Subgroups — C₇×#23199 #13200415

Order 1792.

914 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#495	C₂	1	1	yes	maximal, characteristic
2	C₇×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2949	C₂	1	2	yes	maximal, complemented
4	C₇×#2948	C₂	1	1	yes	maximal, characteristic
5	C₇×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1978	C₂	1	1	yes	maximal, characteristic
7	C₇×#1977	C₂	1	2	yes	maximal, complemented
8	C₇×#1888	C₂	1	2	yes	maximal, complemented
9	C₇×#1885	C₂	1	2	yes	maximal, complemented
10	C₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₇×#124	C₂²	1	2	yes	—
16	C₇×#519	C₂²	1	2	yes	—
17	C₇×#518	C₂²	1	2	yes	—
18	C₇×#495	C₄	1	8	yes	complemented
19	C₇×#442	—	2	2	no	—
20	C₇×#441	—	2	2	no	—
21	C₇×#440	—	2	4	no	—
22	C₄×C₇×Q₁₆	—	2	2	no	—
23	C₄×C₇×SD₁₆	—	2	4	no	—
24	C₄×C₇×D₈	—	2	2	no	—
25	C₂×C₇×#108	C₂²	1	1	yes	characteristic
26	C₂×C₇×#108	C₂²	1	1	yes	characteristic
27	C₇×#427	C₂²	1	1	yes	characteristic
28	C₇×#427	C₂²	1	1	yes	characteristic
29	C₇×#419	C₂²	1	2	yes	—
30	C₇×#419	C₂²	1	2	yes	—
31	C₇×#418	C₂²	1	2	yes	—
32	C₇×#418	C₂²	1	2	yes	—
33	C₂×C₇×#101	C₂²	1	2	yes	—
34	C₂×C₇×#100	C₂²	1	2	yes	—
35	C₇×#405	C₂²	1	2	yes	—
36	C₇×#405	C₂²	1	1	yes	characteristic
37	C₇×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₇×#339	C₂²	1	1	yes	characteristic
40	C₇×#339	C₂²	1	2	yes	—
41	C₇×#339	C₂²	1	1	yes	characteristic
42	#23199	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₇×Q₈	C₂³	1	2	yes	—
44	C₂²×C₇×D₄	C₂³	1	2	yes	—
45	C₂×C₇×Q₁₆	—	2	1	no	—
46	C₂×C₇×Q₁₆	—	2	1	no	—
47	C₂×C₇×Q₁₆	—	2	2	no	—
48	C₂×C₇×Q₁₆	C₂×C₄	1	4	yes	complemented
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₂×C₇×SD₁₆	—	2	4	no	—
52	C₂×C₇×SD₁₆	C₂×C₄	1	8	yes	complemented
53	C₂×C₇×D₈	—	2	1	no	—
54	C₂×C₇×D₈	—	2	1	no	—
55	C₂×C₇×D₈	—	2	2	no	—
56	C₂×C₇×D₈	C₂×C₄	1	4	yes	—
57	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
58	C₂×C₇×M₁₆	C₂³	1	2	yes	—
59	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
60	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₇×#124	—	4	2	no	—
63	C₇×#124	C₂×C₄	1	8	yes	complemented
64	C₄×C₇×Q₈	—	2	4	no	—
65	C₄×C₇×Q₈	—	2	4	no	—
66	C₄×C₇×D₄	—	2	4	no	—
67	C₄×C₇×D₄	—	2	4	no	—
68	C₇×#117	—	4	2	no	—
69	C₇×#117	C₂³	1	1	yes	characteristic
70	C₇×#117	C₂³	1	2	yes	—
71	C₇×#117	C₂³	1	1	yes	characteristic
72	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
73	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#108	—	2	2	no	—
76	C₇×#108	—	2	2	no	—
77	C₇×#107	D₄	1	2	yes	—
78	C₇×#107	D₄	1	2	yes	—
79	C₇×#106	D₄	1	2	yes	—
80	C₇×#106	D₄	1	2	yes	—
81	C₇×#103	—	2	4	no	—
82	C₇×#103	—	2	4	no	—
83	C₇×#102	—	2	4	no	—
84	C₇×#102	—	2	4	no	—
85	C₇×#101	—	4	2	no	—
86	C₇×#100	—	4	2	no	—
87	C₇×#97	—	2	2	no	—
88	C₇×#97	—	2	1	no	—
89	C₇×#97	—	2	1	no	—
90	C₄×C₇×C₈	—	2	1	no	—
91	C₄×C₇×C₈	—	2	2	no	—
92	C₄×C₇×C₈	—	2	1	no	—
93	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
94	C₂×#495	C₂×C₇	1	1	yes	characteristic
95	#2950	C₂×C₇	1	1	yes	characteristic, complemented
