Subgroups — C₇×#61017 #13238233

Order 1792.

1792 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3257	C₂	1	4	yes	maximal, complemented
4	C₇×#3240	C₂	1	2	yes	maximal, complemented
5	C₇×#3235	C₂	1	2	yes	maximal, complemented
6	C₇×#3217	C₂	1	2	yes	maximal, complemented
7	C₇×#3213	C₂	1	2	yes	maximal, complemented
8	C₇×#3200	C₂	1	2	yes	maximal, complemented
9	C₇×#3199	C₂	1	2	yes	maximal, complemented
10	C₇×#3180	C₂	1	2	yes	maximal, complemented
11	C₇×#3171	C₂	1	2	yes	maximal, complemented
12	C₇×#3126	C₂	1	2	yes	maximal, complemented
13	C₇×#3122	C₂	1	2	yes	maximal, complemented
14	C₇×#3118	C₂	1	4	yes	maximal, complemented
15	C₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#559	—	2	2	no	—
17	C₇×#559	—	2	2	no	—
18	C₇×#556	—	2	2	no	—
19	C₇×#551	—	2	2	no	—
20	C₇×#551	—	2	2	no	—
21	C₇×#550	—	2	2	no	—
22	C₇×#546	—	2	2	no	—
23	C₇×#546	—	2	2	no	—
24	C₇×#542	C₂²	1	2	yes	—
25	C₇×#542	C₂²	1	2	yes	complemented
26	C₇×#540	C₂²	1	2	yes	—
27	C₇×#540	C₂²	1	2	yes	complemented
28	C₇×#536	C₂²	1	1	yes	characteristic
29	C₇×#535	C₂²	1	1	yes	characteristic
30	C₇×#535	C₂²	1	2	yes	—
31	C₇×#533	C₂²	1	1	yes	characteristic, complemented
32	C₇×#533	C₂²	1	1	yes	characteristic, complemented
33	C₇×#532	C₂²	1	2	yes	—
34	C₇×#532	C₂²	1	2	yes	complemented
35	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	complemented
38	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
39	C₇×#519	C₂²	1	1	yes	characteristic, complemented
40	C₇×#518	C₂²	1	2	yes	complemented
41	C₇×#518	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₇×#41	C₂²	1	1	yes	characteristic
43	C₇×#501	C₂²	1	2	yes	complemented
44	C₇×#501	C₂²	1	2	yes	complemented
45	C₇×#496	C₂²	1	2	yes	—
46	C₇×#496	C₂²	1	2	yes	—
47	C₇×#490	C₂²	1	2	yes	complemented
48	C₇×#490	C₂²	1	2	yes	complemented
49	C₇×#489	C₂²	1	2	yes	complemented
50	C₇×#489	C₂²	1	2	yes	complemented
51	C₇×#485	C₂²	1	4	yes	complemented
52	C₇×#482	C₂²	1	4	yes	—
53	C₇×#482	C₂²	1	4	yes	complemented
54	C₇×#482	C₂²	1	4	yes	complemented
55	C₇×#479	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	4	yes	complemented
57	C₇×#476	C₂²	1	4	yes	complemented
58	C₇×#474	C₂²	1	4	yes	complemented
59	C₇×#469	C₂²	1	4	yes	complemented
60	C₇×#468	C₂²	1	4	yes	complemented
61	C₇×#466	C₂²	1	4	yes	complemented
62	C₇×#465	C₂²	1	4	yes	complemented
63	C₇×#463	C₂²	1	4	yes	complemented
64	C₇×#463	C₂²	1	4	yes	complemented
65	C₇×#460	C₂²	1	4	yes	complemented
66	C₇×#459	C₂²	1	4	yes	—
67	C₇×#450	C₂²	1	4	yes	complemented
68	C₇×#448	C₂²	1	4	yes	complemented
69	C₇×#447	C₂²	1	4	yes	—
70	C₇×#447	C₂²	1	4	yes	complemented
71	C₇×#442	C₂²	1	4	yes	complemented
72	C₇×#440	C₂²	1	4	yes	complemented
73	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
74	C₄×C₇×D₈	C₂²	1	4	yes	complemented
75	C₇×#433	C₂²	1	2	yes	complemented
76	C₇×#433	C₂²	1	2	yes	complemented
77	C₇×#432	C₂²	1	2	yes	complemented
78	C₇×#432	C₂²	1	2	yes	complemented
79	C₇×#424	C₂²	1	2	yes	complemented
80	C₇×#408	C₂²	1	2	yes	—
81	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
