Finite Group Databasebeta

← #15767719

Subgroups — #15767719

Order 3328.

294 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#13115809C211yesmaximal, characteristic
2#13115011C211yesmaximal, characteristic
3#13113520C211yesmaximal, characteristic
4#13113516C211yesmaximal, characteristic
5#13112695C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic
7C13×#1281C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C13×#431C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×#97C2211yescharacteristic
12C2×#88059—21no—
13C2×#88059—21no—
14#11718597C2211yescharacteristic
15#11718585C2211yescharacteristic
16#11718585C2211yescharacteristic
17#11718143—21no—
18#11718143—21no—
19#11718074—22no—
20#11718073—22no—
21C22×Dic26—21no—
22C22×C8×C13D411yescharacteristic
23C22×C8×C13D411yescharacteristic
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—21no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—21no—
28C2×#6099—21no—
29C2×#6099—21no—
30#88123—21no—
31#88123—21no—
32#88123—21no—
33#88123D412yes—
34C13×C4⋊C8—21no—
35C13×C4⋊C8—21no—
36C13×C22⋊C8—21no—
37C13×C22⋊C8—21no—
38C13×#97—21no—
39C13×#97—21no—
40C4×C8×C13—21no—
41C4×C8×C13—21no—
42#88071—21no—
43#88071—21no—
44#88059—42no—
45#88059—42no—
46C4⋊#1055—21no—
47C4⋊#1055—21no—
48C4⋊#1055—21no—
49C4⋊#1055—21no—
50#10633—131nomaximal, Sylow
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13#4111yescharacteristic
53C22×C4×C13#4111yescharacteristic
54C22×Dic13—41no—
55C22×Dic13—41no—
56C2×Dic26—22no—
57C2×Dic26—41no—
58C2×Dic26—82no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13—21no—
62C2×C8×C13—21no—
63C2×C8×C13—41no—
64C2×C8×C13—41no—
65C2×C8×C13SD1612yes—
66C2×C8×C13Q1612yes—
67C42×C13C2×D411yescharacteristic
68C42×C13#4111yescharacteristic
69C42×C13#4111yescharacteristic
70C42×C13#4111yescharacteristic
71C4⋊Dic13—22no—
72C4⋊Dic13—22no—
73C4⋊Dic13—41no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6099—41no—
78#6099—41no—
79#6099—41no—
80#6099—41no—
81C2×#1055—41no—
82C2×#1055—41no—
83#1993—131no—
84#1849—131no—
85#1549—131no—
86#1548—131no—
87#1286—131no—
88#1286—131no—
89#1281D1311yescharacteristic
90C23×C13#12411yescharacteristic
91C2×C4×C13—41no—
92C2×C4×C13—41no—
93C2×C4×C13#12111yescharacteristic
94C2×C4×C13#12311yescharacteristic
95C2×C4×C13#12311yescharacteristic
96C2×C4×C13#12311yescharacteristic
97C2×C4×C13#12611yescharacteristic
98C2×C4×C13#12611yescharacteristic
99C2×C4×C13C2×SD1611yescharacteristic
100C2×C4×C13C2×Q1611yescharacteristic
101C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C13#13711yescharacteristic
103C2×Dic13—42no—
104C2×Dic13—82no—
105C2×Dic13—81no—
106C2×Dic13—81no—
107C2×Dic13—81no—
108Dic26—82no—
109Dic26—82no—
110C8×C13—22no—
111C8×C13—22no—
112C8×C13—81no—
113C8×C13—81no—
114#1055—81no—
115#1055—81no—
116C2×C4⋊Q8—131no—
117#431C2×D1311yescharacteristic
118#431C2×D1311yescharacteristic
119C2×#108—261no—
120C2×#108—261no—
121#423—131no—
122#423—131no—
123C2×#97C2×D1311yescharacteristic
124#382—131no—
125#340—261no—
126#340—261no—
127#333—262no—
