Subgroups — C₂×#20256721 #27123117

Order 12032.

11662 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625350	C₂	1	2	yes	maximal, complemented
2	#20256721	C₂	1	32	yes	maximal, direct product factor
3	C₂×#15689704	C₂	1	4	yes	maximal, complemented
4	C₂×#15689699	C₂	1	4	yes	maximal, complemented
5	C₂×#15689692	C₂	1	4	yes	maximal, complemented
6	C₂×#15689685	C₂	1	4	yes	maximal, complemented
7	C₂×#15689673	C₂	1	4	yes	maximal, complemented
8	C₂×#15689635	C₂	1	8	yes	maximal, complemented
9	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#10625350	—	2	32	no	—
11	C₂²×#10625350	C₂²	1	4	yes	—
12	C₂²×#10625350	C₂²	1	4	yes	—
13	C₂²×#10625350	C₂²	1	4	yes	complemented
14	C₂²×#10625350	C₂²	1	4	yes	complemented
15	C₂²×#10625350	C₂²	1	32	yes	complemented
16	C₂³×Dic₉₄	C₂²	1	2	yes	complemented
17	C₂³×D₁₈₈	C₂²	1	2	yes	complemented
18	C₂³×C₂²⋊D₄₇	C₂²	1	4	yes	—
19	C₂³×C₄×D₄₇	C₂²	1	4	yes	complemented
20	#15689704	C₂²	1	64	yes	complemented
21	#15689699	C₂²	1	64	yes	complemented
22	#15689692	C₂²	1	64	yes	complemented
23	#15689685	C₂²	1	64	yes	complemented
24	#15689673	C₂²	1	64	yes	complemented
25	C₂×#13094024	C₂²	1	4	yes	complemented
26	C₂×#13094021	C₂²	1	4	yes	complemented
27	C₂×#13094012	C₂²	1	8	yes	complemented
28	#15689635	C₂²	1	128	yes	complemented
29	C₂×#13094008	C₂²	1	16	yes	complemented
30	C₂×#13094004	C₂²	1	16	yes	complemented
31	C₂×#13093999	C₂²	1	16	yes	complemented
32	C₂×#13093998	C₂²	1	16	yes	complemented
33	C₂×#13093994	C₂²	1	16	yes	complemented
34	C₂×C₄×D₁₈₈	C₂²	1	16	yes	complemented
35	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₇	C₂²	1	4	yes	complemented
37	C₂×#117×C₄₇	C₂²	1	4	yes	complemented
38	C₂×#117×C₄₇	C₂²	1	16	yes	complemented
39	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
40	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₂²×C₄²×C₄₇	C₂²	1	2	yes	complemented
42	C₂⁴×D₄₇	C₂³	1	4	yes	—
43	C₂×#10625350	—	2	32	no	—
44	C₂×#10625350	—	2	32	no	—
45	C₂×#10625350	—	2	32	no	—
46	C₂×#10625350	—	2	32	no	—
47	C₂×#10625350	—	2	256	no	—
48	C₂×#10625350	C₂³	1	32	yes	—
49	C₂×#10625350	C₂³	1	32	yes	—
50	C₂×#10625350	C₂³	1	32	yes	complemented
51	C₂×#10625350	C₂³	1	32	yes	complemented
52	C₂²×Dic₉₄	—	2	16	no	—
53	C₂²×Dic₉₄	C₂³	1	4	yes	—
54	C₂²×Dic₉₄	C₂³	1	4	yes	—
55	C₂²×Dic₉₄	C₂³	1	16	yes	complemented
56	C₂²×D₁₈₈	—	2	16	no	—
57	C₂²×D₁₈₈	C₂³	1	4	yes	—
58	C₂²×D₁₈₈	C₂³	1	4	yes	—
59	C₂²×D₁₈₈	C₂³	1	16	yes	—
60	C₂²×D₁₈₈	C₂³	1	16	yes	complemented
61	C₂²×C₂²⋊D₄₇	—	2	32	no	—
62	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
63	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
64	C₂²×C₂²⋊D₄₇	C₂³	1	32	yes	—
65	C₂³×Dic₄₇	C₂³	1	4	yes	—
66	C₂²×C₄×D₄₇	—	2	32	no	—
67	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
68	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
