Subgroups — C₇×#22686 #13199902

Order 1792.

858 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#444	C₂	1	2	yes	maximal
2	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic
3	C₇×#2906	C₂	1	2	yes	maximal, complemented
4	C₇×#1946	C₂	1	2	yes	maximal, complemented
5	C₇×#1866	C₂	1	4	yes	maximal, complemented
6	C₇×#1848	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1806	C₂	1	2	yes	maximal, complemented
8	C₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#135	C₂²	1	1	yes	characteristic
10	C₂×C₇×#131	C₂²	1	4	yes	—
11	C₄×C₇×#41	C₂²	1	2	yes	—
12	C₇×#444	—	2	8	no	—
13	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
14	C₄×C₇×Q₁₆	C₄	1	1	yes	characteristic, complemented
15	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
16	C₄×C₇×SD₁₆	C₄	1	2	yes	complemented
17	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
18	C₄×C₇×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂×C₇×#108	C₂²	1	2	yes	—
20	C₂×C₇×#108	C₂²	1	2	yes	—
21	C₇×#427	C₂²	1	1	yes	characteristic
22	C₇×#424	—	2	4	no	—
23	C₇×#424	C₂²	1	4	yes	—
24	C₇×#423	—	2	2	no	—
25	C₇×#423	C₂²	1	2	yes	—
26	C₂×C₇×C₄⋊C₈	—	2	2	no	—
27	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₇×#104	C₂²	1	4	yes	—
29	C₇×#416	C₂²	1	2	yes	—
30	C₂×C₇×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₇×#339	C₂²	1	4	yes	—
34	C₇×#336	C₂²	1	2	yes	—
35	#22686	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₇×#41	C₂³	1	2	yes	—
37	C₇×#135	D₄	1	4	yes	—
38	C₇×#135	Q₈	1	4	yes	—
39	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₇×SD₁₆	C₂×C₄	1	2	yes	—
41	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
42	C₇×#131	—	2	8	no	—
43	C₇×#131	—	4	4	no	—
44	C₂×C₇×M₁₆	—	2	4	no	—
45	C₂×C₇×M₁₆	C₂³	1	4	yes	—
46	C₂²×C₇×C₈	—	2	4	no	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	2	yes	—
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
51	C₄×C₇×Q₈	C₂×C₄	1	2	yes	—
52	C₄×C₇×D₄	—	2	2	no	—
53	C₄×C₇×D₄	—	2	2	no	—
54	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
55	C₄×C₇×D₄	C₂×C₄	1	2	yes	—
56	C₇×#117	—	2	2	no	—
57	C₇×#117	C₂³	1	2	yes	—
58	C₂×C₇×C₄⋊C₄	—	2	1	no	—
59	C₂×C₄²×C₇	—	2	2	no	—
60	C₂×C₄²×C₇	C₂³	1	2	yes	—
61	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
62	C₇×#108	—	2	4	no	—
63	C₇×#108	—	4	2	no	—
64	C₇×#107	C₂×C₄	1	1	yes	characteristic
65	C₇×#107	C₂×C₄	1	1	yes	characteristic
66	C₇×#106	C₂×C₄	1	2	yes	—
67	C₇×C₄⋊C₈	—	2	4	no	—
68	C₇×C₄⋊C₈	—	2	4	no	—
69	C₇×C₄⋊C₈	—	2	2	no	—
70	C₇×C₄⋊C₈	—	2	2	no	—
71	C₇×C₄⋊C₈	D₄	1	2	yes	—
72	C₇×C₄⋊C₈	D₄	1	2	yes	—
73	C₇×#104	—	2	8	no	—
74	C₇×#103	C₂×C₄	1	2	yes	—
75	C₇×#103	C₂×C₄	1	2	yes	—
76	C₇×#102	C₂×C₄	1	2	yes	—
77	C₇×#102	C₂×C₄	1	2	yes	—
78	C₇×#97	—	2	4	no	—
79	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
80	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₇×C₈	C₂×C₄	1	1	yes	characteristic
83	C₇×#95	—	2	1	no	—
84	C₂×#444	C₂×C₇	1	2	yes	—
85	C₄×#135	C₂×C₇	1	1	yes	characteristic
86	#2906	C₂×C₇	1	2	yes	complemented
87	#1946	C₂×C₇	1	2	yes	complemented
88	#1866	C₂×C₇	1	4	yes	complemented
89	#1848	C₂×C₇	1	1	yes	characteristic, complemented
