Subgroups — C₇×#60457 #13237673

Order 1792.

2756 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#577	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3063	C₂	1	3	yes	maximal, complemented
6	C₇×#3062	C₂	1	3	yes	maximal, complemented
7	C₇×#3060	C₂	1	3	yes	maximal, complemented
8	C₇×#3057	C₂	1	3	yes	maximal, complemented
9	C₇×#3056	C₂	1	3	yes	maximal, complemented
10	C₇×#3055	C₂	1	3	yes	maximal, complemented
11	C₇×#3050	C₂	1	3	yes	maximal, complemented
12	C₂×C₇×#465	C₂	1	3	yes	maximal, complemented
13	C₇×#2912	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₇×#577	—	2	8	no	—
20	C₂×C₇×#137	C₂²	1	3	yes	complemented
21	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
22	C₂×C₇×#135	C₂²	1	3	yes	complemented
23	C₂²×C₇×SD₁₆	C₂²	1	3	yes	complemented
24	C₂×C₇×#131	—	2	8	no	—
25	C₂×C₇×#131	C₂²	1	1	yes	characteristic
26	C₂×C₇×#131	C₂²	1	1	yes	characteristic
27	C₂×C₇×#131	C₂²	1	3	yes	complemented
28	C₂×C₇×#131	C₂²	1	3	yes	complemented
29	C₂²×C₇×M₁₆	C₂²	1	3	yes	complemented
30	C₂³×C₇×C₈	C₂²	1	3	yes	complemented
31	C₇×#550	—	2	1	no	—
32	C₇×D₄×Q₈	—	2	1	no	—
33	C₇×#548	—	2	1	no	—
34	C₇×#548	—	2	1	no	—
35	C₇×#547	—	2	3	no	—
36	C₇×#546	—	2	3	no	—
37	C₇×#546	—	2	3	no	—
38	C₇×D₄²	—	2	3	no	—
39	C₇×#537	C₂²	1	3	yes	—
40	C₇×#537	C₂²	1	3	yes	complemented
41	C₇×#536	C₂²	1	3	yes	complemented
42	C₇×#535	C₂²	1	3	yes	—
43	C₇×#525	C₂²	1	3	yes	—
44	C₇×#525	C₂²	1	3	yes	complemented
45	C₂×C₇×C₂²⋊Q₈	C₂²	1	3	yes	complemented
46	C₂×C₇×#121	C₂²	1	3	yes	—
47	C₇×#520	C₂²	1	1	yes	characteristic
48	C₇×#520	C₂²	1	1	yes	characteristic
49	C₇×#470	C₂²	1	6	yes	complemented
50	C₇×#469	C₂²	1	6	yes	complemented
51	C₇×#468	C₂²	1	6	yes	complemented
52	C₇×#468	C₂²	1	6	yes	complemented
53	C₇×#467	C₂²	1	3	yes	complemented
54	C₇×#467	C₂²	1	3	yes	complemented
55	C₇×#466	C₂²	1	3	yes	complemented
56	C₇×#466	C₂²	1	3	yes	complemented
57	C₇×#465	C₂²	1	3	yes	complemented
58	C₇×#465	C₂²	1	6	yes	complemented
59	C₇×#465	C₂²	1	6	yes	complemented
60	C₇×#465	C₂²	1	6	yes	complemented
61	C₇×#465	C₂²	1	1	yes	characteristic, complemented
62	C₇×#465	C₂²	1	3	yes	complemented
63	C₇×#465	C₂²	1	3	yes	complemented
64	C₇×#428	C₂²	1	3	yes	complemented
65	C₇×#428	C₂²	1	3	yes	complemented
66	C₇×#427	C₂²	1	3	yes	complemented
67	C₂×C₇×#106	C₂²	1	3	yes	complemented
68	C₇×#419	C₂²	1	3	yes	complemented
69	C₇×#418	C₂²	1	3	yes	complemented
70	C₇×#417	C₂²	1	3	yes	complemented
71	C₇×#417	C₂²	1	3	yes	complemented
72	C₇×#416	C₂²	1	3	yes	complemented
73	C₇×#416	C₂²	1	3	yes	complemented
74	C₂×C₇×#103	C₂²	1	3	yes	complemented
75	C₂×C₇×#102	C₂²	1	3	yes	complemented
76	#60457	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₇×2₋¹⁺⁴	—	2	4	no	—
78	C₇×2₋¹⁺⁴	—	2	4	no	—
79	C₇×H(5,𝔽₂)	—	2	4	no	—
80	C₇×H(5,𝔽₂)	—	2	4	no	—
81	C₂×C₇×#41	—	2	4	no	—
82	C₂×C₇×#41	—	2	4	no	—
83	C₂×C₇×#41	—	2	1	no	—
84	C₂×C₇×#41	—	2	3	no	—
85	C₂×C₇×#41	D₄	1	3	yes	—
86	C₂×C₇×#41	D₄	1	1	yes	characteristic
87	C₂×C₇×#41	C₂³	1	3	yes	—
88	C₂×C₇×#41	C₂³	1	3	yes	—
89	C₂×C₇×#41	C₂³	1	3	yes	—
90	C₂×C₇×#41	C₂³	1	1	yes	characteristic
91	C₂²×C₇×Q₈	—	2	1	no	—
92	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
93	C₂²×C₇×Q₈	C₂³	1	3	yes	—
94	C₂²×C₇×D₄	—	2	3	no	—
95	C₂²×C₇×D₄	—	2	3	no	—
96	C₂²×C₇×D₄	D₄	1	3	yes	—
97	C₂²×C₇×D₄	C₂³	1	3	yes	—
98	C₂³×C₄×C₇	C₂³	1	3	yes	—
