Subgroups — C₂²×C₇×#535 #13239890

Order 1792.

14414 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	C₂³×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#535	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₇×#127	C₂	1	2	yes	maximal, complemented
5	C₂²×C₇×#124	C₂	1	2	yes	maximal, complemented
6	C₂²×C₇×#121	C₂	1	4	yes	maximal, complemented
7	C₂²×C₇×#120	C₂	1	4	yes	maximal, complemented
8	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₇	C₂²	1	2	yes	—
10	C₂²×C₇×#41	—	2	16	no	—
11	C₂²×C₇×#41	C₂²	1	24	yes	complemented
12	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂³×C₇×D₄	—	2	16	no	—
14	C₂³×C₇×D₄	C₂²	1	2	yes	—
15	C₂³×C₇×D₄	C₂²	1	2	yes	—
16	C₂³×C₇×D₄	C₂²	1	2	yes	—
17	C₂³×C₇×D₄	C₂²	1	24	yes	complemented
18	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₇×D₄	C₂²	1	8	yes	complemented
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₇	C₂²	1	2	yes	complemented
22	C₇×#535	C₂²	1	256	yes	direct product factor
23	C₂×C₇×#127	C₂²	1	48	yes	complemented
24	C₂×C₇×#124	C₂²	1	48	yes	complemented
25	C₂×C₇×#121	C₂²	1	96	yes	complemented
26	C₂×C₇×#120	C₂²	1	96	yes	complemented
27	C₂×C₇×#117	C₂²	1	24	yes	complemented
28	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	8	yes	complemented
31	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
32	C₂²×#535	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂⁵×C₇	—	2	16	no	—
34	C₂⁵×C₇	—	4	16	no	—
35	C₂⁵×C₇	C₂³	1	4	yes	—
36	C₂⁵×C₇	C₂³	1	2	yes	—
37	C₂⁵×C₇	C₂³	1	1	yes	characteristic
38	C₂⁵×C₇	C₂³	1	24	yes	—
39	C₂×C₇×#41	—	2	192	no	—
40	C₂×C₇×#41	C₂³	1	64	yes	complemented
41	C₂²×C₇×Q₈	—	2	8	no	—
42	C₂²×C₇×Q₈	C₂³	1	12	yes	complemented
43	C₂²×C₇×D₄	—	2	16	no	—
44	C₂²×C₇×D₄	—	2	16	no	—
45	C₂²×C₇×D₄	—	2	16	no	—
46	C₂²×C₇×D₄	—	2	8	no	—
47	C₂²×C₇×D₄	—	2	192	no	—
48	C₂²×C₇×D₄	—	4	32	no	—
49	C₂²×C₇×D₄	C₂³	1	24	yes	—
50	C₂²×C₇×D₄	C₂³	1	24	yes	—
51	C₂²×C₇×D₄	C₂³	1	24	yes	—
52	C₂²×C₇×D₄	C₂³	1	64	yes	complemented
53	C₂²×C₇×D₄	C₂³	1	12	yes	complemented
54	C₂²×C₇×D₄	C₂³	1	96	yes	complemented
55	C₂³×C₄×C₇	—	2	16	no	—
56	C₂³×C₄×C₇	D₄	1	16	yes	complemented
57	C₂³×C₄×C₇	C₂³	1	2	yes	—
58	C₂³×C₄×C₇	C₂³	1	4	yes	—
59	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₇	C₂³	1	12	yes	—
62	C₂³×C₄×C₇	C₂³	1	24	yes	complemented
63	C₇×#127	C₂³	1	128	yes	complemented
64	C₇×#124	C₂³	1	128	yes	complemented
65	C₇×#121	C₂³	1	256	yes	complemented
66	C₇×#120	C₂³	1	256	yes	complemented
67	C₇×#117	C₂³	1	64	yes	complemented
68	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	complemented
