Subgroups — C₇×#60495 #13237711

Order 1792.

2090 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₇×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic
3	C₇×#3084	C₂	1	6	yes	maximal, complemented
4	C₇×#3081	C₂	1	6	yes	maximal, complemented
5	C₇×#3079	C₂	1	3	yes	maximal, complemented
6	C₇×#3077	C₂	1	3	yes	maximal, complemented
7	C₇×#3076	C₂	1	3	yes	maximal, complemented
8	C₂×C₇×#476	C₂	1	3	yes	maximal, complemented
9	C₇×#2912	C₂	1	2	yes	maximal, complemented
10	C₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2897	C₂	1	2	yes	maximal
12	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	C₇×Q₈²	—	2	1	no	—
15	C₇×#557	—	2	1	no	—
16	C₇×#554	—	2	3	no	—
17	C₇×D₄×Q₈	—	2	3	no	—
18	C₇×#544	C₂²	1	6	yes	complemented
19	C₇×#533	C₂²	1	3	yes	complemented
20	C₂×C₇×C₄⋊Q₈	C₂²	1	3	yes	complemented
21	C₇×#520	—	2	1	no	—
22	C₇×#520	C₂²	1	3	yes	—
23	C₇×#520	C₂²	1	1	yes	characteristic
24	C₇×#520	C₂²	1	2	yes	—
25	C₇×#518	—	2	3	no	—
26	C₇×#518	C₂²	1	3	yes	—
27	C₄×C₇×#41	—	2	1	no	—
28	C₄×C₇×#41	C₂²	1	3	yes	—
29	C₄×C₇×#41	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	—	2	3	no	—
31	C₂×C₄×C₇×D₄	C₂²	1	3	yes	—
32	C₇×#479	C₂²	1	6	yes	complemented
33	C₇×#478	C₂²	1	6	yes	complemented
34	C₇×#478	C₂²	1	12	yes	complemented
35	C₇×#477	C₂²	1	3	yes	complemented
36	C₇×#476	C₂²	1	3	yes	complemented
37	C₇×#476	C₂²	1	6	yes	complemented
38	C₇×#476	C₂²	1	12	yes	complemented
39	C₇×#475	C₂²	1	1	yes	characteristic, complemented
40	C₇×#475	C₂²	1	6	yes	complemented
41	C₇×#474	C₂²	1	3	yes	complemented
42	C₇×#474	C₂²	1	6	yes	complemented
43	C₇×#428	C₂²	1	6	yes	complemented
44	C₇×#428	C₂²	1	6	yes	complemented
45	C₇×#427	C₂²	1	6	yes	complemented
46	C₂×C₇×#106	C₂²	1	6	yes	complemented
47	C₇×#424	C₂²	1	6	yes	complemented
48	C₇×#423	C₂²	1	3	yes	complemented
49	C₂×C₇×C₄⋊C₈	C₂²	1	3	yes	complemented
50	C₇×#418	C₂²	1	6	yes	—
51	C₇×#417	C₂²	1	6	yes	—
52	C₇×#416	C₂²	1	6	yes	—
53	C₂×C₇×#102	C₂²	1	6	yes	—
54	#60495	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₇×H(5,𝔽₂)	—	2	4	no	—
56	C₇×H(5,𝔽₂)	Q₈	1	8	yes	complemented
57	C₂×C₇×#41	—	2	1	no	—
58	C₂×C₇×#41	C₂³	1	3	yes	—
59	C₂×C₇×#41	C₂³	1	1	yes	characteristic
60	C₂²×C₇×Q₈	—	2	3	no	—
61	C₂²×C₇×D₄	—	2	3	no	—
62	C₂²×C₇×D₄	C₂³	1	3	yes	—
63	C₂³×C₄×C₇	—	2	3	no	—
64	C₇×#131	—	2	8	no	—
65	C₂×C₇×M₁₆	C₂³	1	6	yes	—
66	C₂²×C₇×C₈	C₂³	1	6	yes	—
67	C₇×C₄⋊Q₈	—	2	6	no	—
68	C₇×C₄⋊Q₈	—	2	3	no	—
69	C₇×C₄⋊Q₈	—	2	3	no	—
70	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
72	C₇×C₄⋊Q₈	C₂³	1	3	yes	—
73	C₇×#125	—	2	6	no	—
