Subgroups — C₂×C₇×#3223 #13238011

Order 1792.

2022 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#536	C₂	1	1	yes	maximal, characteristic
3	C₇×#3223	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₇×#494	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×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₇×#462	C₂	1	2	yes	maximal, complemented
10	C₂×C₇×#452	C₂	1	2	yes	maximal
11	C₂×C₇×#451	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×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
17	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₇×SD₁₆	C₂²	1	2	yes	—
19	C₇×#541	—	2	4	no	—
20	C₇×#541	C₂²	1	8	yes	complemented
21	C₇×#536	—	2	4	no	—
22	C₇×#536	C₂²	1	8	yes	—
23	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×#126	—	2	2	no	—
27	C₂×C₇×#125	—	2	2	no	—
28	C₂×C₇×#125	C₂²	1	1	yes	characteristic
29	C₂×C₇×#124	C₂²	1	1	yes	characteristic
30	C₂×C₇×#124	C₂²	1	1	yes	characteristic
31	C₂×C₇×#123	—	2	2	no	—
32	C₂×C₇×C₂²⋊Q₈	—	2	2	no	—
33	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
35	C₂×C₇×#117	C₂²	1	1	yes	characteristic
36	C₇×#497	C₂²	1	8	yes	complemented
37	C₇×#494	C₂²	1	8	yes	complemented
38	C₇×#491	C₂²	1	8	yes	complemented
39	C₇×#488	C₂²	1	8	yes	complemented
40	C₇×#464	C₂²	1	16	yes	complemented
41	C₇×#462	C₂²	1	16	yes	complemented
42	C₇×#452	C₂²	1	16	yes	—
43	C₇×#451	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×#3223	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	2	yes	—
64	C₂²×C₇×Q₈	C₂³	1	4	yes	—
65	C₂²×C₇×D₄	—	2	1	no	—
66	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₇	—	2	1	no	—
68	C₂³×C₄×C₇	—	2	1	no	—
69	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
70	C₂×C₇×Q₁₆	—	4	4	no	—
71	C₂×C₇×Q₁₆	—	4	4	no	—
72	C₂×C₇×Q₁₆	—	4	4	no	—
73	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
74	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
75	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
76	C₂×C₇×SD₁₆	—	4	4	no	—
77	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
78	C₂²×C₇×C₈	C₂³	1	2	yes	—
79	C₂²×C₇×C₈	C₂³	1	2	yes	—
80	C₇×C₄⋊Q₈	—	2	2	no	—
81	C₇×C₄⋊Q₈	—	2	2	no	—
82	C₇×C₄⋊Q₈	—	2	2	no	—
83	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
84	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
85	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
86	C₇×#126	—	2	16	no	—
87	C₇×#125	—	2	16	no	—
88	C₇×#125	—	2	2	no	—
89	C₇×#125	C₂³	1	4	yes	—
90	C₇×#124	—	2	2	no	—
91	C₇×#124	—	2	2	no	—
92	C₇×#124	C₂³	1	4	yes	—
93	C₇×#124	C₂³	1	4	yes	—
94	C₇×#123	—	2	16	no	—
95	C₇×C₂²⋊Q₈	—	2	4	no	—
96	C₇×C₂²⋊Q₈	—	2	16	no	—
97	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
98	C₄×C₇×Q₈	—	2	4	no	—
99	C₄×C₇×Q₈	C₂³	1	8	yes	—
100	C₇×#117	D₄	1	4	yes	—
101	C₇×#117	C₂³	1	4	yes	—
102	C₂×C₇×C₄⋊C₄	—	2	2	no	—
103	C₂×C₇×C₄⋊C₄	—	2	2	no	—
104	C₂×C₇×C₄⋊C₄	—	2	2	no	—
