Subgroups — C₇×#60214 #13237430

Order 1792.

1960 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₇×#2969	C₂	1	4	yes	maximal, complemented
3	C₇×#2968	C₂	1	4	yes	maximal, complemented
4	C₇×#2967	C₂	1	4	yes	maximal, complemented
5	C₇×#2966	C₂	1	4	yes	maximal, complemented
6	C₇×Q₈×M₁₆	C₂	1	2	yes	maximal, complemented
7	C₇×D₄×M₁₆	C₂	1	2	yes	maximal, complemented
8	C₇×D₄×M₁₆	C₂	1	4	yes	maximal, complemented
9	C₇×#2921	C₂	1	2	yes	maximal, complemented
10	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2873	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×M₁₆	C₂²	1	4	yes	—
15	C₇×#529	C₄	1	2	yes	—
16	C₇×#529	C₄	1	2	yes	—
17	C₇×#529	C₄	1	2	yes	—
18	C₇×#529	C₄	1	2	yes	—
19	C₇×#529	C₂²	1	2	yes	—
20	C₇×#529	C₂²	1	2	yes	—
21	C₇×#529	C₂²	1	2	yes	—
22	C₇×#529	C₂²	1	2	yes	—
23	C₂×C₇×#126	C₄	1	2	yes	—
24	C₂×C₇×#125	C₄	1	1	yes	characteristic
25	C₂×C₇×#124	C₄	1	1	yes	characteristic
26	C₂×C₇×#123	C₄	1	2	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₄	1	1	yes	characteristic
28	C₂×C₇×#121	C₄	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₇×#117	C₂²	1	2	yes	—
33	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
34	C₇×#446	C₂²	1	4	yes	complemented
35	C₇×#446	C₂²	1	8	yes	complemented
36	C₇×C₈×Q₈	C₂²	1	4	yes	complemented
37	C₇×#436	C₂²	1	4	yes	complemented
38	C₇×#436	C₂²	1	8	yes	complemented
39	C₇×#435	C₂²	1	8	yes	complemented
40	C₇×#435	C₂²	1	8	yes	complemented
41	C₇×#435	C₂²	1	8	yes	complemented
42	C₇×C₈×D₄	C₂²	1	8	yes	complemented
43	C₇×C₈×D₄	C₂²	1	4	yes	complemented
44	C₇×#433	C₂²	1	8	yes	complemented
45	C₇×#433	C₂²	1	8	yes	complemented
46	C₇×#432	C₂²	1	2	yes	complemented
47	C₇×#432	C₂²	1	2	yes	complemented
48	C₇×#431	C₂²	1	2	yes	complemented
49	C₇×#431	C₂²	1	2	yes	complemented
50	C₇×#423	C₂²	1	2	yes	—
51	C₇×#423	C₂²	1	4	yes	—
52	C₇×#407	C₂²	1	2	yes	—
53	C₇×#407	C₂²	1	4	yes	—
54	C₇×#405	C₂²	1	8	yes	complemented
55	C₇×#405	C₂²	1	8	yes	complemented
56	C₄×C₇×M₁₆	C₂²	1	2	yes	—
57	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₇×M₁₆	C₂²	1	2	yes	—
59	C₄×C₇×M₁₆	C₂²	1	4	yes	—
60	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
61	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
62	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
63	C₂×C₇×#97	C₂²	1	2	yes	complemented
64	C₂×C₄×C₇×C₈	C₂²	1	2	yes	complemented
65	#60214	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
68	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
70	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₇	C₂³	1	2	yes	—
73	C₂×C₇×M₁₆	—	2	8	no	—
74	C₂×C₇×M₁₆	—	2	16	no	—
75	C₂×C₇×M₁₆	C₂³	1	4	yes	—
76	C₂×C₇×M₁₆	C₂³	1	2	yes	—
77	C₂×C₇×M₁₆	C₂³	1	4	yes	—
78	C₂×C₇×M₁₆	C₂³	1	8	yes	—
79	C₂×C₇×M₁₆	C₂³	1	2	yes	—
80	C₂²×C₇×C₈	C₂³	1	4	yes	—
81	C₂²×C₇×C₈	C₂³	1	8	yes	—
82	C₇×#126	C₂×C₄	1	4	yes	—
83	C₇×#126	C₂×C₄	1	4	yes	—
84	C₇×#126	C₂×C₄	1	4	yes	—
85	C₇×#126	C₂×C₄	1	4	yes	—
86	C₇×#125	C₂×C₄	1	2	yes	—
87	C₇×#125	C₂×C₄	1	2	yes	—
88	C₇×#125	C₂×C₄	1	2	yes	—
89	C₇×#125	C₂×C₄	1	2	yes	—
90	C₇×#124	C₂×C₄	1	2	yes	—
91	C₇×#124	C₂×C₄	1	2	yes	—
92	C₇×#124	C₂×C₄	1	2	yes	—
93	C₇×#124	C₂×C₄	1	2	yes	—
94	C₇×#123	C₂×C₄	1	4	yes	—
95	C₇×#123	C₂×C₄	1	4	yes	—
96	C₇×#123	C₂×C₄	1	4	yes	—
97	C₇×#123	C₂×C₄	1	4	yes	—
98	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
99	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
100	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
101	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
102	C₇×#121	C₂×C₄	1	2	yes	—
103	C₇×#121	C₂×C₄	1	2	yes	—
104	C₇×#121	C₂×C₄	1	2	yes	—
105	C₇×#121	C₂×C₄	1	2	yes	—
106	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
107	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
