Finite Group Databasebeta

← #15873158

Subgroups — #15873158

Order 3328.

1218 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718868C211yesmaximal, characteristic
2C2×C4×C22⋊Dic13C211yesmaximal, characteristic
3#13115019C214yesmaximal, complemented
4#13115018C214yesmaximal, complemented
5#13114814C214yesmaximal, complemented
6C2×C13×#407C211yesmaximal, characteristic
7C24×C4×C13C2211yescharacteristic
8C22×C13×M16C2212yes—
9C22×C22⋊Dic13C412yes—
10C22×C4×Dic13C2212yes—
11C22×#6099C2212yes—
12C13×#407—24no—
13C2×C13×C22⋊C8C2212yes—
14C2×C13×C22⋊C8C2212yes—
15C4×C22⋊Dic13C412yes—
16C4×C22⋊Dic13C412yes—
17C4×C22⋊Dic13C2212yes—
18C4×C22⋊Dic13C2212yes—
19C2×#88071C411yescharacteristic
20C2×#88071C411yescharacteristic
21#11718868—24no—
22C2×C22⋊#1055C2212yes—
23C2×C22⋊#1055C2212yes—
24C2×#88054C2218yescomplemented
25#11718142C2218yescomplemented
26C25×C13C2×C411yescharacteristic
27C23×C4×C13—44no—
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13C2×C411yescharacteristic
30C23×C4×C13C2×C411yescharacteristic
31C23×C4×C13D414yes—
32C23×C4×C13Q814yes—
33C23×C4×C13C2311yescharacteristic
34C23×C4×C13C2311yescharacteristic
35C23×C4×C13C2311yescharacteristic
36C23×Dic13C2×C412yes—
37C23×Dic13C2×C412yes—
38C2×C13×M16—24no—
39C2×C13×M16—44no—
40C22×C8×C13C2314yes—
41C2×C22⋊Dic13—28no—
42C2×C22⋊Dic13C2×C414yes—
43C2×C22⋊Dic13C2×C414yes—
44C2×C4×Dic13—44no—
45C2×C4×Dic13C2×C414yes—
46C2×C4×Dic13C2314yes—
47C2×#6099—24no—
48C2×#6099—44no—
49C22×#1055C2314yes—
50C13×C22⋊C8—24no—
51C13×C22⋊C8—24no—
52#88071C2×C412yes—
53#88071C2×C412yes—
54#88071C2×C412yes—
55#88071C2×C412yes—
56C22⋊#1055—24no—
57C22⋊#1055—24no—
58#88054—48no—
59#21934—131nomaximal, Sylow
60C24×C13—24no—
61C24×C13—42no—
62C24×C13—41no—
63C24×C13—41no—
64C24×C13C4⋊C414yes—
65C24×C13C22×C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C24×C13C22×C411yescharacteristic
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—24no—
71C22×C4×C13—48no—
72C22×C4×C13—48no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13C4⋊C414yes—
77C22×C4×C13C4⋊C414yes—
78C22×C4×C13C4⋊C414yes—
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C22×C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D412yes—
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D412yes—
85C22×C4×C13C2×Q812yes—
86C22×C4×C13C2×Q812yes—
87C22×C4×C13C2×Q812yes—
88C22×C4×C13C2411yescharacteristic
89C22×Dic13—24no—
90C22×Dic13—42no—
91C22×Dic13—42no—
92C22×Dic13—42no—
93C22×Dic13—42no—
94C22×Dic13M1618yescomplemented
95C22×Dic13C22×C414yes—
96C22×Dic13C22×C414yes—
97C13×M16—48no—
98C2×C8×C13—24no—
99C2×C8×C13—28no—
100C22⋊Dic13—28no—
101C22⋊Dic13—28no—
102C4×Dic13—28no—
103C4×Dic13—44no—
104#6099—48no—
105C2×#1055—24no—
106C2×#1055—28no—
107C2×#407—131no—
108C2×#407D1311yescharacteristic
109C2×C4×C22⋊C4—131no—
110#1851—134no—
111#1851—134no—
112#1797—134no—
