Subgroups — C₇×#36829 #13214045

Order 1792.

1462 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2855	C₂	1	2	yes	maximal
2	C₇×#2806	C₂	1	2	yes	maximal, complemented
3	C₇×#2802	C₂	1	2	yes	maximal, complemented
4	C₇×#2776	C₂	1	2	yes	maximal, complemented
5	C₇×#2774	C₂	1	2	yes	maximal, complemented
6	C₇×#2745	C₂	1	2	yes	maximal
7	C₇×#2738	C₂	1	2	yes	maximal
8	C₇×#2698	C₂	1	2	yes	maximal
9	C₇×#2689	C₂	1	2	yes	maximal
10	C₇×#2655	C₂	1	2	yes	maximal, complemented
11	C₇×#2611	C₂	1	1	yes	maximal, characteristic
12	C₇×#2605	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2599	C₂	1	1	yes	maximal, characteristic
14	C₇×#2588	C₂	1	2	yes	maximal, complemented
15	C₇×#2584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2478	C₂	1	2	yes	maximal
17	C₇×#2336	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2320	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2296	C₂	1	1	yes	maximal, characteristic
20	C₂×C₇×#126	C₂²	1	2	yes	—
21	C₂×C₇×#125	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#117	C₂²	1	1	yes	characteristic
25	C₂×C₇×#117	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
27	C₇×#401	C₂²	1	2	yes	—
28	C₇×#400	C₂²	1	2	yes	—
29	C₇×#400	C₂²	1	2	yes	—
30	C₇×#400	C₂²	1	2	yes	—
31	C₇×#400	C₂²	1	2	yes	—
32	C₇×#400	C₂²	1	2	yes	—
33	C₇×#400	C₂²	1	2	yes	—
34	C₇×#400	C₂²	1	2	yes	—
35	C₇×#400	C₂²	1	1	yes	characteristic
36	C₇×#399	C₂²	1	1	yes	characteristic
37	C₇×#398	C₂²	1	2	yes	—
38	C₇×#398	C₂²	1	2	yes	—
39	C₇×#398	C₂²	1	2	yes	—
40	C₇×#398	C₂²	1	2	yes	—
41	C₇×#398	C₂²	1	2	yes	—
42	C₇×#398	C₂²	1	2	yes	—
43	C₇×#398	C₂²	1	2	yes	—
44	C₇×#398	C₂²	1	1	yes	characteristic
45	C₇×#398	C₂²	1	1	yes	characteristic
46	C₇×#397	C₂²	1	1	yes	characteristic
47	C₇×#397	C₂²	1	2	yes	—
48	C₇×#397	C₂²	1	1	yes	characteristic
49	C₇×#397	C₂²	1	2	yes	—
50	C₇×#395	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	—
52	C₇×#395	C₂²	1	2	yes	—
53	C₇×#395	C₂²	1	1	yes	characteristic
54	C₇×#393	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	2	yes	—
58	C₇×#391	C₂²	1	2	yes	—
59	C₇×#391	C₂²	1	2	yes	—
60	C₇×#389	C₂²	1	2	yes	—
61	C₇×#389	C₂²	1	2	yes	—
62	C₇×#389	C₂²	1	2	yes	—
63	C₇×#389	C₂²	1	2	yes	—
64	C₇×#389	C₂²	1	2	yes	—
65	C₇×#389	C₂²	1	2	yes	—
66	C₇×#389	C₂²	1	2	yes	—
67	C₇×#389	C₂²	1	2	yes	—
68	C₇×#389	C₂²	1	2	yes	—
69	C₇×#389	C₂²	1	2	yes	—
70	C₇×#389	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#387	C₂²	1	2	yes	—
90	C₇×#387	C₂²	1	2	yes	—
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#383	C₂²	1	2	yes	—
96	C₇×#383	C₂²	1	1	yes	characteristic
97	C₇×#382	C₂²	1	2	yes	—
98	C₇×#381	C₂²	1	2	yes	—
99	C₇×#381	C₂²	1	2	yes	—
100	C₇×#380	C₂²	1	2	yes	—
101	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
103	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₇×#376	C₂²	1	1	yes	characteristic
107	#36829	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	2	yes	—
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇	C₂³	1	2	yes	—
