Subgroups — C₇×#22452 #13199668

Order 1792.

1368 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#444	C₂	1	2	yes	maximal, complemented
3	C₇×#2880	C₂	1	2	yes	maximal, complemented
4	C₇×#1975	C₂	1	2	yes	maximal, complemented
5	C₇×#1876	C₂	1	4	yes	maximal, complemented
6	C₇×#1810	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1789	C₂	1	2	yes	maximal, complemented
8	C₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₂×C₇×#135	—	2	8	no	—
11	C₂×C₇×#135	C₄	1	1	yes	characteristic, complemented
12	C₂×C₇×#135	C₄	1	2	yes	complemented
13	C₂×C₇×#135	C₄	1	1	yes	characteristic, complemented
14	C₂×C₇×#135	C₂²	1	1	yes	characteristic
15	C₂×C₇×#135	C₂²	1	2	yes	—
16	C₂×C₇×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₇×SD₁₆	C₄	1	2	yes	complemented
19	C₂²×C₇×D₈	C₄	1	1	yes	characteristic, complemented
20	C₂×C₇×#131	C₂²	1	4	yes	complemented
21	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
22	C₇×#444	—	2	8	no	—
23	C₂×C₇×#108	C₂²	1	2	yes	complemented
24	C₂×C₇×#104	C₂²	1	4	yes	complemented
25	C₂×C₇×#104	C₂²	1	4	yes	complemented
26	C₇×#408	—	2	4	no	—
27	C₇×#408	C₂²	1	4	yes	complemented
28	C₇×#407	—	2	2	no	—
29	C₇×#407	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊C₈	—	2	2	no	—
31	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₇×#97	C₂²	1	2	yes	complemented
33	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₇×#341	C₂²	1	2	yes	complemented
35	C₇×#336	C₂²	1	2	yes	complemented
36	#22452	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₇×#41	—	2	2	no	—
38	C₂×C₇×#41	—	2	2	no	—
39	C₂×C₇×#41	—	2	8	no	—
40	C₂×C₇×#41	—	4	4	no	—
41	C₂×C₇×#41	C₂×C₄	1	2	yes	—
42	C₂×C₇×#41	C₂×C₄	1	2	yes	—
43	C₂×C₇×#41	C₂³	1	2	yes	—
44	C₂×C₇×#41	C₂³	1	2	yes	—
45	C₂²×C₇×Q₈	C₂×C₄	1	2	yes	—
46	C₂²×C₇×D₄	—	2	2	no	—
47	C₂²×C₇×D₄	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₇	—	2	2	no	—
49	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
50	C₇×#135	—	2	8	no	—
51	C₇×#135	—	2	4	no	—
52	C₇×#135	—	2	8	no	—
53	C₇×#135	—	2	4	no	—
54	C₇×#135	—	2	4	no	—
55	C₇×#135	D₄	1	8	yes	—
56	C₂×C₇×Q₁₆	—	2	4	no	—
57	C₂×C₇×Q₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₇×SD₁₆	—	2	8	no	—
61	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₇×D₈	—	2	4	no	—
66	C₂×C₇×D₈	C₂×C₄	1	2	yes	—
67	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
68	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
69	C₇×#131	—	2	8	no	—
70	C₇×#131	—	4	4	no	—
71	C₂×C₇×M₁₆	—	2	4	no	—
72	C₂×C₇×M₁₆	C₂³	1	4	yes	—
73	C₂²×C₇×C₈	—	2	4	no	—
74	C₂²×C₇×C₈	—	2	4	no	—
75	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₇×C₈	C₂³	1	2	yes	—
81	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
82	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₄²×C₇	C₂³	1	2	yes	—
84	C₇×#108	—	2	4	no	—
85	C₇×#104	—	2	8	no	—
86	C₇×#104	—	4	4	no	—
87	C₇×C₂²⋊C₈	—	2	2	no	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	4	no	—
90	C₇×C₂²⋊C₈	—	2	4	no	—
91	C₇×C₂²⋊C₈	D₄	1	2	yes	—
92	C₇×C₂²⋊C₈	D₄	1	2	yes	—
93	C₇×#97	—	2	4	no	—
