Subgroups — C₂×C₇×#3122 #13237767

Order 1792.

2338 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3122	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#447	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₇×D₈	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	2	yes	—
14	C₇×#540	—	2	4	no	—
15	C₇×#540	C₂²	1	8	yes	complemented
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₇×#123	—	2	2	no	—
19	C₂×C₇×#121	—	2	2	no	—
20	C₂×C₇×#121	C₂²	1	2	yes	—
21	C₇×#518	—	2	4	no	—
22	C₇×#518	C₂²	1	8	yes	complemented
23	C₂×C₄×C₇×D₄	—	2	2	no	—
24	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
27	C₂×C₇×#117	C₂²	1	1	yes	characteristic
28	C₂×C₇×#117	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₂²⋊C₄	—	2	2	no	—
30	C₇×#482	C₂²	1	16	yes	complemented
31	C₇×#478	C₂²	1	16	yes	complemented
32	C₇×#459	C₂²	1	16	yes	complemented
33	C₇×#447	C₂²	1	16	yes	complemented
34	C₇×#442	C₂²	1	16	yes	complemented
35	C₄×C₇×D₈	C₂²	1	16	yes	complemented
36	C₇×#433	C₂²	1	8	yes	complemented
37	C₂×C₇×#107	C₂²	1	2	yes	complemented
38	C₂×C₇×#106	C₂²	1	2	yes	complemented
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₇×#102	C₂²	1	2	yes	—
41	C₂×C₇×#102	C₂²	1	2	yes	—
42	C₂×C₇×#102	C₂²	1	2	yes	complemented
43	C₂×C₇×#102	C₂²	1	2	yes	complemented
44	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
47	C₂×#3122	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁵×C₇	—	2	1	no	—
49	C₂²×C₇×D₄	—	2	8	no	—
50	C₂²×C₇×D₄	—	2	2	no	—
51	C₂²×C₇×D₄	—	2	1	no	—
52	C₂²×C₇×D₄	—	2	2	no	—
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	C₂³	1	4	yes	—
55	C₂²×C₇×D₄	C₂³	1	2	yes	—
56	C₂²×C₇×D₄	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	—	2	2	no	—
59	C₂³×C₄×C₇	—	2	2	no	—
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₇×D₈	—	2	8	no	—
62	C₂×C₇×D₈	—	2	8	no	—
63	C₂×C₇×D₈	C₂³	1	8	yes	—
64	C₂×C₇×D₈	C₂³	1	8	yes	—
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₂²×C₇×C₈	C₂³	1	2	yes	—
67	C₇×#127	—	2	2	no	—
68	C₇×#127	C₂³	1	4	yes	complemented
69	C₇×#125	—	2	2	no	—
70	C₇×#125	C₂³	1	4	yes	complemented
71	C₇×#123	—	2	16	no	—
72	C₇×#121	—	2	4	no	—
73	C₇×#121	—	2	16	no	—
74	C₇×#121	C₂³	1	8	yes	—
75	C₄×C₇×D₄	—	2	16	no	—
76	C₄×C₇×D₄	—	2	4	no	—
77	C₄×C₇×D₄	—	2	4	no	—
78	C₄×C₇×D₄	—	2	4	no	—
79	C₄×C₇×D₄	C₂³	1	8	yes	—
80	C₄×C₇×D₄	C₂³	1	8	yes	—
81	C₄×C₇×D₄	C₂³	1	8	yes	complemented
82	C₇×#117	—	2	2	no	—
83	C₇×#117	D₄	1	4	yes	—
84	C₇×#117	C₂³	1	4	yes	—
85	C₇×#117	C₂³	1	4	yes	—
86	C₂×C₇×C₄⋊C₄	—	2	2	no	—
87	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
88	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
96	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
97	C₂×C₄²×C₇	—	2	1	no	—
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₇×#107	C₂³	1	8	yes	complemented
101	C₇×#106	C₂³	1	8	yes	complemented
102	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
103	C₇×#102	C₂³	1	8	yes	—
104	C₇×#102	C₂³	1	8	yes	—
105	C₇×#102	C₂³	1	8	yes	complemented
106	C₇×#102	C₂³	1	8	yes	complemented
107	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₇×#97	C₂³	1	4	yes	complemented
