Finite Group Databasebeta

← #15765653

Subgroups — #15765653

Order 3328.

528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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#13125781C211yesmaximal, characteristic
2#13123213C211yesmaximal, characteristic
3#13115814C211yesmaximal, characteristic
4#13113517C211yesmaximal, characteristic
5#13113516C211yesmaximal, characteristic
6#13112668C211yesmaximal, characteristic
7C13×#3209C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#494—21no—
12C13×#487—21no—
13C13×#462—22no—
14C13×#451—22no—
15C13×#431C2211yescharacteristic
16#11718891—22no—
17#11718754—21no—
18#11718753—21no—
19#11718711—22no—
20#11718692—22no—
21#11718638—22no—
22#11718635—22no—
23C42×Dic13C2211yescharacteristic
24#11718586C2211yescharacteristic
25#11718585C2211yescharacteristic
26#11718138—22no—
27#11718124—22no—
28#11718073—22no—
29C22×Q8×C13D412yes—
30C22×Dic26D412yes—
31C2×C13×Q16—24no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8—21no—
36C13×C4⋊Q8D411yescharacteristic
37C13×C4⋊Q8D411yescharacteristic
38C13×#125—21no—
39C13×C22⋊Q8—21no—
40C13×C22⋊Q8—21no—
41C4×Q8×C13—21no—
42C4×Q8×C13—21no—
43C13×#117—21no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C42×C13C2311yescharacteristic
47C2×#6107—24no—
48C2×C4⋊Dic13—21no—
49C2×C4⋊Dic13—21no—
50C2×C4×Dic13—21no—
51C2×C4×Dic13—21no—
52C2×C4×Dic13D412yes—
53C2×#6099—21no—
54#88123—21no—
55#88123—21no—
56#88123—21no—
57#88123—21no—
58C13×C4⋊C8D412yes—
59C13×#103—24no—
60C13×C22⋊C8—21no—
61C4×C8×C13—21no—
62#88071—28no—
63C22⋊#1055—21no—
64#88050—24no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68C4×#1055—21no—
69#10297—131nomaximal, Sylow
70C2×Q8×C13—22no—
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—22no—
74C2×Q8×C13—44no—
75C22×C4×C13—22no—
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×Dic13—22no—
80C22×Dic13—22no—
81C2×Dic26—22no—
82C2×Dic26—22no—
83C2×Dic26—44no—
84C13×Q16—84no—
85C2×C8×C13—22no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—21no—
89C13×C4⋊C4—21no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—41no—
93C13×C4⋊C4—41no—
94C13×C4⋊C4—41no—
95C13×C4⋊C4—41no—
96C13×C22⋊C4—41no—
97C42×C13—41no—
98C42×C13C2×D411yescharacteristic
99C42×C13C2×D411yescharacteristic
100C42×C13C2×D411yescharacteristic
101C42×C13#4111yescharacteristic
102#6107—84no—
103C4⋊Dic13—41no—
104C4⋊Dic13—41no—
105C4⋊Dic13—41no—
106C4⋊Dic13—41no—
107C4×Dic13—22no—
108C4×Dic13—42no—
109C4×Dic13—42no—
110C4×Dic13Q1614yescomplemented
111#6099—42no—
112C2×#1055—22no—
113C2×#1055—41no—
114#3209—131no—
115#3209D1311yescharacteristic
116#2862—131no—
117#1994—131no—
118#1548—131no—
119#1548—131no—
120#1276—131no—
121C23×C13#12011yescharacteristic
122Q8×C13—42no—
123Q8×C13—42no—
124Q8×C13—44no—
125Q8×C13—82no—
126C2×C4×C13—22no—
127C2×C4×C13—22no—
128C2×C4×C13—44no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—42no—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12011yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12711yescharacteristic
138C2×C4×C13C2×Q1612yes—
139C2×C4×C13#13712yes—
140C2×Dic13—24no—
141C2×Dic13—42no—
142C2×Dic13—42no—
143C2×Dic13—44no—
144C2×Dic13—42no—
145Dic26—44no—
146Dic26—82no—
147C8×C13—42no—
148#1055—42no—
149#1055—81no—
150#533C2×D1311yescharacteristic
151C2×C4⋊Q8—131no—
152C2×C4⋊Q8C2×D1311yescharacteristic
153#494—21no—
154#494—261no—
155#487—21no—
156#487—261no—
157#462—22no—
158#462—262no—
159#451—22no—
160#451—262no—
161#431—131no—
