Finite Group Databasebeta

← #15758489

Subgroups — #15758489

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123167C211yesmaximal, characteristic
2C2×#11718062C212yesmaximal
3#13113063C211yesmaximal, characteristic, complemented
4#13112716C212yesmaximal, complemented
5C2×C13×#431C211yesmaximal, characteristic, complemented
6C22×C42×C13C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×#88183—21no—
9C13×#431—24no—
10C2×C13×C4⋊C8—21no—
11C2×C13×C22⋊C8C2212yes—
12C2×C4×C8×C13—21no—
13#11718874—21no—
14#11718873C2211yescharacteristic
15C2×#88071—21no—
16C2×#88071—21no—
17C2×#88071C2212yes—
18#11718601—21no—
19#11718601—21no—
20#11718600C411yescharacteristic, complemented
21#11718600C411yescharacteristic, complemented
22#11718589C411yescharacteristic, complemented
23#11718589C411yescharacteristic, complemented
24#11718062—24no—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13C2311yescharacteristic
28C22×C22⋊D13—21no—
29C23×Dic13—22no—
30C22×D52C2×C411yescharacteristic
31C22×C8×C13—22no—
32C2×C42×C13—22no—
33C2×C42×C13—22no—
34C2×C42×C13C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13D411yescharacteristic
37C2×C42×C13D411yescharacteristic
38C2×C22⋊Dic13—21no—
39#88184—22no—
40#88184—22no—
41#88183—42no—
42#88183—42no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×#6103—21no—
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×C4⋊Dic13C2×C411yescharacteristic
50C2×C4⋊Dic13C2×C411yescharacteristic
51C2×#6101—21no—
52C2×#6101—21no—
53C13×C4⋊C8—24no—
54C13×C22⋊C8—22no—
55C13×C22⋊C8D414yes—
56C4×C8×C13—24no—
57#88071—24no—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—22no—
62#88071—22no—
63#88071—42no—
64#9114—131nomaximal, Sylow
65C24×C13C2×D411yescharacteristic
66C23×D13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13D812yes—
79C22×C4×C13SD1612yes—
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13#4112yes—
84C2×C22⋊D13—42no—
85C2×C22⋊D13—41no—
86C2×C22⋊D13—41no—
87C2×C22⋊D13—42no—
88C22×Dic13—24no—
89C22×Dic13—21no—
90C22×Dic13—21no—
91C22×Dic13—21no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C22×Dic13—42no—
95C22×Dic13—42no—
96C22×Dic13—42no—
97C22×Dic13—42no—
98C2×D52—22no—
99C2×D52—41no—
100C2×D52—41no—
101C2×C8×C13—24no—
102C2×C8×C13—42no—
103C2×C8×C13—42no—
104C42×C13—22no—
105C42×C13—22no—
106C42×C13—21no—
107C42×C13—21no—
108C42×C13—21no—
109C42×C13—21no—
110C22⋊Dic13—41no—
111C22⋊Dic13—41no—
112#6103—42no—
113#6103—42no—
114#6103—42no—
115#6103—42no—
116#6103—41no—
117#6103—41no—
118C4⋊Dic13—22no—
119C4⋊Dic13—41no—
120C4⋊Dic13—41no—
121#6101—42no—
122#6101—42no—
123C2×#431D1311yescharacteristic, complemented
124#2854—131no—
125C2×#327—132no—
126#1434—131no—
127#1294—132no—
128C23×C13—21no—
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13C2×C22⋊C411yescharacteristic
133C23×C13#12112yes—
134C23×C13C2×D811yescharacteristic
135C23×C13C2×SD1611yescharacteristic
136C23×C13#13512yes—
137C22×D13—41no—
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—41no—
144C2×C4×C13—21no—
145C2×C4×C13—21no—
146C2×C4×C13—21no—
147C2×C4×C13—21no—
148C2×C4×C13—21no—