74	C₇×#125	C₂³	1	6	yes	—
75	C₇×C₂²⋊Q₈	—	2	3	no	—
76	C₇×C₂²⋊Q₈	—	2	3	no	—
77	C₇×C₂²⋊Q₈	—	2	12	no	—
78	C₄×C₇×Q₈	—	2	1	no	—
79	C₄×C₇×Q₈	—	2	2	no	—
80	C₄×C₇×Q₈	—	2	3	no	—
81	C₄×C₇×Q₈	—	2	3	no	—
82	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
83	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
84	C₄×C₇×Q₈	C₂³	1	3	yes	—
85	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₄×C₇×D₄	—	2	3	no	—
87	C₄×C₇×D₄	—	2	6	no	—
88	C₄×C₇×D₄	—	2	3	no	—
89	C₄×C₇×D₄	—	2	3	no	—
90	C₄×C₇×D₄	—	2	3	no	—
91	C₄×C₇×D₄	—	2	3	no	—
92	C₄×C₇×D₄	—	2	6	no	—
93	C₄×C₇×D₄	—	2	3	no	—
94	C₄×C₇×D₄	—	2	3	no	—
95	C₄×C₇×D₄	D₄	1	3	yes	—
96	C₄×C₇×D₄	D₄	1	3	yes	—
97	C₄×C₇×D₄	C₂³	1	3	yes	—
98	C₄×C₇×D₄	C₂³	1	3	yes	—
99	C₄×C₇×D₄	C₂³	1	6	yes	—
100	C₇×#117	—	2	3	no	—
101	C₇×#117	—	2	3	no	—
102	C₇×#117	C₂³	1	3	yes	—
103	C₇×#117	C₂³	1	6	yes	—
104	C₇×#117	C₂³	1	3	yes	—
105	C₂×C₇×C₄⋊C₄	—	2	3	no	—
106	C₂×C₇×C₄⋊C₄	—	2	3	no	—
107	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
109	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	6	no	—
111	C₂×C₄²×C₇	—	2	3	no	—
112	C₂×C₄²×C₇	C₂³	1	3	yes	—
113	C₇×#107	C₂³	1	6	yes	—
114	C₇×#107	C₂³	1	6	yes	—
115	C₇×#106	C₂³	1	12	yes	—
116	C₇×#106	C₂³	1	2	yes	—
117	C₇×#106	C₂³	1	6	yes	—
118	C₇×C₄⋊C₈	C₂³	1	6	yes	—
119	C₇×C₄⋊C₈	C₂³	1	3	yes	—
120	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₇×C₄⋊C₈	C₂³	1	6	yes	—
122	C₇×#103	C₂³	1	6	yes	—
123	C₇×#103	C₂³	1	2	yes	—
124	C₇×#102	C₂³	1	12	yes	—
125	C₇×#102	C₂³	1	6	yes	—
126	C₇×#102	C₂³	1	6	yes	—
127	#3503	C₂×C₇	1	1	yes	characteristic, complemented
128	C₄×H(5,𝔽₂)	C₂×C₇	1	1	yes	characteristic
129	#3084	C₂×C₇	1	6	yes	complemented
130	#3081	C₂×C₇	1	6	yes	complemented
131	#3079	C₂×C₇	1	3	yes	complemented
132	#3077	C₂×C₇	1	3	yes	complemented
133	#3076	C₂×C₇	1	3	yes	complemented
134	C₂×#476	C₂×C₇	1	3	yes	complemented
135	#2912	C₂×C₇	1	2	yes	complemented
136	#2906	C₂×C₇	1	1	yes	characteristic, complemented
137	#2897	C₂×C₇	1	2	yes	—
138	C₂⁴×C₇	—	2	3	no	—
139	C₇×#41	—	2	8	no	—
140	C₇×#41	—	2	6	no	—
141	C₇×#41	C₂×Q₈	1	4	yes	—
142	C₇×#41	C₂×Q₈	1	12	yes	complemented
143	C₇×#41	#41	1	4	yes	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	—	2	3	no	—
146	C₂×C₇×Q₈	—	2	6	no	—
147	C₂×C₇×Q₈	—	8	6	no	—
148	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
150	C₂×C₇×D₄	—	2	3	no	—
151	C₂×C₇×D₄	—	2	24	no	—
152	C₂×C₇×D₄	—	2	3	no	—
153	C₂×C₇×D₄	—	2	6	no	—
154	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
155	C₂×C₇×D₄	C₂×Q₈	1	12	yes	complemented
156	C₂×C₇×D₄	C₂⁴	1	3	yes	—
157	C₂²×C₄×C₇	—	2	3	no	—
