Subgroups — C₂×C₇×#3380 #13238569

Order 1792.

1918 conjugacy classes of subgroups.

The subgroup lattice has 356 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×#3380	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#499	C₂	1	2	yes	maximal, complemented
5	C₂×C₇×#478	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal
10	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
11	C₇×#554	—	2	8	no	—
12	C₇×#554	C₂²	1	16	yes	complemented
13	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₇×#125	C₂²	1	4	yes	—
15	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
16	C₂×C₇×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
19	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
20	C₂²×C₇×C₄⋊C₄	—	2	2	no	—
21	C₇×#500	C₂²	1	8	yes	complemented
22	C₇×#499	C₂²	1	16	yes	complemented
23	C₇×#478	C₂²	1	32	yes	complemented
24	C₇×#476	C₂²	1	16	yes	complemented
25	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
26	C₄×C₇×D₈	C₂²	1	16	yes	—
27	C₄×C₇×D₈	C₂²	1	8	yes	—
28	C₂×C₇×#107	C₂²	1	1	yes	characteristic
29	C₂×C₇×#107	C₂²	1	2	yes	—
30	C₂×C₇×#107	C₂²	1	2	yes	—
31	C₂×C₇×#106	C₂²	1	4	yes	—
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₇×#102	C₂²	1	4	yes	—
35	C₂×C₇×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×#3380	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×Q₈	—	2	2	no	—
40	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
41	C₂²×C₇×D₄	C₂³	1	2	yes	—
42	C₂³×C₄×C₇	—	2	2	no	—
43	C₂³×C₄×C₇	—	2	4	no	—
44	C₂×C₇×D₈	Q₈	1	8	yes	complemented
45	C₂×C₇×D₈	C₂³	1	4	yes	—
46	C₂²×C₇×C₈	C₂³	1	2	yes	—
47	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₇×C₄⋊Q₈	—	2	4	no	—
50	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
51	C₇×#125	—	2	8	no	—
52	C₇×#125	C₂³	1	16	yes	—
53	C₇×C₂²⋊Q₈	—	2	16	no	—
54	C₇×C₂²⋊Q₈	—	2	32	no	—
55	C₄×C₇×Q₈	D₄	1	4	yes	—
56	C₄×C₇×Q₈	C₂³	1	4	yes	—
57	C₄×C₇×D₄	—	2	8	no	—
58	C₄×C₇×D₄	—	2	4	no	—
59	C₄×C₇×D₄	C₂³	1	8	yes	—
60	C₄×C₇×D₄	C₂³	1	16	yes	—
61	C₂×C₇×C₄⋊C₄	—	2	4	no	—
62	C₂×C₇×C₄⋊C₄	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	—	2	4	no	—
64	C₂×C₇×C₄⋊C₄	—	2	16	no	—
65	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₄²×C₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
73	C₇×#107	C₂³	1	8	yes	—
74	C₇×#107	C₂³	1	4	yes	—
75	C₇×#107	C₂³	1	8	yes	—
76	C₇×#106	C₂³	1	16	yes	—
77	C₇×C₄⋊C₈	C₂³	1	4	yes	—
78	C₇×C₄⋊C₈	C₂³	1	8	yes	—
79	C₇×#102	C₂³	1	16	yes	—
80	C₇×#102	C₂³	1	8	yes	—
81	C₄×C₇×C₈	C₂³	1	8	yes	—
82	C₄×C₇×C₈	C₂³	1	4	yes	—
83	C₂×#554	C₂×C₇	1	2	yes	complemented
84	#3380	C₂×C₇	1	16	yes	direct product factor
85	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
86	C₂×#499	C₂×C₇	1	2	yes	complemented
87	C₂×#478	C₂×C₇	1	4	yes	complemented
88	C₂×#476	C₂×C₇	1	2	yes	complemented
89	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂×C₄×D₈	C₂×C₇	1	2	yes	—
91	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
92	C₂⁴×C₇	—	2	2	no	—
93	C₂×C₇×Q₈	—	2	4	no	—
94	C₂×C₇×Q₈	—	2	8	no	—
95	C₂×C₇×Q₈	—	8	4	no	—
96	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
