Subgroups — C₇×C₄⋊C₄×SD₁₆ #13199897

Order 1792.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×Q₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₄×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₇×#1941	C₂	1	2	yes	maximal, complemented
6	C₇×#1865	C₂	1	2	yes	maximal, complemented
7	C₇×#1864	C₂	1	2	yes	maximal
8	C₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1802	C₂	1	1	yes	maximal, characteristic
11	C₇×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
16	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
17	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
18	C₄×C₇×SD₁₆	—	2	8	no	—
19	C₄×C₇×SD₁₆	C₄	1	8	yes	complemented
20	C₂×C₇×#106	C₂²	1	2	yes	—
21	C₂×C₇×#106	C₂²	1	2	yes	—
22	C₂×C₇×#106	C₂²	1	1	yes	characteristic
23	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×#103	C₂²	1	2	yes	—
25	C₂×C₇×#103	C₂²	1	1	yes	characteristic
26	C₂×C₇×#102	C₂²	1	2	yes	—
27	C₂×C₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₇×#389	—	2	2	no	—
31	C₇×#389	C₂²	1	2	yes	—
32	C₇×#389	C₂²	1	2	yes	—
33	C₇×#385	—	2	2	no	—
34	C₇×#384	—	2	1	no	—
35	C₇×#384	C₂²	1	1	yes	characteristic
36	C₇×#384	C₂²	1	1	yes	characteristic
37	C₇×#380	—	2	1	no	—
38	C₄×C₇×C₄⋊C₄	—	2	1	no	—
39	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₇×#340	C₂²	1	2	yes	—
41	C₇×#340	C₂²	1	2	yes	—
42	C₇×#336	C₂²	1	2	yes	—
43	C₄⋊C₄×SD₁₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
45	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇	—	2	1	no	—
47	C₂³×C₄×C₇	—	2	2	no	—
48	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	—
49	C₂×C₇×SD₁₆	D₄	1	4	yes	—
50	C₂×C₇×SD₁₆	Q₈	1	4	yes	—
51	C₂²×C₇×C₈	C₂³	1	2	yes	—
52	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₄×C₇×Q₈	—	2	2	no	—
55	C₄×C₇×Q₈	—	2	4	no	—
56	C₄×C₇×Q₈	—	4	2	no	—
57	C₄×C₇×Q₈	C₂×C₄	1	4	yes	complemented
58	C₄×C₇×D₄	—	2	4	no	—
59	C₄×C₇×D₄	—	2	2	no	—
60	C₄×C₇×D₄	—	4	2	no	—
61	C₄×C₇×D₄	C₂×C₄	1	4	yes	—
62	C₂×C₇×C₄⋊C₄	—	2	1	no	—
63	C₂×C₇×C₄⋊C₄	—	2	1	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	1	no	—
66	C₂×C₇×C₄⋊C₄	—	2	2	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	—	2	1	no	—
69	C₂×C₇×C₄⋊C₄	—	2	1	no	—
70	C₂×C₇×C₄⋊C₄	—	4	4	no	—
71	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₄²×C₇	—	2	1	no	—
80	C₂×C₄²×C₇	—	2	2	no	—
81	C₂×C₄²×C₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
83	C₇×#106	—	2	4	no	—
84	C₇×#106	—	4	2	no	—
85	C₇×#106	C₂×C₄	1	4	yes	complemented
86	C₇×C₄⋊C₈	—	2	2	no	—
87	C₇×#103	—	2	4	no	—
88	C₇×#103	C₂×C₄	1	4	yes	complemented
89	C₇×#102	—	2	4	no	—
90	C₇×#102	C₂×C₄	1	4	yes	—
91	C₄×C₇×C₈	—	2	4	no	—
92	C₄×C₇×C₈	C₂×C₄	1	4	yes	complemented
93	C₇×#95	—	2	2	no	—
94	C₇×#95	—	2	2	no	—
95	C₇×#95	D₄	1	2	yes	—
96	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	—
