Finite Group Databasebeta

← #15760586

Subgroups — #15760586

Order 3328.

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

normal subgroups only

This group has 490 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#13123865C211yesmaximal, characteristic
2#13120032C211yesmaximal, characteristic
3#13113462C212yesmaximal, complemented
4#13112693C212yesmaximal, complemented
5C13×#1466C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88124C2211yescharacteristic
8C13×#432C2212yes—
9#11718882C411yescharacteristic
10#11718882C411yescharacteristic
11#11718871—21no—
12#11718871—21no—
13#11718868—21no—
14C2×C22⋊#1055—21no—
15#11718672—24no—
16#11718638C411yescharacteristic
17#11718637C411yescharacteristic
18#11718609—21no—
19#11718609—21no—
20C4×C4⋊Dic13C2211yescharacteristic
21#11718587C2212yes—
22C13×#323—21no—
23C13×#323—21no—
24#11718057—24no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C22⋊C4D411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C42×C13C2311yescharacteristic
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—21no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×#6101—21no—
43C2×#6101—21no—
44C2×#6101—21no—
45C2×C4×Dic13C2×C411yescharacteristic
46C2×C4×Dic13C2×C411yescharacteristic
47C2×#6099—22no—
48C22×#1055—22no—
49#88124—22no—
50#88124—22no—
51C13×C4⋊C8—22no—
52C13×C22⋊C8—22no—
53C13×#97—22no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57C22⋊#1055—22no—
58C22⋊#1055—22no—
59C22⋊#1055—22no—
60C4⋊#1055—22no—
61#88043D414yes—
62#9449—131nomaximal, Sylow
63C24×C13C22⋊C411yescharacteristic
64C24×C13C22⋊C411yescharacteristic
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—41no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—21no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C2×C8×C13—42no—
84C13×C4⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C42×C13C2×D412yes—
88C42×C13#4112yes—
89C22⋊Dic13—42no—
90C22⋊Dic13—42no—
91C22⋊Dic13—81no—
92C22⋊Dic13—81no—
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—42no—
96#6101—41no—
97#6101—42no—
98#6101—41no—
99#6101—81no—
100#6101—81no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103#6099—82no—
104C2×#1055—24no—
105C2×#1055—82no—
106#2973—131no—
107#2566—131no—
108#1534—132no—
109#1466D1311yescharacteristic
110#1285—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—21no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#10112yes—
121C23×C13C2×C22⋊C411yescharacteristic
122D4×C13—44no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—81no—
134C2×C4×C13—81no—
135C2×C4×C13C4×D412yes—
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12112yes—
138C2×C4×C13#12311yescharacteristic
139C2×Dic13—22no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C8×C13—82no—
152#1055—44no—
153C2×#125—131no—
154C2×C4×D4C2×D1311yescharacteristic
155#435—264no—
156#432—132no—
157#432C2×D1312yes—
158#407—261no—
159C2×C22⋊C8—261no—
160#396—261no—
161#396—261no—
162#390—131no—
163#390—131no—
164#385—261no—
165#385—261no—
166#384—131no—
167#382—131no—
168C4×C4⋊C4—131no—
169#330—264no—
170#323—21no—
171#323—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—22no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—41no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13#38611yescharacteristic
185C22×C13C2×#10111yescharacteristic
186C22×C13#41311yescharacteristic
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—41no—
192C4×C13—41no—
193Dic13—42no—
194Dic13—81no—
195Dic13—81no—
196Dic13—81no—
197C22×D4C4×D1311yescharacteristic
198C23×C4D5211yescharacteristic
199C23×C4D5211yescharacteristic
200C2×M16—262no—
201C22×C8—262no—
202#125—262no—
203#125—262no—
204C4×D4—22no—
205C4×D4—22no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—261no—
209C2×C4⋊C4—261no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4C4×D1311yescharacteristic
214C2×C22⋊C4—261no—
215C2×C22⋊C4—261no—
216C2×C22⋊C4—261no—
217C2×C22⋊C4—261no—
218C2×C22⋊C4C22⋊D1311yescharacteristic
219C2×C22⋊C4C22⋊D1311yescharacteristic
220C2×C42—131no—
221C2×C42—131no—
222C2×C42C22×D1311yescharacteristic
223C4⋊C8—22no—
224C4⋊C8—262no—
225C22⋊C8—22no—
226C22⋊C8—262no—
227C22⋊C8—262no—
228C22⋊C8—262no—
229#97—22no—
230#97—134no—
231#95—261no—
232#95—261no—
233#95—261no—
234C2×C13—21no—
235C2×C13—21no—
236C2×C13—42no—
237C2×C13—81no—
238C2×C13#188411yescharacteristic
239C2×C13#190111yescharacteristic
240C2×C13#191111yescharacteristic
241C24#610311yescharacteristic
242C24#610311yescharacteristic
243C2×D4—22no—
244C2×D4—22no—
245C2×D4—41no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—81no—
251C22×C4—81no—
252C22×C4—261no—
253C22×C4—261no—
254C22×C4—261no—
255C22×C4—261no—
256C22×C4#610311yescharacteristic
257C22×C4#610311yescharacteristic
258C22×C4C2×C4×D1311yescharacteristic
259C22×C4C2×D5211yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261M16—1042no—
262C2×C8—42no—
263C2×C8—264no—
264C2×C8—1042no—
265C4⋊C4—22no—
266C4⋊C4—262no—
267C4⋊C4—262no—
268C4⋊C4—522no—
269C4⋊C4—521no—
270C4⋊C4—521no—
271C4⋊C4—522no—
272C4⋊C4—1041no—
273C4⋊C4—1041no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—522no—
277C22⋊C4—522no—
278C22⋊C4—1041no—
279C22⋊C4—1041no—
280C42—521no—
281C42—521no—
282C42D4×D1312yes—
283C42#612912yes—
284C13#944911yescharacteristic, complemented, Sylow
285C23—21no—
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23#8806412yes—
295C23C2×#610311yescharacteristic
296D4—44no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—42no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—262no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4—521no—
314C2×C4—521no—
315C2×C4—521no—
316C2×C4—521no—
317C2×C4—521no—
318C2×C4—521no—
319C2×C4—521no—
320C2×C4—521no—
321C2×C4#8813512yes—
322C2×C4#8813611yescharacteristic
323C2×C4#8814011yescharacteristic
324C2×C4#8819312yes—
325C8—82no—
326C8—524no—
327C22—21no—
328C22—21no—
329C22—22no—
330C22—42no—
331C22—42no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22—81no—
339C22#1171861911yescharacteristic
340C22#1171879311yescharacteristic
341C22C2×#8806411yescharacteristic
342C4—22no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—522no—
349C4—1041no—
350C4—1041no—
351C4—1041no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—81no—
356C2#1311521711yescharacteristic
357C2#1311530211yescharacteristic
358C2#1311536611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1466C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#1466D13
hypocenterC13#9449
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
3. #13113462C2semidirect
4. #13112693C2semidirect
284. C13#9449semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131200322
#131134622
#131126932
C13×#14662
#944913