Subgroups — C₇×#61262 #13238478

Order 1792.

1884 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3494	C₂	1	2	yes	maximal, complemented
2	C₇×#3347	C₂	1	4	yes	maximal, complemented
3	C₇×#3345	C₂	1	4	yes	maximal, complemented
4	C₇×#3341	C₂	1	2	yes	maximal, complemented
5	C₇×#3339	C₂	1	2	yes	maximal, complemented
6	C₇×#3339	C₂	1	2	yes	maximal, complemented
7	C₇×#3334	C₂	1	2	yes	maximal, complemented
8	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3096	C₂	1	2	yes	maximal, complemented
10	C₇×#3094	C₂	1	2	yes	maximal, complemented
11	C₇×#3081	C₂	1	2	yes	maximal, complemented
12	C₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2913	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
21	C₇×#555	C₂²	1	4	yes	complemented
22	C₇×#553	C₂²	1	4	yes	complemented
23	C₇×#553	C₂²	1	4	yes	complemented
24	C₇×#551	—	2	4	no	—
25	C₇×#547	C₂²	1	4	yes	complemented
26	C₇×#546	—	2	4	no	—
27	C₇×#544	C₂²	1	2	yes	—
28	C₇×#542	—	2	2	no	—
29	C₇×#540	—	2	2	no	—
30	C₇×#535	C₂²	1	2	yes	—
31	C₇×#532	—	2	2	no	—
32	C₇×#529	—	2	2	no	—
33	C₇×#525	C₂²	1	1	yes	characteristic
34	C₂×C₇×#121	C₂²	1	2	yes	—
35	C₇×#520	C₂²	1	2	yes	—
36	C₇×#518	C₂²	1	2	yes	—
37	C₂×C₇×#117	C₂²	1	2	yes	—
38	C₇×#501	C₂²	1	4	yes	complemented
39	C₇×#500	C₂²	1	2	yes	complemented
40	C₇×#499	C₂²	1	2	yes	complemented
41	C₇×#482	C₂²	1	4	yes	complemented
42	C₇×#482	C₂²	1	4	yes	complemented
43	C₇×#482	C₂²	1	4	yes	complemented
44	C₇×#482	C₂²	1	4	yes	complemented
45	C₇×#481	C₂²	1	4	yes	complemented
46	C₇×#481	C₂²	1	4	yes	complemented
47	C₇×#480	C₂²	1	4	yes	complemented
48	C₇×#480	C₂²	1	4	yes	complemented
49	C₇×#478	C₂²	1	4	yes	complemented
50	C₇×#478	C₂²	1	4	yes	complemented
51	C₇×#476	C₂²	1	4	yes	complemented
52	C₇×#474	C₂²	1	4	yes	complemented
53	C₇×#469	C₂²	1	4	yes	complemented
54	C₇×#466	C₂²	1	2	yes	—
55	C₇×#466	C₂²	1	2	yes	—
56	C₇×#466	C₂²	1	2	yes	—
57	C₇×#466	C₂²	1	2	yes	—
58	C₇×#466	C₂²	1	2	yes	complemented
59	C₇×#466	C₂²	1	2	yes	complemented
60	C₇×#442	C₂²	1	4	yes	complemented
61	C₄×C₇×D₈	C₂²	1	2	yes	complemented
62	C₄×C₇×D₈	C₂²	1	2	yes	complemented
63	C₇×#435	C₂²	1	2	yes	complemented
64	C₇×#435	C₂²	1	2	yes	complemented
65	C₇×C₈×D₄	C₂²	1	2	yes	complemented
66	C₇×C₈×D₄	C₂²	1	2	yes	complemented
67	C₇×#428	C₂²	1	2	yes	—
68	C₇×#428	C₂²	1	2	yes	—
69	C₇×#428	C₂²	1	4	yes	complemented
70	C₇×#427	C₂²	1	1	yes	characteristic
71	C₇×#427	C₂²	1	1	yes	characteristic
72	C₇×#427	C₂²	1	2	yes	—
73	C₇×#427	C₂²	1	1	yes	characteristic, complemented
74	C₇×#427	C₂²	1	1	yes	characteristic, complemented
75	C₇×#427	C₂²	1	2	yes	complemented
76	C₇×#427	C₂²	1	2	yes	complemented
77	C₂×C₇×#107	C₂²	1	1	yes	characteristic
78	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₇×#107	C₂²	1	2	yes	complemented
81	C₂×C₇×#106	C₂²	1	2	yes	complemented
82	C₇×#424	C₂²	1	1	yes	characteristic
83	C₇×#418	C₂²	1	2	yes	—
84	C₇×#418	C₂²	1	2	yes	—
85	C₂×C₇×#102	C₂²	1	2	yes	—
86	C₇×#408	C₂²	1	1	yes	characteristic
87	C₇×#407	C₂²	1	1	yes	characteristic
88	C₇×#405	C₂²	1	1	yes	characteristic
89	#61262	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	4	no	—
