Subgroups — C₂×C₇×#3389 #13238579

Order 1792.

1898 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#554	C₂	1	2	yes	maximal, complemented
2	C₇×#3389	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#501	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#478	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×#474	C₂	1	2	yes	maximal, complemented
8	C₂×C₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#442	C₂	1	2	yes	maximal
10	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
12	C₇×#554	—	2	8	no	—
13	C₇×#554	C₂²	1	16	yes	complemented
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#125	C₂²	1	2	yes	—
16	C₂×C₇×#125	C₂²	1	2	yes	—
17	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
18	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
22	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
23	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
24	C₂²×C₇×C₄⋊C₄	—	2	2	no	—
25	C₇×#501	C₂²	1	16	yes	complemented
26	C₇×#499	C₂²	1	8	yes	complemented
27	C₇×#478	C₂²	1	16	yes	complemented
28	C₇×#478	C₂²	1	16	yes	complemented
29	C₇×#474	C₂²	1	16	yes	complemented
30	C₇×#446	C₂²	1	8	yes	complemented
31	C₇×#442	C₂²	1	16	yes	—
32	C₄×C₇×D₈	C₂²	1	8	yes	—
33	C₂×C₇×#107	C₂²	1	1	yes	characteristic
34	C₂×C₇×#107	C₂²	1	1	yes	characteristic
35	C₂×C₇×#107	C₂²	1	1	yes	characteristic
36	C₂×C₇×#107	C₂²	1	2	yes	—
37	C₂×C₇×#106	C₂²	1	2	yes	—
38	C₂×C₇×#106	C₂²	1	2	yes	—
39	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₇×#102	C₂²	1	2	yes	—
42	C₂×C₇×#102	C₂²	1	2	yes	—
43	C₂×C₇×#102	C₂²	1	2	yes	—
44	C₂×C₇×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
46	C₂×#3389	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₇×Q₈	—	2	2	no	—
48	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
49	C₂²×C₇×D₄	C₂³	1	2	yes	—
50	C₂³×C₄×C₇	—	2	2	no	—
51	C₂³×C₄×C₇	—	2	2	no	—
52	C₂³×C₄×C₇	—	2	2	no	—
53	C₂×C₇×D₈	Q₈	1	8	yes	complemented
54	C₂×C₇×D₈	C₂³	1	4	yes	—
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₇×C₈	C₂³	1	2	yes	—
57	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
58	C₇×C₄⋊Q₈	—	2	4	no	—
59	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
60	C₇×#125	—	2	4	no	—
61	C₇×#125	—	2	4	no	—
62	C₇×#125	C₂³	1	8	yes	—
63	C₇×#125	C₂³	1	8	yes	—
64	C₇×C₂²⋊Q₈	—	2	16	no	—
65	C₇×C₂²⋊Q₈	—	2	16	no	—
66	C₇×C₂²⋊Q₈	—	2	16	no	—
67	C₄×C₇×Q₈	D₄	1	4	yes	—
68	C₄×C₇×Q₈	C₂³	1	4	yes	—
69	C₄×C₇×D₄	—	2	4	no	—
70	C₄×C₇×D₄	—	2	4	no	—
71	C₄×C₇×D₄	—	2	4	no	—
72	C₄×C₇×D₄	C₂³	1	8	yes	—
73	C₄×C₇×D₄	C₂³	1	8	yes	—
74	C₄×C₇×D₄	C₂³	1	8	yes	—
75	C₂×C₇×C₄⋊C₄	—	2	2	no	—
76	C₂×C₇×C₄⋊C₄	—	2	2	no	—
77	C₂×C₇×C₄⋊C₄	—	2	2	no	—
78	C₂×C₇×C₄⋊C₄	—	2	2	no	—
79	C₂×C₇×C₄⋊C₄	—	2	2	no	—
80	C₂×C₇×C₄⋊C₄	—	2	16	no	—
81	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
82	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
83	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇	C₂³	1	2	yes	—
91	C₇×#107	C₂³	1	4	yes	—
92	C₇×#107	C₂³	1	8	yes	—
93	C₇×#107	C₂³	1	4	yes	—
94	C₇×#107	C₂³	1	4	yes	—
95	C₇×#106	C₂³	1	8	yes	—
96	C₇×#106	C₂³	1	8	yes	—
97	C₇×C₄⋊C₈	C₂³	1	8	yes	—
98	C₇×C₄⋊C₈	C₂³	1	4	yes	—
99	C₇×#102	C₂³	1	8	yes	—
100	C₇×#102	C₂³	1	8	yes	—
101	C₇×#102	C₂³	1	8	yes	—
102	C₇×#97	C₂³	1	8	yes	—
103	C₄×C₇×C₈	C₂³	1	4	yes	—
104	C₂×#554	C₂×C₇	1	2	yes	complemented
105	#3389	C₂×C₇	1	16	yes	direct product factor
106	C₂×#501	C₂×C₇	1	2	yes	complemented
107	C₂×#499	C₂×C₇	1	1	yes	characteristic, complemented
108	C₂×#478	C₂×C₇	1	2	yes	complemented
