Subgroups — C₂²×#15689804 #27123259

Order 12032.

9526 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689804	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094017	C₂	1	2	yes	maximal, complemented
3	C₂²×#13094011	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13094005	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13094005	C₂	1	2	yes	maximal, complemented
6	C₂²×#13094001	C₂	1	2	yes	maximal, complemented
7	C₂²×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
8	C₂²×#13093980	C₂	1	2	yes	maximal, complemented
9	C₂³×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
10	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
12	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
13	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
14	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
15	#15689804	C₂²	1	256	yes	direct product factor
16	C₂×#13094017	C₂²	1	48	yes	complemented
17	C₂×#13094011	C₂²	1	24	yes	complemented
18	C₂×#13094005	C₂²	1	24	yes	complemented
19	C₂×#13094005	C₂²	1	48	yes	complemented
20	C₂×#13094001	C₂²	1	48	yes	complemented
21	C₂×D₄×Dic₄₇	C₂²	1	48	yes	complemented
22	C₂×#13093980	C₂²	1	48	yes	complemented
23	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
24	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
25	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
26	C₂²×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
30	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
31	C₂²×C₂²⋊Dic₄₇	C₂²	1	48	yes	complemented
32	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
36	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
37	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
38	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#120×C₄₇	C₂²	1	24	yes	—
40	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×Dic₉₄	—	4	4	no	—
43	C₂²×Dic₉₄	C₂³	1	12	yes	complemented
44	C₂³×Dic₄₇	—	2	16	no	—
45	C₂³×Dic₄₇	—	4	8	no	—
46	C₂³×Dic₄₇	—	4	4	no	—
47	C₂³×Dic₄₇	C₂³	1	2	yes	—
48	C₂³×Dic₄₇	C₂³	1	2	yes	—
49	C₂³×Dic₄₇	C₂³	1	2	yes	—
50	C₂³×Dic₄₇	C₂³	1	2	yes	—
51	C₂³×Dic₄₇	C₂³	1	24	yes	—
52	C₂³×Dic₄₇	C₂³	1	24	yes	—
53	C₂³×Dic₄₇	C₂³	1	12	yes	complemented
54	#13094017	C₂³	1	128	yes	complemented
55	#13094011	C₂³	1	64	yes	complemented
56	#13094005	C₂³	1	64	yes	complemented
57	#13094005	C₂³	1	128	yes	complemented
58	#13094001	C₂³	1	128	yes	complemented
59	D₄×Dic₄₇	C₂³	1	128	yes	complemented
60	#13093980	C₂³	1	128	yes	complemented
61	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	complemented
62	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	complemented
63	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	complemented
