Subgroups — C₂×C₇×#3341 #13238448

Order 1792.

1982 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#555	C₂	1	2	yes	maximal, complemented
2	C₇×#3341	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#482	C₂	1	4	yes	maximal, complemented
5	C₂×C₇×#476	C₂	1	2	yes	maximal, complemented
6	C₂×C₇×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₇×D₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic
11	C₂³×C₇×C₈	C₂²	1	2	yes	—
12	C₇×#555	—	2	8	no	—
13	C₇×#555	C₂²	1	16	yes	complemented
14	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₇×#124	—	2	4	no	—
16	C₂×C₇×#121	—	2	2	no	—
17	C₂×C₇×#121	C₂²	1	4	yes	—
18	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
19	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₂×C₇×#117	—	2	2	no	—
21	C₂×C₇×#117	C₂²	1	4	yes	—
22	C₇×#500	C₂²	1	8	yes	complemented
23	C₇×#482	C₂²	1	32	yes	complemented
24	C₇×#476	C₂²	1	16	yes	complemented
25	C₇×#466	C₂²	1	16	yes	complemented
26	C₄×C₇×D₈	C₂²	1	8	yes	complemented
27	C₇×C₈×D₄	C₂²	1	8	yes	complemented
28	C₇×#427	C₂²	1	16	yes	complemented
29	C₂×C₇×#107	C₂²	1	2	yes	—
30	C₂×C₇×#107	C₂²	1	2	yes	—
31	C₂×C₇×#107	C₂²	1	1	yes	characteristic
32	C₂×C₇×#106	C₂²	1	4	yes	—
33	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₇×#102	C₂²	1	2	yes	—
35	C₂×C₇×#102	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×#3341	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₇×Q₈	—	2	2	no	—
40	C₂²×C₇×D₄	—	2	4	no	—
41	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
42	C₂²×C₇×D₄	C₂³	1	2	yes	—
43	C₂³×C₄×C₇	—	2	2	no	—
44	C₂³×C₄×C₇	C₂³	1	2	yes	—
45	C₂×C₇×D₈	—	2	4	no	—
46	C₂×C₇×D₈	C₂³	1	4	yes	—
47	C₂²×C₇×C₈	—	2	8	no	—
48	C₂²×C₇×C₈	C₂³	1	8	yes	—
49	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₇×C₈	C₂³	1	2	yes	—
51	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
52	C₇×C₄⋊Q₈	—	2	4	no	—
53	C₇×C₄⋊Q₈	C₂³	1	8	yes	—
54	C₇×#124	—	2	32	no	—
55	C₇×#121	—	2	16	no	—
56	C₇×#121	—	2	8	no	—
57	C₇×#121	C₂³	1	16	yes	—
58	C₄×C₇×D₄	—	2	4	no	—
59	C₄×C₇×D₄	D₄	1	4	yes	—
60	C₄×C₇×D₄	C₂³	1	8	yes	—
61	C₄×C₇×D₄	C₂³	1	4	yes	—
62	C₇×#117	—	2	8	no	—
63	C₇×#117	—	2	16	no	—
64	C₇×#117	C₂³	1	16	yes	—
65	C₂×C₇×C₄⋊C₄	—	2	2	no	—
66	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
69	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
71	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
73	C₂×C₄²×C₇	—	2	4	no	—
74	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
75	C₇×#107	C₂³	1	8	yes	—
76	C₇×#107	C₂³	1	8	yes	—
77	C₇×#107	C₂³	1	4	yes	—
78	C₇×#106	C₂³	1	16	yes	—
79	C₇×C₄⋊C₈	C₂³	1	4	yes	—
80	C₇×#102	C₂³	1	16	yes	—
81	C₇×#102	C₂³	1	8	yes	—
82	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
83	C₄×C₇×C₈	C₂³	1	4	yes	—
84	C₂×#555	C₂×C₇	1	2	yes	complemented
85	#3341	C₂×C₇	1	16	yes	direct product factor
86	C₂×#500	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂×#482	C₂×C₇	1	4	yes	complemented
88	C₂×#476	C₂×C₇	1	2	yes	complemented