108	C₄×C₇×Q₈	C₂³	1	2	yes	—
109	C₄×C₇×Q₈	C₂³	1	2	yes	—
110	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
111	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
112	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
113	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
114	C₄×C₇×D₄	C₂³	1	4	yes	—
115	C₄×C₇×D₄	C₂³	1	2	yes	—
116	C₄×C₇×D₄	C₂³	1	2	yes	—
117	C₄×C₇×D₄	C₂³	1	4	yes	—
118	C₇×#117	C₂×C₄	1	4	yes	—
119	C₇×#117	C₂×C₄	1	4	yes	—
120	C₇×#117	C₂³	1	4	yes	—
121	C₇×#117	C₂³	1	4	yes	—
122	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
123	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
124	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
125	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
126	C₂×C₇×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
127	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
128	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
129	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
130	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
131	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
132	C₂×C₇×C₂²⋊C₄	C₂×C₄	1	2	yes	—
133	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₇	C₂³	1	2	yes	—
146	C₇×C₄⋊C₈	C₂³	1	4	yes	—
147	C₇×C₄⋊C₈	C₂³	1	4	yes	—
148	C₇×C₄⋊C₈	C₂³	1	8	yes	—
149	C₇×C₄⋊C₈	C₂³	1	8	yes	—
150	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
151	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
152	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
153	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
154	C₇×#97	C₂³	1	2	yes	—
155	C₇×#97	C₂³	1	2	yes	—
156	C₇×#97	C₂³	1	4	yes	—
157	C₇×#97	C₂³	1	4	yes	—
158	C₇×#97	C₂³	1	8	yes	—
159	C₄×C₇×C₈	C₂³	1	2	yes	—
160	C₄×C₇×C₈	C₂³	1	2	yes	—
161	C₄×C₇×C₈	C₂³	1	4	yes	—
162	C₄×C₇×C₈	C₂³	1	4	yes	—
163	C₄×C₇×C₈	C₂³	1	8	yes	—
164	C₂×#529	C₂×C₇	1	1	yes	characteristic
165	#2969	C₂×C₇	1	4	yes	complemented
166	#2968	C₂×C₇	1	4	yes	complemented
167	#2967	C₂×C₇	1	4	yes	complemented
168	#2966	C₂×C₇	1	4	yes	complemented
169	Q₈×M₁₆	C₂×C₇	1	2	yes	complemented
170	D₄×M₁₆	C₂×C₇	1	4	yes	complemented
171	D₄×M₁₆	C₂×C₇	1	2	yes	complemented
172	#2921	C₂×C₇	1	2	yes	complemented
173	#2920	C₂×C₇	1	1	yes	characteristic, complemented
174	#2873	C₂×C₇	1	2	yes	complemented
175	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
176	C₂⁴×C₇	C₂²×C₄	1	1	yes	characteristic
177	C₂⁴×C₇	C₂²×C₄	1	2	yes	—
178	C₂×C₇×Q₈	—	4	2	no	—
179	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
180	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
181	C₂×C₇×D₄	—	4	2	no	—
182	C₂×C₇×D₄	—	4	4	no	—
183	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
184	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
185	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
186	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
187	C₂²×C₄×C₇	—	2	4	no	—
188	C₂²×C₄×C₇	—	2	8	no	—
189	C₂²×C₄×C₇	—	4	2	no	—
190	C₂²×C₄×C₇	—	4	2	no	—
191	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
201	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
205	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
206	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
207	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
209	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
210	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
214	C₇×M₁₆	—	2	4	no	—
215	C₇×M₁₆	—	2	8	no	—
216	C₇×M₁₆	—	2	8	no	—
217	C₇×M₁₆	—	2	16	no	—
218	C₇×M₁₆	#41	1	8	yes	—
219	C₂×C₇×C₈	—	2	8	no	—
220	C₂×C₇×C₈	—	2	16	no	—
221	C₂×C₇×C₈	C₂⁴	1	4	yes	—
222	C₂×C₇×C₈	C₂⁴	1	8	yes	—
223	C₂×C₇×C₈	C₂⁴	1	4	yes	—
224	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
