Finite Group Databasebeta

← #15760799

Subgroups — #15760799

Order 3328.

544 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 111 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#13123255C211yesmaximal, characteristic
2#13113283C212yesmaximal, complemented
3#13113170C211yesmaximal, characteristic
4#13112700C212yesmaximal, complemented
5C13×#2599C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C13×#117C2211yescharacteristic
8C22×#6099—21no—
9C13×#398C411yescharacteristic
10C13×#397C411yescharacteristic
11C13×#395C411yescharacteristic
12C13×#393C411yescharacteristic
13C13×#388—21no—
14C13×#387—21no—
15C13×#387—21no—
16C13×#385—21no—
17C13×#383C2211yescharacteristic
18#11718658—24no—
19#11718587C2212yes—
20C4×#6099—21no—
21C4×#6099C2212yes—
22Q8⋊#1055—24no—
23#11718120—21no—
24#11718117—21no—
25C22×Q8×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C13×#117—22no—
30C13×#117—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4D411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13—21no—
42C2×C42×C13D411yescharacteristic
43C2×C42×C13C2311yescharacteristic
44C2×#6099—22no—
45C2×#6099—24no—
46C2×#6099—24no—
47C2×#6099—22no—
48C22×#1055—22no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—21no—
55C13×#95C2×C411yescharacteristic
56C13×#95C2×C411yescharacteristic
57C22⋊#1055—22no—
58C4⋊#1055—22no—
59#88043—22no—
60#88043—22no—
61#88043—22no—
62C4×#1055—22no—
63C4×#1055D414yes—
64#9491—131nomaximal, Sylow
65C24×C13C22⋊C411yescharacteristic
66C2×Q8×C13—22no—
67C2×Q8×C13—42no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
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—22no—
83C13×C4⋊C4—22no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C13×C22⋊C4—22no—
90C13×C22⋊C4—22no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—42no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—42no—
96C42×C13C2×D412yes—
97C42×C13#4112yes—
98#6099—28no—
99#6099—24no—
100#6099—24no—
101C2×#1055—28no—
102C2×#1055—24no—
103C2×#1055—42no—
104#2873—131no—
105#2599D1311yescharacteristic
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
115Q8×C13—24no—
116Q8×C13—42no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13—24no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—22no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13#10412yes—
143C2×C4×C13C4×D412yes—
144C2×C4×C13#12011yescharacteristic
145C2×C4×C13#12112yes—
146C2×C4×C13#12311yescharacteristic
147#1055—28no—
148#1055—82no—
149C22×M16—261no—
150C2×C4×Q8C2×D1311yescharacteristic
151C2×#117C2×D1311yescharacteristic
152#432—132no—
153#405—264no—
154C4×M16—132no—
155C4×M16—261no—
156#398Dic1311yescharacteristic
157#397Dic1311yescharacteristic
158#395Dic1311yescharacteristic
159#393Dic1311yescharacteristic
160#388—21no—
161#387—21no—
162#387—21no—
163#385—21no—
164#383C2×D1311yescharacteristic
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—42no—
185C4×C13—41no—
186C4×C13—81no—
187C4×C13—81no—
188C4×C13—81no—
189C22×Q8C2×Dic1311yescharacteristic
190C23×C4C22⋊D1311yescharacteristic
191C2×M16—264no—
192C2×M16—264no—
193C2×M16—262no—
194C2×M16—262no—
195C22×C8—262no—
196C4×Q8—22no—
197C4×Q8—22no—
198#117—22no—
199#117—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×Dic1311yescharacteristic
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C4⋊C4C22⋊D1311yescharacteristic
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4C2×Dic1311yescharacteristic
209C2×C22⋊C4C22⋊D1311yescharacteristic
210C2×C42—21no—
211C2×C42C22⋊D1311yescharacteristic
212C2×C42C22×D1311yescharacteristic
213C4⋊C8—262no—
214C22⋊C8—262no—
215#97—262no—
216#97—262no—
217#97—262no—
218C4×C8—134no—
219C4×C8—262no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×Dic1311yescharacteristic
227#95C2×Dic1311yescharacteristic
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—42no—
231C2×C13#189111yescharacteristic
232C2×C13#189611yescharacteristic
233C2×C13#190911yescharacteristic
234C24C22⋊Dic1311yescharacteristic
235C2×Q8—22no—
236C2×Q8—42no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4C22⋊Dic1311yescharacteristic
246C22×C4C22⋊Dic1311yescharacteristic
247C22×C4C22⋊Dic1311yescharacteristic
248C22×C4C22×Dic1311yescharacteristic
249C22×C4C2×C22⋊D1311yescharacteristic
250C22×C4C2×C22⋊D1311yescharacteristic
251M16—268no—
252M16—264no—
253M16—264no—
254C2×C8—268no—
255C2×C8—264no—
256C2×C8—522no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C42—21no—
269C42—21no—
270C42—42no—
271C42D4×D1312yes—
272C42#612912yes—
273C13#949111yescharacteristic, complemented, Sylow
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23#8807712yes—
279C23C2×C22⋊Dic1311yescharacteristic
280Q8—24no—
281Q8—42no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—24no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#8807712yes—
308C2×C4D4×Dic1312yes—
309C2×C4#8818911yescharacteristic
310C2×C4#8819111yescharacteristic
311C2×C4#8819312yes—
312C8—268no—
313C8—1042no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22—81no—
321C22#1171888111yescharacteristic
322C22C2×#8807711yescharacteristic
323C22C2×#8807711yescharacteristic
324C4—22no—
325C4—21no—
326C4—22no—
327C4—21no—
328C4—22no—
329C4—41no—
330C4—42no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—42no—
338C2#1311525511yescharacteristic
339C2#1311528011yescharacteristic
340C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2599C2
socleC22×C13#386
prime radicalC24×C13C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2599D13
hypocenterC13#9491
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2599

Complements

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

NH ≅ G/Ntype
2. #13113283C2semidirect
4. #13112700C2semidirect
273. C13#9491semidirect

Maximal subgroups

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

subgroupindex
#131232552
#131132832
#131131702
#131127002
C13×#25992
#949113