Subgroups — C₇×#21419 #13198635

Order 1792.

1122 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	1	yes	maximal, characteristic
2	C₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1897	C₂	1	2	yes	maximal, complemented
9	C₇×#1896	C₂	1	2	yes	maximal, complemented
10	C₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×C₇×#104	C₂	1	2	yes	maximal, complemented
12	C₇×#542	C₄	1	4	yes	complemented
13	C₇×#541	C₄	1	2	yes	complemented
14	C₇×#540	C₄	1	2	yes	complemented
15	C₇×#539	—	2	2	no	—
16	C₇×#538	—	2	2	no	—
17	C₇×#533	C₂²	1	1	yes	characteristic
18	C₇×#532	C₂²	1	1	yes	characteristic
19	C₇×#529	—	2	4	no	—
20	C₇×#525	C₂²	1	2	yes	—
21	C₄×C₇×#41	C₂²	1	2	yes	—
22	C₂×C₇×#117	C₂²	1	1	yes	characteristic
23	C₂×C₇×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
25	C₇×#433	—	2	4	no	—
26	C₇×#423	C₂²	1	1	yes	characteristic
27	C₇×#423	C₂²	1	1	yes	characteristic
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	—
32	C₇×#407	C₂²	1	2	yes	—
33	C₄×C₇×M₁₆	C₂²	1	2	yes	—
34	C₄×C₇×C₄⋊C₄	—	2	2	no	—
35	C₄×C₇×C₂²⋊C₄	—	2	2	no	—
36	C₇×#376	C₂²	1	1	yes	characteristic
37	C₇×#376	C₂²	1	1	yes	characteristic
38	C₄³×C₇	C₂²	1	1	yes	characteristic
39	C₄³×C₇	C₂²	1	1	yes	characteristic
40	C₇×#339	C₂²	1	2	yes	—
41	C₇×#339	C₂²	1	2	yes	—
42	C₇×#339	C₂²	1	2	yes	—
43	C₇×#339	C₂²	1	2	yes	—
44	#21419	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₇×#41	C₂³	1	2	yes	—
46	C₂³×C₄×C₇	—	2	1	no	—
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂×C₇×M₁₆	C₂³	1	2	yes	—
49	C₂×C₇×M₁₆	C₂³	1	2	yes	—
50	C₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
51	C₇×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
52	C₇×#127	C₂×C₄	1	1	yes	characteristic, complemented
53	C₇×#126	—	2	4	no	—
54	C₇×#126	—	2	4	no	—
55	C₇×#125	—	2	4	no	—
56	C₇×#125	C₂×C₄	1	2	yes	complemented
57	C₇×#124	—	2	4	no	—
58	C₇×#124	C₂×C₄	1	2	yes	complemented
59	C₇×#123	—	2	2	no	—
60	C₇×#123	—	2	4	no	—
61	C₇×#123	—	2	4	no	—
62	C₇×C₂²⋊Q₈	—	2	2	no	—
63	C₇×C₂²⋊Q₈	—	2	4	no	—
64	C₇×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
65	C₇×#121	—	2	2	no	—
66	C₇×#121	—	2	4	no	—
67	C₇×#121	C₂×C₄	1	4	yes	—
68	C₇×#120	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
71	C₄×C₇×D₄	—	2	4	no	—
72	C₄×C₇×D₄	—	2	4	no	—
73	C₄×C₇×D₄	—	2	2	no	—
74	C₄×C₇×D₄	C₂×C₄	1	4	yes	complemented
75	C₇×#117	—	2	2	no	—
76	C₇×#117	—	2	2	no	—
77	C₇×#117	—	2	2	no	—
78	C₇×#117	C₂×C₄	1	2	yes	—
79	C₇×#117	C₂×C₄	1	2	yes	—
80	C₇×#117	D₄	1	4	yes	—
81	C₇×#117	C₂³	1	2	yes	—
82	C₂×C₇×C₄⋊C₄	—	2	1	no	—
83	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
84	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
86	C₂×C₄²×C₇	—	2	1	no	—
87	C₂×C₄²×C₇	—	2	2	no	—
88	C₂×C₄²×C₇	—	2	2	no	—
