Subgroups — D₇×#879 #13058071

Order 1344.

492 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10621362	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#879	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
4	D₇×#217	C₂	1	1	yes	maximal, characteristic
5	D₇×#217	C₂	1	1	yes	maximal, characteristic
6	#10621093	C₂	1	1	yes	maximal, characteristic, complemented
7	#10621092	C₂	1	1	yes	maximal, characteristic, complemented
8	D₇×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	D₇×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	D₇×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Dic₃×D₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#10620928	C₂	1	1	yes	maximal, characteristic, complemented
13	#10620925	C₂	1	1	yes	maximal, characteristic, complemented
14	#10620924	C₂	1	1	yes	maximal, characteristic, complemented
15	#10620923	C₂	1	1	yes	maximal, characteristic, complemented
16	D₇×#126	—	3	1	no	maximal, Hall
17	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic
20	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
21	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
22	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
23	C₂×Dic₃×D₇	C₂²	1	1	yes	characteristic
24	C₃×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	#66636	C₂²	1	1	yes	characteristic
26	#66636	C₂²	1	1	yes	characteristic
27	C₄⋊Dic₂₁	C₂²	1	1	yes	characteristic, complemented
28	#66629	C₂²	1	1	yes	characteristic, complemented
29	#66629	C₂²	1	1	yes	characteristic, complemented
30	C₄×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
31	C₇×#217	C₂²	1	1	yes	characteristic
32	C₇×#217	C₂²	1	1	yes	characteristic
33	C₇×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
34	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
35	C₇×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₂²⋊Dic₇	C₂²	1	1	yes	characteristic
38	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×D₇)⋊C₄	C₂²	1	1	yes	characteristic
40	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
41	Dic₃⋊Dic₇	C₂²	1	1	yes	characteristic, complemented
42	#66577	C₂²	1	1	yes	characteristic, complemented
43	#66577	C₂²	1	1	yes	characteristic, complemented
44	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
45	Dic₇⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
46	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic
47	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic
48	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic
49	(C₂×D₇)⋊Dic₃	C₂²	1	1	yes	characteristic
50	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
51	Dic₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
52	C₇×#126	—	3	1	no	—
53	#6461	—	3	1	no	—
54	#6461	—	3	1	no	—
55	#6461	—	3	1	no	—
56	D₇×C₄⋊C₄	—	3	1	no	—
57	D₇×C₄⋊C₄	—	3	1	no	—
58	D₇×C₄⋊C₄	—	3	1	no	—
59	D₇×C₂²⋊C₄	—	3	1	no	—
60	D₇×C₂²⋊C₄	—	3	1	no	—
