Finite Group Databasebeta

← #15766010

Subgroups — #15766010

Order 3328.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#13123212C211yesmaximal, characteristic
2#13115814C211yesmaximal, characteristic
3#13113400C211yesmaximal, characteristic
4#13112695C211yesmaximal, characteristic
5#13112694C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#1518C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×#88142—21no—
10C13×#431C2211yescharacteristic
11C13×#382C2211yescharacteristic
12#11718638—21no—
13#11718597C2211yescharacteristic
14C42×Dic13C2211yescharacteristic
15#11718586C2211yescharacteristic
16#11718585C2211yescharacteristic
17#11718307—22no—
18#11718307—22no—
19C13×#328—22no—
20#11718130—22no—
21#11718124—21no—
22#11718124—21no—
23C22×Dic26—22no—
24C13×C4⋊Q8Q811yescharacteristic, complemented
25C13×C4⋊Q8Q811yescharacteristic, complemented
26C13×#125—21no—
27C13×C22⋊Q8—21no—
28C13×C22⋊Q8—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C13×#117—21no—
32C2×C13×C4⋊C4—21no—
33C2×C42×C13C2311yescharacteristic
34C2×C4⋊Dic13—21no—
35C2×#6101—22no—
36C2×C4×Dic13—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×#6099—21no—
41#88142—42no—
42#88142—42no—
43C13×C4⋊C8—21no—
44C13×C22⋊C8—21no—
45C4×C8×C13—21no—
46C13×#95—21no—
47C13×#95D412yes—
48#88071—24no—
49#88071—21no—
50#88071D412yes—
51C22⋊#1055—21no—
52C4⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4×#1055—21no—
56#10363—131nomaximal, Sylow
57C2×Q8×C13—21no—
58C2×Q8×C13—21no—
59C22×C4×C13—22no—
60C22×C4×C13C2×D411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C22×Dic13—22no—
66C2×Dic26—44no—
67C2×Dic26—44no—
68C2×Dic26—44no—
69C2×C8×C13—41no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—41no—
75C13×C4⋊C4—41no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C22⋊C4—41no—
79C42×C13—41no—
80C42×C13C2×Q811yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—41no—
85C4⋊Dic13—41no—
86#6101—44no—
87C4×Dic13—21no—
88C4×Dic13—21no—
89C4×Dic13—42no—
90C4×Dic13—42no—
91C4×Dic13SD1612yes—
92C4×Dic13Q1612yes—
93#6099—41no—
94#6099—41no—
95C2×#1055—41no—
96C2×#1055—41no—
97#2862—131no—
98#1994—131no—
99#1518—131no—
100#1518D1311yescharacteristic
101#1286—131no—
102#1286—131no—
103#1276—131no—
104C23×C13#12011yescharacteristic
105Q8×C13—81no—
106Q8×C13—81no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—42no—
110C2×C4×C13—42no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—42no—
114C2×C4×C13C22⋊Q811yescharacteristic
115C2×C4×C13C22⋊Q811yescharacteristic
116C2×C4×C13C22⋊Q811yescharacteristic
117C2×C4×C13#12411yescharacteristic
118C2×C4×C13#12411yescharacteristic
119C2×C4×C13#12411yescharacteristic
120C2×C4×C13C2×SD1611yescharacteristic
121C2×C4×C13C2×Q1611yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133Dic26—88no—
134C8×C13—81no—
135#1055—81no—
136#1055—81no—
137#533C2×D1311yescharacteristic
138C2×C4⋊Q8—261no—
139#431—131no—
140#431C2×D1311yescharacteristic
141#423—131no—
142#391—262no—
143#391—262no—
144#382—131no—
145#382—261no—
146#382C2×D1311yescharacteristic
147C43—131no—
148#339—261no—
149#339—261no—
150#328—22no—
151#328—262no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13#39311yescharacteristic
155C22×C13#45011yescharacteristic
156C22×C13#45111yescharacteristic
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—21no—
161C4×C13—82no—
