Subgroups — C₂×C₇×#3315 #13238350

Order 1792.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic
3	C₇×#3315	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
19	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
24	C₇×#552	—	2	4	no	—
25	C₇×#552	C₂²	1	8	yes	complemented
26	C₇×#547	—	2	4	no	—
27	C₇×#547	C₂²	1	8	yes	—
28	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#126	—	2	1	no	—
30	C₂×C₇×#125	—	2	1	no	—
31	C₂×C₇×#125	C₂²	1	1	yes	characteristic
32	C₂×C₇×#123	—	2	1	no	—
33	C₂×C₇×#123	—	2	1	no	—
34	C₂×C₇×#123	—	2	1	no	—
35	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₂×C₇×#121	—	2	1	no	—
40	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	—	2	1	no	—
44	C₂×C₇×#117	C₂²	1	1	yes	characteristic
45	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
46	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₇×#491	C₂²	1	8	yes	complemented
48	C₇×#485	C₂²	1	8	yes	complemented
49	C₇×#484	C₂²	1	8	yes	complemented
50	C₇×#478	C₂²	1	8	yes	complemented
51	C₇×#470	C₂²	1	8	yes	complemented
52	C₇×#467	C₂²	1	8	yes	complemented
53	C₇×#462	C₂²	1	8	yes	complemented
54	C₇×#452	C₂²	1	8	yes	complemented
55	C₇×#452	C₂²	1	8	yes	complemented
56	C₇×#440	C₂²	1	8	yes	complemented
57	C₇×#435	C₂²	1	8	yes	complemented
58	C₂×C₇×#107	C₂²	1	1	yes	characteristic
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic
60	C₂×C₇×#106	C₂²	1	1	yes	characteristic
61	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₇×#417	C₂²	1	8	yes	complemented
63	C₇×#416	C₂²	1	8	yes	complemented
64	C₂×C₇×#103	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×#103	C₂²	1	1	yes	characteristic
70	C₂×C₇×#103	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×#102	C₂²	1	1	yes	characteristic
74	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₇×#97	C₂²	1	1	yes	characteristic
77	C₂×#3315	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂×C₇×#41	—	2	2	no	—
79	C₂×C₇×#41	—	2	2	no	—
80	C₂×C₇×#41	—	2	4	no	—
81	C₂×C₇×#41	—	2	4	no	—
82	C₂×C₇×#41	—	4	2	no	—
83	C₂×C₇×#41	—	4	2	no	—
84	C₂×C₇×#41	C₂³	1	4	yes	—
85	C₂×C₇×#41	C₂³	1	4	yes	—
86	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
89	C₂²×C₇×D₄	—	2	1	no	—
90	C₂²×C₇×D₄	—	2	1	no	—
91	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
92	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇	—	2	1	no	—
94	C₂³×C₄×C₇	—	2	1	no	—
95	C₂³×C₄×C₇	—	2	1	no	—
96	C₂³×C₄×C₇	—	2	1	no	—
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₇×Q₁₆	—	4	2	no	—
100	C₂×C₇×Q₁₆	—	4	2	no	—
101	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
102	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
103	C₂×C₇×SD₁₆	—	2	4	no	—
104	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
105	C₂×C₇×M₁₆	—	4	2	no	—
106	C₂×C₇×M₁₆	C₂³	1	4	yes	—
107	C₂²×C₇×C₈	—	4	2	no	—
108	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
109	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
112	C₂²×C₇×C₈	C₂³	1	4	yes	—
113	C₇×C₄⋊Q₈	—	2	2	no	—
114	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
115	C₇×#126	—	2	8	no	—
116	C₇×#125	—	2	8	no	—
117	C₇×#125	—	2	2	no	—
118	C₇×#125	C₂³	1	4	yes	—
119	C₇×#123	—	2	8	no	—
120	C₇×#123	—	2	8	no	—
121	C₇×#123	—	2	8	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	—	2	2	no	—
