Subgroups — C₂²×C₇×#539 #13239888

Order 1792.

8062 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#539	C₂	1	48	yes	maximal, direct product factor
2	C₂²×C₇×#126	C₂	1	2	yes	maximal, complemented
3	C₂²×C₇×#125	C₂	1	2	yes	maximal, complemented
4	C₂²×C₇×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₇×#123	C₂	1	2	yes	maximal, complemented
6	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×C₇×D₄	C₂	1	2	yes	maximal, complemented
10	C₂³×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
12	C₂³×C₇×D₄	C₂²	1	2	yes	—
13	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
18	C₇×#539	C₂²	1	256	yes	direct product factor
19	C₂×C₇×#126	C₂²	1	48	yes	complemented
20	C₂×C₇×#125	C₂²	1	48	yes	complemented
21	C₂×C₇×#123	C₂²	1	48	yes	complemented
22	C₂×C₇×#123	C₂²	1	48	yes	complemented
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	24	yes	complemented
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	48	yes	complemented
25	C₂×C₇×#121	C₂²	1	24	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	48	yes	complemented
27	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂²×C₇×C₄⋊C₄	C₂²	1	24	yes	complemented
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	2	yes	—
39	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
40	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
41	C₂²×C₄²×C₇	C₂²	1	2	yes	—
42	C₂²×#539	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂⁵×C₇	C₂³	1	2	yes	—
44	C₂⁵×C₇	C₂³	1	1	yes	characteristic
45	C₂²×C₇×Q₈	—	4	4	no	—
46	C₂²×C₇×Q₈	C₂³	1	12	yes	—
47	C₂²×C₇×D₄	—	2	16	no	—
48	C₂²×C₇×D₄	—	4	4	no	—
49	C₂²×C₇×D₄	C₂³	1	24	yes	—
50	C₂²×C₇×D₄	C₂³	1	12	yes	—
51	C₂³×C₄×C₇	—	2	8	no	—
52	C₂³×C₄×C₇	—	4	4	no	—
53	C₂³×C₄×C₇	—	4	8	no	—
54	C₂³×C₄×C₇	—	4	4	no	—
55	C₂³×C₄×C₇	C₂³	1	12	yes	—
56	C₂³×C₄×C₇	C₂³	1	2	yes	—
57	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₇	C₂³	1	2	yes	—
62	C₂³×C₄×C₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₇	C₂³	1	12	yes	—
64	C₂³×C₄×C₇	C₂³	1	12	yes	—
65	C₂³×C₄×C₇	C₂³	1	24	yes	—
66	C₇×#126	C₂³	1	128	yes	complemented
67	C₇×#125	C₂³	1	128	yes	complemented
68	C₇×#123	C₂³	1	128	yes	complemented
69	C₇×#123	C₂³	1	128	yes	complemented
70	C₇×C₂²⋊Q₈	C₂³	1	64	yes	complemented
71	C₇×C₂²⋊Q₈	C₂³	1	128	yes	complemented
72	C₇×#121	C₂³	1	64	yes	—
73	C₄×C₇×D₄	C₂³	1	128	yes	complemented
74	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
75	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
76	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
77	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
78	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
79	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
80	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
81	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
82	C₂×C₇×C₄⋊C₄	C₂³	1	64	yes	complemented
83	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
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×C₄²×C₇	C₂³	1	24	yes	—
89	C₂×#539	C₂×C₇	1	48	yes	direct product factor
90	C₂²×#126	C₂×C₇	1	2	yes	complemented
91	C₂²×#125	C₂×C₇	1	2	yes	complemented
92	C₂²×#123	C₂×C₇	1	2	yes	complemented
93	C₂²×#123	C₂×C₇	1	2	yes	complemented
94	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
