Subgroups — C₂×#20245457 #26370650

Order 12032.

706 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	C₂×#15689563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689558	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689507	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245457	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688944	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688938	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
10	C₂²×#10625325	—	2	1	no	—
11	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
12	C₂×#13094012	—	2	1	no	—
13	#15689563	—	2	2	no	—
14	#15689563	C₂²	1	4	yes	complemented
15	#15689558	—	2	2	no	—
16	#15689558	C₂²	1	4	yes	—
17	C₂×#13093970	—	2	1	no	—
18	C₂×#13093968	—	2	1	no	—
19	C₂×#13093967	—	2	1	no	—
20	C₂×#13093965	—	2	1	no	—
21	C₂×#13093964	C₂²	1	1	yes	characteristic
22	C₂×#13093964	C₂²	1	1	yes	characteristic
23	#15689507	—	2	2	no	—
24	#15689507	C₂²	1	4	yes	complemented
25	#15688944	C₂²	1	4	yes	complemented
26	#15688938	C₂²	1	4	yes	complemented
27	#15688935	C₂²	1	4	yes	complemented
28	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₄₇	—	2	1	no	—
30	C₄₇×#443	—	2	2	no	—
31	C₄₇×#443	C₂²	1	4	yes	complemented
32	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#104×C₄₇	—	2	1	no	—
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₉₄	—	2	1	no	—
36	C₂²×D₁₈₈	—	2	1	no	—
37	C₂×Dic₁₈₈	—	2	1	no	—
38	C₂×Dic₁₈₈	—	2	1	no	—
39	C₂×Dic₁₈₈	—	2	1	no	—
40	C₂×Dic₁₈₈	—	2	1	no	—
41	C₂×Dic₁₈₈	—	2	1	no	—
42	C₂×Dic₁₈₈	C₂³	1	2	yes	—
43	C₂×#10625325	—	2	4	no	—
44	C₂×#10625325	—	4	1	no	—
45	C₂×#10625325	—	4	1	no	—
46	C₂×#10625325	—	4	2	no	—
47	C₂×D₃₇₆	—	2	1	no	—
48	C₂×D₃₇₆	—	2	1	no	—
49	C₂×D₃₇₆	—	2	1	no	—
50	C₂×D₃₇₆	—	2	1	no	—
51	C₂×D₃₇₆	—	2	1	no	—
52	C₂×D₃₇₆	C₂³	1	2	yes	—
53	#13094012	—	2	4	no	—
54	#13094012	—	4	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	—	4	2	no	—
56	#13093970	—	2	4	no	—
57	#13093968	—	2	4	no	—
58	#13093967	—	2	4	no	—
59	#13093965	—	2	4	no	—
60	#13093964	—	2	1	no	—
61	#13093964	—	2	1	no	—
62	#13093964	C₂³	1	2	yes	—
63	#13093964	C₂³	1	2	yes	—
64	C₂×C₄₇⋊C₁₆	—	2	1	no	—
65	C₂×C₄₇⋊C₁₆	—	2	1	no	—
66	C₂×#41×C₄₇	—	2	1	no	—
67	#135×C₄₇	—	2	1	no	—
68	#135×C₄₇	—	2	1	no	—
69	#135×C₄₇	D₄	1	2	yes	—
70	#135×C₄₇	C₂³	1	2	yes	—
71	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₄₇	—	2	1	no	—
73	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
74	#131×C₄₇	—	2	4	no	—
75	#131×C₄₇	—	4	2	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	C₂×M₁₆×C₄₇	—	4	1	no	—
78	C₂²×C₈×C₄₇	—	4	1	no	—
79	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
82	#108×C₄₇	—	2	1	no	—
83	#108×C₄₇	C₂³	1	2	yes	—
84	#104×C₄₇	—	2	4	no	—
85	C₄×C₈×C₄₇	D₄	1	2	yes	—
86	C₄×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂³×D₄₇	—	4	1	no	—
88	#41×C₄₇	—	2	2	no	—
89	#41×C₄₇	—	2	2	no	—
90	#41×C₄₇	—	4	1	no	—
91	#41×C₄₇	—	4	1	no	—
92	C₂×Q₈×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	4	1	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	4	1	no	—
