Subgroups — C₂×C₇×#3058 #13237662

Order 1792.

3062 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#535	C₂	1	2	yes	maximal, complemented
4	C₇×#3058	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#469	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#466	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#418	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
10	C₂³×C₇×D₄	C₂²	1	2	yes	—
11	C₂²×C₇×D₈	—	2	8	no	—
12	C₂²×C₇×D₈	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	2	yes	—
14	C₂²×C₇×D₈	C₂²	1	8	yes	complemented
15	C₂×C₇×#131	—	2	8	no	—
16	C₂×C₇×#131	C₂²	1	8	yes	complemented
17	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₇×M₁₆	C₂²	1	2	yes	complemented
19	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
20	C₂³×C₇×C₈	C₂²	1	2	yes	complemented
21	C₇×#535	—	2	8	no	—
22	C₇×#535	C₂²	1	16	yes	complemented
23	C₂×C₇×#127	—	2	2	no	—
24	C₂×C₇×#124	—	2	2	no	—
25	C₂×C₇×#121	C₂²	1	8	yes	complemented
26	C₂×C₇×#120	—	2	4	no	—
27	C₂×C₇×#117	C₂²	1	2	yes	—
28	C₇×#469	C₂²	1	32	yes	complemented
29	C₇×#466	C₂²	1	32	yes	complemented
30	C₇×#427	C₂²	1	8	yes	complemented
31	C₂×C₇×#107	C₂²	1	2	yes	complemented
32	C₂×C₇×#106	C₂²	1	2	yes	complemented
33	C₇×#418	C₂²	1	16	yes	complemented
34	C₂×C₇×#102	C₂²	1	8	yes	complemented
35	C₂×#3058	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂⁵×C₇	—	2	2	no	—
37	C₂×C₇×#41	—	2	4	no	—
38	C₂×C₇×#41	—	2	4	no	—
39	C₂×C₇×#41	D₄	1	4	yes	—
40	C₂×C₇×#41	C₂³	1	4	yes	—
41	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
42	C₂²×C₇×D₄	—	2	8	no	—
43	C₂²×C₇×D₄	—	2	8	no	—
44	C₂²×C₇×D₄	—	2	2	no	—
45	C₂²×C₇×D₄	—	2	4	no	—
46	C₂²×C₇×D₄	—	2	8	no	—
47	C₂²×C₇×D₄	D₄	1	2	yes	—
48	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
49	C₂²×C₇×D₄	C₂³	1	4	yes	—
50	C₂²×C₇×D₄	C₂³	1	8	yes	—
51	C₂³×C₄×C₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₂×C₇×D₈	—	2	8	no	—
54	C₂×C₇×D₈	—	2	8	no	—
55	C₂×C₇×D₈	—	2	32	no	—
56	C₂×C₇×D₈	C₂³	1	8	yes	—
57	C₂×C₇×D₈	C₂³	1	8	yes	—
58	C₇×#131	—	2	32	no	—
59	C₂×C₇×M₁₆	—	2	4	no	—
60	C₂×C₇×M₁₆	—	2	8	no	—
61	C₂×C₇×M₁₆	C₂³	1	4	yes	—
62	C₂×C₇×M₁₆	C₂³	1	8	yes	complemented
63	C₂²×C₇×C₈	—	2	8	no	—
64	C₂²×C₇×C₈	D₄	1	8	yes	complemented
65	C₂²×C₇×C₈	C₂³	1	2	yes	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₇×C₈	C₂³	1	4	yes	—
69	C₂²×C₇×C₈	C₂³	1	8	yes	complemented
70	C₇×#127	—	2	16	no	—
71	C₇×#124	—	2	16	no	—
72	C₇×#121	—	2	16	no	—
73	C₇×#121	C₂³	1	32	yes	complemented
74	C₇×#120	—	2	32	no	—
75	C₇×#117	—	2	4	no	—
76	C₇×#117	C₂³	1	8	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
80	C₂×C₄²×C₇	—	2	2	no	—
81	C₇×#107	C₂³	1	8	yes	complemented
82	C₇×#106	C₂³	1	8	yes	complemented
83	C₇×#102	C₂³	1	32	yes	complemented
84	C₂³×D₈	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂²×#131	C₂×C₇	1	1	yes	characteristic, complemented
