Subgroups — C₂²×C₇×#450 #13237564

Order 1792.

7126 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₇×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₇×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂²×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#450	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₇×#102	C₂	1	2	yes	maximal, complemented
6	C₂²×C₇×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₇	—	2	1	no	—
8	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
9	C₂³×C₇×D₄	—	2	16	no	—
10	C₂³×C₇×D₄	—	2	6	no	—
11	C₂³×C₇×D₄	—	2	1	no	—
12	C₂³×C₇×D₄	C₂²	1	12	yes	—
13	C₂³×C₇×D₄	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
15	C₂²×C₇×SD₁₆	—	2	16	no	—
16	C₂²×C₇×SD₁₆	C₂²	1	24	yes	complemented
17	C₂³×C₇×C₈	C₂²	1	2	yes	complemented
18	C₂×C₇×C₂²⋊Q₈	—	2	6	no	—
19	C₂×C₇×C₂²⋊Q₈	C₂²	1	12	yes	complemented
20	C₂²×C₇×C₄⋊C₄	—	2	1	no	—
21	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×C₂²⋊C₄	—	2	1	no	—
23	C₇×#450	C₂²	1	64	yes	direct product factor
24	C₂×C₇×#102	C₂²	1	24	yes	complemented
25	C₂×C₇×C₂²⋊C₈	C₂²	1	12	yes	complemented
26	C₂²×#450	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂⁵×C₇	—	2	16	no	—
28	C₂⁵×C₇	—	2	12	no	—
29	C₂⁵×C₇	—	2	2	no	—
30	C₂⁵×C₇	—	4	8	no	—
31	C₂⁵×C₇	—	4	8	no	—
32	C₂⁵×C₇	D₄	1	1	yes	characteristic
33	C₂²×C₇×Q₈	—	2	3	no	—
34	C₂²×C₇×Q₈	—	2	8	no	—
35	C₂²×C₇×Q₈	C₂³	1	6	yes	complemented
36	C₂²×C₇×D₄	—	2	16	no	—
37	C₂²×C₇×D₄	—	2	96	no	—
38	C₂²×C₇×D₄	—	2	96	no	—
39	C₂²×C₇×D₄	—	2	12	no	—
40	C₂²×C₇×D₄	—	2	24	no	—
41	C₂²×C₇×D₄	—	2	6	no	—
42	C₂²×C₇×D₄	—	2	8	no	—
43	C₂²×C₇×D₄	D₄	1	16	yes	—
44	C₂²×C₇×D₄	C₂³	1	16	yes	—
45	C₂²×C₇×D₄	C₂³	1	12	yes	—
46	C₂³×C₄×C₇	—	2	8	no	—
47	C₂³×C₄×C₇	—	2	1	no	—
48	C₂³×C₄×C₇	—	2	1	no	—
49	C₂³×C₄×C₇	D₄	1	6	yes	—
50	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₇	C₂³	1	6	yes	—
52	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
53	C₂×C₇×SD₁₆	—	2	96	no	—
54	C₂×C₇×SD₁₆	C₂³	1	32	yes	complemented
55	C₂²×C₇×C₈	—	2	8	no	—
56	C₂²×C₇×C₈	C₂³	1	12	yes	complemented
57	C₇×C₂²⋊Q₈	—	2	24	no	—
58	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
59	C₂×C₇×C₄⋊C₄	—	2	12	no	—
60	C₂×C₇×C₄⋊C₄	—	2	3	no	—
61	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	complemented
62	C₂×C₇×C₂²⋊C₄	—	2	12	no	—
63	C₇×#102	C₂³	1	32	yes	complemented
64	C₇×C₂²⋊C₈	C₂³	1	16	yes	complemented
65	C₂⁴×D₄	C₂×C₇	1	1	yes	characteristic
66	C₂³×SD₁₆	C₂×C₇	1	2	yes	complemented
67	C₂²×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
68	C₂×#450	C₂×C₇	1	24	yes	direct product factor
69	C₂²×#102	C₂×C₇	1	2	yes	complemented