126	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
130	C₇×#121	—	2	8	no	—
131	C₄×C₇×Q₈	—	2	2	no	—
132	C₄×C₇×Q₈	C₂³	1	4	yes	—
133	C₄×C₇×D₄	—	2	2	no	—
134	C₄×C₇×D₄	D₄	1	4	yes	—
135	C₄×C₇×D₄	C₂³	1	4	yes	—
136	C₄×C₇×D₄	C₂³	1	4	yes	—
137	C₇×#117	—	2	2	no	—
138	C₇×#117	—	2	8	no	—
139	C₇×#117	C₂³	1	4	yes	—
140	C₂×C₇×C₄⋊C₄	—	2	1	no	—
141	C₂×C₇×C₄⋊C₄	—	2	1	no	—
142	C₂×C₇×C₄⋊C₄	—	2	1	no	—
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	2	no	—
145	C₂×C₇×C₄⋊C₄	—	2	1	no	—
146	C₂×C₇×C₄⋊C₄	—	2	1	no	—
147	C₂×C₇×C₄⋊C₄	—	2	1	no	—
148	C₂×C₇×C₄⋊C₄	—	2	1	no	—
149	C₂×C₇×C₄⋊C₄	—	2	1	no	—
150	C₂×C₇×C₄⋊C₄	—	2	1	no	—
151	C₂×C₇×C₄⋊C₄	—	2	8	no	—
152	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
158	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
159	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
160	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
161	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
162	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
163	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
165	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₇	—	2	1	no	—
167	C₂×C₄²×C₇	—	2	1	no	—
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₇×#107	C₂³	1	4	yes	—
170	C₇×#107	C₂³	1	4	yes	—
171	C₇×#106	C₂³	1	4	yes	—
172	C₇×C₄⋊C₈	C₂³	1	4	yes	—
173	C₇×#103	C₂³	1	4	yes	—
174	C₇×#103	C₂³	1	4	yes	—
175	C₇×#103	C₂³	1	4	yes	—
176	C₇×#103	C₂³	1	4	yes	—
177	C₇×#103	C₂³	1	4	yes	—
178	C₇×#103	C₂³	1	4	yes	—
179	C₇×#103	C₂³	1	4	yes	—
180	C₇×#102	C₂³	1	4	yes	—
181	C₇×#102	C₂³	1	4	yes	—
182	C₇×#102	C₂³	1	4	yes	—
183	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
185	C₇×#97	C₂³	1	4	yes	—
186	C₂×#552	C₂×C₇	1	1	yes	characteristic, complemented
187	C₂×#547	C₂×C₇	1	1	yes	characteristic
188	#3315	C₂×C₇	1	16	yes	direct product factor
189	C₂×#491	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#484	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#485	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#478	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#470	C₂×C₇	1	1	yes	characteristic, complemented
194	C₂×#467	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×#452	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂×#435	C₂×C₇	1	1	yes	characteristic, complemented
200	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
201	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
202	C₂⁴×C₇	—	2	1	no	—
203	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
205	C₇×#41	—	2	8	no	—
206	C₇×#41	—	2	8	no	—
207	C₇×#41	—	4	4	no	—
208	C₇×#41	—	4	4	no	—
209	C₇×#41	—	4	8	no	—
210	C₇×#41	—	4	8	no	—
211	C₂×C₇×Q₈	—	2	1	no	—
212	C₂×C₇×Q₈	—	2	1	no	—
213	C₂×C₇×Q₈	—	2	1	no	—
214	C₂×C₇×Q₈	—	2	2	no	—
215	C₂×C₇×Q₈	—	2	2	no	—
216	C₂×C₇×Q₈	—	2	2	no	—
217	C₂×C₇×Q₈	—	2	2	no	—
218	C₂×C₇×Q₈	—	2	2	no	—
219	C₂×C₇×Q₈	—	2	2	no	—
220	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
221	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
222	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
223	C₂×C₇×D₄	—	2	4	no	—
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	1	no	—
226	C₂×C₇×D₄	—	2	2	no	—
227	C₂×C₇×D₄	—	4	2	no	—
228	C₂×C₇×D₄	—	4	4	no	—
229	C₂×C₇×D₄	—	4	4	no	—
