Finite Group Databasebeta

← #15760769

Subgroups — #15760769

Order 3328.

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

normal subgroups only

This group has 626 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
1#13123860C211yesmaximal, characteristic, complemented
2#13114828C211yesmaximal, characteristic, complemented
3#13113261C212yesmaximal, complemented
4#13112694C212yesmaximal, complemented
5C13×#2535C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#397C412yes—
10C13×#392C412yes—
11C13×#386—22no—
12C13×#382C2211yescharacteristic
13C13×#380—21no—
14C2×#88073—21no—
15C2×C22⋊#1055—22no—
16D4×#1055—24no—
17#11718586C2212yes—
18#11718585C2212yes—
19D4⋊#1055—24no—
20#11718122—21no—
21C22×D4×C13—22no—
22C22×D4×C13C2×C411yescharacteristic
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13D412yes—
26C13×#121—42no—
27C13×#121—42no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C13×C22⋊C4—22no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4C2×C412yes—
39C2×C42×C13C2311yescharacteristic
40C2×#6099—22no—
41C22×#1055—24no—
42C13×#95—22no—
43C13×#95—21no—
44C13×#95C2×C412yes—
45#88073—42no—
46C22⋊#1055—24no—
47C22⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055—22no—
51C4×#1055D414yescomplemented
52#9485—131nomaximal, Sylow
53C24×C13—21no—
54C24×C13C22⋊C412yes—
55C2×D4×C13—22no—
56C2×D4×C13—22no—
57C2×D4×C13—22no—
58C2×D4×C13—42no—
59C2×D4×C13—44no—
60C2×D4×C13—44no—
61C2×D4×C13—82no—
62C2×D4×C13D812yes—
63C2×D4×C13SD1612yes—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—42no—
72C22×C4×C13—82no—
73C22×C4×C13C22⋊C412yes—
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C22⋊C4—24no—
82C13×C22⋊C4—44no—
83C13×C22⋊C4—41no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—82no—
86C42×C13C2×D412yes—
87C42×C13#4112yes—
88#6099—42no—
89#6099—42no—
90C2×#1055—24no—
91C2×#1055—42no—
92C2×#1055—84no—
93#2972—131no—
94#2535D1311yescharacteristic
95#1800—131no—
96#1486—132no—
97#1286—132no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—22no—
101C23×C13—42no—
102C23×C13—42no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13#10214yes—
110C23×C13C2×C22⋊C411yescharacteristic
111D4×C13—24no—
112D4×C13—24no—
113D4×C13—24no—
114D4×C13—42no—
115D4×C13—88no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—44no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—82no—
128C2×C4×C13—82no—
129C2×C4×C13—82no—
130C2×C4×C13C4×D412yes—
131C2×C4×C13#12011yescharacteristic
132C2×C4×C13#12112yes—
133C2×C4×C13#12311yescharacteristic
134C2×C4×C13C2×D811yescharacteristic
135C2×C4×C13C2×SD1611yescharacteristic
136C2×C4×C13#13512yes—
137#1055—44no—
138#1055—82no—
139C2×#121—21no—
140C2×C4×D4C2×D1311yescharacteristic
141C2×C4×D4C2×D1311yescharacteristic
142C8×D4—264no—
143#431—132no—
144#423—132no—
145C2×#100—261no—
146C2×C22⋊C8—262no—
147#397Dic1312yes—
148#392Dic1312yes—
149#386—22no—
150#382C2×D1311yescharacteristic
151#380—21no—
152#343—261no—
153D4⋊C8—264no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—24no—
157C22×C13—44no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—42no—
162C22×C13—42no—
163C22×C13—82no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#38611yescharacteristic
169C22×C13C2×#10211yescharacteristic
170C22×C13#41611yescharacteristic
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—42no—
175C4×C13—82no—
176C4×C13—81no—
177C4×C13#46512yes—
178C4×C13#46612yes—
179C22×D4—22no—
180C22×D4C2×Dic1311yescharacteristic
181C22×D4C22⋊D1311yescharacteristic
182C23×C4—21no—
183C23×C4C22⋊D1312yes—
184C2×M16—262no—
185C22×C8—264no—
186#121—42no—
187#121—42no—
188C4×D4—22no—
189C4×D4—22no—
190C4×D4—22no—
191C4×D4—22no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4C2×Dic1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×Dic1312yes—
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—262no—
201C4⋊C8—262no—
202C4⋊C8—262no—
203#100—522no—
204C22⋊C8—264no—
205C22⋊C8—262no—
206C4×C8—134no—
207#95—22no—
208#95—21no—
209#95C2×Dic1312yes—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—44no—
213C2×C13—82no—
214C2×C13#189111yescharacteristic
215C2×C13#189311yescharacteristic
216C2×C13#191111yescharacteristic
217C24—21no—
218C24C22⋊Dic1312yes—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—42no—
223C2×D4—44no—
224C2×D4—44no—
225C2×D4—82no—
226C2×D4#610412yes—
227C2×D4#610512yes—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—82no—
237C22×C4C22⋊Dic1312yes—
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—522no—
242M16—522no—
243C2×C8—264no—
244C2×C8—522no—
245C2×C8—1044no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—24no—
251C22⋊C4—44no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—82no—
255C42D4×D1312yes—
256C42#612912yes—
257C13#948511yescharacteristic, complemented, Sylow
258C23—22no—
259C23—22no—
260C23—22no—
261C23—42no—
262C23—42no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#8807214yes—
270C23C2×C22⋊Dic1311yescharacteristic
271D4—24no—
272D4—24no—
273D4—24no—
274D4—42no—
275D4—88no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—42no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C2×#610411yescharacteristic
291C2×C4C2×#610511yescharacteristic
292C2×C4D4×Dic1312yes—
293C2×C4#8818911yescharacteristic
294C2×C4#8819111yescharacteristic
295C2×C4#8819312yes—
296C2×C4#8820412yes—
297C8—524no—
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C2×#8807211yescharacteristic
314C22#1171888111yescharacteristic
315C22#1171889411yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4#1171869912yes—
323C4#1171870212yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—82no—
328C2#1311525511yescharacteristic
329C2#1311526511yescharacteristic
330C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2535C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#2535D13
hypocenterC13#9485
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #13123860C2semidirect
2. #13114828C2semidirect
3. #13113261C2semidirect
4. #13112694C2semidirect
51. C4×#1055D4semidirect
257. C13#9485semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131148282
#131132612
#131126942
C13×#25352
#948513