Subgroups — C₂²×C₇×#525 #13239875

Order 1792.

14334 conjugacy classes of subgroups.

The subgroup lattice has 396 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	C₂⁵×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇×#525	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₇×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₇×#121	C₂	1	2	yes	maximal, complemented
7	C₂²×C₇×#120	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×C₇×D₄	C₂	1	4	yes	maximal, complemented
9	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₇	C₂²	1	1	yes	characteristic
11	C₂²×C₇×#41	—	2	16	no	—
12	C₂²×C₇×#41	C₂²	1	24	yes	complemented
13	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₇×D₄	C₂²	1	2	yes	—
15	C₂³×C₇×D₄	C₂²	1	4	yes	—
16	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₇	—	2	16	no	—
18	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₇	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₇	C₂²	1	24	yes	complemented
23	C₂⁴×C₄×C₇	C₂²	1	2	yes	complemented
24	C₇×#525	C₂²	1	256	yes	direct product factor
25	C₂×C₇×#123	C₂²	1	48	yes	complemented
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	48	yes	complemented
27	C₂×C₇×#121	C₂²	1	48	yes	complemented
28	C₂×C₇×#120	C₂²	1	48	yes	complemented
29	C₂×C₄×C₇×D₄	C₂²	1	96	yes	complemented
30	C₂×C₇×#117	C₂²	1	24	yes	complemented
31	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×C₇×C₄⋊C₄	C₂²	1	4	yes	complemented
33	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₇×C₂²⋊C₄	C₂²	1	4	yes	complemented
36	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
37	C₂²×#525	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂⁵×C₇	—	2	8	no	—
39	C₂⁵×C₇	—	2	16	no	—
40	C₂⁵×C₇	C₂³	1	2	yes	—
41	C₂⁵×C₇	C₂³	1	12	yes	—
42	C₂⁵×C₇	C₂³	1	1	yes	characteristic
43	C₂⁵×C₇	C₂³	1	2	yes	—
44	C₂×C₇×#41	—	2	192	no	—
45	C₂×C₇×#41	C₂³	1	64	yes	complemented
46	C₂²×C₇×Q₈	—	2	8	no	—
47	C₂²×C₇×Q₈	C₂³	1	12	yes	complemented
48	C₂²×C₇×D₄	—	2	16	no	—
49	C₂²×C₇×D₄	—	2	32	no	—
50	C₂²×C₇×D₄	—	2	8	no	—
51	C₂²×C₇×D₄	C₂³	1	24	yes	—
52	C₂²×C₇×D₄	C₂³	1	48	yes	—
53	C₂²×C₇×D₄	C₂³	1	12	yes	complemented
54	C₂³×C₄×C₇	—	2	8	no	—
55	C₂³×C₄×C₇	—	2	16	no	—
56	C₂³×C₄×C₇	—	2	16	no	—
57	C₂³×C₄×C₇	—	2	16	no	—
58	C₂³×C₄×C₇	—	2	192	no	—
59	C₂³×C₄×C₇	D₄	1	16	yes	complemented
60	C₂³×C₄×C₇	C₂³	1	2	yes	—
61	C₂³×C₄×C₇	C₂³	1	4	yes	—
62	C₂³×C₄×C₇	C₂³	1	2	yes	—
63	C₂³×C₄×C₇	C₂³	1	24	yes	—
64	C₂³×C₄×C₇	C₂³	1	24	yes	—
65	C₂³×C₄×C₇	C₂³	1	12	yes	—
66	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	C₂³	1	12	yes	—
