Subgroups — C₇×#22885 #13200101

Order 1792.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#448	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2363	C₂	1	1	yes	maximal, characteristic
5	C₇×Q₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1933	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1895	C₂	1	1	yes	maximal, characteristic
10	C₇×#1880	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1753	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₇×#121	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₇×#117	C₂²	1	1	yes	characteristic
25	C₇×#448	C₄	1	8	yes	complemented
26	C₄×C₇×SD₁₆	—	2	4	no	—
27	C₂×C₇×#107	C₂²	1	1	yes	characteristic
28	C₂×C₇×#106	C₂²	1	1	yes	characteristic
29	C₇×#419	—	2	4	no	—
30	C₂×C₇×#103	C₂²	1	1	yes	characteristic
31	C₂×C₇×#103	C₂²	1	1	yes	characteristic
32	C₂×C₇×#103	C₂²	1	1	yes	characteristic
33	C₂×C₇×#103	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	1	yes	characteristic
36	C₂×C₇×#102	C₂²	1	1	yes	characteristic
37	C₂×C₇×#102	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₇×#391	—	2	1	no	—
42	C₇×#391	—	2	1	no	—
43	C₇×#391	C₂²	1	1	yes	characteristic
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#390	—	2	1	no	—
46	C₇×#390	C₂²	1	1	yes	characteristic
47	C₇×#389	C₂²	1	1	yes	characteristic
48	C₇×#388	—	2	1	no	—
49	C₇×#386	—	2	1	no	—
50	C₇×#380	—	2	1	no	—
51	C₇×#380	C₂²	1	1	yes	characteristic
52	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
53	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
54	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
55	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
56	C₇×#340	C₂²	1	1	yes	characteristic
57	C₇×#340	C₂²	1	1	yes	characteristic
58	C₇×#340	C₂²	1	1	yes	characteristic
59	C₇×#340	C₂²	1	1	yes	characteristic
60	C₇×#336	C₂²	1	1	yes	characteristic
61	C₇×#336	C₂²	1	1	yes	characteristic
62	#22885	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂²×C₇×Q₈	—	2	1	no	—
64	C₂²×C₇×Q₈	—	2	2	no	—
65	C₂²×C₇×Q₈	—	2	2	no	—
66	C₂²×C₇×Q₈	—	2	2	no	—
67	C₂²×C₇×Q₈	—	4	1	no	—
68	C₂²×C₇×Q₈	—	4	1	no	—
69	C₂²×C₇×Q₈	C₂×C₄	1	4	yes	complemented
70	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×D₄	—	2	1	no	—
73	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₇	—	2	1	no	—
75	C₂³×C₄×C₇	—	2	1	no	—
76	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₇×SD₁₆	—	2	2	no	—
78	C₂×C₇×SD₁₆	—	2	2	no	—
79	C₂×C₇×SD₁₆	—	4	1	no	—
80	C₂×C₇×SD₁₆	—	4	1	no	—
81	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
82	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
83	C₂×C₇×M₁₆	—	2	2	no	—
84	C₂×C₇×M₁₆	—	2	2	no	—
85	C₂×C₇×M₁₆	—	4	1	no	—
86	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₇×#121	—	2	2	no	—
91	C₇×#121	C₂×C₄	1	4	yes	—
92	C₄×C₇×Q₈	—	2	2	no	—
93	C₄×C₇×Q₈	—	2	2	no	—
94	C₄×C₇×Q₈	—	4	1	no	—
95	C₄×C₇×Q₈	—	4	1	no	—
96	C₄×C₇×D₄	—	2	2	no	—
