Subgroups — C₂×#10621572 #13062245

Order 1344.

1796 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66730	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₇×D₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄×D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
5	C₂×D₇×#67	C₂	1	2	yes	maximal, complemented
6	C₂²×#4245	C₂	1	2	yes	maximal, complemented
7	C₂×#66684	C₂	1	2	yes	maximal, complemented
8	#10621572	C₂	1	16	yes	maximal, direct product factor
9	C₂×#66681	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#66676	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#66675	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#6548	—	3	1	no	maximal, Hall
14	C₂³×D₃×C₇	C₂²	1	2	yes	complemented
15	C₂³×C₃×D₇	C₂²	1	2	yes	complemented
16	C₂²×D₃×D₇	C₂²	1	2	yes	complemented
17	C₂×C₃×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
18	C₂×#4268	C₂²	1	2	yes	complemented
19	C₂²×Dic₂₁	C₂²	1	2	yes	complemented
20	#66730	C₂²	1	8	yes	complemented
21	C₂×C₄×D₂₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×Dic₄₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×#67	C₂²	1	2	yes	complemented
24	D₃×C₇×D₄	C₂²	1	8	yes	complemented
25	C₂×C₇×D₁₂	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃×C₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
28	C₃×D₄×D₇	C₂²	1	8	yes	complemented
29	C₂×C₃×D₂₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×D₇	C₂²	1	1	yes	characteristic, complemented
31	D₃×C₂²⋊D₇	C₂²	1	16	yes	complemented
32	D₇×#67	C₂²	1	16	yes	complemented
33	C₂×#4248	C₂²	1	1	yes	characteristic, complemented
34	C₂×#4247	C₂²	1	1	yes	characteristic, complemented
35	C₂×#4246	C₂²	1	1	yes	characteristic, complemented
36	C₂×#4245	C₂²	1	2	yes	complemented
37	C₂×#4245	C₂²	1	1	yes	characteristic, complemented
38	C₂×#4245	C₂²	1	2	yes	complemented
39	C₂×#4245	C₂²	1	2	yes	complemented
40	C₂×#4245	C₂²	1	16	yes	complemented
41	C₂×D₃×Dic₇	C₂²	1	2	yes	complemented
42	#66684	C₂²	1	16	yes	complemented
43	C₂×Dic₃×D₇	C₂²	1	2	yes	complemented
44	#66681	C₂²	1	8	yes	complemented
