Subgroups — C₂²×C₇×#440 #13237368

Order 1792.

3222 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₇×D₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×#440	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₇×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₇×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₇×#102	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
10	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₇	—	2	1	no	—
12	C₂²×C₇×SD₁₆	C₄	1	16	yes	complemented
13	C₂²×C₇×SD₁₆	C₂²	1	12	yes	—
14	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
15	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₇×Q₈	—	2	6	no	—
17	C₂×C₄×C₇×Q₈	C₂²	1	12	yes	complemented
18	C₂×C₄×C₇×D₄	—	2	6	no	—
19	C₂×C₄×C₇×D₄	C₂²	1	12	yes	—
20	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
24	C₂²×C₄²×C₇	—	2	1	no	—
25	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
26	C₇×#440	C₂²	1	64	yes	direct product factor
27	C₂×C₇×#107	C₂²	1	12	yes	complemented
28	C₂×C₇×#103	C₂²	1	12	yes	complemented
29	C₂×C₇×#102	C₂²	1	12	yes	—
30	C₂×C₇×#97	C₂²	1	12	yes	complemented
31	C₂²×#440	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁵×C₇	—	2	1	no	—
33	C₂²×C₇×Q₈	—	2	3	no	—
34	C₂²×C₇×Q₈	—	2	4	no	—
35	C₂²×C₇×Q₈	C₂×C₄	1	8	yes	complemented
36	C₂²×C₇×Q₈	C₂³	1	6	yes	—
37	C₂²×C₇×D₄	—	2	3	no	—
38	C₂²×C₇×D₄	—	2	4	no	—
39	C₂²×C₇×D₄	C₂×C₄	1	8	yes	—
40	C₂²×C₇×D₄	C₂³	1	6	yes	—
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	—	2	12	no	—
45	C₂³×C₄×C₇	—	4	8	no	—
46	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
49	C₂×C₇×SD₁₆	C₂×C₄	1	96	yes	complemented
50	C₂×C₇×SD₁₆	C₂³	1	16	yes	—
51	C₂²×C₇×C₈	—	2	4	no	—
52	C₂²×C₇×C₈	C₂×C₄	1	8	yes	complemented
53	C₂²×C₇×C₈	C₂³	1	6	yes	—
54	C₂²×C₇×C₈	C₂³	1	6	yes	—
55	C₄×C₇×Q₈	—	2	24	no	—
56	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
57	C₄×C₇×D₄	—	2	24	no	—
58	C₄×C₇×D₄	C₂³	1	16	yes	—
59	C₂×C₇×C₄⋊C₄	—	2	12	no	—
60	C₂×C₇×C₄⋊C₄	—	2	3	no	—
61	C₂×C₇×C₄⋊C₄	—	2	3	no	—
62	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
63	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
64	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
65	C₂×C₄²×C₇	—	2	12	no	—
66	C₂×C₄²×C₇	D₄	1	6	yes	—
67	C₂×C₄²×C₇	C₂³	1	6	yes	—
68	C₇×#107	C₂³	1	16	yes	complemented
69	C₇×#103	C₂³	1	16	yes	complemented
70	C₇×#102	C₂³	1	16	yes	—
71	C₇×#97	C₂³	1	16	yes	complemented
72	C₂³×SD₁₆	C₂×C₇	1	1	yes	characteristic
73	C₂²×C₄×Q₈	C₂×C₇	1	1	yes	characteristic, complemented
74	C₂²×C₄×D₄	C₂×C₇	1	1	yes	characteristic
75	C₂×#440	C₂×C₇	1	24	yes	direct product factor