230	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
231	C₂×C₇×D₄	#41	1	4	yes	—
232	C₂×C₇×D₄	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	2	no	—
235	C₂²×C₄×C₇	—	2	2	no	—
236	C₂²×C₄×C₇	—	2	2	no	—
237	C₂²×C₄×C₇	—	2	4	no	—
238	C₂²×C₄×C₇	—	2	1	no	—
239	C₂²×C₄×C₇	—	2	1	no	—
240	C₂²×C₄×C₇	—	2	1	no	—
241	C₂²×C₄×C₇	—	2	1	no	—
242	C₂²×C₄×C₇	—	2	1	no	—
243	C₂²×C₄×C₇	—	2	1	no	—
244	C₂²×C₄×C₇	—	2	1	no	—
245	C₂²×C₄×C₇	—	2	4	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	2	4	no	—
248	C₂²×C₄×C₇	—	4	4	no	—
249	C₂²×C₄×C₇	—	4	4	no	—
250	C₂²×C₄×C₇	—	4	4	no	—
251	C₂²×C₄×C₇	—	4	4	no	—
252	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
261	C₇×Q₁₆	—	4	4	no	—
262	C₇×Q₁₆	—	4	4	no	—
263	C₇×SD₁₆	—	2	8	no	—
264	C₇×M₁₆	—	4	4	no	—
265	C₂×C₇×C₈	—	2	2	no	—
266	C₂×C₇×C₈	—	2	2	no	—
267	C₂×C₇×C₈	—	2	2	no	—
268	C₂×C₇×C₈	—	2	2	no	—
269	C₂×C₇×C₈	—	4	4	no	—
270	C₂×C₇×C₈	C₂⁴	1	2	yes	—
271	C₂×C₇×C₈	C₂⁴	1	2	yes	—
272	C₂×C₇×C₈	C₂⁴	1	2	yes	—
273	C₂×C₇×C₈	C₂⁴	1	2	yes	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	4	no	—
276	C₇×C₄⋊C₄	—	2	4	no	—
277	C₇×C₄⋊C₄	—	2	1	no	—
278	C₇×C₄⋊C₄	—	2	1	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	1	no	—
287	C₇×C₄⋊C₄	—	2	1	no	—
288	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	4	no	—
296	C₇×C₂²⋊C₄	—	2	4	no	—
297	C₇×C₂²⋊C₄	—	2	4	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
300	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
301	C₄²×C₇	—	2	4	no	—
302	C₄²×C₇	—	2	4	no	—
303	C₄²×C₇	C₂×D₄	1	2	yes	—
304	C₄²×C₇	C₂⁴	1	2	yes	—
305	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
307	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
308	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
309	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
311	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
312	#552	—	2	4	no	—
313	#552	C₂²×C₇	1	8	yes	complemented
314	#547	—	2	4	no	—
315	#547	C₂²×C₇	1	8	yes	—
316	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
317	C₂×#126	—	2	1	no	—
318	C₂×#125	—	2	1	no	—
319	C₂×#125	C₂²×C₇	1	1	yes	characteristic
320	C₂×#123	—	2	1	no	—
321	C₂×#123	—	2	1	no	—
322	C₂×#123	—	2	1	no	—
323	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
324	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
325	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
326	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×#121	—	2	1	no	—
328	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
329	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
330	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
331	C₂×#117	—	2	1	no	—
332	C₂×#117	C₂²×C₇	1	1	yes	characteristic
333	C₂²×C₄⋊C₄	—	2	1	no	—
334	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
335	#491	C₂²×C₇	1	8	yes	complemented
336	#485	C₂²×C₇	1	8	yes	complemented
337	#484	C₂²×C₇	1	8	yes	complemented
338	#478	C₂²×C₇	1	8	yes	complemented
339	#470	C₂²×C₇	1	8	yes	complemented
340	#467	C₂²×C₇	1	8	yes	complemented
341	#462	C₂²×C₇	1	8	yes	complemented
342	#452	C₂²×C₇	1	8	yes	complemented
343	#452	C₂²×C₇	1	8	yes	complemented
344	#440	C₂²×C₇	1	8	yes	complemented
345	#435	C₂²×C₇	1	8	yes	complemented
346	C₂×#107	C₂²×C₇	1	1	yes	characteristic
347	C₂×#107	C₂²×C₇	1	1	yes	characteristic
