Subgroups — C₂×C₇×D₄×D₈ #13238255

Order 1792.

3710 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×D₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₇×D₄²	C₂	1	2	yes	maximal, complemented
3	C₇×D₄×D₈	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#459	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#447	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₇×D₄	—	2	2	no	—
11	C₂³×C₇×D₄	C₂²	1	4	yes	complemented
12	C₂²×C₇×D₈	—	2	16	no	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₂²×C₇×D₈	C₂²	1	4	yes	complemented
15	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
16	C₂²×C₇×D₈	C₂²	1	2	yes	complemented
17	C₂²×C₇×D₈	C₂²	1	16	yes	complemented
18	C₂³×C₇×C₈	C₂²	1	2	yes	complemented
19	C₇×D₄²	—	2	8	no	—
20	C₇×D₄²	C₂²	1	16	yes	complemented
21	C₂×C₇×#127	C₂²	1	2	yes	complemented
22	C₂×C₇×#121	—	2	2	no	—
23	C₂×C₇×#121	C₂²	1	4	yes	complemented
24	C₂×C₇×#120	—	2	4	no	—
25	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
27	C₇×#493	C₂²	1	8	yes	complemented
28	C₇×#466	C₂²	1	16	yes	complemented
29	C₇×#459	C₂²	1	16	yes	complemented
30	C₇×#447	C₂²	1	32	yes	complemented
31	C₄×C₇×D₈	C₂²	1	8	yes	complemented
32	C₇×C₈×D₄	C₂²	1	8	yes	complemented
33	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₇×#102	C₂²	1	2	yes	complemented
36	C₂×C₇×#102	C₂²	1	4	yes	complemented
37	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	complemented
38	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×D₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁵×C₇	—	2	4	no	—
41	C₂²×C₇×D₄	—	2	16	no	—
42	C₂²×C₇×D₄	—	2	4	no	—
43	C₂²×C₇×D₄	—	2	16	no	—
44	C₂²×C₇×D₄	—	2	2	no	—
45	C₂²×C₇×D₄	—	2	4	no	—
46	C₂²×C₇×D₄	—	2	8	no	—
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂²×C₇×D₄	—	4	8	no	—
49	C₂²×C₇×D₄	—	4	16	no	—
50	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
51	C₂²×C₇×D₄	C₂³	1	4	yes	—
52	C₂²×C₇×D₄	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	C₂³	1	16	yes	complemented
54	C₂³×C₄×C₇	—	2	2	no	—
55	C₂³×C₄×C₇	C₂³	1	2	yes	—
56	C₂×C₇×D₈	—	2	16	no	—
57	C₂×C₇×D₈	—	2	64	no	—
58	C₂×C₇×D₈	—	2	8	no	—
59	C₂×C₇×D₈	—	4	4	no	—
60	C₂×C₇×D₈	D₄	1	8	yes	direct product factor
61	C₂×C₇×D₈	C₂³	1	4	yes	—
62	C₂×C₇×D₈	C₂³	1	8	yes	complemented
63	C₂×C₇×D₈	C₂³	1	16	yes	complemented
64	C₂×C₇×D₈	C₂³	1	8	yes	complemented
65	C₂²×C₇×C₈	—	2	8	no	—
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₇×C₈	C₂³	1	2	yes	—
68	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇×C₈	C₂³	1	8	yes	complemented
70	C₇×#127	—	2	4	no	—
71	C₇×#127	C₂³	1	8	yes	complemented
72	C₇×#121	—	2	8	no	—
73	C₇×#121	—	2	16	no	—
74	C₇×#121	C₂³	1	16	yes	complemented
75	C₇×#120	—	2	32	no	—
76	C₄×C₇×D₄	—	2	4	no	—
77	C₄×C₇×D₄	D₄	1	4	yes	—
78	C₄×C₇×D₄	C₂³	1	4	yes	—
79	C₄×C₇×D₄	C₂³	1	8	yes	complemented
80	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
84	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
