Finite Group Databasebeta

← #16784521

Subgroups — #16784521

Order 3328.

582 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 148 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#13130768C211yesmaximal, characteristic, complemented
2#13130550C211yesmaximal, characteristic, complemented
3C2×Q8⋊#1057C212yesmaximal, complemented
4C2×D4⋊#1057C212yesmaximal
5#124×Dic13C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic
7C2×Q8×Dic13C2211yescharacteristic
8C2×D4×Dic13C2211yescharacteristic
9C2×C4⋊#1057—22no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12#11718891C411yescharacteristic
13#11718882C411yescharacteristic
14#11718612—22no—
15C22⋊C4×Dic13—22no—
16#11718597C411yescharacteristic
17C42×Dic13C2211yescharacteristic
18Q8⋊#1057—24no—
19D4⋊#1057—24no—
20#11718290—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C22×D4×C13C2×C411yescharacteristic
23C23×Dic13—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C13×#124—22no—
27C13×#124C814yescomplemented
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
44C4⋊#1057—22no—
45C4⋊#1057—22no—
46C4⋊#1057—44no—
47C4×#1057—22no—
48C4×#1057D414yes—
49#88071—22no—
50#88071—22no—
51#9640—131nomaximal, Sylow
52C24×C13—21no—
53C2×Q8×C13—21no—
54C2×Q8×C13—22no—
55C2×Q8×C13—22no—
56C2×Q8×C13C2×C812yes—
57C2×D4×C13—22no—
58C2×D4×C13—21no—
59C2×D4×C13—22no—
60C2×D4×C13C2×C812yes—
61C22×C4×C13—21no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—21no—
65C22×Dic13—21no—
66C22×Dic13—41no—
67C22×Dic13—41no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13C22⋊C412yes—
71C22×Dic13C2×D411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C2×#1057—24no—
74C2×#1057—44no—
75C2×#1057—42no—
76C2×#1057—44no—
77C13×C22⋊C4—28no—
78C42×C13C2×C812yes—
79C42×C13M1612yes—
80C22⋊Dic13—44no—
81C22⋊Dic13—42no—
82C4⋊Dic13—22no—
83C4⋊Dic13—22no—
84C4⋊Dic13—42no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—42no—
89C4×Dic13—41no—
90C4×Dic13—41no—
91C4×Dic13C2×D412yes—
92C4×Dic13#4112yes—
93C4×#124—131no—
94#1842—131no—
95#1744—131no—
96C2×Q8⋊C8—132no—
97C2×D4⋊C8—132no—
98C23×C13—22no—
99C23×C13—41no—
100C23×C13—41no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—24no—
105Q8×C13—42no—
106D4×C13—24no—
107D4×C13—42no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13C22⋊C814yes—
114C2×C4×C13C4×D412yes—
115C2×C4×C13C22×C811yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13#13112yes—
118C2×Dic13—22no—
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#12112yes—
130C2×Dic13#12411yescharacteristic
131C2×Dic13#12711yescharacteristic
132C2×Dic13AGL(1,ℤ/8)12yes—
133C2×Dic13#13712yes—
134#1057—44no—
135#1057—82no—
136C2×#124#26111yescharacteristic
137C2×C4×Q8—131no—
138C2×C4×D4—131no—
139C2×C4⋊C8—132no—
140C2×C4⋊C8—262no—
141C2×C4×C8—132no—
142#391—131no—
143#390—131no—
144#388—262no—
145#382—131no—
146C4×C22⋊C4—262no—
147C43—131no—
148#336—262no—
149Q8⋊C8—264no—
150D4⋊C8—264no—
151C22×C13—42no—
152C22×C13—44no—
153C22×C13—81no—
154C22×C13—81no—
155C22×C13—82no—
156C22×C13#39011yescharacteristic
157C22×C13C2×C22⋊C811yescharacteristic
158C22×C13#40811yescharacteristic
159C22×C13#41712yes—
160C22×C13#42112yes—
161C4×C13—24no—
162C4×C13—42no—
163C4×C13C8×D412yes—
164C4×C13#43612yes—
165Dic13—22no—
166Dic13—42no—
