Subgroups — C₂×C₇×#3325 #13238361

Order 1792.

2630 conjugacy classes of subgroups.

The subgroup lattice has 616 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×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#447	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×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×C₇×D₄	—	2	1	no	—
14	C₂³×C₇×D₄	C₂²	1	2	yes	—
15	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
16	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
17	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
18	C₇×#555	—	2	4	no	—
19	C₇×#555	C₂²	1	8	yes	complemented
20	C₇×D₄²	—	2	4	no	—
21	C₇×D₄²	C₂²	1	8	yes	complemented
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×#127	C₂²	1	1	yes	characteristic
24	C₂×C₇×#124	—	2	2	no	—
25	C₂×C₇×#121	—	2	1	no	—
26	C₂×C₇×#121	—	2	1	no	—
27	C₂×C₇×#121	C₂²	1	2	yes	—
28	C₂×C₇×#121	C₂²	1	2	yes	complemented
29	C₂×C₇×#120	—	2	2	no	—
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×#117	—	2	1	no	—
34	C₂×C₇×#117	C₂²	1	2	yes	complemented
35	C₇×#486	C₂²	1	8	yes	complemented
36	C₇×#482	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#469	C₂²	1	16	yes	complemented
39	C₇×#459	C₂²	1	8	yes	complemented
40	C₇×#447	C₂²	1	16	yes	complemented
41	C₄×C₇×D₈	C₂²	1	8	yes	complemented
42	C₇×#436	C₂²	1	8	yes	complemented
43	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₇×#106	C₂²	1	2	yes	complemented
45	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₇×#418	C₂²	1	16	yes	complemented
47	C₂×C₇×#102	C₂²	1	1	yes	characteristic
48	C₂×C₇×#102	C₂²	1	2	yes	—
49	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₇×#102	C₂²	1	2	yes	complemented
51	C₂×C₇×#102	C₂²	1	2	yes	complemented
52	C₂×C₇×#102	C₂²	1	2	yes	complemented
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
55	C₂×#3325	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₇	—	2	2	no	—
57	C₂²×C₇×Q₈	—	2	1	no	—
58	C₂²×C₇×D₄	—	2	8	no	—
59	C₂²×C₇×D₄	—	2	2	no	—
60	C₂²×C₇×D₄	—	2	2	no	—
61	C₂²×C₇×D₄	—	2	8	no	—
62	C₂²×C₇×D₄	—	2	1	no	—
63	C₂²×C₇×D₄	—	2	2	no	—
64	C₂²×C₇×D₄	—	2	4	no	—
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	—	4	4	no	—
67	C₂²×C₇×D₄	—	4	8	no	—
68	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
69	C₂²×C₇×D₄	C₂³	1	2	yes	—
70	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
71	C₂²×C₇×D₄	C₂³	1	8	yes	—
72	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₇	—	2	1	no	—
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	C₂³	1	2	yes	—
76	C₂×C₇×D₈	—	2	4	no	—
77	C₂×C₇×D₈	—	4	4	no	—
78	C₂×C₇×D₈	C₂³	1	4	yes	—
79	C₂×C₇×D₈	C₂³	1	8	yes	complemented
80	C₂×C₇×M₁₆	—	4	4	no	—
81	C₂×C₇×M₁₆	C₂³	1	8	yes	complemented
82	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×C₈	C₂³	1	2	yes	—
85	C₇×C₄⋊Q₈	—	2	2	no	—
86	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
87	C₇×#127	—	2	2	no	—
