Finite Group Databasebeta

← #16784542

Subgroups — #16784542

Order 3328.

610 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 128 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#13130769C211yesmaximal, characteristic, complemented
2C4×#88110C211yesmaximal, characteristic, complemented
3C2×Q8⋊#1057C212yesmaximal, complemented
4C2×D4⋊#1057C212yesmaximal
5#124×Dic13C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×D4×Dic13C2211yescharacteristic
9C2×#88112—22no—
10C2×#88110—22no—
11C2×C4⋊#1057C2212yes—
12C2×C4×#1057C2212yes—
13#11718891C411yescharacteristic
14#11718882C411yescharacteristic
15#11718612—22no—
16C22⋊C4×Dic13—22no—
17#11718597C411yescharacteristic
18C42×Dic13C2211yescharacteristic
19Q8⋊#1057—24no—
20D4⋊#1057—24no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13C2×C411yescharacteristic
23C23×Dic13—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C13×#124—22no—
27C13×#124—22no—
28C2×C13×C22⋊C4—22no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—21no—
32Q8×Dic13—22no—
33Q8×Dic13—22no—
34D4×Dic13—22no—
35D4×Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4×Dic13—21no—
40C2×C4×Dic13C2×C411yescharacteristic
41C2×C4×Dic13D412yes—
42C2×C4×Dic13D412yes—
43C2×C4×Dic13C2311yescharacteristic
44#88112—44no—
45#88110—28no—
46C4⋊#1057—22no—
47C4⋊#1057—22no—
48C4×#1057—22no—
49C4×#1057D414yes—
50#88071—22no—
51#88071—22no—
52#9646—131nomaximal, Sylow
53C24×C13—21no—
54C2×Q8×C13—21no—
55C2×Q8×C13—22no—
56C2×Q8×C13—22no—
57C2×Q8×C13M1612yes—
58C2×D4×C13—22no—
59C2×D4×C13—21no—
60C2×D4×C13—22no—
61C2×D4×C13M1612yes—
62C22×C4×C13—21no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C22×Dic13—41no—
68C22×Dic13—41no—
69C22×Dic13—42no—
70C22×Dic13—42no—
71C22×Dic13C22⋊C412yes—
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×#1057—28no—
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—44no—
78C13×C22⋊C4—28no—
79C42×C13—21no—
80C42×C13—21no—
81C22⋊Dic13—44no—
82C22⋊Dic13—42no—
83C4⋊Dic13—22no—
84C4⋊Dic13—22no—
85C4⋊Dic13—42no—
86C4×Dic13—22no—
87C4×Dic13—24no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—41no—
91C4×Dic13—41no—
92C4×Dic13C2×D412yes—
93C4×Dic13#4112yes—
94C4×#124—131no—
95#1842—131no—
96C4×#97—131no—
97C2×Q8⋊C8—132no—
98C2×D4⋊C8—132no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13C2×C22⋊C411yescharacteristic
105Q8×C13—24no—
106Q8×C13—42no—
107D4×C13—24no—
108D4×C13—42no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13C4×D412yes—
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13C2×M1611yescharacteristic
118C2×C4×C13#13112yes—
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—22no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—82no—
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13#10414yes—
130C2×Dic13#12112yes—
131C2×Dic13#12411yescharacteristic
132C2×Dic13#12711yescharacteristic
133C2×Dic13AGL(1,ℤ/8)12yes—
134C2×Dic13#13712yes—
135#1057—28no—
136#1057—82no—
137C2×#124#26111yescharacteristic
138C2×C4×Q8—131no—
139C2×C4×D4—131no—
140C2×C4⋊C8—132no—
141C2×C4⋊C8—262no—
142C2×#97—262no—
143C2×C4×C8—132no—
144#391—131no—
145#390—131no—
146#388—262no—
147#382—131no—
148C4×C22⋊C4—262no—
149C43—131no—
150Q8⋊C8—264no—
151D4⋊C8—264no—
152C22×C13—42no—
153C22×C13—44no—
154C22×C13—81no—
155C22×C13—81no—
156C22×C13—82no—
