Subgroups — C₇×#23780 #13200996

Order 1792.

808 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₇×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2094	C₂	1	1	yes	maximal, characteristic
5	C₇×#2088	C₂	1	2	yes	maximal, complemented
6	C₇×#2067	C₂	1	2	yes	maximal
7	C₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2023	C₂	1	1	yes	maximal, characteristic
9	C₇×#1776	C₂	1	2	yes	maximal, complemented
10	C₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1762	C₂	1	2	yes	maximal
12	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	—	2	1	no	—
14	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₇×#117	—	2	1	no	—
16	C₂×C₇×#107	C₂²	1	2	yes	—
17	C₂×C₇×#106	C₂²	1	2	yes	—
18	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₇×#102	C₂²	1	2	yes	—
20	C₂×C₇×#102	C₂²	1	2	yes	—
21	C₂×C₇×#97	C₂²	1	2	yes	—
22	C₇×#391	—	2	1	no	—
23	C₇×#390	C₂²	1	1	yes	characteristic
24	C₇×#390	C₂²	1	1	yes	characteristic
25	C₇×#389	—	2	1	no	—
26	C₇×#389	C₂²	1	1	yes	characteristic
27	C₇×#389	C₂²	1	2	yes	—
28	C₇×#389	C₂²	1	1	yes	characteristic
29	C₇×#388	—	2	1	no	—
30	C₇×#388	—	2	1	no	—
31	C₇×#384	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	—	2	1	no	—
33	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₂²⋊C₄	—	2	1	no	—
36	C₄³×C₇	C₂²	1	1	yes	characteristic
37	C₇×#340	C₂²	1	2	yes	—
38	C₇×#340	C₂²	1	2	yes	—
39	C₇×#340	C₂²	1	2	yes	—
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	1	yes	characteristic
43	#23780	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	—	2	1	no	—
45	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	—	2	1	no	—
47	C₂²×C₇×C₈	C₂³	1	2	yes	—
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₇×C₄⋊Q₈	—	2	4	no	—
50	C₄×C₇×Q₈	—	4	4	no	—
51	C₄×C₇×D₄	—	2	2	no	—
52	C₄×C₇×D₄	Q₈	1	4	yes	complemented
53	C₇×#117	—	4	4	no	—
54	C₂×C₇×C₄⋊C₄	—	2	1	no	—
55	C₂×C₇×C₄⋊C₄	—	2	1	no	—
56	C₂×C₇×C₄⋊C₄	—	2	1	no	—
57	C₂×C₇×C₄⋊C₄	—	2	1	no	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₇×C₄⋊C₄	—	2	2	no	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
66	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₄²×C₇	—	2	1	no	—
71	C₂×C₄²×C₇	—	2	2	no	—
72	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#107	—	2	4	no	—
80	C₇×#106	—	2	4	no	—
81	C₇×C₄⋊C₈	—	2	4	no	—
82	C₇×#102	—	2	4	no	—
83	C₇×#102	—	2	4	no	—
84	C₇×#97	—	2	4	no	—
85	C₇×#95	—	2	1	no	—
86	C₇×#95	—	2	1	no	—
87	C₇×#95	—	2	2	no	—
88	C₇×#95	—	2	1	no	—
89	C₇×#95	—	2	2	no	—
90	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
91	#2293	C₂×C₇	1	1	yes	characteristic
92	#2100	C₂×C₇	1	1	yes	characteristic, complemented
93	#2094	C₂×C₇	1	1	yes	characteristic
94	#2088	C₂×C₇	1	2	yes	complemented
95	#2067	C₂×C₇	1	2	yes	—
96	#2057	C₂×C₇	1	1	yes	characteristic, complemented
97	#2023	C₂×C₇	1	1	yes	characteristic
98	#1776	C₂×C₇	1	2	yes	complemented
99	#1767	C₂×C₇	1	1	yes	characteristic, complemented
100	#1762	C₂×C₇	1	2	yes	—
101	C₂⁴×C₇	—	2	1	no	—
102	C₂×C₇×Q₈	—	2	4	no	—
103	C₂×C₇×Q₈	—	4	2	no	—
104	C₂×C₇×Q₈	—	4	2	no	—
105	C₂×C₇×D₄	—	2	2	no	—
106	C₂×C₇×D₄	—	2	2	no	—
107	C₂×C₇×D₄	—	2	1	no	—
108	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	4	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	1	no	—
114	C₂²×C₄×C₇	—	2	2	no	—
115	C₂²×C₄×C₇	—	4	2	no	—
116	C₂²×C₄×C₇	—	4	2	no	—
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₇×C₈	—	2	2	no	—
125	C₂×C₇×C₈	—	2	2	no	—
126	C₂×C₇×C₈	—	2	2	no	—
127	C₂×C₇×C₈	—	2	2	no	—
128	C₂×C₇×C₈	—	2	2	no	—
129	C₂×C₇×C₈	#41	1	4	yes	—
130	C₇×C₄⋊C₄	—	2	4	no	—
