Finite Group Databasebeta

← #15760208

Subgroups — #15760208

Order 3328.

492 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 103 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#13117651C211yesmaximal, characteristic
2#13115781C211yesmaximal, characteristic, complemented
3#13113434C211yesmaximal, characteristic
4#13113387C211yesmaximal, characteristic, complemented
5#13112702C211yesmaximal, characteristic, complemented
6#13112691C211yesmaximal, characteristic, complemented
7C13×#3215C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C13×#124C2211yescharacteristic
10C13×#497C412yescomplemented
11C13×#489C412yescomplemented
12C13×#464—22no—
13C13×#451—21no—
14C13×#450—21no—
15C13×#432C2211yescharacteristic
16#11718891—21no—
17#11718881—21no—
18#11718612—21no—
19#11718612—21no—
20#11718611—21no—
21C22⋊C4×Dic13—21no—
22#11718598C2211yescharacteristic
23C4×C4⋊Dic13C2211yescharacteristic
24#11718587C2211yescharacteristic
25C4×#6099C2211yescharacteristic
26#11718132—22no—
27#11718130—21no—
28#11718130—21no—
29#11718124—21no—
30#11718124—21no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C23×Dic13—21no—
34C2×C13×Q16—22no—
35C2×C13×SD16—22no—
36C13×C4⋊Q8C2×C411yescharacteristic, complemented
37C13×C4⋊Q8C2×C411yescharacteristic, complemented
38C13×#125—21no—
39C13×#124—21no—
40C13×#124—21no—
41C13×#124C2×C412yes—
42C13×#124D412yes—
43C13×C22⋊Q8—21no—
44C13×C22⋊Q8—21no—
45C4×Q8×C13—21no—
46C4×Q8×C13—21no—
47C13×#117—21no—
48C2×C13×C22⋊C4—21no—
49C2×C13×C22⋊C4—21no—
50C2×C42×C13C2311yescharacteristic
51C2×C22⋊Dic13—21no—
52C2×C22⋊Dic13—21no—
53C2×C22⋊Dic13—21no—
54C2×C4⋊Dic13—21no—
55C2×C4⋊Dic13—21no—
56C2×C4×Dic13—21no—
57C2×C4×Dic13D411yescharacteristic
58C2×C4×Dic13D411yescharacteristic
59C2×#6099—21no—
60C13×C4⋊C8—21no—
61C13×#103—22no—
62C13×#102—22no—
63C13×C22⋊C8—21no—
64C13×#97C2×C412yescomplemented
65#88071—21no—
66#88071—21no—
67#88071—21no—
68#88071—21no—
69#88071—21no—
70#88071D411yescharacteristic
71#88071D411yescharacteristic
72C22⋊#1055—21no—
73C4⋊#1055—21no—
74#88043—21no—
75#88043—21no—
76C4×#1055—21no—
77#9379—131nomaximal, Sylow
78C24×C13—21no—
79C2×Q8×C13—21no—
80C2×Q8×C13—21no—
81C2×Q8×C13—21no—
82C2×Q8×C13—81no—
83C2×Q8×C13C22⋊C412yes—
84C2×D4×C13—21no—
85C2×D4×C13—81no—
86C2×D4×C13C22⋊C412yes—
87C22×C4×C13—21no—
88C22×C4×C13C2×D411yescharacteristic
89C22×C4×C13C2×D411yescharacteristic
90C22×C4×C13C2×D411yescharacteristic
91C22×Dic13—21no—
92C22×Dic13—21no—
93C22×Dic13—21no—
94C22×Dic13—21no—
95C22×Dic13—42no—
96C22×Dic13—81no—
97C22×Dic13—81no—
98C13×Q16—82no—
99C13×SD16—82no—
100C2×C8×C13—22no—
101C13×C4⋊C4—21no—
102C13×C4⋊C4—21no—
103C13×C4⋊C4—21no—
104C13×C4⋊C4—21no—
105C13×C4⋊C4—41no—
106C13×C4⋊C4—41no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4—22no—
110C13×C22⋊C4—22no—
111C13×C22⋊C4—41no—
112C42×C13—41no—
113C42×C13C22×C411yescharacteristic
114C42×C13C2×D411yescharacteristic
115C42×C13#4111yescharacteristic
116C42×C13#4111yescharacteristic
117C22⋊Dic13—42no—
118C22⋊Dic13—81no—
119C22⋊Dic13—81no—
120C4⋊Dic13—42no—
121C4⋊Dic13—81no—
122C4×Dic13—41no—