90	#1806	C₂×C₇	1	2	yes	complemented
91	#1770	C₂×C₇	1	1	yes	characteristic, complemented
92	C₇×#41	—	2	2	no	—
93	C₇×#41	—	2	2	no	—
94	C₇×#41	C₂×D₄	1	4	yes	—
95	C₇×#41	C₂×Q₈	1	4	yes	—
96	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
97	C₂×C₇×D₄	—	2	2	no	—
98	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇	—	2	2	no	—
100	C₂²×C₄×C₇	—	2	2	no	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	2	no	—
103	C₂²×C₄×C₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
106	C₇×Q₁₆	C₄⋊C₄	1	4	yes	complemented
107	C₇×SD₁₆	C₄⋊C₄	1	8	yes	complemented
108	C₇×D₈	C₄⋊C₄	1	4	yes	complemented
109	C₇×M₁₆	—	2	4	no	—
110	C₇×M₁₆	—	2	4	no	—
111	C₇×M₁₆	—	4	8	no	—
112	C₂×C₇×C₈	—	2	2	no	—
113	C₂×C₇×C₈	—	2	1	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	—	2	1	no	—
116	C₂×C₇×C₈	—	2	4	no	—
117	C₂×C₇×C₈	—	4	8	no	—
118	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇×C₈	C₂×D₄	1	4	yes	—
123	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
124	C₂×C₇×C₈	C₂×Q₈	1	2	yes	—
125	C₇×C₄⋊C₄	—	2	2	no	—
126	C₇×C₄⋊C₄	—	2	2	no	—
127	C₇×C₄⋊C₄	—	4	2	no	—
128	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₇×C₄⋊C₄	C₂²×C₄	1	2	yes	—
130	C₇×C₂²⋊C₄	—	2	2	no	—
131	C₇×C₂²⋊C₄	—	2	2	no	—
132	C₇×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₇	—	2	2	no	—
134	C₄²×C₇	—	2	2	no	—
135	C₄²×C₇	—	2	2	no	—
136	C₄²×C₇	—	2	2	no	—
137	C₄²×C₇	—	2	2	no	—
138	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
142	C₂×#135	C₂²×C₇	1	1	yes	characteristic
143	C₂×#131	C₂²×C₇	1	4	yes	—
144	C₄×#41	C₂²×C₇	1	2	yes	—
145	#444	—	2	8	no	—
146	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
147	C₄×Q₁₆	C₄×C₇	1	1	yes	characteristic, complemented
148	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
149	C₄×SD₁₆	C₄×C₇	1	2	yes	complemented
150	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
151	C₄×D₈	C₄×C₇	1	1	yes	characteristic, complemented
152	C₂×#108	C₂²×C₇	1	2	yes	—
153	C₂×#108	C₂²×C₇	1	2	yes	—
154	#427	C₂²×C₇	1	1	yes	characteristic
155	#424	—	2	4	no	—
156	#424	C₂²×C₇	1	4	yes	—
157	#423	—	2	2	no	—
158	#423	C₂²×C₇	1	2	yes	—
159	C₂×C₄⋊C₈	—	2	2	no	—
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×#104	C₂²×C₇	1	4	yes	—
162	#416	C₂²×C₇	1	2	yes	—
163	C₂×#97	C₂²×C₇	1	2	yes	—
164	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
165	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
166	#339	C₂²×C₇	1	4	yes	—
167	#336	C₂²×C₇	1	2	yes	—
168	C₂³×C₇	—	2	2	no	—
169	C₂³×C₇	C₂×#41	1	1	yes	characteristic
170	C₇×Q₈	—	2	2	no	—
171	C₇×Q₈	C₂×C₄⋊C₄	1	4	yes	—
172	C₇×D₄	—	2	4	no	—
173	C₇×D₄	—	2	4	no	—
174	C₇×D₄	—	2	2	no	—
175	C₇×D₄	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	4	no	—
178	C₂×C₄×C₇	—	2	4	no	—
179	C₂×C₄×C₇	—	2	2	no	—
180	C₂×C₄×C₇	—	2	2	no	—
181	C₂×C₄×C₇	—	2	2	no	—
182	C₂×C₄×C₇	—	4	1	no	—
183	C₂×C₄×C₇	—	4	4	no	—
184	C₂×C₄×C₇	—	4	2	no	—
185	C₂×C₄×C₇	—	4	2	no	—
186	C₂×C₄×C₇	—	4	2	no	—
187	C₂×C₄×C₇	—	8	2	no	—
188	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₇	2₋¹⁺⁴	1	1	yes	characteristic
198	C₇×C₈	—	2	1	no	—
199	C₇×C₈	—	2	1	no	—
200	C₇×C₈	—	2	4	no	—