68	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₇	C₂³	1	64	yes	complemented
70	C₂³×C₄×C₇	C₂³	1	24	yes	complemented
71	C₇×#123	C₂³	1	128	yes	complemented
72	C₇×C₂²⋊Q₈	C₂³	1	128	yes	complemented
73	C₇×#121	C₂³	1	128	yes	complemented
74	C₇×#120	C₂³	1	128	yes	complemented
75	C₄×C₇×D₄	C₂³	1	256	yes	complemented
76	C₇×#117	C₂³	1	64	yes	complemented
77	C₂×C₇×C₄⋊C₄	C₂³	1	24	yes	complemented
78	C₂×C₇×C₄⋊C₄	C₂³	1	48	yes	complemented
79	C₂×C₇×C₂²⋊C₄	C₂³	1	24	yes	—
80	C₂×C₇×C₂²⋊C₄	C₂³	1	48	yes	—
81	C₂×C₇×C₂²⋊C₄	C₂³	1	48	yes	complemented
82	C₂×C₄²×C₇	C₂³	1	24	yes	complemented
83	C₂³×#41	C₂×C₇	1	1	yes	characteristic, complemented
84	C₂⁵×C₄	C₂×C₇	1	1	yes	characteristic, complemented
85	C₂×#525	C₂×C₇	1	48	yes	direct product factor
86	C₂²×#123	C₂×C₇	1	2	yes	complemented
87	C₂²×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
88	C₂²×#121	C₂×C₇	1	2	yes	complemented
89	C₂²×#120	C₂×C₇	1	2	yes	complemented
90	C₂²×C₄×D₄	C₂×C₇	1	4	yes	complemented
91	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
92	C₂⁴×C₇	—	2	128	no	—
93	C₂⁴×C₇	—	2	48	no	—
94	C₂⁴×C₇	—	2	8	no	—
95	C₂⁴×C₇	—	2	8	no	—
96	C₂⁴×C₇	—	2	8	no	—
97	C₂⁴×C₇	—	2	96	no	—
98	C₂⁴×C₇	—	2	8	no	—
99	C₂⁴×C₇	—	2	16	no	—
100	C₂⁴×C₇	C₂×D₄	1	8	yes	—
101	C₂⁴×C₇	#41	1	16	yes	complemented
102	C₂⁴×C₇	C₂⁴	1	12	yes	—
103	C₂⁴×C₇	C₂⁴	1	16	yes	—
104	C₂⁴×C₇	C₂⁴	1	6	yes	—
105	C₂⁴×C₇	C₂⁴	1	12	yes	—
106	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
107	C₇×#41	—	2	256	no	—
108	C₂×C₇×Q₈	—	2	48	no	—
109	C₂×C₇×Q₈	C₂⁴	1	16	yes	complemented
110	C₂×C₇×D₄	—	2	96	no	—
111	C₂×C₇×D₄	—	2	192	no	—
112	C₂×C₇×D₄	—	2	48	no	—
113	C₂×C₇×D₄	C₂⁴	1	64	yes	—
114	C₂×C₇×D₄	C₂⁴	1	32	yes	—
115	C₂×C₇×D₄	C₂⁴	1	16	yes	complemented
116	C₂²×C₄×C₇	—	2	48	no	—
117	C₂²×C₄×C₇	—	2	8	no	—
118	C₂²×C₄×C₇	—	2	8	no	—
119	C₂²×C₄×C₇	—	2	16	no	—
120	C₂²×C₄×C₇	—	2	96	no	—
121	C₂²×C₄×C₇	—	2	96	no	—
122	C₂²×C₄×C₇	—	2	96	no	—
123	C₂²×C₄×C₇	—	2	256	no	—
124	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
125	C₂²×C₄×C₇	C₂×D₄	1	8	yes	—
126	C₂²×C₄×C₇	C₂×D₄	1	96	yes	complemented
127	C₂²×C₄×C₇	C₂⁴	1	24	yes	—
128	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
129	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
130	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
131	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
132	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
133	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
