Subgroups — C₇×#17882 #13195098

Order 1792.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2989	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
4	C₇×#1587	C₂	1	2	yes	maximal, complemented
5	C₇×#1586	C₂	1	2	yes	maximal, complemented
6	C₇×#1583	C₂	1	2	yes	maximal, complemented
7	C₇×#1582	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₄	1	1	yes	characteristic
13	C₄×C₇×#41	C₂²	1	1	yes	characteristic
14	C₄×C₇×#41	C₂²	1	1	yes	characteristic
15	C₇×#446	C₂²	1	2	yes	—
16	C₇×C₈×Q₈	C₂²	1	2	yes	—
17	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic
18	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₄×C₇×SD₁₆	C₄	1	1	yes	characteristic
20	C₄×C₇×SD₁₆	C₄	1	1	yes	characteristic
21	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₇×D₈	C₄	1	1	yes	characteristic
24	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
25	C₇×#436	C₂²	1	2	yes	—
26	C₇×#435	—	2	2	no	—
27	C₇×C₈×D₄	—	2	2	no	—
28	C₇×C₈×D₄	C₂²	1	2	yes	—
29	C₇×#432	—	2	1	no	—
30	C₇×#431	—	2	1	no	—
31	C₇×#431	C₂²	1	1	yes	characteristic
32	C₇×#431	C₂²	1	1	yes	characteristic
33	C₇×#427	C₄	1	1	yes	characteristic
34	C₇×#423	—	2	1	no	—
35	C₂×C₇×C₄⋊C₈	—	2	1	no	—
36	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₇×#416	C₄	1	1	yes	characteristic
39	C₇×#416	C₄	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#334	C₂²	1	2	yes	—
42	C₇×#334	C₂²	1	2	yes	—
43	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₇×#322	C₂²	1	2	yes	—
48	C₇×#322	C₂²	1	2	yes	—
49	#17882	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
51	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
52	C₇×#135	—	2	4	no	—
53	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₇×M₁₆	—	2	2	no	—
58	C₂²×C₇×C₈	—	2	1	no	—
59	C₂²×C₇×C₈	—	2	1	no	—
60	C₂²×C₇×C₈	—	2	2	no	—
61	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
63	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
64	C₄×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
66	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
67	C₄×C₇×D₄	—	2	1	no	—
68	C₄×C₇×D₄	—	2	1	no	—
69	C₄×C₇×D₄	—	2	1	no	—
70	C₄×C₇×D₄	—	2	1	no	—
71	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
72	C₄×C₇×D₄	C₂×C₄	1	1	yes	characteristic
73	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
75	C₇×#117	—	2	1	no	—
76	C₇×#117	—	2	1	no	—
77	C₇×#117	C₂×C₄	1	1	yes	characteristic
78	C₇×#117	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₇	—	2	1	no	—
80	C₂×C₄²×C₇	—	2	1	no	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₇×#107	C₂×C₄	1	1	yes	characteristic
83	C₇×#107	C₂×C₄	1	1	yes	characteristic
84	C₇×#106	C₂×C₄	1	1	yes	characteristic
85	C₇×#106	C₂×C₄	1	1	yes	characteristic
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×C₄⋊C₈	—	2	2	no	—
88	C₇×C₄⋊C₈	—	2	1	no	—
89	C₇×C₄⋊C₈	—	2	1	no	—
90	C₇×C₄⋊C₈	—	2	1	no	—
91	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₇×C₄⋊C₈	C₂³	1	2	yes	—
94	C₇×C₄⋊C₈	C₂³	1	2	yes	—
95	C₇×#103	C₂×C₄	1	1	yes	characteristic
96	C₇×#103	C₂×C₄	1	1	yes	characteristic
97	C₇×#103	C₂×C₄	1	1	yes	characteristic
98	C₇×#103	C₂×C₄	1	1	yes	characteristic
99	C₇×#102	C₂×C₄	1	1	yes	characteristic
100	C₇×#102	C₂×C₄	1	1	yes	characteristic
101	C₇×#102	C₂×C₄	1	1	yes	characteristic
102	C₇×#102	C₂×C₄	1	1	yes	characteristic
103	C₇×C₂²⋊C₈	—	2	1	no	—
104	C₇×C₂²⋊C₈	—	2	2	no	—
105	C₇×C₂²⋊C₈	—	2	2	no	—
106	C₇×C₂²⋊C₈	D₄	1	2	yes	—
107	C₇×#97	—	2	2	no	—
108	C₄×C₇×C₈	—	2	2	no	—
109	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	2	yes	—
112	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₇×C₈	C₂³	1	2	yes	—
