Finite Group Databasebeta

← #15844189

Subgroups — #15844189

Order 3328.

850 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 171 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#13126042C212yesmaximal, complemented
2#13125222C211yesmaximal, characteristic
3#13114170C218yesmaximal, complemented
4#13113460C211yesmaximal, characteristic
5#13113438C212yesmaximal, complemented
6C2×C13×#563C211yesmaximal, characteristic
7C13×#563—24no—
8C13×#563—22no—
9C13×#563C2214yes—
10C2×C13×C4⋊Q8—21no—
11C2×C13×#126—22no—
12C2×C13×#125C2212yes—
13C2×C13×#124C2211yescharacteristic
14C2×C13×#123—21no—
15C2×C13×C22⋊Q8—22no—
16#11719175C2211yescharacteristic
17#11718886—21no—
18#11718876—21no—
19#11718730C2214yescomplemented
20#11718726C2214yescomplemented
21#11718724—24no—
22#11718717—22no—
23#11718716C2214yes—
24#11718632—22no—
25#11718631—22no—
26#11718587C2212yes—
27C4×#6099C2211yescharacteristic
28#11718135C2218yescomplemented
29#11718132C2214yes—
30C22×Q8×C13—21no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C23×C4×C13—21no—
34C13×C4⋊Q8—24no—
35C13×C4⋊Q8—24no—
36C13×#126—28no—
37C13×#126—28no—
38C13×#125—22no—
39C13×#125—22no—
40C13×#125D414yes—
41C13×#125C2314yes—
42C13×#124—22no—
43C13×#124D412yes—
44C13×#124C2312yes—
45C13×#123—24no—
46C13×#123—24no—
47C13×C22⋊Q8—28no—
48C13×C22⋊Q8—28no—
49C2×C13×C4⋊C4—22no—
50C2×C13×C4⋊C4—22no—
51C2×C13×C4⋊C4—22no—
52C2×C13×C4⋊C4D412yes—
53C2×C13×C4⋊C4D412yes—
54C2×C13×C22⋊C4—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—22no—
57C2×C42×C13—21no—
58C2×C42×C13C2311yescharacteristic
59#88180—21no—
60#88178—22no—
61C2×#6099—21no—
62#88124—21no—
63#88123C2312yes—
64C4×Dic26—22no—
65#88075—24no—
66#88072—24no—
67C22⋊#1055—22no—
68#88050—24no—
69#88050—24no—
70#88048—24no—
71#88047—24no—
72C4⋊#1055—22no—
73#88043C2312yes—
74#88043C2314yes—
75C4×#1055—21no—
76#18999—131nomaximal, Sylow
77C24×C13—21no—
78C2×Q8×C13—24no—
79C2×Q8×C13—21no—
80C2×Q8×C13—42no—
81C2×Q8×C13—82no—
82C2×Q8×C13C2×D412yes—
83C2×D4×C13—21no—
84C2×D4×C13—42no—
85C2×D4×C13C2×D412yes—
86C22×C4×C13—22no—
87C22×C4×C13—21no—
88C22×C4×C13—22no—
89C22×C4×C13—24no—
90C22×C4×C13—82no—
91C22×C4×C13C2×D411yescharacteristic
92C22×C4×C13C2×D412yes—
93C2×Dic26—22no—
94C13×C4⋊C4—28no—
95C13×C4⋊C4—24no—
96C13×C4⋊C4—24no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—22no—
99C13×C4⋊C4—24no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4C2×D414yes—
102C13×C4⋊C4C2×D414yes—
103C13×C22⋊C4—28no—
104C13×C22⋊C4—24no—
105C13×C22⋊C4—24no—
106C13×C22⋊C4—24no—
107C42×C13—24no—
108C42×C13C2×D412yes—
109C42×C13C2×D411yescharacteristic
110C42×C13C2411yescharacteristic
111C22⋊Dic13—41no—
112C4⋊Dic13—22no—
113C4⋊Dic13—22no—
114#6101—42no—
115C4×Dic13—41no—
116#6099—42no—
117C2×#1055—24no—
118C2×#1055—22no—
119C2×#563D1311yescharacteristic
120#3236—132no—
121#3140—131no—
122#1664—138no—
123#1533—131no—
124#1528—132no—
125C23×C13—22no—
126C23×C13—44no—
127C23×C13—42no—
128C23×C13#12011yescharacteristic
129Q8×C13—42no—
130Q8×C13—81no—
131Q8×C13—84no—
132D4×C13—42no—
133D4×C13—81no—
134C2×C4×C13—22no—
135C2×C4×C13—24no—
136C2×C4×C13—22no—
137C2×C4×C13—24no—
138C2×C4×C13—42no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13—42no—
142C2×C4×C13—84no—
143C2×C4×C13#12011yescharacteristic
144C2×C4×C13#12012yes—
145C2×C4×C13C22×D411yescharacteristic
146C2×C4×C13C22×D412yes—
147C2×Dic13—42no—
148Dic26—44no—
149#1055—44no—
150#1055—42no—
151#563—24no—
152#563—22no—
153#563C2×D1314yes—
154#533—131no—
155C2×C4⋊Q8—21no—
156C2×#126—22no—
157C2×#125C2×D1312yes—
