Subgroups — C₂×#10621596 #13062292

Order 1344.

1796 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#4268	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₇×#67	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₂²⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621596	C₂	1	16	yes	maximal, direct product factor
5	C₂×#66694	C₂	1	2	yes	maximal, complemented
6	C₂×D₃×C₂²⋊D₇	C₂	1	2	yes	maximal, complemented
7	C₂×D₇×#67	C₂	1	2	yes	maximal, complemented
8	C₂×#66686	C₂	1	2	yes	maximal, complemented
9	C₂×#66684	C₂	1	2	yes	maximal, complemented
10	C₂×#66683	C₂	1	2	yes	maximal, complemented
11	C₂×#6548	—	3	1	no	maximal, Hall
12	C₂⁴×C₃×C₇	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₂₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₃×C₇	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₃×D₇	C₂²	1	1	yes	characteristic, complemented
16	C₂²×D₃×D₇	C₂²	1	2	yes	complemented
17	C₂×#4268	C₂²	1	2	yes	complemented
18	C₂×#4268	C₂²	1	2	yes	complemented
19	C₂×#4268	C₂²	1	8	yes	complemented
20	C₂²×Dic₂₁	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#67	C₂²	1	2	yes	complemented
22	C₂×C₇×#67	C₂²	1	2	yes	complemented
23	C₂×C₇×#67	C₂²	1	8	yes	complemented
24	C₂²×C₇×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
26	C₂×C₃×C₂²⋊D₇	C₂²	1	2	yes	complemented
27	C₂×C₃×C₂²⋊D₇	C₂²	1	8	yes	complemented
28	C₂²×C₃×Dic₇	C₂²	1	1	yes	characteristic, complemented
29	#66694	C₂²	1	16	yes	complemented
30	D₃×C₂²⋊D₇	C₂²	1	16	yes	complemented
31	D₇×#67	C₂²	1	16	yes	complemented
32	C₂×#4248	C₂²	1	2	yes	complemented
33	C₂×#4247	C₂²	1	2	yes	complemented
34	C₂×#4246	C₂²	1	2	yes	complemented
35	C₂×#4245	C₂²	1	2	yes	complemented
36	C₂×D₂₁⋊C₄	C₂²	1	2	yes	complemented
37	#66686	C₂²	1	16	yes	complemented
38	C₂×D₃×Dic₇	C₂²	1	2	yes	complemented
39	#66684	C₂²	1	16	yes	complemented
40	#66683	C₂²	1	16	yes	complemented
41	C₂×Dic₃×D₇	C₂²	1	2	yes	complemented
42	C₂²×C₇×D₄	—	3	1	no	—
43	C₂²×C₂²⋊D₇	—	3	1	no	—
44	C₂²×C₂²⋊D₇	—	3	2	no	—
45	C₂²×C₂²⋊D₇	D₃	1	1	yes	characteristic, complemented
46	#6548	—	3	16	no	—
47	C₂×#1159	—	3	2	no	—
48	C₂×#1159	—	3	2	no	—
49	C₂×D₄×D₇	—	3	2	no	—
50	C₂×D₄×D₇	—	3	2	no	—
51	C₂×#1157	—	3	2	no	—
52	C₂×#1004	—	7	1	no	maximal, Hall