91	C₂×C₇×#41	C₂³	1	1	yes	characteristic
92	C₂²×C₇×D₄	—	2	2	no	—
93	C₂²×C₇×D₄	C₂³	1	2	yes	—
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₇×D₈	—	2	4	no	—
96	C₂×C₇×D₈	C₂³	1	2	yes	—
97	C₂×C₇×D₈	C₂³	1	2	yes	—
98	C₇×#131	—	2	4	no	—
99	C₂×C₇×M₁₆	C₂³	1	2	yes	—
100	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
101	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
102	C₂²×C₇×C₈	—	2	4	no	—
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	2	yes	—
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
112	C₇×#127	—	2	2	no	—
113	C₇×#126	—	2	4	no	—
114	C₇×#126	—	2	4	no	—
115	C₇×#125	—	2	2	no	—
116	C₇×#125	C₂³	1	4	yes	—
117	C₇×#124	—	2	2	no	—
118	C₇×#124	—	2	4	no	—
119	C₇×#124	—	2	4	no	—
120	C₇×#123	—	2	4	no	—
121	C₇×#123	—	2	4	no	—
122	C₇×#123	—	2	4	no	—
123	C₇×#123	—	2	4	no	—
124	C₇×#123	D₄	1	2	yes	—
125	C₇×C₂²⋊Q₈	—	2	4	no	—
126	C₇×C₂²⋊Q₈	—	2	4	no	—
127	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
128	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
129	C₇×#121	—	2	4	no	—
130	C₇×#121	—	2	4	no	—
131	C₇×#121	—	2	4	no	—
132	C₇×#121	—	2	2	no	—
133	C₇×#121	—	2	2	no	—
134	C₇×#121	D₄	1	1	yes	characteristic
135	C₇×#121	D₄	1	1	yes	characteristic
136	C₇×#121	C₂³	1	4	yes	—
137	C₇×#121	C₂³	1	4	yes	—
138	C₇×#121	C₂³	1	4	yes	—
139	C₇×#121	C₂³	1	4	yes	—
140	C₇×#120	—	2	4	no	—
141	C₇×#120	D₄	1	2	yes	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×D₄	—	2	2	no	—
144	C₄×C₇×D₄	—	2	4	no	—
145	C₄×C₇×D₄	—	2	2	no	—
146	C₄×C₇×D₄	—	2	2	no	—
147	C₄×C₇×D₄	—	2	4	no	—
148	C₄×C₇×D₄	—	2	4	no	—
149	C₄×C₇×D₄	C₂³	1	4	yes	—
150	C₄×C₇×D₄	C₂³	1	4	yes	—
151	C₄×C₇×D₄	C₂³	1	2	yes	—
152	C₄×C₇×D₄	C₂³	1	2	yes	—
153	C₇×#117	—	2	2	no	—
154	C₇×#117	—	2	2	no	—
155	C₇×#117	—	2	4	no	—
156	C₇×#117	C₂³	1	2	yes	—
157	C₇×#117	C₂³	1	2	yes	—
158	C₇×#117	C₂³	1	4	yes	—
159	C₇×#117	C₂³	1	2	yes	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₇×#117	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
167	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
168	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
169	C₂×C₄²×C₇	—	2	2	no	—
170	C₇×#107	C₂³	1	2	yes	—
171	C₇×#107	C₂³	1	2	yes	—
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#107	C₂³	1	1	yes	characteristic
174	C₇×#107	C₂³	1	2	yes	—
175	C₇×#107	C₂³	1	4	yes	—
176	C₇×#107	C₂³	1	2	yes	—
177	C₇×#107	C₂³	1	4	yes	—
178	C₇×#107	C₂³	1	1	yes	characteristic
179	C₇×#107	C₂³	1	1	yes	characteristic
180	C₇×#106	C₂³	1	2	yes	—
181	C₇×#106	C₂³	1	2	yes	—
182	C₇×#106	C₂³	1	4	yes	—
183	C₇×#106	C₂³	1	2	yes	—
184	C₇×#106	C₂³	1	4	yes	—
185	C₇×#106	C₂³	1	2	yes	—
186	C₇×C₄⋊C₈	C₂³	1	2	yes	—
187	C₇×C₄⋊C₈	C₂³	1	2	yes	—
188	C₇×#102	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×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
198	C₇×#97	C₂³	1	2	yes	—
199	C₄×C₇×C₈	C₂³	1	2	yes	—
200	#3494	C₂×C₇	1	2	yes	complemented
201	#3347	C₂×C₇	1	4	yes	complemented
202	#3345	C₂×C₇	1	4	yes	complemented
203	#3341	C₂×C₇	1	2	yes	complemented
204	#3339	C₂×C₇	1	2	yes	complemented
205	#3339	C₂×C₇	1	2	yes	complemented
206	#3334	C₂×C₇	1	2	yes	complemented
207	#3164	C₂×C₇	1	1	yes	characteristic, complemented