76	C₂²×#107	C₂×C₇	1	1	yes	characteristic, complemented
77	C₂²×#103	C₂×C₇	1	1	yes	characteristic, complemented
78	C₂²×#102	C₂×C₇	1	1	yes	characteristic
79	C₂²×#97	C₂×C₇	1	1	yes	characteristic, complemented
80	C₂⁴×C₇	—	2	8	no	—
81	C₂⁴×C₇	—	2	6	no	—
82	C₂⁴×C₇	—	4	4	no	—
83	C₂⁴×C₇	—	4	4	no	—
84	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
85	C₂×C₇×Q₈	—	2	24	no	—
86	C₂×C₇×Q₈	—	2	6	no	—
87	C₂×C₇×Q₈	—	2	12	no	—
88	C₂×C₇×Q₈	C₂²×C₄	1	24	yes	complemented
89	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
90	C₂×C₇×D₄	—	2	24	no	—
91	C₂×C₇×D₄	—	2	6	no	—
92	C₂×C₇×D₄	—	2	12	no	—
93	C₂×C₇×D₄	C₂²×C₄	1	24	yes	—
94	C₂×C₇×D₄	C₂⁴	1	4	yes	—
95	C₂²×C₄×C₇	—	2	8	no	—
96	C₂²×C₄×C₇	—	2	4	no	—
97	C₂²×C₄×C₇	—	2	4	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	—	2	16	no	—
102	C₂²×C₄×C₇	—	4	48	no	—
103	C₂²×C₄×C₇	—	4	4	no	—
104	C₂²×C₄×C₇	—	4	4	no	—
105	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
107	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
109	C₂²×C₄×C₇	#41	1	4	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
111	C₇×SD₁₆	C₂²×C₄	1	64	yes	complemented
112	C₂×C₇×C₈	—	2	12	no	—
113	C₂×C₇×C₈	C₂²×C₄	1	24	yes	complemented
114	C₂×C₇×C₈	C₂⁴	1	4	yes	—
115	C₂×C₇×C₈	C₂⁴	1	4	yes	—
116	C₇×C₄⋊C₄	—	2	16	no	—
117	C₇×C₄⋊C₄	—	2	6	no	—
118	C₇×C₄⋊C₄	—	2	6	no	—
119	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
120	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
121	C₇×C₂²⋊C₄	—	2	16	no	—
122	C₄²×C₇	—	2	16	no	—
123	C₄²×C₇	C₂×D₄	1	12	yes	—
124	C₄²×C₇	C₂⁴	1	4	yes	—
125	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
126	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
127	C₂⁴×C₄	—	2	1	no	—
128	C₂²×SD₁₆	C₄×C₇	1	16	yes	complemented
129	C₂²×SD₁₆	C₂²×C₇	1	12	yes	—
130	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
131	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic
132	C₂×C₄×Q₈	—	2	6	no	—
133	C₂×C₄×Q₈	C₂²×C₇	1	12	yes	complemented
134	C₂×C₄×D₄	—	2	6	no	—
135	C₂×C₄×D₄	C₂²×C₇	1	12	yes	—
136	C₂²×C₄⋊C₄	—	2	1	no	—
137	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
138	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
139	C₂²×C₂²⋊C₄	—	2	1	no	—
140	C₂²×C₄²	—	2	1	no	—
141	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
142	#440	C₂²×C₇	1	64	yes	direct product factor
143	C₂×#107	C₂²×C₇	1	12	yes	complemented
144	C₂×#103	C₂²×C₇	1	12	yes	complemented
145	C₂×#102	C₂²×C₇	1	12	yes	—
146	C₂×#97	C₂²×C₇	1	12	yes	complemented
147	C₂³×C₇	—	2	24	no	—
148	C₂³×C₇	—	2	4	no	—
149	C₂³×C₇	—	4	12	no	—
150	C₂³×C₇	—	4	12	no	—
151	C₂³×C₇	—	4	32	no	—
