Subgroups — C₇×#19223 #13196439

Order 1792.

584 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×#3248	C₂	1	2	yes	maximal
2	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2966	C₂	1	1	yes	maximal, characteristic
4	C₇×#1700	C₂	1	2	yes	maximal, complemented
5	C₇×#1699	C₂	1	2	yes	maximal, complemented
6	C₇×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1670	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#335	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1552	C₂	1	2	yes	maximal, complemented
12	C₇×#533	C₂²	1	2	yes	—
13	C₇×#529	C₂²	1	1	yes	characteristic
14	C₇×#500	C₂²	1	1	yes	characteristic
15	C₇×#494	C₂²	1	1	yes	characteristic
16	C₇×#487	C₂²	1	2	yes	—
17	C₇×#479	—	2	2	no	—
18	C₇×#475	C₂²	1	2	yes	—
19	C₇×#474	C₂²	1	2	yes	—
20	C₇×#467	—	2	1	no	—
21	C₇×#467	—	2	1	no	—
22	C₇×#467	—	2	2	no	—
23	C₇×#465	—	2	2	no	—
24	C₇×#464	—	2	2	no	—
25	C₇×#462	C₂²	1	2	yes	—
26	C₇×#461	C₂²	1	2	yes	—
27	C₇×#446	C₂²	1	1	yes	characteristic
28	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₄×C₇×Q₁₆	—	2	1	no	—
30	C₄×C₇×Q₁₆	—	2	1	no	—
31	C₇×#436	C₂²	1	1	yes	characteristic
32	C₇×#435	—	2	1	no	—
33	C₇×C₈×D₄	—	2	1	no	—
34	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₇×#433	—	2	1	no	—
36	C₇×#432	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
38	C₇×#405	—	2	1	no	—
39	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
40	C₇×#335	C₂²	1	1	yes	characteristic
41	C₇×#335	C₂²	1	1	yes	characteristic
42	C₇×#335	C₂²	1	2	yes	—
43	C₇×#332	C₂²	1	2	yes	—
44	C₇×#332	C₂²	1	2	yes	—
45	C₇×#332	C₂²	1	2	yes	—
46	C₇×#332	C₂²	1	2	yes	—
47	#19223	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×Q₁₆	—	2	2	no	—
49	C₂×C₇×Q₁₆	—	2	1	no	—
50	C₂×C₇×Q₁₆	—	2	1	no	—
51	C₂×C₇×SD₁₆	—	2	2	no	—
52	C₂×C₇×M₁₆	—	2	1	no	—
53	C₂²×C₇×C₈	—	2	2	no	—
54	C₂²×C₇×C₈	—	2	1	no	—
55	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
57	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₇×#126	—	2	1	no	—
60	C₇×#125	—	2	2	no	—
61	C₇×#125	D₄	1	1	yes	characteristic
62	C₇×#124	D₄	1	1	yes	characteristic
63	C₇×#123	—	2	1	no	—
64	C₇×C₂²⋊Q₈	—	2	2	no	—
65	C₇×C₂²⋊Q₈	—	2	2	no	—
66	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
67	C₇×#121	D₄	1	1	yes	characteristic
68	C₄×C₇×Q₈	—	2	2	no	—
69	C₄×C₇×Q₈	—	2	2	no	—
70	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₇×D₄	—	2	1	no	—
72	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
73	C₇×#117	—	2	1	no	—
74	C₇×#117	—	2	2	no	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#107	—	2	1	no	—
77	C₇×#107	—	2	1	no	—
78	C₇×#107	—	2	2	no	—
79	C₇×#106	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	1	no	—
81	C₇×C₄⋊C₈	—	2	1	no	—
82	C₇×C₄⋊C₈	—	2	2	no	—
83	C₇×C₄⋊C₈	C₂³	1	2	yes	—
84	C₇×C₄⋊C₈	C₂³	1	2	yes	—
85	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₇×#103	—	2	2	no	—
88	C₇×#103	—	2	2	no	—
89	C₇×#103	—	2	2	no	—
90	C₇×#103	—	2	2	no	—
91	C₇×#103	—	2	2	no	—
92	C₇×#102	—	2	2	no	—
93	C₇×C₂²⋊C₈	—	2	1	no	—
94	C₇×C₂²⋊C₈	—	2	1	no	—
95	C₇×C₂²⋊C₈	—	2	1	no	—
96	C₇×#97	—	2	1	no	—
97	C₇×#97	—	2	1	no	—
98	C₄×C₇×C₈	—	2	1	no	—
99	C₄×C₇×C₈	D₄	1	1	yes	characteristic
100	C₄×C₇×C₈	D₄	1	1	yes	characteristic
101	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
103	#3248	C₂×C₇	1	2	yes	—
104	#3170	C₂×C₇	1	1	yes	characteristic, complemented
105	#2966	C₂×C₇	1	1	yes	characteristic
106	#1700	C₂×C₇	1	2	yes	complemented
107	#1699	C₂×C₇	1	2	yes	complemented
108	#1674	C₂×C₇	1	1	yes	characteristic, complemented
109	#1673	C₂×C₇	1	1	yes	characteristic, complemented
110	#1670	C₂×C₇	1	1	yes	characteristic, complemented
111	#1669	C₂×C₇	1	1	yes	characteristic, complemented
112	C₂×#335	C₂×C₇	1	1	yes	characteristic, complemented
