Finite Group Databasebeta

← #15775726

Subgroups — #15775726

Order 3328.

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

normal subgroups only

This group has 456 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#13116000C211yesmaximal, characteristic
2#13113860C212yesmaximal, complemented
3#13112860C212yesmaximal, complemented
4#13112764C211yesmaximal, characteristic
5C13×#2842C211yesmaximal, characteristic
6#11719188C2211yescharacteristic
7C13×#399—21no—
8C13×#399C2212yes—
9C13×#396—22no—
10C13×#396—22no—
11C13×#379—21no—
12C13×#379C2211yescharacteristic
13#11718908—21no—
14#11718631—22no—
15#11718119—21no—
16#11718118C2211yescharacteristic
17#11718117C2212yes—
18#11718044—22no—
19C25×C13D411yescharacteristic
20C2×C13×C4⋊C4—22no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D412yes—
24C2×C13×C22⋊C4—21no—
25C2×C13×C22⋊C4—22no—
26C2×C13×C22⋊C4—21no—
27C2×C13×C22⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2311yescharacteristic
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—21no—
33C2×C22⋊Dic13—42no—
34#88178—22no—
35#88132—42no—
36C13×#95—21no—
37C13×#95D412yes—
38C22⋊#1055—22no—
39#88050—42no—
40#88047—42no—
41#12218—131nomaximal, Sylow
42C24×C13—21no—
43C24×C13—21no—
44C24×C13—41no—
45C24×C13—41no—
46C24×C13—82no—
47C24×C13Q1612yes—
48C24×C13C2×D411yescharacteristic
49C22×C4×C13—22no—
50C22×C4×C13—21no—
51C22×C4×C13—22no—
52C22×C4×C13C2×D412yes—
53C22×Dic13—22no—
54C22×Dic13—41no—
55C2×Dic26—22no—
56C13×C4⋊C4—42no—
57C13×C4⋊C4—82no—
58C13×C4⋊C4—82no—
59C13×C4⋊C4—81no—
60C13×C22⋊C4—41no—
61C13×C22⋊C4—41no—
62C13×C22⋊C4—82no—
63C13×C22⋊C4—82no—
64C13×C22⋊C4—82no—
65C13×C22⋊C4—81no—
66C13×C22⋊C4—81no—
67C22⋊Dic13—41no—
68C22⋊Dic13—41no—
69C22⋊Dic13—41no—
70C22⋊Dic13—41no—
71C22⋊Dic13—84no—
72C4⋊Dic13—22no—
73#6101—42no—
74C2×#1055—42no—
75#2842D1311yescharacteristic
76#2029—131no—
77#1614—132no—
78#1352—132no—
79#1316—131no—
80C23×C13—21no—
81C23×C13—21no—
82C23×C13—22no—
83C23×C13—42no—
84C23×C13—42no—
85C23×C13—42no—
86C23×C13—42no—
87C23×C13—44no—
88C23×C13—41no—
89C23×C13—41no—
90C23×C13—81no—
91C23×C13—82no—
92C23×C13—82no—
93C23×C13—84no—
94C23×C13—82no—
95C23×C13#12011yescharacteristic
96C23×C13C2×Q1611yescharacteristic
97C23×C13#13711yescharacteristic
98C2×C4×C13—22no—
99C2×C4×C13—42no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—42no—
105C2×C4×C13—41no—
106C2×C4×C13—42no—
107C2×C4×C13—42no—
108C2×Dic13—42no—
109C2×Dic13—82no—
110C2×Dic13—81no—
111C2×Dic13—82no—
112Dic26—82no—
113#1055—82no—
114#543—131no—
115#484—262no—
116#399—21no—
117#399C2×D1312yes—
118#396—22no—
119#396—22no—
120#379—21no—
121#379—261no—
122#379C2×D1311yescharacteristic
123#342—131no—
124#342—261no—
125#328—262no—
126#323—132no—
127C22×C13—22no—
128C22×C13—21no—
129C22×C13—21no—
130C22×C13—41no—
131C22×C13—41no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—44no—
136C22×C13—42no—
137C22×C13—81no—
138C22×C13—82no—
139C22×C13—82no—
140C22×C13—84no—
141C22×C13—82no—
