Subgroups — C₂×#20244217 #26220000

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13093951	C₂	1	4	yes	maximal, complemented
3	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244217	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	—	2	2	no	—
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	#15689147	—	2	2	no	—
10	#15689147	C₂²	1	4	yes	complemented
11	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
12	C₂×#13093951	—	2	16	no	—
13	C₂×#13093951	C₂²	1	16	yes	complemented
14	C₄²×Dic₄₇	—	2	2	no	—
15	C₄²×Dic₄₇	C₂²	1	4	yes	complemented
16	C₂²×#41×C₄₇	C₂²	1	2	yes	—
17	C₄₇×#532	—	2	2	no	—
18	C₄₇×#532	—	2	2	no	—
19	C₄₇×#532	C₄	1	4	yes	complemented
20	C₄₇×#532	C₂²	1	4	yes	—
21	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
22	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
23	C₂×#124×C₄₇	C₄	1	2	yes	complemented
24	C₂×#121×C₄₇	—	2	2	no	—
25	C₂×C₄×D₄×C₄₇	—	2	2	no	—
26	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	8	no	—
30	C₂×#10625329	C₂³	1	4	yes	—
31	C₂²×C₄₇⋊C₈	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	16	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	8	no	—
35	C₂×C₄×Dic₄₇	—	2	4	no	—
36	C₂×C₄×Dic₄₇	D₄	1	8	yes	complemented
37	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
38	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
39	#13093951	—	2	32	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	8	no	—
43	C₂×#41×C₄₇	—	2	8	no	—
44	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×#41×C₄₇	C₂³	1	4	yes	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₄₇	—	2	2	no	—
48	C₂²×D₄×C₄₇	—	2	2	no	—
49	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	—	2	2	no	—
51	C₂³×C₄×C₄₇	D₄	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
55	#127×C₄₇	—	2	2	no	—
56	#127×C₄₇	C₂×C₄	1	4	yes	complemented
57	#124×C₄₇	—	2	4	no	—
58	#124×C₄₇	C₂×C₄	1	8	yes	complemented
59	#121×C₄₇	—	2	8	no	—
60	#121×C₄₇	—	2	8	no	—
61	C₄×D₄×C₄₇	—	2	8	no	—
62	C₄×D₄×C₄₇	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	D₄	1	2	yes	—
69	C₂×C₄²×C₄₇	D₄	1	2	yes	—
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₂⁴×C₄₇	—	2	2	no	—
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
74	#41×C₄₇	—	2	16	no	—
75	#41×C₄₇	—	2	8	no	—
76	#41×C₄₇	—	2	8	no	—
77	#41×C₄₇	—	4	8	no	—
78	#41×C₄₇	—	4	4	no	—
79	#41×C₄₇	—	4	4	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	—	2	8	no	—
82	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	4	no	—
85	C₂×D₄×C₄₇	—	2	8	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	8	no	—
88	C₂×D₄×C₄₇	—	4	8	no	—
89	C₂×D₄×C₄₇	—	4	8	no	—
90	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	4	4	no	—
96	C₂²×C₄×C₄₇	—	4	4	no	—
97	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₇	#41	1	4	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	16	no	—
110	C₂²×Dic₄₇	—	2	8	no	—
111	C₂²×Dic₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	—	2	8	no	—
113	C₂²⋊C₄×C₄₇	—	2	16	no	—
114	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
115	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂×D₄	1	4	yes	—
120	C₄×Dic₄₇	—	2	32	no	—
121	C₄×Dic₄₇	—	2	8	no	—
122	C₄×Dic₄₇	—	2	4	no	—
123	C₄×Dic₄₇	C₂×D₄	1	8	yes	complemented
124	#10625329	—	2	8	no	—
125	#10625329	—	4	4	no	—
126	C₂×C₄₇⋊C₈	—	2	4	no	—
127	C₂×C₄₇⋊C₈	—	4	4	no	—
128	C₂³×C₄₇	—	2	4	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	8	no	—
132	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₇	#121	1	4	yes	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	8	no	—
137	Q₈×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	2	8	no	—
139	D₄×C₄₇	—	4	8	no	—
140	D₄×C₄₇	—	4	8	no	—
141	D₄×C₄₇	—	4	4	no	—
142	D₄×C₄₇	—	4	16	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	2	8	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	8	no	—
151	C₂×C₄×C₄₇	#104	1	8	yes	complemented
152	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
