Subgroups — C₇×#19202 #13196418

Order 1792.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3208	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic
4	C₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#1686	C₂	1	4	yes	maximal, complemented
6	C₇×#1666	C₂	1	4	yes	maximal, complemented
7	C₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1545	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₇×SD₁₆	—	2	1	no	—
11	C₂²×C₇×SD₁₆	—	2	1	no	—
12	C₇×#533	C₂²	1	1	yes	characteristic
13	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#127	C₂²	1	1	yes	characteristic
15	C₇×#498	—	2	1	no	—
16	C₇×#492	—	2	1	no	—
17	C₇×#492	—	2	1	no	—
18	C₇×#492	—	2	1	no	—
19	C₇×#492	C₂²	1	2	yes	—
20	C₇×#492	C₂²	1	2	yes	—
21	C₇×#487	—	2	1	no	—
22	C₇×#486	—	2	1	no	—
23	C₇×#483	—	2	2	no	—
24	C₇×#475	C₂²	1	4	yes	complemented
25	C₇×#460	C₂²	1	4	yes	—
26	C₇×#450	—	2	2	no	—
27	C₇×#446	—	2	1	no	—
28	C₇×#446	C₂²	1	2	yes	complemented
29	C₇×C₈×Q₈	—	2	1	no	—
30	C₇×C₈×Q₈	C₂²	1	2	yes	complemented
31	C₇×#431	C₂²	1	1	yes	characteristic
32	C₇×#431	C₂²	1	1	yes	characteristic
33	C₇×#424	—	2	1	no	—
34	C₇×#423	C₂²	1	1	yes	characteristic
35	C₇×#405	—	2	1	no	—
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₇×#335	C₂²	1	2	yes	complemented
38	C₇×#334	C₂²	1	2	yes	complemented
39	C₇×#332	C₂²	1	4	yes	complemented
40	C₇×#331	C₂²	1	4	yes	—
41	#19202	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₇×Q₈	—	2	1	no	—
43	C₂²×C₇×D₄	—	2	1	no	—
44	C₂²×C₇×D₄	—	2	1	no	—
45	C₂²×C₇×D₄	—	2	1	no	—
46	C₂×C₇×SD₁₆	—	2	4	no	—
47	C₂×C₇×SD₁₆	—	2	2	no	—
48	C₂×C₇×SD₁₆	—	2	2	no	—
49	C₂×C₇×SD₁₆	—	2	2	no	—
50	C₂×C₇×SD₁₆	—	2	2	no	—
51	C₂×C₇×SD₁₆	—	4	4	no	—
52	C₂×C₇×SD₁₆	—	4	4	no	—
53	C₂×C₇×M₁₆	—	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	—	2	1	no	—
57	C₇×C₄⋊Q₈	—	2	1	no	—
58	C₇×C₄⋊Q₈	—	2	1	no	—
59	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
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×C₂²⋊Q₈	—	2	1	no	—
68	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₄×C₇×Q₈	—	2	1	no	—
70	C₄×C₇×Q₈	C₂³	1	2	yes	—
71	C₇×#117	—	2	1	no	—
72	C₂×C₇×C₄⋊C₄	—	2	1	no	—
73	C₂×C₇×C₄⋊C₄	—	2	1	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#106	—	2	4	no	—
76	C₇×C₄⋊C₈	—	2	2	no	—
77	C₇×C₄⋊C₈	—	2	2	no	—
78	C₇×C₄⋊C₈	—	2	1	no	—
79	C₇×C₄⋊C₈	C₂³	1	2	yes	—
80	C₇×C₄⋊C₈	C₂³	1	2	yes	—
81	C₇×C₄⋊C₈	C₂³	1	2	yes	—
82	C₇×#103	—	2	4	no	—
83	C₇×#102	—	2	4	no	—
84	C₇×C₂²⋊C₈	—	2	1	no	—
85	C₇×C₂²⋊C₈	—	2	1	no	—
86	C₇×#97	—	2	2	no	—
87	C₄×C₇×C₈	—	2	2	no	—
88	C₄×C₇×C₈	—	2	1	no	—
89	C₄×C₇×C₈	—	2	1	no	—
90	C₄×C₇×C₈	D₄	1	1	yes	characteristic
91	C₄×C₇×C₈	D₄	1	1	yes	characteristic
92	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
94	#3229	C₂×C₇	1	1	yes	characteristic, complemented
95	#3208	C₂×C₇	1	1	yes	characteristic
