Finite Group Databasebeta

← #15757964

Subgroups — #15757964

Order 3328.

740 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 135 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#13117434C211yesmaximal, characteristic
2#13114926C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112715C212yesmaximal, complemented
5C2×C13×#399C211yesmaximal, characteristic
6C22×C13×C4⋊C4—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×C13×C22⋊C4—21no—
9C22×C13×C22⋊C4C2211yescharacteristic
10C13×#399—22no—
11C13×#399C414yescomplemented
12C2×C13×#95C2211yescharacteristic
13#11718908—21no—
14#11718873C2212yes—
15C4×C22⋊Dic13—21no—
16C2×C22⋊#1055C2212yes—
17#11718612—24no—
18#11718121—24no—
19#11718117—22no—
20C25×C13D411yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—24no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—44no—
30C2×C13×C4⋊C4C2×C412yes—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—24no—
34C2×C13×C22⋊C4—44no—
35C2×C13×C22⋊C4C2×C412yes—
36C2×C13×C22⋊C4D412yes—
37C2×C22⋊Dic13—22no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C4⋊Dic13D414yes—
41C2×C4×Dic13—22no—
42C22×#1055—22no—
43C13×#95—21no—
44C13×#95C2×C412yes—
45#88071—22no—
46#88071—22no—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49#9024—131nomaximal, Sylow
50C24×C13—21no—
51C24×C13—22no—
52C24×C13—21no—
53C24×C13—22no—
54C24×C13—42no—
55C24×C13—42no—
56C24×C13C22⋊C412yes—
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—24no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—22no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4112yes—
76C22×Dic13—24no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—48no—
79C13×C4⋊C4—42no—
80C13×C22⋊C4—24no—
81C13×C22⋊C4—24no—
82C13×C22⋊C4—48no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C22⋊Dic13—82no—
86C22⋊Dic13—82no—
87C4⋊Dic13—44no—
88C4×Dic13—82no—
89C2×#1055—44no—
90C2×#1055—42no—
91C2×#399D1311yescharacteristic
92#2312—131no—
93#1824—132no—
94C2×#323—131no—
95#1294—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—48no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—81no—
109C23×C13—81no—
110C23×C13—84no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#12011yescharacteristic
113C23×C13#12311yescharacteristic
114C23×C13#13512yes—
115C23×C13#13712yes—
116C2×C4×C13—24no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—48no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—81no—
131C2×C4×C13—82no—
132C2×C4×C13—82no—
133C2×C4×C13C4×D412yes—
134C2×C4×C13#12112yes—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13—44no—
138#1055—82no—
139C22×C4⋊C4—21no—
140C22×C4⋊C4C2×D1311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C22⋊C4C2×D1311yescharacteristic
143C2×C22⋊C8—132no—
144#399—22no—
145#399Dic1314yescomplemented
146#388—264no—
147#380—132no—
148#379—261no—
149C4×C22⋊C4—261no—
150C2×#95C2×D1311yescharacteristic
151#340—264no—
152#323—262no—
153C22×C13—24no—
154C22×C13—24no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—44no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—82no—
164C22×C13—84no—
165C22×C13—84no—
166C22×C13#38611yescharacteristic
167C22×C13#41611yescharacteristic
168C22×C13#41911yescharacteristic
169C22×C13#45212yes—
170C22×C13#45312yes—
171C22×C13#45812yes—
172C22×C13#48512yes—
173C4×C13—22no—
174C4×C13—22no—
175C4×C13—44no—
176C4×C13—42no—
177C4×C13—82no—
178Dic13—84no—
179C25C22⋊D1311yescharacteristic
180C23×C4—21no—
181C23×C4—21no—
182C23×C4C22⋊D1311yescharacteristic
183C23×C4C22×D1311yescharacteristic
184C22×C8—262no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—134no—
191C2×C4⋊C4C2×Dic1312yes—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—24no—
195C2×C22⋊C4—44no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—262no—
198C2×C22⋊C4—262no—
199C2×C22⋊C4C2×Dic1312yes—
200C2×C22⋊C4C22⋊D1312yes—
201C2×C42—262no—
202C22⋊C8—262no—
203C22⋊C8—262no—
204#95—21no—
205#95—262no—
206#95—262no—
207#95C2×Dic1312yes—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—22no—
211C2×C13—82no—
212C2×C13#161814yes—
213C2×C13#187311yescharacteristic
214C2×C13#188711yescharacteristic
215C2×C13#189011yescharacteristic
216C24—21no—
217C24—22no—
218C24—21no—
219C24—22no—
220C24—42no—
221C24—42no—
222C24C22⋊Dic1312yes—
223C24C2×C22⋊D1311yescharacteristic
224C22×C4—24no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—42no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—264no—
238C22×C4C22⋊Dic1312yes—
239C22×C4D4×D1312yes—
240C22×C4#612912yes—
241C22×C4C22×Dic1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243C2×C8—524no—
244C2×C8—522no—
245C4⋊C4—24no—
246C4⋊C4—48no—
247C4⋊C4—42no—
248C4⋊C4—524no—
249C22⋊C4—24no—
250C22⋊C4—24no—
251C22⋊C4—48no—
252C22⋊C4—522no—
253C22⋊C4—522no—
254C22⋊C4—1042no—
255C22⋊C4—1042no—
256C42—1042no—
257C13#902411yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23—22no—
261C23—22no—
262C23—22no—
263C23—42no—
264C23—42no—
265C23—48no—
266C23—42no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—81no—
271C23—81no—
272C23—84no—
273C23#8818911yescharacteristic
274C23#8819111yescharacteristic
275C23#8819612yes—
276C23#8820412yes—
277C23C2×C22⋊Dic1311yescharacteristic
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—22no—
281C2×C4—42no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—48no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—81no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—524no—
296C2×C4—524no—
297C2×C4—524no—
298C2×C4D4×Dic1312yes—
299C2×C4#8819312yes—
300C8—1042no—
301C22—24no—
302C22—24no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—21no—
307C22—44no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—82no—
312C22—84no—
313C22—84no—
314C22#1171870612yes—
315C22#1171870812yes—
316C22#1171871412yes—
317C22#1171873812yes—
318C22#1171888111yescharacteristic
319C22#1171888611yescharacteristic
320C22#1171889411yescharacteristic
321C4—22no—
322C4—22no—
323C4—44no—
324C4—42no—
325C4—82no—
326C4—1044no—
327C2—21no—
328C2—21no—
329C2—22no—
330C2—82no—
331C2#1311388214yes—
332C2#1311514911yescharacteristic
333C2#1311523511yescharacteristic
334C2#1311525011yescharacteristic
subgroupG/H
centerC23#88191
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#399C2
socleC23×C13#120
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenterC2×#399D13
hypocenterC13#9024
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
2. #13114926C2semidirect
4. #13112715C2semidirect
11. C13×#399C4semidirect
145. #399Dic13semidirect
257. C13#9024semidirect

Maximal subgroups

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

subgroupindex
#131174342
#131149262
C2×#117181172
#131127152
C2×C13×#3992
#902413