Subgroups — C₂×#20258082 #27123707

Order 12032.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258082	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689873	C₂	1	3	yes	maximal, complemented
3	C₂×#15689842	C₂	1	6	yes	maximal, complemented
4	C₂×#15689804	C₂	1	6	yes	maximal, complemented
5	C₂×#15689737	C₂	1	6	yes	maximal, complemented
6	C₂×#15689708	C₂	1	6	yes	maximal, complemented
7	C₂×#15689652	C₂	1	3	yes	maximal, complemented
8	C₂×C₄₇×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689873	C₂²	1	48	yes	complemented
10	#15689842	C₂²	1	96	yes	complemented
11	#15689804	C₂²	1	96	yes	complemented
12	#15689737	C₂²	1	96	yes	complemented
13	#15689708	C₂²	1	96	yes	complemented
14	C₂×#13094022	C₂²	1	6	yes	complemented
15	#15689652	C₂²	1	48	yes	complemented
16	C₂×#13094018	C₂²	1	2	yes	complemented
17	C₂×#13094017	C₂²	1	6	yes	complemented
18	C₂×#13094017	C₂²	1	6	yes	complemented
19	C₂×#13094017	C₂²	1	6	yes	complemented
20	C₂×#13094017	C₂²	1	6	yes	complemented
21	C₂×#13094016	C₂²	1	3	yes	complemented
22	C₂×#13094011	C₂²	1	6	yes	—
23	C₂×#13094010	C₂²	1	6	yes	complemented
24	C₂×#13094006	C₂²	1	6	yes	complemented
25	C₂×#13094005	C₂²	1	6	yes	—
26	C₂×#13094005	C₂²	1	6	yes	—
27	C₂×#13094001	C₂²	1	6	yes	complemented
28	C₂×#13094001	C₂²	1	6	yes	complemented
29	C₂×#13094001	C₂²	1	6	yes	complemented
30	C₂×#13094000	C₂²	1	3	yes	complemented
31	C₂×#13093996	C₂²	1	6	yes	—
32	C₂×#13093995	C₂²	1	3	yes	—
33	C₂×#13093993	C₂²	1	2	yes	complemented
34	C₂×Q₈×Dic₄₇	C₂²	1	3	yes	complemented
35	C₂×C₄×Dic₉₄	C₂²	1	6	yes	complemented
36	C₂×D₄×Dic₄₇	C₂²	1	3	yes	—
37	C₂×D₄×Dic₄₇	C₂²	1	6	yes	—
38	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	6	yes	complemented
39	C₂×#13093980	C₂²	1	6	yes	complemented
40	C₂×#13093980	C₂²	1	6	yes	complemented
41	C₂²×C₂²⋊Dic₄₇	C₂²	1	6	yes	complemented
42	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×H(3,𝔽₄)	C₂²	1	16	yes	complemented
44	C₂×#124×C₄₇	C₂²	1	3	yes	—
45	C₂×#124×C₄₇	C₂²	1	6	yes	—
46	C₂×#120×C₄₇	C₂²	1	6	yes	—
47	C₂²×Dic₉₄	C₂³	1	6	yes	—
48	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
49	C₂³×Dic₄₇	C₂³	1	6	yes	—
50	C₂³×Dic₄₇	C₂³	1	6	yes	—
51	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
52	#13094022	C₂³	1	48	yes	complemented
53	#13094018	C₂³	1	16	yes	complemented
54	#13094017	C₂³	1	48	yes	complemented
55	#13094017	C₂³	1	48	yes	complemented
56	#13094017	C₂³	1	48	yes	complemented
57	#13094017	C₂³	1	48	yes	complemented
58	#13094016	C₂³	1	24	yes	complemented
59	#13094011	C₂³	1	48	yes	—
60	#13094010	C₂³	1	48	yes	complemented
61	#13094006	C₂³	1	48	yes	complemented
62	#13094005	C₂³	1	48	yes	—
63	#13094005	C₂³	1	48	yes	—
64	#13094001	C₂³	1	48	yes	complemented
65	#13094001	C₂³	1	48	yes	complemented
66	#13094001	C₂³	1	48	yes	complemented
67	#13094000	C₂³	1	24	yes	complemented
68	#13093996	C₂³	1	48	yes	—
69	#13093995	C₂³	1	24	yes	—
70	#13093993	C₂³	1	16	yes	complemented
71	Q₈×Dic₄₇	C₂³	1	24	yes	complemented
72	C₄×Dic₉₄	C₂³	1	48	yes	complemented
73	D₄×Dic₄₇	C₂³	1	24	yes	—
74	D₄×Dic₄₇	C₂³	1	48	yes	—
75	(C₂²⋊D₄₇)⋊C₄	C₂³	1	48	yes	complemented
76	#13093980	C₂³	1	48	yes	complemented
77	#13093980	C₂³	1	48	yes	complemented
