Subgroups — C₇×#61475 #13238691

Order 1792.

1900 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	C₇×#3514	C₂	1	2	yes	maximal, complemented
2	C₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Q₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3373	C₂	1	2	yes	maximal, complemented
5	C₇×#3342	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3341	C₂	1	2	yes	maximal, complemented
7	C₇×#3324	C₂	1	2	yes	maximal, complemented
8	C₇×#3319	C₂	1	4	yes	maximal, complemented
9	C₇×#3280	C₂	1	2	yes	maximal, complemented
10	C₇×D₄×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3175	C₂	1	2	yes	maximal, complemented
12	C₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3118	C₂	1	4	yes	maximal, complemented
14	C₇×#3115	C₂	1	2	yes	maximal, complemented
15	C₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2948	C₂	1	2	yes	maximal, complemented
17	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂²×C₇×D₈	C₂²	1	2	yes	—
20	C₇×#559	C₂²	1	2	yes	complemented
21	C₇×#556	C₂²	1	2	yes	—
22	C₇×#555	C₂²	1	4	yes	complemented
23	C₇×#551	—	2	4	no	—
24	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
25	C₇×#548	—	2	2	no	—
26	C₇×#546	—	2	2	no	—
27	C₇×#546	C₂²	1	4	yes	complemented
28	C₇×D₄²	C₂²	1	2	yes	—
29	C₇×#542	C₂²	1	4	yes	complemented
30	C₇×#538	—	2	4	no	—
31	C₇×#532	C₂²	1	2	yes	complemented
32	C₇×#529	—	2	2	no	—
33	C₇×#529	C₂²	1	1	yes	characteristic
34	C₂×C₇×#124	—	2	2	no	—
35	C₇×#518	C₂²	1	4	yes	complemented
36	C₄×C₇×#41	C₂²	1	2	yes	complemented
37	C₇×#500	C₂²	1	1	yes	characteristic, complemented
38	C₇×#500	C₂²	1	2	yes	complemented
39	C₇×#495	C₂²	1	2	yes	complemented
40	C₇×#493	C₂²	1	1	yes	characteristic
41	C₇×#489	C₂²	1	4	yes	complemented
42	C₇×#486	C₂²	1	2	yes	complemented
43	C₇×#485	C₂²	1	4	yes	complemented
44	C₇×#482	C₂²	1	4	yes	complemented
45	C₇×#482	C₂²	1	4	yes	complemented
46	C₇×#476	C₂²	1	4	yes	complemented
47	C₇×#475	C₂²	1	2	yes	complemented
48	C₇×#474	C₂²	1	4	yes	complemented
49	C₇×#474	C₂²	1	2	yes	complemented
50	C₇×#468	C₂²	1	4	yes	complemented
51	C₇×#467	C₂²	1	2	yes	complemented
52	C₇×#466	C₂²	1	2	yes	—
53	C₇×#466	C₂²	1	2	yes	complemented
54	C₇×#466	C₂²	1	2	yes	complemented
55	C₇×#463	C₂²	1	4	yes	complemented
56	C₇×#463	C₂²	1	4	yes	complemented
57	C₇×#460	C₂²	1	2	yes	complemented
58	C₇×#459	C₂²	1	2	yes	—
59	C₇×#450	C₂²	1	4	yes	complemented
60	C₇×#449	C₂²	1	4	yes	complemented
61	C₇×#447	C₂²	1	4	yes	—
62	C₇×#446	C₂²	1	1	yes	characteristic, complemented
63	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₇×#442	C₂²	1	4	yes	complemented
65	C₇×#442	C₂²	1	4	yes	complemented
66	C₇×#440	C₂²	1	4	yes	complemented
67	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
68	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
70	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
71	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
72	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
73	C₄×C₇×D₈	C₂²	1	2	yes	—
74	C₄×C₇×D₈	C₂²	1	2	yes	complemented
75	C₄×C₇×D₈	C₂²	1	2	yes	complemented
76	C₄×C₇×D₈	C₂²	1	2	yes	complemented
77	C₇×#436	C₂²	1	1	yes	characteristic
78	C₇×#435	C₂²	1	2	yes	complemented
79	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
80	C₇×C₈×D₄	C₂²	1	2	yes	complemented
81	C₇×#433	C₂²	1	2	yes	complemented
82	C₇×#432	C₂²	1	1	yes	characteristic, complemented
