Finite Group Databasebeta

← #15846039

Subgroups — #15846039

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13126148C212yesmaximal
2#13123549C211yesmaximal, characteristic
3#13114356C212yesmaximal, complemented
4#13114346C212yesmaximal, complemented
5#13114208C214yesmaximal, complemented
6C2×#11718049C211yesmaximal, characteristic, complemented
7#13113526C212yesmaximal, complemented
8C13×#3160C211yesmaximal, characteristic, complemented
9C13×#533C2212yes—
10C2×#88155—21no—
11#11719182C2211yescharacteristic
12C13×#500C2211yescharacteristic
13C13×#500C2211yescharacteristic
14C13×#499—21no—
15C13×#499—21no—
16C13×#498C2212yes—
17C13×#427—21no—
18C13×#427—21no—
19C2×C4×C8×C13C2211yescharacteristic
20#11718771—21no—
21#11718745C2214yes—
22#11718744C2214yes—
23#11718709—24no—
24#11718688—22no—
25#11718681—22no—
26#11718585C2211yescharacteristic
27C2×C4⋊#1055C2212yes—
28#11718349—21no—
29#11718349C2212yes—
30C8×D52—21no—
31C8×D52C2212yes—
32#11718139C2214yes—
33#11718138C2214yes—
34#11718049C2212yes—
35#11718049C2212yes—
36C2×#6127—21no—
37C22×C8×C13D411yescharacteristic
38C22×C8×C13D411yescharacteristic
39C13×C4⋊Q8C2312yes—
40C13×C4⋊Q8C2312yes—
41C13×#125—22no—
42C13×C22⋊Q8—22no—
43C13×C22⋊Q8—22no—
44C4×Q8×C13—22no—
45C4×Q8×C13—22no—
46C13×#117—22no—
47C2×C42×C13C2311yescharacteristic
48C2×#6106—24no—
49#88184—21no—
50#88184D412yes—
51C2×#6099—21no—
52C22×#1055—22no—
53#88155—44no—
54C2×#6094—22no—
55C2×C8×D13—22no—
56#88129—21no—
57#88128D411yescharacteristic
58C4×D52—21no—
59C4×D52C2312yes—
60#88123D411yescharacteristic
61C13×#107—21no—
62C13×#107—21no—
63C13×#107—21no—
64C13×#107—21no—
65C13×#106—22no—
66C13×#106—22no—
67C4×C8×C13D411yescharacteristic
68C4×C8×C13D411yescharacteristic
69C4×C8×C13C2311yescharacteristic
70C4×C8×C13C2311yescharacteristic
71#88075—24no—
72#88060—22no—
73#88060—22no—
74#88049—24no—
75#88048—24no—
76C4⋊#1055—22no—
77C4⋊#1055—21no—
78C4⋊#1055C2314yes—
79C4⋊#1055C2312yes—
80#19194—131nomaximal, Sylow
81C2×Q8×C13—22no—
82C2×Q8×C13—22no—
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13#4111yescharacteristic
86C2×C22⋊D13—22no—
87#6127—42no—
88#6127—42no—
89C2×D52—21no—
90C2×D52—21no—
91C2×D52C2×D412yes—
92C2×C4×D13—22no—
93C2×Dic26—21no—
94C2×C8×C13—22no—
95C2×C8×C13SD1614yescomplemented
96C2×C8×C13C2×D411yescharacteristic
97C2×C8×C13C2×D411yescharacteristic
98C2×C8×C13C2×D411yescharacteristic
99C2×C8×C13C2×D411yescharacteristic
100C13×C4⋊C4—22no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—22no—
103C13×C4⋊C4—22no—
104C13×C4⋊C4—42no—
105C13×C4⋊C4—42no—
106C13×C22⋊C4—42no—
107C42×C13—42no—
108C42×C13C2×D411yescharacteristic
109C42×C13C2×D411yescharacteristic
110C42×C13#4111yescharacteristic
111C42×C13C2411yescharacteristic
112#6106—84no—
113#6103—22no—
114#6103—22no—