158	C₂²×C₄×C₇	—	2	3	no	—
159	C₂²×C₄×C₇	—	2	6	no	—
160	C₂²×C₄×C₇	—	2	3	no	—
161	C₂²×C₄×C₇	—	2	3	no	—
162	C₂²×C₄×C₇	—	2	6	no	—
163	C₂²×C₄×C₇	—	8	6	no	—
164	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
165	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
166	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
167	C₇×M₁₆	—	2	12	no	—
168	C₂×C₇×C₈	—	2	12	no	—
169	C₂×C₇×C₈	C₂⁴	1	2	yes	—
170	C₂×C₇×C₈	C₂⁴	1	6	yes	—
171	C₇×C₄⋊C₄	—	2	3	no	—
172	C₇×C₄⋊C₄	—	2	3	no	—
173	C₇×C₄⋊C₄	—	2	3	no	—
174	C₇×C₄⋊C₄	—	2	6	no	—
175	C₇×C₄⋊C₄	—	2	6	no	—
176	C₇×C₄⋊C₄	—	2	1	no	—
177	C₇×C₄⋊C₄	—	2	1	no	—
178	C₇×C₄⋊C₄	—	2	6	no	—
179	C₇×C₄⋊C₄	—	2	6	no	—
180	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
181	C₇×C₄⋊C₄	C₂×D₄	1	3	yes	—
182	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
183	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
184	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
185	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
186	C₇×C₂²⋊C₄	—	2	3	no	—
187	C₇×C₂²⋊C₄	—	2	6	no	—
188	C₇×C₂²⋊C₄	—	2	3	no	—
189	C₇×C₂²⋊C₄	—	2	6	no	—
190	C₇×C₂²⋊C₄	—	2	3	no	—
191	C₇×C₂²⋊C₄	C₂×D₄	1	6	yes	—
192	C₄²×C₇	—	2	1	no	—
193	C₄²×C₇	—	2	3	no	—
194	C₄²×C₇	—	2	3	no	—
195	C₄²×C₇	—	2	6	no	—
196	C₄²×C₇	C₂×D₄	1	3	yes	—
197	C₄²×C₇	C₂×D₄	1	3	yes	—
198	C₄²×C₇	C₂⁴	1	1	yes	characteristic
199	C₄²×C₇	C₂⁴	1	3	yes	—
200	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
201	C₂×#131	C₂²×C₇	1	2	yes	—
202	Q₈²	—	2	1	no	—
203	#557	—	2	1	no	—
204	#554	—	2	3	no	—
205	D₄×Q₈	—	2	3	no	—
206	#544	C₂²×C₇	1	6	yes	complemented
207	#533	C₂²×C₇	1	3	yes	complemented
208	C₂×C₄⋊Q₈	C₂²×C₇	1	3	yes	complemented
209	#520	—	2	1	no	—
210	#520	C₂²×C₇	1	3	yes	—
211	#520	C₂²×C₇	1	2	yes	—
212	#520	C₂²×C₇	1	1	yes	characteristic
213	#518	—	2	3	no	—
214	#518	C₂²×C₇	1	3	yes	—
215	C₄×#41	—	2	1	no	—
216	C₄×#41	C₂²×C₇	1	3	yes	—
217	C₄×#41	C₂²×C₇	1	1	yes	characteristic
218	C₂×C₄×D₄	—	2	3	no	—
219	C₂×C₄×D₄	C₂²×C₇	1	3	yes	—
220	#479	C₂²×C₇	1	6	yes	complemented
221	#478	C₂²×C₇	1	6	yes	complemented
222	#478	C₂²×C₇	1	12	yes	complemented
223	#477	C₂²×C₇	1	3	yes	complemented
224	#476	C₂²×C₇	1	3	yes	complemented
225	#476	C₂²×C₇	1	6	yes	complemented
226	#476	C₂²×C₇	1	12	yes	complemented
227	#475	C₂²×C₇	1	1	yes	characteristic, complemented
228	#475	C₂²×C₇	1	6	yes	complemented
229	#474	C₂²×C₇	1	3	yes	complemented
230	#474	C₂²×C₇	1	6	yes	complemented
231	#428	C₂²×C₇	1	6	yes	complemented
232	#428	C₂²×C₇	1	6	yes	complemented
233	#427	C₂²×C₇	1	6	yes	complemented
234	C₂×#106	C₂²×C₇	1	6	yes	complemented