45	#66676	C₂²	1	8	yes	complemented
46	#66675	C₂²	1	8	yes	complemented
47	#66669	C₂²	1	8	yes	complemented
48	C₂²×C₇×D₄	—	3	1	no	—
49	C₂²×C₂²⋊D₇	—	3	2	no	—
50	C₂²×C₂²⋊D₇	—	3	2	no	—
51	#6548	—	3	16	no	—
52	C₂×#1159	—	3	1	no	—
53	C₂×#1159	—	3	2	no	—
54	C₂×#1159	—	3	1	no	—
55	C₂×D₄×D₇	—	3	2	no	—
56	C₂×D₄×D₇	—	3	1	no	—
57	C₂×D₄×D₇	D₃	1	1	yes	characteristic, complemented
58	C₂×#1157	—	3	1	no	—
59	C₂×#1157	—	3	1	no	—
60	C₂×#1004	—	7	1	no	maximal, Hall
61	C₂³×C₃×C₇	C₂³	1	2	yes	—
62	C₂²×D₂₁	C₂³	1	1	yes	characteristic
63	C₂²×D₃×C₇	—	4	4	no	—
64	C₂²×D₃×C₇	C₂³	1	2	yes	—
65	C₂²×D₃×C₇	C₂³	1	1	yes	characteristic
66	C₂²×D₃×C₇	C₂³	1	8	yes	complemented
67	C₂²×C₃×D₇	—	4	4	no	—
68	C₂²×C₃×D₇	C₂³	1	2	yes	—
69	C₂²×C₃×D₇	C₂³	1	1	yes	characteristic
70	C₂²×C₃×D₇	C₂³	1	8	yes	complemented
71	C₂×D₃×D₇	—	4	4	no	—
72	C₂×D₃×D₇	C₂³	1	8	yes	complemented
73	C₃×C₇×D₄	C₂³	1	4	yes	complemented
74	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
75	#4268	C₂³	1	8	yes	complemented
76	C₂×Dic₂₁	C₂³	1	2	yes	—
77	C₂×Dic₂₁	C₂³	1	1	yes	characteristic
78	C₂×Dic₂₁	C₂³	1	8	yes	complemented
79	C₄×D₂₁	C₂³	1	4	yes	complemented
80	Dic₄₂	C₂³	1	4	yes	complemented
81	C₇×#67	C₂³	1	8	yes	complemented
82	C₂×C₇×Dic₃	C₂³	1	1	yes	characteristic
83	C₇×D₁₂	C₂³	1	4	yes	complemented
84	C₄×D₃×C₇	C₂³	1	4	yes	complemented
85	C₃×C₂²⋊D₇	C₂³	1	8	yes	complemented
86	C₂×C₃×Dic₇	C₂³	1	1	yes	characteristic
87	C₃×D₂₈	C₂³	1	4	yes	complemented
88	C₃×C₄×D₇	C₂³	1	4	yes	complemented
89	#4248	C₂³	1	4	yes	complemented
90	#4247	C₂³	1	4	yes	complemented
91	#4246	C₂³	1	4	yes	complemented
92	#4245	C₂³	1	8	yes	complemented
93	#4245	C₂³	1	4	yes	complemented
94	#4245	C₂³	1	8	yes	complemented
95	#4245	C₂³	1	8	yes	complemented
96	D₃×Dic₇	C₂³	1	8	yes	complemented
97	Dic₃×D₇	C₂³	1	8	yes	complemented
98	C₂⁴×C₇	—	3	2	no	—
99	C₂³×D₇	—	3	2	no	—
100	C₂³×D₇	C₂×D₃	1	2	yes	complemented
101	C₂×C₇×D₄	—	3	2	no	—
102	C₂×C₇×D₄	—	3	8	no	—
103	C₂×C₇×D₄	—	3	1	no	—
104	C₂×C₇×D₄	C₂×D₃	1	1	yes	characteristic, complemented
105	C₂²×C₄×C₇	—	3	1	no	—
106	C₂×C₂²⋊D₇	—	3	2	no	—
107	C₂×C₂²⋊D₇	—	3	2	no	—
108	C₂×C₂²⋊D₇	—	3	1	no	—
