Subgroups — C₂×C₄×#13093951 #26213988

Order 12032.

1878 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	C₂²×#13093951	C₂	1	2	yes	maximal
2	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13093951	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688882	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10625329	C₂²	1	2	yes	—
8	C₂²×C₄×Dic₄₇	—	2	2	no	—
9	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
10	C₂×#13093951	C₄	1	16	yes	direct product factor
11	C₂×#13093951	C₂²	1	8	yes	—
12	C₄×#10625329	—	2	2	no	—
13	C₄×#10625329	C₂²	1	4	yes	complemented
14	C₂×#13093935	—	2	1	no	—
15	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
16	C₄²×Dic₄₇	—	2	2	no	—
17	C₄²×Dic₄₇	C₂²	1	4	yes	complemented
18	#15688882	C₂²	1	8	yes	complemented
19	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×#41×C₄₇	—	2	2	no	—
21	C₄×#41×C₄₇	—	2	2	no	—
22	C₄×#41×C₄₇	C₄	1	4	yes	complemented
23	C₄×#41×C₄₇	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	complemented
25	C₂×C₄×D₄×C₄₇	—	2	2	no	—
26	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	complemented
27	C₂×#117×C₄₇	—	2	1	no	—
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	—	2	1	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×Dic₄₇	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	C₂×C₄	1	8	yes	complemented
35	C₂×#10625329	C₂³	1	4	yes	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	16	no	—
38	C₂×C₄×Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	8	no	—
40	C₂×C₄×Dic₄₇	—	2	4	no	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	complemented
42	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
43	#13093951	C₂×C₄	1	32	yes	direct product factor
44	#13093935	—	2	4	no	—
45	C₄×C₄₇⋊C₈	—	2	4	no	—
46	C₂×#41×C₄₇	—	2	1	no	—
47	C₂×#41×C₄₇	—	2	1	no	—
48	C₂×#41×C₄₇	—	2	4	no	—
49	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
50	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×#41×C₄₇	C₂³	1	2	yes	—
52	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂³×C₄×C₄₇	—	2	2	no	—
57	C₂³×C₄×C₄₇	D₄	1	2	yes	—
58	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₄×Q₈×C₄₇	—	2	4	no	—
60	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₄₇	—	2	8	no	—
62	C₄×D₄×C₄₇	—	2	8	no	—
63	C₄×D₄×C₄₇	—	2	4	no	—
64	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
65	#117×C₄₇	—	2	1	no	—
66	#117×C₄₇	—	2	1	no	—
67	#117×C₄₇	—	2	4	no	—
68	#117×C₄₇	—	2	4	no	—
69	#117×C₄₇	C₂×C₄	1	2	yes	—
70	#117×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	—	2	4	no	—
78	C₂×C₄²×C₄₇	—	2	4	no	—
79	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	D₄	1	2	yes	—
82	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	D₄	1	2	yes	—
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
88	#41×C₄₇	—	2	4	no	—
89	#41×C₄₇	—	2	8	no	—
90	#41×C₄₇	—	2	8	no	—
91	#41×C₄₇	—	2	4	no	—
92	#41×C₄₇	C₄²	1	8	yes	complemented
93	#41×C₄₇	C₂²×C₄	1	8	yes	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	C₄²	1	4	yes	complemented
97	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	8	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	C₄²	1	4	yes	complemented
104	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	8	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	8	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	8	no	—
112	C₂²×C₄×C₄₇	—	4	8	no	—
113	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	—	2	16	no	—
126	C₂²×Dic₄₇	—	2	8	no	—
127	C₂²×Dic₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	8	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
131	C₂²⋊C₄×C₄₇	—	2	2	no	—
132	C₂²⋊C₄×C₄₇	—	2	2	no	—
133	C₂²⋊C₄×C₄₇	—	2	8	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	8	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
138	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
139	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
140	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₄²×C₄₇	C₂×D₄	1	2	yes	—
143	C₄×Dic₄₇	—	2	32	no	—
144	C₄×Dic₄₇	—	2	8	no	—
145	C₄×Dic₄₇	—	2	4	no	—
146	C₄×Dic₄₇	C₂²×C₄	1	8	yes	complemented
147	#10625329	—	2	8	no	—
148	#10625329	—	2	4	no	—
149	#10625329	C₂²×C₄	1	8	yes	complemented
150	C₂×C₄₇⋊C₈	—	2	8	no	—
151	C₂×C₄₇⋊C₈	—	2	4	no	—
152	C₂³×C₄₇	—	2	4	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	4	no	—
155	C₂³×C₄₇	—	4	4	no	—
156	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂³×C₄₇	C₄×D₄	1	4	yes	—
159	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₄₇	—	2	2	no	—
161	Q₈×C₄₇	—	2	4	no	—
162	Q₈×C₄₇	C₂×C₄²	1	4	yes	complemented