83	C₇×#427	C₂²	1	1	yes	characteristic, complemented
84	C₇×#427	C₂²	1	2	yes	complemented
85	C₇×#418	C₂²	1	4	yes	complemented
86	C₇×#416	C₂²	1	2	yes	complemented
87	C₇×#405	C₂²	1	2	yes	complemented
88	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
89	#61475	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×C₇×#41	—	2	2	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂²×C₇×Q₈	—	2	2	no	—
93	C₂²×C₇×D₄	—	2	2	no	—
94	C₂²×C₇×D₄	C₂³	1	4	yes	—
95	C₇×#135	—	2	4	no	—
96	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
98	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₇×D₈	—	2	8	no	—
100	C₂×C₇×D₈	C₂³	1	2	yes	—
101	C₂×C₇×D₈	C₂³	1	4	yes	—
102	C₂×C₇×D₈	C₂³	1	2	yes	—
103	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
104	C₂×C₇×M₁₆	C₂³	1	2	yes	—
105	C₂²×C₇×C₈	C₂³	1	2	yes	—
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
110	C₇×#127	C₂³	1	2	yes	—
111	C₇×#126	—	2	4	no	—
112	C₇×#126	—	2	4	no	—
113	C₇×#126	D₄	1	2	yes	—
114	C₇×#125	D₄	1	1	yes	characteristic
115	C₇×#124	—	2	2	no	—
116	C₇×#124	—	2	2	no	—
117	C₇×#124	—	2	4	no	—
118	C₇×#124	—	2	4	no	—
119	C₇×#124	—	2	4	no	—
120	C₇×#124	—	2	2	no	—
121	C₇×#124	D₄	1	1	yes	characteristic
122	C₇×#124	C₂³	1	4	yes	—
123	C₇×#123	—	2	4	no	—
124	C₇×#123	—	2	4	no	—
125	C₇×#123	—	2	4	no	—
126	C₇×#123	D₄	1	2	yes	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	4	no	—
129	C₇×C₂²⋊Q₈	—	2	4	no	—
130	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
131	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
132	C₇×#121	—	2	4	no	—
133	C₇×#121	—	2	2	no	—
134	C₇×#121	—	2	2	no	—
135	C₇×#121	—	2	4	no	—
136	C₇×#121	D₄	1	1	yes	characteristic
137	C₇×#121	C₂³	1	4	yes	—
138	C₇×#121	C₂³	1	4	yes	—
139	C₇×#120	—	2	4	no	—
140	C₇×#120	—	2	4	no	—
141	C₄×C₇×Q₈	—	2	2	no	—
142	C₄×C₇×Q₈	C₂³	1	2	yes	—
143	C₄×C₇×Q₈	C₂³	1	2	yes	—
144	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
150	C₄×C₇×D₄	—	2	2	no	—
151	C₄×C₇×D₄	C₂³	1	2	yes	—
152	C₄×C₇×D₄	C₂³	1	4	yes	—
153	C₄×C₇×D₄	C₂³	1	4	yes	—
154	C₄×C₇×D₄	C₂³	1	2	yes	—
155	C₄×C₇×D₄	C₂³	1	4	yes	—
156	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
157	C₄×C₇×D₄	C₂³	1	2	yes	—
158	C₇×#117	—	2	4	no	—
159	C₇×#117	—	2	2	no	—
160	C₇×#117	C₂³	1	2	yes	—
161	C₇×#117	C₂³	1	4	yes	—
162	C₇×#117	C₂³	1	2	yes	—
163	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
164	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
165	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
166	C₂×C₄²×C₇	—	2	2	no	—
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
168	C₇×#107	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	2	yes	—
170	C₇×#107	C₂³	1	2	yes	—
171	C₇×#107	C₂³	1	4	yes	—
172	C₇×#107	C₂³	1	1	yes	characteristic
173	C₇×#106	C₂³	1	4	yes	—
174	C₇×#106	C₂³	1	2	yes	—
175	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
178	C₇×C₄⋊C₈	C₂³	1	2	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#103	C₂³	1	2	yes	—
181	C₇×#103	C₂³	1	2	yes	—
182	C₇×#102	C₂³	1	4	yes	—
183	C₇×#102	C₂³	1	4	yes	—
184	C₇×#102	C₂³	1	4	yes	—
185	C₇×#102	C₂³	1	2	yes	—
186	C₇×#102	C₂³	1	4	yes	—
187	C₇×#102	C₂³	1	4	yes	—
188	C₇×#102	C₂³	1	2	yes	—
189	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₇×#97	C₂³	1	2	yes	—
193	C₇×#97	C₂³	1	2	yes	—
194	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
195	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
196	C₄×C₇×C₈	C₂³	1	2	yes	—
