Finite Group Databasebeta

← #15758705

Subgroups — #15758705

Order 3328.

648 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 135 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×#11718598C211yesmaximal, characteristic, complemented
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718129C212yesmaximal
4#13112714C212yesmaximal, complemented
5C13×#2854C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C13×#390C412yescomplemented
10C13×#389C412yescomplemented
11C13×#388—22no—
12C13×#386—21no—
13C13×#380C2211yescharacteristic
14C2×#88071—21no—
15C2×#88071—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718598—24no—
19#11718129—24no—
20#11718116—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—22no—
27C13×#123—44no—
28C13×#121—22no—
29C13×#121—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C22⋊C4—21no—
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C42×C13—22no—
38C2×C42×C13—22no—
39C2×C42×C13C2×C412yes—
40C2×C42×C13D412yes—
41C22×#1055—22no—
42C13×#95—22no—
43C13×#95—21no—
44#88071—24no—
45#88071—24no—
46#88071—22no—
47#88071D414yes—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50#9157—131nomaximal, Sylow
51C24×C13—21no—
52C24×C13C2×D411yescharacteristic
53C2×D4×C13—22no—
54C2×D4×C13—42no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13C22⋊C412yes—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D412yes—
73C22×C4×C13C2×D411yescharacteristic
74C22×C4×C13#4112yes—
75C22×Dic13—24no—
76C22×Dic13—44no—
77C22×Dic13—44no—
78C22×Dic13—42no—
79C22×Dic13—42no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—42no—
82C13×C4⋊C4—44no—
83C13×C22⋊C4—44no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C42×C13—24no—
88C42×C13—24no—
89C2×#1055—44no—
90C2×#1055—42no—
91#2854D1311yescharacteristic
92C2×#383—131no—
93#1817—131no—
94C2×#327—132no—
95#1294—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13—42no—
103C23×C13C2×C22⋊C411yescharacteristic
104C23×C13#12011yescharacteristic
105C23×C13#12311yescharacteristic
106C23×C13#13512yes—
107C23×C13AGL(1,ℤ/8)12yes—
108D4×C13—82no—
109D4×C13—82no—
110D4×C13—82no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—42no—
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12112yes—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—84no—
137C2×Dic13—84no—
138#1055—82no—
139C2×#123—21no—
140C2×#121C2×D1311yescharacteristic
141C22×C42C2×D1311yescharacteristic
142C2×C22⋊C8—132no—
143#390Dic1312yescomplemented
144#389Dic1312yescomplemented
145#388—22no—
146#386—21no—
147#383—264no—
148#380C2×D1311yescharacteristic
149C2×#95—132no—
150C2×#95—261no—
151C2×#95—261no—
152#336—262no—
153#327—264no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—24no—
159C22×C13—24no—
160C22×C13—81no—
161C22×C13—81no—
162C22×C13—81no—
163C22×C13—82no—
164C22×C13—82no—
165C22×C13#38611yescharacteristic
166C22×C13#41012yes—
167C22×C13#41611yescharacteristic
168C22×C13#41811yescharacteristic
169C22×C13#42112yes—
170C22×C13#44912yes—
171C22×C13#48212yes—
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—42no—
175C4×C13—42no—
176C4×C13—81no—
177C4×C13—82no—
178Dic13—84no—
179C22×D4—21no—
180C22×D4C2×Dic1311yescharacteristic
181C23×C4—262no—
182C23×C4C22⋊D1311yescharacteristic
183C23×C4C22⋊D1311yescharacteristic
184C23×C4C22×D1311yescharacteristic
185C22×C8—262no—
186#123—44no—
187#121—22no—
188#121—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4C2×Dic1311yescharacteristic
191C2×C4⋊C4C2×Dic1312yes—
192C2×C22⋊C4—21no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4—21no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42C2×Dic1312yes—
199C2×C42C22⋊D1312yes—
200C22⋊C8—262no—
201C22⋊C8—262no—
202#95—22no—
203#95—21no—
204#95—134no—
205#95—264no—
206#95—264no—
207#95—262no—
208C2×C13—22no—
209C2×C13—22no—
210C2×C13—161no—
211C2×C13#151412yes—
212C2×C13#152112yes—
213C2×C13#187511yescharacteristic
214C2×C13#189711yescharacteristic
215C2×C13#189911yescharacteristic
216C24—21no—
217C24C2×C22⋊D1311yescharacteristic
218C2×D4—22no—
219C2×D4—42no—
220C2×D4—42no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C22×C4—22no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—264no—
235C22×C4—524no—
236C22×C4—524no—
237C22×C4—522no—
238C22×C4—522no—
239C22×C4C22⋊Dic1312yes—
240C22×C4C22⋊Dic1312yes—
241C22×C4D4×D1312yes—
242C22×C4#612912yes—
243C22×C4C22×Dic1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245C2×C8—524no—
246C2×C8—522no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—44no—
250C22⋊C4—44no—
251C22⋊C4—44no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C42—24no—
255C42—24no—
256C13#915711yescharacteristic, complemented, Sylow
257C23—22no—
258C23—22no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—42no—
263C23—42no—
264C23#8818612yes—
265C23#8818911yescharacteristic
266C23#8819111yescharacteristic
267C23#8820412yes—
268C23C2×C22⋊Dic1311yescharacteristic
269D4—82no—
270D4—82no—
271D4—82no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—524no—
293C2×C4—524no—
294C2×C4—524no—
295C2×C4—1044no—
296C2×C4—1044no—
297C2×C4D4×Dic1312yes—
298C2×C4#8819312yes—
299C8—1042no—
300C22—24no—
301C22—24no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—82no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22#1171869612yes—
312C22#1171869812yes—
313C22#1171887611yescharacteristic
314C22#1171888111yescharacteristic
315C22#1171889411yescharacteristic
316C22#1171889712yes—
317C22#1171890112yes—
318C4—22no—
319C4—22no—
320C4—42no—
321C4—42no—
322C4—81no—
323C4—82no—
324C4—1044no—
325C2—22no—
326C2—22no—
327C2—161no—
328C2#1311338312yes—
329C2#1311341312yes—
330C2#1311515911yescharacteristic
331C2#1311528511yescharacteristic
332C2#1311529511yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic13
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2854C2
socleC23×C13C2×C22⋊C4
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2854D13
hypocenterC13#9157
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2854

Complements

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

NH ≅ G/Ntype
1. C2×#11718598C2semidirect
2. #13114904C2semidirect
4. #13112714C2semidirect
9. C13×#390C4semidirect
10. C13×#389C4semidirect
143. #390Dic13semidirect
144. #389Dic13semidirect
256. C13#9157semidirect

Maximal subgroups

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

subgroupindex
C2×#117185982
#131149042
C2×#117181292
#131127142
C13×#28542
#915713