Subgroups — C₂×#20257792 #27124079

Order 12032.

8802 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257792	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689865	C₂	1	3	yes	maximal, complemented
3	C₂×#15689835	C₂	1	6	yes	maximal, complemented
4	C₂×#15689755	C₂	1	6	yes	maximal, complemented
5	C₂×#15689691	C₂	1	6	yes	maximal, complemented
6	C₂×#15689688	C₂	1	6	yes	maximal, complemented
7	C₂×#15689672	C₂	1	3	yes	maximal, complemented
8	C₂×C₄₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625354	C₂²	1	3	yes	complemented
10	C₂²×#10625352	C₂²	1	3	yes	complemented
11	C₂³×C₂²⋊D₄₇	C₂²	1	6	yes	complemented
12	C₂²×D₄×D₄₇	C₂²	1	6	yes	complemented
13	#15689865	C₂²	1	48	yes	complemented
14	#15689835	C₂²	1	96	yes	complemented
15	#15689755	C₂²	1	96	yes	complemented
16	#15689691	C₂²	1	96	yes	complemented
17	#15689688	C₂²	1	96	yes	complemented
18	#15689672	C₂²	1	48	yes	complemented
19	C₂×#13094022	C₂²	1	3	yes	complemented
20	C₂×#13094021	C₂²	1	2	yes	complemented
21	C₂×#13094020	C₂²	1	3	yes	—
22	C₂×#13094020	C₂²	1	6	yes	complemented
23	C₂×#13094013	C₂²	1	6	yes	complemented
24	C₂×#13094012	C₂²	1	3	yes	complemented
25	C₂×#13094010	C₂²	1	12	yes	complemented
26	C₂×#13093997	C₂²	1	12	yes	complemented
27	C₂×#13093997	C₂²	1	12	yes	complemented
28	C₂×#13093996	C₂²	1	12	yes	complemented
29	C₂×#13093994	C₂²	1	12	yes	complemented
30	C₂×#13093994	C₂²	1	6	yes	complemented
31	C₂×#13093993	C₂²	1	2	yes	complemented
32	C₂×#13093992	C₂²	1	6	yes	complemented
33	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	12	yes	complemented
34	C₂×#13093981	C₂²	1	6	yes	complemented
35	C₂×#13093980	C₂²	1	6	yes	complemented
36	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
37	C₄₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
38	C₂×#124×C₄₇	C₂²	1	6	yes	complemented
39	C₂×#124×C₄₇	C₂²	1	3	yes	complemented
40	C₂×#120×C₄₇	C₂²	1	6	yes	complemented
41	C₂⁴×D₄₇	C₂³	1	6	yes	—
42	C₂×#10625354	—	4	12	no	—
43	C₂×#10625354	C₂³	1	24	yes	complemented
44	C₂×#10625352	—	4	12	no	—
45	C₂×#10625352	C₂³	1	24	yes	complemented
46	C₂²×Dic₉₄	C₂³	1	3	yes	—
47	C₂²×D₁₈₈	C₂³	1	3	yes	—
48	C₂²×D₁₈₈	C₂³	1	6	yes	—
49	C₂²×D₁₈₈	C₂³	1	6	yes	—
50	C₂²×C₂²⋊D₄₇	—	4	24	no	—
51	C₂²×C₂²⋊D₄₇	C₂³	1	12	yes	—
52	C₂²×C₂²⋊D₄₇	C₂³	1	12	yes	—
53	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
54	C₂²×C₂²⋊D₄₇	C₂³	1	48	yes	complemented
55	C₂×D₄×D₄₇	—	4	24	no	—
56	C₂×D₄×D₄₇	C₂³	1	48	yes	complemented
57	C₂³×Dic₄₇	C₂³	1	6	yes	—
58	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
59	C₂²×C₄×D₄₇	C₂³	1	6	yes	—
60	#13094022	C₂³	1	24	yes	complemented