89	C₂×C₄²×C₇	—	2	2	no	—
90	C₂×C₄²×C₇	—	2	2	no	—
91	C₂×C₄²×C₇	—	2	2	no	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊C₈	—	2	2	no	—
99	C₇×C₄⋊C₈	—	2	2	no	—
100	C₇×#104	—	2	4	no	—
101	C₇×#104	—	2	4	no	—
102	C₇×#104	—	2	4	no	—
103	C₇×#104	—	2	4	no	—
104	C₇×C₂²⋊C₈	—	2	4	no	—
105	C₇×#97	—	2	2	no	—
106	C₄×C₇×C₈	—	2	2	no	—
107	C₇×#95	—	2	2	no	—
108	C₇×#95	—	2	2	no	—
109	#3455	C₂×C₇	1	1	yes	characteristic
110	#2921	C₂×C₇	1	1	yes	characteristic, complemented
111	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
112	#1995	C₂×C₇	1	1	yes	characteristic, complemented
113	#1994	C₂×C₇	1	1	yes	characteristic, complemented
114	#1963	C₂×C₇	1	1	yes	characteristic, complemented
115	#1962	C₂×C₇	1	1	yes	characteristic, complemented
116	#1897	C₂×C₇	1	2	yes	complemented
117	#1896	C₂×C₇	1	2	yes	complemented
118	#1759	C₂×C₇	1	2	yes	complemented
119	C₄×#104	C₂×C₇	1	2	yes	complemented
120	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
121	C₇×#41	—	2	2	no	—
122	C₇×#41	—	2	2	no	—
123	C₇×#41	—	2	2	no	—
124	C₇×#41	—	2	2	no	—
125	C₂×C₇×Q₈	—	2	2	no	—
126	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
127	C₂×C₇×D₄	—	2	2	no	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	2	no	—
130	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇	—	2	1	no	—
132	C₂²×C₄×C₇	—	2	1	no	—
133	C₂²×C₄×C₇	—	2	1	no	—
134	C₂²×C₄×C₇	—	2	1	no	—
135	C₂²×C₄×C₇	—	2	1	no	—
136	C₂²×C₄×C₇	—	2	4	no	—
137	C₂²×C₄×C₇	—	2	1	no	—
138	C₂²×C₄×C₇	—	2	1	no	—
139	C₂²×C₄×C₇	—	2	1	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	4	4	no	—
143	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
149	C₇×M₁₆	—	2	2	no	—
150	C₇×M₁₆	—	2	2	no	—
151	C₇×M₁₆	—	2	2	no	—
152	C₇×M₁₆	—	2	2	no	—
153	C₂×C₇×C₈	—	2	2	no	—
154	C₂×C₇×C₈	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	4	no	—
156	C₇×C₄⋊C₄	—	2	4	no	—
157	C₇×C₄⋊C₄	—	2	2	no	—
158	C₇×C₄⋊C₄	—	2	4	no	—
159	C₇×C₄⋊C₄	—	2	4	no	—
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
162	C₇×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
164	C₇×C₂²⋊C₄	—	2	4	no	—
165	C₇×C₂²⋊C₄	—	2	4	no	—
166	C₇×C₂²⋊C₄	—	2	2	no	—
167	C₇×C₂²⋊C₄	—	2	4	no	—
168	C₇×C₂²⋊C₄	—	2	4	no	—
169	C₇×C₂²⋊C₄	—	2	4	no	—
170	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
171	C₇×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
172	C₄²×C₇	—	2	4	no	—
173	C₄²×C₇	—	2	4	no	—
174	C₄²×C₇	—	2	2	no	—
175	C₄²×C₇	—	2	1	no	—
176	C₄²×C₇	—	2	1	no	—
177	C₄²×C₇	—	2	1	no	—
178	C₄²×C₇	—	2	1	no	—
179	C₄²×C₇	—	4	4	no	—
180	C₄²×C₇	—	4	4	no	—
181	C₄²×C₇	C₂²×C₄	1	2	yes	—
182	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
184	C₄²×C₇	C₂×D₄	1	2	yes	—
185	C₄²×C₇	C₂×D₄	1	2	yes	—
186	C₄²×C₇	#41	1	2	yes	—
187	C₄²×C₇	#41	1	2	yes	—
