Subgroups — C₂×C₇×#3221 #13238010

Order 1792.

2150 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3221	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#496	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₇×#463	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#461	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#449	C₂	1	2	yes	maximal, complemented
11	C₂×C₇×#448	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
17	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₇×D₈	C₂²	1	2	yes	—
19	C₇×#540	—	2	4	no	—
20	C₇×#540	C₂²	1	8	yes	complemented
21	C₇×#536	—	2	4	no	—
22	C₇×#536	C₂²	1	8	yes	complemented
23	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×#127	C₂²	1	1	yes	characteristic
26	C₂×C₇×#125	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#123	—	2	2	no	—
30	C₂×C₇×#123	—	2	2	no	—
31	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₇×#121	—	2	2	no	—
33	C₂×C₇×#121	C₂²	1	2	yes	—
34	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₇×#496	C₂²	1	8	yes	complemented
37	C₇×#492	C₂²	1	8	yes	complemented
38	C₇×#491	C₂²	1	8	yes	complemented
39	C₇×#488	C₂²	1	8	yes	complemented
40	C₇×#463	C₂²	1	16	yes	complemented
41	C₇×#461	C₂²	1	16	yes	complemented
42	C₇×#449	C₂²	1	16	yes	complemented
43	C₇×#448	C₂²	1	16	yes	complemented
44	C₇×#433	C₂²	1	8	yes	complemented
45	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
46	C₂×C₇×#103	C₂²	1	2	yes	—
47	C₂×C₇×#103	C₂²	1	2	yes	—
48	C₂×C₇×#103	C₂²	1	2	yes	—
49	C₂×C₇×#102	C₂²	1	2	yes	—
50	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
51	C₂×C₇×#97	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
53	C₂×#3221	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₇×#41	—	2	2	no	—
55	C₂×C₇×#41	—	4	4	no	—
56	C₂×C₇×#41	C₂³	1	4	yes	—
57	C₂²×C₇×Q₈	—	2	1	no	—
58	C₂²×C₇×Q₈	—	2	2	no	—
59	C₂²×C₇×Q₈	—	4	4	no	—
60	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
61	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
62	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₇×Q₈	C₂³	1	4	yes	—
64	C₂²×C₇×D₄	—	2	1	no	—
65	C₂²×C₇×D₄	—	2	2	no	—
66	C₂²×C₇×D₄	—	2	2	no	—
67	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
68	C₂²×C₇×D₄	C₂³	1	2	yes	—
69	C₂³×C₄×C₇	—	2	1	no	—
70	C₂³×C₄×C₇	—	2	1	no	—
71	C₂³×C₄×C₇	—	2	2	no	—
72	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
73	C₂×C₇×SD₁₆	—	4	4	no	—
74	C₂×C₇×SD₁₆	—	4	4	no	—
75	C₂×C₇×SD₁₆	—	4	4	no	—
76	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
77	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
78	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
79	C₂×C₇×D₈	—	4	4	no	—
80	C₂×C₇×D₈	C₂³	1	8	yes	—
81	C₂²×C₇×C₈	C₂³	1	2	yes	—
82	C₂²×C₇×C₈	C₂³	1	2	yes	—
83	C₇×C₄⋊Q₈	—	2	2	no	—
84	C₇×C₄⋊Q₈	—	2	2	no	—
85	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
87	C₇×#127	—	2	2	no	—
88	C₇×#127	C₂³	1	4	yes	—
89	C₇×#125	—	2	2	no	—
90	C₇×#125	C₂³	1	4	yes	—
91	C₇×#124	—	2	2	no	—
92	C₇×#124	—	2	2	no	—
93	C₇×#124	C₂³	1	4	yes	—
94	C₇×#124	C₂³	1	4	yes	—
95	C₇×#123	—	2	16	no	—
96	C₇×#123	—	2	16	no	—
97	C₇×C₂²⋊Q₈	—	2	16	no	—
98	C₇×#121	—	2	4	no	—
99	C₇×#121	—	2	16	no	—
100	C₇×#121	C₂³	1	8	yes	—
101	C₄×C₇×D₄	—	2	4	no	—
102	C₄×C₇×D₄	C₂³	1	8	yes	—
