Subgroups — C₇×#23043 #13200259

Order 1792.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3067	C₂	1	1	yes	maximal, characteristic
2	C₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2956	C₂	1	2	yes	maximal, complemented
4	C₇×#2916	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1953	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1932	C₂	1	2	yes	maximal, complemented
8	C₇×#1881	C₂	1	2	yes	maximal, complemented
9	C₇×#1858	C₂	1	2	yes	maximal, complemented
10	C₇×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1765	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#575	C₂²	1	2	yes	—
13	C₂×C₇×#135	C₂²	1	1	yes	characteristic
14	C₇×#568	C₂²	1	2	yes	—
15	C₇×#568	C₂²	1	2	yes	—
16	C₂×C₇×#131	C₂²	1	1	yes	characteristic
17	C₇×#473	C₄	1	2	yes	complemented
18	C₇×#472	C₄	1	2	yes	complemented
19	C₇×#471	C₄	1	4	yes	complemented
20	C₇×#444	—	2	2	no	—
21	C₇×#444	—	2	4	no	—
22	C₇×#443	—	2	2	no	—
23	C₇×#443	—	2	4	no	—
24	C₇×#430	—	2	2	no	—
25	C₇×#430	C₂²	1	2	yes	—
26	C₇×#430	C₂²	1	2	yes	—
27	C₂×C₇×#108	—	2	2	no	—
28	C₂×C₇×#108	C₂²	1	1	yes	characteristic
29	C₂×C₇×#108	C₂²	1	1	yes	characteristic
30	C₂×C₇×#108	C₂²	1	1	yes	characteristic
31	C₇×#421	C₂²	1	2	yes	—
32	C₂×C₇×#104	C₂²	1	2	yes	—
33	C₂×C₇×#104	C₂²	1	1	yes	characteristic
34	C₇×#416	C₂²	1	1	yes	characteristic
35	C₇×#413	C₂²	1	2	yes	—
36	C₇×#408	C₂²	1	2	yes	—
37	C₇×#405	C₂²	1	1	yes	characteristic
38	C₄×C₇×M₁₆	C₂²	1	2	yes	—
39	C₂×C₇×#97	C₂²	1	1	yes	characteristic
40	C₇×#344	C₂²	1	2	yes	—
41	C₇×#341	C₂²	1	1	yes	characteristic
42	C₇×#341	C₂²	1	2	yes	—
43	C₇×#339	C₂²	1	1	yes	characteristic
44	#23043	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₇×#41	C₂³	1	2	yes	—
46	C₂×C₇×#41	C₂³	1	1	yes	characteristic
47	C₇×#137	—	2	2	no	—
48	C₇×#137	C₂×C₄	1	4	yes	—
49	C₇×AGL(1,ℤ/8)	—	2	2	no	—
50	C₇×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	—
51	C₇×#135	—	2	4	no	—
52	C₇×#135	—	2	1	no	—
53	C₇×#135	—	2	1	no	—
54	C₇×#135	—	2	1	no	—
55	C₇×#135	—	2	1	no	—
56	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
57	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
59	C₇×#131	—	2	1	no	—
60	C₇×#131	—	2	1	no	—
61	C₇×#131	—	2	4	no	—
62	C₇×#131	—	2	4	no	—
63	C₇×#131	—	2	4	no	—
64	C₇×#131	—	4	2	no	—
65	C₇×#131	C₂×C₄	1	2	yes	—
66	C₇×#131	C₂×C₄	1	2	yes	—
67	C₂×C₇×M₁₆	—	2	1	no	—
68	C₂×C₇×M₁₆	—	2	4	no	—
69	C₂×C₇×M₁₆	—	4	2	no	—
70	C₂×C₇×M₁₆	C₂³	1	2	yes	—
71	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₇×M₁₆	C₂³	1	2	yes	—
73	C₂×C₇×M₁₆	C₂³	1	2	yes	—
74	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
75	C₂²×C₇×C₈	—	2	1	no	—
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
