Finite Group Databasebeta

← #15762050

Subgroups — #15762050

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123137C211yesmaximal, characteristic
2#13114816C211yesmaximal, characteristic, complemented
3C2×#11718044C212yesmaximal, complemented
4C2×#11718043C212yesmaximal
5C4×C13×#95C211yesmaximal, characteristic, complemented
6C22×C42×C13—21no—
7C22×C42×C13C2211yescharacteristic
8C2×#88184C2211yescharacteristic
9C2×#88178C2211yescharacteristic
10C2×#88129C411yescharacteristic, complemented
11C2×C13×#95—21no—
12C2×C13×#95C2212yes—
13#11718874—21no—
14#11718874—21no—
15C2×C22⋊#1055C2212yes—
16#11718601—21no—
17#11718601—21no—
18#11718600C411yescharacteristic, complemented
19#11718597C411yescharacteristic, complemented
20#11718590C411yescharacteristic, complemented
21C2×C4⋊#1055—21no—
22#11718116—21no—
23#11718044—24no—
24#11718043—24no—
25C23×C4×C13—22no—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C23×C4×C13C2311yescharacteristic
29C22×C22⋊D13—21no—
30C22×D52C2×C411yescharacteristic
31C22×Dic26C2×C411yescharacteristic
32C2×C42×C13—24no—
33C2×C42×C13—42no—
34C2×C42×C13—42no—
35C2×C42×C13—42no—
36C2×C42×C13C2×C411yescharacteristic
37C2×C42×C13C2×C411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C22⋊Dic13—21no—
41#88184—22no—
42#88184—22no—
43C2×#6103—21no—
44C2×#6103—21no—
45C2×#6103—21no—
46C2×#6103—21no—
47C2×#6103—21no—
48C2×C4⋊Dic13C2×C411yescharacteristic
49C2×C4⋊Dic13C2×C411yescharacteristic
50#88178—22no—
51#88178—22no—
52C2×#6101—21no—
53C22×#1055—22no—
54#88129—42no—
55C13×#95—24no—
56C13×#95—22no—
57C13×#95D414yes—
58#88071—21no—
59#88071—21no—
60#88071—21no—
61#88071—21no—
62C22⋊#1055—22no—
63C22⋊#1055—22no—
64C4⋊#1055—42no—
65#9713—131nomaximal, Sylow
66C24×C13C2×D411yescharacteristic
67C23×D13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—24no—
73C22×C4×C13—24no—
74C22×C4×C13—24no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—41no—
78C22×C4×C13—41no—
79C22×C4×C13—41no—
80C22×C4×C13—42no—
81C22×C4×C13—42no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D412yes—
91C22×C4×C13#4112yes—
92C2×C22⋊D13—42no—
93C2×C22⋊D13—42no—
94C2×C22⋊D13—41no—
95C2×C22⋊D13—41no—
96C22×Dic13—21no—
97C22×Dic13—21no—
98C22×Dic13—21no—
99C2×D52—22no—
100C2×D52—41no—
101C2×D52—41no—
102C2×Dic26—22no—
103C2×Dic26—41no—
104C2×Dic26—41no—
105C42×C13—22no—
106C42×C13—22no—
107C42×C13—41no—
108C42×C13—41no—
109C42×C13—48no—
110C22⋊Dic13—42no—
111#6103—42no—
112#6103—42no—
113#6103—42no—
114#6103—42no—
115#6103—41no—
116#6103—41no—
117C4⋊Dic13—22no—
118C4⋊Dic13—22no—
119#6101—41no—
120#6101—41no—
121C2×#1055—42no—
122C2×#1055—42no—
123C2×#1055—42no—
124#2850—131no—
125#1797—131no—
126C2×#328—132no—
127C2×#327—132no—
128C4×#95D1311yescharacteristic, complemented
129C23×C13—21no—
130C23×C13—21no—
131C23×C13—21no—
132C23×C13—21no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#12112yes—
135C23×C13#13512yes—
136C23×C13AGL(1,ℤ/8)11yescharacteristic
137C23×C13#13711yescharacteristic
138C22×D13—41no—
139C22×D13—41no—
140C22×D13—41no—
141C22×D13—41no—
142C22×D13—41no—
143C22×D13—41no—
144C22×D13—41no—
