Subgroups — C₂×C₇×#3354 #13238463

Order 1792.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 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×#3354	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#469	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
16	C₇×#555	—	2	4	no	—
17	C₇×#555	C₂²	1	8	yes	complemented
18	C₇×#547	—	2	4	no	—
19	C₇×#547	C₂²	1	8	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#124	—	2	2	no	—
23	C₂×C₇×#123	—	2	2	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×#121	—	2	1	no	—
26	C₂×C₇×#121	C₂²	1	2	yes	—
27	C₂×C₇×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₇×#117	—	2	1	no	—
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₇×#498	C₂²	1	8	yes	complemented
35	C₇×#482	C₂²	1	16	yes	complemented
36	C₇×#481	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#474	C₂²	1	8	yes	complemented
39	C₇×#469	C₂²	1	16	yes	complemented
40	C₄×C₇×D₈	C₂²	1	8	yes	complemented
41	C₇×#436	C₂²	1	8	yes	complemented
42	C₇×#428	C₂²	1	16	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₇×#107	C₂²	1	2	yes	—
45	C₂×C₇×#106	C₂²	1	2	yes	—
46	C₂×C₇×#106	C₂²	1	2	yes	—
47	C₂×C₇×#106	C₂²	1	2	yes	—
48	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#102	C₂²	1	1	yes	characteristic
50	C₂×C₇×#102	C₂²	1	1	yes	characteristic
51	C₂×C₇×#102	C₂²	1	2	yes	—
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×#3354	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	8	no	—
57	C₂×C₇×#41	—	4	8	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	2	1	no	—
60	C₂²×C₇×D₄	—	2	2	no	—
61	C₂²×C₇×D₄	—	2	2	no	—
62	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₇	—	2	2	no	—
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	C₂³	1	2	yes	—
69	C₂×C₇×D₈	—	2	4	no	—
70	C₂×C₇×D₈	C₂³	1	4	yes	—
71	C₂×C₇×M₁₆	—	2	8	no	—
72	C₂×C₇×M₁₆	C₂³	1	8	yes	—
73	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₇×C₈	C₂³	1	2	yes	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₇×C₄⋊Q₈	—	2	2	no	—
77	C₇×C₄⋊Q₈	—	2	2	no	—
78	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
80	C₇×#124	—	2	16	no	—
81	C₇×#123	—	2	16	no	—
82	C₇×C₂²⋊Q₈	—	2	8	no	—
83	C₇×#121	—	2	8	no	—
84	C₇×#121	—	2	4	no	—
85	C₇×#121	—	2	4	no	—
86	C₇×#121	C₂³	1	8	yes	—
87	C₇×#121	C₂³	1	8	yes	—
88	C₄×C₇×D₄	—	2	2	no	—
89	C₄×C₇×D₄	—	2	2	no	—
90	C₄×C₇×D₄	D₄	1	4	yes	—
91	C₄×C₇×D₄	C₂³	1	4	yes	—
92	C₄×C₇×D₄	C₂³	1	4	yes	—
93	C₄×C₇×D₄	C₂³	1	4	yes	—
94	C₇×#117	—	2	4	no	—
95	C₇×#117	—	2	8	no	—
96	C₇×#117	C₂³	1	8	yes	—
97	C₂×C₇×C₄⋊C₄	—	2	2	no	—
98	C₂×C₇×C₄⋊C₄	—	2	4	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
108	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
113	C₂×C₄²×C₇	—	2	2	no	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#107	C₂³	1	8	yes	—
116	C₇×#107	C₂³	1	4	yes	—
117	C₇×#106	C₂³	1	8	yes	—
118	C₇×#106	C₂³	1	8	yes	—
119	C₇×#106	C₂³	1	8	yes	—
120	C₇×C₄⋊C₈	C₂³	1	4	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	4	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#555	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×#547	C₂×C₇	1	1	yes	characteristic, complemented