115C4⋊Dic13—21no—
116C4⋊Dic13C2×D412yes—
117#6099—42no—
118C2×#1055—24no—
119C2×#1055—22no—
120C2×#1055—82no—
121#6094—44no—
122C8×D13—44no—
123#3246—132no—
124#3160D1311yescharacteristic, complemented
125#2931—131no—
126#1695—132no—
127#1693—132no—
128#1671—134no—
129C2×#334—131no—
130#1550—132no—
131C23×C13#12111yescharacteristic
132C22×D13—22no—
133Q8×C13—42no—
134Q8×C13—42no—
135Q8×C13—82no—
136C2×C4×C13—22no—
137C2×C4×C13—41no—
138C2×C4×C13—42no—
139C2×C4×C13—42no—
140C2×C4×C13#12111yescharacteristic
141C2×C4×C13#12111yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13C2×SD1612yes—
144C2×C4×C13#13712yes—
145C2×C4×C13C22×D411yescharacteristic
146C2×C4×C13C22×D411yescharacteristic
147C2×C4×C13C2×#4111yescharacteristic
148C22⋊D13—44no—
149C2×Dic13—22no—
150D52—24no—
151D52—42no—
152D52—42no—
153C4×D13—42no—
154C4×D13—42no—
155Dic26—42no—
156C8×C13—21no—
157C8×C13—21no—
158C8×C13C2×SD1612yes—
159C8×C13C2×SD1612yes—
160#1055—42no—
161#1055—44no—
162C2×#131—261no—
163#533C2×D1312yes—
164#532—131no—
165#500C2×D1311yescharacteristic
166#500C2×D1311yescharacteristic
167#499—21no—
168#499—21no—
169#498C2×D1312yes—
170#476—134no—
171#475—262no—
172#465—264no—
173#461—134no—
174#460—262no—
175#436—132no—
176#436—261no—
177C8×D4—132no—
178C8×D4—261no—
179#427—21no—
180#427—21no—
181#423—131no—
182C2×C4⋊C8—132no—
183#408—261no—
184C2×C4×C8C2×D1311yescharacteristic
185#334—132no—
186#334—132no—
187#333—134no—
188#332—134no—
189C22×C13—21no—
190C22×C13—21no—
191C22×C13#46112yes—
192C22×C13C2×#12111yescharacteristic
193C2×D13—42no—
194C2×D13—42no—
195C2×D13—42no—
196C4×C13—21no—
197C4×C13—21no—
198C4×C13—21no—
199C4×C13—82no—
200C4×C13—82no—
201C4×C13#46112yes—
202C4×C13C22×SD1611yescharacteristic
203C4×C13C2×#13711yescharacteristic
204C4×C13#57712yes—
205Dic13—42no—
206C2×#41—261no—
207C2×SD16—264no—
208#131—524no—
209C2×M16—261no—
210C2×M16—262no—
211C22×C8—262no—
212C22×C8—262no—
213C22×C8C22⋊D1311yescharacteristic
214C22×C8C22⋊D1311yescharacteristic
215C4⋊Q8—131no—
216C4⋊Q8C22×D1312yes—
217C4⋊Q8C22×D1312yes—
218#127—131no—
219#125—22no—
220#124—261no—
221C22⋊Q8—22no—
222C22⋊Q8—22no—
223#121—132no—
224#121—261no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×D4—132no—
228C4×D4—261no—
229#117—22no—
230C2×C42C22×D1311yescharacteristic
231#107—21no—
232#107—21no—
233#107—21no—
234#107—21no—
235#106—22no—
236#106—22no—
237#106—264no—
238C4⋊C8—132no—
239C4⋊C8—134no—
240C4⋊C8—262no—
241C4⋊C8—261no—
242#103—264no—
243#102—264no—
244C22⋊C8—262no—
245C22⋊C8—262no—
246C4×C8C22⋊D1311yescharacteristic
247C4×C8C22⋊D1311yescharacteristic
248C4×C8C22×D1311yescharacteristic
249C4×C8C22×D1311yescharacteristic
250C2×C13—22no—
251C2×C13C2×#46111yescharacteristic
252C2×C13#306011yescharacteristic
253C2×C13#306711yescharacteristic
