Subgroups — C₂×C₇×#3338 #13238445

Order 1792.

1942 conjugacy classes of subgroups.

The subgroup lattice has 366 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
2	C₇×#3338	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#484	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#477	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₇×#107	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₇×C₈	C₂²	1	2	yes	—
12	C₇×#554	—	2	8	no	—
13	C₇×#554	C₂²	1	16	yes	—
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#125	—	2	2	no	—
16	C₂×C₇×C₂²⋊Q₈	—	2	4	no	—
17	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
19	C₂×C₄×C₇×D₄	—	2	2	no	—
20	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	—
22	C₇×#500	C₂²	1	8	yes	complemented
23	C₇×#484	C₂²	1	32	yes	complemented
24	C₇×#477	C₂²	1	16	yes	complemented
25	C₇×#467	C₂²	1	16	yes	complemented
26	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
27	C₇×C₈×D₄	C₂²	1	8	yes	—
28	C₂×C₇×#107	C₂²	1	2	yes	—
29	C₂×C₇×#107	C₂²	1	2	yes	—
30	C₂×C₇×#107	C₂²	1	1	yes	characteristic
31	C₂×C₇×#107	C₂²	1	4	yes	—
32	C₂×C₇×#107	C₂²	1	16	yes	complemented
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	2	yes	—
35	C₂×C₇×#103	C₂²	1	4	yes	—
36	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×#3338	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×Q₈	—	2	2	no	—
40	C₂²×C₇×Q₈	C₂³	1	2	yes	—
41	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₇	—	2	4	no	—
43	C₂³×C₄×C₇	C₂³	1	2	yes	—
44	C₂×C₇×Q₁₆	—	2	4	no	—
45	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
46	C₂²×C₇×C₈	—	2	8	no	—
47	C₂²×C₇×C₈	C₂³	1	8	yes	—
48	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₇×C₈	C₂³	1	2	yes	—
50	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
51	C₇×C₄⋊Q₈	—	2	4	no	—
52	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
53	C₇×#125	—	2	16	no	—
54	C₇×C₂²⋊Q₈	—	2	8	no	—
55	C₇×C₂²⋊Q₈	—	2	32	no	—
56	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
57	C₄×C₇×Q₈	—	2	4	no	—
58	C₄×C₇×Q₈	C₂³	1	8	yes	—
59	C₄×C₇×D₄	—	2	16	no	—
60	C₄×C₇×D₄	D₄	1	4	yes	—
61	C₄×C₇×D₄	C₂³	1	4	yes	—
62	C₂×C₇×C₄⋊C₄	—	2	4	no	—
63	C₂×C₇×C₄⋊C₄	—	2	8	no	—
64	C₂×C₇×C₄⋊C₄	—	2	2	no	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	—	2	4	no	—
67	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	—
69	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
71	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
72	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
73	C₂×C₄²×C₇	—	2	2	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#107	C₂³	1	8	yes	—
76	C₇×#107	C₂³	1	16	yes	—
77	C₇×#107	C₂³	1	8	yes	—
78	C₇×#107	C₂³	1	4	yes	—
79	C₇×C₄⋊C₈	C₂³	1	4	yes	—
80	C₇×#103	C₂³	1	16	yes	—
81	C₇×#103	C₂³	1	8	yes	—
82	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
83	C₄×C₇×C₈	C₂³	1	4	yes	—
84	C₂×#554	C₂×C₇	1	2	yes	—
85	#3338	C₂×C₇	1	16	yes	direct product factor
86	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂×#484	C₂×C₇	1	4	yes	complemented
