Subgroups — C₂×#20243985 #26218520

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689159	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689151	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
4	#20243985	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688887	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688883	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	#15689159	C₄	1	4	yes	complemented
14	#15689159	C₂²	1	4	yes	—
15	C₂×#13093957	C₄	1	1	yes	characteristic, complemented
16	C₂×#13093957	C₄	1	1	yes	characteristic, complemented
17	C₂×#13093955	C₄	1	1	yes	characteristic, complemented
18	C₂×#13093955	C₄	1	1	yes	characteristic, complemented
19	#15689151	—	2	2	no	—
20	#15689151	C₂²	1	4	yes	—
21	C₂×Dic₄₇⋊C₈	—	2	1	no	—
22	C₂×Dic₄₇⋊C₈	—	2	1	no	—
23	#15689079	—	2	2	no	—
24	#15689079	C₂²	1	4	yes	—
25	C₂×#13093935	—	2	1	no	—
26	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
27	#15688887	C₂²	1	4	yes	—
28	#15688883	C₂²	1	4	yes	—
29	#15688878	C₂²	1	4	yes	—
30	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×#339	C₂²	1	4	yes	—
34	C₂×#10625329	—	2	1	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	Q₈	1	4	yes	—
37	C₂×#10625329	C₂³	1	2	yes	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	#13093983	—	2	1	no	—
52	#13093983	—	2	1	no	—
53	#13093983	C₂×C₄	1	2	yes	—
54	#13093983	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄×Dic₄₇	—	2	1	no	—
59	#13093957	C₂×C₄	1	4	yes	complemented
60	#13093957	C₂×C₄	1	4	yes	complemented
61	#13093955	C₂×C₄	1	4	yes	complemented
62	#13093955	C₂×C₄	1	4	yes	complemented
63	Dic₄₇⋊C₈	—	2	4	no	—
64	Dic₄₇⋊C₈	—	2	4	no	—
65	#13093935	—	2	4	no	—
66	C₄×C₄₇⋊C₈	—	2	4	no	—
67	C₂³×C₄×C₄₇	—	2	1	no	—
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₄₇	—	2	1	no	—
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	—	2	1	no	—
74	#117×C₄₇	—	2	1	no	—
75	#117×C₄₇	—	2	1	no	—
76	#117×C₄₇	C₂×C₄	1	2	yes	—
77	#117×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	2	no	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	—	2	1	no	—
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂⁴×C₄₇	#41	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
98	C₂²×C₄×C₄₇	#41	1	2	yes	—
99	C₂²×C₄×C₄₇	#41	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	—	2	1	no	—
104	C₂²×Dic₄₇	—	2	1	no	—
105	M₁₆×C₄₇	—	2	2	no	—
106	M₁₆×C₄₇	—	2	2	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	4	2	no	—
110	C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₄⋊C₄×C₄₇	—	2	1	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₂²⋊C₄×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	4	2	no	—
121	C₂²⋊Dic₄₇	—	2	2	no	—
122	C₂²⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	1	no	—
124	C₄⋊Dic₄₇	—	2	1	no	—
125	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
126	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
127	C₄×Dic₄₇	—	2	2	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	#10625329	—	2	4	no	—
130	#10625329	—	2	2	no	—
131	#10625329	C₂×Q₈	1	4	yes	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	4	no	—
135	C₂×C₄₇⋊C₈	—	2	4	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	4	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₄₇	#125	1	2	yes	—
153	C₂³×C₄₇	#126	1	2	yes	—
154	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	#117	1	2	yes	—
164	C₂×C₄×C₄₇	#117	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
170	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
171	C₂×C₄×C₄₇	#123	1	2	yes	—
172	C₂×C₄×C₄₇	#123	1	2	yes	—
173	C₂×C₄×C₄₇	#125	1	2	yes	—
174	C₂×C₄×C₄₇	#126	1	2	yes	—
175	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	4	2	no	—
185	C₈×C₄₇	—	4	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	2	2	no	—
188	C₄₇⋊C₈	—	2	4	no	—
189	C₄₇⋊C₈	—	2	2	no	—
190	C₄₇⋊C₈	—	2	2	no	—
191	C₂×#1922	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	#387	1	2	yes	—
199	C₂²×C₄₇	#387	1	2	yes	—
200	C₂²×C₄₇	#443	1	2	yes	—
201	C₂²×C₄₇	#444	1	2	yes	—
202	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
205	C₄×C₄₇	—	4	4	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	#387	1	2	yes	—
209	C₄×C₄₇	#387	1	2	yes	—
210	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
211	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
212	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
214	Dic₄₇	—	4	2	no	—
215	Dic₄₇	—	4	2	no	—
216	C₂×#427	—	47	1	no	—
217	C₂×#424	—	47	1	no	—
218	C₂×#405	—	47	1	no	—
219	#1922	—	47	8	no	—
220	C₂×#341	—	47	1	no	—
221	C₂×#339	—	47	1	no	—
222	C₂×#339	D₄₇	1	1	yes	characteristic
223	C₂×#336	—	47	1	no	—
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	—	2	1	no	—
226	C₂×C₄₇	—	2	2	no	—
227	C₂×C₄₇	#1922	1	4	yes	complemented
228	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
231	C₂²×M₁₆	—	47	1	no	—
232	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
233	C₂³×C₈	—	47	1	no	—
234	C₂³×C₈	—	47	1	no	—
235	C₂×#117	—	47	1	no	—
236	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
237	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
238	#427	—	47	4	no	—
239	#427	—	47	4	no	—
240	C₂×#107	—	47	1	no	—
241	C₂×#107	—	47	1	no	—