123C4×Dic13—41no—
124C4×Dic13—81no—
125#6099—22no—
126#6099—41no—
127C2×#1055—41no—
128C2×#1055—41no—
129#3215D1311yescharacteristic
130#2337—131no—
131#1986—131no—
132#1527—131no—
133#1515—131no—
134#1288—131no—
135#1285—131no—
136C23×C13—22no—
137C23×C13—41no—
138C23×C13—41no—
139C23×C13—41no—
140C23×C13—41no—
141C23×C13—41no—
142C23×C13—41no—
143C23×C13#12011yescharacteristic
144Q8×C13—42no—
145Q8×C13—42no—
146Q8×C13—81no—
147Q8×C13—81no—
148D4×C13—42no—
149D4×C13—81no—
150C2×C4×C13—21no—
151C2×C4×C13—21no—
152C2×C4×C13—22no—
153C2×C4×C13—41no—
154C2×C4×C13—41no—
155C2×C4×C13—41no—
156C2×C4×C13—41no—
157C2×C4×C13—41no—
158C2×C4×C13—41no—
159C2×C4×C13C2×C22⋊C411yescharacteristic
160C2×C4×C13C4×D411yescharacteristic
161C2×C4×C13C4×D411yescharacteristic
162C2×C4×C13#12111yescharacteristic
163C2×C4×C13#12111yescharacteristic
164C2×C4×C13#12311yescharacteristic
165C2×Dic13—22no—
166C2×Dic13—41no—
167C2×Dic13—41no—
168C2×Dic13—41no—
169C2×Dic13—41no—
170C2×Dic13—41no—
171C2×Dic13—41no—
172C2×Dic13—41no—
173C2×Dic13—41no—
174C2×Dic13—41no—
175C2×Dic13—41no—
176C2×Dic13—41no—
177C2×Dic13—84no—
178C8×C13—42no—
179#1055—42no—
180#1055—81no—
181#533C2×D1311yescharacteristic
182C2×#124C2×D1311yescharacteristic
183#497Dic1312yescomplemented
184#489Dic1312yescomplemented
185#464—22no—
186#451—21no—
187#450—21no—
188#432—131no—
189#432C2×D1311yescharacteristic
190C4×M16—131no—
191#391—261no—
192#388—261no—
193#388—261no—
194#386—261no—
195#385—261no—
196#383—131no—
197C4×C4⋊C4—131no—
198C4×C22⋊C4—261no—
199#339—261no—
200#339—261no—
201#329—262no—
202#328—261no—
203#328—261no—
204C22×C13—21no—
205C22×C13—21no—
206C22×C13—42no—
207C22×C13—42no—
208C22×C13—42no—
209C22×C13—81no—
210C22×C13—81no—
211C22×C13—81no—
212C22×C13—81no—
213C22×C13#38611yescharacteristic
214C22×C13#45511yescharacteristic
215C22×C13#45611yescharacteristic
216C4×C13—21no—
217C4×C13—21no—
218C4×C13—21no—
219C4×C13—21no—
220C4×C13—21no—
221C4×C13—21no—
222C4×C13—42no—
223C4×C13—81no—
224C4×C13—81no—
225Dic13—42no—
226Dic13—81no—
227Dic13—81no—
228Dic13—81no—
229C22×Q8C22⋊D1311yescharacteristic
230C22×D4C22⋊D1311yescharacteristic
231C23×C4—261no—
232C2×Q16—22no—
233C2×SD16—22no—
234C2×M16—261no—
235C4⋊Q8C2×Dic1311yescharacteristic, complemented
236C4⋊Q8C2×Dic1311yescharacteristic, complemented
237#125—21no—
238#124—21no—
239#124—21no—
240#124C2×Dic1312yes—
241#124C22⋊D1312yes—
242C22⋊Q8—21no—
243C22⋊Q8—21no—
244C4×Q8—21no—
245C4×Q8—21no—
246#117—21no—
247C2×C4⋊C4—261no—
248C2×C4⋊C4—261no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—261no—
252C2×C22⋊C4—261no—
253C2×C22⋊C4—261no—
254C2×C42—131no—
255C2×C42—131no—
256C2×C42—261no—
257C2×C42C22×D1311yescharacteristic
258C4⋊C8—21no—
259C4⋊C8—261no—
260#103—22no—
261#102—22no—
262C22⋊C8—21no—
263C22⋊C8—261no—
264#97—261no—
265#97—261no—
266#97C2×Dic1312yescomplemented
267C4×C8—261no—
268#95—131no—
269#95—131no—
270#95—261no—
271#95—261no—
272#95—261no—
273#95—261no—
274#95—261no—
275C2×C13—21no—
276C2×C13—21no—
277C2×C13—82no—
278C2×C13#188211yescharacteristic
279C2×C13#190611yescharacteristic
