Finite Group Databasebeta

← #16782190

Subgroups — #16782190

Order 3328.

630 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 132 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
2#13130693C211yesmaximal, characteristic
3#13129714C214yesmaximal, complemented
4D13×#384C211yesmaximal, characteristic
5C2×C4⋊C4×D13—21no—
6C2×C4⋊C4×D13—21no—
7C2×C4⋊C4×D13C412yes—
8C2×C42×D13C2211yescharacteristic
9C2×#88112C2212yes—
10C2×#88112C2212yes—
11C2×#88111—21no—
12C2×#88111—21no—
13C13×#384C411yescharacteristic
14#11718637—21no—
15#11718637—21no—
16#11718637C2212yes—
17#11718596C411yescharacteristic
18#11718290—21no—
19#11718290—21no—
20C22×C4×D13—22no—
21C22×C4×D13C2×C411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C412yes—
33C2×#6101—22no—
34C2×#6101—22no—
35C2×#6101—22no—
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13C2311yescharacteristic
39C4⋊C4×D13—44no—
40C4⋊C4×D13—42no—
41C4⋊C4×D13—42no—
42C4⋊C4×D13—44no—
43C42×D13—24no—
44#88112—24no—
45#88112—24no—
46#88111—42no—
47#88111—42no—
48#8724—131nomaximal, Sylow
49C23×D13C22⋊C411yescharacteristic
50C22×C4×C13—22no—
51C22×C4×C13C22⋊C411yescharacteristic
52C22×C4×C13C22⋊C411yescharacteristic
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—22no—
55C22×Dic13C22⋊C411yescharacteristic
56C22×Dic13C2×D411yescharacteristic
57C22×Dic13C2×D411yescharacteristic
58C2×C4×D13—22no—
59C2×C4×D13—22no—
60C2×C4×D13—22no—
61C2×C4×D13—22no—
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—44no—
66C2×C4×D13—44no—
67C2×C4×D13—44no—
68C2×C4×D13D812yes—
69C2×C4×D13SD1612yes—
70C2×C4×D13SD1612yes—
71C2×C4×D13Q1612yes—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C2×#1057—42no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—42no—
81C42×C13—22no—
82C4⋊Dic13—42no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85#6101—44no—
86#6101—42no—
87#6101—42no—
88#6101—44no—
89C4×Dic13—22no—
90C4×Dic13—22no—
91C4×Dic13#4114yes—
92C2×#384—131no—
93#1797—131no—
94#1797—131no—
95#1296—134no—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—21no—
101C22×D13#10112yes—
102C22×D13#10212yes—
103C22×D13#10312yes—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—42no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13#10212yes—
114C2×C4×C13#10312yes—
115C2×C4×C13#11712yes—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—42no—
119C2×Dic13—42no—
120C2×Dic13—42no—
121C2×Dic13#10012yes—
122C2×Dic13#12312yes—
123C2×Dic13#12312yes—
124C2×Dic13C2×D811yescharacteristic
125C2×Dic13C2×SD1611yescharacteristic
126C2×Dic13C2×SD1611yescharacteristic
127C2×Dic13C2×Q1611yescharacteristic
128C2×Dic13AGL(1,ℤ/8)12yes—
129C2×Dic13#13712yes—
130C4×D13—28no—
131C4×D13—24no—
132C4×D13—24no—
133C4×D13—24no—
134C4×D13—24no—
135C4×D13—88no—
136#1057—82no—
137#1057—82no—
138C22×C4⋊C4—132no—
139C22×C4⋊C4—261no—
140C22×C4⋊C4—261no—
141C22×C42—131no—
142C2×C4⋊C8—132no—
143C2×C4⋊C8—132no—
144C2×C22⋊C8—261no—
145C2×C22⋊C8—261no—
146#384—132no—
147#384—131no—
148#384—261no—
149#384—261no—
150#384#26111yescharacteristic
151#336—261no—
152#336—261no—
153C22×C13#38111yescharacteristic
154C22×C13C2×#10011yescharacteristic
155C22×C13C2×#10111yescharacteristic
156C22×C13C2×#10211yescharacteristic
157C22×C13C2×#10311yescharacteristic
158C22×C13#41811yescharacteristic
159C22×C13#41911yescharacteristic
160C2×D13—22no—
161C2×D13—22no—
162C2×D13—22no—
163C2×D13—22no—
164C2×D13—22no—
165C2×D13—22no—
