Subgroups — C₇×#26040 #13203256

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#474	C₂	1	2	yes	maximal
2	C₇×#2551	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₇×#2086	C₂	1	2	yes	maximal, complemented
5	C₇×#2057	C₂	1	2	yes	maximal, complemented
6	C₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1862	C₂	1	2	yes	maximal
9	C₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×C₇×#102	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×C₄⋊Q₈	—	2	1	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
15	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
16	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
17	C₇×#474	—	2	8	no	—
18	C₂×C₇×#107	C₂²	1	2	yes	—
19	C₂×C₇×#107	C₂²	1	2	yes	—
20	C₂×C₇×#107	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₇×#102	C₂²	1	2	yes	—
24	C₂×C₇×#102	C₂²	1	1	yes	characteristic
25	C₂×C₇×#102	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
27	C₇×#395	—	2	2	no	—
28	C₇×#389	—	2	1	no	—
29	C₇×#389	C₂²	1	2	yes	—
30	C₇×#389	C₂²	1	2	yes	—
31	C₇×#385	—	2	2	no	—
32	C₇×#384	C₂²	1	1	yes	characteristic
33	C₇×#384	C₂²	1	1	yes	characteristic
34	C₇×#380	—	2	1	no	—
35	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₇×#340	C₂²	1	1	yes	characteristic
38	C₇×#340	C₂²	1	1	yes	characteristic
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	2	yes	—
42	#26040	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	—	2	2	no	—
44	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇	—	2	1	no	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₇×C₄⋊Q₈	—	2	4	no	—
51	C₇×C₄⋊Q₈	—	4	2	no	—
52	C₇×C₄⋊Q₈	—	4	4	no	—
53	C₄×C₇×D₄	—	2	4	no	—
54	C₄×C₇×D₄	—	2	2	no	—
55	C₄×C₇×D₄	—	4	2	no	—
56	C₄×C₇×D₄	Q₈	1	4	yes	complemented
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	2	no	—
59	C₂×C₇×C₄⋊C₄	—	2	1	no	—
60	C₂×C₇×C₄⋊C₄	—	2	2	no	—
61	C₂×C₇×C₄⋊C₄	—	2	2	no	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	4	4	no	—
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₇	—	2	1	no	—
75	C₂×C₄²×C₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₇×#107	—	2	4	no	—
78	C₇×#107	—	2	4	no	—
79	C₇×#107	—	4	2	no	—
80	C₇×C₄⋊C₈	—	2	4	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×#102	—	2	4	no	—
83	C₇×#102	D₄	1	4	yes	—
84	C₇×#102	Q₈	1	4	yes	complemented
85	C₄×C₇×C₈	—	2	2	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	2	no	—
89	C₇×#95	D₄	1	2	yes	—
90	C₂×#474	C₂×C₇	1	2	yes	—
91	#2551	C₂×C₇	1	1	yes	characteristic, complemented
92	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
93	#2086	C₂×C₇	1	2	yes	complemented
94	#2057	C₂×C₇	1	2	yes	complemented
95	#1947	C₂×C₇	1	1	yes	characteristic, complemented
96	#1939	C₂×C₇	1	1	yes	characteristic, complemented
97	#1862	C₂×C₇	1	2	yes	—
98	#1845	C₂×C₇	1	1	yes	characteristic, complemented
99	#1802	C₂×C₇	1	1	yes	characteristic
100	C₄×#102	C₂×C₇	1	1	yes	characteristic
101	C₂⁴×C₇	—	2	1	no	—
102	C₂×C₇×Q₈	—	4	4	no	—
103	C₂×C₇×Q₈	—	4	4	no	—
104	C₂×C₇×Q₈	—	8	2	no	—
105	C₂×C₇×D₄	—	2	1	no	—
106	C₂×C₇×D₄	—	2	1	no	—
107	C₂×C₇×D₄	—	2	1	no	—
108	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
109	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
110	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
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	4	no	—
115	C₂²×C₄×C₇	—	2	2	no	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	4	4	no	—
118	C₂²×C₄×C₇	—	4	2	no	—
119	C₂²×C₄×C₇	—	4	2	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	—	8	2	no	—
122	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
135	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	2	1	no	—
138	C₇×C₄⋊C₄	—	2	1	no	—
139	C₇×C₄⋊C₄	—	2	1	no	—
140	C₇×C₄⋊C₄	—	2	2	no	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	4	4	no	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	—	4	2	no	—
147	C₇×C₄⋊C₄	—	4	4	no	—
148	C₇×C₄⋊C₄	—	4	2	no	—