94	C₇×#95	—	2	1	no	—
95	C₂²×#135	C₂×C₇	1	1	yes	characteristic
96	C₂×#444	C₂×C₇	1	2	yes	complemented
97	#2880	C₂×C₇	1	2	yes	complemented
98	#1975	C₂×C₇	1	2	yes	complemented
99	#1876	C₂×C₇	1	4	yes	complemented
100	#1810	C₂×C₇	1	1	yes	characteristic, complemented
101	#1789	C₂×C₇	1	2	yes	complemented
102	#1752	C₂×C₇	1	1	yes	characteristic, complemented
103	C₂⁴×C₇	—	2	2	no	—
104	C₂⁴×C₇	#41	1	1	yes	characteristic
105	C₇×#41	—	2	4	no	—
106	C₇×#41	—	2	4	no	—
107	C₇×#41	—	2	4	no	—
108	C₇×#41	—	2	4	no	—
109	C₇×#41	—	2	4	no	—
110	C₇×#41	—	4	8	no	—
111	C₇×#41	—	4	2	no	—
112	C₇×#41	—	4	2	no	—
113	C₇×#41	—	4	8	no	—
114	C₇×#41	C₂×D₄	1	8	yes	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	—	2	4	no	—
117	C₂×C₇×Q₈	—	4	2	no	—
118	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
119	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	4	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	2	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	—	4	2	no	—
127	C₂×C₇×D₄	—	4	8	no	—
128	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
129	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	2	no	—
138	C₂²×C₄×C₇	—	4	8	no	—
139	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇	#41	1	1	yes	characteristic
144	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
145	C₇×Q₁₆	—	2	4	no	—
146	C₇×Q₁₆	—	2	2	no	—
147	C₇×Q₁₆	C₂²⋊C₄	1	4	yes	complemented
148	C₇×SD₁₆	—	2	4	no	—
149	C₇×SD₁₆	—	2	4	no	—
150	C₇×SD₁₆	—	2	4	no	—
151	C₇×SD₁₆	C₂²⋊C₄	1	8	yes	complemented
152	C₇×D₈	—	2	4	no	—
153	C₇×D₈	—	2	2	no	—
154	C₇×D₈	C₂²⋊C₄	1	4	yes	complemented
155	C₇×M₁₆	—	2	4	no	—
156	C₇×M₁₆	—	2	4	no	—
157	C₇×M₁₆	—	4	8	no	—
158	C₂×C₇×C₈	—	2	2	no	—
159	C₂×C₇×C₈	—	2	2	no	—
160	C₂×C₇×C₈	—	2	2	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	2	2	no	—
163	C₂×C₇×C₈	—	2	2	no	—
164	C₂×C₇×C₈	—	2	2	no	—
165	C₂×C₇×C₈	—	2	4	no	—
166	C₂×C₇×C₈	—	4	8	no	—
167	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
172	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
173	C₇×C₂²⋊C₄	—	4	2	no	—
174	C₄²×C₇	—	2	2	no	—
175	C₄²×C₇	—	2	2	no	—
176	C₂²×#41	C₂²×C₇	1	2	yes	—
177	C₂×#135	—	2	8	no	—
178	C₂×#135	C₄×C₇	1	1	yes	characteristic, complemented
179	C₂×#135	C₄×C₇	1	2	yes	complemented
180	C₂×#135	C₄×C₇	1	1	yes	characteristic, complemented
181	C₂×#135	C₂²×C₇	1	2	yes	—
182	C₂×#135	C₂²×C₇	1	1	yes	characteristic
183	C₂×#135	C₂²×C₇	1	1	yes	characteristic
184	C₂²×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
185	C₂²×SD₁₆	C₄×C₇	1	2	yes	complemented
186	C₂²×D₈	C₄×C₇	1	1	yes	characteristic, complemented
187	C₂×#131	C₂²×C₇	1	4	yes	complemented
188	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
189	#444	—	2	8	no	—
190	C₂×#108	C₂²×C₇	1	2	yes	complemented
191	C₂×#104	C₂²×C₇	1	4	yes	complemented
192	C₂×#104	C₂²×C₇	1	4	yes	complemented
193	#408	—	2	4	no	—
194	#408	C₂²×C₇	1	4	yes	complemented
195	#407	—	2	2	no	—
196	#407	C₂²×C₇	1	2	yes	—
197	C₂×C₂²⋊C₈	—	2	2	no	—
198	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂×#97	C₂²×C₇	1	2	yes	complemented
