Finite Group Databasebeta

← #15835335

Subgroups — #15835335

Order 3328.

1054 conjugacy classes of subgroups; only the 183 normal subgroups are shown.

normal subgroups only

This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 183 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124780C212yesmaximal, complemented
2#13119110C211yesmaximal, characteristic
3#13113861C214yesmaximal, complemented
4#13113827C214yesmaximal, complemented
5#13113369C212yesmaximal, complemented
6#13113163C211yesmaximal, characteristic
7C2×C13×#543C211yesmaximal, characteristic
8C13×#543—24no—
9C13×#543—22no—
10C13×#543C2214yes—
11C2×C13×C22⋊Q8—22no—
12C2×C13×C22⋊Q8—21no—
13C2×C13×C22⋊Q8—22no—
14C2×C13×C22⋊Q8C2212yes—
15C22×C13×C22⋊C4—21no—
16C22×C13×C22⋊C4C2211yescharacteristic
17C2×#88180C2211yescharacteristic
18#11718908—21no—
19#11718886—22no—
20#11718872C2211yescharacteristic
21#11718871—21no—
22#11718868C2212yes—
23#11718706—24no—
24#11718705C2214yescomplemented
25#11718704C2214yescomplemented
26#11718625—22no—
27#11718614C2212yes—
28#11718610C2212yes—
29#11718605—22no—
30#11718130C2218yescomplemented
31#11718117C2214yes—
32C25×C13D411yescharacteristic
33C22×Q8×C13—21no—
34C22×Q8×C13D412yes—
35C23×C4×C13—21no—
36C23×C4×C13—21no—
37C23×C4×C13D411yescharacteristic
38C23×C4×C13C2311yescharacteristic
39C13×C22⋊Q8—28no—
40C13×C22⋊Q8—28no—
41C13×C22⋊Q8—24no—
42C13×C22⋊Q8—28no—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—28no—
47C13×C22⋊Q8D414yes—
48C13×C22⋊Q8C2314yes—
49C2×C13×C4⋊C4—21no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4D412yes—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—24no—
55C2×C13×C22⋊C4—22no—
56C2×C13×C22⋊C4—24no—
57C2×C13×C22⋊C4—22no—
58C2×C13×C22⋊C4—22no—
59C2×C13×C22⋊C4D412yes—
60C2×C13×C22⋊C4C2312yes—
61C2×C22⋊Dic13—21no—
62C2×C22⋊Dic13—22no—
63C2×C22⋊Dic13—21no—
64C2×C22⋊Dic13—22no—
65#88180—22no—
66#88180—22no—
67C2×C4⋊Dic13C2311yescharacteristic
68C2×C4⋊Dic13C2311yescharacteristic
69C2×#6101—22no—
70C2×C4×Dic13—21no—
71C2×#6099—22no—
72#88075—24no—
73#88075—24no—
74#88071—21no—
75#88071—22no—
76#88071C2312yes—
77C22⋊#1055—22no—
78C22⋊#1055C2314yes—
79#88048—24no—
80#88047—24no—
81#18138—131nomaximal, Sylow
82C24×C13—21no—
83C24×C13—21no—
84C24×C13—24no—
85C24×C13—42no—
86C24×C13—81no—
87C24×C13C2×D411yescharacteristic
88C24×C13C2×D412yes—
89C2×Q8×C13—24no—
90C2×Q8×C13—22no—
91C2×Q8×C13—44no—
92C2×Q8×C13—82no—
93C2×Q8×C13C2×D414yes—
94C22×C4×C13—22no—
95C22×C4×C13—21no—
96C22×C4×C13—22no—
97C22×C4×C13—24no—
98C22×C4×C13—24no—
99C22×C4×C13—21no—
100C22×C4×C13—42no—
101C22×C4×C13—81no—
102C22×C4×C13—82no—
103C22×C4×C13—82no—
104C22×C4×C13C2×D412yes—
105C22×C4×C13C2×D412yes—
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D412yes—
108C22×C4×C13C2411yescharacteristic
109C22×Dic13—22no—
110C22×Dic13—21no—
111C22×Dic13—21no—
112C13×C4⋊C4—24no—
113C13×C4⋊C4—28no—
114C13×C4⋊C4—24no—
115C13×C4⋊C4—22no—
116C13×C4⋊C4—24no—
117C13×C4⋊C4C2×D414yes—
118C13×C22⋊C4—28no—