69	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
70	C₂×C₇×C₂²⋊C₄	C₂³	1	96	yes	complemented
71	C₂×C₄²×C₇	C₂³	1	24	yes	complemented
72	C₂³×#41	C₂×C₇	1	1	yes	characteristic, complemented
73	C₂⁴×D₄	C₂×C₇	1	1	yes	characteristic, complemented
74	C₂×#535	C₂×C₇	1	48	yes	direct product factor
75	C₂²×#127	C₂×C₇	1	2	yes	complemented
76	C₂²×#124	C₂×C₇	1	2	yes	complemented
77	C₂²×#121	C₂×C₇	1	4	yes	complemented
78	C₂²×#120	C₂×C₇	1	4	yes	complemented
79	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
80	C₂⁴×C₇	—	2	8	no	—
81	C₂⁴×C₇	—	2	8	no	—
82	C₂⁴×C₇	—	2	96	no	—
83	C₂⁴×C₇	—	2	16	no	—
84	C₂⁴×C₇	—	2	16	no	—
85	C₂⁴×C₇	—	2	32	no	—
86	C₂⁴×C₇	—	4	96	no	—
87	C₂⁴×C₇	—	4	128	no	—
88	C₂⁴×C₇	C₂×D₄	1	8	yes	—
89	C₂⁴×C₇	C₂⁴	1	24	yes	—
90	C₂⁴×C₇	C₂⁴	1	12	yes	—
91	C₂⁴×C₇	C₂⁴	1	6	yes	—
92	C₂⁴×C₇	C₂⁴	1	32	yes	—
93	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
94	C₇×#41	—	2	256	no	—
95	C₂×C₇×Q₈	—	2	48	no	—
96	C₂×C₇×Q₈	C₂⁴	1	16	yes	complemented
97	C₂×C₇×D₄	—	2	96	no	—
98	C₂×C₇×D₄	—	2	96	no	—
99	C₂×C₇×D₄	—	2	96	no	—
100	C₂×C₇×D₄	—	2	48	no	—
101	C₂×C₇×D₄	—	2	256	no	—
102	C₂×C₇×D₄	—	4	192	no	—
103	C₂×C₇×D₄	C₂⁴	1	32	yes	—
104	C₂×C₇×D₄	C₂⁴	1	32	yes	—
105	C₂×C₇×D₄	C₂⁴	1	32	yes	—
106	C₂×C₇×D₄	C₂⁴	1	16	yes	complemented
107	C₂×C₇×D₄	C₂⁴	1	128	yes	complemented
108	C₂²×C₄×C₇	—	2	8	no	—
109	C₂²×C₄×C₇	—	2	16	no	—
110	C₂²×C₄×C₇	—	2	96	no	—
111	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₇	C₂×D₄	1	96	yes	complemented
114	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
115	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
116	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
118	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
119	C₂²×C₄×C₇	C₂⁴	1	32	yes	complemented
120	C₇×C₄⋊C₄	C₂⁴	1	32	yes	complemented
121	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
122	C₇×C₂²⋊C₄	C₂⁴	1	128	yes	complemented
123	C₄²×C₇	C₂⁴	1	32	yes	complemented
124	C₂⁶	C₂²×C₇	1	2	yes	—
125	C₂²×#41	—	2	16	no	—
126	C₂²×#41	C₂²×C₇	1	24	yes	complemented
127	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
128	C₂³×D₄	—	2	16	no	—
129	C₂³×D₄	C₂²×C₇	1	2	yes	—
130	C₂³×D₄	C₂²×C₇	1	2	yes	—
131	C₂³×D₄	C₂²×C₇	1	2	yes	—
132	C₂³×D₄	C₂²×C₇	1	24	yes	complemented
133	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
134	C₂³×D₄	C₂²×C₇	1	8	yes	complemented
135	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
136	C₂⁴×C₄	C₂²×C₇	1	2	yes	complemented
137	#535	C₂²×C₇	1	256	yes	direct product factor
