Finite Group Databasebeta

← #15758958

Subgroups — #15758958

Order 3328.

578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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#13123474C211yesmaximal, characteristic, complemented
2#13113504C212yesmaximal, complemented
3#13113150C211yesmaximal, characteristic, complemented
4#13112694C212yesmaximal, complemented
5C13×#2619C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7C2×C13×#121—21no—
8C2×C13×#117C2211yescharacteristic
9C13×#394—21no—
10C13×#394C412yes—
11C13×#392—21no—
12C13×#392C412yes—
13C13×#390—21no—
14C13×#382C2211yescharacteristic
15#11718868—21no—
16#11718661—24no—
17#11718586C2212yes—
18#11718585C2212yes—
19C4×#6099—21no—
20#11718136—24no—
21#11718120—21no—
22#11718117—21no—
23C22×D4×C13—22no—
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13C2×C412yes—
27C23×C4×C13D411yescharacteristic
28C13×#127—22no—
29C13×#127—22no—
30C13×#121—44no—
31C13×#117—22no—
32C13×#117—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4D411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4C2×C411yescharacteristic
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13C2311yescharacteristic
43C2×#6099—22no—
44C13×#95—21no—
45C13×#95C2×C412yes—
46C22⋊#1055—24no—
47C22⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4⋊#1055D414yescomplemented
51#88043—22no—
52C4×#1055—22no—
53C4×#1055—22no—
54#9198—131nomaximal, Sylow
55C24×C13—22no—
56C24×C13C22⋊C411yescharacteristic
57C2×D4×C13—24no—
58C2×D4×C13—44no—
59C2×D4×C13—41no—
60C2×D4×C13—42no—
61C2×D4×C13—41no—
62C2×D4×C13—42no—
63C2×D4×C13—42no—
64C2×D4×C13—82no—
65C2×D4×C13—82no—
66C2×D4×C13—82no—
67C2×D4×C13—82no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—22no—
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—42no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—82no—
86C13×C22⋊C4—82no—
87C42×C13—21no—
88C42×C13—21no—
89C42×C13C2×D412yes—
90C42×C13#4112yes—
91#6099—42no—
92#6099—42no—
93C2×#1055—24no—
94C2×#1055—42no—
95#2921—131no—
96#2619D1311yescharacteristic
97#1545—132no—
98#1458—131no—
99#1286—132no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—42no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13—42no—
109C23×C13—42no—
110C23×C13—42no—
111C23×C13—42no—
112C23×C13C2×C22⋊C411yescharacteristic
113D4×C13—84no—
114D4×C13—84no—
115D4×C13—88no—
116D4×C13—82no—
117D4×C13—82no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13C4×D412yes—
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12112yes—
135C2×C4×C13#12311yescharacteristic
136C2×C4×C13#13512yes—
137C2×C4×C13AGL(1,ℤ/8)12yes—
138#1055—44no—
139#1055—82no—
140C2×#127C2×D1311yescharacteristic
141C2×#121—21no—
142C2×#117C2×D1311yescharacteristic
143#433—264no—
144#431—132no—
145#423—132no—
146#407—261no—
147C4×M16—261no—
148#394—21no—
149#394Dic1312yes—
150#392—21no—
151#392Dic1312yes—
152#390—21no—
153#382C2×D1311yescharacteristic
154#331—264no—
155#324—261no—
156#323—261no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—81no—
164C22×C13—82no—
165C22×C13—82no—
166C22×C13—82no—
167C22×C13—82no—
168C22×C13—82no—
169C22×C13—82no—
170C22×C13—82no—
171C22×C13#38611yescharacteristic
172C22×C13#41611yescharacteristic
173C22×C13#41811yescharacteristic
174C4×C13—22no—
175C4×C13—22no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—82no—
180C4×C13#44912yes—
181C4×C13#48212yes—
182C22×D4—22no—
183C22×D4—21no—
184C22×D4—21no—
185C22×D4C2×Dic1312yes—
186C23×C4C22⋊D1311yescharacteristic
187C2×M16—262no—
188#127—22no—
189#127—22no—
190#121—44no—
191#117—22no—
192#117—22no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4C2×Dic1311yescharacteristic
195C2×C4⋊C4C22⋊D1311yescharacteristic
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—22no—
199C2×C22⋊C4C2×Dic1311yescharacteristic
200C2×C22⋊C4C22⋊D1311yescharacteristic
201C2×C42C22⋊D1311yescharacteristic
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—134no—
204C4⋊C8—262no—
205C4⋊C8—262no—
206C22⋊C8—264no—
207C22⋊C8—262no—
208#97—262no—
209C4×C8—262no—
210C4×C8—262no—
211#95—21no—
212#95C2×Dic1312yes—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—81no—
216C2×C13—162no—
217C2×C13#187511yescharacteristic
218C2×C13#191011yescharacteristic
219C2×C13#191411yescharacteristic
220C24—22no—
221C24C22⋊Dic1311yescharacteristic
222C2×D4—24no—
223C2×D4—44no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—41no—
227C2×D4—42no—
228C2×D4—42no—
229C2×D4—82no—
230C2×D4—82no—
231C2×D4—82no—
232C2×D4—82no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4C22⋊Dic1311yescharacteristic
239C22×C4C22⋊Dic1311yescharacteristic
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22×Dic1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243C22×C4C2×C22⋊D1311yescharacteristic
244M16—522no—
245M16—522no—
246C2×C8—264no—
247C2×C8—522no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—42no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—44no—
254C22⋊C4—82no—
255C22⋊C4—82no—
256C42—21no—
257C42—21no—
258C42D4×D1312yes—
259C42#612912yes—
260C13#919811yescharacteristic, complemented, Sylow
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—42no—
267C23—42no—
268C23—42no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23C2×C22⋊Dic1311yescharacteristic
274D4—84no—
275D4—84no—
276D4—88no—
277D4—82no—
278D4—82no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4#8818612yes—
294C2×C4D4×Dic1312yes—
295C2×C4#8818911yescharacteristic
296C2×C4#8819111yescharacteristic
297C2×C4#8819312yes—
298C2×C4#8820412yes—
299C8—524no—
300C8—1042no—
301C22—21no—
302C22—21no—
303C22—42no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—82no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22#1171887611yescharacteristic
316C22#1171888111yescharacteristic
317C22#1171889411yescharacteristic
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—82no—
324C4#1171869612yes—
325C4#1171869812yes—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—162no—
330C2#1311515911yescharacteristic
331C2#1311536411yescharacteristic
332C2#1311538411yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2619C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#2619D13
hypocenterC13#9198
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2619

Complements

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

NH ≅ G/Ntype
1. #13123474C2semidirect
2. #13113504C2semidirect
3. #13113150C2semidirect
4. #13112694C2semidirect
50. C4⋊#1055D4semidirect
260. C13#9198semidirect

Maximal subgroups

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

subgroupindex
#131234742
#131135042
#131131502
#131126942
C13×#26192
#919813