149C2×C4×C13—21no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—21no—
153C2×C4×C13—21no—
154C2×C4×C13—24no—
155C2×C4×C13—24no—
156C2×C4×C13—21no—
157C2×C4×C13—21no—
158C2×C4×C13—21no—
159C2×C4×C13—42no—
160C2×C4×C13—42no—
161C2×C4×C13—44no—
162C2×C4×C13#10212yes—
163C2×C4×C13#10212yes—
164C2×C4×C13#10412yes—
165C2×C4×C13C4×D412yes—
166C2×C4×C13#12011yescharacteristic
167C2×C4×C13#12311yescharacteristic
168C22⋊D13—82no—
169C22⋊D13—82no—
170C2×Dic13—44no—
171C2×Dic13—44no—
172C2×Dic13—44no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—41no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—82no—
183C2×Dic13—82no—
184C2×Dic13—82no—
185C2×Dic13—82no—
186D52—82no—
187C8×C13—44no—
188C2×#123—261no—
189C2×#121—131no—
190C22×C42C2×D1311yescharacteristic
191#431—24no—
192C2×C4⋊C8—21no—
193C2×C22⋊C8C2×D1312yes—
194C2×C4×C8—21no—
195#390—131no—
196#390—131no—
197#389—131no—
198#389—131no—
199#388—261no—
200#388—261no—
201#386—261no—
202#380—131no—
203C2×#95—132no—
204C2×#95—261no—
205C2×#95—261no—
206#327—264no—
207C22×C13—22no—
208C22×C13—22no—
209C22×C13—22no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—22no—
215C22×C13#38611yescharacteristic
216C22×C13#41011yescharacteristic
217C22×C13#41011yescharacteristic
218C22×C13C2×#10211yescharacteristic
219C22×C13#41611yescharacteristic
220C22×C13C2×#10411yescharacteristic
221C22×C13#42111yescharacteristic
222C22×C13#46512yes—
223C22×C13#46612yes—
224C2×D13—81no—
225C2×D13—81no—
226C2×D13—81no—
227C2×D13—81no—
228C2×D13—81no—
229C2×D13—81no—
230C2×D13—81no—
231C4×C13—22no—
232C4×C13—22no—
233C4×C13—22no—
234C4×C13—21no—
235C4×C13—22no—
236C4×C13—21no—
237C4×C13—41no—
238Dic13—84no—
239Dic13—81no—
240Dic13—81no—
241Dic13—81no—
242C22×D4—131no—
243C22×D4—261no—
244C23×C4—262no—
245C23×C4D5211yescharacteristic
246C23×C4D5211yescharacteristic
247C23×C4C22×D1311yescharacteristic
248C22×C8—22no—
249#123—522no—
250#123—522no—
251#121—262no—
252#121—262no—
253C2×C4⋊C4—131no—
254C2×C4⋊C4—131no—
255C2×C4⋊C4—131no—
256C2×C4⋊C4—261no—
257C2×C4⋊C4—261no—
258C2×C22⋊C4—261no—
259C2×C22⋊C4—261no—
260C2×C22⋊C4—261no—
261C2×C22⋊C4—261no—
262C2×C22⋊C4—261no—
263C2×C22⋊C4—261no—
264C2×C42—22no—
265C2×C42—22no—
266C2×C42C4×D1311yescharacteristic
267C2×C42C4×D1311yescharacteristic
268C2×C42C22⋊D1311yescharacteristic
269C2×C42C22⋊D1311yescharacteristic
270C4⋊C8—24no—
271C22⋊C8—22no—
272C22⋊C8C22⋊D1314yes—
273C4×C8—24no—
274#95—264no—
275#95—261no—
276#95—261no—
277#95—261no—
278#95—262no—
279#95—262no—
280#95—522no—
281C2×C13—22no—
282C2×C13—22no—
283C2×C13#150011yescharacteristic
284C2×C13#150211yescharacteristic
285C2×C13#151711yescharacteristic
286C2×C13#152111yescharacteristic
287C2×C13#187111yescharacteristic
288C2×C13#189311yescharacteristic
289C2×C13#189911yescharacteristic
290D13—161no—
291C24—261no—
292C24C2×D5211yescharacteristic
293C2×D4—262no—
294C2×D4—521no—
295C2×D4—521no—
296C2×D4—521no—
297C2×D4—521no—
298C2×D4—522no—
299C2×D4—522no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—264no—
308C22×C4—261no—
309C22×C4—261no—
310C22×C4—261no—
311C22×C4—522no—
312C22×C4—522no—
313C22×C4—522no—
