Finite Group Databasebeta

← #15759653

Subgroups — #15759653

Order 3328.

508 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125957C211yesmaximal, characteristic
2#13115668C211yesmaximal, characteristic
3#13113508C211yesmaximal, characteristic, complemented
4#13113395C211yesmaximal, characteristic
5#13112694C211yesmaximal, characteristic, complemented
6#13112665C211yesmaximal, characteristic, complemented
7C13×#2327C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Q8×C13—21no—
10#11719182C2211yescharacteristic
11C13×#391—21no—
12C13×#387—22no—
13C13×#387—22no—
14C13×#382C2211yescharacteristic
15C13×#376C2211yescharacteristic
16#11718749C412yescomplemented
17#11718748—22no—
18#11718739C412yescomplemented
19#11718628—22no—
20C2×#88045—21no—
21C2×#88045—21no—
22#11718586C2211yescharacteristic
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25#11718139—22no—
26#11718043—22no—
27C22×Q8×C13—21no—
28C2×#6127—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8C2×C412yes—
32C13×C4⋊Q8D412yes—
33C4×Q8×C13—42no—
34C4×Q8×C13—42no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4—22no—
37C2×C13×C4⋊C4—21no—
38C2×C13×C4⋊C4D412yes—
39C2×C42×C13—22no—
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13C2311yescharacteristic
43#88184—21no—
44#88184—21no—
45C2×#6099—21no—
46#88129—21no—
47#88128C2×C411yescharacteristic
48C4×D52—21no—
49C4×D52—21no—
50#88123C2×C411yescharacteristic
51C13×#95—24no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95D412yes—
56C22⋊#1055—21no—
57C22⋊#1055—21no—
58#88049—24no—
59#88047—24no—
60#88045—42no—
61#88045—42no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4×#1055—21no—
67C4×#1055C2×C412yes—
68#9300—131nomaximal, Sylow
69C2×Q8×C13—22no—
70C2×Q8×C13—22no—
71C2×Q8×C13—41no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C22×C4×C13—21no—
76C22×C4×C13—22no—
77C22×C4×C13—21no—
78C22×C4×C13—22no—
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C2×C22⋊D13—41no—
83#6127—41no—
84#6127—41no—
85#6127—41no—
86#6127—41no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×C4×D13—41no—
91C2×Dic26—21no—
92C13×C4⋊C4—22no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—44no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4C22⋊C414yes—
99C42×C13—21no—
100C42×C13—21no—
101C42×C13—21no—
102C42×C13—44no—
103C42×C13D812yes—
104C42×C13C22×C411yescharacteristic
105C42×C13C2×D411yescharacteristic
106C42×C13#4111yescharacteristic
107C42×C13#4111yescharacteristic
108#6103—41no—
109#6103—41no—
110C4⋊Dic13—21no—
111C4⋊Dic13—21no—
112#6099—41no—
113#6099—41no—
114C2×#1055—22no—
115C2×#1055—41no—
116C2×#1055—41no—
117#3226—131no—
118#2327D1311yescharacteristic, complemented
119#1963—131no—
120#1546—131no—
121#1517—131no—
122#1286—131no—
123#1274—131no—
124C23×C13#12011yescharacteristic
125C22×D13—41no—
126Q8×C13—42no—
127Q8×C13—42no—
128Q8×C13—42no—
129Q8×C13—42no—
130C2×C4×C13—24no—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—42no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13—42no—
143C2×C4×C13—41no—
144C2×C4×C13C2×C22⋊C411yescharacteristic
145C2×C4×C13C4×D411yescharacteristic
146C2×C4×C13C4×D411yescharacteristic
147C2×C4×C13#12111yescharacteristic
148C2×C4×C13#12111yescharacteristic
149C2×C4×C13#12311yescharacteristic
150C2×C4×C13C2×D811yescharacteristic
151C2×C4×C13#13511yescharacteristic
152C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
154C22⋊D13—81no—
155C22⋊D13—81no—
156C2×Dic13—41no—
157D52—42no—
158D52—41no—
159D52—41no—
160D52—81no—
161C4×D13—81no—
162C4×D13—81no—
163Dic26—41no—
164Dic26—41no—
165#1055—42no—
166#1055—81no—
167#1055—81no—
168#532—131no—
169C2×C4⋊Q8C2×D1311yescharacteristic
170C2×C4×Q8—21no—
171#500—132no—
172#486—132no—
173#480—262no—
174#474—262no—
175#431—131no—
176#431—131no—
177#423—131no—
178C2×#104—261no—
179C2×#104—261no—
180#391—21no—
181#387—22no—
182#387—22no—
183#382C2×D1311yescharacteristic
184#376C2×D1311yescharacteristic
185#332—262no—
186#327—262no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13#38611yescharacteristic
190C22×C13#44711yescharacteristic
191C22×C13#44911yescharacteristic
192C2×D13—81no—
193C2×D13—81no—
194C2×D13—81no—
