Finite Group Databasebeta

← #15764832

Subgroups — #15764832

Order 3328.

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

normal subgroups only

This group has 574 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#13125761C211yesmaximal, characteristic
2#13125293C211yesmaximal, characteristic
3#13115826C211yesmaximal, characteristic, complemented
4#13113508C211yesmaximal, characteristic, complemented
5#13113288C211yesmaximal, characteristic
6#13112673C211yesmaximal, characteristic, complemented
7C2×C13×#487C211yesmaximal, characteristic, complemented
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88196—22no—
11#11719182C2211yescharacteristic
12C13×#487—22no—
13C13×#487—22no—
14C2×C13×#103—22no—
15C2×C4×C8×C13C2211yescharacteristic
16#11718888—22no—
17#11718753—21no—
18#11718747—22no—
19#11718746—21no—
20#11718746—21no—
21#11718744—22no—
22#11718742—21no—
23#11718586C2211yescharacteristic
24#11718585C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718139—22no—
27#11718122—22no—
28#11718051—22no—
29C22×Q8×C13—21no—
30C22×Q8×C13D412yes—
31C2×#6127—21no—
32C22×C8×C13—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⋊Q8—21no—
40C13×C4⋊Q8D412yes—
41C2×C13×C4⋊C4—21no—
42C2×C13×C4⋊C4—21no—
43C2×C13×C4⋊C4—21no—
44C2×C13×C4⋊C4—21no—
45C2×C42×C13C2311yescharacteristic
46C2×#6107—24no—
47#88196—44no—
48#88196—44no—
49C2×#6106—24no—
50C2×#6106—24no—
51#88184—21no—
52#88184—21no—
53C2×#6099—21no—
54C2×#6099D412yes—
55#88129—21no—
56#88128D411yescharacteristic
57C4×D52—21no—
58C4×D52—21no—
59#88123D411yescharacteristic
60C13×#103—28no—
61C4×C8×C13—21no—
62C4×C8×C13D412yes—
63#88075—24no—
64C22⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055D412yes—
68#88043—21no—
69C4×#1055—21no—
70C4×#1055—21no—
71#10170—131nomaximal, Sylow
72C2×Q8×C13—22no—
73C2×Q8×C13—22no—
74C2×Q8×C13—22no—
75C2×Q8×C13—44no—
76C2×Q8×C13—41no—
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×C22⋊D13—41no—
85#6127—42no—
86#6127—42no—
87C2×D52—21no—
88C2×D52—21no—
89C2×D52—21no—
90C2×C4×D13—41no—
91C2×Dic26—21no—
92C2×C8×C13—22no—
93C2×C8×C13—42no—
94C13×C4⋊C4—22no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—41no—
97C13×C4⋊C4—41no—
98C13×C4⋊C4—41no—
99C13×C4⋊C4—41no—
100C13×C4⋊C4—41no—
101C13×C4⋊C4—41no—
102C42×C13C2×D411yescharacteristic
103C42×C13C2×D411yescharacteristic
104C42×C13C2×D411yescharacteristic
105C42×C13C2×D411yescharacteristic
106#6107—48no—
107#6106—48no—
108#6106—84no—
109#6103—41no—
110#6103—41no—
111C4⋊Dic13—21no—
112C4⋊Dic13—21no—
113#6099—22no—
114#6099—42no—
115#6099SD1614yescomplemented
116C2×#1055—22no—
117C2×#1055—22no—
118C2×#1055—41no—
119#3206—131no—
120#3152—131no—
121C2×#487D1311yescharacteristic, complemented
122#1997—131no—
123#1546—131no—
124#1492—131no—
125#1278—131no—
126C23×C13#12111yescharacteristic
127C22×D13—41no—
128Q8×C13—44no—
129Q8×C13—44no—
130Q8×C13—44no—
131Q8×C13—81no—
132Q8×C13—81no—
133C2×C4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—82no—
138C2×C4×C13—82no—
139C2×C4×C13#12011yescharacteristic
140C2×C4×C13#12011yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12111yescharacteristic
144C2×C4×C13#12711yescharacteristic
145C2×C4×C13C2×SD1612yes—
146C2×C4×C13AGL(1,ℤ/8)12yes—
147C22⋊D13—82no—
148C2×Dic13—41no—
149D52—42no—
150D52—42no—
151D52—42no—
152C4×D13—81no—
153C4×D13—81no—
154Dic26—42no—
155C8×C13—42no—
156#1055—24no—
157#1055—42no—
158#1055—81no—
159C2×#137—262no—
160#532—131no—
161C2×C4⋊Q8C2×D1311yescharacteristic
162C2×C4⋊Q8C2×D1311yescharacteristic
163#497—262no—
164#494—261no—
165#492—261no—
166#492—261no—
167#487—22no—
168#487—22no—
169#487—261no—
170#461—262no—
171#448—262no—
172#431—131no—
173#423—131no—
174C2×#103—22no—
175C4×M16—131no—