88	C₇×#127	C₂³	1	4	yes	—
89	C₇×#124	—	2	16	no	—
90	C₇×#121	—	2	8	no	—
91	C₇×#121	—	2	4	no	—
92	C₇×#121	—	2	4	no	—
93	C₇×#121	—	2	8	no	—
94	C₇×#121	C₂³	1	8	yes	—
95	C₇×#121	C₂³	1	8	yes	complemented
96	C₇×#120	—	2	16	no	—
97	C₄×C₇×D₄	—	2	2	no	—
98	C₄×C₇×D₄	—	2	2	no	—
99	C₄×C₇×D₄	D₄	1	4	yes	—
100	C₄×C₇×D₄	C₂³	1	4	yes	—
101	C₄×C₇×D₄	C₂³	1	4	yes	—
102	C₄×C₇×D₄	C₂³	1	4	yes	complemented
103	C₇×#117	—	2	4	no	—
104	C₇×#117	—	2	8	no	—
105	C₇×#117	C₂³	1	8	yes	complemented
106	C₂×C₇×C₄⋊C₄	—	2	1	no	—
107	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
116	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
117	C₂×C₄²×C₇	—	2	2	no	—
118	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
119	C₇×#107	C₂³	1	4	yes	complemented
120	C₇×#106	C₂³	1	8	yes	complemented
121	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
122	C₇×#102	C₂³	1	8	yes	—
123	C₇×#102	C₂³	1	4	yes	—
124	C₇×#102	C₂³	1	4	yes	complemented
125	C₇×#102	C₂³	1	8	yes	complemented
126	C₇×#102	C₂³	1	8	yes	complemented
127	C₇×#102	C₂³	1	8	yes	complemented
128	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
129	C₄×C₇×C₈	C₂³	1	4	yes	complemented
130	C₂×#555	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×D₄²	C₂×C₇	1	1	yes	characteristic, complemented
132	#3325	C₂×C₇	1	16	yes	direct product factor
133	C₂×#486	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#482	C₂×C₇	1	2	yes	complemented
135	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
136	C₂×#469	C₂×C₇	1	2	yes	complemented
137	C₂×#459	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂×#447	C₂×C₇	1	2	yes	complemented
139	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
140	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
141	C₂×#418	C₂×C₇	1	2	yes	complemented
142	C₂⁴×C₇	—	2	1	no	—
143	C₂⁴×C₇	—	2	1	no	—
144	C₂⁴×C₇	—	2	2	no	—
145	C₂⁴×C₇	—	2	8	no	—
146	C₂⁴×C₇	—	4	8	no	—
147	C₂⁴×C₇	—	4	8	no	—
148	C₂⁴×C₇	—	8	4	no	—
149	C₂⁴×C₇	C₂×D₄	1	2	yes	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	8	2	no	—
152	C₂×C₇×D₄	—	2	16	no	—
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	8	no	—
159	C₂×C₇×D₄	—	2	2	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	2	no	—
163	C₂×C₇×D₄	—	2	4	no	—
164	C₂×C₇×D₄	—	2	2	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	16	no	—
169	C₂×C₇×D₄	—	4	8	no	—
170	C₂×C₇×D₄	—	4	32	no	—
171	C₂×C₇×D₄	—	4	8	no	—
172	C₂×C₇×D₄	—	4	4	no	—
173	C₂×C₇×D₄	—	8	2	no	—
174	C₂×C₇×D₄	—	8	4	no	—
175	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
176	C₂×C₇×D₄	#41	1	4	yes	—
177	C₂×C₇×D₄	C₂⁴	1	4	yes	—
178	C₂×C₇×D₄	C₂⁴	1	2	yes	—
179	C₂×C₇×D₄	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₇	—	2	4	no	—
181	C₂²×C₄×C₇	—	2	4	no	—
182	C₂²×C₄×C₇	—	2	1	no	—
183	C₂²×C₄×C₇	—	2	2	no	—
184	C₂²×C₄×C₇	—	2	1	no	—
185	C₂²×C₄×C₇	—	2	4	no	—
186	C₂²×C₄×C₇	—	2	4	no	—
187	C₂²×C₄×C₇	—	4	4	no	—
188	C₂²×C₄×C₇	—	4	4	no	—
