Subgroups — C₂²×C₇×#538 #13239887

Order 1792.

9566 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#538	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₇×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₇×#124	C₂	1	2	yes	maximal, complemented
4	C₂²×C₇×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×#121	C₂	1	2	yes	maximal, complemented
7	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₇×#120	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×C₇×D₄	C₂	1	2	yes	maximal, complemented
10	C₂³×C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₇	C₂²	1	1	yes	characteristic
12	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₇×D₄	C₂²	1	2	yes	—
14	C₂³×C₇×D₄	C₂²	1	2	yes	—
15	C₂³×C₇×D₄	C₂²	1	2	yes	—
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
18	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₇	C₂²	1	2	yes	complemented
20	C₇×#538	C₂²	1	256	yes	direct product factor
21	C₂×C₇×#126	C₂²	1	48	yes	complemented
22	C₂×C₇×#124	C₂²	1	48	yes	complemented
23	C₂×C₇×#123	C₂²	1	48	yes	complemented
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	24	yes	complemented
25	C₂×C₇×#121	C₂²	1	48	yes	complemented
26	C₂×C₇×#121	C₂²	1	24	yes	complemented
27	C₂×C₇×#120	C₂²	1	48	yes	complemented
28	C₂×C₄×C₇×D₄	C₂²	1	48	yes	complemented
29	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
30	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
31	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
37	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₂²×C₇×C₂²⋊C₄	C₂²	1	24	yes	complemented
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
41	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
42	C₂²×#538	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂⁵×C₇	—	2	8	no	—
44	C₂⁵×C₇	—	4	4	no	—
45	C₂⁵×C₇	—	4	4	no	—
46	C₂⁵×C₇	C₂³	1	2	yes	—
47	C₂⁵×C₇	C₂³	1	2	yes	—
48	C₂⁵×C₇	C₂³	1	1	yes	characteristic
49	C₂⁵×C₇	C₂³	1	12	yes	—
50	C₂²×C₇×Q₈	—	4	4	no	—
51	C₂²×C₇×Q₈	C₂³	1	12	yes	complemented
52	C₂²×C₇×D₄	—	2	16	no	—
53	C₂²×C₇×D₄	—	4	8	no	—
54	C₂²×C₇×D₄	—	4	8	no	—
55	C₂²×C₇×D₄	—	4	4	no	—
56	C₂²×C₇×D₄	C₂³	1	24	yes	—
57	C₂²×C₇×D₄	C₂³	1	24	yes	—
58	C₂²×C₇×D₄	C₂³	1	24	yes	—
59	C₂²×C₇×D₄	C₂³	1	12	yes	complemented
60	C₂³×C₄×C₇	—	4	4	no	—
61	C₂³×C₄×C₇	—	4	4	no	—
62	C₂³×C₄×C₇	—	4	8	no	—
63	C₂³×C₄×C₇	C₂³	1	2	yes	—
64	C₂³×C₄×C₇	C₂³	1	2	yes	—
65	C₂³×C₄×C₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₇	C₂³	1	12	yes	—
70	C₂³×C₄×C₇	C₂³	1	12	yes	—
71	C₂³×C₄×C₇	C₂³	1	24	yes	complemented
72	C₇×#126	C₂³	1	128	yes	complemented
73	C₇×#124	C₂³	1	128	yes	complemented
74	C₇×#123	C₂³	1	128	yes	complemented
75	C₇×C₂²⋊Q₈	C₂³	1	64	yes	complemented
76	C₇×#121	C₂³	1	128	yes	complemented
77	C₇×#121	C₂³	1	64	yes	complemented
78	C₇×#120	C₂³	1	128	yes	complemented
79	C₄×C₇×D₄	C₂³	1	128	yes	complemented
80	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	complemented
