Finite Group Databasebeta

← #16785085

Subgroups — #16785085

Order 3328.

664 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 122 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#13130692C211yesmaximal, characteristic
2#13130562C211yesmaximal, characteristic
3#13129674C214yesmaximal
4C2×#11718635C211yesmaximal, characteristic
5C23×Dic26C411yescharacteristic
6C22×C13×C4⋊C4C411yescharacteristic
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057C2212yes—
9C2×C22⋊#1057C2212yes—
10C2×#88112—21no—
11C2×#88110—21no—
12C2×#88071C412yes—
13C2×#88071C2212yes—
14#11718635—21no—
15#11718635—21no—
16#11718635—21no—
17#11718635—21no—
18#11718290—21no—
19#11718290—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C23×Dic13C2×C411yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2311yescharacteristic
25C22×Dic26—21no—
26C22×Dic26—21no—
27C22×Dic26—24no—
28C22×Dic26—42no—
29C22×Dic26—42no—
30C22×#1057—22no—
31C22×#1057—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—42no—
35C2×C4×Dic13—42no—
36C2×C4×Dic13D411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C22⋊#1057—22no—
41C22⋊#1057—24no—
42C22⋊#1057Q814yescomplemented
43#88112—42no—
44#88110—42no—
45#88071—22no—
46#88071—22no—
47#88071—22no—
48#88071—22no—
49#9882—131nomaximal, Sylow
50C24×C13C22×C411yescharacteristic
51C22×C4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—24no—
56C22×C4×C13—42no—
57C22×C4×C13—42no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×Dic13—22no—
61C22×Dic13—22no—
62C22×Dic13—22no—
63C22×Dic13—22no—
64C22×Dic13—41no—
65C22×Dic13—41no—
66C22×Dic13—41no—
67C22×Dic13—42no—
68C22×Dic13—42no—
69C22×Dic13C22⋊C411yescharacteristic
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13M1614yes—
72C22×Dic13C2×D411yescharacteristic
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×Q812yes—
75C22×Dic13#4112yes—
76C2×Dic26—24no—
77C2×Dic26—24no—
78C2×Dic26—416no—
79C2×Dic26—42no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—42no—
83C2×#1057—24no—
84C2×#1057—42no—
85C2×#1057—42no—
86C2×#1057—42no—
87C2×#1057—42no—
88C2×#1057—42no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—41no—
94C4×Dic13—41no—
95C2×#391—131no—
96#1797—131no—
97#1749—131no—
98#1280—134no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13C4×Q812yes—
105C23×C13C2×M1612yes—
106C23×C13#13112yes—
107C2×C4×C13—28no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—84no—
116C2×C4×C13#9912yes—
117C2×C4×C13#10012yes—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—24no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—44no—
131C2×Dic13—44no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—44no—
135C2×Dic13#10112yes—
136C2×Dic13C22⋊Q812yes—
137C2×Dic13#12411yescharacteristic
138C2×Dic13C4⋊Q811yescharacteristic
139Dic26—48no—
140Dic26—48no—
141#1057—44no—
142#1057—82no—
143C23×Q8—131no—
144C22×C4⋊C4#26111yescharacteristic
145C22×C42—131no—
146C2×C4⋊C8—261no—
147C2×C22⋊C8—132no—
148C2×C22⋊C8—132no—
149C2×#97—261no—
150#391—261no—
151#391—261no—
152#391—261no—
153#391—261no—
154C2×#95—132no—
155C2×#95—132no—
156#336—261no—
157#336—261no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13#39111yescharacteristic
165C22×C13#40711yescharacteristic
166C22×C13#40811yescharacteristic
167C22×C13C2×#9911yescharacteristic
168C22×C13#41011yescharacteristic
169C22×C13C2×#10011yescharacteristic
170C22×C13C2×#10111yescharacteristic
171C22×C13#44614yes—
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—82no—
175Dic13—22no—
176Dic13—22no—
177Dic13—21no—
178Dic13—21no—
179Dic13—44no—
180Dic13—41no—
181C22×Q8—264no—
182C22×Q8—261no—
183C22×Q8—261no—
184C22×Q8—522no—
185C22×Q8—522no—
186C23×C4—131no—
187C23×C4—131no—
188C23×C4—132no—
189C23×C4C2×#26112yes—
190C23×C4C2×#26111yescharacteristic
191C22×C8—262no—
192C22×C8—262no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—42no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—522no—
201C4⋊C8—522no—
202C22⋊C8—134no—
203C22⋊C8—262no—
204C22⋊C8—264no—
205#97—522no—
206#95—262no—
207#95—262no—
208#95—262no—
209#95—262no—
210C2×C13—24no—
211C2×C13#146211yescharacteristic
212C2×C13#146711yescharacteristic
213C2×C13#146911yescharacteristic
214C2×C13#147211yescharacteristic
215C2×C13#198511yescharacteristic
216C2×C13#199611yescharacteristic
217C2×C13#199711yescharacteristic
218C24C22×#26111yescharacteristic
219C2×Q8—264no—
220C2×Q8—264no—
221C2×Q8—5216no—
222C2×Q8—522no—
223C2×Q8—522no—
224C2×Q8—522no—
225C2×Q8—522no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—24no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—131no—
234C22×C4—131no—
235C22×C4—131no—
236C22×C4—132no—
237C22×C4—132no—
238C22×C4—131no—
239C22×C4—134no—
240C22×C4—262no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4—521no—
245C22×C4—521no—
246C22×C4—521no—
247C22×C4—522no—
248C22×C4—522no—
249C22×C4C22⋊#26111yescharacteristic
250C22×C4C22⋊#26111yescharacteristic
251C2×C8—264no—
252C2×C8—522no—
253C2×C8—522no—
254C2×C8—522no—
255C2×C8—522no—
256C2×C8—522no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C42—262no—
260C42—262no—
261C42—521no—
262C42—521no—
263C13#988211yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23D13⋊M1612yes—
269C23#8823812yes—
270C23Q8×#26112yes—
271C23C2×C22⋊#26111yescharacteristic
272Q8—528no—
273Q8—528no—
274C2×C4—28no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—84no—
283C2×C4—132no—
284C2×C4—132no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—264no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—522no—
298C2×C4—522no—
299C2×C4—524no—
300C2×C4—524no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—524no—
304C2×C4#8810712yes—
305C2×C4#8812112yes—
306C8—524no—
307C8—1042no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22#1171907814yes—
315C22C2×#8810711yescharacteristic
316C22#1171912611yescharacteristic
317C22#1171914211yescharacteristic
318C22#1171914711yescharacteristic
319C22D13⋊#10111yescharacteristic
320C22(C2×#261)⋊Q811yescharacteristic
321C22C2×#8812111yescharacteristic
322C4—22no—
323C4—22no—
324C4—82no—
325C4—262no—
326C4—261no—
327C4—261no—
328C4—262no—
329C4—524no—
330C4—521no—
331C2—24no—
332C2#1313008311yescharacteristic
333C2#1313010011yescharacteristic
334C2#1313010611yescharacteristic
335C2#1313011411yescharacteristic
336C2#1313100811yescharacteristic
337C2#1313102611yescharacteristic
338C2#1313102811yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
cosocleC23×Dic13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#9882
LCSG ▷ C24×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
42. C22⋊#1057Q8semidirect
263. C13#9882semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131305622
#131296742
C2×#117186352
#988213