208	#3096	C₂×C₇	1	2	yes	complemented
209	#3094	C₂×C₇	1	2	yes	complemented
210	#3081	C₂×C₇	1	2	yes	complemented
211	#3058	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
213	#2948	C₂×C₇	1	1	yes	characteristic, complemented
214	#2929	C₂×C₇	1	1	yes	characteristic, complemented
215	#2913	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
217	C₂⁴×C₇	—	2	2	no	—
218	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
219	C₇×#41	—	2	2	no	—
220	C₇×#41	—	2	2	no	—
221	C₇×#41	—	8	8	no	—
222	C₂×C₇×Q₈	—	2	4	no	—
223	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	4	no	—
227	C₂×C₇×D₄	—	2	4	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	—	8	4	no	—
232	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
233	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
234	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
235	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
236	C₂×C₇×D₄	C₂⁴	1	4	yes	—
237	C₂²×C₄×C₇	—	2	2	no	—
238	C₂²×C₄×C₇	—	2	2	no	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	2	no	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
252	C₇×D₈	—	2	4	no	—
253	C₇×D₈	—	2	4	no	—
254	C₇×M₁₆	—	2	2	no	—
255	C₇×M₁₆	—	2	2	no	—
256	C₇×M₁₆	—	2	4	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	2	no	—
260	C₂×C₇×C₈	—	2	2	no	—
261	C₂×C₇×C₈	—	2	2	no	—
262	C₂×C₇×C₈	—	2	4	no	—
263	C₂×C₇×C₈	#41	1	4	yes	complemented
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₇×C₈	C₂⁴	1	2	yes	—
267	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
268	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
269	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
270	C₇×C₄⋊C₄	—	2	2	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
278	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
279	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
280	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
286	C₇×C₂²⋊C₄	—	2	2	no	—
287	C₇×C₂²⋊C₄	—	2	2	no	—
288	C₇×C₂²⋊C₄	—	2	2	no	—
289	C₇×C₂²⋊C₄	—	2	2	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
298	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
299	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
301	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
302	C₄²×C₇	—	2	2	no	—
303	C₄²×C₇	—	2	2	no	—
304	C₄²×C₇	—	2	2	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	—	2	4	no	—
307	C₄²×C₇	C₂⁴	1	2	yes	—
308	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
309	C₂×#131	C₂²×C₇	1	1	yes	characteristic
310	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
311	#555	C₂²×C₇	1	4	yes	complemented
312	#553	C₂²×C₇	1	4	yes	complemented
313	#553	C₂²×C₇	1	4	yes	complemented
314	#551	—	2	4	no	—
315	#547	C₂²×C₇	1	4	yes	complemented
316	#546	—	2	4	no	—
317	#544	C₂²×C₇	1	2	yes	—
318	#542	—	2	2	no	—
319	#540	—	2	2	no	—
320	#535	C₂²×C₇	1	2	yes	—
321	#532	—	2	2	no	—
322	#529	—	2	2	no	—
323	#525	C₂²×C₇	1	1	yes	characteristic
324	C₂×#121	C₂²×C₇	1	2	yes	—
325	#520	C₂²×C₇	1	2	yes	—
326	#518	C₂²×C₇	1	2	yes	—
327	C₂×#117	C₂²×C₇	1	2	yes	—
328	#501	C₂²×C₇	1	4	yes	complemented
