Finite Group Databasebeta

← #15767314

Subgroups — #15767314

Order 3328.

490 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 99 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#13115822C212yesmaximal
2#13115260C212yesmaximal
3#13115013C211yesmaximal, characteristic
4#13112704C211yesmaximal, characteristic
5C13×#3189C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C2212yes—
7C23×#1055C2211yescharacteristic
8C13×#484—22no—
9C13×#467—21no—
10C13×#467—21no—
11C13×#451—22no—
12C2×C13×C22⋊C8C2211yescharacteristic
13C2×#88075—22no—
14#11718873C2212yes—
15C4×C22⋊Dic13C2211yescharacteristic
16C2×#88054—21no—
17#11718142—21no—
18#11718121—22no—
19#11718118—22no—
20#11718118—22no—
21C22×Q8×C13D412yes—
22C23×C4×C13C2311yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C22×C8×C13D411yescharacteristic
26C22×C8×C13D411yescharacteristic
27C13×C22⋊Q8—22no—
28C13×C22⋊Q8—22no—
29C13×C22⋊Q8—22no—
30C13×C22⋊Q8—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C22⋊C4—22no—
34C2×C22⋊Dic13—22no—
35C2×C22⋊Dic13D411yescharacteristic
36C2×C22⋊Dic13D411yescharacteristic
37C2×C4⋊Dic13—22no—
38C2×C4×Dic13—21no—
39C22×#1055—21no—
40C22×#1055—22no—
41C22×#1055—42no—
42C13×#107—21no—
43C13×#107—21no—
44C13×#103—22no—
45C13×#103—22no—
46C13×C22⋊C8—22no—
47#88075—44no—
48#88071—21no—
49#88071—22no—
50#88054—42no—
51#10566—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C2×Q8×C13—22no—
54C2×Q8×C13—22no—
55C2×Q8×C13—42no—
56C2×Q8×C13—42no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C2×D412yes—
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13#4111yescharacteristic
64C22×C4×C13#4112yes—
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—42no—
68C13×Q16—81no—
69C13×Q16—81no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C13×C4⋊C4—22no—
75C13×C4⋊C4—22no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C22⋊Dic13—21no—
81C22⋊Dic13—22no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C22⋊Dic13Q1612yescomplemented
85C4⋊Dic13—42no—
86C4⋊Dic13—42no—
87C4×Dic13—41no—
88C4×Dic13—41no—
89C2×#1055—24no—
90C2×#1055—22no—
91C2×#1055—41no—
92C2×#1055—42no—
93C2×#1055—41no—
94#3189D1311yescharacteristic
95#1996—132no—
96#1892—132no—
97#1850—131no—
98#1289—131no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13#12112yes—
102C23×C13#12111yescharacteristic
103C23×C13C2×Q1611yescharacteristic
104C23×C13#13511yescharacteristic
105C23×C13#13712yes—
106Q8×C13—44no—
107Q8×C13—42no—
108Q8×C13—42no—
109C2×C4×C13—21no—
110C2×C4×C13—22no—
111C2×C4×C13—21no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—82no—
118C2×C4×C13—82no—
119C2×C4×C13#12011yescharacteristic
120C2×C4×C13#12312yes—
121C2×C4×C13#12411yescharacteristic
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—82no—
129C2×Dic13—82no—
130C2×Dic13—82no—
131C8×C13—41no—
132C8×C13—41no—
133#1055—42no—
134C23×C8—131no—
135C2×C22⋊Q8C2×D1312yes—
136#484—22no—
137#467—21no—
138#467—21no—
139#451—22no—
140C2×C4⋊C8—261no—
141C2×#103—262no—
142C2×C22⋊C8C2×D1311yescharacteristic
143#380—132no—
144C4×C22⋊C4—131no—
145#342—262no—
146#342—262no—
147#340—262no—
148#336—261no—
149C22×C13—21no—
150C22×C13—22no—
151C22×C13—21no—
152C22×C13—22no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13#39411yescharacteristic
157C22×C13#46212yes—
158C22×C13#46412yes—
159C22×C13#46711yescharacteristic
160C22×C13#47011yescharacteristic
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—82no—
164C4×C13—82no—
165C4×C13B(4,𝔽2)11yescharacteristic
166C4×C13#45811yescharacteristic
167Dic13—42no—
168Dic13—81no—
169Dic13—162no—
170C22×Q8C22⋊D1312yes—
171C23×C4C22×D1311yescharacteristic
172C2×Q16—21no—
173C2×Q16—21no—
174C22×C8—261no—
175C22×C8—262no—
176C22×C8—522no—
177C22×C8C22⋊D1311yescharacteristic
178C22×C8C22⋊D1311yescharacteristic
179C22⋊Q8—22no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4C22⋊D1312yes—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—131no—
188C2×C22⋊C4—131no—
189C2×C22⋊C4—262no—
190C2×C42—261no—
191#107—21no—
192#107—21no—
193C4⋊C8—522no—
194#103—22no—
195#103—22no—
196#103—524no—
197C22⋊C8—22no—
198#95—261no—
199#95—262no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—22no—
203C2×C13—22no—
204C2×C13#204411yescharacteristic
205C2×C13#205311yescharacteristic
206C2×C13#205611yescharacteristic
207C24D4×D1311yescharacteristic
208C2×Q8—22no—
209C2×Q8—22no—
210C2×Q8—42no—
211C2×Q8—42no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4—522no—
219C22×C4#612911yescharacteristic
220C22×C4#612912yes—
221C22×C4C2×C22⋊D1312yes—
222C22×C4C2×C22⋊D1311yescharacteristic
223Q16—81no—
224Q16—81no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—264no—
230C2×C8—262no—
231C2×C8—521no—
232C2×C8—522no—
233C2×C8—521no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—132no—
243C22⋊C4—261no—
244C22⋊C4—262no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C42—521no—
248C42—521no—
249C13#1056611yescharacteristic, complemented, Sylow
250C23—41no—
251C23—41no—
252C23Q16×D1311yescharacteristic
253C23#8817212yes—
254C23#8817311yescharacteristic
255C23#8819211yescharacteristic
256C23#8819312yes—
257Q8—44no—
258Q8—42no—
259Q8—42no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—262no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—1042no—
277C2×C4—1042no—
278C2×C4—1042no—
279C2×C4#8818912yes—
280C2×C4#8819011yescharacteristic
281C2×C4#8820711yescharacteristic
282C8—41no—
283C8—41no—
284C8—522no—
285C22—22no—
286C22—21no—
287C22—22no—
288C22—21no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22#1171884312yes—
293C22#1171884612yes—
294C22#1171884911yescharacteristic
295C22#1171885011yescharacteristic
296C22#1171888311yescharacteristic
297C4—22no—
298C4—21no—
299C4—82no—
300C4—82no—
301C4—522no—
302C4—1041no—
303C4—2082no—
304C4#1171890411yescharacteristic
305C4#1171890511yescharacteristic
306C2—21no—
307C2—21no—
308C2—22no—
309C2—22no—
310C2#1311608411yescharacteristic
311C2#1311613911yescharacteristic
312C2#1311615611yescharacteristic
subgroupG/H
centerC22#11718883
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#3189C2
socleC22×C13#394
prime radicalC24×C13C2×D4
hypercenter#3189D13
hypocenterC13#10566
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3189

Complements

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

NH ≅ G/Ntype
84. C22⋊Dic13Q16semidirect
249. C13#10566semidirect

Maximal subgroups

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

subgroupindex
#131158222
#131152602
#131150132
#131127042
C13×#31892
#1056613