Finite Group Databasebeta

← #15758665

Subgroups — #15758665

Order 3328.

756 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 143 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×#11718593C211yesmaximal, characteristic, complemented
2#13114904C211yesmaximal, characteristic, complemented
3C2×#11718129C212yesmaximal
4#13112714C212yesmaximal, complemented
5C13×#2854C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C22×C42×C13C2211yescharacteristic
9C22×C4×Dic13—21no—
10C13×#390C412yescomplemented
11C13×#389C412yescomplemented
12C13×#388—22no—
13C13×#386—21no—
14C13×#380C2211yescharacteristic
15C2×#88071—21no—
16C2×#88071C2212yes—
17C2×C22⋊#1055C2212yes—
18#11718593—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—
41C2×C4×Dic13—28no—
42C2×C4×Dic13—24no—
43C22×#1055—22no—
44C13×#95—22no—
45C13×#95—21no—
46#88071—24no—
47#88071—22no—
48#88071D414yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9149—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13C2×D411yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—42no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—24no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—42no—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4112yes—
76C22×Dic13—28no—
77C22×Dic13—24no—
78C22×Dic13—44no—
79C22×Dic13—42no—
80C22×Dic13—42no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—44no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—44no—
87C13×C22⋊C4—42no—
88C42×C13—24no—
89C42×C13—24no—
90C4×Dic13—216no—
91C2×#1055—44no—
92C2×#1055—42no—
93#2854D1311yescharacteristic
94C2×#376—131no—
95#1817—131no—
96C2×#327—132no—
97#1294—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—41no—
101C23×C13—42no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—42no—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13#12011yescharacteristic
107C23×C13#12311yescharacteristic
108C23×C13#13512yes—
109C23×C13AGL(1,ℤ/8)12yes—
110D4×C13—82no—
111D4×C13—82no—
112D4×C13—82no—
113C2×C4×C13—24no—
114C2×C4×C13—24no—
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—22no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13#10414yes—
133C2×C4×C13C4×D412yes—
134C2×C4×C13#12112yes—
135C2×Dic13—28no—
136C2×Dic13—44no—
137C2×Dic13—48no—
138C2×Dic13—48no—
139C2×Dic13—44no—
140#1055—82no—
141C2×#123—21no—
142C2×#121C2×D1311yescharacteristic
143C22×C42—261no—
144C22×C42C2×D1311yescharacteristic
145C2×C22⋊C8—132no—
146#390Dic1312yescomplemented
147#389Dic1312yescomplemented
148#388—22no—
149#386—21no—
150#380C2×D1311yescharacteristic
151#376—264no—
152C2×#95—132no—
153C2×#95—261no—
154#336—262no—
155#327—264no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—24no—
161C22×C13—24no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13#38611yescharacteristic
168C22×C13#41012yes—
169C22×C13#41611yescharacteristic
170C22×C13#41811yescharacteristic
171C22×C13C2×#10412yes—
172C22×C13#44912yes—
173C22×C13#48212yes—
174C4×C13—24no—
175C4×C13—22no—
176C4×C13—22no—
177C4×C13—42no—
178C4×C13—81no—
179C4×C13—82no—
180Dic13—48no—
181C22×D4—21no—
182C22×D4C2×Dic1311yescharacteristic
183C23×C4—262no—
184C23×C4C22⋊D1311yescharacteristic
185C23×C4C22⋊D1311yescharacteristic
186C23×C4C22×D1311yescharacteristic
187C22×C8—262no—
188#123—44no—
189#121—22no—
190#121—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4C2×Dic1311yescharacteristic
193C2×C4⋊C4C2×Dic1312yes—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—21no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—264no—
201C2×C42—268no—
202C2×C42C2×Dic1312yes—
203C2×C42C22⋊D1312yes—
204C22⋊C8—262no—
205C22⋊C8—262no—
206#95—22no—
207#95—21no—
208#95—134no—
209#95—264no—
210#95—262no—
211C2×C13—22no—
212C2×C13—22no—
213C2×C13—161no—
214C2×C13#150012yes—
215C2×C13#150512yes—
216C2×C13#187511yescharacteristic
217C2×C13#189611yescharacteristic
218C2×C13#189911yescharacteristic
219C24—21no—
220C24C2×C22⋊D1311yescharacteristic
221C2×D4—22no—
222C2×D4—42no—
223C2×D4—42no—
224C2×D4—41no—
225C2×D4—41no—
226C2×D4—42no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—24no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—268no—
238C22×C4—264no—
239C22×C4—524no—
240C22×C4—522no—
241C22×C4—522no—
242C22×C4C22⋊Dic1312yes—
243C22×C4C22⋊Dic1312yes—
244C22×C4D4×D1312yes—
245C22×C4#612912yes—
246C22×C4C22×Dic1311yescharacteristic
247C22×C4C2×C22⋊D1311yescharacteristic
248C2×C8—524no—
249C2×C8—522no—
250C4⋊C4—22no—
251C4⋊C4—42no—
252C4⋊C4—44no—
253C22⋊C4—44no—
254C22⋊C4—42no—
255C22⋊C4—44no—
256C22⋊C4—42no—
257C42—24no—
258C42—24no—
259C42—2616no—
260C13#914911yescharacteristic, complemented, Sylow
261C23—22no—
262C23—22no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—42no—
267C23—42no—
268C23#8818612yes—
269C23#8818911yescharacteristic
270C23#8819111yescharacteristic
271C23#8820412yes—
272C23C2×C22⋊Dic1311yescharacteristic
273D4—82no—
274D4—82no—
275D4—82no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—268no—
296C2×C4—528no—
297C2×C4—524no—
298C2×C4—528no—
299C2×C4—524no—
300C2×C4#8807714yes—
301C2×C4D4×Dic1312yes—
302C2×C4#8819312yes—
303C8—1042no—
304C22—24no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—24no—
310C22—82no—
311C22—81no—
312C22—81no—
313C22—81no—
314C22—82no—
315C22#1171869612yes—
316C22#1171869812yes—
317C22#1171887611yescharacteristic
318C22#1171888111yescharacteristic
319C22#1171889411yescharacteristic
320C22C2×#8807712yes—
321C22#1171890112yes—
322C4—24no—
323C4—22no—
324C4—22no—
325C4—42no—
326C4—82no—
327C4—81no—
328C4—528no—
329C2—22no—
330C2—22no—
331C2—161no—
332C2#1311332212yes—
333C2#1311334412yes—
334C2#1311515911yescharacteristic
335C2#1311528011yescharacteristic
336C2#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#9149
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×#11718593C2semidirect
2. #13114904C2semidirect
4. #13112714C2semidirect
10. C13×#390C4semidirect
11. C13×#389C4semidirect
146. #390Dic13semidirect
147. #389Dic13semidirect
260. C13#9149semidirect

Maximal subgroups

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

subgroupindex
C2×#117185932
#131149042
C2×#117181292
#131127142
C13×#28542
#914913