Finite Group Databasebeta

← #15764787

Subgroups — #15764787

Order 3328.

488 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 111 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#13125382C211yesmaximal, characteristic
3C2×#11718742C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic
5#13113290C211yesmaximal, characteristic
6#13112674C211yesmaximal, characteristic
7C13×#1997C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×M16C2211yescharacteristic
13#11718889—22no—
14C2×#88075—22no—
15#11718782—22no—
16#11718753—21no—
17#11718751—22no—
18#11718742—22no—
19#11718742—22no—
20#11718742—21no—
21#11718586C2211yescharacteristic
22C2×C4×#1055C2211yescharacteristic
23#11718363—22no—
24#11718343—21no—
25#11718341—21no—
26C13×#343—22no—
27#11718076—22no—
28#11718073—22no—
29C22×Q8×C13D412yes—
30C22×Dic26—21no—
31C2×C13×M16—21no—
32C2×C13×M16D412yes—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4—21no—
39C2×C42×C13C2311yescharacteristic
40C2×#6107—24no—
41#88180—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—21no—
44#88178—21no—
45#88178—21no—
46C22×#1055—21no—
47#88124—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123D412yes—
52#88123D411yescharacteristic
53#88123D411yescharacteristic
54C4×Dic26—21no—
55C4×Dic26—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×#97—21no—
59C4×C8×C13—21no—
60#88075—28no—
61#88075—24no—
62C22⋊#1055—21no—
63#88058—24no—
64#88057—24no—
65C4⋊#1055D412yes—
66C4×#1055—21no—
67C4×#1055—21no—
68C4×#1055D412yes—
69#10163—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—22no—
72C2×Q8×C13—44no—
73C22×C4×C13—22no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—41no—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26—22no—
81C2×Dic26—41no—
82C2×Dic26—82no—
83C13×M16—22no—
84C13×M16—42no—
85C13×M16Q1614yescomplemented
86C2×C8×C13—22no—
87C2×C8×C13—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C22⋊Dic13—41no—
97#6107—84no—
98C4⋊Dic13—21no—
99C4⋊Dic13—22no—
100C4⋊Dic13—22no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106#6101—41no—
107#6101—41no—
108C4×Dic13—41no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—42no—
112#3209—131no—
113#3165—131no—
114C2×#487—131no—
115#1997D1311yescharacteristic
116#1548—131no—
117#1493—131no—
118#1278—131no—
119C23×C13#12111yescharacteristic
120Q8×C13—44no—
121Q8×C13—44no—
122C2×C4×C13—22no—
123C2×C4×C13—22no—
124C2×C4×C13—42no—
125C2×C4×C13—82no—
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12011yescharacteristic
128C2×C4×C13#12011yescharacteristic
129C2×C4×C13#12111yescharacteristic
130C2×C4×C13#12111yescharacteristic
131C2×C4×C13#12711yescharacteristic
132C2×C4×C13C2×Q1612yes—
133C2×C4×C13#13712yes—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—42no—
137C2×Dic13—82no—
138Dic26—42no—
139Dic26—42no—
140Dic26—82no—
141Dic26—82no—
142C8×C13—24no—
143C8×C13—81no—
144#1055—42no—
145#1055—42no—
146#533—131no—
147C2×C4⋊Q8—131no—
148C2×C4⋊Q8C2×D1311yescharacteristic
149#501—262no—
150#500—261no—
151#498—261no—
152#494—261no—
153#487—262no—
154#487—262no—
155#487—261no—
156#462—262no—
157#451—262no—
158#431—131no—
159#428—262no—
160#423C2×D1311yescharacteristic
161C2×#103—262no—
162C4×M16C2×D1311yescharacteristic
163C2×C4×C8—131no—
164#343—22no—
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#45112yes—
175C4×C13#45512yes—
176C4×C13#47112yes—
177C4×C13#49411yescharacteristic
178C4×C13#49711yescharacteristic
179Dic13—81no—
180Dic13—81no—
181Dic13—82no—
182C22×Q8—261no—
183C22×Q8D5212yes—
184C2×Q16—264no—
185C2×M16—21no—
186C2×M16C22⋊D1312yes—
187C22×C8—261no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—132no—
193C4⋊Q8—131no—
194C4⋊Q8—131no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
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—261no—
207C2×C4⋊C4—261no—
208C2×C42C22×D1311yescharacteristic
209#107—264no—
210#106—264no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—132no—
214#103—268no—
215#103—264no—
216C22⋊C8—261no—
217#97—21no—
218C4×C8—21no—
219C4×C8—132no—
220C4×C8—261no—
221C4×C8—261no—
222C2×C13—22no—
223C2×C13#200411yescharacteristic
224C2×C13#201611yescharacteristic
225C2×C13#201911yescharacteristic
226C2×Q8—22no—
227C2×Q8—22no—
228C2×Q8—44no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—262no—
232C2×Q8—521no—
233C2×Q8—1042no—
234C22×C4—22no—
235C22×C4—521no—
236C22×C4C2×D5211yescharacteristic
237C22×C4#612711yescharacteristic
238C22×C4C2×C22⋊D1311yescharacteristic
239Q16—1044no—
240M16—22no—
241M16—42no—
242M16#610714yescomplemented
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—262no—
246C2×C8—262no—
247C2×C8—522no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—262no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—262no—
257C4⋊C4—261no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C22⋊C4—521no—
263C42—521no—
264C42D4×D1311yescharacteristic
265C42D4×D1311yescharacteristic
266C42D4×D1311yescharacteristic
267C42D4×D1311yescharacteristic
268C13#1016311yescharacteristic, complemented, Sylow
269C23#8818411yescharacteristic
270Q8—44no—
271Q8—44no—
272Q8—522no—
273Q8—522no—
274Q8—1042no—
275Q8—1042no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—522no—
283C2×C4—1042no—
284C2×C4#8813611yescharacteristic
285C2×C4#8813611yescharacteristic
286C2×C4#8813811yescharacteristic
287C2×C4#8813811yescharacteristic
288C2×C4#8819111yescharacteristic
289C2×C4#8819411yescharacteristic
290C2×C4C2×#610712yes—
291C2×C4#8820512yes—
292C8—24no—
293C8—81no—
294C8—522no—
295C8—522no—
296C22—21no—
297C22—21no—
298C22#1171862111yescharacteristic
299C22#1171869212yes—
300C4—21no—
301C4—21no—
302C4—82no—
303C4—1042no—
304C4—1041no—
305C4—1041no—
306C4#1171840712yes—
307C4#1171841512yes—
308C4#1171871112yes—
309C4#1171872111yescharacteristic
310C4#1171875311yescharacteristic
311C2—22no—
312C2#1311586711yescharacteristic
313C2#1311593511yescharacteristic
314C2#1311594911yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1997C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1997D13
hypocenterC13#10163
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
85. C13×M16Q16semidirect
242. M16#6107semidirect
268. C13#10163semidirect

Maximal subgroups

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

subgroupindex
#131257842
#131253822
C2×#117187422
#131135182
#131132902
#131126742
C13×#19972
#1016313