112	C₇×#126	—	4	4	no	—
113	C₇×#125	—	2	4	no	—
114	C₇×C₂²⋊Q₈	—	4	4	no	—
115	C₄×C₇×Q₈	—	2	4	no	—
116	C₇×#117	—	2	4	no	—
117	C₇×#117	—	4	2	no	—
118	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
121	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
123	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
124	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
125	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
130	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₄²×C₇	—	4	2	no	—
154	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
155	C₂×C₄²×C₇	C₂³	1	2	yes	—
156	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₇×#95	C₂³	1	1	yes	characteristic
166	C₇×#95	C₂³	1	1	yes	characteristic
167	C₇×#95	C₂³	1	2	yes	—
168	C₇×#95	C₂³	1	2	yes	—
169	C₇×#95	C₂³	1	2	yes	—
170	C₇×#95	C₂³	1	2	yes	—
171	C₇×#95	C₂³	1	2	yes	—
172	C₇×#95	C₂³	1	2	yes	—
173	C₇×#95	C₂³	1	2	yes	—
174	C₇×#95	C₂³	1	2	yes	—
175	C₇×#95	C₂³	1	2	yes	—
176	C₇×#95	C₂³	1	2	yes	—
177	C₇×#95	C₂³	1	2	yes	—
178	C₇×#95	C₂³	1	2	yes	—
179	C₇×#95	C₂³	1	2	yes	—
180	C₇×#95	C₂³	1	2	yes	—
181	C₇×#95	C₂³	1	2	yes	—
182	C₇×#95	C₂³	1	2	yes	—
183	C₇×#95	C₂³	1	2	yes	—
184	C₇×#95	C₂³	1	2	yes	—
185	C₇×#95	C₂³	1	1	yes	characteristic
186	C₇×#95	C₂³	1	2	yes	—
187	C₇×#95	C₂³	1	2	yes	—
188	C₇×#95	C₂³	1	2	yes	—
189	C₇×#95	C₂³	1	1	yes	characteristic
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	#2855	C₂×C₇	1	2	yes	—
203	#2806	C₂×C₇	1	2	yes	complemented
204	#2802	C₂×C₇	1	2	yes	complemented
205	#2776	C₂×C₇	1	2	yes	complemented
206	#2774	C₂×C₇	1	2	yes	complemented
207	#2745	C₂×C₇	1	2	yes	—
208	#2738	C₂×C₇	1	2	yes	—
209	#2698	C₂×C₇	1	2	yes	—
210	#2689	C₂×C₇	1	2	yes	—
211	#2655	C₂×C₇	1	2	yes	complemented
212	#2611	C₂×C₇	1	1	yes	characteristic
213	#2605	C₂×C₇	1	1	yes	characteristic, complemented
214	#2599	C₂×C₇	1	1	yes	characteristic
215	#2588	C₂×C₇	1	2	yes	complemented
216	#2584	C₂×C₇	1	1	yes	characteristic, complemented
217	#2478	C₂×C₇	1	2	yes	—
218	#2336	C₂×C₇	1	1	yes	characteristic, complemented
219	#2320	C₂×C₇	1	1	yes	characteristic, complemented
220	#2296	C₂×C₇	1	1	yes	characteristic
221	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
222	C₂×C₇×Q₈	—	2	2	no	—
223	C₂×C₇×Q₈	—	2	4	no	—
224	C₂×C₇×Q₈	—	4	2	no	—
225	C₂×C₇×Q₈	—	4	2	no	—
226	C₂×C₇×Q₈	—	4	2	no	—
227	C₂²×C₄×C₇	—	2	2	no	—
228	C₂²×C₄×C₇	—	2	2	no	—
229	C₂²×C₄×C₇	—	2	2	no	—
230	C₂²×C₄×C₇	—	2	4	no	—
231	C₂²×C₄×C₇	—	2	4	no	—
232	C₂²×C₄×C₇	—	4	2	no	—
233	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
234	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂⁴	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	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	4	no	—
255	C₇×C₄⋊C₄	—	2	2	no	—
256	C₇×C₄⋊C₄	—	2	2	no	—
257	C₇×C₄⋊C₄	—	2	4	no	—
258	C₇×C₄⋊C₄	—	2	4	no	—
259	C₇×C₄⋊C₄	—	2	4	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	—	4	2	no	—