61	#13094021	C₂³	1	16	yes	complemented
62	#13094020	C₂³	1	24	yes	—
63	#13094020	C₂³	1	48	yes	complemented
64	#13094013	C₂³	1	48	yes	complemented
65	#13094012	C₂³	1	24	yes	complemented
66	#13094010	C₂³	1	96	yes	complemented
67	#13093997	C₂³	1	96	yes	complemented
68	#13093997	C₂³	1	96	yes	complemented
69	#13093996	C₂³	1	96	yes	complemented
70	#13093994	C₂³	1	96	yes	complemented
71	#13093994	C₂³	1	48	yes	complemented
72	#13093993	C₂³	1	16	yes	complemented
73	#13093992	C₂³	1	48	yes	complemented
74	(C₂²⋊D₄₇)⋊C₄	C₂³	1	96	yes	complemented
75	#13093981	C₂³	1	48	yes	complemented
76	#13093980	C₂³	1	48	yes	complemented
77	C₂×Dic₄₇⋊C₄	C₂³	1	12	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
79	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
80	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	12	yes	—
81	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
82	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
83	C₄²×D₄₇	C₂³	1	8	yes	complemented
84	C₂⁵×C₄₇	C₂³	1	2	yes	—
85	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
86	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
87	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
88	#124×C₄₇	C₂³	1	48	yes	complemented
89	#124×C₄₇	C₂³	1	24	yes	complemented
90	#120×C₄₇	C₂³	1	48	yes	complemented
91	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
95	C₂⁴×C₄₇	—	4	12	no	—
96	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
97	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
98	C₂³×D₄₇	—	4	24	no	—
99	C₂³×D₄₇	—	4	12	no	—
100	C₂³×D₄₇	C₂⁴	1	6	yes	—
101	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
102	C₂³×D₄₇	C₂⁴	1	24	yes	—
103	C₂×Q₈×C₄₇	—	4	6	no	—
104	C₂×Q₈×C₄₇	C₂⁴	1	12	yes	—
105	C₂×D₄×C₄₇	—	4	12	no	—
106	C₂×D₄×C₄₇	—	4	6	no	—
107	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
108	C₂×D₄×C₄₇	C₂⁴	1	24	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
111	C₂×C₂²⋊D₄₇	—	2	48	no	—
112	C₂×C₂²⋊D₄₇	—	4	96	no	—
113	C₂×C₂²⋊D₄₇	—	4	24	no	—
114	C₂×C₂²⋊D₄₇	—	4	12	no	—
115	C₂×C₂²⋊D₄₇	C₂⁴	1	48	yes	—
116	C₂×C₂²⋊D₄₇	C₂⁴	1	48	yes	—
117	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
118	C₂²×Dic₄₇	—	2	24	no	—
119	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
120	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
121	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
122	#10625354	—	4	48	no	—
123	#10625352	—	4	48	no	—
124	D₄×D₄₇	—	4	96	no	—
125	C₂×D₁₈₈	—	4	12	no	—
126	C₂×D₁₈₈	—	4	6	no	—
127	C₂×D₁₈₈	—	4	12	no	—
128	C₂×D₁₈₈	C₂⁴	1	12	yes	—
129	C₂×D₁₈₈	C₂⁴	1	24	yes	—
130	C₂×D₁₈₈	C₂⁴	1	24	yes	—
131	C₂×C₄×D₄₇	—	2	24	no	—
132	C₂×C₄×D₄₇	—	2	12	no	—