145C2×C4×C13—24no—
146C2×C4×C13—24no—
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—21no—
155C2×C4×C13—21no—
156C2×C4×C13—21no—
157C2×C4×C13—28no—
158C2×C4×C13—21no—
159C2×C4×C13—21no—
160C2×C4×C13—21no—
161C2×C4×C13—42no—
162C2×C4×C13—42no—
163C2×C4×C13—44no—
164C2×C4×C13—44no—
165C2×C4×C13—44no—
166C2×C4×C13—44no—
167C2×C4×C13—44no—
168C2×C4×C13—44no—
169C2×C4×C13—44no—
170C2×C4×C13#9912yes—
171C2×C4×C13#10412yes—
172C2×C4×C13#10412yes—
173C2×C4×C13C4×D412yes—
174C2×C4×C13#12411yescharacteristic
175C2×C4×C13#12711yescharacteristic
176C22⋊D13—82no—
177C22⋊D13—82no—
178C2×Dic13—41no—
179C2×Dic13—41no—
180C2×Dic13—41no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—41no—
184C2×Dic13—41no—
185C2×Dic13—41no—
186C2×Dic13—41no—
187D52—82no—
188Dic26—82no—
189#1055—82no—
190C2×#124—131no—
191C2×C22⋊Q8—131no—
192C2×#121—131no—
193C22×C42—21no—
194C22×C42C2×D1311yescharacteristic
195C2×C4⋊C8—261no—
196C2×C22⋊C8—132no—
197#391—131no—
198#390—131no—
199#388—261no—
200#388—261no—
201#386—261no—
202#386—261no—
203#382—131no—
204C2×#95—21no—
205C2×#95C2×D1312yes—
206#336—261no—
207#328—264no—
208#327—264no—
209C22×C13—22no—
210C22×C13—22no—
211C22×C13—22no—
212C22×C13—22no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—21no—
216C22×C13—21no—
217C22×C13#39011yescharacteristic
218C22×C13C2×#9911yescharacteristic
219C22×C13#41011yescharacteristic
220C22×C13#41611yescharacteristic
221C22×C13#41711yescharacteristic
222C22×C13C2×#10411yescharacteristic
223C22×C13C2×#10411yescharacteristic
224C22×C13#46312yes—
225C22×C13#46412yes—
226C2×D13—81no—
227C2×D13—81no—
228C2×D13—81no—
229C2×D13—81no—
230C2×D13—81no—
231C2×D13—81no—
232C2×D13—81no—
233C4×C13—21no—
234C4×C13—22no—
235C4×C13—21no—
236C4×C13—22no—
237C4×C13—22no—
238C4×C13—22no—
239C4×C13—48no—
240C4×C13—41no—
241Dic13—81no—
242Dic13—81no—
243Dic13—81no—
244C22×Q8—131no—
245C22×D4—131no—
246C22×D4—261no—
247C23×C4—22no—
248C23×C4C22⋊D1311yescharacteristic
249C23×C4C22⋊D1311yescharacteristic
250C23×C4C22×D1311yescharacteristic
251C22×C8—262no—
252#124—522no—
253C22⋊Q8—262no—
254C22⋊Q8—262no—
255#121—262no—
256#121—262no—
257C2×C4⋊C4—131no—
258C2×C4⋊C4—131no—
259C2×C4⋊C4—261no—
260C2×C22⋊C4—261no—
261C2×C22⋊C4—261no—
262C2×C22⋊C4—261no—
263C2×C22⋊C4—261no—
264C2×C22⋊C4—261no—
265C2×C22⋊C4—261no—
266C2×C42—24no—
267C2×C42—42no—
268C2×C42—42no—
269C2×C42—42no—
270C2×C42C4×D1311yescharacteristic
271C2×C42C4×D1311yescharacteristic
272C2×C42D5211yescharacteristic
273C2×C42D5211yescharacteristic
274C4⋊C8—522no—
275C22⋊C8—262no—
276C22⋊C8—262no—
277#95—24no—
278#95—22no—
279#95—261no—
280#95—261no—
281#95—261no—
282#95—261no—
283#95D5214yes—
284C2×C13—22no—
285C2×C13—22no—
286C2×C13#150011yescharacteristic
287C2×C13#150111yescharacteristic
288C2×C13#150411yescharacteristic
289C2×C13#150911yescharacteristic
290C2×C13#196211yescharacteristic
291C2×C13#196411yescharacteristic
292C2×C13#198311yescharacteristic
293D13—161no—
294C24—261no—
295C24C2×C22⋊D1311yescharacteristic
296C2×Q8—262no—
297C2×Q8—521no—
298C2×Q8—521no—
299C2×D4—262no—
300C2×D4—521no—
301C2×D4—521no—
302C2×D4—522no—
