Subgroups — C₂×#20252292 #27080584

Order 12032.

2666 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689923	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13094030	C₂	1	2	yes	maximal, complemented
3	#20252292	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689246	C₂	1	4	yes	maximal, complemented
5	C₂×#15689241	C₂	1	4	yes	maximal, complemented
6	C₂×#15689172	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689141	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	2	yes	—
10	#15689923	C₄	1	8	yes	complemented
11	#15689923	C₂²	1	8	yes	—
12	C₂×#13094057	C₄	1	4	yes	complemented
13	C₂×#13094052	C₄	1	4	yes	complemented
14	C₂×#13094046	C₂²	1	4	yes	—
15	C₂×#13094030	—	2	2	no	—
16	C₂×#13094030	—	2	2	no	—
17	C₂×#13094030	—	2	8	no	—
18	C₂×#13094030	C₂²	1	4	yes	complemented
19	C₂×#13094030	C₂²	1	4	yes	complemented
20	C₂×#13094030	C₂²	1	16	yes	complemented
21	C₂²×#10625329	C₂²	1	2	yes	—
22	C₂²×#10625324	—	2	2	no	—
23	C₂²×C₈×D₄₇	—	2	2	no	—
24	#15689246	C₂²	1	32	yes	complemented
25	#15689241	C₂²	1	32	yes	complemented
26	#15689172	C₂²	1	8	yes	complemented
27	C₂×#13093960	C₂²	1	4	yes	complemented
28	#15689141	C₂²	1	16	yes	complemented
29	C₂×#13093952	C₂²	1	8	yes	complemented
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#405	C₂²	1	8	yes	complemented
34	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
35	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
36	C₂×#10625350	—	2	2	no	—
37	C₂×#10625350	—	2	4	no	—
38	C₂×#10625350	—	2	2	no	—
39	C₂×#10625350	—	2	4	no	—
40	C₂×#10625350	C₂×C₄	1	4	yes	—
41	C₂×#10625350	C₂×C₄	1	8	yes	—
42	C₂×#10625350	C₂³	1	4	yes	—
43	C₂×#10625350	C₂³	1	8	yes	—
44	C₂²×Dic₉₄	C₂×C₄	1	2	yes	—
45	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
46	C₂²×C₂²⋊D₄₇	—	2	2	no	—
47	C₂²×C₄×D₄₇	—	2	2	no	—
48	#13094057	C₂×C₄	1	32	yes	complemented
49	#13094052	C₂×C₄	1	32	yes	complemented
50	#13094046	C₂×C₄	1	16	yes	—
51	#13094046	C₂³	1	16	yes	—
52	C₂×Dic₁₈₈	C₂×C₄	1	4	yes	—
53	C₂×#10625325	C₂×C₄	1	8	yes	—
54	C₂×D₃₇₆	C₂×C₄	1	4	yes	—
55	#13094030	—	2	16	no	—
56	#13094030	—	2	16	no	—
57	#13094030	—	2	8	no	—
58	#13094030	—	2	8	no	—
59	#13094030	C₂³	1	16	yes	complemented
60	#13094030	C₂³	1	16	yes	complemented
61	C₂×#10625329	—	2	2	no	—
62	C₂×#10625329	—	2	4	no	—
63	C₂×#10625329	C₂³	1	4	yes	—
64	C₂×#10625329	C₂³	1	8	yes	—
65	C₂×#10625324	—	2	4	no	—
66	C₂×#10625324	—	2	4	no	—
67	C₂×#10625324	—	2	16	no	—
68	C₂²×C₄₇⋊C₈	—	2	2	no	—
69	C₂×C₈×D₄₇	—	2	4	no	—
70	C₂×C₈×D₄₇	—	2	16	no	—
71	C₂×C₈×D₄₇	—	2	4	no	—
72	#13093960	C₂³	1	16	yes	complemented
73	#13093952	C₂³	1	32	yes	complemented
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
77	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
78	C₂²×C₈×C₄₇	D₄	1	2	yes	—
79	C₂²×C₈×C₄₇	D₄	1	2	yes	—
80	C₂²×C₈×C₄₇	D₄	1	4	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
85	#117×C₄₇	—	2	2	no	—