133	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
134	C₂×C₄×D₄₇	C₂⁴	1	24	yes	—
135	C₂×Dic₉₄	—	4	6	no	—
136	C₂×Dic₉₄	C₂⁴	1	12	yes	—
137	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
138	C₂²⋊C₄×C₄₇	C₂⁴	1	48	yes	—
139	C₄²×C₄₇	C₂⁴	1	4	yes	—
140	C₄²×C₄₇	C₂⁴	1	8	yes	—
141	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
142	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
143	(C₂×D₄₇)⋊C₄	C₂⁴	1	48	yes	—
144	Dic₄₇⋊C₄	C₂⁴	1	48	yes	—
145	C₄×Dic₄₇	C₂⁴	1	12	yes	—
146	C₄×Dic₄₇	C₂⁴	1	24	yes	—
147	C₂³×C₄₇	—	2	12	no	—
148	C₂³×C₄₇	—	2	24	no	—
149	C₂³×C₄₇	—	4	24	no	—
150	C₂³×C₄₇	—	8	16	no	—
151	C₂³×C₄₇	C₂⁵	1	12	yes	—
152	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	6	no	—
154	C₂²×D₄₇	—	2	12	no	—
155	C₂²×D₄₇	—	2	24	no	—
156	C₂²×D₄₇	—	4	48	no	—
157	C₂²×D₄₇	—	4	24	no	—
158	C₂²×D₄₇	—	8	48	no	—
159	C₂²×D₄₇	C₂⁵	1	12	yes	—
160	C₂²×D₄₇	C₂⁵	1	2	yes	—
161	Q₈×C₄₇	—	4	12	no	—
162	D₄×C₄₇	—	4	24	no	—
163	D₄×C₄₇	—	4	12	no	—
164	C₂×C₄×C₄₇	—	2	6	no	—
165	C₂×C₄×C₄₇	—	2	12	no	—
166	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
167	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
168	C₂²⋊D₄₇	—	2	96	no	—
169	C₂²⋊D₄₇	—	4	24	no	—
170	C₂²⋊D₄₇	—	4	48	no	—
171	C₂×Dic₄₇	—	2	12	no	—
172	C₂×Dic₄₇	—	2	48	no	—
173	C₂×Dic₄₇	H(5,𝔽₂)	1	12	yes	—
174	C₂×Dic₄₇	C₂⁵	1	12	yes	—
175	C₂×Dic₄₇	C₂⁵	1	6	yes	—
176	D₁₈₈	—	4	24	no	—
177	D₁₈₈	—	4	12	no	—
178	D₁₈₈	—	4	24	no	—
179	C₄×D₄₇	—	2	48	no	—
180	C₄×D₄₇	—	2	24	no	—
181	Dic₉₄	—	4	12	no	—
182	C₂×#3549	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	12	no	—
184	C₂²×C₄₇	—	2	24	no	—
185	C₂²×C₄₇	—	4	24	no	—
186	C₂²×C₄₇	—	8	16	no	—
187	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
188	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
189	C₂×D₄₇	—	2	6	no	—
190	C₂×D₄₇	—	2	12	no	—
191	C₂×D₄₇	—	2	24	no	—
192	C₂×D₄₇	—	4	4	no	—
193	C₂×D₄₇	—	4	24	no	—
194	C₂×D₄₇	—	8	48	no	—
195	C₄×C₄₇	—	2	6	no	—
196	C₄×C₄₇	—	2	12	no	—
197	Dic₄₇	—	2	12	no	—
198	Dic₄₇	C₂×H(5,𝔽₂)	1	12	yes	—
199	#3549	—	47	32	no	—
200	C₂×H(3,𝔽₄)	—	47	3	no	—
201	C₂×H(3,𝔽₄)	D₄₇	1	1	yes	characteristic, complemented
202	C₂×#555	—	47	6	no	—
203	C₂×D₄²	—	47	6	no	—
204	C₂×#535	—	47	6	no	—
205	C₂×#535	—	47	6	no	—
206	C₂×#532	—	47	3	no	—
207	C₂×C₄₇	—	4	12	no	—
208	C₂×C₄₇	#3549	1	4	yes	complemented
209	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	3	yes	—
210	D₄₇	—	4	2	no	—
211	D₄₇	—	4	12	no	—
212	C₂²×#41	—	47	3	no	—
213	C₂²×#41	—	47	3	no	—
214	C₂³×D₄	—	47	6	no	—
215	C₂³×D₄	—	47	6	no	—
216	H(3,𝔽₄)	—	47	48	no	—
217	H(3,𝔽₄)	C₂×D₄₇	1	16	yes	complemented
218	#555	—	47	96	no	—
219	D₄²	—	47	96	no	—