157	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
158	C₂×C₄×C₄₇	#121	1	4	yes	—
159	C₂×C₄×C₄₇	#124	1	2	yes	—
160	C₂×C₄×C₄₇	#124	1	2	yes	—
161	C₂×C₄×C₄₇	#127	1	2	yes	—
162	C₂×C₄×C₄₇	#127	1	2	yes	—
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
167	C₂×Dic₄₇	—	2	16	no	—
168	C₂×Dic₄₇	—	2	32	no	—
169	C₂×Dic₄₇	—	2	8	no	—
170	C₄₇⋊C₈	—	4	4	no	—
171	C₂×#1962	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	8	no	—
175	C₂²×C₄₇	—	4	8	no	—
176	C₂²×C₄₇	—	4	4	no	—
177	C₂²×C₄₇	—	8	8	no	—
178	C₂²×C₄₇	#390	1	2	yes	—
179	C₂²×C₄₇	#390	1	2	yes	—
180	C₂²×C₄₇	C₂×#104	1	4	yes	—
181	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#121	1	2	yes	—
183	C₄×C₄₇	—	2	4	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	#390	1	2	yes	—
186	C₄×C₄₇	#390	1	2	yes	—
187	C₄×C₄₇	C₂×#104	1	8	yes	complemented
188	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
189	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
191	Dic₄₇	—	2	16	no	—
192	C₂×#532	D₄₇	1	1	yes	characteristic
193	C₂×#423	—	47	1	no	—
194	C₂²×#104	—	47	4	no	—
195	C₂×C₄³	—	47	1	no	—
196	#1962	—	47	8	no	—
197	C₂×C₄₇	—	2	2	no	—
198	C₂×C₄₇	—	2	2	no	—
199	C₂×C₄₇	—	8	4	no	—
200	C₂×C₄₇	#1962	1	4	yes	complemented
201	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
202	C₂×C₄₇	C₂²×#104	1	2	yes	—
203	C₂²×#41	C₂×D₄₇	1	2	yes	—
204	C₂²×M₁₆	—	47	2	no	—
205	#532	—	2	2	no	—
206	#532	—	2	2	no	—
207	#532	Dic₄₇	1	4	yes	complemented
208	#532	C₂×D₄₇	1	4	yes	—
209	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic, complemented
210	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
211	C₂×#124	Dic₄₇	1	2	yes	complemented
212	C₂×#121	—	2	2	no	—
213	C₂×C₄×D₄	—	2	2	no	—
214	C₂²×C₄²	—	47	2	no	—
215	C₂²×C₄²	—	94	2	no	—
216	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
217	#423	—	47	4	no	—
218	#423	—	94	2	no	—
219	C₂×C₄⋊C₈	—	94	2	no	—
220	C₂×#104	—	47	16	no	—
221	C₂×#104	—	94	16	no	—
222	C₄³	—	47	4	no	—
223	C₄³	—	94	2	no	—
224	C₄₇	C₂×#1962	1	1	yes	characteristic, complemented, Sylow
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	8	no	—
228	C₂×#41	—	2	8	no	—
229	C₂×#41	C₂×Dic₄₇	1	4	yes	—
230	C₂×#41	C₂²×D₄₇	1	4	yes	—
231	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
232	C₂²×D₄	—	2	2	no	—
233	C₂²×D₄	—	2	2	no	—
234	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	—	94	2	no	—
237	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂×M₁₆	—	47	4	no	—
240	C₂×M₁₆	—	94	2	no	—
241	C₂×M₁₆	—	94	8	no	—
242	C₂²×C₈	—	94	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
245	#127	—	2	2	no	—
246	#127	C₂×Dic₄₇	1	4	yes	complemented
247	#124	—	2	4	no	—
248	#124	C₂×Dic₄₇	1	8	yes	complemented
249	#121	—	2	8	no	—
250	#121	—	2	8	no	—
251	C₄×D₄	—	2	8	no	—
252	C₄×D₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₄²	—	47	8	no	—
256	C₂×C₄²	—	47	4	no	—
257	C₂×C₄²	—	94	16	no	—
258	C₂×C₄²	—	94	4	no	—
259	C₂×C₄²	—	94	8	no	—
260	C₂×C₄²	—	94	2	no	—
261	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
262	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
265	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
266	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
267	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
268	C₄⋊C₈	—	94	8	no	—
269	#104	—	94	32	no	—
270	C₂⁴	—	2	2	no	—
271	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
272	#41	—	2	16	no	—
273	#41	—	2	8	no	—
274	#41	—	2	8	no	—
275	#41	—	4	8	no	—
276	#41	—	4	4	no	—
277	#41	—	4	4	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	4	8	no	—
288	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	—	94	16	no	—
296	C₂²×C₄	—	94	8	no	—
297	C₂²×C₄	—	94	4	no	—
298	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
299	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
300	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
301	C₂²×C₄	D₄×D₄₇	1	4	yes	—
302	C₂²×C₄	#10625352	1	4	yes	—
