Subgroups — C₂×C₇×D₄×Q₁₆ #13238262

Order 1792.

2742 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×Q₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×D₄×Q₈	C₂	1	2	yes	maximal
3	C₇×D₄×Q₁₆	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#451	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₇×Q₈	C₂²	1	4	yes	—
11	C₂²×C₇×Q₁₆	—	2	16	no	—
12	C₂²×C₇×Q₁₆	C₂²	1	4	yes	—
13	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₇×Q₁₆	C₂²	1	16	yes	complemented
17	C₂³×C₇×C₈	C₂²	1	2	yes	—
18	C₇×D₄×Q₈	—	2	8	no	—
19	C₇×D₄×Q₈	C₂²	1	16	yes	—
20	C₂×C₇×C₄⋊Q₈	—	2	2	no	—
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	—	2	4	no	—
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×D₄	—	2	2	no	—
26	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
27	C₇×#494	C₂²	1	8	yes	complemented
28	C₇×#467	C₂²	1	16	yes	complemented
29	C₇×#462	C₂²	1	16	yes	complemented
30	C₇×#451	C₂²	1	32	yes	complemented
31	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
32	C₇×C₈×D₄	C₂²	1	8	yes	—
33	C₂×C₇×#107	C₂²	1	1	yes	characteristic
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₇×#103	C₂²	1	2	yes	—
36	C₂×C₇×#103	C₂²	1	4	yes	—
37	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
39	C₂×D₄×Q₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₇×Q₈	—	2	4	no	—
41	C₂²×C₇×Q₈	—	2	8	no	—
42	C₂²×C₇×Q₈	—	2	16	no	—
43	C₂²×C₇×Q₈	—	4	8	no	—
44	C₂²×C₇×Q₈	C₂³	1	4	yes	—
45	C₂²×C₇×Q₈	C₂³	1	16	yes	—
46	C₂²×C₇×Q₈	C₂³	1	2	yes	—
47	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	—	2	4	no	—
49	C₂³×C₄×C₇	C₂³	1	2	yes	—
50	C₂×C₇×Q₁₆	—	2	16	no	—
51	C₂×C₇×Q₁₆	—	2	64	no	—
52	C₂×C₇×Q₁₆	—	2	8	no	—
53	C₂×C₇×Q₁₆	—	4	4	no	—
54	C₂×C₇×Q₁₆	D₄	1	8	yes	direct product factor
55	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
56	C₂×C₇×Q₁₆	C₂³	1	16	yes	—
57	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
58	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
59	C₂²×C₇×C₈	—	2	8	no	—
60	C₂²×C₇×C₈	C₂³	1	8	yes	—
61	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×C₈	C₂³	1	2	yes	—
63	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
64	C₇×C₄⋊Q₈	—	2	16	no	—
65	C₇×C₄⋊Q₈	—	2	4	no	—
66	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₇×C₂²⋊Q₈	—	2	8	no	—
68	C₇×C₂²⋊Q₈	—	2	32	no	—
69	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
70	C₄×C₇×Q₈	—	2	4	no	—
71	C₄×C₇×Q₈	C₂³	1	8	yes	—
72	C₄×C₇×D₄	—	2	16	no	—
73	C₄×C₇×D₄	D₄	1	4	yes	—
74	C₄×C₇×D₄	C₂³	1	4	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	2	no	—
76	C₂×C₇×C₄⋊C₄	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	4	no	—
79	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
82	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
83	C₂×C₄²×C₇	—	2	2	no	—
84	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
85	C₇×#107	C₂³	1	4	yes	—
86	C₇×C₄⋊C₈	C₂³	1	4	yes	—
87	C₇×#103	C₂³	1	16	yes	—
88	C₇×#103	C₂³	1	8	yes	—
89	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
90	C₄×C₇×C₈	C₂³	1	4	yes	—
91	C₂³×Q₁₆	C₂×C₇	1	2	yes	complemented
92	C₂×D₄×Q₈	C₂×C₇	1	2	yes	—
93	D₄×Q₁₆	C₂×C₇	1	16	yes	direct product factor
94	C₂×#494	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂×#467	C₂×C₇	1	2	yes	complemented
96	C₂×#462	C₂×C₇	1	2	yes	complemented
97	C₂×#451	C₂×C₇	1	4	yes	complemented
98	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
100	C₂⁴×C₇	C₂×D₄	1	2	yes	—
101	C₂×C₇×Q₈	—	2	2	no	—
102	C₂×C₇×Q₈	—	2	16	no	—
103	C₂×C₇×Q₈	—	2	4	no	—