128#332—262no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13#39711yescharacteristic
132C22×C13#48711yescharacteristic
133C22×C13#48911yescharacteristic
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13#46011yescharacteristic
139C4×C13#46211yescharacteristic
140C4×C13#48311yescharacteristic
141C4×C13#48411yescharacteristic
142Dic13—82no—
143Dic13—161no—
144C22×Q8—261no—
145C2×M16—261no—
146C2×M16—261no—
147C22×C8D5211yescharacteristic
148C22×C8D5211yescharacteristic
149C4⋊Q8—132no—
150C4⋊Q8—261no—
151C4⋊Q8—261no—
152C4⋊Q8—261no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C42C22×D1311yescharacteristic
157#108—522no—
158#108—522no—
159C4⋊C8—21no—
160C4⋊C8—21no—
161C4⋊C8—261no—
162C4⋊C8—261no—
163C4⋊C8—261no—
164C4⋊C8—261no—
165C22⋊C8—21no—
166C22⋊C8—21no—
167#97—21no—
168#97—21no—
169C4×C8—21no—
170C4×C8—21no—
171#95—261no—
172#95—261no—
173C2×C13—21no—
174C2×C13—21no—
175C2×C13#207211yescharacteristic
176C2×C13#208111yescharacteristic
177C2×C13#208211yescharacteristic
178C2×Q8—262no—
179C2×Q8—521no—
180C2×Q8—1042no—
181C22×C4—521no—
182C22×C4—521no—
183C22×C4C2×D5211yescharacteristic
184C22×C4#612711yescharacteristic
185C22×C4#612711yescharacteristic
186M16—521no—
187M16—521no—
188M16—521no—
189M16—521no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—521no—
197C2×C8—521no—
198C2×C8#609512yes—
199C2×C8Dic5212yes—
200C4⋊C4—262no—
201C4⋊C4—262no—
202C4⋊C4—521no—
203C4⋊C4—521no—
204C4⋊C4—521no—
205C4⋊C4—521no—
206C42D4×D1311yescharacteristic
207C42#612911yescharacteristic
208C42#612911yescharacteristic
209C42#613111yescharacteristic
210C13#1063311yescharacteristic, complemented, Sylow
211C23#8812911yescharacteristic
212Q8—1042no—
213Q8—1042no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—522no—
217C2×C4—1042no—
218C2×C4—1041no—
219C2×C4—1041no—
220C2×C4—1041no—
221C2×C4#8813711yescharacteristic
222C2×C4#8813711yescharacteristic
223C2×C4#8814011yescharacteristic
224C2×C4#8814911yescharacteristic
225C2×C4#8815211yescharacteristic
226C2×C4#8815211yescharacteristic
227C2×C4C2×#609511yescharacteristic
228C2×C4C2×Dic5211yescharacteristic
229C2×C4#8816211yescharacteristic
230C2×C4#8816311yescharacteristic
231C8—22no—
232C8—22no—
233C8—81no—
234C8—81no—
235C8—1041no—
236C8—1041no—
237C22—21no—
238C22—21no—
239C22#1171833511yescharacteristic
240C22#1171834211yescharacteristic
241C22#1171837511yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—1042no—
247C4—2081no—
248C4#1171838211yescharacteristic
249C4#1171838311yescharacteristic
250C4#1171850911yescharacteristic
251C4#1171851011yescharacteristic
252C2—21no—
253C2—21no—
254C2#1311624611yescharacteristic
255C2#1311629511yescharacteristic
256C2#1311630211yescharacteristic
subgroupG/H
centerC22#11718335
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1281C2
socleC22×C13#397
prime radicalC23×C13#124
hypercenter#1281D13
hypocenterC13#10633
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
210. C13#10633semidirect

Maximal subgroups

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

subgroupindex
#131158092
#131150112
#131135202
#131135162
#131126952
C13×#12812
#1063313