Subgroups — C₇×#23024 #13200240

Order 1792.

982 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic
4	C₇×#2360	C₂	1	2	yes	maximal
5	C₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1928	C₂	1	2	yes	maximal, complemented
8	C₇×#1872	C₂	1	2	yes	maximal
9	C₇×#1863	C₂	1	2	yes	maximal, complemented
10	C₄×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
16	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
17	C₇×#467	C₄	1	8	yes	complemented
18	C₄×C₇×Q₁₆	—	2	4	no	—
19	C₂×C₇×#107	—	2	4	no	—
20	C₂×C₇×#107	C₂²	1	1	yes	characteristic
21	C₂×C₇×#107	C₂²	1	2	yes	—
22	C₂×C₇×#107	C₂²	1	1	yes	characteristic
23	C₂×C₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	2	yes	—
26	C₂×C₇×#103	C₂²	1	2	yes	—
27	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#391	C₂²	1	2	yes	—
31	C₇×#389	—	2	2	no	—
32	C₇×#389	C₂²	1	2	yes	—
33	C₇×#387	—	2	2	no	—
34	C₇×#385	—	2	2	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
37	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#336	C₂²	1	1	yes	characteristic
41	C₇×#336	C₂²	1	1	yes	characteristic
42	#23024	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂³×C₄×C₇	—	2	2	no	—
45	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
46	C₂×C₇×Q₁₆	—	2	2	no	—
47	C₂×C₇×Q₁₆	—	2	2	no	—
48	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂²×C₇×C₈	—	2	2	no	—
50	C₂²×C₇×C₈	—	2	2	no	—
51	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₇×C₂²⋊Q₈	—	2	4	no	—
57	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
58	C₄×C₇×Q₈	—	2	4	no	—
59	C₄×C₇×Q₈	—	4	2	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	4	no	—
62	C₂×C₇×C₄⋊C₄	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	—	2	2	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	4	2	no	—
66	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	2	no	—
77	C₇×#107	—	2	4	no	—
78	C₇×#107	C₂×C₄	1	4	yes	complemented
79	C₇×#107	D₄	1	4	yes	—
80	C₇×#103	—	2	4	no	—
81	C₇×#103	—	4	2	no	—
82	C₇×#103	C₂×C₄	1	8	yes	complemented
83	C₇×C₂²⋊C₈	—	2	2	no	—
84	C₄×C₇×C₈	—	2	2	no	—
85	C₄×C₇×C₈	—	2	2	no	—
86	C₇×#95	—	2	2	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	—	2	2	no	—
90	C₇×#95	D₄	1	1	yes	characteristic
91	C₇×#95	D₄	1	1	yes	characteristic
92	C₂×#467	C₂×C₇	1	1	yes	characteristic
93	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂²×#107	C₂×C₇	1	1	yes	characteristic
95	#2360	C₂×C₇	1	2	yes	—
96	#1969	C₂×C₇	1	1	yes	characteristic, complemented
97	#1942	C₂×C₇	1	1	yes	characteristic, complemented
98	#1928	C₂×C₇	1	2	yes	complemented
99	#1872	C₂×C₇	1	2	yes	—
100	#1863	C₂×C₇	1	2	yes	complemented
101	C₄×#107	C₂×C₇	1	1	yes	characteristic, complemented
102	C₈×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic
103	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
104	C₂×C₇×Q₈	—	2	2	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	1	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	4	4	no	—
119	C₂²×C₄×C₇	—	4	4	no	—
120	C₂²×C₄×C₇	—	8	2	no	—
121	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	#41	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×Q₁₆	—	2	8	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	8	no	—
133	C₂×C₇×C₈	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	1	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
142	C₂×C₇×C₈	#41	1	2	yes	—
143	C₇×C₄⋊C₄	—	2	8	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	4	4	no	—
149	C₇×C₄⋊C₄	—	4	4	no	—
150	C₇×C₄⋊C₄	—	8	2	no	—
151	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
152	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₇×C₂²⋊C₄	—	2	8	no	—
