Subgroups — C₂×#11728461 #13357365

Order 1792.

858 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	C₂²×C₇×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#89897	C₂	1	2	yes	maximal
3	C₂²×#6393	C₂	1	1	yes	maximal, characteristic
4	C₂×#89873	C₂	1	1	yes	maximal, characteristic
5	C₂×#89354	C₂	1	2	yes	maximal
6	#11728461	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₇×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic
9	C₂×#6489	C₂²	1	1	yes	characteristic
10	C₂²×#1136	C₂²	1	2	yes	—
11	C₂²×#1136	C₂²	1	1	yes	characteristic
12	C₂×C₇×#108	C₄	1	4	yes	complemented
13	C₂×C₇×#108	C₄	1	4	yes	complemented
14	C₂×C₇×#108	C₂²	1	4	yes	—
15	#89897	—	2	4	no	—
16	#89897	C₂²	1	8	yes	—
17	C₂×#6393	—	2	1	no	—
18	C₂×#6393	—	2	1	no	—
19	C₂×#6393	—	2	2	no	—
20	C₂×#6393	—	2	4	no	—
21	C₂×#6393	C₂²	1	4	yes	—
22	#89873	—	2	2	no	—
23	#89873	C₂²	1	4	yes	—
24	C₂×#6389	—	2	1	no	—
25	C₂×C₈×Dic₇	—	2	1	no	—
26	#89354	C₂²	1	8	yes	—
27	C₂×#1953	—	7	1	no	maximal, Sylow
28	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
29	C₂×C₇×M₁₆	—	2	2	no	—
30	C₂×C₇×M₁₆	—	2	2	no	—
31	C₂×C₇×M₁₆	—	2	2	no	—
32	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
33	C₂×C₇×M₁₆	C₂×C₄	1	4	yes	—
34	C₂×C₇×M₁₆	C₂³	1	4	yes	—
35	C₂²×C₇×C₈	—	2	2	no	—
36	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
37	C₂²×C₇×C₈	C₂×C₄	1	2	yes	—
38	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
39	C₂²×C₇×C₈	D₄	1	1	yes	characteristic
40	C₂²×C₇×C₈	D₄	1	2	yes	—
41	C₂²×C₇×C₈	Q₈	1	2	yes	—
42	C₂²×C₇×C₈	Q₈	1	2	yes	—
43	C₂²×C₇×C₈	C₂³	1	2	yes	—
44	C₂×C₂²⋊Dic₇	Q₈	1	2	yes	—
45	#6489	—	2	1	no	—
46	#6489	—	2	1	no	—
47	#6489	Q₈	1	2	yes	—
48	#6489	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₇	—	2	1	no	—
50	C₂×C₄×Dic₇	—	2	1	no	—
51	C₂×#1136	—	2	1	no	—
52	C₂×#1136	—	2	1	no	—
53	C₂×#1136	—	2	1	no	—
54	C₂×#1136	—	2	2	no	—
55	C₂×#1136	—	2	2	no	—
56	C₂×#1136	—	2	2	no	—
57	C₂×#1136	—	2	2	no	—
58	C₂×#1136	—	2	2	no	—
59	C₂×#1136	D₄	1	2	yes	—
60	C₂×#1136	D₄	1	2	yes	—
61	C₂×#1136	C₂³	1	4	yes	—
62	C₂×#1136	C₂³	1	2	yes	—
63	C₂²×C₇⋊C₈	—	2	1	no	—
64	C₂²×C₇⋊C₈	—	2	2	no	—
65	C₇×#108	C₂×C₄	1	16	yes	complemented
66	#6393	—	2	4	no	—
67	#6393	—	2	4	no	—
68	#6393	—	2	16	no	—
69	#6389	—	2	4	no	—
70	C₈×Dic₇	—	2	4	no	—
71	C₂×#430	—	7	2	no	—
72	C₂²×#108	—	7	1	no	—
73	C₂²×#108	D₇	1	1	yes	characteristic
74	C₂×#405	—	7	1	no	—
75	#1953	—	7	8	no	—
76	C₂×#344	—	7	2	no	—