86	#117×C₄₇	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
90	#97×C₄₇	C₂³	1	8	yes	complemented
91	C₄×C₈×C₄₇	C₂³	1	8	yes	complemented
92	C₂⁴×C₄₇	#41	1	1	yes	characteristic
93	C₂³×D₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
103	C₂×C₂²⋊D₄₇	—	2	4	no	—
104	C₂×C₂²⋊D₄₇	—	2	8	no	—
105	C₂×C₂²⋊D₄₇	—	2	4	no	—
106	C₂×C₂²⋊D₄₇	—	2	8	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	#10625350	—	2	8	no	—
109	#10625350	—	2	8	no	—
110	#10625350	—	2	8	no	—
111	#10625350	—	2	8	no	—
112	#10625350	—	2	4	no	—
113	#10625350	—	2	4	no	—
114	#10625350	—	2	8	no	—
115	#10625350	C₂²×C₄	1	8	yes	—
116	#10625350	C₂²×C₄	1	16	yes	—
117	#10625350	C₂⁴	1	8	yes	—
118	C₂×D₁₈₈	—	2	2	no	—
119	C₂×D₁₈₈	—	2	4	no	—
120	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
121	C₂×D₁₈₈	C₂²×C₄	1	8	yes	—
122	C₂×C₄×D₄₇	—	2	4	no	—
123	C₂×C₄×D₄₇	—	2	8	no	—
124	C₂×C₄×D₄₇	—	2	4	no	—
125	C₂×C₄×D₄₇	—	2	8	no	—
126	C₂×Dic₉₄	—	2	2	no	—
127	C₂×Dic₉₄	—	2	4	no	—
128	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
129	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
130	M₁₆×C₄₇	C₂²×C₄	1	16	yes	—
131	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	8	yes	—
135	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₇	C₂×D₄	1	8	yes	—
137	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
141	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
142	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
143	C₄⋊C₄×C₄₇	—	2	4	no	—
144	C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	C₂⁴	1	4	yes	—
147	#10625329	—	2	8	no	—
148	#10625329	—	2	4	no	—
149	#10625329	C₂⁴	1	8	yes	—
150	C₂×C₄₇⋊C₈	—	2	4	no	—
151	C₂×C₄₇⋊C₈	—	2	8	no	—
152	Dic₁₈₈	C₂²×C₄	1	16	yes	—
153	D₃₇₆	C₂²×C₄	1	16	yes	—
154	#10625325	C₂²×C₄	1	32	yes	—
155	#10625324	—	2	16	no	—
156	#10625324	—	2	16	no	—
157	C₈×D₄₇	—	2	16	no	—
158	C₈×D₄₇	—	2	16	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₄×D₄	1	2	yes	—
161	C₂³×C₄₇	C₄×D₄	1	2	yes	—
162	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂³×C₄₇	C₂×#41	1	2	yes	—
164	C₂²×D₄₇	—	2	8	no	—
165	C₂²×D₄₇	—	2	4	no	—
166	C₂²×D₄₇	—	4	8	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
171	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
172	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
181	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
182	C₂²⋊D₄₇	—	2	16	no	—
183	C₂²⋊D₄₇	—	2	8	no	—
184	C₂²⋊D₄₇	—	2	8	no	—
185	C₂×Dic₄₇	—	2	8	no	—
186	C₂×Dic₄₇	—	2	4	no	—
187	D₁₈₈	—	2	4	no	—
188	D₁₈₈	—	2	8	no	—
189	D₁₈₈	C₂³×C₄	1	8	yes	—
190	C₄×D₄₇	—	2	16	no	—
191	C₄×D₄₇	—	2	8	no	—
192	C₄×D₄₇	—	2	8	no	—
193	Dic₉₄	—	2	4	no	—
194	Dic₉₄	—	2	8	no	—
195	Dic₉₄	C₂³×C₄	1	8	yes	—
196	C₈×C₄₇	C₂³×C₄	1	8	yes	—
197	C₈×C₄₇	C₂²×D₄	1	2	yes	—
198	C₈×C₄₇	C₂²×D₄	1	4	yes	—
199	C₈×C₄₇	C₂²×D₄	1	2	yes	—
200	C₄₇⋊C₈	—	2	8	no	—
201	C₂×#2955	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	2	4	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
