Subgroups — C₂×C₇×#3285 #13238261

Order 1792.

2794 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#548	C₂	1	2	yes	maximal, complemented
4	C₇×#3285	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#452	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#448	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₂³×C₇×Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#135	—	2	8	no	—
16	C₂×C₇×#135	C₂²	1	8	yes	complemented
17	C₂²×C₇×Q₁₆	—	2	8	no	—
18	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×Q₁₆	C₂²	1	8	yes	complemented
22	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
23	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
24	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
25	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
26	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₇×#548	—	2	8	no	—
28	C₇×#548	C₂²	1	16	yes	complemented
29	C₂×C₇×#124	—	2	2	no	—
30	C₂×C₇×#124	C₂²	1	2	yes	—
31	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₇×#121	—	2	2	no	—
34	C₂×C₇×#121	C₂²	1	2	yes	—
35	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
36	C₂×C₄×C₇×D₄	—	2	2	no	—
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
38	C₇×#495	C₂²	1	8	yes	complemented
39	C₇×#467	C₂²	1	8	yes	complemented
40	C₇×#466	C₂²	1	8	yes	complemented
41	C₇×#464	C₂²	1	16	yes	complemented
42	C₇×#452	C₂²	1	16	yes	complemented
43	C₇×#448	C₂²	1	16	yes	complemented
44	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
45	C₇×C₈×D₄	C₂²	1	8	yes	complemented
46	C₂×C₇×#107	C₂²	1	1	yes	characteristic
47	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₇×#103	C₂²	1	2	yes	—
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	2	yes	—
51	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
54	C₂×#3285	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₇×#41	—	2	4	no	—
56	C₂×C₇×#41	—	2	8	no	—
57	C₂×C₇×#41	—	4	4	no	—
58	C₂×C₇×#41	C₂³	1	8	yes	—
59	C₂²×C₇×Q₈	—	2	2	no	—
60	C₂²×C₇×Q₈	—	2	4	no	—
61	C₂²×C₇×Q₈	—	2	8	no	—
62	C₂²×C₇×Q₈	—	4	4	no	—
63	C₂²×C₇×Q₈	C₂³	1	2	yes	—
64	C₂²×C₇×Q₈	C₂³	1	8	yes	—
65	C₂²×C₇×Q₈	C₂³	1	2	yes	—
66	C₂²×C₇×D₄	—	2	2	no	—
67	C₂²×C₇×D₄	—	2	2	no	—
68	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
69	C₂²×C₇×D₄	C₂³	1	2	yes	—
70	C₂³×C₄×C₇	—	2	2	no	—
71	C₂³×C₄×C₇	—	2	2	no	—
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
74	C₇×#135	—	2	32	no	—
75	C₂×C₇×Q₁₆	—	2	8	no	—
76	C₂×C₇×Q₁₆	—	2	32	no	—
77	C₂×C₇×Q₁₆	—	2	4	no	—
78	C₂×C₇×Q₁₆	D₄	1	8	yes	complemented
79	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
80	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
81	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
82	C₂×C₇×SD₁₆	—	2	8	no	—
83	C₂×C₇×SD₁₆	—	4	4	no	—
84	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
86	C₂×C₇×D₈	—	2	4	no	—
87	C₂×C₇×D₈	C₂³	1	4	yes	—
88	C₂²×C₇×C₈	—	2	4	no	—
89	C₂²×C₇×C₈	—	2	4	no	—
90	C₂²×C₇×C₈	C₂³	1	4	yes	—
91	C₂²×C₇×C₈	C₂³	1	4	yes	—
92	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
95	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
