Subgroups — C₄×D₇×M₃₂ #13506423

Order 1792.

918 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₇×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₇×M₃₂	C₂	1	2	yes	maximal, complemented
5	C₄×#6386	C₂	1	1	yes	maximal, characteristic, complemented
6	#11726825	C₂	1	2	yes	maximal, complemented
7	D₇×#346	C₂	1	2	yes	maximal, complemented
8	C₄×#6372	C₂	1	2	yes	maximal, complemented
9	C₄×D₇×C₁₆	C₂	1	2	yes	maximal, complemented
10	C₂²×C₈×D₇	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₇	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₇	C₄	1	1	yes	characteristic
13	C₂×C₇×M₃₂	C₂²	1	2	yes	—
14	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₇	C₄	1	1	yes	characteristic
16	C₂×C₈×Dic₇	C₂²	1	1	yes	characteristic
17	C₂×#6386	C₂²	1	2	yes	—
18	C₂×C₄×C₇⋊C₈	C₄	1	1	yes	characteristic
19	D₇×M₃₂	C₄	1	16	yes	direct product factor
20	C₂×#6372	C₂²	1	4	yes	—
21	C₂×D₇×C₁₆	C₂²	1	4	yes	—
22	C₄×C₈×D₇	C₄	1	1	yes	characteristic
23	C₄×C₈×D₇	C₄	1	1	yes	characteristic
24	C₄×C₈×D₇	C₄	1	1	yes	characteristic
25	C₄×C₈×D₇	C₄	1	1	yes	characteristic
26	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
30	C₇×#346	C₂²	1	2	yes	complemented
31	C₄×C₇×C₁₆	C₂²	1	2	yes	complemented
32	#89297	C₂²	1	4	yes	complemented
33	C₁₆×Dic₇	C₂²	1	4	yes	complemented
34	#89256	C₂²	1	2	yes	complemented
35	C₄×C₇⋊C₁₆	C₂²	1	2	yes	complemented
36	C₂×C₄×M₃₂	—	7	1	no	maximal, Sylow
37	C₂²×C₄×D₇	C₈	1	2	yes	—
38	C₂²×C₄×D₇	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
41	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₇	C₈	1	2	yes	—
43	C₂×C₄×Dic₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₇	C₈	1	8	yes	—
47	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₇	C₂×C₄	1	8	yes	—
50	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
56	C₄²×D₇	C₈	1	2	yes	—
57	C₄²×D₇	C₈	1	2	yes	—
58	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₇	C₂×C₄	1	1	yes	characteristic
62	C₇×M₃₂	C₂×C₄	1	8	yes	complemented
63	C₂×C₇×C₁₆	C₂³	1	4	yes	—
64	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
68	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
69	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₇	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₇	C₂³	1	1	yes	characteristic
75	C₈×Dic₇	C₂³	1	1	yes	characteristic
76	#6386	C₂×C₄	1	8	yes	complemented
77	C₂×C₇⋊C₁₆	C₂³	1	4	yes	—
78	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	#6372	C₂×C₄	1	16	yes	complemented
