Subgroups — C₇×#23042 #13200258

Order 1792.

824 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	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×#1974	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	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	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×C₄×C₇×C₈	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	#23042	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	2	yes	—
92	C₇×#104	D₄	1	2	yes	—
93	C₇×#103	—	2	1	no	—
94	C₇×#102	—	2	1	no	—
95	C₇×#101	C₂×C₄	1	4	yes	—
96	C₇×#100	C₂×C₄	1	4	yes	—
97	C₇×C₂²⋊C₈	—	4	2	no	—
98	C₇×#97	—	2	1	no	—
99	C₇×#97	—	2	2	no	—
100	C₄×C₇×C₈	—	2	1	no	—
101	C₄×C₇×C₈	—	2	1	no	—
102	C₄×C₇×C₈	—	2	1	no	—
103	C₄×C₇×C₈	—	2	2	no	—
104	#3067	C₂×C₇	1	1	yes	characteristic
105	#2957	C₂×C₇	1	1	yes	characteristic, complemented
106	#2956	C₂×C₇	1	2	yes	complemented
107	#2916	C₂×C₇	1	1	yes	characteristic, complemented
108	#1974	C₂×C₇	1	1	yes	characteristic, complemented
109	#1953	C₂×C₇	1	1	yes	characteristic, complemented
110	#1932	C₂×C₇	1	2	yes	complemented
111	#1881	C₂×C₇	1	2	yes	complemented
112	#1858	C₂×C₇	1	2	yes	complemented
113	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
114	#1764	C₂×C₇	1	1	yes	characteristic, complemented
115	C₇×#41	—	2	1	no	—
116	C₇×#41	—	2	1	no	—
117	C₇×#41	—	2	2	no	—
118	C₇×#41	—	2	2	no	—
119	C₇×#41	—	2	2	no	—
120	C₇×#41	—	2	2	no	—
121	C₇×#41	C₂²×C₄	1	2	yes	—
122	C₇×#41	C₂×D₄	1	2	yes	—
123	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
124	C₂×C₇×Q₈	#41	1	1	yes	characteristic
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	2	no	—
127	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
128	C₂×C₇×D₄	#41	1	1	yes	characteristic
129	C₂²×C₄×C₇	—	2	1	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
133	C₇×Q₁₆	—	2	4	no	—
134	C₇×Q₁₆	—	2	1	no	—
135	C₇×Q₁₆	—	2	1	no	—
136	C₇×SD₁₆	—	2	4	no	—
137	C₇×SD₁₆	—	2	4	no	—
138	C₇×SD₁₆	—	2	2	no	—
139	C₇×SD₁₆	—	2	2	no	—
140	C₇×D₈	—	2	4	no	—
141	C₇×D₈	—	2	1	no	—
142	C₇×D₈	—	2	1	no	—
143	C₇×M₁₆	—	2	1	no	—
144	C₇×M₁₆	—	2	2	no	—
145	C₇×M₁₆	—	2	1	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	—	2	2	no	—
151	C₇×M₁₆	—	4	4	no	—
152	C₇×M₁₆	—	4	4	no	—
153	C₇×M₁₆	C₂²×C₄	1	2	yes	—
154	C₇×M₁₆	C₂²×C₄	1	4	yes	—
155	C₇×M₁₆	C₂×D₄	1	4	yes	—
156	C₇×M₁₆	C₂×D₄	1	2	yes	—
157	C₂×C₇×C₈	—	2	2	no	—
158	C₂×C₇×C₈	—	2	2	no	—
159	C₂×C₇×C₈	—	2	1	no	—
160	C₂×C₇×C₈	—	2	1	no	—
161	C₂×C₇×C₈	—	2	2	no	—
162	C₂×C₇×C₈	—	2	2	no	—
163	C₂×C₇×C₈	—	2	1	no	—
164	C₂×C₇×C₈	—	2	1	no	—
165	C₂×C₇×C₈	—	2	1	no	—
166	C₂×C₇×C₈	—	2	2	no	—
167	C₂×C₇×C₈	—	4	4	no	—
168	C₂×C₇×C₈	—	4	4	no	—
169	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₇×C₈	#41	1	1	yes	characteristic
174	C₂×C₇×C₈	#41	1	1	yes	characteristic
175	C₇×C₄⋊C₄	—	2	1	no	—
176	C₇×C₂²⋊C₄	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	C₄²×C₇	—	2	1	no	—
179	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
181	#575	C₂²×C₇	1	2	yes	—
182	C₂×#135	C₂²×C₇	1	1	yes	characteristic
183	#568	C₂²×C₇	1	2	yes	—
184	#568	C₂²×C₇	1	2	yes	—
185	C₂×#131	C₂²×C₇	1	1	yes	characteristic
186	#473	C₄×C₇	1	2	yes	complemented
187	#472	C₄×C₇	1	2	yes	complemented
188	#471	C₄×C₇	1	4	yes	complemented
189	#444	—	2	2	no	—
190	#444	—	2	4	no	—
191	#443	—	2	2	no	—
192	#443	—	2	4	no	—
193	#430	—	2	2	no	—
194	#430	C₂²×C₇	1	2	yes	—
195	#430	C₂²×C₇	1	2	yes	—
196	C₂×#108	—	2	2	no	—
197	C₂×#108	C₂²×C₇	1	1	yes	characteristic
