Subgroups — C₇×#36595 #13213811

Order 1792.

2706 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	2	yes	maximal, complemented
2	C₇×#2867	C₂	1	1	yes	maximal, characteristic
3	C₇×#2858	C₂	1	2	yes	maximal, complemented
4	C₇×#2548	C₂	1	2	yes	maximal, complemented
5	C₇×#2548	C₂	1	4	yes	maximal, complemented
6	C₇×#2544	C₂	1	4	yes	maximal, complemented
7	C₇×#2445	C₂	1	8	yes	maximal, complemented
8	C₇×#2366	C₂	1	4	yes	maximal, complemented
9	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₇×#127	C₂	1	2	yes	maximal, complemented
11	C₄²×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#559	—	2	16	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#127	C₂²	1	2	yes	—
15	C₂×C₇×#127	C₂²	1	4	yes	—
16	C₂×C₇×#127	C₂²	1	2	yes	—
17	C₂×C₇×#127	C₂²	1	4	yes	—
18	C₂×C₇×#127	C₂²	1	2	yes	—
19	C₂×C₇×#124	C₂²	1	4	yes	—
20	C₂×C₇×#124	C₂²	1	4	yes	—
21	C₂×C₇×#124	C₂²	1	4	yes	—
22	C₂×C₇×#123	C₂²	1	8	yes	—
23	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
24	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
27	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
28	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
29	C₇×#394	C₂²	1	8	yes	—
30	C₇×#394	C₂²	1	16	yes	—
31	C₇×#391	C₂²	1	2	yes	—
32	C₇×#390	C₂²	1	8	yes	—
33	C₇×#390	C₂²	1	8	yes	—
34	C₇×#390	C₂²	1	8	yes	—
35	C₇×#390	C₂²	1	4	yes	—
36	C₇×#390	C₂²	1	8	yes	—
37	C₇×#389	C₂²	1	4	yes	—
38	C₇×#386	C₂²	1	16	yes	—
39	C₇×#384	C₂²	1	1	yes	characteristic
40	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
41	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
42	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
44	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
45	C₄³×C₇	C₂²	1	2	yes	—
46	C₄³×C₇	C₂²	1	1	yes	characteristic
47	#36595	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	C₂³	1	2	yes	—
49	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂³	1	4	yes	—
51	C₂²×C₇×D₄	C₂³	1	4	yes	—
52	C₂²×C₇×D₄	C₂³	1	8	yes	—
53	C₂²×C₇×D₄	C₂³	1	8	yes	—
54	C₂²×C₇×D₄	C₂³	1	4	yes	—
55	C₂³×C₄×C₇	C₂³	1	8	yes	—
56	C₇×C₄⋊Q₈	—	2	4	no	—
57	C₇×#127	—	2	8	no	—
58	C₇×#127	—	2	16	no	—
59	C₇×#127	—	2	8	no	—
60	C₇×#127	—	4	8	no	—
61	C₇×#127	—	4	4	no	—
62	C₇×#124	—	2	16	no	—
63	C₇×#124	—	2	16	no	—
64	C₇×#124	—	4	8	no	—
65	C₇×#123	—	2	32	no	—
66	C₄×C₇×Q₈	—	2	8	no	—
67	C₄×C₇×Q₈	—	2	8	no	—
68	C₄×C₇×Q₈	D₄	1	8	yes	complemented
69	C₄×C₇×D₄	—	2	16	no	—
70	C₄×C₇×D₄	—	2	16	no	—
71	C₄×C₇×D₄	—	4	16	no	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
82	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
83	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
84	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
85	C₂×C₄²×C₇	C₂³	1	4	yes	—
86	C₂×C₄²×C₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₇	C₂³	1	4	yes	—
90	C₂×C₄²×C₇	C₂³	1	4	yes	—
91	C₂×C₄²×C₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂³	1	2	yes	—
95	C₇×#95	C₂³	1	4	yes	—
96	C₇×#95	C₂³	1	2	yes	—
97	C₇×#95	C₂³	1	8	yes	—
98	C₂×#559	C₂×C₇	1	2	yes	complemented
99	#2867	C₂×C₇	1	1	yes	characteristic
100	#2858	C₂×C₇	1	2	yes	complemented
101	#2548	C₂×C₇	1	2	yes	complemented
102	#2548	C₂×C₇	1	4	yes	complemented
