Finite Group Databasebeta

← #15831970

Subgroups — #15831970

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123953C212yesmaximal
2#13113603C214yesmaximal, complemented
3#13113599C212yesmaximal, complemented
4#13113595C212yesmaximal, complemented
5#13113588C212yesmaximal, complemented
6#13113584C211yesmaximal, characteristic, complemented
7C2×#11718050C211yesmaximal, characteristic, complemented
8C4×C13×#131C211yesmaximal, characteristic
9C2×C13×#131C411yescharacteristic
10C2×C13×#131C411yescharacteristic
11C4×C13×#41C2211yescharacteristic
12C13×#405C411yescharacteristic
13C13×#405C412yes—
14C13×#405C412yes—
15C13×#405C411yescharacteristic
16C4×C13×M16C2212yes—
17C4×C13×M16C2211yescharacteristic
18C2×C4×C8×C13C2211yescharacteristic
19C2×C4×C8×C13C2212yes—
20#11718685—22no—
21#11718673—22no—
22#11718672—24no—
23#11718587C2214yes—
24#11718586C2212yes—
25#11718585C2214yes—
26C2×C4⋊#1055C2212yes—
27#11718050C2212yes—
28#11718050C2214yes—
29#11718050C2212yes—
30#11718050C2211yescharacteristic
31#11718050C2211yescharacteristic
32#11718049C2212yes—
33#11718049C2214yes—
34C2×C13×#41C2×C411yescharacteristic
35C13×#131—24no—
36C13×#131—24no—
37C2×C13×M16C2×C411yescharacteristic
38C2×C13×M16C2×C412yes—
39C2×C13×M16C2×C412yes—
40C2×C13×M16C2×C411yescharacteristic
41C22×C8×C13C2×C411yescharacteristic
42C22×C8×C13C2×C412yes—
43C22×C8×C13C2×C412yes—
44C22×C8×C13C2×C411yescharacteristic
45C4×Q8×C13D411yescharacteristic
46C4×Q8×C13Q811yescharacteristic
47C4×D4×C13D412yes—
48C4×D4×C13D411yescharacteristic
49C4×D4×C13Q812yes—
50C4×D4×C13Q811yescharacteristic
51C13×#117C2×C412yes—
52C13×#117C2×C411yescharacteristic
53C2×C42×C13C2311yescharacteristic
54C2×C42×C13C2312yes—
55C2×#6099—24no—
56C22×#1055—22no—
57C13×#97C2×C412yes—
58C13×#97C2×C412yes—
59C13×#97C2×C412yes—
60C4×C8×C13C2×C412yes—
61C4×C8×C13C2×C411yescharacteristic
62C4×C8×C13C2×C411yescharacteristic
63C4×C8×C13C2×C412yes—
64C4×C8×C13C2311yescharacteristic
65C4×C8×C13C2311yescharacteristic
66C4×C8×C13C2312yes—
67C22⋊#1055—22no—
68C22⋊#1055—24no—
69C4⋊#1055—24no—
70C4⋊#1055—22no—
71C4⋊#1055C2312yes—
72C4⋊#1055C2314yes—
73C4⋊#1055C2312yes—
74#88043—24no—
75C4×#1055—22no—
76#17799—131nomaximal, Sylow
77C13×#41—22no—
78C13×#41—22no—
79C2×Q8×C13C4⋊C411yescharacteristic
80C2×D4×C13C4⋊C412yes—
81C2×D4×C13C4⋊C411yescharacteristic
82C22×C4×C13C22×C412yes—
83C22×C4×C13C22×C411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D412yes—
86C22×C4×C13C2×Q812yes—
87C22×C4×C13C2×Q811yescharacteristic
88C13×M16—22no—
89C13×M16—24no—
90C13×M16—24no—
91C13×M16M1614yescomplemented
92C2×C8×C13—22no—
93C2×C8×C13—24no—
94C2×C8×C13—24no—
95C2×C8×C13M1614yescomplemented
96C2×C8×C13C22×C411yescharacteristic
97C2×C8×C13C22×C411yescharacteristic
98C2×C8×C13C22×C412yes—
99C2×C8×C13C22×C411yescharacteristic
100C2×C8×C13C22×C412yes—
101C2×C8×C13C22×C411yescharacteristic
102C13×C4⋊C4C4⋊C412yes—
103C13×C4⋊C4C4⋊C411yescharacteristic
104C13×C4⋊C4C4⋊C412yes—
105C13×C4⋊C4C4⋊C411yescharacteristic
106C13×C22⋊C4C4⋊C412yes—
107C13×C22⋊C4C4⋊C412yes—
108C13×C22⋊C4C4⋊C412yes—
109C42×C13C22×C411yescharacteristic
110C42×C13C22×C412yes—
111C42×C13C2×D411yescharacteristic
