Finite Group Databasebeta

← #15760267

Subgroups — #15760267

Order 3328.

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

normal subgroups only

This group has 446 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#13120534C211yesmaximal, characteristic
3#13113439C212yesmaximal, complemented
4#13112728C212yesmaximal, complemented
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×#88124C2211yescharacteristic
8C13×#432C2212yes—
9#11718871—21no—
10#11718868—21no—
11#11718661—24no—
12#11718647C411yescharacteristic
13#11718644C411yescharacteristic
14#11718633—21no—
15#11718614C411yescharacteristic
16#11718610C411yescharacteristic
17#11718606—21no—
18#11718594—21no—
19#11718593C2211yescharacteristic
20#11718585—21no—
21C4×#6099C2212yes—
22C13×#324—21no—
23C13×#323—21no—
24#11718057—24no—
25C23×C4×C13D411yescharacteristic
26C13×#117—22no—
27C13×#117—22no—
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44#88124—22no—
45#88124—22no—
46C13×C4⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×#97—22no—
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#88043D414yes—
59C4×#1055—22no—
60#9390—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×C8×C13—42no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—22no—
79C13×C22⋊C4—22no—
80C13×C22⋊C4—22no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13C2×D412yes—
84C42×C13#4112yes—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C4⋊Dic13—22no—
88C4⋊Dic13—22no—
89#6101—42no—
90#6101—42no—
91#6101—41no—
92#6101—42no—
93#6101—41no—
94C4×Dic13—42no—
95#6099—42no—
96#6099—42no—
97C2×#1055—24no—
98#2921—131no—
99#2611—131no—
100#1528—132no—
101#1464D1311yescharacteristic
102#1300—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—
138C8×C13—82no—
139#1055—44no—
140C2×#125—131no—
141C2×#117C2×D1311yescharacteristic
142#433—264no—
143#432C2×D1312yes—
144#423—261no—
145#407—261no—
146C4×M16—132no—
147#400—131no—
148#399—131no—
149#398—131no—
150#397—131no—
151#389—261no—
152#388—261no—
153#387—261no—
154#385—261no—
155#376—131no—
156#330—264no—
157#324—21no—
158#323—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—42no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13#38611yescharacteristic
167C22×C13#42111yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176Dic13—42no—
177Dic13—81no—
178Dic13—81no—
179Dic13—81no—
180C23×C4D5211yescharacteristic
181C2×M16—262no—
182#125—262no—
183#125—262no—
184#117—22no—
185#117—22no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4C4×D1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4—261no—
195C2×C22⋊C4—261no—
196C2×C22⋊C4C4×D1311yescharacteristic
197C2×C22⋊C4C22⋊D1311yescharacteristic
198C2×C42—261no—
199C2×C42D5211yescharacteristic
200C2×C42C22×D1311yescharacteristic
201C4⋊C8—22no—
202C4⋊C8—264no—
203C22⋊C8—22no—
204C22⋊C8—264no—
205#97—22no—
206#97—134no—
207C4×C8—262no—
208#95—131no—
209#95—131no—
210#95—261no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215C2×C13—21no—
216C2×C13—21no—
217C2×C13—81no—
218C2×C13#188411yescharacteristic
219C2×C13#189711yescharacteristic
220C2×C13#191511yescharacteristic
221C24#610311yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—261no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4#610311yescharacteristic
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4C2×D5211yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236M16—522no—
237M16—522no—
238C2×C8—42no—
239C2×C8—264no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—262no—
243C4⋊C4—262no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C4⋊C4—521no—
247C4⋊C4—521no—
248C4⋊C4—522no—
249C22⋊C4—22no—
250C22⋊C4—22no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C42—21no—
254C42—21no—
255C42—522no—
256C42D4×D1312yes—
257C42#612912yes—
258C13#939011yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×#610311yescharacteristic
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—262no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4#8813512yes—
291C2×C4#8813611yescharacteristic
292C2×C4#8814011yescharacteristic
293C2×C4#8819312yes—
294C8—82no—
295C8—524no—
296C22—21no—
297C22—21no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1171861911yescharacteristic
304C22#1171880011yescharacteristic
305C22#1171880011yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—22no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—522no—
314C4—1041no—
315C4—1041no—
316C4—1041no—
317C2—21no—
318C2—21no—
319C2—81no—
320C2#1311521711yescharacteristic
321C2#1311528211yescharacteristic
322C2#1311538611yescharacteristic
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#9390
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. #13113439C2semidirect
4. #13112728C2semidirect
258. C13#9390semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131205342
#131134392
#131127282
C13×#14642
#939013