Finite Group Databasebeta

← #15766539

Subgroups — #15766539

Order 3328.

408 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C2×#11718748C211yesmaximal, characteristic
2#13114825C211yesmaximal, characteristic
3#13113608C211yesmaximal, characteristic, complemented
4#13113521C211yesmaximal, characteristic, complemented
5#13113228C211yesmaximal, characteristic
6#13112732C211yesmaximal, characteristic, complemented
7C13×#1548C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×#88063—21no—
13#11718748—22no—
14#11718748—22no—
15C2×#88049—21no—
16C2×#88047—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#333—22no—
21#11718146—21no—
22#11718139—22no—
23#11718072—22no—
24#11718051—22no—
25C22×Q8×C13—21no—
26C22×D52D411yescharacteristic
27C22×C4×D13—21no—
28C2×C13×M16—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8D412yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C42×C13C2311yescharacteristic
36C2×#6103—21no—
37C2×C4⋊Dic13D411yescharacteristic
38C2×#6099—21no—
39C22×#1055—21no—
40C4×D52—21no—
41C4×D52—21no—
42C4×D52—21no—
43C4×D52—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C22⋊C8—21no—
48C4×C8×C13—21no—
49C22⋊#1055—21no—
50#88063—42no—
51#88049—24no—
52#88047—24no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055D412yes—
57C4⋊#1055D412yes—
58C4×#1055—21no—
59#10448—131nomaximal, Sylow
60C23×D13—21no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C2×Q8×C13—82no—
64C22×C4×C13—41no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—21no—
69C2×D52—21no—
70C2×D52—21no—
71C2×D52—21no—
72C2×D52—21no—
73C2×D52—21no—
74C2×D52SD1612yes—
75C2×C4×D13—41no—
76C2×C4×D13—41no—
77C2×C4×D13—82no—
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C42×C13C2×D411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90#6103—41no—
91#6103—41no—
92C4⋊Dic13—21no—
93C4⋊Dic13—21no—
94#6099—41no—
95#6099—41no—
96C2×#1055—22no—
97C2×#1055—22no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#474—131no—
102#1800—131no—
103#1570—131no—
104#1549—131no—
105#1548D1311yescharacteristic, complemented
106#1478—131no—
107#1301—131no—
108C23×C13#12311yescharacteristic
109C22×D13—22no—
110C22×D13—41no—
111C22×D13—41no—
112C22×D13—81no—
113C22×D13—81no—
114Q8×C13—82no—
115Q8×C13—82no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—82no—
120C2×C4×C13#12011yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12111yescharacteristic
124C2×C4×C13#12311yescharacteristic
125C2×C4×C13#12411yescharacteristic
126C2×C4×C13C2×SD1611yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×C4×C13#13711yescharacteristic
130C2×Dic13—41no—
131C2×Dic13—81no—
132D52—22no—
133D52—22no—
134D52—41no—
135D52—41no—
136C4×D13—82no—
137C4×D13—82no—
138C8×C13—81no—
139C8×C13—81no—
140#1055—42no—
141#1055—42no—
142#1055—81no—
143C2×C4⋊Q8C2×D1311yescharacteristic
144C2×C4×D4—131no—
145#474—262no—
146#474—262no—
147#431—131no—
148#431C2×D1311yescharacteristic
149C2×#107—261no—
150#423—131no—
151#423C2×D1311yescharacteristic
152C2×C4⋊C8—131no—
153C2×#102—261no—
154C2×#100—261no—
155#343—261no—
156#334—262no—
157#333—22no—
158#332—262no—
159D4⋊C8—262no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13#39411yescharacteristic
163C22×C13#48311yescharacteristic
164C22×C13#48511yescharacteristic
165C2×D13—42no—
166C2×D13—82no—
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—82no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—82no—