95	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
96	C₂²×#121	C₂×C₇	1	1	yes	characteristic
97	C₂²×C₄×D₄	C₂×C₇	1	2	yes	complemented
98	C₂³×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
99	C₂⁴×C₇	—	2	4	no	—
100	C₂⁴×C₇	—	2	4	no	—
101	C₂⁴×C₇	—	2	8	no	—
102	C₂⁴×C₇	—	2	8	no	—
103	C₂⁴×C₇	—	2	8	no	—
104	C₂⁴×C₇	#41	1	8	yes	—
105	C₂⁴×C₇	C₂⁴	1	12	yes	—
106	C₂⁴×C₇	C₂⁴	1	6	yes	—
107	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₇×Q₈	—	4	24	no	—
109	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
110	C₂×C₇×D₄	—	2	96	no	—
111	C₂×C₇×D₄	—	4	24	no	—
112	C₂×C₇×D₄	C₂⁴	1	32	yes	—
113	C₂×C₇×D₄	C₂⁴	1	16	yes	—
114	C₂²×C₄×C₇	—	2	48	no	—
115	C₂²×C₄×C₇	—	2	8	no	—
116	C₂²×C₄×C₇	—	2	8	no	—
117	C₂²×C₄×C₇	—	2	8	no	—
118	C₂²×C₄×C₇	—	2	4	no	—
119	C₂²×C₄×C₇	—	2	8	no	—
120	C₂²×C₄×C₇	—	2	4	no	—
121	C₂²×C₄×C₇	—	2	8	no	—
122	C₂²×C₄×C₇	—	4	24	no	—
123	C₂²×C₄×C₇	—	4	48	no	—
124	C₂²×C₄×C₇	—	4	24	no	—
125	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
126	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
127	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
131	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
136	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
137	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
138	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
139	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
140	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
141	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
142	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
143	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
144	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
145	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
146	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
147	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
148	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
149	C₄²×C₇	C₂⁴	1	32	yes	—
150	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
151	C₂³×D₄	C₂²×C₇	1	2	yes	—
152	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
153	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
154	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
155	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
156	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
157	#539	C₂²×C₇	1	256	yes	direct product factor
158	C₂×#126	C₂²×C₇	1	48	yes	complemented
159	C₂×#125	C₂²×C₇	1	48	yes	complemented
160	C₂×#123	C₂²×C₇	1	48	yes	complemented
161	C₂×#123	C₂²×C₇	1	48	yes	complemented
162	C₂×C₂²⋊Q₈	C₂²×C₇	1	24	yes	complemented
163	C₂×C₂²⋊Q₈	C₂²×C₇	1	48	yes	complemented
164	C₂×#121	C₂²×C₇	1	24	yes	—
165	C₂×C₄×D₄	C₂²×C₇	1	48	yes	complemented
166	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
167	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
168	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
169	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
170	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
171	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
172	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
173	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
174	C₂²×C₄⋊C₄	C₂²×C₇	1	24	yes	complemented
175	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