99	C₂×D₁₈₈	—	2	2	no	—
100	C₂×D₁₈₈	—	4	1	no	—
101	C₂×D₁₈₈	—	4	1	no	—
102	C₂×D₁₈₈	—	4	1	no	—
103	C₂×D₁₈₈	—	4	1	no	—
104	C₂×D₁₈₈	—	4	1	no	—
105	C₂×Dic₉₄	—	2	2	no	—
106	C₂×Dic₉₄	—	4	1	no	—
107	C₂×Dic₉₄	—	4	1	no	—
108	C₂×Dic₉₄	—	4	1	no	—
109	C₂×Dic₉₄	—	4	1	no	—
110	C₂×Dic₉₄	—	4	1	no	—
111	Q₁₆×C₄₇	—	2	1	no	—
112	Q₁₆×C₄₇	C₂×D₄	1	2	yes	—
113	SD₁₆×C₄₇	—	2	2	no	—
114	SD₁₆×C₄₇	—	2	2	no	—
115	D₈×C₄₇	—	2	1	no	—
116	D₈×C₄₇	C₂×D₄	1	2	yes	—
117	M₁₆×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	4	1	no	—
119	M₁₆×C₄₇	—	4	4	no	—
120	C₂×C₈×C₄₇	—	4	1	no	—
121	C₂×C₈×C₄₇	—	4	4	no	—
122	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
123	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
124	C₂×C₈×C₄₇	D₈	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
130	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
131	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	(C₂×D₄₇)⋊C₄	—	4	8	no	—
135	Dic₁₈₈	—	2	2	no	—
136	Dic₁₈₈	—	2	2	no	—
137	Dic₁₈₈	—	4	1	no	—
138	Dic₁₈₈	—	4	1	no	—
139	D₃₇₆	—	2	2	no	—
140	D₃₇₆	—	2	2	no	—
141	D₃₇₆	—	4	1	no	—
142	D₃₇₆	—	4	1	no	—
143	#10625325	—	4	4	no	—
144	#10625325	—	4	4	no	—
145	C₄₇⋊C₁₆	—	2	2	no	—
146	C₄₇⋊C₁₆	—	2	2	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂²×D₄₇	—	4	2	no	—
150	C₂²×D₄₇	—	8	4	no	—
151	C₂²×D₄₇	—	8	1	no	—
152	C₂²×D₄₇	—	8	1	no	—
153	Q₈×C₄₇	—	2	2	no	—
154	Q₈×C₄₇	—	4	1	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	4	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	8	1	no	—
172	C₂×Dic₄₇	—	8	1	no	—
173	D₁₈₈	—	4	2	no	—
174	D₁₈₈	—	4	2	no	—
175	D₁₈₈	—	8	1	no	—
176	D₁₈₈	—	8	1	no	—
177	Dic₉₄	—	4	2	no	—
178	Dic₉₄	—	4	2	no	—
179	Dic₉₄	—	8	1	no	—
180	Dic₉₄	—	8	1	no	—
181	C₈×C₄₇	—	4	2	no	—
182	C₈×C₄₇	#121	1	1	yes	characteristic
183	C₈×C₄₇	#121	1	1	yes	characteristic
184	C₈×C₄₇	C₂×D₈	1	2	yes	—
185	C₈×C₄₇	C₂×D₈	1	2	yes	—
186	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×#2212	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	#459	1	1	yes	characteristic
193	C₂²×C₄₇	#459	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×D₄₇	—	8	4	no	—
196	C₂×D₄₇	—	8	2	no	—
197	C₂×D₄₇	—	16	2	no	—
198	C₂×D₄₇	—	16	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	#459	1	1	yes	characteristic
202	C₄×C₄₇	#459	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
204	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
205	Dic₄₇	—	8	2	no	—
206	C₂×#510	—	47	1	no	—
207	C₂×#509	—	47	1	no	—
208	C₂×#495	—	47	1	no	—
209	C₂×#443	D₄₇	1	1	yes	characteristic, complemented
210	#2212	—	47	8	no	—
211	C₂×#364	—	47	1	no	—
212	C₂×#362	—	47	1	no	—
213	C₂×#361	—	47	1	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	—	8	2	no	—
217	C₂×C₄₇	#2212	1	2	yes	complemented
218	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
219	D₄₇	—	16	2	no	—
220	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
221	C₂²×Q₁₆	—	47	1	no	—
222	C₂²×SD₁₆	—	94	1	no	—
223	C₂²×D₈	—	47	1	no	—
224	C₂×#131	—	2	1	no	—
225	C₂×#124	—	94	1	no	—
226	#510	—	47	4	no	—
227	#510	—	94	2	no	—
228	#509	—	47	4	no	—