162#431C2×D1311yescharacteristic
163#423—131no—
164#391—262no—
165#391—262no—
166#382—262no—
167C43—131no—
168#339—262no—
169#333—262no—
170#333—262no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13#39211yescharacteristic
174C22×C13#45112yes—
175C4×C13—21no—
176C4×C13—21no—
177C4×C13—82no—
178C4×C13—81no—
179C4×C13—81no—
180C4×C13#45512yes—
181C4×C13#45512yes—
182C4×C13#46212yes—
183C4×C13#49411yescharacteristic
184C4×C13#49711yescharacteristic
185Dic13—44no—
186Dic13—82no—
187C22×Q8—132no—
188C22×Q8C22⋊D1312yes—
189C2×Q16—24no—
190C2×Q16—264no—
191C2×M16—261no—
192C4⋊Q8—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—261no—
197C4⋊Q8—261no—
198C4⋊Q8—261no—
199C4⋊Q8—261no—
200C4⋊Q8C22⋊D1311yescharacteristic
201C4⋊Q8C22⋊D1311yescharacteristic
202#125—21no—
203C22⋊Q8—21no—
204C22⋊Q8—21no—
205C4×Q8—21no—
206C4×Q8—21no—
207#117—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C42—132no—
213C2×C42—261no—
214C2×C42—261no—
215C2×C42C22×D1311yescharacteristic
216C4⋊C8—132no—
217C4⋊C8—261no—
218C4⋊C8—261no—
219C4⋊C8C22⋊D1312yes—
220#103—24no—
221#103—264no—
222C22⋊C8—21no—
223C22⋊C8—261no—
224C4×C8—21no—
225C4×C8—261no—
226#95—268no—
227C2×C13—22no—
228C2×C13#200411yescharacteristic
229C2×C13#200411yescharacteristic
230C2×C13#201611yescharacteristic
231C2×Q8—21no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—21no—
235C2×Q8—44no—
236C2×Q8—262no—
237C2×Q8—262no—
238C2×Q8—524no—
239C22×C4—22no—
240C22×C4—262no—
241C22×C4—262no—
242C22×C4D4×D1311yescharacteristic
243C22×C4D4×D1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245Q16—84no—
246Q16—1044no—
247M16—522no—
248C2×C8—22no—
249C2×C8—262no—
250C2×C8—521no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—521no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C4⋊C4—521no—
265C22⋊C4—41no—
266C42—41no—
267C42—134no—
268C42—262no—
269C42—522no—
270C42—522no—
271C42D4×D1311yescharacteristic
272C42#612911yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C42C2×C22⋊D1311yescharacteristic
275C13#1029711yescharacteristic, complemented, Sylow
276C23#8819111yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—44no—
280Q8—82no—
281Q8—524no—
282Q8—1042no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—44no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4—264no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—524no—
293C2×C4—522no—
294C2×C4Q16×D1312yes—
295C2×C4#8817212yes—
296C2×C4#8819111yescharacteristic
297C2×C4#8819211yescharacteristic
298C2×C4#8819311yescharacteristic
299C2×C4#8819311yescharacteristic
300C2×C4#8819411yescharacteristic
301C2×C4#8820711yescharacteristic
302C8—42no—
303C8—522no—
304C8—1041no—
305C22—21no—
306C22—21no—
307C22#1171884712yes—
308C22#1171888411yescharacteristic
309C4—21no—
310C4—21no—
311C4—81no—
312C4—82no—
313C4—81no—
314C4—524no—
315C4—1042no—
316C4#1171884211yescharacteristic
317C4#1171884312yes—
318C4#1171885111yescharacteristic
319C4#1171886312yes—
320C4#1171890312yes—
321C2—22no—
322C2#1311586211yescharacteristic
323C2#1311586311yescharacteristic
324C2#1311593411yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3209C2
socleC22×C13#392
prime radicalC23×C13#120
hypercenter#3209D13
hypocenterC13#10297
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
110. C4×Dic13Q16semidirect
275. C13#10297semidirect

Maximal subgroups

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

subgroupindex
#131257812
#131232132
#131158142
#131135172
#131135162
#131126682
C13×#32092
#1029713