Finite Group Databasebeta

← #15759562

Subgroups — #15759562

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125961C211yesmaximal, characteristic
2#13115809C211yesmaximal, characteristic, complemented
3#13113518C211yesmaximal, characteristic, complemented
4#13113396C211yesmaximal, characteristic
5#13112696C211yesmaximal, characteristic, complemented
6#13112667C211yesmaximal, characteristic, complemented
7C13×#2932C211yesmaximal, characteristic
8C2×C13×#131—21no—
9C13×#532C2211yescharacteristic
10C2×#88123C2211yescharacteristic
11C13×#435—22no—
12C13×#435—22no—
13C13×#423C2211yescharacteristic
14C13×#408—21no—
15C2×C13×#97C2211yescharacteristic
16#11718740C412yescomplemented
17#11718731C412yescomplemented
18#11718695—22no—
19#11718669—22no—
20#11718597C2211yescharacteristic
21#11718586C2211yescharacteristic
22#11718586C2211yescharacteristic
23#11718143—21no—
24#11718143—21no—
25#11718129—22no—
26#11718073—22no—
27C2×C13×#41—21no—
28C22×Dic26—21no—
29C13×#131—42no—
30C13×#131—42no—
31C2×C13×M16—22no—
32C2×C13×M16—21no—
33C22×C8×C13—22no—
34C22×C8×C13D411yescharacteristic
35C22×C8×C13D411yescharacteristic
36C13×C4⋊Q8C2×C411yescharacteristic
37C13×#127C2×C411yescharacteristic
38C13×#124—21no—
39C13×#121—21no—
40C13×#121D412yes—
41C4×D4×C13—21no—
42C4×D4×C13D412yes—
43C2×C42×C13C2311yescharacteristic
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47#88123—21no—
48#88123—21no—
49#88123—21no—
50#88123C2×C412yes—
51C13×C4⋊C8—21no—
52C13×C4⋊C8D412yes—
53C13×C22⋊C8—24no—
54C13×#97—21no—
55C13×#97—21no—
56#88072—24no—
57#88071—21no—
58#88071—21no—
59C22⋊#1055—21no—
60C22⋊#1055—21no—
61#88048—24no—
62C4⋊#1055—21no—
63C4⋊#1055—21no—
64C4×#1055—21no—
65C4×#1055C2×C412yes—
66#9287—131nomaximal, Sylow
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C2×Q8×C13—21no—
72C2×D4×C13—22no—
73C2×D4×C13—21no—
74C2×D4×C13—21no—
75C2×D4×C13C22⋊C412yes—
76C22×C4×C13—22no—
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13#4111yescharacteristic
80C22×Dic13—41no—
81C22×Dic13—41no—
82C2×Dic26—22no—
83C2×Dic26—41no—
84C2×Dic26—82no—
85C13×M16—44no—
86C13×M16—41no—
87C13×M16—41no—
88C2×C8×C13—21no—
89C2×C8×C13—21no—
90C2×C8×C13—21no—
91C2×C8×C13—22no—
92C2×C8×C13—21no—
93C2×C8×C13—21no—
94C2×C8×C13—44no—
95C2×C8×C13SD1612yes—
96C13×C4⋊C4—21no—
97C13×C4⋊C4C22⋊C412yes—
98C13×C22⋊C4—22no—
99C13×C22⋊C4—22no—
100C42×C13C22×C411yescharacteristic
101C42×C13C2×D411yescharacteristic
102C42×C13C2×D411yescharacteristic
103C42×C13#4111yescharacteristic
104C4⋊Dic13—22no—
105C4⋊Dic13—22no—
106C4⋊Dic13—41no—
107C4⋊Dic13—41no—
108C4⋊Dic13—41no—
109C4⋊Dic13—41no—
110C2×#1055—22no—
111C2×#1055—41no—
112#3227—131no—
113#2932D1311yescharacteristic
114#1993—131no—
115#1548—131no—
116#1517—131no—
117#1286—131no—
118#1275—131no—
119C23×C13—22no—
120C23×C13#12111yescharacteristic
121Q8×C13—41no—
122Q8×C13—41no—
123D4×C13—42no—
124D4×C13—42no—
125D4×C13—42no—
126D4×C13—41no—
127D4×C13—41no—
128D4×C13—81no—
129C2×C4×C13—22no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—42no—
133C2×C4×C13—42no—
134C2×C4×C13C2×C22⋊C411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13C4×D411yescharacteristic
137C2×C4×C13#12011yescharacteristic
138C2×C4×C13#12111yescharacteristic
139C2×C4×C13#12311yescharacteristic
140C2×C4×C13C2×SD1611yescharacteristic
141C2×C4×C13#13511yescharacteristic
142C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C13#13711yescharacteristic
144C2×Dic13—42no—
145C2×Dic13—82no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149Dic26—82no—
150Dic26—82no—
151C8×C13—22no—
152C8×C13—42no—
153C8×C13—41no—
154#1055—42no—
155#1055—81no—
156C2×#131—21no—
157#532C2×D1311yescharacteristic
158C2×C4⋊Q8—131no—
159#498—132no—
160#486—132no—
161#481—262no—
162#476—262no—
163#435—22no—
164#435—22no—
165#431—131no—
166#431—131no—
167#423C2×D1311yescharacteristic
168#408—21no—
169C2×#97C2×D1311yescharacteristic
170#382—131no—
171#340—261no—
172#340—261no—