235	#424	C₂²×C₇	1	6	yes	complemented
236	#423	C₂²×C₇	1	3	yes	complemented
237	C₂×C₄⋊C₈	C₂²×C₇	1	3	yes	complemented
238	#418	C₂²×C₇	1	6	yes	—
239	#417	C₂²×C₇	1	6	yes	—
240	#416	C₂²×C₇	1	6	yes	—
241	C₂×#102	C₂²×C₇	1	6	yes	—
242	C₂³×C₇	—	2	3	no	—
243	C₂³×C₇	—	2	12	no	—
244	C₂³×C₇	—	8	3	no	—
245	C₂³×C₇	—	8	3	no	—
246	C₂³×C₇	C₂²×D₄	1	3	yes	—
247	C₇×Q₈	—	2	1	no	—
248	C₇×Q₈	—	4	6	no	—
249	C₇×Q₈	—	4	2	no	—
250	C₇×Q₈	—	8	6	no	—
251	C₇×Q₈	C₂²⋊Q₈	1	4	yes	—
252	C₇×Q₈	C₂²×Q₈	1	2	yes	—
253	C₇×D₄	—	2	12	no	—
254	C₇×D₄	—	2	12	no	—
255	C₇×D₄	—	2	3	no	—
256	C₇×D₄	C₂²⋊Q₈	1	12	yes	—
257	C₇×D₄	C₂²×Q₈	1	6	yes	—
258	C₂×C₄×C₇	—	2	1	no	—
259	C₂×C₄×C₇	—	2	12	no	—
260	C₂×C₄×C₇	—	2	6	no	—
261	C₂×C₄×C₇	—	2	1	no	—
262	C₂×C₄×C₇	—	2	2	no	—
263	C₂×C₄×C₇	—	2	3	no	—
264	C₂×C₄×C₇	—	2	6	no	—
265	C₂×C₄×C₇	—	4	3	no	—
266	C₂×C₄×C₇	—	4	6	no	—
267	C₂×C₄×C₇	—	8	3	no	—
268	C₂×C₄×C₇	—	8	6	no	—
269	C₂×C₄×C₇	—	8	3	no	—
270	C₂×C₄×C₇	—	8	6	no	—
271	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
272	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
274	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
275	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₇	C₂²×Q₈	1	6	yes	—
277	C₂×C₄×C₇	C₂×#41	1	6	yes	—
278	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
279	C₇×C₈	—	2	2	no	—
280	C₇×C₈	—	2	6	no	—
281	H(5,𝔽₂)	—	2	4	no	—
282	H(5,𝔽₂)	C₇×Q₈	1	8	yes	complemented
283	C₂×#41	—	2	1	no	—
284	C₂×#41	C₂³×C₇	1	3	yes	—
285	C₂×#41	C₂³×C₇	1	1	yes	characteristic
286	C₂²×Q₈	—	2	3	no	—
287	C₂²×D₄	—	2	3	no	—
288	C₂²×D₄	C₂³×C₇	1	3	yes	—
289	C₂³×C₄	—	2	3	no	—
290	#131	—	2	8	no	—
291	C₂×M₁₆	C₂³×C₇	1	6	yes	—
292	C₂²×C₈	C₂³×C₇	1	6	yes	—
293	C₄⋊Q₈	—	2	6	no	—
294	C₄⋊Q₈	—	2	3	no	—
295	C₄⋊Q₈	—	2	3	no	—
296	C₄⋊Q₈	C₂³×C₇	1	3	yes	—
297	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
298	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
299	#125	—	2	6	no	—
300	#125	C₂³×C₇	1	6	yes	—
301	C₂²⋊Q₈	—	2	3	no	—
302	C₂²⋊Q₈	—	2	3	no	—
303	C₂²⋊Q₈	—	2	12	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	3	no	—
307	C₄×Q₈	—	2	3	no	—
308	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
309	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
310	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
311	C₄×Q₈	C₂³×C₇	1	3	yes	—
312	C₄×D₄	—	2	3	no	—
313	C₄×D₄	—	2	6	no	—
314	C₄×D₄	—	2	3	no	—
315	C₄×D₄	—	2	3	no	—
316	C₄×D₄	—	2	3	no	—
317	C₄×D₄	—	2	3	no	—
318	C₄×D₄	—	2	6	no	—
319	C₄×D₄	—	2	3	no	—
320	C₄×D₄	—	2	3	no	—
321	C₄×D₄	C₇×D₄	1	3	yes	—
322	C₄×D₄	C₇×D₄	1	3	yes	—