85	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
86	C₇×#107	C₂³	1	4	yes	complemented
87	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
88	C₇×#102	C₂³	1	16	yes	complemented
89	C₇×#102	C₂³	1	8	yes	complemented
90	C₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
91	C₄×C₇×C₈	C₂³	1	4	yes	complemented
92	C₂³×D₈	C₂×C₇	1	2	yes	complemented
93	C₂×D₄²	C₂×C₇	1	2	yes	complemented
94	D₄×D₈	C₂×C₇	1	16	yes	direct product factor
95	C₂×#493	C₂×C₇	1	1	yes	characteristic, complemented
96	C₂×#466	C₂×C₇	1	2	yes	complemented
97	C₂×#459	C₂×C₇	1	2	yes	complemented
98	C₂×#447	C₂×C₇	1	4	yes	complemented
99	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
101	C₂⁴×C₇	—	2	2	no	—
102	C₂⁴×C₇	—	2	4	no	—
103	C₂⁴×C₇	—	2	16	no	—
104	C₂⁴×C₇	—	4	16	no	—
105	C₂⁴×C₇	—	4	16	no	—
106	C₂⁴×C₇	—	8	8	no	—
107	C₂⁴×C₇	C₂×D₄	1	2	yes	—
108	C₂×C₇×D₄	—	2	32	no	—
109	C₂×C₇×D₄	—	2	16	no	—
110	C₂×C₇×D₄	—	2	2	no	—
111	C₂×C₇×D₄	—	2	8	no	—
112	C₂×C₇×D₄	—	2	16	no	—
113	C₂×C₇×D₄	—	2	4	no	—
114	C₂×C₇×D₄	—	2	8	no	—
115	C₂×C₇×D₄	—	2	8	no	—
116	C₂×C₇×D₄	—	2	4	no	—
117	C₂×C₇×D₄	—	2	8	no	—
118	C₂×C₇×D₄	—	4	16	no	—
119	C₂×C₇×D₄	—	4	32	no	—
120	C₂×C₇×D₄	—	4	16	no	—
121	C₂×C₇×D₄	—	4	16	no	—
122	C₂×C₇×D₄	—	4	64	no	—
123	C₂×C₇×D₄	—	4	8	no	—
124	C₂×C₇×D₄	—	8	4	no	—
125	C₂×C₇×D₄	D₈	1	8	yes	direct product factor
126	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
127	C₂×C₇×D₄	C₂×D₄	1	8	yes	complemented
128	C₂×C₇×D₄	C₂⁴	1	8	yes	—
129	C₂×C₇×D₄	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	4	no	—
132	C₂²×C₄×C₇	—	2	2	no	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	4	8	no	—
135	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
141	C₇×D₈	—	2	32	no	—
142	C₇×D₈	—	2	16	no	—
143	C₇×D₈	—	4	8	no	—
144	C₇×D₈	C₂×D₄	1	16	yes	direct product factor
145	C₂×C₇×C₈	—	2	4	no	—
146	C₂×C₇×C₈	—	2	2	no	—
147	C₂×C₇×C₈	—	2	16	no	—
148	C₂×C₇×C₈	C₂×D₄	1	4	yes	complemented
149	C₂×C₇×C₈	C₂⁴	1	2	yes	—
150	C₂×C₇×C₈	C₂⁴	1	4	yes	—
151	C₂×C₇×C₈	C₂⁴	1	2	yes	—
152	C₇×C₄⋊C₄	—	2	2	no	—
153	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
154	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₇×C₂²⋊C₄	—	2	8	no	—
156	C₇×C₂²⋊C₄	—	2	16	no	—
157	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
158	C₄²×C₇	C₂×D₄	1	2	yes	—
159	C₄²×C₇	C₂⁴	1	2	yes	—
160	C₂³×D₄	—	2	2	no	—
161	C₂³×D₄	C₂²×C₇	1	4	yes	complemented
162	C₂²×D₈	—	2	16	no	—
163	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
164	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
165	C₂²×D₈	C₂²×C₇	1	4	yes	complemented
166	C₂²×D₈	C₂²×C₇	1	2	yes	complemented
167	C₂²×D₈	C₂²×C₇	1	16	yes	complemented
168	C₂³×C₈	C₂²×C₇	1	2	yes	complemented
169	D₄²	—	2	8	no	—
170	D₄²	C₂²×C₇	1	16	yes	complemented
171	C₂×#127	C₂²×C₇	1	2	yes	complemented
172	C₂×#121	—	2	2	no	—
173	C₂×#121	C₂²×C₇	1	4	yes	complemented
174	C₂×#120	—	2	4	no	—
175	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
176	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
