Subgroups — C₂×C₇×#3110 #13237758

Order 1792.

2550 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×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic
3	C₇×#3110	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#484	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#450	C₂	1	2	yes	maximal
8	C₂×C₇×#440	C₂	1	4	yes	maximal, complemented
9	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	—	2	1	no	—
12	C₂²×C₇×SD₁₆	C₂²	1	4	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	—	2	1	no	—
18	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×C₇×Q₈	—	2	1	no	—
21	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
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	—	2	1	no	—
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×#484	C₂²	1	16	yes	complemented
33	C₇×#474	C₂²	1	16	yes	complemented
34	C₇×#461	C₂²	1	16	yes	complemented
35	C₇×#450	C₂²	1	16	yes	—
36	C₇×#440	C₂²	1	32	yes	complemented
37	C₇×#432	C₂²	1	8	yes	complemented
38	C₂×C₇×#107	C₂²	1	4	yes	complemented
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
40	C₂×C₇×#103	C₂²	1	4	yes	complemented
41	C₂×C₇×#102	C₂²	1	4	yes	—
42	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₂×C₇×#97	C₂²	1	2	yes	complemented
44	C₂×#3110	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	C₂³	1	2	yes	—
48	C₂²×C₇×D₄	—	2	8	no	—
49	C₂²×C₇×D₄	—	2	2	no	—
50	C₂²×C₇×D₄	—	2	1	no	—
51	C₂²×C₇×D₄	C₂³	1	4	yes	—
52	C₂²×C₇×D₄	C₂³	1	2	yes	—
53	C₂³×C₄×C₇	—	2	1	no	—
54	C₂³×C₄×C₇	—	2	8	no	—
55	C₂³×C₄×C₇	—	2	2	no	—
56	C₂³×C₄×C₇	—	2	2	no	—
57	C₂³×C₄×C₇	—	4	8	no	—
58	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
59	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂×C₇×SD₁₆	—	2	16	no	—
62	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
63	C₂²×C₇×C₈	C₂³	1	4	yes	—
64	C₇×C₄⋊Q₈	—	2	2	no	—
65	C₇×C₄⋊Q₈	—	2	2	no	—
66	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
67	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
68	C₇×#125	—	2	8	no	—
69	C₇×C₂²⋊Q₈	—	2	8	no	—
70	C₇×C₂²⋊Q₈	—	2	4	no	—
71	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
72	C₄×C₇×Q₈	—	2	8	no	—
73	C₄×C₇×Q₈	—	2	4	no	—
74	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
75	C₄×C₇×D₄	—	2	4	no	—
76	C₄×C₇×D₄	—	2	8	no	—
77	C₄×C₇×D₄	—	2	8	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	8	no	—
82	C₂×C₇×C₄⋊C₄	—	2	2	no	—
83	C₂×C₇×C₄⋊C₄	—	2	1	no	—
84	C₂×C₇×C₄⋊C₄	—	2	1	no	—
85	C₂×C₇×C₄⋊C₄	—	2	1	no	—
86	C₂×C₇×C₄⋊C₄	—	2	1	no	—
87	C₂×C₇×C₄⋊C₄	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	—	2	2	no	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
92	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
94	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₇	—	2	2	no	—
97	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₇	D₄	1	4	yes	—
100	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₇	C₂³	1	4	yes	—
103	C₇×#107	C₂³	1	16	yes	complemented
104	C₇×C₄⋊C₈	C₂³	1	8	yes	complemented