113C23×C13—22no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—22no—
117C23×C13—22no—
118C23×C13—22no—
119C23×C13—22no—
120C23×C13—21no—
121C23×C13—21no—
122C23×C13—21no—
123C23×C13—21no—
124C23×C13—28no—
125C23×C13—44no—
126C23×C13—44no—
127C23×C13—48no—
128C23×C13—48no—
129C23×C13C2×C4⋊C412yes—
130C23×C13C2×C4⋊C412yes—
131C23×C13C2×C4⋊C412yes—
132C23×C13C2×M1614yes—
133C23×C13C23×C411yescharacteristic
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—22no—
137C2×C4×C13—24no—
138C2×C4×C13—24no—
139C2×C4×C13—24no—
140C2×C4×C13—24no—
141C2×C4×C13—24no—
142C2×C4×C13—24no—
143C2×C4×C13—44no—
144C2×C4×C13—44no—
145C2×C4×C13—44no—
146C2×C4×C13C2×C4⋊C412yes—
147C2×C4×C13C2×C4⋊C412yes—
148C2×C4×C13C2×C4⋊C412yes—
149C2×C4×C13C22×D411yescharacteristic
150C2×C4×C13C22×Q811yescharacteristic
151C2×C4×C13H(5,𝔽2)14yes—
152C2×Dic13—24no—
153C2×Dic13—24no—
154C2×Dic13—24no—
155C2×Dic13—24no—
156C2×Dic13—24no—
157C2×Dic13—48no—
158C2×Dic13—48no—
159C2×Dic13C2×M1618yes—
160C8×C13—44no—
161#1055—44no—
162C24×C4C2×D1311yescharacteristic
163C22×M16—132no—
164C22×M16C2×D1312yes—
165C22×C22⋊C4—132no—
166C22×C42—132no—
167C2×C4⋊C8—138no—
168#407—24no—
169#407—264no—
170C2×C22⋊C8—132no—
171C2×C22⋊C8—132no—
172C2×C22⋊C8C2×D1312yes—
173C2×C22⋊C8C2×D1312yes—
174C4×C22⋊C4—132no—
175C4×C22⋊C4—132no—
176C4×C22⋊C4—132no—
177C4×C22⋊C4—132no—
178C2×#95—131no—
179C2×#95—131no—
180#336—138no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13—24no—
184C22×C13—24no—
185C22×C13—22no—
186C22×C13—22no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—416no—
192C22×C13—42no—
193C22×C13—42no—
194C22×C13—42no—
195C22×C13—42no—
196C22×C13#42314yes—
197C22×C13C22×C4⋊C411yescharacteristic
198C22×C13#51812yes—
199C22×C13C22×M1612yes—
200C22×C13#56811yescharacteristic
201C22×C13#56811yescharacteristic
202C4×C13—22no—
203C4×C13—22no—
204C4×C13—22no—
205C4×C13#53412yes—
206C4×C13#54312yes—
207Dic13—28no—
208Dic13—44no—
209C25C4×D1311yescharacteristic
210C23×C4—44no—
211C23×C4—132no—
212C23×C4—132no—
213C23×C4Dic2614yes—
214C23×C4C4×D1311yescharacteristic
215C23×C4C4×D1311yescharacteristic
216C23×C4C4×D1311yescharacteristic
217C23×C4C22⋊D1314yes—
218C23×C4C22×D1311yescharacteristic
219C23×C4C22×D1311yescharacteristic
220C23×C4C22×D1311yescharacteristic
221C2×M16—24no—
222C2×M16—44no—
223C2×M16—264no—
224C2×M16—524no—
225C22×C8—134no—
226C22×C8C22×D1314yes—
227C2×C22⋊C4—134no—
228C2×C22⋊C4—134no—
229C2×C22⋊C4—268no—
230C2×C42—134no—
231C2×C42—134no—
232C2×C42—524no—
233C4⋊C8—528no—
234C22⋊C8—24no—
235C22⋊C8—24no—
236C22⋊C8—264no—
237C22⋊C8—264no—
238#95—132no—
239#95—132no—
240#95—132no—
241#95—132no—
242C2×C13—24no—
243C2×C13—42no—
244C2×C13—42no—
245C2×C13#231511yescharacteristic
246C2×C13C2×#42311yescharacteristic
247C2×C13#290511yescharacteristic
248C2×C13#297312yes—
249C2×C13#297512yes—
250C24—24no—
251C24—42no—
