Finite Group Databasebeta

← C2×#20267936 #27204345

Subgroups — C2×#20267936 #27204345

Order 13184.

812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13110092C211yesmaximal, characteristic, complemented
2C22×#13110090C211yesmaximal, characteristic, complemented
3C2×#15692995C211yesmaximal, characteristic, complemented
4#20267936C218yesmaximal, direct product factor
5C2×#15692945C211yesmaximal, characteristic, complemented
6C2×#15692942C211yesmaximal, characteristic, complemented
7C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
8C22×#41×C103C211yesmaximal, characteristic, complemented
9C22×D412C2211yescharacteristic
10C22×C22⋊D103—21no—
11C2×#13110092—24no—
12C2×#13110092C2214yescomplemented
13C2×#13110090—24no—
14C2×#13110090C2214yescomplemented
15C22×C103⋊C8C2211yescharacteristic
16C22×C103⋊C8C2211yescharacteristic
17#15692995—22no—
18#15692995C2214yescomplemented
19C2×C4⋊Dic103C2211yescharacteristic
20C2×(C2×D103)⋊C4—21no—
21#15692945C2214yescomplemented
22#15692942C2214yescomplemented
23C22⋊(C103⋊C8)C2214yescomplemented
24C2×#41×C103—24no—
25C2×#41×C103—24no—
26C2×#41×C103—22no—
27C2×#41×C103C2214yescomplemented
28C22×Q8×C103C2211yescharacteristic
29C22×D4×C103—21no—
30C22×D4×C103C2211yescharacteristic
31C23×C4×C103—21no—
32C23×C4×C103C2211yescharacteristic
33C23×D103—21no—
34C2×D412—22no—
35C2×D412—22no—
36C2×D412—21no—
37C2×D412C2312yes—
38C2×C22⋊D103—24no—
39C2×C22⋊D103—44no—
40C22×Dic103—21no—
41#13110092—28no—
42#13110090—28no—
43C2×C103⋊C8—22no—
44C2×C103⋊C8—22no—
45C2×C103⋊C8C2312yes—
46C2×C103⋊C8C2312yes—
47C4⋊Dic103—21no—
48C4⋊Dic103C2312yes—
49(C2×D103)⋊C4—24no—
50C24×C103—21no—
51C24×C103D411yescharacteristic
52#41×C103—216no—
53#41×C103—28no—
54#41×C103—28no—
55C2×Q8×C103—22no—
56C2×Q8×C103—21no—
57C2×Q8×C103D414yescomplemented
58C2×Q8×C103C2312yes—
59C2×D4×C103—28no—
60C2×D4×C103—24no—
61C2×D4×C103—21no—
62C2×D4×C103—22no—
63C2×D4×C103D414yescomplemented
64C2×D4×C103C2312yes—
65C22×C4×C103—28no—
66C22×C4×C103—21no—
67C22×C4×C103—24no—
68C22×C4×C103—22no—
69C22×C4×C103—22no—
70C22×C4×C103D411yescharacteristic
71C22×C4×C103D412yes—
72C22×C4×C103C2312yes—
73C22×C4×C103C2311yescharacteristic
74C23×C103—22no—
75C23×C103—24no—
76C23×C103—22no—
77C23×C103—22no—
78C23×C103—22no—
79C23×C103—42no—
80C23×C103—42no—
81C23×C103C2×D412yes—
82C23×C103C2×D411yescharacteristic
83C22×D103—22no—
84C22×D103—42no—
85C22×D103—42no—
86C22×D103—42no—
87Q8×C103—24no—
88Q8×C103—22no—
89Q8×C103C2×D414yescomplemented
90D4×C103—216no—
91D4×C103—24no—
92D4×C103—22no—
93D4×C103C2×D414yescomplemented
94C2×C4×C103—216no—
95C2×C4×C103—22no—
96C2×C4×C103—24no—
97C2×C4×C103—22no—
98C2×C4×C103—24no—
99C2×C4×C103—22no—
100C2×C4×C103—22no—
101C2×C4×C103C2×D412yes—
102C2×C4×C103C2×D411yescharacteristic
103C2×C4×C103C2×D412yes—
104C2×C4×C103C2×D412yes—
105C2×C4×C103C2411yescharacteristic
106C22⋊D103—48no—
107C2×Dic103—22no—
108C2×Dic103—42no—
109D412—22no—
110D412—22no—
111D412—42no—
112C103⋊C8—22no—
113C103⋊C8—22no—
114C22×C103—22no—
115C22×C103—24no—
116C22×C103—22no—
117C22×C103—22no—
118C22×C103—42no—
119C22×C103—42no—
120C22×C103—44no—
121C22×C103—48no—
122C22×C103#12012yes—
123C22×C103#13512yes—
124C22×C103AGL(1,ℤ/8)12yes—
125C22×C103C22×D411yescharacteristic
126C2×D103—42no—
127C2×D103—42no—
128C2×D103—42no—
129C2×D103—84no—
130C4×C103—22no—
131C4×C103—24no—
132C4×C103#12012yes—
133C4×C103C22×D411yescharacteristic
134C4×C103C22×D411yescharacteristic
135Dic103—42no—
136C2×C103—42no—
137C2×C103—44no—
138C2×C103#44914yescomplemented
139C2×C103C2×#12011yescharacteristic
140C2×C103C2×#13511yescharacteristic
141C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
142D103—82no—
143C2×#449—1031nomaximal, Sylow
144C103C2×#44911yescharacteristic, complemented, Sylow
145C22×#41D10311yescharacteristic, complemented
146C22×SD16—1031no—
147C22×D8—1031no—