64	C₂×Dic₄₇⋊C₄	C₂³	1	24	yes	complemented
65	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
67	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
68	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	—
69	C₂×C₂²⋊Dic₄₇	C₂³	1	128	yes	complemented
70	C₂×C₂²⋊Dic₄₇	C₂³	1	24	yes	complemented
71	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	complemented
72	C₂×C₄×Dic₄₇	C₂³	1	12	yes	complemented
73	C₂×C₄×Dic₄₇	C₂³	1	24	yes	complemented
74	C₂⁵×C₄₇	—	2	16	no	—
75	C₂⁵×C₄₇	—	4	4	no	—
76	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
77	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
78	C₂⁵×C₄₇	C₂³	1	12	yes	—
79	C₂⁵×C₄₇	C₂³	1	2	yes	—
80	C₂²×D₄×C₄₇	—	2	16	no	—
81	C₂²×D₄×C₄₇	—	4	4	no	—
82	C₂²×D₄×C₄₇	C₂³	1	24	yes	—
83	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
84	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	#120×C₄₇	C₂³	1	64	yes	—
87	C₂×C₂²⋊C₄×C₄₇	C₂³	1	24	yes	—
88	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
89	C₂⁴×C₄₇	—	2	8	no	—
90	C₂⁴×C₄₇	—	2	8	no	—
91	C₂⁴×C₄₇	—	2	8	no	—
92	C₂⁴×C₄₇	—	2	96	no	—
93	C₂⁴×C₄₇	—	2	8	no	—
94	C₂⁴×C₄₇	—	2	4	no	—
95	C₂⁴×C₄₇	—	2	4	no	—
96	C₂⁴×C₄₇	—	4	24	no	—
97	C₂⁴×C₄₇	—	4	64	no	—
98	C₂⁴×C₄₇	#41	1	16	yes	—
99	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
100	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
101	C₂⁴×C₄₇	C₂⁴	1	16	yes	—
102	C₂⁴×C₄₇	C₂⁴	1	12	yes	—
103	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂×D₄×C₄₇	—	2	96	no	—
105	C₂×D₄×C₄₇	—	4	24	no	—
106	C₂×D₄×C₄₇	C₂⁴	1	32	yes	—
107	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
108	C₂²×C₄×C₄₇	—	2	8	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
112	C₂²×Dic₄₇	—	2	96	no	—
113	C₂²×Dic₄₇	—	2	8	no	—
114	C₂²×Dic₄₇	—	2	8	no	—
115	C₂²×Dic₄₇	—	2	8	no	—
116	C₂²×Dic₄₇	—	2	8	no	—
117	C₂²×Dic₄₇	—	4	48	no	—
118	C₂²×Dic₄₇	—	4	24	no	—
119	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
120	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
121	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
122	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
123	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
124	C₂²×Dic₄₇	C₂⁴	1	32	yes	—
125	C₂²×Dic₄₇	C₂⁴	1	16	yes	complemented
126	C₂×Dic₉₄	—	4	24	no	—
127	C₂×Dic₉₄	C₂⁴	1	16	yes	complemented
128	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
129	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
130	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
131	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
132	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
133	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	—