303	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
306	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
310	M₁₆	—	94	8	no	—
311	M₁₆	—	188	4	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	—	188	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₄²	—	47	8	no	—
317	C₄²	—	94	32	no	—
318	C₄²	—	94	8	no	—
319	C₄²	—	94	4	no	—
320	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
321	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
322	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
323	C₄²	C₂²×Dic₄₇	1	2	yes	—
324	C₄²	C₂²×Dic₄₇	1	2	yes	—
325	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
326	C₂³	—	2	4	no	—
327	C₂³	—	2	4	no	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	8	no	—
330	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
331	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂³	#13093995	1	4	yes	—
333	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
334	Q₈	—	2	8	no	—
335	Q₈	—	4	4	no	—
336	D₄	—	2	8	no	—
337	D₄	—	4	8	no	—
338	D₄	—	4	8	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	16	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	94	16	no	—
350	C₂×C₄	—	94	32	no	—
351	C₂×C₄	—	94	8	no	—
352	C₂×C₄	#13093951	1	8	yes	complemented
353	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
354	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
357	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
358	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
359	C₂×C₄	#13093995	1	4	yes	—
360	C₂×C₄	#13094011	1	2	yes	—
361	C₂×C₄	#13094011	1	2	yes	—
362	C₂×C₄	#13094020	1	2	yes	—
363	C₂×C₄	#13094020	1	2	yes	—
364	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
366	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂×#10625352	1	2	yes	—
368	C₈	—	188	4	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	4	8	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	8	8	no	—
375	C₂²	#15689026	1	2	yes	—
376	C₂²	#15689026	1	2	yes	—
377	C₂²	C₂×#13093951	1	4	yes	—
378	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
379	C₂²	C₂×#13093995	1	2	yes	—
380	C₄	—	2	4	no	—
381	C₄	—	4	4	no	—
382	C₄	—	94	16	no	—
383	C₄	#15689026	1	2	yes	—
384	C₄	#15689026	1	2	yes	—
385	C₄	C₂×#13093951	1	8	yes	complemented
386	C₄	C₂×D₄×Dic₄₇	1	2	yes	—
387	C₄	C₂×#13094011	1	1	yes	characteristic
388	C₄	C₂×#13094020	1	1	yes	characteristic
389	C₂	—	2	2	no	—
390	C₂	—	2	2	no	—
391	C₂	—	8	4	no	—
392	C₂	#20244217	1	4	yes	direct product factor
393	C₂	C₂×#15689026	1	1	yes	characteristic
394	C₂	C₂²×#13093951	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	C₂×#1962
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂×#15689147	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. C₂×C₄²×Dic₄₇	C₂	semidirect
4. #20244217	C₂	direct (N × H)
10. #15689147	C₂²	semidirect
13. C₂×#13093951	C₂²	semidirect
15. C₄²×Dic₄₇	C₂²	semidirect
19. C₄₇×#532	C₄	semidirect
21. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
22. C₂×#127×C₄₇	C₄	semidirect
23. C₂×#124×C₄₇	C₄	semidirect
36. C₂×C₄×Dic₄₇	D₄	semidirect
54. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
56. #127×C₄₇	C₂×C₄	semidirect
58. #124×C₄₇	C₂×C₄	semidirect
123. C₄×Dic₄₇	C₂×D₄	semidirect
151. C₂×C₄×C₄₇	#104	semidirect
187. C₄×C₄₇	C₂×#104	semidirect
200. C₂×C₄₇	#1962	semidirect
207. #532	Dic₄₇	semidirect
209. C₂×C₄⋊Q₈	Dic₄₇	semidirect
210. C₂×#127	Dic₄₇	semidirect
211. C₂×#124	Dic₄₇	semidirect
224. C₄₇	C₂×#1962	semidirect
244. C₄⋊Q₈	C₂×Dic₄₇	semidirect
246. #127	C₂×Dic₄₇	semidirect
248. #124	C₂×Dic₄₇	semidirect
352. C₂×C₄	#13093951	semidirect
385. C₄	C₂×#13093951	semidirect
392. C₂	#20244217	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×#15689147	2
C₂²×#13093951	2
C₂×C₄²×Dic₄₇	2
#20244217	2
C₂×C₄₇×#532	2
C₂×#1962	47

Subgroups — C2×#20244217 #26220000

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244217 #26220000