329	#500	C₂²×C₇	1	2	yes	complemented
330	#499	C₂²×C₇	1	2	yes	complemented
331	#482	C₂²×C₇	1	4	yes	complemented
332	#482	C₂²×C₇	1	4	yes	complemented
333	#482	C₂²×C₇	1	4	yes	complemented
334	#482	C₂²×C₇	1	4	yes	complemented
335	#481	C₂²×C₇	1	4	yes	complemented
336	#481	C₂²×C₇	1	4	yes	complemented
337	#480	C₂²×C₇	1	4	yes	complemented
338	#480	C₂²×C₇	1	4	yes	complemented
339	#478	C₂²×C₇	1	4	yes	complemented
340	#478	C₂²×C₇	1	4	yes	complemented
341	#476	C₂²×C₇	1	4	yes	complemented
342	#474	C₂²×C₇	1	4	yes	complemented
343	#469	C₂²×C₇	1	4	yes	complemented
344	#466	C₂²×C₇	1	2	yes	—
345	#466	C₂²×C₇	1	2	yes	—
346	#466	C₂²×C₇	1	2	yes	—
347	#466	C₂²×C₇	1	2	yes	—
348	#466	C₂²×C₇	1	2	yes	complemented
349	#466	C₂²×C₇	1	2	yes	complemented
350	#442	C₂²×C₇	1	4	yes	complemented
351	C₄×D₈	C₂²×C₇	1	2	yes	complemented
352	C₄×D₈	C₂²×C₇	1	2	yes	complemented
353	#435	C₂²×C₇	1	2	yes	complemented
354	#435	C₂²×C₇	1	2	yes	complemented
355	C₈×D₄	C₂²×C₇	1	2	yes	complemented
356	C₈×D₄	C₂²×C₇	1	2	yes	complemented
357	#428	C₂²×C₇	1	2	yes	—
358	#428	C₂²×C₇	1	2	yes	—
359	#428	C₂²×C₇	1	4	yes	complemented
360	#427	C₂²×C₇	1	2	yes	—
361	#427	C₂²×C₇	1	1	yes	characteristic
362	#427	C₂²×C₇	1	1	yes	characteristic
363	#427	C₂²×C₇	1	1	yes	characteristic, complemented
364	#427	C₂²×C₇	1	2	yes	complemented
365	#427	C₂²×C₇	1	1	yes	characteristic, complemented
366	#427	C₂²×C₇	1	2	yes	complemented
367	C₂×#107	C₂²×C₇	1	1	yes	characteristic
368	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
369	C₂×#107	C₂²×C₇	1	2	yes	complemented
370	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
371	C₂×#106	C₂²×C₇	1	2	yes	complemented
372	#424	C₂²×C₇	1	1	yes	characteristic
373	#418	C₂²×C₇	1	2	yes	—
374	#418	C₂²×C₇	1	2	yes	—
375	C₂×#102	C₂²×C₇	1	2	yes	—
376	#408	C₂²×C₇	1	1	yes	characteristic
377	#407	C₂²×C₇	1	1	yes	characteristic
378	#405	C₂²×C₇	1	1	yes	characteristic
379	C₂³×C₇	—	2	2	no	—
380	C₂³×C₇	—	2	2	no	—
381	C₂³×C₇	—	2	4	no	—
382	C₂³×C₇	—	4	1	no	—
383	C₂³×C₇	—	4	4	no	—
384	C₂³×C₇	—	8	2	no	—
385	C₂³×C₇	—	8	2	no	—
386	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₇	C₂²×D₄	1	2	yes	—
388	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
389	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	8	4	no	—
392	C₇×D₄	—	2	4	no	—
393	C₇×D₄	—	2	4	no	—
394	C₇×D₄	—	2	2	no	—
395	C₇×D₄	—	2	4	no	—
396	C₇×D₄	—	2	4	no	—
397	C₇×D₄	—	4	2	no	—
398	C₇×D₄	—	4	8	no	—
399	C₇×D₄	—	4	4	no	—
400	C₇×D₄	—	8	4	no	—
401	C₇×D₄	—	8	4	no	—
402	C₇×D₄	—	8	4	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	1	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	2	1	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	2	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	4	no	—
417	C₂×C₄×C₇	—	4	4	no	—
418	C₂×C₄×C₇	—	8	4	no	—
419	C₂×C₄×C₇	—	8	4	no	—
420	C₂×C₄×C₇	—	8	2	no	—
421	C₂×C₄×C₇	—	8	2	no	—
422	C₂×C₄×C₇	—	8	4	no	—
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	1	yes	characteristic
429	C₂×C₄×C₇	C₂×#41	1	2	yes	—
430	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
431	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
432	C₇×C₈	—	2	1	no	—
