Subgroups — C₇×#23235 #13200451

Order 1792.

710 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3131	C₂	1	1	yes	maximal, characteristic
2	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2935	C₂	1	1	yes	maximal, characteristic
4	C₇×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1980	C₂	1	1	yes	maximal, characteristic
6	C₇×#1938	C₂	1	2	yes	maximal, complemented
7	C₇×#1929	C₂	1	2	yes	maximal, complemented
8	C₇×#1866	C₂	1	2	yes	maximal, complemented
9	C₄×C₇×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#131	C₂²	1	2	yes	—
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₇×#488	C₄	1	2	yes	complemented
16	C₇×#488	C₄	1	2	yes	complemented
17	C₇×#487	C₄	1	1	yes	characteristic, complemented
18	C₇×#487	C₄	1	1	yes	characteristic, complemented
19	C₇×#486	C₄	1	1	yes	characteristic, complemented
20	C₇×#486	C₄	1	1	yes	characteristic, complemented
21	C₇×#446	—	2	2	no	—
22	C₇×#446	—	2	1	no	—
23	C₇×C₈×Q₈	—	2	1	no	—
24	C₇×#436	—	2	1	no	—
25	C₇×#435	—	2	2	no	—
26	C₇×C₈×D₄	—	2	1	no	—
27	C₂×C₇×#108	C₂²	1	1	yes	characteristic
28	C₂×C₇×#108	C₂²	1	1	yes	characteristic
29	C₇×#424	C₂²	1	2	yes	—
30	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#104	C₂²	1	2	yes	—
32	C₂×C₇×#104	C₂²	1	2	yes	—
33	C₇×#416	C₂²	1	2	yes	—
34	C₇×#416	C₂²	1	2	yes	—
35	C₇×#408	C₂²	1	2	yes	—
36	C₇×#405	C₂²	1	2	yes	—
37	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₇×#97	C₂²	1	2	yes	—
40	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
41	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₇×#341	C₂²	1	1	yes	characteristic
43	C₇×#341	C₂²	1	1	yes	characteristic
44	C₇×#339	C₂²	1	2	yes	—
45	C₇×#339	C₂²	1	2	yes	—
46	C₇×#336	C₂²	1	2	yes	—
47	#23235	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	C₂³	1	2	yes	—
49	C₇×#131	—	2	4	no	—
50	C₇×#131	—	4	2	no	—
51	C₂×C₇×M₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	—	2	2	no	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	2	yes	—
60	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₇×#127	C₂×C₄	1	1	yes	characteristic
64	C₇×#125	C₂×C₄	1	2	yes	—
65	C₇×#124	C₂×C₄	1	2	yes	—
66	C₇×C₂²⋊Q₈	—	2	1	no	—
67	C₇×C₂²⋊Q₈	—	2	1	no	—
68	C₇×#121	—	2	1	no	—
69	C₇×#121	—	2	1	no	—
70	C₄×C₇×Q₈	—	2	1	no	—
71	C₄×C₇×Q₈	—	2	1	no	—
72	C₄×C₇×D₄	—	2	1	no	—
73	C₄×C₇×D₄	—	2	1	no	—
74	C₇×#117	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₄²×C₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#108	—	2	2	no	—
79	C₇×#108	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₇×C₄⋊C₈	D₄	1	2	yes	—
84	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
85	C₇×#104	—	2	4	no	—
86	C₇×#104	—	4	2	no	—
87	C₇×#103	C₂×C₄	1	2	yes	—
88	C₇×#103	C₂×C₄	1	2	yes	—
89	C₇×#103	C₂×C₄	1	2	yes	—
90	C₇×#103	C₂×C₄	1	2	yes	—
91	C₇×#102	C₂×C₄	1	2	yes	—
92	C₇×#102	C₂×C₄	1	2	yes	—
93	C₇×#102	C₂×C₄	1	2	yes	—
94	C₇×#102	C₂×C₄	1	2	yes	—
95	C₇×C₂²⋊C₈	—	2	2	no	—
96	C₇×C₂²⋊C₈	—	2	2	no	—
97	C₇×#97	—	2	2	no	—
98	C₇×#97	—	2	1	no	—
99	C₇×#97	—	2	1	no	—
100	C₇×#97	—	4	2	no	—
101	C₄×C₇×C₈	—	2	2	no	—
102	C₄×C₇×C₈	—	2	1	no	—
103	C₄×C₇×C₈	—	2	1	no	—
104	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
105	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
106	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