103	C₇×#117	D₄	1	4	yes	—
104	C₇×#117	C₂³	1	4	yes	—
105	C₂×C₇×C₄⋊C₄	—	2	2	no	—
106	C₂×C₇×C₄⋊C₄	—	2	2	no	—
107	C₂×C₇×C₄⋊C₄	—	2	2	no	—
108	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
109	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊C₈	C₂³	1	8	yes	—
118	C₇×#103	C₂³	1	8	yes	—
119	C₇×#103	C₂³	1	8	yes	—
120	C₇×#103	C₂³	1	8	yes	—
121	C₇×#102	C₂³	1	8	yes	—
122	C₇×C₂²⋊C₈	C₂³	1	8	yes	—
123	C₇×#97	C₂³	1	4	yes	—
124	C₄×C₇×C₈	C₂³	1	4	yes	—
125	C₂×#540	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#536	C₂×C₇	1	1	yes	characteristic, complemented
127	#3221	C₂×C₇	1	16	yes	direct product factor
128	C₂×#496	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#492	C₂×C₇	1	1	yes	characteristic, complemented
130	C₂×#491	C₂×C₇	1	1	yes	characteristic, complemented
131	C₂×#488	C₂×C₇	1	1	yes	characteristic, complemented
132	C₂×#463	C₂×C₇	1	2	yes	complemented
133	C₂×#461	C₂×C₇	1	2	yes	complemented
134	C₂×#449	C₂×C₇	1	2	yes	complemented
135	C₂×#448	C₂×C₇	1	2	yes	complemented
136	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
137	C₂⁴×C₇	—	2	1	no	—
138	C₂⁴×C₇	—	2	2	no	—
139	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
140	C₇×#41	—	4	8	no	—
141	C₇×#41	—	4	8	no	—
142	C₂×C₇×Q₈	—	2	4	no	—
143	C₂×C₇×Q₈	—	2	1	no	—
144	C₂×C₇×Q₈	—	2	1	no	—
145	C₂×C₇×Q₈	—	2	1	no	—
146	C₂×C₇×Q₈	—	2	4	no	—
147	C₂×C₇×Q₈	—	2	4	no	—
148	C₂×C₇×Q₈	—	2	4	no	—
149	C₂×C₇×Q₈	—	4	8	no	—
150	C₂×C₇×Q₈	—	4	4	no	—
151	C₂×C₇×Q₈	—	4	8	no	—
152	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
153	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
154	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
155	C₂×C₇×D₄	—	2	4	no	—
156	C₂×C₇×D₄	—	2	8	no	—
157	C₂×C₇×D₄	—	2	2	no	—
158	C₂×C₇×D₄	—	2	1	no	—
159	C₂×C₇×D₄	—	2	8	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	2	4	no	—
162	C₂×C₇×D₄	—	2	4	no	—
163	C₂×C₇×D₄	—	4	4	no	—
164	C₂×C₇×D₄	—	8	4	no	—
165	C₂×C₇×D₄	—	8	4	no	—
166	C₂×C₇×D₄	C₂⁴	1	2	yes	—
167	C₂×C₇×D₄	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₇	—	2	4	no	—
169	C₂²×C₄×C₇	—	2	4	no	—
170	C₂²×C₄×C₇	—	2	2	no	—
171	C₂²×C₄×C₇	—	2	1	no	—
172	C₂²×C₄×C₇	—	2	1	no	—
173	C₂²×C₄×C₇	—	2	1	no	—
174	C₂²×C₄×C₇	—	2	4	no	—
175	C₂²×C₄×C₇	—	2	8	no	—
176	C₂²×C₄×C₇	—	4	4	no	—
177	C₂²×C₄×C₇	—	4	4	no	—
178	C₂²×C₄×C₇	—	8	4	no	—
179	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
185	C₇×SD₁₆	—	4	8	no	—
186	C₇×SD₁₆	—	4	8	no	—
187	C₇×SD₁₆	—	4	8	no	—
188	C₇×D₈	—	4	8	no	—
189	C₂×C₇×C₈	—	2	4	no	—
190	C₂×C₇×C₈	—	2	4	no	—
191	C₂×C₇×C₈	C₂⁴	1	4	yes	—
192	C₂×C₇×C₈	C₂⁴	1	4	yes	—
193	C₇×C₄⋊C₄	—	2	8	no	—
194	C₇×C₄⋊C₄	—	2	8	no	—
195	C₇×C₄⋊C₄	—	2	8	no	—
196	C₇×C₄⋊C₄	—	2	2	no	—
197	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
198	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
199	C₇×C₂²⋊C₄	—	2	8	no	—
200	C₇×C₂²⋊C₄	—	2	8	no	—
201	C₇×C₂²⋊C₄	—	2	8	no	—
202	C₇×C₂²⋊C₄	—	2	8	no	—
203	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
204	C₄²×C₇	C₂×D₄	1	2	yes	—
205	C₄²×C₇	C₂×D₄	1	2	yes	—
206	C₄²×C₇	C₂⁴	1	2	yes	—
207	C₄²×C₇	C₂⁴	1	2	yes	—
208	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
209	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
210	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
