Subgroups — C₂×C₇×#3054 #13237657

Order 1792.

2918 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
4	C₇×#3054	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#470	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#468	C₂	1	4	yes	maximal, complemented
8	C₂×C₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#416	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×#41	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₂×C₇×#135	—	2	8	no	—
13	C₂×C₇×#135	C₂²	1	8	yes	complemented
14	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
16	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₇×M₁₆	—	2	8	no	—
18	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
19	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
20	C₂²×C₇×M₁₆	C₂²	1	8	yes	complemented
21	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
22	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
23	C₇×#525	—	2	8	no	—
24	C₇×#525	C₂²	1	16	yes	complemented
25	C₂×C₇×#123	—	2	2	no	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
27	C₂×C₇×#121	C₂²	1	4	yes	—
28	C₂×C₇×#120	—	2	2	no	—
29	C₂×C₄×C₇×D₄	—	2	4	no	—
30	C₂×C₇×#117	C₂²	1	2	yes	—
31	C₇×#470	C₂²	1	16	yes	complemented
32	C₇×#469	C₂²	1	16	yes	complemented
33	C₇×#468	C₂²	1	32	yes	complemented
34	C₇×#427	C₂²	1	8	yes	complemented
35	C₂×C₇×#107	C₂²	1	2	yes	complemented
36	C₂×C₇×#106	C₂²	1	2	yes	complemented
37	C₇×#416	C₂²	1	16	yes	complemented
38	C₂×C₇×#103	C₂²	1	4	yes	complemented
39	C₂×C₇×#102	C₂²	1	4	yes	complemented
40	C₂×#3054	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂⁵×C₇	D₄	1	1	yes	characteristic
42	C₂×C₇×#41	—	2	4	no	—
43	C₂×C₇×#41	—	2	8	no	—
44	C₂×C₇×#41	—	2	8	no	—
45	C₂×C₇×#41	C₂³	1	8	yes	—
46	C₂²×C₇×Q₈	C₂³	1	2	yes	—
47	C₂²×C₇×D₄	—	2	2	no	—
48	C₂²×C₇×D₄	—	2	4	no	—
49	C₂²×C₇×D₄	C₂³	1	2	yes	—
50	C₂³×C₄×C₇	—	2	4	no	—
51	C₂³×C₄×C₇	—	2	4	no	—
52	C₂³×C₄×C₇	—	2	2	no	—
53	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₇	D₄	1	4	yes	—
55	C₂³×C₄×C₇	D₄	1	2	yes	—
56	C₂³×C₄×C₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	C₂³	1	4	yes	—
58	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
59	C₇×#135	—	2	32	no	—
60	C₂×C₇×Q₁₆	—	2	4	no	—
61	C₂×C₇×Q₁₆	C₂³	1	4	yes	complemented
62	C₂×C₇×SD₁₆	—	2	8	no	—
63	C₂×C₇×SD₁₆	C₂³	1	8	yes	complemented
64	C₂×C₇×D₈	—	2	4	no	—
65	C₂×C₇×D₈	C₂³	1	4	yes	complemented
66	C₂×C₇×M₁₆	—	2	8	no	—
67	C₂×C₇×M₁₆	—	2	8	no	—
68	C₂×C₇×M₁₆	—	2	32	no	—
69	C₂×C₇×M₁₆	C₂³	1	8	yes	—
70	C₂×C₇×M₁₆	C₂³	1	8	yes	—
71	C₂²×C₇×C₈	—	2	4	no	—
72	C₂²×C₇×C₈	D₄	1	8	yes	complemented
73	C₂²×C₇×C₈	C₂³	1	2	yes	—
74	C₂²×C₇×C₈	C₂³	1	4	yes	—
75	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₇×C₈	C₂³	1	4	yes	—
78	C₇×#123	—	2	16	no	—
79	C₇×C₂²⋊Q₈	—	2	8	no	—
80	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
81	C₇×#121	—	2	8	no	—
82	C₇×#121	C₂³	1	16	yes	—
83	C₇×#120	—	2	16	no	—
84	C₄×C₇×D₄	—	2	32	no	—
85	C₇×#117	—	2	4	no	—
86	C₇×#117	C₂³	1	8	yes	—
87	C₂×C₇×C₄⋊C₄	—	2	4	no	—
88	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
92	C₂×C₄²×C₇	—	2	2	no	—
93	C₇×#107	C₂³	1	8	yes	complemented
94	C₇×#106	C₂³	1	8	yes	complemented
