Subgroups — C₇×#60804 #13238020

Order 1792.

2164 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×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
3	C₇×#3216	C₂	1	4	yes	maximal, complemented
4	C₇×#3215	C₂	1	4	yes	maximal, complemented
5	C₇×#3210	C₂	1	4	yes	maximal, complemented
6	C₇×#3209	C₂	1	2	yes	maximal, complemented
7	C₇×#3208	C₂	1	2	yes	maximal, complemented
8	C₇×#3152	C₂	1	2	yes	maximal, complemented
9	C₇×#3141	C₂	1	2	yes	maximal, complemented
10	C₇×#3037	C₂	1	4	yes	maximal, complemented
11	C₇×#3007	C₂	1	4	yes	maximal, complemented
12	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	2	yes	—
14	C₂×C₇×#137	C₂²	1	8	yes	complemented
15	C₇×#533	—	2	1	no	—
16	C₇×#533	—	2	1	no	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	C₂²	1	2	yes	—
20	C₇×#533	C₂²	1	2	yes	—
21	C₇×#533	C₂²	1	2	yes	complemented
22	C₇×#533	C₂²	1	2	yes	complemented
23	C₇×#532	—	2	1	no	—
24	C₇×#532	—	2	1	no	—
25	C₇×#532	—	2	1	no	—
26	C₇×#532	—	2	1	no	—
27	C₇×#532	C₂²	1	2	yes	—
28	C₇×#532	C₂²	1	2	yes	—
29	C₇×#532	C₂²	1	2	yes	—
30	C₇×#532	C₂²	1	2	yes	—
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₇×#127	C₂²	1	1	yes	characteristic
35	C₂×C₇×#125	—	2	1	no	—
36	C₂×C₇×#124	C₂²	1	2	yes	—
37	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
38	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
39	C₂×C₇×#121	—	2	1	no	—
40	C₂×C₇×#121	—	2	1	no	—
41	C₂×C₄×C₇×Q₈	—	2	1	no	—
42	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
43	C₂×C₄×C₇×D₄	—	2	1	no	—
44	C₂×C₄×C₇×D₄	—	2	1	no	—
45	C₂×C₇×#117	—	2	1	no	—
46	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
47	C₇×#497	C₂²	1	8	yes	complemented
48	C₇×#494	C₂²	1	4	yes	complemented
49	C₇×#492	C₂²	1	4	yes	complemented
50	C₇×#489	C₂²	1	8	yes	complemented
51	C₇×#487	C₂²	1	4	yes	complemented
52	C₇×#486	C₂²	1	4	yes	complemented
53	C₇×#464	C₂²	1	16	yes	complemented
54	C₇×#462	C₂²	1	8	yes	complemented
55	C₇×#460	C₂²	1	8	yes	complemented
56	C₇×#452	C₂²	1	16	yes	complemented
57	C₇×#451	C₂²	1	8	yes	—
58	C₇×#450	C₂²	1	8	yes	—
59	C₇×#432	C₂²	1	2	yes	—
60	C₇×#432	C₂²	1	2	yes	complemented
61	C₇×#431	C₂²	1	2	yes	—
62	C₇×#431	C₂²	1	2	yes	complemented
63	C₇×#423	C₂²	1	2	yes	complemented
64	C₇×#417	C₂²	1	8	yes	complemented
65	C₇×#407	C₂²	1	2	yes	—
66	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
67	#60804	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂×C₇×#41	—	2	2	no	—
69	C₂×C₇×#41	—	2	2	no	—
70	C₂×C₇×#41	—	4	8	no	—
71	C₂×C₇×#41	C₂³	1	4	yes	—
72	C₂×C₇×#41	C₂³	1	4	yes	—
73	C₂²×C₇×Q₈	—	2	1	no	—
74	C₂²×C₇×Q₈	C₂³	1	2	yes	—
75	C₂²×C₇×Q₈	C₂³	1	2	yes	—
76	C₂²×C₇×D₄	—	2	2	no	—
77	C₂²×C₇×D₄	—	2	1	no	—
78	C₂²×C₇×D₄	—	2	1	no	—
79	C₂²×C₇×D₄	C₂³	1	2	yes	—
80	C₂³×C₄×C₇	—	2	2	no	—
81	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
83	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
84	C₇×#137	—	4	16	no	—
85	C₂×C₇×Q₁₆	C₂³	1	16	yes	—
86	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
87	C₂×C₇×M₁₆	C₂³	1	4	yes	—
88	C₇×C₄⋊Q₈	—	2	1	no	—
89	C₇×C₄⋊Q₈	—	2	1	no	—
90	C₇×C₄⋊Q₈	—	2	1	no	—
91	C₇×C₄⋊Q₈	—	2	1	no	—
92	C₇×C₄⋊Q₈	—	2	1	no	—
93	C₇×C₄⋊Q₈	—	2	1	no	—
