Subgroups — C₂×C₇×#3111 #13237759

Order 1792.

2182 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3111	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#449	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₇×#529	—	2	4	no	—
23	C₇×#529	C₂²	1	8	yes	complemented
24	C₂×C₇×#126	—	2	1	no	—
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#123	—	2	1	no	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₄×C₇×#41	—	2	4	no	—
31	C₄×C₇×#41	C₂²	1	8	yes	complemented
32	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×D₄	—	2	1	no	—
36	C₂×C₄×C₇×D₄	—	2	1	no	—
37	C₂×C₄×C₇×D₄	—	2	1	no	—
38	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₇×#117	—	2	1	no	—
42	C₂×C₇×#117	—	2	1	no	—
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₇	—	2	1	no	—
45	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
46	C₇×#485	C₂²	1	8	yes	complemented
47	C₇×#482	C₂²	1	8	yes	complemented
48	C₇×#479	C₂²	1	8	yes	complemented
49	C₇×#478	C₂²	1	8	yes	complemented
50	C₇×#464	C₂²	1	8	yes	complemented
51	C₇×#463	C₂²	1	8	yes	complemented
52	C₇×#452	C₂²	1	8	yes	complemented
53	C₇×#449	C₂²	1	8	yes	—
54	C₇×#442	C₂²	1	8	yes	complemented
55	C₇×#441	C₂²	1	8	yes	complemented
56	C₇×#440	C₂²	1	8	yes	complemented
57	C₇×#440	C₂²	1	8	yes	complemented
58	C₇×#432	C₂²	1	8	yes	complemented
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic
60	C₂×C₇×#107	C₂²	1	1	yes	characteristic
61	C₂×C₇×#106	C₂²	1	1	yes	characteristic
62	C₂×C₇×#106	C₂²	1	1	yes	characteristic
63	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic
67	C₂×C₇×#103	C₂²	1	1	yes	characteristic
68	C₂×C₇×#103	C₂²	1	1	yes	characteristic
69	C₂×C₇×#102	C₂²	1	1	yes	characteristic
70	C₂×C₇×#102	C₂²	1	1	yes	characteristic
71	C₂×C₇×#102	C₂²	1	1	yes	characteristic
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic
73	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×#97	C₂²	1	1	yes	characteristic
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic
77	C₂×#3111	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₇×#41	—	2	4	no	—
79	C₂×C₇×#41	—	2	4	no	—
80	C₂×C₇×#41	—	2	2	no	—
81	C₂×C₇×#41	C₂³	1	4	yes	—
82	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
83	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇×D₄	—	2	1	no	—
85	C₂²×C₇×D₄	—	2	1	no	—
86	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇	—	2	1	no	—
89	C₂³×C₄×C₇	—	2	1	no	—
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
94	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
95	C₂×C₇×Q₁₆	—	2	4	no	—
96	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
97	C₂×C₇×SD₁₆	—	2	4	no	—
98	C₂×C₇×SD₁₆	—	2	4	no	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
101	C₂×C₇×D₈	—	2	4	no	—
102	C₂×C₇×D₈	C₂³	1	4	yes	—
103	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
