Subgroups — C₂×C₇×#3335 #13238442

Order 1792.

2158 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#547	C₂	1	1	yes	maximal, characteristic
3	C₇×#3335	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#481	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#483	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#465	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₇×#106	C₂	1	2	yes	maximal, complemented
13	C₂²×C₇×#41	—	2	1	no	—
14	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	2	yes	—
16	C₇×#554	—	2	4	no	—
17	C₇×#554	C₂²	1	8	yes	complemented
18	C₇×#547	—	2	4	no	—
19	C₇×#547	C₂²	1	8	yes	—
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#125	—	2	1	no	—
23	C₂×C₇×#123	—	2	2	no	—
24	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂×C₇×#121	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	—	2	1	no	—
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
32	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
34	C₇×#498	C₂²	1	8	yes	complemented
35	C₇×#483	C₂²	1	16	yes	complemented
36	C₇×#481	C₂²	1	16	yes	complemented
37	C₇×#476	C₂²	1	8	yes	complemented
38	C₇×#475	C₂²	1	8	yes	complemented
39	C₇×#465	C₂²	1	16	yes	complemented
40	C₄×C₇×SD₁₆	C₂²	1	8	yes	complemented
41	C₇×C₈×D₄	C₂²	1	8	yes	complemented
42	C₂×C₇×#106	C₂²	1	2	yes	—
43	C₂×C₇×#106	C₂²	1	2	yes	—
44	C₂×C₇×#106	C₂²	1	1	yes	characteristic
45	C₂×C₇×#106	C₂²	1	2	yes	—
46	C₂×C₇×#106	C₂²	1	2	yes	—
47	C₂×C₇×#106	C₂²	1	16	yes	complemented
48	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₇×#103	C₂²	1	1	yes	characteristic
50	C₂×C₇×#103	C₂²	1	2	yes	—
51	C₂×C₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₇×#102	C₂²	1	2	yes	—
53	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
54	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
55	C₂×#3335	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×C₇×#41	—	2	8	no	—
57	C₂×C₇×#41	—	4	8	no	—
58	C₂²×C₇×Q₈	—	2	1	no	—
59	C₂²×C₇×Q₈	—	2	1	no	—
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×D₄	—	2	2	no	—
62	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
63	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₇	—	2	2	no	—
65	C₂³×C₄×C₇	—	2	2	no	—
66	C₂³×C₄×C₇	—	2	1	no	—
67	C₂³×C₄×C₇	C₂³	1	2	yes	—
68	C₂×C₇×SD₁₆	—	2	4	no	—
69	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
70	C₂²×C₇×C₈	—	2	8	no	—
71	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₇×C₈	C₂³	1	2	yes	—
73	C₂²×C₇×C₈	C₂³	1	8	yes	—
74	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
75	C₇×C₄⋊Q₈	—	2	2	no	—
76	C₇×C₄⋊Q₈	—	2	2	no	—
77	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₇×#125	—	2	8	no	—
80	C₇×#123	—	2	16	no	—
81	C₇×C₂²⋊Q₈	—	2	4	no	—
82	C₇×C₂²⋊Q₈	—	2	8	no	—
83	C₇×C₂²⋊Q₈	—	2	16	no	—
84	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
85	C₇×#121	—	2	4	no	—
86	C₇×#121	C₂³	1	8	yes	—
87	C₄×C₇×Q₈	—	2	2	no	—
88	C₄×C₇×Q₈	C₂³	1	4	yes	—
89	C₄×C₇×D₄	—	2	8	no	—
90	C₄×C₇×D₄	—	2	2	no	—
91	C₄×C₇×D₄	D₄	1	4	yes	—
92	C₄×C₇×D₄	C₂³	1	4	yes	—
93	C₄×C₇×D₄	C₂³	1	4	yes	—
94	C₂×C₇×C₄⋊C₄	—	2	2	no	—
95	C₂×C₇×C₄⋊C₄	—	2	2	no	—
96	C₂×C₇×C₄⋊C₄	—	2	4	no	—
97	C₂×C₇×C₄⋊C₄	—	2	4	no	—
98	C₂×C₇×C₄⋊C₄	—	2	1	no	—
99	C₂×C₇×C₄⋊C₄	—	2	1	no	—
100	C₂×C₇×C₄⋊C₄	—	2	2	no	—
101	C₂×C₇×C₄⋊C₄	—	2	1	no	—