265	C₇×C₄⋊C₄	—	4	2	no	—
266	C₇×C₄⋊C₄	—	4	2	no	—
267	C₇×C₄⋊C₄	—	4	2	no	—
268	C₇×C₄⋊C₄	—	4	2	no	—
269	C₇×C₄⋊C₄	—	4	2	no	—
270	C₇×C₄⋊C₄	—	4	2	no	—
271	C₇×C₄⋊C₄	—	4	2	no	—
272	C₇×C₄⋊C₄	—	4	2	no	—
273	C₇×C₄⋊C₄	—	4	2	no	—
274	C₇×C₄⋊C₄	—	4	2	no	—
275	C₇×C₄⋊C₄	—	4	2	no	—
276	C₇×C₄⋊C₄	—	4	2	no	—
277	C₇×C₄⋊C₄	—	4	2	no	—
278	C₇×C₄⋊C₄	—	4	2	no	—
279	C₇×C₂²⋊C₄	—	2	4	no	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	2	no	—
283	C₇×C₂²⋊C₄	—	2	2	no	—
284	C₇×C₂²⋊C₄	—	4	2	no	—
285	C₇×C₂²⋊C₄	—	4	2	no	—
286	C₄²×C₇	—	2	2	no	—
287	C₄²×C₇	—	2	4	no	—
288	C₄²×C₇	—	4	1	no	—
289	C₄²×C₇	—	4	1	no	—
290	C₄²×C₇	—	4	2	no	—
291	C₄²×C₇	—	4	2	no	—
292	C₄²×C₇	—	4	2	no	—
293	C₄²×C₇	—	4	1	no	—
294	C₄²×C₇	—	4	1	no	—
295	C₄²×C₇	—	4	2	no	—
296	C₄²×C₇	#41	1	4	yes	—
297	C₂×#126	C₂²×C₇	1	2	yes	—
298	C₂×#125	C₂²×C₇	1	1	yes	characteristic
299	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
300	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
301	C₂×#117	C₂²×C₇	1	1	yes	characteristic
302	C₂×#117	C₂²×C₇	1	1	yes	characteristic
303	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
304	#401	C₂²×C₇	1	2	yes	—
305	#400	C₂²×C₇	1	2	yes	—
306	#400	C₂²×C₇	1	2	yes	—
307	#400	C₂²×C₇	1	2	yes	—
308	#400	C₂²×C₇	1	1	yes	characteristic
309	#400	C₂²×C₇	1	2	yes	—
310	#400	C₂²×C₇	1	2	yes	—
311	#400	C₂²×C₇	1	2	yes	—
312	#400	C₂²×C₇	1	2	yes	—
313	#399	C₂²×C₇	1	1	yes	characteristic
314	#398	C₂²×C₇	1	2	yes	—
315	#398	C₂²×C₇	1	2	yes	—
316	#398	C₂²×C₇	1	1	yes	characteristic
317	#398	C₂²×C₇	1	1	yes	characteristic
318	#398	C₂²×C₇	1	2	yes	—
319	#398	C₂²×C₇	1	2	yes	—
320	#398	C₂²×C₇	1	2	yes	—
321	#398	C₂²×C₇	1	2	yes	—
322	#398	C₂²×C₇	1	2	yes	—
323	#397	C₂²×C₇	1	1	yes	characteristic
324	#397	C₂²×C₇	1	1	yes	characteristic
325	#397	C₂²×C₇	1	2	yes	—
326	#397	C₂²×C₇	1	2	yes	—
327	#395	C₂²×C₇	1	2	yes	—
328	#395	C₂²×C₇	1	2	yes	—
329	#395	C₂²×C₇	1	1	yes	characteristic
330	#395	C₂²×C₇	1	2	yes	—
331	#393	C₂²×C₇	1	1	yes	characteristic
332	#391	C₂²×C₇	1	2	yes	—
333	#391	C₂²×C₇	1	2	yes	—
334	#391	C₂²×C₇	1	2	yes	—
335	#391	C₂²×C₇	1	2	yes	—
336	#391	C₂²×C₇	1	2	yes	—
337	#389	C₂²×C₇	1	2	yes	—
338	#389	C₂²×C₇	1	2	yes	—
339	#389	C₂²×C₇	1	2	yes	—
340	#389	C₂²×C₇	1	2	yes	—
341	#389	C₂²×C₇	1	2	yes	—
342	#389	C₂²×C₇	1	2	yes	—
343	#389	C₂²×C₇	1	2	yes	—
344	#389	C₂²×C₇	1	2	yes	—
345	#389	C₂²×C₇	1	2	yes	—
346	#389	C₂²×C₇	1	2	yes	—
347	#389	C₂²×C₇	1	2	yes	—
348	#388	C₂²×C₇	1	2	yes	—
349	#388	C₂²×C₇	1	2	yes	—
350	#388	C₂²×C₇	1	2	yes	—
351	#387	C₂²×C₇	1	2	yes	—
352	#387	C₂²×C₇	1	2	yes	—
353	#387	C₂²×C₇	1	2	yes	—
354	#387	C₂²×C₇	1	2	yes	—
355	#387	C₂²×C₇	1	2	yes	—
356	#387	C₂²×C₇	1	2	yes	—
357	#387	C₂²×C₇	1	2	yes	—
358	#387	C₂²×C₇	1	2	yes	—
359	#387	C₂²×C₇	1	2	yes	—
360	#387	C₂²×C₇	1	2	yes	—
361	#387	C₂²×C₇	1	2	yes	—
362	#387	C₂²×C₇	1	2	yes	—
363	#387	C₂²×C₇	1	2	yes	—
364	#387	C₂²×C₇	1	2	yes	—
365	#387	C₂²×C₇	1	2	yes	—
366	#387	C₂²×C₇	1	2	yes	—
367	#387	C₂²×C₇	1	2	yes	—
368	#385	C₂²×C₇	1	2	yes	—