53	C₂³×C₃×C₇	—	4	2	no	—
54	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
55	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
56	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
57	C₂³×C₃×C₇	C₂³	1	4	yes	complemented
58	C₂²×D₂₁	—	4	2	no	—
59	C₂²×D₂₁	C₂³	1	2	yes	—
60	C₂²×D₂₁	C₂³	1	4	yes	complemented
61	C₂²×D₃×C₇	—	4	2	no	—
62	C₂²×D₃×C₇	C₂³	1	2	yes	—
63	C₂²×D₃×C₇	C₂³	1	4	yes	complemented
64	C₂²×C₃×D₇	—	4	2	no	—
65	C₂²×C₃×D₇	C₂³	1	2	yes	—
66	C₂²×C₃×D₇	C₂³	1	4	yes	complemented
67	C₂×D₃×D₇	—	4	4	no	—
68	C₂×D₃×D₇	C₂³	1	8	yes	complemented
69	#4268	C₂³	1	8	yes	complemented
70	#4268	C₂³	1	8	yes	complemented
71	C₂×Dic₂₁	C₂³	1	2	yes	—
72	C₂×Dic₂₁	C₂³	1	4	yes	complemented
73	C₇×#67	C₂³	1	8	yes	complemented
74	C₇×#67	C₂³	1	8	yes	complemented
75	C₂×C₇×Dic₃	C₂³	1	2	yes	—
76	C₂×C₇×Dic₃	C₂³	1	4	yes	complemented
77	C₃×C₂²⋊D₇	C₂³	1	8	yes	complemented
78	C₃×C₂²⋊D₇	C₂³	1	8	yes	complemented
79	C₂×C₃×Dic₇	C₂³	1	2	yes	—
80	C₂×C₃×Dic₇	C₂³	1	4	yes	complemented
81	#4248	C₂³	1	8	yes	complemented
82	#4247	C₂³	1	8	yes	complemented
83	#4246	C₂³	1	8	yes	complemented
84	#4245	C₂³	1	8	yes	complemented
85	D₂₁⋊C₄	C₂³	1	8	yes	complemented
86	D₃×Dic₇	C₂³	1	8	yes	complemented
87	Dic₃×D₇	C₂³	1	8	yes	complemented
88	C₂⁴×C₇	—	3	1	no	—
89	C₂⁴×C₇	C₂×D₃	1	1	yes	characteristic, complemented
90	C₂³×D₇	—	3	1	no	—
91	C₂³×D₇	—	3	2	no	—
92	C₂³×D₇	C₂×D₃	1	1	yes	characteristic, complemented
93	C₂×C₇×D₄	—	3	2	no	—
94	C₂×C₇×D₄	—	3	2	no	—
95	C₂×C₇×D₄	—	3	8	no	—
96	C₂²×C₄×C₇	—	3	1	no	—
97	C₂×C₂²⋊D₇	—	3	2	no	—
98	C₂×C₂²⋊D₇	—	3	2	no	—
99	C₂×C₂²⋊D₇	—	3	8	no	—
100	C₂×C₂²⋊D₇	—	3	2	no	—
101	C₂×C₂²⋊D₇	—	3	16	no	—
102	C₂×C₂²⋊D₇	—	3	2	no	—
103	C₂×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
104	C₂×C₂²⋊D₇	C₂×D₃	1	2	yes	complemented
105	C₂×C₂²⋊D₇	C₂×D₃	1	8	yes	complemented
106	C₂²×Dic₇	—	3	1	no	—
107	C₂²×Dic₇	—	3	2	no	—
108	C₂²×Dic₇	C₂×D₃	1	1	yes	characteristic, complemented
109	#1159	—	3	16	no	—
110	#1159	—	3	16	no	—
111	D₄×D₇	—	3	16	no	—
112	D₄×D₇	—	3	16	no	—
113	#1157	—	3	16	no	—
114	C₂×D₂₈	—	3	2	no	—
115	C₂×C₄×D₇	—	3	2	no	—
116	C₂×C₄×D₇	—	3	2	no	—
117	C₂×Dic₁₄	—	3	2	no	—
118	C₂²×C₃×D₄	—	7	1	no	—
119	C₂²×#67	—	7	1	no	—
120	C₂²×#67	—	7	2	no	—
121	C₂²×#67	D₇	1	1	yes	characteristic, complemented