96	#2949	C₂×C₇	1	2	yes	complemented
97	#2948	C₂×C₇	1	1	yes	characteristic
98	#1979	C₂×C₇	1	1	yes	characteristic, complemented
99	#1978	C₂×C₇	1	1	yes	characteristic
100	#1977	C₂×C₇	1	2	yes	complemented
101	#1888	C₂×C₇	1	2	yes	complemented
102	#1885	C₂×C₇	1	2	yes	complemented
103	#1772	C₂×C₇	1	1	yes	characteristic, complemented
104	#1772	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂⁴×C₇	—	2	2	no	—
106	C₂×C₇×Q₈	—	2	2	no	—
107	C₂×C₇×Q₈	—	2	2	no	—
108	C₂×C₇×Q₈	—	2	2	no	—
109	C₂×C₇×Q₈	—	2	2	no	—
110	C₂×C₇×Q₈	—	2	2	no	—
111	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	2	2	no	—
114	C₂×C₇×D₄	—	2	2	no	—
115	C₂×C₇×D₄	—	2	2	no	—
116	C₂×C₇×D₄	—	2	2	no	—
117	C₂×C₇×D₄	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₇	—	2	1	no	—
119	C₂²×C₄×C₇	—	2	2	no	—
120	C₂²×C₄×C₇	—	4	4	no	—
121	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
122	C₇×Q₁₆	—	2	4	no	—
123	C₇×Q₁₆	—	2	4	no	—
124	C₇×SD₁₆	—	2	8	no	—
125	C₇×SD₁₆	—	2	8	no	—
126	C₇×D₈	—	2	4	no	—
127	C₇×D₈	—	2	4	no	—
128	C₇×M₁₆	—	2	1	no	—
129	C₇×M₁₆	—	2	2	no	—
130	C₇×M₁₆	—	2	1	no	—
131	C₇×M₁₆	—	2	1	no	—
132	C₇×M₁₆	—	2	2	no	—
133	C₇×M₁₆	—	2	1	no	—
134	C₂×C₇×C₈	—	2	1	no	—
135	C₂×C₇×C₈	—	2	2	no	—
136	C₂×C₇×C₈	—	2	1	no	—
137	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
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	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇×C₈	#41	1	2	yes	—
144	C₂×C₇×C₈	#41	1	2	yes	—
145	C₇×C₄⋊C₄	—	4	4	no	—
146	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
147	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
148	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₇×C₂²⋊C₄	—	2	1	no	—
150	C₇×C₂²⋊C₄	—	2	2	no	—
151	C₇×C₂²⋊C₄	—	2	1	no	—
152	C₇×C₂²⋊C₄	—	4	8	no	—
153	C₇×C₂²⋊C₄	—	4	4	no	—
154	C₄²×C₇	—	2	1	no	—
155	C₄²×C₇	—	2	2	no	—
156	C₄²×C₇	—	2	1	no	—
157	C₄²×C₇	—	2	1	no	—
158	C₄²×C₇	—	4	4	no	—
159	C₄²×C₇	C₂²×C₄	1	2	yes	—
160	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
161	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
162	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×#124	C₂²×C₇	1	2	yes	—
164	#519	C₂²×C₇	1	2	yes	—
165	#518	C₂²×C₇	1	2	yes	—
166	#495	C₄×C₇	1	8	yes	complemented
167	#442	—	2	2	no	—
168	#441	—	2	2	no	—
169	#440	—	2	4	no	—
170	C₄×Q₁₆	—	2	2	no	—
171	C₄×SD₁₆	—	2	4	no	—
172	C₄×D₈	—	2	2	no	—
173	C₂×#108	C₂²×C₇	1	1	yes	characteristic
174	C₂×#108	C₂²×C₇	1	1	yes	characteristic
175	#427	C₂²×C₇	1	1	yes	characteristic
176	#427	C₂²×C₇	1	1	yes	characteristic
177	#419	C₂²×C₇	1	2	yes	—
178	#419	C₂²×C₇	1	2	yes	—
179	#418	C₂²×C₇	1	2	yes	—
180	#418	C₂²×C₇	1	2	yes	—
181	C₂×#101	C₂²×C₇	1	2	yes	—
182	C₂×#100	C₂²×C₇	1	2	yes	—
183	#405	C₂²×C₇	1	1	yes	characteristic
184	#405	C₂²×C₇	1	2	yes	—
185	#405	C₂²×C₇	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
187	#339	C₂²×C₇	1	1	yes	characteristic
188	#339	C₂²×C₇	1	2	yes	—
189	#339	C₂²×C₇	1	1	yes	characteristic
190	C₂³×C₇	—	2	4	no	—
191	C₂³×C₇	—	4	2	no	—
