Subgroups — C₂×C₇×#3118 #13237763

Order 1792.

2274 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3118	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×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×#447	C₂	1	1	yes	maximal, characteristic
12	C₂×C₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
21	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
22	C₇×#542	—	2	4	no	—
23	C₇×#542	C₂²	1	8	yes	complemented
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×#126	—	2	1	no	—
26	C₂×C₇×#124	—	2	1	no	—
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₇×#123	—	2	1	no	—
29	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₇×#518	—	2	4	no	—
33	C₇×#518	C₂²	1	8	yes	complemented
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×C₇×D₄	—	2	1	no	—
36	C₂×C₄×C₇×D₄	—	2	1	no	—
37	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
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×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
45	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
46	C₇×#485	C₂²	1	8	yes	complemented
47	C₇×#482	C₂²	1	8	yes	complemented
48	C₇×#476	C₂²	1	8	yes	complemented
49	C₇×#474	C₂²	1	8	yes	complemented
50	C₇×#463	C₂²	1	8	yes	complemented
51	C₇×#463	C₂²	1	8	yes	complemented
52	C₇×#450	C₂²	1	8	yes	complemented
53	C₇×#447	C₂²	1	8	yes	—
54	C₇×#442	C₂²	1	8	yes	complemented
55	C₇×#440	C₂²	1	8	yes	complemented
56	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
57	C₄×C₇×D₈	C₂²	1	8	yes	complemented
58	C₇×#433	C₂²	1	8	yes	complemented
59	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₇×#102	C₂²	1	1	yes	characteristic
68	C₂×C₇×#102	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, complemented
72	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
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, complemented
76	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
77	C₂×#3118	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁵×C₇	—	2	1	no	—
79	C₂²×C₇×Q₈	—	2	1	no	—
80	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
81	C₂²×C₇×D₄	—	2	4	no	—
82	C₂²×C₇×D₄	—	2	4	no	—
83	C₂²×C₇×D₄	—	2	1	no	—
84	C₂²×C₇×D₄	—	2	1	no	—
85	C₂²×C₇×D₄	—	2	2	no	—
86	C₂²×C₇×D₄	C₂³	1	4	yes	—
87	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
88	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
89	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₇	—	2	1	no	—
91	C₂³×C₄×C₇	—	2	1	no	—
92	C₂³×C₄×C₇	—	2	1	no	—
93	C₂³×C₄×C₇	—	2	1	no	—
94	C₂³×C₄×C₇	—	2	1	no	—
95	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
96	C₂×C₇×SD₁₆	—	2	4	no	—
97	C₂×C₇×SD₁₆	—	2	4	no	—
98	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
99	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
100	C₂×C₇×D₈	—	2	4	no	—
101	C₂×C₇×D₈	—	2	4	no	—
102	C₂×C₇×D₈	C₂³	1	4	yes	—
103	C₂×C₇×D₈	C₂³	1	4	yes	—
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	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
108	C₇×C₄⋊Q₈	—	2	2	no	—
109	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
110	C₇×#126	—	2	8	no	—
111	C₇×#124	—	2	8	no	—