229	#509	—	94	2	no	—
230	C₂×Q₃₂	—	94	1	no	—
231	C₂×SD₃₂	—	94	1	no	—
232	C₂×SD₃₂	—	94	1	no	—
233	C₂×D₁₆	—	94	1	no	—
234	C₂×M₃₂	—	47	1	no	—
235	C₂×M₃₂	—	47	1	no	—
236	#495	—	47	4	no	—
237	#495	—	94	2	no	—
238	#443	—	2	2	no	—
239	#443	C₂×D₄₇	1	4	yes	complemented
240	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
241	C₂×#104	—	2	1	no	—
242	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
243	#364	—	47	4	no	—
244	#362	—	47	4	no	—
245	#361	—	47	4	no	—
246	C₄₇	C₂×#2212	1	1	yes	characteristic, complemented, Sylow
247	C₂×#41	—	2	1	no	—
248	C₂²×Q₈	—	94	1	no	—
249	C₂²×D₄	—	94	1	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	D₁₈₈	1	2	yes	—
253	#135	C₂²×D₄₇	1	2	yes	—
254	C₂×Q₁₆	—	47	2	no	—
255	C₂×Q₁₆	—	94	1	no	—
256	C₂×Q₁₆	—	94	1	no	—
257	C₂×Q₁₆	—	94	1	no	—
258	C₂×Q₁₆	—	94	1	no	—
259	C₂×Q₁₆	—	94	1	no	—
260	C₂×Q₁₆	D₁₈₈	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×SD₁₆	—	94	4	no	—
263	C₂×SD₁₆	—	188	1	no	—
264	C₂×SD₁₆	—	188	1	no	—
265	C₂×SD₁₆	—	188	2	no	—
266	C₂×D₈	—	47	2	no	—
267	C₂×D₈	—	94	1	no	—
268	C₂×D₈	—	94	1	no	—
269	C₂×D₈	—	94	1	no	—
270	C₂×D₈	—	94	1	no	—
271	C₂×D₈	—	94	1	no	—
272	C₂×D₈	D₁₈₈	1	1	yes	characteristic
273	#131	—	2	4	no	—
274	#131	—	4	2	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	4	1	no	—
277	C₂²×C₈	—	4	1	no	—
278	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
280	#124	—	94	4	no	—
281	#124	—	188	2	no	—
282	C₂×C₂²⋊C₄	—	188	2	no	—
283	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
284	Q₃₂	—	94	4	no	—
285	SD₃₂	—	94	4	no	—
286	SD₃₂	—	94	4	no	—
287	D₁₆	—	94	4	no	—
288	M₃₂	—	47	2	no	—
289	M₃₂	—	47	2	no	—
290	M₃₂	—	94	1	no	—
291	M₃₂	—	94	1	no	—
292	C₂×C₁₆	—	94	1	no	—
293	C₂×C₁₆	—	94	1	no	—
294	#108	—	2	1	no	—
295	#108	C₂²×D₄₇	1	2	yes	—
296	#104	—	2	4	no	—
297	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
298	C₄×C₈	C₂²×D₄₇	1	2	yes	—
299	C₂⁴	—	188	1	no	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	#41	—	4	1	no	—
303	#41	—	4	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	94	2	no	—
306	C₂×Q₈	—	188	1	no	—
307	C₂×Q₈	—	188	1	no	—
308	C₂×Q₈	—	188	1	no	—
309	C₂×Q₈	—	188	1	no	—
310	C₂×Q₈	—	188	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	188	1	no	—
315	C₂×D₄	—	188	1	no	—
316	C₂×D₄	—	188	1	no	—
317	C₂×D₄	—	188	1	no	—
318	C₂×D₄	—	188	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	188	1	no	—
322	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	94	2	no	—
325	Q₁₆	—	94	2	no	—
326	Q₁₆	—	188	1	no	—
327	Q₁₆	—	188	1	no	—
328	Q₁₆	C₂×D₁₈₈	1	2	yes	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	2	2	no	—
331	SD₁₆	—	188	4	no	—
332	SD₁₆	—	188	4	no	—
333	D₈	—	2	1	no	—
334	D₈	—	94	2	no	—
335	D₈	—	94	2	no	—
336	D₈	—	188	1	no	—
337	D₈	—	188	1	no	—
338	D₈	C₂×D₁₈₈	1	2	yes	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	4	no	—
344	C₂×C₈	#10625334	1	1	yes	characteristic
345	C₂×C₈	#10625334	1	1	yes	characteristic
346	C₂×C₈	#10625334	1	2	yes	—
347	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
