Subgroups — C₇×#23045 #13200261

Order 1792.

844 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	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×#2913	C₂	1	1	yes	maximal, characteristic
5	C₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1952	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×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	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	2	no	—
19	C₇×#441	—	2	2	no	—
20	C₇×#440	—	2	2	no	—
21	C₄×C₇×Q₁₆	—	2	1	no	—
22	C₄×C₇×Q₁₆	—	2	1	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×#107	—	2	1	no	—
32	C₂×C₇×#107	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×C₄×C₇×C₈	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	#23045	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	1	no	—
82	C₇×#107	—	2	1	no	—
83	C₇×#107	—	2	2	no	—
84	C₇×#107	—	2	2	no	—
85	C₇×#107	D₄	1	1	yes	characteristic
86	C₇×#107	D₄	1	1	yes	characteristic
87	C₇×#106	—	2	2	no	—
88	C₇×#106	—	2	2	no	—
89	C₇×#106	D₄	1	2	yes	—
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	1	yes	characteristic
96	C₇×#103	D₄	1	1	yes	characteristic
97	C₇×#102	D₄	1	1	yes	characteristic
98	C₇×#102	D₄	1	1	yes	characteristic
99	C₇×#101	C₂×C₄	1	8	yes	complemented
100	C₇×#97	—	2	2	no	—
101	C₇×#97	—	2	1	no	—
102	C₄×C₇×C₈	—	2	2	no	—
103	C₄×C₇×C₈	—	2	1	no	—
104	C₄×C₇×C₈	—	2	2	no	—
105	C₇×#95	—	4	2	no	—
106	C₂×#473	C₂×C₇	1	1	yes	characteristic
107	#2950	C₂×C₇	1	1	yes	characteristic, complemented
108	#2947	C₂×C₇	1	2	yes	—
109	#2913	C₂×C₇	1	1	yes	characteristic
110	#1969	C₂×C₇	1	1	yes	characteristic, complemented
111	#1952	C₂×C₇	1	1	yes	characteristic, complemented
112	#1930	C₂×C₇	1	2	yes	complemented
113	#1882	C₂×C₇	1	2	yes	—
114	#1857	C₂×C₇	1	2	yes	complemented
115	#1772	C₂×C₇	1	1	yes	characteristic, complemented
116	#1764	C₂×C₇	1	1	yes	characteristic
117	C₇×#41	—	2	1	no	—
118	C₇×#41	—	2	1	no	—
119	C₇×#41	C₂²×C₄	1	2	yes	—
120	C₇×#41	#41	1	2	yes	—
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	—	2	2	no	—
125	C₂×C₇×Q₈	—	2	2	no	—
126	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
127	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	—	2	1	no	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	2	no	—
134	C₂²×C₄×C₇	—	4	2	no	—
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×Q₁₆	—	2	8	no	—
137	C₇×Q₁₆	—	2	4	no	—
138	C₇×Q₁₆	—	2	4	no	—
139	C₇×SD₁₆	—	2	8	no	—
140	C₇×M₁₆	—	2	1	no	—
141	C₇×M₁₆	—	2	2	no	—
142	C₇×M₁₆	—	2	4	no	—
143	C₇×M₁₆	—	2	1	no	—
144	C₇×M₁₆	—	2	1	no	—
145	C₇×M₁₆	C₂²×C₄	1	2	yes	—
146	C₇×M₁₆	C₂²×C₄	1	4	yes	—
147	C₂×C₇×C₈	—	2	2	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	4	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₇×C₈	#41	1	2	yes	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	—	4	2	no	—
162	C₇×C₄⋊C₄	—	4	2	no	—
163	C₇×C₄⋊C₄	—	4	2	no	—
164	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
165	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
166	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
168	C₇×C₂²⋊C₄	—	2	1	no	—
169	C₇×C₂²⋊C₄	—	2	2	no	—
170	C₇×C₂²⋊C₄	—	4	2	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	2	1	no	—
173	C₄²×C₇	—	2	1	no	—
174	C₄²×C₇	—	2	1	no	—
175	C₄²×C₇	—	4	2	no	—
176	C₄²×C₇	—	4	2	no	—
177	C₄²×C₇	—	4	2	no	—
178	C₂×#137	C₂²×C₇	1	2	yes	—
179	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
180	C₂×#131	C₂²×C₇	1	1	yes	characteristic
181	#520	C₂²×C₇	1	2	yes	—
182	#519	C₂²×C₇	1	2	yes	—