97	C₄×C₇×D₄	—	4	1	no	—
98	C₇×#117	—	2	2	no	—
99	C₇×#117	—	4	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	1	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	—	2	1	no	—
103	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
109	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
114	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
115	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₇	—	2	1	no	—
117	C₂×C₄²×C₇	—	2	1	no	—
118	C₂×C₄²×C₇	—	2	1	no	—
119	C₂×C₄²×C₇	—	2	1	no	—
120	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
122	C₇×#107	—	4	1	no	—
123	C₇×#106	—	2	2	no	—
124	C₇×#103	—	2	2	no	—
125	C₇×#103	—	2	2	no	—
126	C₇×#103	—	2	2	no	—
127	C₇×#103	C₂×C₄	1	4	yes	complemented
128	C₇×#103	C₂×C₄	1	4	yes	complemented
129	C₇×#103	D₄	1	4	yes	complemented
130	C₇×#102	—	2	2	no	—
131	C₇×#102	—	4	1	no	—
132	C₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
133	C₇×#97	—	4	1	no	—
134	C₄×C₇×C₈	—	2	2	no	—
135	C₇×#95	—	2	1	no	—
136	C₇×#95	—	2	1	no	—
137	C₇×#95	—	2	1	no	—
138	C₇×#95	—	2	1	no	—
139	C₇×#95	—	2	1	no	—
140	C₇×#95	—	2	1	no	—
141	C₇×#95	—	2	1	no	—
142	C₇×#95	D₄	1	1	yes	characteristic
143	C₇×#95	D₄	1	1	yes	characteristic
144	C₂×#448	C₂×C₇	1	1	yes	characteristic
145	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
146	C₂×#419	C₂×C₇	1	1	yes	characteristic, complemented
147	#2363	C₂×C₇	1	1	yes	characteristic
148	Q₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
149	#1973	C₂×C₇	1	1	yes	characteristic, complemented
150	#1933	C₂×C₇	1	1	yes	characteristic, complemented
151	#1927	C₂×C₇	1	1	yes	characteristic, complemented
152	#1895	C₂×C₇	1	1	yes	characteristic
153	#1880	C₂×C₇	1	1	yes	characteristic, complemented
154	#1877	C₂×C₇	1	1	yes	characteristic, complemented
155	#1863	C₂×C₇	1	1	yes	characteristic, complemented
156	#1854	C₂×C₇	1	1	yes	characteristic, complemented
157	#1763	C₂×C₇	1	1	yes	characteristic, complemented
158	#1753	C₂×C₇	1	1	yes	characteristic, complemented
159	C₂⁴×C₇	—	2	1	no	—
160	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
161	C₂×C₇×Q₈	—	2	4	no	—
162	C₂×C₇×Q₈	—	2	1	no	—
163	C₂×C₇×Q₈	—	2	1	no	—
164	C₂×C₇×Q₈	—	2	1	no	—
165	C₂×C₇×Q₈	—	2	1	no	—
166	C₂×C₇×Q₈	—	2	8	no	—
167	C₂×C₇×Q₈	—	2	1	no	—
168	C₂×C₇×Q₈	—	2	1	no	—
169	C₂×C₇×Q₈	—	2	1	no	—
170	C₂×C₇×Q₈	—	2	1	no	—
171	C₂×C₇×Q₈	—	4	2	no	—
172	C₂×C₇×Q₈	—	4	2	no	—
173	C₂×C₇×Q₈	—	4	4	no	—
174	C₂×C₇×Q₈	—	4	4	no	—
175	C₂×C₇×Q₈	—	4	4	no	—
176	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
177	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
178	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
179	C₂×C₇×Q₈	#41	1	2	yes	—
180	C₂×C₇×D₄	—	2	4	no	—
181	C₂×C₇×D₄	—	2	1	no	—
182	C₂×C₇×D₄	—	2	1	no	—
183	C₂×C₇×D₄	—	2	1	no	—
184	C₂×C₇×D₄	—	2	1	no	—
185	C₂×C₇×D₄	—	2	1	no	—
186	C₂×C₇×D₄	—	8	1	no	—
187	C₂×C₇×D₄	—	8	1	no	—