113	#1552	C₂×C₇	1	2	yes	complemented
114	C₂×C₇×Q₈	—	2	2	no	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₇×D₄	—	2	1	no	—
118	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇	—	2	1	no	—
120	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	#41	1	1	yes	characteristic
123	C₇×Q₁₆	—	4	2	no	—
124	C₇×Q₁₆	—	4	2	no	—
125	C₇×Q₁₆	—	8	2	no	—
126	C₇×SD₁₆	—	8	2	no	—
127	C₇×M₁₆	—	4	2	no	—
128	C₂×C₇×C₈	—	2	2	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	—	4	1	no	—
134	C₂×C₇×C₈	—	4	2	no	—
135	C₂×C₇×C₈	—	8	2	no	—
136	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	1	no	—
143	C₇×C₄⋊C₄	—	2	1	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	2	2	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	4	2	no	—
149	C₇×C₄⋊C₄	—	4	2	no	—
150	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
151	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₇×C₂²⋊C₄	—	2	1	no	—
153	C₇×C₂²⋊C₄	—	2	1	no	—
154	C₇×C₂²⋊C₄	—	2	1	no	—
155	C₇×C₂²⋊C₄	—	2	1	no	—
156	C₇×C₂²⋊C₄	—	2	1	no	—
157	C₇×C₂²⋊C₄	—	4	2	no	—
158	C₄²×C₇	—	2	1	no	—
159	C₄²×C₇	—	4	2	no	—
160	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇	#41	1	1	yes	characteristic
163	C₄²×C₇	C₂⁴	1	1	yes	characteristic
164	#533	C₂²×C₇	1	2	yes	—
165	#529	C₂²×C₇	1	1	yes	characteristic
166	#500	C₂²×C₇	1	1	yes	characteristic
167	#494	C₂²×C₇	1	1	yes	characteristic
168	#487	C₂²×C₇	1	2	yes	—
169	#479	—	2	2	no	—
170	#475	C₂²×C₇	1	2	yes	—
171	#474	C₂²×C₇	1	2	yes	—
172	#467	—	2	1	no	—
173	#467	—	2	1	no	—
174	#467	—	2	2	no	—
175	#465	—	2	2	no	—
176	#464	—	2	2	no	—
177	#462	C₂²×C₇	1	2	yes	—
178	#461	C₂²×C₇	1	2	yes	—
179	#446	C₂²×C₇	1	1	yes	characteristic
180	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
181	C₄×Q₁₆	—	2	1	no	—
182	C₄×Q₁₆	—	2	1	no	—
183	#436	C₂²×C₇	1	1	yes	characteristic
184	#435	—	2	1	no	—
185	C₈×D₄	—	2	1	no	—
186	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
187	#433	—	2	1	no	—
188	#432	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
190	#405	—	2	1	no	—
191	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
192	#335	C₂²×C₇	1	1	yes	characteristic
193	#335	C₂²×C₇	1	1	yes	characteristic
194	#335	C₂²×C₇	1	2	yes	—
195	#332	C₂²×C₇	1	2	yes	—
196	#332	C₂²×C₇	1	2	yes	—
197	#332	C₂²×C₇	1	2	yes	—
198	#332	C₂²×C₇	1	2	yes	—
199	C₂³×C₇	—	2	1	no	—
200	C₂³×C₇	#121	1	1	yes	characteristic
201	C₇×Q₈	—	2	1	no	—
202	C₇×Q₈	—	2	1	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₇×Q₈	—	4	2	no	—
205	C₇×Q₈	—	4	2	no	—
206	C₇×Q₈	—	4	2	no	—
207	C₇×D₄	—	2	1	no	—
208	C₇×D₄	—	2	1	no	—
209	C₇×D₄	—	4	2	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	1	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	2	1	no	—
216	C₂×C₄×C₇	—	2	1	no	—
217	C₂×C₄×C₇	—	2	1	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	1	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	—	4	2	no	—
222	C₂×C₄×C₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
228	C₇×C₈	—	2	1	no	—
229	C₇×C₈	—	2	1	no	—
230	C₇×C₈	—	2	1	no	—
231	C₇×C₈	—	4	1	no	—
232	C₇×C₈	—	4	1	no	—
233	C₇×C₈	—	4	2	no	—
234	C₇×C₈	—	4	2	no	—
235	C₇×C₈	#135	1	2	yes	—
236	C₂×Q₁₆	—	2	2	no	—
237	C₂×Q₁₆	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	1	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
244	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
245	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
247	#126	—	2	1	no	—
248	#125	—	2	2	no	—
249	#125	C₇×D₄	1	1	yes	characteristic
250	#124	C₇×D₄	1	1	yes	characteristic
251	#123	—	2	1	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
255	#121	C₇×D₄	1	1	yes	characteristic
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
261	#117	—	2	1	no	—
