Finite Group Databasebeta

← #15772540

Subgroups — #15772540

Order 3328.

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

normal subgroups only

This group has 616 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#13113174C211yesmaximal, characteristic, complemented
2#13113154C211yesmaximal, characteristic, complemented
3#13112768C214yesmaximal, complemented
4C13×#2541C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×C13×#127C412yes—
7C2×C13×#121—21no—
8C2×C13×#121—21no—
9C2×C4×D4×C13C2211yescharacteristic
10C13×#392—21no—
11C13×#392—21no—
12C13×#390C2212yes—
13C4×C13×C4⋊C4C411yescharacteristic
14#11718868—21no—
15C2×C22⋊#1055—21no—
16#11718120C2212yes—
17#11718120C2212yes—
18#11718117—21no—
19#11718117—21no—
20C22×D4×C13—22no—
21C22×D4×C13—22no—
22C22×D4×C13—21no—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C22×D4×C13C2×C412yes—
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#127—41no—
29C13×#127—41no—
30C13×#127—44no—
31C13×#121—44no—
32C13×#121—44no—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13C2×C412yes—
43C2×#6099—41no—
44C22×#1055—41no—
45C13×#95—21no—
46C22⋊#1055—22no—
47C22⋊#1055—22no—
48C22⋊#1055—41no—
49C22⋊#1055—41no—
50#11563—131nomaximal, Sylow
51C24×C13—22no—
52C24×C13C22⋊C411yescharacteristic
53C24×C13C22⋊C411yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—24no—
57C2×D4×C13—41no—
58C2×D4×C13—42no—
59C2×D4×C13—42no—
60C2×D4×C13—42no—
61C2×D4×C13—42no—
62C2×D4×C13—44no—
63C2×D4×C13—44no—
64C2×D4×C13—42no—
65C2×D4×C13—44no—
66C2×D4×C13—44no—
67C2×D4×C13—41no—
68C2×D4×C13—41no—
69C2×D4×C13—82no—
70C2×D4×C13—82no—
71C2×D4×C13—82no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—42no—
78C22×C4×C13—42no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C13×C4⋊C4—24no—
85C13×C4⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—44no—
89C13×C22⋊C4—44no—
90C42×C13—21no—
91C42×C13—21no—
92C42×C13—42no—
93#6099—82no—
94C2×#1055—42no—
95C2×#1055—42no—
96C2×#1055—82no—
97#2541D1311yescharacteristic
98#1465—131no—
99#1459—131no—
100#1318—134no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—42no—
111C23×C13—42no—
112C23×C13—42no—
113C23×C13—42no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13#10012yes—
118C23×C13C2×C22⋊C411yescharacteristic
119D4×C13—44no—
120D4×C13—82no—
121D4×C13—84no—
122D4×C13—88no—
123D4×C13—88no—
124D4×C13—84no—
125D4×C13—82no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—22no—
129C2×C4×C13—24no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13#9911yescharacteristic
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#13112yes—
145#1055—82no—
146#1055—82no—
147C2×#127Dic1311yescharacteristic
148C2×#127Dic1312yes—
149C2×#121—21no—
150C2×#121—21no—
151C2×C4×D4C2×D1311yescharacteristic
152#407—261no—
153C2×C22⋊C8—261no—
154#392—21no—
155#392—21no—
156#390C2×D1312yes—
157C4×C4⋊C4Dic1311yescharacteristic
158#324—132no—
159#324—132no—
160#323—261no—
161#323—261no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—42no—
166C22×C13—42no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—81no—
173C22×C13—81no—
174C22×C13—82no—
175C22×C13—82no—
176C22×C13—82no—
177C22×C13—82no—
178C22×C13—82no—
179C22×C13—82no—
180C22×C13—82no—
181C22×C13#40811yescharacteristic
182C22×C13C2×#9911yescharacteristic
183C22×C13C2×#10011yescharacteristic
184C4×C13—21no—
185C4×C13—22no—
186C4×C13—44no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13#35312yes—
191C22×D4—22no—
192C22×D4—22no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4C2×Dic1311yescharacteristic
196C22×D4C2×Dic1312yes—
197C23×C4C22⋊D1311yescharacteristic
198C23×C4C22⋊D1311yescharacteristic
199C2×M16—521no—
200C22×C8—521no—
201#127—41no—
202#127—41no—
203#127—44no—
204#121—44no—
205#121—44no—
206C4×D4—41no—
207C4×D4—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4C22×D1311yescharacteristic
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4C22⋊D1311yescharacteristic
213C2×C22⋊C4C22⋊D1311yescharacteristic
214C2×C42C2×Dic1311yescharacteristic
215C2×C42C2×Dic1312yes—
216C22⋊C8—262no—
217C22⋊C8—262no—
218C22⋊C8—521no—
219C22⋊C8—521no—
220#95—21no—
221C2×C13—21no—
222C2×C13—21no—
223C2×C13—42no—
224C2×C13—81no—
225C2×C13—162no—
226C2×C13#147111yescharacteristic
227C2×C13C2×#35311yescharacteristic
228C2×C13#213411yescharacteristic
229C24—22no—
230C24C22⋊Dic1311yescharacteristic
231C24C22⋊Dic1311yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—24no—
235C2×D4—41no—
236C2×D4—42no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—42no—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—42no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—82no—
248C2×D4—82no—
249C2×D4—82no—
250C22×C4—22no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—42no—
257C22×C4C22⋊Dic1311yescharacteristic
258C22×C4C22⋊Dic1311yescharacteristic
259C22×C4C22×Dic1311yescharacteristic
260C22×C4C2×C22⋊D1311yescharacteristic
261C22×C4C2×C22⋊D1311yescharacteristic
262M16—1042no—
263C2×C8—522no—
264C2×C8—522no—
265C2×C8—1042no—
266C4⋊C4—24no—
267C4⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—44no—
271C22⋊C4—44no—
272C42—21no—
273C42—21no—
274C42—42no—
275C13#1156311yescharacteristic, complemented, Sylow
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—42no—
286C23—42no—
287C23—42no—
288C23—42no—
289C23—42no—
290C23—42no—
291C23—42no—
292C23#8807312yes—
293C23C2×C22⋊Dic1311yescharacteristic
294D4—44no—
295D4—84no—
296D4—82no—
297D4—88no—
298D4—88no—
299D4—84no—
300D4—82no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4#8807411yescharacteristic
318C2×C4#8807411yescharacteristic
319C2×C4#8820212yes—
320C8—1042no—
321C8—1042no—
322C22—21no—
323C22—21no—
324C22—22no—
325C22—42no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22—82no—
340C22—82no—
341C22C2×#8807311yescharacteristic
342C22C2×#8807411yescharacteristic
343C22#1171889511yescharacteristic
344C4—21no—
345C4—22no—
346C4—44no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4#1171813712yes—
351C2—21no—
352C2—21no—
353C2—42no—
354C2—81no—
355C2—162no—
356C2#1311319611yescharacteristic
357C2C2×#1171813711yescharacteristic
358C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2541C2
socleC22×C13C2×#99
cosocleC2×C13×C4⋊C4C23
hypercenter#2541D13
hypocenterC13#11563
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13113174C2semidirect
2. #13113154C2semidirect
3. #13112768C2semidirect
275. C13#11563semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131542
#131127682
C13×#25412
#1156313