Subgroups — C₂×C₇×#3355 #13238464

Order 1792.

1962 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#553	C₂	1	2	yes	maximal, complemented
2	C₇×#3355	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#480	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#469	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₇×#428	C₂	1	2	yes	maximal, complemented
11	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
12	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
13	C₇×#553	—	2	8	no	—
14	C₇×#553	C₂²	1	16	yes	complemented
15	C₂×C₇×#126	—	2	2	no	—
16	C₂×C₇×#125	C₂²	1	2	yes	—
17	C₂×C₇×#123	—	2	2	no	—
18	C₂×C₇×#121	—	2	2	no	—
19	C₂×C₇×#121	C₂²	1	2	yes	—
20	C₂×C₇×#121	C₂²	1	2	yes	—
21	C₂×C₄×C₇×D₄	—	2	2	no	—
22	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
23	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
24	C₂×C₇×#117	C₂²	1	2	yes	—
25	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
26	C₇×#499	C₂²	1	8	yes	complemented
27	C₇×#482	C₂²	1	16	yes	complemented
28	C₇×#480	C₂²	1	16	yes	complemented
29	C₇×#478	C₂²	1	16	yes	complemented
30	C₇×#469	C₂²	1	16	yes	complemented
31	C₄×C₇×D₈	C₂²	1	8	yes	complemented
32	C₇×#436	C₂²	1	8	yes	complemented
33	C₇×#428	C₂²	1	16	yes	complemented
34	C₂×C₇×#107	C₂²	1	1	yes	characteristic
35	C₂×C₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₇×#107	C₂²	1	1	yes	characteristic
37	C₂×C₇×#107	C₂²	1	2	yes	—
38	C₂×C₇×#106	C₂²	1	2	yes	—
39	C₂×C₇×#106	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	2	yes	—
42	C₂×C₇×#102	C₂²	1	2	yes	—
43	C₂×C₇×#102	C₂²	1	2	yes	—
44	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₂×#3355	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂²×C₇×D₄	—	2	2	no	—
49	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
50	C₂²×C₇×D₄	C₂³	1	2	yes	—
51	C₂³×C₄×C₇	—	2	2	no	—
52	C₂³×C₄×C₇	—	2	2	no	—
53	C₂³×C₄×C₇	C₂³	1	2	yes	—
54	C₂×C₇×D₈	—	2	4	no	—
55	C₂×C₇×D₈	C₂³	1	4	yes	—
56	C₂×C₇×M₁₆	—	2	8	no	—
57	C₂×C₇×M₁₆	C₂³	1	8	yes	—
58	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₇×C₈	C₂³	1	2	yes	—
60	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
61	C₇×#126	—	2	16	no	—
62	C₇×#125	—	2	4	no	—
63	C₇×#125	C₂³	1	8	yes	—
64	C₇×#123	—	2	16	no	—
65	C₇×#121	—	2	16	no	—
66	C₇×#121	—	2	4	no	—
67	C₇×#121	—	2	4	no	—
68	C₇×#121	C₂³	1	8	yes	—
69	C₇×#121	C₂³	1	8	yes	—
70	C₄×C₇×D₄	—	2	16	no	—
71	C₄×C₇×D₄	—	2	4	no	—
72	C₄×C₇×D₄	D₄	1	4	yes	—
73	C₄×C₇×D₄	C₂³	1	8	yes	—
74	C₄×C₇×D₄	C₂³	1	4	yes	—
75	C₇×#117	—	2	4	no	—
76	C₇×#117	C₂³	1	8	yes	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	4	no	—
79	C₂×C₇×C₄⋊C₄	—	2	2	no	—
80	C₂×C₇×C₄⋊C₄	—	2	2	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
82	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
91	C₂×C₄²×C₇	—	2	2	no	—
92	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
93	C₇×#107	C₂³	1	8	yes	—
94	C₇×#107	C₂³	1	4	yes	—
95	C₇×#107	C₂³	1	4	yes	—
96	C₇×#107	C₂³	1	4	yes	—
97	C₇×#106	C₂³	1	8	yes	—
98	C₇×#106	C₂³	1	8	yes	—
99	C₇×C₄⋊C₈	C₂³	1	4	yes	—
100	C₇×#102	C₂³	1	8	yes	—
101	C₇×#102	C₂³	1	8	yes	—
102	C₇×#102	C₂³	1	8	yes	—
103	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
104	C₄×C₇×C₈	C₂³	1	4	yes	—
105	C₂×#553	C₂×C₇	1	2	yes	complemented
106	#3355	C₂×C₇	1	16	yes	direct product factor
107	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#482	C₂×C₇	1	2	yes	complemented