105	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
106	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
107	C₇×#126	—	2	8	no	—
108	C₇×#125	—	2	2	no	—
109	C₇×#125	C₂³	1	4	yes	—
110	C₇×#124	—	2	2	no	—
111	C₇×#124	C₂³	1	4	yes	—
112	C₇×#123	—	2	8	no	—
113	C₇×C₂²⋊Q₈	—	2	2	no	—
114	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
115	C₇×#121	—	2	2	no	—
116	C₇×#121	C₂³	1	4	yes	—
117	C₄×C₇×Q₈	—	2	2	no	—
118	C₄×C₇×Q₈	—	2	2	no	—
119	C₄×C₇×Q₈	—	2	2	no	—
120	C₄×C₇×Q₈	C₂³	1	4	yes	—
121	C₄×C₇×Q₈	C₂³	1	4	yes	—
122	C₄×C₇×Q₈	C₂³	1	4	yes	—
123	C₄×C₇×D₄	—	2	8	no	—
124	C₄×C₇×D₄	—	2	8	no	—
125	C₄×C₇×D₄	—	2	8	no	—
126	C₄×C₇×D₄	—	2	2	no	—
127	C₄×C₇×D₄	—	2	2	no	—
128	C₄×C₇×D₄	—	2	2	no	—
129	C₄×C₇×D₄	C₂³	1	4	yes	—
130	C₄×C₇×D₄	C₂³	1	4	yes	—
131	C₄×C₇×D₄	C₂³	1	4	yes	—
132	C₇×#117	—	2	2	no	—
133	C₇×#117	—	2	8	no	—
134	C₇×#117	—	2	8	no	—
135	C₇×#117	C₂³	1	4	yes	—
136	C₂×C₇×C₄⋊C₄	—	2	1	no	—
137	C₂×C₇×C₄⋊C₄	—	2	1	no	—
138	C₂×C₇×C₄⋊C₄	—	2	1	no	—
139	C₂×C₇×C₄⋊C₄	—	2	1	no	—
140	C₂×C₇×C₄⋊C₄	—	2	1	no	—
141	C₂×C₇×C₄⋊C₄	—	2	1	no	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
147	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
148	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
149	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
150	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
151	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
152	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
153	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
154	C₂×C₄²×C₇	—	2	1	no	—
155	C₂×C₄²×C₇	—	2	1	no	—
156	C₂×C₄²×C₇	—	2	1	no	—
157	C₂×C₄²×C₇	—	2	1	no	—
158	C₂×C₄²×C₇	—	2	8	no	—
159	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₇	D₄	1	4	yes	—
162	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	4	yes	—
165	C₇×#107	C₂³	1	4	yes	—
166	C₇×#107	C₂³	1	4	yes	—
167	C₇×#106	C₂³	1	4	yes	—
168	C₇×#106	C₂³	1	4	yes	—
169	C₇×C₄⋊C₈	C₂³	1	4	yes	—
170	C₇×C₄⋊C₈	C₂³	1	4	yes	—
171	C₇×#103	C₂³	1	4	yes	—
172	C₇×#103	C₂³	1	4	yes	—
173	C₇×#103	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#102	C₂³	1	4	yes	—
176	C₇×#102	C₂³	1	4	yes	—
177	C₇×#102	C₂³	1	4	yes	—
178	C₇×#102	C₂³	1	4	yes	—
179	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₇×#97	C₂³	1	4	yes	—
182	C₇×#97	C₂³	1	4	yes	—
183	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
185	#3111	C₂×C₇	1	16	yes	direct product factor
186	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#482	C₂×C₇	1	1	yes	characteristic, complemented
188	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
189	C₂×#478	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#449	C₂×C₇	1	1	yes	characteristic
194	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#441	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#432	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	1	no	—
200	C₂⁴×C₇	—	2	1	no	—