220	#535	—	47	96	no	—
221	#535	—	47	96	no	—
222	#532	—	47	48	no	—
223	C₂×C₄⋊Q₈	—	47	3	no	—
224	C₂×#127	—	47	3	no	—
225	C₂×#127	—	47	6	no	—
226	C₂×#127	—	47	2	no	—
227	C₂×#124	—	47	6	no	—
228	C₂×#124	—	47	12	no	—
229	C₂×#124	—	47	3	no	—
230	C₂×#124	C₂×D₄₇	1	3	yes	complemented
231	C₂×#124	C₂×D₄₇	1	6	yes	complemented
232	C₂×#121	—	47	12	no	—
233	C₂×#121	—	47	12	no	—
234	C₂×#121	—	47	12	no	—
235	C₂×#120	—	47	2	no	—
236	C₂×#120	—	47	6	no	—
237	C₂×#120	—	47	6	no	—
238	C₂×#120	—	47	12	no	—
239	C₂×#120	C₂×D₄₇	1	6	yes	complemented
240	C₂×C₄×D₄	—	47	12	no	—
241	C₂×#117	—	47	6	no	—
242	C₂×#117	—	47	6	no	—
243	C₂²×C₄²	—	47	1	no	—
244	C₄₇	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
245	C₂⁵	—	47	6	no	—
246	C₂⁵	C₂²×D₄₇	1	2	yes	—
247	C₂×#41	—	47	24	no	—
248	C₂×#41	—	47	24	no	—
249	C₂×#41	—	188	12	no	—
250	C₂×#41	—	188	12	no	—
251	C₂²×Q₈	—	47	3	no	—
252	C₂²×Q₈	C₂²×D₄₇	1	3	yes	—
253	C₂²×D₄	—	47	12	no	—
254	C₂²×D₄	—	47	12	no	—
255	C₂²×D₄	—	47	6	no	—
256	C₂²×D₄	—	47	48	no	—
257	C₂²×D₄	—	47	48	no	—
258	C₂²×D₄	—	47	3	no	—
259	C₂²×D₄	—	47	6	no	—
260	C₂²×D₄	—	47	6	no	—
261	C₂²×D₄	—	188	24	no	—
262	C₂²×D₄	—	188	24	no	—
263	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
264	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
265	C₂³×C₄	—	47	6	no	—
266	C₂³×C₄	—	47	6	no	—
267	C₂³×C₄	—	47	3	no	—
268	C₄⋊Q₈	—	47	24	no	—
269	#127	—	47	24	no	—
270	#127	—	47	48	no	—
271	#127	—	47	16	no	—
272	#124	—	47	48	no	—
273	#124	—	47	96	no	—
274	#124	—	47	24	no	—
275	#124	C₂²×D₄₇	1	24	yes	complemented
276	#124	C₂²×D₄₇	1	48	yes	complemented
277	#121	—	47	96	no	—
278	#121	—	47	96	no	—
279	#121	—	47	96	no	—
280	#120	—	47	16	no	—
281	#120	—	47	48	no	—
282	#120	—	47	48	no	—
283	#120	—	47	96	no	—
284	#120	C₂²×D₄₇	1	48	yes	complemented
285	C₄×D₄	—	47	96	no	—
286	#117	—	47	48	no	—
287	#117	—	47	48	no	—
288	C₂×C₄⋊C₄	—	47	12	no	—
289	C₂×C₂²⋊C₄	—	47	6	no	—
290	C₂×C₂²⋊C₄	—	47	12	no	—
291	C₂×C₂²⋊C₄	—	47	12	no	—
292	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
293	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
294	C₂×C₄²	—	47	6	no	—
295	C₂×C₄²	—	47	3	no	—
296	C₂×C₄²	—	47	8	no	—
297	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
298	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
299	C₂⁴	—	4	12	no	—
300	C₂⁴	—	47	6	no	—
301	C₂⁴	—	47	1	no	—
302	C₂⁴	—	47	24	no	—
303	C₂⁴	—	188	12	no	—
304	C₂⁴	—	188	24	no	—
305	C₂⁴	C₂³×D₄₇	1	6	yes	—
306	C₂⁴	C₂³×D₄₇	1	8	yes	—
307	#41	—	188	48	no	—
308	#41	—	188	48	no	—
309	C₂×Q₈	—	4	6	no	—
310	C₂×Q₈	—	47	12	no	—
311	C₂×Q₈	—	188	6	no	—
312	C₂×Q₈	C₂³×D₄₇	1	12	yes	—
313	C₂×D₄	—	4	12	no	—
