Subgroups — C₇×#23047 #13200263

Order 1792.

840 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	C₂×C₇×#473	C₂	1	1	yes	maximal, characteristic
2	C₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2947	C₂	1	2	yes	maximal
4	C₇×#2912	C₂	1	1	yes	maximal, characteristic
5	C₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1930	C₂	1	2	yes	maximal, complemented
8	C₇×#1882	C₂	1	2	yes	maximal
9	C₇×#1857	C₂	1	2	yes	maximal, complemented
10	C₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1765	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#137	C₂²	1	2	yes	—
13	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₇×#131	C₂²	1	1	yes	characteristic
15	C₇×#520	C₂²	1	2	yes	—
16	C₇×#519	C₂²	1	2	yes	—
17	C₇×#473	C₄	1	8	yes	complemented
18	C₇×#441	—	2	1	no	—
19	C₇×#441	—	2	1	no	—
20	C₇×#441	—	2	2	no	—
21	C₇×#440	—	2	2	no	—
22	C₄×C₇×Q₁₆	—	2	2	no	—
23	C₄×C₇×Q₁₆	—	2	2	no	—
24	C₄×C₇×SD₁₆	—	2	2	no	—
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₇×#428	—	2	2	no	—
27	C₇×#428	C₂²	1	2	yes	—
28	C₇×#428	C₂²	1	2	yes	—
29	C₇×#427	—	2	1	no	—
30	C₇×#427	C₂²	1	1	yes	characteristic
31	C₂×C₇×#106	—	2	1	no	—
32	C₂×C₇×#106	C₂²	1	1	yes	characteristic
33	C₂×C₇×#104	C₂²	1	1	yes	characteristic
34	C₇×#419	C₂²	1	2	yes	—
35	C₇×#416	C₂²	1	1	yes	characteristic
36	C₂×C₇×#103	C₂²	1	2	yes	—
37	C₂×C₇×#101	C₂²	1	2	yes	—
38	C₇×#405	C₂²	1	2	yes	—
39	C₇×#405	C₂²	1	1	yes	characteristic
40	C₂×C₇×#97	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	2	yes	—
42	C₇×#343	C₂²	1	2	yes	—
43	C₇×#341	C₂²	1	1	yes	characteristic
44	C₇×#339	C₂²	1	1	yes	characteristic
45	C₇×#339	C₂²	1	2	yes	—
46	#23047	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×C₇×#41	C₂³	1	1	yes	characteristic
48	C₂²×C₇×Q₈	C₂³	1	2	yes	—
49	C₇×#137	—	2	4	no	—
50	C₇×#137	C₂×C₄	1	8	yes	—
51	C₂×C₇×Q₁₆	—	2	2	no	—
52	C₂×C₇×Q₁₆	—	2	1	no	—
53	C₂×C₇×Q₁₆	—	2	1	no	—
54	C₂×C₇×Q₁₆	—	2	2	no	—
55	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
56	C₂×C₇×SD₁₆	—	2	2	no	—
57	C₇×#131	—	2	2	no	—
58	C₇×#131	C₂×C₄	1	4	yes	—
59	C₂×C₇×M₁₆	—	2	1	no	—
60	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₇×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₇×C₈	—	2	1	no	—
64	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₄×C₇×Q₈	—	2	2	no	—
67	C₄×C₇×Q₈	—	2	2	no	—
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	—	2	2	no	—
71	C₄×C₇×D₄	—	2	2	no	—
72	C₄×C₇×D₄	—	4	2	no	—
73	C₇×#117	—	2	2	no	—
74	C₇×#117	—	4	2	no	—
75	C₇×#117	C₂³	1	1	yes	characteristic
76	C₇×#117	C₂³	1	2	yes	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
80	C₇×#108	C₂×C₄	1	4	yes	complemented
81	C₇×#107	—	2	2	no	—
82	C₇×#107	—	2	2	no	—
83	C₇×#107	D₄	1	2	yes	—
84	C₇×#106	—	2	1	no	—
85	C₇×#106	—	2	1	no	—
86	C₇×#106	—	2	2	no	—
87	C₇×#106	—	2	2	no	—
88	C₇×#106	D₄	1	1	yes	characteristic
89	C₇×#106	D₄	1	1	yes	characteristic
90	C₇×#104	—	2	2	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#103	—	2	2	no	—
