Subgroups — C₂×C₇×#3126 #13237771

Order 1792.

2122 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3126	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#479	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#460	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#448	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#440	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
14	C₇×#540	—	2	4	no	—
15	C₇×#540	C₂²	1	8	yes	—
16	C₂×C₇×#127	C₂²	1	1	yes	characteristic
17	C₂×C₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₇×#123	—	2	2	no	—
19	C₂×C₇×#121	—	2	2	no	—
20	C₂×C₇×#121	C₂²	1	2	yes	—
21	C₇×#519	—	2	4	no	—
22	C₇×#519	C₂²	1	8	yes	complemented
23	C₂×C₄×C₇×Q₈	—	2	2	no	—
24	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
25	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
27	C₂×C₇×#117	—	2	2	no	—
28	C₂×C₇×#117	C₂²	1	1	yes	characteristic
29	C₂×C₇×#117	C₂²	1	1	yes	characteristic
30	C₇×#482	C₂²	1	16	yes	complemented
31	C₇×#479	C₂²	1	16	yes	complemented
32	C₇×#460	C₂²	1	16	yes	complemented
33	C₇×#448	C₂²	1	16	yes	complemented
34	C₇×#440	C₂²	1	16	yes	complemented
35	C₄×C₇×SD₁₆	C₂²	1	16	yes	complemented
36	C₇×#433	C₂²	1	8	yes	complemented
37	C₂×C₇×#107	C₂²	1	2	yes	—
38	C₂×C₇×#106	C₂²	1	2	yes	—
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₇×#103	C₂²	1	2	yes	—
41	C₂×C₇×#103	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×C₇×#97	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
47	C₂×#3126	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂²×C₇×Q₈	—	2	8	no	—
49	C₂²×C₇×Q₈	—	2	1	no	—
50	C₂²×C₇×Q₈	—	2	2	no	—
51	C₂²×C₇×Q₈	C₂³	1	4	yes	—
52	C₂²×C₇×Q₈	C₂³	1	2	yes	—
53	C₂²×C₇×D₄	—	2	2	no	—
54	C₂²×C₇×D₄	—	2	2	no	—
55	C₂²×C₇×D₄	C₂³	1	2	yes	—
56	C₂³×C₄×C₇	—	2	1	no	—
57	C₂³×C₄×C₇	—	2	2	no	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₂×C₇×SD₁₆	—	2	8	no	—
60	C₂×C₇×SD₁₆	—	2	8	no	—
61	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
62	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
63	C₂²×C₇×C₈	C₂³	1	2	yes	—
64	C₂²×C₇×C₈	C₂³	1	2	yes	—
65	C₇×#127	—	2	2	no	—
66	C₇×#127	C₂³	1	4	yes	—
67	C₇×#125	—	2	2	no	—
68	C₇×#125	C₂³	1	4	yes	—
69	C₇×#123	—	2	16	no	—
70	C₇×#121	—	2	4	no	—
71	C₇×#121	—	2	16	no	—
72	C₇×#121	C₂³	1	8	yes	—
73	C₄×C₇×Q₈	—	2	16	no	—
74	C₄×C₇×Q₈	—	2	4	no	—
75	C₄×C₇×Q₈	—	2	4	no	—
76	C₄×C₇×Q₈	C₂³	1	8	yes	—
77	C₄×C₇×Q₈	C₂³	1	8	yes	—
78	C₄×C₇×D₄	—	2	4	no	—
79	C₄×C₇×D₄	C₂³	1	8	yes	—
80	C₇×#117	—	2	2	no	—
81	C₇×#117	—	2	16	no	—
82	C₇×#117	D₄	1	4	yes	—
83	C₇×#117	C₂³	1	4	yes	—
84	C₇×#117	C₂³	1	4	yes	—
85	C₂×C₇×C₄⋊C₄	—	2	2	no	—
86	C₂×C₇×C₄⋊C₄	—	2	2	no	—
87	C₂×C₇×C₄⋊C₄	—	2	2	no	—