433	C₇×C₈	—	2	1	no	—
434	C₇×C₈	—	2	2	no	—
435	C₇×C₈	—	2	2	no	—
436	C₇×C₈	C₂×#41	1	2	yes	—
437	C₇×C₈	C₂×#41	1	2	yes	—
438	C₂×#41	—	2	4	no	—
439	C₂×#41	C₂³×C₇	1	1	yes	characteristic
440	C₂²×D₄	—	2	2	no	—
441	C₂²×D₄	C₂³×C₇	1	2	yes	—
442	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
443	C₂×D₈	—	2	4	no	—
444	C₂×D₈	C₂³×C₇	1	2	yes	—
445	C₂×D₈	C₂³×C₇	1	2	yes	—
446	#131	—	2	4	no	—
447	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
448	C₂×M₁₆	C₂³×C₇	1	2	yes	—
449	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
450	C₂²×C₈	—	2	4	no	—
451	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
452	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
453	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
454	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
455	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
456	C₂²×C₈	C₂³×C₇	1	2	yes	—
457	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
458	C₄⋊Q₈	—	2	2	no	—
459	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
460	#127	—	2	2	no	—
461	#126	—	2	4	no	—
462	#126	—	2	4	no	—
463	#125	—	2	2	no	—
464	#125	C₂³×C₇	1	4	yes	—
465	#124	—	2	2	no	—
466	#124	—	2	4	no	—
467	#124	—	2	4	no	—
468	#123	—	2	4	no	—
469	#123	—	2	4	no	—
470	#123	—	2	4	no	—
471	#123	—	2	4	no	—
472	#123	C₇×D₄	1	2	yes	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	2	4	no	—
475	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
476	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
477	#121	—	2	4	no	—
478	#121	—	2	4	no	—
479	#121	—	2	4	no	—
480	#121	—	2	2	no	—
481	#121	—	2	2	no	—
482	#121	C₇×D₄	1	1	yes	characteristic
483	#121	C₇×D₄	1	1	yes	characteristic
484	#121	C₂³×C₇	1	4	yes	—
485	#121	C₂³×C₇	1	4	yes	—
486	#121	C₂³×C₇	1	4	yes	—
487	#121	C₂³×C₇	1	4	yes	—
488	#120	—	2	4	no	—
489	#120	C₇×D₄	1	2	yes	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	2	no	—
494	C₄×D₄	—	2	2	no	—
495	C₄×D₄	—	2	4	no	—
496	C₄×D₄	—	2	4	no	—
497	C₄×D₄	C₂³×C₇	1	4	yes	—
498	C₄×D₄	C₂³×C₇	1	4	yes	—
499	C₄×D₄	C₂³×C₇	1	2	yes	—
500	C₄×D₄	C₂³×C₇	1	2	yes	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	—	2	4	no	—
504	#117	C₂³×C₇	1	2	yes	—
505	#117	C₂³×C₇	1	2	yes	—
506	#117	C₂³×C₇	1	2	yes	—
507	#117	C₂³×C₇	1	2	yes	—
508	#117	C₂³×C₇	1	4	yes	—
509	#117	C₂³×C₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
514	C₂×C₂²⋊C₄	—	2	2	no	—
515	C₂×C₂²⋊C₄	—	2	2	no	—
516	C₂×C₂²⋊C₄	—	2	4	no	—
517	C₂×C₄²	—	2	2	no	—
518	#107	C₂³×C₇	1	2	yes	—
519	#107	C₂³×C₇	1	2	yes	—
520	#107	C₂³×C₇	1	1	yes	characteristic
521	#107	C₂³×C₇	1	1	yes	characteristic
522	#107	C₂³×C₇	1	1	yes	characteristic
523	#107	C₂³×C₇	1	1	yes	characteristic
524	#107	C₂³×C₇	1	2	yes	—
525	#107	C₂³×C₇	1	2	yes	—
526	#107	C₂³×C₇	1	4	yes	—
527	#107	C₂³×C₇	1	4	yes	—
528	#106	C₂³×C₇	1	2	yes	—
529	#106	C₂³×C₇	1	2	yes	—
530	#106	C₂³×C₇	1	2	yes	—
531	#106	C₂³×C₇	1	2	yes	—
532	#106	C₂³×C₇	1	4	yes	—
533	#106	C₂³×C₇	1	4	yes	—
534	C₄⋊C₈	C₂³×C₇	1	2	yes	—
535	C₄⋊C₈	C₂³×C₇	1	2	yes	—
536	#102	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	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