70	C₂²×C₂²⋊C₈	C₂×C₇	1	1	yes	characteristic, complemented
71	C₂⁴×C₇	—	2	4	no	—
72	C₂⁴×C₇	—	2	4	no	—
73	C₂⁴×C₇	—	2	96	no	—
74	C₂⁴×C₇	—	2	16	no	—
75	C₂⁴×C₇	—	2	16	no	—
76	C₂⁴×C₇	—	2	12	no	—
77	C₂⁴×C₇	—	4	48	no	—
78	C₂⁴×C₇	—	4	128	no	—
79	C₂⁴×C₇	—	4	8	no	—
80	C₂⁴×C₇	—	4	48	no	—
81	C₂⁴×C₇	—	4	8	no	—
82	C₂⁴×C₇	SD₁₆	1	8	yes	complemented
83	C₂⁴×C₇	C₂×D₄	1	6	yes	—
84	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
85	C₂×C₇×Q₈	—	2	6	no	—
86	C₂×C₇×Q₈	—	2	24	no	—
87	C₂×C₇×Q₈	—	4	12	no	—
88	C₂×C₇×Q₈	C₂⁴	1	4	yes	complemented
89	C₂×C₇×D₄	—	2	96	no	—
90	C₂×C₇×D₄	—	2	192	no	—
91	C₂×C₇×D₄	—	2	64	no	—
92	C₂×C₇×D₄	—	2	48	no	—
93	C₂×C₇×D₄	—	2	16	no	—
94	C₂×C₇×D₄	—	2	12	no	—
95	C₂×C₇×D₄	—	2	24	no	—
96	C₂×C₇×D₄	C₂×D₄	1	48	yes	—
97	C₂×C₇×D₄	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₇	—	2	4	no	—
99	C₂²×C₄×C₇	—	2	24	no	—
100	C₂²×C₄×C₇	—	2	24	no	—
101	C₂²×C₄×C₇	—	2	6	no	—
102	C₂²×C₄×C₇	—	2	6	no	—
103	C₂²×C₄×C₇	—	4	4	no	—
104	C₂²×C₄×C₇	—	4	4	no	—
105	C₂²×C₄×C₇	C₂×D₄	1	6	yes	—
106	C₂²×C₄×C₇	C₂×D₄	1	12	yes	—
107	C₂²×C₄×C₇	C₂×D₄	1	3	yes	—
108	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
109	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
111	C₇×SD₁₆	—	2	64	no	—
112	C₂×C₇×C₈	—	2	24	no	—
113	C₂×C₇×C₈	C₂⁴	1	8	yes	complemented
114	C₇×C₄⋊C₄	—	2	16	no	—
115	C₇×C₄⋊C₄	—	2	6	no	—
116	C₇×C₄⋊C₄	C₂⁴	1	4	yes	complemented
117	C₇×C₂²⋊C₄	—	2	16	no	—
118	C₂⁶	—	2	1	no	—
119	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
120	C₂³×D₄	—	2	16	no	—
121	C₂³×D₄	—	2	1	no	—
122	C₂³×D₄	—	2	6	no	—
123	C₂³×D₄	C₂²×C₇	1	12	yes	—
124	C₂³×D₄	C₂²×C₇	1	2	yes	—
125	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
126	C₂²×SD₁₆	—	2	16	no	—
127	C₂²×SD₁₆	C₂²×C₇	1	24	yes	complemented
128	C₂³×C₈	C₂²×C₇	1	2	yes	complemented
129	C₂×C₂²⋊Q₈	—	2	6	no	—
130	C₂×C₂²⋊Q₈	C₂²×C₇	1	12	yes	complemented
131	C₂²×C₄⋊C₄	—	2	1	no	—
132	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
133	C₂²×C₂²⋊C₄	—	2	1	no	—
134	#450	C₂²×C₇	1	64	yes	direct product factor
135	C₂×#102	C₂²×C₇	1	24	yes	complemented
136	C₂×C₂²⋊C₈	C₂²×C₇	1	12	yes	complemented
137	C₂³×C₇	—	2	12	no	—
138	C₂³×C₇	—	2	12	no	—
139	C₂³×C₇	—	2	32	no	—
140	C₂³×C₇	—	2	64	no	—
141	C₂³×C₇	—	2	48	no	—
142	C₂³×C₇	—	2	8	no	—
143	C₂³×C₇	—	4	384	no	—
144	C₂³×C₇	—	4	32	no	—
145	C₂³×C₇	—	4	24	no	—
146	C₂³×C₇	—	4	32	no	—
147	C₂³×C₇	—	4	24	no	—
148	C₂³×C₇	—	4	64	no	—
149	C₂³×C₇	#120	1	4	yes	—
150	C₂³×C₇	C₂×SD₁₆	1	4	yes	—
151	C₂³×C₇	C₂×SD₁₆	1	24	yes	complemented
152	C₂³×C₇	AGL(1,ℤ/8)	1	4	yes	—
153	C₂³×C₇	C₂²×D₄	1	4	yes	—
154	C₂³×C₇	C₂²×D₄	1	3	yes	—
155	C₇×Q₈	—	2	8	no	—
156	C₇×Q₈	—	4	12	no	—
