Finite Group Databasebeta

← #27205599

Subgroups — #27205599

Order 13184.

552 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#15693054C211yesmaximal, characteristic, complemented
2C2×#15693052C211yesmaximal, characteristic, complemented
3C2×#15693051C211yesmaximal, characteristic, complemented
4#20268337C211yesmaximal, characteristic
5C2×#15693019C211yesmaximal, characteristic, complemented
6#20268184C212yesmaximal, complemented
7#20268182C212yesmaximal, complemented
8#20268169C212yesmaximal, complemented
9#20268162C212yesmaximal, complemented
10M16×Dic103C211yesmaximal, characteristic, complemented
11C2×#137×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C22×Dic206C2211yescharacteristic
14#15693054—24no—
15#15693052—24no—
16#15693051—24no—
17C2×Dic412C2212yes—
18C2×#13110095C2212yes—
19C2×#13110095C2212yes—
20C2×#13110094C2212yes—
21C2×#13110093C2212yes—
22C2×#13110092C2212yes—
23C2×#13110089C2211yescharacteristic
24#15693019—22no—
25#15693019C2212yes—
26#15693019C2212yes—
27#15693019C2211yescharacteristic
28#15693017C2211yescharacteristic
29#15693010C2211yescharacteristic
30#15693008C2211yescharacteristic
31#15692993—22no—
32C4×C22⋊D103—22no—
33C2×Dic103⋊C4—22no—
34C2×C4×Dic103C2211yescharacteristic
35#15692931C2212yes—
36C8×Dic103C2212yes—
37C2×#41×C103C2211yescharacteristic
38C22×Q8×C103C2211yescharacteristic
39#137×C103—24no—
40C2×Q16×C103C2212yes—
41C2×SD16×C103C2212yes—
42C2×M16×C103C2211yescharacteristic
43#13110105—22no—
44#13110105—22no—
45C2×Dic206—22no—
46C2×Dic206—22no—
47C2×Dic206—21no—
48C2×Dic206C2312yes—
49C2×Dic206C2311yescharacteristic
50C2×D412C2311yescharacteristic
51C2×C22⋊D103—21no—
52C2×C22⋊D103—22no—
53C22×Dic103—21no—
54C22×Dic103D412yes—
55C2×C4×D103—21no—
56Dic412—24no—
57#13110095—24no—
58#13110095—24no—
59#13110094—24no—
60#13110093—24no—
61#13110092—24no—
62#13110089D414yescomplemented
63C2×C103⋊C8C2312yes—
64Dic103⋊C4—24no—
65Dic103⋊C4—24no—
66Dic103⋊C4—22no—
67C22⋊Dic103—22no—
68(C2×D103)⋊C4—22no—
69C4×Dic103D412yes—
70C4×Dic103C2311yescharacteristic
71C4×Dic103C2311yescharacteristic
72#41×C103—22no—
73#41×C103—22no—
74C2×Q8×C103—21no—
75C2×Q8×C103—22no—
76C2×Q8×C103—22no—
77C2×Q8×C103C2312yes—
78C2×Q8×C103C2311yescharacteristic
79C2×D4×C103—21no—
80C2×D4×C103C2311yescharacteristic
81C22×C4×C103—21no—
82C22×C4×C103—21no—
83C22×C4×C103C2311yescharacteristic
84Q16×C103—24no—
85SD16×C103—24no—
86M16×C103D414yescomplemented
87C2×C8×C103C2312yes—
88C23×C103—21no—
89C23×C103C2×D411yescharacteristic
90C22×D103—21no—
91Q8×C103—22no—
92Q8×C103—21no—
93Q8×C103—22no—
94Q8×C103—21no—
95Q8×C103—42no—
96D4×C103—21no—
97D4×C103—21no—
98D4×C103—42no—
99C2×C4×C103—21no—
100C2×C4×C103—22no—
101C2×C4×C103—42no—
102C2×C4×C103—42no—
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2×D412yes—
105C2×C4×C103C2×D412yes—
106C2×C4×C103C2411yescharacteristic
107C22⋊D103—42no—
108C22⋊D103—44no—
109C2×Dic103—24no—
110C2×Dic103—21no—
111C2×Dic103—22no—
112C2×Dic103—42no—
113C2×Dic103C2×D412yes—
114C2×Dic103C2×D412yes—
115D412—21no—
116D412—21no—
117C4×D103—42no—
118Dic206—22no—
119Dic206—22no—
120Dic206—21no—
121Dic206—21no—
122Dic206—42no—
123C8×C103C2×D414yes—
124C103⋊C8C2×D414yes—
125C22×C103—22no—
126C22×C103—41no—
127C22×C103—42no—
128C22×C103#12712yes—
129C22×C103C22×D411yescharacteristic
130C2×D103—41no—
131C2×D103—42no—
132C4×C103—41no—
133C4×C103—42no—
134C4×C103#12712yes—
135C4×C103C22×D411yescharacteristic
136C4×C103C22×D411yescharacteristic
137Dic103—22no—
138Dic103—42no—
139Dic103—41no—
140Dic103#13714yescomplemented
141C2×C103—22no—
142C2×C103—81no—
143C2×C103C2×#12711yescharacteristic
