Finite Group Databasebeta

← #15761237

Subgroups — #15761237

Order 3328.

398 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#13115787C211yesmaximal, characteristic
2#13115637C211yesmaximal, characteristic
3#13115597C211yesmaximal, characteristic
4#13114701C211yesmaximal, characteristic
5C2×#11718074C211yesmaximal, characteristic
6#13112670C211yesmaximal, characteristic
7C13×#1296C211yesmaximal, characteristic
8C2×#88123C2211yescharacteristic
9C2×C13×C4⋊C8C2211yescharacteristic
10C2×C13×C4⋊C8C2211yescharacteristic
11C13×#384C2211yescharacteristic
12C2×C8×Dic13—21no—
13C2×#88050—21no—
14C2×#88050—21no—
15C2×#88048—21no—
16C4×C4⋊Dic13C2211yescharacteristic
17C2×C4⋊#1055C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19#11718143—21no—
20#11718143—21no—
21#11718142—21no—
22#11718121—21no—
23#11718074C414yescomplemented
24C22×Dic26—21no—
25C22×C8×C13—21no—
26C22×C8×C13—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C42×C13C2311yescharacteristic
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13D411yescharacteristic
34C2×C4⋊Dic13D411yescharacteristic
35C2×C4×Dic13—21no—
36C22×#1055—21no—
37C22×#1055D411yescharacteristic
38C22×#1055D411yescharacteristic
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—
47#88071—21no—
48C8×Dic13—42no—
49#88050—42no—
50#88050—42no—
51#88048—42no—
52C4⋊#1055—21no—
53C4⋊#1055C2×C412yes—
54C4×#1055—21no—
55C4×#1055—21no—
56#9562—131nomaximal, Sylow
57C22×C4×C13—41no—
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×C4×C13#4111yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—41no—
64C2×Dic26—22no—
65C2×Dic26—41no—
66C2×Dic26—41no—
67C2×Dic26—41no—
68C2×Dic26—41no—
69C2×Dic26—41no—
70C2×C8×C13—22no—
71C2×C8×C13—41no—
72C2×C8×C13—41no—
73C2×C8×C13—41no—
74C2×C8×C13—41no—
75C2×C8×C13—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—81no—
81C42×C13C22×C411yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C42×C13#4111yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89C4⋊Dic13—41no—
90C4⋊Dic13—41no—
91C4⋊Dic13SD1612yes—
92C4⋊Dic13Q1612yes—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#1055—21no—
96C2×#1055—21no—
97C2×#1055—22no—
98C2×#1055—21no—
99C2×#1055—21no—
100C2×#1055—21no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055SD1612yes—
104#1988—131no—
105#1956—131no—
106#1948—131no—
107C8×C4⋊C4—131no—
108C2×#332—131no—
109#1296D1311yescharacteristic
110#1277—131no—
111C23×C13#12111yescharacteristic
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—81no—
115C2×C4×C13—81no—
116C2×C4×C13—81no—
117C2×C4×C13#11711yescharacteristic
118C2×C4×C13C4×D411yescharacteristic
119C2×C4×C13C4×D411yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13#12411yescharacteristic
122C2×C4×C13#12611yescharacteristic
123C2×C4×C13C2×SD1611yescharacteristic
124C2×C4×C13C2×SD1611yescharacteristic
125C2×C4×C13C2×Q1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13511yescharacteristic
128C2×C4×C13#13511yescharacteristic
129C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
131C2×Dic13—22no—
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—42no—
138C2×Dic13—81no—
139C2×Dic13—81no—
140Dic26—42no—
141Dic26—42no—
142Dic26—81no—
143Dic26—81no—
144C8×C13—42no—
145C8×C13—81no—
146#1055—22no—
147#1055—42no—
148#1055—41no—
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×C4×C8—131no—
157C2×C4×C8—261no—
158#384C2×D1311yescharacteristic
159C4×C4⋊C4—131no—
160#340—261no—
161#340—261no—
162#340—261no—
163#336—261no—
164#332—134no—
165C22×C13#38811yescharacteristic
166C22×C13#46011yescharacteristic
167C22×C13#46311yescharacteristic
168C22×C13#46511yescharacteristic
169C22×C13#46711yescharacteristic
170C22×C13#47111yescharacteristic
171C22×C13#47311yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—161no—
175C4×C13C4×SD1611yescharacteristic
