Finite Group Databasebeta

← #15762645

Subgroups — #15762645

Order 3328.

484 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 115 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#13114874C211yesmaximal, characteristic
2#13114612C211yesmaximal, characteristic
3#13113356C212yesmaximal
4#13113200C212yesmaximal
5C2×C13×#467C211yesmaximal, characteristic
6C22×C13×Q16C411yescharacteristic, complemented
7C23×C8×C13C2211yescharacteristic
8C2×C13×C22⋊Q8C2212yes—
9C13×#467—21no—
10C13×#467—21no—
11C13×#467—21no—
12C13×#467—21no—
13C2×C13×#107C411yescharacteristic, complemented
14C2×C13×#103C412yescomplemented
15C4×C22⋊Dic13C2211yescharacteristic
16#11718868C2212yes—
17C2×C22⋊#1055C2211yescharacteristic
18C2×#88059—21no—
19C2×#88055—21no—
20#11718144—21no—
21#11718142—21no—
22#11718130—24no—
23#11718120—24no—
24C22×Q8×C13C2×C412yes—
25C23×C4×C13C2311yescharacteristic
26C2×C13×Q16—21no—
27C2×C13×Q16—21no—
28C2×C13×Q16—42no—
29C22×C8×C13—42no—
30C22×C8×C13C2×C411yescharacteristic
31C22×C8×C13C2×C411yescharacteristic
32C22×C8×C13D411yescharacteristic
33C22×C8×C13D411yescharacteristic
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C13×C22⋊Q8—22no—
39C13×C22⋊Q8—22no—
40C2×C13×C4⋊C4—22no—
41C2×C13×C4⋊C4C2×C412yes—
42C2×C13×C22⋊C4—22no—
43C2×C22⋊Dic13—21no—
44C2×C4×Dic13—21no—
45C2×#6099—22no—
46C22×#1055—21no—
47C13×#107—21no—
48C13×#107—21no—
49C13×#103—22no—
50C13×#103—22no—
51#88071D412yes—
52C22⋊#1055—21no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55C22⋊#1055D412yes—
56#88059—42no—
57#88055—42no—
58#9817—131nomaximal, Sylow
59C24×C13#4111yescharacteristic
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—42no—
63C2×Q8×C13—42no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4111yescharacteristic
74C22×Dic13—22no—
75C13×Q16—42no—
76C13×Q16—42no—
77C2×C8×C13—22no—
78C2×C8×C13—22no—
79C2×C8×C13—22no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C2×C8×C13—41no—
83C2×C8×C13C22⋊C411yescharacteristic
84C2×C8×C13C22⋊C411yescharacteristic
85C2×C8×C13C22⋊C411yescharacteristic
86C2×C8×C13C22⋊C411yescharacteristic
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—42no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C22⋊Dic13—42no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96#6099—42no—
97#6099—42no—
98C2×#1055—22no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—42no—
102C2×#467D1311yescharacteristic
103#1810—131no—
104#1752—131no—
105#1508—132no—
106#1472—132no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—41no—
110C23×C13C4×D411yescharacteristic
111C23×C13#12111yescharacteristic
112C23×C13#12411yescharacteristic
113Q8×C13—42no—
114Q8×C13—42no—
115Q8×C13—82no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—44no—
128C2×C4×C13—82no—
129C2×C4×C13C2×C22⋊C411yescharacteristic
130C2×C4×C13C4×D411yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12711yescharacteristic
133C2×Dic13—42no—
134C2×Dic13—42no—
135C2×Dic13—42no—
136C8×C13—21no—
137C8×C13—21no—
138C8×C13—21no—
139C8×C13#9912yes—
140#1055—42no—
141#1055—82no—
142C22×Q16Dic1311yescharacteristic, complemented
143C23×C8C2×D1311yescharacteristic
144C2×C22⋊Q8C2×D1312yes—
145#467—21no—
146#467—21no—
147#467—21no—
148#467—21no—
149C2×#108—261no—
150C2×#107Dic1311yescharacteristic, complemented
151C2×#103Dic1312yescomplemented
152#407—132no—
153C2×C22⋊C8—131no—
154C2×#97—261no—
155C4×C22⋊C4—131no—
156#341—261no—
157#336—261no—
158#328—264no—
159#324—264no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—44no—
168C22×C13#39011yescharacteristic
