Subgroups — C₂²×#15689243 #27080573

Order 12032.

2710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094044	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13094030	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689243	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093934	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#131×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	C₂×#13094044	C₄	1	12	yes	complemented
11	C₂×#13094044	C₂²	1	12	yes	—
12	C₂²×#10625337	C₄	1	1	yes	characteristic, complemented
13	C₂²×#10625335	C₄	1	1	yes	characteristic, complemented
14	C₂²×#10625336	C₄	1	1	yes	characteristic, complemented
15	C₂²×#10625334	C₄	1	1	yes	characteristic, complemented
16	C₂×#13094030	—	2	6	no	—
17	C₂×#13094030	C₂²	1	12	yes	complemented
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×#10625324	—	2	1	no	—
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₄₇	—	2	1	no	—
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	#15689243	C₂²	1	64	yes	direct product factor
24	C₂×#13093959	C₂²	1	12	yes	complemented
25	C₂×#13093951	C₂²	1	12	yes	complemented
26	C₂×#13093950	C₂²	1	12	yes	complemented
27	C₂×#13093934	C₂²	1	12	yes	complemented
28	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₄₇	—	2	6	no	—
30	C₂×#131×C₄₇	C₂²	1	12	yes	complemented
31	C₂²×M₁₆×C₄₇	—	2	1	no	—
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₄₇	—	2	1	no	—
34	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#10625350	—	2	3	no	—
36	C₂×#10625350	—	2	3	no	—
37	C₂×#10625350	C₂×C₄	1	6	yes	—
38	C₂×#10625350	C₂³	1	6	yes	—
39	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
40	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₂²⋊D₄₇	—	2	1	no	—
42	C₂³×Dic₄₇	—	2	1	no	—
43	C₂²×C₄×D₄₇	—	2	1	no	—
44	#13094044	C₂×C₄	1	48	yes	complemented
45	#13094044	C₂³	1	16	yes	—
46	C₂×#10625337	C₂×C₄	1	12	yes	complemented
47	C₂×#10625335	C₂×C₄	1	12	yes	complemented
48	C₂×#10625336	C₂×C₄	1	12	yes	complemented
49	C₂×#10625334	C₂×C₄	1	12	yes	complemented
50	#13094030	—	2	24	no	—
51	#13094030	C₂³	1	16	yes	complemented
52	C₂×#10625329	—	2	3	no	—
53	C₂×#10625329	C₂³	1	6	yes	—
54	C₂×#10625324	—	2	12	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
59	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
60	C₂×C₈×D₄₇	—	2	12	no	—
61	C₂×C₄×Dic₄₇	—	2	3	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
63	#13093959	C₂³	1	16	yes	complemented
64	#13093951	C₂³	1	16	yes	complemented
65	#13093950	C₂³	1	16	yes	complemented
66	#13093934	C₂³	1	16	yes	complemented
67	C₂×#41×C₄₇	—	2	3	no	—
68	C₂×#41×C₄₇	—	2	3	no	—
69	C₂×#41×C₄₇	C₂×C₄	1	6	yes	—
70	C₂×#41×C₄₇	C₂³	1	6	yes	—
71	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	—	2	1	no	—
75	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
76	#131×C₄₇	—	2	24	no	—
77	#131×C₄₇	C₂³	1	16	yes	complemented
78	C₂×M₁₆×C₄₇	—	2	3	no	—
79	C₂×M₁₆×C₄₇	—	2	12	no	—
80	C₂×M₁₆×C₄₇	C₂³	1	6	yes	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	C₂²×C₈×C₄₇	—	2	12	no	—