189	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
191	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
195	C₇×D₈	—	2	8	no	—
196	C₇×D₈	—	4	8	no	—
197	C₇×M₁₆	—	4	8	no	—
198	C₂×C₇×C₈	—	2	2	no	—
199	C₂×C₇×C₈	—	2	2	no	—
200	C₂×C₇×C₈	—	2	4	no	—
201	C₂×C₇×C₈	C₂⁴	1	2	yes	—
202	C₂×C₇×C₈	C₂⁴	1	2	yes	—
203	C₂×C₇×C₈	C₂⁴	1	4	yes	—
204	C₇×C₄⋊C₄	—	2	4	no	—
205	C₇×C₄⋊C₄	—	2	1	no	—
206	C₇×C₄⋊C₄	—	2	2	no	—
207	C₇×C₄⋊C₄	—	2	1	no	—
208	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
209	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
210	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
211	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
212	C₇×C₂²⋊C₄	—	2	8	no	—
213	C₇×C₂²⋊C₄	—	2	8	no	—
214	C₇×C₂²⋊C₄	—	2	4	no	—
215	C₇×C₂²⋊C₄	—	2	4	no	—
216	C₇×C₂²⋊C₄	—	2	8	no	—
217	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
218	C₄²×C₇	—	2	8	no	—
219	C₄²×C₇	C₂×D₄	1	2	yes	—
220	C₄²×C₇	C₂⁴	1	2	yes	—
221	C₂³×D₄	—	2	1	no	—
222	C₂³×D₄	C₂²×C₇	1	2	yes	—
223	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
225	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
226	#555	—	2	4	no	—
227	#555	C₂²×C₇	1	8	yes	complemented
228	D₄²	—	2	4	no	—
229	D₄²	C₂²×C₇	1	8	yes	complemented
230	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
231	C₂×#127	C₂²×C₇	1	1	yes	characteristic
232	C₂×#124	—	2	2	no	—
233	C₂×#121	—	2	1	no	—
234	C₂×#121	—	2	1	no	—
235	C₂×#121	C₂²×C₇	1	2	yes	—
236	C₂×#121	C₂²×C₇	1	2	yes	complemented
237	C₂×#120	—	2	2	no	—
238	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
240	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
241	C₂×#117	—	2	1	no	—
242	C₂×#117	C₂²×C₇	1	2	yes	complemented
243	#486	C₂²×C₇	1	8	yes	complemented
244	#482	C₂²×C₇	1	16	yes	complemented
245	#476	C₂²×C₇	1	8	yes	complemented
246	#469	C₂²×C₇	1	16	yes	complemented
247	#459	C₂²×C₇	1	8	yes	complemented
248	#447	C₂²×C₇	1	16	yes	complemented
249	C₄×D₈	C₂²×C₇	1	8	yes	complemented
250	#436	C₂²×C₇	1	8	yes	complemented
251	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
252	C₂×#106	C₂²×C₇	1	2	yes	complemented
253	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
254	#418	C₂²×C₇	1	16	yes	complemented
255	C₂×#102	C₂²×C₇	1	1	yes	characteristic
256	C₂×#102	C₂²×C₇	1	2	yes	—
257	C₂×#102	C₂²×C₇	1	2	yes	complemented
258	C₂×#102	C₂²×C₇	1	2	yes	complemented
259	C₂×#102	C₂²×C₇	1	2	yes	complemented
260	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
261	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
262	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
263	C₂³×C₇	—	2	4	no	—
264	C₂³×C₇	—	2	4	no	—
265	C₂³×C₇	—	2	4	no	—
266	C₂³×C₇	—	2	4	no	—
267	C₂³×C₇	—	2	2	no	—
268	C₂³×C₇	—	2	2	no	—
269	C₂³×C₇	—	2	4	no	—
270	C₂³×C₇	—	4	16	no	—
271	C₂³×C₇	—	4	16	no	—
272	C₂³×C₇	—	4	2	no	—
273	C₂³×C₇	—	4	2	no	—
274	C₂³×C₇	—	4	4	no	—
275	C₂³×C₇	—	4	2	no	—
