Subgroups — C₇×#17973 #13195189

Order 1792.

592 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3168	C₂	1	1	yes	maximal, characteristic
2	C₇×#2993	C₂	1	2	yes	maximal, complemented
3	C₇×#1592	C₂	1	2	yes	maximal, complemented
4	C₇×#1591	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₇×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1495	C₂	1	2	yes	maximal, complemented
11	C₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#529	C₂²	1	2	yes	—
13	C₇×#499	C₄	1	1	yes	characteristic
14	C₇×#495	C₄	1	1	yes	characteristic
15	C₇×#488	C₄	1	2	yes	—
16	C₇×#467	C₄	1	1	yes	characteristic
17	C₇×#466	C₄	1	1	yes	characteristic
18	C₇×#465	C₄	1	2	yes	—
19	C₇×#446	C₂²	1	2	yes	—
20	C₇×C₈×Q₈	C₂²	1	2	yes	—
21	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
23	C₄×C₇×D₈	C₂²	1	1	yes	characteristic
24	C₇×#436	—	2	2	no	—
25	C₇×#436	C₂²	1	2	yes	—
26	C₇×#435	—	2	2	no	—
27	C₇×C₈×D₄	C₂²	1	2	yes	—
28	C₇×#433	—	2	2	no	—
29	C₇×#431	C₂²	1	1	yes	characteristic
30	C₇×#431	C₂²	1	1	yes	characteristic
31	C₇×#424	—	2	2	no	—
32	C₇×#423	C₂²	1	2	yes	—
33	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
34	C₇×#335	C₂²	1	1	yes	characteristic
35	C₇×#335	C₂²	1	1	yes	characteristic
36	C₇×#335	C₂²	1	2	yes	—
37	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₇×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₇×D₄⋊C₈	C₂²	1	2	yes	—
40	C₇×D₄⋊C₈	C₂²	1	2	yes	—
41	C₇×#322	C₂²	1	1	yes	characteristic
42	C₇×#322	C₂²	1	1	yes	characteristic
43	C₇×C₈²	C₂²	1	1	yes	characteristic
44	C₇×C₈²	C₂²	1	1	yes	characteristic
45	#17973	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
47	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₇×M₁₆	—	2	2	no	—
50	C₂×C₇×M₁₆	—	2	2	no	—
51	C₂²×C₇×C₈	—	2	2	no	—
52	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
54	C₇×#126	—	2	2	no	—
55	C₇×#125	C₂×C₄	1	2	yes	—
56	C₇×#124	C₂×C₄	1	2	yes	—
57	C₇×#123	—	2	2	no	—
58	C₇×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
59	C₇×#121	C₂×C₄	1	2	yes	—
60	C₄×C₇×Q₈	C₂³	1	2	yes	—
61	C₄×C₇×D₄	—	2	2	no	—
62	C₄×C₇×D₄	C₂³	1	2	yes	—
63	C₇×#117	—	2	2	no	—
64	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
65	C₇×#107	C₂×C₄	1	1	yes	characteristic
66	C₇×#107	C₂×C₄	1	1	yes	characteristic
67	C₇×#106	C₂×C₄	1	2	yes	—
68	C₇×C₄⋊C₈	—	2	2	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	—	2	1	no	—
72	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
73	C₇×C₄⋊C₈	D₄	1	1	yes	characteristic
74	C₇×C₄⋊C₈	C₂³	1	2	yes	—
75	C₇×C₄⋊C₈	C₂³	1	2	yes	—
76	C₇×#103	C₂×C₄	1	2	yes	—
77	C₇×#103	C₂×C₄	1	2	yes	—
78	C₇×#102	C₂×C₄	1	2	yes	—
79	C₇×#102	C₂×C₄	1	2	yes	—
80	C₇×C₂²⋊C₈	—	2	1	no	—
81	C₇×C₂²⋊C₈	—	2	2	no	—
82	C₇×C₂²⋊C₈	—	2	2	no	—
83	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
84	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
85	C₇×#97	—	2	2	no	—
86	C₄×C₇×C₈	—	2	2	no	—
87	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
91	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
95	#3168	C₂×C₇	1	1	yes	characteristic
96	#2993	C₂×C₇	1	2	yes	complemented
97	#1592	C₂×C₇	1	2	yes	complemented
98	#1591	C₂×C₇	1	1	yes	characteristic, complemented
99	#1589	C₂×C₇	1	1	yes	characteristic, complemented
100	SD₁₆⋊C₈	C₂×C₇	1	2	yes	complemented
101	C₈×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
102	C₈×D₈	C₂×C₇	1	1	yes	characteristic, complemented
103	#1567	C₂×C₇	1	1	yes	characteristic, complemented
104	#1495	C₂×C₇	1	2	yes	complemented
105	#1450	C₂×C₇	1	1	yes	characteristic, complemented
106	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
107	C₂×C₇×D₄	—	2	2	no	—
108	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₇	—	2	2	no	—
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	#41	1	1	yes	characteristic