96	C₇×#124	—	2	16	no	—
97	C₇×#124	—	2	4	no	—
98	C₇×#124	C₂³	1	8	yes	—
99	C₇×C₂²⋊Q₈	—	2	4	no	—
100	C₇×C₂²⋊Q₈	—	2	16	no	—
101	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
102	C₇×#121	—	2	16	no	—
103	C₇×#121	—	2	4	no	—
104	C₇×#121	C₂³	1	8	yes	—
105	C₄×C₇×Q₈	—	2	4	no	—
106	C₄×C₇×Q₈	C₂³	1	8	yes	—
107	C₄×C₇×D₄	—	2	16	no	—
108	C₄×C₇×D₄	D₄	1	4	yes	—
109	C₄×C₇×D₄	C₂³	1	4	yes	—
110	C₂×C₇×C₄⋊C₄	—	2	2	no	—
111	C₂×C₇×C₄⋊C₄	—	2	2	no	—
112	C₂×C₇×C₄⋊C₄	D₄	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	2	no	—
116	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
117	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₇	—	2	2	no	—
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×#107	C₂³	1	4	yes	—
123	C₇×C₄⋊C₈	C₂³	1	4	yes	—
124	C₇×#103	C₂³	1	8	yes	—
125	C₇×#103	C₂³	1	8	yes	—
126	C₇×#102	C₂³	1	8	yes	—
127	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
128	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
129	C₄×C₇×C₈	C₂³	1	4	yes	—
130	C₂²×#135	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂³×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#548	C₂×C₇	1	2	yes	complemented
133	#3285	C₂×C₇	1	16	yes	direct product factor
134	C₂×#495	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#464	C₂×C₇	1	2	yes	complemented
138	C₂×#452	C₂×C₇	1	2	yes	complemented
139	C₂×#448	C₂×C₇	1	2	yes	complemented
140	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
142	C₂⁴×C₇	—	2	2	no	—
143	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
145	C₇×#41	—	2	16	no	—
146	C₇×#41	—	4	8	no	—
147	C₇×#41	—	4	16	no	—
148	C₂×C₇×Q₈	—	2	2	no	—
149	C₂×C₇×Q₈	—	2	8	no	—
150	C₂×C₇×Q₈	—	2	2	no	—
151	C₂×C₇×Q₈	—	2	4	no	—
152	C₂×C₇×Q₈	—	2	16	no	—
153	C₂×C₇×Q₈	—	2	4	no	—
154	C₂×C₇×Q₈	—	2	4	no	—
155	C₂×C₇×Q₈	—	4	8	no	—
156	C₂×C₇×Q₈	—	4	8	no	—
157	C₂×C₇×Q₈	—	4	16	no	—
158	C₂×C₇×Q₈	C₂×D₄	1	8	yes	—
159	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
160	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	8	no	—
163	C₂×C₇×D₄	—	2	8	no	—
164	C₂×C₇×D₄	—	2	4	no	—
165	C₂×C₇×D₄	—	2	2	no	—
166	C₂×C₇×D₄	—	2	4	no	—
167	C₂×C₇×D₄	—	4	8	no	—
168	C₂×C₇×D₄	—	4	8	no	—
169	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
170	C₂×C₇×D₄	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₇	—	2	2	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	2	no	—
174	C₂²×C₄×C₇	—	2	2	no	—
175	C₂²×C₄×C₇	—	2	2	no	—
176	C₂²×C₄×C₇	—	2	8	no	—
177	C₂²×C₄×C₇	—	2	2	no	—
178	C₂²×C₄×C₇	—	2	2	no	—
179	C₂²×C₄×C₇	—	2	8	no	—
180	C₂²×C₄×C₇	—	4	8	no	—
181	C₂²×C₄×C₇	—	4	8	no	—
182	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
191	C₇×Q₁₆	—	2	16	no	—
192	C₇×Q₁₆	—	2	8	no	—
193	C₇×Q₁₆	C₂×D₄	1	16	yes	complemented
194	C₇×SD₁₆	—	2	16	no	—
195	C₇×SD₁₆	—	4	8	no	—
196	C₇×D₈	—	2	8	no	—
197	C₂×C₇×C₈	—	2	2	no	—
198	C₂×C₇×C₈	—	2	2	no	—
199	C₂×C₇×C₈	—	2	2	no	—
200	C₂×C₇×C₈	—	2	8	no	—
201	C₂×C₇×C₈	—	2	8	no	—
202	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
203	C₂×C₇×C₈	C₂⁴	1	2	yes	—
204	C₂×C₇×C₈	C₂⁴	1	2	yes	—
