Finite Group Databasebeta

← #16785107

Subgroups — #16785107

Order 3328.

598 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 598 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130563C211yesmaximal, characteristic
2#13130012C211yesmaximal, characteristic
3#13129709C212yesmaximal
4#13129709C212yesmaximal
5#13123187C211yesmaximal, characteristic
6C2×#88150—21no—
7C2×#88142C411yescharacteristic, complemented
8C2×C42×D13C2211yescharacteristic
9C2×(C2×#261)⋊C4—21no—
10C2×(C2×#261)⋊C4—21no—
11C2×(C2×#261)⋊C4C2212yes—
12C2×#88111C2212yes—
13C2×#88110—21no—
14C13×#389C411yescharacteristic, complemented
15#11718648C2211yescharacteristic
16#11718648C2211yescharacteristic
17#11718637C411yescharacteristic, complemented
18#11718633—21no—
19#11718589C411yescharacteristic, complemented
20#11718328—21no—
21#11718307—21no—
22#11718290—21no—
23C23×#261—22no—
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×C4×D13C2311yescharacteristic
27C22×Dic26—21no—
28C22×#1057—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×#6103—21no—
34C2×#6103—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13C2×C411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44#88150—44no—
45#88142—42no—
46C42×D13—42no—
47(C2×#261)⋊C4—24no—
48(C2×#261)⋊C4—24no—
49(C2×#261)⋊C4—42no—
50#88111—22no—
51#88111Q814yescomplemented
52#88110—42no—
53C13×#95—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#9888—131nomaximal, Sylow
58C23×D13C2×D411yescharacteristic
59C22×#261—24no—
60C22×#261—42no—
61C22×#261—42no—
62C22×#261—42no—
63C22×#261—42no—
64C22×#261—42no—
65C22×#261—42no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×Dic13—21no—
72C22×Dic13—21no—
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C22⋊C411yescharacteristic
75C22×Dic13C2×D411yescharacteristic
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13C2×Q812yes—
85C2×C4×D13#4112yes—
86C2×Dic26—42no—
87C2×Dic26—42no—
88C2×Dic26—42no—
89C2×#1057—24no—
90C2×#1057—42no—
91C2×#1057—42no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—42no—
95C42×C13—41no—
96#6103—42no—
97#6103—42no—
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6101—42no—
101#6101—42no—
102#6101—42no—
103#6101—42no—
104C4×Dic13—22no—
105C4×Dic13—22no—
106C4×Dic13—41no—
107#2857—131no—
108#1749—131no—
109#1434—131no—
110#1294—132no—
111#1294—132no—
112C23×C13C2×C22⋊C411yescharacteristic
113C22×D13—21no—
114C22×D13—21no—
115C22×D13—21no—
116C22×D13—21no—
117C22×D13#12411yescharacteristic
118C22×D13C4⋊Q811yescharacteristic
119C22×D13AGL(1,ℤ/8)12yes—
120C22×D13#13712yes—
121C2×#261—44no—
122C2×#261—44no—
123C2×#261—44no—
124C2×#261—82no—
125C2×#261—82no—
126C2×#261—82no—
127C2×#261—82no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13C4×Q812yes—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—21no—
146C2×Dic13—21no—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13#9912yes—
156C2×Dic13#10412yes—
157C2×Dic13C22⋊Q812yes—
158C4×D13—42no—
159C4×D13—42no—
160C4×D13—44no—
161C4×D13—44no—
162Dic26—84no—
163#1057—44no—
164C2×C4⋊Q8—131no—
165C2×C22⋊Q8—261no—
166C22×C42—131no—
167C2×C22⋊C8—132no—
168C2×#97—261no—
169#391—261no—
170#389—131no—
171#389—261no—
172#389#26111yescharacteristic, complemented
173#384—131no—
174#380—131no—
175#380—131no—
176#380—261no—
177C2×#95—132no—
178C2×#95—261no—
179C2×#95—261no—
180#336—261no—
181C22×C13#39111yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13#41011yescharacteristic
184C22×C13#41811yescharacteristic
185C22×C13#41911yescharacteristic
186C22×C13C2×#10411yescharacteristic
187C22×C13#42111yescharacteristic
188C2×D13—21no—
189C2×D13—21no—
190C2×D13—21no—
191C2×D13—21no—
192C2×D13—22no—
193C2×D13—22no—
194C2×D13—22no—
195C2×D13—22no—
196C2×D13#48912yes—
197C2×D13#50112yes—
198#261—84no—
199C4×C13—22no—
200C4×C13—41no—
201C4×C13—41no—
202C4×C13—81no—
203C4×C13—81no—