113	C₇×Q₁₆	—	2	2	no	—
114	C₇×SD₁₆	—	2	4	no	—
115	C₇×D₈	—	2	2	no	—
116	C₇×M₁₆	—	8	2	no	—
117	C₇×M₁₆	—	8	2	no	—
118	C₂×C₇×C₈	—	2	2	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	—	2	2	no	—
122	C₂×C₇×C₈	—	2	1	no	—
123	C₂×C₇×C₈	—	2	1	no	—
124	C₂×C₇×C₈	—	8	2	no	—
125	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
130	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
133	C₇×C₄⋊C₄	—	2	2	no	—
134	C₇×C₄⋊C₄	—	2	2	no	—
135	C₇×C₄⋊C₄	—	2	2	no	—
136	C₇×C₄⋊C₄	—	2	2	no	—
137	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
138	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
139	C₇×C₂²⋊C₄	—	2	2	no	—
140	C₇×C₂²⋊C₄	—	2	2	no	—
141	C₇×C₂²⋊C₄	—	2	2	no	—
142	C₇×C₂²⋊C₄	—	2	2	no	—
143	C₇×C₂²⋊C₄	—	2	2	no	—
144	C₄²×C₇	—	2	2	no	—
145	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₇	#41	1	1	yes	characteristic
148	C₄²×C₇	C₂⁴	1	1	yes	characteristic
149	#529	C₂²×C₇	1	2	yes	—
150	#499	C₄×C₇	1	1	yes	characteristic
151	#495	C₄×C₇	1	1	yes	characteristic
152	#488	C₄×C₇	1	2	yes	—
153	#467	C₄×C₇	1	1	yes	characteristic
154	#466	C₄×C₇	1	1	yes	characteristic
155	#465	C₄×C₇	1	2	yes	—
156	#446	C₂²×C₇	1	2	yes	—
157	C₈×Q₈	C₂²×C₇	1	2	yes	—
158	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
159	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
160	C₄×D₈	C₂²×C₇	1	1	yes	characteristic
161	#436	—	2	2	no	—
162	#436	C₂²×C₇	1	2	yes	—
163	#435	—	2	2	no	—
164	C₈×D₄	C₂²×C₇	1	2	yes	—
165	#433	—	2	2	no	—
166	#431	C₂²×C₇	1	1	yes	characteristic
167	#431	C₂²×C₇	1	1	yes	characteristic
168	#424	—	2	2	no	—
169	#423	C₂²×C₇	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
171	#335	C₂²×C₇	1	1	yes	characteristic
172	#335	C₂²×C₇	1	1	yes	characteristic
173	#335	C₂²×C₇	1	2	yes	—
174	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
175	Q₈⋊C₈	C₂²×C₇	1	2	yes	—
176	D₄⋊C₈	C₂²×C₇	1	2	yes	—
177	D₄⋊C₈	C₂²×C₇	1	2	yes	—
178	#322	C₂²×C₇	1	1	yes	characteristic
179	#322	C₂²×C₇	1	1	yes	characteristic
180	C₈²	C₂²×C₇	1	1	yes	characteristic
181	C₈²	C₂²×C₇	1	1	yes	characteristic
182	C₂³×C₇	—	2	2	no	—
183	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
184	C₇×Q₈	—	2	2	no	—
185	C₇×Q₈	—	2	2	no	—
186	C₇×D₄	—	2	2	no	—
187	C₇×D₄	—	2	2	no	—
188	C₇×D₄	—	8	2	no	—
189	C₂×C₄×C₇	—	2	1	no	—
190	C₂×C₄×C₇	—	2	1	no	—
191	C₂×C₄×C₇	—	2	1	no	—
192	C₂×C₄×C₇	—	2	1	no	—
193	C₂×C₄×C₇	—	2	2	no	—
194	C₂×C₄×C₇	—	2	2	no	—
195	C₂×C₄×C₇	—	2	2	no	—
196	C₂×C₄×C₇	—	4	1	no	—
197	C₂×C₄×C₇	—	4	2	no	—
198	C₂×C₄×C₇	—	4	2	no	—
199	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
205	C₇×C₈	—	2	1	no	—
206	C₇×C₈	—	2	1	no	—
207	C₇×C₈	—	2	1	no	—
208	C₇×C₈	—	2	1	no	—
209	C₇×C₈	—	2	1	no	—
210	C₇×C₈	—	2	1	no	—
211	C₇×C₈	—	4	1	no	—
212	C₇×C₈	—	4	1	no	—
213	C₇×C₈	—	4	2	no	—
214	C₇×C₈	—	4	2	no	—
215	C₇×C₈	#131	1	2	yes	—
216	C₇×C₈	#131	1	2	yes	—
217	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
218	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
219	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
224	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
225	#126	—	2	2	no	—
226	#125	C₂×C₄×C₇	1	2	yes	—
227	#124	C₂×C₄×C₇	1	2	yes	—
228	#123	—	2	2	no	—
229	C₂²⋊Q₈	C₂×C₄×C₇	1	2	yes	—
230	#121	C₂×C₄×C₇	1	2	yes	—
231	C₄×Q₈	C₂³×C₇	1	2	yes	—
232	C₄×D₄	—	2	2	no	—
233	C₄×D₄	C₂³×C₇	1	2	yes	—
234	#117	—	2	2	no	—
235	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
236	#107	C₂×C₄×C₇	1	1	yes	characteristic
237	#107	C₂×C₄×C₇	1	1	yes	characteristic
238	#106	C₂×C₄×C₇	1	2	yes	—
239	C₄⋊C₈	—	2	2	no	—
240	C₄⋊C₈	—	2	2	no	—
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
244	C₄⋊C₈	C₇×D₄	1	1	yes	characteristic
245	C₄⋊C₈	C₂³×C₇	1	2	yes	—
246	C₄⋊C₈	C₂³×C₇	1	2	yes	—
247	#103	C₂×C₄×C₇	1	2	yes	—
