Subgroups — C₇×#22898 #13200114

Order 1792.

996 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3018	C₂	1	1	yes	maximal, characteristic
2	C₇×#2956	C₂	1	2	yes	maximal, complemented
3	C₇×#2901	C₂	1	2	yes	maximal, complemented
4	C₇×#1963	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1932	C₂	1	2	yes	maximal, complemented
6	C₇×#1906	C₂	1	2	yes	maximal, complemented
7	C₇×#1884	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1861	C₂	1	2	yes	maximal, complemented
9	C₇×#1759	C₂	1	2	yes	maximal, complemented
10	C₇×#585	C₂²	1	1	yes	characteristic
11	C₇×#575	C₂²	1	2	yes	—
12	C₇×#568	C₂²	1	2	yes	—
13	C₇×#568	C₂²	1	1	yes	characteristic, complemented
14	C₇×#532	C₂²	1	1	yes	characteristic
15	C₄×C₇×#41	C₂²	1	2	yes	—
16	C₇×#456	C₄	1	2	yes	complemented
17	C₇×#455	C₄	1	2	yes	complemented
18	C₇×#454	C₄	1	2	yes	complemented
19	C₇×#453	C₄	1	2	yes	complemented
20	C₇×#444	—	2	4	no	—
21	C₇×#443	—	2	4	no	—
22	C₇×#430	C₂²	1	2	yes	complemented
23	C₇×#423	C₂²	1	1	yes	characteristic, complemented
24	C₇×#421	—	2	4	no	—
25	C₇×#421	C₂²	1	2	yes	—
26	C₇×#421	C₂²	1	2	yes	—
27	C₂×C₇×#104	—	2	4	no	—
28	C₂×C₇×#104	C₂²	1	2	yes	—
29	C₂×C₇×#104	C₂²	1	2	yes	—
30	C₂×C₇×#104	C₂²	1	2	yes	—
31	C₂×C₇×#104	C₂²	1	2	yes	complemented
32	C₇×#413	C₂²	1	1	yes	characteristic
33	C₇×#410	C₂²	1	1	yes	characteristic, complemented
34	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
35	C₇×#376	C₂²	1	1	yes	characteristic, complemented
36	C₇×#344	C₂²	1	2	yes	complemented
37	C₇×#339	C₂²	1	2	yes	complemented
38	C₇×#339	C₂²	1	2	yes	complemented
39	#22898	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₇×2₋¹⁺⁴	—	2	2	no	—
41	C₇×2₋¹⁺⁴	C₂×C₄	1	2	yes	—
42	C₇×H(5,𝔽₂)	—	2	2	no	—
43	C₇×H(5,𝔽₂)	—	4	1	no	—
44	C₇×H(5,𝔽₂)	C₂×C₄	1	2	yes	—
45	C₂×C₇×#41	—	2	4	no	—
46	C₂×C₇×#41	—	4	1	no	—
47	C₂×C₇×#41	C₂³	1	1	yes	characteristic
48	C₂×C₇×#41	C₂³	1	1	yes	characteristic
49	C₂×C₇×#41	C₂³	1	2	yes	—
50	C₇×#137	—	2	2	no	—
51	C₇×#137	C₂×C₄	1	4	yes	complemented
52	C₇×AGL(1,ℤ/8)	—	2	2	no	—
53	C₇×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	complemented
54	C₇×#135	—	2	4	no	—
55	C₇×#131	—	2	4	no	—
56	C₇×#131	—	2	4	no	—
57	C₇×#131	—	4	2	no	—
58	C₂×C₇×M₁₆	—	2	4	no	—
59	C₂×C₇×M₁₆	—	4	1	no	—
60	C₂×C₇×M₁₆	C₂³	1	2	yes	—
61	C₂×C₇×M₁₆	C₂³	1	2	yes	—
62	C₂×C₇×M₁₆	C₂³	1	2	yes	—
63	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
64	C₇×#127	C₂×C₄	1	1	yes	characteristic, complemented
65	C₇×#124	C₂×C₄	1	1	yes	characteristic, complemented
66	C₇×#124	C₂×C₄	1	1	yes	characteristic, complemented
67	C₇×#121	—	4	1	no	—
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×D₄	—	2	2	no	—
70	C₄×C₇×D₄	—	4	1	no	—
71	C₄×C₇×D₄	—	4	2	no	—
72	C₇×#117	—	2	2	no	—
73	C₇×#117	C₂³	1	2	yes	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₇	C₂³	1	2	yes	—
77	C₇×#108	—	2	4	no	—
78	C₇×C₄⋊C₈	—	4	1	no	—
79	C₇×#104	—	2	4	no	—
80	C₇×#104	—	2	4	no	—
81	C₇×#104	—	2	2	no	—