200	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
201	#341	C₂²×C₇	1	2	yes	complemented
202	#336	C₂²×C₇	1	2	yes	complemented
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	2	no	—
206	C₂³×C₇	—	2	2	no	—
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	—	4	4	no	—
209	C₂³×C₇	—	4	4	no	—
210	C₂³×C₇	—	8	2	no	—
211	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
212	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₇	C₂×#41	1	1	yes	characteristic
214	C₇×Q₈	—	2	2	no	—
215	C₇×Q₈	—	2	2	no	—
216	C₇×Q₈	—	2	2	no	—
217	C₇×Q₈	—	4	4	no	—
218	C₇×Q₈	C₂×C₂²⋊C₄	1	4	yes	—
219	C₇×D₄	—	2	8	no	—
220	C₇×D₄	—	2	2	no	—
221	C₇×D₄	—	2	2	no	—
222	C₇×D₄	—	2	2	no	—
223	C₇×D₄	—	4	4	no	—
224	C₇×D₄	—	4	4	no	—
225	C₇×D₄	—	4	4	no	—
226	C₇×D₄	—	4	4	no	—
227	C₇×D₄	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	1	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	2	8	no	—
235	C₂×C₄×C₇	—	2	2	no	—
236	C₂×C₄×C₇	—	2	2	no	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	4	4	no	—
239	C₂×C₄×C₇	—	4	4	no	—
240	C₂×C₄×C₇	—	4	4	no	—
241	C₂×C₄×C₇	—	4	4	no	—
242	C₂×C₄×C₇	—	4	2	no	—
243	C₂×C₄×C₇	—	4	2	no	—
244	C₂×C₄×C₇	—	4	2	no	—
245	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
251	C₇×C₈	—	2	1	no	—
252	C₇×C₈	—	2	1	no	—
253	C₇×C₈	—	2	4	no	—
254	C₇×C₈	—	4	4	no	—
255	C₇×C₈	C₂×C₂²⋊C₄	1	2	yes	—
256	C₇×C₈	C₂×C₂²⋊C₄	1	2	yes	—
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	—	4	4	no	—
261	C₂×#41	C₂×C₄×C₇	1	2	yes	—
262	C₂×#41	C₂×C₄×C₇	1	2	yes	—
263	C₂×#41	C₂³×C₇	1	2	yes	—
264	C₂×#41	C₂³×C₇	1	2	yes	—
265	C₂²×Q₈	C₂×C₄×C₇	1	2	yes	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	C₂×C₄×C₇	1	2	yes	—
268	C₂³×C₄	—	2	2	no	—
269	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
270	#135	—	2	8	no	—
271	#135	—	2	4	no	—
272	#135	—	2	8	no	—
273	#135	—	2	4	no	—
274	#135	—	2	4	no	—
275	#135	C₇×D₄	1	8	yes	—
276	C₂×Q₁₆	—	2	4	no	—
277	C₂×Q₁₆	C₂×C₄×C₇	1	2	yes	—
278	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
279	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	8	no	—
281	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
282	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
283	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
284	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
285	C₂×D₈	—	2	4	no	—
286	C₂×D₈	C₂×C₄×C₇	1	2	yes	—
287	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
288	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
289	#131	—	2	8	no	—
290	#131	—	4	4	no	—
291	C₂×M₁₆	—	2	4	no	—
292	C₂×M₁₆	C₂³×C₇	1	4	yes	—
293	C₂²×C₈	—	2	4	no	—
294	C₂²×C₈	—	2	4	no	—
295	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
296	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
297	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
298	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₇	1	2	yes	—
301	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂³×C₇	1	2	yes	—
304	#108	—	2	4	no	—
305	#104	—	2	8	no	—