88	C₂×#477	C₂×C₇	1	2	yes	complemented
89	C₂×#467	C₂×C₇	1	2	yes	complemented
90	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic
92	C₂²×#107	C₂×C₇	1	2	yes	complemented
93	C₂⁴×C₇	C₂×D₄	1	2	yes	—
94	C₂×C₇×Q₈	—	2	2	no	—
95	C₂×C₇×Q₈	—	2	8	no	—
96	C₂×C₇×Q₈	—	2	4	no	—
97	C₂×C₇×Q₈	—	2	4	no	—
98	C₂×C₇×Q₈	—	8	4	no	—
99	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
100	C₂×C₇×D₄	Q₁₆	1	8	yes	complemented
101	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₇	—	2	4	no	—
103	C₂²×C₄×C₇	—	2	4	no	—
104	C₂²×C₄×C₇	—	2	2	no	—
105	C₂²×C₄×C₇	—	2	2	no	—
106	C₂²×C₄×C₇	—	2	4	no	—
107	C₂²×C₄×C₇	—	2	16	no	—
108	C₂²×C₄×C₇	—	8	8	no	—
109	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
115	C₇×Q₁₆	—	2	8	no	—
116	C₂×C₇×C₈	—	2	4	no	—
117	C₂×C₇×C₈	—	2	2	no	—
118	C₂×C₇×C₈	—	2	16	no	—
119	C₂×C₇×C₈	#41	1	4	yes	—
120	C₂×C₇×C₈	C₂⁴	1	2	yes	—
121	C₂×C₇×C₈	C₂⁴	1	4	yes	—
122	C₂×C₇×C₈	C₂⁴	1	2	yes	—
123	C₇×C₄⋊C₄	—	2	2	no	—
124	C₇×C₄⋊C₄	—	2	16	no	—
125	C₇×C₄⋊C₄	—	2	4	no	—
126	C₇×C₄⋊C₄	—	2	8	no	—
127	C₇×C₄⋊C₄	—	2	8	no	—
128	C₇×C₄⋊C₄	—	2	16	no	—
129	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
131	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
132	C₇×C₂²⋊C₄	—	2	16	no	—
133	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
134	C₄²×C₇	—	2	8	no	—
135	C₄²×C₇	C₂×D₄	1	2	yes	—
136	C₄²×C₇	C₂⁴	1	2	yes	—
137	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
138	C₂³×C₈	C₂²×C₇	1	2	yes	—
139	#554	—	2	8	no	—
140	#554	C₂²×C₇	1	16	yes	—
141	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
142	C₂×#125	—	2	2	no	—
143	C₂×C₂²⋊Q₈	—	2	4	no	—
144	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	—
145	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
146	C₂×C₄×D₄	—	2	2	no	—
147	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
148	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	—
149	#500	C₂²×C₇	1	8	yes	complemented
150	#484	C₂²×C₇	1	32	yes	complemented
151	#477	C₂²×C₇	1	16	yes	complemented
152	#467	C₂²×C₇	1	16	yes	complemented
153	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
154	C₈×D₄	C₂²×C₇	1	8	yes	—
155	C₂×#107	C₂²×C₇	1	4	yes	—
156	C₂×#107	C₂²×C₇	1	2	yes	—
157	C₂×#107	C₂²×C₇	1	2	yes	—
158	C₂×#107	C₂²×C₇	1	1	yes	characteristic
159	C₂×#107	C₂²×C₇	1	16	yes	complemented
160	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
161	C₂×#103	C₂²×C₇	1	4	yes	—
162	C₂×#103	C₂²×C₇	1	2	yes	—
163	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
164	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
165	C₂³×C₇	—	2	4	no	—
166	C₂³×C₇	—	2	4	no	—
167	C₂³×C₇	C₂×Q₁₆	1	8	yes	—
168	C₂³×C₇	C₂²×D₄	1	4	yes	—
169	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
170	C₇×Q₈	—	2	4	no	—
171	C₇×Q₈	—	2	4	no	—
172	C₇×Q₈	—	4	4	no	—
173	C₇×Q₈	—	8	8	no	—
174	C₇×D₄	C₂×Q₁₆	1	16	yes	complemented
175	C₂×C₄×C₇	—	2	4	no	—
176	C₂×C₄×C₇	—	2	2	no	—
177	C₂×C₄×C₇	—	2	8	no	—
178	C₂×C₄×C₇	—	2	4	no	—
179	C₂×C₄×C₇	—	2	4	no	—
180	C₂×C₄×C₇	—	2	4	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	8	no	—
