Finite Group Databasebeta

← #15772554

Subgroups — #15772554

Order 3328.

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

normal subgroups only

This group has 494 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#13113154C211yesmaximal, characteristic, complemented
3#13112770C212yesmaximal, complemented
4#13112768C212yesmaximal, complemented
5C13×#2544C211yesmaximal, characteristic
6C2×C13×#127C411yescharacteristic
7C2×C13×#124C411yescharacteristic
8C2×C13×#124C411yescharacteristic
9C2×C4×D4×C13C2211yescharacteristic
10C13×#394—21no—
11C13×#394—21no—
12C13×#391C2211yescharacteristic
13C13×#390C2211yescharacteristic
14C13×#386—21no—
15C13×#386—21no—
16C4×C13×C4⋊C4C411yescharacteristic
17#11718868—21no—
18C2×C22⋊#1055—21no—
19#11718120C2212yes—
20#11718120C2212yes—
21#11718117—21no—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13C2×C411yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C23×C4×C13D411yescharacteristic
29C23×C4×C13D411yescharacteristic
30C13×#127—42no—
31C13×#124—41no—
32C13×#124—41no—
33C13×#124—42no—
34C4×D4×C13—41no—
35C4×D4×C13—41no—
36C2×C13×C4⋊C4—21no—
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C13×C22⋊C4—21no—
44C2×C13×C22⋊C4D411yescharacteristic
45C2×C13×C22⋊C4D411yescharacteristic
46C2×C42×C13C2×C411yescharacteristic
47C2×C42×C13C2×C411yescharacteristic
48C2×C42×C13C2×C411yescharacteristic
49C2×#6099—41no—
50C22×#1055—41no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C22⋊#1055—22no—
55C22⋊#1055—22no—
56C22⋊#1055—41no—
57C22⋊#1055—41no—
58#11566—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C24×C13C22⋊C411yescharacteristic
62C2×Q8×C13—22no—
63C2×Q8×C13—41no—
64C2×Q8×C13—41no—
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—81no—
76C2×D4×C13—81no—
77C22×C4×C13—21no—
78C22×C4×C13—21no—
79C22×C4×C13—21no—
80C22×C4×C13—21no—
81C22×C4×C13—21no—
82C22×C4×C13—21no—
83C22×C4×C13—21no—
84C22×C4×C13—81no—
85C22×C4×C13—81no—
86C22×C4×C13C22⋊C411yescharacteristic
87C22×C4×C13C22⋊C411yescharacteristic
88C22×C4×C13C22×C411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
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—81no—
101C13×C22⋊C4—81no—
102C42×C13—21no—
103C42×C13—21no—
104C42×C13—41no—
105C42×C13—41no—
106#6099—82no—
107C2×#1055—42no—
108C2×#1055—42no—
109C2×#1055—82no—
110#2544D1311yescharacteristic
111#1465—131no—
112#1459—131no—
113#1319—132no—
114#1318—132no—
115C23×C13—21no—
116C23×C13—21no—
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—41no—
128C23×C13—41no—
129C23×C13—41no—
130C23×C13—41no—
131C23×C13#10012yes—
132C23×C13C2×C22⋊C411yescharacteristic
133Q8×C13—82no—
134D4×C13—44no—
135D4×C13—82no—
136D4×C13—84no—
137D4×C13—84no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
140C2×C4×C13—22no—
141C2×C4×C13—21no—
142C2×C4×C13—21no—
143C2×C4×C13—21no—
144C2×C4×C13—41no—
145C2×C4×C13—42no—
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—81no—
159C2×C4×C13—81no—
160C2×C4×C13#9911yescharacteristic
161C2×C4×C13#9911yescharacteristic
162C2×C4×C13#13112yes—
163#1055—82no—
164#1055—82no—
165C2×#127Dic1311yescharacteristic
166C2×#124Dic1311yescharacteristic
167C2×#124Dic1311yescharacteristic
168C2×C4×D4C2×D1311yescharacteristic
169#407—261no—
170C2×C22⋊C8—261no—
171#394—21no—
172#394—21no—
173#391C2×D1311yescharacteristic
174#390C2×D1311yescharacteristic
175#386—21no—
176#386—21no—
177C4×C4⋊C4Dic1311yescharacteristic
178#324—132no—
179#324—132no—
180#323—261no—
181#323—261no—
182C22×C13—21no—
183C22×C13—21no—
184C22×C13—22no—
185C22×C13—42no—
186C22×C13—42no—
187C22×C13—41no—
188C22×C13—41no—
189C22×C13—41no—