69	C₂²×C₄×D₄₇	C₂³	1	32	yes	complemented
70	#13094024	C₂³	1	32	yes	complemented
71	#13094021	C₂³	1	32	yes	complemented
72	#13094012	C₂³	1	64	yes	complemented
73	#13094008	C₂³	1	128	yes	complemented
74	#13094004	C₂³	1	128	yes	complemented
75	#13093999	C₂³	1	128	yes	complemented
76	#13093998	C₂³	1	128	yes	complemented
77	#13093994	C₂³	1	128	yes	complemented
78	C₄×D₁₈₈	C₂³	1	128	yes	complemented
79	C₂×C₄⋊Dic₄₇	C₂³	1	16	yes	—
80	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	32	yes	—
81	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	D₄	1	16	yes	complemented
83	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
87	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
89	#117×C₄₇	C₂³	1	32	yes	complemented
90	#117×C₄₇	C₂³	1	32	yes	complemented
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
92	C₂×C₄⋊C₄×C₄₇	C₂³	1	16	yes	complemented
93	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
96	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	16	yes	complemented
98	C₂⁴×C₄₇	—	4	4	no	—
99	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
100	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
101	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
103	C₂³×D₄₇	—	2	16	no	—
104	C₂³×D₄₇	—	4	16	no	—
105	C₂³×D₄₇	C₂⁴	1	8	yes	—
106	C₂³×D₄₇	C₂⁴	1	16	yes	—
107	C₂²×C₄×C₄₇	—	4	8	no	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	64	yes	complemented
113	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₇	—	2	32	no	—
123	C₂×C₂²⋊D₄₇	—	2	32	no	—
124	C₂×C₂²⋊D₄₇	—	2	128	no	—
125	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
126	C₂×C₂²⋊D₄₇	C₂⁴	1	32	yes	—
127	C₂²×Dic₄₇	—	2	16	no	—
128	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
129	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
130	#10625350	—	2	128	no	—
131	#10625350	—	2	128	no	—
132	#10625350	—	2	128	no	—
133	#10625350	—	2	128	no	—
134	C₂×D₁₈₈	—	2	16	no	—
135	C₂×D₁₈₈	—	2	16	no	—
136	C₂×D₁₈₈	—	2	64	no	—
137	C₂×D₁₈₈	—	4	32	no	—
138	C₂×D₁₈₈	C₂⁴	1	16	yes	—
139	C₂×D₁₈₈	C₂⁴	1	16	yes	—
140	C₂×D₁₈₈	C₂⁴	1	64	yes	—
141	C₂×C₄×D₄₇	—	2	32	no	—
142	C₂×C₄×D₄₇	—	2	32	no	—
143	C₂×C₄×D₄₇	—	2	128	no	—
144	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
145	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
146	C₂×Dic₉₄	—	2	16	no	—
147	C₂×Dic₉₄	—	2	16	no	—
148	C₂×Dic₉₄	—	2	64	no	—
149	C₂×Dic₉₄	C₂⁴	1	16	yes	—
150	C₂×Dic₉₄	C₂⁴	1	16	yes	—
151	C₄⋊C₄×C₄₇	C₂⁴	1	32	yes	—
152	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
153	C₄²×C₄₇	C₂⁴	1	16	yes	—
154	C₄²×C₄₇	C₂⁴	1	16	yes	—
155	(C₂×D₄₇)⋊C₄	C₂⁴	1	128	yes	—
156	C₄⋊Dic₄₇	C₂⁴	1	64	yes	—
157	C₂³×C₄₇	—	2	4	no	—
158	C₂³×C₄₇	—	2	8	no	—
159	C₂³×C₄₇	—	4	16	no	—
160	C₂³×C₄₇	—	4	8	no	—
161	C₂³×C₄₇	C₂²×D₄	1	8	yes	—