176	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
177	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
178	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
179	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
180	C₂²×C₄²	C₂²×C₇	1	2	yes	—
181	C₂³×C₇	—	2	32	no	—
182	C₂³×C₇	—	2	12	no	—
183	C₂³×C₇	—	2	12	no	—
184	C₂³×C₇	—	2	24	no	—
185	C₂³×C₇	—	2	24	no	—
186	C₂³×C₇	—	2	24	no	—
187	C₂³×C₇	—	4	32	no	—
188	C₂³×C₇	C₂×#41	1	24	yes	—
189	C₂³×C₇	C₂×#41	1	4	yes	—
190	C₂³×C₇	H(5,𝔽₂)	1	4	yes	—
191	C₂³×C₇	2₋¹⁺⁴	1	4	yes	—
192	C₂³×C₇	C₂⁵	1	8	yes	—
193	C₂³×C₇	C₂⁵	1	4	yes	—
194	C₂³×C₇	C₂⁵	1	3	yes	—
195	C₇×Q₈	—	4	16	no	—
196	C₇×D₄	—	2	64	no	—
197	C₇×D₄	—	4	16	no	—
198	C₂×C₄×C₇	—	2	32	no	—
199	C₂×C₄×C₇	—	2	24	no	—
200	C₂×C₄×C₇	—	2	24	no	—
201	C₂×C₄×C₇	—	2	24	no	—
202	C₂×C₄×C₇	—	2	12	no	—
203	C₂×C₄×C₇	—	2	24	no	—
204	C₂×C₄×C₇	—	2	12	no	—
205	C₂×C₄×C₇	—	2	24	no	—
206	C₂×C₄×C₇	—	4	16	no	—
207	C₂×C₄×C₇	—	4	32	no	—
208	C₂×C₄×C₇	—	4	16	no	—
209	C₂×C₄×C₇	C₂⁵	1	8	yes	—
210	C₂×C₄×C₇	C₂⁵	1	8	yes	—
211	C₂×C₄×C₇	C₂⁵	1	8	yes	—
212	C₂×C₄×C₇	C₂⁵	1	8	yes	—
213	C₂×C₄×C₇	C₂⁵	1	8	yes	—
214	C₂×C₄×C₇	C₂⁵	1	4	yes	—
215	C₂×C₄×C₇	C₂⁵	1	4	yes	—
216	C₂⁵	C₂³×C₇	1	2	yes	—
217	C₂⁵	C₂³×C₇	1	1	yes	characteristic
218	C₂²×Q₈	—	4	4	no	—
219	C₂²×Q₈	C₂³×C₇	1	12	yes	—
220	C₂²×D₄	—	2	16	no	—
221	C₂²×D₄	—	4	4	no	—
222	C₂²×D₄	C₂³×C₇	1	24	yes	—
223	C₂²×D₄	C₂³×C₇	1	12	yes	—
224	C₂³×C₄	—	2	8	no	—
225	C₂³×C₄	—	4	4	no	—
226	C₂³×C₄	—	4	8	no	—
227	C₂³×C₄	—	4	4	no	—
228	C₂³×C₄	C₂³×C₇	1	2	yes	—
229	C₂³×C₄	C₂³×C₇	1	2	yes	—
230	C₂³×C₄	C₂³×C₇	1	2	yes	—
231	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₇	1	2	yes	—
233	C₂³×C₄	C₂³×C₇	1	2	yes	—
234	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
235	C₂³×C₄	C₂³×C₇	1	12	yes	—
236	C₂³×C₄	C₂³×C₇	1	12	yes	—
237	C₂³×C₄	C₂³×C₇	1	12	yes	—
238	C₂³×C₄	C₂³×C₇	1	24	yes	—
239	#126	C₂³×C₇	1	128	yes	complemented
240	#125	C₂³×C₇	1	128	yes	complemented
241	#123	C₂³×C₇	1	128	yes	complemented
242	#123	C₂³×C₇	1	128	yes	complemented
243	C₂²⋊Q₈	C₂³×C₇	1	64	yes	complemented
244	C₂²⋊Q₈	C₂³×C₇	1	128	yes	complemented
245	#121	C₂³×C₇	1	64	yes	—
246	C₄×D₄	C₂³×C₇	1	128	yes	complemented
247	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
248	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
249	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
250	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
251	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
252	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
253	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
254	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
255	C₂×C₄⋊C₄	C₂³×C₇	1	64	yes	complemented
256	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
257	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
258	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
259	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
260	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
261	C₂×C₄²	C₂³×C₇	1	24	yes	—
262	C₂²×C₇	—	2	4	no	—
263	C₂²×C₇	—	2	4	no	—
264	C₂²×C₇	—	2	48	no	—
265	C₂²×C₇	—	2	8	no	—
266	C₂²×C₇	—	2	8	no	—
267	C₂²×C₇	—	2	8	no	—
268	C₂²×C₇	—	4	48	no	—
269	C₂²×C₇	#539	1	16	yes	direct product factor
270	C₂²×C₇	C₂²×#41	1	8	yes	—
