Finite Group Databasebeta

← C2×#23749773 #34053895

Subgroups — C2×#23749773 #34053895

Order 19072.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14558737C211yesmaximal, characteristic, complemented
2C22×#14558723C211yesmaximal, characteristic, complemented
3C22×D1192C211yesmaximal, characteristic, complemented
4C2×#18011886C211yesmaximal, characteristic, complemented
5#23749773C218yesmaximal, direct product factor
6C2×#18011831C211yesmaximal, characteristic, complemented
7C2×#18011823C211yesmaximal, characteristic, complemented
8C2×#103×C149C211yesmaximal, characteristic, complemented
9C2×#14558737—24no—
10C2×#14558737—24no—
11C2×#14558737—22no—
12C2×#14558737C2214yescomplemented
13C22×D596—21no—
14C22×D596—21no—
15C22×D596C2211yescharacteristic
16C22×D596C2211yescharacteristic
17C22×C4×D149—21no—
18C22×C4×D149C2211yescharacteristic
19C2×#14558723—24no—
20C2×#14558723C2214yescomplemented
21C2×D1192—24no—
22C2×D1192C2214yescomplemented
23C22×#11924746C2211yescharacteristic
24#18011886—22no—
25#18011886C2214yescomplemented
26C2×#14558713—21no—
27#18011831C2214yescomplemented
28#18011823C2214yescomplemented
29C22×Q8×C149C2211yescharacteristic
30C22×C8×C149C2211yescharacteristic
31C2×C4⋊C4×C149C2211yescharacteristic
32#103×C149C2214yescomplemented
33C23×D149—21no—
34C23×D149—21no—
35C23×D149D411yescharacteristic
36#14558737—216no—
37#14558737—28no—
38#14558737—28no—
39C2×D596—28no—
40C2×D596—24no—
41C2×D596—24no—
42C2×D596—21no—
43C2×D596—22no—
44C2×D596—22no—
45C2×D596—22no—
46C2×D596—21no—
47C2×D596—44no—
48C2×D596D414yescomplemented
49C2×D596C2312yes—
50C2×D596C2312yes—
51C22×Dic149D411yescharacteristic
52C2×C4×D149—28no—
53C2×C4×D149—24no—
54C2×C4×D149—22no—
55C2×C4×D149—22no—
56C2×C4×D149D412yes—
57C2×C4×D149C2312yes—
58#14558723—28no—
59D1192—28no—
60C2×#11924746—22no—
61C2×#11924746C2312yes—
62#14558713—24no—
63C2×Q8×C149—22no—
64C2×Q8×C149—21no—
65C2×Q8×C149D414yescomplemented
66C2×Q8×C149C2312yes—
67C22×C4×C149—21no—
68C22×C4×C149—21no—
69C22×C4×C149C2311yescharacteristic
70C2×C8×C149—22no—
71C2×C8×C149C2312yes—
72C4⋊C4×C149—21no—
73C4⋊C4×C149C2312yes—
74C22×D149—22no—
75C22×D149—24no—
76C22×D149—22no—
77C22×D149—22no—
78C22×D149—22no—
79C22×D149—22no—
80C22×D149—42no—
81C22×D149—42no—
82C22×D149—42no—
83C22×D149—42no—
84C22×D149—42no—
85C22×D149C2×D412yes—
86D596—216no—
87D596—24no—
88D596—22no—
89D596—22no—
90D596—22no—
91D596—48no—
92D596—42no—
93D596C2×D414yescomplemented
94C2×Dic149—22no—
95C2×Dic149C2×D412yes—
96C4×D149—216no—
97C4×D149—24no—
98C4×D149—22no—
99C4×D149—22no—
100#11924746—22no—
101C23×C149C2×D411yescharacteristic
102Q8×C149—24no—
103Q8×C149—22no—
104Q8×C149C2×D414yescomplemented
105C2×C4×C149—24no—
106C2×C4×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—42no—
109C2×C4×C149C2×D411yescharacteristic
110C2×C4×C149C2×D412yes—
111C2×C4×C149C2×D412yes—
112C2×C4×C149C2411yescharacteristic
113C8×C149—22no—
114C22×C149#12012yes—
115C22×C149#13512yes—
116C22×C149AGL(1,ℤ/8)12yes—
117C22×C149C22×D411yescharacteristic
118C2×D149—22no—
119C2×D149—24no—
120C2×D149—22no—
121C2×D149—22no—
122C2×D149—42no—
123C2×D149—42no—
124C2×D149—44no—
125C2×D149—48no—
126C2×D149—42no—
127C2×D149—42no—
128C2×D149—42no—
129C2×D149—84no—
130C4×C149—24no—
131C4×C149—42no—
132C4×C149#12012yes—
133C4×C149C22×D411yescharacteristic
134C4×C149C22×D411yescharacteristic
135Dic149—22no—
136C2×C149#44914yescomplemented
137C2×C149C2×#12011yescharacteristic
138C2×C149C2×#13511yescharacteristic
139C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
140D149—42no—
141D149—44no—
142D149—82no—
143C149C2×#44911yescharacteristic, complemented, Sylow
144C2×#449—1491nomaximal, Sylow
145C22×#41—1491no—
146C22×SD16—1491no—
147C22×D8—1491no—
148C2×#121—1491no—