97	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic
98	Q₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
99	D₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic
100	#1941	C₂×C₇	1	2	yes	complemented
101	#1865	C₂×C₇	1	2	yes	complemented
102	#1864	C₂×C₇	1	2	yes	—
103	#1844	C₂×C₇	1	1	yes	characteristic, complemented
104	#1803	C₂×C₇	1	1	yes	characteristic, complemented
105	#1802	C₂×C₇	1	1	yes	characteristic
106	C₈×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
107	C₂⁴×C₇	—	2	1	no	—
108	C₂×C₇×Q₈	—	2	1	no	—
109	C₂×C₇×Q₈	—	2	1	no	—
110	C₂×C₇×Q₈	—	2	1	no	—
111	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
112	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
113	C₂×C₇×Q₈	C₂×Q₈	1	2	yes	—
114	C₂×C₇×D₄	—	2	1	no	—
115	C₂×C₇×D₄	—	2	1	no	—
116	C₂×C₇×D₄	—	2	1	no	—
117	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
118	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
119	C₂×C₇×D₄	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₇	—	2	1	no	—
121	C₂²×C₄×C₇	—	2	1	no	—
122	C₂²×C₄×C₇	—	2	1	no	—
123	C₂²×C₄×C₇	—	2	4	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	4	4	no	—
127	C₂²×C₄×C₇	—	4	2	no	—
128	C₂²×C₄×C₇	—	4	2	no	—
129	C₂²×C₄×C₇	—	4	4	no	—
130	C₂²×C₄×C₇	—	8	2	no	—
131	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
136	C₇×SD₁₆	C₄⋊C₄	1	16	yes	direct product factor
137	C₂×C₇×C₈	—	2	1	no	—
138	C₂×C₇×C₈	—	2	1	no	—
139	C₂×C₇×C₈	—	2	2	no	—
140	C₂×C₇×C₈	—	2	2	no	—
141	C₂×C₇×C₈	—	2	2	no	—
142	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
143	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
146	C₇×C₄⋊C₄	—	2	4	no	—
147	C₇×C₄⋊C₄	—	2	2	no	—
148	C₇×C₄⋊C₄	—	2	1	no	—
149	C₇×C₄⋊C₄	—	2	1	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	—	2	2	no	—
154	C₇×C₄⋊C₄	—	4	4	no	—
155	C₇×C₄⋊C₄	—	4	4	no	—
156	C₇×C₄⋊C₄	—	4	2	no	—
157	C₇×C₄⋊C₄	—	4	2	no	—
158	C₇×C₄⋊C₄	—	8	1	no	—
159	C₇×C₄⋊C₄	—	8	1	no	—
160	C₇×C₄⋊C₄	—	8	2	no	—
161	C₇×C₄⋊C₄	SD₁₆	1	4	yes	direct product factor
162	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
163	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
164	C₇×C₂²⋊C₄	—	2	4	no	—
165	C₇×C₂²⋊C₄	—	4	4	no	—
166	C₄²×C₇	—	2	4	no	—
167	C₄²×C₇	—	2	2	no	—
168	C₄²×C₇	—	2	2	no	—
169	C₄²×C₇	—	4	4	no	—
170	C₄²×C₇	C₂²×C₄	1	2	yes	—
171	C₄²×C₇	#41	1	2	yes	—
172	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
173	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
174	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
175	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
177	C₂²×C₄⋊C₄	—	2	1	no	—
178	C₄×SD₁₆	—	2	8	no	—
179	C₄×SD₁₆	C₄×C₇	1	8	yes	complemented
180	C₂×#106	C₂²×C₇	1	2	yes	—
181	C₂×#106	C₂²×C₇	1	2	yes	—
182	C₂×#106	C₂²×C₇	1	1	yes	characteristic
183	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
