Finite Group Databasebeta

← #15758522

Subgroups — #15758522

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88043C211yesmaximal, characteristic
2#13123146C211yesmaximal, characteristic
3C2×#11718057C212yesmaximal, complemented
4#13112718C212yesmaximal, complemented
5C13×#1749C211yesmaximal, characteristic
6C22×C42×C13C2211yescharacteristic
7C23×#1055—21no—
8C2×#88124C2211yescharacteristic
9C2×C13×C22⋊C8—21no—
10C2×C13×#97C2212yes—
11#11718873C411yescharacteristic
12#11718873C411yescharacteristic
13#11718871—21no—
14#11718871—21no—
15#11718597C2211yescharacteristic
16#11718594—21no—
17#11718594—21no—
18#11718589C411yescharacteristic
19#11718589C411yescharacteristic
20C2×#88043—24no—
21C2×#88043—21no—
22C2×#88043C2212yes—
23C13×#336—21no—
24#11718057—24no—
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C22×C8×C13—22no—
29C2×C42×C13—22no—
30C2×C42×C13—22no—
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C22×#1055—24no—
46C22×#1055—24no—
47C22×#1055—24no—
48C22×#1055—22no—
49#88124—22no—
50#88124—22no—
51C13×C22⋊C8—24no—
52C13×#97—22no—
53C13×#97—22no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071—21no—
60#88043—24no—
61#88043—22no—
62#88043D414yes—
63#9121—131nomaximal, Sylow
64C24×C13C22⋊C411yescharacteristic
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—21no—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C2×C8×C13—24no—
86C2×C8×C13—42no—
87C2×C8×C13—42no—
88C42×C13—22no—
89C42×C13—21no—
90C42×C13—22no—
91C42×C13—21no—
92C42×C13C2×D412yes—
93C42×C13#4112yes—
94C22⋊Dic13—42no—
95C22⋊Dic13—42no—
96C4⋊Dic13—22no—
97C4⋊Dic13—22no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6101—42no—
101#6101—42no—
102#6101—41no—
103#6101—42no—
104#6101—41no—
105C2×#1055—216no—
106C2×#1055—24no—
107C2×#1055—24no—
108C2×#1055—24no—
109C22×#97—131no—
110#2851—131no—
111#1749D1311yescharacteristic
112C2×#330—132no—
113#1295—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—21no—
117C23×C13—21no—
118C23×C13#10112yes—
119C23×C13#10412yes—
120C23×C13#10412yes—
121C23×C13C2×C22⋊C411yescharacteristic
122C2×C4×C13—24no—
123C2×C4×C13—24no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—44no—
139C2×C4×C13—44no—
140C2×C4×C13#10412yes—
141C2×C4×C13C4×D412yes—
142C2×C4×C13#12011yescharacteristic
143C2×C4×C13#12112yes—
144C2×C4×C13#12311yescharacteristic
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C8×C13—44no—
158#1055—28no—
159C23×C8—261no—
160C2×#125—131no—
161C22×C42C2×D1311yescharacteristic
162C2×C22⋊C8—21no—
163C2×#97—132no—
164C2×#97—264no—
165C2×#97—261no—
166C2×#97C2×D1312yes—
167#389—131no—
168#389—131no—
169#387—261no—
170#387—261no—
171#385—261no—
172#385—261no—
173#382—131no—
174#380—131no—
175#380—131no—
176#336—21no—
177#330—264no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—22no—
184C22×C13#33014yescomplemented
185C22×C13#38611yescharacteristic
186C22×C13C2×#10111yescharacteristic
187C22×C13#41311yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13C2×#10411yescharacteristic
190C22×C13C2×#10411yescharacteristic
191C22×C13#42111yescharacteristic
192C4×C13—22no—
193C4×C13—21no—
194C4×C13—22no—
195C4×C13—21no—
196C4×C13—22no—
197C4×C13—41no—
198C4×C13—41no—
199Dic13—81no—
200Dic13—81no—
201Dic13—81no—
202Dic13—81no—
203C23×C4C4×D1311yescharacteristic
204C23×C4D5211yescharacteristic
205C23×C4C22⋊D1311yescharacteristic
