Subgroups — C₇×#60685 #13237901

Order 1792.

1878 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	2	yes	maximal, complemented
2	C₇×#3179	C₂	1	8	yes	maximal, complemented
3	C₇×#3178	C₂	1	8	yes	maximal, complemented
4	C₇×#3162	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3131	C₂	1	2	yes	maximal, complemented
7	C₇×#3054	C₂	1	2	yes	maximal, complemented
8	C₇×#3050	C₂	1	2	yes	maximal, complemented
9	C₇×#2943	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#135	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₂²	1	2	yes	—
13	C₂×C₇×#135	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₇×#542	C₂²	1	8	yes	—
17	C₇×#541	C₂²	1	4	yes	—
18	C₇×#540	C₂²	1	4	yes	—
19	C₇×#539	—	2	4	no	—
20	C₇×#538	—	2	4	no	—
21	C₇×#533	C₂²	1	2	yes	—
22	C₇×#532	C₂²	1	2	yes	—
23	C₇×#529	—	2	8	no	—
24	C₇×#525	C₂²	1	4	yes	—
25	C₄×C₇×#41	C₂²	1	4	yes	—
26	C₂×C₇×#117	C₂²	1	1	yes	characteristic
27	C₇×#501	C₂²	1	8	yes	complemented
28	C₇×#497	C₂²	1	4	yes	complemented
29	C₇×#496	C₂²	1	4	yes	complemented
30	C₇×#488	C₂²	1	8	yes	complemented
31	C₇×#487	C₂²	1	4	yes	complemented
32	C₇×#486	C₂²	1	4	yes	complemented
33	C₇×#470	C₂²	1	4	yes	—
34	C₇×#469	C₂²	1	4	yes	—
35	C₇×#468	C₂²	1	8	yes	—
36	C₇×#467	C₂²	1	4	yes	—
37	C₇×#466	C₂²	1	4	yes	—
38	C₇×#465	C₂²	1	8	yes	—
39	C₇×#442	C₂²	1	4	yes	complemented
40	C₇×#441	C₂²	1	4	yes	complemented
41	C₇×#440	C₂²	1	8	yes	complemented
42	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
43	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
44	C₄×C₇×D₈	C₂²	1	4	yes	complemented
45	C₇×#427	C₂²	1	2	yes	—
46	C₇×#427	C₂²	1	2	yes	—
47	C₇×#416	C₂²	1	4	yes	—
48	C₇×#416	C₂²	1	4	yes	—
49	C₇×#405	C₂²	1	8	yes	—
50	C₂×C₇×#97	C₂²	1	1	yes	characteristic
51	C₂×C₇×#97	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
54	#60685	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₇×#41	C₂³	1	4	yes	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₇×#135	—	2	8	no	—
58	C₇×#135	—	2	8	no	—
59	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
60	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
61	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
62	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
63	C₂×C₇×D₈	C₂³	1	2	yes	—
64	C₂×C₇×D₈	C₂³	1	2	yes	—
65	C₂×C₇×M₁₆	—	2	4	no	—
66	C₂×C₇×M₁₆	C₂³	1	4	yes	—
67	C₂²×C₇×C₈	—	2	4	no	—
68	C₂²×C₇×C₈	C₂³	1	4	yes	—
69	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
73	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
74	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
75	C₇×#127	C₂³	1	2	yes	—
76	C₇×#126	—	2	8	no	—
77	C₇×#126	—	2	8	no	—
78	C₇×#125	—	2	8	no	—
79	C₇×#125	C₂³	1	4	yes	—
80	C₇×#124	—	2	8	no	—
81	C₇×#124	C₂³	1	4	yes	—
82	C₇×#123	—	2	4	no	—
83	C₇×#123	—	2	8	no	—
84	C₇×#123	—	2	8	no	—