93	C₇×#103	—	2	2	no	—
94	C₇×#103	—	2	2	no	—
95	C₇×#103	D₄	1	2	yes	—
96	C₇×#102	D₄	1	2	yes	—
97	C₇×#101	C₂×C₄	1	8	yes	complemented
98	C₇×#97	—	2	2	no	—
99	C₇×#97	—	2	1	no	—
100	C₇×#97	—	2	2	no	—
101	C₄×C₇×C₈	—	2	2	no	—
102	C₄×C₇×C₈	—	2	1	no	—
103	C₇×#95	—	4	2	no	—
104	C₂×#473	C₂×C₇	1	1	yes	characteristic
105	#2950	C₂×C₇	1	1	yes	characteristic, complemented
106	#2947	C₂×C₇	1	2	yes	—
107	#2912	C₂×C₇	1	1	yes	characteristic
108	#1971	C₂×C₇	1	1	yes	characteristic, complemented
109	#1951	C₂×C₇	1	1	yes	characteristic, complemented
110	#1930	C₂×C₇	1	2	yes	complemented
111	#1882	C₂×C₇	1	2	yes	—
112	#1857	C₂×C₇	1	2	yes	complemented
113	#1773	C₂×C₇	1	1	yes	characteristic, complemented
114	#1765	C₂×C₇	1	1	yes	characteristic
115	C₇×#41	—	2	1	no	—
116	C₇×#41	—	2	1	no	—
117	C₇×#41	C₂²×C₄	1	2	yes	—
118	C₇×#41	#41	1	2	yes	—
119	C₂×C₇×Q₈	—	2	2	no	—
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	2	2	no	—
122	C₂×C₇×Q₈	—	2	2	no	—
123	C₂×C₇×Q₈	—	2	2	no	—
124	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
125	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇	—	2	1	no	—
129	C₂²×C₄×C₇	—	2	2	no	—
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	4	2	no	—
133	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
134	C₇×Q₁₆	—	2	8	no	—
135	C₇×Q₁₆	—	2	4	no	—
136	C₇×Q₁₆	—	2	4	no	—
137	C₇×SD₁₆	—	2	8	no	—
138	C₇×M₁₆	—	2	1	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	—	2	4	no	—
141	C₇×M₁₆	—	2	1	no	—
142	C₇×M₁₆	—	2	1	no	—
143	C₇×M₁₆	C₂²×C₄	1	2	yes	—
144	C₇×M₁₆	C₂²×C₄	1	4	yes	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	4	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×C₈	#41	1	2	yes	—
156	C₇×C₄⋊C₄	—	2	2	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	4	2	no	—
159	C₇×C₄⋊C₄	—	4	2	no	—
160	C₇×C₄⋊C₄	—	4	2	no	—
161	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
162	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	2	1	no	—
165	C₇×C₂²⋊C₄	—	2	2	no	—
166	C₇×C₂²⋊C₄	—	4	2	no	—
167	C₄²×C₇	—	2	2	no	—
168	C₄²×C₇	—	2	1	no	—
169	C₄²×C₇	—	2	1	no	—
170	C₄²×C₇	—	2	1	no	—
171	C₄²×C₇	—	4	2	no	—
172	C₄²×C₇	—	4	2	no	—
173	C₄²×C₇	—	4	2	no	—
174	C₂×#137	C₂²×C₇	1	2	yes	—
175	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
176	C₂×#131	C₂²×C₇	1	1	yes	characteristic
177	#520	C₂²×C₇	1	2	yes	—
178	#519	C₂²×C₇	1	2	yes	—
179	#473	C₄×C₇	1	8	yes	complemented
180	#441	—	2	1	no	—
181	#441	—	2	1	no	—
182	#441	—	2	2	no	—
183	#440	—	2	2	no	—
184	C₄×Q₁₆	—	2	2	no	—
185	C₄×Q₁₆	—	2	2	no	—
186	C₄×SD₁₆	—	2	2	no	—
187	C₂×#108	C₂²×C₇	1	1	yes	characteristic
188	#428	—	2	2	no	—
189	#428	C₂²×C₇	1	2	yes	—
190	#428	C₂²×C₇	1	2	yes	—
191	#427	—	2	1	no	—
192	#427	C₂²×C₇	1	1	yes	characteristic
193	C₂×#106	—	2	1	no	—
194	C₂×#106	C₂²×C₇	1	1	yes	characteristic
195	C₂×#104	C₂²×C₇	1	1	yes	characteristic
196	#419	C₂²×C₇	1	2	yes	—
197	#416	C₂²×C₇	1	1	yes	characteristic
198	C₂×#103	C₂²×C₇	1	2	yes	—
