Subgroups — C₇×#60693 #13237909

Order 1792.

1998 conjugacy classes of subgroups.

The subgroup lattice has 432 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×#3185	C₂	1	2	yes	maximal, complemented
3	C₇×#3184	C₂	1	2	yes	maximal, complemented
4	C₇×#3183	C₂	1	8	yes	maximal, complemented
5	C₇×#3182	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×#3054	C₂	1	4	yes	maximal, complemented
10	C₇×#2943	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#135	C₂²	1	4	yes	—
13	C₂²×C₇×M₁₆	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×#470	C₂²	1	8	yes	—
37	C₇×#469	C₂²	1	8	yes	—
38	C₇×#468	C₂²	1	16	yes	—
39	C₇×#442	C₂²	1	8	yes	complemented
40	C₇×#441	C₂²	1	8	yes	complemented
41	C₇×#440	C₂²	1	16	yes	complemented
42	C₇×#427	C₂²	1	4	yes	—
43	C₇×#416	C₂²	1	8	yes	—
44	C₄×C₇×M₁₆	C₂²	1	2	yes	—
45	C₄×C₇×M₁₆	C₂²	1	4	yes	—
46	C₄×C₇×M₁₆	C₂²	1	2	yes	—
47	C₂×C₇×#97	C₂²	1	2	yes	—
48	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
50	#60693	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	C₂×C₇×M₁₆	—	2	8	no	—
60	C₂×C₇×M₁₆	C₂³	1	4	yes	—
61	C₂×C₇×M₁₆	C₂³	1	4	yes	—
62	C₂²×C₇×C₈	C₂³	1	2	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	4	yes	—
96	C₂×C₄²×C₇	D₄	1	2	yes	—
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	C₇×#107	C₂³	1	8	yes	—
102	C₇×#106	C₂³	1	8	yes	—
103	C₇×#103	C₂³	1	16	yes	—
104	C₇×#102	C₂³	1	16	yes	—
105	C₇×#97	C₂³	1	4	yes	—
106	C₇×#97	C₂³	1	4	yes	—
107	C₄×C₇×C₈	C₂³	1	2	yes	—
108	C₄×C₇×C₈	C₂³	1	2	yes	—
109	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₄×C₇×C₈	C₂³	1	2	yes	—
112	#3444	C₂×C₇	1	2	yes	complemented
113	#3185	C₂×C₇	1	2	yes	complemented
114	#3184	C₂×C₇	1	2	yes	complemented
115	#3183	C₂×C₇	1	8	yes	complemented
116	#3182	C₂×C₇	1	4	yes	complemented
117	#3160	C₂×C₇	1	1	yes	characteristic, complemented
118	#3147	C₂×C₇	1	1	yes	characteristic, complemented
119	#3131	C₂×C₇	1	2	yes	complemented
120	#3054	C₂×C₇	1	4	yes	complemented
121	#2943	C₂×C₇	1	4	yes	complemented
122	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
123	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
124	C₇×#41	—	2	16	no	—
125	C₇×#41	—	4	16	no	—
126	C₂×C₇×Q₈	—	2	4	no	—
127	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	8	no	—
130	C₂×C₇×D₄	—	2	4	no	—
131	C₂×C₇×D₄	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇	—	2	4	no	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	4	4	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
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	4	yes	—
142	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
144	C₇×Q₁₆	—	2	8	no	—
145	C₇×SD₁₆	—	2	16	no	—
146	C₇×D₈	—	2	8	no	—
147	C₇×M₁₆	—	2	8	no	—
148	C₇×M₁₆	—	2	8	no	—
149	C₂×C₇×C₈	—	2	4	no	—
150	C₂×C₇×C₈	#41	1	8	yes	complemented
151	C₂×C₇×C₈	C₂⁴	1	4	yes	—
152	C₂×C₇×C₈	C₂⁴	1	2	yes	—
153	C₂×C₇×C₈	C₂⁴	1	2	yes	—
154	C₇×C₄⋊C₄	—	2	4	no	—