112C42×C13C2×D412yes—
113C42×C13C2×Q812yes—
114C42×C13C2×Q811yescharacteristic
115C42×C13C2411yescharacteristic
116#6099—84no—
117C2×#1055—22no—
118C2×#1055—24no—
119C2×#1055—22no—
120C2×#1055—82no—
121#2989—132no—
122C4×#131D1311yescharacteristic
123#1569—134no—
124#1568—132no—
125#1567—132no—
126#1565—132no—
127#1564—131no—
128C2×#335—131no—
129C23×C13C2×C4⋊C412yes—
130C23×C13C2×C4⋊C411yescharacteristic
131Q8×C13—22no—
132D4×C13—24no—
133D4×C13—22no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—21no—
137C2×C4×C13—22no—
138C2×C4×C13—21no—
139C2×C4×C13—22no—
140C2×C4×C13—41no—
141C2×C4×C13—42no—
142C2×C4×C13C2×C4⋊C411yescharacteristic
143C2×C4×C13C2×C4⋊C412yes—
144C2×C4×C13C2×C4⋊C411yescharacteristic
145C2×C4×C13C2×C4⋊C412yes—
146C2×C4×C13C2×C4⋊C412yes—
147C2×C4×C13C2×C4⋊C411yescharacteristic
148C2×C4×C13C2×M1612yes—
149C2×C4×C13C2×M1612yes—
150C2×C4×C13C23×C411yescharacteristic
151C2×C4×C13C22×D411yescharacteristic
152C2×C4×C13C22×Q811yescharacteristic
153C8×C13—21no—
154C8×C13—21no—
155C8×C13—22no—
156C8×C13C2×M1612yes—
157C8×C13C2×M1614yes—
158C8×C13C2×M1612yes—
159#1055—44no—
160#1055—42no—
161#1055—42no—
162C2×#131Dic1311yescharacteristic
163C2×#131Dic1311yescharacteristic
164C4×#41C2×D1311yescharacteristic
165#446—262no—
166#436—262no—
167#435—264no—
168#432—134no—
169#431—132no—
170#423—134no—
171C2×C4⋊C8—132no—
172#405Dic1311yescharacteristic
173#405Dic1312yes—
174#405Dic1312yes—
175#405Dic1311yescharacteristic
176C4×M16C2×D1311yescharacteristic
177C4×M16C2×D1312yes—
178C2×C4×C8C2×D1311yescharacteristic
179C2×C4×C8C2×D1312yes—
180#335—132no—
181#335—132no—
182#335—131no—
183#335—131no—
184#335—134no—
185#334—132no—
186#334—134no—
187C22×C13—21no—
188C22×C13—21no—
189C22×C13—22no—
190C22×C13—22no—
191C22×C13—22no—
192C22×C13#42312yes—
193C22×C13C22×C4⋊C411yescharacteristic
194C4×C13—22no—
195C4×C13—21no—
196C4×C13—22no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—22no—
200C4×C13#42312yes—
201C4×C13C22×M1611yescharacteristic
202C4×C13C22×M1611yescharacteristic
203C4×C13#57611yescharacteristic
204C4×C13#57811yescharacteristic
205C2×#41C2×Dic1311yescharacteristic
206#131—24no—
207#131—24no—
208C2×M16—264no—
209C2×M16C2×Dic1311yescharacteristic
210C2×M16C2×Dic1312yes—
211C2×M16C2×Dic1312yes—
212C2×M16C2×Dic1311yescharacteristic
213C22×C8—262no—
214C22×C8C2×Dic1311yescharacteristic
215C22×C8C2×Dic1312yes—
216C22×C8C2×Dic1312yes—
217C22×C8C2×Dic1311yescharacteristic
218C4×Q8Dic2611yescharacteristic
219C4×Q8D5211yescharacteristic
220C4×D4Dic2612yes—
221C4×D4Dic2611yescharacteristic
222C4×D4D5212yes—
223C4×D4D5211yescharacteristic
224#117C2×Dic1312yes—
225#117C2×Dic1311yescharacteristic
226C2×C42C22×D1311yescharacteristic
227C2×C42C22×D1312yes—
228C4⋊C8—132no—
229C4⋊C8—134no—
230C4⋊C8—132no—
231C4⋊C8—262no—
232C4⋊C8—264no—
233C22⋊C8—262no—
234C22⋊C8—264no—
235#97—264no—
236#97C2×Dic1312yes—
237#97C2×Dic1312yes—
238#97C2×Dic1312yes—
239C4×C8—262no—
240C4×C8C2×Dic1312yes—
241C4×C8C2×Dic1311yescharacteristic
242C4×C8C2×Dic1311yescharacteristic
243C4×C8C2×Dic1312yes—
244C4×C8C22×D1311yescharacteristic
245C4×C8C22×D1312yes—
246C4×C8C22×D1311yescharacteristic
247C2×C13—22no—
