Finite Group Databasebeta

← #15775514

Subgroups — #15775514

Order 3328.

372 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 63 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#13116065C211yesmaximal, characteristic
2#13113804C212yesmaximal
3#13112866C212yesmaximal, complemented
4#13112780C211yesmaximal, characteristic, complemented
5C13×#2844C211yesmaximal, characteristic, complemented
6#11719215C2211yescharacteristic
7C13×#400—21no—
8C13×#400—22no—
9C13×#395—22no—
10C13×#395C2212yes—
11C13×#382—21no—
12C13×#382C2211yescharacteristic
13#11718888—22no—
14#11718627—21no—
15C2×#88045—21no—
16#11718122C2211yescharacteristic
17#11718120C2212yes—
18#11718043—22no—
19C22×Q8×C13D412yes—
20C2×#6127—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—21no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4D411yescharacteristic
26C2×C13×C4⋊C4C2311yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×#6106—42no—
29#88184—22no—
30C2×#6099—21no—
31#88151—41no—
32#88149—41no—
33C13×#95—22no—
34C13×#95—22no—
35C13×#95—21no—
36C13×#95—22no—
37C13×#95—22no—
38C13×#95D412yes—
39#88075—42no—
40C22⋊#1055—22no—
41#88050—41no—
42#88049—41no—
43#88045—42no—
44#12184—131nomaximal, Sylow
45C2×Q8×C13—42no—
46C2×Q8×C13—82no—
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C2×D411yescharacteristic
52C22×C4×C13C2×D412yes—
53C2×C22⋊D13—41no—
54#6127—41no—
55#6127—41no—
56#6127—41no—
57#6127—41no—
58C2×D52—21no—
59C2×D52—22no—
60C2×C4×D13—41no—
61C2×Dic26—21no—
62C13×C4⋊C4—41no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—81no—
65C13×C4⋊C4—81no—
66C13×C4⋊C4—82no—
67C13×C4⋊C4—81no—
68C42×C13—21no—
69C42×C13SD1612yescomplemented
70#6106—84no—
71#6103—42no—
72C4⋊Dic13—22no—
73#6099—41no—
74#6099—41no—
75C2×#1055—42no—
76C2×#1055—41no—
77#2844D1311yescharacteristic, complemented
78#2040—131no—
79#1604—132no—
80#1354—132no—
81#1324—131no—
82C23×C13#12011yescharacteristic
83C22×D13—41no—
84Q8×C13—44no—
85Q8×C13—82no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—41no—
91C2×C4×C13—41no—
92C2×C4×C13—42no—
93C2×C4×C13—42no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—42no—
98C2×C4×C13—42no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13C2×SD1611yescharacteristic
102C2×C4×C13#13711yescharacteristic
103C22⋊D13—81no—
104C22⋊D13—81no—
105C2×Dic13—41no—
106D52—41no—
107D52—41no—
108D52—82no—
109C4×D13—81no—
110C4×D13—81no—
111Dic26—41no—
112Dic26—41no—
113#1055—81no—
114#1055—82no—
115#537—131no—
116#448—262no—
117C2×#104—261no—
118#417—261no—
119#400—21no—
120#400—22no—
121#395—22no—
122#395C2×D1312yes—
123#382—21no—
124#382C2×D1311yescharacteristic
125#343—131no—
126#327—262no—
127#324—132no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13#44811yescharacteristic
131C22×C13#45411yescharacteristic
132C22×C13B(4,𝔽2)11yescharacteristic
133C2×D13—81no—
134C2×D13—81no—
135C2×D13—81no—
136C4×C13—21no—
137C4×C13—21no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—82no—
141C4×C13—82no—
142C4×C13—81no—
143Dic13—81no—
144C2×#41—261no—
145C22×Q8C22⋊D1312yes—
146C2×SD16—522no—
147C2×M16—261no—
148C22⋊Q8—521no—
149#121—262no—
150#121—521no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C4⋊C4C22×D1311yescharacteristic
157C2×C42C22⋊D1311yescharacteristic
158#104—522no—
159#103—521no—
160#103—522no—
161#102—521no—
162C22⋊C8—262no—
163#95—22no—
164#95—22no—
165#95—21no—
166#95—22no—
167#95—22no—
168#95C22⋊D1312yes—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13#159911yescharacteristic
172C2×C13#219911yescharacteristic
173C2×C13#220311yescharacteristic
174D13—161no—
175#41—521no—
176#41—521no—
177#41—521no—
178#41—521no—
179C2×Q8—42no—
180C2×Q8—82no—
181C2×Q8—261no—
182C2×D4—261no—
183C2×D4—262no—
184C2×D4—521no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—521no—
190C22×C4C2×C22⋊D1311yescharacteristic
191C22×C4C2×C22⋊D1312yes—
192SD16—1044no—
193M16—521no—
194M16—521no—
195C2×C8—522no—
196C2×C8—521no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—82no—
202C4⋊C4—81no—
203C4⋊C4—262no—
204C22⋊C4—522no—
205C42—21no—
206C42#610612yescomplemented
207C13#1218411yescharacteristic, complemented, Sylow
208C23—521no—
209C23#8820711yescharacteristic
210Q8—44no—
211Q8—82no—
212Q8—521no—
213Q8—521no—
214D4—521no—
215D4—521no—
216D4—1042no—
217D4—1041no—
218D4—1041no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—521no—
235C2×C4—1041no—
236C2×C4—1041no—
237C2×C4C2×#610611yescharacteristic
238C2×C4#8819611yescharacteristic
239C8—1041no—
240C8—1042no—
241C22—21no—
242C22—21no—
243C22—1041no—
244C22—1041no—
245C22—1041no—
246C22#1171888811yescharacteristic
247C22#1171890511yescharacteristic
248C22#1171890611yescharacteristic
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—82no—
254C4—82no—
255C4—81no—
256C4—1041no—
257C2—21no—
258C2—21no—
259C2—2081no—
260C2#1311377611yescharacteristic
261C2#1311683711yescharacteristic
262C2#1311685711yescharacteristic
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2844C2
socleC22×C13B(4,𝔽2)
prime radical#11719215C22
hypercenter#2844D13
hypocenterC13#12184
LCSG ▷ C2×C13×C4⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2844

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112780C2semidirect
5. C13×#2844C2semidirect
69. C42×C13SD16semidirect
77. #2844D13semidirect
206. C42#6106semidirect
207. C13#12184semidirect

Maximal subgroups

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

subgroupindex
#131160652
#131138042
#131128662
#131127802
C13×#28442
#1218413