157	C₇×D₄	—	2	64	no	—
158	C₇×D₄	—	2	48	no	—
159	C₇×D₄	—	2	8	no	—
160	C₇×D₄	C₂²×D₄	1	16	yes	—
161	C₂×C₄×C₇	—	2	12	no	—
162	C₂×C₄×C₇	—	2	24	no	—
163	C₂×C₄×C₇	—	2	8	no	—
164	C₂×C₄×C₇	—	2	4	no	—
165	C₂×C₄×C₇	—	2	4	no	—
166	C₂×C₄×C₇	—	4	12	no	—
167	C₂×C₄×C₇	—	4	12	no	—
168	C₂×C₄×C₇	#120	1	12	yes	—
169	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₇	C₂²×D₄	1	3	yes	—
171	C₂×C₄×C₇	C₂²×D₄	1	12	yes	—
172	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
173	C₇×C₈	—	2	8	no	—
174	C₂⁵	—	2	16	no	—
175	C₂⁵	—	2	12	no	—
176	C₂⁵	—	2	2	no	—
177	C₂⁵	—	4	8	no	—
178	C₂⁵	—	4	8	no	—
179	C₂⁵	C₇×D₄	1	1	yes	characteristic
180	C₂²×Q₈	—	2	3	no	—
181	C₂²×Q₈	—	2	8	no	—
182	C₂²×Q₈	C₂³×C₇	1	6	yes	complemented
183	C₂²×D₄	—	2	16	no	—
184	C₂²×D₄	—	2	96	no	—
185	C₂²×D₄	—	2	96	no	—
186	C₂²×D₄	—	2	12	no	—
187	C₂²×D₄	—	2	24	no	—
188	C₂²×D₄	—	2	6	no	—
189	C₂²×D₄	—	2	8	no	—
190	C₂²×D₄	C₇×D₄	1	16	yes	—
191	C₂²×D₄	C₂³×C₇	1	16	yes	—
192	C₂²×D₄	C₂³×C₇	1	12	yes	—
193	C₂³×C₄	—	2	8	no	—
194	C₂³×C₄	—	2	1	no	—
195	C₂³×C₄	—	2	1	no	—
196	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
197	C₂³×C₄	C₇×D₄	1	6	yes	—
198	C₂³×C₄	C₂³×C₇	1	6	yes	—
199	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
200	C₂×SD₁₆	—	2	96	no	—
201	C₂×SD₁₆	C₂³×C₇	1	32	yes	complemented
202	C₂²×C₈	—	2	8	no	—
203	C₂²×C₈	C₂³×C₇	1	12	yes	complemented
204	C₂²⋊Q₈	—	2	24	no	—
205	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
206	C₂×C₄⋊C₄	—	2	12	no	—
207	C₂×C₄⋊C₄	—	2	3	no	—
208	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	complemented
209	C₂×C₂²⋊C₄	—	2	12	no	—
210	#102	C₂³×C₇	1	32	yes	complemented
211	C₂²⋊C₈	C₂³×C₇	1	16	yes	complemented
212	C₂²×C₇	—	2	4	no	—
213	C₂²×C₇	—	2	48	no	—
214	C₂²×C₇	—	2	4	no	—
215	C₂²×C₇	—	2	16	no	—
216	C₂²×C₇	—	4	128	no	—
217	C₂²×C₇	—	4	96	no	—
218	C₂²×C₇	—	4	8	no	—
219	C₂²×C₇	—	4	8	no	—
220	C₂²×C₇	#450	1	16	yes	direct product factor
221	C₂²×C₇	C₂×#120	1	6	yes	—
222	C₂²×C₇	C₂²×SD₁₆	1	6	yes	—
223	C₂²×C₇	C₂²×SD₁₆	1	8	yes	complemented
224	C₂²×C₇	C₂×AGL(1,ℤ/8)	1	6	yes	—
225	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₇	—	2	4	no	—
227	C₄×C₇	—	4	4	no	—
228	C₄×C₇	—	4	4	no	—
229	C₄×C₇	C₂×#120	1	6	yes	—
230	C₄×C₇	C₂³×D₄	1	2	yes	—
231	C₂⁴	—	2	4	no	—
232	C₂⁴	—	2	4	no	—
233	C₂⁴	—	2	96	no	—
234	C₂⁴	—	2	16	no	—
235	C₂⁴	—	2	16	no	—
236	C₂⁴	—	2	12	no	—
237	C₂⁴	—	4	48	no	—
238	C₂⁴	—	4	128	no	—
239	C₂⁴	—	4	8	no	—
240	C₂⁴	—	4	48	no	—
241	C₂⁴	—	4	8	no	—
242	C₂⁴	C₇×SD₁₆	1	8	yes	complemented
243	C₂⁴	C₂×C₇×D₄	1	6	yes	—
244	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
245	C₂×Q₈	—	2	6	no	—
