Finite Group Databasebeta

← #15751942

Subgroups — #15751942

Order 3328.

682 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 95 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#13116364C211yesmaximal, characteristic, complemented
2#13116239C212yesmaximal, complemented
3#13112657C212yesmaximal, complemented
4#13112657C211yesmaximal, characteristic, complemented
5C13×#2679C211yesmaximal, characteristic
6C2×C13×#120—22no—
7C2×C13×#120—21no—
8C13×#394—21no—
9C13×#394—22no—
10C13×#390C2212yes—
11C13×#390C2211yescharacteristic
12C2×#88072—22no—
13C2×#88072—21no—
14C2×#88047—21no—
15#11718596C2211yescharacteristic, complemented
16#11718121—22no—
17#11718116C2212yescomplemented
18#11718116C2211yescharacteristic, complemented
19C25×C13—21no—
20C22×D4×C13—21no—
21C22×D4×C13—22no—
22C22×D4×C13D412yes—
23C22×D4×C13D411yescharacteristic
24C13×#120—44no—
25C13×#120—42no—
26C13×#120—44no—
27C13×#120—42no—
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C4⋊C4D412yes—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—21no—
32C2×C13×C22⋊C4—22no—
33C2×C13×C22⋊C4—22no—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13—22no—
38C22×#1055—21no—
39C22×#1055—22no—
40C13×#95—21no—
41#88072—42no—
42#88072—44no—
43#88047—42no—
44#7786—131nomaximal, Sylow
45C24×C13—22no—
46C24×C13—21no—
47C24×C13—44no—
48C24×C13—42no—
49C24×C13—81no—
50C24×C13—82no—
51C24×C13—81no—
52C2×D4×C13—22no—
53C2×D4×C13—21no—
54C2×D4×C13—41no—
55C2×D4×C13—42no—
56C2×D4×C13—42no—
57C2×D4×C13—41no—
58C2×D4×C13—44no—
59C2×D4×C13—44no—
60C2×D4×C13—44no—
61C2×D4×C13—81no—
62C2×D4×C13—82no—
63C2×D4×C13D814yes—
64C2×D4×C13SD1612yes—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13C2×D412yes—
68C22×C4×C13C2×D411yescharacteristic
69C22×Dic13—41no—
70C13×C4⋊C4—42no—
71C13×C4⋊C4—41no—
72C13×C22⋊C4—44no—
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—42no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—42no—
78C13×C22⋊C4—42no—
79C13×C22⋊C4—42no—
80C42×C13—41no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—42no—
84C4⋊Dic13—42no—
85C2×#1055—22no—
86C2×#1055—41no—
87C2×#1055—41no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—42no—
91#2679D1311yescharacteristic
92#2093—131no—
93#2071—132no—
94#1270—131no—
95#1270—132no—
96C23×C13—24no—
97C23×C13—22no—
98C23×C13—42no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13—42no—
104C23×C13—42no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—41no—
108C23×C13—84no—
109C23×C13—88no—
110C23×C13—88no—
111C23×C13—84no—
112C23×C13—84no—
113C23×C13#12011yescharacteristic
114D4×C13—44no—
115D4×C13—42no—
116D4×C13—82no—
117D4×C13—81no—
118D4×C13—84no—
119D4×C13—88no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—22no—
123C2×C4×C13—21no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13C2×D812yes—
130C2×C4×C13C2×SD1611yescharacteristic
131C2×C4×C13AGL(1,ℤ/8)12yes—
132C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
133C2×Dic13—82no—
134C2×Dic13—81no—
135#1055—42no—
136#1055—82no—
137C2×#120—22no—
138C2×#120—21no—
139C2×#107—261no—
140C2×#102—262no—
141C2×#102—261no—
142#394—22no—
143#394—21no—
144#390C2×D1312yes—
145#390C2×D1311yescharacteristic
146#384—131no—
147#340—262no—
148#336—132no—
149#336—131no—
150C22×C13—44no—
151C22×C13—42no—
152C22×C13—44no—
153C22×C13—44no—
154C22×C13—44no—
155C22×C13—816no—
156C22×C13—82no—
157C22×C13—82no—
158C22×C13—82no—
159C22×C13—81no—
160C22×C13—82no—
161C22×C13—81no—
162C22×C13—82no—
