Subgroups — C₂×C₇×#3486 #13239998

Order 1792.

11254 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×C₇×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3486	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₇×D₄×Q₈	C₂	1	8	yes	maximal, complemented
5	C₂×C₇×#548	C₂	1	8	yes	maximal, complemented
6	C₂×C₇×#536	C₂	1	6	yes	maximal, complemented
7	C₂×C₇×#525	C₂	1	6	yes	maximal, complemented
8	C₂×C₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₇×2₋¹⁺⁴	—	2	16	no	—
10	C₂×C₇×2₋¹⁺⁴	C₂²	1	16	yes	complemented
11	C₂²×C₇×#41	C₂²	1	6	yes	—
12	C₂²×C₇×#41	C₂²	1	4	yes	complemented
13	C₂³×C₇×Q₈	—	2	16	no	—
14	C₂³×C₇×Q₈	C₂²	1	3	yes	—
15	C₂³×C₇×Q₈	C₂²	1	8	yes	—
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×Q₈	C₂²	1	16	yes	complemented
18	C₂³×C₇×Q₈	C₂²	1	4	yes	complemented
19	C₂⁴×C₄×C₇	C₂²	1	3	yes	—
20	C₇×D₄×Q₈	C₂²	1	128	yes	complemented
21	C₇×#548	C₂²	1	128	yes	complemented
22	C₇×#536	C₂²	1	96	yes	complemented
23	C₂×C₇×C₄⋊Q₈	C₂²	1	12	yes	complemented
24	C₂×C₇×#124	C₂²	1	12	yes	complemented
25	C₇×#525	C₂²	1	96	yes	complemented
26	C₂×C₇×#123	C₂²	1	12	yes	—
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	12	yes	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	24	yes	complemented
29	C₂×C₇×#121	C₂²	1	12	yes	—
30	C₂×C₇×#120	C₂²	1	4	yes	—
31	C₇×#519	C₂²	1	16	yes	complemented
32	C₂×C₄×C₇×Q₈	C₂²	1	8	yes	complemented
33	C₂×C₄×C₇×D₄	C₂²	1	24	yes	—
34	C₂×C₇×#117	C₂²	1	6	yes	—
35	C₂×#3486	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂⁵×C₇	C₂³	1	1	yes	characteristic
37	C₇×2₋¹⁺⁴	—	2	128	no	—
38	C₂×C₇×#41	—	2	32	no	—
39	C₂×C₇×#41	—	2	48	no	—
40	C₂×C₇×#41	C₂³	1	48	yes	—
41	C₂×C₇×#41	C₂³	1	32	yes	complemented
42	C₂²×C₇×Q₈	—	2	64	no	—
43	C₂²×C₇×Q₈	—	2	32	no	—
44	C₂²×C₇×Q₈	—	2	128	no	—
45	C₂²×C₇×Q₈	—	2	24	no	—
46	C₂²×C₇×Q₈	D₄	1	16	yes	complemented
47	C₂²×C₇×Q₈	C₂³	1	12	yes	—
48	C₂²×C₇×Q₈	C₂³	1	24	yes	—
49	C₂²×C₇×Q₈	C₂³	1	64	yes	—
50	C₂²×C₇×Q₈	C₂³	1	6	yes	—
51	C₂²×C₇×Q₈	C₂³	1	4	yes	—
52	C₂²×C₇×Q₈	C₂³	1	8	yes	—
53	C₂²×C₇×Q₈	C₂³	1	32	yes	complemented
54	C₂²×C₇×D₄	C₂³	1	4	yes	—
55	C₂²×C₇×D₄	C₂³	1	6	yes	—
56	C₂²×C₇×D₄	C₂³	1	8	yes	—
57	C₂³×C₄×C₇	—	2	24	no	—
58	C₂³×C₄×C₇	C₂³	1	12	yes	—
59	C₂³×C₄×C₇	C₂³	1	3	yes	—
60	C₂³×C₄×C₇	C₂³	1	24	yes	—
61	C₂³×C₄×C₇	C₂³	1	12	yes	—
62	C₂³×C₄×C₇	C₂³	1	3	yes	—
63	C₇×C₄⋊Q₈	C₂³	1	96	yes	complemented
