Finite Group Databasebeta

← #15773435

Subgroups — #15773435

Order 3328.

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

normal subgroups only

This group has 470 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#13114575C211yesmaximal, characteristic, complemented
2#13113170C211yesmaximal, characteristic, complemented
3#13112866C212yesmaximal, complemented
4#13112839C212yesmaximal, complemented
5C13×#2610C211yesmaximal, characteristic
6C2×C13×#124C411yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#395C2211yescharacteristic
10C13×#394C2211yescharacteristic
11C13×#393C411yescharacteristic
12C13×#392C411yescharacteristic
13C13×#390—21no—
14C13×#388—21no—
15C13×#388—21no—
16C13×#386—21no—
17C13×#376C411yescharacteristic
18#11718587—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13—21no—
25C22×D4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×#124—41no—
28C13×#124—41no—
29C13×#117—41no—
30C13×#117—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4D411yescharacteristic
33C2×C13×C4⋊C4C2311yescharacteristic
34C2×C13×C22⋊C4—21no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13—21no—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×#6099—24no—
46C2×#6099—22no—
47C2×#6099—41no—
48C2×#6099—42no—
49C22×#1055—41no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95C2×C411yescharacteristic
54C13×#95C2×C411yescharacteristic
55C22⋊#1055—22no—
56C4⋊#1055—41no—
57#88043—41no—
58#11765—131nomaximal, Sylow
59C24×C13—21no—
60C24×C13C22⋊C411yescharacteristic
61C2×Q8×C13—41no—
62C2×Q8×C13—81no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C2×D4×C13—42no—
66C2×D4×C13—81no—
67C2×D4×C13—81no—
68C22×C4×C13—22no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—21no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22×C411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×C4×C13C2×D411yescharacteristic
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—81no—
85C13×C22⋊C4—41no—
86C13×C22⋊C4—41no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92C13×C22⋊C4—41no—
93C13×C22⋊C4—81no—
94C13×C22⋊C4—81no—
95C42×C13—21no—
96C42×C13—21no—
97C42×C13—21no—
98C42×C13—21no—
99C42×C13—42no—
100#6099—24no—
101#6099—44no—
102#6099—42no—
103C2×#1055—44no—
104C2×#1055—42no—
105C2×#1055—42no—
106#2610D1311yescharacteristic
107#1742—131no—
108#1464—131no—
109#1354—132no—
110#1345—132no—
111C23×C13—21no—
112C23×C13—21no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13—41no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13—41no—
120C23×C13—41no—
121C23×C13—41no—
122C23×C13#10412yes—
123C23×C13C2×C22⋊C411yescharacteristic
124Q8×C13—82no—
125D4×C13—84no—
126D4×C13—82no—
127C2×C4×C13—22no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—22no—
131C2×C4×C13—21no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—21no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—21no—
138C2×C4×C13—21no—
139C2×C4×C13—21no—
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—41no—
152C2×C4×C13#9911yescharacteristic
153C2×C4×C13#9911yescharacteristic
154C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C13#13711yescharacteristic
156#1055—44no—
157#1055—82no—
158C22×M16—261no—
159C2×#124Dic1311yescharacteristic
160C2×#117C2×D1311yescharacteristic
161#432—261no—
162#395C2×D1311yescharacteristic
163#394C2×D1311yescharacteristic
164#393Dic1311yescharacteristic
165#392Dic1311yescharacteristic
166#390—21no—
167#388—21no—
168#388—21no—
169#386—21no—
170#376Dic1311yescharacteristic
171#343—132no—
172#343—261no—
173#324—132no—
174#323—261no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—22no—
178C22×C13—42no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—81no—
182C22×C13—81no—
183C22×C13—81no—
184C22×C13—81no—
185C22×C13—81no—
186C22×C13—81no—
187C22×C13—81no—
188C22×C13—81no—
189C22×C13C2×#9911yescharacteristic
190C22×C13#41711yescharacteristic
191C22×C13C2×#10411yescharacteristic
192C4×C13—21no—
193C4×C13—21no—
194C4×C13—21no—
195C4×C13—21no—
196C4×C13—42no—
197C4×C13—41no—
198C4×C13—41no—
199C4×C13—41no—
200C4×C13—41no—
201C4×C13—81no—
202C4×C13—81no—
203C22×Q8C2×Dic1311yescharacteristic
204C22×D4—21no—
205C22×D4C2×Dic1311yescharacteristic
206C23×C4C22⋊D1311yescharacteristic
207C2×M16—264no—
208C2×M16—262no—
209C2×M16—521no—
210C2×M16—522no—
211C22×C8—521no—
212#124—41no—
213#124—41no—
214#117—41no—
215#117—41no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4C22⋊D1311yescharacteristic
218C2×C4⋊C4C22×D1311yescharacteristic
219C2×C22⋊C4—21no—
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4C2×Dic1311yescharacteristic
226C2×C22⋊C4C22⋊D1311yescharacteristic
227C2×C42—21no—
228C2×C42C2×Dic1311yescharacteristic
229C2×C42C22⋊D1311yescharacteristic
230C4⋊C8—521no—
231C22⋊C8—262no—
232#97—521no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C2×Dic1311yescharacteristic
237#95C2×Dic1311yescharacteristic
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—42no—
241C2×C13—161no—
242C2×C13#150411yescharacteristic
243C2×C13#212211yescharacteristic
244C2×C13#213211yescharacteristic
245C24—21no—
246C24C22⋊Dic1311yescharacteristic
247C2×Q8—41no—
248C2×Q8—81no—
249C2×D4—41no—
250C2×D4—42no—
251C2×D4—42no—
252C2×D4—81no—
253C2×D4—81no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4C22⋊Dic1311yescharacteristic
263C22×C4C22⋊Dic1311yescharacteristic
264C22×C4C22⋊Dic1311yescharacteristic
265C22×C4C22×Dic1311yescharacteristic
266C22×C4C2×C22⋊D1311yescharacteristic
267C22×C4C2×C22⋊D1311yescharacteristic
268M16—264no—
269M16—524no—
270M16—522no—
271C2×C8—524no—
272C2×C8—522no—
273C2×C8—522no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C22⋊C4—42no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—81no—
286C22⋊C4—81no—
287C42—21no—
288C42—21no—
289C42—21no—
290C42—21no—
291C42—42no—
292C13#1176511yescharacteristic, complemented, Sylow
293C23—21no—
294C23—21no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23#8807712yes—
305C23C2×C22⋊Dic1311yescharacteristic
306Q8—82no—
307D4—84no—
308D4—82no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
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#8807411yescharacteristic
335C2×C4#8807411yescharacteristic
336C2×C4#8820311yescharacteristic
337C2×C4#8820511yescharacteristic
338C8—524no—
339C8—1042no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22C2×#8807411yescharacteristic
355C22#1171889311yescharacteristic
356C22C2×#8807711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—21no—
361C4—42no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4—81no—
367C4—81no—
368C2—21no—
369C2—21no—
370C2—42no—
371C2—161no—
372C2#1311334011yescharacteristic
373C2#1311648611yescharacteristic
374C2#1311652111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2610C2
socleC22×C13C2×#99
prime radicalC13×#392C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2610D13
hypocenterC13#11765
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #13114575C2semidirect
2. #13113170C2semidirect
3. #13112866C2semidirect
4. #13112839C2semidirect
292. C13#11765semidirect

Maximal subgroups

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

subgroupindex
#131145752
#131131702
#131128662
#131128392
C13×#26102
#1176513