109	C₂×#480	C₂×C₇	1	2	yes	complemented
110	C₂×#478	C₂×C₇	1	2	yes	complemented
111	C₂×#469	C₂×C₇	1	2	yes	complemented
112	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#436	C₂×C₇	1	1	yes	characteristic, complemented
114	C₂×#428	C₂×C₇	1	2	yes	complemented
115	C₂⁴×C₇	—	2	2	no	—
116	C₂⁴×C₇	C₂×D₄	1	2	yes	—
117	C₂×C₇×D₄	—	2	8	no	—
118	C₂×C₇×D₄	—	2	8	no	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	4	no	—
121	C₂×C₇×D₄	—	2	4	no	—
122	C₂×C₇×D₄	—	4	2	no	—
123	C₂×C₇×D₄	—	4	8	no	—
124	C₂×C₇×D₄	—	8	4	no	—
125	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
126	C₂×C₇×D₄	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₇	—	2	4	no	—
128	C₂²×C₄×C₇	—	2	4	no	—
129	C₂²×C₄×C₇	—	2	2	no	—
130	C₂²×C₄×C₇	—	2	2	no	—
131	C₂²×C₄×C₇	—	2	2	no	—
132	C₂²×C₄×C₇	—	2	8	no	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	8	4	no	—
135	C₂²×C₄×C₇	—	8	4	no	—
136	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
142	C₇×D₈	—	2	8	no	—
143	C₇×M₁₆	—	2	16	no	—
144	C₂×C₇×C₈	—	2	4	no	—
145	C₂×C₇×C₈	—	2	2	no	—
146	C₂×C₇×C₈	#41	1	4	yes	—
147	C₂×C₇×C₈	C₂⁴	1	2	yes	—
148	C₂×C₇×C₈	C₂⁴	1	4	yes	—
149	C₂×C₇×C₈	C₂⁴	1	2	yes	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	—	2	8	no	—
153	C₇×C₄⋊C₄	—	2	8	no	—
154	C₇×C₄⋊C₄	—	2	8	no	—
155	C₇×C₄⋊C₄	—	2	2	no	—
156	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
157	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
158	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
159	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
160	C₇×C₂²⋊C₄	—	2	8	no	—
161	C₇×C₂²⋊C₄	—	2	8	no	—
162	C₇×C₂²⋊C₄	—	2	8	no	—
163	C₇×C₂²⋊C₄	—	2	8	no	—
164	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
165	C₄²×C₇	—	2	8	no	—
166	C₄²×C₇	C₂×D₄	1	2	yes	—
167	C₄²×C₇	C₂⁴	1	2	yes	—
168	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
169	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
170	#553	—	2	8	no	—
171	#553	C₂²×C₇	1	16	yes	complemented
172	C₂×#126	—	2	2	no	—
173	C₂×#125	C₂²×C₇	1	2	yes	—
174	C₂×#123	—	2	2	no	—
175	C₂×#121	—	2	2	no	—
176	C₂×#121	C₂²×C₇	1	2	yes	—
177	C₂×#121	C₂²×C₇	1	2	yes	—
178	C₂×C₄×D₄	—	2	2	no	—
179	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
180	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
181	C₂×#117	C₂²×C₇	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
183	#499	C₂²×C₇	1	8	yes	complemented
184	#482	C₂²×C₇	1	16	yes	complemented
185	#480	C₂²×C₇	1	16	yes	complemented
186	#478	C₂²×C₇	1	16	yes	complemented
187	#469	C₂²×C₇	1	16	yes	complemented
188	C₄×D₈	C₂²×C₇	1	8	yes	complemented
189	#436	C₂²×C₇	1	8	yes	complemented
190	#428	C₂²×C₇	1	16	yes	complemented
191	C₂×#107	C₂²×C₇	1	2	yes	—
192	C₂×#107	C₂²×C₇	1	1	yes	characteristic
193	C₂×#107	C₂²×C₇	1	1	yes	characteristic
194	C₂×#107	C₂²×C₇	1	1	yes	characteristic
195	C₂×#106	C₂²×C₇	1	2	yes	—
196	C₂×#106	C₂²×C₇	1	2	yes	—
197	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
198	C₂×#102	C₂²×C₇	1	2	yes	—
199	C₂×#102	C₂²×C₇	1	2	yes	—
200	C₂×#102	C₂²×C₇	1	2	yes	—
201	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
202	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
203	C₂³×C₇	—	2	4	no	—
204	C₂³×C₇	—	2	4	no	—
205	C₂³×C₇	—	2	4	no	—
206	C₂³×C₇	—	2	4	no	—
207	C₂³×C₇	—	4	4	no	—
208	C₂³×C₇	—	4	4	no	—
209	C₂³×C₇	—	4	4	no	—
