Finite Group Databasebeta

← #15758965

Subgroups — #15758965

Order 3328.

560 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 127 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#13117454C211yesmaximal, characteristic
3#13113409C212yesmaximal
4#13112704C212yesmaximal
5C2×C13×#324C211yesmaximal, characteristic
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88180—21no—
8C2×#88178C2211yescharacteristic
9C2×C13×C22⋊C8C2212yes—
10#11718873—21no—
11#11718873C2211yescharacteristic
12#11718873C2212yes—
13#11718872—21no—
14#11718871—21no—
15#11718647C412yescomplemented
16#11718646—24no—
17#11718645—22no—
18#11718640C412yescomplemented
19C13×#324—22no—
20#11718059—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C22×C8×C13—22no—
26C2×C13×C4⋊C4—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4C2×C412yes—
29C2×C13×C4⋊C4D412yes—
30C2×C22⋊Dic13—21no—
31C2×C22⋊Dic13—22no—
32C2×C22⋊Dic13—21no—
33#88180—42no—
34#88180—42no—
35C2×C4⋊Dic13—22no—
36C2×C4⋊Dic13—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—22no—
39C2×C4⋊Dic13C2×C411yescharacteristic
40#88178—22no—
41#88178—22no—
42C2×#6101—21no—
43C2×#6101—22no—
44C2×C4×Dic13—22no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47#88071—22no—
48#88071—22no—
49#88071—22no—
50#88071—22no—
51#88071C2×C412yes—
52#88071D414yes—
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—81no—
62C22×C4×C13—81no—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22⋊C412yes—
65C22×C4×C13SD1612yes—
66C22×C4×C13Q1612yes—
67C22×C4×C13C22×C411yescharacteristic
68C22×C4×C13C2×D412yes—
69C22×C4×C13C2×D411yescharacteristic
70C22×C4×C13#4112yes—
71C22×Dic13—21no—
72C22×Dic13—22no—
73C22×Dic13—21no—
74C22×Dic13—24no—
75C2×Dic26—22no—
76C2×Dic26—81no—
77C2×C8×C13—42no—
78C2×C8×C13—82no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—24no—
81C22⋊Dic13—41no—
82C22⋊Dic13—41no—
83C22⋊Dic13—42no—
84C22⋊Dic13—42no—
85C22⋊Dic13—41no—
86C22⋊Dic13—41no—
87C4⋊Dic13—22no—
88C4⋊Dic13—44no—
89C4⋊Dic13—81no—
90C4⋊Dic13—82no—
91C4⋊Dic13—82no—
92#6101—42no—
93#6101—82no—
94C4×Dic13—44no—
95#2627—131no—
96#2316—131no—
97#1520—132no—
98C2×#324D1311yescharacteristic
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—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—81no—
123C2×C4×C13#10314yes—
124C2×C4×C13C4×D412yes—
125C2×C4×C13#12112yes—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—44no—
129C2×Dic13—42no—
130C2×Dic13—44no—
131C2×Dic13—42no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—42no—
135C2×Dic13—44no—
136Dic26—82no—
137C8×C13—82no—
138C2×C22⋊Q8—131no—
139C2×#117—261no—
140C22×C4⋊C4C2×D1311yescharacteristic
141C2×C22⋊C8C2×D1312yes—
142#400—132no—
143#398—262no—
144#395—132no—
145#389—264no—
146#385—261no—
147#381—261no—
148#380—131no—
149#380—132no—
150#380—261no—
151#328—264no—
152#324—22no—
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—
174Dic13—84no—
175Dic13—82no—
176Dic13—81no—
177Dic13—81no—
178C22×Q8—131no—
179C23×C4D5211yescharacteristic
180C23×C4D5211yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—22no—
183C22⋊Q8—262no—
184C22⋊Q8—262no—
185#117—522no—
186#117—522no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—131no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—262no—
193C2×C4⋊C4—262no—
194C2×C4⋊C4—262no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4C4×D1312yes—
197C2×C4⋊C4C22⋊D1312yes—
198C2×C22⋊C4—262no—
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C42—262no—
202C22⋊C8—22no—
203C22⋊C8—22no—
204#95—132no—
205#95—134no—
206#95—262no—
207#95—262no—
208#95—262no—
209#95—262no—
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×D5211yescharacteristic
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—81no—
229C22×C4—81no—
230C22×C4—264no—
231C22×C4—262no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4#609512yes—
235C22×C4Dic5212yes—
236C22×C4#610312yes—
237C22×C4#610312yes—
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4D4×D1312yes—
240C22×C4#612912yes—
241C22×C4C2×C22⋊D1311yescharacteristic
242C2×C8—42no—
243C2×C8—82no—
244C4⋊C4—24no—
245C4⋊C4—24no—
246C4⋊C4—262no—
247C4⋊C4—524no—
248C4⋊C4—522no—
249C4⋊C4—1042no—
250C4⋊C4—1042no—
251C4⋊C4—1041no—
252C4⋊C4—1042no—
253C22⋊C4—521no—
254C22⋊C4—521no—
255C22⋊C4—522no—
256C22⋊C4—522no—
257C22⋊C4—521no—
258C22⋊C4—521no—
259C42—524no—
260C13#920011yescharacteristic, complemented, Sylow
261C23—41no—
262C23—41no—
263C23#8813611yescharacteristic
264C23#8814011yescharacteristic
265C23C2×#609511yescharacteristic
266C23C2×Dic5211yescharacteristic
267C23#8816211yescharacteristic
268C23#8816311yescharacteristic
269C23C2×#610311yescharacteristic
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—81no—
285C2×C4—524no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—524no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4—522no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—524no—
295C2×C4#8805614yes—
296C2×C4#8813512yes—
297C2×C4#8819312yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22#1171838211yescharacteristic
310C22#1171838311yescharacteristic
311C22#1171839211yescharacteristic
312C22#1171840011yescharacteristic
313C22#1171861911yescharacteristic
314C22C2×#8805611yescharacteristic
315C22#1171879411yescharacteristic
316C4—24no—
317C4—22no—
318C4—22no—
319C4—42no—
320C4—1044no—
321C4—1042no—
322C4—1041no—
323C4—1041no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2#1311514111yescharacteristic
331C2#1311537111yescharacteristic
332C2#1311537611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC22×C13#386
prime radicalC24×C13C2×D4
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9200
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
15. #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
#131174542
#131134092
#131127042
C2×C13×#3242
#920013