149#449—1498no—
150C2×#103D14911yescharacteristic, complemented
151C2×#102—1491no—
152C2×C22⋊C8—1491no—
153C2×#41—2984no—
154C2×#41—2984no—
155C2×#41—2982no—
156C2×#41—1494no—
157C22×Q8C2×D14911yescharacteristic
158C22×D4—2981no—
159C22×D4—2981no—
160C22×D4—1491no—
161C22×D4—1491no—
162C23×C4—2981no—
163C23×C4—1491no—
164C2×SD16—2984no—
165C2×SD16—1494no—
166C2×D8—2984no—
167C2×D8—1494no—
168C22×C8—1491no—
169C22×C8C2×D14911yescharacteristic
170#121—2982no—
171#121—1494no—
172C2×C4⋊C4C2×D14911yescharacteristic
173C2×C22⋊C4—2981no—
174#103C2×D14914yescomplemented
175#102—1494no—
176C22⋊C8—1494no—
177C24—2981no—
178C24—2981no—
179C24—1491no—
180#41—29816no—
181#41—2988no—
182#41—2988no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8D59614yescomplemented
186C2×Q8C22×D14912yes—
187C2×D4—2988no—
188C2×D4—2984no—
189C2×D4—2984no—
190C2×D4—2981no—
191C2×D4—2982no—
192C2×D4—2981no—
193C2×D4—2982no—
194C2×D4—2982no—
195C2×D4—5964no—
196C2×D4—1494no—
197C2×D4—1492no—
198C2×D4—1492no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—2988no—
202C22×C4—2984no—
203C22×C4—2982no—
204C22×C4—2982no—
205C22×C4—1491no—
206C22×C4—1492no—
207C22×C4—1492no—
208C22×C4C22×D14911yescharacteristic
209SD16—2988no—
210D8—2988no—
211C2×C8—22no—
212C2×C8—2982no—
213C2×C8—1492no—
214C2×C8C22×D14912yes—
215C4⋊C4—21no—
216C4⋊C4C22×D14912yes—
217C22⋊C4—2984no—
218C23—2982no—
219C23—2982no—
220C23—2982no—
221C23—2982no—
222C23—2984no—
223C23—2982no—
224C23—5962no—
225C23—5962no—
226C23—5962no—
227C23—5962no—
228C23—5962no—
229C23—1492no—
230C23D4×D14911yescharacteristic
231Q8—22no—
232Q8—24no—
233Q8C2×D59614yescomplemented
234D4—29816no—
235D4—2982no—
236D4—2982no—
237D4—2982no—
238D4—2984no—
239D4—5968no—
240D4—5962no—
241D4—1494no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—42no—
246C2×C4—29816no—
247C2×C4—2982no—
248C2×C4—2982no—
249C2×C4—2982no—
250C2×C4—2984no—
251C2×C4—1492no—
252C2×C4D4×D14912yes—
253C2×C4D4×D14911yescharacteristic
254C2×C4C2×D59612yes—
255C2×C4C23×D14911yescharacteristic
256C8—22no—
257C8—2982no—
258C22—2982no—
259C22—2982no—
260C22—2982no—
261C22—2984no—
262C22—5962no—
263C22—5962no—
264C22—5964no—
265C22—5968no—
266C22—5962no—
267C22—5962no—
268C22—5962no—
269C22—11924no—
270C22#1801188112yes—
271C22#1801193412yes—
272C22#1801193812yes—
273C22C2×D4×D14911yescharacteristic
274C4—24no—
275C4—42no—
276C4—2982no—
277C4#1801188112yes—
278C4C2×D4×D14911yescharacteristic
279C4C22×D59611yescharacteristic
280C2—5962no—
281C2—5964no—
282C2—11922no—
283C2#2374977314yesdirect product factor
284C2C2×#1801188111yescharacteristic
285C2C2×#1801193411yescharacteristic
286C2C2×#1801193811yescharacteristic
subgroupG/H
centerC23D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC2×#103×C149C2
socleC23×C149C2×D4
hypercenterC2×#103D149
hypocenterC149C2×#449
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C22×#14558737C2semidirect
2. C22×#14558723C2semidirect
3. C22×D1192C2semidirect
4. C2×#18011886C2semidirect
5. #23749773C2direct (N × H)
6. C2×#18011831C2semidirect
7. C2×#18011823C2semidirect
8. C2×#103×C149C2semidirect
12. C2×#14558737C22semidirect
20. C2×#14558723C22semidirect
22. C2×D1192C22semidirect
25. #18011886C22semidirect
27. #18011831C22semidirect
28. #18011823C22semidirect
32. #103×C149C22semidirect
48. C2×D596D4semidirect
65. C2×Q8×C149D4semidirect
93. D596C2×D4semidirect
104. Q8×C149C2×D4semidirect
136. C2×C149#449semidirect
143. C149C2×#449semidirect
150. C2×#103D149semidirect
174. #103C2×D149semidirect
185. C2×Q8D596semidirect
233. Q8C2×D596semidirect
283. C2#23749773direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145587372
C22×#145587232
C22×D11922
C2×#180118862
#237497732
C2×#180118312
C2×#180118232
C2×#103×C1492
C2×#449149