210	C₂×D₄₇	—	2	8	no	—
211	C₂×D₄₇	—	4	16	no	—
212	C₂×D₄₇	—	4	8	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₇	C₂×C₄×D₄	1	4	yes	—
216	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
218	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
219	Dic₄₇	—	2	8	no	—
220	C₂×#575	—	47	1	no	—
221	C₂²×#131	—	47	2	no	—
222	#2955	—	47	16	no	—
223	C₂×#444	—	47	4	no	—
224	C₂×#443	—	47	4	no	—
225	C₂×#430	—	47	1	no	—
226	C₂×#421	—	47	2	no	—
227	C₂×#405	D₄₇	1	1	yes	characteristic, complemented
228	C₂×C₄₇	—	2	1	no	—
229	C₂×C₄₇	—	2	4	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	#2955	1	2	yes	complemented
232	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
233	D₄₇	—	4	8	no	—
234	C₂²×#41	—	47	2	no	—
235	#575	—	47	8	no	—
236	#575	—	47	8	no	—
237	C₂×#137	—	47	4	no	—
238	C₂×AGL(1,ℤ/8)	—	47	4	no	—
239	C₂×#135	—	47	4	no	—
240	C₂×#131	—	47	4	no	—
241	C₂×#131	—	47	4	no	—
242	C₂×#131	—	47	16	no	—
243	C₂×#131	—	94	2	no	—
244	C₂×#131	—	94	8	no	—
245	C₂×#131	—	94	2	no	—
246	C₂²×M₁₆	—	47	2	no	—
247	C₂²×M₁₆	—	94	2	no	—
248	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
249	C₂³×C₈	—	94	2	no	—
250	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
252	#444	—	47	32	no	—
253	#443	—	47	32	no	—
254	#430	—	47	8	no	—
255	C₂×#108	—	47	4	no	—
256	#421	—	47	16	no	—
257	C₂×#104	—	47	8	no	—
258	#405	C₂×D₄₇	1	8	yes	complemented
259	C₂×#97	C₂×D₄₇	1	2	yes	complemented
260	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	complemented
261	C₄₇	C₂×#2955	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	47	4	no	—
263	C₂×#41	—	47	8	no	—
264	C₂×#41	—	47	4	no	—
265	C₂×#41	—	47	8	no	—
266	C₂×#41	—	94	2	no	—
267	C₂×#41	—	94	4	no	—
268	C₂×#41	—	94	2	no	—
269	C₂×#41	—	94	4	no	—
270	C₂²×Q₈	—	47	2	no	—
271	C₂²×D₄	—	47	2	no	—
272	C₂²×D₄	—	94	2	no	—
273	C₂³×C₄	—	94	2	no	—
274	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
275	#137	—	47	32	no	—
276	AGL(1,ℤ/8)	—	47	32	no	—
277	#135	—	47	16	no	—
278	#135	—	47	16	no	—
279	C₂×Q₁₆	—	47	4	no	—
280	C₂×SD₁₆	—	47	8	no	—
281	C₂×D₈	—	47	4	no	—
282	#131	—	47	16	no	—
283	#131	—	47	16	no	—
284	#131	—	94	16	no	—
285	#131	—	94	16	no	—
286	#131	—	94	8	no	—
287	#131	—	94	8	no	—
288	C₂×M₁₆	—	47	4	no	—
289	C₂×M₁₆	—	47	8	no	—
290	C₂×M₁₆	—	94	2	no	—
291	C₂×M₁₆	—	94	4	no	—
292	C₂×M₁₆	—	94	4	no	—
293	C₂×M₁₆	—	94	4	no	—
294	C₂×M₁₆	—	94	16	no	—
295	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
296	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
297	C₂×M₁₆	C₂²×D₄₇	1	4	yes	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	—	94	4	no	—
300	C₂²×C₈	—	94	16	no	—
301	C₂²×C₈	—	94	4	no	—
302	C₂²×C₈	D₁₈₈	1	2	yes	—
303	C₂²×C₈	D₁₈₈	1	4	yes	—
304	C₂²×C₈	D₁₈₈	1	2	yes	—
305	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
306	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	#117	—	2	2	no	—