262	#117	—	2	2	no	—
263	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	#107	—	2	2	no	—
267	#106	—	2	2	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₇	1	2	yes	—
274	C₄⋊C₈	C₂³×C₇	1	2	yes	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	#97	—	2	1	no	—
285	#97	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	C₇×D₄	1	1	yes	characteristic
288	C₄×C₈	C₇×D₄	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
291	C₂²×C₇	—	2	1	no	—
292	C₂²×C₇	—	2	1	no	—
293	C₂²×C₇	—	4	1	no	—
294	C₂²×C₇	—	4	1	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	#473	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	—	2	1	no	—
301	C₄×C₇	—	2	1	no	—
302	C₄×C₇	—	4	1	no	—
303	C₄×C₇	—	4	1	no	—
304	C₄×C₇	—	4	1	no	—
305	C₄×C₇	—	8	2	no	—
306	C₄×C₇	—	8	2	no	—
307	C₄×C₇	C₂×#135	1	1	yes	characteristic
308	C₄×C₇	#575	1	1	yes	characteristic
309	C₄×C₇	#576	1	1	yes	characteristic
310	C₄×C₇	#578	1	1	yes	characteristic
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₇×#41	1	1	yes	characteristic
320	Q₁₆	—	4	2	no	—
321	Q₁₆	—	4	2	no	—
322	Q₁₆	—	8	2	no	—
323	SD₁₆	—	8	2	no	—
324	M₁₆	—	4	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	—	8	2	no	—
333	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
334	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
348	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
349	C₂²⋊C₄	—	2	1	no	—
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	4	2	no	—
357	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
358	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
359	C₄²	C₇×#41	1	1	yes	characteristic
360	C₄²	C₂⁴×C₇	1	1	yes	characteristic
361	C₂×C₇	—	2	2	no	—
362	C₂×C₇	—	8	1	no	—
363	C₂×C₇	#3035	1	1	yes	characteristic
364	C₂×C₇	#3061	1	1	yes	characteristic
365	C₂×C₇	C₂×#473	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	C₇×#121	1	1	yes	characteristic
368	Q₈	—	2	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	D₄	—	2	1	no	—
375	D₄	—	2	1	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	C₇×#121	1	1	yes	characteristic
390	C₂×C₄	C₇×#121	1	1	yes	characteristic
391	C₂×C₄	C₇×#121	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
393	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	C₇×#135	1	2	yes	—
403	C₇	#19223	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	C₇×#473	1	2	yes	—
410	C₂²	C₂×C₇×#121	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	C₂×C₇×#135	1	1	yes	characteristic
421	C₄	C₇×#575	1	1	yes	characteristic
422	C₄	C₇×#576	1	1	yes	characteristic
423	C₄	C₇×#578	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	8	1	no	—
426	C₂	C₇×#3035	1	1	yes	characteristic
427	C₂	C₇×#3061	1	1	yes	characteristic
428	C₂	C₂×C₇×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₇×#121	D₄
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
2. C₇×#3170	C₂	semidirect
4. C₇×#1700	C₂	semidirect
5. C₇×#1699	C₂	semidirect
6. C₇×#1674	C₂	semidirect
7. C₇×#1673	C₂	semidirect
8. C₇×#1670	C₂	semidirect
9. C₇×#1669	C₂	semidirect
10. C₂×C₇×#335	C₂	semidirect
11. C₇×#1552	C₂	semidirect
47. #19223	C₇	direct (N × H)
104. #3170	C₂×C₇	semidirect
106. #1700	C₂×C₇	semidirect
107. #1699	C₂×C₇	semidirect
108. #1674	C₂×C₇	semidirect
109. #1673	C₂×C₇	semidirect
110. #1670	C₂×C₇	semidirect
111. #1669	C₂×C₇	semidirect
112. C₂×#335	C₂×C₇	semidirect
113. #1552	C₂×C₇	semidirect
403. C₇	#19223	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×#3248	2
C₇×#3170	2
C₇×#2966	2
C₇×#1700	2
C₇×#1699	2
C₇×#1674	2
C₇×#1673	2
C₇×#1670	2
C₇×#1669	2
C₂×C₇×#335	2
C₇×#1552	2
#19223	7

Subgroups — C7×#19223 #13196439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19223 #13196439