Finite Group Databasebeta

← #16779170

Subgroups — #16779170

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719130C211yesmaximal, characteristic
2C2×#11719125C211yesmaximal, characteristic
3#13129674C214yesmaximal
4C2×#11718638C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057C2212yes—
9C2×C22⋊#1057C2212yes—
10#11719130—22no—
11#11719130C414yescomplemented
12#11719125—22no—
13#11719125C414yescomplemented
14C2×#88112—21no—
15C2×#88110—21no—
16C2×C4⋊#1057—21no—
17C2×C4×#1057—21no—
18C2×#88071C412yes—
19C2×#88071C2212yes—
20#11718638—21no—
21#11718638—21no—
22#11718638—21no—
23#11718638—21no—
24C23×C4×C13C2×C412yes—
25C23×C4×C13C2×C411yescharacteristic
26C23×Dic13C2×C411yescharacteristic
27C23×Dic13C2×C412yes—
28C23×Dic13C2311yescharacteristic
29C22×#1057—22no—
30C22×#1057—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—42no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13—42no—
37C2×C4×Dic13C2×C412yes—
38C2×C4×Dic13C2×C412yes—
39C2×C4×Dic13D412yes—
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×C4×Dic13Q812yes—
45C22⋊#1057—22no—
46C22⋊#1057—22no—
47C22⋊#1057C2×C414yes—
48C22⋊#1057C2×C414yes—
49#88112—24no—
50#88110—24no—
51C4⋊#1057—24no—
52C4×#1057—24no—
53#88071—22no—
54#88071—22no—
55#88071—22no—
56#88071—22no—
57#7914—131nomaximal, Sylow
58C24×C13C22×C411yescharacteristic
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—24no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13C4212yes—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C4⋊C412yes—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—24no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13—42no—
76C22×Dic13—42no—
77C22×Dic13C4212yes—
78C22×Dic13C22⋊C411yescharacteristic
79C22×Dic13C22⋊C411yescharacteristic
80C22×Dic13C4⋊C412yes—
81C22×Dic13C22×C411yescharacteristic
82C22×Dic13C22×C411yescharacteristic
83C22×Dic13C2×D411yescharacteristic
84C22×Dic13C2×D411yescharacteristic
85C22×Dic13C2×D411yescharacteristic
86C22×Dic13C2×Q811yescharacteristic
87C2×#1057—24no—
88C2×#1057—24no—
89C2×#1057—42no—
90C2×#1057—42no—
91C2×#1057—42no—
92C2×#1057—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C4⋊Dic13—42no—
96C4⋊Dic13—42no—
97C4×Dic13C22⋊C412yes—
98C4×Dic13C22⋊C412yes—
99C4×Dic13C22⋊C412yes—
100C4×Dic13C22⋊C412yes—
101C4×Dic13C4⋊C412yes—
102C4×Dic13C4⋊C412yes—
103C4×Dic13C4⋊C412yes—
104C4×Dic13C4⋊C412yes—
105C2×#432—131no—
106C2×#431—131no—
107C2×#382—131no—
108#1280—134no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13C2×C4211yescharacteristic
114C23×C13C2×C22⋊C411yescharacteristic
115C23×C13C2×C4⋊C411yescharacteristic
116C23×C13#13112yes—
117C23×C13#13112yes—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—24no—
121C2×C4×C13—24no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—84no—
126C2×C4×C13#9512yes—
127C2×C4×C13#9512yes—
128C2×C4×C13#10012yes—
129C2×C4×C13#10112yes—
130C2×Dic13—24no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—21no—
136C2×Dic13—21no—
137C2×Dic13—21no—
138C2×Dic13—21no—
139C2×Dic13—24no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—42no—
145C2×Dic13—42no—
146C2×Dic13—42no—
147C2×Dic13—84no—
148C2×Dic13#9512yes—
149C2×Dic13#9512yes—
150C2×Dic13C2×C22⋊C411yescharacteristic
151C2×Dic13C2×C22⋊C411yescharacteristic
152C2×Dic13C2×C4⋊C411yescharacteristic
153C2×Dic13C2×C4⋊C411yescharacteristic
154#1057—44no—
155#1057—44no—
156C22×C4⋊C4—131no—
157C22×C4⋊C4#26111yescharacteristic
158C22×C42—131no—
159#432—134no—
160#432—262no—
161#431—134no—
162#431—262no—
163C2×C4⋊C8—261no—
164C2×C4⋊C8—261no—
165C2×C22⋊C8—132no—
166C2×C22⋊C8—132no—
167C2×#97—261no—
168C2×C4×C8—261no—
169#382—261no—
170#382—261no—
171#382—261no—
172#382—261no—
173C2×#95—132no—
174C2×#95—132no—
175C22×C13—22no—
176C22×C13—22no—
177C22×C13—22no—
178C22×C13—22no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13C2×#9511yescharacteristic
184C22×C13#40512yes—
185C22×C13#40811yescharacteristic
186C22×C13#40811yescharacteristic