369	#385	C₂²×C₇	1	2	yes	—
370	#385	C₂²×C₇	1	2	yes	—
371	#385	C₂²×C₇	1	2	yes	—
372	#383	C₂²×C₇	1	2	yes	—
373	#383	C₂²×C₇	1	1	yes	characteristic
374	#382	C₂²×C₇	1	2	yes	—
375	#381	C₂²×C₇	1	2	yes	—
376	#381	C₂²×C₇	1	2	yes	—
377	#380	C₂²×C₇	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
381	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
382	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
383	#376	C₂²×C₇	1	1	yes	characteristic
384	C₂³×C₇	—	2	1	no	—
385	C₂³×C₇	—	2	1	no	—
386	C₂³×C₇	—	2	2	no	—
387	C₂³×C₇	—	2	2	no	—
388	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
389	C₂³×C₇	C₂⁵	1	1	yes	characteristic
390	C₇×Q₈	—	4	4	no	—
391	C₇×Q₈	—	8	4	no	—
392	C₂×C₄×C₇	—	2	8	no	—
393	C₂×C₄×C₇	—	2	1	no	—
394	C₂×C₄×C₇	—	2	1	no	—
395	C₂×C₄×C₇	—	2	1	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	1	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	1	no	—
402	C₂×C₄×C₇	—	2	1	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	2	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	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	2	no	—
418	C₂×C₄×C₇	—	2	2	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	4	8	no	—
439	C₂×C₄×C₇	C₂×#41	1	2	yes	—
440	C₂×C₄×C₇	C₂×#41	1	2	yes	—
441	C₂×C₄×C₇	C₂×#41	1	2	yes	—
442	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
443	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
444	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₇	1	2	yes	—
446	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₇	1	2	yes	—
448	#126	—	4	4	no	—
449	#125	—	2	4	no	—
450	C₂²⋊Q₈	—	4	4	no	—
451	C₄×Q₈	—	2	4	no	—
452	#117	—	2	4	no	—
453	#117	—	4	2	no	—
454	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
463	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
464	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
465	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
466	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
469	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
471	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
472	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
473	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
474	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
479	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
480	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
481	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
488	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
489	C₂×C₄²	—	4	2	no	—
490	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
491	C₂×C₄²	C₂³×C₇	1	2	yes	—
492	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
494	C₂×C₄²	C₂³×C₇	1	2	yes	—
495	C₂×C₄²	C₂³×C₇	1	2	yes	—
496	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
497	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
498	C₂×C₄²	C₂³×C₇	1	2	yes	—
499	C₂×C₄²	C₂³×C₇	1	2	yes	—