109	C₄×C₇×C₈	C₂³	1	4	yes	complemented
110	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
111	C₂×#518	C₂×C₇	1	1	yes	characteristic, complemented
112	#3122	C₂×C₇	1	16	yes	direct product factor
113	C₂×#482	C₂×C₇	1	2	yes	complemented
114	C₂×#478	C₂×C₇	1	2	yes	complemented
115	C₂×#459	C₂×C₇	1	2	yes	complemented
116	C₂×#447	C₂×C₇	1	2	yes	complemented
117	C₂×#442	C₂×C₇	1	2	yes	complemented
118	C₂×C₄×D₈	C₂×C₇	1	2	yes	complemented
119	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂⁴×C₇	—	2	8	no	—
121	C₂⁴×C₇	—	2	2	no	—
122	C₂⁴×C₇	—	2	4	no	—
123	C₂⁴×C₇	—	2	2	no	—
124	C₂⁴×C₇	—	8	4	no	—
125	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇×D₄	—	2	8	no	—
127	C₂×C₇×D₄	—	2	16	no	—
128	C₂×C₇×D₄	—	2	16	no	—
129	C₂×C₇×D₄	—	2	8	no	—
130	C₂×C₇×D₄	—	2	4	no	—
131	C₂×C₇×D₄	—	2	2	no	—
132	C₂×C₇×D₄	—	2	2	no	—
133	C₂×C₇×D₄	—	2	8	no	—
134	C₂×C₇×D₄	—	2	4	no	—
135	C₂×C₇×D₄	—	2	4	no	—
136	C₂×C₇×D₄	—	2	4	no	—
137	C₂×C₇×D₄	—	8	4	no	—
138	C₂×C₇×D₄	—	8	4	no	—
139	C₂×C₇×D₄	#41	1	8	yes	—
140	C₂×C₇×D₄	C₂⁴	1	4	yes	—
141	C₂×C₇×D₄	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₇	—	2	4	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	2	no	—
145	C₂²×C₄×C₇	—	2	8	no	—
146	C₂²×C₄×C₇	—	2	8	no	—
147	C₂²×C₄×C₇	—	2	8	no	—
148	C₂²×C₄×C₇	—	8	4	no	—
149	C₂²×C₄×C₇	—	8	4	no	—
150	C₂²×C₄×C₇	—	8	4	no	—
151	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
157	C₇×D₈	—	2	16	no	—
158	C₇×D₈	—	2	16	no	—
159	C₂×C₇×C₈	—	2	4	no	—
160	C₂×C₇×C₈	—	2	4	no	—
161	C₂×C₇×C₈	C₂⁴	1	4	yes	—
162	C₂×C₇×C₈	C₂⁴	1	4	yes	—
163	C₇×C₄⋊C₄	—	2	8	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
167	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
168	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
169	C₇×C₂²⋊C₄	—	2	4	no	—
170	C₇×C₂²⋊C₄	—	2	8	no	—
171	C₇×C₂²⋊C₄	—	2	8	no	—
172	C₇×C₂²⋊C₄	—	2	8	no	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
175	C₄²×C₇	—	2	4	no	—
176	C₄²×C₇	C₂×D₄	1	2	yes	—
177	C₄²×C₇	C₂×D₄	1	2	yes	—
178	C₄²×C₇	C₂⁴	1	2	yes	—
179	C₄²×C₇	C₂⁴	1	2	yes	—
180	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
181	C₂²×D₈	C₂²×C₇	1	2	yes	—
182	C₂²×D₈	C₂²×C₇	1	2	yes	—
183	#540	—	2	4	no	—
184	#540	C₂²×C₇	1	8	yes	complemented
185	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
186	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
187	C₂×#123	—	2	2	no	—
188	C₂×#121	—	2	2	no	—
189	C₂×#121	C₂²×C₇	1	2	yes	—
190	#518	—	2	4	no	—
191	#518	C₂²×C₇	1	8	yes	complemented
192	C₂×C₄×D₄	—	2	2	no	—
193	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
194	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
195	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
196	C₂×#117	C₂²×C₇	1	1	yes	characteristic
197	C₂×#117	C₂²×C₇	1	1	yes	characteristic
198	C₂²×C₂²⋊C₄	—	2	2	no	—
199	#482	C₂²×C₇	1	16	yes	complemented
200	#478	C₂²×C₇	1	16	yes	complemented
201	#459	C₂²×C₇	1	16	yes	complemented
202	#447	C₂²×C₇	1	16	yes	complemented
203	#442	C₂²×C₇	1	16	yes	complemented
204	C₄×D₈	C₂²×C₇	1	16	yes	complemented
205	#433	C₂²×C₇	1	8	yes	complemented
206	C₂×#107	C₂²×C₇	1	2	yes	complemented