82	C₇×#104	—	2	2	no	—
83	C₇×#104	—	2	2	no	—
84	C₇×#104	—	2	2	no	—
85	C₇×#104	C₂×C₄	1	4	yes	complemented
86	C₇×#104	C₂×C₄	1	4	yes	complemented
87	C₇×#104	D₄	1	4	yes	complemented
88	C₇×#104	D₄	1	4	yes	complemented
89	C₇×#101	C₂×C₄	1	2	yes	complemented
90	C₇×#100	C₂×C₄	1	2	yes	complemented
91	C₇×#99	—	4	1	no	—
92	C₇×#97	—	2	2	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₇×#95	—	4	1	no	—
95	#3018	C₂×C₇	1	1	yes	characteristic
96	#2956	C₂×C₇	1	2	yes	complemented
97	#2901	C₂×C₇	1	2	yes	complemented
98	#1963	C₂×C₇	1	1	yes	characteristic, complemented
99	#1932	C₂×C₇	1	2	yes	complemented
100	#1906	C₂×C₇	1	2	yes	complemented
101	#1884	C₂×C₇	1	1	yes	characteristic, complemented
102	#1861	C₂×C₇	1	2	yes	complemented
103	#1759	C₂×C₇	1	2	yes	complemented
104	C₇×#41	—	2	2	no	—
105	C₇×#41	—	2	2	no	—
106	C₇×#41	—	2	4	no	—
107	C₇×#41	—	2	4	no	—
108	C₇×#41	—	2	2	no	—
109	C₇×#41	—	2	2	no	—
110	C₇×#41	—	2	2	no	—
111	C₇×#41	—	2	2	no	—
112	C₇×#41	—	4	2	no	—
113	C₇×#41	—	4	2	no	—
114	C₇×#41	—	4	4	no	—
115	C₇×#41	—	4	2	no	—
116	C₇×#41	C₂²×C₄	1	4	yes	—
117	C₇×#41	C₂×D₄	1	4	yes	—
118	C₂×C₇×Q₈	—	2	4	no	—
119	C₂×C₇×Q₈	—	4	1	no	—
120	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×Q₈	#41	1	2	yes	—
123	C₂×C₇×D₄	—	2	2	no	—
124	C₂×C₇×D₄	—	2	4	no	—
125	C₂×C₇×D₄	—	2	1	no	—
126	C₂×C₇×D₄	—	2	1	no	—
127	C₂×C₇×D₄	—	4	1	no	—
128	C₂×C₇×D₄	—	4	2	no	—
129	C₂×C₇×D₄	—	4	1	no	—
130	C₂×C₇×D₄	—	4	4	no	—
131	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₇×D₄	#41	1	2	yes	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	1	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	4	2	no	—
140	C₂²×C₄×C₇	—	4	2	no	—
141	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
142	C₇×Q₁₆	—	2	4	no	—
143	C₇×SD₁₆	—	2	4	no	—
144	C₇×SD₁₆	—	2	4	no	—
145	C₇×D₈	—	2	4	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	2	no	—
151	C₇×M₁₆	—	4	4	no	—
152	C₇×M₁₆	C₂²×C₄	1	4	yes	—
153	C₇×M₁₆	C₂×D₄	1	4	yes	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₂×C₇×C₈	—	2	2	no	—
156	C₂×C₇×C₈	—	2	2	no	—
157	C₂×C₇×C₈	—	4	2	no	—
158	C₂×C₇×C₈	—	4	4	no	—
159	C₇×C₄⋊C₄	—	2	2	no	—
160	C₇×C₄⋊C₄	—	4	1	no	—
161	C₇×C₄⋊C₄	—	4	2	no	—
162	C₇×C₂²⋊C₄	—	2	2	no	—
163	C₇×C₂²⋊C₄	—	4	1	no	—
164	C₇×C₂²⋊C₄	—	4	1	no	—
165	C₇×C₂²⋊C₄	—	4	2	no	—
166	C₄²×C₇	—	2	2	no	—
167	C₄²×C₇	—	2	1	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	4	2	no	—
170	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₇	C₂×D₄	1	2	yes	—
173	C₄²×C₇	C₂×D₄	1	2	yes	—
174	#585	C₂²×C₇	1	1	yes	characteristic
175	#575	C₂²×C₇	1	2	yes	—
176	#568	C₂²×C₇	1	2	yes	—
177	#568	C₂²×C₇	1	1	yes	characteristic, complemented
178	#532	C₂²×C₇	1	1	yes	characteristic
179	C₄×#41	C₂²×C₇	1	2	yes	—
180	#456	C₄×C₇	1	2	yes	complemented
181	#455	C₄×C₇	1	2	yes	complemented
182	#454	C₄×C₇	1	2	yes	complemented
183	#453	C₄×C₇	1	2	yes	complemented
184	#444	—	2	4	no	—
185	#443	—	2	4	no	—
