Finite Group Databasebeta

← #15763204

Subgroups — #15763204

Order 3328.

654 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
1C2×#11718704C211yesmaximal, characteristic
2C2×#11718644C211yesmaximal, characteristic
3#13114920C211yesmaximal, characteristic
4C2×#11718130C211yesmaximal, characteristic
5C2×#11718120C211yesmaximal, characteristic
6#13112714C211yesmaximal, characteristic
7C13×#2627C211yesmaximal, characteristic
8C2×C13×C22⋊Q8C2211yescharacteristic
9C22×C13×C4⋊C4C2211yescharacteristic
10C22×C4⋊Dic13C2211yescharacteristic
11C22×#6101—21no—
12C13×#400—21no—
13C13×#398—22no—
14C13×#395—21no—
15C13×#385—21no—
16C13×#381—21no—
17C13×#380C2211yescharacteristic
18C2×#88075—21no—
19C2×#88071—21no—
20C2×#88071C2211yescharacteristic
21C2×C22⋊#1055C2211yescharacteristic
22C2×C22⋊#1055C2211yescharacteristic
23#11718704—22no—
24#11718704—22no—
25#11718644—22no—
26#11718644—22no—
27C2×#88048—21no—
28#11718130—22no—
29#11718121—22no—
30#11718120—22no—
31C22×Q8×C13D411yescharacteristic
32C23×C4×C13D411yescharacteristic
33C23×C4×C13D411yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C23×Dic13—21no—
36C23×Dic13—21no—
37C13×C22⋊Q8—21no—
38C13×C22⋊Q8—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—22no—
49C2×C13×C4⋊C4D411yescharacteristic
50C2×C13×C4⋊C4D412yes—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C4⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4⋊Dic13—21no—
57C2×C4⋊Dic13—21no—
58C2×C4⋊Dic13D412yes—
59C2×#6101—24no—
60C2×#6101—42no—
61C2×#6101—42no—
62C22×#1055—21no—
63C22×#1055—21no—
64C13×#95—22no—
65C13×#95—22no—
66C13×#95—22no—
67C13×#95—21no—
68#88075—24no—
69#88071—24no—
70#88071—21no—
71#88071D412yes—
72C22⋊#1055—21no—
73C22⋊#1055—21no—
74C22⋊#1055—21no—
75C22⋊#1055D412yes—
76#88048—24no—
77#9927—131nomaximal, Sylow
78C24×C13C2×D411yescharacteristic
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—42no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—21no—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—21no—
88C22×C4×C13—21no—
89C22×C4×C13—21no—
90C22×C4×C13—22no—
91C22×C4×C13—21no—
92C22×C4×C13—21no—
93C22×C4×C13—21no—
94C22×C4×C13—42no—
95C22×C4×C13—42no—
96C22×C4×C13SD1612yes—
97C22×C4×C13C2×D411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13#4111yescharacteristic
103C22×Dic13—24no—
104C22×Dic13—22no—
105C22×Dic13—22no—
106C22×Dic13—42no—
107C22×Dic13—41no—
108C22×Dic13—41no—
109C22×Dic13—41no—
110C22×Dic13—41no—
111C22×Dic13—41no—
112C22×Dic13—41no—
113C22×Dic13—41no—
114C22×Dic13—41no—
115C13×C4⋊C4—21no—
116C13×C4⋊C4—21no—
117C13×C4⋊C4—42no—
118C13×C4⋊C4—41no—
119C13×C4⋊C4—41no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C4⋊C4—41no—
123C13×C4⋊C4—41no—
124C13×C4⋊C4—82no—
125C13×C22⋊C4—41no—
126C13×C22⋊C4—41no—
127C13×C22⋊C4—41no—
128C13×C22⋊C4—41no—
129C4⋊Dic13—22no—
130C4⋊Dic13—22no—
131C4⋊Dic13—41no—
132C4⋊Dic13—41no—
133#6101—48no—
134C2×#1055—22no—
135C2×#1055—42no—
136C2×#1055—42no—
137C2×#1055—41no—
138C2×#483—131no—
139#2627D1311yescharacteristic
140C2×#398—131no—
141#1823—131no—
142C2×#328—131no—
