Finite Group Databasebeta

← #15760798

Subgroups — #15760798

Order 3328.

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

normal subgroups only

This group has 544 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#13120413C211yesmaximal, characteristic
2#13113284C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13112701C212yesmaximal, complemented
5C13×#2873C211yesmaximal, characteristic
6C22×C13×M16—21no—
7C2×C13×#117C2211yescharacteristic
8C2×C4×Dic26C2211yescharacteristic
9C13×#405—24no—
10C4×C13×M16—21no—
11C4×C13×M16C2212yes—
12#11718871—21no—
13#11718644C411yescharacteristic
14#11718640C411yescharacteristic
15#11718639—21no—
16#11718614C411yescharacteristic
17#11718608C411yescharacteristic
18#11718605—21no—
19#11718598C2211yescharacteristic
20#11718594—21no—
21#11718587C2212yes—
22#11718120—21no—
23#11718117—21no—
24#11718048—24no—
25C23×C4×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C2×C13×M16—22no—
28C2×C13×M16—24no—
29C2×C13×M16—24no—
30C2×C13×M16—22no—
31C22×C8×C13—22no—
32C13×#117—22no—
33C13×#117—22no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4D411yescharacteristic
38C2×C42×C13D411yescharacteristic
39C2×C42×C13C2311yescharacteristic
40C2×C22⋊Dic13—21no—
41C2×C22⋊Dic13—21no—
42C2×C4⋊Dic13C2×C411yescharacteristic
43C2×#6101—21no—
44C2×#6101—21no—
45C2×#6101—21no—
46C2×C4×Dic13—21no—
47C4×Dic26—22no—
48C4×Dic26—22no—
49C13×#97—22no—
50C13×#97—22no—
51C4×C8×C13—22no—
52C4×C8×C13D414yes—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071C2×C411yescharacteristic
60#88071C2×C411yescharacteristic
61C22⋊#1055—22no—
62C4⋊#1055—22no—
63#88043—22no—
64#9491—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C22×C4×C13—22no—
67C22×C4×C13—22no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C22×Dic13—21no—
79C22×Dic13—21no—
80C2×Dic26—22no—
81C2×Dic26—42no—
82C13×M16—28no—
83C13×M16—24no—
84C13×M16—24no—
85C2×C8×C13—28no—
86C2×C8×C13—24no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13C2×D412yes—
94C42×C13#4112yes—
95C22⋊Dic13—42no—
96C22⋊Dic13—42no—
97C4⋊Dic13—22no—
98#6101—42no—
99#6101—42no—
100#6101—41no—
101#6101—41no—
102C4×Dic13—42no—
103C2×#1055—42no—
104#2873D1311yescharacteristic
105#2599—131no—
106#1491—132no—
107#1464—131no—
108#1288—132no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13#10412yes—
114C23×C13C2×C22⋊C411yescharacteristic
115C2×C4×C13—22no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13#10412yes—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12112yes—
132C2×C4×C13#12311yescharacteristic
133C2×Dic13—22no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144C2×Dic13—41no—
145Dic26—24no—
146Dic26—42no—
147C8×C13—28no—
148#1055—82no—
149C22×M16—21no—
150C2×C4×Q8—131no—
151C2×#117C2×D1311yescharacteristic
152#432—132no—
153#405—24no—
154C4×M16—21no—
155C4×M16C2×D1312yes—
156#398—131no—
157#397—131no—
158#395—131no—
159#393—131no—
160#388—261no—
161#387—261no—
162#387—261no—
163#385—261no—
164#383—131no—
165Q8⋊C8—264no—
166#324—261no—
167#323—261no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—22no—
171C22×C13—42no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13#38611yescharacteristic
176C22×C13C2×#10411yescharacteristic
177C22×C13C2×#10411yescharacteristic
178C4×C13—22no—
179C4×C13—21no—
180C4×C13—22no—
181C4×C13—21no—
182C4×C13—22no—
183C4×C13—41no—
184C4×C13—41no—
185Dic13—42no—
186Dic13—81no—
187Dic13—81no—
188Dic13—81no—
189C22×Q8—131no—
190C23×C4C22⋊D1311yescharacteristic
191C2×M16—22no—
192C2×M16—24no—
193C2×M16—24no—
194C2×M16—22no—
195C22×C8—22no—
196C4×Q8—262no—
197C4×Q8—262no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—261no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4C4×D1311yescharacteristic
205C2×C4⋊C4D5211yescharacteristic
206C2×C22⋊C4—261no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4C4×D1311yescharacteristic
209C2×C22⋊C4D5211yescharacteristic
210C2×C42—261no—
211C2×C42C22⋊D1311yescharacteristic
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—262no—
214C22⋊C8—262no—
215#97—22no—
216#97—22no—
217#97—262no—
218C4×C8—22no—
219C4×C8C22⋊D1314yes—
220#95—131no—
221#95—131no—
222#95—261no—
223#95—261no—
224#95—261no—
225#95—261no—
226#95—261no—
227#95—261no—
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13#189111yescharacteristic
232C2×C13#189611yescharacteristic
233C2×C13#190911yescharacteristic
234C24#610311yescharacteristic
235C2×Q8—262no—
236C2×Q8—522no—
237C22×C4—22no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—22no—
241C22×C4—261no—
242C22×C4—261no—
243C22×C4—261no—
244C22×C4—261no—
245C22×C4#610311yescharacteristic
246C22×C4#610311yescharacteristic
247C22×C4#610311yescharacteristic
248C22×C4C2×C4×D1311yescharacteristic
249C22×C4C2×D5211yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—28no—
252M16—24no—
253M16—24no—
254C2×C8—28no—
255C2×C8—24no—
256C2×C8—522no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—262no—
260C4⋊C4—522no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—522no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—522no—
267C22⋊C4—522no—
268C42—21no—
269C42—21no—
270C42—522no—
271C42#612712yes—
272C42C2×C22⋊D1312yes—
273C13#949111yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#8804512yes—
279C23C2×#610311yescharacteristic
280Q8—264no—
281Q8—522no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—262no—
296C2×C4—521no—
297C2×C4—521no—
298C2×C4—521no—
299C2×C4—521no—
300C2×C4—521no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4#8804512yes—
308C2×C4C4×C22⋊D1312yes—
309C2×C4#8818311yescharacteristic
310C2×C4#8818412yes—
311C2×C4#8820711yescharacteristic
312C8—28no—
313C8—1042no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22C2×#8804511yescharacteristic
322C22C2×#8804511yescharacteristic
323C22#1171887411yescharacteristic
324C4—22no—
325C4—21no—
326C4—21no—
327C4—22no—
328C4—22no—
329C4—41no—
330C4—41no—
331C4—522no—
332C4—1041no—
333C4—1041no—
334C4—1041no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1311525411yescharacteristic
339C2#1311527911yescharacteristic
340C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2873C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2873D13
hypocenterC13#9491
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #13113284C2semidirect
4. #13112701C2semidirect
273. C13#9491semidirect

Maximal subgroups

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

subgroupindex
#131204132
#131132842
#131131702
#131127012
C13×#28732
#949113