248	#103	C₂×C₄×C₇	1	2	yes	—
249	#102	C₂×C₄×C₇	1	2	yes	—
250	#102	C₂×C₄×C₇	1	2	yes	—
251	C₂²⋊C₈	—	2	1	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
255	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
256	#97	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
259	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₇	—	2	1	no	—
267	C₂²×C₇	—	2	1	no	—
268	C₂²×C₇	—	2	1	no	—
269	C₂²×C₇	—	4	2	no	—
270	C₂²×C₇	—	4	2	no	—
271	C₂²×C₇	—	4	2	no	—
272	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
273	C₄×C₇	—	2	1	no	—
274	C₄×C₇	—	2	1	no	—
275	C₄×C₇	—	2	1	no	—
276	C₄×C₇	—	2	1	no	—
277	C₄×C₇	—	4	2	no	—
278	C₄×C₇	—	4	2	no	—
279	C₄×C₇	—	4	2	no	—
280	C₄×C₇	C₂×#131	1	1	yes	characteristic
281	C₄×C₇	C₂×#131	1	1	yes	characteristic
282	C₄×C₇	#576	1	1	yes	characteristic
283	C₄×C₇	#578	1	1	yes	characteristic
284	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
290	C₂²×C₄	C₇×#41	1	1	yes	characteristic
291	Q₁₆	—	2	2	no	—
292	SD₁₆	—	2	4	no	—
293	D₈	—	2	2	no	—
294	M₁₆	—	8	2	no	—
295	M₁₆	—	8	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	8	2	no	—
303	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
304	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
305	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
306	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
307	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
308	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
309	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
310	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
316	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
324	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
325	C₄²	C₇×#41	1	1	yes	characteristic
326	C₄²	C₂⁴×C₇	1	1	yes	characteristic
327	C₂×C₇	—	4	1	no	—
328	C₂×C₇	—	8	2	no	—
329	C₂×C₇	#2931	1	1	yes	characteristic
330	C₂×C₇	#2951	1	1	yes	characteristic
331	C₂×C₇	#2957	1	1	yes	characteristic
332	C₂³	—	2	2	no	—
333	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	8	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
350	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
351	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
352	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
355	C₈	—	2	1	no	—
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₈	C₇×#131	1	2	yes	—
366	C₈	C₇×#131	1	2	yes	—
367	C₇	#17973	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	C₂×C₇×#131	1	1	yes	characteristic
383	C₄	C₂×C₇×#131	1	1	yes	characteristic
384	C₄	C₇×#576	1	1	yes	characteristic
385	C₄	C₇×#578	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	8	2	no	—
388	C₂	C₇×#2931	1	1	yes	characteristic
389	C₂	C₇×#2951	1	1	yes	characteristic
390	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₄²	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2993	C₂	semidirect
3. C₇×#1592	C₂	semidirect
4. C₇×#1591	C₂	semidirect
5. C₇×#1589	C₂	semidirect
6. C₇×SD₁₆⋊C₈	C₂	semidirect
7. C₇×C₈×Q₁₆	C₂	semidirect
8. C₇×C₈×D₈	C₂	semidirect
9. C₇×#1567	C₂	semidirect
10. C₇×#1495	C₂	semidirect
11. C₇×#1450	C₂	semidirect
45. #17973	C₇	direct (N × H)
96. #2993	C₂×C₇	semidirect
97. #1592	C₂×C₇	semidirect
98. #1591	C₂×C₇	semidirect
99. #1589	C₂×C₇	semidirect
100. SD₁₆⋊C₈	C₂×C₇	semidirect
101. C₈×Q₁₆	C₂×C₇	semidirect
102. C₈×D₈	C₂×C₇	semidirect
103. #1567	C₂×C₇	semidirect
104. #1495	C₂×C₇	semidirect
105. #1450	C₂×C₇	semidirect
367. C₇	#17973	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×#3168	2
C₇×#2993	2
C₇×#1592	2
C₇×#1591	2
C₇×#1589	2
C₇×SD₁₆⋊C₈	2
C₇×C₈×Q₁₆	2
C₇×C₈×D₈	2
C₇×#1567	2
C₇×#1495	2
C₇×#1450	2
#17973	7

Subgroups — C7×#17973 #13195189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#17973 #13195189