Finite Group Databasebeta

← #15764867

Subgroups — #15764867

Order 3328.

492 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125980C211yesmaximal, characteristic
2#13125216C211yesmaximal, characteristic
3#13115681C211yesmaximal, characteristic
4#13113508C211yesmaximal, characteristic
5#13113292C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic
7C2×C13×#500C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10#11719175C2211yescharacteristic
11C13×#500—22no—
12C13×#500—22no—
13C2×C13×#107—22no—
14C2×C4×C8×C13C2211yescharacteristic
15C2×#88076—22no—
16#11718886—22no—
17#11718755—22no—
18#11718754—21no—
19#11718743—22no—
20#11718742—21no—
21#11718742—21no—
22#11718740—21no—
23#11718632—22no—
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26C4×#6099C2211yescharacteristic
27#11718139—22no—
28#11718048—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13—21no—
31C22×C8×C13—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8—21no—
37C13×C4⋊Q8—21no—
38C13×C4⋊Q8—21no—
39C13×C4⋊Q8D412yes—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4D412yes—
44C2×C42×C13C2311yescharacteristic
45#88180—21no—
46#88178—21no—
47#88178—21no—
48C2×#6099—21no—
49C2×#6099D412yes—
50#88124—21no—
51#88123D411yescharacteristic
52#88123D411yescharacteristic
53C4×Dic26—21no—
54C4×Dic26—21no—
55C13×#107—28no—
56C4×C8×C13—21no—
57C4×C8×C13D412yes—
58#88076—44no—
59#88075—24no—
60#88075—24no—
61C22⋊#1055—21no—
62#88050—24no—
63#88048—24no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055D412yes—
67#88043—21no—
68C4×#1055—21no—
69C4×#1055—21no—
70#10175—131nomaximal, Sylow
71C2×Q8×C13—22no—
72C2×Q8×C13—41no—
73C2×Q8×C13—41no—
74C2×Q8×C13—41no—
75C2×Q8×C13—42no—
76C2×Q8×C13—42no—
77C2×Q8×C13—42no—
78C2×Q8×C13—42no—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C2×Dic26—21no—
85C2×Dic26—21no—
86C2×C8×C13—24no—
87C2×C8×C13—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—22no—
90C13×C4⋊C4—22no—
91C13×C4⋊C4—22no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C42×C13C2×D411yescharacteristic
97C42×C13C2×D411yescharacteristic
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C22⋊Dic13—41no—
101C4⋊Dic13—21no—
102C4⋊Dic13—21no—
103C4⋊Dic13—21no—
104C4⋊Dic13—21no—
105#6101—41no—
106#6101—41no—
107C4×Dic13—41no—
108#6099—22no—
109#6099—22no—
110#6099—42no—
111C2×#1055—22no—
112C2×#1055—22no—
113C2×#1055—41no—
114#3229—131no—
115C2×#500D1311yescharacteristic
116#3139—131no—
117#1966—131no—
118#1546—131no—
119#1493—131no—
120#1278—131no—
121C23×C13#12111yescharacteristic
122Q8×C13—44no—
123Q8×C13—82no—
124Q8×C13—81no—
125Q8×C13—81no—
126Q8×C13—81no—
127Q8×C13—81no—
128C2×C4×C13—22no—
129C2×C4×C13—22no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—82no—
134C2×C4×C13#12011yescharacteristic
135C2×C4×C13#12011yescharacteristic
136C2×C4×C13#12011yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12711yescharacteristic
140C2×C4×C13#13512yes—
141C2×C4×C13AGL(1,ℤ/8)12yes—
142C2×Dic13—41no—
143C2×Dic13—41no—
144Dic26—42no—
145Dic26—42no—
146C8×C13—24no—
147#1055—42no—
148#1055—42no—
149#1055—81no—
150#533—131no—
151C2×C4⋊Q8C2×D1311yescharacteristic
152C2×C4⋊Q8C2×D1311yescharacteristic
153#500—22no—
154#500—22no—
155#498—261no—
156#491—262no—
157#487—261no—
158#487—261no—
159#487—261no—
160#483—262no—
161#475—262no—
