Subgroups — C₇×#22608 #13199824

Order 1792.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2924	C₂	1	2	yes	maximal
2	C₇×#2911	C₂	1	1	yes	maximal, characteristic
3	C₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1922	C₂	1	2	yes	maximal, complemented
6	C₇×#1922	C₂	1	2	yes	maximal, complemented
7	C₇×#1826	C₂	1	2	yes	maximal
8	C₇×#1811	C₂	1	1	yes	maximal, characteristic
9	C₇×#1773	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₇×#117	C₂²	1	2	yes	—
14	C₇×#433	—	2	2	no	—
15	C₇×#433	—	2	2	no	—
16	C₇×#432	—	2	2	no	—
17	C₇×#431	—	2	2	no	—
18	C₂×C₇×#108	C₂²	1	1	yes	characteristic
19	C₂×C₇×#108	C₂²	1	1	yes	characteristic
20	C₇×#428	C₄	1	2	yes	complemented
21	C₇×#428	C₄	1	2	yes	complemented
22	C₇×#428	C₄	1	2	yes	complemented
23	C₇×#428	C₄	1	2	yes	complemented
24	C₇×#427	C₂²	1	1	yes	characteristic
25	C₇×#427	C₂²	1	2	yes	—
26	C₇×#427	C₂²	1	1	yes	characteristic
27	C₇×#424	C₂²	1	2	yes	—
28	C₇×#424	C₂²	1	2	yes	—
29	C₇×#407	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₇×#405	C₂²	1	2	yes	—
32	C₇×#405	C₂²	1	2	yes	—
33	C₂×C₇×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₇×#341	C₂²	1	2	yes	—
37	C₇×#339	C₂²	1	2	yes	—
38	C₇×#339	C₂²	1	2	yes	—
39	C₇×#339	C₂²	1	2	yes	—
40	C₇×#339	C₂²	1	2	yes	—
41	C₇×#336	C₂²	1	1	yes	characteristic
42	C₇×#336	C₂²	1	1	yes	characteristic
43	#22608	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×M₁₆	—	2	2	no	—
46	C₂×C₇×M₁₆	—	2	2	no	—
47	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₇×M₁₆	C₂³	1	2	yes	—
50	C₂×C₇×M₁₆	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₇×#117	—	2	2	no	—
56	C₇×#117	—	2	2	no	—
57	C₇×#117	C₂×C₄	1	2	yes	—
58	C₇×#117	C₂×C₄	1	2	yes	—
59	C₇×#117	C₂³	1	2	yes	—
60	C₇×#117	C₂³	1	2	yes	—
61	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
62	C₂×C₇×C₄⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
65	C₂×C₄²×C₇	—	2	2	no	—
66	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
68	C₇×#108	—	2	2	no	—
69	C₇×#108	—	2	2	no	—
70	C₇×#107	C₂×C₄	1	2	yes	—
71	C₇×#107	C₂×C₄	1	2	yes	—
72	C₇×#107	C₂×C₄	1	1	yes	characteristic
73	C₇×#107	C₂×C₄	1	1	yes	characteristic
74	C₇×#107	C₂×C₄	1	1	yes	characteristic
75	C₇×#107	C₂×C₄	1	1	yes	characteristic
76	C₇×#106	C₂×C₄	1	2	yes	—
77	C₇×#106	C₂×C₄	1	2	yes	—
78	C₇×#106	C₂×C₄	1	2	yes	—
79	C₇×#106	C₂×C₄	1	2	yes	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×C₄⋊C₈	—	2	2	no	—
84	C₇×C₂²⋊C₈	—	2	2	no	—
85	C₇×C₂²⋊C₈	—	2	2	no	—
86	C₇×C₂²⋊C₈	D₄	1	2	yes	—
87	C₇×C₂²⋊C₈	D₄	1	2	yes	—
88	C₇×#97	—	2	2	no	—
89	C₇×#97	—	2	2	no	—
90	C₇×#97	—	2	2	no	—
91	C₄×C₇×C₈	—	2	2	no	—
92	C₄×C₇×C₈	—	2	2	no	—
93	C₄×C₇×C₈	—	2	2	no	—
94	C₇×#95	—	2	1	no	—
95	#2924	C₂×C₇	1	2	yes	—
96	#2911	C₂×C₇	1	1	yes	characteristic
97	#1946	C₂×C₇	1	1	yes	characteristic, complemented
98	#1945	C₂×C₇	1	1	yes	characteristic, complemented
99	#1922	C₂×C₇	1	2	yes	complemented
100	#1922	C₂×C₇	1	2	yes	complemented
101	#1826	C₂×C₇	1	2	yes	—
102	#1811	C₂×C₇	1	1	yes	characteristic
103	#1773	C₂×C₇	1	1	yes	characteristic, complemented
104	#1772	C₂×C₇	1	1	yes	characteristic, complemented
105	#1753	C₂×C₇	1	1	yes	characteristic
106	C₂⁴×C₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₇	—	2	1	no	—
108	C₂²×C₄×C₇	—	2	1	no	—
109	C₂²×C₄×C₇	—	2	1	no	—
110	C₂²×C₄×C₇	—	2	1	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	1	no	—
113	C₂²×C₄×C₇	—	2	2	no	—
114	C₂²×C₄×C₇	—	2	1	no	—
115	C₂²×C₄×C₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
119	C₇×M₁₆	—	2	4	no	—
120	C₇×M₁₆	—	2	4	no	—
121	C₇×M₁₆	—	2	2	no	—
122	C₇×M₁₆	—	2	2	no	—