64	C₇×#124	C₂³	1	96	yes	complemented
65	C₇×#123	C₂³	1	96	yes	—
66	C₇×C₂²⋊Q₈	C₂³	1	96	yes	—
67	C₇×C₂²⋊Q₈	C₂³	1	192	yes	complemented
68	C₇×#121	C₂³	1	96	yes	—
69	C₇×#120	C₂³	1	32	yes	—
70	C₄×C₇×Q₈	C₂³	1	64	yes	complemented
71	C₄×C₇×D₄	C₂³	1	192	yes	—
72	C₇×#117	C₂³	1	48	yes	—
73	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
74	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	—
75	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
76	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
78	C₂×C₄²×C₇	C₂³	1	12	yes	—
79	C₂²×2₋¹⁺⁴	C₂×C₇	1	1	yes	characteristic, complemented
80	C₂⁴×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
81	#3486	C₂×C₇	1	32	yes	direct product factor
82	C₂×D₄×Q₈	C₂×C₇	1	8	yes	complemented
83	C₂×#548	C₂×C₇	1	8	yes	complemented
84	C₂×#536	C₂×C₇	1	6	yes	complemented
85	C₂×#525	C₂×C₇	1	6	yes	complemented
86	C₂×#519	C₂×C₇	1	1	yes	characteristic, complemented
87	C₂⁴×C₇	—	2	4	no	—
88	C₂⁴×C₇	—	2	8	no	—
89	C₂⁴×C₇	C₂⁴	1	4	yes	—
90	C₂⁴×C₇	C₂⁴	1	4	yes	—
91	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
92	C₂⁴×C₇	C₂⁴	1	2	yes	—
93	C₇×#41	—	2	128	no	—
94	C₇×#41	—	2	192	no	—
95	C₂×C₇×Q₈	—	2	256	no	—
96	C₂×C₇×Q₈	—	2	128	no	—
97	C₂×C₇×Q₈	—	2	48	no	—
98	C₂×C₇×Q₈	—	2	96	no	—
99	C₂×C₇×Q₈	—	2	24	no	—
100	C₂×C₇×Q₈	C₂×D₄	1	32	yes	—
101	C₂×C₇×Q₈	C₂×D₄	1	64	yes	complemented
102	C₂×C₇×Q₈	C₂⁴	1	24	yes	—
103	C₂×C₇×Q₈	C₂⁴	1	48	yes	—
104	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
105	C₂×C₇×D₄	—	2	16	no	—
106	C₂×C₇×D₄	—	2	32	no	—
107	C₂×C₇×D₄	—	2	24	no	—
108	C₂×C₇×D₄	C₂⁴	1	32	yes	—
109	C₂×C₇×D₄	C₂⁴	1	16	yes	—
110	C₂×C₇×D₄	C₂⁴	1	24	yes	—
111	C₂²×C₄×C₇	—	2	12	no	—
112	C₂²×C₄×C₇	—	2	48	no	—
113	C₂²×C₄×C₇	—	2	96	no	—
114	C₂²×C₄×C₇	—	2	48	no	—
115	C₂²×C₄×C₇	C₂×D₄	1	24	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	48	yes	—
117	C₂²×C₄×C₇	C₂⁴	1	48	yes	—
118	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
119	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
121	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
123	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
124	C₇×C₄⋊C₄	C₂⁴	1	48	yes	—
125	C₇×C₄⋊C₄	C₂⁴	1	96	yes	—
126	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
127	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
128	C₇×C₂²⋊C₄	C₂⁴	1	96	yes	—
129	C₄²×C₇	C₂⁴	1	48	yes	—
130	C₂×2₋¹⁺⁴	—	2	16	no	—