86	C₂×#535	C₂×C₇	1	2	yes	complemented
87	#3058	C₂×C₇	1	16	yes	direct product factor
88	C₂×#469	C₂×C₇	1	4	yes	complemented
89	C₂×#466	C₂×C₇	1	4	yes	complemented
90	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×#418	C₂×C₇	1	2	yes	complemented
92	C₂⁴×C₇	—	2	4	no	—
93	C₂⁴×C₇	—	2	8	no	—
94	C₂⁴×C₇	—	4	8	no	—
95	C₂⁴×C₇	—	8	8	no	—
96	C₂⁴×C₇	C₂×D₄	1	2	yes	—
97	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
98	C₇×#41	—	2	16	no	—
99	C₇×#41	—	2	8	no	—
100	C₇×#41	—	2	8	no	—
101	C₂×C₇×Q₈	—	2	4	no	—
102	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
103	C₂×C₇×D₄	—	2	8	no	—
104	C₂×C₇×D₄	—	2	32	no	—
105	C₂×C₇×D₄	—	2	4	no	—
106	C₂×C₇×D₄	—	2	8	no	—
107	C₂×C₇×D₄	—	2	16	no	—
108	C₂×C₇×D₄	—	2	4	no	—
109	C₂×C₇×D₄	—	2	8	no	—
110	C₂×C₇×D₄	—	2	8	no	—
111	C₂×C₇×D₄	—	2	16	no	—
112	C₂×C₇×D₄	—	4	8	no	—
113	C₂×C₇×D₄	—	4	16	no	—
114	C₂×C₇×D₄	—	8	16	no	—
115	C₂×C₇×D₄	C₂×D₄	1	8	yes	—
116	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
117	C₂×C₇×D₄	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	4	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₇	#41	1	4	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
130	C₇×D₈	—	2	16	no	—
131	C₇×D₈	—	2	16	no	—
132	C₇×M₁₆	—	2	8	no	—
133	C₇×M₁₆	—	2	16	no	—
134	C₂×C₇×C₈	—	2	4	no	—
135	C₂×C₇×C₈	—	2	16	no	—
136	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
137	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
138	C₂×C₇×C₈	C₂×D₄	1	16	yes	complemented
139	C₂×C₇×C₈	C₂⁴	1	4	yes	—
140	C₂×C₇×C₈	C₂⁴	1	2	yes	—
141	C₂×C₇×C₈	C₂⁴	1	2	yes	—
142	C₇×C₄⋊C₄	—	2	4	no	—
143	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
144	C₇×C₂²⋊C₄	—	2	8	no	—
145	C₇×C₂²⋊C₄	—	2	32	no	—
146	C₄²×C₇	—	2	8	no	—
147	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
148	C₂³×D₄	C₂²×C₇	1	2	yes	—
149	C₂²×D₈	—	2	8	no	—
150	C₂²×D₈	C₂²×C₇	1	2	yes	—
151	C₂²×D₈	C₂²×C₇	1	2	yes	—
152	C₂²×D₈	C₂²×C₇	1	8	yes	complemented
153	C₂×#131	—	2	8	no	—
154	C₂×#131	C₂²×C₇	1	8	yes	complemented
155	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
156	C₂²×M₁₆	C₂²×C₇	1	2	yes	complemented
157	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂³×C₈	C₂²×C₇	1	2	yes	complemented
159	#535	—	2	8	no	—
160	#535	C₂²×C₇	1	16	yes	complemented
161	C₂×#127	—	2	2	no	—
162	C₂×#124	—	2	2	no	—
163	C₂×#121	C₂²×C₇	1	8	yes	complemented
164	C₂×#120	—	2	4	no	—
165	C₂×#117	C₂²×C₇	1	2	yes	—
166	#469	C₂²×C₇	1	32	yes	complemented
167	#466	C₂²×C₇	1	32	yes	complemented
168	#427	C₂²×C₇	1	8	yes	complemented
169	C₂×#107	C₂²×C₇	1	2	yes	complemented
170	C₂×#106	C₂²×C₇	1	2	yes	complemented
171	#418	C₂²×C₇	1	16	yes	complemented
172	C₂×#102	C₂²×C₇	1	8	yes	complemented
173	C₂³×C₇	—	2	4	no	—
174	C₂³×C₇	—	2	4	no	—
175	C₂³×C₇	—	2	8	no	—
176	C₂³×C₇	—	2	8	no	—
177	C₂³×C₇	—	4	16	no	—
178	C₂³×C₇	—	4	8	no	—