83	#61017	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₇×#41	—	2	2	no	—
85	C₂×C₇×#41	—	2	2	no	—
86	C₂×C₇×#41	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×D₄	—	2	2	no	—
89	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
90	C₂²×C₇×D₄	C₂³	1	2	yes	—
91	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
92	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₇×D₈	C₂³	1	4	yes	—
94	C₂×C₇×D₈	C₂³	1	4	yes	—
95	C₂×C₇×M₁₆	C₂³	1	2	yes	—
96	C₂²×C₇×C₈	C₂³	1	2	yes	—
97	C₇×C₄⋊Q₈	—	2	1	no	—
98	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₇×#127	—	2	2	no	—
101	C₇×#127	—	2	1	no	—
102	C₇×#127	—	2	2	no	—
103	C₇×#127	C₂³	1	2	yes	—
104	C₇×#127	C₂³	1	2	yes	—
105	C₇×#126	—	2	2	no	—
106	C₇×#126	—	2	2	no	—
107	C₇×#126	—	2	2	no	—
108	C₇×#126	—	2	2	no	—
109	C₇×#125	C₂³	1	2	yes	—
110	C₇×#125	C₂³	1	2	yes	—
111	C₇×#124	—	2	1	no	—
112	C₇×#124	—	2	2	no	—
113	C₇×#124	—	2	1	no	—
114	C₇×#124	—	2	2	no	—
115	C₇×#124	—	2	2	no	—
116	C₇×#124	—	2	2	no	—
117	C₇×#124	—	2	2	no	—
118	C₇×#124	—	2	2	no	—
119	C₇×#124	C₂³	1	2	yes	—
120	C₇×#124	C₂³	1	2	yes	—
121	C₇×#123	—	2	1	no	—
122	C₇×#123	—	2	1	no	—
123	C₇×#123	—	2	2	no	—
124	C₇×#123	—	2	2	no	—
125	C₇×#123	—	2	4	no	—
126	C₇×#123	—	2	4	no	—
127	C₇×#123	—	2	2	no	—
128	C₇×#123	—	2	2	no	—
129	C₇×C₂²⋊Q₈	—	2	2	no	—
130	C₇×C₂²⋊Q₈	—	2	2	no	—
131	C₇×C₂²⋊Q₈	—	2	2	no	—
132	C₇×C₂²⋊Q₈	—	2	2	no	—
133	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₇×#121	—	2	2	no	—
136	C₇×#121	—	2	2	no	—
137	C₇×#121	—	2	4	no	—
138	C₇×#121	—	2	4	no	—
139	C₇×#121	C₂³	1	2	yes	—
140	C₇×#121	C₂³	1	4	yes	—
141	C₇×#121	C₂³	1	2	yes	—
142	C₇×#121	C₂³	1	4	yes	—
143	C₇×#120	—	2	2	no	—
144	C₇×#120	—	2	2	no	—
145	C₇×#120	—	2	1	no	—
146	C₇×#120	—	2	1	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	2	no	—
150	C₄×C₇×Q₈	D₄	1	2	yes	—
151	C₄×C₇×Q₈	C₂³	1	2	yes	—
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	D₄	1	2	yes	—
160	C₄×C₇×D₄	D₄	1	2	yes	—
161	C₄×C₇×D₄	D₄	1	2	yes	—
162	C₄×C₇×D₄	C₂³	1	4	yes	—
163	C₄×C₇×D₄	C₂³	1	2	yes	—
164	C₄×C₇×D₄	C₂³	1	2	yes	—
165	C₄×C₇×D₄	C₂³	1	4	yes	—
166	C₇×#117	—	2	2	no	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	—	2	2	no	—
169	C₇×#117	C₂³	1	2	yes	—
170	C₇×#117	C₂³	1	1	yes	characteristic
171	C₇×#117	C₂³	1	1	yes	characteristic
172	C₇×#117	C₂³	1	1	yes	characteristic
173	C₇×#117	C₂³	1	1	yes	characteristic
174	C₇×#117	C₂³	1	1	yes	characteristic
175	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
176	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
177	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₇×#107	C₂³	1	4	yes	—
182	C₇×#107	C₂³	1	4	yes	—
183	C₇×#106	C₂³	1	4	yes	—
184	C₇×#106	C₂³	1	4	yes	—
185	C₇×C₄⋊C₈	C₂³	1	4	yes	—
186	C₇×C₄⋊C₈	C₂³	1	4	yes	—
187	C₇×#103	C₂³	1	4	yes	—
188	C₇×#103	C₂³	1	4	yes	—
189	C₇×#102	C₂³	1	4	yes	—
190	C₇×#102	C₂³	1	4	yes	—
191	C₇×#102	C₂³	1	4	yes	—
192	C₇×#102	C₂³	1	4	yes	—
193	C₇×#102	C₂³	1	4	yes	—
194	C₇×#102	C₂³	1	4	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₇×#97	C₂³	1	2	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₇×#97	C₂³	1	2	yes	—