134	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
135	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
136	C₂²×C₄×C₇	C₂⁴	1	32	yes	complemented
137	C₇×C₄⋊C₄	C₂⁴	1	32	yes	complemented
138	C₇×C₄⋊C₄	C₂⁴	1	64	yes	complemented
139	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
140	C₇×C₂²⋊C₄	C₂⁴	1	64	yes	—
141	C₇×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
142	C₄²×C₇	C₂⁴	1	32	yes	complemented
143	C₂⁶	C₂²×C₇	1	1	yes	characteristic
144	C₂²×#41	—	2	16	no	—
145	C₂²×#41	C₂²×C₇	1	24	yes	complemented
146	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
147	C₂³×D₄	C₂²×C₇	1	2	yes	—
148	C₂³×D₄	C₂²×C₇	1	4	yes	—
149	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
150	C₂⁴×C₄	—	2	16	no	—
151	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
152	C₂⁴×C₄	C₂²×C₇	1	2	yes	—
153	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
154	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
155	C₂⁴×C₄	C₂²×C₇	1	24	yes	complemented
156	C₂⁴×C₄	C₂²×C₇	1	2	yes	complemented
157	#525	C₂²×C₇	1	256	yes	direct product factor
158	C₂×#123	C₂²×C₇	1	48	yes	complemented
159	C₂×C₂²⋊Q₈	C₂²×C₇	1	48	yes	complemented
160	C₂×#121	C₂²×C₇	1	48	yes	complemented
161	C₂×#120	C₂²×C₇	1	48	yes	complemented
162	C₂×C₄×D₄	C₂²×C₇	1	96	yes	complemented
163	C₂×#117	C₂²×C₇	1	24	yes	complemented
164	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
165	C₂²×C₄⋊C₄	C₂²×C₇	1	4	yes	complemented
166	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
167	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
168	C₂²×C₂²⋊C₄	C₂²×C₇	1	4	yes	complemented
169	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
170	C₂³×C₇	—	2	384	no	—
171	C₂³×C₇	—	2	32	no	—
172	C₂³×C₇	—	2	64	no	—
173	C₂³×C₇	—	2	32	no	—
174	C₂³×C₇	—	2	24	no	—
175	C₂³×C₇	—	2	24	no	—
176	C₂³×C₇	—	2	24	no	—
177	C₂³×C₇	—	2	64	no	—
178	C₂³×C₇	—	2	24	no	—
179	C₂³×C₇	—	2	48	no	—
180	C₂³×C₇	—	4	32	no	—
181	C₂³×C₇	C₂²×D₄	1	24	yes	—
182	C₂³×C₇	C₂²×D₄	1	4	yes	—
183	C₂³×C₇	C₂×#41	1	8	yes	—
184	C₂³×C₇	C₂×#41	1	48	yes	complemented
185	C₂³×C₇	C₂⁵	1	8	yes	—
186	C₂³×C₇	C₂⁵	1	4	yes	—
187	C₂³×C₇	C₂⁵	1	8	yes	—
188	C₂³×C₇	C₂⁵	1	3	yes	—
189	C₇×Q₈	—	2	32	no	—
190	C₇×D₄	—	2	64	no	—
191	C₇×D₄	—	2	128	no	—
192	C₇×D₄	—	2	32	no	—
193	C₂×C₄×C₇	—	2	32	no	—
194	C₂×C₄×C₇	—	2	24	no	—
195	C₂×C₄×C₇	—	2	24	no	—
196	C₂×C₄×C₇	—	2	48	no	—
197	C₂×C₄×C₇	—	2	64	no	—
198	C₂×C₄×C₇	—	2	64	no	—
199	C₂×C₄×C₇	—	2	64	no	—
200	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
201	C₂×C₄×C₇	C₂²×D₄	1	24	yes	—
