Finite Group Databasebeta

← #15761317

Subgroups — #15761317

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#13115797C211yesmaximal, characteristic
2#13115758C211yesmaximal, characteristic
3#13115600C211yesmaximal, characteristic
4#13114703C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic
6#13112720C211yesmaximal, characteristic
7C13×#1277C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C2×C4×C8×C13C2211yescharacteristic
12C2×#88057—21no—
13C2×#88056—21no—
14C2×#88056—21no—
15C2×#88055—21no—
16#11718596C2211yescharacteristic
17C4×C4⋊Dic13C2211yescharacteristic
18C2×C4⋊#1055C2211yescharacteristic
19#11718143—21no—
20#11718143—21no—
21#11718143—21no—
22#11718142—21no—
23#11718074C414yescomplemented
24C22×Dic26—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C22×C8×C13D411yescharacteristic
28C22×C8×C13D411yescharacteristic
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13D411yescharacteristic
36C2×C4⋊Dic13D411yescharacteristic
37C2×C4×Dic13—21no—
38C22×#1055—21no—
39#88123—21no—
40#88123—21no—
41#88123—21no—
42#88123C2×C412yes—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8C2×C412yes—
47C4×C8×C13—21no—
48C4×C8×C13—21no—
49#88071—21no—
50#88057—42no—
51#88056—42no—
52#88056—42no—
53#88055—42no—
54C4⋊#1055—21no—
55C4⋊#1055C2×C412yes—
56#9573—131nomaximal, Sylow
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13#4111yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—41no—
63C22×Dic13—41no—
64C2×Dic26—22no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×C8×C13—21no—
71C2×C8×C13—21no—
72C2×C8×C13—22no—
73C2×C8×C13—21no—
74C2×C8×C13—21no—
75C2×C8×C13—21no—
76C2×C8×C13—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C2×C8×C13SD1612yes—
82C42×C13C22×C411yescharacteristic
83C42×C13#4111yescharacteristic
84C42×C13#4111yescharacteristic
85C42×C13#4111yescharacteristic
86C4⋊Dic13—22no—
87C4⋊Dic13—22no—
88C4⋊Dic13—21no—
89C4⋊Dic13—21no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13—41no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—41no—
98C4⋊Dic13—81no—
99C4×Dic13—41no—
100C4×Dic13—41no—
101C2×#1055—22no—
102C2×#1055—41no—
103C2×#1055—41no—
104#1990—131no—
105#1981—131no—
106#1948—131no—
107#1770—131no—
108C2×#332—131no—
109#1296—131no—
110#1277D1311yescharacteristic
111C23×C13#12111yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13#11711yescharacteristic
115C2×C4×C13C4×D411yescharacteristic
116C2×C4×C13C4×D411yescharacteristic
117C2×C4×C13#12311yescharacteristic
118C2×C4×C13#12411yescharacteristic
119C2×C4×C13#12611yescharacteristic
120C2×C4×C13C2×SD1611yescharacteristic
121C2×C4×C13#13511yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C13#13711yescharacteristic
126C2×C4×C13#13711yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×Dic13—42no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—81no—
136C2×Dic13—81no—
137C2×Dic13—81no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140Dic26—42no—
141Dic26—42no—
142Dic26—81no—
143Dic26—81no—
144C8×C13—22no—
145C8×C13—42no—
146C8×C13—41no—
147C8×C13—81no—
148#1055—42no—
149C2×C4⋊Q8—131no—
150C2×#106—261no—
151C2×C4⋊C8—131no—
152C2×C4⋊C8C2×D1311yescharacteristic
153C2×C4⋊C8C2×D1311yescharacteristic
154C2×#103—261no—
155C2×#103—261no—
156C2×#97—261no—
157C2×C4×C8C2×D1311yescharacteristic
158#384—131no—
159C4×C4⋊C4—131no—
160#340—261no—
161#340—261no—
162#340—261no—
163#336—261no—
164#332—134no—
165C22×C13#38811yescharacteristic
166C22×C13#46111yescharacteristic
167C22×C13#46411yescharacteristic
168C22×C13#46811yescharacteristic
169C22×C13#46911yescharacteristic
170C22×C13#47111yescharacteristic
171C22×C13#47311yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13C4×SD1611yescharacteristic
175C4×C13#44011yescharacteristic