96	C₂×#492	C₂×C₇	1	1	yes	characteristic
97	#2960	C₂×C₇	1	1	yes	characteristic, complemented
98	#1686	C₂×C₇	1	4	yes	complemented
99	#1666	C₂×C₇	1	4	yes	complemented
100	#1564	C₂×C₇	1	1	yes	characteristic, complemented
101	#1546	C₂×C₇	1	1	yes	characteristic, complemented
102	#1545	C₂×C₇	1	1	yes	characteristic
103	C₂⁴×C₇	—	4	1	no	—
104	C₂×C₇×Q₈	—	2	1	no	—
105	C₂×C₇×Q₈	—	2	2	no	—
106	C₂×C₇×Q₈	—	4	1	no	—
107	C₂×C₇×Q₈	—	4	2	no	—
108	C₂×C₇×Q₈	—	4	2	no	—
109	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	2	2	no	—
113	C₂×C₇×D₄	—	4	1	no	—
114	C₂×C₇×D₄	—	4	1	no	—
115	C₂×C₇×D₄	—	4	1	no	—
116	C₂×C₇×D₄	—	4	2	no	—
117	C₂×C₇×D₄	—	4	2	no	—
118	C₂×C₇×D₄	—	8	2	no	—
119	C₂×C₇×D₄	—	8	2	no	—
120	C₂²×C₄×C₇	—	4	1	no	—
121	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇	#41	1	1	yes	characteristic
124	C₇×SD₁₆	—	4	4	no	—
125	C₇×SD₁₆	—	4	4	no	—
126	C₇×SD₁₆	—	4	4	no	—
127	C₇×SD₁₆	—	4	4	no	—
128	C₇×SD₁₆	—	8	4	no	—
129	C₇×M₁₆	—	4	2	no	—
130	C₂×C₇×C₈	—	2	2	no	—
131	C₂×C₇×C₈	—	2	2	no	—
132	C₂×C₇×C₈	—	2	2	no	—
133	C₂×C₇×C₈	—	2	2	no	—
134	C₂×C₇×C₈	SD₁₆	1	4	yes	complemented
135	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
139	C₇×C₄⋊C₄	—	2	1	no	—
140	C₇×C₄⋊C₄	—	2	1	no	—
141	C₇×C₄⋊C₄	—	2	1	no	—
142	C₇×C₄⋊C₄	—	2	2	no	—
143	C₇×C₄⋊C₄	—	2	2	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	—	2	2	no	—
146	C₇×C₄⋊C₄	—	4	1	no	—
147	C₇×C₄⋊C₄	—	4	1	no	—
148	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₇×C₂²⋊C₄	—	2	2	no	—
150	C₄²×C₇	—	2	2	no	—
151	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₇	#41	1	1	yes	characteristic
154	C₄²×C₇	C₂⁴	1	1	yes	characteristic
155	C₂²×SD₁₆	—	2	1	no	—
156	C₂²×SD₁₆	—	2	1	no	—
157	#533	C₂²×C₇	1	1	yes	characteristic
158	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
159	C₂×#127	C₂²×C₇	1	1	yes	characteristic
160	#498	—	2	1	no	—
161	#492	—	2	1	no	—
162	#492	—	2	1	no	—
163	#492	—	2	1	no	—
164	#492	C₂²×C₇	1	2	yes	—
165	#492	C₂²×C₇	1	2	yes	—
166	#487	—	2	1	no	—
167	#486	—	2	1	no	—
168	#483	—	2	2	no	—
169	#475	C₂²×C₇	1	4	yes	complemented
170	#460	C₂²×C₇	1	4	yes	—
171	#450	—	2	2	no	—
172	#446	—	2	1	no	—
173	#446	C₂²×C₇	1	2	yes	complemented
174	C₈×Q₈	—	2	1	no	—
175	C₈×Q₈	C₂²×C₇	1	2	yes	complemented
176	#431	C₂²×C₇	1	1	yes	characteristic
177	#431	C₂²×C₇	1	1	yes	characteristic
178	#424	—	2	1	no	—
179	#423	C₂²×C₇	1	1	yes	characteristic
180	#405	—	2	1	no	—
181	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
182	#335	C₂²×C₇	1	2	yes	complemented
183	#334	C₂²×C₇	1	2	yes	complemented
184	#332	C₂²×C₇	1	4	yes	complemented
185	#331	C₂²×C₇	1	4	yes	—
186	C₂³×C₇	—	4	2	no	—
187	C₂³×C₇	—	8	2	no	—
188	C₂³×C₇	—	8	2	no	—
189	C₂³×C₇	—	8	2	no	—
190	C₂³×C₇	#121	1	1	yes	characteristic
191	C₇×Q₈	—	2	4	no	—
192	C₇×Q₈	—	4	2	no	—
193	C₇×Q₈	—	4	2	no	—
194	C₇×Q₈	—	4	2	no	—