202	C₂×C₄×C₇	C₂²×D₄	1	64	yes	complemented
203	C₂×C₄×C₇	C₂⁵	1	16	yes	—
204	C₂×C₄×C₇	C₂⁵	1	8	yes	—
205	C₂×C₄×C₇	C₂⁵	1	8	yes	—
206	C₂×C₄×C₇	C₂⁵	1	4	yes	—
207	C₂×C₄×C₇	C₂⁵	1	4	yes	—
208	C₂⁵	—	2	8	no	—
209	C₂⁵	—	2	16	no	—
210	C₂⁵	C₂³×C₇	1	2	yes	—
211	C₂⁵	C₂³×C₇	1	12	yes	—
212	C₂⁵	C₂³×C₇	1	1	yes	characteristic
213	C₂⁵	C₂³×C₇	1	2	yes	—
214	C₂×#41	—	2	192	no	—
215	C₂×#41	C₂³×C₇	1	64	yes	complemented
216	C₂²×Q₈	—	2	8	no	—
217	C₂²×Q₈	C₂³×C₇	1	12	yes	complemented
218	C₂²×D₄	—	2	16	no	—
219	C₂²×D₄	—	2	32	no	—
220	C₂²×D₄	—	2	8	no	—
221	C₂²×D₄	C₂³×C₇	1	48	yes	—
222	C₂²×D₄	C₂³×C₇	1	24	yes	—
223	C₂²×D₄	C₂³×C₇	1	12	yes	complemented
224	C₂³×C₄	—	2	8	no	—
225	C₂³×C₄	—	2	16	no	—
226	C₂³×C₄	—	2	16	no	—
227	C₂³×C₄	—	2	16	no	—
228	C₂³×C₄	—	2	192	no	—
229	C₂³×C₄	C₇×D₄	1	16	yes	complemented
230	C₂³×C₄	C₂³×C₇	1	4	yes	—
231	C₂³×C₄	C₂³×C₇	1	2	yes	—
232	C₂³×C₄	C₂³×C₇	1	2	yes	—
233	C₂³×C₄	C₂³×C₇	1	24	yes	—
234	C₂³×C₄	C₂³×C₇	1	24	yes	—
235	C₂³×C₄	C₂³×C₇	1	12	yes	—
236	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
238	C₂³×C₄	C₂³×C₇	1	12	yes	—
239	C₂³×C₄	C₂³×C₇	1	64	yes	complemented
240	C₂³×C₄	C₂³×C₇	1	24	yes	complemented
241	#123	C₂³×C₇	1	128	yes	complemented
242	C₂²⋊Q₈	C₂³×C₇	1	128	yes	complemented
243	#121	C₂³×C₇	1	128	yes	complemented
244	#120	C₂³×C₇	1	128	yes	complemented
245	C₄×D₄	C₂³×C₇	1	256	yes	complemented
246	#117	C₂³×C₇	1	64	yes	complemented
247	C₂×C₄⋊C₄	C₂³×C₇	1	24	yes	complemented
248	C₂×C₄⋊C₄	C₂³×C₇	1	48	yes	complemented
249	C₂×C₂²⋊C₄	C₂³×C₇	1	24	yes	—
250	C₂×C₂²⋊C₄	C₂³×C₇	1	48	yes	—
251	C₂×C₂²⋊C₄	C₂³×C₇	1	48	yes	complemented
252	C₂×C₄²	C₂³×C₇	1	24	yes	complemented
253	C₂²×C₇	—	2	128	no	—
254	C₂²×C₇	—	2	8	no	—
255	C₂²×C₇	—	2	8	no	—
256	C₂²×C₇	—	2	8	no	—
257	C₂²×C₇	—	2	48	no	—
258	C₂²×C₇	—	2	96	no	—
259	C₂²×C₇	—	2	8	no	—
260	C₂²×C₇	—	2	16	no	—
261	C₂²×C₇	—	4	48	no	—
262	C₂²×C₇	#525	1	16	yes	direct product factor
263	C₂²×C₇	C₂³×D₄	1	8	yes	—
264	C₂²×C₇	C₂³×D₄	1	6	yes	—
265	C₂²×C₇	C₂²×#41	1	12	yes	—
266	C₂²×C₇	C₂²×#41	1	16	yes	complemented
267	C₂²×C₇	C₂⁶	1	1	yes	characteristic
268	C₄×C₇	—	2	8	no	—
269	C₄×C₇	—	2	8	no	—
270	C₄×C₇	—	2	16	no	—
271	C₄×C₇	C₂³×D₄	1	8	yes	—
272	C₄×C₇	C₂³×D₄	1	8	yes	—
273	C₂⁴	—	2	128	no	—
274	C₂⁴	—	2	48	no	—
275	C₂⁴	—	2	8	no	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	8	no	—
278	C₂⁴	—	2	96	no	—
279	C₂⁴	—	2	8	no	—
280	C₂⁴	—	2	16	no	—
281	C₂⁴	C₂×C₇×D₄	1	8	yes	—
282	C₂⁴	C₇×#41	1	16	yes	complemented
283	C₂⁴	C₂⁴×C₇	1	12	yes	—
284	C₂⁴	C₂⁴×C₇	1	16	yes	—
285	C₂⁴	C₂⁴×C₇	1	6	yes	—