201	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
202	C₇×#41	—	2	16	no	—
203	C₇×#41	—	2	8	no	—
204	C₇×#41	—	2	8	no	—
205	C₂×C₇×Q₈	—	2	1	no	—
206	C₂×C₇×Q₈	—	2	1	no	—
207	C₂×C₇×Q₈	—	2	2	no	—
208	C₂×C₇×Q₈	—	2	2	no	—
209	C₂×C₇×Q₈	—	2	2	no	—
210	C₂×C₇×Q₈	#41	1	4	yes	—
211	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
212	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
213	C₂×C₇×D₄	—	2	8	no	—
214	C₂×C₇×D₄	—	2	4	no	—
215	C₂×C₇×D₄	—	2	4	no	—
216	C₂×C₇×D₄	—	2	1	no	—
217	C₂×C₇×D₄	—	2	1	no	—
218	C₂×C₇×D₄	—	2	2	no	—
219	C₂×C₇×D₄	—	2	2	no	—
220	C₂×C₇×D₄	—	2	2	no	—
221	C₂×C₇×D₄	—	4	4	no	—
222	C₂×C₇×D₄	#41	1	4	yes	—
223	C₂×C₇×D₄	C₂⁴	1	2	yes	—
224	C₂×C₇×D₄	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₇	—	2	8	no	—
226	C₂²×C₄×C₇	—	2	1	no	—
227	C₂²×C₄×C₇	—	2	4	no	—
228	C₂²×C₄×C₇	—	2	2	no	—
229	C₂²×C₄×C₇	—	2	2	no	—
230	C₂²×C₄×C₇	—	2	1	no	—
231	C₂²×C₄×C₇	—	2	1	no	—
232	C₂²×C₄×C₇	—	2	1	no	—
233	C₂²×C₄×C₇	—	2	1	no	—
234	C₂²×C₄×C₇	—	2	1	no	—
235	C₂²×C₄×C₇	—	2	4	no	—
236	C₂²×C₄×C₇	—	2	4	no	—
237	C₂²×C₄×C₇	—	2	4	no	—
238	C₂²×C₄×C₇	—	4	2	no	—
239	C₂²×C₄×C₇	—	4	2	no	—
240	C₂²×C₄×C₇	—	4	4	no	—
241	C₂²×C₄×C₇	—	4	4	no	—
242	C₂²×C₄×C₇	—	4	4	no	—
243	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
244	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
250	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₇×Q₁₆	—	2	8	no	—
254	C₇×SD₁₆	—	2	8	no	—
255	C₇×SD₁₆	—	2	8	no	—
256	C₇×D₈	—	2	8	no	—
257	C₂×C₇×C₈	—	2	2	no	—
258	C₂×C₇×C₈	—	2	2	no	—
259	C₂×C₇×C₈	—	2	2	no	—
260	C₂×C₇×C₈	—	2	2	no	—
261	C₂×C₇×C₈	C₂⁴	1	2	yes	—
262	C₂×C₇×C₈	C₂⁴	1	2	yes	—
263	C₂×C₇×C₈	C₂⁴	1	2	yes	—
264	C₂×C₇×C₈	C₂⁴	1	2	yes	—
265	C₇×C₄⋊C₄	—	2	4	no	—
266	C₇×C₄⋊C₄	—	2	4	no	—
267	C₇×C₄⋊C₄	—	2	4	no	—
268	C₇×C₄⋊C₄	—	2	4	no	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	1	no	—
272	C₇×C₄⋊C₄	—	2	1	no	—
273	C₇×C₄⋊C₄	—	2	1	no	—
274	C₇×C₄⋊C₄	—	2	1	no	—
275	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₂²⋊C₄	—	2	4	no	—
280	C₇×C₂²⋊C₄	—	2	4	no	—
281	C₇×C₂²⋊C₄	—	2	4	no	—
282	C₇×C₂²⋊C₄	—	2	4	no	—
283	C₇×C₂²⋊C₄	—	2	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	4	no	—
287	C₄²×C₇	—	2	4	no	—
288	C₄²×C₇	—	2	4	no	—
289	C₄²×C₇	—	2	4	no	—
290	C₄²×C₇	—	2	4	no	—
291	C₄²×C₇	C₂×D₄	1	4	yes	—
292	C₄²×C₇	C₂×D₄	1	4	yes	—
293	C₄²×C₇	C₂×D₄	1	2	yes	—
294	C₄²×C₇	C₂×D₄	1	2	yes	—
295	C₄²×C₇	C₂⁴	1	2	yes	—
296	C₄²×C₇	C₂⁴	1	2	yes	—
297	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
298	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
299	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
300	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
301	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
302	#529	—	2	4	no	—
303	#529	C₂²×C₇	1	8	yes	complemented
304	C₂×#126	—	2	1	no	—
305	C₂×#125	C₂²×C₇	1	1	yes	characteristic