109	C₂×#478	C₂×C₇	1	2	yes	complemented
110	C₂×#474	C₂×C₇	1	2	yes	complemented
111	C₂×#446	C₂×C₇	1	1	yes	characteristic, complemented
112	C₂×#442	C₂×C₇	1	2	yes	—
113	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
114	C₂⁴×C₇	—	2	2	no	—
115	C₂×C₇×Q₈	—	2	8	no	—
116	C₂×C₇×Q₈	—	4	2	no	—
117	C₂×C₇×Q₈	—	8	4	no	—
118	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
119	C₂×C₇×D₄	—	2	2	no	—
120	C₂×C₇×D₄	—	2	4	no	—
121	C₂×C₇×D₄	C₂×Q₈	1	8	yes	—
122	C₂×C₇×D₄	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₇	—	2	2	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	2	no	—
126	C₂²×C₄×C₇	—	2	8	no	—
127	C₂²×C₄×C₇	—	2	8	no	—
128	C₂²×C₄×C₇	—	2	8	no	—
129	C₂²×C₄×C₇	—	4	8	no	—
130	C₂²×C₄×C₇	—	8	4	no	—
131	C₂²×C₄×C₇	—	8	4	no	—
132	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
137	C₇×D₈	C₂×Q₈	1	16	yes	complemented
138	C₂×C₇×C₈	—	2	2	no	—
139	C₂×C₇×C₈	—	2	4	no	—
140	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
141	C₂×C₇×C₈	C₂⁴	1	2	yes	—
142	C₂×C₇×C₈	C₂⁴	1	4	yes	—
143	C₂×C₇×C₈	C₂⁴	1	2	yes	—
144	C₇×C₄⋊C₄	—	2	8	no	—
145	C₇×C₄⋊C₄	—	2	8	no	—
146	C₇×C₄⋊C₄	—	2	8	no	—
147	C₇×C₄⋊C₄	—	2	8	no	—
148	C₇×C₄⋊C₄	—	2	8	no	—
149	C₇×C₄⋊C₄	—	2	2	no	—
150	C₇×C₄⋊C₄	—	2	2	no	—
151	C₇×C₄⋊C₄	—	2	2	no	—
152	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
153	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
154	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
155	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
156	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
157	C₇×C₂²⋊C₄	—	2	8	no	—
158	C₇×C₂²⋊C₄	—	2	8	no	—
159	C₇×C₂²⋊C₄	—	2	8	no	—
160	C₄²×C₇	C₂×D₄	1	2	yes	—
161	C₄²×C₇	C₂×D₄	1	4	yes	—
162	C₄²×C₇	C₂⁴	1	2	yes	—
163	C₄²×C₇	C₂⁴	1	4	yes	—
164	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
165	#554	—	2	8	no	—
166	#554	C₂²×C₇	1	16	yes	complemented
167	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
168	C₂×#125	C₂²×C₇	1	2	yes	—
169	C₂×#125	C₂²×C₇	1	2	yes	—
170	C₂×C₂²⋊Q₈	—	2	2	no	—
171	C₂×C₂²⋊Q₈	—	2	2	no	—
172	C₂×C₂²⋊Q₈	—	2	2	no	—
173	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
174	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
175	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
176	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
177	C₂²×C₄⋊C₄	—	2	2	no	—
178	#501	C₂²×C₇	1	16	yes	complemented
179	#499	C₂²×C₇	1	8	yes	complemented
180	#478	C₂²×C₇	1	16	yes	complemented
181	#478	C₂²×C₇	1	16	yes	complemented
182	#474	C₂²×C₇	1	16	yes	complemented
183	#446	C₂²×C₇	1	8	yes	complemented
184	#442	C₂²×C₇	1	16	yes	—
185	C₄×D₈	C₂²×C₇	1	8	yes	—
186	C₂×#107	C₂²×C₇	1	1	yes	characteristic
187	C₂×#107	C₂²×C₇	1	2	yes	—
188	C₂×#107	C₂²×C₇	1	1	yes	characteristic
189	C₂×#107	C₂²×C₇	1	1	yes	characteristic
190	C₂×#106	C₂²×C₇	1	2	yes	—
191	C₂×#106	C₂²×C₇	1	2	yes	—
192	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
193	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
194	C₂×#102	C₂²×C₇	1	2	yes	—
195	C₂×#102	C₂²×C₇	1	2	yes	—
196	C₂×#102	C₂²×C₇	1	2	yes	—
197	C₂×#97	C₂²×C₇	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
199	C₂³×C₇	—	2	8	no	—
200	C₂³×C₇	—	2	4	no	—
201	C₂³×C₇	—	4	4	no	—
202	C₂³×C₇	—	4	4	no	—
203	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
204	C₇×Q₈	—	4	4	no	—
205	C₇×Q₈	—	8	8	no	—
206	C₇×D₄	—	2	8	no	—
207	C₇×D₄	—	2	4	no	—
208	C₇×D₄	C₂²×Q₈	1	8	yes	—
209	C₂×C₄×C₇	—	2	4	no	—
210	C₂×C₄×C₇	—	2	2	no	—
211	C₂×C₄×C₇	—	2	2	no	—
212	C₂×C₄×C₇	—	2	4	no	—