276	C₂³×C₇	—	4	2	no	—
277	C₂³×C₇	—	4	4	no	—
278	C₂³×C₇	—	4	2	no	—
279	C₂³×C₇	—	4	4	no	—
280	C₂³×C₇	—	8	8	no	—
281	C₂³×C₇	—	8	32	no	—
282	C₂³×C₇	C₂²×D₄	1	4	yes	—
283	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
284	C₇×Q₈	—	8	4	no	—
285	C₇×D₄	—	2	4	no	—
286	C₇×D₄	—	2	8	no	—
287	C₇×D₄	—	2	2	no	—
288	C₇×D₄	—	2	4	no	—
289	C₇×D₄	—	2	2	no	—
290	C₇×D₄	—	2	2	no	—
291	C₇×D₄	—	2	4	no	—
292	C₇×D₄	—	4	16	no	—
293	C₇×D₄	—	4	16	no	—
294	C₇×D₄	—	4	2	no	—
295	C₇×D₄	—	4	4	no	—
296	C₇×D₄	—	4	8	no	—
297	C₇×D₄	—	8	4	no	—
298	C₇×D₄	—	8	8	no	—
299	C₇×D₄	C₂×#41	1	4	yes	—
300	C₂×C₄×C₇	—	2	4	no	—
301	C₂×C₄×C₇	—	2	2	no	—
302	C₂×C₄×C₇	—	2	8	no	—
303	C₂×C₄×C₇	—	2	4	no	—
304	C₂×C₄×C₇	—	2	4	no	—
305	C₂×C₄×C₇	—	2	2	no	—
306	C₂×C₄×C₇	—	2	4	no	—
307	C₂×C₄×C₇	—	2	2	no	—
308	C₂×C₄×C₇	—	4	2	no	—
309	C₂×C₄×C₇	—	4	2	no	—
310	C₂×C₄×C₇	—	4	4	no	—
311	C₂×C₄×C₇	—	4	8	no	—
312	C₂×C₄×C₇	—	4	8	no	—
313	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
314	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₇	C₂×#41	1	2	yes	—
319	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
320	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
321	C₇×C₈	—	2	2	no	—
322	C₇×C₈	—	2	2	no	—
323	C₇×C₈	—	2	4	no	—
324	C₂⁵	—	2	2	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×D₄	—	2	8	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	8	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	4	4	no	—
335	C₂²×D₄	—	4	8	no	—
336	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
338	C₂²×D₄	C₂³×C₇	1	2	yes	—
339	C₂²×D₄	C₂³×C₇	1	8	yes	—
340	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	C₂³×C₇	1	2	yes	—
344	C₂×D₈	—	2	4	no	—
345	C₂×D₈	—	4	4	no	—
346	C₂×D₈	C₂³×C₇	1	4	yes	—
347	C₂×D₈	C₂³×C₇	1	8	yes	complemented
348	C₂×M₁₆	—	4	4	no	—
349	C₂×M₁₆	C₂³×C₇	1	8	yes	complemented
350	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₇	1	2	yes	—
352	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	2	no	—
354	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
355	#127	—	2	2	no	—
356	#127	C₂³×C₇	1	4	yes	—
357	#124	—	2	16	no	—
358	#121	—	2	8	no	—
359	#121	—	2	4	no	—
360	#121	—	2	4	no	—
361	#121	—	2	8	no	—
362	#121	C₂³×C₇	1	8	yes	—
363	#121	C₂³×C₇	1	8	yes	complemented
364	#120	—	2	16	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	C₇×D₄	1	4	yes	—
368	C₄×D₄	C₂³×C₇	1	4	yes	—
369	C₄×D₄	C₂³×C₇	1	4	yes	—
370	C₄×D₄	C₂³×C₇	1	4	yes	complemented
371	#117	—	2	4	no	—
372	#117	—	2	8	no	—
373	#117	C₂³×C₇	1	8	yes	complemented
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
378	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
387	#107	C₂³×C₇	1	4	yes	complemented
388	#106	C₂³×C₇	1	8	yes	complemented
389	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
390	#102	C₂³×C₇	1	4	yes	—
391	#102	C₂³×C₇	1	8	yes	—
392	#102	C₂³×C₇	1	8	yes	complemented
393	#102	C₂³×C₇	1	8	yes	complemented