131	C₂×2₋¹⁺⁴	C₂²×C₇	1	16	yes	complemented
132	C₂²×#41	C₂²×C₇	1	6	yes	—
133	C₂²×#41	C₂²×C₇	1	4	yes	complemented
134	C₂³×Q₈	—	2	16	no	—
135	C₂³×Q₈	C₂²×C₇	1	3	yes	—
136	C₂³×Q₈	C₂²×C₇	1	8	yes	—
137	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
138	C₂³×Q₈	C₂²×C₇	1	16	yes	complemented
139	C₂³×Q₈	C₂²×C₇	1	4	yes	complemented
140	C₂⁴×C₄	C₂²×C₇	1	3	yes	—
141	D₄×Q₈	C₂²×C₇	1	128	yes	complemented
142	#548	C₂²×C₇	1	128	yes	complemented
143	#536	C₂²×C₇	1	96	yes	complemented
144	C₂×C₄⋊Q₈	C₂²×C₇	1	12	yes	complemented
145	C₂×#124	C₂²×C₇	1	12	yes	complemented
146	#525	C₂²×C₇	1	96	yes	complemented
147	C₂×#123	C₂²×C₇	1	12	yes	—
148	C₂×C₂²⋊Q₈	C₂²×C₇	1	12	yes	—
149	C₂×C₂²⋊Q₈	C₂²×C₇	1	24	yes	complemented
150	C₂×#121	C₂²×C₇	1	12	yes	—
151	C₂×#120	C₂²×C₇	1	4	yes	—
152	#519	C₂²×C₇	1	16	yes	complemented
153	C₂×C₄×Q₈	C₂²×C₇	1	8	yes	complemented
154	C₂×C₄×D₄	C₂²×C₇	1	24	yes	—
155	C₂×#117	C₂²×C₇	1	6	yes	—
156	C₂³×C₇	—	2	32	no	—
157	C₂³×C₇	—	2	8	no	—
158	C₂³×C₇	—	2	4	no	—
159	C₂³×C₇	—	2	4	no	—
160	C₂³×C₇	—	2	4	no	—
161	C₂³×C₇	—	2	16	no	—
162	C₂³×C₇	—	2	8	no	—
163	C₂³×C₇	—	2	16	no	—
164	C₂³×C₇	C₂²×D₄	1	4	yes	—
165	C₂³×C₇	2₋¹⁺⁴	1	8	yes	complemented
166	C₂³×C₇	C₂⁵	1	8	yes	—
167	C₂³×C₇	C₂⁵	1	2	yes	—
168	C₂³×C₇	C₂⁵	1	4	yes	—
169	C₂³×C₇	C₂⁵	1	1	yes	characteristic
170	C₇×Q₈	—	2	96	no	—
171	C₇×Q₈	—	2	48	no	—
172	C₇×Q₈	C₂²×D₄	1	64	yes	—
173	C₇×D₄	—	2	32	no	—
174	C₇×D₄	—	2	64	no	—
175	C₇×D₄	—	2	48	no	—
176	C₂×C₄×C₇	—	2	8	no	—
177	C₂×C₄×C₇	—	2	24	no	—
178	C₂×C₄×C₇	—	2	12	no	—
179	C₂×C₄×C₇	—	2	16	no	—
180	C₂×C₄×C₇	—	2	96	no	—
181	C₂×C₄×C₇	—	2	96	no	—
182	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
183	C₂×C₄×C₇	C₂²×D₄	1	48	yes	—
184	C₂×C₄×C₇	C₂⁵	1	16	yes	—
185	C₂×C₄×C₇	C₂⁵	1	12	yes	—
186	C₂×C₄×C₇	C₂⁵	1	8	yes	—
187	C₂×C₄×C₇	C₂⁵	1	12	yes	—
188	C₂⁵	C₂³×C₇	1	1	yes	characteristic
189	2₋¹⁺⁴	—	2	128	no	—
190	C₂×#41	—	2	32	no	—
191	C₂×#41	—	2	48	no	—
192	C₂×#41	C₂³×C₇	1	48	yes	—
193	C₂×#41	C₂³×C₇	1	32	yes	complemented
194	C₂²×Q₈	—	2	64	no	—
195	C₂²×Q₈	—	2	32	no	—
196	C₂²×Q₈	—	2	128	no	—
197	C₂²×Q₈	—	2	24	no	—
198	C₂²×Q₈	C₇×D₄	1	16	yes	complemented
199	C₂²×Q₈	C₂³×C₇	1	6	yes	—
200	C₂²×Q₈	C₂³×C₇	1	12	yes	—
201	C₂²×Q₈	C₂³×C₇	1	24	yes	—
202	C₂²×Q₈	C₂³×C₇	1	64	yes	—
203	C₂²×Q₈	C₂³×C₇	1	4	yes	—
204	C₂²×Q₈	C₂³×C₇	1	8	yes	—
205	C₂²×Q₈	C₂³×C₇	1	32	yes	complemented
206	C₂²×D₄	C₂³×C₇	1	8	yes	—