131	C₇×C₄⋊C₄	—	2	1	no	—
132	C₇×C₄⋊C₄	—	2	2	no	—
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	—	4	2	no	—
138	C₇×C₄⋊C₄	—	4	2	no	—
139	C₇×C₄⋊C₄	—	4	2	no	—
140	C₇×C₄⋊C₄	—	4	2	no	—
141	C₇×C₄⋊C₄	—	4	4	no	—
142	C₇×C₄⋊C₄	C₂×Q₈	1	2	yes	—
143	C₇×C₄⋊C₄	#41	1	4	yes	—
144	C₇×C₂²⋊C₄	—	2	4	no	—
145	C₇×C₂²⋊C₄	—	4	2	no	—
146	C₇×C₂²⋊C₄	—	4	2	no	—
147	C₇×C₂²⋊C₄	—	4	2	no	—
148	C₇×C₂²⋊C₄	—	4	2	no	—
149	C₄²×C₇	—	2	2	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	—	2	2	no	—
152	C₄²×C₇	—	2	2	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	4	1	no	—
155	C₄²×C₇	—	4	2	no	—
156	C₄²×C₇	—	4	4	no	—
157	C₄²×C₇	C₂×Q₈	1	2	yes	—
158	C₄²×C₇	#41	1	2	yes	—
159	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
160	C₂×C₄×Q₈	—	2	1	no	—
161	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
162	C₂×#117	—	2	1	no	—
163	C₂×#107	C₂²×C₇	1	2	yes	—
164	C₂×#106	C₂²×C₇	1	2	yes	—
165	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
166	C₂×#102	C₂²×C₇	1	2	yes	—
167	C₂×#102	C₂²×C₇	1	2	yes	—
168	C₂×#97	C₂²×C₇	1	2	yes	—
169	#391	—	2	1	no	—
170	#390	C₂²×C₇	1	1	yes	characteristic
171	#390	C₂²×C₇	1	1	yes	characteristic
172	#389	—	2	1	no	—
173	#389	C₂²×C₇	1	2	yes	—
174	#389	C₂²×C₇	1	1	yes	characteristic
175	#389	C₂²×C₇	1	1	yes	characteristic
176	#388	—	2	1	no	—
177	#388	—	2	1	no	—
178	#384	C₂²×C₇	1	1	yes	characteristic
179	C₄×C₄⋊C₄	—	2	1	no	—
180	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
181	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
182	C₄×C₂²⋊C₄	—	2	1	no	—
183	C₄³	C₂²×C₇	1	1	yes	characteristic
184	#340	C₂²×C₇	1	2	yes	—
185	#340	C₂²×C₇	1	2	yes	—
186	#340	C₂²×C₇	1	2	yes	—
187	#340	C₂²×C₇	1	2	yes	—
188	#336	C₂²×C₇	1	1	yes	characteristic
189	#336	C₂²×C₇	1	1	yes	characteristic
190	C₂³×C₇	—	2	2	no	—
191	C₂³×C₇	—	4	1	no	—
192	C₂³×C₇	—	4	1	no	—
193	C₂³×C₇	—	4	1	no	—
194	C₂³×C₇	—	4	1	no	—
195	C₂³×C₇	—	4	1	no	—
196	C₂³×C₇	—	4	1	no	—
197	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
198	C₇×Q₈	—	4	8	no	—
199	C₇×D₄	—	2	4	no	—
200	C₇×D₄	—	4	2	no	—
201	C₂×C₄×C₇	—	2	1	no	—
202	C₂×C₄×C₇	—	2	1	no	—
203	C₂×C₄×C₇	—	2	1	no	—
204	C₂×C₄×C₇	—	2	1	no	—
205	C₂×C₄×C₇	—	2	1	no	—
206	C₂×C₄×C₇	—	2	1	no	—
207	C₂×C₄×C₇	—	2	1	no	—
208	C₂×C₄×C₇	—	2	1	no	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	4	8	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	1	no	—
221	C₂×C₄×C₇	—	4	1	no	—
222	C₂×C₄×C₇	—	4	2	no	—
223	C₂×C₄×C₇	—	4	1	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	—	4	1	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
232	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
234	C₂×C₄×C₇	#137	1	2	yes	—
235	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂×#41	1	2	yes	—
238	C₂×C₄×C₇	C₂×#41	1	2	yes	—
239	C₇×C₈	—	2	4	no	—
240	C₇×C₈	—	4	2	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂²×C₈	C₂³×C₇	1	2	yes	—
245	C₂²×C₈	C₂³×C₇	1	2	yes	—
246	C₄⋊Q₈	—	2	4	no	—
247	C₄×Q₈	—	4	4	no	—
248	C₄×D₄	—	2	2	no	—
249	C₄×D₄	C₇×Q₈	1	4	yes	complemented
250	#117	—	4	4	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
260	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	1	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
270	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
271	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
272	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	#106	—	2	4	no	—
278	C₄⋊C₈	—	2	4	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#97	—	2	4	no	—
282	#95	—	2	1	no	—
283	#95	—	2	1	no	—
284	#95	—	2	2	no	—
