Subgroups — C₇×#19242 #13196458

Order 1792.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3249	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic
3	C₇×#3138	C₂	1	1	yes	maximal, characteristic
4	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1702	C₂	1	2	yes	maximal, complemented
6	C₇×#1698	C₂	1	2	yes	maximal, complemented
7	C₇×#1682	C₂	1	2	yes	maximal, complemented
8	C₇×#1678	C₂	1	2	yes	maximal, complemented
9	C₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#331	C₂	1	1	yes	maximal, characteristic
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₇×#533	C₂²	1	1	yes	characteristic
14	C₂×C₇×#127	C₂²	1	1	yes	characteristic
15	C₇×#492	—	2	1	no	—
16	C₇×#490	—	2	2	no	—
17	C₇×#486	—	2	1	no	—
18	C₇×#486	C₂²	1	2	yes	—
19	C₇×#486	C₂²	1	2	yes	—
20	C₇×#477	—	2	1	no	—
21	C₇×#477	C₂²	1	2	yes	complemented
22	C₇×#467	—	2	2	no	—
23	C₇×#462	—	2	1	no	—
24	C₇×#462	C₂²	1	2	yes	complemented
25	C₇×#460	C₂²	1	2	yes	—
26	C₇×#460	C₂²	1	2	yes	—
27	C₇×#450	—	2	2	no	—
28	C₇×#446	—	2	2	no	—
29	C₇×#446	C₂²	1	2	yes	complemented
30	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
31	C₇×#431	C₂²	1	1	yes	characteristic
32	C₇×#424	—	2	1	no	—
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₇×#418	—	2	1	no	—
36	C₇×#418	—	2	1	no	—
37	C₇×#405	—	2	1	no	—
38	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
39	C₇×#335	C₂²	1	2	yes	complemented
40	C₇×#334	C₂²	1	2	yes	complemented
41	C₇×#333	C₂²	1	1	yes	characteristic, complemented
42	C₇×#333	C₂²	1	1	yes	characteristic, complemented
43	C₇×#332	C₂²	1	1	yes	characteristic, complemented
44	C₇×#332	C₂²	1	1	yes	characteristic, complemented
45	C₇×#331	C₂²	1	2	yes	—
46	C₇×#331	C₂²	1	2	yes	—
47	#19242	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×D₄	—	2	1	no	—
49	C₂²×C₇×D₄	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂×C₇×Q₁₆	—	2	2	no	—
52	C₂×C₇×SD₁₆	—	2	2	no	—
53	C₂×C₇×SD₁₆	—	2	2	no	—
54	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
55	C₂×C₇×M₁₆	D₄	1	1	yes	characteristic
56	C₂²×C₇×C₈	—	2	1	no	—
57	C₂²×C₇×C₈	—	2	1	no	—
58	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
59	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₇×#127	—	2	1	no	—
63	C₇×#127	—	2	1	no	—
64	C₇×#127	—	2	1	no	—
65	C₇×#127	C₂³	1	2	yes	—
66	C₇×#125	—	2	1	no	—
67	C₇×#125	—	2	1	no	—
68	C₇×C₂²⋊Q₈	—	2	1	no	—
69	C₇×C₂²⋊Q₈	—	2	1	no	—
70	C₇×C₂²⋊Q₈	—	2	1	no	—
71	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
72	C₄×C₇×Q₈	—	2	1	no	—
73	C₄×C₇×Q₈	—	2	1	no	—
74	C₄×C₇×Q₈	—	2	1	no	—
75	C₄×C₇×Q₈	C₂³	1	2	yes	—
76	C₇×#117	—	2	1	no	—
77	C₇×#117	—	2	1	no	—
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#107	—	2	2	no	—
80	C₇×C₄⋊C₈	—	2	2	no	—
81	C₇×C₄⋊C₈	—	2	2	no	—
82	C₇×C₄⋊C₈	—	2	1	no	—
83	C₇×C₄⋊C₈	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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×#102	—	2	2	no	—
94	C₇×#102	—	2	2	no	—