286	C₂⁴	C₂⁴×C₇	1	12	yes	—
287	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
288	#41	—	2	256	no	—
289	C₂×Q₈	—	2	48	no	—
290	C₂×Q₈	C₂⁴×C₇	1	16	yes	complemented
291	C₂×D₄	—	2	96	no	—
292	C₂×D₄	—	2	192	no	—
293	C₂×D₄	—	2	48	no	—
294	C₂×D₄	C₂⁴×C₇	1	64	yes	—
295	C₂×D₄	C₂⁴×C₇	1	32	yes	—
296	C₂×D₄	C₂⁴×C₇	1	16	yes	complemented
297	C₂²×C₄	—	2	48	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	16	no	—
301	C₂²×C₄	—	2	96	no	—
302	C₂²×C₄	—	2	96	no	—
303	C₂²×C₄	—	2	96	no	—
304	C₂²×C₄	—	2	256	no	—
305	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
306	C₂²×C₄	C₂×C₇×D₄	1	8	yes	—
307	C₂²×C₄	C₂×C₇×D₄	1	96	yes	complemented
308	C₂²×C₄	C₂⁴×C₇	1	24	yes	—
309	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
310	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
311	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
312	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
313	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
314	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
315	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
316	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
317	C₂²×C₄	C₂⁴×C₇	1	32	yes	complemented
318	C₄⋊C₄	C₂⁴×C₇	1	32	yes	complemented
319	C₄⋊C₄	C₂⁴×C₇	1	64	yes	complemented
320	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
321	C₂²⋊C₄	C₂⁴×C₇	1	64	yes	—
322	C₂²⋊C₄	C₂⁴×C₇	1	64	yes	complemented
323	C₄²	C₂⁴×C₇	1	32	yes	complemented
324	C₂×C₇	—	2	8	no	—
325	C₂×C₇	—	2	16	no	—
326	C₂×C₇	—	4	8	no	—
327	C₂×C₇	C₂×#525	1	12	yes	direct product factor
328	C₂×C₇	C₂⁴×D₄	1	1	yes	characteristic
329	C₂×C₇	C₂³×#41	1	2	yes	—
330	C₂³	—	2	384	no	—
331	C₂³	—	2	32	no	—
332	C₂³	—	2	24	no	—
333	C₂³	—	2	24	no	—
334	C₂³	—	2	24	no	—
335	C₂³	—	2	64	no	—
336	C₂³	—	2	32	no	—
337	C₂³	—	2	64	no	—
338	C₂³	—	2	24	no	—
339	C₂³	—	2	48	no	—
340	C₂³	—	4	32	no	—
341	C₂³	C₂²×C₇×D₄	1	24	yes	—
342	C₂³	C₂²×C₇×D₄	1	4	yes	—
343	C₂³	C₂×C₇×#41	1	8	yes	—
344	C₂³	C₂×C₇×#41	1	48	yes	complemented
345	C₂³	C₂⁵×C₇	1	8	yes	—
346	C₂³	C₂⁵×C₇	1	4	yes	—
347	C₂³	C₂⁵×C₇	1	8	yes	—
348	C₂³	C₂⁵×C₇	1	3	yes	—
349	Q₈	—	2	32	no	—
350	D₄	—	2	64	no	—
351	D₄	—	2	128	no	—
352	D₄	—	2	32	no	—
353	C₂×C₄	—	2	32	no	—
354	C₂×C₄	—	2	24	no	—
355	C₂×C₄	—	2	24	no	—
356	C₂×C₄	—	2	48	no	—
357	C₂×C₄	—	2	64	no	—
358	C₂×C₄	—	2	64	no	—
359	C₂×C₄	—	2	64	no	—
360	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
361	C₂×C₄	C₂²×C₇×D₄	1	24	yes	—
362	C₂×C₄	C₂²×C₇×D₄	1	64	yes	complemented
363	C₂×C₄	C₂⁵×C₇	1	16	yes	—