143C2×#324—131no—
144#1294—131no—
145C23×C13—22no—
146C23×C13—22no—
147C23×C13#12011yescharacteristic
148C23×C13#12011yescharacteristic
149C23×C13#12111yescharacteristic
150C23×C13C2×SD1611yescharacteristic
151C23×C13#13511yescharacteristic
152C23×C13AGL(1,ℤ/8)11yescharacteristic
153C23×C13#13711yescharacteristic
154Q8×C13—42no—
155Q8×C13—81no—
156C2×C4×C13—22no—
157C2×C4×C13—22no—
158C2×C4×C13—22no—
159C2×C4×C13—22no—
160C2×C4×C13—22no—
161C2×C4×C13—41no—
162C2×C4×C13—41no—
163C2×C4×C13—41no—
164C2×C4×C13—41no—
165C2×C4×C13—41no—
166C2×C4×C13—41no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—41no—
171C2×C4×C13—41no—
172C2×C4×C13—41no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—42no—
176C2×C4×C13—42no—
177C2×C4×C13—42no—
178C2×C4×C13—42no—
179C2×C4×C13—81no—
180C2×C4×C13#12011yescharacteristic
181C2×C4×C13#12111yescharacteristic
182C2×C4×C13#12111yescharacteristic
183C2×C4×C13#12711yescharacteristic
184C2×Dic13—24no—
185C2×Dic13—44no—
186C2×Dic13—44no—
187C2×Dic13—42no—
188C2×Dic13—42no—
189C2×Dic13—42no—
190C2×Dic13—42no—
191C2×Dic13—42no—
192C2×Dic13—81no—
193C2×Dic13—81no—
194C2×Dic13—81no—
195C2×Dic13—81no—
196#1055—42no—
197#1055—81no—
198C2×C22⋊Q8C2×D1311yescharacteristic
199C22×C4⋊C4—131no—
200C22×C4⋊C4—261no—
201C22×C4⋊C4C2×D1311yescharacteristic
202#483—262no—
203#483—262no—
204C2×#106—261no—
205C2×#103—261no—
206C2×C22⋊C8—131no—
207C2×C22⋊C8—131no—
208#400—21no—
209#398—22no—
210#398—262no—
211#398—262no—
212#395—21no—
213#385—21no—
214#381—21no—
215#380C2×D1311yescharacteristic
216C2×#95—131no—
217C2×#95—261no—
218#340—262no—
219#328—262no—
220#324—262no—
221C22×C13—22no—
222C22×C13—22no—
223C22×C13—22no—
224C22×C13—22no—
225C22×C13—21no—
226C22×C13—21no—
227C22×C13—21no—
228C22×C13—21no—
229C22×C13#39211yescharacteristic
230C22×C13#44811yescharacteristic
231C22×C13#44911yescharacteristic
232C22×C13#45011yescharacteristic
233C22×C13#45211yescharacteristic
234C22×C13#45612yes—
235C22×C13#45812yes—
236C22×C13#46511yescharacteristic
237C22×C13#46811yescharacteristic
238C4×C13—21no—
239C4×C13—21no—
240C4×C13—21no—
241C4×C13—21no—
242C4×C13—42no—
243C4×C13—82no—
244C4×C13—81no—
245C4×C13—81no—
246C4×C13—81no—
247Dic13—44no—
248Dic13—82no—
249C22×Q8C22⋊D1311yescharacteristic
250C23×C4—261no—
251C23×C4—261no—
252C23×C4C22⋊D1311yescharacteristic
253C23×C4C22⋊D1311yescharacteristic
254C23×C4C22×D1311yescharacteristic
255C22×C8—261no—
256C22×C8—261no—
257C22⋊Q8—21no—
258C22⋊Q8—21no—
259C22⋊Q8—21no—
260C22⋊Q8—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—132no—
270C2×C4⋊C4—261no—
271C2×C4⋊C4—261no—
272C2×C4⋊C4—261no—
273C2×C4⋊C4—261no—
274C2×C4⋊C4—264no—
275C2×C4⋊C4—261no—
276C2×C4⋊C4—522no—
277C2×C4⋊C4—522no—
278C2×C4⋊C4C22⋊D1311yescharacteristic
279C2×C4⋊C4C22⋊D1312yes—
280C2×C22⋊C4—21no—
281C2×C22⋊C4—21no—
282#106—264no—
283#103—264no—
284C22⋊C8—132no—
285C22⋊C8—261no—
286C22⋊C8—261no—
287C22⋊C8—261no—
288#95—22no—
289#95—22no—
290#95—22no—
291#95—21no—
292#95—132no—
293#95—264no—
294#95—261no—
295C2×C13—21no—
296C2×C13—21no—