183	C₂×C₄×C₇	—	4	4	no	—
184	C₂×C₄×C₇	—	4	4	no	—
185	C₂×C₄×C₇	—	4	8	no	—
186	C₂×C₄×C₇	—	8	16	no	—
187	C₂×C₄×C₇	C₂×Q₁₆	1	4	yes	—
188	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₇	C₂×#41	1	2	yes	—
193	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
194	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
195	C₇×C₈	—	2	4	no	—
196	C₇×C₈	—	2	2	no	—
197	C₇×C₈	C₂×#41	1	4	yes	—
198	C₂²×Q₈	—	2	2	no	—
199	C₂²×Q₈	C₂³×C₇	1	2	yes	—
200	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
201	C₂³×C₄	—	2	4	no	—
202	C₂³×C₄	C₂³×C₇	1	2	yes	—
203	C₂×Q₁₆	—	2	4	no	—
204	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
205	C₂²×C₈	—	2	8	no	—
206	C₂²×C₈	C₂³×C₇	1	2	yes	—
207	C₂²×C₈	C₂³×C₇	1	8	yes	—
208	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
210	C₄⋊Q₈	—	2	4	no	—
211	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
212	#125	—	2	16	no	—
213	C₂²⋊Q₈	—	2	8	no	—
214	C₂²⋊Q₈	—	2	32	no	—
215	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	C₂³×C₇	1	8	yes	—
218	C₄×D₄	—	2	16	no	—
219	C₄×D₄	C₇×D₄	1	4	yes	—
220	C₄×D₄	C₂³×C₇	1	4	yes	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	8	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
229	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
234	#107	C₂³×C₇	1	4	yes	—
235	#107	C₂³×C₇	1	8	yes	—
236	#107	C₂³×C₇	1	16	yes	—
237	#107	C₂³×C₇	1	8	yes	—
238	C₄⋊C₈	C₂³×C₇	1	4	yes	—
239	#103	C₂³×C₇	1	8	yes	—
240	#103	C₂³×C₇	1	16	yes	—
241	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
242	C₄×C₈	C₂³×C₇	1	4	yes	—
243	C₂²×C₇	—	2	16	no	—
244	C₂²×C₇	—	2	4	no	—
245	C₂²×C₇	—	2	4	no	—
246	C₂²×C₇	#547	1	2	yes	—
247	C₂²×C₇	C₂²×Q₁₆	1	8	yes	—
248	C₂²×C₇	C₂²×Q₁₆	1	2	yes	—
249	C₂²×C₇	#576	1	2	yes	—
250	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₇	—	2	4	no	—
252	C₄×C₇	—	2	2	no	—
253	C₄×C₇	—	4	4	no	—
254	C₄×C₇	—	4	4	no	—
255	C₄×C₇	—	4	8	no	—
256	C₄×C₇	#547	1	2	yes	—
257	C₄×C₇	C₂²×Q₁₆	1	4	yes	—
258	C₄×C₇	C₂²×#41	1	1	yes	characteristic
259	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
260	C₂⁴	C₂×C₇×D₄	1	2	yes	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	8	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	8	4	no	—
266	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
267	C₂×D₄	C₇×Q₁₆	1	8	yes	complemented
268	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	16	no	—
275	C₂²×C₄	—	8	8	no	—
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	4	yes	—
279	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
282	Q₁₆	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	16	no	—
286	C₂×C₈	C₇×#41	1	4	yes	—
287	C₂×C₈	C₂⁴×C₇	1	2	yes	—
288	C₂×C₈	C₂⁴×C₇	1	4	yes	—
289	C₂×C₈	C₂⁴×C₇	1	2	yes	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
297	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
298	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
301	C₄²	—	2	8	no	—
302	C₄²	C₂×C₇×D₄	1	2	yes	—
303	C₄²	C₂⁴×C₇	1	2	yes	—
304	C₂×C₇	—	2	8	no	—
305	C₂×C₇	#3338	1	4	yes	direct product factor
