Subgroups — C₂×C₇×#1950 #13198392

Order 1792.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#108	C₂	1	2	yes	maximal
2	C₂×C₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₇×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₇×#1950	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₇×#341	C₂	1	2	yes	maximal
7	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
9	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₇×C₈	C₂²	1	2	yes	—
11	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
12	C₂×C₇×#108	—	2	8	no	—
13	C₂×C₇×#108	C₂²	1	8	yes	—
14	C₇×#423	—	2	2	no	—
15	C₇×#423	C₂²	1	4	yes	—
16	C₂×C₇×C₄⋊C₈	—	2	1	no	—
17	C₂×C₇×C₄⋊C₈	—	2	1	no	—
18	C₂×C₇×C₄⋊C₈	C₄	1	2	yes	—
19	C₂×C₇×C₄⋊C₈	C₄	1	4	yes	—
20	C₂×C₇×C₄⋊C₈	C₄	1	2	yes	—
21	C₂×C₇×C₄⋊C₈	C₂²	1	4	yes	—
22	C₄×C₇×M₁₆	—	2	2	no	—
23	C₄×C₇×M₁₆	C₂²	1	4	yes	—
24	C₂×C₇×#97	—	2	1	no	—
25	C₂×C₄×C₇×C₈	—	2	1	no	—
26	C₇×#341	C₂²	1	8	yes	—
27	C₂×#1950	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
29	C₂³×C₄×C₇	Q₈	1	1	yes	characteristic
30	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
31	C₂×C₇×M₁₆	—	2	1	no	—
32	C₂×C₇×M₁₆	—	2	1	no	—
33	C₂×C₇×M₁₆	—	2	2	no	—
34	C₂×C₇×M₁₆	—	2	2	no	—
35	C₂×C₇×M₁₆	—	2	2	no	—
36	C₂×C₇×M₁₆	—	2	4	no	—
37	C₂×C₇×M₁₆	—	2	4	no	—
38	C₂×C₇×M₁₆	D₄	1	4	yes	—
39	C₂×C₇×M₁₆	Q₈	1	4	yes	—
40	C₂×C₇×M₁₆	C₂³	1	4	yes	—
41	C₂×C₇×M₁₆	C₂³	1	2	yes	—
42	C₂×C₇×M₁₆	C₂³	1	2	yes	—
43	C₂²×C₇×C₈	—	2	4	no	—
44	C₂²×C₇×C₈	—	2	1	no	—
45	C₂²×C₇×C₈	—	2	1	no	—
46	C₂²×C₇×C₈	—	2	4	no	—
47	C₂²×C₇×C₈	—	2	2	no	—
48	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
49	C₂²×C₇×C₈	C₂×C₄	1	4	yes	—
50	C₂²×C₇×C₈	C₂³	1	4	yes	—
51	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₇	D₄	1	2	yes	—
55	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₇	Q₈	1	2	yes	—
58	C₂×C₄²×C₇	C₂³	1	2	yes	—
59	C₇×#108	—	2	16	no	—
60	C₇×C₄⋊C₈	—	2	4	no	—
61	C₇×C₄⋊C₈	—	2	4	no	—
62	C₇×C₄⋊C₈	C₂×C₄	1	8	yes	—
63	C₇×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₇×#97	—	2	4	no	—
65	C₄×C₇×C₈	—	2	4	no	—
66	C₂²×#108	C₂×C₇	1	2	yes	—
67	C₂×#423	C₂×C₇	1	1	yes	characteristic
68	C₂²×C₄⋊C₈	C₂×C₇	1	1	yes	characteristic
69	C₂×C₄×M₁₆	C₂×C₇	1	1	yes	characteristic
70	#1950	C₂×C₇	1	8	yes	direct product factor
71	C₂×#341	C₂×C₇	1	2	yes	—
72	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
73	C₂²×C₄×C₇	—	2	4	no	—
74	C₂²×C₄×C₇	—	4	2	no	—
75	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
79	C₂²×C₄×C₇	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
89	C₂²×C₄×C₇	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₇	#41	1	2	yes	—
91	C₂²×C₄×C₇	#41	1	2	yes	—
92	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
93	C₇×M₁₆	—	2	4	no	—
94	C₇×M₁₆	—	2	4	no	—
95	C₇×M₁₆	—	2	2	no	—
96	C₇×M₁₆	—	2	2	no	—
97	C₇×M₁₆	—	2	4	no	—