142C22×C13#45111yescharacteristic
143C22×C13#45511yescharacteristic
144C22×C13B(4,𝔽2)11yescharacteristic
145C4×C13—42no—
146C4×C13—81no—
147C4×C13—82no—
148C4×C13—82no—
149Dic13—82no—
150Dic13—161no—
151C25C22⋊D1311yescharacteristic
152C22⋊Q8—262no—
153C22⋊Q8—522no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4C22⋊D1312yes—
158C2×C22⋊C4—21no—
159C2×C22⋊C4—22no—
160C2×C22⋊C4—21no—
161C2×C22⋊C4—22no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4—261no—
164C2×C22⋊C4—261no—
165C2×C22⋊C4—522no—
166C2×C22⋊C4C22⋊D1311yescharacteristic
167C2×C22⋊C4C22×D1311yescharacteristic
168#107—522no—
169#103—522no—
170C22⋊C8—262no—
171#95—21no—
172#95C22⋊D1312yes—
173C2×C13—21no—
174C2×C13—21no—
175C2×C13—41no—
176C2×C13—41no—
177C2×C13—82no—
178C2×C13#160211yescharacteristic
179C2×C13#220012yes—
180C24—21no—
181C24—21no—
182C24—41no—
183C24—41no—
184C24—82no—
185C24#610712yes—
186C24C2×C22⋊D1311yescharacteristic
187C2×Q8—262no—
188C22×C4—22no—
189C22×C4—21no—
190C22×C4—22no—
191C22×C4—262no—
192C22×C4—521no—
193C22×C4C2×C22⋊D1312yes—
194C2×C8—522no—
195C4⋊C4—42no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C4⋊C4—81no—
199C4⋊C4—262no—
200C4⋊C4—522no—
201C22⋊C4—41no—
202C22⋊C4—41no—
203C22⋊C4—82no—
204C22⋊C4—82no—
205C22⋊C4—82no—
206C22⋊C4—81no—
207C22⋊C4—81no—
208C22⋊C4—521no—
209C22⋊C4—521no—
210C22⋊C4—521no—
211C22⋊C4—521no—
212C22⋊C4—1044no—
213C13#1221811yescharacteristic, complemented, Sylow
214C23—21no—
215C23—21no—
216C23—22no—
217C23—42no—
218C23—42no—
219C23—42no—
220C23—42no—
221C23—44no—
222C23—41no—
223C23—41no—
224C23—81no—
225C23—82no—
226C23—82no—
227C23—82no—
228C23—84no—
229C23#8819611yescharacteristic
230C23C2×#610711yescharacteristic
231C23#8820711yescharacteristic
232Q8—1042no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—522no—
244C2×C4—1042no—
245C2×C4—1041no—
246C2×C4—1042no—
247C8—1042no—
248C22—22no—
249C22—21no—
250C22—21no—
251C22—41no—
252C22—41no—
253C22—42no—
254C22—42no—
255C22—42no—
256C22—44no—
257C22—42no—
258C22—81no—
259C22—82no—
260C22—82no—
261C22—84no—
262C22—82no—
263C22#1171888911yescharacteristic
264C22#1171890311yescharacteristic
265C22#1171890511yescharacteristic
266C4—42no—
267C4—81no—
268C4—82no—
269C4—82no—
270C4—1042no—
271C4—2081no—
272C2—21no—
273C2—21no—
274C2—41no—
275C2—41no—
276C2—82no—
277C2#1311379311yescharacteristic
278C2#1311684312yes—
subgroupG/H
centerC22#11718905
commutator, cosocleC2×C13×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2842C2
socleC22×C13B(4,𝔽2)
prime radicalC25×C13D4
hypercenter#2842D13
hypocenterC13#12218
LCSG ▷ C2×C13×C22⋊C4 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2842

Complements

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

NH ≅ G/Ntype
2. #13113860C2semidirect
3. #13112860C2semidirect
213. C13#12218semidirect

Maximal subgroups

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

subgroupindex
#131160002
#131138602
#131128602
#131127642
C13×#28422
#1221813