348	C₂×#106	C₂²×C₇	1	1	yes	characteristic
349	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
350	#417	C₂²×C₇	1	8	yes	complemented
351	#416	C₂²×C₇	1	8	yes	complemented
352	C₂×#103	C₂²×C₇	1	1	yes	characteristic
353	C₂×#103	C₂²×C₇	1	1	yes	characteristic
354	C₂×#103	C₂²×C₇	1	1	yes	characteristic
355	C₂×#103	C₂²×C₇	1	1	yes	characteristic
356	C₂×#103	C₂²×C₇	1	1	yes	characteristic
357	C₂×#103	C₂²×C₇	1	1	yes	characteristic
358	C₂×#103	C₂²×C₇	1	1	yes	characteristic
359	C₂×#102	C₂²×C₇	1	1	yes	characteristic
360	C₂×#102	C₂²×C₇	1	1	yes	characteristic
361	C₂×#102	C₂²×C₇	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
364	C₂×#97	C₂²×C₇	1	1	yes	characteristic
365	C₂³×C₇	—	2	2	no	—
366	C₂³×C₇	—	2	2	no	—
367	C₂³×C₇	—	2	4	no	—
368	C₂³×C₇	—	2	2	no	—
369	C₂³×C₇	—	2	2	no	—
370	C₂³×C₇	—	2	2	no	—
371	C₂³×C₇	—	2	2	no	—
372	C₂³×C₇	—	2	2	no	—
373	C₂³×C₇	—	4	2	no	—
374	C₂³×C₇	—	4	2	no	—
375	C₂³×C₇	C₂²×D₄	1	2	yes	—
376	C₂³×C₇	C₂²×D₄	1	2	yes	—
377	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
378	C₇×Q₈	—	2	2	no	—
379	C₇×Q₈	—	2	2	no	—
380	C₇×Q₈	—	2	2	no	—
381	C₇×Q₈	—	2	2	no	—
382	C₇×Q₈	—	2	2	no	—
383	C₇×Q₈	—	2	2	no	—
384	C₇×Q₈	—	4	2	no	—
385	C₇×Q₈	—	4	2	no	—
386	C₇×Q₈	—	4	2	no	—
387	C₇×D₄	—	2	4	no	—
388	C₇×D₄	—	2	2	no	—
389	C₇×D₄	—	4	4	no	—
390	C₇×D₄	—	4	8	no	—
391	C₇×D₄	—	4	8	no	—
392	C₇×D₄	C₂×#41	1	4	yes	—
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	4	no	—
398	C₂×C₄×C₇	—	2	4	no	—
399	C₂×C₄×C₇	—	2	2	no	—
400	C₂×C₄×C₇	—	2	2	no	—
401	C₂×C₄×C₇	—	2	2	no	—
402	C₂×C₄×C₇	—	2	2	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	2	no	—
406	C₂×C₄×C₇	—	2	2	no	—
407	C₂×C₄×C₇	—	2	2	no	—
408	C₂×C₄×C₇	—	2	2	no	—
409	C₂×C₄×C₇	—	2	2	no	—
410	C₂×C₄×C₇	—	4	8	no	—
411	C₂×C₄×C₇	—	4	8	no	—
412	C₂×C₄×C₇	—	4	8	no	—
413	C₂×C₄×C₇	—	4	8	no	—
414	C₂×C₄×C₇	—	4	2	no	—
415	C₂×C₄×C₇	—	4	2	no	—
416	C₂×C₄×C₇	—	4	2	no	—
417	C₂×C₄×C₇	—	4	2	no	—
418	C₂×C₄×C₇	—	4	2	no	—
419	C₂×C₄×C₇	—	4	2	no	—
420	C₂×C₄×C₇	—	4	2	no	—
421	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
422	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
423	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
425	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇	C₂×#41	1	2	yes	—
427	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
428	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
429	C₇×C₈	—	2	2	no	—
430	C₇×C₈	—	2	2	no	—
431	C₇×C₈	—	2	2	no	—
432	C₇×C₈	—	2	2	no	—
433	C₂×#41	—	2	2	no	—
434	C₂×#41	—	2	2	no	—
435	C₂×#41	—	2	4	no	—
436	C₂×#41	—	2	4	no	—
437	C₂×#41	—	4	2	no	—
438	C₂×#41	—	4	2	no	—
439	C₂×#41	C₂³×C₇	1	4	yes	—
440	C₂×#41	C₂³×C₇	1	4	yes	—
441	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
442	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
443	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
447	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	—	2	1	no	—
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
454	C₂×Q₁₆	—	4	2	no	—
455	C₂×Q₁₆	—	4	2	no	—
456	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
457	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
458	C₂×SD₁₆	—	2	4	no	—
459	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
460	C₂×M₁₆	—	4	2	no	—
461	C₂×M₁₆	C₂³×C₇	1	4	yes	—