190C22×C13—41no—
191C22×C13—41no—
192C22×C13—81no—
193C22×C13—81no—
194C22×C13—81no—
195C22×C13—81no—
196C22×C13—81no—
197C22×C13—81no—
198C22×C13—81no—
199C22×C13—81no—
200C22×C13—81no—
201C22×C13#40811yescharacteristic
202C22×C13C2×#9911yescharacteristic
203C22×C13C2×#10011yescharacteristic
204C4×C13—21no—
205C4×C13—21no—
206C4×C13—22no—
207C4×C13—42no—
208C4×C13—41no—
209C4×C13—41no—
210C4×C13—41no—
211C4×C13—81no—
212C4×C13—81no—
213C22×Q8C2×Dic1311yescharacteristic
214C22×D4—21no—
215C22×D4—21no—
216C22×D4C2×Dic1311yescharacteristic
217C22×D4C2×Dic1311yescharacteristic
218C23×C4C22⋊D1311yescharacteristic
219C23×C4C22⋊D1311yescharacteristic
220C2×M16—521no—
221C22×C8—521no—
222#127—42no—
223#124—41no—
224#124—41no—
225#124—42no—
226C4×D4—41no—
227C4×D4—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C22×D1311yescharacteristic
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4C22⋊D1311yescharacteristic
237C2×C22⋊C4C22⋊D1311yescharacteristic
238C2×C42C2×Dic1311yescharacteristic
239C2×C42C2×Dic1311yescharacteristic
240C2×C42C2×Dic1311yescharacteristic
241C22⋊C8—262no—
242C22⋊C8—262no—
243C22⋊C8—521no—
244C22⋊C8—521no—
245#95—21no—
246#95—21no—
247#95—21no—
248C2×C13—21no—
249C2×C13—21no—
250C2×C13—42no—
251C2×C13—81no—
252C2×C13—161no—
253C2×C13#147111yescharacteristic
254C2×C13#212711yescharacteristic
255C2×C13#213211yescharacteristic
256C24—21no—
257C24C22⋊Dic1311yescharacteristic
258C24C22⋊Dic1311yescharacteristic
259C2×Q8—22no—
260C2×Q8—41no—
261C2×Q8—41no—
262C2×D4—22no—
263C2×D4—22no—
264C2×D4—22no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—42no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—81no—
273C2×D4—81no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—81no—
282C22×C4—81no—
283C22×C4C22⋊Dic1311yescharacteristic
284C22×C4C22⋊Dic1311yescharacteristic
285C22×C4C22×Dic1311yescharacteristic
286C22×C4C2×C22⋊D1311yescharacteristic
287C22×C4C2×C22⋊D1311yescharacteristic
288M16—1042no—
289C2×C8—522no—
290C2×C8—522no—
291C2×C8—1042no—
292C4⋊C4—41no—
293C4⋊C4—42no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C22⋊C4—42no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C42—21no—
304C42—21no—
305C42—41no—
306C42—41no—
307C13#1156611yescharacteristic, complemented, Sylow
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23#8807312yes—
325C23C2×C22⋊Dic1311yescharacteristic
326Q8—82no—
327D4—44no—
328D4—82no—
329D4—84no—
330D4—84no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4#8807411yescharacteristic
354C2×C4#8807411yescharacteristic
355C2×C4#8820212yes—
356C8—1042no—
357C8—1042no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22C2×#8807311yescharacteristic
378C22C2×#8807411yescharacteristic
379C22#1171889511yescharacteristic
380C4—21no—
381C4—21no—
382C4—22no—
383C4—42no—
384C4—41no—
385C4—41no—
386C4—41no—
387C4—81no—
388C4—81no—
389C2—21no—
390C2—21no—
391C2—42no—
392C2—81no—
393C2—161no—
394C2#1311319611yescharacteristic
395C2#1311650511yescharacteristic
396C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2544C2
socleC22×C13C2×#99
prime radicalC2×C13×#127C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2544D13
hypocenterC13#11566
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2544

Complements

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

NH ≅ G/Ntype
1. #13113174C2semidirect
2. #13113154C2semidirect
3. #13112770C2semidirect
4. #13112768C2semidirect
307. C13#11566semidirect

Maximal subgroups

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

subgroupindex
#131131742
#131131542
#131127702
#131127682
C13×#25442
#1156613