99	C₇×#137	—	2	12	no	—
100	C₇×AGL(1,ℤ/8)	—	2	12	no	—
101	C₇×#135	—	2	12	no	—
102	C₂×C₇×Q₁₆	C₂³	1	3	yes	—
103	C₂×C₇×SD₁₆	—	2	12	no	—
104	C₂×C₇×SD₁₆	C₂³	1	6	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	3	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
107	C₂×C₇×D₈	C₂³	1	3	yes	—
108	C₇×#131	—	2	4	no	—
109	C₇×#131	—	2	12	no	—
110	C₇×#131	—	2	12	no	—
111	C₇×#131	D₄	1	8	yes	complemented
112	C₂×C₇×M₁₆	—	2	12	no	—
113	C₂×C₇×M₁₆	C₂³	1	6	yes	—
114	C₂×C₇×M₁₆	C₂³	1	3	yes	—
115	C₂×C₇×M₁₆	C₂³	1	3	yes	—
116	C₂²×C₇×C₈	—	2	12	no	—
117	C₂²×C₇×C₈	C₂³	1	3	yes	—
118	C₂²×C₇×C₈	C₂³	1	3	yes	—
119	C₂²×C₇×C₈	C₂³	1	3	yes	—
120	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₇×C₈	C₂³	1	3	yes	—
122	C₂²×C₇×C₈	C₂³	1	3	yes	—
123	C₇×C₄⋊Q₈	—	2	3	no	—
124	C₇×#127	—	2	3	no	—
125	C₇×#124	—	2	3	no	—
126	C₇×#124	—	2	3	no	—
127	C₇×#123	—	2	6	no	—
128	C₇×#123	—	2	3	no	—
129	C₇×#123	—	2	3	no	—
130	C₇×C₂²⋊Q₈	—	2	3	no	—
131	C₇×C₂²⋊Q₈	—	2	3	no	—
132	C₇×C₂²⋊Q₈	—	2	3	no	—
133	C₇×C₂²⋊Q₈	—	2	3	no	—
134	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₇×C₂²⋊Q₈	C₂³	1	3	yes	—
136	C₇×C₂²⋊Q₈	C₂³	1	3	yes	—
137	C₇×C₂²⋊Q₈	C₂³	1	3	yes	—
138	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
139	C₇×#121	—	2	6	no	—
140	C₇×#121	—	2	3	no	—
141	C₇×#121	—	2	6	no	—
142	C₇×#121	—	2	3	no	—
143	C₇×#121	—	2	3	no	—
144	C₇×#121	—	2	3	no	—
145	C₇×#121	C₂³	1	1	yes	characteristic
146	C₇×#121	C₂³	1	3	yes	—
147	C₇×#121	C₂³	1	3	yes	—
148	C₇×#121	C₂³	1	3	yes	—
149	C₇×#121	C₂³	1	6	yes	—
150	C₇×#120	—	2	3	no	—
151	C₇×#120	—	2	3	no	—
152	C₇×#120	—	2	6	no	—
153	C₄×C₇×Q₈	—	2	1	no	—
154	C₄×C₇×Q₈	—	2	1	no	—
155	C₄×C₇×D₄	—	2	3	no	—
156	C₄×C₇×D₄	—	2	3	no	—
157	C₄×C₇×D₄	—	2	3	no	—
158	C₄×C₇×D₄	—	2	3	no	—
159	C₄×C₇×D₄	—	2	3	no	—
160	C₄×C₇×D₄	—	2	3	no	—
161	C₇×#117	C₂³	1	3	yes	—
162	C₇×#117	C₂³	1	3	yes	—
163	C₂×C₇×C₄⋊C₄	—	2	3	no	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
166	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
167	C₂×C₇×C₂²⋊C₄	—	2	3	no	—
168	C₇×#107	C₂³	1	3	yes	—
169	C₇×#107	C₂³	1	3	yes	—
170	C₇×#106	C₂³	1	6	yes	—
171	C₇×#106	C₂³	1	3	yes	—
172	C₇×#106	C₂³	1	1	yes	characteristic
173	C₇×#103	C₂³	1	1	yes	characteristic
174	C₇×#103	C₂³	1	3	yes	—
175	C₇×#103	C₂³	1	3	yes	—
176	C₇×#103	C₂³	1	3	yes	—
177	C₇×#103	C₂³	1	6	yes	—
178	C₇×#102	C₂³	1	1	yes	characteristic
179	C₇×#102	C₂³	1	3	yes	—
180	C₇×#102	C₂³	1	3	yes	—
181	C₇×#102	C₂³	1	3	yes	—
182	C₇×#102	C₂³	1	6	yes	—
183	C₂×#577	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂²×#131	C₂×C₇	1	1	yes	characteristic, complemented
185	#3489	C₂×C₇	1	1	yes	characteristic, complemented
186	#3488	C₂×C₇	1	1	yes	characteristic, complemented
187	#3063	C₂×C₇	1	3	yes	complemented
188	#3062	C₂×C₇	1	3	yes	complemented
189	#3060	C₂×C₇	1	3	yes	complemented
190	#3057	C₂×C₇	1	3	yes	complemented
191	#3056	C₂×C₇	1	3	yes	complemented
192	#3055	C₂×C₇	1	3	yes	complemented
193	#3050	C₂×C₇	1	3	yes	complemented
194	C₂×#465	C₂×C₇	1	3	yes	complemented
195	#2912	C₂×C₇	1	1	yes	characteristic, complemented
196	#2898	C₂×C₇	1	1	yes	characteristic, complemented
197	#2897	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂⁴×C₇	—	2	3	no	—
199	C₂⁴×C₇	C₂×D₄	1	3	yes	—
200	C₇×#41	—	2	4	no	—
201	C₇×#41	—	2	12	no	—
202	C₇×#41	—	2	6	no	—
203	C₇×#41	—	2	6	no	—
204	C₇×#41	—	2	6	no	—