201	C₇×C₈	—	4	4	no	—
202	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
203	C₇×C₈	C₂×C₄⋊C₄	1	2	yes	—
204	C₂×#41	C₂³×C₇	1	2	yes	—
205	#135	C₇×D₄	1	4	yes	—
206	#135	C₇×Q₈	1	4	yes	—
207	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
208	C₂×SD₁₆	C₂×C₄×C₇	1	2	yes	—
209	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
210	#131	—	2	8	no	—
211	#131	—	4	4	no	—
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	C₂³×C₇	1	4	yes	—
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
216	C₂²×C₈	C₂³×C₇	1	2	yes	—
217	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
218	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
219	C₄×Q₈	C₂×C₄×C₇	1	2	yes	—
220	C₄×D₄	—	2	2	no	—
221	C₄×D₄	—	2	2	no	—
222	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
223	C₄×D₄	C₂×C₄×C₇	1	2	yes	—
224	#117	—	2	2	no	—
225	#117	C₂³×C₇	1	2	yes	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	C₂³×C₇	1	2	yes	—
229	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
230	#108	—	2	4	no	—
231	#108	—	4	2	no	—
232	#107	C₂×C₄×C₇	1	1	yes	characteristic
233	#107	C₂×C₄×C₇	1	1	yes	characteristic
234	#106	C₂×C₄×C₇	1	2	yes	—
235	C₄⋊C₈	—	2	4	no	—
236	C₄⋊C₈	—	2	4	no	—
237	C₄⋊C₈	—	2	2	no	—
238	C₄⋊C₈	—	2	2	no	—
239	C₄⋊C₈	C₇×D₄	1	2	yes	—
240	C₄⋊C₈	C₇×D₄	1	2	yes	—
241	#104	—	2	8	no	—
242	#103	C₂×C₄×C₇	1	2	yes	—
243	#103	C₂×C₄×C₇	1	2	yes	—
244	#102	C₂×C₄×C₇	1	2	yes	—
245	#102	C₂×C₄×C₇	1	2	yes	—
246	#97	—	2	4	no	—
247	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
248	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
249	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
250	C₄×C₈	C₂×C₄×C₇	1	1	yes	characteristic
251	#95	—	2	1	no	—
252	C₂²×C₇	—	2	1	no	—
253	C₂²×C₇	—	2	1	no	—
254	C₂²×C₇	—	2	4	no	—
255	C₂²×C₇	—	4	2	no	—
256	C₂²×C₇	—	4	2	no	—
257	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₇	#547	1	1	yes	characteristic
259	C₂²×C₇	#554	1	1	yes	characteristic
260	C₄×C₇	—	2	4	no	—
261	C₄×C₇	—	2	1	no	—
262	C₄×C₇	—	2	1	no	—
263	C₄×C₇	—	2	1	no	—
264	C₄×C₇	—	4	2	no	—
265	C₄×C₇	—	4	2	no	—
266	C₄×C₇	—	8	2	no	—
267	C₄×C₇	#444	1	2	yes	complemented
268	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₄×C₇	#520	1	1	yes	characteristic
270	C₄×C₇	D₄²	1	1	yes	characteristic
271	C₄×C₇	D₄×Q₈	1	1	yes	characteristic
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	#41	C₂×C₇×D₄	1	4	yes	—
275	#41	C₂×C₇×Q₈	1	4	yes	—
276	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	C₇×#41	1	1	yes	characteristic
284	C₂²×C₄	C₇×#41	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
286	Q₁₆	C₇×C₄⋊C₄	1	4	yes	complemented
287	SD₁₆	C₇×C₄⋊C₄	1	8	yes	complemented
288	D₈	C₇×C₄⋊C₄	1	4	yes	complemented
289	M₁₆	—	2	4	no	—
290	M₁₆	—	2	4	no	—
291	M₁₆	—	4	8	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	8	no	—
298	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
299	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
300	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
302	C₂×C₈	C₂×C₇×D₄	1	4	yes	—
303	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