115	#2989	C₂×C₇	1	1	yes	characteristic, complemented
116	#2988	C₂×C₇	1	1	yes	characteristic, complemented
117	C₄×#135	C₂×C₇	1	1	yes	characteristic
118	#1587	C₂×C₇	1	2	yes	complemented
119	#1586	C₂×C₇	1	2	yes	complemented
120	#1583	C₂×C₇	1	2	yes	complemented
121	#1582	C₂×C₇	1	2	yes	complemented
122	C₂×#334	C₂×C₇	1	1	yes	characteristic, complemented
123	#1477	C₂×C₇	1	1	yes	characteristic, complemented
124	#1477	C₂×C₇	1	1	yes	characteristic, complemented
125	#1452	C₂×C₇	1	1	yes	characteristic, complemented
126	C₇×#41	—	2	2	no	—
127	C₇×#41	—	2	2	no	—
128	C₇×#41	—	2	2	no	—
129	C₇×#41	M₁₆	1	4	yes	complemented
130	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₇×D₄	—	2	1	no	—
133	C₂×C₇×D₄	—	2	1	no	—
134	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	1	no	—
141	C₂²×C₄×C₇	—	2	1	no	—
142	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	#41	1	1	yes	characteristic
145	C₇×Q₁₆	—	2	2	no	—
146	C₇×SD₁₆	—	2	2	no	—
147	C₇×SD₁₆	—	2	2	no	—
148	C₇×D₈	—	2	2	no	—
149	C₇×M₁₆	—	8	2	no	—
150	C₂×C₇×C₈	—	2	2	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	2	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	8	2	no	—
156	C₂×C₇×C₈	—	8	1	no	—
157	C₂×C₇×C₈	—	8	1	no	—
158	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
163	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
164	C₇×C₄⋊C₄	—	2	1	no	—
165	C₇×C₄⋊C₄	—	2	1	no	—
166	C₇×C₄⋊C₄	—	2	1	no	—
167	C₇×C₄⋊C₄	—	2	1	no	—
168	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
169	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
170	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
171	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
172	C₇×C₂²⋊C₄	—	2	1	no	—
173	C₇×C₂²⋊C₄	—	2	1	no	—
174	C₇×C₂²⋊C₄	—	2	1	no	—
175	C₇×C₂²⋊C₄	—	2	1	no	—
176	C₇×C₂²⋊C₄	—	2	1	no	—
177	C₇×C₂²⋊C₄	—	2	1	no	—
178	C₄²×C₇	—	2	1	no	—
179	C₄²×C₇	—	2	1	no	—
180	C₄²×C₇	—	2	1	no	—
181	C₄²×C₇	—	2	1	no	—
182	C₄²×C₇	—	2	1	no	—
183	C₄²×C₇	—	2	1	no	—
184	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₇	#41	1	1	yes	characteristic
187	C₄²×C₇	C₂⁴	1	1	yes	characteristic
188	C₂×#135	C₄×C₇	1	1	yes	characteristic
189	C₄×#41	C₂²×C₇	1	1	yes	characteristic
190	C₄×#41	C₂²×C₇	1	1	yes	characteristic
191	#446	C₂²×C₇	1	2	yes	—
192	C₈×Q₈	C₂²×C₇	1	2	yes	—
193	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic
194	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
195	C₄×SD₁₆	C₄×C₇	1	1	yes	characteristic
196	C₄×SD₁₆	C₄×C₇	1	1	yes	characteristic
197	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
198	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
199	C₄×D₈	C₄×C₇	1	1	yes	characteristic
200	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
201	#436	C₂²×C₇	1	2	yes	—
202	#435	—	2	2	no	—
203	C₈×D₄	—	2	2	no	—
204	C₈×D₄	C₂²×C₇	1	2	yes	—
205	#432	—	2	1	no	—
206	#431	—	2	1	no	—
207	#431	C₂²×C₇	1	1	yes	characteristic
208	#431	C₂²×C₇	1	1	yes	characteristic
209	#427	C₄×C₇	1	1	yes	characteristic
210	#423	—	2	1	no	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
214	#416	C₄×C₇	1	1	yes	characteristic
215	#416	C₄×C₇	1	1	yes	characteristic
216	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
217	#334	C₂²×C₇	1	2	yes	—
218	#334	C₂²×C₇	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
220	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
221	D₄⋊C₈	C₂²×C₇	1	2	yes	—
222	D₄⋊C₈	C₂²×C₇	1	2	yes	—
223	#322	C₂²×C₇	1	2	yes	—
224	#322	C₂²×C₇	1	2	yes	—
225	C₂³×C₇	—	2	1	no	—
226	C₂³×C₇	—	2	1	no	—
227	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
228	C₇×Q₈	—	2	1	no	—