163	D₄×C₄₇	—	2	8	no	—
164	D₄×C₄₇	—	2	8	no	—
165	D₄×C₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	C₂×C₄²	1	4	yes	complemented
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	8	no	—
172	C₂×C₄×C₄₇	—	2	8	no	—
173	C₂×C₄×C₄₇	—	2	8	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	—	4	16	no	—
178	C₂×C₄×C₄₇	#104	1	8	yes	complemented
179	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
185	C₂×C₄×C₄₇	#117	1	2	yes	—
186	C₂×C₄×C₄₇	#117	1	2	yes	—
187	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
194	C₂×Dic₄₇	—	2	16	no	—
195	C₂×Dic₄₇	—	2	32	no	—
196	C₂×Dic₄₇	—	2	8	no	—
197	C₄₇⋊C₈	—	2	8	no	—
198	C₂×C₄×#104	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	8	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	4	8	no	—
205	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
206	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
207	C₂²×C₄₇	C₂×#104	1	4	yes	—
208	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	4	4	no	—
213	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
214	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
215	C₄×C₄₇	C₂×#104	1	8	yes	complemented
216	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
217	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
218	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
219	Dic₄₇	—	2	16	no	—
220	C₂×C₄×#41	D₄₇	1	1	yes	characteristic
221	C₂²×#104	—	47	2	no	—
222	C₂×C₄×M₁₆	—	47	1	no	—
223	C₂×C₄³	—	47	1	no	—
224	C₄×#104	—	47	8	no	—
225	C₂×#339	—	47	2	no	—
226	C₂×C₄₇	—	2	2	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	4	4	no	—
229	C₂×C₄₇	C₄×#104	1	4	yes	complemented
230	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄₇	C₂²×#104	1	2	yes	—
232	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
233	C₂²×M₁₆	—	47	2	no	—
234	C₄×#41	—	2	2	no	—
235	C₄×#41	—	2	2	no	—
236	C₄×#41	Dic₄₇	1	4	yes	complemented
237	C₄×#41	C₂×D₄₇	1	4	yes	—
238	C₂×C₄×Q₈	Dic₄₇	1	2	yes	complemented
239	C₂×C₄×D₄	—	2	2	no	—
240	C₂×C₄×D₄	Dic₄₇	1	2	yes	complemented
241	C₂×#117	—	2	1	no	—
242	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
243	C₂²×C₄²	—	2	1	no	—
244	C₂²×C₄²	—	47	2	no	—
245	C₂²×C₄²	—	94	2	no	—
246	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
247	C₂×#104	—	47	16	no	—
248	C₂×#104	—	47	8	no	—
249	C₄×M₁₆	—	47	4	no	—
250	C₄×M₁₆	—	94	2	no	—
251	C₂×#97	—	94	1	no	—
252	C₂×C₄×C₈	—	94	1	no	—
253	C₄³	—	47	4	no	—
254	C₄³	—	94	2	no	—
255	#339	—	47	8	no	—
256	C₄₇	C₂×C₄×#104	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂×#41	C₄×D₄₇	1	8	yes	—
261	C₂×#41	C₂×Dic₄₇	1	2	yes	—
262	C₂×#41	C₂²×D₄₇	1	2	yes	—
263	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	—	94	2	no	—
269	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
270	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
271	C₂×M₁₆	—	47	8	no	—
272	C₂×M₁₆	—	47	4	no	—
273	C₂×M₁₆	—	94	4	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂²×C₈	—	94	2	no	—
276	C₄×Q₈	—	2	4	no	—
277	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
278	C₄×D₄	—	2	8	no	—
279	C₄×D₄	—	2	8	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	4	no	—
285	#117	—	2	4	no	—
286	#117	C₂×Dic₄₇	1	2	yes	—
287	#117	C₂²×D₄₇	1	2	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	4	no	—
295	C₂×C₄²	—	2	4	no	—
296	C₂×C₄²	—	47	8	no	—
297	C₂×C₄²	—	47	4	no	—
298	C₂×C₄²	—	94	16	no	—
299	C₂×C₄²	—	94	4	no	—
300	C₂×C₄²	—	94	8	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
303	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
305	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
306	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
307	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
309	#104	—	47	32	no	—
310	#97	—	94	4	no	—
311	C₄×C₈	—	94	4	no	—
312	C₂⁴	—	2	1	no	—
313	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
314	#41	—	2	4	no	—
315	#41	—	2	8	no	—
316	#41	—	2	8	no	—
317	#41	—	2	4	no	—
318	#41	C₄×Dic₄₇	1	8	yes	complemented
319	#41	C₂×C₄×D₄₇	1	8	yes	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₄×Dic₄₇	1	4	yes	complemented
323	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	C₄×Dic₄₇	1	4	yes	complemented
330	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	8	no	—
338	C₂²×C₄	—	4	8	no	—
339	C₂²×C₄	—	94	16	no	—
340	C₂²×C₄	—	94	8	no	—
341	C₂²×C₄	—	94	4	no	—
342	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
344	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
345	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
346	C₂²×C₄	#10625350	1	4	yes	—