306	C₂×#124	C₂²×C₇	1	1	yes	characteristic
307	C₂×#123	—	2	1	no	—
308	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
309	C₂×#121	C₂²×C₇	1	1	yes	characteristic
310	C₄×#41	—	2	4	no	—
311	C₄×#41	C₂²×C₇	1	8	yes	complemented
312	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
313	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
315	C₂×C₄×D₄	—	2	1	no	—
316	C₂×C₄×D₄	—	2	1	no	—
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
319	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
321	C₂×#117	—	2	1	no	—
322	C₂×#117	—	2	1	no	—
323	C₂×#117	C₂²×C₇	1	1	yes	characteristic
324	C₂²×C₄²	—	2	1	no	—
325	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
326	#485	C₂²×C₇	1	8	yes	complemented
327	#482	C₂²×C₇	1	8	yes	complemented
328	#479	C₂²×C₇	1	8	yes	complemented
329	#478	C₂²×C₇	1	8	yes	complemented
330	#464	C₂²×C₇	1	8	yes	complemented
331	#463	C₂²×C₇	1	8	yes	complemented
332	#452	C₂²×C₇	1	8	yes	complemented
333	#449	C₂²×C₇	1	8	yes	—
334	#442	C₂²×C₇	1	8	yes	complemented
335	#441	C₂²×C₇	1	8	yes	complemented
336	#440	C₂²×C₇	1	8	yes	complemented
337	#440	C₂²×C₇	1	8	yes	complemented
338	#432	C₂²×C₇	1	8	yes	complemented
339	C₂×#107	C₂²×C₇	1	1	yes	characteristic
340	C₂×#107	C₂²×C₇	1	1	yes	characteristic
341	C₂×#106	C₂²×C₇	1	1	yes	characteristic
342	C₂×#106	C₂²×C₇	1	1	yes	characteristic
343	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
345	C₂×#103	C₂²×C₇	1	1	yes	characteristic
346	C₂×#103	C₂²×C₇	1	1	yes	characteristic
347	C₂×#103	C₂²×C₇	1	1	yes	characteristic
348	C₂×#103	C₂²×C₇	1	1	yes	characteristic
349	C₂×#102	C₂²×C₇	1	1	yes	characteristic
350	C₂×#102	C₂²×C₇	1	1	yes	characteristic
351	C₂×#102	C₂²×C₇	1	1	yes	characteristic
352	C₂×#102	C₂²×C₇	1	1	yes	characteristic
353	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
355	C₂×#97	C₂²×C₇	1	1	yes	characteristic
356	C₂×#97	C₂²×C₇	1	1	yes	characteristic
357	C₂³×C₇	—	2	2	no	—
358	C₂³×C₇	—	2	4	no	—
359	C₂³×C₇	—	2	2	no	—
360	C₂³×C₇	—	2	2	no	—
361	C₂³×C₇	—	2	2	no	—
362	C₂³×C₇	—	2	2	no	—
363	C₂³×C₇	—	4	2	no	—
364	C₂³×C₇	—	4	2	no	—
365	C₂³×C₇	—	4	2	no	—
366	C₂³×C₇	—	4	2	no	—
367	C₂³×C₇	—	4	2	no	—
368	C₂³×C₇	C₂²×D₄	1	2	yes	—
369	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
370	C₇×Q₈	—	2	4	no	—
371	C₇×Q₈	—	2	2	no	—
372	C₇×Q₈	—	2	2	no	—
373	C₇×Q₈	—	2	2	no	—
374	C₇×Q₈	—	4	2	no	—
375	C₇×Q₈	C₂×#41	1	4	yes	—
376	C₇×D₄	—	2	16	no	—
377	C₇×D₄	—	2	4	no	—
378	C₇×D₄	—	2	2	no	—
379	C₇×D₄	—	2	2	no	—
380	C₇×D₄	—	2	2	no	—
381	C₇×D₄	—	4	8	no	—
382	C₇×D₄	—	4	2	no	—
383	C₇×D₄	C₂×#41	1	4	yes	—
384	C₂×C₄×C₇	—	2	16	no	—
385	C₂×C₄×C₇	—	2	2	no	—
386	C₂×C₄×C₇	—	2	4	no	—
387	C₂×C₄×C₇	—	2	2	no	—
388	C₂×C₄×C₇	—	2	2	no	—
389	C₂×C₄×C₇	—	2	2	no	—
390	C₂×C₄×C₇	—	2	2	no	—
391	C₂×C₄×C₇	—	2	2	no	—
392	C₂×C₄×C₇	—	2	4	no	—
393	C₂×C₄×C₇	—	2	2	no	—
394	C₂×C₄×C₇	—	2	2	no	—
395	C₂×C₄×C₇	—	2	2	no	—