176C4×C13C4×SD1611yescharacteristic
177C4×C13C4×Q1611yescharacteristic
178C4×C13#44211yescharacteristic
179C4×C13#48111yescharacteristic
180C4×C13#48211yescharacteristic
181C4×C13#48711yescharacteristic
182C4×C13#48811yescharacteristic
183Dic13—42no—
184Dic13—42no—
185Dic13—82no—
186C22×Q8—261no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—131no—
190C22×C8—131no—
191C22×C8—261no—
192C4⋊Q8—132no—
193C4⋊Q8—261no—
194C4⋊Q8—261no—
195C4⋊Q8—261no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
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—
214C4×C8—261no—
215C4×C8—261no—
216C4×C8—522no—
217#95—261no—
218C2×C13#166611yescharacteristic
219C2×C13#167011yescharacteristic
220C2×C13#167911yescharacteristic
221C2×C13#168311yescharacteristic
222C2×C13#192611yescharacteristic
223C2×C13#193011yescharacteristic
224C2×C13#193311yescharacteristic
225C2×Q8—262no—
226C2×Q8—521no—
227C2×Q8—521no—
228C2×Q8—521no—
229C2×Q8—521no—
230C2×Q8—521no—
231C22×C4—41no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4—521no—
235C22×C4#612711yescharacteristic
236C22×C4D4×D1311yescharacteristic
237C22×C4D4×D1311yescharacteristic
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—132no—
245C2×C8—261no—
246C2×C8—261no—
247C2×C8—262no—
248C2×C8—261no—
249C2×C8—261no—
250C2×C8—261no—
251C2×C8—521no—
252C2×C8—521no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—81no—
258C4⋊C4—132no—
259C4⋊C4—132no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—262no—
263C4⋊C4—262no—
264C4⋊C4—521no—
265C4⋊C4—521no—
266C42—521no—
267C42—521no—
268C42C2×C4×D1311yescharacteristic
269C42#612711yescharacteristic
270C42#612911yescharacteristic
271C42#613111yescharacteristic
272C13#956211yescharacteristic, complemented, Sylow
273C23#8813811yescharacteristic
274Q8—522no—
275Q8—522no—
276Q8—1041no—
277Q8—1041no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—522no—
290C2×C4—1041no—
291C2×C4—1041no—
292C2×C4#8812611yescharacteristic
293C2×C4#8813511yescharacteristic
294C2×C4#8813911yescharacteristic
295C2×C4#8814711yescharacteristic
296C2×C4#8814811yescharacteristic
297C2×C4#8815211yescharacteristic
298C2×C4#8816511yescharacteristic
299C2×C4#8816611yescharacteristic
300C2×C4SD16×D1311yescharacteristic
301C2×C4SD16×D1311yescharacteristic
302C2×C4#8816811yescharacteristic
303C2×C4#8817011yescharacteristic
304C2×C4Q16×D1311yescharacteristic
305C2×C4#8817311yescharacteristic
306C8—42no—
307C8—81no—
308C8—262no—
309C8—522no—
310C8—521no—
311C22#1171833011yescharacteristic
312C22#1171840911yescharacteristic
313C22#1171841611yescharacteristic
314C22#1171842311yescharacteristic
315C22#1171843911yescharacteristic
316C22#1171847411yescharacteristic
317C22#1171848011yescharacteristic
318C4—21no—
319C4—21no—
320C4—161no—
321C4—522no—
322C4—522no—
323C4—1042no—
324C4#1171842911yescharacteristic
325C4#1171844611yescharacteristic
326C4#1171844911yescharacteristic
327C4#1171845311yescharacteristic
328C4#1171851311yescharacteristic
329C4#1171852411yescharacteristic
330C4#1171853411yescharacteristic
331C4#1171854611yescharacteristic
332C2#1311418311yescharacteristic
333C2#1311420511yescharacteristic
334C2#1311426211yescharacteristic
335C2#1311429011yescharacteristic
336C2#1311546111yescharacteristic
337C2#1311548911yescharacteristic
338C2#1311551011yescharacteristic
subgroupG/H
centerC23#88138
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1296C2
socle, prime radicalC23×C13#121
cosocleC2×C42×C13C23
hypercenter#1296D13
hypocenterC13#9562
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
23. #11718074C4semidirect
272. C13#9562semidirect

Maximal subgroups

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

subgroupindex
#131157872
#131156372
#131155972
#131147012
C2×#117180742
#131126702
C13×#12962
#956213