122	#1004	—	7	16	no	—
123	C₂×#237	—	7	2	no	—
124	C₂×#237	—	7	2	no	—
125	C₂×D₃×D₄	—	7	2	no	—
126	C₂×D₃×D₄	—	7	2	no	—
127	C₂×#235	—	7	2	no	—
128	C₂²×C₃×C₇	—	2	2	no	—
129	C₂²×C₃×C₇	—	2	2	no	—
130	C₂²×C₃×C₇	—	2	2	no	—
131	C₂²×C₃×C₇	—	4	4	no	—
132	C₂²×C₃×C₇	C₂⁴	1	2	yes	—
133	C₂²×C₃×C₇	C₂⁴	1	2	yes	—
134	C₂²×C₃×C₇	C₂⁴	1	2	yes	—
135	C₂²×C₃×C₇	C₂⁴	1	1	yes	characteristic
136	C₂×D₂₁	—	2	4	no	—
137	C₂×D₂₁	—	4	4	no	—
138	C₂×D₂₁	C₂⁴	1	4	yes	—
139	C₂×D₃×C₇	—	2	4	no	—
140	C₂×D₃×C₇	—	4	4	no	—
141	C₂×D₃×C₇	C₂⁴	1	4	yes	—
142	C₂×C₃×D₇	—	2	4	no	—
143	C₂×C₃×D₇	—	4	4	no	—
144	C₂×C₃×D₇	C₂⁴	1	4	yes	—
145	D₃×D₇	—	4	8	no	—
146	Dic₂₁	C₂⁴	1	4	yes	—
147	C₃×Dic₇	C₂⁴	1	4	yes	—
148	C₇×Dic₃	C₂⁴	1	4	yes	—
149	C₂×H(5,𝔽₂)	—	21	1	no	Sylow
150	C₂³×C₇	—	3	2	no	—
151	C₂³×C₇	—	3	4	no	—
152	C₂³×C₇	—	4	2	no	—
153	C₂³×C₇	—	12	2	no	—
154	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
155	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
156	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
157	C₂³×C₇	C₂²×D₃	1	4	yes	complemented
158	C₂²×D₇	—	3	2	no	—
159	C₂²×D₇	—	3	4	no	—
160	C₂²×D₇	—	3	8	no	—
161	C₂²×D₇	—	4	2	no	—
162	C₂²×D₇	—	12	4	no	—
163	C₂²×D₇	—	12	2	no	—
164	C₂²×D₇	C₂²×D₃	1	2	yes	—
165	C₂²×D₇	C₂²×D₃	1	4	yes	complemented
166	C₇×D₄	—	3	8	no	—
167	C₇×D₄	—	3	8	no	—
168	C₂×C₄×C₇	—	3	2	no	—
169	C₂×C₄×C₇	—	3	4	no	—
170	C₂²⋊D₇	—	3	8	no	—
171	C₂²⋊D₇	—	3	8	no	—
172	C₂²⋊D₇	—	3	8	no	—
173	C₂²⋊D₇	—	3	8	no	—
174	C₂²⋊D₇	C₂²×D₃	1	8	yes	complemented
175	C₂²⋊D₇	C₂²×D₃	1	8	yes	complemented
176	C₂×Dic₇	—	3	2	no	—
177	C₂×Dic₇	—	3	4	no	—
178	C₂×Dic₇	—	3	8	no	—
179	C₂×Dic₇	C₂²×D₃	1	2	yes	—
180	C₂×Dic₇	C₂²×D₃	1	4	yes	complemented
181	D₂₈	—	3	8	no	—
182	C₄×D₇	—	3	8	no	—
183	C₄×D₇	—	3	8	no	—
184	Dic₁₄	—	3	8	no	—
185	C₂⁴×C₃	—	7	1	no	—
186	C₂⁴×C₃	C₂×D₇	1	1	yes	characteristic, complemented
187	C₂³×D₃	—	7	1	no	—
188	C₂³×D₃	—	7	2	no	—
189	C₂³×D₃	C₂×D₇	1	1	yes	characteristic, complemented
190	C₂×C₃×D₄	—	7	2	no	—
191	C₂×C₃×D₄	—	7	2	no	—
192	C₂×C₃×D₄	—	7	8	no	—
193	C₂²×C₃×C₄	—	7	1	no	—
194	C₂×#67	—	7	2	no	—
195	C₂×#67	—	7	2	no	—
196	C₂×#67	—	7	8	no	—
197	C₂×#67	—	7	2	no	—
198	C₂×#67	—	7	16	no	—
199	C₂×#67	—	7	2	no	—
200	C₂×#67	C₂×D₇	1	2	yes	complemented
201	C₂×#67	C₂×D₇	1	2	yes	complemented
