Finite Group Databasebeta

← #15758918

Subgroups — #15758918

Order 3328.

436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123921C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13113438C212yesmaximal
4#13112700C212yesmaximal
5C13×#2634C211yesmaximal, characteristic
6C2×C13×#125C2211yescharacteristic
7C2×C4×Q8×C13C2211yescharacteristic
8C13×#400—21no—
9C13×#400C411yescharacteristic
10C13×#400C411yescharacteristic
11C13×#398C411yescharacteristic
12C13×#398C411yescharacteristic
13C13×#395—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#383C2211yescharacteristic
17C2×#88076—21no—
18#11718685—24no—
19#11718587—21no—
20#11718587C2212yes—
21#11718586—21no—
22C4×#6099C2212yes—
23#11718135—24no—
24#11718122—21no—
25C22×Q8×C13D411yescharacteristic
26C13×#125—22no—
27C13×#125—22no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C42×C13D411yescharacteristic
40C2×C42×C13D411yescharacteristic
41C2×C42×C13C2311yescharacteristic
42C2×#6099—22no—
43C13×#95—21no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53#88076—24no—
54C22⋊#1055—22no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57C4⋊#1055—22no—
58#88043—22no—
59#88043—22no—
60#88043D414yes—
61C4×#1055—22no—
62C4×#1055—22no—
63#9190—131nomaximal, Sylow
64C2×Q8×C13—22no—
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—22no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C42×C13—21no—
89C42×C13—21no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13C2×D412yes—
93C42×C13#4112yes—
94#6099—24no—
95#6099—42no—
96C2×#1055—24no—
97C2×#1055—42no—
98#2983—131no—
99#2634D1311yescharacteristic
100C4×#101—131no—
101#1528—132no—
102#1288—132no—
103C23×C13C2×C22⋊C411yescharacteristic
104Q8×C13—44no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13#10412yes—
130C2×C4×C13C4×D412yes—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12112yes—
133C2×C4×C13#12311yescharacteristic
134#1055—44no—
135#1055—44no—
136C2×#125C2×D1311yescharacteristic
137C2×C4×Q8C2×D1311yescharacteristic
138#446—264no—
139#432—132no—
140#432—261no—
141#431—261no—
142C2×#101—261no—
143C4×M16—132no—
144#400—21no—
145#400Dic1311yescharacteristic
146#400Dic1311yescharacteristic
147#398Dic1311yescharacteristic
148#398Dic1311yescharacteristic
149#395—21no—
150#387—21no—
151#387—21no—
152#383C2×D1311yescharacteristic
153#343—261no—
154#330—264no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#38611yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C22×C13#42111yescharacteristic
160C4×C13—22no—
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—22no—
165C4×C13—41no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—81no—
169C4×C13—81no—
170C4×C13—81no—
171C4×C13—81no—
172C22×Q8C22⋊D1311yescharacteristic
173C2×M16—262no—
174#125—22no—
175#125—22no—
176C4×Q8—22no—
177C4×Q8—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4C2×Dic1311yescharacteristic
183C2×C4⋊C4C2×Dic1311yescharacteristic
184C2×C4⋊C4C2×Dic1311yescharacteristic
185C2×C4⋊C4C2×Dic1311yescharacteristic
186C2×C4⋊C4C22⋊D1311yescharacteristic
187C2×C42C22⋊D1311yescharacteristic
188C2×C42C22⋊D1311yescharacteristic
189C2×C42C22×D1311yescharacteristic
190C4⋊C8—262no—
191C4⋊C8—262no—
192C4⋊C8—262no—
193#101—264no—
194C22⋊C8—262no—
195#97—134no—
196#97—262no—
197#97—262no—
198C4×C8—262no—
199C4×C8—262no—
200#95—21no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206#95—21no—
207#95—21no—
208#95C2×Dic1311yescharacteristic
209#95C2×Dic1311yescharacteristic
210C2×C13—21no—
211C2×C13—21no—
212C2×C13#187111yescharacteristic
213C2×C13#191211yescharacteristic
214C2×C13#191511yescharacteristic
215C2×Q8—22no—
216C2×Q8—22no—
217C2×Q8—41no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4C22⋊Dic1311yescharacteristic
223C22×C4C22⋊Dic1311yescharacteristic
224C22×C4C22⋊Dic1311yescharacteristic
225C22×C4C22⋊Dic1311yescharacteristic
226C22×C4C22×Dic1311yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C22×C4C2×C22⋊D1311yescharacteristic
229M16—264no—
230M16—522no—
231C2×C8—264no—
232C2×C8—522no—
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—42no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—21no—
247C42D4×D1312yes—
248C42#612912yes—
249C13#919011yescharacteristic, complemented, Sylow
250C23C2×C22⋊Dic1311yescharacteristic
251Q8—44no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4#8807712yes—
277C2×C4D4×Dic1312yes—
278C2×C4#8818911yescharacteristic
279C2×C4#8819111yescharacteristic
280C2×C4#8819312yes—
281C8—524no—
282C8—524no—
283C22—21no—
284C22—21no—
285C22#1171888111yescharacteristic
286C22C2×#8807711yescharacteristic
287C22#1171889711yescharacteristic
288C4—22no—
289C4—22no—
290C4—21no—
291C4—21no—
292C4—22no—
293C4—41no—
294C4—41no—
295C4—41no—
296C4—81no—
297C4—81no—
298C4—81no—
299C4—81no—
300C2—21no—
301C2—21no—
302C2#1311513911yescharacteristic
303C2#1311537411yescharacteristic
304C2#1311538911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2634C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2634D13
hypocenterC13#9190
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2634

Complements

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

NH ≅ G/Ntype
249. C13#9190semidirect

Maximal subgroups

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

subgroupindex
#131239212
C4×#880762
#131134382
#131127002
C13×#26342
#919013