197	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
198	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
199	#3514	C₂×C₇	1	2	yes	complemented
200	#3396	C₂×C₇	1	1	yes	characteristic, complemented
201	Q₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
202	#3373	C₂×C₇	1	2	yes	complemented
203	#3342	C₂×C₇	1	1	yes	characteristic, complemented
204	#3341	C₂×C₇	1	2	yes	complemented
205	#3324	C₂×C₇	1	2	yes	complemented
206	#3319	C₂×C₇	1	4	yes	complemented
207	#3280	C₂×C₇	1	2	yes	complemented
208	D₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
209	#3175	C₂×C₇	1	2	yes	complemented
210	#3169	C₂×C₇	1	1	yes	characteristic, complemented
211	#3118	C₂×C₇	1	4	yes	complemented
212	#3115	C₂×C₇	1	2	yes	complemented
213	#2966	C₂×C₇	1	1	yes	characteristic, complemented
214	#2948	C₂×C₇	1	2	yes	complemented
215	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
216	C₂⁴×C₇	—	2	4	no	—
217	C₇×#41	—	2	4	no	—
218	C₇×#41	—	4	2	no	—
219	C₇×#41	—	8	4	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	—	2	4	no	—
222	C₂×C₇×Q₈	—	8	4	no	—
223	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
224	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
225	C₂×C₇×D₄	—	2	8	no	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	2	4	no	—
228	C₂×C₇×D₄	—	2	4	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	2	no	—
231	C₂×C₇×D₄	—	2	2	no	—
232	C₂×C₇×D₄	—	4	4	no	—
233	C₂×C₇×D₄	—	8	4	no	—
234	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
235	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
236	C₂×C₇×D₄	C₂⁴	1	4	yes	—
237	C₂×C₇×D₄	C₂⁴	1	2	yes	—
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	4	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
248	C₇×Q₁₆	—	2	2	no	—
249	C₇×SD₁₆	—	2	4	no	—
250	C₇×SD₁₆	—	4	4	no	—
251	C₇×D₈	—	2	8	no	—
252	C₇×D₈	—	2	4	no	—
253	C₇×D₈	—	4	2	no	—
254	C₇×D₈	#41	1	4	yes	complemented
255	C₇×M₁₆	—	4	2	no	—
256	C₂×C₇×C₈	—	2	4	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	4	1	no	—
259	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
260	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
261	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×C₈	C₂⁴	1	2	yes	—
263	C₂×C₇×C₈	C₂⁴	1	2	yes	—
264	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
265	C₇×C₄⋊C₄	—	2	2	no	—
266	C₇×C₄⋊C₄	—	2	2	no	—
267	C₇×C₄⋊C₄	—	2	4	no	—
268	C₇×C₄⋊C₄	—	2	2	no	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
271	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
272	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
273	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
274	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
275	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₂²⋊C₄	—	2	4	no	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	4	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	4	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
291	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
292	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
293	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
294	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
295	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
296	C₄²×C₇	—	2	2	no	—
297	C₄²×C₇	—	2	2	no	—
298	C₄²×C₇	—	2	2	no	—
299	C₄²×C₇	—	2	4	no	—
300	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