229	C₇×Q₈	—	2	1	no	—
230	C₇×Q₈	—	2	1	no	—
231	C₇×Q₈	C₂×M₁₆	1	2	yes	—
232	C₇×D₄	—	2	4	no	—
233	C₇×D₄	—	2	1	no	—
234	C₇×D₄	—	2	1	no	—
235	C₇×D₄	—	2	1	no	—
236	C₇×D₄	—	4	2	no	—
237	C₇×D₄	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	1	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	1	no	—
243	C₂×C₄×C₇	—	2	1	no	—
244	C₂×C₄×C₇	—	2	1	no	—
245	C₂×C₄×C₇	—	2	1	no	—
246	C₂×C₄×C₇	—	2	1	no	—
247	C₂×C₄×C₇	—	4	1	no	—
248	C₂×C₄×C₇	—	4	1	no	—
249	C₂×C₄×C₇	—	4	1	no	—
250	C₂×C₄×C₇	—	4	1	no	—
251	C₂×C₄×C₇	—	4	1	no	—
252	C₂×C₄×C₇	—	4	2	no	—
253	C₂×C₄×C₇	—	8	1	no	—
254	C₂×C₄×C₇	—	8	1	no	—
255	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₇	C₂×M₁₆	1	2	yes	—
259	C₂×C₄×C₇	#131	1	2	yes	—
260	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
261	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
263	C₇×C₈	—	2	1	no	—
264	C₇×C₈	—	2	1	no	—
265	C₇×C₈	—	2	1	no	—
266	C₇×C₈	—	2	1	no	—
267	C₇×C₈	—	2	2	no	—
268	C₇×C₈	—	2	2	no	—
269	C₇×C₈	—	4	2	no	—
270	C₇×C₈	—	4	2	no	—
271	C₇×C₈	—	4	2	no	—
272	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
273	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
274	#135	—	2	4	no	—
275	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
277	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
278	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
279	C₂×M₁₆	—	2	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
284	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
285	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
286	C₄×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
288	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
289	C₄×D₄	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
294	C₄×D₄	C₂×C₄×C₇	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
296	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	C₂×C₄×C₇	1	1	yes	characteristic
300	#117	C₂×C₄×C₇	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
304	#107	C₂×C₄×C₇	1	1	yes	characteristic
305	#107	C₂×C₄×C₇	1	1	yes	characteristic
306	#106	C₂×C₄×C₇	1	1	yes	characteristic
307	#106	C₂×C₄×C₇	1	1	yes	characteristic
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
314	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₇	1	2	yes	—
316	C₄⋊C₈	C₂³×C₇	1	2	yes	—
317	#103	C₂×C₄×C₇	1	1	yes	characteristic
318	#103	C₂×C₄×C₇	1	1	yes	characteristic
319	#103	C₂×C₄×C₇	1	1	yes	characteristic
320	#103	C₂×C₄×C₇	1	1	yes	characteristic
321	#102	C₂×C₄×C₇	1	1	yes	characteristic
322	#102	C₂×C₄×C₇	1	1	yes	characteristic
323	#102	C₂×C₄×C₇	1	1	yes	characteristic
324	#102	C₂×C₄×C₇	1	1	yes	characteristic
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	C₇×D₄	1	2	yes	—
329	#97	—	2	2	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
332	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₇	1	2	yes	—
334	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
335	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
336	C₄×C₈	C₂³×C₇	1	2	yes	—
337	C₂²×C₇	—	2	1	no	—
338	C₂²×C₇	—	2	1	no	—
339	C₂²×C₇	—	2	2	no	—
340	C₂²×C₇	—	4	1	no	—
341	C₂²×C₇	—	4	1	no	—
342	C₂²×C₇	—	4	1	no	—
343	C₂²×C₇	—	4	1	no	—
344	C₂²×C₇	—	4	1	no	—
345	C₂²×C₇	#435	1	2	yes	—
346	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	2	1	no	—
349	C₄×C₇	—	2	1	no	—
350	C₄×C₇	—	2	1	no	—
351	C₄×C₇	—	4	1	no	—
352	C₄×C₇	—	4	1	no	—
353	C₄×C₇	—	4	1	no	—
354	C₄×C₇	—	4	1	no	—
355	C₄×C₇	—	4	1	no	—
356	C₄×C₇	#435	1	2	yes	—
357	C₄×C₇	C₂²×M₁₆	1	1	yes	characteristic
358	C₄×C₇	C₂×#131	1	1	yes	characteristic
359	C₄×C₇	#577	1	1	yes	characteristic
