Finite Group Databasebeta

← #15773965

Subgroups — #15773965

Order 3328.

764 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 107 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#13114828C211yesmaximal, characteristic, complemented
2#13113154C211yesmaximal, characteristic, complemented
3#13112839C214yesmaximal, complemented
4C13×#2408C211yesmaximal, characteristic
5C23×D4×C13C411yescharacteristic
6C2×C13×#121—21no—
7C2×C13×#120—21no—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#394C2212yes—
10C13×#392C412yes—
11C13×#390—21no—
12C13×#380C411yescharacteristic
13C13×#379—21no—
14C2×#88073—21no—
15C2×C22⋊#1055—21no—
16#11718585—21no—
17#11718122C2212yescomplemented
18#11718120C2212yescomplemented
19#11718117—21no—
20C25×C13—21no—
21C22×D4×C13—22no—
22C22×D4×C13—21no—
23C22×D4×C13—41no—
24C22×D4×C13—41no—
25C22×D4×C13—44no—
26C22×D4×C13C2×C412yes—
27C22×D4×C13D411yescharacteristic
28C23×C4×C13C2×C411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#121—44no—
31C13×#120—42no—
32C13×#120—42no—
33C4×D4×C13—41no—
34C4×D4×C13—41no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2311yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—22no—
40C2×C13×C22⋊C4—22no—
41C2×C13×C22⋊C4C2×C411yescharacteristic
42C2×C13×C22⋊C4D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C2×#6099—22no—
45C22×#1055—41no—
46C13×#95C2×C412yes—
47#88073—42no—
48C22⋊#1055—22no—
49C22⋊#1055—41no—
50C4⋊#1055—41no—
51C4⋊#1055—41no—
52#11880—131nomaximal, Sylow
53C24×C13—22no—
54C24×C13—42no—
55C24×C13—44no—
56C24×C13—42no—
57C24×C13—42no—
58C24×C13—82no—
59C24×C13C22⋊C411yescharacteristic
60C24×C13C22⋊C411yescharacteristic
61C2×D4×C13—24no—
62C2×D4×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—48no—
67C2×D4×C13—44no—
68C2×D4×C13—44no—
69C2×D4×C13—44no—
70C2×D4×C13—44no—
71C2×D4×C13—44no—
72C2×D4×C13—41no—
73C2×D4×C13—41no—
74C2×D4×C13—82no—
75C2×D4×C13D812yes—
76C2×D4×C13SD1612yes—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—22no—
82C22×C4×C13—42no—
83C22×C4×C13—42no—
84C22×C4×C13C22⋊C411yescharacteristic
85C22×C4×C13C22⋊C411yescharacteristic
86C22×C4×C13C22×C411yescharacteristic
87C22×C4×C13C2×D411yescharacteristic
88C22×C4×C13C2×D411yescharacteristic
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—44no—
94C13×C22⋊C4—42no—
95C13×C22⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—82no—
98C42×C13—21no—
99C42×C13—21no—
100#6099—42no—
101#6099—42no—
102C2×#1055—42no—
103C2×#1055—42no—
104C2×#1055—82no—
105#2408D1311yescharacteristic
106#1800—131no—
107#1459—131no—
108#1345—134no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—24no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—42no—
119C23×C13—42no—
120C23×C13—42no—
121C23×C13—48no—
122C23×C13—42no—
123C23×C13—42no—
124C23×C13—42no—
125C23×C13—84no—
126C23×C13—88no—
127C23×C13—88no—
128C23×C13—84no—
129C23×C13#10212yes—
130C23×C13#10212yes—
131C23×C13C2×C22⋊C411yescharacteristic
132D4×C13—42no—
133D4×C13—42no—
134D4×C13—44no—
135D4×C13—44no—
136D4×C13—44no—
137D4×C13—44no—
138D4×C13—88no—
139C2×C4×C13—21no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—21no—
145C2×C4×C13—42no—
146C2×C4×C13—42no—
147C2×C4×C13—42no—
148C2×C4×C13—41no—
149C2×C4×C13—41no—
150C2×C4×C13—41no—
151C2×C4×C13—42no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13—81no—
155C2×C4×C13#9911yescharacteristic
156C2×C4×C13#9911yescharacteristic
157C2×C4×C13C2×D811yescharacteristic
158C2×C4×C13C2×SD1611yescharacteristic
159#1055—82no—
160#1055—82no—
161C23×D4Dic1311yescharacteristic
162C2×#121—21no—
163C2×#120—21no—
164C2×C4×D4C2×D1311yescharacteristic
165#423—261no—
166C2×#100—261no—
167C2×C22⋊C8—261no—
168#394C2×D1312yes—
169#392Dic1312yes—
170#390—21no—
171#380Dic1311yescharacteristic
172#379—21no—
173#343—132no—
174#324—132no—
175#323—261no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—22no—
179C22×C13—22no—
180C22×C13—42no—
181C22×C13—42no—
182C22×C13—42no—
183C22×C13—44no—
184C22×C13—44no—
185C22×C13—41no—
