Subgroups — C₂×C₇×#3303 #13238337

Order 1792.

2210 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3303	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#485	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#449	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#416	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
16	C₂³×C₇×C₈	C₂²	1	2	yes	—
17	C₇×#555	—	2	4	no	—
18	C₇×#555	C₂²	1	8	yes	complemented
19	C₇×#547	—	2	4	no	—
20	C₇×#547	C₂²	1	8	yes	complemented
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×#124	—	2	2	no	—
24	C₂×C₇×#123	—	2	2	no	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₇×#121	—	2	1	no	—
27	C₂×C₇×#121	—	2	1	no	—
28	C₂×C₇×#121	C₂²	1	2	yes	—
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₇×#117	—	2	1	no	—
33	C₂×C₇×#117	C₂²	1	2	yes	—
34	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
35	C₇×#487	C₂²	1	8	yes	complemented
36	C₇×#485	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#465	C₂²	1	16	yes	complemented
39	C₇×#461	C₂²	1	8	yes	complemented
40	C₇×#449	C₂²	1	16	yes	complemented
41	C₄×C₇×D₈	C₂²	1	8	yes	complemented
42	C₇×C₈×D₄	C₂²	1	8	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#106	C₂²	1	2	yes	—
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₇×#416	C₂²	1	16	yes	complemented
47	C₂×C₇×#103	C₂²	1	2	yes	—
48	C₂×C₇×#103	C₂²	1	2	yes	—
49	C₂×C₇×#103	C₂²	1	2	yes	—
50	C₂×C₇×#102	C₂²	1	1	yes	characteristic
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3303	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	4	no	—
57	C₂×C₇×#41	—	2	8	no	—
58	C₂×C₇×#41	—	4	4	no	—
59	C₂×C₇×#41	C₂³	1	8	yes	—
60	C₂²×C₇×Q₈	—	2	1	no	—
61	C₂²×C₇×Q₈	C₂³	1	2	yes	—
62	C₂²×C₇×D₄	—	2	2	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
65	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	2	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	C₂³	1	2	yes	—
71	C₂×C₇×SD₁₆	—	4	4	no	—
72	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₇×D₈	—	2	4	no	—
74	C₂×C₇×D₈	C₂³	1	4	yes	—
75	C₂²×C₇×C₈	—	4	4	no	—
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂³	1	2	yes	—
79	C₂²×C₇×C₈	C₂³	1	8	yes	—
80	C₇×C₄⋊Q₈	—	2	2	no	—
81	C₇×C₄⋊Q₈	—	2	2	no	—
82	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
84	C₇×#124	—	2	16	no	—
85	C₇×#123	—	2	16	no	—
86	C₇×C₂²⋊Q₈	—	2	4	no	—
87	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₇×#121	—	2	8	no	—
89	C₇×#121	—	2	8	no	—
90	C₇×#121	—	2	4	no	—
91	C₇×#121	C₂³	1	8	yes	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	—	2	2	no	—
94	C₄×C₇×D₄	D₄	1	4	yes	—
95	C₄×C₇×D₄	C₂³	1	4	yes	—
96	C₄×C₇×D₄	C₂³	1	4	yes	—
97	C₄×C₇×D₄	C₂³	1	4	yes	—
98	C₇×#117	—	2	4	no	—
99	C₇×#117	—	2	8	no	—
100	C₇×#117	C₂³	1	8	yes	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	—	2	1	no	—
104	C₂×C₇×C₄⋊C₄	—	2	1	no	—
105	C₂×C₇×C₄⋊C₄	—	2	8	no	—
106	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	1	no	—
115	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
116	C₂×C₄²×C₇	—	2	2	no	—
117	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
118	C₇×#107	C₂³	1	4	yes	—
119	C₇×#106	C₂³	1	8	yes	—
120	C₇×C₄⋊C₈	C₂³	1	4	yes	—
121	C₇×#103	C₂³	1	8	yes	—
122	C₇×#103	C₂³	1	8	yes	—
123	C₇×#103	C₂³	1	8	yes	—
124	C₇×#102	C₂³	1	8	yes	—
125	C₇×#102	C₂³	1	4	yes	—
126	C₇×#102	C₂³	1	4	yes	—
