Finite Group Databasebeta

← #15766700

Subgroups — #15766700

Order 3328.

366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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#13124637C211yesmaximal, characteristic
2#13114852C211yesmaximal, characteristic
3#13113610C211yesmaximal, characteristic
4#13113400C211yesmaximal, characteristic
5#13113159C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic
7C13×#1542C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88056—21no—
13#11718755—21no—
14#11718752—21no—
15#11718724—22no—
16#11718665—21no—
17#11718656—21no—
18#11718597C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21C13×#333—21no—
22C13×#332—21no—
23#11718143—21no—
24#11718130—22no—
25#11718071—22no—
26#11718061—22no—
27C22×Dic26D411yescharacteristic
28C22×C8×C13—21no—
29C13×C4⋊Q8D411yescharacteristic
30C13×C4⋊Q8D411yescharacteristic
31C13×#125—21no—
32C13×C22⋊Q8—21no—
33C13×C22⋊Q8—21no—
34C4×Q8×C13—21no—
35C4×Q8×C13—21no—
36C13×#117—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13D411yescharacteristic
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×#6099—21no—
43C4×Dic26—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C22⋊C8—21no—
51C4×C8×C13—21no—
52#88071—21no—
53#88071—21no—
54C22⋊#1055D412yes—
55#88056—42no—
56#88050—22no—
57#88050—22no—
58#88048—22no—
59#88047—22no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63C4×#1055—21no—
64#10471—131nomaximal, Sylow
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C22×C4×C13C2×D411yescharacteristic
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—41no—
73C2×Dic26—21no—
74C2×Dic26—21no—
75C2×Dic26—21no—
76C2×Dic26—21no—
77C2×Dic26—21no—
78C2×Dic26Q1612yes—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—41no—
90C42×C13—41no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—41no—
98C4⋊Dic13—41no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103#6099—41no—
104#6099—41no—
105C2×#1055—22no—
106C2×#1055—22no—
107#3078—131no—
108#1805—131no—
109#1571—131no—
110#1542D1311yescharacteristic
111#1518—131no—
112#1461—131no—
113#1286—131no—
114C23×C13#12111yescharacteristic
115Q8×C13—81no—
116Q8×C13—81no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13#12011yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13#12311yescharacteristic
126C2×C4×C13#12411yescharacteristic
127C2×C4×C13C2×Q1611yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13#13711yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139Dic26—22no—
140Dic26—22no—
141Dic26—41no—
142Dic26—41no—
143C8×C13—81no—
144C8×C13—81no—
145#1055—42no—
146#1055—42no—
147#533C2×D1311yescharacteristic
148C2×C4×Q8—131no—
149#479—262no—
150#477—261no—
151#475—261no—
152#431—131no—
153#431C2×D1311yescharacteristic
154#428—261no—
155#423—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157#419—261no—
158C2×#103—261no—
159#382—131no—
160#340—261no—
161#335—262no—
162#333—21no—
163#332—21no—
164#328—262no—
165#324—262no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13#39411yescharacteristic
169C22×C13#46711yescharacteristic
170C22×C13#46811yescharacteristic
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—81no—
176C4×C13—81no—
177C4×C13#44911yescharacteristic
178C4×C13#45111yescharacteristic
179C4×C13#48411yescharacteristic
180C4×C13#48511yescharacteristic
181Dic13—42no—
182Dic13—81no—
183Dic13—161no—
184C22×Q8—131no—
185C2×M16—261no—
186C22×C8—21no—
187C4⋊Q8C22⋊D1311yescharacteristic
188C4⋊Q8C22⋊D1311yescharacteristic
189#125—21no—
190C22⋊Q8—21no—
191C22⋊Q8—21no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—261no—
195C4×Q8—261no—
196C4×Q8—261no—
197C4×Q8—261no—
198#117—21no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C42—261no—
203C2×C42C22×D1311yescharacteristic
204#107—262no—
205#106—262no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—132no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212#103—262no—
213#103—262no—
214#103—522no—
215C22⋊C8—21no—
216C22⋊C8—132no—
217C4×C8—21no—
218C4×C8—261no—
219#95—261no—
220#95—261no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13#203611yescharacteristic
224C2×C13#204911yescharacteristic
225C2×C13#205311yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—132no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—261no—
232C2×Q8—261no—
233C2×Q8—261no—
234C22×C4—261no—
235C22×C4—261no—
236C22×C4—521no—
237C22×C4#612711yescharacteristic
238C22×C4D4×D1311yescharacteristic
239C22×C4D4×D1311yescharacteristic
240M16—521no—
241M16—521no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—262no—
247C2×C8—262no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C22⋊C4—41no—
261C42—41no—
262C42—521no—
263C42—521no—
264C42#612711yescharacteristic
265C42D4×D1311yescharacteristic
266C42#612911yescharacteristic
267C42C2×C22⋊D1311yescharacteristic
268C13#1047111yescharacteristic, complemented, Sylow
269C23#8813811yescharacteristic
270Q8—81no—
271Q8—81no—
272Q8—262no—
273Q8—262no—
274Q8—521no—
275Q8—521no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—1041no—
285C2×C4—1041no—
286C2×C4—1041no—
287C2×C4—1041no—
288C2×C4#8813711yescharacteristic
289C2×C4#8813811yescharacteristic
290C2×C4#8813911yescharacteristic
291C2×C4#8816811yescharacteristic
292C2×C4#8817011yescharacteristic
293C2×C4Q16×D1311yescharacteristic
294C2×C4#8817211yescharacteristic
295C2×C4#8818311yescharacteristic
296C2×C4#8819111yescharacteristic
297C2×C4#8819311yescharacteristic
298C8—81no—
299C8—81no—
300C8—522no—
301C8—522no—
302C22—21no—
303C22—21no—
304C22#1171847311yescharacteristic
305C22#1171847411yescharacteristic
306C22#1171862011yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—81no—
312C4—81no—
313C4—522no—
314C4—1041no—
315C4—2081no—
316C4#1171847011yescharacteristic
317C4#1171847611yescharacteristic
318C4#1171883311yescharacteristic
319C4#1171884711yescharacteristic
320C2—21no—
321C2—21no—
322C2#1311603711yescharacteristic
323C2#1311611611yescharacteristic
324C2#1311614011yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1542C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1542D13
hypocenterC13#10471
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
268. C13#10471semidirect

Maximal subgroups

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

subgroupindex
#131246372
#131148522
#131136102
#131134002
#131131592
#131126952
C13×#15422
#1047113