Subgroups — C₂×C₇×#3077 #13237696

Order 1792.

2530 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#3077	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#478	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#418	C₂	1	2	yes	maximal
10	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	—	2	1	no	—
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₇×#533	—	2	4	no	—
14	C₇×#533	C₂²	1	8	yes	complemented
15	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₇×#125	C₂²	1	2	yes	complemented
18	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×C₇×Q₈	—	2	1	no	—
21	C₂×C₄×C₇×Q₈	—	2	1	no	—
22	C₂×C₄×C₇×D₄	—	2	1	no	—
23	C₂×C₄×C₇×D₄	—	2	1	no	—
24	C₂×C₄×C₇×D₄	—	2	4	no	—
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₄×C₇×D₄	C₂²	1	8	yes	—
28	C₂×C₇×#117	C₂²	1	2	yes	—
29	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
31	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
32	C₇×#478	C₂²	1	32	yes	complemented
33	C₇×#476	C₂²	1	16	yes	complemented
34	C₇×#474	C₂²	1	16	yes	complemented
35	C₇×#428	C₂²	1	16	yes	complemented
36	C₂×C₇×#107	C₂²	1	4	yes	complemented
37	C₂×C₇×#106	C₂²	1	4	yes	complemented
38	C₇×#423	C₂²	1	8	yes	complemented
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
41	C₇×#418	C₂²	1	16	yes	—
42	C₂×C₇×#102	C₂²	1	4	yes	—
43	C₂×C₇×#102	C₂²	1	4	yes	—
44	C₂×#3077	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁵×C₇	—	2	1	no	—
46	C₂²×C₇×Q₈	—	2	1	no	—
47	C₂²×C₇×Q₈	—	2	1	no	—
48	C₂²×C₇×D₄	—	2	2	no	—
49	C₂²×C₇×D₄	—	2	1	no	—
50	C₂²×C₇×D₄	—	2	4	no	—
51	C₂²×C₇×D₄	Q₈	1	8	yes	complemented
52	C₂²×C₇×D₄	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	C₂³	1	4	yes	—
54	C₂³×C₄×C₇	—	2	1	no	—
55	C₂³×C₄×C₇	—	2	8	no	—
56	C₂³×C₄×C₇	—	2	2	no	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	—	4	8	no	—
59	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
62	C₂×C₇×M₁₆	—	2	8	no	—
63	C₂×C₇×M₁₆	C₂³	1	8	yes	—
64	C₂²×C₇×C₈	C₂³	1	4	yes	—
65	C₇×C₄⋊Q₈	—	2	2	no	—
66	C₇×C₄⋊Q₈	—	2	2	no	—
67	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
68	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
69	C₇×#125	—	2	4	no	—
70	C₇×#125	C₂³	1	8	yes	complemented
71	C₇×C₂²⋊Q₈	—	2	8	no	—
72	C₇×C₂²⋊Q₈	—	2	8	no	—
73	C₄×C₇×Q₈	—	2	8	no	—
74	C₄×C₇×Q₈	—	2	8	no	—
75	C₄×C₇×D₄	—	2	8	no	—
76	C₄×C₇×D₄	—	2	8	no	—
77	C₄×C₇×D₄	—	2	4	no	—
78	C₄×C₇×D₄	—	2	4	no	—
79	C₄×C₇×D₄	C₂³	1	8	yes	—
80	C₄×C₇×D₄	C₂³	1	8	yes	—
81	C₇×#117	—	2	4	no	—
82	C₇×#117	C₂³	1	8	yes	—
83	C₂×C₇×C₄⋊C₄	—	2	2	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	2	no	—
86	C₂×C₇×C₄⋊C₄	—	2	2	no	—
87	C₂×C₇×C₄⋊C₄	—	2	1	no	—
88	C₂×C₇×C₄⋊C₄	—	2	1	no	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₄²×C₇	—	2	2	no	—
98	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₇	D₄	1	4	yes	—
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇	C₂³	1	4	yes	—
104	C₇×#107	C₂³	1	16	yes	complemented
105	C₇×#106	C₂³	1	16	yes	complemented
106	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
107	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
108	C₇×#102	C₂³	1	16	yes	—
109	C₇×#102	C₂³	1	16	yes	—
110	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
111	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic
