Finite Group Databasebeta

← #16791102

Subgroups — #16791102

Order 3328.

488 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 84 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#13130700C211yesmaximal, characteristic
2C4×#88119C211yesmaximal, characteristic
3#13129920C214yesmaximal
4#13119147C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic, complemented
6C2×C4×C22⋊D13C2211yescharacteristic
7C2×#88121C2212yes—
8C2×#88119C2212yes—
9C4×C22⋊#261—21no—
10#11719129—21no—
11#11718874C2212yes—
12#11718873C411yescharacteristic, complemented
13#11718871C412yescomplemented
14#11718653—21no—
15#11718648—21no—
16#11718643—21no—
17#11718634—21no—
18#11718291—21no—
19#11718289—21no—
20C23×C4×C13C2×C412yes—
21C23×C4×C13C2×C411yescharacteristic
22C22×C22⋊D13C2311yescharacteristic
23C22×C4×D13D411yescharacteristic
24C2×C22⋊#261—22no—
25C2×#6122—22no—
26C2×C4×#261—41no—
27C2×C13×C4⋊C4—21no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C22⋊Dic13C2×C412yes—
32C2×C22⋊Dic13C2×C411yescharacteristic
33C4×C22⋊D13—41no—
34C4×C22⋊D13—41no—
35C2×#6103—22no—
36C2×#6103D411yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×#6101—22no—
39C2×#6101D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41#88121—24no—
42#88119—22no—
43#88119Q814yes—
44(C2×#261)⋊C4—41no—
45#88112—41no—
46C4⋊#1057—41no—
47#88071—21no—
48#88071—22no—
49#88071—22no—
50#13295—131nomaximal, Sylow
51C24×C13C22×C411yescharacteristic
52C23×D13C2×D411yescharacteristic
53C22×#261—42no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—22no—
57C22×C4×C13—42no—
58C22×C4×C13—42no—
59C22×C4×C13—82no—
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22⋊C411yescharacteristic
62C2×C22⋊D13—41no—
63C2×C22⋊D13—41no—
64C2×C22⋊D13C2×Q812yes—
65C2×C22⋊D13#4112yes—
66C22×Dic13—22no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C411yescharacteristic
69C22×Dic13C2×D411yescharacteristic
70C2×C4×D13—21no—
71C2×C4×D13—21no—
72C2×C4×D13—42no—
73C22⋊#261—24no—
74C22⋊#261—42no—
75#6122—42no—
76#6122—42no—
77C2×#1057—42no—
78C4×#261—82no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C22⋊Dic13—41no—
83C22⋊Dic13—42no—
84#6103—41no—
85#6103—82no—
86C4⋊Dic13—42no—
87#6101—41no—
88#6101—82no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91#2487—131no—
92#1800—131no—
93C4×#99—131no—
94#1390—134no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13C4×Q812yes—
101C22×D13—21no—
102C22×D13—21no—
103C22×D13—41no—
104C22×D13—41no—
105C22×D13C22⋊Q812yes—
106C2×#261—44no—
107C2×#261—82no—
108C2×#261—82no—
109C2×C4×C13—22no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—84no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C22⋊D13—42no—
121C22⋊D13—42no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13#12411yescharacteristic
132C2×Dic13C4⋊Q811yescharacteristic
133C4×D13—42no—
134C4×D13—81no—
135#1057—82no—
136C2×C4×D4—131no—
137C22×C4⋊C4#26111yescharacteristic, complemented
138#423—261no—
139C2×#100—132no—
140C2×#99—132no—
141#400—261no—
142#399—261no—
143#389—261no—
144#386—132no—
145#385—132no—
146#380—131no—
147#380—261no—
148C4×C22⋊C4—261no—
149#343—261no—
150#342—261no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—22no—
154C22×C13—42no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13#39111yescharacteristic
159C22×C13C2×#9911yescharacteristic
160C22×C13#41011yescharacteristic
161C2×D13—22no—
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—42no—
165C2×D13—81no—
166#261—84no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—82no—
170C4×C13#35212yes—
171Dic13—21no—
172Dic13—21no—
173Dic13—41no—
174Dic13—41no—
175Dic13—82no—
176C22×D4—131no—
177C23×C4—131no—
178C23×C4C2×#26112yes—
179C23×C4C2×#26111yescharacteristic
180C2×M16—262no—
181C4×D4—521no—
182C4×D4—521no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—262no—
190C2×C22⋊C4—131no—
191C2×C22⋊C4—131no—
192C2×C22⋊C4—132no—
193C2×C22⋊C4—262no—
194C2×C22⋊C4—262no—
195C2×C42—131no—
196C2×C42—521no—
197C4⋊C8—521no—
198C4⋊C8—521no—
199#100—264no—
200#99—134no—
201#99—262no—
202#95—262no—
203#95—262no—
204#95—261no—
205#95—521no—
206C2×C13—21no—
207C2×C13—21no—
208C2×C13—42no—
209C2×C13#199611yescharacteristic
210C2×C13C2×#35211yescharacteristic
211C2×C13#212211yescharacteristic
212D13—42no—
213C24—131no—
214C24C22×#26111yescharacteristic
215C2×D4—132no—
216C2×D4—132no—
217C2×D4—521no—
218C2×D4—521no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—82no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—262no—
231C22×C4—522no—
232C22×C4—522no—
233C22×C4C22⋊#26111yescharacteristic
234C22×C4C22⋊#26111yescharacteristic
235M16—522no—
236M16—522no—
237C2×C8—522no—
238C4⋊C4—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—1042no—
244C22⋊C4—264no—
245C22⋊C4—521no—
246C22⋊C4—521no—
247C22⋊C4—522no—
248C22⋊C4—522no—
249C22⋊C4—1042no—
250C42—261no—
251C42—261no—
252C42—1042no—
253C13#1329511yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—41no—
257C23—41no—
258C23—132no—
259C23—261no—
260C23—261no—
261C23—521no—
262C23—521no—
263C23Q8×#26112yes—
264C23C2×C22⋊#26111yescharacteristic
265D4—522no—
266D4—522no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—84no—
276C2×C4—131no—
277C2×C4—131no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—522no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—524no—
288C2×C4—522no—
289C2×C4—1041no—
290C2×C4—1042no—
291C2×C4—1042no—
292C2×C4#8811911yescharacteristic
293C2×C4#8811911yescharacteristic
294C8—1042no—
295C22—21no—
296C22—21no—
297C22—22no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—262no—
303C22—522no—
304C22—521no—
305C22—521no—
306C22—1041no—
307C22#1171915611yescharacteristic
308C22(C2×#261)⋊Q811yescharacteristic
309C22C2×#8811911yescharacteristic
310C4—21no—
311C4—41no—
312C4—82no—
313C4—261no—
314C4—261no—
315C4—521no—
316C4—521no—
317C4—1042no—
318C4—1044no—
319C4#1171828812yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—522no—
324C2#1313102511yescharacteristic
325C2C2×#1171828811yescharacteristic
326C2#1313109511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC24×C13C22×C4
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radical, cosocleC22×C22⋊D13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#13295
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. C22×C13×C4⋊C4C4semidirect
12. #11718873C4semidirect
13. #11718871C4semidirect
137. C22×C4⋊C4#261semidirect
253. C13#13295semidirect

Maximal subgroups

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

subgroupindex
#131307002
C4×#881192
#131299202
#131191472
#1329513