187C22×C13#41011yescharacteristic
188C22×C13#41011yescharacteristic
189C22×C13C2×#10011yescharacteristic
190C22×C13C2×#10111yescharacteristic
191C22×C13#42412yes—
192C4×C13—22no—
193C4×C13—82no—
194C4×C13#34314yes—
195Dic13—22no—
196Dic13—22no—
197Dic13—21no—
198Dic13—21no—
199Dic13—21no—
200Dic13—21no—
201Dic13—82no—
202C23×C4—131no—
203C23×C4—131no—
204C23×C4—132no—
205C23×C4C2×#26112yes—
206C23×C4C2×#26111yescharacteristic
207C22×C8—262no—
208C22×C8—262no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—42no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—522no—
215C2×C42—132no—
216C2×C42—132no—
217C2×C42—132no—
218C2×C42—132no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—131no—
223C4⋊C8—264no—
224C4⋊C8—264no—
225C22⋊C8—134no—
226C22⋊C8—134no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#97—264no—
230C4×C8—264no—
231#95—262no—
232#95—262no—
233#95—262no—
234#95—262no—
235C2×C13—22no—
236C2×C13—22no—
237C2×C13#146911yescharacteristic
238C2×C13#146911yescharacteristic
239C2×C13#147011yescharacteristic
240C2×C13#147011yescharacteristic
241C2×C13#172911yescharacteristic
242C2×C13#174011yescharacteristic
243C2×C13C2×#34311yescharacteristic
244C24C22×#26111yescharacteristic
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—132no—
252C22×C4—132no—
253C22×C4—131no—
254C22×C4—131no—
255C22×C4—131no—
256C22×C4—131no—
257C22×C4—131no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—262no—
262C22×C4—262no—
263C22×C4—262no—
264C22×C4—264no—
265C22×C4—521no—
266C22×C4—521no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4C4×#26112yes—
270C22×C4C4⋊#26112yes—
271C22×C4C22⋊#26111yescharacteristic
272C22×C4C22⋊#26111yescharacteristic
273C2×C8—264no—
274C2×C8—264no—
275C2×C8—522no—
276C2×C8—522no—
277C2×C8—522no—
278C2×C8—522no—
279C4⋊C4—42no—
280C4⋊C4—42no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C42—132no—
284C42—132no—
285C42—132no—
286C42—132no—
287C42—132no—
288C42—132no—
289C42—132no—
290C42—132no—
291C13#791411yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—21no—
295C23—21no—
296C23C2×C4×#26111yescharacteristic
297C23C2×C4⋊#26111yescharacteristic
298C23#8823812yes—
299C23#8824012yes—
300C23C2×C22⋊#26111yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—84no—
309C2×C4—131no—
310C2×C4—131no—
311C2×C4—132no—
312C2×C4—132no—
313C2×C4—131no—
314C2×C4—131no—
315C2×C4—264no—
316C2×C4—264no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—261no—
323C2×C4—261no—
324C2×C4—261no—
325C2×C4—521no—
326C2×C4—521no—
327C2×C4—521no—
328C2×C4—521no—
329C2×C4—522no—
330C2×C4—522no—
331C2×C4—522no—
332C2×C4—1044no—
333C2×C4#8811312yes—
334C2×C4(C2×#261)⋊C412yes—
335C2×C4(C2×#261)⋊C412yes—
336C2×C4#8812112yes—
337C8—524no—
338C8—524no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—22no—
344C22—22no—
345C22—22no—
346C22—22no—
347C22#1171907212yes—
348C22#1171907912yes—
349C22C2×#8811311yescharacteristic
350C22C2×(C2×#261)⋊C411yescharacteristic
351C22#1171914211yescharacteristic
352C22#1171914711yescharacteristic
353C22#1171915611yescharacteristic
354C22#1171915911yescharacteristic
355C22C2×#8812111yescharacteristic
356C4—22no—
357C4—82no—
358C4—262no—
359C4—262no—
360C4—261no—
361C4—261no—
362C4—261no—
363C4—261no—
364C4—1042no—
365C4#1171829114yes—
366C2—22no—
367C2—22no—
368C2#1313010611yescharacteristic
369C2#1313010711yescharacteristic
370C2#1313010911yescharacteristic
371C2#1313011011yescharacteristic
372C2#1313050311yescharacteristic
373C2#1313053611yescharacteristic
374C2C2×#1171829111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22×C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#7914
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
11. #11719130C4semidirect
13. #11719125C4semidirect
291. C13#7914semidirect

Maximal subgroups

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

subgroupindex
C2×#117191302
C2×#117191252
#131296742
C2×#117186382
#791413