500	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
501	#95	C₂³×C₇	1	1	yes	characteristic
502	#95	C₂³×C₇	1	1	yes	characteristic
503	#95	C₂³×C₇	1	2	yes	—
504	#95	C₂³×C₇	1	2	yes	—
505	#95	C₂³×C₇	1	2	yes	—
506	#95	C₂³×C₇	1	2	yes	—
507	#95	C₂³×C₇	1	2	yes	—
508	#95	C₂³×C₇	1	2	yes	—
509	#95	C₂³×C₇	1	2	yes	—
510	#95	C₂³×C₇	1	2	yes	—
511	#95	C₂³×C₇	1	2	yes	—
512	#95	C₂³×C₇	1	2	yes	—
513	#95	C₂³×C₇	1	2	yes	—
514	#95	C₂³×C₇	1	2	yes	—
515	#95	C₂³×C₇	1	2	yes	—
516	#95	C₂³×C₇	1	2	yes	—
517	#95	C₂³×C₇	1	2	yes	—
518	#95	C₂³×C₇	1	2	yes	—
519	#95	C₂³×C₇	1	2	yes	—
520	#95	C₂³×C₇	1	2	yes	—
521	#95	C₂³×C₇	1	1	yes	characteristic
522	#95	C₂³×C₇	1	2	yes	—
523	#95	C₂³×C₇	1	2	yes	—
524	#95	C₂³×C₇	1	2	yes	—
525	#95	C₂³×C₇	1	1	yes	characteristic
526	#95	C₂³×C₇	1	2	yes	—
527	#95	C₂³×C₇	1	2	yes	—
528	#95	C₂³×C₇	1	2	yes	—
529	#95	C₂³×C₇	1	2	yes	—
530	#95	C₂³×C₇	1	2	yes	—
531	#95	C₂³×C₇	1	2	yes	—
532	#95	C₂³×C₇	1	2	yes	—
533	#95	C₂³×C₇	1	2	yes	—
534	#95	C₂³×C₇	1	2	yes	—
535	#95	C₂³×C₇	1	2	yes	—
536	#95	C₂³×C₇	1	2	yes	—
537	#95	C₂³×C₇	1	2	yes	—
538	C₂²×C₇	—	2	2	no	—
539	C₂²×C₇	—	2	4	no	—
540	C₂²×C₇	—	4	1	no	—
541	C₂²×C₇	—	4	1	no	—
542	C₂²×C₇	—	4	2	no	—
543	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
544	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
545	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
546	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
547	C₂²×C₇	#585	1	2	yes	—
548	C₄×C₇	—	2	2	no	—
549	C₄×C₇	—	2	2	no	—
550	C₄×C₇	—	2	2	no	—
551	C₄×C₇	—	2	2	no	—
552	C₄×C₇	—	2	4	no	—
553	C₄×C₇	—	4	1	no	—
554	C₄×C₇	—	4	2	no	—
555	C₄×C₇	—	4	2	no	—
556	C₄×C₇	—	4	2	no	—
557	C₄×C₇	—	4	2	no	—
558	C₄×C₇	—	4	1	no	—
559	C₄×C₇	—	4	2	no	—
560	C₄×C₇	—	4	2	no	—
561	C₄×C₇	—	4	2	no	—
562	C₄×C₇	—	4	2	no	—
563	C₄×C₇	—	4	2	no	—
564	C₄×C₇	—	4	2	no	—
565	C₄×C₇	—	4	2	no	—
566	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	4	no	—
569	C₂×Q₈	—	4	2	no	—
570	C₂×Q₈	—	4	2	no	—
571	C₂×Q₈	—	4	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	4	no	—
577	C₂²×C₄	—	4	2	no	—
578	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
581	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
586	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
590	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
592	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
593	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
594	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
595	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	4	2	no	—
610	C₄⋊C₄	—	4	2	no	—
611	C₄⋊C₄	—	4	2	no	—
612	C₄⋊C₄	—	4	2	no	—
613	C₄⋊C₄	—	4	2	no	—
614	C₄⋊C₄	—	4	2	no	—
615	C₄⋊C₄	—	4	2	no	—
616	C₄⋊C₄	—	4	2	no	—
617	C₄⋊C₄	—	4	2	no	—
618	C₄⋊C₄	—	4	2	no	—
619	C₄⋊C₄	—	4	2	no	—
620	C₄⋊C₄	—	4	2	no	—
621	C₄⋊C₄	—	4	2	no	—
622	C₄⋊C₄	—	4	2	no	—
623	C₄⋊C₄	—	4	2	no	—
624	C₂²⋊C₄	—	2	4	no	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	4	2	no	—
630	C₂²⋊C₄	—	4	2	no	—
631	C₄²	—	2	2	no	—