225	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
226	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
227	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
228	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
229	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
230	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
231	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
232	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
233	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
234	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
235	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
236	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
237	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
238	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
239	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
240	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
241	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
242	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
243	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
244	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
245	C₇×C₂²⋊C₄	C₂²×C₄	1	4	yes	—
246	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
247	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
249	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
250	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
251	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
252	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
253	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
254	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
255	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
257	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₇	C₂²×C₄	1	4	yes	—
259	C₄²×C₇	C₂⁴	1	1	yes	characteristic
260	C₄²×C₇	C₂⁴	1	1	yes	characteristic
261	C₄²×C₇	C₂⁴	1	1	yes	characteristic
262	C₄²×C₇	C₂⁴	1	4	yes	—
263	C₄²×C₇	C₂⁴	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
265	C₂²×M₁₆	C₂²×C₇	1	4	yes	—
266	#529	C₄×C₇	1	2	yes	—
267	#529	C₄×C₇	1	2	yes	—
268	#529	C₄×C₇	1	2	yes	—
269	#529	C₄×C₇	1	2	yes	—
270	#529	C₂²×C₇	1	2	yes	—
271	#529	C₂²×C₇	1	2	yes	—
272	#529	C₂²×C₇	1	2	yes	—
273	#529	C₂²×C₇	1	2	yes	—
274	C₂×#126	C₄×C₇	1	2	yes	—
275	C₂×#125	C₄×C₇	1	1	yes	characteristic
276	C₂×#124	C₄×C₇	1	1	yes	characteristic
277	C₂×#123	C₄×C₇	1	2	yes	—
278	C₂×C₂²⋊Q₈	C₄×C₇	1	1	yes	characteristic
279	C₂×#121	C₄×C₇	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
281	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
282	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
283	C₂×#117	C₂²×C₇	1	2	yes	—
284	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
285	#446	C₂²×C₇	1	4	yes	complemented
286	#446	C₂²×C₇	1	8	yes	complemented
287	C₈×Q₈	C₂²×C₇	1	4	yes	complemented
288	#436	C₂²×C₇	1	4	yes	complemented
289	#436	C₂²×C₇	1	8	yes	complemented
290	#435	C₂²×C₇	1	8	yes	complemented
291	#435	C₂²×C₇	1	8	yes	complemented
292	#435	C₂²×C₇	1	8	yes	complemented
293	C₈×D₄	C₂²×C₇	1	8	yes	complemented
294	C₈×D₄	C₂²×C₇	1	4	yes	complemented
295	#433	C₂²×C₇	1	8	yes	complemented
296	#433	C₂²×C₇	1	8	yes	complemented
297	#432	C₂²×C₇	1	2	yes	complemented
298	#432	C₂²×C₇	1	2	yes	complemented
299	#431	C₂²×C₇	1	2	yes	complemented
300	#431	C₂²×C₇	1	2	yes	complemented
301	#423	C₂²×C₇	1	2	yes	—
302	#423	C₂²×C₇	1	4	yes	—
303	#407	C₂²×C₇	1	2	yes	—
304	#407	C₂²×C₇	1	4	yes	—
305	#405	C₂²×C₇	1	8	yes	complemented
306	#405	C₂²×C₇	1	8	yes	complemented
307	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
308	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
