Subgroups — C₇×#60716 #13237932

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3511	C₂	1	2	yes	maximal, complemented
2	C₇×#3185	C₂	1	2	yes	maximal, complemented
3	C₇×#3184	C₂	1	2	yes	maximal, complemented
4	C₇×#3173	C₂	1	8	yes	maximal, complemented
5	C₇×#3167	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3141	C₂	1	2	yes	maximal, complemented
9	C₇×#3060	C₂	1	4	yes	maximal, complemented
10	C₇×#2952	C₂	1	4	yes	maximal, complemented
11	C₄×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₂²	1	4	yes	—
13	C₂×C₇×#131	C₂²	1	2	yes	—
14	C₇×#556	—	2	2	no	—
15	C₇×#555	—	2	2	no	—
16	C₇×#554	—	2	2	no	—
17	C₇×#553	—	2	4	no	—
18	C₇×#548	—	2	4	no	—
19	C₇×#547	—	2	2	no	—
20	C₇×#542	C₂²	1	8	yes	—
21	C₇×#537	C₂²	1	4	yes	—
22	C₇×#533	C₂²	1	4	yes	—
23	C₇×#532	C₂²	1	2	yes	—
24	C₇×#532	C₂²	1	4	yes	—
25	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₇×#520	C₂²	1	4	yes	—
27	C₄×C₇×#41	C₂²	1	1	yes	characteristic
28	C₇×#498	C₂²	1	2	yes	—
29	C₇×#498	C₂²	1	4	yes	—
30	C₇×#498	C₂²	1	2	yes	—
31	C₇×#495	C₂²	1	4	yes	—
32	C₇×#494	C₂²	1	1	yes	characteristic
33	C₇×#493	C₂²	1	1	yes	characteristic
34	C₇×#492	C₂²	1	2	yes	—
35	C₇×#489	C₂²	1	8	yes	—
36	C₇×#487	C₂²	1	4	yes	—
37	C₇×#486	C₂²	1	4	yes	—
38	C₇×#470	C₂²	1	8	yes	—
39	C₇×#469	C₂²	1	8	yes	—
40	C₇×#465	C₂²	1	16	yes	—
41	C₇×#442	C₂²	1	8	yes	—
42	C₇×#441	C₂²	1	8	yes	—
43	C₄×C₇×SD₁₆	C₂²	1	16	yes	—
44	C₂×C₇×#106	C₂²	1	4	yes	—
45	C₇×#417	C₂²	1	8	yes	—
46	C₇×#405	C₂²	1	4	yes	—
47	C₇×#405	C₂²	1	2	yes	—
48	C₄×C₇×M₁₆	C₂²	1	2	yes	—
49	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
52	#60716	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×C₇×#41	—	2	4	no	—
54	C₂×C₇×#41	C₂³	1	4	yes	—
55	C₂×C₇×#41	C₂³	1	1	yes	characteristic
56	C₂²×C₇×Q₈	—	2	2	no	—
57	C₇×#135	—	2	16	no	—
58	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
59	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
60	C₂×C₇×D₈	C₂³	1	4	yes	—
61	C₇×#131	—	2	8	no	—
62	C₂×C₇×M₁₆	C₂³	1	4	yes	—
63	C₂×C₇×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	4	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₇×C₄⋊Q₈	—	2	2	no	—
67	C₇×C₄⋊Q₈	—	2	2	no	—
68	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
70	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
71	C₇×#127	C₂³	1	2	yes	—
72	C₇×#126	—	2	8	no	—
73	C₇×#125	—	2	4	no	—
74	C₇×#124	—	2	8	no	—
75	C₇×#124	—	2	4	no	—
76	C₇×#124	C₂³	1	4	yes	—
77	C₇×#123	—	2	8	no	—
78	C₇×C₂²⋊Q₈	—	2	4	no	—
79	C₇×C₂²⋊Q₈	—	2	4	no	—
80	C₇×C₂²⋊Q₈	—	2	8	no	—
81	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₇×#121	—	2	4	no	—
83	C₇×#121	—	2	8	no	—
84	C₇×#121	—	2	2	no	—
85	C₇×#121	—	2	2	no	—
86	C₇×#121	—	2	4	no	—
87	C₇×#121	C₂³	1	8	yes	—
88	C₄×C₇×Q₈	—	2	4	no	—
89	C₄×C₇×Q₈	D₄	1	2	yes	—
90	C₄×C₇×Q₈	C₂³	1	8	yes	—
91	C₄×C₇×D₄	—	2	8	no	—
92	C₄×C₇×D₄	—	2	2	no	—
93	C₄×C₇×D₄	—	2	4	no	—
94	C₄×C₇×D₄	—	2	2	no	—
95	C₄×C₇×D₄	D₄	1	2	yes	—
96	C₄×C₇×D₄	D₄	1	4	yes	—
97	C₄×C₇×D₄	C₂³	1	8	yes	—
98	C₇×#117	—	2	4	no	—
99	C₇×#117	—	2	4	no	—
100	C₇×#117	C₂³	1	1	yes	characteristic
101	C₇×#117	C₂³	1	2	yes	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	—	2	4	no	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	2	yes	—
107	C₇×#106	C₂³	1	8	yes	—
108	C₇×#106	C₂³	1	8	yes	—