184	C₂×#103	C₂²×C₇	1	2	yes	—
185	C₂×#103	C₂²×C₇	1	1	yes	characteristic
186	C₂×#102	C₂²×C₇	1	2	yes	—
187	C₂×#102	C₂²×C₇	1	1	yes	characteristic
188	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
189	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
190	#389	—	2	2	no	—
191	#389	C₂²×C₇	1	2	yes	—
192	#389	C₂²×C₇	1	2	yes	—
193	#385	—	2	2	no	—
194	#384	—	2	1	no	—
195	#384	C₂²×C₇	1	1	yes	characteristic
196	#384	C₂²×C₇	1	1	yes	characteristic
197	#380	—	2	1	no	—
198	C₄×C₄⋊C₄	—	2	1	no	—
199	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
200	#340	C₂²×C₇	1	2	yes	—
201	#340	C₂²×C₇	1	2	yes	—
202	#336	C₂²×C₇	1	2	yes	—
203	C₂³×C₇	—	2	2	no	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	2	no	—
206	C₂³×C₇	—	4	1	no	—
207	C₂³×C₇	—	4	1	no	—
208	C₂³×C₇	—	4	1	no	—
209	C₂³×C₇	—	4	1	no	—
210	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
211	C₇×Q₈	—	2	2	no	—
212	C₇×Q₈	—	2	2	no	—
213	C₇×Q₈	—	2	2	no	—
214	C₇×Q₈	C₂×C₄⋊C₄	1	4	yes	complemented
215	C₇×D₄	—	2	2	no	—
216	C₇×D₄	—	2	2	no	—
217	C₇×D₄	—	2	2	no	—
218	C₇×D₄	C₂×C₄⋊C₄	1	4	yes	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	2	no	—
223	C₂×C₄×C₇	—	2	1	no	—
224	C₂×C₄×C₇	—	2	1	no	—
225	C₂×C₄×C₇	—	2	2	no	—
226	C₂×C₄×C₇	—	2	2	no	—
227	C₂×C₄×C₇	—	2	2	no	—
228	C₂×C₄×C₇	—	2	2	no	—
229	C₂×C₄×C₇	—	2	2	no	—
230	C₂×C₄×C₇	—	2	2	no	—
231	C₂×C₄×C₇	—	4	1	no	—
232	C₂×C₄×C₇	—	4	1	no	—
233	C₂×C₄×C₇	—	4	1	no	—
234	C₂×C₄×C₇	—	4	1	no	—
235	C₂×C₄×C₇	—	4	8	no	—
236	C₂×C₄×C₇	—	4	2	no	—
237	C₂×C₄×C₇	—	4	2	no	—
238	C₂×C₄×C₇	—	4	2	no	—
239	C₂×C₄×C₇	—	4	2	no	—
240	C₂×C₄×C₇	—	4	2	no	—
241	C₂×C₄×C₇	—	4	2	no	—
242	C₂×C₄×C₇	—	8	8	no	—
243	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
245	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
246	C₂×C₄×C₇	C₂×SD₁₆	1	2	yes	—
247	C₂×C₄×C₇	#135	1	2	yes	—
248	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
251	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
254	C₇×C₈	—	2	2	no	—
255	C₇×C₈	—	4	2	no	—
256	C₇×C₈	C₂×C₄⋊C₄	1	4	yes	complemented
257	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
258	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	—
262	C₂×SD₁₆	C₇×D₄	1	4	yes	—
263	C₂×SD₁₆	C₇×Q₈	1	4	yes	—
264	C₂²×C₈	C₂³×C₇	1	2	yes	—
265	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
267	C₄×Q₈	—	2	2	no	—
268	C₄×Q₈	—	2	4	no	—
269	C₄×Q₈	—	4	2	no	—
270	C₄×Q₈	C₂×C₄×C₇	1	4	yes	complemented
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	4	2	no	—
274	C₄×D₄	C₂×C₄×C₇	1	4	yes	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	4	4	no	—
284	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	C₂³×C₇	1	2	yes	—
295	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
296	#106	—	2	4	no	—
297	#106	—	4	2	no	—
298	#106	C₂×C₄×C₇	1	4	yes	complemented
299	C₄⋊C₈	—	2	2	no	—
