Subgroups — C₂×C₇×#2857 #13213839

Order 1792.

3790 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂³×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
4	C₇×#2857	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₇×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#389	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#380	C₂	1	4	yes	maximal
9	C₂³×C₇×Q₈	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
12	C₂×C₇×C₄⋊Q₈	—	2	8	no	—
13	C₂×C₇×C₄⋊Q₈	C₂²	1	8	yes	complemented
14	C₂×C₇×C₂²⋊Q₈	—	2	16	no	—
15	C₂×C₇×C₂²⋊Q₈	C₂²	1	16	yes	—
16	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
18	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
20	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₄²×C₇	—	2	8	no	—
22	C₂²×C₄²×C₇	C₂²	1	2	yes	—
23	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇	C₂²	1	8	yes	—
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₇×#391	C₂²	1	16	yes	complemented
27	C₇×#389	C₂²	1	32	yes	complemented
28	C₇×#384	C₂²	1	8	yes	complemented
29	C₇×#380	C₂²	1	32	yes	—
30	C₂×C₇×#95	C₂²	1	8	yes	—
31	C₂×#2857	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁵×C₇	C₂³	1	1	yes	characteristic
33	C₂²×C₇×Q₈	—	2	8	no	—
34	C₂²×C₇×Q₈	—	2	8	no	—
35	C₂²×C₇×Q₈	—	2	8	no	—
36	C₂²×C₇×Q₈	C₂³	1	8	yes	—
37	C₂³×C₄×C₇	—	2	4	no	—
38	C₂³×C₄×C₇	—	2	8	no	—
39	C₂³×C₄×C₇	—	2	4	no	—
40	C₂³×C₄×C₇	—	2	8	no	—
41	C₂³×C₄×C₇	D₄	1	8	yes	—
42	C₂³×C₄×C₇	Q₈	1	16	yes	complemented
43	C₂³×C₄×C₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₇	C₂³	1	4	yes	—
45	C₂³×C₄×C₇	C₂³	1	4	yes	—
46	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₇	C₂³	1	8	yes	—
49	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇	C₂³	1	2	yes	—
51	C₇×C₄⋊Q₈	—	2	32	no	—
52	C₇×C₂²⋊Q₈	—	2	64	no	—
53	C₂×C₇×C₄⋊C₄	—	2	8	no	—
54	C₂×C₇×C₄⋊C₄	—	2	16	no	—
55	C₂×C₇×C₄⋊C₄	—	2	16	no	—
56	C₂×C₇×C₄⋊C₄	—	2	16	no	—
57	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
58	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
59	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
61	C₂×C₇×C₂²⋊C₄	—	2	16	no	—
62	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
63	C₂×C₄²×C₇	—	2	4	no	—
64	C₂×C₄²×C₇	—	2	8	no	—
65	C₂×C₄²×C₇	—	2	32	no	—
66	C₂×C₄²×C₇	D₄	1	8	yes	—
67	C₂×C₄²×C₇	C₂³	1	8	yes	—
68	C₂×C₄²×C₇	C₂³	1	4	yes	—
69	C₂×C₄²×C₇	C₂³	1	4	yes	—
70	C₇×#95	C₂³	1	32	yes	—
71	C₂²×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
72	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	—
73	C₂³×C₄²	C₂×C₇	1	1	yes	characteristic
74	#2857	C₂×C₇	1	16	yes	direct product factor
75	C₂×#391	C₂×C₇	1	2	yes	complemented
76	C₂×#389	C₂×C₇	1	4	yes	complemented