632	C₄²	—	2	4	no	—
633	C₄²	—	4	1	no	—
634	C₄²	—	4	1	no	—
635	C₄²	—	4	2	no	—
636	C₄²	—	4	1	no	—
637	C₄²	—	4	1	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	2	no	—
640	C₄²	—	4	2	no	—
641	C₄²	C₇×#41	1	4	yes	—
642	C₂×C₇	—	4	2	no	—
643	C₂×C₇	#3455	1	1	yes	characteristic
644	C₂×C₇	#3492	1	1	yes	characteristic
645	C₂×C₇	#3509	1	1	yes	characteristic
646	C₂×C₇	#3535	1	2	yes	—
647	C₂×C₇	#3555	1	2	yes	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	2	no	—
651	C₂³	—	2	2	no	—
652	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
653	C₂³	C₂⁵×C₇	1	1	yes	characteristic
654	Q₈	—	4	4	no	—
655	Q₈	—	8	4	no	—
656	C₂×C₄	—	2	8	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	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	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	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	C₂×C₇×#41	1	2	yes	—
704	C₂×C₄	C₂×C₇×#41	1	2	yes	—
705	C₂×C₄	C₂×C₇×#41	1	2	yes	—
706	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
707	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
708	C₇	#36829	1	1	yes	characteristic, direct product factor, Sylow
709	C₂²	—	2	2	no	—
710	C₂²	—	2	4	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	4	2	no	—
714	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
715	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
717	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
718	C₂²	C₇×#585	1	2	yes	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	4	no	—
724	C₄	—	4	2	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	2	no	—
731	C₄	—	4	2	no	—
732	C₄	—	4	2	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₂	—	4	2	no	—
738	C₂	C₇×#3455	1	1	yes	characteristic
739	C₂	C₇×#3492	1	1	yes	characteristic
740	C₂	C₇×#3509	1	1	yes	characteristic
741	C₂	C₇×#3535	1	2	yes	—
742	C₂	C₇×#3555	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁴×C₇	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2806	C₂	semidirect
3. C₇×#2802	C₂	semidirect
4. C₇×#2776	C₂	semidirect
5. C₇×#2774	C₂	semidirect
10. C₇×#2655	C₂	semidirect
12. C₇×#2605	C₂	semidirect
14. C₇×#2588	C₂	semidirect
15. C₇×#2584	C₂	semidirect
17. C₇×#2336	C₂	semidirect
18. C₇×#2320	C₂	semidirect
107. #36829	C₇	direct (N × H)
203. #2806	C₂×C₇	semidirect
204. #2802	C₂×C₇	semidirect
205. #2776	C₂×C₇	semidirect
206. #2774	C₂×C₇	semidirect
211. #2655	C₂×C₇	semidirect
213. #2605	C₂×C₇	semidirect
215. #2588	C₂×C₇	semidirect
216. #2584	C₂×C₇	semidirect
218. #2336	C₂×C₇	semidirect
219. #2320	C₂×C₇	semidirect
708. C₇	#36829	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×#2855	2
C₇×#2806	2
C₇×#2802	2
C₇×#2776	2
C₇×#2774	2
C₇×#2745	2
C₇×#2738	2
C₇×#2698	2
C₇×#2689	2
C₇×#2655	2
C₇×#2611	2
C₇×#2605	2
C₇×#2599	2
C₇×#2588	2
C₇×#2584	2
C₇×#2478	2
C₇×#2336	2
C₇×#2320	2
C₇×#2296	2
#36829	7

Subgroups — C7×#36829 #13214045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36829 #13214045