199	C₂×#101	C₂²×C₇	1	2	yes	—
200	#405	C₂²×C₇	1	2	yes	—
201	#405	C₂²×C₇	1	1	yes	characteristic
202	C₂×#97	C₂²×C₇	1	1	yes	characteristic
203	#391	C₂²×C₇	1	2	yes	—
204	#343	C₂²×C₇	1	2	yes	—
205	#341	C₂²×C₇	1	1	yes	characteristic
206	#339	C₂²×C₇	1	1	yes	characteristic
207	#339	C₂²×C₇	1	2	yes	—
208	C₂³×C₇	—	2	1	no	—
209	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
210	C₇×Q₈	—	2	1	no	—
211	C₇×Q₈	—	2	4	no	—
212	C₇×Q₈	—	2	4	no	—
213	C₇×Q₈	—	4	2	no	—
214	C₇×Q₈	—	4	2	no	—
215	C₇×Q₈	C₄×D₄	1	2	yes	—
216	C₇×D₄	—	2	2	no	—
217	C₇×D₄	—	2	2	no	—
218	C₇×D₄	—	2	1	no	—
219	C₇×D₄	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	4	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	2	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	8	2	no	—
233	C₂×C₄×C₇	—	16	2	no	—
234	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇	C₂×#41	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	4	no	—
242	C₇×C₈	—	2	2	no	—
243	C₇×C₈	—	4	1	no	—
244	C₇×C₈	C₄×D₄	1	2	yes	—
245	C₇×C₈	C₄×D₄	1	2	yes	—
246	C₂×#41	C₂³×C₇	1	1	yes	characteristic
247	C₂²×Q₈	C₂³×C₇	1	2	yes	—
248	#137	—	2	4	no	—
249	#137	C₂×C₄×C₇	1	8	yes	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
255	C₂×SD₁₆	—	2	2	no	—
256	#131	—	2	2	no	—
257	#131	C₂×C₄×C₇	1	4	yes	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
260	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
261	C₂×M₁₆	C₂³×C₇	1	2	yes	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	—	4	2	no	—
272	#117	—	2	2	no	—
273	#117	—	4	2	no	—
274	#117	C₂³×C₇	1	1	yes	characteristic
275	#117	C₂³×C₇	1	2	yes	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
278	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
279	#108	C₂×C₄×C₇	1	4	yes	complemented
280	#107	—	2	2	no	—
281	#107	—	2	2	no	—
282	#107	C₇×D₄	1	2	yes	—
283	#106	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	2	no	—
286	#106	—	2	2	no	—
287	#106	C₇×D₄	1	1	yes	characteristic
288	#106	C₇×D₄	1	1	yes	characteristic
289	#104	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	C₇×D₄	1	2	yes	—
295	#102	C₇×D₄	1	2	yes	—
296	#101	C₂×C₄×C₇	1	8	yes	complemented
297	#97	—	2	2	no	—
298	#97	—	2	1	no	—
299	#97	—	2	2	no	—
300	C₄×C₈	—	2	2	no	—
301	C₄×C₈	—	2	1	no	—
302	#95	—	4	2	no	—
303	C₂²×C₇	—	2	2	no	—
304	C₂²×C₇	—	2	2	no	—
305	C₂²×C₇	—	4	2	no	—
306	C₂²×C₇	#520	1	1	yes	characteristic
307	C₂²×C₇	D₄²	1	1	yes	characteristic
308	C₂²×C₇	#553	1	1	yes	characteristic
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	4	4	no	—
311	C₄×C₇	—	4	2	no	—
312	C₄×C₇	—	4	2	no	—
313	C₄×C₇	—	4	2	no	—
314	C₄×C₇	—	8	1	no	—
315	C₄×C₇	—	8	2	no	—
316	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
317	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
318	C₄×C₇	#547	1	1	yes	characteristic
319	C₄×C₇	#548	1	1	yes	characteristic
320	#41	—	2	1	no	—
321	#41	—	2	1	no	—
322	#41	C₂²×C₄×C₇	1	2	yes	—
323	#41	C₇×#41	1	2	yes	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