95	C₇×#103	C₂³	1	16	yes	complemented
96	C₇×#102	C₂³	1	16	yes	complemented
97	C₂²×#135	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂³×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂×#525	C₂×C₇	1	2	yes	complemented
100	#3054	C₂×C₇	1	16	yes	direct product factor
101	C₂×#470	C₂×C₇	1	2	yes	complemented
102	C₂×#469	C₂×C₇	1	2	yes	complemented
103	C₂×#468	C₂×C₇	1	4	yes	complemented
104	C₂×#427	C₂×C₇	1	1	yes	characteristic, complemented
105	C₂×#416	C₂×C₇	1	2	yes	complemented
106	C₂⁴×C₇	—	2	4	no	—
107	C₂⁴×C₇	—	2	2	no	—
108	C₂⁴×C₇	—	4	4	no	—
109	C₂⁴×C₇	C₂×D₄	1	2	yes	—
110	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×C₇	C₂×D₄	1	4	yes	—
112	C₇×#41	—	2	16	no	—
113	C₇×#41	—	2	16	no	—
114	C₇×#41	—	4	16	no	—
115	C₂×C₇×Q₈	—	2	2	no	—
116	C₂×C₇×Q₈	—	2	4	no	—
117	C₂×C₇×Q₈	—	2	4	no	—
118	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
119	C₂×C₇×D₄	—	2	16	no	—
120	C₂×C₇×D₄	—	2	8	no	—
121	C₂×C₇×D₄	—	2	4	no	—
122	C₂×C₇×D₄	—	2	2	no	—
123	C₂×C₇×D₄	—	2	4	no	—
124	C₂×C₇×D₄	—	4	16	no	—
125	C₂×C₇×D₄	—	4	8	no	—
126	C₂×C₇×D₄	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₇	—	2	4	no	—
128	C₂²×C₄×C₇	—	2	8	no	—
129	C₂²×C₄×C₇	—	2	16	no	—
130	C₂²×C₄×C₇	—	2	4	no	—
131	C₂²×C₄×C₇	—	2	8	no	—
132	C₂²×C₄×C₇	—	2	4	no	—
133	C₂²×C₄×C₇	—	2	8	no	—
134	C₂²×C₄×C₇	—	2	4	no	—
135	C₂²×C₄×C₇	—	2	2	no	—
136	C₂²×C₄×C₇	—	2	8	no	—
137	C₂²×C₄×C₇	—	4	8	no	—
138	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
140	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇	#41	1	4	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
149	C₇×Q₁₆	—	2	8	no	—
150	C₇×SD₁₆	—	2	16	no	—
151	C₇×D₈	—	2	8	no	—
152	C₇×M₁₆	—	2	16	no	—
153	C₇×M₁₆	—	2	16	no	—
154	C₂×C₇×C₈	—	2	4	no	—
155	C₂×C₇×C₈	—	2	8	no	—
156	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
157	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
158	C₂×C₇×C₈	C₂×D₄	1	16	yes	complemented
159	C₂×C₇×C₈	C₂⁴	1	4	yes	—
160	C₂×C₇×C₈	C₂⁴	1	2	yes	—
161	C₂×C₇×C₈	C₂⁴	1	2	yes	—
162	C₇×C₄⋊C₄	—	2	16	no	—
163	C₇×C₄⋊C₄	—	2	4	no	—
164	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
165	C₇×C₂²⋊C₄	—	2	8	no	—
166	C₇×C₂²⋊C₄	—	2	16	no	—
167	C₇×C₂²⋊C₄	—	2	16	no	—
168	C₄²×C₇	—	2	8	no	—
169	C₂²×#41	C₂²×C₇	1	2	yes	—
170	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
171	C₂×#135	—	2	8	no	—
172	C₂×#135	C₂²×C₇	1	8	yes	complemented
173	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
174	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
175	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
176	C₂²×M₁₆	—	2	8	no	—
177	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
178	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
179	C₂²×M₁₆	C₂²×C₇	1	8	yes	complemented
180	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
181	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
182	#525	—	2	8	no	—
183	#525	C₂²×C₇	1	16	yes	complemented
184	C₂×#123	—	2	2	no	—
185	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
186	C₂×#121	C₂²×C₇	1	4	yes	—
187	C₂×#120	—	2	2	no	—
188	C₂×C₄×D₄	—	2	4	no	—
189	C₂×#117	C₂²×C₇	1	2	yes	—
190	#470	C₂²×C₇	1	16	yes	complemented
191	#469	C₂²×C₇	1	16	yes	complemented