158C2×#124C2×D1311yescharacteristic
159C2×#123—21no—
160C2×C22⋊Q8—22no—
161#501—134no—
162#491—134no—
163#489—134no—
164#488—262no—
165#484—262no—
166#483—262no—
167#479—264no—
168#432—132no—
169#419—261no—
170#418—261no—
171C4×M16—131no—
172#330—138no—
173#329—134no—
174C22×C13—22no—
175C22×C13—42no—
176C22×C13—44no—
177C22×C13—84no—
178C22×C13#45512yes—
179C22×C13C2×#12011yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—22no—
184C4×C13—44no—
185C4×C13—42no—
186C4×C13—44no—
187Dic13—82no—
188C22×Q8—21no—
189C22×Q8C22⋊D1311yescharacteristic
190C22×D4C22⋊D1311yescharacteristic
191C23×C4—21no—
192C2×M16—261no—
193C4⋊Q8—24no—
194C4⋊Q8—24no—
195C4⋊Q8—132no—
196#126—28no—
197#126—28no—
198#125—22no—
199#125—22no—
200#125—261no—
201#125C22⋊D1314yes—
202#125C22×D1314yes—
203#124—22no—
204#124C22⋊D1312yes—
205#124C22×D1312yes—
206#123—24no—
207#123—24no—
208C22⋊Q8—28no—
209C22⋊Q8—28no—
210C22⋊Q8—262no—
211C4×Q8—262no—
212#117—261no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4C22⋊D1312yes—
217C2×C4⋊C4C22⋊D1312yes—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C42—21no—
222C2×C42C22×D1311yescharacteristic
223#107—264no—
224#106—264no—
225C4⋊C8—262no—
226#103—264no—
227#103—264no—
228#103—264no—
229#102—264no—
230C22⋊C8—262no—
231#97—134no—
232#97—132no—
233C4×C8—261no—
234C2×C13—22no—
235C2×C13—82no—
236C2×C13C2×#45511yescharacteristic
237C2×C13#302012yes—
238C24—21no—
239C2×Q8—24no—
240C2×Q8—21no—
241C2×Q8—42no—
242C2×Q8—82no—
243C2×Q8—262no—
244C2×Q8C2×C22⋊D1312yes—
245C2×D4—21no—
246C2×D4—42no—
247C2×D4C2×C22⋊D1312yes—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—82no—
253C22×C4C2×C22⋊D1311yescharacteristic
254C22×C4C2×C22⋊D1312yes—
255M16—522no—
256C2×C8—262no—
257C2×C8—264no—
258C4⋊C4—28no—
259C4⋊C4—24no—
260C4⋊C4—24no—
261C4⋊C4—22no—
262C4⋊C4—22no—
263C4⋊C4—24no—
264C4⋊C4—24no—
265C4⋊C4—262no—
266C4⋊C4—262no—
267C4⋊C4—522no—
268C4⋊C4C2×C22⋊D1314yes—
269C4⋊C4C2×C22⋊D1314yes—
270C22⋊C4—28no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—24no—
274C22⋊C4—521no—
275C42—24no—
276C42—521no—
277C42C2×C22⋊D1311yescharacteristic
278C42C2×C22⋊D1312yes—
279C42C23×D1311yescharacteristic
280C13#1899911yescharacteristic, complemented, Sylow
281C23—22no—
282C23—44no—
283C23—42no—
284C23#8820711yescharacteristic
285Q8—42no—
286Q8—81no—
287Q8—84no—
288Q8—524no—
289D4—42no—
290D4—81no—
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—42no—
299C2×C4—84no—
300C2×C4—522no—
301C2×C4#8820711yescharacteristic
302C2×C4#8820712yes—
303C2×C4C22×C22⋊D1312yes—
304C2×C4C22×C22⋊D1311yescharacteristic
305C8—524no—
306C8—522no—
307C22—22no—
308C22—42no—
309C22—44no—
310C22—84no—
311C22#1171890312yes—
312C22C2×#8820711yescharacteristic
313C4—21no—
314C4—21no—
315C4—22no—
316C4—22no—
317C4—44no—
318C4—42no—
319C4—44no—
320C4—1042no—
321C2—22no—
322C2—82no—
323C2C2×#1171890311yescharacteristic
324C2#1312420012yes—
subgroupG/H
centerC22C2×#88207
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC2×C13×#563C2
socleC22×C13C2×#120
prime radicalC22×D4×C13D4
hypercenterC2×#563D13
hypocenterC13#18999
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#563

Complements

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

NH ≅ G/Ntype
1. #13126042C2semidirect
3. #13114170C2semidirect
5. #13113438C2semidirect
19. #11718730C22semidirect
20. #11718726C22semidirect
28. #11718135C22semidirect
280. C13#18999semidirect

Maximal subgroups

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

subgroupindex
#131260422
#131252222
#131141702
#131134602
#131134382
C2×C13×#5632
#1899913