78	C₇×#117	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#108	—	2	4	no	—
81	C₇×#108	—	2	4	no	—
82	C₇×#108	—	2	1	no	—
83	C₇×#108	—	2	1	no	—
84	C₇×#108	C₂×C₄	1	2	yes	—
85	C₇×#108	C₂×C₄	1	2	yes	—
86	C₇×#108	D₄	1	2	yes	—
87	C₇×#108	D₄	1	2	yes	—
88	C₇×#104	—	2	4	no	—
89	C₇×#104	—	2	2	no	—
90	C₇×#104	—	2	2	no	—
91	C₇×#104	D₄	1	4	yes	—
92	C₇×#103	—	2	1	no	—
93	C₇×#102	—	2	1	no	—
94	C₇×#101	C₂×C₄	1	4	yes	—
95	C₇×#100	C₂×C₄	1	4	yes	—
96	C₇×C₂²⋊C₈	—	4	2	no	—
97	C₇×#97	—	2	1	no	—
98	C₇×#97	—	2	1	no	—
99	C₇×#97	—	2	1	no	—
100	C₇×#97	—	2	2	no	—
101	C₄×C₇×C₈	—	2	1	no	—
102	C₄×C₇×C₈	—	2	2	no	—
103	#3067	C₂×C₇	1	1	yes	characteristic
104	#2957	C₂×C₇	1	1	yes	characteristic, complemented
105	#2956	C₂×C₇	1	2	yes	complemented
106	#2916	C₂×C₇	1	1	yes	characteristic, complemented
107	#1975	C₂×C₇	1	1	yes	characteristic, complemented
108	#1953	C₂×C₇	1	1	yes	characteristic, complemented
109	#1932	C₂×C₇	1	2	yes	complemented
110	#1881	C₂×C₇	1	2	yes	complemented
111	#1858	C₂×C₇	1	2	yes	complemented
112	#1778	C₂×C₇	1	1	yes	characteristic, complemented
113	#1765	C₂×C₇	1	1	yes	characteristic, complemented
114	C₇×#41	—	2	1	no	—
115	C₇×#41	—	2	1	no	—
116	C₇×#41	—	2	2	no	—
117	C₇×#41	—	2	2	no	—
118	C₇×#41	—	2	2	no	—
119	C₇×#41	—	2	2	no	—
120	C₇×#41	C₂²×C₄	1	2	yes	—
121	C₇×#41	C₂×D₄	1	2	yes	—
122	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
123	C₂×C₇×Q₈	#41	1	1	yes	characteristic
124	C₂×C₇×D₄	—	2	1	no	—
125	C₂×C₇×D₄	—	2	2	no	—
126	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
127	C₂×C₇×D₄	#41	1	1	yes	characteristic
128	C₂²×C₄×C₇	—	2	1	no	—
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
132	C₇×Q₁₆	—	2	4	no	—
133	C₇×Q₁₆	—	2	1	no	—
134	C₇×Q₁₆	—	2	1	no	—
135	C₇×SD₁₆	—	2	4	no	—
136	C₇×SD₁₆	—	2	4	no	—
137	C₇×SD₁₆	—	2	2	no	—
138	C₇×SD₁₆	—	2	2	no	—
139	C₇×D₈	—	2	4	no	—
140	C₇×D₈	—	2	1	no	—
141	C₇×D₈	—	2	1	no	—
142	C₇×M₁₆	—	2	1	no	—
143	C₇×M₁₆	—	2	2	no	—
144	C₇×M₁₆	—	2	1	no	—
145	C₇×M₁₆	—	2	2	no	—
146	C₇×M₁₆	—	2	2	no	—
147	C₇×M₁₆	—	2	2	no	—
148	C₇×M₁₆	—	2	2	no	—
149	C₇×M₁₆	—	2	2	no	—
150	C₇×M₁₆	—	4	4	no	—
151	C₇×M₁₆	—	4	4	no	—
152	C₇×M₁₆	C₂²×C₄	1	2	yes	—
153	C₇×M₁₆	C₂²×C₄	1	4	yes	—
154	C₇×M₁₆	C₂×D₄	1	4	yes	—
155	C₇×M₁₆	C₂×D₄	1	2	yes	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	—	2	1	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	2	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	2	1	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	2	no	—
166	C₂×C₇×C₈	—	4	4	no	—
167	C₂×C₇×C₈	—	4	4	no	—
168	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₇×C₈	#41	1	1	yes	characteristic
173	C₂×C₇×C₈	#41	1	1	yes	characteristic
174	C₇×C₄⋊C₄	—	2	1	no	—
175	C₇×C₂²⋊C₄	—	2	1	no	—