205	C₂×C₇×C₈	C₂⁴	1	2	yes	—
206	C₂×C₇×C₈	C₂⁴	1	2	yes	—
207	C₇×C₄⋊C₄	—	2	8	no	—
208	C₇×C₄⋊C₄	—	2	8	no	—
209	C₇×C₄⋊C₄	—	2	2	no	—
210	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
211	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
212	C₇×C₂²⋊C₄	—	2	8	no	—
213	C₇×C₂²⋊C₄	—	2	8	no	—
214	C₇×C₂²⋊C₄	—	2	8	no	—
215	C₇×C₂²⋊C₄	—	2	8	no	—
216	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
217	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
218	C₄²×C₇	—	2	8	no	—
219	C₄²×C₇	C₂×D₄	1	2	yes	—
220	C₄²×C₇	C₂⁴	1	2	yes	—
221	C₂²×#41	C₂²×C₇	1	2	yes	—
222	C₂³×Q₈	C₂²×C₇	1	2	yes	—
223	C₂×#135	—	2	8	no	—
224	C₂×#135	C₂²×C₇	1	8	yes	complemented
225	C₂²×Q₁₆	—	2	8	no	—
226	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
227	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
228	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
229	C₂²×Q₁₆	C₂²×C₇	1	8	yes	complemented
230	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
231	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
232	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
235	#548	—	2	8	no	—
236	#548	C₂²×C₇	1	16	yes	complemented
237	C₂×#124	—	2	2	no	—
238	C₂×#124	C₂²×C₇	1	2	yes	—
239	C₂×C₂²⋊Q₈	—	2	2	no	—
240	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
241	C₂×#121	—	2	2	no	—
242	C₂×#121	C₂²×C₇	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
244	C₂×C₄×D₄	—	2	2	no	—
245	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
246	#495	C₂²×C₇	1	8	yes	complemented
247	#467	C₂²×C₇	1	8	yes	complemented
248	#466	C₂²×C₇	1	8	yes	complemented
249	#464	C₂²×C₇	1	16	yes	complemented
250	#452	C₂²×C₇	1	16	yes	complemented
251	#448	C₂²×C₇	1	16	yes	complemented
252	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
253	C₈×D₄	C₂²×C₇	1	8	yes	complemented
254	C₂×#107	C₂²×C₇	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂×#103	C₂²×C₇	1	2	yes	—
257	C₂×#103	C₂²×C₇	1	2	yes	—
258	C₂×#102	C₂²×C₇	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
262	C₂³×C₇	—	2	2	no	—
263	C₂³×C₇	—	2	2	no	—
264	C₂³×C₇	—	2	2	no	—
265	C₂³×C₇	—	2	2	no	—
266	C₂³×C₇	—	2	2	no	—
267	C₂³×C₇	—	2	4	no	—
268	C₂³×C₇	—	4	4	no	—
269	C₂³×C₇	—	4	4	no	—
270	C₂³×C₇	—	4	4	no	—
271	C₂³×C₇	#135	1	4	yes	complemented
272	C₂³×C₇	C₂²×D₄	1	2	yes	—
273	C₂³×C₇	C₂²×D₄	1	2	yes	—
274	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
275	C₇×Q₈	—	2	8	no	—
276	C₇×Q₈	—	2	4	no	—
277	C₇×Q₈	—	2	4	no	—
278	C₇×Q₈	—	2	4	no	—
279	C₇×Q₈	—	4	16	no	—
280	C₇×Q₈	—	4	4	no	—
281	C₇×Q₈	C₂²×D₄	1	8	yes	—
282	C₇×D₄	—	2	8	no	—
283	C₇×D₄	—	2	4	no	—
284	C₇×D₄	—	2	4	no	—
285	C₇×D₄	—	4	16	no	—
286	C₇×D₄	—	4	16	no	—
287	C₇×D₄	—	4	4	no	—
288	C₂×C₄×C₇	—	2	2	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	8	no	—
291	C₂×C₄×C₇	—	2	2	no	—
292	C₂×C₄×C₇	—	2	2	no	—
293	C₂×C₄×C₇	—	2	4	no	—
294	C₂×C₄×C₇	—	2	4	no	—
295	C₂×C₄×C₇	—	2	4	no	—
296	C₂×C₄×C₇	—	2	2	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	4	no	—
301	C₂×C₄×C₇	—	2	4	no	—
302	C₂×C₄×C₇	—	4	16	no	—
303	C₂×C₄×C₇	—	4	16	no	—
