Finite Group Databasebeta

← #15774048

Subgroups — #15774048

Order 3328.

452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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#13119153C211yesmaximal, characteristic
2#13114824C211yesmaximal, characteristic
3#13112861C214yesmaximal, complemented
4C13×#1460C211yesmaximal, characteristic
5C2×C4×D4×C13C2211yescharacteristic
6C22×C4⋊Dic13C411yescharacteristic, complemented
7C13×#431—21no—
8#11718881—21no—
9C2×#88074—21no—
10#11718873—21no—
11#11718873—21no—
12#11718873C411yescharacteristic, complemented
13#11718647C412yescomplemented
14#11718610C2212yes—
15#11718607—21no—
16#11718589—21no—
17C13×#323—21no—
18C13×#323C2212yes—
19#11718118C2212yes—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×Dic13—21no—
24C4×D4×C13—41no—
25C4×D4×C13—41no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C22⋊C4D411yescharacteristic
28C2×C13×C22⋊C4C2311yescharacteristic
29C2×C42×C13D411yescharacteristic
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—22no—
33C2×C4⋊Dic13—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13—41no—
36C2×C4⋊Dic13—41no—
37C2×C4⋊Dic13—41no—
38C2×C4⋊Dic13C2×C412yes—
39C2×#6101—22no—
40C13×C4⋊C8—41no—
41C13×C22⋊C8—22no—
42C4×C8×C13—41no—
43#88074—42no—
44#88071—22no—
45#88071—22no—
46#88071—41no—
47#88071C2×C412yes—
48#11899—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C24×C13C2×D411yescharacteristic
51C2×D4×C13—41no—
52C2×D4×C13—41no—
53C2×D4×C13SD1612yes—
54C2×D4×C13Q1612yes—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13—42no—
61C22×C4×C13C22⋊C411yescharacteristic
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D411yescharacteristic
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—42no—
69C22×Dic13—42no—
70C22×Dic13—82no—
71C2×C8×C13—42no—
72C13×C4⋊C4—41no—
73C13×C22⋊C4—41no—
74C13×C22⋊C4—41no—
75C42×C13—21no—
76C42×C13—21no—
77C22⋊Dic13—42no—
78C22⋊Dic13—42no—
79C22⋊Dic13—42no—
80C22⋊Dic13—82no—
81C4⋊Dic13—42no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13—42no—
85C4⋊Dic13—82no—
86#6101—82no—
87#2487—131no—
88#1799—131no—
89#1460D1311yescharacteristic
90#1352—134no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—21no—
95C23×C13—41no—
96C23×C13—41no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13#10312yes—
100C23×C13C2×C22⋊C411yescharacteristic
101C23×C13C2×SD1611yescharacteristic
102C23×C13C2×Q1611yescharacteristic
103D4×C13—42no—
104D4×C13—42no—
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—22no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—81no—
118C2×C4×C13#9911yescharacteristic
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13#10312yes—
121C2×Dic13—42no—
122C2×Dic13—42no—
123C2×Dic13—42no—
124C2×Dic13—42no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—84no—
128C2×Dic13—82no—
129C2×Dic13—82no—
130C2×Dic13—82no—
131C8×C13—82no—
132C2×C4×D4C2×D1311yescharacteristic
133C22×C4⋊C4—131no—
134#431—21no—
135C2×#99—261no—
136#400—132no—
137#399—132no—
138#389—261no—
139#386—261no—
140#385—261no—
141#380—131no—
142#380—261no—
143#380—261no—
144#342—132no—
145#323—21no—
146#323C2×D1312yes—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—22no—
151C22×C13—21no—
152C22×C13—42no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—42no—
156C22×C13—41no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—81no—
161C22×C13C2×#9911yescharacteristic
162C22×C13C2×#10311yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—21no—
165C4×C13—22no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13#35212yes—
170Dic13—82no—
171Dic13—82no—
172Dic13—162no—
173C22×D4D5211yescharacteristic
174C23×C4—261no—
175C23×C4C4×D1311yescharacteristic
176C23×C4D5211yescharacteristic
177C4×D4—41no—
178C4×D4—41no—
179C2×C4⋊C4—132no—
180C2×C4⋊C4—261no—
181C2×C4⋊C4—261no—
182C2×C4⋊C4—262no—
183C2×C4⋊C4—521no—
184C2×C4⋊C4—521no—
185C2×C4⋊C4—521no—
186C2×C4⋊C4C4×D1311yescharacteristic
187C2×C22⋊C4—261no—
188C2×C22⋊C4—262no—
189C2×C22⋊C4—262no—
190C2×C22⋊C4C22⋊D1311yescharacteristic
191C2×C22⋊C4C22×D1311yescharacteristic
192C2×C42C22⋊D1311yescharacteristic
193C4⋊C8—41no—
194#99—522no—
195C22⋊C8—22no—
196C4×C8—41no—
197#95—132no—
198#95—262no—
199#95—262no—
200#95—521no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—41no—
204C2×C13—42no—
205C2×C13—41no—
206C2×C13#152011yescharacteristic
207C2×C13C2×#35211yescharacteristic
208C2×C13#212811yescharacteristic
209C24#610311yescharacteristic
210C24C2×D5211yescharacteristic
211C2×D4—41no—
212C2×D4—41no—
213C2×D4#609512yes—
214C2×D4Dic5212yes—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4—262no—
222C22×C4—262no—
223C22×C4—522no—
224C22×C4—522no—
225C22×C4—1042no—
226C22×C4#610311yescharacteristic
227C22×C4#610311yescharacteristic
228C22×C4#610311yescharacteristic
229C22×C4C2×C4×D1311yescharacteristic
230C22×C4C2×C22⋊D1311yescharacteristic
231C2×C8—42no—
232C4⋊C4—41no—
233C4⋊C4—522no—
234C4⋊C4—522no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C4⋊C4—1042no—
238C4⋊C4—1042no—
239C22⋊C4—41no—
240C22⋊C4—41no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C22⋊C4—1042no—
245C42—21no—
246C42—21no—
247C13#1189911yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23#8805612yes—
257C23C2×#609511yescharacteristic
258C23C2×Dic5211yescharacteristic
259C23C2×#610311yescharacteristic
260D4—42no—
261D4—42no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—522no—
276C2×C4—522no—
277C2×C4—522no—
278C2×C4—522no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—1044no—
282C2×C4—1042no—
283C2×C4—1042no—
284C2×C4—1042no—
285C2×C4#8804611yescharacteristic
286C2×C4#8804611yescharacteristic
287C2×C4#8805612yes—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—41no—
295C22—41no—
296C22—42no—
297C22—42no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22C2×#8804611yescharacteristic
304C22C2×#8805611yescharacteristic
305C22#1171880011yescharacteristic
306C4—21no—
307C4—22no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—1042no—
312C4—1042no—
313C4—2082no—
314C4#1171806812yes—
315C2—21no—
316C2—21no—
317C2—41no—
318C2—42no—
319C2—41no—
320C2#1311340911yescharacteristic
321C2C2×#1171806811yescharacteristic
322C2#1311650711yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1460C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1460D13
hypocenterC13#11899
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13112861C2semidirect
6. C22×C4⋊Dic13C4semidirect
12. #11718873C4semidirect
13. #11718647C4semidirect
247. C13#11899semidirect

Maximal subgroups

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

subgroupindex
#131191532
#131148242
#131128612
C13×#14602
#1189913