109	C₂×C₂²⋊D₇	—	3	2	no	—
110	C₂×C₂²⋊D₇	—	3	2	no	—
111	C₂×C₂²⋊D₇	—	3	16	no	—
112	C₂×C₂²⋊D₇	—	3	16	no	—
113	C₂×C₂²⋊D₇	—	3	1	no	—
114	C₂×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
115	C₂²×Dic₇	—	3	2	no	—
116	C₂²×Dic₇	—	3	2	no	—
117	#1159	—	3	8	no	—
118	#1159	—	3	16	no	—
119	#1159	—	3	8	no	—
120	D₄×D₇	—	3	16	no	—
121	D₄×D₇	—	3	8	no	—
122	D₄×D₇	C₂×D₃	1	8	yes	complemented
123	#1157	—	3	8	no	—
124	#1157	—	3	8	no	—
125	C₂×D₂₈	—	3	1	no	—
126	C₂×D₂₈	C₂×D₃	1	1	yes	characteristic, complemented
127	C₂×C₄×D₇	—	3	2	no	—
128	C₂×C₄×D₇	—	3	1	no	—
129	C₂×C₄×D₇	C₂×D₃	1	1	yes	characteristic, complemented
130	C₂×Dic₁₄	—	3	1	no	—
131	C₂×Dic₁₄	—	3	1	no	—
132	C₂²×C₃×D₄	—	7	1	no	—
133	C₂²×#67	—	7	2	no	—
134	C₂²×#67	—	7	2	no	—
135	#1004	—	7	16	no	—
136	C₂×#237	—	7	1	no	—
137	C₂×#237	—	7	2	no	—
138	C₂×#237	—	7	1	no	—
139	C₂×D₃×D₄	—	7	2	no	—
140	C₂×D₃×D₄	—	7	1	no	—
141	C₂×D₃×D₄	D₇	1	1	yes	characteristic, complemented
142	C₂×#235	—	7	1	no	—
143	C₂×#235	—	7	1	no	—
144	C₂²×C₃×C₇	—	2	4	no	—
145	C₂²×C₃×C₇	C₂⁴	1	4	yes	—
146	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
147	C₂×D₂₁	—	2	2	no	—
148	C₂×D₂₁	C₂⁴	1	2	yes	—
149	C₂×D₃×C₇	—	2	4	no	—
150	C₂×D₃×C₇	—	2	2	no	—
151	C₂×D₃×C₇	—	4	8	no	—
152	C₂×D₃×C₇	C₂⁴	1	4	yes	—
153	C₂×D₃×C₇	C₂⁴	1	2	yes	—
154	C₂×C₃×D₇	—	2	4	no	—
155	C₂×C₃×D₇	—	2	2	no	—
156	C₂×C₃×D₇	—	4	8	no	—
157	C₂×C₃×D₇	C₂⁴	1	4	yes	—
158	C₂×C₃×D₇	C₂⁴	1	2	yes	—
159	D₃×D₇	—	4	8	no	—
160	C₃×C₄×C₇	C₂⁴	1	2	yes	—
161	Dic₂₁	C₂⁴	1	4	yes	—
162	Dic₂₁	C₂⁴	1	2	yes	—
163	C₃×Dic₇	C₂⁴	1	2	yes	—
164	C₇×Dic₃	C₂⁴	1	2	yes	—
165	C₂×H(5,𝔽₂)	—	21	1	no	Sylow
166	C₂³×C₇	—	3	2	no	—
167	C₂³×C₇	—	3	1	no	—
168	C₂³×C₇	—	3	8	no	—
169	C₂³×C₇	—	12	4	no	—
170	C₂³×C₇	C₂²×D₃	1	2	yes	—
171	C₂²×D₇	—	3	1	no	—
172	C₂²×D₇	—	3	8	no	—
173	C₂²×D₇	—	4	4	no	—
174	C₂²×D₇	—	12	4	no	—
175	C₂²×D₇	C₂²×D₃	1	2	yes	—
176	C₂²×D₇	C₂²×D₃	1	1	yes	characteristic
177	C₂²×D₇	C₂²×D₃	1	8	yes	complemented
178	C₇×D₄	—	3	8	no	—
179	C₇×D₄	—	3	4	no	—
180	C₇×D₄	C₂²×D₃	1	4	yes	complemented
181	C₂×C₄×C₇	—	3	1	no	—
182	C₂×C₄×C₇	—	3	4	no	—
183	C₂×C₄×C₇	C₂²×D₃	1	1	yes	characteristic