364	C₂×C₄	C₂⁵×C₇	1	8	yes	—
365	C₂×C₄	C₂⁵×C₇	1	8	yes	—
366	C₂×C₄	C₂⁵×C₇	1	4	yes	—
367	C₂×C₄	C₂⁵×C₇	1	4	yes	—
368	C₇	C₂²×#525	1	1	yes	characteristic, direct product factor, Sylow
369	C₂²	—	2	128	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	48	no	—
374	C₂²	—	2	96	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	48	no	—
378	C₂²	C₇×#525	1	16	yes	direct product factor
379	C₂²	C₂³×C₇×D₄	1	8	yes	—
380	C₂²	C₂³×C₇×D₄	1	6	yes	—
381	C₂²	C₂²×C₇×#41	1	12	yes	—
382	C₂²	C₂²×C₇×#41	1	16	yes	complemented
383	C₂²	C₂⁶×C₇	1	1	yes	characteristic
384	C₄	—	2	8	no	—
385	C₄	—	2	8	no	—
386	C₄	—	2	16	no	—
387	C₄	C₂³×C₇×D₄	1	8	yes	—
388	C₄	C₂³×C₇×D₄	1	8	yes	—
389	C₂	—	2	8	no	—
390	C₂	—	2	16	no	—
391	C₂	—	4	8	no	—
392	C₂	C₂×C₇×#525	1	12	yes	direct product factor
393	C₂	C₂⁴×C₇×D₄	1	1	yes	characteristic
394	C₂	C₂³×C₇×#41	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₇	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂⁴×C₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×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. C₂⁵×C₄×C₇	C₂	semidirect
3. C₂×C₇×#525	C₂	direct (N × H)
4. C₂²×C₇×#123	C₂	semidirect
5. C₂²×C₇×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₇×#121	C₂	semidirect
7. C₂²×C₇×#120	C₂	semidirect
8. C₂²×C₄×C₇×D₄	C₂	semidirect
9. C₂²×C₇×#117	C₂	semidirect
12. C₂²×C₇×#41	C₂²	semidirect
13. C₂³×C₇×Q₈	C₂²	semidirect
16. C₂³×C₇×D₄	C₂²	semidirect
22. C₂⁴×C₄×C₇	C₂²	semidirect
23. C₂⁴×C₄×C₇	C₂²	semidirect
24. C₇×#525	C₂²	direct (N × H)
25. C₂×C₇×#123	C₂²	semidirect
26. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₇×#121	C₂²	semidirect
28. C₂×C₇×#120	C₂²	semidirect
29. C₂×C₄×C₇×D₄	C₂²	semidirect
30. C₂×C₇×#117	C₂²	semidirect
31. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
35. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
36. C₂²×C₄²×C₇	C₂²	semidirect
37. C₂²×#525	C₇	direct (N × H)
45. C₂×C₇×#41	C₂³	semidirect
47. C₂²×C₇×Q₈	C₂³	semidirect
53. C₂²×C₇×D₄	C₂³	semidirect
59. C₂³×C₄×C₇	D₄	semidirect
69. C₂³×C₄×C₇	C₂³	semidirect
70. C₂³×C₄×C₇	C₂³	semidirect
71. C₇×#123	C₂³	semidirect
72. C₇×C₂²⋊Q₈	C₂³	semidirect
73. C₇×#121	C₂³	semidirect
74. C₇×#120	C₂³	semidirect
75. C₄×C₇×D₄	C₂³	semidirect
76. C₇×#117	C₂³	semidirect
77. C₂×C₇×C₄⋊C₄	C₂³	semidirect
78. C₂×C₇×C₄⋊C₄	C₂³	semidirect
81. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
82. C₂×C₄²×C₇	C₂³	semidirect
83. C₂³×#41	C₂×C₇	semidirect
84. C₂⁵×C₄	C₂×C₇	semidirect
85. C₂×#525	C₂×C₇	direct (N × H)
