Subgroups — C₇×#60710 #13237926

Order 1792.

1966 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₇×#3184	C₂	1	2	yes	maximal, complemented
3	C₇×#3183	C₂	1	2	yes	maximal, complemented
4	C₇×#3179	C₂	1	4	yes	maximal, complemented
5	C₇×#3176	C₂	1	2	yes	maximal, complemented
6	C₇×#3173	C₂	1	2	yes	maximal, complemented
7	C₇×#3171	C₂	1	4	yes	maximal, complemented
8	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3055	C₂	1	2	yes	maximal, complemented
12	C₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#469	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₇×#135	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₇×#555	—	2	2	no	—
24	C₇×#553	—	2	2	no	—
25	C₇×#553	—	2	2	no	—
26	C₇×#551	—	2	4	no	—
27	C₇×#547	—	2	2	no	—
28	C₇×#546	—	2	4	no	—
29	C₇×#544	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	4	yes	complemented
31	C₇×#540	C₂²	1	4	yes	complemented
32	C₇×#535	C₂²	1	2	yes	—
33	C₇×#532	C₂²	1	4	yes	complemented
34	C₇×#529	C₂²	1	4	yes	complemented
35	C₇×#525	C₂²	1	2	yes	—
36	C₂×C₇×#121	C₂²	1	2	yes	—
37	C₇×#520	C₂²	1	2	yes	—
38	C₇×#518	C₂²	1	2	yes	—
39	C₂×C₇×#117	C₂²	1	1	yes	characteristic
40	C₇×#501	C₂²	1	4	yes	complemented
41	C₇×#499	C₂²	1	2	yes	complemented
42	C₇×#498	C₂²	1	2	yes	complemented
43	C₇×#496	C₂²	1	4	yes	complemented
44	C₇×#495	C₂²	1	2	yes	complemented
45	C₇×#493	C₂²	1	2	yes	complemented
46	C₇×#490	C₂²	1	4	yes	complemented
47	C₇×#489	C₂²	1	4	yes	complemented
48	C₇×#488	C₂²	1	4	yes	complemented
49	C₇×#486	C₂²	1	4	yes	complemented
50	C₇×#470	C₂²	1	1	yes	characteristic, complemented
51	C₇×#470	C₂²	1	1	yes	characteristic, complemented
52	C₇×#469	C₂²	1	2	yes	—
53	C₇×#469	C₂²	1	2	yes	—
54	C₇×#469	C₂²	1	2	yes	—
55	C₇×#469	C₂²	1	2	yes	—
56	C₇×#469	C₂²	1	4	yes	complemented
57	C₇×#469	C₂²	1	1	yes	characteristic, complemented
58	C₇×#469	C₂²	1	1	yes	characteristic, complemented
59	C₇×#468	C₂²	1	2	yes	complemented
60	C₇×#468	C₂²	1	4	yes	complemented
61	C₇×#468	C₂²	1	2	yes	complemented
62	C₇×#466	C₂²	1	4	yes	complemented
63	C₇×#465	C₂²	1	4	yes	complemented
64	C₇×#442	C₂²	1	2	yes	complemented
65	C₇×#442	C₂²	1	2	yes	complemented
66	C₇×#442	C₂²	1	2	yes	complemented
67	C₇×#442	C₂²	1	4	yes	complemented
68	C₇×#441	C₂²	1	2	yes	complemented
69	C₇×#440	C₂²	1	4	yes	complemented
70	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
71	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
72	C₄×C₇×D₈	C₂²	1	4	yes	complemented
73	C₄×C₇×D₈	C₂²	1	4	yes	complemented
74	C₇×#428	C₂²	1	2	yes	—
75	C₇×#427	C₂²	1	1	yes	characteristic
76	C₂×C₇×#106	C₂²	1	1	yes	characteristic
77	C₇×#418	C₂²	1	2	yes	—
78	C₇×#417	C₂²	1	2	yes	—
79	C₇×#416	C₂²	1	2	yes	—
80	C₂×C₇×#102	C₂²	1	2	yes	—
81	C₇×#405	C₂²	1	1	yes	characteristic
82	C₇×#405	C₂²	1	1	yes	characteristic
83	C₇×#405	C₂²	1	1	yes	characteristic
84	C₇×#405	C₂²	1	1	yes	characteristic
85	C₇×#405	C₂²	1	2	yes	complemented
86	C₇×#405	C₂²	1	2	yes	complemented
87	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
88	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
