Finite Group Databasebeta

← #16792584

Subgroups — #16792584

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719049C211yesmaximal, characteristic
2D13⋊#431C211yesmaximal, characteristic
3#13130040C214yesmaximal, complemented
4#13130034C214yesmaximal, complemented
5M16×#1057C214yesmaximal, complemented
6C4×M16×D13C211yesmaximal, characteristic
7C2×M16×D13C412yes—
8C2×C42×D13C2211yescharacteristic
9#11719125C412yes—
10D13⋊(C22⋊C8)C412yes—
11C2×#88112C412yes—
12C2×#88111C412yes—
13#11719119C2212yes—
14C2×C4×#1057C2212yes—
15#11719051C412yes—
16D13⋊(C4⋊C8)C412yes—
17#11719049C412yes—
18#11719049C412yes—
19#11719049C2212yes—
20#11719049C2212yes—
21#11719049C2212yes—
22C4×D13⋊C8C2212yes—
23C4×C13×M16C411yescharacteristic
24M16×Dic13C2212yes—
25C4×#6099C411yescharacteristic
26#11718368C2212yes—
27D13×#97C412yes—
28C4×#6094C412yes—
29C4×C8×D13C2212yes—
30#11718251C2218yescomplemented
31C8×#1057C2218yescomplemented
32C22×C4×D13C2×C411yescharacteristic
33C22×C4×D13C2×C411yescharacteristic
34C22×C4×D13C2×C411yescharacteristic
35C22×#1057C2×C414yes—
36C2×D13⋊C8C2×C414yes—
37C2×C13×M16C2×C412yes—
38C2×C42×C13C2×C411yescharacteristic
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42C2×#6099C2×C412yes—
43M16×D13C8116yescomplemented
44C2×#6094C2×C414yes—
45C2×C8×D13C2×C414yes—
46C42×D13C2×C411yescharacteristic
47C42×D13C2×C411yescharacteristic
48C42×D13C2×C411yescharacteristic
49C42×D13C2×C411yescharacteristic
50C42×D13C2×C411yescharacteristic
51C42×D13C2×C411yescharacteristic
52C42×D13C2311yescharacteristic
53C42×D13C2311yescharacteristic
54C22⋊#1057C2×C414yes—
55#88112C2×C414yes—
56#88112C2×C414yes—
57#88112C2×C414yes—
58#88111C2×C414yes—
59#88111C2×C414yes—
60#88111C2×C414yes—
61C4⋊#1057C2×C414yes—
62C4×#1057C2×C414yes—
63C4×#1057C2×C414yes—
64C4×#1057C2314yes—
65C4×#1057C2314yes—
66C13×#97C2×C412yes—
67C4×C8×C13C2×C412yes—
68#88055C2×C414yes—
69C8×Dic13C2314yes—
70#88043C2×C412yes—
71C4×#1055C2×C412yes—
72#17314—131nomaximal, Sylow
73C23×D13C4211yescharacteristic
74C22×C4×C13C4211yescharacteristic
75C22×C4×C13C4211yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×Dic13C4211yescharacteristic
78C22×Dic13C22×C411yescharacteristic
79C22×Dic13C22×C411yescharacteristic
80C2×C4×D13—42no—
81C2×C4×D13—42no—
82C2×C4×D13C4211yescharacteristic
83C2×C4×D13C4211yescharacteristic
84C2×C4×D13C4211yescharacteristic
85C2×C4×D13C4211yescharacteristic
86C2×C4×D13C4211yescharacteristic
87C2×C4×D13C4211yescharacteristic
88C2×C4×D13C2×C818yes—
89C2×C4×D13C22×C411yescharacteristic
90C2×C4×D13C22×C411yescharacteristic
91C2×C4×D13C22×C411yescharacteristic
92C2×C4×D13C22×C411yescharacteristic
93C2×C4×D13C22×C411yescharacteristic
94C2×C4×D13C22×C411yescharacteristic
95C2×#1057—44no—
96C2×#1057C22×C418yes—
97C2×#1057C22×C418yes—
98D13⋊C8—44no—
99C13×M16C2×C818yescomplemented
100C2×C8×C13C22×C414yes—
101C42×C13C4211yescharacteristic
102C42×C13C4211yescharacteristic
103C42×C13C22×C411yescharacteristic
104C42×C13C22×C411yescharacteristic
105C4×Dic13C4211yescharacteristic
106C4×Dic13C4211yescharacteristic
107C4×Dic13C4211yescharacteristic
108C4×Dic13C4211yescharacteristic