254D13—82no—
255#41—522no—
256#41—522no—
257C2×Q8—22no—
258C2×Q8—22no—
259C2×Q8—261no—
260C2×D4—132no—
261C2×D4—262no—
262C2×D4—261no—
263C2×D4—261no—
264C22×C4—262no—
265C22×C4D4×D1311yescharacteristic
266C22×C4#612911yescharacteristic
267C22×C4C2×C22⋊D1311yescharacteristic
268SD16—1044no—
269M16—522no—
270M16—524no—
271C2×C8—22no—
272C2×C8—264no—
273C2×C8—262no—
274C2×C8—524no—
275C2×C8—1042no—
276C2×C8#610614yescomplemented
277C2×C8C2×C22⋊D1311yescharacteristic
278C2×C8C2×C22⋊D1311yescharacteristic
279C2×C8C2×C22⋊D1311yescharacteristic
280C2×C8C2×C22⋊D1311yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—42no—
286C4⋊C4—42no—
287C4⋊C4—132no—
288C4⋊C4—261no—
289C22⋊C4—42no—
290C22⋊C4—262no—
291C22⋊C4—262no—
292C42—42no—
293C42D4×D1311yescharacteristic
294C42#612911yescharacteristic
295C42C2×C22⋊D1311yescharacteristic
296C42C23×D1311yescharacteristic
297C13#1919411yescharacteristic, complemented, Sylow
298C23—262no—
299C23#8819211yescharacteristic
300Q8—42no—
301Q8—42no—
302Q8—82no—
303Q8—522no—
304D4—264no—
305D4—522no—
306D4—524no—
307D4—522no—
308C2×C4—22no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—262no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4#8819211yescharacteristic
316C2×C4#8819211yescharacteristic
317C2×C4#8819211yescharacteristic
318C2×C4C2×#610612yes—
319C2×C4#8819612yes—
320C2×C4C2×D4×D1311yescharacteristic
321C2×C4C2×#612911yescharacteristic
322C2×C4C22×C22⋊D1311yescharacteristic
323C8—21no—
324C8—21no—
325C8—524no—
326C8—522no—
327C8C2×#610612yes—
328C8C2×#610612yes—
329C22—21no—
330C22—21no—
331C22—522no—
332C22—522no—
333C22—522no—
334C22#1171874412yes—
335C22C2×#8819211yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—82no—
340C4—82no—
341C4—522no—
342C4#1171874412yes—
343C4#1171947512yes—
344C4C22×#610611yescharacteristic
345C4C2×#8819611yescharacteristic
346C2—22no—
347C2—1042no—
348C2C2×#1171874411yescharacteristic
349C2#1312449411yescharacteristic
350C2#1312455211yescharacteristic
subgroupG/H
centerC22C2×#88192
commutator, cosocleC42×C13C24
FrattiniC42C23×D13
FittingC13×#3160C2
socleC22×C13C2×#121
prime radical#11719182C22
hypercenter#3160D13
hypocenterC13#19194
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3160

Complements

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

NH ≅ G/Ntype
3. #13114356C2semidirect
4. #13114346C2semidirect
5. #13114208C2semidirect
6. C2×#11718049C2semidirect
7. #13113526C2semidirect
8. C13×#3160C2semidirect
95. C2×C8×C13SD16semidirect
124. #3160D13semidirect
276. C2×C8#6106semidirect
297. C13#19194semidirect

Maximal subgroups

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

subgroupindex
#131261482
#131235492
#131143562
#131143462
#131142082
C2×#117180492
#131135262
C13×#31602
#1919413