Finite Group Databasebeta

← #15772523

Subgroups — #15772523

Order 3328.

532 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 91 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#13113157C211yesmaximal, characteristic, complemented
3#13112766C212yesmaximal, complemented
4#13112764C212yesmaximal, complemented
5C13×#2534C211yesmaximal, characteristic
6C2×C13×#123C411yescharacteristic
7C2×C13×#120C411yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C22×C13×C22⋊C4C411yescharacteristic
10C13×#396—21no—
11C13×#394—21no—
12C13×#388—21no—
13C13×#386—21no—
14C13×#381C2211yescharacteristic
15C13×#380C411yescharacteristic
16C13×#379C2211yescharacteristic
17#11718868—21no—
18#11718586—21no—
19#11718120—21no—
20#11718117—21no—
21#11718117C2212yes—
22#11718117C2212yes—
23C25×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13C2×C411yescharacteristic
27C23×C4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C13×#123—42no—
30C13×#120—42no—
31C4×D4×C13—41no—
32C4×D4×C13—41no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—41no—
43C2×C13×C22⋊C4—41no—
44C2×C13×C22⋊C4C2×C411yescharacteristic
45C2×C13×C22⋊C4C2×C411yescharacteristic
46C2×C13×C22⋊C4D411yescharacteristic
47C2×C13×C22⋊C4C2311yescharacteristic
48C2×C42×C13D411yescharacteristic
49C2×#6099—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C22⋊#1055—22no—
54C22⋊#1055—22no—
55C22⋊#1055—41no—
56C4⋊#1055—41no—
57C4×#1055—41no—
58#11559—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13—22no—
61C24×C13—41no—
62C24×C13—42no—
63C24×C13—41no—
64C24×C13—81no—
65C24×C13C22⋊C411yescharacteristic
66C24×C13C22×C411yescharacteristic
67C2×D4×C13—22no—
68C2×D4×C13—22no—
69C2×D4×C13—41no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—81no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—21no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—22no—
81C22×C4×C13—41no—
82C22×C4×C13—41no—
83C22×C4×C13—81no—
84C22×C4×C13—81no—
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C13×C4⋊C4—41no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—41no—
94C13×C22⋊C4—41no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C13×C22⋊C4—41no—
99C13×C22⋊C4—41no—
100C13×C22⋊C4—42no—
101C13×C22⋊C4—41no—
102C13×C22⋊C4—41no—
103C13×C22⋊C4—81no—
104C42×C13—21no—
105C42×C13—21no—
106#6099—82no—
107C2×#1055—42no—
108C2×#1055—42no—
109#2534D1311yescharacteristic
110#1465—131no—
111#1460—131no—
112#1317—132no—
113#1316—132no—
114C23×C13—21no—
115C23×C13—21no—
116C23×C13—22no—
117C23×C13—21no—
118C23×C13—21no—
119C23×C13—21no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13—41no—
123C23×C13—41no—
124C23×C13—41no—
125C23×C13—41no—
126C23×C13—41no—
127C23×C13—42no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13—42no—
132C23×C13—82no—
133C23×C13—84no—
134C23×C13—84no—
135C23×C13—82no—
136C23×C13C2×C22⋊C411yescharacteristic
137C23×C13#13112yes—
138D4×C13—44no—
139D4×C13—84no—
140C2×C4×C13—21no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—41no—
146C2×C4×C13—42no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—41no—
152C2×C4×C13—41no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13—81no—
160C2×C4×C13—81no—
161C2×C4×C13—81no—
162C2×C4×C13—82no—
163C2×C4×C13#9911yescharacteristic
164C2×C4×C13#9911yescharacteristic
165C2×C4×C13#10012yes—
166#1055—82no—
167#1055—82no—
168C2×#123Dic1311yescharacteristic
169C2×#120Dic1311yescharacteristic
170C2×C4×D4C2×D1311yescharacteristic
171C22×C22⋊C4Dic1311yescharacteristic
172#431—261no—
173#407—261no—
174#396—21no—
175#394—21no—
176#388—21no—
177#386—21no—
178#381C2×D1311yescharacteristic
179#380Dic1311yescharacteristic
180#379C2×D1311yescharacteristic
181#324—261no—
182#323—132no—
183#323—132no—
184#323—261no—
185C22×C13—21no—
186C22×C13—21no—
187C22×C13—22no—
188C22×C13—42no—