396	C₂×C₄×C₇	—	2	2	no	—
397	C₂×C₄×C₇	—	2	2	no	—
398	C₂×C₄×C₇	—	2	2	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	4	4	no	—
401	C₂×C₄×C₇	—	4	4	no	—
402	C₂×C₄×C₇	—	4	8	no	—
403	C₂×C₄×C₇	—	4	8	no	—
404	C₂×C₄×C₇	—	4	8	no	—
405	C₂×C₄×C₇	—	4	2	no	—
406	C₂×C₄×C₇	—	4	2	no	—
407	C₂×C₄×C₇	—	4	2	no	—
408	C₂×C₄×C₇	—	4	2	no	—
409	C₂×C₄×C₇	—	4	2	no	—
410	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
412	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
413	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
414	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
415	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₇	C₂×#41	1	2	yes	—
417	C₂×C₄×C₇	C₂×#41	1	2	yes	—
418	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
419	C₇×C₈	—	2	2	no	—
420	C₇×C₈	—	2	2	no	—
421	C₇×C₈	—	2	2	no	—
422	C₇×C₈	—	2	2	no	—
423	C₂×#41	—	2	4	no	—
424	C₂×#41	—	2	4	no	—
425	C₂×#41	—	2	2	no	—
426	C₂×#41	C₂³×C₇	1	4	yes	—
427	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
428	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
429	C₂²×D₄	—	2	1	no	—
430	C₂²×D₄	—	2	1	no	—
431	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
432	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
433	C₂³×C₄	—	2	1	no	—
434	C₂³×C₄	—	2	1	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂³×C₄	—	2	1	no	—
437	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
438	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
440	C₂×Q₁₆	—	2	4	no	—
441	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
442	C₂×SD₁₆	—	2	4	no	—
443	C₂×SD₁₆	—	2	4	no	—
444	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
445	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
446	C₂×D₈	—	2	4	no	—
447	C₂×D₈	C₂³×C₇	1	4	yes	—
448	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
449	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
450	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
451	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
452	#126	—	2	8	no	—
453	#125	—	2	2	no	—
454	#125	C₂³×C₇	1	4	yes	—
455	#124	—	2	2	no	—
456	#124	C₂³×C₇	1	4	yes	—
457	#123	—	2	8	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
460	#121	—	2	2	no	—
461	#121	C₂³×C₇	1	4	yes	—
462	C₄×Q₈	—	2	2	no	—
463	C₄×Q₈	—	2	2	no	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	C₂³×C₇	1	4	yes	—
466	C₄×Q₈	C₂³×C₇	1	4	yes	—
467	C₄×Q₈	C₂³×C₇	1	4	yes	—
468	C₄×D₄	—	2	8	no	—
469	C₄×D₄	—	2	8	no	—
470	C₄×D₄	—	2	8	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	2	no	—
474	C₄×D₄	C₂³×C₇	1	4	yes	—
475	C₄×D₄	C₂³×C₇	1	4	yes	—
476	C₄×D₄	C₂³×C₇	1	4	yes	—
477	#117	—	2	2	no	—
478	#117	—	2	8	no	—
479	#117	—	2	8	no	—
480	#117	C₂³×C₇	1	4	yes	—
481	C₂×C₄⋊C₄	—	2	1	no	—
482	C₂×C₄⋊C₄	—	2	1	no	—
483	C₂×C₄⋊C₄	—	2	1	no	—
484	C₂×C₄⋊C₄	—	2	1	no	—
485	C₂×C₄⋊C₄	—	2	1	no	—
486	C₂×C₄⋊C₄	—	2	1	no	—