173#333—262no—
174#327—262no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—42no—
178C22×C13—42no—
179C22×C13—42no—
180C22×C13#38611yescharacteristic
181C22×C13#46111yescharacteristic
182C22×C13#46311yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—42no—
188C4×C13C4×SD1611yescharacteristic
189C4×C13#44011yescharacteristic
190C4×C13#45011yescharacteristic
191C4×C13#45211yescharacteristic
192Dic13—82no—
193Dic13—161no—
194C2×#41—21no—
195C22×Q8—261no—
196#131—42no—
197#131—42no—
198C2×M16—22no—
199C2×M16—21no—
200C22×C8—22no—
201C22×C8C22⋊D1311yescharacteristic
202C22×C8C22⋊D1311yescharacteristic
203C4⋊Q8—132no—
204C4⋊Q8—261no—
205C4⋊Q8—261no—
206C4⋊Q8—261no—
207C4⋊Q8C4×D1311yescharacteristic
208#127C4×D1311yescharacteristic
209#124—21no—
210#121—21no—
211#121D5212yes—
212C4×D4—21no—
213C4×D4C22⋊D1312yes—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C42C22×D1311yescharacteristic
218#106—264no—
219C4⋊C8—21no—
220C4⋊C8—261no—
221C4⋊C8—261no—
222C4⋊C8C22⋊D1312yes—
223#102—264no—
224C22⋊C8—24no—
225C22⋊C8—261no—
226C22⋊C8—261no—
227#97—21no—
228#97—21no—
229C4×C8—132no—
230C4×C8—261no—
231#95—261no—
232#95—261no—
233C2×C13—21no—
234C2×C13—21no—
235C2×C13—82no—
236C2×C13#187711yescharacteristic
237C2×C13#190311yescharacteristic
238C2×C13#190911yescharacteristic
239#41—41no—
240#41—41no—
241#41—41no—
242#41—41no—
243C2×Q8—21no—
244C2×Q8—262no—
245C2×Q8—521no—
246C2×Q8—1042no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4#610312yes—
251C22×C4—22no—
252C22×C4—521no—
253C22×C4—521no—
254C22×C4C2×D5211yescharacteristic
255C22×C4#612711yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257M16—44no—
258M16—41no—
259M16—41no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—22no—
266C2×C8—44no—
267C2×C8—262no—
268C2×C8—521no—
269C2×C8#610512yes—
270C4⋊C4—21no—
271C4⋊C4—262no—
272C4⋊C4—262no—
273C4⋊C4—521no—
274C4⋊C4—521no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4#610312yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C42C2×C4×D1311yescharacteristic
281C42#612711yescharacteristic
282C42C2×C22⋊D1311yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C13#928711yescharacteristic, complemented, Sylow
285C23—22no—
286C23#8818411yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—1042no—
290Q8—1042no—
291D4—42no—
292D4—42no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297C2×C4—22no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—522no—
303C2×C4—1042no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4C2×#610311yescharacteristic
308C2×C4C4×C22⋊D1311yescharacteristic
309C2×C4C4×C22⋊D1311yescharacteristic
310C2×C4#8818311yescharacteristic
311C2×C4#8818411yescharacteristic
312C2×C4#8818611yescharacteristic
313C2×C4C2×#610511yescharacteristic
314C2×C4#8820411yescharacteristic
315C2×C4#8820511yescharacteristic
316C2×C4#8820711yescharacteristic
317C8—22no—
318C8—42no—
319C8—41no—
320C8—522no—
321C8—1041no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#1171867711yescharacteristic
328C22#1171868011yescharacteristic
329C22#1171887411yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—1042no—
336C4—2081no—
337C4C4×#610511yescharacteristic
338C4#1171867911yescharacteristic
339C4#1171887911yescharacteristic
340C4#1171890011yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1311517011yescharacteristic
345C2#1311531611yescharacteristic
346C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2932C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#2932D13
hypocenterC13#9287
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
2. #13115809C2semidirect
3. #13113518C2semidirect
5. #13112696C2semidirect
6. #13112667C2semidirect
16. #11718740C4semidirect
17. #11718731C4semidirect
284. C13#9287semidirect

Maximal subgroups

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

subgroupindex
#131259612
#131158092
#131135182
#131133962
#131126962
#131126672
C13×#29322
#928713