167Dic13—81no—
168Dic13—81no—
169Dic13#48912yes—
170Dic13#49611yescharacteristic
171Dic13#49711yescharacteristic
172C22×Q8C2×#26111yescharacteristic
173C22×D4C2×#26111yescharacteristic
174C23×C4—261no—
175C22×C8—262no—
176C22×C8—262no—
177#124—22no—
178#124#105714yescomplemented
179C4×Q8—262no—
180C4×Q8—262no—
181C4×D4—262no—
182C4×D4—262no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—261no—
188C2×C22⋊C4—262no—
189C2×C42—131no—
190C2×C42—132no—
191C2×C42—131no—
192C2×C42—132no—
193C2×C42—261no—
194C2×C42C2×#26111yescharacteristic
195C4⋊C8—262no—
196C4⋊C8—262no—
197C4⋊C8—524no—
198C4×C8—134no—
199C4×C8—262no—
200#95—262no—
201#95—262no—
202C2×C13—82no—
203C2×C13#147712yes—
204C2×C13#149512yes—
205C2×C13#195411yescharacteristic
206C2×C13#195911yescharacteristic
207C2×C13#196311yescharacteristic
208C24—21no—
209C2×Q8—21no—
210C2×Q8—22no—
211C2×Q8—22no—
212C2×Q8C2×#105712yes—
213C2×D4—22no—
214C2×D4—22no—
215C2×D4—21no—
216C2×D4C2×#105712yes—
217C22×C4—21no—
218C22×C4—131no—
219C22×C4—131no—
220C22×C4—132no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4—521no—
224C22×C4—521no—
225C22×C4—522no—
226C22×C4—522no—
227C22×C4C22⋊#26112yes—
228C22×C4C22×#26111yescharacteristic
229C2×C8—264no—
230C2×C8—524no—
231C2×C8—522no—
232C2×C8—524no—
233C4⋊C4—262no—
234C4⋊C4—262no—
235C4⋊C4—522no—
236C22⋊C4—28no—
237C22⋊C4—522no—
238C22⋊C4—524no—
239C42—132no—
240C42—132no—
241C42—262no—
242C42—262no—
243C42—262no—
244C42—522no—
245C42—521no—
246C42—521no—
247C42C2×#105712yes—
248C42#612212yes—
249C13#964011yescharacteristic, complemented, Sylow
250C23—22no—
251C23—41no—
252C23—41no—
253C23—42no—
254C23—42no—
255C23C2×C22⋊#26111yescharacteristic
256Q8—24no—
257Q8—42no—
258D4—24no—
259D4—42no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—131no—
266C2×C4—131no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—132no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—262no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—1042no—
279C2×C4—1041no—
280C2×C4—1041no—
281C2×C4C22⋊#105714yes—
282C2×C4#8823812yes—
283C2×C4D4×#26112yes—
284C2×C4C22×#105711yescharacteristic
285C2×C4C2×#612211yescharacteristic
286C8—524no—
287C8—1042no—
288C22—44no—
289C22—42no—
290C22—82no—
291C22—81no—
292C22—81no—
293C22#1171914711yescharacteristic
294C22#1171915111yescharacteristic
295C22#1171916412yes—
296C22#1171916612yes—
297C22C2×C22⋊#105711yescharacteristic
298C4—24no—
299C4—42no—
300C4—132no—
301C4—131no—
302C4—131no—
303C4—262no—
304C4—522no—
305C4—1041no—
306C4—1041no—
307C4D4×#105712yes—
308C4#1171914512yes—
309C2—82no—
310C2#1313013112yes—
311C2#1313019212yes—
312C2#1313095711yescharacteristic
313C2#1313096611yescharacteristic
314C2#1313097311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×#124C4
socleC23×C13C2×C22⋊C4
prime radicalC22×D4×C13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×#124#261
hypocenterC13#9640
LCSG ▷ C2×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. #13130768C2semidirect
2. #13130550C2semidirect
3. C2×Q8⋊#1057C2semidirect
27. C13×#124C8semidirect
178. #124#1057semidirect
249. C13#9640semidirect

Maximal subgroups

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

subgroupindex
#131307682
#131305502
C2×Q8⋊#10572
C2×D4⋊#10572
#124×Dic132
#964013