297C2×C13—21no—
298C2×C13—21no—
299C2×C13#160912yes—
300C2×C13#161112yes—
301C2×C13#200011yescharacteristic
302C2×C13#200511yescharacteristic
303C2×C13#202211yescharacteristic
304C24C2×C22⋊D1311yescharacteristic
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—42no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—42no—
321C22×C4—42no—
322C22×C4—264no—
323C22×C4—262no—
324C22×C4—262no—
325C22×C4—522no—
326C22×C4—521no—
327C22×C4—521no—
328C22×C4—521no—
329C22×C4—521no—
330C22×C4—521no—
331C22×C4—521no—
332C22×C4—521no—
333C22×C4—521no—
334C22×C4#610612yes—
335C22×C4D4×D1311yescharacteristic
336C22×C4D4×D1311yescharacteristic
337C22×C4D4×D1311yescharacteristic
338C22×C4#612911yescharacteristic
339C22×C4C2×C22⋊D1311yescharacteristic
340C22×C4C2×C22⋊D1311yescharacteristic
341C2×C8—262no—
342C2×C8—522no—
343C2×C8—522no—
344C2×C8—521no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—42no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4—82no—
355C4⋊C4—262no—
356C4⋊C4—262no—
357C4⋊C4—528no—
358C4⋊C4—521no—
359C4⋊C4—521no—
360C22⋊C4—41no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C22⋊C4—41no—
364C13#992711yescharacteristic, complemented, Sylow
365C23—22no—
366C23—22no—
367C23#8819111yescharacteristic
368C23#8819311yescharacteristic
369C23C2×#610611yescharacteristic
370C23#8819611yescharacteristic
371C23#8820311yescharacteristic
372C23#8820411yescharacteristic
373C23#8820711yescharacteristic
374Q8—42no—
375Q8—81no—
376C2×C4—22no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—81no—
400C2×C4—264no—
401C2×C4—522no—
402C2×C4—524no—
403C2×C4—524no—
404C2×C4—522no—
405C2×C4—522no—
406C2×C4—522no—
407C2×C4—522no—
408C2×C4—1041no—
409C2×C4—1041no—
410C2×C4—1041no—
411C2×C4—1041no—
412C2×C4#8819111yescharacteristic
413C2×C4#8819211yescharacteristic
414C2×C4#8819311yescharacteristic
415C2×C4#8819411yescharacteristic
416C8—522no—
417C8—1041no—
418C22—21no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—22no—
426C22#1171870711yescharacteristic
427C22#1171870811yescharacteristic
428C22#1171870911yescharacteristic
429C22#1171871011yescharacteristic
430C22#1171888411yescharacteristic
431C22#1171888811yescharacteristic
432C22#1171889911yescharacteristic
433C22#1171890412yes—
434C22#1171890712yes—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—42no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—82no—
444C4—524no—
445C4—1042no—
446C2—21no—
447C2—21no—
448C2—21no—
449C2—21no—
450C2#1311383312yes—
451C2#1311384412yes—
452C2#1311583711yescharacteristic
453C2#1311587011yescharacteristic
454C2#1311596511yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC23×C4×C13C23
FrattiniC23×C4C22×D13
FittingC13×#2627C2
socleC23×C13#120
prime radicalC24×C13C2×D4
hypercenter#2627D13
hypocenterC13#9927
LCSG ▷ C23×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
364. C13#9927semidirect

Maximal subgroups

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

subgroupindex
C2×#117187042
C2×#117186442
#131149202
C2×#117181302
C2×#117181202
#131127142
C13×#26272
#992713