205	C₇×#41	—	2	6	no	—
206	C₇×#41	—	2	6	no	—
207	C₇×#41	—	2	6	no	—
208	C₇×#41	—	4	4	no	—
209	C₇×#41	—	4	12	no	—
210	C₇×#41	C₂×D₄	1	4	yes	—
211	C₇×#41	#41	1	4	yes	—
212	C₂×C₇×Q₈	—	2	4	no	—
213	C₂×C₇×Q₈	—	2	3	no	—
214	C₂×C₇×Q₈	—	2	6	no	—
215	C₂×C₇×Q₈	—	2	6	no	—
216	C₂×C₇×Q₈	—	4	4	no	—
217	C₂×C₇×Q₈	C₂×D₄	1	3	yes	—
218	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
219	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
220	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
221	C₂×C₇×D₄	—	2	12	no	—
222	C₂×C₇×D₄	—	2	1	no	—
223	C₂×C₇×D₄	—	2	3	no	—
224	C₂×C₇×D₄	—	2	3	no	—
225	C₂×C₇×D₄	—	2	3	no	—
226	C₂×C₇×D₄	—	2	3	no	—
227	C₂×C₇×D₄	—	2	3	no	—
228	C₂×C₇×D₄	—	2	6	no	—
229	C₂×C₇×D₄	—	2	6	no	—
230	C₂×C₇×D₄	—	2	3	no	—
231	C₂×C₇×D₄	—	2	6	no	—
232	C₂×C₇×D₄	—	4	12	no	—
233	C₂×C₇×D₄	—	8	6	no	—
234	C₂×C₇×D₄	C₂×D₄	1	6	yes	—
235	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
236	C₂×C₇×D₄	C₂×D₄	1	3	yes	—
237	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
238	C₂×C₇×D₄	C₂⁴	1	3	yes	—
239	C₂²×C₄×C₇	—	2	6	no	—
240	C₂²×C₄×C₇	—	2	6	no	—
241	C₂²×C₄×C₇	—	2	3	no	—
242	C₂²×C₄×C₇	—	2	3	no	—
243	C₂²×C₄×C₇	—	2	3	no	—
244	C₂²×C₄×C₇	—	2	3	no	—
245	C₂²×C₄×C₇	—	2	3	no	—
246	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
247	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
248	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
249	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
252	C₇×Q₁₆	—	2	6	no	—
253	C₇×SD₁₆	—	2	6	no	—
254	C₇×SD₁₆	—	2	12	no	—
255	C₇×SD₁₆	—	2	2	no	—
256	C₇×D₈	—	2	6	no	—
257	C₇×M₁₆	—	2	6	no	—
258	C₇×M₁₆	—	2	12	no	—
259	C₇×M₁₆	C₂×D₄	1	12	yes	complemented
260	C₂×C₇×C₈	—	2	6	no	—
261	C₂×C₇×C₈	—	2	2	no	—
262	C₂×C₇×C₈	—	2	6	no	—
263	C₂×C₇×C₈	—	2	6	no	—
264	C₂×C₇×C₈	—	2	6	no	—
265	C₂×C₇×C₈	C₂×D₄	1	12	yes	complemented
266	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₇×C₈	C₂⁴	1	3	yes	—
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×C₈	C₂⁴	1	3	yes	—
270	C₇×C₄⋊C₄	—	2	3	no	—
271	C₇×C₄⋊C₄	—	2	6	no	—
272	C₇×C₄⋊C₄	—	2	3	no	—
273	C₇×C₄⋊C₄	—	2	3	no	—
274	C₇×C₄⋊C₄	—	2	1	no	—
275	C₇×C₄⋊C₄	—	2	3	no	—
276	C₇×C₄⋊C₄	—	2	3	no	—
277	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
279	C₇×C₄⋊C₄	C₂⁴	1	3	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
281	C₇×C₂²⋊C₄	—	2	3	no	—
282	C₇×C₂²⋊C₄	—	2	6	no	—
283	C₇×C₂²⋊C₄	—	2	3	no	—
284	C₇×C₂²⋊C₄	—	2	3	no	—
285	C₇×C₂²⋊C₄	—	2	1	no	—
286	C₇×C₂²⋊C₄	—	2	3	no	—
287	C₇×C₂²⋊C₄	—	2	3	no	—
288	C₇×C₂²⋊C₄	—	2	3	no	—
289	C₇×C₂²⋊C₄	—	2	6	no	—
290	C₇×C₂²⋊C₄	—	2	1	no	—
291	C₇×C₂²⋊C₄	—	2	3	no	—
292	C₇×C₂²⋊C₄	—	2	3	no	—
293	C₄²×C₇	—	2	3	no	—
294	C₄²×C₇	—	2	3	no	—
295	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
296	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
297	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
298	#577	—	2	8	no	—
299	C₂×#137	C₂²×C₇	1	3	yes	complemented
300	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	3	yes	complemented
301	C₂×#135	C₂²×C₇	1	3	yes	complemented
302	C₂²×SD₁₆	C₂²×C₇	1	3	yes	complemented
303	C₂×#131	—	2	8	no	—
304	C₂×#131	C₂²×C₇	1	1	yes	characteristic
305	C₂×#131	C₂²×C₇	1	1	yes	characteristic
306	C₂×#131	C₂²×C₇	1	3	yes	complemented
307	C₂×#131	C₂²×C₇	1	3	yes	complemented
308	C₂²×M₁₆	C₂²×C₇	1	3	yes	complemented
