Subgroups — C₂²×C₇×#465 #13237650

Order 1792.

3350 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×#465	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
10	C₂³×C₇×D₄	—	2	1	no	—
11	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
13	C₂²×C₇×SD₁₆	—	2	8	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	12	yes	complemented
15	C₂³×C₇×C₈	—	2	8	no	—
16	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
18	C₂³×C₇×C₈	C₂²	1	12	yes	complemented
19	C₂×C₇×C₂²⋊Q₈	—	2	6	no	—
20	C₂×C₇×C₂²⋊Q₈	C₂²	1	12	yes	complemented
21	C₂×C₇×#121	—	2	6	no	—
22	C₂×C₇×#121	C₂²	1	12	yes	—
23	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
24	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
27	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
28	C₇×#465	C₂²	1	64	yes	direct product factor
29	C₂×C₇×#106	C₂²	1	12	yes	complemented
30	C₂×C₇×#103	C₂²	1	12	yes	complemented
31	C₂×C₇×#102	C₂²	1	12	yes	complemented
32	C₂²×#465	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂⁵×C₇	—	2	1	no	—
34	C₂⁵×C₇	D₄	1	1	yes	characteristic
35	C₂²×C₇×Q₈	—	2	3	no	—
36	C₂²×C₇×Q₈	—	2	4	no	—
37	C₂²×C₇×Q₈	—	2	4	no	—
38	C₂²×C₇×Q₈	C₂³	1	6	yes	—
39	C₂²×C₇×D₄	—	2	12	no	—
40	C₂²×C₇×D₄	—	2	4	no	—
41	C₂²×C₇×D₄	—	2	3	no	—
42	C₂²×C₇×D₄	—	2	4	no	—
43	C₂²×C₇×D₄	—	4	8	no	—
44	C₂²×C₇×D₄	C₂³	1	6	yes	—
45	C₂³×C₄×C₇	—	2	4	no	—
46	C₂³×C₄×C₇	—	2	4	no	—
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂³×C₄×C₇	—	2	1	no	—
49	C₂³×C₄×C₇	—	2	1	no	—
50	C₂³×C₄×C₇	D₄	1	6	yes	—
51	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₇	C₂³	1	6	yes	—
53	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
54	C₂×C₇×SD₁₆	—	2	48	no	—
55	C₂×C₇×SD₁₆	C₂³	1	16	yes	complemented
56	C₂²×C₇×C₈	—	2	4	no	—
57	C₂²×C₇×C₈	—	2	48	no	—
58	C₂²×C₇×C₈	D₄	1	8	yes	complemented
59	C₂²×C₇×C₈	C₂³	1	6	yes	—
60	C₂²×C₇×C₈	C₂³	1	6	yes	—
61	C₂²×C₇×C₈	C₂³	1	16	yes	complemented
62	C₇×C₂²⋊Q₈	—	2	24	no	—
63	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
64	C₇×#121	—	2	24	no	—
65	C₇×#121	C₂³	1	16	yes	—
66	C₂×C₇×C₄⋊C₄	—	2	12	no	—
67	C₂×C₇×C₄⋊C₄	—	2	3	no	—
68	C₂×C₇×C₄⋊C₄	—	2	3	no	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
71	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
72	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
73	C₇×#106	C₂³	1	16	yes	complemented
74	C₇×#103	C₂³	1	16	yes	complemented
75	C₇×#102	C₂³	1	16	yes	complemented
76	C₂³×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
77	C₂⁴×C₈	C₂×C₇	1	1	yes	characteristic, complemented
78	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
79	C₂²×#121	C₂×C₇	1	1	yes	characteristic
80	C₂×#465	C₂×C₇	1	24	yes	direct product factor
81	C₂²×#106	C₂×C₇	1	1	yes	characteristic, complemented
82	C₂²×#103	C₂×C₇	1	1	yes	characteristic, complemented
83	C₂²×#102	C₂×C₇	1	1	yes	characteristic, complemented