188	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₇	—	2	1	no	—
190	C₂²×C₄×C₇	—	2	1	no	—
191	C₂²×C₄×C₇	—	2	1	no	—
192	C₂²×C₄×C₇	—	2	1	no	—
193	C₂²×C₄×C₇	—	2	1	no	—
194	C₂²×C₄×C₇	—	2	4	no	—
195	C₂²×C₄×C₇	—	2	1	no	—
196	C₂²×C₄×C₇	—	2	1	no	—
197	C₂²×C₄×C₇	—	2	1	no	—
198	C₂²×C₄×C₇	—	2	1	no	—
199	C₂²×C₄×C₇	—	2	1	no	—
200	C₂²×C₄×C₇	—	2	1	no	—
201	C₂²×C₄×C₇	—	4	2	no	—
202	C₂²×C₄×C₇	—	4	2	no	—
203	C₂²×C₄×C₇	—	4	2	no	—
204	C₂²×C₄×C₇	—	4	2	no	—
205	C₂²×C₄×C₇	—	8	1	no	—
206	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
207	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₇	#41	1	2	yes	—
213	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
214	C₇×SD₁₆	—	2	8	no	—
215	C₇×SD₁₆	—	4	4	no	—
216	C₇×M₁₆	—	4	4	no	—
217	C₂×C₇×C₈	—	2	1	no	—
218	C₂×C₇×C₈	—	2	1	no	—
219	C₂×C₇×C₈	—	2	1	no	—
220	C₂×C₇×C₈	—	2	1	no	—
221	C₂×C₇×C₈	—	2	1	no	—
222	C₂×C₇×C₈	—	2	1	no	—
223	C₂×C₇×C₈	—	2	1	no	—
224	C₂×C₇×C₈	—	2	1	no	—
225	C₂×C₇×C₈	—	2	1	no	—
226	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
227	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
228	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
229	C₇×C₄⋊C₄	—	2	1	no	—
230	C₇×C₄⋊C₄	—	2	1	no	—
231	C₇×C₄⋊C₄	—	2	1	no	—
232	C₇×C₄⋊C₄	—	2	1	no	—
233	C₇×C₄⋊C₄	—	2	1	no	—
234	C₇×C₄⋊C₄	—	2	1	no	—
235	C₇×C₄⋊C₄	—	2	1	no	—
236	C₇×C₄⋊C₄	—	2	1	no	—
237	C₇×C₄⋊C₄	—	4	2	no	—
238	C₇×C₄⋊C₄	—	4	2	no	—
239	C₇×C₄⋊C₄	—	8	1	no	—
240	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
241	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
242	C₇×C₂²⋊C₄	—	2	4	no	—
243	C₇×C₂²⋊C₄	—	2	2	no	—
244	C₇×C₂²⋊C₄	—	4	1	no	—
245	C₇×C₂²⋊C₄	—	4	2	no	—
246	C₇×C₂²⋊C₄	—	4	2	no	—
247	C₇×C₂²⋊C₄	—	4	2	no	—
248	C₇×C₂²⋊C₄	—	4	2	no	—
249	C₇×C₂²⋊C₄	—	8	1	no	—
250	C₄²×C₇	—	2	1	no	—
251	C₄²×C₇	—	2	1	no	—
252	C₄²×C₇	—	2	1	no	—
253	C₄²×C₇	—	2	1	no	—
254	C₄²×C₇	—	4	2	no	—
255	C₄²×C₇	—	4	2	no	—
256	C₄²×C₇	—	4	2	no	—
257	C₄²×C₇	—	8	1	no	—
258	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
259	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
260	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
262	C₂×#121	C₂²×C₇	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
264	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
266	C₂×#117	C₂²×C₇	1	1	yes	characteristic
267	#448	C₄×C₇	1	8	yes	complemented
268	C₄×SD₁₆	—	2	4	no	—
269	C₂×#107	C₂²×C₇	1	1	yes	characteristic
270	C₂×#106	C₂²×C₇	1	1	yes	characteristic
271	#419	—	2	4	no	—
272	C₂×#103	C₂²×C₇	1	1	yes	characteristic
273	C₂×#103	C₂²×C₇	1	1	yes	characteristic
274	C₂×#103	C₂²×C₇	1	1	yes	characteristic
275	C₂×#103	C₂²×C₇	1	1	yes	characteristic
276	C₂×#103	C₂²×C₇	1	1	yes	characteristic
277	C₂×#103	C₂²×C₇	1	1	yes	characteristic
278	C₂×#102	C₂²×C₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₇	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
281	C₂×#97	C₂²×C₇	1	1	yes	characteristic