77	C₂×#384	C₂×C₇	1	1	yes	characteristic, complemented
78	C₂×#380	C₂×C₇	1	4	yes	—
79	C₂⁴×C₇	—	2	2	no	—
80	C₂⁴×C₇	—	2	2	no	—
81	C₂⁴×C₇	—	2	4	no	—
82	C₂⁴×C₇	C₂×D₄	1	4	yes	—
83	C₂⁴×C₇	C₂×Q₈	1	8	yes	—
84	C₂⁴×C₇	C₂⁴	1	2	yes	—
85	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
86	C₂×C₇×Q₈	—	2	16	no	—
87	C₂×C₇×Q₈	—	2	16	no	—
88	C₂×C₇×Q₈	—	2	16	no	—
89	C₂×C₇×Q₈	—	4	32	no	—
90	C₂²×C₄×C₇	—	2	2	no	—
91	C₂²×C₄×C₇	—	2	4	no	—
92	C₂²×C₄×C₇	—	2	2	no	—
93	C₂²×C₄×C₇	—	2	4	no	—
94	C₂²×C₄×C₇	—	2	32	no	—
95	C₂²×C₄×C₇	—	2	64	no	—
96	C₂²×C₄×C₇	—	2	8	no	—
97	C₂²×C₄×C₇	—	2	16	no	—
98	C₂²×C₄×C₇	—	2	8	no	—
99	C₂²×C₄×C₇	—	2	16	no	—
100	C₂²×C₄×C₇	—	2	8	no	—
101	C₂²×C₄×C₇	—	2	8	no	—
102	C₂²×C₄×C₇	—	2	8	no	—
103	C₂²×C₄×C₇	—	2	16	no	—
104	C₂²×C₄×C₇	—	2	8	no	—
105	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₇	C₂×D₄	1	16	yes	—
107	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
111	C₂²×C₄×C₇	C₂×Q₈	1	8	yes	—
112	C₂²×C₄×C₇	C₂×Q₈	1	32	yes	complemented
113	C₂²×C₄×C₇	#41	1	4	yes	—
114	C₂²×C₄×C₇	#41	1	8	yes	—
115	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
121	C₇×C₄⋊C₄	—	2	16	no	—
122	C₇×C₄⋊C₄	—	2	32	no	—
123	C₇×C₄⋊C₄	—	2	32	no	—
124	C₇×C₄⋊C₄	—	2	32	no	—
125	C₇×C₂²⋊C₄	—	2	32	no	—
126	C₄²×C₇	—	2	8	no	—
127	C₄²×C₇	—	2	16	no	—
128	C₄²×C₇	C₂×D₄	1	16	yes	—
129	C₂³×Q₈	C₂²×C₇	1	2	yes	—
130	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
131	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
132	C₂×C₄⋊Q₈	—	2	8	no	—
133	C₂×C₄⋊Q₈	C₂²×C₇	1	8	yes	complemented
134	C₂×C₂²⋊Q₈	—	2	16	no	—
135	C₂×C₂²⋊Q₈	C₂²×C₇	1	16	yes	—
136	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	—
137	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
138	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
139	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
140	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
141	C₂²×C₄²	—	2	8	no	—
142	C₂²×C₄²	C₂²×C₇	1	8	yes	—
143	C₂²×C₄²	C₂²×C₇	1	2	yes	—
144	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
145	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
146	#391	C₂²×C₇	1	16	yes	complemented
147	#389	C₂²×C₇	1	32	yes	complemented
148	#384	C₂²×C₇	1	8	yes	complemented
149	#380	C₂²×C₇	1	32	yes	—
150	C₂×#95	C₂²×C₇	1	8	yes	—
151	C₂³×C₇	—	2	8	no	—
152	C₂³×C₇	—	2	16	no	—
153	C₂³×C₇	—	2	8	no	—
154	C₂³×C₇	—	2	16	no	—
155	C₂³×C₇	—	2	2	no	—
156	C₂³×C₇	—	2	2	no	—
157	C₂³×C₇	—	2	4	no	—
158	C₂³×C₇	C₄⋊Q₈	1	16	yes	complemented
159	C₂³×C₇	C₂²×D₄	1	4	yes	—
160	C₂³×C₇	C₂²×D₄	1	2	yes	—
161	C₂³×C₇	C₂²×D₄	1	2	yes	—
162	C₂³×C₇	C₂²×Q₈	1	8	yes	—
163	C₂³×C₇	C₂²×Q₈	1	4	yes	—
