Finite Group Databasebeta

← #15773613

Subgroups — #15773613

Order 3328.

448 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 79 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#13120578C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic, complemented
3#13112841C212yesmaximal, complemented
4#13112838C212yesmaximal, complemented
5C13×#1821C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C411yescharacteristic
8C2×#88183—21no—
9C13×#407—21no—
10#11718874—21no—
11#11718873C411yescharacteristic
12#11718868—21no—
13#11718655—21no—
14#11718655—21no—
15#11718652C411yescharacteristic
16#11718652C2211yescharacteristic
17#11718644C411yescharacteristic
18#11718644C2211yescharacteristic
19C13×#343—21no—
20C13×#343C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×C22⋊D13—21no—
27C22×D52C2×C411yescharacteristic
28C2×C13×M16—22no—
29C2×C13×C4⋊C4—41no—
30C2×C13×C4⋊C4—41no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic13—21no—
36#88184—41no—
37#88184—41no—
38#88183—44no—
39C2×#6103—21no—
40C2×#6103—21no—
41C2×#6103—21no—
42C2×#6103—21no—
43C2×#6103—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13C2×C411yescharacteristic
46C2×#6101—21no—
47C2×#6101—21no—
48C2×#6099—41no—
49C13×C22⋊C8—41no—
50C13×C22⋊C8—41no—
51#88071—21no—
52#88071—21no—
53#88071C2×C411yescharacteristic
54#88071C2×C411yescharacteristic
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57#11805—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C23×D13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—41no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C2×C22⋊D13—42no—
77C2×C22⋊D13—42no—
78C2×C22⋊D13—41no—
79C2×C22⋊D13—41no—
80C22×Dic13—21no—
81C22×Dic13—21no—
82C22×Dic13—21no—
83C2×D52—41no—
84C2×D52—81no—
85C13×M16—42no—
86C13×M16—42no—
87C2×C8×C13—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C22⋊Dic13—42no—
93#6103—42no—
94#6103—42no—
95#6103—42no—
96#6103—81no—
97#6103—81no—
98C4⋊Dic13—41no—
99C4⋊Dic13—81no—
100#6101—42no—
101#6101—42no—
102#6099—82no—
103C2×#1055—42no—
104#2618—131no—
105#1821D1311yescharacteristic, complemented
106#1463—131no—
107#1346—132no—
108#1345—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#9911yescharacteristic
114C23×C13#9911yescharacteristic
115C23×C13C2×C22⋊C411yescharacteristic
116C22×D13—41no—
117C22×D13—41no—
118C22×D13—41no—
119C22×D13—41no—
120C22×D13—41no—
121C22×D13—41no—
122C22×D13—41no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—21no—
131C2×C4×C13—21no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13—42no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13AGL(1,ℤ/8)12yes—
143C22⋊D13—82no—
144C22⋊D13—82no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—41no—
153C2×Dic13—41no—
154D52—82no—
155C8×C13—82no—
156#1055—82no—
157C2×#123—261no—
158C2×#121—131no—
159C22×C4⋊C4C2×D1311yescharacteristic
160#407—21no—
161#407—261no—
162#398—131no—
163#398—131no—
164#396—261no—
165#396—261no—
166#394—131no—
167#394—131no—
168#386—261no—
169#380—131no—
170#343—21no—
171#343C2×D1312yes—
172#324—132no—
173#324—261no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—21no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13—42no—
183C22×C13—42no—
184C22×C13C2×#9911yescharacteristic
185C22×C13#41811yescharacteristic
186C22×C13#42111yescharacteristic
187C2×D13—81no—
188C2×D13—81no—
189C2×D13—81no—
190C2×D13—81no—
191C2×D13—81no—
192C2×D13—81no—
193C2×D13—81no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200Dic13—81no—
201Dic13—81no—
202Dic13—81no—
203C22×D4—131no—
204C22×D4—261no—
205C23×C4C4×D1311yescharacteristic
206C23×C4D5211yescharacteristic
207C23×C4C22⋊D1311yescharacteristic
208C2×M16—22no—
209C2×M16—521no—
210#123—524no—
211#121—521no—
212#121—521no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4—41no—
215C2×C4⋊C4—131no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C4⋊C4C4×D1311yescharacteristic
220C2×C4⋊C4D5211yescharacteristic
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C4⋊C4C22×D1311yescharacteristic
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225C2×C22⋊C4—261no—
226C2×C22⋊C4—261no—
227C2×C22⋊C4—261no—
228C2×C22⋊C4—261no—
229C22⋊C8—41no—
230C22⋊C8—41no—
231C22⋊C8—262no—
232C22⋊C8—521no—
233#95—131no—
234#95—131no—
235#95—261no—
236#95—261no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—41no—
240C2×C13—41no—
241C2×C13#151011yescharacteristic
242C2×C13#212111yescharacteristic
243C2×C13#213311yescharacteristic
244D13—161no—
245C24—261no—
246C24#610311yescharacteristic
247C2×D4—521no—
248C2×D4—522no—
249C2×D4—522no—
250C2×D4—521no—
251C2×D4—521no—
252C2×D4—1041no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—41no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—261no—
264C22×C4—261no—
265C22×C4—261no—
266C22×C4#610311yescharacteristic
267C22×C4#610311yescharacteristic
268C22×C4#610311yescharacteristic
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272M16—42no—
273M16—42no—
274M16—1042no—
275C2×C8—42no—
276C2×C8—522no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—521no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C4⋊C4—1041no—
285C22⋊C4—522no—
286C22⋊C4—522no—
287C22⋊C4—522no—
288C22⋊C4—522no—
289C22⋊C4—1041no—
290C22⋊C4—1041no—
291C13#1180511yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—521no—
297C23—521no—
298C23—521no—
299C23—521no—
300C23—521no—
301C23—521no—
302C23—521no—
303C23#8804611yescharacteristic
304C23#8804611yescharacteristic
305C23C2×#610311yescharacteristic
306D4—1042no—
307D4—1042no—
308D4—1042no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—521no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—521no—
336C2×C4—521no—
337C2×C4#8820312yes—
338C8—82no—
339C8—1042no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—1041no—
351C22—1041no—
352C22—1041no—
353C22—1041no—
354C22—1041no—
355C22—1041no—
356C22—1041no—
357C22C2×#8804611yescharacteristic
358C22#1171866211yescharacteristic
359C22#1171866611yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—1041no—
367C4—1041no—
368C4—1041no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—2081no—
374C2#1311336411yescharacteristic
375C2#1311648311yescharacteristic
376C2#1311652311yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#1821C2
socleC22×C13C2×#99
prime radicalC2×#88184C4
cosocleC2×C13×C4⋊C4C23
hypercenter#1821D13
hypocenterC13#11805
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
2. #13113166C2semidirect
3. #13112841C2semidirect
4. #13112838C2semidirect
5. C13×#1821C2semidirect
105. #1821D13semidirect
291. C13#11805semidirect

Maximal subgroups

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

subgroupindex
#131205782
#131131662
#131128412
#131128382
C13×#18212
#1180513