Subgroups — C₂×C₇×#3396 #13238608

Order 1792.

2086 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#559	C₂	1	2	yes	maximal, complemented
2	C₇×#3396	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#495	C₂	1	2	yes	maximal, complemented
4	C₂×C₇×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇×#460	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#463	C₂	1	4	yes	maximal, complemented
7	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₇×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×C₇×D₈	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₇×SD₁₆	C₂²	1	4	yes	—
12	C₂²×C₇×D₈	C₂²	1	2	yes	—
13	C₂²×C₇×D₈	C₂²	1	2	yes	—
14	C₇×#559	—	2	8	no	—
15	C₇×#559	C₂²	1	16	yes	complemented
16	C₂×C₇×#127	C₂²	1	2	yes	—
17	C₂×C₇×#124	—	2	2	no	—
18	C₂×C₇×#124	C₂²	1	4	yes	—
19	C₂×C₇×#123	—	2	4	no	—
20	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	—	2	2	no	—
23	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
24	C₇×#495	C₂²	1	16	yes	complemented
25	C₇×#493	C₂²	1	8	yes	—
26	C₇×#463	C₂²	1	32	yes	complemented
27	C₇×#460	C₂²	1	16	yes	complemented
28	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
29	C₄×C₇×Q₁₆	C₂²	1	8	yes	complemented
30	C₄×C₇×D₈	C₂²	1	16	yes	complemented
31	C₂×C₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#103	C₂²	1	2	yes	—
35	C₂×C₇×#102	C₂²	1	4	yes	—
36	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
38	C₂×#3396	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×Q₈	D₄	1	1	yes	characteristic
40	C₂²×C₇×Q₈	C₂³	1	2	yes	—
41	C₂²×C₇×D₄	—	2	2	no	—
42	C₂²×C₇×D₄	—	2	2	no	—
43	C₂²×C₇×D₄	C₂³	1	4	yes	—
44	C₂³×C₄×C₇	—	2	4	no	—
45	C₂×C₇×Q₁₆	—	2	4	no	—
46	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
47	C₂×C₇×SD₁₆	—	4	8	no	—
48	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
49	C₂×C₇×D₈	—	2	8	no	—
50	C₂×C₇×D₈	—	4	4	no	—
51	C₂×C₇×D₈	C₂³	1	8	yes	—
52	C₂×C₇×D₈	C₂³	1	8	yes	—
53	C₂²×C₇×C₈	C₂³	1	2	yes	—
54	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
56	C₇×#127	—	2	4	no	—
57	C₇×#127	C₂³	1	8	yes	—
58	C₇×#124	—	2	16	no	—
59	C₇×#124	—	2	8	no	—
60	C₇×#124	C₂³	1	16	yes	—
61	C₇×#123	—	2	32	no	—
62	C₄×C₇×Q₈	—	2	4	no	—
63	C₄×C₇×Q₈	D₄	1	4	yes	—
64	C₄×C₇×Q₈	C₂³	1	8	yes	—
65	C₄×C₇×Q₈	C₂³	1	4	yes	—
66	C₄×C₇×D₄	—	2	16	no	—
67	C₄×C₇×D₄	—	2	8	no	—
68	C₄×C₇×D₄	C₂³	1	16	yes	—
69	C₂×C₇×C₄⋊C₄	—	2	2	no	—
70	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
72	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₄²×C₇	—	2	2	no	—
77	C₂×C₄²×C₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
79	C₇×#107	C₂³	1	4	yes	—
80	C₇×C₄⋊C₈	C₂³	1	4	yes	—
81	C₇×C₄⋊C₈	C₂³	1	8	yes	—
82	C₇×#103	C₂³	1	8	yes	—
83	C₇×#102	C₂³	1	16	yes	—
84	C₄×C₇×C₈	C₂³	1	4	yes	—
85	C₄×C₇×C₈	C₂³	1	8	yes	—
86	C₂×#559	C₂×C₇	1	2	yes	complemented
87	#3396	C₂×C₇	1	16	yes	direct product factor
88	C₂×#495	C₂×C₇	1	2	yes	complemented
89	C₂×#493	C₂×C₇	1	1	yes	characteristic
90	C₂×#460	C₂×C₇	1	2	yes	complemented
91	C₂×#463	C₂×C₇	1	4	yes	complemented