189C22×C13—42no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13—42no—
193C22×C13—41no—
194C22×C13—41no—
195C22×C13—41no—
196C22×C13—42no—
197C22×C13—41no—
198C22×C13—41no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13—81no—
202C22×C13—84no—
203C22×C13—84no—
204C22×C13—81no—
205C22×C13—81no—
206C22×C13#40811yescharacteristic
207C22×C13C2×#9911yescharacteristic
208C22×C13C2×#10011yescharacteristic
209C4×C13—21no—
210C4×C13—21no—
211C4×C13—22no—
212C4×C13—41no—
213C4×C13—41no—
214C4×C13—41no—
215C4×C13—81no—
216C4×C13—81no—
217C4×C13—81no—
218C25C2×Dic1311yescharacteristic
219C22×D4—21no—
220C22×D4C2×Dic1311yescharacteristic
221C23×C4C2×Dic1311yescharacteristic
222C23×C4C2×Dic1311yescharacteristic
223C23×C4C22⋊D1311yescharacteristic
224C2×M16—521no—
225#123—42no—
226#120—42no—
227C4×D4—41no—
228C4×D4—41no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C22⋊D1311yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—41no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4C2×Dic1311yescharacteristic
241C2×C22⋊C4C2×Dic1311yescharacteristic
242C2×C22⋊C4C22⋊D1311yescharacteristic
243C2×C22⋊C4C22×D1311yescharacteristic
244C2×C42C22⋊D1311yescharacteristic
245C4⋊C8—521no—
246C22⋊C8—262no—
247C22⋊C8—262no—
248C22⋊C8—521no—
249C4×C8—521no—
250#95—21no—
251#95—21no—
252#95—21no—
253C2×C13—21no—
254C2×C13—21no—
255C2×C13—42no—
256C2×C13—81no—
257C2×C13—82no—
258C2×C13#147111yescharacteristic
259C2×C13#212011yescharacteristic
260C2×C13#212111yescharacteristic
261C24—21no—
262C24—22no—
263C24—41no—
264C24—42no—
265C24—41no—
266C24—81no—
267C24C22⋊Dic1311yescharacteristic
268C24C22×Dic1311yescharacteristic
269C2×D4—22no—
270C2×D4—22no—
271C2×D4—41no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—81no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4—81no—
286C22×C4—81no—
287C22×C4C22⋊Dic1311yescharacteristic
288C22×C4C22⋊Dic1311yescharacteristic
289C22×C4C22⋊Dic1311yescharacteristic
290C22×C4C2×C22⋊D1311yescharacteristic
291C22×C4C2×C22⋊D1311yescharacteristic
292M16—1042no—
293C2×C8—522no—
294C2×C8—522no—
295C4⋊C4—41no—
296C4⋊C4—42no—
297C4⋊C4—81no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—81no—
309C42—21no—
310C42—21no—
311C13#1155911yescharacteristic, complemented, Sylow
312C23—21no—
313C23—21no—
314C23—22no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—42no—
326C23—42no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—82no—
331C23—84no—
332C23—84no—
333C23—82no—
334C23#8820212yes—
335C23C2×C22⋊Dic1311yescharacteristic
336D4—44no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—82no—
361C2×C4#8807312yes—
362C2×C4#8807411yescharacteristic
363C2×C4#8807411yescharacteristic
364C8—1042no—
365C8—1042no—
366C22—21no—
367C22—21no—
368C22—22no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—42no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—84no—
384C22—84no—
385C22—81no—
386C22—81no—
387C22C2×#8807311yescharacteristic
388C22C2×#8807411yescharacteristic
389C22#1171889511yescharacteristic
390C4—21no—
391C4—21no—
392C4—22no—
393C4—41no—
394C4—41no—
395C4—41no—
396C4—81no—
397C4—81no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—81no—
403C2—82no—
404C2#1311319611yescharacteristic
405C2#1311647711yescharacteristic
406C2#1311648211yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC24×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2534C2
socleC22×C13C2×#99
prime radicalC2×C13×#120C4
cosocleC2×C13×C22⋊C4C23
hypercenter#2534D13
hypocenterC13#11559
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2534

Complements

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

NH ≅ G/Ntype
1. #13113174C2semidirect
2. #13113157C2semidirect
3. #13112766C2semidirect
4. #13112764C2semidirect
311. C13#11559semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131572
#131127662
#131127642
C13×#25342
#1155913