155	C₇×C₄⋊C₄	—	2	4	no	—
156	C₇×C₄⋊C₄	—	2	8	no	—
157	C₇×C₄⋊C₄	—	2	8	no	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
160	C₇×C₂²⋊C₄	—	2	8	no	—
161	C₇×C₂²⋊C₄	—	2	4	no	—
162	C₇×C₂²⋊C₄	—	2	8	no	—
163	C₇×C₂²⋊C₄	—	2	8	no	—
164	C₇×C₂²⋊C₄	—	2	8	no	—
165	C₄²×C₇	—	2	8	no	—
166	C₄²×C₇	—	2	4	no	—
167	C₄²×C₇	C₂×D₄	1	4	yes	—
168	C₄²×C₇	C₂×D₄	1	4	yes	—
169	C₄²×C₇	C₂×D₄	1	2	yes	—
170	C₄²×C₇	C₂×D₄	1	2	yes	—
171	C₄²×C₇	C₂⁴	1	1	yes	characteristic
172	C₄²×C₇	C₂⁴	1	1	yes	characteristic
173	C₄²×C₇	C₂⁴	1	2	yes	—
174	C₂×#135	C₂²×C₇	1	4	yes	—
175	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
176	#533	C₂²×C₇	1	4	yes	—
177	#533	C₂²×C₇	1	2	yes	—
178	#532	C₂²×C₇	1	2	yes	—
179	#532	C₂²×C₇	1	4	yes	—
180	#529	—	2	4	no	—
181	#529	—	2	4	no	—
182	#529	C₂²×C₇	1	8	yes	—
183	#525	—	2	4	no	—
184	#525	C₂²×C₇	1	4	yes	—
185	C₄×#41	—	2	4	no	—
186	C₄×#41	C₂²×C₇	1	4	yes	—
187	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
188	#500	C₂²×C₇	1	2	yes	complemented
189	#499	C₂²×C₇	1	4	yes	complemented
190	#498	C₂²×C₇	1	2	yes	complemented
191	#495	C₂²×C₇	1	4	yes	complemented
192	#494	C₂²×C₇	1	1	yes	characteristic, complemented
193	#493	C₂²×C₇	1	1	yes	characteristic, complemented
194	#492	C₂²×C₇	1	2	yes	complemented
195	#488	C₂²×C₇	1	8	yes	complemented
196	#487	C₂²×C₇	1	4	yes	complemented
197	#486	C₂²×C₇	1	4	yes	complemented
198	#470	C₂²×C₇	1	8	yes	—
199	#469	C₂²×C₇	1	8	yes	—
200	#468	C₂²×C₇	1	16	yes	—
201	#442	C₂²×C₇	1	8	yes	complemented
202	#441	C₂²×C₇	1	8	yes	complemented
203	#440	C₂²×C₇	1	16	yes	complemented
204	#427	C₂²×C₇	1	4	yes	—
205	#416	C₂²×C₇	1	8	yes	—
206	C₄×M₁₆	C₂²×C₇	1	2	yes	—
207	C₄×M₁₆	C₂²×C₇	1	4	yes	—
208	C₄×M₁₆	C₂²×C₇	1	2	yes	—
209	C₂×#97	C₂²×C₇	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
211	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
212	C₂³×C₇	—	2	2	no	—
213	C₂³×C₇	—	2	4	no	—
214	C₂³×C₇	—	4	2	no	—
215	C₂³×C₇	C₂²×D₄	1	2	yes	—
216	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
217	C₇×Q₈	—	2	8	no	—
218	C₇×Q₈	—	4	8	no	—
219	C₇×D₄	—	2	8	no	—
220	C₇×D₄	—	4	16	no	—
221	C₇×D₄	—	4	8	no	—
222	C₇×D₄	—	4	8	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	4	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	2	8	no	—
227	C₂×C₄×C₇	—	2	4	no	—
228	C₂×C₄×C₇	—	2	4	no	—
229	C₂×C₄×C₇	—	2	8	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	4	no	—
232	C₂×C₄×C₇	—	4	16	no	—
233	C₂×C₄×C₇	—	4	8	no	—
234	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	4	yes	—
240	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
241	C₇×C₈	—	2	4	no	—
242	C₇×C₈	C₂×#41	1	4	yes	—
243	C₇×C₈	C₂×#41	1	4	yes	—
244	C₂×#41	—	2	4	no	—
245	C₂×#41	C₂³×C₇	1	4	yes	—
246	C₂³×C₄	C₇×D₄	1	2	yes	—
247	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
248	#135	—	2	16	no	—
249	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
250	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
