Subgroups — C₂×C₇×#3152 #13237853

Order 1792.

3262 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	C₂²×C₇×#137	C₂	1	4	yes	maximal, complemented
2	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3152	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#497	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#494	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#492	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	C₂²	1	2	yes	—
10	C₂³×C₇×Q₈	C₂²	1	2	yes	—
11	C₂×C₇×#137	—	2	32	no	—
12	C₂×C₇×#137	C₂²	1	32	yes	complemented
13	C₂²×C₇×Q₁₆	C₂²	1	8	yes	—
14	C₂²×C₇×SD₁₆	C₂²	1	8	yes	—
15	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
16	C₇×#532	—	2	4	no	—
17	C₇×#532	C₂²	1	8	yes	—
18	C₂×C₇×C₄⋊Q₈	—	2	2	no	—
19	C₂×C₇×C₄⋊Q₈	—	2	4	no	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊Q₈	C₂²	1	8	yes	complemented
24	C₂×C₇×#127	C₂²	1	1	yes	characteristic
25	C₂×C₇×#124	C₂²	1	2	yes	—
26	C₂×C₇×#121	—	2	2	no	—
27	C₂×C₄×C₇×D₄	—	2	2	no	—
28	C₂²×C₇×C₄⋊C₄	—	2	2	no	—
29	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
30	C₇×#497	C₂²	1	32	yes	complemented
31	C₇×#494	C₂²	1	16	yes	complemented
32	C₇×#492	C₂²	1	16	yes	complemented
33	C₄×C₇×M₁₆	C₂²	1	8	yes	complemented
34	C₂×C₇×#97	C₂²	1	2	yes	—
35	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
36	C₂×#3152	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₇×#41	—	2	4	no	—
38	C₂×C₇×#41	—	2	16	no	—
39	C₂×C₇×#41	C₂³	1	8	yes	—
40	C₂²×C₇×Q₈	—	2	4	no	—
41	C₂²×C₇×Q₈	—	2	2	no	—
42	C₂²×C₇×Q₈	—	2	16	no	—
43	C₂²×C₇×Q₈	C₂³	1	4	yes	—
44	C₂²×C₇×Q₈	C₂³	1	8	yes	—
45	C₂²×C₇×Q₈	C₂³	1	2	yes	—
46	C₂²×C₇×D₄	—	2	2	no	—
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂²×C₇×D₄	C₂³	1	2	yes	—
49	C₂³×C₄×C₇	—	2	2	no	—
50	C₂³×C₄×C₇	—	2	2	no	—
51	C₂³×C₄×C₇	D₄	1	2	yes	—
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₇×#137	—	2	128	no	—
54	C₂×C₇×Q₁₆	—	2	32	no	—
55	C₂×C₇×Q₁₆	C₂³	1	32	yes	—
56	C₂×C₇×SD₁₆	—	2	32	no	—
57	C₂×C₇×SD₁₆	C₂³	1	32	yes	—
58	C₂×C₇×M₁₆	D₄	1	16	yes	complemented
59	C₂×C₇×M₁₆	C₂³	1	8	yes	—
60	C₂²×C₇×C₈	C₂³	1	4	yes	—
61	C₇×C₄⋊Q₈	—	2	4	no	—
62	C₇×C₄⋊Q₈	—	2	4	no	—
63	C₇×C₄⋊Q₈	—	2	16	no	—
64	C₇×C₄⋊Q₈	—	2	2	no	—
65	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
67	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
68	C₇×#127	—	2	2	no	—
69	C₇×#127	C₂³	1	4	yes	—
70	C₇×#124	—	2	4	no	—
71	C₇×#124	C₂³	1	8	yes	—
72	C₇×#121	—	2	16	no	—
73	C₄×C₇×D₄	—	2	16	no	—
74	C₂×C₇×C₄⋊C₄	—	2	4	no	—
75	C₂×C₇×C₄⋊C₄	—	2	4	no	—
76	C₂×C₇×C₄⋊C₄	—	2	16	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
79	C₂×C₄²×C₇	D₄	1	2	yes	—
80	C₂×C₄²×C₇	D₄	1	4	yes	—
81	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₇	C₂³	1	4	yes	—
84	C₇×#97	C₂³	1	8	yes	—
85	C₄×C₇×C₈	C₂³	1	8	yes	—
86	C₂²×#137	C₂×C₇	1	4	yes	complemented
87	C₂×#532	C₂×C₇	1	1	yes	characteristic
88	C₂²×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
89	#3152	C₂×C₇	1	16	yes	direct product factor
90	C₂×#497	C₂×C₇	1	4	yes	complemented
91	C₂×#494	C₂×C₇	1	2	yes	complemented
92	C₂×#492	C₂×C₇	1	2	yes	complemented
93	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂⁴×C₇	—	2	2	no	—
95	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