323	C₄×D₄	C₂³×C₇	1	3	yes	—
324	C₄×D₄	C₂³×C₇	1	6	yes	—
325	C₄×D₄	C₂³×C₇	1	3	yes	—
326	#117	—	2	3	no	—
327	#117	—	2	3	no	—
328	#117	C₂³×C₇	1	3	yes	—
329	#117	C₂³×C₇	1	6	yes	—
330	#117	C₂³×C₇	1	3	yes	—
331	C₂×C₄⋊C₄	—	2	3	no	—
332	C₂×C₄⋊C₄	—	2	3	no	—
333	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
335	C₂×C₂²⋊C₄	—	2	3	no	—
336	C₂×C₂²⋊C₄	—	2	6	no	—
337	C₂×C₄²	—	2	3	no	—
338	C₂×C₄²	C₂³×C₇	1	3	yes	—
339	#107	C₂³×C₇	1	6	yes	—
340	#107	C₂³×C₇	1	6	yes	—
341	#106	C₂³×C₇	1	6	yes	—
342	#106	C₂³×C₇	1	12	yes	—
343	#106	C₂³×C₇	1	2	yes	—
344	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
345	C₄⋊C₈	C₂³×C₇	1	3	yes	—
346	C₄⋊C₈	C₂³×C₇	1	6	yes	—
347	C₄⋊C₈	C₂³×C₇	1	6	yes	—
348	#103	C₂³×C₇	1	2	yes	—
349	#103	C₂³×C₇	1	6	yes	—
350	#102	C₂³×C₇	1	6	yes	—
351	#102	C₂³×C₇	1	12	yes	—
352	#102	C₂³×C₇	1	6	yes	—
353	C₂²×C₇	—	2	3	no	—
354	C₂²×C₇	—	2	3	no	—
355	C₂²×C₇	—	2	6	no	—
356	C₂²×C₇	—	4	3	no	—
357	C₂²×C₇	—	4	3	no	—
358	C₂²×C₇	—	8	12	no	—
359	C₂²×C₇	C₂×C₂²⋊Q₈	1	6	yes	—
360	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
361	C₄×C₇	—	2	1	no	—
362	C₄×C₇	—	2	3	no	—
363	C₄×C₇	—	2	2	no	—
364	C₄×C₇	—	2	3	no	—
365	C₄×C₇	—	4	1	no	—
366	C₄×C₇	—	4	6	no	—
367	C₄×C₇	—	4	3	no	—
368	C₄×C₇	—	4	2	no	—
369	C₄×C₇	C₂×C₂²⋊Q₈	1	6	yes	—
370	C₄×C₇	#577	1	2	yes	—
371	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
372	C₄×C₇	C₂²×#41	1	1	yes	characteristic
373	C₂⁴	—	2	3	no	—
374	#41	—	2	8	no	—
375	#41	—	2	6	no	—
376	#41	C₂×C₇×Q₈	1	4	yes	—
377	#41	C₂×C₇×Q₈	1	12	yes	complemented
378	#41	C₇×#41	1	4	yes	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	3	no	—
381	C₂×Q₈	—	2	6	no	—
382	C₂×Q₈	—	8	6	no	—
383	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
385	C₂×D₄	—	2	3	no	—
386	C₂×D₄	—	2	24	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	2	6	no	—
389	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
390	C₂×D₄	C₂×C₇×Q₈	1	12	yes	complemented
391	C₂×D₄	C₂⁴×C₇	1	3	yes	—
392	C₂²×C₄	—	2	3	no	—
393	C₂²×C₄	—	2	3	no	—
394	C₂²×C₄	—	2	6	no	—
395	C₂²×C₄	—	2	3	no	—
396	C₂²×C₄	—	2	3	no	—
397	C₂²×C₄	—	2	6	no	—
398	C₂²×C₄	—	8	6	no	—
399	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
400	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
401	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
402	M₁₆	—	2	12	no	—
403	C₂×C₈	—	2	12	no	—
404	C₂×C₈	C₂⁴×C₇	1	2	yes	—
405	C₂×C₈	C₂⁴×C₇	1	6	yes	—
406	C₄⋊C₄	—	2	3	no	—
407	C₄⋊C₄	—	2	3	no	—
408	C₄⋊C₄	—	2	3	no	—
409	C₄⋊C₄	—	2	6	no	—
410	C₄⋊C₄	—	2	6	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	6	no	—
414	C₄⋊C₄	—	2	6	no	—