81	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	complemented
82	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	complemented
83	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	complemented
84	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
85	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
86	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
87	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
88	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
89	C₂×C₇×C₂²⋊C₄	C₂³	1	64	yes	complemented
90	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	complemented
91	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	complemented
92	C₂×C₄²×C₇	C₂³	1	24	yes	complemented
93	C₂×#538	C₂×C₇	1	48	yes	direct product factor
94	C₂²×#126	C₂×C₇	1	2	yes	complemented
95	C₂²×#124	C₂×C₇	1	2	yes	complemented
96	C₂²×#123	C₂×C₇	1	2	yes	complemented
97	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
98	C₂²×#121	C₂×C₇	1	2	yes	complemented
99	C₂²×#121	C₂×C₇	1	1	yes	characteristic, complemented
100	C₂²×#120	C₂×C₇	1	2	yes	complemented
101	C₂²×C₄×D₄	C₂×C₇	1	2	yes	complemented
102	C₂³×C₂²⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
103	C₂⁴×C₇	—	2	4	no	—
104	C₂⁴×C₇	—	2	4	no	—
105	C₂⁴×C₇	—	2	8	no	—
106	C₂⁴×C₇	—	2	48	no	—
107	C₂⁴×C₇	—	2	8	no	—
108	C₂⁴×C₇	—	2	8	no	—
109	C₂⁴×C₇	—	2	8	no	—
110	C₂⁴×C₇	—	2	8	no	—
111	C₂⁴×C₇	—	2	8	no	—
112	C₂⁴×C₇	—	4	24	no	—
113	C₂⁴×C₇	—	4	24	no	—
114	C₂⁴×C₇	—	4	64	no	—
115	C₂⁴×C₇	#41	1	8	yes	—
116	C₂⁴×C₇	C₂⁴	1	12	yes	—
117	C₂⁴×C₇	C₂⁴	1	12	yes	—
118	C₂⁴×C₇	C₂⁴	1	6	yes	—
119	C₂⁴×C₇	C₂⁴	1	16	yes	—
120	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₇×Q₈	—	4	24	no	—
122	C₂×C₇×Q₈	C₂⁴	1	16	yes	complemented
123	C₂×C₇×D₄	—	2	96	no	—
124	C₂×C₇×D₄	—	4	48	no	—
125	C₂×C₇×D₄	—	4	48	no	—
126	C₂×C₇×D₄	—	4	24	no	—
127	C₂×C₇×D₄	C₂⁴	1	32	yes	—
128	C₂×C₇×D₄	C₂⁴	1	32	yes	—
129	C₂×C₇×D₄	C₂⁴	1	32	yes	—
130	C₂×C₇×D₄	C₂⁴	1	16	yes	complemented
131	C₂²×C₄×C₇	—	2	8	no	—
132	C₂²×C₄×C₇	—	2	8	no	—
133	C₂²×C₄×C₇	—	2	4	no	—
134	C₂²×C₄×C₇	—	2	8	no	—
135	C₂²×C₄×C₇	—	2	4	no	—
136	C₂²×C₄×C₇	—	2	8	no	—
137	C₂²×C₄×C₇	—	4	24	no	—
138	C₂²×C₄×C₇	—	4	24	no	—
139	C₂²×C₄×C₇	—	4	48	no	—
140	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
141	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
142	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
143	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
144	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
145	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
146	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
147	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
148	C₂²×C₄×C₇	C₂⁴	1	32	yes	complemented
149	C₇×C₄⋊C₄	C₂⁴	1	32	yes	complemented
150	C₇×C₄⋊C₄	C₂⁴	1	32	yes	complemented
151	C₇×C₄⋊C₄	C₂⁴	1	16	yes	complemented
152	C₇×C₄⋊C₄	C₂⁴	1	16	yes	complemented