282	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
283	#391	—	2	1	no	—
284	#391	—	2	1	no	—
285	#391	C₂²×C₇	1	1	yes	characteristic
286	#391	C₂²×C₇	1	1	yes	characteristic
287	#390	—	2	1	no	—
288	#390	C₂²×C₇	1	1	yes	characteristic
289	#389	C₂²×C₇	1	1	yes	characteristic
290	#388	—	2	1	no	—
291	#386	—	2	1	no	—
292	#380	—	2	1	no	—
293	#380	C₂²×C₇	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
295	C₄×C₂²⋊C₄	—	2	1	no	—
296	C₄×C₂²⋊C₄	—	2	1	no	—
297	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
298	#340	C₂²×C₇	1	1	yes	characteristic
299	#340	C₂²×C₇	1	1	yes	characteristic
300	#340	C₂²×C₇	1	1	yes	characteristic
301	#340	C₂²×C₇	1	1	yes	characteristic
302	#336	C₂²×C₇	1	1	yes	characteristic
303	#336	C₂²×C₇	1	1	yes	characteristic
304	C₂³×C₇	—	2	1	no	—
305	C₂³×C₇	—	2	1	no	—
306	C₂³×C₇	—	2	1	no	—
307	C₂³×C₇	—	2	1	no	—
308	C₂³×C₇	—	2	1	no	—
309	C₂³×C₇	—	2	1	no	—
310	C₂³×C₇	—	2	2	no	—
311	C₂³×C₇	—	4	1	no	—
312	C₂³×C₇	—	4	1	no	—
313	C₂³×C₇	—	4	1	no	—
314	C₂³×C₇	—	4	1	no	—
315	C₂³×C₇	—	4	1	no	—
316	C₂³×C₇	—	4	1	no	—
317	C₂³×C₇	C₄×D₄	1	2	yes	—
318	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
319	C₇×Q₈	—	2	2	no	—
320	C₇×Q₈	—	2	2	no	—
321	C₇×Q₈	—	2	2	no	—
322	C₇×Q₈	—	2	2	no	—
323	C₇×Q₈	—	2	2	no	—
324	C₇×Q₈	—	4	8	no	—
325	C₇×Q₈	—	4	1	no	—
326	C₇×Q₈	—	4	1	no	—
327	C₇×Q₈	C₄×D₄	1	4	yes	—
328	C₇×D₄	—	2	2	no	—
329	C₇×D₄	—	2	2	no	—
330	C₇×D₄	—	4	1	no	—
331	C₇×D₄	—	4	1	no	—
332	C₇×D₄	—	8	4	no	—
333	C₂×C₄×C₇	—	2	2	no	—
334	C₂×C₄×C₇	—	2	1	no	—
335	C₂×C₄×C₇	—	2	1	no	—
336	C₂×C₄×C₇	—	2	2	no	—
337	C₂×C₄×C₇	—	2	2	no	—
338	C₂×C₄×C₇	—	2	1	no	—
339	C₂×C₄×C₇	—	2	1	no	—
340	C₂×C₄×C₇	—	2	2	no	—
341	C₂×C₄×C₇	—	2	2	no	—
342	C₂×C₄×C₇	—	2	2	no	—
343	C₂×C₄×C₇	—	2	2	no	—
344	C₂×C₄×C₇	—	2	2	no	—
345	C₂×C₄×C₇	—	2	2	no	—
346	C₂×C₄×C₇	—	2	1	no	—
347	C₂×C₄×C₇	—	2	2	no	—
348	C₂×C₄×C₇	—	2	1	no	—
349	C₂×C₄×C₇	—	2	1	no	—
350	C₂×C₄×C₇	—	2	1	no	—
351	C₂×C₄×C₇	—	2	1	no	—
352	C₂×C₄×C₇	—	2	1	no	—
353	C₂×C₄×C₇	—	2	1	no	—
354	C₂×C₄×C₇	—	2	1	no	—
355	C₂×C₄×C₇	—	2	1	no	—
356	C₂×C₄×C₇	—	4	8	no	—
357	C₂×C₄×C₇	—	4	1	no	—
358	C₂×C₄×C₇	—	4	1	no	—
359	C₂×C₄×C₇	—	4	1	no	—
360	C₂×C₄×C₇	—	4	1	no	—
361	C₂×C₄×C₇	—	4	1	no	—
362	C₂×C₄×C₇	—	4	1	no	—
363	C₂×C₄×C₇	—	4	1	no	—
364	C₂×C₄×C₇	—	4	1	no	—
365	C₂×C₄×C₇	—	4	1	no	—
366	C₂×C₄×C₇	—	4	1	no	—
367	C₂×C₄×C₇	—	4	1	no	—
368	C₂×C₄×C₇	—	4	1	no	—
369	C₂×C₄×C₇	—	4	1	no	—
370	C₂×C₄×C₇	—	4	1	no	—
371	C₂×C₄×C₇	—	4	1	no	—
372	C₂×C₄×C₇	—	8	4	no	—
373	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
374	C₂×C₄×C₇	#137	1	2	yes	—
375	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
376	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
378	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
379	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
381	C₇×C₈	—	2	2	no	—
382	C₇×C₈	—	2	2	no	—
383	C₇×C₈	—	2	2	no	—
384	C₇×C₈	—	4	1	no	—