127	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
128	C₄×C₇×C₈	C₂³	1	4	yes	—
129	C₂×#555	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
131	#3303	C₂×C₇	1	16	yes	direct product factor
132	C₂×#487	C₂×C₇	1	1	yes	characteristic, complemented
133	C₂×#485	C₂×C₇	1	2	yes	complemented
134	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#465	C₂×C₇	1	2	yes	complemented
136	C₂×#461	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#449	C₂×C₇	1	2	yes	complemented
138	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
139	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×#416	C₂×C₇	1	2	yes	complemented
141	C₂⁴×C₇	—	2	1	no	—
142	C₂⁴×C₇	—	2	1	no	—
143	C₂⁴×C₇	C₂×D₄	1	2	yes	—
144	C₇×#41	—	2	16	no	—
145	C₇×#41	—	4	8	no	—
146	C₇×#41	—	4	16	no	—
147	C₂×C₇×Q₈	—	2	2	no	—
148	C₂×C₇×Q₈	—	2	4	no	—
149	C₂×C₇×Q₈	—	2	4	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	8	2	no	—
152	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
153	C₂×C₇×D₄	—	2	8	no	—
154	C₂×C₇×D₄	—	2	8	no	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	1	no	—
157	C₂×C₇×D₄	—	2	1	no	—
158	C₂×C₇×D₄	—	2	2	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	2	no	—
161	C₂×C₇×D₄	—	4	8	no	—
162	C₂×C₇×D₄	—	8	4	no	—
163	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
164	C₂×C₇×D₄	#41	1	4	yes	—
165	C₂×C₇×D₄	C₂⁴	1	2	yes	—
166	C₂×C₇×D₄	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₇	—	2	4	no	—
168	C₂²×C₄×C₇	—	2	4	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	2	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	2	no	—
173	C₂²×C₄×C₇	—	2	4	no	—
174	C₂²×C₄×C₇	—	2	8	no	—
175	C₂²×C₄×C₇	—	2	4	no	—
176	C₂²×C₄×C₇	—	4	8	no	—
177	C₂²×C₄×C₇	—	4	4	no	—
178	C₂²×C₄×C₇	—	4	4	no	—
179	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₇×SD₁₆	—	4	8	no	—
186	C₇×D₈	—	2	8	no	—
187	C₂×C₇×C₈	—	2	2	no	—
188	C₂×C₇×C₈	—	2	2	no	—
189	C₂×C₇×C₈	—	2	4	no	—
190	C₂×C₇×C₈	—	4	8	no	—
191	C₂×C₇×C₈	C₂⁴	1	2	yes	—
192	C₂×C₇×C₈	C₂⁴	1	2	yes	—
193	C₂×C₇×C₈	C₂⁴	1	4	yes	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	—	2	8	no	—
196	C₇×C₄⋊C₄	—	2	4	no	—
197	C₇×C₄⋊C₄	—	2	4	no	—
198	C₇×C₄⋊C₄	—	2	1	no	—
199	C₇×C₄⋊C₄	—	2	2	no	—
200	C₇×C₄⋊C₄	—	2	1	no	—
201	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
202	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
203	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
204	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
205	C₇×C₂²⋊C₄	—	2	8	no	—
206	C₇×C₂²⋊C₄	—	2	8	no	—
207	C₇×C₂²⋊C₄	—	2	8	no	—
208	C₇×C₂²⋊C₄	—	2	4	no	—
209	C₇×C₂²⋊C₄	—	2	4	no	—
210	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
211	C₄²×C₇	—	2	8	no	—
212	C₄²×C₇	C₂×D₄	1	2	yes	—
213	C₄²×C₇	C₂⁴	1	2	yes	—
214	C₂²×#41	C₂²×C₇	1	2	yes	—
215	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
216	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₇	1	2	yes	—
218	#555	—	2	4	no	—
219	#555	C₂²×C₇	1	8	yes	complemented
220	#547	—	2	4	no	—
221	#547	C₂²×C₇	1	8	yes	complemented
222	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
224	C₂×#124	—	2	2	no	—
225	C₂×#123	—	2	2	no	—
226	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
227	C₂×#121	—	2	1	no	—
228	C₂×#121	—	2	1	no	—
229	C₂×#121	C₂²×C₇	1	2	yes	—
230	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