88	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
95	C₂×C₄²×C₇	—	2	2	no	—
96	C₂×C₄²×C₇	—	2	2	no	—
97	C₂×C₄²×C₇	—	2	1	no	—
98	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
100	C₇×#107	C₂³	1	8	yes	—
101	C₇×#106	C₂³	1	8	yes	—
102	C₇×C₄⋊C₈	C₂³	1	8	yes	—
103	C₇×#103	C₂³	1	8	yes	—
104	C₇×#103	C₂³	1	8	yes	—
105	C₇×#102	C₂³	1	8	yes	—
106	C₇×#102	C₂³	1	8	yes	—
107	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
108	C₇×#97	C₂³	1	4	yes	—
109	C₄×C₇×C₈	C₂³	1	4	yes	—
110	C₂×#540	C₂×C₇	1	1	yes	characteristic
111	C₂×#519	C₂×C₇	1	1	yes	characteristic, complemented
112	#3126	C₂×C₇	1	16	yes	direct product factor
113	C₂×#482	C₂×C₇	1	2	yes	complemented
114	C₂×#479	C₂×C₇	1	2	yes	complemented
115	C₂×#460	C₂×C₇	1	2	yes	complemented
116	C₂×#448	C₂×C₇	1	2	yes	complemented
117	C₂×#440	C₂×C₇	1	2	yes	complemented
118	C₂×C₄×SD₁₆	C₂×C₇	1	2	yes	complemented
119	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
120	C₂⁴×C₇	—	2	2	no	—
121	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₇×Q₈	—	2	16	no	—
123	C₂×C₇×Q₈	—	2	8	no	—
124	C₂×C₇×Q₈	—	2	16	no	—
125	C₂×C₇×Q₈	—	2	4	no	—
126	C₂×C₇×Q₈	—	2	2	no	—
127	C₂×C₇×Q₈	—	2	4	no	—
128	C₂×C₇×Q₈	#41	1	8	yes	—
129	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
130	C₂×C₇×D₄	—	2	8	no	—
131	C₂×C₇×D₄	—	2	2	no	—
132	C₂×C₇×D₄	—	2	8	no	—
133	C₂×C₇×D₄	—	2	4	no	—
134	C₂×C₇×D₄	—	2	4	no	—
135	C₂×C₇×D₄	—	8	4	no	—
136	C₂×C₇×D₄	—	8	4	no	—
137	C₂×C₇×D₄	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₇	—	2	8	no	—
139	C₂²×C₄×C₇	—	2	4	no	—
140	C₂²×C₄×C₇	—	2	2	no	—
141	C₂²×C₄×C₇	—	2	4	no	—
142	C₂²×C₄×C₇	—	2	2	no	—
143	C₂²×C₄×C₇	—	2	2	no	—
144	C₂²×C₄×C₇	—	2	8	no	—
145	C₂²×C₄×C₇	—	8	4	no	—
146	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
152	C₇×SD₁₆	—	2	16	no	—
153	C₇×SD₁₆	—	2	16	no	—
154	C₂×C₇×C₈	—	2	4	no	—
155	C₂×C₇×C₈	—	2	4	no	—
156	C₂×C₇×C₈	C₂⁴	1	4	yes	—
157	C₂×C₇×C₈	C₂⁴	1	4	yes	—
158	C₇×C₄⋊C₄	—	2	8	no	—
159	C₇×C₄⋊C₄	—	2	8	no	—
160	C₇×C₄⋊C₄	—	2	8	no	—
161	C₇×C₄⋊C₄	—	2	2	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
164	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
165	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
166	C₇×C₂²⋊C₄	—	2	4	no	—
167	C₇×C₂²⋊C₄	—	2	8	no	—
168	C₇×C₂²⋊C₄	—	2	8	no	—
169	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
170	C₄²×C₇	—	2	8	no	—
171	C₄²×C₇	—	2	8	no	—
172	C₄²×C₇	—	2	4	no	—
173	C₄²×C₇	C₂×D₄	1	2	yes	—
174	C₄²×C₇	C₂×D₄	1	2	yes	—
175	C₄²×C₇	C₂⁴	1	2	yes	—
176	C₄²×C₇	C₂⁴	1	2	yes	—
177	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
178	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
179	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
180	#540	—	2	4	no	—