385	C₂²×Q₈	—	2	1	no	—
386	C₂²×Q₈	—	2	2	no	—
387	C₂²×Q₈	—	2	2	no	—
388	C₂²×Q₈	—	2	2	no	—
389	C₂²×Q₈	—	4	1	no	—
390	C₂²×Q₈	—	4	1	no	—
391	C₂²×Q₈	C₂×C₄×C₇	1	4	yes	complemented
392	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
394	C₂²×D₄	—	2	1	no	—
395	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	4	1	no	—
402	C₂×SD₁₆	—	4	1	no	—
403	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
404	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
405	C₂×M₁₆	—	2	2	no	—
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	4	1	no	—
408	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
412	#121	—	2	2	no	—
413	#121	C₂×C₄×C₇	1	4	yes	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	4	1	no	—
417	C₄×Q₈	—	4	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	—	4	1	no	—
420	#117	—	2	2	no	—
421	#117	—	4	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
444	#107	—	4	1	no	—
445	#106	—	2	2	no	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	C₂×C₄×C₇	1	4	yes	complemented
450	#103	C₂×C₄×C₇	1	4	yes	complemented
451	#103	C₇×D₄	1	4	yes	complemented
452	#102	—	2	2	no	—
453	#102	—	4	1	no	—
454	C₂²⋊C₈	C₂×C₄×C₇	1	4	yes	complemented
455	#97	—	4	1	no	—
456	C₄×C₈	—	2	2	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	C₇×D₄	1	1	yes	characteristic
465	#95	C₇×D₄	1	1	yes	characteristic
466	C₂²×C₇	—	2	2	no	—
467	C₂²×C₇	—	2	2	no	—
468	C₂²×C₇	—	2	2	no	—
469	C₂²×C₇	—	4	1	no	—
470	C₂²×C₇	—	4	1	no	—
471	C₂²×C₇	—	4	1	no	—
472	C₂²×C₇	—	4	1	no	—
473	C₂²×C₇	—	4	2	no	—
474	C₂²×C₇	—	4	2	no	—
475	C₂²×C₇	—	4	2	no	—
476	C₂²×C₇	—	8	1	no	—
477	C₂²×C₇	—	8	1	no	—
478	C₂²×C₇	—	8	1	no	—
479	C₂²×C₇	—	8	1	no	—
480	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
481	C₂²×C₇	D₄²	1	1	yes	characteristic
482	C₂²×C₇	#546	1	1	yes	characteristic
483	C₂²×C₇	C₂×#137	1	1	yes	characteristic
484	C₂²×C₇	#575	1	1	yes	characteristic
485	C₂²×C₇	#577	1	1	yes	characteristic
486	C₂²×C₇	#577	1	1	yes	characteristic
487	C₄×C₇	—	2	2	no	—
488	C₄×C₇	—	2	4	no	—
489	C₄×C₇	—	2	2	no	—
490	C₄×C₇	—	4	1	no	—
491	C₄×C₇	—	4	2	no	—
492	C₄×C₇	—	4	2	no	—
493	C₄×C₇	—	4	2	no	—
494	C₄×C₇	—	4	1	no	—
495	C₄×C₇	—	4	1	no	—
496	C₄×C₇	—	8	1	no	—
497	C₄×C₇	—	8	1	no	—
498	C₄×C₇	—	8	1	no	—
499	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
500	C₄×C₇	#518	1	1	yes	characteristic
501	C₄×C₇	#546	1	1	yes	characteristic
502	C₄×C₇	#551	1	1	yes	characteristic
503	C₂⁴	—	2	1	no	—
504	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	2	8	no	—
511	C₂×Q₈	—	2	1	no	—
512	C₂×Q₈	—	2	1	no	—
513	C₂×Q₈	—	2	1	no	—
514	C₂×Q₈	—	2	1	no	—
515	C₂×Q₈	—	4	2	no	—
516	C₂×Q₈	—	4	2	no	—
517	C₂×Q₈	—	4	4	no	—
518	C₂×Q₈	—	4	4	no	—
519	C₂×Q₈	—	4	4	no	—
520	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
521	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
522	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
523	C₂×Q₈	C₇×#41	1	2	yes	—