89	#60710	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	4	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×D₄	—	2	2	no	—
93	C₂²×C₇×D₄	C₂³	1	2	yes	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₇×AGL(1,ℤ/8)	—	2	8	no	—
96	C₇×#135	—	2	4	no	—
97	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×D₈	—	2	4	no	—
101	C₂×C₇×D₈	C₂³	1	4	yes	—
102	C₂×C₇×D₈	C₂³	1	2	yes	—
103	C₂×C₇×D₈	C₂³	1	2	yes	—
104	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
105	C₂×C₇×M₁₆	—	2	4	no	—
106	C₂×C₇×M₁₆	—	2	4	no	—
107	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
108	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
109	C₂×C₇×M₁₆	C₂³	1	2	yes	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	C₂³	1	2	yes	—
115	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	—	2	2	no	—
118	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
119	C₇×#127	C₂³	1	4	yes	—
120	C₇×#126	—	2	4	no	—
121	C₇×#126	—	2	4	no	—
122	C₇×#125	—	2	2	no	—
123	C₇×#125	C₂³	1	4	yes	—
124	C₇×#124	—	2	4	no	—
125	C₇×#124	—	2	4	no	—
126	C₇×#124	C₂³	1	4	yes	—
127	C₇×#123	—	2	2	no	—
128	C₇×#123	—	2	4	no	—
129	C₇×#123	—	2	4	no	—
130	C₇×#123	—	2	4	no	—
131	C₇×#123	—	2	4	no	—
132	C₇×C₂²⋊Q₈	—	2	4	no	—
133	C₇×C₂²⋊Q₈	—	2	4	no	—
134	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₇×#121	—	2	2	no	—
137	C₇×#121	—	2	2	no	—
138	C₇×#121	—	2	4	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	4	no	—
142	C₇×#121	—	2	4	no	—
143	C₇×#121	C₂³	1	2	yes	—
144	C₇×#121	C₂³	1	4	yes	—
145	C₇×#121	C₂³	1	4	yes	—
146	C₇×#121	C₂³	1	2	yes	—
147	C₇×#120	—	2	2	no	—
148	C₇×#120	—	2	4	no	—
149	C₄×C₇×Q₈	C₂³	1	4	yes	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	—	2	2	no	—
152	C₄×C₇×D₄	—	2	4	no	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	4	no	—
156	C₄×C₇×D₄	—	2	4	no	—
157	C₄×C₇×D₄	C₂³	1	4	yes	—
158	C₄×C₇×D₄	C₂³	1	4	yes	—
159	C₄×C₇×D₄	C₂³	1	4	yes	—
160	C₇×#117	—	2	2	no	—
161	C₇×#117	—	2	4	no	—
162	C₇×#117	D₄	1	2	yes	—
163	C₇×#117	D₄	1	2	yes	—
164	C₇×#117	C₂³	1	2	yes	—
165	C₇×#117	C₂³	1	1	yes	characteristic
166	C₇×#117	C₂³	1	1	yes	characteristic
167	C₇×#117	C₂³	1	2	yes	—
168	C₂×C₇×C₄⋊C₄	—	2	2	no	—
169	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
170	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
172	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
173	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₇×#107	C₂³	1	4	yes	—
176	C₇×#107	C₂³	1	2	yes	—
177	C₇×#106	C₂³	1	2	yes	—
178	C₇×#106	C₂³	1	2	yes	—
179	C₇×#106	C₂³	1	1	yes	characteristic
180	C₇×#106	C₂³	1	1	yes	characteristic
181	C₇×#106	C₂³	1	4	yes	—
182	C₇×#103	C₂³	1	2	yes	—
183	C₇×#103	C₂³	1	2	yes	—
184	C₇×#103	C₂³	1	4	yes	—
185	C₇×#102	C₂³	1	4	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	2	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×#102	C₂³	1	4	yes	—
190	C₇×#102	C₂³	1	4	yes	—
191	C₇×#102	C₂³	1	4	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₇×#97	C₂³	1	2	yes	—
195	C₇×#97	C₂³	1	2	yes	—
196	C₄×C₇×C₈	C₂³	1	2	yes	—
197	C₄×C₇×C₈	C₂³	1	2	yes	—