462	C₂²×C₈	—	4	2	no	—
463	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
467	C₂²×C₈	C₂³×C₇	1	4	yes	—
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
470	#126	—	2	8	no	—
471	#125	—	2	8	no	—
472	#125	—	2	2	no	—
473	#125	C₂³×C₇	1	4	yes	—
474	#123	—	2	8	no	—
475	#123	—	2	8	no	—
476	#123	—	2	8	no	—
477	C₂²⋊Q₈	—	2	2	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	2	no	—
480	C₂²⋊Q₈	—	2	2	no	—
481	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
483	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
484	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
485	#121	—	2	8	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	C₂³×C₇	1	4	yes	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	C₇×D₄	1	4	yes	—
490	C₄×D₄	C₂³×C₇	1	4	yes	—
491	C₄×D₄	C₂³×C₇	1	4	yes	—
492	#117	—	2	2	no	—
493	#117	—	2	8	no	—
494	#117	C₂³×C₇	1	4	yes	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	—	2	1	no	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	—	2	2	no	—
500	C₂×C₄⋊C₄	—	2	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	8	no	—
507	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
521	C₂×C₄²	—	2	1	no	—
522	C₂×C₄²	—	2	1	no	—
523	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
524	#107	C₂³×C₇	1	4	yes	—
525	#107	C₂³×C₇	1	4	yes	—
526	#106	C₂³×C₇	1	4	yes	—
527	C₄⋊C₈	C₂³×C₇	1	4	yes	—
528	#103	C₂³×C₇	1	4	yes	—
529	#103	C₂³×C₇	1	4	yes	—
530	#103	C₂³×C₇	1	4	yes	—
531	#103	C₂³×C₇	1	4	yes	—
532	#103	C₂³×C₇	1	4	yes	—
533	#103	C₂³×C₇	1	4	yes	—
534	#103	C₂³×C₇	1	4	yes	—
535	#102	C₂³×C₇	1	4	yes	—
536	#102	C₂³×C₇	1	4	yes	—
537	#102	C₂³×C₇	1	4	yes	—
538	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
539	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
540	#97	C₂³×C₇	1	4	yes	—
541	C₂²×C₇	—	2	2	no	—
542	C₂²×C₇	—	2	2	no	—
543	C₂²×C₇	—	2	4	no	—
544	C₂²×C₇	—	2	2	no	—
545	C₂²×C₇	—	2	2	no	—
546	C₂²×C₇	—	2	2	no	—
547	C₂²×C₇	—	2	2	no	—
548	C₂²×C₇	—	4	4	no	—
549	C₂²×C₇	—	4	4	no	—
550	C₂²×C₇	—	4	8	no	—
551	C₂²×C₇	—	4	2	no	—
552	C₂²×C₇	—	4	2	no	—
553	C₂²×C₇	#546	1	2	yes	—
554	C₂²×C₇	#575	1	2	yes	—
555	C₂²×C₇	#578	1	2	yes	—
556	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
557	C₄×C₇	—	2	2	no	—
558	C₄×C₇	—	2	2	no	—
559	C₄×C₇	—	2	2	no	—
560	C₄×C₇	—	2	2	no	—
561	C₄×C₇	—	4	2	no	—
562	C₄×C₇	—	4	2	no	—
563	C₄×C₇	—	4	2	no	—
564	C₄×C₇	—	4	2	no	—
565	C₄×C₇	—	4	2	no	—
566	C₄×C₇	—	4	2	no	—
567	C₄×C₇	—	4	2	no	—
568	C₄×C₇	#546	1	2	yes	—
569	C₄×C₇	C₂²×#41	1	1	yes	characteristic
570	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₂⁴	—	2	1	no	—
572	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
573	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
574	#41	—	2	8	no	—
575	#41	—	2	8	no	—
576	#41	—	4	4	no	—
577	#41	—	4	4	no	—
578	#41	—	4	8	no	—
579	#41	—	4	8	no	—
580	C₂×Q₈	—	2	1	no	—
581	C₂×Q₈	—	2	1	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	2	no	—
584	C₂×Q₈	—	2	2	no	—
585	C₂×Q₈	—	2	2	no	—
586	C₂×Q₈	—	2	2	no	—
587	C₂×Q₈	—	2	2	no	—
588	C₂×Q₈	—	2	2	no	—
589	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
590	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
591	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	4	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	—	4	4	no	—