309	C₂³×C₈	C₂²×C₇	1	3	yes	complemented
310	#550	—	2	1	no	—
311	D₄×Q₈	—	2	1	no	—
312	#548	—	2	1	no	—
313	#548	—	2	1	no	—
314	#547	—	2	3	no	—
315	#546	—	2	3	no	—
316	#546	—	2	3	no	—
317	D₄²	—	2	3	no	—
318	#537	C₂²×C₇	1	3	yes	—
319	#537	C₂²×C₇	1	3	yes	complemented
320	#536	C₂²×C₇	1	3	yes	complemented
321	#535	C₂²×C₇	1	3	yes	—
322	#525	C₂²×C₇	1	3	yes	—
323	#525	C₂²×C₇	1	3	yes	complemented
324	C₂×C₂²⋊Q₈	C₂²×C₇	1	3	yes	complemented
325	C₂×#121	C₂²×C₇	1	3	yes	—
326	#520	C₂²×C₇	1	1	yes	characteristic
327	#520	C₂²×C₇	1	1	yes	characteristic
328	#470	C₂²×C₇	1	6	yes	complemented
329	#469	C₂²×C₇	1	6	yes	complemented
330	#468	C₂²×C₇	1	6	yes	complemented
331	#468	C₂²×C₇	1	6	yes	complemented
332	#467	C₂²×C₇	1	3	yes	complemented
333	#467	C₂²×C₇	1	3	yes	complemented
334	#466	C₂²×C₇	1	3	yes	complemented
335	#466	C₂²×C₇	1	3	yes	complemented
336	#465	C₂²×C₇	1	3	yes	complemented
337	#465	C₂²×C₇	1	6	yes	complemented
338	#465	C₂²×C₇	1	6	yes	complemented
339	#465	C₂²×C₇	1	6	yes	complemented
340	#465	C₂²×C₇	1	1	yes	characteristic, complemented
341	#465	C₂²×C₇	1	3	yes	complemented
342	#465	C₂²×C₇	1	3	yes	complemented
343	#428	C₂²×C₇	1	3	yes	complemented
344	#428	C₂²×C₇	1	3	yes	complemented
345	#427	C₂²×C₇	1	3	yes	complemented
346	C₂×#106	C₂²×C₇	1	3	yes	complemented
347	#419	C₂²×C₇	1	3	yes	complemented
348	#418	C₂²×C₇	1	3	yes	complemented
349	#417	C₂²×C₇	1	3	yes	complemented
350	#417	C₂²×C₇	1	3	yes	complemented
351	#416	C₂²×C₇	1	3	yes	complemented
352	#416	C₂²×C₇	1	3	yes	complemented
353	C₂×#103	C₂²×C₇	1	3	yes	complemented
354	C₂×#102	C₂²×C₇	1	3	yes	complemented
355	C₂³×C₇	—	2	6	no	—
356	C₂³×C₇	—	2	6	no	—
357	C₂³×C₇	—	2	1	no	—
358	C₂³×C₇	—	2	3	no	—
359	C₂³×C₇	—	4	3	no	—
360	C₂³×C₇	—	4	6	no	—
361	C₂³×C₇	—	8	3	no	—
362	C₂³×C₇	—	8	3	no	—
363	C₂³×C₇	C₂²×D₄	1	3	yes	—
364	C₂³×C₇	C₂²×D₄	1	3	yes	—
365	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
366	C₇×Q₈	—	2	6	no	—
367	C₇×Q₈	—	2	3	no	—
368	C₇×Q₈	—	2	1	no	—
369	C₇×Q₈	—	2	3	no	—
370	C₇×Q₈	—	2	1	no	—
371	C₇×Q₈	—	4	6	no	—
372	C₇×Q₈	#121	1	4	yes	—
373	C₇×D₄	—	2	12	no	—
374	C₇×D₄	—	2	6	no	—
375	C₇×D₄	—	2	1	no	—
376	C₇×D₄	—	2	3	no	—
377	C₇×D₄	—	2	3	no	—
378	C₇×D₄	—	2	1	no	—
379	C₇×D₄	—	4	6	no	—
380	C₇×D₄	—	4	6	no	—
381	C₇×D₄	—	4	2	no	—
382	C₇×D₄	—	4	6	no	—
383	C₇×D₄	—	4	6	no	—
384	C₇×D₄	—	8	3	no	—
385	C₇×D₄	—	8	3	no	—
386	C₇×D₄	—	8	6	no	—
387	C₇×D₄	#121	1	12	yes	—
388	C₂×C₄×C₇	—	2	6	no	—
389	C₂×C₄×C₇	—	2	6	no	—
390	C₂×C₄×C₇	—	2	6	no	—
391	C₂×C₄×C₇	—	2	1	no	—
392	C₂×C₄×C₇	—	2	3	no	—
393	C₂×C₄×C₇	—	2	1	no	—
394	C₂×C₄×C₇	—	2	3	no	—
395	C₂×C₄×C₇	—	2	1	no	—
396	C₂×C₄×C₇	—	2	1	no	—
397	C₂×C₄×C₇	—	2	3	no	—
398	C₂×C₄×C₇	—	2	3	no	—
399	C₂×C₄×C₇	—	2	1	no	—
400	C₂×C₄×C₇	—	2	3	no	—
401	C₂×C₄×C₇	—	4	6	no	—
402	C₂×C₄×C₇	—	4	6	no	—
403	C₂×C₄×C₇	—	4	6	no	—
404	C₂×C₄×C₇	—	8	3	no	—
405	C₂×C₄×C₇	—	8	3	no	—
406	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
408	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
409	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
410	C₂×C₄×C₇	C₂×#41	1	6	yes	—
411	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
412	C₇×C₈	—	2	1	no	—
413	C₇×C₈	—	2	3	no	—
414	C₇×C₈	C₂²×D₄	1	2	yes	—
415	C₇×C₈	C₂²×D₄	1	6	yes	—
416	2₋¹⁺⁴	—	2	4	no	—
417	2₋¹⁺⁴	—	2	4	no	—
418	H(5,𝔽₂)	—	2	4	no	—
419	H(5,𝔽₂)	—	2	4	no	—
420	C₂×#41	—	2	4	no	—