251	C₂×D₈	C₂³×C₇	1	4	yes	—
252	C₂×M₁₆	—	2	8	no	—
253	C₂×M₁₆	C₂³×C₇	1	4	yes	—
254	C₂×M₁₆	C₂³×C₇	1	4	yes	—
255	C₂²×C₈	C₂³×C₇	1	2	yes	—
256	C₂²×C₈	C₂³×C₇	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
258	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
259	#127	C₂³×C₇	1	2	yes	—
260	#126	—	2	8	no	—
261	#125	—	2	4	no	—
262	#125	C₂³×C₇	1	4	yes	—
263	#124	—	2	4	no	—
264	#124	C₂³×C₇	1	4	yes	—
265	#123	—	2	8	no	—
266	#123	—	2	4	no	—
267	C₂²⋊Q₈	—	2	4	no	—
268	C₂²⋊Q₈	—	2	4	no	—
269	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
270	#121	—	2	4	no	—
271	#121	—	2	4	no	—
272	#121	C₂³×C₇	1	8	yes	—
273	#120	—	2	4	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	C₂³×C₇	1	8	yes	—
277	C₄×D₄	—	2	8	no	—
278	C₄×D₄	—	2	8	no	—
279	C₄×D₄	—	2	8	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	C₂³×C₇	1	8	yes	—
283	#117	—	2	4	no	—
284	#117	—	2	8	no	—
285	#117	—	2	4	no	—
286	#117	C₂³×C₇	1	4	yes	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	C₇×D₄	1	4	yes	—
289	C₂×C₄²	C₇×D₄	1	2	yes	—
290	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₇	1	2	yes	—
292	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₇	1	2	yes	—
294	#107	C₂³×C₇	1	8	yes	—
295	#106	C₂³×C₇	1	8	yes	—
296	#103	C₂³×C₇	1	16	yes	—
297	#102	C₂³×C₇	1	16	yes	—
298	#97	C₂³×C₇	1	4	yes	—
299	#97	C₂³×C₇	1	4	yes	—
300	C₄×C₈	C₂³×C₇	1	2	yes	—
301	C₄×C₈	C₂³×C₇	1	2	yes	—
302	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
304	C₄×C₈	C₂³×C₇	1	2	yes	—
305	C₂²×C₇	—	2	2	no	—
306	C₂²×C₇	—	2	2	no	—
307	C₂²×C₇	—	2	4	no	—
308	C₂²×C₇	—	4	4	no	—
309	C₂²×C₇	—	4	4	no	—
310	C₂²×C₇	—	4	8	no	—
311	C₂²×C₇	#532	1	2	yes	—
312	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
313	C₄×C₇	—	2	2	no	—
314	C₄×C₇	—	2	4	no	—
315	C₄×C₇	—	2	2	no	—
316	C₄×C₇	—	4	4	no	—
317	C₄×C₇	—	4	8	no	—
318	C₄×C₇	#532	1	2	yes	—
319	C₄×C₇	#575	1	4	yes	—
320	C₄×C₇	C₂²×#41	1	2	yes	—
321	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
322	#41	—	2	16	no	—
323	#41	—	4	16	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	C₂⁴×C₇	1	4	yes	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
337	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
338	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
339	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
342	Q₁₆	—	2	8	no	—
343	SD₁₆	—	2	16	no	—
344	D₈	—	2	8	no	—
345	M₁₆	—	2	8	no	—
346	M₁₆	—	2	8	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	C₇×#41	1	8	yes	complemented
349	C₂×C₈	C₂⁴×C₇	1	4	yes	—
350	C₂×C₈	C₂⁴×C₇	1	2	yes	—
351	C₂×C₈	C₂⁴×C₇	1	2	yes	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	8	no	—
357	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₄²	—	2	8	no	—
364	C₄²	—	2	4	no	—
365	C₄²	C₂×C₇×D₄	1	2	yes	—
366	C₄²	C₂×C₇×D₄	1	4	yes	—
367	C₄²	C₂×C₇×D₄	1	2	yes	—
368	C₄²	C₂×C₇×D₄	1	4	yes	—
369	C₄²	C₂⁴×C₇	1	1	yes	characteristic
370	C₄²	C₂⁴×C₇	1	1	yes	characteristic