543	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
544	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
545	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
546	#97	C₂³×C₇	1	2	yes	—
547	C₄×C₈	C₂³×C₇	1	2	yes	—
548	C₂²×C₇	—	2	1	no	—
549	C₂²×C₇	—	2	1	no	—
550	C₂²×C₇	—	2	1	no	—
551	C₂²×C₇	—	2	1	no	—
552	C₂²×C₇	—	2	1	no	—
553	C₂²×C₇	—	2	2	no	—
554	C₂²×C₇	—	2	1	no	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	1	no	—
558	C₂²×C₇	—	4	4	no	—
559	C₂²×C₇	—	4	4	no	—
560	C₂²×C₇	—	4	4	no	—
561	C₂²×C₇	—	4	4	no	—
562	C₂²×C₇	—	16	4	no	—
563	C₂²×C₇	#547	1	2	yes	—
564	C₂²×C₇	#576	1	2	yes	—
565	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₇	—	2	2	no	—
567	C₄×C₇	—	2	1	no	—
568	C₄×C₇	—	2	1	no	—
569	C₄×C₇	—	2	2	no	—
570	C₄×C₇	—	2	2	no	—
571	C₄×C₇	—	4	2	no	—
572	C₄×C₇	—	4	2	no	—
573	C₄×C₇	—	4	2	no	—
574	C₄×C₇	—	4	2	no	—
575	C₄×C₇	—	4	4	no	—
576	C₄×C₇	#547	1	2	yes	—
577	C₄×C₇	C₂²×#41	1	1	yes	characteristic
578	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
579	C₂⁴	—	2	2	no	—
580	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
581	#41	—	2	2	no	—
582	#41	—	2	2	no	—
583	#41	—	8	8	no	—
584	C₂×Q₈	—	2	4	no	—
585	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	2	4	no	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	8	4	no	—
594	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
595	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
596	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
597	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
598	C₂×D₄	C₂⁴×C₇	1	4	yes	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
608	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
609	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
611	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
614	D₈	—	2	4	no	—
615	D₈	—	2	4	no	—
616	M₁₆	—	2	2	no	—
617	M₁₆	—	2	2	no	—
618	M₁₆	—	2	4	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	2	4	no	—
625	C₂×C₈	C₇×#41	1	4	yes	complemented
626	C₂×C₈	C₂⁴×C₇	1	2	yes	—
627	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
628	C₂×C₈	C₂⁴×C₇	1	2	yes	—
629	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
630	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
631	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	4	no	—
636	C₄⋊C₄	—	2	4	no	—
637	C₄⋊C₄	—	2	4	no	—
638	C₄⋊C₄	—	2	4	no	—
639	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
640	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
642	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
644	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
647	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
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	4	no	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
660	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
661	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
662	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
663	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
664	C₄²	—	2	2	no	—
665	C₄²	—	2	2	no	—
666	C₄²	—	2	2	no	—
667	C₄²	—	2	2	no	—
668	C₄²	—	2	4	no	—
669	C₄²	C₂⁴×C₇	1	2	yes	—
