Finite Group Databasebeta

← #15751423

Subgroups — #15751423

Order 3328.

444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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#13123203C211yesmaximal, characteristic
2#13114585C211yesmaximal, characteristic, complemented
3#13112660C212yesmaximal, complemented
4#13112656C212yesmaximal
5C13×#1744C211yesmaximal, characteristic, complemented
6C2×#88130—21no—
7C2×C4×C8×C13—21no—
8C43×C13C2211yescharacteristic
9#11718601—21no—
10#11718601—21no—
11#11718601—21no—
12#11718600C411yescharacteristic
13#11718600C411yescharacteristic
14#11718600C2211yescharacteristic
15#11718589C411yescharacteristic
16#11718589C411yescharacteristic
17#11718589C2211yescharacteristic
18C2×#88043—21no—
19C13×#336—21no—
20C13×#336C2212yes—
21#11718116—21no—
22#11718116C2212yes—
23C22×D52C2×C411yescharacteristic
24C22×C8×C13—22no—
25C2×C42×C13C2×C411yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×C42×C13D411yescharacteristic
28C2×C42×C13D411yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C42×C13D411yescharacteristic
31C2×C42×C13C2311yescharacteristic
32C2×#6103—21no—
33C2×#6103—21no—
34C2×#6103—21no—
35C2×#6103—21no—
36C2×#6103—21no—
37C2×#6103—21no—
38C2×C4⋊Dic13C2×C411yescharacteristic
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C22×#1055—22no—
45#88130—44no—
46C4×C8×C13—24no—
47#88071—21no—
48#88071—21no—
49#88071—21no—
50#88043—24no—
51#7692—131nomaximal, Sylow
52C23×D13—21no—
53C22×C4×C13C22⋊C411yescharacteristic
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×C4×C13C2×D411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13—21no—
63C2×D52—22no—
64C2×D52—41no—
65C2×D52—41no—
66C2×C8×C13—24no—
67C2×C8×C13—42no—
68C2×C8×C13—42no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13—22no—
72C42×C13—22no—
73C42×C13—22no—
74C42×C13—41no—
75C42×C13—41no—
76#6103—42no—
77#6103—42no—
78#6103—42no—
79#6103—42no—
80#6103—42no—
81#6103—42no—
82C4⋊Dic13—22no—
83C4⋊Dic13—41no—
84C4⋊Dic13—41no—
85#6101—42no—
86#6101—42no—
87#6101—42no—
88C2×#1055—24no—
89C2×#1055—42no—
90C2×#1055—42no—
91#2860—131no—
92#1745—131no—
93#1744D1311yescharacteristic, complemented
94#1271—132no—
95#1270—132no—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—41no—
98C22×D13—41no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13—41no—
102C22×D13—41no—
103C22×D13—41no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13#10412yes—
121C2×C4×C13#10412yes—
122C2×C4×C13#13112yes—
123C2×C4×C13#13512yes—
124C2×C4×C13AGL(1,ℤ/8)12yes—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134D52—82no—
135C8×C13—44no—
136#1055—44no—
137C2×#126—261no—
138C2×#97—261no—
139C2×C4×C8—21no—
140#390—131no—
141#390—131no—
142#390—131no—
143#389—131no—
144#389—131no—
145#389—131no—
146#388—261no—
147#388—261no—
148#388—261no—
149C43C2×D1311yescharacteristic
150#336—21no—
151#336—132no—
152#336—261no—
153#336C2×D1312yes—
154C22×C13#40811yescharacteristic
155C22×C13#41011yescharacteristic
156C22×C13#41311yescharacteristic
157C22×C13#41611yescharacteristic
158C22×C13#41811yescharacteristic
159C22×C13C2×#10411yescharacteristic
160C22×C13C2×#10411yescharacteristic
161C2×D13—81no—
162C2×D13—81no—
163C2×D13—81no—
164C2×D13—81no—
165C2×D13—81no—
166C2×D13—81no—
167C2×D13—81no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175Dic13—81no—
176Dic13—81no—
177Dic13—81no—
178C22×D4—131no—
179C22×C8—22no—
180C22×C8—262no—
181#126—524no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—131no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C22⋊C4—261no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4—261no—
191C2×C22⋊C4—261no—
192C2×C22⋊C4—261no—
193C2×C22⋊C4—261no—
194C2×C42C4×D1311yescharacteristic
195C2×C42C4×D1311yescharacteristic
196C2×C42D5211yescharacteristic
197C2×C42D5211yescharacteristic
198C2×C42C22⋊D1311yescharacteristic
199C2×C42C22⋊D1311yescharacteristic
200C2×C42C22×D1311yescharacteristic
201#97—264no—
202C4×C8—24no—
203#95—261no—
204#95—261no—
205#95—261no—
206C2×C13#147311yescharacteristic
207C2×C13#148411yescharacteristic
208C2×C13#149411yescharacteristic
209C2×C13#150011yescharacteristic
210C2×C13#150511yescharacteristic
211C2×C13#152411yescharacteristic
212C2×C13#155311yescharacteristic
213D13—161no—
214C24—261no—
215C2×D4—262no—
216C2×D4—521no—
217C2×D4—521no—
218C22×C4—261no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4#610311yescharacteristic
222C22×C4#610311yescharacteristic
223C22×C4#610311yescharacteristic
224C22×C4#610311yescharacteristic
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4C2×D5211yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C2×C8—24no—
229C2×C8—42no—
230C2×C8—42no—
231C2×C8—264no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—262no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—522no—
238C4⋊C4—522no—
239C4⋊C4—522no—
240C22⋊C4—522no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C22⋊C4—522no—
245C22⋊C4—522no—
246C42—22no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—41no—
252C42—41no—
253C13#769211yescharacteristic, complemented, Sylow
254C23—521no—
255C23—521no—
256C23—521no—
257C23—521no—
258C23—521no—
259C23—521no—
260C23—521no—
261C23C2×#610311yescharacteristic
262D4—1042no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4#8804512yes—
289C2×C4#8806512yes—
290C2×C4#8815512yes—
291C2×C4#8815812yes—
292C2×C4#8820312yes—
293C8—44no—
294C8—524no—
295C22—1041no—
296C22—1041no—
297C22—1041no—
298C22—1041no—
299C22—1041no—
300C22—1041no—
301C22—1041no—
302C22C2×#8804511yescharacteristic
303C22#1171866211yescharacteristic
304C22#1171866711yescharacteristic
305C22#1171877111yescharacteristic
306C22#1171877411yescharacteristic
307C22#1171879311yescharacteristic
308C22C2×#8806511yescharacteristic
309C4—22no—
310C4—22no—
311C4—22no—
312C4—22no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—1041no—
317C4—1041no—
318C4—1041no—
319C2—2081no—
320C2#1311320311yescharacteristic
321C2#1311325211yescharacteristic
322C2#1311329711yescharacteristic
323C2#1311332311yescharacteristic
324C2#1311334311yescharacteristic
325C2#1311342211yescharacteristic
326C2#1311353911yescharacteristic
subgroupG/H
centerC23C2×#6103
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1744C2
socleC23×C13C2×C22⋊C4
prime radicalC22×D52C2×C4
cosocleC2×C42×C13C23
hypercenter#1744D13
hypocenterC13#7692
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C43 ◁ #1744

Complements

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

NH ≅ G/Ntype
2. #13114585C2semidirect
3. #13112660C2semidirect
5. C13×#1744C2semidirect
93. #1744D13semidirect
253. C13#7692semidirect

Maximal subgroups

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

subgroupindex
#131232032
#131145852
#131126602
#131126562
C13×#17442
#769213