309	C₄×M₁₆	C₂²×C₇	1	2	yes	—
310	C₄×M₁₆	C₂²×C₇	1	2	yes	—
311	C₄×M₁₆	C₂²×C₇	1	4	yes	—
312	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
313	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
314	C₂×#97	C₂²×C₇	1	2	yes	complemented
315	C₂×C₄×C₈	C₂²×C₇	1	2	yes	complemented
316	C₂³×C₇	—	2	2	no	—
317	C₂³×C₇	—	2	2	no	—
318	C₂³×C₇	—	2	4	no	—
319	C₂³×C₇	—	4	1	no	—
320	C₂³×C₇	—	4	2	no	—
321	C₂³×C₇	—	4	2	no	—
322	C₂³×C₇	C₂³×C₄	1	4	yes	—
323	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
324	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
325	C₂³×C₇	C₂³×C₄	1	1	yes	characteristic
326	C₇×Q₈	—	2	4	no	—
327	C₇×Q₈	—	4	2	no	—
328	C₇×D₄	—	2	8	no	—
329	C₇×D₄	—	2	4	no	—
330	C₇×D₄	—	4	2	no	—
331	C₇×D₄	—	4	4	no	—
332	C₂×C₄×C₇	—	2	2	no	—
333	C₂×C₄×C₇	—	2	4	no	—
334	C₂×C₄×C₇	—	2	2	no	—
335	C₂×C₄×C₇	—	2	2	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	8	no	—
339	C₂×C₄×C₇	—	2	2	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	2	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	4	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	4	no	—
346	C₂×C₄×C₇	—	4	1	no	—
347	C₂×C₄×C₇	—	4	1	no	—
348	C₂×C₄×C₇	—	4	1	no	—
349	C₂×C₄×C₇	—	4	1	no	—
350	C₂×C₄×C₇	—	4	1	no	—
351	C₂×C₄×C₇	—	4	1	no	—
352	C₂×C₄×C₇	—	4	1	no	—
353	C₂×C₄×C₇	—	4	2	no	—
354	C₂×C₄×C₇	—	4	2	no	—
355	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
356	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
357	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
358	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
359	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
360	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
361	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
362	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
363	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
364	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
365	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
366	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
367	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
369	C₂×C₄×C₇	C₂×#41	1	4	yes	—
370	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
371	C₇×C₈	—	2	4	no	—
372	C₇×C₈	—	2	8	no	—
373	C₇×C₈	C₂×#41	1	8	yes	—
374	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
375	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
376	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
377	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
378	C₂³×C₄	C₂×C₄×C₇	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₇	1	2	yes	—
380	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
381	C₂×M₁₆	—	2	8	no	—
382	C₂×M₁₆	—	2	16	no	—
383	C₂×M₁₆	C₂³×C₇	1	2	yes	—
384	C₂×M₁₆	C₂³×C₇	1	4	yes	—
385	C₂×M₁₆	C₂³×C₇	1	4	yes	—
386	C₂×M₁₆	C₂³×C₇	1	8	yes	—
387	C₂×M₁₆	C₂³×C₇	1	2	yes	—
388	C₂²×C₈	C₂³×C₇	1	4	yes	—
389	C₂²×C₈	C₂³×C₇	1	8	yes	—
390	#126	C₂×C₄×C₇	1	4	yes	—
391	#126	C₂×C₄×C₇	1	4	yes	—
392	#126	C₂×C₄×C₇	1	4	yes	—
393	#126	C₂×C₄×C₇	1	4	yes	—
394	#125	C₂×C₄×C₇	1	2	yes	—
395	#125	C₂×C₄×C₇	1	2	yes	—
396	#125	C₂×C₄×C₇	1	2	yes	—
397	#125	C₂×C₄×C₇	1	2	yes	—
398	#124	C₂×C₄×C₇	1	2	yes	—
399	#124	C₂×C₄×C₇	1	2	yes	—
400	#124	C₂×C₄×C₇	1	2	yes	—
401	#124	C₂×C₄×C₇	1	2	yes	—
402	#123	C₂×C₄×C₇	1	4	yes	—
403	#123	C₂×C₄×C₇	1	4	yes	—
404	#123	C₂×C₄×C₇	1	4	yes	—
405	#123	C₂×C₄×C₇	1	4	yes	—
406	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
407	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
408	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
409	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
410	#121	C₂×C₄×C₇	1	2	yes	—
411	#121	C₂×C₄×C₇	1	2	yes	—
412	#121	C₂×C₄×C₇	1	2	yes	—
413	#121	C₂×C₄×C₇	1	2	yes	—