112	#3077	C₂×C₇	1	16	yes	direct product factor
113	C₂×#478	C₂×C₇	1	4	yes	complemented
114	C₂×#476	C₂×C₇	1	2	yes	complemented
115	C₂×#474	C₂×C₇	1	2	yes	complemented
116	C₂×#428	C₂×C₇	1	2	yes	complemented
117	C₂×#423	C₂×C₇	1	1	yes	characteristic, complemented
118	C₂×#418	C₂×C₇	1	2	yes	—
119	C₂⁴×C₇	—	2	8	no	—
120	C₂⁴×C₇	—	2	4	no	—
121	C₂⁴×C₇	—	2	2	no	—
122	C₂⁴×C₇	—	4	4	no	—
123	C₂⁴×C₇	—	4	4	no	—
124	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
125	C₂×C₇×Q₈	—	2	4	no	—
126	C₂×C₇×Q₈	—	2	4	no	—
127	C₂×C₇×Q₈	—	4	4	no	—
128	C₂×C₇×Q₈	—	4	4	no	—
129	C₂×C₇×D₄	—	2	16	no	—
130	C₂×C₇×D₄	—	2	8	no	—
131	C₂×C₇×D₄	—	2	4	no	—
132	C₂×C₇×D₄	—	2	2	no	—
133	C₂×C₇×D₄	—	2	4	no	—
134	C₂×C₇×D₄	—	2	8	no	—
135	C₂×C₇×D₄	C₂×Q₈	1	8	yes	—
136	C₂×C₇×D₄	C₂×Q₈	1	16	yes	complemented
137	C₂×C₇×D₄	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	2	4	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	8	no	—
144	C₂²×C₄×C₇	—	2	8	no	—
145	C₂²×C₄×C₇	—	4	2	no	—
146	C₂²×C₄×C₇	—	4	8	no	—
147	C₂²×C₄×C₇	—	4	32	no	—
148	C₂²×C₄×C₇	—	4	4	no	—
149	C₂²×C₄×C₇	—	4	8	no	—
150	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
159	C₂²×C₄×C₇	#41	1	4	yes	—
160	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
162	C₇×M₁₆	—	2	16	no	—
163	C₂×C₇×C₈	—	2	8	no	—
164	C₂×C₇×C₈	C₂⁴	1	8	yes	—
165	C₇×C₄⋊C₄	—	2	4	no	—
166	C₇×C₄⋊C₄	—	2	2	no	—
167	C₇×C₄⋊C₄	—	2	8	no	—
168	C₇×C₄⋊C₄	—	2	8	no	—
169	C₇×C₄⋊C₄	—	2	4	no	—
170	C₇×C₄⋊C₄	—	2	4	no	—
171	C₇×C₄⋊C₄	—	2	2	no	—
172	C₇×C₄⋊C₄	—	2	2	no	—
173	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
174	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
175	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₇×C₂²⋊C₄	—	2	8	no	—
177	C₇×C₂²⋊C₄	—	2	8	no	—
178	C₇×C₂²⋊C₄	—	2	8	no	—
179	C₄²×C₇	—	2	8	no	—
180	C₄²×C₇	C₂×D₄	1	4	yes	—
181	C₄²×C₇	C₂×D₄	1	4	yes	—
182	C₄²×C₇	C₂×D₄	1	2	yes	—
183	C₄²×C₇	C₂×D₄	1	2	yes	—
184	C₄²×C₇	C₂⁴	1	2	yes	—
185	C₄²×C₇	C₂⁴	1	2	yes	—
186	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
187	C₂⁴×C₄	—	2	1	no	—
188	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
189	#533	—	2	4	no	—
190	#533	C₂²×C₇	1	8	yes	complemented
191	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
192	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
193	C₂×#125	C₂²×C₇	1	2	yes	complemented
194	C₂×C₂²⋊Q₈	—	2	1	no	—
195	C₂×C₂²⋊Q₈	—	2	1	no	—
196	C₂×C₄×Q₈	—	2	1	no	—
197	C₂×C₄×Q₈	—	2	1	no	—
198	C₂×C₄×D₄	—	2	1	no	—
199	C₂×C₄×D₄	—	2	1	no	—
200	C₂×C₄×D₄	—	2	4	no	—
201	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
202	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
203	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
204	C₂×#117	C₂²×C₇	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
206	C₂²×C₂²⋊C₄	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
208	#478	C₂²×C₇	1	32	yes	complemented
209	#476	C₂²×C₇	1	16	yes	complemented
210	#474	C₂²×C₇	1	16	yes	complemented
211	#428	C₂²×C₇	1	16	yes	complemented
212	C₂×#107	C₂²×C₇	1	4	yes	complemented
213	C₂×#106	C₂²×C₇	1	4	yes	complemented
214	#423	C₂²×C₇	1	8	yes	complemented
215	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
216	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
217	#418	C₂²×C₇	1	16	yes	—