314	C₂×D₄	—	4	6	no	—
315	C₂×D₄	—	47	48	no	—
316	C₂×D₄	—	47	48	no	—
317	C₂×D₄	—	47	24	no	—
318	C₂×D₄	—	47	12	no	—
319	C₂×D₄	—	47	24	no	—
320	C₂×D₄	—	47	24	no	—
321	C₂×D₄	—	94	48	no	—
322	C₂×D₄	—	188	12	no	—
323	C₂×D₄	—	188	12	no	—
324	C₂×D₄	—	188	6	no	—
325	C₂×D₄	—	188	96	no	—
326	C₂×D₄	—	188	96	no	—
327	C₂×D₄	—	188	24	no	—
328	C₂×D₄	—	188	12	no	—
329	C₂×D₄	C₂³×D₄₇	1	12	yes	—
330	C₂×D₄	C₂³×D₄₇	1	24	yes	—
331	C₂²×C₄	—	47	3	no	—
332	C₂²×C₄	—	47	24	no	—
333	C₂²×C₄	—	47	6	no	—
334	C₂²×C₄	—	47	12	no	—
335	C₂²×C₄	—	47	24	no	—
336	C₂²×C₄	—	94	24	no	—
337	C₂²×C₄	—	94	12	no	—
338	C₂²×C₄	—	94	24	no	—
339	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
340	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
341	C₄⋊C₄	—	47	48	no	—
342	C₂²⋊C₄	—	47	24	no	—
343	C₂²⋊C₄	—	47	48	no	—
344	C₂²⋊C₄	—	47	48	no	—
345	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
346	C₂²⋊C₄	C₂³×D₄₇	1	48	yes	—
347	C₄²	—	47	12	no	—
348	C₄²	—	47	24	no	—
349	C₄²	C₂³×D₄₇	1	4	yes	—
350	C₄²	C₂³×D₄₇	1	8	yes	—
351	C₂³	—	2	12	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	4	24	no	—
354	C₂³	—	8	16	no	—
355	C₂³	—	47	12	no	—
356	C₂³	—	47	2	no	—
357	C₂³	—	94	6	no	—
358	C₂³	—	94	12	no	—
359	C₂³	—	94	24	no	—
360	C₂³	—	376	48	no	—
361	C₂³	—	188	24	no	—
362	C₂³	—	188	48	no	—
363	C₂³	C₂⁴×D₄₇	1	12	yes	—
364	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
365	Q₈	—	4	12	no	—
366	Q₈	—	188	12	no	—
367	D₄	—	4	24	no	—
368	D₄	—	4	12	no	—
369	D₄	—	94	96	no	—
370	D₄	—	188	24	no	—
371	D₄	—	188	24	no	—
372	D₄	—	188	12	no	—
373	D₄	—	188	48	no	—
374	D₄	—	188	24	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	47	12	no	—
378	C₂×C₄	—	47	6	no	—
379	C₂×C₄	—	47	12	no	—
380	C₂×C₄	—	94	48	no	—
381	C₂×C₄	—	94	24	no	—
382	C₂×C₄	—	94	48	no	—
383	C₂×C₄	—	94	12	no	—
384	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
385	C₂×C₄	C₂⁴×D₄₇	1	12	yes	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	24	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	94	6	no	—
391	C₂²	—	94	12	no	—
392	C₂²	—	94	24	no	—
393	C₂²	—	376	48	no	—
394	C₂²	—	188	24	no	—
395	C₂²	—	188	4	no	—
396	C₂²	H(5,𝔽₂)×D₄₇	1	6	yes	—
397	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
398	C₄	—	2	12	no	—
399	C₄	—	2	6	no	—
400	C₄	—	47	12	no	—
401	C₄	—	94	12	no	—
402	C₂	—	4	12	no	—
403	C₂	—	188	12	no	—
404	C₂	—	188	2	no	—
405	C₂	#20257792	1	4	yes	direct product factor
406	C₂	C₂×H(5,𝔽₂)×D₄₇	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×H(3,𝔽₄)	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₄₇
hypocenter	C₄₇	C₂×#3549
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #20257792	C₂	direct (N × H)
