Finite Group Databasebeta

← #15760739

Subgroups — #15760739

Order 3328.

838 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117434C211yesmaximal, characteristic, complemented
2#13114780C212yesmaximal, complemented
3#13113163C211yesmaximal, characteristic, complemented
4#13112688C212yesmaximal, complemented
5C13×#2404C211yesmaximal, characteristic
6C22×C13×#41C2211yescharacteristic
7C2×C13×#120—21no—
8C22×C13×C22⋊C4C2211yescharacteristic
9C13×#393C412yescomplemented
10C13×#392C412yescomplemented
11C13×#386—21no—
12C13×#386—22no—
13C13×#381C2211yescharacteristic
14#11718908—21no—
15C2×#88077—24no—
16#11718873—21no—
17C4×C22⋊Dic13C2212yes—
18#11718868C2212yes—
19#11718612—24no—
20#11718117—22no—
21C25×C13D411yescharacteristic
22C2×C13×#41—22no—
23C2×C13×#41—22no—
24C2×C13×#41—44no—
25C22×Q8×C13C2×C411yescharacteristic
26C22×D4×C13—21no—
27C22×D4×C13—22no—
28C22×D4×C13C2×C411yescharacteristic
29C23×C4×C13—21no—
30C23×C4×C13D411yescharacteristic
31C23×C4×C13C2311yescharacteristic
32C13×#120—44no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4C2×C412yes—
39C2×C13×C22⋊C4D412yes—
40C2×C22⋊Dic13—22no—
41C2×C22⋊Dic13—22no—
42C2×C22⋊Dic13—22no—
43C2×C4⋊Dic13—22no—
44C2×C4×Dic13D414yescomplemented
45C2×#6099—22no—
46C13×#95—22no—
47C13×#95—21no—
48C13×#95C2×C412yes—
49#88077—48no—
50#88071—22no—
51#88071—22no—
52C22⋊#1055—22no—
53C22⋊#1055—22no—
54#9479—131nomaximal, Sylow
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—42no—
59C24×C13—42no—
60C24×C13—81no—
61C24×C13C22⋊C412yes—
62C24×C13C2×D411yescharacteristic
63C13×#41—28no—
64C13×#41—44no—
65C13×#41—44no—
66C13×#41—44no—
67C2×Q8×C13—22no—
68C2×Q8×C13—42no—
69C2×D4×C13—24no—
70C2×D4×C13—22no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—41no—
74C2×D4×C13—41no—
75C2×D4×C13—44no—
76C2×D4×C13—44no—
77C2×D4×C13—82no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13—42no—
85C22×C4×C13—42no—
86C22×C4×C13—81no—
87C22×C4×C13C22⋊C412yes—
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D412yes—
90C22×C4×C13C2×D411yescharacteristic
91C22×C4×C13#4112yes—
92C22×Dic13—24no—
93C13×C22⋊C4—24no—
94C13×C22⋊C4—24no—
95C13×C22⋊C4—44no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—82no—
98C22⋊Dic13—44no—
99C22⋊Dic13—82no—
100C22⋊Dic13—82no—
101C4⋊Dic13—82no—
102C4×Dic13—44no—
103#6099—44no—
104C2×#1055—42no—
105#2404D1311yescharacteristic
106#2312—131no—
107#1789—132no—
108#1462—131no—
109#1284—132no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—22no—
113C23×C13—22no—
114C23×C13—22no—
115C23×C13—22no—
116C23×C13—41no—
117C23×C13—42no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—41no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—41no—
125C23×C13—42no—
126C23×C13—42no—
127C23×C13—81no—
128C23×C13—81no—
129C23×C13—88no—
130C23×C13C2×C22⋊C411yescharacteristic
131C23×C13#12011yescharacteristic
132C23×C13#12311yescharacteristic
133Q8×C13—24no—
134Q8×C13—42no—
135D4×C13—24no—
136D4×C13—42no—
137D4×C13—44no—
138D4×C13—44no—
139D4×C13—88no—
140C2×C4×C13—24no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
146C2×C4×C13—48no—
147C2×C4×C13—42no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—42no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—81no—
155C2×C4×C13C4×D412yes—
156C2×C4×C13#12112yes—
157C2×Dic13—44no—
158C2×Dic13—44no—
159C2×Dic13—44no—
160#1055—82no—
161C22×#41C2×D1311yescharacteristic
162C2×#120—21no—
163C22×C22⋊C4C2×D1311yescharacteristic
164C2×#104—264no—
165#407—132no—
166#393Dic1312yescomplemented
167#392Dic1312yescomplemented
168#388—264no—
169#386—21no—
170#386—22no—
171#381C2×D1311yescharacteristic
172#380—261no—
173#379—261no—
174C4×C22⋊C4—132no—
175#323—262no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—21no—
183C22×C13—44no—
184C22×C13—44no—
185C22×C13—44no—
186C22×C13—42no—
