Subgroups — C₂×C₇×#3393 #13238605

Order 1792.

1958 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#556	C₂	1	2	yes	maximal, complemented
2	C₇×#3393	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#495	C₂	1	2	yes	maximal
4	C₂×C₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#464	C₂	1	4	yes	maximal, complemented
6	C₂×C₇×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₇×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₇×Q₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
11	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
12	C₂²×C₇×SD₁₆	C₂²	1	4	yes	—
13	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
14	C₇×#556	—	2	8	no	—
15	C₇×#556	C₂²	1	16	yes	complemented
16	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₇×#126	—	2	4	no	—
18	C₂×C₇×#124	C₂²	1	4	yes	—
19	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
20	C₂×C₄×C₇×Q₈	C₂²	1	4	yes	—
21	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
23	C₂×C₇×#117	—	2	2	no	—
24	C₇×#495	C₂²	1	16	yes	—
25	C₇×#494	C₂²	1	8	yes	complemented
26	C₇×#464	C₂²	1	32	yes	complemented
27	C₇×#461	C₂²	1	16	yes	complemented
28	C₇×C₈×Q₈	C₂²	1	8	yes	complemented
29	C₄×C₇×Q₁₆	C₂²	1	16	yes	complemented
30	C₄×C₇×D₈	C₂²	1	8	yes	—
31	C₂×C₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₇×#103	C₂²	1	4	yes	—
35	C₂×C₇×#102	C₂²	1	2	yes	—
36	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
38	C₂×#3393	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	4	yes	—
41	C₂²×C₇×D₄	C₂³	1	2	yes	—
42	C₂³×C₄×C₇	—	2	2	no	—
43	C₂×C₇×Q₁₆	—	2	8	no	—
44	C₂×C₇×Q₁₆	—	4	4	no	—
45	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
46	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
47	C₂×C₇×SD₁₆	—	4	8	no	—
48	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
49	C₂×C₇×D₈	—	2	4	no	—
50	C₂×C₇×D₈	C₂³	1	4	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₇×C₈	C₂³	1	2	yes	—
53	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
54	C₇×C₄⋊Q₈	—	2	4	no	—
55	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
56	C₇×#126	—	2	32	no	—
57	C₇×#124	—	2	8	no	—
58	C₇×#124	C₂³	1	16	yes	—
59	C₇×C₂²⋊Q₈	—	2	16	no	—
60	C₄×C₇×Q₈	—	2	8	no	—
61	C₄×C₇×Q₈	D₄	1	4	yes	—
62	C₄×C₇×Q₈	C₂³	1	16	yes	—
63	C₄×C₇×Q₈	C₂³	1	4	yes	—
64	C₄×C₇×D₄	—	2	4	no	—
65	C₄×C₇×D₄	C₂³	1	8	yes	—
66	C₇×#117	—	2	16	no	—
67	C₂×C₇×C₄⋊C₄	—	2	2	no	—
68	C₂×C₇×C₄⋊C₄	—	2	4	no	—
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	2	no	—
75	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
76	C₂×C₄²×C₇	—	2	4	no	—
77	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	16	yes	—
83	C₇×#102	C₂³	1	8	yes	—
84	C₄×C₇×C₈	C₂³	1	4	yes	—
85	C₄×C₇×C₈	C₂³	1	8	yes	—
86	C₂×#556	C₂×C₇	1	2	yes	complemented
87	#3393	C₂×C₇	1	16	yes	direct product factor
88	C₂×#495	C₂×C₇	1	2	yes	—
89	C₂×#494	C₂×C₇	1	1	yes	characteristic, complemented
90	C₂×#464	C₂×C₇	1	4	yes	complemented
91	C₂×#461	C₂×C₇	1	2	yes	complemented