89	C₂×#466	C₂×C₇	1	2	yes	complemented
90	C₂×C₄×D₈	C₂×C₇	1	1	yes	characteristic, complemented
91	C₂×C₈×D₄	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂×#427	C₂×C₇	1	2	yes	complemented
93	C₂⁴×C₇	—	2	2	no	—
94	C₂⁴×C₇	C₂×D₄	1	2	yes	—
95	C₂×C₇×Q₈	—	2	8	no	—
96	C₂×C₇×Q₈	—	8	4	no	—
97	C₂×C₇×D₄	—	2	16	no	—
98	C₂×C₇×D₄	—	2	4	no	—
99	C₂×C₇×D₄	—	2	2	no	—
100	C₂×C₇×D₄	—	2	4	no	—
101	C₂×C₇×D₄	—	2	4	no	—
102	C₂×C₇×D₄	—	8	8	no	—
103	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
104	C₂×C₇×D₄	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₇	—	2	4	no	—
106	C₂²×C₄×C₇	—	2	4	no	—
107	C₂²×C₄×C₇	—	2	2	no	—
108	C₂²×C₄×C₇	—	2	4	no	—
109	C₂²×C₄×C₇	—	2	8	no	—
110	C₂²×C₄×C₇	—	4	8	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
117	C₇×D₈	—	2	8	no	—
118	C₂×C₇×C₈	—	2	4	no	—
119	C₂×C₇×C₈	—	2	2	no	—
120	C₂×C₇×C₈	—	2	16	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	2	no	—
127	C₇×C₄⋊C₄	—	2	4	no	—
128	C₇×C₄⋊C₄	C₂×D₄	1	4	yes	—
129	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
130	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
131	C₇×C₂²⋊C₄	—	2	16	no	—
132	C₇×C₂²⋊C₄	—	2	16	no	—
133	C₇×C₂²⋊C₄	—	2	8	no	—
134	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
135	C₄²×C₇	—	2	16	no	—
136	C₄²×C₇	C₂×D₄	1	2	yes	—
137	C₄²×C₇	C₂⁴	1	2	yes	—
138	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic
139	C₂³×C₈	C₂²×C₇	1	2	yes	—
140	#555	—	2	8	no	—
141	#555	C₂²×C₇	1	16	yes	complemented
142	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
143	C₂×#124	—	2	4	no	—
144	C₂×#121	—	2	2	no	—
145	C₂×#121	C₂²×C₇	1	4	yes	—
146	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
147	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
148	C₂×#117	—	2	2	no	—
149	C₂×#117	C₂²×C₇	1	4	yes	—
150	#500	C₂²×C₇	1	8	yes	complemented
151	#482	C₂²×C₇	1	32	yes	complemented
152	#476	C₂²×C₇	1	16	yes	complemented
153	#466	C₂²×C₇	1	16	yes	complemented
154	C₄×D₈	C₂²×C₇	1	8	yes	complemented
155	C₈×D₄	C₂²×C₇	1	8	yes	complemented
156	#427	C₂²×C₇	1	16	yes	complemented
157	C₂×#107	C₂²×C₇	1	2	yes	—
158	C₂×#107	C₂²×C₇	1	2	yes	—
159	C₂×#107	C₂²×C₇	1	1	yes	characteristic
160	C₂×#106	C₂²×C₇	1	4	yes	—
161	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
162	C₂×#102	C₂²×C₇	1	2	yes	—
163	C₂×#102	C₂²×C₇	1	4	yes	—
164	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
165	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
166	C₂³×C₇	—	2	4	no	—
167	C₂³×C₇	—	2	4	no	—
168	C₂³×C₇	—	2	4	no	—
169	C₂³×C₇	—	2	4	no	—
170	C₂³×C₇	—	4	4	no	—
171	C₂³×C₇	—	4	4	no	—
172	C₂³×C₇	—	4	4	no	—
173	C₂³×C₇	C₂²×D₄	1	4	yes	—
174	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
175	C₇×Q₈	—	8	8	no	—
176	C₇×D₄	—	2	8	no	—
177	C₇×D₄	—	2	4	no	—
178	C₇×D₄	—	2	4	no	—
179	C₇×D₄	—	4	4	no	—
180	C₇×D₄	—	8	16	no	—
181	C₂×C₄×C₇	—	2	4	no	—
182	C₂×C₄×C₇	—	2	2	no	—
183	C₂×C₄×C₇	—	2	8	no	—
184	C₂×C₄×C₇	—	2	4	no	—
185	C₂×C₄×C₇	—	2	4	no	—
186	C₂×C₄×C₇	—	2	4	no	—
187	C₂×C₄×C₇	—	2	8	no	—
