Finite Group Databasebeta

← #15755065

Subgroups — #15755065

Order 3328.

746 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 746 conjugacy classes of subgroups — too many to draw. Only its 143 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#13115635C211yesmaximal, characteristic
2#13113536C212yesmaximal, complemented
3#13113451C212yesmaximal, complemented
4#13113177C211yesmaximal, characteristic
5C13×#3501C211yesmaximal, characteristic
6C13×#554—22no—
7C13×#554—24no—
8D4×Q8×C13—22no—
9C13×#544C412yes—
10C13×#543—22no—
11C13×#533C2212yes—
12C2×C13×C22⋊Q8—22no—
13C13×#518C412yes—
14C2×C4×D4×C13C2211yescharacteristic
15C2×C22⋊#1055—22no—
16#11718587C2212yes—
17C2×C4⋊#1055C2211yescharacteristic
18C2×#88043C2211yescharacteristic
19#11718139—22no—
20#11718139—22no—
21#11718135—24no—
22#11718117—22no—
23C22×Q8×C13—22no—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D412yes—
26C13×C4⋊Q8—24no—
27C13×C4⋊Q8D412yes—
28C13×C4⋊Q8D412yes—
29C13×#125—24no—
30C13×#125D414yes—
31C13×C22⋊Q8—24no—
32C13×C22⋊Q8—24no—
33C13×C22⋊Q8—28no—
34C13×C22⋊Q8—28no—
35C13×C22⋊Q8—24no—
36C13×C22⋊Q8—22no—
37C13×C22⋊Q8—22no—
38C4×Q8×C13—22no—
39C4×Q8×C13—22no—
40C4×D4×C13—24no—
41C4×D4×C13—24no—
42C4×D4×C13—22no—
43C4×D4×C13—22no—
44C13×#117C2×C414yes—
45C2×C13×C4⋊C4—22no—
46C2×C13×C4⋊C4—24no—
47C2×C13×C4⋊C4C2×C411yescharacteristic
48C2×C13×C22⋊C4—24no—
49C2×C13×C22⋊C4D412yes—
50C2×C42×C13C2311yescharacteristic
51C22×#1055—21no—
52C22×#1055—21no—
53C22⋊#1055—22no—
54C22⋊#1055—44no—
55C4⋊#1055—22no—
56C4⋊#1055—22no—
57#88043—22no—
58#88043—22no—
59#8457—131nomaximal, Sylow
60C24×C13C22⋊C412yes—
61C2×Q8×C13—24no—
62C2×Q8×C13—22no—
63C2×Q8×C13—22no—
64C2×Q8×C13—82no—
65C2×Q8×C13—82no—
66C2×D4×C13—24no—
67C2×D4×C13—22no—
68C22×C4×C13—24no—
69C22×C4×C13—24no—
70C22×C4×C13—22no—
71C22×C4×C13—22no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13C22⋊C412yes—
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—24no—
79C13×C4⋊C4—28no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—24no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—24no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4C22⋊C414yes—
86C13×C4⋊C4C22⋊C414yes—
87C13×C22⋊C4—28no—
88C13×C22⋊C4—24no—
89C13×C22⋊C4—24no—
90C42×C13—24no—
91C42×C13C2×D412yes—
92C42×C13C2×D412yes—
93C2×#1055—22no—
94C2×#1055—41no—
95C2×#1055—41no—
96C2×#1055—42no—
97C2×#1055—42no—
98C2×#1055—41no—
99#3501D1311yescharacteristic
100#1955—131no—
101#1552—132no—
102#1531—132no—
103#1466—131no—
104C23×C13—22no—
105C23×C13—22no—
106C23×C13—42no—
107C23×C13—42no—
108C23×C13#10114yes—
109C23×C13C2×C22⋊C411yescharacteristic
110Q8×C13—42no—
111Q8×C13—42no—
112Q8×C13—82no—
113Q8×C13—84no—
114D4×C13—28no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—24no—
119C2×C4×C13—24no—
120C2×C4×C13—22no—
121C2×C4×C13—41no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—82no—
126C2×C4×C13—84no—
127C2×C4×C13—84no—
128C2×C4×C13C2×C22⋊C412yes—
129C2×C4×C13#12012yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12011yescharacteristic
132#1055—42no—
133#1055—82no—
134#1055—81no—
135#554—22no—
136#554—24no—
137D4×Q8—22no—
138#544Dic1312yes—
139#543—22no—
140#533C2×D1312yes—
141C2×C22⋊Q8—22no—
142#518Dic1312yes—
143C2×C4×D4C2×D1311yescharacteristic
144#432—132no—
145C2×C4⋊C8—131no—
146C2×C22⋊C8—262no—
147C2×#97—131no—
148#332—262no—
149#332—262no—
150#330—264no—