98	C₇×M₁₆	—	2	4	no	—
99	C₇×M₁₆	—	4	4	no	—
100	C₇×M₁₆	C₂×D₄	1	4	yes	—
101	C₇×M₁₆	C₂×Q₈	1	4	yes	—
102	C₂×C₇×C₈	—	2	8	no	—
103	C₂×C₇×C₈	—	2	8	no	—
104	C₂×C₇×C₈	—	2	4	no	—
105	C₂×C₇×C₈	—	2	4	no	—
106	C₂×C₇×C₈	—	2	2	no	—
107	C₂×C₇×C₈	—	2	2	no	—
108	C₂×C₇×C₈	—	2	4	no	—
109	C₂×C₇×C₈	—	2	4	no	—
110	C₂×C₇×C₈	—	2	4	no	—
111	C₂×C₇×C₈	—	4	4	no	—
112	C₂×C₇×C₈	C₂²×C₄	1	8	yes	—
113	C₄²×C₇	C₄⋊C₄	1	2	yes	—
114	C₄²×C₇	C₄⋊C₄	1	2	yes	—
115	C₄²×C₇	C₄⋊C₄	1	2	yes	—
116	C₄²×C₇	C₄⋊C₄	1	2	yes	—
117	C₄²×C₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₇	C₂×D₄	1	2	yes	—
120	C₄²×C₇	C₂×D₄	1	2	yes	—
121	C₂²×M₁₆	C₂²×C₇	1	2	yes	—
122	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
123	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
124	C₂³×C₈	C₂²×C₇	1	2	yes	—
125	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
126	C₂×#108	—	2	8	no	—
127	C₂×#108	C₂²×C₇	1	8	yes	—
128	#423	—	2	2	no	—
129	#423	C₂²×C₇	1	4	yes	—
130	C₂×C₄⋊C₈	—	2	1	no	—
131	C₂×C₄⋊C₈	—	2	1	no	—
132	C₂×C₄⋊C₈	C₄×C₇	1	2	yes	—
133	C₂×C₄⋊C₈	C₄×C₇	1	4	yes	—
134	C₂×C₄⋊C₈	C₄×C₇	1	2	yes	—
135	C₂×C₄⋊C₈	C₂²×C₇	1	4	yes	—
136	C₄×M₁₆	—	2	2	no	—
137	C₄×M₁₆	C₂²×C₇	1	4	yes	—
138	C₂×#97	—	2	1	no	—
139	C₂×C₄×C₈	—	2	1	no	—
140	#341	C₂²×C₇	1	8	yes	—
141	C₂³×C₇	—	2	2	no	—
142	C₂³×C₇	—	2	2	no	—
143	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂³×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂³×C₇	#125	1	2	yes	—
146	C₂³×C₇	C₄⋊Q₈	1	2	yes	—
147	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₇	—	2	2	no	—
149	C₂×C₄×C₇	—	2	2	no	—
150	C₂×C₄×C₇	—	2	2	no	—
151	C₂×C₄×C₇	—	2	4	no	—
152	C₂×C₄×C₇	—	2	4	no	—
153	C₂×C₄×C₇	—	4	2	no	—
154	C₂×C₄×C₇	—	4	2	no	—
155	C₂×C₄×C₇	#108	1	4	yes	complemented
156	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
165	C₂×C₄×C₇	C₄×Q₈	1	2	yes	—
166	C₂×C₄×C₇	#121	1	2	yes	—
167	C₂×C₄×C₇	#121	1	2	yes	—
168	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₇	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₇	#125	1	2	yes	—
171	C₂×C₄×C₇	C₄⋊Q₈	1	2	yes	—
172	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
178	C₇×C₈	—	2	8	no	—
179	C₇×C₈	—	2	4	no	—
180	C₇×C₈	—	2	4	no	—
181	C₇×C₈	—	4	4	no	—
182	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
183	C₂³×C₄	C₇×Q₈	1	1	yes	characteristic
184	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
185	C₂×M₁₆	—	2	1	no	—
186	C₂×M₁₆	—	2	1	no	—
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	—	2	2	no	—
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	4	no	—
191	C₂×M₁₆	—	2	4	no	—
192	C₂×M₁₆	C₇×D₄	1	4	yes	—
193	C₂×M₁₆	C₇×Q₈	1	4	yes	—
194	C₂×M₁₆	C₂³×C₇	1	4	yes	—
195	C₂×M₁₆	C₂³×C₇	1	2	yes	—
196	C₂×M₁₆	C₂³×C₇	1	2	yes	—
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	—	2	1	no	—
199	C₂²×C₈	—	2	1	no	—