202	C₂×#67	C₂×D₇	1	8	yes	complemented
203	C₂²×Dic₃	—	7	1	no	—
204	C₂²×Dic₃	—	7	2	no	—
205	C₂²×Dic₃	C₂×D₇	1	1	yes	characteristic, complemented
206	#237	—	7	16	no	—
207	#237	—	7	16	no	—
208	D₃×D₄	—	7	16	no	—
209	D₃×D₄	—	7	16	no	—
210	#235	—	7	16	no	—
211	C₂×D₁₂	—	7	2	no	—
212	C₂×C₄×D₃	—	7	2	no	—
213	C₂×C₄×D₃	—	7	2	no	—
214	C₂×Dic₆	—	7	2	no	—
215	C₂×C₃×C₇	—	2	2	no	—
216	C₂×C₃×C₇	—	2	2	no	—
217	C₂×C₃×C₇	—	2	2	no	—
218	C₂×C₃×C₇	H(5,𝔽₂)	1	2	yes	complemented
219	C₂×C₃×C₇	C₂⁵	1	1	yes	characteristic
220	D₂₁	—	2	4	no	—
221	C₃×D₇	—	2	4	no	—
222	D₃×C₇	—	2	4	no	—
223	H(5,𝔽₂)	—	21	16	no	—
224	C₂×#41	—	21	2	no	—
225	C₂×#41	—	21	2	no	—
226	C₂×#41	—	21	2	no	—
227	C₂²×D₄	—	3	1	no	—
228	C₂²×D₄	—	7	1	no	—
229	C₂²×D₄	—	21	2	no	—
230	C₂²×D₄	—	21	2	no	—
231	C₂²×D₄	—	21	2	no	—
232	C₂²×D₄	—	21	1	no	—
233	C₂²×C₇	—	2	2	no	—
234	C₂²×C₇	—	2	2	no	—
235	C₂²×C₇	—	2	2	no	—
236	C₂²×C₇	—	3	4	no	—
237	C₂²×C₇	—	4	4	no	—
238	C₂²×C₇	—	6	4	no	—
239	C₂²×C₇	—	12	4	no	—
240	C₂²×C₇	C₂³×D₃	1	2	yes	—
241	C₂²×C₇	C₂³×D₃	1	2	yes	—
242	C₂²×C₇	C₂³×D₃	1	2	yes	—
243	C₂²×C₇	C₂³×D₃	1	1	yes	characteristic
244	C₂×D₇	—	2	4	no	—
245	C₂×D₇	—	3	4	no	—
246	C₂×D₇	—	4	4	no	—
247	C₂×D₇	—	6	4	no	—
248	C₂×D₇	—	12	8	no	—
249	C₂×D₇	—	12	4	no	—
250	C₂×D₇	C₂³×D₃	1	4	yes	—
251	C₄×C₇	—	3	4	no	—
252	Dic₇	—	3	4	no	—
253	Dic₇	C₂³×D₃	1	4	yes	—
254	C₂³×C₃	—	4	2	no	—
255	C₂³×C₃	—	7	2	no	—
256	C₂³×C₃	—	7	4	no	—
257	C₂³×C₃	—	28	2	no	—
258	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
259	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
260	C₂³×C₃	C₂²×D₇	1	1	yes	characteristic
261	C₂³×C₃	C₂²×D₇	1	4	yes	complemented
262	C₂²×D₃	—	4	2	no	—
263	C₂²×D₃	—	7	2	no	—
264	C₂²×D₃	—	7	4	no	—
265	C₂²×D₃	—	7	8	no	—
266	C₂²×D₃	—	28	4	no	—
267	C₂²×D₃	—	28	2	no	—
268	C₂²×D₃	C₂²×D₇	1	2	yes	—
269	C₂²×D₃	C₂²×D₇	1	4	yes	complemented
270	C₃×D₄	—	7	8	no	—
271	C₃×D₄	—	7	8	no	—
272	C₂×C₃×C₄	—	7	2	no	—
273	C₂×C₃×C₄	—	7	4	no	—
274	#67	—	7	8	no	—
275	#67	—	7	8	no	—
276	#67	—	7	8	no	—
277	#67	—	7	8	no	—
278	#67	C₂²×D₇	1	8	yes	complemented
279	#67	C₂²×D₇	1	8	yes	complemented
280	C₂×Dic₃	—	7	2	no	—
281	C₂×Dic₃	—	7	4	no	—
282	C₂×Dic₃	—	7	8	no	—
283	C₂×Dic₃	C₂²×D₇	1	2	yes	—
284	C₂×Dic₃	C₂²×D₇	1	4	yes	complemented
285	D₁₂	—	7	8	no	—