84	C₂⁴×C₇	—	2	4	no	—
85	C₂⁴×C₇	—	2	4	no	—
86	C₂⁴×C₇	—	2	6	no	—
87	C₂⁴×C₇	—	4	4	no	—
88	C₂⁴×C₇	—	4	4	no	—
89	C₂⁴×C₇	—	4	4	no	—
90	C₂⁴×C₇	SD₁₆	1	8	yes	complemented
91	C₂⁴×C₇	C₂×D₄	1	6	yes	—
92	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
93	C₂×C₇×Q₈	—	2	6	no	—
94	C₂×C₇×Q₈	—	2	12	no	—
95	C₂×C₇×Q₈	—	2	12	no	—
96	C₂×C₇×Q₈	—	4	12	no	—
97	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
98	C₂×C₇×D₄	—	2	16	no	—
99	C₂×C₇×D₄	—	2	12	no	—
100	C₂×C₇×D₄	—	2	6	no	—
101	C₂×C₇×D₄	—	2	12	no	—
102	C₂×C₇×D₄	—	4	48	no	—
103	C₂×C₇×D₄	—	4	12	no	—
104	C₂×C₇×D₄	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₇	—	2	4	no	—
106	C₂²×C₄×C₇	—	2	24	no	—
107	C₂²×C₄×C₇	—	2	12	no	—
108	C₂²×C₄×C₇	—	2	12	no	—
109	C₂²×C₄×C₇	—	2	6	no	—
110	C₂²×C₄×C₇	—	2	6	no	—
111	C₂²×C₄×C₇	—	2	6	no	—
112	C₂²×C₄×C₇	—	4	4	no	—
113	C₂²×C₄×C₇	—	4	4	no	—
114	C₂²×C₄×C₇	—	4	4	no	—
115	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	12	yes	—
117	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
118	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₇	#41	1	4	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
122	C₇×SD₁₆	—	2	32	no	—
123	C₂×C₇×C₈	—	2	12	no	—
124	C₂×C₇×C₈	—	2	32	no	—
125	C₂×C₇×C₈	C₂×D₄	1	24	yes	complemented
126	C₂×C₇×C₈	C₂⁴	1	4	yes	—
127	C₂×C₇×C₈	C₂⁴	1	4	yes	—
128	C₇×C₄⋊C₄	—	2	16	no	—
129	C₇×C₄⋊C₄	—	2	6	no	—
130	C₇×C₄⋊C₄	—	2	6	no	—
131	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
132	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
133	C₇×C₂²⋊C₄	—	2	16	no	—
134	C₇×C₂²⋊C₄	—	2	16	no	—
135	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
136	C₂³×D₄	—	2	1	no	—
137	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
138	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
139	C₂²×SD₁₆	—	2	8	no	—
140	C₂²×SD₁₆	C₂²×C₇	1	12	yes	complemented
141	C₂³×C₈	—	2	8	no	—
142	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
143	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
144	C₂³×C₈	C₂²×C₇	1	12	yes	complemented
145	C₂×C₂²⋊Q₈	—	2	6	no	—
146	C₂×C₂²⋊Q₈	C₂²×C₇	1	12	yes	complemented
147	C₂×#121	—	2	6	no	—
148	C₂×#121	C₂²×C₇	1	12	yes	—
149	C₂²×C₄⋊C₄	—	2	1	no	—
150	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
151	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
152	C₂²×C₂²⋊C₄	—	2	1	no	—
153	C₂²×C₂²⋊C₄	—	2	1	no	—
154	#465	C₂²×C₇	1	64	yes	direct product factor
155	C₂×#106	C₂²×C₇	1	12	yes	complemented
156	C₂×#103	C₂²×C₇	1	12	yes	complemented
157	C₂×#102	C₂²×C₇	1	12	yes	complemented
158	C₂³×C₇	—	2	12	no	—
159	C₂³×C₇	—	2	12	no	—
160	C₂³×C₇	—	2	32	no	—
161	C₂³×C₇	—	2	4	no	—
162	C₂³×C₇	—	4	12	no	—
163	C₂³×C₇	—	4	12	no	—
164	C₂³×C₇	—	4	12	no	—
165	C₂³×C₇	—	8	16	no	—
166	C₂³×C₇	#121	1	4	yes	—
167	C₂³×C₇	C₂×SD₁₆	1	4	yes	—
168	C₂³×C₇	C₂×SD₁₆	1	24	yes	complemented
169	C₂³×C₇	#135	1	4	yes	—
170	C₂³×C₇	C₂²×D₄	1	4	yes	—