154	C₇×C₂²⋊C₄	—	2	2	no	—
155	C₇×C₂²⋊C₄	Q₁₆	1	4	yes	complemented
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	—	4	4	no	—
161	C₄²×C₇	—	8	2	no	—
162	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
163	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
165	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
166	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
167	#467	C₄×C₇	1	8	yes	complemented
168	C₄×Q₁₆	—	2	4	no	—
169	C₂×#107	—	2	4	no	—
170	C₂×#107	C₂²×C₇	1	2	yes	—
171	C₂×#107	C₂²×C₇	1	1	yes	characteristic
172	C₂×#107	C₂²×C₇	1	1	yes	characteristic
173	C₂×#107	C₂²×C₇	1	1	yes	characteristic
174	C₂×#103	C₂²×C₇	1	2	yes	—
175	C₂×#103	C₂²×C₇	1	2	yes	—
176	C₂×#103	C₂²×C₇	1	2	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
179	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
180	#391	C₂²×C₇	1	2	yes	—
181	#389	—	2	2	no	—
182	#389	C₂²×C₇	1	2	yes	—
183	#387	—	2	2	no	—
184	#385	—	2	2	no	—
185	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
186	C₄×C₂²⋊C₄	—	2	2	no	—
187	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
188	#340	C₂²×C₇	1	2	yes	—
189	#340	C₂²×C₇	1	2	yes	—
190	#336	C₂²×C₇	1	1	yes	characteristic
191	#336	C₂²×C₇	1	1	yes	characteristic
192	C₂³×C₇	—	2	1	no	—
193	C₂³×C₇	—	2	1	no	—
194	C₂³×C₇	—	2	1	no	—
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	C₄×D₄	1	2	yes	—
197	C₂³×C₇	C₂×Q₁₆	1	2	yes	—
198	C₂³×C₇	#135	1	2	yes	—
199	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₇×Q₈	—	2	4	no	—
201	C₇×Q₈	—	2	4	no	—
202	C₇×Q₈	—	4	2	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	1	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	2	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	—	8	8	no	—
233	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
234	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
235	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
236	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
241	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
242	C₇×C₈	—	2	2	no	—
243	C₇×C₈	—	4	1	no	—
244	C₇×C₈	—	4	1	no	—
245	C₇×C₈	C₄×D₄	1	4	yes	—
246	C₂²×Q₈	C₂³×C₇	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
255	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
261	C₄×Q₈	—	2	4	no	—
262	C₄×Q₈	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	4	2	no	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	#107	—	2	2	no	—
280	#107	—	2	4	no	—
281	#107	C₂×C₄×C₇	1	4	yes	complemented
282	#107	C₇×D₄	1	4	yes	—
283	#103	—	2	4	no	—
284	#103	—	4	2	no	—
285	#103	C₂×C₄×C₇	1	8	yes	complemented
286	C₂²⋊C₈	—	2	2	no	—
287	C₄×C₈	—	2	2	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	C₇×D₄	1	1	yes	characteristic
294	#95	C₇×D₄	1	1	yes	characteristic
295	C₂²×C₇	—	2	2	no	—
296	C₂²×C₇	—	2	2	no	—
297	C₂²×C₇	—	2	2	no	—
298	C₂²×C₇	—	2	2	no	—
299	C₂²×C₇	—	2	2	no	—
300	C₂²×C₇	—	2	2	no	—
301	C₂²×C₇	C₄×Q₁₆	1	4	yes	complemented
302	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
303	C₂²×C₇	D₄²	1	1	yes	characteristic
304	C₂²×C₇	#547	1	1	yes	characteristic
305	C₂²×C₇	C₂²×Q₁₆	1	1	yes	characteristic
306	C₂²×C₇	C₂×#135	1	1	yes	characteristic
307	C₂²×C₇	#576	1	1	yes	characteristic
308	C₂²×C₇	#578	1	1	yes	characteristic
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	2	2	no	—
312	C₄×C₇	—	4	1	no	—
313	C₄×C₇	—	4	4	no	—
314	C₄×C₇	—	4	4	no	—
315	C₄×C₇	—	4	1	no	—
316	C₄×C₇	—	4	4	no	—
317	C₄×C₇	—	8	2	no	—
318	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
319	C₄×C₇	#520	1	1	yes	characteristic
320	C₄×C₇	#548	1	1	yes	characteristic