198	C₄×C₇×C₈	C₂³	1	2	yes	—
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	#3494	C₂×C₇	1	2	yes	complemented
201	#3184	C₂×C₇	1	2	yes	complemented
202	#3183	C₂×C₇	1	2	yes	complemented
203	#3179	C₂×C₇	1	4	yes	complemented
204	#3176	C₂×C₇	1	2	yes	complemented
205	#3173	C₂×C₇	1	2	yes	complemented
206	#3171	C₂×C₇	1	4	yes	complemented
207	#3163	C₂×C₇	1	1	yes	characteristic, complemented
208	#3155	C₂×C₇	1	1	yes	characteristic, complemented
209	#3136	C₂×C₇	1	2	yes	complemented
210	#3055	C₂×C₇	1	2	yes	complemented
211	#3054	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#469	C₂×C₇	1	1	yes	characteristic, complemented
213	#2952	C₂×C₇	1	1	yes	characteristic, complemented
214	#2948	C₂×C₇	1	1	yes	characteristic, complemented
215	#2946	C₂×C₇	1	2	yes	complemented
216	#2873	C₂×C₇	1	1	yes	characteristic, complemented
217	C₂⁴×C₇	—	2	2	no	—
218	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
219	C₇×#41	—	2	4	no	—
220	C₇×#41	—	2	4	no	—
221	C₇×#41	—	8	8	no	—
222	C₂×C₇×Q₈	—	2	4	no	—
223	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
224	C₂×C₇×D₄	—	2	2	no	—
225	C₂×C₇×D₄	—	2	2	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	2	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	4	no	—
232	C₂×C₇×D₄	—	2	4	no	—
233	C₂×C₇×D₄	—	2	4	no	—
234	C₂×C₇×D₄	—	8	4	no	—
235	C₂×C₇×D₄	C₂⁴	1	4	yes	—
236	C₂×C₇×D₄	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇	—	2	2	no	—
238	C₂²×C₄×C₇	—	2	2	no	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	2	no	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
251	C₇×Q₁₆	—	2	2	no	—
252	C₇×SD₁₆	—	2	4	no	—
253	C₇×SD₁₆	—	2	8	no	—
254	C₇×D₈	—	2	4	no	—
255	C₇×D₈	—	2	4	no	—
256	C₇×D₈	—	2	2	no	—
257	C₇×D₈	—	2	8	no	—
258	C₇×M₁₆	—	2	2	no	—
259	C₇×M₁₆	—	2	4	no	—
260	C₇×M₁₆	—	2	2	no	—
261	C₇×M₁₆	—	2	2	no	—
262	C₇×M₁₆	—	2	2	no	—
263	C₇×M₁₆	—	2	2	no	—
264	C₇×M₁₆	#41	1	4	yes	complemented
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	4	no	—
267	C₂×C₇×C₈	#41	1	4	yes	complemented
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×C₈	C₂⁴	1	2	yes	—
270	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
271	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
272	C₂×C₇×C₈	C₂⁴	1	2	yes	—
273	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
274	C₇×C₄⋊C₄	—	2	2	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	4	no	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	2	no	—
281	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
282	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
283	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
287	C₇×C₂²⋊C₄	—	2	2	no	—
288	C₇×C₂²⋊C₄	—	2	2	no	—
289	C₇×C₂²⋊C₄	—	2	2	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	2	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	2	no	—
299	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
302	C₄²×C₇	—	2	4	no	—
303	C₄²×C₇	—	2	2	no	—
304	C₄²×C₇	C₂×D₄	1	4	yes	—
305	C₄²×C₇	C₂⁴	1	2	yes	—
306	C₄²×C₇	C₂⁴	1	2	yes	—
307	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
