Subgroups — C₇×#19186 #13196402

Order 1792.

778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3205	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1685	C₂	1	4	yes	maximal, complemented
6	C₇×#1665	C₂	1	4	yes	maximal, complemented
7	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₇×SD₁₆	—	2	1	no	—
11	C₂²×C₇×SD₁₆	—	2	1	no	—
12	C₂×C₇×#131	—	2	1	no	—
13	C₇×#532	C₂²	1	1	yes	characteristic
14	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#127	C₂²	1	1	yes	characteristic
16	C₇×#500	—	2	1	no	—
17	C₇×#493	—	2	1	no	—
18	C₇×#492	—	2	1	no	—
19	C₇×#492	—	2	1	no	—
20	C₇×#492	C₂²	1	2	yes	—
21	C₇×#492	C₂²	1	2	yes	—
22	C₇×#486	—	2	1	no	—
23	C₇×#486	—	2	1	no	—
24	C₇×#480	—	2	2	no	—
25	C₇×#474	C₂²	1	4	yes	complemented
26	C₇×#459	C₂²	1	4	yes	—
27	C₇×#447	—	2	2	no	—
28	C₇×#436	—	2	1	no	—
29	C₇×#436	C₂²	1	2	yes	complemented
30	C₇×C₈×D₄	—	2	1	no	—
31	C₇×C₈×D₄	C₂²	1	2	yes	complemented
32	C₇×#431	C₂²	1	1	yes	characteristic
33	C₇×#431	C₂²	1	1	yes	characteristic
34	C₇×#423	C₂²	1	1	yes	characteristic
35	C₇×#408	—	2	1	no	—
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₇×#335	C₂²	1	2	yes	complemented
38	C₇×#334	C₂²	1	2	yes	complemented
39	C₇×#332	C₂²	1	4	yes	complemented
40	C₇×#331	C₂²	1	4	yes	—
41	#19186	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	—	2	1	no	—
43	C₂²×C₇×Q₈	—	2	1	no	—
44	C₂²×C₇×D₄	—	2	1	no	—
45	C₂²×C₇×D₄	—	2	1	no	—
46	C₂²×C₇×D₄	—	2	1	no	—
47	C₂×C₇×SD₁₆	—	2	2	no	—
48	C₂×C₇×SD₁₆	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₂×C₇×SD₁₆	—	4	4	no	—
52	C₂×C₇×SD₁₆	—	4	4	no	—
53	C₂×C₇×D₈	—	2	4	no	—
54	C₇×#131	—	4	4	no	—
55	C₂×C₇×M₁₆	—	2	1	no	—
56	C₂×C₇×M₁₆	—	2	2	no	—
57	C₂²×C₇×C₈	—	2	2	no	—
58	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	—	2	1	no	—
61	C₇×C₄⋊Q₈	—	2	1	no	—
62	C₇×C₄⋊Q₈	—	2	1	no	—
63	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₇×#127	—	2	1	no	—
66	C₇×#127	—	2	1	no	—
67	C₇×#127	—	2	1	no	—
68	C₇×#127	D₄	1	1	yes	characteristic
69	C₇×#127	C₂³	1	2	yes	—
70	C₇×#124	—	2	1	no	—
71	C₇×#121	—	2	1	no	—
72	C₇×#121	D₄	1	2	yes	—
73	C₄×C₇×D₄	—	2	1	no	—
74	C₄×C₇×D₄	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	1	no	—
76	C₂×C₇×C₄⋊C₄	—	2	1	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₇×#107	—	2	4	no	—
79	C₇×C₄⋊C₈	—	2	1	no	—
80	C₇×C₄⋊C₈	C₂³	1	2	yes	—
81	C₇×C₄⋊C₈	C₂³	1	2	yes	—
82	C₇×C₄⋊C₈	C₂³	1	2	yes	—
83	C₇×#102	—	2	4	no	—
84	C₇×#102	—	2	4	no	—
85	C₇×C₂²⋊C₈	—	2	1	no	—
86	C₇×C₂²⋊C₈	—	2	1	no	—
87	C₇×C₂²⋊C₈	—	2	2	no	—
88	C₇×C₂²⋊C₈	—	2	2	no	—
89	C₄×C₇×C₈	—	2	1	no	—
90	C₄×C₇×C₈	—	2	1	no	—
91	C₄×C₇×C₈	D₄	1	1	yes	characteristic
92	C₄×C₇×C₈	D₄	1	1	yes	characteristic
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	#3226	C₂×C₇	1	1	yes	characteristic, complemented
96	#3205	C₂×C₇	1	1	yes	characteristic