210	C₂³×C₇	C₂²×D₄	1	4	yes	—
211	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
212	C₇×D₄	—	2	4	no	—
213	C₇×D₄	—	2	4	no	—
214	C₇×D₄	—	4	4	no	—
215	C₇×D₄	—	4	16	no	—
216	C₇×D₄	—	4	4	no	—
217	C₇×D₄	—	8	8	no	—
218	C₂×C₄×C₇	—	2	4	no	—
219	C₂×C₄×C₇	—	2	2	no	—
220	C₂×C₄×C₇	—	2	2	no	—
221	C₂×C₄×C₇	—	2	8	no	—
222	C₂×C₄×C₇	—	2	4	no	—
223	C₂×C₄×C₇	—	2	4	no	—
224	C₂×C₄×C₇	—	2	4	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	2	4	no	—
227	C₂×C₄×C₇	—	4	4	no	—
228	C₂×C₄×C₇	—	4	4	no	—
229	C₂×C₄×C₇	—	4	4	no	—
230	C₂×C₄×C₇	—	8	8	no	—
231	C₂×C₄×C₇	—	8	8	no	—
232	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂×#41	1	2	yes	—
237	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
238	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
239	C₇×C₈	—	2	4	no	—
240	C₇×C₈	—	2	2	no	—
241	C₇×C₈	C₂×#41	1	4	yes	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
245	C₂²×D₄	C₂³×C₇	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	C₂³×C₇	1	2	yes	—
249	C₂×D₈	—	2	4	no	—
250	C₂×D₈	C₂³×C₇	1	4	yes	—
251	C₂×M₁₆	—	2	8	no	—
252	C₂×M₁₆	C₂³×C₇	1	8	yes	—
253	C₂²×C₈	C₂³×C₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
256	#126	—	2	16	no	—
257	#125	—	2	4	no	—
258	#125	C₂³×C₇	1	8	yes	—
259	#123	—	2	16	no	—
260	#121	—	2	16	no	—
261	#121	—	2	4	no	—
262	#121	—	2	4	no	—
263	#121	C₂³×C₇	1	8	yes	—
264	#121	C₂³×C₇	1	8	yes	—
265	C₄×D₄	—	2	16	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	C₇×D₄	1	4	yes	—
268	C₄×D₄	C₂³×C₇	1	8	yes	—
269	C₄×D₄	C₂³×C₇	1	4	yes	—
270	#117	—	2	4	no	—
271	#117	C₂³×C₇	1	8	yes	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
288	#107	C₂³×C₇	1	4	yes	—
289	#107	C₂³×C₇	1	8	yes	—
290	#107	C₂³×C₇	1	4	yes	—
291	#107	C₂³×C₇	1	4	yes	—
292	#106	C₂³×C₇	1	8	yes	—
293	#106	C₂³×C₇	1	8	yes	—
294	C₄⋊C₈	C₂³×C₇	1	4	yes	—
295	#102	C₂³×C₇	1	8	yes	—
296	#102	C₂³×C₇	1	8	yes	—
297	#102	C₂³×C₇	1	8	yes	—
298	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
299	C₄×C₈	C₂³×C₇	1	4	yes	—
300	C₂²×C₇	—	2	4	no	—
301	C₂²×C₇	—	2	4	no	—
302	C₂²×C₇	—	2	4	no	—
303	C₂²×C₇	—	4	8	no	—
304	C₂²×C₇	—	4	4	no	—
305	C₂²×C₇	—	4	4	no	—
306	C₂²×C₇	—	4	4	no	—
307	C₂²×C₇	—	8	8	no	—
308	C₂²×C₇	#547	1	2	yes	—
309	C₂²×C₇	#575	1	2	yes	—
310	C₂²×C₇	#576	1	2	yes	—
311	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
312	C₄×C₇	—	2	4	no	—
313	C₄×C₇	—	2	2	no	—
314	C₄×C₇	—	2	2	no	—
315	C₄×C₇	—	4	4	no	—
316	C₄×C₇	—	4	4	no	—
317	C₄×C₇	—	4	4	no	—
318	C₄×C₇	#547	1	2	yes	—
319	C₄×C₇	C₂²×#41	1	1	yes	characteristic
320	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×C₇×D₄	1	2	yes	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	8	no	—
330	C₂×D₄	—	8	4	no	—
331	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
332	C₂×D₄	C₂⁴×C₇	1	4	yes	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	8	no	—
340	C₂²×C₄	—	8	4	no	—
341	C₂²×C₄	—	8	4	no	—
342	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
343	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
346	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
348	D₈	—	2	8	no	—
349	M₁₆	—	2	16	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₇×#41	1	4	yes	—
353	C₂×C₈	C₂⁴×C₇	1	2	yes	—
354	C₂×C₈	C₂⁴×C₇	1	4	yes	—
355	C₂×C₈	C₂⁴×C₇	1	2	yes	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
363	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
