Subgroups — C₂×#20244941 #26246160

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689149	C₂	1	2	yes	maximal, complemented
3	C₂×#15689140	C₂	1	2	yes	maximal
4	#20244941	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂×#13093983	C₂²	1	2	yes	—
9	#15689172	—	2	2	no	—
10	#15689172	C₂²	1	4	yes	complemented
11	C₂×#13093960	—	2	2	no	—
12	#15689149	—	2	4	no	—
13	#15689149	C₂²	1	8	yes	complemented
14	C₂×Dic₄₇⋊C₈	—	2	4	no	—
15	#15689140	—	2	4	no	—
16	#15689140	C₂²	1	8	yes	—
17	C₂×#13093951	—	2	4	no	—
18	#15688880	C₂²	1	4	yes	complemented
19	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#408	—	2	2	no	—
23	C₄₇×#408	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	C₂³	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	#13093983	—	2	2	no	—
33	#13093983	—	2	2	no	—
34	#13093983	D₄	1	4	yes	—
35	#13093983	C₂³	1	4	yes	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
39	#13093960	—	2	8	no	—
40	Dic₄₇⋊C₈	—	2	16	no	—
41	#13093951	—	2	16	no	—
42	C₂×#41×C₄₇	—	2	1	no	—
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	Q₈	1	2	yes	—
49	C₂×#41×C₄₇	C₂³	1	2	yes	—
50	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	—	2	1	no	—
54	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₄₇	—	2	2	no	—
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
58	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	—	2	2	no	—
60	C₂²×C₈×C₄₇	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	D₄	1	2	yes	—
64	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
65	C₂²⋊C₈×C₄₇	—	2	8	no	—
66	C₂⁴×C₄₇	—	2	1	no	—
67	C₂⁴×C₄₇	#41	1	1	yes	characteristic
68	#41×C₄₇	—	2	4	no	—
69	#41×C₄₇	—	2	4	no	—
70	#41×C₄₇	—	2	4	no	—
71	#41×C₄₇	—	2	4	no	—
72	#41×C₄₇	—	4	2	no	—
73	#41×C₄₇	—	4	2	no	—
74	#41×C₄₇	—	4	2	no	—
75	#41×C₄₇	—	4	2	no	—
76	C₂×Q₈×C₄₇	—	2	1	no	—
77	C₂×Q₈×C₄₇	—	2	2	no	—
78	C₂×Q₈×C₄₇	—	2	2	no	—
79	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	2	2	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	1	no	—
85	C₂×D₄×C₄₇	—	4	2	no	—
86	C₂×D₄×C₄₇	—	4	2	no	—
87	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	1	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	4	no	—
106	M₁₆×C₄₇	—	2	4	no	—
107	M₁₆×C₄₇	—	2	4	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	2	no	—
113	C₂×C₈×C₄₇	—	4	1	no	—
114	C₂×C₈×C₄₇	—	4	1	no	—
115	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
116	C₂²⋊Dic₄₇	—	2	4	no	—
117	C₂²⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	2	4	no	—
120	C₄×Dic₄₇	—	2	4	no	—
121	C₄×Dic₄₇	C₂×D₄	1	8	yes	—
122	#10625329	—	2	4	no	—
123	#10625329	—	2	4	no	—
124	#10625329	—	4	2	no	—
125	#10625329	—	4	2	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂×C₄₇⋊C₈	—	4	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	1	no	—
133	C₂³×C₄₇	—	4	1	no	—
134	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
136	C₂³×C₄₇	#123	1	2	yes	—
137	C₂³×C₄₇	#123	1	2	yes	—
138	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
139	Q₈×C₄₇	—	2	4	no	—
140	Q₈×C₄₇	—	4	2	no	—
141	D₄×C₄₇	—	2	4	no	—
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	4	no	—
144	D₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#123	1	2	yes	—
161	C₂×C₄×C₄₇	#123	1	2	yes	—
162	C₂×C₄×C₄₇	#123	1	2	yes	—
163	C₂×C₄×C₄₇	#127	1	2	yes	—
164	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
170	C₂×Dic₄₇	—	2	8	no	—
171	C₂×Dic₄₇	—	4	8	no	—
172	C₈×C₄₇	—	2	4	no	—
173	C₈×C₄₇	—	4	2	no	—
174	C₄₇⋊C₈	—	4	4	no	—
175	C₂×#2098	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	—	2	4	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	4	1	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	#399	1	1	yes	characteristic
186	C₂²×C₄₇	#399	1	2	yes	—
187	C₂²×C₄₇	#399	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#123	1	2	yes	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	#399	1	1	yes	characteristic
192	C₄×C₄₇	#399	1	1	yes	characteristic
193	C₄×C₄₇	#399	1	2	yes	—
194	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
195	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
196	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
197	Dic₄₇	—	4	8	no	—
198	C₂×#430	—	47	1	no	—
199	C₂×#424	—	47	2	no	—
200	C₂×#421	—	47	2	no	—
201	C₂×#408	D₄₇	1	1	yes	characteristic
202	#2098	—	47	8	no	—
203	C₂×H(3,ℤ/4)	—	47	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	2	1	no	—
206	C₂×C₄₇	—	2	1	no	—
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	8	2	no	—
209	C₂×C₄₇	#2098	1	2	yes	complemented
210	C₂×C₄₇	C₂×#399	1	1	yes	characteristic
211	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
212	C₂²×M₁₆	—	47	2	no	—
213	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