83	D₇×C₁₆	C₂×C₄	1	16	yes	complemented
84	C₂²×M₃₂	—	7	2	no	—
85	C₂²×C₄×C₈	—	7	1	no	—
86	C₄×M₃₂	—	7	2	no	—
87	C₄×M₃₂	—	7	1	no	—
88	C₄×M₃₂	—	7	2	no	—
89	C₄×M₃₂	—	7	2	no	—
90	C₄×M₃₂	D₇	1	1	yes	characteristic, direct product factor
91	C₂×#346	—	7	2	no	—
92	C₂×C₄×C₁₆	—	7	2	no	—
93	C₂³×D₇	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₇	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₇	C₂×C₈	1	2	yes	—
97	C₂²×Dic₇	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₇	—	2	8	no	—
99	C₂×C₄×D₇	C₄²	1	4	yes	—
100	C₂×C₄×D₇	C₂×C₈	1	2	yes	—
101	C₂×C₄×D₇	C₂×C₈	1	2	yes	—
102	C₂×C₄×D₇	C₂×C₈	1	2	yes	—
103	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₇	C₂×C₈	1	4	yes	—
106	C₂×C₄×D₇	C₂×C₈	1	2	yes	—
107	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₇×C₈	C₂×C₈	1	4	yes	—
110	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
112	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
115	C₄²×C₇	C₂×C₈	1	2	yes	—
116	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
118	C₄×Dic₇	C₂×C₈	1	2	yes	—
119	C₄×Dic₇	C₂×C₈	1	2	yes	—
120	C₄×Dic₇	C₂×C₈	1	2	yes	—
121	C₄×Dic₇	C₂×C₈	1	2	yes	—
122	C₄×Dic₇	C₂×C₈	1	2	yes	—
123	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
124	C₄×Dic₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₇⋊C₈	C₄²	1	4	yes	—
126	C₂×C₇⋊C₈	C₂×C₈	1	4	yes	—
127	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₇	C₄²	1	4	yes	—
132	C₈×D₇	C₄²	1	4	yes	—
133	C₈×D₇	C₂×C₈	1	4	yes	—
134	C₈×D₇	C₂×C₈	1	4	yes	—
135	C₈×D₇	C₂×C₈	1	4	yes	—
136	C₈×D₇	C₂×C₈	1	4	yes	—
137	C₈×D₇	C₂²×C₄	1	4	yes	—
138	C₈×D₇	C₂²×C₄	1	4	yes	—
139	C₇×C₁₆	C₂²×C₄	1	8	yes	complemented
140	C₇⋊C₁₆	C₂²×C₄	1	8	yes	complemented
141	C₂³×C₈	—	7	1	no	—
142	C₂³×C₈	—	7	1	no	—
143	C₂²×C₄²	—	7	1	no	—
144	C₂×M₃₂	—	7	2	no	—
145	C₂×M₃₂	—	7	16	no	—
146	C₂×M₃₂	—	7	4	no	—
147	C₂×M₃₂	C₂×D₇	1	2	yes	—
148	C₂²×C₁₆	—	7	4	no	—
149	C₂×C₄×C₈	—	7	1	no	—
150	C₂×C₄×C₈	—	7	1	no	—
151	C₂×C₄×C₈	—	7	1	no	—
152	C₂×C₄×C₈	—	7	1	no	—
153	C₂×C₄×C₈	—	7	1	no	—
154	C₂×C₄×C₈	—	7	1	no	—
155	C₂×C₄×C₈	—	7	1	no	—
156	C₂×C₄×C₈	—	7	1	no	—
157	C₂×C₄×C₈	—	7	1	no	—
158	C₂×C₄×C₈	—	7	1	no	—
159	C₂×C₄×C₈	—	7	1	no	—
160	C₂×C₄×C₈	C₂×D₇	1	1	yes	characteristic
161	#346	—	7	4	no	—
162	#346	—	7	2	no	—
163	#346	C₂×D₇	1	2	yes	complemented
164	C₄×C₁₆	—	7	4	no	—
165	C₄×C₁₆	—	7	2	no	—
166	C₄×C₁₆	C₂×D₇	1	2	yes	complemented
167	C₂³×C₇	C₂²×C₈	1	1	yes	characteristic
168	C₂²×D₇	—	2	4	no	—
169	C₂²×D₇	C₄×C₈	1	4	yes	—
