Finite Group Databasebeta

← #16788377

Subgroups — #16788377

Order 3328.

452 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 80 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#13130696C211yesmaximal, characteristic
2#13130075C211yesmaximal, characteristic
3#13129833C214yesmaximal, complemented
4#13119147C211yesmaximal, characteristic
5C22×C13×C4⋊C4C411yescharacteristic, complemented
6C2×C4×C22⋊D13C2211yescharacteristic
7C2×#88119—21no—
8#11719136—21no—
9#11719125—21no—
10#11718874—21no—
11#11718873C411yescharacteristic, complemented
12#11718871—21no—
13#11718653C2212yes—
14#11718648—21no—
15#11718643C412yescomplemented
16#11718634—21no—
17#11718305—21no—
18#11718289C2212yes—
19#11718287C2212yes—
20C23×C4×C13—21no—
21C23×C4×C13C2×C411yescharacteristic
22C22×C22⋊D13D411yescharacteristic
23C22×C4×D13D411yescharacteristic
24C2×C22⋊#261—22no—
25C2×C4⋊#261—41no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13D411yescharacteristic
32C4×C22⋊D13—41no—
33C4×C22⋊D13—41no—
34C2×#6103—22no—
35C2×#6103C2311yescharacteristic
36C2×C4⋊Dic13—21no—
37C2×#6101—22no—
38C2×#6101C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C22⋊#1057—22no—
41#88119—42no—
42(C2×#261)⋊C4—41no—
43#88112—41no—
44C4×#1057—41no—
45#88071—22no—
46#88071—22no—
47#88071C2×C412yes—
48#11899—131nomaximal, Sylow
49C24×C13C22⋊C411yescharacteristic
50C23×D13C2×D411yescharacteristic
51C22×#261—42no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—42no—
56C22×C4×C13—42no—
57C22×C4×C13—82no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C2×C22⋊D13—41no—
61C2×C22⋊D13—41no—
62C2×C22⋊D13SD1612yes—
63C2×C22⋊D13Q1612yes—
64C22×Dic13—22no—
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C22⋊C411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C2×C4×D13—21no—
69C2×C4×D13—21no—
70C2×C4×D13—42no—
71C22⋊#261—42no—
72C22⋊#261—42no—
73C2×#1057—42no—
74C4⋊#261—82no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C22⋊Dic13—41no—
79C22⋊Dic13—42no—
80#6103—41no—
81#6103—82no—
82C4⋊Dic13—42no—
83#6101—41no—
84#6101—82no—
85C4×Dic13—21no—
86C4×Dic13—21no—
87#2487—131no—
88#1799—131no—
89#1460—131no—
90#1352—134no—
91C23×C13—21no—
92C23×C13—21no—
93C23×C13—41no—
94C23×C13—41no—
95C23×C13#10312yes—
96C23×C13C2×C22⋊C411yescharacteristic
97C22×D13—21no—
98C22×D13—21no—
99C22×D13—41no—
100C22×D13—41no—
101C22×D13C2×SD1611yescharacteristic
102C22×D13C2×Q1611yescharacteristic
103C2×#261—82no—
104C2×#261—82no—
105C2×#261—82no—
106C2×C4×C13—22no—
107C2×C4×C13—21no—
108C2×C4×C13—42no—
109C2×C4×C13—42no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—42no—
114C2×C4×C13—84no—
115C2×C4×C13#9911yescharacteristic
116C2×C4×C13#9911yescharacteristic
117C22⋊D13—42no—
118C22⋊D13—42no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—41no—
124C2×Dic13—41no—
125C2×Dic13—42no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13#10312yes—
129C4×D13—42no—
130C4×D13—81no—
131#1057—82no—
132C2×C4×D4—131no—
133C22×C4⋊C4#26111yescharacteristic, complemented
134#431—261no—
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—132no—
146#323—261no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—22no—
150C22×C13—42no—
151C22×C13—42no—
152C22×C13—41no—
153C22×C13—41no—
154C22×C13C2×#9911yescharacteristic
155C22×C13C2×#10311yescharacteristic
156C22×C13#42111yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—41no—