421	C₂×#41	—	2	4	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	3	no	—
424	C₂×#41	C₇×D₄	1	3	yes	—
425	C₂×#41	C₇×D₄	1	1	yes	characteristic
426	C₂×#41	C₂³×C₇	1	3	yes	—
427	C₂×#41	C₂³×C₇	1	3	yes	—
428	C₂×#41	C₂³×C₇	1	3	yes	—
429	C₂×#41	C₂³×C₇	1	1	yes	characteristic
430	C₂²×Q₈	—	2	1	no	—
431	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
432	C₂²×Q₈	C₂³×C₇	1	3	yes	—
433	C₂²×D₄	—	2	3	no	—
434	C₂²×D₄	—	2	3	no	—
435	C₂²×D₄	C₇×D₄	1	3	yes	—
436	C₂²×D₄	C₂³×C₇	1	3	yes	—
437	C₂³×C₄	C₂³×C₇	1	3	yes	—
438	#137	—	2	12	no	—
439	AGL(1,ℤ/8)	—	2	12	no	—
440	#135	—	2	12	no	—
441	C₂×Q₁₆	C₂³×C₇	1	3	yes	—
442	C₂×SD₁₆	—	2	12	no	—
443	C₂×SD₁₆	C₂³×C₇	1	3	yes	—
444	C₂×SD₁₆	C₂³×C₇	1	6	yes	—
445	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
446	C₂×D₈	C₂³×C₇	1	3	yes	—
447	#131	—	2	4	no	—
448	#131	—	2	12	no	—
449	#131	—	2	12	no	—
450	#131	C₇×D₄	1	8	yes	complemented
451	C₂×M₁₆	—	2	12	no	—
452	C₂×M₁₆	C₂³×C₇	1	3	yes	—
453	C₂×M₁₆	C₂³×C₇	1	6	yes	—
454	C₂×M₁₆	C₂³×C₇	1	3	yes	—
455	C₂²×C₈	—	2	12	no	—
456	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
457	C₂²×C₈	C₂³×C₇	1	3	yes	—
458	C₂²×C₈	C₂³×C₇	1	3	yes	—
459	C₂²×C₈	C₂³×C₇	1	3	yes	—
460	C₂²×C₈	C₂³×C₇	1	3	yes	—
461	C₂²×C₈	C₂³×C₇	1	3	yes	—
462	C₄⋊Q₈	—	2	3	no	—
463	#127	—	2	3	no	—
464	#124	—	2	3	no	—
465	#124	—	2	3	no	—
466	#123	—	2	6	no	—
467	#123	—	2	3	no	—
468	#123	—	2	3	no	—
469	C₂²⋊Q₈	—	2	3	no	—
470	C₂²⋊Q₈	—	2	3	no	—
471	C₂²⋊Q₈	—	2	3	no	—
472	C₂²⋊Q₈	—	2	3	no	—
473	C₂²⋊Q₈	C₂³×C₇	1	3	yes	—
474	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
475	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
476	C₂²⋊Q₈	C₂³×C₇	1	3	yes	—
477	C₂²⋊Q₈	C₂³×C₇	1	3	yes	—
478	#121	—	2	6	no	—
479	#121	—	2	3	no	—
480	#121	—	2	6	no	—
481	#121	—	2	3	no	—
482	#121	—	2	3	no	—
483	#121	—	2	3	no	—
484	#121	C₂³×C₇	1	3	yes	—
485	#121	C₂³×C₇	1	6	yes	—
486	#121	C₂³×C₇	1	3	yes	—
487	#121	C₂³×C₇	1	1	yes	characteristic
488	#121	C₂³×C₇	1	3	yes	—
489	#120	—	2	3	no	—
490	#120	—	2	3	no	—
491	#120	—	2	6	no	—
492	C₄×Q₈	—	2	1	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×D₄	—	2	3	no	—
495	C₄×D₄	—	2	3	no	—
496	C₄×D₄	—	2	3	no	—
497	C₄×D₄	—	2	3	no	—
498	C₄×D₄	—	2	3	no	—
499	C₄×D₄	—	2	3	no	—
500	#117	C₂³×C₇	1	3	yes	—
501	#117	C₂³×C₇	1	3	yes	—
502	C₂×C₄⋊C₄	—	2	3	no	—
503	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
505	C₂×C₂²⋊C₄	—	2	3	no	—
506	C₂×C₂²⋊C₄	—	2	3	no	—
507	#107	C₂³×C₇	1	3	yes	—
508	#107	C₂³×C₇	1	3	yes	—
509	#106	C₂³×C₇	1	3	yes	—
510	#106	C₂³×C₇	1	6	yes	—
511	#106	C₂³×C₇	1	1	yes	characteristic
512	#103	C₂³×C₇	1	3	yes	—
513	#103	C₂³×C₇	1	6	yes	—
514	#103	C₂³×C₇	1	1	yes	characteristic
515	#103	C₂³×C₇	1	3	yes	—
516	#103	C₂³×C₇	1	3	yes	—
517	#102	C₂³×C₇	1	3	yes	—
518	#102	C₂³×C₇	1	6	yes	—
519	#102	C₂³×C₇	1	1	yes	characteristic
520	#102	C₂³×C₇	1	3	yes	—
521	#102	C₂³×C₇	1	3	yes	—
522	C₂²×C₇	—	2	3	no	—
523	C₂²×C₇	—	2	1	no	—
524	C₂²×C₇	—	2	1	no	—
525	C₂²×C₇	—	2	3	no	—
526	C₂²×C₇	—	2	3	no	—
527	C₂²×C₇	—	2	3	no	—
528	C₂²×C₇	—	2	3	no	—
529	C₂²×C₇	—	4	12	no	—
530	C₂²×C₇	—	4	1	no	—
531	C₂²×C₇	—	4	3	no	—
532	C₂²×C₇	—	4	1	no	—
533	C₂²×C₇	—	4	3	no	—
534	C₂²×C₇	—	4	3	no	—
535	C₂²×C₇	—	4	1	no	—
536	C₂²×C₇	—	16	6	no	—
537	C₂²×C₇	C₂×#121	1	6	yes	—
538	C₂²×C₇	#577	1	2	yes	complemented
539	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