123	C₇×M₁₆	—	2	2	no	—
124	C₇×M₁₆	—	2	2	no	—
125	C₂×C₇×C₈	—	2	1	no	—
126	C₂×C₇×C₈	—	2	1	no	—
127	C₂×C₇×C₈	—	2	1	no	—
128	C₂×C₇×C₈	—	2	1	no	—
129	C₂×C₇×C₈	—	2	1	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×C₈	#41	1	2	yes	—
140	C₂×C₇×C₈	#41	1	2	yes	—
141	C₇×C₄⋊C₄	—	2	2	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
144	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
145	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
146	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
147	C₇×C₂²⋊C₄	—	2	2	no	—
148	C₇×C₂²⋊C₄	—	2	2	no	—
149	C₇×C₂²⋊C₄	—	2	2	no	—
150	C₇×C₂²⋊C₄	—	2	2	no	—
151	C₇×C₂²⋊C₄	—	4	2	no	—
152	C₄²×C₇	—	2	2	no	—
153	C₄²×C₇	—	2	2	no	—
154	C₄²×C₇	—	2	2	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	2	1	no	—
160	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₂×#117	C₂²×C₇	1	2	yes	—
162	#433	—	2	2	no	—
163	#433	—	2	2	no	—
164	#432	—	2	2	no	—
165	#431	—	2	2	no	—
166	C₂×#108	C₂²×C₇	1	1	yes	characteristic
167	C₂×#108	C₂²×C₇	1	1	yes	characteristic
168	#428	C₄×C₇	1	2	yes	complemented
169	#428	C₄×C₇	1	2	yes	complemented
170	#428	C₄×C₇	1	2	yes	complemented
171	#428	C₄×C₇	1	2	yes	complemented
172	#427	C₂²×C₇	1	2	yes	—
173	#427	C₂²×C₇	1	1	yes	characteristic
174	#427	C₂²×C₇	1	1	yes	characteristic
175	#424	C₂²×C₇	1	2	yes	—
176	#424	C₂²×C₇	1	2	yes	—
177	#407	C₂²×C₇	1	2	yes	—
178	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
179	#405	C₂²×C₇	1	2	yes	—
180	#405	C₂²×C₇	1	2	yes	—
181	C₂×#97	C₂²×C₇	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
183	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
184	#341	C₂²×C₇	1	2	yes	—
185	#339	C₂²×C₇	1	2	yes	—
186	#339	C₂²×C₇	1	2	yes	—
187	#339	C₂²×C₇	1	2	yes	—
188	#339	C₂²×C₇	1	2	yes	—
189	#336	C₂²×C₇	1	1	yes	characteristic
190	#336	C₂²×C₇	1	1	yes	characteristic
191	C₂³×C₇	—	2	1	no	—
192	C₂³×C₇	—	2	1	no	—
193	C₂³×C₇	—	4	1	no	—
194	C₂³×C₇	—	4	1	no	—
195	C₂³×C₇	C₄×D₄	1	2	yes	—
196	C₂³×C₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇	—	2	1	no	—
198	C₂×C₄×C₇	—	2	1	no	—
199	C₂×C₄×C₇	—	2	2	no	—
200	C₂×C₄×C₇	—	2	2	no	—
201	C₂×C₄×C₇	—	2	2	no	—
202	C₂×C₄×C₇	—	2	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	4	1	no	—
209	C₂×C₄×C₇	—	4	4	no	—
210	C₂×C₄×C₇	—	4	1	no	—
211	C₂×C₄×C₇	—	4	1	no	—
212	C₂×C₄×C₇	—	4	1	no	—
213	C₂×C₄×C₇	—	4	1	no	—
214	C₂×C₄×C₇	—	8	2	no	—
215	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
221	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
222	C₇×C₈	—	2	2	no	—
223	C₇×C₈	—	2	1	no	—
224	C₇×C₈	—	2	1	no	—
225	C₇×C₈	—	2	2	no	—
226	C₇×C₈	—	4	2	no	—
227	C₇×C₈	—	4	2	no	—
228	C₇×C₈	#117	1	2	yes	—
229	C₇×C₈	#117	1	2	yes	—
230	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
234	C₂×M₁₆	C₂×C₄×C₇	1	2	yes	—
235	C₂×M₁₆	C₂³×C₇	1	2	yes	—
236	C₂×M₁₆	C₂³×C₇	1	2	yes	—
237	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	#117	C₂×C₄×C₇	1	2	yes	—
244	#117	C₂×C₄×C₇	1	2	yes	—
245	#117	C₂³×C₇	1	2	yes	—
246	#117	C₂³×C₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
254	#108	—	2	2	no	—
255	#108	—	2	2	no	—
256	#107	C₂×C₄×C₇	1	2	yes	—
257	#107	C₂×C₄×C₇	1	2	yes	—
258	#107	C₂×C₄×C₇	1	1	yes	characteristic
259	#107	C₂×C₄×C₇	1	1	yes	characteristic
260	#107	C₂×C₄×C₇	1	1	yes	characteristic
261	#107	C₂×C₄×C₇	1	1	yes	characteristic
262	#106	C₂×C₄×C₇	1	2	yes	—
263	#106	C₂×C₄×C₇	1	2	yes	—
264	#106	C₂×C₄×C₇	1	2	yes	—
265	#106	C₂×C₄×C₇	1	2	yes	—
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₂²⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	C₇×D₄	1	2	yes	—
273	C₂²⋊C₈	C₇×D₄	1	2	yes	—
274	#97	—	2	2	no	—
