Subgroups — C₂×C₇×#3568 #13239952

Order 1792.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3568	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₇×#563	C₂	1	3	yes	maximal, complemented
3	C₂×C₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#556	C₂	1	6	yes	maximal, complemented
5	C₂×C₇×#551	C₂	1	6	yes	maximal, complemented
6	C₂×C₇×#542	C₂	1	6	yes	maximal, complemented
7	C₂×C₇×#538	C₂	1	6	yes	maximal, complemented
8	C₂×C₇×#529	C₂	1	3	yes	maximal, complemented
9	C₇×#563	C₂²	1	48	yes	complemented
10	C₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
11	C₇×#556	C₂²	1	96	yes	complemented
12	C₇×#551	C₂²	1	96	yes	complemented
13	C₇×#542	C₂²	1	96	yes	complemented
14	C₇×#538	C₂²	1	96	yes	complemented
15	C₂×C₇×C₄⋊Q₈	C₂²	1	6	yes	complemented
16	C₇×#529	C₂²	1	48	yes	complemented
17	C₂×C₇×#126	C₂²	1	6	yes	complemented
18	C₂×C₇×#126	C₂²	1	6	yes	complemented
19	C₂×C₇×#126	C₂²	1	6	yes	complemented
20	C₂×C₇×#126	C₂²	1	2	yes	complemented
21	C₂×C₇×#126	C₂²	1	6	yes	complemented
22	C₂×C₇×#125	C₂²	1	3	yes	complemented
23	C₂×C₇×#124	C₂²	1	3	yes	—
24	C₂×C₇×#124	C₂²	1	6	yes	—
25	C₂×C₇×#124	C₂²	1	6	yes	—
26	C₂×C₇×#124	C₂²	1	6	yes	complemented
27	C₂×C₇×#123	C₂²	1	6	yes	—
28	C₂×C₇×#123	C₂²	1	6	yes	—
29	C₂×C₇×#123	C₂²	1	6	yes	complemented
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	3	yes	complemented
31	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
32	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
34	C₂×C₇×#121	C₂²	1	3	yes	—
35	C₂×C₇×#121	C₂²	1	6	yes	—
36	C₂×C₇×#120	C₂²	1	6	yes	—
37	C₂×C₇×#120	C₂²	1	2	yes	complemented
38	C₂×C₄×C₇×Q₈	C₂²	1	3	yes	complemented
39	C₂×C₄×C₇×Q₈	C₂²	1	6	yes	complemented
40	C₂×C₄×C₇×D₄	C₂²	1	3	yes	—
41	C₂×C₄×C₇×D₄	C₂²	1	6	yes	—
42	C₂×C₄×C₇×D₄	C₂²	1	6	yes	complemented
43	C₂×C₇×#117	C₂²	1	6	yes	complemented
44	C₂×C₇×#117	C₂²	1	6	yes	complemented
45	C₂²×C₇×C₂²⋊C₄	C₂²	1	6	yes	complemented
46	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic, complemented
47	C₂×#3568	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂⁵×C₇	C₂³	1	2	yes	—
49	C₂²×C₇×Q₈	C₂³	1	6	yes	—
50	C₂²×C₇×Q₈	C₂³	1	3	yes	—
51	C₂²×C₇×D₄	C₂³	1	3	yes	—
52	C₂²×C₇×D₄	C₂³	1	6	yes	—
53	C₂²×C₇×D₄	C₂³	1	6	yes	—
54	C₂³×C₄×C₇	C₂³	1	3	yes	—
55	C₂³×C₄×C₇	C₂³	1	6	yes	—
56	C₂³×C₄×C₇	C₂³	1	6	yes	—
57	C₇×C₄⋊Q₈	C₂³	1	48	yes	complemented
58	C₇×#126	C₂³	1	48	yes	complemented
59	C₇×#126	C₂³	1	48	yes	complemented
60	C₇×#126	C₂³	1	48	yes	complemented
61	C₇×#126	C₂³	1	16	yes	complemented
62	C₇×#126	C₂³	1	48	yes	complemented
63	C₇×#125	C₂³	1	24	yes	complemented
64	C₇×#124	C₂³	1	24	yes	—
65	C₇×#124	C₂³	1	48	yes	—
66	C₇×#124	C₂³	1	48	yes	—
67	C₇×#124	C₂³	1	48	yes	complemented
68	C₇×#123	C₂³	1	48	yes	—
69	C₇×#123	C₂³	1	48	yes	—
70	C₇×#123	C₂³	1	48	yes	complemented
71	C₇×C₂²⋊Q₈	C₂³	1	24	yes	complemented
72	C₇×C₂²⋊Q₈	C₂³	1	48	yes	complemented
73	C₇×C₂²⋊Q₈	C₂³	1	48	yes	complemented
74	C₇×C₂²⋊Q₈	C₂³	1	48	yes	complemented
75	C₇×#121	C₂³	1	24	yes	—
76	C₇×#121	C₂³	1	48	yes	—
77	C₇×#120	C₂³	1	48	yes	—
78	C₇×#120	C₂³	1	16	yes	complemented
79	C₄×C₇×Q₈	C₂³	1	24	yes	complemented
80	C₄×C₇×Q₈	C₂³	1	48	yes	complemented