304	C₂×C₈	C₂×C₇×Q₈	1	2	yes	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
309	C₄⋊C₄	C₂²×C₄×C₇	1	2	yes	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
319	C₄²	C₂²×C₄×C₇	1	1	yes	characteristic
320	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
321	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
322	C₂×C₇	—	2	1	no	—
323	C₂×C₇	—	2	1	no	—
324	C₂×C₇	—	4	4	no	—
325	C₂×C₇	D₄×C₄⋊C₄	1	1	yes	characteristic
326	C₂×C₇	C₂×#444	1	1	yes	characteristic
327	C₂×C₇	#2957	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	C₂×C₇×#41	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	C₂×C₇×C₄⋊C₄	1	4	yes	—
332	D₄	—	2	4	no	—
333	D₄	—	2	4	no	—
334	D₄	—	2	2	no	—
335	D₄	C₂×C₇×C₄⋊C₄	1	4	yes	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
349	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
350	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
351	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
352	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
355	C₂×C₄	C₂²×C₇×Q₈	1	1	yes	characteristic
356	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄	C₇×2₋¹⁺⁴	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	4	no	—
361	C₈	—	4	4	no	—
362	C₈	C₂×C₇×C₄⋊C₄	1	2	yes	—
363	C₈	C₂×C₇×C₄⋊C₄	1	2	yes	—
364	C₇	#22686	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
371	C₂²	C₇×#547	1	1	yes	characteristic
372	C₂²	C₇×#554	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₇×#444	1	2	yes	complemented
381	C₄	C₂²×C₇×C₄⋊C₄	1	1	yes	characteristic
382	C₄	C₇×#520	1	1	yes	characteristic
383	C₄	C₇×D₄²	1	1	yes	characteristic
384	C₄	C₇×D₄×Q₈	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	4	4	no	—
388	C₂	C₇×D₄×C₄⋊C₄	1	1	yes	characteristic
389	C₂	C₂×C₇×#444	1	1	yes	characteristic
390	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₂×C₇×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#2906	C₂	semidirect
4. C₇×#1946	C₂	semidirect
5. C₇×#1866	C₂	semidirect
6. C₇×#1848	C₂	semidirect
7. C₇×#1806	C₂	semidirect
8. C₇×#1770	C₂	semidirect
13. C₄×C₇×Q₁₆	C₄	semidirect
14. C₄×C₇×Q₁₆	C₄	semidirect
15. C₄×C₇×SD₁₆	C₄	semidirect
16. C₄×C₇×SD₁₆	C₄	semidirect
17. C₄×C₇×D₈	C₄	semidirect
18. C₄×C₇×D₈	C₄	semidirect
35. #22686	C₇	direct (N × H)
86. #2906	C₂×C₇	semidirect
87. #1946	C₂×C₇	semidirect
88. #1866	C₂×C₇	semidirect
89. #1848	C₂×C₇	semidirect
90. #1806	C₂×C₇	semidirect
91. #1770	C₂×C₇	semidirect
106. C₇×Q₁₆	C₄⋊C₄	semidirect
107. C₇×SD₁₆	C₄⋊C₄	semidirect
108. C₇×D₈	C₄⋊C₄	semidirect
146. C₄×Q₁₆	C₄×C₇	semidirect
147. C₄×Q₁₆	C₄×C₇	semidirect
148. C₄×SD₁₆	C₄×C₇	semidirect
149. C₄×SD₁₆	C₄×C₇	semidirect
150. C₄×D₈	C₄×C₇	semidirect
151. C₄×D₈	C₄×C₇	semidirect
267. C₄×C₇	#444	semidirect
286. Q₁₆	C₇×C₄⋊C₄	semidirect
287. SD₁₆	C₇×C₄⋊C₄	semidirect
288. D₈	C₇×C₄⋊C₄	semidirect
364. C₇	#22686	direct (N × H)
380. C₄	C₇×#444	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#444	2
C₄×C₇×#135	2
C₇×#2906	2
C₇×#1946	2
C₇×#1866	2
C₇×#1848	2
C₇×#1806	2
C₇×#1770	2
#22686	7

Subgroups — C7×#22686 #13199902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22686 #13199902