231	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
232	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
233	C₂×#117	—	2	1	no	—
234	C₂×#117	C₂²×C₇	1	2	yes	—
235	C₂²×C₄⋊C₄	—	2	1	no	—
236	#487	C₂²×C₇	1	8	yes	complemented
237	#485	C₂²×C₇	1	16	yes	complemented
238	#476	C₂²×C₇	1	8	yes	complemented
239	#465	C₂²×C₇	1	16	yes	complemented
240	#461	C₂²×C₇	1	8	yes	complemented
241	#449	C₂²×C₇	1	16	yes	complemented
242	C₄×D₈	C₂²×C₇	1	8	yes	complemented
243	C₈×D₄	C₂²×C₇	1	8	yes	complemented
244	C₂×#107	C₂²×C₇	1	1	yes	characteristic
245	C₂×#106	C₂²×C₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
247	#416	C₂²×C₇	1	16	yes	complemented
248	C₂×#103	C₂²×C₇	1	2	yes	—
249	C₂×#103	C₂²×C₇	1	2	yes	—
250	C₂×#103	C₂²×C₇	1	2	yes	—
251	C₂×#102	C₂²×C₇	1	1	yes	characteristic
252	C₂×#102	C₂²×C₇	1	2	yes	—
253	C₂×#102	C₂²×C₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
256	C₂³×C₇	—	2	4	no	—
257	C₂³×C₇	—	2	4	no	—
258	C₂³×C₇	—	2	4	no	—
259	C₂³×C₇	—	2	4	no	—
260	C₂³×C₇	—	2	2	no	—
261	C₂³×C₇	—	2	2	no	—
262	C₂³×C₇	—	4	2	no	—
263	C₂³×C₇	—	4	2	no	—
264	C₂³×C₇	—	4	2	no	—
265	C₂³×C₇	—	4	2	no	—
266	C₂³×C₇	—	4	2	no	—
267	C₂³×C₇	C₂²×D₄	1	4	yes	—
268	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
269	C₇×Q₈	—	2	4	no	—
270	C₇×Q₈	—	2	4	no	—
271	C₇×Q₈	—	4	4	no	—
272	C₇×Q₈	—	8	4	no	—
273	C₇×D₄	—	2	4	no	—
274	C₇×D₄	—	2	8	no	—
275	C₇×D₄	—	2	2	no	—
276	C₇×D₄	—	2	2	no	—
277	C₇×D₄	—	2	2	no	—
278	C₇×D₄	—	4	16	no	—
279	C₇×D₄	—	4	2	no	—
280	C₇×D₄	—	8	8	no	—
281	C₇×D₄	C₂×#41	1	4	yes	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	2	2	no	—
284	C₂×C₄×C₇	—	2	8	no	—
285	C₂×C₄×C₇	—	2	4	no	—
286	C₂×C₄×C₇	—	2	4	no	—
287	C₂×C₄×C₇	—	2	2	no	—
288	C₂×C₄×C₇	—	2	4	no	—
289	C₂×C₄×C₇	—	2	2	no	—
290	C₂×C₄×C₇	—	2	4	no	—
291	C₂×C₄×C₇	—	4	16	no	—
292	C₂×C₄×C₇	—	4	4	no	—
293	C₂×C₄×C₇	—	4	2	no	—
294	C₂×C₄×C₇	—	4	2	no	—
295	C₂×C₄×C₇	—	4	4	no	—
296	C₂×C₄×C₇	—	4	8	no	—
297	C₂×C₄×C₇	—	4	8	no	—
298	C₂×C₄×C₇	#135	1	4	yes	—
299	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
300	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
301	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
303	C₂×C₄×C₇	C₂×#41	1	2	yes	—
304	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
305	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
306	C₇×C₈	—	2	2	no	—
307	C₇×C₈	—	2	2	no	—
308	C₇×C₈	—	2	4	no	—
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	8	no	—
311	C₂×#41	—	4	4	no	—
312	C₂×#41	C₂³×C₇	1	8	yes	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×Q₈	C₂³×C₇	1	2	yes	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
318	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	—	2	2	no	—
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	C₂³×C₇	1	2	yes	—
324	C₂×SD₁₆	—	4	4	no	—
325	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
326	C₂×D₈	—	2	4	no	—
327	C₂×D₈	C₂³×C₇	1	4	yes	—
328	C₂²×C₈	—	4	4	no	—
329	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₇	1	2	yes	—
331	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₇	1	8	yes	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
336	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
337	#124	—	2	16	no	—
338	#123	—	2	16	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
341	#121	—	2	8	no	—