207	C₂²×D₄	C₂³×C₇	1	4	yes	—
208	C₂²×D₄	C₂³×C₇	1	6	yes	—
209	C₂³×C₄	—	2	24	no	—
210	C₂³×C₄	C₂³×C₇	1	12	yes	—
211	C₂³×C₄	C₂³×C₇	1	12	yes	—
212	C₂³×C₄	C₂³×C₇	1	3	yes	—
213	C₂³×C₄	C₂³×C₇	1	24	yes	—
214	C₂³×C₄	C₂³×C₇	1	3	yes	—
215	C₄⋊Q₈	C₂³×C₇	1	96	yes	complemented
216	#124	C₂³×C₇	1	96	yes	complemented
217	#123	C₂³×C₇	1	96	yes	—
218	C₂²⋊Q₈	C₂³×C₇	1	96	yes	—
219	C₂²⋊Q₈	C₂³×C₇	1	192	yes	complemented
220	#121	C₂³×C₇	1	96	yes	—
221	#120	C₂³×C₇	1	32	yes	—
222	C₄×Q₈	C₂³×C₇	1	64	yes	complemented
223	C₄×D₄	C₂³×C₇	1	192	yes	—
224	#117	C₂³×C₇	1	48	yes	—
225	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
226	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	—
227	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
228	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
229	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
230	C₂×C₄²	C₂³×C₇	1	12	yes	—
231	C₂²×C₇	—	2	32	no	—
232	C₂²×C₇	—	2	4	no	—
233	C₂²×C₇	—	2	4	no	—
234	C₂²×C₇	—	2	4	no	—
235	C₂²×C₇	—	2	8	no	—
236	C₂²×C₇	—	2	16	no	—
237	C₂²×C₇	—	2	8	no	—
238	C₂²×C₇	—	2	16	no	—
239	C₂²×C₇	—	4	16	no	—
240	C₂²×C₇	C₂³×D₄	1	4	yes	—
241	C₂²×C₇	C₂³×D₄	1	2	yes	—
242	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
243	C₂²×C₇	C₂×2₋¹⁺⁴	1	8	yes	complemented
244	C₂²×C₇	C₂⁶	1	1	yes	characteristic
245	C₄×C₇	—	2	8	no	—
246	C₄×C₇	—	2	12	no	—
247	C₄×C₇	—	2	16	no	—
248	C₄×C₇	C₂³×D₄	1	24	yes	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	8	no	—
251	C₂⁴	C₂⁴×C₇	1	4	yes	—
252	C₂⁴	C₂⁴×C₇	1	4	yes	—
253	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
254	C₂⁴	C₂⁴×C₇	1	2	yes	—
255	#41	—	2	128	no	—
256	#41	—	2	192	no	—
257	C₂×Q₈	—	2	256	no	—
258	C₂×Q₈	—	2	128	no	—
259	C₂×Q₈	—	2	48	no	—
260	C₂×Q₈	—	2	96	no	—
261	C₂×Q₈	—	2	24	no	—
262	C₂×Q₈	C₂×C₇×D₄	1	32	yes	—
263	C₂×Q₈	C₂×C₇×D₄	1	64	yes	complemented
264	C₂×Q₈	C₂⁴×C₇	1	24	yes	—
265	C₂×Q₈	C₂⁴×C₇	1	48	yes	—
266	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
267	C₂×D₄	—	2	16	no	—
268	C₂×D₄	—	2	32	no	—
269	C₂×D₄	—	2	24	no	—
270	C₂×D₄	C₂⁴×C₇	1	32	yes	—
271	C₂×D₄	C₂⁴×C₇	1	16	yes	—
272	C₂×D₄	C₂⁴×C₇	1	24	yes	—
273	C₂²×C₄	—	2	12	no	—
274	C₂²×C₄	—	2	48	no	—
275	C₂²×C₄	—	2	96	no	—
276	C₂²×C₄	—	2	48	no	—
277	C₂²×C₄	C₂×C₇×D₄	1	24	yes	—
278	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
279	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