301	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
302	C₄²×C₇	C₂⁴	1	1	yes	characteristic
303	C₄²×C₇	C₂⁴	1	1	yes	characteristic
304	C₄²×C₇	C₂⁴	1	2	yes	—
305	C₂×#135	C₂²×C₇	1	1	yes	characteristic
306	C₂²×D₈	C₂²×C₇	1	2	yes	—
307	#559	C₂²×C₇	1	2	yes	complemented
308	#556	C₂²×C₇	1	2	yes	—
309	#555	C₂²×C₇	1	4	yes	complemented
310	#551	—	2	4	no	—
311	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
312	#548	—	2	2	no	—
313	#546	—	2	2	no	—
314	#546	C₂²×C₇	1	4	yes	complemented
315	D₄²	C₂²×C₇	1	2	yes	—
316	#542	C₂²×C₇	1	4	yes	complemented
317	#538	—	2	4	no	—
318	#532	C₂²×C₇	1	2	yes	complemented
319	#529	—	2	2	no	—
320	#529	C₂²×C₇	1	1	yes	characteristic
321	C₂×#124	—	2	2	no	—
322	#518	C₂²×C₇	1	4	yes	complemented
323	C₄×#41	C₂²×C₇	1	2	yes	complemented
324	#500	C₂²×C₇	1	2	yes	complemented
325	#500	C₂²×C₇	1	1	yes	characteristic, complemented
326	#495	C₂²×C₇	1	2	yes	complemented
327	#493	C₂²×C₇	1	1	yes	characteristic
328	#489	C₂²×C₇	1	4	yes	complemented
329	#486	C₂²×C₇	1	2	yes	complemented
330	#485	C₂²×C₇	1	4	yes	complemented
331	#482	C₂²×C₇	1	4	yes	complemented
332	#482	C₂²×C₇	1	4	yes	complemented
333	#476	C₂²×C₇	1	4	yes	complemented
334	#475	C₂²×C₇	1	2	yes	complemented
335	#474	C₂²×C₇	1	2	yes	complemented
336	#474	C₂²×C₇	1	4	yes	complemented
337	#468	C₂²×C₇	1	4	yes	complemented
338	#467	C₂²×C₇	1	2	yes	complemented
339	#466	C₂²×C₇	1	2	yes	—
340	#466	C₂²×C₇	1	2	yes	complemented
341	#466	C₂²×C₇	1	2	yes	complemented
342	#463	C₂²×C₇	1	4	yes	complemented
343	#463	C₂²×C₇	1	4	yes	complemented
344	#460	C₂²×C₇	1	2	yes	complemented
345	#459	C₂²×C₇	1	2	yes	—
346	#450	C₂²×C₇	1	4	yes	complemented
347	#449	C₂²×C₇	1	4	yes	complemented
348	#447	C₂²×C₇	1	4	yes	—
349	#446	C₂²×C₇	1	1	yes	characteristic, complemented
350	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
351	#442	C₂²×C₇	1	4	yes	complemented
352	#442	C₂²×C₇	1	4	yes	complemented
353	#440	C₂²×C₇	1	4	yes	complemented
354	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
356	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
357	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
358	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
359	C₄×D₈	C₂²×C₇	1	2	yes	—
360	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
361	C₄×D₈	C₂²×C₇	1	2	yes	complemented
362	C₄×D₈	C₂²×C₇	1	2	yes	complemented
363	C₄×D₈	C₂²×C₇	1	2	yes	complemented
364	#436	C₂²×C₇	1	1	yes	characteristic
365	#435	C₂²×C₇	1	2	yes	complemented
366	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
367	C₈×D₄	C₂²×C₇	1	2	yes	complemented
368	#433	C₂²×C₇	1	2	yes	complemented
369	#432	C₂²×C₇	1	1	yes	characteristic, complemented
370	#427	C₂²×C₇	1	1	yes	characteristic, complemented
371	#427	C₂²×C₇	1	2	yes	complemented
372	#418	C₂²×C₇	1	4	yes	complemented
373	#416	C₂²×C₇	1	2	yes	complemented
374	#405	C₂²×C₇	1	2	yes	complemented
375	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
376	C₂³×C₇	—	2	2	no	—
377	C₂³×C₇	—	2	4	no	—
378	C₂³×C₇	—	4	8	no	—
379	C₂³×C₇	—	8	4	no	—
380	C₂³×C₇	—	8	4	no	—
381	C₂³×C₇	C₂²×D₄	1	2	yes	—
382	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
383	C₇×Q₈	—	2	2	no	—
384	C₇×Q₈	—	2	2	no	—
385	C₇×Q₈	—	2	2	no	—
386	C₇×Q₈	—	4	4	no	—
387	C₇×Q₈	—	8	4	no	—
388	C₇×D₄	—	2	2	no	—
389	C₇×D₄	—	2	4	no	—
390	C₇×D₄	—	2	2	no	—
391	C₇×D₄	—	2	4	no	—
392	C₇×D₄	—	4	2	no	—
393	C₇×D₄	—	4	8	no	—