92	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂×C₄×Q₁₆	C₂×C₇	1	1	yes	characteristic, complemented
94	C₂×C₄×D₈	C₂×C₇	1	2	yes	complemented
95	C₂⁴×C₇	—	2	4	no	—
96	C₂×C₇×Q₈	—	2	4	no	—
97	C₂×C₇×Q₈	—	2	2	no	—
98	C₂×C₇×Q₈	—	2	4	no	—
99	C₂×C₇×Q₈	—	2	4	no	—
100	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
101	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
102	C₂×C₇×D₄	—	2	4	no	—
103	C₂×C₇×D₄	—	2	8	no	—
104	C₂×C₇×D₄	—	2	8	no	—
105	C₂×C₇×D₄	—	2	8	no	—
106	C₂×C₇×D₄	—	2	8	no	—
107	C₂×C₇×D₄	—	4	8	no	—
108	C₂×C₇×D₄	—	8	4	no	—
109	C₂×C₇×D₄	C₂⁴	1	8	yes	—
110	C₂²×C₄×C₇	—	2	2	no	—
111	C₂²×C₄×C₇	—	2	2	no	—
112	C₂²×C₄×C₇	—	2	16	no	—
113	C₂²×C₄×C₇	—	8	8	no	—
114	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
119	C₇×Q₁₆	—	2	8	no	—
120	C₇×SD₁₆	—	4	16	no	—
121	C₇×D₈	—	2	16	no	—
122	C₇×D₈	—	4	8	no	—
123	C₂×C₇×C₈	—	2	2	no	—
124	C₂×C₇×C₈	—	2	4	no	—
125	C₂×C₇×C₈	#41	1	4	yes	—
126	C₂×C₇×C₈	C₂⁴	1	4	yes	—
127	C₂×C₇×C₈	C₂⁴	1	2	yes	—
128	C₂×C₇×C₈	C₂⁴	1	2	yes	—
129	C₇×C₄⋊C₄	—	2	8	no	—
130	C₇×C₄⋊C₄	—	2	2	no	—
131	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
132	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
133	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
134	C₇×C₂²⋊C₄	—	2	16	no	—
135	C₇×C₂²⋊C₄	—	2	16	no	—
136	C₇×C₂²⋊C₄	—	2	16	no	—
137	C₄²×C₇	—	2	8	no	—
138	C₄²×C₇	C₂×D₄	1	4	yes	—
139	C₄²×C₇	C₂×D₄	1	2	yes	—
140	C₄²×C₇	C₂⁴	1	4	yes	—
141	C₄²×C₇	C₂⁴	1	2	yes	—
142	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic
143	C₂²×SD₁₆	C₂²×C₇	1	4	yes	—
144	C₂²×D₈	C₂²×C₇	1	2	yes	—
145	C₂²×D₈	C₂²×C₇	1	2	yes	—
146	#559	—	2	8	no	—
147	#559	C₂²×C₇	1	16	yes	complemented
148	C₂×#127	C₂²×C₇	1	2	yes	—
149	C₂×#124	—	2	2	no	—
150	C₂×#124	C₂²×C₇	1	4	yes	—
151	C₂×#123	—	2	4	no	—
152	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
153	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
154	C₂×C₄×D₄	—	2	2	no	—
155	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
156	#495	C₂²×C₇	1	16	yes	complemented
157	#493	C₂²×C₇	1	8	yes	—
158	#463	C₂²×C₇	1	32	yes	complemented
159	#460	C₂²×C₇	1	16	yes	complemented
160	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
161	C₄×Q₁₆	C₂²×C₇	1	8	yes	complemented
162	C₄×D₈	C₂²×C₇	1	16	yes	complemented
163	C₂×#107	C₂²×C₇	1	1	yes	characteristic
164	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
165	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂×#103	C₂²×C₇	1	2	yes	—
167	C₂×#102	C₂²×C₇	1	4	yes	—
168	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
170	C₂³×C₇	—	2	8	no	—
171	C₂³×C₇	—	4	8	no	—
172	C₂³×C₇	—	4	8	no	—
173	C₂³×C₇	—	4	8	no	—
174	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
175	C₇×Q₈	—	2	8	no	—
176	C₇×Q₈	—	2	4	no	—
177	C₇×Q₈	—	2	4	no	—
178	C₇×Q₈	—	4	4	no	—
179	C₇×D₄	—	2	8	no	—
180	C₇×D₄	—	2	8	no	—
181	C₇×D₄	—	4	8	no	—
182	C₇×D₄	—	4	16	no	—
183	C₇×D₄	—	8	8	no	—
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	4	no	—
186	C₂×C₄×C₇	—	2	2	no	—
187	C₂×C₄×C₇	—	2	4	no	—
188	C₂×C₄×C₇	—	2	4	no	—
189	C₂×C₄×C₇	—	4	4	no	—
190	C₂×C₄×C₇	—	4	4	no	—