153	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
154	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
155	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
156	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
157	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
158	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
159	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
160	C₄²×C₇	C₂⁴	1	32	yes	complemented
161	C₂⁶	C₂²×C₇	1	1	yes	characteristic
162	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
163	C₂³×D₄	C₂²×C₇	1	2	yes	—
164	C₂³×D₄	C₂²×C₇	1	2	yes	—
165	C₂³×D₄	C₂²×C₇	1	2	yes	—
166	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
167	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
168	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
169	C₂⁴×C₄	C₂²×C₇	1	2	yes	complemented
170	#538	C₂²×C₇	1	256	yes	direct product factor
171	C₂×#126	C₂²×C₇	1	48	yes	complemented
172	C₂×#124	C₂²×C₇	1	48	yes	complemented
173	C₂×#123	C₂²×C₇	1	48	yes	complemented
174	C₂×C₂²⋊Q₈	C₂²×C₇	1	24	yes	complemented
175	C₂×#121	C₂²×C₇	1	48	yes	complemented
176	C₂×#121	C₂²×C₇	1	24	yes	complemented
177	C₂×#120	C₂²×C₇	1	48	yes	complemented
178	C₂×C₄×D₄	C₂²×C₇	1	48	yes	complemented
179	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
180	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
181	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
182	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
183	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
184	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
186	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
187	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
188	C₂²×C₂²⋊C₄	C₂²×C₇	1	24	yes	complemented
189	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
190	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
191	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
192	C₂³×C₇	—	2	32	no	—
193	C₂³×C₇	—	2	12	no	—
194	C₂³×C₇	—	2	12	no	—
195	C₂³×C₇	—	2	24	no	—
196	C₂³×C₇	—	2	32	no	—
197	C₂³×C₇	—	2	24	no	—
198	C₂³×C₇	—	2	24	no	—
199	C₂³×C₇	—	2	24	no	—
200	C₂³×C₇	—	2	24	no	—
201	C₂³×C₇	—	2	24	no	—
202	C₂³×C₇	—	4	16	no	—
203	C₂³×C₇	—	4	16	no	—
204	C₂³×C₇	—	4	192	no	—
205	C₂³×C₇	—	4	32	no	—
206	C₂³×C₇	—	4	32	no	—
207	C₂³×C₇	C₂×#41	1	24	yes	—
208	C₂³×C₇	C₂×#41	1	4	yes	—
209	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
210	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
211	C₂³×C₇	C₂⁵	1	8	yes	—
212	C₂³×C₇	C₂⁵	1	8	yes	—
213	C₂³×C₇	C₂⁵	1	4	yes	—
214	C₂³×C₇	C₂⁵	1	3	yes	—
215	C₇×Q₈	—	4	16	no	—
216	C₇×D₄	—	2	64	no	—
217	C₇×D₄	—	4	32	no	—
218	C₇×D₄	—	4	32	no	—
219	C₇×D₄	—	4	16	no	—
220	C₂×C₄×C₇	—	2	24	no	—
221	C₂×C₄×C₇	—	2	24	no	—
222	C₂×C₄×C₇	—	2	12	no	—
223	C₂×C₄×C₇	—	2	24	no	—
224	C₂×C₄×C₇	—	2	12	no	—
225	C₂×C₄×C₇	—	2	24	no	—
226	C₂×C₄×C₇	—	4	16	no	—