170	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
171	C₂²×D₇	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₇	—	2	4	no	—
173	C₂×C₄×C₇	C₂×C₄²	1	2	yes	—
174	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
175	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
176	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
177	C₂×C₄×C₇	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×Dic₇	—	2	4	no	—
180	C₂×Dic₇	C₄×C₈	1	4	yes	—
181	C₂×Dic₇	C₂²×C₈	1	2	yes	—
182	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
183	C₂×Dic₇	C₂²×C₈	1	1	yes	characteristic
184	C₂×Dic₇	C₂²×C₈	1	2	yes	—
185	C₄×D₇	—	2	4	no	—
186	C₄×D₇	—	2	4	no	—
187	C₄×D₇	—	2	4	no	—
188	C₄×D₇	C₄×C₈	1	4	yes	—
189	C₄×D₇	C₄×C₈	1	4	yes	—
190	C₄×D₇	M₃₂	1	8	yes	direct product factor
191	C₄×D₇	C₂×C₄²	1	2	yes	—
192	C₄×D₇	C₂×C₄²	1	2	yes	—
193	C₄×D₇	C₂²×C₈	1	2	yes	—
194	C₄×D₇	C₂²×C₈	1	2	yes	—
195	C₇×C₈	C₂×C₄²	1	2	yes	—
196	C₇×C₈	C₂²×C₈	1	2	yes	—
197	C₇×C₈	C₂²×C₈	1	2	yes	—
198	C₇×C₈	C₂³×C₄	1	2	yes	—
199	C₇⋊C₈	C₂×C₄²	1	2	yes	—
200	C₇⋊C₈	C₂×C₄²	1	2	yes	—
201	C₇⋊C₈	C₂²×C₈	1	2	yes	—
202	C₇⋊C₈	C₂²×C₈	1	2	yes	—
203	C₂³×C₄	—	7	1	no	—
204	C₂³×C₄	—	7	2	no	—
205	C₂²×C₈	—	7	1	no	—
206	C₂²×C₈	—	7	1	no	—
207	C₂²×C₈	—	7	8	no	—
208	C₂²×C₈	—	7	1	no	—
209	C₂²×C₈	—	7	1	no	—
210	C₂²×C₈	—	7	1	no	—
211	C₂²×C₈	—	7	1	no	—
212	C₂²×C₈	—	7	1	no	—
213	C₂²×C₈	—	7	1	no	—
214	C₂²×C₈	—	7	8	no	—
215	C₂²×C₈	—	7	1	no	—
216	C₂²×C₈	—	7	1	no	—
217	C₂²×C₈	C₄×D₇	1	1	yes	characteristic
218	C₂²×C₈	C₂²×D₇	1	1	yes	characteristic
219	C₂×C₄²	—	7	2	no	—
220	C₂×C₄²	—	7	1	no	—
221	C₂×C₄²	—	7	2	no	—
222	C₂×C₄²	—	7	2	no	—
223	C₂×C₄²	—	7	1	no	—
224	C₂×C₄²	—	7	1	no	—
225	C₂×C₄²	—	7	1	no	—
226	C₂×C₄²	—	7	1	no	—
227	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
228	M₃₂	—	7	8	no	—
229	M₃₂	—	7	16	no	—
230	M₃₂	C₄×D₇	1	8	yes	direct product factor
231	C₂×C₁₆	—	7	4	no	—
232	C₂×C₁₆	—	7	16	no	—
233	C₂×C₁₆	C₂²×D₇	1	4	yes	—
234	C₄×C₈	—	7	1	no	—
235	C₄×C₈	—	7	1	no	—
236	C₄×C₈	—	7	1	no	—
237	C₄×C₈	—	7	1	no	—
238	C₄×C₈	—	7	1	no	—
239	C₄×C₈	—	7	1	no	—
240	C₄×C₈	—	7	1	no	—
241	C₄×C₈	—	7	1	no	—
242	C₄×C₈	—	7	1	no	—
243	C₄×C₈	—	7	1	no	—
244	C₄×C₈	—	7	1	no	—
245	C₄×C₈	—	7	1	no	—
246	C₄×C₈	C₄×D₇	1	1	yes	characteristic
247	C₄×C₈	C₄×D₇	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
249	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
250	C₂²×C₇	—	2	2	no	—
251	C₂²×C₇	C₂×C₄×C₈	1	2	yes	—
252	C₂²×C₇	C₂³×C₈	1	1	yes	characteristic