169C22×C13#44412yes—
170C22×C13#47312yes—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—82no—
175C4×C13—82no—
176C4×C13C2×#9911yescharacteristic
177C4×C13#41011yescharacteristic
178Dic13—82no—
179C22×Q8C2×Dic1312yes—
180C23×C4C22×D1311yescharacteristic
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16—42no—
184C2×M16—262no—
185C22×C8—42no—
186C22×C8—261no—
187C22×C8C2×Dic1311yescharacteristic
188C22×C8C2×Dic1311yescharacteristic
189C22×C8C22⋊D1311yescharacteristic
190C22×C8C22⋊D1311yescharacteristic
191C22×C8C22⋊D1311yescharacteristic
192C22×C8C22⋊D1311yescharacteristic
193C22⋊Q8—22no—
194C22⋊Q8—22no—
195C22⋊Q8—22no—
196C22⋊Q8—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C2×Dic1312yes—
199C2×C22⋊C4—22no—
200C2×C22⋊C4—261no—
201C2×C42—261no—
202#108—522no—
203#107—21no—
204#107—21no—
205#103—22no—
206#103—22no—
207C22⋊C8—132no—
208C22⋊C8—261no—
209C22⋊C8—262no—
210C22⋊C8—262no—
211#97—522no—
212#95—132no—
213C2×C13—22no—
214C2×C13—22no—
215C2×C13—41no—
216C2×C13#196411yescharacteristic
217C2×C13#197511yescharacteristic
218C2×C13#197911yescharacteristic
219C24#612911yescharacteristic
220C2×Q8—22no—
221C2×Q8—22no—
222C2×Q8—42no—
223C2×Q8—42no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—262no—
229C22×C4D4×D1311yescharacteristic
230C22×C4D4×D1311yescharacteristic
231C22×C4#612911yescharacteristic
232C22×C4C22×Dic1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235Q16—42no—
236Q16—42no—
237M16—522no—
238M16—522no—
239C2×C8—22no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—262no—
246C2×C8—521no—
247C2×C8—521no—
248C2×C8—522no—
249C2×C8C22⋊Dic1311yescharacteristic
250C2×C8C22⋊Dic1311yescharacteristic
251C2×C8C22⋊Dic1311yescharacteristic
252C2×C8C22⋊Dic1311yescharacteristic
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—522no—
260C42—521no—
261C42—521no—
262C13#981711yescharacteristic, complemented, Sylow
263C23—22no—
264C23—22no—
265C23—41no—
266C23D4×Dic1311yescharacteristic
267C23#8819011yescharacteristic
268C23#8819211yescharacteristic
269Q8—42no—
270Q8—42no—
271Q8—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—44no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—82no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4D4×Dic1311yescharacteristic
289C2×C4#8819211yescharacteristic
290C2×C4#8819411yescharacteristic
291C2×C4C2×C22⋊Dic1311yescharacteristic
292C8—21no—
293C8—21no—
294C8—21no—
295C8—522no—
296C8—1042no—
297C8#8807412yes—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—44no—
306C22#1171885312yes—
307C22#1171885812yes—
308C22#1171888211yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—82no—
313C4—82no—
314C4—1042no—
315C4C2×#8807411yescharacteristic
316C4#1171890111yescharacteristic
317C2—22no—
318C2—22no—
319C2—41no—
320C2#1311567311yescharacteristic
321C2#1311573011yescharacteristic
322C2#1311575211yescharacteristic
subgroupG/H
centerC22#11718882
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#467C2
socleC22×C13#390
prime radicalC24×C13#41
cosocleC23×C4×C13C23
hypercenterC2×#467D13
hypocenterC13#9817
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#467

Complements

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

NH ≅ G/Ntype
6. C22×C13×Q16C4semidirect
13. C2×C13×#107C4semidirect
14. C2×C13×#103C4semidirect
142. C22×Q16Dic13semidirect
150. C2×#107Dic13semidirect
151. C2×#103Dic13semidirect
262. C13#9817semidirect

Maximal subgroups

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

subgroupindex
#131148742
#131146122
#131133562
#131132002
C2×C13×#4672
#981713