Subgroups — C₂²×C₇×#482 #13237718

Order 1792.

2702 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#482	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₇×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₇×D₄	—	2	1	no	—
10	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
12	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₇×#121	—	2	6	no	—
15	C₂×C₇×#121	C₂²	1	12	yes	—
16	C₂×C₇×#117	—	2	6	no	—
17	C₂×C₇×#117	C₂²	1	12	yes	complemented
18	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
22	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
23	C₂²×C₄²×C₇	—	2	1	no	—
24	C₇×#482	C₂²	1	64	yes	direct product factor
25	C₂×C₇×#107	C₂²	1	12	yes	complemented
26	C₂×C₇×#106	C₂²	1	12	yes	complemented
27	C₂×C₇×#102	C₂²	1	12	yes	complemented
28	C₂×C₇×#102	C₂²	1	12	yes	complemented
29	C₂×C₇×C₂²⋊C₈	C₂²	1	12	yes	complemented
30	C₂²×#482	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂⁵×C₇	—	2	1	no	—
32	C₂⁵×C₇	D₄	1	1	yes	characteristic
33	C₂²×C₇×D₄	—	2	12	no	—
34	C₂²×C₇×D₄	—	2	3	no	—
35	C₂²×C₇×D₄	—	2	4	no	—
36	C₂²×C₇×D₄	—	2	4	no	—
37	C₂²×C₇×D₄	—	4	8	no	—
38	C₂²×C₇×D₄	C₂³	1	6	yes	—
39	C₂³×C₄×C₇	—	2	4	no	—
40	C₂³×C₄×C₇	—	2	4	no	—
41	C₂³×C₄×C₇	—	2	1	no	—
42	C₂³×C₄×C₇	—	2	1	no	—
43	C₂³×C₄×C₇	—	2	1	no	—
44	C₂³×C₄×C₇	D₄	1	6	yes	—
45	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₇	C₂³	1	6	yes	—
47	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
48	C₂²×C₇×C₈	—	2	4	no	—
49	C₂²×C₇×C₈	—	2	4	no	—
50	C₂²×C₇×C₈	C₂³	1	6	yes	—
51	C₂²×C₇×C₈	C₂³	1	6	yes	—
52	C₇×#121	—	2	24	no	—
53	C₇×#121	C₂³	1	16	yes	—
54	C₇×#117	—	2	24	no	—
55	C₇×#117	C₂³	1	16	yes	complemented
56	C₂×C₇×C₄⋊C₄	—	2	3	no	—
57	C₂×C₇×C₄⋊C₄	—	2	3	no	—
58	C₂×C₇×C₄⋊C₄	—	2	3	no	—
59	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
60	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
61	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
62	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
63	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
64	C₂×C₄²×C₇	—	2	12	no	—
65	C₇×#107	C₂³	1	16	yes	complemented
66	C₇×#106	C₂³	1	16	yes	complemented
67	C₇×#102	C₂³	1	16	yes	complemented
68	C₇×#102	C₂³	1	16	yes	complemented
69	C₇×C₂²⋊C₈	C₂³	1	16	yes	complemented
70	C₂²×#121	C₂×C₇	1	1	yes	characteristic
71	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
72	C₂×#482	C₂×C₇	1	24	yes	direct product factor
73	C₂²×#107	C₂×C₇	1	1	yes	characteristic, complemented
74	C₂²×#106	C₂×C₇	1	1	yes	characteristic, complemented
75	C₂²×#102	C₂×C₇	1	1	yes	characteristic, complemented
76	C₂²×#102	C₂×C₇	1	1	yes	characteristic, complemented
77	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
78	C₂⁴×C₇	—	2	4	no	—
79	C₂⁴×C₇	—	2	4	no	—
80	C₂⁴×C₇	—	2	4	no	—
81	C₂⁴×C₇	—	2	6	no	—
82	C₂⁴×C₇	—	4	4	no	—
83	C₂⁴×C₇	—	4	4	no	—
84	C₂⁴×C₇	—	4	4	no	—
85	C₂⁴×C₇	C₂×D₄	1	6	yes	—
86	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
87	C₂×C₇×D₄	—	2	16	no	—
88	C₂×C₇×D₄	—	2	6	no	—
89	C₂×C₇×D₄	—	2	12	no	—
90	C₂×C₇×D₄	—	2	12	no	—
91	C₂×C₇×D₄	—	4	48	no	—
92	C₂×C₇×D₄	—	4	12	no	—
93	C₂×C₇×D₄	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₇	—	2	4	no	—
95	C₂²×C₄×C₇	—	2	24	no	—
96	C₂²×C₄×C₇	—	2	12	no	—