164	C₂³×C₇	C₂×#41	1	2	yes	—
165	C₂³×C₇	C₂×#41	1	4	yes	—
166	C₂³×C₇	C₂⁵	1	1	yes	characteristic
167	C₇×Q₈	—	4	32	no	—
168	C₂×C₄×C₇	—	2	8	no	—
169	C₂×C₄×C₇	—	2	16	no	—
170	C₂×C₄×C₇	—	2	2	no	—
171	C₂×C₄×C₇	—	2	4	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	4	no	—
174	C₂×C₄×C₇	—	2	32	no	—
175	C₂×C₄×C₇	—	2	64	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	2	8	no	—
178	C₂×C₄×C₇	—	2	8	no	—
179	C₂×C₄×C₇	—	2	16	no	—
180	C₂×C₄×C₇	—	2	8	no	—
181	C₂×C₄×C₇	—	4	16	no	—
182	C₂×C₄×C₇	—	4	16	no	—
183	C₂×C₄×C₇	#121	1	16	yes	—
184	C₂×C₄×C₇	C₂²⋊Q₈	1	32	yes	complemented
185	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
188	C₂×C₄×C₇	C₂²×D₄	1	8	yes	—
189	C₂×C₄×C₇	C₂²×Q₈	1	8	yes	—
190	C₂×C₄×C₇	C₂²×Q₈	1	8	yes	—
191	C₂×C₄×C₇	C₂×#41	1	4	yes	—
192	C₂×C₄×C₇	C₂×#41	1	8	yes	—
193	C₂⁵	C₂³×C₇	1	1	yes	characteristic
194	C₂²×Q₈	—	2	8	no	—
195	C₂²×Q₈	—	2	8	no	—
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	C₂³×C₇	1	8	yes	—
198	C₂³×C₄	—	2	4	no	—
199	C₂³×C₄	—	2	8	no	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	—	2	8	no	—
202	C₂³×C₄	C₇×D₄	1	8	yes	—
203	C₂³×C₄	C₇×Q₈	1	16	yes	complemented
204	C₂³×C₄	C₂³×C₇	1	4	yes	—
205	C₂³×C₄	C₂³×C₇	1	4	yes	—
206	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₇	1	4	yes	—
208	C₂³×C₄	C₂³×C₇	1	2	yes	—
209	C₂³×C₄	C₂³×C₇	1	8	yes	—
210	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₇	1	2	yes	—
212	C₄⋊Q₈	—	2	32	no	—
213	C₂²⋊Q₈	—	2	64	no	—
214	C₂×C₄⋊C₄	—	2	8	no	—
215	C₂×C₄⋊C₄	—	2	16	no	—
216	C₂×C₄⋊C₄	—	2	16	no	—
217	C₂×C₄⋊C₄	—	2	16	no	—
218	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
220	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
221	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
222	C₂×C₂²⋊C₄	—	2	16	no	—
223	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
224	C₂×C₄²	—	2	4	no	—
225	C₂×C₄²	—	2	8	no	—
226	C₂×C₄²	—	2	32	no	—
227	C₂×C₄²	C₇×D₄	1	8	yes	—
228	C₂×C₄²	C₂³×C₇	1	8	yes	—
229	C₂×C₄²	C₂³×C₇	1	4	yes	—
230	C₂×C₄²	C₂³×C₇	1	4	yes	—
231	#95	C₂³×C₇	1	32	yes	—
232	C₂²×C₇	—	2	32	no	—
233	C₂²×C₇	—	2	4	no	—
234	C₂²×C₇	—	2	8	no	—
235	C₂²×C₇	—	2	4	no	—
236	C₂²×C₇	—	2	8	no	—
237	C₂²×C₇	C₂×#121	1	4	yes	—
238	C₂²×C₇	C₂×C₂²⋊Q₈	1	8	yes	—
239	C₂²×C₇	C₂×C₄⋊Q₈	1	4	yes	—
240	C₂²×C₇	C₂×C₄⋊Q₈	1	8	yes	complemented
241	C₂²×C₇	#532	1	4	yes	—
242	C₂²×C₇	#533	1	8	yes	—
243	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
244	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
245	C₂²×C₇	C₂³×Q₈	1	2	yes	—
246	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
247	C₂²×C₇	C₂²×#41	1	2	yes	—
248	C₄×C₇	—	2	4	no	—
249	C₄×C₇	—	2	8	no	—
250	C₄×C₇	—	4	8	no	—