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—81no—
164#261—162no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—82no—
168C4×C13#35212yes—
169Dic13—22no—
170Dic13—41no—
171Dic13—41no—
172Dic13—82no—
173C22×D4—131no—
174C23×C4—21no—
175C23×C4—131no—
176C23×C4C2×#26111yescharacteristic
177C4×D4—521no—
178C4×D4—521no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—41no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—261no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—521no—
186C2×C4⋊C4C2×#26112yes—
187C2×C22⋊C4—131no—
188C2×C22⋊C4—131no—
189C2×C22⋊C4—261no—
190C2×C22⋊C4—262no—
191C2×C22⋊C4—262no—
192C2×C42—131no—
193C4⋊C8—521no—
194#99—522no—
195C22⋊C8—262no—
196C4×C8—521no—
197#95—132no—
198#95—262no—
199#95—262no—
200#95—521no—
201C2×C13—21no—
202C2×C13—21no—
203C2×C13—42no—
204C2×C13#152011yescharacteristic
205C2×C13C2×#35211yescharacteristic
206C2×C13#212811yescharacteristic
207D13—41no—
208D13—41no—
209C24—131no—
210C24C22⋊#26111yescharacteristic
211C2×D4—132no—
212C2×D4—132no—
213C2×D4—521no—
214C2×D4—521no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—82no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—131no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4—262no—
227C22×C4—522no—
228C22×C4—522no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22×#26111yescharacteristic
231C2×C8—522no—
232C4⋊C4—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—521no—
236C4⋊C4—522no—
237C4⋊C4—1042no—
238C4⋊C4—1042no—
239C22⋊C4—521no—
240C22⋊C4—521no—
241C22⋊C4—522no—
242C22⋊C4—522no—
243C22⋊C4—522no—
244C22⋊C4—1042no—
245C42—261no—
246C42—261no—
247C13#1189911yescharacteristic, complemented, Sylow
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—131no—
253C23—131no—
254C23—261no—
255C23—261no—
256C23—521no—
257C23—521no—
258C23#8811712yes—
259C23C2×C22⋊#26111yescharacteristic
260D4—522no—
261D4—522no—
262C2×C4—22no—
263C2×C4—21no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—84no—
271C2×C4—132no—
272C2×C4—261no—
273C2×C4—261no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—522no—
277C2×C4—521no—
278C2×C4—521no—
279C2×C4—522no—
280C2×C4—522no—
281C2×C4—522no—
282C2×C4—1041no—
283C2×C4—1042no—
284C2×C4—1042no—
285C2×C4—1042no—
286C2×C4#8811911yescharacteristic
287C2×C4#8811911yescharacteristic
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—261no—
297C22—261no—
298C22—521no—
299C22—521no—
300C22—521no—
301C22—521no—
302C22—1041no—
303C22C2×#8811711yescharacteristic
304C22#1171915511yescharacteristic
305C22C2×#8811911yescharacteristic
306C4—21no—
307C4—41no—
308C4—82no—
309C4—262no—
310C4—521no—
311C4—521no—
312C4—1042no—
313C4—2082no—
314C4#1171828812yes—
315C2—21no—
316C2—21no—
317C2—42no—
318C2—521no—
319C2—521no—
320C2#1313027611yescharacteristic
321C2C2×#1171828811yescharacteristic
322C2#1313111511yescharacteristic
subgroupG/H
centerC22C2×#88119
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC22×C13×C4⋊C4C4
socleC22×C13C2×#99
prime radicalC22×C22⋊D13D4
cosocleC2×#6103C23
hypercenterC22×C4⋊C4#261
hypocenterC13#11899
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13129833C2semidirect
5. C22×C13×C4⋊C4C4semidirect
11. #11718873C4semidirect
15. #11718643C4semidirect
133. C22×C4⋊C4#261semidirect
247. C13#11899semidirect

Maximal subgroups

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

subgroupindex
#131306962
#131300752
#131298332
#131191472
#1189913