207	C₂×#106	C₂²×C₇	1	2	yes	complemented
208	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
209	C₂×#102	C₂²×C₇	1	2	yes	—
210	C₂×#102	C₂²×C₇	1	2	yes	—
211	C₂×#102	C₂²×C₇	1	2	yes	complemented
212	C₂×#102	C₂²×C₇	1	2	yes	complemented
213	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
214	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
215	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
216	C₂³×C₇	—	2	16	no	—
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	8	no	—
219	C₂³×C₇	—	2	4	no	—
220	C₂³×C₇	—	2	4	no	—
221	C₂³×C₇	—	2	4	no	—
222	C₂³×C₇	—	4	4	no	—
223	C₂³×C₇	—	4	4	no	—
224	C₂³×C₇	—	4	4	no	—
225	C₂³×C₇	—	4	4	no	—
226	C₂³×C₇	—	4	4	no	—
227	C₂³×C₇	—	8	8	no	—
228	C₂³×C₇	—	8	16	no	—
229	C₂³×C₇	C₂²×D₄	1	2	yes	—
230	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
231	C₇×D₄	—	2	16	no	—
232	C₇×D₄	—	2	8	no	—
233	C₇×D₄	—	2	4	no	—
234	C₇×D₄	—	2	4	no	—
235	C₇×D₄	—	2	4	no	—
236	C₇×D₄	—	4	4	no	—
237	C₇×D₄	—	8	8	no	—
238	C₇×D₄	—	8	8	no	—
239	C₇×D₄	C₂×#41	1	8	yes	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	4	no	—
242	C₂×C₄×C₇	—	2	4	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	4	4	no	—
248	C₂×C₄×C₇	—	4	4	no	—
249	C₂×C₄×C₇	—	8	8	no	—
250	C₂×C₄×C₇	—	8	8	no	—
251	C₂×C₄×C₇	—	8	8	no	—
252	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇	C₂×#41	1	4	yes	—
257	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
258	C₇×C₈	—	2	4	no	—
259	C₇×C₈	—	2	4	no	—
260	C₂⁵	—	2	1	no	—
261	C₂²×D₄	—	2	8	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	C₂³×C₇	1	2	yes	—
267	C₂²×D₄	C₂³×C₇	1	4	yes	—
268	C₂²×D₄	C₂³×C₇	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	—	2	2	no	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
273	C₂×D₈	—	2	8	no	—
274	C₂×D₈	—	2	8	no	—
275	C₂×D₈	C₂³×C₇	1	8	yes	—
276	C₂×D₈	C₂³×C₇	1	8	yes	—
277	C₂²×C₈	C₂³×C₇	1	2	yes	—
278	C₂²×C₈	C₂³×C₇	1	2	yes	—
279	#127	—	2	2	no	—
280	#127	C₂³×C₇	1	4	yes	complemented
281	#125	—	2	2	no	—
282	#125	C₂³×C₇	1	4	yes	complemented
283	#123	—	2	16	no	—
284	#121	—	2	4	no	—
285	#121	—	2	16	no	—
286	#121	C₂³×C₇	1	8	yes	—
287	C₄×D₄	—	2	16	no	—
288	C₄×D₄	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	C₂³×C₇	1	8	yes	—
292	C₄×D₄	C₂³×C₇	1	8	yes	—
293	C₄×D₄	C₂³×C₇	1	8	yes	complemented
294	#117	—	2	2	no	—
295	#117	C₇×D₄	1	4	yes	—
296	#117	C₂³×C₇	1	4	yes	—
297	#117	C₂³×C₇	1	4	yes	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	16	no	—
308	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
312	#107	C₂³×C₇	1	8	yes	complemented
313	#106	C₂³×C₇	1	8	yes	complemented
314	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
315	#102	C₂³×C₇	1	8	yes	—
316	#102	C₂³×C₇	1	8	yes	—
317	#102	C₂³×C₇	1	8	yes	complemented
318	#102	C₂³×C₇	1	8	yes	complemented
319	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
320	#97	C₂³×C₇	1	4	yes	complemented
321	C₄×C₈	C₂³×C₇	1	4	yes	complemented
322	C₂²×C₇	—	2	2	no	—
323	C₂²×C₇	—	2	8	no	—
324	C₂²×C₇	—	2	4	no	—
325	C₂²×C₇	—	4	4	no	—
326	C₂²×C₇	—	4	16	no	—
327	C₂²×C₇	—	4	4	no	—
328	C₂²×C₇	—	4	4	no	—
329	C₂²×C₇	—	4	4	no	—
330	C₂²×C₇	—	4	4	no	—
331	C₂²×C₇	—	4	4	no	—
