Finite Group Databasebeta

← #15764783

Subgroups — #15764783

Order 3328.

488 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125784C211yesmaximal, characteristic
2#13125378C211yesmaximal, characteristic
3#13115826C211yesmaximal, characteristic
4#13113517C211yesmaximal, characteristic
5#13113292C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C2×C13×#487C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#487—22no—
12C13×#487—22no—
13C2×C13×#103—22no—
14C2×C4×C8×C13C2211yescharacteristic
15#11718889—22no—
16#11718753—21no—
17#11718751—22no—
18#11718742—21no—
19#11718741—22no—
20#11718740—21no—
21#11718739—21no—
22#11718625—22no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718138—22no—
27#11718122—22no—
28#11718048—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D412yes—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C42×C13C2311yescharacteristic
45C2×#6107—24no—
46#88180—21no—
47#88178—21no—
48#88178—21no—
49C2×#6099—21no—
50C2×#6099D412yes—
51#88124—21no—
52#88123D411yescharacteristic
53#88123D411yescharacteristic
54C4×Dic26—21no—
55C4×Dic26—21no—
56C13×#103—28no—
57C4×C8×C13—21no—
58C4×C8×C13D412yes—
59#88075—24no—
60C22⋊#1055—21no—
61#88048—24no—
62#88047—24no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055D412yes—
66#88043—21no—
67C4×#1055—21no—
68C4×#1055—21no—
69#10163—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—22no—
72C2×Q8×C13—22no—
73C2×Q8×C13—44no—
74C2×Q8×C13—41no—
75C2×Q8×C13—82no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13#4111yescharacteristic
81C2×Dic26—21no—
82C2×Dic26—21no—
83C2×C8×C13—22no—
84C2×C8×C13—42no—
85C13×C4⋊C4—22no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C22⋊Dic13—41no—
98#6107—84no—
99C4⋊Dic13—21no—
100C4⋊Dic13—21no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103#6101—41no—
104#6101—41no—
105C4×Dic13—41no—
106#6099—22no—
107#6099—42no—
108#6099Q1614yescomplemented
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—41no—
112#3209—131no—
113#3165—131no—
114C2×#487D1311yescharacteristic
115#1997—131no—
116#1548—131no—
117#1493—131no—
118#1278—131no—
119C23×C13#12111yescharacteristic
120Q8×C13—44no—
121Q8×C13—44no—
122Q8×C13—82no—
123Q8×C13—82no—
124C2×C4×C13—22no—
125C2×C4×C13—22no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12711yescharacteristic
136C2×C4×C13C2×Q1612yes—
137C2×C4×C13#13712yes—
138C2×Dic13—41no—
139C2×Dic13—41no—
140Dic26—42no—
141Dic26—42no—
142C8×C13—42no—
143#1055—24no—
144#1055—42no—
145#1055—81no—
146#533—131no—
147C2×C4⋊Q8C2×D1311yescharacteristic
148C2×C4⋊Q8C2×D1311yescharacteristic
149#501—262no—
150#500—261no—
151#498—261no—
152#494—261no—
153#487—22no—
154#487—22no—
155#487—261no—
156#462—262no—
157#451—262no—
158#431—131no—
159#428—262no—
160#423—131no—
161C2×#103—22no—
162C4×M16—131no—
163C2×C4×C8C2×D1311yescharacteristic
164#343—262no—
165#333—262no—
166Q8⋊C8—262no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#39211yescharacteristic
170C22×C13#46212yes—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—82no—
174C4×C13—82no—
175C4×C13#45112yes—
176C4×C13#45512yes—
177C4×C13#47112yes—
178C4×C13#49411yescharacteristic
179C4×C13#49711yescharacteristic
180Dic13—81no—
181Dic13—81no—
182C22×Q8—21no—
183C22×Q8C22⋊D1312yes—
184C2×Q16—264no—
185C2×M16—132no—
186C2×M16—261no—
187C22×C8—21no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—131no—
196C4⋊Q8—131no—
197C4⋊Q8C22⋊D1312yes—
198#125—261no—
199C22⋊Q8—261no—
200C22⋊Q8—261no—
201C4×Q8—261no—
202C4×Q8—261no—
203#117—261no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C42C22×D1311yescharacteristic
209#107—264no—
210#106—264no—
211C4⋊C8—132no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214#103—28no—
215#103—264no—
216C22⋊C8—261no—
217#97—261no—
218C4×C8—21no—
219C4×C8—261no—
220C4×C8—261no—
221C4×C8C22⋊D1312yes—
222C2×C13—22no—
223C2×C13#200411yescharacteristic
224C2×C13#201611yescharacteristic
225C2×C13#201911yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—22no—
229C2×Q8—44no—
230C2×Q8—41no—
231C2×Q8—82no—
232C2×Q8—261no—
233C2×Q8—261no—
234C22×C4—22no—
235C22×C4—41no—
236C22×C4D4×D1311yescharacteristic
237C22×C4#612911yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239Q16—1044no—
240M16—134no—
241M16—262no—
242M16—522no—
243C2×C8—22no—
244C2×C8—42no—
245C2×C8—262no—
246C2×C8—262no—
247C2×C8—521no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C22⋊C4—521no—
263C42—521no—
264C42D4×D1311yescharacteristic
265C42D4×D1311yescharacteristic
266C42C2×C22⋊D1311yescharacteristic
267C42C2×C22⋊D1311yescharacteristic
268C13#1016311yescharacteristic, complemented, Sylow
269C23#8819311yescharacteristic
270Q8—44no—
271Q8—44no—
272Q8—82no—
273Q8—82no—
274Q8—522no—
275Q8—522no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4Q16×D1312yes—
285C2×C4#8817212yes—
286C2×C4#8819111yescharacteristic
287C2×C4#8819111yescharacteristic
288C2×C4#8819211yescharacteristic
289C2×C4#8819311yescharacteristic
290C2×C4#8819411yescharacteristic
291C2×C4#8820711yescharacteristic
292C8—42no—
293C8—264no—
294C8—522no—
295C8—1041no—
296C22—21no—
297C22—21no—
298C22#1171884312yes—
299C22#1171888411yescharacteristic
300C4—21no—
301C4—21no—
302C4—82no—
303C4—82no—
304C4—1041no—
305C4—1041no—
306C4#1171872212yes—
307C4#1171883812yes—
308C4#1171884211yescharacteristic
309C4#1171884712yes—
310C4#1171885111yescharacteristic
311C2—22no—
312C2#1311586511yescharacteristic
313C2#1311593411yescharacteristic
314C2#1311594811yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenterC2×#487D13
hypocenterC13#10163
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
108. #6099Q16semidirect
268. C13#10163semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131253782
#131158262
#131135172
#131132922
#131126732
C2×C13×#4872
#1016313