200	C₄×C₇×C₈	C₂³	1	2	yes	—
201	#3510	C₂×C₇	1	1	yes	characteristic, complemented
202	#3508	C₂×C₇	1	1	yes	characteristic, complemented
203	#3257	C₂×C₇	1	4	yes	complemented
204	#3240	C₂×C₇	1	2	yes	complemented
205	#3235	C₂×C₇	1	2	yes	complemented
206	#3217	C₂×C₇	1	2	yes	complemented
207	#3213	C₂×C₇	1	2	yes	complemented
208	#3200	C₂×C₇	1	2	yes	complemented
209	#3199	C₂×C₇	1	2	yes	complemented
210	#3180	C₂×C₇	1	2	yes	complemented
211	#3171	C₂×C₇	1	2	yes	complemented
212	#3126	C₂×C₇	1	2	yes	complemented
213	#3122	C₂×C₇	1	2	yes	complemented
214	#3118	C₂×C₇	1	4	yes	complemented
215	#2923	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂⁴×C₇	—	2	1	no	—
217	C₂⁴×C₇	—	2	2	no	—
218	C₇×#41	—	4	2	no	—
219	C₇×#41	—	8	4	no	—
220	C₇×#41	—	8	4	no	—
221	C₂×C₇×Q₈	—	2	1	no	—
222	C₂×C₇×Q₈	—	2	2	no	—
223	C₂×C₇×Q₈	—	2	2	no	—
224	C₂×C₇×Q₈	—	4	2	no	—
225	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
226	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	4	no	—
231	C₂×C₇×D₄	—	2	1	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	2	2	no	—
235	C₂×C₇×D₄	—	2	4	no	—
236	C₂×C₇×D₄	—	4	2	no	—
237	C₂×C₇×D₄	—	4	2	no	—
238	C₂×C₇×D₄	—	4	2	no	—
239	C₂×C₇×D₄	—	8	4	no	—
240	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
241	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
242	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
243	C₂×C₇×D₄	C₂⁴	1	2	yes	—
244	C₂×C₇×D₄	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₇	—	2	1	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	2	2	no	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
251	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
252	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
256	C₇×SD₁₆	—	4	4	no	—
257	C₇×SD₁₆	—	4	4	no	—
258	C₇×D₈	—	4	4	no	—
259	C₇×D₈	—	4	4	no	—
260	C₇×M₁₆	—	4	2	no	—
261	C₂×C₇×C₈	—	4	2	no	—
262	C₂×C₇×C₈	C₂⁴	1	4	yes	—
263	C₂×C₇×C₈	C₂⁴	1	4	yes	—
264	C₇×C₄⋊C₄	—	2	2	no	—
265	C₇×C₄⋊C₄	—	2	2	no	—
266	C₇×C₄⋊C₄	—	2	2	no	—
267	C₇×C₄⋊C₄	—	2	2	no	—
268	C₇×C₄⋊C₄	—	2	2	no	—
269	C₇×C₄⋊C₄	—	2	2	no	—
270	C₇×C₄⋊C₄	—	2	2	no	—
271	C₇×C₄⋊C₄	—	2	4	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
274	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
275	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
279	C₇×C₂²⋊C₄	—	2	2	no	—
280	C₇×C₂²⋊C₄	—	2	1	no	—
281	C₇×C₂²⋊C₄	—	2	1	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	2	no	—
284	C₇×C₂²⋊C₄	—	2	2	no	—
285	C₇×C₂²⋊C₄	—	2	2	no	—
286	C₇×C₂²⋊C₄	—	2	4	no	—
287	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	2	no	—
289	C₇×C₂²⋊C₄	—	2	2	no	—
290	C₇×C₂²⋊C₄	—	2	2	no	—
291	C₇×C₂²⋊C₄	—	2	2	no	—
292	C₇×C₂²⋊C₄	—	2	2	no	—
293	C₇×C₂²⋊C₄	—	2	2	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
297	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
299	C₄²×C₇	—	2	2	no	—
300	C₄²×C₇	—	2	2	no	—
301	C₄²×C₇	—	2	2	no	—
302	C₄²×C₇	—	2	1	no	—
303	C₄²×C₇	—	2	1	no	—
304	C₄²×C₇	C₂×D₄	1	2	yes	—
305	C₄²×C₇	C₂×D₄	1	2	yes	—
306	C₄²×C₇	C₂×D₄	1	2	yes	—
