Finite Group Databasebeta

← #15766104

Subgroups — #15766104

Order 3328.

360 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 75 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#13120484C211yesmaximal, characteristic
2#13115781C211yesmaximal, characteristic
3#13113387C211yesmaximal, characteristic
4#13112729C211yesmaximal, characteristic
5#13112702C211yesmaximal, characteristic
6#13112693C211yesmaximal, characteristic
7C13×#1506C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C13×#432C2211yescharacteristic
10C13×#376C2211yescharacteristic
11#11718598C2211yescharacteristic
12C4×C4⋊Dic13C2211yescharacteristic
13#11718594—21no—
14#11718590—21no—
15#11718587C2211yescharacteristic
16C4×#6099C2211yescharacteristic
17#11718321—21no—
18#11718317—21no—
19#11718316—21no—
20#11718307—21no—
21C13×#328—21no—
22C13×#328—21no—
23#11718130—21no—
24#11718130—21no—
25#11718124—21no—
26#11718124—21no—
27C22×Dic26—21no—
28C13×C4⋊Q8Q811yescharacteristic, complemented
29C13×C4⋊Q8Q811yescharacteristic, complemented
30C13×#125—21no—
31C13×C22⋊Q8—21no—
32C13×C22⋊Q8—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C13×#117—21no—
36C2×C42×C13—21no—
37C2×C42×C13C2311yescharacteristic
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×#6101—21no—
41C2×#6101—21no—
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13D411yescharacteristic
44C2×#6099—21no—
45C13×C4⋊C8—21no—
46C13×C22⋊C8—21no—
47C13×#97—21no—
48C13×#95—21no—
49C13×#95D411yescharacteristic
50C13×#95D411yescharacteristic
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#88071—21no—
57#88071—21no—
58#88071D411yescharacteristic
59#88071D411yescharacteristic
60C22⋊#1055—21no—
61C4⋊#1055—21no—
62#88043—21no—
63#88043—21no—
64C4×#1055—21no—
65#10379—131nomaximal, Sylow
66C2×Q8×C13—21no—
67C2×Q8×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13C2×D411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—21no—
74C22×Dic13—21no—
75C22×Dic13—21no—
76C22×Dic13—21no—
77C2×Dic26—42no—
78C2×Dic26—42no—
79C2×Dic26—81no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—21no—
84C13×C4⋊C4—21no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C22⋊C4—41no—
88C42×C13—42no—
89C42×C13—41no—
90C42×C13C2×Q811yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C42×C13#4111yescharacteristic
94C4⋊Dic13—42no—
95C4⋊Dic13—81no—
96#6101—42no—
97#6101—42no—
98C4×Dic13—41no—
99C4×Dic13—41no—
100#6099—22no—
101#6099—41no—
102C2×#1055—41no—
103C2×#1055—41no—
104#2605—131no—
105#1986—131no—
106#1515—131no—
107#1506D1311yescharacteristic
108#1300—131no—
109#1288—131no—
110#1285—131no—
111C23×C13#12011yescharacteristic
112Q8×C13—81no—
113Q8×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—22no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13C22⋊Q811yescharacteristic
127C2×C4×C13C22⋊Q811yescharacteristic
128C2×C4×C13C22⋊Q811yescharacteristic
129C2×C4×C13#12411yescharacteristic
130C2×C4×C13#12411yescharacteristic
131C2×C4×C13#12411yescharacteristic
132C2×Dic13—22no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13—41no—
138C2×Dic13—41no—
139C2×Dic13—41no—
140C2×Dic13—41no—
141C2×Dic13—41no—
142C2×Dic13—41no—
143C2×Dic13—41no—
144Dic26—84no—
145C8×C13—81no—
146#1055—42no—
147#1055—81no—
148#533C2×D1311yescharacteristic
149#432—131no—
150#432C2×D1311yescharacteristic
151C4×M16—131no—
152#400—261no—
153#395—261no—
154#391—261no—
155#391—261no—
156#387—261no—
157#387—261no—
158#383—131no—
159C4×C4⋊C4—131no—
160#376C2×D1311yescharacteristic
161#339—261no—
162#339—261no—
163#328—21no—
164#328—21no—
165#328—261no—
166#328—261no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#39311yescharacteristic
170C22×C13#45511yescharacteristic
171C22×C13#45611yescharacteristic
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—42no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182Dic13—42no—
183Dic13—81no—
184Dic13—81no—
185Dic13—81no—
186C22×Q8—261no—
187C2×M16—261no—
188C4⋊Q8Dic2611yescharacteristic, complemented
189C4⋊Q8Dic2611yescharacteristic, complemented
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4—261no—
198C2×C4⋊C4—261no—
199C2×C4⋊C4—261no—
200C2×C42—21no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42C22×D1311yescharacteristic
204C4⋊C8—21no—
205C4⋊C8—261no—
206C22⋊C8—21no—
207C22⋊C8—261no—
208#97—21no—
209#97—261no—
210#97—261no—
211C4×C8—261no—
212#95—21no—
213#95—131no—
214#95—131no—
215#95—261no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221#95—261no—
222#95C22⋊D1311yescharacteristic
223#95C22⋊D1311yescharacteristic
224C2×C13—21no—
225C2×C13—21no—
226C2×C13#202811yescharacteristic
227C2×C13#203111yescharacteristic
228C2×C13#203111yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—522no—
232C2×Q8—522no—
233C2×Q8—1041no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4D4×D1311yescharacteristic
241C22×C4D4×D1311yescharacteristic
242C22×C4C2×C22⋊D1311yescharacteristic
243M16—262no—
244M16—521no—
245C2×C8—41no—
246C2×C8—521no—
247C2×C8—521no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—522no—
255C4⋊C4—522no—
256C4⋊C4—522no—
257C4⋊C4—1041no—
258C22⋊C4—41no—
259C42—42no—
260C42—41no—
261C42—521no—
262C42—521no—
263C42C2×Dic2611yescharacteristic
264C42#612711yescharacteristic
265C42#612911yescharacteristic
266C42#612911yescharacteristic
267C13#1037911yescharacteristic, complemented, Sylow
268C23#8819111yescharacteristic
269Q8—81no—
270Q8—81no—
271Q8—1044no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—262no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4#8813211yescharacteristic
297C2×C4#8813211yescharacteristic
298C2×C4#8813911yescharacteristic
299C2×C4#8813911yescharacteristic
300C2×C4#8817811yescharacteristic
301C2×C4#8819011yescharacteristic
302C8—81no—
303C8—522no—
304C8—1041no—
305C22—21no—
306C22—21no—
307C22#1171860811yescharacteristic
308C22#1171886311yescharacteristic
309C22#1171886611yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—522no—
321C4—1041no—
322C4—1041no—
323C4—1041no—
324C2—21no—
325C2—21no—
326C2#1311599511yescharacteristic
327C2#1311600811yescharacteristic
328C2#1311601011yescharacteristic
subgroupG/H
centerC22#11718608
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1506C2
socleC22×C13#393
prime radicalC23×C13#120
hypercenter#1506D13
hypocenterC13#10379
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1506

Complements

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

NH ≅ G/Ntype
28. C13×C4⋊Q8Q8semidirect
29. C13×C4⋊Q8Q8semidirect
188. C4⋊Q8Dic26semidirect
189. C4⋊Q8Dic26semidirect
267. C13#10379semidirect

Maximal subgroups

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

subgroupindex
#131204842
#131157812
#131133872
#131127292
#131127022
#131126932
C13×#15062
#1037913