200	C₂²×C₈	—	2	4	no	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
203	C₂²×C₈	C₂×C₄×C₇	1	4	yes	—
204	C₂²×C₈	C₂³×C₇	1	4	yes	—
205	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
206	C₂×C₄²	C₂×C₄×C₇	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₇	1	1	yes	characteristic
208	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
209	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
210	C₂×C₄²	C₇×D₄	1	2	yes	—
211	C₂×C₄²	C₇×Q₈	1	2	yes	—
212	C₂×C₄²	C₂³×C₇	1	2	yes	—
213	#108	—	2	16	no	—
214	C₄⋊C₈	—	2	4	no	—
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	C₂×C₄×C₇	1	8	yes	—
217	C₄⋊C₈	C₂×C₄×C₇	1	8	yes	—
218	#97	—	2	4	no	—
219	C₄×C₈	—	2	4	no	—
220	C₂²×C₇	—	2	1	no	—
221	C₂²×C₇	—	2	1	no	—
222	C₂²×C₇	—	2	1	no	—
223	C₂²×C₇	—	2	1	no	—
224	C₂²×C₇	—	2	4	no	—
225	C₂²×C₇	—	2	4	no	—
226	C₂²×C₇	#389	1	2	yes	—
227	C₂²×C₇	#389	1	2	yes	—
228	C₂²×C₇	C₂×#108	1	2	yes	—
229	C₂²×C₇	#430	1	2	yes	—
230	C₂²×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
231	C₂²×C₇	C₂×#125	1	1	yes	characteristic
232	C₂²×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
233	C₄×C₇	—	2	2	no	—
234	C₄×C₇	—	2	2	no	—
235	C₄×C₇	—	2	2	no	—
236	C₄×C₇	#389	1	2	yes	—
237	C₄×C₇	#389	1	2	yes	—
238	C₄×C₇	C₂×#108	1	4	yes	complemented
239	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
241	C₄×C₇	C₂×#121	1	1	yes	characteristic
242	C₄×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂⁴	C₂×C₇×Q₈	1	1	yes	characteristic
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
247	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
250	C₂²×C₄	C₇×C₄⋊C₄	1	2	yes	—
251	C₂²×C₄	C₇×C₄⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
257	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
258	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
259	C₂²×C₄	C₂×C₇×Q₈	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₇×Q₈	1	2	yes	—
261	C₂²×C₄	C₇×#41	1	2	yes	—
262	C₂²×C₄	C₇×#41	1	2	yes	—
263	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
264	M₁₆	—	2	4	no	—
265	M₁₆	—	2	4	no	—
266	M₁₆	—	2	2	no	—
267	M₁₆	—	2	2	no	—
268	M₁₆	—	2	4	no	—
269	M₁₆	—	2	4	no	—
270	M₁₆	—	4	4	no	—
271	M₁₆	C₂×C₇×D₄	1	4	yes	—
272	M₁₆	C₂×C₇×Q₈	1	4	yes	—
273	C₂×C₈	—	2	8	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	4	4	no	—
283	C₂×C₈	C₂²×C₄×C₇	1	8	yes	—
284	C₄²	C₇×C₄⋊C₄	1	2	yes	—
285	C₄²	C₇×C₄⋊C₄	1	2	yes	—
286	C₄²	C₇×C₄⋊C₄	1	2	yes	—
287	C₄²	C₇×C₄⋊C₄	1	2	yes	—
288	C₄²	C₂²×C₄×C₇	1	2	yes	—
289	C₄²	C₂²×C₄×C₇	1	2	yes	—
290	C₄²	C₂×C₇×D₄	1	2	yes	—
291	C₄²	C₂×C₇×D₄	1	2	yes	—
292	C₂×C₇	—	2	1	no	—
293	C₂×C₇	—	2	1	no	—
294	C₂×C₇	—	2	2	no	—
295	C₂×C₇	#1950	1	4	yes	direct product factor
296	C₂×C₇	C₂×#389	1	1	yes	characteristic
297	C₂×C₇	C₂²×#108	1	1	yes	characteristic
298	C₂×C₇	C₂×#430	1	1	yes	characteristic