285	#95	—	2	1	no	—
286	#95	—	2	2	no	—
287	C₂²×C₇	—	4	2	no	—
288	C₂²×C₇	—	4	2	no	—
289	C₂²×C₇	—	4	2	no	—
290	C₂²×C₇	—	8	1	no	—
291	C₂²×C₇	—	8	1	no	—
292	C₂²×C₇	—	8	1	no	—
293	C₂²×C₇	—	8	1	no	—
294	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
295	C₂²×C₇	#525	1	1	yes	characteristic
296	C₂²×C₇	#532	1	1	yes	characteristic
297	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
298	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
299	C₂²×C₇	C₂×#137	1	1	yes	characteristic
300	C₂²×C₇	#575	1	1	yes	characteristic
301	C₄×C₇	—	2	2	no	—
302	C₄×C₇	—	2	2	no	—
303	C₄×C₇	—	2	2	no	—
304	C₄×C₇	—	2	2	no	—
305	C₄×C₇	—	2	2	no	—
306	C₄×C₇	—	4	2	no	—
307	C₄×C₇	—	4	4	no	—
308	C₄×C₇	—	4	1	no	—
309	C₄×C₇	—	8	1	no	—
310	C₄×C₇	—	8	2	no	—
311	C₄×C₇	—	8	1	no	—
312	C₄×C₇	#529	1	2	yes	—
313	C₄×C₇	#533	1	2	yes	—
314	C₂⁴	—	2	1	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₇×#41	1	4	yes	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	C₂×C₇×Q₈	1	2	yes	—
356	C₄⋊C₄	C₇×#41	1	4	yes	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	4	4	no	—
370	C₄²	C₂×C₇×Q₈	1	2	yes	—
371	C₄²	C₇×#41	1	2	yes	—
372	C₂×C₇	—	8	2	no	—
373	C₂×C₇	#2396	1	1	yes	characteristic
374	C₂×C₇	#3077	1	1	yes	characteristic
375	C₂×C₇	#3079	1	1	yes	characteristic
376	C₂×C₇	#3109	1	1	yes	characteristic
377	C₂×C₇	#3117	1	1	yes	characteristic
378	C₂×C₇	#3180	1	1	yes	characteristic
379	C₂×C₇	#3182	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
388	Q₈	—	4	8	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
421	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
422	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
423	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
424	C₂×C₄	C₇×#137	1	2	yes	—
425	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
426	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
427	C₂×C₄	C₂×C₇×#41	1	2	yes	—
428	C₂×C₄	C₂×C₇×#41	1	2	yes	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₇	#23780	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
440	C₂²	C₇×#525	1	1	yes	characteristic
441	C₂²	C₇×#532	1	1	yes	characteristic
442	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
443	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
444	C₂²	C₂×C₇×#137	1	1	yes	characteristic
445	C₂²	C₇×#575	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	C₇×#529	1	2	yes	—
458	C₄	C₇×#533	1	2	yes	—
459	C₂	—	8	2	no	—
460	C₂	C₇×#2396	1	1	yes	characteristic
461	C₂	C₇×#3077	1	1	yes	characteristic
462	C₂	C₇×#3079	1	1	yes	characteristic
463	C₂	C₇×#3109	1	1	yes	characteristic
464	C₂	C₇×#3117	1	1	yes	characteristic
465	C₂	C₇×#3180	1	1	yes	characteristic
466	C₂	C₇×#3182	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 ◁ C₄³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₇×C₄⋊Q₈	C₂	semidirect
3. C₇×#2100	C₂	semidirect
5. C₇×#2088	C₂	semidirect
7. C₇×#2057	C₂	semidirect
9. C₇×#1776	C₂	semidirect
10. C₇×#1767	C₂	semidirect
43. #23780	C₇	direct (N × H)
52. C₄×C₇×D₄	Q₈	semidirect
90. C₄×C₄⋊Q₈	C₂×C₇	semidirect
92. #2100	C₂×C₇	semidirect
94. #2088	C₂×C₇	semidirect
96. #2057	C₂×C₇	semidirect
98. #1776	C₂×C₇	semidirect
99. #1767	C₂×C₇	semidirect
249. C₄×D₄	C₇×Q₈	semidirect
431. C₇	#23780	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₇×C₄⋊Q₈	2
C₇×#2293	2
C₇×#2100	2
C₇×#2094	2
C₇×#2088	2
C₇×#2067	2
C₇×#2057	2
C₇×#2023	2
C₇×#1776	2
C₇×#1767	2
C₇×#1762	2
#23780	7

Subgroups — C7×#23780 #13200996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23780 #13200996