77	C₂⁴×C₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₇	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₇	#41	1	1	yes	characteristic
88	C₂²×C₄×C₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₇	#41	1	1	yes	characteristic
90	C₂²×C₄×C₇	#41	1	1	yes	characteristic
91	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₇	—	2	2	no	—
93	C₇×M₁₆	—	2	4	no	—
94	C₇×M₁₆	—	2	4	no	—
95	C₇×M₁₆	—	2	4	no	—
96	C₇×M₁₆	C₂²×C₄	1	8	yes	—
97	C₂×C₇×C₈	—	2	4	no	—
98	C₂×C₇×C₈	—	2	4	no	—
99	C₂×C₇×C₈	—	2	4	no	—
100	C₂×C₇×C₈	C₄⋊C₄	1	2	yes	—
101	C₂×C₇×C₈	C₄⋊C₄	1	2	yes	—
102	C₂×C₇×C₈	C₄⋊C₄	1	2	yes	—
103	C₂×C₇×C₈	C₄⋊C₄	1	2	yes	—
104	C₂×C₇×C₈	C₄⋊C₄	1	4	yes	—
105	C₂×C₇×C₈	C₄⋊C₄	1	4	yes	—
106	C₂×C₇×C₈	C₂²×C₄	1	4	yes	—
107	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
108	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
109	C₂×C₇×C₈	C₂×Q₈	1	4	yes	—
110	C₂²⋊Dic₇	—	2	2	no	—
111	C₂²⋊Dic₇	C₂×Q₈	1	4	yes	—
112	C₄⋊Dic₇	—	2	2	no	—
113	C₄⋊Dic₇	—	2	2	no	—
114	C₄×Dic₇	—	2	2	no	—
115	C₄×Dic₇	—	2	2	no	—
116	#1136	—	2	2	no	—
117	#1136	—	2	2	no	—
118	#1136	—	2	2	no	—
119	#1136	—	2	4	no	—
120	#1136	—	2	4	no	—
121	#1136	—	4	2	no	—
122	#1136	—	4	2	no	—
123	#1136	C₂×D₄	1	4	yes	—
124	C₂×C₇⋊C₈	—	2	2	no	—
125	C₂×C₇⋊C₈	—	2	2	no	—
126	C₂×C₇⋊C₈	—	2	2	no	—
127	C₂×C₇⋊C₈	—	2	4	no	—
128	C₂×C₇⋊C₈	—	4	2	no	—
129	C₂×C₇⋊C₈	—	4	2	no	—
130	C₂²×M₁₆	—	7	1	no	—
131	C₂²×M₁₆	—	7	2	no	—
132	C₂²×M₁₆	C₂×D₇	1	2	yes	—
133	C₂³×C₈	C₂×D₇	1	1	yes	characteristic
134	C₂×#117	—	7	1	no	—
135	#430	—	7	8	no	—
136	#430	—	14	4	no	—
137	C₂×#108	—	7	4	no	—
138	C₂×#108	—	14	4	no	—
139	C₂×#108	—	14	1	no	—
140	C₂×#108	—	14	1	no	—
141	C₂×#108	—	14	2	no	—
142	C₂×#108	Dic₇	1	4	yes	complemented
143	C₂×#108	Dic₇	1	4	yes	complemented
144	C₂×#108	C₂×D₇	1	4	yes	—
145	#405	—	7	4	no	—
146	#405	—	14	2	no	—
147	C₂×#97	—	14	1	no	—
148	C₂×C₄×C₈	—	14	1	no	—
149	#344	—	7	8	no	—
150	C₂³×C₇	—	4	2	no	—
151	C₂³×C₇	C₄×Q₈	1	1	yes	characteristic
152	C₂³×C₇	C₄×Q₈	1	1	yes	characteristic
153	C₂³×C₇	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₇	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₇	C₄⋊Q₈	1	1	yes	characteristic
156	C₂³×C₇	C₄⋊Q₈	1	1	yes	characteristic
157	C₂³×C₇	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₇	C₄×Q₈	1	1	yes	characteristic
167	C₂×C₄×C₇	C₄×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₇	#121	1	1	yes	characteristic
171	C₂×C₄×C₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₇	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₇	#125	1	1	yes	characteristic