670	C₂×C₇	—	2	2	no	—
671	C₂×C₇	—	2	2	no	—
672	C₂×C₇	—	4	2	no	—
673	C₂×C₇	—	4	1	no	—
674	C₂×C₇	—	8	4	no	—
675	C₂×C₇	C₂×#547	1	1	yes	characteristic
676	C₂×C₇	C₂×#576	1	1	yes	characteristic
677	C₂×C₇	#3584	1	1	yes	characteristic
678	C₂³	—	2	2	no	—
679	C₂³	—	2	2	no	—
680	C₂³	—	2	4	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	8	2	no	—
684	C₂³	—	8	2	no	—
685	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
686	C₂³	C₂²×C₇×D₄	1	2	yes	—
687	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
688	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
689	Q₈	—	2	2	no	—
690	Q₈	—	8	4	no	—
691	D₄	—	2	4	no	—
692	D₄	—	2	4	no	—
693	D₄	—	2	4	no	—
694	D₄	—	2	4	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	2	no	—
697	D₄	—	4	8	no	—
698	D₄	—	4	4	no	—
699	D₄	—	8	4	no	—
700	D₄	—	8	4	no	—
701	D₄	—	8	4	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	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	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	8	4	no	—
718	C₂×C₄	—	8	4	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	8	4	no	—
722	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
723	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
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	1	yes	characteristic
727	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
728	C₂×C₄	C₂×C₇×#41	1	2	yes	—
729	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
730	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
731	C₈	—	2	1	no	—
732	C₈	—	2	1	no	—
733	C₈	—	2	2	no	—
734	C₈	—	2	2	no	—
735	C₈	C₂×C₇×#41	1	2	yes	—
736	C₈	C₂×C₇×#41	1	2	yes	—
737	C₇	#61262	1	1	yes	characteristic, direct product factor, Sylow
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	2	1	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	1	no	—
745	C₂²	—	2	2	no	—
746	C₂²	—	2	1	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	16	4	no	—
753	C₂²	C₇×#547	1	2	yes	—
754	C₂²	C₇×#576	1	2	yes	—
755	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
756	C₄	—	2	2	no	—
757	C₄	—	2	2	no	—
758	C₄	—	2	1	no	—
759	C₄	—	2	1	no	—
760	C₄	—	2	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	4	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	C₇×#547	1	2	yes	—
767	C₄	C₂²×C₇×#41	1	1	yes	characteristic
768	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
769	C₂	—	2	2	no	—
770	C₂	—	2	2	no	—
771	C₂	—	4	1	no	—
772	C₂	—	4	2	no	—
773	C₂	—	8	4	no	—
774	C₂	C₂×C₇×#547	1	1	yes	characteristic
775	C₂	C₂×C₇×#576	1	1	yes	characteristic
776	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 ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3494	C₂	semidirect
2. C₇×#3347	C₂	semidirect
3. C₇×#3345	C₂	semidirect
4. C₇×#3341	C₂	semidirect
5. C₇×#3339	C₂	semidirect
6. C₇×#3339	C₂	semidirect
7. C₇×#3334	C₂	semidirect
8. C₇×#3164	C₂	semidirect
9. C₇×#3096	C₂	semidirect
10. C₇×#3094	C₂	semidirect
11. C₇×#3081	C₂	semidirect
12. C₇×#3058	C₂	semidirect
13. C₂×C₇×#466	C₂	semidirect
14. C₇×#2948	C₂	semidirect
15. C₇×#2929	C₂	semidirect
16. C₇×#2913	C₂	semidirect
17. C₂×C₇×#427	C₂	semidirect
21. C₇×#555	C₂²	semidirect
