Subgroups — C₇×#60809 #13238025

Order 1792.

2034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3449	C₂	1	1	yes	maximal, characteristic
3	C₇×#3223	C₂	1	8	yes	maximal, complemented
4	C₇×#3222	C₂	1	8	yes	maximal, complemented
5	C₇×#3152	C₂	1	2	yes	maximal, complemented
6	C₇×#3142	C₂	1	2	yes	maximal, complemented
7	C₇×#3037	C₂	1	4	yes	maximal, complemented
8	C₇×#3007	C₂	1	4	yes	maximal, complemented
9	C₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×#41	C₂²	1	2	yes	—
11	C₂×C₇×#137	C₂²	1	8	yes	complemented
12	C₇×#541	—	2	4	no	—
13	C₇×#541	C₂²	1	8	yes	complemented
14	C₇×#537	—	2	2	no	—
15	C₇×#536	C₂²	1	4	yes	—
16	C₇×#535	C₂²	1	4	yes	—
17	C₇×#534	—	2	2	no	—
18	C₇×#532	C₂²	1	2	yes	—
19	C₇×#532	C₂²	1	2	yes	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#126	—	2	2	no	—
22	C₂×C₇×#125	—	2	2	no	—
23	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
24	C₇×#525	—	2	4	no	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
27	C₂×C₇×#117	C₂²	1	1	yes	characteristic
28	C₇×#497	C₂²	1	8	yes	complemented
29	C₇×#494	C₂²	1	4	yes	complemented
30	C₇×#492	C₂²	1	4	yes	complemented
31	C₇×#491	C₂²	1	4	yes	complemented
32	C₇×#490	C₂²	1	4	yes	complemented
33	C₇×#488	C₂²	1	8	yes	complemented
34	C₇×#464	C₂²	1	16	yes	complemented
35	C₇×#462	C₂²	1	8	yes	complemented
36	C₇×#460	C₂²	1	8	yes	complemented
37	C₇×#452	C₂²	1	16	yes	—
38	C₇×#451	C₂²	1	8	yes	complemented
39	C₇×#450	C₂²	1	8	yes	complemented
40	C₇×#433	C₂²	1	8	yes	complemented
41	C₇×#423	C₂²	1	2	yes	complemented
42	C₇×#417	C₂²	1	8	yes	complemented
43	C₇×#407	C₂²	1	2	yes	—
44	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
45	#60809	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×#41	—	2	2	no	—
47	C₂×C₇×#41	—	2	2	no	—
48	C₂×C₇×#41	—	4	8	no	—
49	C₂×C₇×#41	C₂³	1	4	yes	—
50	C₂×C₇×#41	C₂³	1	4	yes	—
51	C₂²×C₇×Q₈	C₂³	1	2	yes	—
52	C₂²×C₇×Q₈	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	C₂³	1	2	yes	—
55	C₂³×C₄×C₇	—	2	2	no	—
56	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
57	C₇×#137	—	4	16	no	—
58	C₂×C₇×Q₁₆	C₂³	1	16	yes	—
59	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
60	C₂×C₇×M₁₆	C₂³	1	4	yes	—
61	C₇×C₄⋊Q₈	—	2	2	no	—
62	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
64	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₇×#127	C₂³	1	2	yes	—
66	C₇×#127	C₂³	1	2	yes	—
67	C₇×#126	—	2	16	no	—
68	C₇×#125	—	2	16	no	—
69	C₇×#125	—	2	2	no	—
70	C₇×#125	C₂³	1	4	yes	—
71	C₇×#124	C₂³	1	4	yes	—
72	C₇×#124	C₂³	1	4	yes	—
73	C₇×#123	—	2	8	no	—
74	C₇×C₂²⋊Q₈	—	2	4	no	—
75	C₇×C₂²⋊Q₈	—	2	8	no	—
76	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
77	C₇×#121	—	2	4	no	—
78	C₇×#121	—	2	4	no	—
79	C₇×#121	—	2	8	no	—
80	C₇×#120	—	2	8	no	—
81	C₄×C₇×Q₈	—	2	4	no	—
82	C₄×C₇×Q₈	C₂³	1	8	yes	—
83	C₄×C₇×D₄	—	2	4	no	—
84	C₄×C₇×D₄	—	2	4	no	—
85	C₇×#117	D₄	1	4	yes	—
86	C₇×#117	C₂³	1	4	yes	—
87	C₂×C₇×C₄⋊C₄	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	—	2	2	no	—
89	C₂×C₇×C₄⋊C₄	—	2	2	no	—
90	C₂×C₇×C₄⋊C₄	—	2	2	no	—
91	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
95	C₂×C₄²×C₇	—	2	2	no	—
96	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊C₈	C₂³	1	8	yes	—
99	C₇×#103	C₂³	1	16	yes	—
100	C₇×#102	C₂³	1	16	yes	—
101	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
102	C₇×#97	C₂³	1	4	yes	—
103	C₄×C₇×C₈	C₂³	1	4	yes	—