186	#430	C₂²×C₇	1	2	yes	complemented
187	#423	C₂²×C₇	1	1	yes	characteristic, complemented
188	#421	—	2	4	no	—
189	#421	C₂²×C₇	1	2	yes	—
190	#421	C₂²×C₇	1	2	yes	—
191	C₂×#104	—	2	4	no	—
192	C₂×#104	C₂²×C₇	1	2	yes	—
193	C₂×#104	C₂²×C₇	1	2	yes	—
194	C₂×#104	C₂²×C₇	1	2	yes	—
195	C₂×#104	C₂²×C₇	1	2	yes	complemented
196	#413	C₂²×C₇	1	1	yes	characteristic
197	#410	C₂²×C₇	1	1	yes	characteristic, complemented
198	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
199	#376	C₂²×C₇	1	1	yes	characteristic, complemented
200	#344	C₂²×C₇	1	2	yes	complemented
201	#339	C₂²×C₇	1	2	yes	complemented
202	#339	C₂²×C₇	1	2	yes	complemented
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	1	no	—
205	C₂³×C₇	—	2	1	no	—
206	C₂³×C₇	—	4	2	no	—
207	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
208	C₇×Q₈	—	2	2	no	—
209	C₇×Q₈	—	2	2	no	—
210	C₇×Q₈	—	2	2	no	—
211	C₇×Q₈	—	4	2	no	—
212	C₇×Q₈	C₄×D₄	1	4	yes	—
213	C₇×D₄	—	2	4	no	—
214	C₇×D₄	—	2	4	no	—
215	C₇×D₄	—	2	2	no	—
216	C₇×D₄	—	2	2	no	—
217	C₇×D₄	—	2	2	no	—
218	C₇×D₄	—	4	4	no	—
219	C₇×D₄	—	4	2	no	—
220	C₇×D₄	—	4	2	no	—
221	C₇×D₄	—	4	2	no	—
222	C₇×D₄	—	8	2	no	—
223	C₇×D₄	C₄×D₄	1	4	yes	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	2	4	no	—
227	C₂×C₄×C₇	—	2	1	no	—
228	C₂×C₄×C₇	—	2	1	no	—
229	C₂×C₄×C₇	—	2	1	no	—
230	C₂×C₄×C₇	—	2	1	no	—
231	C₂×C₄×C₇	—	2	2	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	4	2	no	—
234	C₂×C₄×C₇	—	4	4	no	—
235	C₂×C₄×C₇	—	4	1	no	—
236	C₂×C₄×C₇	—	4	1	no	—
237	C₂×C₄×C₇	—	4	1	no	—
238	C₂×C₄×C₇	—	4	1	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	8	2	no	—
241	C₂×C₄×C₇	—	8	1	no	—
242	C₂×C₄×C₇	—	8	4	no	—
243	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₇	C₂×#41	1	2	yes	—
246	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
247	C₇×C₈	—	2	4	no	—
248	C₇×C₈	—	2	4	no	—
249	C₇×C₈	—	4	2	no	—
250	2₋¹⁺⁴	—	2	2	no	—
251	2₋¹⁺⁴	C₂×C₄×C₇	1	2	yes	—
252	H(5,𝔽₂)	—	2	2	no	—
253	H(5,𝔽₂)	—	4	1	no	—
254	H(5,𝔽₂)	C₂×C₄×C₇	1	2	yes	—
255	C₂×#41	—	2	4	no	—
256	C₂×#41	—	4	1	no	—
257	C₂×#41	C₂³×C₇	1	1	yes	characteristic
258	C₂×#41	C₂³×C₇	1	1	yes	characteristic
259	C₂×#41	C₂³×C₇	1	2	yes	—
260	#137	—	2	2	no	—
261	#137	C₂×C₄×C₇	1	4	yes	complemented
262	AGL(1,ℤ/8)	—	2	2	no	—
263	AGL(1,ℤ/8)	C₂×C₄×C₇	1	4	yes	complemented
264	#135	—	2	4	no	—
265	#131	—	2	4	no	—
266	#131	—	2	4	no	—
267	#131	—	4	2	no	—
268	C₂×M₁₆	—	2	4	no	—
269	C₂×M₁₆	—	4	1	no	—
270	C₂×M₁₆	C₂³×C₇	1	2	yes	—
271	C₂×M₁₆	C₂³×C₇	1	2	yes	—
272	C₂×M₁₆	C₂³×C₇	1	2	yes	—
273	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic, complemented
274	#127	C₂×C₄×C₇	1	1	yes	characteristic, complemented
275	#124	C₂×C₄×C₇	1	1	yes	characteristic, complemented
276	#124	C₂×C₄×C₇	1	1	yes	characteristic, complemented
277	#121	—	4	1	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	—	4	1	no	—
281	C₄×D₄	—	4	2	no	—
282	#117	—	2	2	no	—
283	#117	C₂³×C₇	1	2	yes	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₇	1	2	yes	—
