Finite Group Databasebeta

← #16778672

Subgroups — #16778672

Order 3328.

432 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 104 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#13130621C211yesmaximal, characteristic
2#13130550C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5#13123195C211yesmaximal, characteristic
6C2×#88143—21no—
7C2×#88112—21no—
8C2×#88110—21no—
9C2×C4×#1057—21no—
10C13×#389C411yescharacteristic
11#11718646C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718637C411yescharacteristic
14#11718634C2211yescharacteristic
15#11718633—21no—
16C42×Dic13C2211yescharacteristic
17#11718589C411yescharacteristic
18#11718311—21no—
19#11718308—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13C2×C411yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×#6101—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88143—44no—
45#88112—24no—
46#88110—42no—
47C4×#1057—24no—
48C13×#95—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#7683—131nomaximal, Sylow
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—21no—
59C22×Dic13—21no—
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C2×D411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C2×#1057—24no—
65C2×#1057—24no—
66C2×#1057—42no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C13×C4⋊C4—22no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4—42no—
73C42×C13—22no—
74C4⋊Dic13—22no—
75C4⋊Dic13—42no—
76C4⋊Dic13—41no—
77#6101—42no—
78#6101—42no—
79#6101—42no—
80#6101—42no—
81#6101—42no—
82#6101—42no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—41no—
88C4×Dic13SD1612yes—
89C4×Dic13Q1612yes—
90#2859—131no—
91#1767—131no—
92#1744—131no—
93#1271—132no—
94#1271—132no—
95C23×C13C2×C22⋊C411yescharacteristic
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13#10312yes—
110C2×C4×C13#13112yes—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13#10112yes—
124C2×Dic13#10312yes—
125C2×Dic13#10412yes—
126C2×Dic13#10412yes—
127C2×Dic13C2×SD1611yescharacteristic
128C2×Dic13C2×Q1611yescharacteristic
129C2×Dic13AGL(1,ℤ/8)12yes—
130#1057—44no—
131#1057—44no—
132C2×#125—261no—
133C2×C4⋊C8—261no—
134C2×#97—261no—
135C2×C4×C8—261no—
136#389—131no—
137#389—131no—
138#389—131no—
139#389—261no—
140#389—261no—
141#389#26111yescharacteristic
142#384—131no—
143#384—131no—
144#382—261no—
145C43—131no—
146#336—132no—
147#336—132no—
148#336—261no—
149C22×C13#40811yescharacteristic
150C22×C13#41011yescharacteristic
151C22×C13C2×#10111yescharacteristic
152C22×C13C2×#10311yescharacteristic
153C22×C13#41811yescharacteristic
154C22×C13C2×#10411yescharacteristic
155C22×C13C2×#10411yescharacteristic
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—41no—
159C4×C13—81no—
160C4×C13—81no—
161Dic13—22no—
162Dic13—21no—
163Dic13—21no—
164Dic13—22no—
165Dic13—81no—
166Dic13—81no—
167Dic13#33014yes—
168C22×C8—262no—
169C22×C8—262no—
170#125—524no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—131no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4C2×#26111yescharacteristic
182C2×C4⋊C4C2×#26111yescharacteristic
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—131no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42C2×#26111yescharacteristic
190C4⋊C8—264no—
191#97—522no—
192C4×C8—264no—
193#95—21no—
194#95—261no—
195#95—261no—
196#95—261no—
197C2×C13#147011yescharacteristic
198C2×C13#148411yescharacteristic
199C2×C13#149311yescharacteristic
200C2×C13#150311yescharacteristic
201C2×C13#150511yescharacteristic
202C2×C13C2×#33011yescharacteristic
203C2×C13#154911yescharacteristic
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—261no—
211C22×C4—261no—
212C22×C4C22⋊#26111yescharacteristic
213C22×C4C22⋊#26111yescharacteristic
214C22×C4C22×#26111yescharacteristic
215C2×C8—264no—
216C2×C8—264no—
217C2×C8—522no—
218C2×C8—522no—
219C2×C8—522no—
220C2×C8—522no—
221C4⋊C4—22no—
222C4⋊C4—41no—
223C4⋊C4—42no—
224C4⋊C4—262no—
225C4⋊C4—521no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—522no—
229C4⋊C4—522no—
230C4⋊C4—522no—
231C4⋊C4—522no—
232C4⋊C4—522no—
233C42—22no—
234C42—132no—
235C42—132no—
236C42—262no—
237C42—262no—
238C42—262no—
239C42—262no—
240C42—521no—
241C13#768311yescharacteristic, complemented, Sylow
242C23C2×C22⋊#26111yescharacteristic
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—132no—
257C2×C4—132no—
258C2×C4—132no—
259C2×C4—132no—
260C2×C4—131no—
261C2×C4—132no—
262C2×C4—131no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4#8811712yes—
276C2×C4#8823812yes—
277C8—524no—
278C8—524no—
279C22#1171911611yescharacteristic
280C22#1171913811yescharacteristic
281C22#1171914611yescharacteristic
282C22C2×#8811711yescharacteristic
283C22D13⋊#10111yescharacteristic
284C22D13⋊#10411yescharacteristic
285C22D13⋊#10411yescharacteristic
286C4—22no—
287C4—22no—
288C4—41no—
289C4—81no—
290C4—81no—
291C4—134no—
292C4—262no—
293C4—261no—
294C4—261no—
295C4—262no—
296C4—1041no—
297C4—1041no—
298C2#1313010811yescharacteristic
299C2#1313015511yescharacteristic
300C2#1313018411yescharacteristic
301C2#1313021811yescharacteristic
302C2#1313022611yescharacteristic
303C2D13⋊#33011yescharacteristic
304C2#1313035211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7683
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
241. C13#7683semidirect

Maximal subgroups

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

subgroupindex
#131306212
#131305502
#131296552
#131296542
#131231952
#768313