134	C₂²⋊Dic₄₇	C₂⁴	1	32	yes	complemented
135	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	complemented
136	C₄⋊Dic₄₇	C₂⁴	1	32	yes	complemented
137	Dic₄₇⋊C₄	C₂⁴	1	32	yes	complemented
138	Dic₄₇⋊C₄	C₂⁴	1	32	yes	complemented
139	Dic₄₇⋊C₄	C₂⁴	1	32	yes	complemented
140	C₄×Dic₄₇	C₂⁴	1	16	yes	complemented
141	C₄×Dic₄₇	C₂⁴	1	32	yes	complemented
142	C₂³×C₄₇	—	2	64	no	—
143	C₂³×C₄₇	—	2	24	no	—
144	C₂³×C₄₇	—	2	24	no	—
145	C₂³×C₄₇	—	2	24	no	—
146	C₂³×C₄₇	—	2	64	no	—
147	C₂³×C₄₇	—	2	24	no	—
148	C₂³×C₄₇	—	2	12	no	—
149	C₂³×C₄₇	—	2	12	no	—
150	C₂³×C₄₇	—	4	16	no	—
151	C₂³×C₄₇	—	4	192	no	—
152	C₂³×C₄₇	—	4	16	no	—
153	C₂³×C₄₇	—	4	16	no	—
154	C₂³×C₄₇	C₂×#41	1	48	yes	—
155	C₂³×C₄₇	C₂×#41	1	8	yes	—
156	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
157	C₂³×C₄₇	C₂⁵	1	4	yes	—
158	C₂³×C₄₇	C₂⁵	1	4	yes	—
159	C₂³×C₄₇	C₂⁵	1	8	yes	—
160	C₂³×C₄₇	C₂⁵	1	3	yes	—
161	D₄×C₄₇	—	2	64	no	—
162	D₄×C₄₇	—	4	16	no	—
163	C₂×C₄×C₄₇	—	2	24	no	—
164	C₂×C₄×C₄₇	—	2	12	no	—
165	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
166	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
167	C₂×Dic₄₇	—	2	64	no	—
168	C₂×Dic₄₇	—	2	24	no	—
169	C₂×Dic₄₇	—	2	24	no	—
170	C₂×Dic₄₇	—	2	24	no	—
171	C₂×Dic₄₇	—	2	24	no	—
172	C₂×Dic₄₇	—	4	32	no	—
173	C₂×Dic₄₇	—	4	16	no	—
174	C₂×Dic₄₇	C₂⁵	1	8	yes	—
175	C₂×Dic₄₇	C₂⁵	1	8	yes	—
176	C₂×Dic₄₇	C₂⁵	1	8	yes	—
177	C₂×Dic₄₇	C₂⁵	1	8	yes	—
178	Dic₉₄	—	4	16	no	—
179	C₂²×#551	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	2	8	no	—
182	C₂²×C₄₇	—	2	96	no	—
183	C₂²×C₄₇	—	2	8	no	—
184	C₂²×C₄₇	—	2	8	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	4	64	no	—
188	C₂²×C₄₇	—	4	24	no	—
189	C₂²×C₄₇	—	4	24	no	—
190	C₂²×C₄₇	#551	1	16	yes	complemented
191	C₂²×C₄₇	C₂²×#41	1	16	yes	—
192	C₂²×C₄₇	C₂²×#41	1	12	yes	—
193	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
194	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
195	C₄×C₄₇	—	2	8	no	—
196	C₄×C₄₇	—	2	4	no	—
197	Dic₄₇	—	2	8	no	—
198	Dic₄₇	—	2	8	no	—
199	Dic₄₇	—	2	8	no	—
200	Dic₄₇	—	2	8	no	—
201	C₂×#551	—	47	48	no	—
202	C₂²×#126	—	47	2	no	—
203	C₂²×#124	—	47	1	no	—
204	C₂²×#123	—	47	2	no	—
205	C₂²×#123	—	47	1	no	—
206	C₂²×C₂²⋊Q₈	—	47	2	no	—
207	C₂²×#120	D₄₇	1	1	yes	characteristic
208	C₂²×C₄×D₄	—	47	2	no	—
209	C₂²×#117	—	47	2	no	—
210	C₂³×C₂²⋊C₄	—	47	2	no	—
211	C₂×C₄₇	—	2	16	no	—
212	C₂×C₄₇	—	4	4	no	—
213	C₂×C₄₇	—	4	4	no	—
214	C₂×C₄₇	C₂×#551	1	12	yes	complemented
215	C₂×C₄₇	C₂³×#41	1	2	yes	—
216	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
217	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
218	C₂³×Q₈	—	47	1	no	—
219	C₂³×D₄	C₂×D₄₇	1	2	yes	—
220	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