310	#117	C₂²×D₄₇	1	4	yes	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
314	#108	—	47	16	no	—
315	#104	—	47	32	no	—
316	#97	C₂²×D₄₇	1	8	yes	complemented
317	C₄×C₈	C₂²×D₄₇	1	8	yes	complemented
318	C₂⁴	—	94	2	no	—
319	C₂⁴	#10625350	1	1	yes	characteristic
320	#41	—	47	8	no	—
321	#41	—	47	16	no	—
322	#41	—	47	8	no	—
323	#41	—	94	8	no	—
324	#41	—	94	8	no	—
325	#41	—	94	8	no	—
326	#41	—	94	8	no	—
327	#41	—	94	4	no	—
328	#41	—	94	4	no	—
329	#41	—	94	8	no	—
330	C₂×Q₈	—	47	4	no	—
331	C₂×Q₈	—	47	8	no	—
332	C₂×Q₈	—	94	2	no	—
333	C₂×Q₈	—	94	4	no	—
334	C₂×D₄	—	47	4	no	—
335	C₂×D₄	—	47	8	no	—
336	C₂×D₄	—	94	4	no	—
337	C₂×D₄	—	94	8	no	—
338	C₂×D₄	—	94	4	no	—
339	C₂×D₄	—	94	8	no	—
340	C₂×D₄	—	94	2	no	—
341	C₂×D₄	—	94	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	—	94	4	no	—
345	C₂²×C₄	—	94	8	no	—
346	C₂²×C₄	—	94	4	no	—
347	C₂²×C₄	—	94	8	no	—
348	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
349	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
350	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
351	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
352	C₂²×C₄	#10625350	1	1	yes	characteristic
353	C₂²×C₄	#10625350	1	2	yes	—
354	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
356	Q₁₆	—	47	16	no	—
357	SD₁₆	—	47	32	no	—
358	D₈	—	47	16	no	—
359	M₁₆	—	47	8	no	—
360	M₁₆	—	94	8	no	—
361	M₁₆	—	94	4	no	—
362	M₁₆	—	94	16	no	—
363	M₁₆	—	94	16	no	—
364	M₁₆	C₂×C₄×D₄₇	1	16	yes	—
365	C₂×C₈	—	94	4	no	—
366	C₂×C₈	—	94	8	no	—
367	C₂×C₈	—	94	16	no	—
368	C₂×C₈	—	94	16	no	—
369	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
370	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
371	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
372	C₂×C₈	C₂×D₁₈₈	1	8	yes	—
373	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
374	C₂×C₈	C₂×D₁₈₈	1	8	yes	—
375	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
376	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
377	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
378	C₂×C₈	C₂³×D₄₇	1	4	yes	—
379	C₂×C₈	C₂³×D₄₇	1	2	yes	—
380	C₂×C₈	C₂³×D₄₇	1	2	yes	—
381	C₄⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂³×D₄₇	1	4	yes	—
385	C₂³	—	4	2	no	—
386	C₂³	—	94	8	no	—
387	C₂³	—	94	4	no	—
388	C₂³	—	188	8	no	—
389	C₂³	C₄×D₁₈₈	1	2	yes	—
390	C₂³	C₄×D₁₈₈	1	2	yes	—
391	C₂³	C₂×#10625350	1	1	yes	characteristic
392	C₂³	C₂×#10625350	1	2	yes	—
393	Q₈	—	47	8	no	—
394	Q₈	—	94	8	no	—
395	Q₈	—	94	4	no	—
396	D₄	—	47	8	no	—
397	D₄	—	94	16	no	—
398	D₄	—	94	8	no	—
399	D₄	—	94	8	no	—
400	D₄	—	94	8	no	—
401	D₄	—	94	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	94	8	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	94	8	no	—
407	C₂×C₄	—	94	16	no	—
408	C₂×C₄	—	94	8	no	—
409	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
410	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