85	C₇×C₂²⋊Q₈	—	2	4	no	—
86	C₇×C₂²⋊Q₈	—	2	8	no	—
87	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
88	C₇×#121	—	2	4	no	—
89	C₇×#121	—	2	8	no	—
90	C₇×#121	C₂³	1	8	yes	—
91	C₇×#120	—	2	4	no	—
92	C₄×C₇×Q₈	—	2	4	no	—
93	C₄×C₇×Q₈	C₂³	1	8	yes	—
94	C₄×C₇×D₄	—	2	8	no	—
95	C₄×C₇×D₄	—	2	8	no	—
96	C₄×C₇×D₄	—	2	4	no	—
97	C₄×C₇×D₄	C₂³	1	8	yes	—
98	C₇×#117	—	2	4	no	—
99	C₇×#117	D₄	1	4	yes	—
100	C₇×#117	C₂³	1	4	yes	—
101	C₇×#117	C₂³	1	4	yes	—
102	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
103	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
104	C₂×C₄²×C₇	—	2	4	no	—
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
107	C₇×#107	C₂³	1	4	yes	—
108	C₇×#107	C₂³	1	4	yes	—
109	C₇×#106	C₂³	1	4	yes	—
110	C₇×#106	C₂³	1	4	yes	—
111	C₇×#103	C₂³	1	8	yes	—
112	C₇×#103	C₂³	1	8	yes	—
113	C₇×#102	C₂³	1	8	yes	—
114	C₇×#102	C₂³	1	8	yes	—
115	C₇×#97	C₂³	1	4	yes	—
116	C₇×#97	C₂³	1	4	yes	—
117	C₄×C₇×C₈	C₂³	1	4	yes	—
118	C₄×C₇×C₈	C₂³	1	4	yes	—
119	#3455	C₂×C₇	1	2	yes	complemented
120	#3179	C₂×C₇	1	8	yes	complemented
121	#3178	C₂×C₇	1	8	yes	complemented
122	#3162	C₂×C₇	1	1	yes	characteristic, complemented
123	#3150	C₂×C₇	1	1	yes	characteristic, complemented
124	#3131	C₂×C₇	1	2	yes	complemented
125	#3054	C₂×C₇	1	2	yes	complemented
126	#3050	C₂×C₇	1	2	yes	complemented
127	#2943	C₂×C₇	1	2	yes	complemented
128	C₄×#135	C₂×C₇	1	2	yes	complemented
129	C₂×#405	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
131	C₇×#41	—	2	8	no	—
132	C₇×#41	—	2	8	no	—
133	C₂×C₇×Q₈	—	2	4	no	—
134	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
135	C₂×C₇×D₄	—	2	4	no	—
136	C₂×C₇×D₄	—	2	8	no	—
137	C₂×C₇×D₄	—	2	4	no	—
138	C₂×C₇×D₄	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₇	—	2	2	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	8	no	—
143	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
149	C₇×Q₁₆	—	2	4	no	—
150	C₇×Q₁₆	—	2	4	no	—
151	C₇×SD₁₆	—	2	8	no	—
152	C₇×SD₁₆	—	2	8	no	—
153	C₇×D₈	—	2	4	no	—
154	C₇×D₈	—	2	4	no	—
155	C₇×M₁₆	—	2	8	no	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	—	2	8	no	—
159	C₂×C₇×C₈	#41	1	4	yes	—
160	C₂×C₇×C₈	#41	1	4	yes	—
161	C₂×C₇×C₈	C₂⁴	1	2	yes	—
162	C₂×C₇×C₈	C₂⁴	1	2	yes	—
163	C₂×C₇×C₈	C₂⁴	1	2	yes	—
164	C₂×C₇×C₈	C₂⁴	1	2	yes	—
165	C₇×C₄⋊C₄	—	2	8	no	—
166	C₇×C₄⋊C₄	—	2	4	no	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	—	2	8	no	—
169	C₇×C₄⋊C₄	—	2	4	no	—
170	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
171	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
172	C₇×C₂²⋊C₄	—	2	4	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	2	8	no	—
175	C₇×C₂²⋊C₄	—	2	8	no	—
176	C₇×C₂²⋊C₄	—	2	8	no	—
177	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
178	C₄²×C₇	—	2	8	no	—
179	C₄²×C₇	—	2	4	no	—
180	C₄²×C₇	C₂×D₄	1	2	yes	—
181	C₄²×C₇	C₂×D₄	1	2	yes	—