211	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
213	C₂²×D₈	C₂²×C₇	1	2	yes	—
214	#540	—	2	4	no	—
215	#540	C₂²×C₇	1	8	yes	complemented
216	#536	—	2	4	no	—
217	#536	C₂²×C₇	1	8	yes	complemented
218	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
220	C₂×#127	C₂²×C₇	1	1	yes	characteristic
221	C₂×#125	C₂²×C₇	1	1	yes	characteristic
222	C₂×#124	C₂²×C₇	1	1	yes	characteristic
223	C₂×#124	C₂²×C₇	1	1	yes	characteristic
224	C₂×#123	—	2	2	no	—
225	C₂×#123	—	2	2	no	—
226	C₂×C₂²⋊Q₈	—	2	2	no	—
227	C₂×#121	—	2	2	no	—
228	C₂×#121	C₂²×C₇	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
230	C₂×#117	C₂²×C₇	1	1	yes	characteristic
231	#496	C₂²×C₇	1	8	yes	complemented
232	#492	C₂²×C₇	1	8	yes	complemented
233	#491	C₂²×C₇	1	8	yes	complemented
234	#488	C₂²×C₇	1	8	yes	complemented
235	#463	C₂²×C₇	1	16	yes	complemented
236	#461	C₂²×C₇	1	16	yes	complemented
237	#449	C₂²×C₇	1	16	yes	complemented
238	#448	C₂²×C₇	1	16	yes	complemented
239	#433	C₂²×C₇	1	8	yes	complemented
240	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
241	C₂×#103	C₂²×C₇	1	2	yes	—
242	C₂×#103	C₂²×C₇	1	2	yes	—
243	C₂×#103	C₂²×C₇	1	2	yes	—
244	C₂×#102	C₂²×C₇	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
246	C₂×#97	C₂²×C₇	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
248	C₂³×C₇	—	2	2	no	—
249	C₂³×C₇	—	2	4	no	—
250	C₂³×C₇	—	2	2	no	—
251	C₂³×C₇	—	2	4	no	—
252	C₂³×C₇	—	4	2	no	—
253	C₂³×C₇	—	4	4	no	—
254	C₂³×C₇	—	4	4	no	—
255	C₂³×C₇	—	4	4	no	—
256	C₂³×C₇	—	4	4	no	—
257	C₂³×C₇	C₂²×D₄	1	2	yes	—
258	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
259	C₇×Q₈	—	2	4	no	—
260	C₇×Q₈	—	2	4	no	—
261	C₇×Q₈	—	2	4	no	—
262	C₇×Q₈	—	4	8	no	—
263	C₇×Q₈	—	4	2	no	—
264	C₇×Q₈	—	4	2	no	—
265	C₇×Q₈	—	4	2	no	—
266	C₇×D₄	—	2	4	no	—
267	C₇×D₄	—	2	4	no	—
268	C₇×D₄	—	2	4	no	—
269	C₇×D₄	—	4	8	no	—
270	C₇×D₄	—	4	4	no	—
271	C₇×D₄	—	4	2	no	—
272	C₇×D₄	—	8	8	no	—
273	C₇×D₄	—	8	8	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	2	4	no	—
276	C₂×C₄×C₇	—	2	4	no	—
277	C₂×C₄×C₇	—	2	4	no	—
278	C₂×C₄×C₇	—	2	4	no	—
279	C₂×C₄×C₇	—	2	4	no	—
280	C₂×C₄×C₇	—	2	2	no	—
281	C₂×C₄×C₇	—	2	2	no	—
282	C₂×C₄×C₇	—	2	2	no	—
283	C₂×C₄×C₇	—	4	8	no	—
284	C₂×C₄×C₇	—	4	8	no	—
285	C₂×C₄×C₇	—	4	2	no	—
286	C₂×C₄×C₇	—	4	2	no	—
287	C₂×C₄×C₇	—	4	2	no	—
288	C₂×C₄×C₇	—	4	4	no	—
289	C₂×C₄×C₇	—	8	8	no	—
290	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
291	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
292	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
295	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
296	C₇×C₈	—	2	4	no	—
297	C₇×C₈	—	2	4	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	4	4	no	—
300	C₂×#41	C₂³×C₇	1	4	yes	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	—	4	4	no	—
304	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
306	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
307	C₂²×Q₈	C₂³×C₇	1	4	yes	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	C₂³×C₇	1	2	yes	—
312	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
313	C₂³×C₄	—	2	1	no	—
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
317	C₂×SD₁₆	—	4	4	no	—
318	C₂×SD₁₆	—	4	4	no	—
319	C₂×SD₁₆	—	4	4	no	—
320	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
