Finite Group Databasebeta

← #16784570

Subgroups — #16784570

Order 3328.

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

normal subgroups only

This group has 640 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
3C2×#11718286C214yesmaximal
4C2×#11718634C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic
7C22×#6101C2212yes—
8C22×C4×Dic13C2211yescharacteristic
9C2×C22⋊#1057C2212yes—
10C2×C22⋊#1057C2212yes—
11C2×#88112—21no—
12C2×#88110—21no—
13C2×#88071C412yes—
14#11718634—21no—
15#11718634—21no—
16#11718634—21no—
17#11718634—21no—
18#11718290—21no—
19#11718290—21no—
20#11718286—28no—
21C23×C4×C13C2×C412yes—
22C23×C4×C13C2×C411yescharacteristic
23C23×Dic13C2×C412yes—
24C23×Dic13C2×C411yescharacteristic
25C23×Dic13C2311yescharacteristic
26C22×#1057—22no—
27C22×#1057—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—24no—
34C2×#6101—24no—
35C2×#6101—22no—
36C2×#6101—22no—
37C2×#6101—24no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C22⋊#1057—22no—
44C22⋊#1057—24no—
45C22⋊#1057D414yes—
46#88112—42no—
47#88110—42no—
48#88071—22no—
49#88071—22no—
50#9654—131nomaximal, Sylow
51C24×C13C22×C411yescharacteristic
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—24no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×Dic13—22no—
62C22×Dic13—24no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—24no—
66C22×Dic13—22no—
67C22×Dic13—41no—
68C22×Dic13—41no—
69C22×Dic13—41no—
70C22×Dic13C22⋊C411yescharacteristic
71C22×Dic13C22⋊C411yescharacteristic
72C22×Dic13M1614yes—
73C22×Dic13C2×D411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C22×Dic13C2×D412yes—
76C22×Dic13#4112yes—
77C2×#1057—24no—
78C2×#1057—42no—
79C2×#1057—42no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C4⋊Dic13—24no—
86C4⋊Dic13—24no—
87#6101—44no—
88#6101—42no—
89#6101—42no—
90C4×Dic13—22no—
91C4×Dic13—22no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C2×#389—131no—
95#1797—131no—
96#1749—131no—
97C2×#324—134no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13C4×D412yes—
104C23×C13C2×M1612yes—
105C23×C13#13112yes—
106C2×C4×C13—28no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—84no—
115C2×C4×C13#9912yes—
116C2×C4×C13#10112yes—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—24no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—28no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—44no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—44no—
134C2×Dic13#10112yes—
135C2×Dic13#12112yes—
136C2×Dic13#12411yescharacteristic
137C2×Dic13#12711yescharacteristic
138#1057—44no—
139#1057—82no—
140C22×C4⋊C4—132no—
141C22×C4⋊C4—131no—
142C22×C4⋊C4#26111yescharacteristic
143C22×C42—131no—
144C2×C4⋊C8—261no—
145C2×C22⋊C8—132no—
146C2×C22⋊C8—132no—
147C2×#97—261no—
148#389—261no—
149#389—261no—
150#389—261no—
151#389—261no—
152C2×#95—132no—
153#336—261no—
154#336—261no—
155#324—268no—
156C22×C13—22no—
157C22×C13—22no—
158C22×C13—22no—
159C22×C13—22no—
160C22×C13—22no—
161C22×C13—22no—
162C22×C13#39011yescharacteristic
163C22×C13#40711yescharacteristic
164C22×C13#40811yescharacteristic
165C22×C13C2×#9911yescharacteristic
166C22×C13#41011yescharacteristic
167C22×C13C2×#10111yescharacteristic
168C22×C13C2×#10111yescharacteristic
169C22×C13#43514yes—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—82no—
173Dic13—22no—
174Dic13—21no—
175Dic13—21no—
176Dic13—22no—
177Dic13—44no—
178Dic13—41no—
179C23×C4—131no—
180C23×C4—132no—
181C23×C4—131no—
182C23×C4C2×#26112yes—
183C23×C4C2×#26111yescharacteristic
184C22×C8—262no—
185C22×C8—262no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—264no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—264no—
193C2×C4⋊C4—264no—
194C2×C4⋊C4—262no—
195C2×C4⋊C4—262no—
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—
208C2×C13—24no—
209C2×C13#146311yescharacteristic
210C2×C13#146711yescharacteristic
211C2×C13#147011yescharacteristic
212C2×C13#147211yescharacteristic
213C2×C13#195511yescharacteristic
214C2×C13#196411yescharacteristic
215C2×C13#196611yescharacteristic
216C24C22×#26111yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—132no—
228C22×C4—132no—
229C22×C4—134no—
230C22×C4—131no—
231C22×C4—262no—
232C22×C4—262no—
233C22×C4—264no—
234C22×C4—262no—
235C22×C4—264no—
236C22×C4—262no—
237C22×C4—521no—
238C22×C4—521no—
239C22×C4—521no—
240C22×C4C22⋊#26111yescharacteristic
241C22×C4C22⋊#26111yescharacteristic
242C2×C8—264no—
243C2×C8—522no—
244C2×C8—522no—
245C2×C8—522no—
246C2×C8—522no—
247C2×C8—522no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—264no—
251C4⋊C4—264no—
252C4⋊C4—524no—
253C4⋊C4—522no—
254C4⋊C4—522no—
255C42—262no—
256C42—262no—
257C42—521no—
258C42—521no—
259C13#965411yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23D13⋊M1612yes—
265C23D4×#26112yes—
266C23#8824012yes—
267C23C2×C22⋊#26111yescharacteristic
268C2×C4—28no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—84no—
277C2×C4—132no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—132no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—268no—
288C2×C4—264no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—522no—
293C2×C4—522no—
294C2×C4—524no—
295C2×C4—524no—
296C2×C4—522no—
297C2×C4—522no—
298C2×C4#8811312yes—
299C2×C4#8811912yes—
300C8—524no—
301C8—1042no—
302C22—22no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22#1171907514yes—
309C22#1171912611yescharacteristic
310C22C2×#8811311yescharacteristic
311C22#1171914211yescharacteristic
312C22#1171915111yescharacteristic
313C22#1171915911yescharacteristic
314C22D13⋊#10111yescharacteristic
315C22C2×#8811911yescharacteristic
316C4—22no—
317C4—22no—
318C4—82no—
319C4—262no—
320C4—262no—
321C4—261no—
322C4—261no—
323C4—521no—
324C4—524no—
325C2—24no—
326C2#1313008611yescharacteristic
327C2#1313010011yescharacteristic
328C2#1313011011yescharacteristic
329C2#1313011611yescharacteristic
330C2#1313096211yescharacteristic
331C2#1313097511yescharacteristic
332C2#1313097911yescharacteristic
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#9654
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
259. C13#9654semidirect

Maximal subgroups

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

subgroupindex
#131306922
#131305622
C2×#117182862
C2×#117186342
#965413