248C2×C13—42no—
249C2×C13C2×#42311yescharacteristic
250C2×C13#291311yescharacteristic
251C2×C13#291611yescharacteristic
252#41—22no—
253#41—22no—
254C2×Q8C4⋊Dic1311yescharacteristic
255C2×D4C4⋊Dic1312yes—
256C2×D4C4⋊Dic1311yescharacteristic
257C22×C4C2×Dic2612yes—
258C22×C4C2×Dic2611yescharacteristic
259C22×C4C2×D5211yescharacteristic
260C22×C4C2×D5212yes—
261C22×C4C22×Dic1312yes—
262C22×C4C22×Dic1311yescharacteristic
263M16—22no—
264M16—24no—
265M16—24no—
266M16—1044no—
267M16#609914yescomplemented
268C2×C8—22no—
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—262no—
272C2×C8—262no—
273C2×C8—264no—
274C2×C8—1042no—
275C2×C8#609914yescomplemented
276C2×C8C22×Dic1311yescharacteristic
277C2×C8C22×Dic1311yescharacteristic
278C2×C8C22×Dic1312yes—
279C2×C8C22×Dic1311yescharacteristic
280C2×C8C22×Dic1312yes—
281C2×C8C22×Dic1311yescharacteristic
282C4⋊C4C4⋊Dic1312yes—
283C4⋊C4C4⋊Dic1311yescharacteristic
284C4⋊C4C4⋊Dic1312yes—
285C4⋊C4C4⋊Dic1311yescharacteristic
286C22⋊C4C4⋊Dic1312yes—
287C22⋊C4C4⋊Dic1312yes—
288C22⋊C4C4⋊Dic1312yes—
289C42C2×Dic2612yes—
290C42C2×Dic2611yescharacteristic
291C42C2×D5211yescharacteristic
292C42C2×D5212yes—
293C42C22×Dic1311yescharacteristic
294C42C22×Dic1312yes—
295C42C23×D1311yescharacteristic
296C13#1779911yescharacteristic, complemented, Sylow
297C23C2×C4⋊Dic1312yes—
298C23C2×C4⋊Dic1311yescharacteristic
299Q8—22no—
300D4—24no—
301D4—22no—
302C2×C4—21no—
303C2×C4—22no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—42no—
310C2×C4C2×#609912yes—
311C2×C4C2×#609912yes—
312C2×C4C2×C4⋊Dic1312yes—
313C2×C4C2×C4⋊Dic1311yescharacteristic
314C2×C4C2×C4⋊Dic1312yes—
315C2×C4C2×C4⋊Dic1311yescharacteristic
316C2×C4C2×C4⋊Dic1312yes—
317C2×C4C2×C4⋊Dic1311yescharacteristic
318C2×C4C22×Dic2611yescharacteristic
319C2×C4C22×D5211yescharacteristic
320C2×C4C23×Dic1311yescharacteristic
321C8—21no—
322C8—21no—
323C8—22no—
324C8—524no—
325C8—522no—
326C8—522no—
327C8C2×#609912yes—
328C8C2×#609914yes—
329C8C2×#609912yes—
330C22—21no—
331C22—21no—
332C22—22no—
333C22—22no—
334C22—22no—
335C22#1171858512yes—
336C22C22×C4⋊Dic1311yescharacteristic
337C4—22no—
338C4—21no—
339C4—22no—
340C4—21no—
341C4—21no—
342C4—22no—
343C4#1171858512yes—
344C4#1171945711yescharacteristic
345C4#1171945811yescharacteristic
346C4C22×#609911yescharacteristic
347C4C22×#609911yescharacteristic
348C2—22no—
349C2—42no—
350C2C2×#1171858511yescharacteristic
351C2#1312343611yescharacteristic
352C2#1312344711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC4×C13×#131C2
socleC22×C13C22×C4⋊C4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenterC4×#131D13
hypocenterC13#17799
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #13113603C2semidirect
3. #13113599C2semidirect
4. #13113595C2semidirect
5. #13113588C2semidirect
6. #13113584C2semidirect
7. C2×#11718050C2semidirect
91. C13×M16M16semidirect
95. C2×C8×C13M16semidirect
267. M16#6099semidirect
275. C2×C8#6099semidirect
296. C13#17799semidirect

Maximal subgroups

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

subgroupindex
#131239532
#131136032
#131135992
#131135952
#131135882
#131135842
C2×#117180502
C4×C13×#1312
#1779913