104	C₂×C₇×Q₈	—	2	4	no	—
105	C₂×C₇×Q₈	—	2	32	no	—
106	C₂×C₇×Q₈	—	2	8	no	—
107	C₂×C₇×Q₈	—	2	8	no	—
108	C₂×C₇×Q₈	—	4	16	no	—
109	C₂×C₇×Q₈	—	4	16	no	—
110	C₂×C₇×Q₈	—	4	32	no	—
111	C₂×C₇×Q₈	C₂×D₄	1	8	yes	—
112	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
113	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
114	C₂×C₇×D₄	Q₁₆	1	8	yes	direct product factor
115	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
116	C₂²×C₄×C₇	—	2	2	no	—
117	C₂²×C₄×C₇	—	2	4	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	16	no	—
120	C₂²×C₄×C₇	—	2	2	no	—
121	C₂²×C₄×C₇	—	2	4	no	—
122	C₂²×C₄×C₇	—	4	16	no	—
123	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
129	C₇×Q₁₆	—	2	32	no	—
130	C₇×Q₁₆	—	2	16	no	—
131	C₇×Q₁₆	—	4	8	no	—
132	C₇×Q₁₆	C₂×D₄	1	16	yes	direct product factor
133	C₂×C₇×C₈	—	2	4	no	—
134	C₂×C₇×C₈	—	2	2	no	—
135	C₂×C₇×C₈	—	2	16	no	—
136	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
137	C₂×C₇×C₈	C₂⁴	1	2	yes	—
138	C₂×C₇×C₈	C₂⁴	1	4	yes	—
139	C₂×C₇×C₈	C₂⁴	1	2	yes	—
140	C₇×C₄⋊C₄	—	2	8	no	—
141	C₇×C₄⋊C₄	—	2	8	no	—
142	C₇×C₄⋊C₄	—	2	8	no	—
143	C₇×C₄⋊C₄	—	2	16	no	—
144	C₇×C₄⋊C₄	—	2	2	no	—
145	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
146	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
147	C₇×C₂²⋊C₄	—	2	16	no	—
148	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
149	C₄²×C₇	—	2	8	no	—
150	C₄²×C₇	C₂×D₄	1	2	yes	—
151	C₄²×C₇	C₂⁴	1	2	yes	—
152	C₂³×Q₈	C₂²×C₇	1	4	yes	—
153	C₂²×Q₁₆	—	2	16	no	—
154	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
155	C₂²×Q₁₆	C₂²×C₇	1	4	yes	—
156	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
157	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
158	C₂²×Q₁₆	C₂²×C₇	1	16	yes	complemented
159	C₂³×C₈	C₂²×C₇	1	2	yes	—
160	D₄×Q₈	—	2	8	no	—
161	D₄×Q₈	C₂²×C₇	1	16	yes	—
162	C₂×C₄⋊Q₈	—	2	2	no	—
163	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
164	C₂×C₂²⋊Q₈	—	2	4	no	—
165	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
166	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
167	C₂×C₄×D₄	—	2	2	no	—
168	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
169	#494	C₂²×C₇	1	8	yes	complemented
170	#467	C₂²×C₇	1	16	yes	complemented
171	#462	C₂²×C₇	1	16	yes	complemented
172	#451	C₂²×C₇	1	32	yes	complemented
173	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
174	C₈×D₄	C₂²×C₇	1	8	yes	—
175	C₂×#107	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
177	C₂×#103	C₂²×C₇	1	2	yes	—
178	C₂×#103	C₂²×C₇	1	4	yes	—
179	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
180	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂³×C₇	—	2	4	no	—
182	C₂³×C₇	—	2	4	no	—
183	C₂³×C₇	C₂×Q₁₆	1	8	yes	complemented
184	C₂³×C₇	C₂²×D₄	1	4	yes	—
185	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₇×Q₈	—	2	8	no	—
187	C₇×Q₈	—	2	4	no	—
188	C₇×Q₈	—	2	8	no	—
189	C₇×Q₈	—	2	8	no	—
190	C₇×Q₈	—	4	32	no	—
191	C₇×Q₈	—	4	8	no	—
192	C₇×Q₈	C₂²×D₄	1	8	yes	—
193	C₇×D₄	C₂×Q₁₆	1	16	yes	direct product factor
194	C₂×C₄×C₇	—	2	4	no	—
195	C₂×C₄×C₇	—	2	8	no	—
196	C₂×C₄×C₇	—	2	2	no	—
197	C₂×C₄×C₇	—	2	4	no	—
198	C₂×C₄×C₇	—	2	8	no	—
199	C₂×C₄×C₇	—	2	4	no	—
200	C₂×C₄×C₇	—	2	4	no	—
201	C₂×C₄×C₇	—	2	4	no	—
202	C₂×C₄×C₇	—	2	8	no	—
203	C₂×C₄×C₇	—	4	32	no	—
204	C₂×C₄×C₇	—	4	8	no	—
205	C₂×C₄×C₇	—	4	4	no	—
206	C₂×C₄×C₇	C₂×Q₁₆	1	4	yes	complemented
207	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
209	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
