Finite Group Databasebeta

← #15758967

Subgroups — #15758967

Order 3328.

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

normal subgroups only

This group has 560 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#13120649C211yesmaximal, characteristic
2#13113407C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic
4#13112703C212yesmaximal
5C13×#2316C211yesmaximal, characteristic
6C2×C13×#117—21no—
7C22×C13×C4⋊C4C2211yescharacteristic
8C2×#88178C2211yescharacteristic
9C13×#389—24no—
10C13×#380—21no—
11C13×#380C2212yes—
12#11718873C2211yescharacteristic
13#11718872—21no—
14#11718871—21no—
15C2×C22⋊#1055C2212yes—
16#11718647C412yescomplemented
17#11718645—22no—
18#11718640C412yescomplemented
19#11718120—22no—
20#11718044—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—42no—
26C13×#117—42no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4C2×C412yes—
33C2×C13×C4⋊C4D412yes—
34C2×C13×C22⋊C4—22no—
35C2×C42×C13—22no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40#88178—22no—
41#88178—22no—
42C2×#6101—21no—
43C2×#6101—22no—
44C22×#1055—22no—
45C13×#95—22no—
46C13×#95D414yes—
47#88071—22no—
48#88071—22no—
49#88071—22no—
50#88071C2×C412yes—
51C22⋊#1055—22no—
52C22⋊#1055—22no—
53#9200—131nomaximal, Sylow
54C24×C13C2×D411yescharacteristic
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—24no—
62C22×C4×C13—81no—
63C22×C4×C13—81no—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13SD1612yes—
67C22×C4×C13Q1612yes—
68C22×C4×C13C22×C411yescharacteristic
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13#4112yes—
72C22×Dic13—21no—
73C22×Dic13—22no—
74C22×Dic13—21no—
75C2×Dic26—22no—
76C2×Dic26—81no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—44no—
80C13×C4⋊C4—82no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—42no—
83C13×C22⋊C4—42no—
84C42×C13—44no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C22⋊Dic13—41no—
88C22⋊Dic13—41no—
89C4⋊Dic13—22no—
90C4⋊Dic13—81no—
91#6101—42no—
92#6101—82no—
93C2×#1055—42no—
94C2×#1055—82no—
95#2627—131no—
96#2316D1311yescharacteristic
97#1520—132no—
98C2×#324—131no—
99#1289—132no—
100C23×C13—41no—
101C23×C13—41no—
102C23×C13C2×C22⋊C411yescharacteristic
103C23×C13#12011yescharacteristic
104C23×C13#12311yescharacteristic
105C23×C13C2×SD1611yescharacteristic
106C23×C13C2×Q1611yescharacteristic
107C23×C13AGL(1,ℤ/8)11yescharacteristic
108C23×C13#13711yescharacteristic
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—42no—
117C2×C4×C13—41no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—44no—
123C2×C4×C13—44no—
124C2×C4×C13—44no—
125C2×C4×C13—81no—
126C2×C4×C13#10314yes—
127C2×C4×C13C4×D412yes—
128C2×C4×C13#12112yes—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—42no—
136Dic26—82no—
137#1055—82no—
138C2×C22⋊Q8—131no—
139C2×#117—21no—
140C22×C4⋊C4C2×D1311yescharacteristic
141C2×C22⋊C8—132no—
142#400—132no—
143#398—262no—
144#395—132no—
145#389—24no—
146#385—261no—
147#381—261no—
148#380—21no—
149#380—131no—
150#380C2×D1312yes—
151#328—264no—
152#324—262no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13#38611yescharacteristic
164C22×C13C2×#10311yescharacteristic
165C22×C13#41711yescharacteristic
166C22×C13#45011yescharacteristic
167C22×C13#45111yescharacteristic
168C22×C13#48311yescharacteristic
169C22×C13#48411yescharacteristic
170C4×C13—24no—
171C4×C13—22no—
172C4×C13—22no—
173C4×C13—42no—
174C4×C13—84no—
175Dic13—82no—
176Dic13—81no—
177Dic13—81no—
178C22×Q8—131no—
179C23×C4C22⋊D1311yescharacteristic
180C23×C4C22⋊D1311yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—262no—
183C22⋊Q8—262no—
184C22⋊Q8—262no—
185#117—42no—
186#117—42no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—22no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—131no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4—262no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4C4×D1312yes—
197C2×C4⋊C4D5212yes—
198C2×C22⋊C4—22no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C42—22no—
202C22⋊C8—262no—
203C22⋊C8—262no—
204#95—22no—
205#95—132no—
206#95—262no—
207#95—262no—
208#95—262no—
209#95C22⋊D1314yes—
210C2×C13—21no—
211C2×C13—21no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13#187211yescharacteristic
217C2×C13#191211yescharacteristic
218C2×C13#191311yescharacteristic
219C24C2×C22⋊D1311yescharacteristic
220C2×Q8—262no—
221C2×Q8—1041no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—24no—
229C22×C4—81no—
230C22×C4—81no—
231C22×C4—262no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4#610312yes—
235C22×C4#610312yes—
236C22×C4#610512yes—
237C22×C4#610712yes—
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4C2×D5211yescharacteristic
240C22×C4#612712yes—
241C22×C4C2×C22⋊D1312yes—
242C2×C8—522no—
243C2×C8—1042no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—44no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C4⋊C4—262no—
250C4⋊C4—522no—
251C4⋊C4—1042no—
252C4⋊C4—1041no—
253C22⋊C4—42no—
254C22⋊C4—42no—
255C22⋊C4—521no—
256C22⋊C4—521no—
257C22⋊C4—521no—
258C22⋊C4—521no—
259C42—44no—
260C13#920011yescharacteristic, complemented, Sylow
261C23—41no—
262C23—41no—
263C23C2×#610311yescharacteristic
264C23#8818311yescharacteristic
265C23#8818611yescharacteristic
266C23C2×#610511yescharacteristic
267C23#8819611yescharacteristic
268C23C2×#610711yescharacteristic
269C23#8820711yescharacteristic
270Q8—1042no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—81no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—522no—
295C2×C4#8805014yes—
296C2×C4C4×C22⋊D1312yes—
297C2×C4#8818412yes—
298C8—1042no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1171862711yescharacteristic
310C22C2×#8805011yescharacteristic
311C22#1171863111yescharacteristic
312C22#1171863211yescharacteristic
313C22#1171887411yescharacteristic
314C22#1171887911yescharacteristic
315C22#1171888911yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—84no—
321C4—1042no—
322C4—1041no—
323C4—1041no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1311514311yescharacteristic
331C2#1311537311yescharacteristic
332C2#1311537811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2316C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenter#2316D13
hypocenterC13#9200
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2316

Complements

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

NH ≅ G/Ntype
16. #11718647C4semidirect
18. #11718640C4semidirect
260. C13#9200semidirect

Maximal subgroups

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

subgroupindex
#131206492
#131134072
C2×#117181202
#131127032
C13×#23162
#920013