364	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
365	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
366	C₂²⋊C₄	—	2	8	no	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
371	C₄²	—	2	8	no	—
372	C₄²	C₂×C₇×D₄	1	2	yes	—
373	C₄²	C₂⁴×C₇	1	2	yes	—
374	C₂×C₇	—	4	4	no	—
375	C₂×C₇	—	8	4	no	—
376	C₂×C₇	#3355	1	4	yes	direct product factor
377	C₂×C₇	C₂×#547	1	1	yes	characteristic
378	C₂×C₇	C₂×#575	1	1	yes	characteristic
379	C₂×C₇	C₂×#576	1	1	yes	characteristic
380	C₂³	—	2	4	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	4	4	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	4	no	—
387	C₂³	C₂²×C₇×D₄	1	4	yes	—
388	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	16	no	—
393	D₄	—	4	4	no	—
394	D₄	—	8	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
410	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
411	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
412	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₇×#41	1	2	yes	—
414	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
415	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
416	C₈	—	2	4	no	—
417	C₈	—	2	2	no	—
418	C₈	C₂×C₇×#41	1	4	yes	—
419	C₇	C₂×#3355	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	8	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	8	no	—
428	C₂²	C₇×#547	1	2	yes	—
429	C₂²	C₇×#575	1	2	yes	—
430	C₂²	C₇×#576	1	2	yes	—
431	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	C₇×#547	1	2	yes	—
439	C₄	C₂²×C₇×#41	1	1	yes	characteristic
440	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂	—	4	4	no	—
442	C₂	—	8	4	no	—
443	C₂	C₇×#3355	1	4	yes	direct product factor
444	C₂	C₂×C₇×#547	1	1	yes	characteristic
445	C₂	C₂×C₇×#575	1	1	yes	characteristic
446	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×#553	C₂	semidirect
2. C₇×#3355	C₂	direct (N × H)
3. C₂×C₇×#499	C₂	semidirect
4. C₂×C₇×#482	C₂	semidirect
5. C₂×C₇×#480	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#469	C₂	semidirect
8. C₂×C₄×C₇×D₈	C₂	semidirect
9. C₂×C₇×#436	C₂	semidirect
10. C₂×C₇×#428	C₂	semidirect
14. C₇×#553	C₂²	semidirect
26. C₇×#499	C₂²	semidirect
27. C₇×#482	C₂²	semidirect
28. C₇×#480	C₂²	semidirect
29. C₇×#478	C₂²	semidirect
30. C₇×#469	C₂²	semidirect
31. C₄×C₇×D₈	C₂²	semidirect
32. C₇×#436	C₂²	semidirect
33. C₇×#428	C₂²	semidirect
46. C₂×#3355	C₇	direct (N × H)
105. C₂×#553	C₂×C₇	semidirect
106. #3355	C₂×C₇	direct (N × H)
107. C₂×#499	C₂×C₇	semidirect
108. C₂×#482	C₂×C₇	semidirect
109. C₂×#480	C₂×C₇	semidirect
110. C₂×#478	C₂×C₇	semidirect
111. C₂×#469	C₂×C₇	semidirect
112. C₂×C₄×D₈	C₂×C₇	semidirect
113. C₂×#436	C₂×C₇	semidirect
114. C₂×#428	C₂×C₇	semidirect
171. #553	C₂²×C₇	semidirect
183. #499	C₂²×C₇	semidirect
184. #482	C₂²×C₇	semidirect
185. #480	C₂²×C₇	semidirect
186. #478	C₂²×C₇	semidirect
187. #469	C₂²×C₇	semidirect
188. C₄×D₈	C₂²×C₇	semidirect
189. #436	C₂²×C₇	semidirect
190. #428	C₂²×C₇	semidirect
376. C₂×C₇	#3355	direct (N × H)
419. C₇	C₂×#3355	direct (N × H)
443. C₂	C₇×#3355	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×#553	2
C₇×#3355	2
C₂×C₇×#499	2
C₂×C₇×#482	2
C₂×C₇×#480	2
C₂×C₇×#478	2
C₂×C₇×#469	2
C₂×C₄×C₇×D₈	2
C₂×C₇×#436	2
C₂×C₇×#428	2
C₂×#3355	7

Subgroups — C2×C7×#3355 #13238464

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3355 #13238464