Subgroups — C₇×#19126 #13196342

Order 1792.

618 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3076	C₂	1	2	yes	maximal
3	C₇×C₈×#41	C₂	1	1	yes	maximal, characteristic
4	C₇×#1684	C₂	1	2	yes	maximal, complemented
5	C₇×#1683	C₂	1	2	yes	maximal, complemented
6	C₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1675	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×#1542	C₂	1	2	yes	maximal, complemented
12	C₇×#533	C₂²	1	2	yes	—
13	C₄×C₇×#41	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×#478	—	2	2	no	—
19	C₇×#477	C₂²	1	2	yes	—
20	C₇×#476	C₂²	1	2	yes	—
21	C₇×#475	C₂²	1	2	yes	—
22	C₇×#474	C₂²	1	2	yes	—
23	C₇×#467	—	2	1	no	—
24	C₇×#467	—	2	1	no	—
25	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
26	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
27	C₄×C₇×Q₁₆	—	2	1	no	—
28	C₄×C₇×Q₁₆	—	2	1	no	—
29	C₇×C₈×D₄	—	2	1	no	—
30	C₇×C₈×D₄	—	2	1	no	—
31	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
32	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
33	C₇×#431	—	2	1	no	—
34	C₇×#431	C₂²	1	1	yes	characteristic
35	C₇×#427	—	2	2	no	—
36	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
37	C₇×#416	—	2	2	no	—
38	C₂×C₄×C₇×C₈	—	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×#333	C₂²	1	2	yes	—
44	C₇×#333	C₂²	1	2	yes	—
45	C₇×#332	C₂²	1	2	yes	—
46	C₇×#332	C₂²	1	2	yes	—
47	#19126	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₇×#41	D₄	1	1	yes	characteristic
49	C₂×C₇×Q₁₆	—	2	1	no	—
50	C₂×C₇×Q₁₆	—	2	1	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	—	2	1	no	—
53	C₂²×C₇×C₈	—	2	1	no	—
54	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
55	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
56	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₇×#125	—	2	2	no	—
59	C₇×C₂²⋊Q₈	—	2	2	no	—
60	C₇×C₂²⋊Q₈	—	2	2	no	—
61	C₄×C₇×Q₈	—	2	2	no	—
62	C₄×C₇×Q₈	—	2	2	no	—
63	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
64	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
65	C₄×C₇×D₄	—	2	1	no	—
66	C₄×C₇×D₄	—	2	1	no	—
67	C₄×C₇×D₄	D₄	1	1	yes	characteristic
68	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
69	C₇×#117	—	2	1	no	—
70	C₇×#117	—	2	2	no	—
71	C₇×#117	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₇	—	2	1	no	—
73	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
74	C₇×#107	—	2	1	no	—
75	C₇×#107	—	2	1	no	—
76	C₇×#107	—	2	2	no	—
77	C₇×#107	—	2	2	no	—
78	C₇×#106	—	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×#102	—	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	C₄×C₇×C₈	—	2	1	no	—
97	C₄×C₇×C₈	—	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	#3170	C₂×C₇	1	1	yes	characteristic, complemented
104	#3076	C₂×C₇	1	2	yes	—
105	C₈×#41	C₂×C₇	1	1	yes	characteristic
106	#1684	C₂×C₇	1	2	yes	complemented
107	#1683	C₂×C₇	1	2	yes	complemented
108	#1676	C₂×C₇	1	1	yes	characteristic, complemented
109	#1675	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	#1542	C₂×C₇	1	2	yes	complemented
114	C₇×#41	—	2	2	no	—
115	C₇×#41	Q₁₆	1	4	yes	complemented
116	C₂×C₇×Q₈	—	2	2	no	—
117	C₂×C₇×Q₈	—	2	2	no	—
118	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₇×D₄	—	2	1	no	—
120	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	#41	1	1	yes	characteristic
127	C₇×Q₁₆	—	4	2	no	—
128	C₇×Q₁₆	—	4	2	no	—
129	C₂×C₇×C₈	—	2	2	no	—