162	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
163	C₂³×C₄₇	C₂²×D₄	1	16	yes	—
164	C₂³×C₄₇	C₂⁵	1	4	yes	—
165	C₂³×C₄₇	C₂⁵	1	2	yes	—
166	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
167	C₂²×D₄₇	—	2	32	no	—
168	C₂²×D₄₇	—	2	16	no	—
169	C₂²×D₄₇	—	2	32	no	—
170	C₂²×D₄₇	—	4	32	no	—
171	C₂²×D₄₇	—	4	64	no	—
172	C₂²×D₄₇	C₂⁵	1	16	yes	—
173	C₂×C₄×C₄₇	—	2	16	no	—
174	C₂×C₄×C₄₇	—	4	16	no	—
175	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
177	C₂×C₄×C₄₇	C₂²×D₄	1	32	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	32	yes	—
180	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	16	yes	—
182	C₂×C₄×C₄₇	C₂⁵	1	16	yes	—
183	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
184	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
185	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
186	C₂²⋊D₄₇	—	2	64	no	—
187	C₂²⋊D₄₇	—	2	64	no	—
188	C₂×Dic₄₇	—	2	32	no	—
189	C₂×Dic₄₇	—	2	16	no	—
190	C₂×Dic₄₇	C₂⁵	1	16	yes	—
191	D₁₈₈	—	2	32	no	—
192	D₁₈₈	—	2	32	no	—
193	D₁₈₈	—	4	64	no	—
194	C₄×D₄₇	—	2	64	no	—
195	C₄×D₄₇	—	2	64	no	—
196	Dic₉₄	—	2	32	no	—
197	Dic₉₄	—	2	32	no	—
198	C₂×#3449	—	47	1	no	maximal, Sylow
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	8	no	—
201	C₂²×C₄₇	—	2	16	no	—
202	C₂²×C₄₇	—	2	8	no	—
203	C₂²×C₄₇	—	4	16	no	—
204	C₂²×C₄₇	C₂³×D₄	1	8	yes	—
205	C₂²×C₄₇	C₂³×D₄	1	4	yes	—
206	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
207	C₂²×C₄₇	#585	1	4	yes	—
208	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
209	C₂×D₄₇	—	2	16	no	—
210	C₂×D₄₇	—	2	32	no	—
211	C₂×D₄₇	—	4	64	no	—
212	C₂×D₄₇	—	4	32	no	—
213	C₄×C₄₇	—	2	16	no	—
214	C₄×C₄₇	C₂³×D₄	1	4	yes	—
215	C₄×C₄₇	C₂³×D₄	1	8	yes	—
216	C₄×C₄₇	C₂³×D₄	1	4	yes	—
217	Dic₄₇	—	2	16	no	—
218	C₂³×#41	—	47	2	no	—
219	#3449	—	47	32	no	—
220	C₂×#537	—	47	4	no	—
221	C₂×#536	—	47	4	no	—
222	C₂×#535	—	47	4	no	—
223	C₂×#534	—	47	4	no	—
224	C₂×#532	—	47	4	no	—
225	C₂×#525	—	47	8	no	—
226	C₂²×#117	D₄₇	1	1	yes	characteristic, complemented
227	C₂×C₄₇	—	2	8	no	—
228	C₂×C₄₇	—	2	4	no	—
229	C₂×C₄₇	#3449	1	4	yes	complemented
230	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#585	1	2	yes	—
232	D₄₇	—	4	16	no	—
233	C₂²×#41	—	47	4	no	—
234	C₂²×#41	—	47	4	no	—
235	C₂²×#41	—	47	4	no	—
236	C₂²×#41	—	47	4	no	—
237	C₂²×#41	—	47	32	no	—
238	C₂²×#41	—	94	32	no	—
239	C₂³×Q₈	—	47	2	no	—
240	C₂³×D₄	—	47	4	no	—
241	C₂³×D₄	—	47	2	no	—
242	C₂⁴×C₄	—	47	4	no	—
243	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
244	#537	—	47	64	no	—
245	#536	—	47	64	no	—
246	#535	—	47	64	no	—
247	#534	—	47	64	no	—
248	#532	—	47	64	no	—
249	C₂×C₄⋊Q₈	—	47	4	no	—
250	C₂×#127	—	47	4	no	—
251	C₂×#124	—	47	8	no	—
252	#525	—	47	128	no	—
253	C₂×#123	—	47	16	no	—
254	C₂×C₂²⋊Q₈	—	47	16	no	—
255	C₂×#121	—	47	16	no	—
256	C₂×#121	—	47	16	no	—
257	C₂×#120	—	47	16	no	—