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	C₄²×C₇	C₂×D₄	1	2	yes	—
179	#575	C₂²×C₇	1	2	yes	—
180	C₂×#135	C₂²×C₇	1	1	yes	characteristic
181	#568	C₂²×C₇	1	2	yes	—
182	#568	C₂²×C₇	1	2	yes	—
183	C₂×#131	C₂²×C₇	1	1	yes	characteristic
184	#473	C₄×C₇	1	2	yes	complemented
185	#472	C₄×C₇	1	2	yes	complemented
186	#471	C₄×C₇	1	4	yes	complemented
187	#444	—	2	2	no	—
188	#444	—	2	4	no	—
189	#443	—	2	2	no	—
190	#443	—	2	4	no	—
191	#430	—	2	2	no	—
192	#430	C₂²×C₇	1	2	yes	—
193	#430	C₂²×C₇	1	2	yes	—
194	C₂×#108	—	2	2	no	—
195	C₂×#108	C₂²×C₇	1	1	yes	characteristic
196	C₂×#108	C₂²×C₇	1	1	yes	characteristic
197	C₂×#108	C₂²×C₇	1	1	yes	characteristic
198	#421	C₂²×C₇	1	2	yes	—
199	C₂×#104	C₂²×C₇	1	2	yes	—
200	C₂×#104	C₂²×C₇	1	1	yes	characteristic
201	#416	C₂²×C₇	1	1	yes	characteristic
202	#413	C₂²×C₇	1	2	yes	—
203	#408	C₂²×C₇	1	2	yes	—
204	#405	C₂²×C₇	1	1	yes	characteristic
205	C₄×M₁₆	C₂²×C₇	1	2	yes	—
206	C₂×#97	C₂²×C₇	1	1	yes	characteristic
207	#344	C₂²×C₇	1	2	yes	—
208	#341	C₂²×C₇	1	1	yes	characteristic
209	#341	C₂²×C₇	1	2	yes	—
210	#339	C₂²×C₇	1	1	yes	characteristic
211	C₂³×C₇	—	2	1	no	—
212	C₂³×C₇	—	2	2	no	—
213	C₂³×C₇	2₋¹⁺⁴	1	1	yes	characteristic
214	C₇×Q₈	—	2	1	no	—
215	C₇×Q₈	—	2	2	no	—
216	C₇×Q₈	—	2	2	no	—
217	C₇×Q₈	C₄×D₄	1	2	yes	—
218	C₇×D₄	—	2	2	no	—
219	C₇×D₄	—	2	2	no	—
220	C₇×D₄	—	2	2	no	—
221	C₇×D₄	—	2	2	no	—
222	C₇×D₄	—	2	1	no	—
223	C₇×D₄	—	4	2	no	—
224	C₇×D₄	—	4	2	no	—
225	C₇×D₄	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₇	—	2	1	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	4	2	no	—
232	C₂×C₄×C₇	—	4	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	8	1	no	—
235	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
241	C₇×C₈	—	2	2	no	—
242	C₇×C₈	—	2	4	no	—
243	C₇×C₈	—	2	2	no	—
244	C₇×C₈	—	2	4	no	—
245	C₇×C₈	—	4	2	no	—
246	C₇×C₈	—	4	1	no	—
247	C₇×C₈	C₄×D₄	1	1	yes	characteristic
248	C₇×C₈	C₄×D₄	1	1	yes	characteristic
249	C₇×C₈	C₄×D₄	1	1	yes	characteristic
250	C₇×C₈	C₄×D₄	1	1	yes	characteristic
251	C₂×#41	C₂³×C₇	1	2	yes	—
252	C₂×#41	C₂³×C₇	1	1	yes	characteristic
253	#137	—	2	2	no	—
254	#137	C₂×C₄×C₇	1	4	yes	—
255	AGL(1,ℤ/8)	—	2	2	no	—
256	AGL(1,ℤ/8)	C₂×C₄×C₇	1	4	yes	—
257	#135	—	2	4	no	—
258	#135	—	2	1	no	—
259	#135	—	2	1	no	—
260	#135	—	2	1	no	—
261	#135	—	2	1	no	—
262	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
263	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
264	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
265	#131	—	2	1	no	—
266	#131	—	2	1	no	—
267	#131	—	2	4	no	—
268	#131	—	2	4	no	—
269	#131	—	2	4	no	—
270	#131	—	4	2	no	—
271	#131	C₂×C₄×C₇	1	2	yes	—