81	C₄×C₇×D₄	C₂³	1	24	yes	—
82	C₄×C₇×D₄	C₂³	1	48	yes	—
83	C₄×C₇×D₄	C₂³	1	48	yes	complemented
84	C₇×#117	C₂³	1	48	yes	complemented
85	C₇×#117	C₂³	1	48	yes	complemented
86	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
87	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
88	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
89	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
90	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
91	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
92	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
93	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
94	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
95	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
96	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
97	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
98	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
99	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
100	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
103	C₂×C₇×C₂²⋊C₄	C₂³	1	48	yes	complemented
104	C₂×C₄²×C₇	C₂³	1	3	yes	—
105	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₇	C₂³	1	6	yes	—
107	C₂×C₄²×C₇	C₂³	1	6	yes	—
108	C₂×C₄²×C₇	C₂³	1	2	yes	—
109	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
110	#3568	C₂×C₇	1	32	yes	direct product factor
111	C₂×#563	C₂×C₇	1	3	yes	complemented
112	C₂×H(3,𝔽₄)	C₂×C₇	1	1	yes	characteristic, complemented
113	C₂×#556	C₂×C₇	1	6	yes	complemented
114	C₂×#551	C₂×C₇	1	6	yes	complemented
115	C₂×#542	C₂×C₇	1	6	yes	complemented
116	C₂×#538	C₂×C₇	1	6	yes	complemented
117	C₂×#529	C₂×C₇	1	3	yes	complemented
118	C₂⁴×C₇	—	4	12	no	—
119	C₂⁴×C₇	C₂⁴	1	6	yes	—
120	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
121	C₂⁴×C₇	C₂⁴	1	8	yes	—
122	C₂×C₇×Q₈	—	4	12	no	—
123	C₂×C₇×Q₈	—	4	6	no	—
124	C₂×C₇×Q₈	C₂⁴	1	24	yes	—
125	C₂×C₇×Q₈	C₂⁴	1	12	yes	—
126	C₂×C₇×D₄	—	4	12	no	—
127	C₂×C₇×D₄	—	4	6	no	—
128	C₂×C₇×D₄	—	4	12	no	—
129	C₂×C₇×D₄	C₂⁴	1	12	yes	—
130	C₂×C₇×D₄	C₂⁴	1	24	yes	—
131	C₂×C₇×D₄	C₂⁴	1	24	yes	—
132	C₂²×C₄×C₇	—	4	12	no	—
133	C₂²×C₄×C₇	—	4	6	no	—
134	C₂²×C₄×C₇	—	4	12	no	—
135	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
137	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
138	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
139	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
140	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
141	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
142	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
143	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
144	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
145	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
146	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
147	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
148	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
149	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
150	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
151	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
152	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