188	C₂×C₄×C₇	—	4	4	no	—
189	C₂×C₄×C₇	—	4	8	no	—
190	C₂×C₄×C₇	—	4	16	no	—
191	C₂×C₄×C₇	#135	1	4	yes	—
192	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₇	C₂×#41	1	2	yes	—
197	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
198	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
199	C₇×C₈	—	2	4	no	—
200	C₇×C₈	—	2	2	no	—
201	C₇×C₈	C₂×#41	1	4	yes	—
202	C₂²×Q₈	—	2	2	no	—
203	C₂²×D₄	—	2	4	no	—
204	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
205	C₂²×D₄	C₂³×C₇	1	2	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	C₂³×C₇	1	2	yes	—
208	C₂×D₈	—	2	4	no	—
209	C₂×D₈	C₂³×C₇	1	4	yes	—
210	C₂²×C₈	—	2	8	no	—
211	C₂²×C₈	C₂³×C₇	1	2	yes	—
212	C₂²×C₈	C₂³×C₇	1	8	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	#124	—	2	32	no	—
218	#121	—	2	16	no	—
219	#121	—	2	8	no	—
220	#121	C₂³×C₇	1	16	yes	—
221	C₄×D₄	—	2	4	no	—
222	C₄×D₄	C₇×D₄	1	4	yes	—
223	C₄×D₄	C₂³×C₇	1	8	yes	—
224	C₄×D₄	C₂³×C₇	1	4	yes	—
225	#117	—	2	8	no	—
226	#117	—	2	16	no	—
227	#117	C₂³×C₇	1	16	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
238	#107	C₂³×C₇	1	4	yes	—
239	#107	C₂³×C₇	1	8	yes	—
240	#107	C₂³×C₇	1	8	yes	—
241	#106	C₂³×C₇	1	16	yes	—
242	C₄⋊C₈	C₂³×C₇	1	4	yes	—
243	#102	C₂³×C₇	1	8	yes	—
244	#102	C₂³×C₇	1	16	yes	—
245	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
246	C₄×C₈	C₂³×C₇	1	4	yes	—
247	C₂²×C₇	—	2	4	no	—
248	C₂²×C₇	—	2	4	no	—
249	C₂²×C₇	—	2	4	no	—
250	C₂²×C₇	—	4	8	no	—
251	C₂²×C₇	—	4	4	no	—
252	C₂²×C₇	—	4	4	no	—
253	C₂²×C₇	—	4	4	no	—
254	C₂²×C₇	—	8	8	no	—
255	C₂²×C₇	#547	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	2	no	—
261	C₄×C₇	—	4	4	no	—
262	C₄×C₇	—	4	8	no	—
263	C₄×C₇	#547	1	2	yes	—
264	C₄×C₇	C₂×#135	1	4	yes	—
265	C₄×C₇	C₂²×#41	1	1	yes	characteristic
266	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
267	C₂⁴	—	2	2	no	—
268	C₂⁴	C₂×C₇×D₄	1	2	yes	—
269	C₂×Q₈	—	2	8	no	—
270	C₂×Q₈	—	8	4	no	—
271	C₂×D₄	—	2	16	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	4	no	—
275	C₂×D₄	—	2	4	no	—
276	C₂×D₄	—	8	8	no	—
277	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
278	C₂×D₄	C₂⁴×C₇	1	4	yes	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
286	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
288	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
291	D₈	—	2	8	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	16	no	—
295	C₂×C₈	C₇×#41	1	4	yes	—
296	C₂×C₈	C₂⁴×C₇	1	2	yes	—
297	C₂×C₈	C₂⁴×C₇	1	4	yes	—
298	C₂×C₈	C₂⁴×C₇	1	2	yes	—
299	C₄⋊C₄	—	2	8	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	C₂×C₇×D₄	1	4	yes	—
303	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
304	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
305	C₂²⋊C₄	—	2	16	no	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₂²⋊C₄	—	2	8	no	—
308	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
309	C₄²	—	2	16	no	—
310	C₄²	C₂×C₇×D₄	1	2	yes	—
311	C₄²	C₂⁴×C₇	1	2	yes	—
312	C₂×C₇	—	4	4	no	—
313	C₂×C₇	—	8	4	no	—