304	C₂×C₄×C₇	—	4	4	no	—
305	C₂×C₄×C₇	—	4	4	no	—
306	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
307	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
308	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
312	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
313	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
314	C₇×C₈	—	2	2	no	—
315	C₇×C₈	—	2	2	no	—
316	C₇×C₈	—	2	2	no	—
317	C₇×C₈	C₂²×D₄	1	4	yes	—
318	C₂×#41	—	2	4	no	—
319	C₂×#41	—	2	8	no	—
320	C₂×#41	—	4	4	no	—
321	C₂×#41	C₂³×C₇	1	8	yes	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	4	no	—
324	C₂²×Q₈	—	2	8	no	—
325	C₂²×Q₈	—	4	4	no	—
326	C₂²×Q₈	C₂³×C₇	1	2	yes	—
327	C₂²×Q₈	C₂³×C₇	1	8	yes	—
328	C₂²×Q₈	C₂³×C₇	1	2	yes	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
332	C₂²×D₄	C₂³×C₇	1	2	yes	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
337	#135	—	2	32	no	—
338	C₂×Q₁₆	—	2	8	no	—
339	C₂×Q₁₆	—	2	32	no	—
340	C₂×Q₁₆	—	2	4	no	—
341	C₂×Q₁₆	C₇×D₄	1	8	yes	complemented
342	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
343	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
344	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
345	C₂×SD₁₆	—	2	8	no	—
346	C₂×SD₁₆	—	4	4	no	—
347	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
348	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
349	C₂×D₈	—	2	4	no	—
350	C₂×D₈	C₂³×C₇	1	4	yes	—
351	C₂²×C₈	—	2	4	no	—
352	C₂²×C₈	—	2	4	no	—
353	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₇	1	4	yes	—
356	C₂²×C₈	C₂³×C₇	1	4	yes	—
357	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
359	#124	—	2	16	no	—
360	#124	—	2	4	no	—
361	#124	C₂³×C₇	1	8	yes	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	16	no	—
364	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
365	#121	—	2	16	no	—
366	#121	—	2	4	no	—
367	#121	C₂³×C₇	1	8	yes	—
368	C₄×Q₈	—	2	4	no	—
369	C₄×Q₈	C₂³×C₇	1	8	yes	—
370	C₄×D₄	—	2	16	no	—
371	C₄×D₄	C₇×D₄	1	4	yes	—
372	C₄×D₄	C₂³×C₇	1	4	yes	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₄⋊C₄	—	2	2	no	—
375	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
383	C₂×C₄²	—	2	2	no	—
384	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
385	#107	C₂³×C₇	1	4	yes	—
386	C₄⋊C₈	C₂³×C₇	1	4	yes	—
387	#103	C₂³×C₇	1	8	yes	—
388	#103	C₂³×C₇	1	8	yes	—
389	#102	C₂³×C₇	1	8	yes	—
390	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
391	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
392	C₄×C₈	C₂³×C₇	1	4	yes	—
393	C₂²×C₇	—	2	2	no	—
394	C₂²×C₇	—	2	8	no	—
395	C₂²×C₇	—	2	2	no	—
396	C₂²×C₇	—	2	2	no	—
397	C₂²×C₇	—	2	2	no	—
398	C₂²×C₇	—	2	2	no	—
399	C₂²×C₇	—	4	4	no	—
400	C₂²×C₇	—	4	4	no	—
401	C₂²×C₇	—	4	4	no	—
402	C₂²×C₇	—	4	4	no	—
403	C₂²×C₇	—	8	8	no	—
404	C₂²×C₇	D₄²	1	2	yes	—
405	C₂²×C₇	C₂×#135	1	2	yes	—
406	C₂²×C₇	C₂×#135	1	4	yes	complemented
407	C₂²×C₇	#578	1	2	yes	—
408	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
409	C₄×C₇	—	2	2	no	—
410	C₄×C₇	—	2	2	no	—
411	C₄×C₇	—	2	8	no	—
412	C₄×C₇	—	2	2	no	—
413	C₄×C₇	—	2	2	no	—
414	C₄×C₇	—	4	4	no	—