163C22×C13#44712yes—
164C22×C13#45011yescharacteristic
165C22×C13#45311yescharacteristic
166C22×C13#45512yes—
167C22×C13#45811yescharacteristic
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—81no—
173C4×C13—82no—
174Dic13—161no—
175C25—21no—
176C22×D4—21no—
177C22×D4—22no—
178C22×D4C22⋊D1312yes—
179C22×D4C22⋊D1311yescharacteristic
180C22×C8—261no—
181C22×C8—262no—
182#120—44no—
183#120—42no—
184#120—44no—
185#120—42no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C22⋊D1312yes—
189C2×C4⋊C4C22⋊D1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C42C22×D1311yescharacteristic
196#107—522no—
197#102—522no—
198#102—524no—
199#95—21no—
200C2×C13—84no—
201C2×C13—82no—
202C2×C13#160712yes—
203C2×C13#161311yescharacteristic
204C2×C13#161911yescharacteristic
205C2×C13#163912yes—
206C2×C13#165911yescharacteristic
207C24—22no—
208C24—21no—
209C24—44no—
210C24—42no—
211C24—81no—
212C24—82no—
213C24—81no—
214C2×D4—22no—
215C2×D4—21no—
216C2×D4—41no—
217C2×D4—42no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—44no—
221C2×D4—44no—
222C2×D4—44no—
223C2×D4—81no—
224C2×D4—82no—
225C2×D4#610414yes—
226C2×D4#610512yes—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—521no—
230C22×C4C2×C22⋊D1312yes—
231C22×C4C2×C22⋊D1311yescharacteristic
232C2×C8—262no—
233C2×C8—521no—
234C2×C8—521no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C4⋊C4—521no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C22⋊C4—44no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C22⋊C4—42no—
248C22⋊C4—42no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C42—41no—
253C13#778611yescharacteristic, complemented, Sylow
254C23—24no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—41no—
260C23—42no—
261C23—42no—
262C23—42no—
263C23—42no—
264C23—41no—
265C23—42no—
266C23—84no—
267C23—88no—
268C23—84no—
269C23—88no—
270C23—84no—
271C23#8820711yescharacteristic
272D4—44no—
273D4—42no—
274D4—81no—
275D4—82no—
276D4—84no—
277D4—88no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—21no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—1042no—
288C2×C4—1041no—
289C2×C4C2×#610412yes—
290C2×C4#8818612yes—
291C2×C4#8818611yescharacteristic
292C2×C4C2×#610511yescharacteristic
293C8—522no—
294C8—1042no—
295C22—42no—
296C22—44no—
297C22—44no—
298C22—44no—
299C22—44no—
300C22—816no—
301C22—82no—
302C22—81no—
303C22—82no—
304C22—81no—
305C22—82no—
306C22—82no—
307C22—82no—
308C22#1171887812yes—
309C22#1171887911yescharacteristic
310C22#1171890211yescharacteristic
311C22#1171890312yes—
312C22#1171890411yescharacteristic
313C4—21no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—81no—
318C4—82no—
319C4—2081no—
320C2—82no—
321C2—84no—
322C2#1311382212yes—
323C2#1311385611yescharacteristic
324C2#1311389011yescharacteristic
325C2#1311401512yes—
326C2#1311414211yescharacteristic
subgroupG/H
centerC23#88207
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2679C2
socleC23×C13#120
hypercenter#2679D13
hypocenterC13#7786
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2679

Complements

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

NH ≅ G/Ntype
1. #13116364C2semidirect
2. #13116239C2semidirect
3. #13112657C2semidirect
4. #13112657C2semidirect
15. #11718596C22semidirect
17. #11718116C22semidirect
18. #11718116C22semidirect
253. C13#7786semidirect

Maximal subgroups

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

subgroupindex
#131163642
#131162392
#131126572
C13×#26792
#778613