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	D₄	1	2	yes	—
114	C₂×C₄²×C₇	—	2	2	no	—
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×#541	C₂×C₇	1	1	yes	characteristic, complemented
126	C₂×#536	C₂×C₇	1	1	yes	characteristic
127	#3223	C₂×C₇	1	16	yes	direct product factor
128	C₂×#497	C₂×C₇	1	1	yes	characteristic, complemented
129	C₂×#494	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×#464	C₂×C₇	1	2	yes	complemented
133	C₂×#462	C₂×C₇	1	2	yes	complemented
134	C₂×#452	C₂×C₇	1	2	yes	—
135	C₂×#451	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	C₂×D₄	1	1	yes	characteristic
139	C₇×#41	—	4	8	no	—
140	C₇×#41	—	4	8	no	—
141	C₂×C₇×Q₈	—	2	2	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	—	2	4	no	—
150	C₂×C₇×Q₈	—	2	4	no	—
151	C₂×C₇×Q₈	—	4	8	no	—
152	C₂×C₇×Q₈	—	4	4	no	—
153	C₂×C₇×Q₈	—	4	8	no	—
154	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
155	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
156	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
157	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
158	C₂×C₇×D₄	—	2	4	no	—
159	C₂×C₇×D₄	—	2	1	no	—
160	C₂×C₇×D₄	—	2	4	no	—
161	C₂×C₇×D₄	—	4	4	no	—
162	C₂×C₇×D₄	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₇	—	2	4	no	—
164	C₂²×C₄×C₇	—	2	4	no	—
165	C₂²×C₄×C₇	—	2	2	no	—
166	C₂²×C₄×C₇	—	2	2	no	—
167	C₂²×C₄×C₇	—	2	1	no	—
168	C₂²×C₄×C₇	—	2	1	no	—
169	C₂²×C₄×C₇	—	2	1	no	—
170	C₂²×C₄×C₇	—	2	4	no	—
171	C₂²×C₄×C₇	—	4	4	no	—
172	C₂²×C₄×C₇	—	4	4	no	—
173	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
179	C₇×Q₁₆	—	4	8	no	—
180	C₇×Q₁₆	—	4	8	no	—
181	C₇×Q₁₆	—	4	8	no	—
182	C₇×SD₁₆	—	4	8	no	—
183	C₂×C₇×C₈	—	2	4	no	—
184	C₂×C₇×C₈	—	2	4	no	—
185	C₂×C₇×C₈	C₂⁴	1	4	yes	—
186	C₂×C₇×C₈	C₂⁴	1	4	yes	—
187	C₇×C₄⋊C₄	—	2	8	no	—
188	C₇×C₄⋊C₄	—	2	8	no	—
189	C₇×C₄⋊C₄	—	2	8	no	—
190	C₇×C₄⋊C₄	—	2	8	no	—
191	C₇×C₄⋊C₄	—	2	8	no	—
192	C₇×C₄⋊C₄	—	2	8	no	—
193	C₇×C₄⋊C₄	—	2	2	no	—
194	C₇×C₄⋊C₄	C₂×D₄	1	8	yes	—
195	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
196	C₇×C₂²⋊C₄	—	2	8	no	—
197	C₇×C₂²⋊C₄	—	2	8	no	—
198	C₇×C₂²⋊C₄	—	2	8	no	—
199	C₇×C₂²⋊C₄	C₂×D₄	1	8	yes	—
200	C₄²×C₇	—	2	8	no	—
201	C₄²×C₇	C₂×D₄	1	2	yes	—
202	C₄²×C₇	C₂×D₄	1	2	yes	—
203	C₄²×C₇	C₂⁴	1	2	yes	—
204	C₄²×C₇	C₂⁴	1	2	yes	—
205	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
206	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
207	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
208	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
209	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
210	C₂²×SD₁₆	C₂²×C₇	1	2	yes	—
211	#541	—	2	4	no	—
212	#541	C₂²×C₇	1	8	yes	complemented
213	#536	—	2	4	no	—
214	#536	C₂²×C₇	1	8	yes	—
215	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
216	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
218	C₂×#126	—	2	2	no	—
219	C₂×#125	—	2	2	no	—
220	C₂×#125	C₂²×C₇	1	1	yes	characteristic