181	#540	C₂²×C₇	1	8	yes	—
182	C₂×#127	C₂²×C₇	1	1	yes	characteristic
183	C₂×#125	C₂²×C₇	1	1	yes	characteristic
184	C₂×#123	—	2	2	no	—
185	C₂×#121	—	2	2	no	—
186	C₂×#121	C₂²×C₇	1	2	yes	—
187	#519	—	2	4	no	—
188	#519	C₂²×C₇	1	8	yes	complemented
189	C₂×C₄×Q₈	—	2	2	no	—
190	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
191	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
193	C₂×#117	—	2	2	no	—
194	C₂×#117	C₂²×C₇	1	1	yes	characteristic
195	C₂×#117	C₂²×C₇	1	1	yes	characteristic
196	#482	C₂²×C₇	1	16	yes	complemented
197	#479	C₂²×C₇	1	16	yes	complemented
198	#460	C₂²×C₇	1	16	yes	complemented
199	#448	C₂²×C₇	1	16	yes	complemented
200	#440	C₂²×C₇	1	16	yes	complemented
201	C₄×SD₁₆	C₂²×C₇	1	16	yes	complemented
202	#433	C₂²×C₇	1	8	yes	complemented
203	C₂×#107	C₂²×C₇	1	2	yes	—
204	C₂×#106	C₂²×C₇	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
206	C₂×#103	C₂²×C₇	1	2	yes	—
207	C₂×#103	C₂²×C₇	1	2	yes	—
208	C₂×#102	C₂²×C₇	1	2	yes	—
209	C₂×#102	C₂²×C₇	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
211	C₂×#97	C₂²×C₇	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
213	C₂³×C₇	—	2	2	no	—
214	C₂³×C₇	—	2	4	no	—
215	C₂³×C₇	—	2	4	no	—
216	C₂³×C₇	—	4	4	no	—
217	C₂³×C₇	—	4	4	no	—
218	C₂³×C₇	—	4	4	no	—
219	C₂³×C₇	C₂²×D₄	1	2	yes	—
220	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
221	C₇×Q₈	—	2	16	no	—
222	C₇×Q₈	—	2	8	no	—
223	C₇×Q₈	—	2	4	no	—
224	C₇×Q₈	C₂×#41	1	8	yes	—
225	C₇×D₄	—	2	4	no	—
226	C₇×D₄	—	2	4	no	—
227	C₇×D₄	—	4	4	no	—
228	C₇×D₄	—	8	8	no	—
229	C₇×D₄	—	8	8	no	—
230	C₂×C₄×C₇	—	2	16	no	—
231	C₂×C₄×C₇	—	2	8	no	—
232	C₂×C₄×C₇	—	2	2	no	—
233	C₂×C₄×C₇	—	2	4	no	—
234	C₂×C₄×C₇	—	2	4	no	—
235	C₂×C₄×C₇	—	2	4	no	—
236	C₂×C₄×C₇	—	2	4	no	—
237	C₂×C₄×C₇	—	2	4	no	—
238	C₂×C₄×C₇	—	2	4	no	—
239	C₂×C₄×C₇	—	2	4	no	—
240	C₂×C₄×C₇	—	4	4	no	—
241	C₂×C₄×C₇	—	4	4	no	—
242	C₂×C₄×C₇	—	8	8	no	—
243	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
244	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₇	C₂×#41	1	4	yes	—
248	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
249	C₇×C₈	—	2	4	no	—
250	C₇×C₈	—	2	4	no	—
251	C₂²×Q₈	—	2	8	no	—
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	C₂³×C₇	1	4	yes	—
255	C₂²×Q₈	C₂³×C₇	1	2	yes	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	C₂³×C₇	1	2	yes	—
259	C₂³×C₄	—	2	1	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
262	C₂×SD₁₆	—	2	8	no	—
263	C₂×SD₁₆	—	2	8	no	—
264	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
265	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
266	C₂²×C₈	C₂³×C₇	1	2	yes	—
267	C₂²×C₈	C₂³×C₇	1	2	yes	—
268	#127	—	2	2	no	—
269	#127	C₂³×C₇	1	4	yes	—