102	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
104	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
105	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
113	C₂×C₄²×C₇	—	2	1	no	—
114	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
115	C₇×#106	C₂³	1	8	yes	—
116	C₇×#106	C₂³	1	8	yes	—
117	C₇×#106	C₂³	1	8	yes	—
118	C₇×#106	C₂³	1	8	yes	—
119	C₇×#106	C₂³	1	4	yes	—
120	C₇×C₄⋊C₈	C₂³	1	4	yes	—
121	C₇×#103	C₂³	1	8	yes	—
122	C₇×#103	C₂³	1	4	yes	—
123	C₇×#102	C₂³	1	8	yes	—
124	C₇×#102	C₂³	1	4	yes	—
125	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
126	C₄×C₇×C₈	C₂³	1	4	yes	—
127	C₂×#554	C₂×C₇	1	1	yes	characteristic, complemented
128	C₂×#547	C₂×C₇	1	1	yes	characteristic
129	#3335	C₂×C₇	1	16	yes	direct product factor
130	C₂×#498	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#481	C₂×C₇	1	2	yes	complemented
132	C₂×#483	C₂×C₇	1	2	yes	complemented
133	C₂×#475	C₂×C₇	1	1	yes	characteristic, complemented
134	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
135	C₂×#465	C₂×C₇	1	2	yes	complemented
136	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
138	C₂²×#106	C₂×C₇	1	2	yes	complemented
139	C₂⁴×C₇	—	2	1	no	—
140	C₂⁴×C₇	C₂×D₄	1	2	yes	—
141	C₇×#41	—	4	32	no	—
142	C₂×C₇×Q₈	—	2	1	no	—
143	C₂×C₇×Q₈	—	2	4	no	—
144	C₂×C₇×Q₈	—	2	4	no	—
145	C₂×C₇×Q₈	—	2	2	no	—
146	C₂×C₇×Q₈	—	2	2	no	—
147	C₂×C₇×Q₈	—	4	4	no	—
148	C₂×C₇×Q₈	—	8	2	no	—
149	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
150	C₂×C₇×D₄	—	2	8	no	—
151	C₂×C₇×D₄	—	2	1	no	—
152	C₂×C₇×D₄	—	2	2	no	—
153	C₂×C₇×D₄	—	2	2	no	—
154	C₂×C₇×D₄	—	4	8	no	—
155	C₂×C₇×D₄	SD₁₆	1	8	yes	complemented
156	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
157	C₂×C₇×D₄	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₇	—	2	4	no	—
159	C₂²×C₄×C₇	—	2	4	no	—
160	C₂²×C₄×C₇	—	2	8	no	—
161	C₂²×C₄×C₇	—	2	1	no	—
162	C₂²×C₄×C₇	—	2	1	no	—
163	C₂²×C₄×C₇	—	2	2	no	—
164	C₂²×C₄×C₇	—	2	1	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	8	no	—
167	C₂²×C₄×C₇	—	2	4	no	—
168	C₂²×C₄×C₇	—	4	8	no	—
169	C₂²×C₄×C₇	—	4	4	no	—
170	C₂²×C₄×C₇	—	8	4	no	—
171	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
172	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
177	C₇×SD₁₆	—	2	8	no	—
178	C₂×C₇×C₈	—	2	4	no	—
179	C₂×C₇×C₈	—	2	2	no	—
180	C₂×C₇×C₈	—	2	16	no	—
181	C₂×C₇×C₈	#41	1	4	yes	complemented
182	C₂×C₇×C₈	C₂⁴	1	2	yes	—
183	C₂×C₇×C₈	C₂⁴	1	4	yes	—
184	C₂×C₇×C₈	C₂⁴	1	2	yes	—
185	C₇×C₄⋊C₄	—	2	1	no	—
186	C₇×C₄⋊C₄	—	2	1	no	—
187	C₇×C₄⋊C₄	—	2	2	no	—
188	C₇×C₄⋊C₄	—	2	8	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	2	no	—
191	C₇×C₄⋊C₄	—	2	4	no	—
192	C₇×C₄⋊C₄	—	2	4	no	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	4	no	—
195	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
196	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
197	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
199	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	4	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
204	C₄²×C₇	—	2	4	no	—
205	C₄²×C₇	C₂×D₄	1	2	yes	—
206	C₄²×C₇	C₂⁴	1	2	yes	—
207	C₂²×#41	—	2	1	no	—
208	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₇	1	2	yes	—
210	#554	—	2	4	no	—
211	#554	C₂²×C₇	1	8	yes	complemented