112	C₇×#124	—	2	2	no	—
113	C₇×#124	C₂³	1	4	yes	complemented
114	C₇×#123	—	2	8	no	—
115	C₇×C₂²⋊Q₈	—	2	2	no	—
116	C₇×C₂²⋊Q₈	—	2	8	no	—
117	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
118	C₇×#121	—	2	2	no	—
119	C₇×#121	C₂³	1	4	yes	—
120	C₄×C₇×Q₈	—	2	2	no	—
121	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
122	C₄×C₇×D₄	—	2	8	no	—
123	C₄×C₇×D₄	—	2	8	no	—
124	C₄×C₇×D₄	—	2	2	no	—
125	C₄×C₇×D₄	—	2	2	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	C₄×C₇×D₄	C₂³	1	4	yes	—
133	C₄×C₇×D₄	C₂³	1	4	yes	complemented
134	C₇×#117	—	2	2	no	—
135	C₇×#117	D₄	1	4	yes	—
136	C₇×#117	C₂³	1	4	yes	—
137	C₇×#117	C₂³	1	4	yes	—
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	D₄	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₇×C₂²⋊C₄	—	2	1	no	—
155	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
156	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
157	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
158	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
159	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
160	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₇	—	2	1	no	—
162	C₂×C₄²×C₇	—	2	1	no	—
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
165	C₇×#107	C₂³	1	4	yes	complemented
166	C₇×#107	C₂³	1	4	yes	complemented
167	C₇×#106	C₂³	1	4	yes	complemented
168	C₇×#106	C₂³	1	4	yes	complemented
169	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
170	C₇×C₄⋊C₈	C₂³	1	4	yes	complemented
171	C₇×#103	C₂³	1	4	yes	complemented
172	C₇×#103	C₂³	1	4	yes	complemented
173	C₇×#102	C₂³	1	4	yes	—
174	C₇×#102	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	complemented
178	C₇×#102	C₂³	1	4	yes	complemented
179	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
180	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
181	C₇×#97	C₂³	1	4	yes	complemented
182	C₄×C₇×C₈	C₂³	1	4	yes	complemented
183	C₂×#542	C₂×C₇	1	1	yes	characteristic, complemented
184	C₂×#518	C₂×C₇	1	1	yes	characteristic, complemented
185	#3118	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×#476	C₂×C₇	1	1	yes	characteristic, complemented
189	C₂×#474	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
191	C₂×#463	C₂×C₇	1	1	yes	characteristic, complemented
192	C₂×#450	C₂×C₇	1	1	yes	characteristic, complemented
193	C₂×#447	C₂×C₇	1	1	yes	characteristic
194	C₂×#442	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×#440	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
197	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
198	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
199	C₂⁴×C₇	—	2	8	no	—
200	C₂⁴×C₇	—	2	1	no	—
201	C₂⁴×C₇	—	2	1	no	—
202	C₂⁴×C₇	—	2	4	no	—
203	C₂⁴×C₇	—	2	1	no	—
204	C₂⁴×C₇	—	8	2	no	—
205	C₂⁴×C₇	—	8	2	no	—
206	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
207	C₂×C₇×Q₈	—	2	1	no	—
208	C₂×C₇×Q₈	—	2	4	no	—
209	C₂×C₇×Q₈	—	2	2	no	—
210	C₂×C₇×Q₈	—	2	2	no	—
211	C₂×C₇×Q₈	—	8	2	no	—
212	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
213	C₂×C₇×D₄	—	2	8	no	—
214	C₂×C₇×D₄	—	2	16	no	—
215	C₂×C₇×D₄	—	2	8	no	—
216	C₂×C₇×D₄	—	2	8	no	—