176C4×C13#44111yescharacteristic
177C4×C13#44211yescharacteristic
178C4×C13#48311yescharacteristic
179C4×C13#48511yescharacteristic
180C4×C13#48911yescharacteristic
181C4×C13#49011yescharacteristic
182Dic13—82no—
183Dic13—81no—
184Dic13—81no—
185Dic13—161no—
186C22×Q8—261no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—261no—
190C22×C8D5211yescharacteristic
191C22×C8D5211yescharacteristic
192C4⋊Q8—132no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C42—261no—
204C2×C42C22×D1311yescharacteristic
205#106—522no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—132no—
210C4⋊C8—261no—
211C4⋊C8C4×D1312yes—
212#103—522no—
213#103—522no—
214#97—522no—
215C4×C8—21no—
216C4×C8—21no—
217#95—261no—
218C2×C13#169111yescharacteristic
219C2×C13#169311yescharacteristic
220C2×C13#170011yescharacteristic
221C2×C13#170211yescharacteristic
222C2×C13#192711yescharacteristic
223C2×C13#193011yescharacteristic
224C2×C13#193611yescharacteristic
225C2×Q8—262no—
226C2×Q8—521no—
227C2×Q8—521no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—521no—
234C22×C4—521no—
235C22×C4C2×D5211yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4#613111yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—262no—
250C2×C8—521no—
251C2×C8—521no—
252C2×C8#609512yes—
253C4⋊C4—262no—
254C4⋊C4—262no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—521no—
260C4⋊C4—521no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C4⋊C4—1041no—
266C42—521no—
267C42—521no—
268C42C2×C4×D1311yescharacteristic
269C42#612711yescharacteristic
270C42#612911yescharacteristic
271C42#612911yescharacteristic
272C13#957311yescharacteristic, complemented, Sylow
273C23#8814911yescharacteristic
274Q8—522no—
275Q8—522no—
276Q8—1041no—
277Q8—1041no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—522no—
287C2×C4—1041no—
288C2×C4—1041no—
289C2×C4—1041no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4C4×D5211yescharacteristic
293C2×C4#8813511yescharacteristic
294C2×C4#8813911yescharacteristic
295C2×C4#8814011yescharacteristic
296C2×C4#8814611yescharacteristic
297C2×C4#8815211yescharacteristic
298C2×C4C2×#609511yescharacteristic
299C2×C4#8815811yescharacteristic
300C2×C4#8816311yescharacteristic
301C2×C4#8816311yescharacteristic
302C2×C4#8816511yescharacteristic
303C2×C4#8816811yescharacteristic
304C2×C4#8816811yescharacteristic
305C2×C4#8817211yescharacteristic
306C8—22no—
307C8—42no—
308C8—41no—
309C8—81no—
310C8—522no—
311C22#1171833111yescharacteristic
312C22#1171850211yescharacteristic
313C22#1171850611yescharacteristic
314C22#1171852611yescharacteristic
315C22#1171854711yescharacteristic
316C22#1171855711yescharacteristic
317C22#1171855911yescharacteristic
318C4—21no—
319C4—21no—
320C4—1042no—
321C4—1041no—
322C4—1041no—
323C4—2081no—
324C4C4×#609511yescharacteristic
325C4#1171837711yescharacteristic
326C4#1171838211yescharacteristic
327C4#1171838411yescharacteristic
328C4#1171842511yescharacteristic
329C4#1171844611yescharacteristic
330C4#1171845611yescharacteristic
331C4#1171847811yescharacteristic
332C2#1311433611yescharacteristic
333C2#1311435011yescharacteristic
334C2#1311439111yescharacteristic
335C2#1311440511yescharacteristic
336C2#1311547111yescharacteristic
337C2#1311549211yescharacteristic
338C2#1311553411yescharacteristic
subgroupG/H
centerC23#88149
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1277C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1277D13
hypocenterC13#9573
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
23. #11718074C4semidirect
272. C13#9573semidirect

Maximal subgroups

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

subgroupindex
#131157972
#131157582
#131156002
#131147032
C2×#117180742
#131127202
C13×#12772
#957313