214	C₇×C₈	—	2	4	no	—
215	C₇×C₈	—	2	2	no	—
216	C₇×C₈	C₂²×D₄	1	4	yes	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	—	2	8	no	—
219	C₂²×Q₈	—	2	16	no	—
220	C₂²×Q₈	—	4	8	no	—
221	C₂²×Q₈	C₂³×C₇	1	4	yes	—
222	C₂²×Q₈	C₂³×C₇	1	16	yes	—
223	C₂²×Q₈	C₂³×C₇	1	2	yes	—
224	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
225	C₂³×C₄	—	2	4	no	—
226	C₂³×C₄	C₂³×C₇	1	2	yes	—
227	C₂×Q₁₆	—	2	16	no	—
228	C₂×Q₁₆	—	2	64	no	—
229	C₂×Q₁₆	—	2	8	no	—
230	C₂×Q₁₆	—	4	4	no	—
231	C₂×Q₁₆	C₇×D₄	1	8	yes	direct product factor
232	C₂×Q₁₆	C₂³×C₇	1	16	yes	—
233	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
234	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
235	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
236	C₂²×C₈	—	2	8	no	—
237	C₂²×C₈	C₂³×C₇	1	2	yes	—
238	C₂²×C₈	C₂³×C₇	1	8	yes	—
239	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	16	no	—
242	C₄⋊Q₈	—	2	4	no	—
243	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
244	C₂²⋊Q₈	—	2	8	no	—
245	C₂²⋊Q₈	—	2	32	no	—
246	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	C₂³×C₇	1	8	yes	—
249	C₄×D₄	—	2	16	no	—
250	C₄×D₄	C₇×D₄	1	4	yes	—
251	C₄×D₄	C₂³×C₇	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
262	#107	C₂³×C₇	1	4	yes	—
263	C₄⋊C₈	C₂³×C₇	1	4	yes	—
264	#103	C₂³×C₇	1	8	yes	—
265	#103	C₂³×C₇	1	16	yes	—
266	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
267	C₄×C₈	C₂³×C₇	1	4	yes	—
268	C₂²×C₇	—	2	4	no	—
269	C₂²×C₇	—	2	16	no	—
270	C₂²×C₇	—	2	4	no	—
271	C₂²×C₇	D₄²	1	2	yes	—
272	C₂²×C₇	C₂²×Q₁₆	1	2	yes	—
273	C₂²×C₇	C₂²×Q₁₆	1	8	yes	complemented
274	C₂²×C₇	#578	1	2	yes	—
275	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
276	C₄×C₇	—	2	4	no	—
277	C₄×C₇	—	2	8	no	—
278	C₄×C₇	—	2	2	no	—
279	C₄×C₇	—	4	8	no	—
280	C₄×C₇	—	4	4	no	—
281	C₄×C₇	D₄²	1	2	yes	—
282	C₄×C₇	C₂²×Q₁₆	1	4	yes	complemented
283	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₂⁴	C₂×C₇×D₄	1	2	yes	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	16	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	32	no	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	4	16	no	—
294	C₂×Q₈	—	4	16	no	—
295	C₂×Q₈	—	4	32	no	—
296	C₂×Q₈	C₂×C₇×D₄	1	8	yes	—
297	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
298	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
299	C₂×D₄	C₇×Q₁₆	1	8	yes	direct product factor
300	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	4	16	no	—
308	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
310	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
311	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
313	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
314	Q₁₆	—	2	32	no	—
315	Q₁₆	—	2	16	no	—
316	Q₁₆	—	4	8	no	—
317	Q₁₆	C₂×C₇×D₄	1	16	yes	direct product factor
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	16	no	—
321	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
322	C₂×C₈	C₂⁴×C₇	1	2	yes	—
323	C₂×C₈	C₂⁴×C₇	1	4	yes	—
324	C₂×C₈	C₂⁴×C₇	1	2	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
331	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
332	C₂²⋊C₄	—	2	16	no	—
333	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
334	C₄²	—	2	8	no	—
335	C₄²	C₂×C₇×D₄	1	2	yes	—
336	C₄²	C₂⁴×C₇	1	2	yes	—
337	C₂×C₇	—	2	8	no	—
338	C₂×C₇	D₄×Q₁₆	1	4	yes	direct product factor
339	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
340	C₂×C₇	C₂³×Q₁₆	1	1	yes	characteristic