307	C₄²×C₇	C₂⁴	1	1	yes	characteristic
308	C₄²×C₇	C₂⁴	1	1	yes	characteristic
309	C₄²×C₇	C₂⁴	1	1	yes	characteristic
310	C₄²×C₇	C₂⁴	1	1	yes	characteristic
311	#559	—	2	2	no	—
312	#559	—	2	2	no	—
313	#556	—	2	2	no	—
314	#551	—	2	2	no	—
315	#551	—	2	2	no	—
316	#550	—	2	2	no	—
317	#546	—	2	2	no	—
318	#546	—	2	2	no	—
319	#542	C₂²×C₇	1	2	yes	—
320	#542	C₂²×C₇	1	2	yes	complemented
321	#540	C₂²×C₇	1	2	yes	—
322	#540	C₂²×C₇	1	2	yes	complemented
323	#536	C₂²×C₇	1	1	yes	characteristic
324	#535	C₂²×C₇	1	1	yes	characteristic
325	#535	C₂²×C₇	1	2	yes	—
326	#533	C₂²×C₇	1	1	yes	characteristic, complemented
327	#533	C₂²×C₇	1	1	yes	characteristic, complemented
328	#532	C₂²×C₇	1	2	yes	—
329	#532	C₂²×C₇	1	2	yes	complemented
330	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
331	#529	C₂²×C₇	1	2	yes	—
332	#529	C₂²×C₇	1	2	yes	complemented
333	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
334	#519	C₂²×C₇	1	1	yes	characteristic, complemented
335	#518	C₂²×C₇	1	2	yes	complemented
336	#518	C₂²×C₇	1	1	yes	characteristic, complemented
337	C₄×#41	C₂²×C₇	1	1	yes	characteristic
338	#501	C₂²×C₇	1	2	yes	complemented
339	#501	C₂²×C₇	1	2	yes	complemented
340	#496	C₂²×C₇	1	2	yes	—
341	#496	C₂²×C₇	1	2	yes	—
342	#490	C₂²×C₇	1	2	yes	complemented
343	#490	C₂²×C₇	1	2	yes	complemented
344	#489	C₂²×C₇	1	2	yes	complemented
345	#489	C₂²×C₇	1	2	yes	complemented
346	#485	C₂²×C₇	1	4	yes	complemented
347	#482	C₂²×C₇	1	4	yes	—
348	#482	C₂²×C₇	1	4	yes	complemented
349	#482	C₂²×C₇	1	4	yes	complemented
350	#479	C₂²×C₇	1	4	yes	complemented
351	#478	C₂²×C₇	1	4	yes	complemented
352	#476	C₂²×C₇	1	4	yes	complemented
353	#474	C₂²×C₇	1	4	yes	complemented
354	#469	C₂²×C₇	1	4	yes	complemented
355	#468	C₂²×C₇	1	4	yes	complemented
356	#466	C₂²×C₇	1	4	yes	complemented
357	#465	C₂²×C₇	1	4	yes	complemented
358	#463	C₂²×C₇	1	4	yes	complemented
359	#463	C₂²×C₇	1	4	yes	complemented
360	#460	C₂²×C₇	1	4	yes	complemented
361	#459	C₂²×C₇	1	4	yes	—
362	#450	C₂²×C₇	1	4	yes	complemented
363	#448	C₂²×C₇	1	4	yes	complemented
364	#447	C₂²×C₇	1	4	yes	—
365	#447	C₂²×C₇	1	4	yes	complemented
366	#442	C₂²×C₇	1	4	yes	complemented
367	#440	C₂²×C₇	1	4	yes	complemented
368	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
369	C₄×D₈	C₂²×C₇	1	4	yes	complemented
370	#433	C₂²×C₇	1	2	yes	complemented
371	#433	C₂²×C₇	1	2	yes	complemented
372	#432	C₂²×C₇	1	2	yes	complemented
373	#432	C₂²×C₇	1	2	yes	complemented
374	#424	C₂²×C₇	1	2	yes	complemented
375	#408	C₂²×C₇	1	2	yes	—
376	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
377	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	4	no	—
380	C₂³×C₇	—	4	2	no	—
381	C₂³×C₇	—	4	4	no	—
382	C₂³×C₇	—	8	4	no	—
383	C₂³×C₇	—	8	2	no	—
384	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₇×Q₈	—	2	4	no	—
388	C₇×Q₈	—	4	1	no	—
389	C₇×Q₈	—	4	2	no	—
390	C₇×Q₈	—	4	4	no	—
391	C₇×Q₈	—	8	2	no	—
392	C₇×D₄	—	2	4	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	4	no	—
395	C₇×D₄	—	4	1	no	—
396	C₇×D₄	—	4	1	no	—
397	C₇×D₄	—	4	1	no	—