109C4×Dic13C22×C411yescharacteristic
110C4×Dic13C22×C411yescharacteristic
111C4×Dic13C22×C411yescharacteristic
112C4×Dic13C22×C411yescharacteristic
113C4×Dic13C22×C411yescharacteristic
114C4×Dic13C22×C411yescharacteristic
115C4×Dic13C22×C411yescharacteristic
116C4×Dic13C2411yescharacteristic
117#6099C2×C818yescomplemented
118C2×#1055C22×C414yes—
119#6094C2×C8116yescomplemented
120C8×D13C2×C8116yescomplemented
121C2×#431—131no—
122C2×#431—131no—
123C2×C4×M16—131no—
124#1450—134no—
125C8×M16—134no—
126C8×M16—134no—
127C23×C13C2×C4211yescharacteristic
128C22×D13—41no—
129C22×D13—41no—
130C22×D13C4×C814yes—
131C22×D13C2×C4211yescharacteristic
132C22×D13C2×C4211yescharacteristic
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13C2×C4211yescharacteristic
136C2×C4×C13C2×C4211yescharacteristic
137C2×C4×C13C2×C4211yescharacteristic
138C2×C4×C13C2×C4211yescharacteristic
139C2×C4×C13C2×C4211yescharacteristic
140C2×C4×C13C22×C814yes—
141C2×C4×C13C23×C411yescharacteristic
142C2×Dic13—22no—
143C2×Dic13—22no—
144C2×Dic13C4×C814yes—
145C2×Dic13C2×C4211yescharacteristic
146C2×Dic13C2×C4211yescharacteristic
147C2×Dic13C2×C4211yescharacteristic
148C2×Dic13C2×C4211yescharacteristic
149C2×Dic13C23×C411yescharacteristic
150C2×Dic13C23×C411yescharacteristic
151C4×D13—22no—
152C4×D13—22no—
153C4×D13—22no—
154C4×D13—22no—
155C4×D13—41no—
156C4×D13—41no—
157C4×D13—41no—
158C4×D13—41no—
159C4×D13C4×C814yes—
160C4×D13C4×C814yes—
161C4×D13C22×C814yes—
162C4×D13C22×C814yes—
163#1057—28no—
164#1057—28no—
165C8×C13C22×C818yes—
166#1055C22×C818yes—
167C22×M16—132no—
168C22×C42—131no—
169#431—132no—
170#431—132no—
171#431—132no—
172#431—132no—
173#431—132no—
174#431—132no—
175#431—132no—
176#431—132no—
177C2×C4⋊C8—132no—
178C2×C4⋊C8—132no—
179C2×C22⋊C8—132no—
180C2×C22⋊C8—132no—
181C4×M16—132no—
182C4×M16—131no—
183C4×M16—132no—
184C4×M16—132no—
185C4×M16#26111yescharacteristic
186C2×#97—132no—
187C2×C4×C8—132no—
188C2×C4×C8—132no—
189C2×C4×C8—132no—
190#322—138no—
191C82—138no—
192C22×C13—21no—
193C22×C13—21no—
194C22×C13C2×C4×C812yes—
195C22×C13C22×C4211yescharacteristic
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—44no—
201C2×D13C2×C4×C812yes—
202C2×D13C2×C4×C812yes—
203C4×C13—21no—
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—21no—
207C4×C13C2×C4×C812yes—
208C4×C13C23×C812yes—
209Dic13—21no—
210Dic13—21no—
211Dic13C2×C4×C812yes—
212Dic13C2×C4×C812yes—
213Dic13#56812yes—
214Dic13#56812yes—
215C23×C4—131no—
216C23×C4—131no—
217C23×C4—131no—
218C2×M16—132no—
219C2×M16—1316no—
220C2×M16—134no—
221C2×M16C2×#26112yes—
222C22×C8—134no—
223C22×C8—134no—
224C22×C8—134no—
225C2×C42—131no—
226C2×C42—131no—
227C2×C42—131no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—131no—
232C2×C42—131no—
233C2×C42—131no—
234C2×C42—131no—
235C2×C42—131no—
236C2×C42C2×#26111yescharacteristic
237C4⋊C8—134no—
238C4⋊C8—134no—
239C4⋊C8—134no—
240C4⋊C8—134no—
241C22⋊C8—134no—
242C22⋊C8—134no—
243C22⋊C8—134no—
244C22⋊C8—134no—
245#97—134no—
246#97—132no—
247#97C2×#26112yes—
248C4×C8—134no—
249C4×C8—134no—
250C4×C8—134no—
251C4×C8—134no—
252C4×C8—134no—
253C4×C8—132no—