598	C₂×D₄	—	4	4	no	—
599	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
600	C₂×D₄	C₇×#41	1	4	yes	—
601	C₂×D₄	C₂⁴×C₇	1	2	yes	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	1	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	1	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	2	4	no	—
617	C₂²×C₄	—	4	4	no	—
618	C₂²×C₄	—	4	4	no	—
619	C₂²×C₄	—	4	4	no	—
620	C₂²×C₄	—	4	4	no	—
621	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
622	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
623	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
624	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
625	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
626	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
629	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
630	Q₁₆	—	4	4	no	—
631	Q₁₆	—	4	4	no	—
632	SD₁₆	—	2	8	no	—
633	M₁₆	—	4	4	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	2	2	no	—
638	C₂×C₈	—	4	4	no	—
639	C₂×C₈	C₂⁴×C₇	1	2	yes	—
640	C₂×C₈	C₂⁴×C₇	1	2	yes	—
641	C₂×C₈	C₂⁴×C₇	1	2	yes	—
642	C₂×C₈	C₂⁴×C₇	1	2	yes	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	4	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	1	no	—
656	C₄⋊C₄	—	2	1	no	—
657	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
658	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
659	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
660	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
661	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	—	2	4	no	—
665	C₂²⋊C₄	—	2	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
669	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
670	C₄²	—	2	4	no	—
671	C₄²	—	2	4	no	—
672	C₄²	C₂×C₇×D₄	1	2	yes	—
673	C₄²	C₂⁴×C₇	1	2	yes	—
674	C₂×C₇	—	4	2	no	—
675	C₂×C₇	—	4	2	no	—
676	C₂×C₇	—	4	4	no	—
677	C₂×C₇	#3315	1	4	yes	direct product factor
678	C₂×C₇	C₂×#546	1	1	yes	characteristic
679	C₂×C₇	C₂×#575	1	1	yes	characteristic
680	C₂×C₇	C₂×#578	1	1	yes	characteristic
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	4	2	no	—
690	C₂³	—	4	2	no	—
691	C₂³	C₂²×C₇×D₄	1	2	yes	—
692	C₂³	C₂²×C₇×D₄	1	2	yes	—
693	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	2	2	no	—
697	Q₈	—	2	2	no	—
698	Q₈	—	2	2	no	—
699	Q₈	—	2	2	no	—
700	Q₈	—	4	2	no	—
701	Q₈	—	4	2	no	—
702	Q₈	—	4	2	no	—
703	D₄	—	2	2	no	—
704	D₄	—	2	4	no	—
705	D₄	—	4	4	no	—
706	D₄	—	4	8	no	—
707	D₄	—	4	8	no	—
708	D₄	C₂×C₇×#41	1	4	yes	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	2	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	2	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	4	8	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	4	8	no	—
729	C₂×C₄	—	4	8	no	—
730	C₂×C₄	—	4	2	no	—
731	C₂×C₄	—	4	2	no	—
732	C₂×C₄	—	4	2	no	—
733	C₂×C₄	—	4	2	no	—
734	C₂×C₄	—	4	2	no	—
735	C₂×C₄	—	4	2	no	—
736	C₂×C₄	—	4	2	no	—
737	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
738	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
739	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
740	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
741	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
742	C₂×C₄	C₂×C₇×#41	1	2	yes	—
743	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