94	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
95	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
96	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
98	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₇×#127	—	2	1	no	—
101	C₇×#127	—	2	1	no	—
102	C₇×#127	C₂³	1	2	yes	—
103	C₇×#127	C₂³	1	2	yes	—
104	C₇×#125	—	2	2	no	—
105	C₇×#125	—	2	2	no	—
106	C₇×#125	—	2	2	no	—
107	C₇×#125	—	2	2	no	—
108	C₇×#124	—	2	2	no	—
109	C₇×#124	—	2	2	no	—
110	C₇×#124	C₂³	1	4	yes	—
111	C₇×#124	C₂³	1	4	yes	—
112	C₇×C₂²⋊Q₈	—	2	2	no	—
113	C₇×C₂²⋊Q₈	—	2	2	no	—
114	C₇×C₂²⋊Q₈	—	2	2	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	2	no	—
117	C₇×C₂²⋊Q₈	—	2	2	no	—
118	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
119	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
120	C₇×#121	—	2	2	no	—
121	C₇×#121	—	2	2	no	—
122	C₇×#121	—	2	2	no	—
123	C₇×#121	—	2	2	no	—
124	C₇×#121	—	2	2	no	—
125	C₇×#121	—	2	2	no	—
126	C₇×#121	—	2	2	no	—
127	C₇×#121	—	2	2	no	—
128	C₄×C₇×Q₈	—	2	2	no	—
129	C₄×C₇×Q₈	—	2	2	no	—
130	C₄×C₇×Q₈	—	2	2	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	—	2	2	no	—
133	C₄×C₇×Q₈	—	2	2	no	—
134	C₄×C₇×Q₈	C₂³	1	4	yes	—
135	C₄×C₇×Q₈	C₂³	1	4	yes	—
136	C₄×C₇×D₄	—	2	2	no	—
137	C₄×C₇×D₄	—	2	2	no	—
138	C₄×C₇×D₄	—	2	2	no	—
139	C₄×C₇×D₄	—	2	2	no	—
140	C₄×C₇×D₄	—	2	2	no	—
141	C₄×C₇×D₄	—	2	2	no	—
142	C₄×C₇×D₄	—	2	2	no	—
143	C₄×C₇×D₄	—	2	2	no	—
144	C₇×#117	—	2	2	no	—
145	C₇×#117	—	2	2	no	—
146	C₇×#117	—	2	2	no	—
147	C₇×#117	—	2	2	no	—
148	C₂×C₇×C₄⋊C₄	—	2	1	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	1	no	—
152	C₂×C₇×C₄⋊C₄	—	2	1	no	—
153	C₂×C₇×C₄⋊C₄	—	2	2	no	—
154	C₂×C₇×C₄⋊C₄	—	2	2	no	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
157	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
158	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
159	C₂×C₄²×C₇	—	2	2	no	—
160	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×C₄⋊C₈	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	16	yes	—
175	C₇×#102	C₂³	1	16	yes	—
176	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₇×#97	C₂³	1	4	yes	—
179	C₄×C₇×C₈	C₂³	1	4	yes	—
180	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
181	C₂×#532	C₂×C₇	1	1	yes	characteristic
182	#3216	C₂×C₇	1	4	yes	complemented
183	#3215	C₂×C₇	1	4	yes	complemented
184	#3210	C₂×C₇	1	4	yes	complemented
185	#3209	C₂×C₇	1	2	yes	complemented
186	#3208	C₂×C₇	1	2	yes	complemented
187	#3152	C₂×C₇	1	2	yes	complemented
188	#3141	C₂×C₇	1	2	yes	complemented
189	#3037	C₂×C₇	1	4	yes	complemented
190	#3007	C₂×C₇	1	4	yes	complemented
191	#2920	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂⁴×C₇	—	2	2	no	—
193	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
194	C₇×#41	—	2	16	no	—
195	C₇×#41	—	4	8	no	—
196	C₇×#41	—	4	8	no	—
197	C₇×#41	—	4	8	no	—
198	C₂×C₇×Q₈	—	2	2	no	—
199	C₂×C₇×Q₈	—	2	2	no	—
200	C₂×C₇×Q₈	—	2	2	no	—
201	C₂×C₇×Q₈	—	2	2	no	—
202	C₂×C₇×Q₈	—	2	8	no	—
203	C₂×C₇×Q₈	—	4	4	no	—
204	C₂×C₇×Q₈	—	4	4	no	—
205	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
206	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
207	C₂×C₇×D₄	—	2	4	no	—
208	C₂×C₇×D₄	—	2	4	no	—
209	C₂×C₇×D₄	—	2	2	no	—