254C4×C8C2×#26112yes—
255C2×C13—22no—
256C2×C13C22×C4×C811yescharacteristic
257C2×C13#287311yescharacteristic
258C2×C13#287311yescharacteristic
259D13—22no—
260D13—22no—
261C24—131no—
262C22×C4—131no—
263C22×C4—138no—
264C22×C4—131no—
265C22×C4—131no—
266C22×C4—131no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—131no—
271C22×C4—131no—
272C22×C4—131no—
273C22×C4—131no—
274C22×C4—131no—
275C22×C4—131no—
276C22×C4—131no—
277C22×C4—131no—
278C22×C4—522no—
279C22×C4—522no—
280C22×C4C4×#26111yescharacteristic
281C22×C4C4×#26111yescharacteristic
282C22×C4C22×#26111yescharacteristic
283M16—138no—
284M16—1316no—
285M16D13⋊C818yescomplemented
286C2×C8—134no—
287C2×C8—1316no—
288C2×C8—138no—
289C2×C8—138no—
290C2×C8—524no—
291C2×C8—524no—
292C2×C8C22×#26114yes—
293C42—131no—
294C42—131no—
295C42—131no—
296C42—131no—
297C42—131no—
298C42—131no—
299C42—131no—
300C42—131no—
301C42—131no—
302C42—131no—
303C42—131no—
304C42—131no—
305C42C4×#26111yescharacteristic
306C42C4×#26111yescharacteristic
307C42C22×#26111yescharacteristic
308C42C22×#26111yescharacteristic
309C13#1731411yescharacteristic, complemented, Sylow
310C23—131no—
311C23—131no—
312C23—134no—
313C23—521no—
314C23—521no—
315C23C2×C4×#26111yescharacteristic
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—134no—
319C2×C4—131no—
320C2×C4—131no—
321C2×C4—131no—
322C2×C4—131no—
323C2×C4—134no—
324C2×C4—134no—
325C2×C4—134no—
326C2×C4—134no—
327C2×C4—131no—
328C2×C4—131no—
329C2×C4—262no—
330C2×C4—262no—
331C2×C4—262no—
332C2×C4—262no—
333C2×C4—262no—
334C2×C4—262no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—521no—
339C2×C4C2×D13⋊C814yes—
340C2×C4C2×C4×#26111yescharacteristic
341C2×C4C2×C4×#26111yescharacteristic
342C2×C4C2×C4×#26111yescharacteristic
343C2×C4C2×C4×#26111yescharacteristic
344C2×C4C2×C4×#26111yescharacteristic
345C2×C4C23×#26111yescharacteristic
346C8—138no—
347C8—268no—
348C8—268no—
349C8C2×D13⋊C818yes—
350C22—21no—
351C22—21no—
352C22—132no—
353C22—132no—
354C22—261no—
355C22—261no—
356C22—261no—
357C22—261no—
358C22—524no—
359C22C4×D13⋊C812yes—
360C22C22×C4×#26111yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—132no—
366C4—132no—
367C4—132no—
368C4—132no—
369C4—261no—
370C4—261no—
371C4C4×D13⋊C812yes—
372C4C22×D13⋊C812yes—
373C2—22no—
374C2—262no—
375C2—262no—
376C2C2×C4×D13⋊C811yescharacteristic
377C2#1313139911yescharacteristic
378C2#1313139911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×#261
commutatorC2×C13C22×C4×C8
FittingC4×C13×M16C4
socleC22×C13C22×C42
prime radicalC23×D13C42
cosocleC4×Dic13C24
hypercenterC4×M16#261
hypocenterC13#17314
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #13130040C2semidirect
4. #13130034C2semidirect
5. M16×#1057C2semidirect
30. #11718251C22semidirect
31. C8×#1057C22semidirect
43. M16×D13C8semidirect
99. C13×M16C2×C8semidirect
117. #6099C2×C8semidirect
119. #6094C2×C8semidirect
120. C8×D13C2×C8semidirect
285. M16D13⋊C8semidirect
309. C13#17314semidirect

Maximal subgroups

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

subgroupindex
C2×#117190492
D13⋊#4312
#131300402
#131300342
M16×#10572
C4×M16×D132
#1731413