217	C₂×C₇×D₄	—	2	4	no	—
218	C₂×C₇×D₄	—	2	4	no	—
219	C₂×C₇×D₄	—	2	1	no	—
220	C₂×C₇×D₄	—	2	1	no	—
221	C₂×C₇×D₄	—	2	1	no	—
222	C₂×C₇×D₄	—	2	2	no	—
223	C₂×C₇×D₄	—	2	2	no	—
224	C₂×C₇×D₄	—	2	2	no	—
225	C₂×C₇×D₄	—	2	2	no	—
226	C₂×C₇×D₄	—	8	2	no	—
227	C₂×C₇×D₄	#41	1	4	yes	—
228	C₂×C₇×D₄	#41	1	4	yes	—
229	C₂×C₇×D₄	C₂⁴	1	2	yes	—
230	C₂×C₇×D₄	C₂⁴	1	2	yes	—
231	C₂×C₇×D₄	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇	—	2	2	no	—
233	C₂²×C₄×C₇	—	2	2	no	—
234	C₂²×C₄×C₇	—	2	1	no	—
235	C₂²×C₄×C₇	—	2	1	no	—
236	C₂²×C₄×C₇	—	2	1	no	—
237	C₂²×C₄×C₇	—	2	1	no	—
238	C₂²×C₄×C₇	—	2	1	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	—	2	4	no	—
242	C₂²×C₄×C₇	—	2	4	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	8	2	no	—
245	C₂²×C₄×C₇	—	8	2	no	—
246	C₂²×C₄×C₇	—	8	2	no	—
247	C₂²×C₄×C₇	—	8	2	no	—
248	C₂²×C₄×C₇	—	8	2	no	—
249	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
257	C₇×SD₁₆	—	2	8	no	—
258	C₇×SD₁₆	—	2	8	no	—
259	C₇×D₈	—	2	8	no	—
260	C₇×D₈	—	2	8	no	—
261	C₂×C₇×C₈	—	2	2	no	—
262	C₂×C₇×C₈	—	2	2	no	—
263	C₂×C₇×C₈	—	2	2	no	—
264	C₂×C₇×C₈	—	2	2	no	—
265	C₂×C₇×C₈	C₂⁴	1	2	yes	—
266	C₂×C₇×C₈	C₂⁴	1	2	yes	—
267	C₂×C₇×C₈	C₂⁴	1	2	yes	—
268	C₂×C₇×C₈	C₂⁴	1	2	yes	—
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	4	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	—	2	1	no	—
276	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
277	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	4	no	—
289	C₇×C₂²⋊C₄	—	2	4	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
293	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
294	C₄²×C₇	—	2	4	no	—
295	C₄²×C₇	—	2	4	no	—
296	C₄²×C₇	C₂×D₄	1	2	yes	—
297	C₄²×C₇	C₂×D₄	1	2	yes	—
298	C₄²×C₇	C₂⁴	1	2	yes	—
299	C₄²×C₇	C₂⁴	1	2	yes	—
300	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
301	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
302	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
303	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
304	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
305	#542	—	2	4	no	—
306	#542	C₂²×C₇	1	8	yes	complemented
307	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
308	C₂×#126	—	2	1	no	—
309	C₂×#124	—	2	1	no	—
310	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
311	C₂×#123	—	2	1	no	—
312	C₂×C₂²⋊Q₈	—	2	1	no	—
313	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
314	C₂×#121	C₂²×C₇	1	1	yes	characteristic
315	#518	—	2	4	no	—
316	#518	C₂²×C₇	1	8	yes	complemented
317	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
318	C₂×C₄×D₄	—	2	1	no	—
319	C₂×C₄×D₄	—	2	1	no	—
320	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
321	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
323	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
324	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
325	C₂×#117	C₂²×C₇	1	1	yes	characteristic
326	C₂×#117	C₂²×C₇	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	—	2	1	no	—
328	C₂²×C₂²⋊C₄	—	2	1	no	—
329	#485	C₂²×C₇	1	8	yes	complemented
330	#482	C₂²×C₇	1	8	yes	complemented
331	#476	C₂²×C₇	1	8	yes	complemented