61	D₇×C₂²⋊C₄	D₃	1	1	yes	characteristic
62	#6442	—	3	1	no	—
63	#6442	—	3	1	no	—
64	#6442	—	3	1	no	—
65	#6439	—	3	1	no	—
66	C₄²×D₇	—	3	1	no	—
67	C₂×#879	—	7	1	no	maximal, Hall
68	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
69	C₂²×C₃×D₇	—	2	2	no	—
70	C₂²×C₃×D₇	—	2	2	no	—
71	C₂²×C₃×D₇	—	2	2	no	—
72	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
76	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
77	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
78	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
79	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
80	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
81	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
82	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
83	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
85	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
86	C₃×C₄×D₇	—	2	2	no	—
87	C₃×C₄×D₇	—	2	2	no	—
88	Dic₃×D₇	—	2	2	no	—
89	Dic₃×D₇	—	2	2	no	—
90	Dic₃×D₇	—	2	2	no	—
91	Dic₃×D₇	—	2	2	no	—
92	C₂³×D₇	C₂×D₃	1	1	yes	characteristic
93	C₂×C₄×D₇	—	3	1	no	—
94	C₂×C₄×D₇	—	3	1	no	—
95	C₂×C₄×D₇	—	3	1	no	—
96	C₂×C₄×D₇	—	3	1	no	—
97	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic
98	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic
99	C₇×C₄⋊C₄	—	3	1	no	—
100	C₇×C₄⋊C₄	—	3	1	no	—
101	C₇×C₄⋊C₄	—	3	1	no	—
102	C₇×C₂²⋊C₄	—	3	1	no	—
103	C₇×C₂²⋊C₄	—	3	1	no	—
104	C₇×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
105	C₄²×C₇	—	3	1	no	—
106	C₂²⋊Dic₇	—	3	1	no	—
107	C₂²⋊Dic₇	—	3	1	no	—
108	C₂²⋊Dic₇	C₂×D₃	1	1	yes	characteristic
109	(C₂×D₇)⋊C₄	—	3	1	no	—
110	(C₂×D₇)⋊C₄	—	3	1	no	—
111	(C₂×D₇)⋊C₄	—	3	1	no	—
112	(C₂×D₇)⋊C₄	—	3	1	no	—
113	(C₂×D₇)⋊C₄	C₂×D₃	1	1	yes	characteristic
114	(C₂×D₇)⋊C₄	C₂×D₃	1	1	yes	characteristic
115	C₄⋊Dic₇	—	3	1	no	—
116	C₄⋊Dic₇	—	3	1	no	—
117	C₄⋊Dic₇	—	3	1	no	—
118	Dic₇⋊C₄	—	3	1	no	—
119	Dic₇⋊C₄	—	3	1	no	—
120	Dic₇⋊C₄	—	3	1	no	—
121	Dic₇⋊C₄	—	3	1	no	—
122	Dic₇⋊C₄	—	3	1	no	—
123	Dic₇⋊C₄	—	3	1	no	—
124	C₄×Dic₇	—	3	1	no	—
125	C₄×Dic₇	—	3	1	no	—
126	C₄×Dic₇	—	3	1	no	—
127	C₂×C₃×C₂²⋊C₄	—	7	1	no	—
128	C₂×#217	—	7	1	no	—
129	C₂×#217	—	7	1	no	—
130	C₂×C₄⋊Dic₃	—	7	1	no	—
131	C₂×Dic₃⋊C₄	—	7	1	no	—
132	C₂×Dic₃⋊C₄	—	7	1	no	—
133	C₂×C₄×Dic₃	—	7	1	no	—
134	#879	—	7	1	no	—
135	#879	—	7	1	no	—
136	#879	—	7	1	no	—
137	#879	—	7	1	no	—
138	#879	—	7	1	no	—
139	#879	—	7	1	no	—
140	#879	—	7	1	no	—
141	#879	D₇	1	1	yes	characteristic, direct product factor
142	C₂²×C₃×C₇	—	2	1	no	—
143	C₂²×C₃×C₇	—	2	1	no	—
144	C₂²×C₃×C₇	—	2	1	no	—
145	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₃×D₇	—	2	1	no	—
147	C₂×C₃×D₇	—	2	1	no	—
148	C₂×C₃×D₇	—	2	1	no	—
149	C₂×C₃×D₇	—	4	4	no	—
150	C₂×C₃×D₇	#41	1	2	yes	—
151	C₂×C₃×D₇	#41	1	2	yes	—
152	C₂×C₃×D₇	#41	1	2	yes	—
153	C₃×C₄×C₇	—	2	1	no	—
154	C₃×C₄×C₇	—	2	1	no	—
155	Dic₂₁	—	2	1	no	—
156	Dic₂₁	—	2	1	no	—
157	Dic₂₁	—	2	1	no	—
158	Dic₂₁	—	2	1	no	—