246	C₂×Q₈	—	2	24	no	—
247	C₂×Q₈	—	4	12	no	—
248	C₂×Q₈	C₂⁴×C₇	1	4	yes	complemented
249	C₂×D₄	—	2	96	no	—
250	C₂×D₄	—	2	192	no	—
251	C₂×D₄	—	2	64	no	—
252	C₂×D₄	—	2	48	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	24	no	—
255	C₂×D₄	—	2	12	no	—
256	C₂×D₄	C₂×C₇×D₄	1	48	yes	—
257	C₂×D₄	C₂⁴×C₇	1	8	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	24	no	—
260	C₂²×C₄	—	2	24	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	C₂×C₇×D₄	1	6	yes	—
266	C₂²×C₄	C₂×C₇×D₄	1	12	yes	—
267	C₂²×C₄	C₂×C₇×D₄	1	3	yes	—
268	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
271	SD₁₆	—	2	64	no	—
272	C₂×C₈	—	2	24	no	—
273	C₂×C₈	C₂⁴×C₇	1	8	yes	complemented
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	6	no	—
276	C₄⋊C₄	C₂⁴×C₇	1	4	yes	complemented
277	C₂²⋊C₄	—	2	16	no	—
278	C₂×C₇	—	2	8	no	—
279	C₂×C₇	—	4	16	no	—
280	C₂×C₇	C₂×#450	1	12	yes	direct product factor
281	C₂×C₇	C₂²×#120	1	1	yes	characteristic
282	C₂×C₇	C₂³×SD₁₆	1	1	yes	characteristic
283	C₂×C₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
284	C₂³	—	2	12	no	—
285	C₂³	—	2	12	no	—
286	C₂³	—	2	32	no	—
287	C₂³	—	2	64	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	48	no	—
290	C₂³	—	4	32	no	—
291	C₂³	—	4	384	no	—
292	C₂³	—	4	24	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	4	24	no	—
295	C₂³	—	4	64	no	—
296	C₂³	C₇×#120	1	4	yes	—
297	C₂³	C₂×C₇×SD₁₆	1	4	yes	—
298	C₂³	C₂×C₇×SD₁₆	1	24	yes	complemented
299	C₂³	C₇×AGL(1,ℤ/8)	1	4	yes	—
300	C₂³	C₂²×C₇×D₄	1	4	yes	—
301	C₂³	C₂²×C₇×D₄	1	3	yes	—
302	Q₈	—	2	8	no	—
303	Q₈	—	4	12	no	—
304	D₄	—	2	64	no	—
305	D₄	—	2	8	no	—
306	D₄	—	2	48	no	—
307	D₄	C₂²×C₇×D₄	1	16	yes	—
308	C₂×C₄	—	2	12	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	24	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	12	no	—
314	C₂×C₄	—	4	12	no	—
315	C₂×C₄	C₇×#120	1	12	yes	—
316	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
317	C₂×C₄	C₂²×C₇×D₄	1	12	yes	—
318	C₂×C₄	C₂²×C₇×D₄	1	3	yes	—
319	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
320	C₈	—	2	8	no	—
321	C₇	C₂²×#450	1	1	yes	characteristic, direct product factor, Sylow
322	C₂²	—	2	4	no	—
323	C₂²	—	2	48	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	16	no	—
326	C₂²	—	4	128	no	—
327	C₂²	—	4	8	no	—
328	C₂²	—	4	8	no	—
329	C₂²	—	4	96	no	—
330	C₂²	C₇×#450	1	16	yes	direct product factor
331	C₂²	C₂×C₇×#120	1	6	yes	—
332	C₂²	C₂²×C₇×SD₁₆	1	6	yes	—
333	C₂²	C₂²×C₇×SD₁₆	1	8	yes	complemented
334	C₂²	C₂×C₇×AGL(1,ℤ/8)	1	6	yes	—
335	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	4	4	no	—
338	C₄	—	4	4	no	—
339	C₄	C₂×C₇×#120	1	6	yes	—