174C4×C13#44811yescharacteristic
175C4×C13#45211yescharacteristic
176C4×C13#46511yescharacteristic
177C4×C13#47011yescharacteristic
178C4×C13#47212yes—
179Dic13—81no—
180C22×Q8—21no—
181C22×D4—131no—
182C23×C4—261no—
183C2×M16—21no—
184C2×M16—261no—
185C22×C8—261no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8—21no—
189C4⋊Q8C22⋊D1312yes—
190C4×D4—261no—
191C4×D4—261no—
192C4×D4—261no—
193C4×D4—261no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—131no—
197C2×C22⋊C4—261no—
198C2×C42C22×D1311yescharacteristic
199#107—264no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—132no—
204C4⋊C8—132no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208#102—264no—
209#100—522no—
210C22⋊C8—21no—
211C22⋊C8—261no—
212C4×C8—21no—
213C4×C8—261no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#203511yescharacteristic
217C2×C13#204511yescharacteristic
218C2×C13#204911yescharacteristic
219D13—82no—
220C24—261no—
221C2×Q8—22no—
222C2×Q8—41no—
223C2×Q8—82no—
224C2×D4—132no—
225C2×D4—261no—
226C2×D4—261no—
227C2×D4—261no—
228C2×D4—261no—
229C2×D4—261no—
230C22×C4—41no—
231C22×C4—261no—
232C22×C4—521no—
233C22×C4—521no—
234C22×C4—1042no—
235C22×C4#612711yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4#612911yescharacteristic
238M16—41no—
239M16—41no—
240M16—521no—
241M16—521no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—262no—
245C2×C8—262no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C22⋊C4—521no—
256C22⋊C4—521no—
257C42#612711yescharacteristic
258C42D4×D1311yescharacteristic
259C42D4×D1311yescharacteristic
260C42C2×C22⋊D1311yescharacteristic
261C13#1044811yescharacteristic, complemented, Sylow
262C23—262no—
263C23—521no—
264C23—521no—
265C23—1041no—
266C23—1041no—
267C23#8813711yescharacteristic
268Q8—82no—
269Q8—82no—
270D4—262no—
271D4—262no—
272D4—521no—
273D4—521no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—521no—
279C2×C4—1042no—
280C2×C4—1042no—
281C2×C4—1041no—
282C2×C4#8813811yescharacteristic
283C2×C4#8813811yescharacteristic
284C2×C4#8813911yescharacteristic
285C2×C4SD16×D1311yescharacteristic
286C2×C4#8816911yescharacteristic
287C2×C4#8817211yescharacteristic
288C2×C4#8817311yescharacteristic
289C2×C4#8818311yescharacteristic
290C2×C4#8819111yescharacteristic
291C2×C4#8819311yescharacteristic
292C8—81no—
293C8—81no—
294C8—522no—
295C8—522no—
296C8—1041no—
297C22—21no—
298C22—21no—
299C22—522no—
300C22—1042no—
301C22—1042no—
302C22—1041no—
303C22—1041no—
304C22#1171846611yescharacteristic
305C22#1171847511yescharacteristic
306C22#1171862011yescharacteristic
307C4—21no—
308C4—21no—
309C4—21no—
310C4—82no—
311C4—1041no—
312C4#1171841012yes—
313C4#1171846811yescharacteristic
314C4#1171847711yescharacteristic
315C4#1171883111yescharacteristic
316C4#1171884811yescharacteristic
317C2—21no—
318C2—21no—
319C2—1042no—
320C2#1311603011yescharacteristic
321C2#1311609011yescharacteristic
322C2#1311611411yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#394
prime radicalC22×D52D4
hypercenter#1548D13
hypocenterC13#10448
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
3. #13113608C2semidirect
4. #13113521C2semidirect
6. #13112732C2semidirect
7. C13×#1548C2semidirect
105. #1548D13semidirect
261. C13#10448semidirect

Maximal subgroups

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

subgroupindex
C2×#117187482
#131148252
#131136082
#131135212
#131132282
#131127322
C13×#15482
#1044813