78	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
79	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
80	C₂×C₄⋊Dic₄₇	C₂³	1	3	yes	—
81	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
82	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
83	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
84	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
85	C₂×Dic₄₇⋊C₄	C₂³	1	6	yes	—
86	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
87	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
88	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
89	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
90	C₂×C₂²⋊Dic₄₇	C₂³	1	6	yes	—
91	C₂×C₂²⋊Dic₄₇	C₂³	1	48	yes	complemented
92	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	6	yes	—
93	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
94	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
95	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
96	C₄²×D₄₇	C₂³	1	8	yes	complemented
97	C₂⁵×C₄₇	C₂³	1	2	yes	—
98	C₂²×Q₈×C₄₇	C₂³	1	3	yes	—
99	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
100	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
101	#124×C₄₇	C₂³	1	48	yes	—
102	#124×C₄₇	C₂³	1	24	yes	—
103	#120×C₄₇	C₂³	1	48	yes	—
104	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
105	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
106	C₂×C₂²⋊C₄×C₄₇	C₂³	1	6	yes	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
109	C₂⁴×C₄₇	—	4	12	no	—
110	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
111	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
112	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×Q₈×C₄₇	—	4	6	no	—
114	C₂×Q₈×C₄₇	C₂⁴	1	12	yes	—
115	C₂×D₄×C₄₇	—	4	12	no	—
116	C₂×D₄×C₄₇	—	4	6	no	—
117	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
118	C₂×D₄×C₄₇	C₂⁴	1	24	yes	—
119	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
121	C₂×C₂²⋊D₄₇	—	4	12	no	—
122	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
123	C₂²×Dic₄₇	—	4	12	no	—
124	C₂²×Dic₄₇	—	4	12	no	—
125	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
126	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
127	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
128	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
129	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
130	C₂×C₄×D₄₇	—	4	6	no	—
131	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
132	C₂×Dic₉₄	—	4	12	no	—
133	C₂×Dic₉₄	C₂⁴	1	24	yes	—
134	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
135	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
136	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
137	C₄²×C₄₇	C₂⁴	1	4	yes	—
138	C₄²×C₄₇	C₂⁴	1	8	yes	—
139	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
140	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
141	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
142	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
143	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
144	(C₂×D₄₇)⋊C₄	C₂⁴	1	24	yes	—
145	C₄⋊Dic₄₇	C₂⁴	1	24	yes	—
146	C₄⋊Dic₄₇	C₂⁴	1	12	yes	—
147	C₄⋊Dic₄₇	C₂⁴	1	12	yes	—
148	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
