Subgroups — C₇×#60673 #13237889

Order 1792.

2050 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	2	yes	maximal, complemented
2	C₇×#3170	C₂	1	2	yes	maximal, complemented
3	C₇×#3169	C₂	1	2	yes	maximal, complemented
4	C₇×#3168	C₂	1	8	yes	maximal, complemented
5	C₇×#3167	C₂	1	4	yes	maximal, complemented
6	C₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3131	C₂	1	2	yes	maximal, complemented
9	C₇×#3050	C₂	1	4	yes	maximal, complemented
10	C₄×C₇×#135	C₂	1	4	yes	maximal, complemented
11	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₂²	1	4	yes	—
13	C₂³×C₇×C₈	C₂²	1	2	yes	—
14	C₇×#533	C₂²	1	4	yes	—
15	C₇×#533	C₂²	1	2	yes	—
16	C₇×#532	C₂²	1	2	yes	—
17	C₇×#532	C₂²	1	4	yes	—
18	C₇×#529	—	2	4	no	—
19	C₇×#529	—	2	4	no	—
20	C₇×#529	C₂²	1	8	yes	—
21	C₇×#525	—	2	4	no	—
22	C₇×#525	C₂²	1	4	yes	—
23	C₄×C₇×#41	—	2	4	no	—
24	C₄×C₇×#41	C₂²	1	4	yes	—
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₇×#500	C₂²	1	2	yes	complemented
27	C₇×#499	C₂²	1	4	yes	complemented
28	C₇×#498	C₂²	1	2	yes	complemented
29	C₇×#495	C₂²	1	4	yes	complemented
30	C₇×#494	C₂²	1	1	yes	characteristic, complemented
31	C₇×#493	C₂²	1	1	yes	characteristic, complemented
32	C₇×#492	C₂²	1	2	yes	complemented
33	C₇×#488	C₂²	1	8	yes	complemented
34	C₇×#487	C₂²	1	4	yes	complemented
35	C₇×#486	C₂²	1	4	yes	complemented
36	C₇×#467	C₂²	1	8	yes	—
37	C₇×#466	C₂²	1	8	yes	—
38	C₇×#465	C₂²	1	16	yes	—
39	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
40	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
41	C₄×C₇×D₈	C₂²	1	8	yes	complemented
42	C₇×#427	C₂²	1	4	yes	—
43	C₇×#416	C₂²	1	8	yes	—
44	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
46	C₂×C₄×C₇×C₈	C₂²	1	4	yes	—
47	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
48	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
49	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
50	#60673	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×C₇×#41	—	2	4	no	—
52	C₂×C₇×#41	C₂³	1	4	yes	—
53	C₂³×C₄×C₇	D₄	1	2	yes	—
54	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
55	C₇×#135	—	2	16	no	—
56	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
57	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
58	C₂×C₇×D₈	C₂³	1	4	yes	—
59	C₂²×C₇×C₈	—	2	8	no	—
60	C₂²×C₇×C₈	C₂³	1	4	yes	—
61	C₂²×C₇×C₈	C₂³	1	2	yes	—
62	C₂²×C₇×C₈	C₂³	1	4	yes	—
63	C₂²×C₇×C₈	C₂³	1	2	yes	—
64	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
66	C₇×#127	C₂³	1	2	yes	—
67	C₇×#126	—	2	8	no	—
68	C₇×#125	—	2	4	no	—
69	C₇×#125	C₂³	1	4	yes	—
70	C₇×#124	—	2	4	no	—
71	C₇×#124	C₂³	1	4	yes	—
72	C₇×#123	—	2	8	no	—
73	C₇×#123	—	2	4	no	—
74	C₇×C₂²⋊Q₈	—	2	4	no	—
75	C₇×C₂²⋊Q₈	—	2	4	no	—
76	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
77	C₇×#121	—	2	4	no	—
78	C₇×#121	—	2	4	no	—
79	C₇×#121	C₂³	1	8	yes	—
80	C₇×#120	—	2	4	no	—
81	C₄×C₇×Q₈	—	2	4	no	—
82	C₄×C₇×Q₈	—	2	4	no	—
83	C₄×C₇×Q₈	C₂³	1	8	yes	—
84	C₄×C₇×D₄	—	2	8	no	—
85	C₄×C₇×D₄	—	2	8	no	—