348	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
349	C₂×C₈	#10625350	1	1	yes	characteristic
350	C₂×C₈	#10625350	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
353	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
354	C₂²⋊C₄	—	188	8	no	—
355	C₄²	—	2	1	no	—
356	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
357	C₁₆	—	94	2	no	—
358	C₁₆	—	94	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	376	4	no	—
361	C₂³	—	376	1	no	—
362	C₂³	—	376	1	no	—
363	C₂³	—	188	2	no	—
364	C₂³	#13094049	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	376	1	no	—
368	Q₈	—	376	1	no	—
369	Q₈	—	188	2	no	—
370	Q₈	—	188	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	376	1	no	—
376	D₄	—	376	1	no	—
377	D₄	—	188	2	no	—
378	D₄	—	188	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	376	1	no	—
385	C₂×C₄	—	376	1	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	#13093998	1	1	yes	characteristic
388	C₂×C₄	#13093998	1	1	yes	characteristic
389	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
391	C₂×C₄	#13094049	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	#13093998	1	1	yes	characteristic
395	C₈	#13093998	1	1	yes	characteristic
396	C₈	C₂×#10625334	1	2	yes	—
397	C₈	C₂×#10625334	1	2	yes	—
398	C₈	C₂²×D₁₈₈	1	1	yes	characteristic
399	C₈	C₂×#10625350	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	376	4	no	—
404	C₂²	—	376	2	no	—
405	C₂²	—	752	2	no	—
406	C₂²	—	752	2	no	—
407	C₂²	#15689318	1	1	yes	characteristic
408	C₂²	#15689318	1	1	yes	characteristic
409	C₂²	C₂×#13094049	1	1	yes	characteristic
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	376	2	no	—
413	C₄	#15689318	1	1	yes	characteristic
414	C₄	#15689318	1	1	yes	characteristic
415	C₄	C₂×#13093998	1	1	yes	characteristic
416	C₄	C₂²×#10625334	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	2	no	—
420	C₂	—	752	2	no	—
421	C₂	#20245457	1	2	yes	direct product factor
422	C₂	C₂×#15689318	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689318
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#443	C₂
socle	C₂²×C₄₇	#459
prime radical	C₂×#15689558	C₂
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	C₂×#2212
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×#15689563	C₂	semidirect
3. C₂×#15689507	C₂	semidirect
4. #20245457	C₂	direct (N × H)
5. C₂×#15688944	C₂	semidirect
6. C₂×#15688938	C₂	semidirect
7. C₂×#15688935	C₂	semidirect
8. C₂×C₄₇×#443	C₂	semidirect
14. #15689563	C₂²	semidirect
24. #15689507	C₂²	semidirect
25. #15688944	C₂²	semidirect
26. #15688938	C₂²	semidirect
27. #15688935	C₂²	semidirect
31. C₄₇×#443	C₂²	semidirect
209. C₂×#443	D₄₇	semidirect
217. C₂×C₄₇	#2212	semidirect
239. #443	C₂×D₄₇	semidirect
246. C₄₇	C₂×#2212	semidirect
421. C₂	#20245457	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×#15689563	2
C₂×#15689558	2
C₂×#15689507	2
#20245457	2
C₂×#15688944	2
C₂×#15688938	2
C₂×#15688935	2
C₂×C₄₇×#443	2
C₂×#2212	47

Subgroups — C2×#20245457 #26370650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245457 #26370650