Subgroups — M₁₆×#1136 #13319506

Order 1792.

900 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
2	#11739494	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#1136	C₂	1	1	yes	maximal, characteristic
4	#11727603	C₂	1	4	yes	maximal, complemented
5	#11727601	C₂	1	2	yes	maximal, complemented
6	M₁₆×C₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#11727479	C₂	1	2	yes	maximal, complemented
8	C₈×#1136	C₂	1	2	yes	maximal, complemented
9	C₂²×C₇×M₁₆	C₄	1	2	yes	—
10	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
11	C₂²×#1136	C₄	1	2	yes	—
12	C₄×C₇×M₁₆	C₄	1	2	yes	—
13	C₄×C₇×M₁₆	C₄	1	2	yes	—
14	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
15	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
16	C₄×C₇×M₁₆	C₂²	1	2	yes	—
17	C₂×C₇×#97	C₄	1	2	yes	—
18	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
19	#89979	C₄	1	2	yes	—
20	#89698	C₄	1	2	yes	—
21	#89698	C₄	1	2	yes	—
22	#89697	C₂²	1	2	yes	—
23	#89697	C₂²	1	2	yes	—
24	#89696	C₄	1	2	yes	—
25	C₄×#1136	C₄	1	2	yes	—
26	C₄×#1136	C₄	1	2	yes	—
27	C₄×#1136	C₂²	1	1	yes	characteristic
28	C₄×#1136	C₂²	1	1	yes	characteristic
29	C₄×#1136	C₂²	1	2	yes	—
30	C₄×#1136	C₂²	1	2	yes	—
31	C₂×#6377	C₄	1	2	yes	—
32	C₂×C₄×C₇⋊C₈	C₂²	1	2	yes	—
33	#89250	C₂²	1	4	yes	complemented
34	#89249	C₂²	1	4	yes	complemented
35	#89249	C₂²	1	4	yes	complemented
36	C₈×C₇⋊C₈	C₂²	1	4	yes	complemented
37	M₁₆²	—	7	1	no	maximal, Sylow
38	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇	C₂×C₄	1	1	yes	characteristic
41	C₂×C₇×M₁₆	—	2	8	no	—
42	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
44	C₂×C₇×M₁₆	C₂×C₄	1	2	yes	—
45	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
58	C₂×#1136	—	2	8	no	—
59	C₂×#1136	C₂×C₄	1	2	yes	—
60	C₂×#1136	C₂×C₄	1	4	yes	—
61	C₂×#1136	C₂×C₄	1	4	yes	—
62	C₂×#1136	C₂×C₄	1	2	yes	—
63	C₂²×C₇⋊C₈	C₂×C₄	1	4	yes	—
64	C₇×#97	C₂×C₄	1	2	yes	—
65	C₇×#97	C₂×C₄	1	4	yes	—
66	C₇×#97	C₂×C₄	1	2	yes	—
67	C₄×C₇×C₈	C₂×C₄	1	4	yes	—
68	C₄×C₇×C₈	C₂³	1	2	yes	—
69	C₄×C₇×C₈	C₂³	1	2	yes	—
70	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
71	C₂²⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
72	C₄⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
73	C₄⋊(C₇⋊C₈)	C₂×C₄	1	4	yes	—
74	#6377	C₂×C₄	1	2	yes	—
75	#6377	C₂×C₄	1	4	yes	—
76	#6377	C₂×C₄	1	2	yes	—
77	#6377	C₂×C₄	1	4	yes	—
78	C₄×C₇⋊C₈	C₂×C₄	1	4	yes	—
79	C₄×C₇⋊C₈	C₂³	1	2	yes	—
80	C₄×C₇⋊C₈	C₂³	1	2	yes	—
81	C₄×C₇⋊C₈	C₂³	1	4	yes	—
82	#2920	—	7	1	no	—
83	C₂×C₄×M₁₆	—	7	1	no	—
84	C₂×C₄×M₁₆	D₇	1	1	yes	characteristic
85	#1455	—	7	4	no	—
86	#1451	—	7	2	no	—
87	#1451	—	7	2	no	—
88	C₈×M₁₆	—	7	2	no	—
89	C₈×M₁₆	—	7	2	no	—
90	C₂⁴×C₇	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₇	—	2	4	no	—
92	C₂²×C₄×C₇	—	2	4	no	—
93	C₂²×C₄×C₇	—	4	2	no	—
94	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