221	C₂⁴×C₄	—	47	2	no	—
222	C₂⁴×C₄	—	47	2	no	—
223	C₂⁴×C₄	—	47	1	no	—
224	#551	—	47	256	no	—
225	C₂×#126	—	47	48	no	—
226	C₂×#124	—	47	24	no	—
227	C₂×#123	—	47	48	no	—
228	C₂×#123	—	47	24	no	—
229	C₂×C₂²⋊Q₈	—	47	48	no	—
230	C₂×#120	C₂×D₄₇	1	24	yes	—
231	C₂×C₄×D₄	—	47	48	no	—
232	C₂×#117	—	47	48	no	—
233	C₂²×C₄⋊C₄	—	47	2	no	—
234	C₂²×C₄⋊C₄	—	47	2	no	—
235	C₂²×C₄⋊C₄	—	47	2	no	—
236	C₂²×C₄⋊C₄	—	47	2	no	—
237	C₂²×C₂²⋊C₄	—	47	2	no	—
238	C₂²×C₂²⋊C₄	—	47	2	no	—
239	C₂²×C₂²⋊C₄	—	47	2	no	—
240	C₂²×C₂²⋊C₄	—	47	2	no	—
241	C₂²×C₂²⋊C₄	—	47	48	no	—
242	C₂²×C₂²⋊C₄	—	47	2	no	—
243	C₂²×C₂²⋊C₄	—	47	1	no	—
244	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
245	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
246	C₂²×C₄²	—	47	1	no	—
247	C₂²×C₄²	—	47	2	no	—
248	C₄₇	C₂²×#551	1	1	yes	characteristic, complemented, Sylow
249	C₂⁵	—	2	16	no	—
250	C₂⁵	—	4	4	no	—
251	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
252	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
253	C₂⁵	C₂²×D₄₇	1	12	yes	—
254	C₂⁵	C₂²×D₄₇	1	2	yes	—
255	C₂²×Q₈	—	47	12	no	—
256	C₂²×Q₈	—	188	4	no	—
257	C₂²×D₄	—	2	16	no	—
258	C₂²×D₄	—	4	4	no	—
259	C₂²×D₄	C₂²×D₄₇	1	24	yes	—
260	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
261	C₂³×C₄	—	47	24	no	—
262	C₂³×C₄	—	47	2	no	—
263	C₂³×C₄	—	47	2	no	—
264	C₂³×C₄	—	47	2	no	—
265	C₂³×C₄	—	47	2	no	—
266	C₂³×C₄	—	47	24	no	—
267	C₂³×C₄	—	47	12	no	—
268	C₂³×C₄	—	94	16	no	—
269	C₂³×C₄	—	188	4	no	—
270	C₂³×C₄	—	188	8	no	—
271	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
272	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
273	#126	—	47	128	no	—
274	#124	—	47	64	no	—
275	#123	—	47	128	no	—
276	#123	—	47	64	no	—
277	C₂²⋊Q₈	—	47	128	no	—
278	#120	C₂²×D₄₇	1	64	yes	—
279	C₄×D₄	—	47	128	no	—
280	#117	—	47	128	no	—
281	C₂×C₄⋊C₄	—	47	24	no	—
282	C₂×C₄⋊C₄	—	47	24	no	—
283	C₂×C₄⋊C₄	—	47	24	no	—
284	C₂×C₄⋊C₄	—	47	24	no	—
285	C₂×C₂²⋊C₄	—	47	24	no	—
286	C₂×C₂²⋊C₄	—	47	24	no	—
287	C₂×C₂²⋊C₄	—	47	24	no	—
288	C₂×C₂²⋊C₄	—	47	24	no	—
289	C₂×C₂²⋊C₄	—	47	128	no	—
290	C₂×C₂²⋊C₄	—	47	24	no	—
291	C₂×C₂²⋊C₄	—	47	12	no	—
292	C₂×C₂²⋊C₄	C₂²×D₄₇	1	24	yes	—
293	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
294	C₂×C₄²	—	47	12	no	—
295	C₂×C₄²	—	47	24	no	—
296	C₂⁴	—	2	8	no	—
297	C₂⁴	—	2	8	no	—
298	C₂⁴	—	2	8	no	—
299	C₂⁴	—	2	96	no	—
300	C₂⁴	—	2	8	no	—
301	C₂⁴	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	4	24	no	—
304	C₂⁴	—	4	64	no	—
305	C₂⁴	#10625352	1	16	yes	—
306	C₂⁴	C₂³×D₄₇	1	6	yes	—
307	C₂⁴	C₂³×D₄₇	1	6	yes	—
308	C₂⁴	C₂³×D₄₇	1	16	yes	—
309	C₂⁴	C₂³×D₄₇	1	12	yes	—
310	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
311	C₂×Q₈	—	47	16	no	—
312	C₂×Q₈	—	188	24	no	—