540	C₄×C₇	—	2	1	no	—
541	C₄×C₇	—	2	3	no	—
542	C₄×C₇	—	4	3	no	—
543	C₄×C₇	—	4	1	no	—
544	C₄×C₇	—	4	1	no	—
545	C₄×C₇	—	4	3	no	—
546	C₄×C₇	—	4	3	no	—
547	C₄×C₇	—	4	1	no	—
548	C₄×C₇	C₂×#121	1	6	yes	—
549	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
550	C₄×C₇	C₂²×#41	1	1	yes	characteristic
551	C₂⁴	—	2	3	no	—
552	C₂⁴	C₂×C₇×D₄	1	3	yes	—
553	#41	—	2	4	no	—
554	#41	—	2	12	no	—
555	#41	—	2	6	no	—
556	#41	—	2	6	no	—
557	#41	—	2	6	no	—
558	#41	—	2	6	no	—
559	#41	—	2	6	no	—
560	#41	—	2	6	no	—
561	#41	—	4	4	no	—
562	#41	—	4	12	no	—
563	#41	C₂×C₇×D₄	1	4	yes	—
564	#41	C₇×#41	1	4	yes	—
565	C₂×Q₈	—	2	4	no	—
566	C₂×Q₈	—	2	3	no	—
567	C₂×Q₈	—	2	6	no	—
568	C₂×Q₈	—	2	6	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	C₂×C₇×D₄	1	3	yes	—
571	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
572	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
573	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
574	C₂×D₄	—	2	12	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	3	no	—
577	C₂×D₄	—	2	3	no	—
578	C₂×D₄	—	2	3	no	—
579	C₂×D₄	—	2	3	no	—
580	C₂×D₄	—	2	3	no	—
581	C₂×D₄	—	2	6	no	—
582	C₂×D₄	—	2	6	no	—
583	C₂×D₄	—	2	3	no	—
584	C₂×D₄	—	2	6	no	—
585	C₂×D₄	—	4	12	no	—
586	C₂×D₄	—	8	6	no	—
587	C₂×D₄	C₂×C₇×D₄	1	6	yes	—
588	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
589	C₂×D₄	C₂×C₇×D₄	1	3	yes	—
590	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
591	C₂×D₄	C₂⁴×C₇	1	3	yes	—
592	C₂²×C₄	—	2	6	no	—
593	C₂²×C₄	—	2	6	no	—
594	C₂²×C₄	—	2	3	no	—
595	C₂²×C₄	—	2	3	no	—
596	C₂²×C₄	—	2	3	no	—
597	C₂²×C₄	—	2	3	no	—
598	C₂²×C₄	—	2	3	no	—
599	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
600	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
601	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
602	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
604	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
605	Q₁₆	—	2	6	no	—
606	SD₁₆	—	2	6	no	—
607	SD₁₆	—	2	12	no	—
608	SD₁₆	—	2	2	no	—
609	D₈	—	2	6	no	—
610	M₁₆	—	2	6	no	—
611	M₁₆	—	2	12	no	—
612	M₁₆	C₂×C₇×D₄	1	12	yes	complemented
613	C₂×C₈	—	2	6	no	—
614	C₂×C₈	—	2	2	no	—
615	C₂×C₈	—	2	6	no	—
616	C₂×C₈	—	2	6	no	—
617	C₂×C₈	—	2	6	no	—
618	C₂×C₈	C₂×C₇×D₄	1	12	yes	complemented
619	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₇	1	3	yes	—
621	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
622	C₂×C₈	C₂⁴×C₇	1	3	yes	—
623	C₄⋊C₄	—	2	3	no	—
624	C₄⋊C₄	—	2	6	no	—
625	C₄⋊C₄	—	2	3	no	—
626	C₄⋊C₄	—	2	3	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	3	no	—
629	C₄⋊C₄	—	2	3	no	—
630	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
631	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
632	C₄⋊C₄	C₂⁴×C₇	1	3	yes	—
633	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
634	C₂²⋊C₄	—	2	3	no	—
635	C₂²⋊C₄	—	2	6	no	—
636	C₂²⋊C₄	—	2	3	no	—
637	C₂²⋊C₄	—	2	3	no	—
638	C₂²⋊C₄	—	2	1	no	—
639	C₂²⋊C₄	—	2	3	no	—
640	C₂²⋊C₄	—	2	3	no	—
641	C₂²⋊C₄	—	2	3	no	—
642	C₂²⋊C₄	—	2	6	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	2	3	no	—
645	C₂²⋊C₄	—	2	3	no	—
646	C₄²	—	2	3	no	—
647	C₄²	—	2	3	no	—
648	C₂×C₇	—	2	2	no	—
649	C₂×C₇	—	2	6	no	—
650	C₂×C₇	—	4	3	no	—
651	C₂×C₇	—	8	1	no	—
652	C₂×C₇	—	8	3	no	—
653	C₂×C₇	C₂²×#121	1	1	yes	characteristic
654	C₂×C₇	C₂×#577	1	1	yes	characteristic