104	C₂×#541	C₂×C₇	1	1	yes	characteristic, complemented
105	#3449	C₂×C₇	1	1	yes	characteristic
106	#3223	C₂×C₇	1	8	yes	complemented
107	#3222	C₂×C₇	1	8	yes	complemented
108	#3152	C₂×C₇	1	2	yes	complemented
109	#3142	C₂×C₇	1	2	yes	complemented
110	#3037	C₂×C₇	1	4	yes	complemented
111	#3007	C₂×C₇	1	4	yes	complemented
112	#2921	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂⁴×C₇	—	2	2	no	—
114	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
115	C₇×#41	—	2	16	no	—
116	C₇×#41	—	4	8	no	—
117	C₇×#41	—	4	8	no	—
118	C₇×#41	—	4	8	no	—
119	C₂×C₇×Q₈	—	2	2	no	—
120	C₂×C₇×Q₈	—	2	2	no	—
121	C₂×C₇×Q₈	—	2	8	no	—
122	C₂×C₇×Q₈	—	4	4	no	—
123	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
124	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
125	C₂×C₇×D₄	—	2	4	no	—
126	C₂×C₇×D₄	—	2	4	no	—
127	C₂×C₇×D₄	—	2	2	no	—
128	C₂×C₇×D₄	—	2	4	no	—
129	C₂×C₇×D₄	—	2	4	no	—
130	C₂×C₇×D₄	—	4	4	no	—
131	C₂×C₇×D₄	—	4	8	no	—
132	C₂×C₇×D₄	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	2	2	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	2	no	—
137	C₂²×C₄×C₇	—	2	4	no	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	4	8	no	—
140	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
146	C₇×Q₁₆	—	4	16	no	—
147	C₇×SD₁₆	—	4	16	no	—
148	C₇×M₁₆	—	2	8	no	—
149	C₂×C₇×C₈	C₂⁴	1	8	yes	—
150	C₇×C₄⋊C₄	—	2	8	no	—
151	C₇×C₄⋊C₄	—	2	8	no	—
152	C₇×C₄⋊C₄	—	2	8	no	—
153	C₇×C₄⋊C₄	—	2	8	no	—
154	C₇×C₄⋊C₄	—	2	2	no	—
155	C₇×C₄⋊C₄	—	2	4	no	—
156	C₇×C₄⋊C₄	—	2	4	no	—
157	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
158	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
159	C₇×C₂²⋊C₄	—	2	8	no	—
160	C₇×C₂²⋊C₄	—	2	8	no	—
161	C₇×C₂²⋊C₄	—	2	8	no	—
162	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
163	C₄²×C₇	—	2	8	no	—
164	C₄²×C₇	C₂×D₄	1	2	yes	—
165	C₄²×C₇	C₂×D₄	1	2	yes	—
166	C₄²×C₇	C₂⁴	1	2	yes	—
167	C₄²×C₇	C₂⁴	1	2	yes	—
168	C₂²×#41	C₂²×C₇	1	2	yes	—
169	C₂×#137	C₂²×C₇	1	8	yes	complemented
170	#541	—	2	4	no	—
171	#541	C₂²×C₇	1	8	yes	complemented
172	#537	—	2	2	no	—
173	#536	C₂²×C₇	1	4	yes	—
174	#535	C₂²×C₇	1	4	yes	—
175	#534	—	2	2	no	—
176	#532	C₂²×C₇	1	2	yes	—
177	#532	C₂²×C₇	1	2	yes	—
178	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
179	C₂×#126	—	2	2	no	—
180	C₂×#125	—	2	2	no	—
181	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
182	#525	—	2	4	no	—
183	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
184	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
185	C₂×#117	C₂²×C₇	1	1	yes	characteristic
186	#497	C₂²×C₇	1	8	yes	complemented
187	#494	C₂²×C₇	1	4	yes	complemented
188	#492	C₂²×C₇	1	4	yes	complemented
189	#491	C₂²×C₇	1	4	yes	complemented
190	#490	C₂²×C₇	1	4	yes	complemented
191	#488	C₂²×C₇	1	8	yes	complemented
192	#464	C₂²×C₇	1	16	yes	complemented
193	#462	C₂²×C₇	1	8	yes	complemented
194	#460	C₂²×C₇	1	8	yes	complemented
195	#452	C₂²×C₇	1	16	yes	—
196	#451	C₂²×C₇	1	8	yes	complemented
197	#450	C₂²×C₇	1	8	yes	complemented
198	#433	C₂²×C₇	1	8	yes	complemented
199	#423	C₂²×C₇	1	2	yes	complemented
200	#417	C₂²×C₇	1	8	yes	complemented
201	#407	C₂²×C₇	1	2	yes	—
202	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	4	no	—
205	C₂³×C₇	—	4	2	no	—
206	C₂³×C₇	—	4	4	no	—
207	C₂³×C₇	—	8	4	no	—
208	C₂³×C₇	C₂²×D₄	1	2	yes	—
209	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
210	C₇×Q₈	—	2	8	no	—