218	C₂×#102	C₂²×C₇	1	4	yes	—
219	C₂×#102	C₂²×C₇	1	4	yes	—
220	C₂³×C₇	—	2	2	no	—
221	C₂³×C₇	—	2	2	no	—
222	C₂³×C₇	—	2	8	no	—
223	C₂³×C₇	—	2	16	no	—
224	C₂³×C₇	—	2	4	no	—
225	C₂³×C₇	—	4	8	no	—
226	C₂³×C₇	—	4	32	no	—
227	C₂³×C₇	—	4	8	no	—
228	C₂³×C₇	—	4	4	no	—
229	C₂³×C₇	—	4	4	no	—
230	C₂³×C₇	C₂²⋊Q₈	1	4	yes	—
231	C₂³×C₇	C₂²×D₄	1	2	yes	—
232	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
233	C₇×Q₈	—	4	8	no	—
234	C₇×Q₈	—	4	8	no	—
235	C₇×D₄	—	2	8	no	—
236	C₇×D₄	—	2	16	no	—
237	C₇×D₄	—	2	4	no	—
238	C₇×D₄	C₂²×Q₈	1	8	yes	—
239	C₂×C₄×C₇	—	2	2	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	8	no	—
243	C₂×C₄×C₇	—	2	4	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	4	4	no	—
247	C₂×C₄×C₇	—	4	16	no	—
248	C₂×C₄×C₇	—	4	8	no	—
249	C₂×C₄×C₇	—	4	4	no	—
250	C₂×C₄×C₇	—	4	4	no	—
251	C₂×C₄×C₇	—	4	4	no	—
252	C₂×C₄×C₇	—	4	16	no	—
253	C₂×C₄×C₇	C₂²⋊Q₈	1	8	yes	—
254	C₂×C₄×C₇	C₂²⋊Q₈	1	4	yes	—
255	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
256	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
260	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
263	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
264	C₂×C₄×C₇	C₂×#41	1	2	yes	—
265	C₂×C₄×C₇	C₂×#41	1	4	yes	—
266	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
267	C₇×C₈	—	2	8	no	—
268	C₂⁵	—	2	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	—	2	4	no	—
274	C₂²×D₄	C₇×Q₈	1	8	yes	complemented
275	C₂²×D₄	C₂³×C₇	1	2	yes	—
276	C₂²×D₄	C₂³×C₇	1	4	yes	—
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	—	2	2	no	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	—	4	8	no	—
282	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
283	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
285	C₂×M₁₆	—	2	8	no	—
286	C₂×M₁₆	C₂³×C₇	1	8	yes	—
287	C₂²×C₈	C₂³×C₇	1	4	yes	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
291	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
292	#125	—	2	4	no	—
293	#125	C₂³×C₇	1	8	yes	complemented
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₄×Q₈	—	2	8	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×D₄	—	2	8	no	—
299	C₄×D₄	—	2	8	no	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	C₂³×C₇	1	8	yes	—
303	C₄×D₄	C₂³×C₇	1	8	yes	—
304	#117	—	2	4	no	—
305	#117	C₂³×C₇	1	8	yes	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	8	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
322	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
323	C₂×C₄²	C₇×D₄	1	4	yes	—
324	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
326	C₂×C₄²	C₂³×C₇	1	4	yes	—
327	#107	C₂³×C₇	1	16	yes	complemented
328	#106	C₂³×C₇	1	16	yes	complemented
329	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
330	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
331	#102	C₂³×C₇	1	16	yes	—
332	#102	C₂³×C₇	1	16	yes	—
333	C₂²×C₇	—	2	8	no	—
334	C₂²×C₇	—	2	2	no	—
335	C₂²×C₇	—	2	2	no	—
336	C₂²×C₇	—	2	8	no	—
337	C₂²×C₇	—	4	32	no	—
338	C₂²×C₇	—	4	16	no	—
339	C₂²×C₇	—	4	4	no	—
340	C₂²×C₇	—	4	4	no	—
341	C₂²×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
342	C₂²×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
343	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
344	C₂²×C₇	#575	1	2	yes	—