177	#493	C₂²×C₇	1	8	yes	complemented
178	#466	C₂²×C₇	1	16	yes	complemented
179	#459	C₂²×C₇	1	16	yes	complemented
180	#447	C₂²×C₇	1	32	yes	complemented
181	C₄×D₈	C₂²×C₇	1	8	yes	complemented
182	C₈×D₄	C₂²×C₇	1	8	yes	complemented
183	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
184	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
185	C₂×#102	C₂²×C₇	1	2	yes	complemented
186	C₂×#102	C₂²×C₇	1	4	yes	complemented
187	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	complemented
188	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
189	C₂³×C₇	—	2	4	no	—
190	C₂³×C₇	—	2	4	no	—
191	C₂³×C₇	—	2	8	no	—
192	C₂³×C₇	—	2	4	no	—
193	C₂³×C₇	—	2	8	no	—
194	C₂³×C₇	—	4	32	no	—
195	C₂³×C₇	—	4	4	no	—
196	C₂³×C₇	—	4	4	no	—
197	C₂³×C₇	—	4	8	no	—
198	C₂³×C₇	—	4	8	no	—
199	C₂³×C₇	—	4	32	no	—
200	C₂³×C₇	—	4	8	no	—
201	C₂³×C₇	—	8	16	no	—
202	C₂³×C₇	—	8	64	no	—
203	C₂³×C₇	C₂×D₈	1	8	yes	complemented
204	C₂³×C₇	C₂²×D₄	1	4	yes	—
205	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
206	C₇×D₄	—	2	8	no	—
207	C₇×D₄	—	2	8	no	—
208	C₇×D₄	—	2	4	no	—
209	C₇×D₄	—	2	8	no	—
210	C₇×D₄	—	4	32	no	—
211	C₇×D₄	—	4	32	no	—
212	C₇×D₄	—	4	8	no	—
213	C₇×D₄	—	4	16	no	—
214	C₇×D₄	—	8	8	no	—
215	C₇×D₄	C₂×D₈	1	16	yes	direct product factor
216	C₇×D₄	C₂²×D₄	1	8	yes	complemented
217	C₂×C₄×C₇	—	2	4	no	—
218	C₂×C₄×C₇	—	2	2	no	—
219	C₂×C₄×C₇	—	2	8	no	—
220	C₂×C₄×C₇	—	2	4	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	4	4	no	—
224	C₂×C₄×C₇	—	4	16	no	—
225	C₂×C₄×C₇	C₂×D₈	1	4	yes	complemented
226	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
232	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
233	C₇×C₈	—	2	4	no	—
234	C₇×C₈	—	2	2	no	—
235	C₇×C₈	C₂²×D₄	1	4	yes	complemented
236	C₂⁵	—	2	4	no	—
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	2	4	no	—
239	C₂²×D₄	—	2	16	no	—
240	C₂²×D₄	—	2	4	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	8	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	4	8	no	—
245	C₂²×D₄	—	4	16	no	—
246	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
247	C₂²×D₄	C₂³×C₇	1	4	yes	—
248	C₂²×D₄	C₂³×C₇	1	2	yes	—
249	C₂²×D₄	C₂³×C₇	1	16	yes	complemented
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂³×C₇	1	2	yes	—
252	C₂×D₈	—	2	16	no	—
253	C₂×D₈	—	2	64	no	—
254	C₂×D₈	—	2	8	no	—
255	C₂×D₈	—	4	4	no	—
256	C₂×D₈	C₇×D₄	1	8	yes	direct product factor
257	C₂×D₈	C₂³×C₇	1	4	yes	—
258	C₂×D₈	C₂³×C₇	1	16	yes	complemented
259	C₂×D₈	C₂³×C₇	1	8	yes	complemented
260	C₂×D₈	C₂³×C₇	1	8	yes	complemented
261	C₂²×C₈	—	2	8	no	—
262	C₂²×C₈	C₂³×C₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₇	1	8	yes	complemented
266	#127	—	2	4	no	—
267	#127	C₂³×C₇	1	8	yes	complemented
268	#121	—	2	8	no	—
269	#121	—	2	16	no	—
270	#121	C₂³×C₇	1	16	yes	complemented
271	#120	—	2	32	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	C₇×D₄	1	4	yes	—
274	C₄×D₄	C₂³×C₇	1	4	yes	—
