Finite Group Databasebeta

← #16785153

Subgroups — #16785153

Order 3328.

684 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 120 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#13130693C211yesmaximal, characteristic
2C4×(C2×#261)⋊C4C211yesmaximal, characteristic
3#13129709C212yesmaximal
4#13129709C212yesmaximal
5#13123187C211yesmaximal, characteristic
6C22×C4×#261—21no—
7C2×#88150—21no—
8C2×#88142C411yescharacteristic, complemented
9C2×C42×D13C2211yescharacteristic
10C2×(C2×#261)⋊C4—21no—
11C2×(C2×#261)⋊C4C2212yes—
12C2×#88112—21no—
13C2×#88111C2212yes—
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×C4×#261—24no—
30C2×C4×#261—42no—
31C2×C4×#261—42no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C42×C13C2×C411yescharacteristic
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×#6101—21no—
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×C4×Dic13C2×C411yescharacteristic
45C2×C4×Dic13D411yescharacteristic
46C2×C4×Dic13D411yescharacteristic
47#88150—44no—
48#88142—42no—
49C42×D13—42no—
50(C2×#261)⋊C4—24no—
51(C2×#261)⋊C4—22no—
52(C2×#261)⋊C4Q814yescomplemented
53#88112—42no—
54#88111—24no—
55C13×#95—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#9908—131nomaximal, Sylow
60C23×D13C2×D411yescharacteristic
61C22×#261—24no—
62C22×#261—24no—
63C22×#261—24no—
64C22×#261—42no—
65C22×#261—42no—
66C22×#261—42no—
67C22×#261—42no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22×C411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13C22⋊C411yescharacteristic
76C22×Dic13C22⋊C411yescharacteristic
77C22×Dic13C2×D411yescharacteristic
78C2×C4×D13—22no—
79C2×C4×D13—22no—
80C2×C4×D13—22no—
81C2×C4×D13—22no—
82C2×C4×D13—41no—
83C2×C4×D13—41no—
84C2×C4×D13—41no—
85C2×C4×D13SD1612yes—
86C2×C4×D13Q1612yes—
87C2×C4×D13C2×Q812yes—
88C2×C4×D13#4112yes—
89C2×Dic26—42no—
90C2×Dic26—42no—
91C2×Dic26—42no—
92C2×#1057—42no—
93C2×#1057—42no—
94C2×#1057—42no—
95C4×#261—48no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—42no—
99C42×C13—41no—
100#6103—42no—
101#6103—42no—
102C4⋊Dic13—41no—
103C4⋊Dic13—41no—
104#6101—42no—
105#6101—42no—
106#6101—42no—
107#6101—42no—
108C4×Dic13—22no—
109C4×Dic13—22no—
110C4×Dic13—41no—
111#2857—131no—
112#1797—131no—
113C4×#95—131no—
114#1294—132no—
115#1294—132no—
116C23×C13C2×C22⋊C411yescharacteristic
117C22×D13—21no—
118C22×D13—21no—
119C22×D13—21no—
120C22×D13—21no—
121C22×D13C22⋊Q812yes—
122C22×D13C2×SD1611yescharacteristic
123C22×D13C2×Q1611yescharacteristic
124C22×D13AGL(1,ℤ/8)12yes—
125C2×#261—28no—
126C2×#261—44no—
127C2×#261—44no—
128C2×#261—44no—
129C2×#261—44no—
130C2×#261—44no—
131C2×#261—44no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—21no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13#10312yes—
146C2×C4×C13C4×Q812yes—
147C2×Dic13—21no—
148C2×Dic13—21no—
149C2×Dic13—21no—
150C2×Dic13—21no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154C2×Dic13—41no—
155C2×Dic13—41no—
156C2×Dic13—41no—
157C2×Dic13#9912yes—
158C2×Dic13#10312yes—
159C2×Dic13#10412yes—
160C2×Dic13#10412yes—
161C2×Dic13#12411yescharacteristic
162C2×Dic13C4⋊Q811yescharacteristic
163C4×D13—24no—
164C4×D13—24no—
165C4×D13—42no—
166C4×D13—42no—
167C4×D13—44no—
168Dic26—84no—
169#1057—82no—
170C2×C4⋊Q8—131no—
171C2×C22⋊Q8—261no—
172C22×C42—131no—
173C22×C42—261no—
174C2×C4⋊C8—261no—
175C2×C22⋊C8—132no—
176#391—261no—
177#389—131no—
178#389—261no—
179#389#26111yescharacteristic, complemented
180#384—131no—
181#380—131no—
182#380—131no—
183#380—261no—
184C2×#95—132no—
185C2×#95—261no—
186#336—261no—
187C22×C13#39111yescharacteristic
188C22×C13C2×#9911yescharacteristic
189C22×C13#41011yescharacteristic
190C22×C13C2×#10311yescharacteristic
191C22×C13#41811yescharacteristic
192C22×C13C2×#10411yescharacteristic
193C22×C13C2×#10411yescharacteristic
194C2×D13—22no—
195C2×D13—22no—
196C2×D13—21no—
197C2×D13—21no—
198C2×D13—21no—
199C2×D13—21no—
200C2×D13—22no—
201C2×D13—22no—
202C2×D13#47612yes—
203C2×D13#47712yes—
204#261—48no—
205C4×C13—22no—