414	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
415	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
416	C₄×Q₈	C₂³×C₇	1	2	yes	—
417	C₄×Q₈	C₂³×C₇	1	2	yes	—
418	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
419	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
420	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
421	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
422	C₄×D₄	C₂³×C₇	1	4	yes	—
423	C₄×D₄	C₂³×C₇	1	2	yes	—
424	C₄×D₄	C₂³×C₇	1	2	yes	—
425	C₄×D₄	C₂³×C₇	1	4	yes	—
426	#117	C₂×C₄×C₇	1	4	yes	—
427	#117	C₂×C₄×C₇	1	4	yes	—
428	#117	C₂³×C₇	1	4	yes	—
429	#117	C₂³×C₇	1	4	yes	—
430	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
431	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
432	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
434	C₂×C₄⋊C₄	C₂×C₄×C₇	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
436	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
438	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
439	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
440	C₂×C₂²⋊C₄	C₂×C₄×C₇	1	2	yes	—
441	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
442	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
443	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
444	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
445	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
446	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₇	1	2	yes	—
449	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
454	C₄⋊C₈	C₂³×C₇	1	4	yes	—
455	C₄⋊C₈	C₂³×C₇	1	4	yes	—
456	C₄⋊C₈	C₂³×C₇	1	8	yes	—
457	C₄⋊C₈	C₂³×C₇	1	8	yes	—
458	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
459	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
460	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
461	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
462	#97	C₂³×C₇	1	2	yes	—
463	#97	C₂³×C₇	1	2	yes	—
464	#97	C₂³×C₇	1	4	yes	—
465	#97	C₂³×C₇	1	4	yes	—
466	#97	C₂³×C₇	1	8	yes	—
467	C₄×C₈	C₂³×C₇	1	2	yes	—
468	C₄×C₈	C₂³×C₇	1	2	yes	—
469	C₄×C₈	C₂³×C₇	1	4	yes	—
470	C₄×C₈	C₂³×C₇	1	4	yes	—
471	C₄×C₈	C₂³×C₇	1	8	yes	—
472	C₂²×C₇	—	2	1	no	—
473	C₂²×C₇	—	2	1	no	—
474	C₂²×C₇	—	2	1	no	—
475	C₂²×C₇	—	2	1	no	—
476	C₂²×C₇	—	2	1	no	—
477	C₂²×C₇	—	2	4	no	—
478	C₂²×C₇	—	2	1	no	—
479	C₂²×C₇	—	2	1	no	—
480	C₂²×C₇	—	2	4	no	—
481	C₂²×C₇	—	2	4	no	—
482	C₂²×C₇	—	4	4	no	—
483	C₂²×C₇	—	8	4	no	—
484	C₂²×C₇	C₄×#41	1	2	yes	—
485	C₂²×C₇	#568	1	2	yes	—
486	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
487	C₄×C₇	—	2	1	no	—
488	C₄×C₇	—	2	4	no	—
489	C₄×C₇	—	2	1	no	—
490	C₄×C₇	—	2	1	no	—
491	C₄×C₇	—	2	1	no	—
492	C₄×C₇	—	2	1	no	—
493	C₄×C₇	—	2	1	no	—
494	C₄×C₇	—	2	1	no	—
495	C₄×C₇	—	2	1	no	—
496	C₄×C₇	—	2	1	no	—
497	C₄×C₇	—	2	4	no	—
498	C₄×C₇	—	2	4	no	—
499	C₄×C₇	C₄×#41	1	2	yes	—
500	C₄×C₇	#568	1	2	yes	—
501	C₄×C₇	C₂²×#41	1	2	yes	—
502	C₂⁴	C₂²×C₄×C₇	1	1	yes	characteristic
503	C₂⁴	C₂²×C₄×C₇	1	2	yes	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
506	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
507	C₂×D₄	—	4	2	no	—
508	C₂×D₄	—	4	4	no	—
509	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
510	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
511	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
512	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	8	no	—
515	C₂²×C₄	—	4	2	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
524	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
526	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
527	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
528	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