86	C₄×C₇×D₄	—	2	8	no	—
87	C₄×C₇×D₄	—	2	4	no	—
88	C₄×C₇×D₄	—	2	4	no	—
89	C₄×C₇×D₄	C₂³	1	8	yes	—
90	C₇×#117	—	2	4	no	—
91	C₇×#117	—	2	8	no	—
92	C₇×#117	—	2	4	no	—
93	C₇×#117	C₂³	1	4	yes	—
94	C₂×C₄²×C₇	—	2	4	no	—
95	C₂×C₄²×C₇	D₄	1	2	yes	—
96	C₂×C₄²×C₇	D₄	1	2	yes	—
97	C₂×C₄²×C₇	D₄	1	2	yes	—
98	C₂×C₄²×C₇	C₂³	1	2	yes	—
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇	C₂³	1	2	yes	—
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₇×#107	C₂³	1	8	yes	—
103	C₇×#106	C₂³	1	8	yes	—
104	C₇×#103	C₂³	1	16	yes	—
105	C₇×#102	C₂³	1	16	yes	—
106	C₄×C₇×C₈	C₂³	1	2	yes	—
107	C₄×C₇×C₈	C₂³	1	2	yes	—
108	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	2	yes	—
111	C₄×C₇×C₈	C₂³	1	4	yes	—
112	C₄×C₇×C₈	C₂³	1	4	yes	—
113	#3444	C₂×C₇	1	2	yes	complemented
114	#3170	C₂×C₇	1	2	yes	complemented
115	#3169	C₂×C₇	1	2	yes	complemented
116	#3168	C₂×C₇	1	8	yes	complemented
117	#3167	C₂×C₇	1	4	yes	complemented
118	#3160	C₂×C₇	1	1	yes	characteristic, complemented
119	#3147	C₂×C₇	1	1	yes	characteristic, complemented
120	#3131	C₂×C₇	1	2	yes	complemented
121	#3050	C₂×C₇	1	4	yes	complemented
122	C₄×#135	C₂×C₇	1	4	yes	complemented
123	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
124	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
125	C₇×#41	—	2	16	no	—
126	C₇×#41	—	4	16	no	—
127	C₂×C₇×Q₈	—	2	4	no	—
128	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
129	C₂×C₇×D₄	—	2	4	no	—
130	C₂×C₇×D₄	—	2	8	no	—
131	C₂×C₇×D₄	—	2	4	no	—
132	C₂×C₇×D₄	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	2	4	no	—
136	C₂²×C₄×C₇	—	2	8	no	—
137	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
147	C₇×Q₁₆	—	2	8	no	—
148	C₇×SD₁₆	—	2	16	no	—
149	C₇×D₈	—	2	8	no	—
150	C₂×C₇×C₈	—	2	4	no	—
151	C₂×C₇×C₈	—	2	8	no	—
152	C₂×C₇×C₈	—	2	8	no	—
153	C₂×C₇×C₈	#41	1	8	yes	complemented
154	C₂×C₇×C₈	C₂⁴	1	4	yes	—
155	C₂×C₇×C₈	C₂⁴	1	2	yes	—
156	C₂×C₇×C₈	C₂⁴	1	2	yes	—
157	C₇×C₄⋊C₄	—	2	4	no	—
158	C₇×C₄⋊C₄	—	2	4	no	—
159	C₇×C₄⋊C₄	—	2	8	no	—
160	C₇×C₄⋊C₄	—	2	8	no	—
161	C₇×C₄⋊C₄	—	2	8	no	—
162	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
163	C₇×C₂²⋊C₄	—	2	8	no	—
164	C₇×C₂²⋊C₄	—	2	4	no	—
165	C₇×C₂²⋊C₄	—	2	8	no	—
166	C₇×C₂²⋊C₄	—	2	8	no	—
167	C₇×C₂²⋊C₄	—	2	8	no	—
168	C₄²×C₇	—	2	8	no	—
169	C₄²×C₇	—	2	4	no	—
170	C₄²×C₇	C₂×D₄	1	2	yes	—
171	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₇	C₂×D₄	1	2	yes	—
173	C₄²×C₇	C₂×D₄	1	2	yes	—
174	C₄²×C₇	C₂×D₄	1	2	yes	—
175	C₄²×C₇	C₂×D₄	1	2	yes	—
176	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₇	C₂⁴	1	2	yes	—
178	C₄²×C₇	C₂⁴	1	1	yes	characteristic
179	C₄²×C₇	C₂⁴	1	1	yes	characteristic
180	C₂×#135	C₂²×C₇	1	4	yes	—
181	C₂³×C₈	C₂²×C₇	1	2	yes	—
182	#533	C₂²×C₇	1	4	yes	—
183	#533	C₂²×C₇	1	2	yes	—
184	#532	C₂²×C₇	1	2	yes	—
185	#532	C₂²×C₇	1	4	yes	—
186	#529	—	2	4	no	—
187	#529	—	2	4	no	—
188	#529	C₂²×C₇	1	8	yes	—
189	#525	—	2	4	no	—
190	#525	C₂²×C₇	1	4	yes	—
191	C₄×#41	—	2	4	no	—
192	C₄×#41	C₂²×C₇	1	4	yes	—