211	C₇×Q₈	—	2	8	no	—
212	C₇×Q₈	—	4	4	no	—
213	C₇×Q₈	—	4	4	no	—
214	C₇×D₄	—	2	8	no	—
215	C₇×D₄	—	4	4	no	—
216	C₇×D₄	—	4	8	no	—
217	C₇×D₄	—	4	8	no	—
218	C₇×D₄	—	8	4	no	—
219	C₇×D₄	—	8	4	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	2	4	no	—
224	C₂×C₄×C₇	—	2	4	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	2	no	—
228	C₂×C₄×C₇	—	4	8	no	—
229	C₂×C₄×C₇	—	4	4	no	—
230	C₂×C₄×C₇	—	4	4	no	—
231	C₂×C₄×C₇	—	4	4	no	—
232	C₂×C₄×C₇	—	4	8	no	—
233	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
235	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
238	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
239	C₇×C₈	—	2	8	no	—
240	C₂×#41	—	2	2	no	—
241	C₂×#41	—	2	2	no	—
242	C₂×#41	—	4	8	no	—
243	C₂×#41	C₂³×C₇	1	4	yes	—
244	C₂×#41	C₂³×C₇	1	4	yes	—
245	C₂²×Q₈	C₂³×C₇	1	2	yes	—
246	C₂²×Q₈	C₂³×C₇	1	2	yes	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	C₂³×C₇	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
251	#137	—	4	16	no	—
252	C₂×Q₁₆	C₂³×C₇	1	16	yes	—
253	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
254	C₂×M₁₆	C₂³×C₇	1	4	yes	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
257	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
258	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
259	#127	C₂³×C₇	1	2	yes	—
260	#127	C₂³×C₇	1	2	yes	—
261	#126	—	2	16	no	—
262	#125	—	2	16	no	—
263	#125	—	2	2	no	—
264	#125	C₂³×C₇	1	4	yes	—
265	#124	C₂³×C₇	1	4	yes	—
266	#124	C₂³×C₇	1	4	yes	—
267	#123	—	2	8	no	—
268	C₂²⋊Q₈	—	2	4	no	—
269	C₂²⋊Q₈	—	2	8	no	—
270	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
271	#121	—	2	4	no	—
272	#121	—	2	4	no	—
273	#121	—	2	8	no	—
274	#120	—	2	8	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	C₂³×C₇	1	8	yes	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	#117	C₇×D₄	1	4	yes	—
280	#117	C₂³×C₇	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
292	C₄⋊C₈	C₂³×C₇	1	8	yes	—
293	#103	C₂³×C₇	1	16	yes	—
294	#102	C₂³×C₇	1	16	yes	—
295	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
296	#97	C₂³×C₇	1	4	yes	—
297	C₄×C₈	C₂³×C₇	1	4	yes	—
298	C₂²×C₇	—	2	2	no	—
299	C₂²×C₇	—	2	4	no	—
300	C₂²×C₇	—	2	2	no	—
301	C₂²×C₇	—	4	8	no	—
302	C₂²×C₇	—	4	4	no	—
303	C₂²×C₇	—	8	2	no	—
304	C₂²×C₇	—	8	8	no	—
305	C₂²×C₇	#535	1	2	yes	—
306	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
307	C₄×C₇	—	2	4	no	—
308	C₄×C₇	—	2	4	no	—
309	C₄×C₇	—	2	2	no	—
310	C₄×C₇	—	4	4	no	—
311	C₄×C₇	—	4	4	no	—
312	C₄×C₇	—	4	4	no	—
313	C₄×C₇	#535	1	2	yes	—
314	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
317	#41	—	2	16	no	—
318	#41	—	4	8	no	—
319	#41	—	4	8	no	—
320	#41	—	4	8	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	—	4	4	no	—
325	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
326	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	C₂⁴×C₇	1	4	yes	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
344	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
345	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	Q₁₆	—	4	16	no	—
349	SD₁₆	—	4	16	no	—
350	M₁₆	—	2	8	no	—
351	C₂×C₈	C₂⁴×C₇	1	8	yes	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
360	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
361	C₂²⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
365	C₄²	—	2	8	no	—
366	C₄²	C₂×C₇×D₄	1	2	yes	—
367	C₄²	C₂×C₇×D₄	1	2	yes	—