144C2×C103C2×#13712yes—
145D103—81no—
146#3152—1031nomaximal, Sylow
147C103#315211yescharacteristic, complemented, Sylow
148C2×#137—1031no—
149C2×#137—1031no—
150C2×#137—1031no—
151C2×#137D10311yescharacteristic, complemented
152#532—1031no—
153C2×C4⋊Q8—1031no—
154#497—1032no—
155#497—1032no—
156#494—1032no—
157#492—1032no—
158C4×M16—1031no—
159C2×#41—1031no—
160C2×#41C2×D10311yescharacteristic
161C22×Q8—1031no—
162C22×Q8C2×D10311yescharacteristic
163#137—24no—
164#137—2064no—
165#137—2064no—
166#137—2064no—
167C2×Q16—1032no—
168C2×Q16—1032no—
169C2×Q16—1032no—
170C2×Q16C2×D10312yes—
171C2×SD16—1032no—
172C2×SD16—1032no—
173C2×SD16—1032no—
174C2×SD16C2×D10312yes—
175C2×M16—1031no—
176C2×M16C2×D10311yescharacteristic
177C4⋊Q8—1032no—
178C4⋊Q8—1032no—
179C4⋊Q8—1031no—
180C4⋊Q8—2062no—
181#127—1031no—
182#124—1031no—
183#124—1031no—
184#121—2062no—
185C4×D4—2062no—
186C2×C4⋊C4—2062no—
187C2×C42—1031no—
188#97—1032no—
189C4×C8—1032no—
190#41—22no—
191#41—22no—
192#41—2062no—
193#41—2062no—
194C2×Q8—21no—
195C2×Q8—22no—
196C2×Q8—22no—
197C2×Q8—1031no—
198C2×Q8—1032no—
199C2×Q8—2062no—
200C2×Q8—2062no—
201C2×Q8—2061no—
202C2×Q8C22×D10311yescharacteristic
203C2×Q8C22×D10312yes—
204C2×D4—21no—
205C2×D4—1031no—
206C2×D4—2062no—
207C2×D4—2061no—
208C2×D4C22×D10311yescharacteristic
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—1032no—
212C22×C4—2061no—
213C22×C4—2061no—
214C22×C4C22×D10311yescharacteristic
215Q16—24no—
216Q16—2064no—
217Q16—2064no—
218Q16—2064no—
219SD16—24no—
220SD16—2064no—
221SD16—2064no—
222SD16—2064no—
223M16—1034no—
224M16C22⋊D10314yescomplemented
225C2×C8—1032no—
226C2×C8C22×D10312yes—
227C4⋊C4—2064no—
228C4⋊C4—2064no—
229C4⋊C4—2062no—
230C22⋊C4—2062no—
231C22⋊C4—2062no—
232C42—1032no—
233C42—1031no—
234C42—1031no—
235C23—21no—
236C23—2061no—
237C23D4×D10311yescharacteristic
238Q8—22no—
239Q8—21no—
240Q8—22no—
241Q8—21no—
242Q8—42no—
243Q8—4122no—
244Q8—2062no—
245Q8—2061no—
246Q8—2062no—
247Q8—2061no—
248D4—21no—
249D4—21no—
250D4—42no—
251D4—4124no—
252D4—4122no—
253D4—2061no—
254D4—2061no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—1032no—
260C2×C4—1032no—
261C2×C4—4122no—
262C2×C4—4122no—
263C2×C4—2064no—
264C2×C4—2061no—
265C2×C4—2062no—
266C2×C4D4×D10312yes—
267C2×C4D4×D10311yescharacteristic
268C2×C4C2×C22⋊D10312yes—
269C2×C4C23×D10311yescharacteristic
270C8—1034no—
271C8C2×C22⋊D10314yes—
272C22—22no—
273C22—42no—
274C22—41no—
275C22—4122no—
276C22—4121no—
277C22#1569301712yes—
278C22C2×D4×D10311yescharacteristic
279C4—41no—
280C4—42no—
281C4—1034no—
282C4—4121no—
283C4—4122no—
284C4—2062no—
285C4#1569301712yes—
286C4C2×D4×D10311yescharacteristic
287C4C22×C22⋊D10311yescharacteristic
288C2—22no—
289C2—81no—
290C2—8241no—
291C2C2×#1569301711yescharacteristic
292C2#137×D10312yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#137×C103C2
socleC22×C103C22×D4
prime radical#20268337C2
hypercenterC2×#137D103
hypocenterC103#3152
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#15693054C2semidirect
2. C2×#15693052C2semidirect
3. C2×#15693051C2semidirect
5. C2×#15693019C2semidirect
6. #20268184C2semidirect
7. #20268182C2semidirect
8. #20268169C2semidirect
9. #20268162C2semidirect
10. M16×Dic103C2semidirect
11. C2×#137×C103C2semidirect
62. #13110089D4semidirect
86. M16×C103D4semidirect
140. Dic103#137semidirect
147. C103#3152semidirect
151. C2×#137D103semidirect
224. M16C22⋊D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930542
C2×#156930522
C2×#156930512
#202683372
C2×#156930192
#202681842
#202681822
#202681692
#202681622
M16×Dic1032
C2×#137×C1032
#3152103