138	C₂×#127	C₂²×C₇	1	48	yes	complemented
139	C₂×#124	C₂²×C₇	1	48	yes	complemented
140	C₂×#121	C₂²×C₇	1	96	yes	complemented
141	C₂×#120	C₂²×C₇	1	96	yes	complemented
142	C₂×#117	C₂²×C₇	1	24	yes	complemented
143	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
144	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
145	C₂²×C₂²⋊C₄	C₂²×C₇	1	8	yes	complemented
146	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
147	C₂³×C₇	—	2	32	no	—
148	C₂³×C₇	—	2	24	no	—
149	C₂³×C₇	—	2	24	no	—
150	C₂³×C₇	—	2	64	no	—
151	C₂³×C₇	—	2	48	no	—
152	C₂³×C₇	—	2	48	no	—
153	C₂³×C₇	—	2	96	no	—
154	C₂³×C₇	—	4	64	no	—
155	C₂³×C₇	—	4	384	no	—
156	C₂³×C₇	—	4	32	no	—
157	C₂³×C₇	—	4	64	no	—
158	C₂³×C₇	C₂²×D₄	1	24	yes	—
159	C₂³×C₇	C₂²×D₄	1	4	yes	—
160	C₂³×C₇	H(5,𝔽₂)	1	8	yes	—
161	C₂³×C₇	C₂⁵	1	16	yes	—
162	C₂³×C₇	C₂⁵	1	8	yes	—
163	C₂³×C₇	C₂⁵	1	4	yes	—
164	C₂³×C₇	C₂⁵	1	3	yes	—
165	C₇×Q₈	—	2	32	no	—
166	C₇×D₄	—	2	64	no	—
167	C₇×D₄	—	2	64	no	—
168	C₇×D₄	—	2	64	no	—
169	C₇×D₄	—	2	32	no	—
170	C₇×D₄	—	4	128	no	—
171	C₂×C₄×C₇	—	2	24	no	—
172	C₂×C₄×C₇	—	2	48	no	—
173	C₂×C₄×C₇	—	2	64	no	—
174	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
175	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
176	C₂×C₄×C₇	C₂²×D₄	1	64	yes	complemented
177	C₂×C₄×C₇	C₂⁵	1	16	yes	—
178	C₂×C₄×C₇	C₂⁵	1	8	yes	—
179	C₂×C₄×C₇	C₂⁵	1	4	yes	—
180	C₂×C₄×C₇	C₂⁵	1	4	yes	—
181	C₂⁵	—	2	16	no	—
182	C₂⁵	—	4	16	no	—
183	C₂⁵	C₂³×C₇	1	4	yes	—
184	C₂⁵	C₂³×C₇	1	2	yes	—
185	C₂⁵	C₂³×C₇	1	1	yes	characteristic
186	C₂⁵	C₂³×C₇	1	24	yes	—
187	C₂×#41	—	2	192	no	—
188	C₂×#41	C₂³×C₇	1	64	yes	complemented
189	C₂²×Q₈	—	2	8	no	—
190	C₂²×Q₈	C₂³×C₇	1	12	yes	complemented
191	C₂²×D₄	—	2	16	no	—
192	C₂²×D₄	—	2	16	no	—
193	C₂²×D₄	—	2	16	no	—
194	C₂²×D₄	—	2	8	no	—
195	C₂²×D₄	—	2	192	no	—
196	C₂²×D₄	—	4	32	no	—
197	C₂²×D₄	C₂³×C₇	1	24	yes	—
198	C₂²×D₄	C₂³×C₇	1	24	yes	—
199	C₂²×D₄	C₂³×C₇	1	24	yes	—
200	C₂²×D₄	C₂³×C₇	1	64	yes	complemented
201	C₂²×D₄	C₂³×C₇	1	12	yes	complemented
202	C₂²×D₄	C₂³×C₇	1	96	yes	complemented
203	C₂³×C₄	—	2	16	no	—
204	C₂³×C₄	C₇×D₄	1	16	yes	complemented
205	C₂³×C₄	C₂³×C₇	1	4	yes	—
206	C₂³×C₄	C₂³×C₇	1	2	yes	—
207	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₇	1	12	yes	—
210	C₂³×C₄	C₂³×C₇	1	24	yes	complemented
211	#127	C₂³×C₇	1	128	yes	complemented
212	#124	C₂³×C₇	1	128	yes	complemented
213	#121	C₂³×C₇	1	256	yes	complemented
214	#120	C₂³×C₇	1	256	yes	complemented
215	#117	C₂³×C₇	1	64	yes	complemented
216	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	complemented