184	C₂²⋊D₇	—	3	8	no	—
185	C₂²⋊D₇	—	3	8	no	—
186	C₂²⋊D₇	—	3	4	no	—
187	C₂²⋊D₇	—	3	8	no	—
188	C₂²⋊D₇	—	3	8	no	—
189	C₂²⋊D₇	—	3	4	no	—
190	C₂²⋊D₇	C₂²×D₃	1	8	yes	complemented
191	C₂×Dic₇	—	3	2	no	—
192	C₂×Dic₇	—	3	1	no	—
193	C₂×Dic₇	—	3	8	no	—
194	C₂×Dic₇	—	3	8	no	—
195	C₂×Dic₇	C₂²×D₃	1	1	yes	characteristic
196	D₂₈	—	3	4	no	—
197	D₂₈	C₂²×D₃	1	4	yes	complemented
198	C₄×D₇	—	3	8	no	—
199	C₄×D₇	—	3	4	no	—
200	C₄×D₇	C₂²×D₃	1	4	yes	complemented
201	Dic₁₄	—	3	4	no	—
202	Dic₁₄	—	3	4	no	—
203	C₂⁴×C₃	—	7	2	no	—
204	C₂³×D₃	—	7	2	no	—
205	C₂³×D₃	C₂×D₇	1	2	yes	complemented
206	C₂×C₃×D₄	—	7	2	no	—
207	C₂×C₃×D₄	—	7	8	no	—
208	C₂×C₃×D₄	—	7	1	no	—
209	C₂×C₃×D₄	C₂×D₇	1	1	yes	characteristic, complemented
210	C₂²×C₃×C₄	—	7	1	no	—
211	C₂×#67	—	7	2	no	—
212	C₂×#67	—	7	2	no	—
213	C₂×#67	—	7	1	no	—
214	C₂×#67	—	7	2	no	—
215	C₂×#67	—	7	2	no	—
216	C₂×#67	—	7	16	no	—
217	C₂×#67	—	7	16	no	—
218	C₂×#67	—	7	1	no	—
219	C₂×#67	C₂×D₇	1	2	yes	complemented
220	C₂²×Dic₃	—	7	2	no	—
221	C₂²×Dic₃	—	7	2	no	—
222	#237	—	7	8	no	—
223	#237	—	7	16	no	—
224	#237	—	7	8	no	—
225	D₃×D₄	—	7	16	no	—
226	D₃×D₄	—	7	8	no	—
227	D₃×D₄	C₂×D₇	1	8	yes	complemented
228	#235	—	7	8	no	—
229	#235	—	7	8	no	—
230	C₂×D₁₂	—	7	1	no	—
231	C₂×D₁₂	C₂×D₇	1	1	yes	characteristic, complemented
232	C₂×C₄×D₃	—	7	2	no	—
233	C₂×C₄×D₃	—	7	1	no	—
234	C₂×C₄×D₃	C₂×D₇	1	1	yes	characteristic, complemented
235	C₂×Dic₆	—	7	1	no	—
236	C₂×Dic₆	—	7	1	no	—
237	C₂×C₃×C₇	—	2	4	no	—
238	C₂×C₃×C₇	H(5,𝔽₂)	1	2	yes	complemented
239	C₂×C₃×C₇	C₂⁵	1	1	yes	characteristic
240	D₂₁	—	2	2	no	—
241	C₃×D₇	—	2	4	no	—
242	C₃×D₇	—	2	2	no	—
243	D₃×C₇	—	2	4	no	—
244	D₃×C₇	—	2	2	no	—
245	H(5,𝔽₂)	—	21	16	no	—
246	C₂×#41	—	21	1	no	—
247	C₂×#41	—	21	1	no	—
248	C₂×#41	—	21	1	no	—
249	C₂×#41	—	21	2	no	—
250	C₂×#41	—	21	1	no	—
251	C₂²×D₄	—	3	1	no	—
252	C₂²×D₄	—	7	1	no	—
253	C₂²×D₄	—	21	1	no	—
254	C₂²×D₄	—	21	2	no	—
255	C₂²×D₄	—	21	2	no	—
256	C₂²×D₄	—	21	2	no	—
257	C₂²×C₇	—	2	4	no	—
258	C₂²×C₇	—	3	4	no	—
259	C₂²×C₇	—	3	2	no	—
260	C₂²×C₇	—	6	4	no	—
261	C₂²×C₇	—	6	2	no	—
262	C₂²×C₇	—	12	8	no	—
263	C₂²×C₇	C₂³×D₃	1	4	yes	—