394	#102	C₂³×C₇	1	4	yes	complemented
395	#102	C₂³×C₇	1	8	yes	complemented
396	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
397	C₄×C₈	C₂³×C₇	1	4	yes	complemented
398	C₂²×C₇	—	2	4	no	—
399	C₂²×C₇	—	2	4	no	—
400	C₂²×C₇	—	2	4	no	—
401	C₂²×C₇	—	2	4	no	—
402	C₂²×C₇	—	4	2	no	—
403	C₂²×C₇	—	4	8	no	—
404	C₂²×C₇	—	4	8	no	—
405	C₂²×C₇	—	4	2	no	—
406	C₂²×C₇	—	4	4	no	—
407	C₂²×C₇	—	4	2	no	—
408	C₂²×C₇	—	4	2	no	—
409	C₂²×C₇	—	4	4	no	—
410	C₂²×C₇	—	4	2	no	—
411	C₂²×C₇	—	4	4	no	—
412	C₂²×C₇	—	8	32	no	—
413	C₂²×C₇	—	8	4	no	—
414	C₂²×C₇	—	8	8	no	—
415	C₂²×C₇	#546	1	2	yes	—
416	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
417	C₂²×C₇	#576	1	2	yes	—
418	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
419	C₄×C₇	—	2	4	no	—
420	C₄×C₇	—	2	2	no	—
421	C₄×C₇	—	4	2	no	—
422	C₄×C₇	—	4	2	no	—
423	C₄×C₇	—	4	4	no	—
424	C₄×C₇	#546	1	2	yes	—
425	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
426	C₄×C₇	C₂²×#41	1	1	yes	characteristic
427	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
428	C₂⁴	—	2	1	no	—
429	C₂⁴	—	2	1	no	—
430	C₂⁴	—	2	2	no	—
431	C₂⁴	—	2	8	no	—
432	C₂⁴	—	4	8	no	—
433	C₂⁴	—	4	8	no	—
434	C₂⁴	—	8	4	no	—
435	C₂⁴	C₂×C₇×D₄	1	2	yes	—
436	C₂×Q₈	—	2	4	no	—
437	C₂×Q₈	—	8	2	no	—
438	C₂×D₄	—	2	16	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	4	no	—
453	C₂×D₄	—	4	8	no	—
454	C₂×D₄	—	4	16	no	—
455	C₂×D₄	—	4	8	no	—
456	C₂×D₄	—	4	32	no	—
457	C₂×D₄	—	4	8	no	—
458	C₂×D₄	—	4	4	no	—
459	C₂×D₄	—	8	2	no	—
460	C₂×D₄	—	8	4	no	—
461	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
462	C₂×D₄	C₇×#41	1	4	yes	—
463	C₂×D₄	C₂⁴×C₇	1	4	yes	—
464	C₂×D₄	C₂⁴×C₇	1	2	yes	—
465	C₂×D₄	C₂⁴×C₇	1	2	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	4	4	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
476	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
478	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
481	D₈	—	2	8	no	—
482	D₈	—	4	8	no	—
483	M₁₆	—	4	8	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	4	no	—
487	C₂×C₈	C₂⁴×C₇	1	2	yes	—
488	C₂×C₈	C₂⁴×C₇	1	2	yes	—
489	C₂×C₈	C₂⁴×C₇	1	4	yes	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
497	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
498	C₂²⋊C₄	—	2	8	no	—
499	C₂²⋊C₄	—	2	8	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	8	no	—
503	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
504	C₄²	—	2	8	no	—
505	C₄²	C₂×C₇×D₄	1	2	yes	—
506	C₄²	C₂⁴×C₇	1	2	yes	—
507	C₂×C₇	—	4	4	no	—
508	C₂×C₇	—	4	4	no	—
509	C₂×C₇	—	8	2	no	—
510	C₂×C₇	—	8	4	no	—
511	C₂×C₇	#3325	1	4	yes	direct product factor
512	C₂×C₇	C₂×#546	1	1	yes	characteristic
513	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
514	C₂×C₇	C₂×#576	1	1	yes	characteristic
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	4	no	—
520	C₂³	—	2	2	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	4	16	no	—