105	C₇×#103	C₂³	1	16	yes	complemented
106	C₇×#102	C₂³	1	16	yes	—
107	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₇×#97	C₂³	1	8	yes	complemented
109	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
110	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic
111	#3110	C₂×C₇	1	16	yes	direct product factor
112	C₂×#484	C₂×C₇	1	2	yes	complemented
113	C₂×#474	C₂×C₇	1	2	yes	complemented
114	C₂×#461	C₂×C₇	1	2	yes	complemented
115	C₂×#450	C₂×C₇	1	2	yes	—
116	C₂×#440	C₂×C₇	1	4	yes	complemented
117	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
118	C₂⁴×C₇	—	2	8	no	—
119	C₂⁴×C₇	—	2	4	no	—
120	C₂⁴×C₇	—	2	2	no	—
121	C₂⁴×C₇	—	4	4	no	—
122	C₂⁴×C₇	—	4	4	no	—
123	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇×Q₈	—	2	2	no	—
125	C₂×C₇×Q₈	—	2	4	no	—
126	C₂×C₇×Q₈	—	2	8	no	—
127	C₂×C₇×Q₈	—	4	4	no	—
128	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
129	C₂×C₇×D₄	—	2	8	no	—
130	C₂×C₇×D₄	—	2	16	no	—
131	C₂×C₇×D₄	—	2	16	no	—
132	C₂×C₇×D₄	—	2	4	no	—
133	C₂×C₇×D₄	—	2	2	no	—
134	C₂×C₇×D₄	—	2	4	no	—
135	C₂×C₇×D₄	#41	1	8	yes	—
136	C₂×C₇×D₄	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₇	—	2	4	no	—
138	C₂²×C₄×C₇	—	2	4	no	—
139	C₂²×C₄×C₇	—	2	4	no	—
140	C₂²×C₄×C₇	—	2	4	no	—
141	C₂²×C₄×C₇	—	2	2	no	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	8	no	—
145	C₂²×C₄×C₇	—	2	8	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	2	yes	—
151	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
160	C₇×SD₁₆	—	2	32	no	—
161	C₂×C₇×C₈	—	2	8	no	—
162	C₂×C₇×C₈	C₂⁴	1	8	yes	—
163	C₇×C₄⋊C₄	—	2	4	no	—
164	C₇×C₄⋊C₄	—	2	2	no	—
165	C₇×C₄⋊C₄	—	2	4	no	—
166	C₇×C₄⋊C₄	—	2	4	no	—
167	C₇×C₄⋊C₄	—	2	4	no	—
168	C₇×C₄⋊C₄	—	2	8	no	—
169	C₇×C₄⋊C₄	—	2	8	no	—
170	C₇×C₄⋊C₄	—	2	2	no	—
171	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
172	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
173	C₇×C₂²⋊C₄	—	2	8	no	—
174	C₇×C₂²⋊C₄	—	2	8	no	—
175	C₇×C₂²⋊C₄	—	2	8	no	—
176	C₄²×C₇	—	2	8	no	—
177	C₄²×C₇	C₂×D₄	1	4	yes	—
178	C₄²×C₇	C₂×D₄	1	2	yes	—
179	C₄²×C₇	C₂×D₄	1	4	yes	—
180	C₄²×C₇	C₂×D₄	1	2	yes	—
181	C₄²×C₇	C₂⁴	1	2	yes	—
182	C₄²×C₇	C₂⁴	1	2	yes	—
183	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
184	C₂⁴×C₄	—	2	1	no	—
185	C₂²×SD₁₆	C₂²×C₇	1	4	yes	—
186	#533	—	2	4	no	—
187	#533	C₂²×C₇	1	8	yes	complemented
188	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
189	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
190	C₂×#125	—	2	1	no	—
191	C₂×C₂²⋊Q₈	—	2	1	no	—
192	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
195	C₂×C₄×D₄	—	2	1	no	—
196	C₂×C₄×D₄	—	2	1	no	—
197	C₂×C₄×D₄	—	2	4	no	—
198	C₂×C₄×D₄	C₂²×C₇	1	8	yes	—
199	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
200	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
203	C₂²×C₂²⋊C₄	—	2	1	no	—
204	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
205	#484	C₂²×C₇	1	16	yes	complemented
206	#474	C₂²×C₇	1	16	yes	complemented
207	#461	C₂²×C₇	1	16	yes	complemented