195	C₇×Q₈	—	8	2	no	—
196	C₇×D₄	—	4	2	no	—
197	C₇×D₄	—	4	2	no	—
198	C₇×D₄	—	4	4	no	—
199	C₇×D₄	—	8	2	no	—
200	C₇×D₄	—	8	2	no	—
201	C₇×D₄	—	8	2	no	—
202	C₇×D₄	—	8	2	no	—
203	C₂×C₄×C₇	—	2	2	no	—
204	C₂×C₄×C₇	—	2	2	no	—
205	C₂×C₄×C₇	—	2	2	no	—
206	C₂×C₄×C₇	—	2	2	no	—
207	C₂×C₄×C₇	—	4	2	no	—
208	C₂×C₄×C₇	—	8	2	no	—
209	C₂×C₄×C₇	#121	1	1	yes	characteristic
210	C₂×C₄×C₇	#121	1	1	yes	characteristic
211	C₂×C₄×C₇	#121	1	1	yes	characteristic
212	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
213	C₂×C₄×C₇	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
217	C₇×C₈	—	2	1	no	—
218	C₇×C₈	—	2	1	no	—
219	C₇×C₈	—	4	2	no	—
220	C₇×C₈	—	4	2	no	—
221	C₇×C₈	—	4	2	no	—
222	C₇×C₈	C₂×SD₁₆	1	2	yes	—
223	C₇×C₈	C₂×SD₁₆	1	2	yes	—
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂×SD₁₆	—	2	4	no	—
229	C₂×SD₁₆	—	2	2	no	—
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×SD₁₆	—	2	2	no	—
232	C₂×SD₁₆	—	2	2	no	—
233	C₂×SD₁₆	—	4	4	no	—
234	C₂×SD₁₆	—	4	4	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
237	C₂²×C₈	C₇×D₄	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
242	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
243	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	C₂³×C₇	1	2	yes	—
248	#125	—	2	1	no	—
249	C₂²⋊Q₈	—	2	1	no	—
250	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂³×C₇	1	2	yes	—
253	#117	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
257	#106	—	2	4	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	C₂³×C₇	1	2	yes	—
262	C₄⋊C₈	C₂³×C₇	1	2	yes	—
263	C₄⋊C₈	C₂³×C₇	1	2	yes	—
264	#103	—	2	4	no	—
265	#102	—	2	4	no	—
266	C₂²⋊C₈	—	2	1	no	—
267	C₂²⋊C₈	—	2	1	no	—
268	#97	—	2	2	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	—	2	1	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	C₇×D₄	1	1	yes	characteristic
273	C₄×C₈	C₇×D₄	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
276	C₂²×C₇	—	2	1	no	—
277	C₂²×C₇	—	2	1	no	—
278	C₂²×C₇	—	8	2	no	—
279	C₂²×C₇	—	8	2	no	—
280	C₂²×C₇	—	8	2	no	—
281	C₂²×C₇	—	16	4	no	—
282	C₂²×C₇	#460	1	2	yes	—
283	C₂²×C₇	C₂×#121	1	1	yes	characteristic
284	C₄×C₇	—	2	1	no	—
285	C₄×C₇	—	2	1	no	—
286	C₄×C₇	—	4	2	no	—
287	C₄×C₇	—	4	2	no	—
288	C₄×C₇	—	8	2	no	—
289	C₄×C₇	#460	1	2	yes	—
290	C₄×C₇	#471	1	2	yes	—
291	C₄×C₇	C₂²×SD₁₆	1	1	yes	characteristic
292	C₄×C₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
293	C₄×C₇	#577	1	2	yes	—
294	C₂⁴	—	4	1	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	8	2	no	—
310	C₂×D₄	—	8	2	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₇×#41	1	1	yes	characteristic
315	SD₁₆	—	4	4	no	—
316	SD₁₆	—	4	4	no	—
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	4	4	no	—
319	SD₁₆	—	8	4	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	C₇×SD₁₆	1	4	yes	complemented