193	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
194	#500	C₂²×C₇	1	2	yes	complemented
195	#499	C₂²×C₇	1	4	yes	complemented
196	#498	C₂²×C₇	1	2	yes	complemented
197	#495	C₂²×C₇	1	4	yes	complemented
198	#494	C₂²×C₇	1	1	yes	characteristic, complemented
199	#493	C₂²×C₇	1	1	yes	characteristic, complemented
200	#492	C₂²×C₇	1	2	yes	complemented
201	#488	C₂²×C₇	1	8	yes	complemented
202	#487	C₂²×C₇	1	4	yes	complemented
203	#486	C₂²×C₇	1	4	yes	complemented
204	#467	C₂²×C₇	1	8	yes	—
205	#466	C₂²×C₇	1	8	yes	—
206	#465	C₂²×C₇	1	16	yes	—
207	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
208	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
209	C₄×D₈	C₂²×C₇	1	8	yes	complemented
210	#427	C₂²×C₇	1	4	yes	—
211	#416	C₂²×C₇	1	8	yes	—
212	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
214	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
215	C₂×C₄×C₈	C₂²×C₇	1	4	yes	—
216	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
217	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	4	no	—
220	C₂³×C₇	—	2	4	no	—
221	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
222	C₂³×C₇	C₂²×D₄	1	2	yes	—
223	C₇×Q₈	—	2	8	no	—
224	C₇×Q₈	—	4	8	no	—
225	C₇×D₄	—	2	8	no	—
226	C₇×D₄	—	4	8	no	—
227	C₇×D₄	—	4	16	no	—
228	C₇×D₄	—	4	8	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	4	no	—
231	C₂×C₄×C₇	—	2	4	no	—
232	C₂×C₄×C₇	—	2	4	no	—
233	C₂×C₄×C₇	—	2	4	no	—
234	C₂×C₄×C₇	—	2	4	no	—
235	C₂×C₄×C₇	—	2	4	no	—
236	C₂×C₄×C₇	—	2	4	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	8	no	—
239	C₂×C₄×C₇	—	4	8	no	—
240	C₂×C₄×C₇	—	4	16	no	—
241	C₂×C₄×C₇	#135	1	8	yes	complemented
242	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
243	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₇	C₂×#41	1	4	yes	—
249	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
250	C₇×C₈	—	2	4	no	—
251	C₇×C₈	C₂×#41	1	4	yes	—
252	C₇×C₈	C₂×#41	1	4	yes	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	C₂³×C₇	1	4	yes	—
255	C₂³×C₄	C₇×D₄	1	2	yes	—
256	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
257	#135	—	2	16	no	—
258	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
259	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
260	C₂×D₈	C₂³×C₇	1	4	yes	—
261	C₂²×C₈	—	2	8	no	—
262	C₂²×C₈	C₂³×C₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₇	1	4	yes	—
264	C₂²×C₈	C₂³×C₇	1	4	yes	—
265	C₂²×C₈	C₂³×C₇	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
268	#127	C₂³×C₇	1	2	yes	—
269	#126	—	2	8	no	—
270	#125	—	2	4	no	—
271	#125	C₂³×C₇	1	4	yes	—
272	#124	—	2	4	no	—
273	#124	C₂³×C₇	1	4	yes	—
274	#123	—	2	8	no	—
275	#123	—	2	4	no	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
279	#121	—	2	4	no	—
280	#121	—	2	4	no	—
281	#121	C₂³×C₇	1	8	yes	—
282	#120	—	2	4	no	—
283	C₄×Q₈	—	2	4	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	C₂³×C₇	1	8	yes	—
286	C₄×D₄	—	2	8	no	—
287	C₄×D₄	—	2	8	no	—
288	C₄×D₄	—	2	8	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	C₂³×C₇	1	8	yes	—
