Subgroups — C₇×#23716 #13200932

Order 1792.

816 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2063	C₂	1	2	yes	maximal, complemented
7	C₇×#2051	C₂	1	2	yes	maximal, complemented
8	C₇×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2018	C₂	1	1	yes	maximal, characteristic
10	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₇×#100	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₄×C₇×#41	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
16	C₇×#442	—	2	2	no	—
17	C₇×#440	—	2	2	no	—
18	C₄×C₇×SD₁₆	—	2	2	no	—
19	C₄×C₇×D₈	—	2	2	no	—
20	C₄×C₇×D₈	—	2	2	no	—
21	C₄×C₇×D₈	—	2	2	no	—
22	C₇×#433	—	2	2	no	—
23	C₇×#431	—	2	2	no	—
24	C₂×C₇×#108	C₂²	1	2	yes	—
25	C₇×#428	C₂²	1	2	yes	—
26	C₂×C₇×#107	C₂²	1	1	yes	characteristic
27	C₇×#424	C₂²	1	1	yes	characteristic
28	C₇×#424	C₂²	1	1	yes	characteristic
29	C₇×#418	C₂²	1	2	yes	—
30	C₇×#417	C₂²	1	2	yes	—
31	C₂×C₇×#102	C₂²	1	2	yes	—
32	C₂×C₇×#100	C₂²	1	2	yes	—
33	C₂×C₇×#100	C₂²	1	2	yes	—
34	C₇×#408	C₂²	1	1	yes	characteristic
35	C₇×#408	C₂²	1	1	yes	characteristic
36	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
37	C₄×C₇×M₁₆	C₂²	1	2	yes	—
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#343	C₂²	1	2	yes	—
40	C₇×#343	C₂²	1	2	yes	—
41	C₇×#341	C₂²	1	1	yes	characteristic
42	C₇×#341	C₂²	1	1	yes	characteristic
43	#23716	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₇×#41	C₂³	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂³	1	2	yes	—
46	C₂³×C₄×C₇	—	2	2	no	—
47	C₇×AGL(1,ℤ/8)	—	2	4	no	—
48	C₇×AGL(1,ℤ/8)	—	2	4	no	—
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×D₈	—	2	2	no	—
51	C₂×C₇×D₈	—	2	4	no	—
52	C₂×C₇×D₈	—	2	2	no	—
53	C₂×C₇×M₁₆	C₂³	1	2	yes	—
54	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₇×M₁₆	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
60	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
61	C₄×C₇×D₄	—	2	1	no	—
62	C₄×C₇×D₄	—	2	1	no	—
63	C₄×C₇×D₄	—	2	2	no	—
64	C₄×C₇×D₄	—	2	2	no	—
65	C₄×C₇×D₄	—	2	2	no	—
66	C₄×C₇×D₄	—	2	2	no	—
67	C₄×C₇×D₄	D₄	1	1	yes	characteristic
68	C₄×C₇×D₄	D₄	1	1	yes	characteristic
69	C₇×#117	—	2	1	no	—
70	C₇×#117	C₂³	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₄²×C₇	—	2	1	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#108	—	2	4	no	—
76	C₇×#107	—	2	2	no	—
77	C₇×#107	—	2	2	no	—
78	C₇×#106	—	2	2	no	—
79	C₇×C₄⋊C₈	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×#103	—	2	2	no	—
82	C₇×#102	—	2	2	no	—
83	C₇×#102	—	2	4	no	—
84	C₇×#102	—	2	2	no	—
85	C₇×#102	—	2	2	no	—
86	C₇×#100	—	2	4	no	—
87	C₇×#100	—	2	4	no	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₇×C₂²⋊C₈	—	2	2	no	—
90	C₇×#97	—	2	1	no	—
91	C₇×#97	—	2	2	no	—
92	C₄×C₇×C₈	—	2	1	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₄×C₇×C₈	D₄	1	2	yes	—
95	C₄×C₇×C₈	D₄	1	2	yes	—
96	C₄×AGL(1,ℤ/8)	C₂×C₇	1	2	yes	complemented
97	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
98	#2922	C₂×C₇	1	1	yes	characteristic, complemented
99	#2089	C₂×C₇	1	1	yes	characteristic, complemented
100	#2078	C₂×C₇	1	1	yes	characteristic, complemented
101	#2063	C₂×C₇	1	2	yes	complemented
102	#2051	C₂×C₇	1	2	yes	complemented
103	#2045	C₂×C₇	1	1	yes	characteristic, complemented
104	#2018	C₂×C₇	1	1	yes	characteristic
105	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
106	C₄×#100	C₂×C₇	1	2	yes	complemented
107	C₂⁴×C₇	—	2	2	no	—
108	C₇×#41	—	2	2	no	—
109	C₇×#41	—	2	2	no	—
110	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₇×D₄	—	2	1	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	2	no	—
117	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₇×D₄	#41	1	4	yes	—
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	2	no	—
123	C₂²×C₄×C₇	—	4	2	no	—
124	C₂²×C₄×C₇	—	4	2	no	—
125	C₂²×C₄×C₇	—	8	4	no	—