92	C₂×C₈×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
93	C₂×C₄×Q₁₆	C₂×C₇	1	2	yes	complemented
94	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic
95	C₂⁴×C₇	—	2	2	no	—
96	C₂×C₇×Q₈	—	2	4	no	—
97	C₂×C₇×Q₈	—	2	4	no	—
98	C₂×C₇×Q₈	—	2	8	no	—
99	C₂×C₇×Q₈	—	2	8	no	—
100	C₂×C₇×Q₈	C₂×D₄	1	4	yes	—
101	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
102	C₂×C₇×D₄	—	2	2	no	—
103	C₂×C₇×D₄	—	2	4	no	—
104	C₂×C₇×D₄	—	2	4	no	—
105	C₂×C₇×D₄	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₇	—	2	2	no	—
107	C₂²×C₄×C₇	—	2	4	no	—
108	C₂²×C₄×C₇	—	2	8	no	—
109	C₂²×C₄×C₇	—	4	8	no	—
110	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
115	C₇×Q₁₆	—	2	16	no	—
116	C₇×Q₁₆	—	4	8	no	—
117	C₇×SD₁₆	—	4	16	no	—
118	C₇×D₈	—	2	8	no	—
119	C₂×C₇×C₈	—	2	4	no	—
120	C₂×C₇×C₈	—	2	2	no	—
121	C₂×C₇×C₈	#41	1	4	yes	—
122	C₂×C₇×C₈	C₂⁴	1	2	yes	—
123	C₂×C₇×C₈	C₂⁴	1	4	yes	—
124	C₂×C₇×C₈	C₂⁴	1	2	yes	—
125	C₇×C₄⋊C₄	—	2	8	no	—
126	C₇×C₄⋊C₄	—	2	16	no	—
127	C₇×C₄⋊C₄	—	2	8	no	—
128	C₇×C₄⋊C₄	—	2	2	no	—
129	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
131	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
132	C₇×C₂²⋊C₄	—	2	16	no	—
133	C₇×C₂²⋊C₄	—	2	8	no	—
134	C₇×C₂²⋊C₄	—	2	16	no	—
135	C₄²×C₇	—	2	16	no	—
136	C₄²×C₇	C₂×D₄	1	2	yes	—
137	C₄²×C₇	C₂×D₄	1	4	yes	—
138	C₄²×C₇	C₂⁴	1	2	yes	—
139	C₄²×C₇	C₂⁴	1	4	yes	—
140	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
141	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
142	C₂²×SD₁₆	C₂²×C₇	1	4	yes	—
143	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
144	#556	—	2	8	no	—
145	#556	C₂²×C₇	1	16	yes	complemented
146	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
147	C₂×#126	—	2	4	no	—
148	C₂×#124	C₂²×C₇	1	4	yes	—
149	C₂×C₂²⋊Q₈	—	2	2	no	—
150	C₂×C₄×Q₈	C₂²×C₇	1	4	yes	—
151	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
152	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
153	C₂×#117	—	2	2	no	—
154	#495	C₂²×C₇	1	16	yes	—
155	#494	C₂²×C₇	1	8	yes	complemented
156	#464	C₂²×C₇	1	32	yes	complemented
157	#461	C₂²×C₇	1	16	yes	complemented
158	C₈×Q₈	C₂²×C₇	1	8	yes	complemented
159	C₄×Q₁₆	C₂²×C₇	1	16	yes	complemented
160	C₄×D₈	C₂²×C₇	1	8	yes	—
161	C₂×#107	C₂²×C₇	1	1	yes	characteristic
162	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
163	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
164	C₂×#103	C₂²×C₇	1	4	yes	—
165	C₂×#102	C₂²×C₇	1	2	yes	—
166	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
167	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
168	C₂³×C₇	—	2	4	no	—
169	C₂³×C₇	—	4	4	no	—
170	C₂³×C₇	—	4	4	no	—
171	C₂³×C₇	—	4	4	no	—
172	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
173	C₇×Q₈	—	2	8	no	—
174	C₇×Q₈	—	2	8	no	—
175	C₇×Q₈	—	2	8	no	—
176	C₇×Q₈	—	4	8	no	—
177	C₇×D₄	—	2	4	no	—
178	C₇×D₄	—	2	4	no	—
179	C₇×D₄	—	4	4	no	—
180	C₂×C₄×C₇	—	2	4	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	4	no	—
184	C₂×C₄×C₇	—	2	8	no	—
185	C₂×C₄×C₇	—	4	8	no	—