188	C₄²×C₇	#41	1	2	yes	—
189	C₄²×C₇	#41	1	2	yes	—
190	#542	C₄×C₇	1	4	yes	complemented
191	#541	C₄×C₇	1	2	yes	complemented
192	#540	C₄×C₇	1	2	yes	complemented
193	#539	—	2	2	no	—
194	#538	—	2	2	no	—
195	#533	C₂²×C₇	1	1	yes	characteristic
196	#532	C₂²×C₇	1	1	yes	characteristic
197	#529	—	2	4	no	—
198	#525	C₂²×C₇	1	2	yes	—
199	C₄×#41	C₂²×C₇	1	2	yes	—
200	C₂×#117	C₂²×C₇	1	1	yes	characteristic
201	C₂×#117	C₂²×C₇	1	1	yes	characteristic
202	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
203	#433	—	2	4	no	—
204	#423	C₂²×C₇	1	1	yes	characteristic
205	#423	C₂²×C₇	1	1	yes	characteristic
206	C₂×#104	C₂²×C₇	1	2	yes	—
207	C₂×#104	C₂²×C₇	1	2	yes	—
208	C₂×#104	C₂²×C₇	1	2	yes	—
209	C₂×#104	C₂²×C₇	1	2	yes	—
210	#407	C₂²×C₇	1	2	yes	—
211	C₄×M₁₆	C₂²×C₇	1	2	yes	—
212	C₄×C₄⋊C₄	—	2	2	no	—
213	C₄×C₂²⋊C₄	—	2	2	no	—
214	#376	C₂²×C₇	1	1	yes	characteristic
215	#376	C₂²×C₇	1	1	yes	characteristic
216	C₄³	C₂²×C₇	1	1	yes	characteristic
217	C₄³	C₂²×C₇	1	1	yes	characteristic
218	#339	C₂²×C₇	1	2	yes	—
219	#339	C₂²×C₇	1	2	yes	—
220	#339	C₂²×C₇	1	2	yes	—
221	#339	C₂²×C₇	1	2	yes	—
222	C₂³×C₇	—	2	1	no	—
223	C₂³×C₇	—	2	1	no	—
224	C₂³×C₇	—	2	2	no	—
225	C₂³×C₇	—	4	2	no	—
226	C₂³×C₇	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₇×Q₈	—	2	2	no	—
229	C₇×Q₈	—	2	2	no	—
230	C₇×Q₈	—	8	2	no	—
231	C₇×D₄	—	2	2	no	—
232	C₇×D₄	—	2	2	no	—
233	C₇×D₄	—	4	2	no	—
234	C₇×D₄	—	4	2	no	—
235	C₇×D₄	—	8	2	no	—
236	C₇×D₄	—	8	4	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	1	no	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	1	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	2	no	—
243	C₂×C₄×C₇	—	2	2	no	—
244	C₂×C₄×C₇	—	2	2	no	—
245	C₂×C₄×C₇	—	2	2	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	2	2	no	—
248	C₂×C₄×C₇	—	2	2	no	—
249	C₂×C₄×C₇	—	2	2	no	—
250	C₂×C₄×C₇	—	4	2	no	—
251	C₂×C₄×C₇	—	4	2	no	—
252	C₂×C₄×C₇	—	4	8	no	—
253	C₂×C₄×C₇	—	4	2	no	—
254	C₂×C₄×C₇	—	4	2	no	—
255	C₂×C₄×C₇	—	4	2	no	—
256	C₂×C₄×C₇	—	4	2	no	—
257	C₂×C₄×C₇	—	4	2	no	—
258	C₂×C₄×C₇	—	8	4	no	—
259	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	4	yes	—
260	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
261	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
269	C₇×C₈	—	4	2	no	—
270	C₇×C₈	—	4	2	no	—
271	C₂×#41	C₂³×C₇	1	2	yes	—
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
274	C₂×M₁₆	C₂³×C₇	1	2	yes	—
275	C₂×M₁₆	C₂³×C₇	1	2	yes	—
276	C₄⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic, complemented
277	C₄⋊Q₈	C₂×C₄×C₇	1	2	yes	complemented
278	#127	C₂×C₄×C₇	1	1	yes	characteristic, complemented
279	#126	—	2	4	no	—
280	#126	—	2	4	no	—
281	#125	—	2	4	no	—
282	#125	C₂×C₄×C₇	1	2	yes	complemented
283	#124	—	2	4	no	—