149	C₇×C₄⋊C₄	—	8	1	no	—
150	C₇×C₄⋊C₄	—	8	1	no	—
151	C₇×C₄⋊C₄	D₈	1	4	yes	—
152	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
154	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
155	C₇×C₂²⋊C₄	—	2	4	no	—
156	C₇×C₂²⋊C₄	—	4	4	no	—
157	C₄²×C₇	—	2	2	no	—
158	C₄²×C₇	—	2	2	no	—
159	C₄²×C₇	—	4	2	no	—
160	C₄²×C₇	C₂×Q₈	1	2	yes	—
161	C₄²×C₇	#41	1	2	yes	—
162	C₂×C₄⋊Q₈	—	2	1	no	—
163	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
164	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
165	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
166	C₂²×C₄⋊C₄	—	2	1	no	—
167	#474	—	2	8	no	—
168	C₂×#107	C₂²×C₇	1	2	yes	—
169	C₂×#107	C₂²×C₇	1	2	yes	—
170	C₂×#107	C₂²×C₇	1	2	yes	—
171	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
172	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
173	C₂×#102	C₂²×C₇	1	2	yes	—
174	C₂×#102	C₂²×C₇	1	1	yes	characteristic
175	C₂×#102	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
177	#395	—	2	2	no	—
178	#389	—	2	1	no	—
179	#389	C₂²×C₇	1	2	yes	—
180	#389	C₂²×C₇	1	2	yes	—
181	#385	—	2	2	no	—
182	#384	C₂²×C₇	1	1	yes	characteristic
183	#384	C₂²×C₇	1	1	yes	characteristic
184	#380	—	2	1	no	—
185	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
187	#340	C₂²×C₇	1	1	yes	characteristic
188	#340	C₂²×C₇	1	2	yes	—
189	#340	C₂²×C₇	1	1	yes	characteristic
190	#340	C₂²×C₇	1	2	yes	—
191	#336	C₂²×C₇	1	2	yes	—
192	C₂³×C₇	—	2	2	no	—
193	C₂³×C₇	—	2	2	no	—
194	C₂³×C₇	—	2	2	no	—
195	C₂³×C₇	—	4	1	no	—
196	C₂³×C₇	—	4	1	no	—
197	C₂³×C₇	—	4	1	no	—
198	C₂³×C₇	—	4	1	no	—
199	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
200	C₇×Q₈	—	8	8	no	—
201	C₇×D₄	—	2	2	no	—
202	C₇×D₄	—	2	2	no	—
203	C₇×D₄	—	2	2	no	—
204	C₇×D₄	C₄⋊Q₈	1	4	yes	complemented
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	2	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	2	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	1	no	—
220	C₂×C₄×C₇	—	4	1	no	—
221	C₂×C₄×C₇	—	4	8	no	—
222	C₂×C₄×C₇	—	4	2	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	—	8	8	no	—
229	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
230	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
232	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
233	C₂×C₄×C₇	#137	1	2	yes	—
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	—	2	2	no	—
242	C₇×C₈	—	4	2	no	—
243	C₂²×Q₈	—	2	2	no	—
244	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	2	2	no	—
247	C₂²×C₈	C₂³×C₇	1	2	yes	—
248	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
250	C₄⋊Q₈	—	2	4	no	—
251	C₄⋊Q₈	—	4	2	no	—
252	C₄⋊Q₈	—	4	4	no	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	4	2	no	—
256	C₄×D₄	C₇×Q₈	1	4	yes	complemented
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	4	4	no	—
265	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₇	1	2	yes	—
276	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
277	#107	—	2	4	no	—
278	#107	—	2	4	no	—
279	#107	—	4	2	no	—
280	C₄⋊C₈	—	2	4	no	—
281	C₄⋊C₈	—	2	2	no	—
282	#102	—	2	4	no	—
283	#102	C₇×D₄	1	4	yes	—
284	#102	C₇×Q₈	1	4	yes	complemented
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	1	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	C₇×D₄	1	2	yes	—
290	C₂²×C₇	—	2	4	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	4	2	no	—
293	C₂²×C₇	—	4	2	no	—
294	C₂²×C₇	—	4	2	no	—
295	C₂²×C₇	—	4	2	no	—
296	C₂²×C₇	—	4	2	no	—
297	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
298	C₂²×C₇	D₄²	1	1	yes	characteristic
299	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
300	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
301	C₂²×C₇	C₂×#137	1	1	yes	characteristic
302	C₂²×C₇	#576	1	1	yes	characteristic
303	C₂²×C₇	#578	1	1	yes	characteristic
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	4	no	—
306	C₄×C₇	—	4	2	no	—
307	C₄×C₇	—	4	2	no	—