187C22×C13—42no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—82no—
191C22×C13—82no—
192C22×C13—84no—
193C22×C13—84no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13#38611yescharacteristic
197C22×C13#42112yes—
198C22×C13B(4,𝔽2)12yes—
199C4×C13—22no—
200C4×C13—22no—
201C4×C13—42no—
202C4×C13—42no—
203C4×C13—82no—
204Dic13—84no—
205C25C22⋊D1311yescharacteristic
206C2×#41—22no—
207C2×#41—22no—
208C2×#41—44no—
209C22×Q8C2×Dic1311yescharacteristic
210C22×D4—21no—
211C22×D4—22no—
212C22×D4C2×Dic1311yescharacteristic
213C23×C4—21no—
214C23×C4C22⋊D1311yescharacteristic
215C23×C4C22×D1311yescharacteristic
216C2×M16—262no—
217#120—44no—
218C2×C4⋊C4—262no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—22no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—22no—
224C2×C22⋊C4—262no—
225C2×C22⋊C4—262no—
226C2×C22⋊C4—262no—
227C2×C22⋊C4C2×Dic1312yes—
228C2×C22⋊C4C22⋊D1312yes—
229C2×C42—134no—
230#104—528no—
231C22⋊C8—262no—
232C22⋊C8—262no—
233#95—22no—
234#95—21no—
235#95—262no—
236#95—262no—
237#95C2×Dic1312yes—
238C2×C13—22no—
239C2×C13—22no—
240C2×C13—41no—
241C2×C13—82no—
242C2×C13—82no—
243C2×C13#188911yescharacteristic
244C2×C13#189711yescharacteristic
245C2×C13#191111yescharacteristic
246C24—21no—
247C24—21no—
248C24—21no—
249C24—42no—
250C24—42no—
251C24—81no—
252C24C22⋊Dic1312yes—
253C24C2×C22⋊D1311yescharacteristic
254#41—28no—
255#41—44no—
256#41—44no—
257#41—44no—
258C2×Q8—22no—
259C2×Q8—42no—
260C2×D4—24no—
261C2×D4—22no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—44no—
267C2×D4—44no—
268C2×D4—82no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—22no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—81no—
278C22×C4—264no—
279C22×C4C22⋊Dic1312yes—
280C22×C4D4×D1312yes—
281C22×C4#612912yes—
282C22×C4C22×Dic1311yescharacteristic
283C22×C4C2×C22⋊D1311yescharacteristic
284M16—524no—
285C2×C8—522no—
286C4⋊C4—1042no—
287C22⋊C4—24no—
288C22⋊C4—24no—
289C22⋊C4—44no—
290C22⋊C4—42no—
291C22⋊C4—82no—
292C22⋊C4—524no—
293C22⋊C4—1042no—
294C22⋊C4—1042no—
295C42—524no—
296C13#947911yescharacteristic, complemented, Sylow
297C23—22no—
298C23—22no—
299C23—22no—
300C23—22no—
301C23—22no—
302C23—22no—
303C23—41no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—41no—
313C23—42no—
314C23—81no—
315C23—81no—
316C23—88no—
317C23#8818911yescharacteristic
318C23#8819111yescharacteristic
319C23C2×C22⋊Dic1311yescharacteristic
320Q8—24no—
321Q8—42no—
322D4—24no—
323D4—42no—
324D4—44no—
325D4—44no—
326D4—88no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—48no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—524no—
343C2×C4—524no—
344C2×C4—524no—
345C2×C4D4×Dic1312yes—
346C2×C4#8819312yes—
347C8—1042no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—44no—
356C22—44no—
357C22—44no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—82no—
363C22—82no—
364C22—84no—
365C22—84no—
366C22—81no—
367C22—81no—
368C22#1171869312yes—
369C22#1171888111yescharacteristic
370C22#1171889712yes—
371C4—22no—
372C4—22no—
373C4—42no—
374C4—42no—
375C4—82no—
376C4—1044no—
377C2—22no—
378C2—22no—
379C2—41no—
380C2—82no—
381C2—82no—
382C2#1311524511yescharacteristic
383C2#1311528511yescharacteristic
384C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
Fitting, prime radicalC13×#2404C2
socleC22×C13#386
cosocleC23×C4×C13C23
hypercenter#2404D13
hypocenterC13#9479
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2404

Complements

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

NH ≅ G/Ntype
1. #13117434C2semidirect
2. #13114780C2semidirect
3. #13113163C2semidirect
4. #13112688C2semidirect
9. C13×#393C4semidirect
10. C13×#392C4semidirect
44. C2×C4×Dic13D4semidirect
166. #393Dic13semidirect
167. #392Dic13semidirect
296. C13#9479semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131147802
#131131632
#131126882
C13×#24042
#947913