97	C₂×C₇×D₄	—	2	2	no	—
98	C₂×C₇×D₄	—	2	4	no	—
99	C₂×C₇×D₄	C₂×Q₈	1	8	yes	—
100	C₂×C₇×D₄	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₇	—	2	2	no	—
102	C₂²×C₄×C₇	—	2	4	no	—
103	C₂²×C₄×C₇	—	2	8	no	—
104	C₂²×C₄×C₇	—	2	16	no	—
105	C₂²×C₄×C₇	—	4	8	no	—
106	C₂²×C₄×C₇	—	8	8	no	—
107	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
112	C₇×D₈	C₂×Q₈	1	16	yes	complemented
113	C₂×C₇×C₈	—	2	4	no	—
114	C₂×C₇×C₈	—	2	2	no	—
115	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
116	C₂×C₇×C₈	C₂⁴	1	4	yes	—
117	C₂×C₇×C₈	C₂⁴	1	2	yes	—
118	C₂×C₇×C₈	C₂⁴	1	2	yes	—
119	C₇×C₄⋊C₄	—	2	16	no	—
120	C₇×C₄⋊C₄	—	2	8	no	—
121	C₇×C₄⋊C₄	—	2	16	no	—
122	C₇×C₄⋊C₄	—	2	2	no	—
123	C₇×C₄⋊C₄	—	2	4	no	—
124	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
125	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
126	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
127	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
128	C₇×C₂²⋊C₄	—	2	8	no	—
129	C₇×C₂²⋊C₄	—	2	16	no	—
130	C₄²×C₇	C₂×D₄	1	4	yes	—
131	C₄²×C₇	C₂×D₄	1	2	yes	—
132	C₄²×C₇	C₂⁴	1	4	yes	—
133	C₄²×C₇	C₂⁴	1	2	yes	—
134	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
135	#554	—	2	8	no	—
136	#554	C₂²×C₇	1	16	yes	complemented
137	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
138	C₂×#125	C₂²×C₇	1	4	yes	—
139	C₂×C₂²⋊Q₈	—	2	2	no	—
140	C₂×C₂²⋊Q₈	—	2	4	no	—
141	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
142	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
143	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
144	C₂²×C₄⋊C₄	—	2	2	no	—
145	#500	C₂²×C₇	1	8	yes	complemented
146	#499	C₂²×C₇	1	16	yes	complemented
147	#478	C₂²×C₇	1	32	yes	complemented
148	#476	C₂²×C₇	1	16	yes	complemented
149	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
150	C₄×D₈	C₂²×C₇	1	16	yes	—
151	C₄×D₈	C₂²×C₇	1	8	yes	—
152	C₂×#107	C₂²×C₇	1	2	yes	—
153	C₂×#107	C₂²×C₇	1	1	yes	characteristic
154	C₂×#107	C₂²×C₇	1	2	yes	—
155	C₂×#106	C₂²×C₇	1	4	yes	—
156	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
157	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
158	C₂×#102	C₂²×C₇	1	2	yes	—
159	C₂×#102	C₂²×C₇	1	4	yes	—
160	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
161	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂³×C₇	—	2	8	no	—
163	C₂³×C₇	—	2	4	no	—
164	C₂³×C₇	—	4	4	no	—
165	C₂³×C₇	—	4	4	no	—
166	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
167	C₇×Q₈	—	2	8	no	—
168	C₇×Q₈	—	8	8	no	—
169	C₇×D₄	—	2	8	no	—
170	C₇×D₄	—	2	4	no	—
171	C₇×D₄	C₂²×Q₈	1	8	yes	—
172	C₂×C₄×C₇	—	2	4	no	—
173	C₂×C₄×C₇	—	2	4	no	—
174	C₂×C₄×C₇	—	2	2	no	—
175	C₂×C₄×C₇	—	2	4	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	4	4	no	—
178	C₂×C₄×C₇	—	4	8	no	—
179	C₂×C₄×C₇	—	4	16	no	—
180	C₂×C₄×C₇	—	8	16	no	—
181	C₂×C₄×C₇	#135	1	4	yes	—
182	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
183	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
185	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