264	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
265	C₂×D₇	—	2	2	no	—
266	C₂×D₇	—	2	4	no	—
267	C₂×D₇	—	3	2	no	—
268	C₂×D₇	—	4	8	no	—
269	C₂×D₇	—	6	2	no	—
270	C₂×D₇	—	12	8	no	—
271	C₂×D₇	C₂³×D₃	1	4	yes	—
272	C₂×D₇	C₂³×D₃	1	2	yes	—
273	C₄×C₇	—	3	2	no	—
274	C₄×C₇	C₂³×D₃	1	2	yes	—
275	Dic₇	—	3	4	no	—
276	Dic₇	—	3	2	no	—
277	Dic₇	C₂³×D₃	1	2	yes	—
278	C₂³×C₃	—	7	2	no	—
279	C₂³×C₃	—	7	1	no	—
280	C₂³×C₃	—	7	8	no	—
281	C₂³×C₃	—	28	4	no	—
282	C₂³×C₃	C₂²×D₇	1	2	yes	—
283	C₂²×D₃	—	4	4	no	—
284	C₂²×D₃	—	7	1	no	—
285	C₂²×D₃	—	7	8	no	—
286	C₂²×D₃	—	28	4	no	—
287	C₂²×D₃	C₂²×D₇	1	2	yes	—
288	C₂²×D₃	C₂²×D₇	1	1	yes	characteristic
289	C₂²×D₃	C₂²×D₇	1	8	yes	complemented
290	C₃×D₄	—	7	8	no	—
291	C₃×D₄	—	7	4	no	—
292	C₃×D₄	C₂²×D₇	1	4	yes	complemented
293	C₂×C₃×C₄	—	7	1	no	—
294	C₂×C₃×C₄	—	7	4	no	—
295	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
296	#67	—	7	8	no	—
297	#67	—	7	8	no	—
298	#67	—	7	4	no	—
299	#67	—	7	8	no	—
300	#67	—	7	8	no	—
301	#67	—	7	4	no	—
302	#67	C₂²×D₇	1	8	yes	complemented
303	C₂×Dic₃	—	7	2	no	—
304	C₂×Dic₃	—	7	1	no	—
305	C₂×Dic₃	—	7	8	no	—
306	C₂×Dic₃	—	7	8	no	—
307	C₂×Dic₃	C₂²×D₇	1	1	yes	characteristic
308	D₁₂	—	7	4	no	—
309	D₁₂	C₂²×D₇	1	4	yes	complemented
310	C₄×D₃	—	7	8	no	—
311	C₄×D₃	—	7	4	no	—
312	C₄×D₃	C₂²×D₇	1	4	yes	complemented
313	Dic₆	—	7	4	no	—
314	Dic₆	—	7	4	no	—
315	C₃×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
316	C₂⁴	—	3	2	no	—
317	C₂⁴	—	7	2	no	—
318	C₂⁴	—	21	2	no	—
319	#41	—	21	8	no	—
320	#41	—	21	8	no	—
321	#41	—	21	8	no	—
322	#41	—	21	16	no	—
323	#41	—	21	8	no	—
324	C₂×Q₈	—	21	1	no	—
325	C₂×Q₈	—	21	1	no	—
326	C₂×D₄	—	3	2	no	—
327	C₂×D₄	—	3	8	no	—
328	C₂×D₄	—	3	1	no	—
329	C₂×D₄	—	7	2	no	—
330	C₂×D₄	—	7	8	no	—
331	C₂×D₄	—	7	1	no	—
332	C₂×D₄	—	21	1	no	—
333	C₂×D₄	—	21	1	no	—
334	C₂×D₄	—	21	8	no	—
335	C₂×D₄	—	21	16	no	—
336	C₂×D₄	—	21	16	no	—
337	C₂×D₄	—	21	1	no	—
338	C₂×D₄	—	21	2	no	—
339	C₂×D₄	—	21	2	no	—
340	C₂×D₄	—	21	2	no	—
341	C₂×D₄	—	21	16	no	—
342	C₂×D₄	—	21	2	no	—
343	C₂×D₄	D₃×D₇	1	1	yes	characteristic, complemented