208	#450	C₂²×C₇	1	16	yes	—
209	#440	C₂²×C₇	1	32	yes	complemented
210	#432	C₂²×C₇	1	8	yes	complemented
211	C₂×#107	C₂²×C₇	1	4	yes	complemented
212	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
213	C₂×#103	C₂²×C₇	1	4	yes	complemented
214	C₂×#102	C₂²×C₇	1	4	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
216	C₂×#97	C₂²×C₇	1	2	yes	complemented
217	C₂³×C₇	—	2	2	no	—
218	C₂³×C₇	—	2	2	no	—
219	C₂³×C₇	—	2	16	no	—
220	C₂³×C₇	—	2	8	no	—
221	C₂³×C₇	—	2	4	no	—
222	C₂³×C₇	—	4	8	no	—
223	C₂³×C₇	—	4	32	no	—
224	C₂³×C₇	—	4	4	no	—
225	C₂³×C₇	—	4	8	no	—
226	C₂³×C₇	—	4	4	no	—
227	C₂³×C₇	#137	1	4	yes	—
228	C₂³×C₇	C₂²×D₄	1	2	yes	—
229	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
230	C₇×Q₈	—	2	8	no	—
231	C₇×Q₈	—	4	4	no	—
232	C₇×Q₈	—	4	8	no	—
233	C₇×D₄	—	2	16	no	—
234	C₇×D₄	—	2	8	no	—
235	C₇×D₄	—	2	4	no	—
236	C₇×D₄	C₂×#41	1	8	yes	—
237	C₂×C₄×C₇	—	2	2	no	—
238	C₂×C₄×C₇	—	2	2	no	—
239	C₂×C₄×C₇	—	2	8	no	—
240	C₂×C₄×C₇	—	2	2	no	—
241	C₂×C₄×C₇	—	2	2	no	—
242	C₂×C₄×C₇	—	2	4	no	—
243	C₂×C₄×C₇	—	2	8	no	—
244	C₂×C₄×C₇	—	2	4	no	—
245	C₂×C₄×C₇	—	2	4	no	—
246	C₂×C₄×C₇	—	2	4	no	—
247	C₂×C₄×C₇	—	2	4	no	—
248	C₂×C₄×C₇	—	4	16	no	—
249	C₂×C₄×C₇	—	4	8	no	—
250	C₂×C₄×C₇	—	4	4	no	—
251	C₂×C₄×C₇	—	4	4	no	—
252	C₂×C₄×C₇	—	4	4	no	—
253	C₂×C₄×C₇	—	4	16	no	—
254	C₂×C₄×C₇	AGL(1,ℤ/8)	1	4	yes	—
255	C₂×C₄×C₇	C₂²×D₄	1	2	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	1	yes	characteristic
260	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₇	C₂×#41	1	4	yes	—
262	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
263	C₇×C₈	—	2	8	no	—
264	C₂⁵	—	2	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂²×Q₈	C₂³×C₇	1	2	yes	—
267	C₂²×D₄	—	2	8	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	C₂³×C₇	1	4	yes	—
271	C₂²×D₄	C₂³×C₇	1	2	yes	—
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	—	2	8	no	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	4	8	no	—
277	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
278	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	16	no	—
281	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
282	C₂²×C₈	C₂³×C₇	1	4	yes	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
286	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
287	#125	—	2	8	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
291	C₄×Q₈	—	2	8	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	4	no	—
296	C₄×D₄	—	2	8	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	C₂³×C₇	1	8	yes	—
299	C₄×D₄	C₂³×C₇	1	8	yes	—
300	#117	—	2	8	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
317	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
318	C₂×C₄²	C₇×D₄	1	4	yes	—
319	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₇	1	4	yes	—
322	#107	C₂³×C₇	1	16	yes	complemented
323	C₄⋊C₈	C₂³×C₇	1	8	yes	complemented
324	#103	C₂³×C₇	1	16	yes	complemented
325	#102	C₂³×C₇	1	16	yes	—
326	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