183	#473	C₄×C₇	1	8	yes	complemented
184	#441	—	2	2	no	—
185	#441	—	2	2	no	—
186	#440	—	2	2	no	—
187	C₄×Q₁₆	—	2	1	no	—
188	C₄×Q₁₆	—	2	1	no	—
189	C₄×Q₁₆	—	2	2	no	—
190	C₄×SD₁₆	—	2	2	no	—
191	C₂×#108	C₂²×C₇	1	1	yes	characteristic
192	#428	—	2	2	no	—
193	#428	C₂²×C₇	1	2	yes	—
194	#428	C₂²×C₇	1	2	yes	—
195	#427	—	2	1	no	—
196	#427	C₂²×C₇	1	1	yes	characteristic
197	C₂×#107	—	2	1	no	—
198	C₂×#107	C₂²×C₇	1	1	yes	characteristic
199	C₂×#104	C₂²×C₇	1	1	yes	characteristic
200	#419	C₂²×C₇	1	2	yes	—
201	#416	C₂²×C₇	1	1	yes	characteristic
202	C₂×#103	C₂²×C₇	1	2	yes	—
203	C₂×#101	C₂²×C₇	1	2	yes	—
204	#405	C₂²×C₇	1	2	yes	—
205	#405	C₂²×C₇	1	1	yes	characteristic
206	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
207	#391	C₂²×C₇	1	2	yes	—
208	#343	C₂²×C₇	1	2	yes	—
209	#341	C₂²×C₇	1	1	yes	characteristic
210	#339	C₂²×C₇	1	1	yes	characteristic
211	#339	C₂²×C₇	1	2	yes	—
212	C₂³×C₇	—	2	1	no	—
213	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
214	C₇×Q₈	—	2	1	no	—
215	C₇×Q₈	—	2	4	no	—
216	C₇×Q₈	—	2	4	no	—
217	C₇×Q₈	—	4	2	no	—
218	C₇×Q₈	—	4	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	1	no	—
223	C₇×D₄	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	4	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	1	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	2	no	—
235	C₂×C₄×C₇	—	4	1	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	8	2	no	—
239	C₂×C₄×C₇	—	16	2	no	—
240	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
246	C₇×C₈	—	2	2	no	—
247	C₇×C₈	—	2	4	no	—
248	C₇×C₈	—	2	1	no	—
249	C₇×C₈	—	2	1	no	—
250	C₇×C₈	—	4	1	no	—
251	C₇×C₈	C₄×D₄	1	2	yes	—
252	C₇×C₈	C₄×D₄	1	2	yes	—
253	C₂×#41	C₂³×C₇	1	1	yes	characteristic
254	C₂²×Q₈	C₂³×C₇	1	2	yes	—
255	#137	—	2	4	no	—
256	#137	C₂×C₄×C₇	1	8	yes	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	2	2	no	—
261	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
262	C₂×SD₁₆	—	2	2	no	—
263	#131	—	2	2	no	—
264	#131	C₂×C₄×C₇	1	4	yes	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
267	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
268	C₂×M₁₆	C₂³×C₇	1	2	yes	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	4	2	no	—
279	#117	—	2	2	no	—
280	#117	—	4	2	no	—
281	#117	C₂³×C₇	1	1	yes	characteristic
282	#117	C₂³×C₇	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
285	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
286	#108	C₂×C₄×C₇	1	4	yes	complemented
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#107	—	2	2	no	—
291	#107	C₇×D₄	1	1	yes	characteristic
292	#107	C₇×D₄	1	1	yes	characteristic
293	#106	—	2	2	no	—
294	#106	—	2	2	no	—
295	#106	C₇×D₄	1	2	yes	—
296	#104	—	2	2	no	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	C₇×D₄	1	1	yes	characteristic
302	#103	C₇×D₄	1	1	yes	characteristic
303	#102	C₇×D₄	1	1	yes	characteristic
304	#102	C₇×D₄	1	1	yes	characteristic
305	#101	C₂×C₄×C₇	1	8	yes	complemented
306	#97	—	2	2	no	—
307	#97	—	2	1	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	2	no	—
311	#95	—	4	2	no	—
312	C₂²×C₇	—	2	1	no	—
313	C₂²×C₇	—	2	1	no	—
314	C₂²×C₇	—	2	2	no	—
315	C₂²×C₇	—	4	1	no	—
316	C₂²×C₇	—	4	1	no	—
317	C₂²×C₇	#520	1	1	yes	characteristic
318	C₂²×C₇	D₄²	1	1	yes	characteristic
319	C₂²×C₇	#553	1	1	yes	characteristic
320	C₄×C₇	—	2	2	no	—
321	C₄×C₇	—	4	2	no	—
322	C₄×C₇	—	4	4	no	—
323	C₄×C₇	—	4	1	no	—
324	C₄×C₇	—	4	2	no	—
325	C₄×C₇	—	4	2	no	—
326	C₄×C₇	—	4	1	no	—
327	C₄×C₇	—	8	2	no	—