275	C₄×D₄	C₂³×C₇	1	8	yes	complemented
276	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	4	no	—
280	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
281	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
282	#107	C₂³×C₇	1	4	yes	complemented
283	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
284	#102	C₂³×C₇	1	8	yes	complemented
285	#102	C₂³×C₇	1	16	yes	complemented
286	C₂²⋊C₈	C₂³×C₇	1	8	yes	complemented
287	C₄×C₈	C₂³×C₇	1	4	yes	complemented
288	C₂²×C₇	—	2	4	no	—
289	C₂²×C₇	—	2	16	no	—
290	C₂²×C₇	—	2	4	no	—
291	C₂²×C₇	—	2	8	no	—
292	C₂²×C₇	—	4	16	no	—
293	C₂²×C₇	—	4	4	no	—
294	C₂²×C₇	—	4	4	no	—
295	C₂²×C₇	—	4	8	no	—
296	C₂²×C₇	—	4	8	no	—
297	C₂²×C₇	—	4	8	no	—
298	C₂²×C₇	—	8	64	no	—
299	C₂²×C₇	—	8	16	no	—
300	C₂²×C₇	D₄²	1	2	yes	—
301	C₂²×C₇	C₂²×D₈	1	2	yes	—
302	C₂²×C₇	C₂²×D₈	1	8	yes	complemented
303	C₂²×C₇	#576	1	2	yes	—
304	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
305	C₄×C₇	—	2	4	no	—
306	C₄×C₇	—	2	2	no	—
307	C₄×C₇	—	4	4	no	—
308	C₄×C₇	D₄²	1	2	yes	—
309	C₄×C₇	C₂²×D₈	1	4	yes	complemented
310	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
311	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂⁴	—	2	2	no	—
313	C₂⁴	—	2	4	no	—
314	C₂⁴	—	2	16	no	—
315	C₂⁴	—	4	16	no	—
316	C₂⁴	—	4	16	no	—
317	C₂⁴	—	8	8	no	—
318	C₂⁴	C₂×C₇×D₄	1	2	yes	—
319	C₂×D₄	—	2	32	no	—
320	C₂×D₄	—	2	16	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	4	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	4	16	no	—
330	C₂×D₄	—	4	32	no	—
331	C₂×D₄	—	4	16	no	—
332	C₂×D₄	—	4	16	no	—
333	C₂×D₄	—	4	64	no	—
334	C₂×D₄	—	4	8	no	—
335	C₂×D₄	—	8	4	no	—
336	C₂×D₄	C₇×D₈	1	8	yes	direct product factor
337	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
338	C₂×D₄	C₂×C₇×D₄	1	8	yes	complemented
339	C₂×D₄	C₂⁴×C₇	1	8	yes	—
340	C₂×D₄	C₂⁴×C₇	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	4	8	no	—
346	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
348	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
349	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
352	D₈	—	2	32	no	—
353	D₈	—	2	16	no	—
354	D₈	—	4	8	no	—
355	D₈	C₂×C₇×D₄	1	16	yes	direct product factor
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	16	no	—
359	C₂×C₈	C₂×C₇×D₄	1	4	yes	complemented
360	C₂×C₈	C₂⁴×C₇	1	2	yes	—
361	C₂×C₈	C₂⁴×C₇	1	4	yes	—
362	C₂×C₈	C₂⁴×C₇	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
365	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	16	no	—
368	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
369	C₄²	C₂×C₇×D₄	1	2	yes	—
370	C₄²	C₂⁴×C₇	1	2	yes	—
371	C₂×C₇	—	2	8	no	—
372	C₂×C₇	—	4	8	no	—
373	C₂×C₇	—	8	8	no	—
374	C₂×C₇	D₄×D₈	1	4	yes	direct product factor
375	C₂×C₇	C₂×D₄²	1	1	yes	characteristic
376	C₂×C₇	C₂³×D₈	1	1	yes	characteristic
377	C₂×C₇	C₂×#576	1	1	yes	characteristic
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	2	8	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	4	32	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	8	no	—