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	7	1	no	—
346	C₂²×C₄	—	21	2	no	—
347	C₂²×C₄	—	21	2	no	—
348	C₂²×C₄	—	21	2	no	—
349	C₂²×C₄	—	21	1	no	—
350	C₂×C₇	—	2	4	no	—
351	C₂×C₇	—	6	4	no	—
352	C₂×C₇	—	6	2	no	—
353	C₂×C₇	#1004	1	2	yes	complemented
354	C₂×C₇	C₂⁴×D₃	1	1	yes	characteristic
355	D₇	—	2	2	no	—
356	D₇	—	2	4	no	—
357	D₇	—	6	2	no	—
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	7	4	no	—
360	C₂²×C₃	—	7	2	no	—
361	C₂²×C₃	—	14	4	no	—
362	C₂²×C₃	—	14	2	no	—
363	C₂²×C₃	—	28	8	no	—
364	C₂²×C₃	C₂³×D₇	1	4	yes	—
365	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
366	C₂×D₃	—	2	2	no	—
367	C₂×D₃	—	2	4	no	—
368	C₂×D₃	—	4	8	no	—
369	C₂×D₃	—	7	2	no	—
370	C₂×D₃	—	14	2	no	—
371	C₂×D₃	—	28	8	no	—
372	C₂×D₃	C₂³×D₇	1	4	yes	—
373	C₂×D₃	C₂³×D₇	1	2	yes	—
374	C₃×C₄	—	7	2	no	—
375	C₃×C₄	C₂³×D₇	1	2	yes	—
376	Dic₃	—	7	4	no	—
377	Dic₃	—	7	2	no	—
378	Dic₃	C₂³×D₇	1	2	yes	—
379	C₂³	—	3	1	no	—
380	C₂³	—	3	2	no	—
381	C₂³	—	3	8	no	—
382	C₂³	—	7	1	no	—
383	C₂³	—	7	2	no	—
384	C₂³	—	7	8	no	—
385	C₂³	—	12	4	no	—
386	C₂³	—	21	8	no	—
387	C₂³	—	21	1	no	—
388	C₂³	—	28	4	no	—
389	C₂³	—	84	4	no	—
390	C₂³	C₂×D₃×D₇	1	2	yes	—
391	Q₈	—	21	4	no	—
392	Q₈	—	21	4	no	—
393	D₄	—	3	8	no	—
394	D₄	—	3	4	no	—
395	D₄	—	7	8	no	—
396	D₄	—	7	4	no	—
397	D₄	—	21	4	no	—
398	D₄	—	21	4	no	—
399	D₄	—	21	4	no	—
400	D₄	—	21	8	no	—
401	D₄	—	21	8	no	—
402	D₄	—	21	8	no	—
403	D₄	—	21	8	no	—
404	D₄	C₂×D₃×D₇	1	4	yes	complemented
405	C₂×C₄	—	3	1	no	—
406	C₂×C₄	—	3	4	no	—
407	C₂×C₄	—	7	1	no	—
408	C₂×C₄	—	7	4	no	—
409	C₂×C₄	—	21	8	no	—
410	C₂×C₄	—	21	8	no	—
411	C₂×C₄	—	21	8	no	—
412	C₂×C₄	—	21	2	no	—
413	C₂×C₄	—	21	1	no	—
414	C₂×C₄	—	21	4	no	—
415	C₂×C₄	C₂×D₃×D₇	1	1	yes	characteristic
416	C₇	C₂×#1004	1	1	yes	characteristic, complemented, Sylow
417	C₂×C₃	—	2	4	no	—
418	C₂×C₃	—	14	4	no	—
419	C₂×C₃	—	14	2	no	—
420	C₂×C₃	#6548	1	2	yes	complemented
421	C₂×C₃	C₂⁴×D₇	1	1	yes	characteristic
422	D₃	—	2	2	no	—
423	D₃	—	2	4	no	—
424	D₃	—	14	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	3	2	no	—
427	C₂²	—	3	4	no	—
428	C₂²	—	6	2	no	—
429	C₂²	—	6	4	no	—
430	C₂²	—	7	2	no	—