332	#474	C₂²×C₇	1	8	yes	complemented
333	#463	C₂²×C₇	1	8	yes	complemented
334	#463	C₂²×C₇	1	8	yes	complemented
335	#450	C₂²×C₇	1	8	yes	complemented
336	#447	C₂²×C₇	1	8	yes	—
337	#442	C₂²×C₇	1	8	yes	complemented
338	#440	C₂²×C₇	1	8	yes	complemented
339	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
340	C₄×D₈	C₂²×C₇	1	8	yes	complemented
341	#433	C₂²×C₇	1	8	yes	complemented
342	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
343	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
345	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
346	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
347	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
348	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
349	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
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×#102	C₂²×C₇	1	1	yes	characteristic
354	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
356	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
357	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
358	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
360	C₂³×C₇	—	2	16	no	—
361	C₂³×C₇	—	2	2	no	—
362	C₂³×C₇	—	2	4	no	—
363	C₂³×C₇	—	2	4	no	—
364	C₂³×C₇	—	2	2	no	—
365	C₂³×C₇	—	2	2	no	—
366	C₂³×C₇	—	2	2	no	—
367	C₂³×C₇	—	2	2	no	—
368	C₂³×C₇	—	2	2	no	—
369	C₂³×C₇	—	4	2	no	—
370	C₂³×C₇	—	4	2	no	—
371	C₂³×C₇	—	4	2	no	—
372	C₂³×C₇	—	4	2	no	—
373	C₂³×C₇	—	4	2	no	—
374	C₂³×C₇	—	4	2	no	—
375	C₂³×C₇	—	4	2	no	—
376	C₂³×C₇	—	8	4	no	—
377	C₂³×C₇	—	8	4	no	—
378	C₂³×C₇	—	8	16	no	—
379	C₂³×C₇	C₂²×D₄	1	2	yes	—
380	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
381	C₇×Q₈	—	2	2	no	—
382	C₇×Q₈	—	2	2	no	—
383	C₇×Q₈	—	4	2	no	—
384	C₇×Q₈	—	8	4	no	—
385	C₇×D₄	—	2	16	no	—
386	C₇×D₄	—	2	4	no	—
387	C₇×D₄	—	2	4	no	—
388	C₇×D₄	—	2	2	no	—
389	C₇×D₄	—	2	2	no	—
390	C₇×D₄	—	2	2	no	—
391	C₇×D₄	—	2	2	no	—
392	C₇×D₄	—	4	2	no	—
393	C₇×D₄	—	8	4	no	—
394	C₇×D₄	C₂×#41	1	4	yes	—
395	C₇×D₄	C₂×#41	1	4	yes	—
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	—	2	2	no	—
401	C₂×C₄×C₇	—	2	4	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	—	4	2	no	—
410	C₂×C₄×C₇	—	4	2	no	—
411	C₂×C₄×C₇	—	4	2	no	—
412	C₂×C₄×C₇	—	4	2	no	—
413	C₂×C₄×C₇	—	4	2	no	—
414	C₂×C₄×C₇	—	8	4	no	—
415	C₂×C₄×C₇	—	8	4	no	—
416	C₂×C₄×C₇	—	8	4	no	—
417	C₂×C₄×C₇	—	8	4	no	—
418	C₂×C₄×C₇	—	8	4	no	—
419	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
425	C₂×C₄×C₇	C₂×#41	1	2	yes	—
426	C₂×C₄×C₇	C₂×#41	1	2	yes	—
427	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
428	C₇×C₈	—	2	2	no	—
429	C₇×C₈	—	2	2	no	—
430	C₇×C₈	—	2	2	no	—
431	C₇×C₈	—	2	2	no	—
432	C₂⁵	—	2	1	no	—
433	C₂²×Q₈	—	2	1	no	—
434	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	4	no	—
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	1	no	—
439	C₂²×D₄	—	2	2	no	—
440	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
441	C₂²×D₄	C₂³×C₇	1	4	yes	—
442	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
444	C₂³×C₄	—	2	1	no	—
445	C₂³×C₄	—	2	1	no	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	—	2	1	no	—