280	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₇	1	48	yes	—
282	C₂²×C₄	C₂⁴×C₇	1	48	yes	—
283	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
284	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
285	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
286	C₄⋊C₄	C₂⁴×C₇	1	48	yes	—
287	C₄⋊C₄	C₂⁴×C₇	1	96	yes	—
288	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
289	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
290	C₂²⋊C₄	C₂⁴×C₇	1	96	yes	—
291	C₄²	C₂⁴×C₇	1	48	yes	—
292	C₂×C₇	—	2	4	no	—
293	C₂×C₇	—	2	8	no	—
294	C₂×C₇	—	4	8	no	—
295	C₂×C₇	#3486	1	4	yes	direct product factor
296	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
297	C₂×C₇	C₂²×2₋¹⁺⁴	1	2	yes	—
298	C₂³	—	2	32	no	—
299	C₂³	—	2	8	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	16	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	16	no	—
306	C₂³	C₂²×C₇×D₄	1	4	yes	—
307	C₂³	C₇×2₋¹⁺⁴	1	8	yes	complemented
308	C₂³	C₂⁵×C₇	1	8	yes	—
309	C₂³	C₂⁵×C₇	1	2	yes	—
310	C₂³	C₂⁵×C₇	1	4	yes	—
311	C₂³	C₂⁵×C₇	1	1	yes	characteristic
312	Q₈	—	2	96	no	—
313	Q₈	—	2	48	no	—
314	Q₈	C₂²×C₇×D₄	1	64	yes	—
315	D₄	—	2	32	no	—
316	D₄	—	2	64	no	—
317	D₄	—	2	48	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	12	no	—
321	C₂×C₄	—	2	16	no	—
322	C₂×C₄	—	2	96	no	—
323	C₂×C₄	—	2	96	no	—
324	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
325	C₂×C₄	C₂²×C₇×D₄	1	48	yes	—
326	C₂×C₄	C₂⁵×C₇	1	16	yes	—
327	C₂×C₄	C₂⁵×C₇	1	12	yes	—
328	C₂×C₄	C₂⁵×C₇	1	8	yes	—
329	C₂×C₄	C₂⁵×C₇	1	12	yes	—
330	C₇	C₂×#3486	1	1	yes	characteristic, direct product factor, Sylow
331	C₂²	—	2	32	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	16	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	2	16	no	—
339	C₂²	—	4	16	no	—
340	C₂²	C₂³×C₇×D₄	1	4	yes	—
341	C₂²	C₂³×C₇×D₄	1	2	yes	—
342	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
343	C₂²	C₂×C₇×2₋¹⁺⁴	1	8	yes	complemented
344	C₂²	C₂⁶×C₇	1	1	yes	characteristic
345	C₄	—	2	8	no	—
346	C₄	—	2	12	no	—
347	C₄	—	2	16	no	—
348	C₄	C₂³×C₇×D₄	1	24	yes	—
349	C₂	—	2	4	no	—
350	C₂	—	2	8	no	—
351	C₂	—	4	8	no	—
352	C₂	C₇×#3486	1	4	yes	direct product factor
353	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
354	C₂	C₂²×C₇×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×2₋¹⁺⁴	C₂	semidirect
2. C₂⁴×C₇×Q₈	C₂	semidirect
3. C₇×#3486	C₂	direct (N × H)