210	C₂×C₇×D₄	—	2	2	no	—
211	C₂×C₇×D₄	—	2	2	no	—
212	C₂×C₇×D₄	—	2	2	no	—
213	C₂×C₇×D₄	—	2	2	no	—
214	C₂×C₇×D₄	—	4	4	no	—
215	C₂×C₇×D₄	—	4	4	no	—
216	C₂×C₇×D₄	—	4	8	no	—
217	C₂×C₇×D₄	—	4	4	no	—
218	C₂×C₇×D₄	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₇	—	2	4	no	—
220	C₂²×C₄×C₇	—	2	4	no	—
221	C₂²×C₄×C₇	—	2	2	no	—
222	C₂²×C₄×C₇	—	2	2	no	—
223	C₂²×C₄×C₇	—	2	2	no	—
224	C₂²×C₄×C₇	—	2	4	no	—
225	C₂²×C₄×C₇	—	2	4	no	—
226	C₂²×C₄×C₇	—	4	2	no	—
227	C₂²×C₄×C₇	—	4	8	no	—
228	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
246	C₇×Q₁₆	—	4	16	no	—
247	C₇×SD₁₆	—	4	16	no	—
248	C₇×M₁₆	—	2	8	no	—
249	C₂×C₇×C₈	C₂⁴	1	8	yes	—
250	C₇×C₄⋊C₄	—	2	2	no	—
251	C₇×C₄⋊C₄	—	2	2	no	—
252	C₇×C₄⋊C₄	—	2	2	no	—
253	C₇×C₄⋊C₄	—	2	2	no	—
254	C₇×C₄⋊C₄	—	2	2	no	—
255	C₇×C₄⋊C₄	—	2	2	no	—
256	C₇×C₄⋊C₄	—	2	2	no	—
257	C₇×C₄⋊C₄	—	2	2	no	—
258	C₇×C₄⋊C₄	—	2	2	no	—
259	C₇×C₄⋊C₄	—	2	2	no	—
260	C₇×C₄⋊C₄	—	2	4	no	—
261	C₇×C₄⋊C₄	—	2	4	no	—
262	C₇×C₄⋊C₄	—	2	4	no	—
263	C₇×C₄⋊C₄	—	2	4	no	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
266	C₇×C₂²⋊C₄	—	2	4	no	—
267	C₇×C₂²⋊C₄	—	2	4	no	—
268	C₇×C₂²⋊C₄	—	2	4	no	—
269	C₇×C₂²⋊C₄	—	2	4	no	—
270	C₇×C₂²⋊C₄	—	2	4	no	—
271	C₇×C₂²⋊C₄	—	2	4	no	—
272	C₄²×C₇	—	2	4	no	—
273	C₄²×C₇	—	2	4	no	—
274	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
277	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
285	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
286	C₄²×C₇	C₂⁴	1	1	yes	characteristic
287	C₄²×C₇	C₂⁴	1	1	yes	characteristic
288	C₄²×C₇	C₂⁴	1	1	yes	characteristic
289	C₄²×C₇	C₂⁴	1	1	yes	characteristic
290	C₂²×#41	C₂²×C₇	1	2	yes	—
291	C₂×#137	C₂²×C₇	1	8	yes	complemented
292	#533	—	2	1	no	—
293	#533	—	2	1	no	—
294	#533	—	2	1	no	—
295	#533	—	2	1	no	—
296	#533	C₂²×C₇	1	2	yes	—
297	#533	C₂²×C₇	1	2	yes	—
298	#533	C₂²×C₇	1	2	yes	complemented
299	#533	C₂²×C₇	1	2	yes	complemented
300	#532	—	2	1	no	—
301	#532	—	2	1	no	—
302	#532	—	2	1	no	—
303	#532	—	2	1	no	—
304	#532	C₂²×C₇	1	2	yes	—
305	#532	C₂²×C₇	1	2	yes	—
306	#532	C₂²×C₇	1	2	yes	—
307	#532	C₂²×C₇	1	2	yes	—
308	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
310	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
311	C₂×#127	C₂²×C₇	1	1	yes	characteristic
312	C₂×#125	—	2	1	no	—
313	C₂×#124	C₂²×C₇	1	2	yes	—
314	C₂×C₂²⋊Q₈	—	2	1	no	—
315	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
316	C₂×#121	—	2	1	no	—
317	C₂×#121	—	2	1	no	—
318	C₂×C₄×Q₈	—	2	1	no	—
319	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
320	C₂×C₄×D₄	—	2	1	no	—
321	C₂×C₄×D₄	—	2	1	no	—
322	C₂×#117	—	2	1	no	—
323	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
324	#497	C₂²×C₇	1	8	yes	complemented
325	#494	C₂²×C₇	1	4	yes	complemented
326	#492	C₂²×C₇	1	4	yes	complemented
327	#489	C₂²×C₇	1	8	yes	complemented
328	#487	C₂²×C₇	1	4	yes	complemented
329	#486	C₂²×C₇	1	4	yes	complemented
330	#464	C₂²×C₇	1	16	yes	complemented
331	#462	C₂²×C₇	1	8	yes	complemented
332	#460	C₂²×C₇	1	8	yes	complemented
333	#452	C₂²×C₇	1	16	yes	complemented
334	#451	C₂²×C₇	1	8	yes	—
335	#450	C₂²×C₇	1	8	yes	—
336	#432	C₂²×C₇	1	2	yes	—
337	#432	C₂²×C₇	1	2	yes	complemented
338	#431	C₂²×C₇	1	2	yes	—
