Subgroups — C₂×C₇×#3169 #13237887

Order 1792.

2566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	2	yes	maximal, complemented
2	C₇×#3169	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#486	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#466	C₂	1	4	yes	maximal, complemented
7	C₂×C₄×C₇×D₈	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₇×#41	—	2	2	no	—
10	C₂²×C₇×D₈	C₂²	1	4	yes	—
11	C₂³×C₇×C₈	C₂²	1	2	yes	—
12	C₇×#532	—	2	8	no	—
13	C₇×#532	C₂²	1	16	yes	complemented
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#127	C₂²	1	2	yes	—
16	C₂×C₇×#124	—	2	2	no	—
17	C₂×C₇×#121	—	2	2	no	—
18	C₂×C₇×#121	C₂²	1	4	yes	—
19	C₂×C₄×C₇×D₄	—	2	2	no	—
20	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
21	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
22	C₇×#500	C₂²	1	8	yes	complemented
23	C₇×#493	C₂²	1	8	yes	complemented
24	C₇×#486	C₂²	1	16	yes	complemented
25	C₇×#466	C₂²	1	32	yes	complemented
26	C₄×C₇×D₈	C₂²	1	32	yes	complemented
27	C₂×C₇×#107	C₂²	1	4	yes	—
28	C₂×C₇×#102	C₂²	1	8	yes	—
29	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
31	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇×C₈	C₂²	1	8	yes	complemented
33	C₂×#3169	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂×C₇×#41	—	2	16	no	—
35	C₂×C₇×#41	—	4	16	no	—
36	C₂²×C₇×Q₈	—	2	2	no	—
37	C₂²×C₇×D₄	—	2	4	no	—
38	C₂²×C₇×D₄	—	2	2	no	—
39	C₂²×C₇×D₄	—	2	2	no	—
40	C₂²×C₇×D₄	C₂³	1	4	yes	—
41	C₂³×C₄×C₇	—	2	4	no	—
42	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
45	C₂×C₇×D₈	—	2	16	no	—
46	C₂×C₇×D₈	C₂³	1	16	yes	—
47	C₂²×C₇×C₈	—	2	8	no	—
48	C₂²×C₇×C₈	C₂³	1	8	yes	—
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₇×C₄⋊Q₈	—	2	4	no	—
52	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
53	C₇×#127	—	2	4	no	—
54	C₇×#127	C₂³	1	8	yes	—
55	C₇×#124	—	2	16	no	—
56	C₇×#121	—	2	16	no	—
57	C₇×#121	—	2	8	no	—
58	C₇×#121	C₂³	1	16	yes	—
59	C₄×C₇×D₄	—	2	16	no	—
60	C₄×C₇×D₄	—	2	8	no	—
61	C₄×C₇×D₄	C₂³	1	16	yes	—
62	C₂×C₇×C₄⋊C₄	—	2	2	no	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
65	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
66	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₇	D₄	1	4	yes	—
68	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇	C₂³	1	4	yes	—
71	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
72	C₇×#107	C₂³	1	16	yes	—
73	C₇×#102	C₂³	1	32	yes	—
74	C₄×C₇×C₈	C₂³	1	4	yes	—
75	C₄×C₇×C₈	C₂³	1	4	yes	—
76	C₄×C₇×C₈	C₂³	1	8	yes	—
77	C₂×#532	C₂×C₇	1	2	yes	complemented
78	#3169	C₂×C₇	1	16	yes	direct product factor
79	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
80	C₂×#493	C₂×C₇	1	1	yes	characteristic, complemented
81	C₂×#486	C₂×C₇	1	2	yes	complemented
82	C₂×#466	C₂×C₇	1	4	yes	complemented
83	C₂×C₄×D₈	C₂×C₇	1	4	yes	complemented
84	C₂²×C₄×C₈	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂⁴×C₇	—	2	4	no	—
86	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
87	C₇×#41	—	4	64	no	—
88	C₂×C₇×Q₈	—	2	8	no	—
89	C₂×C₇×Q₈	—	4	8	no	—
90	C₂×C₇×D₄	—	2	16	no	—
91	C₂×C₇×D₄	—	2	4	no	—
92	C₂×C₇×D₄	—	2	8	no	—
93	C₂×C₇×D₄	—	2	8	no	—