179	C₂³×C₇	—	4	16	no	—
180	C₂³×C₇	—	8	16	no	—
181	C₂³×C₇	—	8	32	no	—
182	C₂³×C₇	#121	1	4	yes	—
183	C₂³×C₇	C₂²×D₄	1	4	yes	—
184	C₂³×C₇	C₂²×D₄	1	2	yes	—
185	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₇×Q₈	—	2	8	no	—
187	C₇×D₄	—	2	16	no	—
188	C₇×D₄	—	2	8	no	—
189	C₇×D₄	—	2	8	no	—
190	C₇×D₄	—	2	8	no	—
191	C₇×D₄	—	4	8	no	—
192	C₇×D₄	—	4	16	no	—
193	C₇×D₄	—	8	32	no	—
194	C₂×C₄×C₇	—	2	4	no	—
195	C₂×C₄×C₇	—	2	8	no	—
196	C₂×C₄×C₇	—	2	4	no	—
197	C₂×C₄×C₇	—	2	4	no	—
198	C₂×C₄×C₇	—	2	8	no	—
199	C₂×C₄×C₇	—	4	8	no	—
200	C₂×C₄×C₇	#121	1	4	yes	—
201	C₂×C₄×C₇	#121	1	8	yes	—
202	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
207	C₂×C₄×C₇	C₂×#41	1	2	yes	—
208	C₂×C₄×C₇	C₂×#41	1	4	yes	—
209	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
210	C₇×C₈	—	2	4	no	—
211	C₇×C₈	C₂²×D₄	1	4	yes	—
212	C₇×C₈	C₂²×D₄	1	4	yes	—
213	C₂⁵	—	2	2	no	—
214	C₂×#41	—	2	4	no	—
215	C₂×#41	—	2	4	no	—
216	C₂×#41	C₇×D₄	1	4	yes	—
217	C₂×#41	C₂³×C₇	1	4	yes	—
218	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
219	C₂²×D₄	—	2	8	no	—
220	C₂²×D₄	—	2	8	no	—
221	C₂²×D₄	—	2	2	no	—
222	C₂²×D₄	—	2	4	no	—
223	C₂²×D₄	—	2	8	no	—
224	C₂²×D₄	C₇×D₄	1	2	yes	—
225	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
226	C₂²×D₄	C₂³×C₇	1	4	yes	—
227	C₂²×D₄	C₂³×C₇	1	8	yes	—
228	C₂³×C₄	C₂³×C₇	1	2	yes	—
229	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
230	C₂×D₈	—	2	8	no	—
231	C₂×D₈	—	2	8	no	—
232	C₂×D₈	—	2	32	no	—
233	C₂×D₈	C₂³×C₇	1	8	yes	—
234	C₂×D₈	C₂³×C₇	1	8	yes	—
235	#131	—	2	32	no	—
236	C₂×M₁₆	—	2	4	no	—
237	C₂×M₁₆	—	2	8	no	—
238	C₂×M₁₆	C₂³×C₇	1	4	yes	—
239	C₂×M₁₆	C₂³×C₇	1	8	yes	complemented
240	C₂²×C₈	—	2	8	no	—
241	C₂²×C₈	C₇×D₄	1	8	yes	complemented
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₇	1	4	yes	—
246	C₂²×C₈	C₂³×C₇	1	8	yes	complemented
247	#127	—	2	16	no	—
248	#124	—	2	16	no	—
249	#121	—	2	16	no	—
250	#121	C₂³×C₇	1	32	yes	complemented
251	#120	—	2	32	no	—
252	#117	—	2	4	no	—
253	#117	C₂³×C₇	1	8	yes	—
254	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	8	no	—
257	C₂×C₄²	—	2	2	no	—
258	#107	C₂³×C₇	1	8	yes	complemented
259	#106	C₂³×C₇	1	8	yes	complemented
260	#102	C₂³×C₇	1	32	yes	complemented
261	C₂²×C₇	—	2	8	no	—
262	C₂²×C₇	—	2	4	no	—
263	C₂²×C₇	—	2	4	no	—
264	C₂²×C₇	—	2	8	no	—
265	C₂²×C₇	—	4	8	no	—
266	C₂²×C₇	—	4	8	no	—
267	C₂²×C₇	—	4	16	no	—
268	C₂²×C₇	—	8	32	no	—
269	C₂²×C₇	—	8	16	no	—
270	C₂²×C₇	C₂×#121	1	4	yes	—
271	C₂²×C₇	C₂×#121	1	2	yes	—
272	C₂²×C₇	#576	1	4	yes	—
273	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
274	C₄×C₇	—	2	4	no	—
275	C₄×C₇	—	4	8	no	—
276	C₄×C₇	C₂×#121	1	2	yes	—
277	C₄×C₇	C₂×#121	1	4	yes	—
278	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
279	C₄×C₇	C₂²×#41	1	1	yes	characteristic
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	4	8	no	—
283	C₂⁴	—	8	8	no	—
