Finite Group Databasebeta

← #15872418

Subgroups — #15872418

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#88144C211yesmaximal, characteristic
2C2×#11718379C211yesmaximal, characteristic
3#13117231C211yesmaximal, characteristic
4#13115799C214yesmaximal, complemented
5#13115792C214yesmaximal, complemented
6#13114927C211yesmaximal, characteristic
7#13114924C211yesmaximal, characteristic
8#13114922C211yesmaximal, characteristic
9C13×#1823C211yesmaximal, characteristic
10C22×C13×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic13—21no—
12C22×C4⋊Dic13C2211yescharacteristic
13C22×#6101—21no—
14C22×C4×Dic13C2211yescharacteristic
15C2×#88144—21no—
16C2×#88144—21no—
17C2×#88144—24no—
18C2×#88144C418yescomplemented
19C2×#88144C2212yes—
20C2×#88144C2212yes—
21C2×C13×C22⋊C8C2211yescharacteristic
22C13×#380C2211yescharacteristic
23#11718873C2211yescharacteristic
24C2×C22⋊#1055C2211yescharacteristic
25C2×#88054C2212yes—
26C2×C8×Dic13C2212yes—
27#11718638C2212yes—
28C4⋊C4×Dic13C2212yes—
29#11718604—21no—
30C22⋊C4×Dic13—21no—
31#11718379—24no—
32#11718312—21no—
33#11718309—21no—
34C13×#340C2214yes—
35#11718143C2214yes—
36#11718121C2214yes—
37#11718121C2214yes—
38C23×C4×C13—21no—
39C23×C4×C13C2311yescharacteristic
40C23×Dic13—21no—
41C23×Dic13D411yescharacteristic
42C23×Dic13D411yescharacteristic
43C22×C8×C13C2312yes—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4C2×C414yes—
47C2×C13×C4⋊C4C2312yes—
48C2×C13×C4⋊C4C2312yes—
49C2×C13×C22⋊C4—21no—
50C2×C22⋊Dic13—21no—
51C2×C4⋊Dic13—21no—
52C2×C4⋊Dic13—22no—
53C2×C4⋊Dic13—28no—
54C2×C4⋊Dic13—22no—
55C2×C4⋊Dic13—22no—
56C2×C4⋊Dic13C2×C414yes—
57C2×C4⋊Dic13C2312yes—
58C2×C4⋊Dic13C2312yes—
59C2×#6101—28no—
60C2×#6101—22no—
61C2×#6101—22no—
62C2×C4×Dic13—22no—
63C2×C4×Dic13C2×C414yes—
64C2×C4×Dic13D411yescharacteristic
65C2×C4×Dic13D411yescharacteristic
66C2×C4×Dic13D414yes—
67C2×C4×Dic13C2311yescharacteristic
68C2×C4×Dic13C2311yescharacteristic
69C22×#1055C2312yes—
70#88144—28no—
71#88144—28no—
72#88144—24no—
73#88144—24no—
74#88144C2×C418yes—
75#88144C2×C418yes—
76C13×C22⋊C8—22no—
77C13×#95—21no—
78#88071—21no—
79#88071—22no—
80#88071—22no—
81#88071—22no—
82C22⋊#1055—22no—
83#88054—24no—
84C8×Dic13—24no—
85#21836—131nomaximal, Sylow
86C24×C13C2×D411yescharacteristic
87C22×C4×C13—24no—
88C22×C4×C13—24no—
89C22×C4×C13—22no—
90C22×C4×C13—22no—
91C22×C4×C13—42no—
92C22×C4×C13—42no—
93C22×C4×C13C22×C412yes—
94C22×C4×C13C2×D411yescharacteristic
95C22×C4×C13C2×D412yes—
96C22×C4×C13C2411yescharacteristic
97C22×Dic13—22no—
98C22×Dic13—22no—
99C22×Dic13—24no—
100C22×Dic13—22no—
101C22×Dic13—22no—
102C22×Dic13—42no—
103C22×Dic13—44no—
104C22×Dic13C22⋊C414yes—
105C22×Dic13C22⋊C414yes—
106C22×Dic13C2×D411yescharacteristic
107C22×Dic13C2×D411yescharacteristic
108C22×Dic13C2×D411yescharacteristic
109C22×Dic13C2×D411yescharacteristic
110C2×C8×C13—22no—
111C2×C8×C13—24no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—22no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4C22×C414yes—
