Subgroups — C₂²×C₇×#464 #13237624

Order 1792.

2918 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×Q₁₆	C₂	semidirect
4. C₂²×C₄×C₇×Q₈	C₂	semidirect
5. C₂×C₇×#464	C₂	direct (N × H)
6. C₂²×C₇×C₄⋊C₈	C₂	semidirect
7. C₂²×C₇×#103	C₂	semidirect
13. C₂²×C₇×Q₁₆	C₂²	semidirect
21. C₂×C₄×C₇×Q₈	C₂²	semidirect
28. C₇×#464	C₂²	direct (N × H)
29. C₂×C₇×C₄⋊C₈	C₂²	semidirect
30. C₂×C₇×#103	C₂²	semidirect
32. C₂²×#464	C₇	direct (N × H)
53. C₂×C₇×Q₁₆	C₂³	semidirect
63. C₄×C₇×Q₈	C₂³	semidirect
72. C₇×C₄⋊C₈	C₂³	semidirect
73. C₇×#103	C₂³	semidirect
75. C₂³×Q₁₆	C₂×C₇	semidirect
78. C₂²×C₄×Q₈	C₂×C₇	semidirect
79. C₂×#464	C₂×C₇	direct (N × H)
80. C₂²×C₄⋊C₈	C₂×C₇	semidirect
81. C₂²×#103	C₂×C₇	semidirect
135. C₂²×Q₁₆	C₂²×C₇	semidirect
143. C₂×C₄×Q₈	C₂²×C₇	semidirect
150. #464	C₂²×C₇	direct (N × H)
151. C₂×C₄⋊C₈	C₂²×C₇	semidirect
152. C₂×#103	C₂²×C₇	semidirect
209. C₂×Q₁₆	C₂³×C₇	semidirect
219. C₄×Q₈	C₂³×C₇	semidirect
228. C₄⋊C₈	C₂³×C₇	semidirect
229. #103	C₂³×C₇	semidirect
235. C₂²×C₇	#464	direct (N × H)
297. C₂×C₇	C₂×#464	direct (N × H)
336. C₇	C₂²×#464	direct (N × H)
341. C₂²	C₇×#464	direct (N × H)
355. C₂	C₂×C₇×#464	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×Q₁₆	2
C₂³×C₇×SD₁₆	2
C₂²×C₇×#124	2
C₂²×C₄×C₇×Q₈	2
C₂×C₇×#464	2
C₂²×C₇×C₄⋊C₈	2
C₂²×C₇×#103	2
C₂²×C₇×#102	2
C₂²×#464	7

Subgroups — C22×C7×#464 #13237624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#464 #13237624