253	C₂×D₇	—	2	2	no	—
254	C₂×D₇	—	2	8	no	—
255	C₂×D₇	C₂×C₄×C₈	1	2	yes	—
256	C₂×D₇	C₂×C₄×C₈	1	2	yes	—
257	C₂×D₇	C₂×M₃₂	1	4	yes	—
258	C₄×C₇	—	2	2	no	—
259	C₄×C₇	C₂×C₄×C₈	1	2	yes	—
260	C₄×C₇	C₂×M₃₂	1	4	yes	complemented
261	C₄×C₇	C₂²×C₄²	1	1	yes	characteristic
262	C₄×C₇	C₂³×C₈	1	1	yes	characteristic
263	Dic₇	—	2	2	no	—
264	Dic₇	C₂×C₄×C₈	1	2	yes	—
265	Dic₇	C₂×C₄×C₈	1	2	yes	—
266	Dic₇	C₂×M₃₂	1	4	yes	complemented
267	C₂⁴	—	7	1	no	—
268	C₂²×C₄	—	7	1	no	—
269	C₂²×C₄	—	7	4	no	—
270	C₂²×C₄	—	7	2	no	—
271	C₂²×C₄	—	7	1	no	—
272	C₂²×C₄	—	7	1	no	—
273	C₂²×C₄	—	7	4	no	—
274	C₂²×C₄	—	7	1	no	—
275	C₂²×C₄	—	7	1	no	—
276	C₂²×C₄	—	7	2	no	—
277	C₂²×C₄	—	7	2	no	—
278	C₂²×C₄	—	7	2	no	—
279	C₂²×C₄	—	7	2	no	—
280	C₂²×C₄	—	14	8	no	—
281	C₂²×C₄	C₈×D₇	1	2	yes	—
282	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
283	C₂×C₈	—	7	4	no	—
284	C₂×C₈	—	7	4	no	—
285	C₂×C₈	—	7	1	no	—
286	C₂×C₈	—	7	1	no	—
287	C₂×C₈	—	7	1	no	—
288	C₂×C₈	—	7	1	no	—
289	C₂×C₈	—	7	4	no	—
290	C₂×C₈	—	7	4	no	—
291	C₂×C₈	—	7	4	no	—
292	C₂×C₈	—	7	4	no	—
293	C₂×C₈	—	7	4	no	—
294	C₂×C₈	—	7	4	no	—
295	C₂×C₈	—	7	4	no	—
296	C₂×C₈	—	7	4	no	—
297	C₂×C₈	C₈×D₇	1	4	yes	—
298	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
299	C₂×C₈	C₂×C₄×D₇	1	4	yes	—
300	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
301	C₂×C₈	C₂×C₄×D₇	1	1	yes	characteristic
302	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
303	C₄²	—	7	2	no	—
304	C₄²	—	7	2	no	—
305	C₄²	—	7	2	no	—
306	C₄²	—	7	2	no	—
307	C₄²	—	7	2	no	—
308	C₄²	—	7	1	no	—
309	C₄²	—	7	1	no	—
310	C₄²	C₈×D₇	1	2	yes	—
311	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
312	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
313	C₁₆	—	7	8	no	—
314	C₁₆	C₂×C₄×D₇	1	8	yes	complemented
315	C₂×C₇	—	2	2	no	—
316	C₂×C₇	C₂²×C₄×C₈	1	1	yes	characteristic
317	C₂×C₇	C₂²×M₃₂	1	2	yes	—
318	D₇	—	2	2	no	—
319	D₇	C₄×M₃₂	1	4	yes	direct product factor
320	C₂³	—	7	1	no	—
321	C₂³	—	7	1	no	—
322	C₂³	—	7	4	no	—
323	C₂³	—	14	4	no	—
324	C₂³	C₂×C₈×D₇	1	1	yes	characteristic
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	7	2	no	—
327	C₂×C₄	—	7	1	no	—
328	C₂×C₄	—	7	1	no	—
329	C₂×C₄	—	7	4	no	—
330	C₂×C₄	—	7	2	no	—
331	C₂×C₄	—	7	2	no	—
332	C₂×C₄	—	7	2	no	—
333	C₂×C₄	—	7	2	no	—
334	C₂×C₄	—	7	8	no	—
335	C₂×C₄	—	7	4	no	—
336	C₂×C₄	—	7	4	no	—
337	C₂×C₄	—	7	2	no	—
338	C₂×C₄	—	14	4	no	—
339	C₂×C₄	—	14	4	no	—
340	C₂×C₄	—	14	4	no	—
341	C₂×C₄	—	14	4	no	—
342	C₂×C₄	C₄²×D₇	1	2	yes	—