360	C₄×C₇	#577	1	1	yes	characteristic
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	#41	C₇×M₁₆	1	4	yes	complemented
365	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
366	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
370	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
379	C₂²×C₄	C₇×#41	1	1	yes	characteristic
380	Q₁₆	—	2	2	no	—
381	SD₁₆	—	2	2	no	—
382	SD₁₆	—	2	2	no	—
383	D₈	—	2	2	no	—
384	M₁₆	—	8	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	8	2	no	—
391	C₂×C₈	—	8	1	no	—
392	C₂×C₈	—	8	1	no	—
393	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
394	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
395	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
396	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
397	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
398	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
405	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
406	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
420	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
421	C₄²	C₇×#41	1	1	yes	characteristic
422	C₄²	C₂⁴×C₇	1	1	yes	characteristic
423	C₂×C₇	—	2	2	no	—
424	C₂×C₇	—	4	2	no	—
425	C₂×C₇	—	8	1	no	—
426	C₂×C₇	C₂×#435	1	1	yes	characteristic
427	C₂×C₇	#2952	1	1	yes	characteristic
428	C₂×C₇	#2957	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	—	2	1	no	—
431	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
432	Q₈	—	2	1	no	—
433	Q₈	—	2	1	no	—
434	Q₈	—	2	1	no	—
435	Q₈	C₂×C₇×M₁₆	1	2	yes	—
436	D₄	—	2	4	no	—
437	D₄	—	2	1	no	—
438	D₄	—	2	1	no	—
439	D₄	—	2	1	no	—
440	D₄	—	4	2	no	—
441	D₄	C₂×C₇×M₁₆	1	2	yes	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	8	1	no	—
459	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
460	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
461	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂×C₇×M₁₆	1	2	yes	—
463	C₂×C₄	C₇×#131	1	2	yes	—
464	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
466	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	4	2	no	—
474	C₈	—	4	2	no	—
475	C₈	—	4	2	no	—
476	C₇	#17882	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	C₇×#435	1	2	yes	—
486	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	C₇×#435	1	2	yes	—
497	C₄	C₂²×C₇×M₁₆	1	1	yes	characteristic
498	C₄	C₂×C₇×#131	1	1	yes	characteristic
499	C₄	C₇×#577	1	1	yes	characteristic
500	C₄	C₇×#577	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	8	1	no	—
504	C₂	C₂×C₇×#435	1	1	yes	characteristic
505	C₂	C₇×#2952	1	1	yes	characteristic
506	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2989	C₂	semidirect
2. C₇×#2988	C₂	semidirect
4. C₇×#1587	C₂	semidirect
5. C₇×#1586	C₂	semidirect
6. C₇×#1583	C₂	semidirect
7. C₇×#1582	C₂	semidirect
8. C₂×C₇×#334	C₂	semidirect
9. C₇×#1477	C₂	semidirect
10. C₇×#1477	C₂	semidirect
11. C₇×#1452	C₂	semidirect
49. #17882	C₇	direct (N × H)
115. #2989	C₂×C₇	semidirect
116. #2988	C₂×C₇	semidirect
118. #1587	C₂×C₇	semidirect
119. #1586	C₂×C₇	semidirect
120. #1583	C₂×C₇	semidirect
121. #1582	C₂×C₇	semidirect
122. C₂×#334	C₂×C₇	semidirect
123. #1477	C₂×C₇	semidirect
124. #1477	C₂×C₇	semidirect
125. #1452	C₂×C₇	semidirect
129. C₇×#41	M₁₆	semidirect
364. #41	C₇×M₁₆	semidirect
476. C₇	#17882	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×#2989	2
C₇×#2988	2
C₄×C₇×#135	2
C₇×#1587	2
C₇×#1586	2
C₇×#1583	2
C₇×#1582	2
C₂×C₇×#334	2
C₇×#1477	2
C₇×#1452	2
#17882	7

Subgroups — C7×#17882 #13195098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17882 #13195098