394	C₇×D₄	—	4	4	no	—
395	C₇×D₄	—	4	4	no	—
396	C₇×D₄	—	8	2	no	—
397	C₇×D₄	—	8	4	no	—
398	C₇×D₄	—	8	4	no	—
399	C₇×D₄	C₂×#41	1	4	yes	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	1	no	—
403	C₂×C₄×C₇	—	2	1	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	4	no	—
409	C₂×C₄×C₇	—	4	1	no	—
410	C₂×C₄×C₇	—	4	4	no	—
411	C₂×C₄×C₇	—	4	4	no	—
412	C₂×C₄×C₇	—	8	2	no	—
413	C₂×C₄×C₇	—	8	4	no	—
414	C₂×C₄×C₇	—	8	4	no	—
415	C₂×C₄×C₇	—	8	4	no	—
416	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
419	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
425	C₇×C₈	—	2	2	no	—
426	C₇×C₈	—	2	1	no	—
427	C₇×C₈	—	2	1	no	—
428	C₇×C₈	—	2	1	no	—
429	C₇×C₈	—	2	2	no	—
430	C₇×C₈	C₂×#41	1	2	yes	—
431	C₂×#41	—	2	2	no	—
432	C₂×#41	C₂³×C₇	1	2	yes	—
433	C₂²×Q₈	—	2	2	no	—
434	C₂²×D₄	—	2	2	no	—
435	C₂²×D₄	C₂³×C₇	1	4	yes	—
436	#135	—	2	4	no	—
437	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
438	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
439	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
440	C₂×D₈	—	2	8	no	—
441	C₂×D₈	C₂³×C₇	1	2	yes	—
442	C₂×D₈	C₂³×C₇	1	4	yes	—
443	C₂×D₈	C₂³×C₇	1	2	yes	—
444	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
445	C₂×M₁₆	C₂³×C₇	1	2	yes	—
446	C₂²×C₈	C₂³×C₇	1	2	yes	—
447	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
448	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
449	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
450	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
451	#127	C₂³×C₇	1	2	yes	—
452	#126	—	2	4	no	—
453	#126	—	2	4	no	—
454	#126	C₇×D₄	1	2	yes	—
455	#125	C₇×D₄	1	1	yes	characteristic
456	#124	—	2	2	no	—
457	#124	—	2	2	no	—
458	#124	—	2	4	no	—
459	#124	—	2	4	no	—
460	#124	—	2	4	no	—
461	#124	—	2	2	no	—
462	#124	C₇×D₄	1	1	yes	characteristic
463	#124	C₂³×C₇	1	4	yes	—
464	#123	—	2	4	no	—
465	#123	—	2	4	no	—
466	#123	—	2	4	no	—
467	#123	C₇×D₄	1	2	yes	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	4	no	—
470	C₂²⋊Q₈	—	2	4	no	—
471	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
472	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
473	#121	—	2	4	no	—
474	#121	—	2	2	no	—
475	#121	—	2	2	no	—
476	#121	—	2	4	no	—
477	#121	C₇×D₄	1	1	yes	characteristic
478	#121	C₂³×C₇	1	4	yes	—
479	#121	C₂³×C₇	1	4	yes	—
480	#120	—	2	4	no	—
481	#120	—	2	4	no	—
482	C₄×Q₈	—	2	2	no	—
483	C₄×Q₈	C₂³×C₇	1	2	yes	—
484	C₄×Q₈	C₂³×C₇	1	2	yes	—
485	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
486	C₄×D₄	—	2	2	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	4	no	—
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	2	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	C₂³×C₇	1	2	yes	—
493	C₄×D₄	C₂³×C₇	1	2	yes	—
494	C₄×D₄	C₂³×C₇	1	4	yes	—
495	C₄×D₄	C₂³×C₇	1	4	yes	—
496	C₄×D₄	C₂³×C₇	1	4	yes	—
497	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
498	C₄×D₄	C₂³×C₇	1	2	yes	—
499	#117	—	2	4	no	—
500	#117	—	2	2	no	—
501	#117	C₂³×C₇	1	2	yes	—
502	#117	C₂³×C₇	1	4	yes	—
503	#117	C₂³×C₇	1	2	yes	—
504	C₂×C₂²⋊C₄	—	2	4	no	—
505	C₂×C₂²⋊C₄	—	2	4	no	—
506	C₂×C₂²⋊C₄	—	2	4	no	—
507	C₂×C₄²	—	2	2	no	—
508	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
509	#107	C₂³×C₇	1	1	yes	characteristic
510	#107	C₂³×C₇	1	2	yes	—
511	#107	C₂³×C₇	1	1	yes	characteristic
512	#107	C₂³×C₇	1	2	yes	—
513	#107	C₂³×C₇	1	4	yes	—
514	#106	C₂³×C₇	1	2	yes	—
515	#106	C₂³×C₇	1	4	yes	—