280C2×C13#191111yescharacteristic
281C24—21no—
282C2×Q8—21no—
283C2×Q8—21no—
284C2×Q8—21no—
285C2×Q8—81no—
286C2×Q8C22⋊Dic1312yes—
287C2×D4—21no—
288C2×D4—81no—
289C2×D4C22⋊Dic1312yes—
290C22×C4—21no—
291C22×C4—261no—
292C22×C4—261no—
293C22×C4—261no—
294C22×C4—261no—
295C22×C4—522no—
296C22×C4—1041no—
297C22×C4—1041no—
298C22×C4D4×D1311yescharacteristic
299C22×C4D4×D1311yescharacteristic
300C22×C4C2×C22⋊D1311yescharacteristic
301Q16—82no—
302SD16—82no—
303M16—262no—
304M16—521no—
305C2×C8—22no—
306C2×C8—521no—
307C2×C8—521no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—522no—
315C4⋊C4—1041no—
316C22⋊C4—22no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—522no—
322C22⋊C4—1041no—
323C22⋊C4—1041no—
324C42—41no—
325C42—521no—
326C42—521no—
327C42—1041no—
328C42#612911yescharacteristic
329C42#612911yescharacteristic
330C42C22×Dic1311yescharacteristic
331C42C2×C22⋊D1311yescharacteristic
332C13#937911yescharacteristic, complemented, Sylow
333C23—22no—
334C23—41no—
335C23—41no—
336C23—41no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23#8819111yescharacteristic
341Q8—42no—
342Q8—42no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—81no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—22no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—262no—
357C2×C4—521no—
358C2×C4—521no—
359C2×C4—521no—
360C2×C4—521no—
361C2×C4—521no—
362C2×C4—521no—
363C2×C4—521no—
364C2×C4—521no—
365C2×C4—521no—
366C2×C4—521no—
367C2×C4—521no—
368C2×C4—1044no—
369C2×C4D4×Dic1311yescharacteristic
370C2×C4D4×Dic1311yescharacteristic
371C2×C4#8818911yescharacteristic
372C2×C4#8819311yescharacteristic
373C2×C4#8819311yescharacteristic
374C2×C4C2×C22⋊Dic1311yescharacteristic
375C8—42no—
376C8—522no—
377C8—1041no—
378C22—21no—
379C22—21no—
380C22—42no—
381C22—42no—
382C22—42no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22—81no—
387C22#1171886311yescharacteristic
388C22#1171886611yescharacteristic
389C22#1171888111yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—42no—
397C4—81no—
398C4—81no—
399C4—522no—
400C4—1041no—
401C4—1041no—
402C4—1041no—
403C2—21no—
404C2—21no—
405C2—82no—
406C2#1311520711yescharacteristic
407C2#1311533911yescharacteristic
408C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3215C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#3215D13
hypocenterC13#9379
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3215

Complements

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

NH ≅ G/Ntype
2. #13115781C2semidirect
4. #13113387C2semidirect
5. #13112702C2semidirect
6. #13112691C2semidirect
10. C13×#497C4semidirect
11. C13×#489C4semidirect
36. C13×C4⋊Q8C2×C4semidirect
37. C13×C4⋊Q8C2×C4semidirect
64. C13×#97C2×C4semidirect
183. #497Dic13semidirect
184. #489Dic13semidirect
235. C4⋊Q8C2×Dic13semidirect
236. C4⋊Q8C2×Dic13semidirect
266. #97C2×Dic13semidirect
332. C13#9379semidirect

Maximal subgroups

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

subgroupindex
#131176512
#131157812
#131134342
#131133872
#131127022
#131126912
C13×#32152
#937913