415	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
416	C₄⋊C₄	C₂×C₇×D₄	1	3	yes	—
417	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
418	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
419	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
420	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
421	C₂²⋊C₄	—	2	3	no	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	6	no	—
425	C₂²⋊C₄	—	2	3	no	—
426	C₂²⋊C₄	C₂×C₇×D₄	1	6	yes	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	3	no	—
429	C₄²	—	2	3	no	—
430	C₄²	—	2	6	no	—
431	C₄²	C₂×C₇×D₄	1	3	yes	—
432	C₄²	C₂×C₇×D₄	1	3	yes	—
433	C₄²	C₂⁴×C₇	1	1	yes	characteristic
434	C₄²	C₂⁴×C₇	1	3	yes	—
435	C₂×C₇	—	2	6	no	—
436	C₂×C₇	—	4	6	no	—
437	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
438	C₂×C₇	C₂×#577	1	1	yes	characteristic
439	C₂×C₇	#3585	1	1	yes	characteristic
440	C₂³	—	2	3	no	—
441	C₂³	—	2	12	no	—
442	C₂³	—	8	3	no	—
443	C₂³	—	8	3	no	—
444	C₂³	C₂²×C₇×D₄	1	3	yes	—
445	Q₈	—	2	1	no	—
446	Q₈	—	4	6	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	8	6	no	—
449	Q₈	C₇×C₂²⋊Q₈	1	4	yes	—
450	Q₈	C₂²×C₇×Q₈	1	2	yes	—
451	D₄	—	2	12	no	—
452	D₄	—	2	3	no	—
453	D₄	—	2	12	no	—
454	D₄	C₇×C₂²⋊Q₈	1	12	yes	—
455	D₄	C₂²×C₇×Q₈	1	6	yes	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	12	no	—
458	C₂×C₄	—	2	6	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	4	3	no	—
464	C₂×C₄	—	4	6	no	—
465	C₂×C₄	—	8	3	no	—
466	C₂×C₄	—	8	6	no	—
467	C₂×C₄	—	8	3	no	—
468	C₂×C₄	—	8	6	no	—
469	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
470	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
472	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
473	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
474	C₂×C₄	C₂²×C₇×Q₈	1	6	yes	—
475	C₂×C₄	C₂×C₇×#41	1	6	yes	—
476	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
477	C₈	—	2	2	no	—
478	C₈	—	2	6	no	—
479	C₇	#60495	1	1	yes	characteristic, direct product factor, Sylow
480	C₂²	—	2	3	no	—
481	C₂²	—	2	3	no	—
482	C₂²	—	2	6	no	—
483	C₂²	—	4	3	no	—
484	C₂²	—	4	3	no	—
485	C₂²	—	8	12	no	—
486	C₂²	C₂×C₇×C₂²⋊Q₈	1	6	yes	—
487	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
488	C₄	—	2	3	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	3	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	3	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	6	no	—
496	C₄	C₂×C₇×C₂²⋊Q₈	1	6	yes	—
497	C₄	C₇×#577	1	2	yes	—
498	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
499	C₄	C₂²×C₇×#41	1	1	yes	characteristic
500	C₂	—	2	6	no	—