83	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	D₄	1	6	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	6	yes	—
87	C₂⁴×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	#41	1	1	yes	characteristic
89	C₂³×D₄₇	—	2	1	no	—
90	#41×C₄₇	—	2	12	no	—
91	#41×C₄₇	—	2	6	no	—
92	#41×C₄₇	—	2	6	no	—
93	#41×C₄₇	C₂²×C₄	1	12	yes	—
94	#41×C₄₇	C₂⁴	1	4	yes	—
95	C₂×Q₈×C₄₇	—	2	3	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	6	yes	—
97	C₂×D₄×C₄₇	—	2	6	no	—
98	C₂×D₄×C₄₇	—	2	6	no	—
99	C₂×D₄×C₄₇	—	2	3	no	—
100	C₂×D₄×C₄₇	C₂²×C₄	1	6	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	6	no	—
103	C₂²×C₄×C₄₇	—	2	6	no	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	3	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
110	C₂×C₂²⋊D₄₇	—	2	6	no	—
111	C₂×C₂²⋊D₄₇	—	2	6	no	—
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂²×Dic₄₇	—	2	6	no	—
114	C₂²×Dic₄₇	—	4	4	no	—
115	#10625350	—	2	12	no	—
116	#10625350	—	2	6	no	—
117	#10625350	—	2	6	no	—
118	#10625350	C₂²×C₄	1	12	yes	—
119	#10625350	C₂⁴	1	4	yes	—
120	C₂×D₁₈₈	—	2	3	no	—
121	C₂×D₁₈₈	C₂²×C₄	1	6	yes	—
122	C₂×C₄×D₄₇	—	2	6	no	—
123	C₂×C₄×D₄₇	—	2	6	no	—
124	C₂×Dic₉₄	—	2	3	no	—
125	C₂×Dic₉₄	C₂²×C₄	1	6	yes	—
126	M₁₆×C₄₇	—	2	6	no	—
127	M₁₆×C₄₇	—	2	16	no	—
128	M₁₆×C₄₇	C₂⁴	1	4	yes	—
129	C₂×C₈×C₄₇	—	2	6	no	—
130	C₂×C₈×C₄₇	—	2	16	no	—
131	C₂×C₈×C₄₇	C₂×D₄	1	6	yes	—
132	C₂×C₈×C₄₇	C₂×D₄	1	6	yes	—
133	C₂×C₈×C₄₇	C₂×D₄	1	12	yes	—
134	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
135	#10625337	C₂²×C₄	1	16	yes	complemented
136	#10625336	C₂²×C₄	1	16	yes	complemented
137	#10625335	C₂²×C₄	1	16	yes	complemented
138	#10625334	C₂²×C₄	1	16	yes	complemented
139	C₄×Dic₄₇	—	2	6	no	—
140	C₄×Dic₄₇	C₂⁴	1	4	yes	—
141	#10625329	—	2	6	no	—
142	#10625329	C₂⁴	1	4	yes	—
143	C₂×C₄₇⋊C₈	—	2	6	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	6	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	6	yes	—
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	12	yes	—
147	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
148	#10625324	—	2	16	no	—
149	C₈×D₄₇	—	2	16	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	6	no	—
152	C₂³×C₄₇	—	4	4	no	—
153	C₂³×C₄₇	C₄×D₄	1	3	yes	—
154	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
155	C₂³×C₄₇	C₂×#41	1	3	yes	—
156	C₂²×D₄₇	—	2	6	no	—
157	C₂²×D₄₇	—	4	4	no	—
158	Q₈×C₄₇	—	2	6	no	—
159	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
160	D₄×C₄₇	—	2	12	no	—
161	D₄×C₄₇	—	2	4	no	—
162	D₄×C₄₇	—	2	6	no	—
163	D₄×C₄₇	C₂³×C₄	1	4	yes	—
164	C₂×C₄×C₄₇	—	2	6	no	—
165	C₂×C₄×C₄₇	—	2	12	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	C₄×D₄	1	3	yes	—
168	C₂×C₄×C₄₇	C₄×D₄	1	3	yes	—
169	C₂×C₄×C₄₇	C₄×D₄	1	6	yes	—
170	C₂×C₄×C₄₇	C₂³×C₄	1	3	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	3	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
173	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
174	C₂×C₄×C₄₇	C₂×#41	1	3	yes	—
175	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
176	C₂²⋊D₄₇	—	2	12	no	—