130	C₂×C₇×C₈	—	2	1	no	—
131	C₂×C₇×C₈	—	2	1	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	—	4	1	no	—
135	C₂×C₇×C₈	—	4	2	no	—
136	C₂×C₇×C₈	—	4	4	no	—
137	C₂×C₇×C₈	—	4	2	no	—
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	1	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	C₄×#41	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	#478	—	2	2	no	—
171	#477	C₂²×C₇	1	2	yes	—
172	#476	C₂²×C₇	1	2	yes	—
173	#475	C₂²×C₇	1	2	yes	—
174	#474	C₂²×C₇	1	2	yes	—
175	#467	—	2	1	no	—
176	#467	—	2	1	no	—
177	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
178	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
179	C₄×Q₁₆	—	2	1	no	—
180	C₄×Q₁₆	—	2	1	no	—
181	C₈×D₄	—	2	1	no	—
182	C₈×D₄	—	2	1	no	—
183	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
184	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
185	#431	—	2	1	no	—
186	#431	C₂²×C₇	1	1	yes	characteristic
187	#427	—	2	2	no	—
188	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
189	#416	—	2	2	no	—
190	C₂×C₄×C₈	—	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	#333	C₂²×C₇	1	2	yes	—
196	#333	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	—	4	2	no	—
203	C₇×Q₈	—	4	2	no	—
204	C₇×Q₈	—	8	2	no	—
205	C₇×Q₈	C₂×Q₁₆	1	2	yes	—
206	C₇×D₄	—	2	4	no	—
207	C₇×D₄	—	2	1	no	—
208	C₇×D₄	C₂×Q₁₆	1	2	yes	—
209	C₂×C₄×C₇	—	2	1	no	—
210	C₂×C₄×C₇	—	2	1	no	—
211	C₂×C₄×C₇	—	2	1	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	1	no	—
214	C₂×C₄×C₇	—	2	1	no	—
215	C₂×C₄×C₇	—	4	1	no	—
216	C₂×C₄×C₇	—	4	2	no	—
217	C₂×C₄×C₇	—	4	1	no	—
218	C₂×C₄×C₇	—	4	1	no	—
219	C₂×C₄×C₇	—	4	2	no	—
220	C₂×C₄×C₇	—	4	2	no	—
221	C₂×C₄×C₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₇	C₂×Q₁₆	1	2	yes	—
225	C₂×C₄×C₇	#135	1	2	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
229	C₇×C₈	—	2	1	no	—
230	C₇×C₈	—	2	1	no	—
231	C₇×C₈	—	2	1	no	—
232	C₇×C₈	—	4	1	no	—
233	C₇×C₈	—	4	2	no	—
234	C₇×C₈	—	4	2	no	—
235	C₇×C₈	—	4	1	no	—
236	C₇×C₈	#135	1	2	yes	—
237	C₂×#41	C₇×D₄	1	1	yes	characteristic
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	1	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	#125	—	2	2	no	—
248	C₂²⋊Q₈	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	2	no	—
252	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
253	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
254	C₄×D₄	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	C₇×D₄	1	1	yes	characteristic
257	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
258	#117	—	2	1	no	—
259	#117	—	2	2	no	—
260	#117	C₇×D₄	1	1	yes	characteristic
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
263	#107	—	2	1	no	—
264	#107	—	2	1	no	—
265	#107	—	2	2	no	—
266	#107	—	2	2	no	—
267	#106	—	2	2	no	—
268	#106	—	2	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₇	1	2	yes	—
275	C₄⋊C₈	C₂³×C₇	1	2	yes	—
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	#102	—	2	2	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	C₇×D₄	1	1	yes	characteristic
289	C₄×C₈	C₇×D₄	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
292	C₂²×C₇	—	2	1	no	—
293	C₂²×C₇	—	2	1	no	—
294	C₂²×C₇	—	2	2	no	—
295	C₂²×C₇	—	4	1	no	—
296	C₂²×C₇	—	4	1	no	—
297	C₂²×C₇	#467	1	2	yes	—
298	C₂²×C₇	C₂×#121	1	1	yes	characteristic
299	C₄×C₇	—	2	1	no	—
300	C₄×C₇	—	2	2	no	—
301	C₄×C₇	—	2	1	no	—