221	C₂×#124	C₂²×C₇	1	1	yes	characteristic
222	C₂×#124	C₂²×C₇	1	1	yes	characteristic
223	C₂×#123	—	2	2	no	—
224	C₂×C₂²⋊Q₈	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
227	C₂×#117	C₂²×C₇	1	1	yes	characteristic
228	#497	C₂²×C₇	1	8	yes	complemented
229	#494	C₂²×C₇	1	8	yes	complemented
230	#491	C₂²×C₇	1	8	yes	complemented
231	#488	C₂²×C₇	1	8	yes	complemented
232	#464	C₂²×C₇	1	16	yes	complemented
233	#462	C₂²×C₇	1	16	yes	complemented
234	#452	C₂²×C₇	1	16	yes	—
235	#451	C₂²×C₇	1	16	yes	complemented
236	#433	C₂²×C₇	1	8	yes	complemented
237	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
238	C₂×#103	C₂²×C₇	1	2	yes	—
239	C₂×#103	C₂²×C₇	1	2	yes	—
240	C₂×#103	C₂²×C₇	1	2	yes	—
241	C₂×#102	C₂²×C₇	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
243	C₂×#97	C₂²×C₇	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
245	C₂³×C₇	—	2	2	no	—
246	C₂³×C₇	—	2	4	no	—
247	C₂³×C₇	—	2	2	no	—
248	C₂³×C₇	—	4	2	no	—
249	C₂³×C₇	—	4	4	no	—
250	C₂³×C₇	C₂²×D₄	1	2	yes	—
251	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
252	C₇×Q₈	—	2	4	no	—
253	C₇×Q₈	—	2	4	no	—
254	C₇×Q₈	—	2	4	no	—
255	C₇×Q₈	—	2	4	no	—
256	C₇×Q₈	—	2	4	no	—
257	C₇×Q₈	—	4	8	no	—
258	C₇×Q₈	—	4	4	no	—
259	C₇×Q₈	—	4	2	no	—
260	C₇×Q₈	—	4	2	no	—
261	C₇×Q₈	—	4	2	no	—
262	C₇×D₄	—	2	4	no	—
263	C₇×D₄	—	4	8	no	—
264	C₇×D₄	—	4	2	no	—
265	C₂×C₄×C₇	—	2	2	no	—
266	C₂×C₄×C₇	—	2	4	no	—
267	C₂×C₄×C₇	—	2	4	no	—
268	C₂×C₄×C₇	—	2	4	no	—
269	C₂×C₄×C₇	—	2	4	no	—
270	C₂×C₄×C₇	—	2	4	no	—
271	C₂×C₄×C₇	—	2	4	no	—
272	C₂×C₄×C₇	—	2	2	no	—
273	C₂×C₄×C₇	—	2	2	no	—
274	C₂×C₄×C₇	—	2	2	no	—
275	C₂×C₄×C₇	—	4	8	no	—
276	C₂×C₄×C₇	—	4	8	no	—
277	C₂×C₄×C₇	—	4	2	no	—
278	C₂×C₄×C₇	—	4	2	no	—
279	C₂×C₄×C₇	—	4	2	no	—
280	C₂×C₄×C₇	—	4	4	no	—
281	C₂×C₄×C₇	—	4	4	no	—
282	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
283	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
284	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
287	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
288	C₇×C₈	—	2	4	no	—
289	C₇×C₈	—	2	4	no	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	4	4	no	—
292	C₂×#41	C₂³×C₇	1	4	yes	—
293	C₂²×Q₈	—	2	1	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	—	4	4	no	—
296	C₂²×Q₈	C₂³×C₇	1	2	yes	—
297	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
298	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
299	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
300	C₂²×Q₈	C₂³×C₇	1	4	yes	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
306	C₂×Q₁₆	—	4	4	no	—
307	C₂×Q₁₆	—	4	4	no	—
308	C₂×Q₁₆	—	4	4	no	—
309	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
310	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
311	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
312	C₂×SD₁₆	—	4	4	no	—
313	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
314	C₂²×C₈	C₂³×C₇	1	2	yes	—