116C13×C22⋊C4—42no—
117C22⋊Dic13—42no—
118C4⋊Dic13—24no—
119C4⋊Dic13—22no—
120C4⋊Dic13—28no—
121C4⋊Dic13—28no—
122C4⋊Dic13—24no—
123C4⋊Dic13C22×C414yes—
124#6101—28no—
125#6101—28no—
126C4×Dic13—44no—
127C4×Dic13C22⋊C414yes—
128C4×Dic13C22⋊C414yes—
129C4×Dic13C22×C412yes—
130C4×Dic13C22×C412yes—
131C4×Dic13C2×D412yes—
132C4×Dic13C2×D412yes—
133C2×#1055—22no—
134C2×#1055—24no—
135C22×#125—131no—
136C2×#431—131no—
137#2283—131no—
138#1991—134no—
139#1989—134no—
140#1824—131no—
141#1824—131no—
142#1823—131no—
143#1823D1311yescharacteristic
144C23×C13—22no—
145C23×C13—22no—
146C23×C13C2×C22⋊C412yes—
147C23×C13#13512yes—
148C23×C13#13512yes—
149C23×C13C22×D411yescharacteristic
150C2×C4×C13—22no—
151C2×C4×C13—24no—
152C2×C4×C13—24no—
153C2×C4×C13—24no—
154C2×C4×C13—42no—
155C2×C4×C13—42no—
156C2×C4×C13—48no—
157C2×C4×C13—42no—
158C2×C4×C13—42no—
159C2×C4×C13—42no—
160C2×C4×C13C2×C22⋊C412yes—
161C2×C4×C13C23×C411yescharacteristic
162C2×C4×C13C22×D411yescharacteristic
163C2×C4×C132−1+414yes—
164C2×Dic13—21no—
165C2×Dic13—21no—
166C2×Dic13—21no—
167C2×Dic13—21no—
168C2×Dic13—22no—
169C2×Dic13—22no—
170C2×Dic13—28no—
171C2×Dic13—24no—
172C2×Dic13—44no—
173C2×Dic13—48no—
174C2×Dic13—44no—
175C2×Dic13—42no—
176C2×Dic13—42no—
177C2×Dic13—42no—
178C2×Dic13C2×C22⋊C412yes—
179C2×Dic13C2×C22⋊C412yes—
180C2×Dic13C2×C22⋊C412yes—
181C2×Dic13C2×C22⋊C412yes—
182C8×C13—42no—
183#1055—42no—
184C2×#125—138no—
185C2×#125—132no—
186C2×#125—132no—
187C2×#125—261no—
188C2×#125—261no—
189C2×#125—264no—
190C22×C4⋊C4—131no—
191C22×C4⋊C4—261no—
192C22×C4⋊C4—261no—
193C22×C4⋊C4C2×D1311yescharacteristic
194C22×C42—131no—
195#431—264no—
196C2×C4⋊C8—132no—
197C2×C22⋊C8—131no—
198C2×C22⋊C8C2×D1311yescharacteristic
199C2×C4×C8—132no—
200#383—261no—
201#382—132no—
202#381—261no—
203#380—131no—
204#380C2×D1311yescharacteristic
205C4×C4⋊C4—132no—
206C4×C22⋊C4—261no—
207#376—261no—
208#340—134no—
209#340—134no—
210#340—134no—
211#340C2×D1314yes—
212C22×C13—22no—
213C22×C13—22no—
214C22×C13—24no—
215C22×C13—24no—
216C22×C13#41614yes—
217C22×C13C22×C22⋊C411yescharacteristic
218C22×C13#53612yes—
219C22×C13C2×#13511yescharacteristic
220C22×C13C2×#13511yescharacteristic
221C22×C13#57512yes—
222C4×C13—22no—
223C4×C13—44no—
224C4×C13—82no—
225C4×C13#51912yes—
226C4×C13#53612yes—
227Dic13—22no—
228Dic13—22no—
229Dic13—22no—
230Dic13—22no—
231Dic13—44no—
232Dic13—82no—
233C23×C4—21no—
234C23×C4—131no—
235C23×C4—131no—
236C23×C4—261no—
237C23×C4C22×D1311yescharacteristic
238C22×C8—132no—
239C22×C8C22×D1312yes—
240#125—138no—
241#125—138no—
242#125—268no—
243#125—268no—
244#125—264no—
245#125—264no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—134no—
249C2×C4⋊C4—132no—
250C2×C4⋊C4—132no—
251C2×C4⋊C4—268no—
252C2×C4⋊C4—262no—
253C2×C4⋊C4—262no—
254C2×C4⋊C4—268no—
255C2×C4⋊C4—262no—
256C2×C4⋊C4—262no—
257C2×C4⋊C4—261no—
258C2×C4⋊C4—262no—
259C2×C4⋊C4C4×D1314yes—
260C2×C4⋊C4C22×D1312yes—
261C2×C4⋊C4C22×D1312yes—
262C2×C22⋊C4—21no—
263C2×C22⋊C4—261no—