166C2×D13#33214yes—
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—82no—
171Dic13—22no—
172Dic13—82no—
173Dic13#48012yes—
174Dic13#48112yes—
175Dic13#48312yes—
176Dic13#48412yes—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—131no—
180C23×C4—262no—
181C22×C8—262no—
182C22×C8—262no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—132no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—262no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—522no—
192C2×C4⋊C4—522no—
193C2×C4⋊C4—524no—
194C2×C4⋊C4—524no—
195C2×C4⋊C4C2×#26112yes—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—264no—
200C2×C42C2×#26111yescharacteristic
201C4⋊C8—264no—
202C4⋊C8—264no—
203C22⋊C8—522no—
204C22⋊C8—522no—
205C2×C13C2×#33211yescharacteristic
206C2×C13#154511yescharacteristic
207C2×C13#154811yescharacteristic
208C2×C13#155611yescharacteristic
209C2×C13#182111yescharacteristic
210C2×C13#182311yescharacteristic
211C2×C13#182411yescharacteristic
212D13—24no—
213C24—131no—
214C22×C4—22no—
215C22×C4—131no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—132no—
219C22×C4—132no—
220C22×C4—132no—
221C22×C4—132no—
222C22×C4—262no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4—262no—
226C22×C4—262no—
227C22×C4—262no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—524no—
231C22×C4—524no—
232C22×C4—524no—
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22⋊#26111yescharacteristic
235C22×C4C22×#26111yescharacteristic
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—522no—
239C2×C8—522no—
240C2×C8—522no—
241C2×C8—522no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—522no—
246C4⋊C4—522no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—524no—
250C4⋊C4—524no—
251C4⋊C4—522no—
252C42—22no—
253C42—134no—
254C42—262no—
255C42—262no—
256C13#872411yescharacteristic, complemented, Sylow
257C23—132no—
258C23—132no—
259C23—132no—
260C23—261no—
261C23—261no—
262C23—261no—
263C23—261no—
264C23C2×C22⋊#26111yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—132no—
275C2×C4—132no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—132no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—264no—
284C2×C4—264no—
285C2×C4—264no—
286C2×C4—264no—
287C2×C4—268no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—522no—
293C2×C4—1048no—
294C2×C4#8811512yes—
295C2×C4#8811712yes—
296C2×C4#8823712yes—
297C8—1042no—
298C8—1042no—
299C22—134no—
300C22—262no—
301C22—262no—
302C22—262no—
303C22—262no—
304C22—262no—
305C22—262no—
306C22#1171913511yescharacteristic
307C22C2×#8811511yescharacteristic
308C22#1171913811yescharacteristic
309C22D13⋊#10011yescharacteristic
310C22C2×#8811711yescharacteristic
311C22#1171915311yescharacteristic
312C22D13⋊#10111yescharacteristic
313C4—22no—
314C4—22no—
315C4—22no—
316C4—82no—
317C4—132no—
318C4—132no—
319C4—132no—
320C4—132no—
321C4—262no—
322C4—1042no—
323C2—264no—
324C2D13⋊#33211yescharacteristic
325C2#1313034411yescharacteristic
326C2#1313035011yescharacteristic
327C2#1313036611yescharacteristic
328C2#1313073611yescharacteristic
329C2#1313073911yescharacteristic
330C2#1313074011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#384#261
hypocenterC13#8724
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #13129714C2semidirect
256. C13#8724semidirect

Maximal subgroups

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

subgroupindex
#131306932
#131297142
D13×#3842
#872413