271	C₂²×C₇	C₂²×#41	1	6	yes	—
272	C₂²×C₇	C₂×H(5,𝔽₂)	1	6	yes	—
273	C₂²×C₇	C₂×2₋¹⁺⁴	1	6	yes	—
274	C₂²×C₇	C₂⁶	1	1	yes	characteristic
275	C₄×C₇	—	2	8	no	—
276	C₄×C₇	—	2	8	no	—
277	C₄×C₇	—	2	8	no	—
278	C₄×C₇	—	2	4	no	—
279	C₄×C₇	—	2	8	no	—
280	C₄×C₇	—	2	4	no	—
281	C₄×C₇	—	2	8	no	—
282	C₂⁴	—	2	4	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	8	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	8	no	—
287	C₂⁴	C₇×#41	1	8	yes	—
288	C₂⁴	C₂⁴×C₇	1	12	yes	—
289	C₂⁴	C₂⁴×C₇	1	6	yes	—
290	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
291	C₂×Q₈	—	4	24	no	—
292	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
293	C₂×D₄	—	2	96	no	—
294	C₂×D₄	—	4	24	no	—
295	C₂×D₄	C₂⁴×C₇	1	32	yes	—
296	C₂×D₄	C₂⁴×C₇	1	16	yes	—
297	C₂²×C₄	—	2	48	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	4	24	no	—
306	C₂²×C₄	—	4	48	no	—
307	C₂²×C₄	—	4	24	no	—
308	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
309	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
310	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
311	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
312	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
313	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
314	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
315	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
316	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
317	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
318	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
319	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
320	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
321	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
322	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
323	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
324	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
325	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
326	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
327	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
328	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
329	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
330	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
331	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
332	C₄²	C₂⁴×C₇	1	32	yes	—
333	C₂×C₇	—	2	8	no	—
334	C₂×C₇	—	4	8	no	—
335	C₂×C₇	C₂×#539	1	12	yes	direct product factor
336	C₂×C₇	C₂³×#41	1	1	yes	characteristic
337	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂³	—	2	12	no	—
340	C₂³	—	2	12	no	—
341	C₂³	—	2	32	no	—
342	C₂³	—	2	24	no	—
343	C₂³	—	2	24	no	—
344	C₂³	—	2	24	no	—
345	C₂³	—	4	32	no	—
346	C₂³	C₂×C₇×#41	1	24	yes	—
347	C₂³	C₂×C₇×#41	1	4	yes	—
348	C₂³	C₇×H(5,𝔽₂)	1	4	yes	—
349	C₂³	C₇×2₋¹⁺⁴	1	4	yes	—
350	C₂³	C₂⁵×C₇	1	8	yes	—
351	C₂³	C₂⁵×C₇	1	4	yes	—
352	C₂³	C₂⁵×C₇	1	3	yes	—
353	Q₈	—	4	16	no	—
354	D₄	—	2	64	no	—
355	D₄	—	4	16	no	—
356	C₂×C₄	—	2	32	no	—
357	C₂×C₄	—	2	24	no	—
358	C₂×C₄	—	2	24	no	—
359	C₂×C₄	—	2	24	no	—
360	C₂×C₄	—	2	12	no	—
361	C₂×C₄	—	2	24	no	—
362	C₂×C₄	—	2	12	no	—
363	C₂×C₄	—	2	24	no	—
364	C₂×C₄	—	4	16	no	—
365	C₂×C₄	—	4	32	no	—
366	C₂×C₄	—	4	16	no	—
367	C₂×C₄	C₂⁵×C₇	1	8	yes	—
368	C₂×C₄	C₂⁵×C₇	1	8	yes	—
369	C₂×C₄	C₂⁵×C₇	1	8	yes	—
370	C₂×C₄	C₂⁵×C₇	1	8	yes	—