217	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
218	C₂×C₂²⋊C₄	C₂³×C₇	1	96	yes	complemented
219	C₂×C₄²	C₂³×C₇	1	24	yes	complemented
220	C₂²×C₇	—	2	8	no	—
221	C₂²×C₇	—	2	48	no	—
222	C₂²×C₇	—	2	8	no	—
223	C₂²×C₇	—	2	16	no	—
224	C₂²×C₇	—	2	16	no	—
225	C₂²×C₇	—	2	32	no	—
226	C₂²×C₇	—	4	128	no	—
227	C₂²×C₇	—	4	48	no	—
228	C₂²×C₇	—	4	96	no	—
229	C₂²×C₇	#535	1	16	yes	direct product factor
230	C₂²×C₇	C₂³×D₄	1	8	yes	—
231	C₂²×C₇	C₂³×D₄	1	6	yes	—
232	C₂²×C₇	C₂×H(5,𝔽₂)	1	12	yes	—
233	C₂²×C₇	C₂⁶	1	1	yes	characteristic
234	C₄×C₇	—	2	8	no	—
235	C₄×C₇	—	2	16	no	—
236	C₄×C₇	C₂³×D₄	1	8	yes	—
237	C₄×C₇	C₂³×D₄	1	8	yes	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	8	no	—
240	C₂⁴	—	2	96	no	—
241	C₂⁴	—	2	16	no	—
242	C₂⁴	—	2	16	no	—
243	C₂⁴	—	2	32	no	—
244	C₂⁴	—	4	96	no	—
245	C₂⁴	—	4	128	no	—
246	C₂⁴	C₂×C₇×D₄	1	8	yes	—
247	C₂⁴	C₂⁴×C₇	1	24	yes	—
248	C₂⁴	C₂⁴×C₇	1	12	yes	—
249	C₂⁴	C₂⁴×C₇	1	6	yes	—
250	C₂⁴	C₂⁴×C₇	1	32	yes	—
251	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
252	#41	—	2	256	no	—
253	C₂×Q₈	—	2	48	no	—
254	C₂×Q₈	C₂⁴×C₇	1	16	yes	complemented
255	C₂×D₄	—	2	96	no	—
256	C₂×D₄	—	2	96	no	—
257	C₂×D₄	—	2	96	no	—
258	C₂×D₄	—	2	48	no	—
259	C₂×D₄	—	2	256	no	—
260	C₂×D₄	—	4	192	no	—
261	C₂×D₄	C₂⁴×C₇	1	32	yes	—
262	C₂×D₄	C₂⁴×C₇	1	32	yes	—
263	C₂×D₄	C₂⁴×C₇	1	32	yes	—
264	C₂×D₄	C₂⁴×C₇	1	16	yes	complemented
265	C₂×D₄	C₂⁴×C₇	1	128	yes	complemented
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	2	96	no	—
269	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
270	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
271	C₂²×C₄	C₂×C₇×D₄	1	96	yes	complemented
272	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
273	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
274	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
275	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
276	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
277	C₂²×C₄	C₂⁴×C₇	1	32	yes	complemented
278	C₄⋊C₄	C₂⁴×C₇	1	32	yes	complemented
279	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
280	C₂²⋊C₄	C₂⁴×C₇	1	128	yes	complemented
281	C₄²	C₂⁴×C₇	1	32	yes	complemented
282	C₂×C₇	—	2	8	no	—
283	C₂×C₇	—	4	8	no	—
284	C₂×C₇	—	4	16	no	—
285	C₂×C₇	C₂×#535	1	12	yes	direct product factor
286	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
287	C₂×C₇	C₂²×H(5,𝔽₂)	1	2	yes	—
288	C₂³	—	2	24	no	—
289	C₂³	—	2	32	no	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	64	no	—
292	C₂³	—	2	48	no	—