212	#547	—	2	4	no	—
213	#547	C₂²×C₇	1	8	yes	—
214	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
215	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×#125	—	2	1	no	—
217	C₂×#123	—	2	2	no	—
218	C₂×C₂²⋊Q₈	—	2	1	no	—
219	C₂×C₂²⋊Q₈	—	2	2	no	—
220	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
221	C₂×#121	C₂²×C₇	1	2	yes	—
222	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
223	C₂×C₄×D₄	—	2	1	no	—
224	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
225	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
228	#498	C₂²×C₇	1	8	yes	complemented
229	#483	C₂²×C₇	1	16	yes	complemented
230	#481	C₂²×C₇	1	16	yes	complemented
231	#476	C₂²×C₇	1	8	yes	complemented
232	#475	C₂²×C₇	1	8	yes	complemented
233	#465	C₂²×C₇	1	16	yes	complemented
234	C₄×SD₁₆	C₂²×C₇	1	8	yes	complemented
235	C₈×D₄	C₂²×C₇	1	8	yes	complemented
236	C₂×#106	C₂²×C₇	1	2	yes	—
237	C₂×#106	C₂²×C₇	1	2	yes	—
238	C₂×#106	C₂²×C₇	1	2	yes	—
239	C₂×#106	C₂²×C₇	1	2	yes	—
240	C₂×#106	C₂²×C₇	1	1	yes	characteristic
241	C₂×#106	C₂²×C₇	1	16	yes	complemented
242	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
243	C₂×#103	C₂²×C₇	1	2	yes	—
244	C₂×#103	C₂²×C₇	1	1	yes	characteristic
245	C₂×#102	C₂²×C₇	1	1	yes	characteristic
246	C₂×#102	C₂²×C₇	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
248	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
249	C₂³×C₇	—	2	4	no	—
250	C₂³×C₇	—	2	4	no	—
251	C₂³×C₇	—	2	2	no	—
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	2	no	—
254	C₂³×C₇	—	4	2	no	—
255	C₂³×C₇	C₂×SD₁₆	1	8	yes	—
256	C₂³×C₇	C₂²×D₄	1	4	yes	—
257	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
258	C₇×Q₈	—	2	2	no	—
259	C₇×Q₈	—	2	2	no	—
260	C₇×Q₈	—	4	2	no	—
261	C₇×Q₈	—	4	8	no	—
262	C₇×Q₈	—	8	4	no	—
263	C₇×D₄	—	2	2	no	—
264	C₇×D₄	—	2	2	no	—
265	C₇×D₄	—	4	16	no	—
266	C₇×D₄	—	4	2	no	—
267	C₇×D₄	C₂×SD₁₆	1	16	yes	complemented
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	2	no	—
270	C₂×C₄×C₇	—	2	8	no	—
271	C₂×C₄×C₇	—	2	4	no	—
272	C₂×C₄×C₇	—	2	4	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	2	2	no	—
277	C₂×C₄×C₇	—	2	4	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	—	4	4	no	—
281	C₂×C₄×C₇	—	4	16	no	—
282	C₂×C₄×C₇	—	4	2	no	—
283	C₂×C₄×C₇	—	4	4	no	—
284	C₂×C₄×C₇	—	4	8	no	—
285	C₂×C₄×C₇	—	8	8	no	—
286	C₂×C₄×C₇	C₂×SD₁₆	1	4	yes	—
287	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₇	C₂×#41	1	2	yes	—
292	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
293	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
294	C₇×C₈	—	2	4	no	—
295	C₇×C₈	—	2	2	no	—
296	C₇×C₈	C₂×#41	1	4	yes	complemented
297	C₂×#41	—	2	8	no	—
298	C₂×#41	—	4	8	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
304	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	2	2	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	C₂³×C₇	1	2	yes	—
309	C₂×SD₁₆	—	2	4	no	—
310	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
311	C₂²×C₈	—	2	8	no	—
312	C₂²×C₈	C₂³×C₇	1	2	yes	—
313	C₂²×C₈	C₂³×C₇	1	8	yes	—
314	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
319	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
320	#125	—	2	8	no	—
321	#123	—	2	16	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	8	no	—
324	C₂²⋊Q₈	—	2	16	no	—