448	C₂³×C₄	—	2	1	no	—
449	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
450	C₂×SD₁₆	—	2	4	no	—
451	C₂×SD₁₆	—	2	4	no	—
452	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
453	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
454	C₂×D₈	—	2	4	no	—
455	C₂×D₈	—	2	4	no	—
456	C₂×D₈	C₂³×C₇	1	4	yes	—
457	C₂×D₈	C₂³×C₇	1	4	yes	—
458	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
459	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
460	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
461	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
462	C₄⋊Q₈	—	2	2	no	—
463	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
464	#126	—	2	8	no	—
465	#124	—	2	8	no	—
466	#124	—	2	2	no	—
467	#124	C₂³×C₇	1	4	yes	complemented
468	#123	—	2	8	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	—	2	8	no	—
471	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
472	#121	—	2	2	no	—
473	#121	C₂³×C₇	1	4	yes	—
474	C₄×Q₈	—	2	2	no	—
475	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
476	C₄×D₄	—	2	8	no	—
477	C₄×D₄	—	2	8	no	—
478	C₄×D₄	—	2	2	no	—
479	C₄×D₄	—	2	2	no	—
480	C₄×D₄	—	2	2	no	—
481	C₄×D₄	—	2	2	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	C₂³×C₇	1	4	yes	—
484	C₄×D₄	C₂³×C₇	1	4	yes	—
485	C₄×D₄	C₂³×C₇	1	4	yes	—
486	C₄×D₄	C₂³×C₇	1	4	yes	—
487	C₄×D₄	C₂³×C₇	1	4	yes	complemented
488	#117	—	2	2	no	—
489	#117	C₇×D₄	1	4	yes	—
490	#117	C₂³×C₇	1	4	yes	—
491	#117	C₂³×C₇	1	4	yes	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
497	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
498	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
500	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
501	C₂×C₂²⋊C₄	—	2	1	no	—
502	C₂×C₂²⋊C₄	—	2	1	no	—
503	C₂×C₂²⋊C₄	—	2	1	no	—
504	C₂×C₂²⋊C₄	—	2	1	no	—
505	C₂×C₂²⋊C₄	—	2	1	no	—
506	C₂×C₂²⋊C₄	—	2	1	no	—
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	8	no	—
512	C₂×C₂²⋊C₄	—	2	8	no	—
513	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
515	C₂×C₄²	—	2	1	no	—
516	C₂×C₄²	—	2	1	no	—
517	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
519	#107	C₂³×C₇	1	4	yes	complemented
520	#107	C₂³×C₇	1	4	yes	complemented
521	#106	C₂³×C₇	1	4	yes	complemented
522	#106	C₂³×C₇	1	4	yes	complemented
523	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
524	C₄⋊C₈	C₂³×C₇	1	4	yes	complemented
525	#103	C₂³×C₇	1	4	yes	complemented
526	#103	C₂³×C₇	1	4	yes	complemented
527	#102	C₂³×C₇	1	4	yes	—
528	#102	C₂³×C₇	1	4	yes	—
529	#102	C₂³×C₇	1	4	yes	—
530	#102	C₂³×C₇	1	4	yes	—
531	#102	C₂³×C₇	1	4	yes	complemented
532	#102	C₂³×C₇	1	4	yes	complemented
533	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
534	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
535	#97	C₂³×C₇	1	4	yes	complemented
536	C₄×C₈	C₂³×C₇	1	4	yes	complemented
537	C₂²×C₇	—	2	2	no	—
538	C₂²×C₇	—	2	4	no	—
539	C₂²×C₇	—	2	4	no	—
540	C₂²×C₇	—	2	2	no	—
541	C₂²×C₇	—	2	2	no	—
542	C₂²×C₇	—	4	4	no	—
543	C₂²×C₇	—	4	8	no	—
544	C₂²×C₇	—	4	8	no	—
545	C₂²×C₇	—	4	2	no	—
546	C₂²×C₇	—	4	2	no	—
547	C₂²×C₇	—	4	2	no	—
548	C₂²×C₇	—	4	2	no	—
549	C₂²×C₇	—	4	2	no	—