162#431—131no—
163C2×#107—22no—
164#423—131no—
165#419—262no—
166C2×#101—262no—
167C4×M16—131no—
168C2×C4×C8C2×D1311yescharacteristic
169#332—262no—
170Q8⋊C8—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#39211yescharacteristic
174C22×C13#46312yes—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—82no—
178C4×C13—82no—
179C4×C13#44912yes—
180C4×C13#45612yes—
181C4×C13#47312yes—
182C4×C13#49511yescharacteristic
183C4×C13#49611yescharacteristic
184Dic13—81no—
185Dic13—81no—
186C22×Q8—21no—
187C22×Q8—21no—
188C2×M16—132no—
189C2×M16—261no—
190C22×C8—21no—
191C4⋊Q8—21no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8—21no—
198C4⋊Q8—131no—
199C4⋊Q8—131no—
200C4⋊Q8C22⋊D1312yes—
201#125—261no—
202C22⋊Q8—261no—
203C22⋊Q8—261no—
204C4×Q8—261no—
205C4×Q8—261no—
206#117—261no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C22⋊D1312yes—
211C2×C42C22×D1311yescharacteristic
212#107—28no—
213#106—264no—
214C4⋊C8—132no—
215C4⋊C8—261no—
216C4⋊C8—261no—
217#103—264no—
218#103—264no—
219#103—264no—
220#101—524no—
221C22⋊C8—261no—
222#97—261no—
223C4×C8—21no—
224C4×C8—261no—
225C4×C8—261no—
226C4×C8C22⋊D1312yes—
227C2×C13—22no—
228C2×C13#200511yescharacteristic
229C2×C13#201211yescharacteristic
230C2×C13#202011yescharacteristic
231C2×Q8—22no—
232C2×Q8—42no—
233C2×Q8—42no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—42no—
238C2×Q8—42no—
239C2×Q8—261no—
240C2×Q8—261no—
241C22×C4—22no—
242C22×C4—41no—
243C22×C4D4×D1311yescharacteristic
244C22×C4#612911yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—262no—
247M16—262no—
248M16—522no—
249C2×C8—24no—
250C2×C8—22no—
251C2×C8—262no—
252C2×C8—262no—
253C2×C8—521no—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—22no—
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—521no—
267C4⋊C4—521no—
268C22⋊C4—521no—
269C42—521no—
270C42D4×D1311yescharacteristic
271C42D4×D1311yescharacteristic
272C42C2×C22⋊D1311yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C13#1017511yescharacteristic, complemented, Sylow
275C23#8819311yescharacteristic
276Q8—44no—
277Q8—81no—
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—82no—
282Q8—522no—
283Q8—522no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—44no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4#8816512yes—
293C2×C4#8816612yes—
294C2×C4#8819111yescharacteristic
295C2×C4#8819111yescharacteristic
296C2×C4#8819211yescharacteristic
297C2×C4#8819311yescharacteristic
298C2×C4#8819411yescharacteristic
299C2×C4#8820711yescharacteristic
300C8—24no—
301C8—522no—
302C8—522no—
303C8—1041no—
304C22—21no—
305C22—21no—
306C22#1171881412yes—
307C22#1171888411yescharacteristic
308C4—21no—
309C4—21no—
310C4—82no—
311C4—82no—
312C4—1041no—
313C4—1041no—
314C4#1171875612yes—
315C4#1171881511yescharacteristic
316C4#1171881611yescharacteristic
317C4#1171881912yes—
318C4#1171885312yes—
319C2—22no—
320C2#1311587211yescharacteristic
321C2#1311591111yescharacteristic
322C2#1311595511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#500C2
socleC22×C13#392
prime radicalC23×C13#121
hypercenterC2×#500D13
hypocenterC13#10175
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
274. C13#10175semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131252162
#131156812
#131135082
#131132922
#131126732
C2×C13×#5002
#1017513