326	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
340	C₂²⋊C₄	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
343	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
344	C₄²	C₇×#41	1	1	yes	characteristic
345	C₄²	C₂⁴×C₇	1	1	yes	characteristic
346	C₂×C₇	—	2	2	no	—
347	C₂×C₇	—	16	2	no	—
348	C₂×C₇	C₂×#460	1	1	yes	characteristic
349	C₂×C₇	#3057	1	1	yes	characteristic
350	C₂×C₇	C₂×#471	1	1	yes	characteristic
351	C₂³	—	4	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	—	8	2	no	—
354	C₂³	—	8	2	no	—
355	C₂³	C₇×#121	1	1	yes	characteristic
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	8	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	4	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	C₇×#121	1	1	yes	characteristic
375	C₂×C₄	C₇×#121	1	1	yes	characteristic
376	C₂×C₄	C₇×#121	1	1	yes	characteristic
377	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
378	C₂×C₄	C₇×AGL(1,ℤ/8)	1	2	yes	—
379	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
381	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	C₂×C₇×SD₁₆	1	2	yes	—
388	C₈	C₂×C₇×SD₁₆	1	2	yes	—
389	C₇	#19202	1	1	yes	characteristic, direct product factor, Sylow
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	16	4	no	—
396	C₂²	C₇×#460	1	2	yes	—
397	C₂²	C₂×C₇×#121	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	2	no	—
403	C₄	C₇×#460	1	2	yes	—
404	C₄	C₇×#471	1	2	yes	—
405	C₄	C₂²×C₇×SD₁₆	1	1	yes	characteristic
406	C₄	C₂×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₄	C₇×#577	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	16	2	no	—
410	C₂	C₂×C₇×#460	1	1	yes	characteristic
411	C₂	C₇×#3057	1	1	yes	characteristic
412	C₂	C₂×C₇×#471	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×#3229	C₂	semidirect
4. C₇×#2960	C₂	semidirect
5. C₇×#1686	C₂	semidirect
6. C₇×#1666	C₂	semidirect
7. C₇×#1564	C₂	semidirect
8. C₇×#1546	C₂	semidirect
24. C₇×#475	C₂²	semidirect
28. C₇×#446	C₂²	semidirect
30. C₇×C₈×Q₈	C₂²	semidirect
37. C₇×#335	C₂²	semidirect
38. C₇×#334	C₂²	semidirect
39. C₇×#332	C₂²	semidirect
41. #19202	C₇	direct (N × H)
94. #3229	C₂×C₇	semidirect
97. #2960	C₂×C₇	semidirect
98. #1686	C₂×C₇	semidirect
99. #1666	C₂×C₇	semidirect
100. #1564	C₂×C₇	semidirect
101. #1546	C₂×C₇	semidirect
134. C₂×C₇×C₈	SD₁₆	semidirect
169. #475	C₂²×C₇	semidirect
173. #446	C₂²×C₇	semidirect
175. C₈×Q₈	C₂²×C₇	semidirect
182. #335	C₂²×C₇	semidirect
183. #334	C₂²×C₇	semidirect
184. #332	C₂²×C₇	semidirect
325. C₂×C₈	C₇×SD₁₆	semidirect
389. C₇	#19202	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×#3229	2
C₇×#3208	2
C₂×C₇×#492	2
C₇×#2960	2
C₇×#1686	2
C₇×#1666	2
C₇×#1564	2
C₇×#1546	2
C₇×#1545	2
#19202	7

Subgroups — C7×#19202 #13196418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#19202 #13196418