550	C₂²×C₇	—	4	2	no	—
551	C₂²×C₇	—	4	2	no	—
552	C₂²×C₇	—	8	16	no	—
553	C₂²×C₇	—	8	4	no	—
554	C₂²×C₇	#525	1	2	yes	—
555	C₂²×C₇	#576	1	2	yes	—
556	C₂²×C₇	#577	1	2	yes	—
557	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
558	C₄×C₇	—	2	2	no	—
559	C₄×C₇	—	2	2	no	—
560	C₄×C₇	—	2	2	no	—
561	C₄×C₇	—	2	2	no	—
562	C₄×C₇	—	2	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	#525	1	2	yes	—
569	C₄×C₇	C₂²×#41	1	1	yes	characteristic
570	C₄×C₇	C₂²×#41	1	1	yes	characteristic
571	C₂⁴	—	2	8	no	—
572	C₂⁴	—	2	1	no	—
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	4	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	—	8	2	no	—
577	C₂⁴	—	8	2	no	—
578	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	2	2	no	—
582	C₂×Q₈	—	2	2	no	—
583	C₂×Q₈	—	8	2	no	—
584	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
585	C₂×D₄	—	2	8	no	—
586	C₂×D₄	—	2	16	no	—
587	C₂×D₄	—	2	8	no	—
588	C₂×D₄	—	2	8	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	1	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	2	2	no	—
598	C₂×D₄	—	8	2	no	—
599	C₂×D₄	C₇×#41	1	4	yes	—
600	C₂×D₄	C₇×#41	1	4	yes	—
601	C₂×D₄	C₂⁴×C₇	1	2	yes	—
602	C₂×D₄	C₂⁴×C₇	1	2	yes	—
603	C₂×D₄	C₂⁴×C₇	1	2	yes	—
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	4	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	2	4	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	—	8	2	no	—
619	C₂²×C₄	—	8	2	no	—
620	C₂²×C₄	—	8	2	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	1	yes	characteristic
626	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
629	SD₁₆	—	2	8	no	—
630	SD₁₆	—	2	8	no	—
631	D₈	—	2	8	no	—
632	D₈	—	2	8	no	—
633	C₂×C₈	—	2	2	no	—
634	C₂×C₈	—	2	2	no	—
635	C₂×C₈	—	2	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	C₂⁴×C₇	1	2	yes	—
638	C₂×C₈	C₂⁴×C₇	1	2	yes	—
639	C₂×C₈	C₂⁴×C₇	1	2	yes	—
640	C₂×C₈	C₂⁴×C₇	1	2	yes	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	1	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
649	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
650	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
651	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
665	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	—	2	4	no	—
668	C₄²	C₂×C₇×D₄	1	2	yes	—
669	C₄²	C₂×C₇×D₄	1	2	yes	—
670	C₄²	C₂⁴×C₇	1	2	yes	—
671	C₄²	C₂⁴×C₇	1	2	yes	—
672	C₂×C₇	—	4	2	no	—
673	C₂×C₇	—	4	4	no	—
674	C₂×C₇	—	4	4	no	—
675	C₂×C₇	—	8	2	no	—
676	C₂×C₇	#3118	1	4	yes	direct product factor
677	C₂×C₇	C₂×#525	1	1	yes	characteristic
678	C₂×C₇	C₂×#576	1	1	yes	characteristic
679	C₂×C₇	C₂×#577	1	1	yes	characteristic
680	C₂³	—	2	16	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	2	2	no	—
683	C₂³	—	2	2	no	—
684	C₂³	—	2	4	no	—
685	C₂³	—	2	4	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	—	4	2	no	—
692	C₂³	—	4	2	no	—
693	C₂³	—	4	2	no	—
694	C₂³	—	4	2	no	—
695	C₂³	—	4	2	no	—
696	C₂³	—	8	4	no	—
697	C₂³	—	8	4	no	—
698	C₂³	—	8	16	no	—
699	C₂³	C₂²×C₇×D₄	1	2	yes	—
700	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
701	Q₈	—	2	2	no	—
702	Q₈	—	2	2	no	—
703	Q₈	—	4	2	no	—
704	Q₈	—	8	4	no	—
705	D₄	—	2	16	no	—