177	C₂²⋊D₄₇	—	2	4	no	—
178	C₂×Dic₄₇	—	2	6	no	—
179	C₂×Dic₄₇	—	2	4	no	—
180	C₂×Dic₄₇	—	4	12	no	—
181	D₁₈₈	—	2	6	no	—
182	D₁₈₈	C₂³×C₄	1	4	yes	—
183	C₄×D₄₇	—	2	12	no	—
184	C₄×D₄₇	—	2	4	no	—
185	Dic₉₄	—	2	6	no	—
186	Dic₉₄	C₂³×C₄	1	4	yes	—
187	C₈×C₄₇	—	2	4	no	—
188	C₈×C₄₇	C₂²×D₄	1	4	yes	—
189	C₈×C₄₇	C₂²×D₄	1	4	yes	—
190	C₄₇⋊C₈	—	2	4	no	—
191	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
192	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
193	C₂²×#444	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	—	2	6	no	—
195	C₂²×C₄₇	—	2	6	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	4	12	no	—
198	C₂²×C₄₇	#444	1	4	yes	complemented
199	C₂²×C₄₇	C₂×C₄×D₄	1	3	yes	—
200	C₂²×C₄₇	C₂×C₄×D₄	1	3	yes	—
201	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
202	C₂×D₄₇	—	2	4	no	—
203	C₂×D₄₇	—	4	12	no	—
204	C₄×C₄₇	—	2	4	no	—
205	C₄×C₄₇	C₂×C₄×D₄	1	3	yes	—
206	C₄×C₄₇	C₂×C₄×D₄	1	3	yes	—
207	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
208	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
209	Dic₄₇	—	2	4	no	—
210	Dic₄₇	—	4	4	no	—
211	C₂²×#135	—	47	1	no	—
212	C₂²×#131	—	47	1	no	—
213	C₂²×#131	D₄₇	1	1	yes	characteristic, complemented
214	C₂×#444	—	47	24	no	—
215	C₂²×#108	—	47	1	no	—
216	C₂²×#104	—	47	1	no	—
217	C₂²×#104	—	47	1	no	—
218	C₂²×#97	—	47	1	no	—
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	2	3	no	—
221	C₂×C₄₇	—	4	4	no	—
222	C₂×C₄₇	C₂×#444	1	6	yes	complemented
223	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
224	D₄₇	—	4	4	no	—
225	C₂²×#41	—	47	1	no	—
226	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#135	—	47	12	no	—
228	C₂×#135	—	47	12	no	—
229	C₂²×Q₁₆	—	47	1	no	—
230	C₂²×SD₁₆	—	47	1	no	—
231	C₂²×SD₁₆	—	47	1	no	—
232	C₂²×D₈	—	47	1	no	—
233	C₂×#131	—	2	6	no	—
234	C₂×#131	—	47	12	no	—
235	C₂×#131	—	94	6	no	—
236	C₂×#131	C₂×D₄₇	1	12	yes	complemented
237	C₂²×M₁₆	—	2	1	no	—
238	C₂²×M₁₆	—	47	1	no	—
239	C₂²×M₁₆	—	94	1	no	—
240	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
241	C₂³×C₈	—	2	1	no	—
242	C₂³×C₈	—	47	1	no	—
243	C₂³×C₈	—	94	1	no	—
244	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂²×C₄²	—	47	1	no	—
246	#444	—	47	64	no	—
247	C₂×#108	—	47	12	no	—
248	C₂×#104	—	47	12	no	—
249	C₂×#104	—	47	12	no	—
250	C₂×#97	—	47	12	no	—
251	C₄₇	C₂²×#444	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	2	3	no	—
253	C₂×#41	—	2	3	no	—
254	C₂×#41	—	47	6	no	—
255	C₂×#41	—	47	6	no	—
256	C₂×#41	—	94	3	no	—
257	C₂×#41	—	94	3	no	—
258	C₂×#41	C₄×D₄₇	1	6	yes	—
259	C₂×#41	C₂²×D₄₇	1	6	yes	—
260	C₂²×Q₈	—	47	1	no	—
261	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	—	47	1	no	—
264	C₂²×D₄	—	94	1	no	—
265	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	—	94	1	no	—
268	C₂³×C₄	—	94	1	no	—
269	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
270	#135	—	47	48	no	—
271	#135	—	47	16	no	—
272	C₂×Q₁₆	—	47	12	no	—
273	C₂×SD₁₆	—	47	12	no	—
274	C₂×SD₁₆	—	47	12	no	—
275	C₂×D₈	—	47	12	no	—
276	#131	—	2	24	no	—
277	#131	—	47	16	no	—
278	#131	—	94	24	no	—
