q₈	C₂³×C₇	1	8	yes	—
315	C₄×Q₈	C₂³×C₇	1	4	yes	—
316	C₄×D₄	—	2	4	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	C₂³×C₇	1	4	yes	—
319	C₄×D₄	C₂³×C₇	1	8	yes	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	8	no	—
328	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	—	2	2	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₇	1	2	yes	—
339	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
340	#107	C₂³×C₇	1	8	yes	—
341	#107	C₂³×C₇	1	8	yes	—
342	#107	C₂³×C₇	1	8	yes	—
343	#106	C₂³×C₇	1	4	yes	—
344	#106	C₂³×C₇	1	8	yes	—
345	C₄⋊C₈	C₂³×C₇	1	8	yes	—
346	C₄⋊C₈	C₂³×C₇	1	4	yes	—
347	#103	C₂³×C₇	1	4	yes	—
348	#103	C₂³×C₇	1	8	yes	—
349	#102	C₂³×C₇	1	4	yes	—
350	#102	C₂³×C₇	1	8	yes	—
351	#97	C₂³×C₇	1	8	yes	—
352	C₄×C₈	C₂³×C₇	1	4	yes	—
353	C₂²×C₇	—	2	4	no	—
354	C₂²×C₇	—	4	8	no	—
355	C₂²×C₇	—	4	2	no	—
356	C₂²×C₇	—	4	2	no	—
357	C₂²×C₇	D₄×Q₈	1	2	yes	—
358	C₂²×C₇	C₂×#137	1	2	yes	—
359	C₂²×C₇	#576	1	2	yes	—
360	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₇	—	2	4	no	—
362	C₄×C₇	—	2	4	no	—
363	C₄×C₇	—	2	4	no	—
364	C₄×C₇	—	2	2	no	—
365	C₄×C₇	—	4	2	no	—
366	C₄×C₇	—	4	4	no	—
367	C₄×C₇	—	4	2	no	—
368	C₄×C₇	—	4	4	no	—
369	C₄×C₇	D₄×Q₈	1	2	yes	—
370	C₄×C₇	C₂×#137	1	4	yes	—
371	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
372	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
373	C₂⁴	—	2	1	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	8	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	8	4	no	—
381	C₂×Q₈	—	8	2	no	—
382	C₂×Q₈	—	8	2	no	—
383	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
384	C₂×Q₈	C₂×C₇×Q₈	1	4	yes	—
385	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	C₂×C₇×Q₈	1	4	yes	—
389	C₂×D₄	C₂⁴×C₇	1	2	yes	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	—	8	4	no	—
399	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
400	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
401	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
402	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
404	SD₁₆	C₂×C₇×Q₈	1	16	yes	complemented
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	4	no	—
407	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
408	C₂×C₈	C₂⁴×C₇	1	2	yes	—
409	C₂×C₈	C₂⁴×C₇	1	4	yes	—
410	C₂×C₈	C₂⁴×C₇	1	2	yes	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
423	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
424	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
425	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
426	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
427	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₄²	—	2	8	no	—
431	C₄²	—	2	4	no	—
432	C₄²	C₂×C₇×D₄	1	4	yes	—
433	C₄²	C₂×C₇×D₄	1	2	yes	—
434	C₄²	C₂⁴×C₇	1	2	yes	—
435	C₄²	C₂⁴×C₇	1	4	yes	—
436	C₂×C₇	—	4	4	no	—
437	C₂×C₇	#3385	1	4	yes	direct product factor
438	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
439	C₂×C₇	C₂²×#137	1	1	yes	characteristic
440	C₂×C₇	C₂×#576	1	1	yes	characteristic
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	8	8	no	—
450	Q₈	—	8	4	no	—
451	Q₈	—	8	4	no	—
452	Q₈	C₂²×C₇×Q₈	1	4	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	4	no	—
455	D₄	C₂²×C₇×Q₈	1	4	yes	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	4	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	8	no	—
470	C₂×C₄	—	8	8	no	—
471	C₂×C₄	C₇×#137	1	4	yes	—
472	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
473	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
474	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
475	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
477	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
478	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
479	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	4	no	—
482	C₈	C₂²×C₇×Q₈	1	4	yes	—
483	C₇	C₂×#3385	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²	—	2	4	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	8	no	—
488	C₂²	C₇×D₄×Q₈	1	2	yes	—
489	C₂²	C₂×C₇×#137	1	2	yes	—
490	C₂²	C₇×#576	1	2	yes	—
491	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
492	C₄	—	2	4	no	—
493	C₄	—	2	4	no	—
494	C₄	—	2	2	no	—
495	C₄	—	2	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	4	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	4	no	—
500	C₄	C₇×D₄×Q₈	1	2	yes	—
501	C₄	C₂×C₇×#137	1	4	yes	—
502	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
503	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
504	C₂	—	4	4	no	—
505	C₂	C₇×#3385	1	4	yes	direct product factor
506	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
507	C₂	C₂²×C₇×#137	1	1	yes	characteristic
508	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×D₄	C₂³
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×Q₈²	C₂	semidirect
3. C₇×#3385	C₂	direct (N × H)
4. C₂×C₇×#501	C₂	semidirect
5. C₂×C₇×#500	C₂	semidirect
6. C₂×C₇×#479	C₂	semidirect
7. C₂×C₇×#477	C₂	semidirect
10. C₂×C₇×#446	C₂	semidirect
15. C₇×Q₈²	C₂²	semidirect
33. C₇×#501	C₂²	semidirect
34. C₇×#500	C₂²	semidirect
35. C₇×#479	C₂²	semidirect
36. C₇×#477	C₂²	semidirect
39. C₇×#446	C₂²	semidirect
55. C₂×#3385	C₇	direct (N × H)
64. C₂×C₇×SD₁₆	Q₈	semidirect
125. C₂×Q₈²	C₂×C₇	semidirect
127. #3385	C₂×C₇	direct (N × H)
128. C₂×#501	C₂×C₇	semidirect
129. C₂×#500	C₂×C₇	semidirect
130. C₂×#479	C₂×C₇	semidirect
131. C₂×#477	C₂×C₇	semidirect
134. C₂×#446	C₂×C₇	semidirect
168. C₇×SD₁₆	C₂×Q₈	semidirect
202. Q₈²	C₂²×C₇	semidirect
220. #501	C₂²×C₇	semidirect
221. #500	C₂²×C₇	semidirect
222. #479	C₂²×C₇	semidirect
223. #477	C₂²×C₇	semidirect
226. #446	C₂²×C₇	semidirect
292. C₂×SD₁₆	C₇×Q₈	semidirect
404. SD₁₆	C₂×C₇×Q₈	semidirect
437. C₂×C₇	#3385	direct (N × H)
483. C₇	C₂×#3385	direct (N × H)
505. C₂	C₇×#3385	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×Q₈²	2
C₂×C₇×#554	2
C₇×#3385	2
C₂×C₇×#501	2
C₂×C₇×#500	2
C₂×C₇×#479	2
C₂×C₇×#477	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#446	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×#3385	7

Subgroups — C2×C7×#3385 #13238575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3385 #13238575