191	C₂×C₄×C₇	—	8	16	no	—
192	C₂×C₄×C₇	#135	1	4	yes	—
193	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₇	C₂×#41	1	2	yes	—
199	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
200	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
201	C₇×C₈	—	2	2	no	—
202	C₇×C₈	—	2	4	no	—
203	C₇×C₈	C₂×#41	1	4	yes	—
204	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
205	C₂²×Q₈	C₂³×C₇	1	2	yes	—
206	C₂²×D₄	—	2	2	no	—
207	C₂²×D₄	—	2	2	no	—
208	C₂²×D₄	C₂³×C₇	1	4	yes	—
209	C₂³×C₄	—	2	4	no	—
210	C₂×Q₁₆	—	2	4	no	—
211	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
212	C₂×SD₁₆	—	4	8	no	—
213	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
214	C₂×D₈	—	2	8	no	—
215	C₂×D₈	—	4	4	no	—
216	C₂×D₈	C₂³×C₇	1	8	yes	—
217	C₂×D₈	C₂³×C₇	1	8	yes	—
218	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₇	1	2	yes	—
220	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
221	#127	—	2	4	no	—
222	#127	C₂³×C₇	1	8	yes	—
223	#124	—	2	16	no	—
224	#124	—	2	8	no	—
225	#124	C₂³×C₇	1	16	yes	—
226	#123	—	2	32	no	—
227	C₄×Q₈	—	2	4	no	—
228	C₄×Q₈	C₇×D₄	1	4	yes	—
229	C₄×Q₈	C₂³×C₇	1	8	yes	—
230	C₄×Q₈	C₂³×C₇	1	4	yes	—
231	C₄×D₄	—	2	16	no	—
232	C₄×D₄	—	2	8	no	—
233	C₄×D₄	C₂³×C₇	1	16	yes	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂³×C₇	1	2	yes	—
243	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
244	#107	C₂³×C₇	1	4	yes	—
245	C₄⋊C₈	C₂³×C₇	1	4	yes	—
246	C₄⋊C₈	C₂³×C₇	1	8	yes	—
247	#103	C₂³×C₇	1	8	yes	—
248	#102	C₂³×C₇	1	16	yes	—
249	C₄×C₈	C₂³×C₇	1	8	yes	—
250	C₄×C₈	C₂³×C₇	1	4	yes	—
251	C₂²×C₇	—	4	8	no	—
252	C₂²×C₇	—	4	8	no	—
253	C₂²×C₇	—	4	8	no	—
254	C₂²×C₇	—	8	16	no	—
255	C₂²×C₇	#550	1	2	yes	—
256	C₂²×C₇	C₂×#135	1	2	yes	—
257	C₂²×C₇	#576	1	2	yes	—
258	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
259	C₄×C₇	—	2	4	no	—
260	C₄×C₇	—	2	4	no	—
261	C₄×C₇	—	2	2	no	—
262	C₄×C₇	—	4	4	no	—
263	C₄×C₇	—	4	4	no	—
264	C₄×C₇	#550	1	2	yes	—
265	C₄×C₇	C₂×#135	1	4	yes	—
266	C₄×C₇	C₂²×#41	1	1	yes	characteristic
267	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
268	C₂⁴	—	2	4	no	—
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
274	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	8	no	—
280	C₂×D₄	—	4	8	no	—
281	C₂×D₄	—	8	4	no	—
282	C₂×D₄	C₂⁴×C₇	1	8	yes	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	16	no	—
286	C₂²×C₄	—	8	8	no	—
287	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
288	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
289	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
292	Q₁₆	—	2	8	no	—
293	SD₁₆	—	4	16	no	—
294	D₈	—	2	16	no	—
295	D₈	—	4	8	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	C₇×#41	1	4	yes	—
299	C₂×C₈	C₂⁴×C₇	1	4	yes	—
300	C₂×C₈	C₂⁴×C₇	1	2	yes	—
301	C₂×C₈	C₂⁴×C₇	1	2	yes	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
305	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₄²	—	2	8	no	—
311	C₄²	C₂×C₇×D₄	1	4	yes	—
312	C₄²	C₂×C₇×D₄	1	2	yes	—
313	C₄²	C₂⁴×C₇	1	4	yes	—
314	C₄²	C₂⁴×C₇	1	2	yes	—
315	C₂×C₇	—	8	8	no	—