129	#3354	C₂×C₇	1	16	yes	direct product factor
130	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#481	C₂×C₇	1	2	yes	complemented
132	C₂×#482	C₂×C₇	1	2	yes	complemented
133	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#469	C₂×C₇	1	2	yes	complemented
136	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#428	C₂×C₇	1	2	yes	complemented
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	—	2	1	no	—
141	C₂⁴×C₇	C₂×D₄	1	2	yes	—
142	C₇×#41	—	4	32	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	4	4	no	—
146	C₂×C₇×Q₈	—	8	2	no	—
147	C₂×C₇×D₄	—	2	8	no	—
148	C₂×C₇×D₄	—	2	8	no	—
149	C₂×C₇×D₄	—	2	4	no	—
150	C₂×C₇×D₄	—	2	1	no	—
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	2	no	—
153	C₂×C₇×D₄	—	2	2	no	—
154	C₂×C₇×D₄	—	2	2	no	—
155	C₂×C₇×D₄	—	2	2	no	—
156	C₂×C₇×D₄	—	4	8	no	—
157	C₂×C₇×D₄	—	8	4	no	—
158	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
159	C₂×C₇×D₄	C₂⁴	1	2	yes	—
160	C₂×C₇×D₄	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	—	2	4	no	—
162	C₂²×C₄×C₇	—	2	4	no	—
163	C₂²×C₄×C₇	—	2	8	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	1	no	—
167	C₂²×C₄×C₇	—	2	2	no	—
168	C₂²×C₄×C₇	—	2	4	no	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	4	8	no	—
171	C₂²×C₄×C₇	—	4	4	no	—
172	C₂²×C₄×C₇	—	4	4	no	—
173	C₂²×C₄×C₇	C₂×D₄	1	4	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	4	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
179	C₇×D₈	—	2	8	no	—
180	C₇×M₁₆	—	2	16	no	—
181	C₂×C₇×C₈	—	2	4	no	—
182	C₂×C₇×C₈	—	2	2	no	—
183	C₂×C₇×C₈	#41	1	4	yes	complemented
184	C₂×C₇×C₈	C₂⁴	1	2	yes	—
185	C₂×C₇×C₈	C₂⁴	1	4	yes	—
186	C₂×C₇×C₈	C₂⁴	1	2	yes	—
187	C₇×C₄⋊C₄	—	2	1	no	—
188	C₇×C₄⋊C₄	—	2	2	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	4	no	—
191	C₇×C₄⋊C₄	—	2	4	no	—
192	C₇×C₄⋊C₄	—	2	1	no	—
193	C₇×C₄⋊C₄	—	2	2	no	—
194	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	4	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	4	no	—
202	C₇×C₂²⋊C₄	—	2	4	no	—
203	C₇×C₂²⋊C₄	—	2	8	no	—
204	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
205	C₄²×C₇	—	2	8	no	—
206	C₄²×C₇	C₂×D₄	1	2	yes	—
207	C₄²×C₇	C₂⁴	1	2	yes	—
208	C₂²×#41	—	2	1	no	—
209	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
210	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
211	#555	—	2	4	no	—
212	#555	C₂²×C₇	1	8	yes	complemented
213	#547	—	2	4	no	—
214	#547	C₂²×C₇	1	8	yes	complemented
215	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×#124	—	2	2	no	—
218	C₂×#123	—	2	2	no	—
219	C₂×C₂²⋊Q₈	—	2	1	no	—
220	C₂×#121	—	2	1	no	—
221	C₂×#121	C₂²×C₇	1	2	yes	—
222	C₂×#121	C₂²×C₇	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
226	C₂×#117	—	2	1	no	—
227	C₂×#117	C₂²×C₇	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
229	#498	C₂²×C₇	1	8	yes	complemented
230	#482	C₂²×C₇	1	16	yes	complemented
231	#481	C₂²×C₇	1	16	yes	complemented
232	#476	C₂²×C₇	1	8	yes	complemented
233	#474	C₂²×C₇	1	8	yes	complemented
234	#469	C₂²×C₇	1	16	yes	complemented