206C22×C8—22no—
207C22×C8—264no—
208C22×C8—264no—
209C22×C8—264no—
210C22×C8—262no—
211#125—262no—
212#125—262no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—131no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—131no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4—261no—
220C2×C4⋊C4—261no—
221C2×C22⋊C4—261no—
222C2×C22⋊C4—261no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42C4×D1311yescharacteristic
226C2×C42D5211yescharacteristic
227C2×C42C22⋊D1311yescharacteristic
228C2×C42C22×D1311yescharacteristic
229C22⋊C8—24no—
230#97—22no—
231#97—22no—
232#97—134no—
233#97—264no—
234#97—262no—
235#95—261no—
236#95—261no—
237#95—261no—
238#95—261no—
239#95—261no—
240#95—261no—
241C2×C13—24no—
242C2×C13C2×#33011yescharacteristic
243C2×C13#152411yescharacteristic
244C2×C13#153111yescharacteristic
245C2×C13#153211yescharacteristic
246C2×C13#187111yescharacteristic
247C2×C13#189611yescharacteristic
248C2×C13#190111yescharacteristic
249C24#610311yescharacteristic
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—261no—
261C22×C4—261no—
262C22×C4—261no—
263C22×C4—261no—
264C22×C4#610311yescharacteristic
265C22×C4#610311yescharacteristic
266C22×C4#610311yescharacteristic
267C22×C4C2×C4×D1311yescharacteristic
268C22×C4C2×D5211yescharacteristic
269C22×C4C2×C22⋊D1311yescharacteristic
270C2×C8—24no—
271C2×C8—42no—
272C2×C8—42no—
273C2×C8—2616no—
274C2×C8—264no—
275C2×C8—264no—
276C2×C8—264no—
277C4⋊C4—262no—
278C4⋊C4—262no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4—521no—
284C4⋊C4—521no—
285C4⋊C4—522no—
286C22⋊C4—522no—
287C22⋊C4—522no—
288C42—22no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42D4×D1312yes—
293C42#612912yes—
294C13#912111yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23#8804512yes—
300C23#8806412yes—
301C23#8806512yes—
302C23C2×#610311yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—521no—
322C2×C4—521no—
323C2×C4—521no—
324C2×C4—521no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4#8806512yes—
334C2×C4#8813512yes—
335C2×C4#8813611yescharacteristic
336C2×C4#8814011yescharacteristic
337C2×C4#8819312yes—
338C8—44no—
339C8—268no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22#1171805714yescomplemented
347C22C2×#8804511yescharacteristic
348C22#1171861911yescharacteristic
349C22#1171866611yescharacteristic
350C22#1171879311yescharacteristic
351C22C2×#8806411yescharacteristic
352C22C2×#8806511yescharacteristic
353C22C2×#8806511yescharacteristic
354C4—22no—
355C4—21no—
356C4—22no—
357C4—21no—
358C4—22no—
359C4—41no—
360C4—41no—
361C4—1041no—
362C4—1041no—
363C4—1041no—
364C4—1041no—
365C2—24no—
366C2C2×#1171805711yescharacteristic
367C2#1311342511yescharacteristic
368C2#1311345211yescharacteristic
369C2#1311345711yescharacteristic
370C2#1311513611yescharacteristic
371C2#1311527711yescharacteristic
372C2#1311530211yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1749C2
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1749D13
hypocenterC13#9121
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. C2×#11718057C2semidirect
4. #13112718C2semidirect
184. C22×C13#330semidirect
294. C13#9121semidirect
346. C22#11718057semidirect

Maximal subgroups

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

subgroupindex
C22×#880432
#131231462
C2×#117180572
#131127182
C13×#17492
#912113