119C13×C22⋊C4—24no—
120C13×C22⋊C4—24no—
121C13×C22⋊C4—24no—
122C13×C22⋊C4—24no—
123C22⋊Dic13—42no—
124C22⋊Dic13—41no—
125C22⋊Dic13—41no—
126C22⋊Dic13—44no—
127C22⋊Dic13—82no—
128C4⋊Dic13—22no—
129C4⋊Dic13—22no—
130#6101—82no—
131C4×Dic13—42no—
132#6099—44no—
133C2×#1055—24no—
134C2×#543D1311yescharacteristic
135#3095—132no—
136#2482—131no—
137#1614—134no—
138#1608—134no—
139#1511—132no—
140#1462—131no—
141C23×C13—24no—
142C23×C13—24no—
143C23×C13—22no—
144C23×C13—22no—
145C23×C13—22no—
146C23×C13—22no—
147C23×C13—41no—
148C23×C13—42no—
149C23×C13—42no—
150C23×C13—42no—
151C23×C13—42no—
152C23×C13—81no—
153C23×C13—81no—
154C23×C13—88no—
155C23×C13#12011yescharacteristic
156C23×C13#12011yescharacteristic
157C23×C13#13714yes—
158C23×C13C22×D411yescharacteristic
159Q8×C13—44no—
160Q8×C13—82no—
161Q8×C13—84no—
162C2×C4×C13—24no—
163C2×C4×C13—24no—
164C2×C4×C13—22no—
165C2×C4×C13—24no—
166C2×C4×C13—42no—
167C2×C4×C13—41no—
168C2×C4×C13—41no—
169C2×C4×C13—42no—
170C2×C4×C13—44no—
171C2×C4×C13—44no—
172C2×C4×C13—42no—
173C2×C4×C13—81no—
174C2×C4×C13—84no—
175C2×C4×C13—84no—
176C2×C4×C13#12012yes—
177C2×C4×C13C22×D412yes—
178C2×Dic13—42no—
179C2×Dic13—42no—
180C2×Dic13—42no—
181C2×Dic13—41no—
182C2×Dic13—41no—
183C2×Dic13—42no—
184C2×Dic13—42no—
185#1055—44no—
186#543—24no—
187#543—22no—
188#543C2×D1314yes—
189C2×C22⋊Q8—22no—
190C2×C22⋊Q8—21no—
191C2×C22⋊Q8—22no—
192C2×C22⋊Q8C2×D1312yes—
193C2×#117—131no—
194C22×C22⋊C4—21no—
195C22×C22⋊C4C2×D1311yescharacteristic
196#485—264no—
197#484—134no—
198#483—134no—
199#428—262no—
200#419—262no—
201#407—132no—
202#399—132no—
203#397—132no—
204#388—262no—
205#385—261no—
206#381—131no—
207#379—261no—
208#328—138no—
209#323—134no—
210C22×C13—21no—
211C22×C13—21no—
212C22×C13—21no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—24no—
216C22×C13—21no—
217C22×C13—21no—
218C22×C13—44no—
219C22×C13—44no—
220C22×C13—48no—
221C22×C13—42no—
222C22×C13—42no—
223C22×C13—82no—
224C22×C13—84no—
225C22×C13#45812yes—
226C22×C13C2×#12011yescharacteristic
227C22×C13C2×#13712yes—
228C4×C13—22no—
229C4×C13—22no—
230C4×C13—42no—
231C4×C13—44no—
232C4×C13—44no—
233Dic13—82no—
234Dic13—81no—
235Dic13—81no—
236C25C22⋊D1311yescharacteristic
237C22×Q8—21no—
238C22×Q8C22⋊D1312yes—
239C23×C4—21no—
240C23×C4—21no—
241C23×C4C22⋊D1311yescharacteristic
242C23×C4C22×D1311yescharacteristic
243C2×M16—262no—
244C22⋊Q8—28no—
245C22⋊Q8—28no—
246C22⋊Q8—24no—
247C22⋊Q8—28no—
248C22⋊Q8—24no—
249C22⋊Q8—22no—
250C22⋊Q8—22no—
251C22⋊Q8—28no—
252C22⋊Q8C22⋊D1314yes—
253C22⋊Q8C22×D1314yes—
254#117—262no—
255#117—262no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—131no—
260C2×C4⋊C4—131no—
261C2×C4⋊C4—262no—
262C2×C4⋊C4C22⋊D1312yes—
263C2×C22⋊C4—22no—
264C2×C22⋊C4—24no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—24no—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—261no—
270C2×C22⋊C4—261no—
271C2×C22⋊C4—262no—
272C2×C22⋊C4—262no—
273C2×C22⋊C4C22⋊D1312yes—
274C2×C22⋊C4C22×D1312yes—
275C2×C42—261no—