744	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
745	C₈	—	2	2	no	—
746	C₈	—	2	2	no	—
747	C₈	—	2	2	no	—
748	C₈	—	2	2	no	—
749	C₇	C₂×#3315	1	1	yes	characteristic, direct product factor, Sylow
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	4	no	—
760	C₂²	—	4	4	no	—
761	C₂²	—	4	8	no	—
762	C₂²	C₇×#546	1	2	yes	—
763	C₂²	C₇×#575	1	2	yes	—
764	C₂²	C₇×#578	1	2	yes	—
765	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	2	2	no	—
770	C₄	—	4	2	no	—
771	C₄	—	4	2	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	2	no	—
774	C₄	—	4	2	no	—
775	C₄	—	4	2	no	—
776	C₄	—	4	2	no	—
777	C₄	C₇×#546	1	2	yes	—
778	C₄	C₂²×C₇×#41	1	1	yes	characteristic
779	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
780	C₂	—	4	2	no	—
781	C₂	—	4	2	no	—
782	C₂	—	4	4	no	—
783	C₂	C₇×#3315	1	4	yes	direct product factor
784	C₂	C₂×C₇×#546	1	1	yes	characteristic
785	C₂	C₂×C₇×#575	1	1	yes	characteristic
786	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#547	C₂
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. C₂×C₇×#552	C₂	semidirect
3. C₇×#3315	C₂	direct (N × H)
4. C₂×C₇×#491	C₂	semidirect
5. C₂×C₇×#484	C₂	semidirect
6. C₂×C₇×#485	C₂	semidirect
7. C₂×C₇×#478	C₂	semidirect
8. C₂×C₇×#470	C₂	semidirect
9. C₂×C₇×#467	C₂	semidirect
10. C₂×C₇×#462	C₂	semidirect
11. C₂×C₇×#452	C₂	semidirect
12. C₂×C₇×#452	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₇×#435	C₂	semidirect
15. C₂×C₇×#417	C₂	semidirect
16. C₂×C₇×#416	C₂	semidirect
25. C₇×#552	C₂²	semidirect
47. C₇×#491	C₂²	semidirect
48. C₇×#485	C₂²	semidirect
49. C₇×#484	C₂²	semidirect
50. C₇×#478	C₂²	semidirect
51. C₇×#470	C₂²	semidirect
52. C₇×#467	C₂²	semidirect
53. C₇×#462	C₂²	semidirect
54. C₇×#452	C₂²	semidirect
55. C₇×#452	C₂²	semidirect
56. C₇×#440	C₂²	semidirect
57. C₇×#435	C₂²	semidirect
62. C₇×#417	C₂²	semidirect
63. C₇×#416	C₂²	semidirect
77. C₂×#3315	C₇	direct (N × H)
186. C₂×#552	C₂×C₇	semidirect
188. #3315	C₂×C₇	direct (N × H)
189. C₂×#491	C₂×C₇	semidirect
190. C₂×#484	C₂×C₇	semidirect
191. C₂×#485	C₂×C₇	semidirect
192. C₂×#478	C₂×C₇	semidirect
193. C₂×#470	C₂×C₇	semidirect
194. C₂×#467	C₂×C₇	semidirect
195. C₂×#462	C₂×C₇	semidirect
196. C₂×#452	C₂×C₇	semidirect
197. C₂×#452	C₂×C₇	semidirect
198. C₂×#440	C₂×C₇	semidirect
199. C₂×#435	C₂×C₇	semidirect
200. C₂×#417	C₂×C₇	semidirect
201. C₂×#416	C₂×C₇	semidirect
313. #552	C₂²×C₇	semidirect
335. #491	C₂²×C₇	semidirect
336. #485	C₂²×C₇	semidirect
337. #484	C₂²×C₇	semidirect
338. #478	C₂²×C₇	semidirect
339. #470	C₂²×C₇	semidirect
340. #467	C₂²×C₇	semidirect
341. #462	C₂²×C₇	semidirect
342. #452	C₂²×C₇	semidirect
343. #452	C₂²×C₇	semidirect
344. #440	C₂²×C₇	semidirect
345. #435	C₂²×C₇	semidirect
350. #417	C₂²×C₇	semidirect
351. #416	C₂²×C₇	semidirect
677. C₂×C₇	#3315	direct (N × H)
749. C₇	C₂×#3315	direct (N × H)
783. C₂	C₇×#3315	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×#552	2
C₂×C₇×#547	2
C₇×#3315	2
C₂×C₇×#491	2
C₂×C₇×#484	2
C₂×C₇×#485	2
C₂×C₇×#478	2
C₂×C₇×#470	2
C₂×C₇×#467	2
C₂×C₇×#462	2
C₂×C₇×#452	2
C₂×C₇×#440	2
C₂×C₇×#435	2
C₂×C₇×#417	2
C₂×C₇×#416	2
C₂×#3315	7

Subgroups — C2×C7×#3315 #13238350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3315 #13238350