Finite Group Databasebeta

← #15766702

Subgroups — #15766702

Order 3328.

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

normal subgroups only

This group has 366 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#13124641C211yesmaximal, characteristic
2#13113610C211yesmaximal, characteristic
3#13113494C211yesmaximal, characteristic
4#13113399C211yesmaximal, characteristic
5#13113160C211yesmaximal, characteristic
6#13112694C211yesmaximal, characteristic
7C13×#1805C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C13×#103—21no—
12C13×#382C2211yescharacteristic
13#11718886—21no—
14#11718683—22no—
15#11718682—21no—
16#11718681—21no—
17#11718625—21no—
18#11718586C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21C13×#340—21no—
22#11718120—22no—
23#11718078—21no—
24#11718073—21no—
25#11718071—22no—
26#11718044—22no—
27C22×Q8×C13D411yescharacteristic
28C22×C8×C13—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38#88180—21no—
39#88178—21no—
40#88178—21no—
41C2×#6099—21no—
42#88124—21no—
43#88123D411yescharacteristic
44#88123D411yescharacteristic
45C4×Dic26—21no—
46C4×Dic26—21no—
47C13×C4⋊C8—21no—
48C13×C4⋊C8—21no—
49C13×#103—42no—
50C13×#95—21no—
51C13×#95—21no—
52#88075—22no—
53#88075—22no—
54C22⋊#1055—21no—
55C22⋊#1055D412yes—
56#88048—22no—
57#88047—22no—
58C4⋊#1055—21no—
59C4⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055D412yes—
62C4×#1055—21no—
63C4×#1055—21no—
64#10471—131nomaximal, Sylow
65C2×Q8×C13—21no—
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C2×Q8×C13Q1612yes—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C2×Dic26—21no—
78C2×Dic26—21no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C42×C13—41no—
89C42×C13—41no—
90C42×C13C2×D411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C22⋊Dic13—41no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—41no—
102#6099—41no—
103#6099—41no—
104C2×#1055—22no—
105C2×#1055—22no—
106C2×#1055—41no—
107#3078—131no—
108#1805D1311yescharacteristic
109#1571—131no—
110#1542—131no—
111#1518—131no—
112#1461—131no—
113#1286—131no—
114C23×C13#12111yescharacteristic
115Q8×C13—22no—
116Q8×C13—22no—
117Q8×C13—41no—
118Q8×C13—41no—
119C2×C4×C13—22no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—81no—
126C2×C4×C13—81no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12311yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×C4×C13#12411yescharacteristic
135C2×C4×C13C2×Q1611yescharacteristic
136C2×C4×C13#13511yescharacteristic
137C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C13#13711yescharacteristic
139C2×Dic13—41no—
140C2×Dic13—41no—
141Dic26—81no—
142Dic26—81no—
143C8×C13—81no—
144#1055—42no—
145#1055—42no—
146#1055—81no—
147#533—131no—
148C2×C4×Q8C2×D1311yescharacteristic
149#479—262no—
150#477—261no—
151#475—261no—
152#431—131no—
153#431—131no—
154#428—261no—
155#423—131no—
156C2×C4⋊C8C2×D1311yescharacteristic
157#419—261no—
158C2×#103—21no—
159#382C2×D1311yescharacteristic
160#340—21no—
161#335—262no—
162#333—261no—
163#332—261no—
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—42no—
176C4×C13—81no—
177C4×C13—161no—
178C4×C13#44911yescharacteristic
179C4×C13#45111yescharacteristic
180C4×C13#48411yescharacteristic
181C4×C13#48511yescharacteristic
182Dic13—81no—
183Dic13—81no—
184C22×Q8C22⋊D1311yescharacteristic
185C2×M16—261no—
186C22×C8—21no—
187C4⋊Q8—131no—
188C4⋊Q8—131no—
189#125—261no—
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C4×Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—21no—
196C4×Q8—261no—
197C4×Q8—261no—
198#117—261no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C42—21no—
203C2×C42C22×D1311yescharacteristic
204#107—262no—
205#106—262no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—132no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212#103—42no—
213#103—262no—
214#103—262no—
215C22⋊C8—132no—
216C22⋊C8—261no—
217C4×C8—261no—
218C4×C8—261no—
219#95—21no—
220#95—21no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13#203611yescharacteristic
224C2×C13#204911yescharacteristic
225C2×C13#205311yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—261no—
232C2×Q8—261no—
233C2×Q8#610712yes—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—41no—
237C22×C4D4×D1311yescharacteristic
238C22×C4#612911yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240M16—521no—
241M16—521no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—262no—
246C2×C8—262no—
247C2×C8—521no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C22⋊C4—521no—
261C42—41no—
262C42—41no—
263C42—521no—
264C42#612711yescharacteristic
265C42#612711yescharacteristic
266C42D4×D1311yescharacteristic
267C42D4×D1311yescharacteristic
268C13#1047111yescharacteristic, complemented, Sylow
269C23#8819311yescharacteristic
270Q8—22no—
271Q8—22no—
272Q8—41no—
273Q8—41no—
274Q8—1041no—
275Q8—1041no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4#8813711yescharacteristic
289C2×C4#8813811yescharacteristic
290C2×C4#8813811yescharacteristic
291C2×C4#8813911yescharacteristic
292C2×C4#8818311yescharacteristic
293C2×C4#8818611yescharacteristic
294C2×C4#8819111yescharacteristic
295C2×C4C2×#610711yescharacteristic
296C2×C4#8820411yescharacteristic
297C2×C4#8820511yescharacteristic
298C8—81no—
299C8—522no—
300C8—522no—
301C8—1041no—
302C22—21no—
303C22—21no—
304C22#1171862011yescharacteristic
305C22#1171870311yescharacteristic
306C22#1171871211yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—42no—
312C4—81no—
313C4—161no—
314C4—1041no—
315C4—1041no—
316C4#1171863111yescharacteristic
317C4#1171865711yescharacteristic
318C4#1171869811yescharacteristic
319C4#1171871111yescharacteristic
320C2—21no—
321C2—21no—
322C2#1311603911yescharacteristic
323C2#1311611411yescharacteristic
324C2#1311614011yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1805C2
socleC22×C13#394
prime radicalC23×C13#121
hypercenter#1805D13
hypocenterC13#10471
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1805

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
#131246412
#131136102
#131134942
#131133992
#131131602
#131126942
C13×#18052
#1047113