192	#468	C₂²×C₇	1	32	yes	complemented
193	#427	C₂²×C₇	1	8	yes	complemented
194	C₂×#107	C₂²×C₇	1	2	yes	complemented
195	C₂×#106	C₂²×C₇	1	2	yes	complemented
196	#416	C₂²×C₇	1	16	yes	complemented
197	C₂×#103	C₂²×C₇	1	4	yes	complemented
198	C₂×#102	C₂²×C₇	1	4	yes	complemented
199	C₂³×C₇	—	2	4	no	—
200	C₂³×C₇	—	2	8	no	—
201	C₂³×C₇	—	2	4	no	—
202	C₂³×C₇	—	2	8	no	—
203	C₂³×C₇	—	2	4	no	—
204	C₂³×C₇	—	4	8	no	—
205	C₂³×C₇	—	4	16	no	—
206	C₂³×C₇	—	4	4	no	—
207	C₂³×C₇	—	4	8	no	—
208	C₂³×C₇	#121	1	4	yes	—
209	C₂³×C₇	C₂²×D₄	1	4	yes	—
210	C₂³×C₇	C₂²×D₄	1	2	yes	—
211	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
212	C₇×Q₈	—	2	4	no	—
213	C₇×Q₈	—	2	4	no	—
214	C₇×Q₈	—	4	4	no	—
215	C₇×D₄	—	2	4	no	—
216	C₇×D₄	—	2	4	no	—
217	C₇×D₄	—	4	32	no	—
218	C₇×D₄	—	4	16	no	—
219	C₇×D₄	—	4	4	no	—
220	C₂×C₄×C₇	—	2	8	no	—
221	C₂×C₄×C₇	—	2	4	no	—
222	C₂×C₄×C₇	—	2	16	no	—
223	C₂×C₄×C₇	—	2	8	no	—
224	C₂×C₄×C₇	—	2	4	no	—
225	C₂×C₄×C₇	—	2	4	no	—
226	C₂×C₄×C₇	—	2	8	no	—
227	C₂×C₄×C₇	—	2	4	no	—
228	C₂×C₄×C₇	—	4	4	no	—
229	C₂×C₄×C₇	—	4	8	no	—
230	C₂×C₄×C₇	—	4	16	no	—
231	C₂×C₄×C₇	#121	1	4	yes	—
232	C₂×C₄×C₇	#121	1	8	yes	—
233	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
238	C₂×C₄×C₇	C₂×#41	1	2	yes	—
239	C₂×C₄×C₇	C₂×#41	1	4	yes	—
240	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
241	C₇×C₈	—	2	4	no	—
242	C₇×C₈	C₂²×D₄	1	4	yes	—
243	C₇×C₈	C₂²×D₄	1	4	yes	—
244	C₂⁵	C₇×D₄	1	1	yes	characteristic
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	8	no	—
247	C₂×#41	—	2	8	no	—
248	C₂×#41	C₂³×C₇	1	8	yes	—
249	C₂²×Q₈	C₂³×C₇	1	2	yes	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	C₂³×C₇	1	2	yes	—
253	C₂³×C₄	—	2	4	no	—
254	C₂³×C₄	—	2	4	no	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	C₇×D₄	1	2	yes	—
257	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
258	C₂³×C₄	C₇×D₄	1	4	yes	—
259	C₂³×C₄	C₂³×C₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₇	1	4	yes	—
261	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
262	#135	—	2	32	no	—
263	C₂×Q₁₆	—	2	4	no	—
264	C₂×Q₁₆	C₂³×C₇	1	4	yes	complemented
265	C₂×SD₁₆	—	2	8	no	—
266	C₂×SD₁₆	C₂³×C₇	1	8	yes	complemented
267	C₂×D₈	—	2	4	no	—
268	C₂×D₈	C₂³×C₇	1	4	yes	complemented
269	C₂×M₁₆	—	2	8	no	—
270	C₂×M₁₆	—	2	8	no	—
271	C₂×M₁₆	—	2	32	no	—
272	C₂×M₁₆	C₂³×C₇	1	8	yes	—
273	C₂×M₁₆	C₂³×C₇	1	8	yes	—
274	C₂²×C₈	—	2	4	no	—
275	C₂²×C₈	C₇×D₄	1	8	yes	complemented
276	C₂²×C₈	C₂³×C₇	1	2	yes	—
277	C₂²×C₈	C₂³×C₇	1	4	yes	—
278	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₇	1	4	yes	—
281	#123	—	2	16	no	—
282	C₂²⋊Q₈	—	2	8	no	—
283	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
284	#121	—	2	8	no	—
285	#121	C₂³×C₇	1	16	yes	—
286	#120	—	2	16	no	—
287	C₄×D₄	—	2	32	no	—
288	#117	—	2	4	no	—
289	#117	C₂³×C₇	1	8	yes	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	4	no	—
295	C₂×C₄²	—	2	2	no	—
296	#107	C₂³×C₇	1	8	yes	complemented
297	#106	C₂³×C₇	1	8	yes	complemented
298	#103	C₂³×C₇	1	16	yes	complemented
299	#102	C₂³×C₇	1	16	yes	complemented
300	C₂²×C₇	—	2	8	no	—
301	C₂²×C₇	—	2	4	no	—
302	C₂²×C₇	—	2	4	no	—
303	C₂²×C₇	—	2	8	no	—
304	C₂²×C₇	—	4	16	no	—
305	C₂²×C₇	—	4	8	no	—