321	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
322	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
323	C₂×D₈	—	4	4	no	—
324	C₂×D₈	C₂³×C₇	1	8	yes	—
325	C₂²×C₈	C₂³×C₇	1	2	yes	—
326	C₂²×C₈	C₂³×C₇	1	2	yes	—
327	C₄⋊Q₈	—	2	2	no	—
328	C₄⋊Q₈	—	2	2	no	—
329	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
330	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
331	#127	—	2	2	no	—
332	#127	C₂³×C₇	1	4	yes	—
333	#125	—	2	2	no	—
334	#125	C₂³×C₇	1	4	yes	—
335	#124	—	2	2	no	—
336	#124	—	2	2	no	—
337	#124	C₂³×C₇	1	4	yes	—
338	#124	C₂³×C₇	1	4	yes	—
339	#123	—	2	16	no	—
340	#123	—	2	16	no	—
341	C₂²⋊Q₈	—	2	16	no	—
342	#121	—	2	4	no	—
343	#121	—	2	16	no	—
344	#121	C₂³×C₇	1	8	yes	—
345	C₄×D₄	—	2	4	no	—
346	C₄×D₄	C₂³×C₇	1	8	yes	—
347	#117	C₇×D₄	1	4	yes	—
348	#117	C₂³×C₇	1	4	yes	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
359	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
361	C₄⋊C₈	C₂³×C₇	1	8	yes	—
362	#103	C₂³×C₇	1	8	yes	—
363	#103	C₂³×C₇	1	8	yes	—
364	#103	C₂³×C₇	1	8	yes	—
365	#102	C₂³×C₇	1	8	yes	—
366	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
367	#97	C₂³×C₇	1	4	yes	—
368	C₄×C₈	C₂³×C₇	1	4	yes	—
369	C₂²×C₇	—	2	2	no	—
370	C₂²×C₇	—	2	4	no	—
371	C₂²×C₇	—	4	4	no	—
372	C₂²×C₇	—	4	2	no	—
373	C₂²×C₇	—	4	4	no	—
374	C₂²×C₇	—	4	4	no	—
375	C₂²×C₇	—	4	4	no	—
376	C₂²×C₇	—	4	4	no	—
377	C₂²×C₇	—	8	4	no	—
378	C₂²×C₇	—	8	8	no	—
379	C₂²×C₇	#535	1	2	yes	—
380	C₂²×C₇	#577	1	4	yes	—
381	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₇	—	2	2	no	—
383	C₄×C₇	—	2	4	no	—
384	C₄×C₇	—	2	4	no	—
385	C₄×C₇	—	4	2	no	—
386	C₄×C₇	—	4	2	no	—
387	C₄×C₇	—	4	2	no	—
388	C₄×C₇	—	4	4	no	—
389	C₄×C₇	#535	1	2	yes	—
390	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
394	#41	—	4	8	no	—
395	#41	—	4	8	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	4	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	4	8	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	—	4	8	no	—
406	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
407	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
408	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	4	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	8	4	no	—
419	C₂×D₄	—	8	4	no	—
420	C₂×D₄	C₂⁴×C₇	1	2	yes	—
421	C₂×D₄	C₂⁴×C₇	1	4	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	8	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	8	4	no	—
433	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
434	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
435	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
439	SD₁₆	—	4	8	no	—
440	SD₁₆	—	4	8	no	—
441	SD₁₆	—	4	8	no	—
442	D₈	—	4	8	no	—
443	C₂×C₈	—	2	4	no	—
444	C₂×C₈	—	2	4	no	—
445	C₂×C₈	C₂⁴×C₇	1	4	yes	—
446	C₂×C₈	C₂⁴×C₇	1	4	yes	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
452	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
458	C₄²	C₂×C₇×D₄	1	2	yes	—
459	C₄²	C₂×C₇×D₄	1	2	yes	—
460	C₄²	C₂⁴×C₇	1	2	yes	—
461	C₄²	C₂⁴×C₇	1	2	yes	—
462	C₂×C₇	—	4	2	no	—
463	C₂×C₇	—	8	2	no	—
464	C₂×C₇	—	8	4	no	—
465	C₂×C₇	#3221	1	4	yes	direct product factor
466	C₂×C₇	C₂×#535	1	1	yes	characteristic