339	#431	C₂²×C₇	1	2	yes	complemented
340	#423	C₂²×C₇	1	2	yes	complemented
341	#417	C₂²×C₇	1	8	yes	complemented
342	#407	C₂²×C₇	1	2	yes	—
343	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
344	C₂³×C₇	—	2	2	no	—
345	C₂³×C₇	—	2	2	no	—
346	C₂³×C₇	—	2	4	no	—
347	C₂³×C₇	—	4	1	no	—
348	C₂³×C₇	—	4	4	no	—
349	C₂³×C₇	—	4	4	no	—
350	C₂³×C₇	—	4	4	no	—
351	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
352	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
353	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
354	C₇×Q₈	—	2	8	no	—
355	C₇×Q₈	—	2	8	no	—
356	C₇×Q₈	—	4	4	no	—
357	C₇×Q₈	—	4	4	no	—
358	C₇×Q₈	—	4	4	no	—
359	C₇×Q₈	—	4	4	no	—
360	C₇×D₄	—	2	8	no	—
361	C₇×D₄	—	4	4	no	—
362	C₇×D₄	—	4	4	no	—
363	C₇×D₄	—	4	8	no	—
364	C₇×D₄	—	4	8	no	—
365	C₇×D₄	—	4	4	no	—
366	C₇×D₄	—	4	4	no	—
367	C₇×D₄	—	4	4	no	—
368	C₂×C₄×C₇	—	2	2	no	—
369	C₂×C₄×C₇	—	2	2	no	—
370	C₂×C₄×C₇	—	2	2	no	—
371	C₂×C₄×C₇	—	2	2	no	—
372	C₂×C₄×C₇	—	2	2	no	—
373	C₂×C₄×C₇	—	2	2	no	—
374	C₂×C₄×C₇	—	2	2	no	—
375	C₂×C₄×C₇	—	2	2	no	—
376	C₂×C₄×C₇	—	2	2	no	—
377	C₂×C₄×C₇	—	2	2	no	—
378	C₂×C₄×C₇	—	2	2	no	—
379	C₂×C₄×C₇	—	2	2	no	—
380	C₂×C₄×C₇	—	2	2	no	—
381	C₂×C₄×C₇	—	2	4	no	—
382	C₂×C₄×C₇	—	2	4	no	—
383	C₂×C₄×C₇	—	2	4	no	—
384	C₂×C₄×C₇	—	4	1	no	—
385	C₂×C₄×C₇	—	4	1	no	—
386	C₂×C₄×C₇	—	4	1	no	—
387	C₂×C₄×C₇	—	4	8	no	—
388	C₂×C₄×C₇	—	4	4	no	—
389	C₂×C₄×C₇	—	4	4	no	—
390	C₂×C₄×C₇	—	4	4	no	—
391	C₂×C₄×C₇	—	4	8	no	—
392	C₂×C₄×C₇	#137	1	4	yes	complemented
393	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
405	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
406	C₇×C₈	—	2	8	no	—
407	C₂×#41	—	2	2	no	—
408	C₂×#41	—	2	2	no	—
409	C₂×#41	—	4	8	no	—
410	C₂×#41	C₂³×C₇	1	4	yes	—
411	C₂×#41	C₂³×C₇	1	4	yes	—
412	C₂²×Q₈	—	2	1	no	—
413	C₂²×Q₈	C₂³×C₇	1	2	yes	—
414	C₂²×Q₈	C₂³×C₇	1	2	yes	—
415	C₂²×D₄	—	2	2	no	—
416	C₂²×D₄	—	2	1	no	—
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	C₂³×C₇	1	2	yes	—
419	C₂³×C₄	—	2	2	no	—
420	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
421	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
423	#137	—	4	16	no	—
424	C₂×Q₁₆	C₂³×C₇	1	16	yes	—
425	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
426	C₂×M₁₆	C₂³×C₇	1	4	yes	—
427	C₄⋊Q₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	1	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
434	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
435	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
436	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
437	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
438	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
439	#127	—	2	1	no	—
440	#127	—	2	1	no	—
441	#127	C₂³×C₇	1	2	yes	—
442	#127	C₂³×C₇	1	2	yes	—
443	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#124	—	2	2	no	—
448	#124	—	2	2	no	—
449	#124	C₂³×C₇	1	4	yes	—
450	#124	C₂³×C₇	1	4	yes	—
451	C₂²⋊Q₈	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	2	no	—
457	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
458	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
459	#121	—	2	2	no	—
460	#121	—	2	2	no	—
461	#121	—	2	2	no	—