287	#108	—	2	4	no	—
288	C₄⋊C₈	—	4	1	no	—
289	#104	—	2	4	no	—
290	#104	—	2	4	no	—
291	#104	—	2	2	no	—
292	#104	—	2	2	no	—
293	#104	—	2	2	no	—
294	#104	—	2	2	no	—
295	#104	C₂×C₄×C₇	1	4	yes	complemented
296	#104	C₂×C₄×C₇	1	4	yes	complemented
297	#104	C₇×D₄	1	4	yes	complemented
298	#104	C₇×D₄	1	4	yes	complemented
299	#101	C₂×C₄×C₇	1	2	yes	complemented
300	#100	C₂×C₄×C₇	1	2	yes	complemented
301	#99	—	4	1	no	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	#95	—	4	1	no	—
305	C₂²×C₇	—	2	4	no	—
306	C₂²×C₇	—	4	1	no	—
307	C₂²×C₇	—	4	1	no	—
308	C₂²×C₇	—	4	1	no	—
309	C₂²×C₇	—	8	2	no	—
310	C₂²×C₇	—	8	1	no	—
311	C₂²×C₇	—	8	1	no	—
312	C₂²×C₇	—	16	2	no	—
313	C₂²×C₇	#518	1	1	yes	characteristic
314	C₂²×C₇	#546	1	2	yes	—
315	C₄×C₇	—	2	4	no	—
316	C₄×C₇	—	4	2	no	—
317	C₄×C₇	—	4	1	no	—
318	C₄×C₇	—	4	2	no	—
319	C₄×C₇	—	4	1	no	—
320	C₄×C₇	—	4	1	no	—
321	C₄×C₇	—	4	1	no	—
322	C₄×C₇	—	8	2	no	—
323	C₄×C₇	C₂×C₄×D₄	1	2	yes	—
324	C₄×C₇	D₄²	1	1	yes	characteristic
325	C₄×C₇	#551	1	1	yes	characteristic
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	—	2	2	no	—
333	#41	—	2	2	no	—
334	#41	—	4	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	4	no	—
337	#41	—	4	2	no	—
338	#41	C₂²×C₄×C₇	1	4	yes	—
339	#41	C₂×C₇×D₄	1	4	yes	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
343	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
344	C₂×Q₈	C₇×#41	1	2	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
354	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
355	C₂×D₄	C₇×#41	1	2	yes	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
364	Q₁₆	—	2	4	no	—
365	SD₁₆	—	2	4	no	—
366	SD₁₆	—	2	4	no	—
367	D₈	—	2	4	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	4	2	no	—
373	M₁₆	—	4	4	no	—
374	M₁₆	C₂²×C₄×C₇	1	4	yes	—
375	M₁₆	C₂×C₇×D₄	1	4	yes	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	2	no	—
380	C₂×C₈	—	4	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	4	2	no	—
392	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
393	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
394	C₄²	C₂×C₇×D₄	1	2	yes	—
395	C₄²	C₂×C₇×D₄	1	2	yes	—
396	C₂×C₇	—	2	2	no	—
397	C₂×C₇	—	2	1	no	—
398	C₂×C₇	—	4	4	no	—
399	C₂×C₇	—	8	1	no	—
400	C₂×C₇	—	8	1	no	—
401	C₂×C₇	#2358	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	C₄×C₇×D₄	1	4	yes	—
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	8	2	no	—
422	D₄	C₄×C₇×D₄	1	4	yes	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	4	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	8	1	no	—
441	C₂×C₄	—	8	4	no	—
442	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
443	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
444	C₂×C₄	C₂×C₇×#41	1	2	yes	—
445	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
446	C₈	—	2	4	no	—
447	C₈	—	2	4	no	—
448	C₈	—	4	2	no	—