328	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
329	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
330	C₄×C₇	#547	1	1	yes	characteristic
331	C₄×C₇	#548	1	1	yes	characteristic
332	#41	—	2	1	no	—
333	#41	—	2	1	no	—
334	#41	C₂²×C₄×C₇	1	2	yes	—
335	#41	C₇×#41	1	2	yes	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
342	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
351	Q₁₆	—	2	8	no	—
352	Q₁₆	—	2	4	no	—
353	Q₁₆	—	2	4	no	—
354	SD₁₆	—	2	8	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	C₂²×C₄×C₇	1	2	yes	—
361	M₁₆	C₂²×C₄×C₇	1	4	yes	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
369	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
370	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
371	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
372	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
373	C₂×C₈	C₇×#41	1	2	yes	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
380	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
381	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
382	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	4	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	—	4	2	no	—
393	C₂×C₇	—	2	1	no	—
394	C₂×C₇	—	2	1	no	—
395	C₂×C₇	—	4	2	no	—
396	C₂×C₇	#2361	1	1	yes	characteristic
397	C₂×C₇	#3290	1	1	yes	characteristic
398	C₂×C₇	#3293	1	1	yes	characteristic
399	C₂³	—	2	1	no	—
400	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
401	Q₈	—	2	1	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	C₄×C₇×D₄	1	2	yes	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	1	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	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	16	2	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	C₇×2₋¹⁺⁴	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	4	no	—
435	C₈	—	2	1	no	—
436	C₈	—	2	1	no	—
437	C₈	—	4	1	no	—
438	C₈	C₄×C₇×D₄	1	2	yes	—
439	C₈	C₄×C₇×D₄	1	2	yes	—
440	C₇	#23045	1	1	yes	characteristic, direct product factor, Sylow
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	C₇×#520	1	1	yes	characteristic
447	C₂²	C₇×D₄²	1	1	yes	characteristic
448	C₂²	C₇×#553	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	4	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
458	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
459	C₄	C₇×#547	1	1	yes	characteristic
460	C₄	C₇×#548	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	4	2	no	—
464	C₂	C₇×#2361	1	1	yes	characteristic
465	C₂	C₇×#3290	1	1	yes	characteristic
466	C₂	C₇×#3293	1	1	yes	characteristic

	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×#1969	C₂	semidirect
6. C₇×#1952	C₂	semidirect
7. C₇×#1930	C₂	semidirect
9. C₇×#1857	C₂	semidirect
10. C₇×#1772	C₂	semidirect
17. C₇×#473	C₄	semidirect
46. #23045	C₇	direct (N × H)
55. C₂×C₇×Q₁₆	C₂×C₄	semidirect
80. C₇×#108	C₂×C₄	semidirect
99. C₇×#101	C₂×C₄	semidirect
107. #2950	C₂×C₇	semidirect
110. #1969	C₂×C₇	semidirect
111. #1952	C₂×C₇	semidirect
112. #1930	C₂×C₇	semidirect
114. #1857	C₂×C₇	semidirect
115. #1772	C₂×C₇	semidirect
183. #473	C₄×C₇	semidirect
261. C₂×Q₁₆	C₂×C₄×C₇	semidirect
286. #108	C₂×C₄×C₇	semidirect
305. #101	C₂×C₄×C₇	semidirect
440. C₇	#23045	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×#2913	2
C₇×#1969	2
C₇×#1952	2
C₇×#1930	2
C₇×#1882	2
C₇×#1857	2
C₇×#1772	2
C₇×#1764	2
#23045	7

Subgroups — C7×#23045 #13200261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23045 #13200261