153	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
154	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
155	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
156	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
157	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
158	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
159	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
160	C₄²×C₇	C₂⁴	1	12	yes	—
161	C₄²×C₇	C₂⁴	1	4	yes	—
162	C₄²×C₇	C₂⁴	1	24	yes	—
163	C₄²×C₇	C₂⁴	1	24	yes	—
164	C₄²×C₇	C₂⁴	1	8	yes	—
165	#563	C₂²×C₇	1	48	yes	complemented
166	H(3,𝔽₄)	C₂²×C₇	1	16	yes	complemented
167	#556	C₂²×C₇	1	96	yes	complemented
168	#551	C₂²×C₇	1	96	yes	complemented
169	#542	C₂²×C₇	1	96	yes	complemented
170	#538	C₂²×C₇	1	96	yes	complemented
171	C₂×C₄⋊Q₈	C₂²×C₇	1	6	yes	complemented
172	#529	C₂²×C₇	1	48	yes	complemented
173	C₂×#126	C₂²×C₇	1	6	yes	complemented
174	C₂×#126	C₂²×C₇	1	6	yes	complemented
175	C₂×#126	C₂²×C₇	1	6	yes	complemented
176	C₂×#126	C₂²×C₇	1	2	yes	complemented
177	C₂×#126	C₂²×C₇	1	6	yes	complemented
178	C₂×#125	C₂²×C₇	1	3	yes	complemented
179	C₂×#124	C₂²×C₇	1	3	yes	—
180	C₂×#124	C₂²×C₇	1	6	yes	—
181	C₂×#124	C₂²×C₇	1	6	yes	—
182	C₂×#124	C₂²×C₇	1	6	yes	complemented
183	C₂×#123	C₂²×C₇	1	6	yes	—
184	C₂×#123	C₂²×C₇	1	6	yes	—
185	C₂×#123	C₂²×C₇	1	6	yes	complemented
186	C₂×C₂²⋊Q₈	C₂²×C₇	1	3	yes	complemented
187	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	complemented
188	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	complemented
189	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	complemented
190	C₂×#121	C₂²×C₇	1	3	yes	—
191	C₂×#121	C₂²×C₇	1	6	yes	—
192	C₂×#120	C₂²×C₇	1	6	yes	—
193	C₂×#120	C₂²×C₇	1	2	yes	complemented
194	C₂×C₄×Q₈	C₂²×C₇	1	3	yes	complemented
195	C₂×C₄×Q₈	C₂²×C₇	1	6	yes	complemented
196	C₂×C₄×D₄	C₂²×C₇	1	3	yes	—
197	C₂×C₄×D₄	C₂²×C₇	1	6	yes	—
198	C₂×C₄×D₄	C₂²×C₇	1	6	yes	complemented
199	C₂×#117	C₂²×C₇	1	6	yes	complemented
200	C₂×#117	C₂²×C₇	1	6	yes	complemented
201	C₂²×C₂²⋊C₄	C₂²×C₇	1	6	yes	complemented
202	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic, complemented
203	C₂³×C₇	—	2	6	no	—
204	C₂³×C₇	—	2	12	no	—
205	C₂³×C₇	—	2	12	no	—
206	C₂³×C₇	—	2	12	no	—
207	C₂³×C₇	—	4	24	no	—
208	C₂³×C₇	—	8	16	no	—
209	C₂³×C₇	C₂⁵	1	12	yes	—
210	C₂³×C₇	C₂⁵	1	2	yes	—
211	C₂³×C₇	C₂⁵	1	1	yes	characteristic
212	C₇×Q₈	—	4	24	no	—
213	C₇×Q₈	—	4	12	no	—
214	C₇×D₄	—	4	24	no	—
215	C₇×D₄	—	4	12	no	—
216	C₇×D₄	—	4	24	no	—
217	C₂×C₄×C₇	—	2	6	no	—
218	C₂×C₄×C₇	—	2	12	no	—
219	C₂×C₄×C₇	—	2	6	no	—
220	C₂×C₄×C₇	—	2	12	no	—
221	C₂×C₄×C₇	—	2	12	no	—
222	C₂×C₄×C₇	—	4	24	no	—
223	C₂×C₄×C₇	—	4	12	no	—
224	C₂×C₄×C₇	—	4	24	no	—
225	C₂×C₄×C₇	C₂⁵	1	6	yes	—
226	C₂×C₄×C₇	C₂⁵	1	12	yes	—
227	C₂×C₄×C₇	C₂⁵	1	6	yes	—
228	C₂×C₄×C₇	C₂⁵	1	12	yes	—
229	C₂×C₄×C₇	C₂⁵	1	12	yes	—
230	C₂⁵	C₂³×C₇	1	2	yes	—
231	C₂²×Q₈	C₂³×C₇	1	6	yes	—
232	C₂²×Q₈	C₂³×C₇	1	3	yes	—
233	C₂²×D₄	C₂³×C₇	1	3	yes	—
234	C₂²×D₄	C₂³×C₇	1	6	yes	—
235	C₂²×D₄	C₂³×C₇	1	6	yes	—
236	C₂³×C₄	C₂³×C₇	1	6	yes	—
237	C₂³×C₄	C₂³×C₇	1	6	yes	—
238	C₂³×C₄	C₂³×C₇	1	3	yes	—
239	C₄⋊Q₈	C₂³×C₇	1	48	yes	complemented
