Finite Group Databasebeta

← #15760806

Subgroups — #15760806

Order 3328.

458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123474C211yesmaximal, characteristic
2#13120413C211yesmaximal, characteristic
3#13113282C212yesmaximal, complemented
4#13112702C212yesmaximal, complemented
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#432C2212yes—
9#11718871—21no—
10#11718868—21no—
11#11718661—24no—
12#11718644C411yescharacteristic
13#11718640C411yescharacteristic
14#11718639—21no—
15#11718614C411yescharacteristic
16#11718608C411yescharacteristic
17#11718605—21no—
18#11718598C2211yescharacteristic
19#11718594—21no—
20#11718585—21no—
21C4×#6099C2212yes—
22C13×#324—21no—
23C13×#323—21no—
24#11718076—24no—
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C13×#117—22no—
28C13×#117—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D411yescharacteristic
31C2×C13×C22⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×#6099—22no—
43C4×Dic26—22no—
44C4×Dic26—22no—
45C13×C4⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#97—22no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56C22⋊#1055—24no—
57C4⋊#1055—24no—
58#88043—22no—
59C4×#1055D414yes—
60#9493—131nomaximal, Sylow
61C24×C13C22⋊C411yescharacteristic
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—41no—
65C22×C4×C13—41no—
66C22×C4×C13C22⋊C411yescharacteristic
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×Dic13—21no—
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C2×Dic26—22no—
77C2×Dic26—42no—
78C2×C8×C13—42no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C22⋊C4—22no—
82C13×C22⋊C4—22no—
83C42×C13—21no—
84C42×C13—21no—
85C42×C13C2×D412yes—
86C42×C13#4112yes—
87C22⋊Dic13—42no—
88C22⋊Dic13—42no—
89C4⋊Dic13—22no—
90#6101—42no—
91#6101—42no—
92#6101—41no—
93#6101—41no—
94C4×Dic13—42no—
95#6099—42no—
96#6099—42no—
97C2×#1055—24no—
98#2921—131no—
99#2599—131no—
100#1491—132no—
101#1464D1311yescharacteristic
102#1288—132no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12011yescharacteristic
124C2×C4×C13#12112yes—
125C2×C4×C13#12311yescharacteristic
126C2×Dic13—22no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138Dic26—24no—
139Dic26—42no—
140C8×C13—82no—
141#1055—44no—
142C2×C4×Q8—131no—
143C2×#117C2×D1311yescharacteristic
144#433—264no—
145#432C2×D1312yes—
146#423—261no—
147#407—261no—
148C4×M16—132no—
149#398—131no—
150#397—131no—
151#395—131no—
152#393—131no—
153#388—261no—
154#387—261no—
155#387—261no—
156#385—261no—
157#383—131no—
158Q8⋊C8—264no—
159#324—21no—
160#323—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—42no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—81no—
168C22×C13#38611yescharacteristic
169C22×C13#42111yescharacteristic
170C22×C13#42111yescharacteristic
171C4×C13—22no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—22no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178Dic13—42no—
179Dic13—81no—
180Dic13—81no—
181Dic13—81no—
182C22×Q8—131no—
183C23×C4D5211yescharacteristic
184C2×M16—262no—
185C4×Q8—262no—
186C4×Q8—262no—
187#117—22no—
188#117—22no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4C4×D1311yescharacteristic
194C2×C4⋊C4C22⋊D1311yescharacteristic
195C2×C22⋊C4—261no—
196C2×C22⋊C4—261no—
197C2×C22⋊C4C4×D1311yescharacteristic
198C2×C22⋊C4C22⋊D1311yescharacteristic
199C2×C42—261no—
200C2×C42D5211yescharacteristic
201C2×C42C22×D1311yescharacteristic
202C4⋊C8—22no—
203C4⋊C8—264no—
204C22⋊C8—22no—
205C22⋊C8—264no—
206#97—22no—
207#97—262no—
208C4×C8—134no—
209#95—131no—
210#95—131no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13—81no—
220C2×C13#189111yescharacteristic
221C2×C13#189711yescharacteristic
222C2×C13#190911yescharacteristic
223C24#610311yescharacteristic
224C2×Q8—262no—
225C2×Q8—522no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4#610311yescharacteristic
237C22×C4C2×C4×D1311yescharacteristic
238C22×C4C2×D5211yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240M16—522no—
241M16—522no—
242C2×C8—42no—
243C2×C8—264no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—262no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—521no—
250C4⋊C4—521no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—522no—
254C22⋊C4—522no—
255C42—21no—
256C42—21no—
257C42—522no—
258C42D4×D1312yes—
259C42#612912yes—
260C13#949311yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×#610311yescharacteristic
267Q8—264no—
268Q8—522no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—262no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4#8813512yes—
295C2×C4#8813611yescharacteristic
296C2×C4#8814011yescharacteristic
297C2×C4#8819312yes—
298C8—82no—
299C8—524no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#1171861911yescharacteristic
308C22#1171880011yescharacteristic
309C22#1171880011yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—522no—
318C4—1041no—
319C4—1041no—
320C4—1041no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2#1311525211yescharacteristic
325C2#1311528211yescharacteristic
326C2#1311535611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1464C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1464D13
hypocenterC13#9493
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
3. #13113282C2semidirect
4. #13112702C2semidirect
260. C13#9493semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131204132
#131132822
#131127022
C13×#14642
#949313