171	C₂³×C₇	C₂²×D₄	1	3	yes	—
172	C₇×Q₈	—	2	4	no	—
173	C₇×Q₈	—	2	4	no	—
174	C₇×Q₈	—	4	12	no	—
175	C₇×D₄	—	2	4	no	—
176	C₇×D₄	—	2	4	no	—
177	C₇×D₄	—	4	32	no	—
178	C₇×D₄	—	4	12	no	—
179	C₂×C₄×C₇	—	2	12	no	—
180	C₂×C₄×C₇	—	2	24	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	4	no	—
183	C₂×C₄×C₇	—	2	4	no	—
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	4	no	—
186	C₂×C₄×C₇	—	4	12	no	—
187	C₂×C₄×C₇	—	4	12	no	—
188	C₂×C₄×C₇	—	4	12	no	—
189	C₂×C₄×C₇	#121	1	12	yes	—
190	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
191	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
192	C₂×C₄×C₇	C₂²×D₄	1	6	yes	—
193	C₂×C₄×C₇	C₂×#41	1	6	yes	—
194	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
195	C₇×C₈	—	2	4	no	—
196	C₇×C₈	C₂²×D₄	1	8	yes	complemented
197	C₂⁵	—	2	1	no	—
198	C₂⁵	C₇×D₄	1	1	yes	characteristic
199	C₂²×Q₈	—	2	3	no	—
200	C₂²×Q₈	—	2	4	no	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	C₂³×C₇	1	6	yes	—
203	C₂²×D₄	—	2	12	no	—
204	C₂²×D₄	—	2	4	no	—
205	C₂²×D₄	—	2	3	no	—
206	C₂²×D₄	—	2	4	no	—
207	C₂²×D₄	—	4	8	no	—
208	C₂²×D₄	C₂³×C₇	1	6	yes	—
209	C₂³×C₄	—	2	4	no	—
210	C₂³×C₄	—	2	4	no	—
211	C₂³×C₄	—	2	1	no	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	1	no	—
214	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
215	C₂³×C₄	C₇×D₄	1	6	yes	—
216	C₂³×C₄	C₂³×C₇	1	6	yes	—
217	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
218	C₂×SD₁₆	—	2	48	no	—
219	C₂×SD₁₆	C₂³×C₇	1	16	yes	complemented
220	C₂²×C₈	—	2	4	no	—
221	C₂²×C₈	—	2	48	no	—
222	C₂²×C₈	C₇×D₄	1	8	yes	complemented
223	C₂²×C₈	C₂³×C₇	1	6	yes	—
224	C₂²×C₈	C₂³×C₇	1	6	yes	—
225	C₂²×C₈	C₂³×C₇	1	16	yes	complemented
226	C₂²⋊Q₈	—	2	24	no	—
227	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
228	#121	—	2	24	no	—
229	#121	C₂³×C₇	1	16	yes	—
230	C₂×C₄⋊C₄	—	2	12	no	—
231	C₂×C₄⋊C₄	—	2	3	no	—
232	C₂×C₄⋊C₄	—	2	3	no	—
233	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
234	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
235	C₂×C₂²⋊C₄	—	2	12	no	—
236	C₂×C₂²⋊C₄	—	2	12	no	—
237	#106	C₂³×C₇	1	16	yes	complemented
238	#103	C₂³×C₇	1	16	yes	complemented
239	#102	C₂³×C₇	1	16	yes	complemented
240	C₂²×C₇	—	2	4	no	—
241	C₂²×C₇	—	2	48	no	—
242	C₂²×C₇	—	2	4	no	—
243	C₂²×C₇	—	4	4	no	—
244	C₂²×C₇	—	4	4	no	—
245	C₂²×C₇	—	4	4	no	—
246	C₂²×C₇	—	8	24	no	—
247	C₂²×C₇	#465	1	16	yes	direct product factor
248	C₂²×C₇	C₂×#121	1	6	yes	—
249	C₂²×C₇	C₂²×SD₁₆	1	6	yes	—
250	C₂²×C₇	C₂²×SD₁₆	1	8	yes	complemented
251	C₂²×C₇	C₂×#135	1	6	yes	—
252	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
253	C₄×C₇	—	2	4	no	—
254	C₄×C₇	—	4	4	no	—
255	C₄×C₇	—	4	4	no	—
256	C₄×C₇	—	4	4	no	—
257	C₄×C₇	C₂×#121	1	6	yes	—
258	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
259	C₄×C₇	C₂²×#41	1	1	yes	characteristic
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	2	6	no	—