97	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
98	#2931	C₂×C₇	1	1	yes	characteristic, complemented
99	#1685	C₂×C₇	1	4	yes	complemented
100	#1665	C₂×C₇	1	4	yes	complemented
101	#1564	C₂×C₇	1	1	yes	characteristic, complemented
102	#1546	C₂×C₇	1	1	yes	characteristic, complemented
103	#1545	C₂×C₇	1	1	yes	characteristic, complemented
104	C₂⁴×C₇	—	4	1	no	—
105	C₇×#41	—	4	2	no	—
106	C₇×#41	—	4	2	no	—
107	C₂×C₇×Q₈	—	2	1	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	4	1	no	—
110	C₂×C₇×Q₈	—	4	2	no	—
111	C₂×C₇×Q₈	—	4	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	1	no	—
114	C₂×C₇×D₄	—	2	1	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	2	no	—
117	C₂×C₇×D₄	—	2	2	no	—
118	C₂×C₇×D₄	—	4	1	no	—
119	C₂×C₇×D₄	—	4	1	no	—
120	C₂×C₇×D₄	—	4	1	no	—
121	C₂×C₇×D₄	—	4	2	no	—
122	C₂×C₇×D₄	—	4	2	no	—
123	C₂×C₇×D₄	—	8	2	no	—
124	C₂×C₇×D₄	—	8	2	no	—
125	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇	—	2	2	no	—
127	C₂²×C₄×C₇	—	4	1	no	—
128	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇	#41	1	1	yes	characteristic
131	C₇×SD₁₆	—	4	4	no	—
132	C₇×SD₁₆	—	4	4	no	—
133	C₇×SD₁₆	—	4	4	no	—
134	C₇×SD₁₆	—	4	4	no	—
135	C₇×D₈	—	8	4	no	—
136	C₇×M₁₆	—	4	2	no	—
137	C₇×M₁₆	—	4	4	no	—
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	—	4	4	no	—
143	C₂×C₇×C₈	D₈	1	4	yes	complemented
144	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	4	1	no	—
152	C₇×C₄⋊C₄	—	4	1	no	—
153	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₇×C₂²⋊C₄	—	2	2	no	—
155	C₇×C₂²⋊C₄	—	2	2	no	—
156	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇	#41	1	1	yes	characteristic
159	C₄²×C₇	C₂⁴	1	1	yes	characteristic
160	C₂²×SD₁₆	—	2	1	no	—
161	C₂²×SD₁₆	—	2	1	no	—
162	C₂×#131	—	2	1	no	—
163	#532	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
165	C₂×#127	C₂²×C₇	1	1	yes	characteristic
166	#500	—	2	1	no	—
167	#493	—	2	1	no	—
168	#492	—	2	1	no	—
169	#492	—	2	1	no	—
170	#492	C₂²×C₇	1	2	yes	—
171	#492	C₂²×C₇	1	2	yes	—
172	#486	—	2	1	no	—
173	#486	—	2	1	no	—
174	#480	—	2	2	no	—
175	#474	C₂²×C₇	1	4	yes	complemented
176	#459	C₂²×C₇	1	4	yes	—
177	#447	—	2	2	no	—
178	#436	—	2	1	no	—
179	#436	C₂²×C₇	1	2	yes	complemented
180	C₈×D₄	—	2	1	no	—
181	C₈×D₄	C₂²×C₇	1	2	yes	complemented
182	#431	C₂²×C₇	1	1	yes	characteristic
183	#431	C₂²×C₇	1	1	yes	characteristic
184	#423	C₂²×C₇	1	1	yes	characteristic
185	#408	—	2	1	no	—
186	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
187	#335	C₂²×C₇	1	2	yes	complemented
188	#334	C₂²×C₇	1	2	yes	complemented
189	#332	C₂²×C₇	1	4	yes	complemented
190	#331	C₂²×C₇	1	4	yes	—
191	C₂³×C₇	—	2	2	no	—
192	C₂³×C₇	—	4	2	no	—
193	C₂³×C₇	—	8	2	no	—
194	C₂³×C₇	—	8	2	no	—
195	C₂³×C₇	—	8	2	no	—
196	C₂³×C₇	#121	1	1	yes	characteristic
197	C₇×Q₈	—	4	2	no	—
198	C₇×Q₈	—	4	2	no	—
199	C₇×Q₈	—	4	2	no	—