342	#121	—	2	8	no	—
343	#121	—	2	4	no	—
344	#121	C₂³×C₇	1	8	yes	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	2	2	no	—
347	C₄×D₄	C₇×D₄	1	4	yes	—
348	C₄×D₄	C₂³×C₇	1	4	yes	—
349	C₄×D₄	C₂³×C₇	1	4	yes	—
350	C₄×D₄	C₂³×C₇	1	4	yes	—
351	#117	—	2	4	no	—
352	#117	—	2	8	no	—
353	#117	C₂³×C₇	1	8	yes	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	8	no	—
359	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
371	#107	C₂³×C₇	1	4	yes	—
372	#106	C₂³×C₇	1	8	yes	—
373	C₄⋊C₈	C₂³×C₇	1	4	yes	—
374	#103	C₂³×C₇	1	8	yes	—
375	#103	C₂³×C₇	1	8	yes	—
376	#103	C₂³×C₇	1	8	yes	—
377	#102	C₂³×C₇	1	4	yes	—
378	#102	C₂³×C₇	1	8	yes	—
379	#102	C₂³×C₇	1	4	yes	—
380	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
381	C₄×C₈	C₂³×C₇	1	4	yes	—
382	C₂²×C₇	—	2	4	no	—
383	C₂²×C₇	—	2	4	no	—
384	C₂²×C₇	—	2	4	no	—
385	C₂²×C₇	—	2	4	no	—
386	C₂²×C₇	—	4	8	no	—
387	C₂²×C₇	—	4	8	no	—
388	C₂²×C₇	—	4	2	no	—
389	C₂²×C₇	—	4	2	no	—
390	C₂²×C₇	—	4	2	no	—
391	C₂²×C₇	—	4	2	no	—
392	C₂²×C₇	—	4	2	no	—
393	C₂²×C₇	—	8	4	no	—
394	C₂²×C₇	#546	1	2	yes	—
395	C₂²×C₇	C₂×#135	1	2	yes	—
396	C₂²×C₇	#577	1	2	yes	—
397	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
398	C₄×C₇	—	2	4	no	—
399	C₄×C₇	—	2	2	no	—
400	C₄×C₇	—	4	4	no	—
401	C₄×C₇	—	4	2	no	—
402	C₄×C₇	—	4	2	no	—
403	C₄×C₇	—	4	4	no	—
404	C₄×C₇	#546	1	2	yes	—
405	C₄×C₇	C₂×#135	1	4	yes	—
406	C₄×C₇	C₂²×#41	1	1	yes	characteristic
407	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	C₂×C₇×D₄	1	2	yes	—
411	#41	—	2	16	no	—
412	#41	—	4	8	no	—
413	#41	—	4	16	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	8	2	no	—
419	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	4	8	no	—
429	C₂×D₄	—	8	4	no	—
430	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
431	C₂×D₄	C₇×#41	1	4	yes	—
432	C₂×D₄	C₂⁴×C₇	1	2	yes	—
433	C₂×D₄	C₂⁴×C₇	1	2	yes	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	8	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	4	8	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
447	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
449	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
451	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
452	SD₁₆	—	4	8	no	—
453	D₈	—	2	8	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	4	no	—
457	C₂×C₈	—	4	8	no	—
458	C₂×C₈	C₂⁴×C₇	1	2	yes	—
459	C₂×C₈	C₂⁴×C₇	1	2	yes	—
460	C₂×C₈	C₂⁴×C₇	1	4	yes	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
469	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
471	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
478	C₄²	—	2	8	no	—
479	C₄²	C₂×C₇×D₄	1	2	yes	—
480	C₄²	C₂⁴×C₇	1	2	yes	—
481	C₂×C₇	—	4	4	no	—
482	C₂×C₇	—	4	4	no	—
483	C₂×C₇	—	8	2	no	—
484	C₂×C₇	#3303	1	4	yes	direct product factor
485	C₂×C₇	C₂×#546	1	1	yes	characteristic
486	C₂×C₇	C₂²×#135	1	1	yes	characteristic
487	C₂×C₇	C₂×#577	1	1	yes	characteristic
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	4	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	4	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	C₂²×C₇×D₄	1	4	yes	—
500	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
501	Q₈	—	2	4	no	—
502	Q₈	—	2	4	no	—
503	Q₈	—	4	4	no	—
504	Q₈	—	8	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	4	no	—
509	D₄	—	2	8	no	—