306	C₂²×C₇	—	4	4	no	—
307	C₂²×C₇	—	4	8	no	—
308	C₂²×C₇	—	8	8	no	—
309	C₂²×C₇	C₂×#121	1	4	yes	—
310	C₂²×C₇	C₂×#121	1	2	yes	—
311	C₂²×C₇	#575	1	4	yes	—
312	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
313	C₄×C₇	—	2	4	no	—
314	C₄×C₇	—	4	4	no	—
315	C₄×C₇	—	4	8	no	—
316	C₄×C₇	C₂×#121	1	4	yes	—
317	C₄×C₇	C₂×#121	1	2	yes	—
318	C₄×C₇	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₇	C₂²×#41	1	1	yes	characteristic
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	4	4	no	—
323	C₂⁴	C₂×C₇×D₄	1	2	yes	—
324	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
325	C₂⁴	C₂×C₇×D₄	1	4	yes	—
326	#41	—	2	16	no	—
327	#41	—	2	16	no	—
328	#41	—	4	16	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
333	C₂×D₄	—	2	16	no	—
334	C₂×D₄	—	2	8	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	16	no	—
339	C₂×D₄	—	4	8	no	—
340	C₂×D₄	C₂⁴×C₇	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	16	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	4	8	no	—
352	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
353	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
354	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
355	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
356	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
358	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
359	C₂²×C₄	C₇×#41	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
363	Q₁₆	—	2	8	no	—
364	SD₁₆	—	2	16	no	—
365	D₈	—	2	8	no	—
366	M₁₆	—	2	16	no	—
367	M₁₆	—	2	16	no	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	8	no	—
370	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
371	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
372	C₂×C₈	C₂×C₇×D₄	1	16	yes	complemented
373	C₂×C₈	C₂⁴×C₇	1	4	yes	—
374	C₂×C₈	C₂⁴×C₇	1	2	yes	—
375	C₂×C₈	C₂⁴×C₇	1	2	yes	—
376	C₄⋊C₄	—	2	16	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	16	no	—
381	C₂²⋊C₄	—	2	16	no	—
382	C₄²	—	2	8	no	—
383	C₂×C₇	—	2	4	no	—
384	C₂×C₇	—	4	4	no	—
385	C₂×C₇	—	8	4	no	—
386	C₂×C₇	#3054	1	4	yes	direct product factor
387	C₂×C₇	C₂²×#121	1	1	yes	characteristic
388	C₂×C₇	C₂×#575	1	2	yes	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	8	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	8	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	4	16	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	8	no	—
398	C₂³	C₇×#121	1	4	yes	—
399	C₂³	C₂²×C₇×D₄	1	4	yes	—
400	C₂³	C₂²×C₇×D₄	1	2	yes	—
401	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	32	no	—
408	D₄	—	4	16	no	—
409	D₄	—	4	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	16	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	C₇×#121	1	4	yes	—
422	C₂×C₄	C₇×#121	1	8	yes	—
423	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
424	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
425	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
426	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
427	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
428	C₂×C₄	C₂×C₇×#41	1	2	yes	—
429	C₂×C₄	C₂×C₇×#41	1	4	yes	—
430	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