109	C₇×#103	C₂³	1	16	yes	—
110	C₇×#102	C₂³	1	16	yes	—
111	C₇×#97	C₂³	1	2	yes	—
112	C₇×#97	C₂³	1	4	yes	—
113	C₄×C₇×C₈	C₂³	1	2	yes	—
114	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
115	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₄×C₇×C₈	C₂³	1	2	yes	—
117	C₄×C₇×C₈	C₂³	1	4	yes	—
118	#3511	C₂×C₇	1	2	yes	complemented
119	#3185	C₂×C₇	1	2	yes	complemented
120	#3184	C₂×C₇	1	2	yes	complemented
121	#3173	C₂×C₇	1	8	yes	complemented
122	#3167	C₂×C₇	1	4	yes	complemented
123	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
124	#3147	C₂×C₇	1	1	yes	characteristic, complemented
125	#3141	C₂×C₇	1	2	yes	complemented
126	#3060	C₂×C₇	1	4	yes	complemented
127	#2952	C₂×C₇	1	4	yes	complemented
128	C₄×#131	C₂×C₇	1	1	yes	characteristic, complemented
129	C₇×#41	—	2	4	no	—
130	C₇×#41	—	2	16	no	—
131	C₇×#41	—	8	8	no	—
132	C₂×C₇×Q₈	—	2	4	no	—
133	C₂×C₇×Q₈	—	2	4	no	—
134	C₂×C₇×Q₈	—	8	4	no	—
135	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
137	C₂×C₇×D₄	—	2	4	no	—
138	C₂×C₇×D₄	—	2	8	no	—
139	C₂×C₇×D₄	—	2	2	no	—
140	C₂×C₇×D₄	—	2	2	no	—
141	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
142	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇×D₄	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₇	—	2	4	no	—
145	C₂²×C₄×C₇	—	2	4	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
151	C₇×Q₁₆	—	2	8	no	—
152	C₇×SD₁₆	—	2	16	no	—
153	C₇×D₈	—	2	8	no	—
154	C₇×M₁₆	—	2	4	no	—
155	C₇×M₁₆	—	2	8	no	—
156	C₂×C₇×C₈	—	2	8	no	—
157	C₂×C₇×C₈	#41	1	8	yes	complemented
158	C₂×C₇×C₈	C₂⁴	1	4	yes	—
159	C₂×C₇×C₈	C₂⁴	1	2	yes	—
160	C₂×C₇×C₈	C₂⁴	1	2	yes	—
161	C₇×C₄⋊C₄	—	2	4	no	—
162	C₇×C₄⋊C₄	—	2	4	no	—
163	C₇×C₄⋊C₄	—	2	8	no	—
164	C₇×C₄⋊C₄	—	2	4	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	—	2	2	no	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
169	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
170	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
171	C₇×C₂²⋊C₄	—	2	8	no	—
172	C₇×C₂²⋊C₄	—	2	8	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	2	4	no	—
175	C₇×C₂²⋊C₄	—	2	4	no	—
176	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
177	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
178	C₄²×C₇	—	2	8	no	—
179	C₄²×C₇	C₂×D₄	1	2	yes	—
180	C₄²×C₇	C₂×D₄	1	4	yes	—
181	C₄²×C₇	C₂⁴	1	1	yes	characteristic
182	C₄²×C₇	C₂⁴	1	2	yes	—
183	C₄²×C₇	C₂⁴	1	1	yes	characteristic
184	C₂×#135	C₂²×C₇	1	4	yes	—
185	C₂×#131	C₂²×C₇	1	2	yes	—
186	#556	—	2	2	no	—
187	#555	—	2	2	no	—
188	#554	—	2	2	no	—
189	#553	—	2	4	no	—
190	#548	—	2	4	no	—
191	#547	—	2	2	no	—
192	#542	C₂²×C₇	1	8	yes	—
193	#537	C₂²×C₇	1	4	yes	—
194	#533	C₂²×C₇	1	4	yes	—
195	#532	C₂²×C₇	1	2	yes	—
196	#532	C₂²×C₇	1	4	yes	—
197	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
198	#520	C₂²×C₇	1	4	yes	—
199	C₄×#41	C₂²×C₇	1	1	yes	characteristic
200	#498	C₂²×C₇	1	2	yes	—
201	#498	C₂²×C₇	1	4	yes	—
202	#498	C₂²×C₇	1	2	yes	—
203	#495	C₂²×C₇	1	4	yes	—
204	#494	C₂²×C₇	1	1	yes	characteristic
205	#493	C₂²×C₇	1	1	yes	characteristic
206	#492	C₂²×C₇	1	2	yes	—
207	#489	C₂²×C₇	1	8	yes	—
208	#487	C₂²×C₇	1	4	yes	—
209	#486	C₂²×C₇	1	4	yes	—
210	#470	C₂²×C₇	1	8	yes	—
211	#469	C₂²×C₇	1	8	yes	—
212	#465	C₂²×C₇	1	16	yes	—
213	#442	C₂²×C₇	1	8	yes	—