510	D₄	—	4	16	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	8	no	—
513	D₄	C₂×C₇×#41	1	4	yes	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	4	16	no	—
524	C₂×C₄	—	4	4	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	4	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	4	8	no	—
530	C₂×C₄	C₇×#135	1	4	yes	—
531	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
532	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
533	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
535	C₂×C₄	C₂×C₇×#41	1	2	yes	—
536	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	4	no	—
541	C₇	C₂×#3303	1	1	yes	characteristic, direct product factor, Sylow
542	C₂²	—	2	4	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	8	no	—
549	C₂²	—	4	8	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	4	no	—
554	C₂²	C₇×#546	1	2	yes	—
555	C₂²	C₂×C₇×#135	1	2	yes	—
556	C₂²	C₇×#577	1	2	yes	—
557	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
558	C₄	—	2	2	no	—
559	C₄	—	2	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	4	no	—
564	C₄	C₇×#546	1	2	yes	—
565	C₄	C₂×C₇×#135	1	4	yes	—
566	C₄	C₂²×C₇×#41	1	1	yes	characteristic
567	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
568	C₂	—	4	4	no	—
569	C₂	—	4	4	no	—
570	C₂	—	8	2	no	—
571	C₂	C₇×#3303	1	4	yes	direct product factor
572	C₂	C₂×C₇×#546	1	1	yes	characteristic
573	C₂	C₂²×C₇×#135	1	1	yes	characteristic
574	C₂	C₂×C₇×#577	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. C₂×C₇×#555	C₂	semidirect
2. C₂×C₇×#547	C₂	semidirect
3. C₇×#3303	C₂	direct (N × H)
4. C₂×C₇×#487	C₂	semidirect
5. C₂×C₇×#485	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#465	C₂	semidirect
8. C₂×C₇×#461	C₂	semidirect
9. C₂×C₇×#449	C₂	semidirect
10. C₂×C₄×C₇×D₈	C₂	semidirect
11. C₂×C₇×C₈×D₄	C₂	semidirect
12. C₂×C₇×#416	C₂	semidirect
18. C₇×#555	C₂²	semidirect
20. C₇×#547	C₂²	semidirect
35. C₇×#487	C₂²	semidirect
36. C₇×#485	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#465	C₂²	semidirect
39. C₇×#461	C₂²	semidirect
40. C₇×#449	C₂²	semidirect
41. C₄×C₇×D₈	C₂²	semidirect
42. C₇×C₈×D₄	C₂²	semidirect
46. C₇×#416	C₂²	semidirect
55. C₂×#3303	C₇	direct (N × H)
129. C₂×#555	C₂×C₇	semidirect
130. C₂×#547	C₂×C₇	semidirect
131. #3303	C₂×C₇	direct (N × H)
132. C₂×#487	C₂×C₇	semidirect
133. C₂×#485	C₂×C₇	semidirect
134. C₂×#476	C₂×C₇	semidirect
135. C₂×#465	C₂×C₇	semidirect
136. C₂×#461	C₂×C₇	semidirect
137. C₂×#449	C₂×C₇	semidirect
138. C₂×C₄×D₈	C₂×C₇	semidirect
139. C₂×C₈×D₄	C₂×C₇	semidirect
140. C₂×#416	C₂×C₇	semidirect
219. #555	C₂²×C₇	semidirect
221. #547	C₂²×C₇	semidirect
236. #487	C₂²×C₇	semidirect
237. #485	C₂²×C₇	semidirect
238. #476	C₂²×C₇	semidirect
239. #465	C₂²×C₇	semidirect
240. #461	C₂²×C₇	semidirect
241. #449	C₂²×C₇	semidirect
242. C₄×D₈	C₂²×C₇	semidirect
243. C₈×D₄	C₂²×C₇	semidirect
247. #416	C₂²×C₇	semidirect
484. C₂×C₇	#3303	direct (N × H)
541. C₇	C₂×#3303	direct (N × H)
571. C₂	C₇×#3303	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×#555	2
C₂×C₇×#547	2
C₇×#3303	2
C₂×C₇×#487	2
C₂×C₇×#485	2
C₂×C₇×#476	2
C₂×C₇×#465	2
C₂×C₇×#461	2
C₂×C₇×#449	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#416	2
C₂×#3303	7

Subgroups — C2×C7×#3303 #13238337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3303 #13238337