314	C₂×C₇	#3341	1	4	yes	direct product factor
315	C₂×C₇	C₂×#547	1	1	yes	characteristic
316	C₂×C₇	C₂²×#135	1	1	yes	characteristic
317	C₂×C₇	C₂×#576	1	1	yes	characteristic
318	C₂³	—	2	4	no	—
319	C₂³	—	2	4	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	C₂²×C₇×D₄	1	4	yes	—
326	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
327	Q₈	—	8	8	no	—
328	D₄	—	2	4	no	—
329	D₄	—	2	4	no	—
330	D₄	—	2	8	no	—
331	D₄	—	4	4	no	—
332	D₄	—	8	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	8	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	—	4	16	no	—
343	C₂×C₄	C₇×#135	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	C₇×2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	2	2	no	—
353	C₈	C₂×C₇×#41	1	4	yes	—
354	C₇	C₂×#3341	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	4	8	no	—
359	C₂²	—	4	4	no	—
360	C₂²	—	4	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	C₇×#547	1	2	yes	—
364	C₂²	C₂×C₇×#135	1	2	yes	—
365	C₂²	C₇×#576	1	2	yes	—
366	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	4	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	8	no	—
371	C₄	C₇×#547	1	2	yes	—
372	C₄	C₂×C₇×#135	1	4	yes	—
373	C₄	C₂²×C₇×#41	1	1	yes	characteristic
374	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂	—	4	4	no	—
376	C₂	—	8	4	no	—
377	C₂	C₇×#3341	1	4	yes	direct product factor
378	C₂	C₂×C₇×#547	1	1	yes	characteristic
379	C₂	C₂²×C₇×#135	1	1	yes	characteristic
380	C₂	C₂×C₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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
1. C₂×C₇×#555	C₂	semidirect
2. C₇×#3341	C₂	direct (N × H)
3. C₂×C₇×#500	C₂	semidirect
4. C₂×C₇×#482	C₂	semidirect
5. C₂×C₇×#476	C₂	semidirect
6. C₂×C₇×#466	C₂	semidirect
7. C₂×C₄×C₇×D₈	C₂	semidirect
8. C₂×C₇×C₈×D₄	C₂	semidirect
9. C₂×C₇×#427	C₂	semidirect
13. C₇×#555	C₂²	semidirect
22. C₇×#500	C₂²	semidirect
23. C₇×#482	C₂²	semidirect
24. C₇×#476	C₂²	semidirect
25. C₇×#466	C₂²	semidirect
26. C₄×C₇×D₈	C₂²	semidirect
27. C₇×C₈×D₄	C₂²	semidirect
28. C₇×#427	C₂²	semidirect
38. C₂×#3341	C₇	direct (N × H)
84. C₂×#555	C₂×C₇	semidirect
85. #3341	C₂×C₇	direct (N × H)
86. C₂×#500	C₂×C₇	semidirect
87. C₂×#482	C₂×C₇	semidirect
88. C₂×#476	C₂×C₇	semidirect
89. C₂×#466	C₂×C₇	semidirect
90. C₂×C₄×D₈	C₂×C₇	semidirect
91. C₂×C₈×D₄	C₂×C₇	semidirect
92. C₂×#427	C₂×C₇	semidirect
141. #555	C₂²×C₇	semidirect
150. #500	C₂²×C₇	semidirect
151. #482	C₂²×C₇	semidirect
152. #476	C₂²×C₇	semidirect
153. #466	C₂²×C₇	semidirect
154. C₄×D₈	C₂²×C₇	semidirect
155. C₈×D₄	C₂²×C₇	semidirect
156. #427	C₂²×C₇	semidirect
314. C₂×C₇	#3341	direct (N × H)
354. C₇	C₂×#3341	direct (N × H)
377. C₂	C₇×#3341	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×#555	2
C₇×#3341	2
C₂×C₇×#500	2
C₂×C₇×#482	2
C₂×C₇×#476	2
C₂×C₇×#466	2
C₂×C₄×C₇×D₈	2
C₂×C₇×C₈×D₄	2
C₂×C₇×#427	2
C₂×#3341	7

Subgroups — C2×C7×#3341 #13238448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3341 #13238448