214	#441	C₂²×C₇	1	8	yes	—
215	C₄×SD₁₆	C₂²×C₇	1	16	yes	—
216	C₂×#106	C₂²×C₇	1	4	yes	—
217	#417	C₂²×C₇	1	8	yes	—
218	#405	C₂²×C₇	1	4	yes	—
219	#405	C₂²×C₇	1	2	yes	—
220	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
221	C₄×M₁₆	C₂²×C₇	1	2	yes	—
222	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
224	C₂³×C₇	—	2	4	no	—
225	C₂³×C₇	C₂²×D₄	1	2	yes	—
226	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₇×Q₈	—	2	2	no	—
228	C₇×Q₈	—	2	8	no	—
229	C₇×Q₈	—	4	8	no	—
230	C₇×Q₈	—	8	4	no	—
231	C₇×D₄	—	2	4	no	—
232	C₇×D₄	—	2	2	no	—
233	C₇×D₄	—	2	8	no	—
234	C₇×D₄	—	4	8	no	—
235	C₇×D₄	—	4	4	no	—
236	C₇×D₄	—	4	4	no	—
237	C₇×D₄	—	8	8	no	—
238	C₂×C₄×C₇	—	2	4	no	—
239	C₂×C₄×C₇	—	2	8	no	—
240	C₂×C₄×C₇	—	2	4	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	8	no	—
243	C₂×C₄×C₇	—	4	8	no	—
244	C₂×C₄×C₇	—	8	8	no	—
245	C₂×C₄×C₇	—	8	4	no	—
246	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₇	C₂×#41	1	4	yes	—
252	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
253	C₇×C₈	—	2	4	no	—
254	C₇×C₈	C₂×#41	1	4	yes	—
255	C₇×C₈	C₂×#41	1	4	yes	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	C₂³×C₇	1	4	yes	—
258	C₂×#41	C₂³×C₇	1	1	yes	characteristic
259	C₂²×Q₈	—	2	2	no	—
260	#135	—	2	16	no	—
261	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
262	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
263	C₂×D₈	C₂³×C₇	1	4	yes	—
264	#131	—	2	8	no	—
265	C₂×M₁₆	C₂³×C₇	1	2	yes	—
266	C₂×M₁₆	C₂³×C₇	1	4	yes	—
267	C₂²×C₈	C₂³×C₇	1	4	yes	—
268	C₂²×C₈	C₂³×C₇	1	2	yes	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
272	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
273	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
274	#127	C₂³×C₇	1	2	yes	—
275	#126	—	2	8	no	—
276	#125	—	2	4	no	—
277	#124	—	2	8	no	—
278	#124	—	2	4	no	—
279	#124	C₂³×C₇	1	4	yes	—
280	#123	—	2	8	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	8	no	—
284	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
285	#121	—	2	4	no	—
286	#121	—	2	8	no	—
287	#121	—	2	2	no	—
288	#121	—	2	2	no	—
289	#121	—	2	4	no	—
290	#121	C₂³×C₇	1	8	yes	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	C₇×D₄	1	2	yes	—
293	C₄×Q₈	C₂³×C₇	1	8	yes	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	C₇×D₄	1	2	yes	—
299	C₄×D₄	C₇×D₄	1	4	yes	—
300	C₄×D₄	C₂³×C₇	1	8	yes	—
301	#117	—	2	4	no	—
302	#117	—	2	4	no	—
303	#117	C₂³×C₇	1	1	yes	characteristic
304	#117	C₂³×C₇	1	2	yes	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
308	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₇	1	2	yes	—
310	#106	C₂³×C₇	1	8	yes	—
311	#106	C₂³×C₇	1	8	yes	—
312	#103	C₂³×C₇	1	16	yes	—
313	#102	C₂³×C₇	1	16	yes	—
314	#97	C₂³×C₇	1	4	yes	—
315	#97	C₂³×C₇	1	2	yes	—
316	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
317	C₄×C₈	C₂³×C₇	1	2	yes	—
318	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₇	1	4	yes	—
320	C₄×C₈	C₂³×C₇	1	2	yes	—
321	C₂²×C₇	—	2	2	no	—
322	C₂²×C₇	—	2	2	no	—
323	C₂²×C₇	—	2	4	no	—
324	C₂²×C₇	—	4	4	no	—
325	C₂²×C₇	—	4	4	no	—
326	C₂²×C₇	—	4	4	no	—
327	C₂²×C₇	#532	1	2	yes	—
328	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
329	C₄×C₇	—	2	2	no	—
330	C₄×C₇	—	2	4	no	—
331	C₄×C₇	—	2	2	no	—
332	C₄×C₇	—	4	4	no	—
333	C₄×C₇	—	4	8	no	—
334	C₄×C₇	#532	1	2	yes	—