302	C₄×C₇	—	2	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	#467	1	2	yes	—
308	C₄×C₇	C₂²×Q₁₆	1	1	yes	characteristic
309	C₄×C₇	C₂×#135	1	1	yes	characteristic
310	C₄×C₇	C₂×#135	1	1	yes	characteristic
311	C₄×C₇	#575	1	1	yes	characteristic
312	#41	—	2	2	no	—
313	#41	C₇×Q₁₆	1	4	yes	complemented
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
324	C₂²×C₄	C₇×#41	1	1	yes	characteristic
325	Q₁₆	—	4	2	no	—
326	Q₁₆	—	4	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	4	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
337	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
338	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
339	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
349	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	4	2	no	—
354	C₄²	—	2	1	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	2	no	—
358	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
359	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
360	C₄²	C₇×#41	1	1	yes	characteristic
361	C₄²	C₂⁴×C₇	1	1	yes	characteristic
362	C₂×C₇	—	2	2	no	—
363	C₂×C₇	—	4	2	no	—
364	C₂×C₇	#3035	1	1	yes	characteristic
365	C₂×C₇	C₂×#467	1	1	yes	characteristic
366	C₂×C₇	#3067	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	C₇×#121	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	8	2	no	—
373	Q₈	C₂×C₇×Q₁₆	1	2	yes	—
374	D₄	—	2	4	no	—
375	D₄	—	2	1	no	—
376	D₄	C₂×C₇×Q₁₆	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	4	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	—	4	1	no	—
384	C₂×C₄	—	4	2	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	C₂×C₇×Q₁₆	1	2	yes	—
393	C₂×C₄	C₇×#135	1	2	yes	—
394	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	—	2	1	no	—
400	C₈	—	4	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	1	no	—
404	C₈	C₇×#135	1	2	yes	—
405	C₇	#19126	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	C₇×#467	1	2	yes	—
412	C₂²	C₂×C₇×#121	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	C₇×#467	1	2	yes	—
422	C₄	C₂²×C₇×Q₁₆	1	1	yes	characteristic
423	C₄	C₂×C₇×#135	1	1	yes	characteristic
424	C₄	C₂×C₇×#135	1	1	yes	characteristic
425	C₄	C₇×#575	1	1	yes	characteristic
426	C₂	—	2	2	no	—
427	C₂	—	4	2	no	—
428	C₂	C₇×#3035	1	1	yes	characteristic
429	C₂	C₂×C₇×#467	1	1	yes	characteristic
430	C₂	C₇×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×#121
prime radical	C₂×C₇×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3170	C₂	semidirect
4. C₇×#1684	C₂	semidirect
5. C₇×#1683	C₂	semidirect
6. C₇×#1676	C₂	semidirect
7. C₇×#1675	C₂	semidirect
8. C₇×#1670	C₂	semidirect
9. C₇×#1669	C₂	semidirect
10. C₂×C₇×#335	C₂	semidirect
11. C₇×#1542	C₂	semidirect
47. #19126	C₇	direct (N × H)
103. #3170	C₂×C₇	semidirect
106. #1684	C₂×C₇	semidirect
107. #1683	C₂×C₇	semidirect
108. #1676	C₂×C₇	semidirect
109. #1675	C₂×C₇	semidirect
110. #1670	C₂×C₇	semidirect
111. #1669	C₂×C₇	semidirect
112. C₂×#335	C₂×C₇	semidirect
113. #1542	C₂×C₇	semidirect
115. C₇×#41	Q₁₆	semidirect
313. #41	C₇×Q₁₆	semidirect
405. C₇	#19126	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×#3170	2
C₇×#3076	2
C₇×C₈×#41	2
C₇×#1684	2
C₇×#1683	2
C₇×#1676	2
C₇×#1675	2
C₇×#1670	2
C₇×#1669	2
C₂×C₇×#335	2
C₇×#1542	2
#19126	7

Subgroups — C7×#19126 #13196342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19126 #13196342