264C2×C42—134no—
265C2×C42—131no—
266C2×C42—131no—
267C2×C42—134no—
268C2×C42—131no—
269C2×C42—131no—
270C2×C42—262no—
271C4⋊C8—264no—
272C22⋊C8—22no—
273C22⋊C8—262no—
274C4×C8—264no—
275#95—21no—
276#95—262no—
277#95—262no—
278#95—262no—
279#95—261no—
280C2×C13—24no—
281C2×C13#231011yescharacteristic
282C2×C13C2×#41611yescharacteristic
283C2×C13#289611yescharacteristic
284C2×C13#323212yes—
285C2×C13#323212yes—
286C24D4×D1311yescharacteristic
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—134no—
294C22×C4—131no—
295C22×C4—131no—
296C22×C4—131no—
297C22×C4—131no—
298C22×C4—134no—
299C22×C4—262no—
300C22×C4—262no—
301C22×C4—264no—
302C22×C4—262no—
303C22×C4—262no—
304C22×C4—522no—
305C22×C4—524no—
306C22×C4C2×C4×D1312yes—
307C22×C4D4×D1311yescharacteristic
308C22×C4D4×D1312yes—
309C22×C4C23×D1311yescharacteristic
310C2×C8—22no—
311C2×C8—24no—
312C2×C8—262no—
313C2×C8—264no—
314C4⋊C4—24no—
315C4⋊C4—22no—
316C4⋊C4—24no—
317C4⋊C4—134no—
318C4⋊C4—268no—
319C4⋊C4—268no—
320C4⋊C4—268no—
321C4⋊C4—268no—
322C4⋊C4—264no—
323C4⋊C4—262no—
324C4⋊C4—264no—
325C4⋊C4C2×C4×D1314yes—
326C22⋊C4—42no—
327C22⋊C4—522no—
328C42—134no—
329C42—134no—
330C42—132no—
331C42—132no—
332C42—132no—
333C42—132no—
334C42—524no—
335C13#2183611yescharacteristic, complemented, Sylow
336C23—22no—
337C23—22no—
338C23C22⋊C4×D1312yes—
339C23#8816612yes—
340C23#8817012yes—
341C23C2×D4×D1311yescharacteristic
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—48no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—132no—
353C2×C4—132no—
354C2×C4—132no—
355C2×C4—132no—
356C2×C4—268no—
357C2×C4—261no—
358C2×C4—261no—
359C2×C4—261no—
360C2×C4—261no—
361C2×C4—262no—
362C2×C4—262no—
363C2×C4—264no—
364C2×C4—524no—
365C2×C4—528no—
366C2×C4—524no—
367C2×C4—522no—
368C2×C4—522no—
369C2×C4—522no—
370C2×C4C22⋊C4×D1312yes—
371C2×C4C22×C4×D1311yescharacteristic
372C2×C4C2×D4×D1311yescharacteristic
373C2×C4#8825714yes—
374C8—42no—
375C8—522no—
376C22—22no—
377C22—24no—
378C22—24no—
379C22—22no—
380C22#1171843314yes—
381C22C2×C22⋊C4×D1311yescharacteristic
382C22#1171935312yes—
383C22C2×#8816611yescharacteristic
384C22C2×#8817011yescharacteristic
385C22#1171948212yes—
386C4—22no—
387C4—44no—
388C4—82no—
389C4—262no—
390C4—262no—
391C4—262no—
392C4—262no—
393C4—524no—
394C4—1042no—
395C4#1171922112yes—
396C4#1171935312yes—
397C2—24no—
398C2#1311742111yescharacteristic
399C2C2×#1171843311yescharacteristic
400C2#1312335411yescharacteristic
401C2#1312600112yes—
402C2#1312600712yes—
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1823C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenter#1823D13
hypocenterC13#21836
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #13115799C2semidirect
5. #13115792C2semidirect
18. C2×#88144C4semidirect
335. C13#21836semidirect

Maximal subgroups

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

subgroupindex
C22×#881442
C2×#117183792
#131172312
#131157992
#131157922
#131149272
#131149242
#131149222
C13×#18232
#2183613