176C2×C4×C8C2×D1311yescharacteristic
177#343—262no—
178#332—262no—
179D4⋊C8—262no—
180C22×C13—21no—
181C22×C13—21no—
182C22×C13#39211yescharacteristic
183C22×C13#46012yes—
184C2×D13—81no—
185C2×D13—81no—
186C2×D13—81no—
187C4×C13—21no—
188C4×C13—21no—
189C4×C13—82no—
190C4×C13—82no—
191C4×C13#45012yes—
192C4×C13#45512yes—
193C4×C13#47312yes—
194C4×C13#49211yescharacteristic
195C4×C13#49611yescharacteristic
196Dic13—81no—
197C2×#41—261no—
198C22×Q8—21no—
199C22×Q8C22⋊D1312yes—
200#137—524no—
201#137—524no—
202C2×Q16—264no—
203C2×SD16—264no—
204C2×SD16—264no—
205C2×M16—132no—
206C2×M16—261no—
207C22×C8—21no—
208C4⋊Q8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8—21no—
213C4⋊Q8—21no—
214C4⋊Q8—21no—
215C4⋊Q8—131no—
216C4⋊Q8C22⋊D1312yes—
217#127—131no—
218#124—261no—
219#121—261no—
220#121—261no—
221C4×D4—261no—
222C4×D4—261no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C42C22×D1311yescharacteristic
228C4⋊C8—132no—
229C4⋊C8—261no—
230C4⋊C8—261no—
231#103—28no—
232#103—264no—
233C22⋊C8—261no—
234#97—261no—
235C4×C8—21no—
236C4×C8—261no—
237C4×C8—261no—
238C4×C8C22⋊D1312yes—
239C2×C13—22no—
240C2×C13#200411yescharacteristic
241C2×C13#201411yescharacteristic
242C2×C13#202011yescharacteristic
243D13—161no—
244#41—522no—
245#41—522no—
246C2×Q8—22no—
247C2×Q8—22no—
248C2×Q8—22no—
249C2×Q8—44no—
250C2×Q8—41no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—261no—
254C2×D4—261no—
255C2×D4—261no—
256C2×D4—261no—
257C2×D4—521no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—521no—
261C22×C4D4×D1311yescharacteristic
262C22×C4#612911yescharacteristic
263C22×C4C2×C22⋊D1311yescharacteristic
264Q16—528no—
265SD16—528no—
266SD16—1044no—
267M16—134no—
268M16—262no—
269M16—522no—
270C2×C8—22no—
271C2×C8—42no—
272C2×C8—262no—
273C2×C8—262no—
274C2×C8—521no—
275C4⋊C4—22no—
276C4⋊C4—22no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—261no—
284C4⋊C4—261no—
285C22⋊C4—521no—
286C22⋊C4—521no—
287C42D4×D1311yescharacteristic
288C42D4×D1311yescharacteristic
289C42C2×C22⋊D1311yescharacteristic
290C42C2×C22⋊D1311yescharacteristic
291C13#1017011yescharacteristic, complemented, Sylow
292C23—521no—
293C23#8819311yescharacteristic
294Q8—44no—
295Q8—44no—
296Q8—44no—
297Q8—81no—
298Q8—81no—
299Q8—522no—
300D4—522no—
301D4—522no—
302D4—522no—
303D4—1042no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—521no—
311C2×C4—1041no—
312C2×C4—1041no—
313C2×C4SD16×D1312yes—
314C2×C4#8816812yes—
315C2×C4#8819111yescharacteristic
316C2×C4#8819111yescharacteristic
317C2×C4#8819211yescharacteristic
318C2×C4#8819311yescharacteristic
319C2×C4#8819411yescharacteristic
320C2×C4#8820711yescharacteristic
321C8—42no—
322C8—264no—
323C8—522no—
324C8—1041no—
325C22—21no—
326C22—21no—
327C22—1041no—
328C22—1041no—
329C22—1041no—
330C22#1171882412yes—
331C22#1171888411yescharacteristic
332C4—21no—
333C4—21no—
334C4—82no—
335C4—82no—
336C4—1041no—
337C4#1171872212yes—
338C4#1171883012yes—
339C4#1171883611yescharacteristic
340C4#1171883711yescharacteristic
341C4#1171885312yes—
342C2—22no—
343C2—2081no—
344C2#1311586511yescharacteristic
345C2#1311592211yescharacteristic
346C2#1311595511yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC2×C13×#487C2
socleC22×C13#392
prime radical#11719182C22
hypercenterC2×#487D13
hypocenterC13#10170
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
3. #13115826C2semidirect
4. #13113508C2semidirect
6. #13112673C2semidirect
7. C2×C13×#487C2semidirect
115. #6099SD16semidirect
121. C2×#487D13semidirect
291. C13#10170semidirect

Maximal subgroups

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

subgroupindex
#131257612
#131252932
#131158262
#131135082
#131132882
#131126732
C2×C13×#4872
#1017013