235	C₄×D₈	C₂²×C₇	1	8	yes	complemented
236	#436	C₂²×C₇	1	8	yes	complemented
237	#428	C₂²×C₇	1	16	yes	complemented
238	C₂×#107	C₂²×C₇	1	2	yes	—
239	C₂×#107	C₂²×C₇	1	1	yes	characteristic
240	C₂×#106	C₂²×C₇	1	2	yes	—
241	C₂×#106	C₂²×C₇	1	2	yes	—
242	C₂×#106	C₂²×C₇	1	2	yes	—
243	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
244	C₂×#102	C₂²×C₇	1	1	yes	characteristic
245	C₂×#102	C₂²×C₇	1	2	yes	—
246	C₂×#102	C₂²×C₇	1	1	yes	characteristic
247	C₂×#102	C₂²×C₇	1	2	yes	—
248	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
250	C₂³×C₇	—	2	4	no	—
251	C₂³×C₇	—	2	4	no	—
252	C₂³×C₇	—	2	4	no	—
253	C₂³×C₇	—	2	2	no	—
254	C₂³×C₇	—	2	2	no	—
255	C₂³×C₇	—	4	2	no	—
256	C₂³×C₇	—	4	2	no	—
257	C₂³×C₇	—	4	2	no	—
258	C₂³×C₇	—	4	2	no	—
259	C₂³×C₇	—	4	2	no	—
260	C₂³×C₇	—	4	2	no	—
261	C₂³×C₇	C₂²×D₄	1	4	yes	—
262	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
263	C₇×Q₈	—	4	8	no	—
264	C₇×Q₈	—	8	4	no	—
265	C₇×D₄	—	2	8	no	—
266	C₇×D₄	—	2	2	no	—
267	C₇×D₄	—	2	2	no	—
268	C₇×D₄	—	2	2	no	—
269	C₇×D₄	—	2	2	no	—
270	C₇×D₄	—	4	16	no	—
271	C₇×D₄	—	4	2	no	—
272	C₇×D₄	—	4	2	no	—
273	C₇×D₄	—	8	8	no	—
274	C₂×C₄×C₇	—	2	4	no	—
275	C₂×C₄×C₇	—	2	2	no	—
276	C₂×C₄×C₇	—	2	8	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	4	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	4	no	—
283	C₂×C₄×C₇	—	4	16	no	—
284	C₂×C₄×C₇	—	4	2	no	—
285	C₂×C₄×C₇	—	4	2	no	—
286	C₂×C₄×C₇	—	4	4	no	—
287	C₂×C₄×C₇	—	4	4	no	—
288	C₂×C₄×C₇	—	4	8	no	—
289	C₂×C₄×C₇	—	4	8	no	—
290	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₇	C₂×#41	1	2	yes	—
296	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
297	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
298	C₇×C₈	—	2	4	no	—
299	C₇×C₈	—	2	2	no	—
300	C₇×C₈	C₂×#41	1	4	yes	complemented
301	C₂×#41	—	2	8	no	—
302	C₂×#41	—	4	8	no	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	—	2	2	no	—
307	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
310	C₂³×C₄	—	2	2	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	C₂³×C₇	1	2	yes	—
314	C₂×D₈	—	2	4	no	—
315	C₂×D₈	C₂³×C₇	1	4	yes	—
316	C₂×M₁₆	—	2	8	no	—
317	C₂×M₁₆	C₂³×C₇	1	8	yes	—
318	C₂²×C₈	C₂³×C₇	1	2	yes	—
319	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
324	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
325	#124	—	2	16	no	—
326	#123	—	2	16	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	#121	—	2	8	no	—
329	#121	—	2	4	no	—
330	#121	—	2	4	no	—
331	#121	C₂³×C₇	1	8	yes	—
332	#121	C₂³×C₇	1	8	yes	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	2	no	—
335	C₄×D₄	C₇×D₄	1	4	yes	—
336	C₄×D₄	C₂³×C₇	1	4	yes	—
337	C₄×D₄	C₂³×C₇	1	4	yes	—
338	C₄×D₄	C₂³×C₇	1	4	yes	—
339	#117	—	2	4	no	—
340	#117	—	2	8	no	—
341	#117	C₂³×C₇	1	8	yes	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
350	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
360	#107	C₂³×C₇	1	4	yes	—
361	#107	C₂³×C₇	1	8	yes	—
362	#106	C₂³×C₇	1	8	yes	—
363	#106	C₂³×C₇	1	8	yes	—
364	#106	C₂³×C₇	1	8	yes	—
365	C₄⋊C₈	C₂³×C₇	1	4	yes	—
366	#102	C₂³×C₇	1	4	yes	—
367	#102	C₂³×C₇	1	4	yes	—