292	#117	—	2	4	no	—
293	#117	—	2	8	no	—
294	#117	—	2	4	no	—
295	#117	C₂³×C₇	1	4	yes	—
296	C₂×C₄²	—	2	4	no	—
297	C₂×C₄²	C₇×D₄	1	2	yes	—
298	C₂×C₄²	C₇×D₄	1	2	yes	—
299	C₂×C₄²	C₇×D₄	1	2	yes	—
300	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₇	1	2	yes	—
302	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₇	1	2	yes	—
304	#107	C₂³×C₇	1	8	yes	—
305	#106	C₂³×C₇	1	8	yes	—
306	#103	C₂³×C₇	1	16	yes	—
307	#102	C₂³×C₇	1	16	yes	—
308	C₄×C₈	C₂³×C₇	1	4	yes	—
309	C₄×C₈	C₂³×C₇	1	4	yes	—
310	C₄×C₈	C₂³×C₇	1	2	yes	—
311	C₄×C₈	C₂³×C₇	1	2	yes	—
312	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
313	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
314	C₄×C₈	C₂³×C₇	1	2	yes	—
315	C₂²×C₇	—	2	8	no	—
316	C₂²×C₇	—	2	2	no	—
317	C₂²×C₇	—	2	2	no	—
318	C₂²×C₇	—	2	2	no	—
319	C₂²×C₇	—	4	4	no	—
320	C₂²×C₇	—	4	8	no	—
321	C₂²×C₇	#532	1	2	yes	—
322	C₂²×C₇	C₂×#135	1	4	yes	—
323	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
324	C₄×C₇	—	2	2	no	—
325	C₄×C₇	—	2	2	no	—
326	C₄×C₇	—	2	2	no	—
327	C₄×C₇	—	4	4	no	—
328	C₄×C₇	—	4	8	no	—
329	C₄×C₇	#532	1	2	yes	—
330	C₄×C₇	C₂×#135	1	4	yes	—
331	C₄×C₇	C₂×#135	1	4	yes	—
332	C₄×C₇	C₂²×#41	1	2	yes	—
333	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
334	#41	—	2	16	no	—
335	#41	—	4	16	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	8	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂⁴×C₇	1	4	yes	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
347	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
349	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
350	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
351	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
352	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
353	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
355	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
356	Q₁₆	—	2	8	no	—
357	SD₁₆	—	2	16	no	—
358	D₈	—	2	8	no	—
359	C₂×C₈	—	2	4	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	—	2	8	no	—
362	C₂×C₈	C₇×#41	1	8	yes	complemented
363	C₂×C₈	C₂⁴×C₇	1	4	yes	—
364	C₂×C₈	C₂⁴×C₇	1	2	yes	—
365	C₂×C₈	C₂⁴×C₇	1	2	yes	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	4	no	—
379	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
380	C₄²	C₂×C₇×D₄	1	2	yes	—
381	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
382	C₄²	C₂×C₇×D₄	1	2	yes	—
383	C₄²	C₂×C₇×D₄	1	2	yes	—
384	C₄²	C₂×C₇×D₄	1	2	yes	—
385	C₄²	C₂×C₇×D₄	1	2	yes	—
386	C₄²	C₂⁴×C₇	1	2	yes	—
387	C₄²	C₂⁴×C₇	1	1	yes	characteristic
388	C₄²	C₂⁴×C₇	1	1	yes	characteristic
389	C₂×C₇	—	2	2	no	—
390	C₂×C₇	—	2	4	no	—
391	C₂×C₇	—	8	4	no	—
392	C₂×C₇	C₂×#532	1	1	yes	characteristic
393	C₂×C₇	C₂²×#135	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
398	C₂³	C₂²×C₇×D₄	1	2	yes	—
399	Q₈	—	2	8	no	—
400	Q₈	—	4	8	no	—
401	D₄	—	2	8	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	16	no	—