107	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
108	C₇×#95	—	2	1	no	—
109	#3131	C₂×C₇	1	1	yes	characteristic
110	#2962	C₂×C₇	1	1	yes	characteristic, complemented
111	#2935	C₂×C₇	1	1	yes	characteristic
112	#1986	C₂×C₇	1	1	yes	characteristic, complemented
113	#1980	C₂×C₇	1	1	yes	characteristic
114	#1938	C₂×C₇	1	2	yes	complemented
115	#1929	C₂×C₇	1	2	yes	complemented
116	#1866	C₂×C₇	1	2	yes	complemented
117	C₄×#108	C₂×C₇	1	1	yes	characteristic, complemented
118	#1770	C₂×C₇	1	1	yes	characteristic, complemented
119	#1765	C₂×C₇	1	2	yes	complemented
120	C₇×#41	—	2	2	no	—
121	C₇×#41	—	2	2	no	—
122	C₇×#41	—	2	2	no	—
123	C₇×#41	—	2	2	no	—
124	C₂×C₇×Q₈	—	2	1	no	—
125	C₂×C₇×Q₈	—	2	1	no	—
126	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
127	C₂×C₇×D₄	—	2	2	no	—
128	C₂×C₇×D₄	—	2	1	no	—
129	C₂×C₇×D₄	—	2	1	no	—
130	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	#41	1	1	yes	characteristic
134	C₂²×C₄×C₇	#41	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×M₁₆	—	2	1	no	—
137	C₇×M₁₆	—	2	1	no	—
138	C₇×M₁₆	—	2	1	no	—
139	C₇×M₁₆	—	2	1	no	—
140	C₇×M₁₆	—	2	1	no	—
141	C₇×M₁₆	—	2	1	no	—
142	C₇×M₁₆	—	4	4	no	—
143	C₇×M₁₆	#41	1	2	yes	—
144	C₇×M₁₆	#41	1	2	yes	—
145	C₂×C₇×C₈	—	2	1	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	2	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	2	1	no	—
153	C₂×C₇×C₈	—	2	1	no	—
154	C₂×C₇×C₈	—	2	1	no	—
155	C₂×C₇×C₈	—	4	4	no	—
156	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
161	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
162	C₇×C₄⋊C₄	—	2	1	no	—
163	C₇×C₄⋊C₄	—	2	1	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	2	no	—
166	C₇×C₄⋊C₄	—	2	1	no	—
167	C₇×C₄⋊C₄	—	2	1	no	—
168	C₇×C₄⋊C₄	—	4	2	no	—
169	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
170	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
171	C₇×C₂²⋊C₄	—	2	2	no	—
172	C₇×C₂²⋊C₄	—	2	2	no	—
173	C₇×C₂²⋊C₄	—	2	2	no	—
174	C₄²×C₇	—	2	2	no	—
175	C₄²×C₇	—	2	2	no	—
176	C₄²×C₇	—	2	2	no	—
177	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
181	C₂×#131	C₂²×C₇	1	2	yes	—
182	#533	C₂²×C₇	1	1	yes	characteristic
183	#532	C₂²×C₇	1	1	yes	characteristic
184	#488	C₄×C₇	1	2	yes	complemented
185	#488	C₄×C₇	1	2	yes	complemented
186	#487	C₄×C₇	1	1	yes	characteristic, complemented
187	#487	C₄×C₇	1	1	yes	characteristic, complemented
188	#486	C₄×C₇	1	1	yes	characteristic, complemented
189	#486	C₄×C₇	1	1	yes	characteristic, complemented
190	#446	—	2	2	no	—
191	#446	—	2	1	no	—
192	C₈×Q₈	—	2	1	no	—
193	#436	—	2	1	no	—
194	#435	—	2	2	no	—
195	C₈×D₄	—	2	1	no	—
196	C₂×#108	C₂²×C₇	1	1	yes	characteristic
197	C₂×#108	C₂²×C₇	1	1	yes	characteristic
198	#424	C₂²×C₇	1	2	yes	—
199	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
200	C₂×#104	C₂²×C₇	1	2	yes	—
201	C₂×#104	C₂²×C₇	1	2	yes	—
202	#416	C₂²×C₇	1	2	yes	—
203	#416	C₂²×C₇	1	2	yes	—
204	#408	C₂²×C₇	1	2	yes	—
205	#405	C₂²×C₇	1	2	yes	—
206	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
207	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
208	C₂×#97	C₂²×C₇	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
211	#341	C₂²×C₇	1	1	yes	characteristic
212	#341	C₂²×C₇	1	1	yes	characteristic
213	#339	C₂²×C₇	1	2	yes	—
214	#339	C₂²×C₇	1	2	yes	—
215	#336	C₂²×C₇	1	2	yes	—
216	C₂³×C₇	—	2	2	no	—