198	C₂×#108	C₂²×C₇	1	1	yes	characteristic
199	C₂×#108	C₂²×C₇	1	1	yes	characteristic
200	#421	C₂²×C₇	1	2	yes	—
201	C₂×#104	C₂²×C₇	1	2	yes	—
202	C₂×#104	C₂²×C₇	1	1	yes	characteristic
203	#416	C₂²×C₇	1	1	yes	characteristic
204	#413	C₂²×C₇	1	2	yes	—
205	#408	C₂²×C₇	1	2	yes	—
206	#405	C₂²×C₇	1	1	yes	characteristic
207	C₄×M₁₆	C₂²×C₇	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
209	#344	C₂²×C₇	1	2	yes	—
210	#341	C₂²×C₇	1	1	yes	characteristic
211	#341	C₂²×C₇	1	2	yes	—
212	#339	C₂²×C₇	1	1	yes	characteristic
213	C₂³×C₇	—	2	1	no	—
214	C₂³×C₇	—	2	2	no	—
215	C₂³×C₇	2₋¹⁺⁴	1	1	yes	characteristic
216	C₇×Q₈	—	2	1	no	—
217	C₇×Q₈	—	2	2	no	—
218	C₇×Q₈	—	2	2	no	—
219	C₇×Q₈	C₄×D₄	1	2	yes	—
220	C₇×D₄	—	2	2	no	—
221	C₇×D₄	—	2	2	no	—
222	C₇×D₄	—	2	2	no	—
223	C₇×D₄	—	2	2	no	—
224	C₇×D₄	—	2	1	no	—
225	C₇×D₄	—	4	2	no	—
226	C₇×D₄	—	4	2	no	—
227	C₇×D₄	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	1	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	2	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
244	C₇×C₈	—	2	2	no	—
245	C₇×C₈	—	2	4	no	—
246	C₇×C₈	—	2	2	no	—
247	C₇×C₈	—	2	4	no	—
248	C₇×C₈	—	4	2	no	—
249	C₇×C₈	—	4	1	no	—
250	C₇×C₈	C₄×D₄	1	1	yes	characteristic
251	C₇×C₈	C₄×D₄	1	1	yes	characteristic
252	C₇×C₈	C₄×D₄	1	1	yes	characteristic
253	C₇×C₈	C₄×D₄	1	1	yes	characteristic
254	C₂×#41	C₂³×C₇	1	2	yes	—
255	C₂×#41	C₂³×C₇	1	1	yes	characteristic
256	#137	—	2	2	no	—
257	#137	C₂×C₄×C₇	1	4	yes	—
258	AGL(1,ℤ/8)	—	2	2	no	—
259	AGL(1,ℤ/8)	C₂×C₄×C₇	1	4	yes	—
260	#135	—	2	4	no	—
261	#135	—	2	1	no	—
262	#135	—	2	1	no	—
263	#135	—	2	1	no	—
264	#135	—	2	1	no	—
265	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
266	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
267	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
268	#131	—	2	1	no	—
269	#131	—	2	1	no	—
270	#131	—	2	4	no	—
271	#131	—	2	4	no	—
272	#131	—	2	4	no	—
273	#131	—	4	2	no	—
274	#131	C₂×C₄×C₇	1	2	yes	—
275	#131	C₂×C₄×C₇	1	2	yes	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	4	no	—
278	C₂×M₁₆	—	4	2	no	—
279	C₂×M₁₆	C₂³×C₇	1	2	yes	—
280	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
281	C₂×M₁₆	C₂³×C₇	1	2	yes	—
282	C₂×M₁₆	C₂³×C₇	1	2	yes	—
283	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
287	#117	C₂³×C₇	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
289	#108	—	2	4	no	—
290	#108	—	2	4	no	—
291	#108	—	2	1	no	—
292	#108	—	2	1	no	—
293	#108	C₂×C₄×C₇	1	2	yes	—
294	#108	C₂×C₄×C₇	1	2	yes	—
295	#108	C₇×D₄	1	2	yes	—
296	#108	C₇×D₄	1	2	yes	—
297	#104	—	2	4	no	—
298	#104	—	2	2	no	—
299	#104	—	2	2	no	—
300	#104	C₇×D₄	1	2	yes	—
301	#104	C₇×D₄	1	2	yes	—
302	#103	—	2	1	no	—
303	#102	—	2	1	no	—
304	#101	C₂×C₄×C₇	1	4	yes	—
305	#100	C₂×C₄×C₇	1	4	yes	—
306	C₂²⋊C₈	—	4	2	no	—
307	#97	—	2	1	no	—
308	#97	—	2	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	2	2	no	—
313	C₂²×C₇	—	2	2	no	—
314	C₂²×C₇	—	4	1	no	—
315	C₂²×C₇	—	4	2	no	—
316	C₂²×C₇	—	8	1	no	—
317	C₂²×C₇	—	8	2	no	—
318	C₂²×C₇	#520	1	1	yes	characteristic
319	C₂²×C₇	#547	1	1	yes	characteristic
320	C₂²×C₇	#548	1	1	yes	characteristic
321	C₄×C₇	—	2	2	no	—
322	C₄×C₇	—	2	2	no	—
323	C₄×C₇	—	4	1	no	—
324	C₄×C₇	—	4	2	no	—
325	C₄×C₇	—	8	1	no	—
326	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
327	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
328	C₄×C₇	D₄²	1	1	yes	characteristic
329	C₄×C₇	#553	1	1	yes	characteristic
330	#41	—	2	1	no	—
331	#41	—	2	1	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	C₂²×C₄×C₇	1	2	yes	—