487	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₂²⋊C₄	—	2	1	no	—
493	C₂×C₂²⋊C₄	—	2	1	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₄²	—	2	1	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂×C₄²	—	2	1	no	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	8	no	—
504	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
505	C₂×C₄²	C₇×D₄	1	4	yes	—
506	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
507	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
508	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₄²	C₂³×C₇	1	4	yes	—
510	#107	C₂³×C₇	1	4	yes	—
511	#107	C₂³×C₇	1	4	yes	—
512	#106	C₂³×C₇	1	4	yes	—
513	#106	C₂³×C₇	1	4	yes	—
514	C₄⋊C₈	C₂³×C₇	1	4	yes	—
515	C₄⋊C₈	C₂³×C₇	1	4	yes	—
516	#103	C₂³×C₇	1	4	yes	—
517	#103	C₂³×C₇	1	4	yes	—
518	#103	C₂³×C₇	1	4	yes	—
519	#103	C₂³×C₇	1	4	yes	—
520	#102	C₂³×C₇	1	4	yes	—
521	#102	C₂³×C₇	1	4	yes	—
522	#102	C₂³×C₇	1	4	yes	—
523	#102	C₂³×C₇	1	4	yes	—
524	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
525	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
526	#97	C₂³×C₇	1	4	yes	—
527	#97	C₂³×C₇	1	4	yes	—
528	C₂²×C₇	—	2	2	no	—
529	C₂²×C₇	—	2	4	no	—
530	C₂²×C₇	—	2	2	no	—
531	C₂²×C₇	—	2	2	no	—
532	C₂²×C₇	—	4	4	no	—
533	C₂²×C₇	—	4	8	no	—
534	C₂²×C₇	—	4	2	no	—
535	C₂²×C₇	—	4	2	no	—
536	C₂²×C₇	—	4	2	no	—
537	C₂²×C₇	—	4	2	no	—
538	C₂²×C₇	—	4	2	no	—
539	C₂²×C₇	—	8	4	no	—
540	C₂²×C₇	#525	1	2	yes	—
541	C₂²×C₇	#575	1	2	yes	—
542	C₂²×C₇	#575	1	2	yes	—
543	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
544	C₄×C₇	—	2	2	no	—
545	C₄×C₇	—	2	4	no	—
546	C₄×C₇	—	2	2	no	—
547	C₄×C₇	—	2	2	no	—
548	C₄×C₇	—	2	2	no	—
549	C₄×C₇	—	2	2	no	—
550	C₄×C₇	—	4	2	no	—
551	C₄×C₇	—	4	2	no	—
552	C₄×C₇	—	4	2	no	—
553	C₄×C₇	—	4	2	no	—
554	C₄×C₇	—	4	2	no	—
555	C₄×C₇	#525	1	2	yes	—
556	C₄×C₇	C₂²×#41	1	1	yes	characteristic
557	C₄×C₇	C₂²×#41	1	1	yes	characteristic
558	C₂⁴	—	2	1	no	—
559	C₂⁴	—	2	1	no	—
560	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
561	#41	—	2	16	no	—
562	#41	—	2	8	no	—
563	#41	—	2	8	no	—
564	C₂×Q₈	—	2	1	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	2	no	—
568	C₂×Q₈	—	2	2	no	—
569	C₂×Q₈	C₇×#41	1	4	yes	—
570	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
571	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
572	C₂×D₄	—	2	8	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	4	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	2	2	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	C₇×#41	1	4	yes	—
582	C₂×D₄	C₂⁴×C₇	1	2	yes	—
583	C₂×D₄	C₂⁴×C₇	1	2	yes	—
584	C₂²×C₄	—	2	8	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	4	no	—
600	C₂²×C₄	—	4	4	no	—
601	C₂²×C₄	—	4	4	no	—
602	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
603	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
604	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