462	#121	—	2	2	no	—
463	#121	—	2	2	no	—
464	#121	—	2	2	no	—
465	#121	—	2	2	no	—
466	#121	—	2	2	no	—
467	C₄×Q₈	—	2	2	no	—
468	C₄×Q₈	—	2	2	no	—
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	2	no	—
472	C₄×Q₈	—	2	2	no	—
473	C₄×Q₈	C₂³×C₇	1	4	yes	—
474	C₄×Q₈	C₂³×C₇	1	4	yes	—
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	#117	—	2	2	no	—
484	#117	—	2	2	no	—
485	#117	—	2	2	no	—
486	#117	—	2	2	no	—
487	C₂×C₄⋊C₄	—	2	1	no	—
488	C₂×C₄⋊C₄	—	2	1	no	—
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	—	2	2	no	—
494	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
495	C₂×C₂²⋊C₄	—	2	2	no	—
496	C₂×C₂²⋊C₄	—	2	2	no	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₄²	—	2	2	no	—
499	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
500	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
501	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
502	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
503	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
504	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
505	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
506	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
511	C₄⋊C₈	C₂³×C₇	1	4	yes	—
512	C₄⋊C₈	C₂³×C₇	1	4	yes	—
513	#103	C₂³×C₇	1	16	yes	—
514	#102	C₂³×C₇	1	16	yes	—
515	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
516	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
517	#97	C₂³×C₇	1	4	yes	—
518	C₄×C₈	C₂³×C₇	1	4	yes	—
519	C₂²×C₇	—	2	1	no	—
520	C₂²×C₇	—	2	1	no	—
521	C₂²×C₇	—	2	1	no	—
522	C₂²×C₇	—	2	1	no	—
523	C₂²×C₇	—	2	1	no	—
524	C₂²×C₇	—	2	1	no	—
525	C₂²×C₇	—	2	1	no	—
526	C₂²×C₇	—	4	4	no	—
527	C₂²×C₇	—	4	4	no	—
528	C₂²×C₇	—	4	4	no	—
529	C₂²×C₇	—	4	4	no	—
530	C₂²×C₇	—	8	8	no	—
531	C₂²×C₇	#535	1	2	yes	—
532	C₂²×C₇	C₂×#137	1	2	yes	—
533	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
534	C₄×C₇	—	2	1	no	—
535	C₄×C₇	—	2	1	no	—
536	C₄×C₇	—	2	1	no	—
537	C₄×C₇	—	2	1	no	—
538	C₄×C₇	—	2	1	no	—
539	C₄×C₇	—	2	1	no	—
540	C₄×C₇	—	2	1	no	—
541	C₄×C₇	—	4	4	no	—
542	C₄×C₇	—	4	4	no	—
543	C₄×C₇	—	4	4	no	—
544	C₄×C₇	#535	1	2	yes	—
545	C₄×C₇	C₂×#137	1	2	yes	—
546	C₄×C₇	C₂×#137	1	2	yes	—
547	C₄×C₇	#575	1	2	yes	—
548	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
551	#41	—	2	16	no	—
552	#41	—	4	8	no	—
553	#41	—	4	8	no	—
554	#41	—	4	8	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	8	no	—
560	C₂×Q₈	—	4	4	no	—
561	C₂×Q₈	—	4	4	no	—
562	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
563	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	4	4	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	8	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	C₂⁴×C₇	1	4	yes	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	2	4	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	4	2	no	—
584	C₂²×C₄	—	4	8	no	—
585	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
587	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
588	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
589	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
590	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
591	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