159	C₃×Dic₇	—	2	1	no	—
160	C₃×Dic₇	—	2	1	no	—
161	C₇×Dic₃	—	2	1	no	—
162	C₇×Dic₃	—	2	1	no	—
163	C₇×Dic₃	—	2	1	no	—
164	C₇×Dic₃	—	2	1	no	—
165	C₂×#126	—	21	1	no	Sylow
166	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
167	C₂²×D₇	—	2	2	no	—
168	C₂²×D₇	—	2	2	no	—
169	C₂²×D₇	—	2	2	no	—
170	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
171	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
172	C₂×C₄×C₇	—	3	1	no	—
173	C₂×C₄×C₇	—	3	1	no	—
174	C₂×C₄×C₇	—	3	1	no	—
175	C₂×C₄×C₇	—	3	1	no	—
176	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
178	C₂×Dic₇	—	3	1	no	—
179	C₂×Dic₇	—	3	1	no	—
180	C₂×Dic₇	—	3	1	no	—
181	C₂×Dic₇	—	3	1	no	—
182	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
183	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
184	C₄×D₇	—	2	2	no	—
185	C₄×D₇	—	2	2	no	—
186	C₄×D₇	—	6	2	no	—
187	C₄×D₇	—	6	2	no	—
188	C₄×D₇	—	6	2	no	—
189	C₄×D₇	—	6	2	no	—
190	C₂⁴×C₃	—	7	1	no	—
191	C₂²×C₃×C₄	—	7	1	no	—
192	C₂²×C₃×C₄	—	7	1	no	—
193	C₂²×Dic₃	—	7	1	no	—
194	C₂²×Dic₃	—	7	1	no	—
195	C₂²×Dic₃	—	7	1	no	—
196	C₂²×Dic₃	—	7	1	no	—
197	C₃×C₂²⋊C₄	—	7	1	no	—
198	C₃×C₂²⋊C₄	—	7	1	no	—
199	C₃×C₂²⋊C₄	—	7	1	no	—
200	C₃×C₂²⋊C₄	C₂×D₇	1	1	yes	characteristic
201	#217	—	7	1	no	—
202	#217	—	7	1	no	—
203	#217	—	7	1	no	—
204	#217	—	7	1	no	—
205	#217	—	7	1	no	—
206	#217	—	7	1	no	—
207	#217	C₂×D₇	1	1	yes	characteristic
208	#217	C₂×D₇	1	1	yes	characteristic
209	C₄⋊Dic₃	—	7	1	no	—
210	C₄⋊Dic₃	—	7	1	no	—
211	C₄⋊Dic₃	—	7	1	no	—
212	C₄⋊Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
213	Dic₃⋊C₄	—	7	1	no	—
214	Dic₃⋊C₄	—	7	1	no	—
215	Dic₃⋊C₄	—	7	1	no	—
216	Dic₃⋊C₄	—	7	1	no	—
217	Dic₃⋊C₄	—	7	1	no	—
218	Dic₃⋊C₄	—	7	1	no	—
219	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
220	Dic₃⋊C₄	C₂×D₇	1	1	yes	characteristic, complemented
221	C₄×Dic₃	—	7	1	no	—
222	C₄×Dic₃	—	7	1	no	—
223	C₄×Dic₃	—	7	1	no	—
224	C₄×Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
225	C₂×C₃×C₇	—	4	1	no	—
226	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
227	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₃×C₇	C₂×#41	1	1	yes	characteristic
229	C₃×D₇	—	4	1	no	—
230	C₃×D₇	#126	1	4	yes	complemented
231	#126	—	3	1	no	—
232	#126	—	21	1	no	—
233	#126	—	21	1	no	—
234	#126	—	21	1	no	—
235	#126	—	21	1	no	—
236	#126	—	21	1	no	—
237	#126	—	21	1	no	—
238	#126	—	21	1	no	—
239	C₂×C₄⋊C₄	—	21	1	no	—
240	C₂×C₄⋊C₄	—	21	1	no	—
241	C₂×C₄⋊C₄	—	21	1	no	—
242	C₂×C₂²⋊C₄	—	7	1	no	—
243	C₂×C₂²⋊C₄	—	21	1	no	—
244	C₂×C₂²⋊C₄	—	21	1	no	—
245	C₂×C₄²	—	21	1	no	—
246	C₂²×C₇	—	2	1	no	—
247	C₂²×C₇	—	2	1	no	—
248	C₂²×C₇	—	2	1	no	—
249	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
250	C₂×D₇	—	2	1	no	—
251	C₂×D₇	—	2	1	no	—
252	C₂×D₇	—	2	1	no	—
253	C₂×D₇	—	4	4	no	—
254	C₂×D₇	#235	1	2	yes	—
255	C₂×D₇	#237	1	2	yes	—
256	C₂×D₇	#237	1	2	yes	—
257	C₄×C₇	—	2	1	no	—
258	C₄×C₇	—	2	1	no	—
259	C₄×C₇	—	6	1	no	—
260	C₄×C₇	—	6	1	no	—