103	#2544	C₂×C₇	1	4	yes	complemented
104	#2445	C₂×C₇	1	8	yes	complemented
105	#2366	C₂×C₇	1	4	yes	complemented
106	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
107	C₄×#127	C₂×C₇	1	2	yes	complemented
108	C₄²×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
109	C₂⁴×C₇	C₂⁴	1	8	yes	—
110	C₂×C₇×Q₈	—	2	4	no	—
111	C₂×C₇×Q₈	—	2	4	no	—
112	C₂×C₇×Q₈	—	2	4	no	—
113	C₂×C₇×Q₈	—	2	4	no	—
114	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
115	C₂×C₇×D₄	—	2	8	no	—
116	C₂×C₇×D₄	—	2	8	no	—
117	C₂×C₇×D₄	—	2	8	no	—
118	C₂×C₇×D₄	—	2	16	no	—
119	C₂×C₇×D₄	—	2	8	no	—
120	C₂×C₇×D₄	—	2	16	no	—
121	C₂×C₇×D₄	—	2	16	no	—
122	C₂×C₇×D₄	—	2	16	no	—
123	C₂×C₇×D₄	—	2	16	no	—
124	C₂×C₇×D₄	—	2	8	no	—
125	C₂×C₇×D₄	—	4	8	no	—
126	C₂×C₇×D₄	—	4	8	no	—
127	C₂×C₇×D₄	—	4	8	no	—
128	C₂²×C₄×C₇	—	2	16	no	—
129	C₂²×C₄×C₇	—	4	16	no	—
130	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
140	C₇×C₄⋊C₄	—	2	4	no	—
141	C₇×C₄⋊C₄	—	2	8	no	—
142	C₇×C₄⋊C₄	—	2	8	no	—
143	C₇×C₄⋊C₄	—	2	4	no	—
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	8	no	—
146	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
147	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
148	C₇×C₂²⋊C₄	—	2	16	no	—
149	C₇×C₂²⋊C₄	—	2	16	no	—
150	C₇×C₂²⋊C₄	—	2	16	no	—
151	C₇×C₂²⋊C₄	—	4	16	no	—
152	C₇×C₂²⋊C₄	—	4	16	no	—
153	C₄²×C₇	—	2	8	no	—
154	C₄²×C₇	—	2	8	no	—
155	C₄²×C₇	—	2	8	no	—
156	C₄²×C₇	—	2	4	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	4	no	—
159	C₄²×C₇	C₂×D₄	1	8	yes	—
160	C₄²×C₇	C₂×D₄	1	4	yes	—
161	C₄²×C₇	#41	1	8	yes	—
162	C₄²×C₇	#41	1	4	yes	—
163	#559	—	2	16	no	—
164	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×#127	C₂²×C₇	1	2	yes	—
166	C₂×#127	C₂²×C₇	1	4	yes	—
167	C₂×#127	C₂²×C₇	1	2	yes	—
168	C₂×#127	C₂²×C₇	1	4	yes	—
169	C₂×#127	C₂²×C₇	1	2	yes	—
170	C₂×#124	C₂²×C₇	1	4	yes	—
171	C₂×#124	C₂²×C₇	1	4	yes	—
172	C₂×#124	C₂²×C₇	1	4	yes	—
173	C₂×#123	C₂²×C₇	1	8	yes	—
174	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
175	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
176	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
178	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
179	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
180	#394	C₂²×C₇	1	8	yes	—
181	#394	C₂²×C₇	1	16	yes	—
182	#391	C₂²×C₇	1	2	yes	—
183	#390	C₂²×C₇	1	8	yes	—
184	#390	C₂²×C₇	1	4	yes	—
185	#390	C₂²×C₇	1	8	yes	—
186	#390	C₂²×C₇	1	8	yes	—
187	#390	C₂²×C₇	1	8	yes	—
188	#389	C₂²×C₇	1	4	yes	—
189	#386	C₂²×C₇	1	16	yes	—
190	#384	C₂²×C₇	1	1	yes	characteristic
191	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
192	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
194	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
195	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
196	C₄³	C₂²×C₇	1	2	yes	—
197	C₄³	C₂²×C₇	1	1	yes	characteristic
198	C₂³×C₇	—	2	8	no	—
199	C₂³×C₇	—	2	16	no	—
200	C₂³×C₇	—	2	8	no	—
201	C₂³×C₇	—	2	8	no	—
202	C₂³×C₇	—	2	16	no	—
203	C₂³×C₇	C₂⁵	1	1	yes	characteristic
204	C₇×Q₈	—	2	8	no	—
205	C₇×Q₈	—	4	8	no	—
206	C₇×D₄	—	4	16	no	—
207	C₇×D₄	—	4	16	no	—
208	C₇×D₄	—	4	32	no	—
209	C₇×D₄	—	8	8	no	—
210	C₇×D₄	—	8	16	no	—