258	C₂×C₄×D₄	—	47	16	no	—
259	C₂×#117	C₂×D₄₇	1	4	yes	complemented
260	C₂×#117	C₂×D₄₇	1	4	yes	complemented
261	C₂×#117	C₂×D₄₇	1	16	yes	complemented
262	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	complemented
263	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
264	C₂²×C₄²	C₂×D₄₇	1	2	yes	complemented
265	C₄₇	C₂×#3449	1	1	yes	characteristic, complemented, Sylow
266	C₂⁵	—	47	4	no	—
267	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×#41	—	47	32	no	—
269	C₂×#41	—	47	32	no	—
270	C₂×#41	—	47	32	no	—
271	C₂×#41	—	47	32	no	—
272	C₂×#41	—	94	32	no	—
273	C₂×#41	—	94	32	no	—
274	C₂×#41	—	94	32	no	—
275	C₂×#41	—	94	32	no	—
276	C₂×#41	—	94	256	no	—
277	C₂²×Q₈	—	47	4	no	—
278	C₂²×Q₈	—	47	4	no	—
279	C₂²×Q₈	—	47	16	no	—
280	C₂²×Q₈	—	94	16	no	—
281	C₂²×D₄	—	47	8	no	—
282	C₂²×D₄	—	47	8	no	—
283	C₂²×D₄	—	47	32	no	—
284	C₂²×D₄	—	47	4	no	—
285	C₂²×D₄	—	47	4	no	—
286	C₂²×D₄	—	47	16	no	—
287	C₂²×D₄	—	47	16	no	—
288	C₂²×D₄	—	94	32	no	—
289	C₂²×D₄	—	94	16	no	—
290	C₂³×C₄	—	47	4	no	—
291	C₂³×C₄	—	47	8	no	—
292	C₂³×C₄	—	47	32	no	—
293	C₂³×C₄	—	47	8	no	—
294	C₂³×C₄	—	94	32	no	—
295	C₂³×C₄	D₁₈₈	1	16	yes	complemented
296	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
297	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
298	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
299	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
300	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
302	C₄⋊Q₈	—	47	32	no	—
303	#127	—	47	32	no	—
304	#124	—	47	64	no	—
305	#123	—	47	128	no	—
306	C₂²⋊Q₈	—	47	128	no	—
307	#121	—	47	128	no	—
308	#121	—	47	128	no	—
309	#120	—	47	128	no	—
310	C₄×D₄	—	47	128	no	—
311	#117	C₂²×D₄₇	1	32	yes	complemented
312	#117	C₂²×D₄₇	1	32	yes	complemented
313	C₂×C₄⋊C₄	—	47	16	no	—
314	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	—
315	C₂×C₄⋊C₄	C₂²×D₄₇	1	16	yes	complemented
316	C₂×C₂²⋊C₄	—	47	32	no	—
317	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
319	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
320	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
321	C₂×C₄²	C₂²×D₄₇	1	16	yes	complemented
322	C₂⁴	—	4	4	no	—
323	C₂⁴	—	47	8	no	—
324	C₂⁴	—	47	16	no	—
325	C₂⁴	—	94	16	no	—
326	C₂⁴	—	188	16	no	—
327	C₂⁴	C₂×D₁₈₈	1	8	yes	—
328	C₂⁴	C₂³×D₄₇	1	2	yes	—
329	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
330	C₂⁴	C₂³×D₄₇	1	4	yes	—
331	#41	—	94	128	no	—
332	#41	—	94	128	no	—
333	#41	—	94	128	no	—
334	#41	—	94	128	no	—
335	C₂×Q₈	—	47	16	no	—
336	C₂×Q₈	—	47	16	no	—
337	C₂×Q₈	—	94	16	no	—
338	C₂×Q₈	—	94	16	no	—
339	C₂×Q₈	—	94	64	no	—
340	C₂×D₄	—	47	32	no	—
341	C₂×D₄	—	47	32	no	—
342	C₂×D₄	—	47	16	no	—
343	C₂×D₄	—	47	16	no	—
344	C₂×D₄	—	47	64	no	—
345	C₂×D₄	—	94	32	no	—
346	C₂×D₄	—	94	32	no	—
347	C₂×D₄	—	94	128	no	—
348	C₂×D₄	—	94	16	no	—