22. C₇×#553	C₂²	semidirect
23. C₇×#553	C₂²	semidirect
25. C₇×#547	C₂²	semidirect
38. C₇×#501	C₂²	semidirect
39. C₇×#500	C₂²	semidirect
40. C₇×#499	C₂²	semidirect
41. C₇×#482	C₂²	semidirect
42. C₇×#482	C₂²	semidirect
43. C₇×#482	C₂²	semidirect
44. C₇×#482	C₂²	semidirect
45. C₇×#481	C₂²	semidirect
46. C₇×#481	C₂²	semidirect
47. C₇×#480	C₂²	semidirect
48. C₇×#480	C₂²	semidirect
49. C₇×#478	C₂²	semidirect
50. C₇×#478	C₂²	semidirect
51. C₇×#476	C₂²	semidirect
52. C₇×#474	C₂²	semidirect
53. C₇×#469	C₂²	semidirect
58. C₇×#466	C₂²	semidirect
59. C₇×#466	C₂²	semidirect
60. C₇×#442	C₂²	semidirect
61. C₄×C₇×D₈	C₂²	semidirect
62. C₄×C₇×D₈	C₂²	semidirect
63. C₇×#435	C₂²	semidirect
64. C₇×#435	C₂²	semidirect
65. C₇×C₈×D₄	C₂²	semidirect
66. C₇×C₈×D₄	C₂²	semidirect
69. C₇×#428	C₂²	semidirect
73. C₇×#427	C₂²	semidirect
74. C₇×#427	C₂²	semidirect
75. C₇×#427	C₂²	semidirect
76. C₇×#427	C₂²	semidirect
78. C₂×C₇×#107	C₂²	semidirect
79. C₂×C₇×#107	C₂²	semidirect
80. C₂×C₇×#107	C₂²	semidirect
81. C₂×C₇×#106	C₂²	semidirect
89. #61262	C₇	direct (N × H)
200. #3494	C₂×C₇	semidirect
201. #3347	C₂×C₇	semidirect
202. #3345	C₂×C₇	semidirect
203. #3341	C₂×C₇	semidirect
204. #3339	C₂×C₇	semidirect
205. #3339	C₂×C₇	semidirect
206. #3334	C₂×C₇	semidirect
207. #3164	C₂×C₇	semidirect
208. #3096	C₂×C₇	semidirect
209. #3094	C₂×C₇	semidirect
210. #3081	C₂×C₇	semidirect
211. #3058	C₂×C₇	semidirect
212. C₂×#466	C₂×C₇	semidirect
213. #2948	C₂×C₇	semidirect
214. #2929	C₂×C₇	semidirect
215. #2913	C₂×C₇	semidirect
216. C₂×#427	C₂×C₇	semidirect
263. C₂×C₇×C₈	#41	semidirect
311. #555	C₂²×C₇	semidirect
312. #553	C₂²×C₇	semidirect
313. #553	C₂²×C₇	semidirect
315. #547	C₂²×C₇	semidirect
328. #501	C₂²×C₇	semidirect
329. #500	C₂²×C₇	semidirect
330. #499	C₂²×C₇	semidirect
331. #482	C₂²×C₇	semidirect
332. #482	C₂²×C₇	semidirect
333. #482	C₂²×C₇	semidirect
334. #482	C₂²×C₇	semidirect
335. #481	C₂²×C₇	semidirect
336. #481	C₂²×C₇	semidirect
337. #480	C₂²×C₇	semidirect
338. #480	C₂²×C₇	semidirect
339. #478	C₂²×C₇	semidirect
340. #478	C₂²×C₇	semidirect
341. #476	C₂²×C₇	semidirect
342. #474	C₂²×C₇	semidirect
343. #469	C₂²×C₇	semidirect
348. #466	C₂²×C₇	semidirect
349. #466	C₂²×C₇	semidirect
350. #442	C₂²×C₇	semidirect
351. C₄×D₈	C₂²×C₇	semidirect
352. C₄×D₈	C₂²×C₇	semidirect
353. #435	C₂²×C₇	semidirect
354. #435	C₂²×C₇	semidirect
355. C₈×D₄	C₂²×C₇	semidirect
356. C₈×D₄	C₂²×C₇	semidirect
359. #428	C₂²×C₇	semidirect
363. #427	C₂²×C₇	semidirect
364. #427	C₂²×C₇	semidirect
365. #427	C₂²×C₇	semidirect
366. #427	C₂²×C₇	semidirect
368. C₂×#107	C₂²×C₇	semidirect
369. C₂×#107	C₂²×C₇	semidirect
370. C₂×#107	C₂²×C₇	semidirect
371. C₂×#106	C₂²×C₇	semidirect
625. C₂×C₈	C₇×#41	semidirect
737. C₇	#61262	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3494	2
C₇×#3347	2
C₇×#3345	2
C₇×#3341	2
C₇×#3339	2
C₇×#3334	2
C₇×#3164	2
C₇×#3096	2
C₇×#3094	2
C₇×#3081	2
C₇×#3058	2
C₂×C₇×#466	2
C₇×#2948	2
C₇×#2929	2
C₇×#2913	2
C₂×C₇×#427	2
#61262	7

Subgroups — C7×#61262 #13238478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61262 #13238478