217	C₂³×C₇	C₂×#41	1	1	yes	characteristic
218	C₇×Q₈	—	2	2	no	—
219	C₇×Q₈	—	2	2	no	—
220	C₇×Q₈	—	4	2	no	—
221	C₇×Q₈	—	8	1	no	—
222	C₇×D₄	—	2	2	no	—
223	C₇×D₄	—	2	2	no	—
224	C₇×D₄	—	4	2	no	—
225	C₇×D₄	—	4	2	no	—
226	C₇×D₄	—	4	2	no	—
227	C₇×D₄	—	8	1	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	—	2	2	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	2	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	2	no	—
238	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
243	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
248	C₇×C₈	—	2	1	no	—
249	C₇×C₈	—	2	1	no	—
250	C₇×C₈	—	2	1	no	—
251	C₇×C₈	—	2	1	no	—
252	C₇×C₈	—	2	2	no	—
253	C₇×C₈	—	2	2	no	—
254	C₇×C₈	—	2	2	no	—
255	C₇×C₈	—	2	2	no	—
256	C₇×C₈	—	4	1	no	—
257	C₇×C₈	—	4	1	no	—
258	C₂×#41	C₂³×C₇	1	2	yes	—
259	#131	—	2	4	no	—
260	#131	—	4	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
263	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
264	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
265	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₇	1	2	yes	—
270	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
271	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
272	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
273	#127	C₂×C₄×C₇	1	1	yes	characteristic
274	#125	C₂×C₄×C₇	1	2	yes	—
275	#124	C₂×C₄×C₇	1	2	yes	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	#117	C₂³×C₇	1	2	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄²	C₂³×C₇	1	2	yes	—
287	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
288	#108	—	2	2	no	—
289	#108	—	2	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
293	C₄⋊C₈	C₇×D₄	1	2	yes	—
294	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
295	#104	—	2	4	no	—
296	#104	—	4	2	no	—
297	#103	C₂×C₄×C₇	1	2	yes	—
298	#103	C₂×C₄×C₇	1	2	yes	—
299	#103	C₂×C₄×C₇	1	2	yes	—
300	#103	C₂×C₄×C₇	1	2	yes	—
301	#102	C₂×C₄×C₇	1	2	yes	—
302	#102	C₂×C₄×C₇	1	2	yes	—
303	#102	C₂×C₄×C₇	1	2	yes	—
304	#102	C₂×C₄×C₇	1	2	yes	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	2	2	no	—
307	#97	—	2	2	no	—
308	#97	—	2	1	no	—
309	#97	—	2	1	no	—
310	#97	—	4	2	no	—
311	C₄×C₈	—	2	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
315	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
316	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
317	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
318	#95	—	2	1	no	—
319	C₂²×C₇	—	2	1	no	—
320	C₂²×C₇	—	2	1	no	—
321	C₂²×C₇	—	4	2	no	—
322	C₂²×C₇	—	4	2	no	—
323	C₂²×C₇	—	4	2	no	—
324	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₇	#556	1	1	yes	characteristic
326	C₂²×C₇	#559	1	1	yes	characteristic
327	C₄×C₇	—	2	1	no	—
328	C₄×C₇	—	2	1	no	—
329	C₄×C₇	—	2	1	no	—
330	C₄×C₇	—	4	2	no	—
331	C₄×C₇	—	4	2	no	—
332	C₄×C₇	—	4	2	no	—
333	C₄×C₇	—	8	2	no	—
334	C₄×C₇	#444	1	2	yes	—
335	C₄×C₇	C₄×#41	1	1	yes	characteristic
336	C₄×C₇	#520	1	1	yes	characteristic
337	C₄×C₇	#546	1	1	yes	characteristic
338	C₄×C₇	#548	1	1	yes	characteristic
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	C₇×#41	1	1	yes	characteristic
353	C₂²×C₄	C₇×#41	1	1	yes	characteristic
354	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	1	no	—
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	4	4	no	—
362	M₁₆	C₇×#41	1	2	yes	—