272	#131	C₂×C₄×C₇	1	2	yes	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	2	4	no	—
275	C₂×M₁₆	—	4	2	no	—
276	C₂×M₁₆	C₂³×C₇	1	2	yes	—
277	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
278	C₂×M₁₆	C₂³×C₇	1	2	yes	—
279	C₂×M₁₆	C₂³×C₇	1	2	yes	—
280	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
284	#117	C₂³×C₇	1	1	yes	characteristic
285	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
286	#108	—	2	4	no	—
287	#108	—	2	4	no	—
288	#108	—	2	1	no	—
289	#108	—	2	1	no	—
290	#108	C₂×C₄×C₇	1	2	yes	—
291	#108	C₂×C₄×C₇	1	2	yes	—
292	#108	C₇×D₄	1	2	yes	—
293	#108	C₇×D₄	1	2	yes	—
294	#104	—	2	4	no	—
295	#104	—	2	2	no	—
296	#104	—	2	2	no	—
297	#104	C₇×D₄	1	4	yes	—
298	#103	—	2	1	no	—
299	#102	—	2	1	no	—
300	#101	C₂×C₄×C₇	1	4	yes	—
301	#100	C₂×C₄×C₇	1	4	yes	—
302	C₂²⋊C₈	—	4	2	no	—
303	#97	—	2	1	no	—
304	#97	—	2	1	no	—
305	#97	—	2	1	no	—
306	#97	—	2	2	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	2	2	no	—
309	C₂²×C₇	—	2	2	no	—
310	C₂²×C₇	—	4	1	no	—
311	C₂²×C₇	—	4	2	no	—
312	C₂²×C₇	—	8	1	no	—
313	C₂²×C₇	—	8	2	no	—
314	C₂²×C₇	#520	1	1	yes	characteristic
315	C₂²×C₇	#547	1	1	yes	characteristic
316	C₂²×C₇	#548	1	1	yes	characteristic
317	C₄×C₇	—	2	2	no	—
318	C₄×C₇	—	4	2	no	—
319	C₄×C₇	—	4	2	no	—
320	C₄×C₇	—	8	1	no	—
321	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
322	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
323	C₄×C₇	D₄²	1	1	yes	characteristic
324	C₄×C₇	#553	1	1	yes	characteristic
325	#41	—	2	1	no	—
326	#41	—	2	1	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	2	2	no	—
330	#41	—	2	2	no	—
331	#41	C₂²×C₄×C₇	1	2	yes	—
332	#41	C₂×C₇×D₄	1	2	yes	—
333	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
334	C₂×Q₈	C₇×#41	1	1	yes	characteristic
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
338	C₂×D₄	C₇×#41	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
343	Q₁₆	—	2	4	no	—
344	Q₁₆	—	2	1	no	—
345	Q₁₆	—	2	1	no	—
346	SD₁₆	—	2	4	no	—
347	SD₁₆	—	2	4	no	—
348	SD₁₆	—	2	2	no	—
349	SD₁₆	—	2	2	no	—
350	D₈	—	2	4	no	—
351	D₈	—	2	1	no	—
352	D₈	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	2	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	4	4	no	—
362	M₁₆	—	4	4	no	—
363	M₁₆	C₂²×C₄×C₇	1	2	yes	—
364	M₁₆	C₂²×C₄×C₇	1	4	yes	—
365	M₁₆	C₂×C₇×D₄	1	4	yes	—
366	M₁₆	C₂×C₇×D₄	1	2	yes	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	4	4	no	—
378	C₂×C₈	—	4	4	no	—
379	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
381	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
382	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
383	C₂×C₈	C₇×#41	1	1	yes	characteristic
384	C₂×C₈	C₇×#41	1	1	yes	characteristic
385	C₄⋊C₄	—	2	1	no	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	C₂×C₇×D₄	1	2	yes	—