157C22×C13#39011yescharacteristic
158C22×C13#40711yescharacteristic
159C22×C13#40811yescharacteristic
160C22×C13#41712yes—
161C22×C13C2×#10412yes—
162C4×C13—42no—
163C4×C13—42no—
164C4×C13#43512yes—
165C4×C13#43512yes—
166Dic13—22no—
167Dic13—24no—
168Dic13—81no—
169Dic13—81no—
170Dic13#48912yes—
171Dic13#49611yescharacteristic
172Dic13#49711yescharacteristic
173C22×Q8C2×#26111yescharacteristic
174C22×D4C2×#26111yescharacteristic
175C23×C4—261no—
176C22×C8—262no—
177C22×C8—262no—
178#124—22no—
179#124—22no—
180C4×Q8—262no—
181C4×Q8—262no—
182C4×D4—262no—
183C4×D4—262no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—261no—
187C2×C22⋊C4—22no—
188C2×C22⋊C4—261no—
189C2×C22⋊C4—262no—
190C2×C42—131no—
191C2×C42—132no—
192C2×C42—132no—
193C2×C42—131no—
194C2×C42—261no—
195C2×C42C2×#26111yescharacteristic
196C4⋊C8—262no—
197C4⋊C8—262no—
198C4⋊C8—524no—
199#97—268no—
200C4×C8—134no—
201C4×C8—262no—
202#95—262no—
203#95—262no—
204C2×C13—82no—
205C2×C13#148312yes—
206C2×C13#148912yes—
207C2×C13#195511yescharacteristic
208C2×C13#195911yescharacteristic
209C2×C13#196211yescharacteristic
210C24—21no—
211C2×Q8—21no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8#612212yes—
215C2×D4—22no—
216C2×D4—22no—
217C2×D4—21no—
218C2×D4#612212yes—
219C22×C4—21no—
220C22×C4—131no—
221C22×C4—132no—
222C22×C4—131no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4—522no—
228C22×C4—522no—
229C22×C4C22⋊#26112yes—
230C22×C4C22×#26111yescharacteristic
231C2×C8—264no—
232C2×C8—268no—
233C2×C8—522no—
234C2×C8—524no—
235C4⋊C4—262no—
236C4⋊C4—262no—
237C4⋊C4—522no—
238C22⋊C4—28no—
239C22⋊C4—522no—
240C22⋊C4—524no—
241C42—21no—
242C42—21no—
243C42—132no—
244C42—132no—
245C42—264no—
246C42—262no—
247C42—262no—
248C42—262no—
249C42—521no—
250C42—521no—
251C13#964611yescharacteristic, complemented, Sylow
252C23—22no—
253C23—41no—
254C23—41no—
255C23—42no—
256C23—42no—
257C23C2×C22⋊#26111yescharacteristic
258Q8—24no—
259Q8—42no—
260D4—24no—
261D4—42no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—132no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—134no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—1042no—
282C2×C4—1041no—
283C2×C4—1041no—
284C2×C4#8823812yes—
285C2×C4D4×#26112yes—
286C2×C4C2×#612211yescharacteristic
287C2×C4C2×#612211yescharacteristic
288C8—268no—
289C8—1042no—
290C22—44no—
291C22—42no—
292C22—82no—
293C22—81no—
294C22—81no—
295C22#1171914711yescharacteristic
296C22#1171915111yescharacteristic
297C22D13⋊#10412yes—
298C22#1171916412yes—
299C22#1171916911yescharacteristic
300C4—42no—
301C4—42no—
302C4—132no—
303C4—131no—
304C4—131no—
305C4—264no—
306C4—262no—
307C4—1041no—
308C4—1041no—
309C4#1171914412yes—
310C4#1171914412yes—
311C2—82no—
312C2#1313015212yes—
313C2#1313017112yes—
314C2#1313096011yescharacteristic
315C2#1313096611yescharacteristic
316C2#1313097111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC2×C13×#124C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×#124#261
hypocenterC13#9646
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #13130769C2semidirect
2. C4×#88110C2semidirect
3. C2×Q8⋊#1057C2semidirect
251. C13#9646semidirect

Maximal subgroups

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

subgroupindex
#131307692
C4×#881102
C2×Q8⋊#10572
C2×D4⋊#10572
#124×Dic132
#964613