371	C₂×C₄	C₂⁵×C₇	1	8	yes	—
372	C₂×C₄	C₂⁵×C₇	1	4	yes	—
373	C₂×C₄	C₂⁵×C₇	1	4	yes	—
374	C₇	C₂²×#539	1	1	yes	characteristic, direct product factor, Sylow
375	C₂²	—	2	4	no	—
376	C₂²	—	2	4	no	—
377	C₂²	—	2	48	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	2	8	no	—
380	C₂²	—	2	8	no	—
381	C₂²	—	4	48	no	—
382	C₂²	C₇×#539	1	16	yes	direct product factor
383	C₂²	C₂²×C₇×#41	1	8	yes	—
384	C₂²	C₂²×C₇×#41	1	6	yes	—
385	C₂²	C₂×C₇×H(5,𝔽₂)	1	6	yes	—
386	C₂²	C₂×C₇×2₋¹⁺⁴	1	6	yes	—
387	C₂²	C₂⁶×C₇	1	1	yes	characteristic
388	C₄	—	2	8	no	—
389	C₄	—	2	8	no	—
390	C₄	—	2	8	no	—
391	C₄	—	2	4	no	—
392	C₄	—	2	8	no	—
393	C₄	—	2	4	no	—
394	C₄	—	2	8	no	—
395	C₂	—	2	8	no	—
396	C₂	—	4	8	no	—
397	C₂	C₂×C₇×#539	1	12	yes	direct product factor
398	C₂	C₂³×C₇×#41	1	1	yes	characteristic
399	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
prime radical	C₂²×C₇×#121	C₂
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×#539	C₂	direct (N × H)
2. C₂²×C₇×#126	C₂	semidirect
3. C₂²×C₇×#125	C₂	semidirect
4. C₂²×C₇×#123	C₂	semidirect
5. C₂²×C₇×#123	C₂	semidirect
6. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
7. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
9. C₂²×C₄×C₇×D₄	C₂	semidirect
10. C₂³×C₇×C₄⋊C₄	C₂	semidirect
18. C₇×#539	C₂²	direct (N × H)
19. C₂×C₇×#126	C₂²	semidirect
20. C₂×C₇×#125	C₂²	semidirect
21. C₂×C₇×#123	C₂²	semidirect
22. C₂×C₇×#123	C₂²	semidirect
23. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
24. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
26. C₂×C₄×C₇×D₄	C₂²	semidirect
35. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
42. C₂²×#539	C₇	direct (N × H)
66. C₇×#126	C₂³	semidirect
67. C₇×#125	C₂³	semidirect
68. C₇×#123	C₂³	semidirect
69. C₇×#123	C₂³	semidirect
70. C₇×C₂²⋊Q₈	C₂³	semidirect
71. C₇×C₂²⋊Q₈	C₂³	semidirect
73. C₄×C₇×D₄	C₂³	semidirect
82. C₂×C₇×C₄⋊C₄	C₂³	semidirect
89. C₂×#539	C₂×C₇	direct (N × H)
90. C₂²×#126	C₂×C₇	semidirect
91. C₂²×#125	C₂×C₇	semidirect
92. C₂²×#123	C₂×C₇	semidirect
93. C₂²×#123	C₂×C₇	semidirect
94. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
95. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
97. C₂²×C₄×D₄	C₂×C₇	semidirect
98. C₂³×C₄⋊C₄	C₂×C₇	semidirect
157. #539	C₂²×C₇	direct (N × H)
158. C₂×#126	C₂²×C₇	semidirect
159. C₂×#125	C₂²×C₇	semidirect
160. C₂×#123	C₂²×C₇	semidirect
161. C₂×#123	C₂²×C₇	semidirect
162. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
163. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
165. C₂×C₄×D₄	C₂²×C₇	semidirect
174. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
239. #126	C₂³×C₇	semidirect
240. #125	C₂³×C₇	semidirect
241. #123	C₂³×C₇	semidirect
242. #123	C₂³×C₇	semidirect
243. C₂²⋊Q₈	C₂³×C₇	semidirect
244. C₂²⋊Q₈	C₂³×C₇	semidirect
246. C₄×D₄	C₂³×C₇	semidirect
255. C₂×C₄⋊C₄	C₂³×C₇	semidirect
269. C₂²×C₇	#539	direct (N × H)
335. C₂×C₇	C₂×#539	direct (N × H)
374. C₇	C₂²×#539	direct (N × H)
382. C₂²	C₇×#539	direct (N × H)
397. C₂	C₂×C₇×#539	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×#539	2
C₂²×C₇×#126	2
C₂²×C₇×#125	2
C₂²×C₇×#123	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#121	2
C₂²×C₄×C₇×D₄	2
C₂³×C₇×C₄⋊C₄	2
C₂²×#539	7

Subgroups — C22×C7×#539 #13239888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#539 #13239888