162C4×C13—81no—
163C4×C13—81no—
164C4×C13#47511yescharacteristic
165C4×C13#47711yescharacteristic
166C4×C13#48711yescharacteristic
167C4×C13#48911yescharacteristic
168Dic13—24no—
169Dic13—42no—
170Dic13—82no—
171C22×Q8—262no—
172C2×M16—261no—
173C4⋊Q8—522no—
174C4⋊Q8—522no—
175C4⋊Q8Dic2611yescharacteristic, complemented
176C4⋊Q8Dic2611yescharacteristic, complemented
177#125—21no—
178C22⋊Q8—21no—
179C22⋊Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182#117—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—262no—
185C2×C4⋊C4—261no—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—261no—
189C2×C42—261no—
190C2×C42C22×D1311yescharacteristic
191C4⋊C8—21no—
192C4⋊C8—261no—
193C4⋊C8—261no—
194C4⋊C8—261no—
195C22⋊C8—21no—
196C22⋊C8—261no—
197C4×C8—21no—
198C4×C8—261no—
199#95—21no—
200#95—132no—
201#95—264no—
202#95—261no—
203#95C22⋊D1312yes—
204C2×C13—21no—
205C2×C13—21no—
206C2×C13#202411yescharacteristic
207C2×C13#203111yescharacteristic
208C2×C13#203111yescharacteristic
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—524no—
212C2×Q8—524no—
213C2×Q8—524no—
214C22×C4—22no—
215C22×C4—261no—
216C22×C4—261no—
217C22×C4—262no—
218C22×C4D4×D1311yescharacteristic
219C22×C4D4×D1311yescharacteristic
220C22×C4C2×C22⋊D1311yescharacteristic
221M16—521no—
222M16—521no—
223C2×C8—41no—
224C2×C8—521no—
225C2×C8—521no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—524no—
235C4⋊C4—521no—
236C4⋊C4—521no—
237C22⋊C4—41no—
238C42—41no—
239C42—132no—
240C42—132no—
241C42—261no—
242C42—261no—
243C42—522no—
244C42—522no—
245C42C2×Dic2611yescharacteristic
246C42#612711yescharacteristic
247C42#612911yescharacteristic
248C42#612911yescharacteristic
249C13#1036311yescharacteristic, complemented, Sylow
250C23#8819111yescharacteristic
251Q8—81no—
252Q8—81no—
253Q8—1048no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—262no—
262C2×C4—262no—
263C2×C4—262no—
264C2×C4—262no—
265C2×C4—521no—
266C2×C4—521no—
267C2×C4—522no—
268C2×C4—522no—
269C2×C4—522no—
270C2×C4#8813211yescharacteristic
271C2×C4#8813211yescharacteristic
272C2×C4#8813911yescharacteristic
273C2×C4#8813911yescharacteristic
274C2×C4SD16×D1311yescharacteristic
275C2×C4#8816811yescharacteristic
276C2×C4Q16×D1311yescharacteristic
277C2×C4#8817211yescharacteristic
278C2×C4#8817811yescharacteristic
279C2×C4#8819011yescharacteristic
280C8—81no—
281C8—1041no—
282C8—1041no—
283C22—21no—
284C22—21no—
285C22#1171860811yescharacteristic
286C22#1171883011yescharacteristic
287C22#1171884711yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—264no—
296C4—522no—
297C4—1042no—
298C4#1171845211yescharacteristic
299C4#1171845311yescharacteristic
300C4#1171845511yescharacteristic
301C4#1171845611yescharacteristic
302C2—21no—
303C2—21no—
304C2#1311597511yescharacteristic
305C2#1311600611yescharacteristic
306C2#1311601011yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1518C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1518D13
hypocenterC13#10363
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
24. C13×C4⋊Q8Q8semidirect
25. C13×C4⋊Q8Q8semidirect
175. C4⋊Q8Dic26semidirect
176. C4⋊Q8Dic26semidirect
249. C13#10363semidirect

Maximal subgroups

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

subgroupindex
#131232122
#131158142
#131134002
#131126952
#131126942
#131126682
C13×#15182
#1036313