516	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
517	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
518	C₄⋊C₈	C₂³×C₇	1	2	yes	—
519	C₄⋊C₈	C₂³×C₇	1	2	yes	—
520	#103	C₂³×C₇	1	2	yes	—
521	#103	C₂³×C₇	1	2	yes	—
522	#103	C₂³×C₇	1	4	yes	—
523	#102	C₂³×C₇	1	2	yes	—
524	#102	C₂³×C₇	1	2	yes	—
525	#102	C₂³×C₇	1	4	yes	—
526	#102	C₂³×C₇	1	4	yes	—
527	#102	C₂³×C₇	1	4	yes	—
528	#102	C₂³×C₇	1	4	yes	—
529	#102	C₂³×C₇	1	4	yes	—
530	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
531	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
532	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
533	#97	C₂³×C₇	1	2	yes	—
534	#97	C₂³×C₇	1	2	yes	—
535	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
536	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
537	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
538	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
539	C₄×C₈	C₂³×C₇	1	2	yes	—
540	C₂²×C₇	—	2	1	no	—
541	C₂²×C₇	—	2	2	no	—
542	C₂²×C₇	—	2	1	no	—
543	C₂²×C₇	—	2	2	no	—
544	C₂²×C₇	—	2	4	no	—
545	C₂²×C₇	—	2	1	no	—
546	C₂²×C₇	—	2	2	no	—
547	C₂²×C₇	—	4	2	no	—
548	C₂²×C₇	—	4	2	no	—
549	C₂²×C₇	—	4	4	no	—
550	C₂²×C₇	—	4	4	no	—
551	C₂²×C₇	—	4	4	no	—
552	C₂²×C₇	—	16	8	no	—
553	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
554	C₄×C₇	—	2	1	no	—
555	C₄×C₇	—	2	1	no	—
556	C₄×C₇	—	2	2	no	—
557	C₄×C₇	—	2	1	no	—
558	C₄×C₇	—	2	2	no	—
559	C₄×C₇	—	2	1	no	—
560	C₄×C₇	—	2	2	no	—
561	C₄×C₇	—	4	2	no	—
562	C₄×C₇	—	4	2	no	—
563	C₄×C₇	—	4	2	no	—
564	C₄×C₇	—	4	4	no	—
565	C₄×C₇	#576	1	2	yes	—
566	C₄×C₇	C₂²×#41	1	1	yes	characteristic
567	C₄×C₇	#585	1	1	yes	characteristic
568	C₂⁴	—	2	4	no	—
569	#41	—	2	4	no	—
570	#41	—	4	2	no	—
571	#41	—	8	4	no	—
572	C₂×Q₈	—	2	2	no	—
573	C₂×Q₈	—	2	4	no	—
574	C₂×Q₈	—	8	4	no	—
575	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
576	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
577	C₂×D₄	—	2	8	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	4	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	2	no	—
583	C₂×D₄	—	2	2	no	—
584	C₂×D₄	—	4	4	no	—
585	C₂×D₄	—	8	4	no	—
586	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
587	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
588	C₂×D₄	C₂⁴×C₇	1	4	yes	—
589	C₂×D₄	C₂⁴×C₇	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
597	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
598	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
600	Q₁₆	—	2	2	no	—
601	SD₁₆	—	2	4	no	—
602	SD₁₆	—	4	4	no	—
603	D₈	—	2	8	no	—
604	D₈	—	2	4	no	—
605	D₈	—	4	2	no	—
606	D₈	C₇×#41	1	4	yes	complemented
607	M₁₆	—	4	2	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	2	2	no	—
610	C₂×C₈	—	4	1	no	—
611	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
612	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
613	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
614	C₂×C₈	C₂⁴×C₇	1	2	yes	—
615	C₂×C₈	C₂⁴×C₇	1	2	yes	—
616	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
623	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
624	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
625	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
626	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
627	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
629	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
630	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