182	C₄²×C₇	C₂⁴	1	2	yes	—
183	C₄²×C₇	C₂⁴	1	2	yes	—
184	C₂×#135	C₂²×C₇	1	2	yes	—
185	C₂×#135	C₂²×C₇	1	2	yes	—
186	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
187	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
188	#542	C₂²×C₇	1	8	yes	—
189	#541	C₂²×C₇	1	4	yes	—
190	#540	C₂²×C₇	1	4	yes	—
191	#539	—	2	4	no	—
192	#538	—	2	4	no	—
193	#533	C₂²×C₇	1	2	yes	—
194	#532	C₂²×C₇	1	2	yes	—
195	#529	—	2	8	no	—
196	#525	C₂²×C₇	1	4	yes	—
197	C₄×#41	C₂²×C₇	1	4	yes	—
198	C₂×#117	C₂²×C₇	1	1	yes	characteristic
199	#501	C₂²×C₇	1	8	yes	complemented
200	#497	C₂²×C₇	1	4	yes	complemented
201	#496	C₂²×C₇	1	4	yes	complemented
202	#488	C₂²×C₇	1	8	yes	complemented
203	#487	C₂²×C₇	1	4	yes	complemented
204	#486	C₂²×C₇	1	4	yes	complemented
205	#470	C₂²×C₇	1	4	yes	—
206	#469	C₂²×C₇	1	4	yes	—
207	#468	C₂²×C₇	1	8	yes	—
208	#467	C₂²×C₇	1	4	yes	—
209	#466	C₂²×C₇	1	4	yes	—
210	#465	C₂²×C₇	1	8	yes	—
211	#442	C₂²×C₇	1	4	yes	complemented
212	#441	C₂²×C₇	1	4	yes	complemented
213	#440	C₂²×C₇	1	8	yes	complemented
214	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
215	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
216	C₄×D₈	C₂²×C₇	1	4	yes	complemented
217	#427	C₂²×C₇	1	2	yes	—
218	#427	C₂²×C₇	1	2	yes	—
219	#416	C₂²×C₇	1	4	yes	—
220	#416	C₂²×C₇	1	4	yes	—
221	#405	C₂²×C₇	1	8	yes	—
222	C₂×#97	C₂²×C₇	1	1	yes	characteristic
223	C₂×#97	C₂²×C₇	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
226	C₂³×C₇	—	2	2	no	—
227	C₂³×C₇	—	2	4	no	—
228	C₂³×C₇	—	4	2	no	—
229	C₂³×C₇	C₂²×D₄	1	2	yes	—
230	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₇×Q₈	—	2	4	no	—
232	C₇×Q₈	—	2	4	no	—
233	C₇×Q₈	—	8	4	no	—
234	C₇×D₄	—	2	4	no	—
235	C₇×D₄	—	2	4	no	—
236	C₇×D₄	—	4	8	no	—
237	C₇×D₄	—	8	4	no	—
238	C₇×D₄	—	8	8	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	4	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	8	no	—
245	C₂×C₄×C₇	—	4	2	no	—
246	C₂×C₄×C₇	—	4	2	no	—
247	C₂×C₄×C₇	—	4	8	no	—
248	C₂×C₄×C₇	—	8	8	no	—
249	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₇	C₂×#41	1	2	yes	—
254	C₂×C₄×C₇	C₂×#41	1	2	yes	—
255	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
256	C₇×C₈	—	2	2	no	—
257	C₇×C₈	—	2	2	no	—
258	C₇×C₈	C₂×#41	1	4	yes	—
259	C₇×C₈	C₂×#41	1	4	yes	—
260	C₂×#41	C₂³×C₇	1	4	yes	—
261	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
262	#135	—	2	8	no	—
263	#135	—	2	8	no	—
264	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
265	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
266	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
267	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
268	C₂×D₈	C₂³×C₇	1	2	yes	—
269	C₂×D₈	C₂³×C₇	1	2	yes	—
270	C₂×M₁₆	—	2	4	no	—
271	C₂×M₁₆	C₂³×C₇	1	4	yes	—
272	C₂²×C₈	—	2	4	no	—
273	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₇	1	4	yes	—