4. C₂×C₇×D₄×Q₈	C₂	semidirect
5. C₂×C₇×#548	C₂	semidirect
6. C₂×C₇×#536	C₂	semidirect
7. C₂×C₇×#525	C₂	semidirect
8. C₂×C₇×#519	C₂	semidirect
10. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
12. C₂²×C₇×#41	C₂²	semidirect
17. C₂³×C₇×Q₈	C₂²	semidirect
18. C₂³×C₇×Q₈	C₂²	semidirect
20. C₇×D₄×Q₈	C₂²	semidirect
21. C₇×#548	C₂²	semidirect
22. C₇×#536	C₂²	semidirect
23. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
24. C₂×C₇×#124	C₂²	semidirect
25. C₇×#525	C₂²	semidirect
28. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
31. C₇×#519	C₂²	semidirect
32. C₂×C₄×C₇×Q₈	C₂²	semidirect
35. C₂×#3486	C₇	direct (N × H)
41. C₂×C₇×#41	C₂³	semidirect
46. C₂²×C₇×Q₈	D₄	semidirect
53. C₂²×C₇×Q₈	C₂³	semidirect
63. C₇×C₄⋊Q₈	C₂³	semidirect
64. C₇×#124	C₂³	semidirect
67. C₇×C₂²⋊Q₈	C₂³	semidirect
70. C₄×C₇×Q₈	C₂³	semidirect
79. C₂²×2₋¹⁺⁴	C₂×C₇	semidirect
80. C₂⁴×Q₈	C₂×C₇	semidirect
81. #3486	C₂×C₇	direct (N × H)
82. C₂×D₄×Q₈	C₂×C₇	semidirect
83. C₂×#548	C₂×C₇	semidirect
84. C₂×#536	C₂×C₇	semidirect
85. C₂×#525	C₂×C₇	semidirect
86. C₂×#519	C₂×C₇	semidirect
101. C₂×C₇×Q₈	C₂×D₄	semidirect
131. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
133. C₂²×#41	C₂²×C₇	semidirect
138. C₂³×Q₈	C₂²×C₇	semidirect
139. C₂³×Q₈	C₂²×C₇	semidirect
141. D₄×Q₈	C₂²×C₇	semidirect
142. #548	C₂²×C₇	semidirect
143. #536	C₂²×C₇	semidirect
144. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
145. C₂×#124	C₂²×C₇	semidirect
146. #525	C₂²×C₇	semidirect
149. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
152. #519	C₂²×C₇	semidirect
153. C₂×C₄×Q₈	C₂²×C₇	semidirect
165. C₂³×C₇	2₋¹⁺⁴	semidirect
193. C₂×#41	C₂³×C₇	semidirect
198. C₂²×Q₈	C₇×D₄	semidirect
205. C₂²×Q₈	C₂³×C₇	semidirect
215. C₄⋊Q₈	C₂³×C₇	semidirect
216. #124	C₂³×C₇	semidirect
219. C₂²⋊Q₈	C₂³×C₇	semidirect
222. C₄×Q₈	C₂³×C₇	semidirect
243. C₂²×C₇	C₂×2₋¹⁺⁴	semidirect
263. C₂×Q₈	C₂×C₇×D₄	semidirect
295. C₂×C₇	#3486	direct (N × H)
307. C₂³	C₇×2₋¹⁺⁴	semidirect
330. C₇	C₂×#3486	direct (N × H)
343. C₂²	C₂×C₇×2₋¹⁺⁴	semidirect
352. C₂	C₇×#3486	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×C₇×2₋¹⁺⁴	2
C₂⁴×C₇×Q₈	2
C₇×#3486	2
C₂×C₇×D₄×Q₈	2
C₂×C₇×#548	2
C₂×C₇×#536	2
C₂×C₇×#525	2
C₂×C₇×#519	2
C₂×#3486	7

Subgroups — C2×C7×#3486 #13239998

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3486 #13239998