449	C₇	#22898	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	2	4	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	16	2	no	—
458	C₂²	C₇×#518	1	1	yes	characteristic
459	C₂²	C₇×#546	1	2	yes	—
460	C₄	—	2	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	8	2	no	—
468	C₄	C₂×C₄×C₇×D₄	1	2	yes	—
469	C₄	C₇×D₄²	1	1	yes	characteristic
470	C₄	C₇×#551	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	2	1	no	—
473	C₂	—	4	4	no	—
474	C₂	—	8	1	no	—
475	C₂	—	8	1	no	—
476	C₂	C₇×#2358	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	#2358
prime radical	C₇×#3018	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×#2956	C₂	semidirect
3. C₇×#2901	C₂	semidirect
4. C₇×#1963	C₂	semidirect
5. C₇×#1932	C₂	semidirect
6. C₇×#1906	C₂	semidirect
7. C₇×#1884	C₂	semidirect
8. C₇×#1861	C₂	semidirect
9. C₇×#1759	C₂	semidirect
13. C₇×#568	C₂²	semidirect
16. C₇×#456	C₄	semidirect
17. C₇×#455	C₄	semidirect
18. C₇×#454	C₄	semidirect
19. C₇×#453	C₄	semidirect
22. C₇×#430	C₂²	semidirect
23. C₇×#423	C₂²	semidirect
31. C₂×C₇×#104	C₂²	semidirect
33. C₇×#410	C₂²	semidirect
34. C₄×C₇×M₁₆	C₂²	semidirect
35. C₇×#376	C₂²	semidirect
36. C₇×#344	C₂²	semidirect
37. C₇×#339	C₂²	semidirect
38. C₇×#339	C₂²	semidirect
39. #22898	C₇	direct (N × H)
51. C₇×#137	C₂×C₄	semidirect
53. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
63. C₇×C₄⋊Q₈	C₂×C₄	semidirect
64. C₇×#127	C₂×C₄	semidirect
65. C₇×#124	C₂×C₄	semidirect
66. C₇×#124	C₂×C₄	semidirect
85. C₇×#104	C₂×C₄	semidirect
86. C₇×#104	C₂×C₄	semidirect
87. C₇×#104	D₄	semidirect
88. C₇×#104	D₄	semidirect
89. C₇×#101	C₂×C₄	semidirect
90. C₇×#100	C₂×C₄	semidirect
96. #2956	C₂×C₇	semidirect
97. #2901	C₂×C₇	semidirect
98. #1963	C₂×C₇	semidirect
99. #1932	C₂×C₇	semidirect
100. #1906	C₂×C₇	semidirect
101. #1884	C₂×C₇	semidirect
102. #1861	C₂×C₇	semidirect
103. #1759	C₂×C₇	semidirect
177. #568	C₂²×C₇	semidirect
180. #456	C₄×C₇	semidirect
181. #455	C₄×C₇	semidirect
182. #454	C₄×C₇	semidirect
183. #453	C₄×C₇	semidirect
186. #430	C₂²×C₇	semidirect
187. #423	C₂²×C₇	semidirect
195. C₂×#104	C₂²×C₇	semidirect
197. #410	C₂²×C₇	semidirect
198. C₄×M₁₆	C₂²×C₇	semidirect
199. #376	C₂²×C₇	semidirect
200. #344	C₂²×C₇	semidirect
201. #339	C₂²×C₇	semidirect
202. #339	C₂²×C₇	semidirect
261. #137	C₂×C₄×C₇	semidirect
263. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
273. C₄⋊Q₈	C₂×C₄×C₇	semidirect
274. #127	C₂×C₄×C₇	semidirect
275. #124	C₂×C₄×C₇	semidirect
276. #124	C₂×C₄×C₇	semidirect
295. #104	C₂×C₄×C₇	semidirect
296. #104	C₂×C₄×C₇	semidirect
297. #104	C₇×D₄	semidirect
298. #104	C₇×D₄	semidirect
299. #101	C₂×C₄×C₇	semidirect
300. #100	C₂×C₄×C₇	semidirect
449. C₇	#22898	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×#3018	2
C₇×#2956	2
C₇×#2901	2
C₇×#1963	2
C₇×#1932	2
C₇×#1906	2
C₇×#1884	2
C₇×#1861	2
C₇×#1759	2
#22898	7

Subgroups — C7×#22898 #13200114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22898 #13200114