96	C₇×#41	—	2	32	no	—
97	C₇×#41	—	4	16	no	—
98	C₂×C₇×Q₈	—	2	2	no	—
99	C₂×C₇×Q₈	—	2	8	no	—
100	C₂×C₇×Q₈	—	2	4	no	—
101	C₂×C₇×Q₈	—	2	16	no	—
102	C₂×C₇×Q₈	—	2	8	no	—
103	C₂×C₇×Q₈	—	2	32	no	—
104	C₂×C₇×Q₈	—	4	8	no	—
105	C₂×C₇×Q₈	—	4	16	no	—
106	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
107	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
108	C₂×C₇×D₄	—	2	8	no	—
109	C₂×C₇×D₄	—	2	8	no	—
110	C₂×C₇×D₄	—	2	8	no	—
111	C₂×C₇×D₄	—	2	2	no	—
112	C₂×C₇×D₄	—	4	8	no	—
113	C₂×C₇×D₄	—	4	8	no	—
114	C₂×C₇×D₄	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₇	—	2	8	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	2	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	8	no	—
120	C₂²×C₄×C₇	—	4	8	no	—
121	C₂²×C₄×C₇	—	4	8	no	—
122	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
130	C₇×Q₁₆	—	2	64	no	—
131	C₇×SD₁₆	—	2	64	no	—
132	C₇×M₁₆	C₂×D₄	1	32	yes	complemented
133	C₂×C₇×C₈	C₂×D₄	1	16	yes	—
134	C₂×C₇×C₈	C₂⁴	1	8	yes	—
135	C₇×C₄⋊C₄	—	2	16	no	—
136	C₇×C₄⋊C₄	—	2	16	no	—
137	C₇×C₄⋊C₄	—	2	8	no	—
138	C₇×C₂²⋊C₄	—	2	16	no	—
139	C₄²×C₇	C₂×D₄	1	8	yes	—
140	C₄²×C₇	C₂×D₄	1	2	yes	—
141	C₄²×C₇	C₂×D₄	1	2	yes	—
142	C₄²×C₇	C₂⁴	1	2	yes	—
143	C₄²×C₇	C₂⁴	1	2	yes	—
144	C₂²×#41	C₂²×C₇	1	2	yes	—
145	C₂³×Q₈	C₂²×C₇	1	2	yes	—
146	C₂×#137	—	2	32	no	—
147	C₂×#137	C₂²×C₇	1	32	yes	complemented
148	C₂²×Q₁₆	C₂²×C₇	1	8	yes	—
149	C₂²×SD₁₆	C₂²×C₇	1	8	yes	—
150	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
151	#532	—	2	4	no	—
152	#532	C₂²×C₇	1	8	yes	—
153	C₂×C₄⋊Q₈	—	2	2	no	—
154	C₂×C₄⋊Q₈	—	2	4	no	—
155	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
156	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
157	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
158	C₂×C₄⋊Q₈	C₂²×C₇	1	8	yes	complemented
159	C₂×#127	C₂²×C₇	1	1	yes	characteristic
160	C₂×#124	C₂²×C₇	1	2	yes	—
161	C₂×#121	—	2	2	no	—
162	C₂×C₄×D₄	—	2	2	no	—
163	C₂²×C₄⋊C₄	—	2	2	no	—
164	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
165	#497	C₂²×C₇	1	32	yes	complemented
166	#494	C₂²×C₇	1	16	yes	complemented
167	#492	C₂²×C₇	1	16	yes	complemented
168	C₄×M₁₆	C₂²×C₇	1	8	yes	complemented
169	C₂×#97	C₂²×C₇	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
171	C₂³×C₇	—	2	4	no	—
172	C₂³×C₇	—	2	4	no	—
173	C₂³×C₇	—	4	4	no	—
174	C₂³×C₇	—	4	8	no	—
175	C₂³×C₇	#127	1	4	yes	—
176	C₂³×C₇	C₂²×D₄	1	2	yes	—
177	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
178	C₇×Q₈	—	2	16	no	—
179	C₇×Q₈	—	2	8	no	—
180	C₇×Q₈	—	4	16	no	—
181	C₇×Q₈	—	4	8	no	—
182	C₇×Q₈	—	4	4	no	—
183	C₇×D₄	—	2	8	no	—
184	C₇×D₄	—	4	16	no	—
185	C₇×D₄	—	4	4	no	—
186	C₇×D₄	—	4	16	no	—
187	C₂×C₄×C₇	—	2	4	no	—
188	C₂×C₄×C₇	—	2	16	no	—
189	C₂×C₄×C₇	—	2	4	no	—
190	C₂×C₄×C₇	—	2	8	no	—
191	C₂×C₄×C₇	—	4	4	no	—
192	C₂×C₄×C₇	—	4	16	no	—
193	C₂×C₄×C₇	—	4	8	no	—
194	C₂×C₄×C₇	—	4	16	no	—
195	C₂×C₄×C₇	#127	1	4	yes	—
196	C₂×C₄×C₇	#127	1	8	yes	—
197	C₂×C₄×C₇	#137	1	8	yes	complemented
198	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
203	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
205	C₇×C₈	C₂²×D₄	1	16	yes	—
206	C₂×#41	—	2	4	no	—
207	C₂×#41	—	2	16	no	—
208	C₂×#41	C₂³×C₇	1	8	yes	—
209	C₂²×Q₈	—	2	2	no	—