313	C₂×D₄	—	2	96	no	—
314	C₂×D₄	—	4	24	no	—
315	C₂×D₄	C₂³×D₄₇	1	32	yes	—
316	C₂×D₄	C₂³×D₄₇	1	16	yes	—
317	C₂²×C₄	—	2	8	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	47	12	no	—
320	C₂²×C₄	—	47	12	no	—
321	C₂²×C₄	—	47	12	no	—
322	C₂²×C₄	—	47	12	no	—
323	C₂²×C₄	—	47	32	no	—
324	C₂²×C₄	—	47	32	no	—
325	C₂²×C₄	—	47	16	no	—
326	C₂²×C₄	—	94	96	no	—
327	C₂²×C₄	—	94	8	no	—
328	C₂²×C₄	—	94	8	no	—
329	C₂²×C₄	—	94	8	no	—
330	C₂²×C₄	—	94	8	no	—
331	C₂²×C₄	—	188	24	no	—
332	C₂²×C₄	—	188	48	no	—
333	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
334	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
335	C₄⋊C₄	—	47	32	no	—
336	C₄⋊C₄	—	47	32	no	—
337	C₄⋊C₄	—	47	32	no	—
338	C₄⋊C₄	—	47	32	no	—
339	C₂²⋊C₄	—	47	32	no	—
340	C₂²⋊C₄	—	47	32	no	—
341	C₂²⋊C₄	—	47	32	no	—
342	C₂²⋊C₄	—	47	32	no	—
343	C₂²⋊C₄	—	47	32	no	—
344	C₂²⋊C₄	—	47	16	no	—
345	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
346	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
347	C₄²	—	47	16	no	—
348	C₄²	—	47	32	no	—
349	C₂³	—	2	64	no	—
350	C₂³	—	2	24	no	—
351	C₂³	—	2	24	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	2	64	no	—
354	C₂³	—	2	24	no	—
355	C₂³	—	2	12	no	—
356	C₂³	—	2	12	no	—
357	C₂³	—	4	16	no	—
358	C₂³	—	4	192	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	4	16	no	—
361	C₂³	C₂×#10625352	1	48	yes	—
362	C₂³	C₂×#10625352	1	8	yes	—
363	C₂³	#13094069	1	4	yes	—
364	C₂³	C₂⁴×D₄₇	1	4	yes	—
365	C₂³	C₂⁴×D₄₇	1	4	yes	—
366	C₂³	C₂⁴×D₄₇	1	8	yes	—
367	C₂³	C₂⁴×D₄₇	1	3	yes	—
368	Q₈	—	188	16	no	—
369	D₄	—	2	64	no	—
370	D₄	—	4	16	no	—
371	C₂×C₄	—	2	24	no	—
372	C₂×C₄	—	2	12	no	—
373	C₂×C₄	—	47	8	no	—
374	C₂×C₄	—	47	8	no	—
375	C₂×C₄	—	47	8	no	—
376	C₂×C₄	—	47	8	no	—
377	C₂×C₄	—	94	64	no	—
378	C₂×C₄	—	94	24	no	—
379	C₂×C₄	—	94	24	no	—
380	C₂×C₄	—	94	24	no	—
381	C₂×C₄	—	94	24	no	—
382	C₂×C₄	—	188	16	no	—
383	C₂×C₄	—	188	32	no	—
384	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
385	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
386	C₂²	—	2	96	no	—
387	C₂²	—	2	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	8	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	4	64	no	—
394	C₂²	—	4	24	no	—
395	C₂²	—	4	24	no	—
396	C₂²	#15689804	1	16	yes	direct product factor
397	C₂²	C₂²×#10625352	1	16	yes	—
398	C₂²	C₂²×#10625352	1	12	yes	—
399	C₂²	C₂×#13094069	1	6	yes	—
400	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	4	no	—
403	C₄	—	94	8	no	—
404	C₄	—	94	8	no	—
405	C₄	—	94	8	no	—
406	C₄	—	94	8	no	—
407	C₂	—	2	16	no	—
408	C₂	—	4	4	no	—
409	C₂	—	4	4	no	—
410	C₂	C₂×#15689804	1	12	yes	direct product factor
411	C₂	C₂³×#10625352	1	2	yes	—