126	C₂²×C₄×C₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×SD₁₆	—	2	8	no	—
130	C₇×D₈	—	2	8	no	—
131	C₇×D₈	—	2	8	no	—
132	C₇×M₁₆	—	2	2	no	—
133	C₇×M₁₆	—	2	2	no	—
134	C₇×M₁₆	—	2	2	no	—
135	C₇×M₁₆	—	2	2	no	—
136	C₇×M₁₆	—	2	2	no	—
137	C₇×M₁₆	#41	1	4	yes	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	1	no	—
143	C₂×C₇×C₈	—	2	2	no	—
144	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₇×C₄⋊C₄	—	2	1	no	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	2	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₇×C₂²⋊C₄	—	2	1	no	—
153	C₇×C₂²⋊C₄	—	2	1	no	—
154	C₇×C₂²⋊C₄	—	2	1	no	—
155	C₇×C₂²⋊C₄	—	4	2	no	—
156	C₇×C₂²⋊C₄	—	4	2	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
164	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
165	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
166	C₄×#41	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
168	#442	—	2	2	no	—
169	#440	—	2	2	no	—
170	C₄×SD₁₆	—	2	2	no	—
171	C₄×D₈	—	2	2	no	—
172	C₄×D₈	—	2	2	no	—
173	C₄×D₈	—	2	2	no	—
174	#433	—	2	2	no	—
175	#431	—	2	2	no	—
176	C₂×#108	C₂²×C₇	1	2	yes	—
177	#428	C₂²×C₇	1	2	yes	—
178	C₂×#107	C₂²×C₇	1	1	yes	characteristic
179	#424	C₂²×C₇	1	1	yes	characteristic
180	#424	C₂²×C₇	1	1	yes	characteristic
181	#418	C₂²×C₇	1	2	yes	—
182	#417	C₂²×C₇	1	2	yes	—
183	C₂×#102	C₂²×C₇	1	2	yes	—
184	C₂×#100	C₂²×C₇	1	2	yes	—
185	C₂×#100	C₂²×C₇	1	2	yes	—
186	#408	C₂²×C₇	1	1	yes	characteristic
187	#408	C₂²×C₇	1	1	yes	characteristic
188	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
189	C₄×M₁₆	C₂²×C₇	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
191	#343	C₂²×C₇	1	2	yes	—
192	#343	C₂²×C₇	1	2	yes	—
193	#341	C₂²×C₇	1	1	yes	characteristic
194	#341	C₂²×C₇	1	1	yes	characteristic
195	C₂³×C₇	—	2	1	no	—
196	C₂³×C₇	—	2	4	no	—
197	C₂³×C₇	—	4	2	no	—
198	C₂³×C₇	—	4	2	no	—
199	C₂³×C₇	—	8	2	no	—
200	C₂³×C₇	—	8	2	no	—
201	C₂³×C₇	C₂×#41	1	1	yes	characteristic
202	C₇×Q₈	—	2	2	no	—
203	C₇×D₄	—	2	4	no	—
204	C₇×D₄	—	2	2	no	—
205	C₇×D₄	—	2	4	no	—
206	C₇×D₄	—	4	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₇×D₄	—	4	2	no	—
209	C₂×C₄×C₇	—	2	2	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	4	2	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	1	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	4	2	no	—
219	C₂×C₄×C₇	—	8	4	no	—
220	C₂×C₄×C₇	—	8	4	no	—
221	C₂×C₄×C₇	—	8	2	no	—
222	C₂×C₄×C₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	2	yes	—
229	C₂×C₄×C₇	C₂×#41	1	2	yes	—
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	4	no	—
232	C₇×C₈	—	2	2	no	—
233	C₇×C₈	—	4	1	no	—
234	C₇×C₈	—	4	2	no	—
235	C₇×C₈	—	4	1	no	—
236	C₂×#41	C₂³×C₇	1	1	yes	characteristic
237	C₂²×D₄	C₂³×C₇	1	2	yes	—
238	C₂³×C₄	—	2	2	no	—
239	AGL(1,ℤ/8)	—	2	4	no	—
240	AGL(1,ℤ/8)	—	2	4	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×D₈	—	2	2	no	—
243	C₂×D₈	—	2	4	no	—
244	C₂×D₈	—	2	2	no	—
245	C₂×M₁₆	C₂³×C₇	1	2	yes	—
246	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
247	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
248	C₂×M₁₆	C₂³×C₇	1	2	yes	—
249	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
251	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
252	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₇×D₄	1	1	yes	characteristic
260	C₄×D₄	C₇×D₄	1	1	yes	characteristic
261	#117	—	2	1	no	—
262	#117	C₂³×C₇	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
267	#108	—	2	4	no	—
268	#107	—	2	2	no	—
269	#107	—	2	2	no	—
270	#106	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	2	no	—
274	#102	—	2	2	no	—
275	#102	—	2	4	no	—
276	#102	—	2	2	no	—
277	#102	—	2	2	no	—
278	#100	—	2	4	no	—
279	#100	—	2	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	#97	—	2	1	no	—