151#323—262no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—24no—
155C22×C13—44no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—82no—
159C22×C13#37911yescharacteristic
160C22×C13C2×#10112yes—
161C4×C13—21no—
162C4×C13—22no—
163C4×C13—22no—
164C4×C13—42no—
165C4×C13—44no—
166C4×C13—44no—
167C4×C13#45311yescharacteristic
168C4×C13#45511yescharacteristic
169C22×Q8—22no—
170C22×D4C2×Dic1311yescharacteristic
171C23×C4C22⋊D1312yes—
172C22×C8—261no—
173C22×C8—261no—
174C4⋊Q8—24no—
175C4⋊Q8C22⋊D1312yes—
176C4⋊Q8C22⋊D1312yes—
177#125—24no—
178#125C22⋊D1314yes—
179C22⋊Q8—24no—
180C22⋊Q8—24no—
181C22⋊Q8—28no—
182C22⋊Q8—28no—
183C22⋊Q8—24no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×D4—24no—
189C4×D4—24no—
190C4×D4—22no—
191C4×D4—22no—
192#117C2×Dic1314yes—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4C2×Dic1311yescharacteristic
196C2×C22⋊C4—24no—
197C2×C22⋊C4C22⋊D1312yes—
198C2×C42C22×D1311yescharacteristic
199C4⋊C8—262no—
200C4⋊C8—262no—
201C22⋊C8—262no—
202C22⋊C8—524no—
203#97—262no—
204#97—262no—
205C2×C13—22no—
206C2×C13—44no—
207C2×C13#178411yescharacteristic
208C2×C13#179211yescharacteristic
209C2×C13#179411yescharacteristic
210C24C22⋊Dic1312yes—
211C2×Q8—24no—
212C2×Q8—22no—
213C2×Q8—22no—
214C2×Q8—82no—
215C2×Q8—82no—
216C2×D4—24no—
217C2×D4—22no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4C22⋊Dic1312yes—
225C22×C4C22×Dic1311yescharacteristic
226C22×C4C2×C22⋊D1311yescharacteristic
227C22×C4C2×C22⋊D1311yescharacteristic
228C2×C8—262no—
229C2×C8—521no—
230C2×C8—521no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—521no—
234C4⋊C4—24no—
235C4⋊C4—28no—
236C4⋊C4—22no—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—24no—
240C4⋊C4—22no—
241C4⋊C4C22⋊Dic1314yes—
242C4⋊C4C22⋊Dic1314yes—
243C22⋊C4—28no—
244C22⋊C4—24no—
245C22⋊C4—24no—
246C42—24no—
247C42C2×C22⋊D1312yes—
248C42C2×C22⋊D1312yes—
249C13#845711yescharacteristic, complemented, Sylow
250C23—22no—
251C23—22no—
252C23—42no—
253C23—42no—
254C23#8807614yes—
255C23C2×C22⋊Dic1311yescharacteristic
256Q8—42no—
257Q8—42no—
258Q8—82no—
259Q8—84no—
260D4—28no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—24no—
265C2×C4—24no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—82no—
272C2×C4—84no—
273C2×C4—84no—
274C2×C4C2×C22⋊Dic1312yes—
275C2×C4#8820712yes—
276C2×C4#8820711yescharacteristic
277C2×C4#8820711yescharacteristic
278C8—522no—
279C8—1042no—
280C8—1041no—
281C22—21no—
282C22—21no—
283C22—24no—
284C22—44no—
285C22—42no—
286C22—42no—
287C22—82no—
288C22C2×#8807612yes—
289C22#1171890811yescharacteristic
290C4—22no—
291C4—21no—
292C4—22no—
293C4—42no—
294C4—44no—
295C4—44no—
296C4#1171890211yescharacteristic
297C4#1171890311yescharacteristic
298C2—22no—
299C2—44no—
300C2#1311476011yescharacteristic
301C2#1311479011yescharacteristic
302C2#1311480011yescharacteristic
subgroupG/H
centerC22#11718908
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3501C2
socleC22×C13#379
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#3501D13
hypocenterC13#8457
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3501

Complements

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

NH ≅ G/Ntype
2. #13113536C2semidirect
3. #13113451C2semidirect
249. C13#8457semidirect

Maximal subgroups

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

subgroupindex
#131156352
#131135362
#131134512
#131131772
C13×#35012
#845713