94	C₂×C₇×D₄	—	2	16	no	—
95	C₂×C₇×D₄	—	4	16	no	—
96	C₂×C₇×D₄	—	4	8	no	—
97	C₂×C₇×D₄	—	4	8	no	—
98	C₂×C₇×D₄	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₇	—	2	4	no	—
100	C₂²×C₄×C₇	—	2	4	no	—
101	C₂²×C₄×C₇	—	2	4	no	—
102	C₂²×C₄×C₇	—	2	16	no	—
103	C₂²×C₄×C₇	—	4	16	no	—
104	C₂²×C₄×C₇	D₈	1	8	yes	complemented
105	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
115	C₇×D₈	—	2	32	no	—
116	C₂×C₇×C₈	—	2	4	no	—
117	C₂×C₇×C₈	—	2	16	no	—
118	C₂×C₇×C₈	#41	1	8	yes	complemented
119	C₂×C₇×C₈	C₂⁴	1	4	yes	—
120	C₂×C₇×C₈	C₂⁴	1	4	yes	—
121	C₇×C₄⋊C₄	—	2	8	no	—
122	C₇×C₄⋊C₄	—	2	4	no	—
123	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
124	C₇×C₂²⋊C₄	—	2	16	no	—
125	C₇×C₂²⋊C₄	—	2	16	no	—
126	C₄²×C₇	C₂×D₄	1	4	yes	—
127	C₄²×C₇	C₂×D₄	1	2	yes	—
128	C₄²×C₇	C₂×D₄	1	4	yes	—
129	C₄²×C₇	C₂×D₄	1	2	yes	—
130	C₄²×C₇	C₂⁴	1	2	yes	—
131	C₄²×C₇	C₂⁴	1	2	yes	—
132	C₂²×#41	—	2	2	no	—
133	C₂²×D₈	C₂²×C₇	1	4	yes	—
134	C₂³×C₈	C₂²×C₇	1	2	yes	—
135	#532	—	2	8	no	—
136	#532	C₂²×C₇	1	16	yes	complemented
137	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
138	C₂×#127	C₂²×C₇	1	2	yes	—
139	C₂×#124	—	2	2	no	—
140	C₂×#121	—	2	2	no	—
141	C₂×#121	C₂²×C₇	1	4	yes	—
142	C₂×C₄×D₄	—	2	2	no	—
143	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
144	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
145	#500	C₂²×C₇	1	8	yes	complemented
146	#493	C₂²×C₇	1	8	yes	complemented
147	#486	C₂²×C₇	1	16	yes	complemented
148	#466	C₂²×C₇	1	32	yes	complemented
149	C₄×D₈	C₂²×C₇	1	32	yes	complemented
150	C₂×#107	C₂²×C₇	1	4	yes	—
151	C₂×#102	C₂²×C₇	1	8	yes	—
152	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
153	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
155	C₂×C₄×C₈	C₂²×C₇	1	8	yes	complemented
156	C₂³×C₇	—	2	2	no	—
157	C₂³×C₇	—	2	2	no	—
158	C₂³×C₇	—	2	8	no	—
159	C₂³×C₇	—	4	8	no	—
160	C₂³×C₇	—	4	8	no	—
161	C₂³×C₇	—	4	8	no	—
162	C₂³×C₇	C₂×D₈	1	4	yes	—
163	C₂³×C₇	C₂²×D₄	1	2	yes	—
164	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
165	C₇×Q₈	—	4	16	no	—
166	C₇×D₄	—	2	16	no	—
167	C₇×D₄	—	4	32	no	—
168	C₇×D₄	—	4	8	no	—
169	C₇×D₄	—	4	16	no	—
170	C₇×D₄	—	4	16	no	—
171	C₂×C₄×C₇	—	2	2	no	—
172	C₂×C₄×C₇	—	2	2	no	—
173	C₂×C₄×C₇	—	2	4	no	—
174	C₂×C₄×C₇	—	2	8	no	—
175	C₂×C₄×C₇	—	2	4	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	4	8	no	—
178	C₂×C₄×C₇	—	4	32	no	—
179	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
180	C₂×C₄×C₇	C₂×D₈	1	4	yes	—
181	C₂×C₄×C₇	C₂×D₈	1	16	yes	complemented
182	C₂×C₄×C₇	#135	1	4	yes	—
183	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
184	C₂×C₄×C₇	C₂²×D₄	1	2	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×D₄	1	2	yes	—
188	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₇	C₂×#41	1	4	yes	—
190	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
191	C₇×C₈	—	2	4	no	—
192	C₇×C₈	C₂×#41	1	8	yes	complemented
193	C₂×#41	—	2	16	no	—
194	C₂×#41	—	4	16	no	—
195	C₂²×Q₈	—	2	2	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	2	2	no	—
198	C₂²×D₄	—	2	2	no	—
199	C₂²×D₄	C₂³×C₇	1	4	yes	—
200	C₂³×C₄	—	2	4	no	—
201	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