308	C₂×#135	C₂²×C₇	1	1	yes	characteristic
309	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
311	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
312	#555	—	2	2	no	—
313	#553	—	2	2	no	—
314	#553	—	2	2	no	—
315	#551	—	2	4	no	—
316	#547	—	2	2	no	—
317	#546	—	2	4	no	—
318	#544	C₂²×C₇	1	2	yes	—
319	#542	C₂²×C₇	1	4	yes	complemented
320	#540	C₂²×C₇	1	4	yes	complemented
321	#535	C₂²×C₇	1	2	yes	—
322	#532	C₂²×C₇	1	4	yes	complemented
323	#529	C₂²×C₇	1	4	yes	complemented
324	#525	C₂²×C₇	1	2	yes	—
325	C₂×#121	C₂²×C₇	1	2	yes	—
326	#520	C₂²×C₇	1	2	yes	—
327	#518	C₂²×C₇	1	2	yes	—
328	C₂×#117	C₂²×C₇	1	1	yes	characteristic
329	#501	C₂²×C₇	1	4	yes	complemented
330	#499	C₂²×C₇	1	2	yes	complemented
331	#498	C₂²×C₇	1	2	yes	complemented
332	#496	C₂²×C₇	1	4	yes	complemented
333	#495	C₂²×C₇	1	2	yes	complemented
334	#493	C₂²×C₇	1	2	yes	complemented
335	#490	C₂²×C₇	1	4	yes	complemented
336	#489	C₂²×C₇	1	4	yes	complemented
337	#488	C₂²×C₇	1	4	yes	complemented
338	#486	C₂²×C₇	1	4	yes	complemented
339	#470	C₂²×C₇	1	1	yes	characteristic, complemented
340	#470	C₂²×C₇	1	1	yes	characteristic, complemented
341	#469	C₂²×C₇	1	2	yes	—
342	#469	C₂²×C₇	1	2	yes	—
343	#469	C₂²×C₇	1	2	yes	—
344	#469	C₂²×C₇	1	2	yes	—
345	#469	C₂²×C₇	1	4	yes	complemented
346	#469	C₂²×C₇	1	1	yes	characteristic, complemented
347	#469	C₂²×C₇	1	1	yes	characteristic, complemented
348	#468	C₂²×C₇	1	2	yes	complemented
349	#468	C₂²×C₇	1	4	yes	complemented
350	#468	C₂²×C₇	1	2	yes	complemented
351	#466	C₂²×C₇	1	4	yes	complemented
352	#465	C₂²×C₇	1	4	yes	complemented
353	#442	C₂²×C₇	1	2	yes	complemented
354	#442	C₂²×C₇	1	2	yes	complemented
355	#442	C₂²×C₇	1	2	yes	complemented
356	#442	C₂²×C₇	1	4	yes	complemented
357	#441	C₂²×C₇	1	2	yes	complemented
358	#440	C₂²×C₇	1	4	yes	complemented
359	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
360	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
361	C₄×D₈	C₂²×C₇	1	4	yes	complemented
362	C₄×D₈	C₂²×C₇	1	4	yes	complemented
363	#428	C₂²×C₇	1	2	yes	—
364	#427	C₂²×C₇	1	1	yes	characteristic
365	C₂×#106	C₂²×C₇	1	1	yes	characteristic
366	#418	C₂²×C₇	1	2	yes	—
367	#417	C₂²×C₇	1	2	yes	—
368	#416	C₂²×C₇	1	2	yes	—
369	C₂×#102	C₂²×C₇	1	2	yes	—
370	#405	C₂²×C₇	1	1	yes	characteristic
371	#405	C₂²×C₇	1	1	yes	characteristic
372	#405	C₂²×C₇	1	1	yes	characteristic
373	#405	C₂²×C₇	1	1	yes	characteristic
374	#405	C₂²×C₇	1	2	yes	complemented
375	#405	C₂²×C₇	1	2	yes	complemented
376	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
377	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	4	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	4	2	no	—
382	C₂³×C₇	—	4	4	no	—
383	C₂³×C₇	—	8	2	no	—
384	C₂³×C₇	—	8	2	no	—
385	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
388	C₇×Q₈	—	2	2	no	—
389	C₇×Q₈	—	2	2	no	—
390	C₇×Q₈	—	8	4	no	—
391	C₇×D₄	—	2	4	no	—
392	C₇×D₄	—	2	2	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	2	no	—
395	C₇×D₄	—	4	8	no	—
396	C₇×D₄	—	4	4	no	—
397	C₇×D₄	—	4	4	no	—