308	C₄×C₇	—	4	2	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	8	2	no	—
311	C₄×C₇	—	8	2	no	—
312	C₄×C₇	#474	1	4	yes	complemented
313	C₄×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
314	C₄×C₇	#544	1	1	yes	characteristic
315	C₄×C₇	#547	1	1	yes	characteristic
316	C₄×C₇	#554	1	1	yes	characteristic
317	C₂⁴	—	2	1	no	—
318	C₂×Q₈	—	4	4	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	—	8	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
325	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
326	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
339	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
341	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
351	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	2	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	8	1	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	C₇×D₈	1	4	yes	—
368	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
369	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
370	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	4	2	no	—
376	C₄²	C₂×C₇×Q₈	1	2	yes	—
377	C₄²	C₇×#41	1	2	yes	—
378	C₂×C₇	—	4	4	no	—
379	C₂×C₇	#2440	1	1	yes	characteristic
380	C₂×C₇	C₂×#474	1	1	yes	characteristic
381	C₂×C₇	#3083	1	1	yes	characteristic
382	C₂×C₇	#3276	1	1	yes	characteristic
383	C₂×C₇	D₄×D₈	1	1	yes	characteristic
384	C₂×C₇	Q₈×D₈	1	1	yes	characteristic
385	C₂×C₇	#3385	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
394	Q₈	—	8	8	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	C₇×C₄⋊Q₈	1	4	yes	complemented
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
424	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
425	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
426	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
427	C₂×C₄	C₇×#137	1	2	yes	—
428	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
431	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
432	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₇	#26040	1	1	yes	characteristic, direct product factor, Sylow
438	C₂²	—	2	4	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
446	C₂²	C₇×D₄²	1	1	yes	characteristic
447	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
448	C₂²	C₂²×C₇×D₈	1	1	yes	characteristic
449	C₂²	C₂×C₇×#137	1	1	yes	characteristic
450	C₂²	C₇×#576	1	1	yes	characteristic
451	C₂²	C₇×#578	1	1	yes	characteristic
452	C₄	—	2	4	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₇×#474	1	4	yes	complemented
461	C₄	C₂×C₇×C₄⋊Q₈	1	1	yes	characteristic
462	C₄	C₇×#544	1	1	yes	characteristic
463	C₄	C₇×#547	1	1	yes	characteristic
464	C₄	C₇×#554	1	1	yes	characteristic
465	C₂	—	4	4	no	—
466	C₂	C₇×#2440	1	1	yes	characteristic
467	C₂	C₂×C₇×#474	1	1	yes	characteristic
468	C₂	C₇×#3083	1	1	yes	characteristic
469	C₂	C₇×#3276	1	1	yes	characteristic
470	C₂	C₇×D₄×D₈	1	1	yes	characteristic
471	C₂	C₇×Q₈×D₈	1	1	yes	characteristic
472	C₂	C₇×#3385	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇×#2551	C₂	semidirect
4. C₇×#2086	C₂	semidirect
5. C₇×#2057	C₂	semidirect
6. C₇×#1947	C₂	semidirect
7. C₇×#1939	C₂	semidirect
9. C₇×#1845	C₂	semidirect
42. #26040	C₇	direct (N × H)
56. C₄×C₇×D₄	Q₈	semidirect
84. C₇×#102	Q₈	semidirect
91. #2551	C₂×C₇	semidirect
93. #2086	C₂×C₇	semidirect
94. #2057	C₂×C₇	semidirect
95. #1947	C₂×C₇	semidirect
96. #1939	C₂×C₇	semidirect
98. #1845	C₂×C₇	semidirect
204. C₇×D₄	C₄⋊Q₈	semidirect
256. C₄×D₄	C₇×Q₈	semidirect
284. #102	C₇×Q₈	semidirect
312. C₄×C₇	#474	semidirect
398. D₄	C₇×C₄⋊Q₈	semidirect
437. C₇	#26040	direct (N × H)
460. C₄	C₇×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#474	2
C₇×#2551	2
C₇×D₄×C₄⋊C₄	2
C₇×#2086	2
C₇×#2057	2
C₇×#1947	2
C₇×#1939	2
C₇×#1862	2
C₇×#1845	2
C₇×#1802	2
C₄×C₇×#102	2
#26040	7

Subgroups — C7×#26040 #13203256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#26040 #13203256