523	C₂³	—	4	16	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	4	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	4	no	—
532	C₂³	—	8	8	no	—
533	C₂³	—	8	32	no	—
534	C₂³	C₂²×C₇×D₄	1	4	yes	—
535	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
536	Q₈	—	8	4	no	—
537	D₄	—	2	2	no	—
538	D₄	—	2	4	no	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	8	no	—
544	D₄	—	4	16	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	8	no	—
549	D₄	—	8	4	no	—
550	D₄	—	8	8	no	—
551	D₄	C₂×C₇×#41	1	4	yes	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	4	8	no	—
565	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
566	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
567	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
568	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
569	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
570	C₂×C₄	C₂×C₇×#41	1	2	yes	—
571	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
572	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
573	C₈	—	2	2	no	—
574	C₈	—	2	2	no	—
575	C₈	—	2	4	no	—
576	C₇	C₂×#3325	1	1	yes	characteristic, direct product factor, Sylow
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	8	no	—
584	C₂²	—	4	8	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	8	32	no	—
592	C₂²	—	8	8	no	—
593	C₂²	—	8	4	no	—
594	C₂²	C₇×#546	1	2	yes	—
595	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
596	C₂²	C₇×#576	1	2	yes	—
597	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
598	C₄	—	2	2	no	—
599	C₄	—	2	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	C₇×#546	1	2	yes	—
604	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
605	C₄	C₂²×C₇×#41	1	1	yes	characteristic
606	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂	—	4	4	no	—
608	C₂	—	4	4	no	—
609	C₂	—	8	4	no	—
610	C₂	—	8	2	no	—
611	C₂	C₇×#3325	1	4	yes	direct product factor
612	C₂	C₂×C₇×#546	1	1	yes	characteristic
613	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
614	C₂	C₂×C₇×#576	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×D₄²	C₂	semidirect
3. C₇×#3325	C₂	direct (N × H)
4. C₂×C₇×#486	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#469	C₂	semidirect
8. C₂×C₇×#459	C₂	semidirect
9. C₂×C₇×#447	C₂	semidirect
10. C₂×C₄×C₇×D₈	C₂	semidirect
11. C₂×C₇×#436	C₂	semidirect
12. C₂×C₇×#418	C₂	semidirect
16. C₂²×C₇×D₈	C₂²	semidirect
17. C₂²×C₇×M₁₆	C₂²	semidirect
19. C₇×#555	C₂²	semidirect
21. C₇×D₄²	C₂²	semidirect
22. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
28. C₂×C₇×#121	C₂²	semidirect
32. C₂×C₄×C₇×D₄	C₂²	semidirect
34. C₂×C₇×#117	C₂²	semidirect
35. C₇×#486	C₂²	semidirect
36. C₇×#482	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#469	C₂²	semidirect
39. C₇×#459	C₂²	semidirect
40. C₇×#447	C₂²	semidirect
41. C₄×C₇×D₈	C₂²	semidirect
42. C₇×#436	C₂²	semidirect
43. C₂×C₇×#107	C₂²	semidirect
