Finite Group Databasebeta

← #15764785

Subgroups — #15764785

Order 3328.

488 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 107 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#13125786C211yesmaximal, characteristic
2#13125378C211yesmaximal, characteristic
3C2×#11718754C211yesmaximal, characteristic
4#13115824C211yesmaximal, characteristic
5#13113290C211yesmaximal, characteristic
6#13112672C211yesmaximal, characteristic
7C13×#1548C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9#11719175C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#431C2211yescharacteristic
12C13×#423C2211yescharacteristic
13#11718754—22no—
14#11718754—22no—
15#11718741—22no—
16#11718740—21no—
17#11718739—21no—
18C2×#88050—22no—
19#11718625—22no—
20C4×#6099C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718510—22no—
23#11718400—22no—
24#11718360—21no—
25#11718342—21no—
26C13×#333—22no—
27#11718146—22no—
28#11718076—22no—
29C22×Q8×C13—21no—
30C22×Dic26D412yes—
31C2×C13×M16—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8D412yes—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4—21no—
38C2×C42×C13C2311yescharacteristic
39#88180—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42#88178—21no—
43#88178—21no—
44C2×#6099D412yes—
45C22×#1055—21no—
46C2×Dic52—24no—
47#88124—21no—
48#88123—21no—
49#88123—21no—
50#88123—21no—
51#88123—21no—
52#88123D411yescharacteristic
53#88123D411yescharacteristic
54C4×Dic26—21no—
55C4×Dic26—21no—
56C13×C4⋊C8—21no—
57C13×C4⋊C8—21no—
58C13×C4⋊C8D412yes—
59C13×C22⋊C8—21no—
60C4×C8×C13—21no—
61#88056—24no—
62#88050—28no—
63#88048—24no—
64#88047—24no—
65#88043—21no—
66C4×#1055—21no—
67C4×#1055—21no—
68C4×#1055D412yes—
69#10163—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—82no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4111yescharacteristic
77C22×Dic13—22no—
78C2×Dic26—21no—
79C2×Dic26—22no—
80C2×Dic26—22no—
81C2×Dic26—21no—
82C2×Dic26—44no—
83C13×M16—42no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C13×C4⋊C4—22no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C42×C13C2×D411yescharacteristic
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C22⋊Dic13—41no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—41no—
100C4⋊Dic13—41no—
101C4⋊Dic13—41no—
102C4⋊Dic13—41no—
103#6101—41no—
104#6101—41no—
105C4×Dic13—41no—
106#6099—22no—
107#6099Q1614yescomplemented
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—42no—
111Dic52—84no—
112#3209—131no—
113#3165—131no—
114C2×#487—131no—
115#1997—131no—
116#1548D1311yescharacteristic
117#1493—131no—
118#1278—131no—
119C23×C13#12111yescharacteristic
120Q8×C13—82no—
121Q8×C13—82no—
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—44no—
139Dic26—42no—
140Dic26—44no—
141Dic26—42no—
142C8×C13—42no—
143C8×C13—81no—
144#1055—24no—
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—261no—
154#487—262no—
155#487—262no—
156#462—262no—
157#451—262no—
158#431C2×D1311yescharacteristic
159#428—262no—
160#423C2×D1311yescharacteristic
161C2×#103—262no—
162C4×M16—131no—
163C2×C4×C8—131no—
164#343—262no—
165#333—22no—
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—82no—
180Dic13—81no—
181Dic13—81no—
182C22×Q8—21no—
183C22×Q8—132no—
184C2×Q16—264no—
185C2×M16—21no—
186C2×M16—132no—
187C22×C8—261no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—131no—
192C4⋊Q8—131no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C4⋊Q8—261no—
197C4⋊Q8D5212yes—
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⋊C8C22⋊D1312yes—
214#103—268no—
215#103—264no—
216C22⋊C8—21no—
217#97—261no—
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—41no—
228C2×Q8—82no—
229C2×Q8—262no—
230C2×Q8—261no—
231C2×Q8—262no—
232C2×Q8—261no—
233C2×Q8—524no—
234C22×C4—41no—
235C22×C4—262no—
236C22×C4#612711yescharacteristic
237C22×C4D4×D1311yescharacteristic
238C22×C4D4×D1311yescharacteristic
239Q16—1044no—
240M16—42no—
241M16—134no—
242M16—262no—
243C2×C8—22no—
244C2×C8—41no—
245C2×C8—262no—
246C2×C8—262no—
247C2×C8—522no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—521no—
257C4⋊C4—521no—
258C4⋊C4—521no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C22⋊C4—521no—
263C42—521no—
264C42C2×D5211yescharacteristic
265C42D4×D1311yescharacteristic
266C42D4×D1311yescharacteristic
267C42C2×C22⋊D1311yescharacteristic
268C13#1016311yescharacteristic, complemented, Sylow
269C23#8813811yescharacteristic
270Q8—82no—
271Q8—82no—
272Q8—524no—
273Q8—522no—
274Q8—522no—
275Q8—524no—
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#8816912yes—
288C2×C4Q16×D1312yes—
289C2×C4#8818411yescharacteristic
290C2×C4#8819111yescharacteristic
291C2×C4#8819411yescharacteristic
292C8—42no—
293C8—81no—
294C8—264no—
295C8—522no—
296C22—21no—
297C22—21no—
298C22#1171845412yes—
299C22#1171862111yescharacteristic
300C4—21no—
301C4—21no—
302C4—82no—
303C4—1041no—
304C4—1042no—
305C4—1041no—
306C4#1171840912yes—
307C4#1171846912yes—
308C4#1171882811yescharacteristic
309C4#1171884211yescharacteristic
310C4#1171886312yes—
311C2—22no—
312C2#1311586611yescharacteristic
313C2#1311593711yescharacteristic
314C2#1311595211yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenter#1548D13
hypocenterC13#10163
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
107. #6099Q16semidirect
268. C13#10163semidirect

Maximal subgroups

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

subgroupindex
#131257862
#131253782
C2×#117187542
#131158242
#131132902
#131126722
C13×#15482
#1016313