149	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
150	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
151	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
152	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
153	C₄×Dic₄₇	C₂⁴	1	12	yes	—
154	C₄×Dic₄₇	C₂⁴	1	24	yes	—
155	C₄×Dic₄₇	C₂⁴	1	24	yes	—
156	C₂³×C₄₇	—	2	12	no	—
157	C₂³×C₄₇	—	2	12	no	—
158	C₂³×C₄₇	—	2	12	no	—
159	C₂³×C₄₇	—	4	24	no	—
160	C₂³×C₄₇	—	8	16	no	—
161	C₂³×C₄₇	C₂⁵	1	12	yes	—
162	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
163	C₂²×D₄₇	—	2	6	no	—
164	C₂²×D₄₇	C₂⁵	1	2	yes	—
165	Q₈×C₄₇	—	4	12	no	—
166	D₄×C₄₇	—	4	24	no	—
167	D₄×C₄₇	—	4	12	no	—
168	C₂×C₄×C₄₇	—	2	12	no	—
169	C₂×C₄×C₄₇	—	2	6	no	—
170	C₂×C₄×C₄₇	C₂⁵	1	12	yes	—
171	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
172	C₂²⋊D₄₇	—	4	24	no	—
173	C₂×Dic₄₇	—	2	12	no	—
174	C₂×Dic₄₇	—	2	12	no	—
175	C₂×Dic₄₇	—	2	6	no	—
176	C₂×Dic₄₇	—	4	24	no	—
177	C₂×Dic₄₇	—	4	24	no	—
178	C₂×Dic₄₇	C₂⁵	1	6	yes	—
179	C₂×Dic₄₇	C₂⁵	1	12	yes	—
180	C₂×Dic₄₇	C₂⁵	1	12	yes	—
181	C₄×D₄₇	—	4	12	no	—
182	Dic₉₄	—	4	24	no	—
183	C₂×#3568	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	12	no	—
185	C₂²×C₄₇	—	2	12	no	—
186	C₂²×C₄₇	—	2	12	no	—
187	C₂²×C₄₇	—	4	24	no	—
188	C₂²×C₄₇	—	8	16	no	—
189	C₂²×C₄₇	#585	1	6	yes	—
190	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
191	C₂×D₄₇	—	2	6	no	—
192	C₂×D₄₇	—	4	4	no	—
193	C₄×C₄₇	—	2	12	no	—
194	C₄×C₄₇	—	2	6	no	—
195	Dic₄₇	—	2	12	no	—
196	Dic₄₇	—	2	12	no	—
197	Dic₄₇	—	2	6	no	—
198	#3568	—	47	32	no	—
199	C₂×#563	—	47	3	no	—
200	C₂×H(3,𝔽₄)	D₄₇	1	1	yes	characteristic, complemented
201	C₂×#556	—	47	6	no	—
202	C₂×#551	—	47	6	no	—
203	C₂×#542	—	47	6	no	—
204	C₂×#538	—	47	6	no	—
205	C₂×#529	—	47	3	no	—
206	C₂×C₄₇	—	4	12	no	—
207	C₂×C₄₇	#3568	1	4	yes	complemented
208	C₂×C₄₇	C₂×#585	1	3	yes	—
209	D₄₇	—	4	2	no	—
210	#563	—	47	48	no	—
211	H(3,𝔽₄)	C₂×D₄₇	1	16	yes	complemented
212	#556	—	47	96	no	—
213	#551	—	47	96	no	—
214	#542	—	47	96	no	—
215	#538	—	47	96	no	—
216	C₂×C₄⋊Q₈	—	47	6	no	—
217	#529	—	47	48	no	—
218	C₂×#126	—	47	6	no	—
219	C₂×#126	—	47	6	no	—
220	C₂×#126	—	47	6	no	—
221	C₂×#126	—	47	6	no	—
222	C₂×#126	—	47	2	no	—
223	C₂×#125	—	47	3	no	—
224	C₂×#124	—	47	6	no	—
225	C₂×#124	—	47	6	no	—
226	C₂×#124	C₂×D₄₇	1	3	yes	—
227	C₂×#124	C₂×D₄₇	1	6	yes	—
228	C₂×#123	—	47	6	no	—
229	C₂×#123	—	47	6	no	—
230	C₂×#123	—	47	6	no	—
231	C₂×C₂²⋊Q₈	—	47	3	no	—
232	C₂×C₂²⋊Q₈	—	47	6	no	—
233	C₂×C₂²⋊Q₈	—	47	6	no	—
234	C₂×C₂²⋊Q₈	—	47	6	no	—
235	C₂×#121	—	47	3	no	—
236	C₂×#121	—	47	6	no	—
237	C₂×#120	—	47	2	no	—
238	C₂×#120	C₂×D₄₇	1	6	yes	—
239	C₂×C₄×Q₈	—	47	3	no	—
240	C₂×C₄×Q₈	—	47	6	no	—
241	C₂×C₄×D₄	—	47	3	no	—
242	C₂×C₄×D₄	—	47	6	no	—
243	C₂×C₄×D₄	—	47	6	no	—
244	C₂×#117	—	47	6	no	—
245	C₂×#117	—	47	6	no	—
246	C₂²×C₂²⋊C₄	—	47	6	no	—
247	C₂²×C₄²	—	47	1	no	—
248	C₄₇	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
249	C₂⁵	C₂²×D₄₇	1	2	yes	—
250	C₂²×Q₈	—	47	6	no	—
251	C₂²×Q₈	C₂²×D₄₇	1	3	yes	—
252	C₂²×D₄	—	47	6	no	—
253	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
254	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
255	C₂³×C₄	—	47	6	no	—
256	C₂³×C₄	—	47	6	no	—