95	C₇×#102	—	2	2	no	—
96	C₇×#102	—	2	2	no	—
97	C₇×C₂²⋊C₈	—	2	1	no	—
98	C₇×#97	—	2	2	no	—
99	C₇×#97	D₄	1	2	yes	—
100	C₄×C₇×C₈	—	2	2	no	—
101	C₄×C₇×C₈	—	2	1	no	—
102	C₄×C₇×C₈	C₂³	1	2	yes	—
103	#3249	C₂×C₇	1	1	yes	characteristic, complemented
104	#3208	C₂×C₇	1	1	yes	characteristic
105	#3138	C₂×C₇	1	1	yes	characteristic
106	#2962	C₂×C₇	1	1	yes	characteristic, complemented
107	#1702	C₂×C₇	1	2	yes	complemented
108	#1698	C₂×C₇	1	2	yes	complemented
109	#1682	C₂×C₇	1	2	yes	complemented
110	#1678	C₂×C₇	1	2	yes	complemented
111	#1565	C₂×C₇	1	1	yes	characteristic, complemented
112	#1542	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#331	C₂×C₇	1	1	yes	characteristic
114	C₂⁴×C₇	—	4	1	no	—
115	C₂×C₇×Q₈	—	2	1	no	—
116	C₂×C₇×Q₈	—	2	1	no	—
117	C₂×C₇×Q₈	—	2	1	no	—
118	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	—	2	2	no	—
122	C₂×C₇×D₄	—	4	1	no	—
123	C₂×C₇×D₄	—	4	1	no	—
124	C₂×C₇×D₄	—	4	1	no	—
125	C₂×C₇×D₄	—	4	2	no	—
126	C₂×C₇×D₄	—	4	2	no	—
127	C₂×C₇×D₄	—	8	1	no	—
128	C₂×C₇×D₄	—	8	1	no	—
129	C₂×C₇×D₄	—	8	2	no	—
130	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇	#41	1	1	yes	characteristic
133	C₇×Q₁₆	—	8	2	no	—
134	C₇×SD₁₆	—	8	2	no	—
135	C₇×SD₁₆	—	8	2	no	—
136	C₇×M₁₆	—	2	2	no	—
137	C₇×M₁₆	—	2	2	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	1	no	—
140	C₂×C₇×C₈	—	2	1	no	—
141	C₂×C₇×C₈	—	2	1	no	—
142	C₂×C₇×C₈	—	2	2	no	—
143	C₂×C₇×C₈	—	4	2	no	—
144	C₂×C₇×C₈	—	8	1	no	—
145	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
147	C₇×C₄⋊C₄	—	2	1	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	1	no	—
153	C₇×C₄⋊C₄	—	2	1	no	—
154	C₇×C₄⋊C₄	—	2	1	no	—
155	C₇×C₄⋊C₄	—	2	1	no	—
156	C₇×C₄⋊C₄	—	4	1	no	—
157	C₇×C₄⋊C₄	—	4	1	no	—
158	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
159	C₇×C₂²⋊C₄	—	2	2	no	—
160	C₇×C₂²⋊C₄	—	4	1	no	—
161	C₄²×C₇	—	2	2	no	—
162	C₄²×C₇	—	4	1	no	—
163	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₇	#41	1	1	yes	characteristic
166	C₄²×C₇	C₂⁴	1	1	yes	characteristic
167	#533	C₂²×C₇	1	1	yes	characteristic
168	#533	C₂²×C₇	1	1	yes	characteristic
169	C₂×#127	C₂²×C₇	1	1	yes	characteristic
170	#492	—	2	1	no	—
171	#490	—	2	2	no	—
172	#486	—	2	1	no	—
173	#486	C₂²×C₇	1	2	yes	—
174	#486	C₂²×C₇	1	2	yes	—
175	#477	—	2	1	no	—
176	#477	C₂²×C₇	1	2	yes	complemented
177	#467	—	2	2	no	—
178	#462	—	2	1	no	—
179	#462	C₂²×C₇	1	2	yes	complemented
180	#460	C₂²×C₇	1	2	yes	—
181	#460	C₂²×C₇	1	2	yes	—
182	#450	—	2	2	no	—
183	#446	—	2	2	no	—
184	#446	C₂²×C₇	1	2	yes	complemented
185	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
186	#431	C₂²×C₇	1	1	yes	characteristic
187	#424	—	2	1	no	—
188	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
189	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
190	#418	—	2	1	no	—
191	#418	—	2	1	no	—
192	#405	—	2	1	no	—
193	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
194	#335	C₂²×C₇	1	2	yes	complemented
195	#334	C₂²×C₇	1	2	yes	complemented
