Finite Group Databasebeta

← #16782181

Subgroups — #16782181

Order 3328.

482 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 94 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#13130562C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129712C212yesmaximal, complemented
4#13129712C212yesmaximal, complemented
5#13117231C211yesmaximal, characteristic
6C22×C4×Dic13C2211yescharacteristic
7C2×C22⋊#1057—21no—
8C2×C22⋊#1057—21no—
9C2×#88110C2212yes—
10C2×#88110C2212yes—
11C13×#380C411yescharacteristic
12#11718873C411yescharacteristic
13#11718638C2211yescharacteristic
14#11718638C2211yescharacteristic
15C4⋊C4×Dic13C411yescharacteristic
16C4⋊C4×Dic13C411yescharacteristic
17#11718604—21no—
18C22⋊C4×Dic13—21no—
19#11718312—21no—
20#11718309—21no—
21#11718290—21no—
22#11718290—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×Dic13D411yescharacteristic
25C23×Dic13D411yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C22⋊C4—21no—
31C2×C22⋊Dic13—21no—
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×C4×Dic13—24no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13C2×C411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41C22⋊#1057—24no—
42C22⋊#1057—24no—
43#88110—24no—
44#88110—24no—
45C13×#95—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#8720—131nomaximal, Sylow
54C24×C13C22⋊C411yescharacteristic
55C22×C4×C13—22no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—41no—
59C22×C4×C13—41no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—22no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C2×#1057—24no—
75C2×#1057—24no—
76C2×#1057—42no—
77C2×#1057—42no—
78C2×#1057—42no—
79C2×#1057—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—42no—
83C22⋊Dic13—42no—
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—42no—
90C4×Dic13—42no—
91C4×Dic13#4114yes—
92#2283—131no—
93#1749—131no—
94#1749—131no—
95#1295—132no—
96#1295—132no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13#10412yes—
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—44no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#11712yes—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—44no—
128C2×Dic13—44no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13#10412yes—
136C2×Dic13#12312yes—
137C2×Dic13#12312yes—
138#1057—44no—
139#1057—44no—
140C22×C42—131no—
141C2×C22⋊C8—261no—
142C2×C22⋊C8—261no—
143C2×#97—132no—
144C2×#97—132no—
145#383—261no—
146#382—131no—
147#382—131no—
148#381—261no—
149#380—131no—
150#380#26111yescharacteristic
151C4×C4⋊C4—131no—
152C4×C4⋊C4—131no—
153C4×C22⋊C4—261no—
154#376—261no—
155#336—261no—
156#336—261no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13#38111yescharacteristic
165C22×C13#41311yescharacteristic
166C22×C13#41311yescharacteristic
167C22×C13C2×#10411yescharacteristic
168C22×C13C2×#10411yescharacteristic
169C22×C13#42111yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—41no—
173C4×C13—81no—
174C4×C13—81no—
175Dic13—22no—
176Dic13—22no—
177Dic13—22no—
178Dic13—41no—
179Dic13—81no—
180Dic13—81no—
181C23×C4—131no—
182C23×C4—131no—
183C23×C4C2×#26111yescharacteristic
184C22×C8—262no—
185C22×C8—262no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C22⋊C4—21no—
191C2×C22⋊C4—261no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—264no—
197C2×C42—261no—
198C2×C42—261no—
199C22⋊C8—264no—
200C22⋊C8—264no—
201#97—264no—
202#97—264no—
203#95—21no—
204#95—261no—
205#95—261no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210#95—261no—
211C2×C13—42no—
212C2×C13#152411yescharacteristic
213C2×C13#152911yescharacteristic
214C2×C13#153211yescharacteristic
215C2×C13#153511yescharacteristic
216C2×C13#182211yescharacteristic
217C2×C13#182611yescharacteristic
218C2×C13#182611yescharacteristic
219C24C22⋊#26111yescharacteristic
220C22×C4—22no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—262no—
230C22×C4—262no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—261no—
234C22×C4—261no—
235C22×C4—521no—
236C22×C4—521no—
237C22×C4C22⋊#26111yescharacteristic
238C22×C4C22×#26111yescharacteristic
239C2×C8—264no—
240C2×C8—264no—
241C2×C8—522no—
242C2×C8—522no—
243C2×C8—522no—
244C2×C8—522no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C22⋊C4—42no—
250C22⋊C4—522no—
251C42—134no—
252C42—262no—
253C42—262no—
254C42—262no—
255C42—522no—
256C42—522no—
257C13#872011yescharacteristic, complemented, Sylow
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23#8811812yes—
265C23C2×C22⋊#26111yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—44no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—132no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—524no—
291C2×C4—524no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4#8823712yes—
299C8—524no—
300C8—524no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22#1171913511yescharacteristic
309C22#1171914011yescharacteristic
310C22#1171914811yescharacteristic
311C22#1171914811yescharacteristic
312C22C2×#8811811yescharacteristic
313C22D13⋊#10411yescharacteristic
314C22#1171916611yescharacteristic
315C4—22no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—262no—
320C4—262no—
321C4—262no—
322C4—521no—
323C4—1041no—
324C4—1041no—
325C2—42no—
326C2#1313028911yescharacteristic
327C2#1313030211yescharacteristic
328C2#1313031411yescharacteristic
329C2#1313032111yescharacteristic
330C2#1313073811yescharacteristic
331C2#1313074311yescharacteristic
332C2#1313074411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#380C4
socleC23×C13C2×C22⋊C4
prime radicalC24×C13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#380#261
hypocenterC13#8720
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #13129712C2semidirect
4. #13129712C2semidirect
257. C13#8720semidirect

Maximal subgroups

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

subgroupindex
#131305622
#131297122
#131172312
#872013