204Dic13—22no—
205Dic13—22no—
206Dic13—22no—
207Dic13—81no—
208Dic13—81no—
209C22×Q8—261no—
210C23×C4—131no—
211C23×C4—131no—
212C23×C4—131no—
213C23×C4—262no—
214C22×C8—262no—
215C4⋊Q8—522no—
216C22⋊Q8—524no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—131no—
219C2×C4⋊C4—131no—
220C2×C4⋊C4—261no—
221C2×C4⋊C4—261no—
222C2×C4⋊C4—261no—
223C2×C4⋊C4—261no—
224C2×C4⋊C4C2×#26111yescharacteristic
225C2×C4⋊C4C2×#26111yescharacteristic
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C42—131no—
229C2×C42—131no—
230C2×C42—131no—
231C2×C42—522no—
232C2×C42C2×#26111yescharacteristic
233C22⋊C8—134no—
234C22⋊C8—262no—
235#97—522no—
236#95—21no—
237#95—261no—
238#95—261no—
239#95—264no—
240#95—264no—
241#95—261no—
242#95—522no—
243C2×C13#150611yescharacteristic
244C2×C13#150711yescharacteristic
245C2×C13#151111yescharacteristic
246C2×C13#151411yescharacteristic
247C2×C13#198611yescharacteristic
248C2×C13#199311yescharacteristic
249C2×C13#199611yescharacteristic
250D13—22no—
251D13—22no—
252C24—131no—
253C2×Q8—522no—
254C2×Q8—522no—
255C2×Q8—522no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—131no—
259C22×C4—131no—
260C22×C4—131no—
261C22×C4—132no—
262C22×C4—132no—
263C22×C4—262no—
264C22×C4—262no—
265C22×C4—262no—
266C22×C4—262no—
267C22×C4—264no—
268C22×C4—261no—
269C22×C4—261no—
270C22×C4—521no—
271C22×C4—521no—
272C22×C4—521no—
273C22×C4—521no—
274C22×C4—522no—
275C22×C4—522no—
276C22×C4—522no—
277C22×C4—522no—
278C22×C4—522no—
279C22×C4—522no—
280C22×C4C22⋊#26111yescharacteristic
281C22×C4C22⋊#26111yescharacteristic
282C22×C4C22×#26111yescharacteristic
283C2×C8—264no—
284C2×C8—522no—
285C2×C8—522no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—42no—
289C4⋊C4—521no—
290C4⋊C4—521no—
291C4⋊C4—522no—
292C4⋊C4—522no—
293C4⋊C4—522no—
294C4⋊C4—522no—
295C22⋊C4—522no—
296C22⋊C4—522no—
297C42—41no—
298C42—262no—
299C42—262no—
300C42—521no—
301C13#988811yescharacteristic, complemented, Sylow
302C23—132no—
303C23—132no—
304C23—131no—
305C23—131no—
306C23—261no—
307C23—261no—
308C23—261no—
309C23—261no—
310C23C2×C22⋊#26111yescharacteristic
311Q8—1044no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—132no—
327C2×C4—132no—
328C2×C4—132no—
329C2×C4—261no—
330C2×C4—261no—
331C2×C4—261no—
332C2×C4—261no—
333C2×C4—261no—
334C2×C4—261no—
335C2×C4—522no—
336C2×C4—522no—
337C2×C4—524no—
338C2×C4—524no—
339C2×C4—524no—
340C2×C4—524no—
341C2×C4—524no—
342C2×C4—521no—
343C2×C4—521no—
344C2×C4—521no—
345C2×C4—521no—
346C2×C4—521no—
347C2×C4—521no—
348C2×C4—1042no—
349C2×C4—1042no—
350C2×C4—1042no—
351C2×C4—1042no—
352C2×C4Q8×#26112yes—
353C8—524no—
354C22—132no—
355C22—132no—
356C22—262no—
357C22—261no—
358C22—261no—
359C22—262no—
360C22—261no—
361C22—261no—
362C22—262no—
363C22—262no—
364C22#1171911611yescharacteristic
365C22#1171913811yescharacteristic
366C22D13⋊#9911yescharacteristic
367C22#1171915311yescharacteristic
368C22(C2×#261)⋊Q811yescharacteristic
369C22D13⋊#10411yescharacteristic
370C22#1171916611yescharacteristic
371C4—22no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—262no—
377C4—262no—
378C4—262no—
379C4—1044no—
380C4—1041no—
381C4—1041no—
382C2—262no—
383C2—262no—
384C2#1313022911yescharacteristic
385C2#1313023111yescharacteristic
386C2#1313024511yescharacteristic
387C2#1313025511yescharacteristic
388C2#1313101311yescharacteristic
389C2#1313102011yescharacteristic
390C2#1313102711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#389#261
hypocenterC13#9888
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
7. C2×#88142C4semidirect
14. C13×#389C4semidirect
17. #11718637C4semidirect
19. #11718589C4semidirect
51. #88111Q8semidirect
172. #389#261semidirect
301. C13#9888semidirect

Maximal subgroups

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

subgroupindex
#131305632
#131300122
#131297092
#131231872
#988813