Finite Group Databasebeta

← #15758962

Subgroups — #15758962

Order 3328.

684 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 131 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#13120641C211yesmaximal, characteristic
2#13113407C212yesmaximal, complemented
3C2×#11718117C211yesmaximal, characteristic
4#13112703C212yesmaximal, complemented
5C13×#2315C211yesmaximal, characteristic
6C22×C13×C22⋊C4—21no—
7C22×C13×C22⋊C4C2211yescharacteristic
8C2×#88178C2211yescharacteristic
9C13×#385—24no—
10C13×#380—21no—
11C13×#380C2212yes—
12#11718908—21no—
13#11718873C2211yescharacteristic
14#11718871—21no—
15C2×C22⋊#1055C2212yes—
16#11718610C412yescomplemented
17#11718609—22no—
18#11718608C412yescomplemented
19#11718117—22no—
20#11718044—24no—
21C25×C13D411yescharacteristic
22C23×C4×C13—22no—
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C22×Dic26C2×C411yescharacteristic, complemented
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C22⋊C4—22no—
29C2×C13×C22⋊C4—22no—
30C2×C13×C22⋊C4—22no—
31C2×C13×C22⋊C4—22no—
32C2×C13×C22⋊C4—42no—
33C2×C13×C22⋊C4—42no—
34C2×C13×C22⋊C4C2×C412yes—
35C2×C13×C22⋊C4D412yes—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C22⋊Dic13—22no—
39C2×C22⋊Dic13—22no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic, complemented
42#88178—22no—
43#88178—22no—
44C2×#6101—21no—
45C2×#6101—22no—
46C22×#1055—22no—
47C13×#95—22no—
48C13×#95D414yes—
49#88071—22no—
50#88071C2×C412yescomplemented
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#9199—131nomaximal, Sylow
54C24×C13—21no—
55C24×C13—21no—
56C24×C13—21no—
57C24×C13—21no—
58C24×C13—81no—
59C24×C13—81no—
60C24×C13C22⋊C412yes—
61C24×C13SD1612yes—
62C24×C13Q1612yes—
63C24×C13C2×D411yescharacteristic
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—24no—
67C22×C4×C13—44no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13—82no—
71C22×C4×C13—82no—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D412yes—
76C22×C4×C13#4112yes—
77C22×Dic13—21no—
78C22×Dic13—22no—
79C22×Dic13—21no—
80C2×Dic26—22no—
81C2×Dic26—81no—
82C13×C4⋊C4—82no—
83C13×C4⋊C4—82no—
84C13×C22⋊C4—24no—
85C13×C22⋊C4—24no—
86C13×C22⋊C4—44no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—42no—
89C22⋊Dic13—41no—
90C22⋊Dic13—41no—
91C22⋊Dic13—41no—
92C22⋊Dic13—41no—
93C22⋊Dic13—82no—
94C22⋊Dic13—82no—
95C4⋊Dic13—22no—
96C4⋊Dic13—81no—
97#6101—42no—
98#6101—82no—
99C2×#1055—42no—
100C2×#1055—82no—
101#2626—131no—
102#2315D1311yescharacteristic
103#1520—132no—
104C2×#323—131no—
105#1289—132no—
106C23×C13—22no—
107C23×C13—22no—
108C23×C13—22no—
109C23×C13—22no—
110C23×C13—22no—
111C23×C13—22no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—42no—
115C23×C13—42no—
116C23×C13—42no—
117C23×C13—42no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13—82no—
121C23×C13—82no—
122C23×C13—82no—
123C23×C13—82no—
124C23×C13#10314yes—
125C23×C13C2×C22⋊C411yescharacteristic
126C23×C13#12011yescharacteristic
127C23×C13#12311yescharacteristic
128C23×C13C2×SD1611yescharacteristic
129C23×C13C2×Q1611yescharacteristic
130C23×C13AGL(1,ℤ/8)11yescharacteristic
131C23×C13#13711yescharacteristic
132C2×C4×C13—22no—
133C2×C4×C13—42no—
134C2×C4×C13—41no—
135C2×C4×C13—42no—
136C2×C4×C13—41no—
137C2×C4×C13—42no—
138C2×C4×C13—42no—
139C2×C4×C13—44no—
140C2×C4×C13—44no—
141C2×C4×C13—44no—
142C2×C4×C13—81no—
143C2×C4×C13—88no—
144C2×C4×C13C4×D412yes—
145C2×C4×C13#12112yes—
146C2×Dic13—42no—
147C2×Dic13—42no—
148C2×Dic13—42no—
149C2×Dic13—42no—
150C2×Dic13—41no—
151C2×Dic13—41no—
152C2×Dic13—42no—
153Dic26—82no—
154#1055—82no—
155C2×C22⋊Q8—131no—
156C22×C22⋊C4—21no—
157C22×C22⋊C4C2×D1311yescharacteristic
158C2×C22⋊C8—132no—
159#399—132no—
160#396—262no—
161#393—132no—
162#385—24no—
163#385—261no—
164#380—21no—
165#380—131no—
166#380C2×D1312yes—
167#379—261no—
168#328—264no—
169#323—262no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—21no—
173C22×C13—21no—
174C22×C13—21no—
175C22×C13—21no—
176C22×C13—24no—
177C22×C13—41no—
178C22×C13—41no—
179C22×C13—41no—
180C22×C13—41no—
181C22×C13—44no—
182C22×C13—44no—
183C22×C13—44no—
184C22×C13—42no—
185C22×C13—42no—
186C22×C13—82no—
187C22×C13—82no—
188C22×C13—82no—