415	C₄×C₇	—	4	4	no	—
416	C₄×C₇	D₄²	1	2	yes	—
417	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂⁴	—	2	2	no	—
420	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
421	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
422	#41	—	2	16	no	—
423	#41	—	4	8	no	—
424	#41	—	4	16	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	2	8	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	16	no	—
430	C₂×Q₈	—	2	4	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	4	8	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×Q₈	—	4	16	no	—
435	C₂×Q₈	C₂×C₇×D₄	1	8	yes	—
436	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
437	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	4	8	no	—
445	C₂×D₄	—	4	8	no	—
446	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
447	C₂×D₄	C₂⁴×C₇	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	8	no	—
456	C₂²×C₄	—	2	8	no	—
457	C₂²×C₄	—	4	8	no	—
458	C₂²×C₄	—	4	8	no	—
459	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
464	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
468	Q₁₆	—	2	16	no	—
469	Q₁₆	—	2	8	no	—
470	Q₁₆	C₂×C₇×D₄	1	16	yes	complemented
471	SD₁₆	—	2	16	no	—
472	SD₁₆	—	4	8	no	—
473	D₈	—	2	8	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	8	no	—
478	C₂×C₈	—	2	8	no	—
479	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
480	C₂×C₈	C₂⁴×C₇	1	2	yes	—
481	C₂×C₈	C₂⁴×C₇	1	2	yes	—
482	C₂×C₈	C₂⁴×C₇	1	2	yes	—
483	C₂×C₈	C₂⁴×C₇	1	2	yes	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
488	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
494	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
495	C₄²	—	2	8	no	—
496	C₄²	C₂×C₇×D₄	1	2	yes	—
497	C₄²	C₂⁴×C₇	1	2	yes	—
498	C₂×C₇	—	2	4	no	—
499	C₂×C₇	—	4	2	no	—
500	C₂×C₇	—	8	4	no	—
501	C₂×C₇	#3285	1	4	yes	direct product factor
502	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
503	C₂×C₇	C₂²×#135	1	1	yes	characteristic
504	C₂×C₇	C₂×#578	1	1	yes	characteristic
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	4	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	4	no	—
513	C₂³	—	4	4	no	—
514	C₂³	C₇×#135	1	4	yes	complemented
515	C₂³	C₂²×C₇×D₄	1	2	yes	—
516	C₂³	C₂²×C₇×D₄	1	2	yes	—
517	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
518	Q₈	—	2	4	no	—
519	Q₈	—	2	8	no	—
520	Q₈	—	2	4	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	4	16	no	—
523	Q₈	—	4	4	no	—
524	Q₈	C₂²×C₇×D₄	1	8	yes	—
525	D₄	—	2	8	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	4	no	—
528	D₄	—	4	16	no	—
529	D₄	—	4	16	no	—
530	D₄	—	4	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	8	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	16	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
550	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
551	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
552	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
553	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
554	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