315	C₂²×C₈	C₂³×C₇	1	2	yes	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
320	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
321	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
322	#126	—	2	16	no	—
323	#125	—	2	16	no	—
324	#125	—	2	2	no	—
325	#125	C₂³×C₇	1	4	yes	—
326	#124	—	2	2	no	—
327	#124	—	2	2	no	—
328	#124	C₂³×C₇	1	4	yes	—
329	#124	C₂³×C₇	1	4	yes	—
330	#123	—	2	16	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	16	no	—
333	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
334	C₄×Q₈	—	2	4	no	—
335	C₄×Q₈	C₂³×C₇	1	8	yes	—
336	#117	C₇×D₄	1	4	yes	—
337	#117	C₂³×C₇	1	4	yes	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
353	C₄⋊C₈	C₂³×C₇	1	8	yes	—
354	#103	C₂³×C₇	1	8	yes	—
355	#103	C₂³×C₇	1	8	yes	—
356	#103	C₂³×C₇	1	8	yes	—
357	#102	C₂³×C₇	1	8	yes	—
358	C₂²⋊C₈	C₂³×C₇	1	8	yes	—
359	#97	C₂³×C₇	1	4	yes	—
360	C₄×C₈	C₂³×C₇	1	4	yes	—
361	C₂²×C₇	—	2	2	no	—
362	C₂²×C₇	—	2	4	no	—
363	C₂²×C₇	—	4	4	no	—
364	C₂²×C₇	—	4	2	no	—
365	C₂²×C₇	—	4	4	no	—
366	C₂²×C₇	—	8	4	no	—
367	C₂²×C₇	#535	1	2	yes	—
368	C₂²×C₇	#578	1	4	yes	—
369	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
370	C₄×C₇	—	2	2	no	—
371	C₄×C₇	—	2	4	no	—
372	C₄×C₇	—	2	4	no	—
373	C₄×C₇	—	4	2	no	—
374	C₄×C₇	—	4	2	no	—
375	C₄×C₇	—	4	2	no	—
376	C₄×C₇	—	4	4	no	—
377	C₄×C₇	—	4	4	no	—
378	C₄×C₇	#535	1	2	yes	—
379	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
382	#41	—	4	8	no	—
383	#41	—	4	8	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	4	8	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	8	no	—
397	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
398	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
399	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
400	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	4	4	no	—
405	C₂×D₄	C₂⁴×C₇	1	2	yes	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
417	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
418	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
421	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
422	Q₁₆	—	4	8	no	—
423	Q₁₆	—	4	8	no	—
424	Q₁₆	—	4	8	no	—
425	SD₁₆	—	4	8	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	C₂⁴×C₇	1	4	yes	—
429	C₂×C₈	C₂⁴×C₇	1	4	yes	—
430	C₄⋊C₄	—	2	8	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	C₂×C₇×D₄	1	8	yes	—
438	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	C₂×C₇×D₄	1	8	yes	—
443	C₄²	—	2	8	no	—
444	C₄²	C₂×C₇×D₄	1	2	yes	—
445	C₄²	C₂×C₇×D₄	1	2	yes	—
446	C₄²	C₂⁴×C₇	1	2	yes	—
447	C₄²	C₂⁴×C₇	1	2	yes	—
448	C₂×C₇	—	4	2	no	—
449	C₂×C₇	—	8	2	no	—
450	C₂×C₇	#3223	1	4	yes	direct product factor
451	C₂×C₇	C₂×#535	1	1	yes	characteristic
452	C₂×C₇	C₂×#578	1	2	yes	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	4	no	—
458	C₂³	C₂²×C₇×D₄	1	2	yes	—
459	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