390	C₂×C₇	—	2	1	no	—
391	C₂×C₇	—	2	1	no	—
392	C₂×C₇	—	2	1	no	—
393	C₂×C₇	—	4	2	no	—
394	C₂×C₇	—	8	2	no	—
395	C₂×C₇	#2361	1	1	yes	characteristic
396	C₂³	—	2	1	no	—
397	C₂³	—	2	2	no	—
398	C₂³	C₇×2₋¹⁺⁴	1	1	yes	characteristic
399	Q₈	—	2	1	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	C₄×C₇×D₄	1	2	yes	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	1	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	C₄×C₇×D₄	1	2	yes	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	8	1	no	—
420	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
423	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
425	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	4	no	—
428	C₈	—	2	2	no	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₈	—	4	1	no	—
432	C₈	C₄×C₇×D₄	1	1	yes	characteristic
433	C₈	C₄×C₇×D₄	1	1	yes	characteristic
434	C₈	C₄×C₇×D₄	1	1	yes	characteristic
435	C₈	C₄×C₇×D₄	1	1	yes	characteristic
436	C₇	#23043	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	C₇×#520	1	1	yes	characteristic
443	C₂²	C₇×#547	1	1	yes	characteristic
444	C₂²	C₇×#548	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	8	1	no	—
449	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
450	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
451	C₄	C₇×D₄²	1	1	yes	characteristic
452	C₄	C₇×#553	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	4	2	no	—
457	C₂	—	8	2	no	—
458	C₂	C₇×#2361	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂×C₇	#2361
prime radical	C₇×#3067	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2957	C₂	semidirect
3. C₇×#2956	C₂	semidirect
4. C₇×#2916	C₂	semidirect
5. C₇×#1975	C₂	semidirect
6. C₇×#1953	C₂	semidirect
7. C₇×#1932	C₂	semidirect
8. C₇×#1881	C₂	semidirect
9. C₇×#1858	C₂	semidirect
10. C₇×#1778	C₂	semidirect
11. C₇×#1765	C₂	semidirect
17. C₇×#473	C₄	semidirect
18. C₇×#472	C₄	semidirect
19. C₇×#471	C₄	semidirect
44. #23043	C₇	direct (N × H)
104. #2957	C₂×C₇	semidirect
105. #2956	C₂×C₇	semidirect
106. #2916	C₂×C₇	semidirect
107. #1975	C₂×C₇	semidirect
108. #1953	C₂×C₇	semidirect
109. #1932	C₂×C₇	semidirect
110. #1881	C₂×C₇	semidirect
111. #1858	C₂×C₇	semidirect
112. #1778	C₂×C₇	semidirect
113. #1765	C₂×C₇	semidirect
184. #473	C₄×C₇	semidirect
185. #472	C₄×C₇	semidirect
186. #471	C₄×C₇	semidirect
436. C₇	#23043	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3067	2
C₇×#2957	2
C₇×#2956	2
C₇×#2916	2
C₇×#1975	2
C₇×#1953	2
C₇×#1932	2
C₇×#1881	2
C₇×#1858	2
C₇×#1778	2
C₇×#1765	2
#23043	7

Subgroups — C7×#23043 #13200259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23043 #13200259