293	C₂³	—	2	48	no	—
294	C₂³	—	2	96	no	—
295	C₂³	—	4	64	no	—
296	C₂³	—	4	384	no	—
297	C₂³	—	4	32	no	—
298	C₂³	—	4	64	no	—
299	C₂³	C₂²×C₇×D₄	1	24	yes	—
300	C₂³	C₂²×C₇×D₄	1	4	yes	—
301	C₂³	C₇×H(5,𝔽₂)	1	8	yes	—
302	C₂³	C₂⁵×C₇	1	16	yes	—
303	C₂³	C₂⁵×C₇	1	8	yes	—
304	C₂³	C₂⁵×C₇	1	4	yes	—
305	C₂³	C₂⁵×C₇	1	3	yes	—
306	Q₈	—	2	32	no	—
307	D₄	—	2	64	no	—
308	D₄	—	2	64	no	—
309	D₄	—	2	64	no	—
310	D₄	—	2	32	no	—
311	D₄	—	4	128	no	—
312	C₂×C₄	—	2	24	no	—
313	C₂×C₄	—	2	48	no	—
314	C₂×C₄	—	2	64	no	—
315	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
316	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
317	C₂×C₄	C₂²×C₇×D₄	1	64	yes	complemented
318	C₂×C₄	C₂⁵×C₇	1	16	yes	—
319	C₂×C₄	C₂⁵×C₇	1	8	yes	—
320	C₂×C₄	C₂⁵×C₇	1	4	yes	—
321	C₂×C₄	C₂⁵×C₇	1	4	yes	—
322	C₇	C₂²×#535	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	8	no	—
324	C₂²	—	2	48	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	2	16	no	—
327	C₂²	—	2	16	no	—
328	C₂²	—	2	32	no	—
329	C₂²	—	4	128	no	—
330	C₂²	—	4	96	no	—
331	C₂²	—	4	48	no	—
332	C₂²	C₇×#535	1	16	yes	direct product factor
333	C₂²	C₂³×C₇×D₄	1	8	yes	—
334	C₂²	C₂³×C₇×D₄	1	6	yes	—
335	C₂²	C₂×C₇×H(5,𝔽₂)	1	12	yes	—
336	C₂²	C₂⁶×C₇	1	1	yes	characteristic
337	C₄	—	2	8	no	—
338	C₄	—	2	16	no	—
339	C₄	C₂³×C₇×D₄	1	8	yes	—
340	C₄	C₂³×C₇×D₄	1	8	yes	—
341	C₂	—	2	8	no	—
342	C₂	—	4	16	no	—
343	C₂	—	4	8	no	—
344	C₂	C₂×C₇×#535	1	12	yes	direct product factor
345	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
346	C₂	C₂²×C₇×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₇	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₇×#41	C₂	semidirect
2. C₂⁴×C₇×D₄	C₂	semidirect
3. C₂×C₇×#535	C₂	direct (N × H)
4. C₂²×C₇×#127	C₂	semidirect
5. C₂²×C₇×#124	C₂	semidirect
6. C₂²×C₇×#121	C₂	semidirect
7. C₂²×C₇×#120	C₂	semidirect
8. C₂²×C₇×#117	C₂	semidirect
11. C₂²×C₇×#41	C₂²	semidirect
12. C₂³×C₇×Q₈	C₂²	semidirect
17. C₂³×C₇×D₄	C₂²	semidirect
18. C₂³×C₇×D₄	C₂²	semidirect
19. C₂³×C₇×D₄	C₂²	semidirect
21. C₂⁴×C₄×C₇	C₂²	semidirect
22. C₇×#535	C₂²	direct (N × H)
23. C₂×C₇×#127	C₂²	semidirect
24. C₂×C₇×#124	C₂²	semidirect
25. C₂×C₇×#121	C₂²	semidirect
26. C₂×C₇×#120	C₂²	semidirect
27. C₂×C₇×#117	C₂²	semidirect
28. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
31. C₂²×C₄²×C₇	C₂²	semidirect
32. C₂²×#535	C₇	direct (N × H)
40. C₂×C₇×#41	C₂³	semidirect
42. C₂²×C₇×Q₈	C₂³	semidirect
52. C₂²×C₇×D₄	C₂³	semidirect
53. C₂²×C₇×D₄	C₂³	semidirect
54. C₂²×C₇×D₄	C₂³	semidirect
56. C₂³×C₄×C₇	D₄	semidirect
62. C₂³×C₄×C₇	C₂³	semidirect