275	#97	—	2	2	no	—
276	#97	—	2	2	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	2	2	no	—
280	#95	—	2	1	no	—
281	C₂²×C₇	—	2	1	no	—
282	C₂²×C₇	—	2	1	no	—
283	C₂²×C₇	—	2	2	no	—
284	C₂²×C₇	—	2	2	no	—
285	C₂²×C₇	—	2	2	no	—
286	C₂²×C₇	—	8	1	no	—
287	C₂²×C₇	—	8	1	no	—
288	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₂²×C₇	#552	1	1	yes	characteristic
290	C₂²×C₇	#552	1	1	yes	characteristic
291	C₄×C₇	—	2	2	no	—
292	C₄×C₇	—	4	2	no	—
293	C₄×C₇	—	4	2	no	—
294	C₄×C₇	—	4	2	no	—
295	C₄×C₇	—	4	2	no	—
296	C₄×C₇	—	4	2	no	—
297	C₄×C₇	—	8	1	no	—
298	C₄×C₇	C₂×#117	1	1	yes	characteristic
299	C₄×C₇	#519	1	1	yes	characteristic
300	C₄×C₇	#547	1	1	yes	characteristic
301	C₄×C₇	#547	1	1	yes	characteristic
302	C₂⁴	C₇×#41	1	1	yes	characteristic
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	C₂²×C₄×C₇	1	2	yes	—
312	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
313	C₂²×C₄	C₇×#41	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
315	M₁₆	—	2	4	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
330	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
331	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
334	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂×C₈	C₇×#41	1	2	yes	—
336	C₂×C₈	C₇×#41	1	2	yes	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
340	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
341	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
342	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	2	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₂×C₇	—	2	1	no	—
357	C₂×C₇	—	2	1	no	—
358	C₂×C₇	—	4	2	no	—
359	C₂×C₇	#2344	1	1	yes	characteristic
360	C₂×C₇	#2955	1	1	yes	characteristic
361	C₂×C₇	#2956	1	1	yes	characteristic
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	C₄×C₇×D₄	1	2	yes	—
367	C₂³	C₂×C₇×#41	1	1	yes	characteristic
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
390	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
391	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	2	no	—
399	C₈	C₇×#117	1	2	yes	—
400	C₈	C₇×#117	1	2	yes	—
401	C₇	#22608	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
410	C₂²	C₇×#552	1	1	yes	characteristic
411	C₂²	C₇×#552	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	1	no	—
419	C₄	C₂×C₇×#117	1	1	yes	characteristic
420	C₄	C₇×#519	1	1	yes	characteristic
421	C₄	C₇×#547	1	1	yes	characteristic
422	C₄	C₇×#547	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	C₇×#2344	1	1	yes	characteristic
427	C₂	C₇×#2955	1	1	yes	characteristic
428	C₂	C₇×#2956	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	C₂⁴×C₇	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#1946	C₂	semidirect
4. C₇×#1945	C₂	semidirect
5. C₇×#1922	C₂	semidirect
6. C₇×#1922	C₂	semidirect
9. C₇×#1773	C₂	semidirect
10. C₇×#1772	C₂	semidirect
20. C₇×#428	C₄	semidirect
21. C₇×#428	C₄	semidirect
22. C₇×#428	C₄	semidirect
23. C₇×#428	C₄	semidirect
43. #22608	C₇	direct (N × H)
97. #1946	C₂×C₇	semidirect
98. #1945	C₂×C₇	semidirect
99. #1922	C₂×C₇	semidirect
100. #1922	C₂×C₇	semidirect
103. #1773	C₂×C₇	semidirect
104. #1772	C₂×C₇	semidirect
168. #428	C₄×C₇	semidirect
169. #428	C₄×C₇	semidirect
170. #428	C₄×C₇	semidirect
171. #428	C₄×C₇	semidirect
401. C₇	#22608	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×#2924	2
C₇×#2911	2
C₇×#1946	2
C₇×#1945	2
C₇×#1922	2
C₇×#1826	2
C₇×#1811	2
C₇×#1773	2
C₇×#1772	2
C₇×#1753	2
#22608	7

Subgroups — C7×#22608 #13199824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22608 #13199824