327	#97	C₂³×C₇	1	8	yes	complemented
328	C₂²×C₇	—	2	8	no	—
329	C₂²×C₇	—	2	2	no	—
330	C₂²×C₇	—	2	2	no	—
331	C₂²×C₇	—	2	8	no	—
332	C₂²×C₇	—	4	32	no	—
333	C₂²×C₇	—	4	16	no	—
334	C₂²×C₇	—	4	4	no	—
335	C₂²×C₇	—	4	4	no	—
336	C₂²×C₇	#525	1	2	yes	—
337	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
338	C₂²×C₇	C₂×#137	1	4	yes	—
339	C₂²×C₇	C₂×#137	1	2	yes	—
340	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
341	C₄×C₇	—	2	2	no	—
342	C₄×C₇	—	2	2	no	—
343	C₄×C₇	—	2	2	no	—
344	C₄×C₇	—	2	2	no	—
345	C₄×C₇	—	4	4	no	—
346	C₄×C₇	—	4	4	no	—
347	C₄×C₇	—	4	4	no	—
348	C₄×C₇	#525	1	2	yes	—
349	C₄×C₇	C₂×AGL(1,ℤ/8)	1	4	yes	—
350	C₄×C₇	C₂²×#41	1	2	yes	—
351	C₂⁴	—	2	8	no	—
352	C₂⁴	—	2	4	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	—	4	4	no	—
355	C₂⁴	—	4	4	no	—
356	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	4	no	—
359	C₂×Q₈	—	2	8	no	—
360	C₂×Q₈	—	4	4	no	—
361	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	C₇×#41	1	8	yes	—
369	C₂×D₄	C₂⁴×C₇	1	4	yes	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	4	8	no	—
380	C₂²×C₄	—	4	32	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	8	no	—
383	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
386	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
388	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
390	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
392	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
393	SD₁₆	—	2	32	no	—
394	C₂×C₈	—	2	8	no	—
395	C₂×C₈	C₂⁴×C₇	1	8	yes	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
405	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₄²	—	2	8	no	—
410	C₄²	C₂×C₇×D₄	1	4	yes	—
411	C₄²	C₂×C₇×D₄	1	2	yes	—
412	C₄²	C₂×C₇×D₄	1	4	yes	—
413	C₄²	C₂×C₇×D₄	1	2	yes	—
414	C₄²	C₂⁴×C₇	1	2	yes	—
415	C₄²	C₂⁴×C₇	1	2	yes	—
416	C₂×C₇	—	2	4	no	—
417	C₂×C₇	—	4	8	no	—
418	C₂×C₇	#3110	1	4	yes	direct product factor
419	C₂×C₇	C₂×#525	1	1	yes	characteristic
420	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂×C₇	C₂²×#137	1	1	yes	characteristic
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	4	8	no	—
428	C₂³	—	4	32	no	—
429	C₂³	—	4	4	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	4	no	—
432	C₂³	C₇×#137	1	4	yes	—
433	C₂³	C₂²×C₇×D₄	1	2	yes	—
434	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
435	Q₈	—	2	8	no	—
436	Q₈	—	4	4	no	—
437	Q₈	—	4	8	no	—
438	D₄	—	2	16	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	8	no	—
441	D₄	C₂×C₇×#41	1	8	yes	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	4	16	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	16	no	—
459	C₂×C₄	C₇×AGL(1,ℤ/8)	1	4	yes	—
460	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
461	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
462	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
463	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
464	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
