Finite Group Databasebeta

← #15757958

Subgroups — #15757958

Order 3328.

616 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C2×#11718647C211yesmaximal, characteristic
2#13114924C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112714C212yesmaximal
5C13×#2316C211yesmaximal, characteristic
6C2×C13×#117—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C22×C4⋊Dic13C2211yescharacteristic
9C13×#389—24no—
10C13×#380—21no—
11C13×#380C2212yes—
12C2×#88071—21no—
13C2×#88071—21no—
14C2×#88071C2211yescharacteristic
15C2×C22⋊#1055C2212yes—
16#11718647—22no—
17#11718647C414yescomplemented
18#11718121—24no—
19#11718120—22no—
20C23×C4×C13D411yescharacteristic
21C23×C4×C13D411yescharacteristic
22C23×C4×C13C2311yescharacteristic
23C23×Dic13—21no—
24C23×Dic13—21no—
25C13×#117—42no—
26C13×#117—42no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C412yes—
32C2×C13×C4⋊C4D412yes—
33C2×C13×C4⋊C4D414yes—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13—22no—
36C2×C4⋊Dic13—22no—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C412yes—
40C22×#1055—22no—
41C13×#95—22no—
42C13×#95—22no—
43#88071—24no—
44#88071—24no—
45#88071—21no—
46#88071C2×C412yes—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49#9023—131nomaximal, Sylow
50C24×C13C2×D411yescharacteristic
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—24no—
58C22×C4×C13—42no—
59C22×C4×C13—42no—
60C22×C4×C13C22⋊C412yes—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13SD1612yes—
63C22×C4×C13Q1612yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×C4×C13C2×D412yes—
67C22×C4×C13#4112yes—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—42no—
71C22×Dic13—42no—
72C22×Dic13—44no—
73C22×Dic13—41no—
74C22×Dic13—41no—
75C22×Dic13—41no—
76C22×Dic13—41no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—44no—
80C13×C4⋊C4—44no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—44no—
85C4⋊Dic13—24no—
86C4⋊Dic13—42no—
87C2×#1055—44no—
88C2×#1055—42no—
89C2×#400—131no—
90#2316D1311yescharacteristic
91#1824—132no—
92C2×#324—131no—
93#1294—132no—
94C23×C13—22no—
95C23×C13—22no—
96C23×C13C2×C22⋊C411yescharacteristic
97C23×C13#12011yescharacteristic
98C23×C13#12311yescharacteristic
99C23×C13C2×SD1611yescharacteristic
100C23×C13C2×Q1611yescharacteristic
101C23×C13AGL(1,ℤ/8)11yescharacteristic
102C23×C13#13711yescharacteristic
103C2×C4×C13—22no—
104C2×C4×C13—22no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—24no—
108C2×C4×C13—22no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—44no—
117C2×C4×C13—44no—
118C2×C4×C13—44no—
119C2×C4×C13—81no—
120C2×C4×C13#10314yes—
121C2×C4×C13C4×D412yes—
122C2×C4×C13#12112yes—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—44no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—82no—
129C2×Dic13—82no—
130C2×Dic13—82no—
131C2×Dic13—82no—
132#1055—82no—
133C2×#117—21no—
134C22×C4⋊C4—131no—
135C22×C4⋊C4C2×D1311yescharacteristic
136C2×C22⋊C8—132no—
137#400—134no—
138#400—262no—
139#389—24no—
140#380—21no—
141#380C2×D1312yes—
142C2×#95—131no—
143C2×#95—261no—
144C2×#95—261no—
145#340—264no—
146#324—262no—
147C22×C13—22no—
148C22×C13—22no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13#38611yescharacteristic
156C22×C13C2×#10311yescharacteristic
157C22×C13#41711yescharacteristic
158C22×C13#45011yescharacteristic
159C22×C13#45111yescharacteristic
160C22×C13#45412yes—
161C22×C13#45812yes—
162C22×C13#48311yescharacteristic
163C22×C13#48411yescharacteristic
164C4×C13—24no—
165C4×C13—22no—
166C4×C13—22no—
167C4×C13—42no—
168C4×C13—84no—
169Dic13—82no—
170Dic13—82no—
171C23×C4—261no—
172C23×C4—261no—
173C23×C4C22⋊D1311yescharacteristic
174C23×C4C22⋊D1311yescharacteristic
175C23×C4C22×D1311yescharacteristic
176C22×C8—262no—
177#117—42no—
178#117—42no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—132no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—262no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4C4×D1312yes—
188C2×C4⋊C4D5212yes—
189C2×C4⋊C4C22⋊D1314yes—
190C2×C22⋊C4—22no—
191C2×C42—22no—
192C22⋊C8—262no—
193C22⋊C8—262no—
194#95—22no—
195#95—22no—
196#95—132no—
197#95—264no—
198#95—264no—
199#95—261no—
200C2×C13—21no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—21no—
204C2×C13#161612yes—
205C2×C13#161712yes—
206C2×C13#187211yescharacteristic
207C2×C13#188811yescharacteristic
208C2×C13#189011yescharacteristic
209C24C2×C22⋊D1311yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—21no—
216C22×C4—24no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—522no—
222C22×C4—522no—
223C22×C4—524no—
224C22×C4—521no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4—521no—
228C22×C4#610312yes—
229C22×C4#610312yes—
230C22×C4#610512yes—
231C22×C4#610712yes—
232C22×C4C2×C4×D1311yescharacteristic
233C22×C4C2×D5211yescharacteristic
234C22×C4#612712yes—
235C22×C4C2×C22⋊D1312yes—
236C2×C8—524no—
237C2×C8—522no—
238C4⋊C4—24no—
239C4⋊C4—24no—
240C4⋊C4—44no—
241C4⋊C4—44no—
242C4⋊C4—82no—
243C4⋊C4—264no—
244C4⋊C4—522no—
245C22⋊C4—42no—
246C22⋊C4—42no—
247C42—44no—
248C13#902311yescharacteristic, complemented, Sylow
249C23—22no—
250C23—22no—
251C23C2×#610311yescharacteristic
252C23#8818311yescharacteristic
253C23#8818611yescharacteristic
254C23C2×#610511yescharacteristic
255C23#8819611yescharacteristic
256C23C2×#610711yescharacteristic
257C23#8820711yescharacteristic
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—81no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—524no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—1042no—
281C2×C4—1042no—
282C2×C4—1042no—
283C2×C4—1042no—
284C2×C4#8805014yes—
285C2×C4C4×C22⋊D1312yes—
286C2×C4#8818412yes—
287C8—1042no—
288C22—22no—
289C22—22no—
290C22—22no—
291C22—22no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22#1171862711yescharacteristic
297C22C2×#8805011yescharacteristic
298C22#1171863111yescharacteristic
299C22#1171863211yescharacteristic
300C22#1171887411yescharacteristic
301C22#1171887911yescharacteristic
302C22#1171888911yescharacteristic
303C22#1171890412yes—
304C22#1171890612yes—
305C4—24no—
306C4—22no—
307C4—22no—
308C4—42no—
309C4—84no—
310C4—1042no—
311C4—1042no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2#1311387312yes—
317C2#1311387812yes—
318C2#1311514311yescharacteristic
319C2#1311523911yescharacteristic
320C2#1311524911yescharacteristic
subgroupG/H
centerC23#88207
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2316C2
socleC23×C13#120
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2316D13
hypocenterC13#9023
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
17. #11718647C4semidirect
248. C13#9023semidirect

Maximal subgroups

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

subgroupindex
C2×#117186472
#131149242
C2×#117181202
#131127142
C13×#23162
#902313