257	C₂³×C₄	—	47	3	no	—
258	C₄⋊Q₈	—	47	48	no	—
259	#126	—	47	48	no	—
260	#126	—	47	48	no	—
261	#126	—	47	48	no	—
262	#126	—	47	48	no	—
263	#126	—	47	16	no	—
264	#125	—	47	24	no	—
265	#124	—	47	48	no	—
266	#124	—	47	48	no	—
267	#124	C₂²×D₄₇	1	24	yes	—
268	#124	C₂²×D₄₇	1	48	yes	—
269	#123	—	47	48	no	—
270	#123	—	47	48	no	—
271	#123	—	47	48	no	—
272	C₂²⋊Q₈	—	47	24	no	—
273	C₂²⋊Q₈	—	47	48	no	—
274	C₂²⋊Q₈	—	47	48	no	—
275	C₂²⋊Q₈	—	47	48	no	—
276	#121	—	47	24	no	—
277	#121	—	47	48	no	—
278	#120	—	47	16	no	—
279	#120	C₂²×D₄₇	1	48	yes	—
280	C₄×Q₈	—	47	24	no	—
281	C₄×Q₈	—	47	48	no	—
282	C₄×D₄	—	47	24	no	—
283	C₄×D₄	—	47	48	no	—
284	C₄×D₄	—	47	48	no	—
285	#117	—	47	48	no	—
286	#117	—	47	48	no	—
287	C₂×C₄⋊C₄	—	47	6	no	—
288	C₂×C₄⋊C₄	—	47	6	no	—
289	C₂×C₄⋊C₄	—	47	6	no	—
290	C₂×C₄⋊C₄	—	47	6	no	—
291	C₂×C₄⋊C₄	—	47	3	no	—
292	C₂×C₄⋊C₄	—	47	6	no	—
293	C₂×C₄⋊C₄	—	47	3	no	—
294	C₂×C₄⋊C₄	—	47	6	no	—
295	C₂×C₂²⋊C₄	—	47	6	no	—
296	C₂×C₂²⋊C₄	—	47	6	no	—
297	C₂×C₂²⋊C₄	—	47	6	no	—
298	C₂×C₂²⋊C₄	—	47	6	no	—
299	C₂×C₂²⋊C₄	—	47	48	no	—
300	C₂×C₂²⋊C₄	—	47	6	no	—
301	C₂×C₂²⋊C₄	—	47	6	no	—
302	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
304	C₂×C₂²⋊C₄	C₂²×D₄₇	1	6	yes	—
305	C₂×C₄²	—	47	6	no	—
306	C₂×C₄²	—	47	3	no	—
307	C₂×C₄²	—	47	6	no	—
308	C₂×C₄²	—	47	8	no	—
309	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
310	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
311	C₂⁴	—	4	12	no	—
312	C₂⁴	—	47	1	no	—
313	C₂⁴	C₂³×D₄₇	1	6	yes	—
314	C₂⁴	C₂³×D₄₇	1	8	yes	—
315	C₂×Q₈	—	4	6	no	—
316	C₂×Q₈	—	47	24	no	—
317	C₂×Q₈	—	188	12	no	—
318	C₂×Q₈	C₂³×D₄₇	1	12	yes	—
319	C₂×D₄	—	4	6	no	—
320	C₂×D₄	—	4	12	no	—
321	C₂×D₄	—	47	24	no	—
322	C₂×D₄	—	188	12	no	—
323	C₂×D₄	C₂³×D₄₇	1	12	yes	—
324	C₂×D₄	C₂³×D₄₇	1	24	yes	—
325	C₂²×C₄	—	47	3	no	—
326	C₂²×C₄	—	47	6	no	—
327	C₂²×C₄	—	47	6	no	—
328	C₂²×C₄	—	47	24	no	—
329	C₂²×C₄	—	47	24	no	—
330	C₂²×C₄	—	47	12	no	—
331	C₂²×C₄	—	188	6	no	—
332	C₂²×C₄	—	188	12	no	—
333	C₂²×C₄	—	188	12	no	—
334	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
335	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
336	C₄⋊C₄	—	47	24	no	—
337	C₄⋊C₄	—	47	24	no	—
338	C₄⋊C₄	—	47	24	no	—
339	C₄⋊C₄	—	47	24	no	—
340	C₄⋊C₄	—	47	24	no	—
341	C₄⋊C₄	—	47	24	no	—
342	C₄⋊C₄	—	47	12	no	—
343	C₄⋊C₄	—	47	12	no	—
344	C₂²⋊C₄	—	47	24	no	—
345	C₂²⋊C₄	—	47	24	no	—
346	C₂²⋊C₄	—	47	24	no	—
347	C₂²⋊C₄	—	47	24	no	—
348	C₂²⋊C₄	—	47	24	no	—
349	C₂²⋊C₄	—	47	24	no	—
350	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
351	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
352	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
353	C₄²	—	47	12	no	—
354	C₄²	—	47	24	no	—
355	C₄²	—	47	24	no	—
356	C₄²	C₂³×D₄₇	1	4	yes	—
357	C₄²	C₂³×D₄₇	1	8	yes	—
358	C₂³	—	2	12	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	4	24	no	—
362	C₂³	—	8	16	no	—
363	C₂³	—	47	2	no	—
364	C₂³	—	94	6	no	—
365	C₂³	C₂⁴×D₄₇	1	12	yes	—
366	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
367	Q₈	—	4	12	no	—
368	Q₈	—	188	24	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	24	no	—
371	D₄	—	188	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	47	6	no	—
375	C₂×C₄	—	47	12	no	—
376	C₂×C₄	—	47	12	no	—