284	C₂⁴	C₂×C₇×D₄	1	2	yes	—
285	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
286	#41	—	2	16	no	—
287	#41	—	2	8	no	—
288	#41	—	2	8	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	32	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	8	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	16	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	4	16	no	—
302	C₂×D₄	—	8	16	no	—
303	C₂×D₄	C₂×C₇×D₄	1	8	yes	—
304	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
305	C₂×D₄	C₂⁴×C₇	1	8	yes	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
310	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
311	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
313	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
314	C₂²×C₄	C₇×#41	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
316	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
318	D₈	—	2	16	no	—
319	D₈	—	2	16	no	—
320	M₁₆	—	2	8	no	—
321	M₁₆	—	2	16	no	—
322	C₂×C₈	—	2	4	no	—
323	C₂×C₈	—	2	16	no	—
324	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
325	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
326	C₂×C₈	C₂×C₇×D₄	1	16	yes	complemented
327	C₂×C₈	C₂⁴×C₇	1	4	yes	—
328	C₂×C₈	C₂⁴×C₇	1	2	yes	—
329	C₂×C₈	C₂⁴×C₇	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
332	C₂²⋊C₄	—	2	8	no	—
333	C₂²⋊C₄	—	2	32	no	—
334	C₄²	—	2	8	no	—
335	C₂×C₇	—	2	4	no	—
336	C₂×C₇	—	4	4	no	—
337	C₂×C₇	—	8	8	no	—
338	C₂×C₇	#3058	1	4	yes	direct product factor
339	C₂×C₇	C₂²×#121	1	1	yes	characteristic
340	C₂×C₇	C₂×#576	1	2	yes	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	8	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	4	16	no	—
346	C₂³	—	4	8	no	—
347	C₂³	—	4	16	no	—
348	C₂³	—	8	16	no	—
349	C₂³	—	8	32	no	—
350	C₂³	C₇×#121	1	4	yes	—
351	C₂³	C₂²×C₇×D₄	1	4	yes	—
352	C₂³	C₂²×C₇×D₄	1	2	yes	—
353	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
354	Q₈	—	2	8	no	—
355	D₄	—	2	16	no	—
356	D₄	—	2	8	no	—
357	D₄	—	2	8	no	—
358	D₄	—	2	8	no	—
359	D₄	—	4	8	no	—
360	D₄	—	4	16	no	—
361	D₄	—	8	32	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	8	no	—
368	C₂×C₄	C₇×#121	1	4	yes	—
369	C₂×C₄	C₇×#121	1	8	yes	—
370	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
371	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
372	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
373	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
374	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
375	C₂×C₄	C₂×C₇×#41	1	2	yes	—
376	C₂×C₄	C₂×C₇×#41	1	4	yes	—
377	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
378	C₈	—	2	4	no	—
379	C₈	C₂²×C₇×D₄	1	4	yes	—
380	C₈	C₂²×C₇×D₄	1	4	yes	—
381	C₇	C₂×#3058	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	4	no	—