275	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
278	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
279	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
280	#127	C₂³×C₇	1	2	yes	—
281	#126	—	2	8	no	—
282	#126	—	2	8	no	—
283	#125	—	2	8	no	—
284	#125	C₂³×C₇	1	4	yes	—
285	#124	—	2	8	no	—
286	#124	C₂³×C₇	1	4	yes	—
287	#123	—	2	4	no	—
288	#123	—	2	8	no	—
289	#123	—	2	8	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	8	no	—
292	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
293	#121	—	2	4	no	—
294	#121	—	2	8	no	—
295	#121	C₂³×C₇	1	8	yes	—
296	#120	—	2	4	no	—
297	C₄×Q₈	—	2	4	no	—
298	C₄×Q₈	C₂³×C₇	1	8	yes	—
299	C₄×D₄	—	2	8	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	C₂³×C₇	1	8	yes	—
303	#117	—	2	4	no	—
304	#117	C₇×D₄	1	4	yes	—
305	#117	C₂³×C₇	1	4	yes	—
306	#117	C₂³×C₇	1	4	yes	—
307	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
308	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
312	#107	C₂³×C₇	1	4	yes	—
313	#107	C₂³×C₇	1	4	yes	—
314	#106	C₂³×C₇	1	4	yes	—
315	#106	C₂³×C₇	1	4	yes	—
316	#103	C₂³×C₇	1	8	yes	—
317	#103	C₂³×C₇	1	8	yes	—
318	#102	C₂³×C₇	1	8	yes	—
319	#102	C₂³×C₇	1	8	yes	—
320	#97	C₂³×C₇	1	4	yes	—
321	#97	C₂³×C₇	1	4	yes	—
322	C₄×C₈	C₂³×C₇	1	4	yes	—
323	C₄×C₈	C₂³×C₇	1	4	yes	—
324	C₂²×C₇	—	2	2	no	—
325	C₂²×C₇	—	2	4	no	—
326	C₂²×C₇	—	2	2	no	—
327	C₂²×C₇	—	4	4	no	—
328	C₂²×C₇	—	4	8	no	—
329	C₂²×C₇	—	4	4	no	—
330	C₂²×C₇	#532	1	2	yes	—
331	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
332	C₄×C₇	—	2	4	no	—
333	C₄×C₇	—	2	4	no	—
334	C₄×C₇	—	2	2	no	—
335	C₄×C₇	—	4	8	no	—
336	C₄×C₇	—	4	4	no	—
337	C₄×C₇	#532	1	2	yes	—
338	C₄×C₇	C₂²×#41	1	1	yes	characteristic
339	C₄×C₇	C₂²×#41	1	1	yes	characteristic
340	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
341	#41	—	2	8	no	—
342	#41	—	2	8	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	C₂⁴×C₇	1	4	yes	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
355	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
356	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
359	Q₁₆	—	2	4	no	—
360	Q₁₆	—	2	4	no	—
361	SD₁₆	—	2	8	no	—
362	SD₁₆	—	2	8	no	—
363	D₈	—	2	4	no	—
364	D₈	—	2	4	no	—
365	M₁₆	—	2	8	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	C₇×#41	1	4	yes	—
370	C₂×C₈	C₇×#41	1	4	yes	—
371	C₂×C₈	C₂⁴×C₇	1	2	yes	—
372	C₂×C₈	C₂⁴×C₇	1	2	yes	—
373	C₂×C₈	C₂⁴×C₇	1	2	yes	—
374	C₂×C₈	C₂⁴×C₇	1	2	yes	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
381	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
388	C₄²	—	2	4	no	—
389	C₄²	—	2	8	no	—
390	C₄²	C₂×C₇×D₄	1	2	yes	—
391	C₄²	C₂×C₇×D₄	1	2	yes	—
392	C₄²	C₂⁴×C₇	1	2	yes	—
393	C₄²	C₂⁴×C₇	1	2	yes	—
394	C₂×C₇	—	2	2	no	—
395	C₂×C₇	—	4	2	no	—
396	C₂×C₇	—	8	4	no	—
397	C₂×C₇	C₂×#532	1	1	yes	characteristic