196	#333	C₂²×C₇	1	1	yes	characteristic, complemented
197	#333	C₂²×C₇	1	1	yes	characteristic, complemented
198	#332	C₂²×C₇	1	1	yes	characteristic, complemented
199	#332	C₂²×C₇	1	1	yes	characteristic, complemented
200	#331	C₂²×C₇	1	2	yes	—
201	#331	C₂²×C₇	1	2	yes	—
202	C₂³×C₇	—	4	2	no	—
203	C₂³×C₇	—	8	2	no	—
204	C₂³×C₇	—	8	2	no	—
205	C₂³×C₇	—	8	2	no	—
206	C₂³×C₇	#121	1	1	yes	characteristic
207	C₇×Q₈	—	2	2	no	—
208	C₇×Q₈	—	2	2	no	—
209	C₇×Q₈	—	4	1	no	—
210	C₇×Q₈	—	4	1	no	—
211	C₇×Q₈	—	8	1	no	—
212	C₇×Q₈	—	8	1	no	—
213	C₇×D₄	—	4	2	no	—
214	C₇×D₄	—	4	2	no	—
215	C₇×D₄	—	4	2	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	8	2	no	—
218	C₇×D₄	—	8	2	no	—
219	C₇×D₄	—	8	2	no	—
220	C₇×D₄	—	8	2	no	—
221	C₂×C₄×C₇	—	2	1	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	2	2	no	—
224	C₂×C₄×C₇	—	2	2	no	—
225	C₂×C₄×C₇	—	4	1	no	—
226	C₂×C₄×C₇	—	4	1	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₇	#121	1	1	yes	characteristic
230	C₂×C₄×C₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₇	#135	1	2	yes	—
232	C₂×C₄×C₇	#137	1	2	yes	—
233	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₇×C₈	—	2	2	no	—
237	C₇×C₈	—	2	2	no	—
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	2	no	—
241	C₇×C₈	—	4	1	no	—
242	C₇×C₈	—	4	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
250	C₂×M₁₆	C₇×D₄	1	1	yes	characteristic
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
254	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
257	#127	—	2	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	C₂³×C₇	1	2	yes	—
261	#125	—	2	1	no	—
262	#125	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	C₂²⋊Q₈	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂³×C₇	1	2	yes	—
271	#117	—	2	1	no	—
272	#117	—	2	1	no	—
273	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
280	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
281	C₄⋊C₈	C₂³×C₇	1	2	yes	—
282	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	#97	—	2	2	no	—
294	#97	C₇×D₄	1	2	yes	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	C₂³×C₇	1	2	yes	—
298	C₂²×C₇	—	2	1	no	—
299	C₂²×C₇	—	2	1	no	—
300	C₂²×C₇	—	8	2	no	—
301	C₂²×C₇	—	8	2	no	—
302	C₂²×C₇	—	8	2	no	—
303	C₂²×C₇	—	16	4	no	—
304	C₂²×C₇	#464	1	2	yes	—
305	C₂²×C₇	C₂×#121	1	1	yes	characteristic
306	C₄×C₇	—	2	1	no	—
307	C₄×C₇	—	2	1	no	—
308	C₄×C₇	—	2	1	no	—
309	C₄×C₇	—	4	2	no	—
310	C₄×C₇	—	4	2	no	—
311	C₄×C₇	—	8	1	no	—
312	C₄×C₇	—	8	1	no	—
313	C₄×C₇	#464	1	2	yes	—
314	C₄×C₇	C₂×#135	1	1	yes	characteristic
315	C₄×C₇	C₂×#137	1	1	yes	characteristic
316	C₄×C₇	#576	1	1	yes	characteristic
317	C₄×C₇	#577	1	1	yes	characteristic
318	C₂⁴	—	4	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	8	1	no	—
332	C₂×D₄	—	8	1	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₇×#41	1	1	yes	characteristic
337	Q₁₆	—	8	2	no	—
338	SD₁₆	—	8	2	no	—
339	SD₁₆	—	8	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	2	no	—