368	#102	C₂³×C₇	1	8	yes	—
369	#102	C₂³×C₇	1	8	yes	—
370	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
371	C₄×C₈	C₂³×C₇	1	4	yes	—
372	C₂²×C₇	—	2	4	no	—
373	C₂²×C₇	—	2	4	no	—
374	C₂²×C₇	—	2	4	no	—
375	C₂²×C₇	—	4	8	no	—
376	C₂²×C₇	—	4	2	no	—
377	C₂²×C₇	—	4	2	no	—
378	C₂²×C₇	—	4	2	no	—
379	C₂²×C₇	—	4	2	no	—
380	C₂²×C₇	—	4	2	no	—
381	C₂²×C₇	—	4	2	no	—
382	C₂²×C₇	—	8	4	no	—
383	C₂²×C₇	—	8	4	no	—
384	C₂²×C₇	#547	1	2	yes	—
385	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
386	C₂²×C₇	#577	1	2	yes	—
387	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
388	C₄×C₇	—	2	4	no	—
389	C₄×C₇	—	2	2	no	—
390	C₄×C₇	—	4	2	no	—
391	C₄×C₇	—	4	2	no	—
392	C₄×C₇	—	4	4	no	—
393	C₄×C₇	—	4	4	no	—
394	C₄×C₇	#547	1	2	yes	—
395	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
396	C₄×C₇	C₂²×#41	1	1	yes	characteristic
397	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
398	C₂⁴	—	2	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	C₂×C₇×D₄	1	2	yes	—
401	#41	—	4	32	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	2	4	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	—	8	2	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	8	4	no	—
417	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
418	C₂×D₄	C₂⁴×C₇	1	2	yes	—
419	C₂×D₄	C₂⁴×C₇	1	2	yes	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	4	8	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
433	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
435	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
437	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
438	D₈	—	2	8	no	—
439	M₁₆	—	2	16	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	C₇×#41	1	4	yes	complemented
443	C₂×C₈	C₂⁴×C₇	1	2	yes	—
444	C₂×C₈	C₂⁴×C₇	1	4	yes	—
445	C₂×C₈	C₂⁴×C₇	1	2	yes	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
454	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
455	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
456	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
457	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	8	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
464	C₄²	—	2	8	no	—
465	C₄²	C₂×C₇×D₄	1	2	yes	—
466	C₄²	C₂⁴×C₇	1	2	yes	—
467	C₂×C₇	—	4	4	no	—
468	C₂×C₇	—	8	2	no	—
469	C₂×C₇	—	8	2	no	—
470	C₂×C₇	#3354	1	4	yes	direct product factor
471	C₂×C₇	C₂×#547	1	1	yes	characteristic
472	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₂×C₇	C₂×#577	1	1	yes	characteristic
474	C₂³	—	2	4	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	C₂²×C₇×D₄	1	4	yes	—
486	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
487	Q₈	—	4	8	no	—
488	Q₈	—	8	4	no	—
489	D₄	—	2	2	no	—
490	D₄	—	2	2	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	8	no	—
494	D₄	—	4	16	no	—
495	D₄	—	4	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	8	8	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	16	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	8	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