214	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
215	C₂×#117	—	47	2	no	—
216	#430	—	47	4	no	—
217	#430	—	94	2	no	—
218	C₂×#108	—	94	2	no	—
219	#424	—	47	8	no	—
220	#424	—	94	4	no	—
221	C₂×C₄⋊C₈	—	94	4	no	—
222	#421	—	47	8	no	—
223	#421	—	94	4	no	—
224	C₂×#104	—	94	4	no	—
225	#408	—	2	2	no	—
226	#408	C₂×D₄₇	1	4	yes	—
227	C₂×C₂²⋊C₈	—	2	2	no	—
228	H(3,ℤ/4)	—	47	4	no	—
229	C₄₇	C₂×#2098	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	2	1	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	Dic₉₄	1	2	yes	—
237	C₂×#41	C₂²×D₄₇	1	2	yes	—
238	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	47	4	no	—
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂×M₁₆	—	94	2	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
252	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
259	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
260	#117	—	47	4	no	—
261	#117	—	47	4	no	—
262	#117	—	94	2	no	—
263	#117	—	94	2	no	—
264	C₂×C₄⋊C₄	—	94	2	no	—
265	C₂×C₂²⋊C₄	—	94	2	no	—
266	C₂×C₄²	—	47	4	no	—
267	#108	—	94	8	no	—
268	C₄⋊C₈	—	94	16	no	—
269	#104	—	94	16	no	—
270	C₂²⋊C₈	—	2	8	no	—
271	C₂⁴	—	2	1	no	—
272	C₂⁴	#10625350	1	1	yes	characteristic
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	4	2	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×Dic₉₄	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	C₂×Dic₉₄	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	94	4	no	—
301	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
303	C₂²×C₄	#10625350	1	1	yes	characteristic
304	C₂²×C₄	D₄×D₄₇	1	2	yes	—
305	C₂²×C₄	D₄×D₄₇	1	2	yes	—
306	C₂²×C₄	#10625352	1	2	yes	—
307	C₂²×C₄	#10625352	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	94	4	no	—
314	M₁₆	—	94	4	no	—
315	M₁₆	—	188	2	no	—
316	M₁₆	—	188	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	94	4	no	—
325	C₂×C₈	—	188	2	no	—
326	C₂×C₈	—	188	2	no	—
327	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
328	C₄⋊C₄	—	94	4	no	—
329	C₄⋊C₄	—	94	4	no	—
330	C₂²⋊C₄	—	94	4	no	—
331	C₂²⋊C₄	—	94	4	no	—
332	C₄²	—	47	8	no	—
333	C₄²	—	94	4	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	#13094003	1	1	yes	characteristic
340	C₂³	#13094003	1	1	yes	characteristic
341	C₂³	#13094006	1	2	yes	—
342	C₂³	#13094006	1	2	yes	—
343	C₂³	C₂×#10625350	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	94	8	no	—
358	C₂×C₄	—	188	8	no	—
359	C₂×C₄	#13094001	1	2	yes	—
360	C₂×C₄	#13094001	1	2	yes	—
361	C₂×C₄	#13094001	1	2	yes	—
362	C₂×C₄	#13094001	1	2	yes	—
363	C₂×C₄	#13094003	1	1	yes	characteristic
364	C₂×C₄	#13094003	1	1	yes	characteristic
365	C₂×C₄	#13094005	1	1	yes	characteristic
366	C₂×C₄	#13094005	1	1	yes	characteristic
367	C₂×C₄	#13094005	1	2	yes	—
368	C₂×C₄	#13094006	1	2	yes	—
369	C₂×C₄	#13094006	1	2	yes	—
370	C₂×C₄	#13094020	1	2	yes	—
371	C₂×C₄	#13094020	1	1	yes	characteristic
372	C₂×C₄	#13094020	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
374	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625352	1	2	yes	—
377	C₈	—	2	4	no	—
378	C₈	—	4	2	no	—
379	C₈	—	188	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	#15689059	1	1	yes	characteristic
390	C₂²	#15689059	1	2	yes	—
391	C₂²	#15689059	1	1	yes	characteristic
392	C₂²	C₂×#13094003	1	1	yes	characteristic
393	C₂²	C₂×#13094006	1	2	yes	—
394	C₄	—	4	2	no	—
395	C₄	—	188	8	no	—
396	C₄	#15689059	1	1	yes	characteristic
397	C₄	#15689059	1	1	yes	characteristic
398	C₄	#15689059	1	2	yes	—
399	C₄	C₂×#13094001	1	2	yes	—
400	C₄	C₂×#13094005	1	1	yes	characteristic
401	C₄	C₂×#13094020	1	1	yes	characteristic
402	C₂	—	2	2	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	2	2	no	—
406	C₂	—	8	2	no	—
407	C₂	#20244941	1	2	yes	direct product factor
408	C₂	C₂×#15689059	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13094020
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#408	C₂
socle	C₂²×C₄₇	#399
prime radical	C₂²×#41×C₄₇	C₂²
hypercenter	C₂×#408	D₄₇
hypocenter	C₄₇	C₂×#2098
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#408

Complements

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

N	H ≅ G/N	type
1. C₂×#15689172	C₂	semidirect
2. C₂×#15689149	C₂	semidirect
4. #20244941	C₂	direct (N × H)
5. C₂×#15688880	C₂	semidirect
10. #15689172	C₂²	semidirect
13. #15689149	C₂²	semidirect
18. #15688880	C₂²	semidirect
209. C₂×C₄₇	#2098	semidirect
229. C₄₇	C₂×#2098	semidirect
407. C₂	#20244941	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×#15689172	2
C₂×#15689149	2
C₂×#15689140	2
#20244941	2
C₂×#15688880	2
C₂×C₄₇×#408	2
C₂×#2098	47

Subgroups — C2×#20244941 #26246160

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244941 #26246160