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
302	C₂³	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
303	C₂³	C₇×#125	1	2	yes	—
304	C₂³	C₇×C₄⋊Q₈	1	2	yes	—
305	C₂³	C₂²×C₇×Q₈	1	1	yes	characteristic
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	C₇×#108	1	4	yes	complemented
314	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
315	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
316	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
318	C₂×C₄	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₇×C₄⋊C₄	1	2	yes	—
320	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
321	C₂×C₄	C₄×C₇×D₄	1	2	yes	—
322	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
323	C₂×C₄	C₄×C₇×Q₈	1	2	yes	—
324	C₂×C₄	C₇×#121	1	2	yes	—
325	C₂×C₄	C₇×#121	1	2	yes	—
326	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
327	C₂×C₄	C₇×C₂²⋊Q₈	1	2	yes	—
328	C₂×C₄	C₇×#125	1	2	yes	—
329	C₂×C₄	C₇×C₄⋊Q₈	1	2	yes	—
330	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
333	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
334	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
335	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
336	C₈	—	2	8	no	—
337	C₈	—	2	4	no	—
338	C₈	—	2	4	no	—
339	C₈	—	4	4	no	—
340	C₇	C₂×#1950	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	C₇×#389	1	2	yes	—
348	C₂²	C₇×#389	1	2	yes	—
349	C₂²	C₂×C₇×#108	1	2	yes	—
350	C₂²	C₇×#430	1	2	yes	—
351	C₂²	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
352	C₂²	C₂×C₇×#125	1	1	yes	characteristic
353	C₂²	C₂×C₇×C₄⋊Q₈	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	C₇×#389	1	2	yes	—
358	C₄	C₇×#389	1	2	yes	—
359	C₄	C₂×C₇×#108	1	4	yes	complemented
360	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
361	C₄	C₂×C₄×C₇×Q₈	1	1	yes	characteristic
362	C₄	C₂×C₇×#121	1	1	yes	characteristic
363	C₄	C₂×C₇×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	C₇×#1950	1	4	yes	direct product factor
368	C₂	C₂×C₇×#389	1	1	yes	characteristic
369	C₂	C₂²×C₇×#108	1	1	yes	characteristic
370	C₂	C₂×C₇×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂³×C₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₇	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇×#1950	C₂	direct (N × H)
27. C₂×#1950	C₇	direct (N × H)
70. #1950	C₂×C₇	direct (N × H)
155. C₂×C₄×C₇	#108	semidirect
238. C₄×C₇	C₂×#108	semidirect
295. C₂×C₇	#1950	direct (N × H)
313. C₂×C₄	C₇×#108	semidirect
340. C₇	C₂×#1950	direct (N × H)
359. C₄	C₂×C₇×#108	semidirect
367. C₂	C₇×#1950	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×#108	2
C₂×C₇×#423	2
C₂²×C₇×C₄⋊C₈	2
C₂×C₄×C₇×M₁₆	2
C₇×#1950	2
C₂×C₇×#341	2
C₂×#1950	7

Subgroups — C2×C7×#1950 #13198392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#1950 #13198392