210	C₂²×Q₈	—	2	4	no	—
211	C₂²×Q₈	—	2	16	no	—
212	C₂²×Q₈	C₂³×C₇	1	2	yes	—
213	C₂²×Q₈	C₂³×C₇	1	4	yes	—
214	C₂²×Q₈	C₂³×C₇	1	8	yes	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	C₂³×C₇	1	2	yes	—
218	C₂³×C₄	—	2	2	no	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	C₇×D₄	1	2	yes	—
221	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
222	#137	—	2	128	no	—
223	C₂×Q₁₆	—	2	32	no	—
224	C₂×Q₁₆	C₂³×C₇	1	32	yes	—
225	C₂×SD₁₆	—	2	32	no	—
226	C₂×SD₁₆	C₂³×C₇	1	32	yes	—
227	C₂×M₁₆	C₇×D₄	1	16	yes	complemented
228	C₂×M₁₆	C₂³×C₇	1	8	yes	—
229	C₂²×C₈	C₂³×C₇	1	4	yes	—
230	C₄⋊Q₈	—	2	4	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄⋊Q₈	—	2	16	no	—
233	C₄⋊Q₈	—	2	2	no	—
234	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
235	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
236	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
237	#127	—	2	2	no	—
238	#127	C₂³×C₇	1	4	yes	—
239	#124	—	2	4	no	—
240	#124	C₂³×C₇	1	8	yes	—
241	#121	—	2	16	no	—
242	C₄×D₄	—	2	16	no	—
243	C₂×C₄⋊C₄	—	2	4	no	—
244	C₂×C₄⋊C₄	—	2	4	no	—
245	C₂×C₄⋊C₄	—	2	16	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	C₂×C₄²	C₇×D₄	1	2	yes	—
249	C₂×C₄²	C₇×D₄	1	4	yes	—
250	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₇	1	4	yes	—
253	#97	C₂³×C₇	1	8	yes	—
254	C₄×C₈	C₂³×C₇	1	8	yes	—
255	C₂²×C₇	—	2	8	no	—
256	C₂²×C₇	—	2	4	no	—
257	C₂²×C₇	—	4	4	no	—
258	C₂²×C₇	—	4	8	no	—
259	C₂²×C₇	—	8	8	no	—
260	C₂²×C₇	C₂×#127	1	4	yes	—
261	C₂²×C₇	C₂×#127	1	2	yes	—
262	C₂²×C₇	C₂×#137	1	4	yes	—
263	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
264	C₄×C₇	—	2	4	no	—
265	C₄×C₇	—	4	4	no	—
266	C₄×C₇	—	4	8	no	—
267	C₄×C₇	C₂×#127	1	4	yes	—
268	C₄×C₇	C₂×#127	1	2	yes	—
269	C₄×C₇	C₂×#137	1	8	yes	complemented
270	C₄×C₇	C₂³×D₄	1	2	yes	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
273	#41	—	2	32	no	—
274	#41	—	4	16	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	16	no	—
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	32	no	—
281	C₂×Q₈	—	4	8	no	—
282	C₂×Q₈	—	4	16	no	—
283	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
284	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	8	no	—
290	C₂×D₄	—	4	8	no	—
291	C₂×D₄	C₂⁴×C₇	1	4	yes	—
292	C₂²×C₄	—	2	8	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	4	8	no	—
298	C₂²×C₄	—	4	8	no	—
299	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
300	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
301	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
303	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
304	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
307	Q₁₆	—	2	64	no	—
308	SD₁₆	—	2	64	no	—
309	M₁₆	C₂×C₇×D₄	1	32	yes	complemented
310	C₂×C₈	C₂×C₇×D₄	1	16	yes	—
311	C₂×C₈	C₂⁴×C₇	1	8	yes	—
312	C₄⋊C₄	—	2	16	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₄²	C₂×C₇×D₄	1	8	yes	—
317	C₄²	C₂×C₇×D₄	1	2	yes	—
318	C₄²	C₂×C₇×D₄	1	2	yes	—
319	C₄²	C₂⁴×C₇	1	2	yes	—
320	C₄²	C₂⁴×C₇	1	2	yes	—
321	C₂×C₇	—	2	4	no	—
322	C₂×C₇	—	8	4	no	—
323	C₂×C₇	#3152	1	4	yes	direct product factor
324	C₂×C₇	C₂²×#127	1	1	yes	characteristic
325	C₂×C₇	C₂²×#137	1	2	yes	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	C₇×#127	1	4	yes	—