97	C₂²×C₄×C₇	—	2	12	no	—
98	C₂²×C₄×C₇	—	2	6	no	—
99	C₂²×C₄×C₇	—	2	6	no	—
100	C₂²×C₄×C₇	—	2	6	no	—
101	C₂²×C₄×C₇	—	4	4	no	—
102	C₂²×C₄×C₇	—	4	4	no	—
103	C₂²×C₄×C₇	—	4	4	no	—
104	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
105	C₂²×C₄×C₇	C₂×D₄	1	12	yes	—
106	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
107	C₂²×C₄×C₇	#41	1	4	yes	—
108	C₂²×C₄×C₇	#41	1	4	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
111	C₂×C₇×C₈	—	2	12	no	—
112	C₂×C₇×C₈	—	2	12	no	—
113	C₂×C₇×C₈	C₂⁴	1	4	yes	—
114	C₂×C₇×C₈	C₂⁴	1	4	yes	—
115	C₇×C₄⋊C₄	—	2	6	no	—
116	C₇×C₄⋊C₄	—	2	6	no	—
117	C₇×C₄⋊C₄	—	2	6	no	—
118	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
119	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
120	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
121	C₇×C₂²⋊C₄	—	2	16	no	—
122	C₇×C₂²⋊C₄	—	2	16	no	—
123	C₄²×C₇	—	2	16	no	—
124	C₂³×D₄	—	2	1	no	—
125	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
126	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
127	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
128	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
129	C₂×#121	—	2	6	no	—
130	C₂×#121	C₂²×C₇	1	12	yes	—
131	C₂×#117	—	2	6	no	—
132	C₂×#117	C₂²×C₇	1	12	yes	complemented
133	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
134	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
135	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
136	C₂²×C₂²⋊C₄	—	2	1	no	—
137	C₂²×C₂²⋊C₄	—	2	1	no	—
138	C₂²×C₄²	—	2	1	no	—
139	#482	C₂²×C₇	1	64	yes	direct product factor
140	C₂×#107	C₂²×C₇	1	12	yes	complemented
141	C₂×#106	C₂²×C₇	1	12	yes	complemented
142	C₂×#102	C₂²×C₇	1	12	yes	complemented
143	C₂×#102	C₂²×C₇	1	12	yes	complemented
144	C₂×C₂²⋊C₈	C₂²×C₇	1	12	yes	complemented
145	C₂³×C₇	—	2	12	no	—
146	C₂³×C₇	—	2	12	no	—
147	C₂³×C₇	—	2	12	no	—
148	C₂³×C₇	—	2	4	no	—
149	C₂³×C₇	—	4	16	no	—
150	C₂³×C₇	—	4	12	no	—
151	C₂³×C₇	—	4	12	no	—
152	C₂³×C₇	—	4	12	no	—
153	C₂³×C₇	—	8	16	no	—
154	C₂³×C₇	#123	1	4	yes	—
155	C₂³×C₇	#135	1	4	yes	—
156	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
157	C₂³×C₇	C₂²×D₄	1	4	yes	—
158	C₂³×C₇	C₂²×D₄	1	3	yes	—
159	C₇×D₄	—	2	4	no	—
160	C₇×D₄	—	2	4	no	—
161	C₇×D₄	—	4	32	no	—
162	C₇×D₄	—	4	12	no	—
163	C₂×C₄×C₇	—	2	12	no	—
164	C₂×C₄×C₇	—	2	24	no	—
165	C₂×C₄×C₇	—	2	4	no	—
166	C₂×C₄×C₇	—	2	4	no	—
167	C₂×C₄×C₇	—	2	4	no	—
168	C₂×C₄×C₇	—	2	4	no	—
169	C₂×C₄×C₇	—	2	4	no	—
170	C₂×C₄×C₇	—	4	12	no	—
171	C₂×C₄×C₇	—	4	12	no	—
172	C₂×C₄×C₇	—	4	12	no	—
173	C₂×C₄×C₇	#123	1	12	yes	—
174	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₇	C₂×#41	1	6	yes	—
177	C₂×C₄×C₇	C₂×#41	1	6	yes	—
178	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
179	C₇×C₈	—	2	4	no	—
180	C₇×C₈	—	2	4	no	—
181	C₂⁵	—	2	1	no	—
182	C₂⁵	C₇×D₄	1	1	yes	characteristic
183	C₂²×D₄	—	2	12	no	—
184	C₂²×D₄	—	2	3	no	—
185	C₂²×D₄	—	2	4	no	—
186	C₂²×D₄	—	2	4	no	—
187	C₂²×D₄	—	4	8	no	—
188	C₂²×D₄	C₂³×C₇	1	6	yes	—
189	C₂³×C₄	—	2	4	no	—
190	C₂³×C₄	—	2	4	no	—
191	C₂³×C₄	—	2	1	no	—
192	C₂³×C₄	—	2	1	no	—
193	C₂³×C₄	—	2	1	no	—
194	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
195	C₂³×C₄	C₇×D₄	1	6	yes	—
196	C₂³×C₄	C₂³×C₇	1	6	yes	—
197	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