240	#126	C₂³×C₇	1	48	yes	complemented
241	#126	C₂³×C₇	1	48	yes	complemented
242	#126	C₂³×C₇	1	48	yes	complemented
243	#126	C₂³×C₇	1	16	yes	complemented
244	#126	C₂³×C₇	1	48	yes	complemented
245	#125	C₂³×C₇	1	24	yes	complemented
246	#124	C₂³×C₇	1	24	yes	—
247	#124	C₂³×C₇	1	48	yes	—
248	#124	C₂³×C₇	1	48	yes	—
249	#124	C₂³×C₇	1	48	yes	complemented
250	#123	C₂³×C₇	1	48	yes	—
251	#123	C₂³×C₇	1	48	yes	—
252	#123	C₂³×C₇	1	48	yes	complemented
253	C₂²⋊Q₈	C₂³×C₇	1	24	yes	complemented
254	C₂²⋊Q₈	C₂³×C₇	1	48	yes	complemented
255	C₂²⋊Q₈	C₂³×C₇	1	48	yes	complemented
256	C₂²⋊Q₈	C₂³×C₇	1	48	yes	complemented
257	#121	C₂³×C₇	1	24	yes	—
258	#121	C₂³×C₇	1	48	yes	—
259	#120	C₂³×C₇	1	48	yes	—
260	#120	C₂³×C₇	1	16	yes	complemented
261	C₄×Q₈	C₂³×C₇	1	24	yes	complemented
262	C₄×Q₈	C₂³×C₇	1	48	yes	complemented
263	C₄×D₄	C₂³×C₇	1	24	yes	—
264	C₄×D₄	C₂³×C₇	1	48	yes	—
265	C₄×D₄	C₂³×C₇	1	48	yes	complemented
266	#117	C₂³×C₇	1	48	yes	complemented
267	#117	C₂³×C₇	1	48	yes	complemented
268	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
269	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
273	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
274	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
275	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₇	1	48	yes	complemented
286	C₂×C₄²	C₂³×C₇	1	3	yes	—
287	C₂×C₄²	C₂³×C₇	1	6	yes	—
288	C₂×C₄²	C₂³×C₇	1	6	yes	—
289	C₂×C₄²	C₂³×C₇	1	2	yes	—
290	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
292	C₂²×C₇	—	2	6	no	—
293	C₂²×C₇	—	2	12	no	—
294	C₂²×C₇	—	2	12	no	—
295	C₂²×C₇	—	2	12	no	—
296	C₂²×C₇	—	4	4	no	—
297	C₂²×C₇	—	4	24	no	—
298	C₂²×C₇	—	8	16	no	—
299	C₂²×C₇	#585	1	6	yes	—
300	C₂²×C₇	C₂⁶	1	1	yes	characteristic
301	C₄×C₇	—	2	6	no	—
302	C₄×C₇	—	2	12	no	—
303	C₄×C₇	—	2	6	no	—
304	C₄×C₇	—	2	12	no	—
305	C₄×C₇	—	2	12	no	—
306	C₂⁴	—	4	12	no	—
307	C₂⁴	C₂⁴×C₇	1	6	yes	—
308	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
309	C₂⁴	C₂⁴×C₇	1	8	yes	—
310	C₂×Q₈	—	4	12	no	—
311	C₂×Q₈	—	4	6	no	—
312	C₂×Q₈	C₂⁴×C₇	1	24	yes	—
313	C₂×Q₈	C₂⁴×C₇	1	12	yes	—
314	C₂×D₄	—	4	12	no	—
315	C₂×D₄	—	4	6	no	—
316	C₂×D₄	—	4	12	no	—
317	C₂×D₄	C₂⁴×C₇	1	12	yes	—
318	C₂×D₄	C₂⁴×C₇	1	24	yes	—
319	C₂×D₄	C₂⁴×C₇	1	24	yes	—
320	C₂²×C₄	—	4	12	no	—
321	C₂²×C₄	—	4	6	no	—
322	C₂²×C₄	—	4	12	no	—
323	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
324	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
325	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
326	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
327	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
328	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
329	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
330	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
331	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
332	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
333	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
334	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
335	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
336	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