340	C₄	C₂³×C₇×D₄	1	2	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	C₂×C₇×#450	1	12	yes	direct product factor
344	C₂	C₂²×C₇×#120	1	1	yes	characteristic
345	C₂	C₂³×C₇×SD₁₆	1	1	yes	characteristic
346	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	C₂⁴×C₇×D₄	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. C₂³×C₇×SD₁₆	C₂	semidirect
3. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
4. C₂×C₇×#450	C₂	direct (N × H)
5. C₂²×C₇×#102	C₂	semidirect
6. C₂²×C₇×C₂²⋊C₈	C₂	semidirect
8. C₂³×C₇×Q₈	C₂²	semidirect
16. C₂²×C₇×SD₁₆	C₂²	semidirect
17. C₂³×C₇×C₈	C₂²	semidirect
19. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
21. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
23. C₇×#450	C₂²	direct (N × H)
24. C₂×C₇×#102	C₂²	semidirect
25. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
26. C₂²×#450	C₇	direct (N × H)
35. C₂²×C₇×Q₈	C₂³	semidirect
54. C₂×C₇×SD₁₆	C₂³	semidirect
56. C₂²×C₇×C₈	C₂³	semidirect
58. C₇×C₂²⋊Q₈	C₂³	semidirect
61. C₂×C₇×C₄⋊C₄	C₂³	semidirect
63. C₇×#102	C₂³	semidirect
64. C₇×C₂²⋊C₈	C₂³	semidirect
66. C₂³×SD₁₆	C₂×C₇	semidirect
67. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
68. C₂×#450	C₂×C₇	direct (N × H)
69. C₂²×#102	C₂×C₇	semidirect
70. C₂²×C₂²⋊C₈	C₂×C₇	semidirect
82. C₂⁴×C₇	SD₁₆	semidirect
88. C₂×C₇×Q₈	C₂⁴	semidirect
113. C₂×C₇×C₈	C₂⁴	semidirect
116. C₇×C₄⋊C₄	C₂⁴	semidirect
119. C₂³×Q₈	C₂²×C₇	semidirect
127. C₂²×SD₁₆	C₂²×C₇	semidirect
128. C₂³×C₈	C₂²×C₇	semidirect
130. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
132. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
134. #450	C₂²×C₇	direct (N × H)
135. C₂×#102	C₂²×C₇	semidirect
136. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
151. C₂³×C₇	C₂×SD₁₆	semidirect
182. C₂²×Q₈	C₂³×C₇	semidirect
201. C₂×SD₁₆	C₂³×C₇	semidirect
203. C₂²×C₈	C₂³×C₇	semidirect
205. C₂²⋊Q₈	C₂³×C₇	semidirect
208. C₂×C₄⋊C₄	C₂³×C₇	semidirect
210. #102	C₂³×C₇	semidirect
211. C₂²⋊C₈	C₂³×C₇	semidirect
220. C₂²×C₇	#450	direct (N × H)
223. C₂²×C₇	C₂²×SD₁₆	semidirect
242. C₂⁴	C₇×SD₁₆	semidirect
248. C₂×Q₈	C₂⁴×C₇	semidirect
273. C₂×C₈	C₂⁴×C₇	semidirect
276. C₄⋊C₄	C₂⁴×C₇	semidirect
280. C₂×C₇	C₂×#450	direct (N × H)
298. C₂³	C₂×C₇×SD₁₆	semidirect
321. C₇	C₂²×#450	direct (N × H)
330. C₂²	C₇×#450	direct (N × H)
333. C₂²	C₂²×C₇×SD₁₆	semidirect
343. C₂	C₂×C₇×#450	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₇×D₄	2
C₂³×C₇×SD₁₆	2
C₂²×C₇×C₂²⋊Q₈	2
C₂×C₇×#450	2
C₂²×C₇×#102	2
C₂²×C₇×C₂²⋊C₈	2
C₂²×#450	7

Subgroups — C22×C7×#450 #13237564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#450 #13237564