227	C₂×C₄×C₇	—	4	16	no	—
228	C₂×C₄×C₇	—	4	32	no	—
229	C₂×C₄×C₇	C₂⁵	1	8	yes	—
230	C₂×C₄×C₇	C₂⁵	1	8	yes	—
231	C₂×C₄×C₇	C₂⁵	1	8	yes	—
232	C₂×C₄×C₇	C₂⁵	1	4	yes	—
233	C₂×C₄×C₇	C₂⁵	1	4	yes	—
234	C₂×C₄×C₇	C₂⁵	1	8	yes	—
235	C₂⁵	—	2	8	no	—
236	C₂⁵	—	4	4	no	—
237	C₂⁵	—	4	4	no	—
238	C₂⁵	C₂³×C₇	1	2	yes	—
239	C₂⁵	C₂³×C₇	1	2	yes	—
240	C₂⁵	C₂³×C₇	1	1	yes	characteristic
241	C₂⁵	C₂³×C₇	1	12	yes	—
242	C₂²×Q₈	—	4	4	no	—
243	C₂²×Q₈	C₂³×C₇	1	12	yes	complemented
244	C₂²×D₄	—	2	16	no	—
245	C₂²×D₄	—	4	8	no	—
246	C₂²×D₄	—	4	8	no	—
247	C₂²×D₄	—	4	4	no	—
248	C₂²×D₄	C₂³×C₇	1	24	yes	—
249	C₂²×D₄	C₂³×C₇	1	24	yes	—
250	C₂²×D₄	C₂³×C₇	1	24	yes	—
251	C₂²×D₄	C₂³×C₇	1	12	yes	complemented
252	C₂³×C₄	—	4	4	no	—
253	C₂³×C₄	—	4	4	no	—
254	C₂³×C₄	—	4	8	no	—
255	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₇	1	2	yes	—
257	C₂³×C₄	C₂³×C₇	1	2	yes	—
258	C₂³×C₄	C₂³×C₇	1	2	yes	—
259	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
260	C₂³×C₄	C₂³×C₇	1	2	yes	—
261	C₂³×C₄	C₂³×C₇	1	12	yes	—
262	C₂³×C₄	C₂³×C₇	1	12	yes	—
263	C₂³×C₄	C₂³×C₇	1	24	yes	complemented
264	#126	C₂³×C₇	1	128	yes	complemented
265	#124	C₂³×C₇	1	128	yes	complemented
266	#123	C₂³×C₇	1	128	yes	complemented
267	C₂²⋊Q₈	C₂³×C₇	1	64	yes	complemented
268	#121	C₂³×C₇	1	128	yes	complemented
269	#121	C₂³×C₇	1	64	yes	complemented
270	#120	C₂³×C₇	1	128	yes	complemented
271	C₄×D₄	C₂³×C₇	1	128	yes	complemented
272	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	complemented
273	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	complemented
274	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	complemented
275	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	complemented
276	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₇	1	64	yes	complemented
282	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	complemented
283	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	complemented
284	C₂×C₄²	C₂³×C₇	1	24	yes	complemented
285	C₂²×C₇	—	2	4	no	—
286	C₂²×C₇	—	2	4	no	—
287	C₂²×C₇	—	2	48	no	—
288	C₂²×C₇	—	2	8	no	—
289	C₂²×C₇	—	2	8	no	—
290	C₂²×C₇	—	2	8	no	—
291	C₂²×C₇	—	2	8	no	—
292	C₂²×C₇	—	2	8	no	—
293	C₂²×C₇	—	2	8	no	—
294	C₂²×C₇	—	4	64	no	—
295	C₂²×C₇	—	4	48	no	—
296	C₂²×C₇	—	4	48	no	—
297	C₂²×C₇	#538	1	16	yes	direct product factor
298	C₂²×C₇	C₂²×#41	1	8	yes	—
299	C₂²×C₇	C₂²×#41	1	6	yes	—
300	C₂²×C₇	C₂×H(5,𝔽₂)	1	6	yes	—
301	C₂²×C₇	C₂×H(5,𝔽₂)	1	6	yes	—
302	C₂²×C₇	C₂⁶	1	1	yes	characteristic
303	C₄×C₇	—	2	8	no	—
304	C₄×C₇	—	2	8	no	—
305	C₄×C₇	—	2	4	no	—
306	C₄×C₇	—	2	8	no	—
307	C₄×C₇	—	2	4	no	—
308	C₄×C₇	—	2	8	no	—
309	C₂⁴	—	2	4	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	2	8	no	—
312	C₂⁴	—	2	48	no	—
313	C₂⁴	—	2	8	no	—
314	C₂⁴	—	2	8	no	—
315	C₂⁴	—	2	8	no	—
316	C₂⁴	—	2	8	no	—
317	C₂⁴	—	2	8	no	—
318	C₂⁴	—	4	24	no	—
319	C₂⁴	—	4	24	no	—
320	C₂⁴	—	4	64	no	—
321	C₂⁴	C₇×#41	1	8	yes	—
322	C₂⁴	C₂⁴×C₇	1	12	yes	—