2. C₂×#15689865	C₂	semidirect
3. C₂×#15689835	C₂	semidirect
4. C₂×#15689755	C₂	semidirect
5. C₂×#15689691	C₂	semidirect
6. C₂×#15689688	C₂	semidirect
7. C₂×#15689672	C₂	semidirect
8. C₂×C₄₇×H(3,𝔽₄)	C₂	semidirect
9. C₂²×#10625354	C₂²	semidirect
10. C₂²×#10625352	C₂²	semidirect
11. C₂³×C₂²⋊D₄₇	C₂²	semidirect
12. C₂²×D₄×D₄₇	C₂²	semidirect
13. #15689865	C₂²	semidirect
14. #15689835	C₂²	semidirect
15. #15689755	C₂²	semidirect
16. #15689691	C₂²	semidirect
17. #15689688	C₂²	semidirect
18. #15689672	C₂²	semidirect
19. C₂×#13094022	C₂²	semidirect
20. C₂×#13094021	C₂²	semidirect
22. C₂×#13094020	C₂²	semidirect
23. C₂×#13094013	C₂²	semidirect
24. C₂×#13094012	C₂²	semidirect
25. C₂×#13094010	C₂²	semidirect
26. C₂×#13093997	C₂²	semidirect
27. C₂×#13093997	C₂²	semidirect
28. C₂×#13093996	C₂²	semidirect
29. C₂×#13093994	C₂²	semidirect
30. C₂×#13093994	C₂²	semidirect
31. C₂×#13093993	C₂²	semidirect
32. C₂×#13093992	C₂²	semidirect
33. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
34. C₂×#13093981	C₂²	semidirect
35. C₂×#13093980	C₂²	semidirect
36. C₂×C₄²×D₄₇	C₂²	semidirect
37. C₄₇×H(3,𝔽₄)	C₂²	semidirect
38. C₂×#124×C₄₇	C₂²	semidirect
39. C₂×#124×C₄₇	C₂²	semidirect
40. C₂×#120×C₄₇	C₂²	semidirect
43. C₂×#10625354	C₂³	semidirect
45. C₂×#10625352	C₂³	semidirect
54. C₂²×C₂²⋊D₄₇	C₂³	semidirect
56. C₂×D₄×D₄₇	C₂³	semidirect
60. #13094022	C₂³	semidirect
61. #13094021	C₂³	semidirect
63. #13094020	C₂³	semidirect
64. #13094013	C₂³	semidirect
65. #13094012	C₂³	semidirect
66. #13094010	C₂³	semidirect
67. #13093997	C₂³	semidirect
68. #13093997	C₂³	semidirect
69. #13093996	C₂³	semidirect
70. #13093994	C₂³	semidirect
71. #13093994	C₂³	semidirect
72. #13093993	C₂³	semidirect
73. #13093992	C₂³	semidirect
74. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
75. #13093981	C₂³	semidirect
76. #13093980	C₂³	semidirect
83. C₄²×D₄₇	C₂³	semidirect
88. #124×C₄₇	C₂³	semidirect
89. #124×C₄₇	C₂³	semidirect
90. #120×C₄₇	C₂³	semidirect
201. C₂×H(3,𝔽₄)	D₄₇	semidirect
208. C₂×C₄₇	#3549	semidirect
217. H(3,𝔽₄)	C₂×D₄₇	semidirect
230. C₂×#124	C₂×D₄₇	semidirect
231. C₂×#124	C₂×D₄₇	semidirect
239. C₂×#120	C₂×D₄₇	semidirect
244. C₄₇	C₂×#3549	semidirect
275. #124	C₂²×D₄₇	semidirect
276. #124	C₂²×D₄₇	semidirect
284. #120	C₂²×D₄₇	semidirect
405. C₂	#20257792	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257792	2
C₂×#15689865	2
C₂×#15689835	2
C₂×#15689755	2
C₂×#15689691	2
C₂×#15689688	2
C₂×#15689672	2
C₂×C₄₇×H(3,𝔽₄)	2
C₂×#3549	47

Subgroups — C2×#20257792 #27124079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257792 #27124079