97	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
99	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₇	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
112	C₇×M₁₆	—	2	4	no	—
113	C₇×M₁₆	—	2	8	no	—
114	C₇×M₁₆	M₁₆	1	8	yes	complemented
115	C₂×C₇×C₈	—	2	8	no	—
116	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
117	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
118	C₄²×C₇	C₄²	1	1	yes	characteristic
119	C₄²×C₇	C₄²	1	1	yes	characteristic
120	C₄²×C₇	C₄²	1	1	yes	characteristic
121	C₄²×C₇	C₄²	1	1	yes	characteristic
122	C₄²×C₇	C₄²	1	1	yes	characteristic
123	C₄²×C₇	C₄²	1	1	yes	characteristic
124	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇	C₂⁴	1	1	yes	characteristic
134	#1136	—	2	4	no	—
135	#1136	—	2	8	no	—
136	#1136	—	4	4	no	—
137	#1136	M₁₆	1	8	yes	direct product factor
138	C₂×C₇⋊C₈	—	2	8	no	—
139	C₂×C₇⋊C₈	C₂²×C₄	1	8	yes	—
140	C₂×C₇⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂×C₇⋊C₈	C₂²×C₄	1	4	yes	—
142	C₂²×M₁₆	—	7	2	no	—
143	C₂²×M₁₆	Dic₇	1	2	yes	—
144	C₂²×C₄²	C₂×D₇	1	1	yes	characteristic
145	#432	—	7	2	no	—
146	#432	—	7	2	no	—
147	#431	—	7	2	no	—
148	#431	—	7	2	no	—
149	#423	—	7	2	no	—
150	#407	—	7	2	no	—
151	C₄×M₁₆	—	7	2	no	—
152	C₄×M₁₆	—	7	2	no	—
153	C₄×M₁₆	—	7	1	no	—
154	C₄×M₁₆	—	7	1	no	—
155	C₄×M₁₆	—	7	2	no	—
156	C₄×M₁₆	—	7	2	no	—
157	C₄×M₁₆	Dic₇	1	2	yes	—
158	C₄×M₁₆	Dic₇	1	2	yes	—
159	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
160	C₄×M₁₆	C₂×D₇	1	1	yes	characteristic
161	C₄×M₁₆	C₂×D₇	1	2	yes	—
162	C₂×#97	—	7	2	no	—
163	C₂×#97	Dic₇	1	2	yes	—
164	C₂×C₄×C₈	—	7	2	no	—
165	C₂×C₄×C₈	C₂×D₇	1	2	yes	—
166	#322	—	7	4	no	—
167	#322	—	7	4	no	—
168	#322	—	7	4	no	—
169	C₈²	—	7	4	no	—
170	C₂³×C₇	—	2	2	no	—
171	C₂³×C₇	—	2	2	no	—
172	C₂³×C₇	—	4	1	no	—
173	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
174	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
175	C₂³×C₇	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	2	no	—
178	C₂×C₄×C₇	—	2	2	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	2	no	—
184	C₂×C₄×C₇	—	2	2	no	—
185	C₂×C₄×C₇	—	2	2	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	2	no	—
188	C₂×C₄×C₇	—	2	2	no	—
189	C₂×C₄×C₇	—	4	1	no	—
190	C₂×C₄×C₇	—	4	1	no	—
191	C₂×C₄×C₇	—	4	1	no	—
192	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
193	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
194	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
199	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
200	C₂×C₄×C₇	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
202	C₂×C₄×C₇	C₂×M₁₆	1	4	yes	—
203	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
206	C₇×C₈	—	2	4	no	—
207	C₇×C₈	C₂×M₁₆	1	8	yes	complemented
208	C₇⋊C₈	—	2	4	no	—
209	C₇⋊C₈	—	2	8	no	—
210	C₇⋊C₈	C₂×M₁₆	1	8	yes	complemented
211	C₂³×C₄	C₄×D₇	1	1	yes	characteristic