325	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
326	#121	—	2	4	no	—
327	#121	C₂³×C₇	1	8	yes	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	C₂³×C₇	1	4	yes	—
330	C₄×D₄	—	2	8	no	—
331	C₄×D₄	—	2	2	no	—
332	C₄×D₄	C₇×D₄	1	4	yes	—
333	C₄×D₄	C₂³×C₇	1	4	yes	—
334	C₄×D₄	C₂³×C₇	1	4	yes	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
356	#106	C₂³×C₇	1	4	yes	—
357	#106	C₂³×C₇	1	8	yes	—
358	#106	C₂³×C₇	1	8	yes	—
359	#106	C₂³×C₇	1	8	yes	—
360	#106	C₂³×C₇	1	8	yes	—
361	C₄⋊C₈	C₂³×C₇	1	4	yes	—
362	#103	C₂³×C₇	1	4	yes	—
363	#103	C₂³×C₇	1	8	yes	—
364	#102	C₂³×C₇	1	4	yes	—
365	#102	C₂³×C₇	1	8	yes	—
366	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
367	C₄×C₈	C₂³×C₇	1	4	yes	—
368	C₂²×C₇	—	2	16	no	—
369	C₂²×C₇	—	2	4	no	—
370	C₂²×C₇	—	2	4	no	—
371	C₂²×C₇	—	4	2	no	—
372	C₂²×C₇	—	4	2	no	—
373	C₂²×C₇	—	4	2	no	—
374	C₂²×C₇	—	8	4	no	—
375	C₂²×C₇	#547	1	2	yes	—
376	C₂²×C₇	C₂²×SD₁₆	1	8	yes	—
377	C₂²×C₇	C₂²×SD₁₆	1	2	yes	—
378	C₂²×C₇	#577	1	2	yes	—
379	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₇	—	2	4	no	—
381	C₄×C₇	—	2	2	no	—
382	C₄×C₇	—	4	2	no	—
383	C₄×C₇	—	4	2	no	—
384	C₄×C₇	—	4	4	no	—
385	C₄×C₇	—	4	2	no	—
386	C₄×C₇	—	4	4	no	—
387	C₄×C₇	#547	1	2	yes	—
388	C₄×C₇	C₂²×SD₁₆	1	4	yes	—
389	C₄×C₇	C₂²×#41	1	1	yes	characteristic
390	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
391	C₂⁴	—	2	1	no	—
392	C₂⁴	C₂×C₇×D₄	1	2	yes	—
393	#41	—	4	32	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	4	4	no	—
400	C₂×Q₈	—	8	2	no	—
401	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	8	no	—
407	C₂×D₄	C₇×SD₁₆	1	8	yes	complemented
408	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
409	C₂×D₄	C₂⁴×C₇	1	2	yes	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	8	4	no	—
423	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
425	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
426	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
429	SD₁₆	—	2	8	no	—
430	C₂×C₈	—	2	4	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	16	no	—
433	C₂×C₈	C₇×#41	1	4	yes	complemented
434	C₂×C₈	C₂⁴×C₇	1	2	yes	—
435	C₂×C₈	C₂⁴×C₇	1	4	yes	—
436	C₂×C₈	C₂⁴×C₇	1	2	yes	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
448	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
449	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
450	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
451	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
456	C₄²	—	2	4	no	—
457	C₄²	C₂×C₇×D₄	1	2	yes	—
458	C₄²	C₂⁴×C₇	1	2	yes	—
459	C₂×C₇	—	2	8	no	—
460	C₂×C₇	—	8	2	no	—
461	C₂×C₇	#3335	1	4	yes	direct product factor
462	C₂×C₇	C₂×#547	1	1	yes	characteristic
463	C₂×C₇	C₂³×SD₁₆	1	1	yes	characteristic
464	C₂×C₇	C₂×#577	1	1	yes	characteristic
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	C₂×C₇×SD₁₆	1	8	yes	—
472	C₂³	C₂²×C₇×D₄	1	4	yes	—
473	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	4	8	no	—
478	Q₈	—	8	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	16	no	—
482	D₄	—	4	2	no	—
483	D₄	C₂×C₇×SD₁₆	1	16	yes	complemented
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	16	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	8	8	no	—
502	C₂×C₄	C₂×C₇×SD₁₆	1	4	yes	—
503	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