286	C₄×D₃	—	7	8	no	—
287	C₄×D₃	—	7	8	no	—
288	Dic₆	—	7	8	no	—
289	C₃×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
290	C₂⁴	—	3	1	no	—
291	C₂⁴	—	7	1	no	—
292	C₂⁴	—	21	2	no	—
293	C₂⁴	—	21	1	no	—
294	C₂⁴	D₃×D₇	1	1	yes	characteristic, complemented
295	#41	—	21	16	no	—
296	#41	—	21	16	no	—
297	#41	—	21	16	no	—
298	C₂×Q₈	—	21	2	no	—
299	C₂×D₄	—	3	2	no	—
300	C₂×D₄	—	3	2	no	—
301	C₂×D₄	—	3	8	no	—
302	C₂×D₄	—	7	2	no	—
303	C₂×D₄	—	7	2	no	—
304	C₂×D₄	—	7	8	no	—
305	C₂×D₄	—	21	2	no	—
306	C₂×D₄	—	21	2	no	—
307	C₂×D₄	—	21	16	no	—
308	C₂×D₄	—	21	16	no	—
309	C₂×D₄	—	21	16	no	—
310	C₂×D₄	—	21	2	no	—
311	C₂×D₄	—	21	2	no	—
312	C₂×D₄	—	21	2	no	—
313	C₂×D₄	—	21	8	no	—
314	C₂²×C₄	—	3	1	no	—
315	C₂²×C₄	—	7	1	no	—
316	C₂²×C₄	—	21	2	no	—
317	C₂²×C₄	—	21	2	no	—
318	C₂²×C₄	—	21	2	no	—
319	C₂²×C₄	—	21	1	no	—
320	C₂×C₇	—	2	2	no	—
321	C₂×C₇	—	2	2	no	—
322	C₂×C₇	—	2	2	no	—
323	C₂×C₇	—	6	4	no	—
324	C₂×C₇	#1004	1	2	yes	complemented
325	C₂×C₇	C₂⁴×D₃	1	1	yes	characteristic
326	D₇	—	2	4	no	—
327	D₇	—	6	4	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	4	4	no	—
332	C₂²×C₃	—	7	4	no	—
333	C₂²×C₃	—	14	4	no	—
334	C₂²×C₃	—	28	4	no	—
335	C₂²×C₃	C₂³×D₇	1	2	yes	—
336	C₂²×C₃	C₂³×D₇	1	2	yes	—
337	C₂²×C₃	C₂³×D₇	1	2	yes	—
338	C₂²×C₃	C₂³×D₇	1	1	yes	characteristic
339	C₂×D₃	—	2	4	no	—
340	C₂×D₃	—	4	4	no	—
341	C₂×D₃	—	7	4	no	—
342	C₂×D₃	—	14	4	no	—
343	C₂×D₃	—	28	8	no	—
344	C₂×D₃	—	28	4	no	—
345	C₂×D₃	C₂³×D₇	1	4	yes	—
346	C₃×C₄	—	7	4	no	—
347	Dic₃	—	7	4	no	—
348	Dic₃	C₂³×D₇	1	4	yes	—
349	C₂³	—	3	2	no	—
350	C₂³	—	3	4	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	7	2	no	—
353	C₂³	—	7	4	no	—
354	C₂³	—	12	2	no	—
355	C₂³	—	21	8	no	—
356	C₂³	—	21	2	no	—
357	C₂³	—	21	4	no	—
358	C₂³	—	28	2	no	—
359	C₂³	—	84	2	no	—
360	C₂³	—	84	4	no	—
361	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
362	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
363	C₂³	C₂×D₃×D₇	1	1	yes	characteristic
364	C₂³	C₂×D₃×D₇	1	4	yes	complemented
365	Q₈	—	21	8	no	—
366	D₄	—	3	8	no	—
367	D₄	—	3	8	no	—
368	D₄	—	7	8	no	—
369	D₄	—	7	8	no	—
370	D₄	—	21	8	no	—
371	D₄	—	21	8	no	—
372	D₄	—	21	8	no	—
373	D₄	—	21	8	no	—
374	D₄	—	21	8	no	—
375	C₂×C₄	—	3	4	no	—
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	7	4	no	—