466	C₂×C₄	C₂×C₇×#41	1	4	yes	—
467	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
468	C₈	—	2	8	no	—
469	C₇	C₂×#3110	1	1	yes	characteristic, direct product factor, Sylow
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	8	no	—
473	C₂²	—	2	8	no	—
474	C₂²	—	4	32	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	16	no	—
478	C₂²	C₇×#525	1	2	yes	—
479	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	2	yes	—
480	C₂²	C₂×C₇×#137	1	4	yes	—
481	C₂²	C₂×C₇×#137	1	2	yes	—
482	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	4	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	4	no	—
490	C₄	C₇×#525	1	2	yes	—
491	C₄	C₂×C₇×AGL(1,ℤ/8)	1	4	yes	—
492	C₄	C₂²×C₇×#41	1	2	yes	—
493	C₂	—	2	4	no	—
494	C₂	—	4	8	no	—
495	C₂	C₇×#3110	1	4	yes	direct product factor
496	C₂	C₂×C₇×#525	1	1	yes	characteristic
497	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
498	C₂	C₂²×C₇×#137	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×#3110	C₂	direct (N × H)
4. C₂×C₇×#484	C₂	semidirect
5. C₂×C₇×#474	C₂	semidirect
6. C₂×C₇×#461	C₂	semidirect
8. C₂×C₇×#440	C₂	semidirect
9. C₂×C₇×#432	C₂	semidirect
14. C₇×#533	C₂²	semidirect
15. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₄×C₇×Q₈	C₂²	semidirect
32. C₇×#484	C₂²	semidirect
33. C₇×#474	C₂²	semidirect
34. C₇×#461	C₂²	semidirect
36. C₇×#440	C₂²	semidirect
37. C₇×#432	C₂²	semidirect
38. C₂×C₇×#107	C₂²	semidirect
39. C₂×C₇×C₄⋊C₈	C₂²	semidirect
40. C₂×C₇×#103	C₂²	semidirect
43. C₂×C₇×#97	C₂²	semidirect
44. C₂×#3110	C₇	direct (N × H)
66. C₇×C₄⋊Q₈	C₂³	semidirect
67. C₇×C₄⋊Q₈	C₂³	semidirect
74. C₄×C₇×Q₈	C₂³	semidirect
103. C₇×#107	C₂³	semidirect
104. C₇×C₄⋊C₈	C₂³	semidirect
105. C₇×#103	C₂³	semidirect
108. C₇×#97	C₂³	semidirect
109. C₂×#533	C₂×C₇	semidirect
111. #3110	C₂×C₇	direct (N × H)
112. C₂×#484	C₂×C₇	semidirect
113. C₂×#474	C₂×C₇	semidirect
114. C₂×#461	C₂×C₇	semidirect
116. C₂×#440	C₂×C₇	semidirect
117. C₂×#432	C₂×C₇	semidirect
187. #533	C₂²×C₇	semidirect
188. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
189. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
194. C₂×C₄×Q₈	C₂²×C₇	semidirect
205. #484	C₂²×C₇	semidirect
206. #474	C₂²×C₇	semidirect
207. #461	C₂²×C₇	semidirect
209. #440	C₂²×C₇	semidirect
210. #432	C₂²×C₇	semidirect
211. C₂×#107	C₂²×C₇	semidirect
212. C₂×C₄⋊C₈	C₂²×C₇	semidirect
213. C₂×#103	C₂²×C₇	semidirect
216. C₂×#97	C₂²×C₇	semidirect
285. C₄⋊Q₈	C₂³×C₇	semidirect
286. C₄⋊Q₈	C₂³×C₇	semidirect
293. C₄×Q₈	C₂³×C₇	semidirect
322. #107	C₂³×C₇	semidirect
323. C₄⋊C₈	C₂³×C₇	semidirect
324. #103	C₂³×C₇	semidirect
327. #97	C₂³×C₇	semidirect
418. C₂×C₇	#3110	direct (N × H)
469. C₇	C₂×#3110	direct (N × H)
495. C₂	C₇×#3110	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×#3110	2
C₂×C₇×#484	2
C₂×C₇×#474	2
C₂×C₇×#461	2
C₂×C₇×#450	2
C₂×C₇×#440	2
C₂×C₇×#432	2
C₂×#3110	7

Subgroups — C2×C7×#3110 #13237758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3110 #13237758