655	C₂×C₇	#3584	1	1	yes	characteristic
656	C₂³	—	2	6	no	—
657	C₂³	—	2	6	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	3	no	—
660	C₂³	—	4	3	no	—
661	C₂³	—	4	6	no	—
662	C₂³	—	8	3	no	—
663	C₂³	—	8	3	no	—
664	C₂³	C₂²×C₇×D₄	1	3	yes	—
665	C₂³	C₂²×C₇×D₄	1	3	yes	—
666	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
667	Q₈	—	2	6	no	—
668	Q₈	—	2	3	no	—
669	Q₈	—	2	1	no	—
670	Q₈	—	2	3	no	—
671	Q₈	—	2	1	no	—
672	Q₈	—	4	6	no	—
673	Q₈	C₇×#121	1	4	yes	—
674	D₄	—	2	12	no	—
675	D₄	—	2	1	no	—
676	D₄	—	2	3	no	—
677	D₄	—	2	3	no	—
678	D₄	—	2	1	no	—
679	D₄	—	2	6	no	—
680	D₄	—	4	6	no	—
681	D₄	—	4	6	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	6	no	—
684	D₄	—	4	6	no	—
685	D₄	—	8	3	no	—
686	D₄	—	8	3	no	—
687	D₄	—	8	6	no	—
688	D₄	C₇×#121	1	12	yes	—
689	C₂×C₄	—	2	6	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	3	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	3	no	—
694	C₂×C₄	—	2	6	no	—
695	C₂×C₄	—	2	6	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	3	no	—
699	C₂×C₄	—	2	3	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	3	no	—
702	C₂×C₄	—	4	6	no	—
703	C₂×C₄	—	4	6	no	—
704	C₂×C₄	—	4	6	no	—
705	C₂×C₄	—	8	3	no	—
706	C₂×C₄	—	8	3	no	—
707	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
708	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
709	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
710	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
711	C₂×C₄	C₂×C₇×#41	1	6	yes	—
712	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
713	C₈	—	2	1	no	—
714	C₈	—	2	3	no	—
715	C₈	C₂²×C₇×D₄	1	2	yes	—
716	C₈	C₂²×C₇×D₄	1	6	yes	—
717	C₇	#60457	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	3	no	—
719	C₂²	—	2	3	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	3	no	—
723	C₂²	—	2	3	no	—
724	C₂²	—	2	3	no	—
725	C₂²	—	4	12	no	—
726	C₂²	—	4	3	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	3	no	—
730	C₂²	—	4	1	no	—
731	C₂²	—	4	3	no	—
732	C₂²	—	16	6	no	—
733	C₂²	C₂×C₇×#121	1	6	yes	—
734	C₂²	C₇×#577	1	2	yes	complemented
735	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
736	C₄	—	2	1	no	—
737	C₄	—	2	3	no	—
738	C₄	—	4	3	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	3	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	3	no	—
744	C₄	C₂×C₇×#121	1	6	yes	—
745	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
746	C₄	C₂²×C₇×#41	1	1	yes	characteristic
747	C₂	—	2	2	no	—
748	C₂	—	2	6	no	—
749	C₂	—	4	3	no	—
750	C₂	—	8	3	no	—
751	C₂	—	8	1	no	—
752	C₂	C₂²×C₇×#121	1	1	yes	characteristic
753	C₂	C₂×C₇×#577	1	1	yes	characteristic
754	C₂	C₇×#3584	1	1	yes	characteristic

	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 ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#577	C₂	semidirect
2. C₂²×C₇×#131	C₂	semidirect
3. C₇×#3489	C₂	semidirect
4. C₇×#3488	C₂	semidirect
5. C₇×#3063	C₂	semidirect
6. C₇×#3062	C₂	semidirect
7. C₇×#3060	C₂	semidirect
8. C₇×#3057	C₂	semidirect
9. C₇×#3056	C₂	semidirect
10. C₇×#3055	C₂	semidirect
11. C₇×#3050	C₂	semidirect
12. C₂×C₇×#465	C₂	semidirect
13. C₇×#2912	C₂	semidirect
14. C₇×#2898	C₂	semidirect
15. C₇×#2897	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
21. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
22. C₂×C₇×#135	C₂²	semidirect
23. C₂²×C₇×SD₁₆	C₂²	semidirect