188	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
189	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
190	C₇×C₈	—	2	4	no	—
191	C₇×C₈	—	2	2	no	—
192	C₇×C₈	C₂²×Q₈	1	4	yes	—
193	C₂²×Q₈	—	2	2	no	—
194	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
195	C₂²×D₄	C₂³×C₇	1	2	yes	—
196	C₂³×C₄	—	2	2	no	—
197	C₂³×C₄	—	2	4	no	—
198	C₂×D₈	C₇×Q₈	1	8	yes	complemented
199	C₂×D₈	C₂³×C₇	1	4	yes	—
200	C₂²×C₈	C₂³×C₇	1	2	yes	—
201	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
203	C₄⋊Q₈	—	2	4	no	—
204	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
205	#125	—	2	8	no	—
206	#125	C₂³×C₇	1	16	yes	—
207	C₂²⋊Q₈	—	2	16	no	—
208	C₂²⋊Q₈	—	2	32	no	—
209	C₄×Q₈	C₇×D₄	1	4	yes	—
210	C₄×Q₈	C₂³×C₇	1	4	yes	—
211	C₄×D₄	—	2	8	no	—
212	C₄×D₄	—	2	4	no	—
213	C₄×D₄	C₂³×C₇	1	8	yes	—
214	C₄×D₄	C₂³×C₇	1	16	yes	—
215	C₂×C₄⋊C₄	—	2	4	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	—	2	4	no	—
218	C₂×C₄⋊C₄	—	2	16	no	—
219	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
221	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
223	C₂×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₂²⋊C₄	—	2	4	no	—
225	C₂×C₄²	C₂³×C₇	1	2	yes	—
226	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
227	#107	C₂³×C₇	1	4	yes	—
228	#107	C₂³×C₇	1	8	yes	—
229	#107	C₂³×C₇	1	8	yes	—
230	#106	C₂³×C₇	1	16	yes	—
231	C₄⋊C₈	C₂³×C₇	1	4	yes	—
232	C₄⋊C₈	C₂³×C₇	1	8	yes	—
233	#102	C₂³×C₇	1	16	yes	—
234	#102	C₂³×C₇	1	8	yes	—
235	C₄×C₈	C₂³×C₇	1	8	yes	—
236	C₄×C₈	C₂³×C₇	1	4	yes	—
237	C₂²×C₇	—	2	8	no	—
238	C₂²×C₇	—	4	16	no	—
239	C₂²×C₇	—	4	4	no	—
240	C₂²×C₇	—	4	4	no	—
241	C₂²×C₇	D₄×Q₈	1	2	yes	—
242	C₂²×C₇	C₂×#135	1	2	yes	—
243	C₂²×C₇	#576	1	2	yes	—
244	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₇	—	2	4	no	—
246	C₄×C₇	—	2	4	no	—
247	C₄×C₇	—	2	2	no	—
248	C₄×C₇	—	4	4	no	—
249	C₄×C₇	—	4	8	no	—
250	C₄×C₇	D₄×Q₈	1	2	yes	—
251	C₄×C₇	C₂×#135	1	4	yes	—
252	C₄×C₇	C₂³×Q₈	1	1	yes	characteristic
253	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₂⁴	—	2	2	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	8	no	—
257	C₂×Q₈	—	8	4	no	—
258	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	2	4	no	—
261	C₂×D₄	C₂×C₇×Q₈	1	8	yes	—
262	C₂×D₄	C₂⁴×C₇	1	4	yes	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	16	no	—
267	C₂²×C₄	—	4	8	no	—
268	C₂²×C₄	—	8	8	no	—
269	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
270	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
272	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
273	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
274	D₈	C₂×C₇×Q₈	1	16	yes	complemented
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×C₇×Q₈	1	4	yes	—
278	C₂×C₈	C₂⁴×C₇	1	4	yes	—
279	C₂×C₈	C₂⁴×C₇	1	2	yes	—
280	C₂×C₈	C₂⁴×C₇	1	2	yes	—
281	C₄⋊C₄	—	2	16	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	16	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
287	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
288	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
289	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