363	M₁₆	C₇×#41	1	2	yes	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	4	4	no	—
375	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
376	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
377	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
378	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
379	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
380	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
389	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	2	no	—
395	C₄²	—	2	2	no	—
396	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
397	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
398	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
399	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
400	C₂×C₇	—	2	1	no	—
401	C₂×C₇	—	2	1	no	—
402	C₂×C₇	—	8	2	no	—
403	C₂×C₇	#2367	1	1	yes	characteristic
404	C₂×C₇	C₂×#444	1	1	yes	characteristic
405	C₂×C₇	#2957	1	1	yes	characteristic
406	C₂³	—	2	2	no	—
407	C₂³	C₂×C₇×#41	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	8	1	no	—
412	D₄	—	2	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
429	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
430	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
431	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
432	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
434	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
435	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
436	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₇	#23235	1	1	yes	characteristic, direct product factor, Sylow
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
455	C₂²	C₇×#556	1	1	yes	characteristic
456	C₂²	C₇×#559	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	8	2	no	—
464	C₄	C₇×#444	1	2	yes	—
465	C₄	C₄×C₇×#41	1	1	yes	characteristic
466	C₄	C₇×#520	1	1	yes	characteristic
467	C₄	C₇×#546	1	1	yes	characteristic
468	C₄	C₇×#548	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	8	2	no	—
472	C₂	C₇×#2367	1	1	yes	characteristic
473	C₂	C₂×C₇×#444	1	1	yes	characteristic
474	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2962	C₂	semidirect
4. C₇×#1986	C₂	semidirect
6. C₇×#1938	C₂	semidirect
7. C₇×#1929	C₂	semidirect
8. C₇×#1866	C₂	semidirect
9. C₄×C₇×#108	C₂	semidirect
10. C₇×#1770	C₂	semidirect
11. C₇×#1765	C₂	semidirect
15. C₇×#488	C₄	semidirect
16. C₇×#488	C₄	semidirect
17. C₇×#487	C₄	semidirect
18. C₇×#487	C₄	semidirect
19. C₇×#486	C₄	semidirect
20. C₇×#486	C₄	semidirect
47. #23235	C₇	direct (N × H)
110. #2962	C₂×C₇	semidirect
112. #1986	C₂×C₇	semidirect
114. #1938	C₂×C₇	semidirect
115. #1929	C₂×C₇	semidirect
116. #1866	C₂×C₇	semidirect
117. C₄×#108	C₂×C₇	semidirect
118. #1770	C₂×C₇	semidirect
119. #1765	C₂×C₇	semidirect
184. #488	C₄×C₇	semidirect
185. #488	C₄×C₇	semidirect
186. #487	C₄×C₇	semidirect
187. #487	C₄×C₇	semidirect
188. #486	C₄×C₇	semidirect
189. #486	C₄×C₇	semidirect
448. C₇	#23235	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×#3131	2
C₇×#2962	2
C₇×#2935	2
C₇×#1986	2
C₇×#1980	2
C₇×#1938	2
C₇×#1929	2
C₇×#1866	2
C₄×C₇×#108	2
C₇×#1770	2
C₇×#1765	2
#23235	7

Subgroups — C7×#23235 #13200451

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23235 #13200451