383	C₂²	—	2	8	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	8	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	8	32	no	—
390	C₂²	—	8	16	no	—
391	C₂²	C₂×C₇×#121	1	4	yes	—
392	C₂²	C₂×C₇×#121	1	2	yes	—
393	C₂²	C₇×#576	1	4	yes	—
394	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
395	C₄	—	2	4	no	—
396	C₄	—	4	8	no	—
397	C₄	C₂×C₇×#121	1	2	yes	—
398	C₄	C₂×C₇×#121	1	4	yes	—
399	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
400	C₄	C₂²×C₇×#41	1	1	yes	characteristic
401	C₂	—	2	4	no	—
402	C₂	—	4	4	no	—
403	C₂	—	8	8	no	—
404	C₂	C₇×#3058	1	4	yes	direct product factor
405	C₂	C₂²×C₇×#121	1	1	yes	characteristic
406	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 ◁ C₂²×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×D₈	C₂	semidirect
2. C₂²×C₇×#131	C₂	semidirect
3. C₂×C₇×#535	C₂	semidirect
4. C₇×#3058	C₂	direct (N × H)
5. C₂×C₇×#469	C₂	semidirect
6. C₂×C₇×#466	C₂	semidirect
7. C₂×C₇×#427	C₂	semidirect
8. C₂×C₇×#418	C₂	semidirect
14. C₂²×C₇×D₈	C₂²	semidirect
16. C₂×C₇×#131	C₂²	semidirect
18. C₂²×C₇×M₁₆	C₂²	semidirect
20. C₂³×C₇×C₈	C₂²	semidirect
22. C₇×#535	C₂²	semidirect
25. C₂×C₇×#121	C₂²	semidirect
28. C₇×#469	C₂²	semidirect
29. C₇×#466	C₂²	semidirect
30. C₇×#427	C₂²	semidirect
31. C₂×C₇×#107	C₂²	semidirect
32. C₂×C₇×#106	C₂²	semidirect
33. C₇×#418	C₂²	semidirect
34. C₂×C₇×#102	C₂²	semidirect
35. C₂×#3058	C₇	direct (N × H)
62. C₂×C₇×M₁₆	C₂³	semidirect
64. C₂²×C₇×C₈	D₄	semidirect
69. C₂²×C₇×C₈	C₂³	semidirect
73. C₇×#121	C₂³	semidirect
81. C₇×#107	C₂³	semidirect
82. C₇×#106	C₂³	semidirect
83. C₇×#102	C₂³	semidirect
84. C₂³×D₈	C₂×C₇	semidirect
85. C₂²×#131	C₂×C₇	semidirect
86. C₂×#535	C₂×C₇	semidirect
87. #3058	C₂×C₇	direct (N × H)
88. C₂×#469	C₂×C₇	semidirect
89. C₂×#466	C₂×C₇	semidirect
90. C₂×#427	C₂×C₇	semidirect
91. C₂×#418	C₂×C₇	semidirect
138. C₂×C₇×C₈	C₂×D₄	semidirect
152. C₂²×D₈	C₂²×C₇	semidirect
154. C₂×#131	C₂²×C₇	semidirect
156. C₂²×M₁₆	C₂²×C₇	semidirect
158. C₂³×C₈	C₂²×C₇	semidirect
160. #535	C₂²×C₇	semidirect
163. C₂×#121	C₂²×C₇	semidirect
166. #469	C₂²×C₇	semidirect
167. #466	C₂²×C₇	semidirect
168. #427	C₂²×C₇	semidirect
169. C₂×#107	C₂²×C₇	semidirect
170. C₂×#106	C₂²×C₇	semidirect
171. #418	C₂²×C₇	semidirect
172. C₂×#102	C₂²×C₇	semidirect
239. C₂×M₁₆	C₂³×C₇	semidirect
241. C₂²×C₈	C₇×D₄	semidirect
246. C₂²×C₈	C₂³×C₇	semidirect
250. #121	C₂³×C₇	semidirect
258. #107	C₂³×C₇	semidirect
259. #106	C₂³×C₇	semidirect
260. #102	C₂³×C₇	semidirect
326. C₂×C₈	C₂×C₇×D₄	semidirect
338. C₂×C₇	#3058	direct (N × H)
381. C₇	C₂×#3058	direct (N × H)
404. C₂	C₇×#3058	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×D₈	2
C₂²×C₇×#131	2
C₂×C₇×#535	2
C₇×#3058	2
C₂×C₇×#469	2
C₂×C₇×#466	2
C₂×C₇×#427	2
C₂×C₇×#418	2
C₂×#3058	7

Subgroups — C2×C7×#3058 #13237662

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3058 #13237662