Finite Group Databasebeta

← #16778691

Subgroups — #16778691

Order 3328.

410 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130622C211yesmaximal, characteristic
2C4×#88112C211yesmaximal, characteristic
3#13129656C212yesmaximal
4#13129654C212yesmaximal
5#13123215C211yesmaximal, characteristic
6C2×#88112—21no—
7C2×#88110—21no—
8C2×C4⋊#1057—21no—
9C2×C4×#1057—21no—
10C13×#391C411yescharacteristic
11#11718891C411yescharacteristic
12#11718891C2211yescharacteristic
13#11718646C2211yescharacteristic
14#11718634C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16#11718589C411yescharacteristic
17#11718316—21no—
18#11718314—21no—
19#11718313—21no—
20#11718312—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×#6101—21no—
32C2×#6101—21no—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13C2311yescharacteristic
39#88112—24no—
40#88110—42no—
41C4⋊#1057—24no—
42C4×#1057—42no—
43C13×#95—21no—
44C13×#95—21no—
45#88071—21no—
46#88071—21no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#7689—131nomaximal, Sylow
53C2×Q8×C13—22no—
54C2×Q8×C13—41no—
55C2×Q8×C13—41no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×#1057—24no—
68C2×#1057—24no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—22no—
74C42×C13—41no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77C4⋊Dic13—41no—
78C4⋊Dic13—41no—
79#6101—42no—
80#6101—42no—
81C4×Dic13—22no—
82C4×Dic13—22no—
83C4×Dic13—22no—
84C4×Dic13—21no—
85C4×Dic13—21no—
86C4×Dic13—41no—
87C4×Dic13SD1612yes—
88C4×Dic13Q1612yes—
89#2863—131no—
90#1767—131no—
91C4×C4⋊C8—131no—
92#1272—132no—
93#1271—132no—
94C23×C13C2×C22⋊C411yescharacteristic
95Q8×C13—82no—
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—41no—
103C2×C4×C13—41no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13#10312yes—
109C2×C4×C13#10412yes—
110C2×C4×C13#13112yes—
111C2×Dic13—21no—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—41no—
120C2×Dic13—41no—
121C2×Dic13—41no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13#10312yes—
126C2×Dic13#10412yes—
127C2×Dic13C2×SD1611yescharacteristic
128C2×Dic13C2×Q1611yescharacteristic
129C2×Dic13AGL(1,ℤ/8)11yescharacteristic
130C2×Dic13#13711yescharacteristic
131#1057—44no—
132#1057—44no—
133C2×C4⋊C8—261no—
134C2×C4⋊C8—261no—
135C2×#97—261no—
136C2×C4×C8—261no—
137#391—131no—
138#391—131no—
139#391#26111yescharacteristic
140#389—131no—
141#389—131no—
142#389—131no—
143#387—261no—
144#387—261no—
145#387—261no—
146#383—261no—
147C43—131no—
148#336—132no—
149#336—132no—
150C22×C13#40811yescharacteristic
151C22×C13#41011yescharacteristic
152C22×C13#41311yescharacteristic
153C22×C13C2×#10311yescharacteristic
154C22×C13#41711yescharacteristic
155C22×C13C2×#10411yescharacteristic
156C22×C13C2×#10411yescharacteristic
157C4×C13—22no—
158C4×C13—22no—
159C4×C13—22no—
160C4×C13—81no—
161C4×C13—81no—
162Dic13—22no—
163Dic13—22no—
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—81no—
169Dic13—81no—
170C22×Q8C2×#26111yescharacteristic
171C22×C8—262no—
172C22×C8—262no—
173C2×C4⋊C4—131no—
174C2×C4⋊C4—131no—
175C2×C4⋊C4—261no—
176C2×C4⋊C4—261no—
177C2×C4⋊C4—261no—
178C2×C4⋊C4C2×#26111yescharacteristic
179C2×C42—131no—
180C2×C42—131no—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—131no—
185C2×C42C2×#26111yescharacteristic
186C4⋊C8—264no—
187C4⋊C8—264no—
188#97—522no—
189C4×C8—522no—
190#95—21no—
191#95—21no—
192#95—261no—
193#95—261no—
194#95—261no—
195#95—261no—
196#95—261no—
197#95—261no—
198#95—261no—
199C2×C13#147311yescharacteristic
200C2×C13#148311yescharacteristic
201C2×C13#149311yescharacteristic
202C2×C13#150311yescharacteristic
203C2×C13#150911yescharacteristic
204C2×C13#152411yescharacteristic
205C2×C13#155011yescharacteristic
206C2×Q8—22no—
207C2×Q8—41no—
208C2×Q8—41no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—131no—
212C22×C4—131no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4C22⋊#26111yescharacteristic
218C22×C4C22⋊#26111yescharacteristic
219C22×C4C22×#26111yescharacteristic
220C2×C8—264no—
221C2×C8—264no—
222C2×C8—522no—
223C2×C8—522no—
224C2×C8—522no—
225C2×C8—522no—
226C4⋊C4—22no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C4⋊C4—522no—
230C4⋊C4—521no—
231C4⋊C4—521no—
232C4⋊C4—522no—
233C42—41no—
234C42—132no—
235C42—132no—
236C42—261no—
237C42—262no—
238C42—261no—
239C42—262no—
240C42—262no—
241C42—521no—
242C13#768911yescharacteristic, complemented, Sylow
243C23C2×C22⋊#26111yescharacteristic
244Q8—82no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—131no—
258C2×C4—132no—
259C2×C4—131no—
260C2×C4—132no—
261C2×C4—131no—
262C2×C4—131no—
263C2×C4—261no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—261no—
267C2×C4—261no—
268C2×C4—261no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4—521no—
276C2×C4—521no—
277C2×C4#8811712yes—
278C2×C4#8811812yes—
279C2×C4#8823812yes—
280C8—524no—
281C8—524no—
282C22#1171911611yescharacteristic
283C22#1171914711yescharacteristic
284C22#1171914811yescharacteristic
285C22C2×#8811711yescharacteristic
286C22C2×#8811811yescharacteristic
287C22D13⋊#10411yescharacteristic
288C22#1171916411yescharacteristic
289C4—22no—
290C4—22no—
291C4—22no—
292C4—81no—
293C4—81no—
294C4—261no—
295C4—261no—
296C4—262no—
297C4—262no—
298C4—261no—
299C4—261no—
300C4—1041no—
301C4—1041no—
302C2#1313011711yescharacteristic
303C2#1313015211yescharacteristic
304C2#1313018511yescharacteristic
305C2#1313021811yescharacteristic
306C2#1313024011yescharacteristic
307C2#1313028911yescharacteristic
308C2#1313035411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#391C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#391#261
hypocenterC13#7689
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
242. C13#7689semidirect

Maximal subgroups

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

subgroupindex
#131306222
C4×#881122
#131296562
#131296542
#131232152
#768913