411	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
412	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
416	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
418	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
419	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
420	C₂×C₄	C₂×#10625350	1	2	yes	—
421	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
422	C₈	—	94	8	no	—
423	C₈	C₂²×C₄×D₄₇	1	8	yes	—
424	C₈	C₂²×D₁₈₈	1	2	yes	—
425	C₈	C₂²×D₁₈₈	1	4	yes	—
426	C₈	C₂²×D₁₈₈	1	2	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	94	8	no	—
432	C₂²	—	188	16	no	—
433	C₂²	—	188	8	no	—
434	C₂²	C₂×C₄×D₁₈₈	1	4	yes	—
435	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
436	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
437	C₂²	C₂²×#10625350	1	1	yes	characteristic
438	C₄	—	4	4	no	—
439	C₄	—	94	8	no	—
440	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
441	C₄	C₂×C₄×D₁₈₈	1	4	yes	—
442	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
443	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
444	C₄	C₂³×D₁₈₈	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	4	no	—
447	C₂	—	2	1	no	—
448	C₂	—	188	8	no	—
449	C₂	#20252292	1	2	yes	direct product factor
450	C₂	C₂²×C₄×D₁₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#15689923	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	C₂×#2955
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂²×#13094030	C₂	semidirect
3. #20252292	C₂	direct (N × H)
4. C₂×#15689246	C₂	semidirect
5. C₂×#15689241	C₂	semidirect
6. C₂×#15689172	C₂	semidirect
7. C₂×#15689141	C₂	semidirect
8. C₂×C₄₇×#405	C₂	semidirect
10. #15689923	C₄	semidirect
12. C₂×#13094057	C₄	semidirect
13. C₂×#13094052	C₄	semidirect
18. C₂×#13094030	C₂²	semidirect
19. C₂×#13094030	C₂²	semidirect
20. C₂×#13094030	C₂²	semidirect
24. #15689246	C₂²	semidirect
25. #15689241	C₂²	semidirect
26. #15689172	C₂²	semidirect
27. C₂×#13093960	C₂²	semidirect
28. #15689141	C₂²	semidirect
29. C₂×#13093952	C₂²	semidirect
33. C₄₇×#405	C₂²	semidirect
34. C₂×#97×C₄₇	C₂²	semidirect
35. C₂×C₄×C₈×C₄₇	C₂²	semidirect
48. #13094057	C₂×C₄	semidirect
49. #13094052	C₂×C₄	semidirect
59. #13094030	C₂³	semidirect
60. #13094030	C₂³	semidirect
72. #13093960	C₂³	semidirect
73. #13093952	C₂³	semidirect
90. #97×C₄₇	C₂³	semidirect
91. C₄×C₈×C₄₇	C₂³	semidirect
227. C₂×#405	D₄₇	semidirect
231. C₂×C₄₇	#2955	semidirect
258. #405	C₂×D₄₇	semidirect
259. C₂×#97	C₂×D₄₇	semidirect
260. C₂×C₄×C₈	C₂×D₄₇	semidirect
261. C₄₇	C₂×#2955	semidirect
316. #97	C₂²×D₄₇	semidirect
317. C₄×C₈	C₂²×D₄₇	semidirect
449. C₂	#20252292	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×#15689923	2
C₂²×#13094030	2
#20252292	2
C₂×#15689246	2
C₂×#15689241	2
C₂×#15689172	2
C₂×#15689141	2
C₂×C₄₇×#405	2
C₂×#2955	47

Subgroups — C2×#20252292 #27080584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20252292 #27080584