Finite Group Databasebeta

← #15757993

Subgroups — #15757993

Order 3328.

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

normal subgroups only

This group has 484 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#13118127C211yesmaximal, characteristic
2C4×#88076C211yesmaximal, characteristic
3#13113282C212yesmaximal
4#13112728C212yesmaximal
5C13×#2983C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#446—24no—
9C13×#432—21no—
10C13×#432C2212yes—
11C13×#431—21no—
12#11718890—21no—
13C2×#88076—21no—
14#11718644C411yescharacteristic
15#11718644C411yescharacteristic
16#11718641—21no—
17#11718640C411yescharacteristic
18#11718640C411yescharacteristic
19#11718593C2211yescharacteristic
20C4×#6101—21no—
21C4×#6101—21no—
22C4×#6099C2212yes—
23#11718122—21no—
24#11718076—24no—
25C22×Q8×C13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C4×Q8×C13—22no—
28C4×Q8×C13—22no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4D411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C42×C13D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×#6101—21no—
37C2×#6101—21no—
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C2×#6099—22no—
44C4×Dic26—22no—
45C4×Dic26—22no—
46C13×C4⋊C8—22no—
47C13×C4⋊C8—22no—
48C13×C4⋊C8D414yes—
49C13×C22⋊C8—22no—
50C13×#97—22no—
51C13×#97—22no—
52C4×C8×C13—22no—
53#88076—24no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071—21no—
59#88071C2×C411yescharacteristic
60#88071C2×C411yescharacteristic
61#88043—22no—
62C4×#1055—22no—
63#9030—131nomaximal, Sylow
64C2×Q8×C13—22no—
65C2×Q8×C13—22no—
66C2×Q8×C13—41no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22⋊C411yescharacteristic
71C22×C4×C13C22×C411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13C2×D411yescharacteristic
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—22no—
79C2×Dic26—42no—
80C2×C8×C13—24no—
81C13×C4⋊C4—22no—
82C13×C4⋊C4—22no—
83C13×C4⋊C4—22no—
84C42×C13—21no—
85C42×C13—21no—
86C42×C13—21no—
87C42×C13—21no—
88C42×C13C2×D412yes—
89C42×C13#4112yes—
90C4⋊Dic13—22no—
91#6101—42no—
92#6101—42no—
93#6101—42no—
94#6101—42no—
95#6101—42no—
96C4×Dic13—24no—
97C4×Dic13—41no—
98C4×Dic13—41no—
99#6099—24no—
100#6099—42no—
101C2×#1055—42no—
102#2983D1311yescharacteristic
103#2399—131no—
104C4×#101—131no—
105#1491—132no—
106#1300—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108Q8×C13—44no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#10412yes—
123C2×C4×C13C4×D412yes—
124C2×C4×C13#12011yescharacteristic
125C2×C4×C13#12112yes—
126C2×C4×C13#12311yescharacteristic
127C2×Dic13—22no—
128C2×Dic13—22no—
129C2×Dic13—22no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139Dic26—24no—
140Dic26—42no—
141C8×C13—44no—
142#1055—44no—
143C2×C4×Q8—131no—
144C2×C4×Q8C2×D1311yescharacteristic
145#446—24no—
146#432—21no—
147#432C2×D1312yes—
148#431—21no—
149C2×#101—261no—
150C4×M16—132no—
151#398—131no—
152#398—131no—
153#398—261no—
154#395—131no—
155#395—131no—
156#395—261no—
157C4×C4⋊C4—261no—
158C4×C4⋊C4—261no—
159#376—131no—
160#343—261no—
161Q8⋊C8—264no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10411yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—22no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13#45612yes—
175Dic13—42no—
176Dic13—42no—
177Dic13—42no—
178Dic13—81no—
179C22×Q8—131no—
180C22×Q8D5211yescharacteristic
181C2×M16—262no—
182C4×Q8—22no—
183C4×Q8—22no—
184C4×Q8—262no—
185C4×Q8—262no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4C4×D1311yescharacteristic
193C2×C4⋊C4C4×D1311yescharacteristic
194C2×C4⋊C4D5211yescharacteristic
195C2×C42—261no—
196C2×C42—261no—
197C2×C42C22⋊D1311yescharacteristic
198C2×C42C22⋊D1311yescharacteristic
199C2×C42C22×D1311yescharacteristic
200C4⋊C8—22no—
201C4⋊C8—22no—
202C4⋊C8C22⋊D1314yes—
203#101—264no—
204C22⋊C8—22no—
205#97—22no—
206#97—22no—
207#97—262no—
208C4×C8—22no—
209C4×C8—262no—
210#95—131no—
211#95—131no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13—21no—
218C2×C13—21no—
219C2×C13#187111yescharacteristic
220C2×C13#188611yescharacteristic
221C2×C13#189111yescharacteristic
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—262no—
226C2×Q8—522no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4#610311yescharacteristic
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4#610311yescharacteristic
235C22×C4C2×C4×D1311yescharacteristic
236C22×C4C2×D5211yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238M16—264no—
239M16—522no—
240C2×C8—24no—
241C2×C8—522no—
242C4⋊C4—22no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—262no—
246C4⋊C4—522no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—522no—
250C4⋊C4—522no—
251C42—21no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—264no—
256C42—521no—
257C42—521no—
258C42#612712yes—
259C42C2×C22⋊D1312yes—
260C13#903011yescharacteristic, complemented, Sylow
261C23C2×#610311yescharacteristic
262Q8—44no—
263Q8—264no—
264Q8—522no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4#8806512yes—
291C2×C4C4×C22⋊D1312yes—
292C2×C4#8818311yescharacteristic
293C2×C4#8818412yes—
294C2×C4#8820711yescharacteristic
295C8—44no—
296C8—524no—
297C22—21no—
298C22—21no—
299C22C2×#8806511yescharacteristic
300C22#1171880011yescharacteristic
301C22#1171887411yescharacteristic
302C4—22no—
303C4—22no—
304C4—21no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—522no—
310C4—522no—
311C4—522no—
312C4—1041no—
313C4#1171890712yes—
314C2—21no—
315C2—21no—
316C2#1311513811yescharacteristic
317C2#1311522911yescharacteristic
318C2#1311525411yescharacteristic
subgroupG/H
centerC2×C4#88207
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2983C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#2983D13
hypocenterC13#9030
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
260. C13#9030semidirect

Maximal subgroups

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

subgroupindex
#131181272
C4×#880762
#131132822
#131127282
C13×#29832
#903013