200	C₇×Q₈	—	8	2	no	—
201	C₇×D₄	—	2	4	no	—
202	C₇×D₄	—	4	4	no	—
203	C₇×D₄	—	4	2	no	—
204	C₇×D₄	—	4	2	no	—
205	C₇×D₄	—	4	4	no	—
206	C₇×D₄	—	4	2	no	—
207	C₇×D₄	—	4	2	no	—
208	C₇×D₄	—	8	2	no	—
209	C₇×D₄	—	8	2	no	—
210	C₇×D₄	—	8	2	no	—
211	C₇×D₄	—	8	2	no	—
212	C₂×C₄×C₇	—	2	2	no	—
213	C₂×C₄×C₇	—	2	2	no	—
214	C₂×C₄×C₇	—	2	2	no	—
215	C₂×C₄×C₇	—	4	2	no	—
216	C₂×C₄×C₇	—	4	2	no	—
217	C₂×C₄×C₇	—	4	2	no	—
218	C₂×C₄×C₇	—	8	2	no	—
219	C₂×C₄×C₇	#121	1	1	yes	characteristic
220	C₂×C₄×C₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
227	C₇×C₈	—	2	1	no	—
228	C₇×C₈	—	2	1	no	—
229	C₇×C₈	—	4	2	no	—
230	C₇×C₈	—	4	2	no	—
231	C₇×C₈	—	4	2	no	—
232	C₇×C₈	C₂×D₈	1	2	yes	—
233	C₇×C₈	C₂×D₈	1	2	yes	—
234	C₂×#41	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	—	2	1	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	4	4	no	—
244	C₂×SD₁₆	—	4	4	no	—
245	C₂×D₈	—	2	4	no	—
246	#131	—	4	4	no	—
247	C₂×M₁₆	—	2	1	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
251	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	C₇×D₄	1	1	yes	characteristic
261	#127	C₂³×C₇	1	2	yes	—
262	#124	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	C₇×D₄	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂³×C₇	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
270	#107	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₂³×C₇	1	2	yes	—
273	C₄⋊C₈	C₂³×C₇	1	2	yes	—
274	C₄⋊C₈	C₂³×C₇	1	2	yes	—
275	#102	—	2	4	no	—
276	#102	—	2	4	no	—
277	C₂²⋊C₈	—	2	1	no	—
278	C₂²⋊C₈	—	2	1	no	—
279	C₂²⋊C₈	—	2	2	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₄×C₈	C₇×D₄	1	1	yes	characteristic
284	C₄×C₈	C₇×D₄	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
287	C₂²×C₇	—	2	1	no	—
288	C₂²×C₇	—	2	1	no	—
289	C₂²×C₇	—	4	2	no	—
290	C₂²×C₇	—	4	2	no	—
291	C₂²×C₇	—	4	2	no	—
292	C₂²×C₇	—	8	2	no	—
293	C₂²×C₇	—	8	2	no	—
294	C₂²×C₇	—	8	2	no	—
295	C₂²×C₇	—	16	4	no	—
296	C₂²×C₇	#459	1	2	yes	—
297	C₂²×C₇	C₂×#121	1	1	yes	characteristic
298	C₄×C₇	—	2	1	no	—
299	C₄×C₇	—	2	1	no	—
300	C₄×C₇	—	4	2	no	—
301	C₄×C₇	—	8	2	no	—
302	C₄×C₇	#459	1	2	yes	—
303	C₄×C₇	#471	1	2	yes	—
304	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
305	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄×C₇	#577	1	2	yes	—
307	C₂⁴	—	4	1	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	8	2	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₇×#41	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	4	4	no	—
336	SD₁₆	—	4	4	no	—
337	SD₁₆	—	4	4	no	—
338	D₈	—	8	4	no	—
339	M₁₆	—	4	2	no	—
340	M₁₆	—	4	4	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	4	no	—
346	C₂×C₈	C₇×D₈	1	4	yes	complemented
347	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
348	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
349	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