306	C₂×C₇	C₂×#547	1	1	yes	characteristic
307	C₂×C₇	C₂³×Q₁₆	1	1	yes	characteristic
308	C₂×C₇	C₂×#576	1	1	yes	characteristic
309	C₂³	—	2	4	no	—
310	C₂³	—	2	4	no	—
311	C₂³	C₂×C₇×Q₁₆	1	8	yes	—
312	C₂³	C₂²×C₇×D₄	1	4	yes	—
313	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	2	4	no	—
316	Q₈	—	4	4	no	—
317	Q₈	—	8	8	no	—
318	D₄	C₂×C₇×Q₁₆	1	16	yes	complemented
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	8	16	no	—
331	C₂×C₄	C₂×C₇×Q₁₆	1	4	yes	—
332	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
333	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
334	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
336	C₂×C₄	C₂×C₇×#41	1	2	yes	—
337	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
338	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
339	C₈	—	2	4	no	—
340	C₈	—	2	2	no	—
341	C₈	C₂×C₇×#41	1	4	yes	—
342	C₇	C₂×#3338	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²	—	2	4	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	16	no	—
346	C₂²	C₇×#547	1	2	yes	—
347	C₂²	C₂²×C₇×Q₁₆	1	8	yes	—
348	C₂²	C₂²×C₇×Q₁₆	1	2	yes	—
349	C₂²	C₇×#576	1	2	yes	—
350	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	2	4	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	8	no	—
355	C₄	—	4	4	no	—
356	C₄	C₇×#547	1	2	yes	—
357	C₄	C₂²×C₇×Q₁₆	1	4	yes	—
358	C₄	C₂²×C₇×#41	1	1	yes	characteristic
359	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
360	C₂	—	2	8	no	—
361	C₂	C₇×#3338	1	4	yes	direct product factor
362	C₂	C₂×C₇×#547	1	1	yes	characteristic
363	C₂	C₂³×C₇×Q₁₆	1	1	yes	characteristic
364	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×D₄	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#3338	C₂	direct (N × H)
3. C₂×C₇×#500	C₂	semidirect
4. C₂×C₇×#484	C₂	semidirect
5. C₂×C₇×#477	C₂	semidirect
6. C₂×C₇×#467	C₂	semidirect
7. C₂×C₄×C₇×Q₁₆	C₂	semidirect
9. C₂²×C₇×#107	C₂	semidirect
22. C₇×#500	C₂²	semidirect
23. C₇×#484	C₂²	semidirect
24. C₇×#477	C₂²	semidirect
25. C₇×#467	C₂²	semidirect
26. C₄×C₇×Q₁₆	C₂²	semidirect
32. C₂×C₇×#107	C₂²	semidirect
38. C₂×#3338	C₇	direct (N × H)
85. #3338	C₂×C₇	direct (N × H)
86. C₂×#500	C₂×C₇	semidirect
87. C₂×#484	C₂×C₇	semidirect
88. C₂×#477	C₂×C₇	semidirect
89. C₂×#467	C₂×C₇	semidirect
90. C₂×C₄×Q₁₆	C₂×C₇	semidirect
92. C₂²×#107	C₂×C₇	semidirect
100. C₂×C₇×D₄	Q₁₆	semidirect
149. #500	C₂²×C₇	semidirect
150. #484	C₂²×C₇	semidirect
151. #477	C₂²×C₇	semidirect
152. #467	C₂²×C₇	semidirect
153. C₄×Q₁₆	C₂²×C₇	semidirect
159. C₂×#107	C₂²×C₇	semidirect
174. C₇×D₄	C₂×Q₁₆	semidirect
267. C₂×D₄	C₇×Q₁₆	semidirect
305. C₂×C₇	#3338	direct (N × H)
318. D₄	C₂×C₇×Q₁₆	semidirect
342. C₇	C₂×#3338	direct (N × H)
361. C₂	C₇×#3338	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×#3338	2
C₂×C₇×#500	2
C₂×C₇×#484	2
C₂×C₇×#477	2
C₂×C₇×#467	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₇×C₈×D₄	2
C₂²×C₇×#107	2
C₂×#3338	7

Subgroups — C2×C7×#3338 #13238445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3338 #13238445