Finite Group Databasebeta

← #15759564

Subgroups — #15759564

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#13123554C211yesmaximal, characteristic
2#13115810C211yesmaximal, characteristic, complemented
3#13113517C211yesmaximal, characteristic, complemented
4#13113396C211yesmaximal, characteristic
5#13112695C211yesmaximal, characteristic, complemented
6#13112666C211yesmaximal, characteristic, complemented
7C13×#3227C211yesmaximal, characteristic
8C13×#532C2211yescharacteristic
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×#88202—21no—
11C13×#498C412yescomplemented
12C13×#486C412yescomplemented
13C13×#481—22no—
14C13×#476—22no—
15C13×#431C2211yescharacteristic
16#11718895—21no—
17#11718672—22no—
18#11718672—22no—
19#11718597C2211yescharacteristic
20#11718586C2211yescharacteristic
21#11718585C2211yescharacteristic
22C2×#88043C2211yescharacteristic
23#11718138—22no—
24#11718129—22no—
25#11718121—21no—
26#11718121—21no—
27C2×C13×#41—21no—
28C22×Q8×C13—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8C2×C412yes—
33C13×C4⋊Q8C2×C411yescharacteristic
34C13×#127C2×C411yescharacteristic
35C13×#124—21no—
36C13×#121—21no—
37C13×#121D412yes—
38C4×D4×C13—21no—
39C4×D4×C13D412yes—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C42×C13C2311yescharacteristic
43#88202—42no—
44#88202—42no—
45C2×C4⋊Dic13—21no—
46C2×#6099—22no—
47C2×#6099—21no—
48C22×#1055—22no—
49C22×#1055D411yescharacteristic
50C22×#1055D411yescharacteristic
51C13×#106—24no—
52C13×C4⋊C8—21no—
53C13×#102—24no—
54C13×C22⋊C8—21no—
55C4×C8×C13C2×C412yes—
56#88071—21no—
57#88071—21no—
58C22⋊#1055—24no—
59C22⋊#1055—21no—
60C4⋊#1055—21no—
61C4⋊#1055—21no—
62C4⋊#1055D412yes—
63#88043—21no—
64#88043—21no—
65C4×#1055—21no—
66#9287—131nomaximal, Sylow
67C13×#41—41no—
68C13×#41—41no—
69C13×#41—41no—
70C13×#41—41no—
71C2×Q8×C13—21no—
72C2×Q8×C13—22no—
73C2×Q8×C13—41no—
74C2×Q8×C13—82no—
75C2×D4×C13—22no—
76C2×D4×C13—21no—
77C2×D4×C13—21no—
78C2×D4×C13C22⋊C412yes—
79C22×C4×C13—22no—
80C22×C4×C13—41no—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13#4111yescharacteristic
84C22×Dic13—41no—
85C2×C8×C13—22no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4C22⋊C412yes—
92C13×C22⋊C4—22no—
93C13×C22⋊C4—22no—
94C42×C13C22×C411yescharacteristic
95C42×C13C2×D411yescharacteristic
96C42×C13C2×D411yescharacteristic
97C42×C13#4111yescharacteristic
98C4⋊Dic13—41no—
99C4⋊Dic13—41no—
100#6099—44no—
101#6099—41no—
102#6099—41no—
103C2×#1055—21no—
104C2×#1055—21no—
105C2×#1055—21no—
106C2×#1055—22no—
107C2×#1055—21no—
108C2×#1055—21no—
109C2×#1055—44no—
110C2×#1055—41no—
111C2×#1055SD1612yes—
112#3227D1311yescharacteristic
113#2932—131no—
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—
123Q8×C13—82no—
124Q8×C13—82no—
125D4×C13—42no—
126D4×C13—42no—
127D4×C13—42no—
128D4×C13—41no—
129D4×C13—41no—
130D4×C13—81no—
131C2×C4×C13—22no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13—42no—
136C2×C4×C13—42no—
137C2×C4×C13—82no—
138C2×C4×C13C2×C22⋊C411yescharacteristic
139C2×C4×C13C4×D411yescharacteristic
140C2×C4×C13C4×D411yescharacteristic
141C2×C4×C13#12011yescharacteristic
142C2×C4×C13#12111yescharacteristic
143C2×C4×C13#12311yescharacteristic
144C2×C4×C13C2×SD1611yescharacteristic
145C2×C4×C13#13511yescharacteristic
146C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C13#13711yescharacteristic
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C8×C13—42no—
152#1055—22no—
153#1055—42no—
154#1055—41no—
155#1055—81no—
156C2×#131—261no—
157#532C2×D1311yescharacteristic
158C2×C4⋊Q8C2×D1311yescharacteristic
159#498Dic1312yescomplemented
160#486Dic1312yescomplemented