360	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
361	C₄²	C₇×#41	1	1	yes	characteristic
362	C₄²	C₂⁴×C₇	1	1	yes	characteristic
363	C₂×C₇	—	2	2	no	—
364	C₂×C₇	—	8	2	no	—
365	C₂×C₇	—	16	2	no	—
366	C₂×C₇	C₂×#459	1	1	yes	characteristic
367	C₂×C₇	#3057	1	1	yes	characteristic
368	C₂×C₇	C₂×#471	1	1	yes	characteristic
369	C₂³	—	2	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	C₇×#121	1	1	yes	characteristic
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	D₄	—	2	4	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₇×#121	1	1	yes	characteristic
398	C₂×C₄	C₇×#121	1	1	yes	characteristic
399	C₂×C₄	C₇×#121	1	1	yes	characteristic
400	C₂×C₄	C₂×C₇×D₈	1	2	yes	—
401	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
402	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
404	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
405	C₈	—	2	1	no	—
406	C₈	—	2	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	C₂×C₇×D₈	1	2	yes	—
411	C₈	C₂×C₇×D₈	1	2	yes	—
412	C₇	#19186	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₇×#459	1	2	yes	—
423	C₂²	C₂×C₇×#121	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	2	no	—
428	C₄	C₇×#459	1	2	yes	—
429	C₄	C₇×#471	1	2	yes	—
430	C₄	C₂²×C₇×D₈	1	1	yes	characteristic
431	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₄	C₇×#577	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	8	2	no	—
435	C₂	—	16	2	no	—
436	C₂	C₂×C₇×#459	1	1	yes	characteristic
437	C₂	C₇×#3057	1	1	yes	characteristic
438	C₂	C₂×C₇×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#3205	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3226	C₂	semidirect
3. C₂×C₇×#492	C₂	semidirect
4. C₇×#2931	C₂	semidirect
5. C₇×#1685	C₂	semidirect
6. C₇×#1665	C₂	semidirect
7. C₇×#1564	C₂	semidirect
8. C₇×#1546	C₂	semidirect
9. C₇×#1545	C₂	semidirect
25. C₇×#474	C₂²	semidirect
29. C₇×#436	C₂²	semidirect
31. C₇×C₈×D₄	C₂²	semidirect
37. C₇×#335	C₂²	semidirect
38. C₇×#334	C₂²	semidirect
39. C₇×#332	C₂²	semidirect
41. #19186	C₇	direct (N × H)
95. #3226	C₂×C₇	semidirect
97. C₂×#492	C₂×C₇	semidirect
98. #2931	C₂×C₇	semidirect
99. #1685	C₂×C₇	semidirect
100. #1665	C₂×C₇	semidirect
101. #1564	C₂×C₇	semidirect
102. #1546	C₂×C₇	semidirect
103. #1545	C₂×C₇	semidirect
143. C₂×C₇×C₈	D₈	semidirect
175. #474	C₂²×C₇	semidirect
179. #436	C₂²×C₇	semidirect
181. C₈×D₄	C₂²×C₇	semidirect
187. #335	C₂²×C₇	semidirect
188. #334	C₂²×C₇	semidirect
189. #332	C₂²×C₇	semidirect
346. C₂×C₈	C₇×D₈	semidirect
412. C₇	#19186	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×#3226	2
C₇×#3205	2
C₂×C₇×#492	2
C₇×#2931	2
C₇×#1685	2
C₇×#1665	2
C₇×#1564	2
C₇×#1546	2
C₇×#1545	2
#19186	7

Subgroups — C7×#19186 #13196402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19186 #13196402