27. C₂×C₇×#131	C₂²	semidirect
28. C₂×C₇×#131	C₂²	semidirect
29. C₂²×C₇×M₁₆	C₂²	semidirect
30. C₂³×C₇×C₈	C₂²	semidirect
40. C₇×#537	C₂²	semidirect
41. C₇×#536	C₂²	semidirect
44. C₇×#525	C₂²	semidirect
45. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
49. C₇×#470	C₂²	semidirect
50. C₇×#469	C₂²	semidirect
51. C₇×#468	C₂²	semidirect
52. C₇×#468	C₂²	semidirect
53. C₇×#467	C₂²	semidirect
54. C₇×#467	C₂²	semidirect
55. C₇×#466	C₂²	semidirect
56. C₇×#466	C₂²	semidirect
57. C₇×#465	C₂²	semidirect
58. C₇×#465	C₂²	semidirect
59. C₇×#465	C₂²	semidirect
60. C₇×#465	C₂²	semidirect
61. C₇×#465	C₂²	semidirect
62. C₇×#465	C₂²	semidirect
63. C₇×#465	C₂²	semidirect
64. C₇×#428	C₂²	semidirect
65. C₇×#428	C₂²	semidirect
66. C₇×#427	C₂²	semidirect
67. C₂×C₇×#106	C₂²	semidirect
68. C₇×#419	C₂²	semidirect
69. C₇×#418	C₂²	semidirect
70. C₇×#417	C₂²	semidirect
71. C₇×#417	C₂²	semidirect
72. C₇×#416	C₂²	semidirect
73. C₇×#416	C₂²	semidirect
74. C₂×C₇×#103	C₂²	semidirect
75. C₂×C₇×#102	C₂²	semidirect
76. #60457	C₇	direct (N × H)
111. C₇×#131	D₄	semidirect
183. C₂×#577	C₂×C₇	semidirect
184. C₂²×#131	C₂×C₇	semidirect
185. #3489	C₂×C₇	semidirect
186. #3488	C₂×C₇	semidirect
187. #3063	C₂×C₇	semidirect
188. #3062	C₂×C₇	semidirect
189. #3060	C₂×C₇	semidirect
190. #3057	C₂×C₇	semidirect
191. #3056	C₂×C₇	semidirect
192. #3055	C₂×C₇	semidirect
193. #3050	C₂×C₇	semidirect
194. C₂×#465	C₂×C₇	semidirect
195. #2912	C₂×C₇	semidirect
196. #2898	C₂×C₇	semidirect
197. #2897	C₂×C₇	semidirect
259. C₇×M₁₆	C₂×D₄	semidirect
265. C₂×C₇×C₈	C₂×D₄	semidirect
299. C₂×#137	C₂²×C₇	semidirect
300. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
301. C₂×#135	C₂²×C₇	semidirect
302. C₂²×SD₁₆	C₂²×C₇	semidirect
306. C₂×#131	C₂²×C₇	semidirect
307. C₂×#131	C₂²×C₇	semidirect
308. C₂²×M₁₆	C₂²×C₇	semidirect
309. C₂³×C₈	C₂²×C₇	semidirect
319. #537	C₂²×C₇	semidirect
320. #536	C₂²×C₇	semidirect
323. #525	C₂²×C₇	semidirect
324. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
328. #470	C₂²×C₇	semidirect
329. #469	C₂²×C₇	semidirect
330. #468	C₂²×C₇	semidirect
331. #468	C₂²×C₇	semidirect
332. #467	C₂²×C₇	semidirect
333. #467	C₂²×C₇	semidirect
334. #466	C₂²×C₇	semidirect
335. #466	C₂²×C₇	semidirect
336. #465	C₂²×C₇	semidirect
337. #465	C₂²×C₇	semidirect
338. #465	C₂²×C₇	semidirect
339. #465	C₂²×C₇	semidirect
340. #465	C₂²×C₇	semidirect
341. #465	C₂²×C₇	semidirect
342. #465	C₂²×C₇	semidirect
343. #428	C₂²×C₇	semidirect
344. #428	C₂²×C₇	semidirect
345. #427	C₂²×C₇	semidirect
346. C₂×#106	C₂²×C₇	semidirect
347. #419	C₂²×C₇	semidirect
348. #418	C₂²×C₇	semidirect
349. #417	C₂²×C₇	semidirect
350. #417	C₂²×C₇	semidirect
351. #416	C₂²×C₇	semidirect
352. #416	C₂²×C₇	semidirect
353. C₂×#103	C₂²×C₇	semidirect
354. C₂×#102	C₂²×C₇	semidirect
450. #131	C₇×D₄	semidirect
538. C₂²×C₇	#577	semidirect
612. M₁₆	C₂×C₇×D₄	semidirect
618. C₂×C₈	C₂×C₇×D₄	semidirect
717. C₇	#60457	direct (N × H)
734. C₂²	C₇×#577	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#577	2
C₂²×C₇×#131	2
C₇×#3489	2
C₇×#3488	2
C₇×#3063	2
C₇×#3062	2
C₇×#3060	2
C₇×#3057	2
C₇×#3056	2
C₇×#3055	2
C₇×#3050	2
C₂×C₇×#465	2
C₇×#2912	2
C₇×#2898	2
C₇×#2897	2
#60457	7

Subgroups — C7×#60457 #13237673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60457 #13237673