263	C₂⁴	—	4	4	no	—
264	C₂⁴	—	4	4	no	—
265	C₂⁴	—	4	4	no	—
266	C₂⁴	C₇×SD₁₆	1	8	yes	complemented
267	C₂⁴	C₂×C₇×D₄	1	6	yes	—
268	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
269	C₂×Q₈	—	2	6	no	—
270	C₂×Q₈	—	2	12	no	—
271	C₂×Q₈	—	2	12	no	—
272	C₂×Q₈	—	4	12	no	—
273	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	12	no	—
276	C₂×D₄	—	2	6	no	—
277	C₂×D₄	—	2	12	no	—
278	C₂×D₄	—	4	48	no	—
279	C₂×D₄	—	4	12	no	—
280	C₂×D₄	C₂⁴×C₇	1	4	yes	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	24	no	—
283	C₂²×C₄	—	2	12	no	—
284	C₂²×C₄	—	2	12	no	—
285	C₂²×C₄	—	2	6	no	—
286	C₂²×C₄	—	2	6	no	—
287	C₂²×C₄	—	2	6	no	—
288	C₂²×C₄	—	4	4	no	—
289	C₂²×C₄	—	4	4	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
292	C₂²×C₄	C₂×C₇×D₄	1	12	yes	—
293	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
294	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
295	C₂²×C₄	C₇×#41	1	4	yes	—
296	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
297	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
298	SD₁₆	—	2	32	no	—
299	C₂×C₈	—	2	12	no	—
300	C₂×C₈	—	2	32	no	—
301	C₂×C₈	C₂×C₇×D₄	1	24	yes	complemented
302	C₂×C₈	C₂⁴×C₇	1	4	yes	—
303	C₂×C₈	C₂⁴×C₇	1	4	yes	—
304	C₄⋊C₄	—	2	16	no	—
305	C₄⋊C₄	—	2	6	no	—
306	C₄⋊C₄	—	2	6	no	—
307	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
308	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₂²⋊C₄	—	2	16	no	—
311	C₂×C₇	—	2	8	no	—
312	C₂×C₇	—	8	4	no	—
313	C₂×C₇	C₂×#465	1	12	yes	direct product factor
314	C₂×C₇	C₂²×#121	1	1	yes	characteristic
315	C₂×C₇	C₂³×SD₁₆	1	1	yes	characteristic
316	C₂×C₇	C₂²×#135	1	1	yes	characteristic
317	C₂³	—	2	12	no	—
318	C₂³	—	2	12	no	—
319	C₂³	—	2	32	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	12	no	—
322	C₂³	—	4	12	no	—
323	C₂³	—	4	12	no	—
324	C₂³	—	8	16	no	—
325	C₂³	C₇×#121	1	4	yes	—
326	C₂³	C₂×C₇×SD₁₆	1	4	yes	—
327	C₂³	C₂×C₇×SD₁₆	1	24	yes	complemented
328	C₂³	C₇×#135	1	4	yes	—
329	C₂³	C₂²×C₇×D₄	1	4	yes	—
330	C₂³	C₂²×C₇×D₄	1	3	yes	—
331	Q₈	—	2	4	no	—
332	Q₈	—	2	4	no	—
333	Q₈	—	4	12	no	—
334	D₄	—	2	4	no	—
335	D₄	—	2	4	no	—
336	D₄	—	4	32	no	—
337	D₄	—	4	12	no	—
338	C₂×C₄	—	2	12	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	24	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	12	no	—
346	C₂×C₄	—	4	12	no	—
347	C₂×C₄	—	4	12	no	—
348	C₂×C₄	C₇×#121	1	12	yes	—
349	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
350	C₂×C₄	C₂²×C₇×D₄	1	6	yes	—
351	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
352	C₂×C₄	C₂×C₇×#41	1	6	yes	—
353	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
354	C₈	—	2	4	no	—
355	C₈	C₂²×C₇×D₄	1	8	yes	complemented
356	C₇	C₂²×#465	1	1	yes	characteristic, direct product factor, Sylow
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	48	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	4	no	—