314C22×C4—522no—
315C22×C4—522no—
316C22×C4—522no—
317C22×C4#609512yes—
318C22×C4D10412yes—
319C22×C4#610311yescharacteristic
320C22×C4#610311yescharacteristic
321C22×C4#610311yescharacteristic
322C22×C4#610311yescharacteristic
323C22×C4C2×C4×D1311yescharacteristic
324C22×C4#612712yes—
325C22×C4C2×C22⋊D1311yescharacteristic
326C22×C4C2×C22⋊D1312yes—
327C2×C8—24no—
328C2×C8—42no—
329C2×C8—42no—
330C4⋊C4—262no—
331C4⋊C4—521no—
332C4⋊C4—521no—
333C4⋊C4—522no—
334C4⋊C4—522no—
335C22⋊C4—522no—
336C22⋊C4—521no—
337C22⋊C4—521no—
338C22⋊C4—522no—
339C22⋊C4—521no—
340C22⋊C4—521no—
341C22⋊C4—522no—
342C22⋊C4—522no—
343C42—22no—
344C42—22no—
345C42—21no—
346C42—21no—
347C42—21no—
348C42—21no—
349C13#911411yescharacteristic, complemented, Sylow
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—521no—
355C23—521no—
356C23—521no—
357C23—521no—
358C23—521no—
359C23—521no—
360C23—521no—
361C23C2×#609511yescharacteristic
362C23C2×D10411yescharacteristic
363C23#8815812yes—
364C23C2×#610311yescharacteristic
365C23#8818412yes—
366D4—1042no—
367D4—1042no—
368D4—1042no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—24no—
376C2×C4—24no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—44no—
387C2×C4—524no—
388C2×C4—524no—
389C2×C4—524no—
390C2×C4—521no—
391C2×C4—521no—
392C2×C4—521no—
393C2×C4—521no—
394C2×C4—521no—
395C2×C4—521no—
396C2×C4—521no—
397C2×C4—521no—
398C2×C4—521no—
399C2×C4—1042no—
400C2×C4—1042no—
401C2×C4—1042no—
402C2×C4—1042no—
403C2×C4#8806112yes—
404C2×C4#8806112yes—
405C2×C4#8806512yes—
406C2×C4C4×C22⋊D1312yes—
407C2×C4#8818311yescharacteristic
408C2×C4#8820711yescharacteristic
409C8—44no—
410C22—22no—
411C22—21no—
412C22—21no—
413C22—22no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—1041no—
419C22—1041no—
420C22—1041no—
421C22—1041no—
422C22—1041no—
423C22—1041no—
424C22—1041no—
425C22#1171866711yescharacteristic
426C22#1171866711yescharacteristic
427C22C2×#8806111yescharacteristic
428C22#1171877411yescharacteristic
429C22#1171877512yes—
430C22#1171877612yes—
431C22C2×#8806511yescharacteristic
432C22#1171880011yescharacteristic
433C22#1171887411yescharacteristic
434C4—22no—
435C4—22no—
436C4—22no—
437C4—21no—
438C4—22no—
439C4—21no—
440C4—41no—
441C4—1044no—
442C4—1041no—
443C4—1041no—
444C4—1041no—
445C2—22no—
446C2—22no—
447C2—2081no—
448C2#1311332311yescharacteristic
449C2#1311333211yescharacteristic
450C2#1311339711yescharacteristic
451C2#1311341411yescharacteristic
452C2#1311513811yescharacteristic
453C2#1311526411yescharacteristic
454C2#1311529411yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#431C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×#431D13
hypocenterC13#9114
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #13113063C2semidirect
4. #13112716C2semidirect
5. C2×C13×#431C2semidirect
20. #11718600C4semidirect
21. #11718600C4semidirect
22. #11718589C4semidirect
23. #11718589C4semidirect
123. C2×#431D13semidirect
349. C13#9114semidirect

Maximal subgroups

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

subgroupindex
#131231672
C2×#117180622
#131130632
#131127162
C2×C13×#4312
#911413