175	C₂×C₄×C₇	#125	1	1	yes	characteristic
176	C₂×C₄×C₇	#125	1	1	yes	characteristic
177	C₂×C₄×C₇	#125	1	1	yes	characteristic
178	C₂×C₄×C₇	C₄⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₇	C₄⋊Q₈	1	1	yes	characteristic
180	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
181	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
186	C₂×Dic₇	—	2	4	no	—
187	C₂×Dic₇	—	4	4	no	—
188	C₇×C₈	—	2	8	no	—
189	C₇×C₈	C₂×C₄⋊C₄	1	4	yes	—
190	C₇×C₈	C₂×C₄⋊C₄	1	4	yes	—
191	C₇⋊C₈	—	2	4	no	—
192	C₇⋊C₈	—	4	4	no	—
193	C₂³×C₄	C₂²×D₇	1	1	yes	characteristic
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	—	2	2	no	—
196	C₂×M₁₆	—	2	2	no	—
197	C₂×M₁₆	—	7	2	no	—
198	C₂×M₁₆	—	7	2	no	—
199	C₂×M₁₆	—	7	2	no	—
200	C₂×M₁₆	—	7	4	no	—
201	C₂×M₁₆	—	14	1	no	—
202	C₂×M₁₆	—	14	1	no	—
203	C₂×M₁₆	—	14	1	no	—
204	C₂×M₁₆	—	14	2	no	—
205	C₂×M₁₆	—	14	2	no	—
206	C₂×M₁₆	—	14	2	no	—
207	C₂×M₁₆	—	14	2	no	—
208	C₂×M₁₆	—	14	2	no	—
209	C₂×M₁₆	C₂×Dic₇	1	4	yes	—
210	C₂×M₁₆	C₂×Dic₇	1	4	yes	—
211	C₂×M₁₆	C₂²×D₇	1	4	yes	—
212	C₂²×C₈	—	2	2	no	—
213	C₂²×C₈	—	14	1	no	—
214	C₂²×C₈	—	14	2	no	—
215	C₂²×C₈	Dic₁₄	1	2	yes	—
216	C₂²×C₈	Dic₁₄	1	2	yes	—
217	C₂²×C₈	D₂₈	1	1	yes	characteristic
218	C₂²×C₈	D₂₈	1	1	yes	characteristic
219	C₂²×C₈	D₂₈	1	2	yes	—
220	C₂²×C₈	C₂×Dic₇	1	2	yes	—
221	C₂²×C₈	C₂×Dic₇	1	2	yes	—
222	C₂²×C₈	C₂²×D₇	1	2	yes	—
223	#117	—	7	2	no	—
224	#117	—	7	2	no	—
225	#117	—	14	1	no	—
226	#117	—	14	1	no	—
227	C₂×C₄⋊C₄	—	14	1	no	—
228	C₂×C₂²⋊C₄	—	7	2	no	—
229	C₂×C₄²	—	14	1	no	—
230	#108	—	14	16	no	—
231	#108	—	14	4	no	—
232	#108	—	14	4	no	—
233	#108	C₂×Dic₇	1	16	yes	complemented
234	#97	—	14	4	no	—
235	C₄×C₈	—	14	4	no	—
236	C₂²×C₇	—	2	2	no	—
237	C₂²×C₇	—	2	2	no	—
238	C₂²×C₇	—	2	2	no	—
239	C₂²×C₇	—	4	1	no	—
240	C₂²×C₇	—	4	1	no	—
241	C₂²×C₇	—	4	1	no	—
242	C₂²×C₇	—	4	1	no	—
243	C₂²×C₇	#389	1	1	yes	characteristic
244	C₂²×C₇	#389	1	1	yes	characteristic
245	C₂²×C₇	#389	1	1	yes	characteristic
246	C₂²×C₇	#389	1	1	yes	characteristic
247	C₂²×C₇	C₂×C₄×Q₈	1	1	yes	characteristic
248	C₂²×C₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₂²×C₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
250	C₄×C₇	#389	1	1	yes	characteristic
251	C₄×C₇	#389	1	1	yes	characteristic
252	C₄×C₇	#389	1	1	yes	characteristic
253	C₄×C₇	#389	1	1	yes	characteristic
254	C₄×C₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
255	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₇	C₂×#121	1	1	yes	characteristic
257	C₄×C₇	C₂×#125	1	1	yes	characteristic