398	C₇×D₄	—	4	4	no	—
399	C₇×D₄	—	8	4	no	—
400	C₇×D₄	—	8	4	no	—
401	C₇×D₄	—	8	2	no	—
402	C₇×D₄	—	8	4	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	1	no	—
408	C₂×C₄×C₇	—	2	1	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	2	2	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	4	no	—
414	C₂×C₄×C₇	—	4	4	no	—
415	C₂×C₄×C₇	—	4	4	no	—
416	C₂×C₄×C₇	—	8	4	no	—
417	C₂×C₄×C₇	—	8	4	no	—
418	C₂×C₄×C₇	—	8	4	no	—
419	C₂×C₄×C₇	—	8	2	no	—
420	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
421	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
423	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇	C₂×#41	1	2	yes	—
426	C₂×C₄×C₇	C₂×#41	1	2	yes	—
427	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
428	C₇×C₈	—	2	1	no	—
429	C₇×C₈	—	2	1	no	—
430	C₇×C₈	—	2	2	no	—
431	C₇×C₈	C₂×#41	1	4	yes	—
432	C₇×C₈	C₂×#41	1	2	yes	—
433	C₇×C₈	C₂×#41	1	2	yes	—
434	C₂×#41	—	2	4	no	—
435	C₂×#41	C₂³×C₇	1	2	yes	—
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	C₂³×C₇	1	2	yes	—
438	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
439	AGL(1,ℤ/8)	—	2	8	no	—
440	#135	—	2	4	no	—
441	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
442	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
443	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
444	C₂×D₈	—	2	4	no	—
445	C₂×D₈	C₂³×C₇	1	2	yes	—
446	C₂×D₈	C₂³×C₇	1	2	yes	—
447	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
448	C₂×D₈	C₂³×C₇	1	4	yes	—
449	C₂×M₁₆	—	2	4	no	—
450	C₂×M₁₆	—	2	4	no	—
451	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
452	C₂×M₁₆	C₂³×C₇	1	2	yes	—
453	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
454	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
455	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
456	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
457	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₇	1	2	yes	—
460	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
461	C₄⋊Q₈	—	2	2	no	—
462	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
463	#127	C₂³×C₇	1	4	yes	—
464	#126	—	2	4	no	—
465	#126	—	2	4	no	—
466	#125	—	2	2	no	—
467	#125	C₂³×C₇	1	4	yes	—
468	#124	—	2	4	no	—
469	#124	—	2	4	no	—
470	#124	C₂³×C₇	1	4	yes	—
471	#123	—	2	2	no	—
472	#123	—	2	4	no	—
473	#123	—	2	4	no	—
474	#123	—	2	4	no	—
475	#123	—	2	4	no	—
476	C₂²⋊Q₈	—	2	4	no	—
477	C₂²⋊Q₈	—	2	4	no	—
478	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
479	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
480	#121	—	2	2	no	—
481	#121	—	2	2	no	—
482	#121	—	2	4	no	—
483	#121	—	2	2	no	—
484	#121	—	2	2	no	—
485	#121	—	2	4	no	—
486	#121	—	2	4	no	—
487	#121	C₂³×C₇	1	4	yes	—
488	#121	C₂³×C₇	1	4	yes	—
489	#121	C₂³×C₇	1	2	yes	—
490	#121	C₂³×C₇	1	2	yes	—
491	#120	—	2	2	no	—
492	#120	—	2	4	no	—
493	C₄×Q₈	C₂³×C₇	1	4	yes	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	4	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	C₂³×C₇	1	4	yes	—
502	C₄×D₄	C₂³×C₇	1	4	yes	—
503	C₄×D₄	C₂³×C₇	1	4	yes	—
504	#117	—	2	2	no	—
505	#117	—	2	4	no	—