279	#131	C₂²×D₄₇	1	16	yes	complemented
280	C₂×M₁₆	—	2	3	no	—
281	C₂×M₁₆	—	2	12	no	—
282	C₂×M₁₆	—	47	6	no	—
283	C₂×M₁₆	—	94	3	no	—
284	C₂×M₁₆	—	94	12	no	—
285	C₂×M₁₆	C₂²×D₄₇	1	6	yes	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	12	no	—
288	C₂²×C₈	—	47	1	no	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	6	no	—
291	C₂²×C₈	—	47	6	no	—
292	C₂²×C₈	—	94	1	no	—
293	C₂²×C₈	—	94	12	no	—
294	C₂²×C₈	C₂²⋊D₄₇	1	6	yes	—
295	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₄₇	1	6	yes	—
298	C₂×C₄²	—	47	6	no	—
299	C₂×C₄²	—	94	3	no	—
300	#108	—	47	16	no	—
301	#104	—	47	16	no	—
302	#104	—	47	16	no	—
303	#97	—	47	16	no	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	—	94	1	no	—
306	C₂⁴	#10625350	1	1	yes	characteristic
307	#41	—	2	12	no	—
308	#41	—	2	6	no	—
309	#41	—	2	6	no	—
310	#41	—	47	12	no	—
311	#41	—	47	4	no	—
312	#41	—	94	12	no	—
313	#41	—	94	6	no	—
314	#41	—	94	6	no	—
315	#41	C₂×C₄×D₄₇	1	12	yes	—
316	#41	C₂³×D₄₇	1	4	yes	—
317	C₂×Q₈	—	2	3	no	—
318	C₂×Q₈	—	47	6	no	—
319	C₂×Q₈	—	94	3	no	—
320	C₂×Q₈	C₂×C₄×D₄₇	1	6	yes	—
321	C₂×D₄	—	2	6	no	—
322	C₂×D₄	—	2	6	no	—
323	C₂×D₄	—	2	3	no	—
324	C₂×D₄	—	47	6	no	—
325	C₂×D₄	—	94	6	no	—
326	C₂×D₄	—	94	6	no	—
327	C₂×D₄	—	94	3	no	—
328	C₂×D₄	C₂×C₄×D₄₇	1	6	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	6	no	—
331	C₂²×C₄	—	2	6	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	94	6	no	—
334	C₂²×C₄	—	94	6	no	—
335	C₂²×C₄	—	94	6	no	—
336	C₂²×C₄	—	188	4	no	—
337	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
339	C₂²×C₄	#10625350	1	3	yes	—
340	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
341	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
343	Q₁₆	—	47	16	no	—
344	SD₁₆	—	47	16	no	—
345	SD₁₆	—	47	16	no	—
346	D₈	—	47	16	no	—
347	M₁₆	—	2	6	no	—
348	M₁₆	—	2	16	no	—
349	M₁₆	—	47	4	no	—
350	M₁₆	—	94	6	no	—
351	M₁₆	—	94	16	no	—
352	M₁₆	C₂³×D₄₇	1	4	yes	—
353	C₂×C₈	—	2	6	no	—
354	C₂×C₈	—	2	16	no	—
355	C₂×C₈	—	47	6	no	—
356	C₂×C₈	—	47	6	no	—
357	C₂×C₈	—	47	12	no	—
358	C₂×C₈	—	47	4	no	—
359	C₂×C₈	—	94	6	no	—
360	C₂×C₈	—	94	16	no	—
361	C₂×C₈	C₂×C₂²⋊D₄₇	1	6	yes	—
362	C₂×C₈	C₂×C₂²⋊D₄₇	1	6	yes	—
363	C₂×C₈	C₂×C₂²⋊D₄₇	1	12	yes	—
364	C₂×C₈	C₂³×D₄₇	1	4	yes	—
365	C₄²	—	47	4	no	—
366	C₄²	—	94	6	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	6	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	94	6	no	—
371	C₂³	—	188	4	no	—
372	C₂³	C₄×C₂²⋊D₄₇	1	3	yes	—
373	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂³	C₂×#10625350	1	3	yes	—
375	Q₈	—	2	6	no	—
376	Q₈	—	47	4	no	—
377	Q₈	—	94	6	no	—
378	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
379	D₄	—	2	12	no	—
380	D₄	—	2	4	no	—
381	D₄	—	2	6	no	—
382	D₄	—	47	4	no	—
383	D₄	—	94	12	no	—
384	D₄	—	94	4	no	—
385	D₄	—	94	6	no	—
386	D₄	C₂²×C₄×D₄₇	1	4	yes	—
387	C₂×C₄	—	2	6	no	—
388	C₂×C₄	—	2	12	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	94	6	no	—
391	C₂×C₄	—	94	12	no	—
392	C₂×C₄	—	94	4	no	—
393	C₂×C₄	—	94	4	no	—
394	C₂×C₄	—	188	12	no	—
395	C₂×C₄	C₄×C₂²⋊D₄₇	1	3	yes	—