644	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
645	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
646	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
647	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	4	no	—
652	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
653	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
654	C₄²	C₂⁴×C₇	1	1	yes	characteristic
655	C₄²	C₂⁴×C₇	1	1	yes	characteristic
656	C₄²	C₂⁴×C₇	1	2	yes	—
657	C₂×C₇	—	4	1	no	—
658	C₂×C₇	—	4	2	no	—
659	C₂×C₇	—	4	4	no	—
660	C₂×C₇	—	8	4	no	—
661	C₂×C₇	D₄×#41	1	1	yes	characteristic
662	C₂×C₇	C₂×#576	1	1	yes	characteristic
663	C₂×C₇	#3584	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	4	8	no	—
667	C₂³	—	8	4	no	—
668	C₂³	—	8	4	no	—
669	C₂³	C₂²×C₇×D₄	1	2	yes	—
670	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
671	Q₈	—	2	2	no	—
672	Q₈	—	2	2	no	—
673	Q₈	—	2	2	no	—
674	Q₈	—	4	4	no	—
675	Q₈	—	8	4	no	—
676	D₄	—	2	4	no	—
677	D₄	—	2	2	no	—
678	D₄	—	2	4	no	—
679	D₄	—	2	2	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	8	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	8	2	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	C₂×C₇×#41	1	4	yes	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	8	2	no	—
701	C₂×C₄	—	8	4	no	—
702	C₂×C₄	—	8	4	no	—
703	C₂×C₄	—	8	4	no	—
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	2	yes	—
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	2	yes	—
710	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
711	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
712	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	2	no	—
718	C₈	C₂×C₇×#41	1	2	yes	—
719	C₇	#61475	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	1	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	16	8	no	—
733	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	2	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	2	no	—
739	C₄	—	2	1	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	4	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	C₇×#576	1	2	yes	—
746	C₄	C₂²×C₇×#41	1	1	yes	characteristic
747	C₄	C₇×#585	1	1	yes	characteristic
748	C₂	—	4	2	no	—
749	C₂	—	4	1	no	—
750	C₂	—	4	4	no	—
751	C₂	—	8	4	no	—
752	C₂	C₇×D₄×#41	1	1	yes	characteristic
753	C₂	C₂×C₇×#576	1	1	yes	characteristic
754	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3514	C₂	semidirect
2. C₇×#3396	C₂	semidirect
3. C₇×Q₈×D₈	C₂	semidirect
4. C₇×#3373	C₂	semidirect
5. C₇×#3342	C₂	semidirect
6. C₇×#3341	C₂	semidirect
7. C₇×#3324	C₂	semidirect
8. C₇×#3319	C₂	semidirect
9. C₇×#3280	C₂	semidirect
10. C₇×D₄×D₈	C₂	semidirect
11. C₇×#3175	C₂	semidirect
12. C₇×#3169	C₂	semidirect
13. C₇×#3118	C₂	semidirect
14. C₇×#3115	C₂	semidirect
15. C₇×#2966	C₂	semidirect
16. C₇×#2948	C₂	semidirect
17. C₄×C₇×#135	C₂	semidirect
20. C₇×#559	C₂²	semidirect
22. C₇×#555	C₂²	semidirect
24. C₇×D₄×Q₈	C₂²	semidirect
27. C₇×#546	C₂²	semidirect
29. C₇×#542	C₂²	semidirect
31. C₇×#532	C₂²	semidirect
35. C₇×#518	C₂²	semidirect
36. C₄×C₇×#41	C₂²	semidirect
37. C₇×#500	C₂²	semidirect
38. C₇×#500	C₂²	semidirect
39. C₇×#495	C₂²	semidirect
41. C₇×#489	C₂²	semidirect
42. C₇×#486	C₂²	semidirect
43. C₇×#485	C₂²	semidirect
44. C₇×#482	C₂²	semidirect
45. C₇×#482	C₂²	semidirect
46. C₇×#476	C₂²	semidirect
47. C₇×#475	C₂²	semidirect