524	C₂×D₄	—	2	4	no	—
525	C₂×D₄	—	2	1	no	—
526	C₂×D₄	—	2	1	no	—
527	C₂×D₄	—	2	1	no	—
528	C₂×D₄	—	2	1	no	—
529	C₂×D₄	—	2	1	no	—
530	C₂×D₄	—	8	1	no	—
531	C₂×D₄	—	8	1	no	—
532	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	4	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	4	2	no	—
546	C₂²×C₄	—	4	2	no	—
547	C₂²×C₄	—	4	2	no	—
548	C₂²×C₄	—	4	2	no	—
549	C₂²×C₄	—	8	1	no	—
550	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
551	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
552	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
554	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₇×#41	1	2	yes	—
557	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
558	SD₁₆	—	2	8	no	—
559	SD₁₆	—	4	4	no	—
560	M₁₆	—	4	4	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	2	1	no	—
568	C₂×C₈	—	2	1	no	—
569	C₂×C₈	—	2	1	no	—
570	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
571	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
572	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	4	2	no	—
582	C₄⋊C₄	—	4	2	no	—
583	C₄⋊C₄	—	8	1	no	—
584	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
585	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
586	C₂²⋊C₄	—	2	4	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₂²⋊C₄	—	4	2	no	—
591	C₂²⋊C₄	—	4	2	no	—
592	C₂²⋊C₄	—	4	2	no	—
593	C₂²⋊C₄	—	8	1	no	—
594	C₄²	—	2	1	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	4	2	no	—
599	C₄²	—	4	2	no	—
600	C₄²	—	4	2	no	—
601	C₄²	—	8	1	no	—
602	C₂×C₇	—	4	2	no	—
603	C₂×C₇	—	8	2	no	—
604	C₂×C₇	#2358	1	1	yes	characteristic
605	C₂×C₇	C₄×#137	1	1	yes	characteristic
606	C₂×C₇	#2949	1	1	yes	characteristic
607	C₂×C₇	#3266	1	1	yes	characteristic
608	C₂×C₇	#3271	1	1	yes	characteristic
609	C₂×C₇	#3326	1	1	yes	characteristic
610	C₂×C₇	#3329	1	1	yes	characteristic
611	C₂³	—	2	1	no	—
612	C₂³	—	2	1	no	—
613	C₂³	—	2	1	no	—
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	4	1	no	—
619	C₂³	—	4	1	no	—
620	C₂³	—	4	1	no	—
621	C₂³	—	4	1	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	C₄×C₇×D₄	1	2	yes	—
625	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
626	Q₈	—	2	2	no	—
627	Q₈	—	2	2	no	—
628	Q₈	—	2	2	no	—
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	8	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	C₄×C₇×D₄	1	4	yes	—
635	D₄	—	2	2	no	—
636	D₄	—	2	2	no	—
637	D₄	—	4	1	no	—
638	D₄	—	4	1	no	—
639	D₄	—	8	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	4	8	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	1	no	—
675	C₂×C₄	—	4	1	no	—
676	C₂×C₄	—	4	1	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	1	no	—
679	C₂×C₄	—	8	4	no	—
680	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
681	C₂×C₄	C₇×#137	1	2	yes	—
682	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
684	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