251	C₄×C₇	—	4	8	no	—
252	C₄×C₇	C₂×#121	1	8	yes	—
253	C₄×C₇	C₂×C₂²⋊Q₈	1	16	yes	complemented
254	C₂⁴	—	2	2	no	—
255	C₂⁴	—	2	2	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	C₂×C₇×D₄	1	4	yes	—
258	C₂⁴	C₂×C₇×Q₈	1	8	yes	—
259	C₂⁴	C₂⁴×C₇	1	2	yes	—
260	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	16	no	—
263	C₂×Q₈	—	2	16	no	—
264	C₂×Q₈	—	4	32	no	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	32	no	—
270	C₂²×C₄	—	2	64	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	16	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	2	16	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
281	C₂²×C₄	C₂×C₇×D₄	1	16	yes	—
282	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
283	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
284	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
285	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
286	C₂²×C₄	C₂×C₇×Q₈	1	8	yes	—
287	C₂²×C₄	C₂×C₇×Q₈	1	32	yes	complemented
288	C₂²×C₄	C₇×#41	1	4	yes	—
289	C₂²×C₄	C₇×#41	1	8	yes	—
290	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
291	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
292	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
294	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
296	C₄⋊C₄	—	2	16	no	—
297	C₄⋊C₄	—	2	32	no	—
298	C₄⋊C₄	—	2	32	no	—
299	C₄⋊C₄	—	2	32	no	—
300	C₂²⋊C₄	—	2	32	no	—
301	C₄²	—	2	8	no	—
302	C₄²	—	2	16	no	—
303	C₄²	C₂×C₇×D₄	1	16	yes	—
304	C₂×C₇	—	2	8	no	—
305	C₂×C₇	#2857	1	8	yes	direct product factor
306	C₂×C₇	C₂²×#121	1	1	yes	characteristic
307	C₂×C₇	C₂²×C₂²⋊Q₈	1	2	yes	—
308	C₂×C₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
309	C₂×C₇	C₂×#532	1	1	yes	characteristic
310	C₂×C₇	C₂×#533	1	2	yes	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	4	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	16	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	16	no	—
318	C₂³	C₇×C₄⋊Q₈	1	16	yes	complemented
319	C₂³	C₂²×C₇×D₄	1	4	yes	—
320	C₂³	C₂²×C₇×D₄	1	2	yes	—
321	C₂³	C₂²×C₇×D₄	1	2	yes	—
322	C₂³	C₂²×C₇×Q₈	1	8	yes	—
323	C₂³	C₂²×C₇×Q₈	1	4	yes	—
324	C₂³	C₂×C₇×#41	1	2	yes	—
325	C₂³	C₂×C₇×#41	1	4	yes	—
326	C₂³	C₂⁵×C₇	1	1	yes	characteristic
327	Q₈	—	4	32	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	16	no	—
334	C₂×C₄	—	2	32	no	—
335	C₂×C₄	—	2	64	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	16	no	—
340	C₂×C₄	—	2	8	no	—
341	C₂×C₄	—	4	16	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	C₇×#121	1	16	yes	—
344	C₂×C₄	C₇×C₂²⋊Q₈	1	32	yes	complemented
345	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
346	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