152	C₂³×C₇	C₄×D₄	1	4	yes	—
153	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
154	C₂³×C₇	#137	1	4	yes	—
155	C₂³×C₇	C₂²×D₄	1	3	yes	—
156	C₇×Q₈	—	2	24	no	—
157	C₇×Q₈	—	2	4	no	—
158	C₇×Q₈	C₂³×C₄	1	8	yes	complemented
159	C₇×D₄	—	2	24	no	—
160	C₇×D₄	—	2	4	no	—
161	C₇×D₄	C₂³×C₄	1	8	yes	—
162	C₂×C₄×C₇	—	2	24	no	—
163	C₂×C₄×C₇	—	2	12	no	—
164	C₂×C₄×C₇	—	2	12	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	—	4	32	no	—
169	C₂×C₄×C₇	—	4	12	no	—
170	C₂×C₄×C₇	—	4	12	no	—
171	C₂×C₄×C₇	C₄×D₄	1	12	yes	—
172	C₂×C₄×C₇	C₂³×C₄	1	6	yes	—
173	C₂×C₄×C₇	C₂²×D₄	1	4	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	C₂⁵	1	1	yes	characteristic
178	C₇×C₈	—	2	4	no	—
179	C₇×C₈	C₂³×C₄	1	8	yes	complemented
180	C₂⁵	—	2	1	no	—
181	C₂²×Q₈	—	2	3	no	—
182	C₂²×Q₈	—	2	4	no	—
183	C₂²×Q₈	C₂×C₄×C₇	1	8	yes	complemented
184	C₂²×Q₈	C₂³×C₇	1	6	yes	—
185	C₂²×D₄	—	2	3	no	—
186	C₂²×D₄	—	2	4	no	—
187	C₂²×D₄	C₂×C₄×C₇	1	8	yes	—
188	C₂²×D₄	C₂³×C₇	1	6	yes	—
189	C₂³×C₄	—	2	1	no	—
190	C₂³×C₄	—	2	1	no	—
191	C₂³×C₄	—	2	1	no	—
192	C₂³×C₄	—	2	12	no	—
193	C₂³×C₄	—	4	8	no	—
194	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
195	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
197	C₂×SD₁₆	C₂×C₄×C₇	1	96	yes	complemented
198	C₂×SD₁₆	C₂³×C₇	1	16	yes	—
199	C₂²×C₈	—	2	4	no	—
200	C₂²×C₈	C₂×C₄×C₇	1	8	yes	complemented
201	C₂²×C₈	C₂³×C₇	1	6	yes	—
202	C₂²×C₈	C₂³×C₇	1	6	yes	—
203	C₄×Q₈	—	2	24	no	—
204	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
205	C₄×D₄	—	2	24	no	—
206	C₄×D₄	C₂³×C₇	1	16	yes	—
207	C₂×C₄⋊C₄	—	2	12	no	—
208	C₂×C₄⋊C₄	—	2	3	no	—
209	C₂×C₄⋊C₄	—	2	3	no	—
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×C₄²	—	2	12	no	—
214	C₂×C₄²	C₇×D₄	1	6	yes	—
215	C₂×C₄²	C₂³×C₇	1	6	yes	—
216	#107	C₂³×C₇	1	16	yes	complemented
217	#103	C₂³×C₇	1	16	yes	complemented
218	#102	C₂³×C₇	1	16	yes	—
219	#97	C₂³×C₇	1	16	yes	complemented
220	C₂²×C₇	—	2	8	no	—
221	C₂²×C₇	—	4	48	no	—
222	C₂²×C₇	—	4	4	no	—
223	C₂²×C₇	—	4	4	no	—
224	C₂²×C₇	#440	1	16	yes	direct product factor
225	C₂²×C₇	C₂×C₄×D₄	1	6	yes	—
226	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
227	C₂²×C₇	C₂×#137	1	6	yes	—
228	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
229	C₄×C₇	—	2	8	no	—
230	C₄×C₇	—	2	4	no	—
231	C₄×C₇	—	2	4	no	—
232	C₄×C₇	—	4	4	no	—
233	C₄×C₇	—	4	4	no	—
234	C₄×C₇	C₂×C₄×D₄	1	6	yes	—
235	C₄×C₇	C₂⁴×C₄	1	1	yes	characteristic
236	C₄×C₇	C₂²×#41	1	1	yes	characteristic
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	2	6	no	—
239	C₂⁴	—	4	4	no	—
240	C₂⁴	—	4	4	no	—
241	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
