Finite Group Databasebeta

← #16778806

Subgroups — #16778806

Order 3328.

388 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 96 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#13130764C211yesmaximal, characteristic
2#13130751C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5#13123195C211yesmaximal, characteristic
6C2×#88143—21no—
7C2×C4⋊#1057—21no—
8C13×#389C411yescharacteristic
9#11718646C2211yescharacteristic
10#11718637C411yescharacteristic
11#11718637C411yescharacteristic
12#11718634C2211yescharacteristic
13#11718633—21no—
14C42×Dic13C2211yescharacteristic
15#11718589C411yescharacteristic
16#11718311—21no—
17#11718308—21no—
18#11718290—21no—
19#11718290—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—
45C4⋊#1057—42no—
46C13×#95—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#7720—131nomaximal, Sylow
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13C22⋊C411yescharacteristic
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C2×#1057—42no—
63C2×#1057—42no—
64C2×#1057—42no—
65C2×#1057—42no—
66C2×#1057—42no—
67C2×#1057—42no—
68C13×C4⋊C4—22no—
69C13×C4⋊C4—41no—
70C13×C4⋊C4—42no—
71C42×C13—22no—
72C4⋊Dic13—22no—
73C4⋊Dic13—42no—
74C4⋊Dic13—41no—
75#6101—42no—
76#6101—42no—
77#6101—42no—
78#6101—42no—
79#6101—42no—
80#6101—42no—
81C4×Dic13—22no—
82C4×Dic13—22no—
83C4×Dic13—41no—
84C4×Dic13—41no—
85C4×Dic13—41no—
86C4×Dic13SD1612yes—
87C4×Dic13Q1612yes—
88#2859—131no—
89#1839—131no—
90#1831—131no—
91#1271—132no—
92#1271—132no—
93C23×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—21no—
100C2×C4×C13—21no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13#10312yes—
108C2×C4×C13#13112yes—
109C2×Dic13—21no—
110C2×Dic13—21no—
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×Dic13C2×SD1611yescharacteristic
126C2×Dic13C2×Q1611yescharacteristic
127C2×Dic13AGL(1,ℤ/8)12yes—
128#1057—82no—
129#1057—82no—
130C2×#125—261no—
131C2×C4⋊C8—261no—
132#389—131no—
133#389—131no—
134#389—131no—
135#389—261no—
136#389—261no—
137#389#26111yescharacteristic
138#384—131no—
139#384—131no—
140#382—261no—
141C43—131no—
142#336—132no—
143#336—132no—
144#336—261no—
145#336—261no—
146#336—261no—
147C22×C13#40811yescharacteristic
148C22×C13#41011yescharacteristic
149C22×C13C2×#10111yescharacteristic
150C22×C13C2×#10311yescharacteristic
151C22×C13#41811yescharacteristic
152C22×C13#42111yescharacteristic
153C22×C13#42111yescharacteristic
154C4×C13—22no—
155C4×C13—22no—
156C4×C13—41no—
157C4×C13—81no—
158C4×C13—81no—
159Dic13—22no—
160Dic13—22no—
161Dic13—21no—
162Dic13—21no—
163Dic13—22no—
164Dic13—81no—
165Dic13—81no—
166C22×C8—262no—
167C22×C8—262no—
168#125—524no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—131no—
172C2×C4⋊C4—261no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4—261no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4—261no—
179C2×C4⋊C4C2×#26111yescharacteristic
180C2×C4⋊C4C2×#26111yescharacteristic
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42—131no—
186C2×C42—131no—
187C2×C42C2×#26111yescharacteristic
188C4⋊C8—522no—
189#95—21no—
190#95—261no—
191#95—261no—
192#95—261no—
193C2×C13#147011yescharacteristic
194C2×C13#148111yescharacteristic
195C2×C13#149611yescharacteristic
196C2×C13#151411yescharacteristic
197C2×C13#151811yescharacteristic
198C2×C13#153411yescharacteristic
199C2×C13#154911yescharacteristic
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—131no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—261no—
207C22×C4—261no—
208C22×C4C22⋊#26111yescharacteristic
209C22×C4C22⋊#26111yescharacteristic
210C22×C4C22×#26111yescharacteristic
211C2×C8—522no—
212C2×C8—522no—
213C2×C8—522no—
214C2×C8—522no—
215C2×C8—522no—
216C2×C8—522no—
217C4⋊C4—22no—
218C4⋊C4—41no—
219C4⋊C4—42no—
220C4⋊C4—262no—
221C4⋊C4—521no—
222C4⋊C4—522no—
223C4⋊C4—522no—
224C4⋊C4—522no—
225C4⋊C4—522no—
226C4⋊C4—522no—
227C4⋊C4—522no—
228C4⋊C4—522no—
229C42—22no—
230C42—132no—
231C42—132no—
232C42—262no—
233C42—262no—
234C42—521no—
235C42—521no—
236C42—521no—
237C13#772011yescharacteristic, complemented, Sylow
238C23C2×C22⋊#26111yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—132no—
253C2×C4—131no—
254C2×C4—132no—
255C2×C4—131no—
256C2×C4—132no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—261no—
260C2×C4—261no—
261C2×C4—261no—
262C2×C4—261no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—521no—
268C2×C4—521no—
269C2×C4—521no—
270C2×C4—521no—
271C2×C4#8811712yes—
272C2×C4#8823812yes—
273C8—1042no—
274C8—1042no—
275C22#1171911611yescharacteristic
276C22#1171913811yescharacteristic
277C22#1171914611yescharacteristic
278C22C2×#8811711yescharacteristic
279C22D13⋊#10111yescharacteristic
280C22#1171916611yescharacteristic
281C22#1171916611yescharacteristic
282C4—22no—
283C4—22no—
284C4—41no—
285C4—81no—
286C4—81no—
287C4—262no—
288C4—261no—
289C4—261no—
290C4—262no—
291C4—262no—
292C4—1041no—
293C4—1041no—
294C2#1313010811yescharacteristic
295C2#1313014411yescharacteristic
296C2#1313019511yescharacteristic
297C2#1313025511yescharacteristic
298C2#1313026911yescharacteristic
299C2#1313031911yescharacteristic
300C2#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#7720
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
237. C13#7720semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131307512
#131296552
#131296542
#131231952
#772013