323	C₂⁴	C₂⁴×C₇	1	12	yes	—
324	C₂⁴	C₂⁴×C₇	1	6	yes	—
325	C₂⁴	C₂⁴×C₇	1	16	yes	—
326	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
327	C₂×Q₈	—	4	24	no	—
328	C₂×Q₈	C₂⁴×C₇	1	16	yes	complemented
329	C₂×D₄	—	2	96	no	—
330	C₂×D₄	—	4	48	no	—
331	C₂×D₄	—	4	48	no	—
332	C₂×D₄	—	4	24	no	—
333	C₂×D₄	C₂⁴×C₇	1	32	yes	—
334	C₂×D₄	C₂⁴×C₇	1	32	yes	—
335	C₂×D₄	C₂⁴×C₇	1	32	yes	—
336	C₂×D₄	C₂⁴×C₇	1	16	yes	complemented
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	2	8	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	8	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	4	24	no	—
344	C₂²×C₄	—	4	24	no	—
345	C₂²×C₄	—	4	48	no	—
346	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
347	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
348	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
349	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
350	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
351	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
352	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
353	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
354	C₂²×C₄	C₂⁴×C₇	1	32	yes	complemented
355	C₄⋊C₄	C₂⁴×C₇	1	32	yes	complemented
356	C₄⋊C₄	C₂⁴×C₇	1	32	yes	complemented
357	C₄⋊C₄	C₂⁴×C₇	1	16	yes	complemented
358	C₄⋊C₄	C₂⁴×C₇	1	16	yes	complemented
359	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
360	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
361	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
362	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
363	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
364	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	complemented
365	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	complemented
366	C₄²	C₂⁴×C₇	1	32	yes	complemented
367	C₂×C₇	—	2	8	no	—
368	C₂×C₇	—	4	8	no	—
369	C₂×C₇	—	4	8	no	—
370	C₂×C₇	C₂×#538	1	12	yes	direct product factor
371	C₂×C₇	C₂³×#41	1	1	yes	characteristic
372	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
373	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂³	—	2	12	no	—
375	C₂³	—	2	12	no	—
376	C₂³	—	2	32	no	—
377	C₂³	—	2	24	no	—
378	C₂³	—	2	32	no	—
379	C₂³	—	2	24	no	—
380	C₂³	—	2	24	no	—
381	C₂³	—	2	24	no	—
382	C₂³	—	2	24	no	—
383	C₂³	—	2	24	no	—
384	C₂³	—	4	16	no	—
385	C₂³	—	4	16	no	—
386	C₂³	—	4	192	no	—
387	C₂³	—	4	32	no	—
388	C₂³	—	4	32	no	—
389	C₂³	C₂×C₇×#41	1	24	yes	—
390	C₂³	C₂×C₇×#41	1	4	yes	—
391	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
392	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
393	C₂³	C₂⁵×C₇	1	8	yes	—
394	C₂³	C₂⁵×C₇	1	8	yes	—
395	C₂³	C₂⁵×C₇	1	4	yes	—
396	C₂³	C₂⁵×C₇	1	3	yes	—
397	Q₈	—	4	16	no	—
398	D₄	—	2	64	no	—
399	D₄	—	4	32	no	—
400	D₄	—	4	32	no	—
401	D₄	—	4	16	no	—
402	C₂×C₄	—	2	24	no	—
403	C₂×C₄	—	2	24	no	—
404	C₂×C₄	—	2	12	no	—
405	C₂×C₄	—	2	24	no	—
406	C₂×C₄	—	2	12	no	—
407	C₂×C₄	—	2	24	no	—