348	C₂×C₈	—	8	1	no	—
349	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
350	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
368	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
369	C₄²	C₇×#41	1	1	yes	characteristic
370	C₄²	C₂⁴×C₇	1	1	yes	characteristic
371	C₂×C₇	—	2	2	no	—
372	C₂×C₇	—	16	2	no	—
373	C₂×C₇	C₂×#464	1	1	yes	characteristic
374	C₂×C₇	#3062	1	1	yes	characteristic
375	C₂×C₇	#3068	1	1	yes	characteristic
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	C₇×#121	1	1	yes	characteristic
381	Q₈	—	2	2	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	—	8	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	C₇×#121	1	1	yes	characteristic
403	C₂×C₄	C₇×#121	1	1	yes	characteristic
404	C₂×C₄	C₇×#121	1	1	yes	characteristic
405	C₂×C₄	C₇×#135	1	2	yes	—
406	C₂×C₄	C₇×#137	1	2	yes	—
407	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
409	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₇	#19242	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	16	4	no	—
424	C₂²	C₇×#464	1	2	yes	—
425	C₂²	C₂×C₇×#121	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₇×#464	1	2	yes	—
434	C₄	C₂×C₇×#135	1	1	yes	characteristic
435	C₄	C₂×C₇×#137	1	1	yes	characteristic
436	C₄	C₇×#576	1	1	yes	characteristic
437	C₄	C₇×#577	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₇×#464	1	1	yes	characteristic
441	C₂	C₇×#3062	1	1	yes	characteristic
442	C₂	C₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂²
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×#3249	C₂	semidirect
4. C₇×#2962	C₂	semidirect
5. C₇×#1702	C₂	semidirect
6. C₇×#1698	C₂	semidirect
7. C₇×#1682	C₂	semidirect
8. C₇×#1678	C₂	semidirect
9. C₇×#1565	C₂	semidirect
10. C₇×#1542	C₂	semidirect
21. C₇×#477	C₂²	semidirect
24. C₇×#462	C₂²	semidirect
29. C₇×#446	C₂²	semidirect
30. C₇×C₈×Q₈	C₂²	semidirect
39. C₇×#335	C₂²	semidirect
40. C₇×#334	C₂²	semidirect
41. C₇×#333	C₂²	semidirect
42. C₇×#333	C₂²	semidirect
43. C₇×#332	C₂²	semidirect
44. C₇×#332	C₂²	semidirect
47. #19242	C₇	direct (N × H)
103. #3249	C₂×C₇	semidirect
106. #2962	C₂×C₇	semidirect
107. #1702	C₂×C₇	semidirect
108. #1698	C₂×C₇	semidirect
109. #1682	C₂×C₇	semidirect
110. #1678	C₂×C₇	semidirect
111. #1565	C₂×C₇	semidirect
112. #1542	C₂×C₇	semidirect
176. #477	C₂²×C₇	semidirect
179. #462	C₂²×C₇	semidirect
184. #446	C₂²×C₇	semidirect
185. C₈×Q₈	C₂²×C₇	semidirect
194. #335	C₂²×C₇	semidirect
195. #334	C₂²×C₇	semidirect
196. #333	C₂²×C₇	semidirect
197. #333	C₂²×C₇	semidirect
198. #332	C₂²×C₇	semidirect
199. #332	C₂²×C₇	semidirect
417. C₇	#19242	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×#3249	2
C₇×#3208	2
C₇×#3138	2
C₇×#2962	2
C₇×#1702	2
C₇×#1698	2
C₇×#1682	2
C₇×#1678	2
C₇×#1565	2
C₇×#1542	2
C₂×C₇×#331	2
#19242	7

Subgroups — C7×#19242 #13196458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19242 #13196458