276#107—264no—
277#106—264no—
278#103—264no—
279#103—264no—
280C22⋊C8—134no—
281C22⋊C8—262no—
282#95—132no—
283#95—261no—
284#95—262no—
285C2×C13—22no—
286C2×C13—22no—
287C2×C13—41no—
288C2×C13—44no—
289C2×C13#300411yescharacteristic
290C2×C13#301911yescharacteristic
291C2×C13C2×#45811yescharacteristic
292C24—21no—
293C24—24no—
294C24—21no—
295C24—42no—
296C24—81no—
297C24C2×C22⋊D1311yescharacteristic
298C24C2×C22⋊D1312yes—
299C2×Q8—24no—
300C2×Q8—22no—
301C2×Q8—44no—
302C2×Q8—82no—
303C2×Q8C2×C22⋊D1314yes—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—21no—
310C22×C4—42no—
311C22×C4—81no—
312C22×C4—82no—
313C22×C4—82no—
314C22×C4—262no—
315C22×C4—261no—
316C22×C4—261no—
317C22×C4C2×C22⋊D1312yes—
318C22×C4C2×C22⋊D1312yes—
319C22×C4C2×C22⋊D1311yescharacteristic
320C22×C4C2×C22⋊D1312yes—
321C22×C4C23×D1311yescharacteristic
322M16—524no—
323C2×C8—264no—
324C4⋊C4—24no—
325C4⋊C4—28no—
326C4⋊C4—24no—
327C4⋊C4—22no—
328C4⋊C4—24no—
329C4⋊C4—262no—
330C4⋊C4—262no—
331C4⋊C4—1042no—
332C4⋊C4C2×C22⋊D1314yes—
333C22⋊C4—28no—
334C22⋊C4—24no—
335C22⋊C4—24no—
336C22⋊C4—24no—
337C22⋊C4—24no—
338C22⋊C4—522no—
339C22⋊C4—524no—
340C22⋊C4—521no—
341C22⋊C4—521no—
342C22⋊C4—1042no—
343C42—522no—
344C13#1813811yescharacteristic, complemented, Sylow
345C23—24no—
346C23—24no—
347C23—22no—
348C23—22no—
349C23—22no—
350C23—22no—
351C23—41no—
352C23—42no—
353C23—42no—
354C23—42no—
355C23—42no—
356C23—81no—
357C23—81no—
358C23—88no—
359C23#8819614yes—
360C23#8820711yescharacteristic
361C23#8820711yescharacteristic
362C23C22×C22⋊D1311yescharacteristic
363Q8—44no—
364Q8—82no—
365Q8—84no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—22no—
369C2×C4—24no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—84no—
379C2×C4—84no—
380C2×C4—522no—
381C2×C4—522no—
382C2×C4—522no—
383C2×C4—522no—
384C2×C4—522no—
385C2×C4—521no—
386C2×C4—521no—
387C2×C4#8820712yes—
388C2×C4C22×C22⋊D1312yes—
389C8—524no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—24no—
397C22—21no—
398C22—44no—
399C22—44no—
400C22—48no—
401C22—42no—
402C22—42no—
403C22—82no—
404C22—84no—
405C22#1171890412yes—
406C22C2×#8819612yes—
407C22C2×#8820711yescharacteristic
408C4—22no—
409C4—22no—
410C4—42no—
411C4—44no—
412C4—44no—
413C4—1042no—
414C4—1041no—
415C4—1041no—
416C2—22no—
417C2—22no—
418C2—41no—
419C2—44no—
420C2#1312407011yescharacteristic
421C2#1312419311yescharacteristic
422C2C2×#1171890411yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#543C2
socleC22×C13C2×#120
prime radicalC25×C13D4
hypercenterC2×#543D13
hypocenterC13#18138
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. #13124780C2semidirect
3. #13113861C2semidirect
4. #13113827C2semidirect
5. #13113369C2semidirect
24. #11718705C22semidirect
25. #11718704C22semidirect
30. #11718130C22semidirect
344. C13#18138semidirect

Maximal subgroups

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

subgroupindex
#131247802
#131191102
#131138612
#131138272
#131133692
#131131632
C2×C13×#5432
#1813813