284	#124	C₂×C₄×C₇	1	2	yes	complemented
285	#123	—	2	2	no	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	C₂×C₄×C₇	1	4	yes	—
291	#121	—	2	2	no	—
292	#121	—	2	4	no	—
293	#121	C₂×C₄×C₇	1	4	yes	—
294	#120	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	C₂×C₄×C₇	1	4	yes	complemented
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	C₂×C₄×C₇	1	2	yes	—
305	#117	C₂×C₄×C₇	1	2	yes	—
306	#117	C₇×D₄	1	4	yes	—
307	#117	C₂³×C₇	1	2	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	2	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	2	no	—
326	#104	—	2	4	no	—
327	#104	—	2	4	no	—
328	#104	—	2	4	no	—
329	#104	—	2	4	no	—
330	C₂²⋊C₈	—	2	4	no	—
331	#97	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	C₂²×C₇	—	2	2	no	—
336	C₂²×C₇	—	2	4	no	—
337	C₂²×C₇	—	2	2	no	—
338	C₂²×C₇	—	4	2	no	—
339	C₂²×C₇	—	4	2	no	—
340	C₂²×C₇	—	4	4	no	—
341	C₂²×C₇	—	4	2	no	—
342	C₂²×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₇	#525	1	1	yes	characteristic
344	C₂²×C₇	#525	1	1	yes	characteristic
345	C₄×C₇	—	2	4	no	—
346	C₄×C₇	—	2	4	no	—
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	2	2	no	—
349	C₄×C₇	—	2	2	no	—
350	C₄×C₇	—	4	2	no	—
351	C₄×C₇	—	4	2	no	—
352	C₄×C₇	—	4	2	no	—
353	C₄×C₇	—	4	4	no	—
354	C₄×C₇	—	4	2	no	—
355	C₄×C₇	C₄×#41	1	1	yes	characteristic
356	C₄×C₇	C₄×#41	1	1	yes	characteristic
357	C₄×C₇	#532	1	1	yes	characteristic
358	C₄×C₇	#532	1	1	yes	characteristic
359	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
383	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
385	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
386	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
401	C₄⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
402	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
403	C₂²⋊C₄	—	2	4	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
410	C₂²⋊C₄	C₇×C₂²⋊C₄	1	4	yes	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	4	4	no	—
419	C₄²	—	4	4	no	—
420	C₄²	C₂²×C₄×C₇	1	2	yes	—
421	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
422	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
423	C₄²	C₂×C₇×D₄	1	2	yes	—
424	C₄²	C₂×C₇×D₄	1	2	yes	—
425	C₄²	C₇×#41	1	2	yes	—
426	C₄²	C₇×#41	1	2	yes	—
427	C₄²	C₇×#41	1	2	yes	—
428	C₄²	C₇×#41	1	2	yes	—
429	C₂×C₇	—	2	1	no	—
430	C₂×C₇	—	2	1	no	—
431	C₂×C₇	—	4	2	no	—
432	C₂×C₇	—	8	2	no	—
433	C₂×C₇	#2297	1	1	yes	characteristic
434	C₂×C₇	#2901	1	2	yes	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	C₂×C₇×C₂²⋊C₄	1	2	yes	—
440	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
441	Q₈	—	2	2	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	8	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	2	no	—