270	#125	—	2	2	no	—
271	#125	C₂³×C₇	1	4	yes	—
272	#123	—	2	16	no	—
273	#121	—	2	4	no	—
274	#121	—	2	16	no	—
275	#121	C₂³×C₇	1	8	yes	—
276	C₄×Q₈	—	2	16	no	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	C₂³×C₇	1	8	yes	—
280	C₄×Q₈	C₂³×C₇	1	8	yes	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	C₂³×C₇	1	8	yes	—
283	#117	—	2	2	no	—
284	#117	—	2	16	no	—
285	#117	C₇×D₄	1	4	yes	—
286	#117	C₂³×C₇	1	4	yes	—
287	#117	C₂³×C₇	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
303	#107	C₂³×C₇	1	8	yes	—
304	#106	C₂³×C₇	1	8	yes	—
305	C₄⋊C₈	C₂³×C₇	1	8	yes	—
306	#103	C₂³×C₇	1	8	yes	—
307	#103	C₂³×C₇	1	8	yes	—
308	#102	C₂³×C₇	1	8	yes	—
309	#102	C₂³×C₇	1	8	yes	—
310	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
311	#97	C₂³×C₇	1	4	yes	—
312	C₄×C₈	C₂³×C₇	1	4	yes	—
313	C₂²×C₇	—	2	2	no	—
314	C₂²×C₇	—	2	4	no	—
315	C₂²×C₇	—	4	4	no	—
316	C₂²×C₇	—	4	4	no	—
317	C₂²×C₇	—	4	4	no	—
318	C₂²×C₇	—	4	4	no	—
319	C₂²×C₇	—	8	8	no	—
320	C₂²×C₇	#525	1	2	yes	—
321	C₂²×C₇	#577	1	4	yes	—
322	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
323	C₄×C₇	—	2	8	no	—
324	C₄×C₇	—	2	2	no	—
325	C₄×C₇	—	2	4	no	—
326	C₄×C₇	—	2	4	no	—
327	C₄×C₇	—	4	4	no	—
328	C₄×C₇	—	4	4	no	—
329	C₄×C₇	#525	1	2	yes	—
330	C₄×C₇	C₂²×#41	1	2	yes	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
333	C₂×Q₈	—	2	16	no	—
334	C₂×Q₈	—	2	8	no	—
335	C₂×Q₈	—	2	16	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	C₇×#41	1	8	yes	—
340	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	8	4	no	—
347	C₂×D₄	—	8	4	no	—
348	C₂×D₄	C₂⁴×C₇	1	4	yes	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	8	4	no	—
357	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
358	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
359	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
363	SD₁₆	—	2	16	no	—
364	SD₁₆	—	2	16	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	C₂⁴×C₇	1	4	yes	—
368	C₂×C₈	C₂⁴×C₇	1	4	yes	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
375	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
376	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
381	C₄²	—	2	8	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	4	no	—
384	C₄²	C₂×C₇×D₄	1	2	yes	—
385	C₄²	C₂×C₇×D₄	1	2	yes	—
386	C₄²	C₂⁴×C₇	1	2	yes	—
387	C₄²	C₂⁴×C₇	1	2	yes	—
388	C₂×C₇	—	4	2	no	—
389	C₂×C₇	—	8	4	no	—
390	C₂×C₇	#3126	1	4	yes	direct product factor
391	C₂×C₇	C₂×#525	1	1	yes	characteristic
392	C₂×C₇	C₂×#577	1	2	yes	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	C₂²×C₇×D₄	1	2	yes	—
400	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
401	Q₈	—	2	16	no	—
402	Q₈	—	2	4	no	—
403	Q₈	—	2	8	no	—