261	C₄×C₇	—	6	1	no	—
262	C₄×C₇	—	6	1	no	—
263	Dic₇	—	2	1	no	—
264	Dic₇	—	2	1	no	—
265	Dic₇	—	6	1	no	—
266	Dic₇	—	6	1	no	—
267	Dic₇	—	6	1	no	—
268	Dic₇	—	6	1	no	—
269	C₂³×C₃	—	7	1	no	—
270	C₂³×C₃	—	7	1	no	—
271	C₂³×C₃	—	14	2	no	—
272	C₂³×C₃	—	14	2	no	—
273	C₂³×C₃	—	14	2	no	—
274	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
275	C₂×C₃×C₄	—	7	1	no	—
276	C₂×C₃×C₄	—	7	1	no	—
277	C₂×C₃×C₄	—	14	2	no	—
278	C₂×C₃×C₄	—	14	2	no	—
279	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
281	C₂×Dic₃	—	7	1	no	—
282	C₂×Dic₃	—	7	1	no	—
283	C₂×Dic₃	—	7	1	no	—
284	C₂×Dic₃	—	7	1	no	—
285	C₂×Dic₃	—	14	2	no	—
286	C₂×Dic₃	—	14	2	no	—
287	C₂×Dic₃	—	14	2	no	—
288	C₂×Dic₃	—	14	2	no	—
289	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
290	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
291	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
292	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
293	C₃×C₇	C₂×#126	1	1	yes	characteristic, complemented, Hall
294	C₂⁴	—	7	1	no	—
295	C₂²×C₄	—	7	1	no	—
296	C₂²×C₄	—	7	1	no	—
297	C₂²×C₄	—	21	1	no	—
298	C₂²×C₄	—	21	1	no	—
299	C₂²×C₄	—	21	1	no	—
300	C₂²×C₄	—	21	1	no	—
301	C₄⋊C₄	—	3	1	no	—
302	C₄⋊C₄	—	3	1	no	—
303	C₄⋊C₄	—	3	1	no	—
304	C₄⋊C₄	—	21	1	no	—
305	C₄⋊C₄	—	21	1	no	—
306	C₄⋊C₄	—	21	1	no	—
307	C₄⋊C₄	—	21	1	no	—
308	C₄⋊C₄	—	21	1	no	—
309	C₄⋊C₄	—	21	1	no	—
310	C₄⋊C₄	—	21	1	no	—
311	C₄⋊C₄	—	21	1	no	—
312	C₄⋊C₄	—	21	1	no	—
313	C₂²⋊C₄	—	3	1	no	—
314	C₂²⋊C₄	—	3	1	no	—
315	C₂²⋊C₄	—	7	1	no	—
316	C₂²⋊C₄	—	7	1	no	—
317	C₂²⋊C₄	—	7	1	no	—
318	C₂²⋊C₄	—	21	1	no	—
319	C₂²⋊C₄	—	21	1	no	—
320	C₂²⋊C₄	—	21	1	no	—
321	C₂²⋊C₄	—	21	1	no	—
322	C₂²⋊C₄	—	21	1	no	—
323	C₂²⋊C₄	—	21	1	no	—
324	C₂²⋊C₄	D₃×D₇	1	1	yes	characteristic
325	C₄²	—	3	1	no	—
326	C₄²	—	21	1	no	—
327	C₄²	—	21	1	no	—
328	C₄²	—	21	1	no	—
329	C₂×C₇	—	4	1	no	—
330	C₂×C₇	C₂×#235	1	1	yes	characteristic
331	C₂×C₇	C₂×#237	1	1	yes	characteristic
332	C₂×C₇	C₂×#237	1	1	yes	characteristic
333	D₇	—	4	1	no	—
334	D₇	#879	1	4	yes	direct product factor
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	2	1	no	—
337	C₂²×C₃	—	2	1	no	—
338	C₂²×C₃	—	7	2	no	—
339	C₂²×C₃	—	7	2	no	—
340	C₂²×C₃	—	7	2	no	—
341	C₂²×C₃	—	14	1	no	—
342	C₂²×C₃	—	14	1	no	—
343	C₂²×C₃	—	14	1	no	—
344	C₂²×C₃	—	28	4	no	—
345	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
346	C₃×C₄	—	2	1	no	—
347	C₃×C₄	—	2	1	no	—
348	C₃×C₄	—	14	1	no	—
349	C₃×C₄	—	14	1	no	—
350	Dic₃	—	2	1	no	—
351	Dic₃	—	2	1	no	—
352	Dic₃	—	2	1	no	—
353	Dic₃	—	2	1	no	—
354	Dic₃	—	14	1	no	—
355	Dic₃	—	14	1	no	—
356	Dic₃	—	14	1	no	—
357	Dic₃	—	14	1	no	—
358	C₂³	—	7	1	no	—
359	C₂³	—	7	1	no	—
360	C₂³	—	14	2	no	—
361	C₂³	—	14	2	no	—
362	C₂³	—	14	2	no	—
363	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
364	C₂×C₄	—	3	1	no	—
365	C₂×C₄	—	3	1	no	—
366	C₂×C₄	—	3	1	no	—
367	C₂×C₄	—	3	1	no	—
368	C₂×C₄	—	7	1	no	—
369	C₂×C₄	—	7	1	no	—
370	C₂×C₄	—	14	2	no	—
371	C₂×C₄	—	14	2	no	—
