Finite Group Databasebeta

← #15759677

Subgroups — #15759677

Order 3328.

488 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 113 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#13124629C211yesmaximal, characteristic
2#13123859C211yesmaximal, characteristic
3#13114847C211yesmaximal, characteristic
4#13113400C211yesmaximal, characteristic, complemented
5#13112733C211yesmaximal, characteristic, complemented
6#13112695C211yesmaximal, characteristic, complemented
7C13×#1481C211yesmaximal, characteristic, complemented
8C13×#533C2211yescharacteristic
9C2×C4×D52C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88061—21no—
13#11718748C412yescomplemented
14#11718745C412yescomplemented
15#11718727—22no—
16#11718662—21no—
17#11718656—21no—
18#11718597C2211yescharacteristic
19#11718586C2211yescharacteristic
20#11718585C2211yescharacteristic
21#11718495—22no—
22D13×C22⋊C8—22no—
23C8×D52—22no—
24C13×Q8⋊C8—22no—
25#11718143—21no—
26#11718130—22no—
27C22×D52D411yescharacteristic
28C22×C4×D13—21no—
29C22×C8×C13—21no—
30C13×C4⋊Q8C2×C411yescharacteristic
31C13×C4⋊Q8C2×C411yescharacteristic
32C13×#125—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8—21no—
35C4×Q8×C13—21no—
36C4×Q8×C13—21no—
37C13×#117—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6103—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13D411yescharacteristic
42C2×#6099—21no—
43C2×C8×D13—24no—
44C4×D52—21no—
45C4×D52—21no—
46C4×D52C2×C412yes—
47C4×D52D412yes—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C4×C8×C13D412yes—
53#88071—21no—
54#88071—21no—
55C22⋊#1055D412yes—
56#88061—42no—
57#88060—24no—
58#88049—22no—
59#88049—22no—
60#88048—22no—
61#88047—22no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055C2×C412yes—
65C4×#1055—21no—
66#9303—131nomaximal, Sylow
67C23×D13—21no—
68C2×Q8×C13—21no—
69C2×Q8×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4111yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—41no—
75C2×D52—21no—
76C2×D52—21no—
77C2×D52—21no—
78C2×D52C22⋊C412yes—
79C2×D52SD1612yes—
80C2×D52Q1612yes—
81C2×C4×D13—22no—
82C2×C4×D13—22no—
83C2×C4×D13—82no—
84C2×C8×C13—22no—
85C2×C8×C13—41no—
86C2×C8×C13—41no—
87C2×C8×C13—41no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—21no—
91C13×C4⋊C4—21no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C22⋊C4—41no—
95C42×C13—41no—
96C42×C13C22×C411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13#4111yescharacteristic
100#6103—22no—
101#6103—22no—
102C4⋊Dic13—21no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13C22⋊C412yes—
106#6099—41no—
107#6099—41no—
108C2×#1055—22no—
109C2×#1055—22no—
110C8×D13—84no—
111#3077—131no—
112#2972—131no—
113#1804—131no—
114#1518—131no—
115#1481D1311yescharacteristic, complemented
116#1301—131no—
117#1286—131no—
118C23×C13#12111yescharacteristic
119C22×D13—22no—
120C22×D13—22no—
121C22×D13—22no—
122C22×D13—81no—
123C22×D13—81no—
124Q8×C13—42no—
125Q8×C13—81no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13C2×SD1611yescharacteristic
137C2×C4×C13C2×Q1611yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×Dic13—22no—
141C2×Dic13—81no—
142C2×Dic13—81no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145D52—22no—
146D52—22no—
147D52—22no—
148D52#10314yes—
149C4×D13—44no—
150C4×D13—82no—
151C8×C13—42no—
152C8×C13—81no—
153#1055—42no—
154#1055—42no—
155#533C2×D1311yescharacteristic
156C2×C4×D4—131no—
157#478—262no—
158#476—132no—
159#474—132no—
160C8×D4—262no—
161C8×D4—262no—
162#431—131no—
163#431C2×D1311yescharacteristic
164#428—261no—
165#423—131no—
166C2×C4⋊C8C2×D1311yescharacteristic
167#418—261no—
168C2×#102—261no—
169C2×C22⋊C8—262no—
170#382—131no—
171#340—261no—
172#328—262no—
173Q8⋊C8—22no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13#38611yescharacteristic
177C22×C13#46511yescharacteristic
178C22×C13#46711yescharacteristic
179C2×D13—24no—