283	#97	—	2	2	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	C₇×D₄	1	2	yes	—
287	C₄×C₈	C₇×D₄	1	2	yes	—
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	2	1	no	—
290	C₂²×C₇	—	4	1	no	—
291	C₂²×C₇	—	4	4	no	—
292	C₂²×C₇	—	4	1	no	—
293	C₂²×C₇	—	4	1	no	—
294	C₂²×C₇	—	8	4	no	—
295	C₂²×C₇	—	8	4	no	—
296	C₂²×C₇	—	8	2	no	—
297	C₂²×C₇	—	8	2	no	—
298	C₂²×C₇	C₂×#121	1	1	yes	characteristic
299	C₂²×C₇	#529	1	2	yes	—
300	C₄×C₇	—	2	1	no	—
301	C₄×C₇	—	2	1	no	—
302	C₄×C₇	—	2	1	no	—
303	C₄×C₇	—	4	1	no	—
304	C₄×C₇	—	4	1	no	—
305	C₄×C₇	—	4	1	no	—
306	C₄×C₇	—	8	2	no	—
307	C₄×C₇	#472	1	2	yes	—
308	C₄×C₇	#525	1	1	yes	characteristic
309	C₄×C₇	#525	1	2	yes	—
310	C₄×C₇	#532	1	1	yes	characteristic
311	C₂⁴	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
322	C₂×D₄	C₇×#41	1	4	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	8	4	no	—
330	C₂²×C₄	C₇×#41	1	1	yes	characteristic
331	C₂²×C₄	C₇×#41	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
333	SD₁₆	—	2	8	no	—
334	D₈	—	2	8	no	—
335	D₈	—	2	8	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	C₇×#41	1	4	yes	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
349	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
355	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
356	C₂²⋊C₄	—	2	1	no	—
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
365	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
366	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
367	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
368	C₂×C₇	—	2	2	no	—
369	C₂×C₇	—	8	1	no	—
370	C₂×C₇	—	8	4	no	—
371	C₂×C₇	#2392	1	1	yes	characteristic
372	C₂×C₇	C₂×#472	1	1	yes	characteristic
373	C₂×C₇	#3067	1	1	yes	characteristic
374	C₂³	—	2	1	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	C₂×C₇×#41	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	D₄	—	2	4	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₇×#121	1	1	yes	characteristic
402	C₂×C₄	C₇×#121	1	1	yes	characteristic
403	C₂×C₄	C₇×#121	1	1	yes	characteristic
404	C₂×C₄	C₇×#121	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
407	C₂×C₄	C₂×C₇×#41	1	2	yes	—
408	C₂×C₄	C₂×C₇×#41	1	2	yes	—
409	C₈	—	2	2	no	—
410	C₈	—	2	4	no	—
411	C₈	—	2	2	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	2	no	—
414	C₈	—	4	1	no	—
415	C₇	#23716	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₂×C₇×#121	1	1	yes	characteristic
427	C₂²	C₇×#529	1	2	yes	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₇×#472	1	2	yes	—
436	C₄	C₇×#525	1	1	yes	characteristic
437	C₄	C₇×#525	1	2	yes	—
438	C₄	C₇×#532	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	8	4	no	—
442	C₂	C₇×#2392	1	1	yes	characteristic
443	C₂	C₂×C₇×#472	1	1	yes	characteristic
444	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
prime radical	C₇×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₄×C₇×D₈	C₂	semidirect
3. C₇×#2922	C₂	semidirect
4. C₇×#2089	C₂	semidirect
5. C₇×#2078	C₂	semidirect
6. C₇×#2063	C₂	semidirect
7. C₇×#2051	C₂	semidirect
8. C₇×#2045	C₂	semidirect
10. C₄×C₇×#108	C₂	semidirect
11. C₄×C₇×#100	C₂	semidirect
43. #23716	C₇	direct (N × H)
96. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
97. C₂×C₄×D₈	C₂×C₇	semidirect
98. #2922	C₂×C₇	semidirect
99. #2089	C₂×C₇	semidirect
100. #2078	C₂×C₇	semidirect
101. #2063	C₂×C₇	semidirect
102. #2051	C₂×C₇	semidirect
103. #2045	C₂×C₇	semidirect
105. C₄×#108	C₂×C₇	semidirect
106. C₄×#100	C₂×C₇	semidirect
415. C₇	#23716	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×AGL(1,ℤ/8)	2
C₂×C₄×C₇×D₈	2
C₇×#2922	2
C₇×#2089	2
C₇×#2078	2
C₇×#2063	2
C₇×#2051	2
C₇×#2045	2
C₇×#2018	2
C₄×C₇×#108	2
C₄×C₇×#100	2
#23716	7

Subgroups — C7×#23716 #13200932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23716 #13200932