258	Dic₇	—	4	4	no	—
259	C₂⁴	Q₈×D₇	1	1	yes	characteristic
260	C₂²×C₄	—	14	2	no	—
261	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
262	C₂²×C₄	C₂×Dic₁₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₂₈	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
266	C₂²×C₄	D₄×D₇	1	1	yes	characteristic
267	C₂²×C₄	#1159	1	1	yes	characteristic
268	C₂²×C₄	#1159	1	1	yes	characteristic
269	C₂²×C₄	Q₈×D₇	1	1	yes	characteristic
270	C₂²×C₄	#1161	1	1	yes	characteristic
271	C₂²×C₄	#1161	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₇	1	1	yes	characteristic
274	C₂²×C₄	C₂³×D₇	1	1	yes	characteristic
275	M₁₆	—	2	4	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	4	no	—
278	M₁₆	—	7	4	no	—
279	M₁₆	—	14	2	no	—
280	M₁₆	—	14	2	no	—
281	M₁₆	—	14	2	no	—
282	M₁₆	—	14	4	no	—
283	M₁₆	—	14	4	no	—
284	M₁₆	—	28	2	no	—
285	M₁₆	—	28	2	no	—
286	M₁₆	C₂²×Dic₇	1	8	yes	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	14	2	no	—
291	C₂×C₈	—	14	2	no	—
292	C₂×C₈	—	14	2	no	—
293	C₂×C₈	—	14	4	no	—
294	C₂×C₈	—	28	2	no	—
295	C₂×C₈	—	28	2	no	—
296	C₂×C₈	C₄⋊Dic₇	1	2	yes	—
297	C₂×C₈	C₄⋊Dic₇	1	2	yes	—
298	C₂×C₈	C₄⋊Dic₇	1	2	yes	—
299	C₂×C₈	C₄⋊Dic₇	1	2	yes	—
300	C₂×C₈	C₄⋊Dic₇	1	4	yes	—
301	C₂×C₈	C₄⋊Dic₇	1	4	yes	—
302	C₂×C₈	C₂×Dic₁₄	1	4	yes	—
303	C₂×C₈	C₂×D₂₈	1	2	yes	—
304	C₂×C₈	C₂×D₂₈	1	2	yes	—
305	C₂×C₈	C₂²×Dic₇	1	4	yes	—
306	C₄⋊C₄	—	14	2	no	—
307	C₄⋊C₄	—	14	2	no	—
308	C₂²⋊C₄	—	7	4	no	—
309	C₂²⋊C₄	—	14	2	no	—
310	C₄²	—	14	2	no	—
311	C₄²	—	14	2	no	—
312	C₂×C₇	—	2	1	no	—
313	C₂×C₇	—	2	1	no	—
314	C₂×C₇	—	2	1	no	—
315	C₂×C₇	—	2	1	no	—
316	C₂×C₇	—	2	1	no	—
317	C₂×C₇	—	2	1	no	—
318	C₂×C₇	#1953	1	2	yes	complemented
319	C₂×C₇	C₂×#389	1	1	yes	characteristic
320	C₂³	—	4	2	no	—
321	C₂³	#6451	1	1	yes	characteristic
322	C₂³	#6451	1	1	yes	characteristic
323	C₂³	#6460	1	1	yes	characteristic
324	C₂³	#6460	1	1	yes	characteristic
325	C₂³	Q₈×Dic₇	1	1	yes	characteristic
326	C₂³	Q₈×Dic₇	1	1	yes	characteristic
327	C₂³	C₂×Q₈×D₇	1	1	yes	characteristic
328	C₂×C₄	—	14	4	no	—
329	C₂×C₄	—	28	4	no	—
330	C₂×C₄	#6451	1	1	yes	characteristic
331	C₂×C₄	#6451	1	1	yes	characteristic
332	C₂×C₄	#6453	1	1	yes	characteristic
333	C₂×C₄	#6453	1	1	yes	characteristic
334	C₂×C₄	#6453	1	1	yes	characteristic
335	C₂×C₄	#6453	1	1	yes	characteristic
336	C₂×C₄	#6458	1	1	yes	characteristic
337	C₂×C₄	#6458	1	1	yes	characteristic
338	C₂×C₄	#6458	1	1	yes	characteristic
339	C₂×C₄	#6458	1	1	yes	characteristic