242	C₂×#106	—	47	1	no	—
243	C₂×#106	—	47	1	no	—
244	#424	—	47	4	no	—
245	#424	—	94	2	no	—
246	C₂×C₄⋊C₈	—	94	1	no	—
247	C₂×C₄⋊C₈	—	94	1	no	—
248	#405	—	47	4	no	—
249	#405	—	94	2	no	—
250	C₂×#97	—	94	1	no	—
251	C₂×C₄×C₈	—	94	1	no	—
252	#341	—	47	4	no	—
253	#339	—	47	4	no	—
254	#339	C₂×D₄₇	1	4	yes	—
255	#336	—	47	4	no	—
256	C₄₇	C₂×#1922	1	1	yes	characteristic, complemented, Sylow
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	47	4	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	94	2	no	—
265	C₂×M₁₆	—	94	1	no	—
266	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	2	no	—
271	C₂²×C₈	—	47	2	no	—
272	C₂²×C₈	—	47	1	no	—
273	C₂²×C₈	—	47	1	no	—
274	C₂²×C₈	—	47	2	no	—
275	C₂²×C₈	—	47	2	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	—	94	2	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₂²×C₈	—	94	2	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	47	2	no	—
284	#117	—	47	2	no	—
285	#117	—	94	1	no	—
286	#117	—	94	1	no	—
287	#117	C₄×D₄₇	1	2	yes	—
288	#117	C₂²×D₄₇	1	2	yes	—
289	C₂×C₄⋊C₄	—	47	1	no	—
290	C₂×C₄⋊C₄	—	47	1	no	—
291	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	94	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	94	1	no	—
300	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
301	#107	—	47	4	no	—
302	#107	—	47	4	no	—
303	#106	—	47	4	no	—
304	#106	—	47	4	no	—
305	C₄⋊C₈	—	94	4	no	—
306	C₄⋊C₈	—	94	4	no	—
307	#97	—	94	4	no	—
308	C₄×C₈	—	94	4	no	—
309	C₂⁴	#10625352	1	1	yes	characteristic
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	1	no	—
318	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	#10625350	1	2	yes	—
321	C₂²×C₄	#10625350	1	2	yes	—
322	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
324	C₂²×C₄	#10625352	1	1	yes	characteristic
325	C₂²×C₄	#10625352	1	2	yes	—
326	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
327	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	4	2	no	—
331	M₁₆	—	47	4	no	—
332	M₁₆	—	94	4	no	—
333	M₁₆	—	94	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	47	2	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	4	no	—
343	C₂×C₈	—	94	4	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	4	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	47	2	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₄⋊C₄	—	94	1	no	—
358	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
359	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	94	2	no	—
363	C₂²⋊C₄	—	94	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	2	no	—
369	C₄²	—	94	2	no	—
370	C₄²	—	94	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
374	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
375	C₂³	#13094014	1	2	yes	—
376	C₂³	#13094017	1	2	yes	—
377	C₂³	C₂×#10625352	1	1	yes	characteristic
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	#13093981	1	2	yes	—
391	C₂×C₄	#13093981	1	2	yes	—
392	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	#13093989	1	2	yes	—
395	C₂×C₄	#13093989	1	2	yes	—
396	C₂×C₄	#13094002	1	2	yes	—
397	C₂×C₄	#13094002	1	2	yes	—
398	C₂×C₄	#13094006	1	2	yes	—
399	C₂×C₄	#13094006	1	2	yes	—
400	C₂×C₄	#13094014	1	2	yes	—
401	C₂×C₄	#13094017	1	2	yes	—
402	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
406	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
407	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	94	2	no	—
410	C₈	—	94	2	no	—
411	C₈	—	94	4	no	—
412	C₈	—	94	2	no	—
413	C₈	—	94	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	#15689005	1	2	yes	—
421	C₂²	#15689005	1	2	yes	—
422	C₂²	#15689237	1	2	yes	—
423	C₂²	#15689242	1	2	yes	—
424	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
425	C₂²	C₂×#13094014	1	1	yes	characteristic
426	C₂²	C₂×#13094017	1	1	yes	characteristic
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	188	2	no	—
431	C₄	—	188	2	no	—
432	C₄	#15689005	1	2	yes	—
433	C₄	#15689005	1	2	yes	—
434	C₄	C₂×#13093981	1	1	yes	characteristic
435	C₄	C₂×#13093989	1	1	yes	characteristic
436	C₄	C₂×#13094002	1	1	yes	characteristic
437	C₄	C₂×#13094006	1	1	yes	characteristic
438	C₂	—	2	1	no	—
439	C₂	—	2	2	no	—
440	C₂	—	2	1	no	—
441	C₂	#20243985	1	4	yes	direct product factor
442	C₂	C₂×#15689005	1	1	yes	characteristic
443	C₂	C₂×#15689237	1	1	yes	characteristic
444	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#339	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#339	D₄₇
hypocenter	C₄₇	C₂×#1922
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. #20243985	C₂	direct (N × H)
13. #15689159	C₄	semidirect
15. C₂×#13093957	C₄	semidirect
16. C₂×#13093957	C₄	semidirect
17. C₂×#13093955	C₄	semidirect
18. C₂×#13093955	C₄	semidirect
59. #13093957	C₂×C₄	semidirect
60. #13093957	C₂×C₄	semidirect
61. #13093955	C₂×C₄	semidirect
62. #13093955	C₂×C₄	semidirect
227. C₂×C₄₇	#1922	semidirect
256. C₄₇	C₂×#1922	semidirect
441. C₂	#20243985	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×#15689159	2
C₂×#15689151	2
C₂×#15689079	2
#20243985	2
C₂×#15688887	2
C₂×#15688883	2
C₂×#15688878	2
C₂×C₄₇×#339	2
C₂×#1922	47

Subgroups — C2×#20243985 #26218520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243985 #26218520