192	C₂³×C₇	—	4	2	no	—
193	C₂³×C₇	—	8	4	no	—
194	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₇×Q₈	—	2	4	no	—
196	C₇×Q₈	—	2	4	no	—
197	C₇×Q₈	—	4	2	no	—
198	C₇×Q₈	—	4	2	no	—
199	C₇×D₄	—	2	4	no	—
200	C₇×D₄	—	2	4	no	—
201	C₇×D₄	—	4	2	no	—
202	C₇×D₄	—	4	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	4	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	4	no	—
207	C₂×C₄×C₇	—	2	2	no	—
208	C₂×C₄×C₇	—	4	2	no	—
209	C₂×C₄×C₇	—	4	2	no	—
210	C₂×C₄×C₇	—	4	2	no	—
211	C₂×C₄×C₇	—	16	4	no	—
212	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
218	C₇×C₈	—	4	1	no	—
219	C₇×C₈	—	4	2	no	—
220	C₇×C₈	—	4	1	no	—
221	C₇×C₈	C₄×D₄	1	2	yes	—
222	C₇×C₈	C₄×D₄	1	2	yes	—
223	C₇×C₈	C₄×D₄	1	2	yes	—
224	C₇×C₈	C₄×D₄	1	2	yes	—
225	C₂²×Q₈	C₂³×C₇	1	2	yes	—
226	C₂²×D₄	C₂³×C₇	1	2	yes	—
227	C₂×Q₁₆	—	2	1	no	—
228	C₂×Q₁₆	—	2	1	no	—
229	C₂×Q₁₆	—	2	2	no	—
230	C₂×Q₁₆	C₂×C₄×C₇	1	4	yes	complemented
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	2	4	no	—
234	C₂×SD₁₆	C₂×C₄×C₇	1	8	yes	complemented
235	C₂×D₈	—	2	1	no	—
236	C₂×D₈	—	2	1	no	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	C₂×C₄×C₇	1	4	yes	—
239	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
240	C₂×M₁₆	C₂³×C₇	1	2	yes	—
241	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	#124	—	4	2	no	—
245	#124	C₂×C₄×C₇	1	8	yes	complemented
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	—	2	4	no	—
250	#117	—	4	2	no	—
251	#117	C₂³×C₇	1	1	yes	characteristic
252	#117	C₂³×C₇	1	2	yes	—
253	#117	C₂³×C₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	—	4	2	no	—
255	C₂×C₂²⋊C₄	—	4	2	no	—
256	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
257	#108	—	2	2	no	—
258	#108	—	2	2	no	—
259	#107	C₇×D₄	1	2	yes	—
260	#107	C₇×D₄	1	2	yes	—
261	#106	C₇×D₄	1	2	yes	—
262	#106	C₇×D₄	1	2	yes	—
263	#103	—	2	4	no	—
264	#103	—	2	4	no	—
265	#102	—	2	4	no	—
266	#102	—	2	4	no	—
267	#101	—	4	2	no	—
268	#100	—	4	2	no	—
269	#97	—	2	2	no	—
270	#97	—	2	1	no	—
271	#97	—	2	1	no	—
272	C₄×C₈	—	2	1	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
276	C₂²×C₇	—	2	2	no	—
277	C₂²×C₇	—	4	4	no	—
278	C₂²×C₇	—	8	4	no	—
279	C₂²×C₇	—	8	4	no	—
280	C₂²×C₇	—	16	2	no	—
281	C₂²×C₇	#518	1	1	yes	characteristic
282	C₂²×C₇	D₄²	1	1	yes	characteristic
283	C₂²×C₇	#559	1	1	yes	characteristic
284	C₄×C₇	—	4	2	no	—
285	C₄×C₇	—	4	4	no	—
286	C₄×C₇	—	4	2	no	—
287	C₄×C₇	—	4	4	no	—
288	C₄×C₇	—	4	2	no	—
289	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₇	#550	1	1	yes	characteristic
292	C₄×C₇	#550	1	1	yes	characteristic
293	C₂⁴	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	C₂²×C₄×C₇	1	4	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
310	Q₁₆	—	2	4	no	—
311	Q₁₆	—	2	4	no	—
312	SD₁₆	—	2	8	no	—
313	SD₁₆	—	2	8	no	—
314	D₈	—	2	4	no	—
315	D₈	—	2	4	no	—
316	M₁₆	—	2	1	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	1	no	—
319	M₁₆	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
326	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