340	C₂×C₄	#6460	1	1	yes	characteristic
341	C₂×C₄	#6460	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊Dic₇	1	1	yes	characteristic
346	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
347	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
348	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
349	C₂×C₄	D₄×Dic₇	1	1	yes	characteristic
350	C₂×C₄	Q₈×Dic₇	1	1	yes	characteristic
351	C₂×C₄	Q₈×Dic₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×Dic₁₄	1	1	yes	characteristic
353	C₂×C₄	C₂²×D₂₈	1	1	yes	characteristic
354	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
355	C₂×C₄	C₂×#1159	1	1	yes	characteristic
356	C₂×C₄	C₂×#1161	1	1	yes	characteristic
357	C₂×C₄	C₂³×Dic₇	1	1	yes	characteristic
358	C₈	—	2	8	no	—
359	C₈	—	14	4	no	—
360	C₈	—	28	4	no	—
361	C₈	C₂×C₄⋊Dic₇	1	4	yes	—
362	C₈	C₂×C₄⋊Dic₇	1	4	yes	—
363	C₇	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	#89757	1	1	yes	characteristic
372	C₂²	#89757	1	1	yes	characteristic
373	C₂²	#89757	1	1	yes	characteristic
374	C₂²	#89757	1	1	yes	characteristic
375	C₂²	C₂×#6451	1	1	yes	characteristic
376	C₂²	C₂×#6460	1	1	yes	characteristic
377	C₂²	C₂×Q₈×Dic₇	1	1	yes	characteristic
378	C₄	—	28	4	no	—
379	C₄	#89757	1	1	yes	characteristic
380	C₄	#89757	1	1	yes	characteristic
381	C₄	#89757	1	1	yes	characteristic
382	C₄	#89757	1	1	yes	characteristic
383	C₄	C₂×#6453	1	1	yes	characteristic
384	C₄	C₂×#6458	1	1	yes	characteristic
385	C₄	C₂²×C₄⋊Dic₇	1	1	yes	characteristic
386	C₄	C₂×D₄×Dic₇	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#11728461	1	2	yes	direct product factor
394	C₂	C₂×#89757	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#6458
commutator	C₂×C₄×C₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇
Fitting	C₂²×C₇×#108	C₂
socle	C₂²×C₇	#389
prime radical	C₂⁴×C₇	C₂×Q₈
cosocle	C₂²×C₄×C₇	C₂⁴
hypercenter	C₂²×#108	D₇
hypocenter	C₇	C₂×#1953
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
6. #11728461	C₂	direct (N × H)
12. C₂×C₇×#108	C₄	semidirect
13. C₂×C₇×#108	C₄	semidirect
65. C₇×#108	C₂×C₄	semidirect
142. C₂×#108	Dic₇	semidirect
143. C₂×#108	Dic₇	semidirect
233. #108	C₂×Dic₇	semidirect
318. C₂×C₇	#1953	semidirect
363. C₇	C₂×#1953	semidirect
393. C₂	#11728461	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×C₇×#108	2
C₂×#89897	2
C₂²×#6393	2
C₂×#89873	2
C₂×#89354	2
#11728461	2
C₂×#1953	7

Subgroups — C2×#11728461 #13357365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11728461 #13357365