349	C₂×D₄	—	94	16	no	—
350	C₂×D₄	—	94	64	no	—
351	C₂×D₄	—	188	32	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	—	47	8	no	—
354	C₂²×C₄	—	47	16	no	—
355	C₂²×C₄	—	47	32	no	—
356	C₂²×C₄	—	47	32	no	—
357	C₂²×C₄	—	94	16	no	—
358	C₂²×C₄	—	94	32	no	—
359	C₂²×C₄	—	94	32	no	—
360	C₂²×C₄	—	94	128	no	—
361	C₂²×C₄	C₂×D₁₈₈	1	16	yes	—
362	C₂²×C₄	C₂×D₁₈₈	1	16	yes	—
363	C₂²×C₄	C₂×D₁₈₈	1	8	yes	—
364	C₂²×C₄	C₂×D₁₈₈	1	8	yes	—
365	C₂²×C₄	C₂×D₁₈₈	1	64	yes	complemented
366	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
367	C₂²×C₄	C₂³×D₄₇	1	16	yes	—
368	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
370	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
371	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
372	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
373	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
374	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
375	C₄⋊C₄	—	47	64	no	—
376	C₄⋊C₄	C₂³×D₄₇	1	32	yes	—
377	C₂²⋊C₄	—	47	128	no	—
378	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
379	C₄²	C₂³×D₄₇	1	16	yes	—
380	C₄²	C₂³×D₄₇	1	16	yes	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	8	no	—
383	C₂³	—	4	16	no	—
384	C₂³	—	4	8	no	—
385	C₂³	—	47	16	no	—
386	C₂³	—	94	32	no	—
387	C₂³	—	94	16	no	—
388	C₂³	—	94	32	no	—
389	C₂³	—	188	32	no	—
390	C₂³	—	188	64	no	—
391	C₂³	C₂²×D₁₈₈	1	8	yes	—
392	C₂³	C₂²×D₁₈₈	1	4	yes	—
393	C₂³	C₂²×D₁₈₈	1	16	yes	—
394	C₂³	C₂⁴×D₄₇	1	4	yes	—
395	C₂³	C₂⁴×D₄₇	1	2	yes	—
396	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
397	Q₈	—	94	32	no	—
398	Q₈	—	94	32	no	—
399	D₄	—	94	64	no	—
400	D₄	—	94	64	no	—
401	D₄	—	94	32	no	—
402	D₄	—	94	32	no	—
403	D₄	—	188	64	no	—
404	C₂×C₄	—	2	16	no	—
405	C₂×C₄	—	4	16	no	—
406	C₂×C₄	—	47	16	no	—
407	C₂×C₄	—	94	32	no	—
408	C₂×C₄	—	94	16	no	—
409	C₂×C₄	—	94	64	no	—
410	C₂×C₄	—	94	64	no	—
411	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
412	C₂×C₄	C₂²×D₁₈₈	1	8	yes	—
413	C₂×C₄	C₂²×D₁₈₈	1	32	yes	—
414	C₂×C₄	C₂²×D₁₈₈	1	4	yes	—
415	C₂×C₄	C₂²×D₁₈₈	1	32	yes	—
416	C₂×C₄	C₂²×D₁₈₈	1	16	yes	—
417	C₂×C₄	C₂²×D₁₈₈	1	16	yes	—
418	C₂×C₄	C₂⁴×D₄₇	1	16	yes	—
419	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
420	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
421	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	16	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	4	16	no	—
427	C₂²	—	94	16	no	—
428	C₂²	—	94	32	no	—
429	C₂²	—	188	64	no	—
430	C₂²	—	188	32	no	—
431	C₂²	C₂³×D₁₈₈	1	8	yes	—
432	C₂²	C₂³×D₁₈₈	1	4	yes	—
433	C₂²	C₂³×D₁₈₈	1	2	yes	—
434	C₂²	#15689959	1	4	yes	—
435	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
436	C₄	—	2	16	no	—
437	C₄	—	94	16	no	—
438	C₄	C₂³×D₁₈₈	1	4	yes	—
439	C₄	C₂³×D₁₈₈	1	8	yes	—
440	C₄	C₂³×D₁₈₈	1	4	yes	—
441	C₂	—	2	8	no	—
442	C₂	—	2	4	no	—