148C2×#121—1031no—
149#449—1038no—
150C2×#103—1031no—
151C2×#102—1031no—
152C2×C22⋊C8—1031no—
153C2×#41—24no—
154C2×#41—24no—
155C2×#41—22no—
156C2×#41C2×D10314yescomplemented
157C22×Q8C2×D10311yescharacteristic
158C22×D4—21no—
159C22×D4—1031no—
160C22×D4—2061no—
161C22×D4C2×D10311yescharacteristic
162C23×C4—21no—
163C23×C4C2×D10311yescharacteristic
164C2×SD16—1034no—
165C2×SD16—2064no—
166C2×D8—1034no—
167C2×D8—2064no—
168C22×C8—1031no—
169C22×C8—1031no—
170#121—1034no—
171#121—2062no—
172C2×C4⋊C4—1031no—
173C2×C22⋊C4—2061no—
174#103—1034no—
175#102—1034no—
176C22⋊C8—1034no—
177C24—21no—
178C24—2061no—
179C24C22⋊D10311yescharacteristic
180#41—216no—
181#41—28no—
182#41—28no—
183C2×Q8—21no—
184C2×Q8—22no—
185C2×Q8C22⋊D10314yescomplemented
186C2×Q8C22×D10312yes—
187C2×D4—28no—
188C2×D4—24no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—1032no—
192C2×D4—4124no—
193C2×D4—2064no—
194C2×D4—2061no—
195C2×D4—2062no—
196C2×D4—2062no—
197C2×D4C22⋊D10314yescomplemented
198C2×D4C22×D10312yes—
199C22×C4—28no—
200C22×C4—21no—
201C22×C4—24no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—2061no—
205C22×C4C22⋊D10312yes—
206C22×C4C22⋊D10311yescharacteristic
207C22×C4C22×D10312yes—
208C22×C4C22×D10311yescharacteristic
209SD16—2068no—
210D8—2068no—
211C2×C8—1032no—
212C2×C8—1032no—
213C2×C8—2062no—
214C2×C8—2062no—
215C4⋊C4—1032no—
216C4⋊C4—2061no—
217C22⋊C4—2064no—
218C23—22no—
219C23—22no—
220C23—24no—
221C23—22no—
222C23—22no—
223C23—42no—
224C23—42no—
225C23—4122no—
226C23—4122no—
227C23—4122no—
228C23—2062no—
229C23C2×C22⋊D10312yes—
230C23C2×C22⋊D10311yescharacteristic
231Q8—22no—
232Q8—24no—
233Q8C2×C22⋊D10314yescomplemented
234D4—216no—
235D4—22no—
236D4—24no—
237D4—4128no—
238D4—4122no—
239D4—2062no—
240D4—2062no—
241D4C2×C22⋊D10314yescomplemented
242C2×C4—216no—
243C2×C4—22no—
244C2×C4—22no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—4122no—
250C2×C4—2062no—
251C2×C4C2×C22⋊D10312yes—
252C2×C4C2×C22⋊D10312yes—
253C2×C4C2×C22⋊D10312yes—
254C2×C4C2×C22⋊D10311yescharacteristic
255C2×C4C23×D10311yescharacteristic
256C8—2062no—
257C8—2062no—
258C22—22no—
259C22—22no—
260C22—22no—
261C22—24no—
262C22—42no—
263C22—42no—
264C22—44no—
265C22—48no—
266C22—8244no—
267C22—4122no—
268C22—4122no—
269C22—4122no—
270C22#1569299012yes—
271C22#1569304112yes—
272C22#1569304612yes—
273C22C22×C22⋊D10311yescharacteristic
274C4—22no—
275C4—24no—
276C4—4122no—
277C4#1569299012yes—
278C4C22×C22⋊D10311yescharacteristic
279C4C22×C22⋊D10311yescharacteristic
280C2—42no—
281C2—44no—
282C2—8242no—
283C2#2026793614yesdirect product factor
284C2C2×#1569299011yescharacteristic
285C2C2×#1569304111yescharacteristic
286C2C2×#1569304611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC22×#41×C103C2
socleC23×C103C2×D4
hypercenterC22×#41D103
hypocenterC103C2×#449
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×#13110092C2semidirect
2. C22×#13110090C2semidirect
3. C2×#15692995C2semidirect
4. #20267936C2direct (N × H)
5. C2×#15692945C2semidirect
6. C2×#15692942C2semidirect
7. C2×C22⋊(C103⋊C8)C2semidirect
8. C22×#41×C103C2semidirect
12. C2×#13110092C22semidirect
14. C2×#13110090C22semidirect
18. #15692995C22semidirect
21. #15692945C22semidirect
22. #15692942C22semidirect
23. C22⋊(C103⋊C8)C22semidirect
27. C2×#41×C103C22semidirect
57. C2×Q8×C103D4semidirect
63. C2×D4×C103D4semidirect
89. Q8×C103C2×D4semidirect
93. D4×C103C2×D4semidirect
138. C2×C103#449semidirect
144. C103C2×#449semidirect
145. C22×#41D103semidirect
156. C2×#41C2×D103semidirect
185. C2×Q8C22⋊D103semidirect
197. C2×D4C22⋊D103semidirect
233. Q8C2×C22⋊D103semidirect
241. D4C2×C22⋊D103semidirect
283. C2#20267936direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#131100922
C22×#131100902
C2×#156929952
#202679362
C2×#156929452
C2×#156929422
C2×C22⋊(C103⋊C8)2
C22×#41×C1032
C2×#449103