161#481—22no—
162#476—22no—
163#435—262no—
164#435—262no—
165#431—131no—
166#431C2×D1311yescharacteristic
167#423—131no—
168#408—261no—
169C2×#97—131no—
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×C13—82no—
189C4×C13C4×SD1611yescharacteristic
190C4×C13#44011yescharacteristic
191C4×C13#45011yescharacteristic
192C4×C13#45211yescharacteristic
193Dic13—161no—
194C2×#41—21no—
195C22×Q8—21no—
196#131—522no—
197#131—522no—
198C2×M16—262no—
199C2×M16—261no—
200C22×C8—131no—
201C22×C8—131no—
202C22×C8—262no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8C2×Dic1312yes—
207C4⋊Q8C2×Dic1311yescharacteristic
208#127C2×Dic1311yescharacteristic
209#124—21no—
210#121—21no—
211#121C22⋊D1312yes—
212C4×D4—21no—
213C4×D4C22⋊D1312yes—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—261no—
217C2×C42C22×D1311yescharacteristic
218#106—24no—
219C4⋊C8—21no—
220C4⋊C8—132no—
221C4⋊C8—261no—
222C4⋊C8—261no—
223#102—24no—
224C22⋊C8—21no—
225C22⋊C8—264no—
226C22⋊C8—261no—
227#97—261no—
228#97—261no—
229C4×C8—261no—
230C4×C8C2×Dic1312yes—
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—22no—
245C2×Q8—41no—
246C2×Q8—82no—
247C2×D4—22no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4C22⋊Dic1312yes—
251C22×C4—22no—
252C22×C4—41no—
253C22×C4—521no—
254C22×C4D4×D1311yescharacteristic
255C22×C4#612911yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257M16—524no—
258M16—521no—
259M16—521no—
260C2×C8—22no—
261C2×C8—132no—
262C2×C8—261no—
263C2×C8—261no—
264C2×C8—261no—
265C2×C8—261no—
266C2×C8—261no—
267C2×C8—262no—
268C2×C8—524no—
269C2×C8—521no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—521no—
276C4⋊C4—521no—
277C4⋊C4C22⋊Dic1312yes—
278C22⋊C4—22no—
279C22⋊C4—22no—
280C42D4×D1311yescharacteristic
281C42#612911yescharacteristic
282C42C22×Dic1311yescharacteristic
283C42C2×C22⋊D1311yescharacteristic
284C13#928711yescharacteristic, complemented, Sylow
285C23—22no—
286C23#8819311yescharacteristic
287Q8—41no—
288Q8—41no—
289Q8—82no—
290Q8—82no—
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—42no—
303C2×C4—82no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4SD16×D1311yescharacteristic
308C2×C4#8816811yescharacteristic
309C2×C4#8816911yescharacteristic
310C2×C4#8817011yescharacteristic
311C2×C4D4×Dic1311yescharacteristic
312C2×C4D4×Dic1311yescharacteristic
313C2×C4#8818911yescharacteristic
314C2×C4#8819111yescharacteristic
315C2×C4#8819311yescharacteristic
316C2×C4C2×C22⋊Dic1311yescharacteristic
317C8—42no—
318C8—262no—
319C8—522no—
320C8—521no—
321C8—1041no—
322C22—21no—
323C22—21no—
324C22—42no—
325C22—42no—
326C22—42no—
327C22#1171882311yescharacteristic
328C22#1171882611yescharacteristic
329C22#1171888111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—82no—
336C4—2081no—
337C4SD16×Dic1311yescharacteristic
338C4#1171882511yescharacteristic
339C4#1171883011yescharacteristic
340C4#1171883411yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1311517211yescharacteristic
345C2#1311531811yescharacteristic
346C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#3227C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#3227D13
hypocenterC13#9287
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
2. #13115810C2semidirect
3. #13113517C2semidirect
5. #13112695C2semidirect
6. #13112666C2semidirect
11. C13×#498C4semidirect
12. C13×#486C4semidirect
159. #498Dic13semidirect
160. #486Dic13semidirect
284. C13#9287semidirect

Maximal subgroups

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

subgroupindex
#131235542
#131158102
#131135172
#131133962
#131126952
#131126662
C13×#32272
#928713