706	D₄	—	2	2	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	2	4	no	—
711	D₄	—	2	4	no	—
712	D₄	—	4	2	no	—
713	D₄	—	8	4	no	—
714	D₄	C₂×C₇×#41	1	4	yes	—
715	D₄	C₂×C₇×#41	1	4	yes	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	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	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	2	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	2	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	4	2	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	—	8	4	no	—
735	C₂×C₄	—	8	4	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
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	2	yes	—
742	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
743	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
744	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
745	C₂×C₄	C₂×C₇×#41	1	2	yes	—
746	C₂×C₄	C₂×C₇×#41	1	2	yes	—
747	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
748	C₈	—	2	2	no	—
749	C₈	—	2	2	no	—
750	C₈	—	2	2	no	—
751	C₈	—	2	2	no	—
752	C₇	C₂×#3118	1	1	yes	characteristic, direct product factor, Sylow
753	C₂²	—	2	2	no	—
754	C₂²	—	2	2	no	—
755	C₂²	—	2	2	no	—
756	C₂²	—	2	4	no	—
757	C₂²	—	2	4	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	2	no	—
762	C₂²	—	4	4	no	—
763	C₂²	—	4	8	no	—
764	C₂²	—	4	8	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	8	16	no	—
769	C₂²	—	8	4	no	—
770	C₂²	C₇×#525	1	2	yes	—
771	C₂²	C₇×#576	1	2	yes	—
772	C₂²	C₇×#577	1	2	yes	—
773	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	4	2	no	—
780	C₄	—	4	2	no	—
781	C₄	—	4	2	no	—
782	C₄	—	4	2	no	—
783	C₄	—	4	2	no	—
784	C₄	C₇×#525	1	2	yes	—
785	C₄	C₂²×C₇×#41	1	1	yes	characteristic
786	C₄	C₂²×C₇×#41	1	1	yes	characteristic
787	C₂	—	4	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	4	4	no	—
790	C₂	—	8	2	no	—
791	C₂	C₇×#3118	1	4	yes	direct product factor
792	C₂	C₂×C₇×#525	1	1	yes	characteristic
793	C₂	C₂×C₇×#576	1	1	yes	characteristic
794	C₂	C₂×C₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#542	C₂	semidirect
2. C₂×C₇×#518	C₂	semidirect
3. C₇×#3118	C₂	direct (N × H)
4. C₂×C₇×#485	C₂	semidirect
5. C₂×C₇×#482	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#463	C₂	semidirect
9. C₂×C₇×#463	C₂	semidirect
10. C₂×C₇×#450	C₂	semidirect
12. C₂×C₇×#442	C₂	semidirect
13. C₂×C₇×#440	C₂	semidirect
14. C₂×C₄×C₇×SD₁₆	C₂	semidirect
15. C₂×C₄×C₇×D₈	C₂	semidirect
16. C₂×C₇×#433	C₂	semidirect
23. C₇×#542	C₂²	semidirect
24. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₇×#124	C₂²	semidirect
33. C₇×#518	C₂²	semidirect
34. C₂×C₄×C₇×Q₈	C₂²	semidirect
41. C₂×C₄×C₇×D₄	C₂²	semidirect
46. C₇×#485	C₂²	semidirect
47. C₇×#482	C₂²	semidirect
48. C₇×#476	C₂²	semidirect
49. C₇×#474	C₂²	semidirect
50. C₇×#463	C₂²	semidirect
51. C₇×#463	C₂²	semidirect
52. C₇×#450	C₂²	semidirect
54. C₇×#442	C₂²	semidirect
55. C₇×#440	C₂²	semidirect
56. C₄×C₇×SD₁₆	C₂²	semidirect
57. C₄×C₇×D₈	C₂²	semidirect
58. C₇×#433	C₂²	semidirect
59. C₂×C₇×#107	C₂²	semidirect
60. C₂×C₇×#107	C₂²	semidirect
61. C₂×C₇×#106	C₂²	semidirect
62. C₂×C₇×#106	C₂²	semidirect