306	#104	—	4	4	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	2	4	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	C₂²⋊C₈	C₇×D₄	1	2	yes	—
312	C₂²⋊C₈	C₇×D₄	1	2	yes	—
313	#97	—	2	4	no	—
314	#95	—	2	1	no	—
315	C₂²×C₇	—	2	1	no	—
316	C₂²×C₇	—	2	1	no	—
317	C₂²×C₇	—	2	1	no	—
318	C₂²×C₇	—	2	1	no	—
319	C₂²×C₇	—	2	1	no	—
320	C₂²×C₇	—	2	4	no	—
321	C₂²×C₇	—	2	1	no	—
322	C₂²×C₇	—	2	1	no	—
323	C₂²×C₇	—	4	4	no	—
324	C₂²×C₇	—	4	2	no	—
325	C₂²×C₇	—	4	2	no	—
326	C₂²×C₇	—	4	2	no	—
327	C₂²×C₇	—	4	2	no	—
328	C₂²×C₇	—	4	2	no	—
329	C₂²×C₇	—	8	8	no	—
330	C₂²×C₇	#444	1	2	yes	complemented
331	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂²×C₇	#546	1	2	yes	—
333	C₄×C₇	—	2	1	no	—
334	C₄×C₇	—	2	1	no	—
335	C₄×C₇	—	2	4	no	—
336	C₄×C₇	—	4	2	no	—
337	C₄×C₇	—	8	2	no	—
338	C₄×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
339	C₄×C₇	#518	1	1	yes	characteristic
340	C₄×C₇	D₄²	1	2	yes	—
341	C₂⁴	—	2	2	no	—
342	C₂⁴	C₇×#41	1	1	yes	characteristic
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	#41	—	2	4	no	—
347	#41	—	2	4	no	—
348	#41	—	4	8	no	—
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	#41	—	4	8	no	—
352	#41	C₂×C₇×D₄	1	8	yes	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
357	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	8	no	—
366	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
367	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	8	no	—
377	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
378	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
381	C₂²×C₄	C₇×#41	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
383	Q₁₆	—	2	4	no	—
384	Q₁₆	—	2	2	no	—
385	Q₁₆	C₇×C₂²⋊C₄	1	4	yes	complemented
386	SD₁₆	—	2	4	no	—
387	SD₁₆	—	2	4	no	—
388	SD₁₆	—	2	4	no	—
389	SD₁₆	C₇×C₂²⋊C₄	1	8	yes	complemented
390	D₈	—	2	4	no	—
391	D₈	—	2	2	no	—
392	D₈	C₇×C₂²⋊C₄	1	4	yes	complemented
393	M₁₆	—	2	4	no	—
394	M₁₆	—	2	4	no	—
395	M₁₆	—	4	8	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	4	no	—
404	C₂×C₈	—	4	8	no	—
405	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
406	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
408	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
409	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
410	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₂×C₇	—	2	2	no	—
415	C₂×C₇	—	2	2	no	—
416	C₂×C₇	—	4	1	no	—
417	C₂×C₇	—	4	4	no	—
418	C₂×C₇	—	8	2	no	—
419	C₂×C₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
420	C₂×C₇	C₂×#444	1	1	yes	characteristic
421	C₂×C₇	#2957	1	1	yes	characteristic
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	8	2	no	—
430	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
431	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
432	C₂³	C₂×C₇×#41	1	1	yes	characteristic
433	Q₈	—	2	2	no	—
434	Q₈	—	2	2	no	—
435	Q₈	—	2	2	no	—
436	Q₈	—	4	4	no	—
437	Q₈	C₂×C₇×C₂²⋊C₄	1	4	yes	—
438	D₄	—	2	8	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	4	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	C₂×C₇×C₂²⋊C₄	1	4	yes	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