202	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
204	C₂×D₈	—	2	16	no	—
205	C₂×D₈	C₂³×C₇	1	16	yes	—
206	C₂²×C₈	—	2	8	no	—
207	C₂²×C₈	C₂³×C₇	1	2	yes	—
208	C₂²×C₈	C₂³×C₇	1	8	yes	—
209	C₂²×C₈	C₂³×C₇	1	2	yes	—
210	C₄⋊Q₈	—	2	4	no	—
211	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
212	#127	—	2	4	no	—
213	#127	C₂³×C₇	1	8	yes	—
214	#124	—	2	16	no	—
215	#121	—	2	16	no	—
216	#121	—	2	8	no	—
217	#121	C₂³×C₇	1	16	yes	—
218	C₄×D₄	—	2	16	no	—
219	C₄×D₄	—	2	8	no	—
220	C₄×D₄	C₂³×C₇	1	16	yes	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
223	C₂×C₂²⋊C₄	—	2	4	no	—
224	C₂×C₂²⋊C₄	—	2	4	no	—
225	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
226	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
227	C₂×C₄²	C₇×D₄	1	4	yes	—
228	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₇	1	4	yes	—
231	#107	C₂³×C₇	1	16	yes	—
232	#102	C₂³×C₇	1	32	yes	—
233	C₄×C₈	C₂³×C₇	1	8	yes	—
234	C₄×C₈	C₂³×C₇	1	4	yes	—
235	C₄×C₈	C₂³×C₇	1	4	yes	—
236	C₂²×C₇	—	2	8	no	—
237	C₂²×C₇	—	2	2	no	—
238	C₂²×C₇	—	2	2	no	—
239	C₂²×C₇	—	4	8	no	—
240	C₂²×C₇	—	4	8	no	—
241	C₂²×C₇	—	4	8	no	—
242	C₂²×C₇	—	8	16	no	—
243	C₂²×C₇	#532	1	2	yes	—
244	C₂²×C₇	C₂²×D₈	1	4	yes	—
245	C₂²×C₇	C₂²×D₈	1	2	yes	—
246	C₂²×C₇	C₂×#135	1	2	yes	—
247	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
248	C₄×C₇	—	2	2	no	—
249	C₄×C₇	—	2	2	no	—
250	C₄×C₇	—	4	8	no	—
251	C₄×C₇	#532	1	2	yes	—
252	C₄×C₇	C₂²×D₈	1	4	yes	—
253	C₄×C₇	C₂²×D₈	1	4	yes	—
254	C₄×C₇	C₂×#135	1	4	yes	—
255	C₄×C₇	C₂²×#41	1	2	yes	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
258	#41	—	4	64	no	—
259	C₂×Q₈	—	2	8	no	—
260	C₂×Q₈	—	4	8	no	—
261	C₂×D₄	—	2	16	no	—
262	C₂×D₄	—	2	4	no	—
263	C₂×D₄	—	2	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	16	no	—
266	C₂×D₄	—	4	16	no	—
267	C₂×D₄	—	4	8	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	C₂⁴×C₇	1	8	yes	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	16	no	—
274	C₂²×C₄	—	4	16	no	—
275	C₂²×C₄	C₇×D₈	1	8	yes	complemented
276	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
278	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
280	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
283	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
286	D₈	—	2	32	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	16	no	—
289	C₂×C₈	C₇×#41	1	8	yes	complemented
290	C₂×C₈	C₂⁴×C₇	1	4	yes	—
291	C₂×C₈	C₂⁴×C₇	1	4	yes	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
295	C₂²⋊C₄	—	2	16	no	—
296	C₂²⋊C₄	—	2	16	no	—
297	C₄²	C₂×C₇×D₄	1	4	yes	—
298	C₄²	C₂×C₇×D₄	1	2	yes	—
299	C₄²	C₂×C₇×D₄	1	4	yes	—
300	C₄²	C₂×C₇×D₄	1	2	yes	—
301	C₄²	C₂⁴×C₇	1	2	yes	—
302	C₄²	C₂⁴×C₇	1	2	yes	—
303	C₂×C₇	—	2	4	no	—
304	C₂×C₇	—	8	8	no	—
305	C₂×C₇	#3169	1	4	yes	direct product factor
306	C₂×C₇	C₂×#532	1	1	yes	characteristic
307	C₂×C₇	C₂³×D₈	1	1	yes	characteristic
308	C₂×C₇	C₂²×#135	1	1	yes	characteristic
309	C₂³	—	2	2	no	—
310	C₂³	—	2	2	no	—
311	C₂³	—	2	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	8	no	—
314	C₂³	—	4	8	no	—
315	C₂³	C₂×C₇×D₈	1	4	yes	—
316	C₂³	C₂²×C₇×D₄	1	2	yes	—