347	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
348	C₂×C₄	C₂²×C₇×D₄	1	8	yes	—
349	C₂×C₄	C₂²×C₇×Q₈	1	8	yes	—
350	C₂×C₄	C₂²×C₇×Q₈	1	8	yes	—
351	C₂×C₄	C₂×C₇×#41	1	4	yes	—
352	C₂×C₄	C₂×C₇×#41	1	8	yes	—
353	C₇	C₂×#2857	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	4	no	—
355	C₂²	—	2	8	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	2	32	no	—
359	C₂²	C₂×C₇×#121	1	4	yes	—
360	C₂²	C₂×C₇×C₂²⋊Q₈	1	8	yes	—
361	C₂²	C₂×C₇×C₄⋊Q₈	1	4	yes	—
362	C₂²	C₂×C₇×C₄⋊Q₈	1	8	yes	complemented
363	C₂²	C₇×#532	1	4	yes	—
364	C₂²	C₇×#533	1	8	yes	—
365	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
366	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
367	C₂²	C₂³×C₇×Q₈	1	2	yes	—
368	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
369	C₂²	C₂²×C₇×#41	1	2	yes	—
370	C₄	—	2	4	no	—
371	C₄	—	2	8	no	—
372	C₄	—	4	8	no	—
373	C₄	—	4	8	no	—
374	C₄	C₂×C₇×#121	1	8	yes	—
375	C₄	C₂×C₇×C₂²⋊Q₈	1	16	yes	complemented
376	C₂	—	2	8	no	—
377	C₂	C₇×#2857	1	8	yes	direct product factor
378	C₂	C₂²×C₇×#121	1	1	yes	characteristic
379	C₂	C₂²×C₇×C₂²⋊Q₈	1	2	yes	—
380	C₂	C₂²×C₇×C₄⋊Q₈	1	1	yes	characteristic
381	C₂	C₂×C₇×#532	1	1	yes	characteristic
382	C₂	C₂×C₇×#533	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₄⋊Q₈	C₂	semidirect
4. C₇×#2857	C₂	direct (N × H)
5. C₂×C₇×#391	C₂	semidirect
6. C₂×C₇×#389	C₂	semidirect
7. C₂×C₇×#384	C₂	semidirect
13. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
26. C₇×#391	C₂²	semidirect
27. C₇×#389	C₂²	semidirect
28. C₇×#384	C₂²	semidirect
31. C₂×#2857	C₇	direct (N × H)
42. C₂³×C₄×C₇	Q₈	semidirect
71. C₂²×C₄⋊Q₈	C₂×C₇	semidirect
74. #2857	C₂×C₇	direct (N × H)
75. C₂×#391	C₂×C₇	semidirect
76. C₂×#389	C₂×C₇	semidirect
77. C₂×#384	C₂×C₇	semidirect
112. C₂²×C₄×C₇	C₂×Q₈	semidirect
133. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
146. #391	C₂²×C₇	semidirect
147. #389	C₂²×C₇	semidirect
148. #384	C₂²×C₇	semidirect
158. C₂³×C₇	C₄⋊Q₈	semidirect
184. C₂×C₄×C₇	C₂²⋊Q₈	semidirect
203. C₂³×C₄	C₇×Q₈	semidirect
240. C₂²×C₇	C₂×C₄⋊Q₈	semidirect
253. C₄×C₇	C₂×C₂²⋊Q₈	semidirect
287. C₂²×C₄	C₂×C₇×Q₈	semidirect
305. C₂×C₇	#2857	direct (N × H)
318. C₂³	C₇×C₄⋊Q₈	semidirect
344. C₂×C₄	C₇×C₂²⋊Q₈	semidirect
353. C₇	C₂×#2857	direct (N × H)
362. C₂²	C₂×C₇×C₄⋊Q₈	semidirect
375. C₄	C₂×C₇×C₂²⋊Q₈	semidirect
377. C₂	C₇×#2857	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×C₄⋊Q₈	2
C₂²×C₇×C₂²⋊Q₈	2
C₂³×C₄²×C₇	2
C₇×#2857	2
C₂×C₇×#391	2
C₂×C₇×#389	2
C₂×C₇×#384	2
C₂×C₇×#380	2
C₂×#2857	7

Subgroups — C2×C7×#2857 #13213839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#2857 #13213839