592	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
593	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
594	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
595	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
596	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
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	C₂⁴×C₇	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
603	Q₁₆	—	4	16	no	—
604	SD₁₆	—	4	16	no	—
605	M₁₆	—	2	8	no	—
606	C₂×C₈	C₂⁴×C₇	1	8	yes	—
607	C₄⋊C₄	—	2	2	no	—
608	C₄⋊C₄	—	2	2	no	—
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	2	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	2	no	—
613	C₄⋊C₄	—	2	2	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	4	no	—
618	C₄⋊C₄	—	2	4	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
623	C₂²⋊C₄	—	2	4	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₄²	—	2	4	no	—
630	C₄²	—	2	4	no	—
631	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
632	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
633	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
634	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
635	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
636	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
637	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
638	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
639	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
640	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
641	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
642	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
643	C₄²	C₂⁴×C₇	1	1	yes	characteristic
644	C₄²	C₂⁴×C₇	1	1	yes	characteristic
645	C₄²	C₂⁴×C₇	1	1	yes	characteristic
646	C₄²	C₂⁴×C₇	1	1	yes	characteristic
647	C₂×C₇	—	2	2	no	—
648	C₂×C₇	—	2	2	no	—
649	C₂×C₇	—	4	1	no	—
650	C₂×C₇	—	8	4	no	—
651	C₂×C₇	C₂×#535	1	1	yes	characteristic
652	C₂×C₇	C₂²×#137	1	1	yes	characteristic
653	C₂×C₇	C₂×#575	1	1	yes	characteristic
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	4	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	4	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
662	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
663	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
664	Q₈	—	2	8	no	—
665	Q₈	—	2	8	no	—
666	Q₈	—	4	4	no	—
667	Q₈	—	4	4	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	4	no	—
670	D₄	—	2	8	no	—
671	D₄	—	4	4	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	8	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	8	no	—
702	C₂×C₄	C₇×#137	1	4	yes	complemented
703	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
704	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
705	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
706	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
707	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
708	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
709	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
712	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
