Finite Group Databasebeta

← #15761320

Subgroups — #15761320

Order 3328.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115760C211yesmaximal, characteristic
2#13115592C211yesmaximal, characteristic
3#13114703C211yesmaximal, characteristic
4C2×#11718139C211yesmaximal, characteristic
5#13112719C211yesmaximal, characteristic
6#13112671C211yesmaximal, characteristic
7C13×#1990C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×C8×C13C2211yescharacteristic
10C13×#384C2211yescharacteristic
11C2×#88075—21no—
12C2×#88075—21no—
13C2×#88055—21no—
14C2×#88047—21no—
15C4×C4⋊Dic13C2211yescharacteristic
16C2×C4⋊#1055C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19C13×#340—21no—
20C13×#340—21no—
21#11718142—21no—
22#11718139C414yescomplemented
23#11718121—21no—
24C22×Q8×C13—21no—
25C22×C8×C13D411yescharacteristic
26C22×C8×C13D411yescharacteristic
27C13×C4⋊Q8—21no—
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8C2×C412yes—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13D411yescharacteristic
38C2×C4⋊Dic13D411yescharacteristic
39C2×C4×Dic13—21no—
40C22×#1055—21no—
41C22×#1055—21no—
42C22×#1055—21no—
43C4×C8×C13—21no—
44C4×C8×C13—21no—
45#88075—42no—
46#88075—42no—
47#88071—21no—
48#88055—42no—
49#88047—42no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055C2×C412yes—
55C4⋊#1055C2×C412yes—
56#9574—131nomaximal, Sylow
57C2×Q8×C13—22no—
58C2×Q8×C13—41no—
59C2×Q8×C13—41no—
60C2×Q8×C13—41no—
61C2×Q8×C13—41no—
62C2×Q8×C13—41no—
63C22×C4×C13—41no—
64C22×C4×C13—41no—
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4111yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—21no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13Q1612yes—
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—81no—
85C42×C13C22×C411yescharacteristic
86C42×C13#4111yescharacteristic
87C42×C13#4111yescharacteristic
88C42×C13#4111yescharacteristic
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—21no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—22no—
96C2×#1055—22no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#1990D1311yescharacteristic
105#1981—131no—
106#1947—131no—
107#1770—131no—
108C2×#332—131no—
109#1296—131no—
110#1277—131no—
111C23×C13#12111yescharacteristic
112Q8×C13—42no—
113Q8×C13—42no—
114Q8×C13—81no—
115Q8×C13—81no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—42no—
119C2×C4×C13—81no—
120C2×C4×C13—81no—
121C2×C4×C13—81no—
122C2×C4×C13—81no—
123C2×C4×C13—81no—
124C2×C4×C13#11711yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13C4×D411yescharacteristic
127C2×C4×C13#12311yescharacteristic
128C2×C4×C13#12411yescharacteristic
129C2×C4×C13#12611yescharacteristic
130C2×C4×C13C2×Q1611yescharacteristic
131C2×C4×C13#13511yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C13#13711yescharacteristic
137C2×C4×C13#13711yescharacteristic
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C8×C13—22no—
145C8×C13—41no—
146#1055—42no—
147#1055—42no—
148#1055—81no—
149C2×C4⋊Q8C2×D1311yescharacteristic
150C2×#107—261no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8—131no—
153C2×C4⋊C8—131no—
154C2×#103—261no—
155C2×#103—261no—
156C2×#97—261no—
157C2×C4×C8C2×D1311yescharacteristic
158#384C2×D1311yescharacteristic
159C4×C4⋊C4—131no—
160#340—21no—
161#340—21no—
162#340—261no—
163#336—261no—
164#332—134no—
165C22×C13#38811yescharacteristic
166C22×C13#46211yescharacteristic
167C22×C13#46311yescharacteristic
168C22×C13#46811yescharacteristic
169C22×C13#46911yescharacteristic
170C22×C13#47111yescharacteristic
171C22×C13#47311yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—82no—