685	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
686	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
688	C₈	—	2	2	no	—
689	C₈	—	2	2	no	—
690	C₈	—	2	2	no	—
691	C₈	—	4	1	no	—
692	C₇	#22885	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	4	1	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	8	1	no	—
704	C₂²	—	8	1	no	—
705	C₂²	—	8	1	no	—
706	C₂²	—	8	1	no	—
707	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
708	C₂²	C₇×D₄²	1	1	yes	characteristic
709	C₂²	C₇×#546	1	1	yes	characteristic
710	C₂²	C₂×C₇×#137	1	1	yes	characteristic
711	C₂²	C₇×#575	1	1	yes	characteristic
712	C₂²	C₇×#577	1	1	yes	characteristic
713	C₂²	C₇×#577	1	1	yes	characteristic
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	4	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	8	1	no	—
724	C₄	—	8	1	no	—
725	C₄	—	8	1	no	—
726	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
727	C₄	C₇×#518	1	1	yes	characteristic
728	C₄	C₇×#546	1	1	yes	characteristic
729	C₄	C₇×#551	1	1	yes	characteristic
730	C₂	—	4	2	no	—
731	C₂	—	8	2	no	—
732	C₂	C₇×#2358	1	1	yes	characteristic
733	C₂	C₄×C₇×#137	1	1	yes	characteristic
734	C₂	C₇×#2949	1	1	yes	characteristic
735	C₂	C₇×#3266	1	1	yes	characteristic
736	C₂	C₇×#3271	1	1	yes	characteristic
737	C₂	C₇×#3326	1	1	yes	characteristic
738	C₂	C₇×#3329	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₇×SD₁₆	C₂	semidirect
3. C₂×C₇×#419	C₂	semidirect
5. C₇×Q₈×C₂²⋊C₄	C₂	semidirect
6. C₇×#1973	C₂	semidirect
7. C₇×#1933	C₂	semidirect
8. C₇×#1927	C₂	semidirect
10. C₇×#1880	C₂	semidirect
11. C₇×#1877	C₂	semidirect
12. C₇×#1863	C₂	semidirect
13. C₇×#1854	C₂	semidirect
14. C₇×#1763	C₂	semidirect
15. C₇×#1753	C₂	semidirect
25. C₇×#448	C₄	semidirect
62. #22885	C₇	direct (N × H)
69. C₂²×C₇×Q₈	C₂×C₄	semidirect
127. C₇×#103	C₂×C₄	semidirect
128. C₇×#103	C₂×C₄	semidirect
129. C₇×#103	D₄	semidirect
132. C₇×C₂²⋊C₈	C₂×C₄	semidirect
145. C₂×C₄×SD₁₆	C₂×C₇	semidirect
146. C₂×#419	C₂×C₇	semidirect
148. Q₈×C₂²⋊C₄	C₂×C₇	semidirect
149. #1973	C₂×C₇	semidirect
150. #1933	C₂×C₇	semidirect
151. #1927	C₂×C₇	semidirect
153. #1880	C₂×C₇	semidirect
154. #1877	C₂×C₇	semidirect
155. #1863	C₂×C₇	semidirect
156. #1854	C₂×C₇	semidirect
157. #1763	C₂×C₇	semidirect
158. #1753	C₂×C₇	semidirect
267. #448	C₄×C₇	semidirect
391. C₂²×Q₈	C₂×C₄×C₇	semidirect
449. #103	C₂×C₄×C₇	semidirect
450. #103	C₂×C₄×C₇	semidirect
451. #103	C₇×D₄	semidirect
454. C₂²⋊C₈	C₂×C₄×C₇	semidirect
692. C₇	#22885	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#448	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#419	2
C₇×#2363	2
C₇×Q₈×C₂²⋊C₄	2
C₇×#1973	2
C₇×#1933	2
C₇×#1927	2
C₇×#1895	2
C₇×#1880	2
C₇×#1877	2
C₇×#1863	2
C₇×#1854	2
C₇×#1763	2
C₇×#1753	2
#22885	7

Subgroups — C7×#22885 #13200101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22885 #13200101