337	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
338	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
339	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
340	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
341	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
342	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
343	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
344	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
345	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
346	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
347	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
348	C₄²	C₂⁴×C₇	1	12	yes	—
349	C₄²	C₂⁴×C₇	1	4	yes	—
350	C₄²	C₂⁴×C₇	1	24	yes	—
351	C₄²	C₂⁴×C₇	1	24	yes	—
352	C₄²	C₂⁴×C₇	1	8	yes	—
353	C₂×C₇	—	4	2	no	—
354	C₂×C₇	—	4	12	no	—
355	C₂×C₇	#3568	1	4	yes	direct product factor
356	C₂×C₇	C₂×#585	1	3	yes	—
357	C₂³	—	2	6	no	—
358	C₂³	—	2	12	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	4	24	no	—
362	C₂³	—	8	16	no	—
363	C₂³	C₂⁵×C₇	1	12	yes	—
364	C₂³	C₂⁵×C₇	1	2	yes	—
365	C₂³	C₂⁵×C₇	1	1	yes	characteristic
366	Q₈	—	4	24	no	—
367	Q₈	—	4	12	no	—
368	D₄	—	4	24	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	24	no	—
371	C₂×C₄	—	2	6	no	—
372	C₂×C₄	—	2	12	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	2	12	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	4	24	no	—
377	C₂×C₄	—	4	12	no	—
378	C₂×C₄	—	4	24	no	—
379	C₂×C₄	C₂⁵×C₇	1	6	yes	—
380	C₂×C₄	C₂⁵×C₇	1	12	yes	—
381	C₂×C₄	C₂⁵×C₇	1	6	yes	—
382	C₂×C₄	C₂⁵×C₇	1	12	yes	—
383	C₂×C₄	C₂⁵×C₇	1	12	yes	—
384	C₇	C₂×#3568	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²	—	2	6	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	2	12	no	—
389	C₂²	—	4	24	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	16	no	—
392	C₂²	C₇×#585	1	6	yes	—
393	C₂²	C₂⁶×C₇	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	2	6	no	—
397	C₄	—	2	12	no	—
398	C₄	—	2	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	4	2	no	—
401	C₂	C₇×#3568	1	4	yes	direct product factor
402	C₂	C₂×C₇×#585	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3568	C₂	direct (N × H)
2. C₂×C₇×#563	C₂	semidirect
3. C₂×C₇×H(3,𝔽₄)	C₂	semidirect
4. C₂×C₇×#556	C₂	semidirect
5. C₂×C₇×#551	C₂	semidirect
6. C₂×C₇×#542	C₂	semidirect
7. C₂×C₇×#538	C₂	semidirect
8. C₂×C₇×#529	C₂	semidirect
9. C₇×#563	C₂²	semidirect
10. C₇×H(3,𝔽₄)	C₂²	semidirect
11. C₇×#556	C₂²	semidirect
12. C₇×#551	C₂²	semidirect
13. C₇×#542	C₂²	semidirect
14. C₇×#538	C₂²	semidirect
15. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
16. C₇×#529	C₂²	semidirect
17. C₂×C₇×#126	C₂²	semidirect
18. C₂×C₇×#126	C₂²	semidirect
19. C₂×C₇×#126	C₂²	semidirect
20. C₂×C₇×#126	C₂²	semidirect
21. C₂×C₇×#126	C₂²	semidirect
22. C₂×C₇×#125	C₂²	semidirect
26. C₂×C₇×#124	C₂²	semidirect
29. C₂×C₇×#123	C₂²	semidirect
30. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
32. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
33. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₇×#120	C₂²	semidirect
38. C₂×C₄×C₇×Q₈	C₂²	semidirect
39. C₂×C₄×C₇×Q₈	C₂²	semidirect