186	C₂×C₄×C₇	—	4	4	no	—
187	C₂×C₄×C₇	—	4	16	no	—
188	C₂×C₄×C₇	#135	1	4	yes	—
189	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
197	C₇×C₈	—	2	4	no	—
198	C₇×C₈	—	2	2	no	—
199	C₇×C₈	C₂×#41	1	4	yes	—
200	C₂²×Q₈	C₇×D₄	1	1	yes	characteristic
201	C₂²×Q₈	C₂³×C₇	1	4	yes	—
202	C₂²×D₄	C₂³×C₇	1	2	yes	—
203	C₂³×C₄	—	2	2	no	—
204	C₂×Q₁₆	—	2	8	no	—
205	C₂×Q₁₆	—	4	4	no	—
206	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
207	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
208	C₂×SD₁₆	—	4	8	no	—
209	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
210	C₂×D₈	—	2	4	no	—
211	C₂×D₈	C₂³×C₇	1	4	yes	—
212	C₂²×C₈	C₂³×C₇	1	2	yes	—
213	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
214	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
215	C₄⋊Q₈	—	2	4	no	—
216	C₄⋊Q₈	C₂³×C₇	1	8	yes	—
217	#126	—	2	32	no	—
218	#124	—	2	8	no	—
219	#124	C₂³×C₇	1	16	yes	—
220	C₂²⋊Q₈	—	2	16	no	—
221	C₄×Q₈	—	2	8	no	—
222	C₄×Q₈	C₇×D₄	1	4	yes	—
223	C₄×Q₈	C₂³×C₇	1	16	yes	—
224	C₄×Q₈	C₂³×C₇	1	4	yes	—
225	C₄×D₄	—	2	4	no	—
226	C₄×D₄	C₂³×C₇	1	8	yes	—
227	#117	—	2	16	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
232	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
233	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
234	C₂×C₂²⋊C₄	—	2	4	no	—
235	C₂×C₂²⋊C₄	—	2	2	no	—
236	C₂×C₂²⋊C₄	—	2	4	no	—
237	C₂×C₄²	—	2	4	no	—
238	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
239	C₂×C₄²	C₂³×C₇	1	2	yes	—
240	#107	C₂³×C₇	1	4	yes	—
241	C₄⋊C₈	C₂³×C₇	1	4	yes	—
242	C₄⋊C₈	C₂³×C₇	1	8	yes	—
243	#103	C₂³×C₇	1	16	yes	—
244	#102	C₂³×C₇	1	8	yes	—
245	C₄×C₈	C₂³×C₇	1	4	yes	—
246	C₄×C₈	C₂³×C₇	1	8	yes	—
247	C₂²×C₇	—	4	4	no	—
248	C₂²×C₇	—	4	4	no	—
249	C₂²×C₇	—	4	4	no	—
250	C₂²×C₇	—	8	8	no	—
251	C₂²×C₇	#550	1	2	yes	—
252	C₂²×C₇	C₂×#135	1	2	yes	—
253	C₂²×C₇	#578	1	2	yes	—
254	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₇	—	2	4	no	—
256	C₄×C₇	—	2	4	no	—
257	C₄×C₇	—	2	2	no	—
258	C₄×C₇	—	4	8	no	—
259	C₄×C₇	—	4	4	no	—
260	C₄×C₇	#550	1	2	yes	—
261	C₄×C₇	C₂×#135	1	4	yes	—
262	C₄×C₇	C₂²×#41	1	1	yes	characteristic
263	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
264	C₂⁴	—	2	2	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	2	8	no	—
269	C₂×Q₈	C₂×C₇×D₄	1	4	yes	—
270	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	C₂⁴×C₇	1	4	yes	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
280	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
282	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
284	Q₁₆	—	2	16	no	—
285	Q₁₆	—	4	8	no	—
286	SD₁₆	—	4	16	no	—
287	D₈	—	2	8	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₇×#41	1	4	yes	—
291	C₂×C₈	C₂⁴×C₇	1	2	yes	—
292	C₂×C₈	C₂⁴×C₇	1	4	yes	—
293	C₂×C₈	C₂⁴×C₇	1	2	yes	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	16	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
299	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
300	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