332	C₂²×C₇	—	8	16	no	—
333	C₂²×C₇	—	8	8	no	—
334	C₂²×C₇	#525	1	2	yes	—
335	C₂²×C₇	#576	1	4	yes	—
336	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₇	—	2	2	no	—
338	C₄×C₇	—	2	4	no	—
339	C₄×C₇	—	2	4	no	—
340	C₄×C₇	—	4	4	no	—
341	C₄×C₇	—	4	4	no	—
342	C₄×C₇	#525	1	2	yes	—
343	C₄×C₇	C₂²×#41	1	2	yes	—
344	C₂⁴	—	2	8	no	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	4	no	—
347	C₂⁴	—	2	2	no	—
348	C₂⁴	—	8	4	no	—
349	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂×D₄	—	2	8	no	—
351	C₂×D₄	—	2	16	no	—
352	C₂×D₄	—	2	16	no	—
353	C₂×D₄	—	2	8	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	8	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	8	4	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	C₇×#41	1	8	yes	—
364	C₂×D₄	C₂⁴×C₇	1	4	yes	—
365	C₂×D₄	C₂⁴×C₇	1	4	yes	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	8	no	—
370	C₂²×C₄	—	2	8	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	8	4	no	—
373	C₂²×C₄	—	8	4	no	—
374	C₂²×C₄	—	8	4	no	—
375	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
377	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
378	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
381	D₈	—	2	16	no	—
382	D₈	—	2	16	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	C₂⁴×C₇	1	4	yes	—
386	C₂×C₈	C₂⁴×C₇	1	4	yes	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
391	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
399	C₄²	—	2	4	no	—
400	C₄²	C₂×C₇×D₄	1	2	yes	—
401	C₄²	C₂×C₇×D₄	1	2	yes	—
402	C₄²	C₂⁴×C₇	1	2	yes	—
403	C₄²	C₂⁴×C₇	1	2	yes	—
404	C₂×C₇	—	4	2	no	—
405	C₂×C₇	—	4	8	no	—
406	C₂×C₇	—	8	4	no	—
407	C₂×C₇	#3122	1	4	yes	direct product factor
408	C₂×C₇	C₂×#525	1	1	yes	characteristic
409	C₂×C₇	C₂×#576	1	2	yes	—
410	C₂³	—	2	16	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	8	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	4	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	8	8	no	—
422	C₂³	—	8	16	no	—
423	C₂³	C₂²×C₇×D₄	1	2	yes	—
424	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
425	D₄	—	2	16	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	2	4	no	—
429	D₄	—	2	8	no	—
430	D₄	—	4	4	no	—
431	D₄	—	8	8	no	—
432	D₄	—	8	8	no	—
433	D₄	C₂×C₇×#41	1	8	yes	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	8	8	no	—
444	C₂×C₄	—	8	8	no	—
445	C₂×C₄	—	8	8	no	—
446	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
447	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
448	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
449	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₇×#41	1	4	yes	—
451	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
452	C₈	—	2	4	no	—
453	C₈	—	2	4	no	—
454	C₇	C₂×#3122	1	1	yes	characteristic, direct product factor, Sylow
455	C₂²	—	2	4	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	8	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	4	16	no	—
462	C₂²	—	4	4	no	—
463	C₂²	—	4	4	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	16	no	—
466	C₂²	—	8	8	no	—
467	C₂²	C₇×#525	1	2	yes	—
468	C₂²	C₇×#576	1	4	yes	—