713	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
714	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
715	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
716	C₈	—	2	8	no	—
717	C₇	#60804	1	1	yes	characteristic, direct product factor, Sylow
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	8	8	no	—
730	C₂²	C₇×#535	1	2	yes	—
731	C₂²	C₂×C₇×#137	1	2	yes	—
732	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	C₇×#535	1	2	yes	—
744	C₄	C₂×C₇×#137	1	2	yes	—
745	C₄	C₂×C₇×#137	1	2	yes	—
746	C₄	C₇×#575	1	2	yes	—
747	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
748	C₂	—	2	2	no	—
749	C₂	—	2	2	no	—
750	C₂	—	4	1	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×C₇×#535	1	1	yes	characteristic
753	C₂	C₂²×C₇×#137	1	1	yes	characteristic
754	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3216	C₂	semidirect
4. C₇×#3215	C₂	semidirect
5. C₇×#3210	C₂	semidirect
6. C₇×#3209	C₂	semidirect
7. C₇×#3208	C₂	semidirect
8. C₇×#3152	C₂	semidirect
9. C₇×#3141	C₂	semidirect
10. C₇×#3037	C₂	semidirect
11. C₇×#3007	C₂	semidirect
12. C₇×#2920	C₂	semidirect
14. C₂×C₇×#137	C₂²	semidirect
21. C₇×#533	C₂²	semidirect
22. C₇×#533	C₂²	semidirect
32. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
33. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₄×C₇×Q₈	C₂²	semidirect
47. C₇×#497	C₂²	semidirect
48. C₇×#494	C₂²	semidirect
49. C₇×#492	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#487	C₂²	semidirect
52. C₇×#486	C₂²	semidirect
53. C₇×#464	C₂²	semidirect
54. C₇×#462	C₂²	semidirect
55. C₇×#460	C₂²	semidirect
56. C₇×#452	C₂²	semidirect
60. C₇×#432	C₂²	semidirect
62. C₇×#431	C₂²	semidirect
63. C₇×#423	C₂²	semidirect
64. C₇×#417	C₂²	semidirect
66. C₄×C₇×M₁₆	C₂²	semidirect
67. #60804	C₇	direct (N × H)
180. C₂×#533	C₂×C₇	semidirect
182. #3216	C₂×C₇	semidirect
183. #3215	C₂×C₇	semidirect
184. #3210	C₂×C₇	semidirect
185. #3209	C₂×C₇	semidirect
186. #3208	C₂×C₇	semidirect
187. #3152	C₂×C₇	semidirect
188. #3141	C₂×C₇	semidirect
189. #3037	C₂×C₇	semidirect
190. #3007	C₂×C₇	semidirect
191. #2920	C₂×C₇	semidirect
291. C₂×#137	C₂²×C₇	semidirect
298. #533	C₂²×C₇	semidirect
299. #533	C₂²×C₇	semidirect
309. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
310. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
319. C₂×C₄×Q₈	C₂²×C₇	semidirect
324. #497	C₂²×C₇	semidirect
325. #494	C₂²×C₇	semidirect
326. #492	C₂²×C₇	semidirect
327. #489	C₂²×C₇	semidirect
328. #487	C₂²×C₇	semidirect
329. #486	C₂²×C₇	semidirect
330. #464	C₂²×C₇	semidirect
331. #462	C₂²×C₇	semidirect
332. #460	C₂²×C₇	semidirect
333. #452	C₂²×C₇	semidirect
337. #432	C₂²×C₇	semidirect
339. #431	C₂²×C₇	semidirect
340. #423	C₂²×C₇	semidirect
341. #417	C₂²×C₇	semidirect
343. C₄×M₁₆	C₂²×C₇	semidirect
392. C₂×C₄×C₇	#137	semidirect
702. C₂×C₄	C₇×#137	semidirect
717. C₇	#60804	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×#533	2
C₂×C₇×#532	2
C₇×#3216	2
C₇×#3215	2
C₇×#3210	2
C₇×#3209	2
C₇×#3208	2
C₇×#3152	2
C₇×#3141	2
C₇×#3037	2
C₇×#3007	2
C₇×#2920	2
#60804	7

Subgroups — C7×#60804 #13238020

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60804 #13238020