Finite Group Databasebeta

← #16778662

Subgroups — #16778662

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—42no—
45#88143—42no—
46#88112—24no—
47#88110—42no—
48C4×#1057—24no—
49C13×#95—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#7680—131nomaximal, Sylow
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22×C411yescharacteristic
59C22×Dic13—21no—
60C22×Dic13—21no—
61C22×Dic13C22⋊C411yescharacteristic
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C2×D411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C2×#1057—24no—
66C2×#1057—24no—
67C2×#1057—42no—
68C2×#1057—42no—
69C2×#1057—42no—
70C2×#1057—42no—
71C13×C4⋊C4—22no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4—42no—
74C42×C13—22no—
75C4⋊Dic13—22no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—42no—
81#6101—42no—
82#6101—42no—
83#6101—42no—
84#6101—41no—
85#6101—41no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—22no—
89C4×Dic13—22no—
90C4×Dic13—41no—
91C4×Dic13D812yes—
92C4×Dic13SD1612yes—
93#2859—131no—
94#1767—131no—
95#1744—131no—
96#1271—132no—
97#1271—132no—
98C23×C13C2×C22⋊C411yescharacteristic
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—21no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13#10212yes—
113C2×C4×C13#13112yes—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—41no—
126C2×Dic13#10112yes—
127C2×Dic13#10212yes—
128C2×Dic13#10412yes—
129C2×Dic13#10412yes—
130C2×Dic13C2×D811yescharacteristic
131C2×Dic13C2×SD1611yescharacteristic
132C2×Dic13#13712yes—
133#1057—44no—
134#1057—44no—
135C2×#125—261no—
136C2×C4⋊C8—261no—
137C2×#97—261no—
138C2×C4×C8—261no—
139#389—131no—
140#389—131no—
141#389—131no—
142#389—261no—
143#389—261no—
144#389#26111yescharacteristic
145#384—131no—
146#384—131no—
147#382—261no—
148C43—131no—
149#336—132no—
150#336—132no—
151#336—261no—
152C22×C13#40811yescharacteristic
153C22×C13#41011yescharacteristic
154C22×C13C2×#10111yescharacteristic
155C22×C13C2×#10211yescharacteristic
156C22×C13#41911yescharacteristic
157C22×C13C2×#10411yescharacteristic
158C22×C13C2×#10411yescharacteristic
159C4×C13—22no—
160C4×C13—22no—
161C4×C13—41no—
162C4×C13—81no—
163C4×C13—81no—
164Dic13—22no—
165Dic13—21no—
166Dic13—21no—
167Dic13—22no—
168Dic13—81no—
169Dic13—81no—
170Dic13#33014yes—
171C22×C8—262no—
172C22×C8—262no—
173#125—522no—
174#125—522no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—131no—
177C2×C4⋊C4—131no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4—261no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—261no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4C2×#26111yescharacteristic
186C2×C4⋊C4C2×#26111yescharacteristic
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42C2×#26111yescharacteristic
194C4⋊C8—264no—
195#97—522no—
196C4×C8—264no—
197#95—21no—
198#95—261no—
199#95—261no—
200#95—261no—
201C2×C13#147011yescharacteristic
202C2×C13#148511yescharacteristic
203C2×C13#149211yescharacteristic
204C2×C13#150211yescharacteristic
205C2×C13#150611yescharacteristic
206C2×C13C2×#33011yescharacteristic
207C2×C13#154611yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—261no—
215C22×C4—261no—
216C22×C4C22⋊#26111yescharacteristic
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22×#26111yescharacteristic
219C2×C8—264no—
220C2×C8—264no—
221C2×C8—522no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C4⋊C4—22no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—262no—
229C4⋊C4—521no—
230C4⋊C4—521no—
231C4⋊C4—522no—
232C4⋊C4—522no—
233C4⋊C4—521no—
234C4⋊C4—521no—
235C4⋊C4—521no—
236C4⋊C4—522no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C42—22no—
240C42—132no—
241C42—132no—
242C42—262no—
243C42—262no—
244C42—262no—
245C42—262no—
246C42—521no—
247C13#768011yescharacteristic, complemented, Sylow
248C23C2×C22⋊#26111yescharacteristic
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—132no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—131no—
266C2×C4—132no—
267C2×C4—131no—
268C2×C4—132no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—261no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4#8811512yes—
282C2×C4#8823812yes—
283C8—524no—
284C8—524no—
285C22#1171911611yescharacteristic
286C22C2×#8811511yescharacteristic
287C22#1171914611yescharacteristic
288C22#1171915311yescharacteristic
289C22D13⋊#10111yescharacteristic
290C22D13⋊#10411yescharacteristic
291C22D13⋊#10411yescharacteristic
292C4—22no—
293C4—22no—
294C4—41no—
295C4—81no—
296C4—81no—
297C4—134no—
298C4—262no—
299C4—261no—
300C4—261no—
301C4—262no—
302C4—1041no—
303C4—1041no—
304C2#1313010811yescharacteristic
305C2#1313015811yescharacteristic
306C2#1313018111yescharacteristic
307C2#1313021511yescharacteristic
308C2#1313022911yescharacteristic
309C2D13⋊#33011yescharacteristic
310C2#1313034611yescharacteristic
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#7680
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
247. C13#7680semidirect

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
#768013