345	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₇	—	2	2	no	—
347	C₄×C₇	—	2	2	no	—
348	C₄×C₇	—	2	2	no	—
349	C₄×C₇	—	4	4	no	—
350	C₄×C₇	—	4	4	no	—
351	C₄×C₇	—	4	4	no	—
352	C₄×C₇	C₂×C₂²⋊Q₈	1	4	yes	—
353	C₄×C₇	C₂×C₂²⋊Q₈	1	2	yes	—
354	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
355	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
356	C₄×C₇	C₂²×#41	1	1	yes	characteristic
357	C₂⁴	—	2	8	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	4	4	no	—
361	C₂⁴	—	4	4	no	—
362	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×D₄	—	2	16	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	8	no	—
373	C₂×D₄	C₂×C₇×Q₈	1	8	yes	—
374	C₂×D₄	C₂×C₇×Q₈	1	16	yes	complemented
375	C₂×D₄	C₂⁴×C₇	1	4	yes	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	8	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	4	32	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	8	no	—
388	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
392	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
393	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
394	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
395	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
397	C₂²×C₄	C₇×#41	1	4	yes	—
398	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
399	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
400	M₁₆	—	2	16	no	—
401	C₂×C₈	—	2	8	no	—
402	C₂×C₈	C₂⁴×C₇	1	8	yes	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	8	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
412	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
413	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₄²	—	2	8	no	—
418	C₄²	C₂×C₇×D₄	1	4	yes	—
419	C₄²	C₂×C₇×D₄	1	4	yes	—
420	C₄²	C₂×C₇×D₄	1	2	yes	—
421	C₄²	C₂×C₇×D₄	1	2	yes	—
422	C₄²	C₂⁴×C₇	1	2	yes	—
423	C₄²	C₂⁴×C₇	1	2	yes	—
424	C₂×C₇	—	2	4	no	—
425	C₂×C₇	—	4	8	no	—
426	C₂×C₇	#3077	1	4	yes	direct product factor
427	C₂×C₇	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
428	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂×C₇	C₂×#575	1	1	yes	characteristic
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	16	no	—
435	C₂³	—	4	8	no	—
436	C₂³	—	4	8	no	—
437	C₂³	—	4	32	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	4	no	—
440	C₂³	C₇×C₂²⋊Q₈	1	4	yes	—
441	C₂³	C₂²×C₇×D₄	1	2	yes	—
442	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
443	Q₈	—	4	8	no	—
444	Q₈	—	4	8	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	8	no	—
447	D₄	—	2	16	no	—
448	D₄	C₂²×C₇×Q₈	1	8	yes	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	C₇×C₂²⋊Q₈	1	8	yes	—
464	C₂×C₄	C₇×C₂²⋊Q₈	1	4	yes	—
465	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
466	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
467	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
468	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
469	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
470	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
471	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
472	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
473	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
474	C₂×C₄	C₂×C₇×#41	1	2	yes	—
475	C₂×C₄	C₂×C₇×#41	1	4	yes	—