449	D₄	—	8	4	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	4	yes	—
473	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
474	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
475	C₂×C₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
476	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
479	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
480	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
481	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
482	C₈	—	4	2	no	—
483	C₈	—	4	2	no	—
484	C₇	#21419	1	1	yes	characteristic, direct product factor, Sylow
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
493	C₂²	C₇×#525	1	1	yes	characteristic
494	C₂²	C₇×#525	1	1	yes	characteristic
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	2	no	—
505	C₄	C₄×C₇×#41	1	1	yes	characteristic
506	C₄	C₄×C₇×#41	1	1	yes	characteristic
507	C₄	C₇×#532	1	1	yes	characteristic
508	C₄	C₇×#532	1	1	yes	characteristic
509	C₂	—	2	1	no	—
510	C₂	—	2	1	no	—
511	C₂	—	4	2	no	—
512	C₂	—	8	2	no	—
513	C₂	C₇×#2297	1	1	yes	characteristic
514	C₂	C₇×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂²×C₂²⋊C₄
prime radical	C₇×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2921	C₂	semidirect
3. C₄×C₇×#117	C₂	semidirect
4. C₇×#1995	C₂	semidirect
5. C₇×#1994	C₂	semidirect
6. C₇×#1963	C₂	semidirect
7. C₇×#1962	C₂	semidirect
8. C₇×#1897	C₂	semidirect
9. C₇×#1896	C₂	semidirect
10. C₇×#1759	C₂	semidirect
11. C₄×C₇×#104	C₂	semidirect
12. C₇×#542	C₄	semidirect
13. C₇×#541	C₄	semidirect
14. C₇×#540	C₄	semidirect
44. #21419	C₇	direct (N × H)
50. C₇×C₄⋊Q₈	C₂×C₄	semidirect
51. C₇×C₄⋊Q₈	C₂×C₄	semidirect
52. C₇×#127	C₂×C₄	semidirect
56. C₇×#125	C₂×C₄	semidirect
58. C₇×#124	C₂×C₄	semidirect
70. C₄×C₇×Q₈	C₂×C₄	semidirect
74. C₄×C₇×D₄	C₂×C₄	semidirect
110. #2921	C₂×C₇	semidirect
111. C₄×#117	C₂×C₇	semidirect
112. #1995	C₂×C₇	semidirect
113. #1994	C₂×C₇	semidirect
114. #1963	C₂×C₇	semidirect
115. #1962	C₂×C₇	semidirect
116. #1897	C₂×C₇	semidirect
117. #1896	C₂×C₇	semidirect
118. #1759	C₂×C₇	semidirect
119. C₄×#104	C₂×C₇	semidirect
190. #542	C₄×C₇	semidirect
191. #541	C₄×C₇	semidirect
192. #540	C₄×C₇	semidirect
276. C₄⋊Q₈	C₂×C₄×C₇	semidirect
277. C₄⋊Q₈	C₂×C₄×C₇	semidirect
278. #127	C₂×C₄×C₇	semidirect
282. #125	C₂×C₄×C₇	semidirect
284. #124	C₂×C₄×C₇	semidirect
296. C₄×Q₈	C₂×C₄×C₇	semidirect
300. C₄×D₄	C₂×C₄×C₇	semidirect
484. C₇	#21419	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×#3455	2
C₇×#2921	2
C₄×C₇×#117	2
C₇×#1995	2
C₇×#1994	2
C₇×#1963	2
C₇×#1962	2
C₇×#1897	2
C₇×#1896	2
C₇×#1759	2
C₄×C₇×#104	2
#21419	7

Subgroups — C7×#21419 #13198635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#21419 #13198635