211	C₂×C₄×C₇	—	2	4	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	2	2	no	—
216	C₂×C₄×C₇	—	2	4	no	—
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	4	no	—
219	C₂×C₄×C₇	—	2	4	no	—
220	C₂×C₄×C₇	—	2	4	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	2	8	no	—
224	C₂×C₄×C₇	—	8	16	no	—
225	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₇	C₂×#41	1	4	yes	—
231	C₂×C₄×C₇	C₂×#41	1	4	yes	—
232	C₂×C₄×C₇	C₂×#41	1	2	yes	—
233	C₂×C₄×C₇	C₂×#41	1	4	yes	—
234	C₂×C₄×C₇	C₂×#41	1	4	yes	—
235	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
236	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
237	C₂²×Q₈	C₂³×C₇	1	2	yes	—
238	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
239	C₂²×D₄	C₂³×C₇	1	4	yes	—
240	C₂²×D₄	C₂³×C₇	1	4	yes	—
241	C₂²×D₄	C₂³×C₇	1	8	yes	—
242	C₂²×D₄	C₂³×C₇	1	4	yes	—
243	C₂²×D₄	C₂³×C₇	1	8	yes	—
244	C₂³×C₄	C₂³×C₇	1	8	yes	—
245	C₄⋊Q₈	—	2	4	no	—
246	#127	—	2	8	no	—
247	#127	—	2	16	no	—
248	#127	—	2	8	no	—
249	#127	—	4	8	no	—
250	#127	—	4	4	no	—
251	#124	—	2	16	no	—
252	#124	—	2	16	no	—
253	#124	—	4	8	no	—
254	#123	—	2	32	no	—
255	C₄×Q₈	—	2	8	no	—
256	C₄×Q₈	—	2	8	no	—
257	C₄×Q₈	C₇×D₄	1	8	yes	complemented
258	C₄×D₄	—	2	16	no	—
259	C₄×D₄	—	2	16	no	—
260	C₄×D₄	—	4	16	no	—
261	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
267	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
274	C₂×C₄²	C₂³×C₇	1	4	yes	—
275	C₂×C₄²	C₂³×C₇	1	4	yes	—
276	C₂×C₄²	C₂³×C₇	1	4	yes	—
277	C₂×C₄²	C₂³×C₇	1	2	yes	—
278	C₂×C₄²	C₂³×C₇	1	2	yes	—
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₇	1	2	yes	—
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₇	1	2	yes	—
283	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
284	#95	C₂³×C₇	1	4	yes	—
285	#95	C₂³×C₇	1	2	yes	—
286	#95	C₂³×C₇	1	8	yes	—
287	C₂²×C₇	—	4	8	no	—
288	C₂²×C₇	—	4	8	no	—
289	C₂²×C₇	—	4	16	no	—
290	C₂²×C₇	—	4	8	no	—
291	C₂²×C₇	—	4	16	no	—
292	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
293	C₂²×C₇	C₂²×#41	1	2	yes	—
294	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
295	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂²×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
297	C₄×C₇	—	2	4	no	—
298	C₄×C₇	—	2	4	no	—
299	C₄×C₇	—	2	2	no	—
300	C₄×C₇	—	2	4	no	—
301	C₄×C₇	—	4	4	no	—
302	C₄×C₇	—	4	4	no	—
303	C₄×C₇	—	4	4	no	—
304	C₄×C₇	#532	1	4	yes	—
305	C₄×C₇	#550	1	4	yes	—
306	C₄×C₇	#559	1	8	yes	complemented
307	C₂⁴	C₂⁴×C₇	1	8	yes	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	16	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	16	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	16	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	4	8	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂²×C₄	—	2	16	no	—
327	C₂²×C₄	—	4	16	no	—
328	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
334	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
345	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
346	C₂²⋊C₄	—	2	16	no	—
347	C₂²⋊C₄	—	2	16	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	4	16	no	—
350	C₂²⋊C₄	—	4	16	no	—
351	C₄²	—	2	8	no	—
352	C₄²	—	2	8	no	—
353	C₄²	—	2	8	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	4	no	—