467	C₂×C₇	C₂×#577	1	2	yes	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	4	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	C₂²×C₇×D₄	1	2	yes	—
478	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
479	Q₈	—	2	4	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	2	4	no	—
482	Q₈	—	4	8	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	4	8	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	8	no	—
493	D₄	—	8	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	8	8	no	—
510	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
511	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
512	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
513	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
514	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
515	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
516	C₈	—	2	4	no	—
517	C₈	—	2	4	no	—
518	C₇	C₂×#3221	1	1	yes	characteristic, direct product factor, Sylow
519	C₂²	—	2	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	8	no	—
529	C₂²	C₇×#535	1	2	yes	—
530	C₂²	C₇×#577	1	4	yes	—
531	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
532	C₄	—	2	4	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	C₇×#535	1	2	yes	—
540	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
541	C₂	—	4	2	no	—
542	C₂	—	8	4	no	—
543	C₂	—	8	2	no	—
544	C₂	C₇×#3221	1	4	yes	direct product factor
545	C₂	C₂×C₇×#535	1	1	yes	characteristic
546	C₂	C₂×C₇×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#540	C₂	semidirect
2. C₂×C₇×#536	C₂	semidirect
3. C₇×#3221	C₂	direct (N × H)
4. C₂×C₇×#496	C₂	semidirect
5. C₂×C₇×#492	C₂	semidirect
6. C₂×C₇×#491	C₂	semidirect
7. C₂×C₇×#488	C₂	semidirect
8. C₂×C₇×#463	C₂	semidirect
9. C₂×C₇×#461	C₂	semidirect
10. C₂×C₇×#449	C₂	semidirect
11. C₂×C₇×#448	C₂	semidirect
12. C₂×C₇×#433	C₂	semidirect
20. C₇×#540	C₂²	semidirect
22. C₇×#536	C₂²	semidirect
36. C₇×#496	C₂²	semidirect
37. C₇×#492	C₂²	semidirect
38. C₇×#491	C₂²	semidirect
39. C₇×#488	C₂²	semidirect
40. C₇×#463	C₂²	semidirect
41. C₇×#461	C₂²	semidirect
42. C₇×#449	C₂²	semidirect
43. C₇×#448	C₂²	semidirect
44. C₇×#433	C₂²	semidirect
53. C₂×#3221	C₇	direct (N × H)
125. C₂×#540	C₂×C₇	semidirect
126. C₂×#536	C₂×C₇	semidirect
127. #3221	C₂×C₇	direct (N × H)
128. C₂×#496	C₂×C₇	semidirect
129. C₂×#492	C₂×C₇	semidirect
130. C₂×#491	C₂×C₇	semidirect
131. C₂×#488	C₂×C₇	semidirect
132. C₂×#463	C₂×C₇	semidirect
133. C₂×#461	C₂×C₇	semidirect
134. C₂×#449	C₂×C₇	semidirect
135. C₂×#448	C₂×C₇	semidirect
136. C₂×#433	C₂×C₇	semidirect
215. #540	C₂²×C₇	semidirect
217. #536	C₂²×C₇	semidirect
231. #496	C₂²×C₇	semidirect
232. #492	C₂²×C₇	semidirect
233. #491	C₂²×C₇	semidirect
234. #488	C₂²×C₇	semidirect
235. #463	C₂²×C₇	semidirect
236. #461	C₂²×C₇	semidirect
237. #449	C₂²×C₇	semidirect
238. #448	C₂²×C₇	semidirect
239. #433	C₂²×C₇	semidirect
465. C₂×C₇	#3221	direct (N × H)
518. C₇	C₂×#3221	direct (N × H)
544. C₂	C₇×#3221	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₇×#540	2
C₂×C₇×#536	2
C₇×#3221	2
C₂×C₇×#496	2
C₂×C₇×#492	2
C₂×C₇×#491	2
C₂×C₇×#488	2
C₂×C₇×#463	2
C₂×C₇×#461	2
C₂×C₇×#449	2
C₂×C₇×#448	2
C₂×C₇×#433	2
C₂×#3221	7

Subgroups — C2×C7×#3221 #13238010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3221 #13238010