412	C₂	C₂²×#13094069	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting, prime radical	C₂²×#120×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂²×#120	D₄₇
hypocenter	C₄₇	C₂²×#551
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂×#15689804	C₂	direct (N × H)
2. C₂²×#13094017	C₂	semidirect
3. C₂²×#13094011	C₂	semidirect
4. C₂²×#13094005	C₂	semidirect
5. C₂²×#13094005	C₂	semidirect
6. C₂²×#13094001	C₂	semidirect
7. C₂²×D₄×Dic₄₇	C₂	semidirect
8. C₂²×#13093980	C₂	semidirect
9. C₂³×C₂²⋊Dic₄₇	C₂	semidirect
11. C₂³×Dic₉₄	C₂²	semidirect
14. C₂⁴×Dic₄₇	C₂²	semidirect
15. #15689804	C₂²	direct (N × H)
16. C₂×#13094017	C₂²	semidirect
17. C₂×#13094011	C₂²	semidirect
18. C₂×#13094005	C₂²	semidirect
19. C₂×#13094005	C₂²	semidirect
20. C₂×#13094001	C₂²	semidirect
21. C₂×D₄×Dic₄₇	C₂²	semidirect
22. C₂×#13093980	C₂²	semidirect
23. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
24. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
25. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
26. C₂²×Dic₄₇⋊C₄	C₂²	semidirect
31. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
32. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
33. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
34. C₂²×C₄×Dic₄₇	C₂²	semidirect
35. C₂²×C₄×Dic₄₇	C₂²	semidirect
43. C₂²×Dic₉₄	C₂³	semidirect
53. C₂³×Dic₄₇	C₂³	semidirect
54. #13094017	C₂³	semidirect
55. #13094011	C₂³	semidirect
56. #13094005	C₂³	semidirect
57. #13094005	C₂³	semidirect
58. #13094001	C₂³	semidirect
59. D₄×Dic₄₇	C₂³	semidirect
60. #13093980	C₂³	semidirect
61. C₂×C₄⋊Dic₄₇	C₂³	semidirect
62. C₂×Dic₄₇⋊C₄	C₂³	semidirect
63. C₂×Dic₄₇⋊C₄	C₂³	semidirect
64. C₂×Dic₄₇⋊C₄	C₂³	semidirect
69. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
70. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
71. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
72. C₂×C₄×Dic₄₇	C₂³	semidirect
73. C₂×C₄×Dic₄₇	C₂³	semidirect
125. C₂²×Dic₄₇	C₂⁴	semidirect
127. C₂×Dic₉₄	C₂⁴	semidirect
134. C₂²⋊Dic₄₇	C₂⁴	semidirect
135. C₂²⋊Dic₄₇	C₂⁴	semidirect
136. C₄⋊Dic₄₇	C₂⁴	semidirect
137. Dic₄₇⋊C₄	C₂⁴	semidirect
138. Dic₄₇⋊C₄	C₂⁴	semidirect
139. Dic₄₇⋊C₄	C₂⁴	semidirect
140. C₄×Dic₄₇	C₂⁴	semidirect
141. C₄×Dic₄₇	C₂⁴	semidirect
190. C₂²×C₄₇	#551	semidirect
214. C₂×C₄₇	C₂×#551	semidirect
248. C₄₇	C₂²×#551	semidirect
396. C₂²	#15689804	direct (N × H)
410. C₂	C₂×#15689804	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×#15689804	2
C₂²×#13094017	2
C₂²×#13094011	2
C₂²×#13094005	2
C₂²×#13094001	2
C₂²×D₄×Dic₄₇	2
C₂²×#13093980	2
C₂³×C₂²⋊Dic₄₇	2
C₂²×#120×C₄₇	2
C₂²×#551	47

Subgroups — C22×#15689804 #27123259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689804 #27123259