290	C₂²⋊C₄	—	2	8	no	—
291	C₂²⋊C₄	—	2	16	no	—
292	C₄²	C₂×C₇×D₄	1	4	yes	—
293	C₄²	C₂×C₇×D₄	1	2	yes	—
294	C₄²	C₂⁴×C₇	1	4	yes	—
295	C₄²	C₂⁴×C₇	1	2	yes	—
296	C₂×C₇	—	4	8	no	—
297	C₂×C₇	#3380	1	4	yes	direct product factor
298	C₂×C₇	C₂×D₄×Q₈	1	1	yes	characteristic
299	C₂×C₇	C₂²×#135	1	1	yes	characteristic
300	C₂×C₇	C₂×#576	1	1	yes	characteristic
301	C₂³	—	2	4	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	4	4	no	—
304	C₂³	—	4	4	no	—
305	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
306	Q₈	—	2	8	no	—
307	Q₈	—	8	8	no	—
308	D₄	—	2	4	no	—
309	D₄	—	2	8	no	—
310	D₄	C₂²×C₇×Q₈	1	8	yes	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	8	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	—	8	16	no	—
320	C₂×C₄	C₇×#135	1	4	yes	—
321	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
322	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
323	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
324	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
326	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
327	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
328	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	2	no	—
331	C₈	C₂²×C₇×Q₈	1	4	yes	—
332	C₇	C₂×#3380	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	16	no	—
337	C₂²	C₇×D₄×Q₈	1	2	yes	—
338	C₂²	C₂×C₇×#135	1	2	yes	—
339	C₂²	C₇×#576	1	2	yes	—
340	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	C₇×D₄×Q₈	1	2	yes	—
347	C₄	C₂×C₇×#135	1	4	yes	—
348	C₄	C₂³×C₇×Q₈	1	1	yes	characteristic
349	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
350	C₂	—	4	8	no	—
351	C₂	C₇×#3380	1	4	yes	direct product factor
352	C₂	C₂×C₇×D₄×Q₈	1	1	yes	characteristic
353	C₂	C₂²×C₇×#135	1	1	yes	characteristic
354	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×#3380	C₂	direct (N × H)
3. C₂×C₇×#500	C₂	semidirect
4. C₂×C₇×#499	C₂	semidirect
5. C₂×C₇×#478	C₂	semidirect
6. C₂×C₇×#476	C₂	semidirect
7. C₂×C₇×C₈×Q₈	C₂	semidirect
12. C₇×#554	C₂²	semidirect
21. C₇×#500	C₂²	semidirect
22. C₇×#499	C₂²	semidirect
23. C₇×#478	C₂²	semidirect
24. C₇×#476	C₂²	semidirect
25. C₇×C₈×Q₈	C₂²	semidirect
38. C₂×#3380	C₇	direct (N × H)
44. C₂×C₇×D₈	Q₈	semidirect
83. C₂×#554	C₂×C₇	semidirect
84. #3380	C₂×C₇	direct (N × H)
85. C₂×#500	C₂×C₇	semidirect
86. C₂×#499	C₂×C₇	semidirect
87. C₂×#478	C₂×C₇	semidirect
88. C₂×#476	C₂×C₇	semidirect
89. C₂×C₈×Q₈	C₂×C₇	semidirect
112. C₇×D₈	C₂×Q₈	semidirect
136. #554	C₂²×C₇	semidirect
145. #500	C₂²×C₇	semidirect
146. #499	C₂²×C₇	semidirect
147. #478	C₂²×C₇	semidirect
148. #476	C₂²×C₇	semidirect
149. C₈×Q₈	C₂²×C₇	semidirect
198. C₂×D₈	C₇×Q₈	semidirect
274. D₈	C₂×C₇×Q₈	semidirect
297. C₂×C₇	#3380	direct (N × H)
332. C₇	C₂×#3380	direct (N × H)
351. C₂	C₇×#3380	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×#3380	2
C₂×C₇×#500	2
C₂×C₇×#499	2
C₂×C₇×#478	2
C₂×C₇×#476	2
C₂×C₇×C₈×Q₈	2
C₂×C₄×C₇×D₈	2
C₂×#3380	7

Subgroups — C2×C7×#3380 #13238569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3380 #13238569