242	C₂×Q₈	—	2	24	no	—
243	C₂×Q₈	—	2	6	no	—
244	C₂×Q₈	—	2	12	no	—
245	C₂×Q₈	C₂²×C₄×C₇	1	24	yes	complemented
246	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
247	C₂×D₄	—	2	24	no	—
248	C₂×D₄	—	2	6	no	—
249	C₂×D₄	—	2	12	no	—
250	C₂×D₄	C₂²×C₄×C₇	1	24	yes	—
251	C₂×D₄	C₂⁴×C₇	1	4	yes	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	2	6	no	—
256	C₂²×C₄	—	2	6	no	—
257	C₂²×C₄	—	2	6	no	—
258	C₂²×C₄	—	2	16	no	—
259	C₂²×C₄	—	4	48	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
263	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
264	C₂²×C₄	C₂×C₇×D₄	1	6	yes	—
265	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
266	C₂²×C₄	C₇×#41	1	4	yes	—
267	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
268	SD₁₆	C₂²×C₄×C₇	1	64	yes	complemented
269	C₂×C₈	—	2	12	no	—
270	C₂×C₈	C₂²×C₄×C₇	1	24	yes	complemented
271	C₂×C₈	C₂⁴×C₇	1	4	yes	—
272	C₂×C₈	C₂⁴×C₇	1	4	yes	—
273	C₄⋊C₄	—	2	16	no	—
274	C₄⋊C₄	—	2	6	no	—
275	C₄⋊C₄	—	2	6	no	—
276	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
277	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
278	C₂²⋊C₄	—	2	16	no	—
279	C₄²	—	2	16	no	—
280	C₄²	C₂×C₇×D₄	1	12	yes	—
281	C₄²	C₂⁴×C₇	1	4	yes	—
282	C₂×C₇	—	4	8	no	—
283	C₂×C₇	C₂×#440	1	12	yes	direct product factor
284	C₂×C₇	C₂²×C₄×D₄	1	1	yes	characteristic
285	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
286	C₂×C₇	C₂²×#137	1	1	yes	characteristic
287	C₂³	—	2	4	no	—
288	C₂³	—	2	24	no	—
289	C₂³	—	4	12	no	—
290	C₂³	—	4	12	no	—
291	C₂³	—	4	32	no	—
292	C₂³	C₄×C₇×D₄	1	4	yes	—
293	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
294	C₂³	C₇×#137	1	4	yes	—
295	C₂³	C₂²×C₇×D₄	1	3	yes	—
296	Q₈	—	2	4	no	—
297	Q₈	—	2	24	no	—
298	Q₈	C₂³×C₄×C₇	1	8	yes	complemented
299	D₄	—	2	4	no	—
300	D₄	—	2	24	no	—
301	D₄	C₂³×C₄×C₇	1	8	yes	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	24	no	—
304	C₂×C₄	—	2	12	no	—
305	C₂×C₄	—	2	12	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	4	32	no	—
309	C₂×C₄	—	4	12	no	—
310	C₂×C₄	—	4	12	no	—
311	C₂×C₄	C₄×C₇×D₄	1	12	yes	—
312	C₂×C₄	C₂³×C₄×C₇	1	6	yes	—
313	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
314	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
315	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
316	C₂×C₄	C₂×C₇×#41	1	6	yes	—
317	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
318	C₈	—	2	4	no	—
319	C₈	C₂³×C₄×C₇	1	8	yes	complemented
320	C₇	C₂²×#440	1	1	yes	characteristic, direct product factor, Sylow
321	C₂²	—	2	8	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	48	no	—
325	C₂²	C₇×#440	1	16	yes	direct product factor