175C4×C13—161no—
176C4×C13C4×Q1611yescharacteristic
177C4×C13#44011yescharacteristic
178C4×C13#44011yescharacteristic
179C4×C13#44211yescharacteristic
180C4×C13#48411yescharacteristic
181C4×C13#48511yescharacteristic
182C4×C13#48911yescharacteristic
183C4×C13#49011yescharacteristic
184Dic13—81no—
185Dic13—81no—
186C22×Q8—21no—
187C22×C8—261no—
188C22×C8—261no—
189C22×C8—261no—
190C22×C8C22⋊D1311yescharacteristic
191C22×C8C22⋊D1311yescharacteristic
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8C4×D1312yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C42—261no—
204C2×C42C22×D1311yescharacteristic
205#107—522no—
206C4⋊C8—132no—
207C4⋊C8—132no—
208C4⋊C8—261no—
209C4⋊C8—261no—
210C4⋊C8—261no—
211C4⋊C8—261no—
212#103—522no—
213#103—522no—
214#97—522no—
215C4×C8—21no—
216C4×C8—21no—
217#95—261no—
218C2×C13#169211yescharacteristic
219C2×C13#169411yescharacteristic
220C2×C13#169911yescharacteristic
221C2×C13#170111yescharacteristic
222C2×C13#192811yescharacteristic
223C2×C13#193011yescharacteristic
224C2×C13#193611yescharacteristic
225C2×Q8—22no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4D4×D1311yescharacteristic
236C22×C4#612911yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—262no—
244C2×C8—262no—
245C2×C8—521no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—521no—
249C2×C8—521no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8#610712yes—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C42—521no—
267C42—521no—
268C42C2×C4×D1311yescharacteristic
269C42#612711yescharacteristic
270C42#612911yescharacteristic
271C42#612911yescharacteristic
272C13#957411yescharacteristic, complemented, Sylow
273C23#8819211yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4#8813111yescharacteristic
293C2×C4#8813311yescharacteristic
294C2×C4#8813511yescharacteristic
295C2×C4#8813911yescharacteristic
296C2×C4#8816511yescharacteristic
297C2×C4#8816511yescharacteristic
298C2×C4#8816811yescharacteristic
299C2×C4#8816911yescharacteristic
300C2×C4C4×C22⋊D1311yescharacteristic
301C2×C4#8818911yescharacteristic
302C2×C4#8819611yescharacteristic
303C2×C4C2×#610711yescharacteristic
304C2×C4#8820311yescharacteristic
305C2×C4#8820411yescharacteristic
306C8—22no—
307C8—41no—
308C8—522no—
309C8—522no—
310C8—1041no—
311C22#1171860511yescharacteristic
312C22#1171871811yescharacteristic
313C22#1171875111yescharacteristic
314C22#1171882011yescharacteristic
315C22#1171883511yescharacteristic
316C22#1171883811yescharacteristic
317C22#1171885311yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—161no—
322C4—1041no—
323C4—1041no—
324C4#1171841811yescharacteristic
325C4#1171842511yescharacteristic
326C4#1171842611yescharacteristic
327C4#1171844611yescharacteristic
328C4#1171868711yescharacteristic
329C4C4×#610711yescharacteristic
330C4#1171870511yescharacteristic
331C4#1171870611yescharacteristic
332C2#1311433911yescharacteristic
333C2#1311435111yescharacteristic
334C2#1311438011yescharacteristic
335C2#1311439411yescharacteristic
336C2#1311547411yescharacteristic
337C2#1311548811yescharacteristic
338C2#1311553011yescharacteristic
subgroupG/H
centerC23#88192
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1990C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1990D13
hypocenterC13#9574
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
22. #11718139C4semidirect
272. C13#9574semidirect

Maximal subgroups

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

subgroupindex
#131157602
#131155922
#131147032
C2×#117181392
#131127192
#131126712
C13×#19902
#957413