506	#117	C₇×D₄	1	2	yes	—
507	#117	C₇×D₄	1	2	yes	—
508	#117	C₂³×C₇	1	2	yes	—
509	#117	C₂³×C₇	1	1	yes	characteristic
510	#117	C₂³×C₇	1	1	yes	characteristic
511	#117	C₂³×C₇	1	2	yes	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
518	C₂×C₄²	C₂³×C₇	1	2	yes	—
519	#107	C₂³×C₇	1	2	yes	—
520	#107	C₂³×C₇	1	4	yes	—
521	#106	C₂³×C₇	1	2	yes	—
522	#106	C₂³×C₇	1	2	yes	—
523	#106	C₂³×C₇	1	1	yes	characteristic
524	#106	C₂³×C₇	1	1	yes	characteristic
525	#106	C₂³×C₇	1	4	yes	—
526	#103	C₂³×C₇	1	2	yes	—
527	#103	C₂³×C₇	1	2	yes	—
528	#103	C₂³×C₇	1	4	yes	—
529	#102	C₂³×C₇	1	4	yes	—
530	#102	C₂³×C₇	1	4	yes	—
531	#102	C₂³×C₇	1	2	yes	—
532	#102	C₂³×C₇	1	2	yes	—
533	#102	C₂³×C₇	1	4	yes	—
534	#102	C₂³×C₇	1	4	yes	—
535	#102	C₂³×C₇	1	4	yes	—
536	#97	C₂³×C₇	1	2	yes	—
537	#97	C₂³×C₇	1	2	yes	—
538	#97	C₂³×C₇	1	2	yes	—
539	#97	C₂³×C₇	1	2	yes	—
540	C₄×C₈	C₂³×C₇	1	2	yes	—
541	C₄×C₈	C₂³×C₇	1	2	yes	—
542	C₄×C₈	C₂³×C₇	1	2	yes	—
543	C₄×C₈	C₂³×C₇	1	2	yes	—
544	C₂²×C₇	—	2	2	no	—
545	C₂²×C₇	—	2	2	no	—
546	C₂²×C₇	—	2	2	no	—
547	C₂²×C₇	—	2	1	no	—
548	C₂²×C₇	—	2	1	no	—
549	C₂²×C₇	—	4	2	no	—
550	C₂²×C₇	—	4	4	no	—
551	C₂²×C₇	—	4	4	no	—
552	C₂²×C₇	—	4	2	no	—
553	C₂²×C₇	—	4	2	no	—
554	C₂²×C₇	—	4	4	no	—
555	C₂²×C₇	—	8	2	no	—
556	C₂²×C₇	—	16	4	no	—
557	C₂²×C₇	#532	1	2	yes	—
558	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
559	C₄×C₇	—	2	4	no	—
560	C₄×C₇	—	2	4	no	—
561	C₄×C₇	—	2	1	no	—
562	C₄×C₇	—	2	1	no	—
563	C₄×C₇	—	4	4	no	—
564	C₄×C₇	—	4	2	no	—
565	C₄×C₇	—	4	2	no	—
566	C₄×C₇	—	4	2	no	—
567	C₄×C₇	#532	1	2	yes	—
568	C₄×C₇	C₂²×#41	1	1	yes	characteristic
569	C₄×C₇	C₂²×#41	1	1	yes	characteristic
570	C₂⁴	—	2	2	no	—
571	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
572	#41	—	2	4	no	—
573	#41	—	2	4	no	—
574	#41	—	8	8	no	—
575	C₂×Q₈	—	2	4	no	—
576	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	2	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	8	4	no	—
588	C₂×D₄	C₂⁴×C₇	1	4	yes	—
589	C₂×D₄	C₂⁴×C₇	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
598	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
601	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
604	Q₁₆	—	2	2	no	—
605	SD₁₆	—	2	4	no	—
606	SD₁₆	—	2	8	no	—
607	D₈	—	2	4	no	—
608	D₈	—	2	4	no	—
609	D₈	—	2	2	no	—
610	D₈	—	2	8	no	—
611	M₁₆	—	2	2	no	—
612	M₁₆	—	2	4	no	—
613	M₁₆	—	2	2	no	—
614	M₁₆	—	2	2	no	—
615	M₁₆	—	2	2	no	—
616	M₁₆	—	2	2	no	—
617	M₁₆	C₇×#41	1	4	yes	complemented
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	2	4	no	—
620	C₂×C₈	C₇×#41	1	4	yes	complemented
621	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₇	1	2	yes	—
623	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
624	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
625	C₂×C₈	C₂⁴×C₇	1	2	yes	—
626	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	4	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	4	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
635	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
636	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