189C22×C13#38611yescharacteristic
190C22×C13C2×#10311yescharacteristic
191C22×C13#41711yescharacteristic
192C22×C13#45011yescharacteristic
193C22×C13#45111yescharacteristic
194C22×C13#48311yescharacteristic
195C22×C13#48411yescharacteristic
196C4×C13—22no—
197C4×C13—22no—
198C4×C13—42no—
199C4×C13—84no—
200Dic13—82no—
201Dic13—81no—
202Dic13—81no—
203C25C22⋊D1311yescharacteristic
204C22×Q8—131no—
205C23×C4—22no—
206C23×C4C22⋊D1311yescharacteristic
207C23×C4C22×D1311yescharacteristic
208C22×C8—262no—
209C22⋊Q8—262no—
210C22⋊Q8—262no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—131no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—262no—
216C2×C4⋊C4—261no—
217C2×C22⋊C4—22no—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—42no—
222C2×C22⋊C4—42no—
223C2×C22⋊C4—261no—
224C2×C22⋊C4—261no—
225C2×C22⋊C4—262no—
226C2×C22⋊C4—262no—
227C2×C22⋊C4C4×D1312yes—
228C2×C22⋊C4D5212yes—
229C22⋊C8—262no—
230C22⋊C8—262no—
231#95—22no—
232#95—132no—
233#95—262no—
234#95C22⋊D1314yes—
235C2×C13—21no—
236C2×C13—21no—
237C2×C13—21no—
238C2×C13—21no—
239C2×C13—21no—
240C2×C13—21no—
241C2×C13—44no—
242C2×C13#187211yescharacteristic
243C2×C13#191111yescharacteristic
244C2×C13#191311yescharacteristic
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—81no—
250C24—81no—
251C24#610312yes—
252C24#610512yes—
253C24#610712yes—
254C24C2×C22⋊D1311yescharacteristic
255C2×Q8—262no—
256C2×Q8—1041no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—24no—
260C22×C4—44no—
261C22×C4—81no—
262C22×C4—81no—
263C22×C4—82no—
264C22×C4—82no—
265C22×C4—262no—
266C22×C4—261no—
267C22×C4—261no—
268C22×C4#610312yes—
269C22×C4C2×C4×D1311yescharacteristic
270C22×C4C2×D5211yescharacteristic
271C22×C4#612712yes—
272C22×C4C2×C22⋊D1312yes—
273C2×C8—522no—
274C2×C8—1042no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C4⋊C4—262no—
278C4⋊C4—522no—
279C4⋊C4—1042no—
280C4⋊C4—1041no—
281C22⋊C4—24no—
282C22⋊C4—24no—
283C22⋊C4—44no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C22⋊C4—521no—
287C22⋊C4—521no—
288C22⋊C4—521no—
289C22⋊C4—521no—
290C22⋊C4—1042no—
291C22⋊C4—1042no—
292C13#919911yescharacteristic, complemented, Sylow
293C23—22no—
294C23—22no—
295C23—22no—
296C23—22no—
297C23—22no—
298C23—22no—
299C23—41no—
300C23—41no—
301C23—42no—
302C23—42no—
303C23—42no—
304C23—42no—
305C23—81no—
306C23—81no—
307C23—82no—
308C23—82no—
309C23—82no—
310C23—82no—
311C23#8805014yes—
312C23C2×#610311yescharacteristic
313C23#8818311yescharacteristic
314C23#8818611yescharacteristic
315C23C2×#610511yescharacteristic
316C23#8819611yescharacteristic
317C23C2×#610711yescharacteristic
318C23#8820711yescharacteristic
319Q8—1042no—
320C2×C4—22no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—44no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—81no—
331C2×C4—88no—
332C2×C4—522no—
333C2×C4—522no—
334C2×C4—522no—
335C2×C4—522no—
336C2×C4—521no—
337C2×C4—521no—
338C2×C4—522no—
339C2×C4C4×C22⋊D1312yes—
340C2×C4#8818412yes—
341C8—1042no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—44no—
354C22—44no—
355C22—44no—
356C22—42no—
357C22—42no—
358C22—82no—
359C22—82no—
360C22—82no—
361C22#1171862711yescharacteristic
362C22C2×#8805011yescharacteristic
363C22#1171863111yescharacteristic
364C22#1171863211yescharacteristic
365C22#1171887411yescharacteristic
366C22#1171887911yescharacteristic
367C22#1171888911yescharacteristic
368C4—22no—
369C4—22no—
370C4—42no—
371C4—84no—
372C4—1042no—
373C4—1041no—
374C4—1041no—
375C2—21no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2—44no—
382C2#1311514311yescharacteristic
383C2#1311536811yescharacteristic
384C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2315C2
socleC22×C13#386
prime radicalC25×C13D4
cosocleC23×C4×C13C23
hypercenter#2315D13
hypocenterC13#9199
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #13113407C2semidirect
4. #13112703C2semidirect
16. #11718610C4semidirect
18. #11718608C4semidirect
25. C22×Dic26C2×C4semidirect
41. C2×C4⋊Dic13C2×C4semidirect
50. #88071C2×C4semidirect
292. C13#9199semidirect

Maximal subgroups

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

subgroupindex
#131206412
#131134072
C2×#117181172
#131127032
C13×#23152
#919913