42. C₂×C₄×C₇×D₄	C₂²	semidirect
43. C₂×C₇×#117	C₂²	semidirect
44. C₂×C₇×#117	C₂²	semidirect
45. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
46. C₂²×C₄²×C₇	C₂²	semidirect
47. C₂×#3568	C₇	direct (N × H)
57. C₇×C₄⋊Q₈	C₂³	semidirect
58. C₇×#126	C₂³	semidirect
59. C₇×#126	C₂³	semidirect
60. C₇×#126	C₂³	semidirect
61. C₇×#126	C₂³	semidirect
62. C₇×#126	C₂³	semidirect
63. C₇×#125	C₂³	semidirect
67. C₇×#124	C₂³	semidirect
70. C₇×#123	C₂³	semidirect
71. C₇×C₂²⋊Q₈	C₂³	semidirect
72. C₇×C₂²⋊Q₈	C₂³	semidirect
73. C₇×C₂²⋊Q₈	C₂³	semidirect
74. C₇×C₂²⋊Q₈	C₂³	semidirect
78. C₇×#120	C₂³	semidirect
79. C₄×C₇×Q₈	C₂³	semidirect
80. C₄×C₇×Q₈	C₂³	semidirect
83. C₄×C₇×D₄	C₂³	semidirect
84. C₇×#117	C₂³	semidirect
85. C₇×#117	C₂³	semidirect
103. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
109. C₂×C₄²×C₇	C₂³	semidirect
110. #3568	C₂×C₇	direct (N × H)
111. C₂×#563	C₂×C₇	semidirect
112. C₂×H(3,𝔽₄)	C₂×C₇	semidirect
113. C₂×#556	C₂×C₇	semidirect
114. C₂×#551	C₂×C₇	semidirect
115. C₂×#542	C₂×C₇	semidirect
116. C₂×#538	C₂×C₇	semidirect
117. C₂×#529	C₂×C₇	semidirect
165. #563	C₂²×C₇	semidirect
166. H(3,𝔽₄)	C₂²×C₇	semidirect
167. #556	C₂²×C₇	semidirect
168. #551	C₂²×C₇	semidirect
169. #542	C₂²×C₇	semidirect
170. #538	C₂²×C₇	semidirect
171. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
172. #529	C₂²×C₇	semidirect
173. C₂×#126	C₂²×C₇	semidirect
174. C₂×#126	C₂²×C₇	semidirect
175. C₂×#126	C₂²×C₇	semidirect
176. C₂×#126	C₂²×C₇	semidirect
177. C₂×#126	C₂²×C₇	semidirect
178. C₂×#125	C₂²×C₇	semidirect
182. C₂×#124	C₂²×C₇	semidirect
185. C₂×#123	C₂²×C₇	semidirect
186. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
187. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
188. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
189. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
193. C₂×#120	C₂²×C₇	semidirect
194. C₂×C₄×Q₈	C₂²×C₇	semidirect
195. C₂×C₄×Q₈	C₂²×C₇	semidirect
198. C₂×C₄×D₄	C₂²×C₇	semidirect
199. C₂×#117	C₂²×C₇	semidirect
200. C₂×#117	C₂²×C₇	semidirect
201. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
202. C₂²×C₄²	C₂²×C₇	semidirect
239. C₄⋊Q₈	C₂³×C₇	semidirect
240. #126	C₂³×C₇	semidirect
241. #126	C₂³×C₇	semidirect
242. #126	C₂³×C₇	semidirect
243. #126	C₂³×C₇	semidirect
244. #126	C₂³×C₇	semidirect
245. #125	C₂³×C₇	semidirect
249. #124	C₂³×C₇	semidirect
252. #123	C₂³×C₇	semidirect
253. C₂²⋊Q₈	C₂³×C₇	semidirect
254. C₂²⋊Q₈	C₂³×C₇	semidirect
255. C₂²⋊Q₈	C₂³×C₇	semidirect
256. C₂²⋊Q₈	C₂³×C₇	semidirect
260. #120	C₂³×C₇	semidirect
261. C₄×Q₈	C₂³×C₇	semidirect
262. C₄×Q₈	C₂³×C₇	semidirect
265. C₄×D₄	C₂³×C₇	semidirect
266. #117	C₂³×C₇	semidirect
267. #117	C₂³×C₇	semidirect
285. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
291. C₂×C₄²	C₂³×C₇	semidirect
355. C₂×C₇	#3568	direct (N × H)
384. C₇	C₂×#3568	direct (N × H)
401. C₂	C₇×#3568	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3568	2
C₂×C₇×#563	2
C₂×C₇×H(3,𝔽₄)	2
C₂×C₇×#556	2
C₂×C₇×#551	2
C₂×C₇×#542	2
C₂×C₇×#538	2
C₂×C₇×#529	2
C₂×#3568	7

Subgroups — C2×C7×#3568 #13239952

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3568 #13239952