Finite Group Databasebeta

← #15757607

Subgroups — #15757607

Order 3328.

626 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123860C211yesmaximal, characteristic
2C4×#88189C211yesmaximal, characteristic
3#13114902C212yesmaximal, complemented
4#13112682C212yesmaximal, complemented
5C13×#1459C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189C411yescharacteristic
8C22×C4×Dic13C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10#11718881C411yescharacteristic
11C4×C22⋊Dic13—21no—
12C4×C22⋊Dic13C2211yescharacteristic
13C2×C22⋊#1055—21no—
14C2×C22⋊#1055C2212yes—
15D4×#1055—24no—
16#11718639—21no—
17#11718607C411yescharacteristic
18#11718605—21no—
19#11718604C411yescharacteristic
20C4×#6101—21no—
21#11718586—21no—
22C13×#324—21no—
23C13×#323—21no—
24#11718142—24no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C23×Dic13C2×C411yescharacteristic
29C23×Dic13C2×C411yescharacteristic
30C22×C8×C13—22no—
31C4×D4×C13—22no—
32C4×D4×C13—22no—
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4C2×C411yescharacteristic
35C2×C13×C22⋊C4D411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—21no—
39C2×C22⋊Dic13C2×C411yescharacteristic
40C2×C22⋊Dic13C2×C411yescharacteristic
41#88189—22no—
42#88189C814yescomplemented
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13—21no—
46C2×C4×Dic13—21no—
47C2×C4×Dic13—22no—
48C2×C4×Dic13—21no—
49C2×C4×Dic13—22no—
50C22×#1055—22no—
51C22×#1055D414yes—
52C13×C22⋊C8—22no—
53C13×C22⋊C8—22no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59C22⋊#1055—22no—
60C22⋊#1055—22no—
61C22⋊#1055—22no—
62C4⋊#1055—22no—
63C4×#1055—22no—
64#8966—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13C2×C812yes—
70C2×D4×C13M1612yes—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D412yes—
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13#4112yes—
82C22×Dic13—21no—
83C22×Dic13—21no—
84C22×Dic13—21no—
85C22×Dic13—22no—
86C22×Dic13—22no—
87C22×Dic13—21no—
88C22×Dic13—22no—
89C22×Dic13—21no—
90C22×Dic13—42no—
91C22×Dic13C2×C812yescomplemented
92C2×C8×C13—44no—
93C2×C8×C13—42no—
94C13×C4⋊C4—22no—
95C13×C22⋊C4—22no—
96C13×C22⋊C4—22no—
97C42×C13—21no—
98C42×C13—21no—
99C22⋊Dic13—24no—
100C22⋊Dic13—21no—
101C22⋊Dic13—22no—
102C22⋊Dic13—42no—
103C22⋊Dic13C2×C812yescomplemented
104#6101—24no—
105#6101—42no—
106C4×Dic13—42no—
107C4×Dic13—41no—
108C4×Dic13—42no—
109C4×Dic13—41no—
110C2×#1055—24no—
111C2×#1055—44no—
112C2×#1055—82no—
113#2972—131no—
114C4×#123—131no—
115#1817—132no—
116#1459D1311yescharacteristic
117#1282—132no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13C22⋊C812yes—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13C4×D412yes—
127C23×C13C22×C811yescharacteristic
128C23×C13C2×M1611yescharacteristic
129C23×C13#13112yes—
130D4×C13—24no—
131D4×C13—24no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—24no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—42no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—81no—
144C2×C4×C13C22⋊C812yes—
145C2×C4×C13#12011yescharacteristic
146C2×C4×C13#12112yes—
147C2×C4×C13#12311yescharacteristic
148C2×Dic13—22no—
149C2×Dic13—24no—
150C2×Dic13—22no—
151C2×Dic13—22no—
152C2×Dic13—24no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—42no—
157C2×Dic13—41no—
158C2×Dic13—41no—
159C2×Dic13—41no—
160C2×Dic13—42no—
161C2×Dic13—41no—
162C2×Dic13—41no—
163C2×Dic13—41no—
164C8×C13—82no—
165#1055—44no—
166C2×#123—131no—
167C2×C4×D4C2×D1311yescharacteristic
168C22×C42—131no—
169C8×D4—264no—
170#431—261no—
171C2×C22⋊C8—132no—
172C2×C22⋊C8—261no—
173C2×C22⋊C8C2×D1312yes—
174#388—261no—
175#387—261no—
176#386—131no—
177#385—131no—
178#381—131no—
179C4×C4⋊C4—261no—
180C4×C22⋊C4—131no—
181C4×C22⋊C4—261no—
182#336—264no—
183#324—21no—
184#323—21no—
185C22×C13—21no—
186C22×C13—22no—
187C22×C13—21no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—81no—
197C22×C13#38611yescharacteristic
198C22×C13C2×C22⋊C811yescharacteristic
199C22×C13#40811yescharacteristic
200C22×C13C8×D412yes—
201C22×C13#43512yes—