371	C₄²	C₂⁴×C₇	1	2	yes	—
372	C₂×C₇	—	2	2	no	—
373	C₂×C₇	—	4	2	no	—
374	C₂×C₇	—	8	4	no	—
375	C₂×C₇	C₂×#532	1	1	yes	characteristic
376	C₂×C₇	C₂×#575	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	C₂²×C₇×D₄	1	2	yes	—
381	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	Q₈	—	4	8	no	—
384	D₄	—	2	8	no	—
385	D₄	—	4	16	no	—
386	D₄	—	4	8	no	—
387	D₄	—	4	8	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	16	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
400	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
401	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
402	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
404	C₂×C₄	C₂×C₇×#41	1	4	yes	—
405	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
406	C₈	—	2	4	no	—
407	C₈	C₂×C₇×#41	1	4	yes	—
408	C₈	C₂×C₇×#41	1	4	yes	—
409	C₇	#60693	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	2	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	4	no	—
416	C₂²	C₇×#532	1	2	yes	—
417	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	8	no	—
422	C₄	—	4	4	no	—
423	C₄	C₇×#532	1	2	yes	—
424	C₄	C₇×#575	1	4	yes	—
425	C₄	C₂²×C₇×#41	1	2	yes	—
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	—	8	4	no	—
429	C₂	C₂×C₇×#532	1	1	yes	characteristic
430	C₂	C₂×C₇×#575	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 ◁ 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×#3185	C₂	semidirect
3. C₇×#3184	C₂	semidirect
4. C₇×#3183	C₂	semidirect
5. C₇×#3182	C₂	semidirect
6. C₇×#3160	C₂	semidirect
7. C₇×#3147	C₂	semidirect
8. C₇×#3131	C₂	semidirect
9. C₇×#3054	C₂	semidirect
10. C₇×#2943	C₂	semidirect
11. C₂×C₄×C₇×M₁₆	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. C₇×#442	C₂²	semidirect
40. C₇×#441	C₂²	semidirect
41. C₇×#440	C₂²	semidirect
50. #60693	C₇	direct (N × H)
112. #3444	C₂×C₇	semidirect
113. #3185	C₂×C₇	semidirect
114. #3184	C₂×C₇	semidirect
115. #3183	C₂×C₇	semidirect
116. #3182	C₂×C₇	semidirect
117. #3160	C₂×C₇	semidirect
118. #3147	C₂×C₇	semidirect
119. #3131	C₂×C₇	semidirect
120. #3054	C₂×C₇	semidirect
121. #2943	C₂×C₇	semidirect
122. C₂×C₄×M₁₆	C₂×C₇	semidirect
150. C₂×C₇×C₈	#41	semidirect
188. #500	C₂²×C₇	semidirect
189. #499	C₂²×C₇	semidirect
190. #498	C₂²×C₇	semidirect
191. #495	C₂²×C₇	semidirect
192. #494	C₂²×C₇	semidirect
193. #493	C₂²×C₇	semidirect
194. #492	C₂²×C₇	semidirect
195. #488	C₂²×C₇	semidirect
196. #487	C₂²×C₇	semidirect
197. #486	C₂²×C₇	semidirect
201. #442	C₂²×C₇	semidirect
202. #441	C₂²×C₇	semidirect
203. #440	C₂²×C₇	semidirect
348. C₂×C₈	C₇×#41	semidirect
409. C₇	#60693	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×#3185	2
C₇×#3184	2
C₇×#3183	2
C₇×#3182	2
C₇×#3160	2
C₇×#3147	2
C₇×#3131	2
C₇×#3054	2
C₇×#2943	2
C₂×C₄×C₇×M₁₆	2
#60693	7

Subgroups — C7×#60693 #13237909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60693 #13237909