300	#103	—	2	4	no	—
301	#103	C₂×C₄×C₇	1	4	yes	complemented
302	#102	—	2	4	no	—
303	#102	C₂×C₄×C₇	1	4	yes	—
304	C₄×C₈	—	2	4	no	—
305	C₄×C₈	C₂×C₄×C₇	1	4	yes	complemented
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	C₇×D₄	1	2	yes	—
309	C₂²×C₇	—	2	4	no	—
310	C₂²×C₇	—	4	2	no	—
311	C₂²×C₇	—	4	2	no	—
312	C₂²×C₇	—	4	2	no	—
313	C₂²×C₇	—	4	2	no	—
314	C₂²×C₇	—	4	2	no	—
315	C₂²×C₇	—	4	2	no	—
316	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
317	C₂²×C₇	D₄²	1	1	yes	characteristic
318	C₂²×C₇	D₄×Q₈	1	1	yes	characteristic
319	C₂²×C₇	C₂²×SD₁₆	1	1	yes	characteristic
320	C₂²×C₇	C₂×#135	1	1	yes	characteristic
321	C₂²×C₇	#577	1	1	yes	characteristic
322	C₂²×C₇	#577	1	1	yes	characteristic
323	C₄×C₇	—	2	4	no	—
324	C₄×C₇	—	2	2	no	—
325	C₄×C₇	—	2	4	no	—
326	C₄×C₇	—	4	2	no	—
327	C₄×C₇	—	4	2	no	—
328	C₄×C₇	—	4	2	no	—
329	C₄×C₇	—	8	2	no	—
330	C₄×C₇	—	8	2	no	—
331	C₄×C₇	C₄×SD₁₆	1	4	yes	complemented
332	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
333	C₄×C₇	#520	1	1	yes	characteristic
334	C₄×C₇	#547	1	1	yes	characteristic
335	C₄×C₇	#554	1	1	yes	characteristic
336	C₂⁴	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
341	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
342	C₂×Q₈	C₂×C₇×Q₈	1	2	yes	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
347	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
348	C₂×D₄	C₂×C₇×Q₈	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	8	2	no	—
360	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
361	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
363	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
365	SD₁₆	C₇×C₄⋊C₄	1	16	yes	direct product factor
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
372	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
373	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
374	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	8	1	no	—
388	C₄⋊C₄	—	8	1	no	—
389	C₄⋊C₄	—	8	2	no	—
390	C₄⋊C₄	C₇×SD₁₆	1	4	yes	direct product factor
391	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
392	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	4	no	—
399	C₄²	C₂²×C₄×C₇	1	2	yes	—
400	C₄²	C₇×#41	1	2	yes	—
401	C₂×C₇	—	4	4	no	—
402	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
403	C₂×C₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
404	C₂×C₇	#2952	1	1	yes	characteristic
405	C₂×C₇	D₄×SD₁₆	1	1	yes	characteristic
406	C₂×C₇	#3284	1	1	yes	characteristic
407	C₂×C₇	Q₈×SD₁₆	1	1	yes	characteristic
408	C₂×C₇	#3381	1	1	yes	characteristic
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	C₂×C₇×C₄⋊C₄	1	4	yes	complemented
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	8	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	8	no	—