653	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
654	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
655	C₄²	—	2	4	no	—
656	C₄²	—	2	2	no	—
657	C₄²	C₂×C₇×D₄	1	4	yes	—
658	C₄²	C₂⁴×C₇	1	2	yes	—
659	C₄²	C₂⁴×C₇	1	2	yes	—
660	C₂×C₇	—	2	2	no	—
661	C₂×C₇	—	4	1	no	—
662	C₂×C₇	—	4	1	no	—
663	C₂×C₇	—	8	2	no	—
664	C₂×C₇	—	8	4	no	—
665	C₂×C₇	C₂×#532	1	1	yes	characteristic
666	C₂×C₇	#3585	1	2	yes	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	8	2	no	—
673	C₂³	—	8	2	no	—
674	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
675	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
676	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
677	Q₈	—	2	2	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	8	4	no	—
680	D₄	—	2	4	no	—
681	D₄	—	2	2	no	—
682	D₄	—	2	4	no	—
683	D₄	—	2	2	no	—
684	D₄	—	4	8	no	—
685	D₄	—	4	4	no	—
686	D₄	—	4	4	no	—
687	D₄	—	4	4	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	4	4	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	8	4	no	—
706	C₂×C₄	—	8	4	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	2	no	—
709	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
710	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
712	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
713	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
714	C₂×C₄	C₂×C₇×#41	1	2	yes	—
715	C₂×C₄	C₂×C₇×#41	1	2	yes	—
716	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
717	C₈	—	2	1	no	—
718	C₈	—	2	1	no	—
719	C₈	—	2	2	no	—
720	C₈	C₂×C₇×#41	1	4	yes	—
721	C₈	C₂×C₇×#41	1	2	yes	—
722	C₈	C₂×C₇×#41	1	2	yes	—
723	C₇	#60710	1	1	yes	characteristic, direct product factor, Sylow
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	2	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	4	no	—
735	C₂²	—	8	2	no	—
736	C₂²	—	16	4	no	—
737	C₂²	C₇×#532	1	2	yes	—
738	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
739	C₄	—	2	4	no	—
740	C₄	—	2	4	no	—
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	4	4	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	C₇×#532	1	2	yes	—
748	C₄	C₂²×C₇×#41	1	1	yes	characteristic
749	C₄	C₂²×C₇×#41	1	1	yes	characteristic
750	C₂	—	2	2	no	—
751	C₂	—	4	1	no	—
752	C₂	—	4	1	no	—
753	C₂	—	8	4	no	—
754	C₂	—	8	2	no	—
755	C₂	C₂×C₇×#532	1	1	yes	characteristic
756	C₂	C₇×#3585	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 ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3184	C₂	semidirect
3. C₇×#3183	C₂	semidirect
4. C₇×#3179	C₂	semidirect
5. C₇×#3176	C₂	semidirect
6. C₇×#3173	C₂	semidirect
7. C₇×#3171	C₂	semidirect
8. C₇×#3163	C₂	semidirect
9. C₇×#3155	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3055	C₂	semidirect
12. C₇×#3054	C₂	semidirect
13. C₂×C₇×#469	C₂	semidirect
14. C₇×#2952	C₂	semidirect
15. C₇×#2948	C₂	semidirect
16. C₇×#2946	C₂	semidirect
17. C₇×#2873	C₂	semidirect
30. C₇×#542	C₂²	semidirect
31. C₇×#540	C₂²	semidirect
33. C₇×#532	C₂²	semidirect
34. C₇×#529	C₂²	semidirect
40. C₇×#501	C₂²	semidirect
41. C₇×#499	C₂²	semidirect