252C24—41no—
253C24—41no—
254C24#610114yes—
255C24C2×C4×D1311yescharacteristic
256C24C2×C4×D1311yescharacteristic
257C24C2×C4×D1311yescharacteristic
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—48no—
262C22×C4—48no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—134no—
267C22×C4—138no—
268C22×C4—134no—
269C22×C4—264no—
270C22×C4—522no—
271C22×C4—522no—
272C22×C4—522no—
273C22×C4—522no—
274C22×C4#610114yes—
275C22×C4#610114yes—
276C22×C4#610114yes—
277C22×C4C2×Dic2612yes—
278C22×C4C2×Dic2612yes—
279C22×C4C2×Dic2612yes—
280C22×C4C2×C4×D1311yescharacteristic
281C22×C4C2×C4×D1311yescharacteristic
282C22×C4C2×C4×D1311yescharacteristic
283C22×C4C2×C22⋊D1312yes—
284C22×C4C2×C22⋊D1312yes—
285C22×C4C2×C22⋊D1312yes—
286C22×C4C23×D1311yescharacteristic
287M16—48no—
288M16—528no—
289C2×C8—28no—
290C2×C8—24no—
291C2×C8—268no—
292C2×C8—264no—
293C22⋊C4—268no—
294C22⋊C4—268no—
295C42—268no—
296C42—524no—
297C13#2193411yescharacteristic, complemented, Sylow
298C23—22no—
299C23—21no—
300C23—21no—
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—28no—
310C23—44no—
311C23—44no—
312C23—48no—
313C23—48no—
314C23M16×D1314yes—
315C23C2×#610112yes—
316C23C2×#610112yes—
317C23C2×#610112yes—
318C23C22×C4×D1311yescharacteristic
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—44no—
331C2×C4—138no—
332C2×C4—264no—
333C2×C4—264no—
334C2×C4—264no—
335C2×C4—264no—
336C2×C4—264no—
337C2×C4—528no—
338C2×C4—528no—
339C2×C4C2×#610112yes—
340C2×C4C2×#610112yes—
341C2×C4C2×#610112yes—
342C2×C4C22×Dic2611yescharacteristic
343C2×C4#8825114yes—
344C2×C4C22×C22⋊D1311yescharacteristic
345C8—44no—
346C8—524no—
347C22—22no—
348C22—24no—
349C22—24no—
350C22—22no—
351C22—22no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—416no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22#1171877914yes—
363C22#1171919112yes—
364C22C2×M16×D1312yes—
365C22#1171945011yescharacteristic
366C22#1171945011yescharacteristic
367C22C22×#610111yescharacteristic
368C4—22no—
369C4—22no—
370C4—22no—
371C4—268no—
372C4—524no—
373C4#1171918812yes—
374C4#1171950912yes—
375C2—24no—
376C2—42no—
377C2—42no—
378C2#1311744811yescharacteristic
379C2C2×#1171877911yescharacteristic
380C2#1312339911yescharacteristic
381C2#1312386312yes—
382C2#1312387512yes—
subgroupG/H
center, FrattiniC22×C4C23×D13
commutator, socleC23×C13C23×C4
FittingC2×C13×#407C2
prime radicalC25×C13C2×C4
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13#21934
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13115019C2semidirect
4. #13115018C2semidirect
5. #13114814C2semidirect
24. C2×#88054C22semidirect
25. #11718142C22semidirect
94. C22×Dic13M16semidirect
297. C13#21934semidirect

Maximal subgroups

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

subgroupindex
C2×#117188682
C2×C4×C22⋊Dic132
#131150192
#131150182
#131148142
C2×C13×#4072
#2193413