198	C₂²×C₈	—	2	4	no	—
199	C₂²×C₈	—	2	4	no	—
200	C₂²×C₈	C₂³×C₇	1	6	yes	—
201	C₂²×C₈	C₂³×C₇	1	6	yes	—
202	#121	—	2	24	no	—
203	#121	C₂³×C₇	1	16	yes	—
204	#117	—	2	24	no	—
205	#117	C₂³×C₇	1	16	yes	complemented
206	C₂×C₄⋊C₄	—	2	3	no	—
207	C₂×C₄⋊C₄	—	2	3	no	—
208	C₂×C₄⋊C₄	—	2	3	no	—
209	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
210	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
211	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
212	C₂×C₂²⋊C₄	—	2	12	no	—
213	C₂×C₂²⋊C₄	—	2	12	no	—
214	C₂×C₄²	—	2	12	no	—
215	#107	C₂³×C₇	1	16	yes	complemented
216	#106	C₂³×C₇	1	16	yes	complemented
217	#102	C₂³×C₇	1	16	yes	complemented
218	#102	C₂³×C₇	1	16	yes	complemented
219	C₂²⋊C₈	C₂³×C₇	1	16	yes	complemented
220	C₂²×C₇	—	2	4	no	—
221	C₂²×C₇	—	2	4	no	—
222	C₂²×C₇	—	2	4	no	—
223	C₂²×C₇	—	4	24	no	—
224	C₂²×C₇	—	4	4	no	—
225	C₂²×C₇	—	4	4	no	—
226	C₂²×C₇	—	4	4	no	—
227	C₂²×C₇	—	8	24	no	—
228	C₂²×C₇	#482	1	16	yes	direct product factor
229	C₂²×C₇	C₂×#123	1	6	yes	—
230	C₂²×C₇	C₂×#135	1	6	yes	—
231	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
232	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₇	—	2	4	no	—
234	C₄×C₇	—	4	4	no	—
235	C₄×C₇	—	4	4	no	—
236	C₄×C₇	—	4	4	no	—
237	C₄×C₇	C₂×#123	1	6	yes	—
238	C₄×C₇	C₂²×#41	1	1	yes	characteristic
239	C₄×C₇	C₂²×#41	1	1	yes	characteristic
240	C₂⁴	—	2	4	no	—
241	C₂⁴	—	2	4	no	—
242	C₂⁴	—	2	4	no	—
243	C₂⁴	—	2	6	no	—
244	C₂⁴	—	4	4	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	C₂×C₇×D₄	1	6	yes	—
248	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
249	C₂×D₄	—	2	16	no	—
250	C₂×D₄	—	2	6	no	—
251	C₂×D₄	—	2	12	no	—
252	C₂×D₄	—	2	12	no	—
253	C₂×D₄	—	4	48	no	—
254	C₂×D₄	—	4	12	no	—
255	C₂×D₄	C₂⁴×C₇	1	4	yes	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	24	no	—
258	C₂²×C₄	—	2	12	no	—
259	C₂²×C₄	—	2	12	no	—
260	C₂²×C₄	—	2	6	no	—
261	C₂²×C₄	—	2	6	no	—
262	C₂²×C₄	—	2	6	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	—	4	4	no	—
266	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
267	C₂²×C₄	C₂×C₇×D₄	1	12	yes	—
268	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
269	C₂²×C₄	C₇×#41	1	4	yes	—
270	C₂²×C₄	C₇×#41	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
273	C₂×C₈	—	2	12	no	—
274	C₂×C₈	—	2	12	no	—
275	C₂×C₈	C₂⁴×C₇	1	4	yes	—
276	C₂×C₈	C₂⁴×C₇	1	4	yes	—
277	C₄⋊C₄	—	2	6	no	—
278	C₄⋊C₄	—	2	6	no	—
279	C₄⋊C₄	—	2	6	no	—
280	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
281	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
282	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₄²	—	2	16	no	—
286	C₂×C₇	—	4	4	no	—
287	C₂×C₇	—	8	4	no	—
288	C₂×C₇	C₂×#482	1	12	yes	direct product factor
289	C₂×C₇	C₂²×#123	1	1	yes	characteristic
290	C₂×C₇	C₂²×#135	1	1	yes	characteristic
291	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂³	—	2	12	no	—
293	C₂³	—	2	12	no	—
294	C₂³	—	2	12	no	—
295	C₂³	—	2	4	no	—
296	C₂³	—	4	16	no	—
297	C₂³	—	4	12	no	—
298	C₂³	—	4	12	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	8	16	no	—
301	C₂³	C₇×#123	1	4	yes	—
302	C₂³	C₇×#135	1	4	yes	—
303	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
304	C₂³	C₂²×C₇×D₄	1	4	yes	—
305	C₂³	C₂²×C₇×D₄	1	3	yes	—