431	C₈	—	2	4	no	—
432	C₈	C₂²×C₇×D₄	1	4	yes	—
433	C₈	C₂²×C₇×D₄	1	4	yes	—
434	C₇	C₂×#3054	1	1	yes	characteristic, direct product factor, Sylow
435	C₂²	—	2	4	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	8	no	—
444	C₂²	C₂×C₇×#121	1	4	yes	—
445	C₂²	C₂×C₇×#121	1	2	yes	—
446	C₂²	C₇×#575	1	4	yes	—
447	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	4	8	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×C₇×#121	1	4	yes	—
452	C₄	C₂×C₇×#121	1	2	yes	—
453	C₄	C₂³×C₇×D₄	1	1	yes	characteristic
454	C₄	C₂²×C₇×#41	1	1	yes	characteristic
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	4	no	—
458	C₂	C₇×#3054	1	4	yes	direct product factor
459	C₂	C₂²×C₇×#121	1	1	yes	characteristic
460	C₂	C₂×C₇×#575	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×#135	C₂	semidirect
2. C₂³×C₇×M₁₆	C₂	semidirect
3. C₂×C₇×#525	C₂	semidirect
4. C₇×#3054	C₂	direct (N × H)
5. C₂×C₇×#470	C₂	semidirect
6. C₂×C₇×#469	C₂	semidirect
7. C₂×C₇×#468	C₂	semidirect
8. C₂×C₇×#427	C₂	semidirect
9. C₂×C₇×#416	C₂	semidirect
13. C₂×C₇×#135	C₂²	semidirect
14. C₂²×C₇×Q₁₆	C₂²	semidirect
15. C₂²×C₇×SD₁₆	C₂²	semidirect
16. C₂²×C₇×D₈	C₂²	semidirect
20. C₂²×C₇×M₁₆	C₂²	semidirect
24. C₇×#525	C₂²	semidirect
31. C₇×#470	C₂²	semidirect
32. C₇×#469	C₂²	semidirect
33. C₇×#468	C₂²	semidirect
34. C₇×#427	C₂²	semidirect
35. C₂×C₇×#107	C₂²	semidirect
36. C₂×C₇×#106	C₂²	semidirect
37. C₇×#416	C₂²	semidirect
38. C₂×C₇×#103	C₂²	semidirect
39. C₂×C₇×#102	C₂²	semidirect
40. C₂×#3054	C₇	direct (N × H)
61. C₂×C₇×Q₁₆	C₂³	semidirect
63. C₂×C₇×SD₁₆	C₂³	semidirect
65. C₂×C₇×D₈	C₂³	semidirect
72. C₂²×C₇×C₈	D₄	semidirect
93. C₇×#107	C₂³	semidirect
94. C₇×#106	C₂³	semidirect
95. C₇×#103	C₂³	semidirect
96. C₇×#102	C₂³	semidirect
97. C₂²×#135	C₂×C₇	semidirect
98. C₂³×M₁₆	C₂×C₇	semidirect
99. C₂×#525	C₂×C₇	semidirect
100. #3054	C₂×C₇	direct (N × H)
101. C₂×#470	C₂×C₇	semidirect
102. C₂×#469	C₂×C₇	semidirect
103. C₂×#468	C₂×C₇	semidirect
104. C₂×#427	C₂×C₇	semidirect
105. C₂×#416	C₂×C₇	semidirect
158. C₂×C₇×C₈	C₂×D₄	semidirect
172. C₂×#135	C₂²×C₇	semidirect
173. C₂²×Q₁₆	C₂²×C₇	semidirect
174. C₂²×SD₁₆	C₂²×C₇	semidirect
175. C₂²×D₈	C₂²×C₇	semidirect
179. C₂²×M₁₆	C₂²×C₇	semidirect
183. #525	C₂²×C₇	semidirect
190. #470	C₂²×C₇	semidirect
191. #469	C₂²×C₇	semidirect
192. #468	C₂²×C₇	semidirect
193. #427	C₂²×C₇	semidirect
194. C₂×#107	C₂²×C₇	semidirect
195. C₂×#106	C₂²×C₇	semidirect
196. #416	C₂²×C₇	semidirect
197. C₂×#103	C₂²×C₇	semidirect
198. C₂×#102	C₂²×C₇	semidirect
264. C₂×Q₁₆	C₂³×C₇	semidirect
266. C₂×SD₁₆	C₂³×C₇	semidirect
268. C₂×D₈	C₂³×C₇	semidirect
275. C₂²×C₈	C₇×D₄	semidirect
296. #107	C₂³×C₇	semidirect
297. #106	C₂³×C₇	semidirect
298. #103	C₂³×C₇	semidirect
299. #102	C₂³×C₇	semidirect
372. C₂×C₈	C₂×C₇×D₄	semidirect
386. C₂×C₇	#3054	direct (N × H)
434. C₇	C₂×#3054	direct (N × H)
458. C₂	C₇×#3054	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×#135	2
C₂³×C₇×M₁₆	2
C₂×C₇×#525	2
C₇×#3054	2
C₂×C₇×#470	2
C₂×C₇×#469	2
C₂×C₇×#468	2
C₂×C₇×#427	2
C₂×C₇×#416	2
C₂×#3054	7

Subgroups — C2×C7×#3054 #13237657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3054 #13237657