378	C₂×C₄	—	7	2	no	—
379	C₂×C₄	—	21	8	no	—
380	C₂×C₄	—	21	8	no	—
381	C₂×C₄	—	21	8	no	—
382	C₂×C₄	—	21	4	no	—
383	C₂×C₄	—	21	2	no	—
384	C₇	C₂×#1004	1	1	yes	characteristic, complemented, Sylow
385	C₂×C₃	—	2	2	no	—
386	C₂×C₃	—	2	2	no	—
387	C₂×C₃	—	2	2	no	—
388	C₂×C₃	—	14	4	no	—
389	C₂×C₃	#6548	1	2	yes	complemented
390	C₂×C₃	C₂⁴×D₇	1	1	yes	characteristic
391	D₃	—	2	4	no	—
392	D₃	—	14	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	3	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	6	4	no	—
399	C₂²	—	7	4	no	—
400	C₂²	—	12	4	no	—
401	C₂²	—	14	4	no	—
402	C₂²	—	21	4	no	—
403	C₂²	—	28	4	no	—
404	C₂²	—	42	4	no	—
405	C₂²	—	84	4	no	—
406	C₂²	—	84	8	no	—
407	C₂²	C₂²×D₃×D₇	1	2	yes	—
408	C₂²	C₂²×D₃×D₇	1	2	yes	—
409	C₂²	C₂²×D₃×D₇	1	2	yes	—
410	C₂²	C₂²×D₃×D₇	1	1	yes	characteristic
411	C₄	—	3	4	no	—
412	C₄	—	7	4	no	—
413	C₄	—	21	4	no	—
414	C₃	C₂×#6548	1	1	yes	characteristic, complemented, Sylow
415	C₂	—	2	2	no	—
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	—	6	4	no	—
419	C₂	—	14	4	no	—
420	C₂	—	42	4	no	—
421	C₂	#10621596	1	2	yes	direct product factor
422	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	C₂⁴×C₃×C₇	C₂²
socle	C₂²×C₃×C₇	C₂⁴
hypercenter	C₂⁴	D₃×D₇
hypocenter	C₃×C₇	C₂×H(5,𝔽₂)
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂² ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂²×#4268	C₂	semidirect
2. C₂²×C₇×#67	C₂	semidirect
3. C₂²×C₃×C₂²⋊D₇	C₂	semidirect
4. #10621596	C₂	direct (N × H)
5. C₂×#66694	C₂	semidirect
6. C₂×D₃×C₂²⋊D₇	C₂	semidirect
7. C₂×D₇×#67	C₂	semidirect
8. C₂×#66686	C₂	semidirect
9. C₂×#66684	C₂	semidirect
10. C₂×#66683	C₂	semidirect
12. C₂⁴×C₃×C₇	C₂²	semidirect
13. C₂³×D₂₁	C₂²	semidirect
14. C₂³×D₃×C₇	C₂²	semidirect
15. C₂³×C₃×D₇	C₂²	semidirect
16. C₂²×D₃×D₇	C₂²	semidirect
17. C₂×#4268	C₂²	semidirect
18. C₂×#4268	C₂²	semidirect
19. C₂×#4268	C₂²	semidirect
20. C₂²×Dic₂₁	C₂²	semidirect
21. C₂×C₇×#67	C₂²	semidirect
22. C₂×C₇×#67	C₂²	semidirect
23. C₂×C₇×#67	C₂²	semidirect
24. C₂²×C₇×Dic₃	C₂²	semidirect
25. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
26. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
27. C₂×C₃×C₂²⋊D₇	C₂²	semidirect
28. C₂²×C₃×Dic₇	C₂²	semidirect
29. #66694	C₂²	semidirect