398	C₇×D₄	—	4	4	no	—
399	C₇×D₄	—	4	2	no	—
400	C₇×D₄	—	4	4	no	—
401	C₇×D₄	—	4	4	no	—
402	C₇×D₄	—	8	4	no	—
403	C₇×D₄	—	8	2	no	—
404	C₇×D₄	—	8	2	no	—
405	C₇×D₄	—	8	4	no	—
406	C₇×D₄	—	8	4	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	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	2	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	—	4	2	no	—
417	C₂×C₄×C₇	—	4	2	no	—
418	C₂×C₄×C₇	—	8	2	no	—
419	C₂×C₄×C₇	—	8	2	no	—
420	C₂×C₄×C₇	—	8	4	no	—
421	C₂×C₄×C₇	—	8	4	no	—
422	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
430	C₇×C₈	—	2	4	no	—
431	C₇×C₈	—	2	4	no	—
432	C₂×#41	—	2	2	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	C₂³×C₇	1	1	yes	characteristic
435	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
438	C₂²×D₄	C₂³×C₇	1	2	yes	—
439	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
440	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
441	C₂×D₈	C₂³×C₇	1	4	yes	—
442	C₂×D₈	C₂³×C₇	1	4	yes	—
443	C₂×M₁₆	C₂³×C₇	1	2	yes	—
444	C₂²×C₈	C₂³×C₇	1	2	yes	—
445	C₄⋊Q₈	—	2	1	no	—
446	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
447	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
448	#127	—	2	2	no	—
449	#127	—	2	1	no	—
450	#127	—	2	2	no	—
451	#127	C₂³×C₇	1	2	yes	—
452	#127	C₂³×C₇	1	2	yes	—
453	#126	—	2	2	no	—
454	#126	—	2	2	no	—
455	#126	—	2	2	no	—
456	#126	—	2	2	no	—
457	#125	C₂³×C₇	1	2	yes	—
458	#125	C₂³×C₇	1	2	yes	—
459	#124	—	2	1	no	—
460	#124	—	2	2	no	—
461	#124	—	2	1	no	—
462	#124	—	2	2	no	—
463	#124	—	2	2	no	—
464	#124	—	2	2	no	—
465	#124	—	2	2	no	—
466	#124	—	2	2	no	—
467	#124	C₂³×C₇	1	2	yes	—
468	#124	C₂³×C₇	1	2	yes	—
469	#123	—	2	1	no	—
470	#123	—	2	1	no	—
471	#123	—	2	2	no	—
472	#123	—	2	2	no	—
473	#123	—	2	4	no	—
474	#123	—	2	4	no	—
475	#123	—	2	2	no	—
476	#123	—	2	2	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
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	2	yes	—
488	#121	C₂³×C₇	1	2	yes	—
489	#121	C₂³×C₇	1	4	yes	—
490	#121	C₂³×C₇	1	4	yes	—
491	#120	—	2	2	no	—
492	#120	—	2	2	no	—
493	#120	—	2	1	no	—
494	#120	—	2	1	no	—
495	C₄×Q₈	—	2	2	no	—
496	C₄×Q₈	—	2	2	no	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	C₇×D₄	1	2	yes	—
499	C₄×Q₈	C₂³×C₇	1	2	yes	—
500	C₄×Q₈	C₂³×C₇	1	2	yes	—
501	C₄×D₄	—	2	2	no	—
502	C₄×D₄	—	2	2	no	—
503	C₄×D₄	—	2	4	no	—
504	C₄×D₄	—	2	2	no	—
505	C₄×D₄	—	2	2	no	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	C₇×D₄	1	2	yes	—
508	C₄×D₄	C₇×D₄	1	2	yes	—
509	C₄×D₄	C₇×D₄	1	2	yes	—
510	C₄×D₄	C₂³×C₇	1	2	yes	—
511	C₄×D₄	C₂³×C₇	1	2	yes	—
512	C₄×D₄	C₂³×C₇	1	4	yes	—
513	C₄×D₄	C₂³×C₇	1	4	yes	—
514	#117	—	2	2	no	—
515	#117	—	2	2	no	—
516	#117	—	2	2	no	—
517	#117	C₂³×C₇	1	2	yes	—
518	#117	C₂³×C₇	1	1	yes	characteristic
519	#117	C₂³×C₇	1	1	yes	characteristic
520	#117	C₂³×C₇	1	1	yes	characteristic
521	#117	C₂³×C₇	1	1	yes	characteristic
522	#117	C₂³×C₇	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	—	2	2	no	—
524	C₂×C₂²⋊C₄	—	2	4	no	—
525	C₂×C₂²⋊C₄	—	2	2	no	—
526	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