555	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
556	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	C₂²×C₇×D₄	1	4	yes	—
561	C₇	C₂×#3285	1	1	yes	characteristic, direct product factor, Sylow
562	C₂²	—	2	2	no	—
563	C₂²	—	2	8	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	8	8	no	—
573	C₂²	C₇×D₄²	1	2	yes	—
574	C₂²	C₂×C₇×#135	1	2	yes	—
575	C₂²	C₂×C₇×#135	1	4	yes	complemented
576	C₂²	C₇×#578	1	2	yes	—
577	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	4	no	—
585	C₄	C₇×D₄²	1	2	yes	—
586	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
587	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂	—	2	4	no	—
589	C₂	—	4	2	no	—
590	C₂	—	8	4	no	—
591	C₂	C₇×#3285	1	4	yes	direct product factor
592	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
593	C₂	C₂²×C₇×#135	1	1	yes	characteristic
594	C₂	C₂×C₇×#578	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 ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×#135	C₂	semidirect
2. C₂³×C₇×Q₁₆	C₂	semidirect
3. C₂×C₇×#548	C₂	semidirect
4. C₇×#3285	C₂	direct (N × H)
5. C₂×C₇×#495	C₂	semidirect
6. C₂×C₇×#467	C₂	semidirect
7. C₂×C₇×#466	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#452	C₂	semidirect
10. C₂×C₇×#448	C₂	semidirect
11. C₂×C₄×C₇×Q₁₆	C₂	semidirect
12. C₂×C₇×C₈×D₄	C₂	semidirect
16. C₂×C₇×#135	C₂²	semidirect
21. C₂²×C₇×Q₁₆	C₂²	semidirect
28. C₇×#548	C₂²	semidirect
38. C₇×#495	C₂²	semidirect
39. C₇×#467	C₂²	semidirect
40. C₇×#466	C₂²	semidirect
41. C₇×#464	C₂²	semidirect
42. C₇×#452	C₂²	semidirect
43. C₇×#448	C₂²	semidirect
44. C₄×C₇×Q₁₆	C₂²	semidirect
45. C₇×C₈×D₄	C₂²	semidirect
54. C₂×#3285	C₇	direct (N × H)
78. C₂×C₇×Q₁₆	D₄	semidirect
130. C₂²×#135	C₂×C₇	semidirect
131. C₂³×Q₁₆	C₂×C₇	semidirect
132. C₂×#548	C₂×C₇	semidirect
133. #3285	C₂×C₇	direct (N × H)
134. C₂×#495	C₂×C₇	semidirect
135. C₂×#467	C₂×C₇	semidirect
136. C₂×#466	C₂×C₇	semidirect
137. C₂×#464	C₂×C₇	semidirect
138. C₂×#452	C₂×C₇	semidirect
139. C₂×#448	C₂×C₇	semidirect
140. C₂×C₄×Q₁₆	C₂×C₇	semidirect
141. C₂×C₈×D₄	C₂×C₇	semidirect
193. C₇×Q₁₆	C₂×D₄	semidirect
224. C₂×#135	C₂²×C₇	semidirect
229. C₂²×Q₁₆	C₂²×C₇	semidirect
236. #548	C₂²×C₇	semidirect
246. #495	C₂²×C₇	semidirect
247. #467	C₂²×C₇	semidirect
248. #466	C₂²×C₇	semidirect
249. #464	C₂²×C₇	semidirect
250. #452	C₂²×C₇	semidirect
251. #448	C₂²×C₇	semidirect
252. C₄×Q₁₆	C₂²×C₇	semidirect
253. C₈×D₄	C₂²×C₇	semidirect
271. C₂³×C₇	#135	semidirect
341. C₂×Q₁₆	C₇×D₄	semidirect
406. C₂²×C₇	C₂×#135	semidirect
470. Q₁₆	C₂×C₇×D₄	semidirect
501. C₂×C₇	#3285	direct (N × H)
514. C₂³	C₇×#135	semidirect
561. C₇	C₂×#3285	direct (N × H)
575. C₂²	C₂×C₇×#135	semidirect
591. C₂	C₇×#3285	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×#135	2
C₂³×C₇×Q₁₆	2
C₂×C₇×#548	2
C₇×#3285	2
C₂×C₇×#495	2
C₂×C₇×#467	2
C₂×C₇×#466	2
C₂×C₇×#464	2
C₂×C₇×#452	2
C₂×C₇×#448	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×C₈×D₄	2
C₂×#3285	7

Subgroups — C2×C7×#3285 #13238261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3285 #13238261