317	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
318	Q₈	—	4	16	no	—
319	D₄	—	2	16	no	—
320	D₄	—	4	32	no	—
321	D₄	—	4	8	no	—
322	D₄	—	4	16	no	—
323	D₄	—	4	16	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	8	no	—
331	C₂×C₄	—	4	32	no	—
332	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
333	C₂×C₄	C₂×C₇×D₈	1	4	yes	—
334	C₂×C₄	C₂×C₇×D₈	1	16	yes	complemented
335	C₂×C₄	C₇×#135	1	4	yes	—
336	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
337	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
338	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
340	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
341	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
342	C₂×C₄	C₂×C₇×#41	1	4	yes	—
343	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	C₂×C₇×#41	1	8	yes	complemented
346	C₇	C₂×#3169	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	2	8	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₇×#532	1	2	yes	—
355	C₂²	C₂²×C₇×D₈	1	4	yes	—
356	C₂²	C₂²×C₇×D₈	1	2	yes	—
357	C₂²	C₂×C₇×#135	1	2	yes	—
358	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	4	8	no	—
362	C₄	C₇×#532	1	2	yes	—
363	C₄	C₂²×C₇×D₈	1	4	yes	—
364	C₄	C₂²×C₇×D₈	1	4	yes	—
365	C₄	C₂×C₇×#135	1	4	yes	—
366	C₄	C₂²×C₇×#41	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	—	8	8	no	—
369	C₂	C₇×#3169	1	4	yes	direct product factor
370	C₂	C₂×C₇×#532	1	1	yes	characteristic
371	C₂	C₂³×C₇×D₈	1	1	yes	characteristic
372	C₂	C₂²×C₇×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂³×C₇	C₂²×D₄
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
1. C₂×C₇×#532	C₂	semidirect
2. C₇×#3169	C₂	direct (N × H)
3. C₂×C₇×#500	C₂	semidirect
4. C₂×C₇×#493	C₂	semidirect
5. C₂×C₇×#486	C₂	semidirect
6. C₂×C₇×#466	C₂	semidirect
7. C₂×C₄×C₇×D₈	C₂	semidirect
8. C₂²×C₄×C₇×C₈	C₂	semidirect
13. C₇×#532	C₂²	semidirect
22. C₇×#500	C₂²	semidirect
23. C₇×#493	C₂²	semidirect
24. C₇×#486	C₂²	semidirect
25. C₇×#466	C₂²	semidirect
26. C₄×C₇×D₈	C₂²	semidirect
32. C₂×C₄×C₇×C₈	C₂²	semidirect
33. C₂×#3169	C₇	direct (N × H)
77. C₂×#532	C₂×C₇	semidirect
78. #3169	C₂×C₇	direct (N × H)
79. C₂×#500	C₂×C₇	semidirect
80. C₂×#493	C₂×C₇	semidirect
81. C₂×#486	C₂×C₇	semidirect
82. C₂×#466	C₂×C₇	semidirect
83. C₂×C₄×D₈	C₂×C₇	semidirect
84. C₂²×C₄×C₈	C₂×C₇	semidirect
104. C₂²×C₄×C₇	D₈	semidirect
118. C₂×C₇×C₈	#41	semidirect
136. #532	C₂²×C₇	semidirect
145. #500	C₂²×C₇	semidirect
146. #493	C₂²×C₇	semidirect
147. #486	C₂²×C₇	semidirect
148. #466	C₂²×C₇	semidirect
149. C₄×D₈	C₂²×C₇	semidirect
155. C₂×C₄×C₈	C₂²×C₇	semidirect
181. C₂×C₄×C₇	C₂×D₈	semidirect
192. C₇×C₈	C₂×#41	semidirect
275. C₂²×C₄	C₇×D₈	semidirect
289. C₂×C₈	C₇×#41	semidirect
305. C₂×C₇	#3169	direct (N × H)
334. C₂×C₄	C₂×C₇×D₈	semidirect
345. C₈	C₂×C₇×#41	semidirect
346. C₇	C₂×#3169	direct (N × H)
369. C₂	C₇×#3169	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×#532	2
C₇×#3169	2
C₂×C₇×#500	2
C₂×C₇×#493	2
C₂×C₇×#486	2
C₂×C₇×#466	2
C₂×C₄×C₇×D₈	2
C₂²×C₄×C₇×C₈	2
C₂×#3169	7

Subgroups — C2×C7×#3169 #13237887

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3169 #13237887