330	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
339	Q₁₆	—	2	8	no	—
340	Q₁₆	—	2	4	no	—
341	Q₁₆	—	2	4	no	—
342	SD₁₆	—	2	8	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	C₂²×C₄×C₇	1	2	yes	—
349	M₁₆	C₂²×C₄×C₇	1	4	yes	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
357	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
358	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
360	C₂×C₈	C₇×#41	1	2	yes	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
367	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
368	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	4	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	4	2	no	—
379	C₂×C₇	—	2	1	no	—
380	C₂×C₇	—	2	1	no	—
381	C₂×C₇	—	4	2	no	—
382	C₂×C₇	#2361	1	1	yes	characteristic
383	C₂×C₇	#3289	1	2	yes	—
384	C₂³	—	2	1	no	—
385	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	C₄×C₇×D₄	1	2	yes	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	2	1	no	—
395	D₄	C₄×C₇×D₄	1	2	yes	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	16	2	no	—
410	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
414	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
415	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	4	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	C₄×C₇×D₄	1	2	yes	—
421	C₈	C₄×C₇×D₄	1	2	yes	—
422	C₇	#23047	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	C₇×#520	1	1	yes	characteristic
427	C₂²	C₇×D₄²	1	1	yes	characteristic
428	C₂²	C₇×#553	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	4	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
437	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
438	C₄	C₇×#547	1	1	yes	characteristic
439	C₄	C₇×#548	1	1	yes	characteristic
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	4	2	no	—
443	C₂	C₇×#2361	1	1	yes	characteristic
444	C₂	C₇×#3289	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#41	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2950	C₂	semidirect
5. C₇×#1971	C₂	semidirect
6. C₇×#1951	C₂	semidirect
7. C₇×#1930	C₂	semidirect
9. C₇×#1857	C₂	semidirect
10. C₇×#1773	C₂	semidirect
17. C₇×#473	C₄	semidirect
46. #23047	C₇	direct (N × H)
55. C₂×C₇×Q₁₆	C₂×C₄	semidirect
80. C₇×#108	C₂×C₄	semidirect
97. C₇×#101	C₂×C₄	semidirect
105. #2950	C₂×C₇	semidirect
108. #1971	C₂×C₇	semidirect
109. #1951	C₂×C₇	semidirect
110. #1930	C₂×C₇	semidirect
112. #1857	C₂×C₇	semidirect
113. #1773	C₂×C₇	semidirect
179. #473	C₄×C₇	semidirect
254. C₂×Q₁₆	C₂×C₄×C₇	semidirect
279. #108	C₂×C₄×C₇	semidirect
296. #101	C₂×C₄×C₇	semidirect
422. C₇	#23047	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#473	2
C₇×#2950	2
C₇×#2947	2
C₇×#2912	2
C₇×#1971	2
C₇×#1951	2
C₇×#1930	2
C₇×#1882	2
C₇×#1857	2
C₇×#1773	2
C₇×#1765	2
#23047	7

Subgroups — C7×#23047 #13200263

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23047 #13200263