42. C₇×#498	C₂²	semidirect
43. C₇×#496	C₂²	semidirect
44. C₇×#495	C₂²	semidirect
45. C₇×#493	C₂²	semidirect
46. C₇×#490	C₂²	semidirect
47. C₇×#489	C₂²	semidirect
48. C₇×#488	C₂²	semidirect
49. C₇×#486	C₂²	semidirect
50. C₇×#470	C₂²	semidirect
51. C₇×#470	C₂²	semidirect
56. C₇×#469	C₂²	semidirect
57. C₇×#469	C₂²	semidirect
58. C₇×#469	C₂²	semidirect
59. C₇×#468	C₂²	semidirect
60. C₇×#468	C₂²	semidirect
61. C₇×#468	C₂²	semidirect
62. C₇×#466	C₂²	semidirect
63. C₇×#465	C₂²	semidirect
64. C₇×#442	C₂²	semidirect
65. C₇×#442	C₂²	semidirect
66. C₇×#442	C₂²	semidirect
67. C₇×#442	C₂²	semidirect
68. C₇×#441	C₂²	semidirect
69. C₇×#440	C₂²	semidirect
70. C₄×C₇×SD₁₆	C₂²	semidirect
71. C₄×C₇×SD₁₆	C₂²	semidirect
72. C₄×C₇×D₈	C₂²	semidirect
73. C₄×C₇×D₈	C₂²	semidirect
85. C₇×#405	C₂²	semidirect
86. C₇×#405	C₂²	semidirect
87. C₄×C₇×M₁₆	C₂²	semidirect
88. C₄×C₇×M₁₆	C₂²	semidirect
89. #60710	C₇	direct (N × H)
200. #3494	C₂×C₇	semidirect
201. #3184	C₂×C₇	semidirect
202. #3183	C₂×C₇	semidirect
203. #3179	C₂×C₇	semidirect
204. #3176	C₂×C₇	semidirect
205. #3173	C₂×C₇	semidirect
206. #3171	C₂×C₇	semidirect
207. #3163	C₂×C₇	semidirect
208. #3155	C₂×C₇	semidirect
209. #3136	C₂×C₇	semidirect
210. #3055	C₂×C₇	semidirect
211. #3054	C₂×C₇	semidirect
212. C₂×#469	C₂×C₇	semidirect
213. #2952	C₂×C₇	semidirect
214. #2948	C₂×C₇	semidirect
215. #2946	C₂×C₇	semidirect
216. #2873	C₂×C₇	semidirect
264. C₇×M₁₆	#41	semidirect
267. C₂×C₇×C₈	#41	semidirect
319. #542	C₂²×C₇	semidirect
320. #540	C₂²×C₇	semidirect
322. #532	C₂²×C₇	semidirect
323. #529	C₂²×C₇	semidirect
329. #501	C₂²×C₇	semidirect
330. #499	C₂²×C₇	semidirect
331. #498	C₂²×C₇	semidirect
332. #496	C₂²×C₇	semidirect
333. #495	C₂²×C₇	semidirect
334. #493	C₂²×C₇	semidirect
335. #490	C₂²×C₇	semidirect
336. #489	C₂²×C₇	semidirect
337. #488	C₂²×C₇	semidirect
338. #486	C₂²×C₇	semidirect
339. #470	C₂²×C₇	semidirect
340. #470	C₂²×C₇	semidirect
345. #469	C₂²×C₇	semidirect
346. #469	C₂²×C₇	semidirect
347. #469	C₂²×C₇	semidirect
348. #468	C₂²×C₇	semidirect
349. #468	C₂²×C₇	semidirect
350. #468	C₂²×C₇	semidirect
351. #466	C₂²×C₇	semidirect
352. #465	C₂²×C₇	semidirect
353. #442	C₂²×C₇	semidirect
354. #442	C₂²×C₇	semidirect
355. #442	C₂²×C₇	semidirect
356. #442	C₂²×C₇	semidirect
357. #441	C₂²×C₇	semidirect
358. #440	C₂²×C₇	semidirect
359. C₄×SD₁₆	C₂²×C₇	semidirect
360. C₄×SD₁₆	C₂²×C₇	semidirect
361. C₄×D₈	C₂²×C₇	semidirect
362. C₄×D₈	C₂²×C₇	semidirect
374. #405	C₂²×C₇	semidirect
375. #405	C₂²×C₇	semidirect
376. C₄×M₁₆	C₂²×C₇	semidirect
377. C₄×M₁₆	C₂²×C₇	semidirect
617. M₁₆	C₇×#41	semidirect
620. C₂×C₈	C₇×#41	semidirect
723. C₇	#60710	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×#3494	2
C₇×#3184	2
C₇×#3183	2
C₇×#3179	2
C₇×#3176	2
C₇×#3173	2
C₇×#3171	2
C₇×#3163	2
C₇×#3155	2
C₇×#3136	2
C₇×#3055	2
C₇×#3054	2
C₂×C₇×#469	2
C₇×#2952	2
C₇×#2948	2
C₇×#2946	2
C₇×#2873	2
#60710	7

Subgroups — C7×#60710 #13237926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60710 #13237926