605	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
606	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
607	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
608	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
609	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
610	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
612	Q₁₆	—	2	8	no	—
613	SD₁₆	—	2	8	no	—
614	SD₁₆	—	2	8	no	—
615	D₈	—	2	8	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	C₂⁴×C₇	1	2	yes	—
621	C₂×C₈	C₂⁴×C₇	1	2	yes	—
622	C₂×C₈	C₂⁴×C₇	1	2	yes	—
623	C₂×C₈	C₂⁴×C₇	1	2	yes	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	—	2	4	no	—
646	C₄²	—	2	4	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	C₂×C₇×D₄	1	4	yes	—
651	C₄²	C₂×C₇×D₄	1	4	yes	—
652	C₄²	C₂×C₇×D₄	1	2	yes	—
653	C₄²	C₂×C₇×D₄	1	2	yes	—
654	C₄²	C₂⁴×C₇	1	2	yes	—
655	C₄²	C₂⁴×C₇	1	2	yes	—
656	C₂×C₇	—	4	2	no	—
657	C₂×C₇	—	4	4	no	—
658	C₂×C₇	—	8	2	no	—
659	C₂×C₇	#3111	1	4	yes	direct product factor
660	C₂×C₇	C₂×#525	1	1	yes	characteristic
661	C₂×C₇	C₂×#575	1	1	yes	characteristic
662	C₂×C₇	C₂×#575	1	1	yes	characteristic
663	C₂³	—	2	2	no	—
664	C₂³	—	2	2	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	4	2	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	2	no	—
672	C₂³	—	4	2	no	—
673	C₂³	—	4	2	no	—
674	C₂³	C₂²×C₇×D₄	1	2	yes	—
675	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	4	no	—
678	Q₈	—	2	2	no	—
679	Q₈	—	2	2	no	—
680	Q₈	—	4	2	no	—
681	Q₈	C₂×C₇×#41	1	4	yes	—
682	D₄	—	2	16	no	—
683	D₄	—	2	2	no	—
684	D₄	—	2	2	no	—
685	D₄	—	2	2	no	—
686	D₄	—	2	4	no	—
687	D₄	—	4	8	no	—
688	D₄	—	4	2	no	—
689	D₄	C₂×C₇×#41	1	4	yes	—
690	C₂×C₄	—	2	16	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	4	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	4	4	no	—
707	C₂×C₄	—	4	4	no	—
708	C₂×C₄	—	4	8	no	—
709	C₂×C₄	—	4	8	no	—
710	C₂×C₄	—	4	8	no	—
711	C₂×C₄	—	4	2	no	—
712	C₂×C₄	—	4	2	no	—
713	C₂×C₄	—	4	2	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
717	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
718	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
719	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
720	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
721	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
722	C₂×C₄	C₂×C₇×#41	1	2	yes	—
723	C₂×C₄	C₂×C₇×#41	1	2	yes	—
724	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
725	C₈	—	2	2	no	—
726	C₈	—	2	2	no	—
727	C₈	—	2	2	no	—
728	C₈	—	2	2	no	—
729	C₇	C₂×#3111	1	1	yes	characteristic, direct product factor, Sylow
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	2	2	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	—	4	8	no	—
738	C₂²	—	4	2	no	—
739	C₂²	—	4	2	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	8	4	no	—
742	C₂²	C₇×#525	1	2	yes	—