404	Q₈	C₂×C₇×#41	1	8	yes	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	8	8	no	—
409	D₄	—	8	8	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	8	8	no	—
423	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
424	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
425	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
426	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
427	C₂×C₄	C₂×C₇×#41	1	4	yes	—
428	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
429	C₈	—	2	4	no	—
430	C₈	—	2	4	no	—
431	C₇	C₂×#3126	1	1	yes	characteristic, direct product factor, Sylow
432	C₂²	—	2	4	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	8	no	—
439	C₂²	C₇×#525	1	2	yes	—
440	C₂²	C₇×#577	1	4	yes	—
441	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
442	C₄	—	2	4	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	8	no	—
445	C₄	—	2	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	C₇×#525	1	2	yes	—
449	C₄	C₂²×C₇×#41	1	2	yes	—
450	C₂	—	4	2	no	—
451	C₂	—	8	4	no	—
452	C₂	C₇×#3126	1	4	yes	direct product factor
453	C₂	C₂×C₇×#525	1	1	yes	characteristic
454	C₂	C₂×C₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂×C₇×#540	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
2. C₂×C₇×#519	C₂	semidirect
3. C₇×#3126	C₂	direct (N × H)
4. C₂×C₇×#482	C₂	semidirect
5. C₂×C₇×#479	C₂	semidirect
6. C₂×C₇×#460	C₂	semidirect
7. C₂×C₇×#448	C₂	semidirect
8. C₂×C₇×#440	C₂	semidirect
9. C₂×C₄×C₇×SD₁₆	C₂	semidirect
10. C₂×C₇×#433	C₂	semidirect
22. C₇×#519	C₂²	semidirect
30. C₇×#482	C₂²	semidirect
31. C₇×#479	C₂²	semidirect
32. C₇×#460	C₂²	semidirect
33. C₇×#448	C₂²	semidirect
34. C₇×#440	C₂²	semidirect
35. C₄×C₇×SD₁₆	C₂²	semidirect
36. C₇×#433	C₂²	semidirect
47. C₂×#3126	C₇	direct (N × H)
111. C₂×#519	C₂×C₇	semidirect
112. #3126	C₂×C₇	direct (N × H)
113. C₂×#482	C₂×C₇	semidirect
114. C₂×#479	C₂×C₇	semidirect
115. C₂×#460	C₂×C₇	semidirect
116. C₂×#448	C₂×C₇	semidirect
117. C₂×#440	C₂×C₇	semidirect
118. C₂×C₄×SD₁₆	C₂×C₇	semidirect
119. C₂×#433	C₂×C₇	semidirect
188. #519	C₂²×C₇	semidirect
196. #482	C₂²×C₇	semidirect
197. #479	C₂²×C₇	semidirect
198. #460	C₂²×C₇	semidirect
199. #448	C₂²×C₇	semidirect
200. #440	C₂²×C₇	semidirect
201. C₄×SD₁₆	C₂²×C₇	semidirect
202. #433	C₂²×C₇	semidirect
390. C₂×C₇	#3126	direct (N × H)
431. C₇	C₂×#3126	direct (N × H)
452. C₂	C₇×#3126	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×#540	2
C₂×C₇×#519	2
C₇×#3126	2
C₂×C₇×#482	2
C₂×C₇×#479	2
C₂×C₇×#460	2
C₂×C₇×#448	2
C₂×C₇×#440	2
C₂×C₄×C₇×SD₁₆	2
C₂×C₇×#433	2
C₂×#3126	7

Subgroups — C2×C7×#3126 #13237771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3126 #13237771