326	C₂²	C₂×C₄×C₇×D₄	1	6	yes	—
327	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	6	yes	—
328	C₂²	C₂×C₇×#137	1	6	yes	—
329	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	4	no	—
332	C₄	—	2	8	no	—
333	C₄	—	4	4	no	—
334	C₄	—	4	4	no	—
335	C₄	C₂×C₄×C₇×D₄	1	6	yes	—
336	C₄	C₂⁴×C₄×C₇	1	1	yes	characteristic
337	C₄	C₂²×C₇×#41	1	1	yes	characteristic
338	C₂	—	4	8	no	—
339	C₂	C₂×C₇×#440	1	12	yes	direct product factor
340	C₂	C₂²×C₄×C₇×D₄	1	1	yes	characteristic
341	C₂	C₂²×C₇×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂	C₂²×C₇×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂³×C₇×D₄	C₂²
LCS	G ▷ 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
2. C₂²×C₄×C₇×Q₈	C₂	semidirect
4. C₂×C₇×#440	C₂	direct (N × H)
5. C₂²×C₇×#107	C₂	semidirect
6. C₂²×C₇×#103	C₂	semidirect
8. C₂²×C₇×#97	C₂	semidirect
12. C₂²×C₇×SD₁₆	C₄	semidirect
17. C₂×C₄×C₇×Q₈	C₂²	semidirect
26. C₇×#440	C₂²	direct (N × H)
27. C₂×C₇×#107	C₂²	semidirect
28. C₂×C₇×#103	C₂²	semidirect
30. C₂×C₇×#97	C₂²	semidirect
31. C₂²×#440	C₇	direct (N × H)
35. C₂²×C₇×Q₈	C₂×C₄	semidirect
49. C₂×C₇×SD₁₆	C₂×C₄	semidirect
52. C₂²×C₇×C₈	C₂×C₄	semidirect
56. C₄×C₇×Q₈	C₂³	semidirect
68. C₇×#107	C₂³	semidirect
69. C₇×#103	C₂³	semidirect
71. C₇×#97	C₂³	semidirect
73. C₂²×C₄×Q₈	C₂×C₇	semidirect
75. C₂×#440	C₂×C₇	direct (N × H)
76. C₂²×#107	C₂×C₇	semidirect
77. C₂²×#103	C₂×C₇	semidirect
79. C₂²×#97	C₂×C₇	semidirect
88. C₂×C₇×Q₈	C₂²×C₄	semidirect
111. C₇×SD₁₆	C₂²×C₄	semidirect
113. C₂×C₇×C₈	C₂²×C₄	semidirect
128. C₂²×SD₁₆	C₄×C₇	semidirect
133. C₂×C₄×Q₈	C₂²×C₇	semidirect
142. #440	C₂²×C₇	direct (N × H)
143. C₂×#107	C₂²×C₇	semidirect
144. C₂×#103	C₂²×C₇	semidirect
146. C₂×#97	C₂²×C₇	semidirect
158. C₇×Q₈	C₂³×C₄	semidirect
179. C₇×C₈	C₂³×C₄	semidirect
183. C₂²×Q₈	C₂×C₄×C₇	semidirect
197. C₂×SD₁₆	C₂×C₄×C₇	semidirect
200. C₂²×C₈	C₂×C₄×C₇	semidirect
204. C₄×Q₈	C₂³×C₇	semidirect
216. #107	C₂³×C₇	semidirect
217. #103	C₂³×C₇	semidirect
219. #97	C₂³×C₇	semidirect
224. C₂²×C₇	#440	direct (N × H)
245. C₂×Q₈	C₂²×C₄×C₇	semidirect
268. SD₁₆	C₂²×C₄×C₇	semidirect
270. C₂×C₈	C₂²×C₄×C₇	semidirect
283. C₂×C₇	C₂×#440	direct (N × H)
298. Q₈	C₂³×C₄×C₇	semidirect
319. C₈	C₂³×C₄×C₇	semidirect
320. C₇	C₂²×#440	direct (N × H)
325. C₂²	C₇×#440	direct (N × H)
339. C₂	C₂×C₇×#440	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×SD₁₆	2
C₂²×C₄×C₇×Q₈	2
C₂²×C₄×C₇×D₄	2
C₂×C₇×#440	2
C₂²×C₇×#107	2
C₂²×C₇×#103	2
C₂²×C₇×#102	2
C₂²×C₇×#97	2
C₂²×#440	7

Subgroups — C22×C7×#440 #13237368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#440 #13237368