321	C₄×C₇	#553	1	1	yes	characteristic
322	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	8	2	no	—
340	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
346	C₂²×C₄	C₇×#41	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	Q₁₆	—	2	8	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	8	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
360	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
361	C₂×C₈	C₇×#41	1	2	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
371	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	C₇×Q₁₆	1	4	yes	complemented
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	8	2	no	—
381	C₂×C₇	—	2	4	no	—
382	C₂×C₇	#2361	1	1	yes	characteristic
383	C₂×C₇	C₂×C₄×Q₁₆	1	1	yes	characteristic
384	C₂×C₇	#2951	1	1	yes	characteristic
385	C₂×C₇	#3280	1	1	yes	characteristic
386	C₂×C₇	D₄×Q₁₆	1	1	yes	characteristic
387	C₂×C₇	#3336	1	1	yes	characteristic
388	C₂×C₇	#3338	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	C₄×C₇×D₄	1	2	yes	—
394	C₂³	C₂×C₇×Q₁₆	1	2	yes	—
395	C₂³	C₇×#135	1	2	yes	—
396	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	8	no	—
430	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
431	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
432	C₂×C₄	C₂×C₇×Q₁₆	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
435	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
437	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₈	C₄×C₇×D₄	1	4	yes	—
443	C₇	#23024	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	C₄×C₇×Q₁₆	1	4	yes	complemented
451	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
452	C₂²	C₇×D₄²	1	1	yes	characteristic
453	C₂²	C₇×#547	1	1	yes	characteristic
454	C₂²	C₂²×C₇×Q₁₆	1	1	yes	characteristic
455	C₂²	C₂×C₇×#135	1	1	yes	characteristic
456	C₂²	C₇×#576	1	1	yes	characteristic
457	C₂²	C₇×#578	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	4	no	—
466	C₄	—	8	2	no	—
467	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
468	C₄	C₇×#520	1	1	yes	characteristic
469	C₄	C₇×#548	1	1	yes	characteristic
470	C₄	C₇×#553	1	1	yes	characteristic
471	C₂	—	2	4	no	—
472	C₂	C₇×#2361	1	1	yes	characteristic
473	C₂	C₂×C₄×C₇×Q₁₆	1	1	yes	characteristic
474	C₂	C₇×#2951	1	1	yes	characteristic
475	C₂	C₇×#3280	1	1	yes	characteristic
476	C₂	C₇×D₄×Q₁₆	1	1	yes	characteristic
477	C₂	C₇×#3336	1	1	yes	characteristic
478	C₂	C₇×#3338	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	C₂⁴×C₇	C₂×D₄
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×Q₁₆	C₂	semidirect
5. C₇×#1969	C₂	semidirect
6. C₇×#1942	C₂	semidirect
7. C₇×#1928	C₂	semidirect
9. C₇×#1863	C₂	semidirect
10. C₄×C₇×#107	C₂	semidirect
17. C₇×#467	C₄	semidirect
42. #23024	C₇	direct (N × H)
48. C₂×C₇×Q₁₆	C₂×C₄	semidirect
78. C₇×#107	C₂×C₄	semidirect
82. C₇×#103	C₂×C₄	semidirect
93. C₂×C₄×Q₁₆	C₂×C₇	semidirect
96. #1969	C₂×C₇	semidirect
97. #1942	C₂×C₇	semidirect
98. #1928	C₂×C₇	semidirect
100. #1863	C₂×C₇	semidirect
101. C₄×#107	C₂×C₇	semidirect
155. C₇×C₂²⋊C₄	Q₁₆	semidirect
167. #467	C₄×C₇	semidirect
251. C₂×Q₁₆	C₂×C₄×C₇	semidirect
281. #107	C₂×C₄×C₇	semidirect
285. #103	C₂×C₄×C₇	semidirect
301. C₂²×C₇	C₄×Q₁₆	semidirect
374. C₂²⋊C₄	C₇×Q₁₆	semidirect
443. C₇	#23024	direct (N × H)
450. C₂²	C₄×C₇×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#467	2
C₂×C₄×C₇×Q₁₆	2
C₂²×C₇×#107	2
C₇×#2360	2
C₇×#1969	2
C₇×#1942	2
C₇×#1928	2
C₇×#1872	2
C₇×#1863	2
C₄×C₇×#107	2
C₇×C₈×C₂²⋊C₄	2
#23024	7

Subgroups — C7×#23024 #13200240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23024 #13200240