63. C₂×C₇×C₄⋊C₈	C₂²	semidirect
64. C₂×C₇×C₄⋊C₈	C₂²	semidirect
65. C₂×C₇×#103	C₂²	semidirect
66. C₂×C₇×#103	C₂²	semidirect
71. C₂×C₇×#102	C₂²	semidirect
72. C₂×C₇×#102	C₂²	semidirect
75. C₂×C₇×#97	C₂²	semidirect
76. C₂×C₄×C₇×C₈	C₂²	semidirect
77. C₂×#3118	C₇	direct (N × H)
109. C₇×C₄⋊Q₈	C₂³	semidirect
113. C₇×#124	C₂³	semidirect
121. C₄×C₇×Q₈	C₂³	semidirect
133. C₄×C₇×D₄	C₂³	semidirect
165. C₇×#107	C₂³	semidirect
166. C₇×#107	C₂³	semidirect
167. C₇×#106	C₂³	semidirect
168. C₇×#106	C₂³	semidirect
169. C₇×C₄⋊C₈	C₂³	semidirect
170. C₇×C₄⋊C₈	C₂³	semidirect
171. C₇×#103	C₂³	semidirect
172. C₇×#103	C₂³	semidirect
177. C₇×#102	C₂³	semidirect
178. C₇×#102	C₂³	semidirect
181. C₇×#97	C₂³	semidirect
182. C₄×C₇×C₈	C₂³	semidirect
183. C₂×#542	C₂×C₇	semidirect
184. C₂×#518	C₂×C₇	semidirect
185. #3118	C₂×C₇	direct (N × H)
186. C₂×#485	C₂×C₇	semidirect
187. C₂×#482	C₂×C₇	semidirect
188. C₂×#476	C₂×C₇	semidirect
189. C₂×#474	C₂×C₇	semidirect
190. C₂×#463	C₂×C₇	semidirect
191. C₂×#463	C₂×C₇	semidirect
192. C₂×#450	C₂×C₇	semidirect
194. C₂×#442	C₂×C₇	semidirect
195. C₂×#440	C₂×C₇	semidirect
196. C₂×C₄×SD₁₆	C₂×C₇	semidirect
197. C₂×C₄×D₈	C₂×C₇	semidirect
198. C₂×#433	C₂×C₇	semidirect
306. #542	C₂²×C₇	semidirect
307. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
310. C₂×#124	C₂²×C₇	semidirect
316. #518	C₂²×C₇	semidirect
317. C₂×C₄×Q₈	C₂²×C₇	semidirect
324. C₂×C₄×D₄	C₂²×C₇	semidirect
329. #485	C₂²×C₇	semidirect
330. #482	C₂²×C₇	semidirect
331. #476	C₂²×C₇	semidirect
332. #474	C₂²×C₇	semidirect
333. #463	C₂²×C₇	semidirect
334. #463	C₂²×C₇	semidirect
335. #450	C₂²×C₇	semidirect
337. #442	C₂²×C₇	semidirect
338. #440	C₂²×C₇	semidirect
339. C₄×SD₁₆	C₂²×C₇	semidirect
340. C₄×D₈	C₂²×C₇	semidirect
341. #433	C₂²×C₇	semidirect
342. C₂×#107	C₂²×C₇	semidirect
343. C₂×#107	C₂²×C₇	semidirect
344. C₂×#106	C₂²×C₇	semidirect
345. C₂×#106	C₂²×C₇	semidirect
346. C₂×C₄⋊C₈	C₂²×C₇	semidirect
347. C₂×C₄⋊C₈	C₂²×C₇	semidirect
348. C₂×#103	C₂²×C₇	semidirect
349. C₂×#103	C₂²×C₇	semidirect
354. C₂×#102	C₂²×C₇	semidirect
355. C₂×#102	C₂²×C₇	semidirect
358. C₂×#97	C₂²×C₇	semidirect
359. C₂×C₄×C₈	C₂²×C₇	semidirect
463. C₄⋊Q₈	C₂³×C₇	semidirect
467. #124	C₂³×C₇	semidirect
475. C₄×Q₈	C₂³×C₇	semidirect
487. C₄×D₄	C₂³×C₇	semidirect
519. #107	C₂³×C₇	semidirect
520. #107	C₂³×C₇	semidirect
521. #106	C₂³×C₇	semidirect
522. #106	C₂³×C₇	semidirect
523. C₄⋊C₈	C₂³×C₇	semidirect
524. C₄⋊C₈	C₂³×C₇	semidirect
525. #103	C₂³×C₇	semidirect
526. #103	C₂³×C₇	semidirect
531. #102	C₂³×C₇	semidirect
532. #102	C₂³×C₇	semidirect
535. #97	C₂³×C₇	semidirect
536. C₄×C₈	C₂³×C₇	semidirect
676. C₂×C₇	#3118	direct (N × H)
752. C₇	C₂×#3118	direct (N × H)
791. C₂	C₇×#3118	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×#542	2
C₂×C₇×#518	2
C₇×#3118	2
C₂×C₇×#485	2
C₂×C₇×#482	2
C₂×C₇×#476	2
C₂×C₇×#474	2
C₂×C₇×#463	2
C₂×C₇×#450	2
C₂×C₇×#447	2
C₂×C₇×#442	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#433	2
C₂×#3118	7

Subgroups — C2×C7×#3118 #13237763

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3118 #13237763