465	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
466	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
467	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
468	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
469	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	2	4	no	—
473	C₈	—	4	4	no	—
474	C₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
475	C₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
476	C₇	#22452	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	8	8	no	—
492	C₂²	C₇×#444	1	2	yes	complemented
493	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
494	C₂²	C₇×#546	1	2	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	2	4	no	—
498	C₄	—	4	2	no	—
499	C₄	—	8	2	no	—
500	C₄	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
501	C₄	C₇×#518	1	1	yes	characteristic
502	C₄	C₇×D₄²	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	4	1	no	—
506	C₂	—	4	4	no	—
507	C₂	—	8	2	no	—
508	C₂	C₇×D₄×C₂²⋊C₄	1	1	yes	characteristic
509	C₂	C₂×C₇×#444	1	1	yes	characteristic
510	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂²×C₇×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#444	C₂	semidirect
3. C₇×#2880	C₂	semidirect
4. C₇×#1975	C₂	semidirect
5. C₇×#1876	C₂	semidirect
6. C₇×#1810	C₂	semidirect
7. C₇×#1789	C₂	semidirect
8. C₇×#1752	C₂	semidirect
11. C₂×C₇×#135	C₄	semidirect
12. C₂×C₇×#135	C₄	semidirect
13. C₂×C₇×#135	C₄	semidirect
17. C₂²×C₇×Q₁₆	C₄	semidirect
18. C₂²×C₇×SD₁₆	C₄	semidirect
19. C₂²×C₇×D₈	C₄	semidirect
20. C₂×C₇×#131	C₂²	semidirect
23. C₂×C₇×#108	C₂²	semidirect
24. C₂×C₇×#104	C₂²	semidirect
25. C₂×C₇×#104	C₂²	semidirect
27. C₇×#408	C₂²	semidirect
32. C₂×C₇×#97	C₂²	semidirect
34. C₇×#341	C₂²	semidirect
35. C₇×#336	C₂²	semidirect
36. #22452	C₇	direct (N × H)
96. C₂×#444	C₂×C₇	semidirect
97. #2880	C₂×C₇	semidirect
98. #1975	C₂×C₇	semidirect
99. #1876	C₂×C₇	semidirect
100. #1810	C₂×C₇	semidirect
101. #1789	C₂×C₇	semidirect
102. #1752	C₂×C₇	semidirect
147. C₇×Q₁₆	C₂²⋊C₄	semidirect
151. C₇×SD₁₆	C₂²⋊C₄	semidirect
154. C₇×D₈	C₂²⋊C₄	semidirect
178. C₂×#135	C₄×C₇	semidirect
179. C₂×#135	C₄×C₇	semidirect
180. C₂×#135	C₄×C₇	semidirect
184. C₂²×Q₁₆	C₄×C₇	semidirect
185. C₂²×SD₁₆	C₄×C₇	semidirect
186. C₂²×D₈	C₄×C₇	semidirect
187. C₂×#131	C₂²×C₇	semidirect
190. C₂×#108	C₂²×C₇	semidirect
191. C₂×#104	C₂²×C₇	semidirect
192. C₂×#104	C₂²×C₇	semidirect
194. #408	C₂²×C₇	semidirect
199. C₂×#97	C₂²×C₇	semidirect
201. #341	C₂²×C₇	semidirect
202. #336	C₂²×C₇	semidirect
330. C₂²×C₇	#444	semidirect
385. Q₁₆	C₇×C₂²⋊C₄	semidirect
389. SD₁₆	C₇×C₂²⋊C₄	semidirect
392. D₈	C₇×C₂²⋊C₄	semidirect
476. C₇	#22452	direct (N × H)
492. C₂²	C₇×#444	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×#135	2
C₂×C₇×#444	2
C₇×#2880	2
C₇×#1975	2
C₇×#1876	2
C₇×#1810	2
C₇×#1789	2
C₇×#1752	2
#22452	7

Subgroups — C7×#22452 #13199668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22452 #13199668