63. C₇×#127	C₂³	semidirect
64. C₇×#124	C₂³	semidirect
65. C₇×#121	C₂³	semidirect
66. C₇×#120	C₂³	semidirect
67. C₇×#117	C₂³	semidirect
68. C₂×C₇×C₄⋊C₄	C₂³	semidirect
70. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
71. C₂×C₄²×C₇	C₂³	semidirect
72. C₂³×#41	C₂×C₇	semidirect
73. C₂⁴×D₄	C₂×C₇	semidirect
74. C₂×#535	C₂×C₇	direct (N × H)
75. C₂²×#127	C₂×C₇	semidirect
76. C₂²×#124	C₂×C₇	semidirect
77. C₂²×#121	C₂×C₇	semidirect
78. C₂²×#120	C₂×C₇	semidirect
79. C₂²×#117	C₂×C₇	semidirect
96. C₂×C₇×Q₈	C₂⁴	semidirect
106. C₂×C₇×D₄	C₂⁴	semidirect
107. C₂×C₇×D₄	C₂⁴	semidirect
113. C₂²×C₄×C₇	C₂×D₄	semidirect
119. C₂²×C₄×C₇	C₂⁴	semidirect
120. C₇×C₄⋊C₄	C₂⁴	semidirect
122. C₇×C₂²⋊C₄	C₂⁴	semidirect
123. C₄²×C₇	C₂⁴	semidirect
126. C₂²×#41	C₂²×C₇	semidirect
127. C₂³×Q₈	C₂²×C₇	semidirect
132. C₂³×D₄	C₂²×C₇	semidirect
133. C₂³×D₄	C₂²×C₇	semidirect
134. C₂³×D₄	C₂²×C₇	semidirect
136. C₂⁴×C₄	C₂²×C₇	semidirect
137. #535	C₂²×C₇	direct (N × H)
138. C₂×#127	C₂²×C₇	semidirect
139. C₂×#124	C₂²×C₇	semidirect
140. C₂×#121	C₂²×C₇	semidirect
141. C₂×#120	C₂²×C₇	semidirect
142. C₂×#117	C₂²×C₇	semidirect
143. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
145. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
146. C₂²×C₄²	C₂²×C₇	semidirect
176. C₂×C₄×C₇	C₂²×D₄	semidirect
188. C₂×#41	C₂³×C₇	semidirect
190. C₂²×Q₈	C₂³×C₇	semidirect
200. C₂²×D₄	C₂³×C₇	semidirect
201. C₂²×D₄	C₂³×C₇	semidirect
202. C₂²×D₄	C₂³×C₇	semidirect
204. C₂³×C₄	C₇×D₄	semidirect
210. C₂³×C₄	C₂³×C₇	semidirect
211. #127	C₂³×C₇	semidirect
212. #124	C₂³×C₇	semidirect
213. #121	C₂³×C₇	semidirect
214. #120	C₂³×C₇	semidirect
215. #117	C₂³×C₇	semidirect
216. C₂×C₄⋊C₄	C₂³×C₇	semidirect
218. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
219. C₂×C₄²	C₂³×C₇	semidirect
229. C₂²×C₇	#535	direct (N × H)
254. C₂×Q₈	C₂⁴×C₇	semidirect
264. C₂×D₄	C₂⁴×C₇	semidirect
265. C₂×D₄	C₂⁴×C₇	semidirect
271. C₂²×C₄	C₂×C₇×D₄	semidirect
277. C₂²×C₄	C₂⁴×C₇	semidirect
278. C₄⋊C₄	C₂⁴×C₇	semidirect
280. C₂²⋊C₄	C₂⁴×C₇	semidirect
281. C₄²	C₂⁴×C₇	semidirect
285. C₂×C₇	C₂×#535	direct (N × H)
317. C₂×C₄	C₂²×C₇×D₄	semidirect
322. C₇	C₂²×#535	direct (N × H)
332. C₂²	C₇×#535	direct (N × H)
344. C₂	C₂×C₇×#535	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×#41	2
C₂⁴×C₇×D₄	2
C₂×C₇×#535	2
C₂²×C₇×#127	2
C₂²×C₇×#124	2
C₂²×C₇×#121	2
C₂²×C₇×#120	2
C₂²×C₇×#117	2
C₂²×#535	7

Subgroups — C22×C7×#535 #13239890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#535 #13239890