460	Q₈	—	2	4	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	2	4	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	Q₈	—	4	8	no	—
466	Q₈	—	4	4	no	—
467	Q₈	—	4	2	no	—
468	Q₈	—	4	2	no	—
469	Q₈	—	4	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	8	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
491	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
492	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
493	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
494	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
495	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
496	C₈	—	2	4	no	—
497	C₈	—	2	4	no	—
498	C₇	C₂×#3223	1	1	yes	characteristic, direct product factor, Sylow
499	C₂²	—	2	4	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	8	4	no	—
505	C₂²	C₇×#535	1	2	yes	—
506	C₂²	C₇×#578	1	4	yes	—
507	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
508	C₄	—	2	4	no	—
509	C₄	—	2	4	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	4	no	—
516	C₄	C₇×#535	1	2	yes	—
517	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
518	C₂	—	4	2	no	—
519	C₂	—	8	2	no	—
520	C₂	C₇×#3223	1	4	yes	direct product factor
521	C₂	C₂×C₇×#535	1	1	yes	characteristic
522	C₂	C₂×C₇×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₂²×C₇×#41	C₂²
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×#541	C₂	semidirect
3. C₇×#3223	C₂	direct (N × H)
4. C₂×C₇×#497	C₂	semidirect
5. C₂×C₇×#494	C₂	semidirect
6. C₂×C₇×#491	C₂	semidirect
7. C₂×C₇×#488	C₂	semidirect
8. C₂×C₇×#464	C₂	semidirect
9. C₂×C₇×#462	C₂	semidirect
11. C₂×C₇×#451	C₂	semidirect
12. C₂×C₇×#433	C₂	semidirect
20. C₇×#541	C₂²	semidirect
36. C₇×#497	C₂²	semidirect
37. C₇×#494	C₂²	semidirect
38. C₇×#491	C₂²	semidirect
39. C₇×#488	C₂²	semidirect
40. C₇×#464	C₂²	semidirect
41. C₇×#462	C₂²	semidirect
43. C₇×#451	C₂²	semidirect
44. C₇×#433	C₂²	semidirect
53. C₂×#3223	C₇	direct (N × H)
125. C₂×#541	C₂×C₇	semidirect
127. #3223	C₂×C₇	direct (N × H)
128. C₂×#497	C₂×C₇	semidirect
129. C₂×#494	C₂×C₇	semidirect
130. C₂×#491	C₂×C₇	semidirect
131. C₂×#488	C₂×C₇	semidirect
132. C₂×#464	C₂×C₇	semidirect
133. C₂×#462	C₂×C₇	semidirect
135. C₂×#451	C₂×C₇	semidirect
136. C₂×#433	C₂×C₇	semidirect
212. #541	C₂²×C₇	semidirect
228. #497	C₂²×C₇	semidirect
229. #494	C₂²×C₇	semidirect
230. #491	C₂²×C₇	semidirect
231. #488	C₂²×C₇	semidirect
232. #464	C₂²×C₇	semidirect
233. #462	C₂²×C₇	semidirect
235. #451	C₂²×C₇	semidirect
236. #433	C₂²×C₇	semidirect
450. C₂×C₇	#3223	direct (N × H)
498. C₇	C₂×#3223	direct (N × H)
520. C₂	C₇×#3223	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×#541	2
C₂×C₇×#536	2
C₇×#3223	2
C₂×C₇×#497	2
C₂×C₇×#494	2
C₂×C₇×#491	2
C₂×C₇×#488	2
C₂×C₇×#464	2
C₂×C₇×#462	2
C₂×C₇×#452	2
C₂×C₇×#451	2
C₂×C₇×#433	2
C₂×#3223	7

Subgroups — C2×C7×#3223 #13238011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×#3223 #13238011