301	C₂²⋊C₄	—	2	16	no	—
302	C₂²⋊C₄	—	2	8	no	—
303	C₂²⋊C₄	—	2	16	no	—
304	C₄²	—	2	16	no	—
305	C₄²	C₂×C₇×D₄	1	2	yes	—
306	C₄²	C₂×C₇×D₄	1	4	yes	—
307	C₄²	C₂⁴×C₇	1	2	yes	—
308	C₄²	C₂⁴×C₇	1	4	yes	—
309	C₂×C₇	—	8	4	no	—
310	C₂×C₇	#3393	1	4	yes	direct product factor
311	C₂×C₇	C₂×#550	1	1	yes	characteristic
312	C₂×C₇	C₂²×#135	1	1	yes	characteristic
313	C₂×C₇	C₂×#578	1	1	yes	characteristic
314	C₂³	—	2	4	no	—
315	C₂³	—	4	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
319	Q₈	—	2	8	no	—
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	4	8	no	—
323	D₄	—	2	4	no	—
324	D₄	—	2	4	no	—
325	D₄	—	4	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	C₇×#135	1	4	yes	—
335	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
336	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
337	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
338	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
340	C₂×C₄	C₂×C₇×#41	1	2	yes	—
341	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
342	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
343	C₈	—	2	4	no	—
344	C₈	—	2	2	no	—
345	C₈	C₂×C₇×#41	1	4	yes	—
346	C₇	C₂×#3393	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	8	no	—
351	C₂²	C₇×#550	1	2	yes	—
352	C₂²	C₂×C₇×#135	1	2	yes	—
353	C₂²	C₇×#578	1	2	yes	—
354	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	8	no	—
360	C₄	C₇×#550	1	2	yes	—
361	C₄	C₂×C₇×#135	1	4	yes	—
362	C₄	C₂²×C₇×#41	1	1	yes	characteristic
363	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
364	C₂	—	8	4	no	—
365	C₂	C₇×#3393	1	4	yes	direct product factor
366	C₂	C₂×C₇×#550	1	1	yes	characteristic
367	C₂	C₂²×C₇×#135	1	1	yes	characteristic
368	C₂	C₂×C₇×#578	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×#556	C₂	semidirect
2. C₇×#3393	C₂	direct (N × H)
4. C₂×C₇×#494	C₂	semidirect
5. C₂×C₇×#464	C₂	semidirect
6. C₂×C₇×#461	C₂	semidirect
7. C₂×C₇×C₈×Q₈	C₂	semidirect
8. C₂×C₄×C₇×Q₁₆	C₂	semidirect
15. C₇×#556	C₂²	semidirect
25. C₇×#494	C₂²	semidirect
26. C₇×#464	C₂²	semidirect
27. C₇×#461	C₂²	semidirect
28. C₇×C₈×Q₈	C₂²	semidirect
29. C₄×C₇×Q₁₆	C₂²	semidirect
38. C₂×#3393	C₇	direct (N × H)
86. C₂×#556	C₂×C₇	semidirect
87. #3393	C₂×C₇	direct (N × H)
89. C₂×#494	C₂×C₇	semidirect
90. C₂×#464	C₂×C₇	semidirect
91. C₂×#461	C₂×C₇	semidirect
92. C₂×C₈×Q₈	C₂×C₇	semidirect
93. C₂×C₄×Q₁₆	C₂×C₇	semidirect
145. #556	C₂²×C₇	semidirect
155. #494	C₂²×C₇	semidirect
156. #464	C₂²×C₇	semidirect
157. #461	C₂²×C₇	semidirect
158. C₈×Q₈	C₂²×C₇	semidirect
159. C₄×Q₁₆	C₂²×C₇	semidirect
310. C₂×C₇	#3393	direct (N × H)
346. C₇	C₂×#3393	direct (N × H)
365. C₂	C₇×#3393	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×#556	2
C₇×#3393	2
C₂×C₇×#495	2
C₂×C₇×#494	2
C₂×C₇×#464	2
C₂×C₇×#461	2
C₂×C₇×C₈×Q₈	2
C₂×C₄×C₇×Q₁₆	2
C₂×C₄×C₇×D₈	2
C₂×#3393	7

Subgroups — C2×C7×#3393 #13238605

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3393 #13238605