327	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
328	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
329	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
331	C₂×C₈	C₇×#41	1	2	yes	—
332	C₂×C₈	C₇×#41	1	2	yes	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
335	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
336	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
337	C₂²⋊C₄	—	2	1	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	4	8	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	4	no	—
347	C₄²	C₂²×C₄×C₇	1	2	yes	—
348	C₂×C₇	—	2	1	no	—
349	C₂×C₇	—	2	1	no	—
350	C₂×C₇	—	8	4	no	—
351	C₂×C₇	#2366	1	1	yes	characteristic
352	C₂×C₇	#3290	1	2	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	8	4	no	—
357	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
358	Q₈	—	2	4	no	—
359	Q₈	—	2	4	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	16	4	no	—
375	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
378	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
379	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
380	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	C₄×C₇×D₄	1	2	yes	—
385	C₈	C₄×C₇×D₄	1	2	yes	—
386	C₈	C₄×C₇×D₄	1	2	yes	—
387	C₈	C₄×C₇×D₄	1	2	yes	—
388	C₇	#23199	1	1	yes	characteristic, direct product factor, Sylow
389	C₂²	—	2	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	16	2	no	—
394	C₂²	C₇×#518	1	1	yes	characteristic
395	C₂²	C₇×D₄²	1	1	yes	characteristic
396	C₂²	C₇×#559	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	4	no	—
402	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
403	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
404	C₄	C₇×#550	1	1	yes	characteristic
405	C₄	C₇×#550	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	8	4	no	—
409	C₂	C₇×#2366	1	1	yes	characteristic
410	C₂	C₇×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#2950	C₂	semidirect
3. C₇×#2949	C₂	semidirect
5. C₇×#1979	C₂	semidirect
7. C₇×#1977	C₂	semidirect
8. C₇×#1888	C₂	semidirect
9. C₇×#1885	C₂	semidirect
10. C₇×#1772	C₂	semidirect
11. C₇×#1772	C₂	semidirect
18. C₇×#495	C₄	semidirect
42. #23199	C₇	direct (N × H)
48. C₂×C₇×Q₁₆	C₂×C₄	semidirect
52. C₂×C₇×SD₁₆	C₂×C₄	semidirect
63. C₇×#124	C₂×C₄	semidirect
93. C₄×C₇×C₈	C₂×C₄	semidirect
95. #2950	C₂×C₇	semidirect
96. #2949	C₂×C₇	semidirect
98. #1979	C₂×C₇	semidirect
100. #1977	C₂×C₇	semidirect
101. #1888	C₂×C₇	semidirect
102. #1885	C₂×C₇	semidirect
103. #1772	C₂×C₇	semidirect
104. #1772	C₂×C₇	semidirect
166. #495	C₄×C₇	semidirect
230. C₂×Q₁₆	C₂×C₄×C₇	semidirect
234. C₂×SD₁₆	C₂×C₄×C₇	semidirect
245. #124	C₂×C₄×C₇	semidirect
275. C₄×C₈	C₂×C₄×C₇	semidirect
388. C₇	#23199	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#495	2
C₇×#2950	2
C₇×#2949	2
C₇×#2948	2
C₇×#1979	2
C₇×#1978	2
C₇×#1977	2
C₇×#1888	2
C₇×#1885	2
C₇×#1772	2
#23199	7

Subgroups — C7×#23199 #13200415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#23199 #13200415