212	C₂³×C₄	C₄×D₇	1	1	yes	characteristic
213	C₂³×C₄	C₂×Dic₇	1	1	yes	characteristic
214	C₂×M₁₆	—	2	8	no	—
215	C₂×M₁₆	—	7	2	no	—
216	C₂×M₁₆	—	7	4	no	—
217	C₂×M₁₆	—	7	2	no	—
218	C₂×M₁₆	—	7	4	no	—
219	C₂×M₁₆	—	14	8	no	—
220	C₂×M₁₆	C₂×Dic₇	1	2	yes	—
221	C₂×M₁₆	C₂×Dic₇	1	4	yes	—
222	C₂×M₁₆	C₂×Dic₇	1	2	yes	—
223	C₂²×C₈	—	7	4	no	—
224	C₂²×C₈	C₂×Dic₇	1	4	yes	—
225	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
229	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
230	C₂×C₄²	C₄×D₇	1	1	yes	characteristic
231	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
232	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
235	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
236	C₂×C₄²	C₂²×D₇	1	1	yes	characteristic
237	C₄⋊C₈	—	7	4	no	—
238	C₄⋊C₈	—	7	4	no	—
239	C₂²⋊C₈	—	7	4	no	—
240	C₂²⋊C₈	—	7	4	no	—
241	#97	—	7	2	no	—
242	#97	—	7	4	no	—
243	#97	—	7	2	no	—
244	#97	—	7	4	no	—
245	#97	C₂×Dic₇	1	2	yes	—
246	#97	C₂×Dic₇	1	4	yes	—
247	#97	C₂×Dic₇	1	2	yes	—
248	C₄×C₈	—	7	4	no	—
249	C₄×C₈	—	7	2	no	—
250	C₄×C₈	—	7	4	no	—
251	C₄×C₈	—	7	2	no	—
252	C₄×C₈	C₂×Dic₇	1	4	yes	—
253	C₄×C₈	C₂²×D₇	1	2	yes	—
254	C₄×C₈	C₂²×D₇	1	2	yes	—
255	C₂²×C₇	—	2	1	no	—
256	C₂²×C₇	—	2	1	no	—
257	C₂²×C₇	—	2	1	no	—
258	C₂²×C₇	—	2	1	no	—
259	C₂²×C₇	—	2	1	no	—
260	C₂²×C₇	—	2	1	no	—
261	C₂²×C₇	—	2	1	no	—
262	C₂²×C₇	—	4	4	no	—
263	C₂²×C₇	C₄×M₁₆	1	2	yes	—
264	C₂²×C₇	C₄×M₁₆	1	2	yes	—
265	C₂²×C₇	C₂²×C₄²	1	1	yes	characteristic
266	C₄×C₇	—	2	1	no	—
267	C₄×C₇	—	2	1	no	—
268	C₄×C₇	—	2	1	no	—
269	C₄×C₇	—	2	1	no	—
270	C₄×C₇	—	2	1	no	—
271	C₄×C₇	—	2	1	no	—
272	C₄×C₇	—	2	1	no	—
273	C₄×C₇	C₄×M₁₆	1	2	yes	—
274	C₄×C₇	C₄×M₁₆	1	2	yes	—
275	C₄×C₇	C₂²×M₁₆	1	2	yes	—
276	C₄×C₇	C₂²×M₁₆	1	2	yes	—
277	C₄×C₇	#568	1	2	yes	—
278	C₂⁴	C₄×Dic₇	1	1	yes	characteristic
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
283	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
284	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₇	1	1	yes	characteristic
297	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
300	M₁₆	—	2	4	no	—
301	M₁₆	—	2	8	no	—
302	M₁₆	—	7	8	no	—
303	M₁₆	—	14	8	no	—
304	M₁₆	—	14	4	no	—
305	M₁₆	—	28	4	no	—
306	M₁₆	#1136	1	8	yes	direct product factor
307	C₂×C₈	—	2	8	no	—
308	C₂×C₈	—	7	4	no	—
309	C₂×C₈	—	7	4	no	—
310	C₂×C₈	—	7	8	no	—
311	C₂×C₈	—	14	8	no	—
312	C₂×C₈	C₂²×Dic₇	1	4	yes	—
313	C₂×C₈	C₂²×Dic₇	1	4	yes	—
314	C₄²	C₄×Dic₇	1	1	yes	characteristic
315	C₄²	C₄×Dic₇	1	1	yes	characteristic
316	C₄²	C₄×Dic₇	1	1	yes	characteristic
317	C₄²	C₄×Dic₇	1	1	yes	characteristic
318	C₄²	C₄×Dic₇	1	1	yes	characteristic
319	C₄²	C₄×Dic₇	1	1	yes	characteristic
320	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
321	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
322	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
324	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