388	C₂³	—	4	32	no	—
389	C₂³	—	4	8	no	—
390	C₂³	—	8	16	no	—
391	C₂³	—	8	64	no	—
392	C₂³	C₂×C₇×D₈	1	8	yes	complemented
393	C₂³	C₂²×C₇×D₄	1	4	yes	—
394	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
395	D₄	—	2	8	no	—
396	D₄	—	2	4	no	—
397	D₄	—	2	8	no	—
398	D₄	—	2	8	no	—
399	D₄	—	4	32	no	—
400	D₄	—	4	32	no	—
401	D₄	—	4	8	no	—
402	D₄	—	4	16	no	—
403	D₄	—	8	8	no	—
404	D₄	C₂×C₇×D₈	1	16	yes	direct product factor
405	D₄	C₂²×C₇×D₄	1	8	yes	complemented
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	16	no	—
414	C₂×C₄	C₂×C₇×D₈	1	4	yes	complemented
415	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
416	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
417	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
418	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
420	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
421	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	C₂²×C₇×D₄	1	4	yes	complemented
425	C₇	C₂×D₄×D₈	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	2	4	no	—
427	C₂²	—	2	16	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	8	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	16	no	—
433	C₂²	—	4	8	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	8	64	no	—
437	C₂²	—	8	16	no	—
438	C₂²	C₇×D₄²	1	2	yes	—
439	C₂²	C₂²×C₇×D₈	1	2	yes	—
440	C₂²	C₂²×C₇×D₈	1	8	yes	complemented
441	C₂²	C₇×#576	1	2	yes	—
442	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	4	no	—
446	C₄	C₇×D₄²	1	2	yes	—
447	C₄	C₂²×C₇×D₈	1	4	yes	complemented
448	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
449	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂	—	2	8	no	—
451	C₂	—	4	8	no	—
452	C₂	—	8	8	no	—
453	C₂	C₇×D₄×D₈	1	4	yes	direct product factor
454	C₂	C₂×C₇×D₄²	1	1	yes	characteristic
455	C₂	C₂³×C₇×D₈	1	1	yes	characteristic
456	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×D₈	C₂	semidirect
2. C₂×C₇×D₄²	C₂	semidirect
3. C₇×D₄×D₈	C₂	direct (N × H)
4. C₂×C₇×#493	C₂	semidirect
5. C₂×C₇×#466	C₂	semidirect
6. C₂×C₇×#459	C₂	semidirect
7. C₂×C₇×#447	C₂	semidirect
8. C₂×C₄×C₇×D₈	C₂	semidirect
9. C₂×C₇×C₈×D₄	C₂	semidirect
11. C₂³×C₇×D₄	C₂²	semidirect
14. C₂²×C₇×D₈	C₂²	semidirect
15. C₂²×C₇×D₈	C₂²	semidirect
16. C₂²×C₇×D₈	C₂²	semidirect
17. C₂²×C₇×D₈	C₂²	semidirect
18. C₂³×C₇×C₈	C₂²	semidirect
20. C₇×D₄²	C₂²	semidirect
21. C₂×C₇×#127	C₂²	semidirect
23. C₂×C₇×#121	C₂²	semidirect
26. C₂×C₄×C₇×D₄	C₂²	semidirect
27. C₇×#493	C₂²	semidirect
28. C₇×#466	C₂²	semidirect
29. C₇×#459	C₂²	semidirect
30. C₇×#447	C₂²	semidirect
31. C₄×C₇×D₈	C₂²	semidirect
32. C₇×C₈×D₄	C₂²	semidirect
33. C₂×C₇×#107	C₂²	semidirect
34. C₂×C₇×C₄⋊C₈	C₂²	semidirect
35. C₂×C₇×#102	C₂²	semidirect
36. C₂×C₇×#102	C₂²	semidirect
37. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
38. C₂×C₄×C₇×C₈	C₂²	semidirect
39. C₂×D₄×D₈	C₇	direct (N × H)