357	C₄²	C₂×C₇×D₄	1	8	yes	—
358	C₄²	C₂×C₇×D₄	1	4	yes	—
359	C₄²	C₇×#41	1	8	yes	—
360	C₄²	C₇×#41	1	4	yes	—
361	C₂×C₇	—	8	8	no	—
362	C₂×C₇	C₂×#532	1	1	yes	characteristic
363	C₂×C₇	C₂×#550	1	1	yes	characteristic
364	C₂×C₇	C₂×#559	1	2	yes	—
365	C₂×C₇	#3498	1	1	yes	characteristic
366	C₂×C₇	#3508	1	2	yes	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	16	no	—
369	C₂³	—	2	8	no	—
370	C₂³	—	2	8	no	—
371	C₂³	—	2	16	no	—
372	C₂³	C₂⁵×C₇	1	1	yes	characteristic
373	Q₈	—	2	8	no	—
374	Q₈	—	4	8	no	—
375	D₄	—	4	16	no	—
376	D₄	—	4	16	no	—
377	D₄	—	4	32	no	—
378	D₄	—	8	8	no	—
379	D₄	—	8	16	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	8	16	no	—
394	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
395	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
396	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
397	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
398	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
399	C₂×C₄	C₂×C₇×#41	1	4	yes	—
400	C₂×C₄	C₂×C₇×#41	1	4	yes	—
401	C₂×C₄	C₂×C₇×#41	1	2	yes	—
402	C₂×C₄	C₂×C₇×#41	1	4	yes	—
403	C₂×C₄	C₂×C₇×#41	1	4	yes	—
404	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
405	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
406	C₇	#36595	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	4	8	no	—
408	C₂²	—	4	8	no	—
409	C₂²	—	4	16	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	4	16	no	—
412	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
413	C₂²	C₂²×C₇×#41	1	2	yes	—
414	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
415	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	4	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	4	no	—
423	C₄	—	4	4	no	—
424	C₄	C₇×#532	1	4	yes	—
425	C₄	C₇×#550	1	4	yes	—
426	C₄	C₇×#559	1	8	yes	complemented
427	C₂	—	8	8	no	—
428	C₂	C₂×C₇×#532	1	1	yes	characteristic
429	C₂	C₂×C₇×#550	1	1	yes	characteristic
430	C₂	C₂×C₇×#559	1	2	yes	—
431	C₂	C₇×#3498	1	1	yes	characteristic
432	C₂	C₇×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₇×#2867	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#559	C₂	semidirect
3. C₇×#2858	C₂	semidirect
4. C₇×#2548	C₂	semidirect
5. C₇×#2548	C₂	semidirect
6. C₇×#2544	C₂	semidirect
7. C₇×#2445	C₂	semidirect
8. C₇×#2366	C₂	semidirect
9. C₄×C₇×C₄⋊Q₈	C₂	semidirect
10. C₄×C₇×#127	C₂	semidirect
11. C₄²×C₇×Q₈	C₂	semidirect
47. #36595	C₇	direct (N × H)
68. C₄×C₇×Q₈	D₄	semidirect
98. C₂×#559	C₂×C₇	semidirect
100. #2858	C₂×C₇	semidirect
101. #2548	C₂×C₇	semidirect
102. #2548	C₂×C₇	semidirect
103. #2544	C₂×C₇	semidirect
104. #2445	C₂×C₇	semidirect
105. #2366	C₂×C₇	semidirect
106. C₄×C₄⋊Q₈	C₂×C₇	semidirect
107. C₄×#127	C₂×C₇	semidirect
108. C₄²×Q₈	C₂×C₇	semidirect
257. C₄×Q₈	C₇×D₄	semidirect
306. C₄×C₇	#559	semidirect
406. C₇	#36595	direct (N × H)
426. C₄	C₇×#559	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#559	2
C₇×#2867	2
C₇×#2858	2
C₇×#2548	2
C₇×#2544	2
C₇×#2445	2
C₇×#2366	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄²×C₇×Q₈	2
#36595	7

Subgroups — C7×#36595 #13213811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36595 #13213811