476	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
477	C₈	—	2	8	no	—
478	C₇	C₂×#3077	1	1	yes	characteristic, direct product factor, Sylow
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	8	no	—
483	C₂²	—	4	32	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	16	no	—
487	C₂²	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
488	C₂²	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
489	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
490	C₂²	C₇×#575	1	2	yes	—
491	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	C₂×C₇×C₂²⋊Q₈	1	4	yes	—
499	C₄	C₂×C₇×C₂²⋊Q₈	1	2	yes	—
500	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
501	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
502	C₄	C₂²×C₇×#41	1	1	yes	characteristic
503	C₂	—	2	4	no	—
504	C₂	—	4	8	no	—
505	C₂	C₇×#3077	1	4	yes	direct product factor
506	C₂	C₂²×C₇×C₂²⋊Q₈	1	1	yes	characteristic
507	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
508	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#533	C₂	semidirect
3. C₇×#3077	C₂	direct (N × H)
4. C₂×C₇×#478	C₂	semidirect
5. C₂×C₇×#476	C₂	semidirect
6. C₂×C₇×#474	C₂	semidirect
7. C₂×C₇×#428	C₂	semidirect
8. C₂×C₇×#423	C₂	semidirect
14. C₇×#533	C₂²	semidirect
15. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
17. C₂×C₇×#125	C₂²	semidirect
32. C₇×#478	C₂²	semidirect
33. C₇×#476	C₂²	semidirect
34. C₇×#474	C₂²	semidirect
35. C₇×#428	C₂²	semidirect
36. C₂×C₇×#107	C₂²	semidirect
37. C₂×C₇×#106	C₂²	semidirect
38. C₇×#423	C₂²	semidirect
39. C₂×C₇×C₄⋊C₈	C₂²	semidirect
40. C₂×C₇×C₄⋊C₈	C₂²	semidirect
44. C₂×#3077	C₇	direct (N × H)
51. C₂²×C₇×D₄	Q₈	semidirect
67. C₇×C₄⋊Q₈	C₂³	semidirect
68. C₇×C₄⋊Q₈	C₂³	semidirect
70. C₇×#125	C₂³	semidirect
104. C₇×#107	C₂³	semidirect
105. C₇×#106	C₂³	semidirect
106. C₇×C₄⋊C₈	C₂³	semidirect
107. C₇×C₄⋊C₈	C₂³	semidirect
110. C₂×#533	C₂×C₇	semidirect
112. #3077	C₂×C₇	direct (N × H)
113. C₂×#478	C₂×C₇	semidirect
114. C₂×#476	C₂×C₇	semidirect
115. C₂×#474	C₂×C₇	semidirect
116. C₂×#428	C₂×C₇	semidirect
117. C₂×#423	C₂×C₇	semidirect
136. C₂×C₇×D₄	C₂×Q₈	semidirect
190. #533	C₂²×C₇	semidirect
191. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
192. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
193. C₂×#125	C₂²×C₇	semidirect
208. #478	C₂²×C₇	semidirect
209. #476	C₂²×C₇	semidirect
210. #474	C₂²×C₇	semidirect
211. #428	C₂²×C₇	semidirect
212. C₂×#107	C₂²×C₇	semidirect
213. C₂×#106	C₂²×C₇	semidirect
214. #423	C₂²×C₇	semidirect
215. C₂×C₄⋊C₈	C₂²×C₇	semidirect
216. C₂×C₄⋊C₈	C₂²×C₇	semidirect
274. C₂²×D₄	C₇×Q₈	semidirect
290. C₄⋊Q₈	C₂³×C₇	semidirect
291. C₄⋊Q₈	C₂³×C₇	semidirect
293. #125	C₂³×C₇	semidirect
327. #107	C₂³×C₇	semidirect
328. #106	C₂³×C₇	semidirect
329. C₄⋊C₈	C₂³×C₇	semidirect
330. C₄⋊C₈	C₂³×C₇	semidirect
374. C₂×D₄	C₂×C₇×Q₈	semidirect
426. C₂×C₇	#3077	direct (N × H)
478. C₇	C₂×#3077	direct (N × H)
505. C₂	C₇×#3077	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×C₇×#533	2
C₂²×C₄×C₇×D₄	2
C₇×#3077	2
C₂×C₇×#478	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#428	2
C₂×C₇×#423	2
C₂×C₇×#418	2
C₂×#3077	7

Subgroups — C2×C7×#3077 #13237696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3077 #13237696