303C2×D4—521no—
304C2×D4—521no—
305C2×D4—522no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—42no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—261no—
323C22×C4—261no—
324C22×C4—261no—
325C22×C4#610311yescharacteristic
326C22×C4#610311yescharacteristic
327C22×C4#610311yescharacteristic
328C22×C4#610311yescharacteristic
329C22×C4C2×C4×D1311yescharacteristic
330C22×C4C2×D5211yescharacteristic
331C22×C4C2×D5212yes—
332C22×C4#612712yes—
333C2×C8—522no—
334C2×C8—522no—
335C2×C8—522no—
336C4⋊C4—262no—
337C4⋊C4—262no—
338C4⋊C4—521no—
339C4⋊C4—521no—
340C22⋊C4—522no—
341C22⋊C4—522no—
342C22⋊C4—521no—
343C22⋊C4—521no—
344C22⋊C4—522no—
345C22⋊C4—522no—
346C22⋊C4—522no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—48no—
352C13#971311yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—521no—
358C23—521no—
359C23—521no—
360C23—521no—
361C23—521no—
362C23—521no—
363C23—521no—
364C23C2×#610311yescharacteristic
365C23#8818412yes—
366C23#8818611yescharacteristic
367C23#8819611yescharacteristic
368C23#8820412yes—
369Q8—1042no—
370D4—1042no—
371D4—1042no—
372D4—1042no—
373C2×C4—24no—
374C2×C4—24no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—28no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—44no—
394C2×C4—44no—
395C2×C4—44no—
396C2×C4—44no—
397C2×C4—44no—
398C2×C4—521no—
399C2×C4—521no—
400C2×C4—521no—
401C2×C4—521no—
402C2×C4—521no—
403C2×C4—521no—
404C2×C4—521no—
405C2×C4—521no—
406C2×C4—521no—
407C2×C4#8804512yes—
408C2×C4#8804512yes—
409C2×C4#8804612yes—
410C2×C4C4×D5212yes—
411C2×C4#8812811yescharacteristic
412C2×C4#8812911yescharacteristic
413C8—1042no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—21no—
421C22—21no—
422C22—1041no—
423C22—1041no—
424C22—1041no—
425C22—1041no—
426C22—1041no—
427C22—1041no—
428C22—1041no—
429C22C2×#8804511yescharacteristic
430C22C2×#8804511yescharacteristic
431C22#1171860011yescharacteristic
432C22C2×#8804611yescharacteristic
433C22#1171862711yescharacteristic
434C22#1171866311yescharacteristic
435C22#1171866711yescharacteristic
436C22#1171867712yes—
437C22#1171868912yes—
438C4—21no—
439C4—22no—
440C4—21no—
441C4—22no—
442C4—22no—
443C4—22no—
444C4—48no—
445C4—41no—
446C4—1041no—
447C4—1041no—
448C4—1041no—
449C2—22no—
450C2—22no—
451C2—2081no—
452C2#1311332011yescharacteristic
453C2#1311332511yescharacteristic
454C2#1311333811yescharacteristic
455C2#1311335911yescharacteristic
456C2#1311566411yescharacteristic
457C2#1311567211yescharacteristic
458C2#1311576811yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC4×C13×#95C2
socleC23×C13C2×C22⋊C4
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC4×#95D13
hypocenterC13#9713
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
2. #13114816C2semidirect
3. C2×#11718044C2semidirect
5. C4×C13×#95C2semidirect
10. C2×#88129C4semidirect
18. #11718600C4semidirect
19. #11718597C4semidirect
20. #11718590C4semidirect
128. C4×#95D13semidirect
352. C13#9713semidirect

Maximal subgroups

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

subgroupindex
#131231372
#131148162
C2×#117180442
C2×#117180432
C4×C13×#952
#971313