335	C₄×C₇	#577	1	4	yes	—
336	C₄×C₇	C₂²×#41	1	2	yes	—
337	#41	—	2	4	no	—
338	#41	—	2	16	no	—
339	#41	—	8	8	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	8	4	no	—
343	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
350	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
351	C₂×D₄	C₂⁴×C₇	1	4	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
356	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
359	Q₁₆	—	2	8	no	—
360	SD₁₆	—	2	16	no	—
361	D₈	—	2	8	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	8	no	—
364	C₂×C₈	—	2	8	no	—
365	C₂×C₈	C₇×#41	1	8	yes	complemented
366	C₂×C₈	C₂⁴×C₇	1	4	yes	—
367	C₂×C₈	C₂⁴×C₇	1	2	yes	—
368	C₂×C₈	C₂⁴×C₇	1	2	yes	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
377	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
385	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
386	C₄²	—	2	8	no	—
387	C₄²	C₂×C₇×D₄	1	2	yes	—
388	C₄²	C₂×C₇×D₄	1	4	yes	—
389	C₄²	C₂⁴×C₇	1	1	yes	characteristic
390	C₄²	C₂⁴×C₇	1	2	yes	—
391	C₄²	C₂⁴×C₇	1	1	yes	characteristic
392	C₂×C₇	—	2	2	no	—
393	C₂×C₇	—	4	2	no	—
394	C₂×C₇	—	8	4	no	—
395	C₂×C₇	C₂×#532	1	1	yes	characteristic
396	C₂×C₇	C₂×#577	1	2	yes	—
397	C₂³	—	2	4	no	—
398	C₂³	C₂²×C₇×D₄	1	2	yes	—
399	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	8	no	—
402	Q₈	—	4	8	no	—
403	Q₈	—	8	4	no	—
404	D₄	—	2	4	no	—
405	D₄	—	2	8	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	8	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	8	8	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
420	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
421	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
422	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
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	#60716	1	1	yes	characteristic, direct product factor, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	C₇×#532	1	2	yes	—
437	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	4	no	—
443	C₄	C₇×#532	1	2	yes	—
444	C₄	C₇×#577	1	4	yes	—
445	C₄	C₂²×C₇×#41	1	2	yes	—
446	C₂	—	2	2	no	—
447	C₂	—	4	2	no	—
448	C₂	—	8	4	no	—
449	C₂	C₂×C₇×#532	1	1	yes	characteristic
450	C₂	C₂×C₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×#3511	C₂	semidirect
2. C₇×#3185	C₂	semidirect
3. C₇×#3184	C₂	semidirect
4. C₇×#3173	C₂	semidirect
5. C₇×#3167	C₂	semidirect
6. C₂×C₇×#498	C₂	semidirect
7. C₇×#3147	C₂	semidirect
8. C₇×#3141	C₂	semidirect
9. C₇×#3060	C₂	semidirect
10. C₇×#2952	C₂	semidirect
11. C₄×C₇×#131	C₂	semidirect
52. #60716	C₇	direct (N × H)
118. #3511	C₂×C₇	semidirect
119. #3185	C₂×C₇	semidirect
120. #3184	C₂×C₇	semidirect
121. #3173	C₂×C₇	semidirect
122. #3167	C₂×C₇	semidirect
123. C₂×#498	C₂×C₇	semidirect
124. #3147	C₂×C₇	semidirect
125. #3141	C₂×C₇	semidirect
126. #3060	C₂×C₇	semidirect
127. #2952	C₂×C₇	semidirect
128. C₄×#131	C₂×C₇	semidirect
157. C₂×C₇×C₈	#41	semidirect
365. C₂×C₈	C₇×#41	semidirect
429. C₇	#60716	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×#3511	2
C₇×#3185	2
C₇×#3184	2
C₇×#3173	2
C₇×#3167	2
C₂×C₇×#498	2
C₇×#3147	2
C₇×#3141	2
C₇×#3060	2
C₇×#2952	2
C₄×C₇×#131	2
#60716	7

Subgroups — C7×#60716 #13237932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60716 #13237932