431	C₂²	—	7	4	no	—
432	C₂²	—	12	8	no	—
433	C₂²	—	14	2	no	—
434	C₂²	—	14	4	no	—
435	C₂²	—	21	2	no	—
436	C₂²	—	28	8	no	—
437	C₂²	—	42	2	no	—
438	C₂²	—	84	8	no	—
439	C₂²	C₂²×D₃×D₇	1	4	yes	—
440	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
441	C₄	—	3	2	no	—
442	C₄	—	7	2	no	—
443	C₄	—	21	4	no	—
444	C₄	—	21	2	no	—
445	C₄	C₂²×D₃×D₇	1	2	yes	—
446	C₃	C₂×#6548	1	1	yes	characteristic, complemented, Sylow
447	C₂	—	2	4	no	—
448	C₂	—	6	2	no	—
449	C₂	—	6	4	no	—
450	C₂	—	14	2	no	—
451	C₂	—	14	4	no	—
452	C₂	—	42	2	no	—
453	C₂	#10621572	1	2	yes	direct product factor
454	C₂	C₂³×D₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₃×D₇
commutator, cosocle	C₂×C₃×C₇	C₂⁵
Frattini	C₂	C₂³×D₃×D₇
Fitting	C₂×C₃×C₇×D₄	C₂²
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₂×D₄	D₃×D₇
hypocenter	C₃×C₇	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#66730	C₂	semidirect
2. C₂×D₃×C₇×D₄	C₂	semidirect
3. C₂×C₃×D₄×D₇	C₂	semidirect
4. C₂×D₃×C₂²⋊D₇	C₂	semidirect
5. C₂×D₇×#67	C₂	semidirect
6. C₂²×#4245	C₂	semidirect
7. C₂×#66684	C₂	semidirect
8. #10621572	C₂	direct (N × H)
9. C₂×#66681	C₂	semidirect
10. C₂×#66676	C₂	semidirect
11. C₂×#66675	C₂	semidirect
12. C₂×#66669	C₂	semidirect
14. C₂³×D₃×C₇	C₂²	semidirect
15. C₂³×C₃×D₇	C₂²	semidirect
16. C₂²×D₃×D₇	C₂²	semidirect
17. C₂×C₃×C₇×D₄	C₂²	semidirect
18. C₂×#4268	C₂²	semidirect
19. C₂²×Dic₂₁	C₂²	semidirect
20. #66730	C₂²	semidirect
21. C₂×C₄×D₂₁	C₂²	semidirect
22. C₂×Dic₄₂	C₂²	semidirect
23. C₂×C₇×#67	C₂²	semidirect
24. D₃×C₇×D₄	C₂²	semidirect
25. C₂×C₇×D₁₂	C₂²	semidirect
26. C₂×C₄×D₃×C₇	C₂²	semidirect
27. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
28. C₃×D₄×D₇	C₂²	semidirect
29. C₂×C₃×D₂₈	C₂²	semidirect
30. C₂×C₃×C₄×D₇	C₂²	semidirect
31. D₃×C₂²⋊D₇	C₂²	semidirect
32. D₇×#67	C₂²	semidirect
33. C₂×#4248	C₂²	semidirect
34. C₂×#4247	C₂²	semidirect
35. C₂×#4246	C₂²	semidirect
36. C₂×#4245	C₂²	semidirect
37. C₂×#4245	C₂²	semidirect
38. C₂×#4245	C₂²	semidirect
39. C₂×#4245	C₂²	semidirect
40. C₂×#4245	C₂²	semidirect
41. C₂×D₃×Dic₇	C₂²	semidirect
42. #66684	C₂²	semidirect