195C4×C13—21no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—42no—
200C4×C13—44no—
201C4×C13—82no—
202C4×C13—81no—
203C4×C13C4×D811yescharacteristic
204C4×C13#44211yescharacteristic
205C4×C13#45911yescharacteristic
206C4×C13#46311yescharacteristic
207Dic13—81no—
208C2×#41—261no—
209C22×Q8—21no—
210C2×M16—261no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—131no—
214C4⋊Q8C4×D1312yes—
215C4⋊Q8D5212yes—
216#127—131no—
217#124—261no—
218#121—261no—
219#121—261no—
220C4×Q8—42no—
221C4×Q8—42no—
222C4×D4—261no—
223C4×D4—261no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—22no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4C22⋊D1312yes—
228C2×C42—22no—
229C2×C42C22⋊D1311yescharacteristic
230C2×C42C22⋊D1311yescharacteristic
231C2×C42C22×D1311yescharacteristic
232#107—264no—
233C4⋊C8—261no—
234C4⋊C8—261no—
235C4⋊C8—261no—
236C4⋊C8—261no—
237#104—522no—
238#104—522no—
239#102—264no—
240C22⋊C8—261no—
241C22⋊C8—261no—
242C4×C8—132no—
243C4×C8—261no—
244#95—24no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C22⋊D1312yes—
249C2×C13—21no—
250C2×C13—21no—
251C2×C13#187911yescharacteristic
252C2×C13#190511yescharacteristic
253C2×C13#191211yescharacteristic
254D13—161no—
255#41—521no—
256#41—521no—
257#41—521no—
258#41—521no—
259C2×Q8—22no—
260C2×Q8—22no—
261C2×Q8—41no—
262C2×Q8—41no—
263C2×Q8—41no—
264C2×Q8—41no—
265C2×Q8—261no—
266C2×D4—261no—
267C2×D4—261no—
268C2×D4—261no—
269C2×D4—521no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—22no—
274C22×C4—521no—
275C22×C4C2×C22⋊D1311yescharacteristic
276C22×C4C2×C22⋊D1311yescharacteristic
277C22×C4C2×C22⋊D1311yescharacteristic
278M16—521no—
279M16—521no—
280C2×C8—262no—
281C2×C8—521no—
282C2×C8—521no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—44no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—261no—
290C4⋊C4—261no—
291C4⋊C4#610314yes—
292C22⋊C4—521no—
293C22⋊C4—521no—
294C42—21no—
295C42—21no—
296C42—21no—
297C42—44no—
298C42#610412yes—
299C42C2×C4×D1311yescharacteristic
300C42C2×D5211yescharacteristic
301C42#612711yescharacteristic
302C42#612711yescharacteristic
303C13#930011yescharacteristic, complemented, Sylow
304C23—521no—
305C23#8820711yescharacteristic
306Q8—42no—
307Q8—42no—
308Q8—42no—
309Q8—42no—
310Q8—521no—
311Q8—521no—
312D4—522no—
313D4—521no—
314D4—521no—
315D4—1041no—
316D4—1041no—
317D4—1041no—
318C2×C4—24no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—41no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—521no—
333C2×C4—1041no—
334C2×C4—1041no—
335C2×C4C2×#610311yescharacteristic
336C2×C4C4×C22⋊D1311yescharacteristic
337C2×C4C4×C22⋊D1311yescharacteristic
338C2×C4#8818311yescharacteristic
339C2×C4#8818411yescharacteristic
340C2×C4#8818411yescharacteristic
341C2×C4C2×#610411yescharacteristic
342C2×C4#8818611yescharacteristic
343C2×C4#8820311yescharacteristic
344C2×C4#8820411yescharacteristic
345C8—522no—
346C8—1041no—
347C8—1041no—
348C22—21no—
349C22—21no—
350C22—1041no—
351C22—1041no—
352C22—1041no—
353C22#1171887411yescharacteristic
354C22#1171887811yescharacteristic
355C22#1171889911yescharacteristic
356C4—21no—
357C4—21no—
358C4—21no—
359C4—21no—
360C4—42no—
361C4—44no—
362C4—82no—
363C4—81no—
364C4—1041no—
365C4C4×#610411yescharacteristic
366C4#1171867511yescharacteristic
367C4#1171867611yescharacteristic
368C4#1171867711yescharacteristic
369C2—21no—
370C2—21no—
371C2—2081no—
372C2#1311518411yescharacteristic
373C2#1311533011yescharacteristic
374C2#1311537311yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2327C2
socleC22×C13#386
prime radical#11719182C22
cosocleC2×C42×C13C23
hypercenter#2327D13
hypocenterC13#9300
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2327

Complements

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

NH ≅ G/Ntype
3. #13113508C2semidirect
5. #13112694C2semidirect
6. #13112665C2semidirect
7. C13×#2327C2semidirect
16. #11718749C4semidirect
18. #11718739C4semidirect
118. #2327D13semidirect
303. C13#9300semidirect

Maximal subgroups

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

subgroupindex
#131259572
#131156682
#131135082
#131133952
#131126942
#131126652
C13×#23272
#930013