396	C₂×C₄	C₄×C₂²⋊D₄₇	1	3	yes	—
397	C₂×C₄	C₄×C₂²⋊D₄₇	1	6	yes	—
398	C₂×C₄	C₂²×C₄×D₄₇	1	3	yes	—
399	C₂×C₄	C₂²×C₄×D₄₇	1	3	yes	—
400	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
401	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
402	C₂×C₄	C₂×#10625350	1	3	yes	—
403	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	47	4	no	—
406	C₈	—	47	4	no	—
407	C₈	—	94	4	no	—
408	C₈	C₂²×C₂²⋊D₄₇	1	4	yes	—
409	C₈	C₂²×C₂²⋊D₄₇	1	4	yes	—
410	C₂²	—	2	6	no	—
411	C₂²	—	2	6	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	4	12	no	—
414	C₂²	—	94	4	no	—
415	C₂²	—	188	12	no	—
416	C₂²	#15689243	1	4	yes	direct product factor
417	C₂²	C₂×C₄×C₂²⋊D₄₇	1	3	yes	—
418	C₂²	C₂×C₄×C₂²⋊D₄₇	1	3	yes	—
419	C₂²	C₂²×#10625350	1	1	yes	characteristic
420	C₄	—	2	4	no	—
421	C₄	—	94	4	no	—
422	C₄	—	188	4	no	—
423	C₄	C₂×C₄×C₂²⋊D₄₇	1	3	yes	—
424	C₄	C₂×C₄×C₂²⋊D₄₇	1	3	yes	—
425	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
426	C₄	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	3	no	—
429	C₂	—	4	4	no	—
430	C₂	—	188	4	no	—
431	C₂	C₂×#15689243	1	6	yes	direct product factor
432	C₂	C₂²×C₄×C₂²⋊D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×#131×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#13094044	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×#131	D₄₇
hypocenter	C₄₇	C₂²×#444
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
2. C₂²×#13094030	C₂	semidirect
3. C₂×#15689243	C₂	direct (N × H)
4. C₂²×#13093959	C₂	semidirect
5. C₂²×#13093951	C₂	semidirect
6. C₂²×#13093950	C₂	semidirect
7. C₂²×#13093934	C₂	semidirect
8. C₂²×#131×C₄₇	C₂	semidirect
10. C₂×#13094044	C₄	semidirect
12. C₂²×#10625337	C₄	semidirect
13. C₂²×#10625335	C₄	semidirect
14. C₂²×#10625336	C₄	semidirect
15. C₂²×#10625334	C₄	semidirect
17. C₂×#13094030	C₂²	semidirect
23. #15689243	C₂²	direct (N × H)
24. C₂×#13093959	C₂²	semidirect
25. C₂×#13093951	C₂²	semidirect
26. C₂×#13093950	C₂²	semidirect
27. C₂×#13093934	C₂²	semidirect
30. C₂×#131×C₄₇	C₂²	semidirect
44. #13094044	C₂×C₄	semidirect
46. C₂×#10625337	C₂×C₄	semidirect
47. C₂×#10625335	C₂×C₄	semidirect
48. C₂×#10625336	C₂×C₄	semidirect
49. C₂×#10625334	C₂×C₄	semidirect
51. #13094030	C₂³	semidirect
63. #13093959	C₂³	semidirect
64. #13093951	C₂³	semidirect
65. #13093950	C₂³	semidirect
66. #13093934	C₂³	semidirect
77. #131×C₄₇	C₂³	semidirect
135. #10625337	C₂²×C₄	semidirect
136. #10625336	C₂²×C₄	semidirect
137. #10625335	C₂²×C₄	semidirect
138. #10625334	C₂²×C₄	semidirect
198. C₂²×C₄₇	#444	semidirect
213. C₂²×#131	D₄₇	semidirect
222. C₂×C₄₇	C₂×#444	semidirect
236. C₂×#131	C₂×D₄₇	semidirect
251. C₄₇	C₂²×#444	semidirect
279. #131	C₂²×D₄₇	semidirect
416. C₂²	#15689243	direct (N × H)
431. C₂	C₂×#15689243	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×#13094044	2
C₂²×#13094030	2
C₂×#15689243	2
C₂²×#13093959	2
C₂²×#13093951	2
C₂²×#13093950	2
C₂²×#13093934	2
C₂²×#131×C₄₇	2
C₂²×#444	47

Subgroups — C22×#15689243 #27080573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689243 #27080573