48. C₇×#474	C₂²	semidirect
49. C₇×#474	C₂²	semidirect
50. C₇×#468	C₂²	semidirect
51. C₇×#467	C₂²	semidirect
53. C₇×#466	C₂²	semidirect
54. C₇×#466	C₂²	semidirect
55. C₇×#463	C₂²	semidirect
56. C₇×#463	C₂²	semidirect
57. C₇×#460	C₂²	semidirect
59. C₇×#450	C₂²	semidirect
60. C₇×#449	C₂²	semidirect
62. C₇×#446	C₂²	semidirect
63. C₇×C₈×Q₈	C₂²	semidirect
64. C₇×#442	C₂²	semidirect
65. C₇×#442	C₂²	semidirect
66. C₇×#440	C₂²	semidirect
67. C₄×C₇×Q₁₆	C₂²	semidirect
68. C₄×C₇×Q₁₆	C₂²	semidirect
69. C₄×C₇×SD₁₆	C₂²	semidirect
70. C₄×C₇×SD₁₆	C₂²	semidirect
74. C₄×C₇×D₈	C₂²	semidirect
75. C₄×C₇×D₈	C₂²	semidirect
76. C₄×C₇×D₈	C₂²	semidirect
78. C₇×#435	C₂²	semidirect
80. C₇×C₈×D₄	C₂²	semidirect
81. C₇×#433	C₂²	semidirect
82. C₇×#432	C₂²	semidirect
83. C₇×#427	C₂²	semidirect
84. C₇×#427	C₂²	semidirect
85. C₇×#418	C₂²	semidirect
86. C₇×#416	C₂²	semidirect
87. C₇×#405	C₂²	semidirect
88. C₂×C₄×C₇×C₈	C₂²	semidirect
89. #61475	C₇	direct (N × H)
199. #3514	C₂×C₇	semidirect
200. #3396	C₂×C₇	semidirect
201. Q₈×D₈	C₂×C₇	semidirect
202. #3373	C₂×C₇	semidirect
203. #3342	C₂×C₇	semidirect
204. #3341	C₂×C₇	semidirect
205. #3324	C₂×C₇	semidirect
206. #3319	C₂×C₇	semidirect
207. #3280	C₂×C₇	semidirect
208. D₄×D₈	C₂×C₇	semidirect
209. #3175	C₂×C₇	semidirect
210. #3169	C₂×C₇	semidirect
211. #3118	C₂×C₇	semidirect
212. #3115	C₂×C₇	semidirect
213. #2966	C₂×C₇	semidirect
214. #2948	C₂×C₇	semidirect
215. C₄×#135	C₂×C₇	semidirect
254. C₇×D₈	#41	semidirect
307. #559	C₂²×C₇	semidirect
309. #555	C₂²×C₇	semidirect
311. D₄×Q₈	C₂²×C₇	semidirect
314. #546	C₂²×C₇	semidirect
316. #542	C₂²×C₇	semidirect
318. #532	C₂²×C₇	semidirect
322. #518	C₂²×C₇	semidirect
323. C₄×#41	C₂²×C₇	semidirect
324. #500	C₂²×C₇	semidirect
325. #500	C₂²×C₇	semidirect
326. #495	C₂²×C₇	semidirect
328. #489	C₂²×C₇	semidirect
329. #486	C₂²×C₇	semidirect
330. #485	C₂²×C₇	semidirect
331. #482	C₂²×C₇	semidirect
332. #482	C₂²×C₇	semidirect
333. #476	C₂²×C₇	semidirect
334. #475	C₂²×C₇	semidirect
335. #474	C₂²×C₇	semidirect
336. #474	C₂²×C₇	semidirect
337. #468	C₂²×C₇	semidirect
338. #467	C₂²×C₇	semidirect
340. #466	C₂²×C₇	semidirect
341. #466	C₂²×C₇	semidirect
342. #463	C₂²×C₇	semidirect
343. #463	C₂²×C₇	semidirect
344. #460	C₂²×C₇	semidirect
346. #450	C₂²×C₇	semidirect
347. #449	C₂²×C₇	semidirect
349. #446	C₂²×C₇	semidirect
350. C₈×Q₈	C₂²×C₇	semidirect
351. #442	C₂²×C₇	semidirect
352. #442	C₂²×C₇	semidirect
353. #440	C₂²×C₇	semidirect
354. C₄×Q₁₆	C₂²×C₇	semidirect
355. C₄×Q₁₆	C₂²×C₇	semidirect
356. C₄×SD₁₆	C₂²×C₇	semidirect
357. C₄×SD₁₆	C₂²×C₇	semidirect
361. C₄×D₈	C₂²×C₇	semidirect
362. C₄×D₈	C₂²×C₇	semidirect
363. C₄×D₈	C₂²×C₇	semidirect
365. #435	C₂²×C₇	semidirect
367. C₈×D₄	C₂²×C₇	semidirect
368. #433	C₂²×C₇	semidirect
369. #432	C₂²×C₇	semidirect
370. #427	C₂²×C₇	semidirect
371. #427	C₂²×C₇	semidirect
372. #418	C₂²×C₇	semidirect
373. #416	C₂²×C₇	semidirect
374. #405	C₂²×C₇	semidirect
375. C₂×C₄×C₈	C₂²×C₇	semidirect
606. D₈	C₇×#41	semidirect
719. C₇	#61475	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×#3514	2
C₇×#3396	2
C₇×Q₈×D₈	2
C₇×#3373	2
C₇×#3342	2
C₇×#3341	2
C₇×#3324	2
C₇×#3319	2
C₇×#3280	2
C₇×D₄×D₈	2
C₇×#3175	2
C₇×#3169	2
C₇×#3118	2
C₇×#3115	2
C₇×#2966	2
C₇×#2948	2
C₄×C₇×#135	2
#61475	7

Subgroups — C7×#61475 #13238691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61475 #13238691