363	C₂²	—	8	24	no	—
364	C₂²	C₇×#465	1	16	yes	direct product factor
365	C₂²	C₂×C₇×#121	1	6	yes	—
366	C₂²	C₂²×C₇×SD₁₆	1	6	yes	—
367	C₂²	C₂²×C₇×SD₁₆	1	8	yes	complemented
368	C₂²	C₂×C₇×#135	1	6	yes	—
369	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	4	no	—
374	C₄	C₂×C₇×#121	1	6	yes	—
375	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
376	C₄	C₂²×C₇×#41	1	1	yes	characteristic
377	C₂	—	2	8	no	—
378	C₂	—	8	4	no	—
379	C₂	C₂×C₇×#465	1	12	yes	direct product factor
380	C₂	C₂²×C₇×#121	1	1	yes	characteristic
381	C₂	C₂³×C₇×SD₁₆	1	1	yes	characteristic
382	C₂	C₂²×C₇×#135	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×SD₁₆	C₂	semidirect
2. C₂⁴×C₇×C₈	C₂	semidirect
3. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
5. C₂×C₇×#465	C₂	direct (N × H)
6. C₂²×C₇×#106	C₂	semidirect
7. C₂²×C₇×#103	C₂	semidirect
8. C₂²×C₇×#102	C₂	semidirect
14. C₂²×C₇×SD₁₆	C₂²	semidirect
18. C₂³×C₇×C₈	C₂²	semidirect
20. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
28. C₇×#465	C₂²	direct (N × H)
29. C₂×C₇×#106	C₂²	semidirect
30. C₂×C₇×#103	C₂²	semidirect
31. C₂×C₇×#102	C₂²	semidirect
32. C₂²×#465	C₇	direct (N × H)
55. C₂×C₇×SD₁₆	C₂³	semidirect
58. C₂²×C₇×C₈	D₄	semidirect
61. C₂²×C₇×C₈	C₂³	semidirect
63. C₇×C₂²⋊Q₈	C₂³	semidirect
73. C₇×#106	C₂³	semidirect
74. C₇×#103	C₂³	semidirect
75. C₇×#102	C₂³	semidirect
76. C₂³×SD₁₆	C₂×C₇	semidirect
77. C₂⁴×C₈	C₂×C₇	semidirect
78. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
80. C₂×#465	C₂×C₇	direct (N × H)
81. C₂²×#106	C₂×C₇	semidirect
82. C₂²×#103	C₂×C₇	semidirect
83. C₂²×#102	C₂×C₇	semidirect
90. C₂⁴×C₇	SD₁₆	semidirect
125. C₂×C₇×C₈	C₂×D₄	semidirect
140. C₂²×SD₁₆	C₂²×C₇	semidirect
144. C₂³×C₈	C₂²×C₇	semidirect
146. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
154. #465	C₂²×C₇	direct (N × H)
155. C₂×#106	C₂²×C₇	semidirect
156. C₂×#103	C₂²×C₇	semidirect
157. C₂×#102	C₂²×C₇	semidirect
168. C₂³×C₇	C₂×SD₁₆	semidirect
196. C₇×C₈	C₂²×D₄	semidirect
219. C₂×SD₁₆	C₂³×C₇	semidirect
222. C₂²×C₈	C₇×D₄	semidirect
225. C₂²×C₈	C₂³×C₇	semidirect
227. C₂²⋊Q₈	C₂³×C₇	semidirect
237. #106	C₂³×C₇	semidirect
238. #103	C₂³×C₇	semidirect
239. #102	C₂³×C₇	semidirect
247. C₂²×C₇	#465	direct (N × H)
250. C₂²×C₇	C₂²×SD₁₆	semidirect
266. C₂⁴	C₇×SD₁₆	semidirect
301. C₂×C₈	C₂×C₇×D₄	semidirect
313. C₂×C₇	C₂×#465	direct (N × H)
327. C₂³	C₂×C₇×SD₁₆	semidirect
355. C₈	C₂²×C₇×D₄	semidirect
356. C₇	C₂²×#465	direct (N × H)
364. C₂²	C₇×#465	direct (N × H)
367. C₂²	C₂²×C₇×SD₁₆	semidirect
379. C₂	C₂×C₇×#465	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×SD₁₆	2
C₂⁴×C₇×C₈	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#121	2
C₂×C₇×#465	2
C₂²×C₇×#106	2
C₂²×C₇×#103	2
C₂²×C₇×#102	2
C₂²×#465	7

Subgroups — C22×C7×#465 #13237650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#465 #13237650