Finite Group Databasebeta

← #15773615

Subgroups — #15773615

Order 3328.

448 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114916C211yesmaximal, characteristic, complemented
2#13113166C211yesmaximal, characteristic, complemented
3#13112842C212yesmaximal, complemented
4#13112839C212yesmaximal, complemented
5C13×#2618C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C411yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#398C411yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#396—21no—
12C13×#396—21no—
13C13×#394C411yescharacteristic
14C13×#394C2211yescharacteristic
15C13×#386—21no—
16C13×#380C411yescharacteristic
17#11718868—21no—
18#11718868—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×D4×C13—21no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C23×C4×C13D411yescharacteristic
28C13×#123—44no—
29C13×#121—41no—
30C13×#121—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4—41no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4C2×C411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4D411yescharacteristic
40C2×C13×C4⋊C4C2311yescharacteristic
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4—21no—
45C2×C13×C22⋊C4—21no—
46C2×C13×C22⋊C4—21no—
47C2×#6099—22no—
48C2×#6099—41no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95C2×C411yescharacteristic
52C13×#95C2×C411yescharacteristic
53C22⋊#1055—22no—
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56C22⋊#1055—41no—
57#11805—131nomaximal, Sylow
58C24×C13—21no—
59C24×C13C22⋊C411yescharacteristic
60C2×D4×C13—41no—
61C2×D4×C13—42no—
62C2×D4×C13—42no—
63C2×D4×C13—41no—
64C2×D4×C13—41no—
65C2×D4×C13—81no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—22no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13—41no—
77C22×C4×C13—81no—
78C22×C4×C13—81no—
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22⋊C411yescharacteristic
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C4⋊C4—42no—
92C13×C4⋊C4—81no—
93C13×C22⋊C4—42no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—81no—
98C13×C22⋊C4—81no—
99#6099—42no—
100#6099—42no—
101#6099—82no—
102C2×#1055—42no—
103C2×#1055—42no—
104#2618D1311yescharacteristic
105#1821—131no—
106#1463—131no—
107#1346—132no—
108#1345—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13#9911yescharacteristic
121C23×C13#9911yescharacteristic
122C23×C13C2×C22⋊C411yescharacteristic
123D4×C13—82no—
124D4×C13—82no—
125D4×C13—82no—
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—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—42no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—81no—
152C2×C4×C13—81no—
153C2×C4×C13—81no—
154C2×C4×C13AGL(1,ℤ/8)12yes—
155#1055—82no—
156#1055—82no—
157C2×#123—21no—
158C2×#121Dic1311yescharacteristic
159C22×C4⋊C4C2×D1311yescharacteristic
160#407—261no—
161#407—261no—
162#398Dic1311yescharacteristic
163#398C2×D1311yescharacteristic
164#396—21no—
165#396—21no—
166#394Dic1311yescharacteristic
167#394C2×D1311yescharacteristic
168#386—21no—
169#380Dic1311yescharacteristic
170#343—132no—
171#343—261no—
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×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13—81no—
190C22×C13—81no—
191C22×C13C2×#9911yescharacteristic
192C22×C13#41811yescharacteristic
193C22×C13#42111yescharacteristic
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C22×D4—21no—
204C22×D4C2×Dic1311yescharacteristic
205C23×C4C2×Dic1311yescharacteristic
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22⋊D1311yescharacteristic
208C2×M16—262no—
209C2×M16—521no—
210#123—44no—
211#121—41no—
212#121—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—41no—
217C2×C4⋊C4—41no—
218C2×C4⋊C4C2×Dic1311yescharacteristic
219C2×C4⋊C4C2×Dic1311yescharacteristic
220C2×C4⋊C4C22⋊D1311yescharacteristic
221C2×C4⋊C4C22⋊D1311yescharacteristic
222C2×C4⋊C4C22×D1311yescharacteristic
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C22⋊C8—262no—
230C22⋊C8—521no—
231C22⋊C8—521no—
232C22⋊C8—521no—
233#95—21no—
234#95—21no—
235#95C2×Dic1311yescharacteristic
236#95C2×Dic1311yescharacteristic
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—41no—
240C2×C13—41no—
241C2×C13—161no—
242C2×C13#151011yescharacteristic
243C2×C13#212111yescharacteristic
244C2×C13#213311yescharacteristic
245C24—21no—
246C24C22⋊Dic1311yescharacteristic
247C2×D4—41no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—81no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—41no—
264C22×C4—81no—
265C22×C4—81no—
266C22×C4C22⋊Dic1311yescharacteristic
267C22×C4C22⋊Dic1311yescharacteristic
268C22×C4C22⋊Dic1311yescharacteristic
269C22×C4C22×Dic1311yescharacteristic
270C22×C4C2×C22⋊D1311yescharacteristic
271C22×C4C2×C22⋊D1311yescharacteristic
272M16—522no—
273M16—522no—
274M16—1042no—
275C2×C8—522no—
276C2×C8—522no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C4⋊C4—81no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—42no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C13#1180511yescharacteristic, complemented, Sylow
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23#8807411yescharacteristic
304C23#8807411yescharacteristic
305C23C2×C22⋊Dic1311yescharacteristic
306D4—82no—
307D4—82no—
308D4—82no—
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—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4#8818612yes—
338C8—1042no—
339C8—1042no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22#1171887611yescharacteristic
358C22C2×#8807411yescharacteristic
359C22#1171889711yescharacteristic
360C4—22no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C4—81no—
369C2—21no—
370C2—21no—
371C2—41no—
372C2—41no—
373C2—161no—
374C2#1311336511yescharacteristic
375C2#1311648211yescharacteristic
376C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2618C2
socleC22×C13C2×#99
prime radicalC2×C13×#121C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2618D13
hypocenterC13#11805
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. #13114916C2semidirect
2. #13113166C2semidirect
3. #13112842C2semidirect
4. #13112839C2semidirect
291. C13#11805semidirect

Maximal subgroups

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

subgroupindex
#131149162
#131131662
#131128422
#131128392
C13×#26182
#1180513