180C2×D13—42no—
181C2×D13—42no—
182C2×D13—82no—
183C2×D13—82no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—21no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13C2×#10311yescharacteristic
191C4×C13#41611yescharacteristic
192C4×C13#46511yescharacteristic
193C4×C13#46711yescharacteristic
194Dic13—42no—
195Dic13—161no—
196C22×D4—131no—
197C23×C4—261no—
198C2×M16—261no—
199C22×C8—21no—
200C22×C8—264no—
201C4⋊Q8C4×D1311yescharacteristic
202C4⋊Q8C4×D1311yescharacteristic
203#125—21no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C4×Q8—21no—
207C4×Q8—21no—
208C4×D4—132no—
209C4×D4—132no—
210C4×D4—261no—
211C4×D4—261no—
212#117—21no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C42C22×D1311yescharacteristic
217#107—262no—
218#106—262no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—132no—
223C4⋊C8—261no—
224C4⋊C8—261no—
225#102—262no—
226#102—262no—
227#102—522no—
228C22⋊C8—21no—
229C22⋊C8—132no—
230C22⋊C8—264no—
231C4×C8—261no—
232C4×C8C22⋊D1312yes—
233#95—261no—
234#95—261no—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13#188111yescharacteristic
238C2×C13#189211yescharacteristic
239C2×C13#190411yescharacteristic
240D13—44no—
241C24—261no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×D4—132no—
245C2×D4—132no—
246C2×D4—132no—
247C2×D4—261no—
248C2×D4—261no—
249C2×D4—261no—
250C22×C4—261no—
251C22×C4—262no—
252C22×C4—262no—
253C22×C4—521no—
254C22×C4—1042no—
255C22×C4#612711yescharacteristic
256C22×C4D4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258M16—521no—
259M16—521no—
260C2×C8—22no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—1044no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—132no—
274C4⋊C4—261no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C22⋊C4—41no—
278C22⋊C4—262no—
279C22⋊C4—262no—
280C42—41no—
281C42C2×C4×D1311yescharacteristic
282C42D4×D1311yescharacteristic
283C42#612911yescharacteristic
284C42C2×C22⋊D1311yescharacteristic
285C13#930311yescharacteristic, complemented, Sylow
286C23—262no—
287C23—262no—
288C23—262no—
289C23—1041no—
290C23—1041no—
291C23#8813811yescharacteristic
292Q8—42no—
293Q8—81no—
294D4—134no—
295D4—262no—
296D4—262no—
297D4—262no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—262no—
303C2×C4—524no—
304C2×C4—1042no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4C22⋊C4×D1311yescharacteristic
310C2×C4#8813511yescharacteristic
311C2×C4#8813711yescharacteristic
312C2×C4SD16×D1311yescharacteristic
313C2×C4#8817011yescharacteristic
314C2×C4Q16×D1311yescharacteristic
315C2×C4#8817311yescharacteristic
316C2×C4C4×C22⋊D1311yescharacteristic
317C2×C4#8819111yescharacteristic
318C2×C4#8819211yescharacteristic
319C8—42no—
320C8—81no—
321C8—522no—
322C8—522no—
323C22—21no—
324C22—21no—
325C22—264no—
326C22—522no—
327C22—522no—
328C22—1042no—
329C22—1042no—
330C22#1171846811yescharacteristic
331C22#1171847411yescharacteristic
332C22#1171861711yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—81no—
338C4—81no—
339C4—522no—
340C4—2081no—
341C4D13×#10311yescharacteristic
342C4#1171846511yescharacteristic
343C4#1171883211yescharacteristic
344C4#1171884911yescharacteristic
345C2—21no—
346C2—21no—
347C2—524no—
348C2#1311520111yescharacteristic
349C2#1311525611yescharacteristic
350C2#1311532011yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1481C2
socleC22×C13#386
prime radicalC22×D52D4
cosocleC2×C42×C13C23
hypercenter#1481D13
hypocenterC13#9303
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #13113400C2semidirect
5. #13112733C2semidirect
6. #13112695C2semidirect
7. C13×#1481C2semidirect
13. #11718748C4semidirect
14. #11718745C4semidirect
115. #1481D13semidirect
285. C13#9303semidirect

Maximal subgroups

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

subgroupindex
#131246292
#131238592
#131148472
#131134002
#131127332
#131126952
C13×#14812
#930313