527	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
528	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
529	#107	C₂³×C₇	1	4	yes	—
530	#107	C₂³×C₇	1	4	yes	—
531	#106	C₂³×C₇	1	4	yes	—
532	#106	C₂³×C₇	1	4	yes	—
533	C₄⋊C₈	C₂³×C₇	1	4	yes	—
534	C₄⋊C₈	C₂³×C₇	1	4	yes	—
535	#103	C₂³×C₇	1	4	yes	—
536	#103	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	4	yes	—
538	#102	C₂³×C₇	1	4	yes	—
539	#102	C₂³×C₇	1	4	yes	—
540	#102	C₂³×C₇	1	4	yes	—
541	#102	C₂³×C₇	1	4	yes	—
542	#102	C₂³×C₇	1	4	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
545	#97	C₂³×C₇	1	2	yes	—
546	#97	C₂³×C₇	1	2	yes	—
547	#97	C₂³×C₇	1	2	yes	—
548	C₄×C₈	C₂³×C₇	1	2	yes	—
549	C₂²×C₇	—	2	2	no	—
550	C₂²×C₇	—	2	2	no	—
551	C₂²×C₇	—	2	2	no	—
552	C₂²×C₇	—	2	1	no	—
553	C₂²×C₇	—	2	1	no	—
554	C₂²×C₇	—	2	1	no	—
555	C₂²×C₇	—	4	4	no	—
556	C₂²×C₇	—	4	4	no	—
557	C₂²×C₇	—	4	2	no	—
558	C₂²×C₇	—	4	2	no	—
559	C₂²×C₇	—	4	2	no	—
560	C₂²×C₇	—	4	4	no	—
561	C₂²×C₇	—	16	2	no	—
562	C₂²×C₇	—	16	4	no	—
563	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₇	—	2	2	no	—
565	C₄×C₇	—	2	2	no	—
566	C₄×C₇	—	2	2	no	—
567	C₄×C₇	—	2	2	no	—
568	C₄×C₇	—	2	1	no	—
569	C₄×C₇	—	2	1	no	—
570	C₄×C₇	—	2	1	no	—
571	C₄×C₇	—	4	4	no	—
572	C₄×C₇	—	4	2	no	—
573	C₄×C₇	—	4	2	no	—
574	C₄×C₇	—	4	2	no	—
575	C₄×C₇	#585	1	2	yes	—
576	C₂⁴	—	2	1	no	—
577	C₂⁴	—	2	2	no	—
578	#41	—	4	2	no	—
579	#41	—	8	4	no	—
580	#41	—	8	4	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	4	2	no	—
585	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	2	2	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	4	2	no	—
599	C₂×D₄	—	8	4	no	—
600	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
601	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
602	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
603	C₂×D₄	C₂⁴×C₇	1	2	yes	—
604	C₂×D₄	C₂⁴×C₇	1	4	yes	—
605	C₂²×C₄	—	2	1	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
611	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
612	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
613	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
615	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
616	SD₁₆	—	4	4	no	—
617	SD₁₆	—	4	4	no	—
618	D₈	—	4	4	no	—
619	D₈	—	4	4	no	—
620	M₁₆	—	4	2	no	—
621	C₂×C₈	—	4	2	no	—
622	C₂×C₈	C₂⁴×C₇	1	4	yes	—
623	C₂×C₈	C₂⁴×C₇	1	4	yes	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	2	no	—
628	C₄⋊C₄	—	2	2	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	4	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
634	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
635	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	2	no	—
651	C₂²⋊C₄	—	2	2	no	—
652	C₂²⋊C₄	—	2	2	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
657	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
658	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	2	1	no	—
663	C₄²	—	2	1	no	—
664	C₄²	C₂×C₇×D₄	1	2	yes	—
665	C₄²	C₂×C₇×D₄	1	2	yes	—
666	C₄²	C₂×C₇×D₄	1	2	yes	—
667	C₄²	C₂⁴×C₇	1	1	yes	characteristic
668	C₄²	C₂⁴×C₇	1	1	yes	characteristic