368	C₄²	C₂⁴×C₇	1	2	yes	—
369	C₄²	C₂⁴×C₇	1	2	yes	—
370	C₂×C₇	—	2	2	no	—
371	C₂×C₇	—	4	2	no	—
372	C₂×C₇	—	8	4	no	—
373	C₂×C₇	C₂×#535	1	1	yes	characteristic
374	C₂×C₇	#3586	1	2	yes	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	8	4	no	—
380	C₂³	C₂²×C₇×D₄	1	2	yes	—
381	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
382	Q₈	—	2	8	no	—
383	Q₈	—	2	8	no	—
384	Q₈	—	4	4	no	—
385	Q₈	—	4	4	no	—
386	D₄	—	2	8	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	8	no	—
389	D₄	—	4	8	no	—
390	D₄	—	8	4	no	—
391	D₄	—	8	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	8	no	—
405	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
406	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
407	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
408	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
409	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
410	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
411	C₈	—	2	8	no	—
412	C₇	#60809	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	8	no	—
420	C₂²	C₇×#535	1	2	yes	—
421	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	C₇×#535	1	2	yes	—
429	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
430	C₂	—	2	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	4	no	—
433	C₂	C₂×C₇×#535	1	1	yes	characteristic
434	C₂	C₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#541	C₂	semidirect
3. C₇×#3223	C₂	semidirect
4. C₇×#3222	C₂	semidirect
5. C₇×#3152	C₂	semidirect
6. C₇×#3142	C₂	semidirect
7. C₇×#3037	C₂	semidirect
8. C₇×#3007	C₂	semidirect
9. C₇×#2921	C₂	semidirect
11. C₂×C₇×#137	C₂²	semidirect
13. C₇×#541	C₂²	semidirect
20. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₇×#125	C₂²	semidirect
26. C₂×C₄×C₇×Q₈	C₂²	semidirect
28. C₇×#497	C₂²	semidirect
29. C₇×#494	C₂²	semidirect
30. C₇×#492	C₂²	semidirect
31. C₇×#491	C₂²	semidirect
32. C₇×#490	C₂²	semidirect
33. C₇×#488	C₂²	semidirect
34. C₇×#464	C₂²	semidirect
35. C₇×#462	C₂²	semidirect
36. C₇×#460	C₂²	semidirect
38. C₇×#451	C₂²	semidirect
39. C₇×#450	C₂²	semidirect
40. C₇×#433	C₂²	semidirect
41. C₇×#423	C₂²	semidirect
42. C₇×#417	C₂²	semidirect
44. C₄×C₇×M₁₆	C₂²	semidirect
45. #60809	C₇	direct (N × H)
104. C₂×#541	C₂×C₇	semidirect
106. #3223	C₂×C₇	semidirect
107. #3222	C₂×C₇	semidirect
108. #3152	C₂×C₇	semidirect
109. #3142	C₂×C₇	semidirect
110. #3037	C₂×C₇	semidirect
111. #3007	C₂×C₇	semidirect
112. #2921	C₂×C₇	semidirect
169. C₂×#137	C₂²×C₇	semidirect
171. #541	C₂²×C₇	semidirect
178. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
181. C₂×#125	C₂²×C₇	semidirect
184. C₂×C₄×Q₈	C₂²×C₇	semidirect
186. #497	C₂²×C₇	semidirect
187. #494	C₂²×C₇	semidirect
188. #492	C₂²×C₇	semidirect
189. #491	C₂²×C₇	semidirect
190. #490	C₂²×C₇	semidirect
191. #488	C₂²×C₇	semidirect
192. #464	C₂²×C₇	semidirect
193. #462	C₂²×C₇	semidirect
194. #460	C₂²×C₇	semidirect
196. #451	C₂²×C₇	semidirect
197. #450	C₂²×C₇	semidirect
198. #433	C₂²×C₇	semidirect
199. #423	C₂²×C₇	semidirect
200. #417	C₂²×C₇	semidirect
202. C₄×M₁₆	C₂²×C₇	semidirect
412. C₇	#60809	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×#541	2
C₇×#3449	2
C₇×#3223	2
C₇×#3222	2
C₇×#3152	2
C₇×#3142	2
C₇×#3037	2
C₇×#3007	2
C₇×#2921	2
#60809	7

Subgroups — C7×#60809 #13238025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60809 #13238025