372	C₂×C₄	—	21	1	no	—
373	C₂×C₄	—	21	1	no	—
374	C₂×C₄	—	21	1	no	—
375	C₂×C₄	—	21	1	no	—
376	C₂×C₄	—	42	2	no	—
377	C₂×C₄	—	42	2	no	—
378	C₂×C₄	—	42	2	no	—
379	C₂×C₄	—	42	2	no	—
380	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
381	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
382	C₇	C₂×#879	1	1	yes	characteristic, complemented, Sylow
383	C₂×C₃	—	4	1	no	—
384	C₂×C₃	—	7	4	no	—
385	C₂×C₃	—	28	1	no	—
386	C₂×C₃	D₇×#41	1	1	yes	characteristic
387	C₂×C₃	D₇×#41	1	1	yes	characteristic
388	C₂×C₃	D₇×#41	1	1	yes	characteristic
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	7	2	no	—
393	C₂²	—	7	2	no	—
394	C₂²	—	7	2	no	—
395	C₂²	—	14	1	no	—
396	C₂²	—	14	1	no	—
397	C₂²	—	14	1	no	—
398	C₂²	—	28	4	no	—
399	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	6	1	no	—
403	C₄	—	6	1	no	—
404	C₄	—	6	1	no	—
405	C₄	—	6	1	no	—
406	C₄	—	14	1	no	—
407	C₄	—	14	1	no	—
408	C₄	—	42	1	no	—
409	C₄	—	42	1	no	—
410	C₄	—	42	1	no	—
411	C₄	—	42	1	no	—
412	C₃	D₇×#126	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	4	1	no	—
414	C₂	—	7	4	no	—
415	C₂	—	28	1	no	—
416	C₂	D₇×#235	1	1	yes	characteristic
417	C₂	D₇×#237	1	1	yes	characteristic
418	C₂	D₇×#237	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×D₇
commutator, socle, cosocle	C₂²×C₃×C₇	C₂⁴
Fitting	C₃×C₇×C₂²⋊C₄	C₂²
prime radical	C₂³×C₃×D₇	C₂²
hypercenter	C₂²⋊C₄	D₃×D₇
hypocenter	C₃×C₇	C₂×#126
LCS	G ▷ C₂²×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. #10621362	C₂	semidirect
2. C₇×#879	C₂	semidirect
6. #10621093	C₂	semidirect
7. #10621092	C₂	semidirect
8. D₇×C₄⋊Dic₃	C₂	semidirect
9. D₇×Dic₃⋊C₄	C₂	semidirect
10. D₇×Dic₃⋊C₄	C₂	semidirect
11. C₄×Dic₃×D₇	C₂	semidirect
12. #10620928	C₂	semidirect
13. #10620925	C₂	semidirect
14. #10620924	C₂	semidirect
15. #10620923	C₂	semidirect
27. C₄⋊Dic₂₁	C₂²	semidirect
28. #66629	C₂²	semidirect
29. #66629	C₂²	semidirect
30. C₄×Dic₂₁	C₂²	semidirect
33. C₇×C₄⋊Dic₃	C₂²	semidirect
34. C₇×Dic₃⋊C₄	C₂²	semidirect
35. C₇×Dic₃⋊C₄	C₂²	semidirect
36. C₄×C₇×Dic₃	C₂²	semidirect
40. Dic₃⋊Dic₇	C₂²	semidirect
41. Dic₃⋊Dic₇	C₂²	semidirect
42. #66577	C₂²	semidirect
43. #66577	C₂²	semidirect
44. Dic₇⋊Dic₃	C₂²	semidirect
45. Dic₇⋊Dic₃	C₂²	semidirect
50. Dic₃×Dic₇	C₂²	semidirect
51. Dic₃×Dic₇	C₂²	semidirect
141. #879	D₇	direct (N × H)
212. C₄⋊Dic₃	C₂×D₇	semidirect
219. Dic₃⋊C₄	C₂×D₇	semidirect
220. Dic₃⋊C₄	C₂×D₇	semidirect
224. C₄×Dic₃	C₂×D₇	semidirect
230. C₃×D₇	#126	semidirect
293. C₃×C₇	C₂×#126	semidirect
334. D₇	#879	direct (N × H)
382. C₇	C₂×#879	semidirect
412. C₃	D₇×#126	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10621362	2
C₇×#879	2
C₃×D₇×C₂²⋊C₄	2
D₇×#217	2
#10621093	2
#10621092	2
D₇×C₄⋊Dic₃	2
D₇×Dic₃⋊C₄	2
C₄×Dic₃×D₇	2
#10620928	2
#10620925	2
#10620924	2
#10620923	2
D₇×#126	3
C₂×#879	7

Subgroups — D7×#879 #13058071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#879 #13058071