53. C₂²×C₇×D₄	C₂³	semidirect
60. C₂×C₇×D₈	D₄	direct (N × H)
62. C₂×C₇×D₈	C₂³	semidirect
63. C₂×C₇×D₈	C₂³	semidirect
64. C₂×C₇×D₈	C₂³	semidirect
69. C₂²×C₇×C₈	C₂³	semidirect
71. C₇×#127	C₂³	semidirect
74. C₇×#121	C₂³	semidirect
79. C₄×C₇×D₄	C₂³	semidirect
86. C₇×#107	C₂³	semidirect
87. C₇×C₄⋊C₈	C₂³	semidirect
88. C₇×#102	C₂³	semidirect
89. C₇×#102	C₂³	semidirect
90. C₇×C₂²⋊C₈	C₂³	semidirect
91. C₄×C₇×C₈	C₂³	semidirect
92. C₂³×D₈	C₂×C₇	semidirect
93. C₂×D₄²	C₂×C₇	semidirect
94. D₄×D₈	C₂×C₇	direct (N × H)
95. C₂×#493	C₂×C₇	semidirect
96. C₂×#466	C₂×C₇	semidirect
97. C₂×#459	C₂×C₇	semidirect
98. C₂×#447	C₂×C₇	semidirect
99. C₂×C₄×D₈	C₂×C₇	semidirect
100. C₂×C₈×D₄	C₂×C₇	semidirect
125. C₂×C₇×D₄	D₈	direct (N × H)
127. C₂×C₇×D₄	C₂×D₄	semidirect
144. C₇×D₈	C₂×D₄	direct (N × H)
148. C₂×C₇×C₈	C₂×D₄	semidirect
161. C₂³×D₄	C₂²×C₇	semidirect
164. C₂²×D₈	C₂²×C₇	semidirect
165. C₂²×D₈	C₂²×C₇	semidirect
166. C₂²×D₈	C₂²×C₇	semidirect
167. C₂²×D₈	C₂²×C₇	semidirect
168. C₂³×C₈	C₂²×C₇	semidirect
170. D₄²	C₂²×C₇	semidirect
171. C₂×#127	C₂²×C₇	semidirect
173. C₂×#121	C₂²×C₇	semidirect
176. C₂×C₄×D₄	C₂²×C₇	semidirect
177. #493	C₂²×C₇	semidirect
178. #466	C₂²×C₇	semidirect
179. #459	C₂²×C₇	semidirect
180. #447	C₂²×C₇	semidirect
181. C₄×D₈	C₂²×C₇	semidirect
182. C₈×D₄	C₂²×C₇	semidirect
183. C₂×#107	C₂²×C₇	semidirect
184. C₂×C₄⋊C₈	C₂²×C₇	semidirect
185. C₂×#102	C₂²×C₇	semidirect
186. C₂×#102	C₂²×C₇	semidirect
187. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
188. C₂×C₄×C₈	C₂²×C₇	semidirect
203. C₂³×C₇	C₂×D₈	semidirect
215. C₇×D₄	C₂×D₈	direct (N × H)
216. C₇×D₄	C₂²×D₄	semidirect
225. C₂×C₄×C₇	C₂×D₈	semidirect
235. C₇×C₈	C₂²×D₄	semidirect
249. C₂²×D₄	C₂³×C₇	semidirect
256. C₂×D₈	C₇×D₄	direct (N × H)
258. C₂×D₈	C₂³×C₇	semidirect
259. C₂×D₈	C₂³×C₇	semidirect
260. C₂×D₈	C₂³×C₇	semidirect
265. C₂²×C₈	C₂³×C₇	semidirect
267. #127	C₂³×C₇	semidirect
270. #121	C₂³×C₇	semidirect
275. C₄×D₄	C₂³×C₇	semidirect
282. #107	C₂³×C₇	semidirect
283. C₄⋊C₈	C₂³×C₇	semidirect
284. #102	C₂³×C₇	semidirect
285. #102	C₂³×C₇	semidirect
286. C₂²⋊C₈	C₂³×C₇	semidirect
287. C₄×C₈	C₂³×C₇	semidirect
302. C₂²×C₇	C₂²×D₈	semidirect
309. C₄×C₇	C₂²×D₈	semidirect
336. C₂×D₄	C₇×D₈	direct (N × H)
338. C₂×D₄	C₂×C₇×D₄	semidirect
355. D₈	C₂×C₇×D₄	direct (N × H)
359. C₂×C₈	C₂×C₇×D₄	semidirect
374. C₂×C₇	D₄×D₈	direct (N × H)
392. C₂³	C₂×C₇×D₈	semidirect
404. D₄	C₂×C₇×D₈	direct (N × H)
405. D₄	C₂²×C₇×D₄	semidirect
414. C₂×C₄	C₂×C₇×D₈	semidirect
424. C₈	C₂²×C₇×D₄	semidirect
425. C₇	C₂×D₄×D₈	direct (N × H)
440. C₂²	C₂²×C₇×D₈	semidirect
447. C₄	C₂²×C₇×D₈	semidirect
453. C₂	C₇×D₄×D₈	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×D₈	2
C₂×C₇×D₄²	2
C₇×D₄×D₈	2
C₂×C₇×#493	2
C₂×C₇×#466	2
C₂×C₇×#459	2
C₂×C₇×#447	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂×D₄×D₈	7

Subgroups — C2×C7×D4×D8 #13238255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×D₄×D₈ #13238255