341	C₂×C₇	C₂×#578	1	1	yes	characteristic
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	C₂×C₇×Q₁₆	1	8	yes	complemented
345	C₂³	C₂²×C₇×D₄	1	4	yes	—
346	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	8	no	—
349	Q₈	—	2	8	no	—
350	Q₈	—	2	8	no	—
351	Q₈	—	4	32	no	—
352	Q₈	—	4	8	no	—
353	Q₈	C₂²×C₇×D₄	1	8	yes	—
354	D₄	C₂×C₇×Q₁₆	1	16	yes	direct product factor
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	4	32	no	—
365	C₂×C₄	—	4	8	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	C₂×C₇×Q₁₆	1	4	yes	complemented
368	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
369	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
370	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
371	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
373	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
374	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	2	no	—
377	C₈	C₂²×C₇×D₄	1	4	yes	—
378	C₇	C₂×D₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	4	no	—
380	C₂²	—	2	16	no	—
381	C₂²	—	2	4	no	—
382	C₂²	C₇×D₄²	1	2	yes	—
383	C₂²	C₂²×C₇×Q₁₆	1	2	yes	—
384	C₂²	C₂²×C₇×Q₁₆	1	8	yes	complemented
385	C₂²	C₇×#578	1	2	yes	—
386	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	8	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	8	no	—
392	C₄	C₇×D₄²	1	2	yes	—
393	C₄	C₂²×C₇×Q₁₆	1	4	yes	complemented
394	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
395	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂	—	2	8	no	—
397	C₂	C₇×D₄×Q₁₆	1	4	yes	direct product factor
398	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
399	C₂	C₂³×C₇×Q₁₆	1	1	yes	characteristic
400	C₂	C₂×C₇×#578	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×Q₁₆	C₂	semidirect
3. C₇×D₄×Q₁₆	C₂	direct (N × H)
4. C₂×C₇×#494	C₂	semidirect
5. C₂×C₇×#467	C₂	semidirect
6. C₂×C₇×#462	C₂	semidirect
7. C₂×C₇×#451	C₂	semidirect
8. C₂×C₄×C₇×Q₁₆	C₂	semidirect
16. C₂²×C₇×Q₁₆	C₂²	semidirect
27. C₇×#494	C₂²	semidirect
28. C₇×#467	C₂²	semidirect
29. C₇×#462	C₂²	semidirect
30. C₇×#451	C₂²	semidirect
31. C₄×C₇×Q₁₆	C₂²	semidirect
39. C₂×D₄×Q₁₆	C₇	direct (N × H)
54. C₂×C₇×Q₁₆	D₄	direct (N × H)
91. C₂³×Q₁₆	C₂×C₇	semidirect
93. D₄×Q₁₆	C₂×C₇	direct (N × H)
94. C₂×#494	C₂×C₇	semidirect
95. C₂×#467	C₂×C₇	semidirect
96. C₂×#462	C₂×C₇	semidirect
97. C₂×#451	C₂×C₇	semidirect
98. C₂×C₄×Q₁₆	C₂×C₇	semidirect
114. C₂×C₇×D₄	Q₁₆	direct (N × H)
132. C₇×Q₁₆	C₂×D₄	direct (N × H)
158. C₂²×Q₁₆	C₂²×C₇	semidirect
169. #494	C₂²×C₇	semidirect
170. #467	C₂²×C₇	semidirect
171. #462	C₂²×C₇	semidirect
172. #451	C₂²×C₇	semidirect
173. C₄×Q₁₆	C₂²×C₇	semidirect
183. C₂³×C₇	C₂×Q₁₆	semidirect
193. C₇×D₄	C₂×Q₁₆	direct (N × H)
206. C₂×C₄×C₇	C₂×Q₁₆	semidirect
231. C₂×Q₁₆	C₇×D₄	direct (N × H)
273. C₂²×C₇	C₂²×Q₁₆	semidirect
282. C₄×C₇	C₂²×Q₁₆	semidirect
299. C₂×D₄	C₇×Q₁₆	direct (N × H)
317. Q₁₆	C₂×C₇×D₄	direct (N × H)
338. C₂×C₇	D₄×Q₁₆	direct (N × H)
344. C₂³	C₂×C₇×Q₁₆	semidirect
354. D₄	C₂×C₇×Q₁₆	direct (N × H)
367. C₂×C₄	C₂×C₇×Q₁₆	semidirect
378. C₇	C₂×D₄×Q₁₆	direct (N × H)
384. C₂²	C₂²×C₇×Q₁₆	semidirect
393. C₄	C₂²×C₇×Q₁₆	semidirect
397. C₂	C₇×D₄×Q₁₆	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×Q₁₆	2
C₂×C₇×D₄×Q₈	2
C₇×D₄×Q₁₆	2
C₂×C₇×#494	2
C₂×C₇×#467	2
C₂×C₇×#462	2
C₂×C₇×#451	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×C₈×D₄	2
C₂×D₄×Q₁₆	7

Subgroups — C2×C7×D4×Q16 #13238262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₄×Q₁₆ #13238262