86. C₂²×#123	C₂×C₇	semidirect
87. C₂²×C₂²⋊Q₈	C₂×C₇	semidirect
88. C₂²×#121	C₂×C₇	semidirect
89. C₂²×#120	C₂×C₇	semidirect
90. C₂²×C₄×D₄	C₂×C₇	semidirect
91. C₂²×#117	C₂×C₇	semidirect
101. C₂⁴×C₇	#41	semidirect
109. C₂×C₇×Q₈	C₂⁴	semidirect
115. C₂×C₇×D₄	C₂⁴	semidirect
126. C₂²×C₄×C₇	C₂×D₄	semidirect
136. C₂²×C₄×C₇	C₂⁴	semidirect
137. C₇×C₄⋊C₄	C₂⁴	semidirect
138. C₇×C₄⋊C₄	C₂⁴	semidirect
141. C₇×C₂²⋊C₄	C₂⁴	semidirect
142. C₄²×C₇	C₂⁴	semidirect
145. C₂²×#41	C₂²×C₇	semidirect
146. C₂³×Q₈	C₂²×C₇	semidirect
149. C₂³×D₄	C₂²×C₇	semidirect
155. C₂⁴×C₄	C₂²×C₇	semidirect
156. C₂⁴×C₄	C₂²×C₇	semidirect
157. #525	C₂²×C₇	direct (N × H)
158. C₂×#123	C₂²×C₇	semidirect
159. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
160. C₂×#121	C₂²×C₇	semidirect
161. C₂×#120	C₂²×C₇	semidirect
162. C₂×C₄×D₄	C₂²×C₇	semidirect
163. C₂×#117	C₂²×C₇	semidirect
164. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
165. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
168. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
169. C₂²×C₄²	C₂²×C₇	semidirect
184. C₂³×C₇	C₂×#41	semidirect
202. C₂×C₄×C₇	C₂²×D₄	semidirect
215. C₂×#41	C₂³×C₇	semidirect
217. C₂²×Q₈	C₂³×C₇	semidirect
223. C₂²×D₄	C₂³×C₇	semidirect
229. C₂³×C₄	C₇×D₄	semidirect
239. C₂³×C₄	C₂³×C₇	semidirect
240. C₂³×C₄	C₂³×C₇	semidirect
241. #123	C₂³×C₇	semidirect
242. C₂²⋊Q₈	C₂³×C₇	semidirect
243. #121	C₂³×C₇	semidirect
244. #120	C₂³×C₇	semidirect
245. C₄×D₄	C₂³×C₇	semidirect
246. #117	C₂³×C₇	semidirect
247. C₂×C₄⋊C₄	C₂³×C₇	semidirect
248. C₂×C₄⋊C₄	C₂³×C₇	semidirect
251. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
252. C₂×C₄²	C₂³×C₇	semidirect
262. C₂²×C₇	#525	direct (N × H)
266. C₂²×C₇	C₂²×#41	semidirect
282. C₂⁴	C₇×#41	semidirect
290. C₂×Q₈	C₂⁴×C₇	semidirect
296. C₂×D₄	C₂⁴×C₇	semidirect
307. C₂²×C₄	C₂×C₇×D₄	semidirect
317. C₂²×C₄	C₂⁴×C₇	semidirect
318. C₄⋊C₄	C₂⁴×C₇	semidirect
319. C₄⋊C₄	C₂⁴×C₇	semidirect
322. C₂²⋊C₄	C₂⁴×C₇	semidirect
323. C₄²	C₂⁴×C₇	semidirect
327. C₂×C₇	C₂×#525	direct (N × H)
344. C₂³	C₂×C₇×#41	semidirect
362. C₂×C₄	C₂²×C₇×D₄	semidirect
368. C₇	C₂²×#525	direct (N × H)
378. C₂²	C₇×#525	direct (N × H)
382. C₂²	C₂²×C₇×#41	semidirect
392. C₂	C₂×C₇×#525	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
C₂⁵×C₄×C₇	2
C₂×C₇×#525	2
C₂²×C₇×#123	2
C₂²×C₇×C₂²⋊Q₈	2
C₂²×C₇×#121	2
C₂²×C₇×#120	2
C₂²×C₄×C₇×D₄	2
C₂²×C₇×#117	2
C₂²×#525	7

Subgroups — C22×C7×#525 #13239875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×#525 #13239875