504	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
505	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
507	C₂×C₄	C₂×C₇×#41	1	2	yes	—
508	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
509	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
510	C₈	—	2	4	no	—
511	C₈	—	2	2	no	—
512	C₈	C₂×C₇×#41	1	4	yes	complemented
513	C₇	C₂×#3335	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	4	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	2	16	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	8	4	no	—
521	C₂²	C₇×#547	1	2	yes	—
522	C₂²	C₂²×C₇×SD₁₆	1	8	yes	—
523	C₂²	C₂²×C₇×SD₁₆	1	2	yes	—
524	C₂²	C₇×#577	1	2	yes	—
525	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
526	C₄	—	2	2	no	—
527	C₄	—	2	4	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	C₇×#547	1	2	yes	—
534	C₄	C₂²×C₇×SD₁₆	1	4	yes	—
535	C₄	C₂²×C₇×#41	1	1	yes	characteristic
536	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
537	C₂	—	2	8	no	—
538	C₂	—	8	2	no	—
539	C₂	C₇×#3335	1	4	yes	direct product factor
540	C₂	C₂×C₇×#547	1	1	yes	characteristic
541	C₂	C₂³×C₇×SD₁₆	1	1	yes	characteristic
542	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×#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×#554	C₂	semidirect
3. C₇×#3335	C₂	direct (N × H)
4. C₂×C₇×#498	C₂	semidirect
5. C₂×C₇×#481	C₂	semidirect
6. C₂×C₇×#483	C₂	semidirect
7. C₂×C₇×#475	C₂	semidirect
8. C₂×C₇×#476	C₂	semidirect
9. C₂×C₇×#465	C₂	semidirect
10. C₂×C₄×C₇×SD₁₆	C₂	semidirect
11. C₂×C₇×C₈×D₄	C₂	semidirect
12. C₂²×C₇×#106	C₂	semidirect
17. C₇×#554	C₂²	semidirect
34. C₇×#498	C₂²	semidirect
35. C₇×#483	C₂²	semidirect
36. C₇×#481	C₂²	semidirect
37. C₇×#476	C₂²	semidirect
38. C₇×#475	C₂²	semidirect
39. C₇×#465	C₂²	semidirect
40. C₄×C₇×SD₁₆	C₂²	semidirect
41. C₇×C₈×D₄	C₂²	semidirect
47. C₂×C₇×#106	C₂²	semidirect
55. C₂×#3335	C₇	direct (N × H)
127. C₂×#554	C₂×C₇	semidirect
129. #3335	C₂×C₇	direct (N × H)
130. C₂×#498	C₂×C₇	semidirect
131. C₂×#481	C₂×C₇	semidirect
132. C₂×#483	C₂×C₇	semidirect
133. C₂×#475	C₂×C₇	semidirect
134. C₂×#476	C₂×C₇	semidirect
135. C₂×#465	C₂×C₇	semidirect
136. C₂×C₄×SD₁₆	C₂×C₇	semidirect
137. C₂×C₈×D₄	C₂×C₇	semidirect
138. C₂²×#106	C₂×C₇	semidirect
155. C₂×C₇×D₄	SD₁₆	semidirect
181. C₂×C₇×C₈	#41	semidirect
211. #554	C₂²×C₇	semidirect
228. #498	C₂²×C₇	semidirect
229. #483	C₂²×C₇	semidirect
230. #481	C₂²×C₇	semidirect
231. #476	C₂²×C₇	semidirect
232. #475	C₂²×C₇	semidirect
233. #465	C₂²×C₇	semidirect
234. C₄×SD₁₆	C₂²×C₇	semidirect
235. C₈×D₄	C₂²×C₇	semidirect
241. C₂×#106	C₂²×C₇	semidirect
267. C₇×D₄	C₂×SD₁₆	semidirect
296. C₇×C₈	C₂×#41	semidirect
407. C₂×D₄	C₇×SD₁₆	semidirect
433. C₂×C₈	C₇×#41	semidirect
461. C₂×C₇	#3335	direct (N × H)
483. D₄	C₂×C₇×SD₁₆	semidirect
512. C₈	C₂×C₇×#41	semidirect
513. C₇	C₂×#3335	direct (N × H)
539. C₂	C₇×#3335	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×#554	2
C₂×C₇×#547	2
C₇×#3335	2
C₂×C₇×#498	2
C₂×C₇×#481	2
C₂×C₇×#483	2
C₂×C₇×#475	2
C₂×C₇×#476	2
C₂×C₇×#465	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×C₈×D₄	2
C₂²×C₇×#106	2
C₂×#3335	7

Subgroups — C2×C7×#3335 #13238442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3335 #13238442