30. D₃×C₂²⋊D₇	C₂²	semidirect
31. D₇×#67	C₂²	semidirect
32. C₂×#4248	C₂²	semidirect
33. C₂×#4247	C₂²	semidirect
34. C₂×#4246	C₂²	semidirect
35. C₂×#4245	C₂²	semidirect
36. C₂×D₂₁⋊C₄	C₂²	semidirect
37. #66686	C₂²	semidirect
38. C₂×D₃×Dic₇	C₂²	semidirect
39. #66684	C₂²	semidirect
40. #66683	C₂²	semidirect
41. C₂×Dic₃×D₇	C₂²	semidirect
45. C₂²×C₂²⋊D₇	D₃	semidirect
57. C₂³×C₃×C₇	C₂³	semidirect
60. C₂²×D₂₁	C₂³	semidirect
63. C₂²×D₃×C₇	C₂³	semidirect
66. C₂²×C₃×D₇	C₂³	semidirect
68. C₂×D₃×D₇	C₂³	semidirect
69. #4268	C₂³	semidirect
70. #4268	C₂³	semidirect
72. C₂×Dic₂₁	C₂³	semidirect
73. C₇×#67	C₂³	semidirect
74. C₇×#67	C₂³	semidirect
76. C₂×C₇×Dic₃	C₂³	semidirect
77. C₃×C₂²⋊D₇	C₂³	semidirect
78. C₃×C₂²⋊D₇	C₂³	semidirect
80. C₂×C₃×Dic₇	C₂³	semidirect
81. #4248	C₂³	semidirect
82. #4247	C₂³	semidirect
83. #4246	C₂³	semidirect
84. #4245	C₂³	semidirect
85. D₂₁⋊C₄	C₂³	semidirect
86. D₃×Dic₇	C₂³	semidirect
87. Dic₃×D₇	C₂³	semidirect
89. C₂⁴×C₇	C₂×D₃	semidirect
92. C₂³×D₇	C₂×D₃	semidirect
103. C₂×C₂²⋊D₇	C₂×D₃	semidirect
104. C₂×C₂²⋊D₇	C₂×D₃	semidirect
105. C₂×C₂²⋊D₇	C₂×D₃	semidirect
108. C₂²×Dic₇	C₂×D₃	semidirect
121. C₂²×#67	D₇	semidirect
157. C₂³×C₇	C₂²×D₃	semidirect
165. C₂²×D₇	C₂²×D₃	semidirect
174. C₂²⋊D₇	C₂²×D₃	semidirect
175. C₂²⋊D₇	C₂²×D₃	semidirect
180. C₂×Dic₇	C₂²×D₃	semidirect
186. C₂⁴×C₃	C₂×D₇	semidirect
189. C₂³×D₃	C₂×D₇	semidirect
200. C₂×#67	C₂×D₇	semidirect
201. C₂×#67	C₂×D₇	semidirect
202. C₂×#67	C₂×D₇	semidirect
205. C₂²×Dic₃	C₂×D₇	semidirect
218. C₂×C₃×C₇	H(5,𝔽₂)	semidirect
261. C₂³×C₃	C₂²×D₇	semidirect
269. C₂²×D₃	C₂²×D₇	semidirect
278. #67	C₂²×D₇	semidirect
279. #67	C₂²×D₇	semidirect
284. C₂×Dic₃	C₂²×D₇	semidirect
289. C₃×C₇	C₂×H(5,𝔽₂)	semidirect
294. C₂⁴	D₃×D₇	semidirect
324. C₂×C₇	#1004	semidirect
364. C₂³	C₂×D₃×D₇	semidirect
384. C₇	C₂×#1004	semidirect
389. C₂×C₃	#6548	semidirect
414. C₃	C₂×#6548	semidirect
421. C₂	#10621596	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#4268	2
C₂²×C₇×#67	2
C₂²×C₃×C₂²⋊D₇	2
#10621596	2
C₂×#66694	2
C₂×D₃×C₂²⋊D₇	2
C₂×D₇×#67	2
C₂×#66686	2
C₂×#66684	2
C₂×#66683	2
C₂×#6548	3
C₂×#1004	7

Subgroups — C2×#10621596 #13062292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10621596 #13062292