331	C₂³	C₂²×C₇×D₄	1	2	yes	—
332	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
333	Q₈	—	2	16	no	—
334	Q₈	—	2	8	no	—
335	Q₈	—	4	16	no	—
336	Q₈	—	4	8	no	—
337	Q₈	—	4	4	no	—
338	D₄	—	2	8	no	—
339	D₄	—	4	16	no	—
340	D₄	—	4	4	no	—
341	D₄	—	4	16	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	16	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	16	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	16	no	—
350	C₂×C₄	C₇×#127	1	4	yes	—
351	C₂×C₄	C₇×#127	1	8	yes	—
352	C₂×C₄	C₇×#137	1	8	yes	complemented
353	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
354	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
355	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
356	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
357	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
359	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
360	C₈	C₂²×C₇×D₄	1	16	yes	—
361	C₇	C₂×#3152	1	1	yes	characteristic, direct product factor, Sylow
362	C₂²	—	2	4	no	—
363	C₂²	—	2	8	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	8	8	no	—
367	C₂²	C₂×C₇×#127	1	4	yes	—
368	C₂²	C₂×C₇×#127	1	2	yes	—
369	C₂²	C₂×C₇×#137	1	4	yes	—
370	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
371	C₄	—	2	4	no	—
372	C₄	—	4	4	no	—
373	C₄	—	4	8	no	—
374	C₄	C₂×C₇×#127	1	4	yes	—
375	C₄	C₂×C₇×#127	1	2	yes	—
376	C₄	C₂×C₇×#137	1	8	yes	complemented
377	C₄	C₂³×C₇×D₄	1	2	yes	—
378	C₂	—	2	4	no	—
379	C₂	—	8	4	no	—
380	C₂	C₇×#3152	1	4	yes	direct product factor
381	C₂	C₂²×C₇×#127	1	1	yes	characteristic
382	C₂	C₂²×C₇×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×#137	C₂	semidirect
3. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
4. C₇×#3152	C₂	direct (N × H)
5. C₂×C₇×#497	C₂	semidirect
6. C₂×C₇×#494	C₂	semidirect
7. C₂×C₇×#492	C₂	semidirect
8. C₂×C₄×C₇×M₁₆	C₂	semidirect
12. C₂×C₇×#137	C₂²	semidirect
23. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
30. C₇×#497	C₂²	semidirect
31. C₇×#494	C₂²	semidirect
32. C₇×#492	C₂²	semidirect
33. C₄×C₇×M₁₆	C₂²	semidirect
36. C₂×#3152	C₇	direct (N × H)
58. C₂×C₇×M₁₆	D₄	semidirect
86. C₂²×#137	C₂×C₇	semidirect
88. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
89. #3152	C₂×C₇	direct (N × H)
90. C₂×#497	C₂×C₇	semidirect
91. C₂×#494	C₂×C₇	semidirect
92. C₂×#492	C₂×C₇	semidirect
93. C₂×C₄×M₁₆	C₂×C₇	semidirect
132. C₇×M₁₆	C₂×D₄	semidirect
147. C₂×#137	C₂²×C₇	semidirect
158. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
165. #497	C₂²×C₇	semidirect
166. #494	C₂²×C₇	semidirect
167. #492	C₂²×C₇	semidirect
168. C₄×M₁₆	C₂²×C₇	semidirect
197. C₂×C₄×C₇	#137	semidirect
227. C₂×M₁₆	C₇×D₄	semidirect
269. C₄×C₇	C₂×#137	semidirect
309. M₁₆	C₂×C₇×D₄	semidirect
323. C₂×C₇	#3152	direct (N × H)
352. C₂×C₄	C₇×#137	semidirect
361. C₇	C₂×#3152	direct (N × H)
376. C₄	C₂×C₇×#137	semidirect
380. C₂	C₇×#3152	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×#137	2
C₂×C₇×#532	2
C₂²×C₇×C₄⋊Q₈	2
C₇×#3152	2
C₂×C₇×#497	2
C₂×C₇×#494	2
C₂×C₇×#492	2
C₂×C₄×C₇×M₁₆	2
C₂×#3152	7

Subgroups — C2×C7×#3152 #13237853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3152 #13237853