408	C₂×C₄	—	4	16	no	—
409	C₂×C₄	—	4	16	no	—
410	C₂×C₄	—	4	32	no	—
411	C₂×C₄	C₂⁵×C₇	1	8	yes	—
412	C₂×C₄	C₂⁵×C₇	1	8	yes	—
413	C₂×C₄	C₂⁵×C₇	1	8	yes	—
414	C₂×C₄	C₂⁵×C₇	1	4	yes	—
415	C₂×C₄	C₂⁵×C₇	1	4	yes	—
416	C₂×C₄	C₂⁵×C₇	1	8	yes	—
417	C₇	C₂²×#538	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	48	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	8	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	8	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	4	64	no	—
428	C₂²	—	4	48	no	—
429	C₂²	—	4	48	no	—
430	C₂²	C₇×#538	1	16	yes	direct product factor
431	C₂²	C₂²×C₇×#41	1	8	yes	—
432	C₂²	C₂²×C₇×#41	1	6	yes	—
433	C₂²	C₂×C₇×H(5,𝔽₂)	1	6	yes	—
434	C₂²	C₂×C₇×H(5,𝔽₂)	1	6	yes	—
435	C₂²	C₂⁶×C₇	1	1	yes	characteristic
436	C₄	—	2	8	no	—
437	C₄	—	2	8	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	8	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	8	no	—
442	C₂	—	2	8	no	—
443	C₂	—	4	8	no	—
444	C₂	—	4	8	no	—
445	C₂	C₂×C₇×#538	1	12	yes	direct product factor
446	C₂	C₂³×C₇×#41	1	1	yes	characteristic
447	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#538	C₂	direct (N × H)
2. C₂²×C₇×#126	C₂	semidirect
3. C₂²×C₇×#124	C₂	semidirect
4. C₂²×C₇×#123	C₂	semidirect
5. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₇×#121	C₂	semidirect
7. C₂²×C₇×#121	C₂	semidirect
8. C₂²×C₇×#120	C₂	semidirect
9. C₂²×C₄×C₇×D₄	C₂	semidirect
10. C₂³×C₇×C₂²⋊C₄	C₂	semidirect
12. C₂³×C₇×Q₈	C₂²	semidirect
16. C₂³×C₇×D₄	C₂²	semidirect
19. C₂⁴×C₄×C₇	C₂²	semidirect
20. C₇×#538	C₂²	direct (N × H)
21. C₂×C₇×#126	C₂²	semidirect
22. C₂×C₇×#124	C₂²	semidirect
23. C₂×C₇×#123	C₂²	semidirect
24. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
25. C₂×C₇×#121	C₂²	semidirect
26. C₂×C₇×#121	C₂²	semidirect
27. C₂×C₇×#120	C₂²	semidirect
28. C₂×C₄×C₇×D₄	C₂²	semidirect
29. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
31. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
38. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
39. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
40. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
41. C₂²×C₄²×C₇	C₂²	semidirect
42. C₂²×#538	C₇	direct (N × H)
51. C₂²×C₇×Q₈	C₂³	semidirect
59. C₂²×C₇×D₄	C₂³	semidirect
71. C₂³×C₄×C₇	C₂³	semidirect
72. C₇×#126	C₂³	semidirect
73. C₇×#124	C₂³	semidirect
74. C₇×#123	C₂³	semidirect
75. C₇×C₂²⋊Q₈	C₂³	semidirect
76. C₇×#121	C₂³	semidirect
77. C₇×#121	C₂³	semidirect
78. C₇×#120	C₂³	semidirect
79. C₄×C₇×D₄	C₂³	semidirect
80. C₂×C₇×C₄⋊C₄	C₂³	semidirect
81. C₂×C₇×C₄⋊C₄	C₂³	semidirect
82. C₂×C₇×C₄⋊C₄	C₂³	semidirect
83. C₂×C₇×C₄⋊C₄	C₂³	semidirect
89. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
90. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
91. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
92. C₂×C₄²×C₇	C₂³	semidirect
93. C₂×#538	C₂×C₇	direct (N × H)
94. C₂²×#126	C₂×C₇	semidirect