669	C₄²	C₂⁴×C₇	1	1	yes	characteristic
670	C₄²	C₂⁴×C₇	1	1	yes	characteristic
671	C₂×C₇	—	4	1	no	—
672	C₂×C₇	—	4	1	no	—
673	C₂×C₇	—	4	1	no	—
674	C₂×C₇	—	8	4	no	—
675	C₂×C₇	—	8	2	no	—
676	C₂×C₇	#3449	1	1	yes	characteristic
677	C₂×C₇	#3585	1	2	yes	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	4	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	4	no	—
682	C₂³	—	8	4	no	—
683	C₂³	—	8	2	no	—
684	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
685	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
686	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
687	Q₈	—	2	4	no	—
688	Q₈	—	4	1	no	—
689	Q₈	—	4	2	no	—
690	Q₈	—	4	4	no	—
691	Q₈	—	8	2	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	4	1	no	—
696	D₄	—	4	1	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	4	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	4	no	—
701	D₄	—	4	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	2	no	—
704	D₄	—	8	2	no	—
705	D₄	—	8	4	no	—
706	D₄	—	8	4	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	2	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	4	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
723	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
724	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
725	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
726	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
727	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
729	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
730	C₈	—	2	4	no	—
731	C₈	—	2	4	no	—
732	C₇	#61017	1	1	yes	characteristic, direct product factor, Sylow
733	C₂²	—	2	2	no	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	4	4	no	—
740	C₂²	—	4	4	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	4	no	—
745	C₂²	—	16	4	no	—
746	C₂²	—	16	2	no	—
747	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	2	no	—
752	C₄	—	2	1	no	—
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	4	4	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	C₇×#585	1	2	yes	—
760	C₂	—	4	1	no	—
761	C₂	—	4	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	8	4	no	—
764	C₂	—	8	2	no	—
765	C₂	C₇×#3449	1	1	yes	characteristic
766	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3510	C₂	semidirect
2. C₇×#3508	C₂	semidirect
3. C₇×#3257	C₂	semidirect
4. C₇×#3240	C₂	semidirect
5. C₇×#3235	C₂	semidirect
6. C₇×#3217	C₂	semidirect
7. C₇×#3213	C₂	semidirect
8. C₇×#3200	C₂	semidirect
9. C₇×#3199	C₂	semidirect
10. C₇×#3180	C₂	semidirect
11. C₇×#3171	C₂	semidirect
12. C₇×#3126	C₂	semidirect
13. C₇×#3122	C₂	semidirect
14. C₇×#3118	C₂	semidirect
15. C₇×#2923	C₂	semidirect
25. C₇×#542	C₂²	semidirect
27. C₇×#540	C₂²	semidirect
31. C₇×#533	C₂²	semidirect
32. C₇×#533	C₂²	semidirect
34. C₇×#532	C₂²	semidirect
35. C₂×C₇×#127	C₂²	semidirect
37. C₇×#529	C₂²	semidirect
38. C₂×C₇×#124	C₂²	semidirect
39. C₇×#519	C₂²	semidirect
40. C₇×#518	C₂²	semidirect
41. C₇×#518	C₂²	semidirect
43. C₇×#501	C₂²	semidirect
44. C₇×#501	C₂²	semidirect