398	C₂×C₇	#3584	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂²×C₇×D₄	1	2	yes	—
403	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	4	no	—
406	Q₈	—	8	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	8	no	—
410	D₄	—	8	4	no	—
411	D₄	—	8	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
423	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
424	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
425	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
426	C₂×C₄	C₂×C₇×#41	1	2	yes	—
427	C₂×C₄	C₂×C₇×#41	1	2	yes	—
428	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
431	C₈	C₂×C₇×#41	1	4	yes	—
432	C₈	C₂×C₇×#41	1	4	yes	—
433	C₇	#60685	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	4	no	—
440	C₂²	C₇×#532	1	2	yes	—
441	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	4	8	no	—
446	C₄	—	4	4	no	—
447	C₄	C₇×#532	1	2	yes	—
448	C₄	C₂²×C₇×#41	1	1	yes	characteristic
449	C₄	C₂²×C₇×#41	1	1	yes	characteristic
450	C₂	—	2	2	no	—
451	C₂	—	4	2	no	—
452	C₂	—	8	4	no	—
453	C₂	C₂×C₇×#532	1	1	yes	characteristic
454	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3455	C₂	semidirect
2. C₇×#3179	C₂	semidirect
3. C₇×#3178	C₂	semidirect
4. C₇×#3162	C₂	semidirect
5. C₇×#3150	C₂	semidirect
6. C₇×#3131	C₂	semidirect
7. C₇×#3054	C₂	semidirect
8. C₇×#3050	C₂	semidirect
9. C₇×#2943	C₂	semidirect
10. C₄×C₇×#135	C₂	semidirect
11. C₂×C₇×#405	C₂	semidirect
27. C₇×#501	C₂²	semidirect
28. C₇×#497	C₂²	semidirect
29. C₇×#496	C₂²	semidirect
30. C₇×#488	C₂²	semidirect
31. C₇×#487	C₂²	semidirect
32. C₇×#486	C₂²	semidirect
39. C₇×#442	C₂²	semidirect
40. C₇×#441	C₂²	semidirect
41. C₇×#440	C₂²	semidirect
42. C₄×C₇×Q₁₆	C₂²	semidirect
43. C₄×C₇×SD₁₆	C₂²	semidirect
44. C₄×C₇×D₈	C₂²	semidirect
54. #60685	C₇	direct (N × H)
119. #3455	C₂×C₇	semidirect
120. #3179	C₂×C₇	semidirect
121. #3178	C₂×C₇	semidirect
122. #3162	C₂×C₇	semidirect
123. #3150	C₂×C₇	semidirect
124. #3131	C₂×C₇	semidirect
125. #3054	C₂×C₇	semidirect
126. #3050	C₂×C₇	semidirect
127. #2943	C₂×C₇	semidirect
128. C₄×#135	C₂×C₇	semidirect
129. C₂×#405	C₂×C₇	semidirect
199. #501	C₂²×C₇	semidirect
200. #497	C₂²×C₇	semidirect
201. #496	C₂²×C₇	semidirect
202. #488	C₂²×C₇	semidirect
203. #487	C₂²×C₇	semidirect
204. #486	C₂²×C₇	semidirect
211. #442	C₂²×C₇	semidirect
212. #441	C₂²×C₇	semidirect
213. #440	C₂²×C₇	semidirect
214. C₄×Q₁₆	C₂²×C₇	semidirect
215. C₄×SD₁₆	C₂²×C₇	semidirect
216. C₄×D₈	C₂²×C₇	semidirect
433. C₇	#60685	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×#3455	2
C₇×#3179	2
C₇×#3178	2
C₇×#3162	2
C₇×#3150	2
C₇×#3131	2
C₇×#3054	2
C₇×#3050	2
C₇×#2943	2
C₄×C₇×#135	2
C₂×C₇×#405	2
#60685	7

Subgroups — C7×#60685 #13237901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60685 #13237901