469	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	2	4	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	4	no	—
475	C₄	C₇×#525	1	2	yes	—
476	C₄	C₂²×C₇×#41	1	2	yes	—
477	C₂	—	4	2	no	—
478	C₂	—	4	8	no	—
479	C₂	—	8	4	no	—
480	C₂	C₇×#3122	1	4	yes	direct product factor
481	C₂	C₂×C₇×#525	1	1	yes	characteristic
482	C₂	C₂×C₇×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#540	C₂	semidirect
2. C₂×C₇×#518	C₂	semidirect
3. C₇×#3122	C₂	direct (N × H)
4. C₂×C₇×#482	C₂	semidirect
5. C₂×C₇×#478	C₂	semidirect
6. C₂×C₇×#459	C₂	semidirect
7. C₂×C₇×#447	C₂	semidirect
8. C₂×C₇×#442	C₂	semidirect
9. C₂×C₄×C₇×D₈	C₂	semidirect
10. C₂×C₇×#433	C₂	semidirect
15. C₇×#540	C₂²	semidirect
16. C₂×C₇×#127	C₂²	semidirect
17. C₂×C₇×#125	C₂²	semidirect
22. C₇×#518	C₂²	semidirect
26. C₂×C₄×C₇×D₄	C₂²	semidirect
30. C₇×#482	C₂²	semidirect
31. C₇×#478	C₂²	semidirect
32. C₇×#459	C₂²	semidirect
33. C₇×#447	C₂²	semidirect
34. C₇×#442	C₂²	semidirect
35. C₄×C₇×D₈	C₂²	semidirect
36. C₇×#433	C₂²	semidirect
37. C₂×C₇×#107	C₂²	semidirect
38. C₂×C₇×#106	C₂²	semidirect
39. C₂×C₇×C₄⋊C₈	C₂²	semidirect
42. C₂×C₇×#102	C₂²	semidirect
43. C₂×C₇×#102	C₂²	semidirect
45. C₂×C₇×#97	C₂²	semidirect
46. C₂×C₄×C₇×C₈	C₂²	semidirect
47. C₂×#3122	C₇	direct (N × H)
68. C₇×#127	C₂³	semidirect
70. C₇×#125	C₂³	semidirect
81. C₄×C₇×D₄	C₂³	semidirect
100. C₇×#107	C₂³	semidirect
101. C₇×#106	C₂³	semidirect
102. C₇×C₄⋊C₈	C₂³	semidirect
105. C₇×#102	C₂³	semidirect
106. C₇×#102	C₂³	semidirect
108. C₇×#97	C₂³	semidirect
109. C₄×C₇×C₈	C₂³	semidirect
110. C₂×#540	C₂×C₇	semidirect
111. C₂×#518	C₂×C₇	semidirect
112. #3122	C₂×C₇	direct (N × H)
113. C₂×#482	C₂×C₇	semidirect
114. C₂×#478	C₂×C₇	semidirect
115. C₂×#459	C₂×C₇	semidirect
116. C₂×#447	C₂×C₇	semidirect
117. C₂×#442	C₂×C₇	semidirect
118. C₂×C₄×D₈	C₂×C₇	semidirect
119. C₂×#433	C₂×C₇	semidirect
184. #540	C₂²×C₇	semidirect
185. C₂×#127	C₂²×C₇	semidirect
186. C₂×#125	C₂²×C₇	semidirect
191. #518	C₂²×C₇	semidirect
195. C₂×C₄×D₄	C₂²×C₇	semidirect
199. #482	C₂²×C₇	semidirect
200. #478	C₂²×C₇	semidirect
201. #459	C₂²×C₇	semidirect
202. #447	C₂²×C₇	semidirect
203. #442	C₂²×C₇	semidirect
204. C₄×D₈	C₂²×C₇	semidirect
205. #433	C₂²×C₇	semidirect
206. C₂×#107	C₂²×C₇	semidirect
207. C₂×#106	C₂²×C₇	semidirect
208. C₂×C₄⋊C₈	C₂²×C₇	semidirect
211. C₂×#102	C₂²×C₇	semidirect
212. C₂×#102	C₂²×C₇	semidirect
214. C₂×#97	C₂²×C₇	semidirect
215. C₂×C₄×C₈	C₂²×C₇	semidirect
280. #127	C₂³×C₇	semidirect
282. #125	C₂³×C₇	semidirect
293. C₄×D₄	C₂³×C₇	semidirect
312. #107	C₂³×C₇	semidirect
313. #106	C₂³×C₇	semidirect
314. C₄⋊C₈	C₂³×C₇	semidirect
317. #102	C₂³×C₇	semidirect
318. #102	C₂³×C₇	semidirect
320. #97	C₂³×C₇	semidirect
321. C₄×C₈	C₂³×C₇	semidirect
407. C₂×C₇	#3122	direct (N × H)
454. C₇	C₂×#3122	direct (N × H)
480. C₂	C₇×#3122	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×#540	2
C₂×C₇×#518	2
C₇×#3122	2
C₂×C₇×#482	2
C₂×C₇×#478	2
C₂×C₇×#459	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#433	2
C₂×#3122	7

Subgroups — C2×C7×#3122 #13237767

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3122 #13237767