213	C₂×C₄×C₇	—	2	4	no	—
214	C₂×C₄×C₇	—	2	4	no	—
215	C₂×C₄×C₇	—	2	4	no	—
216	C₂×C₄×C₇	—	4	16	no	—
217	C₂×C₄×C₇	—	4	4	no	—
218	C₂×C₄×C₇	—	4	4	no	—
219	C₂×C₄×C₇	—	4	4	no	—
220	C₂×C₄×C₇	—	8	8	no	—
221	C₂×C₄×C₇	—	8	8	no	—
222	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
224	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
225	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
226	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
228	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
229	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
230	C₇×C₈	—	2	2	no	—
231	C₇×C₈	—	2	4	no	—
232	C₇×C₈	C₂²×Q₈	1	4	yes	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
235	C₂²×D₄	C₂³×C₇	1	2	yes	—
236	C₂³×C₄	—	2	2	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂×D₈	C₇×Q₈	1	8	yes	complemented
240	C₂×D₈	C₂³×C₇	1	4	yes	—
241	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇	1	2	yes	—
243	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	4	no	—
245	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
246	#125	—	2	4	no	—
247	#125	—	2	4	no	—
248	#125	C₂³×C₇	1	8	yes	—
249	#125	C₂³×C₇	1	8	yes	—
250	C₂²⋊Q₈	—	2	16	no	—
251	C₂²⋊Q₈	—	2	16	no	—
252	C₂²⋊Q₈	—	2	16	no	—
253	C₄×Q₈	C₇×D₄	1	4	yes	—
254	C₄×Q₈	C₂³×C₇	1	4	yes	—
255	C₄×D₄	—	2	4	no	—
256	C₄×D₄	—	2	4	no	—
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	C₂³×C₇	1	8	yes	—
259	C₄×D₄	C₂³×C₇	1	8	yes	—
260	C₄×D₄	C₂³×C₇	1	8	yes	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	16	no	—
267	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
268	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₇	1	2	yes	—
277	#107	C₂³×C₇	1	4	yes	—
278	#107	C₂³×C₇	1	4	yes	—
279	#107	C₂³×C₇	1	8	yes	—
280	#107	C₂³×C₇	1	4	yes	—
281	#106	C₂³×C₇	1	8	yes	—
282	#106	C₂³×C₇	1	8	yes	—
283	C₄⋊C₈	C₂³×C₇	1	8	yes	—
284	C₄⋊C₈	C₂³×C₇	1	4	yes	—
285	#102	C₂³×C₇	1	8	yes	—
286	#102	C₂³×C₇	1	8	yes	—
287	#102	C₂³×C₇	1	8	yes	—
288	#97	C₂³×C₇	1	8	yes	—
289	C₄×C₈	C₂³×C₇	1	4	yes	—
290	C₂²×C₇	—	2	8	no	—
291	C₂²×C₇	—	4	16	no	—
292	C₂²×C₇	—	4	4	no	—
293	C₂²×C₇	—	4	4	no	—
294	C₂²×C₇	D₄×Q₈	1	2	yes	—
295	C₂²×C₇	#575	1	2	yes	—
296	C₂²×C₇	#576	1	2	yes	—
297	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
298	C₄×C₇	—	2	4	no	—
299	C₄×C₇	—	2	2	no	—
300	C₄×C₇	—	2	2	no	—
301	C₄×C₇	—	2	4	no	—
302	C₄×C₇	—	4	4	no	—
303	C₄×C₇	—	4	4	no	—
304	C₄×C₇	—	4	4	no	—
305	C₄×C₇	D₄×Q₈	1	2	yes	—
306	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
307	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
308	C₂⁴	—	2	2	no	—
309	C₂×Q₈	—	2	8	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	8	4	no	—
312	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	C₂×C₇×Q₈	1	8	yes	—
316	C₂×D₄	C₂⁴×C₇	1	4	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	8	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	4	8	no	—
324	C₂²×C₄	—	8	4	no	—
325	C₂²×C₄	—	8	4	no	—
326	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
328	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
329	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
330	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
331	D₈	C₂×C₇×Q₈	1	16	yes	complemented
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
335	C₂×C₈	C₂⁴×C₇	1	2	yes	—
336	C₂×C₈	C₂⁴×C₇	1	4	yes	—
337	C₂×C₈	C₂⁴×C₇	1	2	yes	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	2	8	no	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