743	C₂²	C₇×#575	1	2	yes	—
744	C₂²	C₇×#575	1	2	yes	—
745	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
746	C₄	—	2	2	no	—
747	C₄	—	2	2	no	—
748	C₄	—	2	2	no	—
749	C₄	—	2	2	no	—
750	C₄	—	2	2	no	—
751	C₄	—	2	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	C₇×#525	1	2	yes	—
758	C₄	C₂²×C₇×#41	1	1	yes	characteristic
759	C₄	C₂²×C₇×#41	1	1	yes	characteristic
760	C₂	—	4	2	no	—
761	C₂	—	4	4	no	—
762	C₂	—	8	2	no	—
763	C₂	C₇×#3111	1	4	yes	direct product factor
764	C₂	C₂×C₇×#525	1	1	yes	characteristic
765	C₂	C₂×C₇×#575	1	1	yes	characteristic
766	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	C₂×C₇×#449	C₂
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×#529	C₂	semidirect
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₇×#3111	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#479	C₂	semidirect
7. C₂×C₇×#478	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×#452	C₂	semidirect
12. C₂×C₇×#442	C₂	semidirect
13. C₂×C₇×#441	C₂	semidirect
14. C₂×C₇×#440	C₂	semidirect
15. C₂×C₇×#440	C₂	semidirect
16. C₂×C₇×#432	C₂	semidirect
23. C₇×#529	C₂²	semidirect
31. C₄×C₇×#41	C₂²	semidirect
46. C₇×#485	C₂²	semidirect
47. C₇×#482	C₂²	semidirect
48. C₇×#479	C₂²	semidirect
49. C₇×#478	C₂²	semidirect
50. C₇×#464	C₂²	semidirect
51. C₇×#463	C₂²	semidirect
52. C₇×#452	C₂²	semidirect
54. C₇×#442	C₂²	semidirect
55. C₇×#441	C₂²	semidirect
56. C₇×#440	C₂²	semidirect
57. C₇×#440	C₂²	semidirect
58. C₇×#432	C₂²	semidirect
77. C₂×#3111	C₇	direct (N × H)
183. C₂×#529	C₂×C₇	semidirect
184. C₂×C₄×#41	C₂×C₇	semidirect
185. #3111	C₂×C₇	direct (N × H)
186. C₂×#485	C₂×C₇	semidirect
187. C₂×#482	C₂×C₇	semidirect
188. C₂×#479	C₂×C₇	semidirect
189. C₂×#478	C₂×C₇	semidirect
190. C₂×#464	C₂×C₇	semidirect
191. C₂×#463	C₂×C₇	semidirect
192. C₂×#452	C₂×C₇	semidirect
194. C₂×#442	C₂×C₇	semidirect
195. C₂×#441	C₂×C₇	semidirect
196. C₂×#440	C₂×C₇	semidirect
197. C₂×#440	C₂×C₇	semidirect
198. C₂×#432	C₂×C₇	semidirect
303. #529	C₂²×C₇	semidirect
311. C₄×#41	C₂²×C₇	semidirect
326. #485	C₂²×C₇	semidirect
327. #482	C₂²×C₇	semidirect
328. #479	C₂²×C₇	semidirect
329. #478	C₂²×C₇	semidirect
330. #464	C₂²×C₇	semidirect
331. #463	C₂²×C₇	semidirect
332. #452	C₂²×C₇	semidirect
334. #442	C₂²×C₇	semidirect
335. #441	C₂²×C₇	semidirect
336. #440	C₂²×C₇	semidirect
337. #440	C₂²×C₇	semidirect
338. #432	C₂²×C₇	semidirect
659. C₂×C₇	#3111	direct (N × H)
729. C₇	C₂×#3111	direct (N × H)
763. C₂	C₇×#3111	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×#529	2
C₂×C₄×C₇×#41	2
C₇×#3111	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#479	2
C₂×C₇×#478	2
C₂×C₇×#464	2
C₂×C₇×#463	2
C₂×C₇×#452	2
C₂×C₇×#449	2
C₂×C₇×#442	2
C₂×C₇×#441	2
C₂×C₇×#440	2
C₂×C₇×#432	2
C₂×#3111	7

Subgroups — C2×C7×#3111 #13237759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3111 #13237759