404	D₄	—	4	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	16	no	—
417	C₂×C₄	C₇×#135	1	8	yes	complemented
418	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
419	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
420	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
421	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
423	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
424	C₂×C₄	C₂×C₇×#41	1	4	yes	—
425	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
426	C₈	—	2	4	no	—
427	C₈	C₂×C₇×#41	1	4	yes	—
428	C₈	C₂×C₇×#41	1	4	yes	—
429	C₇	#60673	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	8	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₇×#532	1	2	yes	—
437	C₂²	C₂×C₇×#135	1	4	yes	—
438	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	8	no	—
443	C₄	—	4	4	no	—
444	C₄	C₇×#532	1	2	yes	—
445	C₄	C₂×C₇×#135	1	4	yes	—
446	C₄	C₂×C₇×#135	1	4	yes	—
447	C₄	C₂²×C₇×#41	1	2	yes	—
448	C₂	—	2	2	no	—
449	C₂	—	2	4	no	—
450	C₂	—	8	4	no	—
451	C₂	C₂×C₇×#532	1	1	yes	characteristic
452	C₂	C₂²×C₇×#135	1	2	yes	—

	subgroup	G/H
center	C₄²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3444	C₂	semidirect
2. C₇×#3170	C₂	semidirect
3. C₇×#3169	C₂	semidirect
4. C₇×#3168	C₂	semidirect
5. C₇×#3167	C₂	semidirect
6. C₇×#3160	C₂	semidirect
7. C₇×#3147	C₂	semidirect
8. C₇×#3131	C₂	semidirect
9. C₇×#3050	C₂	semidirect
10. C₄×C₇×#135	C₂	semidirect
11. C₂²×C₄×C₇×C₈	C₂	semidirect
26. C₇×#500	C₂²	semidirect
27. C₇×#499	C₂²	semidirect
28. C₇×#498	C₂²	semidirect
29. C₇×#495	C₂²	semidirect
30. C₇×#494	C₂²	semidirect
31. C₇×#493	C₂²	semidirect
32. C₇×#492	C₂²	semidirect
33. C₇×#488	C₂²	semidirect
34. C₇×#487	C₂²	semidirect
35. C₇×#486	C₂²	semidirect
39. C₄×C₇×Q₁₆	C₂²	semidirect
40. C₄×C₇×SD₁₆	C₂²	semidirect
41. C₄×C₇×D₈	C₂²	semidirect
50. #60673	C₇	direct (N × H)
113. #3444	C₂×C₇	semidirect
114. #3170	C₂×C₇	semidirect
115. #3169	C₂×C₇	semidirect
116. #3168	C₂×C₇	semidirect
117. #3167	C₂×C₇	semidirect
118. #3160	C₂×C₇	semidirect
119. #3147	C₂×C₇	semidirect
120. #3131	C₂×C₇	semidirect
121. #3050	C₂×C₇	semidirect
122. C₄×#135	C₂×C₇	semidirect
123. C₂²×C₄×C₈	C₂×C₇	semidirect
153. C₂×C₇×C₈	#41	semidirect
194. #500	C₂²×C₇	semidirect
195. #499	C₂²×C₇	semidirect
196. #498	C₂²×C₇	semidirect
197. #495	C₂²×C₇	semidirect
198. #494	C₂²×C₇	semidirect
199. #493	C₂²×C₇	semidirect
200. #492	C₂²×C₇	semidirect
201. #488	C₂²×C₇	semidirect
202. #487	C₂²×C₇	semidirect
203. #486	C₂²×C₇	semidirect
207. C₄×Q₁₆	C₂²×C₇	semidirect
208. C₄×SD₁₆	C₂²×C₇	semidirect
209. C₄×D₈	C₂²×C₇	semidirect
241. C₂×C₄×C₇	#135	semidirect
362. C₂×C₈	C₇×#41	semidirect
417. C₂×C₄	C₇×#135	semidirect
429. C₇	#60673	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×#3444	2
C₇×#3170	2
C₇×#3169	2
C₇×#3168	2
C₇×#3167	2
C₇×#3160	2
C₇×#3147	2
C₇×#3131	2
C₇×#3050	2
C₄×C₇×#135	2
C₂²×C₄×C₇×C₈	2
#60673	7

Subgroups — C7×#60673 #13237889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60673 #13237889