186C22×C13—41no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—44no—
190C22×C13—81no—
191C22×C13—82no—
192C22×C13—82no—
193C22×C13—816no—
194C22×C13—82no—
195C22×C13—82no—
196C22×C13C2×#9911yescharacteristic
197C22×C13C2×#10211yescharacteristic
198C22×C13#42111yescharacteristic
199C4×C13—21no—
200C4×C13—21no—
201C4×C13—21no—
202C4×C13—41no—
203C4×C13—41no—
204C4×C13—41no—
205C4×C13—82no—
206C4×C13AΣL(1,𝔽16)12yes—
207C25—21no—
208C22×D4—22no—
209C22×D4—21no—
210C22×D4—41no—
211C22×D4—41no—
212C22×D4—44no—
213C22×D4C2×Dic1312yes—
214C22×D4C22⋊D1311yescharacteristic
215C23×C4C2×Dic1311yescharacteristic
216C23×C4C22⋊D1311yescharacteristic
217C2×M16—262no—
218C22×C8—521no—
219#121—44no—
220#120—42no—
221#120—42no—
222C4×D4—41no—
223C4×D4—41no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4C22×D1311yescharacteristic
226C2×C22⋊C4—21no—
227C2×C22⋊C4—22no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4C2×Dic1311yescharacteristic
231C2×C22⋊C4C22⋊D1311yescharacteristic
232C2×C42C22⋊D1311yescharacteristic
233C4⋊C8—521no—
234C4⋊C8—521no—
235#100—522no—
236C22⋊C8—262no—
237C22⋊C8—521no—
238#95C2×Dic1312yes—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—42no—
242C2×C13—42no—
243C2×C13—84no—
244C2×C13#151911yescharacteristic
245C2×C13C2×AΣL(1,𝔽16)11yescharacteristic
246C2×C13#213411yescharacteristic
247C24—22no—
248C24—42no—
249C24—44no—
250C24—42no—
251C24—42no—
252C24—82no—
253C24C22⋊Dic1311yescharacteristic
254C24C22⋊Dic1311yescharacteristic
255C2×D4—24no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—48no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—82no—
269C2×D4#610412yes—
270C2×D4#610512yes—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—22no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4C22⋊Dic1311yescharacteristic
279C22×C4C22⋊Dic1311yescharacteristic
280C22×C4C22×Dic1311yescharacteristic
281C22×C4C2×C22⋊D1311yescharacteristic
282C22×C4C2×C22⋊D1311yescharacteristic
283M16—522no—
284M16—522no—
285C2×C8—522no—
286C2×C8—522no—
287C2×C8—1042no—
288C4⋊C4—41no—
289C4⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—44no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—82no—
297C42—21no—
298C42—21no—
299C13#1188011yescharacteristic, complemented, Sylow
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—24no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—48no—
313C23—42no—
314C23—42no—
315C23—42no—
316C23—84no—
317C23—88no—
318C23—88no—
319C23—84no—
320C23#8807212yes—
321C23#8807212yes—
322C23C2×C22⋊Dic1311yescharacteristic
323D4—42no—
324D4—42no—
325D4—44no—
326D4—44no—
327D4—44no—
328D4—44no—
329D4—88no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—22no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—81no—
346C2×C4#8807411yescharacteristic
347C2×C4#8807411yescharacteristic
348C2×C4C2×#610411yescharacteristic
349C2×C4C2×#610511yescharacteristic
350C8—1042no—
351C8—1042no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—22no—
356C22—42no—
357C22—42no—
358C22—42no—
359C22—44no—
360C22—44no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—44no—
366C22—81no—
367C22—82no—
368C22—82no—
369C22—816no—
370C22—82no—
371C22—82no—
372C22C2×#8807211yescharacteristic
373C22C2×#8807411yescharacteristic
374C22#1171889711yescharacteristic
375C4—21no—
376C4—21no—
377C4—21no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—82no—
382C4#1171812812yes—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—42no—
387C2—84no—
388C2#1311340411yescharacteristic
389C2C2×#1171812811yescharacteristic
390C2#1311652811yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
Fitting, prime radicalC13×#2408C2
socleC22×C13C2×#99
cosocleC2×C13×C4⋊C4C23
hypercenter#2408D13
hypocenterC13#11880
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. #13114828C2semidirect
2. #13113154C2semidirect
3. #13112839C2semidirect
17. #11718122C22semidirect
18. #11718120C22semidirect
299. C13#11880semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131542
#131128392
C13×#24082
#1188013