43. C₂×Dic₃×D₇	C₂²	semidirect
44. #66681	C₂²	semidirect
45. #66676	C₂²	semidirect
46. #66675	C₂²	semidirect
47. #66669	C₂²	semidirect
57. C₂×D₄×D₇	D₃	semidirect
66. C₂²×D₃×C₇	C₂³	semidirect
70. C₂²×C₃×D₇	C₂³	semidirect
72. C₂×D₃×D₇	C₂³	semidirect
73. C₃×C₇×D₄	C₂³	semidirect
75. #4268	C₂³	semidirect
78. C₂×Dic₂₁	C₂³	semidirect
79. C₄×D₂₁	C₂³	semidirect
80. Dic₄₂	C₂³	semidirect
81. C₇×#67	C₂³	semidirect
83. C₇×D₁₂	C₂³	semidirect
84. C₄×D₃×C₇	C₂³	semidirect
85. C₃×C₂²⋊D₇	C₂³	semidirect
87. C₃×D₂₈	C₂³	semidirect
88. C₃×C₄×D₇	C₂³	semidirect
89. #4248	C₂³	semidirect
90. #4247	C₂³	semidirect
91. #4246	C₂³	semidirect
92. #4245	C₂³	semidirect
93. #4245	C₂³	semidirect
94. #4245	C₂³	semidirect
95. #4245	C₂³	semidirect
96. D₃×Dic₇	C₂³	semidirect
97. Dic₃×D₇	C₂³	semidirect
100. C₂³×D₇	C₂×D₃	semidirect
104. C₂×C₇×D₄	C₂×D₃	semidirect
114. C₂×C₂²⋊D₇	C₂×D₃	semidirect
122. D₄×D₇	C₂×D₃	semidirect
126. C₂×D₂₈	C₂×D₃	semidirect
129. C₂×C₄×D₇	C₂×D₃	semidirect
141. C₂×D₃×D₄	D₇	semidirect
177. C₂²×D₇	C₂²×D₃	semidirect
180. C₇×D₄	C₂²×D₃	semidirect
190. C₂²⋊D₇	C₂²×D₃	semidirect
197. D₂₈	C₂²×D₃	semidirect
200. C₄×D₇	C₂²×D₃	semidirect
205. C₂³×D₃	C₂×D₇	semidirect
209. C₂×C₃×D₄	C₂×D₇	semidirect
219. C₂×#67	C₂×D₇	semidirect
227. D₃×D₄	C₂×D₇	semidirect
231. C₂×D₁₂	C₂×D₇	semidirect
234. C₂×C₄×D₃	C₂×D₇	semidirect
238. C₂×C₃×C₇	H(5,𝔽₂)	semidirect
289. C₂²×D₃	C₂²×D₇	semidirect
292. C₃×D₄	C₂²×D₇	semidirect
302. #67	C₂²×D₇	semidirect
309. D₁₂	C₂²×D₇	semidirect
312. C₄×D₃	C₂²×D₇	semidirect
315. C₃×C₇	C₂×H(5,𝔽₂)	semidirect
343. C₂×D₄	D₃×D₇	semidirect
353. C₂×C₇	#1004	semidirect
404. D₄	C₂×D₃×D₇	semidirect
416. C₇	C₂×#1004	semidirect
420. C₂×C₃	#6548	semidirect
446. C₃	C₂×#6548	semidirect
453. C₂	#10621572	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×#66730	2
C₂×D₃×C₇×D₄	2
C₂×C₃×D₄×D₇	2
C₂×D₃×C₂²⋊D₇	2
C₂×D₇×#67	2
C₂²×#4245	2
C₂×#66684	2
#10621572	2
C₂×#66681	2
C₂×#66676	2
C₂×#66675	2
C₂×#66669	2
C₂×#6548	3
C₂×#1004	7

Subgroups — C2×#10621572 #13062245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10621572 #13062245