529	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
530	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
531	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
532	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
533	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
534	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
535	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
537	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
540	M₁₆	—	2	4	no	—
541	M₁₆	—	2	8	no	—
542	M₁₆	—	2	8	no	—
543	M₁₆	—	2	16	no	—
544	M₁₆	C₇×#41	1	8	yes	—
545	C₂×C₈	—	2	8	no	—
546	C₂×C₈	—	2	16	no	—
547	C₂×C₈	C₂⁴×C₇	1	4	yes	—
548	C₂×C₈	C₂⁴×C₇	1	8	yes	—
549	C₂×C₈	C₂⁴×C₇	1	4	yes	—
550	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
551	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
552	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
553	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
554	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
555	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
556	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
557	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
558	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
559	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
560	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
561	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
562	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
563	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
564	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
565	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
566	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
567	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
568	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
569	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
570	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
571	C₂²⋊C₄	C₂²×C₄×C₇	1	4	yes	—
572	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
573	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
574	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
575	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
576	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
577	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
578	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
579	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
580	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
581	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
582	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
583	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
584	C₄²	C₂²×C₄×C₇	1	4	yes	—
585	C₄²	C₂⁴×C₇	1	1	yes	characteristic
586	C₄²	C₂⁴×C₇	1	1	yes	characteristic
587	C₄²	C₂⁴×C₇	1	1	yes	characteristic
588	C₄²	C₂⁴×C₇	1	4	yes	—
589	C₄²	C₂⁴×C₇	1	1	yes	characteristic
590	C₂×C₇	—	2	2	no	—
591	C₂×C₇	—	2	2	no	—
592	C₂×C₇	—	4	1	no	—
593	C₂×C₇	—	4	4	no	—
594	C₂×C₇	C₂×C₄×#41	1	1	yes	characteristic
595	C₂×C₇	C₂×#568	1	1	yes	characteristic
596	C₂×C₇	C₂×#568	1	1	yes	characteristic
597	C₂³	—	2	2	no	—
598	C₂³	—	2	2	no	—
599	C₂³	—	2	4	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	2	no	—
602	C₂³	—	4	2	no	—
603	C₂³	C₂³×C₄×C₇	1	4	yes	—
604	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
605	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
606	C₂³	C₂³×C₄×C₇	1	1	yes	characteristic
607	Q₈	—	2	4	no	—
608	Q₈	—	4	2	no	—
609	D₄	—	2	8	no	—
610	D₄	—	2	4	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	4	1	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	2	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
