Finite Group Databasebeta

← #15760709

Subgroups — #15760709

Order 3328.

556 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 123 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#13123865C211yesmaximal, characteristic
2#13114926C212yesmaximal, complemented
3#13114824C211yesmaximal, characteristic
4#13112703C212yesmaximal, complemented
5C13×#2487C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400C412yescomplemented
9C13×#399C412yescomplemented
10C13×#389—21no—
11C13×#386—21no—
12C13×#385—21no—
13C13×#380—21no—
14C13×#380C2211yescharacteristic
15C2×#88074—21no—
16#11718873C2212yes—
17#11718868—21no—
18C2×C22⋊#1055C2212yes—
19#11718672—24no—
20#11718587—21no—
21#11718121—24no—
22#11718118—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—22no—
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4C2×C411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C22⋊Dic13—22no—
42C2×C4⋊Dic13—22no—
43C2×#6099—22no—
44C22×#1055D414yes—
45C13×#95—22no—
46C13×#95—22no—
47C13×#95C2×C412yes—
48#88074—42no—
49#88071—22no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53C4⋊#1055—22no—
54#88043—22no—
55#9473—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C2×D411yescharacteristic
58C2×D4×C13—22no—
59C2×D4×C13—21no—
60C2×D4×C13—22no—
61C2×D4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—82no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D412yes—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13#4112yes—
77C22×Dic13—42no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—82no—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—82no—
89C42×C13—21no—
90C42×C13—21no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—44no—
94#6099—82no—
95C2×#1055—24no—
96C2×#1055—44no—
97#2973—131no—
98#2487D1311yescharacteristic
99#1824—132no—
100#1799—131no—
101#1289—132no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13C2×C22⋊C411yescharacteristic
110C23×C13#12112yes—
111C23×C13AGL(1,ℤ/8)11yescharacteristic
112C23×C13#13711yescharacteristic
113C23×C13#13712yes—
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—24no—
117C2×C4×C13—22no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—81no—
135C2×C4×C13—84no—
136C2×C4×C13C4×D412yes—
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12311yescharacteristic
139C2×Dic13—82no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142#1055—44no—
143C2×C4×D4C2×D1311yescharacteristic
144C22×C4⋊C4C2×D1311yescharacteristic
145#435—264no—
146#432—261no—
147C2×#99—261no—
148#407—261no—
149C2×C22⋊C8—132no—
150#400Dic1312yescomplemented
151#399Dic1312yescomplemented
152#389—21no—
153#386—21no—
154#385—21no—
155#380—21no—
156#380—132no—
157#380C2×D1311yescharacteristic
158#342—261no—
159#340—264no—
160C22×C13—22no—
161C22×C13—21no—
162C22×C13—22no—
163C22×C13—21no—
164C22×C13—41no—
165C22×C13—42no—
166C22×C13—41no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—81no—
172C22×C13#38611yescharacteristic
173C22×C13#41711yescharacteristic
174C22×C13#41911yescharacteristic
175C22×C13#46812yes—
176C22×C13#47012yes—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—41no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—82no—
183C4×C13—82no—
184C4×C13#45812yes—
185Dic13—162no—
186C22×D4C22⋊D1311yescharacteristic
187C23×C4—21no—
188C23×C4C22⋊D1311yescharacteristic
189C23×C4C22×D1311yescharacteristic
190C2×M16—262no—
191C22×C8—134no—
192C4×D4—22no—
193C4×D4—22no—
194C2×C4⋊C4—22no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4C2×Dic1312yes—
201C2×C4⋊C4C2×Dic1311yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—262no—
205C2×C22⋊C4C2×Dic1311yescharacteristic
206C2×C22⋊C4C22⋊D1311yescharacteristic
207C2×C42C22⋊D1311yescharacteristic
208C4⋊C8—262no—
209#99—522no—
210C22⋊C8—262no—
211C22⋊C8—262no—
212C22⋊C8—262no—
213#97—262no—
214#95—22no—
215#95—22no—
216#95—262no—
217#95C2×Dic1312yes—
218C2×C13—22no—
219C2×C13—21no—
220C2×C13—21no—
221C2×C13—22no—
222C2×C13—81no—
223C2×C13#189011yescharacteristic
224C2×C13#189411yescharacteristic
225C2×C13#191011yescharacteristic
226C24C22⋊Dic1311yescharacteristic
227C24C2×C22⋊D1311yescharacteristic
228C2×D4—22no—
229C2×D4—22no—
230C2×D4—21no—
231C2×D4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—42no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—82no—
240C22×C4—522no—
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4D4×D1312yes—
245C22×C4#612912yes—
246C22×C4C22×Dic1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248M16—1042no—
249C2×C8—264no—
250C2×C8—524no—
251C4⋊C4—22no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—82no—
257C4⋊C4—524no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—82no—
263C22⋊C4—522no—
264C22⋊C4—522no—
265C42—21no—
266C42—21no—
267C13#947311yescharacteristic, complemented, Sylow
268C23—21no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23#8819312yes—
276C23#8819612yes—
277C23#8820311yescharacteristic
278C23#8820511yescharacteristic
279C23C2×C22⋊Dic1311yescharacteristic
280D4—42no—
281D4—42no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—81no—
301C2×C4—84no—
302C2×C4—1042no—
303C2×C4—1042no—
304C2×C4—1042no—
305C2×C4D4×Dic1312yes—
306C2×C4#8818911yescharacteristic
307C2×C4#8819111yescharacteristic
308C8—524no—
309C22—21no—
310C22—22no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1171871012yes—
322C22#1171871312yes—
323C22#1171888111yescharacteristic
324C22#1171888611yescharacteristic
325C22#1171889311yescharacteristic
326C4—21no—
327C4—22no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—82no—
332C4—82no—
333C4—2082no—
334C4#1171871412yes—
335C2—21no—
336C2—22no—
337C2—21no—
338C2—22no—
339C2—81no—
340C2#1311525011yescharacteristic
341C2#1311527011yescharacteristic
342C2#1311536411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2487C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2487D13
hypocenterC13#9473
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2487

Complements

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

NH ≅ G/Ntype
2. #13114926C2semidirect
4. #13112703C2semidirect
8. C13×#400C4semidirect
9. C13×#399C4semidirect
150. #400Dic13semidirect
151. #399Dic13semidirect
267. C13#9473semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131149262
#131148242
#131127032
C13×#24872
#947313