347	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
350	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	M₁₆	—	47	8	no	—
355	M₁₆	—	94	8	no	—
356	M₁₆	—	94	4	no	—
357	C₂×C₈	—	94	8	no	—
358	C₂×C₈	—	94	4	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
362	C₂²⋊C₄	—	2	2	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	47	8	no	—
369	C₄²	—	94	32	no	—
370	C₄²	—	94	8	no	—
371	C₄²	—	94	4	no	—
372	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
373	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
374	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
375	C₄²	C₂²×Dic₄₇	1	4	yes	—
376	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
377	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	4	4	no	—
382	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
383	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
384	C₂³	C₄×C₂²⋊D₄₇	1	4	yes	—
385	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
386	Q₈	—	2	4	no	—
387	Q₈	—	2	2	no	—
388	Q₈	C₂×C₄×Dic₄₇	1	4	yes	complemented
389	D₄	—	2	8	no	—
390	D₄	—	2	8	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	2	no	—
393	D₄	C₂×C₄×Dic₄₇	1	4	yes	complemented
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	16	no	—
404	C₂×C₄	—	94	16	no	—
405	C₂×C₄	—	94	32	no	—
406	C₂×C₄	—	94	8	no	—
407	C₂×C₄	#13093951	1	8	yes	direct product factor
408	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
409	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
411	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
414	C₂×C₄	#13093983	1	2	yes	—
415	C₂×C₄	#13093983	1	2	yes	—
416	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
417	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
418	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
419	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
420	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂×#10625350	1	2	yes	—
423	C₈	—	94	8	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	8	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	8	no	—
430	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
431	C₂²	C₄×C₂²⋊Dic₄₇	1	2	yes	—
432	C₂²	C₂×#13093951	1	4	yes	—
433	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
434	C₂²	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	94	16	no	—
439	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
440	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
441	C₄	C₂×#13093951	1	8	yes	direct product factor
442	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
443	C₄	C₂×#13093983	1	1	yes	characteristic
444	C₄	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	2	2	no	—
447	C₂	—	4	4	no	—
448	C₂	C₄×#13093951	1	4	yes	direct product factor
449	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
450	C₂	C₂²×#13093951	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×#41	D₄₇
hypocenter	C₄₇	C₂×C₄×#104
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#10625329	C₂	semidirect
3. C₂×C₄²×Dic₄₇	C₂	semidirect
4. C₄×#13093951	C₂	direct (N × H)
5. C₂×#15688882	C₂	semidirect
10. C₂×#13093951	C₄	direct (N × H)
13. C₄×#10625329	C₂²	semidirect
17. C₄²×Dic₄₇	C₂²	semidirect
18. #15688882	C₂²	semidirect
22. C₄×#41×C₄₇	C₄	semidirect
24. C₂×C₄×Q₈×C₄₇	C₄	semidirect
26. C₂×C₄×D₄×C₄₇	C₄	semidirect
34. C₂×#10625329	C₂×C₄	semidirect
41. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
43. #13093951	C₂×C₄	direct (N × H)
60. C₄×Q₈×C₄₇	C₂×C₄	semidirect
64. C₄×D₄×C₄₇	C₂×C₄	semidirect
92. #41×C₄₇	C₄²	semidirect
96. C₂×Q₈×C₄₇	C₄²	semidirect
103. C₂×D₄×C₄₇	C₄²	semidirect
146. C₄×Dic₄₇	C₂²×C₄	semidirect
149. #10625329	C₂²×C₄	semidirect
162. Q₈×C₄₇	C₂×C₄²	semidirect
167. D₄×C₄₇	C₂×C₄²	semidirect
178. C₂×C₄×C₄₇	#104	semidirect
215. C₄×C₄₇	C₂×#104	semidirect
229. C₂×C₄₇	C₄×#104	semidirect
236. C₄×#41	Dic₄₇	semidirect
238. C₂×C₄×Q₈	Dic₄₇	semidirect
240. C₂×C₄×D₄	Dic₄₇	semidirect
256. C₄₇	C₂×C₄×#104	semidirect
277. C₄×Q₈	C₂×Dic₄₇	semidirect
281. C₄×D₄	C₂×Dic₄₇	semidirect
318. #41	C₄×Dic₄₇	semidirect
322. C₂×Q₈	C₄×Dic₄₇	semidirect
329. C₂×D₄	C₄×Dic₄₇	semidirect
388. Q₈	C₂×C₄×Dic₄₇	semidirect
393. D₄	C₂×C₄×Dic₄₇	semidirect
407. C₂×C₄	#13093951	direct (N × H)
441. C₄	C₂×#13093951	direct (N × H)
448. C₂	C₄×#13093951	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×#13093951	2
C₂×C₄×#10625329	2
C₂×C₄²×Dic₄₇	2
C₄×#13093951	2
C₂×#15688882	2
C₂×C₄×#41×C₄₇	2
C₂×C₄×#104	47

Subgroups — C2×C4×#13093951 #26213988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#13093951 #26213988