95. C₂²×#124	C₂×C₇	semidirect
96. C₂²×#123	C₂×C₇	semidirect
97. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
98. C₂²×#121	C₂×C₇	semidirect
99. C₂²×#121	C₂×C₇	semidirect
100. C₂²×#120	C₂×C₇	semidirect
101. C₂²×C₄×D₄	C₂×C₇	semidirect
102. C₂³×C₂²⋊C₄	C₂×C₇	semidirect
122. C₂×C₇×Q₈	C₂⁴	semidirect
130. C₂×C₇×D₄	C₂⁴	semidirect
148. C₂²×C₄×C₇	C₂⁴	semidirect
149. C₇×C₄⋊C₄	C₂⁴	semidirect
150. C₇×C₄⋊C₄	C₂⁴	semidirect
151. C₇×C₄⋊C₄	C₂⁴	semidirect
152. C₇×C₄⋊C₄	C₂⁴	semidirect
158. C₇×C₂²⋊C₄	C₂⁴	semidirect
159. C₇×C₂²⋊C₄	C₂⁴	semidirect
160. C₄²×C₇	C₂⁴	semidirect
162. C₂³×Q₈	C₂²×C₇	semidirect
166. C₂³×D₄	C₂²×C₇	semidirect
169. C₂⁴×C₄	C₂²×C₇	semidirect
170. #538	C₂²×C₇	direct (N × H)
171. C₂×#126	C₂²×C₇	semidirect
172. C₂×#124	C₂²×C₇	semidirect
173. C₂×#123	C₂²×C₇	semidirect
174. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
175. C₂×#121	C₂²×C₇	semidirect
176. C₂×#121	C₂²×C₇	semidirect
177. C₂×#120	C₂²×C₇	semidirect
178. C₂×C₄×D₄	C₂²×C₇	semidirect
179. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
180. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
181. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
182. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
188. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
189. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
190. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
191. C₂²×C₄²	C₂²×C₇	semidirect
243. C₂²×Q₈	C₂³×C₇	semidirect
251. C₂²×D₄	C₂³×C₇	semidirect
263. C₂³×C₄	C₂³×C₇	semidirect
264. #126	C₂³×C₇	semidirect
265. #124	C₂³×C₇	semidirect
266. #123	C₂³×C₇	semidirect
267. C₂²⋊Q₈	C₂³×C₇	semidirect
268. #121	C₂³×C₇	semidirect
269. #121	C₂³×C₇	semidirect
270. #120	C₂³×C₇	semidirect
271. C₄×D₄	C₂³×C₇	semidirect
272. C₂×C₄⋊C₄	C₂³×C₇	semidirect
273. C₂×C₄⋊C₄	C₂³×C₇	semidirect
274. C₂×C₄⋊C₄	C₂³×C₇	semidirect
275. C₂×C₄⋊C₄	C₂³×C₇	semidirect
281. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
282. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
283. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
284. C₂×C₄²	C₂³×C₇	semidirect
297. C₂²×C₇	#538	direct (N × H)
328. C₂×Q₈	C₂⁴×C₇	semidirect
336. C₂×D₄	C₂⁴×C₇	semidirect
354. C₂²×C₄	C₂⁴×C₇	semidirect
355. C₄⋊C₄	C₂⁴×C₇	semidirect
356. C₄⋊C₄	C₂⁴×C₇	semidirect
357. C₄⋊C₄	C₂⁴×C₇	semidirect
358. C₄⋊C₄	C₂⁴×C₇	semidirect
364. C₂²⋊C₄	C₂⁴×C₇	semidirect
365. C₂²⋊C₄	C₂⁴×C₇	semidirect
366. C₄²	C₂⁴×C₇	semidirect
370. C₂×C₇	C₂×#538	direct (N × H)
417. C₇	C₂²×#538	direct (N × H)
430. C₂²	C₇×#538	direct (N × H)
445. C₂	C₂×C₇×#538	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×#538	2
C₂²×C₇×#126	2
C₂²×C₇×#124	2
C₂²×C₇×#123	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#121	2
C₂²×C₇×#120	2
C₂²×C₄×C₇×D₄	2
C₂³×C₇×C₂²⋊C₄	2
C₂²×#538	7

Subgroups — C22×C7×#538 #13239887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#538 #13239887