443	C₂	—	188	16	no	—
444	C₂	#20256721	1	4	yes	direct product factor
445	C₂	C₂⁴×D₁₈₈	1	1	yes	characteristic
446	C₂	C₂×#15689959	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂×#3449
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625350	C₂	semidirect
2. #20256721	C₂	direct (N × H)
3. C₂×#15689704	C₂	semidirect
4. C₂×#15689699	C₂	semidirect
5. C₂×#15689692	C₂	semidirect
6. C₂×#15689685	C₂	semidirect
7. C₂×#15689673	C₂	semidirect
8. C₂×#15689635	C₂	semidirect
9. C₂²×#117×C₄₇	C₂	semidirect
13. C₂²×#10625350	C₂²	semidirect
14. C₂²×#10625350	C₂²	semidirect
15. C₂²×#10625350	C₂²	semidirect
16. C₂³×Dic₉₄	C₂²	semidirect
17. C₂³×D₁₈₈	C₂²	semidirect
19. C₂³×C₄×D₄₇	C₂²	semidirect
20. #15689704	C₂²	semidirect
21. #15689699	C₂²	semidirect
22. #15689692	C₂²	semidirect
23. #15689685	C₂²	semidirect
24. #15689673	C₂²	semidirect
25. C₂×#13094024	C₂²	semidirect
26. C₂×#13094021	C₂²	semidirect
27. C₂×#13094012	C₂²	semidirect
28. #15689635	C₂²	semidirect
29. C₂×#13094008	C₂²	semidirect
30. C₂×#13094004	C₂²	semidirect
31. C₂×#13093999	C₂²	semidirect
32. C₂×#13093998	C₂²	semidirect
33. C₂×#13093994	C₂²	semidirect
34. C₂×C₄×D₁₈₈	C₂²	semidirect
36. C₂×#117×C₄₇	C₂²	semidirect
37. C₂×#117×C₄₇	C₂²	semidirect
38. C₂×#117×C₄₇	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
41. C₂²×C₄²×C₄₇	C₂²	semidirect
50. C₂×#10625350	C₂³	semidirect
51. C₂×#10625350	C₂³	semidirect
55. C₂²×Dic₉₄	C₂³	semidirect
60. C₂²×D₁₈₈	C₂³	semidirect
69. C₂²×C₄×D₄₇	C₂³	semidirect
70. #13094024	C₂³	semidirect
71. #13094021	C₂³	semidirect
72. #13094012	C₂³	semidirect
73. #13094008	C₂³	semidirect
74. #13094004	C₂³	semidirect
75. #13093999	C₂³	semidirect
76. #13093998	C₂³	semidirect
77. #13093994	C₂³	semidirect
78. C₄×D₁₈₈	C₂³	semidirect
82. C₂³×C₄×C₄₇	D₄	semidirect
89. #117×C₄₇	C₂³	semidirect
90. #117×C₄₇	C₂³	semidirect
92. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
97. C₂×C₄²×C₄₇	C₂³	semidirect
112. C₂²×C₄×C₄₇	C₂×D₄	semidirect
226. C₂²×#117	D₄₇	semidirect
229. C₂×C₄₇	#3449	semidirect
259. C₂×#117	C₂×D₄₇	semidirect
260. C₂×#117	C₂×D₄₇	semidirect
261. C₂×#117	C₂×D₄₇	semidirect
262. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
264. C₂²×C₄²	C₂×D₄₇	semidirect
265. C₄₇	C₂×#3449	semidirect
295. C₂³×C₄	D₁₈₈	semidirect
311. #117	C₂²×D₄₇	semidirect
312. #117	C₂²×D₄₇	semidirect
315. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
321. C₂×C₄²	C₂²×D₄₇	semidirect
365. C₂²×C₄	C₂×D₁₈₈	semidirect
444. C₂	#20256721	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#10625350	2
#20256721	2
C₂×#15689704	2
C₂×#15689699	2
C₂×#15689692	2
C₂×#15689685	2
C₂×#15689673	2
C₂×#15689635	2
C₂²×#117×C₄₇	2
C₂×#3449	47

Subgroups — C2×#20256721 #27123117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20256721 #27123117