347	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
348	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
349	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
350	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
351	C₂²⋊C₄	—	2	8	no	—
352	C₂²⋊C₄	—	2	8	no	—
353	C₂²⋊C₄	—	2	8	no	—
354	C₄²	C₂×C₇×D₄	1	2	yes	—
355	C₄²	C₂×C₇×D₄	1	4	yes	—
356	C₄²	C₂⁴×C₇	1	2	yes	—
357	C₄²	C₂⁴×C₇	1	4	yes	—
358	C₂×C₇	—	4	8	no	—
359	C₂×C₇	#3389	1	4	yes	direct product factor
360	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
361	C₂×C₇	C₂×#575	1	1	yes	characteristic
362	C₂×C₇	C₂×#576	1	1	yes	characteristic
363	C₂³	—	2	4	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
368	Q₈	—	4	4	no	—
369	Q₈	—	8	8	no	—
370	D₄	—	2	4	no	—
371	D₄	—	2	8	no	—
372	D₄	C₂²×C₇×Q₈	1	8	yes	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	16	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	8	8	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
387	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
388	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
389	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
390	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
392	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
393	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	2	4	no	—
396	C₈	C₂²×C₇×Q₈	1	4	yes	—
397	C₇	C₂×#3389	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	—	2	8	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	16	no	—
402	C₂²	C₇×D₄×Q₈	1	2	yes	—
403	C₂²	C₇×#575	1	2	yes	—
404	C₂²	C₇×#576	1	2	yes	—
405	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
406	C₄	—	2	4	no	—
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	4	no	—
413	C₄	C₇×D₄×Q₈	1	2	yes	—
414	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
415	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂	—	4	8	no	—
417	C₂	C₇×#3389	1	4	yes	direct product factor
418	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
419	C₂	C₂×C₇×#575	1	1	yes	characteristic
420	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#554	C₂	semidirect
2. C₇×#3389	C₂	direct (N × H)
3. C₂×C₇×#501	C₂	semidirect
4. C₂×C₇×#499	C₂	semidirect
5. C₂×C₇×#478	C₂	semidirect
6. C₂×C₇×#478	C₂	semidirect
7. C₂×C₇×#474	C₂	semidirect
8. C₂×C₇×#446	C₂	semidirect
13. C₇×#554	C₂²	semidirect
25. C₇×#501	C₂²	semidirect
26. C₇×#499	C₂²	semidirect
27. C₇×#478	C₂²	semidirect
28. C₇×#478	C₂²	semidirect
29. C₇×#474	C₂²	semidirect
30. C₇×#446	C₂²	semidirect
46. C₂×#3389	C₇	direct (N × H)
53. C₂×C₇×D₈	Q₈	semidirect
104. C₂×#554	C₂×C₇	semidirect
105. #3389	C₂×C₇	direct (N × H)
106. C₂×#501	C₂×C₇	semidirect
107. C₂×#499	C₂×C₇	semidirect
108. C₂×#478	C₂×C₇	semidirect
109. C₂×#478	C₂×C₇	semidirect
110. C₂×#474	C₂×C₇	semidirect
111. C₂×#446	C₂×C₇	semidirect
137. C₇×D₈	C₂×Q₈	semidirect
166. #554	C₂²×C₇	semidirect
178. #501	C₂²×C₇	semidirect
179. #499	C₂²×C₇	semidirect
180. #478	C₂²×C₇	semidirect
181. #478	C₂²×C₇	semidirect
182. #474	C₂²×C₇	semidirect
183. #446	C₂²×C₇	semidirect
239. C₂×D₈	C₇×Q₈	semidirect
331. D₈	C₂×C₇×Q₈	semidirect
359. C₂×C₇	#3389	direct (N × H)
397. C₇	C₂×#3389	direct (N × H)
417. C₂	C₇×#3389	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×#554	2
C₇×#3389	2
C₂×C₇×#501	2
C₂×C₇×#499	2
C₂×C₇×#478	2
C₂×C₇×#474	2
C₂×C₇×#446	2
C₂×C₇×#442	2
C₂×C₄×C₇×D₈	2
C₂×#3389	7

Subgroups — C2×C7×#3389 #13238579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3389 #13238579