377	C₂×C₄	—	94	6	no	—
378	C₂×C₄	—	94	12	no	—
379	C₂×C₄	—	94	12	no	—
380	C₂×C₄	—	188	12	no	—
381	C₂×C₄	—	188	24	no	—
382	C₂×C₄	—	188	24	no	—
383	C₂×C₄	C₂⁴×D₄₇	1	12	yes	—
384	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
385	C₂²	—	2	12	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	94	6	no	—
391	C₂²	—	188	4	no	—
392	C₂²	#15689958	1	6	yes	—
393	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	94	6	no	—
397	C₄	—	94	12	no	—
398	C₄	—	94	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	188	2	no	—
401	C₂	#20258082	1	4	yes	direct product factor
402	C₂	C₂×#15689958	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×H(3,𝔽₄)	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₄₇
hypocenter	C₄₇	C₂×#3568
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #20258082	C₂	direct (N × H)
2. C₂×#15689873	C₂	semidirect
3. C₂×#15689842	C₂	semidirect
4. C₂×#15689804	C₂	semidirect
5. C₂×#15689737	C₂	semidirect
6. C₂×#15689708	C₂	semidirect
7. C₂×#15689652	C₂	semidirect
8. C₂×C₄₇×H(3,𝔽₄)	C₂	semidirect
9. #15689873	C₂²	semidirect
10. #15689842	C₂²	semidirect
11. #15689804	C₂²	semidirect
12. #15689737	C₂²	semidirect
13. #15689708	C₂²	semidirect
14. C₂×#13094022	C₂²	semidirect
15. #15689652	C₂²	semidirect
16. C₂×#13094018	C₂²	semidirect
17. C₂×#13094017	C₂²	semidirect
18. C₂×#13094017	C₂²	semidirect
19. C₂×#13094017	C₂²	semidirect
20. C₂×#13094017	C₂²	semidirect
21. C₂×#13094016	C₂²	semidirect
23. C₂×#13094010	C₂²	semidirect
24. C₂×#13094006	C₂²	semidirect
27. C₂×#13094001	C₂²	semidirect
28. C₂×#13094001	C₂²	semidirect
29. C₂×#13094001	C₂²	semidirect
30. C₂×#13094000	C₂²	semidirect
33. C₂×#13093993	C₂²	semidirect
34. C₂×Q₈×Dic₄₇	C₂²	semidirect
35. C₂×C₄×Dic₉₄	C₂²	semidirect
38. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
39. C₂×#13093980	C₂²	semidirect
40. C₂×#13093980	C₂²	semidirect
41. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
42. C₂×C₄²×D₄₇	C₂²	semidirect
43. C₄₇×H(3,𝔽₄)	C₂²	semidirect
52. #13094022	C₂³	semidirect
53. #13094018	C₂³	semidirect
54. #13094017	C₂³	semidirect
55. #13094017	C₂³	semidirect
56. #13094017	C₂³	semidirect
57. #13094017	C₂³	semidirect
58. #13094016	C₂³	semidirect
60. #13094010	C₂³	semidirect
61. #13094006	C₂³	semidirect
64. #13094001	C₂³	semidirect
65. #13094001	C₂³	semidirect
66. #13094001	C₂³	semidirect
67. #13094000	C₂³	semidirect
70. #13093993	C₂³	semidirect
71. Q₈×Dic₄₇	C₂³	semidirect
72. C₄×Dic₉₄	C₂³	semidirect
75. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
76. #13093980	C₂³	semidirect
77. #13093980	C₂³	semidirect
91. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
96. C₄²×D₄₇	C₂³	semidirect
200. C₂×H(3,𝔽₄)	D₄₇	semidirect
207. C₂×C₄₇	#3568	semidirect
211. H(3,𝔽₄)	C₂×D₄₇	semidirect
248. C₄₇	C₂×#3568	semidirect
401. C₂	#20258082	direct (N × H)

Maximal subgroups

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

subgroup	index
#20258082	2
C₂×#15689873	2
C₂×#15689842	2
C₂×#15689804	2
C₂×#15689737	2
C₂×#15689708	2
C₂×#15689652	2
C₂×C₄₇×H(3,𝔽₄)	2
C₂×#3568	47

Subgroups — C2×#20258082 #27123707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20258082 #27123707