47. C₇×#490	C₂²	semidirect
48. C₇×#490	C₂²	semidirect
49. C₇×#489	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#485	C₂²	semidirect
53. C₇×#482	C₂²	semidirect
54. C₇×#482	C₂²	semidirect
55. C₇×#479	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#476	C₂²	semidirect
58. C₇×#474	C₂²	semidirect
59. C₇×#469	C₂²	semidirect
60. C₇×#468	C₂²	semidirect
61. C₇×#466	C₂²	semidirect
62. C₇×#465	C₂²	semidirect
63. C₇×#463	C₂²	semidirect
64. C₇×#463	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
67. C₇×#450	C₂²	semidirect
68. C₇×#448	C₂²	semidirect
70. C₇×#447	C₂²	semidirect
71. C₇×#442	C₂²	semidirect
72. C₇×#440	C₂²	semidirect
73. C₄×C₇×SD₁₆	C₂²	semidirect
74. C₄×C₇×D₈	C₂²	semidirect
75. C₇×#433	C₂²	semidirect
76. C₇×#433	C₂²	semidirect
77. C₇×#432	C₂²	semidirect
78. C₇×#432	C₂²	semidirect
79. C₇×#424	C₂²	semidirect
81. C₄×C₇×M₁₆	C₂²	semidirect
82. C₂×C₇×#97	C₂²	semidirect
83. #61017	C₇	direct (N × H)
201. #3510	C₂×C₇	semidirect
202. #3508	C₂×C₇	semidirect
203. #3257	C₂×C₇	semidirect
204. #3240	C₂×C₇	semidirect
205. #3235	C₂×C₇	semidirect
206. #3217	C₂×C₇	semidirect
207. #3213	C₂×C₇	semidirect
208. #3200	C₂×C₇	semidirect
209. #3199	C₂×C₇	semidirect
210. #3180	C₂×C₇	semidirect
211. #3171	C₂×C₇	semidirect
212. #3126	C₂×C₇	semidirect
213. #3122	C₂×C₇	semidirect
214. #3118	C₂×C₇	semidirect
215. #2923	C₂×C₇	semidirect
320. #542	C₂²×C₇	semidirect
322. #540	C₂²×C₇	semidirect
326. #533	C₂²×C₇	semidirect
327. #533	C₂²×C₇	semidirect
329. #532	C₂²×C₇	semidirect
330. C₂×#127	C₂²×C₇	semidirect
332. #529	C₂²×C₇	semidirect
333. C₂×#124	C₂²×C₇	semidirect
334. #519	C₂²×C₇	semidirect
335. #518	C₂²×C₇	semidirect
336. #518	C₂²×C₇	semidirect
338. #501	C₂²×C₇	semidirect
339. #501	C₂²×C₇	semidirect
342. #490	C₂²×C₇	semidirect
343. #490	C₂²×C₇	semidirect
344. #489	C₂²×C₇	semidirect
345. #489	C₂²×C₇	semidirect
346. #485	C₂²×C₇	semidirect
348. #482	C₂²×C₇	semidirect
349. #482	C₂²×C₇	semidirect
350. #479	C₂²×C₇	semidirect
351. #478	C₂²×C₇	semidirect
352. #476	C₂²×C₇	semidirect
353. #474	C₂²×C₇	semidirect
354. #469	C₂²×C₇	semidirect
355. #468	C₂²×C₇	semidirect
356. #466	C₂²×C₇	semidirect
357. #465	C₂²×C₇	semidirect
358. #463	C₂²×C₇	semidirect
359. #463	C₂²×C₇	semidirect
360. #460	C₂²×C₇	semidirect
362. #450	C₂²×C₇	semidirect
363. #448	C₂²×C₇	semidirect
365. #447	C₂²×C₇	semidirect
366. #442	C₂²×C₇	semidirect
367. #440	C₂²×C₇	semidirect
368. C₄×SD₁₆	C₂²×C₇	semidirect
369. C₄×D₈	C₂²×C₇	semidirect
370. #433	C₂²×C₇	semidirect
371. #433	C₂²×C₇	semidirect
372. #432	C₂²×C₇	semidirect
373. #432	C₂²×C₇	semidirect
374. #424	C₂²×C₇	semidirect
376. C₄×M₁₆	C₂²×C₇	semidirect
377. C₂×#97	C₂²×C₇	semidirect
732. C₇	#61017	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×#3510	2
C₇×#3508	2
C₇×#3257	2
C₇×#3240	2
C₇×#3235	2
C₇×#3217	2
C₇×#3213	2
C₇×#3200	2
C₇×#3199	2
C₇×#3180	2
C₇×#3171	2
C₇×#3126	2
C₇×#3122	2
C₇×#3118	2
C₇×#2923	2
#61017	7

Subgroups — C7×#61017 #13238233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61017 #13238233