637	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
638	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
640	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
641	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
642	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
645	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
647	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
649	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
650	C₂×C₄	C₂×C₇×#41	1	4	yes	—
651	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
652	C₈	—	2	4	no	—
653	C₈	—	2	8	no	—
654	C₈	C₂×C₇×#41	1	8	yes	—
655	C₇	#60214	1	1	yes	characteristic, direct product factor, Sylow
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	4	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	4	4	no	—
667	C₂²	—	8	4	no	—
668	C₂²	C₄×C₇×#41	1	2	yes	—
669	C₂²	C₇×#568	1	2	yes	—
670	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	4	no	—
679	C₄	—	2	4	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	4	no	—
682	C₄	—	2	1	no	—
683	C₄	C₄×C₇×#41	1	2	yes	—
684	C₄	C₇×#568	1	2	yes	—
685	C₄	C₂²×C₇×#41	1	2	yes	—
686	C₂	—	2	2	no	—
687	C₂	—	2	2	no	—
688	C₂	—	4	1	no	—
689	C₂	—	4	4	no	—
690	C₂	C₂×C₄×C₇×#41	1	1	yes	characteristic
691	C₂	C₂×C₇×#568	1	1	yes	characteristic
692	C₂	C₂×C₇×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂⁴×C₄
prime radical	C₂×C₇×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2969	C₂	semidirect
3. C₇×#2968	C₂	semidirect
4. C₇×#2967	C₂	semidirect
5. C₇×#2966	C₂	semidirect
6. C₇×Q₈×M₁₆	C₂	semidirect
7. C₇×D₄×M₁₆	C₂	semidirect
8. C₇×D₄×M₁₆	C₂	semidirect
9. C₇×#2921	C₂	semidirect
10. C₇×#2920	C₂	semidirect
11. C₇×#2873	C₂	semidirect
12. C₂×C₄×C₇×M₁₆	C₂	semidirect
34. C₇×#446	C₂²	semidirect
35. C₇×#446	C₂²	semidirect
36. C₇×C₈×Q₈	C₂²	semidirect
37. C₇×#436	C₂²	semidirect
38. C₇×#436	C₂²	semidirect
39. C₇×#435	C₂²	semidirect
40. C₇×#435	C₂²	semidirect
41. C₇×#435	C₂²	semidirect
42. C₇×C₈×D₄	C₂²	semidirect
43. C₇×C₈×D₄	C₂²	semidirect
44. C₇×#433	C₂²	semidirect
45. C₇×#433	C₂²	semidirect
46. C₇×#432	C₂²	semidirect
47. C₇×#432	C₂²	semidirect
48. C₇×#431	C₂²	semidirect
49. C₇×#431	C₂²	semidirect
54. C₇×#405	C₂²	semidirect
55. C₇×#405	C₂²	semidirect
61. C₄×C₇×M₁₆	C₂²	semidirect
62. C₄×C₇×M₁₆	C₂²	semidirect
63. C₂×C₇×#97	C₂²	semidirect
64. C₂×C₄×C₇×C₈	C₂²	semidirect
65. #60214	C₇	direct (N × H)
165. #2969	C₂×C₇	semidirect
166. #2968	C₂×C₇	semidirect
167. #2967	C₂×C₇	semidirect
168. #2966	C₂×C₇	semidirect
169. Q₈×M₁₆	C₂×C₇	semidirect
170. D₄×M₁₆	C₂×C₇	semidirect
171. D₄×M₁₆	C₂×C₇	semidirect
172. #2921	C₂×C₇	semidirect
173. #2920	C₂×C₇	semidirect
174. #2873	C₂×C₇	semidirect
175. C₂×C₄×M₁₆	C₂×C₇	semidirect
285. #446	C₂²×C₇	semidirect
286. #446	C₂²×C₇	semidirect
287. C₈×Q₈	C₂²×C₇	semidirect
288. #436	C₂²×C₇	semidirect
289. #436	C₂²×C₇	semidirect
290. #435	C₂²×C₇	semidirect
291. #435	C₂²×C₇	semidirect
292. #435	C₂²×C₇	semidirect
293. C₈×D₄	C₂²×C₇	semidirect
294. C₈×D₄	C₂²×C₇	semidirect
295. #433	C₂²×C₇	semidirect
296. #433	C₂²×C₇	semidirect
297. #432	C₂²×C₇	semidirect
298. #432	C₂²×C₇	semidirect
299. #431	C₂²×C₇	semidirect
300. #431	C₂²×C₇	semidirect
305. #405	C₂²×C₇	semidirect
306. #405	C₂²×C₇	semidirect
312. C₄×M₁₆	C₂²×C₇	semidirect
313. C₄×M₁₆	C₂²×C₇	semidirect
314. C₂×#97	C₂²×C₇	semidirect
315. C₂×C₄×C₈	C₂²×C₇	semidirect
655. C₇	#60214	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#529	2
C₇×#2969	2
C₇×#2968	2
C₇×#2967	2
C₇×#2966	2
C₇×Q₈×M₁₆	2
C₇×D₄×M₁₆	2
C₇×#2921	2
C₇×#2920	2
C₇×#2873	2
C₂×C₄×C₇×M₁₆	2
#60214	7

Subgroups — C7×#60214 #13237430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60214 #13237430