316	C₂×C₇	#3396	1	4	yes	direct product factor
317	C₂×C₇	C₂×#550	1	1	yes	characteristic
318	C₂×C₇	C₂²×#135	1	1	yes	characteristic
319	C₂×C₇	C₂×#576	1	1	yes	characteristic
320	C₂³	—	2	8	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	8	no	—
324	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
325	Q₈	—	2	8	no	—
326	Q₈	—	2	4	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	4	4	no	—
329	D₄	—	2	8	no	—
330	D₄	—	2	8	no	—
331	D₄	—	4	8	no	—
332	D₄	—	4	16	no	—
333	D₄	—	8	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	8	16	no	—
342	C₂×C₄	C₇×#135	1	4	yes	—
343	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
344	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
345	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
346	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
348	C₂×C₄	C₂×C₇×#41	1	2	yes	—
349	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
350	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
351	C₈	—	2	2	no	—
352	C₈	—	2	4	no	—
353	C₈	C₂×C₇×#41	1	4	yes	—
354	C₇	C₂×#3396	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	—	8	16	no	—
359	C₂²	C₇×#550	1	2	yes	—
360	C₂²	C₂×C₇×#135	1	2	yes	—
361	C₂²	C₇×#576	1	2	yes	—
362	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	C₇×#550	1	2	yes	—
369	C₄	C₂×C₇×#135	1	4	yes	—
370	C₄	C₂²×C₇×#41	1	1	yes	characteristic
371	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
372	C₂	—	8	8	no	—
373	C₂	C₇×#3396	1	4	yes	direct product factor
374	C₂	C₂×C₇×#550	1	1	yes	characteristic
375	C₂	C₂²×C₇×#135	1	1	yes	characteristic
376	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	C₂×C₇×#493	C₂
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×#559	C₂	semidirect
2. C₇×#3396	C₂	direct (N × H)
3. C₂×C₇×#495	C₂	semidirect
5. C₂×C₇×#460	C₂	semidirect
6. C₂×C₇×#463	C₂	semidirect
7. C₂×C₇×C₈×Q₈	C₂	semidirect
8. C₂×C₄×C₇×Q₁₆	C₂	semidirect
9. C₂×C₄×C₇×D₈	C₂	semidirect
15. C₇×#559	C₂²	semidirect
24. C₇×#495	C₂²	semidirect
26. C₇×#463	C₂²	semidirect
27. C₇×#460	C₂²	semidirect
28. C₇×C₈×Q₈	C₂²	semidirect
29. C₄×C₇×Q₁₆	C₂²	semidirect
30. C₄×C₇×D₈	C₂²	semidirect
38. C₂×#3396	C₇	direct (N × H)
86. C₂×#559	C₂×C₇	semidirect
87. #3396	C₂×C₇	direct (N × H)
88. C₂×#495	C₂×C₇	semidirect
90. C₂×#460	C₂×C₇	semidirect
91. C₂×#463	C₂×C₇	semidirect
92. C₂×C₈×Q₈	C₂×C₇	semidirect
93. C₂×C₄×Q₁₆	C₂×C₇	semidirect
94. C₂×C₄×D₈	C₂×C₇	semidirect
147. #559	C₂²×C₇	semidirect
156. #495	C₂²×C₇	semidirect
158. #463	C₂²×C₇	semidirect
159. #460	C₂²×C₇	semidirect
160. C₈×Q₈	C₂²×C₇	semidirect
161. C₄×Q₁₆	C₂²×C₇	semidirect
162. C₄×D₈	C₂²×C₇	semidirect
316. C₂×C₇	#3396	direct (N × H)
354. C₇	C₂×#3396	direct (N × H)
373. C₂	C₇×#3396	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×#559	2
C₇×#3396	2
C₂×C₇×#495	2
C₂×C₇×#493	2
C₂×C₇×#460	2
C₂×C₇×#463	2
C₂×C₇×C₈×Q₈	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×D₈	2
C₂×#3396	7

Subgroups — C2×C7×#3396 #13238608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3396 #13238608