44. C₂×C₇×#106	C₂²	semidirect
45. C₂×C₇×C₄⋊C₈	C₂²	semidirect
46. C₇×#418	C₂²	semidirect
49. C₂×C₇×#102	C₂²	semidirect
50. C₂×C₇×#102	C₂²	semidirect
51. C₂×C₇×#102	C₂²	semidirect
52. C₂×C₇×#102	C₂²	semidirect
53. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₇×C₈	C₂²	semidirect
55. C₂×#3325	C₇	direct (N × H)
79. C₂×C₇×D₈	C₂³	semidirect
81. C₂×C₇×M₁₆	C₂³	semidirect
86. C₇×C₄⋊Q₈	C₂³	semidirect
95. C₇×#121	C₂³	semidirect
102. C₄×C₇×D₄	C₂³	semidirect
105. C₇×#117	C₂³	semidirect
119. C₇×#107	C₂³	semidirect
120. C₇×#106	C₂³	semidirect
121. C₇×C₄⋊C₈	C₂³	semidirect
124. C₇×#102	C₂³	semidirect
125. C₇×#102	C₂³	semidirect
126. C₇×#102	C₂³	semidirect
127. C₇×#102	C₂³	semidirect
128. C₇×C₂²⋊C₈	C₂³	semidirect
129. C₄×C₇×C₈	C₂³	semidirect
130. C₂×#555	C₂×C₇	semidirect
131. C₂×D₄²	C₂×C₇	semidirect
132. #3325	C₂×C₇	direct (N × H)
133. C₂×#486	C₂×C₇	semidirect
134. C₂×#482	C₂×C₇	semidirect
135. C₂×#476	C₂×C₇	semidirect
136. C₂×#469	C₂×C₇	semidirect
137. C₂×#459	C₂×C₇	semidirect
138. C₂×#447	C₂×C₇	semidirect
139. C₂×C₄×D₈	C₂×C₇	semidirect
140. C₂×#436	C₂×C₇	semidirect
141. C₂×#418	C₂×C₇	semidirect
224. C₂²×D₈	C₂²×C₇	semidirect
225. C₂²×M₁₆	C₂²×C₇	semidirect
227. #555	C₂²×C₇	semidirect
229. D₄²	C₂²×C₇	semidirect
230. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
236. C₂×#121	C₂²×C₇	semidirect
240. C₂×C₄×D₄	C₂²×C₇	semidirect
242. C₂×#117	C₂²×C₇	semidirect
243. #486	C₂²×C₇	semidirect
244. #482	C₂²×C₇	semidirect
245. #476	C₂²×C₇	semidirect
246. #469	C₂²×C₇	semidirect
247. #459	C₂²×C₇	semidirect
248. #447	C₂²×C₇	semidirect
249. C₄×D₈	C₂²×C₇	semidirect
250. #436	C₂²×C₇	semidirect
251. C₂×#107	C₂²×C₇	semidirect
252. C₂×#106	C₂²×C₇	semidirect
253. C₂×C₄⋊C₈	C₂²×C₇	semidirect
254. #418	C₂²×C₇	semidirect
257. C₂×#102	C₂²×C₇	semidirect
258. C₂×#102	C₂²×C₇	semidirect
259. C₂×#102	C₂²×C₇	semidirect
260. C₂×#102	C₂²×C₇	semidirect
261. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
262. C₂×C₄×C₈	C₂²×C₇	semidirect
347. C₂×D₈	C₂³×C₇	semidirect
349. C₂×M₁₆	C₂³×C₇	semidirect
354. C₄⋊Q₈	C₂³×C₇	semidirect
363. #121	C₂³×C₇	semidirect
370. C₄×D₄	C₂³×C₇	semidirect
373. #117	C₂³×C₇	semidirect
387. #107	C₂³×C₇	semidirect
388. #106	C₂³×C₇	semidirect
389. C₄⋊C₈	C₂³×C₇	semidirect
392. #102	C₂³×C₇	semidirect
393. #102	C₂³×C₇	semidirect
394. #102	C₂³×C₇	semidirect
395. #102	C₂³×C₇	semidirect
396. C₂²⋊C₈	C₂³×C₇	semidirect
397. C₄×C₈	C₂³×C₇	semidirect
511. C₂×C₇	#3325	direct (N × H)
576. C₇	C₂×#3325	direct (N × H)
611. C₂	C₇×#3325	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×D₄²	2
C₇×#3325	2
C₂×C₇×#486	2
C₂×C₇×#482	2
C₂×C₇×#476	2
C₂×C₇×#469	2
C₂×C₇×#459	2
C₂×C₇×#447	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#436	2
C₂×C₇×#418	2
C₂×#3325	7

Subgroups — C2×C7×#3325 #13238361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3325 #13238361