501	C₂	—	4	6	no	—
502	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
503	C₂	C₂×C₇×#577	1	1	yes	characteristic
504	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×H(5,𝔽₂)	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3503	C₂	semidirect
3. C₇×#3084	C₂	semidirect
4. C₇×#3081	C₂	semidirect
5. C₇×#3079	C₂	semidirect
6. C₇×#3077	C₂	semidirect
7. C₇×#3076	C₂	semidirect
8. C₂×C₇×#476	C₂	semidirect
9. C₇×#2912	C₂	semidirect
10. C₇×#2906	C₂	semidirect
18. C₇×#544	C₂²	semidirect
19. C₇×#533	C₂²	semidirect
20. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
32. C₇×#479	C₂²	semidirect
33. C₇×#478	C₂²	semidirect
34. C₇×#478	C₂²	semidirect
35. C₇×#477	C₂²	semidirect
36. C₇×#476	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#476	C₂²	semidirect
39. C₇×#475	C₂²	semidirect
40. C₇×#475	C₂²	semidirect
41. C₇×#474	C₂²	semidirect
42. C₇×#474	C₂²	semidirect
43. C₇×#428	C₂²	semidirect
44. C₇×#428	C₂²	semidirect
45. C₇×#427	C₂²	semidirect
46. C₂×C₇×#106	C₂²	semidirect
47. C₇×#424	C₂²	semidirect
48. C₇×#423	C₂²	semidirect
49. C₂×C₇×C₄⋊C₈	C₂²	semidirect
54. #60495	C₇	direct (N × H)
56. C₇×H(5,𝔽₂)	Q₈	semidirect
127. #3503	C₂×C₇	semidirect
129. #3084	C₂×C₇	semidirect
130. #3081	C₂×C₇	semidirect
131. #3079	C₂×C₇	semidirect
132. #3077	C₂×C₇	semidirect
133. #3076	C₂×C₇	semidirect
134. C₂×#476	C₂×C₇	semidirect
135. #2912	C₂×C₇	semidirect
136. #2906	C₂×C₇	semidirect
142. C₇×#41	C₂×Q₈	semidirect
155. C₂×C₇×D₄	C₂×Q₈	semidirect
206. #544	C₂²×C₇	semidirect
207. #533	C₂²×C₇	semidirect
208. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
220. #479	C₂²×C₇	semidirect
221. #478	C₂²×C₇	semidirect
222. #478	C₂²×C₇	semidirect
223. #477	C₂²×C₇	semidirect
224. #476	C₂²×C₇	semidirect
225. #476	C₂²×C₇	semidirect
226. #476	C₂²×C₇	semidirect
227. #475	C₂²×C₇	semidirect
228. #475	C₂²×C₇	semidirect
229. #474	C₂²×C₇	semidirect
230. #474	C₂²×C₇	semidirect
231. #428	C₂²×C₇	semidirect
232. #428	C₂²×C₇	semidirect
233. #427	C₂²×C₇	semidirect
234. C₂×#106	C₂²×C₇	semidirect
235. #424	C₂²×C₇	semidirect
236. #423	C₂²×C₇	semidirect
237. C₂×C₄⋊C₈	C₂²×C₇	semidirect
282. H(5,𝔽₂)	C₇×Q₈	semidirect
377. #41	C₂×C₇×Q₈	semidirect
390. C₂×D₄	C₂×C₇×Q₈	semidirect
479. C₇	#60495	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3503	2
C₄×C₇×H(5,𝔽₂)	2
C₇×#3084	2
C₇×#3081	2
C₇×#3079	2
C₇×#3077	2
C₇×#3076	2
C₂×C₇×#476	2
C₇×#2912	2
C₇×#2906	2
C₇×#2897	2
#60495	7

Subgroups — C7×#60495 #13237711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60495 #13237711