515	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
516	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
517	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
519	C₂×C₄	C₂×C₇×#41	1	2	yes	—
520	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
521	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
522	C₈	—	2	4	no	—
523	C₈	—	2	2	no	—
524	C₈	C₂×C₇×#41	1	4	yes	complemented
525	C₇	C₂×#3354	1	1	yes	characteristic, direct product factor, Sylow
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	4	no	—
537	C₂²	—	8	4	no	—
538	C₂²	C₇×#547	1	2	yes	—
539	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
540	C₂²	C₇×#577	1	2	yes	—
541	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	C₇×#547	1	2	yes	—
549	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
550	C₄	C₂²×C₇×#41	1	1	yes	characteristic
551	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂	—	4	4	no	—
553	C₂	—	8	2	no	—
554	C₂	—	8	2	no	—
555	C₂	C₇×#3354	1	4	yes	direct product factor
556	C₂	C₂×C₇×#547	1	1	yes	characteristic
557	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
558	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×#3354	C₂	direct (N × H)
4. C₂×C₇×#498	C₂	semidirect
5. C₂×C₇×#481	C₂	semidirect
6. C₂×C₇×#482	C₂	semidirect
7. C₂×C₇×#476	C₂	semidirect
8. C₂×C₇×#474	C₂	semidirect
9. C₂×C₇×#469	C₂	semidirect
10. C₂×C₄×C₇×D₈	C₂	semidirect
11. C₂×C₇×#436	C₂	semidirect
12. C₂×C₇×#428	C₂	semidirect
17. C₇×#555	C₂²	semidirect
19. C₇×#547	C₂²	semidirect
34. C₇×#498	C₂²	semidirect
35. C₇×#482	C₂²	semidirect
36. C₇×#481	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#474	C₂²	semidirect
39. C₇×#469	C₂²	semidirect
40. C₄×C₇×D₈	C₂²	semidirect
41. C₇×#436	C₂²	semidirect
42. C₇×#428	C₂²	semidirect
55. C₂×#3354	C₇	direct (N × H)
127. C₂×#555	C₂×C₇	semidirect
128. C₂×#547	C₂×C₇	semidirect
129. #3354	C₂×C₇	direct (N × H)
130. C₂×#498	C₂×C₇	semidirect
131. C₂×#481	C₂×C₇	semidirect
132. C₂×#482	C₂×C₇	semidirect
133. C₂×#476	C₂×C₇	semidirect
134. C₂×#474	C₂×C₇	semidirect
135. C₂×#469	C₂×C₇	semidirect
136. C₂×C₄×D₈	C₂×C₇	semidirect
137. C₂×#436	C₂×C₇	semidirect
138. C₂×#428	C₂×C₇	semidirect
183. C₂×C₇×C₈	#41	semidirect
212. #555	C₂²×C₇	semidirect
214. #547	C₂²×C₇	semidirect
229. #498	C₂²×C₇	semidirect
230. #482	C₂²×C₇	semidirect
231. #481	C₂²×C₇	semidirect
232. #476	C₂²×C₇	semidirect
233. #474	C₂²×C₇	semidirect
234. #469	C₂²×C₇	semidirect
235. C₄×D₈	C₂²×C₇	semidirect
236. #436	C₂²×C₇	semidirect
237. #428	C₂²×C₇	semidirect
300. C₇×C₈	C₂×#41	semidirect
442. C₂×C₈	C₇×#41	semidirect
470. C₂×C₇	#3354	direct (N × H)
524. C₈	C₂×C₇×#41	semidirect
525. C₇	C₂×#3354	direct (N × H)
555. C₂	C₇×#3354	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×#3354	2
C₂×C₇×#498	2
C₂×C₇×#481	2
C₂×C₇×#482	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#469	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#436	2
C₂×C₇×#428	2
C₂×#3354	7

Subgroups — C2×C7×#3354 #13238463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3354 #13238463