343	C₂×C₄	C₂×C₈×D₇	1	2	yes	—
344	C₂×C₄	C₂×C₈×D₇	1	2	yes	—
345	C₂×C₄	C₂×C₈×D₇	1	2	yes	—
346	C₂×C₄	C₂×C₈×D₇	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
348	C₈	—	7	2	no	—
349	C₈	—	7	2	no	—
350	C₈	—	7	2	no	—
351	C₈	—	7	2	no	—
352	C₈	C₄²×D₇	1	2	yes	—
353	C₈	C₂×C₈×D₇	1	2	yes	—
354	C₈	C₂×C₈×D₇	1	2	yes	—
355	C₈	C₂²×C₄×D₇	1	2	yes	—
356	C₇	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
357	C₂²	—	2	2	no	—
358	C₂²	—	7	4	no	—
359	C₂²	—	7	2	no	—
360	C₂²	—	7	2	no	—
361	C₂²	—	14	8	no	—
362	C₂²	—	14	2	no	—
363	C₂²	C₄×C₈×D₇	1	2	yes	—
364	C₂²	C₂²×C₈×D₇	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	7	4	no	—
367	C₄	—	7	2	no	—
368	C₄	—	7	2	no	—
369	C₄	—	14	2	no	—
370	C₄	C₄×C₈×D₇	1	2	yes	—
371	C₄	D₇×M₃₂	1	4	yes	direct product factor
372	C₄	C₂×C₄²×D₇	1	1	yes	characteristic
373	C₄	C₂²×C₈×D₇	1	1	yes	characteristic
374	C₂	—	2	2	no	—
375	C₂	—	7	4	no	—
376	C₂	—	14	2	no	—
377	C₂	C₂×C₄×C₈×D₇	1	1	yes	characteristic
378	C₂	C₂×D₇×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂²×D₇
commutator	C₂×C₇	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₇
Fitting	C₄×C₇×M₃₂	C₂
socle	C₂²×C₇	C₂³×C₈
prime radical	C₂³×D₇	C₂×C₈
cosocle	C₂×C₇×C₈	C₂⁴
hypercenter	C₄×M₃₂	D₇
hypocenter	C₇	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. C₄×C₇×M₃₂	C₂	semidirect
4. Dic₇×M₃₂	C₂	semidirect
5. C₄×#6386	C₂	semidirect
6. #11726825	C₂	semidirect
7. D₇×#346	C₂	semidirect
8. C₄×#6372	C₂	semidirect
9. C₄×D₇×C₁₆	C₂	semidirect
19. D₇×M₃₂	C₄	direct (N × H)
30. C₇×#346	C₂²	semidirect
31. C₄×C₇×C₁₆	C₂²	semidirect
32. #89297	C₂²	semidirect
33. C₁₆×Dic₇	C₂²	semidirect
34. #89256	C₂²	semidirect
35. C₄×C₇⋊C₁₆	C₂²	semidirect
62. C₇×M₃₂	C₂×C₄	semidirect
76. #6386	C₂×C₄	semidirect
82. #6372	C₂×C₄	semidirect
83. D₇×C₁₆	C₂×C₄	semidirect
90. C₄×M₃₂	D₇	direct (N × H)
139. C₇×C₁₆	C₂²×C₄	semidirect
140. C₇⋊C₁₆	C₂²×C₄	semidirect
163. #346	C₂×D₇	semidirect
166. C₄×C₁₆	C₂×D₇	semidirect
190. C₄×D₇	M₃₂	direct (N × H)
230. M₃₂	C₄×D₇	direct (N × H)
260. C₄×C₇	C₂×M₃₂	semidirect
266. Dic₇	C₂×M₃₂	semidirect
314. C₁₆	C₂×C₄×D₇	semidirect
319. D₇	C₄×M₃₂	direct (N × H)
356. C₇	C₂×C₄×M₃₂	semidirect
371. C₄	D₇×M₃₂	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×D₇×M₃₂	2
C₂×C₄×C₈×D₇	2
C₄×C₇×M₃₂	2
Dic₇×M₃₂	2
C₄×#6386	2
#11726825	2
D₇×#346	2
C₄×#6372	2
C₄×D₇×C₁₆	2
C₂×C₄×M₃₂	7

Subgroups — C4×D7×M32 #13506423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₇×M₃₂ #13506423