306	D₄	—	2	4	no	—
307	D₄	—	2	4	no	—
308	D₄	—	4	32	no	—
309	D₄	—	4	12	no	—
310	C₂×C₄	—	2	12	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	24	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	4	12	no	—
318	C₂×C₄	—	4	12	no	—
319	C₂×C₄	—	4	12	no	—
320	C₂×C₄	C₇×#123	1	12	yes	—
321	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
322	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
323	C₂×C₄	C₂×C₇×#41	1	6	yes	—
324	C₂×C₄	C₂×C₇×#41	1	6	yes	—
325	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
326	C₈	—	2	4	no	—
327	C₈	—	2	4	no	—
328	C₇	C₂²×#482	1	1	yes	characteristic, direct product factor, Sylow
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	24	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	8	24	no	—
337	C₂²	C₇×#482	1	16	yes	direct product factor
338	C₂²	C₂×C₇×#123	1	6	yes	—
339	C₂²	C₂×C₇×#135	1	6	yes	—
340	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	6	yes	—
341	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	4	no	—
346	C₄	C₂×C₇×#123	1	6	yes	—
347	C₄	C₂²×C₇×#41	1	1	yes	characteristic
348	C₄	C₂²×C₇×#41	1	1	yes	characteristic
349	C₂	—	4	4	no	—
350	C₂	—	8	4	no	—
351	C₂	C₂×C₇×#482	1	12	yes	direct product factor
352	C₂	C₂²×C₇×#123	1	1	yes	characteristic
353	C₂	C₂²×C₇×#135	1	1	yes	characteristic
354	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ C₂⁴×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₇×#117	C₂	semidirect
3. C₂×C₇×#482	C₂	direct (N × H)
4. C₂²×C₇×#107	C₂	semidirect
5. C₂²×C₇×#106	C₂	semidirect
6. C₂²×C₇×#102	C₂	semidirect
7. C₂²×C₇×#102	C₂	semidirect
8. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
17. C₂×C₇×#117	C₂²	semidirect
24. C₇×#482	C₂²	direct (N × H)
25. C₂×C₇×#107	C₂²	semidirect
26. C₂×C₇×#106	C₂²	semidirect
27. C₂×C₇×#102	C₂²	semidirect
28. C₂×C₇×#102	C₂²	semidirect
29. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
30. C₂²×#482	C₇	direct (N × H)
55. C₇×#117	C₂³	semidirect
65. C₇×#107	C₂³	semidirect
66. C₇×#106	C₂³	semidirect
67. C₇×#102	C₂³	semidirect
68. C₇×#102	C₂³	semidirect
69. C₇×C₂²⋊C₈	C₂³	semidirect
71. C₂²×#117	C₂×C₇	semidirect
72. C₂×#482	C₂×C₇	direct (N × H)
73. C₂²×#107	C₂×C₇	semidirect
74. C₂²×#106	C₂×C₇	semidirect
75. C₂²×#102	C₂×C₇	semidirect
76. C₂²×#102	C₂×C₇	semidirect
77. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
132. C₂×#117	C₂²×C₇	semidirect
139. #482	C₂²×C₇	direct (N × H)
140. C₂×#107	C₂²×C₇	semidirect
141. C₂×#106	C₂²×C₇	semidirect
142. C₂×#102	C₂²×C₇	semidirect
143. C₂×#102	C₂²×C₇	semidirect
144. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
205. #117	C₂³×C₇	semidirect
215. #107	C₂³×C₇	semidirect
216. #106	C₂³×C₇	semidirect
217. #102	C₂³×C₇	semidirect
218. #102	C₂³×C₇	semidirect
219. C₂²⋊C₈	C₂³×C₇	semidirect
228. C₂²×C₇	#482	direct (N × H)
288. C₂×C₇	C₂×#482	direct (N × H)
328. C₇	C₂²×#482	direct (N × H)
337. C₂²	C₇×#482	direct (N × H)
351. C₂	C₂×C₇×#482	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇×#121	2
C₂²×C₇×#117	2
C₂×C₇×#482	2
C₂²×C₇×#107	2
C₂²×C₇×#106	2
C₂²×C₇×#102	2
C₂²×C₇×C₂²⋊C₈	2
C₂²×#482	7

Subgroups — C22×C7×#482 #13237718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#482 #13237718