337	#41	C₂×C₇×D₄	1	2	yes	—
338	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
339	C₂×Q₈	C₇×#41	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
343	C₂×D₄	C₇×#41	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	Q₁₆	—	2	4	no	—
349	Q₁₆	—	2	1	no	—
350	Q₁₆	—	2	1	no	—
351	SD₁₆	—	2	4	no	—
352	SD₁₆	—	2	4	no	—
353	SD₁₆	—	2	2	no	—
354	SD₁₆	—	2	2	no	—
355	D₈	—	2	4	no	—
356	D₈	—	2	1	no	—
357	D₈	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	4	4	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	C₂²×C₄×C₇	1	2	yes	—
369	M₁₆	C₂²×C₄×C₇	1	4	yes	—
370	M₁₆	C₂×C₇×D₄	1	4	yes	—
371	M₁₆	C₂×C₇×D₄	1	2	yes	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₂×C₈	—	4	4	no	—
384	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
385	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
386	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
387	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
388	C₂×C₈	C₇×#41	1	1	yes	characteristic
389	C₂×C₈	C₇×#41	1	1	yes	characteristic
390	C₄⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
395	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
396	C₂×C₇	—	2	1	no	—
397	C₂×C₇	—	2	1	no	—
398	C₂×C₇	—	2	1	no	—
399	C₂×C₇	—	4	2	no	—
400	C₂×C₇	—	8	2	no	—
401	C₂×C₇	#2361	1	1	yes	characteristic
402	C₂³	—	2	1	no	—
403	C₂³	—	2	2	no	—
404	C₂³	C₇×2₋¹⁺⁴	1	1	yes	characteristic
405	Q₈	—	2	1	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	2	2	no	—
408	Q₈	C₄×C₇×D₄	1	2	yes	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	2	2	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	C₄×C₇×D₄	1	2	yes	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
430	C₂×C₄	C₂×C₇×#41	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	C₈	—	2	2	no	—
434	C₈	—	2	4	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₈	—	4	2	no	—
438	C₈	—	4	1	no	—
439	C₈	C₄×C₇×D₄	1	1	yes	characteristic
440	C₈	C₄×C₇×D₄	1	1	yes	characteristic
441	C₈	C₄×C₇×D₄	1	1	yes	characteristic
442	C₈	C₄×C₇×D₄	1	1	yes	characteristic
443	C₇	#23042	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	8	1	no	—
448	C₂²	—	8	2	no	—
449	C₂²	C₇×#520	1	1	yes	characteristic
450	C₂²	C₇×#547	1	1	yes	characteristic
451	C₂²	C₇×#548	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
458	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
459	C₄	C₇×D₄²	1	1	yes	characteristic
460	C₄	C₇×#553	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	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×#1974	C₂	semidirect
6. C₇×#1953	C₂	semidirect
7. C₇×#1932	C₂	semidirect
8. C₇×#1881	C₂	semidirect
9. C₇×#1858	C₂	semidirect
10. C₄×C₇×#108	C₂	semidirect
11. C₇×#1764	C₂	semidirect
17. C₇×#473	C₄	semidirect
18. C₇×#472	C₄	semidirect
19. C₇×#471	C₄	semidirect
44. #23042	C₇	direct (N × H)
105. #2957	C₂×C₇	semidirect
106. #2956	C₂×C₇	semidirect
107. #2916	C₂×C₇	semidirect
108. #1974	C₂×C₇	semidirect
109. #1953	C₂×C₇	semidirect
110. #1932	C₂×C₇	semidirect
111. #1881	C₂×C₇	semidirect
112. #1858	C₂×C₇	semidirect
113. C₄×#108	C₂×C₇	semidirect
114. #1764	C₂×C₇	semidirect
186. #473	C₄×C₇	semidirect
187. #472	C₄×C₇	semidirect
188. #471	C₄×C₇	semidirect
443. C₇	#23042	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×#1974	2
C₇×#1953	2
C₇×#1932	2
C₇×#1881	2
C₇×#1858	2
C₄×C₇×#108	2
C₇×#1764	2
#23042	7

Subgroups — C7×#23042 #13200258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23042 #13200258