449	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
450	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
451	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
452	C₂×C₄	C₂×C₇×SD₁₆	1	2	yes	—
453	C₂×C₄	C₇×#135	1	2	yes	—
454	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
457	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
458	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	4	2	no	—
462	C₈	C₂×C₇×C₄⋊C₄	1	4	yes	complemented
463	C₇	C₄⋊C₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
472	C₂²	C₇×D₄²	1	1	yes	characteristic
473	C₂²	C₇×D₄×Q₈	1	1	yes	characteristic
474	C₂²	C₂²×C₇×SD₁₆	1	1	yes	characteristic
475	C₂²	C₂×C₇×#135	1	1	yes	characteristic
476	C₂²	C₇×#577	1	1	yes	characteristic
477	C₂²	C₇×#577	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	8	2	no	—
485	C₄	—	8	2	no	—
486	C₄	C₄×C₇×SD₁₆	1	4	yes	complemented
487	C₄	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
488	C₄	C₇×#520	1	1	yes	characteristic
489	C₄	C₇×#547	1	1	yes	characteristic
490	C₄	C₇×#554	1	1	yes	characteristic
491	C₂	—	4	4	no	—
492	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
493	C₂	C₂×C₄×C₇×SD₁₆	1	1	yes	characteristic
494	C₂	C₇×#2952	1	1	yes	characteristic
495	C₂	C₇×D₄×SD₁₆	1	1	yes	characteristic
496	C₂	C₇×#3284	1	1	yes	characteristic
497	C₂	C₇×Q₈×SD₁₆	1	1	yes	characteristic
498	C₂	C₇×#3381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₄×C₇×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×Q₈×C₄⋊C₄	C₂	semidirect
5. C₇×#1941	C₂	semidirect
6. C₇×#1865	C₂	semidirect
8. C₇×#1844	C₂	semidirect
9. C₇×#1803	C₂	semidirect
11. C₇×C₈×C₄⋊C₄	C₂	semidirect
19. C₄×C₇×SD₁₆	C₄	semidirect
43. C₄⋊C₄×SD₁₆	C₇	direct (N × H)
57. C₄×C₇×Q₈	C₂×C₄	semidirect
85. C₇×#106	C₂×C₄	semidirect
88. C₇×#103	C₂×C₄	semidirect
92. C₄×C₇×C₈	C₂×C₄	semidirect
98. Q₈×C₄⋊C₄	C₂×C₇	semidirect
100. #1941	C₂×C₇	semidirect
101. #1865	C₂×C₇	semidirect
103. #1844	C₂×C₇	semidirect
104. #1803	C₂×C₇	semidirect
106. C₈×C₄⋊C₄	C₂×C₇	semidirect
136. C₇×SD₁₆	C₄⋊C₄	direct (N × H)
161. C₇×C₄⋊C₄	SD₁₆	direct (N × H)
179. C₄×SD₁₆	C₄×C₇	semidirect
214. C₇×Q₈	C₂×C₄⋊C₄	semidirect
256. C₇×C₈	C₂×C₄⋊C₄	semidirect
270. C₄×Q₈	C₂×C₄×C₇	semidirect
298. #106	C₂×C₄×C₇	semidirect
301. #103	C₂×C₄×C₇	semidirect
305. C₄×C₈	C₂×C₄×C₇	semidirect
331. C₄×C₇	C₄×SD₁₆	semidirect
365. SD₁₆	C₇×C₄⋊C₄	direct (N × H)
390. C₄⋊C₄	C₇×SD₁₆	direct (N × H)
420. Q₈	C₂×C₇×C₄⋊C₄	semidirect
462. C₈	C₂×C₇×C₄⋊C₄	semidirect
463. C₇	C₄⋊C₄×SD₁₆	direct (N × H)
486. C₄	C₄×C₇×SD₁₆	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×SD₁₆	2
C₇×Q₈×C₄⋊C₄	2
C₇×D₄×C₄⋊C₄	2
C₇×#1941	2
C₇×#1865	2
C₇×#1864	2
C₇×#1844	2
C₇×#1803	2
C₇×#1802	2
C₇×C₈×C₄⋊C₄	2
C₄⋊C₄×SD₁₆	7

Subgroups — C7×C4⋊C4×SD16 #13199897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₄⋊C₄×SD₁₆ #13199897