325	C₄²	C₂×C₄×D₇	1	1	yes	characteristic
326	C₄²	C₂²×Dic₇	1	1	yes	characteristic
327	C₄²	C₂²×Dic₇	1	1	yes	characteristic
328	C₄²	C₂²×Dic₇	1	1	yes	characteristic
329	C₄²	C₂³×D₇	1	1	yes	characteristic
330	C₂×C₇	—	2	2	no	—
331	C₂×C₇	—	2	2	no	—
332	C₂×C₇	—	4	1	no	—
333	C₂×C₇	C₂×C₄×M₁₆	1	1	yes	characteristic
334	C₂×C₇	C₂×C₄×M₁₆	1	1	yes	characteristic
335	C₂×C₇	#2873	1	1	yes	characteristic
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	4	1	no	—
339	C₂³	C₂×C₄×Dic₇	1	1	yes	characteristic
340	C₂³	C₂×C₄×Dic₇	1	1	yes	characteristic
341	C₂³	C₂×C₄×Dic₇	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	D₇×M₁₆	1	4	yes	—
359	C₂×C₄	C₂×#1136	1	4	yes	—
360	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
362	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
363	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
365	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
366	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
367	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₇	1	1	yes	characteristic
369	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₇	1	1	yes	characteristic
371	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
372	C₈	—	2	4	no	—
373	C₈	—	7	8	no	—
374	C₈	—	14	4	no	—
375	C₈	—	14	8	no	—
376	C₈	C₂×#1136	1	8	yes	complemented
377	C₇	M₁₆²	1	1	yes	characteristic, complemented, Sylow
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₄×#1136	1	2	yes	—
387	C₂²	M₁₆×Dic₇	1	2	yes	—
388	C₂²	C₂²×C₄×Dic₇	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	C₄×#1136	1	2	yes	—
397	C₄	M₁₆×Dic₇	1	2	yes	—
398	C₄	C₂×D₇×M₁₆	1	2	yes	—
399	C₄	#90436	1	2	yes	—
400	C₄	C₂²×#1136	1	2	yes	—
401	C₂	—	2	2	no	—
402	C₂	—	2	2	no	—
403	C₂	—	4	1	no	—
404	C₂	C₂×C₄×#1136	1	1	yes	characteristic
405	C₂	C₂×M₁₆×Dic₇	1	1	yes	characteristic
406	C₂	#11741192	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₇
commutator, socle	C₂²×C₇	C₂²×C₄²
Fitting	C₂×C₄×C₇×M₁₆	C₂
prime radical	C₂⁴×C₇	C₄²
cosocle	C₄²×C₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₇
hypocenter	C₇	M₁₆²
LCS	G ▷ C₂²×C₇ ▷ C₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11727603	C₂	semidirect
5. #11727601	C₂	semidirect
6. M₁₆×C₇⋊C₈	C₂	semidirect
7. #11727479	C₂	semidirect
8. C₈×#1136	C₂	semidirect
33. #89250	C₂²	semidirect
34. #89249	C₂²	semidirect
35. #89249	C₂²	semidirect
36. C₈×C₇⋊C₈	C₂²	semidirect
114. C₇×M₁₆	M₁₆	semidirect
137. #1136	M₁₆	direct (N × H)
207. C₇×C₈	C₂×M₁₆	semidirect
210. C₇⋊C₈	C₂×M₁₆	semidirect
306. M₁₆	#1136	direct (N × H)
376. C₈	C₂×#1136	semidirect
377. C₇	M₁₆²	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₇×M₁₆	2
#11739494	2
C₂×C₄×#1136	2
#11727603	2
#11727601	2
M₁₆×C₇⋊C₈	2
#11727479	2
C₈×#1136	2
M₁₆²	7

Subgroups — M16×#1136 #13319506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#1136 #13319506