206C4×C13—22no—
207C4×C13—41no—
208C4×C13—81no—
209C4×C13—81no—
210Dic13—21no—
211Dic13—21no—
212Dic13—22no—
213Dic13—81no—
214Dic13—81no—
215Dic13#32814yes—
216C22×Q8—261no—
217C23×C4—131no—
218C23×C4—131no—
219C23×C4—131no—
220C23×C4—262no—
221C22×C8—262no—
222C4⋊Q8—522no—
223C22⋊Q8—524no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—131no—
226C2×C4⋊C4—131no—
227C2×C4⋊C4—261no—
228C2×C4⋊C4—261no—
229C2×C4⋊C4—261no—
230C2×C4⋊C4—261no—
231C2×C4⋊C4C2×#26111yescharacteristic
232C2×C4⋊C4C2×#26111yescharacteristic
233C2×C22⋊C4—261no—
234C2×C22⋊C4—261no—
235C2×C42—131no—
236C2×C42—131no—
237C2×C42—131no—
238C2×C42—264no—
239C2×C42—522no—
240C2×C42—522no—
241C2×C42—522no—
242C2×C42C2×#26111yescharacteristic
243C4⋊C8—522no—
244C22⋊C8—264no—
245#95—21no—
246#95—134no—
247#95—261no—
248#95—261no—
249#95—262no—
250#95—264no—
251#95—261no—
252C2×C13C2×#32811yescharacteristic
253C2×C13#150311yescharacteristic
254C2×C13#150511yescharacteristic
255C2×C13#150711yescharacteristic
256C2×C13#198711yescharacteristic
257C2×C13#199411yescharacteristic
258C2×C13#199611yescharacteristic
259D13—22no—
260D13—22no—
261C24—131no—
262C2×Q8—522no—
263C2×Q8—522no—
264C2×Q8—522no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—131no—
268C22×C4—131no—
269C22×C4—131no—
270C22×C4—132no—
271C22×C4—132no—
272C22×C4—132no—
273C22×C4—132no—
274C22×C4—262no—
275C22×C4—262no—
276C22×C4—262no—
277C22×C4—262no—
278C22×C4—264no—
279C22×C4—264no—
280C22×C4—264no—
281C22×C4—261no—
282C22×C4—261no—
283C22×C4—521no—
284C22×C4—521no—
285C22×C4—521no—
286C22×C4—522no—
287C22×C4—522no—
288C22×C4—522no—
289C22×C4—522no—
290C22×C4C22⋊#26111yescharacteristic
291C22×C4C22⋊#26111yescharacteristic
292C22×C4C22×#26111yescharacteristic
293C2×C8—522no—
294C2×C8—522no—
295C2×C8—522no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—42no—
299C4⋊C4—521no—
300C4⋊C4—521no—
301C4⋊C4—522no—
302C4⋊C4—522no—
303C4⋊C4—522no—
304C4⋊C4—522no—
305C22⋊C4—522no—
306C22⋊C4—522no—
307C42—41no—
308C42—262no—
309C42—262no—
310C42—521no—
311C42—528no—
312C13#990811yescharacteristic, complemented, Sylow
313C23—132no—
314C23—131no—
315C23—131no—
316C23—132no—
317C23—261no—
318C23—261no—
319C23—261no—
320C23—261no—
321C23C2×C22⋊#26111yescharacteristic
322Q8—1044no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—132no—
337C2×C4—132no—
338C2×C4—132no—
339C2×C4—131no—
340C2×C4—131no—
341C2×C4—132no—
342C2×C4—264no—
343C2×C4—264no—
344C2×C4—261no—
345C2×C4—261no—
346C2×C4—261no—
347C2×C4—261no—
348C2×C4—268no—
349C2×C4—522no—
350C2×C4—522no—
351C2×C4—524no—
352C2×C4—524no—
353C2×C4—524no—
354C2×C4—524no—
355C2×C4—524no—
356C2×C4—524no—
357C2×C4—524no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4#8811712yes—
365C2×C4Q8×#26112yes—
366C8—1042no—
367C22—132no—
368C22—132no—
369C22—262no—
370C22—262no—
371C22—261no—
372C22—261no—
373C22—261no—
374C22—261no—
375C22—262no—
376C22—262no—
377C22#1171911611yescharacteristic
378C22#1171913811yescharacteristic
379C22D13⋊#9911yescharacteristic
380C22C2×#8811711yescharacteristic
381C22(C2×#261)⋊Q811yescharacteristic
382C22D13⋊#10411yescharacteristic
383C22D13⋊#10411yescharacteristic
384C4—22no—
385C4—22no—
386C4—41no—
387C4—81no—
388C4—81no—
389C4—134no—
390C4—261no—
391C4—261no—
392C4—262no—
393C4—528no—
394C4—1041no—
395C4—1041no—
396C2—262no—
397C2—262no—
398C2D13⋊#32811yescharacteristic
399C2#1313021811yescharacteristic
400C2#1313022611yescharacteristic
401C2#1313023111yescharacteristic
402C2#1313101411yescharacteristic
403C2#1313102211yescharacteristic
404C2#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#9908
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
8. C2×#88142C4semidirect
14. C13×#389C4semidirect
17. #11718637C4semidirect
19. #11718589C4semidirect
52. (C2×#261)⋊C4Q8semidirect
179. #389#261semidirect
312. C13#9908semidirect

Maximal subgroups

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

subgroupindex
#131306932
C4×(C2×#261)⋊C42
#131297092
#131231872
#990813