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—21no—
205C4×C13—41no—
206C4×C13—41no—
207C4×C13#45812yes—
208Dic13—42no—
209Dic13—42no—
210Dic13—42no—
211Dic13—81no—
212C22×D4C4×D1311yescharacteristic
213C23×C4—131no—
214C23×C4—131no—
215C23×C4D5211yescharacteristic
216C23×C4C22×D1311yescharacteristic
217C22×C8—22no—
218C22×C8—134no—
219C22×C8—262no—
220#123—134no—
221#123—262no—
222C4×D4—22no—
223C4×D4—22no—
224C2×C4⋊C4—261no—
225C2×C4⋊C4—261no—
226C2×C4⋊C4C22⋊D1311yescharacteristic
227C2×C22⋊C4—131no—
228C2×C22⋊C4—131no—
229C2×C22⋊C4—261no—
230C2×C22⋊C4—261no—
231C2×C22⋊C4C4×D1311yescharacteristic
232C2×C22⋊C4C22⋊D1311yescharacteristic
233C2×C42—261no—
234C2×C42—261no—
235C2×C42—262no—
236C2×C42—262no—
237C2×C42—261no—
238C2×C42D5211yescharacteristic
239C4⋊C8—262no—
240C22⋊C8—22no—
241C22⋊C8—22no—
242C22⋊C8—262no—
243C22⋊C8—262no—
244C22⋊C8—262no—
245C4×C8—262no—
246#95—261no—
247#95—261no—
248#95—261no—
249#95—261no—
250#95—261no—
251C2×C13—21no—
252C2×C13—21no—
253C2×C13—22no—
254C2×C13—22no—
255C2×C13—42no—
256C2×C13#186911yescharacteristic
257C2×C13#189011yescharacteristic
258C2×C13#189111yescharacteristic
259C24#610311yescharacteristic
260C24C2×C4×D1311yescharacteristic
261C2×D4—22no—
262C2×D4—22no—
263C2×D4C8×D1312yes—
264C2×D4#609412yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—132no—
270C22×C4—262no—
271C22×C4—262no—
272C22×C4—261no—
273C22×C4—262no—
274C22×C4—261no—
275C22×C4—261no—
276C22×C4—261no—
277C22×C4—261no—
278C22×C4—522no—
279C22×C4#610311yescharacteristic
280C22×C4#610311yescharacteristic
281C22×C4#610311yescharacteristic
282C22×C4C2×D5211yescharacteristic
283C22×C4D4×D1312yes—
284C22×C4#612912yes—
285C22×C4C2×C22⋊D1311yescharacteristic
286C2×C8—44no—
287C2×C8—42no—
288C2×C8—264no—
289C2×C8—524no—
290C2×C8—1042no—
291C4⋊C4—22no—
292C4⋊C4—264no—
293C4⋊C4—522no—
294C22⋊C4—22no—
295C22⋊C4—22no—
296C22⋊C4—132no—
297C22⋊C4—261no—
298C22⋊C4—264no—
299C22⋊C4—262no—
300C22⋊C4—522no—
301C42—21no—
302C42—21no—
303C42—522no—
304C42—521no—
305C42—521no—
306C42—522no—
307C13#896611yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23#8806012yes—
315C23#8813512yes—
316C23C2×C8×D1311yescharacteristic
317C23C2×#609411yescharacteristic
318C23#8816112yes—
319C23C2×#610311yescharacteristic
320D4—24no—
321D4—24no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—22no—
325C2×C4—24no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—81no—
334C2×C4—262no—
335C2×C4—264no—
336C2×C4—262no—
337C2×C4—262no—
338C2×C4—264no—
339C2×C4—521no—
340C2×C4—521no—
341C2×C4—521no—
342C2×C4—522no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—522no—
347C2×C4—521no—
348C2×C4—521no—
349C2×C4—521no—
350C2×C4#8806012yes—
351C2×C4#8813611yescharacteristic
352C2×C4#8814011yescharacteristic
353C2×C4#8819312yes—
354C8—82no—
355C8—524no—
356C22—21no—
357C22—22no—
358C22—21no—
359C22—22no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—42no—
364C22—42no—
365C22—41no—
366C22—41no—
367C22—81no—
368C22#1171838612yes—
369C22#1171839112yes—
370C22#1171861911yescharacteristic
371C22C2×#8806011yescharacteristic
372C22#1171879011yescharacteristic
373C4—22no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—522no—
379C4—522no—
380C4—522no—
381C4—1041no—
382C4#1171840312yes—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—22no—
387C2—42no—
388C2#1311512611yescharacteristic
389C2#1311524711yescharacteristic
390C2#1311525211yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC23×C13C22×C8
FrattiniC23×C4C22×D13
FittingC13×#1459C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC23×C4×C13C23
hypercenter#1459D13
hypocenterC13#8966
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
3. #13114902C2semidirect
4. #13112682C2semidirect
42. #88189C8semidirect
91. C22×Dic13C2×C8semidirect
103. C22⋊Dic13C2×C8semidirect
307. C13#8966semidirect

Maximal subgroups

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

subgroupindex
#131238602
C4×#881892
#131149022
#131126822
C13×#14592
#896613